LMFDB - Embedded newform 72.5.m.a.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,5,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, 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:	$7.44263734204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	72.41
Dual form			72.5.m.a.65.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.21271 + 8.40705i) q^{3} +(36.5152 + 21.0820i) q^{5} +(-13.5757 - 23.5138i) q^{7} +(-60.3569 + 54.0189i) q^{9} +O(q^{10})$	\(q+(3.21271 + 8.40705i) q^{3} +(36.5152 + 21.0820i) q^{5} +(-13.5757 - 23.5138i) q^{7} +(-60.3569 + 54.0189i) q^{9} +(62.1394 - 35.8762i) q^{11} +(-77.8791 + 134.890i) q^{13} +(-59.9250 + 374.715i) q^{15} +266.582i q^{17} +404.309 q^{19} +(154.067 - 189.674i) q^{21} +(-733.066 - 423.236i) q^{23} +(576.404 + 998.362i) q^{25} +(-648.049 - 333.877i) q^{27} +(786.534 - 454.106i) q^{29} +(-92.9311 + 160.961i) q^{31} +(501.249 + 407.149i) q^{33} -1144.81i q^{35} +1242.05 q^{37} +(-1384.23 - 221.369i) q^{39} +(-1800.50 - 1039.52i) q^{41} +(-1135.43 - 1966.61i) q^{43} +(-3342.77 + 700.061i) q^{45} +(3348.82 - 1933.44i) q^{47} +(831.902 - 1440.90i) q^{49} +(-2241.17 + 856.453i) q^{51} -4584.58i q^{53} +3025.37 q^{55} +(1298.93 + 3399.05i) q^{57} +(2294.86 + 1324.94i) q^{59} +(3399.92 + 5888.83i) q^{61} +(2089.57 + 685.876i) q^{63} +(-5687.53 + 3283.70i) q^{65} +(-2414.00 + 4181.17i) q^{67} +(1203.03 - 7522.65i) q^{69} -1946.43i q^{71} +4098.42 q^{73} +(-6541.45 + 8053.31i) q^{75} +(-1687.17 - 974.087i) q^{77} +(-963.790 - 1669.33i) q^{79} +(724.921 - 6520.83i) q^{81} +(-4204.15 + 2427.27i) q^{83} +(-5620.10 + 9734.30i) q^{85} +(6344.60 + 5153.52i) q^{87} +3890.92i q^{89} +4229.04 q^{91} +(-1651.77 - 264.154i) q^{93} +(14763.4 + 8523.66i) q^{95} +(-6132.12 - 10621.1i) q^{97} +(-1812.55 + 5522.08i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 100 * q^9	$ 24 q + 4 q^{3} - 100 q^{9} + 252 q^{11} - 80 q^{15} - 408 q^{19} + 24 q^{21} + 720 q^{23} + 1500 q^{25} - 1280 q^{27} + 2376 q^{29} - 1104 q^{31} - 1412 q^{33} - 4184 q^{39} + 1980 q^{41} + 1476 q^{43} - 4696 q^{45} + 4536 q^{47} - 6084 q^{49} - 7828 q^{51} + 2544 q^{55} - 1204 q^{57} + 10332 q^{59} + 2784 q^{61} + 9072 q^{63} + 17280 q^{65} - 2604 q^{67} + 5680 q^{69} + 5112 q^{73} - 15412 q^{75} - 28368 q^{77} + 3480 q^{79} - 26548 q^{81} - 23400 q^{83} + 7392 q^{85} - 3192 q^{87} - 14208 q^{91} + 39488 q^{93} + 57528 q^{95} - 4020 q^{97} + 50744 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	3.21271	+	8.40705i	0.356968	+	0.934117i
$3$	3.21271	+	8.40705i	0.356968	+	0.934117i
$4$		0			0
$5$	36.5152	+	21.0820i	1.46061	+	0.843281i	0.999039	−	0.0438239i	$-0.0139541\pi$
$5$	36.5152	+	21.0820i	1.46061	+	0.843281i	0.461567	+	0.887105i	$0.347287\pi$
$6$		0			0
$7$	−13.5757	−	23.5138i	−0.277055	−	0.479873i	0.693597	−	0.720363i	$-0.256025\pi$
$7$	−13.5757	−	23.5138i	−0.277055	−	0.479873i	−0.970651	+	0.240491i	$0.922692\pi$
$8$		0			0
$9$	−60.3569	+	54.0189i	−0.745147	+	0.666900i
$10$		0			0
$11$	62.1394	−	35.8762i	0.513548	−	0.296497i	−0.220743	−	0.975332i	$-0.570848\pi$
$11$	62.1394	−	35.8762i	0.513548	−	0.296497i	0.734291	+	0.678835i	$0.237515\pi$
$12$		0			0
$13$	−77.8791	+	134.890i	−0.460823	+	0.798169i	−0.999002	−	0.0446617i	$-0.985779\pi$
$13$	−77.8791	+	134.890i	−0.460823	+	0.798169i	0.538179	+	0.842830i	$0.319112\pi$
$14$		0			0
$15$	−59.9250	+	374.715i	−0.266333	+	1.66540i
$16$		0			0
$17$			266.582i			0.922431i	0.887288	+	0.461215i	$0.152586\pi$
$17$			266.582i			0.922431i	−0.887288	+	0.461215i	$0.847414\pi$
$18$		0			0
$19$	404.309			1.11997			0.559985	−	0.828503i	$-0.310807\pi$
$19$	404.309			1.11997			0.559985	+	0.828503i	$0.310807\pi$
$20$		0			0
$21$	154.067	−	189.674i	0.349357	−	0.430100i
$22$		0			0
$23$	−733.066	−	423.236i	−1.38576	−	0.800067i	−0.392924	−	0.919571i	$-0.628536\pi$
$23$	−733.066	−	423.236i	−1.38576	−	0.800067i	−0.992834	+	0.119504i	$0.961870\pi$
$24$		0			0
$25$	576.404	+	998.362i	0.922247	+	1.59738i
$26$		0			0
$27$	−648.049	−	333.877i	−0.888956	−	0.457993i
$28$		0			0
$29$	786.534	−	454.106i	0.935237	−	0.539959i	0.0467730	−	0.998906i	$-0.485106\pi$
$29$	786.534	−	454.106i	0.935237	−	0.539959i	0.888464	+	0.458946i	$0.151773\pi$
$30$		0			0
$31$	−92.9311	+	160.961i	−0.0967025	+	0.167494i	−0.910318	−	0.413910i	$-0.864163\pi$
$31$	−92.9311	+	160.961i	−0.0967025	+	0.167494i	0.813615	+	0.581404i	$0.197496\pi$
$32$		0			0
$33$	501.249	+	407.149i	0.460284	+	0.373874i
$34$		0			0
$35$		−	1144.81i		−	0.934540i
$36$		0			0
$37$	1242.05			0.907272			0.453636	−	0.891187i	$-0.350127\pi$
$37$	1242.05			0.907272			0.453636	+	0.891187i	$0.350127\pi$
$38$		0			0
$39$	−1384.23	−	221.369i	−0.910082	−	0.145541i
$40$		0			0
$41$	−1800.50	−	1039.52i	−1.07109	−	0.618392i	−0.142609	−	0.989779i	$-0.545549\pi$
$41$	−1800.50	−	1039.52i	−1.07109	−	0.618392i	−0.928478	+	0.371387i	$0.878882\pi$
$42$		0			0
$43$	−1135.43	−	1966.61i	−0.614075	−	1.06361i	−0.990546	−	0.137181i	$-0.956196\pi$
$43$	−1135.43	−	1966.61i	−0.614075	−	1.06361i	0.376471	−	0.926429i	$-0.377138\pi$
$44$		0			0
$45$	−3342.77	+	700.061i	−1.65075	+	0.345709i
$46$		0			0
$47$	3348.82	−	1933.44i	1.51599	−	0.875257i	0.516166	−	0.856489i	$-0.327359\pi$
$47$	3348.82	−	1933.44i	1.51599	−	0.875257i	0.999824	−	0.0187685i	$-0.00597456\pi$
$48$		0			0
$49$	831.902	−	1440.90i	0.346482	−	0.600124i
$50$		0			0
$51$	−2241.17	+	856.453i	−0.861658	+	0.329278i
$52$		0			0
$53$		−	4584.58i		−	1.63210i	−0.577979	−	0.816052i	$-0.696158\pi$
$53$		−	4584.58i		−	1.63210i	0.577979	−	0.816052i	$-0.303842\pi$
$54$		0			0
$55$	3025.37			1.00012
$56$		0			0
$57$	1298.93	+	3399.05i	0.399794	+	1.04618i
$58$		0			0
$59$	2294.86	+	1324.94i	0.659254	+	0.380621i	0.791993	−	0.610530i	$-0.209044\pi$
$59$	2294.86	+	1324.94i	0.659254	+	0.380621i	−0.132739	+	0.991151i	$0.542377\pi$
$60$		0			0
$61$	3399.92	+	5888.83i	0.913710	+	1.58259i	0.808779	+	0.588113i	$0.200129\pi$
$61$	3399.92	+	5888.83i	0.913710	+	1.58259i	0.104931	+	0.994479i	$0.466538\pi$
$62$		0			0
$63$	2089.57	+	685.876i	0.526473	+	0.172808i
$64$		0			0
$65$	−5687.53	+	3283.70i	−1.34616	+	0.777207i
$66$		0			0
$67$	−2414.00	+	4181.17i	−0.537758	+	0.931425i	0.461266	+	0.887262i	$0.347395\pi$
$67$	−2414.00	+	4181.17i	−0.537758	+	0.931425i	−0.999024	+	0.0441630i	$0.985938\pi$
$68$		0			0
$69$	1203.03	−	7522.65i	0.252685	−	1.58006i
$70$		0			0
$71$		−	1946.43i		−	0.386120i	−0.981187	−	0.193060i	$-0.938159\pi$
$71$		−	1946.43i		−	0.386120i	0.981187	−	0.193060i	$-0.0618413\pi$
$72$		0			0
$73$	4098.42			0.769079			0.384539	−	0.923109i	$-0.374360\pi$
$73$	4098.42			0.769079			0.384539	+	0.923109i	$0.374360\pi$
$74$		0			0
$75$	−6541.45	+	8053.31i	−1.16293	+	1.43170i
$76$		0			0
$77$	−1687.17	−	974.087i	−0.284562	−	0.164292i
$78$		0			0
$79$	−963.790	−	1669.33i	−0.154429	−	0.267478i	0.778422	−	0.627741i	$-0.216020\pi$
$79$	−963.790	−	1669.33i	−0.154429	−	0.267478i	−0.932851	+	0.360263i	$0.882687\pi$
$80$		0			0
$81$	724.921	−	6520.83i	0.110489	−	0.993877i
$82$		0			0
$83$	−4204.15	+	2427.27i	−0.610270	+	0.352339i	−0.773071	−	0.634319i	$-0.781280\pi$
$83$	−4204.15	+	2427.27i	−0.610270	+	0.352339i	0.162801	+	0.986659i	$0.447947\pi$
$84$		0			0
$85$	−5620.10	+	9734.30i	−0.777869	+	1.34731i
$86$		0			0
$87$	6344.60	+	5153.52i	0.838235	+	0.680872i
$88$		0			0
$89$			3890.92i			0.491215i	0.969369	+	0.245608i	$0.0789875\pi$
$89$			3890.92i			0.491215i	−0.969369	+	0.245608i	$0.921013\pi$
$90$		0			0
$91$	4229.04			0.510692
$92$		0			0
$93$	−1651.77	−	264.154i	−0.190978	−	0.0305415i
$94$		0			0
$95$	14763.4	+	8523.66i	1.63583	+	0.944450i
$96$		0			0
$97$	−6132.12	−	10621.1i	−0.651729	−	1.12883i	−0.982703	−	0.185188i	$-0.940711\pi$
$97$	−6132.12	−	10621.1i	−0.651729	−	1.12883i	0.330974	−	0.943640i	$-0.392623\pi$
$98$		0			0
$99$	−1812.55	+	5522.08i	−0.184935	+	0.563420i
$100$		0			0
$101$	3727.37	−	2152.00i	0.365392	−	0.210959i	−0.306051	−	0.952015i	$-0.599008\pi$
$101$	3727.37	−	2152.00i	0.365392	−	0.210959i	0.671444	+	0.741056i	$0.265675\pi$
$102$		0			0
$103$	4651.41	−	8056.49i	0.438440	−	0.759401i	−0.559129	−	0.829081i	$-0.688864\pi$
$103$	4651.41	−	8056.49i	0.438440	−	0.759401i	0.997569	+	0.0696796i	$0.0221977\pi$
$104$		0			0
$105$	9624.49	−	3677.95i	0.872969	−	0.333601i
$106$		0			0
$107$			1104.60i			0.0964802i	0.998836	+	0.0482401i	$0.0153613\pi$
$107$			1104.60i			0.0964802i	−0.998836	+	0.0482401i	$0.984639\pi$
$108$		0			0
$109$	−4058.15			−0.341566			−0.170783	−	0.985309i	$-0.554630\pi$
$109$	−4058.15			−0.341566			−0.170783	+	0.985309i	$0.554630\pi$
$110$		0			0
$111$	3990.37	+	10442.0i	0.323867	+	0.847497i
$112$		0			0
$113$	−12170.6	−	7026.70i	−0.953137	−	0.550294i	−0.0590829	−	0.998253i	$-0.518818\pi$
$113$	−12170.6	−	7026.70i	−0.953137	−	0.550294i	−0.894054	+	0.447959i	$0.852151\pi$
$114$		0			0
$115$	−17845.3	−	30909.0i	−1.34936	−	2.33717i
$116$		0			0
$117$	−2586.09	−	12348.5i	−0.188917	−	0.902076i
$118$		0			0
$119$	6268.36	−	3619.04i	0.442649	−	0.255564i
$120$		0			0
$121$	−4746.30	+	8220.83i	−0.324179	+	0.561494i
$122$		0			0
$123$	2954.79	−	18476.5i	0.195307	−	1.22127i
$124$		0			0
$125$			22254.6i			1.42429i
$126$		0			0
$127$	−10448.8			−0.647827			−0.323914	−	0.946087i	$-0.604999\pi$
$127$	−10448.8			−0.647827			−0.323914	+	0.946087i	$0.604999\pi$
$128$		0			0
$129$	12885.6	−	15863.7i	0.774330	−	0.953293i
$130$		0			0
$131$	−405.818	−	234.299i	−0.0236477	−	0.0136530i	0.488130	−	0.872771i	$-0.337679\pi$
$131$	−405.818	−	234.299i	−0.0236477	−	0.0136530i	−0.511777	+	0.859118i	$0.671013\pi$
$132$		0			0
$133$	−5488.77	−	9506.82i	−0.310293	−	0.537443i
$134$		0			0
$135$	−16624.8	−	25853.7i	−0.912198	−	1.41859i
$136$		0			0
$137$	−10655.0	+	6151.69i	−0.567694	+	0.327758i	−0.756228	−	0.654308i	$-0.772960\pi$
$137$	−10655.0	+	6151.69i	−0.567694	+	0.327758i	0.188534	+	0.982067i	$0.439626\pi$
$138$		0			0
$139$	−12966.4	+	22458.4i	−0.671103	+	1.16238i	0.306489	+	0.951874i	$0.400846\pi$
$139$	−12966.4	+	22458.4i	−0.671103	+	1.16238i	−0.977592	+	0.210510i	$0.932488\pi$
$140$		0			0
$141$	27013.4	+	21942.1i	1.35875	+	1.10367i
$142$		0			0
$143$			11176.0i			0.546531i
$144$		0			0
$145$	38293.9			1.82135
$146$		0			0
$147$	14786.4	+	2364.65i	0.684268	+	0.109429i
$148$		0			0
$149$	−15908.0	−	9184.47i	−0.716543	−	0.413696i	0.0969362	−	0.995291i	$-0.469096\pi$
$149$	−15908.0	−	9184.47i	−0.716543	−	0.413696i	−0.813479	+	0.581595i	$0.802429\pi$
$150$		0			0
$151$	−2827.61	−	4897.56i	−0.124012	−	0.214796i	0.797334	−	0.603538i	$-0.206243\pi$
$151$	−2827.61	−	4897.56i	−0.124012	−	0.214796i	−0.921346	+	0.388742i	$0.872910\pi$
$152$		0			0
$153$	−14400.5	−	16090.1i	−0.615169	−	0.687347i
$154$		0			0
$155$	−6786.79	+	3918.35i	−0.282489	+	0.163095i
$156$		0			0
$157$	−5449.09	+	9438.10i	−0.221067	+	0.382900i	−0.955132	−	0.296179i	$-0.904287\pi$
$157$	−5449.09	+	9438.10i	−0.221067	+	0.382900i	0.734065	+	0.679079i	$0.237621\pi$
$158$		0			0
$159$	38542.8	−	14728.9i	1.52458	−	0.582609i
$160$		0			0
$161$			22982.8i			0.886649i
$162$		0			0
$163$	−30912.5			−1.16348			−0.581741	−	0.813374i	$-0.697628\pi$
$163$	−30912.5			−1.16348			−0.581741	+	0.813374i	$0.697628\pi$
$164$		0			0
$165$	9719.65	+	25434.4i	0.357012	+	0.934231i
$166$		0			0
$167$	11623.4	+	6710.79i	0.416775	+	0.240625i	0.693697	−	0.720267i	$-0.255981\pi$
$167$	11623.4	+	6710.79i	0.416775	+	0.240625i	−0.276922	+	0.960893i	$0.589314\pi$
$168$		0			0
$169$	2150.20	+	3724.26i	0.0752846	+	0.130397i
$170$		0			0
$171$	−24402.9	+	21840.3i	−0.834543	+	0.746907i
$172$		0			0
$173$	21187.2	−	12232.4i	0.707915	−	0.408715i	−0.102373	−	0.994746i	$-0.532644\pi$
$173$	21187.2	−	12232.4i	0.707915	−	0.408715i	0.810289	+	0.586031i	$0.199310\pi$
$174$		0			0
$175$	15650.2	−	27106.9i	0.511026	−	0.885122i
$176$		0			0
$177$	−3766.10	+	23549.7i	−0.120211	+	0.751690i
$178$		0			0
$179$		−	2795.04i		−	0.0872333i	−0.999048	−	0.0436167i	$-0.986112\pi$
$179$		−	2795.04i		−	0.0872333i	0.999048	−	0.0436167i	$-0.0138880\pi$
$180$		0			0
$181$	10760.7			0.328460			0.164230	−	0.986422i	$-0.447486\pi$
$181$	10760.7			0.328460			0.164230	+	0.986422i	$0.447486\pi$
$182$		0			0
$183$	−38584.7	+	47502.4i	−1.15216	+	1.41845i
$184$		0			0
$185$	45353.8	+	26185.0i	1.32517	+	0.765085i
$186$		0			0
$187$	9563.96	+	16565.3i	0.273498	+	0.473713i
$188$		0			0
$189$	947.008	+	19770.7i	0.0265112	+	0.553475i
$190$		0			0
$191$	−13059.0	+	7539.60i	−0.357966	+	0.206672i	−0.668188	−	0.743992i	$-0.732930\pi$
$191$	−13059.0	+	7539.60i	−0.357966	+	0.206672i	0.310222	+	0.950664i	$0.399597\pi$
$192$		0			0
$193$	−29135.7	+	50464.6i	−0.782189	+	1.35479i	0.148475	+	0.988916i	$0.452563\pi$
$193$	−29135.7	+	50464.6i	−0.782189	+	1.35479i	−0.930664	+	0.365875i	$0.880770\pi$
$194$		0			0
$195$	−45878.6	−	37265.8i	−1.20654	−	0.980034i
$196$		0			0
$197$		−	16205.3i		−	0.417565i	−0.977962	−	0.208782i	$-0.933050\pi$
$197$		−	16205.3i		−	0.417565i	0.977962	−	0.208782i	$-0.0669500\pi$
$198$		0			0
$199$	54924.2			1.38694			0.693469	−	0.720486i	$-0.256081\pi$
$199$	54924.2			1.38694			0.693469	+	0.720486i	$0.256081\pi$
$200$		0			0
$201$	−42906.8	−	6861.71i	−1.06202	−	0.169840i
$202$		0			0
$203$	−21355.5	−	12329.6i	−0.518223	−	0.299196i
$204$		0			0
$205$	−43830.3	−	75916.3i	−1.04296	−	1.80646i
$206$		0			0
$207$	67108.3	−	14054.2i	1.56616	−	0.327993i
$208$		0			0
$209$	25123.5	−	14505.1i	0.575159	−	0.332068i
$210$		0			0
$211$	−14345.0	+	24846.3i	−0.322207	+	0.558080i	−0.980943	−	0.194295i	$-0.937758\pi$
$211$	−14345.0	+	24846.3i	−0.322207	+	0.558080i	0.658736	+	0.752374i	$0.271092\pi$
$212$		0			0
$213$	16363.8	−	6253.33i	0.360682	−	0.137833i
$214$		0			0
$215$		−	95748.3i		−	2.07135i
$216$		0			0
$217$	5046.41			0.107168
$218$		0			0
$219$	13167.1	+	34455.6i	0.274537	+	0.718409i
$220$		0			0
$221$	−35959.4	−	20761.2i	−0.736255	−	0.425077i
$222$		0			0
$223$	35511.7	+	61508.2i	0.714105	+	1.23687i	0.963304	+	0.268414i	$0.0864996\pi$
$223$	35511.7	+	61508.2i	0.714105	+	1.23687i	−0.249198	+	0.968453i	$0.580167\pi$
$224$		0			0
$225$	−88720.4	−	29121.3i	−1.75250	−	0.575236i
$226$		0			0
$227$	−57302.4	+	33083.5i	−1.11204	+	0.642037i	−0.939357	−	0.342940i	$-0.888577\pi$
$227$	−57302.4	+	33083.5i	−1.11204	+	0.642037i	−0.172684	+	0.984977i	$0.555244\pi$
$228$		0			0
$229$	17111.1	−	29637.4i	0.326293	−	0.565156i	−0.655480	−	0.755212i	$-0.727534\pi$
$229$	17111.1	−	29637.4i	0.326293	−	0.565156i	0.981773	+	0.190056i	$0.0608670\pi$
$230$		0			0
$231$	2768.81	−	17313.6i	0.0518882	−	0.324461i
$232$		0			0
$233$		−	43761.3i		−	0.806081i	−0.915182	−	0.403040i	$-0.867953\pi$
$233$		−	43761.3i		−	0.806081i	0.915182	−	0.403040i	$-0.132047\pi$
$234$		0			0
$235$	163044.			2.95235
$236$		0			0
$237$	10937.8	−	13465.7i	0.194730	−	0.239736i
$238$		0			0
$239$	731.380	+	422.262i	0.0128040	+	0.00739242i	0.506388	−	0.862306i	$-0.330980\pi$
$239$	731.380	+	422.262i	0.0128040	+	0.00739242i	−0.493584	+	0.869698i	$0.664314\pi$
$240$		0			0
$241$	40944.4	+	70917.8i	0.704953	+	1.22101i	0.966708	+	0.255880i	$0.0823654\pi$
$241$	40944.4	+	70917.8i	0.704953	+	1.22101i	−0.261755	+	0.965134i	$0.584301\pi$
$242$		0			0
$243$	57149.9	−	14855.1i	0.967838	−	0.251573i
$244$		0			0
$245$	60754.1	−	35076.4i	1.01215	−	0.584363i
$246$		0			0
$247$	−31487.2	+	54537.4i	−0.516108	+	0.893925i
$248$		0			0
$249$	−33912.9	−	27546.4i	−0.546973	−	0.444289i
$250$		0			0
$251$		−	71221.9i		−	1.13049i	−0.824923	−	0.565244i	$-0.808782\pi$
$251$		−	71221.9i		−	1.13049i	0.824923	−	0.565244i	$-0.191218\pi$
$252$		0			0
$253$	−60736.3			−0.948872
$254$		0			0
$255$	−99892.5	−	15974.9i	−1.53622	−	0.245674i
$256$		0			0
$257$	−49166.6	−	28386.4i	−0.744396	−	0.429777i	0.0792696	−	0.996853i	$-0.474741\pi$
$257$	−49166.6	−	28386.4i	−0.744396	−	0.429777i	−0.823665	+	0.567076i	$0.808075\pi$
$258$		0			0
$259$	−16861.7	−	29205.4i	−0.251364	−	0.435375i
$260$		0			0
$261$	−22942.5	+	69896.1i	−0.336791	+	1.02606i
$262$		0			0
$263$	−71029.6	+	41009.0i	−1.02690	+	0.592881i	−0.916095	−	0.400961i	$-0.868676\pi$
$263$	−71029.6	+	41009.0i	−1.02690	+	0.592881i	−0.110805	+	0.993842i	$0.535343\pi$
$264$		0			0
$265$	96652.3	−	167407.i	1.37632	−	2.38386i
$266$		0			0
$267$	−32711.1	+	12500.4i	−0.458852	+	0.175348i
$268$		0			0
$269$		−	52979.7i		−	0.732158i	−0.930584	−	0.366079i	$-0.880700\pi$
$269$		−	52979.7i		−	0.732158i	0.930584	−	0.366079i	$-0.119300\pi$
$270$		0			0
$271$	−134817.			−1.83571			−0.917857	−	0.396912i	$-0.870082\pi$
$271$	−134817.			−1.83571			−0.917857	+	0.396912i	$0.870082\pi$
$272$		0			0
$273$	13586.7	+	35553.8i	0.182301	+	0.477046i
$274$		0			0
$275$	71634.8	+	41358.4i	0.947237	+	0.546888i
$276$		0			0
$277$	−11389.2	−	19726.6i	−0.148434	−	0.257095i	0.782215	−	0.623009i	$-0.214090\pi$
$277$	−11389.2	−	19726.6i	−0.148434	−	0.257095i	−0.930649	+	0.365914i	$0.880757\pi$
$278$		0			0
$279$	−3085.92	−	14735.2i	−0.0396439	−	0.189298i
$280$		0			0
$281$	51021.8	−	29457.4i	0.646164	−	0.373063i	−0.140821	−	0.990035i	$-0.544974\pi$
$281$	51021.8	−	29457.4i	0.646164	−	0.373063i	0.786985	+	0.616972i	$0.211641\pi$
$282$		0			0
$283$	−30254.6	+	52402.5i	−0.377762	+	0.654303i	−0.990736	−	0.135800i	$-0.956640\pi$
$283$	−30254.6	+	52402.5i	−0.377762	+	0.654303i	0.612974	+	0.790103i	$0.289973\pi$
$284$		0			0
$285$	−24228.2	+	151501.i	−0.298285	+	1.86520i
$286$		0			0
$287$			56448.6i			0.685314i
$288$		0			0
$289$	12454.8			0.149122
$290$		0			0
$291$	69591.7	−	85675.7i	0.821810	−	1.01175i
$292$		0			0
$293$	18933.3	+	10931.1i	0.220541	+	0.127330i	0.606201	−	0.795312i	$-0.292693\pi$
$293$	18933.3	+	10931.1i	0.220541	+	0.127330i	−0.385659	+	0.922641i	$0.626026\pi$
$294$		0			0
$295$	55864.9	+	96760.8i	0.641941	+	1.11187i
$296$		0			0
$297$	−52247.6	+	2502.64i	−0.592316	+	0.0283717i
$298$		0			0
$299$	114181.	−	65922.4i	1.27718	−	0.737379i
$300$		0			0
$301$	−30828.3	+	53396.2i	−0.340265	+	0.589356i
$302$		0			0
$303$	30066.9	+	24422.4i	0.327494	+	0.266013i
$304$		0			0
$305$			286709.i			3.08206i
$306$		0			0
$307$	66154.5			0.701912			0.350956	−	0.936392i	$-0.385857\pi$
$307$	66154.5			0.701912			0.350956	+	0.936392i	$0.385857\pi$
$308$		0			0
$309$	82674.9	+	13221.5i	0.865878	+	0.138472i
$310$		0			0
$311$	−30715.5	−	17733.6i	−0.317568	−	0.183348i	0.332740	−	0.943019i	$-0.392027\pi$
$311$	−30715.5	−	17733.6i	−0.317568	−	0.183348i	−0.650308	+	0.759671i	$0.725360\pi$
$312$		0			0
$313$	2946.58	+	5103.63i	0.0300767	+	0.0520944i	0.880672	−	0.473727i	$-0.157092\pi$
$313$	2946.58	+	5103.63i	0.0300767	+	0.0520944i	−0.850595	+	0.525821i	$0.823758\pi$
$314$		0			0
$315$	61841.4	+	69097.3i	0.623244	+	0.696370i
$316$		0			0
$317$	108043.	−	62378.9i	1.07518	−	0.620753i	0.145585	−	0.989346i	$-0.453494\pi$
$317$	108043.	−	62378.9i	1.07518	−	0.620753i	0.929591	+	0.368593i	$0.120160\pi$
$318$		0			0
$319$	32583.2	−	56435.7i	0.320193	−	0.554591i
$320$		0			0
$321$	−9286.45	+	3548.77i	−0.0901238	+	0.0344404i
$322$		0			0
$323$			107782.i			1.03309i
$324$		0			0
$325$	−179559.			−1.69997
$326$		0			0
$327$	−13037.7	−	34117.0i	−0.121928	−	0.319063i
$328$		0			0
$329$	−90925.0	−	52495.6i	−0.840024	−	0.484988i
$330$		0			0
$331$	−4789.87	−	8296.30i	−0.0437188	−	0.0757232i	0.843338	−	0.537384i	$-0.180587\pi$
$331$	−4789.87	−	8296.30i	−0.0437188	−	0.0757232i	−0.887057	+	0.461660i	$0.847254\pi$
$332$		0			0
$333$	−74966.6	+	67094.4i	−0.676051	+	0.605059i
$334$		0			0
$335$	−176295.	+	101784.i	−1.57091	+	0.906963i
$336$		0			0
$337$	20485.4	−	35481.8i	0.180379	−	0.312425i	−0.761631	−	0.648011i	$-0.775601\pi$
$337$	20485.4	−	35481.8i	0.180379	−	0.312425i	0.942010	+	0.335586i	$0.108934\pi$
$338$		0			0
$339$	19973.2	−	124894.i	0.173799	−	1.08678i
$340$		0			0
$341$			13336.1i			0.114688i
$342$		0			0
$343$	−110365.			−0.938086
$344$		0			0
$345$	202522.	−	249329.i	1.70151	−	2.09476i
$346$		0			0
$347$	−85852.9	−	49567.2i	−0.713011	−	0.411657i	0.0991642	−	0.995071i	$-0.468383\pi$
$347$	−85852.9	−	49567.2i	−0.713011	−	0.411657i	−0.812175	+	0.583414i	$0.801716\pi$
$348$		0			0
$349$	68555.3	+	118741.i	0.562847	+	0.974880i	0.997246	+	0.0741593i	$0.0236273\pi$
$349$	68555.3	+	118741.i	0.562847	+	0.974880i	−0.434399	+	0.900720i	$0.643039\pi$
$350$		0			0
$351$	95506.2	−	61413.6i	0.775207	−	0.498483i
$352$		0			0
$353$	−163579.	+	94442.2i	−1.31274	+	0.757908i	−0.982548	−	0.186008i	$-0.940445\pi$
$353$	−163579.	+	94442.2i	−1.31274	+	0.757908i	−0.330187	+	0.943916i	$0.607112\pi$
$354$		0			0
$355$	41034.8	−	71074.3i	0.325608	−	0.563970i
$356$		0			0
$357$	50563.8	+	41071.4i	0.396738	+	0.322258i
$358$		0			0
$359$		−	149533.i		−	1.16024i	−0.814530	−	0.580121i	$-0.803005\pi$
$359$		−	149533.i		−	1.16024i	0.814530	−	0.580121i	$-0.196995\pi$
$360$		0			0
$361$	33144.8			0.254332
$362$		0			0
$363$	−84361.4	−	13491.2i	−0.640222	−	0.102385i
$364$		0			0
$365$	149655.	+	86403.1i	1.12332	+	0.648550i
$366$		0			0
$367$	−84970.2	−	147173.i	−0.630862	−	1.09269i	−0.987376	−	0.158395i	$-0.949368\pi$
$367$	−84970.2	−	147173.i	−0.630862	−	1.09269i	0.356514	−	0.934290i	$-0.383965\pi$
$368$		0			0
$369$	164826.	−	34518.7i	1.21052	−	0.253514i
$370$		0			0
$371$	−107801.	+	62238.8i	−0.783202	+	0.452182i
$372$		0			0
$373$	−37928.1	+	65693.5i	−0.272611	+	0.472177i	−0.969530	−	0.244974i	$-0.921221\pi$
$373$	−37928.1	+	65693.5i	−0.272611	+	0.472177i	0.696918	+	0.717150i	$0.254554\pi$
$374$		0			0
$375$	−187095.	+	71497.6i	−1.33046	+	0.508427i
$376$		0			0
$377$			141461.i			0.995303i
$378$		0			0
$379$	−177671.			−1.23691			−0.618457	−	0.785819i	$-0.712242\pi$
$379$	−177671.			−1.23691			−0.618457	+	0.785819i	$0.712242\pi$
$380$		0			0
$381$	−33569.0	−	87843.6i	−0.231254	−	0.605146i
$382$		0			0
$383$	97889.8	+	56516.7i	0.667329	+	0.385283i	0.795064	−	0.606526i	$-0.207437\pi$
$383$	97889.8	+	56516.7i	0.667329	+	0.385283i	−0.127735	+	0.991808i	$0.540771\pi$
$384$		0			0
$385$	−41071.5	−	71137.9i	−0.277089	−	0.479932i
$386$		0			0
$387$	174765.	+	57364.4i	1.16690	+	0.383019i
$388$		0			0
$389$	231900.	−	133888.i	1.53251	−	0.884792i	0.533260	−	0.845951i	$-0.320967\pi$
$389$	231900.	−	133888.i	1.53251	−	0.884792i	0.999245	−	0.0388408i	$-0.0123665\pi$
$390$		0			0
$391$	112827.	−	195422.i	0.738007	−	1.27827i
$392$		0			0
$393$	665.988	−	4164.47i	0.00431202	−	0.0269634i
$394$		0			0
$395$		−	81274.6i		−	0.520908i
$396$		0			0
$397$	−221153.			−1.40317			−0.701587	−	0.712584i	$-0.747525\pi$
$397$	−221153.			−1.40317			−0.701587	+	0.712584i	$0.747525\pi$
$398$		0			0
$399$	62290.5	−	76687.0i	0.391270	−	0.481700i
$400$		0			0
$401$	34988.0	+	20200.3i	0.217586	+	0.125623i	0.604832	−	0.796353i	$-0.293240\pi$
$401$	34988.0	+	20200.3i	0.217586	+	0.125623i	−0.387246	+	0.921976i	$0.626574\pi$
$402$		0			0
$403$	−14474.8	−	25071.1i	−0.0891255	−	0.154370i
$404$		0			0
$405$	163943.	−	222826.i	0.999500	−	1.35849i
$406$		0			0
$407$	77180.5	−	44560.2i	0.465928	−	0.269004i
$408$		0			0
$409$	82781.2	−	143381.i	0.494863	−	0.857128i	−0.505119	−	0.863049i	$-0.668552\pi$
$409$	82781.2	−	143381.i	0.494863	−	0.857128i	0.999982	+	0.00592156i	$0.00188490\pi$
$410$		0			0
$411$	−85949.2	−	69813.9i	−0.508813	−	0.413293i
$412$		0			0
$413$		−	71947.8i		−	0.421811i
$414$		0			0
$415$	−204687.			−1.18849
$416$		0			0
$417$	−230466.	−	36856.5i	−1.32536	−	0.211954i
$418$		0			0
$419$	291062.	+	168045.i	1.65790	+	0.957186i	0.973684	+	0.227902i	$0.0731867\pi$
$419$	291062.	+	168045.i	1.65790	+	0.957186i	0.684211	+	0.729284i	$0.260147\pi$
$420$		0			0
$421$	−40957.5	−	70940.4i	−0.231084	−	0.400248i	0.727044	−	0.686591i	$-0.240894\pi$
$421$	−40957.5	−	70940.4i	−0.231084	−	0.400248i	−0.958127	+	0.286343i	$0.907560\pi$
$422$		0			0
$423$	−97682.2	+	297596.i	−0.545927	+	1.66321i
$424$		0			0
$425$	−266146.	+	153659.i	−1.47347	+	0.850709i
$426$		0			0
$427$	92312.3	−	159890.i	0.506295	−	0.876929i
$428$		0			0
$429$	−93957.3	+	35905.3i	−0.510524	+	0.195094i
$430$		0			0
$431$			8293.28i			0.0446449i	0.999751	+	0.0223224i	$0.00710604\pi$
$431$			8293.28i			0.0446449i	−0.999751	+	0.0223224i	$0.992894\pi$
$432$		0			0
$433$	267935.			1.42907			0.714536	−	0.699599i	$-0.246638\pi$
$433$	267935.			1.42907			0.714536	+	0.699599i	$0.246638\pi$
$434$		0			0
$435$	123027.	+	321939.i	0.650164	+	1.70135i
$436$		0			0
$437$	−296385.	−	171118.i	−1.55201	−	0.896051i
$438$		0			0
$439$	49835.2	+	86317.0i	0.258587	+	0.447886i	0.965864	−	0.259051i	$-0.0834098\pi$
$439$	49835.2	+	86317.0i	0.258587	+	0.447886i	−0.707277	+	0.706937i	$0.750076\pi$
$440$		0			0
$441$	27624.6	+	131907.i	0.142042	+	0.678249i
$442$		0			0
$443$	100669.	−	58121.1i	0.512964	−	0.296160i	−0.221087	−	0.975254i	$-0.570961\pi$
$443$	100669.	−	58121.1i	0.512964	−	0.296160i	0.734051	+	0.679094i	$0.237627\pi$
$444$		0			0
$445$	−82028.4	+	142077.i	−0.414233	+	0.717472i
$446$		0			0
$447$	26106.5	−	163246.i	0.130657	−	0.817011i
$448$		0			0
$449$			18692.8i			0.0927217i	0.998925	+	0.0463608i	$0.0147624\pi$
$449$			18692.8i			0.0927217i	−0.998925	+	0.0463608i	$0.985238\pi$
$450$		0			0
$451$	−149176.			−0.733407
$452$		0			0
$453$	32089.7	−	39506.3i	0.156376	−	0.192517i
$454$		0			0
$455$	154424.	+	89156.8i	0.745920	+	0.430657i
$456$		0			0
$457$	97568.3	+	168993.i	0.467172	+	0.809165i	0.999297	−	0.0375009i	$-0.0119397\pi$
$457$	97568.3	+	168993.i	0.467172	+	0.809165i	−0.532125	+	0.846666i	$0.678606\pi$
$458$		0			0
$459$	89005.6	−	172758.i	0.422466	−	0.820000i
$460$		0			0
$461$	−233270.	+	134678.i	−1.09763	+	0.633718i	−0.935598	−	0.353067i	$-0.885139\pi$
$461$	−233270.	+	134678.i	−1.09763	+	0.633718i	−0.162034	+	0.986785i	$0.551806\pi$
$462$		0			0
$463$	−111589.	+	193278.i	−0.520546	+	0.901612i	0.479169	+	0.877723i	$0.340938\pi$
$463$	−111589.	+	193278.i	−0.520546	+	0.901612i	−0.999715	+	0.0238890i	$0.992395\pi$
$464$		0			0
$465$	−54745.8	−	44468.3i	−0.253189	−	0.205658i
$466$		0			0
$467$		−	18160.1i		−	0.0832693i	−0.999133	−	0.0416346i	$-0.986743\pi$
$467$		−	18160.1i		−	0.0832693i	0.999133	−	0.0416346i	$-0.0132565\pi$
$468$		0			0
$469$	131087.			0.595954
$470$		0			0
$471$	−96852.9	−	15488.8i	−0.436587	−	0.0698196i
$472$		0			0
$473$	−141109.	−	81469.4i	−0.630715	−	0.364143i
$474$		0			0
$475$	233046.	+	403647.i	1.03289	+	1.78902i
$476$		0			0
$477$	247654.	+	276711.i	1.08845	+	1.21616i
$478$		0			0
$479$	−16180.3	+	9341.71i	−0.0705206	+	0.0407151i	−0.534846	−	0.844950i	$-0.679630\pi$
$479$	−16180.3	+	9341.71i	−0.0705206	+	0.0407151i	0.464325	+	0.885665i	$0.346297\pi$
$480$		0			0
$481$	−96730.1	+	167541.i	−0.418092	+	0.724156i
$482$		0			0
$483$	−193218.	+	73837.3i	−0.828234	+	0.316506i
$484$		0			0
$485$		−	517110.i		−	2.19836i
$486$		0			0
$487$	287143.			1.21071			0.605355	−	0.795956i	$-0.293031\pi$
$487$	287143.			1.21071			0.605355	+	0.795956i	$0.293031\pi$
$488$		0			0
$489$	−99313.1	−	259883.i	−0.415326	−	1.08683i
$490$		0			0
$491$	−41490.2	−	23954.4i	−0.172101	−	0.0993625i	0.411475	−	0.911421i	$-0.365014\pi$
$491$	−41490.2	−	23954.4i	−0.172101	−	0.0993625i	−0.583576	+	0.812058i	$0.698347\pi$
$492$		0			0
$493$	121057.	+	209676.i	0.498075	+	0.862691i
$494$		0			0
$495$	−182602.	+	163427.i	−0.745239	+	0.666982i
$496$		0			0
$497$	−45768.0	+	26424.1i	−0.185289	+	0.106976i
$498$		0			0
$499$	84460.5	−	146290.i	0.339197	−	0.587507i	−0.645085	−	0.764111i	$-0.723178\pi$
$499$	84460.5	−	146290.i	0.339197	−	0.587507i	0.984282	+	0.176604i	$0.0565112\pi$
$500$		0			0
$501$	−19075.2	+	119279.i	−0.0759965	+	0.475212i
$502$		0			0
$503$			390496.i			1.54341i	0.635981	+	0.771705i	$0.280596\pi$
$503$			390496.i			1.54341i	−0.635981	+	0.771705i	$0.719404\pi$
$504$		0			0
$505$	181474.			0.711592
$506$		0			0
$507$	−24402.0	+	30041.8i	−0.0949315	+	0.116872i
$508$		0			0
$509$	−26718.3	−	15425.8i	−0.103127	−	0.0595406i	0.447549	−	0.894259i	$-0.352297\pi$
$509$	−26718.3	−	15425.8i	−0.103127	−	0.0595406i	−0.550677	+	0.834719i	$0.685630\pi$
$510$		0			0
$511$	−55638.8	−	96369.3i	−0.213077	−	0.369060i
$512$		0			0
$513$	−262012.	−	134989.i	−0.995604	−	0.512938i
$514$		0			0
$515$	339694.	−	196123.i	1.28078	−	0.739457i
$516$		0			0
$517$	138729.	−	240286.i	0.519023	−	0.898974i
$518$		0			0
$519$	170907.	+	138822.i	0.634491	+	0.515377i
$520$		0			0
$521$			60361.1i			0.222373i	0.993800	+	0.111186i	$0.0354650\pi$
$521$			60361.1i			0.222373i	−0.993800	+	0.111186i	$0.964535\pi$
$522$		0			0
$523$	−186623.			−0.682278			−0.341139	−	0.940013i	$-0.610813\pi$
$523$	−186623.			−0.682278			−0.341139	+	0.940013i	$0.610813\pi$
$524$		0			0
$525$	278168.	+	44485.0i	1.00923	+	0.161397i
$526$		0			0
$527$	−42909.5	−	24773.8i	−0.154501	−	0.0892014i
$528$		0			0
$529$	218336.	+	378170.i	0.780216	+	1.35137i
$530$		0			0
$531$	−210083.	+	43996.6i	−0.745077	+	0.156038i
$532$		0			0
$533$	280442.	−	161913.i	0.987162	−	0.569939i
$534$		0			0
$535$	−23287.3	+	40334.7i	−0.0813600	+	0.140920i
$536$		0			0
$537$	23498.1	−	8979.67i	0.0814861	−	0.0311395i
$538$		0			0
$539$		−	119382.i		−	0.410923i
$540$		0			0
$541$	−172373.			−0.588944			−0.294472	−	0.955660i	$-0.595144\pi$
$541$	−172373.			−0.588944			−0.294472	+	0.955660i	$0.595144\pi$
$542$		0			0
$543$	34571.0	+	90465.6i	0.117250	+	0.306820i
$544$		0			0
$545$	−148184.	−	85554.0i	−0.498894	−	0.288036i
$546$		0			0
$547$	−112933.	−	195606.i	−0.377438	−	0.653742i	0.613250	−	0.789889i	$-0.289862\pi$
$547$	−112933.	−	195606.i	−0.377438	−	0.653742i	−0.990689	+	0.136146i	$0.956528\pi$
$548$		0			0
$549$	−523316.	−	171772.i	−1.73628	−	0.569912i
$550$		0			0
$551$	318003.	−	183599.i	1.04744	−	0.604738i
$552$		0			0
$553$	−26168.2	+	45324.6i	−0.0855704	+	0.148212i
$554$		0			0
$555$	−74430.1	+	465417.i	−0.241637	+	1.51097i
$556$		0			0
$557$			184989.i			0.596259i	0.954525	+	0.298129i	$0.0963627\pi$
$557$			184989.i			0.596259i	−0.954525	+	0.298129i	$0.903637\pi$
$558$		0			0
$559$	353703.			1.13192
$560$		0			0
$561$	−108539.	+	133624.i	−0.344873	+	0.424580i
$562$		0			0
$563$	−501090.	−	289305.i	−1.58088	−	0.912722i	−0.994731	−	0.102520i	$-0.967310\pi$
$563$	−501090.	−	289305.i	−1.58088	−	0.912722i	−0.586150	−	0.810202i	$-0.699357\pi$
$564$		0			0
$565$	−296274.	−	513162.i	−0.928105	−	1.60753i
$566$		0			0
$567$	−163170.	+	71479.0i	−0.507546	+	0.222337i
$568$		0			0
$569$	406755.	−	234840.i	1.25634	−	0.725350i	0.283982	−	0.958830i	$-0.408344\pi$
$569$	406755.	−	234840.i	1.25634	−	0.725350i	0.972362	+	0.233479i	$0.0750111\pi$
$570$		0			0
$571$	92597.5	−	160384.i	0.284006	−	0.491912i	−0.688362	−	0.725367i	$-0.741670\pi$
$571$	92597.5	−	160384.i	0.284006	−	0.491912i	0.972368	+	0.233455i	$0.0750032\pi$
$572$		0			0
$573$	−105341.	−	85564.8i	−0.320838	−	0.260607i
$574$		0			0
$575$		−	975820.i		−	2.95144i
$576$		0			0
$577$	−47668.0			−0.143178			−0.0715888	−	0.997434i	$-0.522807\pi$
$577$	−47668.0			−0.143178			−0.0715888	+	0.997434i	$0.522807\pi$
$578$		0			0
$579$	−517863.	−	82817.4i	−1.54475	−	0.247038i
$580$		0			0
$581$	114148.	+	65903.6i	0.338156	+	0.195234i
$582$		0			0
$583$	−164477.	−	284883.i	−0.483914	−	0.838164i
$584$		0			0
$585$	165900.	−	505428.i	0.484770	−	1.47689i
$586$		0			0
$587$	−361008.	+	208428.i	−1.04771	+	0.604895i	−0.922007	−	0.387173i	$-0.873452\pi$
$587$	−361008.	+	208428.i	−1.04771	+	0.604895i	−0.125702	+	0.992068i	$0.540118\pi$
$588$		0			0
$589$	−37572.9	+	65078.2i	−0.108304	+	0.187588i
$590$		0			0
$591$	136238.	−	52062.9i	0.390054	−	0.149057i
$592$		0			0
$593$		−	79264.3i		−	0.225408i	−0.993629	−	0.112704i	$-0.964049\pi$
$593$		−	79264.3i		−	0.225408i	0.993629	−	0.112704i	$-0.0359511\pi$
$594$		0			0
$595$	305187.			0.862048
$596$		0			0
$597$	176456.	+	461750.i	0.495093	+	1.29556i
$598$		0			0
$599$	−25721.0	−	14850.0i	−0.0716861	−	0.0413880i	0.463729	−	0.885977i	$-0.346511\pi$
$599$	−25721.0	−	14850.0i	−0.0716861	−	0.0413880i	−0.535415	+	0.844589i	$0.679845\pi$
$600$		0			0
$601$	132293.	+	229139.i	0.366259	+	0.634380i	0.988977	−	0.148066i	$-0.0473049\pi$
$601$	132293.	+	229139.i	0.366259	+	0.634380i	−0.622718	+	0.782446i	$0.713972\pi$
$602$		0			0
$603$	−80160.4	−	382764.i	−0.220458	−	1.05268i
$604$		0			0
$605$	−346624.	+	200123.i	−0.946995	+	0.546748i
$606$		0			0
$607$	−92600.9	+	160389.i	−0.251326	+	0.435310i	−0.963891	−	0.266296i	$-0.914200\pi$
$607$	−92600.9	+	160389.i	−0.251326	+	0.435310i	0.712565	+	0.701606i	$0.247533\pi$
$608$		0			0
$609$	35046.4	−	219148.i	0.0944951	−	0.590885i
$610$		0			0
$611$			602299.i			1.61335i
$612$		0			0
$613$	247948.			0.659841			0.329920	−	0.944009i	$-0.392978\pi$
$613$	247948.			0.659841			0.329920	+	0.944009i	$0.392978\pi$
$614$		0			0
$615$	497418.	−	612381.i	1.31514	−	1.61909i
$616$		0			0
$617$	392212.	+	226444.i	1.03027	+	0.594826i	0.917062	−	0.398746i	$-0.130554\pi$
$617$	392212.	+	226444.i	1.03027	+	0.594826i	0.113207	+	0.993571i	$0.463888\pi$
$618$		0			0
$619$	−155258.	−	268915.i	−0.405203	−	0.701833i	0.589142	−	0.808030i	$-0.299466\pi$
$619$	−155258.	−	268915.i	−0.405203	−	0.701833i	−0.994345	+	0.106197i	$0.966133\pi$
$620$		0			0
$621$	333754.	+	519031.i	0.865452	+	1.34589i
$622$		0			0
$623$	91490.1	−	52821.8i	0.235721	−	0.136093i
$624$		0			0
$625$	−108919.	+	188653.i	−0.278832	+	0.482952i
$626$		0			0
$627$	202659.	+	164614.i	0.515504	+	0.418728i
$628$		0			0
$629$			331110.i			0.836895i
$630$		0			0
$631$	475076.			1.19317			0.596587	−	0.802548i	$-0.296523\pi$
$631$	475076.			1.19317			0.596587	+	0.802548i	$0.296523\pi$
$632$		0			0
$633$	−254970.	−	40775.2i	−0.636329	−	0.101763i
$634$		0			0
$635$	−381540.	−	220282.i	−0.946220	−	0.546300i
$636$		0			0
$637$	129576.	+	224431.i	0.319333	+	0.553101i
$638$		0			0
$639$	105144.	+	117481.i	0.257504	+	0.287717i
$640$		0			0
$641$	−161749.	+	93386.1i	−0.393665	+	0.227282i	−0.683747	−	0.729719i	$-0.739651\pi$
$641$	−161749.	+	93386.1i	−0.393665	+	0.227282i	0.290082	+	0.957002i	$0.406317\pi$
$642$		0			0
$643$	−336575.	+	582964.i	−0.814066	+	1.41000i	0.0959311	+	0.995388i	$0.469417\pi$
$643$	−336575.	+	582964.i	−0.814066	+	1.41000i	−0.909997	+	0.414615i	$0.863916\pi$
$644$		0			0
$645$	804961.	−	307612.i	1.93489	−	0.739407i
$646$		0			0
$647$			172889.i			0.413009i	0.978446	+	0.206504i	$0.0662088\pi$
$647$			172889.i			0.413009i	−0.978446	+	0.206504i	$0.933791\pi$
$648$		0			0
$649$	190135.			0.451412
$650$		0			0
$651$	16212.7	+	42425.4i	0.0382554	+	0.100107i
$652$		0			0
$653$	−48978.2	−	28277.6i	−0.114862	−	0.0663156i	0.441468	−	0.897277i	$-0.354458\pi$
$653$	−48978.2	−	28277.6i	−0.114862	−	0.0663156i	−0.556330	+	0.830961i	$0.687791\pi$
$654$		0			0
$655$	−9879.01	−	17110.9i	−0.0230267	−	0.0398833i
$656$		0			0
$657$	−247368.	+	221392.i	−0.573077	+	0.512899i
$658$		0			0
$659$	86580.6	−	49987.3i	0.199365	−	0.115104i	−0.396994	−	0.917821i	$-0.629947\pi$
$659$	86580.6	−	49987.3i	0.199365	−	0.115104i	0.596359	+	0.802718i	$0.296613\pi$
$660$		0			0
$661$	−145897.	+	252702.i	−0.333922	+	0.578370i	−0.983277	−	0.182116i	$-0.941706\pi$
$661$	−145897.	+	252702.i	−0.333922	+	0.578370i	0.649355	+	0.760485i	$0.275039\pi$
$662$		0			0
$663$	59013.0	−	369013.i	0.134252	−	0.839487i
$664$		0			0
$665$		−	462858.i		−	1.04666i
$666$		0			0
$667$	−768775.			−1.72802
$668$		0			0
$669$	−403013.	+	496157.i	−0.900465	+	1.10858i
$670$		0			0
$671$	422537.	+	243952.i	0.938469	+	0.541825i
$672$		0			0
$673$	−385663.	−	667988.i	−0.851486	−	1.47482i	−0.879867	−	0.475221i	$-0.842368\pi$
$673$	−385663.	−	667988.i	−0.851486	−	1.47482i	0.0283803	−	0.999597i	$-0.490965\pi$
$674$		0			0
$675$	−40208.6	−	839435.i	−0.0882494	−	1.84238i
$676$		0			0
$677$	−381716.	+	220384.i	−0.832842	+	0.480842i	−0.854825	−	0.518917i	$-0.826335\pi$
$677$	−381716.	+	220384.i	−0.832842	+	0.480842i	0.0219828	+	0.999758i	$0.493002\pi$
$678$		0			0
$679$	−166495.	+	288378.i	−0.361129	+	0.625494i
$680$		0			0
$681$	−462231.	−	375456.i	−0.996701	−	0.809589i
$682$		0			0
$683$			862783.i			1.84953i	0.380544	+	0.924763i	$0.375737\pi$
$683$			862783.i			1.84953i	−0.380544	+	0.924763i	$0.624263\pi$
$684$		0			0
$685$	−518761.			−1.10557
$686$		0			0
$687$	304136.	+	48637.8i	0.644398	+	0.103053i
$688$		0			0
$689$	618416.	+	357043.i	1.30269	+	0.752111i
$690$		0			0
$691$	114452.	+	198236.i	0.239699	+	0.415171i	0.960628	−	0.277838i	$-0.0896178\pi$
$691$	114452.	+	198236.i	0.239699	+	0.415171i	−0.720929	+	0.693009i	$0.756284\pi$
$692$		0			0
$693$	154451.	−	32346.0i	0.321607	−	0.0673526i
$694$		0			0
$695$	−946939.	+	546715.i	−1.96043	+	1.13186i
$696$		0			0
$697$	277117.	−	479981.i	0.570424	−	0.988003i
$698$		0			0
$699$	367904.	−	140593.i	0.752973	−	0.287745i
$700$		0			0
$701$		−	55341.5i		−	0.112620i	−0.998413	−	0.0563099i	$-0.982067\pi$
$701$		−	55341.5i		−	0.112620i	0.998413	−	0.0563099i	$-0.0179335\pi$
$702$		0			0
$703$	502174.			1.01612
$704$		0			0
$705$	523813.	+	1.37072e6i	1.05390	+	2.75784i
$706$		0			0
$707$	−101203.	−	58429.6i	−0.202467	−	0.116894i
$708$		0			0
$709$	−322439.	−	558481.i	−0.641439	−	1.11101i	−0.985112	−	0.171916i	$-0.945004\pi$
$709$	−322439.	−	558481.i	−0.641439	−	1.11101i	0.343673	−	0.939090i	$-0.388329\pi$
$710$		0			0
$711$	148347.	+	48693.0i	0.293453	+	0.0963224i
$712$		0			0
$713$	136249.	−	78663.5i	0.268013	−	0.154737i
$714$		0			0
$715$	−235613.	+	408094.i	−0.460879	+	0.798267i
$716$		0			0
$717$	−1200.27	+	7505.35i	−0.00233474	+	0.0145993i
$718$		0			0
$719$			75266.7i			0.145594i	0.997347	+	0.0727972i	$0.0231926\pi$
$719$			75266.7i			0.145594i	−0.997347	+	0.0727972i	$0.976807\pi$
$720$		0			0
$721$	−252584.			−0.485888
$722$		0			0
$723$	−464666.	+	572060.i	−0.888924	+	1.09437i
$724$		0			0
$725$	906724.	+	523497.i	1.72504	+	0.995952i
$726$		0			0
$727$	−324522.	−	562089.i	−0.614010	−	1.06350i	−0.990557	−	0.137099i	$-0.956222\pi$
$727$	−324522.	−	562089.i	−0.614010	−	1.06350i	0.376547	−	0.926397i	$-0.377111\pi$
$728$		0			0
$729$	308494.	+	432737.i	0.580486	+	0.814271i
$730$		0			0
$731$	524265.	−	302684.i	0.981106	−	0.566442i
$732$		0			0
$733$	368327.	−	637961.i	0.685528	−	1.18737i	−0.287742	−	0.957708i	$-0.592905\pi$
$733$	368327.	−	637961.i	0.685528	−	1.18737i	0.973270	−	0.229662i	$-0.0737621\pi$
$734$		0			0
$735$	490074.	+	398072.i	0.907167	+	0.736864i
$736$		0			0
$737$			346420.i			0.637776i
$738$		0			0
$739$	19217.4			0.0351890			0.0175945	−	0.999845i	$-0.494399\pi$
$739$	19217.4			0.0351890			0.0175945	+	0.999845i	$0.494399\pi$
$740$		0			0
$741$	−559658.	−	89501.3i	−1.01926	−	0.163002i
$742$		0			0
$743$	581985.	+	336009.i	1.05423	+	0.608659i	0.923830	−	0.382803i	$-0.125041\pi$
$743$	581985.	+	336009.i	1.05423	+	0.608659i	0.130398	+	0.991462i	$0.458375\pi$
$744$		0			0
$745$	−387254.	−	670744.i	−0.697724	−	1.20849i
$746$		0			0
$747$	122631.	−	373606.i	0.219766	−	0.669534i
$748$		0			0
$749$	25973.4	−	14995.7i	0.0462982	−	0.0267303i
$750$		0			0
$751$	−256433.	+	444155.i	−0.454668	+	0.787508i	−0.998669	−	0.0515767i	$-0.983575\pi$
$751$	−256433.	+	444155.i	−0.454668	+	0.787508i	0.544001	+	0.839084i	$0.316909\pi$
$752$		0			0
$753$	598766.	−	228816.i	1.05601	−	0.403549i
$754$		0			0
$755$		−	238447.i		−	0.418309i
$756$		0			0
$757$	557746.			0.973296			0.486648	−	0.873598i	$-0.338219\pi$
$757$	557746.			0.973296			0.486648	+	0.873598i	$0.338219\pi$
$758$		0			0
$759$	−195128.	−	510613.i	−0.338717	−	0.886357i
$760$		0			0
$761$	−337594.	−	194910.i	−0.582943	−	0.336562i	0.179359	−	0.983784i	$-0.442598\pi$
$761$	−337594.	−	194910.i	−0.582943	−	0.336562i	−0.762302	+	0.647222i	$0.775931\pi$
$762$		0			0
$763$	55092.1	+	95422.3i	0.0946324	+	0.163908i
$764$		0			0
$765$	−186624.	−	891124.i	−0.318893	−	1.52270i
$766$		0			0
$767$	−357444.	+	206370.i	−0.607599	+	0.350797i
$768$		0			0
$769$	−337667.	+	584856.i	−0.570999	+	0.989000i	0.425464	+	0.904975i	$0.360111\pi$
$769$	−337667.	+	584856.i	−0.570999	+	0.989000i	−0.996464	+	0.0840247i	$0.973223\pi$
$770$		0			0
$771$	80687.2	−	504543.i	0.135736	−	0.848769i
$772$		0			0
$773$		−	560744.i		−	0.938439i	−0.883082	−	0.469219i	$-0.844535\pi$
$773$		−	560744.i		−	0.938439i	0.883082	−	0.469219i	$-0.155465\pi$
$774$		0			0
$775$	−214264.			−0.356735
$776$		0			0
$777$	191359.	−	235586.i	0.316962	−	0.390218i
$778$		0			0
$779$	−727957.	−	420286.i	−1.19958	−	0.692580i
$780$		0			0
$781$	−69830.6	−	120950.i	−0.114484	−	0.198292i
$782$		0			0
$783$	−661328.	+	31677.4i	−1.07868	+	0.0516685i
$784$		0			0
$785$	−397949.	+	229756.i	−0.645784	+	0.372844i
$786$		0			0
$787$	618135.	−	1.07064e6i	0.998007	−	1.72860i	0.444360	−	0.895848i	$-0.353431\pi$
$787$	618135.	−	1.07064e6i	0.998007	−	1.72860i	0.553647	−	0.832751i	$-0.313236\pi$
$788$		0			0
$789$	−572962.	−	465399.i	−0.920390	−	0.747604i
$790$		0			0
$791$			381569.i			0.609846i
$792$		0			0
$793$	−1.05913e6			−1.68423
$794$		0			0
$795$	1.71791e6	+	274731.i	2.71811	+	0.434683i
$796$		0			0
$797$	−106275.	−	61357.9i	−0.167307	−	0.0965948i	0.414008	−	0.910273i	$-0.364128\pi$
$797$	−106275.	−	61357.9i	−0.167307	−	0.0965948i	−0.581315	+	0.813678i	$0.697462\pi$
$798$		0			0
$799$	515422.	+	892737.i	0.807364	+	1.39840i
$800$		0			0
$801$	−210183.	−	234844.i	−0.327591	−	0.366028i
$802$		0			0
$803$	254673.	−	147036.i	0.394959	−	0.228030i
$804$		0			0
$805$	−484525.	+	839222.i	−0.747695	+	1.29505i
$806$		0			0
$807$	445403.	−	170209.i	0.683921	−	0.261357i
$808$		0			0
$809$		−	694344.i		−	1.06091i	−0.847714	−	0.530454i	$-0.822021\pi$
$809$		−	694344.i		−	1.06091i	0.847714	−	0.530454i	$-0.177979\pi$
$810$		0			0
$811$	739442.			1.12425			0.562125	−	0.827053i	$-0.309984\pi$
$811$	739442.			1.12425			0.562125	+	0.827053i	$0.309984\pi$
$812$		0			0
$813$	−433127.	−	1.13341e6i	−0.655291	−	1.71477i
$814$		0			0
$815$	−1.12878e6	−	651699.i	−1.69939	−	0.981142i
$816$		0			0
$817$	−459063.	−	795120.i	−0.687746	−	1.19121i
$818$		0			0
$819$	−255252.	+	228448.i	−0.380541	+	0.340581i
$820$		0			0
$821$	308186.	−	177931.i	0.457221	−	0.263977i	−0.253654	−	0.967295i	$-0.581632\pi$
$821$	308186.	−	177931.i	0.457221	−	0.263977i	0.710875	+	0.703318i	$0.248299\pi$
$822$		0			0
$823$	151832.	−	262981.i	0.224163	−	0.388262i	−0.731905	−	0.681407i	$-0.761368\pi$
$823$	151832.	−	262981.i	0.224163	−	0.388262i	0.956068	+	0.293145i	$0.0947018\pi$
$824$		0			0
$825$	−117560.	+	735110.i	−0.172723	+	1.08005i
$826$		0			0
$827$			908378.i			1.32818i	0.747655	+	0.664088i	$0.231180\pi$
$827$			908378.i			1.32818i	−0.747655	+	0.664088i	$0.768820\pi$
$828$		0			0
$829$	289286.			0.420939			0.210469	−	0.977600i	$-0.432501\pi$
$829$	289286.			0.420939			0.210469	+	0.977600i	$0.432501\pi$
$830$		0			0
$831$	129253.	−	159125.i	0.187171	−	0.230429i
$832$		0			0
$833$	384118.	+	221771.i	0.553572	+	0.319605i
$834$		0			0
$835$	282954.	+	490091.i	0.405829	+	0.702917i
$836$		0			0
$837$	113965.	−	73283.4i	0.162675	−	0.104605i
$838$		0			0
$839$	691754.	−	399384.i	0.982716	−	0.567371i	0.0796267	−	0.996825i	$-0.474627\pi$
$839$	691754.	−	399384.i	0.982716	−	0.567371i	0.903089	+	0.429454i	$0.141294\pi$
$840$		0			0
$841$	58783.7	−	101816.i	0.0831122	−	0.143955i
$842$		0			0
$843$	411568.	+	334304.i	0.579144	+	0.470421i
$844$		0			0
$845$			181323.i			0.253944i
$846$		0			0
$847$	257737.			0.359261
$848$		0			0
$849$	−537749.	−	85997.6i	−0.746044	−	0.119308i
$850$		0			0
$851$	−910508.	−	525682.i	−1.25726	−	0.725879i
$852$		0			0
$853$	142800.	+	247336.i	0.196259	+	0.339930i	0.947312	−	0.320311i	$-0.103787\pi$
$853$	142800.	+	247336.i	0.196259	+	0.339930i	−0.751054	+	0.660241i	$0.770454\pi$
$854$		0			0
$855$	−1.35151e6	+	283041.i	−1.84879	+	0.387184i
$856$		0			0
$857$	−661445.	+	381886.i	−0.900601	+	0.519962i	−0.877395	−	0.479769i	$-0.840721\pi$
$857$	−661445.	+	381886.i	−0.900601	+	0.519962i	−0.0232057	+	0.999731i	$0.507387\pi$
$858$		0			0
$859$	−502881.	+	871016.i	−0.681521	+	1.18043i	0.292996	+	0.956114i	$0.405348\pi$
$859$	−502881.	+	871016.i	−0.681521	+	1.18043i	−0.974517	+	0.224315i	$0.927986\pi$
$860$		0			0
$861$	−474566.	+	181353.i	−0.640163	+	0.244635i
$862$		0			0
$863$		−	688011.i		−	0.923792i	−0.886934	−	0.461896i	$-0.847169\pi$
$863$		−	688011.i		−	0.923792i	0.886934	−	0.461896i	$-0.152831\pi$
$864$		0			0
$865$	1.03154e6			1.37865
$866$		0			0
$867$	40013.7	+	104708.i	0.0532317	+	0.139297i
$868$		0			0
$869$	−119779.	−	69154.2i	−0.158613	−	0.0915754i
$870$		0			0
$871$	−376000.	−	651251.i	−0.495623	−	0.858444i
$872$		0			0
$873$	943858.	+	309809.i	1.23845	+	0.406505i
$874$		0			0
$875$	523289.	−	302121.i	0.683479	−	0.394607i
$876$		0			0
$877$	154630.	−	267827.i	0.201045	−	0.348221i	−0.747820	−	0.663901i	$-0.768899\pi$
$877$	154630.	−	267827.i	0.201045	−	0.348221i	0.948866	+	0.315680i	$0.102233\pi$
$878$		0			0
$879$	−31071.4	+	194291.i	−0.0402145	+	0.251464i
$880$		0			0
$881$			14534.0i			0.0187255i	0.999956	+	0.00936273i	$0.00298029\pi$
$881$			14534.0i			0.0187255i	−0.999956	+	0.00936273i	$0.997020\pi$
$882$		0			0
$883$	658359.			0.844387			0.422194	−	0.906506i	$-0.361260\pi$
$883$	658359.			0.844387			0.422194	+	0.906506i	$0.361260\pi$
$884$		0			0
$885$	−633995.	+	780523.i	−0.809467	+	0.996551i
$886$		0			0
$887$	154470.	+	89183.3i	0.196335	+	0.113354i	0.594945	−	0.803767i	$-0.297174\pi$
$887$	154470.	+	89183.3i	0.196335	+	0.113354i	−0.398610	+	0.917121i	$0.630507\pi$
$888$		0			0
$889$	141850.	+	245691.i	0.179483	+	0.310874i
$890$		0			0
$891$	−188896.	−	431208.i	−0.237940	−	0.543164i
$892$		0			0
$893$	1.35396e6	−	781708.i	1.69786	−	0.980261i
$894$		0			0
$895$	58925.2	−	102061.i	0.0735623	−	0.127414i
$896$		0			0
$897$	921044.	+	748135.i	1.14471	+	0.929812i
$898$		0			0
$899$			168802.i			0.208862i
$900$		0			0
$901$	1.22217e6			1.50550
$902$		0			0
$903$	−547947.	−	87628.5i	−0.671991	−	0.107466i
$904$		0			0
$905$	392928.	+	226857.i	0.479751	+	0.276984i
$906$		0			0
$907$	−149790.	−	259444.i	−0.182082	−	0.315376i	0.760507	−	0.649330i	$-0.224950\pi$
$907$	−149790.	−	259444.i	−0.182082	−	0.315376i	−0.942589	+	0.333954i	$0.891617\pi$
$908$		0			0
$909$	−108724.	+	331236.i	−0.131582	+	0.400876i
$910$		0			0
$911$	359297.	−	207440.i	0.432930	−	0.249952i	−0.267664	−	0.963512i	$-0.586252\pi$
$911$	359297.	−	207440.i	0.432930	−	0.249952i	0.700594	+	0.713560i	$0.252918\pi$
$912$		0			0
$913$	−174162.	+	301658.i	−0.208935	+	0.361887i
$914$		0			0
$915$	−2.41037e6	+	921112.i	−2.87900	+	1.10020i
$916$		0			0
$917$			12723.1i			0.0151305i
$918$		0			0
$919$	−1.61551e6			−1.91284			−0.956422	−	0.291987i	$-0.905684\pi$
$919$	−1.61551e6			−1.91284			−0.956422	+	0.291987i	$0.905684\pi$
$920$		0			0
$921$	212535.	+	556164.i	0.250560	+	0.655667i
$922$		0			0
$923$	262555.	+	151586.i	0.308189	+	0.177933i
$924$		0			0
$925$	715926.	+	1.24002e6i	0.836729	+	1.44926i
$926$		0			0
$927$	154457.	+	737529.i	0.179742	+	0.858262i
$928$		0			0
$929$	655036.	−	378185.i	0.758986	−	0.438201i	−0.0699457	−	0.997551i	$-0.522283\pi$
$929$	655036.	−	378185.i	0.758986	−	0.438201i	0.828931	+	0.559350i	$0.188949\pi$
$930$		0			0
$931$	336346.	−	582568.i	0.388049	−	0.672120i
$932$		0			0
$933$	50407.2	−	315200.i	0.0579067	−	0.362095i
$934$		0			0
$935$			806511.i			0.922544i
$936$		0			0
$937$	−509731.			−0.580580			−0.290290	−	0.956939i	$-0.593752\pi$
$937$	−509731.			−0.580580			−0.290290	+	0.956939i	$0.593752\pi$
$938$		0			0
$939$	−33440.0	+	41168.6i	−0.0379258	+	0.0466912i
$940$		0			0
$941$	−202787.	−	117079.i	−0.229013	−	0.132221i	0.381104	−	0.924532i	$-0.375544\pi$
$941$	−202787.	−	117079.i	−0.229013	−	0.132221i	−0.610117	+	0.792312i	$0.708877\pi$
$942$		0			0
$943$	879922.	+	1.52407e6i	0.989511	+	1.71388i
$944$		0			0
$945$	−382226.	+	741894.i	−0.428012	+	0.830765i
$946$		0			0
$947$	338121.	−	195214.i	0.377027	−	0.217677i	−0.299497	−	0.954097i	$-0.596819\pi$
$947$	338121.	−	195214.i	0.377027	−	0.217677i	0.676524	+	0.736421i	$0.263485\pi$
$948$		0			0
$949$	−319181.	+	552838.i	−0.354409	+	0.613855i
$950$		0			0
$951$	871535.	+	707920.i	0.963660	+	0.782751i
$952$		0			0
$953$		−	1.19963e6i		−	1.32087i	−0.750883	−	0.660435i	$-0.770372\pi$
$953$		−	1.19963e6i		−	1.32087i	0.750883	−	0.660435i	$-0.229628\pi$
$954$		0			0
$955$	−635801.			−0.697131
$956$		0			0
$957$	579138.	+	92616.5i	0.632351	+	0.101126i
$958$		0			0
$959$	289299.	+	167027.i	0.314564	+	0.181614i
$960$		0			0
$961$	444488.	+	769876.i	0.481297	+	0.833631i
$962$		0			0
$963$	−59669.4	−	66670.4i	−0.0643427	−	0.0718920i
$964$		0			0
$965$	−2.12779e6	+	1.22848e6i	−2.28494	+	1.31921i
$966$		0			0
$967$	785526.	−	1.36057e6i	0.840055	−	1.45502i	−0.0497929	−	0.998760i	$-0.515856\pi$
$967$	785526.	−	1.36057e6i	0.840055	−	1.45502i	0.889848	−	0.456258i	$-0.150811\pi$
$968$		0			0
$969$	−906126.	+	346272.i	−0.965031	+	0.368782i
$970$		0			0
$971$		−	1.61621e6i		−	1.71419i	−0.515161	−	0.857094i	$-0.672268\pi$
$971$		−	1.61621e6i		−	1.71419i	0.515161	−	0.857094i	$-0.327732\pi$
$972$		0			0
$973$	704109.			0.743728
$974$		0			0
$975$	−576873.	−	1.50956e6i	−0.606835	−	1.58797i
$976$		0			0
$977$	−1.58350e6	−	914234.i	−1.65893	−	0.957786i	−0.973208	−	0.229926i	$-0.926152\pi$
$977$	−1.58350e6	−	914234.i	−1.65893	−	0.957786i	−0.685726	−	0.727860i	$-0.740515\pi$
$978$		0			0
$979$	139591.	+	241779.i	0.145644	+	0.252263i
$980$		0			0
$981$	244937.	−	219217.i	0.254517	−	0.227790i
$982$		0			0
$983$	−848695.	+	489994.i	−0.878303	+	0.507089i	−0.870099	−	0.492878i	$-0.835945\pi$
$983$	−848695.	+	489994.i	−0.878303	+	0.507089i	−0.00820475	+	0.999966i	$0.502612\pi$
$984$		0			0
$985$	341640.	−	591738.i	0.352124	−	0.609897i
$986$		0			0
$987$	149217.	−	933064.i	0.153174	−	0.957805i
$988$		0			0
$989$			1.92221e6i			1.96521i
$990$		0			0
$991$	−596898.			−0.607789			−0.303895	−	0.952706i	$-0.598287\pi$
$991$	−596898.			−0.607789			−0.303895	+	0.952706i	$0.598287\pi$
$992$		0			0
$993$	54358.9	−	66922.4i	0.0551280	−	0.0678692i
$994$		0			0
$995$	2.00556e6	+	1.15791e6i	2.02577	+	1.16958i
$996$		0			0
$997$	261524.	+	452974.i	0.263101	+	0.455704i	0.967064	−	0.254532i	$-0.0819215\pi$
$997$	261524.	+	452974.i	0.263101	+	0.455704i	−0.703964	+	0.710236i	$0.748588\pi$
$998$		0			0
$999$	−804912.	−	414693.i	−0.806525	−	0.415524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.m.a.41.8	✓	24
3.2	odd	2		216.5.m.a.17.2		24
4.3	odd	2		144.5.q.d.113.5		24
9.2	odd	6	inner	72.5.m.a.65.8	yes	24
9.4	even	3		648.5.e.c.161.2		24
9.5	odd	6		648.5.e.c.161.23		24
9.7	even	3		216.5.m.a.89.2		24
12.11	even	2		432.5.q.d.17.2		24
36.7	odd	6		432.5.q.d.305.2		24
36.11	even	6		144.5.q.d.65.5		24
36.23	even	6		1296.5.e.j.161.23		24
36.31	odd	6		1296.5.e.j.161.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.m.a.41.8	✓	24	1.1	even	1	trivial
72.5.m.a.65.8	yes	24	9.2	odd	6	inner
144.5.q.d.65.5		24	36.11	even	6
144.5.q.d.113.5		24	4.3	odd	2
216.5.m.a.17.2		24	3.2	odd	2
216.5.m.a.89.2		24	9.7	even	3
432.5.q.d.17.2		24	12.11	even	2
432.5.q.d.305.2		24	36.7	odd	6
648.5.e.c.161.2		24	9.4	even	3
648.5.e.c.161.23		24	9.5	odd	6
1296.5.e.j.161.2		24	36.31	odd	6
1296.5.e.j.161.23		24	36.23	even	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.21271 + 8.40705i) q^{3} +(36.5152 + 21.0820i) q^{5} +(-13.5757 - 23.5138i) q^{7} +(-60.3569 + 54.0189i) q^{9} +O(q^{10})\)	\(q+(3.21271 + 8.40705i) q^{3} +(36.5152 + 21.0820i) q^{5} +(-13.5757 - 23.5138i) q^{7} +(-60.3569 + 54.0189i) q^{9} +(62.1394 - 35.8762i) q^{11} +(-77.8791 + 134.890i) q^{13} +(-59.9250 + 374.715i) q^{15} +266.582i q^{17} +404.309 q^{19} +(154.067 - 189.674i) q^{21} +(-733.066 - 423.236i) q^{23} +(576.404 + 998.362i) q^{25} +(-648.049 - 333.877i) q^{27} +(786.534 - 454.106i) q^{29} +(-92.9311 + 160.961i) q^{31} +(501.249 + 407.149i) q^{33} -1144.81i q^{35} +1242.05 q^{37} +(-1384.23 - 221.369i) q^{39} +(-1800.50 - 1039.52i) q^{41} +(-1135.43 - 1966.61i) q^{43} +(-3342.77 + 700.061i) q^{45} +(3348.82 - 1933.44i) q^{47} +(831.902 - 1440.90i) q^{49} +(-2241.17 + 856.453i) q^{51} -4584.58i q^{53} +3025.37 q^{55} +(1298.93 + 3399.05i) q^{57} +(2294.86 + 1324.94i) q^{59} +(3399.92 + 5888.83i) q^{61} +(2089.57 + 685.876i) q^{63} +(-5687.53 + 3283.70i) q^{65} +(-2414.00 + 4181.17i) q^{67} +(1203.03 - 7522.65i) q^{69} -1946.43i q^{71} +4098.42 q^{73} +(-6541.45 + 8053.31i) q^{75} +(-1687.17 - 974.087i) q^{77} +(-963.790 - 1669.33i) q^{79} +(724.921 - 6520.83i) q^{81} +(-4204.15 + 2427.27i) q^{83} +(-5620.10 + 9734.30i) q^{85} +(6344.60 + 5153.52i) q^{87} +3890.92i q^{89} +4229.04 q^{91} +(-1651.77 - 264.154i) q^{93} +(14763.4 + 8523.66i) q^{95} +(-6132.12 - 10621.1i) q^{97} +(-1812.55 + 5522.08i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 100 * q^9	\( 24 q + 4 q^{3} - 100 q^{9} + 252 q^{11} - 80 q^{15} - 408 q^{19} + 24 q^{21} + 720 q^{23} + 1500 q^{25} - 1280 q^{27} + 2376 q^{29} - 1104 q^{31} - 1412 q^{33} - 4184 q^{39} + 1980 q^{41} + 1476 q^{43} - 4696 q^{45} + 4536 q^{47} - 6084 q^{49} - 7828 q^{51} + 2544 q^{55} - 1204 q^{57} + 10332 q^{59} + 2784 q^{61} + 9072 q^{63} + 17280 q^{65} - 2604 q^{67} + 5680 q^{69} + 5112 q^{73} - 15412 q^{75} - 28368 q^{77} + 3480 q^{79} - 26548 q^{81} - 23400 q^{83} + 7392 q^{85} - 3192 q^{87} - 14208 q^{91} + 39488 q^{93} + 57528 q^{95} - 4020 q^{97} + 50744 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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