LMFDB - Embedded newform 36.4.h.b.11.5

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			11.5
Character	$\chi$	$=$	36.11
Dual form			36.4.h.b.23.5

$q$-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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

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

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	0.328178	−	0.944616i	$-0.393565\pi$
$5$	14.6499	−	8.45813i	1.31033	−	0.756519i	0.982150	+	0.188097i	$0.0602320\pi$
$6$	14.3030	+	3.38006i	0.973194	+	0.229984i
$7$	−3.08966	−	1.78382i	−0.166826	−	0.0963170i	0.414262	−	0.910157i	$-0.364040\pi$
$7$	−3.08966	−	1.78382i	−0.166826	−	0.0963170i	−0.581088	+	0.813841i	$0.697373\pi$
$8$	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	−0.285620	−	0.958343i	$-0.592199\pi$
$11$	25.0688	−	43.4205i	0.687139	−	1.19016i	0.972759	−	0.231817i	$-0.0744672\pi$
$12$	−28.1185	+	30.6162i	−0.676426	+	0.736511i
$13$	−18.9966	−	32.9032i	−0.405286	−	0.701977i	0.589068	−	0.808083i	$-0.299495\pi$
$13$	−18.9966	−	32.9032i	−0.405286	−	0.701977i	−0.994355	+	0.106107i	$0.966162\pi$
$14$	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	$0.205601\pi$
$17$			84.3819i			1.20386i	−0.798549	+	0.601930i	$0.794399\pi$
$18$	−3.56618	−	76.2842i	−0.0466976	−	0.998909i
$19$			62.9237i			0.759773i	0.925033	+	0.379887i	$0.124037\pi$
$19$			62.9237i			0.759773i	−0.925033	+	0.379887i	$0.875963\pi$
$20$	−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	0.984607	−	0.174784i	$-0.0559227\pi$
$23$	37.6066	+	65.1366i	0.340936	+	0.590518i	−0.643671	+	0.765302i	$0.722589\pi$
$24$	−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	0.798524	−	0.601963i	$-0.205614\pi$
$29$	105.644	+	60.9938i	0.676471	+	0.390561i	−0.122053	+	0.992524i	$0.538948\pi$
$30$	238.126	−	71.4589i	1.44919	−	0.434885i
$31$	−17.2800	+	9.97659i	−0.100115	+	0.0578016i	−0.549222	−	0.835677i	$-0.685076\pi$
$31$	−17.2800	+	9.97659i	−0.100115	+	0.0578016i	0.449106	+	0.893478i	$0.351742\pi$
$32$	−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	0.192969	−	0.981205i	$-0.438188\pi$
$41$	299.072	−	172.670i	1.13920	−	0.657718i	0.946233	+	0.323486i	$0.104855\pi$
$42$	−38.1619	−	35.9571i	−0.140203	−	0.132102i
$43$	113.206	+	65.3596i	0.401483	+	0.231796i	0.687124	−	0.726540i	$-0.258873\pi$
$43$	113.206	+	65.3596i	0.401483	+	0.231796i	−0.285641	+	0.958337i	$0.592206\pi$
$44$	−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	−0.999593	−	0.0285243i	$-0.990919\pi$
$47$	−153.083	+	265.147i	−0.475094	+	0.822887i	0.524499	+	0.851411i	$0.324253\pi$
$48$	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	$0.213401\pi$
$53$			479.464i			1.24263i	−0.783561	+	0.621315i	$0.786599\pi$
$54$	−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	−0.998770	−	0.0495801i	$-0.984212\pi$
$59$	−245.774	−	425.693i	−0.542323	−	0.939330i	0.456447	−	0.889750i	$-0.349122\pi$
$60$	−152.978	+	686.355i	−0.329156	+	1.47680i
$61$	−49.9168	+	86.4585i	−0.104774	+	0.181473i	−0.913646	−	0.406511i	$-0.866745\pi$
$61$	−49.9168	+	86.4585i	−0.104774	+	0.181473i	0.808872	+	0.587985i	$0.200079\pi$
$62$	−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	−0.901839	−	0.432071i	$-0.857783\pi$
$67$	−536.669	+	309.846i	−0.978575	+	0.564980i	−0.0767351	+	0.997052i	$0.524450\pi$
$68$	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	0.964812	−	0.262942i	$-0.0846928\pi$
$79$	856.295	+	494.382i	1.21950	+	0.704080i	0.254691	+	0.967022i	$0.418026\pi$
$80$	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	−0.650150	−	0.759806i	$-0.725294\pi$
$83$	251.755	−	436.053i	0.332936	−	0.576663i	0.983086	+	0.183143i	$0.0586272\pi$
$84$	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	$-0.792239\pi$
$89$		−	1019.86i		−	1.21467i	0.794448	−	0.607333i	$-0.207761\pi$
$90$	−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	0.472369	+	0.881401i	$0.343399\pi$
$97$	−503.589	+	872.242i	−0.527131	+	0.913018i	−0.999500	+	0.0316171i	$0.989934\pi$
$98$	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	0.309540	−	0.950886i	$-0.399825\pi$
$101$	−364.582	−	210.492i	−0.359181	−	0.207373i	−0.668721	+	0.743513i	$0.733158\pi$
$102$	−285.216	+	1206.91i	−0.276869	+	1.17159i
$103$	−1496.60	+	864.065i	−1.43170	+	0.826591i	−0.997250	−	0.0741066i	$-0.976389\pi$
$103$	−1496.60	+	864.065i	−1.43170	+	0.826591i	−0.434447	+	0.900697i	$0.643056\pi$
$104$	−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	−0.822983	−	0.568065i	$-0.807692\pi$
$113$	−891.915	+	514.947i	−0.742516	+	0.428692i	0.0804674	+	0.996757i	$0.474359\pi$
$114$	−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	$-0.910471\pi$
$127$		−	794.523i		−	0.555138i	0.960706	−	0.277569i	$-0.0895287\pi$
$128$	−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	0.826619	−	0.562763i	$-0.190262\pi$
$131$	−111.039	−	192.325i	−0.0740575	−	0.128271i	−0.900676	+	0.434491i	$0.856928\pi$
$132$	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	0.791312	−	0.611412i	$-0.209398\pi$
$137$	1054.28	+	608.690i	0.657470	+	0.379591i	−0.133842	+	0.991003i	$0.542732\pi$
$138$	317.721	+	1058.76i	0.195987	+	0.653099i
$139$	1909.09	−	1102.21i	1.16494	−	0.672578i	0.212457	−	0.977170i	$-0.431854\pi$
$139$	1909.09	−	1102.21i	1.16494	−	0.672578i	0.952483	+	0.304592i	$0.0985202\pi$
$140$	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	−0.593668	−	0.804710i	$-0.702321\pi$
$149$	−352.120	+	203.297i	−0.193603	+	0.111777i	0.400065	+	0.916487i	$0.368987\pi$
$150$	1624.29	−	1723.88i	0.884149	−	0.938363i
$151$	−2990.17	−	1726.37i	−1.61150	−	0.930399i	−0.989023	−	0.147759i	$-0.952794\pi$
$151$	−2990.17	−	1726.37i	−1.61150	−	0.930399i	−0.622475	−	0.782640i	$-0.713873\pi$
$152$	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	0.955963	−	0.293488i	$-0.0948160\pi$
$157$	440.287	+	762.599i	0.223813	+	0.387656i	−0.732149	+	0.681144i	$0.761483\pi$
$158$	−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	$-0.866609\pi$
$163$		−	1693.56i		−	0.813802i	0.913472	−	0.406901i	$-0.133391\pi$
$164$	−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	0.611075	−	0.791573i	$-0.290737\pi$
$167$	−820.051	−	1420.37i	−0.379985	−	0.658153i	−0.991060	+	0.133420i	$0.957404\pi$
$168$	−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	0.853933	−	0.520383i	$-0.174211\pi$
$173$	1889.17	+	1090.71i	0.830234	+	0.479336i	−0.0236985	+	0.999719i	$0.507544\pi$
$174$	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	0.205239	+	0.978712i	$0.434203\pi$
$191$	−1966.48	+	3406.04i	−0.744970	+	1.29033i	−0.950209	+	0.311614i	$0.899130\pi$
$192$	−925.600	−	2494.22i	−0.347914	−	0.937527i
$193$	−1356.60	−	2349.69i	−0.505958	−	0.876346i	−0.999976	−	0.00689392i	$-0.997806\pi$
$193$	−1356.60	−	2349.69i	−0.505958	−	0.876346i	0.494018	−	0.869452i	$-0.335528\pi$
$194$	−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	$0.117661\pi$
$197$			1997.91i			0.722565i	−0.932456	+	0.361282i	$0.882339\pi$
$198$	−3401.70	−	1757.51i	−1.22095	−	0.630812i
$199$			2409.09i			0.858170i	0.903264	+	0.429085i	$0.141164\pi$
$199$			2409.09i			0.858170i	−0.903264	+	0.429085i	$0.858836\pi$
$200$	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	−0.734515	−	0.678592i	$-0.762590\pi$
$211$	−1575.68	+	909.717i	−0.514095	+	0.296813i	0.220420	+	0.975405i	$0.429257\pi$
$212$	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	0.110160	−	0.993914i	$-0.464864\pi$
$223$	−2316.13	−	1337.22i	−0.695514	−	0.401555i	−0.805674	+	0.592359i	$0.798197\pi$
$224$	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	−0.00715576	−	0.999974i	$-0.502278\pi$
$227$	2949.58	−	5108.82i	0.862425	−	1.49376i	0.869581	−	0.493790i	$-0.164389\pi$
$228$	−1926.48	−	1769.32i	−0.559581	−	0.513930i
$229$	−1516.38	−	2626.44i	−0.437576	−	0.757904i	0.559926	−	0.828543i	$-0.310830\pi$
$229$	−1516.38	−	2626.44i	−0.437576	−	0.757904i	−0.997502	+	0.0706386i	$0.977496\pi$
$230$	−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	$0.0582356\pi$
$233$			1294.13i			0.363867i	−0.983311	+	0.181934i	$0.941764\pi$
$234$	−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	0.933008	+	0.359856i	$0.117174\pi$
$239$	2875.14	+	4979.89i	0.778149	+	1.34779i	−0.154859	+	0.987937i	$0.549492\pi$
$240$	5322.35	−	1821.98i	1.43148	−	0.490034i
$241$	−3008.82	+	5211.43i	−0.804212	+	1.39294i	0.112611	+	0.993639i	$0.464079\pi$
$241$	−3008.82	+	5211.43i	−0.804212	+	1.39294i	−0.916822	+	0.399296i	$0.869255\pi$
$242$	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	−0.773445	−	0.633863i	$-0.781468\pi$
$257$	−2518.27	+	1453.92i	−0.611226	+	0.352892i	0.162219	+	0.986755i	$0.448135\pi$
$258$	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	−0.883740	−	0.467979i	$-0.844982\pi$
$263$	−156.053	+	270.292i	−0.0365880	+	0.0633723i	0.847152	+	0.531351i	$0.178316\pi$
$264$	−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	$-0.933640\pi$
$269$		−	1826.27i		−	0.413939i	0.978347	−	0.206969i	$-0.0663600\pi$
$270$	−4434.84	+	5039.06i	−0.999614	+	1.13581i
$271$		−	4987.26i		−	1.11791i	−0.829197	−	0.558956i	$-0.811202\pi$
$271$		−	4987.26i		−	1.11791i	0.829197	−	0.558956i	$-0.188798\pi$
$272$	−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	−0.999018	−	0.0443112i	$-0.985891\pi$
$277$	−2125.92	+	3682.20i	−0.461134	+	0.798708i	0.537884	+	0.843019i	$0.319224\pi$
$278$	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	0.205326	−	0.978694i	$-0.434175\pi$
$281$	−2541.67	−	1467.43i	−0.539585	−	0.311529i	−0.744911	+	0.667164i	$0.767508\pi$
$282$	−3085.75	+	3274.96i	−0.651609	+	0.691565i
$283$	3467.24	−	2001.81i	0.728289	−	0.420478i	−0.0895066	−	0.995986i	$-0.528529\pi$
$283$	3467.24	−	2001.81i	0.728289	−	0.420478i	0.817796	+	0.575508i	$0.195196\pi$
$284$	−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	−0.248899	−	0.968530i	$-0.580069\pi$
$293$	2334.26	−	1347.69i	0.465423	−	0.268712i	0.714322	+	0.699817i	$0.246735\pi$
$294$	−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	$0.139822\pi$
$307$			4575.16i			0.850547i	−0.905065	+	0.425274i	$0.860178\pi$
$308$	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	0.947289	+	0.320381i	$0.103811\pi$
$311$	4119.46	+	7135.11i	0.751103	+	1.30095i	−0.196186	+	0.980567i	$0.562856\pi$
$312$	−2979.42	+	3328.35i	−0.540629	+	0.603944i
$313$	2659.91	−	4607.09i	0.480341	−	0.831975i	−0.519405	−	0.854528i	$-0.673846\pi$
$313$	2659.91	−	4607.09i	0.480341	−	0.831975i	0.999746	+	0.0225534i	$0.00717958\pi$
$314$	−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	−0.365092	−	0.930971i	$-0.618962\pi$
$317$	−7641.35	−	4411.73i	−1.35388	−	0.781665i	−0.988791	+	0.149307i	$0.952296\pi$
$318$	−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	0.319462	−	0.947599i	$-0.396498\pi$
$331$	−2056.23	−	1187.17i	−0.341452	−	0.197138i	−0.660914	+	0.750462i	$0.729831\pi$
$332$	−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	0.890868	−	0.454263i	$-0.150097\pi$
$337$	321.888	+	557.527i	0.0520308	+	0.0901199i	−0.838837	+	0.544383i	$0.816764\pi$
$338$	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	0.800459	−	0.599387i	$-0.204589\pi$
$347$	−768.265	−	1330.67i	−0.118855	−	0.205863i	−0.919314	+	0.393525i	$0.871256\pi$
$348$	−4837.96	+	1519.37i	−0.745235	+	0.234043i
$349$	−3432.65	+	5945.53i	−0.526492	+	0.911910i	0.473032	+	0.881045i	$0.343160\pi$
$349$	−3432.65	+	5945.53i	−0.526492	+	0.911910i	−0.999524	+	0.0308650i	$0.990174\pi$
$350$	−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	0.508118	−	0.861288i	$-0.330342\pi$
$353$	107.968	+	62.3355i	0.0162792	+	0.00939881i	−0.491838	+	0.870687i	$0.663675\pi$
$354$	−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	0.445640	−	0.895212i	$-0.352976\pi$
$367$	−750.997	−	433.589i	−0.106817	−	0.0616707i	−0.552457	+	0.833542i	$0.686310\pi$
$368$	−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	0.976401	−	0.215964i	$-0.0692895\pi$
$373$	2169.58	+	3757.82i	0.301170	+	0.521642i	−0.675231	+	0.737606i	$0.735956\pi$
$374$	−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	$0.404455\pi$
$379$			14096.9i			1.91058i	−0.295677	+	0.955288i	$0.595545\pi$
$380$	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	−0.998160	−	0.0606386i	$-0.980686\pi$
$383$	−4134.45	−	7161.08i	−0.551594	−	0.955390i	0.446565	−	0.894751i	$-0.352647\pi$
$384$	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	0.787756	−	0.615987i	$-0.211243\pi$
$389$	4972.96	+	2871.14i	0.648173	+	0.374223i	−0.139583	+	0.990210i	$0.544576\pi$
$390$	−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	−0.870813	−	0.491614i	$-0.836407\pi$
$401$	−7070.19	+	4081.97i	−0.880469	+	0.508339i	−0.00965631	+	0.999953i	$0.503074\pi$
$402$	−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	0.716183	−	0.697913i	$-0.245888\pi$
$409$	−2037.43	−	3528.93i	−0.246319	−	0.426637i	−0.962502	+	0.271276i	$0.912554\pi$
$410$	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	0.885520	−	0.464601i	$-0.153802\pi$
$419$	346.536	+	600.219i	0.0404043	+	0.0699823i	−0.845116	+	0.534583i	$0.820469\pi$
$420$	1696.98	−	1847.72i	0.197153	−	0.214665i
$421$	5362.68	−	9288.44i	0.620810	−	1.07527i	−0.368525	−	0.929618i	$-0.620137\pi$
$421$	5362.68	−	9288.44i	0.620810	−	1.07527i	0.989335	−	0.145657i	$-0.0465296\pi$
$422$	−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	0.775731	−	0.631063i	$-0.217381\pi$
$439$	5675.95	+	3277.01i	0.617080	+	0.356271i	−0.158651	+	0.987335i	$0.550715\pi$
$440$	−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	−0.664224	−	0.747533i	$-0.731238\pi$
$443$	2939.61	−	5091.55i	0.315271	−	0.546065i	0.979495	+	0.201468i	$0.0645713\pi$
$444$	−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	$-0.884374\pi$
$449$		−	6761.00i		−	0.710627i	0.934747	−	0.355313i	$-0.115626\pi$
$450$	−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	−0.151954	−	0.988388i	$-0.548557\pi$
$457$	7620.16	−	13198.5i	0.779992	−	1.35099i	0.931946	−	0.362598i	$-0.118110\pi$
$458$	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	0.961064	−	0.276327i	$-0.0891171\pi$
$461$	11900.4	+	6870.68i	1.20229	+	0.694142i	0.241226	+	0.970469i	$0.422450\pi$
$462$	−2517.95	+	755.606i	−0.253562	+	0.0760908i
$463$	−15291.7	+	8828.66i	−1.53491	+	0.886183i	−0.535789	+	0.844352i	$0.679986\pi$
$463$	−15291.7	+	8828.66i	−1.53491	+	0.886183i	−0.999125	+	0.0418305i	$0.986681\pi$
$464$	−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	−0.0751944	−	0.997169i	$-0.523958\pi$
$479$	8659.06	−	14997.9i	0.825976	−	1.43063i	0.901171	−	0.433464i	$-0.142709\pi$
$480$	−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	$0.111121\pi$
$487$			7352.14i			0.684101i	−0.939682	+	0.342050i	$0.888879\pi$
$488$	−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	0.992179	−	0.124822i	$-0.0398360\pi$
$491$	4221.27	+	7311.46i	0.387991	+	0.672019i	−0.604189	+	0.796841i	$0.706503\pi$
$492$	−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	−0.176956	−	0.984219i	$-0.556625\pi$
$499$	6542.34	−	3777.22i	0.586924	−	0.338861i	0.763880	+	0.645358i	$0.223292\pi$
$500$	−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	−0.0617925	−	0.998089i	$-0.519682\pi$
$509$	8861.66	−	5116.28i	0.771682	−	0.445531i	0.833474	+	0.552558i	$0.186348\pi$
$510$	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	$-0.717058\pi$
$521$		−	18465.3i		−	1.55274i	0.630276	−	0.776371i	$-0.282942\pi$
$522$	4276.12	−	8276.51i	0.358545	−	0.693971i
$523$		−	15941.5i		−	1.33284i	−0.745579	−	0.666418i	$-0.767827\pi$
$523$		−	15941.5i		−	1.33284i	0.745579	−	0.666418i	$-0.232173\pi$
$524$	−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	0.485272	−	0.874363i	$-0.338720\pi$
$547$	−374.999	−	216.506i	−0.0293122	−	0.0169234i	−0.514585	+	0.857440i	$0.672054\pi$
$548$	−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	$0.113610\pi$
$557$			9185.88i			0.698776i	−0.936978	+	0.349388i	$0.886390\pi$
$558$	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	0.999880	−	0.0155079i	$-0.00493650\pi$
$563$	6499.11	+	11256.8i	0.486510	+	0.842659i	−0.513370	+	0.858167i	$0.671603\pi$
$564$	−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	0.686335	−	0.727286i	$-0.259218\pi$
$569$	5424.42	+	3131.79i	0.399655	+	0.230741i	−0.286680	+	0.958026i	$0.592552\pi$
$570$	4496.46	+	14983.8i	0.330414	+	1.10106i
$571$	−21837.8	+	12608.1i	−1.60050	+	0.924047i	−0.609109	+	0.793086i	$0.708473\pi$
$571$	−21837.8	+	12608.1i	−1.60050	+	0.924047i	−0.991388	+	0.130961i	$0.958194\pi$
$572$	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	0.136551	−	0.990633i	$-0.456398\pi$
$587$	13172.1	−	22814.8i	0.926189	−	1.60421i	0.789638	−	0.613573i	$-0.210268\pi$
$588$	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	$-0.868035\pi$
$593$		−	11633.4i		−	0.805609i	0.915286	−	0.402804i	$-0.131965\pi$
$594$	−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	−0.945645	−	0.325200i	$-0.894568\pi$
$599$	−11060.5	−	19157.3i	−0.754454	−	1.30675i	0.191191	−	0.981553i	$-0.438765\pi$
$600$	−18545.8	−	3885.83i	−1.26188	−	0.264397i
$601$	846.923	−	1466.91i	0.0574820	−	0.0995618i	−0.835852	−	0.548954i	$-0.815026\pi$
$601$	846.923	−	1466.91i	0.0574820	−	0.0995618i	0.893334	+	0.449392i	$0.148359\pi$
$602$	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	−0.0670351	−	0.997751i	$-0.521354\pi$
$607$	11418.4	−	6592.43i	0.763525	−	0.440821i	0.830560	+	0.556929i	$0.188021\pi$
$608$	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	−0.967658	−	0.252266i	$-0.918824\pi$
$617$	−18897.2	+	10910.3i	−1.23302	+	0.711884i	−0.265361	+	0.964149i	$0.585491\pi$
$618$	−24326.5	+	7300.09i	−1.58342	+	0.475166i
$619$	−15640.0	−	9029.74i	−1.01555	−	0.586326i	−0.102736	−	0.994709i	$-0.532760\pi$
$619$	−15640.0	−	9029.74i	−1.01555	−	0.586326i	−0.912811	+	0.408382i	$0.866093\pi$
$620$	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	$0.0739829\pi$
$631$			7301.94i			0.460674i	−0.973111	+	0.230337i	$0.926017\pi$
$632$	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	0.522504	−	0.852637i	$-0.324998\pi$
$641$	735.990	+	424.924i	0.0453508	+	0.0261833i	−0.477153	+	0.878820i	$0.658331\pi$
$642$	903.386	+	213.487i	0.0555355	+	0.0131241i
$643$	−984.538	+	568.423i	−0.0603832	+	0.0348622i	−0.529888	−	0.848068i	$-0.677766\pi$
$643$	−984.538	+	568.423i	−0.0603832	+	0.0348622i	0.469504	+	0.882930i	$0.344433\pi$
$644$	−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	0.468654	−	0.883382i	$-0.344739\pi$
$653$	24496.2	−	14142.9i	1.46801	−	0.847557i	0.999358	+	0.0358245i	$0.0114057\pi$
$654$	−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	0.194831	+	0.980837i	$0.437584\pi$
$659$	−12722.0	+	22035.1i	−0.752014	+	1.30253i	−0.946845	+	0.321690i	$0.895749\pi$
$660$	25966.9	+	23848.5i	1.53145	+	1.40652i
$661$	2109.30	+	3653.42i	0.124119	+	0.214980i	0.921388	−	0.388644i	$-0.127056\pi$
$661$	2109.30	+	3653.42i	0.124119	+	0.214980i	−0.797269	+	0.603624i	$0.793723\pi$
$662$	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	−0.995230	−	0.0975565i	$-0.968897\pi$
$673$	−7212.87	+	12493.0i	−0.413129	+	0.715560i	0.582101	+	0.813116i	$0.302231\pi$
$674$	−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	−0.994537	−	0.104382i	$-0.966713\pi$
$677$	−27870.5	−	16091.1i	−1.58220	−	0.913486i	−0.587666	−	0.809103i	$-0.699953\pi$
$678$	−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	0.621063	−	0.783761i	$-0.286701\pi$
$691$	4592.61	+	2651.54i	0.252838	+	0.145976i	−0.368225	+	0.929737i	$0.620034\pi$
$692$	−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	$0.0876056\pi$
$701$			10087.7i			0.543519i	−0.962365	+	0.271760i	$0.912394\pi$
$702$	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	−0.292754	−	0.956188i	$-0.594572\pi$
$709$	12869.6	−	22290.9i	0.681706	−	1.18075i	0.974460	−	0.224561i	$-0.0720949\pi$
$710$	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	0.887147	−	0.461487i	$-0.152684\pi$
$727$	18250.7	+	10537.0i	0.931061	+	0.537548i	0.0439138	+	0.999035i	$0.486017\pi$
$728$	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	−0.999938	−	0.0111727i	$-0.996444\pi$
$733$	−10114.0	−	17518.0i	−0.509645	−	0.882730i	0.490293	−	0.871558i	$-0.336890\pi$
$734$	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	$-0.929855\pi$
$739$		−	8782.55i		−	0.437173i	0.975818	−	0.218587i	$-0.0701447\pi$
$740$	−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	0.995871	+	0.0907800i	$0.0289360\pi$
$743$	11676.8	+	20224.8i	0.576553	+	0.998620i	−0.419318	+	0.907840i	$0.637731\pi$
$744$	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	−0.100662	−	0.994921i	$-0.532096\pi$
$751$	14625.3	−	8443.94i	0.710634	−	0.410285i	0.811296	+	0.584636i	$0.198763\pi$
$752$	−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	−0.901271	−	0.433256i	$-0.857365\pi$
$761$	−20503.9	+	11837.9i	−0.976696	+	0.563896i	−0.0754248	+	0.997151i	$0.524031\pi$
$762$	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	−0.868322	−	0.496002i	$-0.834801\pi$
$769$	−18418.7	−	31902.0i	−0.863711	−	1.49599i	0.00461075	−	0.999989i	$-0.498532\pi$
$770$	−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	$0.0558680\pi$
$773$			7505.51i			0.349230i	−0.984637	+	0.174615i	$0.944132\pi$
$774$	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	−0.0668382	−	0.997764i	$-0.521291\pi$
$787$	16864.0	−	9736.41i	0.763832	−	0.440998i	0.830670	+	0.556765i	$0.187958\pi$
$788$	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	−0.991803	−	0.127773i	$-0.959217\pi$
$797$	−30984.0	+	17888.6i	−1.37705	+	0.795040i	−0.385247	+	0.922814i	$0.625884\pi$
$798$	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	$-0.883129\pi$
$809$		−	16519.8i		−	0.717932i	0.933351	−	0.358966i	$-0.116871\pi$
$810$	31514.1	+	14949.2i	1.36703	+	0.648472i
$811$		−	18594.4i		−	0.805103i	−0.915397	−	0.402552i	$-0.868123\pi$
$811$		−	18594.4i		−	0.805103i	0.915397	−	0.402552i	$-0.131877\pi$
$812$	−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	0.999784	+	0.0207677i	$0.00661104\pi$
$821$	35701.8	+	20612.4i	1.51766	+	0.876222i	0.517878	+	0.855455i	$0.326722\pi$
$822$	13022.0	+	12269.6i	0.552547	+	0.520623i
$823$	3713.28	−	2143.86i	0.157274	−	0.0908025i	−0.419297	−	0.907849i	$-0.637723\pi$
$823$	3713.28	−	2143.86i	0.157274	−	0.0908025i	0.576572	+	0.817047i	$0.304390\pi$
$824$	−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	−0.703972	−	0.710228i	$-0.748592\pi$
$839$	6393.60	−	11074.0i	0.263089	−	0.455683i	0.967061	+	0.254544i	$0.0819254\pi$
$840$	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	0.183132	−	0.983088i	$-0.441376\pi$
$853$	23491.5	−	40688.4i	0.942946	−	1.63323i	0.759813	−	0.650141i	$-0.225290\pi$
$854$	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	0.992607	+	0.121375i	$0.0387305\pi$
$857$	39991.4	+	23089.0i	1.59402	+	0.920310i	0.601418	+	0.798935i	$0.294603\pi$
$858$	−27245.7	−	6438.66i	−1.08409	−	0.256191i
$859$	−5670.77	+	3274.02i	−0.225244	+	0.130045i	−0.608376	−	0.793649i	$-0.708179\pi$
$859$	−5670.77	+	3274.02i	−0.225244	+	0.130045i	0.383132	+	0.923694i	$0.374845\pi$
$860$	−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	0.987378	+	0.158383i	$0.0506282\pi$
$877$	16384.3	+	28378.4i	0.630853	+	1.09267i	−0.356525	+	0.934286i	$0.616039\pi$
$878$	−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	$-0.906882\pi$
$881$		−	15082.2i		−	0.576769i	0.957515	−	0.288384i	$-0.0931181\pi$
$882$	−21230.2	+	13617.3i	−0.810497	+	0.519861i
$883$			425.340i			0.0162105i	0.999967	+	0.00810523i	$0.00258000\pi$
$883$			425.340i			0.0162105i	−0.999967	+	0.00810523i	$0.997420\pi$
$884$	−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	0.727742	−	0.685851i	$-0.240570\pi$
$887$	−6078.41	−	10528.1i	−0.230094	−	0.398534i	−0.957835	+	0.287317i	$0.907237\pi$
$888$	−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	−0.453832	−	0.891087i	$-0.649944\pi$
$907$	−39674.6	−	22906.2i	−1.45245	−	0.838574i	−0.998620	+	0.0525131i	$0.983277\pi$
$908$	−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	−0.475471	−	0.879732i	$-0.657722\pi$
$911$	14411.9	−	24962.1i	0.524134	−	0.907827i	0.999605	−	0.0280960i	$-0.00894440\pi$
$912$	−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	$0.267360\pi$
$919$			41488.4i			1.48920i	−0.667511	+	0.744600i	$0.732640\pi$
$920$	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	0.563234	−	0.826297i	$-0.309557\pi$
$929$	3659.97	+	2113.09i	0.129257	+	0.0746266i	−0.433977	+	0.900924i	$0.642890\pi$
$930$	−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	−0.842836	−	0.538171i	$-0.819116\pi$
$941$	−23040.3	+	13302.3i	−0.798185	+	0.460832i	0.0446514	+	0.999003i	$0.485782\pi$
$942$	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	−0.0410299	+	0.999158i	$0.513064\pi$
$947$	−25814.6	+	44712.3i	−0.885811	+	1.53427i	−0.844781	+	0.535112i	$0.820269\pi$
$948$	−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	$0.144283\pi$
$953$			25766.7i			0.875829i	−0.899017	+	0.437915i	$0.855717\pi$
$954$	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	−0.984443	−	0.175705i	$-0.943779\pi$
$967$	−39828.3	+	22994.9i	−1.32450	+	0.764700i	−0.340056	+	0.940405i	$0.610446\pi$
$968$	−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	−0.997564	−	0.0697519i	$-0.977779\pi$
$977$	−43850.9	+	25317.3i	−1.43594	+	0.829040i	−0.438375	+	0.898792i	$0.644446\pi$
$978$	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	−0.730061	−	0.683382i	$-0.760509\pi$
$983$	6989.79	−	12106.7i	0.226795	−	0.392821i	0.956856	+	0.290561i	$0.0938419\pi$
$984$	−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	$0.156911\pi$
$991$			29526.4i			0.946456i	−0.880940	+	0.473228i	$0.843089\pi$
$992$	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	−0.903187	−	0.429247i	$-0.858779\pi$
$997$	−2513.86	+	4354.14i	−0.0798545	+	0.138312i	0.823333	+	0.567559i	$0.192112\pi$
$998$	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.11.5	✓	24
3.2	odd	2		108.4.h.b.35.8		24
4.3	odd	2	inner	36.4.h.b.11.9	yes	24
9.2	odd	6		324.4.b.c.323.2		24
9.4	even	3		108.4.h.b.71.4		24
9.5	odd	6	inner	36.4.h.b.23.9	yes	24
9.7	even	3		324.4.b.c.323.23		24
12.11	even	2		108.4.h.b.35.4		24
36.7	odd	6		324.4.b.c.323.1		24
36.11	even	6		324.4.b.c.323.24		24
36.23	even	6	inner	36.4.h.b.23.5	yes	24
36.31	odd	6		108.4.h.b.71.8		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
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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