LMFDB - Embedded newform 48.4.j.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77551 + 0.544550i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(7.40693 - 3.02281i) q^{4} +(-3.72414 + 3.72414i) q^{5} +(7.04291 + 4.73259i) q^{6} +20.2675i q^{7} +(-18.9120 + 12.4233i) q^{8} +9.00000i q^{9} +O(q^{10})$	\(q+(-2.77551 + 0.544550i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(7.40693 - 3.02281i) q^{4} +(-3.72414 + 3.72414i) q^{5} +(7.04291 + 4.73259i) q^{6} +20.2675i q^{7} +(-18.9120 + 12.4233i) q^{8} +9.00000i q^{9} +(8.30842 - 12.3644i) q^{10} +(-47.5467 + 47.5467i) q^{11} +(-22.1248 - 9.30013i) q^{12} +(27.8636 + 27.8636i) q^{13} +(-11.0367 - 56.2527i) q^{14} +15.8002 q^{15} +(45.7253 - 44.7795i) q^{16} +56.3788 q^{17} +(-4.90095 - 24.9796i) q^{18} +(-66.1489 - 66.1489i) q^{19} +(-16.3271 + 38.8418i) q^{20} +(42.9939 - 42.9939i) q^{21} +(106.075 - 157.858i) q^{22} -3.66579i q^{23} +(66.4721 + 13.7646i) q^{24} +97.2615i q^{25} +(-92.5089 - 62.1627i) q^{26} +(19.0919 - 19.0919i) q^{27} +(61.2648 + 150.120i) q^{28} +(-86.8428 - 86.8428i) q^{29} +(-43.8536 + 8.60399i) q^{30} -102.846 q^{31} +(-102.526 + 149.186i) q^{32} +201.724 q^{33} +(-156.480 + 30.7011i) q^{34} +(-75.4791 - 75.4791i) q^{35} +(27.2053 + 66.6624i) q^{36} +(66.8267 - 66.8267i) q^{37} +(219.618 + 147.576i) q^{38} -118.215i q^{39} +(24.1647 - 116.697i) q^{40} +29.5734i q^{41} +(-95.9178 + 142.742i) q^{42} +(-372.929 + 372.929i) q^{43} +(-208.451 + 495.900i) q^{44} +(-33.5173 - 33.5173i) q^{45} +(1.99620 + 10.1744i) q^{46} +539.082 q^{47} +(-191.990 - 2.00634i) q^{48} -67.7725 q^{49} +(-52.9637 - 269.951i) q^{50} +(-119.598 - 119.598i) q^{51} +(290.610 + 122.158i) q^{52} +(385.376 - 385.376i) q^{53} +(-42.5933 + 63.3862i) q^{54} -354.142i q^{55} +(-251.789 - 383.298i) q^{56} +280.646i q^{57} +(288.323 + 193.743i) q^{58} +(71.0380 - 71.0380i) q^{59} +(117.031 - 47.7610i) q^{60} +(-155.133 - 155.133i) q^{61} +(285.449 - 56.0045i) q^{62} -182.408 q^{63} +(203.324 - 469.897i) q^{64} -207.536 q^{65} +(-559.886 + 109.849i) q^{66} +(-178.141 - 178.141i) q^{67} +(417.594 - 170.422i) q^{68} +(-7.77631 + 7.77631i) q^{69} +(250.595 + 168.391i) q^{70} +483.585i q^{71} +(-111.810 - 170.208i) q^{72} +908.791i q^{73} +(-149.088 + 221.869i) q^{74} +(206.323 - 206.323i) q^{75} +(-689.916 - 290.005i) q^{76} +(-963.654 - 963.654i) q^{77} +(64.3741 + 328.108i) q^{78} +1066.46 q^{79} +(-3.52228 + 337.053i) q^{80} -81.0000 q^{81} +(-16.1042 - 82.0814i) q^{82} +(871.541 + 871.541i) q^{83} +(188.491 - 448.415i) q^{84} +(-209.963 + 209.963i) q^{85} +(831.990 - 1238.15i) q^{86} +368.443i q^{87} +(308.515 - 1489.89i) q^{88} +185.044i q^{89} +(111.279 + 74.7758i) q^{90} +(-564.727 + 564.727i) q^{91} +(-11.0810 - 27.1522i) q^{92} +(218.168 + 218.168i) q^{93} +(-1496.23 + 293.557i) q^{94} +492.696 q^{95} +(533.962 - 98.9792i) q^{96} -725.140 q^{97} +(188.103 - 36.9055i) q^{98} +(-427.921 - 427.921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.77551	+	0.544550i	−0.981292	+	0.192527i
$2$	−2.77551	+	0.544550i	−0.981292	+	0.192527i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$	7.40693	−	3.02281i	0.925866	−	0.377851i
$5$	−3.72414	+	3.72414i	−0.333097	+	0.333097i	−0.853762	−	0.520664i	$-0.825684\pi$
$5$	−3.72414	+	3.72414i	−0.333097	+	0.333097i	0.520664	+	0.853762i	$0.325684\pi$
$6$	7.04291	+	4.73259i	0.479210	+	0.322012i
$7$			20.2675i			1.09434i	0.837020	+	0.547172i	$0.184296\pi$
$7$			20.2675i			1.09434i	−0.837020	+	0.547172i	$0.815704\pi$
$8$	−18.9120	+	12.4233i	−0.835798	+	0.549037i
$9$			9.00000i			0.333333i
$10$	8.30842	−	12.3644i	0.262735	−	0.390996i
$11$	−47.5467	+	47.5467i	−1.30326	+	1.30326i	−0.377081	+	0.926180i	$0.623072\pi$
$11$	−47.5467	+	47.5467i	−1.30326	+	1.30326i	−0.926180	+	0.377081i	$0.876928\pi$
$12$	−22.1248	−	9.30013i	−0.532240	−	0.223726i
$13$	27.8636	+	27.8636i	0.594460	+	0.594460i	0.938833	−	0.344373i	$-0.111909\pi$
$13$	27.8636	+	27.8636i	0.594460	+	0.594460i	−0.344373	+	0.938833i	$0.611909\pi$
$14$	−11.0367	−	56.2527i	−0.210691	−	1.07387i
$15$	15.8002			0.271973
$16$	45.7253	−	44.7795i	0.714457	−	0.699679i
$17$	56.3788			0.804345			0.402173	−	0.915564i	$-0.368255\pi$
$17$	56.3788			0.804345			0.402173	+	0.915564i	$0.368255\pi$
$18$	−4.90095	−	24.9796i	−0.0641758	−	0.327097i
$19$	−66.1489	−	66.1489i	−0.798716	−	0.798716i	0.184177	−	0.982893i	$-0.441038\pi$
$19$	−66.1489	−	66.1489i	−0.798716	−	0.798716i	−0.982893	+	0.184177i	$0.941038\pi$
$20$	−16.3271	+	38.8418i	−0.182543	+	0.434265i
$21$	42.9939	−	42.9939i	0.446764	−	0.446764i
$22$	106.075	−	157.858i	1.02797	−	1.52979i
$23$		−	3.66579i		−	0.0332335i	−0.999862	−	0.0166167i	$-0.994710\pi$
$23$		−	3.66579i		−	0.0332335i	0.999862	−	0.0166167i	$-0.00528951\pi$
$24$	66.4721	+	13.7646i	0.565356	+	0.117070i
$25$			97.2615i			0.778092i
$26$	−92.5089	−	62.1627i	−0.697788	−	0.468889i
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$	61.2648	+	150.120i	0.413499	+	1.01322i
$29$	−86.8428	−	86.8428i	−0.556079	−	0.556079i	0.372109	−	0.928189i	$-0.378635\pi$
$29$	−86.8428	−	86.8428i	−0.556079	−	0.556079i	−0.928189	+	0.372109i	$0.878635\pi$
$30$	−43.8536	+	8.60399i	−0.266885	+	0.0523622i
$31$	−102.846			−0.595858			−0.297929	−	0.954588i	$-0.596296\pi$
$31$	−102.846			−0.595858			−0.297929	+	0.954588i	$0.596296\pi$
$32$	−102.526	+	149.186i	−0.566383	+	0.824142i
$33$	201.724			1.06411
$34$	−156.480	+	30.7011i	−0.789297	+	0.154859i
$35$	−75.4791	−	75.4791i	−0.364523	−	0.364523i
$36$	27.2053	+	66.6624i	0.125950	+	0.308622i
$37$	66.8267	−	66.8267i	0.296925	−	0.296925i	−0.542883	−	0.839808i	$-0.682667\pi$
$37$	66.8267	−	66.8267i	0.296925	−	0.296925i	0.839808	+	0.542883i	$0.182667\pi$
$38$	219.618	+	147.576i	0.937547	+	0.629998i
$39$		−	118.215i		−	0.485374i
$40$	24.1647	−	116.697i	0.0955195	−	0.461285i
$41$			29.5734i			0.112649i	0.998413	+	0.0563243i	$0.0179381\pi$
$41$			29.5734i			0.112649i	−0.998413	+	0.0563243i	$0.982062\pi$
$42$	−95.9178	+	142.742i	−0.352391	+	0.524420i
$43$	−372.929	+	372.929i	−1.32258	+	1.32258i	−0.410905	+	0.911678i	$0.634787\pi$
$43$	−372.929	+	372.929i	−1.32258	+	1.32258i	−0.911678	+	0.410905i	$0.865213\pi$
$44$	−208.451	+	495.900i	−0.714207	+	1.69908i
$45$	−33.5173	−	33.5173i	−0.111032	−	0.111032i
$46$	1.99620	+	10.1744i	0.00639835	+	0.0326117i
$47$	539.082			1.67305			0.836524	−	0.547930i	$-0.184584\pi$
$47$	539.082			1.67305			0.836524	+	0.547930i	$0.184584\pi$
$48$	−191.990	−	2.00634i	−0.577319	−	0.00603312i
$49$	−67.7725			−0.197587
$50$	−52.9637	−	269.951i	−0.149804	−	0.763535i
$51$	−119.598	−	119.598i	−0.328373	−	0.328373i
$52$	290.610	+	122.158i	0.775008	+	0.325773i
$53$	385.376	−	385.376i	0.998781	−	0.998781i	−0.00121789	−	0.999999i	$-0.500388\pi$
$53$	385.376	−	385.376i	0.998781	−	0.998781i	0.999999	+	0.00121789i	$0.000387665\pi$
$54$	−42.5933	+	63.3862i	−0.107337	+	0.159737i
$55$		−	354.142i		−	0.868226i
$56$	−251.789	−	383.298i	−0.600835	−	0.914650i
$57$			280.646i			0.652149i
$58$	288.323	+	193.743i	0.652737	+	0.438616i
$59$	71.0380	−	71.0380i	0.156752	−	0.156752i	−0.624374	−	0.781126i	$-0.714646\pi$
$59$	71.0380	−	71.0380i	0.156752	−	0.156752i	0.781126	+	0.624374i	$0.214646\pi$
$60$	117.031	−	47.7610i	0.251811	−	0.102765i
$61$	−155.133	−	155.133i	−0.325619	−	0.325619i	0.525299	−	0.850918i	$-0.323954\pi$
$61$	−155.133	−	155.133i	−0.325619	−	0.325619i	−0.850918	+	0.525299i	$0.823954\pi$
$62$	285.449	−	56.0045i	0.584711	−	0.114719i
$63$	−182.408			−0.364781
$64$	203.324	−	469.897i	0.397117	−	0.917768i
$65$	−207.536			−0.396026
$66$	−559.886	+	109.849i	−1.04420	+	0.204870i
$67$	−178.141	−	178.141i	−0.324827	−	0.324827i	0.525788	−	0.850615i	$-0.323770\pi$
$67$	−178.141	−	178.141i	−0.324827	−	0.324827i	−0.850615	+	0.525788i	$0.823770\pi$
$68$	417.594	−	170.422i	0.744716	−	0.303923i
$69$	−7.77631	+	7.77631i	−0.0135675	+	0.0135675i
$70$	250.595	+	168.391i	0.427884	+	0.287523i
$71$			483.585i			0.808323i	0.914688	+	0.404162i	$0.132437\pi$
$71$			483.585i			0.808323i	−0.914688	+	0.404162i	$0.867563\pi$
$72$	−111.810	−	170.208i	−0.183012	−	0.278599i
$73$			908.791i			1.45707i	0.685010	+	0.728534i	$0.259798\pi$
$73$			908.791i			1.45707i	−0.685010	+	0.728534i	$0.740202\pi$
$74$	−149.088	+	221.869i	−0.234204	+	0.348537i
$75$	206.323	−	206.323i	0.317655	−	0.317655i
$76$	−689.916	−	290.005i	−1.04130	−	0.437708i
$77$	−963.654	−	963.654i	−1.42622	−	1.42622i
$78$	64.3741	+	328.108i	0.0934479	+	0.476294i
$79$	1066.46			1.51882			0.759409	−	0.650613i	$-0.225488\pi$
$79$	1066.46			1.51882			0.759409	+	0.650613i	$0.225488\pi$
$80$	−3.52228	+	337.053i	−0.00492253	+	0.471045i
$81$	−81.0000			−0.111111
$82$	−16.1042	−	82.0814i	−0.0216880	−	0.110541i
$83$	871.541	+	871.541i	1.15258	+	1.15258i	0.986034	+	0.166544i	$0.0532609\pi$
$83$	871.541	+	871.541i	1.15258	+	1.15258i	0.166544	+	0.986034i	$0.446739\pi$
$84$	188.491	−	448.415i	0.244833	−	0.582454i
$85$	−209.963	+	209.963i	−0.267925	+	0.267925i
$86$	831.990	−	1238.15i	1.04321	−	1.55247i
$87$			368.443i			0.454037i
$88$	308.515	−	1489.89i	0.373725	−	1.80480i
$89$			185.044i			0.220388i	0.993910	+	0.110194i	$0.0351473\pi$
$89$			185.044i			0.220388i	−0.993910	+	0.110194i	$0.964853\pi$
$90$	111.279	+	74.7758i	0.130332	+	0.0875784i
$91$	−564.727	+	564.727i	−0.650543	+	0.650543i
$92$	−11.0810	−	27.1522i	−0.0125573	−	0.0307697i
$93$	218.168	+	218.168i	0.243258	+	0.243258i
$94$	−1496.23	+	293.557i	−1.64175	+	0.322108i
$95$	492.696			0.532100
$96$	533.962	−	98.9792i	0.567680	−	0.105229i
$97$	−725.140			−0.759039			−0.379519	−	0.925184i	$-0.623911\pi$
$97$	−725.140			−0.759039			−0.379519	+	0.925184i	$0.623911\pi$
$98$	188.103	−	36.9055i	0.193891	−	0.0380410i
$99$	−427.921	−	427.921i	−0.434420	−	0.434420i
$100$	294.003	+	720.409i	0.294003	+	0.720409i
$101$	−1141.34	+	1141.34i	−1.12443	+	1.12443i	−0.133359	+	0.991068i	$0.542576\pi$
$101$	−1141.34	+	1141.34i	−1.12443	+	1.12443i	−0.991068	+	0.133359i	$0.957424\pi$
$102$	397.071	+	266.818i	0.385450	+	0.259009i
$103$		−	1099.46i		−	1.05177i	−0.850555	−	0.525886i	$-0.823734\pi$
$103$		−	1099.46i		−	1.05177i	0.850555	−	0.525886i	$-0.176266\pi$
$104$	−873.113	−	180.798i	−0.823229	−	0.170468i
$105$			320.231i			0.297632i
$106$	−859.758	+	1279.47i	−0.787803	+	1.17239i
$107$	361.438	−	361.438i	0.326556	−	0.326556i	−0.524719	−	0.851275i	$-0.675830\pi$
$107$	361.438	−	361.438i	0.326556	−	0.326556i	0.851275	+	0.524719i	$0.175830\pi$
$108$	83.7012	−	199.123i	0.0745754	−	0.177413i
$109$	1405.61	+	1405.61i	1.23517	+	1.23517i	0.961953	+	0.273215i	$0.0880871\pi$
$109$	1405.61	+	1405.61i	1.23517	+	1.23517i	0.273215	+	0.961953i	$0.411913\pi$
$110$	192.848	+	982.924i	0.167157	+	0.851983i
$111$	−283.522			−0.242439
$112$	907.569	+	926.738i	0.765689	+	0.781861i
$113$	−290.830			−0.242115			−0.121058	−	0.992645i	$-0.538629\pi$
$113$	−290.830			−0.242115			−0.121058	+	0.992645i	$0.538629\pi$
$114$	−152.826	−	778.936i	−0.125556	−	0.639948i
$115$	13.6519	+	13.6519i	0.0110700	+	0.0110700i
$116$	−905.748	−	380.730i	−0.724971	−	0.304740i
$117$	−250.773	+	250.773i	−0.198153	+	0.198153i
$118$	−158.483	+	235.851i	−0.123640	+	0.183998i
$119$			1142.66i			0.880230i
$120$	−298.813	+	196.290i	−0.227314	+	0.149323i
$121$		−	3190.38i		−	2.39698i
$122$	515.052	+	346.096i	0.382218	+	0.256837i
$123$	62.7347	−	62.7347i	0.0459886	−	0.0459886i
$124$	−761.770	+	310.882i	−0.551685	+	0.225146i
$125$	−827.734	−	827.734i	−0.592278	−	0.592278i
$126$	506.275	−	99.3301i	0.357957	−	0.0702304i
$127$	278.588			0.194651			0.0973256	−	0.995253i	$-0.468971\pi$
$127$	278.588			0.194651			0.0973256	+	0.995253i	$0.468971\pi$
$128$	−308.446	+	1414.93i	−0.212993	+	0.977054i
$129$	1582.20			1.07988
$130$	576.019	−	113.014i	0.388617	−	0.0762459i
$131$	−666.234	−	666.234i	−0.444345	−	0.444345i	0.449124	−	0.893469i	$-0.351736\pi$
$131$	−666.234	−	666.234i	−0.444345	−	0.444345i	−0.893469	+	0.449124i	$0.851736\pi$
$132$	1494.15	−	609.772i	0.985222	−	0.402075i
$133$	1340.67	−	1340.67i	0.874069	−	0.874069i
$134$	591.440	+	397.426i	0.381288	+	0.256212i
$135$			142.202i			0.0906576i
$136$	−1066.23	+	700.410i	−0.672271	+	0.441615i
$137$		−	632.580i		−	0.394489i	−0.980354	−	0.197244i	$-0.936801\pi$
$137$		−	632.580i		−	0.394489i	0.980354	−	0.197244i	$-0.0631992\pi$
$138$	17.3487	−	25.8178i	0.0107016	−	0.0159258i
$139$	1097.95	−	1097.95i	0.669976	−	0.669976i	−0.287734	−	0.957710i	$-0.592902\pi$
$139$	1097.95	−	1097.95i	0.669976	−	0.669976i	0.957710	+	0.287734i	$0.0929019\pi$
$140$	−787.228	−	330.910i	−0.475235	−	0.199764i
$141$	−1143.57	−	1143.57i	−0.683019	−	0.683019i
$142$	−263.336	−	1342.20i	−0.155624	−	0.793201i
$143$	−2649.65			−1.54947
$144$	403.015	+	411.527i	0.233226	+	0.238152i
$145$	646.830			0.370457
$146$	−494.882	−	2522.36i	−0.280526	−	1.42981i
$147$	143.767	+	143.767i	0.0806647	+	0.0806647i
$148$	292.976	−	696.985i	0.162720	−	0.387107i
$149$	963.349	−	963.349i	0.529669	−	0.529669i	−0.390805	−	0.920474i	$-0.627803\pi$
$149$	963.349	−	963.349i	0.529669	−	0.529669i	0.920474	+	0.390805i	$0.127803\pi$
$150$	−460.298	+	685.005i	−0.250555	+	0.372869i
$151$		−	2047.36i		−	1.10339i	−0.834046	−	0.551694i	$-0.813981\pi$
$151$		−	2047.36i		−	1.10339i	0.834046	−	0.551694i	$-0.186019\pi$
$152$	2072.79	+	429.219i	1.10609	+	0.229041i
$153$			507.409i			0.268115i
$154$	3199.39	+	2149.88i	1.67412	+	1.12495i
$155$	383.011	−	383.011i	0.198479	−	0.198479i
$156$	−357.342	−	875.613i	−0.183399	−	0.449392i
$157$	2663.57	+	2663.57i	1.35399	+	1.35399i	0.881147	+	0.472843i	$0.156772\pi$
$157$	2663.57	+	2663.57i	1.35399	+	1.35399i	0.472843	+	0.881147i	$0.343228\pi$
$158$	−2959.99	+	580.743i	−1.49040	+	0.292414i
$159$	−1635.01			−0.815502
$160$	−173.766	−	937.411i	−0.0858587	−	0.463180i
$161$	74.2964			0.0363688
$162$	224.816	−	44.1085i	0.109032	−	0.0213919i
$163$	1003.92	+	1003.92i	0.482410	+	0.482410i	0.905900	−	0.423491i	$-0.139195\pi$
$163$	1003.92	+	1003.92i	0.482410	+	0.482410i	−0.423491	+	0.905900i	$0.639195\pi$
$164$	89.3948	+	219.048i	0.0425644	+	0.104298i
$165$	−751.248	+	751.248i	−0.354452	+	0.354452i
$166$	−2893.57	−	1944.37i	−1.35292	−	0.909113i
$167$			1282.05i			0.594061i	0.954868	+	0.297031i	$0.0959964\pi$
$167$			1282.05i			0.594061i	−0.954868	+	0.297031i	$0.904004\pi$
$168$	−278.973	+	1347.22i	−0.128115	+	0.618694i
$169$		−	644.238i		−	0.293235i
$170$	468.419	−	697.089i	0.211330	−	0.314496i
$171$	595.340	−	595.340i	0.266239	−	0.266239i
$172$	−1634.97	+	3889.55i	−0.724796	+	1.72428i
$173$	1974.96	+	1974.96i	0.867937	+	0.867937i	0.992244	−	0.124306i	$-0.0396706\pi$
$173$	1974.96	+	1974.96i	0.867937	+	0.867937i	−0.124306	+	0.992244i	$0.539671\pi$
$174$	−200.635	−	1022.62i	−0.0874146	−	0.445543i
$175$	−1971.25			−0.851500
$176$	−44.9695	+	4303.20i	−0.0192597	+	1.84299i
$177$	−301.389			−0.127987
$178$	−100.765	−	513.591i	−0.0424308	−	0.216265i
$179$	66.3425	+	66.3425i	0.0277021	+	0.0277021i	0.720822	−	0.693120i	$-0.243764\pi$
$179$	66.3425	+	66.3425i	0.0277021	+	0.0277021i	−0.693120	+	0.720822i	$0.743764\pi$
$180$	−349.577	−	146.944i	−0.144755	−	0.0608475i
$181$	−371.784	+	371.784i	−0.152677	+	0.152677i	−0.779312	−	0.626636i	$-0.784431\pi$
$181$	−371.784	+	371.784i	−0.152677	+	0.152677i	0.626636	+	0.779312i	$0.284431\pi$
$182$	1259.88	−	1874.93i	0.513125	−	0.763620i
$183$			658.174i			0.265867i
$184$	45.5411	+	69.3272i	0.0182464	+	0.0277765i
$185$			497.744i			0.197810i
$186$	−724.332	−	486.725i	−0.285541	−	0.191873i
$187$	−2680.63	+	2680.63i	−1.04827	+	1.04827i
$188$	3992.95	−	1629.54i	1.54902	−	0.632163i
$189$	386.945	+	386.945i	0.148921	+	0.148921i
$190$	−1367.48	+	268.297i	−0.522145	+	0.102444i
$191$	−2857.35			−1.08246			−0.541232	−	0.840873i	$-0.682042\pi$
$191$	−2857.35			−1.08246			−0.541232	+	0.840873i	$0.682042\pi$
$192$	−1428.12	+	565.487i	−0.536800	+	0.212555i
$193$	−4318.58			−1.61066			−0.805332	−	0.592824i	$-0.798013\pi$
$193$	−4318.58			−1.61066			−0.805332	+	0.592824i	$0.798013\pi$
$194$	2012.63	−	394.875i	0.744839	−	0.146136i
$195$	440.251	+	440.251i	0.161677	+	0.161677i
$196$	−501.986	+	204.863i	−0.182939	+	0.0746586i
$197$	−1400.78	+	1400.78i	−0.506605	+	0.506605i	−0.913483	−	0.406878i	$-0.866618\pi$
$197$	−1400.78	+	1400.78i	−0.506605	+	0.506605i	0.406878	+	0.913483i	$0.366618\pi$
$198$	1420.72	+	954.674i	0.509931	+	0.342655i
$199$			2154.43i			0.767454i	0.923447	+	0.383727i	$0.125360\pi$
$199$			2154.43i			0.767454i	−0.923447	+	0.383727i	$0.874640\pi$
$200$	−1208.31	−	1839.41i	−0.427201	−	0.650328i
$201$			755.789i			0.265220i
$202$	2546.28	−	3789.30i	0.886908	−	1.31987i
$203$	1760.09	−	1760.09i	0.608542	−	0.608542i
$204$	−1247.37	−	524.330i	−0.428105	−	0.179953i
$205$	−110.136	−	110.136i	−0.0375230	−	0.0375230i
$206$	598.708	+	3051.55i	0.202495	+	1.03210i
$207$	32.9921			0.0110778
$208$	2521.79	+	26.3533i	0.840647	+	0.00878496i
$209$	6290.33			2.08187
$210$	−174.382	−	888.805i	−0.0573023	−	0.292064i
$211$	663.531	+	663.531i	0.216490	+	0.216490i	0.807017	−	0.590528i	$-0.201080\pi$
$211$	663.531	+	663.531i	0.216490	+	0.216490i	−0.590528	+	0.807017i	$0.701080\pi$
$212$	1689.53	−	4019.37i	0.547348	−	1.30213i
$213$	1025.84	−	1025.84i	0.329997	−	0.329997i
$214$	−806.354	+	1200.00i	−0.257576	+	0.383318i
$215$		−	2777.68i		−	0.881098i
$216$	−123.881	+	598.249i	−0.0390233	+	0.188452i
$217$		−	2084.42i		−	0.652073i
$218$	−4666.72	−	3135.87i	−1.44986	−	0.974256i
$219$	1927.84	−	1927.84i	0.594846	−	0.594846i
$220$	−1070.50	−	2623.10i	−0.328060	−	0.803861i
$221$	1570.92	+	1570.92i	0.478151	+	0.478151i
$222$	786.917	−	154.392i	0.237903	−	0.0466761i
$223$	432.791			0.129963			0.0649816	−	0.997886i	$-0.479301\pi$
$223$	432.791			0.129963			0.0649816	+	0.997886i	$0.479301\pi$
$224$	−3023.62	−	2077.96i	−0.901894	−	0.619818i
$225$	−875.354			−0.259364
$226$	807.202	−	158.371i	0.237585	−	0.0466138i
$227$	482.544	+	482.544i	0.141091	+	0.141091i	0.774124	−	0.633034i	$-0.218191\pi$
$227$	482.544	+	482.544i	0.141091	+	0.141091i	−0.633034	+	0.774124i	$0.718191\pi$
$228$	848.339	+	2078.73i	0.246415	+	0.603802i
$229$	−2717.39	+	2717.39i	−0.784150	+	0.784150i	−0.980528	−	0.196378i	$-0.937082\pi$
$229$	−2717.39	+	2717.39i	−0.784150	+	0.784150i	0.196378	+	0.980528i	$0.437082\pi$
$230$	−45.3252	−	30.4569i	−0.0129942	−	0.00873161i
$231$			4088.44i			1.16450i
$232$	2721.24	+	563.495i	0.770078	+	0.159462i
$233$		−	1214.38i		−	0.341445i	−0.985319	−	0.170722i	$-0.945390\pi$
$233$		−	1214.38i		−	0.341445i	0.985319	−	0.170722i	$-0.0546102\pi$
$234$	559.464	−	832.580i	0.156296	−	0.232596i
$235$	−2007.62	+	2007.62i	−0.557288	+	0.557288i
$236$	311.440	−	740.908i	0.0859025	−	0.204360i
$237$	−2262.31	−	2262.31i	−0.620055	−	0.620055i
$238$	−622.235	−	3171.46i	−0.169468	−	0.863762i
$239$	2676.38			0.724353			0.362177	−	0.932110i	$-0.382034\pi$
$239$	2676.38			0.724353			0.362177	+	0.932110i	$0.382034\pi$
$240$	722.468	−	707.524i	0.194313	−	0.190294i
$241$	−2415.81			−0.645708			−0.322854	−	0.946449i	$-0.604642\pi$
$241$	−2415.81			−0.645708			−0.322854	+	0.946449i	$0.604642\pi$
$242$	1737.32	+	8854.94i	0.461484	+	2.35214i
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$	−1618.00	−	680.123i	−0.424515	−	0.178444i
$245$	252.394	−	252.394i	0.0658158	−	0.0658158i
$246$	−139.959	+	208.283i	−0.0362742	+	0.0539823i
$247$		−	3686.29i		−	0.949609i
$248$	1945.01	−	1277.68i	0.498017	−	0.327148i
$249$		−	3697.63i		−	0.941076i
$250$	2748.13	+	1846.64i	0.695227	+	0.467168i
$251$	1492.39	−	1492.39i	0.375295	−	0.375295i	−0.494106	−	0.869402i	$-0.664505\pi$
$251$	1492.39	−	1492.39i	0.375295	−	0.375295i	0.869402	+	0.494106i	$0.164505\pi$
$252$	−1351.08	+	551.383i	−0.337739	+	0.137833i
$253$	174.296	+	174.296i	0.0433119	+	0.0433119i
$254$	−773.225	+	151.705i	−0.191010	+	0.0374757i
$255$	890.797			0.218760
$256$	85.5990	−	4095.11i	0.0208982	−	0.999782i
$257$	−3266.32			−0.792791			−0.396395	−	0.918080i	$-0.629739\pi$
$257$	−3266.32			−0.792791			−0.396395	+	0.918080i	$0.629739\pi$
$258$	−4391.42	+	861.588i	−1.05968	+	0.207907i
$259$	1354.41	+	1354.41i	0.324938	+	0.324938i
$260$	−1537.21	+	627.342i	−0.366667	+	0.149639i
$261$	781.585	−	781.585i	0.185360	−	0.185360i
$262$	2211.94	+	1486.34i	0.521580	+	0.350483i
$263$		−	893.279i		−	0.209437i	−0.994502	−	0.104719i	$-0.966606\pi$
$263$		−	893.279i		−	0.209437i	0.994502	−	0.104719i	$-0.0333942\pi$
$264$	−3814.99	+	2506.07i	−0.889380	+	0.584235i
$265$			2870.39i			0.665383i
$266$	−2990.99	+	4451.12i	−0.689434	+	1.02600i
$267$	392.537	−	392.537i	0.0899732	−	0.0899732i
$268$	−1857.97	−	780.993i	−0.423483	−	0.178010i
$269$	−2619.13	−	2619.13i	−0.593647	−	0.593647i	0.344967	−	0.938615i	$-0.387890\pi$
$269$	−2619.13	−	2619.13i	−0.593647	−	0.593647i	−0.938615	+	0.344967i	$0.887890\pi$
$270$	−77.4359	−	394.683i	−0.0174541	−	0.0889616i
$271$	5424.67			1.21596			0.607980	−	0.793952i	$-0.291980\pi$
$271$	5424.67			1.21596			0.607980	+	0.793952i	$0.291980\pi$
$272$	2577.94	−	2524.61i	0.574670	−	0.562784i
$273$	2395.93			0.531166
$274$	344.471	+	1755.73i	0.0759499	+	0.387108i
$275$	−4624.47	−	4624.47i	−1.01406	−	1.01406i
$276$	−34.0923	+	81.1049i	−0.00743520	+	0.0176882i
$277$	2242.55	−	2242.55i	0.486432	−	0.486432i	−0.420746	−	0.907178i	$-0.638232\pi$
$277$	2242.55	−	2242.55i	0.486432	−	0.486432i	0.907178	+	0.420746i	$0.138232\pi$
$278$	−2449.48	+	3645.25i	−0.528453	+	0.786431i
$279$		−	925.610i		−	0.198619i
$280$	2365.16	+	489.760i	0.504804	+	0.104531i
$281$			3622.87i			0.769119i	0.923100	+	0.384559i	$0.125647\pi$
$281$			3622.87i			0.769119i	−0.923100	+	0.384559i	$0.874353\pi$
$282$	3796.71	+	2551.25i	0.801741	+	0.538741i
$283$	−0.00634733	+	0.00634733i	−1.33325e−6	+	1.33325e-6i	−0.707107	−	0.707106i	$-0.750000\pi$
$283$	−0.00634733	+	0.00634733i	−1.33325e−6	+	1.33325e-6i	0.707106	+	0.707107i	$0.250000\pi$
$284$	1461.78	+	3581.88i	0.305426	+	0.748399i
$285$	−1045.17	−	1045.17i	−0.217229	−	0.217229i
$286$	7354.13	−	1442.86i	1.52048	−	0.298316i
$287$	−599.380			−0.123276
$288$	−1342.67	−	922.737i	−0.274714	−	0.188794i
$289$	−1734.43			−0.353028
$290$	−1795.28	+	352.231i	−0.363527	+	0.0713232i
$291$	1538.25	+	1538.25i	0.309876	+	0.309876i
$292$	2747.10	+	6731.35i	0.550555	+	1.34905i
$293$	−24.9384	+	24.9384i	−0.00497241	+	0.00497241i	−0.709589	−	0.704616i	$-0.751119\pi$
$293$	−24.9384	+	24.9384i	−0.00497241	+	0.00497241i	0.704616	+	0.709589i	$0.251119\pi$
$294$	−477.316	−	320.739i	−0.0946858	−	0.0636254i
$295$			529.112i			0.104427i
$296$	−433.617	+	2094.03i	−0.0851468	+	0.411193i
$297$			1815.51i			0.354703i
$298$	−2149.20	+	3198.38i	−0.417784	+	0.621735i
$299$	102.142	−	102.142i	0.0197560	−	0.0197560i
$300$	904.545	−	2151.89i	0.174080	−	0.414132i
$301$	−7558.34	−	7558.34i	−1.44736	−	1.44736i
$302$	1114.89	+	5682.47i	0.212433	+	1.08275i
$303$	4842.28			0.918091
$304$	−5986.79	−	62.5633i	−1.12949	−	0.0118035i
$305$	1155.48			0.216926
$306$	−276.310	−	1408.32i	−0.0516195	−	0.263099i
$307$	−618.757	−	618.757i	−0.115030	−	0.115030i	0.647249	−	0.762279i	$-0.275920\pi$
$307$	−618.757	−	618.757i	−0.115030	−	0.115030i	−0.762279	+	0.647249i	$0.775920\pi$
$308$	−10050.7	−	4224.78i	−1.85938	−	0.781588i
$309$	−2332.30	+	2332.30i	−0.429384	+	0.429384i
$310$	−854.484	+	1271.62i	−0.156553	+	0.232978i
$311$			4183.92i			0.762856i	0.924399	+	0.381428i	$0.124568\pi$
$311$			4183.92i			0.762856i	−0.924399	+	0.381428i	$0.875432\pi$
$312$	1468.62	+	2235.68i	0.266488	+	0.405675i
$313$		−	2124.18i		−	0.383597i	−0.981434	−	0.191799i	$-0.938568\pi$
$313$		−	2124.18i		−	0.383597i	0.981434	−	0.191799i	$-0.0614321\pi$
$314$	−8843.23	−	5942.33i	−1.58934	−	1.06798i
$315$	679.312	−	679.312i	0.121508	−	0.121508i
$316$	7899.23	−	3223.72i	1.40622	−	0.573887i
$317$	1064.95	+	1064.95i	0.188687	+	0.188687i	0.795128	−	0.606442i	$-0.207404\pi$
$317$	1064.95	+	1064.95i	0.188687	+	0.188687i	−0.606442	+	0.795128i	$0.707404\pi$
$318$	4537.99	−	890.344i	0.800245	−	0.157006i
$319$	8258.18			1.44943
$320$	992.756	+	2507.17i	0.173427	+	0.437985i
$321$	−1533.45			−0.266632
$322$	−206.211	+	40.4581i	−0.0356884	+	0.00700199i
$323$	−3729.40	−	3729.40i	−0.642443	−	0.642443i
$324$	−599.961	+	244.847i	−0.102874	+	0.0419834i
$325$	−2710.06	+	2710.06i	−0.462545	+	0.462545i
$326$	−3333.06	−	2239.70i	−0.566262	−	0.380508i
$327$		−	5963.51i		−	1.00851i
$328$	−367.399	−	559.292i	−0.0618482	−	0.0941516i
$329$			10925.9i			1.83089i
$330$	1676.01	−	2494.19i	0.279579	−	0.416062i
$331$	−1785.55	+	1785.55i	−0.296504	+	0.296504i	−0.839643	−	0.543139i	$-0.817236\pi$
$331$	−1785.55	+	1785.55i	−0.296504	+	0.296504i	0.543139	+	0.839643i	$0.317236\pi$
$332$	9089.94	+	3820.94i	1.50264	+	0.631631i
$333$	601.440	+	601.440i	0.0989751	+	0.0989751i
$334$	−698.142	−	3558.35i	−0.114373	−	0.582947i
$335$	1326.85			0.216398
$336$	40.6635	−	3891.15i	0.00660230	−	0.631785i
$337$	549.365			0.0888006			0.0444003	−	0.999014i	$-0.485862\pi$
$337$	549.365			0.0888006			0.0444003	+	0.999014i	$0.485862\pi$
$338$	350.819	+	1788.09i	0.0564558	+	0.287749i
$339$	616.944	+	616.944i	0.0988430	+	0.0988430i
$340$	−920.503	+	2189.86i	−0.146827	+	0.349299i
$341$	4889.97	−	4889.97i	0.776559	−	0.776559i
$342$	−1328.18	+	1976.57i	−0.209999	+	0.312516i
$343$			5578.18i			0.878115i
$344$	2419.81	−	11685.8i	0.379266	−	1.83156i
$345$		−	57.9202i		−	0.00903860i
$346$	−6556.98	−	4406.05i	−1.01880	−	0.684598i
$347$	−6594.28	+	6594.28i	−1.02017	+	1.02017i	−0.0203788	+	0.999792i	$0.506487\pi$
$347$	−6594.28	+	6594.28i	−1.02017	+	1.02017i	−0.999792	+	0.0203788i	$0.993513\pi$
$348$	1113.73	+	2729.03i	0.171558	+	0.420378i
$349$	6550.56	+	6550.56i	1.00471	+	1.00471i	0.999989	+	0.00471950i	$0.00150227\pi$
$349$	6550.56	+	6550.56i	1.00471	+	1.00471i	0.00471950	+	0.999989i	$0.498498\pi$
$350$	5471.23	−	1073.44i	0.835570	−	0.163937i
$351$	1063.94			0.161791
$352$	−2218.49	−	11968.1i	−0.335927	−	1.81222i
$353$	−939.592			−0.141670			−0.0708349	−	0.997488i	$-0.522566\pi$
$353$	−939.592			−0.141670			−0.0708349	+	0.997488i	$0.522566\pi$
$354$	836.508	−	164.121i	0.125593	−	0.0246411i
$355$	−1800.94	−	1800.94i	−0.269250	−	0.269250i
$356$	559.351	+	1370.60i	0.0832740	+	0.204050i
$357$	2423.95	−	2423.95i	0.359352	−	0.359352i
$358$	−220.261	−	148.008i	−0.0325172	−	0.0218504i
$359$		−	11175.4i		−	1.64294i	−0.570254	−	0.821469i	$-0.693155\pi$
$359$		−	11175.4i		−	1.64294i	0.570254	−	0.821469i	$-0.306845\pi$
$360$	1050.27	+	217.483i	0.153762	+	0.0318398i
$361$			1892.35i			0.275893i
$362$	829.435	−	1234.34i	0.120426	−	0.179215i
$363$	−6767.82	+	6767.82i	−0.978563	+	0.978563i
$364$	−2475.83	+	5889.95i	−0.356508	+	0.848124i
$365$	−3384.47	−	3384.47i	−0.485346	−	0.485346i
$366$	−358.409	−	1826.77i	−0.0511867	−	0.260893i
$367$	−10474.8			−1.48986			−0.744930	−	0.667143i	$-0.767517\pi$
$367$	−10474.8			−1.48986			−0.744930	+	0.667143i	$0.767517\pi$
$368$	−164.152	−	167.619i	−0.0232528	−	0.0237439i
$369$	−266.161			−0.0375496
$370$	−271.046	−	1381.49i	−0.0380839	−	0.194109i
$371$	7810.61	+	7810.61i	1.09301	+	1.09301i
$372$	2275.44	+	956.477i	0.317140	+	0.133309i
$373$	7160.10	−	7160.10i	0.993930	−	0.993930i	−0.00605119	−	0.999982i	$-0.501926\pi$
$373$	7160.10	−	7160.10i	0.993930	−	0.993930i	0.999982	+	0.00605119i	$0.00192617\pi$
$374$	5980.38	−	8899.85i	0.826840	−	1.23048i
$375$			3511.78i			0.483593i
$376$	−10195.1	+	6697.17i	−1.39833	+	0.918565i
$377$		−	4839.51i		−	0.661134i
$378$	−1284.68	−	863.260i	−0.174807	−	0.117464i
$379$	3707.91	−	3707.91i	0.502540	−	0.502540i	−0.409687	−	0.912226i	$-0.634362\pi$
$379$	3707.91	−	3707.91i	0.502540	−	0.502540i	0.912226	+	0.409687i	$0.134362\pi$
$380$	3649.36	−	1489.32i	0.492654	−	0.201055i
$381$	−590.975	−	590.975i	−0.0794660	−	0.0794660i
$382$	7930.61	−	1555.97i	1.06221	−	0.208404i
$383$	1619.09			0.216010			0.108005	−	0.994150i	$-0.465554\pi$
$383$	1619.09			0.216010			0.108005	+	0.994150i	$0.465554\pi$
$384$	3655.82	−	2347.20i	0.485834	−	0.311927i
$385$	7177.57			0.950137
$386$	11986.3	−	2351.68i	1.58053	−	0.310097i
$387$	−3356.36	−	3356.36i	−0.440861	−	0.440861i
$388$	−5371.06	+	2191.96i	−0.702769	+	0.286804i
$389$	−3130.25	+	3130.25i	−0.407995	+	0.407995i	−0.881039	−	0.473044i	$-0.843155\pi$
$389$	−3130.25	+	3130.25i	−0.407995	+	0.407995i	0.473044	+	0.881039i	$0.343155\pi$
$390$	−1461.66	−	982.183i	−0.189779	−	0.127525i
$391$		−	206.673i		−	0.0267312i
$392$	1281.71	−	841.956i	0.165143	−	0.108483i
$393$			2826.59i			0.362806i
$394$	3125.08	−	4650.66i	0.399592	−	0.594663i
$395$	−3971.67	+	3971.67i	−0.505914	+	0.505914i
$396$	−4463.10	−	1876.06i	−0.566362	−	0.238069i
$397$	−4797.49	−	4797.49i	−0.606497	−	0.606497i	0.335532	−	0.942029i	$-0.391084\pi$
$397$	−4797.49	−	4797.49i	−0.606497	−	0.606497i	−0.942029	+	0.335532i	$0.891084\pi$
$398$	−1173.19	−	5979.64i	−0.147756	−	0.753097i
$399$	−5688.00			−0.713674
$400$	4355.32	+	4447.31i	0.544415	+	0.555914i
$401$	10424.9			1.29825			0.649123	−	0.760684i	$-0.275136\pi$
$401$	10424.9			1.29825			0.649123	+	0.760684i	$0.275136\pi$
$402$	−411.565	−	2097.70i	−0.0510622	−	0.260258i
$403$	−2865.65	−	2865.65i	−0.354214	−	0.354214i
$404$	−5003.76	+	11903.8i	−0.616203	+	1.46594i
$405$	301.656	−	301.656i	0.0370108	−	0.0370108i
$406$	−3926.69	+	5843.60i	−0.479996	+	0.714318i
$407$			6354.78i			0.773943i
$408$	3747.62	+	776.029i	0.454742	+	0.0941647i
$409$			12366.0i			1.49501i	0.664255	+	0.747506i	$0.268749\pi$
$409$			12366.0i			1.49501i	−0.664255	+	0.747506i	$0.731251\pi$
$410$	365.657	+	245.709i	0.0440452	+	0.0295968i
$411$	−1341.90	+	1341.90i	−0.161049	+	0.161049i
$412$	−3323.44	−	8143.59i	−0.397413	−	0.973801i
$413$	1439.77	+	1439.77i	0.171540	+	0.171540i
$414$	−91.5699	+	17.9658i	−0.0108706	+	0.00213278i
$415$	−6491.48			−0.767842
$416$	−7013.61	+	1300.10i	−0.826611	+	0.153227i
$417$	−4658.20			−0.547034
$418$	−17458.9	+	3425.39i	−2.04292	+	0.400817i
$419$	−1809.65	−	1809.65i	−0.210996	−	0.210996i	0.593694	−	0.804691i	$-0.297669\pi$
$419$	−1809.65	−	1809.65i	−0.210996	−	0.210996i	−0.804691	+	0.593694i	$0.797669\pi$
$420$	967.997	+	2371.93i	0.112460	+	0.275567i
$421$	2481.06	−	2481.06i	0.287219	−	0.287219i	−0.548760	−	0.835980i	$-0.684900\pi$
$421$	2481.06	−	2481.06i	0.287219	−	0.287219i	0.835980	+	0.548760i	$0.184900\pi$
$422$	−2202.96	−	1480.31i	−0.254120	−	0.170759i
$423$			4851.74i			0.557683i
$424$	−2500.58	+	12075.8i	−0.286412	+	1.38315i
$425$			5483.49i			0.625855i
$426$	−2288.61	+	3405.85i	−0.260289	+	0.387356i
$427$	3144.17	−	3144.17i	0.356339	−	0.356339i
$428$	1584.59	−	3769.70i	0.178958	−	0.425737i
$429$	5620.75	+	5620.75i	0.632570	+	0.632570i
$430$	1512.58	+	7709.48i	0.169636	+	0.864614i
$431$	−4925.25			−0.550443			−0.275221	−	0.961381i	$-0.588751\pi$
$431$	−4925.25			−0.550443			−0.275221	+	0.961381i	$0.588751\pi$
$432$	18.0570	−	1727.91i	0.00201104	−	0.192440i
$433$	13472.5			1.49526			0.747630	−	0.664115i	$-0.231192\pi$
$433$	13472.5			1.49526			0.747630	+	0.664115i	$0.231192\pi$
$434$	1135.07	+	5785.34i	0.125542	+	0.639874i
$435$	−1372.13	−	1372.13i	−0.151239	−	0.151239i
$436$	14660.2	+	6162.38i	1.61031	+	0.676891i
$437$	−242.488	+	242.488i	−0.0265441	+	0.0265441i
$438$	−4300.93	+	6400.54i	−0.469193	+	0.698241i
$439$		−	13.7683i		−	0.00149687i	−1.00000		0.000748434i	$-0.999762\pi$
$439$		−	13.7683i		−	0.00149687i	1.00000		0.000748434i	$-0.000238234\pi$
$440$	4399.60	+	6697.51i	0.476688	+	0.725662i
$441$		−	609.952i		−	0.0658624i
$442$	−5215.54	−	3504.66i	−0.561263	−	0.377148i
$443$	−112.762	+	112.762i	−0.0120936	+	0.0120936i	−0.713128	−	0.701034i	$-0.752722\pi$
$443$	−112.762	+	112.762i	−0.0120936	+	0.0120936i	0.701034	+	0.713128i	$0.252722\pi$
$444$	−2100.02	+	857.031i	−0.224466	+	0.0916057i
$445$	−689.129	−	689.129i	−0.0734108	−	0.0734108i
$446$	−1201.22	+	235.676i	−0.127532	+	0.0250215i
$447$	−4087.14			−0.432473
$448$	9523.65	+	4120.88i	1.00435	+	0.434583i
$449$	−17094.6			−1.79676			−0.898380	−	0.439218i	$-0.855255\pi$
$449$	−17094.6			−1.79676			−0.898380	+	0.439218i	$0.855255\pi$
$450$	2429.55	−	476.674i	0.254512	−	0.0499347i
$451$	−1406.12	−	1406.12i	−0.146811	−	0.146811i
$452$	−2154.16	+	879.124i	−0.224166	+	0.0914834i
$453$	−4343.10	+	4343.10i	−0.450457	+	0.450457i
$454$	−1602.08	−	1076.54i	−0.165615	−	0.111287i
$455$		−	4206.24i		−	0.433389i
$456$	−3486.54	−	5307.56i	−0.358053	−	0.545065i
$457$		−	4074.04i		−	0.417015i	−0.978021	−	0.208507i	$-0.933140\pi$
$457$		−	4074.04i		−	0.417015i	0.978021	−	0.208507i	$-0.0668605\pi$
$458$	6062.40	−	9021.91i	0.618509	−	0.920450i
$459$	1076.38	−	1076.38i	0.109458	−	0.109458i
$460$	142.386	+	59.8517i	0.0144321	+	0.00606652i
$461$	2329.41	+	2329.41i	0.235339	+	0.235339i	0.814917	−	0.579578i	$-0.196783\pi$
$461$	2329.41	+	2329.41i	0.235339	+	0.235339i	−0.579578	+	0.814917i	$0.696783\pi$
$462$	−2226.36	−	11347.5i	−0.224198	−	1.14271i
$463$	12448.0			1.24948			0.624738	−	0.780834i	$-0.285206\pi$
$463$	12448.0			1.24948			0.624738	+	0.780834i	$0.285206\pi$
$464$	−7859.68	−	82.1356i	−0.786372	−	0.00821778i
$465$	−1624.98			−0.162057
$466$	661.290	+	3370.53i	0.0657375	+	0.335057i
$467$	366.937	+	366.937i	0.0363594	+	0.0363594i	0.725053	−	0.688693i	$-0.241815\pi$
$467$	366.937	+	366.937i	0.0363594	+	0.0363594i	−0.688693	+	0.725053i	$0.741815\pi$
$468$	−1099.42	+	2615.49i	−0.108591	+	0.258336i
$469$	3610.48	−	3610.48i	0.355472	−	0.355472i
$470$	4478.92	−	6665.42i	0.439569	−	0.654155i
$471$		−	11300.6i		−	1.10553i
$472$	−460.943	+	2225.99i	−0.0449504	+	0.217076i
$473$		−	35463.1i		−	3.44734i
$474$	7511.02	+	5047.13i	0.727832	+	0.489077i
$475$	6433.74	−	6433.74i	0.621474	−	0.621474i
$476$	3454.04	+	8463.60i	0.332596	+	0.814975i
$477$	3468.38	+	3468.38i	0.332927	+	0.332927i
$478$	−7428.31	+	1457.42i	−0.710802	+	0.139458i
$479$	18458.4			1.76072			0.880361	−	0.474304i	$-0.157300\pi$
$479$	18458.4			1.76072			0.880361	+	0.474304i	$0.157300\pi$
$480$	−1619.94	+	2357.16i	−0.154041	+	0.224144i
$481$	3724.07			0.353020
$482$	6705.10	−	1315.53i	0.633628	−	0.124317i
$483$	−157.607	−	157.607i	−0.0148475	−	0.0148475i
$484$	−9643.91	−	23630.9i	−0.905702	−	2.21928i
$485$	2700.52	−	2700.52i	0.252834	−	0.252834i
$486$	−570.476	−	383.339i	−0.0532455	−	0.0357791i
$487$		−	3880.55i		−	0.361077i	−0.983568	−	0.180538i	$-0.942216\pi$
$487$		−	3880.55i		−	0.361077i	0.983568	−	0.180538i	$-0.0577840\pi$
$488$	4861.13	+	1006.61i	0.450929	+	0.0933751i
$489$		−	4259.26i		−	0.393886i
$490$	−563.082	+	837.965i	−0.0519132	+	0.0772559i
$491$	3893.20	−	3893.20i	0.357836	−	0.357836i	−0.505179	−	0.863015i	$-0.668573\pi$
$491$	3893.20	−	3893.20i	0.357836	−	0.357836i	0.863015	+	0.505179i	$0.168573\pi$
$492$	275.037	−	654.307i	0.0252025	−	0.0599562i
$493$	−4896.10	−	4896.10i	−0.447280	−	0.447280i
$494$	2007.37	+	10231.4i	0.182826	+	0.931843i
$495$	3187.27			0.289409
$496$	−4702.64	+	4605.37i	−0.425715	+	0.416909i
$497$	−9801.06			−0.884583
$498$	2013.55	+	10262.8i	0.181183	+	0.923470i
$499$	−5061.87	−	5061.87i	−0.454110	−	0.454110i	0.442606	−	0.896716i	$-0.354054\pi$
$499$	−5061.87	−	5061.87i	−0.454110	−	0.454110i	−0.896716	+	0.442606i	$0.854054\pi$
$500$	−8633.05	−	3628.89i	−0.772163	−	0.324577i
$501$	2719.65	−	2719.65i	0.242525	−	0.242525i
$502$	−3329.48	+	4954.84i	−0.296019	+	0.440529i
$503$			11814.7i			1.04730i	0.851933	+	0.523651i	$0.175430\pi$
$503$			11814.7i			1.04730i	−0.851933	+	0.523651i	$0.824570\pi$
$504$	3449.69	−	2266.10i	0.304883	−	0.200278i
$505$		−	8500.99i		−	0.749088i
$506$	−578.674	−	388.848i	−0.0508403	−	0.0341629i
$507$	−1366.63	+	1366.63i	−0.119713	+	0.119713i
$508$	2063.48	−	842.119i	0.180221	−	0.0735492i
$509$	7553.16	+	7553.16i	0.657737	+	0.657737i	0.954844	−	0.297107i	$-0.0960219\pi$
$509$	7553.16	+	7553.16i	0.657737	+	0.657737i	−0.297107	+	0.954844i	$0.596022\pi$
$510$	−2472.42	+	485.083i	−0.214668	+	0.0421173i
$511$	−18418.9			−1.59453
$512$	1992.41	+	11412.6i	0.171978	+	0.985101i
$513$	−2525.81			−0.217383
$514$	9065.70	−	1778.67i	0.777959	−	0.152634i
$515$	4094.53	+	4094.53i	0.350343	+	0.350343i
$516$	11719.3	−	4782.69i	0.999829	−	0.408036i
$517$	−25631.6	+	25631.6i	−2.18042	+	2.18042i
$518$	−4496.73	−	3021.64i	−0.381419	−	0.256300i
$519$		−	8379.03i		−	0.708668i
$520$	3924.92	−	2578.28i	0.330998	−	0.217433i
$521$			1696.39i			0.142649i	0.997453	+	0.0713245i	$0.0227226\pi$
$521$			1696.39i			0.142649i	−0.997453	+	0.0713245i	$0.977277\pi$
$522$	−1743.69	+	2594.91i	−0.146205	+	0.217579i
$523$	6684.89	−	6684.89i	0.558910	−	0.558910i	−0.370087	−	0.928997i	$-0.620672\pi$
$523$	6684.89	−	6684.89i	0.558910	−	0.558910i	0.928997	+	0.370087i	$0.120672\pi$
$524$	−6948.65	−	2920.85i	−0.579300	−	0.243508i
$525$	4181.65	+	4181.65i	0.347623	+	0.347623i
$526$	486.435	+	2479.31i	0.0403224	+	0.205519i
$527$	−5798.31			−0.479276
$528$	9223.87	−	9033.08i	0.760260	−	0.744535i
$529$	12153.6			0.998896
$530$	−1563.07	−	7966.79i	−0.128104	−	0.652935i
$531$	639.342	+	639.342i	0.0522506	+	0.0522506i
$532$	5877.68	−	13982.9i	0.479003	−	1.13954i
$533$	−824.023	+	824.023i	−0.0669651	+	0.0669651i
$534$	−875.734	+	1303.25i	−0.0709677	+	0.105612i
$535$			2692.09i			0.217550i
$536$	5582.10	+	1155.90i	0.449832	+	0.0931479i
$537$		−	281.468i		−	0.0226187i
$538$	8695.67	+	5843.18i	0.696834	+	0.468248i
$539$	3222.36	−	3222.36i	0.257508	−	0.257508i
$540$	429.849	+	1053.28i	0.0342551	+	0.0839369i
$541$	−5108.56	−	5108.56i	−0.405978	−	0.405978i	0.474355	−	0.880333i	$-0.342681\pi$
$541$	−5108.56	−	5108.56i	−0.405978	−	0.405978i	−0.880333	+	0.474355i	$0.842681\pi$
$542$	−15056.2	+	2954.00i	−1.19321	+	0.234106i
$543$	1577.34			0.124660
$544$	−5780.32	+	8410.91i	−0.455568	+	0.662895i
$545$	−10469.4			−0.822863
$546$	−6649.94	+	1304.70i	−0.521229	+	0.102264i
$547$	13162.0	+	13162.0i	1.02883	+	1.02883i	0.999572	+	0.0292549i	$0.00931345\pi$
$547$	13162.0	+	13162.0i	1.02883	+	1.02883i	0.0292549	+	0.999572i	$0.490687\pi$
$548$	−1912.17	−	4685.48i	−0.149058	−	0.365244i
$549$	1396.20	−	1396.20i	0.108540	−	0.108540i
$550$	15353.5	+	10317.0i	1.19032	+	0.799852i
$551$			11489.1i			0.888299i
$552$	50.4579	−	243.673i	0.00389064	−	0.0187888i
$553$			21614.6i			1.66211i
$554$	−5003.04	+	7445.40i	−0.383680	+	0.570983i
$555$	1055.87	−	1055.87i	0.0807557	−	0.0807557i
$556$	4813.54	−	11451.3i	0.367157	−	0.873460i
$557$	−10462.8	−	10462.8i	−0.795911	−	0.795911i	0.186537	−	0.982448i	$-0.440274\pi$
$557$	−10462.8	−	10462.8i	−0.795911	−	0.795911i	−0.982448	+	0.186537i	$0.940274\pi$
$558$	504.040	+	2569.04i	0.0382397	+	0.194904i
$559$	−20782.3			−1.57245
$560$	−6831.22	−	71.3879i	−0.515485	−	0.00538694i
$561$	11372.9			0.855911
$562$	−1972.83	−	10055.3i	−0.148076	−	0.754730i
$563$	11673.6	+	11673.6i	0.873857	+	0.873857i	0.992890	−	0.119033i	$-0.0379795\pi$
$563$	11673.6	+	11673.6i	0.873857	+	0.873857i	−0.119033	+	0.992890i	$0.537980\pi$
$564$	−11927.1	−	5013.54i	−0.890464	−	0.374305i
$565$	1083.09	−	1083.09i	0.0806479	−	0.0806479i
$566$	0.0141606	−	0.0210735i	1.05162e−6	−	1.56499e-6i
$567$		−	1641.67i		−	0.121594i
$568$	−6007.71	−	9145.53i	−0.443799	−	0.675595i
$569$		−	238.804i		−	0.0175943i	−0.999961	−	0.00879717i	$-0.997200\pi$
$569$		−	238.804i		−	0.0175943i	0.999961	−	0.00879717i	$-0.00280026\pi$
$570$	3470.01	+	2331.72i	0.254988	+	0.171342i
$571$	14395.8	−	14395.8i	1.05507	−	1.05507i	0.0566747	−	0.998393i	$-0.481950\pi$
$571$	14395.8	−	14395.8i	1.05507	−	1.05507i	0.998393	−	0.0566747i	$-0.0180498\pi$
$572$	−19625.8	+	8009.38i	−1.43461	+	0.585470i
$573$	6061.36	+	6061.36i	0.441914	+	0.441914i
$574$	1663.59	−	326.392i	0.120970	−	0.0237341i
$575$	356.540			0.0258587
$576$	4229.07	+	1829.92i	0.305923	+	0.132372i
$577$	−14732.2			−1.06293			−0.531463	−	0.847081i	$-0.678358\pi$
$577$	−14732.2			−1.06293			−0.531463	+	0.847081i	$0.678358\pi$
$578$	4813.93	−	944.482i	0.346424	−	0.0679676i
$579$	9161.09	+	9161.09i	0.657551	+	0.657551i
$580$	4791.03	−	1955.24i	0.342994	−	0.139978i
$581$	−17664.0	+	17664.0i	−1.26132	+	1.26132i
$582$	−5107.10	−	3431.79i	−0.363739	−	0.244419i
$583$			36646.7i			2.60335i
$584$	−11290.2	−	17187.0i	−0.799984	−	1.21782i
$585$		−	1867.83i		−	0.132009i
$586$	55.6366	−	82.7970i	0.00392206	−	0.00583671i
$587$	−4120.47	+	4120.47i	−0.289727	+	0.289727i	−0.836972	−	0.547245i	$-0.815677\pi$
$587$	−4120.47	+	4120.47i	−0.289727	+	0.289727i	0.547245	+	0.836972i	$0.315677\pi$
$588$	1499.45	+	630.293i	0.105164	+	0.0442055i
$589$	6803.12	+	6803.12i	0.475921	+	0.475921i
$590$	−288.128	−	1468.56i	−0.0201051	−	0.102474i
$591$	5942.99			0.413641
$592$	63.2044	−	6048.13i	0.00438798	−	0.419893i
$593$	−18995.5			−1.31543			−0.657716	−	0.753266i	$-0.728477\pi$
$593$	−18995.5			−1.31543			−0.657716	+	0.753266i	$0.728477\pi$
$594$	−988.637	−	5038.98i	−0.0682900	−	0.348067i
$595$	−4255.43	−	4255.43i	−0.293202	−	0.293202i
$596$	4223.44	−	10047.5i	0.290267	−	0.690538i
$597$	4570.23	−	4570.23i	0.313312	−	0.313312i
$598$	−227.875	+	339.118i	−0.0155828	+	0.0231899i
$599$		−	19402.7i		−	1.32349i	−0.749728	−	0.661747i	$-0.769815\pi$
$599$		−	19402.7i		−	1.32349i	0.749728	−	0.661747i	$-0.230185\pi$
$600$	−1338.76	+	6465.18i	−0.0910912	+	0.439899i
$601$		−	14134.5i		−	0.959329i	−0.877452	−	0.479665i	$-0.840758\pi$
$601$		−	14134.5i		−	0.959329i	0.877452	−	0.479665i	$-0.159242\pi$
$602$	25094.2	+	16862.4i	1.69894	+	1.14163i
$603$	1603.27	−	1603.27i	0.108276	−	0.108276i
$604$	−6188.77	−	15164.6i	−0.416917	−	1.02159i
$605$	11881.4	+	11881.4i	0.798428	+	0.798428i
$606$	−13439.8	+	2636.86i	−0.900915	+	0.176758i
$607$	−2098.86			−0.140346			−0.0701731	−	0.997535i	$-0.522355\pi$
$607$	−2098.86			−0.140346			−0.0701731	+	0.997535i	$0.522355\pi$
$608$	16650.5	−	3086.46i	1.11063	−	0.205876i
$609$	−7467.42			−0.496872
$610$	−3207.04	+	629.214i	−0.212867	+	0.0417642i
$611$	15020.8	+	15020.8i	0.994560	+	0.994560i
$612$	1533.80	+	3758.35i	0.101308	+	0.248239i
$613$	6577.63	−	6577.63i	0.433390	−	0.433390i	−0.456390	−	0.889780i	$-0.650858\pi$
$613$	6577.63	−	6577.63i	0.433390	−	0.433390i	0.889780	+	0.456390i	$0.150858\pi$
$614$	2054.31	+	1380.42i	0.135025	+	0.0907318i
$615$			467.266i			0.0306374i
$616$	30196.3	+	6252.84i	1.97507	+	0.408984i
$617$		−	8011.43i		−	0.522736i	−0.965239	−	0.261368i	$-0.915826\pi$
$617$		−	8011.43i		−	0.522736i	0.965239	−	0.261368i	$-0.0841736\pi$
$618$	5203.27	−	7743.37i	0.338683	−	0.504019i
$619$	−7930.76	+	7930.76i	−0.514966	+	0.514966i	−0.916044	−	0.401078i	$-0.868636\pi$
$619$	−7930.76	+	7930.76i	−0.514966	+	0.514966i	0.401078	+	0.916044i	$0.368636\pi$
$620$	1679.17	−	3994.71i	0.108769	−	0.258760i
$621$	−69.9868	−	69.9868i	−0.00452250	−	0.00452250i
$622$	−2278.35	−	11612.5i	−0.146871	−	0.748584i
$623$	−3750.37			−0.241181
$624$	−5293.62	−	5405.43i	−0.339606	−	0.346779i
$625$	−5992.49			−0.383520
$626$	1156.72	+	5895.70i	0.0738530	+	0.376421i
$627$	−13343.8	−	13343.8i	−0.849920	−	0.849920i
$628$	27780.4	+	11677.4i	1.76522	+	0.742007i
$629$	3767.61	−	3767.61i	0.238831	−	0.238831i
$630$	−1515.52	+	2255.36i	−0.0958409	+	0.142628i
$631$			205.500i			0.0129649i	0.999979	+	0.00648243i	$0.00206344\pi$
$631$			205.500i			0.0129649i	−0.999979	+	0.00648243i	$0.997937\pi$
$632$	−20168.9	+	13249.0i	−1.26943	+	0.833887i
$633$		−	2815.12i		−	0.176763i
$634$	−3535.70	−	2375.87i	−0.221484	−	0.148829i
$635$	−1037.50	+	1037.50i	−0.0648378	+	0.0648378i
$636$	−12110.4	+	4942.32i	−0.755046	+	0.308138i
$637$	−1888.39	−	1888.39i	−0.117458	−	0.117458i
$638$	−22920.7	+	4496.99i	−1.42232	+	0.279056i
$639$	−4352.26			−0.269441
$640$	−4120.69	−	6418.08i	−0.254507	−	0.396401i
$641$	24945.2			1.53709			0.768545	−	0.639795i	$-0.220981\pi$
$641$	24945.2			1.53709			0.768545	+	0.639795i	$0.220981\pi$
$642$	4256.11	−	835.040i	0.261644	−	0.0513340i
$643$	2568.72	+	2568.72i	0.157543	+	0.157543i	0.781477	−	0.623934i	$-0.214467\pi$
$643$	2568.72	+	2568.72i	0.157543	+	0.157543i	−0.623934	+	0.781477i	$0.714467\pi$
$644$	550.309	−	224.584i	0.0336727	−	0.0137420i
$645$	−5892.35	+	5892.35i	−0.359707	+	0.359707i
$646$	12381.8	+	8320.14i	0.754112	+	0.506736i
$647$		−	24443.7i		−	1.48529i	−0.669687	−	0.742643i	$-0.733572\pi$
$647$		−	24443.7i		−	1.48529i	0.669687	−	0.742643i	$-0.266428\pi$
$648$	1531.87	−	1006.29i	0.0928665	−	0.0610041i
$649$			6755.25i			0.408578i
$650$	6046.04	−	8997.56i	0.364839	−	0.542944i
$651$	−4421.73	+	4421.73i	−0.266208	+	0.266208i
$652$	10470.6	+	4401.29i	0.628926	+	0.264368i
$653$	−9074.73	−	9074.73i	−0.543831	−	0.543831i	0.380819	−	0.924650i	$-0.375642\pi$
$653$	−9074.73	−	9074.73i	−0.543831	−	0.543831i	−0.924650	+	0.380819i	$0.875642\pi$
$654$	3247.43	+	16551.8i	0.194166	+	0.989643i
$655$	4962.30			0.296020
$656$	1324.28	+	1352.25i	0.0788179	+	0.0804826i
$657$	−8179.12			−0.485689
$658$	−5949.68	−	30324.9i	−0.352496	−	1.79664i
$659$	−7745.96	−	7745.96i	−0.457875	−	0.457875i	0.440082	−	0.897957i	$-0.354949\pi$
$659$	−7745.96	−	7745.96i	−0.457875	−	0.457875i	−0.897957	+	0.440082i	$0.854949\pi$
$660$	−3293.56	+	7835.32i	−0.194245	+	0.462105i
$661$	−6346.77	+	6346.77i	−0.373465	+	0.373465i	−0.868738	−	0.495272i	$-0.835068\pi$
$661$	−6346.77	+	6346.77i	−0.373465	+	0.373465i	0.495272	+	0.868738i	$0.335068\pi$
$662$	3983.49	−	5928.13i	0.233871	−	0.348042i
$663$		−	6664.84i		−	0.390409i
$664$	−27309.9	−	5655.14i	−1.59613	−	0.330515i
$665$			9985.72i			0.582300i
$666$	−1996.82	−	1341.79i	−0.116179	−	0.0780680i
$667$	−318.347	+	318.347i	−0.0184804	+	0.0184804i
$668$	3875.40	+	9496.08i	0.224467	+	0.550022i
$669$	−918.088	−	918.088i	−0.0530573	−	0.0530573i
$670$	−3682.68	+	722.534i	−0.212350	+	0.0416626i
$671$	14752.1			0.848734
$672$	2006.06	+	10822.1i	0.115157	+	0.621236i
$673$	−10029.4			−0.574450			−0.287225	−	0.957863i	$-0.592733\pi$
$673$	−10029.4			−0.574450			−0.287225	+	0.957863i	$0.592733\pi$
$674$	−1524.77	+	299.156i	−0.0871393	+	0.0170965i
$675$	1856.91	+	1856.91i	0.105885	+	0.105885i
$676$	−1947.41	−	4771.82i	−0.110799	−	0.271497i
$677$	16757.3	−	16757.3i	0.951309	−	0.951309i	−0.0475592	−	0.998868i	$-0.515144\pi$
$677$	16757.3	−	16757.3i	0.951309	−	0.951309i	0.998868	+	0.0475592i	$0.0151443\pi$
$678$	−2048.29	−	1376.38i	−0.116024	−	0.0779639i
$679$		−	14696.8i		−	0.830649i
$680$	1362.38	−	6579.23i	0.0768307	−	0.371032i
$681$		−	2047.26i		−	0.115200i
$682$	−10909.3	+	16235.0i	−0.612522	+	0.911540i
$683$	15221.0	−	15221.0i	0.852731	−	0.852731i	−0.137738	−	0.990469i	$-0.543983\pi$
$683$	15221.0	−	15221.0i	0.852731	−	0.852731i	0.990469	+	0.137738i	$0.0439832\pi$
$684$	2610.04	−	6209.24i	0.145903	−	0.347100i
$685$	2355.82	+	2355.82i	0.131403	+	0.131403i
$686$	−3037.60	−	15482.3i	−0.169061	−	0.861687i
$687$	11528.9			0.640256
$688$	−352.714	+	33751.8i	−0.0195452	+	1.87031i
$689$	21475.9			1.18747
$690$	31.5404	+	160.758i	0.00174018	+	0.00886950i
$691$	−12184.0	−	12184.0i	−0.670769	−	0.670769i	0.287125	−	0.957893i	$-0.407301\pi$
$691$	−12184.0	−	12184.0i	−0.670769	−	0.670769i	−0.957893	+	0.287125i	$0.907301\pi$
$692$	20598.3	+	8658.45i	1.13155	+	0.475643i
$693$	8672.89	−	8672.89i	0.475405	−	0.475405i
$694$	14711.6	−	21893.4i	0.804674	−	1.19750i
$695$			8177.83i			0.446335i
$696$	−4577.27	−	6967.97i	−0.249283	−	0.379483i
$697$			1667.32i			0.0906084i
$698$	−21748.2	−	14614.0i	−1.17935	−	0.792478i
$699$	−2576.09	+	2576.09i	−0.139394	+	0.139394i
$700$	−14600.9	+	5958.71i	−0.788375	+	0.321740i
$701$	−420.818	−	420.818i	−0.0226734	−	0.0226734i	0.695679	−	0.718353i	$-0.255104\pi$
$701$	−420.818	−	420.818i	−0.0226734	−	0.0226734i	−0.718353	+	0.695679i	$0.755104\pi$
$702$	−2952.97	+	579.367i	−0.158765	+	0.0311493i
$703$	−8841.02			−0.474318
$704$	12674.7	+	32009.5i	0.678544	+	1.71364i
$705$	8517.61			0.455024
$706$	2607.85	−	511.655i	0.139019	−	0.0272753i
$707$	−23132.0	−	23132.0i	−1.23051	−	1.23051i
$708$	−2232.37	+	911.041i	−0.118499	+	0.0483602i
$709$	9956.34	−	9956.34i	0.527388	−	0.527388i	−0.392405	−	0.919793i	$-0.628357\pi$
$709$	9956.34	−	9956.34i	0.527388	−	0.527388i	0.919793	+	0.392405i	$0.128357\pi$
$710$	5979.23	+	4017.83i	0.316051	+	0.212375i
$711$			9598.18i			0.506273i
$712$	−2298.85	−	3499.54i	−0.121001	−	0.184200i
$713$			377.010i			0.0198024i
$714$	−5407.73	+	8047.65i	−0.283444	+	0.421815i
$715$	9867.67	−	9867.67i	0.516126	−	0.516126i
$716$	691.935	+	290.854i	0.0361157	+	0.0151812i
$717$	−5677.45	−	5677.45i	−0.295716	−	0.295716i
$718$	6085.56	+	31017.4i	0.316310	+	1.61220i
$719$	−20878.5			−1.08295			−0.541473	−	0.840718i	$-0.682133\pi$
$719$	−20878.5			−1.08295			−0.541473	+	0.840718i	$0.682133\pi$
$720$	−3033.47	−	31.7005i	−0.157015	−	0.00164084i
$721$	22283.2			1.15100
$722$	−1030.48	−	5252.24i	−0.0531170	−	0.270732i
$723$	5124.70	+	5124.70i	0.263609	+	0.263609i
$724$	−1629.94	+	3877.61i	−0.0836691	+	0.199047i
$725$	8446.46	−	8446.46i	0.432681	−	0.432681i
$726$	15098.8	−	22469.6i	0.771856	−	1.14866i
$727$		−	2726.84i		−	0.139110i	−0.997578	−	0.0695549i	$-0.977842\pi$
$727$		−	2726.84i		−	0.139110i	0.997578	−	0.0695549i	$-0.0221579\pi$
$728$	3664.33	−	17695.8i	0.186551	−	0.900895i
$729$		−	729.000i		−	0.0370370i
$730$	11236.6	+	7550.62i	0.569708	+	0.382823i
$731$	−21025.3	+	21025.3i	−1.06381	+	1.06381i
$732$	1989.53	+	4875.05i	0.100458	+	0.246157i
$733$	−1081.50	−	1081.50i	−0.0544967	−	0.0544967i	0.679333	−	0.733830i	$-0.262269\pi$
$733$	−1081.50	−	1081.50i	−0.0544967	−	0.0544967i	−0.733830	+	0.679333i	$0.762269\pi$
$734$	29072.8	−	5704.03i	1.46199	−	0.286839i
$735$	−1070.82			−0.0537384
$736$	546.883	+	375.840i	0.0273891	+	0.0188229i
$737$	16940.1			0.846669
$738$	738.733	−	144.938i	0.0368471	−	0.00722932i
$739$	−15055.3	−	15055.3i	−0.749416	−	0.749416i	0.224954	−	0.974369i	$-0.427777\pi$
$739$	−15055.3	−	15055.3i	−0.749416	−	0.749416i	−0.974369	+	0.224954i	$0.927777\pi$
$740$	1504.59	+	3686.76i	0.0747428	+	0.183146i
$741$	−7819.81	+	7819.81i	−0.387676	+	0.387676i
$742$	−25931.7	−	17425.2i	−1.28300	−	0.862127i
$743$			21909.2i			1.08179i	0.841090	+	0.540896i	$0.181915\pi$
$743$			21909.2i			1.08179i	−0.841090	+	0.540896i	$0.818085\pi$
$744$	−6836.36	−	1415.62i	−0.336872	−	0.0697571i
$745$			7175.30i			0.352863i
$746$	−15973.9	+	23772.0i	−0.783977	+	1.16669i
$747$	−7843.86	+	7843.86i	−0.384193	+	0.384193i
$748$	−11752.2	+	27958.3i	−0.574469	+	1.36665i
$749$	7325.45	+	7325.45i	0.357365	+	0.357365i
$750$	−1912.34	−	9746.98i	−0.0931049	−	0.474546i
$751$	4501.15			0.218707			0.109354	−	0.994003i	$-0.465122\pi$
$751$	4501.15			0.218707			0.109354	+	0.994003i	$0.465122\pi$
$752$	24649.7	−	24139.8i	1.19532	−	1.17060i
$753$	−6331.69			−0.306427
$754$	2635.35	+	13432.1i	0.127286	+	0.648765i
$755$	7624.66	+	7624.66i	0.367536	+	0.367536i
$756$	4035.74	+	1696.42i	0.194151	+	0.0816111i
$757$	−3638.27	+	3638.27i	−0.174683	+	0.174683i	−0.789034	−	0.614350i	$-0.789418\pi$
$757$	−3638.27	+	3638.27i	−0.174683	+	0.174683i	0.614350	+	0.789034i	$0.289418\pi$
$758$	−8272.20	+	12310.5i	−0.396385	+	0.589890i
$759$		−	739.476i		−	0.0353640i
$760$	−9317.84	+	6120.90i	−0.444728	+	0.292143i
$761$			7208.65i			0.343381i	0.985151	+	0.171691i	$0.0549230\pi$
$761$			7208.65i			0.343381i	−0.985151	+	0.171691i	$0.945077\pi$
$762$	1962.07	+	1318.44i	0.0932787	+	0.0626799i
$763$	−28488.3	+	28488.3i	−1.35170	+	1.35170i
$764$	−21164.2	+	8637.22i	−1.00222	+	0.409010i
$765$	−1889.66	−	1889.66i	−0.0893085	−	0.0893085i
$766$	−4493.82	+	881.678i	−0.211969	+	0.0415879i
$767$	3958.75			0.186365
$768$	−8868.61	+	8505.45i	−0.416691	+	0.399627i
$769$	−6428.86			−0.301470			−0.150735	−	0.988574i	$-0.548164\pi$
$769$	−6428.86			−0.301470			−0.150735	+	0.988574i	$0.548164\pi$
$770$	−19921.4	+	3908.54i	−0.932362	+	0.182927i
$771$	6928.90	+	6928.90i	0.323655	+	0.323655i
$772$	−31987.4	+	13054.2i	−1.49126	+	0.608591i
$773$	21187.9	−	21187.9i	0.985867	−	0.985867i	−0.0140348	−	0.999902i	$-0.504468\pi$
$773$	21187.9	−	21187.9i	0.985867	−	0.985867i	0.999902	+	0.0140348i	$0.00446757\pi$
$774$	11143.3	+	7487.91i	0.517491	+	0.347735i
$775$		−	10002.9i		−	0.463633i
$776$	13713.8	−	9008.61i	0.634403	−	0.416740i
$777$		−	5746.28i		−	0.265311i
$778$	6983.48	−	10392.6i	0.321812	−	0.478913i
$779$	1956.25	−	1956.25i	0.0899742	−	0.0899742i
$780$	4591.70	+	1930.11i	0.210781	+	0.0886015i
$781$	−22992.9	−	22992.9i	−1.05346	−	1.05346i
$782$	112.544	+	573.623i	0.00514649	+	0.0262311i
$783$	−3315.99			−0.151346
$784$	−3098.91	+	3034.81i	−0.141168	+	0.138248i
$785$	−19839.1			−0.902021
$786$	−1539.22	−	7845.24i	−0.0698501	−	0.356019i
$787$	25780.3	+	25780.3i	1.16769	+	1.16769i	0.982751	+	0.184935i	$0.0592074\pi$
$787$	25780.3	+	25780.3i	1.16769	+	1.16769i	0.184935	+	0.982751i	$0.440793\pi$
$788$	−6141.18	+	14609.7i	−0.277627	+	0.660470i
$789$	−1894.93	+	1894.93i	−0.0855024	+	0.0855024i
$790$	8860.64	−	13186.2i	0.399047	−	0.593852i
$791$		−	5894.41i		−	0.264957i
$792$	13409.0	+	2776.64i	0.601601	+	0.124575i
$793$		−	8645.14i		−	0.387135i
$794$	15928.0	+	10703.0i	0.711918	+	0.478383i
$795$	6089.01	−	6089.01i	0.271641	−	0.271641i
$796$	6512.43	+	15957.7i	0.289983	+	0.710560i
$797$	19825.4	+	19825.4i	0.881121	+	0.881121i	0.993649	−	0.112528i	$-0.0358948\pi$
$797$	19825.4	+	19825.4i	0.881121	+	0.881121i	−0.112528	+	0.993649i	$0.535895\pi$
$798$	15787.1	−	3097.40i	0.700323	−	0.137402i
$799$	30392.8			1.34571
$800$	−14510.0	−	9971.87i	−0.641258	−	0.440699i
$801$	−1665.39			−0.0734628
$802$	−28934.5	+	5676.90i	−1.27396	+	0.249948i
$803$	−43210.0	−	43210.0i	−1.89894	−	1.89894i
$804$	2284.61	+	5598.08i	0.100214	+	0.245558i
$805$	−276.691	+	276.691i	−0.0121144	+	0.0121144i
$806$	9514.13	+	6393.15i	0.415783	+	0.279391i
$807$			11112.0i			0.484711i
$808$	7405.75	−	35764.0i	0.322443	−	1.55715i
$809$			40019.8i			1.73921i	0.493749	+	0.869605i	$0.335626\pi$
$809$			40019.8i			1.73921i	−0.493749	+	0.869605i	$0.664374\pi$
$810$	−672.982	+	1001.51i	−0.0291928	+	0.0434440i
$811$	−24193.5	+	24193.5i	−1.04753	+	1.04753i	−0.0487212	+	0.998812i	$0.515515\pi$
$811$	−24193.5	+	24193.5i	−1.04753	+	1.04753i	−0.998812	+	0.0487212i	$0.984485\pi$
$812$	7716.45	−	18357.3i	0.333490	−	0.793367i
$813$	−11507.5	−	11507.5i	−0.496414	−	0.496414i
$814$	−3460.49	−	17637.8i	−0.149005	−	0.759464i
$815$	−7477.45			−0.321379
$816$	−10824.1	−	113.115i	−0.464364	−	0.00485271i
$817$	49337.6			2.11274
$818$	−6733.91	−	34322.0i	−0.287831	−	1.46704i
$819$	−5082.54	−	5082.54i	−0.216848	−	0.216848i
$820$	−1148.69	−	482.848i	−0.0489194	−	0.0205632i
$821$	−18924.0	+	18924.0i	−0.804450	+	0.804450i	−0.983788	−	0.179338i	$-0.942605\pi$
$821$	−18924.0	+	18924.0i	−0.804450	+	0.804450i	0.179338	+	0.983788i	$0.442605\pi$
$822$	2993.74	−	4455.21i	0.127030	−	0.189043i
$823$			4894.21i			0.207292i	0.994614	+	0.103646i	$0.0330509\pi$
$823$			4894.21i			0.207292i	−0.994614	+	0.103646i	$0.966949\pi$
$824$	13658.8	+	20792.9i	0.577462	+	0.879070i
$825$			19620.0i			0.827975i
$826$	−4780.11	−	3212.06i	−0.201357	−	0.135305i
$827$	−19015.3	+	19015.3i	−0.799549	+	0.799549i	−0.983024	−	0.183475i	$-0.941265\pi$
$827$	−19015.3	+	19015.3i	−0.799549	+	0.799549i	0.183475	+	0.983024i	$0.441265\pi$
$828$	244.370	−	99.7288i	0.0102566	−	0.00418577i
$829$	−7608.33	−	7608.33i	−0.318755	−	0.318755i	0.529534	−	0.848289i	$-0.322367\pi$
$829$	−7608.33	−	7608.33i	−0.318755	−	0.318755i	−0.848289	+	0.529534i	$0.822367\pi$
$830$	18017.2	−	3534.93i	0.753477	−	0.147831i
$831$	−9514.33			−0.397170
$832$	18758.4	−	7427.69i	0.781646	−	0.309506i
$833$	−3820.93			−0.158928
$834$	12928.9	−	2536.62i	0.536799	−	0.105319i
$835$	−4774.55	−	4774.55i	−0.197880	−	0.197880i
$836$	46592.0	−	19014.4i	1.92753	−	0.786637i
$837$	−1963.51	+	1963.51i	−0.0810860	+	0.0810860i
$838$	6008.16	+	4037.27i	0.247671	+	0.166426i
$839$		−	31098.4i		−	1.27966i	−0.768517	−	0.639830i	$-0.779005\pi$
$839$		−	31098.4i		−	1.27966i	0.768517	−	0.639830i	$-0.220995\pi$
$840$	−3978.32	−	6056.19i	−0.163411	−	0.248760i
$841$		−	9305.65i		−	0.381551i
$842$	−5535.15	+	8237.27i	−0.226548	+	0.337144i
$843$	7685.27	−	7685.27i	0.313991	−	0.313991i
$844$	6920.46	+	2909.00i	0.282242	+	0.118640i
$845$	2399.23	+	2399.23i	0.0976759	+	0.0976759i
$846$	−2642.01	−	13466.1i	−0.107369	−	0.547249i
$847$	64661.1			2.62312
$848$	364.487	−	34878.3i	0.0147601	−	1.41241i
$849$	0.0269294			1.08859e−6
$850$	−2986.03	−	15219.5i	−0.120494	−	0.614146i
$851$	−244.972	−	244.972i	−0.00986786	−	0.00986786i
$852$	4497.40	−	10699.2i	0.180843	−	0.430222i
$853$	28324.9	−	28324.9i	1.13696	−	1.13696i	0.147968	−	0.988992i	$-0.452727\pi$
$853$	28324.9	−	28324.9i	1.13696	−	1.13696i	0.988992	−	0.147968i	$-0.0472733\pi$
$854$	−7014.51	+	10438.8i	−0.281068	+	0.418278i
$855$			4434.26i			0.177367i
$856$	−2345.25	+	11325.7i	−0.0936438	+	0.452226i
$857$			14990.8i			0.597520i	0.954328	+	0.298760i	$0.0965730\pi$
$857$			14990.8i			0.597520i	−0.954328	+	0.298760i	$0.903427\pi$
$858$	−18661.2	−	12539.7i	−0.742522	−	0.498948i
$859$	19751.5	−	19751.5i	0.784533	−	0.784533i	−0.196059	−	0.980592i	$-0.562815\pi$
$859$	19751.5	−	19751.5i	0.784533	−	0.784533i	0.980592	+	0.196059i	$0.0628146\pi$
$860$	−8396.39	−	20574.1i	−0.332924	−	0.815779i
$861$	1271.48	+	1271.48i	0.0503273	+	0.0503273i
$862$	13670.1	−	2682.04i	0.540145	−	0.105975i
$863$	−9084.96			−0.358349			−0.179175	−	0.983817i	$-0.557343\pi$
$863$	−9084.96			−0.358349			−0.179175	+	0.983817i	$0.557343\pi$
$864$	890.813	+	4805.66i	0.0350765	+	0.189227i
$865$	−14710.0			−0.578215
$866$	−37393.1	+	7336.45i	−1.46729	+	0.287879i
$867$	3679.28	+	3679.28i	0.144123	+	0.144123i
$868$	−6300.81	−	15439.2i	−0.246387	−	0.603733i
$869$	−50706.9	+	50706.9i	−1.97942	+	1.97942i
$870$	4555.57	+	3061.18i	0.177527	+	0.119292i
$871$		−	9927.32i		−	0.386193i
$872$	−44045.2	−	9120.57i	−1.71050	−	0.354199i
$873$		−	6526.26i		−	0.253013i
$874$	540.981	−	805.074i	0.0209370	−	0.0311580i
$875$	16776.1	−	16776.1i	0.648155	−	0.648155i
$876$	8451.88	−	20106.8i	0.325985	−	0.775511i
$877$	18336.8	+	18336.8i	0.706031	+	0.706031i	0.965698	−	0.259668i	$-0.0836130\pi$
$877$	18336.8	+	18336.8i	0.706031	+	0.706031i	−0.259668	+	0.965698i	$0.583613\pi$
$878$	7.49752	+	38.2141i	0.000288188	+	0.00146886i
$879$	105.805			0.00405995
$880$	−15858.3	−	16193.2i	−0.607480	−	0.620310i
$881$	13402.7			0.512543			0.256271	−	0.966605i	$-0.417506\pi$
$881$	13402.7			0.512543			0.256271	+	0.966605i	$0.417506\pi$
$882$	332.149	+	1692.93i	0.0126803	+	0.0646303i
$883$	16285.1	+	16285.1i	0.620656	+	0.620656i	0.945699	−	0.325044i	$-0.105379\pi$
$883$	16285.1	+	16285.1i	0.620656	+	0.620656i	−0.325044	+	0.945699i	$0.605379\pi$
$884$	16384.3	+	6887.10i	0.623374	+	0.262034i
$885$	1122.42	−	1122.42i	0.0426323	−	0.0426323i
$886$	251.567	−	374.376i	0.00953901	−	0.0141957i
$887$			35406.7i			1.34029i	0.742229	+	0.670146i	$0.233769\pi$
$887$			35406.7i			1.34029i	−0.742229	+	0.670146i	$0.766231\pi$
$888$	5361.95	−	3522.27i	0.202630	−	0.133108i
$889$			5646.29i			0.213015i
$890$	2287.95	+	1537.42i	0.0861710	+	0.0579038i
$891$	3851.28	−	3851.28i	0.144807	−	0.144807i
$892$	3205.65	−	1308.24i	0.120329	−	0.0491067i
$893$	−35659.7	−	35659.7i	−1.33629	−	1.33629i
$894$	11343.9	−	2225.65i	0.424382	−	0.0832628i
$895$	−494.138			−0.0184550
$896$	−28677.0	−	6251.44i	−1.06923	−	0.233087i
$897$	−433.352			−0.0161307
$898$	47446.3	−	9308.88i	1.76315	−	0.345926i
$899$	8931.39	+	8931.39i	0.331344	+	0.331344i
$900$	−6483.68	+	2646.03i	−0.240136	+	0.0980010i
$901$	21727.0	−	21727.0i	0.803365	−	0.803365i
$902$	4668.40	+	3137.00i	0.172329	+	0.115799i
$903$			32067.3i			1.18176i
$904$	5500.17	−	3613.06i	0.202359	−	0.132930i
$905$		−	2769.15i		−	0.101712i
$906$	9689.30	−	14419.4i	0.355304	−	0.528755i
$907$	−8884.93	+	8884.93i	−0.325269	+	0.325269i	−0.850784	−	0.525515i	$-0.823873\pi$
$907$	−8884.93	+	8884.93i	−0.325269	+	0.325269i	0.525515	+	0.850784i	$0.323873\pi$
$908$	5032.81	+	2115.53i	0.183942	+	0.0773199i
$909$	−10272.0	−	10272.0i	−0.374809	−	0.374809i
$910$	2290.51	+	11674.5i	0.0834392	+	0.425280i
$911$	16668.9			0.606219			0.303110	−	0.952956i	$-0.401975\pi$
$911$	16668.9			0.606219			0.303110	+	0.952956i	$0.401975\pi$
$912$	12567.2	+	12832.6i	0.456295	+	0.465932i
$913$	−82877.8			−3.00422
$914$	2218.52	+	11307.6i	0.0802867	+	0.409213i
$915$	−2451.14	−	2451.14i	−0.0885596	−	0.0885596i
$916$	−11913.4	+	28341.7i	−0.429726	+	1.02231i
$917$	13502.9	−	13502.9i	0.486266	−	0.486266i
$918$	−2401.36	+	3573.64i	−0.0863362	+	0.128483i
$919$		−	26028.5i		−	0.934276i	−0.884184	−	0.467138i	$-0.845285\pi$
$919$		−	26028.5i		−	0.934276i	0.884184	−	0.467138i	$-0.154715\pi$
$920$	−427.786	−	88.5828i	−0.0153301	−	0.00317445i
$921$			2625.16i			0.0939218i
$922$	−7733.77	−	5196.82i	−0.276245	−	0.185627i
$923$	−13474.4	+	13474.4i	−0.480516	+	0.480516i
$924$	12358.6	+	30282.8i	0.440008	+	1.07817i
$925$	6499.66	+	6499.66i	0.231035	+	0.231035i
$926$	−34549.6	+	6778.55i	−1.22610	+	0.240558i
$927$	9895.10			0.350591
$928$	21859.4	−	4052.02i	0.773243	−	0.143334i
$929$	−13806.2			−0.487584			−0.243792	−	0.969828i	$-0.578391\pi$
$929$	−13806.2			−0.487584			−0.243792	+	0.969828i	$0.578391\pi$
$930$	4510.15	−	884.882i	0.159025	−	0.0312005i
$931$	4483.07	+	4483.07i	0.157816	+	0.157816i
$932$	−3670.84	−	8994.83i	−0.129015	−	0.316132i
$933$	8875.43	−	8875.43i	0.311435	−	0.311435i
$934$	−1218.25	−	818.623i	−0.0426793	−	0.0286790i
$935$		−	19966.1i		−	0.698354i
$936$	1627.18	−	7858.02i	0.0568227	−	0.274410i
$937$		−	1798.08i		−	0.0626901i	−0.999509	−	0.0313451i	$-0.990021\pi$
$937$		−	1798.08i		−	0.0626901i	0.999509	−	0.0313451i	$-0.00997908\pi$
$938$	−8054.85	+	11987.0i	−0.280384	+	0.417260i
$939$	−4506.08	+	4506.08i	−0.156603	+	0.156603i
$940$	−8801.65	+	20939.0i	−0.305402	+	0.726546i
$941$	−8722.11	−	8722.11i	−0.302160	−	0.302160i	0.539698	−	0.841858i	$-0.318538\pi$
$941$	−8722.11	−	8722.11i	−0.302160	−	0.302160i	−0.841858	+	0.539698i	$0.818538\pi$
$942$	6153.73	+	31364.9i	0.212844	+	1.08485i
$943$	108.410			0.00374371
$944$	67.1875	−	6429.28i	0.00231649	−	0.221669i
$945$	−2882.08			−0.0992106
$946$	19311.4	+	98428.2i	0.663708	+	3.38285i
$947$	15872.2	+	15872.2i	0.544644	+	0.544644i	0.924887	−	0.380243i	$-0.124160\pi$
$947$	15872.2	+	15872.2i	0.544644	+	0.544644i	−0.380243	+	0.924887i	$0.624160\pi$
$948$	−23595.3	−	9918.26i	−0.808376	−	0.339800i
$949$	−25322.2	+	25322.2i	−0.866168	+	0.866168i
$950$	−14353.4	+	21360.4i	−0.490197	+	0.729498i
$951$		−	4518.21i		−	0.154062i
$952$	−14195.6	−	21609.9i	−0.483279	−	0.735695i
$953$			34643.6i			1.17756i	0.808292	+	0.588782i	$0.200392\pi$
$953$			34643.6i			1.17756i	−0.808292	+	0.588782i	$0.799608\pi$
$954$	−11515.2	−	7737.83i	−0.390796	−	0.262601i
$955$	10641.2	−	10641.2i	0.360566	−	0.360566i
$956$	19823.7	−	8090.17i	0.670654	−	0.273698i
$957$	−17518.2	−	17518.2i	−0.591729	−	0.591729i
$958$	−51231.5	+	10051.5i	−1.72778	+	0.338987i
$959$	12820.8			0.431706
$960$	3212.56	−	7424.47i	0.108005	−	0.249608i
$961$	−19213.8			−0.644953
$962$	−10336.2	+	2027.94i	−0.346416	+	0.0679661i
$963$	3252.94	+	3252.94i	0.108852	+	0.108852i
$964$	−17893.7	+	7302.52i	−0.597840	+	0.243982i
$965$	16083.0	−	16083.0i	0.536508	−	0.536508i
$966$	523.263	+	351.614i	0.0174283	+	0.0117112i
$967$		−	22531.8i		−	0.749301i	−0.927166	−	0.374650i	$-0.877763\pi$
$967$		−	22531.8i		−	0.749301i	0.927166	−	0.374650i	$-0.122237\pi$
$968$	39635.0	+	60336.4i	1.31603	+	2.00339i
$969$			15822.5i			0.524553i
$970$	−6024.77	+	8965.90i	−0.199426	+	0.296781i
$971$	5854.80	−	5854.80i	0.193501	−	0.193501i	−0.603706	−	0.797207i	$-0.706310\pi$
$971$	5854.80	−	5854.80i	0.193501	−	0.193501i	0.797207	+	0.603706i	$0.206310\pi$
$972$	1792.11	+	753.310i	0.0591378	+	0.0248585i
$973$	22252.7	+	22252.7i	0.733184	+	0.733184i
$974$	2113.15	+	10770.5i	0.0695171	+	0.354321i
$975$	11497.8			0.377666
$976$	−14040.3	−	146.724i	−0.460470	−	0.00481202i
$977$	50312.5			1.64753			0.823766	−	0.566930i	$-0.191869\pi$
$977$	50312.5			1.64753			0.823766	+	0.566930i	$0.191869\pi$
$978$	2319.38	+	11821.6i	0.0758338	+	0.386517i
$979$	−8798.21	−	8798.21i	−0.287224	−	0.287224i
$980$	1106.53	−	2632.41i	0.0360681	−	0.0858053i
$981$	−12650.5	+	12650.5i	−0.411723	+	0.411723i
$982$	−8685.57	+	12925.7i	−0.282248	+	0.420035i
$983$		−	1796.13i		−	0.0582783i	−0.999575	−	0.0291391i	$-0.990723\pi$
$983$		−	1796.13i		−	0.0582783i	0.999575	−	0.0291391i	$-0.00927659\pi$
$984$	−407.065	+	1965.81i	−0.0131878	+	0.0636867i
$985$		−	10433.4i		−	0.337498i
$986$	16255.3	+	10923.0i	0.525026	+	0.352798i
$987$	23177.3	−	23177.3i	0.747457	−	0.747457i
$988$	−11143.0	−	27304.1i	−0.358811	−	0.879211i
$989$	1367.08	+	1367.08i	0.0439540	+	0.0439540i
$990$	−8846.32	+	1735.63i	−0.283994	+	0.0557191i
$991$	−32363.5			−1.03740			−0.518698	−	0.854958i	$-0.673583\pi$
$991$	−32363.5			−1.03740			−0.518698	+	0.854958i	$0.673583\pi$
$992$	10544.4	−	15343.1i	0.337484	−	0.491072i
$993$	7575.45			0.242094
$994$	27203.0	−	5337.17i	0.868034	−	0.170306i
$995$	−8023.40	−	8023.40i	−0.255637	−	0.255637i
$996$	−11177.2	−	27388.1i	−0.355587	−	0.871311i
$997$	680.434	−	680.434i	0.0216144	−	0.0216144i	−0.696217	−	0.717831i	$-0.745135\pi$
$997$	680.434	−	680.434i	0.0216144	−	0.0216144i	0.717831	+	0.696217i	$0.245135\pi$
$998$	16805.7	+	11292.9i	0.533042	+	0.358185i
$999$		−	2551.69i		−	0.0808128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.13.1	✓	24
3.2	odd	2		144.4.k.b.109.12		24
4.3	odd	2		192.4.j.a.145.9		24
8.3	odd	2		384.4.j.a.289.5		24
8.5	even	2		384.4.j.b.289.8		24
12.11	even	2		576.4.k.b.145.8		24
16.3	odd	4		384.4.j.a.97.5		24
16.5	even	4	inner	48.4.j.a.37.1	yes	24
16.11	odd	4		192.4.j.a.49.9		24
16.13	even	4		384.4.j.b.97.8		24
48.5	odd	4		144.4.k.b.37.12		24
48.11	even	4		576.4.k.b.433.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.1	✓	24	1.1	even	1	trivial
48.4.j.a.37.1	yes	24	16.5	even	4	inner
144.4.k.b.37.12		24	48.5	odd	4
144.4.k.b.109.12		24	3.2	odd	2
192.4.j.a.49.9		24	16.11	odd	4
192.4.j.a.145.9		24	4.3	odd	2
384.4.j.a.97.5		24	16.3	odd	4
384.4.j.a.289.5		24	8.3	odd	2
384.4.j.b.97.8		24	16.13	even	4
384.4.j.b.289.8		24	8.5	even	2
576.4.k.b.145.8		24	12.11	even	2
576.4.k.b.433.8		24	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.77551 + 0.544550i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(7.40693 - 3.02281i) q^{4} +(-3.72414 + 3.72414i) q^{5} +(7.04291 + 4.73259i) q^{6} +20.2675i q^{7} +(-18.9120 + 12.4233i) q^{8} +9.00000i q^{9} +O(q^{10})\)	\(q+(-2.77551 + 0.544550i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(7.40693 - 3.02281i) q^{4} +(-3.72414 + 3.72414i) q^{5} +(7.04291 + 4.73259i) q^{6} +20.2675i q^{7} +(-18.9120 + 12.4233i) q^{8} +9.00000i q^{9} +(8.30842 - 12.3644i) q^{10} +(-47.5467 + 47.5467i) q^{11} +(-22.1248 - 9.30013i) q^{12} +(27.8636 + 27.8636i) q^{13} +(-11.0367 - 56.2527i) q^{14} +15.8002 q^{15} +(45.7253 - 44.7795i) q^{16} +56.3788 q^{17} +(-4.90095 - 24.9796i) q^{18} +(-66.1489 - 66.1489i) q^{19} +(-16.3271 + 38.8418i) q^{20} +(42.9939 - 42.9939i) q^{21} +(106.075 - 157.858i) q^{22} -3.66579i q^{23} +(66.4721 + 13.7646i) q^{24} +97.2615i q^{25} +(-92.5089 - 62.1627i) q^{26} +(19.0919 - 19.0919i) q^{27} +(61.2648 + 150.120i) q^{28} +(-86.8428 - 86.8428i) q^{29} +(-43.8536 + 8.60399i) q^{30} -102.846 q^{31} +(-102.526 + 149.186i) q^{32} +201.724 q^{33} +(-156.480 + 30.7011i) q^{34} +(-75.4791 - 75.4791i) q^{35} +(27.2053 + 66.6624i) q^{36} +(66.8267 - 66.8267i) q^{37} +(219.618 + 147.576i) q^{38} -118.215i q^{39} +(24.1647 - 116.697i) q^{40} +29.5734i q^{41} +(-95.9178 + 142.742i) q^{42} +(-372.929 + 372.929i) q^{43} +(-208.451 + 495.900i) q^{44} +(-33.5173 - 33.5173i) q^{45} +(1.99620 + 10.1744i) q^{46} +539.082 q^{47} +(-191.990 - 2.00634i) q^{48} -67.7725 q^{49} +(-52.9637 - 269.951i) q^{50} +(-119.598 - 119.598i) q^{51} +(290.610 + 122.158i) q^{52} +(385.376 - 385.376i) q^{53} +(-42.5933 + 63.3862i) q^{54} -354.142i q^{55} +(-251.789 - 383.298i) q^{56} +280.646i q^{57} +(288.323 + 193.743i) q^{58} +(71.0380 - 71.0380i) q^{59} +(117.031 - 47.7610i) q^{60} +(-155.133 - 155.133i) q^{61} +(285.449 - 56.0045i) q^{62} -182.408 q^{63} +(203.324 - 469.897i) q^{64} -207.536 q^{65} +(-559.886 + 109.849i) q^{66} +(-178.141 - 178.141i) q^{67} +(417.594 - 170.422i) q^{68} +(-7.77631 + 7.77631i) q^{69} +(250.595 + 168.391i) q^{70} +483.585i q^{71} +(-111.810 - 170.208i) q^{72} +908.791i q^{73} +(-149.088 + 221.869i) q^{74} +(206.323 - 206.323i) q^{75} +(-689.916 - 290.005i) q^{76} +(-963.654 - 963.654i) q^{77} +(64.3741 + 328.108i) q^{78} +1066.46 q^{79} +(-3.52228 + 337.053i) q^{80} -81.0000 q^{81} +(-16.1042 - 82.0814i) q^{82} +(871.541 + 871.541i) q^{83} +(188.491 - 448.415i) q^{84} +(-209.963 + 209.963i) q^{85} +(831.990 - 1238.15i) q^{86} +368.443i q^{87} +(308.515 - 1489.89i) q^{88} +185.044i q^{89} +(111.279 + 74.7758i) q^{90} +(-564.727 + 564.727i) q^{91} +(-11.0810 - 27.1522i) q^{92} +(218.168 + 218.168i) q^{93} +(-1496.23 + 293.557i) q^{94} +492.696 q^{95} +(533.962 - 98.9792i) q^{96} -725.140 q^{97} +(188.103 - 36.9055i) q^{98} +(-427.921 - 427.921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

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