LMFDB - Embedded newform 690.3.f.a.229.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(229,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.f (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.24
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(3.16709 - 3.86905i) q^{5} +2.44949 q^{6} -4.38904 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(3.16709 - 3.86905i) q^{5} +2.44949 q^{6} -4.38904 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(5.47167 + 4.47894i) q^{10} +2.89637i q^{11} +3.46410i q^{12} +1.58189i q^{13} -6.20704i q^{14} +(-6.70139 - 5.48556i) q^{15} +4.00000 q^{16} +3.92071 q^{17} -4.24264i q^{18} -23.3725i q^{19} +(-6.33417 + 7.73810i) q^{20} +7.60204i q^{21} -4.09608 q^{22} +(22.3520 - 5.42118i) q^{23} -4.89898 q^{24} +(-4.93912 - 24.5072i) q^{25} -2.23713 q^{26} +5.19615i q^{27} +8.77808 q^{28} -8.38570 q^{29} +(7.75775 - 9.47720i) q^{30} -32.5278 q^{31} +5.65685i q^{32} +5.01666 q^{33} +5.54473i q^{34} +(-13.9005 + 16.9814i) q^{35} +6.00000 q^{36} -49.8194 q^{37} +33.0537 q^{38} +2.73992 q^{39} +(-10.9433 - 8.95787i) q^{40} -67.7817 q^{41} -10.7509 q^{42} -16.2354 q^{43} -5.79274i q^{44} +(-9.50126 + 11.6072i) q^{45} +(7.66671 + 31.6105i) q^{46} -84.9146i q^{47} -6.92820i q^{48} -29.7363 q^{49} +(34.6585 - 6.98497i) q^{50} -6.79088i q^{51} -3.16378i q^{52} +1.17306 q^{53} -7.34847 q^{54} +(11.2062 + 9.17305i) q^{55} +12.4141i q^{56} -40.4824 q^{57} -11.8592i q^{58} -103.019 q^{59} +(13.4028 + 10.9711i) q^{60} +12.6631i q^{61} -46.0013i q^{62} +13.1671 q^{63} -8.00000 q^{64} +(6.12042 + 5.00999i) q^{65} +7.09463i q^{66} +125.456 q^{67} -7.84143 q^{68} +(-9.38976 - 38.7148i) q^{69} +(-24.0153 - 19.6582i) q^{70} -27.4629 q^{71} +8.48528i q^{72} -25.1610i q^{73} -70.4553i q^{74} +(-42.4478 + 8.55481i) q^{75} +46.7450i q^{76} -12.7123i q^{77} +3.87483i q^{78} -25.5000i q^{79} +(12.6683 - 15.4762i) q^{80} +9.00000 q^{81} -95.8578i q^{82} +110.184 q^{83} -15.2041i q^{84} +(12.4172 - 15.1694i) q^{85} -22.9603i q^{86} +14.5245i q^{87} +8.19217 q^{88} -14.4878i q^{89} +(-16.4150 - 13.4368i) q^{90} -6.94298i q^{91} +(-44.7039 + 10.8424i) q^{92} +56.3399i q^{93} +120.087 q^{94} +(-90.4294 - 74.0227i) q^{95} +9.79796 q^{96} -63.9628 q^{97} -42.0535i q^{98} -8.68911i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 96 * q^4 - 144 * q^9	$ 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) $ 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−2.00000			−0.500000
$5$	3.16709	−	3.86905i	0.633417	−	0.773810i
$5$	3.16709	−	3.86905i	0.633417	−	0.773810i
$6$	2.44949			0.408248
$7$	−4.38904			−0.627005			−0.313503	−	0.949587i	$-0.601502\pi$
$7$	−4.38904			−0.627005			−0.313503	+	0.949587i	$0.601502\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.00000			−0.333333
$10$	5.47167	+	4.47894i	0.547167	+	0.447894i
$11$			2.89637i			0.263306i	0.991296	+	0.131653i	$0.0420285\pi$
$11$			2.89637i			0.263306i	−0.991296	+	0.131653i	$0.957971\pi$
$12$			3.46410i			0.288675i
$13$			1.58189i			0.121684i	0.998147	+	0.0608420i	$0.0193786\pi$
$13$			1.58189i			0.121684i	−0.998147	+	0.0608420i	$0.980621\pi$
$14$		−	6.20704i		−	0.443360i
$15$	−6.70139	−	5.48556i	−0.446760	−	0.365704i
$16$	4.00000			0.250000
$17$	3.92071			0.230630			0.115315	−	0.993329i	$-0.463212\pi$
$17$	3.92071			0.230630			0.115315	+	0.993329i	$0.463212\pi$
$18$		−	4.24264i		−	0.235702i
$19$		−	23.3725i		−	1.23013i	−0.788476	−	0.615066i	$-0.789129\pi$
$19$		−	23.3725i		−	1.23013i	0.788476	−	0.615066i	$-0.210871\pi$
$20$	−6.33417	+	7.73810i	−0.316709	+	0.386905i
$21$			7.60204i			0.362002i
$22$	−4.09608			−0.186186
$23$	22.3520	−	5.42118i	0.971825	−	0.235704i
$23$	22.3520	−	5.42118i	0.971825	−	0.235704i
$24$	−4.89898			−0.204124
$25$	−4.93912	−	24.5072i	−0.197565	−	0.980290i
$26$	−2.23713			−0.0860436
$27$			5.19615i			0.192450i
$28$	8.77808			0.313503
$29$	−8.38570			−0.289162			−0.144581	−	0.989493i	$-0.546183\pi$
$29$	−8.38570			−0.289162			−0.144581	+	0.989493i	$0.546183\pi$
$30$	7.75775	−	9.47720i	0.258592	−	0.315907i
$31$	−32.5278			−1.04929			−0.524643	−	0.851323i	$-0.675801\pi$
$31$	−32.5278			−1.04929			−0.524643	+	0.851323i	$0.675801\pi$
$32$			5.65685i			0.176777i
$33$	5.01666			0.152020
$34$			5.54473i			0.163080i
$35$	−13.9005	+	16.9814i	−0.397156	+	0.485183i
$36$	6.00000			0.166667
$37$	−49.8194			−1.34647			−0.673236	−	0.739428i	$-0.735096\pi$
$37$	−49.8194			−1.34647			−0.673236	+	0.739428i	$0.735096\pi$
$38$	33.0537			0.869834
$39$	2.73992			0.0702543
$40$	−10.9433	−	8.95787i	−0.273583	−	0.223947i
$41$	−67.7817			−1.65321			−0.826606	−	0.562781i	$-0.809731\pi$
$41$	−67.7817			−1.65321			−0.826606	+	0.562781i	$0.809731\pi$
$42$	−10.7509			−0.255974
$43$	−16.2354			−0.377566			−0.188783	−	0.982019i	$-0.560454\pi$
$43$	−16.2354			−0.377566			−0.188783	+	0.982019i	$0.560454\pi$
$44$		−	5.79274i		−	0.131653i
$45$	−9.50126	+	11.6072i	−0.211139	+	0.257937i
$46$	7.66671	+	31.6105i	0.166668	+	0.687184i
$47$		−	84.9146i		−	1.80669i	−0.428912	−	0.903347i	$-0.641103\pi$
$47$		−	84.9146i		−	1.80669i	0.428912	−	0.903347i	$-0.358897\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−29.7363			−0.606864
$50$	34.6585	−	6.98497i	0.693170	−	0.139699i
$51$		−	6.79088i		−	0.133154i
$52$		−	3.16378i		−	0.0608420i
$53$	1.17306			0.0221333			0.0110666	−	0.999939i	$-0.496477\pi$
$53$	1.17306			0.0221333			0.0110666	+	0.999939i	$0.496477\pi$
$54$	−7.34847			−0.136083
$55$	11.2062	+	9.17305i	0.203749	+	0.166783i
$56$			12.4141i			0.221680i
$57$	−40.4824			−0.710217
$58$		−	11.8592i		−	0.204468i
$59$	−103.019			−1.74608			−0.873041	−	0.487647i	$-0.837855\pi$
$59$	−103.019			−1.74608			−0.873041	+	0.487647i	$0.837855\pi$
$60$	13.4028	+	10.9711i	0.223380	+	0.182852i
$61$			12.6631i			0.207592i	0.994599	+	0.103796i	$0.0330989\pi$
$61$			12.6631i			0.207592i	−0.994599	+	0.103796i	$0.966901\pi$
$62$		−	46.0013i		−	0.741957i
$63$	13.1671			0.209002
$64$	−8.00000			−0.125000
$65$	6.12042	+	5.00999i	0.0941603	+	0.0770767i
$66$			7.09463i			0.107494i
$67$	125.456			1.87247			0.936236	−	0.351371i	$-0.114284\pi$
$67$	125.456			1.87247			0.936236	+	0.351371i	$0.114284\pi$
$68$	−7.84143			−0.115315
$69$	−9.38976	−	38.7148i	−0.136084	−	0.561083i
$70$	−24.0153	−	19.6582i	−0.343076	−	0.280832i
$71$	−27.4629			−0.386801			−0.193400	−	0.981120i	$-0.561952\pi$
$71$	−27.4629			−0.386801			−0.193400	+	0.981120i	$0.561952\pi$
$72$			8.48528i			0.117851i
$73$		−	25.1610i		−	0.344672i	−0.985038	−	0.172336i	$-0.944869\pi$
$73$		−	25.1610i		−	0.344672i	0.985038	−	0.172336i	$-0.0551314\pi$
$74$		−	70.4553i		−	0.952099i
$75$	−42.4478	+	8.55481i	−0.565971	+	0.114064i
$76$			46.7450i			0.615066i
$77$		−	12.7123i		−	0.165094i
$78$			3.87483i			0.0496773i
$79$		−	25.5000i		−	0.322785i	−0.986890	−	0.161392i	$-0.948402\pi$
$79$		−	25.5000i		−	0.322785i	0.986890	−	0.161392i	$-0.0515985\pi$
$80$	12.6683	−	15.4762i	0.158354	−	0.193453i
$81$	9.00000			0.111111
$82$		−	95.8578i		−	1.16900i
$83$	110.184			1.32751			0.663757	−	0.747948i	$-0.268961\pi$
$83$	110.184			1.32751			0.663757	+	0.747948i	$0.268961\pi$
$84$		−	15.2041i		−	0.181001i
$85$	12.4172	−	15.1694i	0.146085	−	0.178464i
$86$		−	22.9603i		−	0.266980i
$87$			14.5245i			0.166948i
$88$	8.19217			0.0930928
$89$		−	14.4878i		−	0.162785i	−0.996682	−	0.0813923i	$-0.974063\pi$
$89$		−	14.4878i		−	0.162785i	0.996682	−	0.0813923i	$-0.0259367\pi$
$90$	−16.4150	−	13.4368i	−0.182389	−	0.149298i
$91$		−	6.94298i		−	0.0762965i
$92$	−44.7039	+	10.8424i	−0.485912	+	0.117852i
$93$			56.3399i			0.605805i
$94$	120.087			1.27752
$95$	−90.4294	−	74.0227i	−0.951888	−	0.779187i
$96$	9.79796			0.102062
$97$	−63.9628			−0.659410			−0.329705	−	0.944084i	$-0.606949\pi$
$97$	−63.9628			−0.659410			−0.329705	+	0.944084i	$0.606949\pi$
$98$		−	42.0535i		−	0.429118i
$99$		−	8.68911i		−	0.0877687i
$100$	9.87824	+	49.0145i	0.0987824	+	0.490145i
$101$	−87.1443			−0.862815			−0.431407	−	0.902157i	$-0.641983\pi$
$101$	−87.1443			−0.862815			−0.431407	+	0.902157i	$0.641983\pi$
$102$	9.60375			0.0941544
$103$	135.577			1.31628			0.658141	−	0.752894i	$-0.271343\pi$
$103$	135.577			1.31628			0.658141	+	0.752894i	$0.271343\pi$
$104$	4.47426			0.0430218
$105$	29.4127	+	24.0763i	0.280121	+	0.229298i
$106$			1.65896i			0.0156506i
$107$	−124.682			−1.16525			−0.582627	−	0.812740i	$-0.697975\pi$
$107$	−124.682			−1.16525			−0.582627	+	0.812740i	$0.697975\pi$
$108$		−	10.3923i		−	0.0962250i
$109$		−	99.8206i		−	0.915785i	−0.889008	−	0.457893i	$-0.848604\pi$
$109$		−	99.8206i		−	0.915785i	0.889008	−	0.457893i	$-0.151396\pi$
$110$	−12.9727	+	15.8480i	−0.117933	+	0.144072i
$111$			86.2898i			0.777386i
$112$	−17.5562			−0.156751
$113$	−43.7120			−0.386832			−0.193416	−	0.981117i	$-0.561957\pi$
$113$	−43.7120			−0.386832			−0.193416	+	0.981117i	$0.561957\pi$
$114$		−	57.2507i		−	0.502199i
$115$	49.8158	−	103.650i	0.433181	−	0.901307i
$116$	16.7714			0.144581
$117$		−	4.74567i		−	0.0405613i
$118$		−	145.691i		−	1.23467i
$119$	−17.2082			−0.144606
$120$	−15.5155	+	18.9544i	−0.129296	+	0.157953i
$121$	112.611			0.930670
$122$	−17.9083			−0.146789
$123$			117.401i			0.954482i
$124$	65.0557			0.524643
$125$	−110.462	−	58.5069i	−0.883699	−	0.468055i
$126$			18.6211i			0.147787i
$127$			90.0283i			0.708884i	0.935078	+	0.354442i	$0.115329\pi$
$127$			90.0283i			0.708884i	−0.935078	+	0.354442i	$0.884671\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			28.1205i			0.217988i
$130$	−7.08519	+	8.65558i	−0.0545015	+	0.0665814i
$131$	127.511			0.973363			0.486681	−	0.873580i	$-0.338207\pi$
$131$	127.511			0.973363			0.486681	+	0.873580i	$0.338207\pi$
$132$	−10.0333			−0.0760100
$133$			102.583i			0.771299i
$134$			177.421i			1.32404i
$135$	20.1042	+	16.4567i	0.148920	+	0.121901i
$136$		−	11.0895i		−	0.0815401i
$137$	113.969			0.831891			0.415945	−	0.909390i	$-0.363451\pi$
$137$	113.969			0.831891			0.415945	+	0.909390i	$0.363451\pi$
$138$	54.7509	−	13.2791i	0.396746	−	0.0962256i
$139$	202.788			1.45890			0.729452	−	0.684032i	$-0.239775\pi$
$139$	202.788			1.45890			0.729452	+	0.684032i	$0.239775\pi$
$140$	27.8009	−	33.9628i	0.198578	−	0.242592i
$141$	−147.076			−1.04309
$142$		−	38.8384i		−	0.273510i
$143$	−4.58174			−0.0320401
$144$	−12.0000			−0.0833333
$145$	−26.5582	+	32.4447i	−0.183160	+	0.223757i
$146$	35.5831			0.243720
$147$			51.5049i			0.350373i
$148$	99.6389			0.673236
$149$		−	88.7811i		−	0.595846i	−0.954590	−	0.297923i	$-0.903706\pi$
$149$		−	88.7811i		−	0.595846i	0.954590	−	0.297923i	$-0.0962939\pi$
$150$	−12.0983	−	60.0302i	−0.0806555	−	0.400202i
$151$	106.644			0.706250			0.353125	−	0.935576i	$-0.385119\pi$
$151$	106.644			0.706250			0.353125	+	0.935576i	$0.385119\pi$
$152$	−66.1074			−0.434917
$153$	−11.7621			−0.0768768
$154$	17.9779			0.116739
$155$	−103.018	+	125.852i	−0.664635	+	0.811948i
$156$	−5.47983			−0.0351271
$157$	33.6167			0.214119			0.107060	−	0.994253i	$-0.465856\pi$
$157$	33.6167			0.214119			0.107060	+	0.994253i	$0.465856\pi$
$158$	36.0624			0.228243
$159$		−	2.03181i		−	0.0127787i
$160$	21.8867	+	17.9157i	0.136792	+	0.111973i
$161$	−98.1037	+	23.7938i	−0.609339	+	0.147787i
$162$			12.7279i			0.0785674i
$163$		−	273.536i		−	1.67813i	−0.544027	−	0.839067i	$-0.683101\pi$
$163$		−	273.536i		−	1.67813i	0.544027	−	0.839067i	$-0.316899\pi$
$164$	135.563			0.826606
$165$	15.8882	−	19.4097i	0.0962921	−	0.117635i
$166$			155.823i			0.938695i
$167$			62.4430i			0.373910i	0.982368	+	0.186955i	$0.0598619\pi$
$167$			62.4430i			0.373910i	−0.982368	+	0.186955i	$0.940138\pi$
$168$	21.5018			0.127987
$169$	166.498			0.985193
$170$	21.4528	+	17.5606i	0.126193	+	0.103298i
$171$			70.1175i			0.410044i
$172$	32.4707			0.188783
$173$			187.243i			1.08233i	0.840917	+	0.541164i	$0.182016\pi$
$173$			187.243i			1.08233i	−0.840917	+	0.541164i	$0.817984\pi$
$174$	−20.5407			−0.118050
$175$	21.6780	+	107.563i	0.123874	+	0.614647i
$176$			11.5855i			0.0658266i
$177$			178.434i			1.00810i
$178$	20.4889			0.115106
$179$	−151.065			−0.843937			−0.421968	−	0.906611i	$-0.638661\pi$
$179$	−151.065			−0.843937			−0.421968	+	0.906611i	$0.638661\pi$
$180$	19.0025	−	23.2143i	0.105570	−	0.128968i
$181$			295.157i			1.63070i	0.578968	+	0.815350i	$0.303456\pi$
$181$			295.157i			1.63070i	−0.578968	+	0.815350i	$0.696544\pi$
$182$	9.81886			0.0539498
$183$	21.9331			0.119853
$184$	−15.3334	−	63.2209i	−0.0833338	−	0.343592i
$185$	−157.782	+	192.754i	−0.852878	+	1.04191i
$186$	−79.6766			−0.428369
$187$			11.3558i			0.0607264i
$188$			169.829i			0.903347i
$189$		−	22.8061i		−	0.120667i
$190$	104.684	−	127.886i	0.550968	−	0.673087i
$191$		−	339.920i		−	1.77969i	−0.456267	−	0.889843i	$-0.650814\pi$
$191$		−	339.920i		−	1.77969i	0.456267	−	0.889843i	$-0.349186\pi$
$192$			13.8564i			0.0721688i
$193$			205.591i			1.06524i	0.846354	+	0.532620i	$0.178793\pi$
$193$			205.591i			1.06524i	−0.846354	+	0.532620i	$0.821207\pi$
$194$		−	90.4570i		−	0.466273i
$195$	8.67755	−	10.6009i	0.0445003	−	0.0543635i
$196$	59.4727			0.303432
$197$		−	239.594i		−	1.21621i	−0.793856	−	0.608106i	$-0.791930\pi$
$197$		−	239.594i		−	1.21621i	0.793856	−	0.608106i	$-0.208070\pi$
$198$	12.2883			0.0620619
$199$			12.7701i			0.0641713i	0.999485	+	0.0320856i	$0.0102149\pi$
$199$			12.7701i			0.0641713i	−0.999485	+	0.0320856i	$0.989785\pi$
$200$	−69.3170	+	13.9699i	−0.346585	+	0.0698497i
$201$		−	217.296i		−	1.08107i
$202$		−	123.241i		−	0.610102i
$203$	36.8052			0.181306
$204$			13.5818i			0.0665772i
$205$	−214.670	+	262.251i	−1.04717	+	1.27927i
$206$			191.735i			0.930753i
$207$	−67.0559	+	16.2635i	−0.323942	+	0.0785679i
$208$			6.32757i			0.0304210i
$209$	67.6954			0.323901
$210$	−34.0490	+	41.5958i	−0.162138	+	0.198075i
$211$	−84.8656			−0.402207			−0.201103	−	0.979570i	$-0.564453\pi$
$211$	−84.8656			−0.402207			−0.201103	+	0.979570i	$0.564453\pi$
$212$	−2.34613			−0.0110666
$213$			47.5671i			0.223320i
$214$		−	176.327i		−	0.823959i
$215$	−51.4188	+	62.8154i	−0.239157	+	0.292165i
$216$	14.6969			0.0680414
$217$	142.766			0.657907
$218$	141.168			0.647558
$219$	−43.5802			−0.198996
$220$	−22.4124	−	18.3461i	−0.101875	−	0.0833914i
$221$			6.20214i			0.0280640i
$222$	−122.032			−0.549695
$223$			44.0312i			0.197449i	0.995115	+	0.0987246i	$0.0314763\pi$
$223$			44.0312i			0.197449i	−0.995115	+	0.0987246i	$0.968524\pi$
$224$		−	24.8281i		−	0.110840i
$225$	14.8174	+	73.5217i	0.0658549	+	0.326763i
$226$		−	61.8181i		−	0.273532i
$227$	−343.150			−1.51167			−0.755837	−	0.654760i	$-0.772770\pi$
$227$	−343.150			−1.51167			−0.755837	+	0.654760i	$0.772770\pi$
$228$	80.9647			0.355108
$229$			54.4435i			0.237745i	0.992910	+	0.118872i	$0.0379279\pi$
$229$			54.4435i			0.237745i	−0.992910	+	0.118872i	$0.962072\pi$
$230$	146.584	+	70.4502i	0.637320	+	0.306305i
$231$	−22.0183			−0.0953173
$232$			23.7183i			0.102234i
$233$			118.133i			0.507010i	0.967334	+	0.253505i	$0.0815834\pi$
$233$			118.133i			0.507010i	−0.967334	+	0.253505i	$0.918417\pi$
$234$	6.71140			0.0286812
$235$	−328.539	−	268.932i	−1.39804	−	1.14439i
$236$	206.038			0.873041
$237$	−44.1673			−0.186360
$238$		−	24.3360i		−	0.102252i
$239$	34.1084			0.142713			0.0713564	−	0.997451i	$-0.477267\pi$
$239$	34.1084			0.142713			0.0713564	+	0.997451i	$0.477267\pi$
$240$	−26.8056	−	21.9422i	−0.111690	−	0.0914259i
$241$		−	151.731i		−	0.629590i	−0.949160	−	0.314795i	$-0.898064\pi$
$241$		−	151.731i		−	0.629590i	0.949160	−	0.314795i	$-0.101936\pi$
$242$			159.256i			0.658083i
$243$		−	15.5885i		−	0.0641500i
$244$		−	25.3262i		−	0.103796i
$245$	−94.1776	+	115.051i	−0.384398	+	0.469598i
$246$	−166.031			−0.674921
$247$	36.9728			0.149687
$248$			92.0026i			0.370978i
$249$		−	190.844i		−	0.766441i
$250$	82.7412	−	156.217i	0.330965	−	0.624870i
$251$			31.1868i			0.124250i	0.998068	+	0.0621252i	$0.0197878\pi$
$251$			31.1868i			0.124250i	−0.998068	+	0.0621252i	$0.980212\pi$
$252$	−26.3342			−0.104501
$253$	15.7017	+	64.7396i	0.0620622	+	0.255888i
$254$	−127.319			−0.501257
$255$	−26.2743	−	21.5073i	−0.103036	−	0.0843423i
$256$	16.0000			0.0625000
$257$			487.515i			1.89695i	0.316858	+	0.948473i	$0.397372\pi$
$257$			487.515i			1.89695i	−0.316858	+	0.948473i	$0.602628\pi$
$258$	−39.7683			−0.154141
$259$	218.659			0.844245
$260$	−12.2408	−	10.0200i	−0.0470802	−	0.0385384i
$261$	25.1571			0.0963874
$262$			180.327i			0.688272i
$263$	296.073			1.12575			0.562876	−	0.826541i	$-0.309695\pi$
$263$	296.073			1.12575			0.562876	+	0.826541i	$0.309695\pi$
$264$		−	14.1893i		−	0.0537472i
$265$	3.71520	−	4.53865i	0.0140196	−	0.0171270i
$266$	−145.074			−0.545391
$267$	−25.0936			−0.0939837
$268$	−250.911			−0.936236
$269$	−69.7280			−0.259212			−0.129606	−	0.991566i	$-0.541371\pi$
$269$	−69.7280			−0.259212			−0.129606	+	0.991566i	$0.541371\pi$
$270$	−23.2732	+	28.4316i	−0.0861972	+	0.105302i
$271$	356.089			1.31398			0.656991	−	0.753898i	$-0.271829\pi$
$271$	356.089			1.31398			0.656991	+	0.753898i	$0.271829\pi$
$272$	15.6829			0.0576576
$273$	−12.0256			−0.0440498
$274$			161.177i			0.588235i
$275$	70.9820	−	14.3055i	0.258116	−	0.0520201i
$276$	18.7795	+	77.4295i	0.0680418	+	0.280542i
$277$		−	38.0169i		−	0.137245i	−0.997643	−	0.0686225i	$-0.978140\pi$
$277$		−	38.0169i		−	0.137245i	0.997643	−	0.0686225i	$-0.0218604\pi$
$278$			286.785i			1.03160i
$279$	97.5835			0.349762
$280$	48.0307	+	39.3164i	0.171538	+	0.140416i
$281$		−	311.125i		−	1.10721i	−0.832781	−	0.553603i	$-0.813253\pi$
$281$		−	311.125i		−	1.10721i	0.832781	−	0.553603i	$-0.186747\pi$
$282$		−	207.997i		−	0.737579i
$283$	106.374			0.375879			0.187939	−	0.982181i	$-0.439819\pi$
$283$	106.374			0.375879			0.187939	+	0.982181i	$0.439819\pi$
$284$	54.9257			0.193400
$285$	−128.211	+	156.628i	−0.449864	+	0.549573i
$286$		−	6.47956i		−	0.0226558i
$287$	297.496			1.03657
$288$		−	16.9706i		−	0.0589256i
$289$	−273.628			−0.946810
$290$	−45.8837	−	37.5590i	−0.158220	−	0.129514i
$291$			110.787i			0.380710i
$292$			50.3221i			0.172336i
$293$	235.464			0.803631			0.401815	−	0.915721i	$-0.368379\pi$
$293$	235.464			0.803631			0.401815	+	0.915721i	$0.368379\pi$
$294$	−72.8389			−0.247751
$295$	−326.270	+	398.585i	−1.10600	+	1.35114i
$296$			140.911i			0.476050i
$297$	−15.0500			−0.0506733
$298$	125.555			0.421327
$299$	8.57572	+	35.3584i	0.0286813	+	0.118256i
$300$	84.8956	−	17.1096i	0.282985	−	0.0570321i
$301$	71.2576			0.236736
$302$			150.817i			0.499394i
$303$			150.938i			0.498146i
$304$		−	93.4900i		−	0.307533i
$305$	48.9942	+	40.1051i	0.160637	+	0.131492i
$306$		−	16.6342i		−	0.0543601i
$307$		−	35.2062i		−	0.114678i	−0.998355	−	0.0573391i	$-0.981738\pi$
$307$		−	35.2062i		−	0.114678i	0.998355	−	0.0573391i	$-0.0182616\pi$
$308$			25.4245i			0.0825472i
$309$		−	234.826i		−	0.759956i
$310$	−177.981	−	145.690i	−0.574134	−	0.469968i
$311$	−174.212			−0.560166			−0.280083	−	0.959976i	$-0.590362\pi$
$311$	−174.212			−0.560166			−0.280083	+	0.959976i	$0.590362\pi$
$312$		−	7.74965i		−	0.0248386i
$313$	212.916			0.680244			0.340122	−	0.940381i	$-0.389532\pi$
$313$	212.916			0.680244			0.340122	+	0.940381i	$0.389532\pi$
$314$			47.5412i			0.151405i
$315$	41.7014	−	50.9442i	0.132385	−	0.161728i
$316$			51.0000i			0.161392i
$317$			220.794i			0.696511i	0.937400	+	0.348256i	$0.113226\pi$
$317$			220.794i			0.696511i	−0.937400	+	0.348256i	$0.886774\pi$
$318$	2.87341			0.00903588
$319$		−	24.2881i		−	0.0761382i
$320$	−25.3367	+	30.9524i	−0.0791772	+	0.0967263i
$321$			215.956i			0.672759i
$322$	−33.6495	−	138.740i	−0.104501	−	0.430868i
$323$		−	91.6369i		−	0.283706i
$324$	−18.0000			−0.0555556
$325$	38.7678	−	7.81315i	0.119286	−	0.0240405i
$326$	386.838			1.18662
$327$	−172.894			−0.528729
$328$			191.716i			0.584499i
$329$			372.693i			1.13281i
$330$	27.4495	+	22.4693i	0.0831802	+	0.0680888i
$331$	328.021			0.990999			0.495499	−	0.868608i	$-0.334985\pi$
$331$	328.021			0.990999			0.495499	+	0.868608i	$0.334985\pi$
$332$	−220.367			−0.663757
$333$	149.458			0.448824
$334$	−88.3078			−0.264395
$335$	397.329	−	485.395i	1.18606	−	1.44894i
$336$			30.4081i			0.0905004i
$337$	−97.1617			−0.288314			−0.144157	−	0.989555i	$-0.546047\pi$
$337$	−97.1617			−0.288314			−0.144157	+	0.989555i	$0.546047\pi$
$338$			235.463i			0.696637i
$339$			75.7115i			0.223338i
$340$	−24.8345	+	30.3389i	−0.0730426	+	0.0892320i
$341$		−	94.2126i		−	0.276283i
$342$	−99.1611			−0.289945
$343$	345.577			1.00751
$344$			45.9205i			0.133490i
$345$	−179.528	−	86.2835i	−0.520370	−	0.250097i
$346$	−264.801			−0.765321
$347$		−	346.996i		−	0.999987i	−0.866029	−	0.499994i	$-0.833336\pi$
$347$		−	346.996i		−	0.999987i	0.866029	−	0.499994i	$-0.166664\pi$
$348$		−	29.0489i		−	0.0834739i
$349$	−428.347			−1.22735			−0.613677	−	0.789557i	$-0.710310\pi$
$349$	−428.347			−1.22735			−0.613677	+	0.789557i	$0.710310\pi$
$350$	−152.117	+	30.6573i	−0.434621	+	0.0875923i
$351$	−8.21975			−0.0234181
$352$	−16.3843			−0.0465464
$353$		−	285.410i		−	0.808527i	−0.914643	−	0.404263i	$-0.867528\pi$
$353$		−	285.410i		−	0.808527i	0.914643	−	0.404263i	$-0.132472\pi$
$354$	−252.344			−0.712835
$355$	−86.9773	+	106.255i	−0.245006	+	0.299311i
$356$			28.9756i			0.0813923i
$357$			29.8054i			0.0834885i
$358$		−	213.638i		−	0.596753i
$359$			448.742i			1.24998i	0.780634	+	0.624988i	$0.214896\pi$
$359$			448.742i			1.24998i	−0.780634	+	0.624988i	$0.785104\pi$
$360$	32.8300	+	26.8736i	0.0911944	+	0.0746490i
$361$	−185.274			−0.513224
$362$	−417.415			−1.15308
$363$		−	195.048i		−	0.537322i
$364$			13.8860i			0.0381482i
$365$	−97.3493	−	79.6872i	−0.266710	−	0.218321i
$366$			31.0181i			0.0847489i
$367$	259.468			0.706998			0.353499	−	0.935435i	$-0.384992\pi$
$367$	259.468			0.706998			0.353499	+	0.935435i	$0.384992\pi$
$368$	89.4079	−	21.6847i	0.242956	−	0.0589259i
$369$	203.345			0.551071
$370$	−272.595	−	223.138i	−0.736744	−	0.603076i
$371$	−5.14862			−0.0138777
$372$		−	112.680i		−	0.302903i
$373$	173.652			0.465555			0.232778	−	0.972530i	$-0.425219\pi$
$373$	173.652			0.465555			0.232778	+	0.972530i	$0.425219\pi$
$374$	−16.0596			−0.0429400
$375$	−101.337	+	191.327i	−0.270232	+	0.510204i
$376$	−240.175			−0.638762
$377$		−	13.2653i		−	0.0351864i
$378$	32.2527			0.0853246
$379$		−	243.255i		−	0.641833i	−0.947107	−	0.320917i	$-0.896009\pi$
$379$		−	243.255i		−	0.641833i	0.947107	−	0.320917i	$-0.103991\pi$
$380$	180.859	+	148.045i	0.475944	+	0.389593i
$381$	155.934			0.409275
$382$	480.720			1.25843
$383$	−46.0197			−0.120156			−0.0600779	−	0.998194i	$-0.519135\pi$
$383$	−46.0197			−0.120156			−0.0600779	+	0.998194i	$0.519135\pi$
$384$	−19.5959			−0.0510310
$385$	−49.1844	−	40.2609i	−0.127752	−	0.104574i
$386$	−290.750			−0.753239
$387$	48.7061			0.125855
$388$	127.926			0.329705
$389$			403.468i			1.03719i	0.855019	+	0.518597i	$0.173545\pi$
$389$			403.468i			1.03719i	−0.855019	+	0.518597i	$0.826455\pi$
$390$	14.9919	+	12.2719i	0.0384408	+	0.0314664i
$391$	87.6357	−	21.2549i	0.224132	−	0.0543604i
$392$			84.1071i			0.214559i
$393$		−	220.855i		−	0.561971i
$394$	338.837			0.859992
$395$	−98.6608	−	80.7607i	−0.249774	−	0.204457i
$396$			17.3782i			0.0438844i
$397$		−	333.085i		−	0.839005i	−0.907754	−	0.419502i	$-0.862205\pi$
$397$		−	333.085i		−	0.839005i	0.907754	−	0.419502i	$-0.137795\pi$
$398$	−18.0596			−0.0453760
$399$	177.679			0.445310
$400$	−19.7565	−	98.0290i	−0.0493912	−	0.245072i
$401$		−	498.274i		−	1.24258i	−0.783582	−	0.621289i	$-0.786609\pi$
$401$		−	498.274i		−	1.24258i	0.783582	−	0.621289i	$-0.213391\pi$
$402$	307.302			0.764434
$403$		−	51.4555i		−	0.127681i
$404$	174.289			0.431407
$405$	28.5038	−	34.8215i	0.0703797	−	0.0859789i
$406$			52.0503i			0.128203i
$407$		−	144.295i		−	0.354534i
$408$	−19.2075			−0.0470772
$409$	415.197			1.01515			0.507576	−	0.861607i	$-0.330542\pi$
$409$	415.197			1.01515			0.507576	+	0.861607i	$0.330542\pi$
$410$	−370.879	−	303.590i	−0.904582	−	0.740463i
$411$		−	197.400i		−	0.480292i
$412$	−271.154			−0.658141
$413$	452.154			1.09480
$414$	−23.0001	−	94.8314i	−0.0555559	−	0.229061i
$415$	348.961	−	426.307i	0.840871	−	1.02724i
$416$	−8.94853			−0.0215109
$417$		−	351.238i		−	0.842298i
$418$			95.7357i			0.229033i
$419$			297.163i			0.709221i	0.935014	+	0.354610i	$0.115386\pi$
$419$			297.163i			0.709221i	−0.935014	+	0.354610i	$0.884614\pi$
$420$	−58.8253	−	48.1526i	−0.140060	−	0.114649i
$421$		−	281.558i		−	0.668783i	−0.942434	−	0.334392i	$-0.891469\pi$
$421$		−	281.558i		−	0.668783i	0.942434	−	0.334392i	$-0.108531\pi$
$422$		−	120.018i		−	0.284403i
$423$			254.744i			0.602231i
$424$		−	3.31793i		−	0.00782530i
$425$	−19.3649	−	96.0859i	−0.0455644	−	0.226084i
$426$	−67.2700			−0.157911
$427$		−	55.5788i		−	0.130161i
$428$	249.364			0.582627
$429$			7.93581i			0.0184984i
$430$	−88.8345	−	72.7172i	−0.206592	−	0.169110i
$431$		−	782.410i		−	1.81534i	−0.419689	−	0.907668i	$-0.637861\pi$
$431$		−	782.410i		−	1.81534i	0.419689	−	0.907668i	$-0.362139\pi$
$432$			20.7846i			0.0481125i
$433$	153.757			0.355096			0.177548	−	0.984112i	$-0.443183\pi$
$433$	153.757			0.355096			0.177548	+	0.984112i	$0.443183\pi$
$434$			201.901i			0.465211i
$435$	56.1959	+	46.0002i	0.129186	+	0.105748i
$436$			199.641i			0.457893i
$437$	−126.707	−	522.421i	−0.289946	−	1.19547i
$438$		−	61.6317i		−	0.140712i
$439$	−446.096			−1.01616			−0.508082	−	0.861309i	$-0.669645\pi$
$439$	−446.096			−1.01616			−0.508082	+	0.861309i	$0.669645\pi$
$440$	25.9453	−	31.6959i	0.0589666	−	0.0720362i
$441$	89.2090			0.202288
$442$	−8.77116			−0.0198442
$443$		−	726.162i		−	1.63919i	−0.572942	−	0.819596i	$-0.694198\pi$
$443$		−	726.162i		−	1.63919i	0.572942	−	0.819596i	$-0.305802\pi$
$444$		−	172.580i		−	0.388693i
$445$	−56.0541	−	45.8842i	−0.125964	−	0.103111i
$446$	−62.2695			−0.139618
$447$	−153.773			−0.344012
$448$	35.1123			0.0783757
$449$	118.414			0.263728			0.131864	−	0.991268i	$-0.457904\pi$
$449$	118.414			0.263728			0.131864	+	0.991268i	$0.457904\pi$
$450$	−103.975	+	20.9549i	−0.231057	+	0.0465665i
$451$		−	196.321i		−	0.435301i
$452$	87.4241			0.193416
$453$		−	184.712i		−	0.407754i
$454$		−	485.287i		−	1.06891i
$455$	−26.8628	−	21.9890i	−0.0590390	−	0.0483275i
$456$			114.501i			0.251100i
$457$	27.9007			0.0610518			0.0305259	−	0.999534i	$-0.490282\pi$
$457$	27.9007			0.0610518			0.0305259	+	0.999534i	$0.490282\pi$
$458$	−76.9947			−0.168111
$459$			20.3726i			0.0443848i
$460$	−99.6316	+	207.301i	−0.216590	+	0.450653i
$461$	382.827			0.830427			0.415214	−	0.909724i	$-0.363707\pi$
$461$	382.827			0.830427			0.415214	+	0.909724i	$0.363707\pi$
$462$		−	31.1386i		−	0.0673995i
$463$		−	58.0745i		−	0.125431i	−0.998031	−	0.0627154i	$-0.980024\pi$
$463$		−	58.0745i		−	0.125431i	0.998031	−	0.0627154i	$-0.0199760\pi$
$464$	−33.5428			−0.0722905
$465$	217.982	+	178.433i	0.468778	+	0.383727i
$466$	−167.066			−0.358510
$467$	−384.852			−0.824095			−0.412047	−	0.911162i	$-0.635186\pi$
$467$	−384.852			−0.824095			−0.412047	+	0.911162i	$0.635186\pi$
$468$			9.49135i			0.0202807i
$469$	−550.630			−1.17405
$470$	380.327	−	464.624i	0.809206	−	0.988562i
$471$		−	58.2258i		−	0.123622i
$472$			291.381i			0.617333i
$473$		−	47.0236i		−	0.0994156i
$474$		−	62.4620i		−	0.131776i
$475$	−572.796	+	115.440i	−1.20589	+	0.243031i
$476$	34.4163			0.0723032
$477$	−3.51919			−0.00737776
$478$			48.2365i			0.100913i
$479$			557.765i			1.16444i	0.813033	+	0.582218i	$0.197815\pi$
$479$			557.765i			1.16444i	−0.813033	+	0.582218i	$0.802185\pi$
$480$	31.0310	−	37.9088i	0.0646479	−	0.0789767i
$481$		−	78.8089i		−	0.163844i
$482$	214.580			0.445188
$483$	41.2120	+	169.921i	0.0853251	+	0.351802i
$484$	−225.222			−0.465335
$485$	−202.576	+	247.475i	−0.417682	+	0.510258i
$486$	22.0454			0.0453609
$487$		−	651.144i		−	1.33705i	−0.743689	−	0.668525i	$-0.766926\pi$
$487$		−	651.144i		−	1.33705i	0.743689	−	0.668525i	$-0.233074\pi$
$488$	35.8166			0.0733947
$489$	−473.778			−0.968872
$490$	−162.707	−	133.187i	−0.332056	−	0.271811i
$491$	492.791			1.00365			0.501824	−	0.864970i	$-0.332662\pi$
$491$	492.791			1.00365			0.501824	+	0.864970i	$0.332662\pi$
$492$		−	234.803i		−	0.477241i
$493$	−32.8779			−0.0666895
$494$			52.2874i			0.105845i
$495$	−33.6186	−	27.5192i	−0.0679164	−	0.0555942i
$496$	−130.111			−0.262321
$497$	120.536			0.242526
$498$	269.894			0.541956
$499$	506.096			1.01422			0.507110	−	0.861881i	$-0.330714\pi$
$499$	506.096			1.01422			0.507110	+	0.861881i	$0.330714\pi$
$500$	220.925	+	117.014i	0.441850	+	0.234027i
$501$	108.154			0.215877
$502$	−44.1048			−0.0878583
$503$	73.5526			0.146228			0.0731139	−	0.997324i	$-0.476706\pi$
$503$	73.5526			0.146228			0.0731139	+	0.997324i	$0.476706\pi$
$504$		−	37.2422i		−	0.0738933i
$505$	−275.994	+	337.166i	−0.546522	+	0.667655i
$506$	−91.5556	+	22.2056i	−0.180940	+	0.0438846i
$507$		−	288.382i		−	0.568801i
$508$		−	180.057i		−	0.354442i
$509$	−725.849			−1.42603			−0.713015	−	0.701149i	$-0.752671\pi$
$509$	−725.849			−1.42603			−0.713015	+	0.701149i	$0.752671\pi$
$510$	30.4159	−	37.1574i	0.0596390	−	0.0728577i
$511$			110.433i			0.216111i
$512$			22.6274i			0.0441942i
$513$	121.447			0.236739
$514$	−689.451			−1.34134
$515$	429.385	−	524.555i	0.833756	−	1.01855i
$516$		−	56.2409i		−	0.108994i
$517$	245.944			0.475714
$518$			309.231i			0.596971i
$519$	324.314			0.624882
$520$	14.1704	−	17.3112i	0.0272507	−	0.0332907i
$521$		−	90.1740i		−	0.173079i	−0.996248	−	0.0865394i	$-0.972419\pi$
$521$		−	90.1740i		−	0.173079i	0.996248	−	0.0865394i	$-0.0275808\pi$
$522$			35.5775i			0.0681562i
$523$	355.009			0.678794			0.339397	−	0.940643i	$-0.389777\pi$
$523$	355.009			0.678794			0.339397	+	0.940643i	$0.389777\pi$
$524$	−255.021			−0.486681
$525$	186.305	−	37.5474i	0.354867	−	0.0715188i
$526$			418.710i			0.796027i
$527$	−127.532			−0.241997
$528$	20.0666			0.0380050
$529$	470.222	−	242.348i	0.888888	−	0.458125i
$530$	6.41862	+	5.25408i	0.0121106	+	0.00991336i
$531$	309.057			0.582027
$532$		−	205.166i		−	0.385650i
$533$		−	107.223i		−	0.201169i
$534$		−	35.4878i		−	0.0664565i
$535$	−394.879	+	482.402i	−0.738092	+	0.901685i
$536$		−	354.842i		−	0.662019i
$537$			261.652i			0.487247i
$538$		−	98.6102i		−	0.183290i
$539$		−	86.1274i		−	0.159791i
$540$	−40.2084	−	32.9133i	−0.0744599	−	0.0609506i
$541$	−692.660			−1.28033			−0.640166	−	0.768236i	$-0.721135\pi$
$541$	−692.660			−1.28033			−0.640166	+	0.768236i	$0.721135\pi$
$542$			503.586i			0.929126i
$543$	511.226			0.941485
$544$			22.1789i			0.0407701i
$545$	−386.211	−	316.140i	−0.708644	−	0.580074i
$546$		−	17.0068i		−	0.0311479i
$547$			571.267i			1.04436i	0.852834	+	0.522181i	$0.174882\pi$
$547$			571.267i			1.04436i	−0.852834	+	0.522181i	$0.825118\pi$
$548$	−227.938			−0.415945
$549$		−	37.9893i		−	0.0691972i
$550$	20.2311	+	100.384i	0.0367837	+	0.182516i
$551$			195.995i			0.355707i
$552$	−109.502	+	26.5583i	−0.198373	+	0.0481128i
$553$			111.920i			0.202388i
$554$	53.7640			0.0970469
$555$	333.860	+	273.287i	0.601549	+	0.492410i
$556$	−405.575			−0.729452
$557$	−614.979			−1.10409			−0.552045	−	0.833814i	$-0.686152\pi$
$557$	−614.979			−1.10409			−0.552045	+	0.833814i	$0.686152\pi$
$558$			138.004i			0.247319i
$559$		−	25.6826i		−	0.0459438i
$560$	−55.6019	+	67.9257i	−0.0992890	+	0.121296i
$561$	19.6689			0.0350604
$562$	439.997			0.782913
$563$	158.051			0.280731			0.140365	−	0.990100i	$-0.455172\pi$
$563$	158.051			0.280731			0.140365	+	0.990100i	$0.455172\pi$
$564$	294.153			0.521547
$565$	−138.440	+	169.124i	−0.245026	+	0.299335i
$566$			150.435i			0.265786i
$567$	−39.5013			−0.0696673
$568$			77.6767i			0.136755i
$569$			460.419i			0.809173i	0.914500	+	0.404586i	$0.132584\pi$
$569$			460.419i			0.809173i	−0.914500	+	0.404586i	$0.867416\pi$
$570$	−221.506	−	181.318i	−0.388607	−	0.318102i
$571$		−	1109.86i		−	1.94371i	−0.235580	−	0.971855i	$-0.575699\pi$
$571$		−	1109.86i		−	1.94371i	0.235580	−	0.971855i	$-0.424301\pi$
$572$	9.16348			0.0160201
$573$	−588.759			−1.02750
$574$			420.723i			0.732968i
$575$	−243.257	−	521.009i	−0.423056	−	0.906103i
$576$	24.0000			0.0416667
$577$			554.867i			0.961642i	0.876819	+	0.480821i	$0.159661\pi$
$577$			554.867i			0.961642i	−0.876819	+	0.480821i	$0.840339\pi$
$578$		−	386.968i		−	0.669496i
$579$	356.095			0.615017
$580$	53.1165	−	64.8894i	0.0915801	−	0.111878i
$581$	−483.601			−0.832359
$582$	−156.676			−0.269203
$583$			3.39763i			0.00582783i
$584$	−71.1661			−0.121860
$585$	−18.3613	−	15.0300i	−0.0313868	−	0.0256922i
$586$			332.996i			0.568253i
$587$		−	880.384i		−	1.49980i	−0.661550	−	0.749901i	$-0.730101\pi$
$587$		−	880.384i		−	1.49980i	0.661550	−	0.749901i	$-0.269899\pi$
$588$		−	103.010i		−	0.175187i
$589$			760.257i			1.29076i
$590$	−563.685	−	461.415i	−0.955398	−	0.782059i
$591$	−414.989			−0.702180
$592$	−199.278			−0.336618
$593$			474.560i			0.800270i	0.916456	+	0.400135i	$0.131037\pi$
$593$			474.560i			0.800270i	−0.916456	+	0.400135i	$0.868963\pi$
$594$		−	21.2839i		−	0.0358314i
$595$	−54.4997	+	66.5793i	−0.0915962	+	0.111898i
$596$			177.562i			0.297923i
$597$	22.1184			0.0370493
$598$	−50.0043	+	12.1279i	−0.0836193	+	0.0202808i
$599$	−150.075			−0.250542			−0.125271	−	0.992123i	$-0.539980\pi$
$599$	−150.075			−0.250542			−0.125271	+	0.992123i	$0.539980\pi$
$600$	24.1967	+	120.060i	0.0403278	+	0.200101i
$601$	−346.698			−0.576868			−0.288434	−	0.957500i	$-0.593135\pi$
$601$	−346.698			−0.576868			−0.288434	+	0.957500i	$0.593135\pi$
$602$			100.773i			0.167398i
$603$	−376.367			−0.624158
$604$	−213.288			−0.353125
$605$	356.649	−	435.698i	0.589502	−	0.720162i
$606$	−213.459			−0.352243
$607$			717.693i			1.18236i	0.806540	+	0.591180i	$0.201338\pi$
$607$			717.693i			1.18236i	−0.806540	+	0.591180i	$0.798662\pi$
$608$	132.215			0.217459
$609$		−	63.7484i		−	0.104677i
$610$	−56.7172	+	69.2882i	−0.0929790	+	0.113587i
$611$	134.326			0.219846
$612$	23.5243			0.0384384
$613$	−1059.01			−1.72759			−0.863796	−	0.503841i	$-0.831920\pi$
$613$	−1059.01			−1.72759			−0.863796	+	0.503841i	$0.831920\pi$
$614$	49.7891			0.0810897
$615$	454.232	+	371.820i	0.738588	+	0.604586i
$616$	−35.9557			−0.0583697
$617$	−832.513			−1.34929			−0.674646	−	0.738142i	$-0.735704\pi$
$617$	−832.513			−1.34929			−0.674646	+	0.738142i	$0.735704\pi$
$618$	332.095			0.537370
$619$			1204.47i			1.94583i	0.231168	+	0.972914i	$0.425745\pi$
$619$			1204.47i			1.94583i	−0.231168	+	0.972914i	$0.574255\pi$
$620$	206.037	−	251.704i	0.332318	−	0.405974i
$621$	28.1693	+	116.144i	0.0453612	+	0.187028i
$622$		−	246.373i		−	0.396097i
$623$			63.5876i			0.102067i
$624$	10.9597			0.0175636
$625$	−576.210	+	242.089i	−0.921936	+	0.387342i
$626$			301.109i			0.481005i
$627$		−	117.252i		−	0.187004i
$628$	−67.2334			−0.107060
$629$	−195.328			−0.310537
$630$	72.0460	+	58.9747i	0.114359	+	0.0936106i
$631$		−	383.040i		−	0.607037i	−0.952826	−	0.303518i	$-0.901839\pi$
$631$		−	383.040i		−	0.607037i	0.952826	−	0.303518i	$-0.0981613\pi$
$632$	−72.1249			−0.114122
$633$			146.992i			0.232214i
$634$	−312.250			−0.492508
$635$	348.324	+	285.128i	0.548542	+	0.449020i
$636$			4.06361i			0.00638933i
$637$		−	47.0397i		−	0.0738456i
$638$	34.3485			0.0538378
$639$	82.3886			0.128934
$640$	−43.7733	−	35.8315i	−0.0683958	−	0.0559867i
$641$			439.350i			0.685413i	0.939443	+	0.342706i	$0.111344\pi$
$641$			439.350i			0.685413i	−0.939443	+	0.342706i	$0.888656\pi$
$642$	−305.408			−0.475713
$643$	715.156			1.11222			0.556109	−	0.831109i	$-0.312294\pi$
$643$	715.156			1.11222			0.556109	+	0.831109i	$0.312294\pi$
$644$	196.207	−	47.5875i	0.304670	−	0.0738937i
$645$	108.800	+	89.0600i	0.168681	+	0.138077i
$646$	129.594			0.200610
$647$			117.314i			0.181319i	0.995882	+	0.0906596i	$0.0288975\pi$
$647$			117.314i			0.181319i	−0.995882	+	0.0906596i	$0.971102\pi$
$648$		−	25.4558i		−	0.0392837i
$649$		−	298.381i		−	0.459754i
$650$	11.0495	+	54.8260i	0.0169992	+	0.0843476i
$651$		−	247.278i		−	0.379843i
$652$			547.072i			0.839067i
$653$		−	135.228i		−	0.207087i	−0.994625	−	0.103543i	$-0.966982\pi$
$653$		−	135.228i		−	0.207087i	0.994625	−	0.103543i	$-0.0330181\pi$
$654$		−	244.509i		−	0.373868i
$655$	403.837	−	493.345i	0.616545	−	0.753198i
$656$	−271.127			−0.413303
$657$			75.4831i			0.114891i
$658$	−527.068			−0.801015
$659$			548.436i			0.832224i	0.909313	+	0.416112i	$0.136608\pi$
$659$			548.436i			0.832224i	−0.909313	+	0.416112i	$0.863392\pi$
$660$	−31.7764	+	38.8194i	−0.0481460	+	0.0588173i
$661$		−	77.7084i		−	0.117562i	−0.998271	−	0.0587809i	$-0.981279\pi$
$661$		−	77.7084i		−	0.117562i	0.998271	−	0.0587809i	$-0.0187213\pi$
$662$			463.891i			0.700742i
$663$	10.7424			0.0162028
$664$		−	311.647i		−	0.469347i
$665$	396.898	+	324.889i	0.596839	+	0.488554i
$666$			211.366i			0.317366i
$667$	−187.437	+	45.4604i	−0.281015	+	0.0681565i
$668$		−	124.886i		−	0.186955i
$669$	76.2642			0.113997
$670$	686.452	+	561.908i	1.02455	+	0.838669i
$671$	−36.6770			−0.0546602
$672$	−43.0036			−0.0639935
$673$			384.159i			0.570816i	0.958406	+	0.285408i	$0.0921291\pi$
$673$			384.159i			0.570816i	−0.958406	+	0.285408i	$0.907871\pi$
$674$		−	137.407i		−	0.203869i
$675$	127.343	−	25.6644i	0.188657	−	0.0380214i
$676$	−332.995			−0.492597
$677$	960.270			1.41842			0.709210	−	0.704998i	$-0.249052\pi$
$677$	960.270			1.41842			0.709210	+	0.704998i	$0.249052\pi$
$678$	−107.072			−0.157924
$679$	280.735			0.413454
$680$	−42.9057	−	35.1213i	−0.0630966	−	0.0516489i
$681$			594.353i			0.872765i
$682$	133.237			0.195362
$683$		−	250.745i		−	0.367122i	−0.983008	−	0.183561i	$-0.941237\pi$
$683$		−	250.745i		−	0.367122i	0.983008	−	0.183561i	$-0.0587626\pi$
$684$		−	140.235i		−	0.205022i
$685$	360.950	−	440.952i	0.526934	−	0.643725i
$686$			488.719i			0.712419i
$687$	94.2989			0.137262
$688$	−64.9414			−0.0943916
$689$			1.85566i			0.00269327i
$690$	122.023	−	253.890i	0.176845	−	0.367957i
$691$	239.207			0.346175			0.173087	−	0.984906i	$-0.444626\pi$
$691$	239.207			0.346175			0.173087	+	0.984906i	$0.444626\pi$
$692$		−	374.485i		−	0.541164i
$693$			38.1368i			0.0550315i
$694$	490.726			0.707098
$695$	642.246	−	784.596i	0.924095	−	1.12891i
$696$	41.0814			0.0590250
$697$	−265.753			−0.381281
$698$		−	605.774i		−	0.867870i
$699$	204.613			0.292722
$700$	−43.3560	−	215.126i	−0.0619371	−	0.307323i
$701$		−	1147.70i		−	1.63723i	−0.574339	−	0.818617i	$-0.694741\pi$
$701$		−	1147.70i		−	1.63723i	0.574339	−	0.818617i	$-0.305259\pi$
$702$		−	11.6245i		−	0.0165591i
$703$			1164.40i			1.65634i
$704$		−	23.1709i		−	0.0329133i
$705$	−465.804	+	569.046i	−0.660714	+	0.807157i
$706$	403.631			0.571715
$707$	382.480			0.540990
$708$		−	356.868i		−	0.504051i
$709$		−	1366.04i		−	1.92671i	−0.268225	−	0.963356i	$-0.586437\pi$
$709$		−	1366.04i		−	1.92671i	0.268225	−	0.963356i	$-0.413563\pi$
$710$	−150.268	−	123.004i	−0.211645	−	0.173246i
$711$			76.5000i			0.107595i
$712$	−40.9778			−0.0575530
$713$	−727.061	+	176.339i	−1.01972	+	0.247320i
$714$	−42.1512			−0.0590353
$715$	−14.5108	+	17.7270i	−0.0202948	+	0.0247930i
$716$	302.129			0.421968
$717$		−	59.0774i		−	0.0823953i
$718$	−634.616			−0.883867
$719$	−491.364			−0.683400			−0.341700	−	0.939809i	$-0.611003\pi$
$719$	−491.364			−0.683400			−0.341700	+	0.939809i	$0.611003\pi$
$720$	−38.0050	+	46.4286i	−0.0527848	+	0.0644842i
$721$	−595.053			−0.825316
$722$		−	262.017i		−	0.362904i
$723$	−262.806			−0.363494
$724$		−	590.313i		−	0.815350i
$725$	41.4180	+	205.510i	0.0571283	+	0.283463i
$726$	275.840			0.379944
$727$	106.511			0.146507			0.0732536	−	0.997313i	$-0.476662\pi$
$727$	106.511			0.146507			0.0732536	+	0.997313i	$0.476662\pi$
$728$	−19.6377			−0.0269749
$729$	−27.0000			−0.0370370
$730$	112.695	−	137.673i	0.154376	−	0.188593i
$731$	−63.6542			−0.0870783
$732$	−43.8662			−0.0599266
$733$	23.9903			0.0327289			0.0163645	−	0.999866i	$-0.494791\pi$
$733$	23.9903			0.0327289			0.0163645	+	0.999866i	$0.494791\pi$
$734$			366.944i			0.499923i
$735$	199.275	+	163.120i	0.271122	+	0.221933i
$736$	30.6668	+	126.442i	0.0416669	+	0.171796i
$737$			363.366i			0.493034i
$738$			287.573i			0.389666i
$739$	256.204			0.346691			0.173345	−	0.984861i	$-0.444542\pi$
$739$	256.204			0.346691			0.173345	+	0.984861i	$0.444542\pi$
$740$	315.565	−	385.508i	0.426439	−	0.520957i
$741$		−	64.0387i		−	0.0864220i
$742$		−	7.28125i		−	0.00981301i
$743$	500.539			0.673673			0.336836	−	0.941563i	$-0.390643\pi$
$743$	500.539			0.673673			0.336836	+	0.941563i	$0.390643\pi$
$744$	159.353			0.214184
$745$	−343.499	−	281.177i	−0.461072	−	0.377419i
$746$			245.581i			0.329197i
$747$	−330.551			−0.442505
$748$		−	22.7117i		−	0.0303632i
$749$	547.234			0.730620
$750$	−270.577	−	143.312i	−0.360769	−	0.191083i
$751$			869.309i			1.15754i	0.815492	+	0.578768i	$0.196466\pi$
$751$			869.309i			1.15754i	−0.815492	+	0.578768i	$0.803534\pi$
$752$		−	339.658i		−	0.451673i
$753$	54.0172			0.0717360
$754$	18.7599			0.0248805
$755$	337.750	−	412.610i	0.447351	−	0.546504i
$756$			45.6122i			0.0603336i
$757$	642.801			0.849142			0.424571	−	0.905395i	$-0.360425\pi$
$757$	642.801			0.849142			0.424571	+	0.905395i	$0.360425\pi$
$758$	344.014			0.453844
$759$	112.132	−	27.1962i	0.147737	−	0.0358316i
$760$	−209.368	+	255.773i	−0.275484	+	0.336543i
$761$	985.400			1.29487			0.647437	−	0.762119i	$-0.275841\pi$
$761$	985.400			1.29487			0.647437	+	0.762119i	$0.275841\pi$
$762$			220.523i			0.289401i
$763$			438.116i			0.574202i
$764$			679.840i			0.889843i
$765$	−37.2517	+	45.5083i	−0.0486951	+	0.0594880i
$766$		−	65.0816i		−	0.0849630i
$767$		−	162.965i		−	0.212470i
$768$		−	27.7128i		−	0.0360844i
$769$		−	504.152i		−	0.655594i	−0.944748	−	0.327797i	$-0.893694\pi$
$769$		−	504.152i		−	0.655594i	0.944748	−	0.327797i	$-0.106306\pi$
$770$	56.9375	−	69.5573i	0.0739448	−	0.0903341i
$771$	844.401			1.09520
$772$		−	411.183i		−	0.532620i
$773$	238.172			0.308114			0.154057	−	0.988062i	$-0.450766\pi$
$773$	238.172			0.308114			0.154057	+	0.988062i	$0.450766\pi$
$774$			68.8808i			0.0889933i
$775$	160.659	+	797.168i	0.207302	+	1.02860i
$776$			180.914i			0.233137i
$777$		−	378.729i		−	0.487425i
$778$	−570.590			−0.733406
$779$			1584.23i			2.03367i
$780$	−17.3551	+	21.2018i	−0.0222501	+	0.0271817i
$781$		−	79.5426i		−	0.101847i
$782$	30.0590	+	123.936i	0.0384386	+	0.158485i
$783$		−	43.5734i		−	0.0556493i
$784$	−118.945			−0.151716
$785$	106.467	−	130.065i	0.135627	−	0.165688i
$786$	312.336			0.397374
$787$	−1475.14			−1.87439			−0.937193	−	0.348811i	$-0.886585\pi$
$787$	−1475.14			−1.87439			−0.937193	+	0.348811i	$0.886585\pi$
$788$			479.187i			0.608106i
$789$		−	512.813i		−	0.649953i
$790$	114.213	−	139.527i	0.144573	−	0.176617i
$791$	191.854			0.242546
$792$	−24.5765			−0.0310309
$793$	−20.0316			−0.0252606
$794$	471.053			0.593266
$795$	−7.86117	−	6.43491i	−0.00988826	−	0.00809423i
$796$		−	25.5402i		−	0.0320856i
$797$	−711.412			−0.892613			−0.446306	−	0.894880i	$-0.647261\pi$
$797$	−711.412			−0.892613			−0.446306	+	0.894880i	$0.647261\pi$
$798$			251.275i			0.314882i
$799$		−	332.926i		−	0.416678i
$800$	138.634	−	27.9399i	0.173292	−	0.0349249i
$801$			43.4635i			0.0542615i
$802$	704.666			0.878635
$803$	72.8756			0.0907542
$804$			434.591i			0.540536i
$805$	−218.643	+	454.925i	−0.271607	+	0.565124i
$806$	72.7691			0.0902842
$807$			120.772i			0.149656i
$808$			246.481i			0.305051i
$809$	−208.458			−0.257674			−0.128837	−	0.991666i	$-0.541124\pi$
$809$	−208.458			−0.257674			−0.128837	+	0.991666i	$0.541124\pi$
$810$	49.2450	+	40.3104i	0.0607963	+	0.0497660i
$811$	1248.40			1.53934			0.769668	−	0.638445i	$-0.220422\pi$
$811$	1248.40			1.53934			0.769668	+	0.638445i	$0.220422\pi$
$812$	−73.6103			−0.0906531
$813$		−	616.765i		−	0.758628i
$814$	204.065			0.250694
$815$	−1058.32	−	866.312i	−1.29856	−	1.06296i
$816$		−	27.1635i		−	0.0332886i
$817$			379.461i			0.464456i
$818$			587.177i			0.717820i
$819$			20.8289i			0.0254322i
$820$	429.341	−	524.502i	0.523587	−	0.639636i
$821$	988.320			1.20380			0.601900	−	0.798572i	$-0.294411\pi$
$821$	988.320			1.20380			0.601900	+	0.798572i	$0.294411\pi$
$822$	279.166			0.339618
$823$		−	672.949i		−	0.817677i	−0.912607	−	0.408839i	$-0.865934\pi$
$823$		−	672.949i		−	0.817677i	0.912607	−	0.408839i	$-0.134066\pi$
$824$		−	383.470i		−	0.465376i
$825$	−24.7779	−	122.944i	−0.0300338	−	0.149024i
$826$			639.442i			0.774143i
$827$	1421.35			1.71868			0.859339	−	0.511406i	$-0.170875\pi$
$827$	1421.35			1.71868			0.859339	+	0.511406i	$0.170875\pi$
$828$	134.112	−	32.5271i	0.161971	−	0.0392839i
$829$	−1150.45			−1.38775			−0.693875	−	0.720095i	$-0.744098\pi$
$829$	−1150.45			−1.38775			−0.693875	+	0.720095i	$0.744098\pi$
$830$	602.889	+	493.506i	0.726372	+	0.594586i
$831$	−65.8472			−0.0792385
$832$		−	12.6551i		−	0.0152105i
$833$	−116.588			−0.139961
$834$	496.726			0.595595
$835$	241.595	+	197.762i	0.289336	+	0.236841i
$836$	−135.391			−0.161951
$837$		−	169.020i		−	0.201935i
$838$	−420.253			−0.501495
$839$			967.070i			1.15265i	0.817222	+	0.576323i	$0.195513\pi$
$839$			967.070i			1.15265i	−0.817222	+	0.576323i	$0.804487\pi$
$840$	68.0981	−	83.1916i	0.0810691	−	0.0990376i
$841$	−770.680			−0.916385
$842$	398.183			0.472901
$843$	−538.884			−0.639246
$844$	169.731			0.201103
$845$	527.312	−	644.188i	0.624038	−	0.762353i
$846$	−360.262			−0.425842
$847$	−494.254			−0.583535
$848$	4.69226			0.00553332
$849$		−	184.245i		−	0.217014i
$850$	135.886	−	27.3861i	0.159866	−	0.0322189i
$851$	−1113.56	+	270.080i	−1.30853	+	0.317368i
$852$		−	95.1342i		−	0.111660i
$853$			885.948i			1.03863i	0.854584	+	0.519313i	$0.173812\pi$
$853$			885.948i			1.03863i	−0.854584	+	0.519313i	$0.826188\pi$
$854$	78.6003			0.0920378
$855$	271.288	+	222.068i	0.317296	+	0.259729i
$856$			352.654i			0.411979i
$857$		−	219.985i		−	0.256692i	−0.991729	−	0.128346i	$-0.959033\pi$
$857$		−	219.985i		−	0.256692i	0.991729	−	0.128346i	$-0.0409668\pi$
$858$	−11.2229			−0.0130803
$859$	−248.800			−0.289639			−0.144820	−	0.989458i	$-0.546260\pi$
$859$	−248.800			−0.289639			−0.144820	+	0.989458i	$0.546260\pi$
$860$	102.838	−	125.631i	0.119579	−	0.146082i
$861$		−	515.279i		−	0.598465i
$862$	1106.49			1.28364
$863$		−	730.096i		−	0.845998i	−0.906130	−	0.422999i	$-0.860977\pi$
$863$		−	730.096i		−	0.845998i	0.906130	−	0.422999i	$-0.139023\pi$
$864$	−29.3939			−0.0340207
$865$	724.452	+	593.014i	0.837516	+	0.685565i
$866$			217.445i			0.251091i
$867$			473.938i			0.546641i
$868$	−285.532			−0.328954
$869$	73.8574			0.0849912
$870$	−65.0541	+	79.4730i	−0.0747749	+	0.0913482i
$871$			198.457i			0.227850i
$872$	−282.335			−0.323779
$873$	191.888			0.219803
$874$	738.816	−	179.190i	0.845327	−	0.205023i
$875$	484.824	+	256.789i	0.554084	+	0.293473i
$876$	87.1604			0.0994981
$877$			1341.09i			1.52918i	0.644514	+	0.764592i	$0.277060\pi$
$877$			1341.09i			1.52918i	−0.644514	+	0.764592i	$0.722940\pi$
$878$		−	630.875i		−	0.718536i
$879$		−	407.835i		−	0.463976i
$880$	44.8248	+	36.6922i	0.0509373	+	0.0416957i
$881$		−	168.776i		−	0.191573i	−0.995402	−	0.0957864i	$-0.969463\pi$
$881$		−	168.776i		−	0.191573i	0.995402	−	0.0957864i	$-0.0305366\pi$
$882$			126.161i			0.143039i
$883$		−	516.266i		−	0.584673i	−0.956316	−	0.292336i	$-0.905567\pi$
$883$		−	516.266i		−	0.584673i	0.956316	−	0.292336i	$-0.0944327\pi$
$884$		−	12.4043i		−	0.0140320i
$885$	690.370	+	565.116i	0.780079	+	0.638549i
$886$	1026.95			1.15908
$887$			531.793i			0.599541i	0.954011	+	0.299771i	$0.0969102\pi$
$887$			531.793i			0.599541i	−0.954011	+	0.299771i	$0.903090\pi$
$888$	244.064			0.274847
$889$		−	395.138i		−	0.444474i
$890$	64.8901	−	79.2725i	0.0729102	−	0.0890702i
$891$			26.0673i			0.0292562i
$892$		−	88.0624i		−	0.0987246i
$893$	−1984.67			−2.22247
$894$		−	217.468i		−	0.243253i
$895$	−478.435	+	584.477i	−0.534564	+	0.653047i
$896$			49.6563i			0.0554200i
$897$	61.2425	−	14.8536i	0.0682749	−	0.0165592i
$898$			167.463i			0.186484i
$899$	272.769			0.303413
$900$	−29.6347	−	147.043i	−0.0329275	−	0.163382i
$901$	4.59925			0.00510461
$902$	277.639			0.307804
$903$		−	123.422i		−	0.136680i
$904$			123.636i			0.136766i
$905$	1141.98	+	934.787i	1.26185	+	1.03291i
$906$	261.223			0.288325
$907$	842.943			0.929375			0.464687	−	0.885475i	$-0.346167\pi$
$907$	842.943			0.929375			0.464687	+	0.885475i	$0.346167\pi$
$908$	686.300			0.755837
$909$	261.433			0.287605
$910$	31.0972	−	37.9897i	0.0341727	−	0.0417469i
$911$			1240.10i			1.36125i	0.732631	+	0.680626i	$0.238292\pi$
$911$			1240.10i			1.36125i	−0.732631	+	0.680626i	$0.761708\pi$
$912$	−161.929			−0.177554
$913$			319.133i			0.349543i
$914$			39.4575i			0.0431701i
$915$	69.4641	−	84.8604i	0.0759170	−	0.0927436i
$916$		−	108.887i		−	0.118872i
$917$	−559.649			−0.610304
$918$	−28.8112			−0.0313848
$919$		−	293.548i		−	0.319421i	−0.987164	−	0.159711i	$-0.948944\pi$
$919$		−	293.548i		−	0.319421i	0.987164	−	0.159711i	$-0.0510561\pi$
$920$	−293.167	−	140.900i	−0.318660	−	0.153153i
$921$	−60.9789			−0.0662094
$922$			541.399i			0.587201i
$923$		−	43.4433i		−	0.0470675i
$924$	44.0366			0.0476587
$925$	246.064	+	1220.94i	0.266015	+	1.31993i
$926$	82.1297			0.0886930
$927$	−406.731			−0.438761
$928$		−	47.4367i		−	0.0511171i
$929$	326.931			0.351917			0.175959	−	0.984398i	$-0.443698\pi$
$929$	326.931			0.351917			0.175959	+	0.984398i	$0.443698\pi$
$930$	−252.343	+	308.273i	−0.271336	+	0.331476i
$931$			695.013i			0.746523i
$932$		−	236.267i		−	0.253505i
$933$			301.743i			0.323412i
$934$		−	544.263i		−	0.582723i
$935$	43.9363	+	35.9649i	0.0469907	+	0.0384651i
$936$	−13.4228			−0.0143406
$937$	364.741			0.389265			0.194632	−	0.980876i	$-0.437649\pi$
$937$	364.741			0.389265			0.194632	+	0.980876i	$0.437649\pi$
$938$		−	778.708i		−	0.830179i
$939$		−	368.782i		−	0.392739i
$940$	657.078	+	537.864i	0.699019	+	0.572195i
$941$			114.607i			0.121793i	0.998144	+	0.0608964i	$0.0193959\pi$
$941$			114.607i			0.121793i	−0.998144	+	0.0608964i	$0.980604\pi$
$942$	82.3437			0.0874137
$943$	−1515.05	+	367.457i	−1.60663	+	0.389668i
$944$	−412.075			−0.436521
$945$	−88.2380	−	72.2289i	−0.0933736	−	0.0764327i
$946$	66.5014			0.0702975
$947$		−	352.179i		−	0.371889i	−0.982560	−	0.185945i	$-0.940466\pi$
$947$		−	352.179i		−	0.371889i	0.982560	−	0.185945i	$-0.0595345\pi$
$948$	88.3346			0.0931799
$949$	39.8020			0.0419410
$950$	−163.256	−	810.055i	−0.171849	−	0.852690i
$951$	382.427			0.402131
$952$			48.6720i			0.0511261i
$953$	−1802.34			−1.89123			−0.945614	−	0.325290i	$-0.894538\pi$
$953$	−1802.34			−1.89123			−0.945614	+	0.325290i	$0.894538\pi$
$954$		−	4.97689i		−	0.00521687i
$955$	−1315.17	−	1076.56i	−1.37714	−	1.12728i
$956$	−68.2167			−0.0713564
$957$	−42.0682			−0.0439584
$958$	−788.798			−0.823380
$959$	−500.214			−0.521600
$960$	53.6112	+	43.8844i	0.0558450	+	0.0457130i
$961$	97.0602			0.100999
$962$	111.453			0.115855
$963$	374.046			0.388418
$964$			303.463i			0.314795i
$965$	795.444	+	651.126i	0.824294	+	0.674742i
$966$	−240.304	+	58.2826i	−0.248762	+	0.0603340i
$967$			402.567i			0.416305i	0.978096	+	0.208152i	$0.0667450\pi$
$967$			402.567i			0.416305i	−0.978096	+	0.208152i	$0.933255\pi$
$968$		−	318.512i		−	0.329041i
$969$	−158.720			−0.163797
$970$	−349.983	−	286.485i	−0.360807	−	0.295346i
$971$		−	1053.48i		−	1.08494i	−0.840075	−	0.542470i	$-0.817489\pi$
$971$		−	1053.48i		−	1.08494i	0.840075	−	0.542470i	$-0.182511\pi$
$972$			31.1769i			0.0320750i
$973$	−890.042			−0.914740
$974$	920.856			0.945438
$975$	−13.5328	−	67.1478i	−0.0138798	−	0.0688695i
$976$			50.6524i			0.0518979i
$977$	1151.57			1.17868			0.589341	−	0.807884i	$-0.299387\pi$
$977$	1151.57			1.17868			0.589341	+	0.807884i	$0.299387\pi$
$978$		−	670.024i		−	0.685096i
$979$	41.9621			0.0428622
$980$	188.355	−	230.103i	0.192199	−	0.234799i
$981$			299.462i			0.305262i
$982$			696.912i			0.709687i
$983$	−583.591			−0.593683			−0.296842	−	0.954927i	$-0.595933\pi$
$983$	−583.591			−0.593683			−0.296842	+	0.954927i	$0.595933\pi$
$984$	332.061			0.337460
$985$	−927.001	−	758.814i	−0.941117	−	0.770370i
$986$		−	46.4964i		−	0.0471566i
$987$	645.524			0.654026
$988$	−73.9455			−0.0748436
$989$	−362.892	+	88.0148i	−0.366929	+	0.0889938i
$990$	38.9180	−	47.5439i	0.0393111	−	0.0480241i
$991$	−970.432			−0.979245			−0.489622	−	0.871935i	$-0.662865\pi$
$991$	−970.432			−0.979245			−0.489622	+	0.871935i	$0.662865\pi$
$992$		−	184.005i		−	0.185489i
$993$		−	568.148i		−	0.572154i
$994$			170.463i			0.171492i
$995$	49.4081	+	40.4440i	0.0496564	+	0.0406472i
$996$			381.688i			0.383221i
$997$		−	418.055i		−	0.419312i	−0.977775	−	0.209656i	$-0.932766\pi$
$997$		−	418.055i		−	0.419312i	0.977775	−	0.209656i	$-0.0672345\pi$
$998$			715.728i			0.717162i
$999$		−	258.869i		−	0.259129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.24	yes	48
5.4	even	2	inner	690.3.f.a.229.21	✓	48
23.22	odd	2	inner	690.3.f.a.229.23	yes	48
115.114	odd	2	inner	690.3.f.a.229.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.21	✓	48	5.4	even	2	inner
690.3.f.a.229.22	yes	48	115.114	odd	2	inner
690.3.f.a.229.23	yes	48	23.22	odd	2	inner
690.3.f.a.229.24	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(3.16709 - 3.86905i) q^{5} +2.44949 q^{6} -4.38904 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(3.16709 - 3.86905i) q^{5} +2.44949 q^{6} -4.38904 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(5.47167 + 4.47894i) q^{10} +2.89637i q^{11} +3.46410i q^{12} +1.58189i q^{13} -6.20704i q^{14} +(-6.70139 - 5.48556i) q^{15} +4.00000 q^{16} +3.92071 q^{17} -4.24264i q^{18} -23.3725i q^{19} +(-6.33417 + 7.73810i) q^{20} +7.60204i q^{21} -4.09608 q^{22} +(22.3520 - 5.42118i) q^{23} -4.89898 q^{24} +(-4.93912 - 24.5072i) q^{25} -2.23713 q^{26} +5.19615i q^{27} +8.77808 q^{28} -8.38570 q^{29} +(7.75775 - 9.47720i) q^{30} -32.5278 q^{31} +5.65685i q^{32} +5.01666 q^{33} +5.54473i q^{34} +(-13.9005 + 16.9814i) q^{35} +6.00000 q^{36} -49.8194 q^{37} +33.0537 q^{38} +2.73992 q^{39} +(-10.9433 - 8.95787i) q^{40} -67.7817 q^{41} -10.7509 q^{42} -16.2354 q^{43} -5.79274i q^{44} +(-9.50126 + 11.6072i) q^{45} +(7.66671 + 31.6105i) q^{46} -84.9146i q^{47} -6.92820i q^{48} -29.7363 q^{49} +(34.6585 - 6.98497i) q^{50} -6.79088i q^{51} -3.16378i q^{52} +1.17306 q^{53} -7.34847 q^{54} +(11.2062 + 9.17305i) q^{55} +12.4141i q^{56} -40.4824 q^{57} -11.8592i q^{58} -103.019 q^{59} +(13.4028 + 10.9711i) q^{60} +12.6631i q^{61} -46.0013i q^{62} +13.1671 q^{63} -8.00000 q^{64} +(6.12042 + 5.00999i) q^{65} +7.09463i q^{66} +125.456 q^{67} -7.84143 q^{68} +(-9.38976 - 38.7148i) q^{69} +(-24.0153 - 19.6582i) q^{70} -27.4629 q^{71} +8.48528i q^{72} -25.1610i q^{73} -70.4553i q^{74} +(-42.4478 + 8.55481i) q^{75} +46.7450i q^{76} -12.7123i q^{77} +3.87483i q^{78} -25.5000i q^{79} +(12.6683 - 15.4762i) q^{80} +9.00000 q^{81} -95.8578i q^{82} +110.184 q^{83} -15.2041i q^{84} +(12.4172 - 15.1694i) q^{85} -22.9603i q^{86} +14.5245i q^{87} +8.19217 q^{88} -14.4878i q^{89} +(-16.4150 - 13.4368i) q^{90} -6.94298i q^{91} +(-44.7039 + 10.8424i) q^{92} +56.3399i q^{93} +120.087 q^{94} +(-90.4294 - 74.0227i) q^{95} +9.79796 q^{96} -63.9628 q^{97} -42.0535i q^{98} -8.68911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 96 * q^4 - 144 * q^9	\( 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) \) 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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