LMFDB - Embedded newform 230.4.l.a.217.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.33
Character	$\chi$	$=$	230.217
Dual form			230.4.l.a.53.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.142678 - 1.99490i) q^{2} +(6.09912 - 1.32678i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(2.72190 + 10.8440i) q^{5} +(-1.77659 - 12.3565i) q^{6} +(-27.2494 + 14.8793i) q^{7} +(-1.70052 + 7.81717i) q^{8} +(10.8788 - 4.96819i) q^{9} +(22.0210 - 3.88273i) q^{10} +(22.6211 + 19.6013i) q^{11} +(-24.9034 + 1.78113i) q^{12} +(-1.13736 + 2.08291i) q^{13} +(25.7949 + 56.4829i) q^{14} +(30.9887 + 62.5272i) q^{15} +(15.3519 + 4.50772i) q^{16} +(79.5992 + 59.5872i) q^{17} +(-8.35890 - 22.4111i) q^{18} +(-11.7162 + 81.4881i) q^{19} +(-4.60375 - 44.4838i) q^{20} +(-146.456 + 126.905i) q^{21} +(42.3302 - 42.3302i) q^{22} +(29.4175 - 106.309i) q^{23} +49.9341i q^{24} +(-110.183 + 59.0322i) q^{25} +(3.99294 + 2.56610i) q^{26} +(-75.1537 + 56.2594i) q^{27} +(116.358 - 43.3994i) q^{28} +(201.669 - 28.9956i) q^{29} +(129.157 - 52.8983i) q^{30} +(-155.812 + 100.134i) q^{31} +(11.1829 - 29.9824i) q^{32} +(163.975 + 89.5373i) q^{33} +(130.228 - 150.291i) q^{34} +(-235.520 - 254.991i) q^{35} +(-45.9006 + 13.4776i) q^{36} +(-227.244 - 84.7578i) q^{37} +(160.889 + 34.9993i) q^{38} +(-4.17330 + 14.2130i) q^{39} +(-89.3977 + 2.83716i) q^{40} +(75.4444 - 165.200i) q^{41} +(232.266 + 310.272i) q^{42} +(53.1987 + 244.551i) q^{43} +(-78.4052 - 90.4844i) q^{44} +(83.4859 + 104.447i) q^{45} +(-207.879 - 73.8531i) q^{46} +(77.5288 + 77.5288i) q^{47} +(99.6137 + 7.12452i) q^{48} +(335.696 - 522.353i) q^{49} +(102.043 + 228.226i) q^{50} +(564.544 + 257.819i) q^{51} +(5.68884 - 7.59940i) q^{52} +(134.039 + 245.473i) q^{53} +(101.509 + 157.951i) q^{54} +(-150.983 + 298.655i) q^{55} +(-69.9758 - 238.316i) q^{56} +(36.6583 + 512.551i) q^{57} +(-29.0697 - 406.447i) q^{58} +(-136.931 - 466.345i) q^{59} +(-87.0991 - 265.204i) q^{60} +(-180.929 - 281.531i) q^{61} +(177.527 + 325.117i) q^{62} +(-222.518 + 297.250i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(-25.6828 - 6.66396i) q^{65} +(202.014 - 314.340i) q^{66} +(673.011 + 48.1347i) q^{67} +(-281.235 - 281.235i) q^{68} +(38.3721 - 687.422i) q^{69} +(-542.287 + 433.459i) q^{70} +(316.520 + 365.283i) q^{71} +(20.3376 + 93.4902i) q^{72} +(-482.161 - 644.092i) q^{73} +(-201.507 + 441.238i) q^{74} +(-593.694 + 506.233i) q^{75} +(92.7758 - 315.965i) q^{76} +(-908.064 - 197.537i) q^{77} +(27.7580 + 10.3532i) q^{78} +(651.571 - 191.318i) q^{79} +(-7.09525 + 178.745i) q^{80} +(-595.188 + 686.884i) q^{81} +(-318.794 - 174.075i) q^{82} +(-53.4826 + 143.392i) q^{83} +(652.101 - 419.080i) q^{84} +(-429.500 + 1025.36i) q^{85} +(495.445 - 71.2343i) q^{86} +(1191.53 - 444.418i) q^{87} +(-191.694 + 143.501i) q^{88} +(848.401 + 545.234i) q^{89} +(220.273 - 151.644i) q^{90} -73.6812i q^{91} +(-176.990 + 404.162i) q^{92} +(-817.459 + 817.459i) q^{93} +(165.724 - 143.601i) q^{94} +(-915.544 + 94.7521i) q^{95} +(28.4255 - 197.703i) q^{96} +(-24.1568 - 64.7669i) q^{97} +(-994.148 - 744.210i) q^{98} +(343.474 + 100.853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.142678	−	1.99490i	0.0504444	−	0.705305i
$2$	0.142678	−	1.99490i	0.0504444	−	0.705305i
$3$	6.09912	−	1.32678i	1.17378	−	0.255339i	0.416934	−	0.908937i	$-0.363105\pi$
$3$	6.09912	−	1.32678i	1.17378	−	0.255339i	0.756842	+	0.653598i	$0.226741\pi$
$4$	−3.95929	−	0.569259i	−0.494911	−	0.0711574i
$5$	2.72190	+	10.8440i	0.243454	+	0.969912i
$5$	2.72190	+	10.8440i	0.243454	+	0.969912i
$6$	−1.77659	−	12.3565i	−0.120882	−	0.840751i
$7$	−27.2494	+	14.8793i	−1.47133	+	0.803406i	−0.997034	−	0.0769600i	$-0.975479\pi$
$7$	−27.2494	+	14.8793i	−1.47133	+	0.803406i	−0.474295	+	0.880366i	$0.657297\pi$
$8$	−1.70052	+	7.81717i	−0.0751532	+	0.345474i
$9$	10.8788	−	4.96819i	0.402920	−	0.184007i
$10$	22.0210	−	3.88273i	0.696365	−	0.122783i
$11$	22.6211	+	19.6013i	0.620047	+	0.537274i	0.907248	−	0.420597i	$-0.138179\pi$
$11$	22.6211	+	19.6013i	0.620047	+	0.537274i	−0.287201	+	0.957870i	$0.592725\pi$
$12$	−24.9034	+	1.78113i	−0.599084	+	0.0428473i
$13$	−1.13736	+	2.08291i	−0.0242651	+	0.0444382i	−0.889530	−	0.456876i	$-0.848968\pi$
$13$	−1.13736	+	2.08291i	−0.0242651	+	0.0444382i	0.865265	+	0.501314i	$0.167150\pi$
$14$	25.7949	+	56.4829i	0.492426	+	1.07826i
$15$	30.9887	+	62.5272i	0.533417	+	1.07630i
$16$	15.3519	+	4.50772i	0.239873	+	0.0704331i
$17$	79.5992	+	59.5872i	1.13563	+	0.850119i	0.990256	−	0.139258i	$-0.0444718\pi$
$17$	79.5992	+	59.5872i	1.13563	+	0.850119i	0.145370	+	0.989377i	$0.453563\pi$
$18$	−8.35890	−	22.4111i	−0.109456	−	0.293463i
$19$	−11.7162	+	81.4881i	−0.141468	+	0.983929i	0.788171	+	0.615457i	$0.211028\pi$
$19$	−11.7162	+	81.4881i	−0.141468	+	0.983929i	−0.929639	+	0.368473i	$0.879881\pi$
$20$	−4.60375	−	44.4838i	−0.0514714	−	0.497344i
$21$	−146.456	+	126.905i	−1.52187	+	1.31871i
$22$	42.3302	−	42.3302i	0.410220	−	0.410220i
$23$	29.4175	−	106.309i	0.266695	−	0.963781i
$23$	29.4175	−	106.309i	0.266695	−	0.963781i
$24$			49.9341i			0.424698i
$25$	−110.183	+	59.0322i	−0.881460	+	0.472258i
$26$	3.99294	+	2.56610i	0.0301184	+	0.0193559i
$27$	−75.1537	+	56.2594i	−0.535679	+	0.401004i
$28$	116.358	−	43.3994i	0.785345	−	0.292918i
$29$	201.669	−	28.9956i	1.29134	−	0.185667i	0.537804	−	0.843070i	$-0.319254\pi$
$29$	201.669	−	28.9956i	1.29134	−	0.185667i	0.753539	+	0.657403i	$0.228345\pi$
$30$	129.157	−	52.8983i	0.786025	−	0.321929i
$31$	−155.812	+	100.134i	−0.902730	+	0.580149i	−0.907599	−	0.419839i	$-0.862087\pi$
$31$	−155.812	+	100.134i	−0.902730	+	0.580149i	0.00486857	+	0.999988i	$0.498450\pi$
$32$	11.1829	−	29.9824i	0.0617771	−	0.165631i
$33$	163.975	+	89.5373i	0.864983	+	0.472317i
$34$	130.228	−	150.291i	0.656879	−	0.758079i
$35$	−235.520	−	254.991i	−1.13743	−	1.23147i
$36$	−45.9006	+	13.4776i	−0.212503	+	0.0623964i
$37$	−227.244	−	84.7578i	−1.00970	−	0.376597i	−0.210452	−	0.977604i	$-0.567494\pi$
$37$	−227.244	−	84.7578i	−1.00970	−	0.376597i	−0.799244	+	0.601007i	$0.794766\pi$
$38$	160.889	+	34.9993i	0.686834	+	0.149412i
$39$	−4.17330	+	14.2130i	−0.0171349	+	0.0583563i
$40$	−89.3977	+	2.83716i	−0.353375	+	0.0112149i
$41$	75.4444	−	165.200i	0.287377	−	0.629267i	−0.709796	−	0.704407i	$-0.751213\pi$
$41$	75.4444	−	165.200i	0.287377	−	0.629267i	0.997173	+	0.0751400i	$0.0239404\pi$
$42$	232.266	+	310.272i	0.853321	+	1.13990i
$43$	53.1987	+	244.551i	0.188668	+	0.867293i	0.969986	+	0.243160i	$0.0781841\pi$
$43$	53.1987	+	244.551i	0.188668	+	0.867293i	−0.781318	+	0.624133i	$0.785452\pi$
$44$	−78.4052	−	90.4844i	−0.268637	−	0.310023i
$45$	83.4859	+	104.447i	0.276563	+	0.345999i
$46$	−207.879	−	73.8531i	−0.666306	−	0.236719i
$47$	77.5288	+	77.5288i	0.240611	+	0.240611i	0.817103	−	0.576492i	$-0.195579\pi$
$47$	77.5288	+	77.5288i	0.240611	+	0.240611i	−0.576492	+	0.817103i	$0.695579\pi$
$48$	99.6137	+	7.12452i	0.299542	+	0.0214237i
$49$	335.696	−	522.353i	0.978706	−	1.52290i
$50$	102.043	+	228.226i	0.288621	+	0.645521i
$51$	564.544	+	257.819i	1.55004	+	0.707879i
$52$	5.68884	−	7.59940i	0.0151711	−	0.0202663i
$53$	134.039	+	245.473i	0.347389	+	0.636196i	0.991701	−	0.128567i	$-0.0410379\pi$
$53$	134.039	+	245.473i	0.347389	+	0.636196i	−0.644312	+	0.764763i	$0.722856\pi$
$54$	101.509	+	157.951i	0.255808	+	0.398046i
$55$	−150.983	+	298.655i	−0.370156	+	0.732193i
$56$	−69.9758	−	238.316i	−0.166981	−	0.568684i
$57$	36.6583	+	512.551i	0.0851845	+	1.19103i
$58$	−29.0697	−	406.447i	−0.0658109	−	0.920157i
$59$	−136.931	−	466.345i	−0.302152	−	1.02903i	−0.960952	−	0.276716i	$-0.910754\pi$
$59$	−136.931	−	466.345i	−0.302152	−	1.02903i	0.658800	−	0.752318i	$-0.271064\pi$
$60$	−87.0991	−	265.204i	−0.187407	−	0.570627i
$61$	−180.929	−	281.531i	−0.379764	−	0.590925i	0.597779	−	0.801661i	$-0.296050\pi$
$61$	−180.929	−	281.531i	−0.379764	−	0.590925i	−0.977543	+	0.210737i	$0.932414\pi$
$62$	177.527	+	325.117i	0.363645	+	0.665966i
$63$	−222.518	+	297.250i	−0.444995	+	0.594443i
$64$	−58.2164	−	26.5866i	−0.113704	−	0.0519269i
$65$	−25.6828	−	6.66396i	−0.0490085	−	0.0127164i
$66$	202.014	−	314.340i	0.376761	−	0.586251i
$67$	673.011	+	48.1347i	1.22718	+	0.0877699i	0.669836	−	0.742509i	$-0.266364\pi$
$67$	673.011	+	48.1347i	1.22718	+	0.0877699i	0.557348	+	0.830279i	$0.311819\pi$
$68$	−281.235	−	281.235i	−0.501541	−	0.501541i
$69$	38.3721	−	687.422i	0.0669486	−	1.19936i
$70$	−542.287	+	433.459i	−0.925938	+	0.740118i
$71$	316.520	+	365.283i	0.529070	+	0.610580i	0.955878	−	0.293762i	$-0.0949075\pi$
$71$	316.520	+	365.283i	0.529070	+	0.610580i	−0.426808	+	0.904342i	$0.640362\pi$
$72$	20.3376	+	93.4902i	0.0332889	+	0.153027i
$73$	−482.161	−	644.092i	−0.773051	−	1.03267i	−0.998295	−	0.0583724i	$-0.981409\pi$
$73$	−482.161	−	644.092i	−0.773051	−	1.03267i	0.225244	−	0.974302i	$-0.427682\pi$
$74$	−201.507	+	441.238i	−0.316549	+	0.693147i
$75$	−593.694	+	506.233i	−0.914051	+	0.779396i
$76$	92.7758	−	315.965i	0.140028	−	0.476891i
$77$	−908.064	−	197.537i	−1.34394	−	0.292357i
$78$	27.7580	+	10.3532i	0.0402946	+	0.0150291i
$79$	651.571	−	191.318i	0.927942	−	0.272468i	0.217367	−	0.976090i	$-0.430253\pi$
$79$	651.571	−	191.318i	0.927942	−	0.272468i	0.710575	+	0.703621i	$0.248435\pi$
$80$	−7.09525	+	178.745i	−0.00991592	+	0.249803i
$81$	−595.188	+	686.884i	−0.816444	+	0.942227i
$82$	−318.794	−	174.075i	−0.429329	−	0.234431i
$83$	−53.4826	+	143.392i	−0.0707286	+	0.189631i	−0.967504	−	0.252855i	$-0.918631\pi$
$83$	−53.4826	+	143.392i	−0.0707286	+	0.189631i	0.896776	+	0.442486i	$0.145903\pi$
$84$	652.101	−	419.080i	0.847025	−	0.544350i
$85$	−429.500	+	1025.36i	−0.548069	+	1.30842i
$86$	495.445	−	71.2343i	0.621224	−	0.0893185i
$87$	1191.53	−	444.418i	1.46834	−	0.547662i
$88$	−191.694	+	143.501i	−0.232212	+	0.173832i
$89$	848.401	+	545.234i	1.01045	+	0.649379i	0.937510	−	0.347957i	$-0.113125\pi$
$89$	848.401	+	545.234i	1.01045	+	0.649379i	0.0729428	+	0.997336i	$0.476761\pi$
$90$	220.273	−	151.644i	0.257986	−	0.177608i
$91$		−	73.6812i		−	0.0848778i
$92$	−176.990	+	404.162i	−0.200570	+	0.458008i
$93$	−817.459	+	817.459i	−0.911468	+	0.911468i
$94$	165.724	−	143.601i	0.181842	−	0.157567i
$95$	−915.544	+	94.7521i	−0.988766	+	0.102330i
$96$	28.4255	−	197.703i	0.0302204	−	0.210188i
$97$	−24.1568	−	64.7669i	−0.0252861	−	0.0677947i	0.923693	−	0.383133i	$-0.125155\pi$
$97$	−24.1568	−	64.7669i	−0.0252861	−	0.0677947i	−0.948979	+	0.315338i	$0.897882\pi$
$98$	−994.148	−	744.210i	−1.02474	−	0.767108i
$99$	343.474	+	100.853i	0.348691	+	0.102385i
$100$	469.849	−	171.003i	0.469849	−	0.171003i
$101$	−46.4841	−	101.786i	−0.0457954	−	0.100278i	0.885351	−	0.464922i	$-0.153918\pi$
$101$	−46.4841	−	101.786i	−0.0457954	−	0.100278i	−0.931147	+	0.364644i	$0.881191\pi$
$102$	594.872	−	1089.43i	0.577462	−	1.05754i
$103$	−1536.91	+	109.922i	−1.47026	+	0.105155i	−0.783346	−	0.621586i	$-0.786489\pi$
$103$	−1536.91	+	109.922i	−1.47026	+	0.105155i	−0.686912	+	0.726741i	$0.741034\pi$
$104$	−14.3484	−	12.4330i	−0.0135286	−	0.0117226i
$105$	−1774.78	−	1242.74i	−1.64954	−	1.15504i
$106$	508.820	−	232.370i	0.466236	−	0.212923i
$107$	250.300	−	1150.61i	0.226144	−	1.03957i	−0.714358	−	0.699781i	$-0.753281\pi$
$107$	250.300	−	1150.61i	0.226144	−	1.03957i	0.940502	−	0.339788i	$-0.110355\pi$
$108$	329.581	−	179.965i	0.293648	−	0.160344i
$109$	−121.145	−	842.582i	−0.106455	−	0.740410i	−0.971212	−	0.238219i	$-0.923436\pi$
$109$	−121.145	−	842.582i	−0.106455	−	0.740410i	0.864757	−	0.502191i	$-0.167473\pi$
$110$	574.246	+	343.808i	0.497747	+	0.298008i
$111$	−1498.45	−	215.444i	−1.28132	−	0.184226i
$112$	−485.401	+	105.593i	−0.409519	+	0.0890854i
$113$	27.0405	−	378.076i	0.0225112	−	0.314747i	−0.973703	−	0.227819i	$-0.926840\pi$
$113$	27.0405	−	378.076i	0.0225112	−	0.314747i	0.996215	−	0.0869279i	$-0.0277050\pi$
$114$	1027.72			0.844340
$115$	1232.88	+	29.6401i	0.999711	+	0.0240343i
$116$	−814.970			−0.652311
$117$	−2.02479	+	28.3103i	−0.00159993	+	0.0223700i
$118$	−949.851	+	206.628i	−0.741025	+	0.161200i
$119$	−3055.65	−	439.335i	−2.35387	−	0.338435i
$120$	−541.483	+	135.915i	−0.411920	+	0.103394i
$121$	−61.9177	−	430.647i	−0.0465197	−	0.323552i
$122$	−587.443	+	320.768i	−0.435939	+	0.238041i
$123$	240.960	−	1107.67i	0.176639	−	0.811997i
$124$	673.906	−	307.763i	0.488053	−	0.222886i
$125$	−940.048	−	1034.13i	−0.672644	−	0.739967i
$126$	561.236	+	486.314i	0.396816	+	0.343843i
$127$	−294.825	+	21.0863i	−0.205996	+	0.0147331i	−0.173956	−	0.984753i	$-0.555655\pi$
$127$	−294.825	+	21.0863i	−0.205996	+	0.0147331i	−0.0320403	+	0.999487i	$0.510200\pi$
$128$	−61.3439	+	112.343i	−0.0423600	+	0.0775766i
$129$	648.930	+	1420.96i	0.442908	+	0.969833i
$130$	−16.9583	+	50.2839i	−0.0114411	+	0.0339245i
$131$	2445.42	+	718.039i	1.63097	+	0.478896i	0.963936	−	0.266133i	$-0.0857460\pi$
$131$	2445.42	+	718.039i	1.63097	+	0.478896i	0.667033	+	0.745029i	$0.267564\pi$
$132$	−598.255	−	447.848i	−0.394481	−	0.295304i
$133$	−893.226	−	2394.83i	−0.582350	−	1.56134i
$134$	192.048	−	1335.72i	0.123809	−	0.861112i
$135$	−814.635	−	661.831i	−0.519352	−	0.421936i
$136$	−601.164	+	520.912i	−0.379040	+	0.328440i
$137$	−38.8234	+	38.8234i	−0.0242110	+	0.0242110i	−0.719109	−	0.694898i	$-0.755450\pi$
$137$	−38.8234	+	38.8234i	−0.0242110	+	0.0242110i	0.694898	+	0.719109i	$0.255450\pi$
$138$	−1365.87	−	174.629i	−0.842538	−	0.107720i
$139$			2367.17i			1.44447i	0.691649	+	0.722233i	$0.256884\pi$
$139$			2367.17i			1.44447i	−0.691649	+	0.722233i	$0.743116\pi$
$140$	787.336	+	1143.65i	0.475300	+	0.690403i
$141$	575.721	+	369.994i	0.343861	+	0.220986i
$142$	773.866	−	579.309i	0.457334	−	0.342356i
$143$	−66.5560	+	24.8241i	−0.0389209	+	0.0145168i
$144$	189.406	−	27.2324i	0.109610	−	0.0157595i
$145$	863.348	+	2107.96i	0.494463	+	1.20729i
$146$	−1353.70	+	869.967i	−0.767347	+	0.493144i
$147$	1354.40	−	3631.29i	0.759926	−	2.03744i
$148$	851.476	+	464.941i	0.472912	+	0.258229i
$149$	−548.468	+	632.965i	−0.301559	+	0.348017i	−0.886224	−	0.463258i	$-0.846680\pi$
$149$	−548.468	+	632.965i	−0.301559	+	0.348017i	0.584665	+	0.811275i	$0.301226\pi$
$150$	925.179	+	1256.59i	0.503603	+	0.684001i
$151$	−743.342	+	218.265i	−0.400611	+	0.117630i	−0.475831	−	0.879537i	$-0.657852\pi$
$151$	−743.342	+	218.265i	−0.400611	+	0.117630i	0.0752194	+	0.997167i	$0.476034\pi$
$152$	−617.083	−	230.160i	−0.329290	−	0.122819i
$153$	1161.99	+	252.775i	0.613994	+	0.133566i
$154$	−523.629	+	1783.32i	−0.273995	+	0.933141i
$155$	−1509.95	−	1417.06i	−0.782467	−	0.734330i
$156$	24.6141	−	53.8975i	0.0126327	−	0.0276619i
$157$	1716.07	+	2292.40i	0.872337	+	1.16531i	0.985151	+	0.171690i	$0.0549227\pi$
$157$	1716.07	+	2292.40i	0.872337	+	1.16531i	−0.112814	+	0.993616i	$0.535986\pi$
$158$	−288.697	−	1327.12i	−0.145364	−	0.668227i
$159$	1143.21	+	1319.33i	0.570203	+	0.658049i
$160$	355.566	+	39.6573i	0.175687	+	0.0195949i
$161$	780.193	+	3334.57i	0.381912	+	1.63230i
$162$	1285.35	+	1285.35i	0.623373	+	0.623373i
$163$	2613.86	+	186.947i	1.25603	+	0.0898332i	0.683440	−	0.730007i	$-0.260483\pi$
$163$	2613.86	+	186.947i	1.25603	+	0.0898332i	0.572593	+	0.819840i	$0.305938\pi$
$164$	−392.748	+	611.128i	−0.187003	+	0.290982i
$165$	−524.614	+	2021.85i	−0.247522	+	0.953945i
$166$	278.423	+	127.152i	0.130180	+	0.0594511i
$167$	−1037.21	+	1385.55i	−0.480608	+	0.642017i	−0.973666	−	0.227979i	$-0.926788\pi$
$167$	−1037.21	+	1385.55i	−0.480608	+	0.642017i	0.493058	+	0.869996i	$0.335879\pi$
$168$	−742.984	−	1360.67i	−0.341205	−	0.624871i
$169$	1184.74	+	1843.50i	0.539255	+	0.839097i
$170$	1984.21	+	1003.11i	0.895190	+	0.452558i
$171$	277.390	+	944.704i	0.124050	+	0.422475i
$172$	−71.4162	−	998.529i	−0.0316595	−	0.442658i
$173$	−188.217	−	2631.62i	−0.0827162	−	1.15652i	−0.854085	−	0.520134i	$-0.825882\pi$
$173$	−188.217	−	2631.62i	−0.0827162	−	1.15652i	0.771368	−	0.636389i	$-0.219573\pi$
$174$	−716.566	−	2440.40i	−0.312199	−	1.06325i
$175$	2124.05	−	3248.03i	0.917503	−	1.40302i
$176$	258.919	+	402.886i	0.110891	+	0.172549i
$177$	−1453.90	−	2662.62i	−0.617411	−	1.13070i
$178$	1208.74	−	1614.69i	0.508982	−	0.679920i
$179$	4021.18	+	1836.41i	1.67909	+	0.766814i	0.999446	+	0.0332714i	$0.0105926\pi$
$179$	4021.18	+	1836.41i	1.67909	+	0.766814i	0.679643	+	0.733543i	$0.262135\pi$
$180$	−271.087	−	461.059i	−0.112254	−	0.190918i
$181$	2159.02	−	3359.50i	0.886622	−	1.37961i	−0.0382238	−	0.999269i	$-0.512170\pi$
$181$	2159.02	−	3359.50i	0.886622	−	1.37961i	0.924846	−	0.380342i	$-0.124194\pi$
$182$	−146.987	−	10.5127i	−0.0598648	−	0.00428161i
$183$	−1477.04	−	1477.04i	−0.596644	−	0.596644i
$184$	781.011	+	410.743i	0.312918	+	0.164567i
$185$	300.573	−	2694.93i	0.119452	−	1.07100i
$186$	1514.12	+	1747.39i	0.596885	+	0.688841i
$187$	632.635	+	2908.17i	0.247395	+	1.13726i
$188$	−262.825	−	351.093i	−0.101960	−	0.136202i
$189$	1210.79	−	2651.27i	0.465991	−	1.02038i
$190$	58.3931	+	1839.94i	0.0222962	+	0.702544i
$191$	−1166.72	+	3973.48i	−0.441994	+	1.50529i	0.374109	+	0.927385i	$0.377949\pi$
$191$	−1166.72	+	3973.48i	−0.441994	+	1.50529i	−0.816102	+	0.577907i	$0.803870\pi$
$192$	−390.344	−	84.9140i	−0.146722	−	0.0319174i
$193$	1322.16	+	493.138i	0.493113	+	0.183922i	0.583704	−	0.811967i	$-0.301603\pi$
$193$	1322.16	+	493.138i	0.493113	+	0.183922i	−0.0905910	+	0.995888i	$0.528876\pi$
$194$	−132.650	+	38.9497i	−0.0490915	+	0.0144146i
$195$	−165.484	−	6.56887i	−0.0607720	−	0.00241234i
$196$	−1626.47	+	1877.05i	−0.592737	+	0.684055i
$197$	545.291	+	297.752i	0.197210	+	0.107685i	0.574820	−	0.818280i	$-0.305072\pi$
$197$	545.291	+	297.752i	0.197210	+	0.107685i	−0.377610	+	0.925965i	$0.623254\pi$
$198$	250.199	−	670.808i	0.0898022	−	0.240769i
$199$	3836.05	−	2465.28i	1.36648	−	0.878186i	0.367822	−	0.929896i	$-0.380104\pi$
$199$	3836.05	−	2465.28i	1.36648	−	0.878186i	0.998662	+	0.0517104i	$0.0164673\pi$
$200$	−274.097	−	961.702i	−0.0969081	−	0.340013i
$201$	4168.64	−	599.359i	1.46285	−	0.210326i
$202$	−209.685	+	78.2086i	−0.0730367	+	0.0272413i
$203$	−5063.92	+	3790.80i	−1.75082	+	1.31065i
$204$	−2088.43	−	1342.15i	−0.716760	−	0.460634i
$205$	1996.78	+	368.458i	0.680297	+	0.125533i
$206$			3081.68i			1.04228i
$207$	−208.136	−	1302.67i	−0.0698861	−	0.437400i
$208$	−26.8498	+	26.8498i	−0.00895046	+	0.00895046i
$209$	−1862.31	+	1613.70i	−0.616356	+	0.534075i
$210$	−2732.36	+	3363.21i	−0.897862	+	1.10516i
$211$	373.550	−	2598.10i	0.121878	−	0.847680i	−0.833548	−	0.552448i	$-0.813694\pi$
$211$	373.550	−	2598.10i	0.121878	−	0.847680i	0.955426	−	0.295232i	$-0.0953969\pi$
$212$	−390.959	−	1048.20i	−0.126657	−	0.339579i
$213$	2415.14	+	1807.95i	0.776915	+	0.581591i
$214$	−2259.65	−	663.493i	−0.721806	−	0.211941i
$215$	−2507.09	+	1242.53i	−0.795267	+	0.394137i
$216$	−311.989	−	683.160i	−0.0982785	−	0.215200i
$217$	2755.85	−	5046.97i	0.862117	−	1.57885i
$218$	−1698.15	+	121.454i	−0.527585	+	0.0377336i
$219$	−3795.33	−	3288.67i	−1.17107	−	1.01474i
$220$	767.797	−	1096.51i	0.235295	−	0.336031i
$221$	−214.648	+	98.0263i	−0.0653338	+	0.0298369i
$222$	−643.586	+	2958.52i	−0.194571	+	0.894426i
$223$	−4990.21	+	2724.86i	−1.49852	+	0.818252i	−0.998849	−	0.0479647i	$-0.984726\pi$
$223$	−4990.21	+	2724.86i	−1.49852	+	0.818252i	−0.499668	+	0.866217i	$0.666545\pi$
$224$	141.391	+	983.395i	0.0421744	+	0.293330i
$225$	−905.374	+	1189.61i	−0.268259	+	0.352477i
$226$	−750.368	−	107.887i	−0.220857	−	0.0317545i
$227$	−1374.33	+	298.967i	−0.401839	+	0.0874147i	−0.408943	−	0.912560i	$-0.634102\pi$
$227$	−1374.33	+	298.967i	−0.401839	+	0.0874147i	0.00710376	+	0.999975i	$0.497739\pi$
$228$	146.633	−	2050.20i	0.0425922	−	0.595517i
$229$	4042.53			1.16654			0.583270	−	0.812278i	$-0.301773\pi$
$229$	4042.53			1.16654			0.583270	+	0.812278i	$0.301773\pi$
$230$	235.035	−	2455.25i	0.0673814	−	0.703889i
$231$	−5800.48			−1.65214
$232$	−116.279	+	1625.79i	−0.0329055	+	0.460078i
$233$	2478.12	−	539.082i	0.696768	−	0.151573i	0.149788	−	0.988718i	$-0.452141\pi$
$233$	2478.12	−	539.082i	0.696768	−	0.151573i	0.546980	+	0.837145i	$0.315777\pi$
$234$	56.1874	+	8.07852i	0.0156969	+	0.00225688i
$235$	−629.693	+	1051.74i	−0.174794	+	0.291950i
$236$	276.679	+	1924.34i	0.0763147	+	0.530780i
$237$	3720.17	−	2031.37i	1.01962	−	0.556757i
$238$	−1312.41	+	6033.04i	−0.357440	+	1.64312i
$239$	−6107.44	+	2789.17i	−1.65296	+	0.754881i	−0.999997	−	0.00250874i	$-0.999201\pi$
$239$	−6107.44	+	2789.17i	−1.65296	+	0.754881i	−0.652963	+	0.757390i	$0.726474\pi$
$240$	193.880	+	1099.60i	0.0521455	+	0.295745i
$241$	325.875	+	282.372i	0.0871014	+	0.0754738i	0.697323	−	0.716757i	$-0.254374\pi$
$241$	325.875	+	282.372i	0.0871014	+	0.0754738i	−0.610222	+	0.792231i	$0.708920\pi$
$242$	−867.934	+	62.0759i	−0.230549	+	0.0164892i
$243$	−1504.01	+	2754.40i	−0.397047	+	0.727138i
$244$	556.086	+	1217.66i	0.145901	+	0.319478i
$245$	6578.10	+	2218.48i	1.71535	+	0.578504i
$246$	−2175.32	−	638.733i	−0.563795	−	0.165545i
$247$	−156.407	−	117.085i	−0.0402913	−	0.0301617i
$248$	−517.805	−	1388.29i	−0.132583	−	0.355470i
$249$	−135.946	+	945.527i	−0.0345994	+	0.240644i
$250$	−2197.12	+	1727.76i	−0.555833	+	0.437092i
$251$	3192.15	−	2766.02i	0.802737	−	0.695575i	−0.153507	−	0.988148i	$-0.549057\pi$
$251$	3192.15	−	2766.02i	0.802737	−	0.695575i	0.956243	+	0.292572i	$0.0945112\pi$
$252$	1050.23	−	1050.23i	0.262532	−	0.262532i
$253$	2749.25	−	1828.20i	0.683177	−	0.454301i
$254$			591.157i			0.146033i
$255$	−1259.14	+	6823.65i	−0.309218	+	1.67574i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	3079.16	−	2305.03i	0.747365	−	0.559471i	−0.156300	−	0.987710i	$-0.549957\pi$
$257$	3079.16	−	2305.03i	0.747365	−	0.559471i	0.903666	+	0.428239i	$0.140866\pi$
$258$	2927.27	−	1091.81i	0.706371	−	0.263463i
$259$	7453.41	−	1071.64i	1.78816	−	0.257098i
$260$	97.8919	+	41.0047i	0.0233500	+	0.00978078i
$261$	2049.86	−	1317.37i	0.486143	−	0.312425i
$262$	1781.33	−	4775.92i	0.420041	−	1.12617i
$263$	−7016.77	−	3831.45i	−1.64514	−	0.898316i	−0.989714	−	0.143060i	$-0.954306\pi$
$263$	−7016.77	−	3831.45i	−1.64514	−	0.898316i	−0.655430	−	0.755256i	$-0.727512\pi$
$264$	−978.773	+	1129.56i	−0.228179	+	0.263333i
$265$	−2297.06	+	2121.66i	−0.532481	+	0.491821i
$266$	−4904.90	+	1440.21i	−1.13060	+	0.331973i
$267$	5897.91	+	2199.80i	1.35186	+	0.504217i
$268$	−2637.24	−	573.697i	−0.601101	−	0.130762i
$269$	1902.67	−	6479.89i	0.431255	−	1.46872i	−0.401902	−	0.915683i	$-0.631651\pi$
$269$	1902.67	−	6479.89i	0.431255	−	1.46872i	0.833157	−	0.553037i	$-0.186531\pi$
$270$	−1436.52	+	1530.69i	−0.323792	+	0.345018i
$271$	1739.23	−	3808.39i	0.389856	−	0.853666i	−0.608343	−	0.793674i	$-0.708165\pi$
$271$	1739.23	−	3808.39i	0.389856	−	0.853666i	0.998199	−	0.0599913i	$-0.0191073\pi$
$272$	953.395	+	1273.59i	0.212530	+	0.283907i
$273$	−97.7588	−	449.390i	−0.0216726	−	0.0996276i
$274$	71.9097	+	82.9882i	0.0158548	+	0.0182974i
$275$	−3649.56	−	824.347i	−0.800279	−	0.180764i
$276$	−543.247	+	2699.86i	−0.118477	+	0.588813i
$277$	−3887.90	−	3887.90i	−0.843326	−	0.843326i	0.145964	−	0.989290i	$-0.453372\pi$
$277$	−3887.90	−	3887.90i	−0.843326	−	0.843326i	−0.989290	+	0.145964i	$0.953372\pi$
$278$	4722.28	+	337.744i	1.01879	+	0.0728653i
$279$	−1197.56	+	1863.45i	−0.256976	+	0.399862i
$280$	2393.82	−	1407.49i	0.510921	−	0.300405i
$281$	5202.31	+	2375.82i	1.10443	+	0.504375i	0.882321	−	0.470648i	$-0.155980\pi$
$281$	5202.31	+	2375.82i	1.10443	+	0.504375i	0.222106	+	0.975023i	$0.428707\pi$
$282$	820.245	−	1095.72i	0.173209	−	0.231380i
$283$	162.695	+	297.954i	0.0341740	+	0.0625850i	0.894208	−	0.447652i	$-0.147740\pi$
$283$	162.695	+	297.954i	0.0341740	+	0.0625850i	−0.860034	+	0.510237i	$0.829558\pi$
$284$	−1045.25	−	1626.44i	−0.218395	−	0.339830i
$285$	−5458.29	+	1792.63i	−1.13446	+	0.372583i
$286$	40.0256	+	136.315i	0.00827540	+	0.0281834i
$287$	402.248	+	5624.17i	0.0827316	+	1.15674i
$288$	−27.3020	−	381.732i	−0.00558606	−	0.0781034i
$289$	1401.24	+	4772.20i	0.285212	+	0.971342i
$290$	4328.37	−	1421.54i	0.876450	−	0.287847i
$291$	−233.267	−	362.970i	−0.0469909	−	0.0731192i
$292$	1542.36	+	2824.62i	0.309109	+	0.566090i
$293$	2962.64	−	3957.63i	0.590714	−	0.789102i	−0.401203	−	0.915989i	$-0.631408\pi$
$293$	2962.64	−	3957.63i	0.590714	−	0.789102i	0.991917	+	0.126887i	$0.0404986\pi$
$294$	−7050.83	−	3220.01i	−1.39868	−	0.638757i
$295$	4684.31	−	2754.22i	0.924513	−	0.543583i
$296$	1049.00	−	1632.28i	0.205986	−	0.320521i
$297$	−2802.82	−	200.461i	−0.547595	−	0.0391648i
$298$	1184.45	+	1184.45i	0.230246	+	0.230246i
$299$	187.974	+	182.185i	0.0363573	+	0.0352376i
$300$	2638.78	−	1666.35i	0.507833	−	0.320690i
$301$	−5088.37	−	5872.29i	−0.974382	−	1.12450i
$302$	329.359	+	1514.04i	0.0627565	+	0.288487i
$303$	−418.559	−	559.130i	−0.0793584	−	0.106010i
$304$	−547.192	+	1198.18i	−0.103236	+	0.226054i
$305$	2560.44	−	2728.29i	0.480690	−	0.512201i
$306$	670.052	−	2281.99i	0.125178	−	0.426315i
$307$	−5668.31	−	1233.06i	−1.05377	−	0.229234i	−0.347868	−	0.937543i	$-0.613094\pi$
$307$	−5668.31	−	1233.06i	−1.05377	−	0.229234i	−0.705902	+	0.708310i	$0.749458\pi$
$308$	3482.84	+	1299.03i	0.644328	+	0.240322i
$309$	−9227.97	+	2709.58i	−1.69890	+	0.498843i
$310$	−3042.34	+	2810.03i	−0.557398	+	0.514835i
$311$	−1233.94	+	1424.04i	−0.224985	+	0.259646i	−0.857008	−	0.515303i	$-0.827679\pi$
$311$	−1233.94	+	1424.04i	−0.224985	+	0.259646i	0.632023	+	0.774950i	$0.282225\pi$
$312$	−104.008	−	56.7929i	−0.0188728	−	0.0103053i
$313$	737.434	−	1977.14i	0.133170	−	0.357043i	−0.853200	−	0.521583i	$-0.825342\pi$
$313$	737.434	−	1977.14i	0.133170	−	0.357043i	0.986370	+	0.164541i	$0.0526142\pi$
$314$	4817.95	−	3096.31i	0.865901	−	0.556481i
$315$	−3829.03	−	1603.89i	−0.684894	−	0.286886i
$316$	−2688.66	+	386.572i	−0.478637	+	0.0688176i
$317$	−7710.11	+	2875.72i	−1.36607	+	0.509516i	−0.922247	−	0.386601i	$-0.873649\pi$
$317$	−7710.11	+	2875.72i	−1.36607	+	0.509516i	−0.443818	+	0.896117i	$0.646376\pi$
$318$	2795.05	−	2092.35i	0.492889	−	0.368972i
$319$	5130.32	+	3297.06i	0.900447	+	0.578682i
$320$	129.844	−	703.662i	0.0226829	−	0.122925i
$321$		−	7349.81i		−	1.27796i
$322$	6763.46	−	1080.64i	1.17054	−	0.187024i
$323$	−5788.25	+	5788.25i	−0.997111	+	0.997111i
$324$	2747.53	−	2380.75i	0.471114	−	0.408222i
$325$	2.35785	−	296.641i	0.000402431	−	0.0506298i
$326$	745.883	−	5187.73i	0.126720	−	0.881355i
$327$	−1856.80	−	4978.27i	−0.314010	−	0.841893i
$328$	1163.10	+	870.689i	0.195798	+	0.146572i
$329$	−3266.19	−	959.039i	−0.547327	−	0.160710i
$330$	3958.55	+	1335.03i	0.660336	+	0.222700i
$331$	−149.631	−	327.645i	−0.0248473	−	0.0544079i	0.896801	−	0.442433i	$-0.145885\pi$
$331$	−149.631	−	327.645i	−0.0248473	−	0.0544079i	−0.921649	+	0.388025i	$0.873157\pi$
$332$	293.380	−	537.286i	0.0484980	−	0.0888175i
$333$	−2893.25	+	206.929i	−0.476123	+	0.0340530i
$334$	2616.05	+	2266.82i	0.428574	+	0.371361i
$335$	1309.90	+	7429.11i	0.213634	+	1.21163i
$336$	−2820.42	+	1288.04i	−0.457936	+	0.209133i
$337$	−2176.62	+	10005.7i	−0.351833	+	1.61735i	0.372589	+	0.927996i	$0.378470\pi$
$337$	−2176.62	+	10005.7i	−0.351833	+	1.61735i	−0.724423	+	0.689356i	$0.757894\pi$
$338$	3846.64	−	2100.42i	0.619022	−	0.338011i
$339$	−336.701	−	2341.81i	−0.0539442	−	0.375190i
$340$	2284.21	−	3815.20i	0.364349	−	0.608553i
$341$	−5487.39	−	788.968i	−0.871434	−	0.125293i
$342$	1924.17	−	418.578i	0.304232	−	0.0661816i
$343$	−615.564	+	8606.70i	−0.0969018	+	1.35486i
$344$	−2002.16			−0.313806
$345$	7558.82	−	1454.99i	1.17957	−	0.227055i
$346$	−5276.69			−0.819874
$347$	690.543	−	9655.05i	0.106831	−	1.49369i	−0.607745	−	0.794132i	$-0.707926\pi$
$347$	690.543	−	9655.05i	0.106831	−	1.49369i	0.714576	−	0.699558i	$-0.246620\pi$
$348$	−4970.60	+	1081.29i	−0.765667	+	0.166561i
$349$	9447.11	+	1358.29i	1.44897	+	0.208331i	0.821456	−	0.570271i	$-0.193162\pi$
$349$	9447.11	+	1358.29i	1.44897	+	0.208331i	0.627518	+	0.778602i	$0.284071\pi$
$350$	−6176.45	−	4700.70i	−0.943272	−	0.717894i
$351$	−31.7068	−	220.526i	−0.00482161	−	0.0335350i
$352$	840.662	−	459.036i	0.127294	−	0.0695077i
$353$	1014.43	−	4663.27i	0.152954	−	0.703119i	−0.835237	−	0.549891i	$-0.814669\pi$
$353$	1014.43	−	4663.27i	0.152954	−	0.703119i	0.988191	−	0.153228i	$-0.0489670\pi$
$354$	−5519.11	+	2520.49i	−0.828636	+	0.378425i
$355$	−3099.58	+	4426.59i	−0.463405	+	0.661800i
$356$	−3048.68	−	2641.70i	−0.453876	−	0.393286i
$357$	−19219.6	+	1374.62i	−2.84933	+	0.203788i
$358$	4237.20	−	7759.85i	0.625539	−	1.14559i
$359$	3808.35	+	8339.12i	0.559880	+	1.22597i	0.952013	+	0.306058i	$0.0990102\pi$
$359$	3808.35	+	8339.12i	0.559880	+	1.22597i	−0.392132	+	0.919909i	$0.628262\pi$
$360$	−958.447	+	475.010i	−0.140318	+	0.0695423i
$361$	78.1182	+	22.9376i	0.0113891	+	0.00334416i
$362$	−6393.83	−	4786.36i	−0.928322	−	0.694933i
$363$	−949.019	−	2544.42i	−0.137219	−	0.367899i
$364$	−41.9437	+	291.725i	−0.00603969	+	0.0420070i
$365$	5672.11	−	6981.68i	0.813402	−	1.00120i
$366$	−3157.29	+	2735.81i	−0.450914	+	0.390719i
$367$	−3249.01	+	3249.01i	−0.462117	+	0.462117i	−0.899349	−	0.437232i	$-0.855959\pi$
$367$	−3249.01	+	3249.01i	−0.462117	+	0.462117i	0.437232	+	0.899349i	$0.355959\pi$
$368$	930.826	−	1499.44i	0.131855	−	0.212401i
$369$		−	2172.01i		−	0.306423i
$370$	−5333.24	−	984.123i	−0.749357	−	0.138276i
$371$	−7304.94	−	4694.60i	−1.02225	−	0.656958i
$372$	3701.90	−	2771.21i	0.515953	−	0.386238i
$373$	4065.30	−	1516.28i	0.564325	−	0.210482i	−0.0510783	−	0.998695i	$-0.516266\pi$
$373$	4065.30	−	1516.28i	0.564325	−	0.210482i	0.615404	+	0.788212i	$0.288993\pi$
$374$	5891.79	−	847.112i	0.814592	−	0.117121i
$375$	−7105.54	−	5060.07i	−0.978475	−	0.696802i
$376$	−737.896	+	474.217i	−0.101208	+	0.0650422i
$377$	−168.974	+	453.037i	−0.0230838	+	0.0618901i
$378$	−5116.27	−	2793.70i	−0.696171	−	0.380138i
$379$	−2752.44	+	3176.48i	−0.373043	+	0.430514i	−0.910967	−	0.412479i	$-0.864663\pi$
$379$	−2752.44	+	3176.48i	−0.373043	+	0.430514i	0.537924	+	0.842993i	$0.319209\pi$
$380$	3678.84	+	146.031i	0.496633	+	0.0197138i
$381$	−1770.20	+	519.777i	−0.238031	+	0.0698923i
$382$	7760.24	+	2894.42i	1.03939	+	0.387674i
$383$	−872.312	−	189.760i	−0.116379	−	0.0253167i	0.153999	−	0.988071i	$-0.450785\pi$
$383$	−872.312	−	189.760i	−0.116379	−	0.0253167i	−0.270377	+	0.962754i	$0.587148\pi$
$384$	−225.089	+	766.583i	−0.0299128	+	0.101874i
$385$	−329.572	−	10384.7i	−0.0436274	−	1.37468i
$386$	1172.41	−	2567.21i	0.154596	−	0.338517i
$387$	1793.71	+	2396.12i	0.235606	+	0.314733i
$388$	58.7745	+	270.182i	0.00769027	+	0.0353516i
$389$	1601.34	+	1848.04i	0.208717	+	0.240873i	0.850450	−	0.526056i	$-0.176330\pi$
$389$	1601.34	+	1848.04i	0.208717	+	0.240873i	−0.641733	+	0.766928i	$0.721784\pi$
$390$	−36.7152	+	329.187i	−0.00476705	+	0.0427411i
$391$	8676.27	−	6709.21i	1.12219	−	0.867773i
$392$	3512.47	+	3512.47i	0.452567	+	0.452567i
$393$	15867.6	+	1134.87i	2.03667	+	0.145666i
$394$	671.787	−	1045.32i	0.0858989	−	0.133661i
$395$	3848.16	+	6544.85i	0.490182	+	0.833689i
$396$	−1302.50	−	594.832i	−0.165286	−	0.0754834i
$397$	2100.28	−	2805.64i	0.265516	−	0.354688i	−0.647893	−	0.761732i	$-0.724349\pi$
$397$	2100.28	−	2805.64i	0.265516	−	0.354688i	0.913409	+	0.407044i	$0.133440\pi$
$398$	−4370.67	−	8004.29i	−0.550458	−	1.00809i
$399$	−8625.31	−	13421.2i	−1.08222	−	1.68397i
$400$	−1957.61	+	409.584i	−0.244701	+	0.0511980i
$401$	−2784.35	−	9482.62i	−0.346742	−	1.18090i	−0.929677	−	0.368377i	$-0.879914\pi$
$401$	−2784.35	−	9482.62i	−0.346742	−	1.18090i	0.582934	−	0.812519i	$-0.301905\pi$
$402$	−600.890	−	8401.54i	−0.0745515	−	1.04237i
$403$	−31.3572	−	438.431i	−0.00387596	−	0.0541930i
$404$	126.101	+	429.461i	0.0155291	+	0.0528873i
$405$	−9068.57	−	4584.56i	−1.11264	−	0.562491i
$406$	6839.77	+	10642.9i	0.836089	+	1.30098i
$407$	−3479.16	−	6371.60i	−0.423723	−	0.775991i
$408$	−2975.43	+	3974.71i	−0.361044	+	0.482298i
$409$	4569.86	+	2086.98i	0.552482	+	0.252310i	0.672037	−	0.740518i	$-0.265420\pi$
$409$	4569.86	+	2086.98i	0.552482	+	0.252310i	−0.119555	+	0.992828i	$0.538147\pi$
$410$	1019.93	−	3930.80i	0.122856	−	0.473484i
$411$	−185.278	+	288.299i	−0.0222363	+	0.0346003i
$412$	6147.65	+	439.689i	0.735129	+	0.0525774i
$413$	10670.2	+	10670.2i	1.27130	+	1.27130i
$414$	−2628.40	+	229.348i	−0.312026	+	0.0272267i
$415$	−1700.51	−	189.663i	−0.201144	−	0.0224342i
$416$	49.7318	+	57.3936i	0.00586130	+	0.00676431i
$417$	3140.72	+	14437.7i	0.368829	+	1.69548i
$418$	2953.46	+	3945.36i	0.345594	+	0.461660i
$419$	−2383.48	+	5219.09i	−0.277901	+	0.608519i	−0.996188	−	0.0872279i	$-0.972199\pi$
$419$	−2383.48	+	5219.09i	−0.277901	+	0.608519i	0.718287	+	0.695747i	$0.244926\pi$
$420$	6319.44	+	5930.66i	0.734183	+	0.689016i
$421$	−3255.29	+	11086.5i	−0.376848	+	1.28343i	0.524900	+	0.851164i	$0.324103\pi$
$421$	−3255.29	+	11086.5i	−0.376848	+	1.28343i	−0.901748	+	0.432262i	$0.857715\pi$
$422$	−5129.66	−	1115.89i	−0.591725	−	0.128722i
$423$	1228.60	+	458.244i	0.141221	+	0.0526728i
$424$	−2146.84	+	630.370i	−0.245896	+	0.0722016i
$425$	−12288.0	−	1866.55i	−1.40248	−	0.213038i
$426$	3951.28	−	4560.02i	0.449390	−	0.518624i
$427$	9119.20	+	4979.46i	1.03351	+	0.564339i
$428$	−1646.01	+	4413.12i	−0.185894	+	0.498402i
$429$	−372.997	+	239.711i	−0.0419778	+	0.0269775i
$430$	2121.01	+	5178.69i	0.237870	+	0.580788i
$431$	3833.88	−	551.228i	0.428472	−	0.0616049i	0.0752945	−	0.997161i	$-0.476010\pi$
$431$	3833.88	−	551.228i	0.428472	−	0.0616049i	0.353177	+	0.935556i	$0.385101\pi$
$432$	−1407.35	+	524.916i	−0.156739	+	0.0584607i
$433$	2074.20	−	1552.73i	0.230207	−	0.172331i	−0.477947	−	0.878389i	$-0.658619\pi$
$433$	2074.20	−	1552.73i	0.230207	−	0.172331i	0.708155	+	0.706057i	$0.249528\pi$
$434$	−9675.01	−	6217.75i	−1.07008	−	0.687700i
$435$	8062.47	+	11711.2i	0.888657	+	1.29083i
$436$			3404.98i			0.374012i
$437$	8318.26	+	3642.72i	0.910564	+	0.398753i
$438$	−7102.09	+	7102.09i	−0.774774	+	0.774774i
$439$	5494.03	−	4760.61i	0.597303	−	0.517566i	−0.302908	−	0.953020i	$-0.597958\pi$
$439$	5494.03	−	4760.61i	0.597303	−	0.517566i	0.900211	+	0.435454i	$0.143412\pi$
$440$	−2077.89	−	1688.13i	−0.225135	−	0.182906i
$441$	1056.83	−	7350.40i	0.114116	−	0.793694i
$442$	164.927	+	442.188i	0.0177484	+	0.0475853i
$443$	9250.09	+	6924.53i	0.992065	+	0.742651i	0.966406	−	0.257020i	$-0.0827406\pi$
$443$	9250.09	+	6924.53i	0.992065	+	0.742651i	0.0256593	+	0.999671i	$0.491831\pi$
$444$	5810.13	+	1706.01i	0.621028	+	0.182350i
$445$	−3603.23	+	10684.1i	−0.383842	+	1.13814i
$446$	4723.84	+	10343.8i	0.501526	+	1.09819i
$447$	−2505.36	+	4588.23i	−0.265100	+	0.485494i
$448$	1981.95	−	141.752i	0.209014	−	0.0149490i
$449$	3532.47	+	3060.90i	0.371286	+	0.321722i	0.820440	−	0.571733i	$-0.193729\pi$
$449$	3532.47	+	3060.90i	0.371286	+	0.321722i	−0.449153	+	0.893455i	$0.648274\pi$
$450$	2243.98	+	1975.87i	0.235072	+	0.206985i
$451$	4944.77	−	2258.20i	0.516276	−	0.235775i
$452$	−322.285	+	1481.52i	−0.0335376	+	0.154170i
$453$	−4244.14	+	2317.48i	−0.440192	+	0.240363i
$454$	400.324	+	2784.31i	0.0413835	+	0.287829i
$455$	798.995	−	200.552i	0.0823241	−	0.0206638i
$456$	−4069.04	−	585.039i	−0.417873	−	0.0600811i
$457$	−689.214	+	149.929i	−0.0705472	+	0.0153466i	−0.247700	−	0.968837i	$-0.579675\pi$
$457$	−689.214	+	149.929i	−0.0705472	+	0.0153466i	0.177153	+	0.984183i	$0.443311\pi$
$458$	576.781	−	8064.45i	0.0588454	−	0.822767i
$459$	−9334.52			−0.949233
$460$	−4864.46	−	819.183i	−0.493058	−	0.0830317i
$461$	8359.09			0.844516			0.422258	−	0.906476i	$-0.361238\pi$
$461$	8359.09			0.844516			0.422258	+	0.906476i	$0.361238\pi$
$462$	−827.603	+	11571.4i	−0.0833411	+	1.16526i
$463$	−12979.0	+	2823.42i	−1.30278	+	0.283402i	−0.809835	−	0.586658i	$-0.800443\pi$
$463$	−12979.0	+	2823.42i	−1.30278	+	0.283402i	−0.492945	+	0.870060i	$0.664080\pi$
$464$	3226.70	+	463.929i	0.322836	+	0.0464168i
$465$	−11089.5	−	6639.44i	−1.10594	−	0.662144i
$466$	−721.843	−	5020.53i	−0.0717569	−	0.499080i
$467$	−8652.42	+	4724.58i	−0.857358	+	0.468153i	−0.846875	−	0.531792i	$-0.821519\pi$
$467$	−8652.42	+	4724.58i	−0.857358	+	0.468153i	−0.0104830	+	0.999945i	$0.503337\pi$
$468$	24.1326	−	110.936i	0.00238361	−	0.0109573i
$469$	−19055.3	+	8702.28i	−1.87611	+	0.856789i
$470$	2008.28	+	1406.24i	0.197096	+	0.138011i
$471$	13508.0	+	11704.7i	1.32148	+	1.14507i
$472$	3878.36	−	277.386i	0.378212	−	0.0270502i
$473$	−3590.09	+	6574.76i	−0.348991	+	0.639129i
$474$	−3521.59	−	7711.21i	−0.341249	−	0.747232i
$475$	−3519.50	−	9670.20i	−0.339970	−	0.934104i
$476$	11848.1	+	3478.91i	1.14087	+	0.334991i
$477$	2677.74	+	2004.53i	0.257034	+	0.192414i
$478$	4692.73	+	12581.7i	0.449039	+	1.20392i
$479$	1656.24	−	11519.4i	0.157987	−	1.09882i	−0.744349	−	0.667790i	$-0.767240\pi$
$479$	1656.24	−	11519.4i	0.157987	−	1.09882i	0.902336	−	0.431033i	$-0.141851\pi$
$480$	2221.26	−	229.884i	0.211221	−	0.0218598i
$481$	435.001	−	376.930i	0.0412356	−	0.0357309i
$482$	609.801	−	609.801i	0.0576258	−	0.0576258i
$483$	9182.74	+	19302.8i	0.865070	+	1.81844i
$484$			1740.30i			0.163439i
$485$	636.577	−	438.244i	0.0595989	−	0.0410302i
$486$	5280.16	+	3393.36i	0.492825	+	0.316720i
$487$	−16446.7	+	12311.9i	−1.53033	+	1.14559i	−0.588992	+	0.808139i	$0.700475\pi$
$487$	−16446.7	+	12311.9i	−1.53033	+	1.14559i	−0.941342	+	0.337454i	$0.890434\pi$
$488$	2508.45	−	935.605i	0.232689	−	0.0867886i
$489$	16190.3	−	2327.81i	1.49724	−	0.215270i
$490$	5364.21	−	12806.2i	0.494552	−	1.18066i
$491$	3299.25	−	2120.30i	0.303244	−	0.194883i	−0.380165	−	0.924919i	$-0.624133\pi$
$491$	3299.25	−	2120.30i	0.303244	−	0.194883i	0.683409	+	0.730035i	$0.260496\pi$
$492$	−1584.58	+	4248.43i	−0.145200	+	0.389297i
$493$	17780.4	+	9708.86i	1.62432	+	0.886947i
$494$	−255.889	+	295.312i	−0.0233057	+	0.0268962i
$495$	−158.745	+	3999.13i	−0.0144143	+	0.363126i
$496$	−2843.38	+	834.893i	−0.257403	+	0.0755802i
$497$	−14060.1	−	5244.16i	−1.26898	−	0.473305i
$498$	1866.84	+	406.106i	0.167982	+	0.0365423i
$499$	21.3350	−	72.6603i	0.00191400	−	0.00651848i	−0.958530	−	0.284990i	$-0.908010\pi$
$499$	21.3350	−	72.6603i	0.00191400	−	0.00651848i	0.960444	+	0.278472i	$0.0898278\pi$
$500$	3133.23	+	4629.57i	0.280244	+	0.414081i
$501$	−4487.73	+	9826.76i	−0.400194	+	0.876302i
$502$	−5062.49	−	6762.69i	−0.450099	−	0.601262i
$503$	−2252.25	−	10353.4i	−0.199647	−	0.917765i	−0.962519	−	0.271215i	$-0.912575\pi$
$503$	−2252.25	−	10353.4i	−0.199647	−	0.917765i	0.762871	−	0.646550i	$-0.223789\pi$
$504$	−1945.25	−	2244.94i	−0.171922	−	0.198408i
$505$	977.236	−	781.121i	0.0861118	−	0.0688306i
$506$	−3254.84	−	5745.34i	−0.285959	−	0.504766i
$507$	9671.80	+	9671.80i	0.847219	+	0.847219i
$508$	1179.30	+	84.3453i	0.102998	+	0.00736657i
$509$	−9619.11	+	14967.6i	−0.837641	+	1.30340i	0.113154	+	0.993577i	$0.463905\pi$
$509$	−9619.11	+	14967.6i	−0.837641	+	1.30340i	−0.950796	+	0.309818i	$0.899732\pi$
$510$	13432.9	+	3485.46i	1.16631	+	0.302625i
$511$	22722.2	+	10376.9i	1.96707	+	0.898330i
$512$	306.830	−	409.877i	0.0264846	−	0.0353793i
$513$	−3703.95	−	6783.28i	−0.318779	−	0.583800i
$514$	−4158.99	−	6471.51i	−0.356897	−	0.555343i
$515$	−5375.31	−	16367.0i	−0.459931	−	1.40042i
$516$	−1760.41	−	5995.39i	−0.150189	−	0.511497i
$517$	234.122	+	3273.45i	0.0199162	+	0.278465i
$518$	−1074.38	−	15021.7i	−0.0911300	−	1.27416i
$519$	−4639.55	−	15800.8i	−0.392396	−	1.33638i
$520$	95.7675	−	189.434i	0.00807631	−	0.0159755i
$521$	−4412.55	−	6866.07i	−0.371051	−	0.577366i	0.604645	−	0.796495i	$-0.293315\pi$
$521$	−4412.55	−	6866.07i	−0.371051	−	0.577366i	−0.975696	+	0.219129i	$0.929679\pi$
$522$	−2335.55	−	4277.24i	−0.195832	−	0.358640i
$523$	6024.94	−	8048.37i	0.503733	−	0.672908i	−0.474539	−	0.880234i	$-0.657385\pi$
$523$	6024.94	−	8048.37i	0.503733	−	0.672908i	0.978272	+	0.207326i	$0.0664762\pi$
$524$	−9273.35	−	4235.00i	−0.773107	−	0.353066i
$525$	8645.40	−	22628.3i	0.718698	−	1.88110i
$526$	−8644.51	+	13451.1i	−0.716576	+	1.11501i
$527$	−18369.2	−	1313.79i	−1.51836	−	0.108595i
$528$	2113.72	+	2113.72i	0.174220	+	0.174220i
$529$	−10436.2	−	6254.70i	−0.857748	−	0.514071i
$530$	3904.77	+	4885.14i	0.320023	+	0.400371i
$531$	−3806.55	−	4392.99i	−0.311092	−	0.359020i
$532$	2173.26	+	9990.30i	0.177110	+	0.814162i
$533$	258.290	+	345.036i	0.0209902	+	0.0280397i
$534$	5229.90	−	11451.9i	0.423820	−	0.928037i
$535$	13158.5	−	417.603i	1.06335	−	0.0337468i
$536$	−1520.75	+	5179.19i	−0.122549	+	0.417363i
$537$	26962.2	+	5865.26i	2.16667	+	0.471331i
$538$	−12655.3	−	4720.18i	−1.01414	−	0.378255i
$539$	17832.6	−	5236.13i	1.42506	−	0.418434i
$540$	2848.62	+	3084.12i	0.227009	+	0.245776i
$541$	7306.22	−	8431.82i	0.580626	−	0.670078i	−0.387113	−	0.922032i	$-0.626528\pi$
$541$	7306.22	−	8431.82i	0.580626	−	0.670078i	0.967739	+	0.251954i	$0.0810731\pi$
$542$	−7349.23	−	4012.98i	−0.582429	−	0.318030i
$543$	8710.79	−	23354.5i	0.688427	−	1.84574i
$544$	2676.71	−	1720.22i	0.210962	−	0.135577i
$545$	8807.17	−	3607.11i	0.692216	−	0.283508i
$546$	−910.438	+	130.901i	−0.0713611	+	0.0102602i
$547$	−8511.52	+	3174.63i	−0.665313	+	0.248149i	−0.659353	−	0.751833i	$-0.729170\pi$
$547$	−8511.52	+	3174.63i	−0.665313	+	0.248149i	−0.00595979	+	0.999982i	$0.501897\pi$
$548$	175.813	−	131.612i	0.0137051	−	0.0102595i
$549$	−3367.00	−	2163.84i	−0.261749	−	0.168216i
$550$	−2165.21	+	7162.90i	−0.167863	+	0.555322i
$551$			16773.3i			1.29686i
$552$	5308.45	+	1468.94i	0.409316	+	0.113265i
$553$	−14908.2	+	14908.2i	−1.14641	+	1.14641i
$554$	−8310.71	+	7201.27i	−0.637343	+	0.552261i
$555$	−1742.35	−	16835.5i	−0.133259	−	1.28762i
$556$	1347.53	−	9372.31i	0.102785	−	0.714882i
$557$	1427.63	+	3827.61i	0.108600	+	0.291169i	0.979870	−	0.199635i	$-0.0639757\pi$
$557$	1427.63	+	3827.61i	0.108600	+	0.291169i	−0.871270	+	0.490804i	$0.836703\pi$
$558$	3546.53	+	2654.90i	0.269062	+	0.201417i
$559$	−569.883	−	167.333i	−0.0431190	−	0.0126609i
$560$	−2466.25	−	4976.26i	−0.186104	−	0.375509i
$561$	7717.03	+	16897.9i	0.580772	+	1.27171i
$562$	5481.78	−	10039.1i	0.411450	−	0.753515i
$563$	−1989.36	+	142.282i	−0.148919	+	0.0106509i	−0.145600	−	0.989344i	$-0.546511\pi$
$563$	−1989.36	+	142.282i	−0.148919	+	0.0106509i	−0.00331941	+	0.999994i	$0.501057\pi$
$564$	−2068.82	−	1792.64i	−0.154456	−	0.133837i
$565$	4173.44	−	735.858i	0.310758	−	0.0547925i
$566$	617.603	−	282.050i	0.0458654	−	0.0209460i
$567$	5998.17	−	27573.1i	0.444267	−	2.04226i
$568$	−3393.73	+	1853.12i	−0.250700	+	0.136893i
$569$	2045.93	+	14229.8i	0.150738	+	1.04840i	0.914987	+	0.403484i	$0.132201\pi$
$569$	2045.93	+	14229.8i	0.150738	+	1.04840i	−0.764249	+	0.644921i	$0.776890\pi$
$570$	2797.35	+	11144.5i	0.205558	+	0.818936i
$571$	−12178.0	−	1750.93i	−0.892529	−	0.128326i	−0.319235	−	0.947676i	$-0.603426\pi$
$571$	−12178.0	−	1750.93i	−0.892529	−	0.128326i	−0.573294	+	0.819349i	$0.694335\pi$
$572$	277.646	−	60.3981i	0.0202954	−	0.00441499i
$573$	−1844.01	+	25782.7i	−0.134441	+	1.87973i
$574$	11277.1			0.820027
$575$	3034.36	+	13450.0i	0.220072	+	0.975484i
$576$	−765.414			−0.0553685
$577$	783.773	−	10958.6i	0.0565492	−	0.790661i	−0.887490	−	0.460827i	$-0.847553\pi$
$577$	783.773	−	10958.6i	0.0565492	−	0.790661i	0.944039	−	0.329834i	$-0.106993\pi$
$578$	9720.01	−	2114.46i	0.699480	−	0.152162i
$579$	8718.27	+	1253.50i	0.625767	+	0.0899717i
$580$	−2218.26	−	8837.50i	−0.158808	−	0.632685i
$581$	−676.209	−	4703.14i	−0.0482855	−	0.335833i
$582$	−757.373	+	413.557i	−0.0539418	+	0.0294544i
$583$	−1779.50	+	8180.21i	−0.126414	+	0.581114i
$584$	5854.90	−	2673.85i	0.414859	−	0.189460i
$585$	−312.506	+	55.1009i	−0.0220864	+	0.00389426i
$586$	−7472.38	−	6474.85i	−0.526760	−	0.456440i
$587$	−7237.88	+	517.663i	−0.508926	+	0.0363991i	−0.323441	−	0.946248i	$-0.604840\pi$
$587$	−7237.88	+	517.663i	−0.508926	+	0.0363991i	−0.185484	+	0.982647i	$0.559385\pi$
$588$	−7429.61	+	13606.3i	−0.521075	+	0.954277i
$589$	−6334.22	−	13870.0i	−0.443119	−	0.970295i
$590$	−4826.06	−	9737.72i	−0.336755	−	0.679484i
$591$	3720.85	+	1092.54i	0.258977	+	0.0760424i
$592$	−3106.57	−	2325.55i	−0.215674	−	0.161452i
$593$	3242.76	+	8694.19i	0.224560	+	0.602070i	0.999553	−	0.0299006i	$-0.00951907\pi$
$593$	3242.76	+	8694.19i	0.224560	+	0.602070i	−0.774992	+	0.631971i	$0.782246\pi$
$594$	−799.802	+	5562.75i	−0.0552463	+	0.384246i
$595$	−3553.02	−	34331.1i	−0.244806	−	2.36544i
$596$	2531.86	−	2193.87i	0.174009	−	0.150779i
$597$	20125.6	−	20125.6i	1.37971	−	1.37971i
$598$	390.262	−	348.997i	0.0266873	−	0.0238654i
$599$			1499.97i			0.102316i	0.998691	+	0.0511578i	$0.0162911\pi$
$599$			1499.97i			0.102316i	−0.998691	+	0.0511578i	$0.983709\pi$
$600$	−2947.72	−	5501.87i	−0.200567	−	0.374355i
$601$	−17455.2	−	11217.8i	−1.18472	−	0.761371i	−0.208468	−	0.978029i	$-0.566848\pi$
$601$	−17455.2	−	11217.8i	−1.18472	−	0.761371i	−0.976247	+	0.216658i	$0.930484\pi$
$602$	−12440.7	+	9312.96i	−0.842265	+	0.630512i
$603$	7560.71	−	2820.00i	0.510607	−	0.190447i
$604$	3067.35	−	441.019i	0.206637	−	0.0297099i
$605$	4501.38	−	1843.61i	0.302491	−	0.123890i
$606$	−1175.13	+	755.210i	−0.0787729	+	0.0506243i
$607$	−463.914	+	1243.80i	−0.0310209	+	0.0831703i	−0.951537	−	0.307535i	$-0.900496\pi$
$607$	−463.914	+	1243.80i	−0.0310209	+	0.0831703i	0.920516	+	0.390705i	$0.127769\pi$
$608$	2312.19	+	1262.55i	0.154230	+	0.0842157i
$609$	−25855.9	+	29839.3i	−1.72041	+	1.98546i
$610$	−5077.35	−	5497.10i	−0.337010	−	0.364871i
$611$	−249.664	+	73.3079i	−0.0165308	+	0.00485388i
$612$	−4456.74	−	1662.28i	−0.294368	−	0.109794i
$613$	−14137.5	−	3075.43i	−0.931499	−	0.202635i	−0.278884	−	0.960325i	$-0.589964\pi$
$613$	−14137.5	−	3075.43i	−0.931499	−	0.202635i	−0.652615	+	0.757690i	$0.726328\pi$
$614$	−3268.59	+	11131.8i	−0.214837	+	0.731666i
$615$	12667.4	−	402.019i	0.830569	−	0.0263593i
$616$	3088.37	−	6762.58i	0.202003	−	0.442325i
$617$	5765.48	+	7701.78i	0.376190	+	0.502532i	0.948182	−	0.317728i	$-0.102920\pi$
$617$	5765.48	+	7701.78i	0.376190	+	0.502532i	−0.571991	+	0.820260i	$0.693829\pi$
$618$	4088.71	+	18795.5i	0.266136	+	1.22341i
$619$	1511.68	+	1744.57i	0.0981573	+	0.113280i	0.802703	−	0.596379i	$-0.203395\pi$
$619$	1511.68	+	1744.57i	0.0981573	+	0.113280i	−0.704545	+	0.709659i	$0.748849\pi$
$620$	5171.66	+	6470.11i	0.334998	+	0.419106i
$621$	3770.04	+	9644.53i	0.243618	+	0.623223i
$622$	2664.77	+	2664.77i	0.171781	+	0.171781i
$623$	−31231.1	−	2233.69i	−2.00842	−	0.143645i
$624$	−128.136	+	199.384i	−0.00822043	+	0.0127912i
$625$	8655.39	−	13008.6i	0.553945	−	0.832553i
$626$	−3838.98	−	1753.20i	−0.245106	−	0.111936i
$627$	−9217.40	+	12313.0i	−0.587093	+	0.784265i
$628$	−5489.43	−	10053.1i	−0.348809	−	0.638796i
$629$	−13038.0	−	20287.5i	−0.826485	−	1.28604i
$630$	−3745.94	+	7409.71i	−0.236891	+	0.468587i
$631$	3314.21	+	11287.2i	0.209092	+	0.712100i	0.995531	+	0.0944333i	$0.0301039\pi$
$631$	3314.21	+	11287.2i	0.209092	+	0.712100i	−0.786440	+	0.617667i	$0.788078\pi$
$632$	387.559	+	5418.78i	0.0243928	+	0.341056i
$633$	−1168.78	−	16341.7i	−0.0733885	−	1.02611i
$634$	4636.72	+	15791.2i	0.290454	+	0.989195i
$635$	−1031.14	−	3139.68i	−0.0644404	−	0.196212i
$636$	−3775.24	−	5874.39i	−0.235374	−	0.366250i
$637$	706.210	+	1293.33i	0.0439263	+	0.0804451i
$638$	7309.30	−	9764.08i	0.453570	−	0.605899i
$639$	5258.16	+	2401.32i	0.325524	+	0.148662i
$640$	−1385.21	−	359.424i	−0.0855552	−	0.0221992i
$641$	−5549.84	+	8635.72i	−0.341974	+	0.532122i	−0.969059	−	0.246829i	$-0.920611\pi$
$641$	−5549.84	+	8635.72i	−0.341974	+	0.532122i	0.627085	+	0.778951i	$0.284248\pi$
$642$	−14662.2	−	1048.66i	−0.901355	−	0.0644662i
$643$	3375.34	+	3375.34i	0.207014	+	0.207014i	0.802997	−	0.595983i	$-0.203237\pi$
$643$	3375.34	+	3375.34i	0.207014	+	0.207014i	−0.595983	+	0.802997i	$0.703237\pi$
$644$	−1190.77	−	13646.6i	−0.0728619	−	0.835020i
$645$	−13642.5	+	10904.7i	−0.832826	+	0.665692i
$646$	10721.2	+	12372.9i	0.652969	+	0.753567i
$647$	5045.49	+	23193.8i	0.306582	+	1.40934i	0.830239	+	0.557407i	$0.188204\pi$
$647$	5045.49	+	23193.8i	0.306582	+	1.40934i	−0.523657	+	0.851929i	$0.675433\pi$
$648$	−4357.36	−	5820.75i	−0.264156	−	0.352871i
$649$	6043.43	−	13233.3i	0.365525	−	0.800387i
$650$	−591.435	−	47.0280i	−0.0356892	−	0.00283783i
$651$	10112.0	−	34438.5i	0.608790	−	2.07335i
$652$	−10242.6	−	2228.14i	−0.615232	−	0.133835i
$653$	22733.5	+	8479.14i	1.36237	+	0.508139i	0.921132	−	0.389250i	$-0.127266\pi$
$653$	22733.5	+	8479.14i	1.36237	+	0.508139i	0.441240	+	0.897389i	$0.354539\pi$
$654$	−10196.1	+	2993.85i	−0.609632	+	0.179004i
$655$	−1130.21	+	28472.4i	−0.0674213	+	1.69849i
$656$	1902.89	−	2196.05i	0.113255	−	0.130703i
$657$	−8445.32	−	4611.50i	−0.501497	−	0.273838i
$658$	−2379.20	+	6378.90i	−0.140959	+	0.377926i
$659$	−9307.19	+	5981.37i	−0.550162	+	0.353568i	−0.786002	−	0.618224i	$-0.787852\pi$
$659$	−9307.19	+	5981.37i	−0.550162	+	0.353568i	0.235840	+	0.971792i	$0.424216\pi$
$660$	3228.06	−	7706.45i	0.190382	−	0.454505i
$661$	−30201.4	+	4342.31i	−1.77716	+	0.255516i	−0.951278	−	0.308333i	$-0.900229\pi$
$661$	−30201.4	+	4342.31i	−1.77716	+	0.255516i	−0.825877	+	0.563850i	$0.809320\pi$
$662$	−674.970	+	251.751i	−0.0396276	+	0.0147803i
$663$	−1179.10	+	882.665i	−0.0690687	+	0.0517041i
$664$	−1029.97	−	661.925i	−0.0601970	−	0.0386862i
$665$	23538.2	−	16204.6i	1.37259	−	0.944942i
$666$			5801.27i			0.337530i
$667$	2850.10	−	22292.2i	0.165452	−	1.29409i
$668$	4895.34	−	4895.34i	0.283542	−	0.283542i
$669$	−26820.6	+	23240.2i	−1.54999	+	1.34308i
$670$	15007.3	−	1553.14i	0.865345	−	0.0895569i
$671$	1425.56	−	9914.99i	0.0820166	−	0.570438i
$672$	2167.11	+	5810.25i	0.124402	+	0.333534i
$673$	−23254.3	−	17408.0i	−1.33193	−	0.997069i	−0.998526	−	0.0542842i	$-0.982712\pi$
$673$	−23254.3	−	17408.0i	−1.33193	−	0.997069i	−0.333402	−	0.942785i	$-0.608197\pi$
$674$	19649.9	+	5769.75i	1.12298	+	0.329736i
$675$	4959.51	−	10635.3i	0.282803	−	0.606448i
$676$	−3641.31	−	7973.35i	−0.207175	−	0.453650i
$677$	14203.0	−	26010.8i	0.806301	−	1.47663i	−0.0714146	−	0.997447i	$-0.522751\pi$
$677$	14203.0	−	26010.8i	0.806301	−	1.47663i	0.877715	−	0.479183i	$-0.159067\pi$
$678$	−4719.72	+	337.561i	−0.267345	+	0.0191209i
$679$	1621.94	+	1405.42i	0.0916708	+	0.0794332i
$680$	−7285.05	−	5101.13i	−0.410836	−	0.287675i
$681$	−7985.53	+	3646.87i	−0.449348	+	0.205211i
$682$	−2356.85	+	10834.3i	−0.132329	+	0.608307i
$683$	−6105.77	+	3334.00i	−0.342066	+	0.186782i	−0.641094	−	0.767462i	$-0.721519\pi$
$683$	−6105.77	+	3334.00i	−0.342066	+	0.186782i	0.299029	+	0.954244i	$0.403337\pi$
$684$	−560.485	−	3898.26i	−0.0313314	−	0.217915i
$685$	−526.672	−	315.326i	−0.0293768	−	0.0175883i
$686$	17081.7	+	2455.98i	0.950704	+	0.136691i
$687$	24655.8	−	5363.55i	1.36926	−	0.297863i
$688$	−285.665	+	3994.12i	−0.0158298	+	0.221329i
$689$	−663.749			−0.0367008
$690$	−1824.08	−	15286.7i	−0.100640	−	0.843413i
$691$	−34.8587			−0.00191908			−0.000959542	−	1.00000i	$-0.500305\pi$
$691$	−34.8587			−0.00191908			−0.000959542		1.00000i	$0.500305\pi$
$692$	−752.869	+	10526.5i	−0.0413581	+	0.578262i
$693$	−10860.1	+	2362.47i	−0.595296	+	0.129499i
$694$	−19162.4	−	2755.13i	−1.04812	−	0.150697i
$695$	−25669.5	+	6443.20i	−1.40101	+	0.351661i
$696$	1447.87	+	10070.1i	0.0788525	+	0.548431i
$697$	15849.1	−	8654.28i	0.861304	−	0.470308i
$698$	4057.55	−	18652.3i	0.220030	−	1.01146i
$699$	14399.1	−	6575.85i	0.779148	−	0.355825i
$700$	−10258.7	+	11650.7i	−0.553917	+	0.629081i
$701$	−24807.3	−	21495.6i	−1.33660	−	1.15817i	−0.974082	−	0.226196i	$-0.927371\pi$
$701$	−24807.3	−	21495.6i	−1.33660	−	1.15817i	−0.362520	−	0.931976i	$-0.618084\pi$
$702$	−444.451	+	31.7878i	−0.0238956	+	0.00170905i
$703$	9569.20	−	17524.7i	0.513384	−	0.940193i
$704$	−795.789	−	1742.53i	−0.0426029	−	0.0932873i
$705$	−2445.14	+	7250.18i	−0.130623	+	0.387316i
$706$	−9158.04	−	2689.04i	−0.488198	−	0.143348i
$707$	2781.16	+	2081.95i	0.147944	+	0.110750i
$708$	4240.68	+	11369.7i	0.225105	+	0.603531i
$709$	1432.63	−	9964.14i	0.0758864	−	0.527801i	−0.916050	−	0.401064i	$-0.868640\pi$
$709$	1432.63	−	9964.14i	0.0758864	−	0.527801i	0.991936	−	0.126737i	$-0.0404505\pi$
$710$	8388.38	+	6814.95i	0.443395	+	0.360226i
$711$	6137.82	−	5318.45i	0.323750	−	0.280531i
$712$	−5704.92	+	5704.92i	−0.300282	+	0.300282i
$713$	6061.57	+	19509.9i	0.318384	+	1.02476i
$714$			38537.5i			2.01993i
$715$	−450.350	−	654.162i	−0.0235554	−	0.0342157i
$716$	−14875.6	−	9559.97i	−0.776435	−	0.498984i
$717$	−33549.4	+	25114.7i	−1.74745	+	1.30813i
$718$	17179.1	−	6407.48i	0.892924	−	0.333043i
$719$	17933.5	−	2578.45i	0.930192	−	0.133741i	0.339470	−	0.940617i	$-0.389752\pi$
$719$	17933.5	−	2578.45i	0.930192	−	0.133741i	0.590722	+	0.806875i	$0.298843\pi$
$720$	810.850	+	1979.78i	0.0419703	+	0.102475i
$721$	40244.4	−	25863.5i	2.07875	−	1.33593i
$722$	56.9040	−	152.566i	0.00293317	−	0.00786413i
$723$	2362.20	+	1289.86i	0.121509	+	0.0663489i
$724$	−10460.6	+	12072.2i	−0.536968	+	0.619695i
$725$	−20508.7	+	15099.8i	−1.05059	+	0.773505i
$726$	−5211.27	+	1530.17i	−0.266403	+	0.0782229i
$727$	−22884.7	−	8535.55i	−1.16746	−	0.435441i	−0.310377	−	0.950614i	$-0.600455\pi$
$727$	−22884.7	−	8535.55i	−1.16746	−	0.435441i	−0.857087	+	0.515172i	$0.827728\pi$
$728$	575.978	+	125.296i	0.0293231	+	0.00637884i
$729$	1394.95	−	4750.77i	0.0708709	−	0.241364i
$730$	−13118.5	−	12311.4i	−0.665120	−	0.624202i
$731$	−10337.5	+	22636.0i	−0.523046	+	1.14531i
$732$	5007.20	+	6688.84i	0.252830	+	0.337741i
$733$	3043.99	+	13993.0i	0.153386	+	0.705106i	0.988023	+	0.154305i	$0.0493139\pi$
$733$	3043.99	+	13993.0i	0.153386	+	0.705106i	−0.834637	+	0.550801i	$0.814322\pi$
$734$	6017.90	+	6945.03i	0.302622	+	0.349245i
$735$	43064.1	+	4803.06i	2.16115	+	0.241039i
$736$	−2858.43	−	2070.85i	−0.143156	−	0.103713i
$737$	14280.7	+	14280.7i	0.713755	+	0.713755i
$738$	−4332.95	−	309.899i	−0.216122	−	0.0154573i
$739$	4742.65	−	7379.71i	0.236077	−	0.367344i	−0.702919	−	0.711270i	$-0.748121\pi$
$739$	4742.65	−	7379.71i	0.236077	−	0.367344i	0.938997	+	0.343926i	$0.111757\pi$
$740$	−2724.17	+	10498.9i	−0.135328	+	0.521550i
$741$	−1109.29	−	506.597i	−0.0549944	−	0.0251151i
$742$	−10407.5	+	13902.8i	−0.514923	+	0.687856i
$743$	−4893.23	−	8961.28i	−0.241609	−	0.442473i	0.728534	−	0.685010i	$-0.240202\pi$
$743$	−4893.23	−	8961.28i	−0.241609	−	0.442473i	−0.970142	+	0.242537i	$0.922020\pi$
$744$	−5000.11	−	7780.32i	−0.246388	−	0.383388i
$745$	−8356.72	−	4224.69i	−0.410962	−	0.207759i
$746$	−2444.80	−	8326.23i	−0.119987	−	0.408639i
$747$	130.573	+	1825.65i	0.00639548	+	0.0894206i
$748$	−849.276	−	11874.4i	−0.0415142	−	0.580444i
$749$	10299.8	+	35077.8i	0.502463	+	1.71123i
$750$	−11108.2	+	13452.9i	−0.540817	+	0.654974i
$751$	−7581.15	−	11796.5i	−0.368362	−	0.573183i	0.606750	−	0.794892i	$-0.292473\pi$
$751$	−7581.15	−	11796.5i	−0.368362	−	0.573183i	−0.975113	+	0.221709i	$0.928836\pi$
$752$	840.735	+	1539.69i	0.0407692	+	0.0746633i
$753$	15799.4	−	21105.5i	0.764625	−	1.02142i
$754$	879.656	+	401.725i	0.0424870	+	0.0194032i
$755$	−4390.15	−	7466.67i	−0.211621	−	0.359920i
$756$	−6303.14	+	9807.87i	−0.303231	+	0.471837i
$757$	−3548.74	−	253.811i	−0.170384	−	0.0121861i	−0.0141137	−	0.999900i	$-0.504493\pi$
$757$	−3548.74	−	253.811i	−0.170384	−	0.0121861i	−0.156271	+	0.987714i	$0.549947\pi$
$758$	5944.07	+	5944.07i	0.284826	+	0.284826i
$759$	14342.4	−	14798.1i	0.685896	−	0.707690i
$760$	816.209	−	7318.09i	0.0389566	−	0.349283i
$761$	−24838.9	−	28665.7i	−1.18319	−	1.36548i	−0.915672	−	0.401927i	$-0.868341\pi$
$761$	−24838.9	−	28665.7i	−1.18319	−	1.36548i	−0.267522	−	0.963552i	$-0.586205\pi$
$762$	784.336	+	3605.54i	0.0372881	+	0.171411i
$763$	15838.1	+	21157.3i	0.751480	+	1.00386i
$764$	6881.31	−	15068.0i	0.325860	−	0.713534i
$765$	421.731	+	13288.6i	0.0199317	+	0.628038i
$766$	−503.013	+	1713.11i	−0.0237266	+	0.0808055i
$767$	1127.10	+	245.185i	0.0530601	+	0.0115425i
$768$	1497.14	+	558.406i	0.0703431	+	0.0262366i
$769$	21135.7	−	6206.01i	0.991124	−	0.291020i	0.254315	−	0.967121i	$-0.418150\pi$
$769$	21135.7	−	6206.01i	0.991124	−	0.291020i	0.736809	+	0.676101i	$0.236332\pi$
$770$	−20763.5	−	824.204i	−0.971771	−	0.0385743i
$771$	15721.9	−	18144.0i	0.734384	−	0.847525i
$772$	−4954.07	−	2705.13i	−0.230960	−	0.126113i
$773$	2187.20	−	5864.10i	0.101770	−	0.272855i	−0.876079	−	0.482167i	$-0.839850\pi$
$773$	2187.20	−	5864.10i	0.101770	−	0.272855i	0.977849	+	0.209312i	$0.0671225\pi$
$774$	5035.96	−	3236.41i	0.233868	−	0.150298i
$775$	11256.6	−	20231.0i	0.521741	−	0.937700i
$776$	547.373	−	78.7004i	0.0253216	−	0.00364070i
$777$	44037.4	−	16425.1i	2.03325	−	0.758362i
$778$	3915.14	−	2930.84i	0.180417	−	0.135059i
$779$	12577.9	+	8083.35i	0.578500	+	0.371779i
$780$	651.459	+	120.211i	0.0299051	+	0.00551827i
$781$			14467.3i			0.662844i
$782$	−12146.3	−	18265.6i	−0.555436	−	0.835264i
$783$	−13524.9	+	13524.9i	−0.617292	+	0.617292i
$784$	7508.19	−	6505.88i	0.342028	−	0.296369i
$785$	−20187.7	+	24848.6i	−0.917871	+	1.12979i
$786$	4527.91	−	31492.3i	0.205478	−	1.42913i
$787$	3376.95	+	9053.95i	0.152954	+	0.410087i	0.990716	−	0.135950i	$-0.0434086\pi$
$787$	3376.95	+	9053.95i	0.152954	+	0.410087i	−0.837761	+	0.546037i	$0.816136\pi$
$788$	−1989.47	−	1489.30i	−0.0899389	−	0.0673274i
$789$	−47879.6	−	14058.7i	−2.16041	−	0.634352i
$790$	13605.4	−	6742.89i	0.612732	−	0.303673i
$791$	4888.67	+	10704.7i	0.219748	+	0.481182i
$792$	−1372.47	+	2513.49i	−0.0615766	+	0.112769i
$793$	792.186	−	56.6583i	0.0354746	−	0.00253719i
$794$	−5297.32	−	4590.15i	−0.236769	−	0.205162i
$795$	−11195.1	+	15988.0i	−0.499432	+	0.713251i
$796$	−16591.4	+	7577.04i	−0.738777	+	0.337388i
$797$	2411.53	−	11085.6i	0.107178	−	0.492689i	−0.891996	−	0.452044i	$-0.850695\pi$
$797$	2411.53	−	11085.6i	0.107178	−	0.492689i	0.999174	−	0.0406450i	$-0.0129413\pi$
$798$	−28004.7	+	15291.7i	−1.24230	+	0.678348i
$799$	1551.51	+	10791.0i	0.0686963	+	0.477793i
$800$	537.772	+	3963.69i	0.0237664	+	0.175172i
$801$	11938.4	+	1716.49i	0.526622	+	0.0757168i
$802$	−19314.2	+	4201.54i	−0.850384	+	0.184990i
$803$	1718.02	−	24021.0i	0.0755013	−	1.05565i
$804$	−16846.0			−0.738946
$805$	−34036.3	+	17536.7i	−1.49021	+	0.767812i
$806$	−879.101			−0.0384181
$807$	3007.19	−	42046.0i	0.131175	−	1.83406i
$808$	874.725	−	190.285i	0.0380851	−	0.00828490i
$809$	−25480.2	−	3663.50i	−1.10734	−	0.159211i	−0.435700	−	0.900092i	$-0.643499\pi$
$809$	−25480.2	−	3663.50i	−1.10734	−	0.159211i	−0.671636	+	0.740881i	$0.734408\pi$
$810$	−10439.7	+	17436.8i	−0.452854	+	0.756379i
$811$	3155.69	+	21948.3i	0.136635	+	0.950321i	0.936632	+	0.350316i	$0.113926\pi$
$811$	3155.69	+	21948.3i	0.136635	+	0.950321i	−0.799996	+	0.600005i	$0.795165\pi$
$812$	22207.4	−	12126.2i	0.959764	−	0.524071i
$813$	5554.89	−	25535.4i	0.239629	−	1.10156i
$814$	−13207.1	+	6031.49i	−0.568685	+	0.259710i
$815$	5087.41	+	28853.4i	0.218656	+	1.24011i
$816$	7504.64	+	6502.81i	0.321955	+	0.278975i
$817$	−20551.3	+	1469.85i	−0.880046	+	0.0629421i
$818$	4815.36	−	8818.66i	0.205825	−	0.376941i
$819$	−366.062	−	801.565i	−0.0156181	−	0.0341989i
$820$	−7696.06	−	2595.51i	−0.327754	−	0.110536i
$821$	2989.77	+	877.875i	0.127093	+	0.0373180i	0.344661	−	0.938727i	$-0.387994\pi$
$821$	2989.77	+	877.875i	0.127093	+	0.0373180i	−0.217567	+	0.976045i	$0.569812\pi$
$822$	548.693	+	410.746i	0.0232821	+	0.0174287i
$823$	12906.6	+	34604.0i	0.546655	+	1.46564i	0.857151	+	0.515065i	$0.172232\pi$
$823$	12906.6	+	34604.0i	0.546655	+	1.46564i	−0.310496	+	0.950575i	$0.600495\pi$
$824$	1754.27	−	12201.2i	0.0741663	−	0.515838i
$825$	−23352.8	−	185.620i	−0.985504	−	0.00783327i
$826$	22808.4	−	19763.6i	0.960782	−	0.832522i
$827$	16064.9	−	16064.9i	0.675490	−	0.675490i	−0.283486	−	0.958976i	$-0.591491\pi$
$827$	16064.9	−	16064.9i	0.675490	−	0.675490i	0.958976	+	0.283486i	$0.0914910\pi$
$828$	82.5117	+	5276.13i	0.00346314	+	0.221447i
$829$			8670.64i			0.363261i	0.983367	+	0.181631i	$0.0581375\pi$
$829$			8670.64i			0.363261i	−0.983367	+	0.181631i	$0.941862\pi$
$830$	−620.987	+	3365.30i	−0.0259696	+	0.140737i
$831$	−28871.2	−	18554.4i	−1.20521	−	0.774541i
$832$	121.590	−	91.0214i	0.00506657	−	0.00379279i
$833$	57846.7	−	21575.7i	2.40609	−	0.897424i
$834$	29249.9	−	4205.49i	1.21444	−	0.174610i
$835$	−17848.0	−	7476.11i	−0.739706	−	0.309846i
$836$	8292.01	−	5328.95i	0.343045	−	0.220461i
$837$	6076.35	−	16291.3i	0.250931	−	0.672773i
$838$	10071.5	+	5499.47i	0.415173	+	0.226702i
$839$	3558.58	−	4106.82i	0.146431	−	0.168991i	−0.677796	−	0.735250i	$-0.737065\pi$
$839$	3558.58	−	4106.82i	0.146431	−	0.168991i	0.824227	+	0.566260i	$0.191610\pi$
$840$	12732.8	−	11760.5i	0.523002	−	0.483066i
$841$	16428.5	−	4823.84i	0.673602	−	0.197787i
$842$	21652.0	+	8075.79i	0.886197	+	0.330535i
$843$	34881.7	+	7588.05i	1.42514	+	0.310019i
$844$	−2957.98	+	10074.0i	−0.120637	+	0.410853i
$845$	−16766.0	+	17865.1i	−0.682567	+	0.727311i
$846$	1089.45	−	2385.56i	0.0442742	−	0.0969471i
$847$	8094.95	+	10813.6i	0.328389	+	0.438677i
$848$	951.220	+	4372.69i	0.0385201	+	0.177074i
$849$	1387.62	+	1601.40i	0.0560930	+	0.0647348i
$850$	−5476.83	+	24247.1i	−0.221004	+	0.978433i
$851$	−15695.5	+	21664.8i	−0.632238	+	0.872689i
$852$	−8533.05	−	8533.05i	−0.343119	−	0.343119i
$853$	2799.16	+	200.200i	0.112358	+	0.00803601i	0.127405	−	0.991851i	$-0.459335\pi$
$853$	2799.16	+	200.200i	0.112358	+	0.00803601i	−0.0150469	+	0.999887i	$0.504790\pi$
$854$	11234.7	−	17481.5i	0.450166	−	0.700472i
$855$	−9489.30	+	5579.39i	−0.379564	+	0.223171i
$856$	8568.90	+	3913.28i	0.342148	+	0.156254i
$857$	2846.84	−	3802.94i	0.113473	−	0.151582i	−0.740209	−	0.672377i	$-0.765273\pi$
$857$	2846.84	−	3802.94i	0.113473	−	0.151582i	0.853682	+	0.520795i	$0.174364\pi$
$858$	424.981	+	778.294i	0.0169098	+	0.0309680i
$859$	−23105.4	−	35952.7i	−0.917749	−	1.42805i	−0.903710	−	0.428145i	$-0.859167\pi$
$859$	−23105.4	−	35952.7i	−0.917749	−	1.42805i	−0.0140392	−	0.999901i	$-0.504469\pi$
$860$	10633.6	−	3492.33i	0.421632	−	0.138474i
$861$	9915.40	+	33768.8i	0.392469	+	1.33663i
$862$	−552.636	−	7726.87i	−0.0218363	−	0.305311i
$863$	−263.281	−	3681.15i	−0.0103849	−	0.145200i	−0.999999	−	0.00145011i	$-0.999538\pi$
$863$	−263.281	−	3681.15i	−0.0103849	−	0.145200i	0.989614	−	0.143750i	$-0.0459161\pi$
$864$	846.357	+	2882.43i	0.0333260	+	0.113498i
$865$	28024.9	−	9204.02i	1.10159	−	0.361787i
$866$	−2801.60	−	4359.38i	−0.109933	−	0.171060i
$867$	14878.0	+	27247.1i	0.582796	+	1.06731i
$868$	−13784.2	+	18413.6i	−0.539018	+	0.720044i
$869$	18489.3	+	8443.79i	0.721758	+	0.329616i
$870$	24513.1	−	14412.9i	0.955257	−	0.561659i
$871$	−865.713	+	1347.08i	−0.0336780	+	0.0524041i
$872$	6792.62	+	485.818i	0.263792	+	0.0188668i
$873$	−584.572	−	584.572i	−0.0226630	−	0.0226630i
$874$	8453.71	−	16074.4i	0.327175	−	0.622110i
$875$	41002.9	+	14192.3i	1.58417	+	0.548328i
$876$	13154.7	+	15181.3i	0.507369	+	0.585535i
$877$	3162.10	+	14535.9i	0.121752	+	0.559685i	0.997094	+	0.0761809i	$0.0242727\pi$
$877$	3162.10	+	14535.9i	0.121752	+	0.559685i	−0.875342	+	0.483504i	$0.839364\pi$
$878$	−8713.07	−	11639.3i	−0.334911	−	0.447389i
$879$	12818.6	−	28068.8i	0.491878	−	1.07706i
$880$	−3664.13	+	3904.32i	−0.140361	+	0.149562i
$881$	−7981.36	+	27182.0i	−0.305220	+	1.03948i	0.653922	+	0.756562i	$0.273122\pi$
$881$	−7981.36	+	27182.0i	−0.305220	+	1.03948i	−0.959143	+	0.282923i	$0.908696\pi$
$882$	−14512.5	−	3157.01i	−0.554040	−	0.120524i
$883$	6261.44	+	2335.40i	0.238635	+	0.0890061i	0.465936	−	0.884818i	$-0.345718\pi$
$883$	6261.44	+	2335.40i	0.238635	+	0.0890061i	−0.227302	+	0.973824i	$0.572990\pi$
$884$	905.654	−	265.924i	0.0344575	−	0.0101176i
$885$	24915.9	−	23013.4i	0.946373	−	0.874109i
$886$	15133.6	−	17465.1i	0.573840	−	0.662246i
$887$	−11976.6	−	6539.72i	−0.453365	−	0.247556i	0.236306	−	0.971679i	$-0.424063\pi$
$887$	−11976.6	−	6539.72i	−0.453365	−	0.247556i	−0.689671	+	0.724123i	$0.742245\pi$
$888$	4232.30	−	11347.2i	0.159940	−	0.428816i
$889$	7720.06	−	4961.38i	0.291252	−	0.187176i
$890$	20799.6	+	8712.49i	0.783377	+	0.328139i
$891$	−26927.6	+	3871.60i	−1.01247	+	0.145571i
$892$	21308.8	−	7947.78i	0.799857	−	0.298331i
$893$	−7226.02	+	5409.33i	−0.270783	+	0.202706i
$894$	8795.61	+	5652.60i	0.329048	+	0.211467i
$895$	−8968.72	+	48604.0i	−0.334962	+	1.81525i
$896$		−	3974.03i		−	0.148173i
$897$	1388.20	+	861.769i	0.0516729	+	0.0320776i
$898$	6610.22	−	6610.22i	0.245641	−	0.245641i
$899$	−28518.9	+	24711.8i	−1.05802	+	0.916779i
$900$	4261.83	−	4194.61i	0.157846	−	0.155356i
$901$	−3957.71	+	27526.5i	−0.146338	+	1.01780i
$902$	−3799.38	−	10186.5i	−0.140250	−	0.376025i
$903$	−38825.8	−	29064.7i	−1.43083	−	1.07111i
$904$	2909.50	+	854.308i	0.107045	+	0.0314313i
$905$	42306.9	+	14268.1i	1.55395	+	0.524074i
$906$	4017.60	+	8797.31i	0.147324	+	0.322595i
$907$	−23078.1	+	42264.3i	−0.844867	+	1.54726i	−0.00792444	+	0.999969i	$0.502522\pi$
$907$	−23078.1	+	42264.3i	−0.844867	+	1.54726i	−0.836943	+	0.547290i	$0.815659\pi$
$908$	5611.55	−	401.346i	0.205095	−	0.0146687i
$909$	−1011.38	−	876.369i	−0.0369037	−	0.0319773i
$910$	−286.084	−	1622.53i	−0.0104215	−	0.0591060i
$911$	16365.0	−	7473.63i	0.595165	−	0.271803i	−0.0949736	−	0.995480i	$-0.530277\pi$
$911$	16365.0	−	7473.63i	0.595165	−	0.271803i	0.690139	+	0.723677i	$0.257549\pi$
$912$	−1747.66	+	8033.86i	−0.0634548	+	0.291697i
$913$	−4020.51	+	2195.36i	−0.145739	+	0.0795794i
$914$	200.759	+	1396.31i	0.00726533	+	0.0505315i
$915$	11996.6	−	20037.3i	0.433437	−	0.723948i
$916$	−16005.5	−	2301.25i	−0.577333	−	0.0830080i
$917$	−77320.0	+	16819.9i	−2.78444	+	0.605718i
$918$	−1331.83	+	18621.5i	−0.0478835	+	0.669499i
$919$	50913.0			1.82749			0.913746	−	0.406286i	$-0.133176\pi$
$919$	50913.0			1.82749			0.913746	+	0.406286i	$0.133176\pi$
$920$	−2328.24	+	9587.25i	−0.0834347	+	0.343568i
$921$	−36207.7			−1.29542
$922$	1192.66	−	16675.6i	0.0426011	−	0.595641i
$923$	−1120.85	+	243.826i	−0.0399710	+	0.00869515i
$924$	22965.8	+	3301.98i	0.817660	+	0.117562i
$925$	30041.8	−	4075.92i	1.06786	−	0.144881i
$926$	3780.62	+	26294.8i	0.134167	+	0.933153i
$927$	−16173.7	+	8831.51i	−0.573046	+	0.312907i
$928$	1385.88	−	6370.77i	0.0490233	−	0.225356i
$929$	20159.8	−	9206.65i	0.711970	−	0.325146i	−0.0262972	−	0.999654i	$-0.508372\pi$
$929$	20159.8	−	9206.65i	0.711970	−	0.325146i	0.738267	+	0.674508i	$0.235644\pi$
$930$	−14827.3	+	21175.2i	−0.522802	+	0.746627i
$931$	38632.5	+	33475.3i	1.35997	+	1.17842i
$932$	−10118.5	+	723.687i	−0.355624	+	0.0254347i
$933$	−5636.55	+	10322.6i	−0.197784	+	0.362214i
$934$	8190.57	+	17934.8i	0.286942	+	0.628315i
$935$	−29814.1	+	14776.0i	−1.04281	+	0.516821i
$936$	−217.863	−	63.9704i	−0.00760799	−	0.00223391i
$937$	12975.5	+	9713.35i	0.452392	+	0.338657i	0.801054	−	0.598592i	$-0.204273\pi$
$937$	12975.5	+	9713.35i	0.452392	+	0.338657i	−0.348662	+	0.937249i	$0.613364\pi$
$938$	14641.4	+	39255.2i	0.509659	+	1.36645i
$939$	1874.47	−	13037.2i	0.0651447	−	0.453092i
$940$	3091.85	−	3805.70i	0.107282	−	0.132051i
$941$	−8515.14	+	7378.41i	−0.294990	+	0.255610i	−0.789763	−	0.613412i	$-0.789797\pi$
$941$	−8515.14	+	7378.41i	−0.294990	+	0.255610i	0.494773	+	0.869022i	$0.335251\pi$
$942$	25277.1	−	25277.1i	0.874282	−	0.874282i
$943$	−15342.9	−	12880.2i	−0.529834	−	0.444790i
$944$		−	7776.53i		−	0.268119i
$945$	32045.9	+	5913.31i	1.10312	+	0.203555i
$946$	12603.8	+	8099.97i	0.433176	+	0.278385i
$947$	6392.10	−	4785.07i	0.219341	−	0.164196i	−0.483957	−	0.875092i	$-0.660801\pi$
$947$	6392.10	−	4785.07i	0.219341	−	0.164196i	0.703298	+	0.710895i	$0.251710\pi$
$948$	−15885.6	+	5925.02i	−0.544240	+	0.202991i
$949$	1889.98	−	271.738i	0.0646483	−	0.00929502i
$950$	−19793.3	+	5641.34i	−0.675978	+	0.192662i
$951$	−43209.4	+	27769.0i	−1.47335	+	0.946868i
$952$	8630.56	−	23139.4i	0.293821	−	0.787765i
$953$	−27816.2	−	15188.8i	−0.945494	−	0.516279i	−0.0689607	−	0.997619i	$-0.521968\pi$
$953$	−27816.2	−	15188.8i	−0.945494	−	0.516279i	−0.876534	+	0.481340i	$0.840150\pi$
$954$	4380.91	−	5055.84i	0.148676	−	0.171582i
$955$	−46263.9	−	1836.44i	−1.56761	−	0.0622260i
$956$	25768.9	−	7566.42i	0.871783	−	0.255979i
$957$	35664.9	+	13302.3i	1.20468	+	0.449324i
$958$	−22743.8	−	4947.62i	−0.767036	−	0.166858i
$959$	480.249	−	1635.58i	0.0161711	−	0.0550736i
$960$	−141.671	−	4463.99i	−0.00476293	−	0.150078i
$961$	1874.85	−	4105.34i	0.0629334	−	0.137805i
$962$	−689.875	−	921.565i	−0.0231211	−	0.0308861i
$963$	−2993.49	−	13760.9i	−0.100170	−	0.460475i
$964$	−1129.49	−	1303.50i	−0.0377369	−	0.0435507i
$965$	−1748.80	+	15679.7i	−0.0583376	+	0.523053i
$966$	39817.4	−	15564.6i	1.32619	−	0.518408i
$967$	1273.20	+	1273.20i	0.0423407	+	0.0423407i	0.727960	−	0.685619i	$-0.240469\pi$
$967$	1273.20	+	1273.20i	0.0423407	+	0.0423407i	−0.685619	+	0.727960i	$0.740469\pi$
$968$	3471.74	+	248.304i	0.115275	+	0.00824461i
$969$	−27623.5	+	42983.0i	−0.915784	+	1.42499i
$970$	−783.429	−	1332.44i	−0.0259324	−	0.0441052i
$971$	3254.06	+	1486.08i	0.107547	+	0.0491148i	0.468462	−	0.883484i	$-0.344808\pi$
$971$	3254.06	+	1486.08i	0.107547	+	0.0491148i	−0.360915	+	0.932599i	$0.617536\pi$
$972$	7522.78	−	10049.3i	0.248244	−	0.331616i
$973$	−35221.8	−	64504.0i	−1.16049	−	2.12529i
$974$	22214.4	+	34566.3i	0.730796	+	1.13714i
$975$	−379.198	−	1812.38i	−0.0124554	−	0.0595308i
$976$	−1508.54	−	5137.62i	−0.0494746	−	0.168495i
$977$	−1588.73	−	22213.3i	−0.0520244	−	0.727396i	−0.954793	−	0.297270i	$-0.903924\pi$
$977$	−1588.73	−	22213.3i	−0.0520244	−	0.727396i	0.902769	−	0.430126i	$-0.141531\pi$
$978$	−2333.76	−	32630.2i	−0.0763040	−	1.06687i
$979$	8504.46	+	28963.5i	0.277634	+	0.945535i
$980$	−24781.7	−	12528.2i	−0.807778	−	0.408367i
$981$	−5504.02	−	8564.43i	−0.179134	−	0.278737i
$982$	−3759.06	−	6884.20i	−0.122155	−	0.223711i
$983$	11122.8	−	14858.4i	0.360898	−	0.482104i	−0.582938	−	0.812517i	$-0.698097\pi$
$983$	11122.8	−	14858.4i	0.360898	−	0.482104i	0.943837	+	0.330413i	$0.107188\pi$
$984$	8249.12	+	3767.25i	0.267248	+	0.122048i
$985$	−1744.58	+	6723.56i	−0.0564334	+	0.217493i
$986$	21905.1	−	34085.0i	0.707506	−	1.10090i
$987$	−21193.3	−	1515.77i	−0.683475	−	0.0488831i
$988$	552.609	+	552.609i	0.0177944	+	0.0177944i
$989$	27562.9	+	1538.57i	0.886198	+	0.0494678i
$990$	7955.23	+	887.270i	0.255388	+	0.0284841i
$991$	−18027.8	−	20805.2i	−0.577873	−	0.666901i	0.389273	−	0.921122i	$-0.372726\pi$
$991$	−18027.8	−	20805.2i	−0.577873	−	0.666901i	−0.967146	+	0.254222i	$0.918181\pi$
$992$	1259.84	+	5791.40i	0.0403226	+	0.185360i
$993$	−1347.33	−	1799.82i	−0.0430576	−	0.0575182i
$994$	−12467.7	+	27300.4i	−0.397837	+	0.871143i
$995$	37174.7	+	34887.7i	1.18444	+	1.11157i
$996$	1076.50	−	3666.22i	0.0342472	−	0.116635i
$997$	−30321.9	−	6596.13i	−0.963194	−	0.209530i	−0.296642	−	0.954989i	$-0.595867\pi$
$997$	−30321.9	−	6596.13i	−0.963194	−	0.209530i	−0.666552	+	0.745459i	$0.732231\pi$
$998$	−141.906	−	52.9283i	−0.00450097	−	0.00167877i
$999$	21846.7	−	6414.77i	0.691890	−	0.203157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.217.33	yes	720
5.3	odd	4	inner	230.4.l.a.33.15	yes	720
23.7	odd	22	inner	230.4.l.a.7.15	✓	720
115.53	even	44	inner	230.4.l.a.53.33	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.15	✓	720	23.7	odd	22	inner
230.4.l.a.33.15	yes	720	5.3	odd	4	inner
230.4.l.a.53.33	yes	720	115.53	even	44	inner
230.4.l.a.217.33	yes	720	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142678 - 1.99490i) q^{2} +(6.09912 - 1.32678i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(2.72190 + 10.8440i) q^{5} +(-1.77659 - 12.3565i) q^{6} +(-27.2494 + 14.8793i) q^{7} +(-1.70052 + 7.81717i) q^{8} +(10.8788 - 4.96819i) q^{9} +(22.0210 - 3.88273i) q^{10} +(22.6211 + 19.6013i) q^{11} +(-24.9034 + 1.78113i) q^{12} +(-1.13736 + 2.08291i) q^{13} +(25.7949 + 56.4829i) q^{14} +(30.9887 + 62.5272i) q^{15} +(15.3519 + 4.50772i) q^{16} +(79.5992 + 59.5872i) q^{17} +(-8.35890 - 22.4111i) q^{18} +(-11.7162 + 81.4881i) q^{19} +(-4.60375 - 44.4838i) q^{20} +(-146.456 + 126.905i) q^{21} +(42.3302 - 42.3302i) q^{22} +(29.4175 - 106.309i) q^{23} +49.9341i q^{24} +(-110.183 + 59.0322i) q^{25} +(3.99294 + 2.56610i) q^{26} +(-75.1537 + 56.2594i) q^{27} +(116.358 - 43.3994i) q^{28} +(201.669 - 28.9956i) q^{29} +(129.157 - 52.8983i) q^{30} +(-155.812 + 100.134i) q^{31} +(11.1829 - 29.9824i) q^{32} +(163.975 + 89.5373i) q^{33} +(130.228 - 150.291i) q^{34} +(-235.520 - 254.991i) q^{35} +(-45.9006 + 13.4776i) q^{36} +(-227.244 - 84.7578i) q^{37} +(160.889 + 34.9993i) q^{38} +(-4.17330 + 14.2130i) q^{39} +(-89.3977 + 2.83716i) q^{40} +(75.4444 - 165.200i) q^{41} +(232.266 + 310.272i) q^{42} +(53.1987 + 244.551i) q^{43} +(-78.4052 - 90.4844i) q^{44} +(83.4859 + 104.447i) q^{45} +(-207.879 - 73.8531i) q^{46} +(77.5288 + 77.5288i) q^{47} +(99.6137 + 7.12452i) q^{48} +(335.696 - 522.353i) q^{49} +(102.043 + 228.226i) q^{50} +(564.544 + 257.819i) q^{51} +(5.68884 - 7.59940i) q^{52} +(134.039 + 245.473i) q^{53} +(101.509 + 157.951i) q^{54} +(-150.983 + 298.655i) q^{55} +(-69.9758 - 238.316i) q^{56} +(36.6583 + 512.551i) q^{57} +(-29.0697 - 406.447i) q^{58} +(-136.931 - 466.345i) q^{59} +(-87.0991 - 265.204i) q^{60} +(-180.929 - 281.531i) q^{61} +(177.527 + 325.117i) q^{62} +(-222.518 + 297.250i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(-25.6828 - 6.66396i) q^{65} +(202.014 - 314.340i) q^{66} +(673.011 + 48.1347i) q^{67} +(-281.235 - 281.235i) q^{68} +(38.3721 - 687.422i) q^{69} +(-542.287 + 433.459i) q^{70} +(316.520 + 365.283i) q^{71} +(20.3376 + 93.4902i) q^{72} +(-482.161 - 644.092i) q^{73} +(-201.507 + 441.238i) q^{74} +(-593.694 + 506.233i) q^{75} +(92.7758 - 315.965i) q^{76} +(-908.064 - 197.537i) q^{77} +(27.7580 + 10.3532i) q^{78} +(651.571 - 191.318i) q^{79} +(-7.09525 + 178.745i) q^{80} +(-595.188 + 686.884i) q^{81} +(-318.794 - 174.075i) q^{82} +(-53.4826 + 143.392i) q^{83} +(652.101 - 419.080i) q^{84} +(-429.500 + 1025.36i) q^{85} +(495.445 - 71.2343i) q^{86} +(1191.53 - 444.418i) q^{87} +(-191.694 + 143.501i) q^{88} +(848.401 + 545.234i) q^{89} +(220.273 - 151.644i) q^{90} -73.6812i q^{91} +(-176.990 + 404.162i) q^{92} +(-817.459 + 817.459i) q^{93} +(165.724 - 143.601i) q^{94} +(-915.544 + 94.7521i) q^{95} +(28.4255 - 197.703i) q^{96} +(-24.1568 - 64.7669i) q^{97} +(-994.148 - 744.210i) q^{98} +(343.474 + 100.853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more