LMFDB - Embedded newform 152.6.b.b.75.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,6,Mod(75,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("152.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	152.b (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:	$24.3783406116$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.15
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.93864 - 2.75858i) q^{2} +1.79162i q^{3} +(16.7804 + 27.2473i) q^{4} -26.9679i q^{5} +(4.94234 - 8.84819i) q^{6} +21.5599i q^{7} +(-7.70850 - 180.855i) q^{8} +239.790 q^{9} +O(q^{10})$	\(q+(-4.93864 - 2.75858i) q^{2} +1.79162i q^{3} +(16.7804 + 27.2473i) q^{4} -26.9679i q^{5} +(4.94234 - 8.84819i) q^{6} +21.5599i q^{7} +(-7.70850 - 180.855i) q^{8} +239.790 q^{9} +(-74.3932 + 133.185i) q^{10} -90.3444 q^{11} +(-48.8170 + 30.0642i) q^{12} -419.826 q^{13} +(59.4749 - 106.477i) q^{14} +48.3163 q^{15} +(-460.835 + 914.444i) q^{16} -215.062 q^{17} +(-1184.24 - 661.481i) q^{18} +(1355.34 - 799.470i) q^{19} +(734.804 - 452.533i) q^{20} -38.6273 q^{21} +(446.179 + 249.223i) q^{22} +3077.62i q^{23} +(324.024 - 13.8107i) q^{24} +2397.73 q^{25} +(2073.37 + 1158.13i) q^{26} +864.978i q^{27} +(-587.451 + 361.785i) q^{28} -6155.92 q^{29} +(-238.617 - 133.285i) q^{30} +3059.38 q^{31} +(4798.47 - 3244.86i) q^{32} -161.863i q^{33} +(1062.12 + 593.268i) q^{34} +581.426 q^{35} +(4023.78 + 6533.64i) q^{36} +9295.40 q^{37} +(-8898.95 + 209.478i) q^{38} -752.170i q^{39} +(-4877.28 + 207.882i) q^{40} -17772.2i q^{41} +(190.767 + 106.557i) q^{42} +7152.73 q^{43} +(-1516.02 - 2461.65i) q^{44} -6466.64i q^{45} +(8489.88 - 15199.3i) q^{46} -23161.1i q^{47} +(-1638.34 - 825.642i) q^{48} +16342.2 q^{49} +(-11841.5 - 6614.35i) q^{50} -385.311i q^{51} +(-7044.86 - 11439.1i) q^{52} +11807.4 q^{53} +(2386.11 - 4271.82i) q^{54} +2436.40i q^{55} +(3899.23 - 166.195i) q^{56} +(1432.35 + 2428.26i) q^{57} +(30401.9 + 16981.6i) q^{58} -42428.8i q^{59} +(810.769 + 1316.49i) q^{60} -45648.8i q^{61} +(-15109.2 - 8439.54i) q^{62} +5169.86i q^{63} +(-32649.2 + 2788.24i) q^{64} +11321.8i q^{65} +(-446.513 + 799.385i) q^{66} +33058.2i q^{67} +(-3608.84 - 5859.88i) q^{68} -5513.94 q^{69} +(-2871.46 - 1603.91i) q^{70} +29886.8 q^{71} +(-1848.42 - 43367.3i) q^{72} -39654.0 q^{73} +(-45906.7 - 25642.1i) q^{74} +4295.83i q^{75} +(44526.6 + 23514.0i) q^{76} -1947.82i q^{77} +(-2074.92 + 3714.70i) q^{78} +62295.5 q^{79} +(24660.6 + 12427.7i) q^{80} +56719.3 q^{81} +(-49026.1 + 87770.5i) q^{82} +107005. q^{83} +(-648.183 - 1052.49i) q^{84} +5799.78i q^{85} +(-35324.8 - 19731.4i) q^{86} -11029.1i q^{87} +(696.420 + 16339.3i) q^{88} +92408.3i q^{89} +(-17838.8 + 31936.4i) q^{90} -9051.43i q^{91} +(-83857.0 + 51643.8i) q^{92} +5481.25i q^{93} +(-63891.9 + 114385. i) q^{94} +(-21560.0 - 36550.7i) q^{95} +(5813.57 + 8597.05i) q^{96} +76257.9i q^{97} +(-80708.2 - 45081.2i) q^{98} -21663.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−4.93864	−	2.75858i	−0.873037	−	0.487653i
$2$	−4.93864	−	2.75858i	−0.873037	−	0.487653i
$3$			1.79162i			0.114933i	0.998347	+	0.0574664i	$0.0183022\pi$
$3$			1.79162i			0.114933i	−0.998347	+	0.0574664i	$0.981698\pi$
$4$	16.7804	+	27.2473i	0.524388	+	0.851479i
$5$		−	26.9679i		−	0.482417i	−0.970473	−	0.241208i	$-0.922456\pi$
$5$		−	26.9679i		−	0.482417i	0.970473	−	0.241208i	$-0.0775437\pi$
$6$	4.94234	−	8.84819i	0.0560473	−	0.100341i
$7$			21.5599i			0.166304i	0.996537	+	0.0831520i	$0.0264987\pi$
$7$			21.5599i			0.166304i	−0.996537	+	0.0831520i	$0.973501\pi$
$8$	−7.70850	−	180.855i	−0.0425838	−	0.999093i
$9$	239.790			0.986790
$10$	−74.3932	+	133.185i	−0.235252	+	0.421168i
$11$	−90.3444			−0.225123			−0.112561	−	0.993645i	$-0.535906\pi$
$11$	−90.3444			−0.225123			−0.112561	+	0.993645i	$0.535906\pi$
$12$	−48.8170	+	30.0642i	−0.0978628	+	0.0602694i
$13$	−419.826			−0.688987			−0.344493	−	0.938789i	$-0.611949\pi$
$13$	−419.826			−0.688987			−0.344493	+	0.938789i	$0.611949\pi$
$14$	59.4749	−	106.477i	0.0810987	−	0.145190i
$15$	48.3163			0.0554454
$16$	−460.835	+	914.444i	−0.450034	+	0.893012i
$17$	−215.062			−0.180485			−0.0902427	−	0.995920i	$-0.528764\pi$
$17$	−215.062			−0.180485			−0.0902427	+	0.995920i	$0.528764\pi$
$18$	−1184.24	−	661.481i	−0.861505	−	0.481212i
$19$	1355.34	−	799.470i	0.861320	−	0.508064i
$19$	1355.34	−	799.470i	0.861320	−	0.508064i
$20$	734.804	−	452.533i	0.410768	−	0.252974i
$21$	−38.6273			−0.0191138
$22$	446.179	+	249.223i	0.196541	+	0.109782i
$23$			3077.62i			1.21310i	0.795046	+	0.606549i	$0.207446\pi$
$23$			3077.62i			1.21310i	−0.795046	+	0.606549i	$0.792554\pi$
$24$	324.024	−	13.8107i	0.114828	−	0.00489428i
$25$	2397.73			0.767274
$26$	2073.37	+	1158.13i	0.601511	+	0.335987i
$27$			864.978i			0.228347i
$28$	−587.451	+	361.785i	−0.141604	+	0.0872078i
$29$	−6155.92			−1.35925			−0.679623	−	0.733561i	$-0.737857\pi$
$29$	−6155.92			−1.35925			−0.679623	+	0.733561i	$0.737857\pi$
$30$	−238.617	−	133.285i	−0.0484059	−	0.0270382i
$31$	3059.38			0.571779			0.285890	−	0.958263i	$-0.407711\pi$
$31$	3059.38			0.571779			0.285890	+	0.958263i	$0.407711\pi$
$32$	4798.47	−	3244.86i	0.828376	−	0.560172i
$33$		−	161.863i		−	0.0258740i
$34$	1062.12	+	593.268i	0.157571	+	0.0880144i
$35$	581.426			0.0802278
$36$	4023.78	+	6533.64i	0.517461	+	0.840232i
$37$	9295.40			1.11626			0.558128	−	0.829755i	$-0.311520\pi$
$37$	9295.40			1.11626			0.558128	+	0.829755i	$0.311520\pi$
$38$	−8898.95	+	209.478i	−0.999723	+	0.0235331i
$39$		−	752.170i		−	0.0791871i
$40$	−4877.28	+	207.882i	−0.481979	+	0.0205431i
$41$		−	17772.2i		−	1.65113i	−0.564307	−	0.825565i	$-0.690857\pi$
$41$		−	17772.2i		−	1.65113i	0.564307	−	0.825565i	$-0.309143\pi$
$42$	190.767	+	106.557i	0.0166870	+	0.00932089i
$43$	7152.73			0.589930			0.294965	−	0.955508i	$-0.404692\pi$
$43$	7152.73			0.589930			0.294965	+	0.955508i	$0.404692\pi$
$44$	−1516.02	−	2461.65i	−0.118052	−	0.191687i
$45$		−	6466.64i		−	0.476044i
$46$	8489.88	−	15199.3i	0.591571	−	1.05908i
$47$		−	23161.1i		−	1.52938i	−0.644400	−	0.764689i	$-0.722893\pi$
$47$		−	23161.1i		−	1.52938i	0.644400	−	0.764689i	$-0.277107\pi$
$48$	−1638.34	−	825.642i	−0.102636	−	0.0517236i
$49$	16342.2			0.972343
$50$	−11841.5	−	6614.35i	−0.669859	−	0.374164i
$51$		−	385.311i		−	0.0207437i
$52$	−7044.86	−	11439.1i	−0.361297	−	0.586658i
$53$	11807.4			0.577383			0.288691	−	0.957422i	$-0.406780\pi$
$53$	11807.4			0.577383			0.288691	+	0.957422i	$0.406780\pi$
$54$	2386.11	−	4271.82i	0.111354	−	0.199356i
$55$			2436.40i			0.108603i
$56$	3899.23	−	166.195i	0.166153	−	0.00708186i
$57$	1432.35	+	2428.26i	0.0583931	+	0.0989938i
$58$	30401.9	+	16981.6i	1.18667	+	0.662841i
$59$		−	42428.8i		−	1.58683i	−0.608680	−	0.793416i	$-0.708301\pi$
$59$		−	42428.8i		−	1.58683i	0.608680	−	0.793416i	$-0.291699\pi$
$60$	810.769	+	1316.49i	0.0290749	+	0.0472106i
$61$		−	45648.8i		−	1.57074i	−0.619025	−	0.785372i	$-0.712472\pi$
$61$		−	45648.8i		−	1.57074i	0.619025	−	0.785372i	$-0.287528\pi$
$62$	−15109.2	−	8439.54i	−0.499185	−	0.278830i
$63$			5169.86i			0.164107i
$64$	−32649.2	+	2788.24i	−0.996373	+	0.0850904i
$65$			11321.8i			0.332379i
$66$	−446.513	+	799.385i	−0.0126175	+	0.0225890i
$67$			33058.2i			0.899690i	0.893107	+	0.449845i	$0.148521\pi$
$67$			33058.2i			0.899690i	−0.893107	+	0.449845i	$0.851479\pi$
$68$	−3608.84	−	5859.88i	−0.0946445	−	0.153680i
$69$	−5513.94			−0.139425
$70$	−2871.46	−	1603.91i	−0.0700418	−	0.0391233i
$71$	29886.8			0.703612			0.351806	−	0.936073i	$-0.385568\pi$
$71$	29886.8			0.703612			0.351806	+	0.936073i	$0.385568\pi$
$72$	−1848.42	−	43367.3i	−0.0420213	−	0.985895i
$73$	−39654.0			−0.870924			−0.435462	−	0.900207i	$-0.643415\pi$
$73$	−39654.0			−0.870924			−0.435462	+	0.900207i	$0.643415\pi$
$74$	−45906.7	−	25642.1i	−0.974533	−	0.544346i
$75$			4295.83i			0.0881849i
$76$	44526.6	+	23514.0i	0.884272	+	0.466973i
$77$		−	1947.82i		−	0.0374388i
$78$	−2074.92	+	3714.70i	−0.0386159	+	0.0691333i
$79$	62295.5			1.12302			0.561512	−	0.827469i	$-0.310220\pi$
$79$	62295.5			1.12302			0.561512	+	0.827469i	$0.310220\pi$
$80$	24660.6	+	12427.7i	0.430804	+	0.217104i
$81$	56719.3			0.960546
$82$	−49026.1	+	87770.5i	−0.805179	+	1.44150i
$83$	107005.			1.70494			0.852468	−	0.522780i	$-0.175105\pi$
$83$	107005.			1.70494			0.852468	+	0.522780i	$0.175105\pi$
$84$	−648.183	−	1052.49i	−0.0100230	−	0.0162750i
$85$			5799.78i			0.0870692i
$86$	−35324.8	−	19731.4i	−0.515031	−	0.287681i
$87$		−	11029.1i		−	0.156222i
$88$	696.420	+	16339.3i	0.00958660	+	0.224919i
$89$			92408.3i			1.23662i	0.785935	+	0.618310i	$0.212182\pi$
$89$			92408.3i			1.23662i	−0.785935	+	0.618310i	$0.787818\pi$
$90$	−17838.8	+	31936.4i	−0.232145	+	0.415604i
$91$		−	9051.43i		−	0.114581i
$92$	−83857.0	+	51643.8i	−1.03293	+	0.636134i
$93$			5481.25i			0.0657162i
$94$	−63891.9	+	114385.i	−0.745806	+	1.33520i
$95$	−21560.0	−	36550.7i	−0.245098	−	0.415515i
$96$	5813.57	+	8597.05i	0.0643821	+	0.0952075i
$97$			76257.9i			0.822916i	0.911429	+	0.411458i	$0.134980\pi$
$97$			76257.9i			0.822916i	−0.911429	+	0.411458i	$0.865020\pi$
$98$	−80708.2	−	45081.2i	−0.848892	−	0.474166i
$99$	−21663.7			−0.222149
$100$	40235.0	+	65331.8i	0.402350	+	0.653318i
$101$		−	144178.i		−	1.40636i	−0.711012	−	0.703180i	$-0.751763\pi$
$101$		−	144178.i		−	1.40636i	0.711012	−	0.703180i	$-0.248237\pi$
$102$	−1062.91	+	1902.91i	−0.0101157	+	0.0181100i
$103$	44423.8			0.412594			0.206297	−	0.978489i	$-0.433859\pi$
$103$	44423.8			0.412594			0.206297	+	0.978489i	$0.433859\pi$
$104$	3236.23	+	75927.7i	0.0293397	+	0.688362i
$105$			1041.70i			0.00922079i
$106$	−58312.4	−	32571.6i	−0.504077	−	0.281563i
$107$			64037.4i			0.540722i	0.962759	+	0.270361i	$0.0871431\pi$
$107$			64037.4i			0.540722i	−0.962759	+	0.270361i	$0.912857\pi$
$108$	−23568.3	+	14514.7i	−0.194433	+	0.119743i
$109$	−53855.6			−0.434175			−0.217087	−	0.976152i	$-0.569656\pi$
$109$	−53855.6			−0.434175			−0.217087	+	0.976152i	$0.569656\pi$
$110$	6721.02	−	12032.5i	0.0529606	−	0.0948145i
$111$			16653.9i			0.128294i
$112$	−19715.4	−	9935.57i	−0.148511	−	0.0748424i
$113$			63828.3i			0.470238i	0.971967	+	0.235119i	$0.0755479\pi$
$113$			63828.3i			0.470238i	−0.971967	+	0.235119i	$0.924452\pi$
$114$	−375.305	−	15943.6i	−0.00270472	−	0.114901i
$115$	82997.0			0.585218
$116$	−103299.	−	167733.i	−0.712773	−	1.15737i
$117$	−100670.			−0.679886
$118$	−117043.	+	209541.i	−0.773824	+	1.38536i
$119$		−	4636.73i		−	0.0300154i
$120$	−372.446	−	8738.26i	−0.00236108	−	0.0553951i
$121$	−152889.			−0.949320
$122$	−125926.	+	225443.i	−0.765978	+	1.37132i
$123$	31841.1			0.189769
$124$	51337.6	+	83359.8i	0.299834	+	0.486858i
$125$		−	148937.i		−	0.852562i
$126$	14261.5	−	25532.1i	0.0800274	−	0.143272i
$127$	245386.			1.35002			0.675010	−	0.737808i	$-0.264139\pi$
$127$	245386.			1.35002			0.675010	+	0.737808i	$0.264139\pi$
$128$	168934.	+	76295.3i	0.911366	+	0.411598i
$129$			12815.0i			0.0678023i
$130$	31232.2	−	55914.5i	0.162086	−	0.290179i
$131$	−184118.			−0.937387			−0.468693	−	0.883361i	$-0.655275\pi$
$131$	−184118.			−0.937387			−0.468693	+	0.883361i	$0.655275\pi$
$132$	4410.34	−	2716.13i	0.0220312	−	0.0135680i
$133$	17236.5	+	29221.1i	0.0844930	+	0.143241i
$134$	91194.0	−	163263.i	0.438737	−	0.785463i
$135$	23326.6			0.110158
$136$	1657.81	+	38895.1i	0.00768576	+	0.180322i
$137$	164046.			0.746732			0.373366	−	0.927684i	$-0.378204\pi$
$137$	164046.			0.746732			0.373366	+	0.927684i	$0.378204\pi$
$138$	27231.4	+	15210.7i	0.121723	+	0.0679908i
$139$	−87851.9			−0.385668			−0.192834	−	0.981231i	$-0.561768\pi$
$139$	−87851.9			−0.385668			−0.192834	+	0.981231i	$0.561768\pi$
$140$	9756.58	+	15842.3i	0.0420705	+	0.0683123i
$141$	41496.0			0.175776
$142$	−147600.	−	82445.2i	−0.614280	−	0.343119i
$143$	37928.9			0.155107
$144$	−110504.	+	219275.i	−0.444089	+	0.881215i
$145$			166012.i			0.655723i
$146$	195837.	+	109389.i	0.760349	+	0.424709i
$147$			29279.0i			0.111754i
$148$	155981.	+	253275.i	0.585351	+	0.950468i
$149$		−	12580.6i		−	0.0464232i	−0.999731	−	0.0232116i	$-0.992611\pi$
$149$		−	12580.6i		−	0.0464232i	0.999731	−	0.0232116i	$-0.00738915\pi$
$150$	11850.4	−	21215.6i	0.0430037	−	0.0769887i
$151$	−6755.65			−0.0241115			−0.0120558	−	0.999927i	$-0.503838\pi$
$151$	−6755.65			−0.0241115			−0.0120558	+	0.999927i	$0.503838\pi$
$152$	−155036.	−	238958.i	−0.544281	−	0.838903i
$153$	−51569.8			−0.178101
$154$	−5373.23	+	9619.60i	−0.0182572	+	0.0326855i
$155$		−	82504.9i		−	0.275836i
$156$	20494.6	−	12621.7i	0.0674262	−	0.0415248i
$157$		−	298532.i		−	0.966588i	−0.875458	−	0.483294i	$-0.839440\pi$
$157$		−	298532.i		−	0.966588i	0.875458	−	0.483294i	$-0.160560\pi$
$158$	−307655.	−	171847.i	−0.980441	−	0.547646i
$159$			21154.4i			0.0663601i
$160$	−87507.1	−	129405.i	−0.270236	−	0.399622i
$161$	−66353.3			−0.201743
$162$	−280116.	−	156465.i	−0.838592	−	0.468413i
$163$	225736.			0.665476			0.332738	−	0.943019i	$-0.392028\pi$
$163$	225736.			0.665476			0.332738	+	0.943019i	$0.392028\pi$
$164$	484245.	−	298225.i	1.40590	−	0.865833i
$165$	−4365.11			−0.0124820
$166$	−528459.	−	295182.i	−1.48847	−	0.831417i
$167$	581701.			1.61402			0.807009	−	0.590539i	$-0.201085\pi$
$167$	581701.			1.61402			0.807009	+	0.590539i	$0.201085\pi$
$168$	297.758	+	6985.95i	0.000813937	+	0.0190964i
$169$	−195039.			−0.525297
$170$	15999.2	−	28643.1i	0.0424596	−	0.0760146i
$171$	324997.	−	191705.i	0.849942	−	0.501352i
$172$	120026.	+	194893.i	0.309352	+	0.502313i
$173$	−626577.			−1.59169			−0.795846	−	0.605499i	$-0.792974\pi$
$173$	−626577.			−1.59169			−0.795846	+	0.605499i	$0.792974\pi$
$174$	−30424.7	+	54468.8i	−0.0761821	+	0.136388i
$175$			51695.0i			0.127601i
$176$	41633.8	−	82614.9i	0.101313	−	0.201037i
$177$	76016.4			0.182379
$178$	254916.	−	456372.i	0.603042	−	1.07961i
$179$		−	446020.i		−	1.04045i	−0.854029	−	0.520226i	$-0.825848\pi$
$179$		−	446020.i		−	1.04045i	0.854029	−	0.520226i	$-0.174152\pi$
$180$	176199.	−	108513.i	0.405342	−	0.249632i
$181$	−645175.			−1.46380			−0.731899	−	0.681413i	$-0.761366\pi$
$181$	−645175.			−1.46380			−0.731899	+	0.681413i	$0.761366\pi$
$182$	−24969.1	+	44701.8i	−0.0558759	+	0.100034i
$183$	81785.5			0.180530
$184$	556604.	−	23723.8i	1.21200	−	0.0516583i
$185$		−	250677.i		−	0.538500i
$186$	15120.5	−	27069.9i	0.0320467	−	0.0573727i
$187$	19429.7			0.0406314
$188$	631079.	−	388653.i	1.30223	−	0.801988i
$189$	−18648.9			−0.0379750
$190$	5649.17	+	239986.i	0.0113527	+	0.482283i
$191$			497589.i			0.986932i	0.869765	+	0.493466i	$0.164270\pi$
$191$			497589.i			0.986932i	−0.869765	+	0.493466i	$0.835730\pi$
$192$	−4995.48	−	58495.0i	−0.00977967	−	0.114516i
$193$			41507.7i			0.0802112i	0.999195	+	0.0401056i	$0.0127694\pi$
$193$			41507.7i			0.0802112i	−0.999195	+	0.0401056i	$0.987231\pi$
$194$	210364.	−	376611.i	0.401298	−	0.718437i
$195$	−20284.5			−0.0382012
$196$	274229.	+	445281.i	0.509885	+	0.827930i
$197$			140183.i			0.257354i	0.991687	+	0.128677i	$0.0410730\pi$
$197$			140183.i			0.257354i	−0.991687	+	0.128677i	$0.958927\pi$
$198$	106989.	+	59761.1i	0.193944	+	0.108332i
$199$			745266.i			1.33407i	0.745026	+	0.667035i	$0.232437\pi$
$199$			745266.i			1.33407i	−0.745026	+	0.667035i	$0.767563\pi$
$200$	−18482.9	−	433642.i	−0.0326735	−	0.766578i
$201$	−59227.9			−0.103404
$202$	−397728.	+	712045.i	−0.685816	+	1.22780i
$203$		−	132721.i		−	0.226048i
$204$	10498.7	−	6465.68i	0.0176628	−	0.0108777i
$205$	−479279.			−0.796533
$206$	−219393.	−	122547.i	−0.360210	−	0.201203i
$207$			737983.i			1.19707i
$208$	193470.	−	383907.i	0.310067	−	0.615273i
$209$	−122447.	+	72227.7i	−0.193903	+	0.114377i
$210$	2873.61	−	5144.57i	0.00449655	−	0.00805010i
$211$		−	759403.i		−	1.17426i	−0.809491	−	0.587132i	$-0.800257\pi$
$211$		−	759403.i		−	1.17426i	0.809491	−	0.587132i	$-0.199743\pi$
$212$	198133.	+	321720.i	0.302773	+	0.491629i
$213$			53545.9i			0.0808680i
$214$	176653.	−	316258.i	0.263685	−	0.472071i
$215$		−	192894.i		−	0.284592i
$216$	156436.	−	6667.68i	0.228140	−	0.00972390i
$217$			65960.0i			0.0950892i
$218$	265974.	+	148565.i	0.379051	+	0.211727i
$219$		−	71045.1i		−	0.100098i
$220$	−66385.4	+	40883.8i	−0.0924732	+	0.0569502i
$221$	90288.8			0.124352
$222$	45941.1	−	82247.5i	0.0625631	−	0.112006i
$223$	354973.			0.478006			0.239003	−	0.971019i	$-0.423179\pi$
$223$	354973.			0.478006			0.239003	+	0.971019i	$0.423179\pi$
$224$	69959.0	+	103455.i	0.0931588	+	0.137762i
$225$	574952.			0.757139
$226$	176076.	−	315225.i	0.229313	−	0.410535i
$227$		−	521607.i		−	0.671860i	−0.941887	−	0.335930i	$-0.890949\pi$
$227$		−	521607.i		−	0.671860i	0.941887	−	0.335930i	$-0.109051\pi$
$228$	−42128.2	+	79774.9i	−0.0536705	+	0.101632i
$229$			921989.i			1.16182i	0.813969	+	0.580908i	$0.197302\pi$
$229$			921989.i			1.16182i	−0.813969	+	0.580908i	$0.802698\pi$
$230$	−409893.	−	228954.i	−0.510917	−	0.285384i
$231$	3489.76			0.00430295
$232$	47452.9	+	1.11333e6i	0.0578819	+	1.35801i
$233$	−1.42390e6			−1.71826			−0.859132	−	0.511754i	$-0.828996\pi$
$233$	−1.42390e6			−1.71826			−0.859132	+	0.511754i	$0.828996\pi$
$234$	497174.	+	277707.i	0.593566	+	0.331549i
$235$	−624607.			−0.737797
$236$	1.15607e6	−	711973.i	1.35115	−	0.832116i
$237$			111610.i			0.129072i
$238$	−12790.8	+	22899.2i	−0.0146371	+	0.0262046i
$239$		−	316371.i		−	0.358263i	−0.983825	−	0.179132i	$-0.942671\pi$
$239$		−	316371.i		−	0.358263i	0.983825	−	0.179132i	$-0.0573288\pi$
$240$	−22265.8	+	44182.6i	−0.0249523	+	0.0495134i
$241$			485506.i			0.538458i	0.963076	+	0.269229i	$0.0867689\pi$
$241$			485506.i			0.538458i	−0.963076	+	0.269229i	$0.913231\pi$
$242$	755064.	+	421757.i	0.828792	+	0.462939i
$243$			311809.i			0.338745i
$244$	1.24381e6	−	766007.i	1.33746	−	0.823679i
$245$		−	440714.i		−	0.469074i
$246$	−157252.	−	87836.3i	−0.165675	−	0.0925414i
$247$	−569007.	+	335638.i	−0.593438	+	0.350049i
$248$	−23583.2	−	553304.i	−0.0243486	−	0.571261i
$249$			191712.i			0.195953i
$250$	−410854.	+	735545.i	−0.415755	+	0.744319i
$251$	788575.			0.790058			0.395029	−	0.918669i	$-0.370735\pi$
$251$	788575.			0.790058			0.395029	+	0.918669i	$0.370735\pi$
$252$	−140865.	+	86752.5i	−0.139734	+	0.0860559i
$253$		−	278046.i		−	0.273096i
$254$	−1.21187e6	−	676918.i	−1.17862	−	0.658342i
$255$	−10391.0			−0.0100071
$256$	−623839.	−	842815.i	−0.594939	−	0.803771i
$257$		−	743793.i		−	0.702456i	−0.936290	−	0.351228i	$-0.885764\pi$
$257$		−	743793.i		−	0.702456i	0.936290	−	0.351228i	$-0.114236\pi$
$258$	35351.2	−	63288.7i	0.0330640	−	0.0591939i
$259$			200408.i			0.185638i
$260$	−308490.	+	189985.i	−0.283014	+	0.174296i
$261$	−1.47613e6			−1.34129
$262$	909295.	+	507906.i	0.818373	+	0.457120i
$263$			1.46320e6i			1.30441i	0.758043	+	0.652205i	$0.226156\pi$
$263$			1.46320e6i			1.30441i	−0.758043	+	0.652205i	$0.773844\pi$
$264$	−29273.8	+	1247.72i	−0.0258505	+	0.00110181i
$265$		−	318420.i		−	0.278539i
$266$	−4516.32	−	191861.i	−0.00391364	−	0.166258i
$267$	−165561.			−0.142128
$268$	−900749.	+	554731.i	−0.766067	+	0.471787i
$269$	397571.			0.334992			0.167496	−	0.985873i	$-0.446432\pi$
$269$	397571.			0.334992			0.167496	+	0.985873i	$0.446432\pi$
$270$	−115202.	−	64348.5i	−0.0961725	−	0.0537192i
$271$		−	1.02186e6i		−	0.845217i	−0.906312	−	0.422608i	$-0.861115\pi$
$271$		−	1.02186e6i		−	0.845217i	0.906312	−	0.422608i	$-0.138885\pi$
$272$	99108.2	−	196663.i	0.0812246	−	0.161176i
$273$	16216.7			0.0131691
$274$	−810165.	−	452535.i	−0.651925	−	0.364146i
$275$	−216622.			−0.172731
$276$	−92526.2	−	150240.i	−0.0731126	−	0.118717i
$277$		−	482020.i		−	0.377455i	−0.982029	−	0.188728i	$-0.939564\pi$
$277$		−	482020.i		−	0.377455i	0.982029	−	0.188728i	$-0.0604363\pi$
$278$	433869.	+	242347.i	0.336703	+	0.188072i
$279$	733608.			0.564227
$280$	−4481.92	−	105154.i	−0.00341641	−	0.0801550i
$281$			1.37395e6i			1.03802i	0.854768	+	0.519010i	$0.173699\pi$
$281$			1.37395e6i			1.03802i	−0.854768	+	0.519010i	$0.826301\pi$
$282$	−204934.	−	114470.i	−0.153459	−	0.0857175i
$283$	−539885.			−0.400715			−0.200357	−	0.979723i	$-0.564210\pi$
$283$	−539885.			−0.400715			−0.200357	+	0.979723i	$0.564210\pi$
$284$	501513.	+	814335.i	0.368966	+	0.599111i
$285$	65485.1	−	38627.5i	0.0477562	−	0.0281698i
$286$	−187318.	−	104630.i	−0.135414	−	0.0756383i
$287$	383167.			0.274589
$288$	1.15063e6	−	778086.i	0.817434	−	0.552772i
$289$	−1.37361e6			−0.967425
$290$	457959.	−	819876.i	0.319766	−	0.572471i
$291$	−136626.			−0.0945800
$292$	−665412.	−	1.08047e6i	−0.456702	−	0.741574i
$293$	−522263.			−0.355402			−0.177701	−	0.984085i	$-0.556866\pi$
$293$	−522263.			−0.355402			−0.177701	+	0.984085i	$0.556866\pi$
$294$	80768.6	−	144599.i	0.0544972	−	0.0975654i
$295$	−1.14422e6			−0.765514
$296$	−71653.5	−	1.68112e6i	−0.0475344	−	1.11524i
$297$		−	78146.0i		−	0.0514062i
$298$	−34704.6	+	62131.1i	−0.0226384	+	0.0405292i
$299$		−	1.29207e6i		−	0.835808i
$300$	−117050.	+	72085.9i	−0.0750876	+	0.0462431i
$301$			154212.i			0.0981077i
$302$	33363.8	+	18636.0i	0.0210503	+	0.0117581i
$303$	258313.			0.161637
$304$	106483.	+	1.60781e6i	0.0660838	+	0.997814i
$305$	−1.23105e6			−0.757752
$306$	254685.	+	142260.i	0.155489	+	0.0868517i
$307$			1.90603e6i			1.15421i	0.816670	+	0.577105i	$0.195818\pi$
$307$			1.90603e6i			1.15421i	−0.816670	+	0.577105i	$0.804182\pi$
$308$	53072.9	−	32685.3i	0.0318784	−	0.0196325i
$309$			79590.7i			0.0474205i
$310$	−227597.	+	407463.i	−0.134512	+	0.240815i
$311$			37265.3i			0.0218476i	0.999940	+	0.0109238i	$0.00347723\pi$
$311$			37265.3i			0.0218476i	−0.999940	+	0.0109238i	$0.996523\pi$
$312$	−136034.	+	5798.10i	−0.0791153	+	0.00337209i
$313$	1.34915e6			0.778396			0.389198	−	0.921154i	$-0.372752\pi$
$313$	1.34915e6			0.778396			0.389198	+	0.921154i	$0.372752\pi$
$314$	−823525.	+	1.47434e6i	−0.471360	+	0.843868i
$315$	139420.			0.0791680
$316$	1.04534e6	+	1.69739e6i	0.588900	+	0.956231i
$317$	695473.			0.388716			0.194358	−	0.980931i	$-0.437738\pi$
$317$	695473.			0.388716			0.194358	+	0.980931i	$0.437738\pi$
$318$	58356.1	−	104474.i	0.0323608	−	0.0579349i
$319$	556153.			0.305998
$320$	75193.1	+	880479.i	0.0410490	+	0.480667i
$321$	−114731.			−0.0621467
$322$	327696.	+	183041.i	0.176129	+	0.0983806i
$323$	−291483.	+	171936.i	−0.155456	+	0.0916981i
$324$	951774.	+	1.54545e6i	0.503699	+	0.817885i
$325$	−1.00663e6			−0.528642
$326$	−1.11483e6	−	622712.i	−0.580985	−	0.324521i
$327$		−	96488.9i		−	0.0499009i
$328$	−3.21419e6	+	136997.i	−1.64963	+	0.0703115i
$329$	499352.			0.254342
$330$	21557.7	+	12041.5i	0.0108973	+	0.00608691i
$331$			2.30186e6i			1.15481i	0.816459	+	0.577404i	$0.195934\pi$
$331$			2.30186e6i			1.15481i	−0.816459	+	0.577404i	$0.804066\pi$
$332$	1.79559e6	+	2.91559e6i	0.894048	+	1.45172i
$333$	2.22894e6			1.10151
$334$	−2.87281e6	−	1.60467e6i	−1.40910	−	0.787082i
$335$	891512.			0.434025
$336$	17800.8	−	35322.5i	0.00860184	−	0.0170688i
$337$			3.72058e6i			1.78458i	0.451464	+	0.892290i	$0.350902\pi$
$337$			3.72058e6i			1.78458i	−0.451464	+	0.892290i	$0.649098\pi$
$338$	963229.	+	538032.i	0.458604	+	0.256163i
$339$	−114356.			−0.0540457
$340$	−158029.	+	97322.8i	−0.0741376	+	0.0456581i
$341$	−276398.			−0.128721
$342$	−2.13388e6	+	50230.6i	−0.986517	+	0.0232222i
$343$			714694.i			0.328008i
$344$	−55136.8	−	1.29361e6i	−0.0251215	−	0.589395i
$345$			148699.i			0.0672607i
$346$	3.09444e6	+	1.72847e6i	1.38961	+	0.776194i
$347$	−102106.			−0.0455225			−0.0227613	−	0.999741i	$-0.507246\pi$
$347$	−102106.			−0.0455225			−0.0227613	+	0.999741i	$0.507246\pi$
$348$	300513.	−	185073.i	0.133020	−	0.0819209i
$349$		−	2.09248e6i		−	0.919597i	−0.888023	−	0.459799i	$-0.847922\pi$
$349$		−	2.09248e6i		−	0.919597i	0.888023	−	0.459799i	$-0.152078\pi$
$350$	142605.	−	255303.i	0.0622249	−	0.111400i
$351$		−	363140.i		−	0.157328i
$352$	−433515.	+	293155.i	−0.186487	+	0.126108i
$353$	1.29274e6			0.552173			0.276086	−	0.961133i	$-0.410962\pi$
$353$	1.29274e6			0.552173			0.276086	+	0.961133i	$0.410962\pi$
$354$	−375418.	−	209698.i	−0.159223	−	0.0889376i
$355$		−	805984.i		−	0.339434i
$356$	−2.51788e6	+	1.55065e6i	−1.05296	+	0.648469i
$357$	8307.28			0.00344976
$358$	−1.23038e6	+	2.20273e6i	−0.507380	+	0.908353i
$359$		−	4.19203e6i		−	1.71667i	−0.513086	−	0.858337i	$-0.671498\pi$
$359$		−	4.19203e6i		−	1.71667i	0.513086	−	0.858337i	$-0.328502\pi$
$360$	−1.16952e6	+	49848.0i	−0.475612	+	0.0202718i
$361$	1.19779e6	−	2.16711e6i	0.483743	−	0.875210i
$362$	3.18629e6	+	1.77977e6i	1.27795	+	0.713826i
$363$		−	273919.i		−	0.109108i
$364$	246627.	−	151887.i	0.0975635	−	0.0600851i
$365$			1.06939e6i			0.420148i
$366$	−403910.	−	225612.i	−0.157609	−	0.0880359i
$367$			1.08261e6i			0.419571i	0.977747	+	0.209785i	$0.0672765\pi$
$367$			1.08261e6i			0.419571i	−0.977747	+	0.209785i	$0.932723\pi$
$368$	−2.81431e6	−	1.41827e6i	−1.08331	−	0.545935i
$369$		−	4.26160e6i		−	1.62932i
$370$	−691515.	+	1.23801e6i	−0.262601	+	0.470131i
$371$			254566.i			0.0960210i
$372$	−149349.	+	91977.7i	−0.0559559	+	0.0344608i
$373$	2.51466e6			0.935851			0.467925	−	0.883768i	$-0.345002\pi$
$373$	2.51466e6			0.935851			0.467925	+	0.883768i	$0.345002\pi$
$374$	−95956.4	−	53598.4i	−0.0354727	−	0.0198140i
$375$	266838.			0.0979873
$376$	−4.18881e6	+	178537.i	−1.52799	+	0.0651268i
$377$	2.58442e6			0.936503
$378$	92100.2	+	51444.5i	0.0331536	+	0.0185187i
$379$			2.81311e6i			1.00598i	0.864292	+	0.502990i	$0.167767\pi$
$379$			2.81311e6i			1.00598i	−0.864292	+	0.502990i	$0.832233\pi$
$380$	634122.	−	1.20079e6i	0.225276	−	0.426587i
$381$			439639.i			0.155161i
$382$	1.37264e6	−	2.45741e6i	0.481281	−	0.861628i
$383$	−4.38136e6			−1.52620			−0.763101	−	0.646279i	$-0.776324\pi$
$383$	−4.38136e6			−1.52620			−0.763101	+	0.646279i	$0.776324\pi$
$384$	−136692.	+	302666.i	−0.0473060	+	0.104746i
$385$	−52528.6			−0.0180611
$386$	114502.	−	204992.i	0.0391153	−	0.0700274i
$387$	1.71515e6			0.582137
$388$	−2.07783e6	+	1.27964e6i	−0.700696	+	0.431528i
$389$			1.39789e6i			0.468381i	0.972191	+	0.234191i	$0.0752440\pi$
$389$			1.39789e6i			0.468381i	−0.972191	+	0.234191i	$0.924756\pi$
$390$	100178.	+	55956.4i	0.0333511	+	0.0186289i
$391$		−	661881.i		−	0.218946i
$392$	−125974.	−	2.95557e6i	−0.0414061	−	0.971461i
$393$		−	329871.i		−	0.107736i
$394$	386707.	−	692315.i	0.125499	−	0.224679i
$395$		−	1.67998e6i		−	0.541765i
$396$	−363526.	−	590278.i	−0.116492	−	0.189155i
$397$		−	139153.i		−	0.0443115i	−0.999755	−	0.0221557i	$-0.992947\pi$
$397$		−	139153.i		−	0.0443115i	0.999755	−	0.0221557i	$-0.00705297\pi$
$398$	2.05588e6	−	3.68061e6i	0.650564	−	1.16469i
$399$	−52353.1	+	30881.4i	−0.0164631	+	0.00971101i
$400$	−1.10496e6	+	2.19259e6i	−0.345299	+	0.685185i
$401$		−	2.89612e6i		−	0.899404i	−0.893179	−	0.449702i	$-0.851530\pi$
$401$		−	2.89612e6i		−	0.899404i	0.893179	−	0.449702i	$-0.148470\pi$
$402$	292506.	+	163385.i	0.0902754	+	0.0504252i
$403$	−1.28441e6			−0.393949
$404$	3.92847e6	−	2.41937e6i	1.19749	−	0.737479i
$405$		−	1.52960e6i		−	0.463383i
$406$	−366123.	+	655464.i	−0.110233	+	0.197348i
$407$	−839787.			−0.251295
$408$	−69685.5	+	2970.17i	−0.0207249	+	0.000883346i
$409$			4.18231e6i			1.23626i	0.786078	+	0.618128i	$0.212109\pi$
$409$			4.18231e6i			1.23626i	−0.786078	+	0.618128i	$0.787891\pi$
$410$	2.36699e6	+	1.32213e6i	0.695403	+	0.388432i
$411$			293909.i			0.0858239i
$412$	745450.	+	1.21043e6i	0.216359	+	0.351315i
$413$	914762.			0.263896
$414$	2.03579e6	−	3.64464e6i	0.583757	−	1.04509i
$415$		−	2.88569e6i		−	0.822489i
$416$	−2.01452e6	+	1.36228e6i	−0.570741	+	0.385951i
$417$		−	157397.i		−	0.0443259i
$418$	803971.	−	18925.1i	0.225061	−	0.00529783i
$419$	5.33921e6			1.48574			0.742869	−	0.669437i	$-0.233465\pi$
$419$	5.33921e6			1.48574			0.742869	+	0.669437i	$0.233465\pi$
$420$	−28383.5	+	17480.1i	−0.00785131	+	0.00483528i
$421$	5.84059e6			1.60602			0.803011	−	0.595964i	$-0.203230\pi$
$421$	5.84059e6			1.60602			0.803011	+	0.595964i	$0.203230\pi$
$422$	−2.09488e6	+	3.75042e6i	−0.572634	+	1.02518i
$423$		−	5.55381e6i		−	1.50918i
$424$	−91017.1	−	2.13542e6i	−0.0245872	−	0.576859i
$425$	−515662.			−0.138482
$426$	147711.	−	264444.i	0.0394356	−	0.0706008i
$427$	984186.			0.261221
$428$	−1.74485e6	+	1.07457e6i	−0.460414	+	0.283548i
$429$			67954.4i			0.0178268i
$430$	−532115.	+	952635.i	−0.138782	+	0.248459i
$431$	−3.18075e6			−0.824777			−0.412388	−	0.911008i	$-0.635305\pi$
$431$	−3.18075e6			−0.824777			−0.412388	+	0.911008i	$0.635305\pi$
$432$	−790974.	−	398612.i	−0.203917	−	0.102764i
$433$		−	2.87889e6i		−	0.737913i	−0.929447	−	0.368956i	$-0.879715\pi$
$433$		−	2.87889e6i		−	0.737913i	0.929447	−	0.368956i	$-0.120285\pi$
$434$	181956.	−	325753.i	0.0463706	−	0.0830164i
$435$	−297432.			−0.0753640
$436$	−903720.	−	1.46742e6i	−0.227676	−	0.369691i
$437$	2.46047e6	+	4.17122e6i	0.616330	+	1.04486i
$438$	−195984.	+	350867.i	−0.0488130	+	0.0873890i
$439$	4.54057e6			1.12447			0.562236	−	0.826977i	$-0.309941\pi$
$439$	4.54057e6			1.12447			0.562236	+	0.826977i	$0.309941\pi$
$440$	440635.	−	18781.0i	0.108505	−	0.00462473i
$441$	3.91869e6			0.959499
$442$	−445904.	−	249069.i	−0.108564	−	0.0606407i
$443$	−3.58650e6			−0.868284			−0.434142	−	0.900845i	$-0.642948\pi$
$443$	−3.58650e6			−0.868284			−0.434142	+	0.900845i	$0.642948\pi$
$444$	−453773.	+	279459.i	−0.109240	+	0.0672760i
$445$	2.49206e6			0.596566
$446$	−1.75309e6	−	979223.i	−0.417317	−	0.233101i
$447$	22539.7			0.00533555
$448$	−60114.4	−	703914.i	−0.0141509	−	0.165701i
$449$		−	2.78600e6i		−	0.652178i	−0.945339	−	0.326089i	$-0.894269\pi$
$449$		−	2.78600e6i		−	0.652178i	0.945339	−	0.326089i	$-0.105731\pi$
$450$	−2.83949e6	−	1.58605e6i	−0.661011	−	0.369221i
$451$			1.60562e6i			0.371707i
$452$	−1.73915e6	+	1.07107e6i	−0.400398	+	0.246587i
$453$		−	12103.6i		−	0.00277120i
$454$	−1.43890e6	+	2.57603e6i	−0.327635	+	0.586559i
$455$	−244098.			−0.0552759
$456$	428122.	−	277766.i	0.0964174	−	0.0625557i
$457$	6.01508e6			1.34726			0.673629	−	0.739069i	$-0.264734\pi$
$457$	6.01508e6			1.34726			0.673629	+	0.739069i	$0.264734\pi$
$458$	2.54339e6	−	4.55338e6i	0.566563	−	1.01431i
$459$		−	186024.i		−	0.0412134i
$460$	1.39273e6	+	2.26145e6i	0.306882	+	0.498301i
$461$		−	5.49794e6i		−	1.20489i	−0.798160	−	0.602445i	$-0.794193\pi$
$461$		−	5.49794e6i		−	1.20489i	0.798160	−	0.602445i	$-0.205807\pi$
$462$	−17234.7	−	9626.80i	−0.00375663	−	0.00209835i
$463$		−	6.80325e6i		−	1.47490i	−0.675400	−	0.737452i	$-0.736029\pi$
$463$		−	6.80325e6i		−	1.47490i	0.675400	−	0.737452i	$-0.263971\pi$
$464$	2.83686e6	−	5.62925e6i	0.611707	−	1.21382i
$465$	147818.			0.0317026
$466$	7.03214e6	+	3.92795e6i	1.50011	+	0.837917i
$467$	−3.92402e6			−0.832606			−0.416303	−	0.909226i	$-0.636674\pi$
$467$	−3.92402e6			−0.832606			−0.416303	+	0.909226i	$0.636674\pi$
$468$	−1.68929e6	−	2.74299e6i	−0.356524	−	0.578909i
$469$	−712734.			−0.149622
$470$	3.08471e6	+	1.72303e6i	0.644125	+	0.359789i
$471$	534857.			0.111093
$472$	−7.67347e6	+	327062.i	−1.58539	+	0.0675734i
$473$	−646209.			−0.132807
$474$	307886.	−	551202.i	0.0629425	−	0.112685i
$475$	3.24974e6	−	1.91691e6i	0.660868	−	0.389824i
$476$	126339.	−	77806.4i	0.0255575	−	0.0157397i
$477$	2.83129e6			0.569756
$478$	−872737.	+	1.56245e6i	−0.174708	+	0.312777i
$479$			4.25311e6i			0.846969i	0.905903	+	0.423485i	$0.139193\pi$
$479$			4.25311e6i			0.846969i	−0.905903	+	0.423485i	$0.860807\pi$
$480$	231844.	−	156780.i	0.0459297	−	0.0310590i
$481$	−3.90245e6			−0.769086
$482$	1.33931e6	−	2.39774e6i	0.262581	−	0.470094i
$483$		−	118880.i		−	0.0231868i
$484$	−2.56554e6	−	4.16581e6i	−0.497812	−	0.808326i
$485$	2.05652e6			0.396988
$486$	860152.	−	1.53992e6i	0.165190	−	0.295737i
$487$	−1.02183e7			−1.95235			−0.976174	−	0.216988i	$-0.930377\pi$
$487$	−1.02183e7			−1.95235			−0.976174	+	0.216988i	$0.930377\pi$
$488$	−8.25583e6	+	351884.i	−1.56932	+	0.0668883i
$489$			404434.i			0.0764849i
$490$	−1.21575e6	+	2.17653e6i	−0.228746	+	0.409519i
$491$	3.32334e6			0.622116			0.311058	−	0.950391i	$-0.399317\pi$
$491$	3.32334e6			0.622116			0.311058	+	0.950391i	$0.399317\pi$
$492$	534307.	+	867584.i	0.0995126	+	0.161584i
$493$	1.32391e6			0.245324
$494$	3.73601e6	−	87944.1i	0.688796	−	0.0162140i
$495$			584225.i			0.107168i
$496$	−1.40987e6	+	2.79763e6i	−0.257320	+	0.510606i
$497$			644357.i			0.117013i
$498$	528854.	−	946799.i	0.0955571	−	0.171074i
$499$	−5.52536e6			−0.993366			−0.496683	−	0.867932i	$-0.665449\pi$
$499$	−5.52536e6			−0.993366			−0.496683	+	0.867932i	$0.665449\pi$
$500$	4.05812e6	−	2.49922e6i	0.725939	−	0.447074i
$501$			1.04219e6i			0.185504i
$502$	−3.89449e6	−	2.17535e6i	−0.689750	−	0.385274i
$503$			2.18871e6i			0.385716i	0.981227	+	0.192858i	$0.0617756\pi$
$503$			2.18871e6i			0.385716i	−0.981227	+	0.192858i	$0.938224\pi$
$504$	934996.	−	39851.9i	0.163958	−	0.00698831i
$505$	−3.88819e6			−0.678451
$506$	−767013.	+	1.37317e6i	−0.133176	+	0.238423i
$507$		−	349437.i		−	0.0603738i
$508$	4.11768e6	+	6.68611e6i	0.707935	+	1.14951i
$509$	−6.27300e6			−1.07320			−0.536600	−	0.843836i	$-0.680292\pi$
$509$	−6.27300e6			−1.07320			−0.536600	+	0.843836i	$0.680292\pi$
$510$	51317.6	+	28664.5i	0.00873657	+	0.00487999i
$511$		−	854939.i		−	0.144838i
$512$	755944.	+	5.88327e6i	0.127443	+	0.991846i
$513$	691524.	+	1.17234e6i	0.116015	+	0.196680i
$514$	−2.05182e6	+	3.67333e6i	−0.342555	+	0.613271i
$515$		−	1.19802e6i		−	0.199042i
$516$	−349174.	+	215041.i	−0.0577322	+	0.0355547i
$517$			2.09248e6i			0.344298i
$518$	552843.	−	989745.i	0.0905268	−	0.162069i
$519$		−	1.12259e6i		−	0.182938i
$520$	2.04761e6	−	87274.3i	0.332077	−	0.0141540i
$521$		−	1.45769e6i		−	0.235273i	−0.993057	−	0.117636i	$-0.962468\pi$
$521$		−	1.45769e6i		−	0.235273i	0.993057	−	0.117636i	$-0.0375317\pi$
$522$	7.29008e6	+	4.07203e6i	1.17100	+	0.654085i
$523$			1.24010e7i			1.98245i	0.132178	+	0.991226i	$0.457803\pi$
$523$			1.24010e7i			1.98245i	−0.132178	+	0.991226i	$0.542197\pi$
$524$	−3.08958e6	−	5.01673e6i	−0.491555	−	0.798165i
$525$	−92617.9			−0.0146655
$526$	4.03636e6	−	7.22622e6i	0.636100	−	1.13880i
$527$	−657957.			−0.103198
$528$	148015.	+	74592.2i	0.0231058	+	0.0116442i
$529$	−3.03541e6			−0.471605
$530$	−878389.	+	1.57256e6i	−0.135830	+	0.243175i
$531$		−	1.01740e7i		−	1.56587i
$532$	−506960.	+	959991.i	−0.0776595	+	0.147058i
$533$			7.46123e6i			1.13761i
$534$	817647.	+	456714.i	0.124083	+	0.0693092i
$535$	1.72695e6			0.260853
$536$	5.97875e6	−	254829.i	0.898874	−	0.0383122i
$537$	799100.			0.119582
$538$	−1.96346e6	−	1.09673e6i	−0.292460	−	0.163360i
$539$	−1.47642e6			−0.218897
$540$	391431.	+	635589.i	0.0577658	+	0.0937976i
$541$			6.25172e6i			0.918346i	0.888347	+	0.459173i	$0.151854\pi$
$541$			6.25172e6i			0.918346i	−0.888347	+	0.459173i	$0.848146\pi$
$542$	−2.81889e6	+	5.04660e6i	−0.412173	+	0.737906i
$543$		−	1.15591e6i		−	0.168238i
$544$	−1.03197e6	+	697848.i	−0.149510	+	0.101103i
$545$			1.45237e6i			0.209453i
$546$	−80088.7	−	44735.3i	−0.0114971	−	0.00642197i
$547$			8.68527e6i			1.24112i	0.784158	+	0.620561i	$0.213095\pi$
$547$			8.68527e6i			1.24112i	−0.784158	+	0.620561i	$0.786905\pi$
$548$	2.75276e6	+	4.46982e6i	0.391577	+	0.635826i
$549$		−	1.09461e7i		−	1.54999i
$550$	1.06982e6	+	597569.i	0.150801	+	0.0842329i
$551$	−8.34337e6	+	4.92147e6i	−1.17075	+	0.690584i
$552$	42504.2	+	997224.i	0.00593723	+	0.139298i
$553$			1.34309e6i			0.186763i
$554$	−1.32969e6	+	2.38052e6i	−0.184067	+	0.329532i
$555$	449120.			0.0618913
$556$	−1.47419e6	−	2.39373e6i	−0.202240	−	0.328389i
$557$			1.26351e7i			1.72560i	0.505544	+	0.862801i	$0.331292\pi$
$557$			1.26351e7i			1.72560i	−0.505544	+	0.862801i	$0.668708\pi$
$558$	−3.62303e6	−	2.02372e6i	−0.492591	−	0.275147i
$559$	−3.00290e6			−0.406454
$560$	−267941.	+	531682.i	−0.0361052	+	0.0716443i
$561$			34810.7i			0.00466988i
$562$	3.79016e6	−	6.78546e6i	0.506194	−	0.906231i
$563$			2.22227e6i			0.295478i	0.989026	+	0.147739i	$0.0471996\pi$
$563$			2.22227e6i			0.295478i	−0.989026	+	0.147739i	$0.952800\pi$
$564$	696321.	+	1.13066e6i	0.0921746	+	0.149669i
$565$	1.72132e6			0.226850
$566$	2.66630e6	+	1.48932e6i	0.349839	+	0.195410i
$567$			1.22286e6i			0.159743i
$568$	−230382.	−	5.40518e6i	−0.0299625	−	0.702974i
$569$		−	8.80479e6i		−	1.14009i	−0.821614	−	0.570044i	$-0.806926\pi$
$569$		−	8.80479e6i		−	1.14009i	0.821614	−	0.570044i	$-0.193074\pi$
$570$	−429965.	+	10121.2i	−0.0554301	+	0.00130480i
$571$	−1.03222e7			−1.32490			−0.662450	−	0.749106i	$-0.730483\pi$
$571$	−1.03222e7			−1.32490			−0.662450	+	0.749106i	$0.730483\pi$
$572$	636464.	+	1.03346e6i	0.0813362	+	0.132070i
$573$	−891491.			−0.113431
$574$	−1.89233e6	−	1.05700e6i	−0.239727	−	0.133904i
$575$			7.37931e6i			0.930778i
$576$	−7.82894e6	+	668593.i	−0.983212	+	0.0839664i
$577$	−2.38619e6			−0.298378			−0.149189	−	0.988809i	$-0.547666\pi$
$577$	−2.38619e6			−0.298378			−0.149189	+	0.988809i	$0.547666\pi$
$578$	6.78375e6	+	3.78921e6i	0.844598	+	0.471768i
$579$	−74366.1			−0.00921889
$580$	−4.52339e6	+	2.78576e6i	−0.558334	+	0.343853i
$581$			2.30702e6i			0.283537i
$582$	674745.	+	376893.i	0.0825719	+	0.0461223i
$583$	−1.06673e6			−0.129982
$584$	305673.	+	7.17164e6i	0.0370873	+	0.870134i
$585$			2.71486e6i			0.327988i
$586$	2.57927e6	+	1.44071e6i	0.310279	+	0.173313i
$587$	−4.97228e6			−0.595608			−0.297804	−	0.954627i	$-0.596254\pi$
$587$	−4.97228e6			−0.595608			−0.297804	+	0.954627i	$0.596254\pi$
$588$	−797775.	+	491314.i	−0.0951562	+	0.0586025i
$589$	4.14649e6	−	2.44588e6i	0.492485	−	0.290500i
$590$	5.65088e6	+	3.15642e6i	0.668322	+	0.373305i
$591$	−251156.			−0.0295784
$592$	−4.28364e6	+	8.50012e6i	−0.502353	+	0.996829i
$593$	550883.			0.0643313			0.0321657	−	0.999483i	$-0.489760\pi$
$593$	550883.			0.0643313			0.0321657	+	0.999483i	$0.489760\pi$
$594$	−215572.	+	385935.i	−0.0250684	+	0.0448795i
$595$	−125043.			−0.0144799
$596$	342788.	−	211108.i	0.0395284	−	0.0243438i
$597$	−1.33524e6			−0.153328
$598$	−3.56427e6	+	6.38105e6i	−0.407585	+	0.729692i
$599$	4.35875e6			0.496357			0.248179	−	0.968714i	$-0.420168\pi$
$599$	4.35875e6			0.496357			0.248179	+	0.968714i	$0.420168\pi$
$600$	776923.	−	33114.4i	0.0881049	−	0.00375525i
$601$		−	387678.i		−	0.0437809i	−0.999760	−	0.0218905i	$-0.993031\pi$
$601$		−	387678.i		−	0.0437809i	0.999760	−	0.0218905i	$-0.00696851\pi$
$602$	425408.	−	761600.i	0.0478425	−	0.0856517i
$603$			7.92704e6i			0.887805i
$604$	−113363.	−	184074.i	−0.0126438	−	0.0205305i
$605$			4.12309e6i			0.457968i
$606$	−1.27572e6	−	712579.i	−0.141115	−	0.0788227i
$607$	−3.69831e6			−0.407410			−0.203705	−	0.979032i	$-0.565298\pi$
$607$	−3.69831e6			−0.407410			−0.203705	+	0.979032i	$0.565298\pi$
$608$	3.90939e6	−	8.23412e6i	0.428894	−	0.903355i
$609$	237787.			0.0259803
$610$	6.07974e6	+	3.39596e6i	0.661546	+	0.369521i
$611$			9.72364e6i			1.05372i
$612$	−865364.	−	1.40514e6i	−0.0933943	−	0.151650i
$613$			2.46872e6i			0.265351i	0.991160	+	0.132675i	$0.0423568\pi$
$613$			2.46872e6i			0.265351i	−0.991160	+	0.132675i	$0.957643\pi$
$614$	5.25796e6	−	9.41323e6i	0.562854	−	1.00767i
$615$		−	858687.i		−	0.0915476i
$616$	−352273.	+	15014.8i	−0.0374049	+	0.00159429i
$617$	−6.46330e6			−0.683504			−0.341752	−	0.939790i	$-0.611020\pi$
$617$	−6.46330e6			−0.683504			−0.341752	+	0.939790i	$0.611020\pi$
$618$	219558.	−	393070.i	0.0231248	−	0.0413999i
$619$	1.08579e6			0.113899			0.0569494	−	0.998377i	$-0.481863\pi$
$619$	1.08579e6			0.113899			0.0569494	+	0.998377i	$0.481863\pi$
$620$	2.24804e6	−	1.38447e6i	0.234869	−	0.144645i
$621$	−2.66207e6			−0.277007
$622$	102800.	−	184040.i	0.0106541	−	0.0190738i
$623$	−1.99232e6			−0.205655
$624$	687817.	+	346626.i	0.0707150	+	0.0356369i
$625$	3.47641e6			0.355984
$626$	−6.66299e6	−	3.72175e6i	−0.679569	−	0.379587i
$627$	−129405.	−	219380.i	−0.0131456	−	0.0222858i
$628$	8.13420e6	−	5.00949e6i	0.823030	−	0.506868i
$629$	−1.99909e6			−0.201468
$630$	−688547.	−	384603.i	−0.0691166	−	0.0386065i
$631$		−	4.86063e6i		−	0.485981i	−0.970029	−	0.242991i	$-0.921872\pi$
$631$		−	4.86063e6i		−	0.485981i	0.970029	−	0.242991i	$-0.0781284\pi$
$632$	−480205.	−	1.12665e7i	−0.0478226	−	1.12200i
$633$	1.36056e6			0.134961
$634$	−3.43470e6	−	1.91852e6i	−0.339363	−	0.189559i
$635$		−	6.61754e6i		−	0.651272i
$636$	−576400.	+	354979.i	−0.0565043	+	0.0347985i
$637$	−6.86087e6			−0.669932
$638$	−2.74664e6	−	1.53420e6i	−0.267147	−	0.149221i
$639$	7.16655e6			0.694318
$640$	2.05752e6	−	4.55580e6i	0.198562	−	0.439658i
$641$			7.52432e6i			0.723306i	0.932313	+	0.361653i	$0.117788\pi$
$641$			7.52432e6i			0.723306i	−0.932313	+	0.361653i	$0.882212\pi$
$642$	566615.	+	316495.i	0.0542564	+	0.0303060i
$643$	3.17853e6			0.303178			0.151589	−	0.988444i	$-0.451561\pi$
$643$	3.17853e6			0.303178			0.151589	+	0.988444i	$0.451561\pi$
$644$	−1.11344e6	−	1.80795e6i	−0.105792	−	0.171780i
$645$	345594.			0.0327089
$646$	1.91383e6	−	45050.8i	0.180435	−	0.00424738i
$647$			1.27831e7i			1.20054i	0.799798	+	0.600269i	$0.204940\pi$
$647$			1.27831e7i			1.20054i	−0.799798	+	0.600269i	$0.795060\pi$
$648$	−437220.	−	1.02580e7i	−0.0409037	−	0.959675i
$649$			3.83321e6i			0.357232i
$650$	4.97139e6	+	2.77687e6i	0.461524	+	0.257794i
$651$	−118175.			−0.0109289
$652$	3.78795e6	+	6.15071e6i	0.348968	+	0.566639i
$653$		−	1.25243e7i		−	1.14940i	−0.818365	−	0.574699i	$-0.805119\pi$
$653$		−	1.25243e7i		−	1.14940i	0.818365	−	0.574699i	$-0.194881\pi$
$654$	−266173.	+	476525.i	−0.0243343	+	0.0435653i
$655$			4.96529e6i			0.452211i
$656$	1.62517e7	+	8.19004e6i	1.47448	+	0.743064i
$657$	−9.50865e6			−0.859420
$658$	−2.46612e6	−	1.37751e6i	−0.222050	−	0.124031i
$659$		−	1.95227e7i		−	1.75116i	−0.483075	−	0.875579i	$-0.660480\pi$
$659$		−	1.95227e7i		−	1.75116i	0.483075	−	0.875579i	$-0.339520\pi$
$660$	−73248.4	−	118938.i	−0.00654544	−	0.0106282i
$661$	1.17749e6			0.104822			0.0524110	−	0.998626i	$-0.483309\pi$
$661$	1.17749e6			0.104822			0.0524110	+	0.998626i	$0.483309\pi$
$662$	6.34988e6	−	1.13681e7i	0.563146	−	1.00819i
$663$			161764.i			0.0142921i
$664$	−824846.	−	1.93524e7i	−0.0726027	−	1.70339i
$665$	788031.	−	464833.i	0.0691017	−	0.0407608i
$666$	−1.10080e7	−	6.14873e6i	−0.961660	−	0.537155i
$667$		−	1.89456e7i		−	1.64890i
$668$	9.76119e6	+	1.58498e7i	0.846373	+	1.37430i
$669$			635978.i			0.0549385i
$670$	−4.40286e6	−	2.45931e6i	−0.378920	−	0.211654i
$671$			4.12412e6i			0.353610i
$672$	−185352.	+	125340.i	−0.0158334	+	0.0107070i
$673$		−	1.92406e7i		−	1.63750i	−0.574151	−	0.818749i	$-0.694668\pi$
$673$		−	1.92406e7i		−	1.63750i	0.574151	−	0.818749i	$-0.305332\pi$
$674$	1.02635e7	−	1.83746e7i	0.870256	−	1.55800i
$675$			2.07399e6i			0.175205i
$676$	−3.27284e6	−	5.31430e6i	−0.275460	−	0.447279i
$677$	−1.22877e7			−1.03039			−0.515194	−	0.857074i	$-0.672280\pi$
$677$	−1.22877e7			−1.03039			−0.515194	+	0.857074i	$0.672280\pi$
$678$	564765.	+	315462.i	0.0471839	+	0.0263556i
$679$	−1.64412e6			−0.136854
$680$	1.04892e6	−	44707.6i	0.0869902	−	0.00370774i
$681$	934523.			0.0772187
$682$	1.36503e6	+	762466.i	0.112378	+	0.0627711i
$683$		−	2.78444e6i		−	0.228395i	−0.993458	−	0.114197i	$-0.963570\pi$
$683$		−	2.78444e6i		−	0.228395i	0.993458	−	0.114197i	$-0.0364296\pi$
$684$	1.06770e7	+	5.63842e6i	0.872591	+	0.460805i
$685$		−	4.42398e6i		−	0.360236i
$686$	1.97154e6	−	3.52962e6i	0.159954	−	0.286364i
$687$	−1.65186e6			−0.133531
$688$	−3.29622e6	+	6.54077e6i	−0.265488	+	0.526814i
$689$	−4.95704e6			−0.397809
$690$	410200.	−	734373.i	0.0327999	−	0.0587211i
$691$	−5.06792e6			−0.403771			−0.201885	−	0.979409i	$-0.564707\pi$
$691$	−5.06792e6			−0.403771			−0.201885	+	0.979409i	$0.564707\pi$
$692$	−1.05142e7	−	1.70726e7i	−0.834665	−	1.35529i
$693$		−	467068.i		−	0.0369443i
$694$	504264.	+	281667.i	0.0397429	+	0.0221992i
$695$			2.36918e6i			0.186053i
$696$	−1.99467e6	+	85017.8i	−0.156080	+	0.00665253i
$697$			3.82213e6i			0.298005i
$698$	−5.77228e6	+	1.03340e7i	−0.448445	+	0.802843i
$699$		−	2.55109e6i		−	0.197485i
$700$	−1.40855e6	+	867464.i	−0.108649	+	0.0669123i
$701$			1.84189e7i			1.41569i	0.706366	+	0.707847i	$0.250333\pi$
$701$			1.84189e7i			1.41569i	−0.706366	+	0.707847i	$0.749667\pi$
$702$	−1.00175e6	+	1.79342e6i	−0.0767216	+	0.137353i
$703$	1.25984e7	−	7.43139e6i	0.961453	−	0.567129i
$704$	2.94967e6	−	251902.i	0.224306	−	0.0191558i
$705$		−	1.11906e6i		−	0.0847970i
$706$	−6.38439e6	−	3.56614e6i	−0.482068	−	0.269269i
$707$	3.10848e6			0.233883
$708$	1.27559e6	+	2.07125e6i	0.0956373	+	0.155292i
$709$		−	1.41054e7i		−	1.05383i	−0.849918	−	0.526915i	$-0.823349\pi$
$709$		−	1.41054e7i		−	1.05383i	0.849918	−	0.526915i	$-0.176651\pi$
$710$	−2.22337e6	+	3.98047e6i	−0.165526	+	0.296339i
$711$	1.49378e7			1.10819
$712$	1.67125e7	−	712329.i	1.23550	−	0.0526600i
$713$			9.41560e6i			0.693624i
$714$	−41026.7	−	22916.3i	−0.00301177	−	0.00168229i
$715$		−	1.02286e6i		−	0.0748261i
$716$	1.21529e7	−	7.48441e6i	0.885923	−	0.545600i
$717$	566819.			0.0411762
$718$	−1.15641e7	+	2.07029e7i	−0.837142	+	1.49872i
$719$		−	3.59772e6i		−	0.259540i	−0.991544	−	0.129770i	$-0.958576\pi$
$719$		−	3.59772e6i		−	0.259540i	0.991544	−	0.129770i	$-0.0414240\pi$
$720$	5.91338e6	+	2.98005e6i	0.425113	+	0.214236i
$721$			957774.i			0.0686159i
$722$	−1.18936e7	+	7.39835e6i	−0.849125	+	0.528192i
$723$	−869844.			−0.0618865
$724$	−1.08263e7	−	1.75793e7i	−0.767598	−	1.24639i
$725$	−1.47603e7			−1.04291
$726$	−755629.	+	1.35279e6i	−0.0532068	+	0.0952552i
$727$		−	4.42128e6i		−	0.310250i	−0.987895	−	0.155125i	$-0.950422\pi$
$727$		−	4.42128e6i		−	0.310250i	0.987895	−	0.155125i	$-0.0495781\pi$
$728$	−1.63700e6	+	69772.9i	−0.114477	+	0.00487931i
$729$	1.32241e7			0.921613
$730$	2.94999e6	−	5.28132e6i	0.204887	−	0.366805i
$731$	−1.53828e6			−0.106474
$732$	1.37240e6	+	2.22844e6i	0.0946677	+	0.153717i
$733$		−	5.89336e6i		−	0.405138i	−0.979268	−	0.202569i	$-0.935071\pi$
$733$		−	5.89336e6i		−	0.405138i	0.979268	−	0.202569i	$-0.0649291\pi$
$734$	2.98646e6	−	5.34661e6i	0.204605	−	0.366301i
$735$	789594.			0.0539120
$736$	9.98646e6	+	1.47679e7i	0.679543	+	1.00490i
$737$		−	2.98663e6i		−	0.202541i
$738$	−1.17560e7	+	2.10465e7i	−0.794543	+	1.42246i
$739$	2.27527e7			1.53258			0.766288	−	0.642497i	$-0.222102\pi$
$739$	2.27527e7			1.53258			0.766288	+	0.642497i	$0.222102\pi$
$740$	6.83029e6	−	4.20647e6i	0.458522	−	0.282383i
$741$	−601337.	−	1.01945e6i	−0.0402321	−	0.0682054i
$742$	702243.	−	1.25721e6i	0.0468250	−	0.0838299i
$743$	341178.			0.0226730			0.0113365	−	0.999936i	$-0.496391\pi$
$743$	341178.			0.0226730			0.0113365	+	0.999936i	$0.496391\pi$
$744$	991312.	−	42252.2i	0.0656565	−	0.00279845i
$745$	−339272.			−0.0223953
$746$	−1.24190e7	−	6.93689e6i	−0.817033	−	0.456371i
$747$	2.56587e7			1.68241
$748$	326039.	+	529407.i	0.0213066	+	0.0345968i
$749$	−1.38064e6			−0.0899242
$750$	−1.31782e6	−	736096.i	−0.0855466	−	0.0477838i
$751$	6.71971e6			0.434761			0.217380	−	0.976087i	$-0.430249\pi$
$751$	6.71971e6			0.434761			0.217380	+	0.976087i	$0.430249\pi$
$752$	2.11795e7	+	1.06734e7i	1.36575	+	0.688272i
$753$			1.41283e6i			0.0908035i
$754$	−1.27635e7	−	7.12933e6i	−0.817602	−	0.456689i
$755$			182186.i			0.0116318i
$756$	−312936.	−	508132.i	−0.0199137	−	0.0323350i
$757$		−	8.93104e6i		−	0.566451i	−0.959053	−	0.283226i	$-0.908595\pi$
$757$		−	8.93104e6i		−	0.566451i	0.959053	−	0.283226i	$-0.0914045\pi$
$758$	7.76021e6	−	1.38930e7i	0.490570	−	0.878258i
$759$	498154.			0.0313877
$760$	−6.44418e6	+	4.18099e6i	−0.404701	+	0.262570i
$761$	−1.57336e7			−0.984839			−0.492419	−	0.870358i	$-0.663887\pi$
$761$	−1.57336e7			−0.984839			−0.492419	+	0.870358i	$0.663887\pi$
$762$	1.21278e6	−	2.17122e6i	0.0756650	−	0.135462i
$763$		−	1.16112e6i		−	0.0722050i
$764$	−1.35580e7	+	8.34975e6i	−0.840352	+	0.517535i
$765$			1.39073e6i			0.0859190i
$766$	2.16380e7	+	1.20864e7i	1.33243	+	0.744258i
$767$			1.78127e7i			1.09331i
$768$	1.51001e6	−	1.11768e6i	0.0923795	−	0.0683780i
$769$	5.08185e6			0.309889			0.154944	−	0.987923i	$-0.450480\pi$
$769$	5.08185e6			0.309889			0.154944	+	0.987923i	$0.450480\pi$
$770$	259420.	+	144905.i	0.0157680	+	0.00880756i
$771$	1.33260e6			0.0807352
$772$	−1.13097e6	+	696516.i	−0.0682982	+	0.0420618i
$773$	1.30205e7			0.783755			0.391877	−	0.920017i	$-0.371826\pi$
$773$	1.30205e7			0.783755			0.391877	+	0.920017i	$0.371826\pi$
$774$	−8.47053e6	−	4.73139e6i	−0.508228	−	0.283881i
$775$	7.33556e6			0.438712
$776$	1.37916e7	−	587834.i	0.822170	−	0.0350429i
$777$	−359056.			−0.0213358
$778$	3.85620e6	−	6.90369e6i	0.228408	−	0.408914i
$779$	−1.42083e7	−	2.40874e7i	−0.838879	−	1.42215i
$780$	−340382.	−	552697.i	−0.0200323	−	0.0325275i
$781$	−2.70010e6			−0.158399
$782$	−1.82585e6	+	3.26879e6i	−0.106770	+	0.191148i
$783$		−	5.32474e6i		−	0.310380i
$784$	−7.53104e6	+	1.49440e7i	−0.437587	+	0.868314i
$785$	−8.05078e6			−0.466298
$786$	−909976.	+	1.62911e6i	−0.0525380	+	0.0940579i
$787$		−	5.56173e6i		−	0.320091i	−0.987110	−	0.160045i	$-0.948836\pi$
$787$		−	5.56173e6i		−	0.320091i	0.987110	−	0.160045i	$-0.0511641\pi$
$788$	−3.81962e6	+	2.35233e6i	−0.219131	+	0.134953i
$789$	−2.62150e6			−0.149919
$790$	−4.63436e6	+	8.29682e6i	−0.264194	+	0.472981i
$791$	−1.37614e6			−0.0782024
$792$	166995.	+	3.91799e6i	0.00945996	+	0.221948i
$793$			1.91646e7i			1.08222i
$794$	−383865.	+	687227.i	−0.0216086	+	0.0386856i
$795$	570489.			0.0320132
$796$	−2.03065e7	+	1.25059e7i	−1.13593	+	0.699571i
$797$	−2.16448e7			−1.20700			−0.603502	−	0.797361i	$-0.706228\pi$
$797$	−2.16448e7			−1.20700			−0.603502	+	0.797361i	$0.706228\pi$
$798$	343742.	−	8091.55i	0.0191085	−	0.000449805i
$799$			4.98109e6i			0.276031i
$800$	1.15054e7	−	7.78031e6i	0.635592	−	0.429805i
$801$			2.21586e7i			1.22028i
$802$	−7.98918e6	+	1.43029e7i	−0.438597	+	0.785213i
$803$	3.58252e6			0.196065
$804$	−993870.	−	1.61380e6i	−0.0542237	−	0.0880462i
$805$			1.78941e6i			0.0973241i
$806$	6.34322e6	+	3.54314e6i	0.343932	+	0.192110i
$807$			712298.i			0.0385015i
$808$	−2.60754e7	+	1.11140e6i	−1.40508	+	0.0598882i
$809$	2.25215e7			1.20983			0.604917	−	0.796289i	$-0.293206\pi$
$809$	2.25215e7			1.20983			0.604917	+	0.796289i	$0.293206\pi$
$810$	−4.21953e6	+	7.55415e6i	−0.225970	+	0.404551i
$811$			8.93759e6i			0.477165i	0.971122	+	0.238582i	$0.0766827\pi$
$811$			8.93759e6i			0.477165i	−0.971122	+	0.238582i	$0.923317\pi$
$812$	3.61630e6	−	2.22712e6i	0.192475	−	0.118537i
$813$	1.83079e6			0.0971430
$814$	4.14741e6	+	2.31662e6i	0.219390	+	0.122545i
$815$		−	6.08763e6i		−	0.321036i
$816$	352345.	+	177565.i	0.0185243	+	0.00933536i
$817$	9.69438e6	−	5.71839e6i	0.508118	−	0.299722i
$818$	1.15373e7	−	2.06550e7i	0.602864	−	1.07930i
$819$		−	2.17044e6i		−	0.113068i
$820$	−8.04250e6	−	1.30591e7i	−0.417692	−	0.678231i
$821$		−	3.29211e7i		−	1.70457i	−0.523074	−	0.852287i	$-0.675215\pi$
$821$		−	3.29211e7i		−	1.70457i	0.523074	−	0.852287i	$-0.324785\pi$
$822$	810772.	−	1.45151e6i	0.0418523	−	0.0749274i
$823$			6.73875e6i			0.346801i	0.984851	+	0.173400i	$0.0554754\pi$
$823$			6.73875e6i			0.346801i	−0.984851	+	0.173400i	$0.944525\pi$
$824$	−342441.	−	8.03427e6i	−0.0175698	−	0.412219i
$825$		−	388105.i		−	0.0198524i
$826$	−4.51769e6	−	2.52345e6i	−0.230391	−	0.128690i
$827$			2.63122e7i			1.33781i	0.743349	+	0.668904i	$0.233236\pi$
$827$			2.63122e7i			1.33781i	−0.743349	+	0.668904i	$0.766764\pi$
$828$	−2.01081e7	+	1.23837e7i	−1.01928	+	0.627731i
$829$	5.20905e6			0.263252			0.131626	−	0.991299i	$-0.457980\pi$
$829$	5.20905e6			0.263252			0.131626	+	0.991299i	$0.457980\pi$
$830$	−7.96043e6	+	1.42514e7i	−0.401090	+	0.718064i
$831$	863598.			0.0433819
$832$	1.37070e7	−	1.17058e6i	0.686488	−	0.0586262i
$833$	−3.51459e6			−0.175494
$834$	−434194.	+	777330.i	−0.0216157	+	0.0386982i
$835$		−	1.56873e7i		−	0.778629i
$836$	−4.02273e6	−	2.12436e6i	−0.199070	−	0.105126i
$837$			2.64629e6i			0.130564i
$838$	−2.63685e7	−	1.47287e7i	−1.29710	−	0.724525i
$839$	3.75422e7			1.84126			0.920630	−	0.390437i	$-0.127676\pi$
$839$	3.75422e7			1.84126			0.920630	+	0.390437i	$0.127676\pi$
$840$	188396.	−	8029.92i	0.00921243	−	0.000392657i
$841$	1.73842e7			0.847551
$842$	−2.88446e7	−	1.61118e7i	−1.40212	−	0.783182i
$843$	−2.46161e6			−0.119302
$844$	2.06917e7	−	1.27431e7i	0.999862	−	0.615771i
$845$			5.25980e6i			0.253412i
$846$	−1.53206e7	+	2.74283e7i	−0.735955	+	1.31757i
$847$		−	3.29628e6i		−	0.157876i
$848$	−5.44125e6	+	1.07972e7i	−0.259842	+	0.515609i
$849$		−	967271.i		−	0.0460552i
$850$	2.54667e6	+	1.42250e6i	0.120900	+	0.0675311i
$851$			2.86077e7i			1.35413i
$852$	−1.45898e6	+	898522.i	−0.0688574	+	0.0424062i
$853$		−	4.33902e6i		−	0.204183i	−0.994775	−	0.102091i	$-0.967447\pi$
$853$		−	4.33902e6i		−	0.204183i	0.994775	−	0.102091i	$-0.0325534\pi$
$854$	−4.86055e6	−	2.71496e6i	−0.228055	−	0.127385i
$855$	−5.16988e6	−	8.76449e6i	−0.241861	−	0.410026i
$856$	1.15815e7	−	493632.i	0.540232	−	0.0230260i
$857$		−	3.19143e7i		−	1.48434i	−0.670213	−	0.742169i	$-0.733797\pi$
$857$		−	3.19143e7i		−	1.48434i	0.670213	−	0.742169i	$-0.266203\pi$
$858$	187458.	−	335603.i	0.00869332	−	0.0155635i
$859$	2.97907e7			1.37752			0.688761	−	0.724989i	$-0.258155\pi$
$859$	2.97907e7			1.37752			0.688761	+	0.724989i	$0.258155\pi$
$860$	5.25585e6	−	3.23685e6i	0.242324	−	0.149237i
$861$			686492.i			0.0315593i
$862$	1.57086e7	+	8.77437e6i	0.720061	+	0.402205i
$863$	−1.38627e6			−0.0633609			−0.0316804	−	0.999498i	$-0.510086\pi$
$863$	−1.38627e6			−0.0633609			−0.0316804	+	0.999498i	$0.510086\pi$
$864$	2.80673e6	+	4.15057e6i	0.127914	+	0.189157i
$865$			1.68975e7i			0.767859i
$866$	−7.94166e6	+	1.42178e7i	−0.359846	+	0.644226i
$867$		−	2.46098e6i		−	0.111189i
$868$	−1.79723e6	+	1.10684e6i	−0.0809664	+	0.0498636i
$869$	−5.62805e6			−0.252818
$870$	1.46891e6	+	820490.i	0.0657956	+	0.0367515i
$871$		−	1.38787e7i		−	0.619875i
$872$	415146.	+	9.74006e6i	0.0184888	+	0.433781i
$873$			1.82859e7i			0.812046i
$874$	−644693.	−	2.73876e7i	−0.0285479	−	1.21276i
$875$	3.21106e6			0.141784
$876$	1.93579e6	−	1.19217e6i	0.0852311	−	0.0524900i
$877$	1.65815e6			0.0727987			0.0363994	−	0.999337i	$-0.488411\pi$
$877$	1.65815e6			0.0727987			0.0363994	+	0.999337i	$0.488411\pi$
$878$	−2.24243e7	−	1.25255e7i	−0.981707	−	0.548353i
$879$		−	935698.i		−	0.0408473i
$880$	−2.22795e6	−	1.12278e6i	−0.0969838	−	0.0488750i
$881$	−2.95505e7			−1.28270			−0.641349	−	0.767249i	$-0.721625\pi$
$881$	−2.95505e7			−1.28270			−0.641349	+	0.767249i	$0.721625\pi$
$882$	−1.93530e7	−	1.08100e7i	−0.837678	−	0.467903i
$883$	−1.95346e7			−0.843146			−0.421573	−	0.906794i	$-0.638522\pi$
$883$	−1.95346e7			−0.843146			−0.421573	+	0.906794i	$0.638522\pi$
$884$	1.51508e6	+	2.46013e6i	0.0652088	+	0.105883i
$885$		−	2.05000e6i		−	0.0879825i
$886$	1.77125e7	+	9.89367e6i	0.758044	+	0.423422i
$887$	1.11186e7			0.474506			0.237253	−	0.971448i	$-0.423753\pi$
$887$	1.11186e7			0.474506			0.237253	+	0.971448i	$0.423753\pi$
$888$	3.01193e6	−	128376.i	0.128178	−	0.00546326i
$889$			5.29051e6i			0.224514i
$890$	−1.23074e7	−	6.87455e6i	−0.520824	−	0.290917i
$891$	−5.12427e6			−0.216241
$892$	5.95660e6	+	9.67207e6i	0.250661	+	0.407012i
$893$	−1.85166e7	−	3.13912e7i	−0.777021	−	1.31728i
$894$	−111315.	−	62177.6i	−0.00465813	−	0.00260190i
$895$	−1.20282e7			−0.501931
$896$	−1.64492e6	+	3.64221e6i	−0.0684503	+	0.151564i
$897$	2.31489e6			0.0960617
$898$	−7.68543e6	+	1.37591e7i	−0.318037	+	0.569376i
$899$	−1.88333e7			−0.777189
$900$	9.64795e6	+	1.56659e7i	0.397035	+	0.644688i
$901$	−2.53932e6			−0.104209
$902$	4.42923e6	−	7.92958e6i	0.181264	−	0.324514i
$903$	−276291.			−0.0112758
$904$	1.15437e7	−	492020.i	0.469811	−	0.0200245i
$905$			1.73990e7i			0.706160i
$906$	−33388.8	+	59775.3i	−0.00135139	+	0.00241936i
$907$			2.35927e7i			0.952270i	0.879372	+	0.476135i	$0.157963\pi$
$907$			2.35927e7i			0.952270i	−0.879372	+	0.476135i	$0.842037\pi$
$908$	1.42124e7	−	8.75279e6i	0.572075	−	0.352315i
$909$		−	3.45725e7i		−	1.38778i
$910$	1.20551e6	+	673365.i	0.0482579	+	0.0269555i
$911$	3.38240e7			1.35030			0.675148	−	0.737682i	$-0.264080\pi$
$911$	3.38240e7			1.35030			0.675148	+	0.737682i	$0.264080\pi$
$912$	−2.88058e6	+	190777.i	−0.114681	+	0.00759518i
$913$	−9.66729e6			−0.383820
$914$	−2.97063e7	−	1.65931e7i	−1.17621	−	0.656995i
$915$		−	2.20558e6i		−	0.0870905i
$916$	−2.51218e7	+	1.54714e7i	−0.989262	+	0.609243i
$917$		−	3.96958e6i		−	0.155891i
$918$	−513164.	+	918708.i	−0.0200978	+	0.0359808i
$919$		−	5.37265e6i		−	0.209845i	−0.994480	−	0.104923i	$-0.966540\pi$
$919$		−	5.37265e6i		−	0.209845i	0.994480	−	0.104923i	$-0.0334595\pi$
$920$	−639782.	−	1.50104e7i	−0.0249208	−	0.584687i
$921$	−3.41490e6			−0.132656
$922$	−1.51665e7	+	2.71524e7i	−0.587569	+	1.05191i
$923$	−1.25472e7			−0.484779
$924$	58559.7	+	95086.7i	0.00225641	+	0.00366387i
$925$	2.22879e7			0.856474
$926$	−1.87673e7	+	3.35988e7i	−0.719242	+	1.28765i
$927$	1.06524e7			0.407143
$928$	−2.95390e7	+	1.99751e7i	−1.12597	+	0.761412i
$929$	−1.92859e7			−0.733164			−0.366582	−	0.930386i	$-0.619472\pi$
$929$	−1.92859e7			−0.733164			−0.366582	+	0.930386i	$0.619472\pi$
$930$	−730020.	−	407768.i	−0.0276775	−	0.0154599i
$931$	2.21492e7	−	1.30651e7i	0.837498	−	0.494012i
$932$	−2.38937e7	−	3.87975e7i	−0.901038	−	1.46307i
$933$	−66765.5			−0.00251101
$934$	1.93794e7	+	1.08247e7i	0.726896	+	0.406023i
$935$		−	523978.i		−	0.0196013i
$936$	776015.	+	1.82067e7i	0.0289521	+	0.679269i
$937$	1.41288e7			0.525721			0.262861	−	0.964834i	$-0.415334\pi$
$937$	1.41288e7			0.525721			0.262861	+	0.964834i	$0.415334\pi$
$938$	3.51994e6	+	1.96614e6i	0.130626	+	0.0729637i
$939$			2.41717e6i			0.0894631i
$940$	−1.04812e7	−	1.70189e7i	−0.386892	−	0.628219i
$941$	−2.19479e7			−0.808012			−0.404006	−	0.914756i	$-0.632383\pi$
$941$	−2.19479e7			−0.808012			−0.404006	+	0.914756i	$0.632383\pi$
$942$	−2.64147e6	−	1.47545e6i	−0.0969880	−	0.0541747i
$943$	5.46961e7			2.00298
$944$	3.87988e7	+	1.95527e7i	1.41706	+	0.714128i
$945$			502921.i			0.0183198i
$946$	3.19140e6	+	1.78262e6i	0.115945	+	0.0647637i
$947$	−8.42285e6			−0.305200			−0.152600	−	0.988288i	$-0.548765\pi$
$947$	−8.42285e6			−0.305200			−0.152600	+	0.988288i	$0.548765\pi$
$948$	−3.04108e6	+	1.87286e6i	−0.109902	+	0.0676839i
$949$	1.66478e7			0.600055
$950$	−2.13373e7	+	502271.i	−0.767062	+	0.0180563i
$951$			1.24603e6i			0.0446762i
$952$	−838577.	+	35742.2i	−0.0299882	+	0.00127817i
$953$			4.19088e7i			1.49477i	0.664394	+	0.747383i	$0.268690\pi$
$953$			4.19088e7i			1.49477i	−0.664394	+	0.747383i	$0.731310\pi$
$954$	−1.39827e7	−	7.81036e6i	−0.497418	−	0.277843i
$955$	1.34189e7			0.476112
$956$	8.62028e6	−	5.30885e6i	0.305054	−	0.187869i
$957$			996418.i			0.0351691i
$958$	1.17326e7	−	2.10046e7i	0.413027	−	0.739436i
$959$			3.53682e6i			0.124184i
$960$	−1.57749e6	+	134718.i	−0.0552444	+	0.00471788i
$961$	−1.92694e7			−0.673068
$962$	1.92728e7	+	1.07652e7i	0.671440	+	0.375047i
$963$			1.53555e7i			0.533580i
$964$	−1.32287e7	+	8.14700e6i	−0.458486	+	0.282361i
$965$	1.11937e6			0.0386952
$966$	−327941.	+	587107.i	−0.0113071	+	0.0202430i
$967$			1.10867e7i			0.381272i	0.981661	+	0.190636i	$0.0610550\pi$
$967$			1.10867e7i			0.381272i	−0.981661	+	0.190636i	$0.938945\pi$
$968$	1.17854e6	+	2.76507e7i	0.0404257	+	0.948459i
$969$	−308044.	−	522227.i	−0.0105391	−	0.0178669i
$970$	−1.01564e7	−	5.67307e6i	−0.346586	−	0.193593i
$971$		−	2.03318e7i		−	0.692035i	−0.938228	−	0.346018i	$-0.887534\pi$
$971$		−	2.03318e7i		−	0.692035i	0.938228	−	0.346018i	$-0.112466\pi$
$972$	−8.49597e6	+	5.23229e6i	−0.288435	+	0.177634i
$973$		−	1.89408e6i		−	0.0641382i
$974$	5.04647e7	+	2.81881e7i	1.70447	+	0.952069i
$975$		−	1.80350e6i		−	0.0607582i
$976$	4.17433e7	+	2.10366e7i	1.40269	+	0.706887i
$977$		−	1.13639e7i		−	0.380884i	−0.981698	−	0.190442i	$-0.939008\pi$
$977$		−	1.13639e7i		−	0.380884i	0.981698	−	0.190442i	$-0.0609921\pi$
$978$	1.11567e6	−	1.99736e6i	0.0372981	−	0.0667742i
$979$		−	8.34858e6i		−	0.278391i
$980$	1.20083e7	−	7.39537e6i	0.399407	−	0.245977i
$981$	−1.29140e7			−0.428439
$982$	−1.64128e7	−	9.16772e6i	−0.543130	−	0.303377i
$983$	−3.96913e7			−1.31012			−0.655060	−	0.755577i	$-0.727357\pi$
$983$	−3.96913e7			−1.31012			−0.655060	+	0.755577i	$0.727357\pi$
$984$	−245447.	−	5.75862e6i	−0.00808109	−	0.189597i
$985$	3.78045e6			0.124152
$986$	−6.53831e6	−	3.65211e6i	−0.214177	−	0.119633i
$987$			894651.i			0.0292322i
$988$	−1.86934e7	−	9.87177e6i	−0.609252	−	0.321738i
$989$			2.20134e7i			0.715643i
$990$	1.61163e6	−	2.88528e6i	0.0522610	−	0.0935620i
$991$	−5.69524e7			−1.84216			−0.921081	−	0.389372i	$-0.872692\pi$
$991$	−5.69524e7			−1.84216			−0.921081	+	0.389372i	$0.872692\pi$
$992$	1.46803e7	−	9.92725e6i	0.473649	−	0.320295i
$993$	−4.12407e6			−0.132725
$994$	1.77751e6	−	3.18225e6i	0.0570620	−	0.102157i
$995$	2.00983e7			0.643578
$996$	−5.22365e6	+	3.21701e6i	−0.166850	+	0.102755i
$997$			1.02156e7i			0.325483i	0.986669	+	0.162741i	$0.0520336\pi$
$997$			1.02156e7i			0.325483i	−0.986669	+	0.162741i	$0.947966\pi$
$998$	2.72878e7	+	1.52422e7i	0.867246	+	0.484418i
$999$			8.04031e6i			0.254894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.15	✓	96
4.3	odd	2		608.6.b.b.303.45		96
8.3	odd	2	inner	152.6.b.b.75.81	yes	96
8.5	even	2		608.6.b.b.303.46		96
19.18	odd	2	inner	152.6.b.b.75.82	yes	96
76.75	even	2		608.6.b.b.303.51		96
152.37	odd	2		608.6.b.b.303.52		96
152.75	even	2	inner	152.6.b.b.75.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.15	✓	96	1.1	even	1	trivial
152.6.b.b.75.16	yes	96	152.75	even	2	inner
152.6.b.b.75.81	yes	96	8.3	odd	2	inner
152.6.b.b.75.82	yes	96	19.18	odd	2	inner
608.6.b.b.303.45		96	4.3	odd	2
608.6.b.b.303.46		96	8.5	even	2
608.6.b.b.303.51		96	76.75	even	2
608.6.b.b.303.52		96	152.37	odd	2

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.93864 - 2.75858i) q^{2} +1.79162i q^{3} +(16.7804 + 27.2473i) q^{4} -26.9679i q^{5} +(4.94234 - 8.84819i) q^{6} +21.5599i q^{7} +(-7.70850 - 180.855i) q^{8} +239.790 q^{9} +O(q^{10})\)	\(q+(-4.93864 - 2.75858i) q^{2} +1.79162i q^{3} +(16.7804 + 27.2473i) q^{4} -26.9679i q^{5} +(4.94234 - 8.84819i) q^{6} +21.5599i q^{7} +(-7.70850 - 180.855i) q^{8} +239.790 q^{9} +(-74.3932 + 133.185i) q^{10} -90.3444 q^{11} +(-48.8170 + 30.0642i) q^{12} -419.826 q^{13} +(59.4749 - 106.477i) q^{14} +48.3163 q^{15} +(-460.835 + 914.444i) q^{16} -215.062 q^{17} +(-1184.24 - 661.481i) q^{18} +(1355.34 - 799.470i) q^{19} +(734.804 - 452.533i) q^{20} -38.6273 q^{21} +(446.179 + 249.223i) q^{22} +3077.62i q^{23} +(324.024 - 13.8107i) q^{24} +2397.73 q^{25} +(2073.37 + 1158.13i) q^{26} +864.978i q^{27} +(-587.451 + 361.785i) q^{28} -6155.92 q^{29} +(-238.617 - 133.285i) q^{30} +3059.38 q^{31} +(4798.47 - 3244.86i) q^{32} -161.863i q^{33} +(1062.12 + 593.268i) q^{34} +581.426 q^{35} +(4023.78 + 6533.64i) q^{36} +9295.40 q^{37} +(-8898.95 + 209.478i) q^{38} -752.170i q^{39} +(-4877.28 + 207.882i) q^{40} -17772.2i q^{41} +(190.767 + 106.557i) q^{42} +7152.73 q^{43} +(-1516.02 - 2461.65i) q^{44} -6466.64i q^{45} +(8489.88 - 15199.3i) q^{46} -23161.1i q^{47} +(-1638.34 - 825.642i) q^{48} +16342.2 q^{49} +(-11841.5 - 6614.35i) q^{50} -385.311i q^{51} +(-7044.86 - 11439.1i) q^{52} +11807.4 q^{53} +(2386.11 - 4271.82i) q^{54} +2436.40i q^{55} +(3899.23 - 166.195i) q^{56} +(1432.35 + 2428.26i) q^{57} +(30401.9 + 16981.6i) q^{58} -42428.8i q^{59} +(810.769 + 1316.49i) q^{60} -45648.8i q^{61} +(-15109.2 - 8439.54i) q^{62} +5169.86i q^{63} +(-32649.2 + 2788.24i) q^{64} +11321.8i q^{65} +(-446.513 + 799.385i) q^{66} +33058.2i q^{67} +(-3608.84 - 5859.88i) q^{68} -5513.94 q^{69} +(-2871.46 - 1603.91i) q^{70} +29886.8 q^{71} +(-1848.42 - 43367.3i) q^{72} -39654.0 q^{73} +(-45906.7 - 25642.1i) q^{74} +4295.83i q^{75} +(44526.6 + 23514.0i) q^{76} -1947.82i q^{77} +(-2074.92 + 3714.70i) q^{78} +62295.5 q^{79} +(24660.6 + 12427.7i) q^{80} +56719.3 q^{81} +(-49026.1 + 87770.5i) q^{82} +107005. q^{83} +(-648.183 - 1052.49i) q^{84} +5799.78i q^{85} +(-35324.8 - 19731.4i) q^{86} -11029.1i q^{87} +(696.420 + 16339.3i) q^{88} +92408.3i q^{89} +(-17838.8 + 31936.4i) q^{90} -9051.43i q^{91} +(-83857.0 + 51643.8i) q^{92} +5481.25i q^{93} +(-63891.9 + 114385. i) q^{94} +(-21560.0 - 36550.7i) q^{95} +(5813.57 + 8597.05i) q^{96} +76257.9i q^{97} +(-80708.2 - 45081.2i) q^{98} -21663.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Introduction

L-functions

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