LMFDB - Embedded newform 690.3.f.a.229.46

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			229.46
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.95471 - 0.671486i) q^{5} +2.44949 q^{6} +12.0941 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.95471 - 0.671486i) q^{5} +2.44949 q^{6} +12.0941 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(-0.949624 - 7.00701i) q^{10} +20.5287i q^{11} -3.46410i q^{12} +13.6717i q^{13} -17.1037i q^{14} +(1.16305 + 8.58180i) q^{15} +4.00000 q^{16} +0.319227 q^{17} +4.24264i q^{18} -6.05163i q^{19} +(-9.90941 + 1.34297i) q^{20} +20.9477i q^{21} +29.0320 q^{22} +(-20.7175 + 9.98930i) q^{23} -4.89898 q^{24} +(24.0982 - 6.65403i) q^{25} +19.3347 q^{26} -5.19615i q^{27} -24.1883 q^{28} -6.76339 q^{29} +(12.1365 - 1.64480i) q^{30} -30.6209 q^{31} -5.65685i q^{32} -35.5568 q^{33} -0.451455i q^{34} +(59.9229 - 8.12105i) q^{35} +6.00000 q^{36} -71.2469 q^{37} -8.55830 q^{38} -23.6800 q^{39} +(1.89925 + 14.0140i) q^{40} +12.7925 q^{41} +29.6245 q^{42} +0.0776096 q^{43} -41.0575i q^{44} +(-14.8641 + 2.01446i) q^{45} +(14.1270 + 29.2989i) q^{46} +35.9738i q^{47} +6.92820i q^{48} +97.2684 q^{49} +(-9.41022 - 34.0800i) q^{50} +0.552917i q^{51} -27.3433i q^{52} +11.2637 q^{53} -7.34847 q^{54} +(13.7848 + 101.714i) q^{55} +34.2074i q^{56} +10.4817 q^{57} +9.56487i q^{58} +47.3445 q^{59} +(-2.32609 - 17.1636i) q^{60} -42.0557i q^{61} +43.3045i q^{62} -36.2824 q^{63} -8.00000 q^{64} +(9.18033 + 67.7391i) q^{65} +50.2849i q^{66} +75.9168 q^{67} -0.638454 q^{68} +(-17.3020 - 35.8837i) q^{69} +(-11.4849 - 84.7438i) q^{70} +104.642 q^{71} -8.48528i q^{72} -107.046i q^{73} +100.758i q^{74} +(11.5251 + 41.7393i) q^{75} +12.1033i q^{76} +248.278i q^{77} +33.4886i q^{78} +68.2847i q^{79} +(19.8188 - 2.68594i) q^{80} +9.00000 q^{81} -18.0913i q^{82} +103.809 q^{83} -41.8954i q^{84} +(1.58167 - 0.214356i) q^{85} -0.109757i q^{86} -11.7145i q^{87} -58.0640 q^{88} -50.8054i q^{89} +(2.84887 + 21.0210i) q^{90} +165.347i q^{91} +(41.4350 - 19.9786i) q^{92} -53.0370i q^{93} +50.8747 q^{94} +(-4.06358 - 29.9841i) q^{95} +9.79796 q^{96} +39.8613 q^{97} -137.558i q^{98} -61.5862i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	4.95471	−	0.671486i	0.990941	−	0.134297i
$5$	4.95471	−	0.671486i	0.990941	−	0.134297i
$6$	2.44949			0.408248
$7$	12.0941			1.72774			0.863868	−	0.503719i	$-0.168035\pi$
$7$	12.0941			1.72774			0.863868	+	0.503719i	$0.168035\pi$
$8$			2.82843i			0.353553i
$9$	−3.00000			−0.333333
$10$	−0.949624	−	7.00701i	−0.0949624	−	0.700701i
$11$			20.5287i			1.86625i	0.359554	+	0.933124i	$0.382929\pi$
$11$			20.5287i			1.86625i	−0.359554	+	0.933124i	$0.617071\pi$
$12$		−	3.46410i		−	0.288675i
$13$			13.6717i			1.05167i	0.850588	+	0.525833i	$0.176246\pi$
$13$			13.6717i			1.05167i	−0.850588	+	0.525833i	$0.823754\pi$
$14$		−	17.1037i		−	1.22169i
$15$	1.16305	+	8.58180i	0.0775365	+	0.572120i
$16$	4.00000			0.250000
$17$	0.319227			0.0187780			0.00938902	−	0.999956i	$-0.497011\pi$
$17$	0.319227			0.0187780			0.00938902	+	0.999956i	$0.497011\pi$
$18$			4.24264i			0.235702i
$19$		−	6.05163i		−	0.318507i	−0.987238	−	0.159253i	$-0.949091\pi$
$19$		−	6.05163i		−	0.318507i	0.987238	−	0.159253i	$-0.0509087\pi$
$20$	−9.90941	+	1.34297i	−0.495471	+	0.0671486i
$21$			20.9477i			0.997508i
$22$	29.0320			1.31964
$23$	−20.7175	+	9.98930i	−0.900760	+	0.434318i
$23$	−20.7175	+	9.98930i	−0.900760	+	0.434318i
$24$	−4.89898			−0.204124
$25$	24.0982	−	6.65403i	0.963929	−	0.266161i
$26$	19.3347			0.743641
$27$		−	5.19615i		−	0.192450i
$28$	−24.1883			−0.863868
$29$	−6.76339			−0.233220			−0.116610	−	0.993178i	$-0.537203\pi$
$29$	−6.76339			−0.233220			−0.116610	+	0.993178i	$0.537203\pi$
$30$	12.1365	−	1.64480i	0.404550	−	0.0548266i
$31$	−30.6209			−0.987771			−0.493886	−	0.869527i	$-0.664424\pi$
$31$	−30.6209			−0.987771			−0.493886	+	0.869527i	$0.664424\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−35.5568			−1.07748
$34$		−	0.451455i		−	0.0132781i
$35$	59.9229	−	8.12105i	1.71208	−	0.232030i
$36$	6.00000			0.166667
$37$	−71.2469			−1.92559			−0.962795	−	0.270232i	$-0.912900\pi$
$37$	−71.2469			−1.92559			−0.962795	+	0.270232i	$0.912900\pi$
$38$	−8.55830			−0.225218
$39$	−23.6800			−0.607180
$40$	1.89925	+	14.0140i	0.0474812	+	0.350351i
$41$	12.7925			0.312012			0.156006	−	0.987756i	$-0.450138\pi$
$41$	12.7925			0.312012			0.156006	+	0.987756i	$0.450138\pi$
$42$	29.6245			0.705345
$43$	0.0776096			0.00180487			0.000902437	−	1.00000i	$-0.499713\pi$
$43$	0.0776096			0.00180487			0.000902437		1.00000i	$0.499713\pi$
$44$		−	41.0575i		−	0.933124i
$45$	−14.8641	+	2.01446i	−0.330314	+	0.0447657i
$46$	14.1270	+	29.2989i	0.307109	+	0.636933i
$47$			35.9738i			0.765400i	0.923873	+	0.382700i	$0.125006\pi$
$47$			35.9738i			0.765400i	−0.923873	+	0.382700i	$0.874994\pi$
$48$			6.92820i			0.144338i
$49$	97.2684			1.98507
$50$	−9.41022	−	34.0800i	−0.188204	−	0.681600i
$51$			0.552917i			0.0108415i
$52$		−	27.3433i		−	0.525833i
$53$	11.2637			0.212522			0.106261	−	0.994338i	$-0.466112\pi$
$53$	11.2637			0.212522			0.106261	+	0.994338i	$0.466112\pi$
$54$	−7.34847			−0.136083
$55$	13.7848	+	101.714i	0.250632	+	1.84934i
$56$			34.2074i			0.610847i
$57$	10.4817			0.183890
$58$			9.56487i			0.164912i
$59$	47.3445			0.802449			0.401224	−	0.915980i	$-0.368585\pi$
$59$	47.3445			0.802449			0.401224	+	0.915980i	$0.368585\pi$
$60$	−2.32609	−	17.1636i	−0.0387682	−	0.286060i
$61$		−	42.0557i		−	0.689438i	−0.938706	−	0.344719i	$-0.887974\pi$
$61$		−	42.0557i		−	0.689438i	0.938706	−	0.344719i	$-0.112026\pi$
$62$			43.3045i			0.698460i
$63$	−36.2824			−0.575912
$64$	−8.00000			−0.125000
$65$	9.18033	+	67.7391i	0.141236	+	1.04214i
$66$			50.2849i			0.761893i
$67$	75.9168			1.13309			0.566543	−	0.824032i	$-0.308281\pi$
$67$	75.9168			1.13309			0.566543	+	0.824032i	$0.308281\pi$
$68$	−0.638454			−0.00938902
$69$	−17.3020	−	35.8837i	−0.250753	−	0.520054i
$70$	−11.4849	−	84.7438i	−0.164070	−	1.21063i
$71$	104.642			1.47384			0.736918	−	0.675982i	$-0.236280\pi$
$71$	104.642			1.47384			0.736918	+	0.675982i	$0.236280\pi$
$72$		−	8.48528i		−	0.117851i
$73$		−	107.046i		−	1.46638i	−0.680025	−	0.733189i	$-0.738031\pi$
$73$		−	107.046i		−	1.46638i	0.680025	−	0.733189i	$-0.261969\pi$
$74$			100.758i			1.36160i
$75$	11.5251	+	41.7393i	0.153668	+	0.556524i
$76$			12.1033i			0.159253i
$77$			248.278i			3.22438i
$78$			33.4886i			0.429341i
$79$			68.2847i			0.864364i	0.901786	+	0.432182i	$0.142256\pi$
$79$			68.2847i			0.864364i	−0.901786	+	0.432182i	$0.857744\pi$
$80$	19.8188	−	2.68594i	0.247735	−	0.0335743i
$81$	9.00000			0.111111
$82$		−	18.0913i		−	0.220626i
$83$	103.809			1.25071			0.625357	−	0.780339i	$-0.284953\pi$
$83$	103.809			1.25071			0.625357	+	0.780339i	$0.284953\pi$
$84$		−	41.8954i		−	0.498754i
$85$	1.58167	−	0.214356i	0.0186079	−	0.00252184i
$86$		−	0.109757i		−	0.00127624i
$87$		−	11.7145i		−	0.134650i
$88$	−58.0640			−0.659819
$89$		−	50.8054i		−	0.570847i	−0.958402	−	0.285423i	$-0.907866\pi$
$89$		−	50.8054i		−	0.570847i	0.958402	−	0.285423i	$-0.0921342\pi$
$90$	2.84887	+	21.0210i	0.0316541	+	0.233567i
$91$			165.347i			1.81700i
$92$	41.4350	−	19.9786i	0.450380	−	0.217159i
$93$		−	53.0370i		−	0.570290i
$94$	50.8747			0.541220
$95$	−4.06358	−	29.9841i	−0.0427746	−	0.315622i
$96$	9.79796			0.102062
$97$	39.8613			0.410941			0.205471	−	0.978663i	$-0.434128\pi$
$97$	39.8613			0.410941			0.205471	+	0.978663i	$0.434128\pi$
$98$		−	137.558i		−	1.40366i
$99$		−	61.5862i		−	0.622083i
$100$	−48.1964	+	13.3081i	−0.481964	+	0.133081i
$101$	148.892			1.47418			0.737090	−	0.675795i	$-0.236199\pi$
$101$	148.892			1.47418			0.737090	+	0.675795i	$0.236199\pi$
$102$	0.781943			0.00766610
$103$	22.1086			0.214646			0.107323	−	0.994224i	$-0.465772\pi$
$103$	22.1086			0.214646			0.107323	+	0.994224i	$0.465772\pi$
$104$	−38.6693			−0.371820
$105$	14.0661	+	103.790i	0.133963	+	0.988472i
$106$		−	15.9292i		−	0.150276i
$107$	−107.230			−1.00215			−0.501076	−	0.865403i	$-0.667062\pi$
$107$	−107.230			−1.00215			−0.501076	+	0.865403i	$0.667062\pi$
$108$			10.3923i			0.0962250i
$109$		−	128.876i		−	1.18234i	−0.806545	−	0.591172i	$-0.798665\pi$
$109$		−	128.876i		−	1.18234i	0.806545	−	0.591172i	$-0.201335\pi$
$110$	143.845	−	19.4946i	1.30768	−	0.177223i
$111$		−	123.403i		−	1.11174i
$112$	48.3766			0.431934
$113$	−133.471			−1.18116			−0.590579	−	0.806979i	$-0.701101\pi$
$113$	−133.471			−1.18116			−0.590579	+	0.806979i	$0.701101\pi$
$114$		−	14.8234i		−	0.130030i
$115$	−95.9413	+	63.4055i	−0.834272	+	0.551353i
$116$	13.5268			0.116610
$117$		−	41.0150i		−	0.350556i
$118$		−	66.9552i		−	0.567417i
$119$	3.86078			0.0324435
$120$	−24.2730	+	3.28959i	−0.202275	+	0.0274133i
$121$	−300.429			−2.48288
$122$	−59.4757			−0.487506
$123$			22.1573i			0.180140i
$124$	61.2418			0.493886
$125$	114.931	−	49.1504i	0.919452	−	0.393203i
$126$			51.3111i			0.407231i
$127$		−	224.615i		−	1.76862i	−0.466896	−	0.884312i	$-0.654628\pi$
$127$		−	224.615i		−	1.76862i	0.466896	−	0.884312i	$-0.345372\pi$
$128$			11.3137i			0.0883883i
$129$			0.134424i			0.00104204i
$130$	95.7975	−	12.9829i	0.736904	−	0.0998688i
$131$	−18.3056			−0.139738			−0.0698688	−	0.997556i	$-0.522258\pi$
$131$	−18.3056			−0.139738			−0.0698688	+	0.997556i	$0.522258\pi$
$132$	71.1136			0.538740
$133$		−	73.1893i		−	0.550296i
$134$		−	107.363i		−	0.801213i
$135$	−3.48914	−	25.7454i	−0.0258455	−	0.190707i
$136$			0.902910i			0.00663904i
$137$	−63.2308			−0.461539			−0.230769	−	0.973008i	$-0.574124\pi$
$137$	−63.2308			−0.461539			−0.230769	+	0.973008i	$0.574124\pi$
$138$	−50.7472	+	24.4687i	−0.367734	+	0.177309i
$139$	−7.37996			−0.0530932			−0.0265466	−	0.999648i	$-0.508451\pi$
$139$	−7.37996			−0.0530932			−0.0265466	+	0.999648i	$0.508451\pi$
$140$	−119.846	+	16.2421i	−0.856042	+	0.116015i
$141$	−62.3085			−0.441904
$142$		−	147.987i		−	1.04216i
$143$	−280.662			−1.96267
$144$	−12.0000			−0.0833333
$145$	−33.5106	+	4.54152i	−0.231108	+	0.0313208i
$146$	−151.385			−1.03689
$147$			168.474i			1.14608i
$148$	142.494			0.962795
$149$			248.032i			1.66464i	0.554295	+	0.832321i	$0.312988\pi$
$149$			248.032i			1.66464i	−0.554295	+	0.832321i	$0.687012\pi$
$150$	59.0283	−	16.2990i	0.393522	−	0.108660i
$151$	91.1561			0.603683			0.301841	−	0.953358i	$-0.402399\pi$
$151$	91.1561			0.603683			0.301841	+	0.953358i	$0.402399\pi$
$152$	17.1166			0.112609
$153$	−0.957680			−0.00625935
$154$	351.117			2.27998
$155$	−151.718	+	20.5615i	−0.978823	+	0.132655i
$156$	47.3600			0.303590
$157$	195.178			1.24317			0.621587	−	0.783345i	$-0.286488\pi$
$157$	195.178			1.24317			0.621587	+	0.783345i	$0.286488\pi$
$158$	96.5692			0.611197
$159$			19.5092i			0.122700i
$160$	−3.79850	−	28.0280i	−0.0237406	−	0.175175i
$161$	−250.560	+	120.812i	−1.55627	+	0.750386i
$162$		−	12.7279i		−	0.0785674i
$163$		−	265.545i		−	1.62911i	−0.580087	−	0.814555i	$-0.696981\pi$
$163$		−	265.545i		−	1.62911i	0.580087	−	0.814555i	$-0.303019\pi$
$164$	−25.5850			−0.156006
$165$	−176.174	+	23.8759i	−1.06772	+	0.144702i
$166$		−	146.808i		−	0.884388i
$167$		−	171.565i		−	1.02733i	−0.857990	−	0.513667i	$-0.828287\pi$
$167$		−	171.565i		−	1.02733i	0.857990	−	0.513667i	$-0.171713\pi$
$168$	−59.2490			−0.352672
$169$	−17.9144			−0.106003
$170$	−0.303145	−	2.23683i	−0.00178321	−	0.0131578i
$171$			18.1549i			0.106169i
$172$	−0.155219			−0.000902437
$173$			88.8667i			0.513681i	0.966454	+	0.256840i	$0.0826814\pi$
$173$			88.8667i			0.513681i	−0.966454	+	0.256840i	$0.917319\pi$
$174$	−16.5668			−0.0952118
$175$	291.447	−	80.4748i	1.66541	−	0.459856i
$176$			82.1149i			0.466562i
$177$			82.0030i			0.463294i
$178$	−71.8497			−0.403650
$179$	204.622			1.14314			0.571570	−	0.820553i	$-0.306334\pi$
$179$	204.622			1.14314			0.571570	+	0.820553i	$0.306334\pi$
$180$	29.7282	−	4.02891i	0.165157	−	0.0223829i
$181$			23.8445i			0.131738i	0.997828	+	0.0658689i	$0.0209819\pi$
$181$			23.8445i			0.131738i	−0.997828	+	0.0658689i	$0.979018\pi$
$182$	233.836			1.28481
$183$	72.8426			0.398047
$184$	−28.2540	−	58.5979i	−0.153554	−	0.318467i
$185$	−353.007	+	47.8412i	−1.90815	+	0.258601i
$186$	−75.0056			−0.403256
$187$			6.55332i			0.0350445i
$188$		−	71.9476i		−	0.382700i
$189$		−	62.8430i		−	0.332503i
$190$	−42.4039	+	5.74678i	−0.223178	+	0.0302462i
$191$		−	176.236i		−	0.922701i	−0.887218	−	0.461351i	$-0.847365\pi$
$191$		−	176.236i		−	0.922701i	0.887218	−	0.461351i	$-0.152635\pi$
$192$		−	13.8564i		−	0.0721688i
$193$			185.881i			0.963112i	0.876415	+	0.481556i	$0.159928\pi$
$193$			185.881i			0.963112i	−0.876415	+	0.481556i	$0.840072\pi$
$194$		−	56.3724i		−	0.290579i
$195$	−117.328	+	15.9008i	−0.601680	+	0.0815425i
$196$	−194.537			−0.992534
$197$			234.176i			1.18871i	0.804203	+	0.594355i	$0.202592\pi$
$197$			234.176i			1.18871i	−0.804203	+	0.594355i	$0.797408\pi$
$198$	−87.0960			−0.439879
$199$		−	322.699i		−	1.62160i	−0.585322	−	0.810801i	$-0.699032\pi$
$199$		−	322.699i		−	1.62160i	0.585322	−	0.810801i	$-0.300968\pi$
$200$	18.8204	+	68.1600i	0.0941022	+	0.340800i
$201$			131.492i			0.654187i
$202$		−	210.565i		−	1.04240i
$203$	−81.7974			−0.402943
$204$		−	1.10583i		−	0.00542075i
$205$	63.3831	−	8.58998i	0.309186	−	0.0419024i
$206$		−	31.2662i		−	0.151778i
$207$	62.1524	−	29.9679i	0.300253	−	0.144773i
$208$			54.6867i			0.262917i
$209$	124.232			0.594413
$210$	146.781	−	19.8924i	0.698955	−	0.0947258i
$211$	376.722			1.78541			0.892707	−	0.450638i	$-0.148804\pi$
$211$	376.722			1.78541			0.892707	+	0.450638i	$0.148804\pi$
$212$	−22.5273			−0.106261
$213$			181.246i			0.850919i
$214$			151.646i			0.708628i
$215$	0.384533	−	0.0521137i	0.00178852	−	0.000242390i
$216$	14.6969			0.0680414
$217$	−370.334			−1.70661
$218$	−182.258			−0.836044
$219$	185.408			0.846613
$220$	−27.5695	−	203.428i	−0.125316	−	0.924671i
$221$			4.36436i			0.0197482i
$222$	−174.518			−0.786119
$223$			183.455i			0.822670i	0.911484	+	0.411335i	$0.134937\pi$
$223$			183.455i			0.822670i	−0.911484	+	0.411335i	$0.865063\pi$
$224$		−	68.4148i		−	0.305423i
$225$	−72.2946	+	19.9621i	−0.321310	+	0.0887204i
$226$			188.756i			0.835205i
$227$	122.555			0.539889			0.269945	−	0.962876i	$-0.412995\pi$
$227$	122.555			0.539889			0.269945	+	0.962876i	$0.412995\pi$
$228$	−20.9635			−0.0919450
$229$		−	361.955i		−	1.58059i	−0.612728	−	0.790294i	$-0.709928\pi$
$229$		−	361.955i		−	1.58059i	0.612728	−	0.790294i	$-0.290072\pi$
$230$	89.6690	+	135.682i	0.389865	+	0.589920i
$231$	−430.029			−1.86160
$232$		−	19.1297i		−	0.0824558i
$233$			273.642i			1.17443i	0.809432	+	0.587214i	$0.199775\pi$
$233$			273.642i			1.17443i	−0.809432	+	0.587214i	$0.800225\pi$
$234$	−58.0040			−0.247880
$235$	24.1559	+	178.240i	0.102791	+	0.758467i
$236$	−94.6889			−0.401224
$237$	−118.273			−0.499041
$238$		−	5.45996i		−	0.0229410i
$239$	−244.161			−1.02159			−0.510797	−	0.859702i	$-0.670649\pi$
$239$	−244.161			−1.02159			−0.510797	+	0.859702i	$0.670649\pi$
$240$	4.65219	+	34.3272i	0.0193841	+	0.143030i
$241$		−	49.0776i		−	0.203641i	−0.994803	−	0.101821i	$-0.967533\pi$
$241$		−	49.0776i		−	0.203641i	0.994803	−	0.101821i	$-0.0324668\pi$
$242$			424.871i			1.75566i
$243$			15.5885i			0.0641500i
$244$			84.1114i			0.344719i
$245$	481.936	−	65.3143i	1.96709	−	0.266589i
$246$	31.3351			0.127378
$247$	82.7359			0.334963
$248$		−	86.6090i		−	0.349230i
$249$			179.803i			0.722100i
$250$	−69.5091	−	162.538i	−0.278036	−	0.650151i
$251$		−	354.418i		−	1.41202i	−0.708201	−	0.706011i	$-0.750493\pi$
$251$		−	354.418i		−	1.41202i	0.708201	−	0.706011i	$-0.249507\pi$
$252$	72.5649			0.287956
$253$	−205.068	−	425.304i	−0.810545	−	1.68104i
$254$	−317.654			−1.25061
$255$	0.371276	+	2.73954i	0.00145598	+	0.0107433i
$256$	16.0000			0.0625000
$257$			116.570i			0.453580i	0.973944	+	0.226790i	$0.0728231\pi$
$257$			116.570i			0.453580i	−0.973944	+	0.226790i	$0.927177\pi$
$258$	0.190104			0.000736837
$259$	−861.670			−3.32691
$260$	−18.3607	−	135.478i	−0.0706179	−	0.521070i
$261$	20.2902			0.0777401
$262$			25.8881i			0.0988094i
$263$	−258.714			−0.983704			−0.491852	−	0.870679i	$-0.663680\pi$
$263$	−258.714			−0.983704			−0.491852	+	0.870679i	$0.663680\pi$
$264$		−	100.570i		−	0.380946i
$265$	55.8082	−	7.56339i	0.210597	−	0.0285411i
$266$	−103.505			−0.389118
$267$	87.9975			0.329579
$268$	−151.834			−0.566543
$269$	115.192			0.428221			0.214111	−	0.976809i	$-0.431315\pi$
$269$	115.192			0.428221			0.214111	+	0.976809i	$0.431315\pi$
$270$	−36.4095	+	4.93439i	−0.134850	+	0.0182755i
$271$	73.8741			0.272598			0.136299	−	0.990668i	$-0.456479\pi$
$271$	73.8741			0.272598			0.136299	+	0.990668i	$0.456479\pi$
$272$	1.27691			0.00469451
$273$	−286.390			−1.04905
$274$			89.4219i			0.326357i
$275$	136.599	+	494.706i	0.496723	+	1.79893i
$276$	34.6040	+	71.7674i	0.125377	+	0.260027i
$277$		−	240.607i		−	0.868617i	−0.900764	−	0.434309i	$-0.856993\pi$
$277$		−	240.607i		−	0.868617i	0.900764	−	0.434309i	$-0.143007\pi$
$278$			10.4368i			0.0375426i
$279$	91.8627			0.329257
$280$	22.9698	+	169.488i	0.0820350	+	0.605313i
$281$		−	178.599i		−	0.635584i	−0.948160	−	0.317792i	$-0.897059\pi$
$281$		−	178.599i		−	0.635584i	0.948160	−	0.317792i	$-0.102941\pi$
$282$			88.1175i			0.312473i
$283$	−262.744			−0.928425			−0.464212	−	0.885724i	$-0.653663\pi$
$283$	−262.744			−0.928425			−0.464212	+	0.885724i	$0.653663\pi$
$284$	−209.285			−0.736918
$285$	51.9339	−	7.03834i	0.182224	−	0.0246959i
$286$			396.916i			1.38782i
$287$	154.714			0.539075
$288$			16.9706i			0.0589256i
$289$	−288.898			−0.999647
$290$	6.42268	+	47.3911i	0.0221472	+	0.163418i
$291$			69.0418i			0.237257i
$292$			214.091i			0.733189i
$293$	−300.663			−1.02615			−0.513076	−	0.858343i	$-0.671494\pi$
$293$	−300.663			−1.02615			−0.513076	+	0.858343i	$0.671494\pi$
$294$	238.258			0.810401
$295$	234.578	−	31.7911i	0.795179	−	0.107767i
$296$		−	201.517i		−	0.680799i
$297$	106.670			0.359160
$298$	350.770			1.17708
$299$	−136.570	−	283.242i	−0.456757	−	0.947299i
$300$	−23.0502	−	83.4787i	−0.0768341	−	0.278262i
$301$	0.938622			0.00311835
$302$		−	128.914i		−	0.426868i
$303$			257.889i			0.851118i
$304$		−	24.2065i		−	0.0796267i
$305$	−28.2398	−	208.374i	−0.0925895	−	0.683192i
$306$			1.35436i			0.00442603i
$307$		−	413.963i		−	1.34841i	−0.738542	−	0.674207i	$-0.764485\pi$
$307$		−	413.963i		−	1.34841i	0.738542	−	0.674207i	$-0.235515\pi$
$308$		−	496.555i		−	1.61219i
$309$			38.2932i			0.123926i
$310$	29.0784	+	214.561i	0.0938012	+	0.692133i
$311$	382.590			1.23019			0.615097	−	0.788451i	$-0.289117\pi$
$311$	382.590			1.23019			0.615097	+	0.788451i	$0.289117\pi$
$312$		−	66.9772i		−	0.214671i
$313$	−15.8544			−0.0506529			−0.0253265	−	0.999679i	$-0.508063\pi$
$313$	−15.8544			−0.0506529			−0.0253265	+	0.999679i	$0.508063\pi$
$314$		−	276.024i		−	0.879057i
$315$	−179.769	+	24.3631i	−0.570695	+	0.0773433i
$316$		−	136.569i		−	0.432182i
$317$			500.084i			1.57755i	0.614680	+	0.788776i	$0.289285\pi$
$317$			500.084i			1.57755i	−0.614680	+	0.788776i	$0.710715\pi$
$318$	27.5902			0.0867618
$319$		−	138.844i		−	0.435247i
$320$	−39.6376	+	5.37189i	−0.123868	+	0.0167871i
$321$		−	185.728i		−	0.578593i
$322$	170.854	+	354.346i	0.530603	+	1.10045i
$323$		−	1.93184i		−	0.00598094i
$324$	−18.0000			−0.0555556
$325$	90.9716	+	329.463i	0.279913	+	1.01373i
$326$	−375.537			−1.15195
$327$	223.219			0.682627
$328$			36.1827i			0.110313i
$329$			435.073i			1.32241i
$330$	33.7656	+	249.147i	0.102320	+	0.754991i
$331$	−11.6405			−0.0351678			−0.0175839	−	0.999845i	$-0.505597\pi$
$331$	−11.6405			−0.0351678			−0.0175839	+	0.999845i	$0.505597\pi$
$332$	−207.619			−0.625357
$333$	213.741			0.641864
$334$	−242.629			−0.726434
$335$	376.145	−	50.9770i	1.12282	−	0.152170i
$336$			83.7907i			0.249377i
$337$	−500.602			−1.48547			−0.742733	−	0.669588i	$-0.766471\pi$
$337$	−500.602			−1.48547			−0.742733	+	0.669588i	$0.766471\pi$
$338$			25.3348i			0.0749551i
$339$		−	231.178i		−	0.681942i
$340$	−3.16335	+	0.428712i	−0.00930397	+	0.00126092i
$341$		−	628.609i		−	1.84343i
$342$	25.6749			0.0750728
$343$	583.765			1.70194
$344$			0.219513i			0.000638120i
$345$	−109.822	−	166.175i	−0.318324	−	0.481667i
$346$	125.677			0.363227
$347$		−	90.5681i		−	0.261003i	−0.991448	−	0.130502i	$-0.958341\pi$
$347$		−	90.5681i		−	0.261003i	0.991448	−	0.130502i	$-0.0416588\pi$
$348$			23.4291i			0.0673249i
$349$	338.922			0.971122			0.485561	−	0.874203i	$-0.338615\pi$
$349$	338.922			0.971122			0.485561	+	0.874203i	$0.338615\pi$
$350$	−113.809	−	412.169i	−0.325167	−	1.17762i
$351$	71.0401			0.202393
$352$	116.128			0.329909
$353$		−	526.786i		−	1.49231i	−0.665771	−	0.746156i	$-0.731897\pi$
$353$		−	526.786i		−	1.49231i	0.665771	−	0.746156i	$-0.268103\pi$
$354$	115.970			0.327598
$355$	518.472	−	70.2658i	1.46048	−	0.197932i
$356$			101.611i			0.285423i
$357$			6.68706i			0.0187313i
$358$		−	289.380i		−	0.808323i
$359$			396.636i			1.10483i	0.833568	+	0.552417i	$0.186295\pi$
$359$			396.636i			1.10483i	−0.833568	+	0.552417i	$0.813705\pi$
$360$	−5.69775	−	42.0421i	−0.0158271	−	0.116784i
$361$	324.378			0.898553
$362$	33.7213			0.0931527
$363$		−	520.358i		−	1.43349i
$364$		−	330.694i		−	0.908501i
$365$	−71.8795	−	530.379i	−0.196930	−	1.45309i
$366$		−	103.015i		−	0.281462i
$367$	48.7560			0.132850			0.0664251	−	0.997791i	$-0.478841\pi$
$367$	48.7560			0.132850			0.0664251	+	0.997791i	$0.478841\pi$
$368$	−82.8699	+	39.9572i	−0.225190	+	0.108579i
$369$	−38.3775			−0.104004
$370$	67.6577	+	499.228i	0.182859	+	1.34926i
$371$	136.224			0.367182
$372$			106.074i			0.285145i
$373$	−521.630			−1.39847			−0.699236	−	0.714891i	$-0.746476\pi$
$373$	−521.630			−1.39847			−0.699236	+	0.714891i	$0.746476\pi$
$374$	9.26780			0.0247802
$375$	85.1309	+	199.067i	0.227016	+	0.530846i
$376$	−101.749			−0.270610
$377$		−	92.4668i		−	0.245270i
$378$	−88.8735			−0.235115
$379$			553.263i			1.45980i	0.683556	+	0.729898i	$0.260433\pi$
$379$			553.263i			1.45980i	−0.683556	+	0.729898i	$0.739567\pi$
$380$	8.12717	+	59.9681i	0.0213873	+	0.157811i
$381$	389.045			1.02112
$382$	−249.235			−0.652448
$383$	−248.722			−0.649405			−0.324703	−	0.945816i	$-0.605264\pi$
$383$	−248.722			−0.649405			−0.324703	+	0.945816i	$0.605264\pi$
$384$	−19.5959			−0.0510310
$385$	166.715	+	1230.14i	0.433025	+	3.19517i
$386$	262.875			0.681023
$387$	−0.232829			−0.000601625
$388$	−79.7226			−0.205471
$389$			443.911i			1.14116i	0.821242	+	0.570580i	$0.193282\pi$
$389$			443.911i			1.14116i	−0.821242	+	0.570580i	$0.806718\pi$
$390$	22.4871	+	165.926i	0.0576593	+	0.425452i
$391$	−6.61357	+	3.18885i	−0.0169145	+	0.00815563i
$392$			275.116i			0.701828i
$393$		−	31.7063i		−	0.0806776i
$394$	331.175			0.840544
$395$	45.8522	+	338.331i	0.116082	+	0.856534i
$396$			123.172i			0.311041i
$397$			549.866i			1.38505i	0.721392	+	0.692527i	$0.243503\pi$
$397$			549.866i			1.38505i	−0.721392	+	0.692527i	$0.756497\pi$
$398$	−456.365			−1.14665
$399$	126.768			0.317713
$400$	96.3929	−	26.6161i	0.240982	−	0.0665403i
$401$			22.4686i			0.0560314i	0.999607	+	0.0280157i	$0.00891884\pi$
$401$			22.4686i			0.0560314i	−0.999607	+	0.0280157i	$0.991081\pi$
$402$	185.957			0.462580
$403$		−	418.639i		−	1.03881i
$404$	−297.784			−0.737090
$405$	44.5923	−	6.04337i	0.110105	−	0.0149219i
$406$			115.679i			0.284924i
$407$		−	1462.61i		−	3.59363i
$408$	−1.56389			−0.00383305
$409$	−451.796			−1.10464			−0.552318	−	0.833634i	$-0.686256\pi$
$409$	−451.796			−1.10464			−0.552318	+	0.833634i	$0.686256\pi$
$410$	−12.1481	−	89.6372i	−0.0296294	−	0.218627i
$411$		−	109.519i		−	0.266470i
$412$	−44.2171			−0.107323
$413$	572.591			1.38642
$414$	−42.3810	−	87.8968i	−0.102370	−	0.212311i
$415$	514.344	−	69.7064i	1.23938	−	0.167967i
$416$	77.3386			0.185910
$417$		−	12.7825i		−	0.0306534i
$418$		−	175.691i		−	0.420314i
$419$			242.846i			0.579586i	0.957089	+	0.289793i	$0.0935864\pi$
$419$			242.846i			0.579586i	−0.957089	+	0.289793i	$0.906414\pi$
$420$	−28.1321	−	207.579i	−0.0669813	−	0.494236i
$421$			275.398i			0.654151i	0.944998	+	0.327076i	$0.106063\pi$
$421$			275.398i			0.654151i	−0.944998	+	0.327076i	$0.893937\pi$
$422$		−	532.766i		−	1.26248i
$423$		−	107.921i		−	0.255133i
$424$			31.8585i			0.0751379i
$425$	7.69279	−	2.12414i	0.0181007	−	0.00499799i
$426$	256.320			0.601691
$427$		−	508.628i		−	1.19117i
$428$	214.460			0.501076
$429$		−	486.121i		−	1.13315i
$430$	−0.0737000	−	0.543811i	−0.000171395	−	0.00126468i
$431$			137.991i			0.320166i	0.987104	+	0.160083i	$0.0511762\pi$
$431$			137.991i			0.320166i	−0.987104	+	0.160083i	$0.948824\pi$
$432$		−	20.7846i		−	0.0481125i
$433$	−522.317			−1.20627			−0.603137	−	0.797637i	$-0.706083\pi$
$433$	−522.317			−1.20627			−0.603137	+	0.797637i	$0.706083\pi$
$434$			523.731i			1.20675i
$435$	−7.86614	−	58.0421i	−0.0180831	−	0.133430i
$436$			257.751i			0.591172i
$437$	60.4516	+	125.375i	0.138333	+	0.286898i
$438$		−	262.207i		−	0.598646i
$439$	−105.152			−0.239526			−0.119763	−	0.992803i	$-0.538213\pi$
$439$	−105.152			−0.239526			−0.119763	+	0.992803i	$0.538213\pi$
$440$	−287.690	+	38.9892i	−0.653841	+	0.0886117i
$441$	−291.805			−0.661690
$442$	6.17214			0.0139641
$443$		−	134.158i		−	0.302840i	−0.988470	−	0.151420i	$-0.951615\pi$
$443$		−	134.158i		−	0.302840i	0.988470	−	0.151420i	$-0.0483846\pi$
$444$			246.806i			0.555870i
$445$	−34.1151	−	251.726i	−0.0766631	−	0.565676i
$446$	259.445			0.581715
$447$	−429.603			−0.961081
$448$	−96.7532			−0.215967
$449$	182.896			0.407340			0.203670	−	0.979040i	$-0.434713\pi$
$449$	182.896			0.407340			0.203670	+	0.979040i	$0.434713\pi$
$450$	28.2306	+	102.240i	0.0627348	+	0.227200i
$451$			262.614i			0.582293i
$452$	266.942			0.590579
$453$			157.887i			0.348536i
$454$		−	173.319i		−	0.381759i
$455$	111.028	+	819.246i	0.244018	+	1.80054i
$456$			29.6468i			0.0650150i
$457$	605.882			1.32578			0.662890	−	0.748717i	$-0.269330\pi$
$457$	605.882			1.32578			0.662890	+	0.748717i	$0.269330\pi$
$458$	−511.881			−1.11764
$459$		−	1.65875i		−	0.00361384i
$460$	191.883	−	126.811i	0.417136	−	0.275676i
$461$	162.714			0.352959			0.176479	−	0.984304i	$-0.443529\pi$
$461$	162.714			0.352959			0.176479	+	0.984304i	$0.443529\pi$
$462$			608.153i			1.31635i
$463$		−	357.244i		−	0.771586i	−0.922585	−	0.385793i	$-0.873928\pi$
$463$		−	357.244i		−	0.771586i	0.922585	−	0.385793i	$-0.126072\pi$
$464$	−27.0536			−0.0583051
$465$	−35.6136	−	262.783i	−0.0765883	−	0.565124i
$466$	386.988			0.830446
$467$	926.354			1.98363			0.991814	−	0.127695i	$-0.0407578\pi$
$467$	926.354			1.98363			0.991814	+	0.127695i	$0.0407578\pi$
$468$			82.0300i			0.175278i
$469$	918.148			1.95767
$470$	252.069	−	34.1616i	0.536317	−	0.0726843i
$471$			338.059i			0.717747i
$472$			133.910i			0.283708i
$473$			1.59323i			0.00336835i
$474$			167.263i			0.352875i
$475$	−40.2677	−	145.834i	−0.0847742	−	0.307018i
$476$	−7.72155			−0.0162217
$477$	−33.7910			−0.0708407
$478$			345.295i			0.722375i
$479$			398.719i			0.832398i	0.909274	+	0.416199i	$0.136638\pi$
$479$			398.719i			0.832398i	−0.909274	+	0.416199i	$0.863362\pi$
$480$	48.5460	−	6.57919i	0.101138	−	0.0137066i
$481$		−	974.063i		−	2.02508i
$482$	−69.4062			−0.143996
$483$	−209.253	−	433.983i	−0.433235	−	0.898515i
$484$	600.858			1.24144
$485$	197.501	−	26.7663i	0.407218	−	0.0551882i
$486$	22.0454			0.0453609
$487$			671.551i			1.37895i	0.724308	+	0.689477i	$0.242160\pi$
$487$			671.551i			1.37895i	−0.724308	+	0.689477i	$0.757840\pi$
$488$	118.951			0.243753
$489$	459.937			0.940567
$490$	−92.3684	−	681.561i	−0.188507	−	1.39094i
$491$	401.963			0.818662			0.409331	−	0.912386i	$-0.365762\pi$
$491$	401.963			0.818662			0.409331	+	0.912386i	$0.365762\pi$
$492$		−	44.3145i		−	0.0900702i
$493$	−2.15905			−0.00437942
$494$		−	117.006i		−	0.236855i
$495$	−41.3543	−	305.142i	−0.0835440	−	0.616448i
$496$	−122.484			−0.246943
$497$	1265.56			2.54640
$498$	254.280			0.510602
$499$	177.256			0.355222			0.177611	−	0.984101i	$-0.443163\pi$
$499$	177.256			0.355222			0.177611	+	0.984101i	$0.443163\pi$
$500$	−229.863	+	98.3007i	−0.459726	+	0.196601i
$501$	297.159			0.593131
$502$	−501.222			−0.998451
$503$	−42.6526			−0.0847964			−0.0423982	−	0.999101i	$-0.513500\pi$
$503$	−42.6526			−0.0847964			−0.0423982	+	0.999101i	$0.513500\pi$
$504$		−	102.622i		−	0.203616i
$505$	737.717	−	99.9789i	1.46083	−	0.197978i
$506$	−601.470	+	290.010i	−1.18868	+	0.573142i
$507$		−	31.0287i		−	0.0612006i
$508$			449.231i			0.884312i
$509$	−476.572			−0.936292			−0.468146	−	0.883651i	$-0.655078\pi$
$509$	−476.572			−0.936292			−0.468146	+	0.883651i	$0.655078\pi$
$510$	3.87430	−	0.525063i	0.00759666	−	0.00102954i
$511$		−	1294.62i		−	2.53351i
$512$		−	22.6274i		−	0.0441942i
$513$	−31.4452			−0.0612967
$514$	164.855			0.320730
$515$	109.541	−	14.8456i	0.212702	−	0.0288264i
$516$		−	0.268848i		−	0.000521022i
$517$	−738.497			−1.42843
$518$			1218.59i			2.35248i
$519$	−153.922			−0.296574
$520$	−191.595	+	25.9659i	−0.368452	+	0.0499344i
$521$		−	160.588i		−	0.308230i	−0.988053	−	0.154115i	$-0.950747\pi$
$521$		−	160.588i		−	0.308230i	0.988053	−	0.154115i	$-0.0492527\pi$
$522$		−	28.6946i		−	0.0549705i
$523$	−586.487			−1.12139			−0.560695	−	0.828023i	$-0.689466\pi$
$523$	−586.487			−1.12139			−0.560695	+	0.828023i	$0.689466\pi$
$524$	36.6113			0.0698688
$525$	139.386	+	504.802i	0.265498	+	0.961527i
$526$			365.877i			0.695584i
$527$	−9.77501			−0.0185484
$528$	−142.227			−0.269370
$529$	329.428	−	413.906i	0.622737	−	0.782432i
$530$	−10.6963	−	78.9247i	−0.0201816	−	0.148914i
$531$	−142.033			−0.267483
$532$			146.379i			0.275148i
$533$			174.895i			0.328133i
$534$		−	124.447i		−	0.233047i
$535$	−531.294	+	72.0036i	−0.993073	+	0.134586i
$536$			214.725i			0.400606i
$537$			354.416i			0.659993i
$538$		−	162.905i		−	0.302798i
$539$			1996.80i			3.70463i
$540$	6.97828	+	51.4908i	0.0129227	+	0.0953534i
$541$	−148.856			−0.275149			−0.137574	−	0.990491i	$-0.543931\pi$
$541$	−148.856			−0.275149			−0.137574	+	0.990491i	$0.543931\pi$
$542$		−	104.474i		−	0.192756i
$543$	−41.3000			−0.0760588
$544$		−	1.80582i		−	0.00331952i
$545$	−86.5381	−	638.541i	−0.158786	−	1.17163i
$546$			405.016i			0.741788i
$547$			479.298i			0.876231i	0.898919	+	0.438115i	$0.144354\pi$
$547$			479.298i			0.876231i	−0.898919	+	0.438115i	$0.855646\pi$
$548$	126.462			0.230769
$549$			126.167i			0.229813i
$550$	699.620	−	193.180i	1.27204	−	0.351236i
$551$			40.9295i			0.0742823i
$552$	101.494	−	48.9374i	0.183867	−	0.0886547i
$553$			825.846i			1.49339i
$554$	−340.270			−0.614205
$555$	−82.8635	−	611.426i	−0.149304	−	1.10167i
$556$	14.7599			0.0265466
$557$	−579.354			−1.04013			−0.520067	−	0.854126i	$-0.674093\pi$
$557$	−579.354			−1.04013			−0.520067	+	0.854126i	$0.674093\pi$
$558$		−	129.914i		−	0.232820i
$559$			1.06105i			0.00189813i
$560$	239.692	−	32.4842i	0.428021	−	0.0580075i
$561$	−11.3507			−0.0202330
$562$	−252.577			−0.449426
$563$	−85.3556			−0.151609			−0.0758043	−	0.997123i	$-0.524152\pi$
$563$	−85.3556			−0.151609			−0.0758043	+	0.997123i	$0.524152\pi$
$564$	124.617			0.220952
$565$	−661.309	+	89.6238i	−1.17046	+	0.158626i
$566$			371.576i			0.656495i
$567$	108.847			0.191971
$568$			295.973i			0.521080i
$569$		−	117.341i		−	0.206224i	−0.994670	−	0.103112i	$-0.967120\pi$
$569$		−	117.341i		−	0.206224i	0.994670	−	0.103112i	$-0.0328800\pi$
$570$	−9.95371	−	73.4456i	−0.0174626	−	0.128852i
$571$			211.007i			0.369540i	0.982782	+	0.184770i	$0.0591540\pi$
$571$			211.007i			0.369540i	−0.982782	+	0.184770i	$0.940846\pi$
$572$	561.324			0.981336
$573$	305.250			0.532722
$574$		−	218.799i		−	0.381183i
$575$	−432.785	+	378.579i	−0.752670	+	0.658398i
$576$	24.0000			0.0416667
$577$			38.2624i			0.0663127i	0.999450	+	0.0331564i	$0.0105559\pi$
$577$			38.2624i			0.0663127i	−0.999450	+	0.0331564i	$0.989444\pi$
$578$			408.564i			0.706857i
$579$	−321.955			−0.556053
$580$	67.0212	−	9.08304i	0.115554	−	0.0156604i
$581$	1255.48			2.16090
$582$	97.6398			0.167766
$583$			231.229i			0.396619i
$584$	302.770			0.518443
$585$	−27.5410	−	203.217i	−0.0470786	−	0.347380i
$586$			425.201i			0.725599i
$587$		−	1046.43i		−	1.78268i	−0.453338	−	0.891339i	$-0.649767\pi$
$587$		−	1046.43i		−	1.78268i	0.453338	−	0.891339i	$-0.350233\pi$
$588$		−	336.948i		−	0.573040i
$589$			185.307i			0.314612i
$590$	−44.9594	−	331.743i	−0.0762025	−	0.562277i
$591$	−405.604			−0.686302
$592$	−284.987			−0.481398
$593$			797.943i			1.34560i	0.739823	+	0.672802i	$0.234909\pi$
$593$			797.943i			1.34560i	−0.739823	+	0.672802i	$0.765091\pi$
$594$		−	150.855i		−	0.253964i
$595$	19.1290	−	2.59246i	0.0321496	−	0.00435707i
$596$		−	496.063i		−	0.832321i
$597$	558.931			0.936233
$598$	−400.565	+	193.140i	−0.669842	+	0.322976i
$599$	259.288			0.432869			0.216434	−	0.976297i	$-0.430557\pi$
$599$	259.288			0.432869			0.216434	+	0.976297i	$0.430557\pi$
$600$	−118.057	+	32.5979i	−0.196761	+	0.0543299i
$601$	−876.688			−1.45872			−0.729358	−	0.684132i	$-0.760181\pi$
$601$	−876.688			−1.45872			−0.729358	+	0.684132i	$0.760181\pi$
$602$		−	1.32741i		−	0.00220500i
$603$	−227.750			−0.377695
$604$	−182.312			−0.301841
$605$	−1488.54	+	201.734i	−2.46039	+	0.333444i
$606$	364.710			0.601831
$607$		−	336.337i		−	0.554098i	−0.960856	−	0.277049i	$-0.910644\pi$
$607$		−	336.337i		−	0.554098i	0.960856	−	0.277049i	$-0.0893564\pi$
$608$	−34.2332			−0.0563046
$609$		−	141.677i		−	0.232639i
$610$	−294.685	+	39.9371i	−0.483090	+	0.0654707i
$611$	−491.822			−0.804946
$612$	1.91536			0.00312967
$613$	584.386			0.953322			0.476661	−	0.879087i	$-0.341847\pi$
$613$	584.386			0.953322			0.476661	+	0.879087i	$0.341847\pi$
$614$	−585.432			−0.953473
$615$	14.8783	+	109.783i	0.0241923	+	0.178509i
$616$	−702.235			−1.13999
$617$	−1174.78			−1.90402			−0.952010	−	0.306066i	$-0.900987\pi$
$617$	−1174.78			−1.90402			−0.952010	+	0.306066i	$0.900987\pi$
$618$	54.1547			0.0876290
$619$			797.546i			1.28844i	0.764839	+	0.644221i	$0.222818\pi$
$619$			797.546i			1.28844i	−0.764839	+	0.644221i	$0.777182\pi$
$620$	303.435	−	41.1230i	0.489412	−	0.0663274i
$621$	51.9059	+	107.651i	0.0835845	+	0.173351i
$622$		−	541.065i		−	0.869879i
$623$		−	614.448i		−	0.986272i
$624$	−94.7201			−0.151795
$625$	536.448	−	320.700i	0.858317	−	0.513121i
$626$			22.4215i			0.0358170i
$627$			215.177i			0.343185i
$628$	−390.357			−0.621587
$629$	−22.7439			−0.0361588
$630$	34.4547	+	254.231i	0.0546900	+	0.403542i
$631$		−	593.058i		−	0.939870i	−0.882701	−	0.469935i	$-0.844277\pi$
$631$		−	593.058i		−	0.939870i	0.882701	−	0.469935i	$-0.155723\pi$
$632$	−193.138			−0.305599
$633$			652.502i			1.03081i
$634$	707.226			1.11550
$635$	−150.826	−	1112.90i	−0.237521	−	1.75260i
$636$		−	39.0185i		−	0.0613498i
$637$			1329.82i			2.08763i
$638$	−196.355			−0.307766
$639$	−313.927			−0.491279
$640$	7.59699	+	56.0561i	0.0118703	+	0.0875876i
$641$		−	535.781i		−	0.835852i	−0.908481	−	0.417926i	$-0.862757\pi$
$641$		−	535.781i		−	0.835852i	0.908481	−	0.417926i	$-0.137243\pi$
$642$	−262.659			−0.409127
$643$	−547.232			−0.851060			−0.425530	−	0.904944i	$-0.639912\pi$
$643$	−547.232			−0.851060			−0.425530	+	0.904944i	$0.639912\pi$
$644$	501.120	−	241.624i	0.778137	−	0.375193i
$645$	0.0902637	+	0.666030i	0.000139944	+	0.00103261i
$646$	−2.73204			−0.00422916
$647$			617.708i			0.954726i	0.878706	+	0.477363i	$0.158407\pi$
$647$			617.708i			0.954726i	−0.878706	+	0.477363i	$0.841593\pi$
$648$			25.4558i			0.0392837i
$649$			971.922i			1.49757i
$650$	465.931	−	128.653i	0.716816	−	0.197928i
$651$		−	641.437i		−	0.985310i
$652$			531.090i			0.814555i
$653$		−	935.181i		−	1.43213i	−0.698034	−	0.716065i	$-0.745941\pi$
$653$		−	935.181i		−	1.43213i	0.698034	−	0.716065i	$-0.254059\pi$
$654$		−	315.679i		−	0.482690i
$655$	−90.6990	+	12.2920i	−0.138472	+	0.0187664i
$656$	51.1700			0.0780031
$657$			321.137i			0.488792i
$658$	615.286			0.935084
$659$		−	683.679i		−	1.03745i	−0.854942	−	0.518724i	$-0.826407\pi$
$659$		−	683.679i		−	1.03745i	0.854942	−	0.518724i	$-0.173593\pi$
$660$	352.347	−	47.7518i	0.533859	−	0.0723512i
$661$		−	236.085i		−	0.357164i	−0.983925	−	0.178582i	$-0.942849\pi$
$661$		−	236.085i		−	0.357164i	0.983925	−	0.178582i	$-0.0571510\pi$
$662$			16.4622i			0.0248674i
$663$	−7.55930			−0.0114017
$664$			293.617i			0.442194i
$665$	−49.1456	−	362.632i	−0.0739031	−	0.545311i
$666$		−	302.275i		−	0.453866i
$667$	140.120	−	67.5615i	0.210075	−	0.101292i
$668$			343.129i			0.513667i
$669$	−317.754			−0.474969
$670$	−72.0924	−	531.950i	−0.107601	−	0.793955i
$671$	863.350			1.28666
$672$	118.498			0.176336
$673$			703.521i			1.04535i	0.852532	+	0.522675i	$0.175066\pi$
$673$			703.521i			1.04535i	−0.852532	+	0.522675i	$0.824934\pi$
$674$			707.958i			1.05038i
$675$	−34.5753	−	125.218i	−0.0512227	−	0.185508i
$676$	35.8289			0.0530013
$677$	−1030.88			−1.52272			−0.761359	−	0.648331i	$-0.775468\pi$
$677$	−1030.88			−1.52272			−0.761359	+	0.648331i	$0.775468\pi$
$678$	−326.936			−0.482206
$679$	482.088			0.709997
$680$	0.606291	+	4.47365i	0.000891604	+	0.00657890i
$681$			212.271i			0.311705i
$682$	−888.987			−1.30350
$683$		−	932.286i		−	1.36499i	−0.730892	−	0.682494i	$-0.760895\pi$
$683$		−	932.286i		−	1.36499i	0.730892	−	0.682494i	$-0.239105\pi$
$684$		−	36.3098i		−	0.0530845i
$685$	−313.290	+	42.4586i	−0.457358	+	0.0619833i
$686$		−	825.568i		−	1.20345i
$687$	626.924			0.912553
$688$	0.310438			0.000451219
$689$			153.993i			0.223502i
$690$	−235.007	+	155.311i	−0.340590	+	0.225089i
$691$	−21.5824			−0.0312336			−0.0156168	−	0.999878i	$-0.504971\pi$
$691$	−21.5824			−0.0312336			−0.0156168	+	0.999878i	$0.504971\pi$
$692$		−	177.733i		−	0.256840i
$693$		−	744.833i		−	1.07479i
$694$	−128.083			−0.184557
$695$	−36.5655	+	4.95554i	−0.0526123	+	0.00713027i
$696$	33.1337			0.0476059
$697$	4.08371			0.00585898
$698$		−	479.308i		−	0.686687i
$699$	−473.961			−0.678056
$700$	−582.895	+	160.950i	−0.832707	+	0.229928i
$701$			753.621i			1.07507i	0.843243	+	0.537533i	$0.180644\pi$
$701$			753.621i			1.07507i	−0.843243	+	0.537533i	$0.819356\pi$
$702$		−	100.466i		−	0.143114i
$703$			431.160i			0.613314i
$704$		−	164.230i		−	0.233281i
$705$	−308.720	+	41.8393i	−0.437901	+	0.0593465i
$706$	−744.988			−1.05522
$707$	1800.72			2.54699
$708$		−	164.006i		−	0.231647i
$709$		−	1093.91i		−	1.54289i	−0.636297	−	0.771444i	$-0.719535\pi$
$709$		−	1093.91i		−	1.54289i	0.636297	−	0.771444i	$-0.280465\pi$
$710$	−99.3709	−	733.230i	−0.139959	−	1.03272i
$711$		−	204.854i		−	0.288121i
$712$	143.699			0.201825
$713$	634.388	−	305.882i	0.889745	−	0.429006i
$714$	9.45693			0.0132450
$715$	−1390.60	+	188.461i	−1.94489	+	0.263581i
$716$	−409.244			−0.571570
$717$		−	422.899i		−	0.589817i
$718$	560.928			0.781236
$719$	661.633			0.920213			0.460106	−	0.887864i	$-0.347811\pi$
$719$	661.633			0.920213			0.460106	+	0.887864i	$0.347811\pi$
$720$	−59.4565	+	8.05783i	−0.0825784	+	0.0111914i
$721$	267.384			0.370852
$722$		−	458.739i		−	0.635373i
$723$	85.0048			0.117572
$724$		−	47.6891i		−	0.0658689i
$725$	−162.986	+	45.0038i	−0.224808	+	0.0620742i
$726$	−735.898			−1.01363
$727$	1032.59			1.42035			0.710175	−	0.704025i	$-0.248616\pi$
$727$	1032.59			1.42035			0.710175	+	0.704025i	$0.248616\pi$
$728$	−467.672			−0.642407
$729$	−27.0000			−0.0370370
$730$	−750.069	+	101.653i	−1.02749	+	0.139251i
$731$	0.0247751			3.38920e−5
$732$	−145.685			−0.199024
$733$	−61.3572			−0.0837070			−0.0418535	−	0.999124i	$-0.513326\pi$
$733$	−61.3572			−0.0837070			−0.0418535	+	0.999124i	$0.513326\pi$
$734$		−	68.9514i		−	0.0939392i
$735$	113.128	+	834.738i	0.153915	+	1.13570i
$736$	56.5080	+	117.196i	0.0767772	+	0.159233i
$737$			1558.47i			2.11462i
$738$			54.2740i			0.0735420i
$739$	−382.298			−0.517318			−0.258659	−	0.965969i	$-0.583281\pi$
$739$	−382.298			−0.517318			−0.258659	+	0.965969i	$0.583281\pi$
$740$	706.014	−	95.6825i	0.954073	−	0.129301i
$741$			143.303i			0.193391i
$742$		−	192.650i		−	0.259637i
$743$	−628.380			−0.845734			−0.422867	−	0.906192i	$-0.638976\pi$
$743$	−628.380			−0.845734			−0.422867	+	0.906192i	$0.638976\pi$
$744$	150.011			0.201628
$745$	166.550	+	1228.92i	0.223557	+	1.64956i
$746$			737.696i			0.988869i
$747$	−311.428			−0.416905
$748$		−	13.1066i		−	0.0175223i
$749$	−1296.86			−1.73145
$750$	281.523	−	120.393i	0.375365	−	0.160524i
$751$		−	1078.88i		−	1.43659i	−0.695740	−	0.718294i	$-0.744923\pi$
$751$		−	1078.88i		−	1.43659i	0.695740	−	0.718294i	$-0.255077\pi$
$752$			143.895i			0.191350i
$753$	613.869			0.815232
$754$	−130.768			−0.173432
$755$	451.652	−	61.2100i	0.598214	−	0.0810729i
$756$			125.686i			0.166251i
$757$	171.766			0.226903			0.113452	−	0.993544i	$-0.463809\pi$
$757$	171.766			0.226903			0.113452	+	0.993544i	$0.463809\pi$
$758$	782.432			1.03223
$759$	736.647	−	355.188i	0.970550	−	0.467968i
$760$	84.8077	−	11.4936i	0.111589	−	0.0151231i
$761$	−338.552			−0.444877			−0.222439	−	0.974947i	$-0.571402\pi$
$761$	−338.552			−0.444877			−0.222439	+	0.974947i	$0.571402\pi$
$762$		−	550.193i		−	0.722038i
$763$		−	1558.64i		−	2.04278i
$764$			352.472i			0.461351i
$765$	−4.74502	+	0.643069i	−0.00620265	+	0.000840613i
$766$			351.746i			0.459199i
$767$			647.278i			0.843908i
$768$			27.7128i			0.0360844i
$769$			763.085i			0.992308i	0.868235	+	0.496154i	$0.165255\pi$
$769$			763.085i			0.992308i	−0.868235	+	0.496154i	$0.834745\pi$
$770$	1739.68	−	235.770i	2.25933	−	0.306195i
$771$	−201.905			−0.261875
$772$		−	371.761i		−	0.481556i
$773$	455.189			0.588861			0.294430	−	0.955673i	$-0.404870\pi$
$773$	455.189			0.588861			0.294430	+	0.955673i	$0.404870\pi$
$774$			0.329270i			0.000425413i
$775$	−737.909	+	203.752i	−0.952141	+	0.262906i
$776$			112.745i			0.145290i
$777$		−	1492.46i		−	1.92079i
$778$	627.786			0.806922
$779$		−	77.4155i		−	0.0993781i
$780$	234.655	−	31.8016i	0.300840	−	0.0407713i
$781$			2148.17i			2.75054i
$782$	4.50972	+	9.35300i	0.00576690	+	0.0119604i
$783$			35.1436i			0.0448833i
$784$	389.073			0.496267
$785$	967.051	−	131.059i	1.23191	−	0.166955i
$786$	−44.8395			−0.0570477
$787$	681.842			0.866382			0.433191	−	0.901302i	$-0.357388\pi$
$787$	681.842			0.866382			0.433191	+	0.901302i	$0.357388\pi$
$788$		−	468.351i		−	0.594355i
$789$		−	448.106i		−	0.567942i
$790$	478.472	−	64.8448i	0.605661	−	0.0820821i
$791$	−1614.22			−2.04073
$792$	174.192			0.219940
$793$	574.972			0.725059
$794$	777.628			0.979381
$795$	13.1002	+	96.6626i	0.0164782	+	0.121588i
$796$			645.398i			0.810801i
$797$	−263.083			−0.330092			−0.165046	−	0.986286i	$-0.552777\pi$
$797$	−263.083			−0.330092			−0.165046	+	0.986286i	$0.552777\pi$
$798$		−	179.277i		−	0.224657i
$799$			11.4838i			0.0143727i
$800$	−37.6409	−	136.320i	−0.0470511	−	0.170400i
$801$			152.416i			0.190282i
$802$	31.7754			0.0396202
$803$	2197.51			2.73662
$804$		−	262.983i		−	0.327094i
$805$	−1160.33	+	766.836i	−1.44140	+	0.952591i
$806$	−592.045			−0.734547
$807$			199.518i			0.247234i
$808$			421.131i			0.521201i
$809$	−788.964			−0.975233			−0.487617	−	0.873058i	$-0.662134\pi$
$809$	−788.964			−0.975233			−0.487617	+	0.873058i	$0.662134\pi$
$810$	−8.54662	−	63.0631i	−0.0105514	−	0.0778557i
$811$	472.336			0.582412			0.291206	−	0.956660i	$-0.405943\pi$
$811$	472.336			0.582412			0.291206	+	0.956660i	$0.405943\pi$
$812$	163.595			0.201471
$813$			127.954i			0.157385i
$814$	−2068.44			−2.54108
$815$	−178.310	−	1315.70i	−0.218785	−	1.61435i
$816$			2.21167i			0.00271038i
$817$		−	0.469665i		−	0.000574865i
$818$			638.936i			0.781095i
$819$		−	496.041i		−	0.605667i
$820$	−126.766	+	17.1800i	−0.154593	+	0.0209512i
$821$	1233.71			1.50269			0.751347	−	0.659908i	$-0.229405\pi$
$821$	1233.71			1.50269			0.751347	+	0.659908i	$0.229405\pi$
$822$	−154.883			−0.188422
$823$			405.241i			0.492394i	0.969220	+	0.246197i	$0.0791811\pi$
$823$			405.241i			0.492394i	−0.969220	+	0.246197i	$0.920819\pi$
$824$			62.5325i			0.0758889i
$825$	−856.856	+	236.596i	−1.03861	+	0.286783i
$826$		−	809.766i		−	0.980346i
$827$	127.687			0.154397			0.0771986	−	0.997016i	$-0.475402\pi$
$827$	127.687			0.154397			0.0771986	+	0.997016i	$0.475402\pi$
$828$	−124.305	+	59.9358i	−0.150127	+	0.0723863i
$829$	−730.117			−0.880721			−0.440360	−	0.897821i	$-0.645149\pi$
$829$	−730.117			−0.880721			−0.440360	+	0.897821i	$0.645149\pi$
$830$	−98.5798	−	727.393i	−0.118771	−	0.876377i
$831$	416.743			0.501496
$832$		−	109.373i		−	0.131458i
$833$	31.0507			0.0372757
$834$	−18.0771			−0.0216752
$835$	−115.203	−	850.052i	−0.137968	−	1.01803i
$836$	−248.465			−0.297207
$837$			159.111i			0.190097i
$838$	343.437			0.409829
$839$			704.305i			0.839458i	0.907649	+	0.419729i	$0.137875\pi$
$839$			704.305i			0.839458i	−0.907649	+	0.419729i	$0.862125\pi$
$840$	−293.561	+	39.7848i	−0.349478	+	0.0473629i
$841$	−795.257			−0.945608
$842$	389.471			0.462555
$843$	309.343			0.366955
$844$	−753.444			−0.892707
$845$	−88.7607	+	12.0293i	−0.105042	+	0.0142358i
$846$	−152.624			−0.180407
$847$	−3633.43			−4.28977
$848$	45.0547			0.0531305
$849$		−	455.086i		−	0.536026i
$850$	−3.00399	−	10.8793i	−0.00353411	−	0.0127991i
$851$	1476.05	−	711.706i	1.73449	−	0.836318i
$852$		−	362.492i		−	0.425460i
$853$		−	1263.95i		−	1.48177i	−0.671633	−	0.740884i	$-0.734407\pi$
$853$		−	1263.95i		−	1.48177i	0.671633	−	0.740884i	$-0.265593\pi$
$854$	−719.308			−0.842281
$855$	12.1908	+	89.9522i	0.0142582	+	0.105207i
$856$		−	303.293i		−	0.354314i
$857$		−	1093.23i		−	1.27564i	−0.770184	−	0.637821i	$-0.779836\pi$
$857$		−	1093.23i		−	1.27564i	0.770184	−	0.637821i	$-0.220164\pi$
$858$	−687.479			−0.801257
$859$	−994.497			−1.15774			−0.578869	−	0.815421i	$-0.696506\pi$
$859$	−994.497			−1.15774			−0.578869	+	0.815421i	$0.696506\pi$
$860$	−0.769066	+	0.104227i	−0.000894262	+	0.000121195i
$861$			267.973i			0.311235i
$862$	195.149			0.226391
$863$		−	704.337i		−	0.816149i	−0.912949	−	0.408074i	$-0.866200\pi$
$863$		−	704.337i		−	0.816149i	0.912949	−	0.408074i	$-0.133800\pi$
$864$	−29.3939			−0.0340207
$865$	59.6727	+	440.309i	0.0689858	+	0.509027i
$866$			738.668i			0.852965i
$867$		−	500.386i		−	0.577147i
$868$	740.668			0.853304
$869$	−1401.80			−1.61312
$870$	−82.0839	+	11.1244i	−0.0943493	+	0.0127867i
$871$			1037.91i			1.19163i
$872$	364.515			0.418022
$873$	−119.584			−0.136980
$874$	177.306	−	85.4915i	0.202868	−	0.0978163i
$875$	1390.00	−	594.432i	1.58857	−	0.679350i
$876$	−370.817			−0.423307
$877$		−	1265.04i		−	1.44246i	−0.692697	−	0.721229i	$-0.743578\pi$
$877$		−	1265.04i		−	1.44246i	0.692697	−	0.721229i	$-0.256422\pi$
$878$			148.707i			0.169371i
$879$		−	520.763i		−	0.592449i
$880$	55.1390	+	406.855i	0.0626580	+	0.462336i
$881$		−	966.222i		−	1.09673i	−0.836238	−	0.548367i	$-0.815250\pi$
$881$		−	966.222i		−	1.09673i	0.836238	−	0.548367i	$-0.184750\pi$
$882$			412.675i			0.467885i
$883$			932.122i			1.05563i	0.849359	+	0.527816i	$0.176989\pi$
$883$			932.122i			1.05563i	−0.849359	+	0.527816i	$0.823011\pi$
$884$		−	8.72872i		−	0.00987412i
$885$	55.0639	+	406.301i	0.0622190	+	0.459097i
$886$	−189.728			−0.214140
$887$			732.602i			0.825932i	0.910746	+	0.412966i	$0.135507\pi$
$887$			732.602i			0.825932i	−0.910746	+	0.412966i	$0.864493\pi$
$888$	349.037			0.393060
$889$		−	2716.53i		−	3.05572i
$890$	−355.994	+	48.2460i	−0.399993	+	0.0542090i
$891$			184.759i			0.207361i
$892$		−	366.911i		−	0.411335i
$893$	217.700			0.243785
$894$			607.551i			0.679587i
$895$	1013.84	−	137.401i	1.13279	−	0.153521i
$896$			136.830i			0.152712i
$897$	490.590	−	236.547i	0.546923	−	0.263709i
$898$		−	258.654i		−	0.288033i
$899$	207.101			0.230368
$900$	144.589	−	39.9242i	0.160655	−	0.0443602i
$901$	3.59566			0.00399075
$902$	371.392			0.411743
$903$			1.62574i			0.00180038i
$904$		−	377.513i		−	0.417603i
$905$	16.0113	+	118.143i	0.0176920	+	0.130544i
$906$	223.286			0.246453
$907$	−449.388			−0.495467			−0.247733	−	0.968828i	$-0.579686\pi$
$907$	−449.388			−0.495467			−0.247733	+	0.968828i	$0.579686\pi$
$908$	−245.110			−0.269945
$909$	−446.676			−0.491393
$910$	1158.59	−	157.018i	1.27317	−	0.172547i
$911$			18.1325i			0.0199040i	0.999950	+	0.00995200i	$0.00316787\pi$
$911$			18.1325i			0.0199040i	−0.999950	+	0.00995200i	$0.996832\pi$
$912$	41.9269			0.0459725
$913$			2131.07i			2.33414i
$914$		−	856.846i		−	0.937468i
$915$	360.914	−	48.9128i	0.394441	−	0.0534566i
$916$			723.909i			0.790294i
$917$	−221.391			−0.241430
$918$	−2.34583			−0.00255537
$919$		−	1170.30i		−	1.27345i	−0.771091	−	0.636725i	$-0.780289\pi$
$919$		−	1170.30i		−	1.27345i	0.771091	−	0.636725i	$-0.219711\pi$
$920$	−179.338	−	271.363i	−0.194933	−	0.294960i
$921$	717.005			0.778507
$922$		−	230.112i		−	0.249579i
$923$			1430.64i			1.54998i
$924$	860.059			0.930799
$925$	−1716.92	+	474.079i	−1.85613	+	0.512517i
$926$	−505.220			−0.545594
$927$	−66.3257			−0.0715488
$928$			38.2595i			0.0412279i
$929$	−966.715			−1.04060			−0.520298	−	0.853984i	$-0.674179\pi$
$929$	−966.715			−1.04060			−0.520298	+	0.853984i	$0.674179\pi$
$930$	−371.631	+	50.3652i	−0.399603	+	0.0541561i
$931$		−	588.632i		−	0.632258i
$932$		−	547.283i		−	0.587214i
$933$			662.666i			0.710253i
$934$		−	1310.06i		−	1.40264i
$935$	4.40046	+	32.4698i	0.00470638	+	0.0347270i
$936$	116.008			0.123940
$937$	372.607			0.397659			0.198830	−	0.980034i	$-0.436286\pi$
$937$	372.607			0.397659			0.198830	+	0.980034i	$0.436286\pi$
$938$		−	1298.46i		−	1.38428i
$939$		−	27.4606i		−	0.0292445i
$940$	−48.3118	−	356.479i	−0.0513955	−	0.379233i
$941$			166.501i			0.176941i	0.996079	+	0.0884704i	$0.0281979\pi$
$941$			166.501i			0.176941i	−0.996079	+	0.0884704i	$0.971802\pi$
$942$	478.087			0.507524
$943$	−265.028	+	127.788i	−0.281048	+	0.135512i
$944$	189.378			0.200612
$945$	−42.1982	−	311.369i	−0.0446542	−	0.329491i
$946$	2.25316			0.00238178
$947$		−	479.382i		−	0.506211i	−0.967439	−	0.253106i	$-0.918548\pi$
$947$		−	479.382i		−	0.506211i	0.967439	−	0.253106i	$-0.0814520\pi$
$948$	236.545			0.249520
$949$	1463.49			1.54214
$950$	−206.240	+	56.9472i	−0.217095	+	0.0599444i
$951$	−866.171			−0.910800
$952$			10.9199i			0.0114705i
$953$	−1140.58			−1.19683			−0.598415	−	0.801186i	$-0.704203\pi$
$953$	−1140.58			−1.19683			−0.598415	+	0.801186i	$0.704203\pi$
$954$			47.7877i			0.0500919i
$955$	−118.340	−	873.197i	−0.123916	−	0.914342i
$956$	488.322			0.510797
$957$	240.485			0.251290
$958$	563.873			0.588594
$959$	−764.723			−0.797417
$960$	−9.30438	−	68.6544i	−0.00969206	−	0.0715150i
$961$	−23.3598			−0.0243078
$962$	−1377.53			−1.43195
$963$	321.691			0.334051
$964$			98.1551i			0.101821i
$965$	124.816	+	920.984i	0.129343	+	0.954387i
$966$	−613.745	+	295.928i	−0.635346	+	0.306344i
$967$		−	20.5686i		−	0.0212705i	−0.999943	−	0.0106353i	$-0.996615\pi$
$967$		−	20.5686i		−	0.0212705i	0.999943	−	0.0106353i	$-0.00338538\pi$
$968$		−	849.741i		−	0.877832i
$969$	3.34605			0.00345310
$970$	−37.8532	−	279.309i	−0.0390240	−	0.287947i
$971$			584.768i			0.602233i	0.953587	+	0.301116i	$0.0973592\pi$
$971$			584.768i			0.602233i	−0.953587	+	0.301116i	$0.902641\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−89.2543			−0.0917311
$974$	949.716			0.975068
$975$	−570.646	+	157.568i	−0.585278	+	0.161608i
$976$		−	168.223i		−	0.172359i
$977$	−1537.56			−1.57375			−0.786876	−	0.617112i	$-0.788303\pi$
$977$	−1537.56			−1.57375			−0.786876	+	0.617112i	$0.788303\pi$
$978$		−	650.449i		−	0.665081i
$979$	1042.97			1.06534
$980$	−963.872	+	130.629i	−0.983543	+	0.133295i
$981$			386.627i			0.394115i
$982$		−	568.462i		−	0.578881i
$983$	−717.423			−0.729830			−0.364915	−	0.931041i	$-0.618902\pi$
$983$	−717.423			−0.729830			−0.364915	+	0.931041i	$0.618902\pi$
$984$	−62.6702			−0.0636892
$985$	157.246	+	1160.27i	0.159640	+	1.17794i
$986$			3.05336i			0.00309672i
$987$	−753.568			−0.763493
$988$	−165.472			−0.167482
$989$	−1.60788	+	0.775266i	−0.00162576	+	0.000783889i
$990$	−431.535	+	58.4838i	−0.435894	+	0.0590745i
$991$	211.667			0.213590			0.106795	−	0.994281i	$-0.465941\pi$
$991$	211.667			0.213590			0.106795	+	0.994281i	$0.465941\pi$
$992$			173.218i			0.174615i
$993$		−	20.1620i		−	0.0203041i
$994$		−	1789.77i		−	1.80058i
$995$	−216.688	−	1598.88i	−0.217777	−	1.60691i
$996$		−	359.606i		−	0.361050i
$997$		−	460.147i		−	0.461532i	−0.973009	−	0.230766i	$-0.925877\pi$
$997$		−	460.147i		−	0.461532i	0.973009	−	0.230766i	$-0.0741232\pi$
$998$		−	250.677i		−	0.251180i
$999$			370.210i			0.370580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.46	yes	48
5.4	even	2	inner	690.3.f.a.229.47	yes	48
23.22	odd	2	inner	690.3.f.a.229.45	✓	48
115.114	odd	2	inner	690.3.f.a.229.48	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.45	✓	48	23.22	odd	2	inner
690.3.f.a.229.46	yes	48	1.1	even	1	trivial
690.3.f.a.229.47	yes	48	5.4	even	2	inner
690.3.f.a.229.48	yes	48	115.114	odd	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.95471 - 0.671486i) q^{5} +2.44949 q^{6} +12.0941 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.95471 - 0.671486i) q^{5} +2.44949 q^{6} +12.0941 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(-0.949624 - 7.00701i) q^{10} +20.5287i q^{11} -3.46410i q^{12} +13.6717i q^{13} -17.1037i q^{14} +(1.16305 + 8.58180i) q^{15} +4.00000 q^{16} +0.319227 q^{17} +4.24264i q^{18} -6.05163i q^{19} +(-9.90941 + 1.34297i) q^{20} +20.9477i q^{21} +29.0320 q^{22} +(-20.7175 + 9.98930i) q^{23} -4.89898 q^{24} +(24.0982 - 6.65403i) q^{25} +19.3347 q^{26} -5.19615i q^{27} -24.1883 q^{28} -6.76339 q^{29} +(12.1365 - 1.64480i) q^{30} -30.6209 q^{31} -5.65685i q^{32} -35.5568 q^{33} -0.451455i q^{34} +(59.9229 - 8.12105i) q^{35} +6.00000 q^{36} -71.2469 q^{37} -8.55830 q^{38} -23.6800 q^{39} +(1.89925 + 14.0140i) q^{40} +12.7925 q^{41} +29.6245 q^{42} +0.0776096 q^{43} -41.0575i q^{44} +(-14.8641 + 2.01446i) q^{45} +(14.1270 + 29.2989i) q^{46} +35.9738i q^{47} +6.92820i q^{48} +97.2684 q^{49} +(-9.41022 - 34.0800i) q^{50} +0.552917i q^{51} -27.3433i q^{52} +11.2637 q^{53} -7.34847 q^{54} +(13.7848 + 101.714i) q^{55} +34.2074i q^{56} +10.4817 q^{57} +9.56487i q^{58} +47.3445 q^{59} +(-2.32609 - 17.1636i) q^{60} -42.0557i q^{61} +43.3045i q^{62} -36.2824 q^{63} -8.00000 q^{64} +(9.18033 + 67.7391i) q^{65} +50.2849i q^{66} +75.9168 q^{67} -0.638454 q^{68} +(-17.3020 - 35.8837i) q^{69} +(-11.4849 - 84.7438i) q^{70} +104.642 q^{71} -8.48528i q^{72} -107.046i q^{73} +100.758i q^{74} +(11.5251 + 41.7393i) q^{75} +12.1033i q^{76} +248.278i q^{77} +33.4886i q^{78} +68.2847i q^{79} +(19.8188 - 2.68594i) q^{80} +9.00000 q^{81} -18.0913i q^{82} +103.809 q^{83} -41.8954i q^{84} +(1.58167 - 0.214356i) q^{85} -0.109757i q^{86} -11.7145i q^{87} -58.0640 q^{88} -50.8054i q^{89} +(2.84887 + 21.0210i) q^{90} +165.347i q^{91} +(41.4350 - 19.9786i) q^{92} -53.0370i q^{93} +50.8747 q^{94} +(-4.06358 - 29.9841i) q^{95} +9.79796 q^{96} +39.8613 q^{97} -137.558i q^{98} -61.5862i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 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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