LMFDB - Embedded newform 112.4.j.b.83.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,4,Mod(27,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.27"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	112.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.60821392064$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.10
Character	$\chi$	$=$	112.83
Dual form			112.4.j.b.27.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.35605 - 1.56494i) q^{2} +(4.79702 + 4.79702i) q^{3} +(3.10192 + 7.37415i) q^{4} +(-2.04624 - 2.04624i) q^{5} +(-3.79496 - 18.8091i) q^{6} +(13.3740 - 12.8115i) q^{7} +(4.23184 - 22.2282i) q^{8} +19.0229i q^{9} +(1.61879 + 8.02329i) q^{10} +(34.5515 + 34.5515i) q^{11} +(-20.4940 + 50.2540i) q^{12} +(7.32563 - 7.32563i) q^{13} +(-51.5591 + 9.25497i) q^{14} -19.6317i q^{15} +(-44.7562 + 45.7480i) q^{16} +133.707i q^{17} +(29.7697 - 44.8188i) q^{18} +(13.6735 + 13.6735i) q^{19} +(8.74201 - 21.4366i) q^{20} +(125.613 + 2.69841i) q^{21} +(-27.3339 - 135.476i) q^{22} +129.773 q^{23} +(126.929 - 86.3288i) q^{24} -116.626i q^{25} +(-28.7237 + 5.79535i) q^{26} +(38.2664 - 38.2664i) q^{27} +(135.959 + 58.8819i) q^{28} +(85.7909 + 85.7909i) q^{29} +(-30.7225 + 46.2533i) q^{30} -239.073 q^{31} +(177.041 - 37.7438i) q^{32} +331.489i q^{33} +(209.244 - 315.021i) q^{34} +(-53.5820 - 1.15105i) q^{35} +(-140.278 + 59.0074i) q^{36} +(-50.7975 + 50.7975i) q^{37} +(-10.8172 - 53.6135i) q^{38} +70.2824 q^{39} +(-54.1436 + 36.8248i) q^{40} -118.276 q^{41} +(-291.727 - 202.934i) q^{42} +(-75.4750 - 75.4750i) q^{43} +(-147.612 + 361.964i) q^{44} +(38.9254 - 38.9254i) q^{45} +(-305.751 - 203.087i) q^{46} -169.043 q^{47} +(-434.151 + 4.75794i) q^{48} +(14.7299 - 342.684i) q^{49} +(-182.512 + 274.776i) q^{50} +(-641.398 + 641.398i) q^{51} +(76.7438 + 31.2968i) q^{52} +(482.264 - 482.264i) q^{53} +(-150.042 + 30.2728i) q^{54} -141.401i q^{55} +(-228.180 - 351.497i) q^{56} +131.184i q^{57} +(-67.8698 - 336.385i) q^{58} +(-285.231 + 285.231i) q^{59} +(144.767 - 60.8961i) q^{60} +(313.070 - 313.070i) q^{61} +(563.267 + 374.135i) q^{62} +(243.712 + 254.413i) q^{63} +(-476.183 - 188.132i) q^{64} -29.9800 q^{65} +(518.760 - 781.003i) q^{66} +(-58.2711 + 58.2711i) q^{67} +(-985.979 + 414.750i) q^{68} +(622.523 + 622.523i) q^{69} +(124.440 + 86.5645i) q^{70} -374.109 q^{71} +(422.844 + 80.5018i) q^{72} -610.003 q^{73} +(199.176 - 40.1862i) q^{74} +(559.457 - 559.457i) q^{75} +(-58.4162 + 143.244i) q^{76} +(904.751 + 19.4359i) q^{77} +(-165.589 - 109.988i) q^{78} -460.899i q^{79} +(185.193 - 2.02957i) q^{80} +880.748 q^{81} +(278.664 + 185.095i) q^{82} +(-875.405 - 875.405i) q^{83} +(369.742 + 934.658i) q^{84} +(273.598 - 273.598i) q^{85} +(59.7088 + 295.937i) q^{86} +823.082i q^{87} +(914.233 - 621.800i) q^{88} +633.231 q^{89} +(-152.626 + 30.7941i) q^{90} +(4.12080 - 191.826i) q^{91} +(402.545 + 956.964i) q^{92} +(-1146.84 - 1146.84i) q^{93} +(398.272 + 264.542i) q^{94} -55.9584i q^{95} +(1030.33 + 668.211i) q^{96} +946.138i q^{97} +(-570.984 + 784.327i) q^{98} +(-657.269 + 657.269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} + 24 q^{4} - 4 q^{7} + 80 q^{8} + 112 q^{11} - 24 q^{14} + 240 q^{16} + 68 q^{18} + 52 q^{21} - 120 q^{22} + 160 q^{23} + 96 q^{28} + 528 q^{29} - 552 q^{30} - 984 q^{32} + 476 q^{35} + 32 q^{36}+ \cdots + 7592 q^{99}+O(q^{100}) $ 88 * q - 4 * q^2 + 24 * q^4 - 4 * q^7 + 80 * q^8 + 112 * q^11 - 24 * q^14 + 240 * q^16 + 68 * q^18 + 52 * q^21 - 120 * q^22 + 160 * q^23 + 96 * q^28 + 528 * q^29 - 552 * q^30 - 984 * q^32 + 476 * q^35 + 32 * q^36 - 896 * q^37 - 8 * q^39 + 640 * q^42 + 40 * q^43 - 1024 * q^44 + 664 * q^46 - 1376 * q^49 + 2356 * q^50 + 1504 * q^51 - 1560 * q^53 - 3624 * q^56 + 1880 * q^58 - 1704 * q^60 - 6720 * q^64 - 8 * q^65 + 648 * q^67 + 4192 * q^70 - 456 * q^71 - 1744 * q^72 + 1224 * q^74 + 292 * q^77 + 9272 * q^78 - 1952 * q^81 - 4192 * q^84 + 496 * q^85 + 2592 * q^86 - 1472 * q^88 - 1964 * q^91 - 840 * q^92 - 112 * q^93 - 3268 * q^98 + 7592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.35605	−	1.56494i	−0.832989	−	0.553290i
$2$	−2.35605	−	1.56494i	−0.832989	−	0.553290i
$3$	4.79702	+	4.79702i	0.923188	+	0.923188i	0.997253	−	0.0740657i	$-0.0235974\pi$
$3$	4.79702	+	4.79702i	0.923188	+	0.923188i	−0.0740657	+	0.997253i	$0.523597\pi$
$4$	3.10192	+	7.37415i	0.387740	+	0.921769i
$5$	−2.04624	−	2.04624i	−0.183021	−	0.183021i	0.609650	−	0.792671i	$-0.291310\pi$
$5$	−2.04624	−	2.04624i	−0.183021	−	0.183021i	−0.792671	+	0.609650i	$0.791310\pi$
$6$	−3.79496	−	18.8091i	−0.258214	−	1.27980i
$7$	13.3740	−	12.8115i	0.722130	−	0.691757i
$7$	13.3740	−	12.8115i	0.722130	−	0.691757i
$8$	4.23184	−	22.2282i	0.187023	−	0.982356i
$9$			19.0229i			0.704551i
$10$	1.61879	+	8.02329i	0.0511908	+	0.253719i
$11$	34.5515	+	34.5515i	0.947061	+	0.947061i	0.998668	−	0.0516064i	$-0.0164341\pi$
$11$	34.5515	+	34.5515i	0.947061	+	0.947061i	−0.0516064	+	0.998668i	$0.516434\pi$
$12$	−20.4940	+	50.2540i	−0.493009	+	1.20892i
$13$	7.32563	−	7.32563i	0.156290	−	0.156290i	−0.624631	−	0.780920i	$-0.714750\pi$
$13$	7.32563	−	7.32563i	0.156290	−	0.156290i	0.780920	+	0.624631i	$0.214750\pi$
$14$	−51.5591	+	9.25497i	−0.984269	+	0.176678i
$15$		−	19.6317i		−	0.337926i
$16$	−44.7562	+	45.7480i	−0.699315	+	0.714813i
$17$			133.707i			1.90758i	0.300477	+	0.953789i	$0.402854\pi$
$17$			133.707i			1.90758i	−0.300477	+	0.953789i	$0.597146\pi$
$18$	29.7697	−	44.8188i	0.389821	−	0.586883i
$19$	13.6735	+	13.6735i	0.165100	+	0.165100i	0.784822	−	0.619722i	$-0.212754\pi$
$19$	13.6735	+	13.6735i	0.165100	+	0.165100i	−0.619722	+	0.784822i	$0.712754\pi$
$20$	8.74201	−	21.4366i	0.0977387	−	0.239668i
$21$	125.613	+	2.69841i	1.30528	+	0.0280401i
$22$	−27.3339	−	135.476i	−0.264891	−	1.31289i
$23$	129.773			1.17650			0.588250	−	0.808679i	$-0.299817\pi$
$23$	129.773			1.17650			0.588250	+	0.808679i	$0.299817\pi$
$24$	126.929	−	86.3288i	1.07956	−	0.734242i
$25$		−	116.626i		−	0.933006i
$26$	−28.7237	+	5.79535i	−0.216661	+	0.0437139i
$27$	38.2664	−	38.2664i	0.272755	−	0.272755i
$28$	135.959	+	58.8819i	0.917639	+	0.397415i
$29$	85.7909	+	85.7909i	0.549344	+	0.549344i	0.926251	−	0.376907i	$-0.123012\pi$
$29$	85.7909	+	85.7909i	0.549344	+	0.549344i	−0.376907	+	0.926251i	$0.623012\pi$
$30$	−30.7225	+	46.2533i	−0.186971	+	0.281489i
$31$	−239.073			−1.38512			−0.692560	−	0.721360i	$-0.743517\pi$
$31$	−239.073			−1.38512			−0.692560	+	0.721360i	$0.743517\pi$
$32$	177.041	−	37.7438i	0.978021	−	0.208507i
$33$			331.489i			1.74863i
$34$	209.244	−	315.021i	1.05544	−	1.58899i
$35$	−53.5820	−	1.15105i	−0.258772	−	0.00555893i
$36$	−140.278	+	59.0074i	−0.649433	+	0.273183i
$37$	−50.7975	+	50.7975i	−0.225704	+	0.225704i	−0.810895	−	0.585191i	$-0.801019\pi$
$37$	−50.7975	+	50.7975i	−0.225704	+	0.225704i	0.585191	+	0.810895i	$0.301019\pi$
$38$	−10.8172	−	53.6135i	−0.0461783	−	0.228875i
$39$	70.2824			0.288569
$40$	−54.1436	+	36.8248i	−0.214021	+	0.145563i
$41$	−118.276			−0.450527			−0.225264	−	0.974298i	$-0.572324\pi$
$41$	−118.276			−0.450527			−0.225264	+	0.974298i	$0.572324\pi$
$42$	−291.727	−	202.934i	−1.07177	−	0.745558i
$43$	−75.4750	−	75.4750i	−0.267671	−	0.267671i	0.560490	−	0.828161i	$-0.310613\pi$
$43$	−75.4750	−	75.4750i	−0.267671	−	0.267671i	−0.828161	+	0.560490i	$0.810613\pi$
$44$	−147.612	+	361.964i	−0.505758	+	1.24018i
$45$	38.9254	−	38.9254i	0.128948	−	0.128948i
$46$	−305.751	−	203.087i	−0.980011	−	0.650946i
$47$	−169.043			−0.524625			−0.262313	−	0.964983i	$-0.584485\pi$
$47$	−169.043			−0.524625			−0.262313	+	0.964983i	$0.584485\pi$
$48$	−434.151	+	4.75794i	−1.30551	+	0.0143073i
$49$	14.7299	−	342.684i	0.0429442	−	0.999077i
$50$	−182.512	+	274.776i	−0.516223	+	0.777184i
$51$	−641.398	+	641.398i	−1.76105	+	1.76105i
$52$	76.7438	+	31.2968i	0.204662	+	0.0834631i
$53$	482.264	−	482.264i	1.24989	−	1.24989i	0.294118	−	0.955769i	$-0.404974\pi$
$53$	482.264	−	482.264i	1.24989	−	1.24989i	0.955769	−	0.294118i	$-0.0950257\pi$
$54$	−150.042	+	30.2728i	−0.378114	+	0.0762891i
$55$		−	141.401i		−	0.346665i
$56$	−228.180	−	351.497i	−0.544497	−	0.838763i
$57$			131.184i			0.304837i
$58$	−67.8698	−	336.385i	−0.153651	−	0.761544i
$59$	−285.231	+	285.231i	−0.629389	+	0.629389i	−0.947914	−	0.318525i	$-0.896812\pi$
$59$	−285.231	+	285.231i	−0.629389	+	0.629389i	0.318525	+	0.947914i	$0.396812\pi$
$60$	144.767	−	60.8961i	0.311490	−	0.131027i
$61$	313.070	−	313.070i	0.657124	−	0.657124i	−0.297575	−	0.954699i	$-0.596178\pi$
$61$	313.070	−	313.070i	0.657124	−	0.657124i	0.954699	+	0.297575i	$0.0961777\pi$
$62$	563.267	+	374.135i	1.15379	+	0.766373i
$63$	243.712	+	254.413i	0.487378	+	0.508778i
$64$	−476.183	−	188.132i	−0.930045	−	0.367446i
$65$	−29.9800			−0.0572086
$66$	518.760	−	781.003i	0.967500	−	1.45659i
$67$	−58.2711	+	58.2711i	−0.106253	+	0.106253i	−0.758235	−	0.651982i	$-0.773938\pi$
$67$	−58.2711	+	58.2711i	−0.106253	+	0.106253i	0.651982	+	0.758235i	$0.273938\pi$
$68$	−985.979	+	414.750i	−1.75835	+	0.739644i
$69$	622.523	+	622.523i	1.08613	+	1.08613i
$70$	124.440	+	86.5645i	0.212478	+	0.147806i
$71$	−374.109			−0.625331			−0.312666	−	0.949863i	$-0.601222\pi$
$71$	−374.109			−0.625331			−0.312666	+	0.949863i	$0.601222\pi$
$72$	422.844	+	80.5018i	0.692120	+	0.131767i
$73$	−610.003			−0.978020			−0.489010	−	0.872278i	$-0.662642\pi$
$73$	−610.003			−0.978020			−0.489010	+	0.872278i	$0.662642\pi$
$74$	199.176	−	40.1862i	0.312889	−	0.0631291i
$75$	559.457	−	559.457i	0.861340	−	0.861340i
$76$	−58.4162	+	143.244i	−0.0881683	+	0.216200i
$77$	904.751	+	19.4359i	1.33904	+	0.0287652i
$78$	−165.589	−	109.988i	−0.240375	−	0.159662i
$79$		−	460.899i		−	0.656395i	−0.944609	−	0.328198i	$-0.893559\pi$
$79$		−	460.899i		−	0.656395i	0.944609	−	0.328198i	$-0.106441\pi$
$80$	185.193	−	2.02957i	0.258816	−	0.00283641i
$81$	880.748			1.20816
$82$	278.664	+	185.095i	0.375284	+	0.249272i
$83$	−875.405	−	875.405i	−1.15769	−	1.15769i	−0.984971	−	0.172717i	$-0.944745\pi$
$83$	−875.405	−	875.405i	−1.15769	−	1.15769i	−0.172717	−	0.984971i	$-0.555255\pi$
$84$	369.742	+	934.658i	0.480264	+	1.21404i
$85$	273.598	−	273.598i	0.349128	−	0.349128i
$86$	59.7088	+	295.937i	0.0748670	+	0.371066i
$87$			823.082i			1.01430i
$88$	914.233	−	621.800i	1.10747	−	0.753229i
$89$	633.231			0.754184			0.377092	−	0.926176i	$-0.376924\pi$
$89$	633.231			0.754184			0.377092	+	0.926176i	$0.376924\pi$
$90$	−152.626	+	30.7941i	−0.178758	+	0.0360665i
$91$	4.12080	−	191.826i	0.00474700	−	0.220976i
$92$	402.545	+	956.964i	0.456176	+	1.08446i
$93$	−1146.84	−	1146.84i	−1.27873	−	1.27873i
$94$	398.272	+	264.542i	0.437007	+	0.290270i
$95$		−	55.9584i		−	0.0604338i
$96$	1030.33	+	668.211i	1.09539	+	0.710406i
$97$			946.138i			0.990368i	0.868788	+	0.495184i	$0.164899\pi$
$97$			946.138i			0.990368i	−0.868788	+	0.495184i	$0.835101\pi$
$98$	−570.984	+	784.327i	−0.588552	+	0.808460i
$99$	−657.269	+	657.269i	−0.667253	+	0.667253i
$100$	860.016	−	361.764i	0.860016	−	0.361764i
$101$	−141.100	−	141.100i	−0.139010	−	0.139010i	0.634178	−	0.773187i	$-0.281339\pi$
$101$	−141.100	−	141.100i	−0.139010	−	0.139010i	−0.773187	+	0.634178i	$0.781339\pi$
$102$	2514.91	−	507.414i	2.44131	−	0.492564i
$103$		−	891.445i		−	0.852784i	−0.904539	−	0.426392i	$-0.859784\pi$
$103$		−	891.445i		−	0.852784i	0.904539	−	0.426392i	$-0.140216\pi$
$104$	−131.834	−	193.836i	−0.124302	−	0.182762i
$105$	−251.512	−	262.556i	−0.233763	−	0.244027i
$106$	−1890.95	+	381.522i	−1.73269	+	0.349591i
$107$	−727.560	−	727.560i	−0.657345	−	0.657345i	0.297406	−	0.954751i	$-0.403878\pi$
$107$	−727.560	−	727.560i	−0.657345	−	0.657345i	−0.954751	+	0.297406i	$0.903878\pi$
$108$	400.882	+	163.483i	0.357175	+	0.145659i
$109$	−1136.70	−	1136.70i	−0.998867	−	0.998867i	0.00113245	−	0.999999i	$-0.499640\pi$
$109$	−1136.70	−	1136.70i	−0.998867	−	0.998867i	−0.999999	+	0.00113245i	$0.999640\pi$
$110$	−221.285	+	333.149i	−0.191806	+	0.288768i
$111$	−487.353			−0.416735
$112$	−12.4690	+	1185.23i	−0.0105198	+	0.999945i
$113$	−556.606			−0.463373			−0.231686	−	0.972791i	$-0.574424\pi$
$113$	−556.606			−0.463373			−0.231686	+	0.972791i	$0.574424\pi$
$114$	205.295	−	309.075i	0.168663	−	0.253926i
$115$	−265.546	−	265.546i	−0.215325	−	0.215325i
$116$	−366.519	+	898.752i	−0.293366	+	0.719371i
$117$	139.355	+	139.355i	0.110114	+	0.110114i
$118$	1118.39	−	225.648i	0.872509	−	0.176039i
$119$	1713.00	+	1788.21i	1.31958	+	1.37752i
$120$	−436.378	−	83.0784i	−0.331964	−	0.0631999i
$121$			1056.61i			0.793849i
$122$	−1227.55	+	247.672i	−0.910957	+	0.183796i
$123$	−567.373	−	567.373i	−0.415921	−	0.415921i
$124$	−741.584	−	1762.96i	−0.537066	−	1.27676i
$125$	−494.425	+	494.425i	−0.353781	+	0.353781i
$126$	−176.056	−	980.803i	−0.124479	−	0.693468i
$127$			1588.68i			1.11002i	0.831843	+	0.555011i	$0.187286\pi$
$127$			1588.68i			1.11002i	−0.831843	+	0.555011i	$0.812714\pi$
$128$	827.494	+	1188.45i	0.571413	+	0.820663i
$129$		−	724.111i		−	0.494220i
$130$	70.6343	+	46.9169i	0.0476541	+	0.0316530i
$131$	−1500.21	−	1500.21i	−1.00057	−	1.00057i	−1.00000		0.000565274i	$-0.999820\pi$
$131$	−1500.21	−	1500.21i	−1.00057	−	1.00057i	−0.000565274	−	1.00000i	$-0.500180\pi$
$132$	−2444.45	+	1028.25i	−1.61183	+	0.678014i
$133$	358.047	+	7.69157i	0.233433	+	0.00501461i
$134$	228.480	−	46.0986i	0.147296	−	0.0297188i
$135$	−156.605			−0.0998399
$136$	2972.07	+	565.829i	1.87392	+	0.356760i
$137$			2259.10i			1.40882i	0.709795	+	0.704408i	$0.248788\pi$
$137$			2259.10i			1.40882i	−0.709795	+	0.704408i	$0.751212\pi$
$138$	−492.482	−	2440.91i	−0.303789	−	1.50568i
$139$	2145.82	−	2145.82i	1.30940	−	1.30940i	0.387547	−	0.921850i	$-0.373323\pi$
$139$	2145.82	−	2145.82i	1.30940	−	1.30940i	0.921850	−	0.387547i	$-0.126677\pi$
$140$	−157.719	−	398.692i	−0.0952120	−	0.240683i
$141$	−810.901	−	810.901i	−0.484328	−	0.484328i
$142$	881.418	+	585.458i	0.520894	+	0.345990i
$143$	506.223			0.296031
$144$	−870.259	−	851.392i	−0.503622	−	0.492703i
$145$		−	351.098i		−	0.201083i
$146$	1437.20	+	954.618i	0.814679	+	0.541129i
$147$	1714.52	−	1573.20i	0.961982	−	0.882690i
$148$	−532.158	−	217.019i	−0.295561	−	0.120533i
$149$	−1085.99	+	1085.99i	−0.597100	+	0.597100i	−0.939540	−	0.342440i	$-0.888747\pi$
$149$	−1085.99	+	1085.99i	−0.597100	+	0.597100i	0.342440	+	0.939540i	$0.388747\pi$
$150$	−2193.62	+	442.590i	−1.19406	+	0.240915i
$151$	257.765			0.138918			0.0694590	−	0.997585i	$-0.477873\pi$
$151$	257.765			0.138918			0.0694590	+	0.997585i	$0.477873\pi$
$152$	361.800	−	246.072i	0.193065	−	0.131310i
$153$	−2543.50			−1.34399
$154$	−2101.22	−	1461.67i	−1.09949	−	0.764838i
$155$	489.200	+	489.200i	0.253507	+	0.253507i
$156$	218.010	+	518.273i	0.111890	+	0.265994i
$157$	1532.56	−	1532.56i	0.779053	−	0.779053i	−0.200617	−	0.979670i	$-0.564295\pi$
$157$	1532.56	−	1532.56i	0.779053	−	0.779053i	0.979670	+	0.200617i	$0.0642946\pi$
$158$	−721.280	+	1085.90i	−0.363177	+	0.546770i
$159$	4626.86			2.30776
$160$	−439.501	−	285.035i	−0.217160	−	0.140838i
$161$	1735.59	−	1662.59i	0.849586	−	0.813852i
$162$	−2075.08	−	1378.32i	−1.00638	−	0.668462i
$163$	−177.457	+	177.457i	−0.0852729	+	0.0852729i	−0.748457	−	0.663184i	$-0.769205\pi$
$163$	−177.457	+	177.457i	−0.0852729	+	0.0852729i	0.663184	+	0.748457i	$0.269205\pi$
$164$	−366.883	−	872.186i	−0.174687	−	0.415282i
$165$	678.306	−	678.306i	0.320037	−	0.320037i
$166$	692.539	+	3432.45i	0.323804	+	1.60488i
$167$			1722.29i			0.798054i	0.916939	+	0.399027i	$0.130652\pi$
$167$			1722.29i			0.798054i	−0.916939	+	0.399027i	$0.869348\pi$
$168$	591.554	−	2780.72i	0.271663	−	1.27701i
$169$			2089.67i			0.951147i
$170$	−1072.77	+	216.445i	−0.483988	+	0.0976504i
$171$	−260.108	+	260.108i	−0.116322	+	0.116322i
$172$	322.447	−	790.682i	0.142944	−	0.350517i
$173$	−1795.20	+	1795.20i	−0.788939	+	0.788939i	−0.981320	−	0.192381i	$-0.938379\pi$
$173$	−1795.20	+	1795.20i	−0.788939	+	0.788939i	0.192381	+	0.981320i	$0.438379\pi$
$174$	1288.08	−	1939.22i	0.561200	−	0.844896i
$175$	−1494.15	−	1559.76i	−0.645414	−	0.673752i
$176$	−3127.06	+	34.2700i	−1.33927	+	0.0146773i
$177$	−2736.52			−1.16209
$178$	−1491.92	−	990.969i	−0.628226	−	0.417282i
$179$	−953.910	+	953.910i	−0.398316	+	0.398316i	−0.877639	−	0.479323i	$-0.840882\pi$
$179$	−953.910	+	953.910i	−0.398316	+	0.398316i	0.479323	+	0.877639i	$0.340882\pi$
$180$	407.785	+	166.298i	0.168858	+	0.0688619i
$181$	1780.34	+	1780.34i	0.731114	+	0.731114i	0.970840	−	0.239727i	$-0.0770578\pi$
$181$	1780.34	+	1780.34i	0.731114	+	0.731114i	−0.239727	+	0.970840i	$0.577058\pi$
$182$	−309.905	+	445.502i	−0.126218	+	0.181444i
$183$	3003.61			1.21330
$184$	549.178	−	2884.61i	0.220032	−	1.15574i
$185$	207.888			0.0826173
$186$	907.271	+	4496.74i	0.357658	+	1.77267i
$187$	−4619.79	+	4619.79i	−1.80659	+	1.80659i
$188$	−524.356	−	1246.55i	−0.203418	−	0.483583i
$189$	21.5256	−	1002.03i	0.00828442	−	0.385645i
$190$	−87.5715	+	131.841i	−0.0334374	+	0.0503406i
$191$		−	2064.00i		−	0.781916i	−0.920409	−	0.390958i	$-0.872144\pi$
$191$		−	2064.00i		−	0.781916i	0.920409	−	0.390958i	$-0.127856\pi$
$192$	−1381.79	−	3186.74i	−0.519385	−	1.19783i
$193$	1142.67			0.426172			0.213086	−	0.977033i	$-0.431649\pi$
$193$	1142.67			0.426172			0.213086	+	0.977033i	$0.431649\pi$
$194$	1480.65	−	2229.15i	0.547961	−	0.824965i
$195$	−143.815	−	143.815i	−0.0528143	−	0.0528143i
$196$	2572.69	−	954.357i	0.937570	−	0.347798i
$197$	837.511	−	837.511i	0.302894	−	0.302894i	−0.539251	−	0.842145i	$-0.681292\pi$
$197$	837.511	−	837.511i	0.302894	−	0.302894i	0.842145	+	0.539251i	$0.181292\pi$
$198$	2577.14	−	519.970i	0.924998	−	0.186630i
$199$			2165.33i			0.771338i	0.922637	+	0.385669i	$0.126029\pi$
$199$			2165.33i			0.771338i	−0.922637	+	0.385669i	$0.873971\pi$
$200$	−2592.38	−	493.542i	−0.916544	−	0.174493i
$201$	−559.056			−0.196183
$202$	111.625	+	553.251i	0.0388808	+	0.192706i
$203$	2246.48	+	48.2590i	0.776710	+	0.0166853i
$204$	−6719.33	−	2740.20i	−2.30611	−	0.940453i
$205$	242.021	+	242.021i	0.0824561	+	0.0824561i
$206$	−1395.06	+	2100.29i	−0.471837	+	0.710359i
$207$			2468.65i			0.828904i
$208$	7.26595	+	663.000i	0.00242213	+	0.221013i
$209$			944.877i			0.312720i
$210$	181.691	+	1012.20i	0.0597042	+	0.332610i
$211$	130.423	−	130.423i	0.0425531	−	0.0425531i	−0.685510	−	0.728063i	$-0.740421\pi$
$211$	130.423	−	130.423i	0.0425531	−	0.0425531i	0.728063	+	0.685510i	$0.240421\pi$
$212$	5052.23	+	2060.34i	1.63674	+	0.667476i
$213$	−1794.61	−	1794.61i	−0.577298	−	0.577298i
$214$	575.578	+	2852.76i	0.183858	+	0.911263i
$215$			308.880i			0.0979789i
$216$	−688.656	−	1012.53i	−0.216931	−	0.318954i
$217$	−3197.37	+	3062.89i	−1.00024	+	0.958167i
$218$	899.254	+	4457.00i	0.279381	+	1.38471i
$219$	−2926.20	−	2926.20i	−0.902896	−	0.902896i
$220$	1042.72	−	438.616i	0.319545	−	0.134416i
$221$	979.491	+	979.491i	0.298134	+	0.298134i
$222$	1148.23	+	762.679i	0.347135	+	0.230575i
$223$	−1221.92			−0.366933			−0.183466	−	0.983026i	$-0.558732\pi$
$223$	−1221.92			−0.366933			−0.183466	+	0.983026i	$0.558732\pi$
$224$	1884.19	−	2772.95i	0.562022	−	0.827122i
$225$	2218.56			0.657351
$226$	1311.39	+	871.056i	0.385984	+	0.256380i
$227$	3515.16	+	3515.16i	1.02780	+	1.02780i	0.999602	+	0.0281934i	$0.00897542\pi$
$227$	3515.16	+	3515.16i	1.02780	+	1.02780i	0.0281934	+	0.999602i	$0.491025\pi$
$228$	−967.369	+	406.922i	−0.280989	+	0.118198i
$229$	−3345.39	−	3345.39i	−0.965369	−	0.965369i	0.0340515	−	0.999420i	$-0.489159\pi$
$229$	−3345.39	−	3345.39i	−0.965369	−	0.965369i	−0.999420	+	0.0340515i	$0.989159\pi$
$230$	210.075	+	1041.20i	0.0602259	+	0.298500i
$231$	4246.88	+	4433.34i	1.20963	+	1.26274i
$232$	2270.03	−	1543.92i	0.642391	−	0.436911i
$233$			537.847i			0.151225i	0.997137	+	0.0756127i	$0.0240913\pi$
$233$			537.847i			0.151225i	−0.997137	+	0.0756127i	$0.975909\pi$
$234$	−110.244	−	546.408i	−0.0307987	−	0.152649i
$235$	345.902	+	345.902i	0.0960177	+	0.0960177i
$236$	−2988.10	−	1218.57i	−0.824191	−	0.336112i
$237$	2210.95	−	2210.95i	0.605976	−	0.605976i
$238$	−1237.46	−	6893.84i	−0.337027	−	1.87757i
$239$		−	6403.30i		−	1.73303i	−0.499149	−	0.866516i	$-0.666354\pi$
$239$		−	6403.30i		−	1.73303i	0.499149	−	0.866516i	$-0.333646\pi$
$240$	898.113	+	878.642i	0.241554	+	0.236317i
$241$		−	1648.67i		−	0.440664i	−0.975425	−	0.220332i	$-0.929286\pi$
$241$		−	1648.67i		−	0.440664i	0.975425	−	0.220332i	$-0.0707140\pi$
$242$	1653.54	−	2489.43i	0.439229	−	0.661268i
$243$	3191.77	+	3191.77i	0.842603	+	0.842603i
$244$	3279.75	+	1337.51i	0.860509	+	0.350923i
$245$	−731.354	+	671.072i	−0.190712	+	0.174993i
$246$	448.853	+	2224.66i	0.116333	+	0.576583i
$247$	200.333			0.0516069
$248$	−1011.72	+	5314.15i	−0.259049	+	1.36068i
$249$		−	8398.68i		−	2.13753i
$250$	1938.63	−	391.143i	0.490440	−	0.0989521i
$251$	3775.90	−	3775.90i	0.949534	−	0.949534i	−0.0492528	−	0.998786i	$-0.515684\pi$
$251$	3775.90	−	3775.90i	0.949534	−	0.949534i	0.998786	+	0.0492528i	$0.0156840\pi$
$252$	−1120.10	+	2586.34i	−0.279999	+	0.646523i
$253$	4483.84	+	4483.84i	1.11422	+	1.11422i
$254$	2486.20	−	3743.01i	0.614165	−	0.924636i
$255$	2624.91			0.644620
$256$	−89.7669	−	4095.02i	−0.0219157	−	0.999760i
$257$			6959.86i			1.68928i	0.535337	+	0.844638i	$0.320185\pi$
$257$			6959.86i			1.68928i	−0.535337	+	0.844638i	$0.679815\pi$
$258$	−1133.19	+	1706.04i	−0.273447	+	0.411680i
$259$	−28.5745	+	1330.16i	−0.00685534	+	0.319120i
$260$	−92.9956	−	221.077i	−0.0221821	−	0.0527331i
$261$	−1631.99	+	1631.99i	−0.387041	+	0.387041i
$262$	1186.83	+	5882.31i	0.279856	+	1.38706i
$263$	−4461.40			−1.04602			−0.523008	−	0.852328i	$-0.675190\pi$
$263$	−4461.40			−1.04602			−0.523008	+	0.852328i	$0.675190\pi$
$264$	7368.39	+	1402.81i	1.71778	+	0.327034i
$265$	−1973.66			−0.457512
$266$	−831.539	−	578.444i	−0.191673	−	0.133333i
$267$	3037.62	+	3037.62i	0.696253	+	0.696253i
$268$	−610.452	−	248.948i	−0.139139	−	0.0567421i
$269$	2252.15	−	2252.15i	0.510469	−	0.510469i	−0.404201	−	0.914670i	$-0.632450\pi$
$269$	2252.15	−	2252.15i	0.510469	−	0.510469i	0.914670	+	0.404201i	$0.132450\pi$
$270$	368.968	+	245.077i	0.0831655	+	0.0552405i
$271$	−6670.05			−1.49512			−0.747559	−	0.664196i	$-0.768774\pi$
$271$	−6670.05			−1.49512			−0.747559	+	0.664196i	$0.768774\pi$
$272$	−6116.85	−	5984.24i	−1.36356	−	1.33400i
$273$	939.960	−	900.425i	0.208384	−	0.199620i
$274$	3535.36	−	5322.55i	0.779485	−	1.17353i
$275$	4029.60	−	4029.60i	0.883614	−	0.883614i
$276$	−2659.56	+	6521.59i	−0.580025	+	1.42230i
$277$	−1517.50	+	1517.50i	−0.329161	+	0.329161i	−0.852267	−	0.523106i	$-0.824773\pi$
$277$	−1517.50	+	1517.50i	−0.329161	+	0.329161i	0.523106	+	0.852267i	$0.324773\pi$
$278$	−8413.74	+	1697.57i	−1.81519	+	0.366236i
$279$		−	4547.85i		−	0.975888i
$280$	−252.336	+	1186.16i	−0.0538570	+	0.253166i
$281$			559.278i			0.118732i	0.998236	+	0.0593661i	$0.0189079\pi$
$281$			559.278i			0.118732i	−0.998236	+	0.0593661i	$0.981092\pi$
$282$	641.509	+	3179.53i	0.135466	+	0.671413i
$283$	−25.8379	+	25.8379i	−0.00542721	+	0.00542721i	−0.709815	−	0.704388i	$-0.751222\pi$
$283$	−25.8379	+	25.8379i	−0.00542721	+	0.00542721i	0.704388	+	0.709815i	$0.251222\pi$
$284$	−1160.45	−	2758.73i	−0.242466	−	0.576411i
$285$	268.434	−	268.434i	0.0557917	−	0.0557917i
$286$	−1192.69	−	792.209i	−0.246591	−	0.163791i
$287$	−1581.83	+	1515.30i	−0.325339	+	0.311655i
$288$	717.995	+	3367.82i	0.146904	+	0.689066i
$289$	−12964.7			−2.63885
$290$	−549.447	+	827.203i	−0.111257	+	0.167500i
$291$	−4538.65	+	4538.65i	−0.914296	+	0.914296i
$292$	−1892.18	−	4498.25i	−0.379217	−	0.901508i
$293$	3862.53	+	3862.53i	0.770142	+	0.770142i	0.978131	−	0.207989i	$-0.0666918\pi$
$293$	3862.53	+	3862.53i	0.770142	+	0.770142i	−0.207989	+	0.978131i	$0.566692\pi$
$294$	−6501.46	+	1023.41i	−1.28970	+	0.203016i
$295$	1167.30			0.230383
$296$	914.168	+	1344.10i	0.179510	+	0.263933i
$297$	2644.33			0.516631
$298$	4258.16	−	859.135i	0.827747	−	0.167008i
$299$	950.667	−	950.667i	0.183875	−	0.183875i
$300$	5860.91	+	2390.13i	1.12793	+	0.459980i
$301$	−1976.36	−	42.4561i	−0.378456	−	0.00812999i
$302$	−607.307	−	403.387i	−0.115717	−	0.0768620i
$303$		−	1353.72i		−	0.256664i
$304$	−1237.51	+	13.5621i	−0.233473	+	0.00255868i
$305$	−1281.23			−0.240535
$306$	5992.61	+	3980.43i	1.11952	+	0.743614i
$307$	−2044.42	−	2044.42i	−0.380069	−	0.380069i	0.491058	−	0.871127i	$-0.336610\pi$
$307$	−2044.42	−	2044.42i	−0.380069	−	0.380069i	−0.871127	+	0.491058i	$0.836610\pi$
$308$	2663.14	+	6732.06i	0.492684	+	1.24544i
$309$	4276.28	−	4276.28i	0.787279	−	0.787279i
$310$	−387.010	−	1918.15i	−0.0709054	−	0.351431i
$311$		−	9371.35i		−	1.70868i	−0.519711	−	0.854342i	$-0.673960\pi$
$311$		−	9371.35i		−	1.70868i	0.519711	−	0.854342i	$-0.326040\pi$
$312$	297.424	−	1562.25i	0.0539690	−	0.283477i
$313$	8978.95			1.62147			0.810735	−	0.585413i	$-0.199068\pi$
$313$	8978.95			1.62147			0.810735	+	0.585413i	$0.199068\pi$
$314$	−6009.14	+	1212.42i	−1.07998	+	0.217900i
$315$	21.8962	−	1019.28i	0.00391655	−	0.182318i
$316$	3398.74	−	1429.67i	0.605045	−	0.254511i
$317$	−1767.75	−	1767.75i	−0.313207	−	0.313207i	0.532944	−	0.846151i	$-0.321086\pi$
$317$	−1767.75	−	1767.75i	−0.313207	−	0.313207i	−0.846151	+	0.532944i	$0.821086\pi$
$318$	−10901.1	−	7240.76i	−1.92234	−	1.27686i
$319$			5928.41i			1.04052i
$320$	589.422	+	1359.35i	0.102968	+	0.237469i
$321$		−	6980.25i		−	1.21371i
$322$	−6690.97	+	1201.04i	−1.15799	+	0.207862i
$323$	−1828.24	+	1828.24i	−0.314942	+	0.314942i
$324$	2732.01	+	6494.77i	0.468451	+	1.11364i
$325$	−854.357	−	854.357i	−0.145819	−	0.145819i
$326$	695.806	−	140.387i	0.118212	−	0.0238507i
$327$		−	10905.6i		−	1.84428i
$328$	−500.525	+	2629.06i	−0.0842588	+	0.442578i
$329$	−2260.78	+	2165.69i	−0.378848	+	0.362913i
$330$	−2659.63	+	536.612i	−0.443660	+	0.0895138i
$331$	4730.32	+	4730.32i	0.785504	+	0.785504i	0.980754	−	0.195250i	$-0.0625518\pi$
$331$	4730.32	+	4730.32i	0.785504	+	0.785504i	−0.195250	+	0.980754i	$0.562552\pi$
$332$	3739.93	−	9170.80i	0.618239	−	1.51600i
$333$	−966.314	−	966.314i	−0.159020	−	0.159020i
$334$	2695.29	−	4057.80i	0.441555	−	0.664770i
$335$	238.473			0.0388931
$336$	−5745.40	+	5625.77i	−0.932848	+	0.913425i
$337$	1717.91			0.277688			0.138844	−	0.990314i	$-0.455661\pi$
$337$	1717.91			0.277688			0.138844	+	0.990314i	$0.455661\pi$
$338$	3270.21	−	4923.36i	0.526260	−	0.792295i
$339$	−2670.05	−	2670.05i	−0.427780	−	0.427780i
$340$	2866.23	+	1168.87i	0.457186	+	0.186444i
$341$	−8260.32	−	8260.32i	−1.31179	−	1.31179i
$342$	1019.88	−	205.773i	0.161254	−	0.0325350i
$343$	−4193.30	−	4771.78i	−0.660108	−	0.751171i
$344$	−1997.07	+	1358.27i	−0.313008	+	0.212887i
$345$		−	2547.66i		−	0.397570i
$346$	7038.96	−	1420.19i	1.09369	−	0.220665i
$347$	−7793.80	−	7793.80i	−1.20574	−	1.20574i	−0.972392	−	0.233352i	$-0.925031\pi$
$347$	−7793.80	−	7793.80i	−1.20574	−	1.20574i	−0.233352	−	0.972392i	$-0.574969\pi$
$348$	−6069.53	+	2553.13i	−0.934946	+	0.393283i
$349$	−4211.57	+	4211.57i	−0.645960	+	0.645960i	−0.952014	−	0.306054i	$-0.900991\pi$
$349$	−4211.57	+	4211.57i	−0.645960	+	0.645960i	0.306054	+	0.952014i	$0.400991\pi$
$350$	1079.37	+	6013.13i	0.164842	+	0.918329i
$351$		−	560.652i		−	0.0852574i
$352$	7421.13	+	4812.92i	1.12371	+	0.728777i
$353$			7172.87i			1.08151i	0.841180	+	0.540755i	$0.181862\pi$
$353$			7172.87i			1.08151i	−0.841180	+	0.540755i	$0.818138\pi$
$354$	6447.38	+	4282.50i	0.968007	+	0.642972i
$355$	765.516	+	765.516i	0.114449	+	0.114449i
$356$	1964.23	+	4669.54i	0.292427	+	0.695183i
$357$	−360.798	+	16795.4i	−0.0534887	+	2.48993i
$358$	3740.27	−	754.644i	0.552177	−	0.111408i
$359$	−12810.1			−1.88326			−0.941630	−	0.336650i	$-0.890706\pi$
$359$	−12810.1			−1.88326			−0.941630	+	0.336650i	$0.890706\pi$
$360$	−700.514	−	1029.97i	−0.102557	−	0.150789i
$361$		−	6485.07i		−	0.945484i
$362$	−1408.44	−	6980.69i	−0.204491	−	1.01353i
$363$	−5068.60	+	5068.60i	−0.732872	+	0.732872i
$364$	1427.33	−	564.640i	0.205529	−	0.0813055i
$365$	1248.21	+	1248.21i	0.178998	+	0.178998i
$366$	−7076.65	−	4700.48i	−1.01066	−	0.671305i
$367$	−5502.08			−0.782578			−0.391289	−	0.920268i	$-0.627971\pi$
$367$	−5502.08			−0.782578			−0.391289	+	0.920268i	$0.627971\pi$
$368$	−5808.13	+	5936.85i	−0.822744	+	0.840977i
$369$		−	2249.95i		−	0.317419i
$370$	−489.793	−	325.332i	−0.0688193	−	0.0457114i
$371$	271.282	−	12628.3i	0.0379630	−	1.76720i
$372$	4899.55	−	12014.4i	0.682877	−	1.67450i
$373$	−5026.12	+	5026.12i	−0.697702	+	0.697702i	−0.963914	−	0.266213i	$-0.914228\pi$
$373$	−5026.12	+	5026.12i	−0.697702	+	0.697702i	0.266213	+	0.963914i	$0.414228\pi$
$374$	18114.2	−	3654.75i	2.50444	−	0.505301i
$375$	−4743.53			−0.653213
$376$	−715.361	+	3757.51i	−0.0981169	+	0.515369i
$377$	1256.94			0.171713
$378$	−1618.83	+	2327.14i	−0.220274	+	0.316654i
$379$	6001.11	+	6001.11i	0.813342	+	0.813342i	0.985133	−	0.171792i	$-0.0549556\pi$
$379$	6001.11	+	6001.11i	0.813342	+	0.813342i	−0.171792	+	0.985133i	$0.554956\pi$
$380$	412.645	−	173.578i	0.0557060	−	0.0234326i
$381$	−7620.96	+	7620.96i	−1.02476	+	1.02476i
$382$	−3230.04	+	4862.88i	−0.432626	+	0.651327i
$383$	12452.4			1.66133			0.830665	−	0.556773i	$-0.187961\pi$
$383$	12452.4			1.66133			0.830665	+	0.556773i	$0.187961\pi$
$384$	−1731.50	+	9670.52i	−0.230104	+	1.28515i
$385$	−1811.57	−	1891.11i	−0.239808	−	0.250337i
$386$	−2692.19	−	1788.21i	−0.354997	−	0.235797i
$387$	1435.75	−	1435.75i	0.188588	−	0.188588i
$388$	−6976.96	+	2934.84i	−0.912891	+	0.384005i
$389$	7568.58	−	7568.58i	0.986483	−	0.986483i	−0.0134265	−	0.999910i	$-0.504274\pi$
$389$	7568.58	−	7568.58i	0.986483	−	0.986483i	0.999910	+	0.0134265i	$0.00427393\pi$
$390$	113.773	+	563.896i	0.0147721	+	0.0732154i
$391$			17351.6i			2.24426i
$392$	−7554.89	−	1777.60i	−0.973418	−	0.229037i
$393$		−	14393.1i		−	1.84742i
$394$	−3283.87	+	662.561i	−0.419896	+	0.0847191i
$395$	−943.111	+	943.111i	−0.120134	+	0.120134i
$396$	−6885.60	−	2808.01i	−0.873773	−	0.356332i
$397$	746.476	−	746.476i	0.0943692	−	0.0943692i	−0.658346	−	0.752715i	$-0.728744\pi$
$397$	746.476	−	746.476i	0.0943692	−	0.0943692i	0.752715	+	0.658346i	$0.228744\pi$
$398$	3388.62	−	5101.62i	0.426774	−	0.642516i
$399$	1680.66	+	1754.46i	0.210873	+	0.220132i
$400$	5335.40	+	5219.73i	0.666925	+	0.652466i
$401$	8402.79			1.04642			0.523211	−	0.852203i	$-0.324734\pi$
$401$	8402.79			1.04642			0.523211	+	0.852203i	$0.324734\pi$
$402$	1317.16	+	874.889i	0.163418	+	0.108546i
$403$	−1751.36	+	1751.36i	−0.216480	+	0.216480i
$404$	602.811	−	1478.17i	0.0742351	−	0.182034i
$405$	−1802.22	−	1802.22i	−0.221119	−	0.221119i
$406$	−5217.30	−	3629.31i	−0.637759	−	0.443645i
$407$	−3510.26			−0.427511
$408$	11542.8	+	16971.4i	1.40062	+	2.05934i
$409$	8430.15			1.01918			0.509589	−	0.860418i	$-0.329797\pi$
$409$	8430.15			1.01918			0.509589	+	0.860418i	$0.329797\pi$
$410$	−191.465	−	948.963i	−0.0230628	−	0.114307i
$411$	−10837.0	+	10837.0i	−1.30060	+	1.30060i
$412$	6573.65	−	2765.19i	0.786069	−	0.330658i
$413$	−160.448	+	7468.95i	−0.0191165	+	0.889886i
$414$	3863.29	−	5816.26i	0.458624	−	0.690468i
$415$			3582.58i			0.423764i
$416$	1020.44	−	1573.43i	0.120267	−	0.185442i
$417$	20587.1			2.41764
$418$	1478.68	−	2226.18i	0.173025	−	0.260492i
$419$	8672.14	+	8672.14i	1.01113	+	1.01113i	0.999937	+	0.0111887i	$0.00356153\pi$
$419$	8672.14	+	8672.14i	1.01113	+	1.01113i	0.0111887	+	0.999937i	$0.496438\pi$
$420$	1155.95	−	2669.12i	0.134297	−	0.310094i
$421$	10398.8	−	10398.8i	1.20382	−	1.20382i	0.230818	−	0.972997i	$-0.425860\pi$
$421$	10398.8	−	10398.8i	1.20382	−	1.20382i	0.972997	−	0.230818i	$-0.0741403\pi$
$422$	−511.387	+	103.179i	−0.0589904	+	0.0119020i
$423$		−	3215.68i		−	0.369625i
$424$	−8678.97	−	12760.7i	−0.994076	−	1.46159i
$425$	15593.7			1.77978
$426$	1419.73	+	7036.64i	0.161469	+	0.800296i
$427$	176.108	−	8197.92i	0.0199589	−	0.929099i
$428$	3108.31	−	7621.97i	0.351041	−	0.860799i
$429$	2428.36	+	2428.36i	0.273293	+	0.273293i
$430$	483.379	−	727.736i	0.0542107	−	0.0816153i
$431$			12243.6i			1.36834i	0.729322	+	0.684170i	$0.239835\pi$
$431$			12243.6i			1.36834i	−0.729322	+	0.684170i	$0.760165\pi$
$432$	37.9547	+	3463.28i	0.00422707	+	0.385710i
$433$		−	8787.77i		−	0.975320i	−0.873034	−	0.487660i	$-0.837851\pi$
$433$		−	8787.77i		−	0.975320i	0.873034	−	0.487660i	$-0.162149\pi$
$434$	12326.4	−	2212.61i	1.36333	−	0.244721i
$435$	1684.22	−	1684.22i	0.185638	−	0.185638i
$436$	4856.26	−	11908.2i	0.533424	−	1.30802i
$437$	1774.44	+	1774.44i	0.194240	+	0.194240i
$438$	2314.93	+	11473.6i	0.252538	+	1.25167i
$439$		−	6163.76i		−	0.670115i	−0.942198	−	0.335057i	$-0.891244\pi$
$439$		−	6163.76i		−	0.670115i	0.942198	−	0.335057i	$-0.108756\pi$
$440$	−3143.10	−	598.388i	−0.340548	−	0.0648342i
$441$	6518.83	+	280.204i	0.703901	+	0.0302564i
$442$	−774.882	−	3840.57i	−0.0833877	−	0.413297i
$443$	705.371	+	705.371i	0.0756505	+	0.0756505i	0.743920	−	0.668269i	$-0.232965\pi$
$443$	705.371	+	705.371i	0.0756505	+	0.0756505i	−0.668269	+	0.743920i	$0.732965\pi$
$444$	−1511.73	−	3593.82i	−0.161585	−	0.384133i
$445$	−1295.74	−	1295.74i	−0.138032	−	0.138032i
$446$	2878.91	+	1912.24i	0.305651	+	0.203020i
$447$	−10419.1			−1.10247
$448$	−8778.75	+	3584.54i	−0.925797	+	0.378022i
$449$	1808.14			0.190048			0.0950240	−	0.995475i	$-0.469707\pi$
$449$	1808.14			0.190048			0.0950240	+	0.995475i	$0.469707\pi$
$450$	−5227.03	−	3471.91i	−0.547566	−	0.363706i
$451$	−4086.62	−	4086.62i	−0.426677	−	0.426677i
$452$	−1726.55	−	4104.50i	−0.179668	−	0.427123i
$453$	1236.51	+	1236.51i	0.128247	+	0.128247i
$454$	−2780.87	−	13782.9i	−0.287473	−	1.42481i
$455$	−400.954	+	384.089i	−0.0413121	+	0.0395745i
$456$	2915.98	+	555.149i	0.299458	+	0.0570115i
$457$			13173.0i			1.34838i	0.738560	+	0.674188i	$0.235506\pi$
$457$			13173.0i			1.34838i	−0.738560	+	0.674188i	$0.764494\pi$
$458$	2646.56	+	13117.2i	0.270012	+	1.33827i
$459$	5116.51	+	5116.51i	0.520301	+	0.520301i
$460$	1134.48	−	2781.88i	0.114990	−	0.281969i
$461$	2780.05	−	2780.05i	0.280867	−	0.280867i	−0.552588	−	0.833455i	$-0.686360\pi$
$461$	2780.05	−	2780.05i	0.280867	−	0.280867i	0.833455	+	0.552588i	$0.186360\pi$
$462$	−3067.92	−	17091.3i	−0.308945	−	1.72112i
$463$			3630.01i			0.364365i	0.983265	+	0.182182i	$0.0583161\pi$
$463$			3630.01i			0.364365i	−0.983265	+	0.182182i	$0.941684\pi$
$464$	−7764.44	+	85.0920i	−0.776843	+	0.00851357i
$465$			4693.41i			0.468068i
$466$	841.699	−	1267.19i	0.0836716	−	0.125969i
$467$	39.0209	+	39.0209i	0.00386654	+	0.00386654i	0.709037	−	0.705171i	$-0.249130\pi$
$467$	39.0209	+	39.0209i	0.00386654	+	0.00386654i	−0.705171	+	0.709037i	$0.749130\pi$
$468$	−595.355	+	1459.89i	−0.0588040	+	0.144195i
$469$	−32.7786	+	1525.86i	−0.00322723	+	0.150230i
$470$	−273.645	−	1356.28i	−0.0268560	−	0.133107i
$471$	14703.4			1.43842
$472$	5133.12	+	7547.23i	0.500574	+	0.735994i
$473$		−	5215.55i		−	0.507001i
$474$	−8669.09	+	1749.09i	−0.840052	+	0.169491i
$475$	1594.68	−	1594.68i	0.154040	−	0.154040i
$476$	−7872.95	+	18178.8i	−0.758101	+	1.75047i
$477$	9174.04	+	9174.04i	0.880609	+	0.880609i
$478$	−10020.8	+	15086.5i	−0.958870	+	1.44360i
$479$	1088.16			0.103798			0.0518990	−	0.998652i	$-0.483473\pi$
$479$	1088.16			0.103798			0.0518990	+	0.998652i	$0.483473\pi$
$480$	−740.976	−	3475.62i	−0.0704599	−	0.330499i
$481$			744.247i			0.0705504i
$482$	−2580.06	+	3884.34i	−0.243815	+	0.367068i
$483$	16301.1	+	350.181i	1.53567	+	0.0329892i
$484$	−7791.63	+	3277.53i	−0.731746	+	0.307807i
$485$	1936.03	−	1936.03i	0.181259	−	0.181259i
$486$	−2525.03	−	12514.9i	−0.235675	−	1.16808i
$487$	−17740.1			−1.65068			−0.825339	−	0.564638i	$-0.809016\pi$
$487$	−17740.1			−1.65068			−0.825339	+	0.564638i	$0.809016\pi$
$488$	−5634.12	−	8283.85i	−0.522632	−	0.768426i
$489$	−1702.53			−0.157446
$490$	2773.29	−	436.552i	0.255683	−	0.0402478i
$491$	5821.10	+	5821.10i	0.535036	+	0.535036i	0.922067	−	0.387031i	$-0.126499\pi$
$491$	5821.10	+	5821.10i	0.535036	+	0.535036i	−0.387031	+	0.922067i	$0.626499\pi$
$492$	2423.95	−	5943.84i	0.222114	−	0.544653i
$493$	−11470.9	+	11470.9i	−1.04792	+	1.04792i
$494$	−471.995	−	313.510i	−0.0429880	−	0.0285536i
$495$	2689.86			0.244243
$496$	10700.0	−	10937.1i	0.968636	−	0.990102i
$497$	−5003.34	+	4792.90i	−0.451571	+	0.432577i
$498$	−13143.4	+	19787.7i	−1.18267	+	1.78054i
$499$	4283.85	−	4283.85i	0.384312	−	0.384312i	−0.488341	−	0.872653i	$-0.662398\pi$
$499$	4283.85	−	4283.85i	0.384312	−	0.384312i	0.872653	+	0.488341i	$0.162398\pi$
$500$	−5179.63	−	2112.30i	−0.463280	−	0.188930i
$501$	−8261.88	+	8261.88i	−0.736753	+	0.736753i
$502$	−14805.3	+	2987.14i	−1.31632	+	0.265583i
$503$		−	743.585i		−	0.0659142i	−0.999457	−	0.0329571i	$-0.989508\pi$
$503$		−	743.585i		−	0.0659142i	0.999457	−	0.0329571i	$-0.0104925\pi$
$504$	6686.48	−	4340.64i	0.590951	−	0.383626i
$505$			577.449i			0.0508834i
$506$	−3547.20	−	17581.1i	−0.311645	−	1.54462i
$507$	−10024.2	+	10024.2i	−0.878087	+	0.878087i
$508$	−11715.2	+	4927.97i	−1.02318	+	0.430400i
$509$	−6189.71	+	6189.71i	−0.539006	+	0.539006i	−0.923237	−	0.384231i	$-0.874467\pi$
$509$	−6189.71	+	6189.71i	−0.539006	+	0.539006i	0.384231	+	0.923237i	$0.374467\pi$
$510$	−6184.41	−	4107.83i	−0.536961	−	0.356662i
$511$	−8158.20	+	7815.06i	−0.706258	+	0.676552i
$512$	−6196.96	+	9788.53i	−0.534902	+	0.844914i
$513$	1046.47			0.0900638
$514$	10891.8	−	16397.8i	0.934660	−	1.40715i
$515$	−1824.11	+	1824.11i	−0.156078	+	0.156078i
$516$	5339.70	−	2246.13i	0.455557	−	0.191629i
$517$	−5840.68	−	5840.68i	−0.496852	−	0.496852i
$518$	2148.94	−	3089.20i	0.182276	−	0.262030i
$519$	−17223.2			−1.45668
$520$	−126.871	+	666.401i	−0.0106993	+	0.0561992i
$521$	−11779.3			−0.990521			−0.495260	−	0.868745i	$-0.664927\pi$
$521$	−11779.3			−0.990521			−0.495260	+	0.868745i	$0.664927\pi$
$522$	6399.01	−	1291.08i	0.536547	−	0.108255i
$523$	1261.69	−	1261.69i	0.105488	−	0.105488i	−0.652393	−	0.757881i	$-0.726235\pi$
$523$	1261.69	−	1261.69i	0.105488	−	0.105488i	0.757881	+	0.652393i	$0.226235\pi$
$524$	6409.25	−	15716.3i	0.534331	−	1.31025i
$525$	314.705	−	14649.7i	0.0261616	−	1.21784i
$526$	10511.3	+	6981.83i	0.871319	+	0.578750i
$527$		−	31965.8i		−	2.64222i
$528$	−15165.0	−	14836.2i	−1.24994	−	1.22284i
$529$	4673.97			0.384151
$530$	4650.03	+	3088.65i	0.381102	+	0.253137i
$531$	−5425.92	−	5425.92i	−0.443437	−	0.443437i
$532$	1053.91	+	2664.15i	0.0858891	+	0.217116i
$533$	−866.447	+	866.447i	−0.0704127	+	0.0704127i
$534$	−2403.08	−	11910.5i	−0.194741	−	0.965201i
$535$			2977.53i			0.240616i
$536$	1048.67	+	1541.85i	0.0845064	+	0.124250i
$537$	−9151.86			−0.735441
$538$	−8830.67	+	1781.69i	−0.707653	+	0.142777i
$539$	12349.2	−	11331.3i	0.986858	−	0.905517i
$540$	−485.775	−	1154.83i	−0.0387119	−	0.0920293i
$541$	3180.80	+	3180.80i	0.252778	+	0.252778i	0.822109	−	0.569330i	$-0.192797\pi$
$541$	3180.80	+	3180.80i	0.252778	+	0.252778i	−0.569330	+	0.822109i	$0.692797\pi$
$542$	15715.0	+	10438.2i	1.24542	+	0.827234i
$543$			17080.7i			1.34991i
$544$	5046.62	+	23671.7i	0.397743	+	1.86565i
$545$			4651.94i			0.365628i
$546$	−3623.70	+	650.462i	−0.284030	+	0.0509839i
$547$	−2706.48	+	2706.48i	−0.211555	+	0.211555i	−0.804928	−	0.593373i	$-0.797796\pi$
$547$	−2706.48	+	2706.48i	−0.211555	+	0.211555i	0.593373	+	0.804928i	$0.297796\pi$
$548$	−16658.9	+	7007.55i	−1.29860	+	0.546255i
$549$	5955.50	+	5955.50i	0.462977	+	0.462977i
$550$	−15800.0	+	3187.84i	−1.22494	+	0.247145i
$551$			2346.12i			0.181394i
$552$	16472.0	−	11203.1i	1.27010	−	0.863835i
$553$	−5904.82	−	6164.09i	−0.454066	−	0.474003i
$554$	5950.09	−	1200.50i	0.456309	−	0.0920659i
$555$	997.242	+	997.242i	0.0762713	+	0.0762713i
$556$	22479.8	+	9167.44i	1.71467	+	0.699256i
$557$	−1976.55	−	1976.55i	−0.150358	−	0.150358i	0.627920	−	0.778278i	$-0.283906\pi$
$557$	−1976.55	−	1976.55i	−0.150358	−	0.150358i	−0.778278	+	0.627920i	$0.783906\pi$
$558$	−7117.12	+	10715.0i	−0.539949	+	0.812903i
$559$	−1105.80			−0.0836682
$560$	2450.78	−	2399.75i	0.184937	−	0.181086i
$561$	−44322.5			−3.33565
$562$	875.237	−	1317.69i	0.0656933	−	0.0989025i
$563$	1969.01	+	1969.01i	0.147396	+	0.147396i	0.776954	−	0.629558i	$-0.216764\pi$
$563$	1969.01	+	1969.01i	0.147396	+	0.147396i	−0.629558	+	0.776954i	$0.716764\pi$
$564$	3464.36	−	8495.06i	0.258645	−	0.634231i
$565$	1138.95	+	1138.95i	0.0848071	+	0.0848071i
$566$	101.310	−	20.4405i	0.00752363	−	0.00151798i
$567$	11779.2	−	11283.7i	0.872448	−	0.835752i
$568$	−1583.17	+	8315.75i	−0.116951	+	0.614298i
$569$		−	12025.5i		−	0.886004i	−0.896521	−	0.443002i	$-0.853913\pi$
$569$		−	12025.5i		−	0.886004i	0.896521	−	0.443002i	$-0.146087\pi$
$570$	−1052.53	+	212.360i	−0.0773429	+	0.0156049i
$571$	−3067.62	−	3067.62i	−0.224826	−	0.224826i	0.585701	−	0.810527i	$-0.300819\pi$
$571$	−3067.62	−	3067.62i	−0.224826	−	0.224826i	−0.810527	+	0.585701i	$0.800819\pi$
$572$	1570.26	+	3732.96i	0.114783	+	0.272873i
$573$	9901.06	−	9901.06i	0.721855	−	0.721855i
$574$	6098.21	−	1094.64i	0.443440	−	0.0795984i
$575$		−	15134.8i		−	1.09768i
$576$	3578.81	−	9058.37i	0.258884	−	0.655264i
$577$		−	4574.91i		−	0.330080i	−0.986287	−	0.165040i	$-0.947225\pi$
$577$		−	4574.91i		−	0.330080i	0.986287	−	0.165040i	$-0.0527753\pi$
$578$	30545.4	+	20289.0i	2.19813	+	1.46005i
$579$	5481.42	+	5481.42i	0.393437	+	0.393437i
$580$	2589.05	−	1089.08i	0.185352	−	0.0779681i
$581$	−22923.0	−	492.431i	−1.63684	−	0.0351626i
$582$	17796.0	−	3590.55i	1.26747	−	0.255727i
$583$	33325.9			2.36744
$584$	−2581.43	+	13559.2i	−0.182912	+	0.960763i
$585$		−	570.306i		−	0.0403064i
$586$	−3055.68	−	15145.0i	−0.215408	−	1.06763i
$587$	−1826.09	+	1826.09i	−0.128400	+	0.128400i	−0.768386	−	0.639986i	$-0.778940\pi$
$587$	−1826.09	+	1826.09i	−0.128400	+	0.128400i	0.639986	+	0.768386i	$0.278940\pi$
$588$	16919.3	+	7763.19i	1.18664	+	0.544470i
$589$	−3268.95	−	3268.95i	−0.228684	−	0.228684i
$590$	−2750.23	−	1826.76i	−0.191907	−	0.127469i
$591$	8035.12			0.559257
$592$	−50.3836	−	4597.39i	−0.00349789	−	0.319175i
$593$		−	5705.55i		−	0.395107i	−0.980292	−	0.197554i	$-0.936700\pi$
$593$		−	5705.55i		−	0.395107i	0.980292	−	0.197554i	$-0.0632997\pi$
$594$	−6230.16	−	4138.22i	−0.430348	−	0.285847i
$595$	153.904	−	7164.31i	0.0106041	−	0.493627i
$596$	−11376.9	−	4639.61i	−0.781908	−	0.318869i
$597$	−10387.1	+	10387.1i	−0.712090	+	0.712090i
$598$	−3727.55	+	752.079i	−0.254901	+	0.0514294i
$599$	10497.7			0.716070			0.358035	−	0.933708i	$-0.383447\pi$
$599$	10497.7			0.716070			0.358035	+	0.933708i	$0.383447\pi$
$600$	−10068.2	−	14803.2i	−0.685052	−	1.00723i
$601$	9375.74			0.636347			0.318173	−	0.948033i	$-0.396931\pi$
$601$	9375.74			0.636347			0.318173	+	0.948033i	$0.396931\pi$
$602$	4589.95	+	3192.91i	0.310751	+	0.216168i
$603$	−1108.48	−	1108.48i	−0.0748606	−	0.0748606i
$604$	799.566	+	1900.80i	0.0538641	+	0.128050i
$605$	2162.09	−	2162.09i	0.145291	−	0.145291i
$606$	−2118.49	+	3189.43i	−0.142010	+	0.213798i
$607$	−5702.60			−0.381320			−0.190660	−	0.981656i	$-0.561063\pi$
$607$	−5702.60			−0.381320			−0.190660	+	0.981656i	$0.561063\pi$
$608$	2936.85	+	1904.67i	0.195896	+	0.127047i
$609$	10544.9	+	11007.9i	0.701646	+	0.732453i
$610$	3018.65	+	2005.06i	0.200363	+	0.133086i
$611$	−1238.34	+	1238.34i	−0.0819934	+	0.0819934i
$612$	−7889.73	−	18756.2i	−0.521117	−	1.23884i
$613$	7424.25	−	7424.25i	0.489172	−	0.489172i	−0.418873	−	0.908045i	$-0.637575\pi$
$613$	7424.25	−	7424.25i	0.489172	−	0.489172i	0.908045	+	0.418873i	$0.137575\pi$
$614$	1617.35	+	8016.15i	0.106305	+	0.526882i
$615$			2321.96i			0.152245i
$616$	4260.78	−	20028.7i	0.278688	−	1.31003i
$617$			22808.8i			1.48825i	0.668043	+	0.744123i	$0.267132\pi$
$617$			22808.8i			1.48825i	−0.668043	+	0.744123i	$0.732868\pi$
$618$	−16767.3	+	3383.00i	−1.09139	+	0.220201i
$619$	15749.6	−	15749.6i	1.02267	−	1.02267i	0.0229291	−	0.999737i	$-0.492701\pi$
$619$	15749.6	−	15749.6i	1.02267	−	1.02267i	0.999737	−	0.0229291i	$-0.00729921\pi$
$620$	−2089.98	+	5124.90i	−0.135380	+	0.331969i
$621$	4965.94	−	4965.94i	0.320896	−	0.320896i
$622$	−14665.6	+	22079.4i	−0.945398	+	1.42331i
$623$	8468.86	−	8112.65i	0.544619	−	0.521712i
$624$	−3145.57	+	3215.28i	−0.201801	+	0.206273i
$625$	−12554.8			−0.803507
$626$	−21154.8	−	14051.5i	−1.35067	−	0.897144i
$627$	−4532.60	+	4532.60i	−0.288699	+	0.288699i
$628$	16055.2	+	6547.44i	1.02018	+	0.416037i
$629$	−6792.00	−	6792.00i	−0.430548	−	0.430548i
$630$	−1646.71	+	2367.21i	−0.104137	+	0.149702i
$631$	−7632.20			−0.481510			−0.240755	−	0.970586i	$-0.577395\pi$
$631$	−7632.20			−0.481510			−0.240755	+	0.970586i	$0.577395\pi$
$632$	−10244.9	−	1950.45i	−0.644814	−	0.122761i
$633$	1251.29			0.0785689
$634$	1398.48	+	6931.32i	0.0876036	+	0.434193i
$635$	3250.83	−	3250.83i	0.203158	−	0.203158i
$636$	14352.1	+	34119.2i	0.894811	+	2.12722i
$637$	−2402.47	−	2618.28i	−0.149434	−	0.162857i
$638$	9277.61	−	13967.6i	0.575712	−	0.866745i
$639$		−	7116.62i		−	0.440578i
$640$	738.596	−	4125.10i	0.0456181	−	0.254780i
$641$	18811.7			1.15915			0.579576	−	0.814918i	$-0.303218\pi$
$641$	18811.7			1.15915			0.579576	+	0.814918i	$0.303218\pi$
$642$	−10923.7	+	16445.8i	−0.671531	+	1.01100i
$643$	14360.3	+	14360.3i	0.880740	+	0.880740i	0.993610	−	0.112869i	$-0.0360042\pi$
$643$	14360.3	+	14360.3i	0.880740	+	0.880740i	−0.112869	+	0.993610i	$0.536004\pi$
$644$	17643.8	+	7641.26i	1.07960	+	0.467559i
$645$	−1481.71	+	1481.71i	−0.0904529	+	0.0904529i
$646$	7168.52	−	1446.33i	0.436597	−	0.0880887i
$647$		−	13880.5i		−	0.843430i	−0.906728	−	0.421715i	$-0.861428\pi$
$647$		−	13880.5i		−	0.843430i	0.906728	−	0.421715i	$-0.138572\pi$
$648$	3727.18	−	19577.4i	0.225953	−	1.18684i
$649$	−19710.4			−1.19214
$650$	675.888	+	3349.92i	0.0407854	+	0.202146i
$651$	−30030.6	−	645.117i	−1.80797	−	0.0388389i
$652$	−1859.05	−	758.136i	−0.111666	−	0.0455382i
$653$	6926.86	+	6926.86i	0.415113	+	0.415113i	0.883515	−	0.468402i	$-0.155170\pi$
$653$	6926.86	+	6926.86i	0.415113	+	0.415113i	−0.468402	+	0.883515i	$0.655170\pi$
$654$	−17066.6	+	25694.1i	−1.02042	+	1.53627i
$655$			6139.59i			0.366250i
$656$	5293.59	−	5410.90i	0.315061	−	0.322043i
$657$		−	11604.0i		−	0.689065i
$658$	8715.69	−	1564.48i	0.516372	−	0.0926899i
$659$	−21306.6	+	21306.6i	−1.25947	+	1.25947i	−0.308118	+	0.951348i	$0.599699\pi$
$659$	−21306.6	+	21306.6i	−1.25947	+	1.25947i	−0.951348	+	0.308118i	$0.900301\pi$
$660$	7105.98	+	2897.88i	0.419091	+	0.170909i
$661$	−9192.89	−	9192.89i	−0.540941	−	0.540941i	0.382864	−	0.923805i	$-0.374938\pi$
$661$	−9192.89	−	9192.89i	−0.540941	−	0.540941i	−0.923805	+	0.382864i	$0.874938\pi$
$662$	−3742.18	−	18547.5i	−0.219704	−	1.08893i
$663$			9397.29i			0.550468i
$664$	−23163.2	+	15754.1i	−1.35378	+	0.920748i
$665$	−716.912	−	748.389i	−0.0418055	−	0.0436410i
$666$	764.457	+	3788.91i	0.0444777	+	0.220446i
$667$	11133.3	+	11133.3i	0.646303	+	0.646303i
$668$	−12700.4	+	5342.41i	−0.735621	+	0.309437i
$669$	−5861.59	−	5861.59i	−0.338748	−	0.338748i
$670$	−561.855	−	373.197i	−0.0323975	−	0.0215192i
$671$	21634.1			1.24467
$672$	22340.4	−	4263.37i	1.28244	−	0.244737i
$673$	−24859.6			−1.42388			−0.711938	−	0.702242i	$-0.752182\pi$
$673$	−24859.6			−1.42388			−0.711938	+	0.702242i	$0.752182\pi$
$674$	−4047.49	−	2688.43i	−0.231311	−	0.153642i
$675$	−4462.85	−	4462.85i	−0.254482	−	0.254482i
$676$	−15409.5	+	6481.99i	−0.876738	+	0.368798i
$677$	11098.7	+	11098.7i	0.630070	+	0.630070i	0.948086	−	0.318016i	$-0.103016\pi$
$677$	11098.7	+	11098.7i	0.630070	+	0.630070i	−0.318016	+	0.948086i	$0.603016\pi$
$678$	2112.30	+	10469.3i	0.119649	+	0.593022i
$679$	12121.5	+	12653.7i	0.685094	+	0.715175i
$680$	−4923.75	−	7239.40i	−0.277673	−	0.408262i
$681$			33724.7i			1.89770i
$682$	6534.80	+	32388.6i	0.366907	+	1.81851i
$683$	−5129.88	−	5129.88i	−0.287393	−	0.287393i	0.548656	−	0.836048i	$-0.315140\pi$
$683$	−5129.88	−	5129.88i	−0.287393	−	0.287393i	−0.836048	+	0.548656i	$0.815140\pi$
$684$	−2724.91	−	1111.24i	−0.152324	−	0.0621191i
$685$	4622.66	−	4622.66i	0.257844	−	0.257844i
$686$	2412.07	+	17804.8i	0.134247	+	0.990948i
$687$		−	32095.8i		−	1.78243i
$688$	6830.81	−	74.8601i	0.378521	−	0.00414828i
$689$		−	7065.77i		−	0.390688i
$690$	−3986.94	+	6002.42i	−0.219972	+	0.331171i
$691$	1243.53	+	1243.53i	0.0684606	+	0.0684606i	0.740508	−	0.672047i	$-0.234585\pi$
$691$	1243.53	+	1243.53i	0.0684606	+	0.0684606i	−0.672047	+	0.740508i	$0.734585\pi$
$692$	−18806.6	−	7669.51i	−1.03312	−	0.421316i
$693$	−369.726	+	17211.0i	−0.0202666	+	0.943420i
$694$	6165.73	+	30559.4i	0.337245	+	1.67150i
$695$	−8781.73			−0.479295
$696$	18295.6	+	3483.15i	0.996399	+	0.189696i
$697$		−	15814.4i		−	0.859416i
$698$	16513.5	−	3331.80i	0.895481	−	0.180674i
$699$	−2580.07	+	2580.07i	−0.139609	+	0.139609i
$700$	6867.15	−	15856.4i	0.370791	−	0.856163i
$701$	8513.11	+	8513.11i	0.458681	+	0.458681i	0.898223	−	0.439541i	$-0.144859\pi$
$701$	8513.11	+	8513.11i	0.458681	+	0.458681i	−0.439541	+	0.898223i	$0.644859\pi$
$702$	−877.387	+	1320.92i	−0.0471721	+	0.0710185i
$703$	−1389.15			−0.0745276
$704$	−9952.59	−	22953.1i	−0.532816	−	1.22880i
$705$			3318.60i			0.177285i
$706$	11225.1	−	16899.6i	0.598389	−	0.900886i
$707$	−3694.78	−	79.3713i	−0.196544	−	0.00422216i
$708$	−8488.48	−	20179.5i	−0.450588	−	1.07118i
$709$	20499.4	−	20499.4i	1.08585	−	1.08585i	0.0899043	−	0.995950i	$-0.471344\pi$
$709$	20499.4	−	20499.4i	1.08585	−	1.08585i	0.995950	−	0.0899043i	$-0.0286561\pi$
$710$	−605.605	−	3001.58i	−0.0320112	−	0.158658i
$711$	8767.63			0.462464
$712$	2679.73	−	14075.6i	0.141049	−	0.740877i
$713$	−31025.1			−1.62959
$714$	27133.8	−	39006.0i	1.42221	−	2.04449i
$715$	−1035.85	−	1035.85i	−0.0541801	−	0.0541801i
$716$	−9993.23	−	4075.32i	−0.521598	−	0.212712i
$717$	30716.8	−	30716.8i	1.59991	−	1.59991i
$718$	30181.2	+	20047.0i	1.56873	+	1.04199i
$719$	−14074.7			−0.730037			−0.365018	−	0.931000i	$-0.618937\pi$
$719$	−14074.7			−0.730037			−0.365018	+	0.931000i	$0.618937\pi$
$720$	38.6083	+	3522.91i	0.00199840	+	0.182349i
$721$	−11420.8	−	11922.2i	−0.589919	−	0.615821i
$722$	−10148.8	+	15279.1i	−0.523127	+	0.787577i
$723$	7908.69	−	7908.69i	0.406815	−	0.406815i
$724$	−7606.02	+	18651.0i	−0.390436	+	0.957400i
$725$	10005.4	−	10005.4i	0.512541	−	0.512541i
$726$	19873.9	−	4009.80i	1.01596	−	0.204983i
$727$		−	95.2264i		−	0.00485798i	−0.999997	−	0.00242899i	$-0.999227\pi$
$727$		−	95.2264i		−	0.00485798i	0.999997	−	0.00242899i	$-0.000773172\pi$
$728$	−4246.50	−	903.374i	−0.216189	−	0.0459907i
$729$			6841.84i			0.347602i
$730$	−987.469	−	4894.23i	−0.0500656	−	0.248142i
$731$	10091.6	−	10091.6i	0.510602	−	0.510602i
$732$	9316.96	+	22149.1i	0.470444	+	1.11838i
$733$	13958.3	−	13958.3i	0.703357	−	0.703357i	−0.261772	−	0.965130i	$-0.584307\pi$
$733$	13958.3	−	13958.3i	0.703357	−	0.703357i	0.965130	+	0.261772i	$0.0843070\pi$
$734$	12963.2	+	8610.42i	0.651878	+	0.432993i
$735$	−6727.47	−	289.173i	−0.337614	−	0.0145120i
$736$	22975.1	−	4898.11i	1.15064	−	0.245308i
$737$	−4026.71			−0.201256
$738$	−3521.04	+	5300.99i	−0.175625	+	0.264407i
$739$	22132.3	−	22132.3i	1.10169	−	1.10169i	0.107485	−	0.994207i	$-0.465720\pi$
$739$	22132.3	−	22132.3i	1.10169	−	1.10169i	0.994207	−	0.107485i	$-0.0342797\pi$
$740$	644.851	+	1533.00i	0.0320340	+	0.0761541i
$741$	961.004	+	961.004i	0.0476428	+	0.0476428i
$742$	−20401.8	+	29328.4i	−1.00940	+	1.45105i
$743$	−5532.55			−0.273176			−0.136588	−	0.990628i	$-0.543614\pi$
$743$	−5532.55			−0.273176			−0.136588	+	0.990628i	$0.543614\pi$
$744$	−30345.3	+	20638.9i	−1.49531	+	1.01701i
$745$	4444.40			0.218564
$746$	19707.4	−	3976.20i	0.967209	−	0.195146i
$747$	16652.7	−	16652.7i	0.815651	−	0.815651i
$748$	−48397.3	−	19736.8i	−2.36575	−	0.964773i
$749$	−19051.6	−	409.266i	−0.929412	−	0.0199656i
$750$	11176.0	+	7423.35i	0.544119	+	0.361417i
$751$			36330.7i			1.76528i	0.470048	+	0.882641i	$0.344236\pi$
$751$			36330.7i			1.76528i	−0.470048	+	0.882641i	$0.655764\pi$
$752$	7565.70	−	7733.37i	0.366879	−	0.375009i
$753$	36226.2			1.75320
$754$	−2961.42	−	1967.04i	−0.143035	−	0.0950073i
$755$	−527.449	−	527.449i	−0.0254250	−	0.0254250i
$756$	7455.88	−	2949.48i	0.358687	−	0.141894i
$757$	15674.3	−	15674.3i	0.752564	−	0.752564i	−0.222393	−	0.974957i	$-0.571387\pi$
$757$	15674.3	−	15674.3i	0.752564	−	0.752564i	0.974957	+	0.222393i	$0.0713869\pi$
$758$	−4747.52	−	23530.3i	−0.227490	−	1.12752i
$759$			43018.2i			2.05726i
$760$	−1243.85	−	236.807i	−0.0593674	−	0.0113025i
$761$	−16656.7			−0.793437			−0.396718	−	0.917940i	$-0.629851\pi$
$761$	−16656.7			−0.793437			−0.396718	+	0.917940i	$0.629851\pi$
$762$	29881.7	−	6028.99i	1.42060	−	0.286624i
$763$	−29765.2	−	639.417i	−1.41229	−	0.0303387i
$764$	15220.3	−	6402.37i	0.720745	−	0.303180i
$765$	5204.62	+	5204.62i	0.245978	+	0.245978i
$766$	−29338.5	−	19487.3i	−1.38387	−	0.919198i
$767$			4179.00i			0.196734i
$768$	19213.3	−	20074.5i	0.902734	−	0.943198i
$769$			9190.37i			0.430966i	0.976508	+	0.215483i	$0.0691327\pi$
$769$			9190.37i			0.430966i	−0.976508	+	0.215483i	$0.930867\pi$
$770$	1308.67	+	7290.54i	0.0612481	+	0.341211i
$771$	−33386.6	+	33386.6i	−1.55952	+	1.55952i
$772$	3544.47	+	8426.23i	0.165244	+	0.392832i
$773$	3285.14	+	3285.14i	0.152857	+	0.152857i	0.779393	−	0.626536i	$-0.215528\pi$
$773$	3285.14	+	3285.14i	0.152857	+	0.152857i	−0.626536	+	0.779393i	$0.715528\pi$
$774$	−5629.57	+	1135.83i	−0.261435	+	0.0527476i
$775$			27882.0i			1.29233i
$776$	21030.9	+	4003.90i	0.972894	+	0.185221i
$777$	−6517.88	+	6243.74i	−0.300937	+	0.288279i
$778$	−29676.3	+	5987.55i	−1.36754	+	0.275918i
$779$	−1617.24	−	1617.24i	−0.0743822	−	0.0743822i
$780$	614.410	−	1506.61i	0.0282044	−	0.0691608i
$781$	−12926.0	−	12926.0i	−0.592227	−	0.592227i
$782$	27154.2	−	40881.2i	1.24173	−	1.86945i
$783$	6565.83			0.299672
$784$	15017.9	+	16011.1i	0.684122	+	0.729367i
$785$	−6271.96			−0.285167
$786$	−22524.3	+	33910.8i	−1.02216	+	1.53888i
$787$	11875.1	+	11875.1i	0.537867	+	0.537867i	0.922902	−	0.385035i	$-0.125811\pi$
$787$	11875.1	+	11875.1i	0.537867	+	0.537867i	−0.385035	+	0.922902i	$0.625811\pi$
$788$	8773.83	+	3578.04i	0.396643	+	0.161754i
$789$	−21401.5	−	21401.5i	−0.965668	−	0.965668i
$790$	3697.93	−	746.101i	0.166540	−	0.0336014i
$791$	−7444.08	+	7130.98i	−0.334616	+	0.320541i
$792$	11828.4	+	17391.3i	0.530688	+	0.780271i
$793$		−	4586.87i		−	0.205403i
$794$	−2926.92	+	590.542i	−0.130822	+	0.0263949i
$795$	−9467.67	−	9467.67i	−0.422369	−	0.422369i
$796$	−15967.5	+	6716.68i	−0.710995	+	0.299079i
$797$	−27267.4	+	27267.4i	−1.21187	+	1.21187i	−0.241460	+	0.970411i	$0.577626\pi$
$797$	−27267.4	+	27267.4i	−1.21187	+	1.21187i	−0.970411	+	0.241460i	$0.922374\pi$
$798$	−1214.10	−	6763.72i	−0.0538581	−	0.300042i
$799$		−	22602.3i		−	1.00076i
$800$	−4401.90	−	20647.5i	−0.194538	−	0.912500i
$801$			12045.9i			0.531361i
$802$	−19797.4	−	13149.9i	−0.871658	−	0.578975i
$803$	−21076.5	−	21076.5i	−0.926244	−	0.926244i
$804$	−1734.15	−	4122.56i	−0.0760679	−	0.180835i
$805$	−6953.48	−	149.375i	−0.304445	−	0.00654008i
$806$	6867.05	−	1385.51i	0.300101	−	0.0605490i
$807$	21607.3			0.942518
$808$	−3733.51	+	2539.28i	−0.162555	+	0.110559i
$809$			37899.6i			1.64707i	0.567265	+	0.823535i	$0.308001\pi$
$809$			37899.6i			1.64707i	−0.567265	+	0.823535i	$0.691999\pi$
$810$	1425.75	+	7066.49i	0.0618466	+	0.306532i
$811$	−2453.46	+	2453.46i	−0.106230	+	0.106230i	−0.758224	−	0.651994i	$-0.773933\pi$
$811$	−2453.46	+	2453.46i	−0.106230	+	0.106230i	0.651994	+	0.758224i	$0.273933\pi$
$812$	6612.54	+	16715.6i	0.285782	+	0.722417i
$813$	−31996.4	−	31996.4i	−1.38027	−	1.38027i
$814$	8270.34	+	5493.35i	0.356112	+	0.236538i
$815$	726.238			0.0312135
$816$	−636.172	−	58049.2i	−0.0272923	−	2.49035i
$817$		−	2064.01i		−	0.0883850i
$818$	−19861.8	−	13192.7i	−0.848964	−	0.563902i
$819$	3649.08	+	78.3895i	0.155689	+	0.00334451i
$820$	−1033.97	+	2535.43i	−0.0440340	+	0.107977i
$821$	−16123.1	+	16123.1i	−0.685385	+	0.685385i	−0.961208	−	0.275823i	$-0.911050\pi$
$821$	−16123.1	+	16123.1i	−0.685385	+	0.685385i	0.275823	+	0.961208i	$0.411050\pi$
$822$	42491.6	−	8573.19i	1.80300	−	0.363776i
$823$	24632.9			1.04332			0.521658	−	0.853155i	$-0.325314\pi$
$823$	24632.9			1.04332			0.521658	+	0.853155i	$0.325314\pi$
$824$	−19815.2	−	3772.45i	−0.837737	−	0.159490i
$825$	38660.1			1.63148
$826$	12066.5	−	17346.1i	0.508289	−	0.730688i
$827$	1089.80	+	1089.80i	0.0458236	+	0.0458236i	0.729647	−	0.683824i	$-0.239684\pi$
$827$	1089.80	+	1089.80i	0.0458236	+	0.0458236i	−0.683824	+	0.729647i	$0.739684\pi$
$828$	−18204.2	+	7657.56i	−0.764058	+	0.321399i
$829$	−4055.04	+	4055.04i	−0.169888	+	0.169888i	−0.786930	−	0.617042i	$-0.788331\pi$
$829$	−4055.04	+	4055.04i	−0.169888	+	0.169888i	0.617042	+	0.786930i	$0.288331\pi$
$830$	5606.53	−	8440.73i	0.234464	−	0.352990i
$831$	−14559.0			−0.607755
$832$	−4866.53	+	2110.15i	−0.202784	+	0.0879284i
$833$	45819.4	+	1969.49i	1.90582	+	0.0819194i
$834$	−48504.2	−	32217.6i	−2.01386	−	1.33766i
$835$	3524.22	−	3524.22i	0.146061	−	0.146061i
$836$	−6967.67	+	2930.93i	−0.288256	+	0.121254i
$837$	−9148.46	+	9148.46i	−0.377798	+	0.377798i
$838$	−6860.59	−	34003.4i	−0.282810	−	1.40170i
$839$		−	35349.1i		−	1.45457i	−0.686335	−	0.727285i	$-0.740782\pi$
$839$		−	35349.1i		−	1.45457i	0.686335	−	0.727285i	$-0.259218\pi$
$840$	−6900.49	+	4479.57i	−0.283440	+	0.184000i
$841$		−	9668.83i		−	0.396442i
$842$	−40773.5	+	8226.55i	−1.66882	+	0.336705i
$843$	−2682.87	+	2682.87i	−0.109612	+	0.109612i
$844$	1366.32	+	557.197i	0.0557236	+	0.0227246i
$845$	4275.97	−	4275.97i	0.174080	−	0.174080i
$846$	−5032.34	+	7576.29i	−0.204510	+	0.307894i
$847$	13536.8	+	14131.2i	0.549151	+	0.573263i
$848$	478.335	+	43646.9i	0.0193704	+	1.76750i
$849$	−247.890			−0.0100207
$850$	−36739.6	−	24403.3i	−1.48254	−	0.984736i
$851$	−6592.13	+	6592.13i	−0.265541	+	0.265541i
$852$	7666.98	−	18800.4i	0.308294	−	0.755977i
$853$	28356.9	+	28356.9i	1.13824	+	1.13824i	0.988765	+	0.149477i	$0.0477591\pi$
$853$	28356.9	+	28356.9i	1.13824	+	1.13824i	0.149477	+	0.988765i	$0.452241\pi$
$854$	−13244.2	+	19039.1i	−0.530687	+	0.762886i
$855$	1064.49			0.0425787
$856$	−19251.3	+	13093.4i	−0.768685	+	0.522808i
$857$	−5617.28			−0.223900			−0.111950	−	0.993714i	$-0.535710\pi$
$857$	−5617.28			−0.223900			−0.111950	+	0.993714i	$0.535710\pi$
$858$	−1921.09	−	9521.59i	−0.0764395	−	0.378860i
$859$	26923.7	−	26923.7i	1.06941	−	1.06941i	0.0720059	−	0.997404i	$-0.477060\pi$
$859$	26923.7	−	26923.7i	1.06941	−	1.06941i	0.997404	−	0.0720059i	$-0.0229400\pi$
$860$	−2277.73	+	958.122i	−0.0903139	+	0.0379903i
$861$	−14857.0	−	319.158i	−0.588066	−	0.0126328i
$862$	19160.6	−	28846.6i	0.757089	−	1.13981i
$863$		−	7764.09i		−	0.306249i	−0.988207	−	0.153124i	$-0.951067\pi$
$863$		−	7764.09i		−	0.306249i	0.988207	−	0.153124i	$-0.0489335\pi$
$864$	5330.40	−	8219.04i	0.209889	−	0.323631i
$865$	7346.82			0.288785
$866$	−13752.3	+	20704.4i	−0.539635	+	0.812430i
$867$	−62191.9	−	62191.9i	−2.43616	−	2.43616i
$868$	−32504.2	−	14077.0i	−1.27104	−	0.550468i
$869$	15924.8	−	15924.8i	0.621646	−	0.621646i
$870$	−6603.83	+	1332.40i	−0.257346	+	0.0519226i
$871$			853.745i			0.0332124i
$872$	−30077.2	+	20456.5i	−1.16805	+	0.794432i
$873$	−17998.3			−0.697765
$874$	−1403.77	−	6957.57i	−0.0543287	−	0.269271i
$875$	−278.123	+	12946.8i	−0.0107455	+	0.500207i
$876$	12501.4	−	30655.1i	0.482172	−	1.18235i
$877$	15619.2	+	15619.2i	0.601396	+	0.601396i	0.940683	−	0.339287i	$-0.110186\pi$
$877$	15619.2	+	15619.2i	0.601396	+	0.601396i	−0.339287	+	0.940683i	$0.610186\pi$
$878$	−9645.93	+	14522.1i	−0.370768	+	0.558198i
$879$			37057.3i			1.42197i
$880$	6468.84	+	6328.59i	0.247801	+	0.242428i
$881$			45320.9i			1.73314i	0.499053	+	0.866571i	$0.333681\pi$
$881$			45320.9i			1.73314i	−0.499053	+	0.866571i	$0.666319\pi$
$882$	−14920.2	−	10861.8i	−0.569601	−	0.414665i
$883$	−5998.33	+	5998.33i	−0.228607	+	0.228607i	−0.812110	−	0.583504i	$-0.801681\pi$
$883$	−5998.33	+	5998.33i	−0.228607	+	0.228607i	0.583504	+	0.812110i	$0.301681\pi$
$884$	−4184.61	+	10261.2i	−0.159212	+	0.390410i
$885$	5599.59	+	5599.59i	0.212687	+	0.212687i
$886$	−558.023	−	2765.75i	−0.0211593	−	0.104873i
$887$			25507.8i			0.965578i	0.875737	+	0.482789i	$0.160376\pi$
$887$			25507.8i			0.965578i	−0.875737	+	0.482789i	$0.839624\pi$
$888$	−2062.40	+	10833.0i	−0.0779388	+	0.409381i
$889$	20353.5	+	21247.1i	0.767866	+	0.801581i
$890$	1025.07	+	5080.59i	0.0386073	+	0.191350i
$891$	30431.2	+	30431.2i	1.14420	+	1.14420i
$892$	−3790.31	−	9010.65i	−0.142275	−	0.338227i
$893$	−2311.40	−	2311.40i	−0.0866158	−	0.0866158i
$894$	24547.8	+	16305.2i	0.918346	+	0.609986i
$895$	3903.86			0.145801
$896$	26292.7	+	5292.87i	0.980334	+	0.197346i
$897$	9120.74			0.339501
$898$	−4260.07	−	2829.64i	−0.158308	−	0.105152i
$899$	−20510.3	−	20510.3i	−0.760907	−	0.760907i
$900$	6881.79	+	16360.0i	0.254881	+	0.605925i
$901$	64482.2	+	64482.2i	2.38426	+	2.38426i
$902$	3232.95	+	16023.6i	0.119341	+	0.591493i
$903$	−9276.96	−	9684.29i	−0.341880	−	0.356891i
$904$	−2355.47	+	12372.3i	−0.0866612	+	0.455197i
$905$		−	7286.01i		−	0.267619i
$906$	−978.207	−	4848.32i	−0.0358706	−	0.177787i
$907$	−26334.9	−	26334.9i	−0.964096	−	0.964096i	0.0352818	−	0.999377i	$-0.488767\pi$
$907$	−26334.9	−	26334.9i	−0.964096	−	0.964096i	−0.999377	+	0.0352818i	$0.988767\pi$
$908$	−15017.6	+	36825.1i	−0.548873	+	1.34591i
$909$	2684.13	−	2684.13i	0.0979393	−	0.0979393i
$910$	1545.74	−	277.464i	0.0563087	−	0.0101075i
$911$			16395.8i			0.596285i	0.954521	+	0.298142i	$0.0963671\pi$
$911$			16395.8i			0.596285i	−0.954521	+	0.298142i	$0.903633\pi$
$912$	−6001.40	−	5871.29i	−0.217902	−	0.213177i
$913$		−	60493.1i		−	2.19280i
$914$	20615.0	−	31036.3i	0.746043	−	1.12318i
$915$	−6146.11	−	6146.11i	−0.222059	−	0.222059i
$916$	14292.3	−	35046.5i	0.515535	−	1.26416i
$917$	−39283.9	−	843.896i	−1.41469	−	0.0303903i
$918$	−4047.70	−	20061.8i	−0.145527	−	0.721282i
$919$	−26851.4			−0.963815			−0.481908	−	0.876222i	$-0.660056\pi$
$919$	−26851.4			−0.963815			−0.481908	+	0.876222i	$0.660056\pi$
$920$	−7026.36	+	4778.86i	−0.251796	+	0.171255i
$921$		−	19614.3i		−	0.701750i
$922$	−10900.5	+	2199.31i	−0.389360	+	0.0785581i
$923$	−2740.58	+	2740.58i	−0.0977327	+	0.0977327i
$924$	−19518.7	+	45069.0i	−0.694932	+	1.60461i
$925$	5924.29	+	5924.29i	0.210583	+	0.210583i
$926$	5680.75	−	8552.48i	0.201599	−	0.303512i
$927$	16957.9			0.600830
$928$	18426.6	+	11950.4i	0.651812	+	0.422728i
$929$			19627.5i			0.693171i	0.938018	+	0.346585i	$0.112659\pi$
$929$			19627.5i			0.693171i	−0.938018	+	0.346585i	$0.887341\pi$
$930$	7344.91	−	11057.9i	0.258978	−	0.389896i
$931$	4887.08	−	4484.26i	0.172038	−	0.157858i
$932$	−3966.16	+	1668.36i	−0.139395	+	0.0586361i
$933$	44954.6	−	44954.6i	1.57744	−	1.57744i
$934$	−30.8697	−	153.001i	−0.00108146	−	0.00536010i
$935$	18906.4			0.661290
$936$	3687.32	−	2507.87i	0.128765	−	0.0875772i
$937$	4230.42			0.147494			0.0737469	−	0.997277i	$-0.476504\pi$
$937$	4230.42			0.147494			0.0737469	+	0.997277i	$0.476504\pi$
$938$	2465.11	−	3543.70i	0.0858089	−	0.123354i
$939$	43072.2	+	43072.2i	1.49692	+	1.49692i
$940$	−1477.77	+	3623.69i	−0.0512762	+	0.125736i
$941$	−3133.94	+	3133.94i	−0.108569	+	0.108569i	−0.759305	−	0.650735i	$-0.774461\pi$
$941$	−3133.94	+	3133.94i	−0.108569	+	0.108569i	0.650735	+	0.759305i	$0.274461\pi$
$942$	−34642.0	−	23010.0i	−1.19819	−	0.795866i
$943$	−15349.0			−0.530045
$944$	−282.908	−	25814.7i	−0.00975409	−	0.890038i
$945$	−2094.44	+	2006.35i	−0.0720974	+	0.0690650i
$946$	−8162.03	+	12288.1i	−0.280519	+	0.422326i
$947$	273.354	−	273.354i	0.00937997	−	0.00937997i	−0.702401	−	0.711781i	$-0.747889\pi$
$947$	273.354	−	273.354i	0.00937997	−	0.00937997i	0.711781	+	0.702401i	$0.247889\pi$
$948$	23162.0	+	9445.67i	0.793531	+	0.323609i
$949$	−4468.65	+	4468.65i	−0.152854	+	0.152854i
$950$	−6252.71	+	1261.56i	−0.213542	+	0.0430846i
$951$		−	16959.9i		−	0.578298i
$952$	46997.7	−	30509.4i	1.60001	−	1.03867i
$953$			20906.0i			0.710610i	0.934750	+	0.355305i	$0.115623\pi$
$953$			20906.0i			0.710610i	−0.934750	+	0.355305i	$0.884377\pi$
$954$	−7257.64	−	35971.3i	−0.246305	−	1.22077i
$955$	−4223.44	+	4223.44i	−0.143107	+	0.143107i
$956$	47218.9	−	19862.5i	1.59746	−	0.671966i
$957$	−28438.7	+	28438.7i	−0.960599	+	0.960599i
$958$	−2563.76	−	1702.91i	−0.0864626	−	0.0574304i
$959$	28942.5	+	30213.3i	0.974559	+	1.01735i
$960$	−3693.36	+	9348.30i	−0.124169	+	0.314287i
$961$	27364.8			0.918558
$962$	1164.70	−	1753.48i	0.0390348	−	0.0587677i
$963$	13840.3	−	13840.3i	0.463133	−	0.463133i
$964$	12157.5	−	5114.03i	0.406190	−	0.170863i
$965$	−2338.18	−	2338.18i	−0.0779986	−	0.0779986i
$966$	−37858.2	−	26335.3i	−1.26094	−	0.877148i
$967$	9771.57			0.324956			0.162478	−	0.986712i	$-0.448051\pi$
$967$	9771.57			0.324956			0.162478	+	0.986712i	$0.448051\pi$
$968$	23486.6	+	4471.42i	0.779842	+	0.148468i
$969$	−17540.3			−0.581501
$970$	−7591.13	+	1531.60i	−0.251275	+	0.0506977i
$971$	−9977.45	+	9977.45i	−0.329754	+	0.329754i	−0.852493	−	0.522739i	$-0.824910\pi$
$971$	−9977.45	+	9977.45i	−0.329754	+	0.329754i	0.522739	+	0.852493i	$0.324910\pi$
$972$	−13636.0	+	33437.3i	−0.449974	+	1.10340i
$973$	1207.06	−	56189.5i	0.0397705	−	1.85134i
$974$	41796.5	+	27762.2i	1.37500	+	0.913304i
$975$		−	8196.74i		−	0.269237i
$976$	310.520	+	28334.2i	0.0101839	+	0.929258i
$977$	15291.4			0.500732			0.250366	−	0.968151i	$-0.419449\pi$
$977$	15291.4			0.500732			0.250366	+	0.968151i	$0.419449\pi$
$978$	4011.24	+	2664.36i	0.131150	+	0.0871132i
$979$	21879.1	+	21879.1i	0.714258	+	0.714258i
$980$	−7217.19	−	3311.50i	−0.235250	−	0.107941i
$981$	21623.4	−	21623.4i	0.703753	−	0.703753i
$982$	−4605.11	−	22824.5i	−0.149649	−	0.741709i
$983$			14778.2i			0.479504i	0.970834	+	0.239752i	$0.0770661\pi$
$983$			14778.2i			0.479504i	−0.970834	+	0.239752i	$0.922934\pi$
$984$	−15012.7	+	10210.6i	−0.486369	+	0.330796i
$985$	−3427.50			−0.110872
$986$	44977.2	−	9074.69i	1.45270	−	0.293101i
$987$	−21233.9	−	456.147i	−0.684785	−	0.0147106i
$988$	621.418	+	1477.29i	0.0200101	+	0.0475696i
$989$	−9794.60	−	9794.60i	−0.314914	−	0.314914i
$990$	−6337.44	−	4209.48i	−0.203452	−	0.135137i
$991$		−	7672.15i		−	0.245927i	−0.992411	−	0.122964i	$-0.960760\pi$
$991$		−	7672.15i		−	0.245927i	0.992411	−	0.122964i	$-0.0392398\pi$
$992$	−42325.6	+	9023.51i	−1.35468	+	0.288807i
$993$			45382.9i			1.45033i
$994$	19288.7	−	3462.36i	0.615494	−	0.110482i
$995$	4430.79	−	4430.79i	0.141171	−	0.141171i
$996$	61933.1	−	26052.0i	1.97031	−	0.828805i
$997$	28731.6	+	28731.6i	0.912677	+	0.912677i	0.996482	−	0.0838054i	$-0.0267074\pi$
$997$	28731.6	+	28731.6i	0.912677	+	0.912677i	−0.0838054	+	0.996482i	$0.526707\pi$
$998$	−16796.9	+	3388.98i	−0.532763	+	0.107491i
$999$			3887.68i			0.123124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.4.j.b.83.10	yes	88
4.3	odd	2		448.4.j.b.111.8		88
7.6	odd	2	inner	112.4.j.b.83.9	yes	88
16.5	even	4		448.4.j.b.335.37		88
16.11	odd	4	inner	112.4.j.b.27.9	✓	88
28.27	even	2		448.4.j.b.111.37		88
112.27	even	4	inner	112.4.j.b.27.10	yes	88
112.69	odd	4		448.4.j.b.335.8		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.4.j.b.27.9	✓	88	16.11	odd	4	inner
112.4.j.b.27.10	yes	88	112.27	even	4	inner
112.4.j.b.83.9	yes	88	7.6	odd	2	inner
112.4.j.b.83.10	yes	88	1.1	even	1	trivial
448.4.j.b.111.8		88	4.3	odd	2
448.4.j.b.111.37		88	28.27	even	2
448.4.j.b.335.8		88	112.69	odd	4
448.4.j.b.335.37		88	16.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	112.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35605 - 1.56494i) q^{2} +(4.79702 + 4.79702i) q^{3} +(3.10192 + 7.37415i) q^{4} +(-2.04624 - 2.04624i) q^{5} +(-3.79496 - 18.8091i) q^{6} +(13.3740 - 12.8115i) q^{7} +(4.23184 - 22.2282i) q^{8} +19.0229i q^{9} +(1.61879 + 8.02329i) q^{10} +(34.5515 + 34.5515i) q^{11} +(-20.4940 + 50.2540i) q^{12} +(7.32563 - 7.32563i) q^{13} +(-51.5591 + 9.25497i) q^{14} -19.6317i q^{15} +(-44.7562 + 45.7480i) q^{16} +133.707i q^{17} +(29.7697 - 44.8188i) q^{18} +(13.6735 + 13.6735i) q^{19} +(8.74201 - 21.4366i) q^{20} +(125.613 + 2.69841i) q^{21} +(-27.3339 - 135.476i) q^{22} +129.773 q^{23} +(126.929 - 86.3288i) q^{24} -116.626i q^{25} +(-28.7237 + 5.79535i) q^{26} +(38.2664 - 38.2664i) q^{27} +(135.959 + 58.8819i) q^{28} +(85.7909 + 85.7909i) q^{29} +(-30.7225 + 46.2533i) q^{30} -239.073 q^{31} +(177.041 - 37.7438i) q^{32} +331.489i q^{33} +(209.244 - 315.021i) q^{34} +(-53.5820 - 1.15105i) q^{35} +(-140.278 + 59.0074i) q^{36} +(-50.7975 + 50.7975i) q^{37} +(-10.8172 - 53.6135i) q^{38} +70.2824 q^{39} +(-54.1436 + 36.8248i) q^{40} -118.276 q^{41} +(-291.727 - 202.934i) q^{42} +(-75.4750 - 75.4750i) q^{43} +(-147.612 + 361.964i) q^{44} +(38.9254 - 38.9254i) q^{45} +(-305.751 - 203.087i) q^{46} -169.043 q^{47} +(-434.151 + 4.75794i) q^{48} +(14.7299 - 342.684i) q^{49} +(-182.512 + 274.776i) q^{50} +(-641.398 + 641.398i) q^{51} +(76.7438 + 31.2968i) q^{52} +(482.264 - 482.264i) q^{53} +(-150.042 + 30.2728i) q^{54} -141.401i q^{55} +(-228.180 - 351.497i) q^{56} +131.184i q^{57} +(-67.8698 - 336.385i) q^{58} +(-285.231 + 285.231i) q^{59} +(144.767 - 60.8961i) q^{60} +(313.070 - 313.070i) q^{61} +(563.267 + 374.135i) q^{62} +(243.712 + 254.413i) q^{63} +(-476.183 - 188.132i) q^{64} -29.9800 q^{65} +(518.760 - 781.003i) q^{66} +(-58.2711 + 58.2711i) q^{67} +(-985.979 + 414.750i) q^{68} +(622.523 + 622.523i) q^{69} +(124.440 + 86.5645i) q^{70} -374.109 q^{71} +(422.844 + 80.5018i) q^{72} -610.003 q^{73} +(199.176 - 40.1862i) q^{74} +(559.457 - 559.457i) q^{75} +(-58.4162 + 143.244i) q^{76} +(904.751 + 19.4359i) q^{77} +(-165.589 - 109.988i) q^{78} -460.899i q^{79} +(185.193 - 2.02957i) q^{80} +880.748 q^{81} +(278.664 + 185.095i) q^{82} +(-875.405 - 875.405i) q^{83} +(369.742 + 934.658i) q^{84} +(273.598 - 273.598i) q^{85} +(59.7088 + 295.937i) q^{86} +823.082i q^{87} +(914.233 - 621.800i) q^{88} +633.231 q^{89} +(-152.626 + 30.7941i) q^{90} +(4.12080 - 191.826i) q^{91} +(402.545 + 956.964i) q^{92} +(-1146.84 - 1146.84i) q^{93} +(398.272 + 264.542i) q^{94} -55.9584i q^{95} +(1030.33 + 668.211i) q^{96} +946.138i q^{97} +(-570.984 + 784.327i) q^{98} +(-657.269 + 657.269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} + 24 q^{4} - 4 q^{7} + 80 q^{8} + 112 q^{11} - 24 q^{14} + 240 q^{16} + 68 q^{18} + 52 q^{21} - 120 q^{22} + 160 q^{23} + 96 q^{28} + 528 q^{29} - 552 q^{30} - 984 q^{32} + 476 q^{35} + 32 q^{36}+ \cdots + 7592 q^{99}+O(q^{100}) \) 88 * q - 4 * q^2 + 24 * q^4 - 4 * q^7 + 80 * q^8 + 112 * q^11 - 24 * q^14 + 240 * q^16 + 68 * q^18 + 52 * q^21 - 120 * q^22 + 160 * q^23 + 96 * q^28 + 528 * q^29 - 552 * q^30 - 984 * q^32 + 476 * q^35 + 32 * q^36 - 896 * q^37 - 8 * q^39 + 640 * q^42 + 40 * q^43 - 1024 * q^44 + 664 * q^46 - 1376 * q^49 + 2356 * q^50 + 1504 * q^51 - 1560 * q^53 - 3624 * q^56 + 1880 * q^58 - 1704 * q^60 - 6720 * q^64 - 8 * q^65 + 648 * q^67 + 4192 * q^70 - 456 * q^71 - 1744 * q^72 + 1224 * q^74 + 292 * q^77 + 9272 * q^78 - 1952 * q^81 - 4192 * q^84 + 496 * q^85 + 2592 * q^86 - 1472 * q^88 - 1964 * q^91 - 840 * q^92 - 112 * q^93 - 3268 * q^98 + 7592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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