LMFDB - Embedded newform 231.4.g.a.197.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [231,4,Mod(197,231)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("231.197"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(231, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.5
Character	$\chi$	$=$	231.197
Dual form			231.4.g.a.197.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.08922 q^{2} +(2.66331 - 4.46170i) q^{3} +17.9001 q^{4} +19.3058i q^{5} +(-13.5542 + 22.7066i) q^{6} -7.00000i q^{7} -50.3840 q^{8} +(-12.8135 - 23.7658i) q^{9} -98.2512i q^{10} +(-31.1051 - 19.0650i) q^{11} +(47.6737 - 79.8651i) q^{12} +5.35526i q^{13} +35.6245i q^{14} +(86.1365 + 51.4173i) q^{15} +113.214 q^{16} +44.3368 q^{17} +(65.2108 + 120.949i) q^{18} -15.3030i q^{19} +345.576i q^{20} +(-31.2319 - 18.6432i) q^{21} +(158.301 + 97.0260i) q^{22} -110.289i q^{23} +(-134.188 + 224.798i) q^{24} -247.712 q^{25} -27.2541i q^{26} +(-140.162 - 6.12574i) q^{27} -125.301i q^{28} +188.065 q^{29} +(-438.367 - 261.674i) q^{30} +323.720 q^{31} -173.099 q^{32} +(-167.905 + 88.0054i) q^{33} -225.640 q^{34} +135.140 q^{35} +(-229.364 - 425.411i) q^{36} -12.7844 q^{37} +77.8805i q^{38} +(23.8936 + 14.2627i) q^{39} -972.701i q^{40} +338.470 q^{41} +(158.946 + 94.8793i) q^{42} +125.542i q^{43} +(-556.785 - 341.266i) q^{44} +(458.817 - 247.375i) q^{45} +561.287i q^{46} -408.178i q^{47} +(301.525 - 505.127i) q^{48} -49.0000 q^{49} +1260.66 q^{50} +(118.083 - 197.817i) q^{51} +95.8599i q^{52} -303.069i q^{53} +(713.317 + 31.1752i) q^{54} +(368.064 - 600.507i) q^{55} +352.688i q^{56} +(-68.2775 - 40.7568i) q^{57} -957.106 q^{58} -18.6625i q^{59} +(1541.86 + 920.377i) q^{60} -922.178i q^{61} -1647.48 q^{62} +(-166.361 + 89.6946i) q^{63} -24.7739 q^{64} -103.387 q^{65} +(854.505 - 447.879i) q^{66} +284.742 q^{67} +793.635 q^{68} +(-492.078 - 293.735i) q^{69} -687.758 q^{70} +558.799i q^{71} +(645.596 + 1197.42i) q^{72} -846.812i q^{73} +65.0624 q^{74} +(-659.735 + 1105.22i) q^{75} -273.926i q^{76} +(-133.455 + 217.735i) q^{77} +(-121.600 - 72.5862i) q^{78} -221.581i q^{79} +2185.68i q^{80} +(-400.627 + 609.047i) q^{81} -1722.55 q^{82} +899.959 q^{83} +(-559.055 - 333.716i) q^{84} +855.955i q^{85} -638.913i q^{86} +(500.877 - 839.091i) q^{87} +(1567.20 + 960.571i) q^{88} +587.363i q^{89} +(-2335.02 + 1258.94i) q^{90} +37.4868 q^{91} -1974.20i q^{92} +(862.168 - 1444.34i) q^{93} +2077.31i q^{94} +295.437 q^{95} +(-461.017 + 772.315i) q^{96} -680.065 q^{97} +249.372 q^{98} +(-54.5300 + 983.527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 288 q^{4} + 4 q^{9} + 16 q^{12} + 20 q^{15} + 1248 q^{16} + 384 q^{22} - 1824 q^{25} - 900 q^{27} + 264 q^{31} - 964 q^{33} - 1008 q^{34} + 48 q^{36} - 24 q^{37} + 1524 q^{45} + 192 q^{48} - 3528 q^{49}+ \cdots - 1260 q^{99}+O(q^{100}) $ 72 * q + 288 * q^4 + 4 * q^9 + 16 * q^12 + 20 * q^15 + 1248 * q^16 + 384 * q^22 - 1824 * q^25 - 900 * q^27 + 264 * q^31 - 964 * q^33 - 1008 * q^34 + 48 * q^36 - 24 * q^37 + 1524 * q^45 + 192 * q^48 - 3528 * q^49 + 1728 * q^55 - 3612 * q^58 - 3172 * q^60 + 5844 * q^64 - 2748 * q^66 + 624 * q^67 + 804 * q^69 - 756 * q^70 - 4516 * q^75 - 1268 * q^78 + 4796 * q^81 + 10056 * q^82 + 7428 * q^88 - 1008 * q^91 - 3916 * q^93 + 168 * q^97 - 1260 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−5.08922			−1.79931			−0.899655	−	0.436601i	$-0.856182\pi$
$2$	−5.08922			−1.79931			−0.899655	+	0.436601i	$0.856182\pi$
$3$	2.66331	−	4.46170i	0.512555	−	0.858654i
$3$	2.66331	−	4.46170i	0.512555	−	0.858654i
$4$	17.9001			2.23752
$5$			19.3058i			1.72676i	0.504555	+	0.863380i	$0.331657\pi$
$5$			19.3058i			1.72676i	−0.504555	+	0.863380i	$0.668343\pi$
$6$	−13.5542	+	22.7066i	−0.922246	+	1.54499i
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$	−50.3840			−2.22668
$9$	−12.8135	−	23.7658i	−0.474575	−	0.880215i
$10$		−	98.2512i		−	3.10698i
$11$	−31.1051	−	19.0650i	−0.852594	−	0.522574i
$11$	−31.1051	−	19.0650i	−0.852594	−	0.522574i
$12$	47.6737	−	79.8651i	1.14685	−	1.92125i
$13$			5.35526i			0.114252i	0.998367	+	0.0571262i	$0.0181938\pi$
$13$			5.35526i			0.114252i	−0.998367	+	0.0571262i	$0.981806\pi$
$14$			35.6245i			0.680075i
$15$	86.1365	+	51.4173i	1.48269	+	0.885059i
$16$	113.214			1.76897
$17$	44.3368			0.632544			0.316272	−	0.948669i	$-0.397569\pi$
$17$	44.3368			0.632544			0.316272	+	0.948669i	$0.397569\pi$
$18$	65.2108	+	120.949i	0.853907	+	1.58378i
$19$		−	15.3030i		−	0.184777i	−0.995723	−	0.0923883i	$-0.970550\pi$
$19$		−	15.3030i		−	0.184777i	0.995723	−	0.0923883i	$-0.0294501\pi$
$20$			345.576i			3.86366i
$21$	−31.2319	−	18.6432i	−0.324541	−	0.193728i
$22$	158.301	+	97.0260i	1.53408	+	0.940273i
$23$		−	110.289i		−	0.999867i	−0.866064	−	0.499933i	$-0.833358\pi$
$23$		−	110.289i		−	0.999867i	0.866064	−	0.499933i	$-0.166642\pi$
$24$	−134.188	+	224.798i	−1.14130	+	1.91195i
$25$	−247.712			−1.98170
$26$		−	27.2541i		−	0.205576i
$27$	−140.162	−	6.12574i	−0.999046	−	0.0436630i
$28$		−	125.301i		−	0.845702i
$29$	188.065			1.20424			0.602119	−	0.798407i	$-0.294323\pi$
$29$	188.065			1.20424			0.602119	+	0.798407i	$0.294323\pi$
$30$	−438.367	−	261.674i	−2.66782	−	1.59250i
$31$	323.720			1.87554			0.937772	−	0.347252i	$-0.112885\pi$
$31$	323.720			1.87554			0.937772	+	0.347252i	$0.112885\pi$
$32$	−173.099			−0.956246
$33$	−167.905	+	88.0054i	−0.885712	+	0.464235i
$34$	−225.640			−1.13814
$35$	135.140			0.652654
$36$	−229.364	−	425.411i	−1.06187	−	1.96950i
$37$	−12.7844			−0.0568037			−0.0284018	−	0.999597i	$-0.509042\pi$
$37$	−12.7844			−0.0568037			−0.0284018	+	0.999597i	$0.509042\pi$
$38$			77.8805i			0.332470i
$39$	23.8936	+	14.2627i	0.0981034	+	0.0585607i
$40$		−	972.701i		−	3.84494i
$41$	338.470			1.28927			0.644635	−	0.764491i	$-0.277009\pi$
$41$	338.470			1.28927			0.644635	+	0.764491i	$0.277009\pi$
$42$	158.946	+	94.8793i	0.583950	+	0.348576i
$43$			125.542i			0.445234i	0.974906	+	0.222617i	$0.0714599\pi$
$43$			125.542i			0.445234i	−0.974906	+	0.222617i	$0.928540\pi$
$44$	−556.785	−	341.266i	−1.90769	−	1.16927i
$45$	458.817	−	247.375i	1.51992	−	0.819476i
$46$			561.287i			1.79907i
$47$		−	408.178i		−	1.26679i	−0.773830	−	0.633393i	$-0.781662\pi$
$47$		−	408.178i		−	1.26679i	0.773830	−	0.633393i	$-0.218338\pi$
$48$	301.525	−	505.127i	0.906694	−	1.51893i
$49$	−49.0000			−0.142857
$50$	1260.66			3.56569
$51$	118.083	−	197.817i	0.324214	−	0.543137i
$52$			95.8599i			0.255642i
$53$		−	303.069i		−	0.785468i	−0.919652	−	0.392734i	$-0.871529\pi$
$53$		−	303.069i		−	0.785468i	0.919652	−	0.392734i	$-0.128471\pi$
$54$	713.317	+	31.1752i	1.79759	+	0.0785632i
$55$	368.064	−	600.507i	0.902360	−	1.47222i
$56$			352.688i			0.841606i
$57$	−68.2775	−	40.7568i	−0.158659	−	0.0947082i
$58$	−957.106			−2.16680
$59$		−	18.6625i		−	0.0411805i	−0.999788	−	0.0205903i	$-0.993445\pi$
$59$		−	18.6625i		−	0.0411805i	0.999788	−	0.0205903i	$-0.00655455\pi$
$60$	1541.86	+	920.377i	3.31754	+	1.98034i
$61$		−	922.178i		−	1.93562i	−0.251684	−	0.967809i	$-0.580984\pi$
$61$		−	922.178i		−	1.93562i	0.251684	−	0.967809i	$-0.419016\pi$
$62$	−1647.48			−3.37469
$63$	−166.361	+	89.6946i	−0.332690	+	0.179372i
$64$	−24.7739			−0.0483865
$65$	−103.387			−0.197287
$66$	854.505	−	447.879i	1.59367	−	0.835304i
$67$	284.742			0.519206			0.259603	−	0.965715i	$-0.416408\pi$
$67$	284.742			0.519206			0.259603	+	0.965715i	$0.416408\pi$
$68$	793.635			1.41533
$69$	−492.078	−	293.735i	−0.858540	−	0.512487i
$70$	−687.758			−1.17433
$71$			558.799i			0.934045i	0.884245	+	0.467023i	$0.154673\pi$
$71$			558.799i			0.934045i	−0.884245	+	0.467023i	$0.845327\pi$
$72$	645.596	+	1197.42i	1.05673	+	1.95996i
$73$		−	846.812i		−	1.35770i	−0.734279	−	0.678848i	$-0.762480\pi$
$73$		−	846.812i		−	1.35770i	0.734279	−	0.678848i	$-0.237520\pi$
$74$	65.0624			0.102207
$75$	−659.735	+	1105.22i	−1.01573	+	1.70159i
$76$		−	273.926i		−	0.413441i
$77$	−133.455	+	217.735i	−0.197514	+	0.322250i
$78$	−121.600	−	72.5862i	−0.176518	−	0.105369i
$79$		−	221.581i		−	0.315567i	−0.987474	−	0.157783i	$-0.949565\pi$
$79$		−	221.581i		−	0.315567i	0.987474	−	0.157783i	$-0.0504348\pi$
$80$			2185.68i			3.05458i
$81$	−400.627	+	609.047i	−0.549558	+	0.835456i
$82$	−1722.55			−2.31980
$83$	899.959			1.19016			0.595080	−	0.803666i	$-0.297120\pi$
$83$	899.959			1.19016			0.595080	+	0.803666i	$0.297120\pi$
$84$	−559.055	−	333.716i	−0.726166	−	0.433469i
$85$			855.955i			1.09225i
$86$		−	638.913i		−	0.801114i
$87$	500.877	−	839.091i	0.617238	−	1.03402i
$88$	1567.20	+	960.571i	1.89845	+	1.16361i
$89$			587.363i			0.699555i	0.936833	+	0.349778i	$0.113743\pi$
$89$			587.363i			0.699555i	−0.936833	+	0.349778i	$0.886257\pi$
$90$	−2335.02	+	1258.94i	−2.73481	+	1.47449i
$91$	37.4868			0.0431834
$92$		−	1974.20i		−	2.23722i
$93$	862.168	−	1444.34i	0.961319	−	1.61044i
$94$			2077.31i			2.27934i
$95$	295.437			0.319065
$96$	−461.017	+	772.315i	−0.490128	+	0.821085i
$97$	−680.065			−0.711857			−0.355928	−	0.934513i	$-0.615835\pi$
$97$	−680.065			−0.711857			−0.355928	+	0.934513i	$0.615835\pi$
$98$	249.372			0.257044
$99$	−54.5300	+	983.527i	−0.0553583	+	0.998467i
$100$	−4434.08			−4.43408
$101$	−1493.24			−1.47112			−0.735559	−	0.677460i	$-0.763081\pi$
$101$	−1493.24			−1.47112			−0.735559	+	0.677460i	$0.763081\pi$
$102$	−600.949	+	1006.74i	−0.583361	+	0.977272i
$103$	2040.28			1.95180			0.975899	−	0.218223i	$-0.0700261\pi$
$103$	2040.28			1.95180			0.975899	+	0.218223i	$0.0700261\pi$
$104$		−	269.819i		−	0.254404i
$105$	359.921	−	602.955i	0.334521	−	0.560404i
$106$			1542.39i			1.41330i
$107$	−1153.93			−1.04256			−0.521282	−	0.853385i	$-0.674546\pi$
$107$	−1153.93			−1.04256			−0.521282	+	0.853385i	$0.674546\pi$
$108$	−2508.93	−	109.652i	−2.23538	−	0.0976967i
$109$			385.169i			0.338463i	0.985576	+	0.169231i	$0.0541285\pi$
$109$			385.169i			0.338463i	−0.985576	+	0.169231i	$0.945871\pi$
$110$	−1873.16	+	3056.11i	−1.62363	+	2.64899i
$111$	−34.0488	+	57.0400i	−0.0291150	+	0.0487747i
$112$		−	792.498i		−	0.668608i
$113$		−	1410.54i		−	1.17427i	−0.809488	−	0.587136i	$-0.800255\pi$
$113$		−	1410.54i		−	1.17427i	0.809488	−	0.587136i	$-0.199745\pi$
$114$	347.479	+	207.420i	0.285477	+	0.170409i
$115$	2129.22			1.72653
$116$	3366.40			2.69450
$117$	127.272	−	68.6197i	0.100567	−	0.0542213i
$118$			94.9776i			0.0740965i
$119$		−	310.358i		−	0.239079i
$120$	−4339.90	−	2590.61i	−3.30147	−	1.97074i
$121$	604.051	+	1186.04i	0.453832	+	0.891087i
$122$			4693.16i			3.48278i
$123$	901.451	−	1510.15i	0.660822	−	1.10704i
$124$	5794.64			4.19656
$125$		−	2369.05i		−	1.69516i
$126$	846.646	−	456.476i	0.598613	−	0.322747i
$127$		−	1501.87i		−	1.04937i	−0.851298	−	0.524683i	$-0.824184\pi$
$127$		−	1501.87i		−	1.04937i	0.851298	−	0.524683i	$-0.175816\pi$
$128$	1510.87			1.04331
$129$	560.133	+	334.359i	0.382302	+	0.228207i
$130$	526.161			0.354980
$131$	1508.86			1.00633			0.503166	−	0.864190i	$-0.332168\pi$
$131$	1508.86			1.00633			0.503166	+	0.864190i	$0.332168\pi$
$132$	−3005.52	+	1575.31i	−1.98180	+	1.03874i
$133$	−107.121			−0.0698390
$134$	−1449.12			−0.934213
$135$	118.262	−	2705.94i	0.0753954	−	1.72511i
$136$	−2233.87			−1.40847
$137$		−	1408.49i		−	0.878360i	−0.898399	−	0.439180i	$-0.855269\pi$
$137$		−	1408.49i		−	0.878360i	0.898399	−	0.439180i	$-0.144731\pi$
$138$	2504.29	+	1494.88i	1.54478	+	0.922123i
$139$			1180.45i			0.720322i	0.932890	+	0.360161i	$0.117278\pi$
$139$			1180.45i			0.720322i	−0.932890	+	0.360161i	$0.882722\pi$
$140$	2419.03			1.46032
$141$	−1821.17	−	1087.11i	−1.08773	−	0.649297i
$142$		−	2843.85i		−	1.68064i
$143$	102.098	−	166.576i	0.0597054	−	0.0974109i
$144$	−1450.67	−	2690.62i	−0.839508	−	1.55707i
$145$			3630.75i			2.07943i
$146$			4309.61i			2.44292i
$147$	−130.502	+	218.623i	−0.0732221	+	0.122665i
$148$	−228.842			−0.127099
$149$	−2628.81			−1.44537			−0.722685	−	0.691177i	$-0.757092\pi$
$149$	−2628.81			−1.44537			−0.722685	+	0.691177i	$0.757092\pi$
$150$	3357.54	−	5624.69i	1.82761	−	3.06169i
$151$			1583.26i			0.853268i	0.904424	+	0.426634i	$0.140301\pi$
$151$			1583.26i			0.853268i	−0.904424	+	0.426634i	$0.859699\pi$
$152$			771.028i			0.411438i
$153$	−568.110	−	1053.70i	−0.300190	−	0.556775i
$154$	679.182	−	1108.10i	0.355390	−	0.579828i
$155$			6249.66i			3.23861i
$156$	427.698	+	255.305i	0.219508	+	0.131031i
$157$	−1060.25			−0.538962			−0.269481	−	0.963006i	$-0.586852\pi$
$157$	−1060.25			−0.538962			−0.269481	+	0.963006i	$0.586852\pi$
$158$			1127.67i			0.567803i
$159$	−1352.20	−	807.169i	−0.674445	−	0.402595i
$160$		−	3341.81i		−	1.65121i
$161$	−772.026			−0.377914
$162$	2038.88	−	3099.57i	0.988825	−	1.50324i
$163$	1225.66			0.588963			0.294481	−	0.955657i	$-0.404853\pi$
$163$	1225.66			0.588963			0.294481	+	0.955657i	$0.404853\pi$
$164$	6058.65			2.88476
$165$	−1699.01	−	3241.53i	−0.801623	−	1.52941i
$166$	−4580.09			−2.14147
$167$	3263.64			1.51227			0.756133	−	0.654418i	$-0.227086\pi$
$167$	3263.64			1.51227			0.756133	+	0.654418i	$0.227086\pi$
$168$	1573.59	+	939.319i	0.722648	+	0.431369i
$169$	2168.32			0.986946
$170$		−	4356.14i		−	1.96530i
$171$	−363.689	+	196.086i	−0.162643	+	0.0876903i
$172$			2247.23i			0.996218i
$173$	−1598.62			−0.702546			−0.351273	−	0.936273i	$-0.614251\pi$
$173$	−1598.62			−0.702546			−0.351273	+	0.936273i	$0.614251\pi$
$174$	−2549.07	+	4270.32i	−1.11060	+	1.86053i
$175$			1733.99i			0.749011i
$176$	−3521.53	−	2158.43i	−1.50821	−	0.924418i
$177$	−83.2665	−	49.7041i	−0.0353598	−	0.0211073i
$178$		−	2989.22i		−	1.25872i
$179$		−	562.245i		−	0.234772i	−0.993086	−	0.117386i	$-0.962549\pi$
$179$		−	562.245i		−	0.234772i	0.993086	−	0.117386i	$-0.0374514\pi$
$180$	8212.89	−	4428.04i	3.40085	−	1.83359i
$181$	−1921.89			−0.789242			−0.394621	−	0.918844i	$-0.629124\pi$
$181$	−1921.89			−0.789242			−0.394621	+	0.918844i	$0.629124\pi$
$182$	−190.779			−0.0777003
$183$	−4114.48	−	2456.05i	−1.66203	−	0.992111i
$184$			5556.82i			2.22638i
$185$		−	246.812i		−	0.0980863i
$186$	−4387.76	+	7350.57i	−1.72971	+	2.89769i
$187$	−1379.10	−	845.281i	−0.539303	−	0.330551i
$188$		−	7306.45i		−	2.83446i
$189$	−42.8802	+	981.136i	−0.0165030	+	0.377604i
$190$	−1503.54			−0.574096
$191$			2473.38i			0.937001i	0.883463	+	0.468500i	$0.155206\pi$
$191$			2473.38i			0.937001i	−0.883463	+	0.468500i	$0.844794\pi$
$192$	−65.9806	+	110.534i	−0.0248007	+	0.0415473i
$193$		−	4618.34i		−	1.72246i	−0.508213	−	0.861231i	$-0.669694\pi$
$193$		−	4618.34i		−	1.72246i	0.508213	−	0.861231i	$-0.330306\pi$
$194$	3461.00			1.28085
$195$	−275.353	+	461.283i	−0.101120	+	0.169401i
$196$	−877.107			−0.319645
$197$	1312.52			0.474684			0.237342	−	0.971426i	$-0.423724\pi$
$197$	1312.52			0.474684			0.237342	+	0.971426i	$0.423724\pi$
$198$	277.515	−	5005.38i	0.0996067	−	1.79655i
$199$	649.120			0.231231			0.115615	−	0.993294i	$-0.463116\pi$
$199$	649.120			0.231231			0.115615	+	0.993294i	$0.463116\pi$
$200$	12480.7			4.41261
$201$	758.358	−	1270.43i	0.266122	−	0.445818i
$202$	7599.43			2.64700
$203$		−	1316.46i		−	0.455159i
$204$	2113.70	−	3540.96i	0.725434	−	1.21528i
$205$			6534.41i			2.22626i
$206$	−10383.5			−3.51189
$207$	−2621.12	+	1413.20i	−0.880098	+	0.474512i
$208$			606.291i			0.202109i
$209$	−291.752	+	476.002i	−0.0965595	+	0.157539i
$210$	−1831.72	+	3068.57i	−0.601907	+	1.00834i
$211$		−	2047.96i		−	0.668188i	−0.942540	−	0.334094i	$-0.891570\pi$
$211$		−	2047.96i		−	0.668188i	0.942540	−	0.334094i	$-0.108430\pi$
$212$		−	5424.99i		−	1.75750i
$213$	2493.19	+	1488.26i	0.802022	+	0.478750i
$214$	5872.58			1.87590
$215$	−2423.69			−0.768811
$216$	7061.94	+	308.639i	2.22456	+	0.0972234i
$217$		−	2266.04i		−	0.708889i
$218$		−	1960.21i		−	0.609000i
$219$	−3778.22	−	2255.32i	−1.16579	−	0.695894i
$220$	6588.41	−	10749.2i	2.01905	−	3.29413i
$221$			237.435i			0.0722697i
$222$	173.282	−	290.289i	0.0523870	−	0.0877609i
$223$	−389.399			−0.116933			−0.0584665	−	0.998289i	$-0.518621\pi$
$223$	−389.399			−0.116933			−0.0584665	+	0.998289i	$0.518621\pi$
$224$			1211.69i			0.361427i
$225$	3174.07	+	5887.08i	0.940464	+	1.74432i
$226$			7178.56i			2.11288i
$227$	−4194.16			−1.22633			−0.613164	−	0.789956i	$-0.710103\pi$
$227$	−4194.16			−1.22633			−0.613164	+	0.789956i	$0.710103\pi$
$228$	−1222.18	−	729.552i	−0.355003	−	0.211911i
$229$	−2762.08			−0.797044			−0.398522	−	0.917159i	$-0.630477\pi$
$229$	−2762.08			−0.797044			−0.398522	+	0.917159i	$0.630477\pi$
$230$	−10836.1			−3.10656
$231$	616.038	+	1175.33i	0.175464	+	0.334768i
$232$	−9475.49			−2.68145
$233$	−2543.40			−0.715124			−0.357562	−	0.933889i	$-0.616392\pi$
$233$	−2543.40			−0.715124			−0.357562	+	0.933889i	$0.616392\pi$
$234$	−647.716	+	349.221i	−0.180951	+	0.0975610i
$235$	7880.19			2.18743
$236$		−	334.061i		−	0.0921422i
$237$	−988.627	−	590.139i	−0.270963	−	0.161745i
$238$			1579.48i			0.430178i
$239$	3145.26			0.851255			0.425627	−	0.904898i	$-0.360053\pi$
$239$	3145.26			0.851255			0.425627	+	0.904898i	$0.360053\pi$
$240$	9751.86	+	5821.16i	2.62283	+	1.56564i
$241$			2067.13i			0.552513i	0.961084	+	0.276257i	$0.0890940\pi$
$241$			2067.13i			0.552513i	−0.961084	+	0.276257i	$0.910906\pi$
$242$	−3074.15	−	6036.00i	−0.816585	−	1.60334i
$243$	1650.39	+	3409.56i	0.435689	+	0.900097i
$244$		−	16507.1i		−	4.33098i
$245$		−	945.982i		−	0.246680i
$246$	−4587.68	+	7685.48i	−1.18902	+	1.99190i
$247$	81.9517			0.0211112
$248$	−16310.3			−4.17623
$249$	2396.87	−	4015.35i	0.610023	−	1.02194i
$250$			12056.6i			3.05011i
$251$		−	2034.49i		−	0.511616i	−0.966728	−	0.255808i	$-0.917659\pi$
$251$		−	2034.49i		−	0.511616i	0.966728	−	0.255808i	$-0.0823415\pi$
$252$	−2977.88	+	1605.55i	−0.744400	+	0.401349i
$253$	−2102.67	+	3430.56i	−0.522505	+	0.852480i
$254$			7643.35i			1.88813i
$255$	3819.02	+	2279.68i	0.937867	+	0.559839i
$256$	−7490.96			−1.82885
$257$			4128.28i			1.00201i	0.865446	+	0.501003i	$0.167035\pi$
$257$			4128.28i			1.00201i	−0.865446	+	0.501003i	$0.832965\pi$
$258$	−2850.64	−	1701.63i	−0.687880	−	0.410615i
$259$			89.4906i			0.0214698i
$260$	−1850.65			−0.441432
$261$	−2409.78	−	4469.53i	−0.571501	−	1.05999i
$262$	−7678.91			−1.81071
$263$	−2804.26			−0.657483			−0.328741	−	0.944420i	$-0.606624\pi$
$263$	−2804.26			−0.657483			−0.328741	+	0.944420i	$0.606624\pi$
$264$	8459.72	−	4434.06i	1.97220	−	1.03370i
$265$	5850.98			1.35631
$266$	545.163			0.125662
$267$	2620.64	+	1564.33i	0.600676	+	0.358560i
$268$	5096.93			1.16173
$269$		−	355.233i		−	0.0805165i	−0.999189	−	0.0402582i	$-0.987182\pi$
$269$		−	355.233i		−	0.0805165i	0.999189	−	0.0402582i	$-0.0128181\pi$
$270$	−601.862	+	13771.1i	−0.135660	+	3.10401i
$271$			4496.47i			1.00790i	0.863733	+	0.503950i	$0.168120\pi$
$271$			4496.47i			1.00790i	−0.863733	+	0.503950i	$0.831880\pi$
$272$	5019.55			1.11895
$273$	99.8392	−	167.255i	0.0221339	−	0.0370796i
$274$			7168.11i			1.58044i
$275$	7705.11	+	4722.64i	1.68958	+	1.03558i
$276$	−8808.27	−	5257.91i	−1.92100	−	1.14670i
$277$			2716.98i			0.589342i	0.955599	+	0.294671i	$0.0952101\pi$
$277$			2716.98i			0.589342i	−0.955599	+	0.294671i	$0.904790\pi$
$278$		−	6007.59i		−	1.29608i
$279$	−4147.99	−	7693.47i	−0.890086	−	1.65088i
$280$	−6808.91			−1.45325
$281$	298.561			0.0633832			0.0316916	−	0.999498i	$-0.489911\pi$
$281$	298.561			0.0633832			0.0316916	+	0.999498i	$0.489911\pi$
$282$	9268.33	+	5532.52i	1.95717	+	1.16829i
$283$			5011.77i			1.05272i	0.850263	+	0.526358i	$0.176443\pi$
$283$			5011.77i			1.05272i	−0.850263	+	0.526358i	$0.823557\pi$
$284$			10002.6i			2.08994i
$285$	786.840	−	1318.15i	0.163538	−	0.273966i
$286$	−519.600	+	847.740i	−0.107429	+	0.175273i
$287$		−	2369.29i		−	0.487298i
$288$	2218.01	+	4113.84i	0.453810	+	0.841702i
$289$	−2947.25			−0.599888
$290$		−	18477.7i		−	3.74154i
$291$	−1811.23	+	3034.24i	−0.364866	+	0.611239i
$292$		−	15158.0i		−	3.03787i
$293$	−68.5089			−0.0136598			−0.00682992	−	0.999977i	$-0.502174\pi$
$293$	−68.5089			−0.0136598			−0.00682992	+	0.999977i	$0.502174\pi$
$294$	664.155	−	1112.62i	0.131749	−	0.220712i
$295$	360.294			0.0711088
$296$	644.128			0.126484
$297$	4242.97	+	2862.74i	0.828964	+	0.559303i
$298$	13378.6			2.60067
$299$	590.629			0.114237
$300$	−11809.4	+	19783.6i	−2.27271	+	3.80735i
$301$	878.797			0.168282
$302$		−	8057.53i		−	1.53529i
$303$	−3976.97	+	6662.39i	−0.754029	+	1.26318i
$304$		−	1732.52i		−	0.326864i
$305$	17803.3			3.34235
$306$	2891.24	+	5362.51i	0.540134	+	1.00181i
$307$		−	3943.18i		−	0.733059i	−0.930406	−	0.366529i	$-0.880546\pi$
$307$		−	3943.18i		−	0.733059i	0.930406	−	0.366529i	$-0.119454\pi$
$308$	−2388.87	+	3897.50i	−0.441942	+	0.721041i
$309$	5433.92	−	9103.13i	1.00040	−	1.67592i
$310$		−	31805.9i		−	5.82727i
$311$			4735.59i			0.863442i	0.902007	+	0.431721i	$0.142094\pi$
$311$			4735.59i			0.863442i	−0.902007	+	0.431721i	$0.857906\pi$
$312$	−1203.85	−	718.614i	−0.218445	−	0.130396i
$313$	2998.16			0.541426			0.270713	−	0.962660i	$-0.412741\pi$
$313$	2998.16			0.541426			0.270713	+	0.962660i	$0.412741\pi$
$314$	5395.84			0.969761
$315$	−1731.62	−	3211.72i	−0.309733	−	0.574476i
$316$		−	3966.33i		−	0.706087i
$317$			2760.19i			0.489047i	0.969643	+	0.244523i	$0.0786315\pi$
$317$			2760.19i			0.489047i	−0.969643	+	0.244523i	$0.921369\pi$
$318$	6881.66	+	4107.86i	1.21354	+	0.724394i
$319$	−5849.79	−	3585.47i	−1.02673	−	0.629303i
$320$		−	478.279i		−	0.0835518i
$321$	−3073.27	+	5148.47i	−0.534371	+	0.895202i
$322$	3929.01			0.679985
$323$		−	678.487i		−	0.116879i
$324$	−7171.29	+	10902.0i	−1.22965	+	1.86935i
$325$		−	1326.56i		−	0.226414i
$326$	−6237.64			−1.05973
$327$	1718.51	+	1025.82i	0.290623	+	0.173481i
$328$	−17053.4			−2.87079
$329$	−2857.25			−0.478800
$330$	8646.63	+	16496.9i	1.44237	+	2.75189i
$331$	−3459.72			−0.574512			−0.287256	−	0.957854i	$-0.592743\pi$
$331$	−3459.72			−0.574512			−0.287256	+	0.957854i	$0.592743\pi$
$332$	16109.4			2.66301
$333$	163.813	+	303.831i	0.0269576	+	0.0499995i
$334$	−16609.4			−2.72104
$335$			5497.16i			0.896544i
$336$	−3535.89	−	2110.67i	−0.574103	−	0.342698i
$337$		−	4834.04i		−	0.781386i	−0.920521	−	0.390693i	$-0.872235\pi$
$337$		−	4834.04i		−	0.781386i	0.920521	−	0.390693i	$-0.127765\pi$
$338$	−11035.1			−1.77582
$339$	−6293.42	−	3756.72i	−1.00829	−	0.601879i
$340$			15321.7i			2.44393i
$341$	−10069.3	−	6171.73i	−1.59908	−	0.980111i
$342$	1850.89	−	997.923i	0.292646	−	0.157782i
$343$			343.000i			0.0539949i
$344$		−	6325.33i		−	0.991393i
$345$	5670.78	−	9499.94i	0.884941	−	1.48249i
$346$	8135.71			1.26410
$347$	−9893.29			−1.53055			−0.765273	−	0.643706i	$-0.777396\pi$
$347$	−9893.29			−1.53055			−0.765273	+	0.643706i	$0.777396\pi$
$348$	8965.78	−	15019.9i	1.38108	−	2.31365i
$349$		−	7531.68i		−	1.15519i	−0.816323	−	0.577595i	$-0.803991\pi$
$349$		−	7531.68i		−	1.15519i	0.816323	−	0.577595i	$-0.196009\pi$
$350$		−	8824.63i		−	1.34770i
$351$	32.8050	−	750.606i	0.00498860	−	0.114144i
$352$	5384.26	+	3300.13i	0.815289	+	0.499709i
$353$			7982.30i			1.20355i	0.798664	+	0.601777i	$0.205541\pi$
$353$			7982.30i			1.20355i	−0.798664	+	0.601777i	$0.794459\pi$
$354$	423.761	+	252.955i	0.0636233	+	0.0379786i
$355$	−10788.0			−1.61287
$356$			10513.9i			1.56527i
$357$	−1384.72	−	826.580i	−0.205286	−	0.122541i
$358$			2861.39i			0.422427i
$359$	12947.6			1.90348			0.951742	−	0.306900i	$-0.0992916\pi$
$359$	12947.6			1.90348			0.951742	+	0.306900i	$0.0992916\pi$
$360$	−23117.0	+	12463.7i	−3.38437	+	1.82471i
$361$	6624.82			0.965858
$362$	9780.90			1.42009
$363$	6900.52	+	463.695i	0.997750	+	0.0670460i
$364$	671.020			0.0966236
$365$	16348.3			2.34441
$366$	20939.5	+	12499.4i	2.99050	+	1.78512i
$367$	−4168.83			−0.592947			−0.296473	−	0.955041i	$-0.595811\pi$
$367$	−4168.83			−0.592947			−0.296473	+	0.955041i	$0.595811\pi$
$368$		−	12486.3i		−	1.76873i
$369$	−4336.99	−	8044.00i	−0.611855	−	1.13483i
$370$			1256.08i			0.176488i
$371$	−2121.49			−0.296879
$372$	15432.9	−	25853.9i	2.15097	−	3.60340i
$373$			3855.42i			0.535190i	0.963531	+	0.267595i	$0.0862289\pi$
$373$			3855.42i			0.535190i	−0.963531	+	0.267595i	$0.913771\pi$
$374$	7018.54	+	4301.82i	0.970374	+	0.594764i
$375$	−10570.0	−	6309.53i	−1.45555	−	0.868860i
$376$			20565.7i			2.82073i
$377$			1007.14i			0.137587i
$378$	218.227	−	4993.22i	0.0296941	−	0.679427i
$379$	5187.84			0.703118			0.351559	−	0.936166i	$-0.385652\pi$
$379$	5187.84			0.703118			0.351559	+	0.936166i	$0.385652\pi$
$380$	5288.36			0.713913
$381$	−6700.89	−	3999.95i	−0.901043	−	0.537858i
$382$		−	12587.5i		−	1.68596i
$383$		−	8321.35i		−	1.11019i	−0.831788	−	0.555093i	$-0.812683\pi$
$383$		−	8321.35i		−	1.11019i	0.831788	−	0.555093i	$-0.187317\pi$
$384$	4023.92	−	6741.05i	0.534753	−	0.895841i
$385$	−4203.55	−	2576.45i	−0.556448	−	0.341060i
$386$			23503.7i			3.09925i
$387$	2983.62	−	1608.64i	0.391901	−	0.211297i
$388$	−12173.3			−1.59279
$389$		−	1196.59i		−	0.155963i	−0.996955	−	0.0779816i	$-0.975152\pi$
$389$		−	1196.59i		−	0.155963i	0.996955	−	0.0779816i	$-0.0248476\pi$
$390$	1401.33	−	2347.57i	0.181947	−	0.304805i
$391$		−	4889.88i		−	0.632460i
$392$	2468.82			0.318097
$393$	4018.56	−	6732.07i	0.515801	−	0.864092i
$394$	−6679.68			−0.854105
$395$	4277.78			0.544908
$396$	−976.095	+	17605.3i	−0.123865	+	2.23409i
$397$	−6109.12			−0.772312			−0.386156	−	0.922433i	$-0.626197\pi$
$397$	−6109.12			−0.772312			−0.386156	+	0.922433i	$0.626197\pi$
$398$	−3303.51			−0.416056
$399$	−285.297	+	477.943i	−0.0357963	+	0.0599676i
$400$	−28044.5			−3.50556
$401$			13781.5i			1.71625i	0.513438	+	0.858126i	$0.328371\pi$
$401$			13781.5i			1.71625i	−0.513438	+	0.858126i	$0.671629\pi$
$402$	−3859.45	+	6465.52i	−0.478835	+	0.802166i
$403$			1733.61i			0.214286i
$404$	−26729.2			−3.29165
$405$	−11758.1	−	7734.42i	−1.44263	−	0.948954i
$406$			6699.74i			0.818972i
$407$	397.659	+	243.734i	0.0484305	+	0.0296841i
$408$	−5949.48	+	9966.83i	−0.721920	+	1.20939i
$409$			8693.30i			1.05099i	0.850796	+	0.525496i	$0.176120\pi$
$409$			8693.30i			1.05099i	−0.850796	+	0.525496i	$0.823880\pi$
$410$		−	33255.0i		−	4.00573i
$411$	−6284.25	−	3751.25i	−0.754208	−	0.450208i
$412$	36521.4			4.36718
$413$	−130.638			−0.0155648
$414$	13339.4	−	7192.06i	1.58357	−	0.853794i
$415$			17374.4i			2.05512i
$416$		−	926.990i		−	0.109253i
$417$	5266.83	+	3143.92i	0.618508	+	0.369205i
$418$	1484.79	−	2422.48i	0.173740	−	0.283462i
$419$			512.168i			0.0597160i	0.999554	+	0.0298580i	$0.00950552\pi$
$419$			512.168i			0.0597160i	−0.999554	+	0.0298580i	$0.990494\pi$
$420$	6442.64	−	10793.0i	0.748497	−	1.25391i
$421$	12376.8			1.43280			0.716399	−	0.697691i	$-0.245789\pi$
$421$	12376.8			1.43280			0.716399	+	0.697691i	$0.245789\pi$
$422$			10422.5i			1.20228i
$423$	−9700.69	+	5230.20i	−1.11504	+	0.601185i
$424$			15269.8i			1.74898i
$425$	−10982.8			−1.25351
$426$	−12688.4	−	7574.06i	−1.44309	−	0.861419i
$427$	−6455.24			−0.731595
$428$	−20655.4			−2.33275
$429$	−471.292	−	899.175i	−0.0530400	−	0.101195i
$430$	12334.7			1.38333
$431$	−11336.6			−1.26697			−0.633487	−	0.773753i	$-0.718377\pi$
$431$	−11336.6			−1.26697			−0.633487	+	0.773753i	$0.718377\pi$
$432$	−15868.3	−	693.520i	−1.76728	−	0.0772384i
$433$	1811.36			0.201035			0.100518	−	0.994935i	$-0.467950\pi$
$433$	1811.36			0.201035			0.100518	+	0.994935i	$0.467950\pi$
$434$			11532.4i			1.27551i
$435$	16199.3	+	9669.81i	1.78551	+	1.06582i
$436$			6894.57i			0.757317i
$437$	−1687.76			−0.184752
$438$	19228.2	+	11477.8i	2.09762	+	1.25213i
$439$			1173.94i			0.127629i	0.997962	+	0.0638145i	$0.0203266\pi$
$439$			1173.94i			0.127629i	−0.997962	+	0.0638145i	$0.979673\pi$
$440$	−18544.6	+	30255.9i	−2.00927	+	3.27817i
$441$	627.862	+	1164.52i	0.0677964	+	0.125745i
$442$		−	1208.36i		−	0.130036i
$443$		−	11990.3i		−	1.28595i	−0.765888	−	0.642975i	$-0.777700\pi$
$443$		−	11990.3i		−	1.28595i	0.765888	−	0.642975i	$-0.222300\pi$
$444$	−609.478	+	1021.02i	−0.0651454	+	0.109134i
$445$	−11339.5			−1.20796
$446$	1981.73			0.210399
$447$	−7001.34	+	11728.9i	−0.740832	+	1.24107i
$448$			173.417i			0.0182884i
$449$			17778.6i			1.86865i	0.356417	+	0.934327i	$0.383998\pi$
$449$			17778.6i			1.86865i	−0.356417	+	0.934327i	$0.616002\pi$
$450$	−16153.5	−	29960.6i	−1.69219	−	3.13857i
$451$	−10528.1	−	6452.92i	−1.09922	−	0.673739i
$452$		−	25248.9i		−	2.62745i
$453$	7064.01	+	4216.71i	0.732662	+	0.437347i
$454$	21345.0			2.20654
$455$			723.711i			0.0745673i
$456$	3440.09	+	2053.49i	0.353283	+	0.210885i
$457$		−	1089.90i		−	0.111561i	−0.998443	−	0.0557807i	$-0.982235\pi$
$457$		−	1089.90i		−	0.111561i	0.998443	−	0.0557807i	$-0.0177648\pi$
$458$	14056.8			1.43413
$459$	−6214.35	−	271.596i	−0.631941	−	0.0276188i
$460$	38113.4			3.86314
$461$	−2110.05			−0.213178			−0.106589	−	0.994303i	$-0.533993\pi$
$461$	−2110.05			−0.213178			−0.106589	+	0.994303i	$0.533993\pi$
$462$	−3135.15	−	5981.53i	−0.315715	−	0.602351i
$463$	−9497.11			−0.953279			−0.476639	−	0.879099i	$-0.658145\pi$
$463$	−9497.11			−0.953279			−0.476639	+	0.879099i	$0.658145\pi$
$464$	21291.6			2.13026
$465$	27884.1	+	16644.8i	2.78085	+	1.65997i
$466$	12943.9			1.28673
$467$		−	3480.44i		−	0.344873i	−0.985021	−	0.172437i	$-0.944836\pi$
$467$		−	3480.44i		−	0.344873i	0.985021	−	0.172437i	$-0.0551640\pi$
$468$	2278.19	−	1228.30i	0.225020	−	0.121321i
$469$		−	1993.20i		−	0.196241i
$470$	−40104.0			−3.93587
$471$	−2823.78	+	4730.51i	−0.276248	+	0.462782i
$472$			940.292i			0.0916958i
$473$	2393.47	−	3905.01i	0.232668	−	0.379603i
$474$	5031.34	+	3003.35i	0.487546	+	0.291030i
$475$			3790.75i			0.366171i
$476$		−	5555.45i		−	0.534944i
$477$	−7202.69	+	3883.39i	−0.691381	+	0.372763i
$478$	−16006.9			−1.53167
$479$	14854.9			1.41699			0.708496	−	0.705715i	$-0.249374\pi$
$479$	14854.9			1.41699			0.708496	+	0.705715i	$0.249374\pi$
$480$	−14910.1	−	8900.28i	−1.41782	−	0.846334i
$481$		−	68.4636i		−	0.00648996i
$482$		−	10520.1i		−	0.994143i
$483$	−2056.15	+	3444.55i	−0.193702	+	0.324498i
$484$	10812.6	+	21230.2i	1.01546	+	1.99382i
$485$		−	13129.2i		−	1.22921i
$486$	−8399.19	−	17352.0i	−0.783940	−	1.61955i
$487$	6600.15			0.614130			0.307065	−	0.951689i	$-0.400653\pi$
$487$	6600.15			0.614130			0.307065	+	0.951689i	$0.400653\pi$
$488$			46463.0i			4.31000i
$489$	3264.31	−	5468.52i	0.301876	−	0.505716i
$490$			4814.31i			0.443854i
$491$	768.249			0.0706122			0.0353061	−	0.999377i	$-0.488759\pi$
$491$	768.249			0.0706122			0.0353061	+	0.999377i	$0.488759\pi$
$492$	16136.1	−	27031.9i	1.47860	−	2.47702i
$493$	8338.22			0.761733
$494$	−417.070			−0.0379856
$495$	−18987.7	−	1052.74i	−1.72411	−	0.0955904i
$496$	36649.7			3.31778
$497$	3911.59			0.353036
$498$	−12198.2	+	20435.0i	−1.09762	+	1.83878i
$499$	2674.41			0.239926			0.119963	−	0.992778i	$-0.461722\pi$
$499$	2674.41			0.239926			0.119963	+	0.992778i	$0.461722\pi$
$500$		−	42406.4i		−	3.79294i
$501$	8692.11	−	14561.4i	0.775119	−	1.29851i
$502$			10353.9i			0.920556i
$503$	−1280.71			−0.113527			−0.0567635	−	0.998388i	$-0.518078\pi$
$503$	−1280.71			−0.113527			−0.0567635	+	0.998388i	$0.518078\pi$
$504$	8381.92	−	4519.17i	0.740794	−	0.399405i
$505$		−	28828.1i		−	2.54027i
$506$	10700.9	−	17458.9i	0.940148	−	1.53388i
$507$	5774.92	−	9674.40i	0.505864	−	0.847446i
$508$		−	26883.7i		−	2.34797i
$509$		−	20562.6i		−	1.79061i	−0.445451	−	0.895306i	$-0.646957\pi$
$509$		−	20562.6i		−	1.79061i	0.445451	−	0.895306i	$-0.353043\pi$
$510$	−19435.8	−	11601.8i	−1.68751	−	1.00732i
$511$	−5927.68			−0.513161
$512$	26036.2			2.24736
$513$	−93.7424	+	2144.91i	−0.00806789	+	0.184600i
$514$		−	21009.7i		−	1.80292i
$515$			39389.2i			3.37028i
$516$	10026.5	+	5985.07i	0.855407	+	0.510617i
$517$	−7781.92	+	12696.4i	−0.661990	+	1.08005i
$518$		−	455.437i		−	0.0386308i
$519$	−4257.62	+	7132.54i	−0.360094	+	0.603245i
$520$	5209.07			0.439294
$521$		−	5933.99i		−	0.498988i	−0.968376	−	0.249494i	$-0.919736\pi$
$521$		−	5933.99i		−	0.498988i	0.968376	−	0.249494i	$-0.0802643\pi$
$522$	12263.9	+	22746.4i	1.02831	+	1.90725i
$523$		−	7681.86i		−	0.642265i	−0.947034	−	0.321132i	$-0.895937\pi$
$523$		−	7681.86i		−	0.642265i	0.947034	−	0.321132i	$-0.104063\pi$
$524$	27008.8			2.25169
$525$	7736.52	+	4618.15i	0.643142	+	0.383909i
$526$	14271.5			1.18302
$527$	14352.7			1.18636
$528$	−19009.2	+	9963.44i	−1.56680	+	0.821218i
$529$	3.23965			0.000266265
$530$	−29776.9			−2.44043
$531$	−443.529	+	239.132i	−0.0362477	+	0.0195432i
$532$	−1917.48			−0.156266
$533$			1812.59i			0.147302i
$534$	−13337.0	−	7961.23i	−1.08080	−	0.645162i
$535$		−	22277.4i		−	1.80026i
$536$	−14346.5			−1.15611
$537$	−2508.57	−	1497.43i	−0.201588	−	0.120333i
$538$			1807.86i			0.144874i
$539$	1524.15	+	934.185i	0.121799	+	0.0746535i
$540$	2116.91	−	48436.7i	0.168699	−	3.85997i
$541$		−	3969.52i		−	0.315458i	−0.987482	−	0.157729i	$-0.949583\pi$
$541$		−	3969.52i		−	0.315458i	0.987482	−	0.157729i	$-0.0504173\pi$
$542$		−	22883.5i		−	1.81352i
$543$	−5118.59	+	8574.88i	−0.404530	+	0.677686i
$544$	−7674.65			−0.604868
$545$	−7435.97			−0.584444
$546$	−508.103	+	851.197i	−0.0398257	+	0.0667177i
$547$			1248.29i			0.0975743i	0.998809	+	0.0487871i	$0.0155356\pi$
$547$			1248.29i			0.0975743i	−0.998809	+	0.0487871i	$0.984464\pi$
$548$		−	25212.2i		−	1.96535i
$549$	−21916.3	+	11816.3i	−1.70376	+	0.918596i
$550$	−39213.0	−	24034.5i	−3.04008	−	1.86334i
$551$		−	2877.97i		−	0.222515i
$552$	24792.9	+	14799.6i	1.91169	+	1.14114i
$553$	−1551.07			−0.119273
$554$		−	13827.3i		−	1.06041i
$555$	−1101.20	−	657.337i	−0.0842222	−	0.0502746i
$556$			21130.3i			1.61173i
$557$	7821.05			0.594953			0.297476	−	0.954729i	$-0.403855\pi$
$557$	7821.05			0.594953			0.297476	+	0.954729i	$0.403855\pi$
$558$	21110.1	+	39153.8i	1.60154	+	2.97045i
$559$	−672.313			−0.0508690
$560$	15299.8			1.15452
$561$	−7444.37	+	3901.88i	−0.560252	+	0.293649i
$562$	−1519.44			−0.114046
$563$	7575.96			0.567120			0.283560	−	0.958954i	$-0.408484\pi$
$563$	7575.96			0.567120			0.283560	+	0.958954i	$0.408484\pi$
$564$	−32599.2	−	19459.4i	−2.43382	−	1.45281i
$565$	27231.6			2.02768
$566$		−	25506.0i		−	1.89416i
$567$	4263.33	+	2804.39i	0.315773	+	0.207713i
$568$		−	28154.5i		−	2.07982i
$569$	−6621.75			−0.487870			−0.243935	−	0.969792i	$-0.578438\pi$
$569$	−6621.75			−0.487870			−0.243935	+	0.969792i	$0.578438\pi$
$570$	−4004.40	+	6708.35i	−0.294256	+	0.492950i
$571$			17750.7i			1.30095i	0.759526	+	0.650477i	$0.225431\pi$
$571$			17750.7i			1.30095i	−0.759526	+	0.650477i	$0.774569\pi$
$572$	1827.57	−	2981.73i	0.133592	−	0.217959i
$573$	11035.5	+	6587.37i	0.804560	+	0.480264i
$574$			12057.8i			0.876801i
$575$			27320.0i			1.98143i
$576$	317.441	+	588.771i	0.0229630	+	0.0425905i
$577$	−2101.26			−0.151606			−0.0758029	−	0.997123i	$-0.524152\pi$
$577$	−2101.26			−0.151606			−0.0758029	+	0.997123i	$0.524152\pi$
$578$	14999.2			1.07938
$579$	−20605.6	−	12300.1i	−1.47900	−	0.882857i
$580$			64990.9i			4.65276i
$581$		−	6299.71i		−	0.449838i
$582$	9217.72	−	15441.9i	0.656507	−	1.09981i
$583$	−5778.02	+	9427.00i	−0.410465	+	0.669685i
$584$			42665.8i			3.02315i
$585$	1324.76	+	2457.08i	0.0936272	+	0.173655i
$586$	348.657			0.0245783
$587$		−	4200.54i		−	0.295357i	−0.989035	−	0.147679i	$-0.952820\pi$
$587$		−	4200.54i		−	0.295357i	0.989035	−	0.147679i	$-0.0471801\pi$
$588$	−2336.01	+	3913.39i	−0.163836	+	0.274465i
$589$		−	4953.90i		−	0.346557i
$590$	−1833.61			−0.127947
$591$	3495.64	−	5856.05i	0.243302	−	0.407590i
$592$	−1447.37			−0.100484
$593$	22724.7			1.57368			0.786839	−	0.617158i	$-0.211716\pi$
$593$	22724.7			1.57368			0.786839	+	0.617158i	$0.211716\pi$
$594$	−21593.4	−	14569.1i	−1.49156	−	1.00636i
$595$	5991.69			0.412832
$596$	−47056.0			−3.23404
$597$	1728.81	−	2896.18i	0.118518	−	0.198547i
$598$	−3005.84			−0.205548
$599$			12256.4i			0.836029i	0.908440	+	0.418015i	$0.137274\pi$
$599$			12256.4i			0.836029i	−0.908440	+	0.418015i	$0.862726\pi$
$600$	33240.1	−	55685.3i	2.26170	−	3.78890i
$601$			2009.00i			0.136354i	0.997673	+	0.0681772i	$0.0217183\pi$
$601$			2009.00i			0.136354i	−0.997673	+	0.0681772i	$0.978282\pi$
$602$	−4472.39			−0.302792
$603$	−3648.55	−	6767.13i	−0.246402	−	0.457013i
$604$			28340.5i			1.90920i
$605$	−22897.3	+	11661.7i	−1.53869	+	0.783659i
$606$	20239.7	−	33906.4i	1.35673	−	2.27286i
$607$		−	11582.1i		−	0.774469i	−0.921981	−	0.387234i	$-0.873430\pi$
$607$		−	11582.1i		−	0.774469i	0.921981	−	0.387234i	$-0.126570\pi$
$608$			2648.94i			0.176692i
$609$	−5873.64	−	3506.14i	−0.390824	−	0.233294i
$610$	−90605.1			−6.01392
$611$	2185.90			0.144733
$612$	−10169.3	−	18861.4i	−0.671680	−	1.24579i
$613$		−	17850.5i		−	1.17614i	−0.808810	−	0.588070i	$-0.799888\pi$
$613$		−	17850.5i		−	1.17614i	0.808810	−	0.588070i	$-0.200112\pi$
$614$			20067.7i			1.31900i
$615$	29154.6	+	17403.2i	1.91159	+	1.14108i
$616$	6724.00	−	10970.4i	0.439801	−	0.717548i
$617$		−	7771.43i		−	0.507076i	−0.967325	−	0.253538i	$-0.918406\pi$
$617$		−	7771.43i		−	0.507076i	0.967325	−	0.253538i	$-0.0815943\pi$
$618$	−27654.4	+	46327.8i	−1.80004	+	3.01550i
$619$	−1198.31			−0.0778094			−0.0389047	−	0.999243i	$-0.512387\pi$
$619$	−1198.31			−0.0778094			−0.0389047	+	0.999243i	$0.512387\pi$
$620$			111870.i			7.24646i
$621$	−675.605	+	15458.4i	−0.0436571	+	0.998913i
$622$		−	24100.4i		−	1.55360i
$623$	4111.54			0.264407
$624$	2705.09	+	1614.74i	0.173542	+	0.103592i
$625$	14772.3			0.945428
$626$	−15258.3			−0.974193
$627$	1346.75	+	2569.45i	0.0857798	+	0.163659i
$628$	−18978.6			−1.20594
$629$	−566.818			−0.0359309
$630$	8812.61	+	16345.1i	0.557306	+	1.03366i
$631$	5841.29			0.368523			0.184262	−	0.982877i	$-0.441011\pi$
$631$	5841.29			0.368523			0.184262	+	0.982877i	$0.441011\pi$
$632$			11164.1i			0.702666i
$633$	−9137.40	−	5454.37i	−0.573742	−	0.342483i
$634$		−	14047.2i		−	0.879947i
$635$	28994.7			1.81200
$636$	−24204.7	−	14448.4i	−1.50908	−	0.900814i
$637$		−	262.408i		−	0.0163218i
$638$	29770.9	+	18247.2i	1.84740	+	1.13231i
$639$	13280.3	−	7160.18i	0.822161	−	0.443274i
$640$			29168.5i			1.80154i
$641$		−	15867.0i		−	0.977704i	−0.872367	−	0.488852i	$-0.837416\pi$
$641$		−	15867.0i		−	0.977704i	0.872367	−	0.488852i	$-0.162584\pi$
$642$	15640.5	−	26201.7i	0.961499	−	1.61075i
$643$	−24781.4			−1.51988			−0.759941	−	0.649992i	$-0.774772\pi$
$643$	−24781.4			−1.51988			−0.759941	+	0.649992i	$0.774772\pi$
$644$	−13819.4			−0.845590
$645$	−6455.05	+	10813.8i	−0.394058	+	0.660143i
$646$			3452.97i			0.210302i
$647$		−	3705.33i		−	0.225149i	−0.993643	−	0.112575i	$-0.964090\pi$
$647$		−	3705.33i		−	0.225149i	0.993643	−	0.112575i	$-0.0359098\pi$
$648$	20185.2	−	30686.2i	1.22369	−	1.86029i
$649$	−355.801	+	580.498i	−0.0215199	+	0.0351103i
$650$			6751.17i			0.407389i
$651$	−10110.4	−	6035.18i	−0.608691	−	0.363345i
$652$	21939.5			1.31782
$653$		−	20988.0i		−	1.25777i	−0.777499	−	0.628884i	$-0.783512\pi$
$653$		−	20988.0i		−	1.25777i	0.777499	−	0.628884i	$-0.216488\pi$
$654$	−8745.85	−	5220.65i	−0.522920	−	0.312146i
$655$			29129.7i			1.73769i
$656$	38319.5			2.28068
$657$	−20125.2	+	10850.6i	−1.19506	+	0.644328i
$658$	14541.2			0.861510
$659$	19842.5			1.17292			0.586458	−	0.809979i	$-0.300522\pi$
$659$	19842.5			1.17292			0.586458	+	0.809979i	$0.300522\pi$
$660$	−30412.5	−	58023.9i	−1.79365	−	3.42209i
$661$	−9896.73			−0.582357			−0.291179	−	0.956669i	$-0.594047\pi$
$661$	−9896.73			−0.582357			−0.291179	+	0.956669i	$0.594047\pi$
$662$	17607.3			1.03373
$663$	1059.36	+	632.364i	0.0620547	+	0.0370422i
$664$	−45343.5			−2.65011
$665$		−	2068.06i		−	0.120595i
$666$	−833.679	−	1546.26i	−0.0485051	−	0.0899646i
$667$		−	20741.6i		−	1.20408i
$668$	58419.7			3.38372
$669$	−1037.09	+	1737.38i	−0.0599346	+	0.100405i
$670$		−	27976.3i		−	1.61316i
$671$	−17581.3	+	28684.4i	−1.01150	+	1.65030i
$672$	5406.21	+	3227.12i	0.310341	+	0.185251i
$673$			9024.80i			0.516910i	0.966023	+	0.258455i	$0.0832134\pi$
$673$			9024.80i			0.516910i	−0.966023	+	0.258455i	$0.916787\pi$
$674$			24601.5i			1.40596i
$675$	34719.9	+	1517.42i	1.97981	+	0.0865268i
$676$	38813.3			2.20831
$677$	−15168.3			−0.861101			−0.430551	−	0.902566i	$-0.641681\pi$
$677$	−15168.3			−0.861101			−0.430551	+	0.902566i	$0.641681\pi$
$678$	32028.6	+	19118.8i	1.81423	+	1.08297i
$679$			4760.45i			0.269057i
$680$		−	43126.5i		−	2.43209i
$681$	−11170.4	+	18713.1i	−0.628560	+	1.05299i
$682$	51245.1	+	31409.3i	2.87724	+	1.76352i
$683$			12158.0i			0.681133i	0.940220	+	0.340567i	$0.110619\pi$
$683$			12158.0i			0.681133i	−0.940220	+	0.340567i	$0.889381\pi$
$684$	−6510.08	+	3509.96i	−0.363917	+	0.196209i
$685$	27191.9			1.51672
$686$		−	1745.60i		−	0.0971536i
$687$	−7356.27	+	12323.6i	−0.408529	+	0.684385i
$688$			14213.2i			0.787605i
$689$	1623.02			0.0897416
$690$	−28859.9	+	48347.3i	−1.59228	+	2.66746i
$691$	9147.68			0.503609			0.251805	−	0.967778i	$-0.418976\pi$
$691$	9147.68			0.503609			0.251805	+	0.967778i	$0.418976\pi$
$692$	−28615.5			−1.57196
$693$	6884.69	+	381.710i	0.377385	+	0.0209235i
$694$	50349.1			2.75393
$695$	−22789.6			−1.24382
$696$	−25236.2	+	42276.8i	−1.37439	+	2.30244i
$697$	15006.7			0.815520
$698$			38330.4i			2.07855i
$699$	−6773.88	+	11347.9i	−0.366540	+	0.614044i
$700$			31038.6i			1.67593i
$701$	−17573.0			−0.946823			−0.473411	−	0.880841i	$-0.656978\pi$
$701$	−17573.0			−0.946823			−0.473411	+	0.880841i	$0.656978\pi$
$702$	−166.952	+	3820.00i	−0.00897604	+	0.205380i
$703$			195.640i			0.0104960i
$704$	770.593	+	472.314i	0.0412540	+	0.0252855i
$705$	20987.4	−	35159.0i	1.12118	−	1.87825i
$706$		−	40623.7i		−	2.16557i
$707$			10452.7i			0.556031i
$708$	−1490.48	−	889.711i	−0.0791183	−	0.0472279i
$709$	−13023.4			−0.689849			−0.344924	−	0.938631i	$-0.612095\pi$
$709$	−13023.4			−0.689849			−0.344924	+	0.938631i	$0.612095\pi$
$710$	54902.7			2.90206
$711$	−5266.05	+	2839.23i	−0.277767	+	0.149760i
$712$		−	29593.7i		−	1.55768i
$713$		−	35702.9i		−	1.87529i
$714$	7047.15	+	4206.64i	0.369374	+	0.220490i
$715$	3215.87	+	1971.08i	0.168205	+	0.103097i
$716$		−	10064.3i		−	0.525306i
$717$	8376.81	−	14033.2i	0.436315	−	0.730934i
$718$	−65893.4			−3.42496
$719$			1181.05i			0.0612599i	0.999531	+	0.0306300i	$0.00975135\pi$
$719$			1181.05i			0.0612599i	−0.999531	+	0.0306300i	$0.990249\pi$
$720$	51944.5	−	28006.3i	2.68869	−	1.44963i
$721$		−	14282.0i		−	0.737710i
$722$	−33715.1			−1.73788
$723$	9222.93	+	5505.42i	0.474418	+	0.283194i
$724$	−34402.1			−1.76594
$725$	−46586.1			−2.38643
$726$	−35118.2	−	2359.85i	−1.79526	−	0.120637i
$727$	5915.80			0.301795			0.150897	−	0.988549i	$-0.451784\pi$
$727$	5915.80			0.301795			0.150897	+	0.988549i	$0.451784\pi$
$728$	−1888.74			−0.0961555
$729$	19608.0	+	1717.20i	0.996187	+	0.0872426i
$730$	−83200.3			−4.21833
$731$			5566.15i			0.281630i
$732$	−73649.8	−	43963.6i	−3.71882	−	2.21987i
$733$			34504.2i			1.73867i	0.494226	+	0.869334i	$0.335452\pi$
$733$			34504.2i			1.73867i	−0.494226	+	0.869334i	$0.664548\pi$
$734$	21216.1			1.06690
$735$	−4220.69	−	2519.45i	−0.211813	−	0.126437i
$736$			19091.0i			0.956118i
$737$	−8856.93	−	5428.61i	−0.442672	−	0.271324i
$738$	22071.9	+	40937.7i	1.10092	+	2.04192i
$739$		−	3219.32i		−	0.160250i	−0.996785	−	0.0801248i	$-0.974468\pi$
$739$		−	3219.32i		−	0.160250i	0.996785	−	0.0801248i	$-0.0255319\pi$
$740$		−	4417.97i		−	0.219470i
$741$	218.263	−	365.644i	0.0108206	−	0.0181272i
$742$	10796.7			0.534177
$743$	−18197.0			−0.898495			−0.449248	−	0.893407i	$-0.648308\pi$
$743$	−18197.0			−0.898495			−0.449248	+	0.893407i	$0.648308\pi$
$744$	−43439.5	+	72771.7i	−2.14055	+	3.58594i
$745$		−	50751.1i		−	2.49581i
$746$		−	19621.1i		−	0.962973i
$747$	−11531.6	−	21388.2i	−0.564820	−	1.04760i
$748$	−24686.1	−	15130.7i	−1.20670	−	0.739615i
$749$			8077.48i			0.394052i
$750$	53793.0	+	32110.6i	2.61899	+	1.56335i
$751$	−19418.9			−0.943549			−0.471774	−	0.881719i	$-0.656386\pi$
$751$	−19418.9			−0.943549			−0.471774	+	0.881719i	$0.656386\pi$
$752$		−	46211.5i		−	2.24090i
$753$	−9077.26	−	5418.47i	−0.439301	−	0.262231i
$754$		−	5125.55i		−	0.247562i
$755$	−30565.9			−1.47339
$756$	−767.562	+	17562.5i	−0.0369259	+	0.844896i
$757$	951.894			0.0457030			0.0228515	−	0.999739i	$-0.492726\pi$
$757$	951.894			0.0457030			0.0228515	+	0.999739i	$0.492726\pi$
$758$	−26402.1			−1.26513
$759$	9706.06	+	18518.1i	0.464174	+	0.885594i
$760$	−14885.3			−0.710455
$761$	3967.66			0.188998			0.0944990	−	0.995525i	$-0.469875\pi$
$761$	3967.66			0.188998			0.0944990	+	0.995525i	$0.469875\pi$
$762$	34102.3	+	20356.6i	1.62126	+	0.967773i
$763$	2696.18			0.127927
$764$			44273.8i			2.09656i
$765$	20342.5	−	10967.8i	0.961417	−	0.518355i
$766$			42349.2i			1.99757i
$767$	99.9426			0.00470498
$768$	−19950.8	+	33422.4i	−0.937385	+	1.57035i
$769$		−	7769.69i		−	0.364346i	−0.983266	−	0.182173i	$-0.941687\pi$
$769$		−	7769.69i		−	0.364346i	0.983266	−	0.182173i	$-0.0583131\pi$
$770$	21392.8	+	13112.1i	1.00122	+	0.613673i
$771$	18419.2	+	10994.9i	0.860376	+	0.513583i
$772$		−	82668.9i		−	3.85404i
$773$			28786.3i			1.33942i	0.742623	+	0.669710i	$0.233581\pi$
$773$			28786.3i			1.33942i	−0.742623	+	0.669710i	$0.766419\pi$
$774$	−15184.3	+	8186.72i	−0.705152	+	0.380188i
$775$	−80189.4			−3.71676
$776$	34264.4			1.58508
$777$	399.280	+	238.341i	0.0184351	+	0.0110044i
$778$			6089.73i			0.280626i
$779$		−	5179.61i		−	0.238227i
$780$	−4928.86	+	8257.04i	−0.226258	+	0.379038i
$781$	10653.5	−	17381.5i	0.488108	−	0.796361i
$782$			24885.7i			1.13799i
$783$	−26359.7	−	1152.04i	−1.20309	−	0.0525806i
$784$	−5547.49			−0.252710
$785$		−	20468.9i		−	0.930658i
$786$	−20451.4	+	34261.0i	−0.928086	+	1.55477i
$787$			9026.09i			0.408825i	0.978885	+	0.204413i	$0.0655284\pi$
$787$			9026.09i			0.408825i	−0.978885	+	0.204413i	$0.934472\pi$
$788$	23494.2			1.06212
$789$	−7468.62	+	12511.8i	−0.336996	+	0.564550i
$790$	−21770.6			−0.980459
$791$	−9873.80			−0.443833
$792$	2747.44	−	49554.0i	0.123265	−	2.22326i
$793$	4938.50			0.221149
$794$	31090.6			1.38963
$795$	15583.0	−	26105.3i	0.695185	−	1.16460i
$796$	11619.3			0.517383
$797$		−	22813.9i		−	1.01394i	−0.861964	−	0.506969i	$-0.830766\pi$
$797$		−	22813.9i		−	1.01394i	0.861964	−	0.506969i	$-0.169234\pi$
$798$	1451.94	−	2432.35i	0.0644087	−	0.107900i
$799$		−	18097.3i		−	0.801298i
$800$	42878.7			1.89499
$801$	13959.2	−	7526.19i	0.615759	−	0.331991i
$802$		−	70137.3i		−	3.08807i
$803$	−16144.5	+	26340.1i	−0.709497	+	1.15756i
$804$	13574.7	−	22741.0i	0.595452	−	0.997527i
$805$		−	14904.5i		−	0.652567i
$806$		−	8822.70i		−	0.385566i
$807$	−1584.94	−	946.097i	−0.0691358	−	0.0412691i
$808$	75235.4			3.27571
$809$	29900.1			1.29942			0.649710	−	0.760182i	$-0.274890\pi$
$809$	29900.1			1.29942			0.649710	+	0.760182i	$0.274890\pi$
$810$	59839.6	+	39362.1i	2.59574	+	1.70746i
$811$		−	14200.0i		−	0.614832i	−0.951575	−	0.307416i	$-0.900536\pi$
$811$		−	14200.0i		−	0.614832i	0.951575	−	0.307416i	$-0.0994643\pi$
$812$		−	23564.8i		−	1.01843i
$813$	20061.9	+	11975.5i	0.865438	+	0.516604i
$814$	−2023.77	−	1240.42i	−0.0871415	−	0.0534110i
$815$			23662.3i			1.01700i
$816$	13368.6	−	22395.7i	0.573524	−	0.960793i
$817$	1921.18			0.0822688
$818$		−	44242.1i		−	1.89106i
$819$	−480.338	−	890.905i	−0.0204937	−	0.0380107i
$820$			116967.i			4.98129i
$821$	26294.6			1.11777			0.558883	−	0.829246i	$-0.311230\pi$
$821$	26294.6			1.11777			0.558883	+	0.829246i	$0.311230\pi$
$822$	31981.9	+	19090.9i	1.35705	+	0.810064i
$823$	31406.6			1.33021			0.665107	−	0.746748i	$-0.268386\pi$
$823$	31406.6			1.33021			0.665107	+	0.746748i	$0.268386\pi$
$824$	−102798.			−4.34603
$825$	41592.1	−	21800.0i	1.75521	−	0.919974i
$826$	664.843			0.0280059
$827$	34810.1			1.46368			0.731841	−	0.681476i	$-0.238662\pi$
$827$	34810.1			1.46368			0.731841	+	0.681476i	$0.238662\pi$
$828$	−46918.4	+	25296.4i	−1.96924	+	1.06173i
$829$	−29176.1			−1.22235			−0.611176	−	0.791495i	$-0.709303\pi$
$829$	−29176.1			−1.22235			−0.611176	+	0.791495i	$0.709303\pi$
$830$		−	88422.0i		−	3.69780i
$831$	12122.4	+	7236.18i	0.506041	+	0.302070i
$832$		−	132.671i		−	0.00552828i
$833$	−2172.50			−0.0903635
$834$	−26804.0	−	16000.1i	−1.11289	−	0.664314i
$835$			63007.1i			2.61132i
$836$	−5222.41	+	8520.50i	−0.216054	+	0.352497i
$837$	−45373.4	−	1983.03i	−1.87376	−	0.0818918i
$838$		−	2606.53i		−	0.107448i
$839$		−	40421.4i		−	1.66329i	−0.555307	−	0.831645i	$-0.687399\pi$
$839$		−	40421.4i		−	1.66329i	0.555307	−	0.831645i	$-0.312601\pi$
$840$	−18134.3	+	30379.3i	−0.744871	+	1.24784i
$841$	10979.6			0.450187
$842$	−62988.2			−2.57805
$843$	795.163	−	1332.09i	0.0324874	−	0.0544243i
$844$		−	36658.8i		−	1.49508i
$845$			41861.1i			1.70422i
$846$	49368.9	−	26617.6i	2.00631	−	1.08172i
$847$	8302.26	−	4228.36i	0.336799	−	0.171532i
$848$		−	34311.7i		−	1.38947i
$849$	22361.0	+	13347.9i	0.903919	+	0.539575i
$850$	55893.7			2.25546
$851$			1409.98i			0.0567961i
$852$	44628.5	+	26640.0i	1.79454	+	1.07121i
$853$			8072.68i			0.324037i	0.986788	+	0.162018i	$0.0518004\pi$
$853$			8072.68i			0.324037i	−0.986788	+	0.162018i	$0.948200\pi$
$854$	32852.1			1.31637
$855$	−3785.58	−	7021.29i	−0.151420	−	0.280846i
$856$	58139.4			2.32145
$857$	−39705.8			−1.58264			−0.791321	−	0.611401i	$-0.790606\pi$
$857$	−39705.8			−1.58264			−0.791321	+	0.611401i	$0.790606\pi$
$858$	2398.51	+	4576.10i	0.0954355	+	0.182081i
$859$	−33321.0			−1.32351			−0.661757	−	0.749719i	$-0.730189\pi$
$859$	−33321.0			−1.32351			−0.661757	+	0.749719i	$0.730189\pi$
$860$	−43384.4			−1.72023
$861$	−10571.0	−	6310.15i	−0.418421	−	0.249767i
$862$	57694.6			2.27968
$863$		−	48839.3i		−	1.92643i	−0.268733	−	0.963215i	$-0.586605\pi$
$863$		−	48839.3i		−	1.92643i	0.268733	−	0.963215i	$-0.413395\pi$
$864$	24262.0	+	1060.36i	0.955334	+	0.0417525i
$865$		−	30862.5i		−	1.21313i
$866$	−9218.39			−0.361725
$867$	−7849.45	+	13149.7i	−0.307475	+	0.515096i
$868$		−	40562.5i		−	1.58615i
$869$	−4224.44	+	6892.28i	−0.164907	+	0.269050i
$870$	−82441.8	−	49211.8i	−3.21269	−	1.91774i
$871$			1524.87i			0.0593206i
$872$		−	19406.3i		−	0.753648i
$873$	8714.02	+	16162.3i	0.337829	+	0.626587i
$874$	8589.39			0.332426
$875$	−16583.4			−0.640709
$876$	−67630.7	−	40370.6i	−2.60848	−	1.55707i
$877$			28801.3i			1.10895i	0.832199	+	0.554476i	$0.187081\pi$
$877$			28801.3i			1.10895i	−0.832199	+	0.554476i	$0.812919\pi$
$878$		−	5974.44i		−	0.229644i
$879$	−182.461	+	305.666i	−0.00700142	+	0.0117291i
$880$	41670.1	−	67985.8i	1.59625	−	2.60432i
$881$			24899.5i			0.952197i	0.879392	+	0.476099i	$0.157949\pi$
$881$			24899.5i			0.952197i	−0.879392	+	0.476099i	$0.842051\pi$
$882$	−3195.33	−	5926.52i	−0.121987	−	0.226254i
$883$	43258.8			1.64867			0.824335	−	0.566102i	$-0.191549\pi$
$883$	43258.8			1.64867			0.824335	+	0.566102i	$0.191549\pi$
$884$			4250.12i			0.161705i
$885$	959.575	−	1607.52i	0.0364472	−	0.0610579i
$886$			61021.2i			2.31382i
$887$	−18076.2			−0.684263			−0.342131	−	0.939652i	$-0.611149\pi$
$887$	−18076.2			−0.684263			−0.342131	+	0.939652i	$0.611149\pi$
$888$	1715.51	−	2873.90i	0.0648298	−	0.108606i
$889$	−10513.1			−0.396623
$890$	57709.2			2.17350
$891$	24073.0	−	11306.5i	0.905137	−	0.425120i
$892$	−6970.29			−0.261640
$893$	−6246.36			−0.234072
$894$	35631.3	−	59691.2i	1.33299	−	2.23308i
$895$	10854.6			0.405394
$896$		−	10576.1i		−	0.394333i
$897$	1573.03	−	2635.21i	0.0585529	−	0.0980903i
$898$		−	90479.4i		−	3.36229i
$899$	60880.6			2.25860
$900$	56816.2	+	105380.i	2.10430	+	3.90295i
$901$		−	13437.1i		−	0.496843i
$902$	53579.9	+	32840.3i	1.97784	+	1.21227i
$903$	2340.51	−	3920.93i	0.0862540	−	0.144497i
$904$			71068.8i			2.61473i
$905$		−	37103.5i		−	1.36283i
$906$	−35950.3	−	21459.7i	−1.31829	−	0.786923i
$907$	6196.80			0.226859			0.113430	−	0.993546i	$-0.463816\pi$
$907$	6196.80			0.226859			0.113430	+	0.993546i	$0.463816\pi$
$908$	−75076.1			−2.74393
$909$	19133.7	+	35488.1i	0.698156	+	1.29490i
$910$		−	3683.13i		−	0.134170i
$911$		−	39268.2i		−	1.42811i	−0.700087	−	0.714057i	$-0.746856\pi$
$911$		−	39268.2i		−	1.42811i	0.700087	−	0.714057i	$-0.253144\pi$
$912$	−7729.97	−	4614.24i	−0.280663	−	0.167536i
$913$	−27993.3	−	17157.7i	−1.01472	−	0.621947i
$914$			5546.76i			0.200734i
$915$	47415.9	−	79433.1i	1.71314	−	2.86992i
$916$	−49441.6			−1.78340
$917$		−	10562.0i		−	0.380358i
$918$	31626.2	+	1382.21i	1.13706	+	0.0496947i
$919$		−	28397.6i		−	1.01931i	−0.860378	−	0.509657i	$-0.829772\pi$
$919$		−	28397.6i		−	1.01931i	0.860378	−	0.509657i	$-0.170228\pi$
$920$	−107279.			−3.84443
$921$	−17593.3	−	10501.9i	−0.629444	−	0.375733i
$922$	10738.5			0.383573
$923$	−2992.51			−0.106717
$924$	11027.2	+	21038.7i	0.392605	+	0.749049i
$925$	3166.84			0.112568
$926$	48332.9			1.71524
$927$	−26143.2	−	48489.0i	−0.926274	−	1.71800i
$928$	−32553.9			−1.15155
$929$		−	25873.6i		−	0.913762i	−0.889528	−	0.456881i	$-0.848966\pi$
$929$		−	25873.6i		−	0.913762i	0.889528	−	0.456881i	$-0.151034\pi$
$930$	−141908.	−	84709.1i	−5.00361	−	2.98680i
$931$			749.848i			0.0263967i
$932$	−45527.3			−1.60010
$933$	21128.8	+	12612.4i	0.741399	+	0.442562i
$934$			17712.7i			0.620534i
$935$	16318.8	−	26624.6i	0.570783	−	0.931247i
$936$	−6412.48	+	3457.34i	−0.223930	+	0.120734i
$937$			43297.4i			1.50957i	0.655974	+	0.754783i	$0.272258\pi$
$937$			43297.4i			1.50957i	−0.655974	+	0.754783i	$0.727742\pi$
$938$			10143.8i			0.353099i
$939$	7985.05	−	13376.9i	0.277511	−	0.464898i
$940$	141057.			4.89442
$941$	29358.7			1.01707			0.508537	−	0.861040i	$-0.330187\pi$
$941$	29358.7			1.01707			0.508537	+	0.861040i	$0.330187\pi$
$942$	14370.8	−	24074.6i	0.497056	−	0.832689i
$943$		−	37329.6i		−	1.28910i
$944$		−	2112.86i		−	0.0728471i
$945$	−18941.6	−	827.835i	−0.652031	−	0.0284968i
$946$	−12180.9	+	19873.4i	−0.418641	+	0.683024i
$947$			28664.4i			0.983598i	0.870709	+	0.491799i	$0.163661\pi$
$947$			28664.4i			0.983598i	−0.870709	+	0.491799i	$0.836339\pi$
$948$	−17696.6	−	10563.6i	−0.606284	−	0.361908i
$949$	4534.90			0.155120
$950$		−	19291.9i		−	0.658856i
$951$	12315.1	+	7351.26i	0.419922	+	0.250663i
$952$			15637.1i			0.532353i
$953$	13033.7			0.443027			0.221513	−	0.975157i	$-0.428900\pi$
$953$	13033.7			0.443027			0.221513	+	0.975157i	$0.428900\pi$
$954$	36656.1	−	19763.4i	1.24401	−	0.670717i
$955$	−47750.4			−1.61797
$956$	56300.6			1.90470
$957$	−31577.1	+	16550.8i	−1.06661	+	0.559049i
$958$	−75600.0			−2.54961
$959$	−9859.42			−0.331989
$960$	−2133.94	−	1273.81i	−0.0717421	−	0.0428249i
$961$	75003.8			2.51766
$962$			348.426i			0.0116775i
$963$	14785.9	+	27424.0i	0.494774	+	0.917680i
$964$			37002.0i			1.23626i
$965$	89160.5			2.97428
$966$	10464.2	−	17530.1i	0.348530	−	0.583872i
$967$			52979.8i			1.76186i	0.473250	+	0.880928i	$0.343081\pi$
$967$			52979.8i			1.76186i	−0.473250	+	0.880928i	$0.656919\pi$
$968$	−30434.5	−	59757.3i	−1.01054	−	1.98417i
$969$	−3027.21	−	1807.02i	−0.100359	−	0.0599071i
$970$			66817.2i			2.21172i
$971$			7741.94i			0.255871i	0.991783	+	0.127935i	$0.0408350\pi$
$971$			7741.94i			0.255871i	−0.991783	+	0.127935i	$0.959165\pi$
$972$	29542.2	+	61031.7i	0.974863	+	2.01398i
$973$	8263.18			0.272256
$974$	−33589.6			−1.10501
$975$	−5918.73	−	3533.05i	−0.194411	−	0.116050i
$976$		−	104403.i		−	3.42405i
$977$		−	2451.15i		−	0.0802654i	−0.999194	−	0.0401327i	$-0.987222\pi$
$977$		−	2451.15i		−	0.0802654i	0.999194	−	0.0401327i	$-0.0127781\pi$
$978$	−16612.8	+	27830.5i	−0.543168	+	0.909939i
$979$	11198.1	−	18270.0i	0.365569	−	0.596436i
$980$		−	16933.2i		−	0.551951i
$981$	9153.84	−	4935.36i	0.297920	−	0.160626i
$982$	−3909.78			−0.127053
$983$		−	45946.2i		−	1.49080i	−0.666617	−	0.745400i	$-0.732258\pi$
$983$		−	45946.2i		−	1.49080i	0.666617	−	0.745400i	$-0.267742\pi$
$984$	−45418.7	+	76087.4i	−1.47144	+	2.46502i
$985$			25339.1i			0.819666i
$986$	−42435.0			−1.37059
$987$	−7609.75	+	12748.2i	−0.245411	+	0.411124i
$988$	1466.95			0.0472367
$989$	13846.0			0.445174
$990$	96632.7	+	5357.64i	3.10221	+	0.171997i
$991$	34744.4			1.11371			0.556857	−	0.830608i	$-0.312007\pi$
$991$	34744.4			1.11371			0.556857	+	0.830608i	$0.312007\pi$
$992$	−56035.6			−1.79348
$993$	−9214.32	+	15436.2i	−0.294469	+	0.493307i
$994$	−19906.9			−0.635221
$995$			12531.7i			0.399280i
$996$	42904.4	−	71875.3i	1.36494	−	2.28660i
$997$			48583.2i			1.54328i	0.636063	+	0.771638i	$0.280562\pi$
$997$			48583.2i			1.54328i	−0.636063	+	0.771638i	$0.719438\pi$
$998$	−13610.7			−0.431701
$999$	1791.89	+	78.3137i	0.0567495	+	0.00248022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.g.a.197.5	✓	72
3.2	odd	2	inner	231.4.g.a.197.68	yes	72
11.10	odd	2	inner	231.4.g.a.197.67	yes	72
33.32	even	2	inner	231.4.g.a.197.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.g.a.197.5	✓	72	1.1	even	1	trivial
231.4.g.a.197.6	yes	72	33.32	even	2	inner
231.4.g.a.197.67	yes	72	11.10	odd	2	inner
231.4.g.a.197.68	yes	72	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.08922 q^{2} +(2.66331 - 4.46170i) q^{3} +17.9001 q^{4} +19.3058i q^{5} +(-13.5542 + 22.7066i) q^{6} -7.00000i q^{7} -50.3840 q^{8} +(-12.8135 - 23.7658i) q^{9} -98.2512i q^{10} +(-31.1051 - 19.0650i) q^{11} +(47.6737 - 79.8651i) q^{12} +5.35526i q^{13} +35.6245i q^{14} +(86.1365 + 51.4173i) q^{15} +113.214 q^{16} +44.3368 q^{17} +(65.2108 + 120.949i) q^{18} -15.3030i q^{19} +345.576i q^{20} +(-31.2319 - 18.6432i) q^{21} +(158.301 + 97.0260i) q^{22} -110.289i q^{23} +(-134.188 + 224.798i) q^{24} -247.712 q^{25} -27.2541i q^{26} +(-140.162 - 6.12574i) q^{27} -125.301i q^{28} +188.065 q^{29} +(-438.367 - 261.674i) q^{30} +323.720 q^{31} -173.099 q^{32} +(-167.905 + 88.0054i) q^{33} -225.640 q^{34} +135.140 q^{35} +(-229.364 - 425.411i) q^{36} -12.7844 q^{37} +77.8805i q^{38} +(23.8936 + 14.2627i) q^{39} -972.701i q^{40} +338.470 q^{41} +(158.946 + 94.8793i) q^{42} +125.542i q^{43} +(-556.785 - 341.266i) q^{44} +(458.817 - 247.375i) q^{45} +561.287i q^{46} -408.178i q^{47} +(301.525 - 505.127i) q^{48} -49.0000 q^{49} +1260.66 q^{50} +(118.083 - 197.817i) q^{51} +95.8599i q^{52} -303.069i q^{53} +(713.317 + 31.1752i) q^{54} +(368.064 - 600.507i) q^{55} +352.688i q^{56} +(-68.2775 - 40.7568i) q^{57} -957.106 q^{58} -18.6625i q^{59} +(1541.86 + 920.377i) q^{60} -922.178i q^{61} -1647.48 q^{62} +(-166.361 + 89.6946i) q^{63} -24.7739 q^{64} -103.387 q^{65} +(854.505 - 447.879i) q^{66} +284.742 q^{67} +793.635 q^{68} +(-492.078 - 293.735i) q^{69} -687.758 q^{70} +558.799i q^{71} +(645.596 + 1197.42i) q^{72} -846.812i q^{73} +65.0624 q^{74} +(-659.735 + 1105.22i) q^{75} -273.926i q^{76} +(-133.455 + 217.735i) q^{77} +(-121.600 - 72.5862i) q^{78} -221.581i q^{79} +2185.68i q^{80} +(-400.627 + 609.047i) q^{81} -1722.55 q^{82} +899.959 q^{83} +(-559.055 - 333.716i) q^{84} +855.955i q^{85} -638.913i q^{86} +(500.877 - 839.091i) q^{87} +(1567.20 + 960.571i) q^{88} +587.363i q^{89} +(-2335.02 + 1258.94i) q^{90} +37.4868 q^{91} -1974.20i q^{92} +(862.168 - 1444.34i) q^{93} +2077.31i q^{94} +295.437 q^{95} +(-461.017 + 772.315i) q^{96} -680.065 q^{97} +249.372 q^{98} +(-54.5300 + 983.527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 288 q^{4} + 4 q^{9} + 16 q^{12} + 20 q^{15} + 1248 q^{16} + 384 q^{22} - 1824 q^{25} - 900 q^{27} + 264 q^{31} - 964 q^{33} - 1008 q^{34} + 48 q^{36} - 24 q^{37} + 1524 q^{45} + 192 q^{48} - 3528 q^{49}+ \cdots - 1260 q^{99}+O(q^{100}) \) 72 * q + 288 * q^4 + 4 * q^9 + 16 * q^12 + 20 * q^15 + 1248 * q^16 + 384 * q^22 - 1824 * q^25 - 900 * q^27 + 264 * q^31 - 964 * q^33 - 1008 * q^34 + 48 * q^36 - 24 * q^37 + 1524 * q^45 + 192 * q^48 - 3528 * q^49 + 1728 * q^55 - 3612 * q^58 - 3172 * q^60 + 5844 * q^64 - 2748 * q^66 + 624 * q^67 + 804 * q^69 - 756 * q^70 - 4516 * q^75 - 1268 * q^78 + 4796 * q^81 + 10056 * q^82 + 7428 * q^88 - 1008 * q^91 - 3916 * q^93 + 168 * q^97 - 1260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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