LMFDB - Embedded newform 460.2.x.a.337.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			337.7
Character	$\chi$	$=$	460.337
Dual form			460.2.x.a.273.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.343687 - 0.128189i) q^{3} +(1.40466 - 1.73981i) q^{5} +(-4.20215 + 0.914122i) q^{7} +(-2.16556 - 1.87647i) q^{9} +O(q^{10})$	\(q+(-0.343687 - 0.128189i) q^{3} +(1.40466 - 1.73981i) q^{5} +(-4.20215 + 0.914122i) q^{7} +(-2.16556 - 1.87647i) q^{9} +(-3.69025 + 0.530577i) q^{11} +(0.169917 - 0.781095i) q^{13} +(-0.705786 + 0.417889i) q^{15} +(-0.545291 + 0.998626i) q^{17} +(-3.11483 - 0.914597i) q^{19} +(1.56141 + 0.224496i) q^{21} +(0.0291979 + 4.79574i) q^{23} +(-1.05388 - 4.88767i) q^{25} +(1.03112 + 1.88836i) q^{27} +(-0.349392 - 1.18992i) q^{29} +(3.27559 - 7.17255i) q^{31} +(1.33630 + 0.290695i) q^{33} +(-4.31218 + 8.59497i) q^{35} +(0.556344 + 7.77871i) q^{37} +(-0.158526 + 0.246671i) q^{39} +(-5.31900 - 6.13845i) q^{41} +(1.92286 - 5.15539i) q^{43} +(-6.30657 + 1.13187i) q^{45} +(-7.22140 - 7.22140i) q^{47} +(10.4550 - 4.77465i) q^{49} +(0.315422 - 0.273315i) q^{51} +(-0.639416 - 2.93935i) q^{53} +(-4.26043 + 7.16561i) q^{55} +(0.953286 + 0.713621i) q^{57} +(2.17041 + 3.37722i) q^{59} +(-10.1219 - 4.62252i) q^{61} +(10.8153 + 5.90562i) q^{63} +(-1.12028 - 1.39279i) q^{65} +(5.73836 + 7.66555i) q^{67} +(0.604725 - 1.65198i) q^{69} +(0.934198 - 6.49749i) q^{71} +(-0.184431 + 0.100707i) q^{73} +(-0.264340 + 1.81493i) q^{75} +(15.0220 - 5.60290i) q^{77} +(6.63906 - 4.26667i) q^{79} +(1.11107 + 7.72766i) q^{81} +(6.25864 - 0.447627i) q^{83} +(0.971473 + 2.35143i) q^{85} +(-0.0324527 + 0.453748i) q^{87} +(6.66413 + 14.5924i) q^{89} +3.43760i q^{91} +(-2.04522 + 2.04522i) q^{93} +(-5.96649 + 4.13452i) q^{95} +(6.60153 + 0.472150i) q^{97} +(8.98706 + 5.77563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{22}\right)$

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			0
$2$		0			0
$3$	−0.343687	−	0.128189i	−0.198428	−	0.0740098i	0.248285	−	0.968687i	$-0.420133\pi$
$3$	−0.343687	−	0.128189i	−0.198428	−	0.0740098i	−0.446713	+	0.894677i	$0.647406\pi$
$4$		0			0
$5$	1.40466	−	1.73981i	0.628182	−	0.778067i
$5$	1.40466	−	1.73981i	0.628182	−	0.778067i
$6$		0			0
$7$	−4.20215	+	0.914122i	−1.58826	+	0.345506i	−0.917989	−	0.396607i	$-0.870188\pi$
$7$	−4.20215	+	0.914122i	−1.58826	+	0.345506i	−0.670275	+	0.742112i	$0.733824\pi$
$8$		0			0
$9$	−2.16556	−	1.87647i	−0.721853	−	0.625490i
$10$		0			0
$11$	−3.69025	+	0.530577i	−1.11265	+	0.159975i	−0.674035	−	0.738699i	$-0.735440\pi$
$11$	−3.69025	+	0.530577i	−1.11265	+	0.159975i	−0.438616	+	0.898674i	$0.644531\pi$
$12$		0			0
$13$	0.169917	−	0.781095i	0.0471264	−	0.216637i	−0.947561	−	0.319574i	$-0.896460\pi$
$13$	0.169917	−	0.781095i	0.0471264	−	0.216637i	0.994688	+	0.102937i	$0.0328240\pi$
$14$		0			0
$15$	−0.705786	+	0.417889i	−0.182233	+	0.107899i
$16$		0			0
$17$	−0.545291	+	0.998626i	−0.132252	+	0.242202i	−0.935410	−	0.353564i	$-0.884970\pi$
$17$	−0.545291	+	0.998626i	−0.132252	+	0.242202i	0.803158	+	0.595766i	$0.203152\pi$
$18$		0			0
$19$	−3.11483	−	0.914597i	−0.714591	−	0.209823i	−0.0958250	−	0.995398i	$-0.530549\pi$
$19$	−3.11483	−	0.914597i	−0.714591	−	0.209823i	−0.618766	+	0.785575i	$0.712367\pi$
$20$		0			0
$21$	1.56141	+	0.224496i	0.340727	+	0.0489891i
$22$		0			0
$23$	0.0291979	+	4.79574i	0.00608819	+	0.999981i
$23$	0.0291979	+	4.79574i	0.00608819	+	0.999981i
$24$		0			0
$25$	−1.05388	−	4.88767i	−0.210776	−	0.977534i
$26$		0			0
$27$	1.03112	+	1.88836i	0.198439	+	0.363414i
$28$		0			0
$29$	−0.349392	−	1.18992i	−0.0648805	−	0.220963i	0.920671	−	0.390340i	$-0.127643\pi$
$29$	−0.349392	−	1.18992i	−0.0648805	−	0.220963i	−0.985551	+	0.169377i	$0.945824\pi$
$30$		0			0
$31$	3.27559	−	7.17255i	0.588314	−	1.28823i	−0.348142	−	0.937442i	$-0.613187\pi$
$31$	3.27559	−	7.17255i	0.588314	−	1.28823i	0.936456	−	0.350786i	$-0.114086\pi$
$32$		0			0
$33$	1.33630	+	0.290695i	0.232621	+	0.0506035i
$34$		0			0
$35$	−4.31218	+	8.59497i	−0.728892	+	1.45282i
$36$		0			0
$37$	0.556344	+	7.77871i	0.0914624	+	1.27881i	0.811284	+	0.584652i	$0.198769\pi$
$37$	0.556344	+	7.77871i	0.0914624	+	1.27881i	−0.719821	+	0.694159i	$0.755776\pi$
$38$		0			0
$39$	−0.158526	+	0.246671i	−0.0253844	+	0.0394989i
$40$		0			0
$41$	−5.31900	−	6.13845i	−0.830688	−	0.958665i	0.168949	−	0.985625i	$-0.445963\pi$
$41$	−5.31900	−	6.13845i	−0.830688	−	0.958665i	−0.999637	+	0.0269601i	$0.991417\pi$
$42$		0			0
$43$	1.92286	−	5.15539i	0.293234	−	0.786190i	−0.703884	−	0.710315i	$-0.748552\pi$
$43$	1.92286	−	5.15539i	0.293234	−	0.786190i	0.997117	−	0.0758749i	$-0.0241750\pi$
$44$		0			0
$45$	−6.30657	+	1.13187i	−0.940128	+	0.168729i
$46$		0			0
$47$	−7.22140	−	7.22140i	−1.05335	−	1.05335i	−0.998494	−	0.0548557i	$-0.982530\pi$
$47$	−7.22140	−	7.22140i	−1.05335	−	1.05335i	−0.0548557	−	0.998494i	$-0.517470\pi$
$48$		0			0
$49$	10.4550	−	4.77465i	1.49358	−	0.682094i
$50$		0			0
$51$	0.315422	−	0.273315i	0.0441679	−	0.0382717i
$52$		0			0
$53$	−0.639416	−	2.93935i	−0.0878305	−	0.403750i	0.912151	−	0.409855i	$-0.134421\pi$
$53$	−0.639416	−	2.93935i	−0.0878305	−	0.403750i	−0.999981	+	0.00610432i	$0.998057\pi$
$54$		0			0
$55$	−4.26043	+	7.16561i	−0.574476	+	0.966210i
$56$		0			0
$57$	0.953286	+	0.713621i	0.126266	+	0.0945214i
$58$		0			0
$59$	2.17041	+	3.37722i	0.282563	+	0.439676i	0.953303	−	0.302016i	$-0.0976597\pi$
$59$	2.17041	+	3.37722i	0.282563	+	0.439676i	−0.670740	+	0.741693i	$0.734023\pi$
$60$		0			0
$61$	−10.1219	−	4.62252i	−1.29598	−	0.591853i	−0.356445	−	0.934316i	$-0.616011\pi$
$61$	−10.1219	−	4.62252i	−1.29598	−	0.591853i	−0.939531	+	0.342464i	$0.888739\pi$
$62$		0			0
$63$	10.8153	+	5.90562i	1.36260	+	0.744038i
$64$		0			0
$65$	−1.12028	−	1.39279i	−0.138954	−	0.172755i
$66$		0			0
$67$	5.73836	+	7.66555i	0.701052	+	0.936496i	0.999841	−	0.0178230i	$-0.00567353\pi$
$67$	5.73836	+	7.66555i	0.701052	+	0.936496i	−0.298789	+	0.954319i	$0.596583\pi$
$68$		0			0
$69$	0.604725	−	1.65198i	0.0728003	−	0.198875i
$70$		0			0
$71$	0.934198	−	6.49749i	0.110869	−	0.771110i	−0.856209	−	0.516630i	$-0.827186\pi$
$71$	0.934198	−	6.49749i	0.110869	−	0.771110i	0.967078	−	0.254481i	$-0.0819045\pi$
$72$		0			0
$73$	−0.184431	+	0.100707i	−0.0215860	+	0.0117868i	−0.490006	−	0.871719i	$-0.663005\pi$
$73$	−0.184431	+	0.100707i	−0.0215860	+	0.0117868i	0.468420	+	0.883506i	$0.344824\pi$
$74$		0			0
$75$	−0.264340	+	1.81493i	−0.0305233	+	0.209570i
$76$		0			0
$77$	15.0220	−	5.60290i	1.71191	−	0.638510i
$78$		0			0
$79$	6.63906	−	4.26667i	0.746953	−	0.480037i	−0.110965	−	0.993824i	$-0.535394\pi$
$79$	6.63906	−	4.26667i	0.746953	−	0.480037i	0.857918	+	0.513787i	$0.171758\pi$
$80$		0			0
$81$	1.11107	+	7.72766i	0.123452	+	0.858629i
$82$		0			0
$83$	6.25864	−	0.447627i	0.686975	−	0.0491334i	0.276512	−	0.961011i	$-0.410822\pi$
$83$	6.25864	−	0.447627i	0.686975	−	0.0491334i	0.410463	+	0.911877i	$0.365367\pi$
$84$		0			0
$85$	0.971473	+	2.35143i	0.105371	+	0.255048i
$86$		0			0
$87$	−0.0324527	+	0.453748i	−0.00347930	+	0.0486469i
$88$		0			0
$89$	6.66413	+	14.5924i	0.706397	+	1.54679i	0.832039	+	0.554717i	$0.187174\pi$
$89$	6.66413	+	14.5924i	0.706397	+	1.54679i	−0.125642	+	0.992076i	$0.540099\pi$
$90$		0			0
$91$			3.43760i			0.360359i
$92$		0			0
$93$	−2.04522	+	2.04522i	−0.212079	+	0.212079i
$94$		0			0
$95$	−5.96649	+	4.13452i	−0.612149	+	0.424193i
$96$		0			0
$97$	6.60153	+	0.472150i	0.670283	+	0.0479396i	0.402333	−	0.915493i	$-0.368199\pi$
$97$	6.60153	+	0.472150i	0.670283	+	0.0479396i	0.267950	+	0.963433i	$0.413654\pi$
$98$		0			0
$99$	8.98706	+	5.77563i	0.903234	+	0.580473i
$100$		0			0
$101$	4.18957	−	4.83502i	0.416877	−	0.481102i	−0.508006	−	0.861354i	$-0.669617\pi$
$101$	4.18957	−	4.83502i	0.416877	−	0.481102i	0.924883	+	0.380252i	$0.124163\pi$
$102$		0			0
$103$	−8.38333	+	11.1988i	−0.826034	+	1.10345i	0.167038	+	0.985950i	$0.446580\pi$
$103$	−8.38333	+	11.1988i	−0.826034	+	1.10345i	−0.993073	+	0.117502i	$0.962511\pi$
$104$		0			0
$105$	2.58382	−	2.40121i	0.252155	−	0.234334i
$106$		0			0
$107$	−3.22835	−	8.65554i	−0.312096	−	0.836763i	−0.994399	−	0.105693i	$-0.966294\pi$
$107$	−3.22835	−	8.65554i	−0.312096	−	0.836763i	0.682302	−	0.731070i	$-0.260979\pi$
$108$		0			0
$109$	6.50609	−	1.91036i	0.623171	−	0.182979i	0.0451217	−	0.998981i	$-0.485632\pi$
$109$	6.50609	−	1.91036i	0.623171	−	0.182979i	0.578049	+	0.816002i	$0.303814\pi$
$110$		0			0
$111$	0.805934	−	2.74476i	0.0764959	−	0.260521i
$112$		0			0
$113$	7.05690	−	5.28273i	0.663857	−	0.496957i	−0.213408	−	0.976963i	$-0.568456\pi$
$113$	7.05690	−	5.28273i	0.663857	−	0.496957i	0.877265	+	0.480006i	$0.159366\pi$
$114$		0			0
$115$	8.38470	+	6.68557i	0.781877	+	0.623433i
$116$		0			0
$117$	−1.83366	+	1.37266i	−0.169522	+	0.126903i
$118$		0			0
$119$	1.37853	−	4.69484i	0.126370	−	0.430375i
$120$		0			0
$121$	2.78199	−	0.816865i	0.252908	−	0.0742604i
$122$		0			0
$123$	1.04119	+	2.79154i	0.0938810	+	0.251705i
$124$		0			0
$125$	−9.98396	−	5.03195i	−0.892993	−	0.450071i
$126$		0			0
$127$	−6.02422	+	8.04741i	−0.534563	+	0.714093i	−0.983790	−	0.179325i	$-0.942609\pi$
$127$	−6.02422	+	8.04741i	−0.534563	+	0.714093i	0.449227	+	0.893418i	$0.351699\pi$
$128$		0			0
$129$	−1.32173	+	1.52535i	−0.116372	+	0.134300i
$130$		0			0
$131$	−15.5724	−	10.0078i	−1.36057	−	0.874382i	−0.362232	−	0.932088i	$-0.617985\pi$
$131$	−15.5724	−	10.0078i	−1.36057	−	0.874382i	−0.998334	+	0.0577055i	$0.981622\pi$
$132$		0			0
$133$	13.9250	+	0.995939i	1.20745	+	0.0863588i
$134$		0			0
$135$	4.73375	+	0.858538i	0.407416	+	0.0738912i
$136$		0			0
$137$	0.824279	−	0.824279i	0.0704229	−	0.0704229i	−0.671018	−	0.741441i	$-0.734143\pi$
$137$	0.824279	−	0.824279i	0.0704229	−	0.0704229i	0.741441	+	0.671018i	$0.234143\pi$
$138$		0			0
$139$		−	3.37271i		−	0.286070i	−0.989718	−	0.143035i	$-0.954314\pi$
$139$		−	3.37271i		−	0.286070i	0.989718	−	0.143035i	$-0.0456861\pi$
$140$		0			0
$141$	1.55620	+	3.40761i	0.131056	+	0.286972i
$142$		0			0
$143$	−0.212604	+	2.97259i	−0.0177788	+	0.248580i
$144$		0			0
$145$	−2.56101	−	1.06355i	−0.212680	−	0.0883233i
$146$		0			0
$147$	−4.20532	+	0.300770i	−0.346849	+	0.0248071i
$148$		0			0
$149$	−2.65165	−	18.4426i	−0.217231	−	1.51088i	−0.748193	−	0.663482i	$-0.769078\pi$
$149$	−2.65165	−	18.4426i	−0.217231	−	1.51088i	0.530961	−	0.847396i	$-0.321831\pi$
$150$		0			0
$151$	−0.445897	+	0.286561i	−0.0362866	+	0.0233200i	−0.558658	−	0.829398i	$-0.688684\pi$
$151$	−0.445897	+	0.286561i	−0.0362866	+	0.0233200i	0.522372	+	0.852718i	$0.325047\pi$
$152$		0			0
$153$	3.05475	−	1.13936i	0.246962	−	0.0921120i
$154$		0			0
$155$	−7.87779	−	15.7739i	−0.632759	−	1.26699i
$156$		0			0
$157$	−21.7298	+	11.8654i	−1.73423	+	0.946959i	−0.792972	+	0.609259i	$0.791467\pi$
$157$	−21.7298	+	11.8654i	−1.73423	+	0.946959i	−0.941254	+	0.337700i	$0.890351\pi$
$158$		0			0
$159$	−0.157032	+	1.09218i	−0.0124534	+	0.0866156i
$160$		0			0
$161$	−4.50659	−	20.1257i	−0.355169	−	1.58613i
$162$		0			0
$163$	1.21553	+	1.62376i	0.0952079	+	0.127183i	0.845615	−	0.533793i	$-0.179234\pi$
$163$	1.21553	+	1.62376i	0.0952079	+	0.127183i	−0.750408	+	0.660975i	$0.770143\pi$
$164$		0			0
$165$	2.38280	−	1.91659i	0.185501	−	0.149206i
$166$		0			0
$167$	−5.44440	−	2.97287i	−0.421300	−	0.230047i	0.254591	−	0.967049i	$-0.418059\pi$
$167$	−5.44440	−	2.97287i	−0.421300	−	0.230047i	−0.675891	+	0.737001i	$0.736241\pi$
$168$		0			0
$169$	11.2440	+	5.13495i	0.864921	+	0.394996i
$170$		0			0
$171$	5.02914	+	7.82550i	0.384588	+	0.598431i
$172$		0			0
$173$	−8.61314	−	6.44771i	−0.654845	−	0.490210i	0.219439	−	0.975626i	$-0.429577\pi$
$173$	−8.61314	−	6.44771i	−0.654845	−	0.490210i	−0.874283	+	0.485416i	$0.838668\pi$
$174$		0			0
$175$	8.89649	+	19.5754i	0.672511	+	1.47976i
$176$		0			0
$177$	−0.313020	−	1.43893i	−0.0235280	−	0.108156i
$178$		0			0
$179$	−18.7677	+	16.2623i	−1.40277	+	1.21550i	−0.457497	+	0.889211i	$0.651254\pi$
$179$	−18.7677	+	16.2623i	−1.40277	+	1.21550i	−0.945269	+	0.326292i	$0.894201\pi$
$180$		0			0
$181$	11.8447	−	5.40929i	0.880410	−	0.402070i	0.0766739	−	0.997056i	$-0.475570\pi$
$181$	11.8447	−	5.40929i	0.880410	−	0.402070i	0.803736	+	0.594987i	$0.202843\pi$
$182$		0			0
$183$	2.88621	+	2.88621i	0.213355	+	0.213355i
$184$		0			0
$185$	14.3149	+	9.95848i	1.05246	+	0.732162i
$186$		0			0
$187$	1.48241	−	3.97449i	0.108405	−	0.290644i
$188$		0			0
$189$	−6.05911	−	6.99259i	−0.440736	−	0.508636i
$190$		0			0
$191$	2.45981	−	3.82754i	0.177986	−	0.276951i	−0.740786	−	0.671742i	$-0.765547\pi$
$191$	2.45981	−	3.82754i	0.177986	−	0.276951i	0.918771	+	0.394791i	$0.129183\pi$
$192$		0			0
$193$	1.48171	+	20.7170i	0.106656	+	1.49124i	0.715869	+	0.698235i	$0.246031\pi$
$193$	1.48171	+	20.7170i	0.106656	+	1.49124i	−0.609213	+	0.793007i	$0.708514\pi$
$194$		0			0
$195$	0.206486	+	0.622292i	0.0147868	+	0.0445633i
$196$		0			0
$197$	−3.77681	−	0.821596i	−0.269087	−	0.0585363i	0.0759972	−	0.997108i	$-0.475786\pi$
$197$	−3.77681	−	0.821596i	−0.269087	−	0.0585363i	−0.345084	+	0.938572i	$0.612150\pi$
$198$		0			0
$199$	2.68916	−	5.88845i	0.190630	−	0.417421i	−0.790050	−	0.613043i	$-0.789945\pi$
$199$	2.68916	−	5.88845i	0.190630	−	0.417421i	0.980679	+	0.195622i	$0.0626725\pi$
$200$		0			0
$201$	−0.989564	−	3.37014i	−0.0697984	−	0.237712i
$202$		0			0
$203$	2.55593	+	4.68084i	0.179391	+	0.328530i
$204$		0			0
$205$	−18.1511	+	0.631631i	−1.26773	+	0.0441150i
$206$		0			0
$207$	8.93583	−	10.4403i	0.621083	−	0.725648i
$208$		0			0
$209$	11.9798	+	1.72243i	0.828657	+	0.119143i
$210$		0			0
$211$	−13.9374	−	4.09239i	−0.959490	−	0.281732i	−0.235757	−	0.971812i	$-0.575757\pi$
$211$	−13.9374	−	4.09239i	−0.959490	−	0.281732i	−0.723733	+	0.690080i	$0.757575\pi$
$212$		0			0
$213$	−1.15398	+	2.11335i	−0.0790692	+	0.144804i
$214$		0			0
$215$	−6.26845	−	10.5870i	−0.427504	−	0.722026i
$216$		0			0
$217$	−7.20795	+	33.1344i	−0.489308	+	2.24931i
$218$		0			0
$219$	0.0762960	−	0.0109697i	0.00515560	−	0.000741264i
$220$		0			0
$221$	0.687367	+	0.595607i	0.0462373	+	0.0400649i
$222$		0			0
$223$	11.1239	−	2.41986i	0.744913	−	0.162046i	0.175938	−	0.984401i	$-0.443704\pi$
$223$	11.1239	−	2.41986i	0.744913	−	0.162046i	0.568974	+	0.822355i	$0.307340\pi$
$224$		0			0
$225$	−6.88932	+	12.5621i	−0.459288	+	0.837475i
$226$		0			0
$227$	10.0279	+	3.74021i	0.665575	+	0.248247i	0.659466	−	0.751735i	$-0.270783\pi$
$227$	10.0279	+	3.74021i	0.665575	+	0.248247i	0.00610923	+	0.999981i	$0.498055\pi$
$228$		0			0
$229$	−13.9527			−0.922019			−0.461009	−	0.887395i	$-0.652513\pi$
$229$	−13.9527			−0.922019			−0.461009	+	0.887395i	$0.652513\pi$
$230$		0			0
$231$	−5.88108			−0.386947
$232$		0			0
$233$	−5.28142	−	1.96987i	−0.345998	−	0.129050i	0.170457	−	0.985365i	$-0.445476\pi$
$233$	−5.28142	−	1.96987i	−0.345998	−	0.129050i	−0.516454	+	0.856315i	$0.672748\pi$
$234$		0			0
$235$	−22.7075	+	2.42028i	−1.48127	+	0.157882i
$236$		0			0
$237$	−2.82870	+	0.615346i	−0.183744	+	0.0399710i
$238$		0			0
$239$	−19.2547	−	16.6843i	−1.24548	−	1.07922i	−0.993774	−	0.111415i	$-0.964462\pi$
$239$	−19.2547	−	16.6843i	−1.24548	−	1.07922i	−0.251710	−	0.967803i	$-0.580993\pi$
$240$		0			0
$241$	22.8968	−	3.29206i	1.47491	−	0.212060i	0.642528	−	0.766263i	$-0.277886\pi$
$241$	22.8968	−	3.29206i	1.47491	−	0.212060i	0.832382	+	0.554203i	$0.186977\pi$
$242$		0			0
$243$	1.98076	−	9.10542i	0.127066	−	0.584113i
$244$		0			0
$245$	6.37874	−	24.8965i	0.407523	−	1.59058i
$246$		0			0
$247$	−1.24365	+	2.27757i	−0.0791315	+	0.144918i
$248$		0			0
$249$	−2.20839	−	0.648443i	−0.139951	−	0.0410934i
$250$		0			0
$251$	−4.98207	−	0.716313i	−0.314465	−	0.0452133i	−0.0167248	−	0.999860i	$-0.505324\pi$
$251$	−4.98207	−	0.716313i	−0.314465	−	0.0452133i	−0.297740	+	0.954647i	$0.596233\pi$
$252$		0			0
$253$	−2.65226	−	17.6820i	−0.166746	−	1.11166i
$254$		0			0
$255$	−0.0324561	−	0.932688i	−0.00203248	−	0.0584072i
$256$		0			0
$257$	−14.1228	−	25.8639i	−0.880953	−	1.61335i	−0.786308	−	0.617834i	$-0.788010\pi$
$257$	−14.1228	−	25.8639i	−0.880953	−	1.61335i	−0.0946451	−	0.995511i	$-0.530172\pi$
$258$		0			0
$259$	−9.44853	−	32.1787i	−0.587103	−	1.99949i
$260$		0			0
$261$	−1.47622	+	3.23247i	−0.0913756	+	0.200085i
$262$		0			0
$263$	−7.95757	−	1.73106i	−0.490684	−	0.106742i	−0.0395862	−	0.999216i	$-0.512604\pi$
$263$	−7.95757	−	1.73106i	−0.490684	−	0.106742i	−0.451098	+	0.892474i	$0.648968\pi$
$264$		0			0
$265$	−6.01206	−	3.01631i	−0.369318	−	0.185290i
$266$		0			0
$267$	−0.419794	−	5.86949i	−0.0256910	−	0.359207i
$268$		0			0
$269$	−8.70662	+	13.5478i	−0.530852	+	0.826022i	−0.998317	−	0.0579895i	$-0.981531\pi$
$269$	−8.70662	+	13.5478i	−0.530852	+	0.826022i	0.467465	+	0.884012i	$0.345167\pi$
$270$		0			0
$271$	13.6575	+	15.7616i	0.829633	+	0.957447i	0.999608	−	0.0280012i	$-0.00891422\pi$
$271$	13.6575	+	15.7616i	0.829633	+	0.957447i	−0.169975	+	0.985448i	$0.554369\pi$
$272$		0			0
$273$	0.440662	−	1.18146i	0.0266701	−	0.0715052i
$274$		0			0
$275$	6.48236	+	17.4776i	0.390901	+	1.05394i
$276$		0			0
$277$	−12.9909	−	12.9909i	−0.780547	−	0.780547i	0.199376	−	0.979923i	$-0.436109\pi$
$277$	−12.9909	−	12.9909i	−0.780547	−	0.780547i	−0.979923	+	0.199376i	$0.936109\pi$
$278$		0			0
$279$	−20.5526	+	9.38604i	−1.23045	+	0.561927i
$280$		0			0
$281$	−15.8433	+	13.7283i	−0.945132	+	0.818961i	−0.983612	−	0.180298i	$-0.942294\pi$
$281$	−15.8433	+	13.7283i	−0.945132	+	0.818961i	0.0384805	+	0.999259i	$0.487748\pi$
$282$		0			0
$283$	−7.04116	−	32.3677i	−0.418554	−	1.92406i	−0.380491	−	0.924785i	$-0.624245\pi$
$283$	−7.04116	−	32.3677i	−0.418554	−	1.92406i	−0.0380630	−	0.999275i	$-0.512119\pi$
$284$		0			0
$285$	2.58061	−	0.656144i	0.152862	−	0.0388666i
$286$		0			0
$287$	27.9625	+	20.9325i	1.65058	+	1.23561i
$288$		0			0
$289$	8.49098	+	13.2122i	0.499470	+	0.777190i
$290$		0			0
$291$	−2.20834	−	1.00851i	−0.129455	−	0.0591201i
$292$		0			0
$293$	−10.6953	−	5.84007i	−0.624825	−	0.341180i	0.135447	−	0.990785i	$-0.456753\pi$
$293$	−10.6953	−	5.84007i	−0.624825	−	0.341180i	−0.760273	+	0.649604i	$0.774935\pi$
$294$		0			0
$295$	8.92439	+	0.967737i	0.519598	+	0.0563438i
$296$		0			0
$297$	−4.80701	−	6.42141i	−0.278931	−	0.372608i
$298$		0			0
$299$	3.75089	+	0.792071i	0.216920	+	0.0458066i
$300$		0			0
$301$	−3.36750	+	23.4215i	−0.194100	+	1.34999i
$302$		0			0
$303$	−2.05969	+	1.12468i	−0.118326	+	0.0646111i
$304$		0			0
$305$	−22.2601	+	11.1171i	−1.27461	+	0.636565i
$306$		0			0
$307$	22.1757	−	8.27111i	1.26563	−	0.472057i	0.375105	−	0.926982i	$-0.377607\pi$
$307$	22.1757	−	8.27111i	1.26563	−	0.472057i	0.890530	+	0.454925i	$0.150334\pi$
$308$		0			0
$309$	4.31681	−	2.77424i	0.245575	−	0.157821i
$310$		0			0
$311$	−0.981677	−	6.82771i	−0.0556658	−	0.387164i	−0.998540	−	0.0540155i	$-0.982798\pi$
$311$	−0.981677	−	6.82771i	−0.0556658	−	0.387164i	0.942874	−	0.333149i	$-0.108111\pi$
$312$		0			0
$313$	−23.6755	+	1.69330i	−1.33822	+	0.0957112i	−0.722016	−	0.691877i	$-0.756784\pi$
$313$	−23.6755	+	1.69330i	−1.33822	+	0.0957112i	−0.616202	+	0.787588i	$0.711330\pi$
$314$		0			0
$315$	25.4665	−	10.5213i	1.43487	−	0.592806i
$316$		0			0
$317$	−0.0537117	+	0.750988i	−0.00301675	+	0.0421797i	−0.998738	−	0.0502334i	$-0.984003\pi$
$317$	−0.0537117	+	0.750988i	−0.00301675	+	0.0421797i	0.995721	+	0.0924131i	$0.0294580\pi$
$318$		0			0
$319$	1.92069	+	4.20572i	0.107538	+	0.235475i
$320$		0			0
$321$			3.38864i			0.189135i
$322$		0			0
$323$	2.61183	−	2.61183i	0.145326	−	0.145326i
$324$		0			0
$325$	−3.99681	−	0.00731802i	−0.221703	−	0.000405931i
$326$		0			0
$327$	−2.48095	−	0.177441i	−0.137197	−	0.00981250i
$328$		0			0
$329$	36.9467	+	23.7442i	2.03694	+	1.30906i
$330$		0			0
$331$	13.1452	−	15.1704i	0.722528	−	0.833842i	−0.269081	−	0.963118i	$-0.586720\pi$
$331$	13.1452	−	15.1704i	0.722528	−	0.833842i	0.991609	+	0.129276i	$0.0412653\pi$
$332$		0			0
$333$	13.3917	−	17.8892i	0.733861	−	0.980323i
$334$		0			0
$335$	21.3970	+	0.783811i	1.16904	+	0.0428242i
$336$		0			0
$337$	9.55634	+	25.6215i	0.520567	+	1.39569i	0.885491	+	0.464657i	$0.153822\pi$
$337$	9.55634	+	25.6215i	0.520567	+	1.39569i	−0.364924	+	0.931037i	$0.618905\pi$
$338$		0			0
$339$	−3.10255	+	0.910991i	−0.168507	+	0.0494782i
$340$		0			0
$341$	−8.28215	+	28.2064i	−0.448504	+	1.52746i
$342$		0			0
$343$	−15.4703	+	11.5809i	−0.835319	+	0.625312i
$344$		0			0
$345$	−2.02470	−	3.37257i	−0.109006	−	0.181573i
$346$		0			0
$347$	1.47225	−	1.10212i	0.0790348	−	0.0591647i	−0.559030	−	0.829148i	$-0.688826\pi$
$347$	1.47225	−	1.10212i	0.0790348	−	0.0591647i	0.638064	+	0.769983i	$0.279735\pi$
$348$		0			0
$349$	4.65035	−	15.8376i	0.248928	−	0.847770i	−0.736320	−	0.676634i	$-0.763438\pi$
$349$	4.65035	−	15.8376i	0.248928	−	0.847770i	0.985247	−	0.171136i	$-0.0547438\pi$
$350$		0			0
$351$	1.65019	−	0.484539i	0.0880806	−	0.0258628i
$352$		0			0
$353$	4.60494	+	12.3463i	0.245096	+	0.657128i	0.999999	+	0.00129186i	$0.000411212\pi$
$353$	4.60494	+	12.3463i	0.245096	+	0.657128i	−0.754903	+	0.655837i	$0.772316\pi$
$354$		0			0
$355$	−9.99217	−	10.7521i	−0.530329	−	0.570661i
$356$		0			0
$357$	−1.07561	+	1.43684i	−0.0569272	+	0.0760459i
$358$		0			0
$359$	−12.9289	+	14.9207i	−0.682360	+	0.787486i	−0.986257	−	0.165219i	$-0.947167\pi$
$359$	−12.9289	+	14.9207i	−0.682360	+	0.787486i	0.303897	+	0.952705i	$0.401712\pi$
$360$		0			0
$361$	−7.11814	−	4.57455i	−0.374639	−	0.240766i
$362$		0			0
$363$	−1.06085	−	0.0758732i	−0.0556799	−	0.00398231i
$364$		0			0
$365$	−0.0838512	+	0.462333i	−0.00438897	+	0.0241996i
$366$		0			0
$367$	21.8618	−	21.8618i	1.14118	−	1.14118i	0.152940	−	0.988235i	$-0.451126\pi$
$367$	21.8618	−	21.8618i	1.14118	−	1.14118i	0.988235	−	0.152940i	$-0.0488742\pi$
$368$		0			0
$369$			23.2741i			1.21160i
$370$		0			0
$371$	5.37384	+	11.7671i	0.278996	+	0.610916i
$372$		0			0
$373$	−0.0679602	+	0.950208i	−0.00351885	+	0.0491999i	−0.998908	−	0.0467175i	$-0.985124\pi$
$373$	−0.0679602	+	0.950208i	−0.00351885	+	0.0491999i	0.995389	+	0.0959174i	$0.0305785\pi$
$374$		0			0
$375$	2.78632	+	3.00925i	0.143885	+	0.155397i
$376$		0			0
$377$	−0.988807	+	0.0707209i	−0.0509262	+	0.00364231i
$378$		0			0
$379$	3.40094	+	23.6541i	0.174695	+	1.21503i	0.868803	+	0.495158i	$0.164890\pi$
$379$	3.40094	+	23.6541i	0.174695	+	1.21503i	−0.694108	+	0.719871i	$0.744201\pi$
$380$		0			0
$381$	3.10203	−	1.99356i	0.158922	−	0.102133i
$382$		0			0
$383$	3.35132	−	1.24998i	0.171245	−	0.0638709i	−0.262380	−	0.964965i	$-0.584507\pi$
$383$	3.35132	−	1.24998i	0.171245	−	0.0638709i	0.433624	+	0.901094i	$0.357235\pi$
$384$		0			0
$385$	11.3527	−	34.0055i	0.578588	−	1.73308i
$386$		0			0
$387$	−13.8380	+	7.55613i	−0.703426	+	0.384099i
$388$		0			0
$389$	3.01023	−	20.9366i	0.152625	−	1.06153i	−0.759173	−	0.650889i	$-0.774396\pi$
$389$	3.01023	−	20.9366i	0.152625	−	1.06153i	0.911797	−	0.410640i	$-0.134695\pi$
$390$		0			0
$391$	−4.80507	−	2.58592i	−0.243003	−	0.130775i
$392$		0			0
$393$	4.06915	+	5.43574i	0.205261	+	0.274197i
$394$		0			0
$395$	1.90241	−	17.5439i	0.0957208	−	0.882730i
$396$		0			0
$397$	−21.4991	−	11.7394i	−1.07901	−	0.589185i	−0.161491	−	0.986874i	$-0.551630\pi$
$397$	−21.4991	−	11.7394i	−1.07901	−	0.589185i	−0.917520	+	0.397690i	$0.869812\pi$
$398$		0			0
$399$	−4.65819	−	2.12732i	−0.233201	−	0.106499i
$400$		0			0
$401$	20.5109	+	31.9156i	1.02427	+	1.59379i	0.781699	+	0.623656i	$0.214353\pi$
$401$	20.5109	+	31.9156i	1.02427	+	1.59379i	0.242568	+	0.970134i	$0.422010\pi$
$402$		0			0
$403$	−5.04586	−	3.77728i	−0.251352	−	0.188160i
$404$		0			0
$405$	15.0053	+	8.92166i	0.745621	+	0.443321i
$406$		0			0
$407$	−6.18025	−	28.4102i	−0.306344	−	1.40824i
$408$		0			0
$409$	12.5576	−	10.8812i	0.620933	−	0.538042i	−0.286585	−	0.958055i	$-0.592520\pi$
$409$	12.5576	−	10.8812i	0.620933	−	0.538042i	0.907518	+	0.420013i	$0.137975\pi$
$410$		0			0
$411$	−0.388957	+	0.177631i	−0.0191858	+	0.00876188i
$412$		0			0
$413$	−12.2076	−	12.2076i	−0.600695	−	0.600695i
$414$		0			0
$415$	8.01245	−	11.5176i	0.393316	−	0.565377i
$416$		0			0
$417$	−0.432344	+	1.15916i	−0.0211720	+	0.0567642i
$418$		0			0
$419$	1.22392	+	1.41247i	0.0597922	+	0.0690039i	0.784858	−	0.619676i	$-0.212736\pi$
$419$	1.22392	+	1.41247i	0.0597922	+	0.0690039i	−0.725066	+	0.688680i	$0.758191\pi$
$420$		0			0
$421$	−12.8860	+	20.0510i	−0.628026	+	0.977228i	0.370796	+	0.928714i	$0.379085\pi$
$421$	−12.8860	+	20.0510i	−0.628026	+	0.977228i	−0.998823	+	0.0485139i	$0.984551\pi$
$422$		0			0
$423$	2.08765	+	29.1891i	0.101505	+	1.41922i
$424$		0			0
$425$	5.45563	+	1.61277i	0.264637	+	0.0782310i
$426$		0			0
$427$	46.7593	+	10.1719i	2.26284	+	0.492251i
$428$		0			0
$429$	0.454121	−	0.994386i	0.0219252	−	0.0480094i
$430$		0			0
$431$	−6.34581	−	21.6118i	−0.305667	−	1.04101i	−0.958875	−	0.283827i	$-0.908396\pi$
$431$	−6.34581	−	21.6118i	−0.305667	−	1.04101i	0.653209	−	0.757178i	$-0.273422\pi$
$432$		0			0
$433$	1.65762	+	3.03571i	0.0796602	+	0.145887i	0.914473	−	0.404648i	$-0.132606\pi$
$433$	1.65762	+	3.03571i	0.0796602	+	0.145887i	−0.834813	+	0.550534i	$0.814424\pi$
$434$		0			0
$435$	0.743851	+	0.693822i	0.0356649	+	0.0332662i
$436$		0			0
$437$	4.29522	−	14.9646i	0.205468	−	0.715855i
$438$		0			0
$439$	21.7715	+	3.13027i	1.03910	+	0.149400i	0.640683	−	0.767806i	$-0.278651\pi$
$439$	21.7715	+	3.13027i	1.03910	+	0.149400i	0.398415	+	0.917205i	$0.369560\pi$
$440$		0			0
$441$	−31.6005	−	9.27874i	−1.50479	−	0.441845i
$442$		0			0
$443$	−10.7320	+	19.6542i	−0.509892	+	0.933797i	0.488241	+	0.872709i	$0.337639\pi$
$443$	−10.7320	+	19.6542i	−0.509892	+	0.933797i	−0.998132	+	0.0610879i	$0.980543\pi$
$444$		0			0
$445$	34.7489	+	8.90301i	1.64725	+	0.422043i
$446$		0			0
$447$	−1.45280	+	6.67840i	−0.0687149	+	0.315878i
$448$		0			0
$449$	11.1774	−	1.60706i	0.527492	−	0.0758419i	0.126576	−	0.991957i	$-0.459601\pi$
$449$	11.1774	−	1.60706i	0.527492	−	0.0758419i	0.400916	+	0.916115i	$0.368692\pi$
$450$		0			0
$451$	22.8853	+	19.8303i	1.07763	+	0.933770i
$452$		0			0
$453$	0.189983	−	0.0413283i	0.00892618	−	0.00194177i
$454$		0			0
$455$	5.98078	+	4.82865i	0.280383	+	0.226371i
$456$		0			0
$457$	−7.94233	−	2.96234i	−0.371527	−	0.138572i	0.156764	−	0.987636i	$-0.449894\pi$
$457$	−7.94233	−	2.96234i	−0.371527	−	0.138572i	−0.528290	+	0.849064i	$0.677167\pi$
$458$		0			0
$459$	−2.44802			−0.114264
$460$		0			0
$461$	22.2123			1.03453			0.517264	−	0.855826i	$-0.326951\pi$
$461$	22.2123			1.03453			0.517264	+	0.855826i	$0.326951\pi$
$462$		0			0
$463$	1.65223	+	0.616251i	0.0767858	+	0.0286396i	0.387564	−	0.921843i	$-0.373317\pi$
$463$	1.65223	+	0.616251i	0.0767858	+	0.0286396i	−0.310778	+	0.950483i	$0.600589\pi$
$464$		0			0
$465$	0.685462	+	6.43112i	0.0317876	+	0.298236i
$466$		0			0
$467$	−2.27926	+	0.495823i	−0.105472	+	0.0229440i	−0.264991	−	0.964251i	$-0.585369\pi$
$467$	−2.27926	+	0.495823i	−0.105472	+	0.0229440i	0.159520	+	0.987195i	$0.449005\pi$
$468$		0			0
$469$	−31.1207	−	26.9663i	−1.43702	−	1.24519i
$470$		0			0
$471$	8.98925	−	1.29246i	0.414203	−	0.0595534i
$472$		0			0
$473$	−4.36050	+	20.0449i	−0.200496	+	0.921666i
$474$		0			0
$475$	−1.18759	+	16.1881i	−0.0544906	+	0.742763i
$476$		0			0
$477$	−4.13090	+	7.56517i	−0.189141	+	0.346386i
$478$		0			0
$479$	−29.9443	−	8.79245i	−1.36819	−	0.401737i	−0.486548	−	0.873654i	$-0.661744\pi$
$479$	−29.9443	−	8.79245i	−1.36819	−	0.401737i	−0.881643	+	0.471917i	$0.843562\pi$
$480$		0			0
$481$	6.17044	+	0.887175i	0.281348	+	0.0404517i
$482$		0			0
$483$	−1.03104	+	7.49465i	−0.0469138	+	0.341019i
$484$		0			0
$485$	10.0943	−	10.8222i	0.458360	−	0.491410i
$486$		0			0
$487$	−14.6086	−	26.7536i	−0.661978	−	1.21232i	−0.965725	−	0.259569i	$-0.916420\pi$
$487$	−14.6086	−	26.7536i	−0.661978	−	1.21232i	0.303747	−	0.952753i	$-0.401762\pi$
$488$		0			0
$489$	−0.209615	−	0.713884i	−0.00947912	−	0.0322829i
$490$		0			0
$491$	14.1288	−	30.9377i	0.637623	−	1.39620i	−0.264358	−	0.964425i	$-0.585160\pi$
$491$	14.1288	−	30.9377i	0.637623	−	1.39620i	0.901981	−	0.431776i	$-0.142113\pi$
$492$		0			0
$493$	1.37880	+	0.299941i	0.0620982	+	0.0135086i
$494$		0			0
$495$	22.6722	−	7.52300i	1.01904	−	0.338134i
$496$		0			0
$497$	2.01386	+	28.1574i	0.0903339	+	1.26303i
$498$		0			0
$499$	−7.31967	+	11.3896i	−0.327673	+	0.509870i	−0.965532	−	0.260284i	$-0.916184\pi$
$499$	−7.31967	+	11.3896i	−0.327673	+	0.509870i	0.637859	+	0.770153i	$0.279820\pi$
$500$		0			0
$501$	1.49008	+	1.71965i	0.0665720	+	0.0768282i
$502$		0			0
$503$	11.4074	−	30.5845i	0.508633	−	1.36370i	−0.388301	−	0.921532i	$-0.626938\pi$
$503$	11.4074	−	30.5845i	0.508633	−	1.36370i	0.896934	−	0.442164i	$-0.145789\pi$
$504$		0			0
$505$	−2.52711	−	14.0806i	−0.112455	−	0.626578i
$506$		0			0
$507$	−3.20617	−	3.20617i	−0.142391	−	0.142391i
$508$		0			0
$509$	27.1275	−	12.3887i	1.20241	−	0.549121i	0.289457	−	0.957191i	$-0.406525\pi$
$509$	27.1275	−	12.3887i	1.20241	−	0.549121i	0.912951	+	0.408070i	$0.133798\pi$
$510$		0			0
$511$	0.682948	−	0.591778i	0.0302118	−	0.0261787i
$512$		0			0
$513$	−1.48468	−	6.82497i	−0.0655503	−	0.301330i
$514$		0			0
$515$	7.70812	+	30.3159i	0.339660	+	1.33588i
$516$		0			0
$517$	30.4803	+	22.8172i	1.34052	+	1.00350i
$518$		0			0
$519$	2.13370	+	3.32010i	0.0936590	+	0.145736i
$520$		0			0
$521$	12.4291	+	5.67619i	0.544530	+	0.248678i	0.668635	−	0.743591i	$-0.266879\pi$
$521$	12.4291	+	5.67619i	0.544530	+	0.248678i	−0.124105	+	0.992269i	$0.539606\pi$
$522$		0			0
$523$	26.7183	+	14.5893i	1.16831	+	0.637945i	0.941836	−	0.336073i	$-0.109099\pi$
$523$	26.7183	+	14.5893i	1.16831	+	0.637945i	0.226473	+	0.974018i	$0.427281\pi$
$524$		0			0
$525$	−0.548269	−	7.86823i	−0.0239284	−	0.343398i
$526$		0			0
$527$	5.37654	+	7.18222i	0.234206	+	0.312862i
$528$		0			0
$529$	−22.9983	+	0.280052i	−0.999926	+	0.0121762i
$530$		0			0
$531$	1.63710	−	11.3863i	0.0710440	−	0.494122i
$532$		0			0
$533$	−5.69850	+	3.11161i	−0.246829	+	0.134779i
$534$		0			0
$535$	−19.5937	−	6.54135i	−0.847110	−	0.282807i
$536$		0			0
$537$	8.53487	−	3.18334i	0.368307	−	0.137371i
$538$		0			0
$539$	−36.0483	+	23.1669i	−1.55271	+	0.997867i
$540$		0			0
$541$	3.36965	+	23.4364i	0.144872	+	1.00761i	0.924450	+	0.381304i	$0.124525\pi$
$541$	3.36965	+	23.4364i	0.144872	+	1.00761i	−0.779578	+	0.626306i	$0.784566\pi$
$542$		0			0
$543$	−4.76428	+	0.340748i	−0.204455	+	0.0146229i
$544$		0			0
$545$	5.81516	−	14.0028i	0.249094	−	0.599813i
$546$		0			0
$547$	1.65010	−	23.0714i	0.0705533	−	0.986464i	−0.831691	−	0.555239i	$-0.812627\pi$
$547$	1.65010	−	23.0714i	0.0705533	−	0.986464i	0.902244	−	0.431225i	$-0.141919\pi$
$548$		0			0
$549$	13.2456	+	29.0038i	0.565307	+	1.23785i
$550$		0			0
$551$			4.02595i			0.171511i
$552$		0			0
$553$	−23.9981	+	23.9981i	−1.02050	+	1.02050i
$554$		0			0
$555$	−3.64330	−	5.25762i	−0.154649	−	0.223173i
$556$		0			0
$557$	−22.1660	−	1.58534i	−0.939203	−	0.0671731i	−0.406663	−	0.913578i	$-0.633308\pi$
$557$	−22.1660	−	1.58534i	−0.939203	−	0.0671731i	−0.532540	+	0.846405i	$0.678762\pi$
$558$		0			0
$559$	−3.70012	−	2.37793i	−0.156499	−	0.100576i
$560$		0			0
$561$	−1.01897	+	1.17595i	−0.0430210	+	0.0496488i
$562$		0			0
$563$	−3.82795	+	5.11354i	−0.161329	+	0.215510i	−0.873920	−	0.486069i	$-0.838430\pi$
$563$	−3.82795	+	5.11354i	−0.161329	+	0.215510i	0.712592	+	0.701579i	$0.247521\pi$
$564$		0			0
$565$	0.721576	−	19.6981i	0.0303569	−	0.828704i
$566$		0			0
$567$	−11.7329	−	31.4571i	−0.492736	−	1.32108i
$568$		0			0
$569$	−14.5403	+	4.26941i	−0.609560	+	0.178983i	−0.571921	−	0.820309i	$-0.693802\pi$
$569$	−14.5403	+	4.26941i	−0.609560	+	0.178983i	−0.0376385	+	0.999291i	$0.511984\pi$
$570$		0			0
$571$	−2.62519	+	8.94056i	−0.109861	+	0.374151i	−0.996009	−	0.0892503i	$-0.971553\pi$
$571$	−2.62519	+	8.94056i	−0.109861	+	0.374151i	0.886149	+	0.463401i	$0.153371\pi$
$572$		0			0
$573$	−1.33605	+	1.00016i	−0.0558144	+	0.0417821i
$574$		0			0
$575$	23.4092	−	5.19684i	0.976233	−	0.216723i
$576$		0			0
$577$	25.6128	−	19.1735i	1.06628	−	0.798205i	0.0860912	−	0.996287i	$-0.472562\pi$
$577$	25.6128	−	19.1735i	1.06628	−	0.798205i	0.980185	+	0.198083i	$0.0634714\pi$
$578$		0			0
$579$	2.14644	−	7.31010i	0.0892030	−	0.303798i
$580$		0			0
$581$	−25.8906	+	7.60216i	−1.07412	+	0.315391i
$582$		0			0
$583$	3.91915	+	10.5077i	0.162315	+	0.435183i
$584$		0			0
$585$	−0.187494	+	5.11835i	−0.00775193	+	0.211618i
$586$		0			0
$587$	−7.46220	+	9.96833i	−0.307998	+	0.411437i	−0.927657	−	0.373434i	$-0.878180\pi$
$587$	−7.46220	+	9.96833i	−0.307998	+	0.411437i	0.619659	+	0.784871i	$0.287271\pi$
$588$		0			0
$589$	−16.7629	+	19.3454i	−0.690704	+	0.797114i
$590$		0			0
$591$	1.19272	+	0.766517i	0.0490621	+	0.0315303i
$592$		0			0
$593$	−2.89695	−	0.207194i	−0.118963	−	0.00850842i	0.0117306	−	0.999931i	$-0.496266\pi$
$593$	−2.89695	−	0.207194i	−0.118963	−	0.00850842i	−0.130694	+	0.991423i	$0.541721\pi$
$594$		0			0
$595$	−6.23177	−	8.99302i	−0.255478	−	0.368678i
$596$		0			0
$597$	−1.67906	+	1.67906i	−0.0687195	+	0.0687195i
$598$		0			0
$599$		−	22.5754i		−	0.922407i	−0.887294	−	0.461204i	$-0.847418\pi$
$599$		−	22.5754i		−	0.922407i	0.887294	−	0.461204i	$-0.152582\pi$
$600$		0			0
$601$	12.4720	+	27.3098i	0.508743	+	1.11399i	0.973528	+	0.228568i	$0.0734043\pi$
$601$	12.4720	+	27.3098i	0.508743	+	1.11399i	−0.464785	+	0.885424i	$0.653868\pi$
$602$		0			0
$603$	1.95740	−	27.3681i	0.0797116	−	1.11451i
$604$		0			0
$605$	2.48654	−	5.98754i	0.101092	−	0.243428i
$606$		0			0
$607$	−12.9013	+	0.922718i	−0.523647	+	0.0374520i	−0.330661	−	0.943750i	$-0.607272\pi$
$607$	−12.9013	+	0.922718i	−0.523647	+	0.0374520i	−0.192986	+	0.981202i	$0.561817\pi$
$608$		0			0
$609$	−0.278410	−	1.93638i	−0.0112817	−	0.0784663i
$610$		0			0
$611$	−6.86764	+	4.41356i	−0.277835	+	0.178554i
$612$		0			0
$613$	−45.0233	+	16.7928i	−1.81847	+	0.678256i	−0.824873	+	0.565319i	$0.808753\pi$
$613$	−45.0233	+	16.7928i	−1.81847	+	0.678256i	−0.993602	+	0.112937i	$0.963974\pi$
$614$		0			0
$615$	6.31927	+	2.10968i	0.254817	+	0.0850706i
$616$		0			0
$617$	−0.351689	+	0.192037i	−0.0141585	+	0.00773111i	−0.486313	−	0.873785i	$-0.661658\pi$
$617$	−0.351689	+	0.192037i	−0.0141585	+	0.00773111i	0.472154	+	0.881516i	$0.343477\pi$
$618$		0			0
$619$	4.23051	−	29.4238i	0.170039	−	1.18264i	−0.708759	−	0.705450i	$-0.750745\pi$
$619$	4.23051	−	29.4238i	0.170039	−	1.18264i	0.878798	−	0.477194i	$-0.158346\pi$
$620$		0			0
$621$	−9.02596	+	5.00012i	−0.362199	+	0.200648i
$622$		0			0
$623$	−41.3429	−	55.2277i	−1.65637	−	2.21265i
$624$		0			0
$625$	−22.7787	+	10.3020i	−0.911147	+	0.412081i
$626$		0			0
$627$	−3.89649	−	2.12765i	−0.155611	−	0.0849700i
$628$		0			0
$629$	−8.07139	−	3.68608i	−0.321827	−	0.146974i
$630$		0			0
$631$	9.65970	+	15.0308i	0.384547	+	0.598366i	0.978528	−	0.206112i	$-0.0660812\pi$
$631$	9.65970	+	15.0308i	0.384547	+	0.598366i	−0.593982	+	0.804479i	$0.702445\pi$
$632$		0			0
$633$	4.26550	+	3.19312i	0.169539	+	0.126915i
$634$		0			0
$635$	5.53901	+	21.7849i	0.219809	+	0.864506i
$636$		0			0
$637$	−1.95297	−	8.97767i	−0.0773796	−	0.355708i
$638$		0			0
$639$	−14.2154	+	12.3177i	−0.562352	+	0.487281i
$640$		0			0
$641$	−16.7632	+	7.65550i	−0.662107	+	0.302374i	−0.717980	−	0.696064i	$-0.754933\pi$
$641$	−16.7632	+	7.65550i	−0.662107	+	0.302374i	0.0558729	+	0.998438i	$0.482206\pi$
$642$		0			0
$643$	0.157120	+	0.157120i	0.00619622	+	0.00619622i	0.710198	−	0.704002i	$-0.248605\pi$
$643$	0.157120	+	0.157120i	0.00619622	+	0.00619622i	−0.704002	+	0.710198i	$0.748605\pi$
$644$		0			0
$645$	0.797254	+	4.44215i	0.0313918	+	0.174910i
$646$		0			0
$647$	−3.04960	+	8.17631i	−0.119892	+	0.321444i	−0.983008	−	0.183562i	$-0.941237\pi$
$647$	−3.04960	+	8.17631i	−0.119892	+	0.321444i	0.863116	+	0.505006i	$0.168510\pi$
$648$		0			0
$649$	−9.80121	−	11.3112i	−0.384731	−	0.444003i
$650$		0			0
$651$	6.72474	−	10.4639i	0.263563	−	0.410113i
$652$		0			0
$653$	−3.24803	−	45.4134i	−0.127105	−	1.77716i	−0.516689	−	0.856173i	$-0.672836\pi$
$653$	−3.24803	−	45.4134i	−0.127105	−	1.77716i	0.389584	−	0.920991i	$-0.372619\pi$
$654$		0			0
$655$	−39.2855	+	13.0355i	−1.53501	+	0.509340i
$656$		0			0
$657$	0.588369	+	0.127992i	0.0229545	+	0.00499344i
$658$		0			0
$659$	−2.92430	+	6.40332i	−0.113914	+	0.249438i	−0.957999	−	0.286773i	$-0.907418\pi$
$659$	−2.92430	+	6.40332i	−0.113914	+	0.249438i	0.844084	+	0.536211i	$0.180145\pi$
$660$		0			0
$661$	11.0030	+	37.4729i	0.427968	+	1.45753i	0.838109	+	0.545504i	$0.183662\pi$
$661$	11.0030	+	37.4729i	0.427968	+	1.45753i	−0.410140	+	0.912022i	$0.634520\pi$
$662$		0			0
$663$	−0.159889	−	0.292815i	−0.00620958	−	0.0113720i
$664$		0			0
$665$	21.2926	−	22.8280i	0.825694	−	0.885231i
$666$		0			0
$667$	5.69635	−	1.71034i	0.220563	−	0.0662245i
$668$		0			0
$669$	−4.13335	−	0.594286i	−0.159804	−	0.0229764i
$670$		0			0
$671$	39.8049	+	11.6878i	1.53665	+	0.451201i
$672$		0			0
$673$	22.4251	−	41.0685i	0.864425	−	1.58308i	0.0530189	−	0.998594i	$-0.483116\pi$
$673$	22.4251	−	41.0685i	0.864425	−	1.58308i	0.811406	−	0.584483i	$-0.198703\pi$
$674$		0			0
$675$	8.14299	−	7.02988i	0.313424	−	0.270580i
$676$		0			0
$677$	−1.50363	+	6.91209i	−0.0577893	+	0.265653i	−0.996972	−	0.0777657i	$-0.975221\pi$
$677$	−1.50363	+	6.91209i	−0.0577893	+	0.265653i	0.939182	+	0.343419i	$0.111585\pi$
$678$		0			0
$679$	−28.1722	+	4.05055i	−1.08115	+	0.155446i
$680$		0			0
$681$	−2.96701	−	2.57093i	−0.113696	−	0.0985181i
$682$		0			0
$683$	14.8316	−	3.22641i	0.567514	−	0.123455i	0.0803515	−	0.996767i	$-0.474396\pi$
$683$	14.8316	−	3.22641i	0.567514	−	0.123455i	0.487162	+	0.873312i	$0.338032\pi$
$684$		0			0
$685$	−0.276260	−	2.59192i	−0.0105553	−	0.0990321i
$686$		0			0
$687$	4.79535	+	1.78857i	0.182954	+	0.0682384i
$688$		0			0
$689$	−2.40456			−0.0916063
$690$		0			0
$691$	−3.42547			−0.130311			−0.0651555	−	0.997875i	$-0.520754\pi$
$691$	−3.42547			−0.130311			−0.0651555	+	0.997875i	$0.520754\pi$
$692$		0			0
$693$	−43.0446	−	16.0548i	−1.63513	−	0.609872i
$694$		0			0
$695$	−5.86788	−	4.73750i	−0.222581	−	0.179704i
$696$		0			0
$697$	9.03042	−	1.96445i	0.342051	−	0.0744087i
$698$		0			0
$699$	1.56264	+	1.35404i	0.0591046	+	0.0512144i
$700$		0			0
$701$	−5.12609	+	0.737021i	−0.193610	+	0.0278369i	−0.238437	−	0.971158i	$-0.576635\pi$
$701$	−5.12609	+	0.737021i	−0.193610	+	0.0278369i	0.0448277	+	0.998995i	$0.485726\pi$
$702$		0			0
$703$	5.38146	−	24.7382i	0.202966	−	0.933018i
$704$		0			0
$705$	8.11452	+	2.07902i	0.305610	+	0.0783005i
$706$		0			0
$707$	−13.1854	+	24.1473i	−0.495888	+	0.908151i
$708$		0			0
$709$	−18.0375	−	5.29627i	−0.677411	−	0.198906i	−0.0751103	−	0.997175i	$-0.523931\pi$
$709$	−18.0375	−	5.29627i	−0.677411	−	0.198906i	−0.602300	+	0.798269i	$0.705749\pi$
$710$		0			0
$711$	−22.3836	−	3.21827i	−0.839449	−	0.120695i
$712$		0			0
$713$	34.4933	+	15.4995i	1.29179	+	0.580460i
$714$		0			0
$715$	4.87310	+	4.54535i	0.182244	+	0.169987i
$716$		0			0
$717$	4.47886	+	8.20242i	0.167266	+	0.306325i
$718$		0			0
$719$	8.10533	+	27.6042i	0.302278	+	1.02946i	0.960878	+	0.276971i	$0.0893305\pi$
$719$	8.10533	+	27.6042i	0.302278	+	1.02946i	−0.658601	+	0.752493i	$0.728851\pi$
$720$		0			0
$721$	24.9909	−	54.7225i	0.930711	−	2.03797i
$722$		0			0
$723$	−8.29132	−	1.80367i	−0.308358	−	0.0670791i
$724$		0			0
$725$	−5.44772	+	2.96174i	−0.202323	+	0.109996i
$726$		0			0
$727$	1.47192	+	20.5801i	0.0545905	+	0.763275i	0.948850	+	0.315727i	$0.102248\pi$
$727$	1.47192	+	20.5801i	0.0545905	+	0.763275i	−0.894260	+	0.447548i	$0.852297\pi$
$728$		0			0
$729$	10.8146	−	16.8278i	0.400540	−	0.623252i
$730$		0			0
$731$	4.09979	+	4.73141i	0.151636	+	0.174998i
$732$		0			0
$733$	6.61364	−	17.7319i	0.244280	−	0.654941i	−0.755720	−	0.654895i	$-0.772713\pi$
$733$	6.61364	−	17.7319i	0.244280	−	0.654941i	1.00000		4.58548e-5i	$-1.45960e-5\pi$
$734$		0			0
$735$	−5.38375	+	7.73893i	−0.198582	+	0.285455i
$736$		0			0
$737$	−25.2431	−	25.2431i	−0.929843	−	0.929843i
$738$		0			0
$739$	21.2043	−	9.68366i	0.780011	−	0.356219i	0.0147101	−	0.999892i	$-0.495317\pi$
$739$	21.2043	−	9.68366i	0.780011	−	0.356219i	0.765301	+	0.643673i	$0.222590\pi$
$740$		0			0
$741$	0.719385	−	0.623351i	0.0264273	−	0.0228994i
$742$		0			0
$743$	1.21883	+	5.60288i	0.0447146	+	0.205550i	0.994084	−	0.108611i	$-0.0346404\pi$
$743$	1.21883	+	5.60288i	0.0447146	+	0.205550i	−0.949370	+	0.314161i	$0.898277\pi$
$744$		0			0
$745$	−35.8113	−	21.2922i	−1.31202	−	0.780085i
$746$		0			0
$747$	−14.3934	−	10.7748i	−0.526628	−	0.394229i
$748$		0			0
$749$	21.4782	+	33.4208i	0.784798	+	1.22117i
$750$		0			0
$751$	−24.7519	−	11.3038i	−0.903210	−	0.412482i	−0.0910021	−	0.995851i	$-0.529007\pi$
$751$	−24.7519	−	11.3038i	−0.903210	−	0.412482i	−0.812207	+	0.583369i	$0.801734\pi$
$752$		0			0
$753$	1.62045	+	0.884832i	0.0590524	+	0.0322451i
$754$		0			0
$755$	−0.127771	+	1.17830i	−0.00465007	+	0.0428826i
$756$		0			0
$757$	0.709928	+	0.948353i	0.0258028	+	0.0344685i	0.813257	−	0.581905i	$-0.197692\pi$
$757$	0.709928	+	0.948353i	0.0258028	+	0.0344685i	−0.787454	+	0.616373i	$0.788601\pi$
$758$		0			0
$759$	−1.35508	+	6.41706i	−0.0491864	+	0.232925i
$760$		0			0
$761$	−1.82246	+	12.6755i	−0.0660641	+	0.459486i	0.929758	+	0.368171i	$0.120016\pi$
$761$	−1.82246	+	12.6755i	−0.0660641	+	0.459486i	−0.995822	+	0.0913147i	$0.970893\pi$
$762$		0			0
$763$	−25.5933	+	13.9750i	−0.926539	+	0.505929i
$764$		0			0
$765$	2.30860	−	6.91510i	0.0834676	−	0.250016i
$766$		0			0
$767$	3.00671	−	1.12145i	0.108566	−	0.0404931i
$768$		0			0
$769$	15.5273	−	9.97881i	0.559930	−	0.359845i	−0.229859	−	0.973224i	$-0.573827\pi$
$769$	15.5273	−	9.97881i	0.559930	−	0.359845i	0.789789	+	0.613379i	$0.210190\pi$
$770$		0			0
$771$	1.53835	+	10.6995i	0.0554024	+	0.385332i
$772$		0			0
$773$	29.4404	−	2.10562i	1.05890	−	0.0757339i	0.468989	−	0.883204i	$-0.344618\pi$
$773$	29.4404	−	2.10562i	1.05890	−	0.0757339i	0.589909	+	0.807470i	$0.299164\pi$
$774$		0			0
$775$	−38.5091	−	8.45103i	−1.38329	−	0.303570i
$776$		0			0
$777$	−0.877612	+	12.2706i	−0.0314841	+	0.440206i
$778$		0			0
$779$	10.9536	+	23.9850i	0.392452	+	0.859351i
$780$		0			0
$781$			24.4730i			0.875713i
$782$		0			0
$783$	1.88673	−	1.88673i	0.0674261	−	0.0674261i
$784$		0			0
$785$	−9.87941	+	54.4725i	−0.352611	+	1.94421i
$786$		0			0
$787$	0.502751	+	0.0359575i	0.0179211	+	0.00128175i	0.0802969	−	0.996771i	$-0.474413\pi$
$787$	0.502751	+	0.0359575i	0.0179211	+	0.00128175i	−0.0623757	+	0.998053i	$0.519868\pi$
$788$		0			0
$789$	2.51301	+	1.61501i	0.0894655	+	0.0574960i
$790$		0			0
$791$	−24.8251	+	28.6497i	−0.882679	+	1.01867i
$792$		0			0
$793$	−5.33050	+	7.12072i	−0.189292	+	0.252864i
$794$		0			0
$795$	1.67961	+	1.80735i	0.0595697	+	0.0641000i
$796$		0			0
$797$	−13.8592	−	37.1578i	−0.490916	−	1.31620i	−0.912377	−	0.409351i	$-0.865755\pi$
$797$	−13.8592	−	37.1578i	−0.490916	−	1.31620i	0.421461	−	0.906847i	$-0.361518\pi$
$798$		0			0
$799$	11.1492	−	3.27371i	0.394432	−	0.115816i
$800$		0			0
$801$	12.9506	−	44.1058i	0.457588	−	1.55840i
$802$		0			0
$803$	0.627162	−	0.469488i	0.0221321	−	0.0165679i
$804$		0			0
$805$	−41.3452	−	20.4292i	−1.45723	−	0.720033i
$806$		0			0
$807$	4.72902	−	3.54010i	0.166470	−	0.124618i
$808$		0			0
$809$	7.35715	−	25.0562i	0.258664	−	0.880927i	−0.723087	−	0.690757i	$-0.757278\pi$
$809$	7.35715	−	25.0562i	0.258664	−	0.880927i	0.981751	−	0.190171i	$-0.0609042\pi$
$810$		0			0
$811$	9.45413	−	2.77598i	0.331980	−	0.0974780i	−0.111495	−	0.993765i	$-0.535564\pi$
$811$	9.45413	−	2.77598i	0.331980	−	0.0974780i	0.443474	+	0.896287i	$0.353746\pi$
$812$		0			0
$813$	−2.67344	−	7.16778i	−0.0937618	−	0.251385i
$814$		0			0
$815$	4.53244	+	0.166031i	0.158765	+	0.00581583i
$816$		0			0
$817$	−10.7045	+	14.2995i	−0.374503	+	0.500277i
$818$		0			0
$819$	6.45055	−	7.44434i	0.225401	−	0.260126i
$820$		0			0
$821$	−26.3218	−	16.9160i	−0.918636	−	0.590371i	−0.00637434	−	0.999980i	$-0.502029\pi$
$821$	−26.3218	−	16.9160i	−0.918636	−	0.590371i	−0.912262	+	0.409608i	$0.865665\pi$
$822$		0			0
$823$	−8.01564	−	0.573290i	−0.279408	−	0.0199836i	−0.0690679	−	0.997612i	$-0.522003\pi$
$823$	−8.01564	−	0.573290i	−0.279408	−	0.0199836i	−0.210340	+	0.977628i	$0.567457\pi$
$824$		0			0
$825$	0.0125197	−	6.83778i	0.000435881	−	0.238061i
$826$		0			0
$827$	−30.2966	+	30.2966i	−1.05352	+	1.05352i	−0.0550305	+	0.998485i	$0.517526\pi$
$827$	−30.2966	+	30.2966i	−1.05352	+	1.05352i	−0.998485	+	0.0550305i	$0.982474\pi$
$828$		0			0
$829$		−	17.3791i		−	0.603601i	−0.953371	−	0.301801i	$-0.902412\pi$
$829$		−	17.3791i		−	0.603601i	0.953371	−	0.301801i	$-0.0975877\pi$
$830$		0			0
$831$	2.79952	+	6.13009i	0.0971142	+	0.212650i
$832$		0			0
$833$	−0.932943	+	13.0442i	−0.0323246	+	0.451956i
$834$		0			0
$835$	−12.8197	+	5.29637i	−0.443645	+	0.183288i
$836$		0			0
$837$	16.9219	−	1.21027i	0.584905	−	0.0418332i
$838$		0			0
$839$	1.16494	+	8.10232i	0.0402181	+	0.279723i	0.999999	−	0.00102533i	$-0.000326372\pi$
$839$	1.16494	+	8.10232i	0.0402181	+	0.279723i	−0.959781	+	0.280749i	$0.909417\pi$
$840$		0			0
$841$	23.1025	−	14.8471i	0.796639	−	0.511969i
$842$		0			0
$843$	7.20495	−	2.68731i	0.248152	−	0.0925557i
$844$		0			0
$845$	24.7278	−	12.3495i	0.850661	−	0.424837i
$846$		0			0
$847$	−10.9436	+	5.97566i	−0.376027	+	0.205326i
$848$		0			0
$849$	−1.72922	+	12.0270i	−0.0593465	+	0.412764i
$850$		0			0
$851$	−37.2884	+	2.89521i	−1.27823	+	0.0992464i
$852$		0			0
$853$	5.30198	+	7.08261i	0.181536	+	0.242504i	0.882073	−	0.471112i	$-0.156147\pi$
$853$	5.30198	+	7.08261i	0.181536	+	0.242504i	−0.700537	+	0.713616i	$0.747056\pi$
$854$		0			0
$855$	20.6791	+	2.24238i	0.707210	+	0.0766879i
$856$		0			0
$857$	37.8587	+	20.6724i	1.29323	+	0.706157i	0.970675	−	0.240394i	$-0.0772766\pi$
$857$	37.8587	+	20.6724i	1.29323	+	0.706157i	0.322554	+	0.946551i	$0.395458\pi$
$858$		0			0
$859$	7.73560	+	3.53273i	0.263935	+	0.120535i	0.542988	−	0.839741i	$-0.317293\pi$
$859$	7.73560	+	3.53273i	0.263935	+	0.120535i	−0.279052	+	0.960276i	$0.590020\pi$
$860$		0			0
$861$	−6.92705	−	10.7787i	−0.236073	−	0.367337i
$862$		0			0
$863$	45.6361	+	34.1627i	1.55347	+	1.16291i	0.921794	+	0.387681i	$0.126724\pi$
$863$	45.6361	+	34.1627i	1.55347	+	1.16291i	0.631677	+	0.775232i	$0.282367\pi$
$864$		0			0
$865$	−23.3163	+	5.92840i	−0.792778	+	0.201572i
$866$		0			0
$867$	−1.22458	−	5.62932i	−0.0415890	−	0.191182i
$868$		0			0
$869$	−22.2360	+	19.2676i	−0.754304	+	0.653608i
$870$		0			0
$871$	6.96257	−	3.17970i	0.235918	−	0.107740i
$872$		0			0
$873$	−13.4100	−	13.4100i	−0.453861	−	0.453861i
$874$		0			0
$875$	46.5539	+	12.0185i	1.57381	+	0.406298i
$876$		0			0
$877$	6.50510	−	17.4409i	0.219662	−	0.588936i	−0.779643	−	0.626224i	$-0.784599\pi$
$877$	6.50510	−	17.4409i	0.219662	−	0.588936i	0.999305	+	0.0372887i	$0.0118721\pi$
$878$		0			0
$879$	2.92720	+	3.37817i	0.0987321	+	0.113943i
$880$		0			0
$881$	12.1472	−	18.9015i	0.409251	−	0.636806i	−0.574045	−	0.818824i	$-0.694626\pi$
$881$	12.1472	−	18.9015i	0.409251	−	0.636806i	0.983295	+	0.182018i	$0.0582628\pi$
$882$		0			0
$883$	2.95294	+	41.2874i	0.0993742	+	1.38943i	0.765424	+	0.643526i	$0.222529\pi$
$883$	2.95294	+	41.2874i	0.0993742	+	1.38943i	−0.666050	+	0.745907i	$0.732016\pi$
$884$		0			0
$885$	−2.94315	−	1.47660i	−0.0989328	−	0.0496355i
$886$		0			0
$887$	−24.2424	−	5.27361i	−0.813980	−	0.177071i	−0.213740	−	0.976891i	$-0.568565\pi$
$887$	−24.2424	−	5.27361i	−0.813980	−	0.177071i	−0.600240	+	0.799820i	$0.704928\pi$
$888$		0			0
$889$	17.9584	−	39.3233i	0.602304	−	1.31886i
$890$		0			0
$891$	−8.20024	−	27.9275i	−0.274718	−	0.935605i
$892$		0			0
$893$	15.8888	+	29.0981i	0.531698	+	0.973731i
$894$		0			0
$895$	1.93115	+	55.4953i	0.0645512	+	1.85500i
$896$		0			0
$897$	−1.18760	−	0.753046i	−0.0396528	−	0.0251435i
$898$		0			0
$899$	−9.67922	−	1.39166i	−0.322820	−	0.0464145i
$900$		0			0
$901$	3.28397	+	0.964262i	0.109405	+	0.0321242i
$902$		0			0
$903$	4.15974	−	7.61799i	0.138427	−	0.253511i
$904$		0			0
$905$	7.22659	−	28.2057i	0.240220	−	0.937590i
$906$		0			0
$907$	−2.71475	+	12.4795i	−0.0901417	+	0.414375i	−1.00000		0.000544843i	$-0.999827\pi$
$907$	−2.71475	+	12.4795i	−0.0901417	+	0.414375i	0.909858	+	0.414919i	$0.136190\pi$
$908$		0			0
$909$	−18.1455	+	2.60893i	−0.601849	+	0.0865328i
$910$		0			0
$911$	19.5396	+	16.9312i	0.647377	+	0.560955i	0.915444	−	0.402445i	$-0.131839\pi$
$911$	19.5396	+	16.9312i	0.647377	+	0.560955i	−0.268067	+	0.963400i	$0.586385\pi$
$912$		0			0
$913$	−22.8584	+	4.97255i	−0.756503	+	0.164567i
$914$		0			0
$915$	9.07560	−	0.967324i	0.300030	−	0.0319787i
$916$		0			0
$917$	74.5858	+	27.8191i	2.46304	+	0.918667i
$918$		0			0
$919$	41.0798			1.35510			0.677548	−	0.735479i	$-0.263043\pi$
$919$	41.0798			1.35510			0.677548	+	0.735479i	$0.263043\pi$
$920$		0			0
$921$	−8.68177			−0.286074
$922$		0			0
$923$	−4.91642	−	1.83373i	−0.161826	−	0.0603579i
$924$		0			0
$925$	37.4335	−	10.9170i	1.23080	−	0.358950i
$926$		0			0
$927$	39.1688	−	8.52066i	1.28647	−	0.279855i
$928$		0			0
$929$	11.4837	+	9.95071i	0.376769	+	0.326472i	0.822574	−	0.568658i	$-0.192537\pi$
$929$	11.4837	+	9.95071i	0.376769	+	0.326472i	−0.445805	+	0.895130i	$0.647083\pi$
$930$		0			0
$931$	−36.9325	+	5.31010i	−1.21042	+	0.174031i
$932$		0			0
$933$	−0.537846	+	2.47244i	−0.0176083	+	0.0809440i
$934$		0			0
$935$	−4.83259	−	8.16191i	−0.158043	−	0.266923i
$936$		0			0
$937$	2.74738	−	5.03144i	0.0897528	−	0.164370i	−0.828946	−	0.559328i	$-0.811059\pi$
$937$	2.74738	−	5.03144i	0.0897528	−	0.164370i	0.918699	+	0.394958i	$0.129241\pi$
$938$		0			0
$939$	8.35403	+	2.45296i	0.272623	+	0.0800494i
$940$		0			0
$941$	56.1581	+	8.07431i	1.83070	+	0.263215i	0.969507	−	0.245063i	$-0.0788086\pi$
$941$	56.1581	+	8.07431i	1.83070	+	0.263215i	0.861193	+	0.508278i	$0.169718\pi$
$942$		0			0
$943$	29.2831	−	25.6878i	0.953590	−	0.836509i
$944$		0			0
$945$	−20.6767	+	0.719519i	−0.672615	+	0.0234060i
$946$		0			0
$947$	−23.3936	−	42.8421i	−0.760188	−	1.39218i	−0.914677	−	0.404186i	$-0.867555\pi$
$947$	−23.3936	−	42.8421i	−0.760188	−	1.39218i	0.154488	−	0.987995i	$-0.450627\pi$
$948$		0			0
$949$	0.0473237	+	0.161170i	0.00153619	+	0.00523179i
$950$		0			0
$951$	0.114728	−	0.251220i	0.00372031	−	0.00814635i
$952$		0			0
$953$	56.8820	+	12.3739i	1.84259	+	0.400831i	0.992130	−	0.125210i	$-0.0399605\pi$
$953$	56.8820	+	12.3739i	1.84259	+	0.400831i	0.850459	+	0.526041i	$0.176324\pi$
$954$		0			0
$955$	−3.20400	−	9.65598i	−0.103679	−	0.312460i
$956$		0			0
$957$	−0.120990	−	1.69166i	−0.00391105	−	0.0546836i
$958$		0			0
$959$	−2.71025	+	4.21724i	−0.0875186	+	0.136182i
$960$		0			0
$961$	−20.4153	−	23.5605i	−0.658557	−	0.760015i
$962$		0			0
$963$	−9.25066	+	24.8020i	−0.298098	+	0.799233i
$964$		0			0
$965$	38.1249	+	26.5224i	1.22728	+	0.853785i
$966$		0			0
$967$	20.1939	+	20.1939i	0.649392	+	0.649392i	0.952846	−	0.303454i	$-0.0981400\pi$
$967$	20.1939	+	20.1939i	0.649392	+	0.649392i	−0.303454	+	0.952846i	$0.598140\pi$
$968$		0			0
$969$	−1.23246	+	0.562845i	−0.0395923	+	0.0180812i
$970$		0			0
$971$	14.3272	−	12.4146i	0.459783	−	0.398404i	−0.393936	−	0.919138i	$-0.628887\pi$
$971$	14.3272	−	12.4146i	0.459783	−	0.398404i	0.853719	+	0.520734i	$0.174342\pi$
$972$		0			0
$973$	3.08307	+	14.1726i	0.0988387	+	0.454354i
$974$		0			0
$975$	1.37271	+	0.514860i	0.0439620	+	0.0164887i
$976$		0			0
$977$	−25.5352	−	19.1154i	−0.816944	−	0.611557i	0.106924	−	0.994267i	$-0.465900\pi$
$977$	−25.5352	−	19.1154i	−0.816944	−	0.611557i	−0.923868	+	0.382711i	$0.874991\pi$
$978$		0			0
$979$	−32.3347	−	50.3138i	−1.03342	−	1.60804i
$980$		0			0
$981$	−17.6741	−	8.07148i	−0.564290	−	0.257702i
$982$		0			0
$983$	3.50161	+	1.91203i	0.111684	+	0.0609842i	0.534120	−	0.845409i	$-0.320643\pi$
$983$	3.50161	+	1.91203i	0.111684	+	0.0609842i	−0.422436	+	0.906393i	$0.638825\pi$
$984$		0			0
$985$	−6.73455	+	5.41688i	−0.214581	+	0.172596i
$986$		0			0
$987$	−9.65436	−	12.8967i	−0.307302	−	0.410507i
$988$		0			0
$989$	24.7801	+	9.07103i	0.787961	+	0.288442i
$990$		0			0
$991$	3.92460	−	27.2962i	0.124669	−	0.867092i	−0.827488	−	0.561483i	$-0.810231\pi$
$991$	3.92460	−	27.2962i	0.124669	−	0.867092i	0.952157	−	0.305609i	$-0.0988599\pi$
$992$		0			0
$993$	−6.46253	+	3.52881i	−0.205082	+	0.111983i
$994$		0			0
$995$	−6.46743	−	12.9499i	−0.205031	−	0.410539i
$996$		0			0
$997$	−34.8689	+	13.0054i	−1.10431	+	0.411886i	−0.834489	−	0.551025i	$-0.814237\pi$
$997$	−34.8689	+	13.0054i	−1.10431	+	0.411886i	−0.269820	+	0.962911i	$0.586964\pi$
$998$		0			0
$999$	−14.1153	+	9.07136i	−0.446589	+	0.287005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.337.7	yes	240
5.3	odd	4	inner	460.2.x.a.153.6	✓	240
23.20	odd	22	inner	460.2.x.a.457.6	yes	240
115.43	even	44	inner	460.2.x.a.273.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.153.6	✓	240	5.3	odd	4	inner
460.2.x.a.273.7	yes	240	115.43	even	44	inner
460.2.x.a.337.7	yes	240	1.1	even	1	trivial
460.2.x.a.457.6	yes	240	23.20	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.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.343687 - 0.128189i) q^{3} +(1.40466 - 1.73981i) q^{5} +(-4.20215 + 0.914122i) q^{7} +(-2.16556 - 1.87647i) q^{9} +O(q^{10})\)	\(q+(-0.343687 - 0.128189i) q^{3} +(1.40466 - 1.73981i) q^{5} +(-4.20215 + 0.914122i) q^{7} +(-2.16556 - 1.87647i) q^{9} +(-3.69025 + 0.530577i) q^{11} +(0.169917 - 0.781095i) q^{13} +(-0.705786 + 0.417889i) q^{15} +(-0.545291 + 0.998626i) q^{17} +(-3.11483 - 0.914597i) q^{19} +(1.56141 + 0.224496i) q^{21} +(0.0291979 + 4.79574i) q^{23} +(-1.05388 - 4.88767i) q^{25} +(1.03112 + 1.88836i) q^{27} +(-0.349392 - 1.18992i) q^{29} +(3.27559 - 7.17255i) q^{31} +(1.33630 + 0.290695i) q^{33} +(-4.31218 + 8.59497i) q^{35} +(0.556344 + 7.77871i) q^{37} +(-0.158526 + 0.246671i) q^{39} +(-5.31900 - 6.13845i) q^{41} +(1.92286 - 5.15539i) q^{43} +(-6.30657 + 1.13187i) q^{45} +(-7.22140 - 7.22140i) q^{47} +(10.4550 - 4.77465i) q^{49} +(0.315422 - 0.273315i) q^{51} +(-0.639416 - 2.93935i) q^{53} +(-4.26043 + 7.16561i) q^{55} +(0.953286 + 0.713621i) q^{57} +(2.17041 + 3.37722i) q^{59} +(-10.1219 - 4.62252i) q^{61} +(10.8153 + 5.90562i) q^{63} +(-1.12028 - 1.39279i) q^{65} +(5.73836 + 7.66555i) q^{67} +(0.604725 - 1.65198i) q^{69} +(0.934198 - 6.49749i) q^{71} +(-0.184431 + 0.100707i) q^{73} +(-0.264340 + 1.81493i) q^{75} +(15.0220 - 5.60290i) q^{77} +(6.63906 - 4.26667i) q^{79} +(1.11107 + 7.72766i) q^{81} +(6.25864 - 0.447627i) q^{83} +(0.971473 + 2.35143i) q^{85} +(-0.0324527 + 0.453748i) q^{87} +(6.66413 + 14.5924i) q^{89} +3.43760i q^{91} +(-2.04522 + 2.04522i) q^{93} +(-5.96649 + 4.13452i) q^{95} +(6.60153 + 0.472150i) q^{97} +(8.98706 + 5.77563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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