LMFDB - Embedded newform 36.4.h.b.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,4,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (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:	$2.12406876021$
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			23.5
Character	$\chi$	$=$	36.23
Dual form			36.4.h.b.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38284 - 2.46734i) q^{2} +(-1.42987 + 4.99554i) q^{3} +(-4.17551 + 6.82387i) q^{4} +(14.6499 + 8.45813i) q^{5} +(14.3030 - 3.38006i) q^{6} +(-3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +(-22.9109 - 14.2860i) q^{9} +O(q^{10})$	\(q+(-1.38284 - 2.46734i) q^{2} +(-1.42987 + 4.99554i) q^{3} +(-4.17551 + 6.82387i) q^{4} +(14.6499 + 8.45813i) q^{5} +(14.3030 - 3.38006i) q^{6} +(-3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +(-22.9109 - 14.2860i) q^{9} +(0.610574 - 47.8425i) q^{10} +(25.0688 + 43.4205i) q^{11} +(-28.1185 - 30.6162i) q^{12} +(-18.9966 + 32.9032i) q^{13} +(8.67378 + 5.15650i) q^{14} +(-63.2005 + 61.0903i) q^{15} +(-29.1303 - 56.9862i) q^{16} -84.3819i q^{17} +(-3.56618 + 76.2842i) q^{18} -62.9237i q^{19} +(-118.888 + 64.6521i) q^{20} +(-4.49331 - 17.9852i) q^{21} +(72.4668 - 121.897i) q^{22} +(37.6066 - 65.1366i) q^{23} +(-36.6571 + 111.715i) q^{24} +(80.5801 + 139.569i) q^{25} +(107.453 + 1.37133i) q^{26} +(104.126 - 94.0254i) q^{27} +(0.728372 - 28.5317i) q^{28} +(105.644 - 60.9938i) q^{29} +(238.126 + 71.4589i) q^{30} +(-17.2800 - 9.97659i) q^{31} +(-100.322 + 150.677i) q^{32} +(-252.754 + 63.1467i) q^{33} +(-208.199 + 116.687i) q^{34} -60.3510 q^{35} +(193.150 - 96.6899i) q^{36} +17.7622 q^{37} +(-155.254 + 87.0135i) q^{38} +(-137.206 - 141.946i) q^{39} +(323.922 + 203.933i) q^{40} +(299.072 + 172.670i) q^{41} +(-38.1619 + 35.9571i) q^{42} +(113.206 - 65.3596i) q^{43} +(-400.970 - 10.2362i) q^{44} +(-214.811 - 403.072i) q^{45} +(-212.718 - 2.71474i) q^{46} +(-153.083 - 265.147i) q^{47} +(326.330 - 64.0387i) q^{48} +(-165.136 + 286.024i) q^{49} +(232.934 - 391.820i) q^{50} +(421.534 + 120.655i) q^{51} +(-145.206 - 267.018i) q^{52} -479.464i q^{53} +(-375.982 - 126.892i) q^{54} +848.142i q^{55} +(-71.4047 + 37.6577i) q^{56} +(314.338 + 89.9729i) q^{57} +(-296.581 - 176.316i) q^{58} +(-245.774 + 425.693i) q^{59} +(-152.978 - 686.355i) q^{60} +(-49.9168 - 86.4585i) q^{61} +(-0.720188 + 56.4315i) q^{62} +(96.2705 + 3.26994i) q^{63} +(510.500 + 39.1649i) q^{64} +(-556.599 + 321.352i) q^{65} +(505.323 + 536.308i) q^{66} +(-536.669 - 309.846i) q^{67} +(575.811 + 352.337i) q^{68} +(271.620 + 281.003i) q^{69} +(83.4558 + 148.906i) q^{70} +254.455 q^{71} +(-505.663 - 342.860i) q^{72} +100.485 q^{73} +(-24.5622 - 43.8253i) q^{74} +(-812.441 + 202.976i) q^{75} +(429.383 + 262.738i) q^{76} +(-154.908 - 89.4363i) q^{77} +(-160.494 + 534.823i) q^{78} +(856.295 - 494.382i) q^{79} +(55.2404 - 1081.23i) q^{80} +(320.821 + 654.610i) q^{81} +(12.4646 - 976.687i) q^{82} +(251.755 + 436.053i) q^{83} +(141.490 + 44.4354i) q^{84} +(713.714 - 1236.19i) q^{85} +(-317.810 - 188.936i) q^{86} +(153.639 + 614.964i) q^{87} +(529.222 + 1003.48i) q^{88} +1019.86i q^{89} +(-697.466 + 1087.39i) q^{90} -135.546i q^{91} +(287.457 + 528.601i) q^{92} +(74.5466 - 72.0576i) q^{93} +(-442.518 + 744.363i) q^{94} +(532.217 - 921.828i) q^{95} +(-609.267 - 716.610i) q^{96} +(-503.589 - 872.242i) q^{97} +(934.074 + 11.9208i) q^{98} +(45.9541 - 1352.94i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38284	−	2.46734i	−0.488908	−	0.872335i
$2$	−1.38284	−	2.46734i	−0.488908	−	0.872335i
$3$	−1.42987	+	4.99554i	−0.275179	+	0.961393i
$3$	−1.42987	+	4.99554i	−0.275179	+	0.961393i
$4$	−4.17551	+	6.82387i	−0.521938	+	0.852983i
$5$	14.6499	+	8.45813i	1.31033	+	0.756519i	0.982150	−	0.188097i	$-0.0602320\pi$
$5$	14.6499	+	8.45813i	1.31033	+	0.756519i	0.328178	+	0.944616i	$0.393565\pi$
$6$	14.3030	−	3.38006i	0.973194	−	0.229984i
$7$	−3.08966	+	1.78382i	−0.166826	+	0.0963170i	−0.581088	−	0.813841i	$-0.697373\pi$
$7$	−3.08966	+	1.78382i	−0.166826	+	0.0963170i	0.414262	+	0.910157i	$0.364040\pi$
$8$	22.6108	+	0.866066i	0.999267	+	0.0382750i
$9$	−22.9109	−	14.2860i	−0.848553	−	0.529110i
$10$	0.610574	−	47.8425i	0.0193080	−	1.51291i
$11$	25.0688	+	43.4205i	0.687139	+	1.19016i	0.972759	+	0.231817i	$0.0744672\pi$
$11$	25.0688	+	43.4205i	0.687139	+	1.19016i	−0.285620	+	0.958343i	$0.592199\pi$
$12$	−28.1185	−	30.6162i	−0.676426	−	0.736511i
$13$	−18.9966	+	32.9032i	−0.405286	+	0.701977i	−0.994355	−	0.106107i	$-0.966162\pi$
$13$	−18.9966	+	32.9032i	−0.405286	+	0.701977i	0.589068	+	0.808083i	$0.299495\pi$
$14$	8.67378	+	5.15650i	0.165583	+	0.0984380i
$15$	−63.2005	+	61.0903i	−1.08789	+	1.05156i
$16$	−29.1303	−	56.9862i	−0.455161	−	0.890409i
$17$		−	84.3819i		−	1.20386i	−0.798549	−	0.601930i	$-0.794399\pi$
$17$		−	84.3819i		−	1.20386i	0.798549	−	0.601930i	$-0.205601\pi$
$18$	−3.56618	+	76.2842i	−0.0466976	+	0.998909i
$19$		−	62.9237i		−	0.759773i	−0.925033	−	0.379887i	$-0.875963\pi$
$19$		−	62.9237i		−	0.759773i	0.925033	−	0.379887i	$-0.124037\pi$
$20$	−118.888	+	64.6521i	−1.32921	+	0.722832i
$21$	−4.49331	−	17.9852i	−0.0466915	−	0.186890i
$22$	72.4668	−	121.897i	0.702271	−	1.18129i
$23$	37.6066	−	65.1366i	0.340936	−	0.590518i	−0.643671	−	0.765302i	$-0.722589\pi$
$23$	37.6066	−	65.1366i	0.340936	−	0.590518i	0.984607	+	0.174784i	$0.0559227\pi$
$24$	−36.6571	+	111.715i	−0.311775	+	0.950156i
$25$	80.5801	+	139.569i	0.644641	+	1.11655i
$26$	107.453	+	1.37133i	0.810507	+	0.0103438i
$27$	104.126	−	94.0254i	0.742187	−	0.670193i
$28$	0.728372	−	28.5317i	0.00491605	−	0.192571i
$29$	105.644	−	60.9938i	0.676471	−	0.390561i	−0.122053	−	0.992524i	$-0.538948\pi$
$29$	105.644	−	60.9938i	0.676471	−	0.390561i	0.798524	+	0.601963i	$0.205614\pi$
$30$	238.126	+	71.4589i	1.44919	+	0.434885i
$31$	−17.2800	−	9.97659i	−0.100115	−	0.0578016i	0.449106	−	0.893478i	$-0.351742\pi$
$31$	−17.2800	−	9.97659i	−0.100115	−	0.0578016i	−0.549222	+	0.835677i	$0.685076\pi$
$32$	−100.322	+	150.677i	−0.554204	+	0.832381i
$33$	−252.754	+	63.1467i	−1.33330	+	0.333104i
$34$	−208.199	+	116.687i	−1.05017	+	0.588577i
$35$	−60.3510			−0.291462
$36$	193.150	−	96.6899i	0.894215	−	0.447638i
$37$	17.7622			0.0789211			0.0394606	−	0.999221i	$-0.487436\pi$
$37$	17.7622			0.0789211			0.0394606	+	0.999221i	$0.487436\pi$
$38$	−155.254	+	87.0135i	−0.662777	+	0.371459i
$39$	−137.206	−	141.946i	−0.563349	−	0.582809i
$40$	323.922	+	203.933i	1.28041	+	0.806117i
$41$	299.072	+	172.670i	1.13920	+	0.657718i	0.946233	−	0.323486i	$-0.104855\pi$
$41$	299.072	+	172.670i	1.13920	+	0.657718i	0.192969	+	0.981205i	$0.438188\pi$
$42$	−38.1619	+	35.9571i	−0.140203	+	0.132102i
$43$	113.206	−	65.3596i	0.401483	−	0.231796i	−0.285641	−	0.958337i	$-0.592206\pi$
$43$	113.206	−	65.3596i	0.401483	−	0.231796i	0.687124	+	0.726540i	$0.258873\pi$
$44$	−400.970	−	10.2362i	−1.37383	−	0.0350718i
$45$	−214.811	−	403.072i	−0.711601	−	1.33525i
$46$	−212.718	−	2.71474i	−0.681816	−	0.00870145i
$47$	−153.083	−	265.147i	−0.475094	−	0.822887i	0.524499	−	0.851411i	$-0.324253\pi$
$47$	−153.083	−	265.147i	−0.475094	−	0.822887i	−0.999593	+	0.0285243i	$0.990919\pi$
$48$	326.330	−	64.0387i	0.981284	−	0.192567i
$49$	−165.136	+	286.024i	−0.481446	+	0.833889i
$50$	232.934	−	391.820i	0.658837	−	1.10823i
$51$	421.534	+	120.655i	1.15738	+	0.331277i
$52$	−145.206	−	267.018i	−0.387240	−	0.712091i
$53$		−	479.464i		−	1.24263i	−0.783561	−	0.621315i	$-0.786599\pi$
$53$		−	479.464i		−	1.24263i	0.783561	−	0.621315i	$-0.213401\pi$
$54$	−375.982	−	126.892i	−0.947494	−	0.319774i
$55$			848.142i			2.07933i
$56$	−71.4047	+	37.6577i	−0.170390	+	0.0898611i
$57$	314.338	+	89.9729i	0.730441	+	0.209074i
$58$	−296.581	−	176.316i	−0.671432	−	0.399161i
$59$	−245.774	+	425.693i	−0.542323	+	0.939330i	0.456447	+	0.889750i	$0.349122\pi$
$59$	−245.774	+	425.693i	−0.542323	+	0.939330i	−0.998770	+	0.0495801i	$0.984212\pi$
$60$	−152.978	−	686.355i	−0.329156	−	1.47680i
$61$	−49.9168	−	86.4585i	−0.104774	−	0.181473i	0.808872	−	0.587985i	$-0.200079\pi$
$61$	−49.9168	−	86.4585i	−0.104774	−	0.181473i	−0.913646	+	0.406511i	$0.866745\pi$
$62$	−0.720188	+	56.4315i	−0.00147523	+	0.115594i
$63$	96.2705	+	3.26994i	0.192523	+	0.00653927i
$64$	510.500	+	39.1649i	0.997070	+	0.0764940i
$65$	−556.599	+	321.352i	−1.06212	+	0.613213i
$66$	505.323	+	536.308i	0.942438	+	1.00023i
$67$	−536.669	−	309.846i	−0.978575	−	0.564980i	−0.0767351	−	0.997052i	$-0.524450\pi$
$67$	−536.669	−	309.846i	−0.978575	−	0.564980i	−0.901839	+	0.432071i	$0.857783\pi$
$68$	575.811	+	352.337i	1.02687	+	0.628341i
$69$	271.620	+	281.003i	0.473902	+	0.490272i
$70$	83.4558	+	148.906i	0.142498	+	0.254253i
$71$	254.455			0.425327			0.212663	−	0.977125i	$-0.431786\pi$
$71$	254.455			0.425327			0.212663	+	0.977125i	$0.431786\pi$
$72$	−505.663	−	342.860i	−0.827679	−	0.561201i
$73$	100.485			0.161108			0.0805541	−	0.996750i	$-0.474331\pi$
$73$	100.485			0.161108			0.0805541	+	0.996750i	$0.474331\pi$
$74$	−24.5622	−	43.8253i	−0.0385852	−	0.0688457i
$75$	−812.441	+	202.976i	−1.25084	+	0.312502i
$76$	429.383	+	262.738i	0.648074	+	0.396555i
$77$	−154.908	−	89.4363i	−0.229265	−	0.132366i
$78$	−160.494	+	534.823i	−0.232979	+	0.776369i
$79$	856.295	−	494.382i	1.21950	−	0.704080i	0.254691	−	0.967022i	$-0.418026\pi$
$79$	856.295	−	494.382i	1.21950	−	0.704080i	0.964812	+	0.262942i	$0.0846928\pi$
$80$	55.2404	−	1081.23i	0.0772008	−	1.51107i
$81$	320.821	+	654.610i	0.440084	+	0.897956i
$82$	12.4646	−	976.687i	0.0167864	−	1.31533i
$83$	251.755	+	436.053i	0.332936	+	0.576663i	0.983086	−	0.183143i	$-0.0586272\pi$
$83$	251.755	+	436.053i	0.332936	+	0.576663i	−0.650150	+	0.759806i	$0.725294\pi$
$84$	141.490	+	44.4354i	0.183784	+	0.0577178i
$85$	713.714	−	1236.19i	0.910743	−	1.57745i
$86$	−317.810	−	188.936i	−0.398492	−	0.236901i
$87$	153.639	+	614.964i	0.189332	+	0.757829i
$88$	529.222	+	1003.48i	0.641082	+	1.21559i
$89$			1019.86i			1.21467i	0.794448	+	0.607333i	$0.207761\pi$
$89$			1019.86i			1.21467i	−0.794448	+	0.607333i	$0.792239\pi$
$90$	−697.466	+	1087.39i	−0.816882	+	1.27357i
$91$		−	135.546i		−	0.156144i
$92$	287.457	+	528.601i	0.325755	+	0.599027i
$93$	74.5466	−	72.0576i	0.0831196	−	0.0803443i
$94$	−442.518	+	744.363i	−0.485556	+	0.816757i
$95$	532.217	−	921.828i	0.574783	−	0.995553i
$96$	−609.267	−	716.610i	−0.647740	−	0.761861i
$97$	−503.589	−	872.242i	−0.527131	−	0.913018i	−0.999500	−	0.0316171i	$-0.989934\pi$
$97$	−503.589	−	872.242i	−0.527131	−	0.913018i	0.472369	−	0.881401i	$-0.343399\pi$
$98$	934.074	+	11.9208i	0.962814	+	0.0122876i
$99$	45.9541	−	1352.94i	0.0466521	−	1.37349i
$100$	−1288.86	−	32.9027i	−1.28886	−	0.0329027i
$101$	−364.582	+	210.492i	−0.359181	+	0.207373i	−0.668721	−	0.743513i	$-0.733158\pi$
$101$	−364.582	+	210.492i	−0.359181	+	0.207373i	0.309540	+	0.950886i	$0.399825\pi$
$102$	−285.216	−	1206.91i	−0.276869	−	1.17159i
$103$	−1496.60	−	864.065i	−1.43170	−	0.826591i	−0.434447	−	0.900697i	$-0.643056\pi$
$103$	−1496.60	−	864.065i	−1.43170	−	0.826591i	−0.997250	+	0.0741066i	$0.976389\pi$
$104$	−458.026	+	727.516i	−0.431858	+	0.685950i
$105$	86.2942	−	301.486i	0.0802043	−	0.280210i
$106$	−1183.00	+	663.022i	−1.08399	+	0.607532i
$107$	63.1607			0.0570652			0.0285326	−	0.999593i	$-0.490917\pi$
$107$	63.1607			0.0570652			0.0285326	+	0.999593i	$0.490917\pi$
$108$	206.838	+	1103.15i	0.184287	+	0.982872i
$109$	−835.373			−0.734076			−0.367038	−	0.930206i	$-0.619628\pi$
$109$	−835.373			−0.734076			−0.367038	+	0.930206i	$0.619628\pi$
$110$	2092.65	−	1172.84i	1.81388	−	1.01660i
$111$	−25.3976	+	88.7317i	−0.0217174	+	0.0758742i
$112$	191.656	+	124.105i	0.161694	+	0.104704i
$113$	−891.915	−	514.947i	−0.742516	−	0.428692i	0.0804674	−	0.996757i	$-0.474359\pi$
$113$	−891.915	−	514.947i	−0.742516	−	0.428692i	−0.822983	+	0.568065i	$0.807692\pi$
$114$	−212.686	−	899.997i	−0.174736	−	0.739407i
$115$	1101.87	−	636.164i	0.893476	−	0.515849i
$116$	−24.9051	+	975.583i	−0.0199343	+	0.780867i
$117$	905.285	−	482.456i	0.715330	−	0.381223i
$118$	1390.19	+	17.7419i	1.08456	+	0.0138413i
$119$	150.522	+	260.711i	0.115952	+	0.200835i
$120$	−1481.92	+	1326.57i	−1.12734	+	1.00915i
$121$	−591.391	+	1024.32i	−0.444321	+	0.769587i
$122$	−144.295	+	242.720i	−0.107081	+	0.180122i
$123$	−1290.21	+	1247.13i	−0.945810	+	0.914230i
$124$	140.231	−	76.2588i	0.101558	−	0.0552278i
$125$			611.695i			0.437693i
$126$	−125.059	−	242.054i	−0.0884215	−	0.171142i
$127$			794.523i			0.555138i	0.960706	+	0.277569i	$0.0895287\pi$
$127$			794.523i			0.555138i	−0.960706	+	0.277569i	$0.910471\pi$
$128$	−609.307	−	1313.73i	−0.420747	−	0.907178i
$129$	164.636	+	658.982i	0.112368	+	0.449769i
$130$	1562.57	+	928.938i	1.05420	+	0.626717i
$131$	−111.039	+	192.325i	−0.0740575	+	0.128271i	−0.900676	−	0.434491i	$-0.856928\pi$
$131$	−111.039	+	192.325i	−0.0740575	+	0.128271i	0.826619	+	0.562763i	$0.190262\pi$
$132$	624.472	−	1988.43i	0.411767	−	1.31114i
$133$	112.244	+	194.413i	0.0731791	+	0.126750i
$134$	−22.3671	+	1752.61i	−0.0144196	+	1.12987i
$135$	2320.72	−	496.754i	1.47952	−	0.316694i
$136$	73.0803	−	1907.95i	0.0460778	−	1.20298i
$137$	1054.28	−	608.690i	0.657470	−	0.379591i	−0.133842	−	0.991003i	$-0.542732\pi$
$137$	1054.28	−	608.690i	0.657470	−	0.379591i	0.791312	+	0.611412i	$0.209398\pi$
$138$	317.721	−	1058.76i	0.195987	−	0.653099i
$139$	1909.09	+	1102.21i	1.16494	+	0.672578i	0.952483	−	0.304592i	$-0.0985202\pi$
$139$	1909.09	+	1102.21i	1.16494	+	0.672578i	0.212457	+	0.977170i	$0.431854\pi$
$140$	251.996	−	411.827i	0.152125	−	0.248612i
$141$	1543.44	−	385.605i	0.921853	−	0.230311i
$142$	−351.870	−	627.826i	−0.207946	−	0.371028i
$143$	−1904.89			−1.11395
$144$	−146.701	+	1721.76i	−0.0848967	+	0.996390i
$145$	2063.57			1.18187
$146$	−138.955	−	247.931i	−0.0787671	−	0.140540i
$147$	−1192.72	−	1233.92i	−0.669211	−	0.692328i
$148$	−74.1660	+	121.207i	−0.0411920	+	0.0673184i
$149$	−352.120	−	203.297i	−0.193603	−	0.111777i	0.400065	−	0.916487i	$-0.368987\pi$
$149$	−352.120	−	203.297i	−0.193603	−	0.111777i	−0.593668	+	0.804710i	$0.702321\pi$
$150$	1624.29	+	1723.88i	0.884149	+	0.938363i
$151$	−2990.17	+	1726.37i	−1.61150	+	0.930399i	−0.622475	+	0.782640i	$0.713873\pi$
$151$	−2990.17	+	1726.37i	−1.61150	+	0.930399i	−0.989023	+	0.147759i	$0.952794\pi$
$152$	54.4961	−	1422.76i	0.0290804	−	0.759217i
$153$	−1205.48	+	1933.27i	−0.636975	+	1.02154i
$154$	−6.45621	+	505.887i	−0.00337829	+	0.264711i
$155$	−168.767	−	292.312i	−0.0874559	−	0.151478i
$156$	1541.53	−	343.582i	0.791159	−	0.176337i
$157$	440.287	−	762.599i	0.223813	−	0.387656i	−0.732149	−	0.681144i	$-0.761483\pi$
$157$	440.287	−	762.599i	0.223813	−	0.387656i	0.955963	+	0.293488i	$0.0948160\pi$
$158$	−2403.93	−	1429.12i	−1.21042	−	0.719585i
$159$	2395.18	+	685.572i	1.19466	+	0.341946i
$160$	−2744.15	+	1358.87i	−1.35590	+	0.671427i
$161$			268.333i			0.131352i
$162$	1171.50	−	1696.80i	0.568159	−	0.822919i
$163$			1693.56i			0.813802i	0.913472	+	0.406901i	$0.133391\pi$
$163$			1693.56i			0.813802i	−0.913472	+	0.406901i	$0.866609\pi$
$164$	−2427.05	+	1319.85i	−1.15562	+	0.628432i
$165$	−4236.93	−	1212.73i	−1.99906	−	0.572189i
$166$	727.752	−	1224.16i	0.340268	−	0.572367i
$167$	−820.051	+	1420.37i	−0.379985	+	0.658153i	−0.991060	−	0.133420i	$-0.957404\pi$
$167$	−820.051	+	1420.37i	−0.379985	+	0.658153i	0.611075	+	0.791573i	$0.290737\pi$
$168$	−86.0212	−	410.551i	−0.0395040	−	0.188540i
$169$	376.755	+	652.558i	0.171486	+	0.297022i
$170$	−4037.05	−	51.5214i	−1.82134	−	0.0232442i
$171$	−898.927	+	1441.64i	−0.402004	+	0.644708i
$172$	−26.6878	+	1045.41i	−0.0118310	+	0.463442i
$173$	1889.17	−	1090.71i	0.830234	−	0.479336i	−0.0236985	−	0.999719i	$-0.507544\pi$
$173$	1889.17	−	1090.71i	0.830234	−	0.479336i	0.853933	+	0.520383i	$0.174211\pi$
$174$	1304.87	−	1229.48i	0.568515	−	0.535669i
$175$	−497.930	−	287.480i	−0.215085	−	0.124180i
$176$	1744.10	−	2693.43i	0.746971	−	1.15355i
$177$	−1775.14	−	1836.46i	−0.753830	−	0.779869i
$178$	2516.35	−	1410.31i	1.05960	−	0.593859i
$179$	2350.24			0.981370			0.490685	−	0.871337i	$-0.336747\pi$
$179$	2350.24			0.981370			0.490685	+	0.871337i	$0.336747\pi$
$180$	3647.45	+	217.192i	1.51036	+	0.0899364i
$181$	−2280.14			−0.936362			−0.468181	−	0.883633i	$-0.655090\pi$
$181$	−2280.14			−0.936362			−0.468181	+	0.883633i	$0.655090\pi$
$182$	−334.438	+	187.439i	−0.136210	+	0.0763399i
$183$	503.282	−	125.737i	0.203299	−	0.0507910i
$184$	906.730	−	1440.22i	0.363288	−	0.577036i
$185$	260.214	+	150.235i	0.103413	+	0.0597053i
$186$	−280.876	−	84.2876i	−0.110725	−	0.0332272i
$187$	3663.90	−	2115.36i	1.43279	−	0.827220i
$188$	2448.53	+	62.5071i	0.949878	+	0.0242489i
$189$	−153.990	+	476.248i	−0.0592651	+	0.183291i
$190$	−3010.43	−	38.4196i	−1.14947	−	0.0146697i
$191$	−1966.48	−	3406.04i	−0.744970	−	1.29033i	−0.950209	−	0.311614i	$-0.899130\pi$
$191$	−1966.48	−	3406.04i	−0.744970	−	1.29033i	0.205239	−	0.978712i	$-0.434203\pi$
$192$	−925.600	+	2494.22i	−0.347914	+	0.937527i
$193$	−1356.60	+	2349.69i	−0.505958	+	0.876346i	0.494018	+	0.869452i	$0.335528\pi$
$193$	−1356.60	+	2349.69i	−0.505958	+	0.876346i	−0.999976	+	0.00689392i	$0.997806\pi$
$194$	−1455.73	+	2448.70i	−0.538739	+	0.906217i
$195$	−809.465	−	3240.01i	−0.297267	−	1.18985i
$196$	−1262.26	−	2321.16i	−0.460008	−	0.845904i
$197$		−	1997.91i		−	0.722565i	−0.932456	−	0.361282i	$-0.882339\pi$
$197$		−	1997.91i		−	0.722565i	0.932456	−	0.361282i	$-0.117661\pi$
$198$	−3401.70	+	1757.51i	−1.22095	+	0.630812i
$199$		−	2409.09i		−	0.858170i	−0.903264	−	0.429085i	$-0.858836\pi$
$199$		−	2409.09i		−	0.858170i	0.903264	−	0.429085i	$-0.141164\pi$
$200$	1701.11	+	3225.55i	0.601432	+	1.14041i
$201$	2315.22	−	2237.91i	0.812451	−	0.785324i
$202$	1023.51	+	608.471i	0.356505	+	0.211940i
$203$	−217.603	+	376.900i	−0.0752353	+	0.130311i
$204$	−2583.45	+	2372.69i	−0.886656	+	0.814322i
$205$	2920.92	+	5059.19i	0.995152	+	1.72365i
$206$	−62.3750	+	4887.49i	−0.0210965	+	1.65305i
$207$	−1792.14	+	955.093i	−0.601752	+	0.320693i
$208$	2428.40	+	124.068i	0.809517	+	0.0413584i
$209$	2732.18	−	1577.42i	0.904252	−	0.522070i
$210$	−863.199	+	203.990i	−0.283649	+	0.0670317i
$211$	−1575.68	−	909.717i	−0.514095	−	0.296813i	0.220420	−	0.975405i	$-0.429257\pi$
$211$	−1575.68	−	909.717i	−0.514095	−	0.296813i	−0.734515	+	0.678592i	$0.762590\pi$
$212$	3271.80	+	2002.00i	1.05994	+	0.648577i
$213$	−363.838	+	1271.14i	−0.117041	+	0.408906i
$214$	−87.3411	−	155.839i	−0.0278996	−	0.0497800i
$215$	2211.28			0.701433
$216$	2435.81	−	2035.81i	0.767295	−	0.641294i
$217$	71.1856			0.0222691
$218$	1155.19	+	2061.15i	0.358895	+	0.640360i
$219$	−143.681	+	501.978i	−0.0443336	+	0.154888i
$220$	−5787.61	−	3541.42i	−1.77364	−	1.08528i
$221$	2776.43	+	1602.97i	0.845082	+	0.487908i
$222$	254.052	−	60.0372i	0.0768056	−	0.0181506i
$223$	−2316.13	+	1337.22i	−0.695514	+	0.401555i	−0.805674	−	0.592359i	$-0.798197\pi$
$223$	−2316.13	+	1337.22i	−0.695514	+	0.401555i	0.110160	+	0.993914i	$0.464864\pi$
$224$	41.1795	−	644.496i	0.0122831	−	0.192242i
$225$	147.713	−	4348.82i	0.0437667	−	1.28854i
$226$	−37.1729	+	2912.74i	−0.0109412	+	0.857314i
$227$	2949.58	+	5108.82i	0.862425	+	1.49376i	0.869581	+	0.493790i	$0.164389\pi$
$227$	2949.58	+	5108.82i	0.862425	+	1.49376i	−0.00715576	+	0.999974i	$0.502278\pi$
$228$	−1926.48	+	1769.32i	−0.559581	+	0.513930i
$229$	−1516.38	+	2626.44i	−0.437576	+	0.757904i	−0.997502	−	0.0706386i	$-0.977496\pi$
$229$	−1516.38	+	2626.44i	−0.437576	+	0.757904i	0.559926	+	0.828543i	$0.310830\pi$
$230$	−3093.34	−	1838.97i	−0.886821	−	0.527208i
$231$	668.282	−	645.968i	0.190345	−	0.183990i
$232$	2441.53	−	1287.63i	0.690924	−	0.364383i
$233$		−	1294.13i		−	0.363867i	−0.983311	−	0.181934i	$-0.941764\pi$
$233$		−	1294.13i		−	0.363867i	0.983311	−	0.181934i	$-0.0582356\pi$
$234$	−2442.25	−	1566.48i	−0.682285	−	0.437625i
$235$		−	5179.18i		−	1.43767i
$236$	−1878.64	−	3454.61i	−0.518174	−	0.952865i
$237$	1245.32	+	4984.56i	0.341316	+	1.36617i
$238$	435.115	−	731.910i	0.118506	−	0.199339i
$239$	2875.14	−	4979.89i	0.778149	−	1.34779i	−0.154859	−	0.987937i	$-0.549492\pi$
$239$	2875.14	−	4979.89i	0.778149	−	1.34779i	0.933008	−	0.359856i	$-0.117174\pi$
$240$	5322.35	+	1821.98i	1.43148	+	0.490034i
$241$	−3008.82	−	5211.43i	−0.804212	−	1.39294i	−0.916822	−	0.399296i	$-0.869255\pi$
$241$	−3008.82	−	5211.43i	−0.804212	−	1.39294i	0.112611	−	0.993639i	$-0.464079\pi$
$242$	3345.14	+	42.6912i	0.888570	+	0.0113401i
$243$	−3728.87	+	666.669i	−0.984391	+	0.175995i
$244$	798.409	+	20.3822i	0.209479	+	0.00534769i
$245$	−4838.46	+	2793.49i	−1.26171	+	0.728446i
$246$	4861.26	+	1458.81i	1.25993	+	0.378090i
$247$	2070.39	+	1195.34i	0.533343	+	0.307926i
$248$	−382.074	−	240.545i	−0.0978295	−	0.0615911i
$249$	−2538.30	+	634.154i	−0.646017	+	0.161397i
$250$	1509.26	−	845.876i	0.381815	−	0.213992i
$251$	−3207.28			−0.806541			−0.403270	−	0.915081i	$-0.632127\pi$
$251$	−3207.28			−0.806541			−0.403270	+	0.915081i	$0.632127\pi$
$252$	−424.292	+	643.283i	−0.106063	+	0.160806i
$253$	3771.02			0.937082
$254$	1960.36	−	1098.70i	0.484266	−	0.271411i
$255$	5154.91	+	5332.98i	1.26593	+	1.30966i
$256$	−2398.85	+	3320.05i	−0.585657	+	0.810559i
$257$	−2518.27	−	1453.92i	−0.611226	−	0.352892i	0.162219	−	0.986755i	$-0.448135\pi$
$257$	−2518.27	−	1453.92i	−0.611226	−	0.352892i	−0.773445	+	0.633863i	$0.781468\pi$
$258$	1398.27	−	1317.48i	0.337412	−	0.317918i
$259$	−54.8790	+	31.6844i	−0.0131661	+	0.00760144i
$260$	131.215	−	5139.96i	0.0312986	−	1.22603i
$261$	−3291.77	−	111.809i	−0.780671	−	0.0265164i
$262$	628.081	+	8.01567i	0.148103	+	0.00189011i
$263$	−156.053	−	270.292i	−0.0365880	−	0.0633723i	0.847152	−	0.531351i	$-0.178316\pi$
$263$	−156.053	−	270.292i	−0.0365880	−	0.0633723i	−0.883740	+	0.467979i	$0.844982\pi$
$264$	−5769.67	+	1208.90i	−1.34507	+	0.281828i
$265$	4055.37	−	7024.11i	0.940073	−	1.62825i
$266$	324.466	−	545.787i	0.0747906	−	0.125806i
$267$	−5094.77	−	1458.27i	−1.16777	−	0.334251i
$268$	4355.21	−	2368.39i	0.992674	−	0.539823i
$269$			1826.27i			0.413939i	0.978347	+	0.206969i	$0.0663600\pi$
$269$			1826.27i			0.413939i	−0.978347	+	0.206969i	$0.933640\pi$
$270$	−4434.84	−	5039.06i	−0.999614	−	1.13581i
$271$			4987.26i			1.11791i	0.829197	+	0.558956i	$0.188798\pi$
$271$			4987.26i			1.11791i	−0.829197	+	0.558956i	$0.811202\pi$
$272$	−4808.60	+	2458.07i	−1.07193	+	0.547950i
$273$	677.126	+	193.814i	0.150116	+	0.0429675i
$274$	−2959.75	−	1759.55i	−0.652573	−	0.387950i
$275$	−4040.09	+	6997.65i	−0.885916	+	1.53445i
$276$	−3051.68	+	680.171i	−0.665541	+	0.148339i
$277$	−2125.92	−	3682.20i	−0.461134	−	0.798708i	0.537884	−	0.843019i	$-0.319224\pi$
$277$	−2125.92	−	3682.20i	−0.461134	−	0.798708i	−0.999018	+	0.0443112i	$0.985891\pi$
$278$	79.5662	−	6234.54i	0.0171657	−	1.34505i
$279$	253.375	+	475.434i	0.0543697	+	0.102020i
$280$	−1364.59	−	52.2679i	−0.291249	−	0.0111557i
$281$	−2541.67	+	1467.43i	−0.539585	+	0.311529i	−0.744911	−	0.667164i	$-0.767508\pi$
$281$	−2541.67	+	1467.43i	−0.539585	+	0.311529i	0.205326	+	0.978694i	$0.434175\pi$
$282$	−3085.75	−	3274.96i	−0.651609	−	0.691565i
$283$	3467.24	+	2001.81i	0.728289	+	0.420478i	0.817796	−	0.575508i	$-0.195196\pi$
$283$	3467.24	+	2001.81i	0.728289	+	0.420478i	−0.0895066	+	0.995986i	$0.528529\pi$
$284$	−1062.48	+	1736.36i	−0.221994	+	0.362797i
$285$	3844.03	+	3976.81i	0.798949	+	0.826547i
$286$	2634.16	+	4700.02i	0.544620	+	0.971741i
$287$	−1232.04			−0.253398
$288$	4451.03	−	2018.96i	0.910693	−	0.413084i
$289$	−2207.31			−0.449280
$290$	−2853.59	−	5091.53i	−0.577823	−	1.03098i
$291$	5077.39	−	1268.51i	1.02282	−	0.255537i
$292$	−419.576	+	685.697i	−0.0840886	+	0.137423i
$293$	2334.26	+	1347.69i	0.465423	+	0.268712i	0.714322	−	0.699817i	$-0.246735\pi$
$293$	2334.26	+	1347.69i	0.465423	+	0.268712i	−0.248899	+	0.968530i	$0.580069\pi$
$294$	−1395.16	+	4649.16i	−0.276759	+	0.922261i
$295$	−7201.14	+	4157.58i	−1.42124	+	0.820554i
$296$	401.617	+	15.3832i	0.0788633	+	0.00302071i
$297$	6692.94	+	2164.09i	1.30762	+	0.422806i
$298$	−14.6755	+	1149.93i	−0.00285279	+	0.223535i
$299$	1428.80	+	2474.75i	0.276353	+	0.478658i
$300$	2007.27	−	6391.52i	0.386300	−	1.23005i
$301$	−233.179	+	403.878i	−0.0446518	+	0.0773393i
$302$	8394.46	+	4990.45i	1.59949	+	0.950888i
$303$	−530.214	−	2122.26i	−0.100528	−	0.402379i
$304$	−3585.78	+	1832.99i	−0.676509	+	0.345819i
$305$		−	1688.81i		−	0.317053i
$306$	6437.01	+	300.921i	1.20255	+	0.0562174i
$307$		−	4575.16i		−	0.850547i	−0.905065	−	0.425274i	$-0.860178\pi$
$307$		−	4575.16i		−	0.850547i	0.905065	−	0.425274i	$-0.139822\pi$
$308$	1257.12	−	683.631i	0.232569	−	0.126472i
$309$	6456.43	−	6240.85i	1.18865	−	1.14896i
$310$	−487.856	+	820.626i	−0.0893818	+	0.150350i
$311$	4119.46	−	7135.11i	0.751103	−	1.30095i	−0.196186	−	0.980567i	$-0.562856\pi$
$311$	4119.46	−	7135.11i	0.751103	−	1.30095i	0.947289	−	0.320381i	$-0.103811\pi$
$312$	−2979.42	−	3328.35i	−0.540629	−	0.603944i
$313$	2659.91	+	4607.09i	0.480341	+	0.831975i	0.999746	−	0.0225534i	$-0.00717958\pi$
$313$	2659.91	+	4607.09i	0.480341	+	0.831975i	−0.519405	+	0.854528i	$0.673846\pi$
$314$	−2490.44	−	31.7833i	−0.447591	−	0.00571222i
$315$	1382.70	+	862.173i	0.247321	+	0.154216i
$316$	−201.867	+	7907.54i	−0.0359365	+	1.40770i
$317$	−7641.35	+	4411.73i	−1.35388	+	0.781665i	−0.988791	−	0.149307i	$-0.952296\pi$
$317$	−7641.35	+	4411.73i	−1.35388	+	0.781665i	−0.365092	+	0.930971i	$0.618962\pi$
$318$	−1620.62	−	6857.76i	−0.285785	−	1.20932i
$319$	5296.76	+	3058.08i	0.929660	+	0.536739i
$320$	7147.52	+	4891.64i	1.24862	+	0.854534i
$321$	−90.3117	+	315.522i	−0.0157031	+	0.0548620i
$322$	662.068	−	371.062i	0.114583	−	0.0642189i
$323$	−5309.63			−0.914661
$324$	−5806.56	−	544.087i	−0.995639	−	0.0932933i
$325$	−6123.01			−1.04506
$326$	4178.58	−	2341.92i	0.709908	−	0.397874i
$327$	1194.48	−	4173.14i	0.202002	−	0.705735i
$328$	6612.74	+	4163.22i	1.11319	+	0.700840i
$329$	945.947	+	546.143i	0.158516	+	0.0915192i
$330$	2866.77	+	12131.0i	0.478214	+	2.02360i
$331$	−2056.23	+	1187.17i	−0.341452	+	0.197138i	−0.660914	−	0.750462i	$-0.729831\pi$
$331$	−2056.23	+	1187.17i	−0.341452	+	0.197138i	0.319462	+	0.947599i	$0.396498\pi$
$332$	−4026.77	−	102.797i	−0.665656	−	0.0169932i
$333$	−406.948	−	253.750i	−0.0669688	−	0.0417580i
$334$	4638.53	+	59.1977i	0.759908	+	0.00969806i
$335$	−5241.43	−	9078.43i	−0.854836	−	1.48062i
$336$	−894.014	+	779.970i	−0.145156	+	0.126639i
$337$	321.888	−	557.527i	0.0520308	−	0.0901199i	−0.838837	−	0.544383i	$-0.816764\pi$
$337$	321.888	−	557.527i	0.0520308	−	0.0901199i	0.890868	+	0.454263i	$0.150097\pi$
$338$	1089.09	−	1831.96i	0.175262	−	0.294810i
$339$	3847.77	−	3719.29i	0.616466	−	0.595883i
$340$	5455.47	+	10032.0i	0.870189	+	1.60018i
$341$		−	1000.41i		−	0.158871i
$342$	4800.09	+	224.397i	0.758945	+	0.0354796i
$343$		−	2401.99i		−	0.378120i
$344$	2616.29	−	1379.79i	0.410061	−	0.216260i
$345$	1602.45	+	6414.07i	0.250067	+	1.00093i
$346$	−5303.56	−	3152.93i	−0.824050	−	0.489892i
$347$	−768.265	+	1330.67i	−0.118855	+	0.205863i	−0.919314	−	0.393525i	$-0.871256\pi$
$347$	−768.265	+	1330.67i	−0.118855	+	0.205863i	0.800459	+	0.599387i	$0.204589\pi$
$348$	−4837.96	−	1519.37i	−0.745235	−	0.234043i
$349$	−3432.65	−	5945.53i	−0.526492	−	0.911910i	−0.999524	−	0.0308650i	$-0.990174\pi$
$349$	−3432.65	−	5945.53i	−0.526492	−	0.911910i	0.473032	−	0.881045i	$-0.343160\pi$
$350$	−20.7525	+	1626.10i	−0.00316934	+	0.248339i
$351$	1115.69	+	5212.24i	0.169661	+	0.792618i
$352$	−9057.41	−	578.715i	−1.37148	−	0.0876296i
$353$	107.968	−	62.3355i	0.0162792	−	0.00939881i	−0.491838	−	0.870687i	$-0.663675\pi$
$353$	107.968	−	62.3355i	0.0162792	−	0.00939881i	0.508118	+	0.861288i	$0.330342\pi$
$354$	−2076.43	+	6919.41i	−0.311754	+	1.03888i
$355$	3727.74	+	2152.21i	0.557318	+	0.321768i
$356$	−6959.41	−	4258.44i	−1.03609	−	0.633980i
$357$	−1517.62	+	379.154i	−0.224989	+	0.0562100i
$358$	−3250.01	−	5798.84i	−0.479799	−	0.856084i
$359$	4489.49			0.660017			0.330009	−	0.943978i	$-0.392948\pi$
$359$	4489.49			0.660017			0.330009	+	0.943978i	$0.392948\pi$
$360$	−4507.96	−	9299.84i	−0.659973	−	1.36151i
$361$	2899.60			0.422744
$362$	3153.07	+	5625.87i	0.457794	+	0.816821i
$363$	−4271.42	−	4418.97i	−0.617607	−	0.638941i
$364$	924.948	+	565.973i	0.133188	+	0.0814974i
$365$	1472.10	+	849.917i	0.211105	+	0.121881i
$366$	−1006.19	−	1067.89i	−0.143701	−	0.152513i
$367$	−750.997	+	433.589i	−0.106817	+	0.0616707i	−0.552457	−	0.833542i	$-0.686310\pi$
$367$	−750.997	+	433.589i	−0.106817	+	0.0616707i	0.445640	+	0.895212i	$0.352976\pi$
$368$	−4807.38	−	245.610i	−0.680984	−	0.0347916i
$369$	−4385.27	−	8228.56i	−0.618667	−	1.16087i
$370$	10.8451	−	849.787i	0.00152381	−	0.119401i
$371$	855.275	+	1481.38i	0.119686	+	0.207303i
$372$	180.441	+	809.573i	0.0251490	+	0.112834i
$373$	2169.58	−	3757.82i	0.301170	−	0.521642i	−0.675231	−	0.737606i	$-0.735956\pi$
$373$	2169.58	−	3757.82i	0.301170	−	0.521642i	0.976401	+	0.215964i	$0.0692895\pi$
$374$	−10285.9	−	6114.89i	−1.42211	−	0.845436i
$375$	−3055.75	−	874.646i	−0.420795	−	0.120444i
$376$	−3231.69	−	6127.78i	−0.443250	−	0.840468i
$377$			4634.71i			0.633156i
$378$	1388.01	−	278.630i	0.188866	−	0.0379132i
$379$		−	14096.9i		−	1.91058i	−0.295677	−	0.955288i	$-0.595545\pi$
$379$		−	14096.9i		−	1.91058i	0.295677	−	0.955288i	$-0.404455\pi$
$380$	4068.15	+	7480.88i	0.549189	+	1.00990i
$381$	−3969.07	−	1136.07i	−0.533706	−	0.152762i
$382$	−5684.52	+	9561.97i	−0.761375	+	1.28071i
$383$	−4134.45	+	7161.08i	−0.551594	+	0.955390i	0.446565	+	0.894751i	$0.352647\pi$
$383$	−4134.45	+	7161.08i	−0.551594	+	0.955390i	−0.998160	+	0.0606386i	$0.980686\pi$
$384$	7434.05	−	1165.35i	0.987935	−	0.154867i
$385$	−1512.93	−	2620.47i	−0.200275	−	0.346887i
$386$	7673.45	+	97.9297i	1.01183	+	0.0129132i
$387$	−3527.38	−	119.812i	−0.463326	−	0.0157374i
$388$	8054.80	+	205.627i	1.05392	+	0.0269050i
$389$	4972.96	−	2871.14i	0.648173	−	0.374223i	−0.139583	−	0.990210i	$-0.544576\pi$
$389$	4972.96	−	2871.14i	0.648173	−	0.374223i	0.787756	+	0.615987i	$0.211243\pi$
$390$	−6874.83	+	6477.63i	−0.892617	+	0.841046i
$391$	−5496.35	−	3173.32i	−0.710902	−	0.410439i
$392$	−3981.58	+	6324.22i	−0.513010	+	0.814851i
$393$	−801.999	−	829.702i	−0.102940	−	0.106496i
$394$	−4929.52	+	2762.79i	−0.630319	+	0.353267i
$395$	16726.2			2.13060
$396$	9040.37	+	5962.78i	1.14721	+	0.756669i
$397$	10494.4			1.32670			0.663349	−	0.748310i	$-0.269134\pi$
$397$	10494.4			1.32670			0.663349	+	0.748310i	$0.269134\pi$
$398$	−5944.04	+	3331.39i	−0.748612	+	0.419566i
$399$	−1131.69	+	282.736i	−0.141994	+	0.0354749i
$400$	5606.17	−	8657.63i	0.700771	−	1.08220i
$401$	−7070.19	−	4081.97i	−0.880469	−	0.508339i	−0.00965631	−	0.999953i	$-0.503074\pi$
$401$	−7070.19	−	4081.97i	−0.880469	−	0.508339i	−0.870813	+	0.491614i	$0.836407\pi$
$402$	−8723.26	−	2617.74i	−1.08228	−	0.324779i
$403$	656.523	−	379.044i	0.0811507	−	0.0468524i
$404$	85.9485	−	3366.77i	0.0105844	−	0.414611i
$405$	−836.774	+	12303.5i	−0.102666	+	1.50955i
$406$	1230.85	+	15.7083i	0.150458	+	0.00192017i
$407$	445.277	+	771.242i	0.0542298	+	0.0939288i
$408$	9426.73	+	3093.20i	1.14386	+	0.375333i
$409$	−2037.43	+	3528.93i	−0.246319	+	0.426637i	−0.962502	−	0.271276i	$-0.912554\pi$
$409$	−2037.43	+	3528.93i	−0.246319	+	0.426637i	0.716183	+	0.697913i	$0.245888\pi$
$410$	8443.56	−	14203.0i	1.01707	−	1.71081i
$411$	1533.25	+	6137.06i	0.184014	+	0.736543i
$412$	12145.3	−	6604.72i	1.45233	−	0.789784i
$413$		−	1753.66i		−	0.208940i
$414$	4834.78	+	3101.08i	0.573953	+	0.368140i
$415$			8517.52i			1.00749i
$416$	−3051.98	−	6163.26i	−0.359701	−	0.726391i
$417$	−8235.90	+	7960.90i	−0.967179	+	0.934885i
$418$	−7670.20	−	4559.88i	−0.897516	−	0.533567i
$419$	346.536	−	600.219i	0.0404043	−	0.0699823i	−0.845116	−	0.534583i	$-0.820469\pi$
$419$	346.536	−	600.219i	0.0404043	−	0.0699823i	0.885520	+	0.464601i	$0.153802\pi$
$420$	1696.98	+	1847.72i	0.197153	+	0.214665i
$421$	5362.68	+	9288.44i	0.620810	+	1.07527i	0.989335	+	0.145657i	$0.0465296\pi$
$421$	5362.68	+	9288.44i	0.620810	+	1.07527i	−0.368525	+	0.929618i	$0.620137\pi$
$422$	−65.6705	+	5145.72i	−0.00757533	+	0.593577i
$423$	−280.618	+	8261.70i	−0.0322556	+	0.949640i
$424$	415.247	−	10841.1i	0.0475618	−	1.24172i
$425$	11777.1	−	6799.50i	1.34417	−	0.776057i
$426$	3639.46	−	860.073i	0.413926	−	0.0978184i
$427$	308.452	+	178.085i	0.0349579	+	0.0201830i
$428$	−263.728	+	431.000i	−0.0297845	+	0.0486756i
$429$	2723.76	−	9515.98i	0.306536	−	1.07095i
$430$	−3057.85	−	5455.98i	−0.342936	−	0.611885i
$431$	−10013.8			−1.11914			−0.559569	−	0.828784i	$-0.689033\pi$
$431$	−10013.8			−1.11914			−0.559569	+	0.828784i	$0.689033\pi$
$432$	−8391.37	−	3194.75i	−0.934560	−	0.355805i
$433$	−9726.02			−1.07945			−0.539726	−	0.841841i	$-0.681472\pi$
$433$	−9726.02			−1.07945			−0.539726	+	0.841841i	$0.681472\pi$
$434$	−98.4383	−	175.639i	−0.0108875	−	0.0194261i
$435$	−2950.65	+	10308.7i	−0.325225	+	1.13624i
$436$	3488.11	−	5700.47i	0.383142	−	0.626154i
$437$	−4098.64	−	2366.35i	−0.448660	−	0.259034i
$438$	1437.24	−	339.646i	0.156790	−	0.0370523i
$439$	5675.95	−	3277.01i	0.617080	−	0.356271i	−0.158651	−	0.987335i	$-0.550715\pi$
$439$	5675.95	−	3277.01i	0.617080	−	0.356271i	0.775731	+	0.631063i	$0.217381\pi$
$440$	−734.546	+	19177.2i	−0.0795866	+	2.07781i
$441$	7869.55	−	4193.94i	0.849752	−	0.452861i
$442$	115.715	−	9067.05i	0.0124525	−	0.975737i
$443$	2939.61	+	5091.55i	0.315271	+	0.546065i	0.979495	−	0.201468i	$-0.0645713\pi$
$443$	2939.61	+	5091.55i	0.315271	+	0.546065i	−0.664224	+	0.747533i	$0.731238\pi$
$444$	−499.445	−	543.810i	−0.0533843	−	0.0581263i
$445$	−8626.14	+	14940.9i	−0.918917	+	1.59161i
$446$	6502.21	+	3865.52i	0.690333	+	0.410398i
$447$	1519.07	−	1468.34i	0.160737	−	0.155370i
$448$	−1647.13	+	789.631i	−0.173705	+	0.0832736i
$449$			6761.00i			0.710627i	0.934747	+	0.355313i	$0.115626\pi$
$449$			6761.00i			0.710627i	−0.934747	+	0.355313i	$0.884374\pi$
$450$	−10934.3	+	5649.26i	−1.14544	+	0.591797i
$451$			17314.5i			1.80778i
$452$	7238.13	−	3936.14i	0.753214	−	0.409603i
$453$	−4348.62	−	17406.0i	−0.451028	−	1.80531i
$454$	8526.39	−	14342.3i	0.881417	−	1.48264i
$455$	1146.47	−	1985.74i	0.118126	−	0.204600i
$456$	7029.53	+	2306.60i	0.721903	+	0.236878i
$457$	7620.16	+	13198.5i	0.779992	+	1.35099i	0.931946	+	0.362598i	$0.118110\pi$
$457$	7620.16	+	13198.5i	0.779992	+	1.35099i	−0.151954	+	0.988388i	$0.548557\pi$
$458$	8577.22	+	109.464i	0.875081	+	0.0111679i
$459$	−7934.05	−	8786.35i	−0.806818	−	0.893490i
$460$	−259.760	+	10175.3i	−0.0263291	+	1.03136i
$461$	11900.4	−	6870.68i	1.20229	−	0.694142i	0.241226	−	0.970469i	$-0.422450\pi$
$461$	11900.4	−	6870.68i	1.20229	−	0.694142i	0.961064	+	0.276327i	$0.0891171\pi$
$462$	−2517.95	−	755.606i	−0.253562	−	0.0760908i
$463$	−15291.7	−	8828.66i	−1.53491	−	0.886183i	−0.999125	−	0.0418305i	$-0.986681\pi$
$463$	−15291.7	−	8828.66i	−1.53491	−	0.886183i	−0.535789	−	0.844352i	$-0.679986\pi$
$464$	−6553.25	−	4243.50i	−0.655662	−	0.424568i
$465$	1701.57	−	425.112i	0.169696	−	0.0423959i
$466$	−3193.05	+	1789.57i	−0.317414	+	0.177898i
$467$	−6165.12			−0.610895			−0.305447	−	0.952209i	$-0.598806\pi$
$467$	−6165.12			−0.610895			−0.305447	+	0.952209i	$0.598806\pi$
$468$	−487.806	+	8192.04i	−0.0481813	+	0.809139i
$469$	2210.83			0.217669
$470$	−12778.8	+	7161.97i	−1.25413	+	0.702888i
$471$	3180.04	+	3289.89i	0.311101	+	0.321848i
$472$	−5925.83	+	9412.42i	−0.577878	+	0.917885i
$473$	5675.89	+	3276.98i	0.551750	+	0.318553i
$474$	10576.5	−	9965.47i	1.02489	−	0.965673i
$475$	8782.19	−	5070.40i	0.848325	−	0.489781i
$476$	−2407.56	−	61.4614i	−0.231829	−	0.00591824i
$477$	−6849.61	+	10985.0i	−0.657489	+	1.05444i
$478$	−16262.9	−	207.550i	−1.55617	−	0.0198601i
$479$	8659.06	+	14997.9i	0.825976	+	1.43063i	0.901171	+	0.433464i	$0.142709\pi$
$479$	8659.06	+	14997.9i	0.825976	+	1.43063i	−0.0751944	+	0.997169i	$0.523958\pi$
$480$	−2864.53	−	15651.5i	−0.272390	−	1.48832i
$481$	−337.422	+	584.431i	−0.0319857	+	0.0554008i
$482$	−8697.63	+	14630.3i	−0.821921	+	1.38256i
$483$	−1340.47	−	383.682i	−0.126281	−	0.0361452i
$484$	−4520.46	−	8312.63i	−0.424536	−	0.780675i
$485$		−	17037.7i		−	1.59514i
$486$	6801.33	+	8278.48i	0.634803	+	0.772674i
$487$		−	7352.14i		−	0.684101i	−0.939682	−	0.342050i	$-0.888879\pi$
$487$		−	7352.14i		−	0.684101i	0.939682	−	0.342050i	$-0.111121\pi$
$488$	−1053.78	−	1998.13i	−0.0977510	−	0.185351i
$489$	−8460.25	−	2421.57i	−0.782384	−	0.223941i
$490$	13583.3	+	8075.16i	1.25231	+	0.744487i
$491$	4221.27	−	7311.46i	0.387991	−	0.672019i	−0.604189	−	0.796841i	$-0.706503\pi$
$491$	4221.27	−	7311.46i	0.387991	−	0.672019i	0.992179	+	0.124822i	$0.0398360\pi$
$492$	−3122.98	−	14011.7i	−0.286168	−	1.28393i
$493$	−5146.77	−	8914.47i	−0.470181	−	0.814377i
$494$	86.2890	−	6761.31i	0.00785896	−	0.615801i
$495$	12116.5	−	19431.7i	1.10020	−	1.76443i
$496$	−65.1574	+	1275.34i	−0.00589850	+	0.115453i
$497$	−786.178	+	453.900i	−0.0709555	+	0.0409662i
$498$	5074.73	+	5385.90i	0.456635	+	0.484635i
$499$	6542.34	+	3777.22i	0.586924	+	0.338861i	0.763880	−	0.645358i	$-0.223292\pi$
$499$	6542.34	+	3777.22i	0.586924	+	0.338861i	−0.176956	+	0.984219i	$0.556625\pi$
$500$	−4174.12	−	2554.14i	−0.373345	−	0.228449i
$501$	−5922.95	−	6127.55i	−0.528180	−	0.546425i
$502$	4435.16	+	7913.44i	0.394324	+	0.703574i
$503$	−604.632			−0.0535968			−0.0267984	−	0.999641i	$-0.508531\pi$
$503$	−604.632			−0.0535968			−0.0267984	+	0.999641i	$0.508531\pi$
$504$	2173.92	+	157.313i	0.192132	+	0.0139033i
$505$	−7121.47			−0.627527
$506$	−5214.71	−	9304.37i	−0.458147	−	0.817450i
$507$	−3798.59	+	949.020i	−0.332745	+	0.0831311i
$508$	−5421.72	−	3317.54i	−0.473523	−	0.289748i
$509$	8861.66	+	5116.28i	0.771682	+	0.445531i	0.833474	−	0.552558i	$-0.186348\pi$
$509$	8861.66	+	5116.28i	0.771682	+	0.445531i	−0.0617925	+	0.998089i	$0.519682\pi$
$510$	6029.84	−	20093.6i	0.523541	−	1.74462i
$511$	−310.465	+	179.247i	−0.0268770	+	0.0155175i
$512$	11508.9	+	1327.68i	0.993412	+	0.114601i
$513$	−5916.43	−	6552.00i	−0.509195	−	0.563894i
$514$	−104.955	+	8223.96i	−0.00900659	+	0.705726i
$515$	−14616.8	−	25317.0i	−1.25066	−	2.16621i
$516$	−5184.25	−	1628.13i	−0.442294	−	0.138904i
$517$	7675.21	−	13293.8i	0.652911	−	1.13088i
$518$	154.065	+	91.5906i	0.0130680	+	0.00776884i
$519$	2747.43	+	10997.0i	0.232367	+	0.930085i
$520$	−12863.5	+	6784.00i	−1.08481	+	0.572111i
$521$			18465.3i			1.55274i	0.630276	+	0.776371i	$0.282942\pi$
$521$			18465.3i			1.55274i	−0.630276	+	0.776371i	$0.717058\pi$
$522$	4276.12	+	8276.51i	0.358545	+	0.693971i
$523$			15941.5i			1.33284i	0.745579	+	0.666418i	$0.232173\pi$
$523$			15941.5i			1.33284i	−0.745579	+	0.666418i	$0.767827\pi$
$524$	−848.759	−	1560.77i	−0.0707599	−	0.130120i
$525$	2148.09	−	2076.37i	0.178572	−	0.172610i
$526$	−451.105	+	758.807i	−0.0373938	+	0.0629003i
$527$	−841.844	+	1458.12i	−0.0695850	+	0.120525i
$528$	10961.3	+	12564.0i	0.903464	+	1.03557i
$529$	3254.98	+	5637.79i	0.267525	+	0.463368i
$530$	−22938.8	−	292.748i	−1.87999	−	0.0239928i
$531$	11712.4	−	6241.90i	0.957199	−	0.510123i
$532$	−1795.32	−	45.8319i	−0.146310	−	0.00373508i
$533$	−11362.7	+	6560.29i	−0.923406	+	0.533129i
$534$	3447.20	+	14587.1i	0.279354	+	1.18211i
$535$	925.299	+	534.221i	0.0747741	+	0.0431709i
$536$	−11866.2	−	7470.66i	−0.956233	−	0.602021i
$537$	−3360.54	+	11740.7i	−0.270052	+	0.943482i
$538$	4506.02	−	2525.44i	0.361093	−	0.202378i
$539$	−16559.1			−1.32328
$540$	−6300.39	+	17910.5i	−0.502084	+	1.42730i
$541$	7256.04			0.576638			0.288319	−	0.957534i	$-0.406904\pi$
$541$	7256.04			0.576638			0.288319	+	0.957534i	$0.406904\pi$
$542$	12305.2	−	6896.58i	0.975195	−	0.546556i
$543$	3260.31	−	11390.5i	0.257667	−	0.900211i
$544$	12714.4	+	8465.33i	1.00207	+	0.667184i
$545$	−12238.1	−	7065.70i	−0.961880	−	0.555342i
$546$	−458.154	−	1938.71i	−0.0359106	−	0.151958i
$547$	−374.999	+	216.506i	−0.0293122	+	0.0169234i	−0.514585	−	0.857440i	$-0.672054\pi$
$547$	−374.999	+	216.506i	−0.0293122	+	0.0169234i	0.485272	+	0.874363i	$0.338720\pi$
$548$	−248.542	+	9735.87i	−0.0193744	+	0.758934i
$549$	−91.5034	+	2693.96i	−0.00711342	+	0.209427i
$550$	22852.4	+	291.646i	1.77169	+	0.0226106i
$551$	−3837.96	−	6647.54i	−0.296738	−	0.513965i
$552$	5898.19	+	6588.95i	0.454789	+	0.508051i
$553$	−1763.77	+	3054.94i	−0.135630	+	0.234918i
$554$	−6145.43	+	10337.3i	−0.471289	+	0.792758i
$555$	−1122.58	+	1085.10i	−0.0858572	+	0.0829905i
$556$	−15492.7	+	8425.06i	−1.18172	+	0.642630i
$557$		−	9185.88i		−	0.698776i	−0.936978	−	0.349388i	$-0.886390\pi$
$557$		−	9185.88i		−	0.698776i	0.936978	−	0.349388i	$-0.113610\pi$
$558$	822.680	−	1282.61i	0.0624136	−	0.0973068i
$559$			4966.45i			0.375776i
$560$	1758.04	+	3439.17i	0.132662	+	0.259521i
$561$	5328.44	+	21327.9i	0.401010	+	1.60510i
$562$	7135.38	+	4241.93i	0.535565	+	0.318390i
$563$	6499.11	−	11256.8i	0.486510	−	0.842659i	−0.513370	−	0.858167i	$-0.671603\pi$
$563$	6499.11	−	11256.8i	0.486510	−	0.842659i	0.999880	+	0.0155079i	$0.00493650\pi$
$564$	−3813.34	+	12142.3i	−0.284699	+	0.906533i
$565$	−8710.99	−	15087.9i	−0.648627	−	1.12345i
$566$	144.506	−	11323.0i	0.0107315	−	0.840888i
$567$	−2158.93	−	1450.24i	−0.159906	−	0.107415i
$568$	5753.43	+	220.374i	0.425015	+	0.0162794i
$569$	5424.42	−	3131.79i	0.399655	−	0.230741i	−0.286680	−	0.958026i	$-0.592552\pi$
$569$	5424.42	−	3131.79i	0.399655	−	0.230741i	0.686335	+	0.727286i	$0.259218\pi$
$570$	4496.46	−	14983.8i	0.330414	−	1.10106i
$571$	−21837.8	−	12608.1i	−1.60050	−	0.924047i	−0.991388	−	0.130961i	$-0.958194\pi$
$571$	−21837.8	−	12608.1i	−1.60050	−	0.924047i	−0.609109	−	0.793086i	$-0.708473\pi$
$572$	7953.90	−	12998.7i	0.581415	−	0.950183i
$573$	19826.8	−	4953.42i	1.44551	−	0.361138i
$574$	1703.72	+	3039.86i	0.123888	+	0.221048i
$575$	12121.4			0.879125
$576$	−11136.5	−	8190.30i	−0.805593	−	0.592469i
$577$	18112.2			1.30680			0.653398	−	0.757014i	$-0.273343\pi$
$577$	18112.2			1.30680			0.653398	+	0.757014i	$0.273343\pi$
$578$	3052.36	+	5446.18i	0.219656	+	0.391923i
$579$	−9798.24	−	10136.7i	−0.703283	−	0.727577i
$580$	−8616.47	+	14081.6i	−0.616861	+	1.00811i
$581$	−1555.67	−	898.169i	−0.111085	−	0.0641348i
$582$	−10151.1	−	10773.5i	−0.722981	−	0.767312i
$583$	20818.6	−	12019.6i	1.47893	−	0.853861i
$584$	2272.05	+	87.0268i	0.160990	+	0.00616643i
$585$	17343.0	+	589.076i	1.22572	+	0.0416330i
$586$	97.2865	−	7623.04i	0.00685813	−	0.537380i
$587$	13172.1	+	22814.8i	0.926189	+	1.60421i	0.789638	+	0.613573i	$0.210268\pi$
$587$	13172.1	+	22814.8i	0.926189	+	1.60421i	0.136551	+	0.990633i	$0.456398\pi$
$588$	13400.3	−	2986.73i	0.939831	−	0.209474i
$589$	−627.764	+	1087.32i	−0.0439161	+	0.0760649i
$590$	20216.2	+	12018.4i	1.41065	+	0.838624i
$591$	9980.65	+	2856.76i	0.694669	+	0.198835i
$592$	−517.417	−	1012.20i	−0.0359218	−	0.0702721i
$593$			11633.4i			0.805609i	0.915286	+	0.402804i	$0.131965\pi$
$593$			11633.4i			0.805609i	−0.915286	+	0.402804i	$0.868035\pi$
$594$	−3915.73	−	19506.3i	−0.270479	−	1.34740i
$595$			5092.53i			0.350880i
$596$	2857.55	−	1553.96i	0.196392	−	0.106799i
$597$	12034.7	+	3444.69i	0.825039	+	0.236150i
$598$	4130.25	−	6947.52i	0.282439	−	0.475092i
$599$	−11060.5	+	19157.3i	−0.754454	+	1.30675i	0.191191	+	0.981553i	$0.438765\pi$
$599$	−11060.5	+	19157.3i	−0.754454	+	1.30675i	−0.945645	+	0.325200i	$0.894568\pi$
$600$	−18545.8	+	3885.83i	−1.26188	+	0.264397i
$601$	846.923	+	1466.91i	0.0574820	+	0.0995618i	0.893334	−	0.449392i	$-0.148359\pi$
$601$	846.923	+	1466.91i	0.0574820	+	0.0995618i	−0.835852	+	0.548954i	$0.815026\pi$
$602$	1318.95	+	16.8327i	0.0892964	+	0.00113962i
$603$	7869.13	+	14765.7i	0.531435	+	0.997190i
$604$	704.917	−	27613.0i	0.0474879	−	1.86019i
$605$	−17327.7	+	10004.1i	−1.16441	+	0.672274i
$606$	−4503.14	+	4242.97i	−0.301860	+	0.284420i
$607$	11418.4	+	6592.43i	0.763525	+	0.440821i	0.830560	−	0.556929i	$-0.188021\pi$
$607$	11418.4	+	6592.43i	0.763525	+	0.440821i	−0.0670351	+	0.997751i	$0.521354\pi$
$608$	9481.16	+	6312.61i	0.632421	+	0.421069i
$609$	−1571.68	−	1625.97i	−0.104577	−	0.108190i
$610$	−4166.87	+	2335.36i	−0.276577	+	0.155010i
$611$	11632.2			0.770196
$612$	−8158.88	−	16298.4i	−0.538894	−	1.07651i
$613$	−18052.3			−1.18944			−0.594719	−	0.803934i	$-0.702737\pi$
$613$	−18052.3			−1.18944			−0.594719	+	0.803934i	$0.702737\pi$
$614$	−11288.5	+	6326.71i	−0.741962	+	0.415839i
$615$	−29450.0	+	7357.61i	−1.93095	+	0.482419i
$616$	−3425.15	−	2156.39i	−0.224031	−	0.141045i
$617$	−18897.2	−	10910.3i	−1.23302	−	0.711884i	−0.265361	−	0.964149i	$-0.585491\pi$
$617$	−18897.2	−	10910.3i	−1.23302	−	0.711884i	−0.967658	+	0.252266i	$0.918824\pi$
$618$	−24326.5	−	7300.09i	−1.58342	−	0.475166i
$619$	−15640.0	+	9029.74i	−1.01555	+	0.586326i	−0.912811	−	0.408382i	$-0.866093\pi$
$619$	−15640.0	+	9029.74i	−1.01555	+	0.586326i	−0.102736	+	0.994709i	$0.532760\pi$
$620$	2699.39	+	68.9112i	0.174855	+	0.00446378i
$621$	−2208.67	−	10318.4i	−0.142723	−	0.666768i
$622$	−23301.3	−	297.374i	−1.50208	−	0.0191698i
$623$	−1819.25	−	3151.03i	−0.116993	−	0.202638i
$624$	−4092.09	+	11953.8i	−0.262524	+	0.766883i
$625$	4898.71	−	8484.82i	0.313518	−	0.543028i
$626$	7689.02	−	12933.8i	0.490919	−	0.825778i
$627$	3973.42	+	15904.2i	0.253083	+	1.01300i
$628$	3365.45	+	6188.70i	0.213848	+	0.393242i
$629$		−	1498.81i		−	0.0950100i
$630$	215.223	−	4603.83i	0.0136106	−	0.291144i
$631$		−	7301.94i		−	0.460674i	−0.973111	−	0.230337i	$-0.926017\pi$
$631$		−	7301.94i		−	0.460674i	0.973111	−	0.230337i	$-0.0739829\pi$
$632$	19789.7	−	10436.8i	1.24556	−	0.656888i
$633$	6797.55	−	6570.58i	0.426822	−	0.412571i
$634$	21452.0	+	12753.1i	1.34380	+	0.798878i
$635$	−6720.18	+	11639.7i	−0.419972	+	0.727413i
$636$	−14679.4	+	13481.8i	−0.915211	+	0.840547i
$637$	−6274.06	−	10867.0i	−0.390247	−	0.675928i
$638$	220.756	−	17297.7i	0.0136988	−	1.07339i
$639$	−5829.79	−	3635.14i	−0.360912	−	0.225045i
$640$	2185.45	−	24399.7i	0.134980	−	1.50700i
$641$	735.990	−	424.924i	0.0453508	−	0.0261833i	−0.477153	−	0.878820i	$-0.658331\pi$
$641$	735.990	−	424.924i	0.0453508	−	0.0261833i	0.522504	+	0.852637i	$0.324998\pi$
$642$	903.386	−	213.487i	0.0555355	−	0.0131241i
$643$	−984.538	−	568.423i	−0.0603832	−	0.0348622i	0.469504	−	0.882930i	$-0.344433\pi$
$643$	−984.538	−	568.423i	−0.0603832	−	0.0348622i	−0.529888	+	0.848068i	$0.677766\pi$
$644$	−1831.07	−	1120.43i	−0.112041	−	0.0685575i
$645$	−3161.85	+	11046.6i	−0.193020	+	0.674353i
$646$	7342.37	+	13100.6i	0.447185	+	0.797891i
$647$	995.889			0.0605138			0.0302569	−	0.999542i	$-0.490367\pi$
$647$	995.889			0.0605138			0.0302569	+	0.999542i	$0.490367\pi$
$648$	6687.11	+	15079.1i	0.405392	+	0.914143i
$649$	−24645.0			−1.49061
$650$	8467.14	+	15107.5i	0.510936	+	0.911640i
$651$	−101.786	+	355.611i	−0.00612799	+	0.0214093i
$652$	−11556.6	−	7071.46i	−0.694160	−	0.424754i
$653$	24496.2	+	14142.9i	1.46801	+	0.847557i	0.999358	−	0.0358245i	$-0.0114057\pi$
$653$	24496.2	+	14142.9i	1.46801	+	0.847557i	0.468654	+	0.883382i	$0.344739\pi$
$654$	−11948.3	+	2823.61i	−0.714398	+	0.168826i
$655$	−3253.43	+	1878.37i	−0.194079	+	0.112052i
$656$	1127.71	−	22072.9i	0.0671185	−	1.31372i
$657$	−2302.21	−	1435.53i	−0.136709	−	0.0852440i
$658$	39.4248	−	3089.20i	0.00233577	−	0.183023i
$659$	−12722.0	−	22035.1i	−0.752014	−	1.30253i	−0.946845	−	0.321690i	$-0.895749\pi$
$659$	−12722.0	−	22035.1i	−0.752014	−	1.30253i	0.194831	−	0.980837i	$-0.437584\pi$
$660$	25966.9	−	23848.5i	1.53145	−	1.40652i
$661$	2109.30	−	3653.42i	0.124119	−	0.214980i	−0.797269	−	0.603624i	$-0.793723\pi$
$661$	2109.30	−	3653.42i	0.124119	−	0.214980i	0.921388	+	0.388644i	$0.127056\pi$
$662$	5772.58	+	3431.76i	0.338909	+	0.201479i
$663$	−11977.7	+	11577.7i	−0.701620	+	0.678193i
$664$	5314.74	+	10077.6i	0.310621	+	0.588983i
$665$			3797.51i			0.221445i
$666$	−63.3431	+	1354.97i	−0.00368543	+	0.0788350i
$667$		−	9175.09i		−	0.532625i
$668$	−6268.29	−	11526.7i	−0.363065	−	0.667636i
$669$	−3368.36	−	13482.4i	−0.194661	−	0.779162i
$670$	−15151.5	+	25486.4i	−0.873661	+	1.46959i
$671$	2502.71	−	4334.83i	0.143988	−	0.249395i
$672$	3160.73	+	1127.26i	0.181440	+	0.0647099i
$673$	−7212.87	−	12493.0i	−0.413129	−	0.715560i	0.582101	−	0.813116i	$-0.302231\pi$
$673$	−7212.87	−	12493.0i	−0.413129	−	0.715560i	−0.995230	+	0.0975565i	$0.968897\pi$
$674$	−1820.73	−	23.2364i	−0.104053	−	0.00132794i
$675$	21513.5	+	6956.16i	1.22675	+	0.396656i
$676$	−6026.11	−	153.837i	−0.342860	−	0.00875270i
$677$	−27870.5	+	16091.1i	−1.58220	+	0.913486i	−0.587666	+	0.809103i	$0.699953\pi$
$677$	−27870.5	+	16091.1i	−1.58220	+	0.913486i	−0.994537	+	0.104382i	$0.966713\pi$
$678$	−14497.6	−	4350.55i	−0.821205	−	0.246434i
$679$	3111.84	+	1796.62i	0.175878	+	0.101543i
$680$	17208.3	−	27333.1i	0.970452	−	1.54144i
$681$	−29738.9	+	7429.80i	−1.67342	+	0.418077i
$682$	−2468.34	+	1383.40i	−0.138589	+	0.0776732i
$683$	28383.3			1.59012			0.795062	−	0.606528i	$-0.207438\pi$
$683$	28383.3			1.59012			0.795062	+	0.606528i	$0.207438\pi$
$684$	−6084.09	−	12153.7i	−0.340104	−	0.679401i
$685$	20593.5			1.14867
$686$	−5926.51	+	3321.56i	−0.329847	+	0.184866i
$687$	−10952.3	−	11330.6i	−0.608232	−	0.629242i
$688$	−7022.32	−	4547.24i	−0.389133	−	0.251980i
$689$	15775.9	+	9108.21i	0.872298	+	0.503621i
$690$	13609.7	−	12823.4i	0.750889	−	0.707506i
$691$	4592.61	−	2651.54i	0.252838	−	0.145976i	−0.368225	−	0.929737i	$-0.620034\pi$
$691$	4592.61	−	2651.54i	0.252838	−	0.145976i	0.621063	+	0.783761i	$0.286701\pi$
$692$	−445.362	+	17445.7i	−0.0244655	+	0.958360i
$693$	2271.41	+	4262.08i	0.124507	+	0.233627i
$694$	4345.61	+	55.4594i	0.237690	+	0.00303344i
$695$	18645.3	+	32294.6i	1.01764	+	1.76260i
$696$	2941.31	+	14037.9i	0.160187	+	0.764520i
$697$	14570.2	−	25236.3i	0.791801	−	1.37144i
$698$	−9922.81	+	16691.2i	−0.538086	+	0.905117i
$699$	6464.87	+	1850.44i	0.349819	+	0.100129i
$700$	4040.83	−	2197.43i	0.218185	−	0.118650i
$701$		−	10087.7i		−	0.543519i	−0.962365	−	0.271760i	$-0.912394\pi$
$701$		−	10087.7i		−	0.543519i	0.962365	−	0.271760i	$-0.0876056\pi$
$702$	11317.5	−	9960.48i	0.608480	−	0.535519i
$703$		−	1117.66i		−	0.0599622i
$704$	11097.1	+	23148.0i	0.594086	+	1.23924i
$705$	25872.8	+	7405.56i	1.38216	+	0.395616i
$706$	−303.105	−	180.194i	−0.0161580	−	0.00960579i
$707$	750.956	−	1300.69i	0.0399471	−	0.0691905i
$708$	19943.9	−	4445.18i	1.05867	−	0.235961i
$709$	12869.6	+	22290.9i	0.681706	+	1.18075i	0.974460	+	0.224561i	$0.0720949\pi$
$709$	12869.6	+	22290.9i	0.681706	+	1.18075i	−0.292754	+	0.956188i	$0.594572\pi$
$710$	155.363	−	12173.8i	0.00821223	−	0.643483i
$711$	−26681.3	−	906.260i	−1.40735	−	0.0478023i
$712$	−883.268	+	23059.9i	−0.0464914	+	1.21378i
$713$	−1299.68	+	750.372i	−0.0682658	+	0.0394133i
$714$	3034.13	+	3220.18i	0.159033	+	0.168784i
$715$	−27906.5	−	16111.9i	−1.45964	−	0.842726i
$716$	−9813.44	+	16037.7i	−0.512215	+	0.837092i
$717$	20766.2	+	21483.5i	1.08163	+	1.11899i
$718$	−6208.25	−	11077.1i	−0.322688	−	0.575757i
$719$	−7178.86			−0.372359			−0.186180	−	0.982516i	$-0.559611\pi$
$719$	−7178.86			−0.372359			−0.186180	+	0.982516i	$0.559611\pi$
$720$	−16712.1	+	23982.8i	−0.865030	+	1.24137i
$721$	6165.33			0.318459
$722$	−4009.69	−	7154.30i	−0.206683	−	0.368775i
$723$	30336.1	−	7579.01i	1.56046	−	0.389857i
$724$	9520.74	−	15559.4i	0.488723	−	0.798701i
$725$	17025.7	+	9829.77i	0.872161	+	0.503543i
$726$	−4996.39	+	16649.8i	−0.255418	+	0.851144i
$727$	18250.7	−	10537.0i	0.931061	−	0.537548i	0.0439138	−	0.999035i	$-0.486017\pi$
$727$	18250.7	−	10537.0i	0.931061	−	0.537548i	0.887147	+	0.461487i	$0.152684\pi$
$728$	117.392	−	3064.81i	0.00597641	−	0.156029i
$729$	2001.43	−	19581.0i	0.101683	−	0.994817i
$730$	61.3537	−	4807.47i	0.00311069	−	0.243743i
$731$	−5515.17	−	9552.55i	−0.279050	−	0.483330i
$732$	−1243.44	+	3959.35i	−0.0627855	+	0.199920i
$733$	−10114.0	+	17518.0i	−0.509645	+	0.882730i	0.490293	+	0.871558i	$0.336890\pi$
$733$	−10114.0	+	17518.0i	−0.509645	+	0.882730i	−0.999938	+	0.0111727i	$0.996444\pi$
$734$	2108.32	+	1253.38i	0.106021	+	0.0630288i
$735$	−7036.60	−	28165.1i	−0.353128	−	1.41345i
$736$	6041.83	+	12201.1i	0.302588	+	0.611056i
$737$		−	31069.9i		−	1.55288i
$738$	−14238.5	+	22198.7i	−0.710199	+	1.10725i
$739$			8782.55i			0.437173i	0.975818	+	0.218587i	$0.0701447\pi$
$739$			8782.55i			0.437173i	−0.975818	+	0.218587i	$0.929855\pi$
$740$	−2111.71	+	1148.36i	−0.104903	+	0.0570467i
$741$	−8931.77	+	8633.54i	−0.442803	+	0.428018i
$742$	2472.36	−	4158.76i	0.122322	−	0.205759i
$743$	11676.8	−	20224.8i	0.576553	−	0.998620i	−0.419318	−	0.907840i	$-0.637731\pi$
$743$	11676.8	−	20224.8i	0.576553	−	0.998620i	0.995871	−	0.0907800i	$-0.0289360\pi$
$744$	1747.97	−	1564.72i	0.0861339	−	0.0771040i
$745$	−3439.02	−	5956.56i	−0.169122	−	0.292928i
$746$	−12272.0	−	156.617i	−0.602291	−	0.00768654i
$747$	461.497	−	13586.9i	0.0226041	−	0.665489i
$748$	−863.747	+	33834.7i	−0.0422216	+	1.65390i
$749$	−195.145	+	112.667i	−0.00951995	+	0.00549634i
$750$	2067.57	+	8749.06i	0.100662	+	0.425961i
$751$	14625.3	+	8443.94i	0.710634	+	0.410285i	0.811296	−	0.584636i	$-0.198763\pi$
$751$	14625.3	+	8443.94i	0.710634	+	0.410285i	−0.100662	+	0.994921i	$0.532096\pi$
$752$	−10650.4	+	16447.4i	−0.516462	+	0.797574i
$753$	4586.00	−	16022.1i	0.221943	−	0.775403i
$754$	11435.4	−	6409.06i	0.552324	−	0.309555i
$755$	−58407.6			−2.81546
$756$	−2606.87	−	3039.38i	−0.125411	−	0.146219i
$757$	6838.01			0.328311			0.164156	−	0.986434i	$-0.447510\pi$
$757$	6838.01			0.328311			0.164156	+	0.986434i	$0.447510\pi$
$758$	−34781.8	+	19493.7i	−1.66666	+	0.934095i
$759$	−5392.07	+	18838.3i	−0.257865	+	0.900904i
$760$	12832.2	−	20382.4i	0.612466	−	0.972824i
$761$	−20503.9	−	11837.9i	−0.976696	−	0.563896i	−0.0754248	−	0.997151i	$-0.524031\pi$
$761$	−20503.9	−	11837.9i	−0.976696	−	0.563896i	−0.901271	+	0.433256i	$0.857365\pi$
$762$	2685.54	+	11364.0i	0.127673	+	0.540257i
$763$	2581.02	−	1490.15i	0.122463	−	0.0707039i
$764$	31453.4	+	802.957i	1.48945	+	0.0380235i
$765$	−34012.0	+	18126.1i	−1.60746	+	0.856669i
$766$	23386.1	+	298.457i	1.10310	+	0.0140779i
$767$	−9337.76	−	16173.5i	−0.439592	−	0.761396i
$768$	−13155.4	−	16730.8i	−0.618105	−	0.786095i
$769$	−18418.7	+	31902.0i	−0.863711	+	1.49599i	0.00461075	+	0.999989i	$0.498532\pi$
$769$	−18418.7	+	31902.0i	−0.863711	+	1.49599i	−0.868322	+	0.496002i	$0.834801\pi$
$770$	−4373.44	+	7356.59i	−0.204686	+	0.344303i
$771$	10863.9	−	10501.2i	0.507464	−	0.490520i
$772$	−10369.5	−	19068.4i	−0.483429	−	0.888972i
$773$		−	7505.51i		−	0.349230i	−0.984637	−	0.174615i	$-0.944132\pi$
$773$		−	7505.51i		−	0.349230i	0.984637	−	0.174615i	$-0.0558680\pi$
$774$	4582.19	+	8868.93i	0.212795	+	0.411869i
$775$		−	3215.66i		−	0.149045i
$776$	−10631.2	−	20158.3i	−0.491799	−	0.932525i
$777$	−79.8109	−	319.455i	−0.00368494	−	0.0147495i
$778$	−13960.9	−	8299.65i	−0.643345	−	0.382464i
$779$	10865.0	−	18818.8i	0.499717	−	0.865535i
$780$	25489.3	+	8004.99i	1.17008	+	0.367467i
$781$	6378.88	+	11048.5i	0.292259	+	0.506207i
$782$	−229.075	+	17949.6i	−0.0104753	+	0.820812i
$783$	5265.35	−	16284.3i	0.240317	−	0.743235i
$784$	21109.9	+	1078.51i	0.961638	+	0.0491303i
$785$	12900.3	−	7448.01i	0.586538	−	0.338638i
$786$	−938.119	+	3126.15i	−0.0425720	+	0.141865i
$787$	16864.0	+	9736.41i	0.763832	+	0.440998i	0.830670	−	0.556765i	$-0.187958\pi$
$787$	16864.0	+	9736.41i	0.763832	+	0.440998i	−0.0668382	+	0.997764i	$0.521291\pi$
$788$	13633.5	+	8342.29i	0.616335	+	0.377134i
$789$	1573.39	−	393.088i	0.0709940	−	0.0177367i
$790$	−23129.7	−	41269.2i	−1.04167	−	1.85860i
$791$	3674.28			0.165161
$792$	2210.79	−	30551.2i	0.0991882	−	1.37069i
$793$	3793.01			0.169853
$794$	−14512.1	−	25893.2i	−0.648633	−	1.15733i
$795$	29290.6	+	30302.4i	1.30670	+	1.35184i
$796$	16439.3	+	10059.2i	0.732005	+	0.447912i
$797$	−30984.0	−	17888.6i	−1.37705	−	0.795040i	−0.385247	−	0.922814i	$-0.625884\pi$
$797$	−30984.0	−	17888.6i	−1.37705	−	0.795040i	−0.991803	+	0.127773i	$0.959217\pi$
$798$	2262.56	+	2401.29i	0.100368	+	0.106522i
$799$	−22373.6	+	12917.4i	−0.990640	+	0.571947i
$800$	−29113.7	−	1860.20i	−1.28666	−	0.0822098i
$801$	14569.7	−	23366.0i	0.642692	−	1.03071i
$802$	−294.669	+	23089.3i	−0.0129740	+	1.01660i
$803$	2519.04	+	4363.11i	0.110704	+	0.191745i
$804$	5604.01	+	25143.1i	0.245819	+	1.10290i
$805$	−2269.60	+	3931.06i	−0.0993700	+	0.172114i
$806$	−1843.09	−	1095.71i	−0.0805462	−	0.0478841i
$807$	−9123.20	−	2611.33i	−0.397958	−	0.113907i
$808$	−8425.81	+	4443.64i	−0.366855	+	0.193474i
$809$			16519.8i			0.717932i	0.933351	+	0.358966i	$0.116871\pi$
$809$			16519.8i			0.717932i	−0.933351	+	0.358966i	$0.883129\pi$
$810$	31514.1	−	14949.2i	1.36703	−	0.648472i
$811$			18594.4i			0.805103i	0.915397	+	0.402552i	$0.131877\pi$
$811$			18594.4i			0.805103i	−0.915397	+	0.402552i	$0.868123\pi$
$812$	−1663.31	−	3058.64i	−0.0718852	−	0.132189i
$813$	−24914.1	−	7131.14i	−1.07475	−	0.307626i
$814$	1287.17	−	2165.15i	0.0554240	−	0.0932291i
$815$	−14324.3	+	24810.5i	−0.615656	+	1.06635i
$816$	−5403.71	−	27536.3i	−0.231823	−	1.18133i
$817$	−4112.67	−	7123.35i	−0.176113	−	0.305036i
$818$	11524.5	+	147.078i	0.492598	+	0.00628661i
$819$	−1936.41	+	3105.49i	−0.0826173	+	0.132496i
$820$	−46719.6	−	1192.68i	−1.98966	−	0.0507929i
$821$	35701.8	−	20612.4i	1.51766	−	0.876222i	0.517878	−	0.855455i	$-0.326722\pi$
$821$	35701.8	−	20612.4i	1.51766	−	0.876222i	0.999784	−	0.0207677i	$-0.00661104\pi$
$822$	13022.0	−	12269.6i	0.552547	−	0.520623i
$823$	3713.28	+	2143.86i	0.157274	+	0.0908025i	0.576572	−	0.817047i	$-0.304390\pi$
$823$	3713.28	+	2143.86i	0.157274	+	0.0908025i	−0.419297	+	0.907849i	$0.637723\pi$
$824$	−33091.1	−	20833.4i	−1.39901	−	0.880783i
$825$	−29180.2	−	30188.2i	−1.23143	−	1.27396i
$826$	−4326.87	+	2425.03i	−0.182265	+	0.102152i
$827$	24944.4			1.04885			0.524426	−	0.851456i	$-0.324280\pi$
$827$	24944.4			1.04885			0.524426	+	0.851456i	$0.324280\pi$
$828$	965.683	−	16217.3i	0.0405311	−	0.680666i
$829$	−31040.8			−1.30047			−0.650235	−	0.759733i	$-0.725330\pi$
$829$	−31040.8			−1.30047			−0.650235	+	0.759733i	$0.725330\pi$
$830$	21015.6	−	11778.4i	0.878869	−	0.492570i
$831$	21434.4	−	5355.05i	0.894767	−	0.223544i
$832$	−10986.4	+	16053.1i	−0.457796	+	0.668918i
$833$	24135.3	+	13934.5i	1.00389	+	0.579594i
$834$	31031.2	+	9312.08i	1.28839	+	0.386632i
$835$	−24027.4	+	13872.2i	−0.995810	+	0.574931i
$836$	−644.098	+	25230.6i	−0.0266466	+	1.04380i
$837$	−2737.35	+	585.934i	−0.113042	+	0.0241969i
$838$	−1960.15	−	25.0157i	−0.0808021	−	0.00103121i
$839$	6393.60	+	11074.0i	0.263089	+	0.455683i	0.967061	−	0.254544i	$-0.0819254\pi$
$839$	6393.60	+	11074.0i	0.263089	+	0.455683i	−0.703972	+	0.710228i	$0.748592\pi$
$840$	2212.29	−	6742.12i	0.0908706	−	0.276935i
$841$	−4754.02	+	8234.20i	−0.194925	+	0.337619i
$842$	15502.0	−	26076.0i	0.634481	−	1.06727i
$843$	−3696.37	−	14795.3i	−0.151020	−	0.604479i
$844$	12787.0	−	6953.67i	0.521502	−	0.283596i
$845$			12746.6i			0.518929i
$846$	20772.5	−	10732.2i	0.844175	−	0.436149i
$847$		−	4219.73i		−	0.171183i
$848$	−27322.8	+	13966.9i	−1.10645	+	0.565597i
$849$	−14957.8	+	14458.4i	−0.604655	+	0.584466i
$850$	−33062.5	−	19655.4i	−1.33416	−	0.793147i
$851$	667.975	−	1156.97i	0.0269070	−	0.0466044i
$852$	−7154.88	−	7790.43i	−0.287702	−	0.313258i
$853$	23491.5	+	40688.4i	0.942946	+	1.63323i	0.759813	+	0.650141i	$0.225290\pi$
$853$	23491.5	+	40688.4i	0.942946	+	1.63323i	0.183132	+	0.983088i	$0.441376\pi$
$854$	12.8556	−	1007.32i	0.000515115	−	0.0403627i
$855$	−25362.8	+	13516.7i	−1.01449	+	0.540656i
$856$	1428.12	+	54.7013i	0.0570234	+	0.00218417i
$857$	39991.4	−	23089.0i	1.59402	−	0.920310i	0.601418	−	0.798935i	$-0.294603\pi$
$857$	39991.4	−	23089.0i	1.59402	−	0.920310i	0.992607	−	0.121375i	$-0.0387305\pi$
$858$	−27245.7	+	6438.66i	−1.08409	+	0.256191i
$859$	−5670.77	−	3274.02i	−0.225244	−	0.130045i	0.383132	−	0.923694i	$-0.374845\pi$
$859$	−5670.77	−	3274.02i	−0.225244	−	0.130045i	−0.608376	+	0.793649i	$0.708179\pi$
$860$	−9233.22	+	15089.5i	−0.366105	+	0.598311i
$861$	1761.66	−	6154.72i	0.0697298	−	0.243615i
$862$	13847.5	+	24707.5i	0.547156	+	0.976264i
$863$	−29442.2			−1.16133			−0.580663	−	0.814144i	$-0.697207\pi$
$863$	−29442.2			−1.16133			−0.580663	+	0.814144i	$0.697207\pi$
$864$	3721.39	+	25122.2i	0.146533	+	0.989206i
$865$	36901.5			1.45051
$866$	13449.5	+	23997.4i	0.527752	+	0.941644i
$867$	3156.17	−	11026.7i	0.123632	−	0.431934i
$868$	−297.236	+	485.761i	−0.0116231	+	0.0189952i
$869$	42932.6	+	24787.2i	1.67594	+	0.967603i
$870$	29515.3	−	6975.01i	1.15019	−	0.271810i
$871$	20389.8	−	11772.1i	0.793206	−	0.457958i
$872$	−18888.5	−	723.488i	−0.733538	−	0.0280968i
$873$	−923.138	+	27178.1i	−0.0357886	+	1.05365i
$874$	−170.822	+	13385.0i	−0.00661113	+	0.518026i
$875$	−1091.15	−	1889.93i	−0.0421573	−	0.0730186i
$876$	−2825.49	−	3076.47i	−0.108978	−	0.118658i
$877$	16384.3	−	28378.4i	0.630853	−	1.09267i	−0.356525	−	0.934286i	$-0.616039\pi$
$877$	16384.3	−	28378.4i	0.630853	−	1.09267i	0.987378	−	0.158383i	$-0.0506282\pi$
$878$	−15934.4	−	9472.89i	−0.612483	−	0.364117i
$879$	−10070.1	+	9733.88i	−0.386413	+	0.373510i
$880$	48332.4	−	24706.6i	1.85146	−	0.946432i
$881$			15082.2i			0.576769i	0.957515	+	0.288384i	$0.0931181\pi$
$881$			15082.2i			0.576769i	−0.957515	+	0.288384i	$0.906882\pi$
$882$	−21230.2	−	13617.3i	−0.810497	−	0.519861i
$883$		−	425.340i		−	0.0162105i	−0.999967	−	0.00810523i	$-0.997420\pi$
$883$		−	425.340i		−	0.0162105i	0.999967	−	0.00810523i	$-0.00258000\pi$
$884$	−22531.5	+	12252.8i	−0.857258	+	0.466183i
$885$	−10472.7	−	41918.4i	−0.397779	−	1.59217i
$886$	8497.56	−	14293.8i	0.322214	−	0.541997i
$887$	−6078.41	+	10528.1i	−0.230094	+	0.398534i	−0.957835	−	0.287317i	$-0.907237\pi$
$887$	−6078.41	+	10528.1i	−0.230094	+	0.398534i	0.727742	+	0.685851i	$0.240570\pi$
$888$	−651.109	+	1984.30i	−0.0246056	+	0.0749874i
$889$	−1417.28	−	2454.80i	−0.0534692	−	0.0926114i
$890$	48792.8	+	622.702i	1.83768	+	0.0234528i
$891$	−20380.9	+	30340.5i	−0.766313	+	1.14079i
$892$	546.017	−	21388.5i	0.0204955	−	0.802849i
$893$	−16684.0	+	9632.54i	−0.625207	+	0.360964i
$894$	−5723.53	−	1717.56i	−0.214120	−	0.0642548i
$895$	34430.8	+	19878.7i	1.28592	+	0.742425i
$896$	4226.01	+	2972.10i	0.157568	+	0.110816i
$897$	−14405.7	+	3599.05i	−0.536225	+	0.133967i
$898$	16681.7	−	9349.38i	0.619905	−	0.347431i
$899$	−2434.04			−0.0903001
$900$	29059.0	+	19166.5i	1.07626	+	0.709870i
$901$	−40458.1			−1.49595
$902$	42720.7	−	23943.2i	1.57699	−	0.883836i
$903$	−1684.17	−	1742.35i	−0.0620662	−	0.0642101i
$904$	−19721.0	−	12415.8i	−0.725564	−	0.456798i
$905$	−33403.9	−	19285.7i	−1.22694	−	0.708375i
$906$	−36933.0	+	34799.2i	−1.35432	+	1.27608i
$907$	−39674.6	+	22906.2i	−1.45245	+	0.838574i	−0.998620	−	0.0525131i	$-0.983277\pi$
$907$	−39674.6	+	22906.2i	−1.45245	+	0.838574i	−0.453832	+	0.891087i	$0.649944\pi$
$908$	−47177.9	−	1204.38i	−1.72429	−	0.0440185i
$909$	11360.0	+	385.856i	0.414508	+	0.0140792i
$910$	−6484.87	−	82.7609i	−0.236232	−	0.00301483i
$911$	14411.9	+	24962.1i	0.524134	+	0.907827i	0.999605	+	0.0280960i	$0.00894440\pi$
$911$	14411.9	+	24962.1i	0.524134	+	0.907827i	−0.475471	+	0.879732i	$0.657722\pi$
$912$	−4029.56	−	20533.9i	−0.146307	−	0.745553i
$913$	−12622.4	+	21862.7i	−0.457547	+	0.792495i
$914$	22027.7	−	37052.9i	0.797168	−	1.34092i
$915$	8436.54	+	2414.79i	0.304813	+	0.0872464i
$916$	−11590.8	−	21314.3i	−0.418092	−	0.768824i
$917$		−	792.293i		−	0.0285320i
$918$	−10707.4	+	31726.1i	−0.384963	+	1.14065i
$919$		−	41488.4i		−	1.48920i	−0.667511	−	0.744600i	$-0.732640\pi$
$919$		−	41488.4i		−	1.48920i	0.667511	−	0.744600i	$-0.267360\pi$
$920$	25465.1	−	13429.9i	0.912566	−	0.481273i
$921$	22855.4	+	6541.89i	0.817710	+	0.234053i
$922$	−33408.6	−	19861.2i	−1.19333	−	0.709428i
$923$	−4833.79	+	8372.36i	−0.172379	+	0.298570i
$924$	1617.59	+	7257.51i	0.0575916	+	0.258392i
$925$	1431.28	+	2479.04i	0.0508758	+	0.0881194i
$926$	−637.321	+	49938.4i	−0.0226174	+	1.77222i
$927$	21944.6	+	41177.0i	0.777513	+	1.45893i
$928$	−1408.04	+	22037.2i	−0.0498075	+	0.779532i
$929$	3659.97	−	2113.09i	0.129257	−	0.0746266i	−0.433977	−	0.900924i	$-0.642890\pi$
$929$	3659.97	−	2113.09i	0.129257	−	0.0746266i	0.563234	+	0.826297i	$0.309557\pi$
$930$	−3401.90	−	3610.50i	−0.119949	−	0.127304i
$931$	17997.7	+	10391.0i	0.633567	+	0.365790i
$932$	8830.95	+	5403.64i	0.310373	+	0.189916i
$933$	29753.5	+	30781.2i	1.04403	+	1.08010i
$934$	8525.38	+	15211.4i	0.298671	+	0.532905i
$935$	71567.8			2.50323
$936$	20887.1	−	10124.7i	0.729397	−	0.353564i
$937$	31514.2			1.09875			0.549373	−	0.835577i	$-0.314867\pi$
$937$	31514.2			1.09875			0.549373	+	0.835577i	$0.314867\pi$
$938$	−3057.22	−	5454.86i	−0.106420	−	0.189880i
$939$	−26818.3	+	6700.12i	−0.932035	+	0.232854i
$940$	35342.0	+	21625.7i	1.22631	+	0.750374i
$941$	−23040.3	−	13302.3i	−0.798185	−	0.460832i	0.0446514	−	0.999003i	$-0.485782\pi$
$941$	−23040.3	−	13302.3i	−0.798185	−	0.460832i	−0.842836	+	0.538171i	$0.819116\pi$
$942$	3719.78	−	12395.6i	0.128659	−	0.428738i
$943$	22494.2	−	12987.0i	0.776790	−	0.448480i
$944$	31418.1	+	1605.16i	1.08323	+	0.0553426i
$945$	−6284.11	+	5674.53i	−0.216320	+	0.195336i
$946$	236.558	−	18535.9i	0.00813018	−	0.637054i
$947$	−25814.6	−	44712.3i	−0.885811	−	1.53427i	−0.844781	−	0.535112i	$-0.820269\pi$
$947$	−25814.6	−	44712.3i	−0.885811	−	1.53427i	−0.0410299	−	0.999158i	$-0.513064\pi$
$948$	−39213.8	−	12315.2i	−1.34347	−	0.421919i
$949$	−1908.88	+	3306.28i	−0.0652950	+	0.113094i
$950$	−24654.8	−	14657.1i	−0.842006	−	0.500567i
$951$	−11112.9	−	44480.9i	−0.378927	−	1.51671i
$952$	3177.63	+	6025.26i	0.108180	+	0.205126i
$953$		−	25766.7i		−	0.875829i	−0.899017	−	0.437915i	$-0.855717\pi$
$953$		−	25766.7i		−	0.875829i	0.899017	−	0.437915i	$-0.144283\pi$
$954$	36575.5	+	1709.86i	1.24128	+	0.0580279i
$955$		−	66530.9i		−	2.25433i
$956$	21976.9	+	40413.2i	0.743499	+	1.36721i
$957$	−22850.5	+	22087.5i	−0.771840	+	0.746069i
$958$	25030.9	−	42104.6i	0.844166	−	1.41998i
$959$	−2171.58	+	3761.29i	−0.0731220	+	0.126651i
$960$	−34656.4	+	28711.3i	−1.16514	+	0.965265i
$961$	−14696.4	−	25455.0i	−0.493318	−	0.854452i
$962$	1908.59	+	24.3577i	0.0639661	+	0.000816346i
$963$	−1447.07	−	902.312i	−0.0484228	−	0.0301938i
$964$	48125.4	+	1228.57i	1.60790	+	0.0410472i
$965$	−39748.1	+	22948.6i	−1.32594	+	0.765534i
$966$	906.983	+	3837.96i	0.0302088	+	0.127831i
$967$	−39828.3	−	22994.9i	−1.32450	−	0.764700i	−0.340056	−	0.940405i	$-0.610446\pi$
$967$	−39828.3	−	22994.9i	−1.32450	−	0.764700i	−0.984443	+	0.175705i	$0.943779\pi$
$968$	−14259.0	+	22648.5i	−0.473451	+	0.752016i
$969$	7592.09	−	26524.5i	0.251696	−	0.879349i
$970$	−42037.7	+	23560.4i	−1.39150	+	0.779876i
$971$	22109.4			0.730714			0.365357	−	0.930867i	$-0.380947\pi$
$971$	22109.4			0.730714			0.365357	+	0.930867i	$0.380947\pi$
$972$	11020.7	−	28229.0i	0.363670	−	0.931528i
$973$	−7864.57			−0.259123
$974$	−18140.2	+	10166.8i	−0.596765	+	0.334462i
$975$	8755.12	−	30587.7i	0.287578	−	1.00471i
$976$	−3472.85	+	5363.13i	−0.113897	+	0.175891i
$977$	−43850.9	−	25317.3i	−1.43594	−	0.829040i	−0.438375	−	0.898792i	$-0.644446\pi$
$977$	−43850.9	−	25317.3i	−1.43594	−	0.829040i	−0.997564	+	0.0697519i	$0.977779\pi$
$978$	5724.33	+	24222.9i	0.187162	+	0.791988i
$979$	−44282.9	+	25566.8i	−1.44565	+	0.834645i
$980$	1140.64	−	44681.2i	0.0371801	−	1.45642i
$981$	19139.2	+	11934.1i	0.622902	+	0.388407i
$982$	−23877.2	−	304.724i	−0.775918	−	0.00990239i
$983$	6989.79	+	12106.7i	0.226795	+	0.392821i	0.956856	−	0.290561i	$-0.0938419\pi$
$983$	6989.79	+	12106.7i	0.226795	+	0.392821i	−0.730061	+	0.683382i	$0.760509\pi$
$984$	−30252.9	+	27081.3i	−0.980110	+	0.877359i
$985$	16898.6	−	29269.2i	0.546633	−	0.946797i
$986$	−14877.8	+	25026.1i	−0.480535	+	0.808310i
$987$	−4080.86	+	3944.60i	−0.131606	+	0.127212i
$988$	−16801.8	+	9136.91i	−0.541028	+	0.294215i
$989$		−	9831.82i		−	0.316111i
$990$	−64699.8	−	3024.63i	−2.07707	−	0.0971000i
$991$		−	29526.4i		−	0.946456i	−0.880940	−	0.473228i	$-0.843089\pi$
$991$		−	29526.4i		−	0.946456i	0.880940	−	0.473228i	$-0.156911\pi$
$992$	3236.80	−	1602.83i	0.103597	−	0.0513002i
$993$	−2990.39	−	11969.5i	−0.0955661	−	0.382518i
$994$	2207.08	+	1312.10i	0.0704270	+	0.0418683i
$995$	20376.4	−	35293.0i	0.649222	−	1.12448i
$996$	6271.30	−	19968.9i	0.199512	−	0.635281i
$997$	−2513.86	−	4354.14i	−0.0798545	−	0.138312i	0.823333	−	0.567559i	$-0.192112\pi$
$997$	−2513.86	−	4354.14i	−0.0798545	−	0.138312i	−0.903187	+	0.429247i	$0.858779\pi$
$998$	272.669	−	21365.4i	0.00864849	−	0.677667i
$999$	1849.50	−	1670.10i	0.0585742	−	0.0528924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.23.5	yes	24
3.2	odd	2		108.4.h.b.71.8		24
4.3	odd	2	inner	36.4.h.b.23.9	yes	24
9.2	odd	6	inner	36.4.h.b.11.9	yes	24
9.4	even	3		324.4.b.c.323.24		24
9.5	odd	6		324.4.b.c.323.1		24
9.7	even	3		108.4.h.b.35.4		24
12.11	even	2		108.4.h.b.71.4		24
36.7	odd	6		108.4.h.b.35.8		24
36.11	even	6	inner	36.4.h.b.11.5	✓	24
36.23	even	6		324.4.b.c.323.23		24
36.31	odd	6		324.4.b.c.323.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.5	✓	24	36.11	even	6	inner
36.4.h.b.11.9	yes	24	9.2	odd	6	inner
36.4.h.b.23.5	yes	24	1.1	even	1	trivial
36.4.h.b.23.9	yes	24	4.3	odd	2	inner
108.4.h.b.35.4		24	9.7	even	3
108.4.h.b.35.8		24	36.7	odd	6
108.4.h.b.71.4		24	12.11	even	2
108.4.h.b.71.8		24	3.2	odd	2
324.4.b.c.323.1		24	9.5	odd	6
324.4.b.c.323.2		24	36.31	odd	6
324.4.b.c.323.23		24	36.23	even	6
324.4.b.c.323.24		24	9.4	even	3

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38284 - 2.46734i) q^{2} +(-1.42987 + 4.99554i) q^{3} +(-4.17551 + 6.82387i) q^{4} +(14.6499 + 8.45813i) q^{5} +(14.3030 - 3.38006i) q^{6} +(-3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +(-22.9109 - 14.2860i) q^{9} +O(q^{10})\)	\(q+(-1.38284 - 2.46734i) q^{2} +(-1.42987 + 4.99554i) q^{3} +(-4.17551 + 6.82387i) q^{4} +(14.6499 + 8.45813i) q^{5} +(14.3030 - 3.38006i) q^{6} +(-3.08966 + 1.78382i) q^{7} +(22.6108 + 0.866066i) q^{8} +(-22.9109 - 14.2860i) q^{9} +(0.610574 - 47.8425i) q^{10} +(25.0688 + 43.4205i) q^{11} +(-28.1185 - 30.6162i) q^{12} +(-18.9966 + 32.9032i) q^{13} +(8.67378 + 5.15650i) q^{14} +(-63.2005 + 61.0903i) q^{15} +(-29.1303 - 56.9862i) q^{16} -84.3819i q^{17} +(-3.56618 + 76.2842i) q^{18} -62.9237i q^{19} +(-118.888 + 64.6521i) q^{20} +(-4.49331 - 17.9852i) q^{21} +(72.4668 - 121.897i) q^{22} +(37.6066 - 65.1366i) q^{23} +(-36.6571 + 111.715i) q^{24} +(80.5801 + 139.569i) q^{25} +(107.453 + 1.37133i) q^{26} +(104.126 - 94.0254i) q^{27} +(0.728372 - 28.5317i) q^{28} +(105.644 - 60.9938i) q^{29} +(238.126 + 71.4589i) q^{30} +(-17.2800 - 9.97659i) q^{31} +(-100.322 + 150.677i) q^{32} +(-252.754 + 63.1467i) q^{33} +(-208.199 + 116.687i) q^{34} -60.3510 q^{35} +(193.150 - 96.6899i) q^{36} +17.7622 q^{37} +(-155.254 + 87.0135i) q^{38} +(-137.206 - 141.946i) q^{39} +(323.922 + 203.933i) q^{40} +(299.072 + 172.670i) q^{41} +(-38.1619 + 35.9571i) q^{42} +(113.206 - 65.3596i) q^{43} +(-400.970 - 10.2362i) q^{44} +(-214.811 - 403.072i) q^{45} +(-212.718 - 2.71474i) q^{46} +(-153.083 - 265.147i) q^{47} +(326.330 - 64.0387i) q^{48} +(-165.136 + 286.024i) q^{49} +(232.934 - 391.820i) q^{50} +(421.534 + 120.655i) q^{51} +(-145.206 - 267.018i) q^{52} -479.464i q^{53} +(-375.982 - 126.892i) q^{54} +848.142i q^{55} +(-71.4047 + 37.6577i) q^{56} +(314.338 + 89.9729i) q^{57} +(-296.581 - 176.316i) q^{58} +(-245.774 + 425.693i) q^{59} +(-152.978 - 686.355i) q^{60} +(-49.9168 - 86.4585i) q^{61} +(-0.720188 + 56.4315i) q^{62} +(96.2705 + 3.26994i) q^{63} +(510.500 + 39.1649i) q^{64} +(-556.599 + 321.352i) q^{65} +(505.323 + 536.308i) q^{66} +(-536.669 - 309.846i) q^{67} +(575.811 + 352.337i) q^{68} +(271.620 + 281.003i) q^{69} +(83.4558 + 148.906i) q^{70} +254.455 q^{71} +(-505.663 - 342.860i) q^{72} +100.485 q^{73} +(-24.5622 - 43.8253i) q^{74} +(-812.441 + 202.976i) q^{75} +(429.383 + 262.738i) q^{76} +(-154.908 - 89.4363i) q^{77} +(-160.494 + 534.823i) q^{78} +(856.295 - 494.382i) q^{79} +(55.2404 - 1081.23i) q^{80} +(320.821 + 654.610i) q^{81} +(12.4646 - 976.687i) q^{82} +(251.755 + 436.053i) q^{83} +(141.490 + 44.4354i) q^{84} +(713.714 - 1236.19i) q^{85} +(-317.810 - 188.936i) q^{86} +(153.639 + 614.964i) q^{87} +(529.222 + 1003.48i) q^{88} +1019.86i q^{89} +(-697.466 + 1087.39i) q^{90} -135.546i q^{91} +(287.457 + 528.601i) q^{92} +(74.5466 - 72.0576i) q^{93} +(-442.518 + 744.363i) q^{94} +(532.217 - 921.828i) q^{95} +(-609.267 - 716.610i) q^{96} +(-503.589 - 872.242i) q^{97} +(934.074 + 11.9208i) q^{98} +(45.9541 - 1352.94i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

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