LMFDB - Embedded newform 112.4.j.b.27.9

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			27.9
Character	$\chi$	$=$	112.27
Dual form			112.4.j.b.83.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-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} +(-11.4606 + 51.1141i) 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} +(-2.69841 + 125.613i) 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} +(-52.9889 - 138.362i) 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} +(1.15105 - 53.5820i) 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} +(-190.219 - 300.172i) 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} +(341.373 + 243.064i) 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} +(81.1407 + 128.043i) 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} +(19.4359 - 904.751i) 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} +(917.917 + 409.539i) 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} +(-191.826 - 4.12080i) 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} +(501.575 + 830.430i) 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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$ .

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

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	$-0.976403\pi$
$3$	−4.79702	+	4.79702i	−0.923188	+	0.923188i	0.0740657	+	0.997253i	$0.476403\pi$
$4$	3.10192	−	7.37415i	0.387740	−	0.921769i
$5$	2.04624	−	2.04624i	0.183021	−	0.183021i	−0.609650	−	0.792671i	$-0.708690\pi$
$5$	2.04624	−	2.04624i	0.183021	−	0.183021i	0.792671	+	0.609650i	$0.208690\pi$
$6$	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	−0.0516064	−	0.998668i	$-0.516434\pi$
$11$	34.5515	−	34.5515i	0.947061	−	0.947061i	0.998668	+	0.0516064i	$0.0164341\pi$
$12$	20.4940	+	50.2540i	0.493009	+	1.20892i
$13$	−7.32563	−	7.32563i	−0.156290	−	0.156290i	0.624631	−	0.780920i	$-0.285250\pi$
$13$	−7.32563	−	7.32563i	−0.156290	−	0.156290i	−0.780920	+	0.624631i	$0.785250\pi$
$14$	−11.4606	+	51.1141i	−0.218784	+	0.975773i
$15$			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	$-0.787246\pi$
$19$	−13.6735	+	13.6735i	−0.165100	+	0.165100i	0.619722	+	0.784822i	$0.287246\pi$
$20$	−8.74201	−	21.4366i	−0.0977387	−	0.239668i
$21$	−2.69841	+	125.613i	−0.0280401	+	1.30528i
$22$	−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
$28$	−52.9889	−	138.362i	−0.357641	−	0.933859i
$29$	85.7909	−	85.7909i	0.549344	−	0.549344i	−0.376907	−	0.926251i	$-0.623012\pi$
$29$	85.7909	−	85.7909i	0.549344	−	0.549344i	0.926251	+	0.376907i	$0.123012\pi$
$30$	−30.7225	−	46.2533i	−0.186971	−	0.281489i
$31$	239.073			1.38512			0.692560	−	0.721360i	$-0.256483\pi$
$31$	239.073			1.38512			0.692560	+	0.721360i	$0.256483\pi$
$32$	177.041	+	37.7438i	0.978021	+	0.208507i
$33$			331.489i			1.74863i
$34$	−209.244	−	315.021i	−1.05544	−	1.58899i
$35$	1.15105	−	53.5820i	0.00555893	−	0.258772i
$36$	−140.278	−	59.0074i	−0.649433	−	0.273183i
$37$	−50.7975	−	50.7975i	−0.225704	−	0.225704i	0.585191	−	0.810895i	$-0.301019\pi$
$37$	−50.7975	−	50.7975i	−0.225704	−	0.225704i	−0.810895	+	0.585191i	$0.801019\pi$
$38$	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	$-0.427676\pi$
$41$	118.276			0.450527			0.225264	+	0.974298i	$0.427676\pi$
$42$	−190.219	−	300.172i	−0.698843	−	1.10280i
$43$	−75.4750	+	75.4750i	−0.267671	+	0.267671i	−0.828161	−	0.560490i	$-0.810613\pi$
$43$	−75.4750	+	75.4750i	−0.267671	+	0.267671i	0.560490	+	0.828161i	$0.310613\pi$
$44$	−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	$-0.415515\pi$
$47$	169.043			0.524625			0.262313	+	0.964983i	$0.415515\pi$
$48$	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	0.955769	+	0.294118i	$0.0950257\pi$
$53$	482.264	+	482.264i	1.24989	+	1.24989i	0.294118	+	0.955769i	$0.404974\pi$
$54$	150.042	+	30.2728i	0.378114	+	0.0762891i
$55$		−	141.401i		−	0.346665i
$56$	341.373	+	243.064i	0.814606	+	0.580014i
$57$		−	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	$-0.103188\pi$
$59$	285.231	+	285.231i	0.629389	+	0.629389i	−0.318525	+	0.947914i	$0.603188\pi$
$60$	144.767	+	60.8961i	0.311490	+	0.131027i
$61$	−313.070	−	313.070i	−0.657124	−	0.657124i	0.297575	−	0.954699i	$-0.403822\pi$
$61$	−313.070	−	313.070i	−0.657124	−	0.657124i	−0.954699	+	0.297575i	$0.903822\pi$
$62$	−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	0.651982	−	0.758235i	$-0.273938\pi$
$67$	−58.2711	−	58.2711i	−0.106253	−	0.106253i	−0.758235	+	0.651982i	$0.773938\pi$
$68$	985.979	+	414.750i	1.75835	+	0.739644i
$69$	−622.523	+	622.523i	−1.08613	+	1.08613i
$70$	81.1407	+	128.043i	0.138545	+	0.218629i
$71$	−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	$-0.337358\pi$
$73$	610.003			0.978020			0.489010	+	0.872278i	$0.337358\pi$
$74$	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
$77$	19.4359	−	904.751i	0.0287652	−	1.33904i
$78$	−165.589	+	109.988i	−0.240375	+	0.159662i
$79$			460.899i			0.656395i	0.944609	+	0.328198i	$0.106441\pi$
$79$			460.899i			0.656395i	−0.944609	+	0.328198i	$0.893559\pi$
$80$	−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	0.172717	−	0.984971i	$-0.444745\pi$
$83$	875.405	−	875.405i	1.15769	−	1.15769i	0.984971	−	0.172717i	$-0.0552548\pi$
$84$	917.917	+	409.539i	1.19230	+	0.531957i
$85$	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	$-0.623076\pi$
$89$	−633.231			−0.754184			−0.377092	+	0.926176i	$0.623076\pi$
$90$	152.626	+	30.7941i	0.178758	+	0.0360665i
$91$	−191.826	−	4.12080i	−0.220976	−	0.00474700i
$92$	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	$0.835101\pi$
$98$	501.575	+	830.430i	0.517008	+	0.855981i
$99$	−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	$-0.718661\pi$
$101$	141.100	−	141.100i	0.139010	−	0.139010i	0.773187	+	0.634178i	$0.218661\pi$
$102$	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	−0.954751	−	0.297406i	$-0.903878\pi$
$107$	−727.560	+	727.560i	−0.657345	+	0.657345i	0.297406	+	0.954751i	$0.403878\pi$
$108$	−400.882	+	163.483i	−0.357175	+	0.145659i
$109$	−1136.70	+	1136.70i	−0.998867	+	0.998867i	−0.999999	−	0.00113245i	$-0.999640\pi$
$109$	−1136.70	+	1136.70i	−0.998867	+	0.998867i	0.00113245	+	0.999999i	$0.499640\pi$
$110$	221.285	+	333.149i	0.191806	+	0.288768i
$111$	487.353			0.416735
$112$	−1184.67	−	38.4413i	−0.999474	−	0.0324318i
$113$	−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
$126$	972.338	+	218.014i	0.687482	+	0.154144i
$127$		−	1588.68i		−	1.11002i	−0.831843	−	0.555011i	$-0.812714\pi$
$127$		−	1588.68i		−	1.11002i	0.831843	−	0.555011i	$-0.187286\pi$
$128$	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	0.000565274	−	1.00000i	$-0.499820\pi$
$131$	1500.21	−	1500.21i	1.00057	−	1.00057i	1.00000		0.000565274i	$-0.000179932\pi$
$132$	2444.45	+	1028.25i	1.61183	+	0.678014i
$133$	−7.69157	+	358.047i	−0.00501461	+	0.233433i
$134$	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	$-0.751212\pi$
$137$		−	2259.10i		−	1.40882i	0.709795	−	0.704408i	$-0.248788\pi$
$138$	492.482	−	2440.91i	0.303789	−	1.50568i
$139$	−2145.82	−	2145.82i	−1.30940	−	1.30940i	−0.921850	−	0.387547i	$-0.873323\pi$
$139$	−2145.82	−	2145.82i	−1.30940	−	1.30940i	−0.387547	−	0.921850i	$-0.626677\pi$
$140$	−391.551	−	174.695i	−0.236372	−	0.105460i
$141$	−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
$147$	1573.20	+	1714.52i	0.882690	+	0.961982i
$148$	−532.158	+	217.019i	−0.295561	+	0.120533i
$149$	−1085.99	−	1085.99i	−0.597100	−	0.597100i	0.342440	−	0.939540i	$-0.388747\pi$
$149$	−1085.99	−	1085.99i	−0.597100	−	0.597100i	−0.939540	+	0.342440i	$0.888747\pi$
$150$	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
$154$	1370.09	+	2162.05i	0.716915	+	1.13132i
$155$	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	$-0.435705\pi$
$157$	−1532.56	−	1532.56i	−0.779053	−	0.779053i	−0.979670	+	0.200617i	$0.935705\pi$
$158$	−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	0.663184	−	0.748457i	$-0.269205\pi$
$163$	−177.457	−	177.457i	−0.0852729	−	0.0852729i	−0.748457	+	0.663184i	$0.769205\pi$
$164$	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	$0.869348\pi$
$168$	−2803.56	+	471.592i	−1.28750	+	0.216572i
$169$		−	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	$-0.0616210\pi$
$173$	1795.20	+	1795.20i	0.788939	+	0.788939i	−0.192381	+	0.981320i	$0.561621\pi$
$174$	−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	0.479323	−	0.877639i	$-0.340882\pi$
$179$	−953.910	−	953.910i	−0.398316	−	0.398316i	−0.877639	+	0.479323i	$0.840882\pi$
$180$	−407.785	+	166.298i	−0.168858	+	0.0688619i
$181$	−1780.34	+	1780.34i	−0.731114	+	0.731114i	−0.970840	−	0.239727i	$-0.922942\pi$
$181$	−1780.34	+	1780.34i	−0.731114	+	0.731114i	0.239727	+	0.970840i	$0.422942\pi$
$182$	458.399	−	290.487i	0.186697	−	0.118310i
$183$	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
$189$	−1002.03	−	21.5256i	−0.385645	−	0.00828442i
$190$	−87.5715	−	131.841i	−0.0334374	−	0.0503406i
$191$			2064.00i			0.781916i	0.920409	+	0.390958i	$0.127856\pi$
$191$			2064.00i			0.781916i	−0.920409	+	0.390958i	$0.872144\pi$
$192$	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
$196$	−2481.31	−	1171.60i	−0.904267	−	0.426967i
$197$	837.511	+	837.511i	0.302894	+	0.302894i	0.842145	−	0.539251i	$-0.181292\pi$
$197$	837.511	+	837.511i	0.302894	+	0.302894i	−0.539251	+	0.842145i	$0.681292\pi$
$198$	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
$203$	48.2590	−	2246.48i	0.0166853	−	0.776710i
$204$	−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
$210$	−1003.46	−	224.991i	−0.329739	−	0.0739328i
$211$	130.423	+	130.423i	0.0425531	+	0.0425531i	0.728063	−	0.685510i	$-0.240421\pi$
$211$	130.423	+	130.423i	0.0425531	+	0.0425531i	−0.685510	+	0.728063i	$0.740421\pi$
$212$	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	$-0.441268\pi$
$223$	1221.92			0.366933			0.183466	+	0.983026i	$0.441268\pi$
$224$	2851.30	−	1763.37i	0.850495	−	0.525984i
$225$	2218.56			0.657351
$226$	1311.39	−	871.056i	0.385984	−	0.256380i
$227$	−3515.16	+	3515.16i	−1.02780	+	1.02780i	−0.0281934	+	0.999602i	$0.508975\pi$
$227$	−3515.16	+	3515.16i	−1.02780	+	1.02780i	−0.999602	+	0.0281934i	$0.991025\pi$
$228$	−967.369	−	406.922i	−0.280989	−	0.118198i
$229$	3345.39	−	3345.39i	0.965369	−	0.965369i	−0.0340515	−	0.999420i	$-0.510841\pi$
$229$	3345.39	−	3345.39i	0.965369	−	0.965369i	0.999420	+	0.0340515i	$0.0108410\pi$
$230$	−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	$-0.975909\pi$
$233$		−	537.847i		−	0.151225i	0.997137	−	0.0756127i	$-0.0240913\pi$
$234$	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
$238$	−6834.34	−	1532.37i	−1.86136	−	0.417347i
$239$			6403.30i			1.73303i	0.499149	+	0.866516i	$0.333646\pi$
$239$			6403.30i			1.73303i	−0.499149	+	0.866516i	$0.666354\pi$
$240$	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
$245$	−671.072	−	731.354i	−0.174993	−	0.190712i
$246$	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	$-0.484316\pi$
$251$	−3775.90	−	3775.90i	−0.949534	−	0.949534i	−0.998786	+	0.0492528i	$0.984316\pi$
$252$	−2632.05	+	1008.00i	−0.657951	+	0.251977i
$253$	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
$259$	−1330.16	−	28.5745i	−0.319120	−	0.00685534i
$260$	−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
$266$	−542.201	−	855.613i	−0.124979	−	0.197222i
$267$	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	$-0.367550\pi$
$269$	−2252.15	−	2252.15i	−0.510469	−	0.510469i	−0.914670	+	0.404201i	$0.867550\pi$
$270$	368.968	−	245.077i	0.0831655	−	0.0552405i
$271$	6670.05			1.49512			0.747559	−	0.664196i	$-0.231226\pi$
$271$	6670.05			1.49512			0.747559	+	0.664196i	$0.231226\pi$
$272$	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	0.523106	−	0.852267i	$-0.324773\pi$
$277$	−1517.50	−	1517.50i	−0.329161	−	0.329161i	−0.852267	+	0.523106i	$0.824773\pi$
$278$	8413.74	+	1697.57i	1.81519	+	0.366236i
$279$		−	4547.85i		−	0.975888i
$280$	1195.90	−	201.165i	0.255245	−	0.0429353i
$281$		−	559.278i		−	0.118732i	−0.998236	−	0.0593661i	$-0.981092\pi$
$281$		−	559.278i		−	0.118732i	0.998236	−	0.0593661i	$-0.0189079\pi$
$282$	641.509	−	3179.53i	0.135466	−	0.671413i
$283$	25.8379	+	25.8379i	0.00542721	+	0.00542721i	0.709815	−	0.704388i	$-0.248778\pi$
$283$	25.8379	+	25.8379i	0.00542721	+	0.00542721i	−0.704388	+	0.709815i	$0.748778\pi$
$284$	−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	$-0.933308\pi$
$293$	−3862.53	+	3862.53i	−0.770142	+	0.770142i	0.207989	+	0.978131i	$0.433308\pi$
$294$	−6389.66	−	1577.52i	−1.26753	−	0.312936i
$295$	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
$301$	−42.4561	+	1976.36i	−0.00812999	+	0.378456i
$302$	−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	$-0.663390\pi$
$307$	2044.42	−	2044.42i	0.380069	−	0.380069i	0.871127	+	0.491058i	$0.163390\pi$
$308$	−6611.48	−	2949.79i	−1.22313	−	0.545713i
$309$	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	$-0.800932\pi$
$313$	−8978.95			−1.62147			−0.810735	+	0.585413i	$0.800932\pi$
$314$	6009.14	+	1212.42i	1.07998	+	0.217900i
$315$	−1019.28	−	21.8962i	−0.182318	−	0.00391655i
$316$	3398.74	+	1429.67i	0.605045	+	0.254511i
$317$	−1767.75	+	1767.75i	−0.313207	+	0.313207i	−0.846151	−	0.532944i	$-0.821086\pi$
$317$	−1767.75	+	1767.75i	−0.313207	+	0.313207i	0.532944	+	0.846151i	$0.321086\pi$
$318$	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
$322$	−1487.27	+	6633.22i	−0.257399	+	1.14800i
$323$	−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	−0.195250	−	0.980754i	$-0.562552\pi$
$331$	4730.32	−	4730.32i	0.785504	−	0.785504i	0.980754	+	0.195250i	$0.0625518\pi$
$332$	−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
$336$	5867.31	−	5498.50i	0.952643	−	0.892761i
$337$	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	−0.233352	+	0.972392i	$0.574969\pi$
$347$	−7793.80	+	7793.80i	−1.20574	+	1.20574i	−0.972392	+	0.233352i	$0.925031\pi$
$348$	6069.53	+	2553.13i	0.934946	+	0.393283i
$349$	4211.57	+	4211.57i	0.645960	+	0.645960i	0.952014	−	0.306054i	$-0.0990088\pi$
$349$	4211.57	+	4211.57i	0.645960	+	0.645960i	−0.306054	+	0.952014i	$0.599009\pi$
$350$	−5961.23	−	1336.60i	−0.910403	−	0.204127i
$351$			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
$357$	−16795.4	−	360.798i	−2.48993	−	0.0534887i
$358$	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
$364$	−625.415	+	1401.77i	−0.0900568	+	0.201848i
$365$	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	$-0.372029\pi$
$367$	5502.08			0.782578			0.391289	+	0.920268i	$0.372029\pi$
$368$	−5808.13	−	5936.85i	−0.822744	−	0.840977i
$369$		−	2249.95i		−	0.317419i
$370$	489.793	−	325.332i	0.0688193	−	0.0457114i
$371$	12628.3	+	271.282i	1.76720	+	0.0379630i
$372$	4899.55	+	12014.4i	0.682877	+	1.67450i
$373$	−5026.12	−	5026.12i	−0.697702	−	0.697702i	0.266213	−	0.963914i	$-0.414228\pi$
$373$	−5026.12	−	5026.12i	−0.697702	−	0.697702i	−0.963914	+	0.266213i	$0.914228\pi$
$374$	−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
$378$	2394.51	−	1517.40i	0.325821	−	0.206473i
$379$	6001.11	−	6001.11i	0.813342	−	0.813342i	−0.171792	−	0.985133i	$-0.554956\pi$
$379$	6001.11	−	6001.11i	0.813342	−	0.813342i	0.985133	+	0.171792i	$0.0549556\pi$
$380$	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	$-0.812039\pi$
$383$	−12452.4			−1.66133			−0.830665	+	0.556773i	$0.812039\pi$
$384$	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	0.999910	−	0.0134265i	$-0.00427393\pi$
$389$	7568.58	+	7568.58i	0.986483	+	0.986483i	−0.0134265	+	0.999910i	$0.504274\pi$
$390$	−113.773	+	563.896i	−0.0147721	+	0.0732154i
$391$			17351.6i			2.24426i
$392$	7679.56	−	1122.76i	0.989481	−	0.144664i
$393$			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	$-0.271256\pi$
$397$	−746.476	−	746.476i	−0.0943692	−	0.0943692i	−0.752715	+	0.658346i	$0.771256\pi$
$398$	−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
$406$	3401.91	+	5368.34i	0.415848	+	0.656223i
$407$	−3510.26			−0.427511
$408$	11542.8	−	16971.4i	1.40062	−	2.05934i
$409$	−8430.15			−1.01918			−0.509589	−	0.860418i	$-0.670203\pi$
$409$	−8430.15			−1.01918			−0.509589	+	0.860418i	$0.670203\pi$
$410$	−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
$413$	7468.95	+	160.448i	0.889886	+	0.0191165i
$414$	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	−0.0111887	+	0.999937i	$0.503562\pi$
$419$	−8672.14	+	8672.14i	−1.01113	+	1.01113i	−0.999937	+	0.0111887i	$0.996438\pi$
$420$	2716.30	−	1040.26i	0.315575	−	0.120856i
$421$	10398.8	+	10398.8i	1.20382	+	1.20382i	0.972997	+	0.230818i	$0.0741403\pi$
$421$	10398.8	+	10398.8i	1.20382	+	1.20382i	0.230818	+	0.972997i	$0.425860\pi$
$422$	−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
$427$	−8197.92	−	176.108i	−0.929099	−	0.0199589i
$428$	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	$-0.760165\pi$
$431$		−	12243.6i		−	1.36834i	0.729322	−	0.684170i	$-0.239835\pi$
$432$	−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	$-0.162149\pi$
$434$	−2739.92	+	12220.0i	−0.303042	+	1.35156i
$435$	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	−0.668269	−	0.743920i	$-0.732965\pi$
$443$	705.371	−	705.371i	0.0756505	−	0.0756505i	0.743920	+	0.668269i	$0.232965\pi$
$444$	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
$448$	−3958.23	+	8616.72i	−0.417431	+	0.908709i
$449$	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	$-0.764494\pi$
$457$		−	13173.0i		−	1.34838i	0.738560	−	0.674188i	$-0.235506\pi$
$458$	−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	$-0.313640\pi$
$461$	−2780.05	−	2780.05i	−0.280867	−	0.280867i	−0.833455	+	0.552588i	$0.813640\pi$
$462$	−16943.8	−	3799.06i	−1.70627	−	0.382572i
$463$		−	3630.01i		−	0.364365i	−0.983265	−	0.182182i	$-0.941684\pi$
$463$		−	3630.01i		−	0.364365i	0.983265	−	0.182182i	$-0.0583161\pi$
$464$	−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	$-0.750870\pi$
$467$	−39.0209	+	39.0209i	−0.00386654	+	0.00386654i	0.705171	+	0.709037i	$0.250870\pi$
$468$	595.355	+	1459.89i	0.0588040	+	0.144195i
$469$	−1525.86	−	32.7786i	−0.150230	−	0.00322723i
$470$	−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
$476$	18500.1	−	7085.01i	1.78141	−	0.682229i
$477$	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	$-0.516527\pi$
$479$	−1088.16			−0.103798			−0.0518990	+	0.998652i	$0.516527\pi$
$480$	−740.976	+	3475.62i	−0.0704599	+	0.330499i
$481$			744.247i			0.0705504i
$482$	2580.06	+	3884.34i	0.243815	+	0.367068i
$483$	−350.181	+	16301.1i	−0.0329892	+	1.53567i
$484$	−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
$490$	2725.60	+	672.916i	0.251286	+	0.0620393i
$491$	5821.10	−	5821.10i	0.535036	−	0.535036i	−0.387031	−	0.922067i	$-0.626499\pi$
$491$	5821.10	−	5821.10i	0.535036	−	0.535036i	0.922067	+	0.387031i	$0.126499\pi$
$492$	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	0.872653	−	0.488341i	$-0.162398\pi$
$499$	4283.85	+	4283.85i	0.384312	+	0.384312i	−0.488341	+	0.872653i	$0.662398\pi$
$500$	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	$-0.0104925\pi$
$504$	4623.78	−	6493.91i	0.408650	−	0.573932i
$505$		−	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	$-0.125533\pi$
$509$	6189.71	+	6189.71i	0.539006	+	0.539006i	−0.384231	+	0.923237i	$0.625533\pi$
$510$	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
$518$	3178.64	−	2014.30i	0.269616	−	0.170856i
$519$	−17223.2			−1.45668
$520$	−126.871	−	666.401i	−0.0106993	−	0.0561992i
$521$	11779.3			0.990521			0.495260	−	0.868745i	$-0.335073\pi$
$521$	11779.3			0.990521			0.495260	+	0.868745i	$0.335073\pi$
$522$	6399.01	+	1291.08i	0.536547	+	0.108255i
$523$	−1261.69	−	1261.69i	−0.105488	−	0.105488i	0.652393	−	0.757881i	$-0.273765\pi$
$523$	−1261.69	−	1261.69i	−0.105488	−	0.105488i	−0.757881	+	0.652393i	$0.773765\pi$
$524$	−6409.25	−	15716.3i	−0.534331	−	1.31025i
$525$	−14649.7	−	314.705i	−1.21784	−	0.0261616i
$526$	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
$532$	2616.43	+	1167.35i	0.213227	+	0.0951337i
$533$	−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
$539$	−11331.3	−	12349.2i	−0.905517	−	0.986858i
$540$	−485.775	+	1154.83i	−0.0387119	+	0.0920293i
$541$	3180.80	−	3180.80i	0.252778	−	0.252778i	−0.569330	−	0.822109i	$-0.692797\pi$
$541$	3180.80	−	3180.80i	0.252778	−	0.252778i	0.822109	+	0.569330i	$0.192797\pi$
$542$	−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
$546$	−805.479	+	3592.43i	−0.0631343	+	0.281578i
$547$	−2706.48	−	2706.48i	−0.211555	−	0.211555i	0.593373	−	0.804928i	$-0.297796\pi$
$547$	−2706.48	−	2706.48i	−0.211555	−	0.211555i	−0.804928	+	0.593373i	$0.797796\pi$
$548$	−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	−0.778278	−	0.627920i	$-0.783906\pi$
$557$	−1976.55	+	1976.55i	−0.150358	+	0.150358i	0.627920	+	0.778278i	$0.283906\pi$
$558$	7117.12	+	10715.0i	0.539949	+	0.812903i
$559$	1105.80			0.0836682
$560$	−2502.79	+	2345.47i	−0.188861	+	0.176989i
$561$	−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	$-0.783236\pi$
$563$	−1969.01	+	1969.01i	−0.147396	+	0.147396i	0.629558	+	0.776954i	$0.283236\pi$
$564$	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	$0.146087\pi$
$569$			12025.5i			0.886004i	−0.896521	+	0.443002i	$0.853913\pi$
$570$	1052.53	+	212.360i	0.0773429	+	0.0156049i
$571$	−3067.62	+	3067.62i	−0.224826	+	0.224826i	−0.810527	−	0.585701i	$-0.800819\pi$
$571$	−3067.62	+	3067.62i	−0.224826	+	0.224826i	0.585701	+	0.810527i	$0.300819\pi$
$572$	−1570.26	+	3732.96i	−0.114783	+	0.272873i
$573$	−9901.06	−	9901.06i	−0.721855	−	0.721855i
$574$	−1355.51	+	6045.58i	−0.0985681	+	0.439613i
$575$			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
$581$	492.431	−	22923.0i	0.0351626	−	1.63684i
$582$	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	$-0.221060\pi$
$587$	1826.09	+	1826.09i	0.128400	+	0.128400i	−0.639986	+	0.768386i	$0.721060\pi$
$588$	17523.1	−	6282.72i	1.22898	−	0.440638i
$589$	−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
$595$	7164.31	+	153.904i	0.493627	+	0.0106041i
$596$	−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	$-0.603069\pi$
$601$	−9375.74			−0.636347			−0.318173	+	0.948033i	$0.603069\pi$
$602$	−2992.85	−	4722.83i	−0.202624	−	0.319748i
$603$	−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	$-0.438937\pi$
$607$	5702.60			0.381320			0.190660	+	0.981656i	$0.438937\pi$
$608$	−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	0.908045	−	0.418873i	$-0.137575\pi$
$613$	7424.25	+	7424.25i	0.489172	+	0.489172i	−0.418873	+	0.908045i	$0.637575\pi$
$614$	−1617.35	+	8016.15i	−0.106305	+	0.526882i
$615$			2321.96i			0.152245i
$616$	20193.2	−	3396.74i	1.32079	−	0.222173i
$617$		−	22808.8i		−	1.48825i	−0.668043	−	0.744123i	$-0.732868\pi$
$617$		−	22808.8i		−	1.48825i	0.668043	−	0.744123i	$-0.267132\pi$
$618$	−16767.3	−	3383.00i	−1.09139	−	0.220201i
$619$	−15749.6	−	15749.6i	−1.02267	−	1.02267i	−0.999737	−	0.0229291i	$-0.992701\pi$
$619$	−15749.6	−	15749.6i	−1.02267	−	1.02267i	−0.0229291	−	0.999737i	$-0.507299\pi$
$620$	−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
$630$	2435.75	−	1543.53i	0.154036	−	0.0976122i
$631$	−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
$637$	−2618.28	+	2402.47i	−0.162857	+	0.149434i
$638$	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	$-0.963996\pi$
$643$	−14360.3	+	14360.3i	−0.880740	+	0.880740i	0.112869	+	0.993610i	$0.463996\pi$
$644$	−6876.51	−	17955.7i	−0.420765	−	1.09868i
$645$	−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
$651$	−645.117	+	30030.6i	−0.0388389	+	1.80797i
$652$	−1859.05	+	758.136i	−0.111666	+	0.0455382i
$653$	6926.86	−	6926.86i	0.415113	−	0.415113i	−0.468402	−	0.883515i	$-0.655170\pi$
$653$	6926.86	−	6926.86i	0.415113	−	0.415113i	0.883515	+	0.468402i	$0.155170\pi$
$654$	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
$658$	−1937.33	+	8640.46i	−0.114780	+	0.511915i
$659$	−21306.6	−	21306.6i	−1.25947	−	1.25947i	−0.951348	−	0.308118i	$-0.900301\pi$
$659$	−21306.6	−	21306.6i	−1.25947	−	1.25947i	−0.308118	−	0.951348i	$-0.599699\pi$
$660$	7105.98	−	2897.88i	0.419091	−	0.170909i
$661$	9192.89	−	9192.89i	0.540941	−	0.540941i	−0.382864	−	0.923805i	$-0.625062\pi$
$661$	9192.89	−	9192.89i	0.540941	−	0.540941i	0.923805	+	0.382864i	$0.125062\pi$
$662$	−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
$672$	−5218.83	+	22136.7i	−0.299584	+	1.27075i
$673$	−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	$-0.896984\pi$
$677$	−11098.7	+	11098.7i	−0.630070	+	0.630070i	0.318016	+	0.948086i	$0.396984\pi$
$678$	−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	−0.836048	−	0.548656i	$-0.815140\pi$
$683$	−5129.88	+	5129.88i	−0.287393	+	0.287393i	0.548656	+	0.836048i	$0.315140\pi$
$684$	2724.91	−	1111.24i	0.152324	−	0.0621191i
$685$	−4622.66	−	4622.66i	−0.257844	−	0.257844i
$686$	17347.2	+	4680.26i	0.965478	+	0.260486i
$687$			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	$-0.765415\pi$
$691$	−1243.53	+	1243.53i	−0.0684606	+	0.0684606i	0.672047	+	0.740508i	$0.265415\pi$
$692$	18806.6	−	7669.51i	1.03312	−	0.421316i
$693$	−17211.0	−	369.726i	−0.943420	−	0.0202666i
$694$	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
$700$	16136.6	−	6179.87i	0.871296	−	0.333682i
$701$	8513.11	−	8513.11i	0.458681	−	0.458681i	−0.439541	−	0.898223i	$-0.644859\pi$
$701$	8513.11	−	8513.11i	0.458681	−	0.458681i	0.898223	+	0.439541i	$0.144859\pi$
$702$	−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
$707$	79.3713	−	3694.78i	0.00422216	−	0.196544i
$708$	−8488.48	+	20179.5i	−0.450588	+	1.07118i
$709$	20499.4	+	20499.4i	1.08585	+	1.08585i	0.995950	+	0.0899043i	$0.0286561\pi$
$709$	20499.4	+	20499.4i	1.08585	+	1.08585i	0.0899043	+	0.995950i	$0.471344\pi$
$710$	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
$714$	40135.3	−	25433.7i	2.10368	−	1.33310i
$715$	−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	$-0.381063\pi$
$719$	14074.7			0.730037			0.365018	+	0.931000i	$0.381063\pi$
$720$	−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	$-0.000773172\pi$
$728$	−720.178	−	4281.37i	−0.0366642	−	0.217965i
$729$		−	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	$-0.415693\pi$
$733$	−13958.3	−	13958.3i	−0.703357	−	0.703357i	−0.965130	+	0.261772i	$0.915693\pi$
$734$	−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	0.994207	+	0.107485i	$0.0342797\pi$
$739$	22132.3	+	22132.3i	1.10169	+	1.10169i	0.107485	+	0.994207i	$0.465720\pi$
$740$	−644.851	+	1533.00i	−0.0320340	+	0.0761541i
$741$	−961.004	+	961.004i	−0.0476428	+	0.0476428i
$742$	−30177.5	+	19123.5i	−1.49306	+	0.946151i
$743$	−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
$749$	−409.266	+	19051.6i	−0.0199656	+	0.929412i
$750$	11176.0	−	7423.35i	0.544119	−	0.361417i
$751$		−	36330.7i		−	1.76528i	−0.470048	−	0.882641i	$-0.655764\pi$
$751$		−	36330.7i		−	1.76528i	0.470048	−	0.882641i	$-0.344236\pi$
$752$	−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
$756$	−3266.94	+	7322.34i	−0.157166	+	0.352263i
$757$	15674.3	+	15674.3i	0.752564	+	0.752564i	0.974957	−	0.222393i	$-0.0713869\pi$
$757$	15674.3	+	15674.3i	0.752564	+	0.752564i	−0.222393	+	0.974957i	$0.571387\pi$
$758$	−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	$-0.370149\pi$
$761$	16656.7			0.793437			0.396718	+	0.917940i	$0.370149\pi$
$762$	−29881.7	−	6028.99i	−1.42060	−	0.286624i
$763$	−639.417	+	29765.2i	−0.0303387	+	1.41229i
$764$	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	$0.930867\pi$
$770$	7227.61	+	1620.55i	0.338266	+	0.0758447i
$771$	−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	$-0.784472\pi$
$773$	−3285.14	+	3285.14i	−0.152857	+	0.152857i	0.626536	+	0.779393i	$0.284472\pi$
$774$	−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
$784$	−16336.4	+	14663.3i	−0.744185	+	0.667973i
$785$	−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	$-0.874189\pi$
$787$	−11875.1	+	11875.1i	−0.537867	+	0.537867i	0.385035	+	0.922902i	$0.374189\pi$
$788$	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	0.970411	+	0.241460i	$0.0776263\pi$
$797$	27267.4	+	27267.4i	1.21187	+	1.21187i	0.241460	+	0.970411i	$0.422374\pi$
$798$	6705.35	+	1503.44i	0.297452	+	0.0666934i
$799$			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
$805$	149.375	−	6953.48i	0.00654008	−	0.304445i
$806$	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	$-0.691999\pi$
$809$		−	37899.6i		−	1.64707i	0.567265	−	0.823535i	$-0.308001\pi$
$810$	−1425.75	+	7066.49i	−0.0618466	+	0.306532i
$811$	2453.46	+	2453.46i	0.106230	+	0.106230i	0.758224	−	0.651994i	$-0.226067\pi$
$811$	2453.46	+	2453.46i	0.106230	+	0.106230i	−0.651994	+	0.758224i	$0.726067\pi$
$812$	−16416.2	−	7324.28i	−0.709478	−	0.316542i
$813$	−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
$819$	−78.3895	+	3649.08i	−0.00334451	+	0.155689i
$820$	−1033.97	−	2535.43i	−0.0440340	−	0.107977i
$821$	−16123.1	−	16123.1i	−0.685385	−	0.685385i	0.275823	−	0.961208i	$-0.411050\pi$
$821$	−16123.1	−	16123.1i	−0.685385	−	0.685385i	−0.961208	+	0.275823i	$0.911050\pi$
$822$	−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
$826$	−17848.3	+	11310.4i	−0.751842	+	0.476441i
$827$	1089.80	−	1089.80i	0.0458236	−	0.0458236i	−0.683824	−	0.729647i	$-0.739684\pi$
$827$	1089.80	−	1089.80i	0.0458236	−	0.0458236i	0.729647	+	0.683824i	$0.239684\pi$
$828$	−18204.2	−	7657.56i	−0.764058	−	0.321399i
$829$	4055.04	+	4055.04i	0.169888	+	0.169888i	0.786930	−	0.617042i	$-0.211669\pi$
$829$	4055.04	+	4055.04i	0.169888	+	0.169888i	−0.617042	+	0.786930i	$0.711669\pi$
$830$	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	$-0.259218\pi$
$840$	−4771.77	+	6701.75i	−0.196002	+	0.275277i
$841$			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	−0.149477	+	0.988765i	$0.547759\pi$
$853$	−28356.9	+	28356.9i	−1.13824	+	1.13824i	−0.988765	+	0.149477i	$0.952241\pi$
$854$	19590.3	−	12414.3i	0.784972	−	0.497436i
$855$	1064.49			0.0425787
$856$	−19251.3	−	13093.4i	−0.768685	−	0.522808i
$857$	5617.28			0.223900			0.111950	−	0.993714i	$-0.464290\pi$
$857$	5617.28			0.223900			0.111950	+	0.993714i	$0.464290\pi$
$858$	−1921.09	+	9521.59i	−0.0764395	+	0.378860i
$859$	−26923.7	−	26923.7i	−1.06941	−	1.06941i	−0.997404	−	0.0720059i	$-0.977060\pi$
$859$	−26923.7	−	26923.7i	−1.06941	−	1.06941i	−0.0720059	−	0.997404i	$-0.522940\pi$
$860$	2277.73	+	958.122i	0.0903139	+	0.0379903i
$861$	−319.158	+	14857.0i	−0.0126328	+	0.588066i
$862$	19160.6	+	28846.6i	0.757089	+	1.13981i
$863$			7764.09i			0.306249i	0.988207	+	0.153124i	$0.0489335\pi$
$863$			7764.09i			0.306249i	−0.988207	+	0.153124i	$0.951067\pi$
$864$	−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
$868$	−12668.2	−	33078.7i	−0.495376	−	1.29351i
$869$	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
$875$	12946.8	+	278.123i	0.500207	+	0.0107455i
$876$	12501.4	+	30655.1i	0.482172	+	1.18235i
$877$	15619.2	−	15619.2i	0.601396	−	0.601396i	−0.339287	−	0.940683i	$-0.610186\pi$
$877$	15619.2	−	15619.2i	0.601396	−	0.601396i	0.940683	+	0.339287i	$0.110186\pi$
$878$	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	$0.666319\pi$
$882$	15797.2	−	9541.41i	0.603082	−	0.364258i
$883$	−5998.33	−	5998.33i	−0.228607	−	0.228607i	0.583504	−	0.812110i	$-0.301681\pi$
$883$	−5998.33	−	5998.33i	−0.228607	−	0.228607i	−0.812110	+	0.583504i	$0.801681\pi$
$884$	−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
$896$	−4158.87	−	26495.8i	−0.155065	−	0.987904i
$897$	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	−0.999377	−	0.0352818i	$-0.988767\pi$
$907$	−26334.9	+	26334.9i	−0.964096	+	0.964096i	0.0352818	+	0.999377i	$0.488767\pi$
$908$	15017.6	+	36825.1i	0.548873	+	1.34591i
$909$	−2684.13	−	2684.13i	−0.0979393	−	0.0979393i
$910$	343.589	−	1532.40i	0.0125163	−	0.0558227i
$911$		−	16395.8i		−	0.596285i	−0.954521	−	0.298142i	$-0.903633\pi$
$911$		−	16395.8i		−	0.596285i	0.954521	−	0.298142i	$-0.0963671\pi$
$912$	−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
$917$	843.896	−	39283.9i	0.0303903	−	1.41469i
$918$	−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
$924$	45865.6	−	17565.2i	1.63297	−	0.625383i
$925$	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
$931$	4484.26	+	4887.08i	0.157858	+	0.172038i
$932$	−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	$-0.523496\pi$
$937$	−4230.42			−0.147494			−0.0737469	+	0.997277i	$0.523496\pi$
$938$	3646.30	−	2310.65i	0.126925	−	0.0804324i
$939$	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	$-0.225539\pi$
$941$	3133.94	+	3133.94i	0.108569	+	0.108569i	−0.650735	+	0.759305i	$0.725539\pi$
$942$	−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	0.711781	−	0.702401i	$-0.247889\pi$
$947$	273.354	+	273.354i	0.00937997	+	0.00937997i	−0.702401	+	0.711781i	$0.747889\pi$
$948$	−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
$952$	−32499.5	+	45644.2i	−1.10642	+	1.55392i
$953$		−	20906.0i		−	0.710610i	−0.934750	−	0.355305i	$-0.884377\pi$
$953$		−	20906.0i		−	0.710610i	0.934750	−	0.355305i	$-0.115623\pi$
$954$	−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
$966$	−24685.2	−	38954.2i	−0.822189	−	1.29744i
$967$	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	$-0.175090\pi$
$971$	9977.45	+	9977.45i	0.329754	+	0.329754i	−0.522739	+	0.852493i	$0.675090\pi$
$972$	13636.0	+	33437.3i	0.449974	+	1.10340i
$973$	−56189.5	−	1207.06i	−1.85134	−	0.0397705i
$974$	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
$980$	−7474.73	+	2679.99i	−0.243644	+	0.0873562i
$981$	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
$987$	−456.147	+	21233.9i	−0.0147106	+	0.684785i
$988$	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	$0.0392398\pi$
$991$			7672.15i			0.245927i	−0.992411	+	0.122964i	$0.960760\pi$
$992$	42325.6	+	9023.51i	1.35468	+	0.288807i
$993$			45382.9i			1.45033i
$994$	4287.51	−	19122.2i	0.136812	−	0.610182i
$995$	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	$-0.973293\pi$
$997$	−28731.6	+	28731.6i	−0.912677	+	0.912677i	0.0838054	+	0.996482i	$0.473293\pi$
$998$	−16796.9	−	3388.98i	−0.532763	−	0.107491i
$999$			3887.68i			0.123124i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.4.j.b.27.9	✓	88	1.1	even	1	trivial
112.4.j.b.27.10	yes	88	7.6	odd	2	inner
112.4.j.b.83.9	yes	88	112.83	even	4	inner
112.4.j.b.83.10	yes	88	16.3	odd	4	inner
448.4.j.b.111.8		88	16.13	even	4
448.4.j.b.111.37		88	112.13	odd	4
448.4.j.b.335.8		88	28.27	even	2
448.4.j.b.335.37		88	4.3	odd	2

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	112.4.j.b.27.9

Level	$112$
Weight	$4$
Character	112.27
Analytic conductor	$6.608$
Analytic rank	$0$
Dimension	$88$
Inner twists	$4$