LMFDB - Embedded newform 36.5.d.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.d (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:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.5.d.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30278 - 2.25647i) q^{2} +(5.81665 + 14.9053i) q^{4} +22.8444 q^{5} -56.8882i q^{7} +(14.4222 - 62.3538i) q^{8} +O(q^{10})$	\(q+(-3.30278 - 2.25647i) q^{2} +(5.81665 + 14.9053i) q^{4} +22.8444 q^{5} -56.8882i q^{7} +(14.4222 - 62.3538i) q^{8} +(-75.4500 - 51.5478i) q^{10} -134.561i q^{11} +247.066 q^{13} +(-128.367 + 187.889i) q^{14} +(-188.333 + 173.397i) q^{16} +92.3112 q^{17} -29.5600i q^{19} +(132.878 + 340.502i) q^{20} +(-303.633 + 444.425i) q^{22} +571.038i q^{23} -103.133 q^{25} +(-816.005 - 557.499i) q^{26} +(847.933 - 330.899i) q^{28} -20.0891 q^{29} -474.736i q^{31} +(1013.29 - 147.724i) q^{32} +(-304.883 - 208.298i) q^{34} -1299.58i q^{35} -755.867 q^{37} +(-66.7013 + 97.6300i) q^{38} +(329.467 - 1424.44i) q^{40} -541.822 q^{41} +3097.06i q^{43} +(2005.67 - 782.695i) q^{44} +(1288.53 - 1886.01i) q^{46} +1050.16i q^{47} -835.266 q^{49} +(340.625 + 232.717i) q^{50} +(1437.10 + 3682.59i) q^{52} -1768.35 q^{53} -3073.97i q^{55} +(-3547.20 - 820.453i) q^{56} +(66.3499 + 45.3306i) q^{58} +2582.98i q^{59} -2403.33 q^{61} +(-1071.23 + 1567.95i) q^{62} +(-3680.00 - 1798.56i) q^{64} +5644.09 q^{65} -379.816i q^{67} +(536.942 + 1375.92i) q^{68} +(-2932.46 + 4292.21i) q^{70} -702.517i q^{71} +9824.92 q^{73} +(2496.46 + 1705.59i) q^{74} +(440.599 - 171.940i) q^{76} -7654.93 q^{77} +3756.40i q^{79} +(-4302.36 + 3961.16i) q^{80} +(1789.52 + 1222.61i) q^{82} -10433.6i q^{83} +2108.79 q^{85} +(6988.43 - 10228.9i) q^{86} +(-8390.39 - 1940.67i) q^{88} +11923.5 q^{89} -14055.2i q^{91} +(-8511.46 + 3321.53i) q^{92} +(2369.66 - 3468.45i) q^{94} -675.280i q^{95} -2199.06 q^{97} +(2758.70 + 1884.76i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5}+O(q^{10}) $ 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5	$ 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5} - 172 q^{10} + 296 q^{13} - 600 q^{14} + 112 q^{16} + 600 q^{17} + 1368 q^{20} - 1128 q^{22} + 972 q^{25} - 1692 q^{26} + 1488 q^{28} - 888 q^{29} + 2784 q^{32} - 484 q^{34} - 4408 q^{37} - 4680 q^{38} + 1664 q^{40} - 552 q^{41} + 3696 q^{44} - 384 q^{46} - 572 q^{49} + 1038 q^{50} + 6008 q^{52} - 5112 q^{53} - 1728 q^{56} - 124 q^{58} + 4232 q^{61} + 7224 q^{62} - 14720 q^{64} + 18192 q^{65} - 5496 q^{68} + 6096 q^{70} + 8840 q^{73} + 4116 q^{74} - 1872 q^{76} - 20928 q^{77} - 25632 q^{80} + 3740 q^{82} - 10256 q^{85} + 19560 q^{86} - 8640 q^{88} + 25080 q^{89} - 18816 q^{92} - 5232 q^{94} + 23048 q^{97} + 5850 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5 - 172 * q^10 + 296 * q^13 - 600 * q^14 + 112 * q^16 + 600 * q^17 + 1368 * q^20 - 1128 * q^22 + 972 * q^25 - 1692 * q^26 + 1488 * q^28 - 888 * q^29 + 2784 * q^32 - 484 * q^34 - 4408 * q^37 - 4680 * q^38 + 1664 * q^40 - 552 * q^41 + 3696 * q^44 - 384 * q^46 - 572 * q^49 + 1038 * q^50 + 6008 * q^52 - 5112 * q^53 - 1728 * q^56 - 124 * q^58 + 4232 * q^61 + 7224 * q^62 - 14720 * q^64 + 18192 * q^65 - 5496 * q^68 + 6096 * q^70 + 8840 * q^73 + 4116 * q^74 - 1872 * q^76 - 20928 * q^77 - 25632 * q^80 + 3740 * q^82 - 10256 * q^85 + 19560 * q^86 - 8640 * q^88 + 25080 * q^89 - 18816 * q^92 - 5232 * q^94 + 23048 * q^97 + 5850 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

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 $

$2$	−3.30278	−	2.25647i	−0.825694	−	0.564118i
$2$	−3.30278	−	2.25647i	−0.825694	−	0.564118i
$3$		0			0
$3$		0			0
$4$	5.81665	+	14.9053i	0.363541	+	0.931578i
$5$	22.8444			0.913776			0.456888	−	0.889524i	$-0.348964\pi$
$5$	22.8444			0.913776			0.456888	+	0.889524i	$0.348964\pi$
$6$		0			0
$7$		−	56.8882i		−	1.16098i	−0.814266	−	0.580492i	$-0.802860\pi$
$7$		−	56.8882i		−	1.16098i	0.814266	−	0.580492i	$-0.197140\pi$
$8$	14.4222	−	62.3538i	0.225347	−	0.974279i
$9$		0			0
$10$	−75.4500	−	51.5478i	−0.754500	−	0.515478i
$11$		−	134.561i		−	1.11207i	−0.831157	−	0.556037i	$-0.812321\pi$
$11$		−	134.561i		−	1.11207i	0.831157	−	0.556037i	$-0.187679\pi$
$12$		0			0
$13$	247.066			1.46193			0.730966	−	0.682414i	$-0.239070\pi$
$13$	247.066			1.46193			0.730966	+	0.682414i	$0.239070\pi$
$14$	−128.367	+	187.889i	−0.654932	+	0.958617i
$15$		0			0
$16$	−188.333	+	173.397i	−0.735676	+	0.677334i
$17$	92.3112			0.319416			0.159708	−	0.987164i	$-0.448945\pi$
$17$	92.3112			0.319416			0.159708	+	0.987164i	$0.448945\pi$
$18$		0			0
$19$		−	29.5600i		−	0.0818836i	−0.999162	−	0.0409418i	$-0.986964\pi$
$19$		−	29.5600i		−	0.0818836i	0.999162	−	0.0409418i	$-0.0130358\pi$
$20$	132.878	+	340.502i	0.332195	+	0.851254i
$21$		0			0
$22$	−303.633	+	444.425i	−0.627342	+	0.918233i
$23$			571.038i			1.07947i	0.841836	+	0.539733i	$0.181475\pi$
$23$			571.038i			1.07947i	−0.841836	+	0.539733i	$0.818525\pi$
$24$		0			0
$25$	−103.133			−0.165013
$26$	−816.005	−	557.499i	−1.20711	−	0.824703i
$27$		0			0
$28$	847.933	−	330.899i	1.08155	−	0.422065i
$29$	−20.0891			−0.0238872			−0.0119436	−	0.999929i	$-0.503802\pi$
$29$	−20.0891			−0.0238872			−0.0119436	+	0.999929i	$0.503802\pi$
$30$		0			0
$31$		−	474.736i		−	0.494002i	−0.969015	−	0.247001i	$-0.920555\pi$
$31$		−	474.736i		−	0.494002i	0.969015	−	0.247001i	$-0.0794452\pi$
$32$	1013.29	−	147.724i	0.989540	−	0.144262i
$33$		0			0
$34$	−304.883	−	208.298i	−0.263740	−	0.180188i
$35$		−	1299.58i		−	1.06088i
$36$		0			0
$37$	−755.867			−0.552131			−0.276065	−	0.961139i	$-0.589031\pi$
$37$	−755.867			−0.552131			−0.276065	+	0.961139i	$0.589031\pi$
$38$	−66.7013	+	97.6300i	−0.0461920	+	0.0676108i
$39$		0			0
$40$	329.467	−	1424.44i	0.205917	−	0.890273i
$41$	−541.822			−0.322321			−0.161161	−	0.986928i	$-0.551524\pi$
$41$	−541.822			−0.322321			−0.161161	+	0.986928i	$0.551524\pi$
$42$		0			0
$43$			3097.06i			1.67499i	0.546444	+	0.837496i	$0.315981\pi$
$43$			3097.06i			1.67499i	−0.546444	+	0.837496i	$0.684019\pi$
$44$	2005.67	−	782.695i	1.03598	−	0.404284i
$45$		0			0
$46$	1288.53	−	1886.01i	0.608947	−	0.891309i
$47$			1050.16i			0.475401i	0.971338	+	0.237701i	$0.0763937\pi$
$47$			1050.16i			0.475401i	−0.971338	+	0.237701i	$0.923606\pi$
$48$		0			0
$49$	−835.266			−0.347882
$50$	340.625	+	232.717i	0.136250	+	0.0930867i
$51$		0			0
$52$	1437.10	+	3682.59i	0.531472	+	1.36190i
$53$	−1768.35			−0.629532			−0.314766	−	0.949169i	$-0.601926\pi$
$53$	−1768.35			−0.629532			−0.314766	+	0.949169i	$0.601926\pi$
$54$		0			0
$55$		−	3073.97i		−	1.01619i
$56$	−3547.20	−	820.453i	−1.13112	−	0.261624i
$57$		0			0
$58$	66.3499	+	45.3306i	0.0197235	+	0.0134752i
$59$			2582.98i			0.742024i	0.928628	+	0.371012i	$0.120989\pi$
$59$			2582.98i			0.742024i	−0.928628	+	0.371012i	$0.879011\pi$
$60$		0			0
$61$	−2403.33			−0.645883			−0.322941	−	0.946419i	$-0.604672\pi$
$61$	−2403.33			−0.645883			−0.322941	+	0.946419i	$0.604672\pi$
$62$	−1071.23	+	1567.95i	−0.278676	+	0.407895i
$63$		0			0
$64$	−3680.00	−	1798.56i	−0.898438	−	0.439101i
$65$	5644.09			1.33588
$66$		0			0
$67$		−	379.816i		−	0.0846104i	−0.999105	−	0.0423052i	$-0.986530\pi$
$67$		−	379.816i		−	0.0846104i	0.999105	−	0.0423052i	$-0.0134702\pi$
$68$	536.942	+	1375.92i	0.116121	+	0.297561i
$69$		0			0
$70$	−2932.46	+	4292.21i	−0.598462	+	0.875962i
$71$		−	702.517i		−	0.139361i	−0.997569	−	0.0696803i	$-0.977802\pi$
$71$		−	702.517i		−	0.139361i	0.997569	−	0.0696803i	$-0.0221979\pi$
$72$		0			0
$73$	9824.92			1.84367			0.921836	−	0.387581i	$-0.126689\pi$
$73$	9824.92			1.84367			0.921836	+	0.387581i	$0.126689\pi$
$74$	2496.46	+	1705.59i	0.455891	+	0.311467i
$75$		0			0
$76$	440.599	−	171.940i	0.0762810	−	0.0297680i
$77$	−7654.93			−1.29110
$78$		0			0
$79$			3756.40i			0.601890i	0.953641	+	0.300945i	$0.0973021\pi$
$79$			3756.40i			0.601890i	−0.953641	+	0.300945i	$0.902698\pi$
$80$	−4302.36	+	3961.16i	−0.672243	+	0.618931i
$81$		0			0
$82$	1789.52	+	1222.61i	0.266139	+	0.181827i
$83$		−	10433.6i		−	1.51452i	−0.653111	−	0.757262i	$-0.726537\pi$
$83$		−	10433.6i		−	1.51452i	0.653111	−	0.757262i	$-0.273463\pi$
$84$		0			0
$85$	2108.79			0.291875
$86$	6988.43	−	10228.9i	0.944893	−	1.38303i
$87$		0			0
$88$	−8390.39	−	1940.67i	−1.08347	−	0.250603i
$89$	11923.5			1.50530			0.752651	−	0.658419i	$-0.228775\pi$
$89$	11923.5			1.50530			0.752651	+	0.658419i	$0.228775\pi$
$90$		0			0
$91$		−	14055.2i		−	1.69728i
$92$	−8511.46	+	3321.53i	−1.00561	+	0.392430i
$93$		0			0
$94$	2369.66	−	3468.45i	0.268183	−	0.392536i
$95$		−	675.280i		−	0.0748233i
$96$		0			0
$97$	−2199.06			−0.233718			−0.116859	−	0.993148i	$-0.537283\pi$
$97$	−2199.06			−0.233718			−0.116859	+	0.993148i	$0.537283\pi$
$98$	2758.70	+	1884.76i	0.287244	+	0.196247i
$99$		0			0
$100$	−599.889	−	1537.22i	−0.0599889	−	0.153722i
$101$	874.835			0.0857597			0.0428799	−	0.999080i	$-0.486347\pi$
$101$	874.835			0.0857597			0.0428799	+	0.999080i	$0.486347\pi$
$102$		0			0
$103$			3036.94i			0.286260i	0.989704	+	0.143130i	$0.0457168\pi$
$103$			3036.94i			0.286260i	−0.989704	+	0.143130i	$0.954283\pi$
$104$	3563.24	−	15405.5i	0.329442	−	1.42433i
$105$		0			0
$106$	5840.48	+	3990.25i	0.519801	+	0.355131i
$107$			19057.6i			1.66457i	0.554350	+	0.832284i	$0.312967\pi$
$107$			19057.6i			1.66457i	−0.554350	+	0.832284i	$0.687033\pi$
$108$		0			0
$109$	−13132.7			−1.10535			−0.552675	−	0.833397i	$-0.686393\pi$
$109$	−13132.7			−1.10535			−0.552675	+	0.833397i	$0.686393\pi$
$110$	−6936.32	+	10152.6i	−0.573250	+	0.839060i
$111$		0			0
$112$	9864.26	+	10713.9i	0.786373	+	0.854108i
$113$	−14541.5			−1.13882			−0.569408	−	0.822055i	$-0.692827\pi$
$113$	−14541.5			−1.13882			−0.569408	+	0.822055i	$0.692827\pi$
$114$		0			0
$115$			13045.0i			0.986391i
$116$	−116.852	−	299.434i	−0.00868397	−	0.0222528i
$117$		0			0
$118$	5828.44	−	8531.02i	0.418589	−	0.612685i
$119$		−	5251.42i		−	0.370836i
$120$		0			0
$121$	−3465.66			−0.236709
$122$	7937.66	+	5423.05i	0.533301	+	0.364354i
$123$		0			0
$124$	7076.06	−	2761.38i	0.460202	−	0.179590i
$125$	−16633.8			−1.06456
$126$		0			0
$127$			25959.7i			1.60951i	0.593609	+	0.804753i	$0.297702\pi$
$127$			25959.7i			1.60951i	−0.593609	+	0.804753i	$0.702298\pi$
$128$	8095.81	+	14244.1i	0.494129	+	0.869388i
$129$		0			0
$130$	−18641.2	−	12735.7i	−1.10303	−	0.753594i
$131$			16440.3i			0.958003i	0.877814	+	0.479002i	$0.159001\pi$
$131$			16440.3i			0.958003i	−0.877814	+	0.479002i	$0.840999\pi$
$132$		0			0
$133$	−1681.61			−0.0950655
$134$	−857.045	+	1254.45i	−0.0477303	+	0.0698623i
$135$		0			0
$136$	1331.33	−	5755.96i	0.0719794	−	0.311200i
$137$	31618.7			1.68462			0.842312	−	0.538990i	$-0.181194\pi$
$137$	31618.7			1.68462			0.842312	+	0.538990i	$0.181194\pi$
$138$		0			0
$139$		−	12895.9i		−	0.667453i	−0.942670	−	0.333726i	$-0.891694\pi$
$139$		−	12895.9i		−	0.667453i	0.942670	−	0.333726i	$-0.108306\pi$
$140$	19370.5	−	7559.19i	0.988292	−	0.385673i
$141$		0			0
$142$	−1585.21	+	2320.25i	−0.0786159	+	0.115069i
$143$		−	33245.5i		−	1.62578i
$144$		0			0
$145$	−458.924			−0.0218276
$146$	−32449.5	−	22169.7i	−1.52231	−	1.04005i
$147$		0			0
$148$	−4396.62	−	11266.4i	−0.200722	−	0.514353i
$149$	−31474.8			−1.41772			−0.708859	−	0.705350i	$-0.750790\pi$
$149$	−31474.8			−1.41772			−0.708859	+	0.705350i	$0.750790\pi$
$150$		0			0
$151$		−	39479.3i		−	1.73147i	−0.500502	−	0.865735i	$-0.666851\pi$
$151$		−	39479.3i		−	1.73147i	0.500502	−	0.865735i	$-0.333149\pi$
$152$	−1843.18	−	426.320i	−0.0797774	−	0.0184522i
$153$		0			0
$154$	25282.5	+	17273.1i	1.06605	+	0.728333i
$155$		−	10845.1i		−	0.451408i
$156$		0			0
$157$	2619.07			0.106255			0.0531273	−	0.998588i	$-0.483081\pi$
$157$	2619.07			0.106255			0.0531273	+	0.998588i	$0.483081\pi$
$158$	8476.21	−	12406.5i	0.339537	−	0.496977i
$159$		0			0
$160$	23148.0	−	3374.67i	0.904218	−	0.131823i
$161$	32485.3			1.25324
$162$		0			0
$163$			7123.14i			0.268100i	0.990975	+	0.134050i	$0.0427982\pi$
$163$			7123.14i			0.268100i	−0.990975	+	0.134050i	$0.957202\pi$
$164$	−3151.59	−	8075.99i	−0.117177	−	0.300267i
$165$		0			0
$166$	−23543.0	+	34459.7i	−0.854371	+	1.25053i
$167$			48670.8i			1.74516i	0.488472	+	0.872580i	$0.337555\pi$
$167$			48670.8i			1.74516i	−0.488472	+	0.872580i	$0.662445\pi$
$168$		0			0
$169$	32480.8			1.13724
$170$	−6964.87	−	4758.44i	−0.240999	−	0.164652i
$171$		0			0
$172$	−46162.4	+	18014.5i	−1.56039	+	0.608928i
$173$	27575.9			0.921377			0.460689	−	0.887562i	$-0.347603\pi$
$173$	27575.9			0.921377			0.460689	+	0.887562i	$0.347603\pi$
$174$		0			0
$175$			5867.05i			0.191577i
$176$	23332.5	+	25342.3i	0.753245	+	0.818126i
$177$		0			0
$178$	−39380.7	−	26905.1i	−1.24292	−	0.849169i
$179$		−	42280.0i		−	1.31956i	−0.751459	−	0.659780i	$-0.770649\pi$
$179$		−	42280.0i		−	1.31956i	0.751459	−	0.659780i	$-0.229351\pi$
$180$		0			0
$181$	−1006.79			−0.0307313			−0.0153657	−	0.999882i	$-0.504891\pi$
$181$	−1006.79			−0.0307313			−0.0153657	+	0.999882i	$0.504891\pi$
$182$	−31715.1	+	46421.1i	−0.957466	+	1.40143i
$183$		0			0
$184$	35606.4	+	8235.62i	1.05170	+	0.243254i
$185$	−17267.3			−0.504524
$186$		0			0
$187$		−	12421.5i		−	0.355214i
$188$	−15652.9	+	6108.43i	−0.442874	+	0.172828i
$189$		0			0
$190$	−1523.75	+	2230.30i	−0.0422092	+	0.0617811i
$191$		−	6906.62i		−	0.189321i	−0.995510	−	0.0946605i	$-0.969823\pi$
$191$		−	6906.62i		−	0.189321i	0.995510	−	0.0946605i	$-0.0301766\pi$
$192$		0			0
$193$	28207.8			0.757278			0.378639	−	0.925545i	$-0.376392\pi$
$193$	28207.8			0.757278			0.378639	+	0.925545i	$0.376392\pi$
$194$	7262.99	+	4962.11i	0.192980	+	0.131845i
$195$		0			0
$196$	−4858.45	−	12449.8i	−0.126469	−	0.324080i
$197$	−38453.6			−0.990843			−0.495422	−	0.868653i	$-0.664986\pi$
$197$	−38453.6			−0.990843			−0.495422	+	0.868653i	$0.664986\pi$
$198$		0			0
$199$			5490.10i			0.138635i	0.997595	+	0.0693176i	$0.0220822\pi$
$199$			5490.10i			0.138635i	−0.997595	+	0.0693176i	$0.977918\pi$
$200$	−1487.40	+	6430.73i	−0.0371851	+	0.160768i
$201$		0			0
$202$	−2889.38	−	1974.04i	−0.0708113	−	0.0483787i
$203$			1142.83i			0.0277326i
$204$		0			0
$205$	−12377.6			−0.294529
$206$	6852.77	−	10030.3i	0.161485	−	0.236363i
$207$		0			0
$208$	−46530.8	+	42840.7i	−1.07551	+	0.990215i
$209$	−3977.62			−0.0910606
$210$		0			0
$211$			46471.5i			1.04381i	0.853004	+	0.521905i	$0.174778\pi$
$211$			46471.5i			1.04381i	−0.853004	+	0.521905i	$0.825222\pi$
$212$	−10285.9	−	26357.8i	−0.228861	−	0.586458i
$213$		0			0
$214$	43003.0	−	62943.1i	0.939013	−	1.37442i
$215$			70750.5i			1.53057i
$216$		0			0
$217$	−27006.9			−0.573529
$218$	43374.2	+	29633.5i	0.912681	+	0.623548i
$219$		0			0
$220$	45818.2	−	17880.2i	0.946658	−	0.369426i
$221$	22807.0			0.466964
$222$		0			0
$223$		−	48307.2i		−	0.971409i	−0.874123	−	0.485704i	$-0.838563\pi$
$223$		−	48307.2i		−	0.971409i	0.874123	−	0.485704i	$-0.161437\pi$
$224$	−8403.75	−	57644.1i	−0.167486	−	1.14884i
$225$		0			0
$226$	48027.4	+	32812.6i	0.940313	+	0.642427i
$227$		−	19108.6i		−	0.370832i	−0.982660	−	0.185416i	$-0.940637\pi$
$227$		−	19108.6i		−	0.370832i	0.982660	−	0.185416i	$-0.0593633\pi$
$228$		0			0
$229$	−73378.5			−1.39926			−0.699629	−	0.714506i	$-0.746651\pi$
$229$	−73378.5			−1.39926			−0.699629	+	0.714506i	$0.746651\pi$
$230$	29435.7	−	43084.8i	0.556441	−	0.814457i
$231$		0			0
$232$	−289.730	+	1252.63i	−0.00538291	+	0.0232728i
$233$	34041.9			0.627049			0.313524	−	0.949580i	$-0.398490\pi$
$233$	34041.9			0.627049			0.313524	+	0.949580i	$0.398490\pi$
$234$		0			0
$235$			23990.3i			0.434411i
$236$	−38500.0	+	15024.3i	−0.691253	+	0.269756i
$237$		0			0
$238$	−11849.7	+	17344.2i	−0.209196	+	0.306197i
$239$		−	35114.3i		−	0.614735i	−0.951591	−	0.307368i	$-0.900552\pi$
$239$		−	35114.3i		−	0.614735i	0.951591	−	0.307368i	$-0.0994482\pi$
$240$		0			0
$241$	−19621.0			−0.337821			−0.168910	−	0.985631i	$-0.554025\pi$
$241$	−19621.0			−0.337821			−0.168910	+	0.985631i	$0.554025\pi$
$242$	11446.3	+	7820.17i	0.195449	+	0.133532i
$243$		0			0
$244$	−13979.3	−	35822.2i	−0.234805	−	0.601690i
$245$	−19081.2			−0.317887
$246$		0			0
$247$		−	7303.28i		−	0.119708i
$248$	−29601.6	−	6846.74i	−0.481296	−	0.111322i
$249$		0			0
$250$	54937.6	+	37533.7i	0.879002	+	0.600539i
$251$			560.729i			0.00890032i	0.999990	+	0.00445016i	$0.00141654\pi$
$251$			560.729i			0.00890032i	−0.999990	+	0.00445016i	$0.998583\pi$
$252$		0			0
$253$	76839.4			1.20045
$254$	58577.5	−	85739.2i	0.907952	−	1.32896i
$255$		0			0
$256$	5402.70	−	65312.9i	0.0824386	−	0.996596i
$257$	−80511.1			−1.21896			−0.609480	−	0.792801i	$-0.708622\pi$
$257$	−80511.1			−1.21896			−0.609480	+	0.792801i	$0.708622\pi$
$258$		0			0
$259$			42999.9i			0.641015i
$260$	32829.7	+	84126.5i	0.485647	+	1.24448i
$261$		0			0
$262$	37097.1	−	54298.6i	0.540427	−	0.791017i
$263$		−	34821.7i		−	0.503430i	−0.967801	−	0.251715i	$-0.919005\pi$
$263$		−	34821.7i		−	0.503430i	0.967801	−	0.251715i	$-0.0809945\pi$
$264$		0			0
$265$	−40397.0			−0.575251
$266$	5553.99	+	3794.52i	0.0784950	+	0.0536282i
$267$		0			0
$268$	5661.26	−	2209.26i	0.0788212	−	0.0307593i
$269$	28469.5			0.393438			0.196719	−	0.980460i	$-0.436971\pi$
$269$	28469.5			0.393438			0.196719	+	0.980460i	$0.436971\pi$
$270$		0			0
$271$			37653.7i			0.512706i	0.966583	+	0.256353i	$0.0825210\pi$
$271$			37653.7i			0.512706i	−0.966583	+	0.256353i	$0.917479\pi$
$272$	−17385.2	+	16006.5i	−0.234987	+	0.216351i
$273$		0			0
$274$	−104429.	−	71346.8i	−1.39098	−	0.950327i
$275$			13877.7i			0.183506i
$276$		0			0
$277$	25920.1			0.337814			0.168907	−	0.985632i	$-0.445976\pi$
$277$	25920.1			0.337814			0.168907	+	0.985632i	$0.445976\pi$
$278$	−29099.2	+	42592.1i	−0.376522	+	0.551112i
$279$		0			0
$280$	−81033.6	−	18742.8i	−1.03359	−	0.239066i
$281$	−49815.6			−0.630889			−0.315444	−	0.948944i	$-0.602154\pi$
$281$	−49815.6			−0.630889			−0.315444	+	0.948944i	$0.602154\pi$
$282$		0			0
$283$		−	73403.9i		−	0.916530i	−0.888816	−	0.458265i	$-0.848471\pi$
$283$		−	73403.9i		−	0.916530i	0.888816	−	0.458265i	$-0.151529\pi$
$284$	10471.2	−	4086.30i	0.129825	−	0.0506633i
$285$		0			0
$286$	−75017.6	+	109802.i	−0.917131	+	1.34239i
$287$			30823.3i			0.374209i
$288$		0			0
$289$	−74999.6			−0.897974
$290$	1515.72	+	1035.55i	0.0180229	+	0.0123133i
$291$		0			0
$292$	57148.2	+	146443.i	0.670250	+	1.71752i
$293$	130683.			1.52224			0.761120	−	0.648611i	$-0.224650\pi$
$293$	130683.			1.52224			0.761120	+	0.648611i	$0.224650\pi$
$294$		0			0
$295$			59006.8i			0.678044i
$296$	−10901.3	+	47131.2i	−0.124421	+	0.537929i
$297$		0			0
$298$	103954.	+	71022.0i	1.17060	+	0.799761i
$299$			141084.i			1.57811i
$300$		0			0
$301$	176186.			1.94464
$302$	−89083.9	+	130391.i	−0.976754	+	1.42966i
$303$		0			0
$304$	5125.62	+	5567.12i	0.0554625	+	0.0602398i
$305$	−54902.6			−0.590192
$306$		0			0
$307$		−	139512.i		−	1.48025i	−0.672469	−	0.740126i	$-0.734766\pi$
$307$		−	139512.i		−	1.48025i	0.672469	−	0.740126i	$-0.265234\pi$
$308$	−44526.1	−	114099.i	−0.469368	−	1.20276i
$309$		0			0
$310$	−24471.6	+	35818.8i	−0.254647	+	0.372725i
$311$		−	132034.i		−	1.36510i	−0.730837	−	0.682552i	$-0.760870\pi$
$311$		−	132034.i		−	1.36510i	0.730837	−	0.682552i	$-0.239130\pi$
$312$		0			0
$313$	39526.3			0.403458			0.201729	−	0.979441i	$-0.435344\pi$
$313$	39526.3			0.403458			0.201729	+	0.979441i	$0.435344\pi$
$314$	−8650.20	−	5909.86i	−0.0877338	−	0.0599402i
$315$		0			0
$316$	−55990.0	+	21849.7i	−0.560708	+	0.218812i
$317$	91959.1			0.915116			0.457558	−	0.889180i	$-0.348724\pi$
$317$	91959.1			0.915116			0.457558	+	0.889180i	$0.348724\pi$
$318$		0			0
$319$			2703.21i			0.0265643i
$320$	−84067.4	−	41087.0i	−0.820971	−	0.401241i
$321$		0			0
$322$	−107292.	−	73302.2i	−1.03479	−	0.706977i
$323$		−	2728.72i		−	0.0261549i
$324$		0			0
$325$	−25480.7			−0.241237
$326$	16073.2	−	23526.1i	0.151240	−	0.221368i
$327$		0			0
$328$	−7814.26	+	33784.7i	−0.0726341	+	0.314031i
$329$	59741.8			0.551933
$330$		0			0
$331$		−	3244.08i		−	0.0296098i	−0.999890	−	0.0148049i	$-0.995287\pi$
$331$		−	3244.08i		−	0.0296098i	0.999890	−	0.0148049i	$-0.00471272\pi$
$332$	155515.	−	60688.4i	1.41090	−	0.550591i
$333$		0			0
$334$	109824.	−	160749.i	0.984477	−	1.44097i
$335$		−	8676.68i		−	0.0773150i
$336$		0			0
$337$	5591.21			0.0492318			0.0246159	−	0.999697i	$-0.492164\pi$
$337$	5591.21			0.0492318			0.0246159	+	0.999697i	$0.492164\pi$
$338$	−107277.	−	73292.1i	−0.939016	−	0.641540i
$339$		0			0
$340$	12266.1	+	31432.1i	0.106108	+	0.271904i
$341$	−63881.0			−0.549367
$342$		0			0
$343$		−	89071.8i		−	0.757098i
$344$	193113.	+	44666.4i	1.63191	+	0.377454i
$345$		0			0
$346$	−91077.0	−	62224.3i	−0.760775	−	0.519766i
$347$		−	170630.i		−	1.41708i	−0.705668	−	0.708542i	$-0.749353\pi$
$347$		−	170630.i		−	1.41708i	0.705668	−	0.708542i	$-0.250647\pi$
$348$		0			0
$349$	−96101.4			−0.789003			−0.394502	−	0.918895i	$-0.629083\pi$
$349$	−96101.4			−0.789003			−0.394502	+	0.918895i	$0.629083\pi$
$350$	13238.8	−	19377.5i	0.108072	−	0.158184i
$351$		0			0
$352$	−19877.9	−	136349.i	−0.160430	−	1.10044i
$353$	−205914.			−1.65248			−0.826242	−	0.563316i	$-0.809526\pi$
$353$	−205914.			−1.65248			−0.826242	+	0.563316i	$0.809526\pi$
$354$		0			0
$355$		−	16048.6i		−	0.127344i
$356$	69354.9	+	177723.i	0.547239	+	1.40231i
$357$		0			0
$358$	−95403.8	+	139641.i	−0.744388	+	1.08955i
$359$		−	78435.2i		−	0.608586i	−0.952578	−	0.304293i	$-0.901580\pi$
$359$		−	78435.2i		−	0.608586i	0.952578	−	0.304293i	$-0.0984202\pi$
$360$		0			0
$361$	129447.			0.993295
$362$	3325.20	+	2271.79i	0.0253747	+	0.0173361i
$363$		0			0
$364$	209496.	−	81754.0i	1.58115	−	0.617030i
$365$	224445.			1.68470
$366$		0			0
$367$			221785.i			1.64664i	0.567574	+	0.823322i	$0.307882\pi$
$367$			221785.i			1.64664i	−0.567574	+	0.823322i	$0.692118\pi$
$368$	−99016.5	−	107545.i	−0.731159	−	0.794138i
$369$		0			0
$370$	57030.1	+	38963.3i	0.416582	+	0.284611i
$371$			100599.i			0.730876i
$372$		0			0
$373$	−25883.8			−0.186042			−0.0930208	−	0.995664i	$-0.529652\pi$
$373$	−25883.8			−0.186042			−0.0930208	+	0.995664i	$0.529652\pi$
$374$	−28028.7	+	41025.4i	−0.200383	+	0.293298i
$375$		0			0
$376$	65481.6	+	15145.6i	0.463173	+	0.107130i
$377$	−4963.35			−0.0349214
$378$		0			0
$379$			147801.i			1.02896i	0.857503	+	0.514479i	$0.172015\pi$
$379$			147801.i			1.02896i	−0.857503	+	0.514479i	$0.827985\pi$
$380$	10065.2	−	3927.87i	0.0697038	−	0.0272013i
$381$		0			0
$382$	−15584.6	+	22811.0i	−0.106800	+	0.156321i
$383$			226231.i			1.54225i	0.636683	+	0.771126i	$0.280306\pi$
$383$			226231.i			1.54225i	−0.636683	+	0.771126i	$0.719694\pi$
$384$		0			0
$385$	−174872.			−1.17978
$386$	−93164.2	−	63650.2i	−0.625280	−	0.427194i
$387$		0			0
$388$	−12791.2	−	32777.5i	−0.0849662	−	0.217727i
$389$	−256419.			−1.69453			−0.847267	−	0.531167i	$-0.821754\pi$
$389$	−256419.			−1.69453			−0.847267	+	0.531167i	$0.821754\pi$
$390$		0			0
$391$			52713.2i			0.344799i
$392$	−12046.4	+	52082.0i	−0.0783943	+	0.338934i
$393$		0			0
$394$	127004.	+	86769.6i	0.818133	+	0.558953i
$395$			85812.7i			0.549993i
$396$		0			0
$397$	−56667.7			−0.359546			−0.179773	−	0.983708i	$-0.557536\pi$
$397$	−56667.7			−0.359546			−0.179773	+	0.983708i	$0.557536\pi$
$398$	12388.3	−	18132.6i	0.0782067	−	0.114470i
$399$		0			0
$400$	19423.3	−	17883.0i	0.121396	−	0.111769i
$401$	−10912.0			−0.0678605			−0.0339302	−	0.999424i	$-0.510802\pi$
$401$	−10912.0			−0.0678605			−0.0339302	+	0.999424i	$0.510802\pi$
$402$		0			0
$403$		−	117291.i		−	0.722198i
$404$	5088.61	+	13039.6i	0.0311772	+	0.0798919i
$405$		0			0
$406$	2578.77	−	3774.52i	0.0156445	−	0.0228987i
$407$			101710.i			0.614010i
$408$		0			0
$409$	−289576.			−1.73108			−0.865538	−	0.500844i	$-0.833023\pi$
$409$	−289576.			−1.73108			−0.865538	+	0.500844i	$0.833023\pi$
$410$	40880.4	+	27929.7i	0.243191	+	0.166149i
$411$		0			0
$412$	−45266.3	+	17664.8i	−0.266674	+	0.104067i
$413$	146941.			0.861477
$414$		0			0
$415$		−	238348.i		−	1.38394i
$416$	250350.	−	36497.7i	1.44664	−	0.210901i
$417$		0			0
$418$	13137.2	+	8975.39i	0.0751882	+	0.0513690i
$419$			69837.9i			0.397798i	0.980020	+	0.198899i	$0.0637366\pi$
$419$			69837.9i			0.397798i	−0.980020	+	0.198899i	$0.936263\pi$
$420$		0			0
$421$	16207.0			0.0914405			0.0457203	−	0.998954i	$-0.485442\pi$
$421$	16207.0			0.0914405			0.0457203	+	0.998954i	$0.485442\pi$
$422$	104862.	−	153485.i	0.588832	−	0.861867i
$423$		0			0
$424$	−25503.6	+	110264.i	−0.141863	+	0.613339i
$425$	−9520.32			−0.0527077
$426$		0			0
$427$			136721.i			0.749859i
$428$	−284059.	+	110852.i	−1.55067	+	0.605138i
$429$		0			0
$430$	159647.	−	233673.i	0.863421	−	1.26378i
$431$		−	105264.i		−	0.566662i	−0.959022	−	0.283331i	$-0.908560\pi$
$431$		−	105264.i		−	0.566662i	0.959022	−	0.283331i	$-0.0914395\pi$
$432$		0			0
$433$	131799.			0.702970			0.351485	−	0.936193i	$-0.385677\pi$
$433$	131799.			0.702970			0.351485	+	0.936193i	$0.385677\pi$
$434$	89197.7	+	60940.3i	0.473559	+	0.323538i
$435$		0			0
$436$	−76388.1	−	195746.i	−0.401840	−	1.02972i
$437$	16879.9			0.0883906
$438$		0			0
$439$			149053.i			0.773414i	0.922203	+	0.386707i	$0.126388\pi$
$439$			149053.i			0.773414i	−0.922203	+	0.386707i	$0.873612\pi$
$440$	−191674.	−	44333.4i	−0.990049	−	0.228995i
$441$		0			0
$442$	−75326.4	−	51463.4i	−0.385569	−	0.263423i
$443$		−	248933.i		−	1.26845i	−0.773147	−	0.634227i	$-0.781318\pi$
$443$		−	248933.i		−	1.26845i	0.773147	−	0.634227i	$-0.218682\pi$
$444$		0			0
$445$	272385.			1.37551
$446$	−109004.	+	159548.i	−0.547990	+	0.802086i
$447$		0			0
$448$	−102317.	+	209349.i	−0.509789	+	1.04307i
$449$	−243749.			−1.20906			−0.604532	−	0.796581i	$-0.706640\pi$
$449$	−243749.			−1.20906			−0.604532	+	0.796581i	$0.706640\pi$
$450$		0			0
$451$			72908.1i			0.358445i
$452$	−84583.1	−	216745.i	−0.414006	−	1.06090i
$453$		0			0
$454$	−43118.1	+	63111.5i	−0.209193	+	0.306194i
$455$		−	321082.i		−	1.55093i
$456$		0			0
$457$	343278.			1.64367			0.821833	−	0.569729i	$-0.192952\pi$
$457$	343278.			1.64367			0.821833	+	0.569729i	$0.192952\pi$
$458$	242353.	+	165577.i	1.15536	+	0.789347i
$459$		0			0
$460$	−194439.	+	75878.4i	−0.918900	+	0.358593i
$461$	155524.			0.731804			0.365902	−	0.930653i	$-0.380761\pi$
$461$	155524.			0.731804			0.365902	+	0.930653i	$0.380761\pi$
$462$		0			0
$463$		−	321457.i		−	1.49955i	−0.661694	−	0.749774i	$-0.730162\pi$
$463$		−	321457.i		−	1.49955i	0.661694	−	0.749774i	$-0.269838\pi$
$464$	3783.45	−	3483.40i	0.0175732	−	0.0161796i
$465$		0			0
$466$	−112433.	−	76814.6i	−0.517750	−	0.353730i
$467$		−	81219.7i		−	0.372415i	−0.982510	−	0.186208i	$-0.940380\pi$
$467$		−	81219.7i		−	0.372415i	0.982510	−	0.186208i	$-0.0596197\pi$
$468$		0			0
$469$	−21607.1			−0.0982313
$470$	54133.5	−	79234.7i	0.245059	−	0.358690i
$471$		0			0
$472$	161059.	+	37252.3i	0.722938	+	0.167213i
$473$	416743.			1.86271
$474$		0			0
$475$			3048.61i			0.0135118i
$476$	78273.7	−	30545.7i	0.345463	−	0.134814i
$477$		0			0
$478$	−79234.5	+	115975.i	−0.346784	+	0.507583i
$479$			346051.i			1.50824i	0.656738	+	0.754119i	$0.271936\pi$
$479$			346051.i			1.50824i	−0.656738	+	0.754119i	$0.728064\pi$
$480$		0			0
$481$	−186749.			−0.807178
$482$	64803.6	+	44274.2i	0.278936	+	0.190571i
$483$		0			0
$484$	−20158.5	−	51656.5i	−0.0860534	−	0.220513i
$485$	−50236.2			−0.213566
$486$		0			0
$487$		−	94439.7i		−	0.398196i	−0.979980	−	0.199098i	$-0.936199\pi$
$487$		−	94439.7i		−	0.398196i	0.979980	−	0.199098i	$-0.0638012\pi$
$488$	−34661.3	+	149857.i	−0.145548	+	0.629270i
$489$		0			0
$490$	63020.8	+	43056.1i	0.262477	+	0.179326i
$491$		−	175728.i		−	0.728915i	−0.931220	−	0.364458i	$-0.881254\pi$
$491$		−	175728.i		−	0.728915i	0.931220	−	0.364458i	$-0.118746\pi$
$492$		0			0
$493$	−1854.45			−0.00762995
$494$	−16479.7	+	24121.1i	−0.0675296	+	0.0988424i
$495$		0			0
$496$	82318.0	+	89408.5i	0.334604	+	0.363426i
$497$	−39964.9			−0.161795
$498$		0			0
$499$			37294.6i			0.149777i	0.997192	+	0.0748885i	$0.0238601\pi$
$499$			37294.6i			0.149777i	−0.997192	+	0.0748885i	$0.976140\pi$
$500$	−96752.9	−	247930.i	−0.387011	−	0.991722i
$501$		0			0
$502$	1265.27	−	1851.96i	0.00502084	−	0.00734894i
$503$			250727.i			0.990979i	0.868614	+	0.495489i	$0.165011\pi$
$503$			250727.i			0.990979i	−0.868614	+	0.495489i	$0.834989\pi$
$504$		0			0
$505$	19985.1			0.0783652
$506$	−253783.	−	173386.i	−0.991202	−	0.677194i
$507$		0			0
$508$	−386936.	+	150999.i	−1.49938	+	0.585121i
$509$	−151144.			−0.583383			−0.291692	−	0.956512i	$-0.594218\pi$
$509$	−151144.			−0.583383			−0.291692	+	0.956512i	$0.594218\pi$
$510$		0			0
$511$		−	558922.i		−	2.14047i
$512$	−165221.	+	203523.i	−0.630267	+	0.776378i
$513$		0			0
$514$	265910.	+	181671.i	1.00649	+	0.687638i
$515$			69377.0i			0.261578i
$516$		0			0
$517$	141311.			0.528682
$518$	97028.2	−	142019.i	0.361608	−	0.529282i
$519$		0			0
$520$	81400.2	−	351930.i	0.301036	−	1.30152i
$521$	179715.			0.662079			0.331039	−	0.943617i	$-0.392601\pi$
$521$	179715.			0.662079			0.331039	+	0.943617i	$0.392601\pi$
$522$		0			0
$523$			305226.i			1.11588i	0.829881	+	0.557941i	$0.188408\pi$
$523$			305226.i			1.11588i	−0.829881	+	0.557941i	$0.811592\pi$
$524$	−245047.	+	95627.5i	−0.892455	+	0.348273i
$525$		0			0
$526$	−78574.3	+	115008.i	−0.283994	+	0.415679i
$527$		−	43823.5i		−	0.157792i
$528$		0			0
$529$	−46243.2			−0.165248
$530$	133422.	+	91154.8i	0.474982	+	0.324510i
$531$		0			0
$532$	−9781.36	−	25064.9i	−0.0345602	−	0.0885609i
$533$	−133866.			−0.471211
$534$		0			0
$535$			435360.i			1.52104i
$536$	−23683.0	−	5477.79i	−0.0824341	−	0.0190667i
$537$		0			0
$538$	−94028.5	−	64240.8i	−0.324859	−	0.221945i
$539$			112394.i			0.386871i
$540$		0			0
$541$	−282083.			−0.963789			−0.481895	−	0.876229i	$-0.660051\pi$
$541$	−282083.			−0.963789			−0.481895	+	0.876229i	$0.660051\pi$
$542$	84964.5	−	124362.i	0.289227	−	0.423338i
$543$		0			0
$544$	93537.9	−	13636.6i	0.316075	−	0.0460795i
$545$	−300008.			−1.01004
$546$		0			0
$547$		−	296270.i		−	0.990176i	−0.868843	−	0.495088i	$-0.835136\pi$
$547$		−	296270.i		−	0.990176i	0.868843	−	0.495088i	$-0.164864\pi$
$548$	183915.	+	471285.i	0.612430	+	1.56936i
$549$		0			0
$550$	31314.6	−	45834.8i	0.103519	−	0.151520i
$551$			593.834i			0.00195597i
$552$		0			0
$553$	213695.			0.698785
$554$	−85608.4	−	58488.1i	−0.278931	−	0.190567i
$555$		0			0
$556$	192216.	−	75010.7i	0.621785	−	0.242646i
$557$	116573.			0.375739			0.187869	−	0.982194i	$-0.439842\pi$
$557$	116573.			0.375739			0.187869	+	0.982194i	$0.439842\pi$
$558$		0			0
$559$			765179.i			2.44872i
$560$	225343.	+	244753.i	0.718569	+	0.780463i
$561$		0			0
$562$	164530.	+	112408.i	0.520921	+	0.355896i
$563$			117383.i			0.370329i	0.982708	+	0.185164i	$0.0592817\pi$
$563$			117383.i			0.370329i	−0.982708	+	0.185164i	$0.940718\pi$
$564$		0			0
$565$	−332193.			−1.04062
$566$	−165634.	+	242437.i	−0.517031	+	0.756773i
$567$		0			0
$568$	−43804.6	−	10131.8i	−0.135776	−	0.0314045i
$569$	222193.			0.686288			0.343144	−	0.939283i	$-0.388508\pi$
$569$	222193.			0.686288			0.343144	+	0.939283i	$0.388508\pi$
$570$		0			0
$571$		−	117091.i		−	0.359131i	−0.983746	−	0.179565i	$-0.942531\pi$
$571$		−	117091.i		−	0.359131i	0.983746	−	0.179565i	$-0.0574691\pi$
$572$	495533.	−	193378.i	1.51454	−	0.591036i
$573$		0			0
$574$	69551.9	−	101802.i	0.211098	−	0.308982i
$575$		−	58892.8i		−	0.178126i
$576$		0			0
$577$	−335932.			−1.00902			−0.504510	−	0.863406i	$-0.668327\pi$
$577$	−335932.			−1.00902			−0.504510	+	0.863406i	$0.668327\pi$
$578$	247707.	+	169235.i	0.741451	+	0.506563i
$579$		0			0
$580$	−2669.40	−	6840.38i	−0.00793521	−	0.0203341i
$581$	−593546.			−1.75834
$582$		0			0
$583$			237952.i			0.700086i
$584$	141697.	−	612622.i	0.415466	−	1.79625i
$585$		0			0
$586$	−431616.	−	294882.i	−1.25690	−	0.858723i
$587$		−	396842.i		−	1.15170i	−0.817554	−	0.575852i	$-0.804670\pi$
$587$		−	396842.i		−	1.15170i	0.817554	−	0.575852i	$-0.195330\pi$
$588$		0			0
$589$	−14033.2			−0.0404507
$590$	133147.	−	194886.i	0.382497	−	0.559857i
$591$		0			0
$592$	142355.	−	131065.i	0.406189	−	0.373977i
$593$	−13679.6			−0.0389012			−0.0194506	−	0.999811i	$-0.506192\pi$
$593$	−13679.6			−0.0389012			−0.0194506	+	0.999811i	$0.506192\pi$
$594$		0			0
$595$		−	119965.i		−	0.338862i
$596$	−183078.	−	469139.i	−0.515399	−	1.32072i
$597$		0			0
$598$	318353.	−	465970.i	0.890239	−	1.30303i
$599$			124021.i			0.345654i	0.984952	+	0.172827i	$0.0552902\pi$
$599$			124021.i			0.345654i	−0.984952	+	0.172827i	$0.944710\pi$
$600$		0			0
$601$	484678.			1.34185			0.670926	−	0.741525i	$-0.265897\pi$
$601$	484678.			1.34185			0.670926	+	0.741525i	$0.265897\pi$
$602$	−581903.	−	397559.i	−1.60567	−	1.09701i
$603$		0			0
$604$	588448.	−	229637.i	1.61300	−	0.629460i
$605$	−79170.9			−0.216299
$606$		0			0
$607$		−	298924.i		−	0.811303i	−0.914028	−	0.405651i	$-0.867045\pi$
$607$		−	298924.i		−	0.811303i	0.914028	−	0.405651i	$-0.132955\pi$
$608$	−4366.72	−	29952.8i	−0.0118127	−	0.0810271i
$609$		0			0
$610$	181331.	+	123886.i	0.487318	+	0.332938i
$611$			259460.i			0.695004i
$612$		0			0
$613$	−155694.			−0.414334			−0.207167	−	0.978306i	$-0.566424\pi$
$613$	−155694.			−0.414334			−0.207167	+	0.978306i	$0.566424\pi$
$614$	−314806.	+	460777.i	−0.835037	+	1.22223i
$615$		0			0
$616$	−110401.	+	477314.i	−0.290945	+	1.25789i
$617$	625050.			1.64189			0.820946	−	0.571007i	$-0.193447\pi$
$617$	625050.			1.64189			0.820946	+	0.571007i	$0.193447\pi$
$618$		0			0
$619$		−	368822.i		−	0.962576i	−0.876563	−	0.481288i	$-0.840169\pi$
$619$		−	368822.i		−	0.962576i	0.876563	−	0.481288i	$-0.159831\pi$
$620$	161649.	−	63082.0i	0.420522	−	0.164105i
$621$		0			0
$622$	−297932.	+	436079.i	−0.770080	+	1.12716i
$623$		−	678307.i		−	1.74763i
$624$		0			0
$625$	−315531.			−0.807758
$626$	−130547.	−	89190.1i	−0.333133	−	0.227598i
$627$		0			0
$628$	15234.2	+	39037.9i	0.0386279	+	0.0989845i
$629$	−69775.0			−0.176359
$630$		0			0
$631$		−	457172.i		−	1.14821i	−0.818782	−	0.574105i	$-0.805350\pi$
$631$		−	457172.i		−	1.14821i	0.818782	−	0.574105i	$-0.194650\pi$
$632$	234226.	+	54175.5i	0.586409	+	0.135634i
$633$		0			0
$634$	−303720.	−	207503.i	−0.755606	−	0.516234i
$635$			593035.i			1.47073i
$636$		0			0
$637$	−206366.			−0.508580
$638$	6099.73	−	8928.11i	0.0149854	−	0.0219340i
$639$		0			0
$640$	184944.	+	325397.i	0.451524	+	0.794427i
$641$	728866.			1.77391			0.886955	−	0.461855i	$-0.152816\pi$
$641$	728866.			1.77391			0.886955	+	0.461855i	$0.152816\pi$
$642$		0			0
$643$			201261.i			0.486786i	0.969928	+	0.243393i	$0.0782604\pi$
$643$			201261.i			0.486786i	−0.969928	+	0.243393i	$0.921740\pi$
$644$	188956.	+	484202.i	0.455605	+	1.16749i
$645$		0			0
$646$	−6157.28	+	9012.34i	−0.0147545	+	0.0215960i
$647$		−	284857.i		−	0.680484i	−0.940338	−	0.340242i	$-0.889491\pi$
$647$		−	284857.i		−	0.680484i	0.940338	−	0.340242i	$-0.110509\pi$
$648$		0			0
$649$	347569.			0.825186
$650$	84157.0	+	57496.5i	0.199188	+	0.136086i
$651$		0			0
$652$	−106172.	+	41432.8i	−0.249756	+	0.0974652i
$653$	−639617.			−1.50001			−0.750005	−	0.661433i	$-0.769949\pi$
$653$	−639617.			−1.50001			−0.750005	+	0.661433i	$0.769949\pi$
$654$		0			0
$655$			375569.i			0.875401i
$656$	102043.	−	93950.5i	0.237124	−	0.218319i
$657$		0			0
$658$	−197314.	−	134806.i	−0.455728	−	0.311356i
$659$			372398.i			0.857505i	0.903422	+	0.428753i	$0.141047\pi$
$659$			372398.i			0.857505i	−0.903422	+	0.428753i	$0.858953\pi$
$660$		0			0
$661$	−137125.			−0.313843			−0.156922	−	0.987611i	$-0.550157\pi$
$661$	−137125.			−0.313843			−0.156922	+	0.987611i	$0.550157\pi$
$662$	−7320.19	+	10714.5i	−0.0167035	+	0.0244487i
$663$		0			0
$664$	−650572.	−	150475.i	−1.47557	−	0.341293i
$665$	−38415.5			−0.0868686
$666$		0			0
$667$		−	11471.7i		−	0.0257854i
$668$	−725450.	+	283101.i	−1.62575	+	0.634437i
$669$		0			0
$670$	−19578.7	+	28657.1i	−0.0436148	+	0.0638385i
$671$			323394.i			0.718269i
$672$		0			0
$673$	840931.			1.85665			0.928325	−	0.371770i	$-0.121249\pi$
$673$	840931.			1.85665			0.928325	+	0.371770i	$0.121249\pi$
$674$	−18466.5	−	12616.4i	−0.0406504	−	0.0277726i
$675$		0			0
$676$	188930.	+	484135.i	0.413435	+	1.05943i
$677$	−207006.			−0.451653			−0.225827	−	0.974168i	$-0.572508\pi$
$677$	−207006.			−0.451653			−0.225827	+	0.974168i	$0.572508\pi$
$678$		0			0
$679$			125100.i			0.271343i
$680$	30413.5	−	131491.i	0.0657731	−	0.284367i
$681$		0			0
$682$	210985.	+	144146.i	0.453609	+	0.309908i
$683$		−	241334.i		−	0.517341i	−0.965966	−	0.258670i	$-0.916716\pi$
$683$		−	241334.i		−	0.517341i	0.965966	−	0.258670i	$-0.0832844\pi$
$684$		0			0
$685$	722311.			1.53937
$686$	−200988.	+	294184.i	−0.427093	+	0.625131i
$687$		0			0
$688$	−537022.	−	583279.i	−1.13453	−	1.23225i
$689$	−436901.			−0.920333
$690$		0			0
$691$			628208.i			1.31567i	0.753161	+	0.657836i	$0.228528\pi$
$691$			628208.i			1.31567i	−0.753161	+	0.657836i	$0.771472\pi$
$692$	160399.	+	411026.i	0.334958	+	0.858335i
$693$		0			0
$694$	−385022.	+	563552.i	−0.799404	+	1.17008i
$695$		−	294598.i		−	0.609903i
$696$		0			0
$697$	−50016.2			−0.102954
$698$	317401.	+	216850.i	0.651475	+	0.445091i
$699$		0			0
$700$	−87449.8	+	34126.6i	−0.178469	+	0.0696461i
$701$	470333.			0.957127			0.478563	−	0.878053i	$-0.341158\pi$
$701$	470333.			0.957127			0.478563	+	0.878053i	$0.341158\pi$
$702$		0			0
$703$			22343.4i			0.0452105i
$704$	−242016.	+	495184.i	−0.488313	+	0.999129i
$705$		0			0
$706$	680089.	+	464640.i	1.36445	+	0.932196i
$707$		−	49767.8i		−	0.0995656i
$708$		0			0
$709$	−666498.			−1.32589			−0.662944	−	0.748669i	$-0.730693\pi$
$709$	−666498.			−1.32589			−0.662944	+	0.748669i	$0.730693\pi$
$710$	−36213.2	+	53004.9i	−0.0718373	+	0.105147i
$711$		0			0
$712$	171963.	−	743476.i	0.339215	−	1.46658i
$713$	271092.			0.533259
$714$		0			0
$715$		−	759474.i		−	1.48560i
$716$	630195.	−	245928.i	1.22927	−	0.479714i
$717$		0			0
$718$	−176987.	+	259054.i	−0.343315	+	0.502506i
$719$		−	551482.i		−	1.06678i	−0.845870	−	0.533388i	$-0.820918\pi$
$719$		−	551482.i		−	1.06678i	0.845870	−	0.533388i	$-0.179082\pi$
$720$		0			0
$721$	172766.			0.332344
$722$	−427535.	−	292094.i	−0.820158	−	0.560336i
$723$		0			0
$724$	−5856.14	−	15006.4i	−0.0111721	−	0.0286286i
$725$	2071.85			0.00394169
$726$		0			0
$727$		−	735388.i		−	1.39139i	−0.718339	−	0.695694i	$-0.755097\pi$
$727$		−	735388.i		−	1.39139i	0.718339	−	0.695694i	$-0.244903\pi$
$728$	−876393.	−	202706.i	−1.65362	−	0.382477i
$729$		0			0
$730$	−741290.	−	506453.i	−1.39105	−	0.950372i
$731$			285893.i			0.535019i
$732$		0			0
$733$	372734.			0.693731			0.346866	−	0.937915i	$-0.387246\pi$
$733$	372734.			0.693731			0.346866	+	0.937915i	$0.387246\pi$
$734$	500452.	−	732506.i	0.928902	−	1.35962i
$735$		0			0
$736$	84356.0	+	578626.i	0.155726	+	1.06817i
$737$	−51108.4			−0.0940931
$738$		0			0
$739$		−	962125.i		−	1.76174i	−0.473356	−	0.880871i	$-0.656957\pi$
$739$		−	962125.i		−	1.76174i	0.473356	−	0.880871i	$-0.343043\pi$
$740$	−100438.	−	257374.i	−0.183415	−	0.470004i
$741$		0			0
$742$	226998.	−	332254.i	0.412301	−	0.603480i
$743$			557423.i			1.00973i	0.863197	+	0.504867i	$0.168459\pi$
$743$			557423.i			1.00973i	−0.863197	+	0.504867i	$0.831541\pi$
$744$		0			0
$745$	−719022.			−1.29548
$746$	85488.3	+	58406.1i	0.153613	+	0.104949i
$747$		0			0
$748$	185145.	−	72251.5i	0.330910	−	0.129135i
$749$	1.08415e6			1.93254
$750$		0			0
$751$			619927.i			1.09916i	0.835441	+	0.549580i	$0.185212\pi$
$751$			619927.i			1.09916i	−0.835441	+	0.549580i	$0.814788\pi$
$752$	−182095.	−	197780.i	−0.322005	−	0.349741i
$753$		0			0
$754$	16392.8	+	11199.7i	0.0288344	+	0.0196998i
$755$		−	901881.i		−	1.58218i
$756$		0			0
$757$	−66502.8			−0.116051			−0.0580254	−	0.998315i	$-0.518480\pi$
$757$	−66502.8			−0.116051			−0.0580254	+	0.998315i	$0.518480\pi$
$758$	333508.	−	488152.i	0.580454	−	0.849604i
$759$		0			0
$760$	−42106.3	−	9739.03i	−0.0728987	−	0.0168612i
$761$	−417057.			−0.720156			−0.360078	−	0.932922i	$-0.617250\pi$
$761$	−417057.			−0.720156			−0.360078	+	0.932922i	$0.617250\pi$
$762$		0			0
$763$			747093.i			1.28329i
$764$	102945.	−	40173.4i	0.176367	−	0.0688260i
$765$		0			0
$766$	510485.	−	747192.i	0.870013	−	1.27343i
$767$			638169.i			1.08479i
$768$		0			0
$769$	−284602.			−0.481266			−0.240633	−	0.970616i	$-0.577355\pi$
$769$	−284602.			−0.481266			−0.240633	+	0.970616i	$0.577355\pi$
$770$	577564.	+	394595.i	0.974134	+	0.665534i
$771$		0			0
$772$	164075.	+	420445.i	0.275301	+	0.705463i
$773$	−690220.			−1.15512			−0.577562	−	0.816347i	$-0.695996\pi$
$773$	−690220.			−1.15512			−0.577562	+	0.816347i	$0.695996\pi$
$774$		0			0
$775$			48960.9i			0.0815167i
$776$	−31715.3	+	137120.i	−0.0526677	+	0.227707i
$777$		0			0
$778$	846893.	+	578602.i	1.39917	+	0.955918i
$779$			16016.2i			0.0263928i
$780$		0			0
$781$	−94531.3			−0.154979
$782$	118946.	−	174100.i	0.194507	−	0.284698i
$783$		0			0
$784$	157308.	−	144833.i	0.255929	−	0.235632i
$785$	59831.1			0.0970929
$786$		0			0
$787$			855688.i			1.38155i	0.723071	+	0.690774i	$0.242730\pi$
$787$			855688.i			1.38155i	−0.723071	+	0.690774i	$0.757270\pi$
$788$	−223672.	−	573161.i	−0.360212	−	0.923048i
$789$		0			0
$790$	193634.	−	283420.i	0.310261	−	0.454126i
$791$			827242.i			1.32215i
$792$		0			0
$793$	−593782.			−0.944236
$794$	187161.	+	127869.i	0.296875	+	0.202827i
$795$		0			0
$796$	−81831.3	+	31934.0i	−0.129150	+	0.0503996i
$797$	−579975.			−0.913046			−0.456523	−	0.889712i	$-0.650905\pi$
$797$	−579975.			−0.913046			−0.456523	+	0.889712i	$0.650905\pi$
$798$		0			0
$799$			96941.7i			0.151851i
$800$	−104503.	+	15235.2i	−0.163287	+	0.0238050i
$801$		0			0
$802$	36040.0	+	24622.7i	0.0560320	+	0.0382814i
$803$		−	1.32205e6i		−	2.05030i
$804$		0			0
$805$	742108.			1.14518
$806$	−264665.	+	387387.i	−0.407405	+	0.596314i
$807$		0			0
$808$	12617.1	−	54549.3i	0.0193257	−	0.0835539i
$809$	60860.6			0.0929907			0.0464953	−	0.998919i	$-0.485195\pi$
$809$	60860.6			0.0929907			0.0464953	+	0.998919i	$0.485195\pi$
$810$		0			0
$811$			103330.i			0.157103i	0.996910	+	0.0785515i	$0.0250295\pi$
$811$			103330.i			0.157103i	−0.996910	+	0.0785515i	$0.974970\pi$
$812$	−17034.2	+	6647.47i	−0.0258351	+	0.0100819i
$813$		0			0
$814$	229506.	−	335926.i	0.346375	−	0.506985i
$815$			162724.i			0.244983i
$816$		0			0
$817$	91549.0			0.137154
$818$	956404.	+	653421.i	1.42934	+	0.976531i
$819$		0			0
$820$	−71996.2	−	184491.i	−0.107073	−	0.274377i
$821$	−533333.			−0.791247			−0.395623	−	0.918413i	$-0.629471\pi$
$821$	−533333.			−0.791247			−0.395623	+	0.918413i	$0.629471\pi$
$822$		0			0
$823$		−	728807.i		−	1.07600i	−0.842945	−	0.538000i	$-0.819180\pi$
$823$		−	728807.i		−	1.07600i	0.842945	−	0.538000i	$-0.180820\pi$
$824$	189365.	+	43799.3i	0.278897	+	0.0645079i
$825$		0			0
$826$	−485314.	−	331569.i	−0.711317	−	0.485975i
$827$			768434.i			1.12356i	0.827287	+	0.561779i	$0.189883\pi$
$827$			768434.i			1.12356i	−0.827287	+	0.561779i	$0.810117\pi$
$828$		0			0
$829$	−401672.			−0.584471			−0.292235	−	0.956346i	$-0.594399\pi$
$829$	−401672.			−0.584471			−0.292235	+	0.956346i	$0.594399\pi$
$830$	−537827.	+	787211.i	−0.780704	+	1.14271i
$831$		0			0
$832$	−909205.	−	444364.i	−1.31345	−	0.641936i
$833$	−77104.4			−0.111119
$834$		0			0
$835$			1.11185e6i			1.59469i
$836$	−23136.4	−	59287.4i	−0.0331043	−	0.0848301i
$837$		0			0
$838$	157587.	−	230659.i	0.224405	−	0.328460i
$839$		−	429703.i		−	0.610443i	−0.952281	−	0.305221i	$-0.901270\pi$
$839$		−	429703.i		−	0.610443i	0.952281	−	0.305221i	$-0.0987305\pi$
$840$		0			0
$841$	−706877.			−0.999429
$842$	−53528.1	−	36570.7i	−0.0755019	−	0.0515833i
$843$		0			0
$844$	−692669.	+	270308.i	−0.972391	+	0.379468i
$845$	742006.			1.03919
$846$		0			0
$847$			197155.i			0.274815i
$848$	333040.	−	306628.i	0.463132	−	0.426403i
$849$		0			0
$850$	31443.5	+	21482.4i	0.0435204	+	0.0297334i
$851$		−	431629.i		−	0.596007i
$852$		0			0
$853$	−732176.			−1.00628			−0.503138	−	0.864206i	$-0.667821\pi$
$853$	−732176.			−1.00628			−0.503138	+	0.864206i	$0.667821\pi$
$854$	308507.	−	451559.i	0.423009	−	0.619154i
$855$		0			0
$856$	1.18832e6	+	274853.i	1.62175	+	0.375105i
$857$	−430159.			−0.585689			−0.292844	−	0.956160i	$-0.594602\pi$
$857$	−430159.			−0.585689			−0.292844	+	0.956160i	$0.594602\pi$
$858$		0			0
$859$		−	489975.i		−	0.664030i	−0.943274	−	0.332015i	$-0.892272\pi$
$859$		−	489975.i		−	0.664030i	0.943274	−	0.332015i	$-0.107728\pi$
$860$	−1.05455e6	+	411531.i	−1.42584	+	0.556424i
$861$		0			0
$862$	−237525.	+	347662.i	−0.319665	+	0.467890i
$863$			999093.i			1.34148i	0.741692	+	0.670740i	$0.234023\pi$
$863$			999093.i			1.34148i	−0.741692	+	0.670740i	$0.765977\pi$
$864$		0			0
$865$	629955.			0.841933
$866$	−435303.	−	297401.i	−0.580438	−	0.396559i
$867$		0			0
$868$	−157090.	−	402544.i	−0.208501	−	0.534287i
$869$	505464.			0.669347
$870$		0			0
$871$		−	93839.8i		−	0.123695i
$872$	−189402.	+	818872.i	−0.249087	+	1.07692i
$873$		0			0
$874$	−55750.4	−	38089.0i	−0.0729836	−	0.0498628i
$875$			946265.i			1.23594i
$876$		0			0
$877$	634599.			0.825087			0.412544	−	0.910938i	$-0.364640\pi$
$877$	634599.			0.825087			0.412544	+	0.910938i	$0.364640\pi$
$878$	336334.	−	492289.i	0.436297	−	0.638603i
$879$		0			0
$880$	533018.	+	578930.i	0.688298	+	0.747585i
$881$	−312649.			−0.402815			−0.201407	−	0.979508i	$-0.564552\pi$
$881$	−312649.			−0.402815			−0.201407	+	0.979508i	$0.564552\pi$
$882$		0			0
$883$		−	209047.i		−	0.268116i	−0.990973	−	0.134058i	$-0.957199\pi$
$883$		−	209047.i		−	0.268116i	0.990973	−	0.134058i	$-0.0428008\pi$
$884$	132660.	+	339944.i	0.169761	+	0.435014i
$885$		0			0
$886$	−561710.	+	822169.i	−0.715558	+	1.04735i
$887$		−	178008.i		−	0.226252i	−0.993581	−	0.113126i	$-0.963914\pi$
$887$		−	178008.i		−	0.226252i	0.993581	−	0.113126i	$-0.0360864\pi$
$888$		0			0
$889$	1.47680e6			1.86861
$890$	−899628.	−	614631.i	−1.13575	−	0.775951i
$891$		0			0
$892$	720031.	−	280986.i	0.904943	−	0.353147i
$893$	31042.8			0.0389276
$894$		0			0
$895$		−	965863.i		−	1.20578i
$896$	810319.	−	460556.i	1.00935	−	0.573676i
$897$		0			0
$898$	805047.	+	550012.i	0.998317	+	0.682055i
$899$			9537.04i			0.0118003i
$900$		0			0
$901$	−163239.			−0.201082
$902$	164515.	−	240799.i	0.202205	−	0.295966i
$903$		0			0
$904$	−209721.	+	906720.i	−0.256629	+	1.10952i
$905$	−22999.5			−0.0280815
$906$		0			0
$907$		−	62871.2i		−	0.0764253i	−0.999270	−	0.0382126i	$-0.987834\pi$
$907$		−	62871.2i		−	0.0764253i	0.999270	−	0.0382126i	$-0.0121664\pi$
$908$	284819.	−	111148.i	0.345459	−	0.134813i
$909$		0			0
$910$	−724513.	+	1.06046e6i	−0.874910	+	1.28060i
$911$		−	1.45791e6i		−	1.75669i	−0.478027	−	0.878345i	$-0.658648\pi$
$911$		−	1.45791e6i		−	1.75669i	0.478027	−	0.878345i	$-0.341352\pi$
$912$		0			0
$913$	−1.40395e6			−1.68426
$914$	−1.13377e6	−	774598.i	−1.35716	−	0.927222i
$915$		0			0
$916$	−426817.	−	1.09372e6i	−0.508687	−	1.30352i
$917$	935258.			1.11223
$918$		0			0
$919$		−	315989.i		−	0.374146i	−0.982346	−	0.187073i	$-0.940100\pi$
$919$		−	315989.i		−	0.374146i	0.982346	−	0.187073i	$-0.0599001\pi$
$920$	813407.	+	188138.i	0.961020	+	0.222280i
$921$		0			0
$922$	−513660.	−	350935.i	−0.604246	−	0.412824i
$923$		−	173568.i		−	0.203736i
$924$		0			0
$925$	77954.8			0.0911086
$926$	−725358.	+	1.06170e6i	−0.845923	+	1.23817i
$927$		0			0
$928$	−20356.1	+	2967.65i	−0.0236373	+	0.00344601i
$929$	−122547.			−0.141994			−0.0709971	−	0.997477i	$-0.522618\pi$
$929$	−122547.			−0.141994			−0.0709971	+	0.997477i	$0.522618\pi$
$930$		0			0
$931$			24690.4i			0.0284859i
$932$	198010.	+	507403.i	0.227958	+	0.584145i
$933$		0			0
$934$	−183270.	+	268250.i	−0.210086	+	0.307501i
$935$		−	283761.i		−	0.324586i
$936$		0			0
$937$	495399.			0.564256			0.282128	−	0.959377i	$-0.408960\pi$
$937$	495399.			0.564256			0.282128	+	0.959377i	$0.408960\pi$
$938$	71363.3	+	48755.7i	0.0811090	+	0.0554141i
$939$		0			0
$940$	−357582.	+	139543.i	−0.404687	+	0.157926i
$941$	1.14226e6			1.28999			0.644994	−	0.764188i	$-0.276860\pi$
$941$	1.14226e6			1.28999			0.644994	+	0.764188i	$0.276860\pi$
$942$		0			0
$943$		−	309401.i		−	0.347935i
$944$	−447883.	−	486461.i	−0.502598	−	0.545889i
$945$		0			0
$946$	−1.37641e6	−	940370.i	−1.53803	−	1.05079i
$947$			527337.i			0.588015i	0.955803	+	0.294007i	$0.0949890\pi$
$947$			527337.i			0.588015i	−0.955803	+	0.294007i	$0.905011\pi$
$948$		0			0
$949$	2.42741e6			2.69532
$950$	6879.10	−	10068.9i	0.00762227	−	0.0111566i
$951$		0			0
$952$	−327446.	−	75737.0i	−0.361298	−	0.0835669i
$953$	259379.			0.285594			0.142797	−	0.989752i	$-0.454390\pi$
$953$	259379.			0.285594			0.142797	+	0.989752i	$0.454390\pi$
$954$		0			0
$955$		−	157778.i		−	0.172997i
$956$	523387.	−	204248.i	0.572674	−	0.223481i
$957$		0			0
$958$	780856.	−	1.14293e6i	0.850824	−	1.24534i
$959$		−	1.79873e6i		−	1.95582i
$960$		0			0
$961$	698146.			0.755962
$962$	616791.	+	421395.i	0.666482	+	0.455344i
$963$		0			0
$964$	−114128.	−	292455.i	−0.122812	−	0.314706i
$965$	644391.			0.691982
$966$		0			0
$967$			1.03870e6i			1.11081i	0.831581	+	0.555403i	$0.187436\pi$
$967$			1.03870e6i			1.11081i	−0.831581	+	0.555403i	$0.812564\pi$
$968$	−49982.4	+	216097.i	−0.0533417	+	0.230621i
$969$		0			0
$970$	165919.	+	113357.i	0.176341	+	0.120477i
$971$		−	1.15698e6i		−	1.22713i	−0.789646	−	0.613563i	$-0.789736\pi$
$971$		−	1.15698e6i		−	1.22713i	0.789646	−	0.613563i	$-0.210264\pi$
$972$		0			0
$973$	−733622.			−0.774902
$974$	−213101.	+	311913.i	−0.224630	+	0.328788i
$975$		0			0
$976$	452626.	−	416731.i	0.475160	−	0.437478i
$977$	−1.09732e6			−1.14960			−0.574799	−	0.818295i	$-0.694920\pi$
$977$	−1.09732e6			−1.14960			−0.574799	+	0.818295i	$0.694920\pi$
$978$		0			0
$979$		−	1.60444e6i		−	1.67401i
$980$	−110988.	−	284409.i	−0.115565	−	0.296136i
$981$		0			0
$982$	−396525.	+	580389.i	−0.411195	+	0.601861i
$983$			1.71299e6i			1.77276i	0.462963	+	0.886378i	$0.346786\pi$
$983$			1.71299e6i			1.77276i	−0.462963	+	0.886378i	$0.653214\pi$
$984$		0			0
$985$	−878451.			−0.905409
$986$	6124.84	+	4184.52i	0.00630000	+	0.00430419i
$987$		0			0
$988$	108857.	−	42480.6i	0.111518	−	0.0435188i
$989$	−1.76854e6			−1.80810
$990$		0			0
$991$			1.03974e6i			1.05872i	0.848399	+	0.529358i	$0.177567\pi$
$991$			1.03974e6i			1.05872i	−0.848399	+	0.529358i	$0.822433\pi$
$992$	−70130.0	−	481045.i	−0.0712657	−	0.488835i
$993$		0			0
$994$	131995.	+	90179.7i	0.133593	+	0.0912717i
$995$			125418.i			0.126682i
$996$		0			0
$997$	−1.11868e6			−1.12542			−0.562709	−	0.826655i	$-0.690241\pi$
$997$	−1.11868e6			−1.12542			−0.562709	+	0.826655i	$0.690241\pi$
$998$	84154.4	−	123176.i	0.0844920	−	0.123670i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.d.b.19.1		4
3.2	odd	2		12.5.d.a.7.4	yes	4
4.3	odd	2	inner	36.5.d.b.19.2		4
8.3	odd	2		576.5.g.m.127.2		4
8.5	even	2		576.5.g.m.127.1		4
12.11	even	2		12.5.d.a.7.3	✓	4
15.2	even	4		300.5.f.a.199.4		8
15.8	even	4		300.5.f.a.199.5		8
15.14	odd	2		300.5.c.a.151.1		4
24.5	odd	2		192.5.g.d.127.4		4
24.11	even	2		192.5.g.d.127.2		4
48.5	odd	4		768.5.b.g.127.2		8
48.11	even	4		768.5.b.g.127.6		8
48.29	odd	4		768.5.b.g.127.7		8
48.35	even	4		768.5.b.g.127.3		8
60.23	odd	4		300.5.f.a.199.3		8
60.47	odd	4		300.5.f.a.199.6		8
60.59	even	2		300.5.c.a.151.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.3	✓	4	12.11	even	2
12.5.d.a.7.4	yes	4	3.2	odd	2
36.5.d.b.19.1		4	1.1	even	1	trivial
36.5.d.b.19.2		4	4.3	odd	2	inner
192.5.g.d.127.2		4	24.11	even	2
192.5.g.d.127.4		4	24.5	odd	2
300.5.c.a.151.1		4	15.14	odd	2
300.5.c.a.151.2		4	60.59	even	2
300.5.f.a.199.3		8	60.23	odd	4
300.5.f.a.199.4		8	15.2	even	4
300.5.f.a.199.5		8	15.8	even	4
300.5.f.a.199.6		8	60.47	odd	4
576.5.g.m.127.1		4	8.5	even	2
576.5.g.m.127.2		4	8.3	odd	2
768.5.b.g.127.2		8	48.5	odd	4
768.5.b.g.127.3		8	48.35	even	4
768.5.b.g.127.6		8	48.11	even	4
768.5.b.g.127.7		8	48.29	odd	4

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.30278 - 2.25647i) q^{2} +(5.81665 + 14.9053i) q^{4} +22.8444 q^{5} -56.8882i q^{7} +(14.4222 - 62.3538i) q^{8} +O(q^{10})\)	\(q+(-3.30278 - 2.25647i) q^{2} +(5.81665 + 14.9053i) q^{4} +22.8444 q^{5} -56.8882i q^{7} +(14.4222 - 62.3538i) q^{8} +(-75.4500 - 51.5478i) q^{10} -134.561i q^{11} +247.066 q^{13} +(-128.367 + 187.889i) q^{14} +(-188.333 + 173.397i) q^{16} +92.3112 q^{17} -29.5600i q^{19} +(132.878 + 340.502i) q^{20} +(-303.633 + 444.425i) q^{22} +571.038i q^{23} -103.133 q^{25} +(-816.005 - 557.499i) q^{26} +(847.933 - 330.899i) q^{28} -20.0891 q^{29} -474.736i q^{31} +(1013.29 - 147.724i) q^{32} +(-304.883 - 208.298i) q^{34} -1299.58i q^{35} -755.867 q^{37} +(-66.7013 + 97.6300i) q^{38} +(329.467 - 1424.44i) q^{40} -541.822 q^{41} +3097.06i q^{43} +(2005.67 - 782.695i) q^{44} +(1288.53 - 1886.01i) q^{46} +1050.16i q^{47} -835.266 q^{49} +(340.625 + 232.717i) q^{50} +(1437.10 + 3682.59i) q^{52} -1768.35 q^{53} -3073.97i q^{55} +(-3547.20 - 820.453i) q^{56} +(66.3499 + 45.3306i) q^{58} +2582.98i q^{59} -2403.33 q^{61} +(-1071.23 + 1567.95i) q^{62} +(-3680.00 - 1798.56i) q^{64} +5644.09 q^{65} -379.816i q^{67} +(536.942 + 1375.92i) q^{68} +(-2932.46 + 4292.21i) q^{70} -702.517i q^{71} +9824.92 q^{73} +(2496.46 + 1705.59i) q^{74} +(440.599 - 171.940i) q^{76} -7654.93 q^{77} +3756.40i q^{79} +(-4302.36 + 3961.16i) q^{80} +(1789.52 + 1222.61i) q^{82} -10433.6i q^{83} +2108.79 q^{85} +(6988.43 - 10228.9i) q^{86} +(-8390.39 - 1940.67i) q^{88} +11923.5 q^{89} -14055.2i q^{91} +(-8511.46 + 3321.53i) q^{92} +(2369.66 - 3468.45i) q^{94} -675.280i q^{95} -2199.06 q^{97} +(2758.70 + 1884.76i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5}+O(q^{10}) \) 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5	\( 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5} - 172 q^{10} + 296 q^{13} - 600 q^{14} + 112 q^{16} + 600 q^{17} + 1368 q^{20} - 1128 q^{22} + 972 q^{25} - 1692 q^{26} + 1488 q^{28} - 888 q^{29} + 2784 q^{32} - 484 q^{34} - 4408 q^{37} - 4680 q^{38} + 1664 q^{40} - 552 q^{41} + 3696 q^{44} - 384 q^{46} - 572 q^{49} + 1038 q^{50} + 6008 q^{52} - 5112 q^{53} - 1728 q^{56} - 124 q^{58} + 4232 q^{61} + 7224 q^{62} - 14720 q^{64} + 18192 q^{65} - 5496 q^{68} + 6096 q^{70} + 8840 q^{73} + 4116 q^{74} - 1872 q^{76} - 20928 q^{77} - 25632 q^{80} + 3740 q^{82} - 10256 q^{85} + 19560 q^{86} - 8640 q^{88} + 25080 q^{89} - 18816 q^{92} - 5232 q^{94} + 23048 q^{97} + 5850 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5 - 172 * q^10 + 296 * q^13 - 600 * q^14 + 112 * q^16 + 600 * q^17 + 1368 * q^20 - 1128 * q^22 + 972 * q^25 - 1692 * q^26 + 1488 * q^28 - 888 * q^29 + 2784 * q^32 - 484 * q^34 - 4408 * q^37 - 4680 * q^38 + 1664 * q^40 - 552 * q^41 + 3696 * q^44 - 384 * q^46 - 572 * q^49 + 1038 * q^50 + 6008 * q^52 - 5112 * q^53 - 1728 * q^56 - 124 * q^58 + 4232 * q^61 + 7224 * q^62 - 14720 * q^64 + 18192 * q^65 - 5496 * q^68 + 6096 * q^70 + 8840 * q^73 + 4116 * q^74 - 1872 * q^76 - 20928 * q^77 - 25632 * q^80 + 3740 * q^82 - 10256 * q^85 + 19560 * q^86 - 8640 * q^88 + 25080 * q^89 - 18816 * q^92 - 5232 * q^94 + 23048 * q^97 + 5850 * q^98

Introduction

L-functions

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Database

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