LMFDB - Embedded newform 105.4.g.b.104.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(104,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.104");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			104.18
Character	$\chi$	$=$	105.104
Dual form			105.4.g.b.104.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22256 q^{2} +(-4.91936 + 1.67328i) q^{3} -6.50535 q^{4} +(-9.89077 + 5.21274i) q^{5} +(6.01420 - 2.04568i) q^{6} +(-1.55936 + 18.4545i) q^{7} +17.7336 q^{8} +(21.4003 - 16.4630i) q^{9} +O(q^{10})$	\(q-1.22256 q^{2} +(-4.91936 + 1.67328i) q^{3} -6.50535 q^{4} +(-9.89077 + 5.21274i) q^{5} +(6.01420 - 2.04568i) q^{6} +(-1.55936 + 18.4545i) q^{7} +17.7336 q^{8} +(21.4003 - 16.4630i) q^{9} +(12.0920 - 6.37288i) q^{10} -54.5342i q^{11} +(32.0022 - 10.8853i) q^{12} -24.4972 q^{13} +(1.90640 - 22.5617i) q^{14} +(39.9339 - 42.1934i) q^{15} +30.3625 q^{16} -36.0147i q^{17} +(-26.1630 + 20.1269i) q^{18} +99.5921i q^{19} +(64.3430 - 33.9107i) q^{20} +(-23.2085 - 93.3936i) q^{21} +66.6712i q^{22} +97.3866 q^{23} +(-87.2381 + 29.6733i) q^{24} +(70.6546 - 103.116i) q^{25} +29.9492 q^{26} +(-77.7285 + 116.796i) q^{27} +(10.1442 - 120.053i) q^{28} -14.1008i q^{29} +(-48.8215 + 51.5839i) q^{30} -186.132i q^{31} -178.989 q^{32} +(91.2510 + 268.273i) q^{33} +44.0300i q^{34} +(-80.7753 - 190.658i) q^{35} +(-139.216 + 107.097i) q^{36} +199.381i q^{37} -121.757i q^{38} +(120.510 - 40.9906i) q^{39} +(-175.399 + 92.4408i) q^{40} +313.963 q^{41} +(28.3738 + 114.179i) q^{42} -30.0581i q^{43} +354.764i q^{44} +(-125.848 + 274.385i) q^{45} -119.061 q^{46} -514.304i q^{47} +(-149.364 + 50.8049i) q^{48} +(-338.137 - 57.5542i) q^{49} +(-86.3794 + 126.065i) q^{50} +(60.2627 + 177.169i) q^{51} +159.363 q^{52} -451.022 q^{53} +(95.0275 - 142.790i) q^{54} +(284.273 + 539.385i) q^{55} +(-27.6530 + 327.265i) q^{56} +(-166.646 - 489.930i) q^{57} +17.2390i q^{58} +355.610 q^{59} +(-259.784 + 274.483i) q^{60} -656.101i q^{61} +227.557i q^{62} +(270.445 + 420.603i) q^{63} -24.0755 q^{64} +(242.296 - 127.697i) q^{65} +(-111.560 - 327.980i) q^{66} -73.7273i q^{67} +234.288i q^{68} +(-479.080 + 162.955i) q^{69} +(98.7524 + 233.090i) q^{70} -611.294i q^{71} +(379.504 - 291.948i) q^{72} -424.158 q^{73} -243.755i q^{74} +(-175.034 + 625.490i) q^{75} -647.882i q^{76} +(1006.40 + 85.0382i) q^{77} +(-147.331 + 50.1134i) q^{78} +814.120 q^{79} +(-300.308 + 158.272i) q^{80} +(186.942 - 704.623i) q^{81} -383.838 q^{82} -585.698i q^{83} +(150.980 + 607.558i) q^{84} +(187.735 + 356.213i) q^{85} +36.7477i q^{86} +(23.5946 + 69.3670i) q^{87} -967.089i q^{88} -732.894 q^{89} +(153.856 - 335.452i) q^{90} +(38.1998 - 452.083i) q^{91} -633.535 q^{92} +(311.451 + 915.650i) q^{93} +628.766i q^{94} +(-519.148 - 985.043i) q^{95} +(880.511 - 299.499i) q^{96} +272.613 q^{97} +(413.392 + 70.3633i) q^{98} +(-897.794 - 1167.05i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) $ 40 * q + 184 * q^4 + 4 * q^9	$ 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) $ 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.22256			−0.432239			−0.216120	−	0.976367i	$-0.569340\pi$
$2$	−1.22256			−0.432239			−0.216120	+	0.976367i	$0.569340\pi$
$3$	−4.91936	+	1.67328i	−0.946732	+	0.322023i
$3$	−4.91936	+	1.67328i	−0.946732	+	0.322023i
$4$	−6.50535			−0.813169
$5$	−9.89077	+	5.21274i	−0.884657	+	0.466242i
$5$	−9.89077	+	5.21274i	−0.884657	+	0.466242i
$6$	6.01420	−	2.04568i	0.409215	−	0.139191i
$7$	−1.55936	+	18.4545i	−0.0841973	+	0.996449i
$7$	−1.55936	+	18.4545i	−0.0841973	+	0.996449i
$8$	17.7336			0.783723
$9$	21.4003	−	16.4630i	0.792602	−	0.609739i
$10$	12.0920	−	6.37288i	0.382384	−	0.201528i
$11$		−	54.5342i		−	1.49479i	−0.664381	−	0.747394i	$-0.731305\pi$
$11$		−	54.5342i		−	1.49479i	0.664381	−	0.747394i	$-0.268695\pi$
$12$	32.0022	−	10.8853i	0.769853	−	0.261859i
$13$	−24.4972			−0.522637			−0.261319	−	0.965253i	$-0.584157\pi$
$13$	−24.4972			−0.522637			−0.261319	+	0.965253i	$0.584157\pi$
$14$	1.90640	−	22.5617i	0.0363934	−	0.430704i
$15$	39.9339	−	42.1934i	0.687393	−	0.726286i
$16$	30.3625			0.474413
$17$		−	36.0147i		−	0.513815i	−0.966436	−	0.256907i	$-0.917296\pi$
$17$		−	36.0147i		−	0.513815i	0.966436	−	0.256907i	$-0.0827035\pi$
$18$	−26.1630	+	20.1269i	−0.342594	+	0.263553i
$19$			99.5921i			1.20253i	0.799051	+	0.601263i	$0.205336\pi$
$19$			99.5921i			1.20253i	−0.799051	+	0.601263i	$0.794664\pi$
$20$	64.3430	−	33.9107i	0.719376	−	0.379133i
$21$	−23.2085	−	93.3936i	−0.241167	−	0.970484i
$22$			66.6712i			0.646106i
$23$	97.3866			0.882892			0.441446	−	0.897288i	$-0.354466\pi$
$23$	97.3866			0.882892			0.441446	+	0.897288i	$0.354466\pi$
$24$	−87.2381	+	29.6733i	−0.741975	+	0.252377i
$25$	70.6546	−	103.116i	0.565237	−	0.824928i
$26$	29.9492			0.225904
$27$	−77.7285	+	116.796i	−0.554032	+	0.832496i
$28$	10.1442	−	120.053i	0.0684666	−	0.810282i
$29$		−	14.1008i		−	0.0902915i	−0.998980	−	0.0451457i	$-0.985625\pi$
$29$		−	14.1008i		−	0.0902915i	0.998980	−	0.0451457i	$-0.0143752\pi$
$30$	−48.8215	+	51.5839i	−0.297118	+	0.313929i
$31$		−	186.132i		−	1.07840i	−0.842179	−	0.539198i	$-0.818728\pi$
$31$		−	186.132i		−	1.07840i	0.842179	−	0.539198i	$-0.181272\pi$
$32$	−178.989			−0.988783
$33$	91.2510	+	268.273i	0.481356	+	1.41516i
$34$			44.0300i			0.222091i
$35$	−80.7753	−	190.658i	−0.390101	−	0.920772i
$36$	−139.216	+	107.097i	−0.644520	+	0.495821i
$37$			199.381i			0.885894i	0.896548	+	0.442947i	$0.146067\pi$
$37$			199.381i			0.885894i	−0.896548	+	0.442947i	$0.853933\pi$
$38$		−	121.757i		−	0.519779i
$39$	120.510	−	40.9906i	0.494798	−	0.168301i
$40$	−175.399	+	92.4408i	−0.693326	+	0.365404i
$41$	313.963			1.19592			0.597961	−	0.801525i	$-0.295978\pi$
$41$	313.963			1.19592			0.597961	+	0.801525i	$0.295978\pi$
$42$	28.3738	+	114.179i	0.104242	+	0.419481i
$43$		−	30.0581i		−	0.106600i	−0.998579	−	0.0533002i	$-0.983026\pi$
$43$		−	30.0581i		−	0.106600i	0.998579	−	0.0533002i	$-0.0169740\pi$
$44$			354.764i			1.21552i
$45$	−125.848	+	274.385i	−0.416896	+	0.908954i
$46$	−119.061			−0.381621
$47$		−	514.304i		−	1.59615i	−0.602559	−	0.798074i	$-0.705852\pi$
$47$		−	514.304i		−	1.59615i	0.602559	−	0.798074i	$-0.294148\pi$
$48$	−149.364	+	50.8049i	−0.449142	+	0.152772i
$49$	−338.137	−	57.5542i	−0.985822	−	0.167797i
$50$	−86.3794	+	126.065i	−0.244318	+	0.356567i
$51$	60.2627	+	177.169i	0.165460	+	0.486445i
$52$	159.363			0.424993
$53$	−451.022			−1.16892			−0.584458	−	0.811424i	$-0.698693\pi$
$53$	−451.022			−1.16892			−0.584458	+	0.811424i	$0.698693\pi$
$54$	95.0275	−	142.790i	0.239474	−	0.359837i
$55$	284.273	+	539.385i	0.696933	+	1.32238i
$56$	−27.6530	+	327.265i	−0.0659873	+	0.780940i
$57$	−166.646	−	489.930i	−0.387241	−	1.13847i
$58$			17.2390i			0.0390275i
$59$	355.610			0.784686			0.392343	−	0.919819i	$-0.371665\pi$
$59$	355.610			0.784686			0.392343	+	0.919819i	$0.371665\pi$
$60$	−259.784	+	274.483i	−0.558966	+	0.590593i
$61$		−	656.101i		−	1.37713i	−0.725173	−	0.688566i	$-0.758240\pi$
$61$		−	656.101i		−	1.37713i	0.725173	−	0.688566i	$-0.241760\pi$
$62$			227.557i			0.466125i
$63$	270.445	+	420.603i	0.540839	+	0.841126i
$64$	−24.0755			−0.0470224
$65$	242.296	−	127.697i	0.462355	−	0.243675i
$66$	−111.560	−	327.980i	−0.208061	−	0.611689i
$67$		−	73.7273i		−	0.134436i	−0.997738	−	0.0672181i	$-0.978588\pi$
$67$		−	73.7273i		−	0.134436i	0.997738	−	0.0672181i	$-0.0214123\pi$
$68$			234.288i			0.417818i
$69$	−479.080	+	162.955i	−0.835862	+	0.284312i
$70$	98.7524	+	233.090i	0.168617	+	0.397994i
$71$		−	611.294i		−	1.02179i	−0.859643	−	0.510896i	$-0.829314\pi$
$71$		−	611.294i		−	1.02179i	0.859643	−	0.510896i	$-0.170686\pi$
$72$	379.504	−	291.948i	0.621181	−	0.477866i
$73$	−424.158			−0.680053			−0.340027	−	0.940416i	$-0.610436\pi$
$73$	−424.158			−0.680053			−0.340027	+	0.940416i	$0.610436\pi$
$74$		−	243.755i		−	0.382918i
$75$	−175.034	+	625.490i	−0.269482	+	0.963005i
$76$		−	647.882i		−	0.977858i
$77$	1006.40	+	85.0382i	1.48948	+	0.125857i
$78$	−147.331	+	50.1134i	−0.213871	+	0.0727465i
$79$	814.120			1.15944			0.579719	−	0.814816i	$-0.303162\pi$
$79$	814.120			1.15944			0.579719	+	0.814816i	$0.303162\pi$
$80$	−300.308	+	158.272i	−0.419693	+	0.221191i
$81$	186.942	−	704.623i	0.256437	−	0.966561i
$82$	−383.838			−0.516925
$83$		−	585.698i		−	0.774562i	−0.921962	−	0.387281i	$-0.873414\pi$
$83$		−	585.698i		−	0.774562i	0.921962	−	0.387281i	$-0.126586\pi$
$84$	150.980	+	607.558i	0.196110	+	0.789167i
$85$	187.735	+	356.213i	0.239562	+	0.454550i
$86$			36.7477i			0.0460769i
$87$	23.5946	+	69.3670i	0.0290759	+	0.0854818i
$88$		−	967.089i		−	1.17150i
$89$	−732.894			−0.872883			−0.436442	−	0.899733i	$-0.643761\pi$
$89$	−732.894			−0.872883			−0.436442	+	0.899733i	$0.643761\pi$
$90$	153.856	−	335.452i	0.180199	−	0.392886i
$91$	38.1998	−	452.083i	0.0440047	−	0.520782i
$92$	−633.535			−0.717941
$93$	311.451	+	915.650i	0.347268	+	1.02095i
$94$			628.766i			0.689918i
$95$	−519.148	−	985.043i	−0.560668	−	1.06382i
$96$	880.511	−	299.499i	0.936112	−	0.318411i
$97$	272.613			0.285357			0.142678	−	0.989769i	$-0.454429\pi$
$97$	272.613			0.285357			0.142678	+	0.989769i	$0.454429\pi$
$98$	413.392	+	70.3633i	0.426111	+	0.0725283i
$99$	−897.794	−	1167.05i	−0.911431	−	1.18477i
$100$	−459.633	+	670.806i	−0.459633	+	0.670806i
$101$	1204.16			1.18632			0.593161	−	0.805084i	$-0.297880\pi$
$101$	1204.16			1.18632			0.593161	+	0.805084i	$0.297880\pi$
$102$	−73.6746	−	216.600i	−0.0715184	−	0.210260i
$103$	1737.25			1.66190			0.830952	−	0.556344i	$-0.187796\pi$
$103$	1737.25			1.66190			0.830952	+	0.556344i	$0.187796\pi$
$104$	−434.423			−0.409603
$105$	716.387	+	802.755i	0.665831	+	0.746103i
$106$	551.400			0.505252
$107$	939.557			0.848882			0.424441	−	0.905456i	$-0.360471\pi$
$107$	939.557			0.848882			0.424441	+	0.905456i	$0.360471\pi$
$108$	505.651	−	759.799i	0.450522	−	0.676960i
$109$	515.039			0.452585			0.226293	−	0.974059i	$-0.427339\pi$
$109$	515.039			0.452585			0.226293	+	0.974059i	$0.427339\pi$
$110$	−347.540	−	659.429i	−0.301242	−	0.571583i
$111$	−333.621	−	980.829i	−0.285278	−	0.838704i
$112$	−47.3459	+	560.324i	−0.0399443	+	0.472729i
$113$	−371.631			−0.309381			−0.154691	−	0.987963i	$-0.549438\pi$
$113$	−371.631			−0.309381			−0.154691	+	0.987963i	$0.549438\pi$
$114$	203.734	+	598.967i	0.167381	+	0.492092i
$115$	−963.229	+	507.651i	−0.781057	+	0.411641i
$116$			91.7307i			0.0734223i
$117$	−524.245	+	403.295i	−0.414244	+	0.318672i
$118$	−434.753			−0.339172
$119$	664.633	+	56.1597i	0.511990	+	0.0432618i
$120$	708.173	−	748.242i	0.538725	−	0.569207i
$121$	−1642.98			−1.23439
$122$			802.121i			0.595251i
$123$	−1544.50	+	525.349i	−1.13222	+	0.385115i
$124$			1210.85i			0.876918i
$125$	−161.311	+	1388.20i	−0.115425	+	0.993316i
$126$	−330.634	−	514.211i	−0.233772	−	0.363568i
$127$		−	56.0497i		−	0.0391623i	−0.999808	−	0.0195811i	$-0.993767\pi$
$127$		−	56.0497i		−	0.0391623i	0.999808	−	0.0195811i	$-0.00623327\pi$
$128$	1461.34			1.00911
$129$	50.2956	+	147.867i	0.0343278	+	0.100922i
$130$	−296.220	+	156.117i	−0.199848	+	0.105326i
$131$	−2147.48			−1.43226			−0.716132	−	0.697965i	$-0.754089\pi$
$131$	−2147.48			−1.43226			−0.716132	+	0.697965i	$0.754089\pi$
$132$	−593.620	−	1745.21i	−0.391424	−	1.15077i
$133$	−1837.92	−	155.300i	−1.19826	−	0.101249i
$134$			90.1358i			0.0581086i
$135$	159.968	−	1560.38i	0.101984	−	0.994786i
$136$		−	638.671i		−	0.402688i
$137$	−2872.66			−1.79145			−0.895724	−	0.444611i	$-0.853342\pi$
$137$	−2872.66			−1.79145			−0.895724	+	0.444611i	$0.853342\pi$
$138$	585.703	−	199.222i	0.361292	−	0.122891i
$139$		−	651.443i		−	0.397516i	−0.980049	−	0.198758i	$-0.936309\pi$
$139$		−	651.443i		−	0.397516i	0.980049	−	0.198758i	$-0.0636907\pi$
$140$	525.472	+	1240.30i	0.317218	+	0.748744i
$141$	860.576	+	2530.05i	0.513997	+	1.51112i
$142$			747.342i			0.441659i
$143$			1335.93i			0.781233i
$144$	649.764	−	499.856i	0.376021	−	0.289268i
$145$	73.5038	+	139.468i	0.0420977	+	0.0798770i
$146$	518.557			0.293946
$147$	1759.72	−	282.668i	0.987343	−	0.158599i
$148$		−	1297.05i		−	0.720382i
$149$			2941.51i			1.61730i	0.588288	+	0.808652i	$0.299802\pi$
$149$			2941.51i			1.61730i	−0.588288	+	0.808652i	$0.700198\pi$
$150$	213.989	−	764.698i	0.116481	−	0.416249i
$151$	717.383			0.386621			0.193311	−	0.981138i	$-0.438077\pi$
$151$	717.383			0.386621			0.193311	+	0.981138i	$0.438077\pi$
$152$			1766.13i			0.942448i
$153$	−592.908	−	770.724i	−0.313293	−	0.407251i
$154$	−1230.38	−	103.964i	−0.643812	−	0.0544004i
$155$	970.257	+	1840.99i	0.502793	+	0.954010i
$156$	−783.963	+	266.658i	−0.402354	+	0.136857i
$157$	725.468			0.368781			0.184391	−	0.982853i	$-0.440969\pi$
$157$	725.468			0.368781			0.184391	+	0.982853i	$0.440969\pi$
$158$	−995.308			−0.501155
$159$	2218.74	−	754.686i	1.10665	−	0.376418i
$160$	1770.34	−	933.023i	0.874734	−	0.461012i
$161$	−151.860	+	1797.22i	−0.0743371	+	0.879757i
$162$	−228.548	+	861.442i	−0.110842	+	0.417786i
$163$		−	2478.01i		−	1.19076i	−0.803446	−	0.595378i	$-0.797002\pi$
$163$		−	2478.01i		−	1.19076i	0.803446	−	0.595378i	$-0.202998\pi$
$164$	−2042.44			−0.972487
$165$	−2300.98	−	2177.76i	−1.08564	−	1.02751i
$166$			716.049i			0.334796i
$167$		−	392.827i		−	0.182023i	−0.995850	−	0.0910117i	$-0.970990\pi$
$167$		−	392.827i		−	0.182023i	0.995850	−	0.0910117i	$-0.0290101\pi$
$168$	−411.571	−	1656.21i	−0.189008	−	0.760590i
$169$	−1596.89			−0.726850
$170$	−229.517	−	435.491i	−0.103548	−	0.196474i
$171$	1639.58	+	2131.30i	0.733227	+	0.953125i
$172$			195.538i			0.0866841i
$173$		−	1758.06i		−	0.772615i	−0.922370	−	0.386308i	$-0.873750\pi$
$173$		−	1758.06i		−	0.772615i	0.922370	−	0.386308i	$-0.126250\pi$
$174$	−28.8458	−	84.8051i	−0.0125678	−	0.0369486i
$175$	1792.78	+	1464.69i	0.774408	+	0.632687i
$176$		−	1655.79i		−	0.709148i
$177$	−1749.37	+	595.035i	−0.742887	+	0.252687i
$178$	896.005			0.377294
$179$		−	561.038i		−	0.234268i	−0.993116	−	0.117134i	$-0.962629\pi$
$179$		−	561.038i		−	0.234268i	0.993116	−	0.117134i	$-0.0373707\pi$
$180$	818.685	−	1784.97i	0.339007	−	0.739134i
$181$			3519.60i			1.44536i	0.691183	+	0.722680i	$0.257090\pi$
$181$			3519.60i			1.44536i	−0.691183	+	0.722680i	$0.742910\pi$
$182$	−46.7014	+	552.697i	−0.0190205	+	0.225102i
$183$	1097.84	+	3227.60i	0.443469	+	1.30378i
$184$	1727.02			0.691943
$185$	−1039.32	−	1972.03i	−0.413041	−	0.783712i
$186$	−380.766	−	1119.43i	−0.150103	−	0.441295i
$187$	−1964.03			−0.768044
$188$			3345.73i			1.29794i
$189$	−2034.20	−	1616.57i	−0.782891	−	0.622158i
$190$	634.688	+	1204.27i	0.242343	+	0.459826i
$191$		−	2737.21i		−	1.03695i	−0.855093	−	0.518475i	$-0.826500\pi$
$191$		−	2737.21i		−	1.03695i	0.855093	−	0.518475i	$-0.173500\pi$
$192$	118.436	−	40.2851i	0.0445176	−	0.0151423i
$193$		−	1381.34i		−	0.515186i	−0.966253	−	0.257593i	$-0.917071\pi$
$193$		−	1381.34i		−	0.515186i	0.966253	−	0.257593i	$-0.0829294\pi$
$194$	−333.284			−0.123342
$195$	−978.267	+	1033.62i	−0.359257	+	0.379584i
$196$	2199.70	+	374.411i	0.801640	+	0.136447i
$197$	474.652			0.171663			0.0858314	−	0.996310i	$-0.472645\pi$
$197$	474.652			0.171663			0.0858314	+	0.996310i	$0.472645\pi$
$198$	1097.60	+	1426.78i	0.393956	+	0.512105i
$199$		−	3657.03i		−	1.30271i	−0.758772	−	0.651357i	$-0.774200\pi$
$199$		−	3657.03i		−	1.30271i	0.758772	−	0.651357i	$-0.225800\pi$
$200$	1252.96	−	1828.62i	0.442989	−	0.646515i
$201$	123.366	+	362.691i	0.0432915	+	0.127275i
$202$	−1472.16			−0.512775
$203$	260.223	+	21.9882i	0.0899709	+	0.00760230i
$204$	−392.030	−	1152.55i	−0.134547	−	0.395562i
$205$	−3105.34	+	1636.61i	−1.05798	+	0.557589i
$206$	−2123.88			−0.718340
$207$	2084.10	−	1603.27i	0.699782	−	0.538334i
$208$	−743.794			−0.247946
$209$	5431.18			1.79752
$210$	−875.824	−	981.413i	−0.287798	−	0.322495i
$211$	−266.470			−0.0869410			−0.0434705	−	0.999055i	$-0.513841\pi$
$211$	−266.470			−0.0869410			−0.0434705	+	0.999055i	$0.513841\pi$
$212$	2934.05			0.950527
$213$	1022.87	+	3007.18i	0.329041	+	0.967363i
$214$	−1148.66			−0.366920
$215$	156.685	+	297.298i	0.0497015	+	0.0943048i
$216$	−1378.41	+	2071.21i	−0.434207	+	0.652446i
$217$	3434.97	+	290.246i	1.07457	+	0.0907979i
$218$	−629.665			−0.195625
$219$	2086.58	−	709.735i	0.643828	−	0.218993i
$220$	−1849.29	−	3508.89i	−0.566724	−	1.07532i
$221$			882.258i			0.268539i
$222$	407.871	+	1199.12i	0.123308	+	0.362521i
$223$	1634.62			0.490863			0.245431	−	0.969414i	$-0.421070\pi$
$223$	1634.62			0.490863			0.245431	+	0.969414i	$0.421070\pi$
$224$	279.107	−	3303.15i	0.0832528	−	0.985272i
$225$	−185.567	−	3369.89i	−0.0549829	−	0.998487i
$226$	454.340			0.133727
$227$		−	2561.56i		−	0.748972i	−0.927232	−	0.374486i	$-0.877819\pi$
$227$		−	2561.56i		−	0.748972i	0.927232	−	0.374486i	$-0.122181\pi$
$228$	1084.09	+	3187.17i	0.314893	+	0.925769i
$229$		−	4252.03i		−	1.22699i	−0.789697	−	0.613497i	$-0.789762\pi$
$229$		−	4252.03i		−	1.22699i	0.789697	−	0.613497i	$-0.210238\pi$
$230$	1177.60	−	620.633i	0.337604	−	0.177928i
$231$	−5093.14	+	1265.66i	−1.45067	+	0.360494i
$232$		−	250.058i		−	0.0707635i
$233$	−3657.28			−1.02831			−0.514156	−	0.857697i	$-0.671895\pi$
$233$	−3657.28			−1.02831			−0.514156	+	0.857697i	$0.671895\pi$
$234$	640.920	−	493.052i	0.179052	−	0.137743i
$235$	2680.94	+	5086.86i	0.744191	+	1.41204i
$236$	−2313.37			−0.638082
$237$	−4004.95	+	1362.25i	−1.09768	+	0.373366i
$238$	−812.552	−	68.6585i	−0.221302	−	0.0186994i
$239$		−	1938.73i		−	0.524710i	−0.964971	−	0.262355i	$-0.915501\pi$
$239$		−	1938.73i		−	0.524710i	0.964971	−	0.262355i	$-0.0844992\pi$
$240$	1212.49	−	1281.10i	0.326108	−	0.344560i
$241$			5100.72i			1.36334i	0.731658	+	0.681672i	$0.238747\pi$
$241$			5100.72i			1.36334i	−0.731658	+	0.681672i	$0.761253\pi$
$242$	2008.63			0.533553
$243$	259.395	+	3779.10i	0.0684782	+	0.997653i
$244$			4268.17i			1.11984i
$245$	3644.45	−	1193.36i	0.950348	−	0.311189i
$246$	1888.24	−	642.269i	0.489389	−	0.166462i
$247$		−	2439.72i		−	0.628485i
$248$		−	3300.79i		−	0.845163i
$249$	980.037	+	2881.26i	0.249427	+	0.733303i
$250$	197.212	−	1697.16i	0.0498912	−	0.429350i
$251$	1834.02			0.461205			0.230603	−	0.973048i	$-0.425930\pi$
$251$	1834.02			0.461205			0.230603	+	0.973048i	$0.425930\pi$
$252$	−1759.34	−	2736.17i	−0.439794	−	0.683978i
$253$		−	5310.90i		−	1.31974i
$254$			68.5240i			0.0169275i
$255$	−1519.58	−	1438.21i	−0.373176	−	0.353192i
$256$	−1593.97			−0.389154
$257$		−	7667.08i		−	1.86093i	−0.366380	−	0.930465i	$-0.619403\pi$
$257$		−	7667.08i		−	1.86093i	0.366380	−	0.930465i	$-0.380597\pi$
$258$	−61.4893	−	180.775i	−0.0148378	−	0.0436224i
$259$	−3679.48	−	310.906i	−0.882748	−	0.0745898i
$260$	−1576.22	+	830.716i	−0.375973	+	0.198149i
$261$	−232.141	−	301.761i	−0.0550542	−	0.0715652i
$262$	2625.42			0.619081
$263$	6022.49			1.41203			0.706013	−	0.708199i	$-0.250492\pi$
$263$	6022.49			1.41203			0.706013	+	0.708199i	$0.250492\pi$
$264$	1618.21	+	4757.46i	0.377250	+	1.10910i
$265$	4460.95	−	2351.06i	1.03409	−	0.544998i
$266$	2246.97	+	189.863i	0.517934	+	0.0437640i
$267$	3605.37	−	1226.34i	0.826386	−	0.281089i
$268$			479.622i			0.109319i
$269$	−3060.15			−0.693609			−0.346805	−	0.937937i	$-0.612733\pi$
$269$	−3060.15			−0.693609			−0.346805	+	0.937937i	$0.612733\pi$
$270$	−195.570	+	1907.65i	−0.0440815	+	0.429986i
$271$			4427.98i			0.992547i	0.868166	+	0.496274i	$0.165299\pi$
$271$			4427.98i			0.992547i	−0.868166	+	0.496274i	$0.834701\pi$
$272$		−	1093.49i		−	0.243760i
$273$	568.543	+	2287.88i	0.126043	+	0.507211i
$274$	3512.00			0.774334
$275$	−5623.35	−	3853.09i	−1.23309	−	0.844910i
$276$	3116.59	−	1060.08i	0.679697	−	0.231193i
$277$			2979.18i			0.646216i	0.946362	+	0.323108i	$0.104728\pi$
$277$			2979.18i			0.646216i	−0.946362	+	0.323108i	$0.895272\pi$
$278$			796.426i			0.171822i
$279$	−3064.28	−	3983.27i	−0.657540	−	0.854738i
$280$	−1432.44	−	3381.05i	−0.305731	−	0.721630i
$281$			2966.90i			0.629859i	0.949115	+	0.314930i	$0.101981\pi$
$281$			2966.90i			0.629859i	−0.949115	+	0.314930i	$0.898019\pi$
$282$	−1052.10	−	3093.13i	−0.222170	−	0.653167i
$283$	−5731.24			−1.20384			−0.601920	−	0.798556i	$-0.705598\pi$
$283$	−5731.24			−1.20384			−0.601920	+	0.798556i	$0.705598\pi$
$284$			3976.68i			0.830890i
$285$	4202.13	+	3977.10i	0.873378	+	0.826608i
$286$		−	1633.25i		−	0.337679i
$287$	−489.580	+	5794.03i	−0.100693	+	1.19168i
$288$	−3830.41	+	2946.69i	−0.783712	+	0.602900i
$289$	3615.94			0.735995
$290$	−89.8627	−	170.507i	−0.0181963	−	0.0345260i
$291$	−1341.08	+	456.157i	−0.270156	+	0.0918915i
$292$	2759.29			0.552998
$293$		−	1743.02i		−	0.347537i	−0.984787	−	0.173768i	$-0.944406\pi$
$293$		−	1743.02i		−	0.347537i	0.984787	−	0.173768i	$-0.0555944\pi$
$294$	−2151.36	+	345.578i	−0.426768	+	0.0685527i
$295$	−3517.25	+	1853.70i	−0.694178	+	0.365853i
$296$			3535.75i			0.694295i
$297$	6369.37	+	4238.86i	1.24440	+	0.828160i
$298$		−	3596.17i		−	0.699062i
$299$	−2385.70			−0.461432
$300$	1138.66	−	4069.04i	0.219134	−	0.783086i
$301$	554.707	+	46.8712i	0.106222	+	0.00897546i
$302$	−877.042			−0.167113
$303$	−5923.71	+	2014.90i	−1.12313	+	0.382023i
$304$			3023.86i			0.570495i
$305$	3420.08	+	6489.34i	0.642077	+	1.21829i
$306$	724.864	+	942.254i	0.135417	+	0.176030i
$307$	−10595.5			−1.96976			−0.984878	−	0.173247i	$-0.944574\pi$
$307$	−10595.5			−1.96976			−0.984878	+	0.173247i	$0.944574\pi$
$308$	−6546.99	−	553.203i	−1.21120	−	0.102343i
$309$	−8546.15	+	2906.90i	−1.57338	+	0.535171i
$310$	−1186.19	−	2250.71i	−0.217327	−	0.412361i
$311$	3683.11			0.671543			0.335772	−	0.941943i	$-0.391003\pi$
$311$	3683.11			0.671543			0.335772	+	0.941943i	$0.391003\pi$
$312$	2137.09	−	726.912i	0.387784	−	0.131902i
$313$	82.6926			0.0149331			0.00746655	−	0.999972i	$-0.497623\pi$
$313$	82.6926			0.0149331			0.00746655	+	0.999972i	$0.497623\pi$
$314$	−886.926			−0.159402
$315$	−4867.40	−	2750.32i	−0.870625	−	0.491947i
$316$	−5296.14			−0.942820
$317$	−8772.72			−1.55434			−0.777168	−	0.629293i	$-0.783345\pi$
$317$	−8772.72			−1.55434			−0.777168	+	0.629293i	$0.783345\pi$
$318$	−2712.53	+	922.647i	−0.478338	+	0.162703i
$319$	−768.976			−0.134967
$320$	238.125	−	125.499i	0.0415987	−	0.0219238i
$321$	−4622.02	+	1572.14i	−0.803664	+	0.273360i
$322$	185.658	−	2197.21i	0.0321314	−	0.380266i
$323$	3586.78			0.617876
$324$	−1216.13	+	4583.82i	−0.208526	+	0.785978i
$325$	−1730.84	+	2526.05i	−0.295414	+	0.431139i
$326$			3029.51i			0.514691i
$327$	−2533.66	+	861.805i	−0.428477	+	0.145743i
$328$	5567.71			0.937272
$329$	9491.22	+	801.983i	1.59048	+	0.134391i
$330$	2813.08	+	2662.44i	0.469258	+	0.444129i
$331$	6259.67			1.03946			0.519732	−	0.854329i	$-0.326032\pi$
$331$	6259.67			1.03946			0.519732	+	0.854329i	$0.326032\pi$
$332$			3810.17i			0.629850i
$333$	3282.40	+	4266.81i	0.540164	+	0.702161i
$334$			480.254i			0.0786776i
$335$	384.321	+	729.220i	0.0626797	+	0.118930i
$336$	−704.668	−	2835.66i	−0.114413	−	0.460410i
$337$			8203.39i			1.32602i	0.748612	+	0.663008i	$0.230720\pi$
$337$			8203.39i			1.32602i	−0.748612	+	0.663008i	$0.769280\pi$
$338$	1952.29			0.314173
$339$	1828.19	−	621.843i	0.292901	−	0.0996279i
$340$	−1221.28	−	2317.29i	−0.194804	−	0.369626i
$341$	−10150.5			−1.61197
$342$	−2004.48	−	2605.63i	−0.316930	−	0.411978i
$343$	1589.41	−	6150.40i	0.250204	−	0.968193i
$344$		−	533.039i		−	0.0835451i
$345$	3889.03	−	4109.07i	0.606893	−	0.641232i
$346$			2149.32i			0.333955i
$347$	2993.06			0.463043			0.231521	−	0.972830i	$-0.425630\pi$
$347$	2993.06			0.463043			0.231521	+	0.972830i	$0.425630\pi$
$348$	−153.491	−	451.257i	−0.0236437	−	0.0695112i
$349$		−	7305.70i		−	1.12053i	−0.828313	−	0.560265i	$-0.810699\pi$
$349$		−	7305.70i		−	1.12053i	0.828313	−	0.560265i	$-0.189301\pi$
$350$	−2191.78	−	1790.67i	−0.334729	−	0.273472i
$351$	1904.13	−	2861.17i	0.289558	−	0.435093i
$352$			9761.01i			1.47802i
$353$		−	6126.46i		−	0.923735i	−0.886949	−	0.461867i	$-0.847180\pi$
$353$		−	6126.46i		−	0.923735i	0.886949	−	0.461867i	$-0.152820\pi$
$354$	2138.71	−	727.465i	0.321105	−	0.109221i
$355$	3186.52	+	6046.17i	0.476402	+	0.903936i
$356$	4767.74			0.709802
$357$	−3363.54	+	835.848i	−0.498649	+	0.123915i
$358$			685.901i			0.101260i
$359$		−	8351.09i		−	1.22773i	−0.789413	−	0.613863i	$-0.789615\pi$
$359$		−	8351.09i		−	1.22773i	0.789413	−	0.613863i	$-0.210385\pi$
$360$	−2231.74	+	4865.85i	−0.326731	+	0.712368i
$361$	−3059.59			−0.446070
$362$		−	4302.92i		−	0.624741i
$363$	8082.40	−	2749.16i	1.16864	−	0.397503i
$364$	−248.503	+	2940.96i	−0.0357832	+	0.423484i
$365$	4195.24	−	2211.02i	0.601614	−	0.317069i
$366$	−1342.17	−	3945.92i	−0.191685	−	0.563543i
$367$	10233.1			1.45549			0.727745	−	0.685848i	$-0.240568\pi$
$367$	10233.1			1.45549			0.727745	+	0.685848i	$0.240568\pi$
$368$	2956.90			0.418856
$369$	6718.90	−	5168.76i	0.947891	−	0.729201i
$370$	1270.63	+	2410.92i	0.178532	+	0.338751i
$371$	703.303	−	8323.37i	0.0984196	−	1.16477i
$372$	−2026.10	−	5956.62i	−0.282388	−	0.830206i
$373$		−	9039.05i		−	1.25476i	−0.778715	−	0.627378i	$-0.784128\pi$
$373$		−	9039.05i		−	1.25476i	0.778715	−	0.627378i	$-0.215872\pi$
$374$	2401.14			0.331979
$375$	−1529.30	−	7098.99i	−0.210594	−	0.977574i
$376$		−	9120.48i		−	1.25094i
$377$			345.429i			0.0471897i
$378$	2486.93	+	1976.35i	0.338396	+	0.268921i
$379$	5342.32			0.724054			0.362027	−	0.932168i	$-0.382085\pi$
$379$	5342.32			0.724054			0.362027	+	0.932168i	$0.382085\pi$
$380$	3377.24	+	6408.05i	0.455918	+	0.865069i
$381$	93.7869	+	275.729i	0.0126112	+	0.0370762i
$382$			3346.40i			0.448211i
$383$		−	2265.22i		−	0.302213i	−0.988518	−	0.151106i	$-0.951716\pi$
$383$		−	2265.22i		−	0.302213i	0.988518	−	0.151106i	$-0.0482836\pi$
$384$	−7188.88	+	2445.24i	−0.955355	+	0.324956i
$385$	−10397.4	+	4405.02i	−1.37636	+	0.583118i
$386$			1688.77i			0.222684i
$387$	−494.845	−	643.251i	−0.0649984	−	0.0844917i
$388$	−1773.44			−0.232043
$389$		−	2359.74i		−	0.307567i	−0.988105	−	0.153783i	$-0.950854\pi$
$389$		−	2359.74i		−	0.307567i	0.988105	−	0.153783i	$-0.0491458\pi$
$390$	1195.99	−	1263.66i	0.155285	−	0.164071i
$391$		−	3507.35i		−	0.453643i
$392$	−5996.39	−	1020.65i	−0.772611	−	0.131506i
$393$	10564.3	−	3593.35i	1.35597	−	0.461222i
$394$	−580.289			−0.0741994
$395$	−8052.27	+	4243.80i	−1.02571	+	0.540579i
$396$	5840.47	+	7592.05i	0.741148	+	0.963421i
$397$	−3203.32			−0.404962			−0.202481	−	0.979286i	$-0.564900\pi$
$397$	−3203.32			−0.404962			−0.202481	+	0.979286i	$0.564900\pi$
$398$			4470.93i			0.563084i
$399$	9301.27	−	2311.39i	1.16703	−	0.290010i
$400$	2145.25	−	3130.86i	0.268156	−	0.391357i
$401$		−	4753.14i		−	0.591921i	−0.955200	−	0.295961i	$-0.904360\pi$
$401$		−	4753.14i		−	0.591921i	0.955200	−	0.295961i	$-0.0956397\pi$
$402$	−150.823	−	443.411i	−0.0187123	−	0.0550132i
$403$			4559.70i			0.563610i
$404$	−7833.50			−0.964681
$405$	1824.01	+	7943.75i	0.223793	+	0.974637i
$406$	−318.138	−	26.8818i	−0.0388889	−	0.00328601i
$407$	10873.1			1.32422
$408$	1068.68	+	3141.86i	0.129675	+	0.381238i
$409$		−	1599.93i		−	0.193427i	−0.995312	−	0.0967134i	$-0.969167\pi$
$409$		−	1599.93i		−	0.193427i	0.995312	−	0.0967134i	$-0.0308330\pi$
$410$	3796.45	−	2000.85i	0.457301	−	0.241012i
$411$	14131.7	−	4806.78i	1.69602	−	0.576887i
$412$	−11301.4			−1.35141
$413$	−554.522	+	6562.60i	−0.0660684	+	0.781899i
$414$	−2547.93	+	1960.09i	−0.302473	+	0.232689i
$415$	3053.09	+	5793.00i	0.361133	+	0.685222i
$416$	4384.72			0.516775
$417$	1090.05	+	3204.68i	0.128009	+	0.376341i
$418$	−6639.92			−0.776960
$419$	−6140.88			−0.715995			−0.357997	−	0.933723i	$-0.616540\pi$
$419$	−6140.88			−0.715995			−0.357997	+	0.933723i	$0.616540\pi$
$420$	−4660.35	−	5222.20i	−0.541433	−	0.606708i
$421$	2459.78			0.284757			0.142378	−	0.989812i	$-0.454525\pi$
$421$	2459.78			0.284757			0.142378	+	0.989812i	$0.454525\pi$
$422$	325.775			0.0375793
$423$	−8466.97	−	11006.2i	−0.973234	−	1.26511i
$424$	−7998.25			−0.916107
$425$	−3713.69	−	2544.61i	−0.423860	−	0.290427i
$426$	−1250.51	−	3676.45i	−0.142224	−	0.418132i
$427$	12108.0	+	1023.09i	1.37224	+	0.115951i
$428$	−6112.15			−0.690285
$429$	−2235.39	−	6571.93i	−0.251575	−	0.739618i
$430$	−191.556	−	363.463i	−0.0214830	−	0.0407622i
$431$		−	5814.41i		−	0.649815i	−0.945746	−	0.324907i	$-0.894667\pi$
$431$		−	5814.41i		−	0.649815i	0.945746	−	0.324907i	$-0.105333\pi$
$432$	−2360.03	+	3546.21i	−0.262840	+	0.394947i
$433$	6273.51			0.696272			0.348136	−	0.937444i	$-0.386815\pi$
$433$	6273.51			0.696272			0.348136	+	0.937444i	$0.386815\pi$
$434$	−4199.44	−	354.842i	−0.464470	−	0.0392464i
$435$	−594.961	−	563.100i	−0.0655775	−	0.0620657i
$436$	−3350.51			−0.368028
$437$			9698.94i			1.06170i
$438$	−2550.97	+	867.691i	−0.278288	+	0.0946573i
$439$			8309.95i			0.903445i	0.892158	+	0.451723i	$0.149190\pi$
$439$			8309.95i			0.903445i	−0.892158	+	0.451723i	$0.850810\pi$
$440$	5041.18	+	9565.25i	0.546202	+	1.03638i
$441$	−8183.73	+	4335.06i	−0.883677	+	0.468098i
$442$		−	1078.61i		−	0.116073i
$443$	−2263.02			−0.242707			−0.121354	−	0.992609i	$-0.538724\pi$
$443$	−2263.02			−0.242707			−0.121354	+	0.992609i	$0.538724\pi$
$444$	2170.32	+	6380.64i	0.231979	+	0.682008i
$445$	7248.89	−	3820.39i	0.772203	−	0.406975i
$446$	−1998.42			−0.212170
$447$	−4921.98	−	14470.4i	−0.520809	−	1.53115i
$448$	37.5422	−	444.301i	0.00395916	−	0.0468555i
$449$			1895.08i			0.199186i	0.995028	+	0.0995928i	$0.0317540\pi$
$449$			1895.08i			0.199186i	−0.995028	+	0.0995928i	$0.968246\pi$
$450$	226.866	+	4119.89i	0.0237658	+	0.431585i
$451$		−	17121.7i		−	1.78765i
$452$	2417.59			0.251579
$453$	−3529.07	+	1200.38i	−0.366027	+	0.124501i
$454$			3131.65i			0.323735i
$455$	1978.76	+	4670.57i	0.203881	+	0.481230i
$456$	−2955.23	−	8688.23i	−0.303490	−	0.892245i
$457$		−	10430.5i		−	1.06766i	−0.845592	−	0.533829i	$-0.820752\pi$
$457$		−	10430.5i		−	1.06766i	0.845592	−	0.533829i	$-0.179248\pi$
$458$			5198.35i			0.530355i
$459$	4206.37	+	2799.37i	0.427748	+	0.284670i
$460$	6266.14	−	3302.45i	0.635131	−	0.334734i
$461$	7025.94			0.709828			0.354914	−	0.934899i	$-0.384510\pi$
$461$	7025.94			0.709828			0.354914	+	0.934899i	$0.384510\pi$
$462$	6226.66	−	1547.34i	0.627036	−	0.155820i
$463$			12799.1i			1.28472i	0.766405	+	0.642358i	$0.222044\pi$
$463$			12799.1i			1.28472i	−0.766405	+	0.642358i	$0.777956\pi$
$464$		−	428.135i		−	0.0428355i
$465$	−7853.53	−	7432.97i	−0.783223	−	0.741281i
$466$	4471.24			0.444476
$467$			14926.4i			1.47904i	0.673134	+	0.739520i	$0.264948\pi$
$467$			14926.4i			1.47904i	−0.673134	+	0.739520i	$0.735052\pi$
$468$	3410.40	−	2623.58i	0.336850	−	0.259135i
$469$	1360.60	+	114.967i	0.133959	+	0.0113192i
$470$	−3277.60	−	6218.98i	−0.321669	−	0.610341i
$471$	−3568.84	+	1213.91i	−0.349137	+	0.118756i
$472$	6306.25			0.614976
$473$	−1639.19			−0.159345
$474$	4896.28	−	1665.43i	0.474459	−	0.161383i
$475$	10269.5	+	7036.65i	0.991998	+	0.679713i
$476$	−4323.67	−	365.339i	−0.416335	−	0.0351792i
$477$	−9651.98	+	7425.15i	−0.926486	+	0.712734i
$478$			2370.20i			0.226800i
$479$	1243.12			0.118579			0.0592897	−	0.998241i	$-0.481116\pi$
$479$	1243.12			0.118579			0.0592897	+	0.998241i	$0.481116\pi$
$480$	−7147.72	+	7552.15i	−0.679682	+	0.718139i
$481$		−	4884.27i		−	0.463001i
$482$		−	6235.92i		−	0.589291i
$483$	−2260.20	−	9095.29i	−0.212925	−	0.856832i
$484$	10688.1			1.00377
$485$	−2696.35	+	1421.06i	−0.252443	+	0.133045i
$486$	−317.126	−	4620.17i	−0.0295990	−	0.431225i
$487$		−	11664.2i		−	1.08533i	−0.839949	−	0.542665i	$-0.817415\pi$
$487$		−	11664.2i		−	1.08533i	0.839949	−	0.542665i	$-0.182585\pi$
$488$		−	11635.0i		−	1.07929i
$489$	4146.41	+	12190.3i	0.383451	+	1.12733i
$490$	−4455.55	+	1458.96i	−0.410778	+	0.134508i
$491$			15943.8i			1.46544i	0.680530	+	0.732721i	$0.261750\pi$
$491$			15943.8i			1.46544i	−0.680530	+	0.732721i	$0.738250\pi$
$492$	10047.5	−	3417.58i	0.920685	−	0.313163i
$493$	−507.836			−0.0463931
$494$			2982.70i			0.271656i
$495$	14963.4	+	6863.01i	1.35869	+	0.623171i
$496$		−	5651.42i		−	0.511605i
$497$	11281.1	+	953.224i	1.01816	+	0.0860321i
$498$	−1198.15	−	3522.50i	−0.107812	−	0.316962i
$499$	−20046.9			−1.79844			−0.899221	−	0.437494i	$-0.855866\pi$
$499$	−20046.9			−1.79844			−0.899221	+	0.437494i	$0.855866\pi$
$500$	1049.39	−	9030.74i	0.0938601	−	0.807734i
$501$	657.311	+	1932.46i	0.0586157	+	0.172327i
$502$	−2242.20			−0.199351
$503$			20523.9i			1.81931i	0.415361	+	0.909657i	$0.363655\pi$
$503$			20523.9i			1.81931i	−0.415361	+	0.909657i	$0.636345\pi$
$504$	4795.97	+	7458.81i	0.423868	+	0.659210i
$505$	−11910.1	+	6276.99i	−1.04949	+	0.553113i
$506$			6492.88i			0.570442i
$507$	7855.68	−	2672.05i	0.688132	−	0.234063i
$508$			364.623i			0.0318455i
$509$	−9493.01			−0.826661			−0.413330	−	0.910581i	$-0.635635\pi$
$509$	−9493.01			−0.826661			−0.413330	+	0.910581i	$0.635635\pi$
$510$	1857.78	+	1758.29i	0.161301	+	0.152664i
$511$	661.412	−	7827.61i	0.0572586	−	0.677638i
$512$	−9742.03			−0.840900
$513$	−11632.0	−	7741.15i	−1.00110	−	0.666238i
$514$			9373.44i			0.804367i
$515$	−17182.7	+	9055.82i	−1.47022	+	0.774849i
$516$	−327.191	−	961.925i	−0.0279143	−	0.0820666i
$517$	−28047.2			−2.38590
$518$	4498.37	+	380.101i	0.381558	+	0.0322407i
$519$	2941.72	+	8648.51i	0.248800	+	0.731460i
$520$	4296.78	−	2264.54i	0.362358	−	0.190974i
$521$	−6019.18			−0.506152			−0.253076	−	0.967446i	$-0.581442\pi$
$521$	−6019.18			−0.506152			−0.253076	+	0.967446i	$0.581442\pi$
$522$	283.806	+	368.920i	0.0237966	+	0.0309333i
$523$	−464.284			−0.0388178			−0.0194089	−	0.999812i	$-0.506178\pi$
$523$	−464.284			−0.0388178			−0.0194089	+	0.999812i	$0.506178\pi$
$524$	13970.1			1.16467
$525$	−11270.2	−	4205.52i	−0.936896	−	0.349607i
$526$	−7362.84			−0.610333
$527$	−6703.48			−0.554095
$528$	2770.60	+	8145.44i	0.228362	+	0.671373i
$529$	−2682.84			−0.220502
$530$	−5453.77	+	2874.30i	−0.446975	+	0.235569i
$531$	7610.14	−	5854.39i	0.621944	−	0.478453i
$532$	11956.3	+	1010.28i	0.974385	+	0.0823329i
$533$	−7691.21			−0.625034
$534$	−4407.77	+	1499.27i	−0.357197	+	0.121498i
$535$	−9292.94	+	4897.67i	−0.750970	+	0.395784i
$536$		−	1307.45i		−	0.105361i
$537$	938.774	+	2759.95i	0.0754396	+	0.221789i
$538$	3741.21			0.299805
$539$	−3138.67	+	18440.0i	−0.250820	+	1.47359i
$540$	−1040.65	+	10150.8i	−0.0829302	+	0.808929i
$541$	9639.52			0.766054			0.383027	−	0.923737i	$-0.374882\pi$
$541$	9639.52			0.766054			0.383027	+	0.923737i	$0.374882\pi$
$542$		−	5413.45i		−	0.429018i
$543$	−5889.28	−	17314.2i	−0.465439	−	1.36837i
$544$			6446.23i			0.508051i
$545$	−5094.13	+	2684.77i	−0.400383	+	0.211014i
$546$	−695.076	−	2797.06i	−0.0544808	−	0.219237i
$547$		−	24026.4i		−	1.87806i	−0.343842	−	0.939028i	$-0.611728\pi$
$547$		−	24026.4i		−	1.87806i	0.343842	−	0.939028i	$-0.388272\pi$
$548$	18687.7			1.45675
$549$	−10801.4	−	14040.7i	−0.839691	−	1.09152i
$550$	6874.87	+	4710.63i	0.532992	+	0.365203i
$551$	1404.33			0.108578
$552$	−8495.83	+	2889.79i	−0.655084	+	0.222822i
$553$	−1269.50	+	15024.2i	−0.0976215	+	1.15532i
$554$		−	3642.22i		−	0.279320i
$555$	8412.57	+	7962.07i	0.643412	+	0.608957i
$556$			4237.87i			0.323247i
$557$	−266.067			−0.0202399			−0.0101199	−	0.999949i	$-0.503221\pi$
$557$	−266.067			−0.0202399			−0.0101199	+	0.999949i	$0.503221\pi$
$558$	3746.26	+	4869.77i	0.284214	+	0.369452i
$559$			736.337i			0.0557133i
$560$	−2452.54	−	5788.83i	−0.185069	−	0.436827i
$561$	9661.79	−	3286.38i	0.727132	−	0.247328i
$562$		−	3627.21i		−	0.272250i
$563$			5312.19i			0.397659i	0.980034	+	0.198829i	$0.0637140\pi$
$563$			5312.19i			0.397659i	−0.980034	+	0.198829i	$0.936286\pi$
$564$	−5598.35	−	16458.9i	−0.417966	−	1.22880i
$565$	3675.71	−	1937.21i	0.273696	−	0.144246i
$566$	7006.77			0.520347
$567$	12712.0	+	4548.68i	0.941538	+	0.336908i
$568$		−	10840.5i		−	0.800802i
$569$		−	3367.91i		−	0.248137i	−0.992274	−	0.124069i	$-0.960406\pi$
$569$		−	3367.91i		−	0.248137i	0.992274	−	0.124069i	$-0.0395943\pi$
$570$	−5137.35	−	4862.24i	−0.377508	−	0.357292i
$571$	−17311.2			−1.26874			−0.634371	−	0.773029i	$-0.718741\pi$
$571$	−17311.2			−1.26874			−0.634371	+	0.773029i	$0.718741\pi$
$572$		−	8690.71i		−	0.635274i
$573$	4580.12	+	13465.3i	0.333922	+	0.981714i
$574$	598.540	−	7083.54i	0.0435236	−	0.515089i
$575$	6880.82	−	10042.1i	0.499043	−	0.728323i
$576$	−515.222	+	396.354i	−0.0372701	+	0.0286714i
$577$	14972.0			1.08023			0.540114	−	0.841592i	$-0.318381\pi$
$577$	14972.0			1.08023			0.540114	+	0.841592i	$0.318381\pi$
$578$	−4420.70			−0.318126
$579$	2311.37	+	6795.31i	0.165902	+	0.487743i
$580$	−478.168	−	907.287i	−0.0342325	−	0.0649535i
$581$	10808.8	+	913.311i	0.771812	+	0.0652160i
$582$	1639.55	−	557.679i	0.116772	−	0.0397191i
$583$			24596.1i			1.74728i
$584$	−7521.85			−0.532973
$585$	3082.92	−	6721.66i	0.217885	−	0.475054i
$586$			2130.94i			0.150219i
$587$		−	13991.7i		−	0.983812i	−0.870648	−	0.491906i	$-0.836300\pi$
$587$		−	13991.7i		−	0.983812i	0.870648	−	0.491906i	$-0.163700\pi$
$588$	−11447.6	+	1838.85i	−0.802877	+	0.128968i
$589$	18537.3			1.29680
$590$	4300.05	−	2266.26i	0.300051	−	0.158136i
$591$	−2334.99	+	794.226i	−0.162519	+	0.0552794i
$592$			6053.70i			0.420280i
$593$			2682.43i			0.185758i	0.995677	+	0.0928788i	$0.0296069\pi$
$593$			2682.43i			0.185758i	−0.995677	+	0.0928788i	$0.970393\pi$
$594$	−7786.92	−	5182.25i	−0.537881	−	0.357963i
$595$	−6866.48	+	2909.10i	−0.473106	+	0.200439i
$596$		−	19135.6i		−	1.31514i
$597$	6119.24	+	17990.3i	0.419504	+	1.23332i
$598$	2916.65			0.199449
$599$		−	10409.6i		−	0.710060i	−0.934855	−	0.355030i	$-0.884471\pi$
$599$		−	10409.6i		−	0.710060i	0.934855	−	0.355030i	$-0.115529\pi$
$600$	−3103.98	+	11092.2i	−0.211199	+	0.754729i
$601$			9004.50i			0.611150i	0.952168	+	0.305575i	$0.0988487\pi$
$601$			9004.50i			0.611150i	−0.952168	+	0.305575i	$0.901151\pi$
$602$	−678.161	−	57.3028i	−0.0459132	−	0.00387955i
$603$	−1213.77	−	1577.78i	−0.0819710	−	0.106554i
$604$	−4666.83			−0.314388
$605$	16250.3	−	8564.42i	1.09201	−	0.575526i
$606$	7242.08	−	2463.33i	0.485461	−	0.165125i
$607$	−7532.63			−0.503690			−0.251845	−	0.967768i	$-0.581037\pi$
$607$	−7532.63			−0.503690			−0.251845	+	0.967768i	$0.581037\pi$
$608$		−	17825.9i		−	1.18904i
$609$	−1316.92	+	327.259i	−0.0876264	+	0.0217754i
$610$	−4181.25	−	7933.59i	−0.277531	−	0.526593i
$611$			12599.0i			0.834207i
$612$	3857.08	+	5013.83i	0.254760	+	0.331164i
$613$			5607.50i			0.369469i	0.982788	+	0.184735i	$0.0591426\pi$
$613$			5607.50i			0.369469i	−0.982788	+	0.184735i	$0.940857\pi$
$614$	12953.6			0.851406
$615$	12537.8	−	13247.2i	0.822068	−	0.868582i
$616$	17847.1	+	1508.04i	1.16734	+	0.0986371i
$617$	−6623.55			−0.432178			−0.216089	−	0.976374i	$-0.569330\pi$
$617$	−6623.55			−0.432178			−0.216089	+	0.976374i	$0.569330\pi$
$618$	10448.2	−	3553.86i	0.680075	−	0.231322i
$619$			89.5674i			0.00581586i	0.999996	+	0.00290793i	$0.000925625\pi$
$619$			89.5674i			0.00581586i	−0.999996	+	0.00290793i	$0.999074\pi$
$620$	−6311.86	−	11976.3i	−0.408856	−	0.775772i
$621$	−7569.72	+	11374.4i	−0.489150	+	0.735004i
$622$	−4502.81			−0.290267
$623$	1142.84	−	13525.2i	0.0734944	−	0.869784i
$624$	3658.99	−	1244.58i	0.234739	−	0.0798444i
$625$	−5640.84	−	14571.3i	−0.361014	−	0.932560i
$626$	−101.096			−0.00645468
$627$	−26717.9	+	9087.88i	−1.70177	+	0.578844i
$628$	−4719.42			−0.299881
$629$	7180.65			0.455185
$630$	5950.68	+	3362.43i	0.376318	+	0.212639i
$631$	−4797.64			−0.302680			−0.151340	−	0.988482i	$-0.548359\pi$
$631$	−4797.64			−0.302680			−0.151340	+	0.988482i	$0.548359\pi$
$632$	14437.3			0.908678
$633$	1310.86	−	445.879i	0.0823099	−	0.0279970i
$634$	10725.1			0.671845
$635$	292.173	+	554.375i	0.0182591	+	0.0346452i
$636$	−14433.7	+	4909.50i	−0.899894	+	0.306092i
$637$	8283.39	+	1409.91i	0.515227	+	0.0876968i
$638$	940.117			0.0583379
$639$	−10063.7	−	13081.8i	−0.623026	−	0.809875i
$640$	−14453.8	+	7617.61i	−0.892715	+	0.470488i
$641$		−	17890.0i		−	1.10236i	−0.834387	−	0.551179i	$-0.814178\pi$
$641$		−	17890.0i		−	1.10236i	0.834387	−	0.551179i	$-0.185822\pi$
$642$	5650.69	−	1922.04i	0.347375	−	0.118157i
$643$	4734.63			0.290382			0.145191	−	0.989404i	$-0.453620\pi$
$643$	4734.63			0.290382			0.145191	+	0.989404i	$0.453620\pi$
$644$	987.905	−	11691.6i	0.0604486	−	0.715391i
$645$	−1268.25	−	1200.34i	−0.0774223	−	0.0732763i
$646$	−4385.05			−0.267070
$647$			6925.33i			0.420808i	0.977615	+	0.210404i	$0.0674779\pi$
$647$			6925.33i			0.420808i	−0.977615	+	0.210404i	$0.932522\pi$
$648$	3315.17	−	12495.5i	0.200975	−	0.757516i
$649$		−	19392.9i		−	1.17294i
$650$	2116.05	−	3088.24i	0.127690	−	0.186355i
$651$	−17383.5	+	4319.84i	−1.04656	+	0.260074i
$652$			16120.4i			0.968285i
$653$	16122.5			0.966192			0.483096	−	0.875567i	$-0.339512\pi$
$653$	16122.5			0.966192			0.483096	+	0.875567i	$0.339512\pi$
$654$	3097.55	−	1053.61i	0.185205	−	0.0629958i
$655$	21240.3	−	11194.3i	1.26706	−	0.667781i
$656$	9532.69			0.567362
$657$	−9077.08	+	6982.89i	−0.539012	+	0.414655i
$658$	−11603.6	−	980.470i	−0.687468	−	0.0580892i
$659$			17386.0i			1.02771i	0.857877	+	0.513855i	$0.171783\pi$
$659$			17386.0i			1.02771i	−0.857877	+	0.513855i	$0.828217\pi$
$660$	14968.7	+	14167.1i	0.882812	+	0.835537i
$661$			16253.3i			0.956401i	0.878251	+	0.478201i	$0.158711\pi$
$661$			16253.3i			0.956401i	−0.878251	+	0.478201i	$0.841289\pi$
$662$	−7652.81			−0.449297
$663$	−1476.26	−	4340.15i	−0.0864757	−	0.254234i
$664$		−	10386.5i		−	0.607042i
$665$	18988.0	−	8044.59i	1.10725	−	0.469106i
$666$	−4012.93	−	5216.42i	−0.233480	−	0.303502i
$667$		−	1373.23i		−	0.0797176i
$668$			2555.48i			0.148016i
$669$	−8041.30	+	2735.18i	−0.464715	+	0.158069i
$670$	−469.855	−	891.513i	−0.0270926	−	0.0514062i
$671$	−35779.9			−2.05852
$672$	4154.07	+	16716.4i	0.238462	+	0.959598i
$673$			14216.2i			0.814255i	0.913371	+	0.407128i	$0.133470\pi$
$673$			14216.2i			0.814255i	−0.913371	+	0.407128i	$0.866530\pi$
$674$		−	10029.1i		−	0.573156i
$675$	6551.65	+	16267.2i	0.373590	+	0.927594i
$676$	10388.3			0.591052
$677$		−	24424.5i		−	1.38657i	−0.720663	−	0.693286i	$-0.756162\pi$
$677$		−	24424.5i		−	1.38657i	0.720663	−	0.693286i	$-0.243838\pi$
$678$	−2235.06	+	760.238i	−0.126603	+	0.0430631i
$679$	−425.100	+	5030.93i	−0.0240263	+	0.284344i
$680$	3329.23	+	6316.95i	0.187750	+	0.356241i
$681$	4286.21	+	12601.2i	0.241186	+	0.709076i
$682$	12409.6			0.696758
$683$	−31372.1			−1.75757			−0.878785	−	0.477217i	$-0.841646\pi$
$683$	−31372.1			−1.75757			−0.878785	+	0.477217i	$0.841646\pi$
$684$	−10666.1	−	13864.8i	−0.596238	−	0.775052i
$685$	28412.9	−	14974.5i	1.58482	−	0.835248i
$686$	−1943.14	+	7519.21i	−0.108148	+	0.418491i
$687$	7114.83	+	20917.3i	0.395121	+	1.16163i
$688$		−	912.637i		−	0.0505726i
$689$	11048.7			0.610920
$690$	−4754.56	+	5023.58i	−0.262323	+	0.277166i
$691$			7582.28i			0.417429i	0.977977	+	0.208715i	$0.0669280\pi$
$691$			7582.28i			0.417429i	−0.977977	+	0.208715i	$0.933072\pi$
$692$			11436.8i			0.628267i
$693$	22937.2	−	14748.5i	1.25731	−	0.808440i
$694$	−3659.19			−0.200145
$695$	3395.80	+	6443.27i	0.185338	+	0.351665i
$696$	418.418	+	1230.13i	0.0227875	+	0.0669941i
$697$		−	11307.3i		−	0.614482i
$698$			8931.64i			0.484337i
$699$	17991.5	−	6119.66i	0.973535	−	0.331140i
$700$	−11662.7	−	9528.33i	−0.629725	−	0.514481i
$701$		−	6851.81i		−	0.369172i	−0.982816	−	0.184586i	$-0.940906\pi$
$701$		−	6851.81i		−	0.369172i	0.982816	−	0.184586i	$-0.0590944\pi$
$702$	−2327.90	+	3497.94i	−0.125158	+	0.188064i
$703$	−19856.8			−1.06531
$704$			1312.94i			0.0702886i
$705$	−21700.2	−	20538.2i	−1.15926	−	1.09718i
$706$			7489.95i			0.399275i
$707$	−1877.72	+	22222.2i	−0.0998851	+	1.18211i
$708$	11380.3	−	3870.91i	0.604093	−	0.205477i
$709$	2516.36			0.133292			0.0666459	−	0.997777i	$-0.478770\pi$
$709$	2516.36			0.133292			0.0666459	+	0.997777i	$0.478770\pi$
$710$	−3895.70	−	7391.79i	−0.205920	−	0.390717i
$711$	17422.4	−	13402.8i	0.918973	−	0.706955i
$712$	−12996.9			−0.684099
$713$		−	18126.7i		−	0.952106i
$714$	4112.12	−	1021.87i	0.215536	−	0.0535611i
$715$	−6963.87	−	13213.4i	−0.364243	−	0.691123i
$716$			3649.75i			0.190499i
$717$	3244.03	+	9537.30i	0.168969	+	0.496760i
$718$			10209.7i			0.530671i
$719$	4061.37			0.210658			0.105329	−	0.994437i	$-0.466410\pi$
$719$	4061.37			0.210658			0.105329	+	0.994437i	$0.466410\pi$
$720$	−3821.05	+	8331.01i	−0.197781	+	0.431220i
$721$	−2708.99	+	32060.0i	−0.139928	+	1.65600i
$722$	3740.53			0.192809
$723$	−8534.93	−	25092.3i	−0.439028	−	1.29072i
$724$		−	22896.3i		−	1.17532i
$725$	−1454.02	−	996.287i	−0.0744840	−	0.0510361i
$726$	−9881.20	+	3361.01i	−0.505132	+	0.171816i
$727$	−22093.5			−1.12710			−0.563551	−	0.826081i	$-0.690565\pi$
$727$	−22093.5			−1.12710			−0.563551	+	0.826081i	$0.690565\pi$
$728$	677.420	−	8017.06i	0.0344875	−	0.408149i
$729$	−7599.56	−	18156.7i	−0.386098	−	0.922458i
$730$	−5128.93	+	2703.10i	−0.260041	+	0.137050i
$731$	−1082.53			−0.0547728
$732$	−7141.84	−	20996.7i	−0.360615	−	1.06019i
$733$	35895.7			1.80878			0.904391	−	0.426705i	$-0.140326\pi$
$733$	35895.7			1.80878			0.904391	+	0.426705i	$0.140326\pi$
$734$	−12510.6			−0.629120
$735$	−15931.5	+	11968.8i	−0.799515	+	0.600646i
$736$	−17431.1			−0.872989
$737$	−4020.66			−0.200954
$738$	−8214.24	+	6319.11i	−0.409716	+	0.315189i
$739$	8613.60			0.428764			0.214382	−	0.976750i	$-0.431226\pi$
$739$	8613.60			0.428764			0.214382	+	0.976750i	$0.431226\pi$
$740$	6761.16	+	12828.8i	0.335872	+	0.637291i
$741$	4082.34	+	12001.9i	0.202387	+	0.595007i
$742$	−859.828	+	10175.8i	−0.0425408	+	0.503458i
$743$	636.669			0.0314362			0.0157181	−	0.999876i	$-0.494997\pi$
$743$	636.669			0.0314362			0.0157181	+	0.999876i	$0.494997\pi$
$744$	5523.15	+	16237.8i	0.272162	+	0.800143i
$745$	−15333.3	−	29093.8i	−0.754054	−	1.43076i
$746$			11050.8i			0.542355i
$747$	−9642.31	−	12534.1i	−0.472281	−	0.613920i
$748$	12776.7			0.624550
$749$	−1465.10	+	17339.1i	−0.0714736	+	0.845868i
$750$	1869.66	+	8678.92i	0.0910271	+	0.422546i
$751$	26006.9			1.26366			0.631828	−	0.775109i	$-0.282305\pi$
$751$	26006.9			1.26366			0.631828	+	0.775109i	$0.282305\pi$
$752$		−	15615.5i		−	0.757234i
$753$	−9022.23	+	3068.84i	−0.436638	+	0.148519i
$754$		−	422.307i		−	0.0203973i
$755$	−7095.47	+	3739.53i	−0.342027	+	0.180259i
$756$	13233.2	+	10516.3i	0.636623	+	0.505920i
$757$		−	17235.8i		−	0.827537i	−0.910382	−	0.413769i	$-0.864212\pi$
$757$		−	17235.8i		−	0.827537i	0.910382	−	0.413769i	$-0.135788\pi$
$758$	−6531.29			−0.312965
$759$	8886.63	+	26126.2i	0.424986	+	1.24944i
$760$	−9206.38	−	17468.4i	−0.439409	−	0.833743i
$761$	18532.2			0.882775			0.441388	−	0.897317i	$-0.354486\pi$
$761$	18532.2			0.882775			0.441388	+	0.897317i	$0.354486\pi$
$762$	−114.660	−	337.094i	−0.00545104	−	0.0160258i
$763$	−803.129	+	9504.79i	−0.0381065	+	0.450978i
$764$			17806.5i			0.843216i
$765$	9881.90	+	4532.38i	0.467034	+	0.214207i
$766$			2769.36i			0.130628i
$767$	−8711.43			−0.410106
$768$	7841.33	−	2667.17i	0.368424	−	0.125316i
$769$			14838.4i			0.695822i	0.937528	+	0.347911i	$0.113109\pi$
$769$			14838.4i			0.695822i	−0.937528	+	0.347911i	$0.886891\pi$
$770$	12711.4	−	5385.38i	0.594917	−	0.252046i
$771$	12829.2	+	37717.1i	0.599263	+	1.76180i
$772$			8986.10i			0.418933i
$773$		−	21416.9i		−	0.996525i	−0.867026	−	0.498262i	$-0.833972\pi$
$773$		−	21416.9i		−	0.996525i	0.867026	−	0.498262i	$-0.166028\pi$
$774$	604.976	+	786.411i	0.0280949	+	0.0365206i
$775$	−19193.2	−	13151.1i	−0.889599	−	0.609549i
$776$	4834.41			0.223641
$777$	18620.9	−	4627.34i	0.859745	−	0.213649i
$778$			2884.91i			0.132942i
$779$			31268.3i			1.43813i
$780$	6363.97	−	6724.05i	0.292137	−	0.308666i
$781$	−33336.4			−1.52736
$782$			4287.94i			0.196082i
$783$	1646.92	+	1096.03i	0.0751673	+	0.0500244i
$784$	−10266.7	−	1747.49i	−0.467687	−	0.0796049i
$785$	−7175.43	+	3781.68i	−0.326245	+	0.171941i
$786$	−12915.4	+	4393.07i	−0.586104	+	0.199358i
$787$	22017.8			0.997270			0.498635	−	0.866812i	$-0.333835\pi$
$787$	22017.8			0.997270			0.498635	+	0.866812i	$0.333835\pi$
$788$	−3087.78			−0.139591
$789$	−29626.8	+	10077.3i	−1.33681	+	0.454705i
$790$	9844.36	−	5188.28i	0.443350	−	0.233659i
$791$	579.504	−	6858.26i	0.0260491	−	0.308283i
$792$	−15921.1	−	20696.0i	−0.714309	−	0.928534i
$793$			16072.6i			0.719741i
$794$	3916.24			0.175041
$795$	−18011.0	+	19030.1i	−0.803504	+	0.848968i
$796$			23790.3i			1.05933i
$797$		−	23577.1i		−	1.04786i	−0.851761	−	0.523931i	$-0.824465\pi$
$797$		−	23577.1i		−	1.04786i	0.851761	−	0.523931i	$-0.175535\pi$
$798$	−11371.3	+	2825.80i	−0.504437	+	0.125354i
$799$	−18522.5			−0.820124
$800$	−12646.4	+	18456.6i	−0.558897	+	0.815675i
$801$	−15684.1	+	12065.6i	−0.691849	+	0.532231i
$802$			5810.98i			0.255852i
$803$			23131.1i			1.01654i
$804$	−802.542	−	2359.43i	−0.0352033	−	0.103496i
$805$	−7866.44	−	18567.5i	−0.344417	−	0.812943i
$806$		−	5574.49i		−	0.243614i
$807$	15054.0	−	5120.50i	0.656662	−	0.223358i
$808$	21354.2			0.929748
$809$		−	9941.71i		−	0.432054i	−0.976387	−	0.216027i	$-0.930690\pi$
$809$		−	9941.71i		−	0.432054i	0.976387	−	0.216027i	$-0.0693100\pi$
$810$	−2229.96	−	9711.68i	−0.0967320	−	0.421276i
$811$		−	21344.4i		−	0.924171i	−0.886835	−	0.462085i	$-0.847101\pi$
$811$		−	21344.4i		−	0.924171i	0.886835	−	0.462085i	$-0.152899\pi$
$812$	−1692.84	−	143.041i	−0.0731615	−	0.00618195i
$813$	−7409.25	−	21782.8i	−0.319623	−	0.939676i
$814$	−13293.0			−0.572382
$815$	12917.3	+	24509.5i	0.555180	+	1.05341i
$816$	1829.72	+	5379.30i	0.0784965	+	0.230776i
$817$	2993.55			0.128190
$818$			1956.01i			0.0836067i
$819$	−6625.13	−	10303.6i	−0.282663	−	0.439604i
$820$	20201.3	−	10646.7i	0.860318	−	0.453414i
$821$		−	20727.6i		−	0.881117i	−0.897724	−	0.440559i	$-0.854780\pi$
$821$		−	20727.6i		−	0.881117i	0.897724	−	0.440559i	$-0.145220\pi$
$822$	−17276.8	+	5876.56i	−0.733087	+	0.249353i
$823$			393.084i			0.0166489i	0.999965	+	0.00832444i	$0.00264978\pi$
$823$			393.084i			0.0166489i	−0.999965	+	0.00832444i	$0.997350\pi$
$824$	30807.7			1.30247
$825$	34110.6	+	9545.32i	1.43949	+	0.402819i
$826$	677.935	−	8023.15i	0.0285574	−	0.337968i
$827$	13189.7			0.554596			0.277298	−	0.960784i	$-0.410561\pi$
$827$	13189.7			0.554596			0.277298	+	0.960784i	$0.410561\pi$
$828$	−13557.8	+	10429.8i	−0.569041	+	0.437756i
$829$			17264.1i			0.723289i	0.932316	+	0.361645i	$0.117785\pi$
$829$			17264.1i			0.723289i	−0.932316	+	0.361645i	$0.882215\pi$
$830$	−3732.58	−	7082.27i	−0.156096	−	0.296180i
$831$	−4985.01	−	14655.7i	−0.208096	−	0.611793i
$832$	589.781			0.0245757
$833$	−2072.80	+	12177.9i	−0.0862163	+	0.506530i
$834$	−1332.65	−	3917.91i	−0.0553306	−	0.162669i
$835$	2047.71	+	3885.36i	0.0848669	+	0.161028i
$836$	−35331.7			−1.46169
$837$	21739.4	+	14467.7i	0.897759	+	0.597465i
$838$	7507.58			0.309481
$839$	−22957.9			−0.944690			−0.472345	−	0.881414i	$-0.656592\pi$
$839$	−22957.9			−0.944690			−0.472345	+	0.881414i	$0.656592\pi$
$840$	12704.1	+	14235.7i	0.521827	+	0.584738i
$841$	24190.2			0.991847
$842$	−3007.23			−0.123083
$843$	−4964.46	−	14595.3i	−0.202829	−	0.596308i
$844$	1733.48			0.0706978
$845$	15794.5	−	8324.17i	0.643013	−	0.338888i
$846$	10351.4	+	13455.8i	0.420670	+	0.546831i
$847$	2561.99	−	30320.3i	0.103933	−	1.23001i
$848$	−13694.1			−0.554550
$849$	28194.1	−	9589.98i	1.13971	−	0.387664i
$850$	4540.20	+	3110.93i	0.183209	+	0.125534i
$851$			19417.1i			0.782149i
$852$	−6654.11	−	19562.7i	−0.267566	−	0.786630i
$853$	−29182.4			−1.17138			−0.585689	−	0.810536i	$-0.699176\pi$
$853$	−29182.4			−1.17138			−0.585689	+	0.810536i	$0.699176\pi$
$854$	−14802.7	−	1250.79i	−0.593137	−	0.0501185i
$855$	−27326.6	−	12533.5i	−1.09304	−	0.501328i
$856$	16661.8			0.665289
$857$			33378.4i			1.33044i	0.746648	+	0.665219i	$0.231662\pi$
$857$			33378.4i			1.33044i	−0.746648	+	0.665219i	$0.768338\pi$
$858$	2732.89	+	8034.57i	0.108741	+	0.319692i
$859$			5538.66i			0.219996i	0.993932	+	0.109998i	$0.0350845\pi$
$859$			5538.66i			0.219996i	−0.993932	+	0.109998i	$0.964916\pi$
$860$	−1019.29	−	1934.03i	−0.0404158	−	0.0766857i
$861$	−7286.62	−	29322.2i	−0.288418	−	1.16062i
$862$			7108.44i			0.280875i
$863$	24503.6			0.966527			0.483263	−	0.875475i	$-0.339451\pi$
$863$	24503.6			0.966527			0.483263	+	0.875475i	$0.339451\pi$
$864$	13912.5	−	20905.2i	0.547817	−	0.823157i
$865$	9164.29	+	17388.5i	0.360226	+	0.683500i
$866$	−7669.73			−0.300956
$867$	−17788.1	+	6050.49i	−0.696789	+	0.237007i
$868$	−22345.7	−	1888.15i	−0.873804	−	0.0738341i
$869$		−	44397.4i		−	1.73312i
$870$	727.374	+	688.422i	0.0283452	+	0.0268272i
$871$			1806.11i			0.0702614i
$872$	9133.51			0.354702
$873$	5833.98	−	4488.01i	0.226174	−	0.173993i
$874$		−	11857.5i		−	0.458909i
$875$	−25367.0	−	5141.62i	−0.980071	−	0.198650i
$876$	−13574.0	+	4617.08i	−0.523541	+	0.178078i
$877$			5474.16i			0.210775i	0.994431	+	0.105387i	$0.0336082\pi$
$877$			5474.16i			0.210775i	−0.994431	+	0.105387i	$0.966392\pi$
$878$		−	10159.4i		−	0.390505i
$879$	2916.56	+	8574.55i	0.111915	+	0.329024i
$880$	8631.21	+	16377.1i	0.330634	+	0.627353i
$881$	−13195.1			−0.504600			−0.252300	−	0.967649i	$-0.581187\pi$
$881$	−13195.1			−0.504600			−0.252300	+	0.967649i	$0.581187\pi$
$882$	10005.1	−	5299.85i	0.381960	−	0.202330i
$883$			13041.2i			0.497023i	0.968629	+	0.248511i	$0.0799413\pi$
$883$			13041.2i			0.497023i	−0.968629	+	0.248511i	$0.920059\pi$
$884$		−	5739.40i		−	0.218367i
$885$	14200.9	−	15004.4i	0.539387	−	0.569906i
$886$	2766.67			0.104908
$887$			41932.8i			1.58733i	0.608352	+	0.793667i	$0.291831\pi$
$887$			41932.8i			1.58733i	−0.608352	+	0.793667i	$0.708169\pi$
$888$	−5916.31	−	17393.6i	−0.223579	−	0.657311i
$889$	1034.37	+	87.4014i	0.0390232	+	0.00329736i
$890$	−8862.18	+	4670.64i	−0.333776	+	0.175910i
$891$	−38426.0	−	10194.7i	−1.44480	−	0.383319i
$892$	−10633.8			−0.399154
$893$	51220.7			1.91941
$894$	6017.40	+	17690.9i	0.225114	+	0.661824i
$895$	2924.54	+	5549.09i	0.109225	+	0.207247i
$896$	−2278.76	+	26968.4i	−0.0849641	+	1.00552i
$897$	11736.1	−	3991.94i	0.436853	−	0.148592i
$898$		−	2316.84i		−	0.0860959i
$899$	−2624.61			−0.0973699
$900$	1207.18	+	21922.4i	0.0447104	+	0.811939i
$901$			16243.4i			0.600606i
$902$			20932.3i			0.772693i
$903$	−2807.23	+	697.604i	−0.103454	+	0.0257085i
$904$	−6590.36			−0.242469
$905$	−18346.8	−	34811.6i	−0.673887	−	1.27865i
$906$	4314.49	−	1467.54i	0.158211	−	0.0538142i
$907$		−	21860.2i		−	0.800283i	−0.916453	−	0.400142i	$-0.868961\pi$
$907$		−	21860.2i		−	0.800283i	0.916453	−	0.400142i	$-0.131039\pi$
$908$			16663.9i			0.609041i
$909$	25769.4	−	19824.1i	0.940282	−	0.723347i
$910$	−2419.15	−	5710.04i	−0.0881254	−	0.208007i
$911$		−	14163.2i		−	0.515091i	−0.966266	−	0.257545i	$-0.917086\pi$
$911$		−	14163.2i		−	0.515091i	0.966266	−	0.257545i	$-0.0829136\pi$
$912$	−5059.77	−	14875.5i	−0.183712	−	0.540105i
$913$	−31940.5			−1.15781
$914$			12751.9i			0.461484i
$915$	−27683.1	−	26200.7i	−1.00019	−	0.946631i
$916$			27660.9i			0.997754i
$917$	3348.69	−	39630.7i	0.120593	−	1.42718i
$918$	−5142.53	−	3422.39i	−0.184890	−	0.123045i
$919$	17539.6			0.629575			0.314787	−	0.949162i	$-0.398067\pi$
$919$	17539.6			0.629575			0.314787	+	0.949162i	$0.398067\pi$
$920$	−17081.5	+	9002.50i	−0.612132	+	0.322613i
$921$	52123.0	−	17729.2i	1.86483	−	0.634307i
$922$	−8589.61			−0.306815
$923$			14975.0i			0.534027i
$924$	33132.7	−	8233.55i	1.17964	−	0.293143i
$925$	20559.4	+	14087.2i	0.730799	+	0.500740i
$926$		−	15647.6i		−	0.555304i
$927$	37177.6	−	28600.2i	1.31723	−	1.01333i
$928$			2523.89i			0.0892787i
$929$	−22741.0			−0.803129			−0.401564	−	0.915831i	$-0.631533\pi$
$929$	−22741.0			−0.803129			−0.401564	+	0.915831i	$0.631533\pi$
$930$	9601.39	+	9087.23i	0.338540	+	0.320411i
$931$	5731.95	−	33675.8i	0.201780	−	1.18548i
$932$	23791.9			0.836191
$933$	−18118.5	+	6162.88i	−0.635771	+	0.216252i
$934$		−	18248.4i		−	0.639299i
$935$	19425.8	−	10238.0i	0.679456	−	0.358094i
$936$	−9296.77	+	7151.89i	−0.324652	+	0.249751i
$937$	12779.2			0.445549			0.222775	−	0.974870i	$-0.428489\pi$
$937$	12779.2			0.445549			0.222775	+	0.974870i	$0.428489\pi$
$938$	−1663.41	−	140.554i	−0.0579022	−	0.00489258i
$939$	−406.795	+	138.368i	−0.0141376	+	0.00480881i
$940$	−17440.4	−	33091.9i	−0.605153	−	1.14823i
$941$	−2629.15			−0.0910817			−0.0455408	−	0.998962i	$-0.514501\pi$
$941$	−2629.15			−0.0910817			−0.0455408	+	0.998962i	$0.514501\pi$
$942$	4363.11	−	1484.08i	0.150911	−	0.0513310i
$943$	30575.8			1.05587
$944$	10797.2			0.372265
$945$	28546.6	+	5385.31i	0.982667	+	0.185380i
$946$	2004.01			0.0688752
$947$	−14698.9			−0.504383			−0.252192	−	0.967677i	$-0.581151\pi$
$947$	−14698.9			−0.504383			−0.252192	+	0.967677i	$0.581151\pi$
$948$	26053.6	−	8861.93i	0.892597	−	0.303610i
$949$	10390.7			0.355421
$950$	−12555.1	−	8602.70i	−0.428781	−	0.293799i
$951$	43156.2	−	14679.2i	1.47154	−	0.500532i
$952$	11786.4	+	995.915i	0.401258	+	0.0339053i
$953$	−14010.3			−0.476219			−0.238110	−	0.971238i	$-0.576528\pi$
$953$	−14010.3			−0.476219			−0.238110	+	0.971238i	$0.576528\pi$
$954$	11800.1	−	9077.67i	0.400464	−	0.308072i
$955$	14268.4	+	27073.1i	0.483470	+	0.917346i
$956$			12612.1i			0.426678i
$957$	3782.87	−	1286.71i	0.127777	−	0.0434624i
$958$	−1519.78			−0.0512546
$959$	4479.50	−	53013.6i	0.150835	−	1.78509i
$960$	−961.428	+	1015.83i	−0.0323229	+	0.0341517i
$961$	−4854.03			−0.162936
$962$			5971.30i			0.200127i
$963$	20106.8	−	15467.9i	0.672826	−	0.517597i
$964$		−	33182.0i		−	1.10863i
$965$	7200.56	+	13662.5i	0.240201	+	0.455763i
$966$	2763.22	+	11119.5i	0.0920345	+	0.370357i
$967$			36963.6i			1.22923i	0.788826	+	0.614617i	$0.210689\pi$
$967$			36963.6i			1.22923i	−0.788826	+	0.614617i	$0.789311\pi$
$968$	−29135.9			−0.967422
$969$	−17644.7	+	6001.69i	−0.584963	+	0.198970i
$970$	3296.44	−	1737.33i	0.109116	−	0.0575074i
$971$	59617.4			1.97036			0.985178	−	0.171538i	$-0.0548736\pi$
$971$	59617.4			1.97036			0.985178	+	0.171538i	$0.0548736\pi$
$972$	−1687.46	−	24584.4i	−0.0556844	−	0.811260i
$973$	12022.0	+	1015.83i	0.396104	+	0.0334697i
$974$			14260.2i			0.469122i
$975$	4287.83	−	15322.7i	0.140841	−	0.503303i
$976$		−	19920.8i		−	0.653330i
$977$	22596.1			0.739932			0.369966	−	0.929045i	$-0.379369\pi$
$977$	22596.1			0.739932			0.369966	+	0.929045i	$0.379369\pi$
$978$	−5069.23	−	14903.3i	−0.165742	−	0.487274i
$979$			39967.8i			1.30478i
$980$	−23708.4	+	7763.26i	−0.772794	+	0.253049i
$981$	11022.0	−	8479.07i	0.358720	−	0.275959i
$982$		−	19492.2i		−	0.633421i
$983$			21849.2i			0.708932i	0.935069	+	0.354466i	$0.115337\pi$
$983$			21849.2i			0.708932i	−0.935069	+	0.354466i	$0.884663\pi$
$984$	−27389.6	+	9316.34i	−0.887345	+	0.301823i
$985$	−4694.67	+	2474.24i	−0.151863	+	0.0800364i
$986$	620.859			0.0200529
$987$	−48032.7	+	11936.2i	−1.54904	+	0.384939i
$988$			15871.3i			0.511065i
$989$		−	2927.26i		−	0.0941166i
$990$	−18293.6	−	8390.43i	−0.587281	−	0.269359i
$991$	−48955.2			−1.56924			−0.784618	−	0.619980i	$-0.787141\pi$
$991$	−48955.2			−1.56924			−0.784618	+	0.619980i	$0.787141\pi$
$992$			33315.5i			1.06630i
$993$	−30793.6	+	10474.2i	−0.984094	+	0.334732i
$994$	−13791.8	−	1165.37i	−0.440090	−	0.0371865i
$995$	19063.1	+	36170.8i	0.607379	+	1.15245i
$996$	−6375.49	−	18743.6i	−0.202826	−	0.596299i
$997$	−21348.2			−0.678140			−0.339070	−	0.940761i	$-0.610112\pi$
$997$	−21348.2			−0.678140			−0.339070	+	0.940761i	$0.610112\pi$
$998$	24508.5			0.777358
$999$	−23286.9	−	15497.6i	−0.737503	−	0.490813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.g.b.104.18	yes	40
3.2	odd	2	inner	105.4.g.b.104.21	yes	40
5.4	even	2	inner	105.4.g.b.104.23	yes	40
7.6	odd	2	inner	105.4.g.b.104.19	yes	40
15.14	odd	2	inner	105.4.g.b.104.20	yes	40
21.20	even	2	inner	105.4.g.b.104.24	yes	40
35.34	odd	2	inner	105.4.g.b.104.22	yes	40
105.104	even	2	inner	105.4.g.b.104.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.g.b.104.17	✓	40	105.104	even	2	inner
105.4.g.b.104.18	yes	40	1.1	even	1	trivial
105.4.g.b.104.19	yes	40	7.6	odd	2	inner
105.4.g.b.104.20	yes	40	15.14	odd	2	inner
105.4.g.b.104.21	yes	40	3.2	odd	2	inner
105.4.g.b.104.22	yes	40	35.34	odd	2	inner
105.4.g.b.104.23	yes	40	5.4	even	2	inner
105.4.g.b.104.24	yes	40	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.22256 q^{2} +(-4.91936 + 1.67328i) q^{3} -6.50535 q^{4} +(-9.89077 + 5.21274i) q^{5} +(6.01420 - 2.04568i) q^{6} +(-1.55936 + 18.4545i) q^{7} +17.7336 q^{8} +(21.4003 - 16.4630i) q^{9} +O(q^{10})\)	\(q-1.22256 q^{2} +(-4.91936 + 1.67328i) q^{3} -6.50535 q^{4} +(-9.89077 + 5.21274i) q^{5} +(6.01420 - 2.04568i) q^{6} +(-1.55936 + 18.4545i) q^{7} +17.7336 q^{8} +(21.4003 - 16.4630i) q^{9} +(12.0920 - 6.37288i) q^{10} -54.5342i q^{11} +(32.0022 - 10.8853i) q^{12} -24.4972 q^{13} +(1.90640 - 22.5617i) q^{14} +(39.9339 - 42.1934i) q^{15} +30.3625 q^{16} -36.0147i q^{17} +(-26.1630 + 20.1269i) q^{18} +99.5921i q^{19} +(64.3430 - 33.9107i) q^{20} +(-23.2085 - 93.3936i) q^{21} +66.6712i q^{22} +97.3866 q^{23} +(-87.2381 + 29.6733i) q^{24} +(70.6546 - 103.116i) q^{25} +29.9492 q^{26} +(-77.7285 + 116.796i) q^{27} +(10.1442 - 120.053i) q^{28} -14.1008i q^{29} +(-48.8215 + 51.5839i) q^{30} -186.132i q^{31} -178.989 q^{32} +(91.2510 + 268.273i) q^{33} +44.0300i q^{34} +(-80.7753 - 190.658i) q^{35} +(-139.216 + 107.097i) q^{36} +199.381i q^{37} -121.757i q^{38} +(120.510 - 40.9906i) q^{39} +(-175.399 + 92.4408i) q^{40} +313.963 q^{41} +(28.3738 + 114.179i) q^{42} -30.0581i q^{43} +354.764i q^{44} +(-125.848 + 274.385i) q^{45} -119.061 q^{46} -514.304i q^{47} +(-149.364 + 50.8049i) q^{48} +(-338.137 - 57.5542i) q^{49} +(-86.3794 + 126.065i) q^{50} +(60.2627 + 177.169i) q^{51} +159.363 q^{52} -451.022 q^{53} +(95.0275 - 142.790i) q^{54} +(284.273 + 539.385i) q^{55} +(-27.6530 + 327.265i) q^{56} +(-166.646 - 489.930i) q^{57} +17.2390i q^{58} +355.610 q^{59} +(-259.784 + 274.483i) q^{60} -656.101i q^{61} +227.557i q^{62} +(270.445 + 420.603i) q^{63} -24.0755 q^{64} +(242.296 - 127.697i) q^{65} +(-111.560 - 327.980i) q^{66} -73.7273i q^{67} +234.288i q^{68} +(-479.080 + 162.955i) q^{69} +(98.7524 + 233.090i) q^{70} -611.294i q^{71} +(379.504 - 291.948i) q^{72} -424.158 q^{73} -243.755i q^{74} +(-175.034 + 625.490i) q^{75} -647.882i q^{76} +(1006.40 + 85.0382i) q^{77} +(-147.331 + 50.1134i) q^{78} +814.120 q^{79} +(-300.308 + 158.272i) q^{80} +(186.942 - 704.623i) q^{81} -383.838 q^{82} -585.698i q^{83} +(150.980 + 607.558i) q^{84} +(187.735 + 356.213i) q^{85} +36.7477i q^{86} +(23.5946 + 69.3670i) q^{87} -967.089i q^{88} -732.894 q^{89} +(153.856 - 335.452i) q^{90} +(38.1998 - 452.083i) q^{91} -633.535 q^{92} +(311.451 + 915.650i) q^{93} +628.766i q^{94} +(-519.148 - 985.043i) q^{95} +(880.511 - 299.499i) q^{96} +272.613 q^{97} +(413.392 + 70.3633i) q^{98} +(-897.794 - 1167.05i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) 40 * q + 184 * q^4 + 4 * q^9	\( 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) \) 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more