LMFDB - Embedded newform 684.3.g.d.343.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, 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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.14
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690218 + 1.87713i) q^{2} +(-3.04720 - 2.59125i) q^{4} +8.91109 q^{5} -7.74115i q^{7} +(6.96733 - 3.93145i) q^{8} +O(q^{10})$	\(q+(-0.690218 + 1.87713i) q^{2} +(-3.04720 - 2.59125i) q^{4} +8.91109 q^{5} -7.74115i q^{7} +(6.96733 - 3.93145i) q^{8} +(-6.15059 + 16.7272i) q^{10} +16.0761i q^{11} -6.44347 q^{13} +(14.5311 + 5.34308i) q^{14} +(2.57085 + 15.7921i) q^{16} -1.80859 q^{17} +4.35890i q^{19} +(-27.1539 - 23.0909i) q^{20} +(-30.1768 - 11.0960i) q^{22} -9.27915i q^{23} +54.4076 q^{25} +(4.44740 - 12.0952i) q^{26} +(-20.0592 + 23.5888i) q^{28} +40.7713 q^{29} +25.0573i q^{31} +(-31.4182 - 6.07418i) q^{32} +(1.24832 - 3.39496i) q^{34} -68.9821i q^{35} +71.0299 q^{37} +(-8.18220 - 3.00859i) q^{38} +(62.0865 - 35.0335i) q^{40} +49.0888 q^{41} -30.1441i q^{43} +(41.6572 - 48.9871i) q^{44} +(17.4181 + 6.40463i) q^{46} -82.6289i q^{47} -10.9254 q^{49} +(-37.5531 + 102.130i) q^{50} +(19.6345 + 16.6966i) q^{52} -35.2383 q^{53} +143.256i q^{55} +(-30.4339 - 53.9351i) q^{56} +(-28.1410 + 76.5328i) q^{58} +80.2683i q^{59} +51.2987 q^{61} +(-47.0358 - 17.2950i) q^{62} +(33.0874 - 54.7834i) q^{64} -57.4184 q^{65} +4.89367i q^{67} +(5.51115 + 4.68652i) q^{68} +(129.488 + 47.6126i) q^{70} -96.5570i q^{71} -117.120 q^{73} +(-49.0261 + 133.332i) q^{74} +(11.2950 - 13.2824i) q^{76} +124.447 q^{77} -6.35313i q^{79} +(22.9091 + 140.725i) q^{80} +(-33.8819 + 92.1458i) q^{82} +91.5054i q^{83} -16.1166 q^{85} +(56.5842 + 20.8060i) q^{86} +(63.2024 + 112.007i) q^{88} +87.1610 q^{89} +49.8799i q^{91} +(-24.0446 + 28.2754i) q^{92} +(155.105 + 57.0319i) q^{94} +38.8426i q^{95} -107.608 q^{97} +(7.54088 - 20.5083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.690218	+	1.87713i	−0.345109	+	0.938563i
$2$	−0.690218	+	1.87713i	−0.345109	+	0.938563i
$3$		0			0
$3$		0			0
$4$	−3.04720	−	2.59125i	−0.761800	−	0.647812i
$5$	8.91109			1.78222			0.891109	−	0.453789i	$-0.149928\pi$
$5$	8.91109			1.78222			0.891109	+	0.453789i	$0.149928\pi$
$6$		0			0
$7$		−	7.74115i		−	1.10588i	−0.833222	−	0.552939i	$-0.813506\pi$
$7$		−	7.74115i		−	1.10588i	0.833222	−	0.552939i	$-0.186494\pi$
$8$	6.96733	−	3.93145i	0.870916	−	0.491431i
$9$		0			0
$10$	−6.15059	+	16.7272i	−0.615059	+	1.67272i
$11$			16.0761i			1.46146i	0.682665	+	0.730732i	$0.260821\pi$
$11$			16.0761i			1.46146i	−0.682665	+	0.730732i	$0.739179\pi$
$12$		0			0
$13$	−6.44347			−0.495652			−0.247826	−	0.968805i	$-0.579716\pi$
$13$	−6.44347			−0.495652			−0.247826	+	0.968805i	$0.579716\pi$
$14$	14.5311	+	5.34308i	1.03794	+	0.381648i
$15$		0			0
$16$	2.57085	+	15.7921i	0.160678	+	0.987007i
$17$	−1.80859			−0.106388			−0.0531939	−	0.998584i	$-0.516940\pi$
$17$	−1.80859			−0.106388			−0.0531939	+	0.998584i	$0.516940\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−27.1539	−	23.0909i	−1.35769	−	1.15454i
$21$		0			0
$22$	−30.1768	−	11.0960i	−1.37167	−	0.504364i
$23$		−	9.27915i		−	0.403441i	−0.979443	−	0.201721i	$-0.935347\pi$
$23$		−	9.27915i		−	0.403441i	0.979443	−	0.201721i	$-0.0646533\pi$
$24$		0			0
$25$	54.4076			2.17630
$26$	4.44740	−	12.0952i	0.171054	−	0.465200i
$27$		0			0
$28$	−20.0592	+	23.5888i	−0.716402	+	0.842458i
$29$	40.7713			1.40591			0.702953	−	0.711237i	$-0.251865\pi$
$29$	40.7713			1.40591			0.702953	+	0.711237i	$0.251865\pi$
$30$		0			0
$31$			25.0573i			0.808302i	0.914692	+	0.404151i	$0.132433\pi$
$31$			25.0573i			0.808302i	−0.914692	+	0.404151i	$0.867567\pi$
$32$	−31.4182	−	6.07418i	−0.981819	−	0.189818i
$33$		0			0
$34$	1.24832	−	3.39496i	0.0367154	−	0.0998517i
$35$		−	68.9821i		−	1.97092i
$36$		0			0
$37$	71.0299			1.91973			0.959864	−	0.280466i	$-0.0904890\pi$
$37$	71.0299			1.91973			0.959864	+	0.280466i	$0.0904890\pi$
$38$	−8.18220	−	3.00859i	−0.215321	−	0.0791734i
$39$		0			0
$40$	62.0865	−	35.0335i	1.55216	−	0.875838i
$41$	49.0888			1.19729			0.598643	−	0.801016i	$-0.295707\pi$
$41$	49.0888			1.19729			0.598643	+	0.801016i	$0.295707\pi$
$42$		0			0
$43$		−	30.1441i		−	0.701025i	−0.936558	−	0.350512i	$-0.886007\pi$
$43$		−	30.1441i		−	0.701025i	0.936558	−	0.350512i	$-0.113993\pi$
$44$	41.6572	−	48.9871i	0.946754	−	1.11334i
$45$		0			0
$46$	17.4181	+	6.40463i	0.378655	+	0.139231i
$47$		−	82.6289i		−	1.75806i	−0.476764	−	0.879031i	$-0.658190\pi$
$47$		−	82.6289i		−	1.75806i	0.476764	−	0.879031i	$-0.341810\pi$
$48$		0			0
$49$	−10.9254			−0.222967
$50$	−37.5531	+	102.130i	−0.751061	+	2.04260i
$51$		0			0
$52$	19.6345	+	16.6966i	0.377587	+	0.321089i
$53$	−35.2383			−0.664874			−0.332437	−	0.943125i	$-0.607871\pi$
$53$	−35.2383			−0.664874			−0.332437	+	0.943125i	$0.607871\pi$
$54$		0			0
$55$			143.256i			2.60465i
$56$	−30.4339	−	53.9351i	−0.543463	−	0.963127i
$57$		0			0
$58$	−28.1410	+	76.5328i	−0.485190	+	1.31953i
$59$			80.2683i			1.36048i	0.732990	+	0.680240i	$0.238124\pi$
$59$			80.2683i			1.36048i	−0.732990	+	0.680240i	$0.761876\pi$
$60$		0			0
$61$	51.2987			0.840962			0.420481	−	0.907301i	$-0.361861\pi$
$61$	51.2987			0.840962			0.420481	+	0.907301i	$0.361861\pi$
$62$	−47.0358	−	17.2950i	−0.758642	−	0.278952i
$63$		0			0
$64$	33.0874	−	54.7834i	0.516991	−	0.855991i
$65$	−57.4184			−0.883360
$66$		0			0
$67$			4.89367i			0.0730399i	0.999333	+	0.0365200i	$0.0116272\pi$
$67$			4.89367i			0.0730399i	−0.999333	+	0.0365200i	$0.988373\pi$
$68$	5.51115	+	4.68652i	0.0810463	+	0.0689194i
$69$		0			0
$70$	129.488	+	47.6126i	1.84983	+	0.680181i
$71$		−	96.5570i		−	1.35996i	−0.733232	−	0.679979i	$-0.761989\pi$
$71$		−	96.5570i		−	1.35996i	0.733232	−	0.679979i	$-0.238011\pi$
$72$		0			0
$73$	−117.120			−1.60439			−0.802193	−	0.597064i	$-0.796334\pi$
$73$	−117.120			−1.60439			−0.802193	+	0.597064i	$0.796334\pi$
$74$	−49.0261	+	133.332i	−0.662515	+	1.80179i
$75$		0			0
$76$	11.2950	−	13.2824i	0.148618	−	0.174769i
$77$	124.447			1.61620
$78$		0			0
$79$		−	6.35313i		−	0.0804193i	−0.999191	−	0.0402097i	$-0.987197\pi$
$79$		−	6.35313i		−	0.0804193i	0.999191	−	0.0402097i	$-0.0128026\pi$
$80$	22.9091	+	140.725i	0.286364	+	1.75906i
$81$		0			0
$82$	−33.8819	+	92.1458i	−0.413194	+	1.12373i
$83$			91.5054i			1.10247i	0.834348	+	0.551237i	$0.185844\pi$
$83$			91.5054i			1.10247i	−0.834348	+	0.551237i	$0.814156\pi$
$84$		0			0
$85$	−16.1166			−0.189606
$86$	56.5842	+	20.8060i	0.657956	+	0.241930i
$87$		0			0
$88$	63.2024	+	112.007i	0.718209	+	1.27281i
$89$	87.1610			0.979337			0.489668	−	0.871909i	$-0.337118\pi$
$89$	87.1610			0.979337			0.489668	+	0.871909i	$0.337118\pi$
$90$		0			0
$91$			49.8799i			0.548130i
$92$	−24.0446	+	28.2754i	−0.261354	+	0.307342i
$93$		0			0
$94$	155.105	+	57.0319i	1.65005	+	0.606723i
$95$			38.8426i			0.408869i
$96$		0			0
$97$	−107.608			−1.10937			−0.554683	−	0.832062i	$-0.687160\pi$
$97$	−107.608			−1.10937			−0.554683	+	0.832062i	$0.687160\pi$
$98$	7.54088	−	20.5083i	0.0769478	−	0.209268i
$99$		0			0
$100$	−165.791	−	140.984i	−1.65791	−	1.40984i
$101$	179.796			1.78016			0.890080	−	0.455804i	$-0.150648\pi$
$101$	179.796			1.78016			0.890080	+	0.455804i	$0.150648\pi$
$102$		0			0
$103$			26.0507i			0.252920i	0.991972	+	0.126460i	$0.0403615\pi$
$103$			26.0507i			0.252920i	−0.991972	+	0.126460i	$0.959638\pi$
$104$	−44.8938	+	25.3322i	−0.431671	+	0.243579i
$105$		0			0
$106$	24.3221	−	66.1468i	0.229454	−	0.624026i
$107$			24.0268i			0.224550i	0.993677	+	0.112275i	$0.0358137\pi$
$107$			24.0268i			0.224550i	−0.993677	+	0.112275i	$0.964186\pi$
$108$		0			0
$109$	24.3822			0.223690			0.111845	−	0.993726i	$-0.464324\pi$
$109$	24.3822			0.223690			0.111845	+	0.993726i	$0.464324\pi$
$110$	−268.909	−	98.8775i	−2.44462	−	0.898887i
$111$		0			0
$112$	122.249	−	19.9013i	1.09151	−	0.177691i
$113$	−80.5460			−0.712796			−0.356398	−	0.934334i	$-0.615995\pi$
$113$	−80.5460			−0.712796			−0.356398	+	0.934334i	$0.615995\pi$
$114$		0			0
$115$		−	82.6874i		−	0.719021i
$116$	−124.238	−	105.648i	−1.07102	−	0.910763i
$117$		0			0
$118$	−150.674	−	55.4026i	−1.27690	−	0.469513i
$119$			14.0006i			0.117652i
$120$		0			0
$121$	−137.441			−1.13587
$122$	−35.4073	+	96.2941i	−0.290223	+	0.789296i
$123$		0			0
$124$	64.9298	−	76.3547i	0.523628	−	0.615764i
$125$	262.054			2.09643
$126$		0			0
$127$		−	156.407i		−	1.23155i	−0.787921	−	0.615776i	$-0.788843\pi$
$127$		−	156.407i		−	1.23155i	0.787921	−	0.615776i	$-0.211157\pi$
$128$	79.9979	+	99.9217i	0.624983	+	0.780638i
$129$		0			0
$130$	39.6312	−	107.782i	0.304855	−	0.829089i
$131$			15.8524i			0.121010i	0.998168	+	0.0605052i	$0.0192712\pi$
$131$			15.8524i			0.121010i	−0.998168	+	0.0605052i	$0.980729\pi$
$132$		0			0
$133$	33.7429			0.253706
$134$	−9.18604	−	3.37770i	−0.0685525	−	0.0252067i
$135$		0			0
$136$	−12.6011	+	7.11040i	−0.0926550	+	0.0522823i
$137$	−79.6097			−0.581093			−0.290546	−	0.956861i	$-0.593837\pi$
$137$	−79.6097			−0.581093			−0.290546	+	0.956861i	$0.593837\pi$
$138$		0			0
$139$			107.505i			0.773414i	0.922203	+	0.386707i	$0.126388\pi$
$139$			107.505i			0.773414i	−0.922203	+	0.386707i	$0.873612\pi$
$140$	−178.750	+	210.202i	−1.27678	+	1.50144i
$141$		0			0
$142$	181.250	+	66.6453i	1.27641	+	0.469333i
$143$		−	103.586i		−	0.724377i
$144$		0			0
$145$	363.316			2.50563
$146$	80.8384	−	219.849i	0.553688	−	1.50582i
$147$		0			0
$148$	−216.442	−	184.056i	−1.46245	−	1.24362i
$149$	−114.197			−0.766425			−0.383212	−	0.923660i	$-0.625182\pi$
$149$	−114.197			−0.766425			−0.383212	+	0.923660i	$0.625182\pi$
$150$		0			0
$151$			286.626i			1.89818i	0.314999	+	0.949092i	$0.397996\pi$
$151$			286.626i			1.89818i	−0.314999	+	0.949092i	$0.602004\pi$
$152$	17.1368	+	30.3699i	0.112742	+	0.199802i
$153$		0			0
$154$	−85.8958	+	233.603i	−0.557765	+	1.51691i
$155$			223.288i			1.44057i
$156$		0			0
$157$	−113.974			−0.725949			−0.362975	−	0.931799i	$-0.618239\pi$
$157$	−113.974			−0.725949			−0.362975	+	0.931799i	$0.618239\pi$
$158$	11.9256	+	4.38504i	0.0754786	+	0.0277534i
$159$		0			0
$160$	−279.971	−	54.1276i	−1.74982	−	0.338297i
$161$	−71.8313			−0.446157
$162$		0			0
$163$		−	8.95098i		−	0.0549140i	−0.999623	−	0.0274570i	$-0.991259\pi$
$163$		−	8.95098i		−	0.0549140i	0.999623	−	0.0274570i	$-0.00874093\pi$
$164$	−149.583	−	127.201i	−0.912093	−	0.775617i
$165$		0			0
$166$	−171.767	−	63.1586i	−1.03474	−	0.380474i
$167$			2.62249i			0.0157036i	0.999969	+	0.00785178i	$0.00249932\pi$
$167$			2.62249i			0.0157036i	−0.999969	+	0.00785178i	$0.997501\pi$
$168$		0			0
$169$	−127.482			−0.754329
$170$	11.1239	−	30.2528i	0.0654349	−	0.177958i
$171$		0			0
$172$	−78.1108	+	91.8550i	−0.454133	+	0.534041i
$173$	−16.2314			−0.0938230			−0.0469115	−	0.998899i	$-0.514938\pi$
$173$	−16.2314			−0.0938230			−0.0469115	+	0.998899i	$0.514938\pi$
$174$		0			0
$175$		−	421.177i		−	2.40673i
$176$	−253.875	+	41.3292i	−1.44247	+	0.234825i
$177$		0			0
$178$	−60.1600	+	163.612i	−0.337978	+	0.919169i
$179$		−	107.999i		−	0.603349i	−0.953411	−	0.301674i	$-0.902454\pi$
$179$		−	107.999i		−	0.603349i	0.953411	−	0.301674i	$-0.0975456\pi$
$180$		0			0
$181$	104.811			0.579069			0.289534	−	0.957168i	$-0.406500\pi$
$181$	104.811			0.579069			0.289534	+	0.957168i	$0.406500\pi$
$182$	−93.6308	−	34.4280i	−0.514455	−	0.189165i
$183$		0			0
$184$	−36.4805	−	64.6509i	−0.198264	−	0.351364i
$185$	632.954			3.42138
$186$		0			0
$187$		−	29.0751i		−	0.155482i
$188$	−214.112	+	251.787i	−1.13889	+	1.33929i
$189$		0			0
$190$	−72.9124	−	26.8098i	−0.383749	−	0.141104i
$191$		−	295.930i		−	1.54937i	−0.632345	−	0.774687i	$-0.717907\pi$
$191$		−	295.930i		−	1.54937i	0.632345	−	0.774687i	$-0.282093\pi$
$192$		0			0
$193$	−194.495			−1.00775			−0.503874	−	0.863777i	$-0.668092\pi$
$193$	−194.495			−1.00775			−0.503874	+	0.863777i	$0.668092\pi$
$194$	74.2733	−	201.995i	0.382852	−	1.04121i
$195$		0			0
$196$	33.2918	+	28.3104i	0.169856	+	0.144441i
$197$	−130.284			−0.661340			−0.330670	−	0.943746i	$-0.607275\pi$
$197$	−130.284			−0.661340			−0.330670	+	0.943746i	$0.607275\pi$
$198$		0			0
$199$		−	270.765i		−	1.36063i	−0.732921	−	0.680313i	$-0.761844\pi$
$199$		−	270.765i		−	1.36063i	0.732921	−	0.680313i	$-0.238156\pi$
$200$	379.076	−	213.901i	1.89538	−	1.06950i
$201$		0			0
$202$	−124.098	+	337.500i	−0.614349	+	1.67079i
$203$		−	315.616i		−	1.55476i
$204$		0			0
$205$	437.435			2.13383
$206$	−48.9005	−	17.9807i	−0.237381	−	0.0872849i
$207$		0			0
$208$	−16.5652	−	101.756i	−0.0796404	−	0.489212i
$209$	−70.0741			−0.335283
$210$		0			0
$211$			183.580i			0.870048i	0.900419	+	0.435024i	$0.143260\pi$
$211$			183.580i			0.870048i	−0.900419	+	0.435024i	$0.856740\pi$
$212$	107.378	+	91.3113i	0.506501	+	0.430714i
$213$		0			0
$214$	−45.1013	−	16.5837i	−0.210754	−	0.0774940i
$215$		−	268.617i		−	1.24938i
$216$		0			0
$217$	193.973			0.893883
$218$	−16.8290	+	45.7685i	−0.0771974	+	0.209947i
$219$		0			0
$220$	371.211	−	436.528i	1.68732	−	1.98422i
$221$	11.6536			0.0527313
$222$		0			0
$223$			168.708i			0.756538i	0.925696	+	0.378269i	$0.123481\pi$
$223$			168.708i			0.756538i	−0.925696	+	0.378269i	$0.876519\pi$
$224$	−47.0211	+	243.213i	−0.209916	+	1.08577i
$225$		0			0
$226$	55.5943	−	151.195i	0.245992	−	0.669004i
$227$			249.037i			1.09708i	0.836124	+	0.548540i	$0.184816\pi$
$227$			249.037i			1.09708i	−0.836124	+	0.548540i	$0.815184\pi$
$228$		0			0
$229$	−283.680			−1.23878			−0.619388	−	0.785085i	$-0.712619\pi$
$229$	−283.680			−1.23878			−0.619388	+	0.785085i	$0.712619\pi$
$230$	155.215	+	57.0723i	0.674846	+	0.248140i
$231$		0			0
$232$	284.067	−	160.290i	1.22443	−	0.690906i
$233$	77.8448			0.334098			0.167049	−	0.985949i	$-0.446576\pi$
$233$	77.8448			0.334098			0.167049	+	0.985949i	$0.446576\pi$
$234$		0			0
$235$		−	736.314i		−	3.13325i
$236$	207.995	−	244.593i	0.881335	−	1.03641i
$237$		0			0
$238$	−26.2809	−	9.66346i	−0.110424	−	0.0406028i
$239$		−	31.9668i		−	0.133752i	−0.997761	−	0.0668762i	$-0.978697\pi$
$239$		−	31.9668i		−	0.133752i	0.997761	−	0.0668762i	$-0.0213032\pi$
$240$		0			0
$241$	45.2991			0.187963			0.0939815	−	0.995574i	$-0.470041\pi$
$241$	45.2991			0.187963			0.0939815	+	0.995574i	$0.470041\pi$
$242$	94.8641	−	257.994i	0.392000	−	1.06609i
$243$		0			0
$244$	−156.317	−	132.928i	−0.640645	−	0.544786i
$245$	−97.3570			−0.397375
$246$		0			0
$247$		−	28.0864i		−	0.113710i
$248$	98.5117	+	174.583i	0.397225	+	0.703963i
$249$		0			0
$250$	−180.874	+	491.908i	−0.723496	+	1.96763i
$251$			16.0745i			0.0640416i	0.999487	+	0.0320208i	$0.0101943\pi$
$251$			16.0745i			0.0640416i	−0.999487	+	0.0320208i	$0.989806\pi$
$252$		0			0
$253$	149.173			0.589615
$254$	293.596	+	107.955i	1.15589	+	0.425019i
$255$		0			0
$256$	−242.781	+	81.1983i	−0.948365	+	0.317181i
$257$	342.048			1.33093			0.665463	−	0.746431i	$-0.268234\pi$
$257$	342.048			1.33093			0.665463	+	0.746431i	$0.268234\pi$
$258$		0			0
$259$		−	549.853i		−	2.12299i
$260$	174.965	+	148.785i	0.672943	+	0.572251i
$261$		0			0
$262$	−29.7569	−	10.9416i	−0.113576	−	0.0417617i
$263$		−	306.233i		−	1.16438i	−0.813052	−	0.582192i	$-0.802195\pi$
$263$		−	306.233i		−	1.16438i	0.813052	−	0.582192i	$-0.197805\pi$
$264$		0			0
$265$	−314.012			−1.18495
$266$	−23.2899	+	63.3396i	−0.0875561	+	0.238119i
$267$		0			0
$268$	12.6807	−	14.9120i	0.0473162	−	0.0556418i
$269$	−110.529			−0.410889			−0.205444	−	0.978669i	$-0.565864\pi$
$269$	−110.529			−0.410889			−0.205444	+	0.978669i	$0.565864\pi$
$270$		0			0
$271$		−	177.256i		−	0.654081i	−0.945010	−	0.327040i	$-0.893949\pi$
$271$		−	177.256i		−	0.654081i	0.945010	−	0.327040i	$-0.106051\pi$
$272$	−4.64963	−	28.5615i	−0.0170942	−	0.105006i
$273$		0			0
$274$	54.9480	−	149.437i	0.200540	−	0.545392i
$275$			874.662i			3.18059i
$276$		0			0
$277$	−337.347			−1.21786			−0.608929	−	0.793225i	$-0.708400\pi$
$277$	−337.347			−1.21786			−0.608929	+	0.793225i	$0.708400\pi$
$278$	−201.800	−	74.2015i	−0.725898	−	0.266912i
$279$		0			0
$280$	−271.200	−	480.621i	−0.968570	−	1.71650i
$281$	−250.838			−0.892661			−0.446331	−	0.894868i	$-0.647269\pi$
$281$	−250.838			−0.892661			−0.446331	+	0.894868i	$0.647269\pi$
$282$		0			0
$283$			417.902i			1.47668i	0.674427	+	0.738342i	$0.264391\pi$
$283$			417.902i			1.47668i	−0.674427	+	0.738342i	$0.735609\pi$
$284$	−250.203	+	294.229i	−0.880998	+	1.03602i
$285$		0			0
$286$	194.444	+	71.4968i	0.679873	+	0.249989i
$287$		−	380.003i		−	1.32405i
$288$		0			0
$289$	−285.729			−0.988682
$290$	−250.767	+	681.991i	−0.864715	+	2.35169i
$291$		0			0
$292$	356.889	+	303.488i	1.22222	+	1.03934i
$293$	−210.732			−0.719223			−0.359612	−	0.933102i	$-0.617091\pi$
$293$	−210.732			−0.719223			−0.359612	+	0.933102i	$0.617091\pi$
$294$		0			0
$295$			715.278i			2.42467i
$296$	494.889	−	279.251i	1.67192	−	0.943414i
$297$		0			0
$298$	78.8210	−	214.363i	0.264500	−	0.719338i
$299$			59.7900i			0.199966i
$300$		0			0
$301$	−233.350			−0.775248
$302$	−538.033	−	197.834i	−1.78156	−	0.655080i
$303$		0			0
$304$	−68.8362	+	11.2061i	−0.226435	+	0.0368621i
$305$	457.128			1.49878
$306$		0			0
$307$			282.598i			0.920514i	0.887786	+	0.460257i	$0.152243\pi$
$307$			282.598i			0.920514i	−0.887786	+	0.460257i	$0.847757\pi$
$308$	−379.216	−	322.474i	−1.23122	−	1.04699i
$309$		0			0
$310$	−419.140	−	154.118i	−1.35207	−	0.497153i
$311$			44.9288i			0.144466i	0.997388	+	0.0722328i	$0.0230125\pi$
$311$			44.9288i			0.144466i	−0.997388	+	0.0722328i	$0.976988\pi$
$312$		0			0
$313$	−511.392			−1.63384			−0.816921	−	0.576750i	$-0.804321\pi$
$313$	−511.392			−1.63384			−0.816921	+	0.576750i	$0.804321\pi$
$314$	78.6669	−	213.944i	0.250531	−	0.681349i
$315$		0			0
$316$	−16.4625	+	19.3592i	−0.0520966	+	0.0612634i
$317$	419.477			1.32327			0.661636	−	0.749825i	$-0.269863\pi$
$317$	419.477			1.32327			0.661636	+	0.749825i	$0.269863\pi$
$318$		0			0
$319$			655.443i			2.05468i
$320$	294.845	−	488.180i	0.921390	−	1.52556i
$321$		0			0
$322$	49.5792	−	134.836i	0.153973	−	0.418746i
$323$		−	7.88348i		−	0.0244071i
$324$		0			0
$325$	−350.574			−1.07869
$326$	16.8021	+	6.17813i	0.0515402	+	0.0189513i
$327$		0			0
$328$	342.018	−	192.990i	1.04274	−	0.588384i
$329$	−639.643			−1.94420
$330$		0			0
$331$			355.767i			1.07482i	0.843320	+	0.537412i	$0.180598\pi$
$331$			355.767i			1.07482i	−0.843320	+	0.537412i	$0.819402\pi$
$332$	237.113	−	278.835i	0.714197	−	0.839865i
$333$		0			0
$334$	−4.92275	−	1.81009i	−0.0147388	−	0.00541943i
$335$			43.6080i			0.130173i
$336$		0			0
$337$	298.046			0.884410			0.442205	−	0.896914i	$-0.354196\pi$
$337$	298.046			0.884410			0.442205	+	0.896914i	$0.354196\pi$
$338$	87.9901	−	239.299i	0.260326	−	0.707985i
$339$		0			0
$340$	49.1103	+	41.7620i	0.144442	+	0.122829i
$341$	−402.824			−1.18130
$342$		0			0
$343$		−	294.741i		−	0.859304i
$344$	−118.510	−	210.024i	−0.344506	−	0.610534i
$345$		0			0
$346$	11.2032	−	30.4683i	0.0323791	−	0.0880587i
$347$		−	174.610i		−	0.503199i	−0.967831	−	0.251599i	$-0.919043\pi$
$347$		−	174.610i		−	0.503199i	0.967831	−	0.251599i	$-0.0809565\pi$
$348$		0			0
$349$	41.7325			0.119577			0.0597887	−	0.998211i	$-0.480957\pi$
$349$	41.7325			0.119577			0.0597887	+	0.998211i	$0.480957\pi$
$350$	790.602	+	290.704i	2.25886	+	0.830583i
$351$		0			0
$352$	97.6491	−	505.082i	0.277412	−	1.43489i
$353$	−385.808			−1.09294			−0.546470	−	0.837478i	$-0.684029\pi$
$353$	−385.808			−1.09294			−0.546470	+	0.837478i	$0.684029\pi$
$354$		0			0
$355$		−	860.429i		−	2.42374i
$356$	−265.597	−	225.856i	−0.746059	−	0.634426i
$357$		0			0
$358$	202.729	+	74.5431i	0.566281	+	0.208221i
$359$			702.253i			1.95614i	0.208287	+	0.978068i	$0.433211\pi$
$359$			702.253i			1.95614i	−0.208287	+	0.978068i	$0.566789\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−72.3427	+	196.744i	−0.199842	+	0.543492i
$363$		0			0
$364$	129.251	−	151.994i	0.355086	−	0.417566i
$365$	−1043.67			−2.85937
$366$		0			0
$367$			384.653i			1.04810i	0.851687	+	0.524051i	$0.175580\pi$
$367$			384.653i			1.04810i	−0.851687	+	0.524051i	$0.824420\pi$
$368$	146.537	−	23.8553i	0.398200	−	0.0648242i
$369$		0			0
$370$	−436.876	+	1188.13i	−1.18075	+	3.21118i
$371$			272.785i			0.735270i
$372$		0			0
$373$	−425.180			−1.13989			−0.569946	−	0.821682i	$-0.693036\pi$
$373$	−425.180			−1.13989			−0.569946	+	0.821682i	$0.693036\pi$
$374$	54.5777	+	20.0682i	0.145930	+	0.0536582i
$375$		0			0
$376$	−324.852	−	575.703i	−0.863967	−	1.53113i
$377$	−262.708			−0.696839
$378$		0			0
$379$		−	531.642i		−	1.40275i	−0.712793	−	0.701375i	$-0.752570\pi$
$379$		−	531.642i		−	1.40275i	0.712793	−	0.701375i	$-0.247430\pi$
$380$	100.651	−	118.361i	0.264870	−	0.311476i
$381$		0			0
$382$	555.499	+	204.256i	1.45418	+	0.534703i
$383$		−	676.483i		−	1.76627i	−0.469116	−	0.883137i	$-0.655427\pi$
$383$		−	676.483i		−	1.76627i	0.469116	−	0.883137i	$-0.344573\pi$
$384$		0			0
$385$	1108.96			2.88042
$386$	134.244	−	365.092i	0.347783	−	0.945834i
$387$		0			0
$388$	327.905	+	278.840i	0.845115	+	0.718661i
$389$	38.8036			0.0997521			0.0498760	−	0.998755i	$-0.484117\pi$
$389$	38.8036			0.0997521			0.0498760	+	0.998755i	$0.484117\pi$
$390$		0			0
$391$			16.7822i			0.0429213i
$392$	−76.1207	+	42.9525i	−0.194185	+	0.109573i
$393$		0			0
$394$	89.9243	−	244.559i	0.228234	−	0.620709i
$395$		−	56.6133i		−	0.143325i
$396$		0			0
$397$	−28.6954			−0.0722806			−0.0361403	−	0.999347i	$-0.511506\pi$
$397$	−28.6954			−0.0722806			−0.0361403	+	0.999347i	$0.511506\pi$
$398$	508.259	+	186.887i	1.27703	+	0.469564i
$399$		0			0
$400$	139.874	+	859.211i	0.349685	+	2.14803i
$401$	−402.321			−1.00329			−0.501647	−	0.865073i	$-0.667272\pi$
$401$	−402.321			−1.00329			−0.501647	+	0.865073i	$0.667272\pi$
$402$		0			0
$403$		−	161.456i		−	0.400636i
$404$	−547.875	−	465.897i	−1.35613	−	1.15321i
$405$		0			0
$406$	592.451	+	217.844i	1.45924	+	0.536561i
$407$			1141.88i			2.80561i
$408$		0			0
$409$	299.164			0.731451			0.365726	−	0.930723i	$-0.380821\pi$
$409$	299.164			0.731451			0.365726	+	0.930723i	$0.380821\pi$
$410$	−301.925	+	821.120i	−0.736402	+	2.00273i
$411$		0			0
$412$	67.5040	−	79.3818i	0.163845	−	0.192674i
$413$	621.369			1.50452
$414$		0			0
$415$			815.413i			1.96485i
$416$	202.442	+	39.1388i	0.486640	+	0.0940837i
$417$		0			0
$418$	48.3664	−	131.538i	0.115709	−	0.314684i
$419$			55.9282i			0.133480i	0.997770	+	0.0667401i	$0.0212598\pi$
$419$			55.9282i			0.133480i	−0.997770	+	0.0667401i	$0.978740\pi$
$420$		0			0
$421$	657.497			1.56175			0.780875	−	0.624687i	$-0.214774\pi$
$421$	657.497			1.56175			0.780875	+	0.624687i	$0.214774\pi$
$422$	−344.603	−	126.710i	−0.816594	−	0.300261i
$423$		0			0
$424$	−245.517	+	138.538i	−0.579050	+	0.326740i
$425$	−98.4012			−0.231532
$426$		0			0
$427$		−	397.111i		−	0.930002i
$428$	62.2595	−	73.2145i	0.145466	−	0.171062i
$429$		0			0
$430$	504.227	+	185.404i	1.17262	+	0.431172i
$431$			627.989i			1.45705i	0.685019	+	0.728525i	$0.259794\pi$
$431$			627.989i			1.45705i	−0.685019	+	0.728525i	$0.740206\pi$
$432$		0			0
$433$	−285.023			−0.658251			−0.329125	−	0.944286i	$-0.606754\pi$
$433$	−285.023			−0.658251			−0.329125	+	0.944286i	$0.606754\pi$
$434$	−133.883	+	364.111i	−0.308487	+	0.838965i
$435$		0			0
$436$	−74.2975	−	63.1804i	−0.170407	−	0.144909i
$437$	40.4469			0.0925558
$438$		0			0
$439$			28.8089i			0.0656239i	0.999462	+	0.0328120i	$0.0104462\pi$
$439$			28.8089i			0.0656239i	−0.999462	+	0.0328120i	$0.989554\pi$
$440$	563.202	+	998.109i	1.28001	+	2.26843i
$441$		0			0
$442$	−8.04354	+	21.8753i	−0.0181980	+	0.0494917i
$443$		−	290.870i		−	0.656591i	−0.944575	−	0.328295i	$-0.893526\pi$
$443$		−	290.870i		−	0.656591i	0.944575	−	0.328295i	$-0.106474\pi$
$444$		0			0
$445$	776.700			1.74539
$446$	−316.686	−	116.445i	−0.710058	−	0.261088i
$447$		0			0
$448$	−424.087	−	256.134i	−0.946622	−	0.571729i
$449$	12.6985			0.0282817			0.0141409	−	0.999900i	$-0.495499\pi$
$449$	12.6985			0.0282817			0.0141409	+	0.999900i	$0.495499\pi$
$450$		0			0
$451$			789.156i			1.74979i
$452$	245.440	+	208.715i	0.543008	+	0.461758i
$453$		0			0
$454$	−467.474	−	171.890i	−1.02968	−	0.378612i
$455$			444.484i			0.976888i
$456$		0			0
$457$	118.476			0.259248			0.129624	−	0.991563i	$-0.458623\pi$
$457$	118.476			0.259248			0.129624	+	0.991563i	$0.458623\pi$
$458$	195.801	−	532.502i	0.427512	−	1.16267i
$459$		0			0
$460$	−214.264	+	251.965i	−0.465791	+	0.547750i
$461$	−189.946			−0.412029			−0.206015	−	0.978549i	$-0.566049\pi$
$461$	−189.946			−0.412029			−0.206015	+	0.978549i	$0.566049\pi$
$462$		0			0
$463$		−	493.864i		−	1.06666i	−0.845907	−	0.533331i	$-0.820940\pi$
$463$		−	493.864i		−	1.06666i	0.845907	−	0.533331i	$-0.179060\pi$
$464$	104.817	+	643.864i	0.225898	+	1.38764i
$465$		0			0
$466$	−53.7299	+	146.125i	−0.115300	+	0.313572i
$467$		−	79.7951i		−	0.170867i	−0.996344	−	0.0854337i	$-0.972772\pi$
$467$		−	79.7951i		−	0.170867i	0.996344	−	0.0854337i	$-0.0272276\pi$
$468$		0			0
$469$	37.8827			0.0807732
$470$	1382.15	+	508.217i	2.94075	+	1.08131i
$471$		0			0
$472$	315.571	+	559.256i	0.668582	+	1.18486i
$473$	484.599			1.02452
$474$		0			0
$475$			237.157i			0.499278i
$476$	36.2790	−	42.6626i	0.0762165	−	0.0896273i
$477$		0			0
$478$	60.0057	+	22.0640i	0.125535	+	0.0461591i
$479$			229.249i			0.478600i	0.970946	+	0.239300i	$0.0769179\pi$
$479$			229.249i			0.478600i	−0.970946	+	0.239300i	$0.923082\pi$
$480$		0			0
$481$	−457.679			−0.951516
$482$	−31.2662	+	85.0321i	−0.0648677	+	0.176415i
$483$		0			0
$484$	418.810	+	356.144i	0.865309	+	0.735834i
$485$	−958.909			−1.97713
$486$		0			0
$487$		−	842.418i		−	1.72981i	−0.501934	−	0.864906i	$-0.667378\pi$
$487$		−	842.418i		−	1.72981i	0.501934	−	0.864906i	$-0.332622\pi$
$488$	357.415	−	201.678i	0.732408	−	0.413275i
$489$		0			0
$490$	67.1975	−	182.751i	0.137138	−	0.372962i
$491$		−	385.037i		−	0.784190i	−0.919925	−	0.392095i	$-0.871750\pi$
$491$		−	385.037i		−	0.784190i	0.919925	−	0.392095i	$-0.128250\pi$
$492$		0			0
$493$	−73.7387			−0.149571
$494$	52.7218	+	19.3858i	0.106724	+	0.0392424i
$495$		0			0
$496$	−395.708	+	64.4187i	−0.797799	+	0.129876i
$497$	−747.462			−1.50395
$498$		0			0
$499$			709.613i			1.42207i	0.703156	+	0.711035i	$0.251773\pi$
$499$			709.613i			1.42207i	−0.703156	+	0.711035i	$0.748227\pi$
$500$	−798.530	−	679.047i	−1.59706	−	1.35809i
$501$		0			0
$502$	−30.1738	−	11.0949i	−0.0601071	−	0.0221013i
$503$		−	607.671i		−	1.20809i	−0.796949	−	0.604047i	$-0.793554\pi$
$503$		−	607.671i		−	1.20809i	0.796949	−	0.604047i	$-0.206446\pi$
$504$		0			0
$505$	1602.18			3.17263
$506$	−102.962	+	280.016i	−0.203481	+	0.553391i
$507$		0			0
$508$	−405.290	+	476.604i	−0.797815	+	0.938196i
$509$	−42.8187			−0.0841232			−0.0420616	−	0.999115i	$-0.513393\pi$
$509$	−42.8187			−0.0841232			−0.0420616	+	0.999115i	$0.513393\pi$
$510$		0			0
$511$			906.645i			1.77426i
$512$	15.1526	−	511.776i	0.0295949	−	0.999562i
$513$		0			0
$514$	−236.088	+	642.067i	−0.459314	+	1.24916i
$515$			232.141i			0.450759i
$516$		0			0
$517$	1328.35			2.56934
$518$	1032.14	+	379.518i	1.99255	+	0.732661i
$519$		0			0
$520$	−400.053	+	225.738i	−0.769333	+	0.434111i
$521$	261.985			0.502849			0.251425	−	0.967877i	$-0.419101\pi$
$521$	261.985			0.502849			0.251425	+	0.967877i	$0.419101\pi$
$522$		0			0
$523$		−	509.423i		−	0.974039i	−0.873391	−	0.487020i	$-0.838084\pi$
$523$		−	509.423i		−	0.974039i	0.873391	−	0.487020i	$-0.161916\pi$
$524$	41.0774	−	48.3053i	0.0783920	−	0.0921857i
$525$		0			0
$526$	574.837	+	211.367i	1.09285	+	0.401839i
$527$		−	45.3186i		−	0.0859935i
$528$		0			0
$529$	442.897			0.837235
$530$	216.737	−	589.440i	0.408937	−	1.11215i
$531$		0			0
$532$	−102.821	−	87.4362i	−0.193273	−	0.164354i
$533$	−316.302			−0.593437
$534$		0			0
$535$			214.105i			0.400196i
$536$	19.2392	+	34.0958i	0.0358941	+	0.0636116i
$537$		0			0
$538$	76.2891	−	207.477i	0.141801	−	0.385645i
$539$		−	175.637i		−	0.325858i
$540$		0			0
$541$	−990.355			−1.83060			−0.915301	−	0.402772i	$-0.868047\pi$
$541$	−990.355			−1.83060			−0.915301	+	0.402772i	$0.868047\pi$
$542$	332.732	+	122.345i	0.613896	+	0.225729i
$543$		0			0
$544$	56.8228	+	10.9857i	0.104454	+	0.0201944i
$545$	217.272			0.398665
$546$		0			0
$547$			547.139i			1.00025i	0.865952	+	0.500127i	$0.166713\pi$
$547$			547.139i			1.00025i	−0.865952	+	0.500127i	$0.833287\pi$
$548$	242.587	+	206.289i	0.442677	+	0.376439i
$549$		0			0
$550$	−1641.85	−	603.707i	−2.98518	−	1.09765i
$551$			177.718i			0.322537i
$552$		0			0
$553$	−49.1805			−0.0889340
$554$	232.843	−	633.242i	0.420293	−	1.14304i
$555$		0			0
$556$	278.571	−	327.588i	0.501027	−	0.589187i
$557$	−54.9787			−0.0987050			−0.0493525	−	0.998781i	$-0.515716\pi$
$557$	−54.9787			−0.0987050			−0.0493525	+	0.998781i	$0.515716\pi$
$558$		0			0
$559$			194.233i			0.347464i
$560$	1089.37	−	177.343i	1.94531	−	0.316683i
$561$		0			0
$562$	173.133	−	470.854i	0.308065	−	0.837818i
$563$		−	126.028i		−	0.223851i	−0.993717	−	0.111925i	$-0.964298\pi$
$563$		−	126.028i		−	0.223851i	0.993717	−	0.111925i	$-0.0357018\pi$
$564$		0			0
$565$	−717.753			−1.27036
$566$	−784.454	−	288.443i	−1.38596	−	0.509617i
$567$		0			0
$568$	−379.609	−	672.745i	−0.668326	−	1.18441i
$569$	−162.688			−0.285919			−0.142959	−	0.989729i	$-0.545662\pi$
$569$	−162.688			−0.285919			−0.142959	+	0.989729i	$0.545662\pi$
$570$		0			0
$571$		−	414.403i		−	0.725749i	−0.931838	−	0.362875i	$-0.881795\pi$
$571$		−	414.403i		−	0.725749i	0.931838	−	0.362875i	$-0.118205\pi$
$572$	−268.417	+	315.647i	−0.469260	+	0.551830i
$573$		0			0
$574$	713.314	+	262.285i	1.24271	+	0.456942i
$575$		−	504.856i		−	0.878011i
$576$		0			0
$577$	−648.643			−1.12416			−0.562082	−	0.827081i	$-0.690000\pi$
$577$	−648.643			−1.12416			−0.562082	+	0.827081i	$0.690000\pi$
$578$	197.215	−	536.349i	0.341203	−	0.927940i
$579$		0			0
$580$	−1107.10	−	941.444i	−1.90879	−	1.62318i
$581$	708.357			1.21920
$582$		0			0
$583$		−	566.495i		−	0.971689i
$584$	−816.015	+	460.452i	−1.39729	+	0.788446i
$585$		0			0
$586$	145.451	−	395.571i	0.248210	−	0.675036i
$587$		−	1032.50i		−	1.75895i	−0.475948	−	0.879473i	$-0.657895\pi$
$587$		−	1032.50i		−	1.75895i	0.475948	−	0.879473i	$-0.342105\pi$
$588$		0			0
$589$	−109.222			−0.185437
$590$	−1342.67	−	493.698i	−2.27571	−	0.836775i
$591$		0			0
$592$	182.607	+	1121.71i	0.308458	+	1.89478i
$593$	−820.949			−1.38440			−0.692199	−	0.721706i	$-0.743358\pi$
$593$	−820.949			−1.38440			−0.692199	+	0.721706i	$0.743358\pi$
$594$		0			0
$595$			124.761i			0.209682i
$596$	347.982	+	295.914i	0.583862	+	0.496499i
$597$		0			0
$598$	−112.233	−	41.2681i	−0.187681	−	0.0690102i
$599$			185.031i			0.308899i	0.988001	+	0.154450i	$0.0493604\pi$
$599$			185.031i			0.308899i	−0.988001	+	0.154450i	$0.950640\pi$
$600$		0			0
$601$	−57.8307			−0.0962241			−0.0481120	−	0.998842i	$-0.515320\pi$
$601$	−57.8307			−0.0962241			−0.0481120	+	0.998842i	$0.515320\pi$
$602$	161.062	−	438.027i	0.267545	−	0.727619i
$603$		0			0
$604$	742.719	−	873.406i	1.22967	−	1.44604i
$605$	−1224.75			−2.02438
$606$		0			0
$607$			1027.52i			1.69278i	0.532565	+	0.846389i	$0.321228\pi$
$607$			1027.52i			1.69278i	−0.532565	+	0.846389i	$0.678772\pi$
$608$	26.4767	−	136.949i	0.0435473	−	0.225245i
$609$		0			0
$610$	−315.517	+	858.086i	−0.517242	+	1.40670i
$611$			532.417i			0.871387i
$612$		0			0
$613$	−1130.78			−1.84466			−0.922330	−	0.386404i	$-0.873717\pi$
$613$	−1130.78			−1.84466			−0.922330	+	0.386404i	$0.873717\pi$
$614$	−530.471	−	195.054i	−0.863960	−	0.317677i
$615$		0			0
$616$	867.066	−	489.259i	1.40758	−	0.794251i
$617$	831.065			1.34694			0.673472	−	0.739212i	$-0.264802\pi$
$617$	831.065			1.34694			0.673472	+	0.739212i	$0.264802\pi$
$618$		0			0
$619$		−	702.202i		−	1.13441i	−0.823575	−	0.567207i	$-0.808024\pi$
$619$		−	702.202i		−	1.13441i	0.823575	−	0.567207i	$-0.191976\pi$
$620$	578.596	−	680.404i	0.933219	−	1.09743i
$621$		0			0
$622$	−84.3370	−	31.0107i	−0.135590	−	0.0498564i
$623$		−	674.726i		−	1.08303i
$624$		0			0
$625$	974.996			1.55999
$626$	352.972	−	959.948i	0.563853	−	1.53346i
$627$		0			0
$628$	347.302	+	295.335i	0.553028	+	0.470279i
$629$	−128.464			−0.204236
$630$		0			0
$631$			56.3471i			0.0892981i	0.999003	+	0.0446490i	$0.0142170\pi$
$631$			56.3471i			0.0892981i	−0.999003	+	0.0446490i	$0.985783\pi$
$632$	−24.9770	−	44.2643i	−0.0395206	−	0.0700385i
$633$		0			0
$634$	−289.530	+	787.411i	−0.456673	+	1.24197i
$635$		−	1393.76i		−	2.19490i
$636$		0			0
$637$	70.3973			0.110514
$638$	−1230.35	−	452.398i	−1.92845	−	0.709088i
$639$		0			0
$640$	712.868	+	890.411i	1.11386	+	1.39127i
$641$	−472.269			−0.736768			−0.368384	−	0.929674i	$-0.620089\pi$
$641$	−472.269			−0.736768			−0.368384	+	0.929674i	$0.620089\pi$
$642$		0			0
$643$		−	507.477i		−	0.789233i	−0.918846	−	0.394616i	$-0.870878\pi$
$643$		−	507.477i		−	0.789233i	0.918846	−	0.394616i	$-0.129122\pi$
$644$	218.884	+	186.133i	0.339882	+	0.289026i
$645$		0			0
$646$	14.7983	+	5.44132i	0.0229076	+	0.00842309i
$647$			1010.69i			1.56212i	0.624457	+	0.781059i	$0.285320\pi$
$647$			1010.69i			1.56212i	−0.624457	+	0.781059i	$0.714680\pi$
$648$		0			0
$649$	−1290.40			−1.98829
$650$	241.972	−	658.071i	0.372265	−	1.01242i
$651$		0			0
$652$	−23.1942	+	27.2754i	−0.0355740	+	0.0418335i
$653$	961.670			1.47270			0.736348	−	0.676603i	$-0.236549\pi$
$653$	961.670			1.47270			0.736348	+	0.676603i	$0.236549\pi$
$654$		0			0
$655$			141.262i			0.215667i
$656$	126.200	+	775.215i	0.192378	+	1.18173i
$657$		0			0
$658$	441.493	−	1200.69i	0.670962	−	1.82476i
$659$			373.680i			0.567041i	0.958966	+	0.283521i	$0.0915024\pi$
$659$			373.680i			0.567041i	−0.958966	+	0.283521i	$0.908498\pi$
$660$		0			0
$661$	254.841			0.385538			0.192769	−	0.981244i	$-0.438253\pi$
$661$	254.841			0.385538			0.192769	+	0.981244i	$0.438253\pi$
$662$	−667.819	−	245.556i	−1.00879	−	0.370931i
$663$		0			0
$664$	359.749	+	637.548i	0.541791	+	0.960163i
$665$	300.686			0.452159
$666$		0			0
$667$		−	378.323i		−	0.567201i
$668$	6.79553	−	7.99126i	0.0101730	−	0.0119630i
$669$		0			0
$670$	−81.8577	−	30.0990i	−0.122176	−	0.0449239i
$671$			824.683i			1.22904i
$672$		0			0
$673$	166.830			0.247891			0.123945	−	0.992289i	$-0.460445\pi$
$673$	166.830			0.247891			0.123945	+	0.992289i	$0.460445\pi$
$674$	−205.717	+	559.470i	−0.305218	+	0.830075i
$675$		0			0
$676$	388.462	+	330.337i	0.574648	+	0.488664i
$677$	43.7097			0.0645639			0.0322819	−	0.999479i	$-0.489723\pi$
$677$	43.7097			0.0645639			0.0322819	+	0.999479i	$0.489723\pi$
$678$		0			0
$679$			833.013i			1.22682i
$680$	−112.289	+	63.3614i	−0.165131	+	0.0931786i
$681$		0			0
$682$	278.036	−	756.152i	0.407678	−	1.10873i
$683$			398.448i			0.583379i	0.956513	+	0.291689i	$0.0942174\pi$
$683$			398.448i			0.583379i	−0.956513	+	0.291689i	$0.905783\pi$
$684$		0			0
$685$	−709.410			−1.03563
$686$	553.266	+	203.436i	0.806511	+	0.296553i
$687$		0			0
$688$	476.038	−	77.4959i	0.691916	−	0.112639i
$689$	227.057			0.329546
$690$		0			0
$691$		−	1092.32i		−	1.58078i	−0.612605	−	0.790389i	$-0.709878\pi$
$691$		−	1092.32i		−	1.58078i	0.612605	−	0.790389i	$-0.290122\pi$
$692$	49.4602	+	42.0595i	0.0714743	+	0.0607797i
$693$		0			0
$694$	327.765	+	120.519i	0.472283	+	0.173658i
$695$			957.983i			1.37839i
$696$		0			0
$697$	−88.7817			−0.127377
$698$	−28.8045	+	78.3372i	−0.0412672	+	0.112231i
$699$		0			0
$700$	−1091.38	+	1283.41i	−1.55911	+	1.83344i
$701$	828.024			1.18120			0.590602	−	0.806963i	$-0.298890\pi$
$701$	828.024			1.18120			0.590602	+	0.806963i	$0.298890\pi$
$702$		0			0
$703$			309.612i			0.440416i
$704$	880.704	+	531.916i	1.25100	+	0.755563i
$705$		0			0
$706$	266.292	−	724.210i	0.377184	−	1.02579i
$707$		−	1391.83i		−	1.96864i
$708$		0			0
$709$	−1287.71			−1.81623			−0.908117	−	0.418717i	$-0.862480\pi$
$709$	−1287.71			−1.81623			−0.908117	+	0.418717i	$0.862480\pi$
$710$	1615.13	+	593.883i	2.27483	+	0.836455i
$711$		0			0
$712$	607.279	−	342.669i	0.852920	−	0.481277i
$713$	232.511			0.326102
$714$		0			0
$715$		−	923.063i		−	1.29100i
$716$	−279.854	+	329.096i	−0.390857	+	0.459631i
$717$		0			0
$718$	−1318.22	−	484.707i	−1.83596	−	0.675080i
$719$		−	915.858i		−	1.27379i	−0.770949	−	0.636897i	$-0.780218\pi$
$719$		−	915.858i		−	1.27379i	0.770949	−	0.636897i	$-0.219782\pi$
$720$		0			0
$721$	201.663			0.279699
$722$	13.1141	−	35.6654i	0.0181636	−	0.0493980i
$723$		0			0
$724$	−319.381	−	271.593i	−0.441135	−	0.375128i
$725$	2218.27			3.05968
$726$		0			0
$727$			913.562i			1.25662i	0.777963	+	0.628310i	$0.216253\pi$
$727$			913.562i			1.25662i	−0.777963	+	0.628310i	$0.783747\pi$
$728$	196.100	+	347.530i	0.269368	+	0.477376i
$729$		0			0
$730$	720.359	−	1959.10i	0.986793	−	2.68370i
$731$			54.5184i			0.0745806i
$732$		0			0
$733$	269.142			0.367179			0.183590	−	0.983003i	$-0.441228\pi$
$733$	269.142			0.367179			0.183590	+	0.983003i	$0.441228\pi$
$734$	−722.042	−	265.494i	−0.983709	−	0.361709i
$735$		0			0
$736$	−56.3633	+	291.534i	−0.0765805	+	0.396107i
$737$	−78.6712			−0.106745
$738$		0			0
$739$		−	816.781i		−	1.10525i	−0.833429	−	0.552626i	$-0.813626\pi$
$739$		−	816.781i		−	1.10525i	0.833429	−	0.552626i	$-0.186374\pi$
$740$	−1928.74	−	1640.14i	−2.60640	−	2.21641i
$741$		0			0
$742$	−512.052	−	188.281i	−0.690097	−	0.253748i
$743$			889.227i			1.19681i	0.801195	+	0.598403i	$0.204198\pi$
$743$			889.227i			1.19681i	−0.801195	+	0.598403i	$0.795802\pi$
$744$		0			0
$745$	−1017.62			−1.36594
$746$	293.467	−	798.116i	0.393387	−	1.06986i
$747$		0			0
$748$	−75.3409	+	88.5977i	−0.100723	+	0.118446i
$749$	185.995			0.248325
$750$		0			0
$751$		−	517.950i		−	0.689680i	−0.938661	−	0.344840i	$-0.887933\pi$
$751$		−	517.950i		−	0.689680i	0.938661	−	0.344840i	$-0.112067\pi$
$752$	1304.89	−	212.427i	1.73522	−	0.282482i
$753$		0			0
$754$	181.326	−	493.137i	0.240485	−	0.654027i
$755$			2554.15i			3.38298i
$756$		0			0
$757$	−378.920			−0.500555			−0.250278	−	0.968174i	$-0.580522\pi$
$757$	−378.920			−0.500555			−0.250278	+	0.968174i	$0.580522\pi$
$758$	997.959	+	366.949i	1.31657	+	0.484101i
$759$		0			0
$760$	152.708	+	270.629i	0.200931	+	0.356091i
$761$	−702.253			−0.922803			−0.461401	−	0.887192i	$-0.652653\pi$
$761$	−702.253			−0.922803			−0.461401	+	0.887192i	$0.652653\pi$
$762$		0			0
$763$		−	188.746i		−	0.247374i
$764$	−766.830	+	901.759i	−1.00370	+	1.18031i
$765$		0			0
$766$	1269.84	+	466.920i	1.65776	+	0.609556i
$767$		−	517.206i		−	0.674324i
$768$		0			0
$769$	206.234			0.268185			0.134092	−	0.990969i	$-0.457188\pi$
$769$	206.234			0.268185			0.134092	+	0.990969i	$0.457188\pi$
$770$	−765.425	+	2081.66i	−0.994059	+	2.70346i
$771$		0			0
$772$	592.666	+	503.986i	0.767702	+	0.652831i
$773$	−364.309			−0.471293			−0.235646	−	0.971839i	$-0.575721\pi$
$773$	−364.309			−0.471293			−0.235646	+	0.971839i	$0.575721\pi$
$774$		0			0
$775$			1363.31i			1.75911i
$776$	−749.744	+	423.057i	−0.966165	+	0.545177i
$777$		0			0
$778$	−26.7829	+	72.8392i	−0.0344253	+	0.0936236i
$779$			213.973i			0.274676i
$780$		0			0
$781$	1552.26			1.98753
$782$	−31.5023	−	11.5834i	−0.0402843	−	0.0148125i
$783$		0			0
$784$	−28.0875	−	172.535i	−0.0358259	−	0.220070i
$785$	−1015.63			−1.29380
$786$		0			0
$787$		−	844.845i		−	1.07350i	−0.843741	−	0.536750i	$-0.819652\pi$
$787$		−	844.845i		−	1.07350i	0.843741	−	0.536750i	$-0.180348\pi$
$788$	397.001	+	337.598i	0.503809	+	0.428424i
$789$		0			0
$790$	106.270	+	39.0755i	0.134519	+	0.0494627i
$791$			623.518i			0.788266i
$792$		0			0
$793$	−330.542			−0.416824
$794$	19.8061	−	53.8648i	0.0249447	−	0.0678399i
$795$		0			0
$796$	−701.619	+	825.074i	−0.881431	+	1.03653i
$797$	1155.32			1.44958			0.724791	−	0.688969i	$-0.241936\pi$
$797$	1155.32			1.44958			0.724791	+	0.688969i	$0.241936\pi$
$798$		0			0
$799$			149.442i			0.187037i
$800$	−1709.39	−	330.482i	−2.13674	−	0.413102i
$801$		0			0
$802$	277.689	−	755.206i	0.346245	−	0.941654i
$803$		−	1882.84i		−	2.34475i
$804$		0			0
$805$	−640.095			−0.795150
$806$	303.074	+	111.440i	0.376022	+	0.138263i
$807$		0			0
$808$	1252.70	−	706.860i	1.55037	−	0.874826i
$809$	−95.4530			−0.117989			−0.0589944	−	0.998258i	$-0.518789\pi$
$809$	−95.4530			−0.117989			−0.0589944	+	0.998258i	$0.518789\pi$
$810$		0			0
$811$		−	917.758i		−	1.13164i	−0.824530	−	0.565818i	$-0.808560\pi$
$811$		−	917.758i		−	1.13164i	0.824530	−	0.565818i	$-0.191440\pi$
$812$	−817.841	+	961.746i	−1.00719	+	1.18442i
$813$		0			0
$814$	−2143.46	−	788.148i	−2.63324	−	0.968241i
$815$		−	79.7631i		−	0.0978688i
$816$		0			0
$817$	131.395			0.160826
$818$	−206.488	+	561.568i	−0.252430	+	0.686513i
$819$		0			0
$820$	−1332.95	−	1133.50i	−1.62555	−	1.38232i
$821$	958.146			1.16705			0.583524	−	0.812096i	$-0.301673\pi$
$821$	958.146			1.16705			0.583524	+	0.812096i	$0.301673\pi$
$822$		0			0
$823$			63.1070i			0.0766793i	0.999265	+	0.0383396i	$0.0122069\pi$
$823$			63.1070i			0.0766793i	−0.999265	+	0.0383396i	$0.987793\pi$
$824$	102.417	+	181.504i	0.124293	+	0.220272i
$825$		0			0
$826$	−428.880	+	1166.39i	−0.519225	+	1.41209i
$827$		−	1430.65i		−	1.72993i	−0.501836	−	0.864963i	$-0.667342\pi$
$827$		−	1430.65i		−	1.72993i	0.501836	−	0.864963i	$-0.332658\pi$
$828$		0			0
$829$	−706.756			−0.852541			−0.426270	−	0.904596i	$-0.640173\pi$
$829$	−706.756			−0.852541			−0.426270	+	0.904596i	$0.640173\pi$
$830$	−1530.63	−	562.812i	−1.84414	−	0.678087i
$831$		0			0
$832$	−213.198	+	352.996i	−0.256247	+	0.424273i
$833$	19.7596			0.0237210
$834$		0			0
$835$			23.3693i			0.0279872i
$836$	213.530	+	181.579i	0.255418	+	0.217200i
$837$		0			0
$838$	−104.984	−	38.6026i	−0.125279	−	0.0460652i
$839$			240.681i			0.286867i	0.989660	+	0.143433i	$0.0458142\pi$
$839$			240.681i			0.286867i	−0.989660	+	0.143433i	$0.954186\pi$
$840$		0			0
$841$	821.295			0.976570
$842$	−453.816	+	1234.20i	−0.538974	+	1.46580i
$843$		0			0
$844$	475.702	−	559.405i	0.563628	−	0.662802i
$845$	−1136.00			−1.34438
$846$		0			0
$847$			1063.95i			1.25614i
$848$	−90.5925	−	556.488i	−0.106831	−	0.656236i
$849$		0			0
$850$	67.9183	−	184.711i	0.0799038	−	0.217308i
$851$		−	659.098i		−	0.774498i
$852$		0			0
$853$	1178.74			1.38188			0.690940	−	0.722912i	$-0.257197\pi$
$853$	1178.74			1.38188			0.690940	+	0.722912i	$0.257197\pi$
$854$	745.427	+	274.093i	0.872865	+	0.320952i
$855$		0			0
$856$	94.4602	+	167.403i	0.110351	+	0.195564i
$857$	−424.112			−0.494880			−0.247440	−	0.968903i	$-0.579589\pi$
$857$	−424.112			−0.494880			−0.247440	+	0.968903i	$0.579589\pi$
$858$		0			0
$859$		−	695.559i		−	0.809731i	−0.914376	−	0.404866i	$-0.867318\pi$
$859$		−	695.559i		−	0.809731i	0.914376	−	0.404866i	$-0.132682\pi$
$860$	−696.053	+	818.529i	−0.809364	+	0.951777i
$861$		0			0
$862$	−1178.81	−	433.449i	−1.36753	−	0.502841i
$863$		−	788.782i		−	0.914000i	−0.889467	−	0.457000i	$-0.848924\pi$
$863$		−	788.782i		−	0.914000i	0.889467	−	0.457000i	$-0.151076\pi$
$864$		0			0
$865$	−144.639			−0.167213
$866$	196.728	−	535.023i	0.227168	−	0.617810i
$867$		0			0
$868$	−591.073	−	502.632i	−0.680960	−	0.579069i
$869$	102.133			0.117530
$870$		0			0
$871$		−	31.5323i		−	0.0362024i
$872$	169.879	−	95.8575i	0.194815	−	0.109928i
$873$		0			0
$874$	−27.9172	+	75.9239i	−0.0319418	+	0.0868694i
$875$		−	2028.60i		−	2.31840i
$876$		0			0
$877$	−636.075			−0.725285			−0.362642	−	0.931928i	$-0.618125\pi$
$877$	−636.075			−0.725285			−0.362642	+	0.931928i	$0.618125\pi$
$878$	−54.0779	−	19.8844i	−0.0615922	−	0.0226474i
$879$		0			0
$880$	−2262.31	+	368.289i	−2.57080	+	0.418510i
$881$	60.4939			0.0686650			0.0343325	−	0.999410i	$-0.489069\pi$
$881$	60.4939			0.0686650			0.0343325	+	0.999410i	$0.489069\pi$
$882$		0			0
$883$			494.131i			0.559604i	0.960058	+	0.279802i	$0.0902689\pi$
$883$			494.131i			0.559604i	−0.960058	+	0.279802i	$0.909731\pi$
$884$	−35.5109	−	30.1975i	−0.0401707	−	0.0341600i
$885$		0			0
$886$	545.999	+	200.763i	0.616251	+	0.226595i
$887$			1459.45i			1.64538i	0.568494	+	0.822688i	$0.307526\pi$
$887$			1459.45i			1.64538i	−0.568494	+	0.822688i	$0.692474\pi$
$888$		0			0
$889$	−1210.77			−1.36195
$890$	−536.092	+	1457.96i	−0.602350	+	1.63816i
$891$		0			0
$892$	437.164	−	514.087i	0.490095	−	0.576331i
$893$	360.171			0.403327
$894$		0			0
$895$		−	962.393i		−	1.07530i
$896$	773.509	−	619.275i	0.863291	−	0.691155i
$897$		0			0
$898$	−8.76472	+	23.8366i	−0.00976026	+	0.0265442i
$899$			1021.62i			1.13640i
$900$		0			0
$901$	63.7319			0.0707346
$902$	−1481.34	−	544.689i	−1.64229	−	0.603868i
$903$		0			0
$904$	−561.191	+	316.663i	−0.620786	+	0.350290i
$905$	933.985			1.03203
$906$		0			0
$907$			253.406i			0.279389i	0.990195	+	0.139695i	$0.0446120\pi$
$907$			253.406i			0.279389i	−0.990195	+	0.139695i	$0.955388\pi$
$908$	645.317	−	758.866i	0.710702	−	0.835755i
$909$		0			0
$910$	−834.353	−	306.791i	−0.916871	−	0.337133i
$911$		−	11.8641i		−	0.0130231i	−0.999979	−	0.00651156i	$-0.997927\pi$
$911$		−	11.8641i		−	0.0130231i	0.999979	−	0.00651156i	$-0.00207271\pi$
$912$		0			0
$913$	−1471.05			−1.61123
$914$	−81.7745	+	222.395i	−0.0894688	+	0.243321i
$915$		0			0
$916$	864.428	+	735.085i	0.943699	+	0.802494i
$917$	122.715			0.133823
$918$		0			0
$919$			1222.00i			1.32971i	0.746974	+	0.664853i	$0.231506\pi$
$919$			1222.00i			1.32971i	−0.746974	+	0.664853i	$0.768494\pi$
$920$	−325.081	−	576.111i	−0.353349	−	0.626207i
$921$		0			0
$922$	131.104	−	356.552i	0.142195	−	0.386715i
$923$			622.163i			0.674066i
$924$		0			0
$925$	3864.57			4.17791
$926$	927.045	+	340.874i	1.00113	+	0.368114i
$927$		0			0
$928$	−1280.96	−	247.652i	−1.38034	−	0.266866i
$929$	772.022			0.831024			0.415512	−	0.909588i	$-0.363602\pi$
$929$	772.022			0.831024			0.415512	+	0.909588i	$0.363602\pi$
$930$		0			0
$931$		−	47.6226i		−	0.0511521i
$932$	−237.209	−	201.715i	−0.254516	−	0.216433i
$933$		0			0
$934$	149.785	+	55.0760i	0.160370	+	0.0589678i
$935$		−	259.091i		−	0.277103i
$936$		0			0
$937$	193.066			0.206047			0.103023	−	0.994679i	$-0.467148\pi$
$937$	193.066			0.206047			0.103023	+	0.994679i	$0.467148\pi$
$938$	−26.1473	+	71.1105i	−0.0278756	+	0.0758108i
$939$		0			0
$940$	−1907.97	+	2243.70i	−2.02976	+	2.38691i
$941$	356.077			0.378402			0.189201	−	0.981938i	$-0.439410\pi$
$941$	356.077			0.378402			0.189201	+	0.981938i	$0.439410\pi$
$942$		0			0
$943$		−	455.502i		−	0.483035i
$944$	−1267.61	+	206.358i	−1.34280	+	0.218599i
$945$		0			0
$946$	−334.479	+	909.653i	−0.353572	+	0.961578i
$947$			828.719i			0.875100i	0.899194	+	0.437550i	$0.144154\pi$
$947$			828.719i			0.875100i	−0.899194	+	0.437550i	$0.855846\pi$
$948$		0			0
$949$	754.661			0.795217
$950$	−445.174	−	163.690i	−0.468604	−	0.172305i
$951$		0			0
$952$	55.0426	+	97.5468i	0.0578179	+	0.102465i
$953$	72.8231			0.0764146			0.0382073	−	0.999270i	$-0.487835\pi$
$953$	72.8231			0.0764146			0.0382073	+	0.999270i	$0.487835\pi$
$954$		0			0
$955$		−	2637.06i		−	2.76132i
$956$	−82.8340	+	97.4092i	−0.0866464	+	0.101892i
$957$		0			0
$958$	−430.330	−	158.232i	−0.449196	−	0.165169i
$959$			616.271i			0.642618i
$960$		0			0
$961$	333.129			0.346649
$962$	315.898	−	859.122i	0.328377	−	0.893058i
$963$		0			0
$964$	−138.035	−	117.381i	−0.143190	−	0.121765i
$965$	−1733.17			−1.79603
$966$		0			0
$967$		−	1333.39i		−	1.37889i	−0.724336	−	0.689447i	$-0.757854\pi$
$967$		−	1333.39i		−	1.37889i	0.724336	−	0.689447i	$-0.242146\pi$
$968$	−957.596	+	540.342i	−0.989252	+	0.558204i
$969$		0			0
$970$	661.856	−	1799.99i	0.682326	−	1.85566i
$971$		−	749.276i		−	0.771654i	−0.922571	−	0.385827i	$-0.873916\pi$
$971$		−	749.276i		−	0.771654i	0.922571	−	0.385827i	$-0.126084\pi$
$972$		0			0
$973$	832.209			0.855302
$974$	1581.32	+	581.452i	1.62354	+	0.596973i
$975$		0			0
$976$	131.881	+	810.115i	0.135124	+	0.830036i
$977$	943.603			0.965817			0.482908	−	0.875671i	$-0.339580\pi$
$977$	943.603			0.965817			0.482908	+	0.875671i	$0.339580\pi$
$978$		0			0
$979$			1401.21i			1.43126i
$980$	296.666	+	252.276i	0.302721	+	0.257425i
$981$		0			0
$982$	722.764	+	265.760i	0.736012	+	0.270631i
$983$		−	650.742i		−	0.661996i	−0.943632	−	0.330998i	$-0.892615\pi$
$983$		−	650.742i		−	0.661996i	0.943632	−	0.330998i	$-0.107385\pi$
$984$		0			0
$985$	−1160.97			−1.17865
$986$	50.8957	−	138.417i	0.0516184	−	0.140382i
$987$		0			0
$988$	−72.7790	+	85.5850i	−0.0736629	+	0.0866245i
$989$	−279.711			−0.282823
$990$		0			0
$991$		−	1136.18i		−	1.14650i	−0.819380	−	0.573251i	$-0.805682\pi$
$991$		−	1136.18i		−	1.14650i	0.819380	−	0.573251i	$-0.194318\pi$
$992$	152.203	−	787.257i	0.153430	−	0.793606i
$993$		0			0
$994$	515.911	−	1403.08i	0.519026	−	1.41155i
$995$		−	2412.81i		−	2.42493i
$996$		0			0
$997$	−1161.15			−1.16465			−0.582324	−	0.812957i	$-0.697856\pi$
$997$	−1161.15			−1.16465			−0.582324	+	0.812957i	$0.697856\pi$
$998$	−1332.03	−	489.788i	−1.33470	−	0.490769i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.14	yes	36
3.2	odd	2	inner	684.3.g.d.343.23	yes	36
4.3	odd	2	inner	684.3.g.d.343.13	✓	36
12.11	even	2	inner	684.3.g.d.343.24	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.13	✓	36	4.3	odd	2	inner
684.3.g.d.343.14	yes	36	1.1	even	1	trivial
684.3.g.d.343.23	yes	36	3.2	odd	2	inner
684.3.g.d.343.24	yes	36	12.11	even	2	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690218 + 1.87713i) q^{2} +(-3.04720 - 2.59125i) q^{4} +8.91109 q^{5} -7.74115i q^{7} +(6.96733 - 3.93145i) q^{8} +O(q^{10})\)	\(q+(-0.690218 + 1.87713i) q^{2} +(-3.04720 - 2.59125i) q^{4} +8.91109 q^{5} -7.74115i q^{7} +(6.96733 - 3.93145i) q^{8} +(-6.15059 + 16.7272i) q^{10} +16.0761i q^{11} -6.44347 q^{13} +(14.5311 + 5.34308i) q^{14} +(2.57085 + 15.7921i) q^{16} -1.80859 q^{17} +4.35890i q^{19} +(-27.1539 - 23.0909i) q^{20} +(-30.1768 - 11.0960i) q^{22} -9.27915i q^{23} +54.4076 q^{25} +(4.44740 - 12.0952i) q^{26} +(-20.0592 + 23.5888i) q^{28} +40.7713 q^{29} +25.0573i q^{31} +(-31.4182 - 6.07418i) q^{32} +(1.24832 - 3.39496i) q^{34} -68.9821i q^{35} +71.0299 q^{37} +(-8.18220 - 3.00859i) q^{38} +(62.0865 - 35.0335i) q^{40} +49.0888 q^{41} -30.1441i q^{43} +(41.6572 - 48.9871i) q^{44} +(17.4181 + 6.40463i) q^{46} -82.6289i q^{47} -10.9254 q^{49} +(-37.5531 + 102.130i) q^{50} +(19.6345 + 16.6966i) q^{52} -35.2383 q^{53} +143.256i q^{55} +(-30.4339 - 53.9351i) q^{56} +(-28.1410 + 76.5328i) q^{58} +80.2683i q^{59} +51.2987 q^{61} +(-47.0358 - 17.2950i) q^{62} +(33.0874 - 54.7834i) q^{64} -57.4184 q^{65} +4.89367i q^{67} +(5.51115 + 4.68652i) q^{68} +(129.488 + 47.6126i) q^{70} -96.5570i q^{71} -117.120 q^{73} +(-49.0261 + 133.332i) q^{74} +(11.2950 - 13.2824i) q^{76} +124.447 q^{77} -6.35313i q^{79} +(22.9091 + 140.725i) q^{80} +(-33.8819 + 92.1458i) q^{82} +91.5054i q^{83} -16.1166 q^{85} +(56.5842 + 20.8060i) q^{86} +(63.2024 + 112.007i) q^{88} +87.1610 q^{89} +49.8799i q^{91} +(-24.0446 + 28.2754i) q^{92} +(155.105 + 57.0319i) q^{94} +38.8426i q^{95} -107.608 q^{97} +(7.54088 - 20.5083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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