LMFDB - Embedded newform 152.6.b.b.75.11

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			75.11
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.42318 - 1.60907i) q^{2} +14.2121i q^{3} +(26.8218 + 17.4525i) q^{4} -9.24558i q^{5} +(22.8682 - 77.0746i) q^{6} +124.323i q^{7} +(-117.377 - 137.806i) q^{8} +41.0170 q^{9} +O(q^{10})$	\(q+(-5.42318 - 1.60907i) q^{2} +14.2121i q^{3} +(26.8218 + 17.4525i) q^{4} -9.24558i q^{5} +(22.8682 - 77.0746i) q^{6} +124.323i q^{7} +(-117.377 - 137.806i) q^{8} +41.0170 q^{9} +(-14.8768 + 50.1404i) q^{10} +365.060 q^{11} +(-248.037 + 381.193i) q^{12} +366.232 q^{13} +(200.045 - 674.228i) q^{14} +131.399 q^{15} +(414.817 + 936.217i) q^{16} +1513.21 q^{17} +(-222.443 - 65.9992i) q^{18} +(-794.804 - 1358.08i) q^{19} +(161.359 - 247.983i) q^{20} -1766.89 q^{21} +(-1979.79 - 587.407i) q^{22} -2261.20i q^{23} +(1958.52 - 1668.17i) q^{24} +3039.52 q^{25} +(-1986.14 - 589.293i) q^{26} +4036.47i q^{27} +(-2169.76 + 3334.57i) q^{28} +2188.28 q^{29} +(-712.599 - 211.430i) q^{30} -7701.88 q^{31} +(-743.189 - 5744.75i) q^{32} +5188.26i q^{33} +(-8206.40 - 2434.86i) q^{34} +1149.44 q^{35} +(1100.15 + 715.851i) q^{36} +2009.12 q^{37} +(2125.12 + 8644.02i) q^{38} +5204.91i q^{39} +(-1274.10 + 1085.22i) q^{40} +10836.3i q^{41} +(9582.18 + 2843.05i) q^{42} +6494.00 q^{43} +(9791.57 + 6371.23i) q^{44} -379.226i q^{45} +(-3638.42 + 12262.9i) q^{46} +11509.4i q^{47} +(-13305.6 + 5895.41i) q^{48} +1350.71 q^{49} +(-16483.9 - 4890.80i) q^{50} +21505.8i q^{51} +(9823.00 + 6391.68i) q^{52} +31071.7 q^{53} +(6494.96 - 21890.5i) q^{54} -3375.19i q^{55} +(17132.6 - 14592.7i) q^{56} +(19301.2 - 11295.8i) q^{57} +(-11867.4 - 3521.09i) q^{58} +34078.2i q^{59} +(3524.35 + 2293.24i) q^{60} +54487.2i q^{61} +(41768.7 + 12392.9i) q^{62} +5099.37i q^{63} +(-5213.24 + 32350.6i) q^{64} -3386.03i q^{65} +(8348.27 - 28136.9i) q^{66} -40891.1i q^{67} +(40586.9 + 26409.3i) q^{68} +32136.3 q^{69} +(-6233.63 - 1849.53i) q^{70} +3893.87 q^{71} +(-4814.45 - 5652.41i) q^{72} -79369.5 q^{73} +(-10895.8 - 3232.82i) q^{74} +43197.9i q^{75} +(2383.93 - 50297.5i) q^{76} +45385.5i q^{77} +(8375.07 - 28227.2i) q^{78} -18972.8 q^{79} +(8655.87 - 3835.22i) q^{80} -47399.5 q^{81} +(17436.4 - 58767.3i) q^{82} -77330.3 q^{83} +(-47391.2 - 30836.8i) q^{84} -13990.5i q^{85} +(-35218.1 - 10449.3i) q^{86} +31100.0i q^{87} +(-42849.7 - 50307.6i) q^{88} +90614.0i q^{89} +(-610.200 + 2056.61i) q^{90} +45531.2i q^{91} +(39463.7 - 60649.4i) q^{92} -109460. i q^{93} +(18519.5 - 62417.8i) q^{94} +(-12556.2 + 7348.42i) q^{95} +(81644.7 - 10562.3i) q^{96} -41798.6i q^{97} +(-7325.15 - 2173.39i) q^{98} +14973.7 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 $

$2$	−5.42318	−	1.60907i	−0.958692	−	0.284446i
$2$	−5.42318	−	1.60907i	−0.958692	−	0.284446i
$3$			14.2121i			0.911705i	0.890055	+	0.455852i	$0.150666\pi$
$3$			14.2121i			0.911705i	−0.890055	+	0.455852i	$0.849334\pi$
$4$	26.8218	+	17.4525i	0.838181	+	0.545392i
$5$		−	9.24558i		−	0.165390i	−0.996575	−	0.0826949i	$-0.973647\pi$
$5$		−	9.24558i		−	0.165390i	0.996575	−	0.0826949i	$-0.0263527\pi$
$6$	22.8682	−	77.0746i	0.259331	−	0.874044i
$7$			124.323i			0.958975i	0.877549	+	0.479488i	$0.159178\pi$
$7$			124.323i			0.958975i	−0.877549	+	0.479488i	$0.840822\pi$
$8$	−117.377	−	137.806i	−0.648423	−	0.761280i
$9$	41.0170			0.168794
$10$	−14.8768	+	50.1404i	−0.0470445	+	0.158558i
$11$	365.060			0.909667			0.454834	−	0.890576i	$-0.349699\pi$
$11$	365.060			0.909667			0.454834	+	0.890576i	$0.349699\pi$
$12$	−248.037	+	381.193i	−0.497237	+	0.764174i
$13$	366.232			0.601032			0.300516	−	0.953777i	$-0.402841\pi$
$13$	366.232			0.601032			0.300516	+	0.953777i	$0.402841\pi$
$14$	200.045	−	674.228i	0.272777	−	0.919362i
$15$	131.399			0.150787
$16$	414.817	+	936.217i	0.405095	+	0.914275i
$17$	1513.21			1.26992			0.634960	−	0.772545i	$-0.281017\pi$
$17$	1513.21			1.26992			0.634960	+	0.772545i	$0.281017\pi$
$18$	−222.443	−	65.9992i	−0.161822	−	0.0480128i
$19$	−794.804	−	1358.08i	−0.505098	−	0.863062i
$19$	−794.804	−	1358.08i	−0.505098	−	0.863062i
$20$	161.359	−	247.983i	0.0902023	−	0.138627i
$21$	−1766.89			−0.874303
$22$	−1979.79	−	587.407i	−0.872091	−	0.258751i
$23$		−	2261.20i		−	0.891290i	−0.895210	−	0.445645i	$-0.852974\pi$
$23$		−	2261.20i		−	0.891290i	0.895210	−	0.445645i	$-0.147026\pi$
$24$	1958.52	−	1668.17i	0.694063	−	0.591170i
$25$	3039.52			0.972646
$26$	−1986.14	−	589.293i	−0.576205	−	0.170961i
$27$			4036.47i			1.06560i
$28$	−2169.76	+	3334.57i	−0.523018	+	0.803795i
$29$	2188.28			0.483178			0.241589	−	0.970379i	$-0.422331\pi$
$29$	2188.28			0.483178			0.241589	+	0.970379i	$0.422331\pi$
$30$	−712.599	−	211.430i	−0.144558	−	0.0428907i
$31$	−7701.88			−1.43944			−0.719719	−	0.694266i	$-0.755729\pi$
$31$	−7701.88			−1.43944			−0.719719	+	0.694266i	$0.755729\pi$
$32$	−743.189	−	5744.75i	−0.128299	−	0.991735i
$33$			5188.26i			0.829348i
$34$	−8206.40	−	2434.86i	−1.21746	−	0.361223i
$35$	1149.44			0.158605
$36$	1100.15	+	715.851i	0.141480	+	0.0920590i
$37$	2009.12			0.241269			0.120635	−	0.992697i	$-0.461507\pi$
$37$	2009.12			0.241269			0.120635	+	0.992697i	$0.461507\pi$
$38$	2125.12	+	8644.02i	0.238739	+	0.971084i
$39$			5204.91i			0.547964i
$40$	−1274.10	+	1085.22i	−0.125908	+	0.107243i
$41$			10836.3i			1.00675i	0.864068	+	0.503375i	$0.167909\pi$
$41$			10836.3i			1.00675i	−0.864068	+	0.503375i	$0.832091\pi$
$42$	9582.18	+	2843.05i	0.838187	+	0.248692i
$43$	6494.00			0.535600			0.267800	−	0.963474i	$-0.413703\pi$
$43$	6494.00			0.535600			0.267800	+	0.963474i	$0.413703\pi$
$44$	9791.57	+	6371.23i	0.762466	+	0.496126i
$45$		−	379.226i		−	0.0279169i
$46$	−3638.42	+	12262.9i	−0.253524	+	0.854472i
$47$			11509.4i			0.759993i	0.924988	+	0.379997i	$0.124075\pi$
$47$			11509.4i			0.759993i	−0.924988	+	0.379997i	$0.875925\pi$
$48$	−13305.6	+	5895.41i	−0.833549	+	0.369327i
$49$	1350.71			0.0803660
$50$	−16483.9	−	4890.80i	−0.932468	−	0.276665i
$51$			21505.8i			1.15779i
$52$	9823.00	+	6391.68i	0.503774	+	0.327798i
$53$	31071.7			1.51941			0.759705	−	0.650268i	$-0.225343\pi$
$53$	31071.7			1.51941			0.759705	+	0.650268i	$0.225343\pi$
$54$	6494.96	−	21890.5i	0.303104	−	1.02158i
$55$		−	3375.19i		−	0.150450i
$56$	17132.6	−	14592.7i	0.730049	−	0.621822i
$57$	19301.2	−	11295.8i	0.786858	−	0.460501i
$58$	−11867.4	−	3521.09i	−0.463219	−	0.137438i
$59$			34078.2i			1.27452i	0.770648	+	0.637261i	$0.219932\pi$
$59$			34078.2i			1.27452i	−0.770648	+	0.637261i	$0.780068\pi$
$60$	3524.35	+	2293.24i	0.126387	+	0.0822379i
$61$			54487.2i			1.87487i	0.348165	+	0.937433i	$0.386805\pi$
$61$			54487.2i			1.87487i	−0.348165	+	0.937433i	$0.613195\pi$
$62$	41768.7	+	12392.9i	1.37998	+	0.409442i
$63$			5099.37i			0.161870i
$64$	−5213.24	+	32350.6i	−0.159096	+	0.987263i
$65$		−	3386.03i		−	0.0994047i
$66$	8348.27	−	28136.9i	0.235905	−	0.795090i
$67$		−	40891.1i		−	1.11286i	−0.830894	−	0.556431i	$-0.812170\pi$
$67$		−	40891.1i		−	1.11286i	0.830894	−	0.556431i	$-0.187830\pi$
$68$	40586.9	+	26409.3i	1.06442	+	0.692604i
$69$	32136.3			0.812593
$70$	−6233.63	−	1849.53i	−0.152053	−	0.0451145i
$71$	3893.87			0.0916719			0.0458359	−	0.998949i	$-0.485405\pi$
$71$	3893.87			0.0916719			0.0458359	+	0.998949i	$0.485405\pi$
$72$	−4814.45	−	5652.41i	−0.109450	−	0.128500i
$73$	−79369.5			−1.74320			−0.871598	−	0.490221i	$-0.836916\pi$
$73$	−79369.5			−1.74320			−0.871598	+	0.490221i	$0.836916\pi$
$74$	−10895.8	−	3232.82i	−0.231303	−	0.0686281i
$75$			43197.9i			0.886766i
$76$	2383.93	−	50297.5i	0.0473433	−	0.998879i
$77$			45385.5i			0.872349i
$78$	8375.07	−	28227.2i	0.155866	−	0.525329i
$79$	−18972.8			−0.342030			−0.171015	−	0.985268i	$-0.554705\pi$
$79$	−18972.8			−0.342030			−0.171015	+	0.985268i	$0.554705\pi$
$80$	8655.87	−	3835.22i	0.151212	−	0.0669986i
$81$	−47399.5			−0.802714
$82$	17436.4	−	58767.3i	0.286366	−	0.965163i
$83$	−77330.3			−1.23212			−0.616062	−	0.787698i	$-0.711273\pi$
$83$	−77330.3			−1.23212			−0.616062	+	0.787698i	$0.711273\pi$
$84$	−47391.2	−	30836.8i	−0.732824	−	0.476838i
$85$		−	13990.5i		−	0.210032i
$86$	−35218.1	−	10449.3i	−0.513476	−	0.152349i
$87$			31100.0i			0.440516i
$88$	−42849.7	−	50307.6i	−0.589849	−	0.692512i
$89$			90614.0i			1.21261i	0.795233	+	0.606304i	$0.207348\pi$
$89$			90614.0i			1.21261i	−0.795233	+	0.606304i	$0.792652\pi$
$90$	−610.200	+	2056.61i	−0.00794084	+	0.0267637i
$91$			45531.2i			0.576375i
$92$	39463.7	−	60649.4i	0.486102	−	0.747062i
$93$		−	109460.i		−	1.31234i
$94$	18519.5	−	62417.8i	0.216177	−	0.728600i
$95$	−12556.2	+	7348.42i	−0.142742	+	0.0835382i
$96$	81644.7	−	10562.3i	0.904170	−	0.116971i
$97$		−	41798.6i		−	0.451058i	−0.974236	−	0.225529i	$-0.927589\pi$
$97$		−	41798.6i		−	0.451058i	0.974236	−	0.225529i	$-0.0724110\pi$
$98$	−7325.15	−	2173.39i	−0.0770462	−	0.0228598i
$99$	14973.7			0.153547
$100$	81525.4	+	53047.4i	0.815254	+	0.530474i
$101$		−	132278.i		−	1.29028i	−0.764063	−	0.645141i	$-0.776798\pi$
$101$		−	132278.i		−	1.29028i	0.764063	−	0.645141i	$-0.223202\pi$
$102$	34604.3	−	116630.i	0.329329	−	1.10997i
$103$	−94980.3			−0.882146			−0.441073	−	0.897471i	$-0.645402\pi$
$103$	−94980.3			−0.882146			−0.441073	+	0.897471i	$0.645402\pi$
$104$	−42987.2	−	50469.1i	−0.389723	−	0.457554i
$105$			16335.9i			0.144601i
$106$	−168507.	−	49996.5i	−1.45665	−	0.432190i
$107$			26503.0i			0.223787i	0.993720	+	0.111894i	$0.0356916\pi$
$107$			26503.0i			0.223787i	−0.993720	+	0.111894i	$0.964308\pi$
$108$	−70446.7	+	108265.i	−0.581167	+	0.893162i
$109$	189293.			1.52605			0.763026	−	0.646368i	$-0.223713\pi$
$109$	189293.			1.52605			0.763026	+	0.646368i	$0.223713\pi$
$110$	−5430.92	+	18304.3i	−0.0427948	+	0.144235i
$111$			28553.8i			0.219966i
$112$	−116394.	+	51571.4i	−0.876767	+	0.388476i
$113$			2785.22i			0.0205194i	0.999947	+	0.0102597i	$0.00326582\pi$
$113$			2785.22i			0.0205194i	−0.999947	+	0.0102597i	$0.996734\pi$
$114$	−122849.	+	30202.3i	−0.885342	+	0.217660i
$115$	−20906.1			−0.147410
$116$	58693.5	+	38191.0i	0.404991	+	0.263522i
$117$	15021.7			0.101451
$118$	54834.2	−	184812.i	0.362532	−	1.22187i
$119$			188127.i			1.21782i
$120$	−15423.2	−	18107.6i	−0.0977736	−	0.114791i
$121$	−27782.1			−0.172505
$122$	87673.8	−	295494.i	0.533298	−	1.79742i
$123$	−154006.			−0.917859
$124$	−206578.	−	134417.i	−1.20651	−	0.785058i
$125$		−	56994.5i		−	0.326256i
$126$	8205.24	−	27654.8i	0.0460431	−	0.155183i
$127$	256840.			1.41304			0.706518	−	0.707695i	$-0.250265\pi$
$127$	256840.			1.41304			0.706518	+	0.707695i	$0.250265\pi$
$128$	80326.8	−	167055.i	0.433347	−	0.901227i
$129$			92293.2i			0.488310i
$130$	−5448.35	+	18363.0i	−0.0282753	+	0.0952985i
$131$	243483.			1.23963			0.619814	−	0.784749i	$-0.287208\pi$
$131$	243483.			1.23963			0.619814	+	0.784749i	$0.287208\pi$
$132$	−90548.4	+	139158.i	−0.452320	+	0.695144i
$133$	168841.	−	98812.7i	0.827655	−	0.484377i
$134$	−65796.6	+	221760.i	−0.316549	+	1.06689i
$135$	37319.5			0.176239
$136$	−177616.	−	208530.i	−0.823445	−	0.966765i
$137$	−179062.			−0.815082			−0.407541	−	0.913187i	$-0.633614\pi$
$137$	−179062.			−0.815082			−0.407541	+	0.913187i	$0.633614\pi$
$138$	−174281.	−	51709.5i	−0.779027	−	0.231139i
$139$	−199170.			−0.874351			−0.437176	−	0.899376i	$-0.644021\pi$
$139$	−199170.			−0.874351			−0.437176	+	0.899376i	$0.644021\pi$
$140$	30830.1	+	20060.7i	0.132940	+	0.0865018i
$141$	−163573.			−0.692890
$142$	−21117.2	−	6265.51i	−0.0878851	−	0.0260757i
$143$	133697.			0.546740
$144$	17014.5	+	38400.8i	0.0683776	+	0.154324i
$145$		−	20231.9i		−	0.0799128i
$146$	430435.	+	127711.i	1.67119	+	0.495845i
$147$			19196.4i			0.0732701i
$148$	53888.2	+	35064.3i	0.202227	+	0.131586i
$149$		−	54501.3i		−	0.201114i	−0.994931	−	0.100557i	$-0.967938\pi$
$149$		−	54501.3i		−	0.201114i	0.994931	−	0.100557i	$-0.0320624\pi$
$150$	69508.4	−	234270.i	0.252237	−	0.850136i
$151$	121160.			0.432432			0.216216	−	0.976346i	$-0.430628\pi$
$151$	121160.			0.432432			0.216216	+	0.976346i	$0.430628\pi$
$152$	−93860.7	+	268937.i	−0.329515	+	0.944150i
$153$	62067.2			0.214355
$154$	73028.4	−	246134.i	0.248136	−	0.836314i
$155$			71208.3i			0.238068i
$156$	−90839.0	+	139605.i	−0.298855	+	0.459293i
$157$		−	471348.i		−	1.52613i	−0.646320	−	0.763067i	$-0.723693\pi$
$157$		−	471348.i		−	1.52613i	0.646320	−	0.763067i	$-0.276307\pi$
$158$	102893.	+	30528.6i	0.327902	+	0.0972892i
$159$			441593.i			1.38525i
$160$	−53113.5	+	6871.21i	−0.164023	+	0.0212194i
$161$	281120.			0.854725
$162$	257056.	+	76269.0i	0.769556	+	0.228329i
$163$	502273.			1.48071			0.740356	−	0.672215i	$-0.234657\pi$
$163$	502273.			1.48071			0.740356	+	0.672215i	$0.234657\pi$
$164$	−189121.	+	290649.i	−0.549074	+	0.843839i
$165$	47968.5			0.137166
$166$	419376.	+	124430.i	1.18123	+	0.350473i
$167$	−373307.			−1.03580			−0.517898	−	0.855442i	$-0.673285\pi$
$167$	−373307.			−1.03580			−0.517898	+	0.855442i	$0.673285\pi$
$168$	207393.	+	243489.i	0.566918	+	0.665589i
$169$	−237167.			−0.638760
$170$	−22511.6	+	75872.9i	−0.0597427	+	0.201356i
$171$	−32600.5	−	55704.4i	−0.0852577	−	0.145680i
$172$	174181.	+	113337.i	0.448930	+	0.292112i
$173$	365898.			0.929491			0.464745	−	0.885444i	$-0.346146\pi$
$173$	365898.			0.929491			0.464745	+	0.885444i	$0.346146\pi$
$174$	50042.0	−	168661.i	0.125303	−	0.422319i
$175$			377883.i			0.932744i
$176$	151433.	+	341776.i	0.368501	+	0.831686i
$177$	−484322.			−1.16199
$178$	145804.	−	491416.i	0.344921	−	1.16252i
$179$			156783.i			0.365735i	0.983138	+	0.182867i	$0.0585379\pi$
$179$			156783.i			0.365735i	−0.983138	+	0.182867i	$0.941462\pi$
$180$	6618.46	−	10171.5i	0.0152256	−	0.0233994i
$181$	−391539.			−0.888339			−0.444169	−	0.895943i	$-0.646501\pi$
$181$	−391539.			−0.888339			−0.444169	+	0.895943i	$0.646501\pi$
$182$	73262.8	−	246924.i	0.163948	−	0.552566i
$183$	−774377.			−1.70932
$184$	−311608.	+	265413.i	−0.678521	+	0.577933i
$185$		−	18575.5i		−	0.0399035i
$186$	−176128.	+	593620.i	−0.373290	+	1.25813i
$187$	552412.			1.15520
$188$	−200869.	+	308704.i	−0.414494	+	0.637012i
$189$	−501827.			−1.02188
$190$	79918.9	−	19647.9i	0.160607	−	0.0394851i
$191$			559199.i			1.10913i	0.832140	+	0.554566i	$0.187116\pi$
$191$			559199.i			1.10913i	−0.832140	+	0.554566i	$0.812884\pi$
$192$	−459770.	−	74091.0i	−0.900093	−	0.145048i
$193$		−	36191.3i		−	0.0699377i	−0.999388	−	0.0349688i	$-0.988867\pi$
$193$		−	36191.3i		−	0.0699377i	0.999388	−	0.0349688i	$-0.0111332\pi$
$194$	−67256.8	+	226681.i	−0.128302	+	0.432426i
$195$	48122.4			0.0906277
$196$	36228.5	+	23573.4i	0.0673612	+	0.0438310i
$197$		−	616594.i		−	1.13197i	−0.824417	−	0.565983i	$-0.808497\pi$
$197$		−	616594.i		−	1.13197i	0.824417	−	0.565983i	$-0.191503\pi$
$198$	−81204.9	−	24093.7i	−0.147204	−	0.0436757i
$199$			155213.i			0.277840i	0.990304	+	0.138920i	$0.0443631\pi$
$199$			155213.i			0.277840i	−0.990304	+	0.138920i	$0.955637\pi$
$200$	−356770.	−	418865.i	−0.630686	−	0.740456i
$201$	581147.			1.01460
$202$	−212845.	+	717369.i	−0.367016	+	1.23698i
$203$			272054.i			0.463356i
$204$	−375331.	+	576824.i	−0.631450	+	0.970439i
$205$	100188.			0.166506
$206$	515095.	+	152830.i	0.845706	+	0.250923i
$207$		−	92747.5i		−	0.150445i
$208$	151919.	+	342873.i	0.243475	+	0.549509i
$209$	−290151.	−	495781.i	−0.459472	−	0.785099i
$210$	26285.7	−	88592.7i	0.0411311	−	0.138628i
$211$		−	339665.i		−	0.525225i	−0.964901	−	0.262612i	$-0.915416\pi$
$211$		−	339665.i		−	0.525225i	0.964901	−	0.262612i	$-0.0845840\pi$
$212$	833398.	+	542280.i	1.27354	+	0.828675i
$213$			55340.0i			0.0835777i
$214$	42645.1	−	143730.i	0.0636554	−	0.214543i
$215$		−	60040.7i		−	0.0885829i
$216$	556252.	−	473789.i	0.811217	−	0.690956i
$217$		−	957524.i		−	1.38038i
$218$	−1.02657e6	−	304586.i	−1.46301	−	0.434079i
$219$		−	1.12800e6i		−	1.58928i
$220$	58905.7	−	90528.7i	0.0820541	−	0.126104i
$221$	554185.			0.763263
$222$	45945.0	−	154852.i	0.0625685	−	0.210880i
$223$	−1.08038e6			−1.45483			−0.727415	−	0.686198i	$-0.759279\pi$
$223$	−1.08038e6			−1.45483			−0.727415	+	0.686198i	$0.759279\pi$
$224$	714206.	−	92395.8i	0.951050	−	0.123036i
$225$	124672.			0.164177
$226$	4481.62	−	15104.8i	0.00583665	−	0.0196718i
$227$		−	105829.i		−	0.136314i	−0.997675	−	0.0681569i	$-0.978288\pi$
$227$		−	105829.i		−	0.136314i	0.997675	−	0.0681569i	$-0.0217119\pi$
$228$	714832.	+	33880.5i	0.910683	+	0.0431631i
$229$		−	285269.i		−	0.359473i	−0.983715	−	0.179736i	$-0.942475\pi$
$229$		−	285269.i		−	0.359473i	0.983715	−	0.179736i	$-0.0575245\pi$
$230$	113377.	+	33639.3i	0.141321	+	0.0419303i
$231$	−645022.			−0.795325
$232$	−256854.	−	301559.i	−0.313304	−	0.367834i
$233$	981311.			1.18418			0.592089	−	0.805873i	$-0.298303\pi$
$233$	981311.			1.18418			0.592089	+	0.805873i	$0.298303\pi$
$234$	−81465.6	−	24171.0i	−0.0972601	−	0.0288573i
$235$	106411.			0.125695
$236$	−594752.	+	914039.i	−0.695114	+	1.06828i
$237$		−	269643.i		−	0.311831i
$238$	302709.	−	1.02025e6i	0.346404	−	1.16752i
$239$			1.21758e6i			1.37881i	0.724377	+	0.689404i	$0.242127\pi$
$239$			1.21758e6i			1.37881i	−0.724377	+	0.689404i	$0.757873\pi$
$240$	54506.5	+	123018.i	0.0610829	+	0.137861i
$241$			696863.i			0.772867i	0.922317	+	0.386434i	$0.126293\pi$
$241$			696863.i			0.772867i	−0.922317	+	0.386434i	$0.873707\pi$
$242$	150668.	+	44703.4i	0.165379	+	0.0490684i
$243$			307217.i			0.333757i
$244$	−950941.	+	1.46145e6i	−1.02254	+	1.57148i
$245$		−	12488.1i		−	0.0132917i
$246$	835205.	+	247807.i	0.879944	+	0.261081i
$247$	−291083.	−	497373.i	−0.303580	−	0.518728i
$248$	904024.	+	1.06137e6i	0.933364	+	1.09582i
$249$		−	1.09902e6i		−	1.12333i
$250$	−91708.1	+	309092.i	−0.0928021	+	0.312779i
$251$	567572.			0.568639			0.284319	−	0.958730i	$-0.408232\pi$
$251$	567572.			0.568639			0.284319	+	0.958730i	$0.408232\pi$
$252$	−88997.0	+	136774.i	−0.0882824	+	0.135676i
$253$		−	825473.i		−	0.810777i
$254$	−1.39289e6	−	413273.i	−1.35467	−	0.401932i
$255$	198834.			0.191487
$256$	−704430.	+	776718.i	−0.671797	+	0.740736i
$257$			172685.i			0.163088i	0.996670	+	0.0815441i	$0.0259851\pi$
$257$			172685.i			0.163088i	−0.996670	+	0.0815441i	$0.974015\pi$
$258$	148506.	−	500523.i	0.138898	−	0.468139i
$259$			249781.i			0.231371i
$260$	59094.8	−	90819.3i	0.0542145	−	0.0833191i
$261$	89756.6			0.0815577
$262$	−1.32046e6	−	391782.i	−1.18842	−	0.352607i
$263$			678009.i			0.604430i	0.953240	+	0.302215i	$0.0977261\pi$
$263$			678009.i			0.604430i	−0.953240	+	0.302215i	$0.902274\pi$
$264$	714976.	−	608983.i	0.631367	−	0.537768i
$265$		−	287276.i		−	0.251295i
$266$	−1.07465e6	+	264202.i	−0.931245	+	0.228945i
$267$	−1.28781e6			−1.10554
$268$	713654.	−	1.09677e6i	0.606947	−	0.932780i
$269$	1.02017e6			0.859591			0.429796	−	0.902926i	$-0.358586\pi$
$269$	1.02017e6			0.859591			0.429796	+	0.902926i	$0.358586\pi$
$270$	−202390.	−	60049.6i	−0.168959	−	0.0501304i
$271$		−	2.30195e6i		−	1.90403i	−0.306055	−	0.952014i	$-0.599009\pi$
$271$		−	2.30195e6i		−	1.90403i	0.306055	−	0.952014i	$-0.400991\pi$
$272$	627704.	+	1.41669e6i	0.514438	+	1.16106i
$273$	−647092.			−0.525484
$274$	971084.	+	288123.i	0.781413	+	0.231847i
$275$	1.10961e6			0.884785
$276$	861953.	+	560860.i	0.681100	+	0.443182i
$277$			608040.i			0.476138i	0.971248	+	0.238069i	$0.0765145\pi$
$277$			608040.i			0.476138i	−0.971248	+	0.238069i	$0.923486\pi$
$278$	1.08013e6	+	320478.i	0.838233	+	0.248706i
$279$	−315908.			−0.242969
$280$	−134918.	−	158400.i	−0.102843	−	0.120743i
$281$		−	49508.2i		−	0.0374034i	−0.999825	−	0.0187017i	$-0.994047\pi$
$281$		−	49508.2i		−	0.0374034i	0.999825	−	0.0187017i	$-0.00595328\pi$
$282$	887087.	+	263200.i	0.664268	+	0.197090i
$283$	−300557.			−0.223080			−0.111540	−	0.993760i	$-0.535578\pi$
$283$	−300557.			−0.223080			−0.111540	+	0.993760i	$0.535578\pi$
$284$	104441.	+	67958.0i	0.0768376	+	0.0499971i
$285$	−104436.	−	178450.i	−0.0761621	−	0.130138i
$286$	−725061.	−	215127.i	−0.524155	−	0.155518i
$287$	−1.34721e6			−0.965449
$288$	−30483.4	−	235632.i	−0.0216562	−	0.167399i
$289$	869939.			0.612695
$290$	−32554.5	+	109721.i	−0.0227309	+	0.0766118i
$291$	594044.			0.411232
$292$	−2.12883e6	−	1.38520e6i	−1.46111	−	0.950726i
$293$	1.81073e6			1.23221			0.616104	−	0.787664i	$-0.288710\pi$
$293$	1.81073e6			1.23221			0.616104	+	0.787664i	$0.288710\pi$
$294$	30888.3	−	104106.i	0.0208414	−	0.0702434i
$295$	315073.			0.210793
$296$	−235825.	−	276870.i	−0.156444	−	0.183674i
$297$			1.47355e6i			0.969337i
$298$	−87696.4	+	295571.i	−0.0572059	+	0.192806i
$299$		−	828123.i		−	0.535694i
$300$	−753913.	+	1.15864e6i	−0.483635	+	0.743271i
$301$			807355.i			0.513628i
$302$	−657074.	−	194955.i	−0.414569	−	0.123004i
$303$	1.87995e6			1.17636
$304$	941761.	−	1.30746e6i	0.584463	−	0.811420i
$305$	503766.			0.310084
$306$	−336602.	−	99870.4i	−0.205500	−	0.0609724i
$307$			2.34882e6i			1.42234i	0.703018	+	0.711172i	$0.251835\pi$
$307$			2.34882e6i			1.42234i	−0.703018	+	0.711172i	$0.748165\pi$
$308$	−792092.	+	1.21732e6i	−0.475772	+	0.731186i
$309$		−	1.34987e6i		−	0.804256i
$310$	114579.	−	386176.i	0.0677176	−	0.228234i
$311$		−	3.13408e6i		−	1.83743i	−0.394926	−	0.918713i	$-0.629230\pi$
$311$		−	3.13408e6i		−	1.83743i	0.394926	−	0.918713i	$-0.370770\pi$
$312$	717271.	−	610938.i	0.417154	−	0.355312i
$313$	−2.28638e6			−1.31913			−0.659565	−	0.751648i	$-0.729259\pi$
$313$	−2.28638e6			−1.31913			−0.659565	+	0.751648i	$0.729259\pi$
$314$	−758432.	+	2.55621e6i	−0.434102	+	1.46309i
$315$	47146.6			0.0267716
$316$	−508886.	−	331124.i	−0.286683	−	0.186541i
$317$	−96347.3			−0.0538507			−0.0269254	−	0.999637i	$-0.508572\pi$
$317$	−96347.3			−0.0538507			−0.0269254	+	0.999637i	$0.508572\pi$
$318$	710554.	−	2.39484e6i	0.394030	−	1.32803i
$319$	798853.			0.439532
$320$	299100.	+	48199.4i	0.163283	+	0.0263128i
$321$	−376662.			−0.204028
$322$	−1.52456e6	−	452341.i	−0.819418	−	0.243123i
$323$	−1.20270e6	−	2.05506e6i	−0.641434	−	1.09602i
$324$	−1.27134e6	−	827242.i	−0.672820	−	0.437794i
$325$	1.11317e6			0.584592
$326$	−2.72392e6	−	808192.i	−1.41955	−	0.421183i
$327$			2.69025e6i			1.39131i
$328$	1.49331e6	−	1.27193e6i	0.766419	−	0.652800i
$329$	−1.43089e6			−0.728815
$330$	−260142.	−	77184.6i	−0.131500	−	0.0390163i
$331$			601438.i			0.301731i	0.988554	+	0.150866i	$0.0482061\pi$
$331$			601438.i			0.301731i	−0.988554	+	0.150866i	$0.951794\pi$
$332$	−2.07414e6	−	1.34961e6i	−1.03274	−	0.671990i
$333$	82408.1			0.0407249
$334$	2.02451e6	+	600676.i	0.993010	+	0.294628i
$335$	−378062.			−0.184056
$336$	−732937.	−	1.65419e6i	−0.354175	−	0.799353i
$337$		−	3.82139e6i		−	1.83294i	−0.400109	−	0.916468i	$-0.631028\pi$
$337$		−	3.82139e6i		−	1.83294i	0.400109	−	0.916468i	$-0.368972\pi$
$338$	1.28620e6	+	381618.i	0.612374	+	0.181693i
$339$	−39583.8			−0.0187076
$340$	244169.	−	375250.i	0.114550	−	0.176045i
$341$	−2.81165e6			−1.30941
$342$	87165.9	+	354552.i	0.0402978	+	0.163913i
$343$			2.25743e6i			1.03604i
$344$	−762246.	−	894915.i	−0.347296	−	0.407742i
$345$		−	297119.i		−	0.134395i
$346$	−1.98433e6	−	588756.i	−0.891096	−	0.264390i
$347$	−1.55563e6			−0.693556			−0.346778	−	0.937947i	$-0.612724\pi$
$347$	−1.55563e6			−0.693556			−0.346778	+	0.937947i	$0.612724\pi$
$348$	−542774.	+	834157.i	−0.240254	+	0.369232i
$349$		−	1.01085e6i		−	0.444246i	−0.975019	−	0.222123i	$-0.928701\pi$
$349$		−	1.01085e6i		−	0.444246i	0.975019	−	0.222123i	$-0.0712987\pi$
$350$	608040.	−	2.04933e6i	0.265315	−	0.894214i
$351$			1.47828e6i			0.640457i
$352$	−271309.	−	2.09718e6i	−0.116710	−	0.902149i
$353$	1.24723e6			0.532731			0.266366	−	0.963872i	$-0.414177\pi$
$353$	1.24723e6			0.532731			0.266366	+	0.963872i	$0.414177\pi$
$354$	2.62657e6	+	779308.i	1.11399	+	0.330523i
$355$		−	36001.1i		−	0.0151616i
$356$	−1.58145e6	+	2.43043e6i	−0.661347	+	1.01638i
$357$	−2.67367e6			−1.11029
$358$	252274.	−	850262.i	0.104032	−	0.350627i
$359$		−	1.07100e6i		−	0.438584i	−0.975659	−	0.219292i	$-0.929625\pi$
$359$		−	1.07100e6i		−	0.438584i	0.975659	−	0.219292i	$-0.0703747\pi$
$360$	−52259.8	+	44512.4i	−0.0212526	+	0.0181019i
$361$	−1.21267e6	+	2.15882e6i	−0.489751	+	0.871862i
$362$	2.12339e6	+	630013.i	0.851643	+	0.252684i
$363$		−	394842.i		−	0.157274i
$364$	−794635.	+	1.22123e6i	−0.314351	+	0.483107i
$365$			733816.i			0.288307i
$366$	4.19959e6	+	1.24603e6i	1.63872	+	0.486211i
$367$		−	2.89160e6i		−	1.12066i	−0.828270	−	0.560329i	$-0.810675\pi$
$367$		−	2.89160e6i		−	1.12066i	0.828270	−	0.560329i	$-0.189325\pi$
$368$	2.11697e6	−	937983.i	0.814884	−	0.361057i
$369$			444473.i			0.169934i
$370$	−29889.2	+	100738.i	−0.0113504	+	0.0382552i
$371$			3.86294e6i			1.45708i
$372$	1.91035e6	−	2.93591e6i	0.715741	−	1.09998i
$373$	1.47047e6			0.547247			0.273624	−	0.961837i	$-0.411778\pi$
$373$	1.47047e6			0.547247			0.273624	+	0.961837i	$0.411778\pi$
$374$	−2.99583e6	−	888869.i	−1.10749	−	0.328593i
$375$	810010.			0.297449
$376$	1.58608e6	−	1.35095e6i	0.578568	−	0.492797i
$377$	801417.			0.290406
$378$	2.72150e6	+	807475.i	0.979668	+	0.290670i
$379$		−	1.89549e6i		−	0.677833i	−0.940816	−	0.338917i	$-0.889940\pi$
$379$		−	1.89549e6i		−	0.677833i	0.940816	−	0.338917i	$-0.110060\pi$
$380$	−465030.	−	22040.8i	−0.165204	−	0.00783011i
$381$			3.65023e6i			1.28827i
$382$	899790.	−	3.03264e6i	0.315488	−	1.06332i
$383$	3.50444e6			1.22073			0.610367	−	0.792119i	$-0.291022\pi$
$383$	3.50444e6			1.22073			0.610367	+	0.792119i	$0.291022\pi$
$384$	2.37420e6	+	1.14161e6i	0.821653	+	0.395084i
$385$	419615.			0.144278
$386$	−58234.4	+	196272.i	−0.0198935	+	0.0670487i
$387$	266364.			0.0904063
$388$	729492.	−	1.12111e6i	0.246003	−	0.378068i
$389$			4.31747e6i			1.44662i	0.690523	+	0.723311i	$0.257381\pi$
$389$			4.31747e6i			1.44662i	−0.690523	+	0.723311i	$0.742619\pi$
$390$	−260977.	−	77432.3i	−0.0868841	−	0.0257787i
$391$		−	3.42166e6i		−	1.13187i
$392$	−158543.	−	186137.i	−0.0521111	−	0.0611811i
$393$			3.46041e6i			1.13017i
$394$	−992142.	+	3.34390e6i	−0.321983	+	1.08521i
$395$			175415.i			0.0565684i
$396$	401621.	+	261329.i	0.128700	+	0.0837431i
$397$		−	391751.i		−	0.124748i	−0.998053	−	0.0623740i	$-0.980133\pi$
$397$		−	391751.i		−	0.124748i	0.998053	−	0.0623740i	$-0.0198671\pi$
$398$	249748.	−	841746.i	0.0790304	−	0.266363i
$399$	1.40433e6	+	2.39958e6i	0.441609	+	0.754577i
$400$	1.26084e6	+	2.84565e6i	0.394014	+	0.889266i
$401$			5.15441e6i			1.60073i	0.599514	+	0.800364i	$0.295361\pi$
$401$			5.15441e6i			1.60073i	−0.599514	+	0.800364i	$0.704639\pi$
$402$	−3.15167e6	−	935106.i	−0.972691	−	0.288600i
$403$	−2.82068e6			−0.865148
$404$	2.30859e6	−	3.54794e6i	0.703710	−	1.08149i
$405$			438235.i			0.132761i
$406$	437754.	−	1.47540e6i	0.131800	−	0.444216i
$407$	733450.			0.219475
$408$	2.96364e6	−	2.52429e6i	0.881404	−	0.750739i
$409$			4.89993e6i			1.44838i	0.689602	+	0.724189i	$0.257786\pi$
$409$			4.89993e6i			1.44838i	−0.689602	+	0.724189i	$0.742214\pi$
$410$	−543337.	−	161209.i	−0.159628	−	0.0473620i
$411$		−	2.54484e6i		−	0.743114i
$412$	−2.54754e6	−	1.65765e6i	−0.739398	−	0.481115i
$413$	−4.23672e6			−1.22223
$414$	−149237.	+	502987.i	−0.0427933	+	0.144230i
$415$			714963.i			0.203781i
$416$	−272180.	−	2.10391e6i	−0.0771121	−	0.596065i
$417$		−	2.83061e6i		−	0.797150i
$418$	775796.	+	3.15559e6i	0.217173	+	0.883363i
$419$	4.28386e6			1.19207			0.596033	−	0.802960i	$-0.296743\pi$
$419$	4.28386e6			1.19207			0.596033	+	0.802960i	$0.296743\pi$
$420$	−285104.	+	438159.i	−0.0788642	+	0.121202i
$421$	−2.52522e6			−0.694375			−0.347188	−	0.937796i	$-0.612863\pi$
$421$	−2.52522e6			−0.694375			−0.347188	+	0.937796i	$0.612863\pi$
$422$	−546545.	+	1.84207e6i	−0.149398	+	0.503529i
$423$			472083.i			0.128282i
$424$	−3.64710e6	−	4.28188e6i	−0.985221	−	1.15670i
$425$	4.59942e6			1.23518
$426$	89045.9	−	300119.i	0.0237733	−	0.0801253i
$427$	−6.77404e6			−1.79795
$428$	−462545.	+	710858.i	−0.122052	+	0.187574i
$429$			1.90011e6i			0.498465i
$430$	−96609.7	+	325612.i	−0.0251970	+	0.0849237i
$431$	−1.42046e6			−0.368328			−0.184164	−	0.982896i	$-0.558958\pi$
$431$	−1.42046e6			−0.368328			−0.184164	+	0.982896i	$0.558958\pi$
$432$	−3.77901e6	+	1.67440e6i	−0.974247	+	0.431667i
$433$			178506.i			0.0457543i	0.999738	+	0.0228772i	$0.00728266\pi$
$433$			178506.i			0.0457543i	−0.999738	+	0.0228772i	$0.992717\pi$
$434$	−1.54072e6	+	5.19282e6i	−0.392645	+	1.32336i
$435$	287537.			0.0728569
$436$	5.07719e6	+	3.30365e6i	1.27911	+	0.832297i
$437$	−3.07089e6	+	1.79721e6i	−0.769238	+	0.450189i
$438$	−1.81504e6	+	6.11737e6i	−0.452064	+	1.52363i
$439$	6.49147e6			1.60761			0.803807	−	0.594891i	$-0.202805\pi$
$439$	6.49147e6			1.60761			0.803807	+	0.594891i	$0.202805\pi$
$440$	−465123.	+	396170.i	−0.114534	+	0.0975551i
$441$	55402.1			0.0135653
$442$	−3.00544e6	−	891722.i	−0.731734	−	0.217107i
$443$	−1.04834e6			−0.253800			−0.126900	−	0.991915i	$-0.540503\pi$
$443$	−1.04834e6			−0.253800			−0.126900	+	0.991915i	$0.540503\pi$
$444$	−498336.	+	765864.i	−0.119968	+	0.184372i
$445$	837779.			0.200553
$446$	5.85907e6	+	1.73840e6i	1.39473	+	0.413821i
$447$	774577.			0.183356
$448$	−4.02194e6	−	648128.i	−0.946761	−	0.152569i
$449$		−	1.14659e6i		−	0.268407i	−0.990954	−	0.134203i	$-0.957152\pi$
$449$		−	1.14659e6i		−	0.268407i	0.990954	−	0.134203i	$-0.0428476\pi$
$450$	−676119.	−	200606.i	−0.157395	−	0.0466995i
$451$			3.95590e6i			0.915808i
$452$	−48609.3	+	74704.7i	−0.0111911	+	0.0171989i
$453$			1.72194e6i			0.394251i
$454$	−170286.	+	573930.i	−0.0387739	+	0.130683i
$455$	420962.			0.0953266
$456$	−3.82215e6	−	1.33395e6i	−0.860787	−	0.300420i
$457$	−3.64223e6			−0.815786			−0.407893	−	0.913030i	$-0.633736\pi$
$457$	−3.64223e6			−0.815786			−0.407893	+	0.913030i	$0.633736\pi$
$458$	−459018.	+	1.54707e6i	−0.102251	+	0.344624i
$459$			6.10802e6i			1.35322i
$460$	−560738.	−	364864.i	−0.123557	−	0.0803964i
$461$			2.78881e6i			0.611177i	0.952164	+	0.305589i	$0.0988533\pi$
$461$			2.78881e6i			0.611177i	−0.952164	+	0.305589i	$0.901147\pi$
$462$	3.49807e6	+	1.03788e6i	0.762471	+	0.226227i
$463$			1.15763e6i			0.250968i	0.992096	+	0.125484i	$0.0400483\pi$
$463$			1.15763e6i			0.250968i	−0.992096	+	0.125484i	$0.959952\pi$
$464$	907735.	+	2.04870e6i	0.195733	+	0.441758i
$465$	−1.01202e6			−0.217048
$466$	−5.32183e6	−	1.57900e6i	−1.13526	−	0.336835i
$467$	5.45656e6			1.15778			0.578891	−	0.815405i	$-0.303486\pi$
$467$	5.45656e6			1.15778			0.578891	+	0.815405i	$0.303486\pi$
$468$	402910.	+	262168.i	0.0850341	+	0.0553305i
$469$	5.08371e6			1.06721
$470$	−577089.	−	171223.i	−0.120503	−	0.0357535i
$471$	6.69883e6			1.39138
$472$	4.69620e6	−	4.00000e6i	0.970268	−	0.826429i
$473$	2.37070e6			0.487218
$474$	−433875.	+	1.46233e6i	−0.0886990	+	0.298950i
$475$	−2.41582e6	−	4.12792e6i	−0.491282	−	0.839454i
$476$	−3.28330e6	+	5.04590e6i	−0.664190	+	1.02075i
$477$	1.27447e6			0.256468
$478$	1.95917e6	−	6.60317e6i	0.392196	−	1.32185i
$479$		−	4.48505e6i		−	0.893157i	−0.894744	−	0.446579i	$-0.852642\pi$
$479$		−	4.48505e6i		−	0.893157i	0.894744	−	0.446579i	$-0.147358\pi$
$480$	−97654.2	−	754853.i	−0.0193458	−	0.149541i
$481$	735805.			0.145011
$482$	1.12130e6	−	3.77921e6i	0.219839	−	0.740941i
$483$			3.99529e6i			0.779257i
$484$	−745166.	−	484869.i	−0.144591	−	0.0940830i
$485$	−386452.			−0.0746004
$486$	494334.	−	1.66610e6i	0.0949358	−	0.319970i
$487$	−3.10015e6			−0.592326			−0.296163	−	0.955137i	$-0.595707\pi$
$487$	−3.10015e6			−0.592326			−0.296163	+	0.955137i	$0.595707\pi$
$488$	7.50870e6	−	6.39555e6i	1.42730	−	1.21571i
$489$			7.13834e6i			1.34997i
$490$	−20094.2	+	67725.2i	−0.00378078	+	0.0127427i
$491$	1.43332e6			0.268312			0.134156	−	0.990960i	$-0.457168\pi$
$491$	1.43332e6			0.268312			0.134156	+	0.990960i	$0.457168\pi$
$492$	−4.13073e6	−	2.68780e6i	−0.769332	−	0.500593i
$493$	3.31132e6			0.613597
$494$	778286.	+	3.16572e6i	0.143490	+	0.583653i
$495$		−	138440.i		−	0.0253951i
$496$	−3.19487e6	−	7.21064e6i	−0.583108	−	1.31604i
$497$			484099.i			0.0879111i
$498$	−1.76840e6	+	5.96020e6i	−0.319528	+	1.07693i
$499$	3.39259e6			0.609930			0.304965	−	0.952364i	$-0.401355\pi$
$499$	3.39259e6			0.609930			0.304965	+	0.952364i	$0.401355\pi$
$500$	994700.	−	1.52870e6i	0.177937	−	0.273461i
$501$		−	5.30546e6i		−	0.944341i
$502$	−3.07804e6	−	913262.i	−0.545150	−	0.161747i
$503$		−	5.68066e6i		−	1.00110i	−0.865707	−	0.500552i	$-0.833131\pi$
$503$		−	5.68066e6i		−	1.00110i	0.865707	−	0.500552i	$-0.166869\pi$
$504$	702726.	−	598549.i	0.123228	−	0.104960i
$505$	−1.22299e6			−0.213400
$506$	−1.32824e6	+	4.47669e6i	−0.230622	+	0.777286i
$507$		−	3.37064e6i		−	0.582361i
$508$	6.88890e6	+	4.48251e6i	1.18438	+	0.770659i
$509$	−3.22322e6			−0.551436			−0.275718	−	0.961239i	$-0.588916\pi$
$509$	−3.22322e6			−0.551436			−0.275718	+	0.961239i	$0.588916\pi$
$510$	−1.07831e6	−	319937.i	−0.183577	−	0.0544677i
$511$		−	9.86747e6i		−	1.67168i
$512$	5.07004e6	−	3.07880e6i	0.854745	−	0.519048i
$513$	5.48186e6	−	3.20820e6i	0.919675	−	0.538230i
$514$	277863.	−	936504.i	0.0463898	−	0.156351i
$515$			878147.i			0.145898i
$516$	−1.61075e6	+	2.47547e6i	−0.266320	+	0.409292i
$517$			4.20164e6i			0.691341i
$518$	401914.	−	1.35461e6i	0.0658126	−	0.221814i
$519$			5.20017e6i			0.847421i
$520$	−466616.	+	397442.i	−0.0756748	+	0.0644563i
$521$		−	1.11994e7i		−	1.80759i	−0.427962	−	0.903797i	$-0.640768\pi$
$521$		−	1.11994e7i		−	1.80759i	0.427962	−	0.903797i	$-0.359232\pi$
$522$	−486766.	−	144425.i	−0.0781887	−	0.0231988i
$523$		−	2.39158e6i		−	0.382323i	−0.981559	−	0.191161i	$-0.938775\pi$
$523$		−	2.39158e6i		−	0.382323i	0.981559	−	0.191161i	$-0.0612254\pi$
$524$	6.53066e6	+	4.24941e6i	1.03903	+	0.676083i
$525$	−5.37050e6			−0.850387
$526$	1.09096e6	−	3.67697e6i	0.171928	−	0.579462i
$527$	−1.16545e7			−1.82797
$528$	−4.85734e6	+	2.15218e6i	−0.758252	+	0.335965i
$529$	1.32333e6			0.205603
$530$	−462246.	+	1.55795e6i	−0.0714799	+	0.240915i
$531$			1.39779e6i			0.215132i
$532$	6.25316e6	+	296378.i	0.957900	+	0.0454011i
$533$			3.96860e6i			0.605089i
$534$	6.98404e6	+	2.07218e6i	1.05987	+	0.314467i
$535$	245035.			0.0370121
$536$	−5.63505e6	+	4.79968e6i	−0.847200	+	0.721606i
$537$	−2.22821e6			−0.333442
$538$	−5.53257e6	−	1.64152e6i	−0.824083	−	0.244507i
$539$	493091.			0.0731063
$540$	1.00098e6	+	651320.i	0.147720	+	0.0961192i
$541$			5.07981e6i			0.746198i	0.927792	+	0.373099i	$0.121705\pi$
$541$			5.07981e6i			0.746198i	−0.927792	+	0.373099i	$0.878295\pi$
$542$	−3.70400e6	+	1.24839e7i	−0.541593	+	1.82538i
$543$		−	5.56458e6i		−	0.809903i
$544$	−1.12460e6	−	8.69299e6i	−0.162930	−	1.25942i
$545$		−	1.75013e6i		−	0.252394i
$546$	3.50930e6	+	1.04122e6i	0.503778	+	0.149472i
$547$		−	4.98971e6i		−	0.713028i	−0.934290	−	0.356514i	$-0.883965\pi$
$547$		−	4.98971e6i		−	0.713028i	0.934290	−	0.356514i	$-0.116035\pi$
$548$	−4.80276e6	−	3.12508e6i	−0.683186	−	0.444539i
$549$			2.23490e6i			0.316467i
$550$	−6.01760e6	−	1.78543e6i	−0.848236	−	0.251673i
$551$	−1.73925e6	−	2.97186e6i	−0.244053	−	0.417013i
$552$	−3.77207e6	−	4.42859e6i	−0.526904	−	0.618611i
$553$		−	2.35877e6i		−	0.327999i
$554$	978379.	−	3.29751e6i	0.135436	−	0.456470i
$555$	263996.			0.0363802
$556$	−5.34208e6	−	3.47602e6i	−0.732864	−	0.476864i
$557$		−	4.63835e6i		−	0.633469i	−0.948514	−	0.316735i	$-0.897414\pi$
$557$		−	4.63835e6i		−	0.633469i	0.948514	−	0.316735i	$-0.102586\pi$
$558$	1.71323e6	+	508318.i	0.232932	+	0.0691114i
$559$	2.37831e6			0.321913
$560$	476808.	+	1.07613e6i	0.0642500	+	0.145008i
$561$			7.85091e6i			1.05321i
$562$	−79662.1	+	268492.i	−0.0106392	+	0.0358583i
$563$		−	1.49382e7i		−	1.98622i	−0.117175	−	0.993111i	$-0.537384\pi$
$563$		−	1.49382e7i		−	1.98622i	0.117175	−	0.993111i	$-0.462616\pi$
$564$	−4.38732e6	−	2.85477e6i	−0.580767	−	0.377897i
$565$	25751.0			0.00339370
$566$	1.62997e6	+	483616.i	0.213865	+	0.0634541i
$567$		−	5.89286e6i		−	0.769783i
$568$	−457052.	−	536601.i	−0.0594421	−	0.0697880i
$569$		−	1.32859e7i		−	1.72033i	−0.510017	−	0.860164i	$-0.670361\pi$
$569$		−	1.32859e7i		−	1.72033i	0.510017	−	0.860164i	$-0.329639\pi$
$570$	279238.	+	1.13581e6i	0.0359987	+	0.146427i
$571$	−9.39535e6			−1.20593			−0.602966	−	0.797767i	$-0.706014\pi$
$571$	−9.39535e6			−1.20593			−0.602966	+	0.797767i	$0.706014\pi$
$572$	3.58598e6	+	2.33335e6i	0.458267	+	0.298187i
$573$	−7.94738e6			−1.01120
$574$	7.30614e6	+	2.16775e6i	0.925568	+	0.274618i
$575$		−	6.87295e6i		−	0.866909i
$576$	−213832.	+	1.32693e6i	−0.0268544	+	0.166644i
$577$	−837200.			−0.104686			−0.0523431	−	0.998629i	$-0.516669\pi$
$577$	−837200.			−0.104686			−0.0523431	+	0.998629i	$0.516669\pi$
$578$	−4.71784e6	−	1.39979e6i	−0.587386	−	0.174279i
$579$	514354.			0.0637625
$580$	353098.	−	542655.i	0.0435838	−	0.0669814i
$581$		−	9.61395e6i		−	1.18158i
$582$	−3.22161e6	−	955859.i	−0.394244	−	0.116973i
$583$	1.13430e7			1.38216
$584$	9.31615e6	+	1.09376e7i	1.13033	+	1.32706i
$585$		−	138885.i		−	0.0167789i
$586$	−9.81991e6	−	2.91359e6i	−1.18131	−	0.350497i
$587$	−3.77948e6			−0.452727			−0.226364	−	0.974043i	$-0.572684\pi$
$587$	−3.77948e6			−0.452727			−0.226364	+	0.974043i	$0.572684\pi$
$588$	−335026.	+	514882.i	−0.0399609	+	0.0614136i
$589$	6.12149e6	+	1.04598e7i	0.727057	+	1.24232i
$590$	−1.70870e6	−	506974.i	−0.202085	−	0.0599592i
$591$	8.76308e6			1.03202
$592$	833418.	+	1.88097e6i	0.0977369	+	0.220586i
$593$	−5.96912e6			−0.697065			−0.348532	−	0.937297i	$-0.613320\pi$
$593$	−5.96912e6			−0.697065			−0.348532	+	0.937297i	$0.613320\pi$
$594$	2.37105e6	−	7.99135e6i	0.275724	−	0.929296i
$595$	1.73934e6			0.201415
$596$	951187.	−	1.46182e6i	0.109686	−	0.168570i
$597$	−2.20589e6			−0.253308
$598$	−1.33251e6	+	4.49106e6i	−0.152376	+	0.513566i
$599$	−1.72710e7			−1.96675			−0.983376	−	0.181581i	$-0.941879\pi$
$599$	−1.72710e7			−1.96675			−0.983376	+	0.181581i	$0.941879\pi$
$600$	5.95295e6	−	5.07044e6i	0.675078	−	0.575000i
$601$		−	3.08241e6i		−	0.348100i	−0.984737	−	0.174050i	$-0.944315\pi$
$601$		−	3.08241e6i		−	0.348100i	0.984737	−	0.174050i	$-0.0556854\pi$
$602$	1.29909e6	−	4.37843e6i	0.146099	−	0.492411i
$603$		−	1.67723e6i		−	0.187845i
$604$	3.24974e6	+	2.11456e6i	0.362456	+	0.235845i
$605$			256862.i			0.0285306i
$606$	−1.01953e7	−	3.02497e6i	−1.12776	−	0.334610i
$607$	−1.07721e7			−1.18667			−0.593334	−	0.804957i	$-0.702189\pi$
$607$	−1.07721e7			−1.18667			−0.593334	+	0.804957i	$0.702189\pi$
$608$	−7.21114e6	+	5.57526e6i	−0.791125	+	0.611654i
$609$	−3.86645e6			−0.422444
$610$	−2.73201e6	−	810594.i	−0.297275	−	0.0882021i
$611$			4.21513e6i			0.456781i
$612$	1.66475e6	+	1.08323e6i	0.179668	+	0.116908i
$613$		−	3.17483e6i		−	0.341248i	−0.985336	−	0.170624i	$-0.945422\pi$
$613$		−	3.17483e6i		−	0.341248i	0.985336	−	0.170624i	$-0.0545783\pi$
$614$	3.77942e6	−	1.27381e7i	0.404580	−	1.36359i
$615$			1.42388e6i			0.151805i
$616$	6.25441e6	−	5.32722e6i	0.664102	−	0.565651i
$617$	3.57680e6			0.378253			0.189126	−	0.981953i	$-0.439434\pi$
$617$	3.57680e6			0.378253			0.189126	+	0.981953i	$0.439434\pi$
$618$	−2.17203e6	+	7.32057e6i	−0.228767	+	0.771034i
$619$	−1.81270e7			−1.90151			−0.950757	−	0.309937i	$-0.899692\pi$
$619$	−1.81270e7			−1.90151			−0.950757	+	0.309937i	$0.899692\pi$
$620$	−1.24277e6	+	1.90994e6i	−0.129841	+	0.199544i
$621$	9.12726e6			0.949754
$622$	−5.04296e6	+	1.69967e7i	−0.522648	+	1.76153i
$623$	−1.12654e7			−1.16286
$624$	−4.87293e6	+	2.15909e6i	−0.500990	+	0.221977i
$625$	8.97155e6			0.918687
$626$	1.23994e7	+	3.67894e6i	1.26464	+	0.375221i
$627$	7.04608e6	−	4.12365e6i	0.715779	−	0.418902i
$628$	8.22622e6	−	1.26424e7i	0.832341	−	1.27918i
$629$	3.04022e6			0.306392
$630$	−255685.	−	75862.1i	−0.0256657	−	0.00761507i
$631$			5.80712e6i			0.580614i	0.956934	+	0.290307i	$0.0937574\pi$
$631$			5.80712e6i			0.580614i	−0.956934	+	0.290307i	$0.906243\pi$
$632$	2.22698e6	+	2.61458e6i	0.221780	+	0.260381i
$633$	4.82735e6			0.478850
$634$	522509.	+	155030.i	0.0516262	+	0.0153176i
$635$		−	2.37463e6i		−	0.233702i
$636$	−7.70692e6	+	1.18443e7i	−0.755507	+	1.16109i
$637$	494674.			0.0483026
$638$	−4.33232e6	−	1.28541e6i	−0.421375	−	0.125023i
$639$	159715.			0.0154737
$640$	−1.54452e6	−	742667.i	−0.149054	−	0.0716712i
$641$		−	1.04768e7i		−	1.00712i	−0.863960	−	0.503560i	$-0.832023\pi$
$641$		−	1.04768e7i		−	1.00712i	0.863960	−	0.503560i	$-0.167977\pi$
$642$	2.04271e6	+	606076.i	0.195600	+	0.0580349i
$643$	−3.09642e6			−0.295347			−0.147674	−	0.989036i	$-0.547179\pi$
$643$	−3.09642e6			−0.295347			−0.147674	+	0.989036i	$0.547179\pi$
$644$	7.54013e6	+	4.90625e6i	0.716414	+	0.466160i
$645$	853303.			0.0807615
$646$	3.21574e6	+	1.30802e7i	0.303180	+	1.23320i
$647$			6.31465e6i			0.593046i	0.955026	+	0.296523i	$0.0958271\pi$
$647$			6.31465e6i			0.593046i	−0.955026	+	0.296523i	$0.904173\pi$
$648$	5.56361e6	+	6.53195e6i	0.520498	+	0.611091i
$649$			1.24406e7i			1.15939i
$650$	−6.03692e6	−	1.79117e6i	−0.560444	−	0.166285i
$651$	1.36084e7			1.25850
$652$	1.34719e7	+	8.76594e6i	1.24111	+	0.807569i
$653$		−	9.24440e6i		−	0.848390i	−0.905571	−	0.424195i	$-0.860557\pi$
$653$		−	9.24440e6i		−	0.848390i	0.905571	−	0.424195i	$-0.139443\pi$
$654$	4.32880e6	−	1.45897e7i	0.395752	−	1.33384i
$655$		−	2.25115e6i		−	0.205022i
$656$	−1.01451e7	+	4.49508e6i	−0.920446	+	0.407829i
$657$	−3.25550e6			−0.294241
$658$	7.75999e6	+	2.30241e6i	0.698709	+	0.207308i
$659$			2.03128e6i			0.182203i	0.995842	+	0.0911015i	$0.0290388\pi$
$659$			2.03128e6i			0.182203i	−0.995842	+	0.0911015i	$0.970961\pi$
$660$	1.28660e6	+	837172.i	0.114970	+	0.0748092i
$661$	−7.84907e6			−0.698738			−0.349369	−	0.936985i	$-0.613604\pi$
$661$	−7.84907e6			−0.698738			−0.349369	+	0.936985i	$0.613604\pi$
$662$	967755.	−	3.26171e6i	0.0858263	−	0.289268i
$663$			7.87612e6i			0.695870i
$664$	9.07680e6	+	1.06566e7i	0.798937	+	0.937991i
$665$	−913580.	−	1.56103e6i	−0.0801110	−	0.136886i
$666$	−446914.	−	132600.i	−0.0390426	−	0.0115840i
$667$		−	4.94813e6i		−	0.430652i
$668$	−1.00128e7	−	6.51515e6i	−0.868185	−	0.564916i
$669$		−	1.53544e7i		−	1.32638i
$670$	2.05030e6	+	608327.i	0.176453	+	0.0523540i
$671$			1.98911e7i			1.70550i
$672$	1.31314e6	+	1.01503e7i	0.112172	+	0.867077i
$673$		−	1.23851e7i		−	1.05405i	−0.849850	−	0.527025i	$-0.823307\pi$
$673$		−	1.23851e7i		−	1.05405i	0.849850	−	0.527025i	$-0.176693\pi$
$674$	−6.14889e6	+	2.07241e7i	−0.521371	+	1.75722i
$675$			1.22689e7i			1.03645i
$676$	−6.36125e6	−	4.13917e6i	−0.535397	−	0.348375i
$677$	4.80364e6			0.402808			0.201404	−	0.979508i	$-0.435450\pi$
$677$	4.80364e6			0.402808			0.201404	+	0.979508i	$0.435450\pi$
$678$	214670.	+	63693.1i	0.0179348	+	0.00532130i
$679$	5.19654e6			0.432553
$680$	−1.92798e6	+	1.64216e6i	−0.159893	+	0.136189i
$681$	1.50405e6			0.124278
$682$	1.52481e7	+	4.52414e6i	1.25532	+	0.372456i
$683$		−	1.17375e7i		−	0.962769i	−0.876510	−	0.481384i	$-0.840134\pi$
$683$		−	1.17375e7i		−	0.962769i	0.876510	−	0.481384i	$-0.159866\pi$
$684$	97781.5	−	2.06305e6i	0.00799128	−	0.168605i
$685$			1.65553e6i			0.134806i
$686$	3.63236e6	−	1.22424e7i	0.294699	−	0.993248i
$687$	4.05427e6			0.327733
$688$	2.69382e6	+	6.07979e6i	0.216969	+	0.489686i
$689$	1.13794e7			0.913215
$690$	−478084.	+	1.61133e6i	−0.0382280	+	0.128843i
$691$	1.58528e7			1.26302			0.631512	−	0.775366i	$-0.282435\pi$
$691$	1.58528e7			1.26302			0.631512	+	0.775366i	$0.282435\pi$
$692$	9.81405e6	+	6.38586e6i	0.779082	+	0.506937i
$693$			1.86158e6i			0.147247i
$694$	8.43645e6	+	2.50311e6i	0.664907	+	0.197279i
$695$			1.84144e6i			0.144609i
$696$	4.28578e6	−	3.65042e6i	0.335356	−	0.285641i
$697$			1.63976e7i			1.27849i
$698$	−1.62653e6	+	5.48203e6i	−0.126364	+	0.425896i
$699$			1.39465e7i			1.07962i
$700$	−6.59502e6	+	1.01355e7i	−0.508711	+	0.781808i
$701$		−	6.17197e6i		−	0.474382i	−0.971463	−	0.237191i	$-0.923773\pi$
$701$		−	6.17197e6i		−	0.474382i	0.971463	−	0.237191i	$-0.0762268\pi$
$702$	2.37866e6	−	8.01700e6i	0.182175	−	0.614001i
$703$	−1.59686e6	−	2.72855e6i	−0.121865	−	0.208230i
$704$	−1.90315e6	+	1.18099e7i	−0.144724	+	0.898081i
$705$			1.51233e6i			0.114597i
$706$	−6.76393e6	−	2.00687e6i	−0.510725	−	0.151533i
$707$	1.64453e7			1.23735
$708$	−1.29904e7	−	8.45266e6i	−0.973956	−	0.633739i
$709$			1.38638e7i			1.03577i	0.855449	+	0.517887i	$0.173281\pi$
$709$			1.38638e7i			1.03577i	−0.855449	+	0.517887i	$0.826719\pi$
$710$	−57928.3	+	195241.i	−0.00431266	+	0.0145353i
$711$	−778209.			−0.0577327
$712$	1.24872e7	−	1.06360e7i	0.923135	−	0.786283i
$713$			1.74155e7i			1.28296i
$714$	1.44998e7	+	4.30213e6i	1.06443	+	0.315819i
$715$		−	1.23610e6i		−	0.0904252i
$716$	−2.73626e6	+	4.20520e6i	−0.199469	+	0.306552i
$717$	−1.73044e7			−1.25707
$718$	−1.72331e6	+	5.80821e6i	−0.124753	+	0.420467i
$719$			1.32215e7i			0.953804i	0.878956	+	0.476902i	$0.158240\pi$
$719$			1.32215e7i			0.953804i	−0.878956	+	0.476902i	$0.841760\pi$
$720$	355038.	−	157309.i	0.0255237	−	0.0113090i
$721$		−	1.18083e7i		−	0.845956i
$722$	1.00502e7	−	9.75638e6i	0.717518	−	0.696540i
$723$	−9.90387e6			−0.704627
$724$	−1.05018e7	−	6.83335e6i	−0.744588	−	0.484493i
$725$	6.65131e6			0.469962
$726$	−635327.	+	2.14130e6i	−0.0447359	+	0.150777i
$727$		−	1.08625e7i		−	0.762242i	−0.924525	−	0.381121i	$-0.875538\pi$
$727$		−	1.08625e7i		−	0.762242i	0.924525	−	0.381121i	$-0.124462\pi$
$728$	6.27449e6	−	5.34432e6i	0.438783	−	0.373735i
$729$	−1.58843e7			−1.10700
$730$	1.18076e6	−	3.97962e6i	0.0820078	−	0.276398i
$731$	9.82676e6			0.680169
$732$	−2.07702e7	−	1.35148e7i	−1.43272	−	0.932252i
$733$		−	5.85557e6i		−	0.402540i	−0.979536	−	0.201270i	$-0.935493\pi$
$733$		−	5.85557e6i		−	0.402540i	0.979536	−	0.201270i	$-0.0645069\pi$
$734$	−4.65278e6	+	1.56817e7i	−0.318767	+	1.07437i
$735$	177482.			0.0121181
$736$	−1.29900e7	+	1.68050e6i	−0.883924	+	0.114352i
$737$		−	1.49277e7i		−	1.01233i
$738$	715188.	−	2.41046e6i	0.0483369	−	0.162914i
$739$	1.67168e7			1.12601			0.563005	−	0.826453i	$-0.309645\pi$
$739$	1.67168e7			1.12601			0.563005	+	0.826453i	$0.309645\pi$
$740$	324190.	−	498228.i	0.0217631	−	0.0334463i
$741$	7.06870e6	−	4.13689e6i	0.472927	−	0.276776i
$742$	6.21573e6	−	2.09494e7i	0.414460	−	1.39689i
$743$	5.07962e6			0.337566			0.168783	−	0.985653i	$-0.446016\pi$
$743$	5.07962e6			0.337566			0.168783	+	0.985653i	$0.446016\pi$
$744$	−1.50843e7	+	1.28481e7i	−0.999060	+	0.850952i
$745$	−503896.			−0.0332621
$746$	−7.97461e6	−	2.36608e6i	−0.524641	−	0.155662i
$747$	−3.17185e6			−0.207975
$748$	1.48167e7	+	9.64099e6i	0.968270	+	0.630039i
$749$	−3.29494e6			−0.214606
$750$	−4.39283e6	−	1.30336e6i	−0.285162	−	0.0846081i
$751$	6.62925e6			0.428908			0.214454	−	0.976734i	$-0.431203\pi$
$751$	6.62925e6			0.428908			0.214454	+	0.976734i	$0.431203\pi$
$752$	−1.07753e7	+	4.77431e6i	−0.694843	+	0.307869i
$753$			8.06637e6i			0.518431i
$754$	−4.34623e6	−	1.28954e6i	−0.278410	−	0.0826048i
$755$		−	1.12020e6i		−	0.0715199i
$756$	−1.34599e7	−	8.75817e6i	−0.856520	−	0.557325i
$757$		−	1.78443e7i		−	1.13177i	−0.824483	−	0.565887i	$-0.808534\pi$
$757$		−	1.78443e7i		−	1.13177i	0.824483	−	0.565887i	$-0.191466\pi$
$758$	−3.04997e6	+	1.02796e7i	−0.192807	+	0.649833i
$759$	1.17317e7			0.739190
$760$	2.48648e6	+	867796.i	0.156153	+	0.0544984i
$761$	−5.27818e6			−0.330387			−0.165193	−	0.986261i	$-0.552825\pi$
$761$	−5.27818e6			−0.330387			−0.165193	+	0.986261i	$0.552825\pi$
$762$	5.87347e6	−	1.97958e7i	0.366444	−	1.23506i
$763$			2.35336e7i			1.46345i
$764$	−9.75945e6	+	1.49987e7i	−0.604912	+	0.929653i
$765$		−	573847.i		−	0.0354522i
$766$	−1.90052e7	−	5.63888e6i	−1.17031	−	0.347233i
$767$			1.24805e7i			0.766028i
$768$	−1.10388e7	−	1.00114e7i	−0.675332	−	0.612480i
$769$	1.13899e7			0.694549			0.347275	−	0.937763i	$-0.387107\pi$
$769$	1.13899e7			0.694549			0.347275	+	0.937763i	$0.387107\pi$
$770$	−2.27565e6	−	675190.i	−0.138318	−	0.0410392i
$771$	−2.45422e6			−0.148688
$772$	631631.	−	970716.i	0.0381435	−	0.0586204i
$773$	−2.00043e6			−0.120414			−0.0602068	−	0.998186i	$-0.519176\pi$
$773$	−2.00043e6			−0.120414			−0.0602068	+	0.998186i	$0.519176\pi$
$774$	−1.44454e6	−	428599.i	−0.0866718	−	0.0257157i
$775$	−2.34100e7			−1.40006
$776$	−5.76011e6	+	4.90620e6i	−0.343381	+	0.292476i
$777$	−3.54990e6			−0.210942
$778$	6.94710e6	−	2.34144e7i	0.411486	−	1.38686i
$779$	1.47166e7	−	8.61274e6i	0.868888	−	0.508508i
$780$	1.29073e6	+	839859.i	0.0759624	+	0.0494277i
$781$	1.42150e6			0.0833909
$782$	−5.50569e6	+	1.85563e7i	−0.321955	+	1.08511i
$783$			8.83292e6i			0.514873i
$784$	560298.	+	1.26456e6i	0.0325558	+	0.0734766i
$785$	−4.35788e6			−0.252407
$786$	5.56803e6	−	1.87664e7i	0.321474	−	1.08349i
$787$			6.23690e6i			0.358948i	0.983763	+	0.179474i	$0.0574397\pi$
$787$			6.23690e6i			0.358948i	−0.983763	+	0.179474i	$0.942560\pi$
$788$	1.07611e7	−	1.65381e7i	0.617366	−	0.948793i
$789$	−9.63591e6			−0.551062
$790$	282255.	−	951306.i	0.0160906	−	0.0542316i
$791$	−346268.			−0.0196776
$792$	−1.75757e6	−	2.06347e6i	−0.0995631	−	0.116892i
$793$			1.99550e7i			1.12686i
$794$	−630354.	+	2.12453e6i	−0.0354840	+	0.119595i
$795$	4.08278e6			0.229107
$796$	−2.70886e6	+	4.16308e6i	−0.151532	+	0.232880i
$797$	9.80871e6			0.546973			0.273487	−	0.961876i	$-0.411823\pi$
$797$	9.80871e6			0.546973			0.273487	+	0.961876i	$0.411823\pi$
$798$	−3.75485e6	−	1.52730e7i	−0.208730	−	0.849021i
$799$			1.74162e7i			0.965130i
$800$	−2.25894e6	−	1.74613e7i	−0.124790	−	0.964608i
$801$			3.71671e6i			0.204681i
$802$	8.29380e6	−	2.79533e7i	0.455321	−	1.53461i
$803$	−2.89746e7			−1.58573
$804$	1.55874e7	+	1.01425e7i	0.850420	+	0.553356i
$805$		−	2.59911e6i		−	0.141363i
$806$	1.52970e7	+	4.53866e6i	0.829411	+	0.246088i
$807$			1.44987e7i			0.783693i
$808$	−1.82288e7	+	1.55264e7i	−0.982267	+	0.836649i
$809$	−1.57251e7			−0.844738			−0.422369	−	0.906424i	$-0.638801\pi$
$809$	−1.57251e7			−0.844738			−0.422369	+	0.906424i	$0.638801\pi$
$810$	705151.	−	2.37663e6i	0.0377633	−	0.127277i
$811$			6.29338e6i			0.335994i	0.985788	+	0.167997i	$0.0537299\pi$
$811$			6.29338e6i			0.335994i	−0.985788	+	0.167997i	$0.946270\pi$
$812$	−4.74804e6	+	7.29697e6i	−0.252711	+	0.388376i
$813$	3.27155e7			1.73591
$814$	−3.97763e6	−	1.18017e6i	−0.210409	−	0.0624287i
$815$		−	4.64380e6i		−	0.244895i
$816$	−2.01341e7	+	8.92098e6i	−1.05854	+	0.469015i
$817$	−5.16145e6	−	8.81938e6i	−0.270531	−	0.462256i
$818$	7.88433e6	−	2.65732e7i	0.411985	−	1.38855i
$819$			1.86755e6i			0.0972888i
$820$	2.68722e6	+	1.74853e6i	0.139562	+	0.0908112i
$821$		−	2.12117e7i		−	1.09829i	−0.835726	−	0.549146i	$-0.814953\pi$
$821$		−	2.12117e7i		−	1.09829i	0.835726	−	0.549146i	$-0.185047\pi$
$822$	−4.09482e6	+	1.38011e7i	−0.211376	+	0.712418i
$823$			1.52175e7i			0.783146i	0.920147	+	0.391573i	$0.128069\pi$
$823$			1.52175e7i			0.783146i	−0.920147	+	0.391573i	$0.871931\pi$
$824$	1.11485e7	+	1.30889e7i	0.572003	+	0.671560i
$825$			1.57698e7i			0.806662i
$826$	2.29765e7	+	6.81718e6i	1.17175	+	0.347660i
$827$			4.76448e6i			0.242243i	0.992638	+	0.121122i	$0.0386491\pi$
$827$			4.76448e6i			0.242243i	−0.992638	+	0.121122i	$0.961351\pi$
$828$	1.61868e6	−	2.48765e6i	0.0820513	−	0.126100i
$829$	−2.38161e7			−1.20361			−0.601804	−	0.798644i	$-0.705551\pi$
$829$	−2.38161e7			−1.20361			−0.601804	+	0.798644i	$0.705551\pi$
$830$	1.15042e6	−	3.87737e6i	0.0579646	−	0.195363i
$831$	−8.64151e6			−0.434097
$832$	−1.90926e6	+	1.18478e7i	−0.0956216	+	0.593377i
$833$	2.04391e6			0.102058
$834$	−4.55465e6	+	1.53509e7i	−0.226746	+	0.764222i
$835$			3.45144e6i			0.171310i
$836$	870276.	−	1.83616e7i	0.0430667	−	0.908647i
$837$		−	3.10884e7i		−	1.53386i
$838$	−2.32322e7	−	6.89303e6i	−1.14282	−	0.339078i
$839$	−1.66134e7			−0.814805			−0.407402	−	0.913249i	$-0.633565\pi$
$839$	−1.66134e7			−0.814805			−0.407402	+	0.913249i	$0.633565\pi$
$840$	2.25120e6	−	1.91746e6i	0.110082	−	0.0937625i
$841$	−1.57226e7			−0.766539
$842$	1.36947e7	+	4.06326e6i	0.665692	+	0.197512i
$843$	703614.			0.0341009
$844$	5.92803e6	−	9.11043e6i	0.286453	−	0.440233i
$845$			2.19275e6i			0.105644i
$846$	759614.	−	2.56019e6i	0.0364894	−	0.122983i
$847$		−	3.45397e6i		−	0.165428i
$848$	1.28891e7	+	2.90899e7i	0.615505	+	1.38916i
$849$		−	4.27153e6i		−	0.203383i
$850$	−2.49435e7	−	7.40079e6i	−1.18416	−	0.351343i
$851$		−	4.54302e6i		−	0.215041i
$852$	−965824.	+	1.48432e6i	−0.0455826	+	0.0700532i
$853$			3.11169e7i			1.46428i	0.681155	+	0.732139i	$0.261478\pi$
$853$			3.11169e7i			1.46428i	−0.681155	+	0.732139i	$0.738522\pi$
$854$	3.67368e7	+	1.08999e7i	1.72368	+	0.511420i
$855$	−515019.	+	301410.i	−0.0240940	+	0.0141008i
$856$	3.65228e6	−	3.11084e6i	0.170365	−	0.145109i
$857$		−	2.33524e7i		−	1.08612i	−0.839692	−	0.543062i	$-0.817265\pi$
$857$		−	2.33524e7i		−	1.08612i	0.839692	−	0.543062i	$-0.182735\pi$
$858$	3.05740e6	−	1.03046e7i	0.141786	−	0.477875i
$859$	−8.80191e6			−0.407000			−0.203500	−	0.979075i	$-0.565232\pi$
$859$	−8.80191e6			−0.407000			−0.203500	+	0.979075i	$0.565232\pi$
$860$	1.04786e6	−	1.61040e6i	0.0483124	−	0.0742485i
$861$		−	1.91466e7i		−	0.880204i
$862$	7.70339e6	+	2.28561e6i	0.353113	+	0.104769i
$863$	4.16374e7			1.90308			0.951539	−	0.307530i	$-0.0995023\pi$
$863$	4.16374e7			1.90308			0.951539	+	0.307530i	$0.0995023\pi$
$864$	2.31885e7	−	2.99986e6i	1.05679	−	0.136715i
$865$		−	3.38294e6i		−	0.153728i
$866$	287228.	−	968068.i	0.0130146	−	0.0438643i
$867$			1.23636e7i			0.558597i
$868$	1.67112e7	−	2.56825e7i	0.752851	−	1.15701i
$869$	−6.92623e6			−0.311134
$870$	−1.55937e6	−	462667.i	−0.0698473	−	0.0207238i
$871$		−	1.49756e7i		−	0.668866i
$872$	−2.22187e7	−	2.60859e7i	−0.989527	−	1.16175i
$873$		−	1.71445e6i		−	0.0761359i
$874$	1.95458e7	−	4.80531e6i	0.865517	−	0.212786i
$875$	7.08575e6			0.312871
$876$	1.96866e7	−	3.02551e7i	0.866781	−	1.33210i
$877$	2.62664e7			1.15319			0.576597	−	0.817029i	$-0.304380\pi$
$877$	2.62664e7			1.15319			0.576597	+	0.817029i	$0.304380\pi$
$878$	−3.52044e7	−	1.04452e7i	−1.54121	−	0.457279i
$879$			2.57342e7i			1.12341i
$880$	3.15991e6	−	1.40009e6i	0.137552	−	0.0609464i
$881$	3.51136e6			0.152418			0.0762088	−	0.997092i	$-0.475718\pi$
$881$	3.51136e6			0.152418			0.0762088	+	0.997092i	$0.475718\pi$
$882$	−300456.	−	89145.8i	−0.0130050	−	0.00385860i
$883$	−3.99212e7			−1.72307			−0.861533	−	0.507702i	$-0.830495\pi$
$883$	−3.99212e7			−1.72307			−0.861533	+	0.507702i	$0.830495\pi$
$884$	1.48642e7	+	9.67194e6i	0.639752	+	0.416277i
$885$			4.47784e6i			0.192181i
$886$	5.68533e6	+	1.68685e6i	0.243316	+	0.0721925i
$887$	−1.51954e7			−0.648492			−0.324246	−	0.945973i	$-0.605111\pi$
$887$	−1.51954e7			−0.648492			−0.324246	+	0.945973i	$0.605111\pi$
$888$	3.93490e6	−	3.35156e6i	0.167456	−	0.142631i
$889$			3.19312e7i			1.35507i
$890$	−4.54343e6	−	1.34804e6i	−0.192269	−	0.0570465i
$891$	−1.73037e7			−0.730203
$892$	−2.89776e7	−	1.88553e7i	−1.21941	−	0.793453i
$893$	1.56308e7	−	9.14775e6i	0.655921	−	0.383871i
$894$	−4.20067e6	−	1.24635e6i	−0.175782	−	0.0521549i
$895$	1.44955e6			0.0604888
$896$	2.07688e7	+	9.98649e6i	0.864255	+	0.415569i
$897$	1.17693e7			0.488395
$898$	−1.84495e6	+	6.21818e6i	−0.0763472	+	0.257320i
$899$	−1.68539e7			−0.695505
$900$	3.34392e6	+	2.17584e6i	0.137610	+	0.0895409i
$901$	4.70179e7			1.92953
$902$	6.36532e6	−	2.14536e7i	0.260498	−	0.877978i
$903$	−1.14742e7			−0.468277
$904$	383822.	−	326921.i	0.0156210	−	0.0133052i
$905$			3.62000e6i			0.146922i
$906$	2.77072e6	−	9.33839e6i	0.112143	−	0.377965i
$907$		−	1.67286e6i		−	0.0675215i	−0.999430	−	0.0337607i	$-0.989252\pi$
$907$		−	1.67286e6i		−	0.0675215i	0.999430	−	0.0337607i	$-0.0107484\pi$
$908$	1.84699e6	−	2.83852e6i	0.0743445	−	0.114256i
$909$		−	5.42565e6i		−	0.217792i
$910$	−2.28295e6	−	677357.i	−0.0913889	−	0.0271153i
$911$	4.59483e6			0.183431			0.0917156	−	0.995785i	$-0.470765\pi$
$911$	4.59483e6			0.183431			0.0917156	+	0.995785i	$0.470765\pi$
$912$	1.85818e7	+	1.33844e7i	0.739776	+	0.532858i
$913$	−2.82302e7			−1.12082
$914$	1.97524e7	+	5.86059e6i	0.782088	+	0.232047i
$915$			7.15956e6i			0.282705i
$916$	4.97868e6	−	7.65143e6i	0.196054	−	0.301303i
$917$			3.02707e7i			1.18877i
$918$	9.82822e6	−	3.31249e7i	0.384918	−	1.29732i
$919$			3.90980e7i			1.52709i	0.645752	+	0.763547i	$0.276544\pi$
$919$			3.90980e7i			1.52709i	−0.645752	+	0.763547i	$0.723456\pi$
$920$	2.45389e6	+	2.88099e6i	0.0955842	+	0.112221i
$921$	−3.33817e7			−1.29676
$922$	4.48740e6	−	1.51242e7i	0.173847	−	0.585931i
$923$	1.42606e6			0.0550977
$924$	−1.73006e7	−	1.12573e7i	−0.666626	−	0.433764i
$925$	6.10676e6			0.234670
$926$	1.86271e6	−	6.27805e6i	0.0713868	−	0.240601i
$927$	−3.89580e6			−0.148901
$928$	−1.62630e6	−	1.25711e7i	−0.0619915	−	0.479185i
$929$	1.09135e7			0.414881			0.207440	−	0.978248i	$-0.433487\pi$
$929$	1.09135e7			0.414881			0.207440	+	0.978248i	$0.433487\pi$
$930$	5.48836e6	+	1.62841e6i	0.208082	+	0.0617384i
$931$	−1.07355e6	−	1.83438e6i	−0.0405927	−	0.0693608i
$932$	2.63205e7	+	1.71264e7i	0.992555	+	0.645841i
$933$	4.45418e7			1.67519
$934$	−2.95919e7	−	8.77998e6i	−1.10996	−	0.329326i
$935$		−	5.10736e6i		−	0.191059i
$936$	−1.76321e6	−	2.07009e6i	−0.0657830	−	0.0772325i
$937$	−2.77150e7			−1.03126			−0.515628	−	0.856813i	$-0.672441\pi$
$937$	−2.77150e7			−1.03126			−0.515628	+	0.856813i	$0.672441\pi$
$938$	−2.75699e7	−	8.18005e6i	−1.02312	−	0.303563i
$939$		−	3.24942e7i		−	1.20266i
$940$	2.85415e6	+	1.85715e6i	0.105355	+	0.0685532i
$941$	5.89140e6			0.216893			0.108446	−	0.994102i	$-0.465412\pi$
$941$	5.89140e6			0.216893			0.108446	+	0.994102i	$0.465412\pi$
$942$	−3.63290e7	−	1.07789e7i	−1.33391	−	0.395773i
$943$	2.45030e7			0.897306
$944$	−3.19046e7	+	1.41362e7i	−1.16526	+	0.516302i
$945$			4.63968e6i			0.169009i
$946$	−1.28567e7	−	3.81462e6i	−0.467092	−	0.138587i
$947$	−1.18149e6			−0.0428111			−0.0214055	−	0.999771i	$-0.506814\pi$
$947$	−1.18149e6			−0.0428111			−0.0214055	+	0.999771i	$0.506814\pi$
$948$	4.70596e6	−	7.23232e6i	0.170070	−	0.261371i
$949$	−2.90676e7			−1.04772
$950$	6.45934e6	+	2.62737e7i	0.232209	+	0.944521i
$951$		−	1.36929e6i		−	0.0490960i
$952$	2.59251e7	−	2.20818e7i	0.927104	−	0.789663i
$953$			1.68084e7i			0.599508i	0.954017	+	0.299754i	$0.0969046\pi$
$953$			1.68084e7i			0.599508i	−0.954017	+	0.299754i	$0.903095\pi$
$954$	−6.91167e6	−	2.05071e6i	−0.245874	−	0.0729512i
$955$	5.17012e6			0.183439
$956$	−2.12499e7	+	3.26577e7i	−0.751991	+	1.15569i
$957$			1.13534e7i			0.400723i
$958$	−7.21675e6	+	2.43232e7i	−0.254055	+	0.856263i
$959$		−	2.22616e7i		−	0.781644i
$960$	−685014.	+	4.25083e6i	−0.0239895	+	0.148866i
$961$	3.06898e7			1.07198
$962$	−3.99040e6	−	1.18396e6i	−0.139021	−	0.0412477i
$963$			1.08707e6i			0.0377740i
$964$	−1.21620e7	+	1.86911e7i	−0.421516	+	0.647802i
$965$	−334610.			−0.0115670
$966$	6.42870e6	−	2.16672e7i	0.221656	−	0.747067i
$967$		−	4.47806e7i		−	1.54001i	−0.638037	−	0.770006i	$-0.720253\pi$
$967$		−	4.47806e7i		−	1.54001i	0.638037	−	0.770006i	$-0.279747\pi$
$968$	3.26098e6	+	3.82856e6i	0.111856	+	0.131325i
$969$	2.92066e7	−	1.70929e7i	0.999246	−	0.584799i
$970$	2.09580e6	+	621828.i	0.0715188	+	0.0212198i
$971$		−	4.12614e7i		−	1.40441i	−0.711972	−	0.702207i	$-0.752198\pi$
$971$		−	4.12614e7i		−	1.40441i	0.711972	−	0.702207i	$-0.247802\pi$
$972$	−5.36173e6	+	8.24012e6i	−0.182028	+	0.279749i
$973$		−	2.47614e7i		−	0.838481i
$974$	1.68127e7	+	4.98836e6i	0.567858	+	0.168485i
$975$			1.58204e7i			0.532975i
$976$	−5.10119e7	+	2.26022e7i	−1.71414	+	0.759498i
$977$		−	5.25883e7i		−	1.76260i	−0.472560	−	0.881299i	$-0.656670\pi$
$977$		−	5.25883e7i		−	1.76260i	0.472560	−	0.881299i	$-0.343330\pi$
$978$	1.14861e7	−	3.87125e7i	0.383994	−	1.29421i
$979$			3.30796e7i			1.10307i
$980$	217949.	−	334953.i	0.00724920	−	0.0111409i
$981$	7.76425e6			0.257589
$982$	−7.77317e6	−	2.30632e6i	−0.257229	−	0.0763203i
$983$	−2.31566e7			−0.764347			−0.382173	−	0.924091i	$-0.624824\pi$
$983$	−2.31566e7			−0.764347			−0.382173	+	0.924091i	$0.624824\pi$
$984$	1.80768e7	+	2.12231e7i	0.595161	+	0.698748i
$985$	−5.70076e6			−0.187216
$986$	−1.79579e7	−	5.32814e6i	−0.588251	−	0.174535i
$987$		−	2.03360e7i		−	0.664464i
$988$	873070.	−	1.84206e7i	0.0284549	−	0.600358i
$989$		−	1.46842e7i		−	0.477375i
$990$	−222760.	+	750786.i	−0.00722352	+	0.0243460i
$991$	−2.99104e7			−0.967472			−0.483736	−	0.875214i	$-0.660721\pi$
$991$	−2.99104e7			−0.967472			−0.483736	+	0.875214i	$0.660721\pi$
$992$	5.72396e6	+	4.42454e7i	0.184679	+	1.42754i
$993$	−8.54768e6			−0.275090
$994$	778949.	−	2.62536e6i	0.0250059	−	0.0842796i
$995$	1.43503e6			0.0459519
$996$	1.91808e7	−	2.94778e7i	0.612657	−	0.941556i
$997$			5.73919e7i			1.82858i	0.405065	+	0.914288i	$0.367249\pi$
$997$			5.73919e7i			1.82858i	−0.405065	+	0.914288i	$0.632751\pi$
$998$	−1.83986e7	−	5.45891e6i	−0.584735	−	0.173492i
$999$			8.10976e6i			0.257095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.11	✓	96
4.3	odd	2		608.6.b.b.303.27		96
8.3	odd	2	inner	152.6.b.b.75.85	yes	96
8.5	even	2		608.6.b.b.303.28		96
19.18	odd	2	inner	152.6.b.b.75.86	yes	96
76.75	even	2		608.6.b.b.303.69		96
152.37	odd	2		608.6.b.b.303.70		96
152.75	even	2	inner	152.6.b.b.75.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.11	✓	96	1.1	even	1	trivial
152.6.b.b.75.12	yes	96	152.75	even	2	inner
152.6.b.b.75.85	yes	96	8.3	odd	2	inner
152.6.b.b.75.86	yes	96	19.18	odd	2	inner
608.6.b.b.303.27		96	4.3	odd	2
608.6.b.b.303.28		96	8.5	even	2
608.6.b.b.303.69		96	76.75	even	2
608.6.b.b.303.70		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)

\(f(q)\)	\(=\)	\(q+(-5.42318 - 1.60907i) q^{2} +14.2121i q^{3} +(26.8218 + 17.4525i) q^{4} -9.24558i q^{5} +(22.8682 - 77.0746i) q^{6} +124.323i q^{7} +(-117.377 - 137.806i) q^{8} +41.0170 q^{9} +O(q^{10})\)	\(q+(-5.42318 - 1.60907i) q^{2} +14.2121i q^{3} +(26.8218 + 17.4525i) q^{4} -9.24558i q^{5} +(22.8682 - 77.0746i) q^{6} +124.323i q^{7} +(-117.377 - 137.806i) q^{8} +41.0170 q^{9} +(-14.8768 + 50.1404i) q^{10} +365.060 q^{11} +(-248.037 + 381.193i) q^{12} +366.232 q^{13} +(200.045 - 674.228i) q^{14} +131.399 q^{15} +(414.817 + 936.217i) q^{16} +1513.21 q^{17} +(-222.443 - 65.9992i) q^{18} +(-794.804 - 1358.08i) q^{19} +(161.359 - 247.983i) q^{20} -1766.89 q^{21} +(-1979.79 - 587.407i) q^{22} -2261.20i q^{23} +(1958.52 - 1668.17i) q^{24} +3039.52 q^{25} +(-1986.14 - 589.293i) q^{26} +4036.47i q^{27} +(-2169.76 + 3334.57i) q^{28} +2188.28 q^{29} +(-712.599 - 211.430i) q^{30} -7701.88 q^{31} +(-743.189 - 5744.75i) q^{32} +5188.26i q^{33} +(-8206.40 - 2434.86i) q^{34} +1149.44 q^{35} +(1100.15 + 715.851i) q^{36} +2009.12 q^{37} +(2125.12 + 8644.02i) q^{38} +5204.91i q^{39} +(-1274.10 + 1085.22i) q^{40} +10836.3i q^{41} +(9582.18 + 2843.05i) q^{42} +6494.00 q^{43} +(9791.57 + 6371.23i) q^{44} -379.226i q^{45} +(-3638.42 + 12262.9i) q^{46} +11509.4i q^{47} +(-13305.6 + 5895.41i) q^{48} +1350.71 q^{49} +(-16483.9 - 4890.80i) q^{50} +21505.8i q^{51} +(9823.00 + 6391.68i) q^{52} +31071.7 q^{53} +(6494.96 - 21890.5i) q^{54} -3375.19i q^{55} +(17132.6 - 14592.7i) q^{56} +(19301.2 - 11295.8i) q^{57} +(-11867.4 - 3521.09i) q^{58} +34078.2i q^{59} +(3524.35 + 2293.24i) q^{60} +54487.2i q^{61} +(41768.7 + 12392.9i) q^{62} +5099.37i q^{63} +(-5213.24 + 32350.6i) q^{64} -3386.03i q^{65} +(8348.27 - 28136.9i) q^{66} -40891.1i q^{67} +(40586.9 + 26409.3i) q^{68} +32136.3 q^{69} +(-6233.63 - 1849.53i) q^{70} +3893.87 q^{71} +(-4814.45 - 5652.41i) q^{72} -79369.5 q^{73} +(-10895.8 - 3232.82i) q^{74} +43197.9i q^{75} +(2383.93 - 50297.5i) q^{76} +45385.5i q^{77} +(8375.07 - 28227.2i) q^{78} -18972.8 q^{79} +(8655.87 - 3835.22i) q^{80} -47399.5 q^{81} +(17436.4 - 58767.3i) q^{82} -77330.3 q^{83} +(-47391.2 - 30836.8i) q^{84} -13990.5i q^{85} +(-35218.1 - 10449.3i) q^{86} +31100.0i q^{87} +(-42849.7 - 50307.6i) q^{88} +90614.0i q^{89} +(-610.200 + 2056.61i) q^{90} +45531.2i q^{91} +(39463.7 - 60649.4i) q^{92} -109460. i q^{93} +(18519.5 - 62417.8i) q^{94} +(-12556.2 + 7348.42i) q^{95} +(81644.7 - 10562.3i) q^{96} -41798.6i q^{97} +(-7325.15 - 2173.39i) q^{98} +14973.7 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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