LMFDB - Embedded newform 36.4.h.b.11.9

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			11.9
Character	$\chi$	$=$	36.11
Dual form			36.4.h.b.23.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44536 - 2.43124i) q^{2} +(1.42987 + 4.99554i) q^{3} +(-3.82189 - 7.02803i) q^{4} +(14.6499 - 8.45813i) q^{5} +(14.2121 + 3.74398i) q^{6} +(3.08966 + 1.78382i) q^{7} +(-22.6108 - 0.866066i) q^{8} +(-22.9109 + 14.2860i) q^{9} +O(q^{10})$	\(q+(1.44536 - 2.43124i) q^{2} +(1.42987 + 4.99554i) q^{3} +(-3.82189 - 7.02803i) q^{4} +(14.6499 - 8.45813i) q^{5} +(14.2121 + 3.74398i) 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} +(29.6440 - 29.1416i) q^{12} +(-18.9966 - 32.9032i) q^{13} +(8.80255 - 4.93346i) q^{14} +(63.2005 + 61.0903i) q^{15} +(-34.7863 + 53.7207i) q^{16} +84.3819i q^{17} +(1.61823 + 76.3504i) q^{18} -62.9237i q^{19} +(-115.434 - 70.6340i) q^{20} +(-4.49331 + 17.9852i) q^{21} +(69.3323 + 123.706i) q^{22} +(-37.6066 - 65.1366i) q^{23} +(-28.0041 - 114.192i) 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} +(239.873 - 65.3586i) q^{30} +(17.2800 - 9.97659i) q^{31} +(80.3294 + 162.220i) q^{32} +(-252.754 - 63.1467i) q^{33} +(205.153 + 121.962i) q^{34} +60.3510 q^{35} +(187.965 + 106.419i) q^{36} +17.7622 q^{37} +(-152.983 - 90.9472i) q^{38} +(137.206 - 141.946i) q^{39} +(-338.572 + 178.558i) q^{40} +(299.072 - 172.670i) q^{41} +(37.2319 + 36.9193i) 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} +(-318.104 - 96.9630i) q^{48} +(-165.136 - 286.024i) q^{49} +(-222.859 - 397.636i) q^{50} +(-421.534 + 120.655i) q^{51} +(-158.641 + 259.261i) q^{52} +479.464i q^{53} +(-379.098 + 117.255i) q^{54} +848.142i q^{55} +(-68.3149 - 43.0094i) q^{56} +(314.338 - 89.9729i) q^{57} +(300.984 - 168.689i) q^{58} +(245.774 + 425.693i) q^{59} +(187.799 - 677.655i) 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} +(-518.845 + 523.237i) q^{66} +(536.669 - 309.846i) q^{67} +(593.039 - 322.498i) q^{68} +(271.620 - 281.003i) q^{69} +(87.2287 - 146.728i) q^{70} -254.455 q^{71} +(530.408 - 303.176i) q^{72} +100.485 q^{73} +(25.6727 - 43.1841i) q^{74} +(812.441 + 202.976i) q^{75} +(-442.230 + 240.488i) q^{76} +(-154.908 + 89.4363i) q^{77} +(-146.793 - 538.745i) 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} +(143.573 - 37.1581i) q^{84} +(713.714 + 1236.19i) q^{85} +(-322.528 + 180.764i) q^{86} +(-153.639 + 614.964i) q^{87} +(604.432 - 960.062i) q^{88} -1019.86i q^{89} +(669.489 + 1104.84i) q^{90} -135.546i q^{91} +(-314.053 + 513.245i) q^{92} +(74.5466 + 72.0576i) q^{93} +(-423.378 - 755.413i) q^{94} +(-532.217 - 921.828i) q^{95} +(-695.514 + 633.242i) 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 $

$2$	1.44536	−	2.43124i	0.511011	−	0.859574i
$2$	1.44536	−	2.43124i	0.511011	−	0.859574i
$3$	1.42987	+	4.99554i	0.275179	+	0.961393i
$3$	1.42987	+	4.99554i	0.275179	+	0.961393i
$4$	−3.82189	−	7.02803i	−0.477736	−	0.878503i
$5$	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	$0.0602320\pi$
$6$	14.2121	+	3.74398i	0.967008	+	0.254745i
$7$	3.08966	+	1.78382i	0.166826	+	0.0963170i	0.581088	−	0.813841i	$-0.302627\pi$
$7$	3.08966	+	1.78382i	0.166826	+	0.0963170i	−0.414262	+	0.910157i	$0.635960\pi$
$8$	−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	$0.407801\pi$
$11$	−25.0688	+	43.4205i	−0.687139	+	1.19016i	−0.972759	+	0.231817i	$0.925533\pi$
$12$	29.6440	−	29.1416i	0.713124	−	0.701038i
$13$	−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	$0.966162\pi$
$14$	8.80255	−	4.93346i	0.168041	−	0.0941802i
$15$	63.2005	+	61.0903i	1.08789	+	1.05156i
$16$	−34.7863	+	53.7207i	−0.543537	+	0.839386i
$17$			84.3819i			1.20386i	0.798549	+	0.601930i	$0.205601\pi$
$17$			84.3819i			1.20386i	−0.798549	+	0.601930i	$0.794399\pi$
$18$	1.61823	+	76.3504i	0.0211901	+	0.999775i
$19$		−	62.9237i		−	0.759773i	−0.925033	−	0.379887i	$-0.875963\pi$
$19$		−	62.9237i		−	0.759773i	0.925033	−	0.379887i	$-0.124037\pi$
$20$	−115.434	−	70.6340i	−1.29060	−	0.789712i
$21$	−4.49331	+	17.9852i	−0.0466915	+	0.186890i
$22$	69.3323	+	123.706i	0.671896	+	1.19883i
$23$	−37.6066	−	65.1366i	−0.340936	−	0.590518i	0.643671	−	0.765302i	$-0.277411\pi$
$23$	−37.6066	−	65.1366i	−0.340936	−	0.590518i	−0.984607	+	0.174784i	$0.944077\pi$
$24$	−28.0041	−	114.192i	−0.238180	−	0.971221i
$25$	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	$0.538948\pi$
$30$	239.873	−	65.3586i	1.45982	−	0.397760i
$31$	17.2800	−	9.97659i	0.100115	−	0.0578016i	−0.449106	−	0.893478i	$-0.648258\pi$
$31$	17.2800	−	9.97659i	0.100115	−	0.0578016i	0.549222	+	0.835677i	$0.314924\pi$
$32$	80.3294	+	162.220i	0.443761	+	0.896145i
$33$	−252.754	−	63.1467i	−1.33330	−	0.333104i
$34$	205.153	+	121.962i	1.03481	+	0.615186i
$35$	60.3510			0.291462
$36$	187.965	+	106.419i	0.870210	+	0.492682i
$37$	17.7622			0.0789211			0.0394606	−	0.999221i	$-0.487436\pi$
$37$	17.7622			0.0789211			0.0394606	+	0.999221i	$0.487436\pi$
$38$	−152.983	−	90.9472i	−0.653082	−	0.388252i
$39$	137.206	−	141.946i	0.563349	−	0.582809i
$40$	−338.572	+	178.558i	−1.33832	+	0.705811i
$41$	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	$0.104855\pi$
$42$	37.2319	+	36.9193i	0.136786	+	0.135637i
$43$	−113.206	−	65.3596i	−0.401483	−	0.231796i	0.285641	−	0.958337i	$-0.407794\pi$
$43$	−113.206	−	65.3596i	−0.401483	−	0.231796i	−0.687124	+	0.726540i	$0.741127\pi$
$44$	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	$-0.675747\pi$
$47$	153.083	−	265.147i	0.475094	−	0.822887i	0.999593	+	0.0285243i	$0.00908080\pi$
$48$	−318.104	−	96.9630i	−0.956549	−	0.291571i
$49$	−165.136	−	286.024i	−0.481446	−	0.833889i
$50$	−222.859	−	397.636i	−0.630340	−	1.12469i
$51$	−421.534	+	120.655i	−1.15738	+	0.331277i
$52$	−158.641	+	259.261i	−0.423069	+	0.691405i
$53$			479.464i			1.24263i	0.783561	+	0.621315i	$0.213401\pi$
$53$			479.464i			1.24263i	−0.783561	+	0.621315i	$0.786599\pi$
$54$	−379.098	+	117.255i	−0.955346	+	0.295489i
$55$			848.142i			2.07933i
$56$	−68.3149	−	43.0094i	−0.163017	−	0.102632i
$57$	314.338	−	89.9729i	0.730441	−	0.209074i
$58$	300.984	−	168.689i	0.681400	−	0.381896i
$59$	245.774	+	425.693i	0.542323	+	0.939330i	0.998770	+	0.0495801i	$0.0157883\pi$
$59$	245.774	+	425.693i	0.542323	+	0.939330i	−0.456447	+	0.889750i	$0.650878\pi$
$60$	187.799	−	677.655i	0.404079	−	1.45808i
$61$	−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
$66$	−518.845	+	523.237i	−0.967657	+	0.975849i
$67$	536.669	−	309.846i	0.978575	−	0.564980i	0.0767351	−	0.997052i	$-0.475550\pi$
$67$	536.669	−	309.846i	0.978575	−	0.564980i	0.901839	+	0.432071i	$0.142217\pi$
$68$	593.039	−	322.498i	1.05760	−	0.575127i
$69$	271.620	−	281.003i	0.473902	−	0.490272i
$70$	87.2287	−	146.728i	0.148940	−	0.250534i
$71$	−254.455			−0.425327			−0.212663	−	0.977125i	$-0.568214\pi$
$71$	−254.455			−0.425327			−0.212663	+	0.977125i	$0.568214\pi$
$72$	530.408	−	303.176i	0.868183	−	0.496244i
$73$	100.485			0.161108			0.0805541	−	0.996750i	$-0.474331\pi$
$73$	100.485			0.161108			0.0805541	+	0.996750i	$0.474331\pi$
$74$	25.6727	−	43.1841i	0.0403295	−	0.0678386i
$75$	812.441	+	202.976i	1.25084	+	0.312502i
$76$	−442.230	+	240.488i	−0.667464	+	0.362971i
$77$	−154.908	+	89.4363i	−0.229265	+	0.132366i
$78$	−146.793	−	538.745i	−0.213090	−	0.782062i
$79$	−856.295	−	494.382i	−1.21950	−	0.704080i	−0.254691	−	0.967022i	$-0.581974\pi$
$79$	−856.295	−	494.382i	−1.21950	−	0.704080i	−0.964812	+	0.262942i	$0.915307\pi$
$80$	−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	$-0.941373\pi$
$83$	−251.755	+	436.053i	−0.332936	+	0.576663i	0.650150	+	0.759806i	$0.274706\pi$
$84$	143.573	−	37.1581i	0.186489	−	0.0482653i
$85$	713.714	+	1236.19i	0.910743	+	1.57745i
$86$	−322.528	+	180.764i	−0.404408	+	0.226654i
$87$	−153.639	+	614.964i	−0.189332	+	0.757829i
$88$	604.432	−	960.062i	0.732189	−	1.16299i
$89$		−	1019.86i		−	1.21467i	−0.794448	−	0.607333i	$-0.792239\pi$
$89$		−	1019.86i		−	1.21467i	0.794448	−	0.607333i	$-0.207761\pi$
$90$	669.489	+	1104.84i	0.784115	+	1.29400i
$91$		−	135.546i		−	0.156144i
$92$	−314.053	+	513.245i	−0.355895	+	0.581625i
$93$	74.5466	+	72.0576i	0.0831196	+	0.0803443i
$94$	−423.378	−	755.413i	−0.464554	−	0.828882i
$95$	−532.217	−	921.828i	−0.574783	−	0.995553i
$96$	−695.514	+	633.242i	−0.739434	+	0.673229i
$97$	−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	$0.733158\pi$
$102$	−315.924	+	1199.24i	−0.306678	+	1.16414i
$103$	1496.60	−	864.065i	1.43170	−	0.826591i	0.434447	−	0.900697i	$-0.356944\pi$
$103$	1496.60	−	864.065i	1.43170	−	0.826591i	0.997250	+	0.0741066i	$0.0236105\pi$
$104$	401.034	+	760.420i	0.378121	+	0.716975i
$105$	86.2942	+	301.486i	0.0802043	+	0.280210i
$106$	1165.69	+	692.996i	1.06813	+	0.634998i
$107$	−63.1607			−0.0570652			−0.0285326	−	0.999593i	$-0.509083\pi$
$107$	−63.1607			−0.0570652			−0.0285326	+	0.999593i	$0.509083\pi$
$108$	−262.856	+	1091.15i	−0.234197	+	0.972189i
$109$	−835.373			−0.734076			−0.367038	−	0.930206i	$-0.619628\pi$
$109$	−835.373			−0.734076			−0.367038	+	0.930206i	$0.619628\pi$
$110$	2062.04	+	1225.87i	1.78734	+	1.06256i
$111$	25.3976	+	88.7317i	0.0217174	+	0.0758742i
$112$	−203.306	+	103.926i	−0.171523	+	0.0876794i
$113$	−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	$0.474359\pi$
$114$	235.585	−	894.276i	0.193549	−	0.734707i
$115$	−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
$120$	−1376.11	−	1436.04i	−1.04684	−	1.09243i
$121$	−591.391	−	1024.32i	−0.444321	−	0.769587i
$122$	138.054	+	246.323i	0.102449	+	0.182796i
$123$	1290.21	+	1247.13i	0.945810	+	0.914230i
$124$	−136.158	−	83.3146i	−0.0986075	−	0.0603377i
$125$		−	611.695i		−	0.437693i
$126$	−131.195	+	238.783i	−0.0927603	+	0.168829i
$127$			794.523i			0.555138i	0.960706	+	0.277569i	$0.0895287\pi$
$127$			794.523i			0.555138i	−0.960706	+	0.277569i	$0.910471\pi$
$128$	833.074	−	1184.54i	0.575266	−	0.817967i
$129$	164.636	−	658.982i	0.112368	−	0.449769i
$130$	−1585.77	+	888.758i	−1.06986	+	0.599610i
$131$	111.039	+	192.325i	0.0740575	+	0.128271i	0.900676	−	0.434491i	$-0.143072\pi$
$131$	111.039	+	192.325i	0.0740575	+	0.128271i	−0.826619	+	0.562763i	$0.809738\pi$
$132$	522.201	+	2017.70i	0.344332	+	1.33044i
$133$	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	$0.542732\pi$
$138$	−290.598	−	1066.52i	−0.179256	−	0.657888i
$139$	−1909.09	+	1102.21i	−1.16494	+	0.672578i	−0.952483	−	0.304592i	$-0.901480\pi$
$139$	−1909.09	+	1102.21i	−1.16494	+	0.672578i	−0.212457	+	0.977170i	$0.568146\pi$
$140$	−230.655	−	424.148i	−0.139242	−	0.256051i
$141$	1543.44	+	385.605i	0.921853	+	0.230311i
$142$	−367.778	+	618.641i	−0.217347	+	0.365600i
$143$	1904.89			1.11395
$144$	29.5348	−	1727.75i	0.0170919	−	0.999854i
$145$	2063.57			1.18187
$146$	145.237	−	244.304i	0.0823280	−	0.138485i
$147$	1192.72	−	1233.92i	0.669211	−	0.692328i
$148$	−67.8850	−	124.833i	−0.0377035	−	0.0693325i
$149$	−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	$0.368987\pi$
$150$	1667.75	−	1681.87i	0.907809	−	0.915494i
$151$	2990.17	+	1726.37i	1.61150	+	0.930399i	0.989023	+	0.147759i	$0.0472060\pi$
$151$	2990.17	+	1726.37i	1.61150	+	0.930399i	0.622475	+	0.782640i	$0.286127\pi$
$152$	−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
$156$	−1521.99	−	421.789i	−0.781132	−	0.216475i
$157$	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	$0.761483\pi$
$158$	−2439.62	+	1367.30i	−1.22839	+	0.688461i
$159$	−2395.18	+	685.572i	−1.19466	+	0.341946i
$160$	2548.89	+	1697.07i	1.25942	+	0.838531i
$161$		−	268.333i		−	0.131352i
$162$	−1127.82	−	1726.14i	−0.546973	−	0.837151i
$163$			1693.56i			0.813802i	0.913472	+	0.406901i	$0.133391\pi$
$163$			1693.56i			0.813802i	−0.913472	+	0.406901i	$0.866609\pi$
$164$	−2356.55	−	1441.97i	−1.12205	−	0.686577i
$165$	−4236.93	+	1212.73i	−1.99906	+	0.572189i
$166$	696.274	+	1242.33i	0.325550	+	0.580864i
$167$	820.051	+	1420.37i	0.379985	+	0.658153i	0.991060	−	0.133420i	$-0.0425959\pi$
$167$	820.051	+	1420.37i	0.379985	+	0.658153i	−0.611075	+	0.791573i	$0.709263\pi$
$168$	117.174	−	402.768i	0.0538105	−	0.184966i
$169$	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	$0.507544\pi$
$174$	1273.06	+	1262.38i	0.554660	+	0.550003i
$175$	497.930	−	287.480i	0.215085	−	0.124180i
$176$	−1460.52	−	2857.15i	−0.625518	−	1.22367i
$177$	−1775.14	+	1836.46i	−0.753830	+	0.779869i
$178$	−2479.53	−	1474.07i	−1.04410	−	0.620707i
$179$	−2350.24			−0.981370			−0.490685	−	0.871337i	$-0.663253\pi$
$179$	−2350.24			−0.981370			−0.490685	+	0.871337i	$0.663253\pi$
$180$	3653.78	−	30.8028i	1.51298	−	0.0127550i
$181$	−2280.14			−0.936362			−0.468181	−	0.883633i	$-0.655090\pi$
$181$	−2280.14			−0.936362			−0.468181	+	0.883633i	$0.655090\pi$
$182$	−329.545	−	195.912i	−0.134217	−	0.0797912i
$183$	−503.282	−	125.737i	−0.203299	−	0.0507910i
$184$	793.905	+	1505.36i	0.318084	+	0.603135i
$185$	260.214	−	150.235i	0.103413	−	0.0597053i
$186$	282.936	−	77.0921i	0.111537	−	0.0303907i
$187$	−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	$-0.565797\pi$
$191$	1966.48	−	3406.04i	0.744970	−	1.29033i	0.950209	−	0.311614i	$-0.100870\pi$
$192$	534.299	+	2606.23i	0.200832	+	0.979626i
$193$	−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	$-0.335528\pi$
$194$	1392.77	+	2485.05i	0.515437	+	0.919671i
$195$	809.465	−	3240.01i	0.297267	−	1.18985i
$196$	−1379.05	+	2253.73i	−0.502570	+	0.821331i
$197$			1997.91i			0.722565i	0.932456	+	0.361282i	$0.117661\pi$
$197$			1997.91i			0.722565i	−0.932456	+	0.361282i	$0.882339\pi$
$198$	−3355.74	−	1843.75i	−1.20445	−	0.661766i
$199$		−	2409.09i		−	0.858170i	−0.903264	−	0.429085i	$-0.858836\pi$
$199$		−	2409.09i		−	0.858170i	0.903264	−	0.429085i	$-0.141164\pi$
$200$	−1942.86	+	3085.98i	−0.686904	+	1.09106i
$201$	2315.22	+	2237.91i	0.812451	+	0.785324i
$202$	−1038.71	+	582.153i	−0.361798	+	0.202773i
$203$	217.603	+	376.900i	0.0752353	+	0.130311i
$204$	2459.02	+	2501.42i	0.843952	+	0.858502i
$205$	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
$210$	857.712	+	225.953i	0.281846	+	0.0742486i
$211$	1575.68	−	909.717i	0.514095	−	0.296813i	−0.220420	−	0.975405i	$-0.570743\pi$
$211$	1575.68	−	909.717i	0.514095	−	0.296813i	0.734515	+	0.678592i	$0.237410\pi$
$212$	3369.69	−	1832.46i	1.09166	−	0.593650i
$213$	−363.838	−	1271.14i	−0.117041	−	0.408906i
$214$	−91.2897	+	153.559i	−0.0291609	+	0.0490518i
$215$	−2211.28			−0.701433
$216$	2272.94	+	2216.17i	0.715992	+	0.698109i
$217$	71.1856			0.0222691
$218$	−1207.41	+	2031.00i	−0.375120	+	0.630992i
$219$	143.681	+	501.978i	0.0443336	+	0.154888i
$220$	5960.76	−	3241.50i	1.82670	−	0.993373i
$221$	2776.43	−	1602.97i	0.845082	−	0.487908i
$222$	252.437	+	66.5011i	0.0763174	+	0.0201048i
$223$	2316.13	+	1337.22i	0.695514	+	0.401555i	0.805674	−	0.592359i	$-0.201803\pi$
$223$	2316.13	+	1337.22i	0.695514	+	0.401555i	−0.110160	+	0.993914i	$0.535136\pi$
$224$	−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	$0.497722\pi$
$227$	−2949.58	+	5108.82i	−0.862425	+	1.49376i	−0.869581	+	0.493790i	$0.835611\pi$
$228$	−1833.70	−	1865.31i	−0.532630	−	0.541813i
$229$	−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	$0.977496\pi$
$230$	−3139.26	+	1759.43i	−0.899986	+	0.504405i
$231$	−668.282	−	645.968i	−0.190345	−	0.183990i
$232$	−2335.88	−	1470.62i	−0.661027	−	0.416167i
$233$			1294.13i			0.363867i	0.983311	+	0.181934i	$0.0582356\pi$
$233$			1294.13i			0.363867i	−0.983311	+	0.181934i	$0.941764\pi$
$234$	2481.43	−	1503.65i	0.693231	−	0.420070i
$235$		−	5179.18i		−	1.43767i
$236$	2052.46	−	3354.26i	0.566118	−	0.925184i
$237$	1245.32	−	4984.56i	0.341316	−	1.36617i
$238$	416.295	+	742.776i	0.113380	+	0.202298i
$239$	−2875.14	−	4979.89i	−0.778149	−	1.34779i	−0.933008	−	0.359856i	$-0.882826\pi$
$239$	−2875.14	−	4979.89i	−0.778149	−	1.34779i	0.154859	−	0.987937i	$-0.450508\pi$
$240$	−5480.32	+	1270.07i	−1.47397	+	0.341594i
$241$	−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
$246$	4896.91	−	1334.27i	1.26917	−	0.345813i
$247$	−2070.39	+	1195.34i	−0.533343	+	0.307926i
$248$	−399.355	+	210.613i	−0.102254	+	0.0539273i
$249$	−2538.30	−	634.154i	−0.646017	−	0.161397i
$250$	−1487.18	−	884.117i	−0.376230	−	0.223666i
$251$	3207.28			0.806541			0.403270	−	0.915081i	$-0.367873\pi$
$251$	3207.28			0.806541			0.403270	+	0.915081i	$0.367873\pi$
$252$	390.916	+	664.094i	0.0977199	+	0.166008i
$253$	3771.02			0.937082
$254$	1931.68	+	1148.37i	0.477182	+	0.283681i
$255$	−5154.91	+	5332.98i	−1.26593	+	1.30966i
$256$	−1675.82	−	3737.49i	−0.409136	−	0.912473i
$257$	−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	$0.448135\pi$
$258$	−1364.19	−	1352.74i	−0.329188	−	0.326425i
$259$	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	$-0.821684\pi$
$263$	156.053	−	270.292i	0.0365880	−	0.0633723i	0.883740	+	0.467979i	$0.155018\pi$
$264$	5660.29	+	1646.70i	1.31957	+	0.383892i
$265$	4055.37	+	7024.11i	0.940073	+	1.62825i
$266$	−310.432	−	553.889i	−0.0715556	−	0.127673i
$267$	5094.77	−	1458.27i	1.16777	−	0.334251i
$268$	−4228.69	−	2587.53i	−0.963838	−	0.589770i
$269$		−	1826.27i		−	0.413939i	−0.978347	−	0.206969i	$-0.933640\pi$
$269$		−	1826.27i		−	0.413939i	0.978347	−	0.206969i	$-0.0663600\pi$
$270$	−4561.99	+	4924.24i	−1.02827	+	1.10993i
$271$			4987.26i			1.11791i	0.829197	+	0.558956i	$0.188798\pi$
$271$			4987.26i			1.11791i	−0.829197	+	0.558956i	$0.811202\pi$
$272$	−4533.05	−	2935.34i	−1.01050	−	0.654342i
$273$	677.126	−	193.814i	0.150116	−	0.0429675i
$274$	3003.69	−	1683.44i	0.662261	−	0.371170i
$275$	4040.09	+	6997.65i	0.885916	+	1.53445i
$276$	−3013.00	−	834.993i	−0.657105	−	0.182104i
$277$	−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	$0.767508\pi$
$282$	3168.32	−	3195.15i	0.669046	−	0.674710i
$283$	−3467.24	+	2001.81i	−0.728289	+	0.420478i	−0.817796	−	0.575508i	$-0.804804\pi$
$283$	−3467.24	+	2001.81i	−0.728289	+	0.420478i	0.0895066	+	0.995986i	$0.471471\pi$
$284$	972.497	+	1788.31i	0.203194	+	0.373651i
$285$	3844.03	−	3976.81i	0.798949	−	0.826547i
$286$	2753.25	−	4631.26i	0.569242	−	0.957525i
$287$	1232.04			0.253398
$288$	−4157.89	−	2569.02i	−0.850715	−	0.525628i
$289$	−2207.31			−0.449280
$290$	2982.60	−	5017.05i	0.603946	−	1.01590i
$291$	−5077.39	−	1268.51i	−1.02282	−	0.255537i
$292$	−384.043	−	706.213i	−0.0769672	−	0.141534i
$293$	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	$0.246735\pi$
$294$	−1276.06	−	4683.25i	−0.253133	−	0.929024i
$295$	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
$300$	−1678.54	−	6485.61i	−0.323035	−	1.24816i
$301$	−233.179	−	403.878i	−0.0446518	−	0.0773393i
$302$	8519.09	−	4774.60i	1.62324	−	0.909759i
$303$	530.214	−	2122.26i	0.100528	−	0.402379i
$304$	3380.31	+	2188.89i	0.637743	+	0.412965i
$305$			1688.81i			0.317053i
$306$	−6442.59	+	136.550i	−1.20359	+	0.0255099i
$307$		−	4575.16i		−	0.850547i	−0.905065	−	0.425274i	$-0.860178\pi$
$307$		−	4575.16i		−	0.850547i	0.905065	−	0.425274i	$-0.139822\pi$
$308$	1220.60	+	746.883i	0.225813	+	0.138174i
$309$	6456.43	+	6240.85i	1.18865	+	1.14896i
$310$	−466.755	−	832.809i	−0.0855158	−	0.152582i
$311$	−4119.46	−	7135.11i	−0.751103	−	1.30095i	−0.947289	−	0.320381i	$-0.896189\pi$
$311$	−4119.46	−	7135.11i	−0.751103	−	1.30095i	0.196186	−	0.980567i	$-0.437144\pi$
$312$	−3225.29	+	3090.69i	−0.585243	+	0.560819i
$313$	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	$0.952296\pi$
$318$	−1795.10	+	6814.17i	−0.316554	+	1.20163i
$319$	−5296.76	+	3058.08i	−0.929660	+	0.536739i
$320$	7810.04	−	3744.11i	1.36436	−	0.654070i
$321$	−90.3117	−	315.522i	−0.0157031	−	0.0548620i
$322$	−652.383	−	387.837i	−0.112907	−	0.0671221i
$323$	5309.63			0.914661
$324$	−5826.76	+	247.106i	−0.999102	+	0.0423706i
$325$	−6123.01			−1.04506
$326$	4117.45	+	2447.80i	0.699523	+	0.415862i
$327$	−1194.48	−	4173.14i	−0.202002	−	0.705735i
$328$	−6911.82	+	3645.19i	−1.16354	+	0.613633i
$329$	945.947	−	546.143i	0.158516	−	0.0915192i
$330$	−3175.42	+	12053.8i	−0.529701	+	2.01073i
$331$	2056.23	+	1187.17i	0.341452	+	0.197138i	0.660914	−	0.750462i	$-0.270169\pi$
$331$	2056.23	+	1187.17i	0.341452	+	0.197138i	−0.319462	+	0.947599i	$0.603502\pi$
$332$	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
$336$	−809.869	−	867.021i	−0.131494	−	0.140773i
$337$	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	$0.816764\pi$
$338$	−1041.98	−	1859.16i	−0.167682	−	0.299187i
$339$	−3847.77	−	3719.29i	−0.616466	−	0.595883i
$340$	5960.23	−	9740.57i	0.950703	−	1.55370i
$341$			1000.41i			0.158871i
$342$	4804.25	−	101.825i	0.759603	−	0.0160997i
$343$		−	2401.99i		−	0.378120i
$344$	2503.08	+	1575.88i	0.392317	+	0.246993i
$345$	1602.45	−	6414.07i	0.250067	−	1.00093i
$346$	5382.30	−	3016.56i	0.836284	−	0.468702i
$347$	768.265	+	1330.67i	0.118855	+	0.205863i	0.919314	−	0.393525i	$-0.128744\pi$
$347$	768.265	+	1330.67i	0.118855	+	0.205863i	−0.800459	+	0.599387i	$0.795411\pi$
$348$	4909.18	−	1270.54i	0.756206	−	0.195714i
$349$	−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	$0.663675\pi$
$354$	1899.17	+	6970.14i	0.285140	+	1.04649i
$355$	−3727.74	+	2152.21i	−0.557318	+	0.321768i
$356$	−7167.62	+	3897.80i	−1.06709	+	0.580289i
$357$	−1517.62	−	379.154i	−0.224989	−	0.0562100i
$358$	−3396.94	+	5714.01i	−0.501491	+	0.843560i
$359$	−4489.49			−0.660017			−0.330009	−	0.943978i	$-0.607052\pi$
$359$	−4489.49			−0.660017			−0.330009	+	0.943978i	$0.607052\pi$
$360$	5206.13	−	8927.76i	0.762187	−	1.30704i
$361$	2899.60			0.422744
$362$	−3295.61	+	5543.57i	−0.478491	+	0.804872i
$363$	4271.42	−	4418.97i	0.617607	−	0.638941i
$364$	−952.621	+	518.042i	−0.137173	+	0.0745955i
$365$	1472.10	−	849.917i	0.211105	−	0.121881i
$366$	−1033.12	+	1041.87i	−0.147547	+	0.148796i
$367$	750.997	+	433.589i	0.106817	+	0.0616707i	0.552457	−	0.833542i	$-0.313690\pi$
$367$	750.997	+	433.589i	0.106817	+	0.0616707i	−0.445640	+	0.895212i	$0.647024\pi$
$368$	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
$372$	221.514	−	799.312i	0.0308735	−	0.111404i
$373$	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	$0.735956\pi$
$374$	−10438.6	+	5850.40i	−1.44323	+	0.808869i
$375$	3055.75	−	874.646i	0.420795	−	0.120444i
$376$	−3690.96	+	5862.62i	−0.506242	+	0.804099i
$377$		−	4634.71i		−	0.633156i
$378$	−1380.44	−	313.962i	−0.187837	−	0.0427208i
$379$		−	14096.9i		−	1.91058i	−0.295677	−	0.955288i	$-0.595545\pi$
$379$		−	14096.9i		−	1.91058i	0.295677	−	0.955288i	$-0.404455\pi$
$380$	−4444.55	+	7263.56i	−0.600002	+	0.980560i
$381$	−3969.07	+	1136.07i	−0.533706	+	0.152762i
$382$	−5438.65	−	9703.92i	−0.728443	−	1.29973i
$383$	4134.45	+	7161.08i	0.551594	+	0.955390i	0.998160	+	0.0606386i	$0.0193137\pi$
$383$	4134.45	+	7161.08i	0.551594	+	0.955390i	−0.446565	+	0.894751i	$0.647353\pi$
$384$	7108.62	+	2467.91i	0.944688	+	0.327969i
$385$	−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	$0.544576\pi$
$390$	−6707.28	−	6650.97i	−0.870862	−	0.863551i
$391$	5496.35	−	3173.32i	0.710902	−	0.410439i
$392$	3486.15	+	6610.26i	0.449176	+	0.851705i
$393$	−801.999	+	829.702i	−0.102940	+	0.106496i
$394$	4857.41	+	2887.69i	0.621098	+	0.369238i
$395$	−16726.2			−2.13060
$396$	−9332.84	+	5493.74i	−1.18433	+	0.697148i
$397$	10494.4			1.32670			0.663349	−	0.748310i	$-0.269134\pi$
$397$	10494.4			1.32670			0.663349	+	0.748310i	$0.269134\pi$
$398$	−5857.08	−	3481.99i	−0.737661	−	0.438534i
$399$	1131.69	+	282.736i	0.141994	+	0.0354749i
$400$	4694.64	+	9183.90i	0.586830	+	1.14799i
$401$	−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	$0.503074\pi$
$402$	8787.22	−	2394.27i	1.09022	−	0.297053i
$403$	−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
$408$	9635.73	−	2363.04i	1.16921	−	0.286736i
$409$	−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	$0.912554\pi$
$410$	−8078.34	−	14413.8i	−0.973076	−	1.73621i
$411$	−1533.25	+	6137.06i	−0.184014	+	0.736543i
$412$	−11792.5	−	7215.82i	−1.41014	−	0.862859i
$413$			1753.66i			0.208940i
$414$	4912.35	−	2976.69i	0.583161	−	0.353372i
$415$			8517.52i			1.00749i
$416$	3811.55	−	5724.72i	0.449222	−	0.674705i
$417$	−8235.90	−	7960.90i	−0.967179	−	0.934885i
$418$	7784.07	−	4362.65i	0.910841	−	0.510489i
$419$	−346.536	−	600.219i	−0.0404043	−	0.0699823i	0.845116	−	0.534583i	$-0.179531\pi$
$419$	−346.536	−	600.219i	−0.0404043	−	0.0699823i	−0.885520	+	0.464601i	$0.846198\pi$
$420$	1789.05	−	1758.72i	0.207849	−	0.204326i
$421$	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
$426$	−3616.33	−	952.672i	−0.411295	−	0.108350i
$427$	−308.452	+	178.085i	−0.0349579	+	0.0201830i
$428$	241.393	+	443.895i	0.0272621	+	0.0501319i
$429$	2723.76	+	9515.98i	0.306536	+	1.07095i
$430$	−3196.09	+	5376.16i	−0.358440	+	0.602934i
$431$	10013.8			1.11914			0.559569	−	0.828784i	$-0.310967\pi$
$431$	10013.8			1.11914			0.559569	+	0.828784i	$0.310967\pi$
$432$	8673.27	−	2322.92i	0.965956	−	0.258707i
$433$	−9726.02			−1.07945			−0.539726	−	0.841841i	$-0.681472\pi$
$433$	−9726.02			−1.07945			−0.539726	+	0.841841i	$0.681472\pi$
$434$	102.889	−	173.069i	0.0113797	−	0.0191419i
$435$	2950.65	+	10308.7i	0.325225	+	1.13624i
$436$	3192.70	+	5871.03i	0.350694	+	0.644888i
$437$	−4098.64	+	2366.35i	−0.448660	+	0.259034i
$438$	1428.10	+	376.214i	0.155793	+	0.0410416i
$439$	−5675.95	−	3277.01i	−0.617080	−	0.356271i	0.158651	−	0.987335i	$-0.449285\pi$
$439$	−5675.95	−	3277.01i	−0.617080	−	0.356271i	−0.775731	+	0.631063i	$0.782619\pi$
$440$	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	$-0.935429\pi$
$443$	−2939.61	+	5091.55i	−0.315271	+	0.546065i	0.664224	+	0.747533i	$0.268762\pi$
$444$	526.542	−	517.618i	0.0562806	−	0.0553267i
$445$	−8626.14	−	14940.9i	−0.918917	−	1.59161i
$446$	6598.74	−	3698.32i	0.700582	−	0.392647i
$447$	−1519.07	−	1468.34i	−0.160737	−	0.155370i
$448$	1507.41	+	1031.64i	0.158969	+	0.108796i
$449$		−	6761.00i		−	0.710627i	−0.934747	−	0.355313i	$-0.884374\pi$
$449$		−	6761.00i		−	0.710627i	0.934747	−	0.355313i	$-0.115626\pi$
$450$	10786.5	+	5926.46i	1.12996	+	0.620836i
$451$			17314.5i			1.80778i
$452$	7027.86	+	4300.33i	0.731334	+	0.447501i
$453$	−4348.62	+	17406.0i	−0.451028	+	1.80531i
$454$	8157.60	+	14555.2i	0.843293	+	1.50465i
$455$	−1146.47	−	1985.74i	−0.118126	−	0.204600i
$456$	−7185.38	+	1762.13i	−0.737908	+	0.180963i
$457$	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	$0.422450\pi$
$462$	−2536.41	+	691.101i	−0.255421	+	0.0695951i
$463$	15291.7	−	8828.66i	1.53491	−	0.886183i	0.535789	−	0.844352i	$-0.320014\pi$
$463$	15291.7	−	8828.66i	1.53491	−	0.886183i	0.999125	−	0.0418305i	$-0.0133190\pi$
$464$	−6951.61	+	3553.53i	−0.695518	+	0.355536i
$465$	1701.57	+	425.112i	0.169696	+	0.0423959i
$466$	3146.34	+	1870.48i	0.312771	+	0.185940i
$467$	6165.12			0.610895			0.305447	−	0.952209i	$-0.401194\pi$
$467$	6165.12			0.610895			0.305447	+	0.952209i	$0.401194\pi$
$468$	−69.1820	−	8206.26i	−0.00683320	−	0.810544i
$469$	2210.83			0.217669
$470$	−12591.8	−	7485.76i	−1.23578	−	0.734664i
$471$	−3180.04	+	3289.89i	−0.311101	+	0.321848i
$472$	−5188.48	−	9838.13i	−0.505972	−	0.959400i
$473$	5675.89	−	3276.98i	0.551750	−	0.318553i
$474$	−10318.8	−	10232.1i	−0.999908	−	0.991514i
$475$	−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	$0.476042\pi$
$479$	−8659.06	+	14997.9i	−0.825976	+	1.43063i	−0.901171	+	0.433464i	$0.857291\pi$
$480$	−4833.18	+	15159.7i	−0.459591	+	1.44155i
$481$	−337.422	−	584.431i	−0.0319857	−	0.0554008i
$482$	8321.43	+	14847.5i	0.786371	+	1.40308i
$483$	1340.47	−	383.682i	0.126281	−	0.0361452i
$484$	−4938.72	+	8071.15i	−0.463816	+	0.757997i
$485$			17037.7i			1.59514i
$486$	7010.38	−	8102.21i	0.654315	−	0.756222i
$487$		−	7352.14i		−	0.684101i	−0.939682	−	0.342050i	$-0.888879\pi$
$487$		−	7352.14i		−	0.684101i	0.939682	−	0.342050i	$-0.111121\pi$
$488$	1203.54	−	1911.67i	0.111643	−	0.177330i
$489$	−8460.25	+	2421.57i	−0.782384	+	0.223941i
$490$	−13784.9	+	7725.89i	−1.27090	+	0.712286i
$491$	−4221.27	−	7311.46i	−0.387991	−	0.672019i	0.604189	−	0.796841i	$-0.293497\pi$
$491$	−4221.27	−	7311.46i	−0.387991	−	0.672019i	−0.992179	+	0.124822i	$0.960164\pi$
$492$	3833.84	−	13834.1i	0.351307	−	1.26766i
$493$	−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
$498$	−5210.53	+	5254.64i	−0.468854	+	0.472824i
$499$	−6542.34	+	3777.22i	−0.586924	+	0.338861i	−0.763880	−	0.645358i	$-0.776708\pi$
$499$	−6542.34	+	3777.22i	−0.586924	+	0.338861i	0.176956	+	0.984219i	$0.443375\pi$
$500$	−4299.01	+	2337.83i	−0.384515	+	0.209102i
$501$	−5922.95	+	6127.55i	−0.528180	+	0.546425i
$502$	4635.66	−	7797.68i	0.412151	−	0.693282i
$503$	604.632			0.0535968			0.0267984	−	0.999641i	$-0.491469\pi$
$503$	604.632			0.0535968			0.0267984	+	0.999641i	$0.491469\pi$
$504$	2179.59	+	9.44045i	0.192632	+	0.000834348i
$505$	−7121.47			−0.627527
$506$	5450.46	−	9168.26i	0.478859	−	0.805492i
$507$	3798.59	+	949.020i	0.332745	+	0.0831311i
$508$	5583.93	−	3036.58i	0.487691	−	0.265209i
$509$	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	$0.186348\pi$
$510$	5515.08	+	20240.9i	0.478847	+	1.75742i
$511$	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
$516$	−5260.57	+	1361.49i	−0.448805	+	0.116155i
$517$	7675.21	+	13293.8i	0.652911	+	1.13088i
$518$	156.352	−	87.6290i	0.0132620	−	0.00743281i
$519$	−2747.43	+	10997.0i	−0.232367	+	0.930085i
$520$	12306.9	+	7748.10i	1.03787	+	0.653416i
$521$		−	18465.3i		−	1.55274i	−0.630276	−	0.776371i	$-0.717058\pi$
$521$		−	18465.3i		−	1.55274i	0.630276	−	0.776371i	$-0.282942\pi$
$522$	−4485.94	+	8164.69i	−0.376139	+	0.684595i
$523$			15941.5i			1.33284i	0.745579	+	0.666418i	$0.232173\pi$
$523$			15941.5i			1.33284i	−0.745579	+	0.666418i	$0.767827\pi$
$524$	927.289	−	1515.43i	0.0773069	−	0.126340i
$525$	2148.09	+	2076.37i	0.178572	+	0.172610i
$526$	−431.593	−	770.072i	−0.0357764	−	0.0638341i
$527$	841.844	+	1458.12i	0.0695850	+	0.120525i
$528$	12184.7	−	11381.5i	1.00430	−	0.938097i
$529$	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
$534$	3818.34	−	14494.3i	0.309430	−	1.17459i
$535$	−925.299	+	534.221i	−0.0747741	+	0.0431709i
$536$	−12402.9	+	6541.08i	−0.999482	+	0.527111i
$537$	−3360.54	−	11740.7i	−0.270052	−	0.943482i
$538$	−4440.10	−	2639.61i	−0.355811	−	0.211527i
$539$	16559.1			1.32328
$540$	5378.32	+	18208.6i	0.428604	+	1.45106i
$541$	7256.04			0.576638			0.288319	−	0.957534i	$-0.406904\pi$
$541$	7256.04			0.576638			0.288319	+	0.957534i	$0.406904\pi$
$542$	12125.2	+	7208.37i	0.960929	+	0.571265i
$543$	−3260.31	−	11390.5i	−0.257667	−	0.900211i
$544$	−13688.4	+	6778.35i	−1.07883	+	0.534227i
$545$	−12238.1	+	7065.70i	−0.961880	+	0.555342i
$546$	507.481	−	1926.39i	0.0397769	−	0.150992i
$547$	374.999	+	216.506i	0.0293122	+	0.0169234i	0.514585	−	0.857440i	$-0.327946\pi$
$547$	374.999	+	216.506i	0.0293122	+	0.0169234i	−0.485272	+	0.874363i	$0.661280\pi$
$548$	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
$552$	−6384.93	+	6118.46i	−0.492320	+	0.471774i
$553$	−1763.77	−	3054.94i	−0.135630	−	0.234918i
$554$	5879.62	+	10490.7i	0.450904	+	0.804527i
$555$	1122.58	+	1085.10i	0.0858572	+	0.0829905i
$556$	15042.7	+	9204.58i	1.14740	+	0.702089i
$557$			9185.88i			0.698776i	0.936978	+	0.349388i	$0.113610\pi$
$557$			9185.88i			0.698776i	−0.936978	+	0.349388i	$0.886390\pi$
$558$	789.679	+	1303.19i	0.0599100	+	0.0988679i
$559$			4966.45i			0.375776i
$560$	−2099.39	+	3242.10i	−0.158420	+	0.244649i
$561$	5328.44	−	21327.9i	0.401010	−	1.60510i
$562$	−7241.31	+	4058.45i	−0.543516	+	0.304618i
$563$	−6499.11	−	11256.8i	−0.486510	−	0.842659i	0.513370	−	0.858167i	$-0.328397\pi$
$563$	−6499.11	−	11256.8i	−0.486510	−	0.842659i	−0.999880	+	0.0155079i	$0.995063\pi$
$564$	−3188.82	−	12321.1i	−0.238074	−	0.919879i
$565$	−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	$0.592552\pi$
$570$	−4112.61	−	15093.7i	−0.302207	−	1.10913i
$571$	21837.8	−	12608.1i	1.60050	−	0.924047i	0.609109	−	0.793086i	$-0.291527\pi$
$571$	21837.8	−	12608.1i	1.60050	−	0.924047i	0.991388	−	0.130961i	$-0.0418063\pi$
$572$	−7280.29	−	13387.6i	−0.532175	−	0.978611i
$573$	19826.8	+	4953.42i	1.44551	+	0.361138i
$574$	1780.74	−	2995.39i	0.129489	−	0.217814i
$575$	−12121.4			−0.879125
$576$	−12255.5	+	6395.69i	−0.886541	+	0.462651i
$577$	18112.2			1.30680			0.653398	−	0.757014i	$-0.273343\pi$
$577$	18112.2			1.30680			0.653398	+	0.757014i	$0.273343\pi$
$578$	−3190.35	+	5366.51i	−0.229587	+	0.386189i
$579$	9798.24	−	10136.7i	0.703283	−	0.727577i
$580$	−7886.75	−	14502.9i	−0.564620	−	1.03827i
$581$	−1555.67	+	898.169i	−0.111085	+	0.0641348i
$582$	−10422.7	+	10510.9i	−0.742327	+	0.748612i
$583$	−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	$0.543602\pi$
$587$	−13172.1	+	22814.8i	−0.926189	+	1.60421i	−0.789638	+	0.613573i	$0.789732\pi$
$588$	−13230.5	−	3666.57i	−0.927919	−	0.257154i
$589$	−627.764	−	1087.32i	−0.0439161	−	0.0760649i
$590$	20516.3	−	11498.5i	1.43160	−	0.802351i
$591$	−9980.65	+	2856.76i	−0.694669	+	0.198835i
$592$	−617.881	+	954.195i	−0.0428965	+	0.0662453i
$593$		−	11633.4i		−	0.805609i	−0.915286	−	0.402804i	$-0.868035\pi$
$593$		−	11633.4i		−	0.805609i	0.915286	−	0.402804i	$-0.131965\pi$
$594$	4412.26	−	19400.1i	0.304776	−	1.34006i
$595$			5092.53i			0.350880i
$596$	2774.54	+	1697.73i	0.190687	+	0.116681i
$597$	12034.7	−	3444.69i	0.825039	−	0.236150i
$598$	3951.60	+	7050.66i	0.270223	+	0.482146i
$599$	11060.5	+	19157.3i	0.754454	+	1.30675i	0.945645	+	0.325200i	$0.105432\pi$
$599$	11060.5	+	19157.3i	0.754454	+	1.30675i	−0.191191	+	0.981553i	$0.561235\pi$
$600$	−18194.2	−	5293.08i	−1.23796	−	0.360148i
$601$	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
$606$	−4393.39	−	4356.51i	−0.294504	−	0.292031i
$607$	−11418.4	+	6592.43i	−0.763525	+	0.440821i	−0.830560	−	0.556929i	$-0.811979\pi$
$607$	−11418.4	+	6592.43i	−0.763525	+	0.440821i	0.0670351	+	0.997751i	$0.478646\pi$
$608$	10207.5	−	5054.62i	0.680867	−	0.337158i
$609$	−1571.68	+	1625.97i	−0.104577	+	0.108190i
$610$	4105.92	+	2440.94i	0.272531	+	0.162018i
$611$	−11632.2			−0.770196
$612$	−8979.86	+	15860.9i	−0.593120	+	1.04761i
$613$	−18052.3			−1.18944			−0.594719	−	0.803934i	$-0.702737\pi$
$613$	−18052.3			−1.18944			−0.594719	+	0.803934i	$0.702737\pi$
$614$	−11123.3	−	6612.73i	−0.731108	−	0.434639i
$615$	29450.0	+	7357.61i	1.93095	+	0.482419i
$616$	3580.06	−	1888.07i	0.234164	−	0.123494i
$617$	−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	$0.585491\pi$
$618$	24504.9	−	6676.89i	1.59503	−	0.434602i
$619$	15640.0	+	9029.74i	1.01555	+	0.586326i	0.912811	−	0.408382i	$-0.133907\pi$
$619$	15640.0	+	9029.74i	1.01555	+	0.586326i	0.102736	+	0.994709i	$0.467240\pi$
$620$	−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
$624$	2852.52	+	12308.6i	0.183000	+	0.789645i
$625$	4898.71	+	8484.82i	0.313518	+	0.543028i
$626$	−7356.45	−	13125.8i	−0.469685	−	0.838037i
$627$	−3973.42	+	15904.2i	−0.253083	+	1.01300i
$628$	3676.84	−	6008.92i	0.233634	−	0.381818i
$629$			1498.81i			0.0950100i
$630$	97.6620	+	4607.82i	0.00617611	+	0.291397i
$631$		−	7301.94i		−	0.460674i	−0.973111	−	0.230337i	$-0.926017\pi$
$631$		−	7301.94i		−	0.460674i	0.973111	−	0.230337i	$-0.0739829\pi$
$632$	18933.4	+	11920.0i	1.19166	+	0.750241i
$633$	6797.55	+	6570.58i	0.426822	+	0.412571i
$634$	−21770.5	+	12201.4i	−1.36375	+	0.764324i
$635$	6720.18	+	11639.7i	0.419972	+	0.727413i
$636$	13972.3	+	14213.2i	0.871131	+	0.886150i
$637$	−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	$0.658331\pi$
$642$	−897.643	−	236.472i	−0.0551825	−	0.0145371i
$643$	984.538	−	568.423i	0.0603832	−	0.0348622i	−0.469504	−	0.882930i	$-0.655567\pi$
$643$	984.538	−	568.423i	0.0603832	−	0.0348622i	0.529888	+	0.848068i	$0.322234\pi$
$644$	−1885.85	+	1025.54i	−0.115393	+	0.0627514i
$645$	−3161.85	−	11046.6i	−0.193020	−	0.674353i
$646$	7674.30	−	12909.0i	0.467402	−	0.786219i
$647$	−995.889			−0.0605138			−0.0302569	−	0.999542i	$-0.509633\pi$
$647$	−995.889			−0.0605138			−0.0302569	+	0.999542i	$0.509633\pi$
$648$	−7820.98	+	14523.4i	−0.474131	+	0.880454i
$649$	−24645.0			−1.49061
$650$	−8849.93	+	14886.5i	−0.534035	+	0.898303i
$651$	101.786	+	355.611i	0.00612799	+	0.0214093i
$652$	11902.4	−	6472.59i	0.714928	−	0.388783i
$653$	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	$0.0114057\pi$
$654$	−11872.4	−	3127.62i	−0.709857	−	0.187002i
$655$	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	$-0.562416\pi$
$659$	12722.0	−	22035.1i	0.752014	−	1.30253i	0.946845	−	0.321690i	$-0.104251\pi$
$660$	24716.2	+	25142.3i	1.45769	+	1.48282i
$661$	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	$0.793723\pi$
$662$	5858.28	−	3283.32i	0.343940	−	0.192764i
$663$	11977.7	+	11577.7i	0.701620	+	0.678193i
$664$	6070.04	−	9641.48i	0.354764	−	0.563497i
$665$		−	3797.51i		−	0.221445i
$666$	28.7433	+	1356.15i	0.00167234	+	0.0789034i
$667$		−	9175.09i		−	0.532625i
$668$	6848.26	−	11191.8i	0.396657	−	0.648241i
$669$	−3368.36	+	13482.4i	−0.194661	+	0.779162i
$670$	−14496.1	−	25864.8i	−0.835872	−	1.49141i
$671$	−2502.71	−	4334.83i	−0.143988	−	0.249395i
$672$	−3278.49	+	715.833i	−0.188200	+	0.0410920i
$673$	−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	$-0.699953\pi$
$678$	−14603.9	+	3979.15i	−0.827226	+	0.225396i
$679$	−3111.84	+	1796.62i	−0.175878	+	0.101543i
$680$	−15067.0	−	28569.4i	−0.849698	−	1.61116i
$681$	−29738.9	−	7429.80i	−1.67342	−	0.418077i
$682$	2432.23	+	1445.94i	0.136561	+	0.0811847i
$683$	−28383.3			−1.59012			−0.795062	−	0.606528i	$-0.792562\pi$
$683$	−28383.3			−1.59012			−0.795062	+	0.606528i	$0.792562\pi$
$684$	6696.30	−	11827.5i	0.374326	−	0.661162i
$685$	20593.5			1.14867
$686$	−5839.81	−	3471.73i	−0.325022	−	0.193223i
$687$	10952.3	−	11330.6i	0.608232	−	0.629242i
$688$	7449.19	−	3807.89i	0.412787	−	0.211009i
$689$	15775.9	−	9108.21i	0.872298	−	0.503621i
$690$	−13278.0	−	13166.6i	−0.732589	−	0.726439i
$691$	−4592.61	−	2651.54i	−0.252838	−	0.145976i	0.368225	−	0.929737i	$-0.379966\pi$
$691$	−4592.61	−	2651.54i	−0.252838	−	0.145976i	−0.621063	+	0.783761i	$0.713299\pi$
$692$	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
$696$	4006.51	−	13771.8i	0.218199	−	0.750027i
$697$	14570.2	+	25236.3i	0.791801	+	1.37144i
$698$	9493.61	+	16939.0i	0.514812	+	0.918555i
$699$	−6464.87	+	1850.44i	−0.349819	+	0.100129i
$700$	−3923.45	−	2400.75i	−0.211846	−	0.129628i
$701$			10087.7i			0.543519i	0.962365	+	0.271760i	$0.0876056\pi$
$701$			10087.7i			0.543519i	−0.962365	+	0.271760i	$0.912394\pi$
$702$	11059.7	+	10246.1i	0.594615	+	0.550873i
$703$		−	1117.66i		−	0.0599622i
$704$	−14498.2	+	21184.3i	−0.776166	+	1.13411i
$705$	25872.8	−	7405.56i	1.38216	−	0.395616i
$706$	307.605	−	172.400i	0.0163978	−	0.00919031i
$707$	−750.956	−	1300.69i	−0.0399471	−	0.0691905i
$708$	19691.1	+	5457.00i	1.04525	+	0.289670i
$709$	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
$714$	−3115.32	+	3141.70i	−0.163288	+	0.164671i
$715$	27906.5	−	16111.9i	1.45964	−	0.842726i
$716$	8982.36	+	16517.6i	0.468836	+	0.862137i
$717$	20766.2	−	21483.5i	1.08163	−	1.11899i
$718$	−6488.92	+	10915.0i	−0.337276	+	0.567334i
$719$	7178.86			0.372359			0.186180	−	0.982516i	$-0.440389\pi$
$719$	7178.86			0.372359			0.186180	+	0.982516i	$0.440389\pi$
$720$	−14180.8	−	25561.2i	−0.734012	−	1.32307i
$721$	6165.33			0.318459
$722$	4190.96	−	7049.64i	0.216027	−	0.363380i
$723$	−30336.1	−	7579.01i	−1.56046	−	0.389857i
$724$	8714.44	+	16024.9i	0.447334	+	0.822597i
$725$	17025.7	−	9829.77i	0.872161	−	0.503543i
$726$	−4569.86	−	16771.9i	−0.233614	−	0.857385i
$727$	−18250.7	−	10537.0i	−0.931061	−	0.537548i	−0.0439138	−	0.999035i	$-0.513983\pi$
$727$	−18250.7	−	10537.0i	−0.931061	−	0.537548i	−0.887147	+	0.461487i	$0.847316\pi$
$728$	−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
$732$	1039.80	+	4017.63i	0.0525031	+	0.202863i
$733$	−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	$-0.336890\pi$
$734$	2139.62	−	1199.17i	0.107595	−	0.0603026i
$735$	7036.60	−	28165.1i	0.353128	−	1.41345i
$736$	7545.52	−	11332.9i	0.377896	−	0.567577i
$737$			31069.9i			1.55288i
$738$	13667.4	+	22554.9i	0.681711	+	1.12501i
$739$			8782.55i			0.437173i	0.975818	+	0.218587i	$0.0701447\pi$
$739$			8782.55i			0.437173i	−0.975818	+	0.218587i	$0.929855\pi$
$740$	−2050.36	−	1254.61i	−0.101855	−	0.0623250i
$741$	−8931.77	−	8633.54i	−0.442803	−	0.428018i
$742$	2365.42	+	4220.50i	0.117031	+	0.208813i
$743$	−11676.8	−	20224.8i	−0.576553	−	0.998620i	−0.995871	−	0.0907800i	$-0.971064\pi$
$743$	−11676.8	−	20224.8i	−0.576553	−	0.998620i	0.419318	−	0.907840i	$-0.362269\pi$
$744$	−1623.16	−	1693.84i	−0.0799835	−	0.0834668i
$745$	−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
$750$	2290.17	−	8693.44i	0.111500	−	0.423253i
$751$	−14625.3	+	8443.94i	−0.710634	+	0.410285i	−0.811296	−	0.584636i	$-0.801237\pi$
$751$	−14625.3	+	8443.94i	−0.710634	+	0.410285i	0.100662	+	0.994921i	$0.467904\pi$
$752$	8918.69	+	17447.2i	0.432488	+	0.846056i
$753$	4586.00	+	16022.1i	0.221943	+	0.775403i
$754$	−11268.1	−	6698.81i	−0.544244	−	0.323549i
$755$	58407.6			2.81546
$756$	−2758.55	+	2902.41i	−0.132708	+	0.139629i
$757$	6838.01			0.328311			0.164156	−	0.986434i	$-0.447510\pi$
$757$	6838.01			0.328311			0.164156	+	0.986434i	$0.447510\pi$
$758$	−34272.9	−	20375.0i	−1.64228	−	0.976325i
$759$	5392.07	+	18838.3i	0.257865	+	0.900904i
$760$	11235.5	+	21304.2i	0.536257	+	1.01682i
$761$	−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	$0.524031\pi$
$762$	−2974.67	+	11291.8i	−0.141419	+	0.536823i
$763$	−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
$768$	16274.6	−	13715.8i	0.764660	−	0.644434i
$769$	−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	$-0.498532\pi$
$770$	4184.28	+	7465.81i	0.195832	+	0.349414i
$771$	−10863.9	−	10501.2i	−0.507464	−	0.490520i
$772$	−11329.0	+	18514.5i	−0.528158	+	0.863148i
$773$			7505.51i			0.349230i	0.984637	+	0.174615i	$0.0558680\pi$
$773$			7505.51i			0.349230i	−0.984637	+	0.174615i	$0.944132\pi$
$774$	4807.04	−	8749.10i	0.223237	−	0.406305i
$775$		−	3215.66i		−	0.149045i
$776$	12142.0	−	19286.0i	0.561691	−	0.892173i
$777$	−79.8109	+	319.455i	−0.00368494	+	0.0147495i
$778$	14168.2	−	7940.66i	0.652896	−	0.365921i
$779$	−10865.0	−	18818.8i	−0.499717	−	0.865535i
$780$	−25864.5	+	6694.00i	−1.18731	+	0.307287i
$781$	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
$786$	858.033	+	3149.07i	0.0389377	+	0.142905i
$787$	−16864.0	+	9736.41i	−0.763832	+	0.440998i	−0.830670	−	0.556765i	$-0.812042\pi$
$787$	−16864.0	+	9736.41i	−0.763832	+	0.440998i	0.0668382	+	0.997764i	$0.478709\pi$
$788$	14041.4	−	7635.79i	0.634775	−	0.345195i
$789$	1573.39	+	393.088i	0.0709940	+	0.0177367i
$790$	−24175.3	+	40665.5i	−1.08876	+	1.83141i
$791$	−3674.28			−0.165161
$792$	−132.671	+	30630.8i	−0.00595236	+	1.37427i
$793$	3793.01			0.169853
$794$	15168.2	−	25514.5i	0.677957	−	1.14040i
$795$	−29290.6	+	30302.4i	−1.30670	+	1.35184i
$796$	−16931.2	+	9207.27i	−0.753906	+	0.409979i
$797$	−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	$0.625884\pi$
$798$	2323.10	−	2342.77i	0.103054	−	0.103926i
$799$	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
$804$	6879.61	−	24824.4i	0.301773	−	1.08892i
$805$	−2269.60	−	3931.06i	−0.0993700	−	0.172114i
$806$	−1870.46	+	1048.31i	−0.0817420	+	0.0458130i
$807$	9123.20	−	2611.33i	0.397958	−	0.113907i
$808$	8061.21	+	5075.14i	0.350981	+	0.220969i
$809$		−	16519.8i		−	0.717932i	−0.933351	−	0.358966i	$-0.883129\pi$
$809$		−	16519.8i		−	0.717932i	0.933351	−	0.358966i	$-0.116871\pi$
$810$	−31122.3	−	15748.6i	−1.35003	−	0.683147i
$811$			18594.4i			0.805103i	0.915397	+	0.402552i	$0.131877\pi$
$811$			18594.4i			0.805103i	−0.915397	+	0.402552i	$0.868123\pi$
$812$	1817.21	−	2969.79i	0.0785363	−	0.128349i
$813$	−24914.1	+	7131.14i	−1.07475	+	0.307626i
$814$	1231.49	+	2197.29i	0.0530268	+	0.0946132i
$815$	14324.3	+	24810.5i	0.615656	+	1.06635i
$816$	8181.93	−	26842.2i	0.351011	−	1.15155i
$817$	−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	$0.326722\pi$
$822$	12704.6	+	12597.9i	0.539080	+	0.534555i
$823$	−3713.28	+	2143.86i	−0.157274	+	0.0908025i	−0.576572	−	0.817047i	$-0.695610\pi$
$823$	−3713.28	+	2143.86i	−0.157274	+	0.0908025i	0.419297	+	0.907849i	$0.362277\pi$
$824$	−34587.8	+	18241.1i	−1.46229	+	0.771187i
$825$	−29180.2	+	30188.2i	−1.23143	+	1.27396i
$826$	4263.58	+	2534.67i	0.179599	+	0.106770i
$827$	−24944.4			−1.04885			−0.524426	−	0.851456i	$-0.675720\pi$
$827$	−24944.4			−1.04885			−0.524426	+	0.851456i	$0.675720\pi$
$828$	−136.956	−	16245.5i	−0.00574824	−	0.681848i
$829$	−31040.8			−1.30047			−0.650235	−	0.759733i	$-0.725330\pi$
$829$	−31040.8			−1.30047			−0.650235	+	0.759733i	$0.725330\pi$
$830$	20708.2	+	12310.8i	0.866013	+	0.514838i
$831$	−21434.4	−	5355.05i	−0.894767	−	0.223544i
$832$	−8409.14	−	17541.1i	−0.350402	−	0.730922i
$833$	24135.3	−	13934.5i	1.00389	−	0.579594i
$834$	−31258.7	+	8517.12i	−1.29784	+	0.353626i
$835$	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	$-0.918075\pi$
$839$	−6393.60	+	11074.0i	−0.263089	+	0.455683i	0.703972	+	0.710228i	$0.251408\pi$
$840$	−1690.08	−	6891.59i	−0.0694205	−	0.283074i
$841$	−4754.02	−	8234.20i	−0.194925	−	0.337619i
$842$	−14831.5	−	26463.1i	−0.607038	−	1.08311i
$843$	3696.37	−	14795.3i	0.151020	−	0.604479i
$844$	−12415.6	−	7597.06i	−0.506353	−	0.309836i
$845$		−	12746.6i		−	0.518929i
$846$	20491.8	+	11258.9i	0.832769	+	0.457550i
$847$		−	4219.73i		−	0.171183i
$848$	−25757.1	−	16678.8i	−1.04305	−	0.675415i
$849$	−14957.8	−	14458.4i	−0.604655	−	0.584466i
$850$	33553.3	−	18805.3i	1.35396	−	0.758841i
$851$	−667.975	−	1156.97i	−0.0269070	−	0.0466044i
$852$	−7543.06	+	7415.22i	−0.303311	+	0.298170i
$853$	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	$0.294603\pi$
$858$	27072.5	+	7131.88i	1.07720	+	0.283774i
$859$	5670.77	−	3274.02i	0.225244	−	0.130045i	−0.383132	−	0.923694i	$-0.625155\pi$
$859$	5670.77	−	3274.02i	0.225244	−	0.130045i	0.608376	+	0.793649i	$0.291821\pi$
$860$	8451.27	+	15540.9i	0.335100	+	0.616211i
$861$	1761.66	+	6154.72i	0.0697298	+	0.243615i
$862$	14473.5	−	24346.0i	0.571892	−	0.961983i
$863$	29442.2			1.16133			0.580663	−	0.814144i	$-0.302793\pi$
$863$	29442.2			1.16133			0.580663	+	0.814144i	$0.302793\pi$
$864$	6888.40	−	24444.3i	0.271236	−	0.962513i
$865$	36901.5			1.45051
$866$	−14057.6	+	23646.3i	−0.551611	+	0.927869i
$867$	−3156.17	−	11026.7i	−0.123632	−	0.431934i
$868$	−272.063	−	500.294i	−0.0106387	−	0.0195635i
$869$	42932.6	−	24787.2i	1.67594	−	0.967603i
$870$	29327.6	+	7725.97i	1.14287	+	0.301075i
$871$	−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
$876$	2978.78	−	2928.30i	0.114890	−	0.112943i
$877$	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	$0.616039\pi$
$878$	−16171.0	+	9063.16i	−0.621576	+	0.348368i
$879$	10070.1	+	9733.88i	0.386413	+	0.373510i
$880$	−45562.7	−	29503.7i	−1.74536	−	1.13019i
$881$		−	15082.2i		−	0.576769i	−0.957515	−	0.288384i	$-0.906882\pi$
$881$		−	15082.2i		−	0.576769i	0.957515	−	0.288384i	$-0.0931181\pi$
$882$	21570.8	−	13071.1i	0.823500	−	0.499008i
$883$		−	425.340i		−	0.0162105i	−0.999967	−	0.00810523i	$-0.997420\pi$
$883$		−	425.340i		−	0.0162105i	0.999967	−	0.00810523i	$-0.00258000\pi$
$884$	−21877.0	−	13386.5i	−0.832355	−	0.509316i
$885$	−10472.7	+	41918.4i	−0.397779	+	1.59217i
$886$	8130.01	+	14506.0i	0.308277	+	0.550044i
$887$	6078.41	+	10528.1i	0.230094	+	0.398534i	0.957835	−	0.287317i	$-0.0927634\pi$
$887$	6078.41	+	10528.1i	0.230094	+	0.398534i	−0.727742	+	0.685851i	$0.759430\pi$
$888$	−497.414	−	2028.29i	−0.0187974	−	0.0766499i
$889$	−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
$894$	−5765.49	+	1570.94i	−0.215690	+	0.0587695i
$895$	−34430.8	+	19878.7i	−1.28592	+	0.742425i
$896$	4686.92	−	2173.78i	0.174753	−	0.0810501i
$897$	−14405.7	−	3599.05i	−0.536225	−	0.133967i
$898$	−16437.6	−	9772.06i	−0.610836	−	0.363138i
$899$	2434.04			0.0903001
$900$	29999.1	−	17658.8i	1.11108	−	0.654030i
$901$	−40458.1			−1.49595
$902$	42095.7	+	25025.6i	1.55392	+	0.923793i
$903$	1684.17	−	1742.35i	0.0620662	−	0.0642101i
$904$	20612.9	−	10870.9i	0.758380	−	0.399958i
$905$	−33403.9	+	19285.7i	−1.22694	+	0.708375i
$906$	36032.9	+	35730.4i	1.32132	+	1.31022i
$907$	39674.6	+	22906.2i	1.45245	+	0.838574i	0.998620	−	0.0525131i	$-0.0167231\pi$
$907$	39674.6	+	22906.2i	1.45245	+	0.838574i	0.453832	+	0.891087i	$0.350056\pi$
$908$	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	$0.342278\pi$
$911$	−14411.9	+	24962.1i	−0.524134	+	0.907827i	−0.999605	+	0.0280960i	$0.991056\pi$
$912$	−6101.27	+	20016.3i	−0.221528	+	0.726761i
$913$	−12622.4	−	21862.7i	−0.457547	−	0.792495i
$914$	−21074.9	−	37603.0i	−0.762688	−	1.36083i
$915$	−8436.54	+	2414.79i	−0.304813	+	0.0872464i
$916$	−12663.3	+	20695.1i	−0.456775	+	0.746490i
$917$			792.293i			0.0285320i
$918$	−9894.23	−	31989.0i	−0.355728	−	1.15010i
$919$		−	41488.4i		−	1.48920i	−0.667511	−	0.744600i	$-0.732640\pi$
$919$		−	41488.4i		−	1.48920i	0.667511	−	0.744600i	$-0.267360\pi$
$920$	24363.2	+	15338.5i	0.873077	+	0.549669i
$921$	22855.4	−	6541.89i	0.817710	−	0.234053i
$922$	33904.6	−	19002.1i	1.21105	−	0.678743i
$923$	4833.79	+	8372.36i	0.172379	+	0.298570i
$924$	−1985.78	+	7165.52i	−0.0707008	+	0.255117i
$925$	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	$0.642890\pi$
$930$	3492.93	−	3522.50i	0.123159	−	0.124202i
$931$	−17997.7	+	10391.0i	−0.633567	+	0.365790i
$932$	9095.16	−	4946.01i	0.319659	−	0.173833i
$933$	29753.5	−	30781.2i	1.04403	−	1.08010i
$934$	8910.80	−	14988.9i	0.312174	−	0.525109i
$935$	−71567.8			−2.50323
$936$	−20051.4	−	11692.8i	−0.700215	−	0.408323i
$937$	31514.2			1.09875			0.549373	−	0.835577i	$-0.314867\pi$
$937$	31514.2			1.09875			0.549373	+	0.835577i	$0.314867\pi$
$938$	3195.44	−	5375.07i	0.111231	−	0.187102i
$939$	26818.3	+	6700.12i	0.932035	+	0.232854i
$940$	−36399.4	+	19794.2i	−1.26300	+	0.686826i
$941$	−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	$0.485782\pi$
$942$	3402.23	+	12486.5i	0.117676	+	0.431882i
$943$	−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	$-0.486936\pi$
$947$	25814.6	−	44712.3i	0.885811	−	1.53427i	0.844781	−	0.535112i	$-0.179731\pi$
$948$	−39791.1	+	10298.3i	−1.36324	+	0.352821i
$949$	−1908.88	−	3306.28i	−0.0652950	−	0.113094i
$950$	−25020.8	+	14023.1i	−0.854506	+	0.478915i
$951$	11112.9	−	44480.9i	0.378927	−	1.51671i
$952$	3629.22	−	5764.54i	0.123554	−	0.196250i
$953$			25766.7i			0.875829i	0.899017	+	0.437915i	$0.144283\pi$
$953$			25766.7i			0.875829i	−0.899017	+	0.437915i	$0.855717\pi$
$954$	−36607.3	+	775.885i	−1.24235	+	0.0263314i
$955$		−	66530.9i		−	2.25433i
$956$	−24010.4	+	39239.2i	−0.812291	+	1.32750i
$957$	−22850.5	−	22087.5i	−0.771840	−	0.746069i
$958$	23948.2	+	42729.7i	0.807653	+	1.44106i
$959$	2171.58	+	3761.29i	0.0731220	+	0.126651i
$960$	29871.3	+	33661.8i	1.00426	+	1.13170i
$961$	−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
$966$	1004.63	−	3813.57i	0.0334612	−	0.127018i
$967$	39828.3	−	22994.9i	1.32450	−	0.764700i	0.340056	−	0.940405i	$-0.389554\pi$
$967$	39828.3	−	22994.9i	1.32450	−	0.764700i	0.984443	+	0.175705i	$0.0562205\pi$
$968$	12484.7	+	23672.9i	0.414540	+	0.786029i
$969$	7592.09	+	26524.5i	0.251696	+	0.879349i
$970$	41422.8	+	24625.6i	1.37114	+	0.815133i
$971$	−22109.4			−0.730714			−0.365357	−	0.930867i	$-0.619053\pi$
$971$	−22109.4			−0.730714			−0.365357	+	0.930867i	$0.619053\pi$
$972$	−9565.95	−	28754.5i	−0.315667	−	0.948870i
$973$	−7864.57			−0.259123
$974$	−17874.8	−	10626.5i	−0.588036	−	0.349583i
$975$	−8755.12	−	30587.7i	−0.287578	−	1.00471i
$976$	−2908.19	−	5689.14i	−0.0953778	−	0.186583i
$977$	−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	$0.644446\pi$
$978$	−6340.64	+	24069.0i	−0.207312	+	0.786953i
$979$	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	$-0.906158\pi$
$983$	−6989.79	+	12106.7i	−0.226795	+	0.392821i	0.730061	+	0.683382i	$0.239491\pi$
$984$	−28092.7	−	29316.2i	−0.910125	−	0.949761i
$985$	16898.6	+	29269.2i	0.546633	+	0.946797i
$986$	14234.3	+	25397.7i	0.459750	+	0.820310i
$987$	4080.86	+	3944.60i	0.131606	+	0.127212i
$988$	16313.7	+	9982.30i	0.525311	+	0.321437i
$989$			9831.82i			0.316111i
$990$	−64756.0	+	1372.49i	−2.07887	+	0.0440613i
$991$		−	29526.4i		−	0.946456i	−0.880940	−	0.473228i	$-0.843089\pi$
$991$		−	29526.4i		−	0.946456i	0.880940	−	0.473228i	$-0.156911\pi$
$992$	3006.49	+	2001.73i	0.0962258	+	0.0640677i
$993$	−2990.39	+	11969.5i	−0.0955661	+	0.382518i
$994$	−2239.85	+	1255.34i	−0.0714725	+	0.0400574i
$995$	−20376.4	−	35293.0i	−0.649222	−	1.12448i
$996$	5244.24	+	20262.9i	0.166837	+	0.644633i
$997$	−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.11.9	yes	24
3.2	odd	2		108.4.h.b.35.4		24
4.3	odd	2	inner	36.4.h.b.11.5	✓	24
9.2	odd	6		324.4.b.c.323.24		24
9.4	even	3		108.4.h.b.71.8		24
9.5	odd	6	inner	36.4.h.b.23.5	yes	24
9.7	even	3		324.4.b.c.323.1		24
12.11	even	2		108.4.h.b.35.8		24
36.7	odd	6		324.4.b.c.323.23		24
36.11	even	6		324.4.b.c.323.2		24
36.23	even	6	inner	36.4.h.b.23.9	yes	24
36.31	odd	6		108.4.h.b.71.4		24

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

\(f(q)\)	\(=\)	\(q+(1.44536 - 2.43124i) q^{2} +(1.42987 + 4.99554i) q^{3} +(-3.82189 - 7.02803i) q^{4} +(14.6499 - 8.45813i) q^{5} +(14.2121 + 3.74398i) q^{6} +(3.08966 + 1.78382i) q^{7} +(-22.6108 - 0.866066i) q^{8} +(-22.9109 + 14.2860i) q^{9} +O(q^{10})\)	\(q+(1.44536 - 2.43124i) q^{2} +(1.42987 + 4.99554i) q^{3} +(-3.82189 - 7.02803i) q^{4} +(14.6499 - 8.45813i) q^{5} +(14.2121 + 3.74398i) 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} +(29.6440 - 29.1416i) q^{12} +(-18.9966 - 32.9032i) q^{13} +(8.80255 - 4.93346i) q^{14} +(63.2005 + 61.0903i) q^{15} +(-34.7863 + 53.7207i) q^{16} +84.3819i q^{17} +(1.61823 + 76.3504i) q^{18} -62.9237i q^{19} +(-115.434 - 70.6340i) q^{20} +(-4.49331 + 17.9852i) q^{21} +(69.3323 + 123.706i) q^{22} +(-37.6066 - 65.1366i) q^{23} +(-28.0041 - 114.192i) 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} +(239.873 - 65.3586i) q^{30} +(17.2800 - 9.97659i) q^{31} +(80.3294 + 162.220i) q^{32} +(-252.754 - 63.1467i) q^{33} +(205.153 + 121.962i) q^{34} +60.3510 q^{35} +(187.965 + 106.419i) q^{36} +17.7622 q^{37} +(-152.983 - 90.9472i) q^{38} +(137.206 - 141.946i) q^{39} +(-338.572 + 178.558i) q^{40} +(299.072 - 172.670i) q^{41} +(37.2319 + 36.9193i) 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} +(-318.104 - 96.9630i) q^{48} +(-165.136 - 286.024i) q^{49} +(-222.859 - 397.636i) q^{50} +(-421.534 + 120.655i) q^{51} +(-158.641 + 259.261i) q^{52} +479.464i q^{53} +(-379.098 + 117.255i) q^{54} +848.142i q^{55} +(-68.3149 - 43.0094i) q^{56} +(314.338 - 89.9729i) q^{57} +(300.984 - 168.689i) q^{58} +(245.774 + 425.693i) q^{59} +(187.799 - 677.655i) 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} +(-518.845 + 523.237i) q^{66} +(536.669 - 309.846i) q^{67} +(593.039 - 322.498i) q^{68} +(271.620 - 281.003i) q^{69} +(87.2287 - 146.728i) q^{70} -254.455 q^{71} +(530.408 - 303.176i) q^{72} +100.485 q^{73} +(25.6727 - 43.1841i) q^{74} +(812.441 + 202.976i) q^{75} +(-442.230 + 240.488i) q^{76} +(-154.908 + 89.4363i) q^{77} +(-146.793 - 538.745i) 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} +(143.573 - 37.1581i) q^{84} +(713.714 + 1236.19i) q^{85} +(-322.528 + 180.764i) q^{86} +(-153.639 + 614.964i) q^{87} +(604.432 - 960.062i) q^{88} -1019.86i q^{89} +(669.489 + 1104.84i) q^{90} -135.546i q^{91} +(-314.053 + 513.245i) q^{92} +(74.5466 + 72.0576i) q^{93} +(-423.378 - 755.413i) q^{94} +(-532.217 - 921.828i) q^{95} +(-695.514 + 633.242i) 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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