LMFDB - Embedded newform 684.3.m.a.353.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (of order $6$, degree $2$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.14
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60029 - 2.53754i) q^{3} +1.56237i q^{5} +(-4.59594 + 7.96040i) q^{7} +(-3.87817 + 8.12156i) q^{9} +O(q^{10})$	\(q+(-1.60029 - 2.53754i) q^{3} +1.56237i q^{5} +(-4.59594 + 7.96040i) q^{7} +(-3.87817 + 8.12156i) q^{9} +(-18.3761 - 10.6095i) q^{11} +(0.163320 - 0.282878i) q^{13} +(3.96458 - 2.50024i) q^{15} +(22.8775 + 13.2083i) q^{17} +(8.51862 - 16.9833i) q^{19} +(27.5546 - 1.07655i) q^{21} +(-2.17715 - 1.25698i) q^{23} +22.5590 q^{25} +(26.8149 - 3.15581i) q^{27} -52.9670i q^{29} +(-4.11110 - 7.12064i) q^{31} +(2.48516 + 63.6082i) q^{33} +(-12.4371 - 7.18057i) q^{35} +30.2712 q^{37} +(-0.979172 + 0.0382561i) q^{39} +10.9070i q^{41} +(30.7940 + 53.3368i) q^{43} +(-12.6889 - 6.05915i) q^{45} +41.4547i q^{47} +(-17.7453 - 30.7358i) q^{49} +(-3.09392 - 79.1895i) q^{51} +(54.4144 - 31.4162i) q^{53} +(16.5759 - 28.7104i) q^{55} +(-56.7280 + 5.56184i) q^{57} -78.8050i q^{59} -57.7876 q^{61} +(-46.8270 - 68.1980i) q^{63} +(0.441962 + 0.255167i) q^{65} +(30.3656 - 52.5947i) q^{67} +(0.294435 + 7.53613i) q^{69} +(48.8284 + 28.1911i) q^{71} +(30.1874 - 52.2860i) q^{73} +(-36.1008 - 57.2442i) q^{75} +(168.911 - 97.5209i) q^{77} +(-34.6994 - 60.1011i) q^{79} +(-50.9195 - 62.9937i) q^{81} +(1.98665 + 1.14700i) q^{83} +(-20.6363 + 35.7431i) q^{85} +(-134.406 + 84.7623i) q^{87} +(92.6623 - 53.4986i) q^{89} +(1.50122 + 2.60018i) q^{91} +(-11.4899 + 21.8271i) q^{93} +(26.5343 + 13.3093i) q^{95} +(13.8646 + 24.0142i) q^{97} +(157.431 - 108.098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.60029	−	2.53754i	−0.533428	−	0.845845i
$3$	−1.60029	−	2.53754i	−0.533428	−	0.845845i
$4$		0			0
$5$			1.56237i			0.312475i	0.987720	+	0.156237i	$0.0499365\pi$
$5$			1.56237i			0.312475i	−0.987720	+	0.156237i	$0.950064\pi$
$6$		0			0
$7$	−4.59594	+	7.96040i	−0.656563	+	1.13720i	0.324937	+	0.945736i	$0.394657\pi$
$7$	−4.59594	+	7.96040i	−0.656563	+	1.13720i	−0.981500	+	0.191464i	$0.938676\pi$
$8$		0			0
$9$	−3.87817	+	8.12156i	−0.430908	+	0.902396i
$10$		0			0
$11$	−18.3761	−	10.6095i	−1.67056	−	0.964496i	−0.967326	−	0.253535i	$-0.918407\pi$
$11$	−18.3761	−	10.6095i	−1.67056	−	0.964496i	−0.703231	−	0.710962i	$-0.748260\pi$
$12$		0			0
$13$	0.163320	−	0.282878i	0.0125631	−	0.0217599i	−0.859676	−	0.510840i	$-0.829334\pi$
$13$	0.163320	−	0.282878i	0.0125631	−	0.0217599i	0.872239	+	0.489081i	$0.162668\pi$
$14$		0			0
$15$	3.96458	−	2.50024i	0.264305	−	0.166683i
$16$		0			0
$17$	22.8775	+	13.2083i	1.34573	+	0.776960i	0.987642	−	0.156727i	$-0.0500942\pi$
$17$	22.8775	+	13.2083i	1.34573	+	0.776960i	0.358092	+	0.933686i	$0.383428\pi$
$18$		0			0
$19$	8.51862	−	16.9833i	0.448349	−	0.893859i
$19$	8.51862	−	16.9833i	0.448349	−	0.893859i
$20$		0			0
$21$	27.5546	−	1.07655i	1.31212	−	0.0512644i
$22$		0			0
$23$	−2.17715	−	1.25698i	−0.0946589	−	0.0546513i	0.451923	−	0.892057i	$-0.350738\pi$
$23$	−2.17715	−	1.25698i	−0.0946589	−	0.0546513i	−0.546582	+	0.837405i	$0.684071\pi$
$24$		0			0
$25$	22.5590			0.902360
$26$		0			0
$27$	26.8149	−	3.15581i	0.993146	−	0.116882i
$28$		0			0
$29$		−	52.9670i		−	1.82645i	−0.407458	−	0.913224i	$-0.633585\pi$
$29$		−	52.9670i		−	1.82645i	0.407458	−	0.913224i	$-0.366415\pi$
$30$		0			0
$31$	−4.11110	−	7.12064i	−0.132616	−	0.229698i	0.792068	−	0.610433i	$-0.209004\pi$
$31$	−4.11110	−	7.12064i	−0.132616	−	0.229698i	−0.924684	+	0.380735i	$0.875671\pi$
$32$		0			0
$33$	2.48516	+	63.6082i	0.0753079	+	1.92752i
$34$		0			0
$35$	−12.4371	−	7.18057i	−0.355346	−	0.205159i
$36$		0			0
$37$	30.2712			0.818141			0.409071	−	0.912503i	$-0.365853\pi$
$37$	30.2712			0.818141			0.409071	+	0.912503i	$0.365853\pi$
$38$		0			0
$39$	−0.979172	+	0.0382561i	−0.0251070	+	0.000980925i
$40$		0			0
$41$			10.9070i			0.266025i	0.991114	+	0.133012i	$0.0424650\pi$
$41$			10.9070i			0.266025i	−0.991114	+	0.133012i	$0.957535\pi$
$42$		0			0
$43$	30.7940	+	53.3368i	0.716140	+	1.24039i	0.962518	+	0.271218i	$0.0874263\pi$
$43$	30.7940	+	53.3368i	0.716140	+	1.24039i	−0.246378	+	0.969174i	$0.579240\pi$
$44$		0			0
$45$	−12.6889	−	6.05915i	−0.281976	−	0.134648i
$46$		0			0
$47$			41.4547i			0.882015i	0.897503	+	0.441008i	$0.145379\pi$
$47$			41.4547i			0.882015i	−0.897503	+	0.441008i	$0.854621\pi$
$48$		0			0
$49$	−17.7453	−	30.7358i	−0.362149	−	0.627261i
$50$		0			0
$51$	−3.09392	−	79.1895i	−0.0606650	−	1.55273i
$52$		0			0
$53$	54.4144	−	31.4162i	1.02669	−	0.592758i	0.110653	−	0.993859i	$-0.464706\pi$
$53$	54.4144	−	31.4162i	1.02669	−	0.592758i	0.916034	+	0.401101i	$0.131372\pi$
$54$		0			0
$55$	16.5759	−	28.7104i	0.301381	−	0.522007i
$56$		0			0
$57$	−56.7280	+	5.56184i	−0.995228	+	0.0975762i
$58$		0			0
$59$		−	78.8050i		−	1.33568i	−0.744305	−	0.667839i	$-0.767219\pi$
$59$		−	78.8050i		−	1.33568i	0.744305	−	0.667839i	$-0.232781\pi$
$60$		0			0
$61$	−57.7876			−0.947337			−0.473669	−	0.880703i	$-0.657071\pi$
$61$	−57.7876			−0.947337			−0.473669	+	0.880703i	$0.657071\pi$
$62$		0			0
$63$	−46.8270	−	68.1980i	−0.743286	−	1.08251i
$64$		0			0
$65$	0.441962	+	0.255167i	0.00679941	+	0.00392564i
$66$		0			0
$67$	30.3656	−	52.5947i	0.453218	−	0.784996i	−0.545366	−	0.838198i	$-0.683609\pi$
$67$	30.3656	−	52.5947i	0.453218	−	0.784996i	0.998584	+	0.0532020i	$0.0169427\pi$
$68$		0			0
$69$	0.294435	+	7.53613i	0.00426717	+	0.109219i
$70$		0			0
$71$	48.8284	+	28.1911i	0.687724	+	0.397058i	0.802759	−	0.596304i	$-0.203365\pi$
$71$	48.8284	+	28.1911i	0.687724	+	0.397058i	−0.115035	+	0.993361i	$0.536698\pi$
$72$		0			0
$73$	30.1874	−	52.2860i	0.413526	−	0.716247i	−0.581747	−	0.813370i	$-0.697631\pi$
$73$	30.1874	−	52.2860i	0.413526	−	0.716247i	0.995272	+	0.0971226i	$0.0309639\pi$
$74$		0			0
$75$	−36.1008	−	57.2442i	−0.481344	−	0.763257i
$76$		0			0
$77$	168.911	−	97.5209i	2.19365	−	1.26650i
$78$		0			0
$79$	−34.6994	−	60.1011i	−0.439232	−	0.760773i	0.558398	−	0.829573i	$-0.311416\pi$
$79$	−34.6994	−	60.1011i	−0.439232	−	0.760773i	−0.997630	+	0.0688003i	$0.978083\pi$
$80$		0			0
$81$	−50.9195	−	62.9937i	−0.628636	−	0.777699i
$82$		0			0
$83$	1.98665	+	1.14700i	0.0239356	+	0.0138192i	0.511920	−	0.859033i	$-0.328934\pi$
$83$	1.98665	+	1.14700i	0.0239356	+	0.0138192i	−0.487984	+	0.872852i	$0.662268\pi$
$84$		0			0
$85$	−20.6363	+	35.7431i	−0.242780	+	0.420507i
$86$		0			0
$87$	−134.406	+	84.7623i	−1.54489	+	0.974279i
$88$		0			0
$89$	92.6623	−	53.4986i	1.04115	−	0.601108i	0.120991	−	0.992654i	$-0.461393\pi$
$89$	92.6623	−	53.4986i	1.04115	−	0.601108i	0.920159	+	0.391545i	$0.128059\pi$
$90$		0			0
$91$	1.50122	+	2.60018i	0.0164969	+	0.0285734i
$92$		0			0
$93$	−11.4899	+	21.8271i	−0.123548	+	0.234700i
$94$		0			0
$95$	26.5343	+	13.3093i	0.279308	+	0.140098i
$96$		0			0
$97$	13.8646	+	24.0142i	0.142934	+	0.247569i	0.928600	−	0.371082i	$-0.121013\pi$
$97$	13.8646	+	24.0142i	0.142934	+	0.247569i	−0.785666	+	0.618650i	$0.787680\pi$
$98$		0			0
$99$	157.431	−	108.098i	1.59021	−	1.09189i
$100$		0			0
$101$			14.4308i			0.142879i	0.997445	+	0.0714394i	$0.0227593\pi$
$101$			14.4308i			0.142879i	−0.997445	+	0.0714394i	$0.977241\pi$
$102$		0			0
$103$	83.0455	+	143.839i	0.806267	+	1.39650i	0.915432	+	0.402472i	$0.131849\pi$
$103$	83.0455	+	143.839i	0.806267	+	1.39650i	−0.109165	+	0.994024i	$0.534818\pi$
$104$		0			0
$105$	1.68198	+	43.0506i	0.0160188	+	0.410006i
$106$		0			0
$107$		−	131.867i		−	1.23241i	−0.787587	−	0.616203i	$-0.788670\pi$
$107$		−	131.867i		−	1.23241i	0.787587	−	0.616203i	$-0.211330\pi$
$108$		0			0
$109$	−73.6078	+	127.492i	−0.675301	+	1.16965i	0.301080	+	0.953599i	$0.402653\pi$
$109$	−73.6078	+	127.492i	−0.675301	+	1.16965i	−0.976381	+	0.216056i	$0.930681\pi$
$110$		0			0
$111$	−48.4426	−	76.8143i	−0.436420	−	0.692021i
$112$		0			0
$113$	7.71947	−	4.45684i	0.0683139	−	0.0394411i	−0.465454	−	0.885072i	$-0.654109\pi$
$113$	7.71947	−	4.45684i	0.0683139	−	0.0394411i	0.533768	+	0.845631i	$0.320776\pi$
$114$		0			0
$115$	1.96387	−	3.40153i	0.0170771	−	0.0295785i
$116$		0			0
$117$	1.66403	+	2.42346i	0.0142225	+	0.0207134i
$118$		0			0
$119$	−210.287	+	121.409i	−1.76712	+	1.02025i
$120$		0			0
$121$	164.621	+	285.132i	1.36051	+	2.35647i
$122$		0			0
$123$	27.6769	−	17.4543i	0.225016	−	0.141905i
$124$		0			0
$125$			74.3049i			0.594439i
$126$		0			0
$127$	−54.7983	−	94.9135i	−0.431483	−	0.747351i	0.565518	−	0.824736i	$-0.308676\pi$
$127$	−54.7983	−	94.9135i	−0.431483	−	0.747351i	−0.997001	+	0.0773852i	$0.975343\pi$
$128$		0			0
$129$	86.0649	−	163.495i	0.667170	−	1.26740i
$130$		0			0
$131$		−	36.4161i		−	0.277985i	−0.990293	−	0.138993i	$-0.955614\pi$
$131$		−	36.4161i		−	0.277985i	0.990293	−	0.138993i	$-0.0443864\pi$
$132$		0			0
$133$	96.0429	+	145.866i	0.722127	+	1.09674i
$134$		0			0
$135$	4.93056	+	41.8949i	0.0365226	+	0.310333i
$136$		0			0
$137$		−	219.638i		−	1.60320i	−0.597860	−	0.801600i	$-0.703982\pi$
$137$		−	219.638i		−	1.60320i	0.597860	−	0.801600i	$-0.296018\pi$
$138$		0			0
$139$	−66.5128	+	115.204i	−0.478509	+	0.828803i	−0.999696	−	0.0246398i	$-0.992156\pi$
$139$	−66.5128	+	115.204i	−0.478509	+	0.828803i	0.521187	+	0.853443i	$0.325489\pi$
$140$		0			0
$141$	105.193	−	66.3394i	0.746048	−	0.470492i
$142$		0			0
$143$	−6.00237	+	3.46547i	−0.0419746	+	0.0242341i
$144$		0			0
$145$	82.7542			0.570718
$146$		0			0
$147$	−49.5956	+	94.2154i	−0.337385	+	0.640921i
$148$		0			0
$149$		−	93.6039i		−	0.628214i	−0.949388	−	0.314107i	$-0.898295\pi$
$149$		−	93.6039i		−	0.628214i	0.949388	−	0.314107i	$-0.101705\pi$
$150$		0			0
$151$	−1.49138	+	2.58314i	−0.00987668	+	0.0171069i	−0.870922	−	0.491422i	$-0.836477\pi$
$151$	−1.49138	+	2.58314i	−0.00987668	+	0.0171069i	0.861045	+	0.508529i	$0.169811\pi$
$152$		0			0
$153$	−195.995	+	134.577i	−1.28101	+	0.879586i
$154$		0			0
$155$	11.1251	−	6.42307i	0.0717748	−	0.0414392i
$156$		0			0
$157$	−40.0109			−0.254847			−0.127423	−	0.991848i	$-0.540671\pi$
$157$	−40.0109			−0.254847			−0.127423	+	0.991848i	$0.540671\pi$
$158$		0			0
$159$	−166.798	−	87.8036i	−1.04905	−	0.552224i
$160$		0			0
$161$	20.0121	−	11.5540i	0.124299	−	0.0717640i
$162$		0			0
$163$	−73.5546			−0.451255			−0.225628	−	0.974214i	$-0.572443\pi$
$163$	−73.5546			−0.451255			−0.225628	+	0.974214i	$0.572443\pi$
$164$		0			0
$165$	−99.3798	+	3.88275i	−0.602302	+	0.0235318i
$166$		0			0
$167$	−85.1627	−	49.1687i	−0.509956	−	0.294423i	0.222860	−	0.974851i	$-0.428461\pi$
$167$	−85.1627	−	49.1687i	−0.509956	−	0.294423i	−0.732816	+	0.680427i	$0.761794\pi$
$168$		0			0
$169$	84.4467	+	146.266i	0.499684	+	0.865479i
$170$		0			0
$171$	104.894	+	135.049i	0.613417	+	0.789759i
$172$		0			0
$173$	−40.7061	+	23.5017i	−0.235296	+	0.135848i	−0.613013	−	0.790073i	$-0.710043\pi$
$173$	−40.7061	+	23.5017i	−0.235296	+	0.135848i	0.377717	+	0.925921i	$0.376709\pi$
$174$		0			0
$175$	−103.680	+	179.579i	−0.592456	+	1.02616i
$176$		0			0
$177$	−199.971	+	126.111i	−1.12978	+	0.712489i
$178$		0			0
$179$		−	250.921i		−	1.40179i	−0.713262	−	0.700897i	$-0.752783\pi$
$179$		−	250.921i		−	1.40179i	0.713262	−	0.700897i	$-0.247217\pi$
$180$		0			0
$181$	122.712	+	212.544i	0.677969	+	1.17428i	0.975591	+	0.219594i	$0.0704732\pi$
$181$	122.712	+	212.544i	0.677969	+	1.17428i	−0.297622	+	0.954684i	$0.596193\pi$
$182$		0			0
$183$	92.4766	+	146.638i	0.505337	+	0.801301i
$184$		0			0
$185$			47.2949i			0.255648i
$186$		0			0
$187$	−280.266	−	485.435i	−1.49875	−	2.59591i
$188$		0			0
$189$	−98.1183	+	227.962i	−0.519144	+	1.20615i
$190$		0			0
$191$	240.460	+	138.830i	1.25895	+	0.726857i	0.972871	−	0.231348i	$-0.0743137\pi$
$191$	240.460	+	138.830i	1.25895	+	0.726857i	0.286082	+	0.958205i	$0.407647\pi$
$192$		0			0
$193$	229.151			1.18731			0.593654	−	0.804720i	$-0.297685\pi$
$193$	229.151			1.18731			0.593654	+	0.804720i	$0.297685\pi$
$194$		0			0
$195$	−0.0597702	−	1.52983i	−0.000306514	−	0.00784529i
$196$		0			0
$197$			174.829i			0.887455i	0.896162	+	0.443727i	$0.146344\pi$
$197$			174.829i			0.887455i	−0.896162	+	0.443727i	$0.853656\pi$
$198$		0			0
$199$	163.425	+	283.060i	0.821230	+	1.42241i	0.904767	+	0.425907i	$0.140045\pi$
$199$	163.425	+	283.060i	0.821230	+	1.42241i	−0.0835370	+	0.996505i	$0.526622\pi$
$200$		0			0
$201$	−182.055	+	7.11283i	−0.905744	+	0.0353872i
$202$		0			0
$203$	421.638	+	243.433i	2.07704	+	1.19918i
$204$		0			0
$205$	−17.0408			−0.0831259
$206$		0			0
$207$	18.6520	−	12.8071i	0.0901064	−	0.0618701i
$208$		0			0
$209$	−336.723	+	221.710i	−1.61112	+	1.06081i
$210$		0			0
$211$	60.2414			0.285504			0.142752	−	0.989758i	$-0.454405\pi$
$211$	60.2414			0.285504			0.142752	+	0.989758i	$0.454405\pi$
$212$		0			0
$213$	−6.60348	−	169.018i	−0.0310023	−	0.793510i
$214$		0			0
$215$	−83.3320	+	48.1118i	−0.387591	+	0.223776i
$216$		0			0
$217$	75.5775			0.348283
$218$		0			0
$219$	−180.986	+	7.07109i	−0.826421	+	0.0322881i
$220$		0			0
$221$	7.47269	−	4.31436i	0.0338131	−	0.0195220i
$222$		0			0
$223$	−130.050	−	225.254i	−0.583185	−	1.01011i	−0.995099	−	0.0988836i	$-0.968473\pi$
$223$	−130.050	−	225.254i	−0.583185	−	1.01011i	0.411914	−	0.911223i	$-0.364860\pi$
$224$		0			0
$225$	−87.4877	+	183.214i	−0.388834	+	0.814286i
$226$		0			0
$227$	−143.205	−	82.6796i	−0.630860	−	0.364227i	0.150225	−	0.988652i	$-0.452000\pi$
$227$	−143.205	−	82.6796i	−0.630860	−	0.364227i	−0.781085	+	0.624425i	$0.785333\pi$
$228$		0			0
$229$	−166.723	−	288.773i	−0.728048	−	1.26102i	−0.957707	−	0.287745i	$-0.907095\pi$
$229$	−166.723	−	288.773i	−0.728048	−	1.26102i	0.229659	−	0.973271i	$-0.426239\pi$
$230$		0			0
$231$	−517.769	−	272.557i	−2.24142	−	1.17990i
$232$		0			0
$233$	−46.3651	−	26.7689i	−0.198992	−	0.114888i	0.397193	−	0.917735i	$-0.369984\pi$
$233$	−46.3651	−	26.7689i	−0.198992	−	0.114888i	−0.596185	+	0.802847i	$0.703318\pi$
$234$		0			0
$235$	−64.7677			−0.275607
$236$		0			0
$237$	−96.9797	+	184.230i	−0.409197	+	0.777341i
$238$		0			0
$239$	364.835	−	210.637i	1.52651	−	0.881328i	0.527000	−	0.849865i	$-0.323317\pi$
$239$	364.835	−	210.637i	1.52651	−	0.881328i	0.999505	−	0.0314631i	$-0.0100167\pi$
$240$		0			0
$241$	141.455			0.586949			0.293475	−	0.955967i	$-0.405188\pi$
$241$	141.455			0.586949			0.293475	+	0.955967i	$0.405188\pi$
$242$		0			0
$243$	−78.3628	+	230.018i	−0.322481	+	0.946576i
$244$		0			0
$245$	48.0208	−	27.7248i	0.196003	−	0.113162i
$246$		0			0
$247$	−3.41295	−	5.18345i	−0.0138176	−	0.0209856i
$248$		0			0
$249$	−0.268672	−	6.87672i	−0.00107900	−	0.0276174i
$250$		0			0
$251$	111.588	−	64.4253i	0.444573	−	0.256675i	−0.260962	−	0.965349i	$-0.584040\pi$
$251$	111.588	−	64.4253i	0.444573	−	0.256675i	0.705536	+	0.708674i	$0.250706\pi$
$252$		0			0
$253$	26.6718	+	46.1969i	0.105422	+	0.182596i
$254$		0			0
$255$	123.723	−	4.83385i	0.485190	−	0.0189563i
$256$		0			0
$257$	−4.49375	−	2.59447i	−0.0174854	−	0.0100952i	0.491232	−	0.871029i	$-0.336547\pi$
$257$	−4.49375	−	2.59447i	−0.0174854	−	0.0100952i	−0.508717	+	0.860934i	$0.669880\pi$
$258$		0			0
$259$	−139.125	+	240.971i	−0.537161	+	0.930390i
$260$		0			0
$261$	430.175	+	205.415i	1.64818	+	0.787031i
$262$		0			0
$263$	−18.3290	+	10.5822i	−0.0696919	+	0.0402366i	−0.534441	−	0.845206i	$-0.679478\pi$
$263$	−18.3290	+	10.5822i	−0.0696919	+	0.0402366i	0.464749	+	0.885442i	$0.346145\pi$
$264$		0			0
$265$	49.0838	+	85.0156i	0.185222	+	0.320813i
$266$		0			0
$267$	−284.041	−	149.521i	−1.06382	−	0.560003i
$268$		0			0
$269$	−180.342	−	104.121i	−0.670418	−	0.387066i	0.125817	−	0.992053i	$-0.459845\pi$
$269$	−180.342	−	104.121i	−0.670418	−	0.387066i	−0.796235	+	0.604988i	$0.793178\pi$
$270$		0			0
$271$	150.784	−	261.165i	0.556398	−	0.963710i	−0.441395	−	0.897313i	$-0.645516\pi$
$271$	150.784	−	261.165i	0.556398	−	0.963710i	0.997793	−	0.0663970i	$-0.0211504\pi$
$272$		0			0
$273$	4.19568	−	7.97043i	0.0153688	−	0.0291957i
$274$		0			0
$275$	−414.547	−	239.339i	−1.50744	−	0.870323i
$276$		0			0
$277$	−106.417	+	184.320i	−0.384177	+	0.665414i	−0.991655	−	0.128923i	$-0.958848\pi$
$277$	−106.417	+	184.320i	−0.384177	+	0.665414i	0.607478	+	0.794337i	$0.292181\pi$
$278$		0			0
$279$	73.7743	−	5.77350i	0.264424	−	0.0206936i
$280$		0			0
$281$		−	242.264i		−	0.862150i	−0.902316	−	0.431075i	$-0.858134\pi$
$281$		−	242.264i		−	0.862150i	0.902316	−	0.431075i	$-0.141866\pi$
$282$		0			0
$283$	336.324			1.18843			0.594213	−	0.804308i	$-0.297464\pi$
$283$	336.324			1.18843			0.594213	+	0.804308i	$0.297464\pi$
$284$		0			0
$285$	−8.68967	−	88.6303i	−0.0304901	−	0.310983i
$286$		0			0
$287$	−86.8242	−	50.1280i	−0.302523	−	0.174662i
$288$		0			0
$289$	204.419	+	354.064i	0.707333	+	1.22514i
$290$		0			0
$291$	38.7495	−	73.6114i	0.133160	−	0.252960i
$292$		0			0
$293$	179.353	−	103.550i	0.612127	−	0.353412i	−0.161670	−	0.986845i	$-0.551688\pi$
$293$	179.353	−	103.550i	0.612127	−	0.353412i	0.773797	+	0.633433i	$0.218355\pi$
$294$		0			0
$295$	123.123			0.417366
$296$		0			0
$297$	−526.236	−	226.500i	−1.77184	−	0.762628i
$298$		0			0
$299$	−0.711145	+	0.410580i	−0.00237841	+	0.00137318i
$300$		0			0
$301$	−566.110			−1.88076
$302$		0			0
$303$	36.6186	−	23.0933i	0.120853	−	0.0762156i
$304$		0			0
$305$		−	90.2858i		−	0.296019i
$306$		0			0
$307$	137.863	−	238.786i	0.449066	−	0.777806i	−0.549259	−	0.835652i	$-0.685090\pi$
$307$	137.863	−	238.786i	0.449066	−	0.777806i	0.998325	+	0.0578463i	$0.0184233\pi$
$308$		0			0
$309$	232.100	−	440.915i	0.751133	−	1.42691i
$310$		0			0
$311$	237.877	−	137.339i	0.764879	−	0.441603i	−0.0661657	−	0.997809i	$-0.521077\pi$
$311$	237.877	−	137.339i	0.764879	−	0.441603i	0.831045	+	0.556205i	$0.187743\pi$
$312$		0			0
$313$	−485.034			−1.54963			−0.774815	−	0.632189i	$-0.782157\pi$
$313$	−485.034			−1.54963			−0.774815	+	0.632189i	$0.782157\pi$
$314$		0			0
$315$	106.551	−	73.1613i	0.338256	−	0.232258i
$316$		0			0
$317$			406.534i			1.28244i	0.767357	+	0.641220i	$0.221571\pi$
$317$			406.534i			1.28244i	−0.767357	+	0.641220i	$0.778429\pi$
$318$		0			0
$319$	−561.951	+	973.328i	−1.76160	+	3.05118i
$320$		0			0
$321$	−334.618	+	211.026i	−1.04243	+	0.657401i
$322$		0			0
$323$	419.206	−	276.019i	1.29785	−	0.854547i
$324$		0			0
$325$	3.68433	−	6.38145i	0.0113364	−	0.0196352i
$326$		0			0
$327$	441.310	−	17.2419i	1.34957	−	0.0527275i
$328$		0			0
$329$	−329.996	−	190.523i	−1.00303	−	0.579098i
$330$		0			0
$331$	−114.803	+	198.845i	−0.346838	+	0.600741i	−0.985686	−	0.168592i	$-0.946078\pi$
$331$	−114.803	+	198.845i	−0.346838	+	0.600741i	0.638848	+	0.769333i	$0.279411\pi$
$332$		0			0
$333$	−117.397	+	245.850i	−0.352544	+	0.738287i
$334$		0			0
$335$	82.1726	+	47.4424i	0.245291	+	0.141619i
$336$		0			0
$337$	444.001			1.31751			0.658755	−	0.752358i	$-0.271083\pi$
$337$	444.001			1.31751			0.658755	+	0.752358i	$0.271083\pi$
$338$		0			0
$339$	−23.6627	−	12.4562i	−0.0698016	−	0.0367440i
$340$		0			0
$341$			174.466i			0.511631i
$342$		0			0
$343$	−124.176			−0.362030
$344$		0			0
$345$	−11.7742	+	0.460017i	−0.0341283	+	0.00133338i
$346$		0			0
$347$			53.3296i			0.153688i	0.997043	+	0.0768439i	$0.0244843\pi$
$347$			53.3296i			0.153688i	−0.997043	+	0.0768439i	$0.975516\pi$
$348$		0			0
$349$	−174.035	+	301.437i	−0.498666	+	0.863715i	−0.999999	−	0.00153938i	$-0.999510\pi$
$349$	−174.035	+	301.437i	−0.498666	+	0.863715i	0.501333	+	0.865255i	$0.332843\pi$
$350$		0			0
$351$	3.48670	−	8.10077i	0.00993362	−	0.0230791i
$352$		0			0
$353$	−155.310	−	89.6686i	−0.439973	−	0.254019i	0.263613	−	0.964628i	$-0.415086\pi$
$353$	−155.310	−	89.6686i	−0.439973	−	0.254019i	−0.703586	+	0.710610i	$0.748419\pi$
$354$		0			0
$355$	−44.0450	+	76.2882i	−0.124070	+	0.214896i
$356$		0			0
$357$	644.599	+	339.321i	1.80560	+	0.950479i
$358$		0			0
$359$	192.832	+	111.332i	0.537138	+	0.310117i	0.743918	−	0.668271i	$-0.232965\pi$
$359$	192.832	+	111.332i	0.537138	+	0.310117i	−0.206780	+	0.978387i	$0.566299\pi$
$360$		0			0
$361$	−215.866	−	289.349i	−0.597967	−	0.801521i
$362$		0			0
$363$	460.093	−	874.026i	1.26747	−	2.40778i
$364$		0			0
$365$	81.6903	+	47.1639i	0.223809	+	0.129216i
$366$		0			0
$367$	466.936			1.27231			0.636153	−	0.771563i	$-0.280525\pi$
$367$	466.936			1.27231			0.636153	+	0.771563i	$0.280525\pi$
$368$		0			0
$369$	−88.5820	−	42.2993i	−0.240060	−	0.114632i
$370$		0			0
$371$			577.547i			1.55673i
$372$		0			0
$373$	−29.7770	−	51.5752i	−0.0798310	−	0.138271i	0.823346	−	0.567540i	$-0.192105\pi$
$373$	−29.7770	−	51.5752i	−0.0798310	−	0.138271i	−0.903177	+	0.429269i	$0.858771\pi$
$374$		0			0
$375$	188.551	−	118.909i	0.502803	−	0.317091i
$376$		0			0
$377$	−14.9832	−	8.65056i	−0.0397433	−	0.0229458i
$378$		0			0
$379$	61.2909			0.161717			0.0808587	−	0.996726i	$-0.474234\pi$
$379$	61.2909			0.161717			0.0808587	+	0.996726i	$0.474234\pi$
$380$		0			0
$381$	−153.153	+	290.941i	−0.401978	+	0.763626i
$382$		0			0
$383$			202.153i			0.527814i	0.964548	+	0.263907i	$0.0850112\pi$
$383$			202.153i			0.527814i	−0.964548	+	0.263907i	$0.914989\pi$
$384$		0			0
$385$	152.364	+	263.902i	0.395751	+	0.685460i
$386$		0			0
$387$	−552.603	+	43.2462i	−1.42791	+	0.111747i
$388$		0			0
$389$		−	773.464i		−	1.98834i	−0.107826	−	0.994170i	$-0.534389\pi$
$389$		−	773.464i		−	1.98834i	0.107826	−	0.994170i	$-0.465611\pi$
$390$		0			0
$391$	−33.2052	−	57.5131i	−0.0849237	−	0.147092i
$392$		0			0
$393$	−92.4070	+	58.2761i	−0.235132	+	0.148285i
$394$		0			0
$395$	93.9003	−	54.2133i	0.237722	−	0.137249i
$396$		0			0
$397$	111.155	−	192.525i	0.279986	−	0.484951i	−0.691395	−	0.722477i	$-0.743003\pi$
$397$	111.155	−	192.525i	0.279986	−	0.484951i	0.971381	+	0.237527i	$0.0763367\pi$
$398$		0			0
$399$	216.444	−	477.139i	0.542466	−	1.19584i
$400$		0			0
$401$			495.758i			1.23630i	0.786058	+	0.618152i	$0.212119\pi$
$401$			495.758i			1.23630i	−0.786058	+	0.618152i	$0.787881\pi$
$402$		0			0
$403$	−2.68570			−0.00666427
$404$		0			0
$405$	98.4196	−	79.5553i	0.243011	−	0.196433i
$406$		0			0
$407$	−556.268	−	321.161i	−1.36675	−	0.789094i
$408$		0			0
$409$	403.387	−	698.686i	0.986275	−	1.70828i	0.350149	−	0.936694i	$-0.386131\pi$
$409$	403.387	−	698.686i	0.986275	−	1.70828i	0.636126	−	0.771585i	$-0.280536\pi$
$410$		0			0
$411$	−557.340	+	351.484i	−1.35606	+	0.855193i
$412$		0			0
$413$	627.320	+	362.183i	1.51893	+	0.876957i
$414$		0			0
$415$	−1.79203	+	3.10389i	−0.00431815	+	0.00747926i
$416$		0			0
$417$	398.773	−	15.5800i	0.956289	−	0.0373620i
$418$		0			0
$419$	235.914	−	136.205i	0.563041	−	0.325072i	−0.191324	−	0.981527i	$-0.561278\pi$
$419$	235.914	−	136.205i	0.563041	−	0.325072i	0.754365	+	0.656455i	$0.227945\pi$
$420$		0			0
$421$	400.333	+	693.396i	0.950909	+	1.64702i	0.743465	+	0.668775i	$0.233181\pi$
$421$	400.333	+	693.396i	0.950909	+	1.64702i	0.207444	+	0.978247i	$0.433486\pi$
$422$		0			0
$423$	−336.677	−	160.769i	−0.795927	−	0.380068i
$424$		0			0
$425$	516.093	+	297.966i	1.21434	+	0.701097i
$426$		0			0
$427$	265.588	−	460.012i	0.621987	−	1.07731i
$428$		0			0
$429$	18.3993	+	9.68549i	0.0428887	+	0.0225769i
$430$		0			0
$431$	76.3653	−	44.0895i	0.177182	−	0.102296i	−0.408786	−	0.912630i	$-0.634048\pi$
$431$	76.3653	−	44.0895i	0.177182	−	0.102296i	0.585968	+	0.810334i	$0.300714\pi$
$432$		0			0
$433$	−405.267	−	701.944i	−0.935952	−	1.62112i	−0.772927	−	0.634495i	$-0.781208\pi$
$433$	−405.267	−	701.944i	−0.935952	−	1.62112i	−0.163026	−	0.986622i	$-0.552125\pi$
$434$		0			0
$435$	−132.430	−	209.992i	−0.304437	−	0.482739i
$436$		0			0
$437$	−39.8940	+	26.2675i	−0.0912907	+	0.0601088i
$438$		0			0
$439$	4.18943	+	7.25630i	0.00954312	+	0.0165292i	0.870758	−	0.491713i	$-0.163629\pi$
$439$	4.18943	+	7.25630i	0.00954312	+	0.0165292i	−0.861214	+	0.508242i	$0.830296\pi$
$440$		0			0
$441$	318.442	−	24.9210i	0.722091	−	0.0565101i
$442$		0			0
$443$			93.4493i			0.210947i	0.994422	+	0.105473i	$0.0336358\pi$
$443$			93.4493i			0.210947i	−0.994422	+	0.105473i	$0.966364\pi$
$444$		0			0
$445$	83.5848	+	144.773i	0.187831	+	0.325333i
$446$		0			0
$447$	−237.523	+	149.793i	−0.531372	+	0.335107i
$448$		0			0
$449$			122.697i			0.273268i	0.990622	+	0.136634i	$0.0436284\pi$
$449$			122.697i			0.273268i	−0.990622	+	0.136634i	$0.956372\pi$
$450$		0			0
$451$	115.717	−	200.429i	0.256580	−	0.444409i
$452$		0			0
$453$	8.94145	−	0.349341i	0.0197383	−	0.000771172i
$454$		0			0
$455$	−4.06246	+	2.34546i	−0.00892848	+	0.00515486i
$456$		0			0
$457$	213.401	−	369.622i	0.466962	−	0.808801i	−0.532326	−	0.846539i	$-0.678682\pi$
$457$	213.401	−	369.622i	0.466962	−	0.808801i	0.999288	+	0.0377382i	$0.0120153\pi$
$458$		0			0
$459$	655.141	+	281.983i	1.42732	+	0.614342i
$460$		0			0
$461$	144.545	−	83.4531i	0.313546	−	0.181026i	−0.334966	−	0.942230i	$-0.608725\pi$
$461$	144.545	−	83.4531i	0.313546	−	0.181026i	0.648512	+	0.761204i	$0.275391\pi$
$462$		0			0
$463$	−422.303	−	731.450i	−0.912101	−	1.57980i	−0.811092	−	0.584919i	$-0.801126\pi$
$463$	−422.303	−	731.450i	−0.912101	−	1.57980i	−0.101009	−	0.994886i	$-0.532207\pi$
$464$		0			0
$465$	−34.1021	−	17.9516i	−0.0733378	−	0.0386055i
$466$		0			0
$467$			612.701i			1.31199i	0.754764	+	0.655997i	$0.227752\pi$
$467$			612.701i			1.31199i	−0.754764	+	0.655997i	$0.772248\pi$
$468$		0			0
$469$	279.117	+	483.444i	0.595132	+	1.03080i
$470$		0			0
$471$	64.0289	+	101.529i	0.135942	+	0.215561i
$472$		0			0
$473$		−	1306.83i		−	2.76286i
$474$		0			0
$475$	192.172	−	383.126i	0.404572	−	0.806582i
$476$		0			0
$477$	44.1199	+	563.767i	0.0924945	+	1.18190i
$478$		0			0
$479$		−	138.380i		−	0.288892i	−0.989513	−	0.144446i	$-0.953860\pi$
$479$		−	138.380i		−	0.288892i	0.989513	−	0.144446i	$-0.0461401\pi$
$480$		0			0
$481$	4.94389	−	8.56308i	0.0102784	−	0.0178027i
$482$		0			0
$483$	−61.3438	−	32.2918i	−0.127006	−	0.0668567i
$484$		0			0
$485$	−37.5191	+	21.6616i	−0.0773589	+	0.0446632i
$486$		0			0
$487$	−767.796			−1.57658			−0.788291	−	0.615302i	$-0.789034\pi$
$487$	−767.796			−1.57658			−0.788291	+	0.615302i	$0.789034\pi$
$488$		0			0
$489$	117.708	+	186.647i	0.240712	+	0.381692i
$490$		0			0
$491$			20.6719i			0.0421017i	0.999778	+	0.0210508i	$0.00670118\pi$
$491$			20.6719i			0.0421017i	−0.999778	+	0.0210508i	$0.993299\pi$
$492$		0			0
$493$	699.605	−	1211.75i	1.41908	−	2.45791i
$494$		0			0
$495$	168.889	+	245.966i	0.341189	+	0.496901i
$496$		0			0
$497$	−448.825	+	259.129i	−0.903068	+	0.521387i
$498$		0			0
$499$	−821.607			−1.64651			−0.823253	−	0.567674i	$-0.807843\pi$
$499$	−821.607			−1.64651			−0.823253	+	0.567674i	$0.807843\pi$
$500$		0			0
$501$	11.5173	+	294.787i	0.0229886	+	0.588398i
$502$		0			0
$503$	−331.574	+	191.434i	−0.659192	+	0.380585i	−0.791969	−	0.610561i	$-0.790944\pi$
$503$	−331.574	+	191.434i	−0.659192	+	0.380585i	0.132777	+	0.991146i	$0.457611\pi$
$504$		0			0
$505$	−22.5462			−0.0446460
$506$		0			0
$507$	236.016	−	448.354i	0.465515	−	0.884327i
$508$		0			0
$509$	−483.713	−	279.272i	−0.950321	−	0.548668i	−0.0571400	−	0.998366i	$-0.518198\pi$
$509$	−483.713	−	279.272i	−0.950321	−	0.548668i	−0.893180	+	0.449698i	$0.851531\pi$
$510$		0			0
$511$	277.479	+	480.607i	0.543011	+	0.940523i
$512$		0			0
$513$	174.830	−	482.290i	0.340800	−	0.940136i
$514$		0			0
$515$	−224.730	+	129.748i	−0.436369	+	0.251938i
$516$		0			0
$517$	439.812	−	761.777i	0.850701	−	1.47346i
$518$		0			0
$519$	124.778	+	65.6838i	0.240420	+	0.126558i
$520$		0			0
$521$			1013.96i			1.94618i	0.230417	+	0.973092i	$0.425991\pi$
$521$			1013.96i			1.94618i	−0.230417	+	0.973092i	$0.574009\pi$
$522$		0			0
$523$	400.647	+	693.941i	0.766056	+	1.32685i	0.939687	+	0.342036i	$0.111117\pi$
$523$	400.647	+	693.941i	0.766056	+	1.32685i	−0.173631	+	0.984811i	$0.555550\pi$
$524$		0			0
$525$	621.604	−	24.2859i	1.18401	−	0.0462589i
$526$		0			0
$527$		−	217.203i		−	0.412150i
$528$		0			0
$529$	−261.340	−	452.654i	−0.494026	−	0.855679i
$530$		0			0
$531$	640.020	+	305.620i	1.20531	+	0.575555i
$532$		0			0
$533$	3.08536	+	1.78133i	0.00578866	+	0.00334209i
$534$		0			0
$535$	206.026			0.385096
$536$		0			0
$537$	−636.721	+	401.546i	−1.18570	+	0.747757i
$538$		0			0
$539$			753.073i			1.39717i
$540$		0			0
$541$	−12.7450	−	22.0750i	−0.0235582	−	0.0408040i	0.854006	−	0.520263i	$-0.174166\pi$
$541$	−12.7450	−	22.0750i	−0.0235582	−	0.0408040i	−0.877564	+	0.479459i	$0.840833\pi$
$542$		0			0
$543$	342.964	−	651.519i	0.631609	−	1.19985i
$544$		0			0
$545$	−199.191	−	115.003i	−0.365487	−	0.211014i
$546$		0			0
$547$	7.32208			0.0133859			0.00669295	−	0.999978i	$-0.497870\pi$
$547$	7.32208			0.0133859			0.00669295	+	0.999978i	$0.497870\pi$
$548$		0			0
$549$	224.110	−	469.325i	0.408215	−	0.854873i
$550$		0			0
$551$	−899.555	−	451.206i	−1.63259	−	0.818885i
$552$		0			0
$553$	637.905			1.15353
$554$		0			0
$555$	120.013	−	75.6854i	0.216239	−	0.136370i
$556$		0			0
$557$	235.341	−	135.874i	0.422514	−	0.243939i	−0.273638	−	0.961833i	$-0.588227\pi$
$557$	235.341	−	135.874i	0.422514	−	0.243939i	0.696153	+	0.717894i	$0.254894\pi$
$558$		0			0
$559$	20.1171			0.0359877
$560$		0			0
$561$	−783.303	+	1488.02i	−1.39626	+	2.65244i
$562$		0			0
$563$	−125.587	+	72.5078i	−0.223068	+	0.128788i	−0.607370	−	0.794419i	$-0.707775\pi$
$563$	−125.587	+	72.5078i	−0.223068	+	0.128788i	0.384302	+	0.923207i	$0.374442\pi$
$564$		0			0
$565$	6.96324	+	12.0607i	0.0123243	+	0.0213464i
$566$		0			0
$567$	735.478	−	115.825i	1.29714	−	0.204277i
$568$		0			0
$569$	−944.345	−	545.218i	−1.65966	−	0.958204i	−0.972872	−	0.231344i	$-0.925688\pi$
$569$	−944.345	−	545.218i	−1.65966	−	0.958204i	−0.686785	−	0.726860i	$-0.740979\pi$
$570$		0			0
$571$	−234.969	−	406.979i	−0.411505	−	0.712748i	0.583549	−	0.812078i	$-0.301663\pi$
$571$	−234.969	−	406.979i	−0.411505	−	0.712748i	−0.995055	+	0.0993297i	$0.968330\pi$
$572$		0			0
$573$	−32.5195	−	832.343i	−0.0567530	−	1.45261i
$574$		0			0
$575$	−49.1144	−	28.3562i	−0.0854163	−	0.0493151i
$576$		0			0
$577$	−43.8582			−0.0760107			−0.0380053	−	0.999278i	$-0.512100\pi$
$577$	−43.8582			−0.0760107			−0.0380053	+	0.999278i	$0.512100\pi$
$578$		0			0
$579$	−366.706	−	581.478i	−0.633344	−	1.00428i
$580$		0			0
$581$	−18.2611	+	10.5430i	−0.0314304	+	0.0181464i
$582$		0			0
$583$	−1333.23			−2.28685
$584$		0			0
$585$	−3.78635	+	2.59984i	−0.00647240	+	0.00444417i
$586$		0			0
$587$	373.819	−	215.824i	0.636829	−	0.367674i	−0.146563	−	0.989201i	$-0.546821\pi$
$587$	373.819	−	215.824i	0.636829	−	0.367674i	0.783392	+	0.621528i	$0.213488\pi$
$588$		0			0
$589$	−155.953	+	9.16212i	−0.264776	+	0.0155554i
$590$		0			0
$591$	443.634	−	279.776i	0.750650	−	0.473394i
$592$		0			0
$593$	839.777	−	484.845i	1.41615	−	0.817614i	0.420191	−	0.907435i	$-0.361963\pi$
$593$	839.777	−	484.845i	1.41615	−	0.817614i	0.995958	+	0.0898213i	$0.0286296\pi$
$594$		0			0
$595$	−189.686	−	328.547i	−0.318801	−	0.552179i
$596$		0			0
$597$	456.748	−	867.673i	0.765073	−	1.45339i
$598$		0			0
$599$	−721.606	−	416.619i	−1.20468	−	0.695525i	−0.243091	−	0.970003i	$-0.578161\pi$
$599$	−721.606	−	416.619i	−1.20468	−	0.695525i	−0.961593	+	0.274479i	$0.911495\pi$
$600$		0			0
$601$	−39.4076	+	68.2560i	−0.0655701	+	0.113571i	−0.896947	−	0.442139i	$-0.854220\pi$
$601$	−39.4076	+	68.2560i	−0.0655701	+	0.113571i	0.831377	+	0.555709i	$0.187553\pi$
$602$		0			0
$603$	309.388	+	450.587i	0.513082	+	0.747243i
$604$		0			0
$605$	−445.483	+	257.200i	−0.736336	+	0.425124i
$606$		0			0
$607$	−237.075	−	410.626i	−0.390568	−	0.676484i	0.601956	−	0.798529i	$-0.294388\pi$
$607$	−237.075	−	410.626i	−0.390568	−	0.676484i	−0.992525	+	0.122045i	$0.961055\pi$
$608$		0			0
$609$	−57.0218	−	1459.48i	−0.0936318	−	2.39653i
$610$		0			0
$611$	11.7266	+	6.77038i	0.0191925	+	0.0110808i
$612$		0			0
$613$	197.970	−	342.894i	0.322953	−	0.559370i	−0.658143	−	0.752893i	$-0.728658\pi$
$613$	197.970	−	342.894i	0.322953	−	0.559370i	0.981096	+	0.193522i	$0.0619912\pi$
$614$		0			0
$615$	27.2702	+	43.2417i	0.0443417	+	0.0703117i
$616$		0			0
$617$	−657.897	−	379.837i	−1.06628	−	0.615619i	−0.139120	−	0.990276i	$-0.544427\pi$
$617$	−657.897	−	379.837i	−1.06628	−	0.615619i	−0.927164	+	0.374657i	$0.877761\pi$
$618$		0			0
$619$	267.269	−	462.924i	0.431776	−	0.747857i	−0.565251	−	0.824919i	$-0.691221\pi$
$619$	267.269	−	462.924i	0.431776	−	0.747857i	0.997026	+	0.0770618i	$0.0245539\pi$
$620$		0			0
$621$	−62.3470	−	26.8352i	−0.100398	−	0.0432128i
$622$		0			0
$623$			983.506i			1.57866i
$624$		0			0
$625$	447.883			0.716613
$626$		0			0
$627$	1101.45	+	499.648i	1.75670	+	0.796887i
$628$		0			0
$629$	692.529	+	399.832i	1.10100	+	0.635663i
$630$		0			0
$631$	−316.906	−	548.898i	−0.502229	−	0.869886i	−0.999997	−	0.00257536i	$-0.999180\pi$
$631$	−316.906	−	548.898i	−0.502229	−	0.869886i	0.497768	−	0.867310i	$-0.334153\pi$
$632$		0			0
$633$	−96.4035	−	152.865i	−0.152296	−	0.241493i
$634$		0			0
$635$	148.290	−	85.6154i	0.233528	−	0.134827i
$636$		0			0
$637$	−11.5927			−0.0181988
$638$		0			0
$639$	−418.321	+	287.233i	−0.654649	+	0.449504i
$640$		0			0
$641$	−7.78120	+	4.49248i	−0.0121392	+	0.00700855i	−0.506057	−	0.862500i	$-0.668898\pi$
$641$	−7.78120	+	4.49248i	−0.0121392	+	0.00700855i	0.493918	+	0.869508i	$0.335564\pi$
$642$		0			0
$643$	396.064			0.615963			0.307982	−	0.951392i	$-0.400346\pi$
$643$	396.064			0.615963			0.307982	+	0.951392i	$0.400346\pi$
$644$		0			0
$645$	255.440	+	134.465i	0.396032	+	0.208474i
$646$		0			0
$647$			749.207i			1.15797i	0.815338	+	0.578985i	$0.196551\pi$
$647$			749.207i			1.15797i	−0.815338	+	0.578985i	$0.803449\pi$
$648$		0			0
$649$	−836.079	+	1448.13i	−1.28826	+	2.23133i
$650$		0			0
$651$	−120.946	−	191.781i	−0.185784	−	0.294594i
$652$		0			0
$653$	411.871	−	237.794i	0.630737	−	0.364156i	−0.150301	−	0.988640i	$-0.548024\pi$
$653$	411.871	−	237.794i	0.630737	−	0.364156i	0.781037	+	0.624484i	$0.214691\pi$
$654$		0			0
$655$	56.8955			0.0868633
$656$		0			0
$657$	307.573	+	447.943i	0.468147	+	0.681801i
$658$		0			0
$659$		−	69.8374i		−	0.105975i	−0.998595	−	0.0529874i	$-0.983126\pi$
$659$		−	69.8374i		−	0.105975i	0.998595	−	0.0529874i	$-0.0168743\pi$
$660$		0			0
$661$	−185.179	+	320.740i	−0.280150	+	0.485234i	−0.971421	−	0.237361i	$-0.923718\pi$
$661$	−185.179	+	320.740i	−0.280150	+	0.485234i	0.691272	+	0.722595i	$0.257051\pi$
$662$		0			0
$663$	−22.9063	−	12.0580i	−0.0345495	−	0.0181871i
$664$		0			0
$665$	−227.897	+	150.055i	−0.342702	+	0.225646i
$666$		0			0
$667$	−66.5785	+	115.317i	−0.0998178	+	0.172889i
$668$		0			0
$669$	−363.472	+	690.478i	−0.543306	+	1.03210i
$670$		0			0
$671$	1061.91	+	613.095i	1.58258	+	0.913704i
$672$		0			0
$673$	96.0890	−	166.431i	0.142777	−	0.247297i	−0.785764	−	0.618526i	$-0.787730\pi$
$673$	96.0890	−	166.431i	0.142777	−	0.247297i	0.928541	+	0.371229i	$0.121063\pi$
$674$		0			0
$675$	604.918	−	71.1920i	0.896175	−	0.105470i
$676$		0			0
$677$	−610.979	−	352.749i	−0.902480	−	0.521047i	−0.0244761	−	0.999700i	$-0.507792\pi$
$677$	−610.979	−	352.749i	−0.902480	−	0.521047i	−0.878004	+	0.478653i	$0.841125\pi$
$678$		0			0
$679$	−254.883			−0.375380
$680$		0			0
$681$	19.3669	+	495.699i	0.0284389	+	0.727899i
$682$		0			0
$683$			563.037i			0.824358i	0.911103	+	0.412179i	$0.135232\pi$
$683$			563.037i			0.824358i	−0.911103	+	0.412179i	$0.864768\pi$
$684$		0			0
$685$	343.157			0.500959
$686$		0			0
$687$	−465.966	+	885.184i	−0.678263	+	1.28848i
$688$		0			0
$689$		−	20.5235i		−	0.0297874i
$690$		0			0
$691$	−533.521	+	924.086i	−0.772100	+	1.33732i	0.164310	+	0.986409i	$0.447460\pi$
$691$	−533.521	+	924.086i	−0.772100	+	1.33732i	−0.936410	+	0.350908i	$0.885873\pi$
$692$		0			0
$693$	136.955	+	1750.03i	0.197627	+	2.52529i
$694$		0			0
$695$	−179.991	−	103.918i	−0.258980	−	0.149522i
$696$		0			0
$697$	−144.063	+	249.525i	−0.206690	+	0.357998i
$698$		0			0
$699$	6.27034	+	160.491i	0.00897045	+	0.229601i
$700$		0			0
$701$	−19.1885	−	11.0785i	−0.0273730	−	0.0158038i	0.486251	−	0.873819i	$-0.338364\pi$
$701$	−19.1885	−	11.0785i	−0.0273730	−	0.0158038i	−0.513624	+	0.858015i	$0.671697\pi$
$702$		0			0
$703$	257.869	−	514.106i	0.366812	−	0.731303i
$704$		0			0
$705$	103.647	+	164.350i	0.147017	+	0.233121i
$706$		0			0
$707$	−114.875	−	66.3229i	−0.162482	−	0.0938089i
$708$		0			0
$709$	499.221			0.704120			0.352060	−	0.935977i	$-0.385481\pi$
$709$	499.221			0.704120			0.352060	+	0.935977i	$0.385481\pi$
$710$		0			0
$711$	622.685	−	48.7307i	0.875787	−	0.0685382i
$712$		0			0
$713$			20.6703i			0.0289906i
$714$		0			0
$715$	−5.41436	−	9.37795i	−0.00757253	−	0.0131160i
$716$		0			0
$717$	−1118.34	−	588.701i	−1.55975	−	0.821062i
$718$		0			0
$719$	802.059	+	463.069i	1.11552	+	0.644046i	0.940254	−	0.340475i	$-0.110588\pi$
$719$	802.059	+	463.069i	1.11552	+	0.644046i	0.175267	+	0.984521i	$0.443921\pi$
$720$		0			0
$721$	−1526.69			−2.11746
$722$		0			0
$723$	−226.368	−	358.947i	−0.313095	−	0.496468i
$724$		0			0
$725$		−	1194.88i		−	1.64811i
$726$		0			0
$727$	164.277	+	284.536i	0.225965	+	0.391384i	0.956609	−	0.291376i	$-0.0941130\pi$
$727$	164.277	+	284.536i	0.225965	+	0.391384i	−0.730643	+	0.682759i	$0.760780\pi$
$728$		0			0
$729$	709.082	−	169.246i	0.972677	−	0.232162i
$730$		0			0
$731$			1626.95i			2.22565i
$732$		0			0
$733$	−208.671	−	361.428i	−0.284680	−	0.493080i	0.687851	−	0.725852i	$-0.258554\pi$
$733$	−208.671	−	361.428i	−0.284680	−	0.493080i	−0.972532	+	0.232771i	$0.925221\pi$
$734$		0			0
$735$	−147.200	−	77.4868i	−0.200272	−	0.105424i
$736$		0			0
$737$	−1116.00	+	644.325i	−1.51425	+	0.874253i
$738$		0			0
$739$	293.870	−	508.998i	0.397659	−	0.688766i	−0.595778	−	0.803149i	$-0.703156\pi$
$739$	293.870	−	508.998i	0.397659	−	0.688766i	0.993437	+	0.114384i	$0.0364894\pi$
$740$		0			0
$741$	−7.69149	+	16.9555i	−0.0103799	+	0.0228819i
$742$		0			0
$743$			308.182i			0.414781i	0.978258	+	0.207390i	$0.0664970\pi$
$743$			308.182i			0.414781i	−0.978258	+	0.207390i	$0.933503\pi$
$744$		0			0
$745$	146.244			0.196301
$746$		0			0
$747$	−17.0200	+	11.6865i	−0.0227844	+	0.0156446i
$748$		0			0
$749$	1049.72	+	606.055i	1.40149	+	0.809152i
$750$		0			0
$751$	67.4421	−	116.813i	0.0898031	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$751$	67.4421	−	116.813i	0.0898031	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$752$		0			0
$753$	−342.054	−	180.059i	−0.454255	−	0.239123i
$754$		0			0
$755$	−4.03584	−	2.33009i	−0.00534548	−	0.00308621i
$756$		0			0
$757$	−323.700	+	560.665i	−0.427609	+	0.740641i	−0.996660	−	0.0816616i	$-0.973977\pi$
$757$	−323.700	+	560.665i	−0.427609	+	0.740641i	0.569051	+	0.822302i	$0.307311\pi$
$758$		0			0
$759$	74.5437	−	141.609i	0.0982131	−	0.186573i
$760$		0			0
$761$	−913.138	+	527.201i	−1.19992	+	0.692773i	−0.960537	−	0.278152i	$-0.910278\pi$
$761$	−913.138	+	527.201i	−1.19992	+	0.692773i	−0.239382	+	0.970926i	$0.576945\pi$
$762$		0			0
$763$	−676.594	−	1171.89i	−0.886754	−	1.53590i
$764$		0			0
$765$	−210.259	−	306.217i	−0.274848	−	0.400284i
$766$		0			0
$767$	−22.2922	−	12.8704i	−0.0290642	−	0.0167802i
$768$		0			0
$769$	137.478	−	238.119i	0.178775	−	0.309647i	−0.762686	−	0.646769i	$-0.776120\pi$
$769$	137.478	−	238.119i	0.178775	−	0.309647i	0.941461	+	0.337121i	$0.109453\pi$
$770$		0			0
$771$	0.607728	+	15.5549i	0.000788234	+	0.0201750i
$772$		0			0
$773$	−568.785	+	328.388i	−0.735815	+	0.424823i	−0.820546	−	0.571581i	$-0.806330\pi$
$773$	−568.785	+	328.388i	−0.735815	+	0.424823i	0.0847310	+	0.996404i	$0.472997\pi$
$774$		0			0
$775$	−92.7423	−	160.634i	−0.119667	−	0.207270i
$776$		0			0
$777$	834.112	−	32.5886i	1.07350	−	0.0419415i
$778$		0			0
$779$	185.237	+	92.9127i	0.237788	+	0.119272i
$780$		0			0
$781$	−598.185	−	1036.09i	−0.765922	−	1.32662i
$782$		0			0
$783$	−167.154	−	1420.31i	−0.213479	−	1.81393i
$784$		0			0
$785$		−	62.5120i		−	0.0796331i
$786$		0			0
$787$	266.659	+	461.866i	0.338829	+	0.586869i	0.984213	−	0.176989i	$-0.0566358\pi$
$787$	266.659	+	461.866i	0.338829	+	0.586869i	−0.645384	+	0.763859i	$0.723302\pi$
$788$		0			0
$789$	56.1844	+	29.5758i	0.0712096	+	0.0374852i
$790$		0			0
$791$			81.9335i			0.103582i
$792$		0			0
$793$	−9.43786	+	16.3469i	−0.0119015	+	0.0206139i
$794$		0			0
$795$	137.182	−	260.601i	0.172556	−	0.327800i
$796$		0			0
$797$	−9.48311	+	5.47507i	−0.0118985	+	0.00686960i	−0.505937	−	0.862570i	$-0.668853\pi$
$797$	−9.48311	+	5.47507i	−0.0118985	+	0.00686960i	0.494039	+	0.869440i	$0.335520\pi$
$798$		0			0
$799$	−547.547	+	948.379i	−0.685290	+	1.18696i
$800$		0			0
$801$	75.1318	+	960.040i	0.0937975	+	1.19855i
$802$		0			0
$803$	−1109.45	+	640.543i	−1.38164	+	0.797688i
$804$		0			0
$805$	18.0517	+	31.2664i	0.0224244	+	0.0388403i
$806$		0			0
$807$	24.3892	+	624.248i	0.0302221	+	0.773542i
$808$		0			0
$809$		−	200.785i		−	0.248189i	−0.992270	−	0.124095i	$-0.960397\pi$
$809$		−	200.785i		−	0.248189i	0.992270	−	0.124095i	$-0.0396027\pi$
$810$		0			0
$811$	252.299	+	436.995i	0.311096	+	0.538835i	0.978600	−	0.205772i	$-0.0659705\pi$
$811$	252.299	+	436.995i	0.311096	+	0.538835i	−0.667504	+	0.744606i	$0.732637\pi$
$812$		0			0
$813$	−904.014	+	35.3196i	−1.11195	+	0.0434436i
$814$		0			0
$815$		−	114.920i		−	0.141006i
$816$		0			0
$817$	1168.16	−	68.6284i	1.42982	−	0.0840005i
$818$		0			0
$819$	−26.9395	+	2.10826i	−0.0328932	+	0.00257419i
$820$		0			0
$821$			758.721i			0.924142i	0.886843	+	0.462071i	$0.152894\pi$
$821$			758.721i			0.924142i	−0.886843	+	0.462071i	$0.847106\pi$
$822$		0			0
$823$	−397.225	+	688.013i	−0.482654	+	0.835982i	−0.999802	−	0.0199144i	$-0.993661\pi$
$823$	−397.225	+	688.013i	−0.482654	+	0.835982i	0.517147	+	0.855896i	$0.326994\pi$
$824$		0			0
$825$	56.0627	+	1434.94i	0.0679548	+	1.73932i
$826$		0			0
$827$	−154.964	+	89.4686i	−0.187381	+	0.108184i	−0.590756	−	0.806850i	$-0.701170\pi$
$827$	−154.964	+	89.4686i	−0.187381	+	0.108184i	0.403375	+	0.915035i	$0.367837\pi$
$828$		0			0
$829$	742.995			0.896255			0.448127	−	0.893970i	$-0.352091\pi$
$829$	742.995			0.896255			0.448127	+	0.893970i	$0.352091\pi$
$830$		0			0
$831$	638.015	−	24.9271i	0.767768	−	0.0299965i
$832$		0			0
$833$		−	937.543i		−	1.12550i
$834$		0			0
$835$	76.8198	−	133.056i	0.0919998	−	0.159348i
$836$		0			0
$837$	−132.710	−	177.966i	−0.158555	−	0.212623i
$838$		0			0
$839$	741.832	−	428.297i	0.884185	−	0.510485i	0.0121493	−	0.999926i	$-0.496133\pi$
$839$	741.832	−	428.297i	0.884185	−	0.510485i	0.872036	+	0.489442i	$0.162799\pi$
$840$		0			0
$841$	−1964.50			−2.33591
$842$		0			0
$843$	−614.754	+	387.692i	−0.729246	+	0.459896i
$844$		0			0
$845$	−228.522	+	131.937i	−0.270440	+	0.156139i
$846$		0			0
$847$	−3026.36			−3.57303
$848$		0			0
$849$	−538.215	−	853.435i	−0.633940	−	1.00522i
$850$		0			0
$851$	−65.9051	−	38.0503i	−0.0774443	−	0.0447125i
$852$		0			0
$853$	376.897	+	652.805i	0.441849	+	0.765305i	0.997827	−	0.0658925i	$-0.0209895\pi$
$853$	376.897	+	652.805i	0.441849	+	0.765305i	−0.555978	+	0.831197i	$0.687656\pi$
$854$		0			0
$855$	−210.997	+	163.884i	−0.246780	+	0.191677i
$856$		0			0
$857$	908.400	−	524.465i	1.05998	−	0.611978i	0.134551	−	0.990907i	$-0.457041\pi$
$857$	908.400	−	524.465i	1.05998	−	0.611978i	0.925426	+	0.378929i	$0.123708\pi$
$858$		0			0
$859$	318.090	−	550.949i	0.370303	−	0.641384i	−0.619309	−	0.785147i	$-0.712587\pi$
$859$	318.090	−	550.949i	0.370303	−	0.641384i	0.989612	+	0.143763i	$0.0459205\pi$
$860$		0			0
$861$	11.7420	+	300.538i	0.0136376	+	0.349057i
$862$		0			0
$863$			1603.33i			1.85786i	0.370255	+	0.928930i	$0.379270\pi$
$863$			1603.33i			1.85786i	−0.370255	+	0.928930i	$0.620730\pi$
$864$		0			0
$865$	−36.7184	−	63.5981i	−0.0424490	−	0.0735239i
$866$		0			0
$867$	571.322	−	1085.32i	0.658964	−	1.25182i
$868$		0			0
$869$			1472.57i			1.69455i
$870$		0			0
$871$	−9.91861	−	17.1795i	−0.0113876	−	0.0197239i
$872$		0			0
$873$	−248.802	+	19.4710i	−0.284996	+	0.0223035i
$874$		0			0
$875$	−591.497	−	341.501i	−0.675996	−	0.390287i
$876$		0			0
$877$	−310.652			−0.354221			−0.177111	−	0.984191i	$-0.556675\pi$
$877$	−310.652			−0.354221			−0.177111	+	0.984191i	$0.556675\pi$
$878$		0			0
$879$	−549.777	−	289.406i	−0.625458	−	0.329245i
$880$		0			0
$881$		−	1186.34i		−	1.34659i	−0.739375	−	0.673293i	$-0.764879\pi$
$881$		−	1186.34i		−	1.34659i	0.739375	−	0.673293i	$-0.235121\pi$
$882$		0			0
$883$	160.019	+	277.162i	0.181223	+	0.313887i	0.942297	−	0.334778i	$-0.108661\pi$
$883$	160.019	+	277.162i	0.181223	+	0.313887i	−0.761075	+	0.648664i	$0.775328\pi$
$884$		0			0
$885$	−197.032	−	312.429i	−0.222635	−	0.353027i
$886$		0			0
$887$	263.073	+	151.885i	0.296587	+	0.171235i	0.640909	−	0.767617i	$-0.278558\pi$
$887$	263.073	+	151.885i	0.296587	+	0.171235i	−0.344322	+	0.938852i	$0.611891\pi$
$888$		0			0
$889$	1007.40			1.13318
$890$		0			0
$891$	267.375	+	1697.81i	0.300084	+	1.90551i
$892$		0			0
$893$	704.039	+	353.137i	0.788397	+	0.395450i
$894$		0			0
$895$	392.032			0.438025
$896$		0			0
$897$	2.17990	+	1.14751i	0.00243021	+	0.00127928i
$898$		0			0
$899$	−377.159	+	217.753i	−0.419531	+	0.242217i
$900$		0			0
$901$	1659.82			1.84220
$902$		0			0
$903$	905.938	+	1436.52i	1.00325	+	1.59084i
$904$		0			0
$905$	−332.073	+	191.723i	−0.366932	+	0.211848i
$906$		0			0
$907$	−424.741	−	735.674i	−0.468293	−	0.811107i	0.531051	−	0.847340i	$-0.321797\pi$
$907$	−424.741	−	735.674i	−0.468293	−	0.811107i	−0.999343	+	0.0362335i	$0.988464\pi$
$908$		0			0
$909$	−117.200	−	55.9650i	−0.128933	−	0.0615676i
$910$		0			0
$911$	−342.761	−	197.893i	−0.376247	−	0.217226i	0.299937	−	0.953959i	$-0.403034\pi$
$911$	−342.761	−	197.893i	−0.376247	−	0.217226i	−0.676184	+	0.736733i	$0.736368\pi$
$912$		0			0
$913$	−24.3380	−	42.1546i	−0.0266572	−	0.0461716i
$914$		0			0
$915$	−229.103	+	144.483i	−0.250386	+	0.157905i
$916$		0			0
$917$	289.886	+	167.366i	0.316125	+	0.182515i
$918$		0			0
$919$	1265.47			1.37700			0.688502	−	0.725235i	$-0.258269\pi$
$919$	1265.47			1.37700			0.688502	+	0.725235i	$0.258269\pi$
$920$		0			0
$921$	−826.550	+	32.2931i	−0.897448	+	0.0350631i
$922$		0			0
$923$	15.9493	−	9.20834i	0.0172799	−	0.00997653i
$924$		0			0
$925$	682.888			0.738258
$926$		0			0
$927$	−1490.26	+	116.627i	−1.60762	+	0.125811i
$928$		0			0
$929$	732.006	−	422.624i	0.787950	−	0.454923i	−0.0512902	−	0.998684i	$-0.516333\pi$
$929$	732.006	−	422.624i	0.787950	−	0.454923i	0.839240	+	0.543760i	$0.183000\pi$
$930$		0			0
$931$	−673.161	+	39.5477i	−0.723052	+	0.0424787i
$932$		0			0
$933$	−729.173	−	383.841i	−0.781536	−	0.411406i
$934$		0			0
$935$	758.431	−	437.880i	0.811156	−	0.468321i
$936$		0			0
$937$	119.492	+	206.966i	0.127526	+	0.220882i	0.922718	−	0.385477i	$-0.125963\pi$
$937$	119.492	+	206.966i	0.127526	+	0.220882i	−0.795191	+	0.606358i	$0.792630\pi$
$938$		0			0
$939$	776.193	+	1230.79i	0.826616	+	1.31075i
$940$		0			0
$941$	−1439.49	−	831.093i	−1.52975	−	0.883201i	−0.999372	−	0.0354402i	$-0.988717\pi$
$941$	−1439.49	−	831.093i	−1.52975	−	0.883201i	−0.530378	−	0.847761i	$-0.677950\pi$
$942$		0			0
$943$	13.7099	−	23.7462i	0.0145386	−	0.0251816i
$944$		0			0
$945$	−356.161	−	153.297i	−0.376890	−	0.162219i
$946$		0			0
$947$	−1181.93	+	682.387i	−1.24808	+	0.720577i	−0.970726	−	0.240191i	$-0.922790\pi$
$947$	−1181.93	+	682.387i	−1.24808	+	0.720577i	−0.277351	+	0.960769i	$0.589457\pi$
$948$		0			0
$949$	−9.86040	−	17.0787i	−0.0103903	−	0.0179965i
$950$		0			0
$951$	1031.59	−	650.570i	1.08475	−	0.684090i
$952$		0			0
$953$	−797.996	−	460.723i	−0.837352	−	0.483445i	0.0190116	−	0.999819i	$-0.493948\pi$
$953$	−797.996	−	460.723i	−0.837352	−	0.483445i	−0.856363	+	0.516374i	$0.827281\pi$
$954$		0			0
$955$	−216.904	+	375.688i	−0.227124	+	0.393391i
$956$		0			0
$957$	3369.14	−	131.631i	3.52052	−	0.137546i
$958$		0			0
$959$	1748.41	+	1009.45i	1.82316	+	1.05260i
$960$		0			0
$961$	446.698	−	773.703i	0.464826	−	0.805102i
$962$		0			0
$963$	1070.97	+	511.405i	1.11212	+	0.531054i
$964$		0			0
$965$			358.019i			0.371004i
$966$		0			0
$967$	189.011			0.195461			0.0977307	−	0.995213i	$-0.468842\pi$
$967$	189.011			0.195461			0.0977307	+	0.995213i	$0.468842\pi$
$968$		0			0
$969$	−1371.26	−	622.040i	−1.41512	−	0.641940i
$970$		0			0
$971$	−393.888	−	227.411i	−0.405652	−	0.234203i	0.283268	−	0.959041i	$-0.408581\pi$
$971$	−393.888	−	227.411i	−0.405652	−	0.234203i	−0.688920	+	0.724838i	$0.741915\pi$
$972$		0			0
$973$	−611.378	−	1058.94i	−0.628343	−	1.08832i
$974$		0			0
$975$	−22.0891	+	0.863018i	−0.0226555	+	0.000885147i
$976$		0			0
$977$	536.712	−	309.871i	0.549347	−	0.317166i	−0.199511	−	0.979896i	$-0.563935\pi$
$977$	536.712	−	309.871i	0.549347	−	0.317166i	0.748859	+	0.662730i	$0.230602\pi$
$978$		0			0
$979$	−2270.37			−2.31907
$980$		0			0
$981$	−749.974	−	1092.25i	−0.764499	−	1.11340i
$982$		0			0
$983$	377.628	−	218.024i	0.384159	−	0.221794i	−0.295467	−	0.955353i	$-0.595475\pi$
$983$	377.628	−	218.024i	0.384159	−	0.221794i	0.679626	+	0.733559i	$0.262142\pi$
$984$		0			0
$985$	−273.148			−0.277307
$986$		0			0
$987$	44.6282	+	1142.27i	0.0452160	+	1.15731i
$988$		0			0
$989$		−	154.830i		−	0.156552i
$990$		0			0
$991$	278.088	−	481.663i	0.280614	−	0.486038i	−0.690922	−	0.722929i	$-0.742795\pi$
$991$	278.088	−	481.663i	0.280614	−	0.486038i	0.971536	+	0.236892i	$0.0761286\pi$
$992$		0			0
$993$	688.295	−	26.8916i	0.693148	−	0.0270811i
$994$		0			0
$995$	−442.245	+	255.330i	−0.444468	+	0.256613i
$996$		0			0
$997$	1624.38			1.62927			0.814633	−	0.579977i	$-0.196939\pi$
$997$	1624.38			1.62927			0.814633	+	0.579977i	$0.196939\pi$
$998$		0			0
$999$	811.721	−	95.5304i	0.812534	−	0.0956260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.14	✓	80
3.2	odd	2		2052.3.m.a.1493.17		80
9.4	even	3		2052.3.be.a.125.24		80
9.5	odd	6		684.3.be.a.581.40	yes	80
19.7	even	3		684.3.be.a.425.40	yes	80
57.26	odd	6		2052.3.be.a.197.24		80
171.121	even	3		2052.3.m.a.881.24		80
171.140	odd	6	inner	684.3.m.a.653.14	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.14	✓	80	1.1	even	1	trivial
684.3.m.a.653.14	yes	80	171.140	odd	6	inner
684.3.be.a.425.40	yes	80	19.7	even	3
684.3.be.a.581.40	yes	80	9.5	odd	6
2052.3.m.a.881.24		80	171.121	even	3
2052.3.m.a.1493.17		80	3.2	odd	2
2052.3.be.a.125.24		80	9.4	even	3
2052.3.be.a.197.24		80	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60029 - 2.53754i) q^{3} +1.56237i q^{5} +(-4.59594 + 7.96040i) q^{7} +(-3.87817 + 8.12156i) q^{9} +O(q^{10})\)	\(q+(-1.60029 - 2.53754i) q^{3} +1.56237i q^{5} +(-4.59594 + 7.96040i) q^{7} +(-3.87817 + 8.12156i) q^{9} +(-18.3761 - 10.6095i) q^{11} +(0.163320 - 0.282878i) q^{13} +(3.96458 - 2.50024i) q^{15} +(22.8775 + 13.2083i) q^{17} +(8.51862 - 16.9833i) q^{19} +(27.5546 - 1.07655i) q^{21} +(-2.17715 - 1.25698i) q^{23} +22.5590 q^{25} +(26.8149 - 3.15581i) q^{27} -52.9670i q^{29} +(-4.11110 - 7.12064i) q^{31} +(2.48516 + 63.6082i) q^{33} +(-12.4371 - 7.18057i) q^{35} +30.2712 q^{37} +(-0.979172 + 0.0382561i) q^{39} +10.9070i q^{41} +(30.7940 + 53.3368i) q^{43} +(-12.6889 - 6.05915i) q^{45} +41.4547i q^{47} +(-17.7453 - 30.7358i) q^{49} +(-3.09392 - 79.1895i) q^{51} +(54.4144 - 31.4162i) q^{53} +(16.5759 - 28.7104i) q^{55} +(-56.7280 + 5.56184i) q^{57} -78.8050i q^{59} -57.7876 q^{61} +(-46.8270 - 68.1980i) q^{63} +(0.441962 + 0.255167i) q^{65} +(30.3656 - 52.5947i) q^{67} +(0.294435 + 7.53613i) q^{69} +(48.8284 + 28.1911i) q^{71} +(30.1874 - 52.2860i) q^{73} +(-36.1008 - 57.2442i) q^{75} +(168.911 - 97.5209i) q^{77} +(-34.6994 - 60.1011i) q^{79} +(-50.9195 - 62.9937i) q^{81} +(1.98665 + 1.14700i) q^{83} +(-20.6363 + 35.7431i) q^{85} +(-134.406 + 84.7623i) q^{87} +(92.6623 - 53.4986i) q^{89} +(1.50122 + 2.60018i) q^{91} +(-11.4899 + 21.8271i) q^{93} +(26.5343 + 13.3093i) q^{95} +(13.8646 + 24.0142i) q^{97} +(157.431 - 108.098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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