LMFDB - Embedded newform 152.6.b.b.75.4

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			75.4
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.61333 + 0.700358i) q^{2} +4.49700i q^{3} +(31.0190 - 7.86269i) q^{4} -93.3850i q^{5} +(-3.14951 - 25.2431i) q^{6} +95.0367i q^{7} +(-168.613 + 65.8603i) q^{8} +222.777 q^{9} +O(q^{10})$	\(q+(-5.61333 + 0.700358i) q^{2} +4.49700i q^{3} +(31.0190 - 7.86269i) q^{4} -93.3850i q^{5} +(-3.14951 - 25.2431i) q^{6} +95.0367i q^{7} +(-168.613 + 65.8603i) q^{8} +222.777 q^{9} +(65.4030 + 524.201i) q^{10} +300.630 q^{11} +(35.3585 + 139.492i) q^{12} +276.831 q^{13} +(-66.5598 - 533.473i) q^{14} +419.952 q^{15} +(900.356 - 487.785i) q^{16} -1297.16 q^{17} +(-1250.52 + 156.024i) q^{18} +(654.993 + 1430.76i) q^{19} +(-734.257 - 2896.71i) q^{20} -427.380 q^{21} +(-1687.53 + 210.548i) q^{22} -2226.45i q^{23} +(-296.174 - 758.253i) q^{24} -5595.77 q^{25} +(-1553.95 + 193.881i) q^{26} +2094.60i q^{27} +(747.244 + 2947.94i) q^{28} +3508.64 q^{29} +(-2357.33 + 294.117i) q^{30} +3472.71 q^{31} +(-4712.37 + 3368.67i) q^{32} +1351.93i q^{33} +(7281.37 - 908.474i) q^{34} +8875.01 q^{35} +(6910.32 - 1751.63i) q^{36} -5424.58 q^{37} +(-4678.74 - 7572.62i) q^{38} +1244.91i q^{39} +(6150.37 + 15746.0i) q^{40} -19973.8i q^{41} +(2399.03 - 299.319i) q^{42} +15101.0 q^{43} +(9325.23 - 2363.76i) q^{44} -20804.0i q^{45} +(1559.31 + 12497.8i) q^{46} -4008.50i q^{47} +(2193.57 + 4048.90i) q^{48} +7775.02 q^{49} +(31410.9 - 3919.04i) q^{50} -5833.31i q^{51} +(8587.03 - 2176.64i) q^{52} +3492.83 q^{53} +(-1466.97 - 11757.7i) q^{54} -28074.3i q^{55} +(-6259.15 - 16024.5i) q^{56} +(-6434.14 + 2945.50i) q^{57} +(-19695.2 + 2457.30i) q^{58} -5272.90i q^{59} +(13026.5 - 3301.95i) q^{60} -5218.99i q^{61} +(-19493.5 + 2432.14i) q^{62} +21172.0i q^{63} +(24092.8 - 22209.8i) q^{64} -25851.9i q^{65} +(-946.836 - 7588.84i) q^{66} -44164.6i q^{67} +(-40236.5 + 10199.1i) q^{68} +10012.3 q^{69} +(-49818.4 + 6215.69i) q^{70} +59386.9 q^{71} +(-37563.2 + 14672.2i) q^{72} +67977.3 q^{73} +(30450.0 - 3799.15i) q^{74} -25164.2i q^{75} +(31566.9 + 39230.8i) q^{76} +28570.9i q^{77} +(-871.883 - 6988.10i) q^{78} -2688.59 q^{79} +(-45551.9 - 84079.8i) q^{80} +44715.4 q^{81} +(13988.8 + 112119. i) q^{82} -53937.2 q^{83} +(-13256.9 + 3360.35i) q^{84} +121135. i q^{85} +(-84767.2 + 10576.1i) q^{86} +15778.3i q^{87} +(-50690.1 + 19799.6i) q^{88} +46866.4i q^{89} +(14570.3 + 116780. i) q^{90} +26309.2i q^{91} +(-17505.9 - 69062.2i) q^{92} +15616.8i q^{93} +(2807.38 + 22501.0i) q^{94} +(133612. - 61166.6i) q^{95} +(-15148.9 - 21191.5i) q^{96} -81391.3i q^{97} +(-43643.8 + 5445.30i) q^{98} +66973.4 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 $

$2$	−5.61333	+	0.700358i	−0.992306	+	0.123807i
$2$	−5.61333	+	0.700358i	−0.992306	+	0.123807i
$3$			4.49700i			0.288483i	0.989543	+	0.144241i	$0.0460741\pi$
$3$			4.49700i			0.288483i	−0.989543	+	0.144241i	$0.953926\pi$
$4$	31.0190	−	7.86269i	0.969344	−	0.245709i
$5$		−	93.3850i		−	1.67052i	−0.549853	−	0.835261i	$-0.685316\pi$
$5$		−	93.3850i		−	1.67052i	0.549853	−	0.835261i	$-0.314684\pi$
$6$	−3.14951	−	25.2431i	−0.0357162	−	0.286263i
$7$			95.0367i			0.733072i	0.930404	+	0.366536i	$0.119456\pi$
$7$			95.0367i			0.733072i	−0.930404	+	0.366536i	$0.880544\pi$
$8$	−168.613	+	65.8603i	−0.931465	+	0.363830i
$9$	222.777			0.916778
$10$	65.4030	+	524.201i	0.206822	+	1.65767i
$11$	300.630			0.749118			0.374559	−	0.927203i	$-0.377794\pi$
$11$	300.630			0.749118			0.374559	+	0.927203i	$0.377794\pi$
$12$	35.3585	+	139.492i	0.0708827	+	0.279639i
$13$	276.831			0.454315			0.227158	−	0.973858i	$-0.427057\pi$
$13$	276.831			0.454315			0.227158	+	0.973858i	$0.427057\pi$
$14$	−66.5598	−	533.473i	−0.0907594	−	0.727432i
$15$	419.952			0.481917
$16$	900.356	−	487.785i	0.879254	−	0.476353i
$17$	−1297.16			−1.08860			−0.544302	−	0.838889i	$-0.683206\pi$
$17$	−1297.16			−1.08860			−0.544302	+	0.838889i	$0.683206\pi$
$18$	−1250.52	+	156.024i	−0.909724	+	0.113504i
$19$	654.993	+	1430.76i	0.416248	+	0.909251i
$19$	654.993	+	1430.76i	0.416248	+	0.909251i
$20$	−734.257	−	2896.71i	−0.410462	−	1.61931i
$21$	−427.380			−0.211478
$22$	−1687.53	+	210.548i	−0.743354	+	0.0927460i
$23$		−	2226.45i		−	0.877592i	−0.898587	−	0.438796i	$-0.855405\pi$
$23$		−	2226.45i		−	0.877592i	0.898587	−	0.438796i	$-0.144595\pi$
$24$	−296.174	−	758.253i	−0.104959	−	0.268712i
$25$	−5595.77			−1.79065
$26$	−1553.95	+	193.881i	−0.450820	+	0.0562474i
$27$			2094.60i			0.552957i
$28$	747.244	+	2947.94i	0.180122	+	0.710598i
$29$	3508.64			0.774718			0.387359	−	0.921929i	$-0.373387\pi$
$29$	3508.64			0.774718			0.387359	+	0.921929i	$0.373387\pi$
$30$	−2357.33	+	294.117i	−0.478209	+	0.0596647i
$31$	3472.71			0.649028			0.324514	−	0.945881i	$-0.394799\pi$
$31$	3472.71			0.649028			0.324514	+	0.945881i	$0.394799\pi$
$32$	−4712.37	+	3368.67i	−0.813514	+	0.581546i
$33$			1351.93i			0.216107i
$34$	7281.37	−	908.474i	1.08023	−	0.134777i
$35$	8875.01			1.22461
$36$	6910.32	−	1751.63i	0.888673	−	0.225261i
$37$	−5424.58			−0.651422			−0.325711	−	0.945469i	$-0.605604\pi$
$37$	−5424.58			−0.651422			−0.325711	+	0.945469i	$0.605604\pi$
$38$	−4678.74	−	7572.62i	−0.525618	−	0.850721i
$39$			1244.91i			0.131062i
$40$	6150.37	+	15746.0i	0.607786	+	1.55603i
$41$		−	19973.8i		−	1.85567i	−0.372992	−	0.927834i	$-0.621668\pi$
$41$		−	19973.8i		−	1.85567i	0.372992	−	0.927834i	$-0.378332\pi$
$42$	2399.03	−	299.319i	0.209851	−	0.0261825i
$43$	15101.0			1.24548			0.622739	−	0.782430i	$-0.286020\pi$
$43$	15101.0			1.24548			0.622739	+	0.782430i	$0.286020\pi$
$44$	9325.23	−	2363.76i	0.726152	−	0.184065i
$45$		−	20804.0i		−	1.53150i
$46$	1559.31	+	12497.8i	0.108652	+	0.870840i
$47$		−	4008.50i		−	0.264690i	−0.991204	−	0.132345i	$-0.957749\pi$
$47$		−	4008.50i		−	0.264690i	0.991204	−	0.132345i	$-0.0422506\pi$
$48$	2193.57	+	4048.90i	0.137419	+	0.253650i
$49$	7775.02			0.462606
$50$	31410.9	−	3919.04i	1.77687	−	0.221694i
$51$		−	5833.31i		−	0.314043i
$52$	8587.03	−	2176.64i	0.440387	−	0.111629i
$53$	3492.83			0.170800			0.0854001	−	0.996347i	$-0.472783\pi$
$53$	3492.83			0.170800			0.0854001	+	0.996347i	$0.472783\pi$
$54$	−1466.97	−	11757.7i	−0.0684599	−	0.548703i
$55$		−	28074.3i		−	1.25142i
$56$	−6259.15	−	16024.5i	−0.266713	−	0.682831i
$57$	−6434.14	+	2945.50i	−0.262303	+	0.120080i
$58$	−19695.2	+	2457.30i	−0.768758	+	0.0959156i
$59$		−	5272.90i		−	0.197206i	−0.995127	−	0.0986028i	$-0.968563\pi$
$59$		−	5272.90i		−	0.197206i	0.995127	−	0.0986028i	$-0.0314373\pi$
$60$	13026.5	−	3301.95i	0.467143	−	0.118411i
$61$		−	5218.99i		−	0.179582i	−0.995961	−	0.0897909i	$-0.971380\pi$
$61$		−	5218.99i		−	0.179582i	0.995961	−	0.0897909i	$-0.0286199\pi$
$62$	−19493.5	+	2432.14i	−0.644035	+	0.0803543i
$63$			21172.0i			0.672064i
$64$	24092.8	−	22209.8i	0.735255	−	0.677790i
$65$		−	25851.9i		−	0.758943i
$66$	−946.836	−	7588.84i	−0.0267556	−	0.214445i
$67$		−	44164.6i		−	1.20195i	−0.799267	−	0.600976i	$-0.794779\pi$
$67$		−	44164.6i		−	1.20195i	0.799267	−	0.600976i	$-0.205221\pi$
$68$	−40236.5	+	10199.1i	−1.05523	+	0.267480i
$69$	10012.3			0.253170
$70$	−49818.4	+	6215.69i	−1.21519	+	0.151616i
$71$	59386.9			1.39812			0.699061	−	0.715062i	$-0.253602\pi$
$71$	59386.9			1.39812			0.699061	+	0.715062i	$0.253602\pi$
$72$	−37563.2	+	14672.2i	−0.853947	+	0.333551i
$73$	67977.3			1.49299			0.746495	−	0.665391i	$-0.231735\pi$
$73$	67977.3			1.49299			0.746495	+	0.665391i	$0.231735\pi$
$74$	30450.0	−	3799.15i	0.646410	−	0.0806506i
$75$		−	25164.2i		−	0.516570i
$76$	31566.9	+	39230.8i	0.626899	+	0.779101i
$77$			28570.9i			0.549157i
$78$	−871.883	−	6988.10i	−0.0162264	−	0.130054i
$79$	−2688.59			−0.0484681			−0.0242341	−	0.999706i	$-0.507715\pi$
$79$	−2688.59			−0.0484681			−0.0242341	+	0.999706i	$0.507715\pi$
$80$	−45551.9	−	84079.8i	−0.795758	−	1.46881i
$81$	44715.4			0.757259
$82$	13988.8	+	112119.i	0.229745	+	1.84139i
$83$	−53937.2			−0.859395			−0.429698	−	0.902973i	$-0.641380\pi$
$83$	−53937.2			−0.859395			−0.429698	+	0.902973i	$0.641380\pi$
$84$	−13256.9	+	3360.35i	−0.204995	+	0.0519621i
$85$			121135.i			1.81854i
$86$	−84767.2	+	10576.1i	−1.23590	+	0.154199i
$87$			15778.3i			0.223493i
$88$	−50690.1	+	19799.6i	−0.697777	+	0.272552i
$89$			46866.4i			0.627172i	0.949560	+	0.313586i	$0.101530\pi$
$89$			46866.4i			0.627172i	−0.949560	+	0.313586i	$0.898470\pi$
$90$	14570.3	+	116780.i	0.189610	+	1.51972i
$91$			26309.2i			0.333045i
$92$	−17505.9	−	69062.2i	−0.215632	−	0.850689i
$93$			15616.8i			0.187233i
$94$	2807.38	+	22501.0i	0.0327704	+	0.262653i
$95$	133612.	−	61166.6i	1.51892	−	0.695352i
$96$	−15148.9	−	21191.5i	−0.167766	−	0.234685i
$97$		−	81391.3i		−	0.878311i	−0.898411	−	0.439156i	$-0.855278\pi$
$97$		−	81391.3i		−	0.878311i	0.898411	−	0.439156i	$-0.144722\pi$
$98$	−43643.8	+	5445.30i	−0.459047	+	0.0572739i
$99$	66973.4			0.686774
$100$	−173575.	+	43997.8i	−1.73575	+	0.439978i
$101$			2539.86i			0.0247746i	0.999923	+	0.0123873i	$0.00394310\pi$
$101$			2539.86i			0.0247746i	−0.999923	+	0.0123873i	$0.996057\pi$
$102$	4085.41	+	32744.3i	0.0388808	+	0.311627i
$103$	−92949.2			−0.863282			−0.431641	−	0.902045i	$-0.642065\pi$
$103$	−92949.2			−0.863282			−0.431641	+	0.902045i	$0.642065\pi$
$104$	−46677.5	+	18232.2i	−0.423179	+	0.165293i
$105$			39910.9i			0.353279i
$106$	−19606.4	+	2446.24i	−0.169486	+	0.0211463i
$107$		−	168149.i		−	1.41983i	−0.704288	−	0.709914i	$-0.748734\pi$
$107$		−	168149.i		−	1.41983i	0.704288	−	0.709914i	$-0.251266\pi$
$108$	16469.2	+	64972.3i	0.135866	+	0.536005i
$109$	−190552.			−1.53620			−0.768098	−	0.640332i	$-0.778797\pi$
$109$	−190552.			−1.53620			−0.768098	+	0.640332i	$0.778797\pi$
$110$	19662.1	+	157590.i	0.154934	+	1.24179i
$111$		−	24394.3i		−	0.187924i
$112$	46357.5	+	85566.9i	0.349201	+	0.644556i
$113$		−	200780.i		−	1.47919i	−0.673050	−	0.739597i	$-0.735016\pi$
$113$		−	200780.i		−	1.47919i	0.673050	−	0.739597i	$-0.264984\pi$
$114$	34054.1	−	21040.3i	0.245418	−	0.151632i
$115$	−207917.			−1.46604
$116$	108834.	−	27587.3i	0.750968	−	0.190355i
$117$	61671.7			0.416506
$118$	3692.92	+	29598.5i	0.0244154	+	0.195688i
$119$		−	123278.i		−	0.798025i
$120$	−70809.5	+	27658.2i	−0.448889	+	0.175336i
$121$	−70672.8			−0.438823
$122$	3655.17	+	29296.0i	0.0222335	+	0.178200i
$123$	89822.0			0.535328
$124$	107720.	−	27304.8i	0.629132	−	0.159472i
$125$			230733.i			1.32079i
$126$	−14828.0	−	118845.i	−0.0832062	−	0.666893i
$127$	−360363.			−1.98258			−0.991292	−	0.131684i	$-0.957962\pi$
$127$	−360363.			−1.98258			−0.991292	+	0.131684i	$0.957962\pi$
$128$	−119686.	+	141545.i	−0.645683	+	0.763605i
$129$			67909.4i			0.359299i
$130$	18105.6	+	145115.i	0.0939625	+	0.753104i
$131$	145926.			0.742943			0.371472	−	0.928444i	$-0.378853\pi$
$131$	145926.			0.742943			0.371472	+	0.928444i	$0.378853\pi$
$132$	10629.8	+	41935.5i	0.0530995	+	0.209482i
$133$	−135975.	+	62248.4i	−0.666546	+	0.305140i
$134$	30931.0	+	247911.i	0.148810	+	1.19270i
$135$	195604.			0.923727
$136$	218718.	−	85431.1i	1.01400	−	0.396067i
$137$	−65742.5			−0.299257			−0.149629	−	0.988742i	$-0.547808\pi$
$137$	−65742.5			−0.299257			−0.149629	+	0.988742i	$0.547808\pi$
$138$	−56202.5	+	7012.22i	−0.251222	+	0.0313442i
$139$	220332.			0.967253			0.483627	−	0.875274i	$-0.339319\pi$
$139$	220332.			0.967253			0.483627	+	0.875274i	$0.339319\pi$
$140$	275294.	−	69781.4i	1.18707	−	0.300898i
$141$	18026.2			0.0763583
$142$	−333359.	+	41592.1i	−1.38737	+	0.173097i
$143$	83223.7			0.340335
$144$	200579.	−	108667.i	0.806081	−	0.436710i
$145$		−	327654.i		−	1.29418i
$146$	−381579.	+	47608.5i	−1.48150	+	0.184843i
$147$			34964.3i			0.133454i
$148$	−168265.	+	42651.8i	−0.631451	+	0.160060i
$149$			311465.i			1.14933i	0.818390	+	0.574663i	$0.194867\pi$
$149$			311465.i			1.14933i	−0.818390	+	0.574663i	$0.805133\pi$
$150$	17623.9	+	141255.i	0.0639550	+	0.512596i
$151$	171779.			0.613093			0.306547	−	0.951856i	$-0.400826\pi$
$151$	171779.			0.613093			0.306547	+	0.951856i	$0.400826\pi$
$152$	−204671.	−	198108.i	−0.718534	−	0.695492i
$153$	−288977.			−0.998008
$154$	−20009.8	−	160378.i	−0.0679895	−	0.544932i
$155$		−	324299.i		−	1.08422i
$156$	9788.34	+	38615.9i	0.0322031	+	0.127044i
$157$		−	60313.0i		−	0.195282i	−0.995222	−	0.0976409i	$-0.968870\pi$
$157$		−	60313.0i		−	0.195282i	0.995222	−	0.0976409i	$-0.0311297\pi$
$158$	15091.9	−	1882.97i	0.0480952	−	0.00600070i
$159$			15707.3i			0.0492729i
$160$	314584.	+	440065.i	0.971485	+	1.35899i
$161$	211594.			0.643338
$162$	−251002.	+	31316.8i	−0.751433	+	0.0937540i
$163$	134718.			0.397153			0.198576	−	0.980085i	$-0.436368\pi$
$163$	134718.			0.397153			0.198576	+	0.980085i	$0.436368\pi$
$164$	−157048.	−	619566.i	−0.455954	−	1.79878i
$165$	126250.			0.361012
$166$	302767.	−	37775.4i	0.852784	−	0.106399i
$167$	459295.			1.27438			0.637192	−	0.770705i	$-0.280096\pi$
$167$	459295.			1.27438			0.637192	+	0.770705i	$0.280096\pi$
$168$	72061.9	−	28147.4i	0.196985	−	0.0769422i
$169$	−294657.			−0.793598
$170$	−84837.9	−	679971.i	−0.225148	−	1.80455i
$171$	145917.	+	318741.i	0.381607	+	0.833581i
$172$	468419.	−	118735.i	1.20730	−	0.306025i
$173$	254781.			0.647219			0.323609	−	0.946191i	$-0.395104\pi$
$173$	254781.			0.647219			0.323609	+	0.946191i	$0.395104\pi$
$174$	−11050.5	−	88569.1i	−0.0276700	−	0.221773i
$175$		−	531803.i		−	1.31267i
$176$	270674.	−	146643.i	0.658665	−	0.356844i
$177$	23712.2			0.0568904
$178$	−32823.3	−	263077.i	−0.0776483	−	0.622346i
$179$			616670.i			1.43853i	0.694734	+	0.719267i	$0.255522\pi$
$179$			616670.i			1.43853i	−0.694734	+	0.719267i	$0.744478\pi$
$180$	−163576.	−	645320.i	−0.376303	−	1.48455i
$181$	493543.			1.11977			0.559885	−	0.828571i	$-0.310845\pi$
$181$	493543.			1.11977			0.559885	+	0.828571i	$0.310845\pi$
$182$	−18425.8	−	147682.i	−0.0412334	−	0.330483i
$183$	23469.8			0.0518062
$184$	146634.	+	375408.i	0.319295	+	0.817447i
$185$			506575.i			1.08821i
$186$	−10937.3	−	87662.0i	−0.0231808	−	0.185793i
$187$	−389964.			−0.815493
$188$	−31517.6	−	124340.i	−0.0650366	−	0.256575i
$189$	−199064.			−0.405357
$190$	−707169.	+	436924.i	−1.42115	+	0.878056i
$191$		−	839278.i		−	1.66465i	−0.554290	−	0.832324i	$-0.687010\pi$
$191$		−	839278.i		−	1.66465i	0.554290	−	0.832324i	$-0.312990\pi$
$192$	99877.6	+	108345.i	0.195531	+	0.212108i
$193$			85037.8i			0.164331i	0.996619	+	0.0821653i	$0.0261835\pi$
$193$			85037.8i			0.164331i	−0.996619	+	0.0821653i	$0.973816\pi$
$194$	57003.0	+	456876.i	0.108741	+	0.871554i
$195$	116256.			0.218942
$196$	241173.	−	61132.5i	0.448424	−	0.113666i
$197$			932798.i			1.71247i	0.516589	+	0.856233i	$0.327201\pi$
$197$			932798.i			1.71247i	−0.516589	+	0.856233i	$0.672799\pi$
$198$	−375944.	+	46905.3i	−0.681491	+	0.0850275i
$199$		−	158415.i		−	0.283573i	−0.989897	−	0.141786i	$-0.954715\pi$
$199$		−	158415.i		−	0.283573i	0.989897	−	0.141786i	$-0.0452846\pi$
$200$	943520.	−	368539.i	1.66792	−	0.651491i
$201$	198608.			0.346742
$202$	−1778.81	−	14257.1i	−0.00306727	−	0.0245840i
$203$			333450.i			0.567924i
$204$	−45865.5	−	180943.i	−0.0771633	−	0.304416i
$205$	−1.86525e6			−3.09994
$206$	521755.	−	65097.8i	0.856640	−	0.106880i
$207$		−	496001.i		−	0.804557i
$208$	249247.	−	135034.i	0.399458	−	0.216414i
$209$	196910.	+	430130.i	0.311819	+	0.681136i
$210$	−27951.9	−	224033.i	−0.0437385	−	0.350561i
$211$			140861.i			0.217813i	0.994052	+	0.108907i	$0.0347350\pi$
$211$			140861.i			0.217813i	−0.994052	+	0.108907i	$0.965265\pi$
$212$	108344.	−	27463.1i	0.165564	−	0.0419671i
$213$			267063.i			0.403334i
$214$	117765.	+	943878.i	0.175785	+	1.40890i
$215$		−	1.41021e6i		−	2.08060i
$216$	−137951.	−	353177.i	−0.201182	−	0.515060i
$217$			330035.i			0.475784i
$218$	1.06963e6	−	133454.i	1.52438	−	0.190192i
$219$			305694.i			0.430702i
$220$	−220739.	−	870837.i	−0.307485	−	1.21305i
$221$	−359094.			−0.494569
$222$	17084.8	+	136934.i	0.0232663	+	0.186478i
$223$	−2964.04			−0.00399137			−0.00199568	−	0.999998i	$-0.500635\pi$
$223$	−2964.04			−0.00399137			−0.00199568	+	0.999998i	$0.500635\pi$
$224$	−320148.	−	447849.i	−0.426315	−	0.596364i
$225$	−1.24661e6			−1.64162
$226$	140618.	+	1.12705e6i	0.183135	+	1.46781i
$227$		−	447740.i		−	0.576715i	−0.957523	−	0.288358i	$-0.906891\pi$
$227$		−	447740.i		−	0.576715i	0.957523	−	0.288358i	$-0.0931092\pi$
$228$	−176421.	+	141956.i	−0.224757	+	0.180849i
$229$		−	99233.7i		−	0.125046i	−0.998044	−	0.0625231i	$-0.980085\pi$
$229$		−	99233.7i		−	0.125046i	0.998044	−	0.0625231i	$-0.0199147\pi$
$230$	1.16711e6	−	145616.i	1.45476	−	0.181506i
$231$	−128483.			−0.158422
$232$	−591603.	+	231080.i	−0.721623	+	0.281866i
$233$	1.17832e6			1.42192			0.710960	−	0.703232i	$-0.248261\pi$
$233$	1.17832e6			1.42192			0.710960	+	0.703232i	$0.248261\pi$
$234$	−346184.	+	43192.3i	−0.413301	+	0.0515664i
$235$	−374334.			−0.442170
$236$	−41459.1	−	163560.i	−0.0484552	−	0.191160i
$237$		−	12090.6i		−	0.0139822i
$238$	86338.4	+	691998.i	0.0988011	+	0.791885i
$239$			1.16687e6i			1.32138i	0.750658	+	0.660690i	$0.229736\pi$
$239$			1.16687e6i			1.32138i	−0.750658	+	0.660690i	$0.770264\pi$
$240$	378107.	−	204847.i	0.423727	−	0.229562i
$241$			1.02176e6i			1.13320i	0.823994	+	0.566599i	$0.191741\pi$
$241$			1.02176e6i			1.13320i	−0.823994	+	0.566599i	$0.808259\pi$
$242$	396710.	−	49496.3i	0.435447	−	0.0543293i
$243$			710072.i			0.771413i
$244$	−41035.3	−	161888.i	−0.0441249	−	0.174076i
$245$		−	726071.i		−	0.772794i
$246$	−504201.	+	62907.6i	−0.531209	+	0.0662774i
$247$	181323.	+	396080.i	0.189108	+	0.413086i
$248$	−585544.	+	228713.i	−0.604548	+	0.236136i
$249$		−	242555.i		−	0.247921i
$250$	−161595.	−	1.29518e6i	−0.163523	−	1.31063i
$251$	−786942.			−0.788421			−0.394211	−	0.919020i	$-0.628982\pi$
$251$	−786942.			−0.788421			−0.394211	+	0.919020i	$0.628982\pi$
$252$	166469.	+	656734.i	0.165132	+	0.651461i
$253$		−	669336.i		−	0.657420i
$254$	2.02284e6	−	252384.i	1.96733	−	0.245458i
$255$	−544744.			−0.524617
$256$	572707.	−	878361.i	0.546176	−	0.837670i
$257$			680976.i			0.643130i	0.946887	+	0.321565i	$0.104209\pi$
$257$			680976.i			0.643130i	−0.946887	+	0.321565i	$0.895791\pi$
$258$	−47560.9	−	381198.i	−0.0444837	−	0.356534i
$259$		−	515535.i		−	0.477539i
$260$	−203266.	−	801901.i	−0.186479	−	0.735677i
$261$	781644.			0.710245
$262$	−819134.	+	102201.i	−0.737227	+	0.0919816i
$263$			702665.i			0.626411i	0.949685	+	0.313205i	$0.101403\pi$
$263$			702665.i			0.626411i	−0.949685	+	0.313205i	$0.898597\pi$
$264$	−89038.5	−	227953.i	−0.0786264	−	0.201297i
$265$		−	326179.i		−	0.285326i
$266$	719677.	−	444652.i	0.623639	−	0.385315i
$267$	−210758.			−0.180928
$268$	−347252.	−	1.36994e6i	−0.295330	−	1.16510i
$269$	−954364.			−0.804144			−0.402072	−	0.915608i	$-0.631710\pi$
$269$	−954364.			−0.804144			−0.402072	+	0.915608i	$0.631710\pi$
$270$	−1.09799e6	+	136993.i	−0.916620	+	0.114364i
$271$		−	1.30739e6i		−	1.08139i	−0.841219	−	0.540695i	$-0.818161\pi$
$271$		−	1.30739e6i		−	1.08139i	0.841219	−	0.540695i	$-0.181839\pi$
$272$	−1.16790e6	+	632734.i	−0.957160	+	0.518560i
$273$	−118312.			−0.0960778
$274$	369035.	−	46043.3i	0.296955	−	0.0370502i
$275$	−1.68225e6			−1.34140
$276$	310572.	−	78723.8i	0.245409	−	0.0622062i
$277$			2.32222e6i			1.81846i	0.416290	+	0.909232i	$0.363330\pi$
$277$			2.32222e6i			1.81846i	−0.416290	+	0.909232i	$0.636670\pi$
$278$	−1.23680e6	+	154311.i	−0.959812	+	0.119753i
$279$	773639.			0.595015
$280$	−1.49644e6	+	584511.i	−1.14068	+	0.445551i
$281$		−	1.63016e6i		−	1.23158i	−0.787909	−	0.615792i	$-0.788836\pi$
$281$		−	1.63016e6i		−	1.23158i	0.787909	−	0.615792i	$-0.211164\pi$
$282$	−101187.	+	12624.8i	−0.0757708	+	0.00945370i
$283$	821287.			0.609577			0.304789	−	0.952420i	$-0.401414\pi$
$283$	821287.			0.609577			0.304789	+	0.952420i	$0.401414\pi$
$284$	1.84212e6	−	466941.i	1.35526	−	0.343531i
$285$	275066.	+	600852.i	0.200597	+	0.438183i
$286$	−467162.	+	58286.4i	−0.337717	+	0.0421359i
$287$	1.89824e6			1.36034
$288$	−1.04981e6	+	750463.i	−0.745811	+	0.533148i
$289$	262758.			0.185060
$290$	229476.	+	1.83923e6i	0.160229	+	1.28423i
$291$	366016.			0.253378
$292$	2.10859e6	−	534484.i	1.44722	−	0.366841i
$293$	2.23127e6			1.51839			0.759194	−	0.650864i	$-0.225593\pi$
$293$	2.23127e6			1.51839			0.759194	+	0.650864i	$0.225593\pi$
$294$	−24487.5	−	196266.i	−0.0165225	−	0.132427i
$295$	−492410.			−0.329436
$296$	914657.	−	357265.i	0.606777	−	0.237007i
$297$			629698.i			0.414230i
$298$	−218137.	−	1.74835e6i	−0.142295	−	1.14048i
$299$		−	616351.i		−	0.398703i
$300$	−197858.	−	780567.i	−0.126926	−	0.500734i
$301$			1.43515e6i			0.913024i
$302$	−964250.	+	120306.i	−0.608376	+	0.0759052i
$303$	−11421.8			−0.00714704
$304$	1.28763e6	+	968701.i	0.799112	+	0.601182i
$305$	−487376.			−0.299995
$306$	1.62212e6	−	202387.i	0.990330	−	0.123560i
$307$			1.82839e6i			1.10719i	0.832786	+	0.553595i	$0.186745\pi$
$307$			1.82839e6i			1.10719i	−0.832786	+	0.553595i	$0.813255\pi$
$308$	224644.	+	886239.i	0.134933	+	0.532322i
$309$		−	417992.i		−	0.249042i
$310$	227125.	+	1.82040e6i	0.134234	+	1.07588i
$311$			1.90568e6i			1.11724i	0.829422	+	0.558622i	$0.188670\pi$
$311$			1.90568e6i			1.11724i	−0.829422	+	0.558622i	$0.811330\pi$
$312$	−81990.2	−	209908.i	−0.0476843	−	0.122080i
$313$	−2.31801e6			−1.33738			−0.668688	−	0.743543i	$-0.733144\pi$
$313$	−2.31801e6			−1.33738			−0.668688	+	0.743543i	$0.733144\pi$
$314$	42240.7	+	338557.i	0.0241773	+	0.193779i
$315$	1.97715e6			1.12270
$316$	−83397.3	+	21139.5i	−0.0469823	+	0.0119091i
$317$	−2.82404e6			−1.57842			−0.789211	−	0.614122i	$-0.789510\pi$
$317$	−2.82404e6			−1.57842			−0.789211	+	0.614122i	$0.789510\pi$
$318$	−11000.7	−	88170.1i	−0.00610033	−	0.0488938i
$319$	1.05480e6			0.580355
$320$	−2.07407e6	−	2.24991e6i	−1.13226	−	1.22826i
$321$	756167.			0.409596
$322$	−1.18775e6	+	148192.i	−0.638388	+	0.0796498i
$323$	−849628.	−	1.85592e6i	−0.453130	−	0.989815i
$324$	1.38703e6	−	351583.i	0.734045	−	0.186065i
$325$	−1.54908e6			−0.813517
$326$	−756219.	+	94351.1i	−0.394097	+	0.0491703i
$327$		−	856911.i		−	0.443166i
$328$	1.31548e6	+	3.36784e6i	0.675148	+	1.72849i
$329$	380954.			0.194036
$330$	−708684.	+	88420.3i	−0.358235	+	0.0446958i
$331$			2.30744e6i			1.15760i	0.815468	+	0.578802i	$0.196479\pi$
$331$			2.30744e6i			1.15760i	−0.815468	+	0.578802i	$0.803521\pi$
$332$	−1.67308e6	+	424091.i	−0.833050	+	0.211161i
$333$	−1.20847e6			−0.597209
$334$	−2.57818e6	+	321671.i	−1.26458	+	0.157778i
$335$	−4.12431e6			−2.00789
$336$	−384794.	+	208470.i	−0.185943	+	0.100738i
$337$		−	1.22825e6i		−	0.589130i	−0.955631	−	0.294565i	$-0.904825\pi$
$337$		−	1.22825e6i		−	0.589130i	0.955631	−	0.294565i	$-0.0951748\pi$
$338$	1.65401e6	−	206366.i	0.787492	−	0.0982530i
$339$	902909.			0.426722
$340$	952447.	+	3.75749e6i	0.446831	+	1.76279i
$341$	1.04400e6			0.486199
$342$	−1.04232e6	−	1.68701e6i	−0.481875	−	0.779922i
$343$			2.33619e6i			1.07219i
$344$	−2.54624e6	+	994559.i	−1.16012	+	0.453142i
$345$		−	935002.i		−	0.422926i
$346$	−1.43017e6	+	178438.i	−0.642239	+	0.0801302i
$347$	884418.			0.394307			0.197153	−	0.980373i	$-0.436830\pi$
$347$	884418.			0.394307			0.197153	+	0.980373i	$0.436830\pi$
$348$	124060.	+	489428.i	0.0549142	+	0.216641i
$349$			1.51416e6i			0.665438i	0.943026	+	0.332719i	$0.107966\pi$
$349$			1.51416e6i			0.665438i	−0.943026	+	0.332719i	$0.892034\pi$
$350$	372453.	+	2.98519e6i	0.162518	+	1.30257i
$351$			579851.i			0.251217i
$352$	−1.41668e6	+	1.01272e6i	−0.609417	+	0.435646i
$353$	−924516.			−0.394892			−0.197446	−	0.980314i	$-0.563265\pi$
$353$	−924516.			−0.394892			−0.197446	+	0.980314i	$0.563265\pi$
$354$	−133105.	+	16607.0i	−0.0564527	+	0.00704343i
$355$		−	5.54585e6i		−	2.33559i
$356$	368496.	+	1.45375e6i	0.154102	+	0.607945i
$357$	554379.			0.230216
$358$	−431890.	−	3.46157e6i	−0.178101	−	1.42747i
$359$		−	3.57999e6i		−	1.46604i	−0.680208	−	0.733019i	$-0.738111\pi$
$359$		−	3.57999e6i		−	1.46604i	0.680208	−	0.733019i	$-0.261889\pi$
$360$	1.37016e6	+	3.50784e6i	0.557205	+	1.42654i
$361$	−1.61807e6	+	1.87428e6i	−0.653474	+	0.756949i
$362$	−2.77042e6	+	345657.i	−1.11115	+	0.138635i
$363$		−	317816.i		−	0.126593i
$364$	206861.	+	816084.i	0.0818322	+	0.322835i
$365$		−	6.34807e6i		−	2.49407i
$366$	−131744.	+	16437.3i	−0.0514076	+	0.00641397i
$367$			1.35151e6i			0.523787i	0.965097	+	0.261893i	$0.0843469\pi$
$367$			1.35151e6i			0.523787i	−0.965097	+	0.261893i	$0.915653\pi$
$368$	−1.08603e6	−	2.00460e6i	−0.418044	−	0.771627i
$369$		−	4.44970e6i		−	1.70124i
$370$	−354784.	−	2.84357e6i	−0.134729	−	1.07984i
$371$			331948.i			0.125209i
$372$	122790.	+	484416.i	0.0460049	+	0.181494i
$373$	4.87847e6			1.81556			0.907781	−	0.419443i	$-0.137775\pi$
$373$	4.87847e6			1.81556			0.907781	+	0.419443i	$0.137775\pi$
$374$	2.18900e6	−	273114.i	0.809219	−	0.100964i
$375$	−1.03760e6			−0.381025
$376$	264001.	+	675886.i	0.0963020	+	0.246549i
$377$	971302.			0.351966
$378$	1.11741e6	−	139416.i	0.402238	−	0.0501860i
$379$			2.12271e6i			0.759088i	0.925174	+	0.379544i	$0.123919\pi$
$379$			2.12271e6i			0.759088i	−0.925174	+	0.379544i	$0.876081\pi$
$380$	3.66357e6	−	2.94787e6i	1.30151	−	1.04725i
$381$		−	1.62055e6i		−	0.571941i
$382$	587795.	+	4.71114e6i	0.206095	+	1.65184i
$383$	−506796.			−0.176537			−0.0882687	−	0.996097i	$-0.528133\pi$
$383$	−506796.			−0.176537			−0.0882687	+	0.996097i	$0.528133\pi$
$384$	−636527.	−	538229.i	−0.220287	−	0.186268i
$385$	2.66809e6			0.917379
$386$	−59556.9	−	477345.i	−0.0203453	−	0.163066i
$387$	3.36417e6			1.14183
$388$	−639954.	−	2.52468e6i	−0.215809	−	0.851386i
$389$			1.63640e6i			0.548296i	0.961688	+	0.274148i	$0.0883958\pi$
$389$			1.63640e6i			0.548296i	−0.961688	+	0.274148i	$0.911604\pi$
$390$	−652584.	+	81420.9i	−0.217257	+	0.0271065i
$391$			2.88805e6i			0.955351i
$392$	−1.31097e6	+	512065.i	−0.430902	+	0.168310i
$393$			656231.i			0.214326i
$394$	−653293.	−	5.23611e6i	−0.212015	−	1.69929i
$395$			251074.i			0.0809671i
$396$	2.07745e6	−	526591.i	0.665720	−	0.168747i
$397$		−	2.66069e6i		−	0.847261i	−0.905835	−	0.423631i	$-0.860755\pi$
$397$		−	2.66069e6i		−	0.847261i	0.905835	−	0.423631i	$-0.139245\pi$
$398$	110947.	+	889238.i	0.0351083	+	0.281391i
$399$	−279931.	−	611480.i	−0.0880275	−	0.192287i
$400$	−5.03818e6	+	2.72953e6i	−1.57443	+	0.852979i
$401$			4.45829e6i			1.38454i	0.721636	+	0.692272i	$0.243390\pi$
$401$			4.45829e6i			1.38454i	−0.721636	+	0.692272i	$0.756610\pi$
$402$	−1.11485e6	+	139097.i	−0.344075	+	0.0429291i
$403$	961354.			0.294863
$404$	19970.1	+	78784.0i	0.00608734	+	0.0240151i
$405$		−	4.17575e6i		−	1.26502i
$406$	−233534.	−	1.87176e6i	−0.0703130	−	0.563555i
$407$	−1.63079e6			−0.487991
$408$	384183.	+	983573.i	0.114258	+	0.292521i
$409$		−	4.62121e6i		−	1.36599i	−0.730424	−	0.682994i	$-0.760677\pi$
$409$		−	4.62121e6i		−	1.36599i	0.730424	−	0.682994i	$-0.239323\pi$
$410$	1.04703e7	−	1.30634e6i	3.07609	−	0.383794i
$411$		−	295644.i		−	0.0863306i
$412$	−2.88319e6	+	730831.i	−0.836817	+	0.212116i
$413$	501119.			0.144566
$414$	347379.	+	2.78422e6i	0.0996098	+	0.798367i
$415$			5.03693e6i			1.43564i
$416$	−1.30453e6	+	932555.i	−0.369591	+	0.264205i
$417$			990832.i			0.279036i
$418$	−1.40657e6	−	2.27655e6i	−0.393749	−	0.637290i
$419$	−4.42550e6			−1.23148			−0.615740	−	0.787950i	$-0.711143\pi$
$419$	−4.42550e6			−1.23148			−0.615740	+	0.787950i	$0.711143\pi$
$420$	313807.	+	1.23800e6i	0.0868039	+	0.342449i
$421$	2.80313e6			0.770793			0.385396	−	0.922751i	$-0.374065\pi$
$421$	2.80313e6			0.770793			0.385396	+	0.922751i	$0.374065\pi$
$422$	−98653.1	−	790699.i	−0.0269668	−	0.216138i
$423$		−	893001.i		−	0.242662i
$424$	−588938.	+	230039.i	−0.159094	+	0.0621422i
$425$	7.25858e6			1.94930
$426$	−187040.	−	1.49911e6i	−0.0499356	−	0.400231i
$427$	495996.			0.131646
$428$	−1.32211e6	−	5.21583e6i	−0.348865	−	1.37630i
$429$			374257.i			0.0981808i
$430$	987654.	+	7.91599e6i	0.257593	+	2.06459i
$431$	3.60636e6			0.935137			0.467569	−	0.883957i	$-0.345130\pi$
$431$	3.60636e6			0.935137			0.467569	+	0.883957i	$0.345130\pi$
$432$	1.02171e6	+	1.88588e6i	0.263403	+	0.486190i
$433$		−	5.37862e6i		−	1.37864i	−0.724457	−	0.689320i	$-0.757909\pi$
$433$		−	5.37862e6i		−	1.37864i	0.724457	−	0.689320i	$-0.242091\pi$
$434$	−231142.	−	1.85259e6i	−0.0589054	−	0.472124i
$435$	1.47346e6			0.373350
$436$	−5.91072e6	+	1.49825e6i	−1.48910	+	0.377457i
$437$	3.18552e6	−	1.45831e6i	0.797952	−	0.365297i
$438$	−214095.	−	1.71596e6i	−0.0533239	−	0.427388i
$439$	1.29172e6			0.319894			0.159947	−	0.987126i	$-0.448868\pi$
$439$	1.29172e6			0.319894			0.159947	+	0.987126i	$0.448868\pi$
$440$	1.84898e6	+	4.73370e6i	0.455303	+	1.16565i
$441$	1.73210e6			0.424107
$442$	2.01571e6	−	251494.i	0.490764	−	0.0612312i
$443$	2.33522e6			0.565352			0.282676	−	0.959215i	$-0.408778\pi$
$443$	2.33522e6			0.565352			0.282676	+	0.959215i	$0.408778\pi$
$444$	−191805.	−	756688.i	−0.0461746	−	0.182163i
$445$	4.37662e6			1.04770
$446$	16638.1	−	2075.89i	0.00396066	−	0.000494159i
$447$	−1.40066e6			−0.331560
$448$	2.11075e6	+	2.28971e6i	0.496869	+	0.538995i
$449$			2.56046e6i			0.599379i	0.954037	+	0.299690i	$0.0968831\pi$
$449$			2.56046e6i			0.599379i	−0.954037	+	0.299690i	$0.903117\pi$
$450$	6.99763e6	−	873072.i	1.62899	−	0.203245i
$451$		−	6.00471e6i		−	1.39011i
$452$	−1.57867e6	−	6.22801e6i	−0.363451	−	1.43385i
$453$			772488.i			0.176867i
$454$	313579.	+	2.51331e6i	0.0714014	+	0.572278i
$455$	2.45688e6			0.556360
$456$	890889.	−	920405.i	0.200637	−	0.207284i
$457$	−2.84015e6			−0.636138			−0.318069	−	0.948068i	$-0.603034\pi$
$457$	−2.84015e6			−0.636138			−0.318069	+	0.948068i	$0.603034\pi$
$458$	69499.1	+	557031.i	0.0154816	+	0.124084i
$459$		−	2.71702e6i		−	0.601951i
$460$	−6.44937e6	+	1.63479e6i	−1.42109	+	0.360219i
$461$		−	3.23395e6i		−	0.708730i	−0.935107	−	0.354365i	$-0.884697\pi$
$461$		−	3.23395e6i		−	0.708730i	0.935107	−	0.354365i	$-0.115303\pi$
$462$	721218.	−	89984.2i	0.157203	−	0.0196138i
$463$			8.68840e6i			1.88360i	0.336180	+	0.941798i	$0.390865\pi$
$463$			8.68840e6i			1.88360i	−0.336180	+	0.941798i	$0.609135\pi$
$464$	3.15903e6	−	1.71146e6i	0.681174	−	0.369039i
$465$	1.45837e6			0.312778
$466$	−6.61433e6	+	825249.i	−1.41098	+	0.176044i
$467$	−7.68880e6			−1.63142			−0.815711	−	0.578459i	$-0.803654\pi$
$467$	−7.68880e6			−1.63142			−0.815711	+	0.578459i	$0.803654\pi$
$468$	1.91299e6	−	484905.i	0.403737	−	0.102339i
$469$	4.19726e6			0.881117
$470$	2.10126e6	−	262168.i	0.438768	−	0.0547437i
$471$	271227.			0.0563354
$472$	347275.	+	889080.i	0.0717493	+	0.183690i
$473$	4.53982e6			0.933009
$474$	8467.73	+	67868.4i	0.00173110	+	0.0138746i
$475$	−3.66519e6	−	8.00622e6i	−0.745353	−	1.62815i
$476$	−969292.	−	3.82394e6i	−0.196082	−	0.773560i
$477$	778123.			0.156586
$478$	−817228.	−	6.55003e6i	−0.163596	−	1.31121i
$479$		−	6.32466e6i		−	1.25950i	−0.776797	−	0.629751i	$-0.783157\pi$
$479$		−	6.32466e6i		−	1.25950i	0.776797	−	0.629751i	$-0.216843\pi$
$480$	−1.97897e6	+	1.41468e6i	−0.392046	+	0.280257i
$481$	−1.50170e6			−0.295951
$482$	−715597.	−	5.73547e6i	−0.140298	−	1.12448i
$483$			951539.i			0.185592i
$484$	−2.19220e6	+	555678.i	−0.425370	+	0.107823i
$485$	−7.60073e6			−1.46724
$486$	−497305.	−	3.98587e6i	−0.0955063	−	0.765478i
$487$	−1.68772e6			−0.322462			−0.161231	−	0.986917i	$-0.551546\pi$
$487$	−1.68772e6			−0.322462			−0.161231	+	0.986917i	$0.551546\pi$
$488$	343724.	+	879992.i	0.0653373	+	0.167274i
$489$			605828.i			0.114572i
$490$	508510.	+	4.07568e6i	0.0956773	+	0.766848i
$491$	−4.39190e6			−0.822146			−0.411073	−	0.911602i	$-0.634846\pi$
$491$	−4.39190e6			−0.822146			−0.411073	+	0.911602i	$0.634846\pi$
$492$	2.78619e6	−	706242.i	0.518917	−	0.131535i
$493$	−4.55126e6			−0.843362
$494$	−1.29522e6	−	2.09634e6i	−0.238796	−	0.386495i
$495$		−	6.25431e6i		−	1.14727i
$496$	3.12667e6	−	1.69393e6i	0.570661	−	0.309167i
$497$			5.64394e6i			1.02492i
$498$	169876.	+	1.36154e6i	0.0306943	+	0.246013i
$499$	5.21260e6			0.937137			0.468568	−	0.883427i	$-0.344770\pi$
$499$	5.21260e6			0.937137			0.468568	+	0.883427i	$0.344770\pi$
$500$	1.81418e6	+	7.15709e6i	0.324530	+	1.28030i
$501$			2.06545e6i			0.367638i
$502$	4.41736e6	−	551141.i	0.782355	−	0.0976121i
$503$			1.33359e6i			0.235018i	0.993072	+	0.117509i	$0.0374909\pi$
$503$			1.33359e6i			0.235018i	−0.993072	+	0.117509i	$0.962509\pi$
$504$	−1.39439e6	−	3.56988e6i	−0.244517	−	0.626004i
$505$	237185.			0.0413865
$506$	468775.	+	3.75721e6i	0.0813932	+	0.652362i
$507$		−	1.32507e6i		−	0.228939i
$508$	−1.11781e7	+	2.83343e6i	−1.92180	+	0.487139i
$509$	960938.			0.164400			0.0821998	−	0.996616i	$-0.473805\pi$
$509$	960938.			0.164400			0.0821998	+	0.996616i	$0.473805\pi$
$510$	3.05783e6	−	381516.i	0.520580	−	0.0649512i
$511$			6.46034e6i			1.09447i
$512$	−2.59963e6	+	5.33163e6i	−0.438264	+	0.898846i
$513$	−2.99687e6	+	1.37195e6i	−0.502777	+	0.230167i
$514$	−476927.	−	3.82254e6i	−0.0796240	−	0.638182i
$515$			8.68007e6i			1.44213i
$516$	533950.	+	2.10648e6i	0.0882829	+	0.348284i
$517$		−	1.20507e6i		−	0.198284i
$518$	361059.	+	2.89387e6i	0.0591226	+	0.473865i
$519$			1.14575e6i			0.186711i
$520$	1.70261e6	+	4.35898e6i	0.276126	+	0.706930i
$521$		−	1.08312e7i		−	1.74816i	−0.485782	−	0.874080i	$-0.661465\pi$
$521$		−	1.08312e7i		−	1.74816i	0.485782	−	0.874080i	$-0.338535\pi$
$522$	−4.38763e6	+	547431.i	−0.704780	+	0.0879333i
$523$			3.86911e6i			0.618524i	0.950977	+	0.309262i	$0.100082\pi$
$523$			3.86911e6i			0.618524i	−0.950977	+	0.309262i	$0.899918\pi$
$524$	4.52649e6	−	1.14737e6i	0.720168	−	0.182548i
$525$	2.39152e6			0.378683
$526$	−492117.	−	3.94429e6i	−0.0775540	−	0.621591i
$527$	−4.50464e6			−0.706535
$528$	659452.	+	1.21722e6i	0.102943	+	0.190013i
$529$	1.47928e6			0.229832
$530$	228442.	+	1.83095e6i	0.0353253	+	0.283130i
$531$		−	1.17468e6i		−	0.180794i
$532$	−3.72837e6	+	3.00001e6i	−0.571136	+	0.459562i
$533$		−	5.52937e6i		−	0.843058i
$534$	1.18305e6	−	147606.i	0.179536	−	0.0224002i
$535$	−1.57026e7			−2.37186
$536$	2.90869e6	+	7.44674e6i	0.437306	+	1.11958i
$537$	−2.77316e6			−0.414992
$538$	5.35716e6	−	668397.i	0.797957	−	0.0995586i
$539$	2.33740e6			0.346546
$540$	6.06744e6	−	1.53797e6i	0.895409	−	0.226968i
$541$		−	9.20084e6i		−	1.35156i	−0.737105	−	0.675779i	$-0.763807\pi$
$541$		−	9.20084e6i		−	1.35156i	0.737105	−	0.675779i	$-0.236193\pi$
$542$	915642.	+	7.33882e6i	0.133884	+	1.07307i
$543$			2.21946e6i			0.323034i
$544$	6.11269e6	−	4.36970e6i	0.885595	−	0.633073i
$545$			1.77947e7i			2.56625i
$546$	664126.	−	82860.9i	0.0953386	−	0.0118951i
$547$			1.36673e7i			1.95306i	0.215380	+	0.976530i	$0.430901\pi$
$547$			1.36673e7i			1.95306i	−0.215380	+	0.976530i	$0.569099\pi$
$548$	−2.03927e6	+	516913.i	−0.290083	+	0.0735302i
$549$		−	1.16267e6i		−	0.164637i
$550$	9.44305e6	−	1.17818e6i	1.33108	−	0.166075i
$551$	2.29813e6	+	5.02003e6i	0.322475	+	0.704413i
$552$	−1.68821e6	+	659415.i	−0.235819	+	0.0921109i
$553$		−	255515.i		−	0.0355306i
$554$	−1.62639e6	−	1.30354e7i	−0.225139	−	1.80447i
$555$	−2.27807e6			−0.313931
$556$	6.83447e6	−	1.73240e6i	0.937601	−	0.237663i
$557$			4.93456e6i			0.673923i	0.941518	+	0.336962i	$0.109399\pi$
$557$			4.93456e6i			0.673923i	−0.941518	+	0.336962i	$0.890601\pi$
$558$	−4.34269e6	+	541824.i	−0.590437	+	0.0736670i
$559$	4.18045e6			0.565839
$560$	7.99067e6	−	4.32910e6i	1.07675	−	0.583348i
$561$		−	1.75367e6i		−	0.235255i
$562$	1.14169e6	+	9.15062e6i	0.152479	+	1.22211i
$563$			4.87905e6i			0.648730i	0.945932	+	0.324365i	$0.105151\pi$
$563$			4.87905e6i			0.648730i	−0.945932	+	0.324365i	$0.894849\pi$
$564$	559155.	−	141734.i	0.0740175	−	0.0187619i
$565$	−1.87499e7			−2.47103
$566$	−4.61016e6	+	575195.i	−0.604888	+	0.0754700i
$567$			4.24961e6i			0.555125i
$568$	−1.00134e7	+	3.91124e6i	−1.30230	+	0.508679i
$569$			3.03918e6i			0.393528i	0.980451	+	0.196764i	$0.0630433\pi$
$569$			3.03918e6i			0.393528i	−0.980451	+	0.196764i	$0.936957\pi$
$570$	−1.96485e6	−	3.18014e6i	−0.253304	−	0.409977i
$571$	715082.			0.0917837			0.0458919	−	0.998946i	$-0.485387\pi$
$571$	715082.			0.0917837			0.0458919	+	0.998946i	$0.485387\pi$
$572$	2.58152e6	−	654362.i	0.329902	−	0.0836235i
$573$	3.77423e6			0.480222
$574$	−1.06555e7	+	1.32945e6i	−1.34987	+	0.168419i
$575$			1.24587e7i			1.57146i
$576$	5.36733e6	−	4.94784e6i	0.674066	−	0.621383i
$577$	−7.57765e6			−0.947534			−0.473767	−	0.880650i	$-0.657106\pi$
$577$	−7.57765e6			−0.947534			−0.473767	+	0.880650i	$0.657106\pi$
$578$	−1.47495e6	+	184025.i	−0.183636	+	0.0229117i
$579$	−382415.			−0.0474065
$580$	−2.57624e6	−	1.01635e7i	−0.317993	−	1.25451i
$581$		−	5.12601e6i		−	0.629998i
$582$	−2.05457e6	+	256343.i	−0.251428	+	0.0313699i
$583$	1.05005e6			0.127949
$584$	−1.14619e7	+	4.47701e6i	−1.39067	+	0.543195i
$585$		−	5.75921e6i		−	0.695783i
$586$	−1.25249e7	+	1.56269e6i	−1.50671	+	0.187987i
$587$	7.04413e6			0.843785			0.421893	−	0.906646i	$-0.361366\pi$
$587$	7.04413e6			0.843785			0.421893	+	0.906646i	$0.361366\pi$
$588$	274913.	+	1.08456e6i	0.0327908	+	0.129363i
$589$	2.27460e6	+	4.96862e6i	0.270157	+	0.590130i
$590$	2.76406e6	−	344863.i	0.326902	−	0.0407865i
$591$	−4.19479e6			−0.494017
$592$	−4.88406e6	+	2.64603e6i	−0.572765	+	0.310307i
$593$	−1.54904e7			−1.80895			−0.904473	−	0.426531i	$-0.859736\pi$
$593$	−1.54904e7			−1.80895			−0.904473	+	0.426531i	$0.859736\pi$
$594$	−441014.	−	3.53471e6i	−0.0512846	−	0.411043i
$595$	−1.15123e7			−1.33312
$596$	2.44895e6	+	9.66132e6i	0.282400	+	1.11409i
$597$	712393.			0.0818058
$598$	431666.	+	3.45978e6i	0.0493623	+	0.395636i
$599$	−8.16729e6			−0.930059			−0.465030	−	0.885295i	$-0.653956\pi$
$599$	−8.16729e6			−0.930059			−0.465030	+	0.885295i	$0.653956\pi$
$600$	1.65732e6	+	4.24301e6i	0.187944	+	0.481167i
$601$		−	5.00996e6i		−	0.565781i	−0.959152	−	0.282891i	$-0.908707\pi$
$601$		−	5.00996e6i		−	0.565781i	0.959152	−	0.282891i	$-0.0912933\pi$
$602$	−1.00512e6	−	8.05600e6i	−0.113039	−	0.906000i
$603$		−	9.83886e6i		−	1.10192i
$604$	5.32840e6	−	1.35064e6i	0.594298	−	0.150642i
$605$			6.59979e6i			0.733063i
$606$	64114.1	−	7999.32i	0.00709205	−	0.000884854i
$607$	1.30779e7			1.44068			0.720338	−	0.693623i	$-0.243987\pi$
$607$	1.30779e7			1.44068			0.720338	+	0.693623i	$0.243987\pi$
$608$	−7.90635e6	−	4.53583e6i	−0.867395	−	0.497621i
$609$	−1.49952e6			−0.163836
$610$	2.73580e6	−	341338.i	0.297687	−	0.0371415i
$611$		−	1.10968e6i		−	0.120252i
$612$	−8.96377e6	+	2.27213e6i	−0.967413	+	0.245220i
$613$			3.44034e6i			0.369785i	0.982759	+	0.184893i	$0.0591937\pi$
$613$			3.44034e6i			0.369785i	−0.982759	+	0.184893i	$0.940806\pi$
$614$	−1.28053e6	−	1.02633e7i	−0.137078	−	1.09867i
$615$		−	8.38803e6i		−	0.894278i
$616$	−1.88168e6	−	4.81742e6i	−0.199800	−	0.511521i
$617$	−1.31680e7			−1.39254			−0.696269	−	0.717781i	$-0.745158\pi$
$617$	−1.31680e7			−1.39254			−0.696269	+	0.717781i	$0.745158\pi$
$618$	292744.	+	2.34633e6i	0.0308331	+	0.247126i
$619$	1.10190e7			1.15589			0.577945	−	0.816076i	$-0.303855\pi$
$619$	1.10190e7			1.15589			0.577945	+	0.816076i	$0.303855\pi$
$620$	−2.54986e6	−	1.00594e7i	−0.266402	−	1.05098i
$621$	4.66351e6			0.485271
$622$	−1.33466e6	−	1.06972e7i	−0.138323	−	1.10865i
$623$	−4.45403e6			−0.459762
$624$	607249.	+	1.12086e6i	0.0624317	+	0.115237i
$625$	4.06021e6			0.415765
$626$	1.30117e7	−	1.62343e6i	1.32709	−	0.165577i
$627$	−1.93429e6	+	885505.i	−0.196496	+	0.0899544i
$628$	−474222.	−	1.87085e6i	−0.0479825	−	0.189295i
$629$	7.03653e6			0.709140
$630$	−1.10984e7	+	1.38471e6i	−1.11406	+	0.138998i
$631$			6.53113e6i			0.653003i	0.945197	+	0.326501i	$0.105870\pi$
$631$			6.53113e6i			0.653003i	−0.945197	+	0.326501i	$0.894130\pi$
$632$	453331.	−	177071.i	0.0451464	−	0.0176342i
$633$	−633452.			−0.0628354
$634$	1.58523e7	−	1.97784e6i	1.56628	−	0.195420i
$635$			3.36526e7i			3.31195i
$636$	123501.	+	487224.i	0.0121068	+	0.0477623i
$637$	2.15237e6			0.210169
$638$	−5.92095e6	+	738739.i	−0.575890	+	0.0718520i
$639$	1.32300e7			1.28177
$640$	1.32182e7	+	1.11769e7i	1.27562	+	1.07863i
$641$			1.26861e7i			1.21950i	0.792594	+	0.609750i	$0.208730\pi$
$641$			1.26861e7i			1.21950i	−0.792594	+	0.609750i	$0.791270\pi$
$642$	−4.24462e6	+	529588.i	−0.406444	+	0.0507108i
$643$	8.74310e6			0.833946			0.416973	−	0.908919i	$-0.363091\pi$
$643$	8.74310e6			0.833946			0.416973	+	0.908919i	$0.363091\pi$
$644$	6.56344e6	−	1.66370e6i	0.623616	−	0.158074i
$645$	6.34172e6			0.600216
$646$	6.06906e6	+	9.82287e6i	0.572190	+	0.926099i
$647$			2.39445e6i			0.224877i	0.993659	+	0.112438i	$0.0358661\pi$
$647$			2.39445e6i			0.224877i	−0.993659	+	0.112438i	$0.964134\pi$
$648$	−7.53961e6	+	2.94497e6i	−0.705361	+	0.275514i
$649$		−	1.58519e6i		−	0.147730i
$650$	8.69552e6	−	1.08491e6i	0.807258	−	0.100719i
$651$	−1.48416e6			−0.137255
$652$	4.17883e6	−	1.05925e6i	0.384978	−	0.0975840i
$653$		−	4.14995e6i		−	0.380855i	−0.981701	−	0.190428i	$-0.939013\pi$
$653$		−	4.14995e6i		−	0.380855i	0.981701	−	0.190428i	$-0.0609874\pi$
$654$	600145.	+	4.81013e6i	0.0548670	+	0.439756i
$655$		−	1.36273e7i		−	1.24110i
$656$	−9.74291e6	−	1.79835e7i	−0.883953	−	1.63160i
$657$	1.51438e7			1.36874
$658$	−2.13842e6	+	266805.i	−0.192544	+	0.0240231i
$659$		−	1.08924e7i		−	0.977036i	−0.872554	−	0.488518i	$-0.837538\pi$
$659$		−	1.08924e7i		−	0.977036i	0.872554	−	0.488518i	$-0.162462\pi$
$660$	3.91615e6	−	992665.i	0.349945	−	0.0887039i
$661$	−3.44356e6			−0.306552			−0.153276	−	0.988183i	$-0.548982\pi$
$661$	−3.44356e6			−0.306552			−0.153276	+	0.988183i	$0.548982\pi$
$662$	−1.61603e6	−	1.29524e7i	−0.143319	−	1.14870i
$663$		−	1.61484e6i		−	0.142675i
$664$	9.09452e6	−	3.55232e6i	0.800497	−	0.312674i
$665$	5.81307e6	+	1.26980e7i	0.509743	+	1.11348i
$666$	6.78356e6	−	846364.i	0.592614	−	0.0739386i
$667$		−	7.81180e6i		−	0.679887i
$668$	1.42469e7	−	3.61129e6i	1.23532	−	0.313128i
$669$		−	13329.3i		−	0.00115144i
$670$	2.31511e7	−	2.88850e6i	1.99244	−	0.248591i
$671$		−	1.56898e6i		−	0.134528i
$672$	2.01397e6	−	1.43970e6i	0.172041	−	0.122984i
$673$		−	1.24306e7i		−	1.05792i	−0.848645	−	0.528962i	$-0.822581\pi$
$673$		−	1.24306e7i		−	1.05792i	0.848645	−	0.528962i	$-0.177419\pi$
$674$	860213.	+	6.89456e6i	0.0729384	+	0.584597i
$675$		−	1.17209e7i		−	0.990150i
$676$	−9.13997e6	+	2.31680e6i	−0.769269	+	0.194994i
$677$	−1.41359e7			−1.18536			−0.592681	−	0.805437i	$-0.701931\pi$
$677$	−1.41359e7			−1.18536			−0.592681	+	0.805437i	$0.701931\pi$
$678$	−5.06833e6	+	632360.i	−0.423439	+	0.0528311i
$679$	7.73516e6			0.643865
$680$	−7.97799e6	−	2.04250e7i	−0.661639	−	1.69391i
$681$	2.01349e6			0.166372
$682$	−5.86031e6	+	731173.i	−0.482458	+	0.0601948i
$683$			1.02525e7i			0.840967i	0.907300	+	0.420484i	$0.138140\pi$
$683$			1.02525e7i			0.840967i	−0.907300	+	0.420484i	$0.861860\pi$
$684$	7.03237e6	+	8.73973e6i	0.574727	+	0.714262i
$685$			6.13937e6i			0.499916i
$686$	−1.63617e6	−	1.31138e7i	−0.132745	−	1.06395i
$687$	446254.			0.0360736
$688$	1.35963e7	−	7.36607e6i	1.09509	−	0.593287i
$689$	966927.			0.0775971
$690$	654836.	+	5.24848e6i	0.0523612	+	0.419672i
$691$	−2.17104e6			−0.172971			−0.0864854	−	0.996253i	$-0.527564\pi$
$691$	−2.17104e6			−0.172971			−0.0864854	+	0.996253i	$0.527564\pi$
$692$	7.90304e6	−	2.00326e6i	0.627378	−	0.159027i
$693$			6.36493e6i			0.503455i
$694$	−4.96453e6	+	619410.i	−0.391273	+	0.0488179i
$695$		−	2.05757e7i		−	1.61582i
$696$	−1.03917e6	−	2.66044e6i	−0.0813134	−	0.208176i
$697$			2.59091e7i			2.02009i
$698$	−1.06045e6	−	8.49948e6i	−0.0823859	−	0.660319i
$699$			5.29892e6i			0.410199i
$700$	−4.18140e6	−	1.64960e7i	−0.322535	−	1.27243i
$701$			1.47483e7i			1.13357i	0.823866	+	0.566785i	$0.191813\pi$
$701$			1.47483e7i			1.13357i	−0.823866	+	0.566785i	$0.808187\pi$
$702$	−406103.	−	3.25489e6i	−0.0311024	−	0.249284i
$703$	−3.55306e6	−	7.76130e6i	−0.271153	−	0.592306i
$704$	7.24302e6	−	6.67693e6i	0.550793	−	0.507745i
$705$		−	1.68338e6i		−	0.127558i
$706$	5.18962e6	−	647493.i	0.391853	−	0.0488903i
$707$	−241380.			−0.0181616
$708$	735529.	−	186442.i	0.0551463	−	0.0139785i
$709$			579292.i			0.0432795i	0.999766	+	0.0216397i	$0.00688868\pi$
$709$			579292.i			0.0432795i	−0.999766	+	0.0216397i	$0.993111\pi$
$710$	3.88408e6	+	3.11307e7i	0.289163	+	2.31762i
$711$	−598955.			−0.0444345
$712$	−3.08663e6	−	7.90229e6i	−0.228184	−	0.584189i
$713$		−	7.73180e6i		−	0.569582i
$714$	−3.11191e6	+	388264.i	−0.228445	+	0.0285024i
$715$		−	7.77185e6i		−	0.568538i
$716$	4.84868e6	+	1.91285e7i	0.353461	+	1.39443i
$717$	−5.24742e6			−0.381195
$718$	2.50727e6	+	2.00957e7i	0.181506	+	1.45476i
$719$		−	2.45890e7i		−	1.77386i	−0.461906	−	0.886929i	$-0.652834\pi$
$719$		−	2.45890e7i		−	1.77386i	0.461906	−	0.886929i	$-0.347166\pi$
$720$	−1.01479e7	−	1.87310e7i	−0.729533	−	1.34658i
$721$		−	8.83359e6i		−	0.632848i
$722$	7.77008e6	−	1.16542e7i	0.554731	−	0.832030i
$723$	−4.59485e6			−0.326908
$724$	1.53092e7	−	3.88057e6i	1.08544	−	0.275137i
$725$	−1.96335e7			−1.38725
$726$	222585.	+	1.78400e6i	0.0156731	+	0.125619i
$727$		−	1.45708e7i		−	1.02246i	−0.859443	−	0.511232i	$-0.829189\pi$
$727$		−	1.45708e7i		−	1.02246i	0.859443	−	0.511232i	$-0.170811\pi$
$728$	−1.73273e6	−	4.43607e6i	−0.121172	−	0.310220i
$729$	7.67265e6			0.534720
$730$	4.44592e6	+	3.56338e7i	0.308784	+	2.47488i
$731$	−1.95884e7			−1.35583
$732$	728010.	−	184536.i	0.0502180	−	0.0127292i
$733$		−	1.87450e6i		−	0.128862i	−0.997922	−	0.0644311i	$-0.979477\pi$
$733$		−	1.87450e6i		−	0.128862i	0.997922	−	0.0644311i	$-0.0205233\pi$
$734$	−946542.	−	7.58648e6i	−0.0648485	−	0.519757i
$735$	3.26514e6			0.222938
$736$	7.50017e6	+	1.04919e7i	0.510360	+	0.713933i
$737$		−	1.32772e7i		−	0.900404i
$738$	3.11638e6	+	2.49776e7i	0.210625	+	1.68815i
$739$	−1.58113e7			−1.06502			−0.532508	−	0.846425i	$-0.678750\pi$
$739$	−1.58113e7			−1.06502			−0.532508	+	0.846425i	$0.678750\pi$
$740$	3.98304e6	+	1.57134e7i	0.267384	+	1.05485i
$741$	−1.78117e6	+	815408.i	−0.119168	+	0.0545543i
$742$	−232482.	−	1.86333e6i	−0.0155017	−	0.124245i
$743$	1.94622e7			1.29336			0.646680	−	0.762761i	$-0.276157\pi$
$743$	1.94622e7			1.29336			0.646680	+	0.762761i	$0.276157\pi$
$744$	−1.02852e6	−	2.63319e6i	−0.0681211	−	0.174401i
$745$	2.90861e7			1.91997
$746$	−2.73845e7	+	3.41667e6i	−1.80159	+	0.224779i
$747$	−1.20160e7			−0.787875
$748$	−1.20963e7	+	3.06616e6i	−0.790493	+	0.200374i
$749$	1.59804e7			1.04084
$750$	5.82442e6	−	726695.i	0.378094	−	0.0471736i
$751$	−2.18798e7			−1.41561			−0.707804	−	0.706409i	$-0.750314\pi$
$751$	−2.18798e7			−1.41561			−0.707804	+	0.706409i	$0.750314\pi$
$752$	−1.95529e6	−	3.60907e6i	−0.126086	−	0.232729i
$753$		−	3.53887e6i		−	0.227446i
$754$	−5.45224e6	+	680259.i	−0.349258	+	0.0435759i
$755$		−	1.60415e7i		−	1.02419i
$756$	−6.17476e6	+	1.56518e6i	−0.392930	+	0.0995999i
$757$		−	2.59831e7i		−	1.64797i	−0.566608	−	0.823987i	$-0.691745\pi$
$757$		−	2.59831e7i		−	1.64797i	0.566608	−	0.823987i	$-0.308255\pi$
$758$	−1.48665e6	−	1.19155e7i	−0.0939804	−	0.753247i
$759$	3.01000e6			0.189654
$760$	−1.85003e7	+	1.91132e7i	−1.16183	+	1.20033i
$761$	−1.42185e7			−0.890006			−0.445003	−	0.895529i	$-0.646797\pi$
$761$	−1.42185e7			−0.890006			−0.445003	+	0.895529i	$0.646797\pi$
$762$	1.13497e6	+	9.09671e6i	0.0708103	+	0.567540i
$763$		−	1.81094e7i		−	1.12614i
$764$	−6.59898e6	−	2.60336e7i	−0.409019	−	1.61362i
$765$			2.69861e7i			1.66720i
$766$	2.84482e6	−	354939.i	0.175179	−	0.0218566i
$767$		−	1.45970e6i		−	0.0895935i
$768$	3.94999e6	+	2.57546e6i	0.241653	+	0.157562i
$769$	1.06124e7			0.647142			0.323571	−	0.946204i	$-0.395117\pi$
$769$	1.06124e7			0.647142			0.323571	+	0.946204i	$0.395117\pi$
$770$	−1.49769e7	+	1.86862e6i	−0.910321	+	0.113578i
$771$	−3.06235e6			−0.185532
$772$	668625.	+	2.63779e6i	0.0403775	+	0.159293i
$773$	−2.24785e7			−1.35306			−0.676531	−	0.736414i	$-0.736517\pi$
$773$	−2.24785e7			−1.35306			−0.676531	+	0.736414i	$0.736517\pi$
$774$	−1.88842e7	+	2.35612e6i	−1.13304	+	0.141366i
$775$	−1.94325e7			−1.16218
$776$	5.36045e6	+	1.37236e7i	0.319556	+	0.818117i
$777$	2.31836e6			0.137762
$778$	−1.14606e6	−	9.18565e6i	−0.0678829	−	0.544078i
$779$	2.85777e7	−	1.30827e7i	1.68727	−	0.772419i
$780$	3.60615e6	−	914085.i	0.212230	−	0.0537960i
$781$	1.78535e7			1.04736
$782$	−2.02267e6	−	1.62116e7i	−0.118279	−	0.948001i
$783$			7.34919e6i			0.428386i
$784$	7.00029e6	−	3.79254e6i	0.406748	−	0.220364i
$785$	−5.63233e6			−0.326223
$786$	−459597.	−	3.68364e6i	−0.0265351	−	0.212677i
$787$			3.06719e7i			1.76524i	0.470088	+	0.882619i	$0.344222\pi$
$787$			3.06719e7i			1.76524i	−0.470088	+	0.882619i	$0.655778\pi$
$788$	7.33430e6	+	2.89345e7i	0.420768	+	1.65997i
$789$	−3.15988e6			−0.180709
$790$	−175842.	−	1.40936e6i	−0.0100243	−	0.0803442i
$791$	1.90815e7			1.08435
$792$	−1.12926e7	+	4.41088e6i	−0.639707	+	0.249869i
$793$		−	1.44478e6i		−	0.0815867i
$794$	1.86343e6	+	1.49353e7i	0.104897	+	0.840743i
$795$	1.46682e6			0.0823114
$796$	−1.24557e6	−	4.91388e6i	−0.0696764	−	0.274879i
$797$	2.18608e7			1.21905			0.609524	−	0.792767i	$-0.291360\pi$
$797$	2.18608e7			1.21905			0.609524	+	0.792767i	$0.291360\pi$
$798$	1.99960e6	+	3.23639e6i	0.111157	+	0.179909i
$799$			5.19965e6i			0.288142i
$800$	2.63693e7	−	1.88503e7i	1.45671	−	1.04134i
$801$			1.04408e7i			0.574977i
$802$	−3.12240e6	−	2.50258e7i	−0.171416	−	1.37389i
$803$	2.04360e7			1.11843
$804$	6.16062e6	−	1.56159e6i	0.336112	−	0.0851977i
$805$		−	1.97597e7i		−	1.07471i
$806$	−5.39640e6	+	673292.i	−0.292595	+	0.0365062i
$807$		−	4.29178e6i		−	0.231981i
$808$	−167276.	−	428254.i	−0.00901375	−	0.0230767i
$809$	−2.05190e7			−1.10226			−0.551131	−	0.834419i	$-0.685803\pi$
$809$	−2.05190e7			−1.10226			−0.551131	+	0.834419i	$0.685803\pi$
$810$	2.92452e6	+	2.34399e7i	0.156618	+	1.25529i
$811$		−	8.82513e6i		−	0.471160i	−0.971855	−	0.235580i	$-0.924301\pi$
$811$		−	8.82513e6i		−	0.471160i	0.971855	−	0.235580i	$-0.0756990\pi$
$812$	2.62181e6	+	1.03433e7i	0.139544	+	0.550513i
$813$	5.87933e6			0.311962
$814$	9.15417e6	−	1.14214e6i	0.484237	−	0.0604168i
$815$		−	1.25807e7i		−	0.663453i
$816$	−2.84540e6	−	5.25206e6i	−0.149595	−	0.276124i
$817$	9.89108e6	+	2.16060e7i	0.518428	+	1.13245i
$818$	3.23650e6	+	2.59404e7i	0.169119	+	1.35548i
$819$			5.86108e6i			0.305329i
$820$	−5.78582e7	+	1.46659e7i	−3.00490	+	0.761682i
$821$			2.37349e7i			1.22894i	0.788942	+	0.614468i	$0.210629\pi$
$821$			2.37349e7i			1.22894i	−0.788942	+	0.614468i	$0.789371\pi$
$822$	207057.	+	1.65955e6i	0.0106883	+	0.0856664i
$823$			2.05277e7i			1.05643i	0.849110	+	0.528215i	$0.177139\pi$
$823$			2.05277e7i			1.05643i	−0.849110	+	0.528215i	$0.822861\pi$
$824$	1.56725e7	−	6.12166e6i	0.804117	−	0.314088i
$825$		−	7.56509e6i		−	0.386972i
$826$	−2.81295e6	+	350963.i	−0.143454	+	0.0178983i
$827$			3.05316e7i			1.55234i	0.630526	+	0.776168i	$0.282839\pi$
$827$			3.05316e7i			1.55234i	−0.630526	+	0.776168i	$0.717161\pi$
$828$	−3.89990e6	−	1.53855e7i	−0.197687	−	0.779892i
$829$	2.25540e6			0.113982			0.0569911	−	0.998375i	$-0.481849\pi$
$829$	2.25540e6			0.113982			0.0569911	+	0.998375i	$0.481849\pi$
$830$	−3.52765e6	−	2.82739e7i	−0.177742	−	1.42459i
$831$	−1.04430e7			−0.524595
$832$	6.66966e6	−	6.14838e6i	0.334038	−	0.307930i
$833$	−1.00854e7			−0.503595
$834$	−693937.	−	5.56187e6i	−0.0345466	−	0.276889i
$835$		−	4.28913e7i		−	2.12889i
$836$	9.48993e6	+	1.17939e7i	0.469621	+	0.583638i
$837$			7.27392e6i			0.358885i
$838$	2.48418e7	−	3.09943e6i	1.22200	−	0.152466i
$839$	1.74935e7			0.857969			0.428984	−	0.903312i	$-0.358872\pi$
$839$	1.74935e7			0.857969			0.428984	+	0.903312i	$0.358872\pi$
$840$	−2.62854e6	−	6.72951e6i	−0.128534	−	0.329067i
$841$	−8.20059e6			−0.399812
$842$	−1.57349e7	+	1.96319e6i	−0.764862	+	0.0954295i
$843$	7.33082e6			0.355290
$844$	1.10755e6	+	4.36937e6i	0.0535187	+	0.211136i
$845$			2.75166e7i			1.32572i
$846$	625420.	+	5.01271e6i	0.0300432	+	0.240795i
$847$		−	6.71652e6i		−	0.321688i
$848$	3.14480e6	−	1.70375e6i	0.150177	−	0.0813612i
$849$			3.69333e6i			0.175852i
$850$	−4.07448e7	+	5.08361e6i	−1.93431	+	0.241338i
$851$			1.20776e7i			0.571683i
$852$	2.09983e6	+	8.28402e6i	0.0991027	+	0.390969i
$853$			3.59976e7i			1.69395i	0.531631	+	0.846976i	$0.321579\pi$
$853$			3.59976e7i			1.69395i	−0.531631	+	0.846976i	$0.678421\pi$
$854$	−2.78419e6	+	347375.i	−0.130633	+	0.0162987i
$855$	2.97657e7	−	1.36265e7i	1.39252	−	0.637484i
$856$	1.10744e7	+	2.83522e7i	0.516576	+	1.32252i
$857$		−	1.66793e7i		−	0.775758i	−0.921710	−	0.387879i	$-0.873208\pi$
$857$		−	1.66793e7i		−	0.775758i	0.921710	−	0.387879i	$-0.126792\pi$
$858$	−262114.	−	2.10083e6i	−0.0121555	−	0.0974255i
$859$	3.05812e7			1.41407			0.707036	−	0.707178i	$-0.250032\pi$
$859$	3.05812e7			1.41407			0.707036	+	0.707178i	$0.250032\pi$
$860$	−1.10881e7	−	4.37434e7i	−0.511222	−	2.01681i
$861$			8.53639e6i			0.392434i
$862$	−2.02437e7	+	2.52574e6i	−0.927943	+	0.115777i
$863$	2.23026e7			1.01936			0.509682	−	0.860363i	$-0.329763\pi$
$863$	2.23026e7			1.01936			0.509682	+	0.860363i	$0.329763\pi$
$864$	−7.05602e6	−	9.87053e6i	−0.321570	−	0.449838i
$865$		−	2.37927e7i		−	1.08119i
$866$	3.76696e6	+	3.01920e7i	0.170685	+	1.36803i
$867$			1.18162e6i			0.0533864i
$868$	2.59496e6	+	1.02373e7i	0.116904	+	0.461199i
$869$	−808269.			−0.0363083
$870$	−8.27103e6	+	1.03195e6i	−0.370477	+	0.0462233i
$871$		−	1.22262e7i		−	0.546065i
$872$	3.21295e7	−	1.25498e7i	1.43091	−	0.558914i
$873$		−	1.81321e7i		−	0.805216i
$874$	−1.68600e7	+	1.04170e7i	−0.746586	+	0.461278i
$875$	−2.19281e7			−0.968234
$876$	2.40358e6	+	9.48232e6i	0.105827	+	0.417498i
$877$	−4.16206e7			−1.82730			−0.913648	−	0.406505i	$-0.866747\pi$
$877$	−4.16206e7			−1.82730			−0.913648	+	0.406505i	$0.866747\pi$
$878$	−7.25083e6	+	904664.i	−0.317433	+	0.0396051i
$879$			1.00340e7i			0.438029i
$880$	−1.36942e7	−	2.52769e7i	−0.596116	−	1.10031i
$881$	−7.80431e6			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$881$	−7.80431e6			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$882$	−9.72283e6	+	1.21309e6i	−0.420844	+	0.0525074i
$883$	2.87613e7			1.24139			0.620693	−	0.784054i	$-0.286851\pi$
$883$	2.87613e7			1.24139			0.620693	+	0.784054i	$0.286851\pi$
$884$	−1.11387e7	+	2.82344e6i	−0.479408	+	0.121520i
$885$		−	2.21437e6i		−	0.0950367i
$886$	−1.31084e7	+	1.63549e6i	−0.561002	+	0.0699945i
$887$	−1.02058e7			−0.435550			−0.217775	−	0.975999i	$-0.569880\pi$
$887$	−1.02058e7			−0.435550			−0.217775	+	0.975999i	$0.569880\pi$
$888$	1.60662e6	+	4.11321e6i	0.0683723	+	0.175044i
$889$		−	3.42478e7i		−	1.45338i
$890$	−2.45674e7	+	3.06520e6i	−1.03964	+	0.129713i
$891$	1.34428e7			0.567276
$892$	−91941.5	+	23305.3i	−0.00386901	+	0.000980714i
$893$	5.73521e6	−	2.62554e6i	0.240669	−	0.110177i
$894$	7.86235e6	−	980961.i	0.329009	−	0.0410495i
$895$	5.75877e7			2.40310
$896$	−1.34520e7	−	1.13746e7i	−0.559777	−	0.473332i
$897$	2.77173e6			0.115019
$898$	−1.79324e6	−	1.43727e7i	−0.0742074	−	0.594768i
$899$	1.21845e7			0.502814
$900$	−3.86685e7	+	9.80169e6i	−1.59130	+	0.403362i
$901$	−4.53075e6			−0.185934
$902$	4.20545e6	+	3.37064e7i	0.172106	+	1.37942i
$903$	−6.45389e6			−0.263392
$904$	1.32235e7	+	3.38542e7i	0.538175	+	1.37782i
$905$		−	4.60895e7i		−	1.87060i
$906$	−541018.	−	4.33623e6i	−0.0218973	−	0.175506i
$907$		−	2.99715e7i		−	1.20974i	−0.796325	−	0.604868i	$-0.793226\pi$
$907$		−	2.99715e7i		−	1.20974i	0.796325	−	0.604868i	$-0.206774\pi$
$908$	−3.52044e6	−	1.38885e7i	−0.141704	−	0.559035i
$909$			565823.i			0.0227128i
$910$	−1.37913e7	+	1.72070e6i	−0.552079	+	0.0688813i
$911$	−3.93768e7			−1.57197			−0.785985	−	0.618246i	$-0.787844\pi$
$911$	−3.93768e7			−1.57197			−0.785985	+	0.618246i	$0.787844\pi$
$912$	−4.35624e6	+	5.79048e6i	−0.173430	+	0.230530i
$913$	−1.62151e7			−0.643788
$914$	1.59427e7	−	1.98912e6i	0.631244	−	0.0787583i
$915$		−	2.19173e6i		−	0.0865434i
$916$	−780243.	−	3.07813e6i	−0.0307250	−	0.121213i
$917$			1.38684e7i			0.544631i
$918$	1.90289e6	+	1.52515e7i	0.0745258	+	0.597320i
$919$		−	1.74439e7i		−	0.681326i	−0.940185	−	0.340663i	$-0.889348\pi$
$919$		−	1.74439e7i		−	0.681326i	0.940185	−	0.340663i	$-0.110652\pi$
$920$	3.50575e7	−	1.36935e7i	1.36556	−	0.533389i
$921$	−8.22226e6			−0.319405
$922$	2.26492e6	+	1.81532e7i	0.0877457	+	0.703277i
$923$	1.64402e7			0.635188
$924$	−3.98542e6	+	1.01022e6i	−0.153566	+	0.0389257i
$925$	3.03547e7			1.16646
$926$	−6.08500e6	−	4.87709e7i	−0.233202	−	1.86910i
$927$	−2.07069e7			−0.791438
$928$	−1.65340e7	+	1.18195e7i	−0.630244	+	0.450534i
$929$	−2.13025e7			−0.809824			−0.404912	−	0.914356i	$-0.632698\pi$
$929$	−2.13025e7			−0.809824			−0.404912	+	0.914356i	$0.632698\pi$
$930$	−8.18632e6	+	1.02138e6i	−0.310371	+	0.0387241i
$931$	5.09258e6	+	1.11242e7i	0.192559	+	0.420625i
$932$	3.65504e7	−	9.26480e6i	1.37833	−	0.349378i
$933$	−8.56982e6			−0.322305
$934$	4.31598e7	−	5.38491e6i	1.61887	−	0.201982i
$935$			3.64168e7i			1.36230i
$936$	−1.03987e7	+	4.06171e6i	−0.387961	+	0.151537i
$937$	−333669.			−0.0124156			−0.00620778	−	0.999981i	$-0.501976\pi$
$937$	−333669.			−0.0124156			−0.00620778	+	0.999981i	$0.501976\pi$
$938$	−2.35606e7	+	2.93958e6i	−0.874338	+	0.109088i
$939$		−	1.04241e7i		−	0.385810i
$940$	−1.16115e7	+	2.94327e6i	−0.428615	+	0.108645i
$941$	−4.98749e7			−1.83615			−0.918076	−	0.396405i	$-0.870257\pi$
$941$	−4.98749e7			−1.83615			−0.918076	+	0.396405i	$0.870257\pi$
$942$	−1.52249e6	+	189956.i	−0.0559020	+	0.00697472i
$943$	−4.44706e7			−1.62852
$944$	−2.57204e6	−	4.74749e6i	−0.0939395	−	0.173394i
$945$			1.85896e7i			0.677158i
$946$	−2.54835e7	+	3.17950e6i	−0.925831	+	0.115513i
$947$	3.12985e7			1.13409			0.567047	−	0.823685i	$-0.308086\pi$
$947$	3.12985e7			1.13409			0.567047	+	0.823685i	$0.308086\pi$
$948$	−95064.4	−	375037.i	−0.00343556	−	0.0135536i
$949$	1.88183e7			0.678288
$950$	2.61811e7	+	4.23746e7i	0.941195	+	1.52334i
$951$		−	1.26997e7i		−	0.455347i
$952$	8.11909e6	+	2.07862e7i	0.290345	+	0.743333i
$953$		−	6.44799e6i		−	0.229981i	−0.993367	−	0.114991i	$-0.963316\pi$
$953$		−	6.44799e6i		−	0.229981i	0.993367	−	0.114991i	$-0.0366838\pi$
$954$	−4.36786e6	+	544965.i	−0.155381	+	0.0193864i
$955$	−7.83760e7			−2.78083
$956$	9.17474e6	+	3.61952e7i	0.324675	+	1.28087i
$957$			4.74344e6i			0.167422i
$958$	4.42953e6	+	3.55024e7i	0.155935	+	1.24981i
$959$		−	6.24795e6i		−	0.219377i
$960$	1.01178e7	−	9.32707e6i	0.354332	−	0.326638i
$961$	−1.65695e7			−0.578762
$962$	8.42952e6	−	1.05172e6i	0.293674	−	0.0366408i
$963$		−	3.74598e7i		−	1.30167i
$964$	8.03377e6	+	3.16939e7i	0.278437	+	1.09846i
$965$	7.94125e6			0.274518
$966$	−666418.	−	5.34130e6i	−0.0229776	−	0.184164i
$967$			3.65275e7i			1.25619i	0.778139	+	0.628093i	$0.216164\pi$
$967$			3.65275e7i			1.25619i	−0.778139	+	0.628093i	$0.783836\pi$
$968$	1.19164e7	−	4.65453e6i	0.408748	−	0.159657i
$969$	8.34609e6	−	3.82078e6i	0.285544	−	0.130720i
$970$	4.26654e7	−	5.32323e6i	1.45595	−	0.181654i
$971$			1.46193e7i			0.497598i	0.968555	+	0.248799i	$0.0800358\pi$
$971$			1.46193e7i			0.497598i	−0.968555	+	0.248799i	$0.919964\pi$
$972$	5.58308e6	+	2.20257e7i	0.189543	+	0.747764i
$973$			2.09396e7i			0.709066i
$974$	9.47373e6	−	1.18201e6i	0.319981	−	0.0399230i
$975$		−	6.96623e6i		−	0.234685i
$976$	−2.54575e6	−	4.69895e6i	−0.0855443	−	0.157898i
$977$			1.70811e7i			0.572505i	0.958154	+	0.286252i	$0.0924096\pi$
$977$			1.70811e7i			0.572505i	−0.958154	+	0.286252i	$0.907590\pi$
$978$	−424297.	−	3.40071e6i	−0.0141848	−	0.113690i
$979$			1.40894e7i			0.469825i
$980$	−5.70887e6	−	2.25220e7i	−0.189882	−	0.749103i
$981$	−4.24506e7			−1.40835
$982$	2.46532e7	−	3.07591e6i	0.815821	−	0.101787i
$983$	−4.08627e7			−1.34879			−0.674394	−	0.738372i	$-0.735595\pi$
$983$	−4.08627e7			−1.34879			−0.674394	+	0.738372i	$0.735595\pi$
$984$	−1.51452e7	+	5.91570e6i	−0.498640	+	0.194768i
$985$	8.71094e7			2.86071
$986$	2.55477e7	−	3.18751e6i	0.836873	−	0.104414i
$987$			1.71315e6i			0.0559761i
$988$	8.73870e6	+	1.08603e7i	0.284810	+	0.353957i
$989$		−	3.36217e7i		−	1.09302i
$990$	4.38026e6	+	3.51075e7i	0.142040	+	1.13845i
$991$	4.47322e7			1.44689			0.723446	−	0.690381i	$-0.242557\pi$
$991$	4.47322e7			1.44689			0.723446	+	0.690381i	$0.242557\pi$
$992$	−1.63647e7	+	1.16984e7i	−0.527994	+	0.377440i
$993$	−1.03765e7			−0.333948
$994$	−3.95278e6	−	3.16813e7i	−0.126893	−	1.01704i
$995$	−1.47936e7			−0.473715
$996$	−1.90714e6	−	7.52383e6i	−0.0609163	−	0.240320i
$997$		−	3.59648e7i		−	1.14588i	−0.819597	−	0.572941i	$-0.805802\pi$
$997$		−	3.59648e7i		−	1.14588i	0.819597	−	0.572941i	$-0.194198\pi$
$998$	−2.92601e7	+	3.65069e6i	−0.929927	+	0.116024i
$999$		−	1.13623e7i		−	0.360208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.4	yes	96
4.3	odd	2		608.6.b.b.303.41		96
8.3	odd	2	inner	152.6.b.b.75.94	yes	96
8.5	even	2		608.6.b.b.303.42		96
19.18	odd	2	inner	152.6.b.b.75.93	yes	96
76.75	even	2		608.6.b.b.303.55		96
152.37	odd	2		608.6.b.b.303.56		96
152.75	even	2	inner	152.6.b.b.75.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.3	✓	96	152.75	even	2	inner
152.6.b.b.75.4	yes	96	1.1	even	1	trivial
152.6.b.b.75.93	yes	96	19.18	odd	2	inner
152.6.b.b.75.94	yes	96	8.3	odd	2	inner
608.6.b.b.303.41		96	4.3	odd	2
608.6.b.b.303.42		96	8.5	even	2
608.6.b.b.303.55		96	76.75	even	2
608.6.b.b.303.56		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)

\(f(q)\)	\(=\)	\(q+(-5.61333 + 0.700358i) q^{2} +4.49700i q^{3} +(31.0190 - 7.86269i) q^{4} -93.3850i q^{5} +(-3.14951 - 25.2431i) q^{6} +95.0367i q^{7} +(-168.613 + 65.8603i) q^{8} +222.777 q^{9} +O(q^{10})\)	\(q+(-5.61333 + 0.700358i) q^{2} +4.49700i q^{3} +(31.0190 - 7.86269i) q^{4} -93.3850i q^{5} +(-3.14951 - 25.2431i) q^{6} +95.0367i q^{7} +(-168.613 + 65.8603i) q^{8} +222.777 q^{9} +(65.4030 + 524.201i) q^{10} +300.630 q^{11} +(35.3585 + 139.492i) q^{12} +276.831 q^{13} +(-66.5598 - 533.473i) q^{14} +419.952 q^{15} +(900.356 - 487.785i) q^{16} -1297.16 q^{17} +(-1250.52 + 156.024i) q^{18} +(654.993 + 1430.76i) q^{19} +(-734.257 - 2896.71i) q^{20} -427.380 q^{21} +(-1687.53 + 210.548i) q^{22} -2226.45i q^{23} +(-296.174 - 758.253i) q^{24} -5595.77 q^{25} +(-1553.95 + 193.881i) q^{26} +2094.60i q^{27} +(747.244 + 2947.94i) q^{28} +3508.64 q^{29} +(-2357.33 + 294.117i) q^{30} +3472.71 q^{31} +(-4712.37 + 3368.67i) q^{32} +1351.93i q^{33} +(7281.37 - 908.474i) q^{34} +8875.01 q^{35} +(6910.32 - 1751.63i) q^{36} -5424.58 q^{37} +(-4678.74 - 7572.62i) q^{38} +1244.91i q^{39} +(6150.37 + 15746.0i) q^{40} -19973.8i q^{41} +(2399.03 - 299.319i) q^{42} +15101.0 q^{43} +(9325.23 - 2363.76i) q^{44} -20804.0i q^{45} +(1559.31 + 12497.8i) q^{46} -4008.50i q^{47} +(2193.57 + 4048.90i) q^{48} +7775.02 q^{49} +(31410.9 - 3919.04i) q^{50} -5833.31i q^{51} +(8587.03 - 2176.64i) q^{52} +3492.83 q^{53} +(-1466.97 - 11757.7i) q^{54} -28074.3i q^{55} +(-6259.15 - 16024.5i) q^{56} +(-6434.14 + 2945.50i) q^{57} +(-19695.2 + 2457.30i) q^{58} -5272.90i q^{59} +(13026.5 - 3301.95i) q^{60} -5218.99i q^{61} +(-19493.5 + 2432.14i) q^{62} +21172.0i q^{63} +(24092.8 - 22209.8i) q^{64} -25851.9i q^{65} +(-946.836 - 7588.84i) q^{66} -44164.6i q^{67} +(-40236.5 + 10199.1i) q^{68} +10012.3 q^{69} +(-49818.4 + 6215.69i) q^{70} +59386.9 q^{71} +(-37563.2 + 14672.2i) q^{72} +67977.3 q^{73} +(30450.0 - 3799.15i) q^{74} -25164.2i q^{75} +(31566.9 + 39230.8i) q^{76} +28570.9i q^{77} +(-871.883 - 6988.10i) q^{78} -2688.59 q^{79} +(-45551.9 - 84079.8i) q^{80} +44715.4 q^{81} +(13988.8 + 112119. i) q^{82} -53937.2 q^{83} +(-13256.9 + 3360.35i) q^{84} +121135. i q^{85} +(-84767.2 + 10576.1i) q^{86} +15778.3i q^{87} +(-50690.1 + 19799.6i) q^{88} +46866.4i q^{89} +(14570.3 + 116780. i) q^{90} +26309.2i q^{91} +(-17505.9 - 69062.2i) q^{92} +15616.8i q^{93} +(2807.38 + 22501.0i) q^{94} +(133612. - 61166.6i) q^{95} +(-15148.9 - 21191.5i) q^{96} -81391.3i q^{97} +(-43643.8 + 5445.30i) q^{98} +66973.4 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

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