LMFDB - Embedded newform 230.4.e.a.137.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.e (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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.6
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(-3.58924 + 3.58924i) q^{3} +4.00000i q^{4} +(11.1634 + 0.614616i) q^{5} +10.1519 q^{6} +(-16.2976 + 16.2976i) q^{7} +(5.65685 - 5.65685i) q^{8} +1.23476i q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(-3.58924 + 3.58924i) q^{3} +4.00000i q^{4} +(11.1634 + 0.614616i) q^{5} +10.1519 q^{6} +(-16.2976 + 16.2976i) q^{7} +(5.65685 - 5.65685i) q^{8} +1.23476i q^{9} +(-14.9183 - 16.6567i) q^{10} +34.5362i q^{11} +(-14.3569 - 14.3569i) q^{12} +(23.5981 - 23.5981i) q^{13} +46.0964 q^{14} +(-42.2742 + 37.8622i) q^{15} -16.0000 q^{16} +(55.6511 - 55.6511i) q^{17} +(1.74622 - 1.74622i) q^{18} -29.0874 q^{19} +(-2.45846 + 44.6537i) q^{20} -116.992i q^{21} +(48.8416 - 48.8416i) q^{22} +(-109.205 - 15.5323i) q^{23} +40.6076i q^{24} +(124.244 + 13.7224i) q^{25} -66.7456 q^{26} +(-101.341 - 101.341i) q^{27} +(-65.1902 - 65.1902i) q^{28} +293.672i q^{29} +(113.330 + 6.23951i) q^{30} -254.453 q^{31} +(22.6274 + 22.6274i) q^{32} +(-123.959 - 123.959i) q^{33} -157.405 q^{34} +(-191.953 + 171.920i) q^{35} -4.93905 q^{36} +(-82.6349 + 82.6349i) q^{37} +(41.1358 + 41.1358i) q^{38} +169.399i q^{39} +(66.6267 - 59.6731i) q^{40} -292.497 q^{41} +(-165.451 + 165.451i) q^{42} +(-295.293 - 295.293i) q^{43} -138.145 q^{44} +(-0.758904 + 13.7842i) q^{45} +(132.473 + 176.405i) q^{46} +(277.347 + 277.347i) q^{47} +(57.4278 - 57.4278i) q^{48} -188.220i q^{49} +(-156.302 - 195.115i) q^{50} +399.490i q^{51} +(94.3925 + 94.3925i) q^{52} +(-185.792 - 185.792i) q^{53} +286.636i q^{54} +(-21.2265 + 385.543i) q^{55} +184.386i q^{56} +(104.402 - 104.402i) q^{57} +(415.314 - 415.314i) q^{58} +26.0941i q^{59} +(-151.449 - 169.097i) q^{60} -191.833i q^{61} +(359.851 + 359.851i) q^{62} +(-20.1236 - 20.1236i) q^{63} -64.0000i q^{64} +(277.940 - 248.932i) q^{65} +350.608i q^{66} +(-94.6227 + 94.6227i) q^{67} +(222.604 + 222.604i) q^{68} +(447.712 - 336.214i) q^{69} +(514.595 + 28.3316i) q^{70} +17.9990 q^{71} +(6.98487 + 6.98487i) q^{72} +(-272.645 + 272.645i) q^{73} +233.727 q^{74} +(-495.196 + 396.690i) q^{75} -116.350i q^{76} +(-562.856 - 562.856i) q^{77} +(239.566 - 239.566i) q^{78} +1034.70 q^{79} +(-178.615 - 9.83385i) q^{80} +694.137 q^{81} +(413.653 + 413.653i) q^{82} +(-819.532 - 819.532i) q^{83} +467.966 q^{84} +(655.461 - 587.053i) q^{85} +835.215i q^{86} +(-1054.06 - 1054.06i) q^{87} +(195.366 + 195.366i) q^{88} -394.478 q^{89} +(20.5670 - 18.4205i) q^{90} +769.184i q^{91} +(62.1294 - 436.820i) q^{92} +(913.292 - 913.292i) q^{93} -784.455i q^{94} +(-324.716 - 17.8776i) q^{95} -162.430 q^{96} +(-587.067 + 587.067i) q^{97} +(-266.184 + 266.184i) q^{98} -42.6441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) $ 72 * q - 16 * q^3 - 16 * q^6	$ 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) $ 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	−3.58924	+	3.58924i	−0.690749	+	0.690749i	−0.962397	−	0.271648i	$-0.912431\pi$
$3$	−3.58924	+	3.58924i	−0.690749	+	0.690749i	0.271648	+	0.962397i	$0.412431\pi$
$4$			4.00000i			0.500000i
$5$	11.1634	+	0.614616i	0.998488	+	0.0549729i
$5$	11.1634	+	0.614616i	0.998488	+	0.0549729i
$6$	10.1519			0.690749
$7$	−16.2976	+	16.2976i	−0.879985	+	0.879985i	−0.993533	−	0.113547i	$-0.963779\pi$
$7$	−16.2976	+	16.2976i	−0.879985	+	0.879985i	0.113547	+	0.993533i	$0.463779\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$			1.23476i			0.0457320i
$10$	−14.9183	−	16.6567i	−0.471757	−	0.526730i
$11$			34.5362i			0.946642i	0.880890	+	0.473321i	$0.156945\pi$
$11$			34.5362i			0.946642i	−0.880890	+	0.473321i	$0.843055\pi$
$12$	−14.3569	−	14.3569i	−0.345374	−	0.345374i
$13$	23.5981	−	23.5981i	0.503457	−	0.503457i	−0.409053	−	0.912511i	$-0.634141\pi$
$13$	23.5981	−	23.5981i	0.503457	−	0.503457i	0.912511	+	0.409053i	$0.134141\pi$
$14$	46.0964			0.879985
$15$	−42.2742	+	37.8622i	−0.727677	+	0.651732i
$16$	−16.0000			−0.250000
$17$	55.6511	−	55.6511i	0.793963	−	0.793963i	−0.188173	−	0.982136i	$-0.560256\pi$
$17$	55.6511	−	55.6511i	0.793963	−	0.793963i	0.982136	+	0.188173i	$0.0602565\pi$
$18$	1.74622	−	1.74622i	0.0228660	−	0.0228660i
$19$	−29.0874			−0.351217			−0.175608	−	0.984460i	$-0.556189\pi$
$19$	−29.0874			−0.351217			−0.175608	+	0.984460i	$0.556189\pi$
$20$	−2.45846	+	44.6537i	−0.0274864	+	0.499244i
$21$		−	116.992i		−	1.21570i
$22$	48.8416	−	48.8416i	0.473321	−	0.473321i
$23$	−109.205	−	15.5323i	−0.990036	−	0.140814i
$23$	−109.205	−	15.5323i	−0.990036	−	0.140814i
$24$			40.6076i			0.345374i
$25$	124.244	+	13.7224i	0.993956	+	0.109780i
$26$	−66.7456			−0.503457
$27$	−101.341	−	101.341i	−0.722338	−	0.722338i
$28$	−65.1902	−	65.1902i	−0.439993	−	0.439993i
$29$			293.672i			1.88046i	0.340535	+	0.940232i	$0.389392\pi$
$29$			293.672i			1.88046i	−0.340535	+	0.940232i	$0.610608\pi$
$30$	113.330	+	6.23951i	0.689704	+	0.0379725i
$31$	−254.453			−1.47423			−0.737115	−	0.675767i	$-0.763812\pi$
$31$	−254.453			−1.47423			−0.737115	+	0.675767i	$0.763812\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−123.959	−	123.959i	−0.653892	−	0.653892i
$34$	−157.405			−0.793963
$35$	−191.953	+	171.920i	−0.927030	+	0.830279i
$36$	−4.93905			−0.0228660
$37$	−82.6349	+	82.6349i	−0.367165	+	0.367165i	−0.866442	−	0.499277i	$-0.833599\pi$
$37$	−82.6349	+	82.6349i	−0.367165	+	0.367165i	0.499277	+	0.866442i	$0.333599\pi$
$38$	41.1358	+	41.1358i	0.175608	+	0.175608i
$39$			169.399i			0.695525i
$40$	66.6267	−	59.6731i	0.263365	−	0.235879i
$41$	−292.497			−1.11415			−0.557077	−	0.830461i	$-0.688077\pi$
$41$	−292.497			−1.11415			−0.557077	+	0.830461i	$0.688077\pi$
$42$	−165.451	+	165.451i	−0.607849	+	0.607849i
$43$	−295.293	−	295.293i	−1.04725	−	1.04725i	−0.998827	−	0.0484242i	$-0.984580\pi$
$43$	−295.293	−	295.293i	−1.04725	−	1.04725i	−0.0484242	−	0.998827i	$-0.515420\pi$
$44$	−138.145			−0.473321
$45$	−0.758904	+	13.7842i	−0.00251402	+	0.0456628i
$46$	132.473	+	176.405i	0.424611	+	0.565425i
$47$	277.347	+	277.347i	0.860748	+	0.860748i	0.991425	−	0.130677i	$-0.0417150\pi$
$47$	277.347	+	277.347i	0.860748	+	0.860748i	−0.130677	+	0.991425i	$0.541715\pi$
$48$	57.4278	−	57.4278i	0.172687	−	0.172687i
$49$		−	188.220i		−	0.548747i
$50$	−156.302	−	195.115i	−0.442088	−	0.551868i
$51$			399.490i			1.09686i
$52$	94.3925	+	94.3925i	0.251729	+	0.251729i
$53$	−185.792	−	185.792i	−0.481519	−	0.481519i	0.424097	−	0.905617i	$-0.360591\pi$
$53$	−185.792	−	185.792i	−0.481519	−	0.481519i	−0.905617	+	0.424097i	$0.860591\pi$
$54$			286.636i			0.722338i
$55$	−21.2265	+	385.543i	−0.0520397	+	0.945211i
$56$			184.386i			0.439993i
$57$	104.402	−	104.402i	0.242602	−	0.242602i
$58$	415.314	−	415.314i	0.940232	−	0.940232i
$59$			26.0941i			0.0575789i	0.999585	+	0.0287895i	$0.00916524\pi$
$59$			26.0941i			0.0575789i	−0.999585	+	0.0287895i	$0.990835\pi$
$60$	−151.449	−	169.097i	−0.325866	−	0.363838i
$61$		−	191.833i		−	0.402652i	−0.979524	−	0.201326i	$-0.935475\pi$
$61$		−	191.833i		−	0.402652i	0.979524	−	0.201326i	$-0.0645250\pi$
$62$	359.851	+	359.851i	0.737115	+	0.737115i
$63$	−20.1236	−	20.1236i	−0.0402434	−	0.0402434i
$64$		−	64.0000i		−	0.125000i
$65$	277.940	−	248.932i	0.530372	−	0.475019i
$66$			350.608i			0.653892i
$67$	−94.6227	+	94.6227i	−0.172537	+	0.172537i	−0.788093	−	0.615556i	$-0.788932\pi$
$67$	−94.6227	+	94.6227i	−0.172537	+	0.172537i	0.615556	+	0.788093i	$0.288932\pi$
$68$	222.604	+	222.604i	0.396982	+	0.396982i
$69$	447.712	−	336.214i	0.781133	−	0.586599i
$70$	514.595	+	28.3316i	0.878654	+	0.0483753i
$71$	17.9990			0.0300857			0.0150429	−	0.999887i	$-0.495212\pi$
$71$	17.9990			0.0300857			0.0150429	+	0.999887i	$0.495212\pi$
$72$	6.98487	+	6.98487i	0.0114330	+	0.0114330i
$73$	−272.645	+	272.645i	−0.437132	+	0.437132i	−0.891046	−	0.453914i	$-0.850027\pi$
$73$	−272.645	+	272.645i	−0.437132	+	0.437132i	0.453914	+	0.891046i	$0.350027\pi$
$74$	233.727			0.367165
$75$	−495.196	+	396.690i	−0.762404	+	0.610744i
$76$		−	116.350i		−	0.175608i
$77$	−562.856	−	562.856i	−0.833031	−	0.833031i
$78$	239.566	−	239.566i	0.347763	−	0.347763i
$79$	1034.70			1.47358			0.736788	−	0.676123i	$-0.236341\pi$
$79$	1034.70			1.47358			0.736788	+	0.676123i	$0.236341\pi$
$80$	−178.615	−	9.83385i	−0.249622	−	0.0137432i
$81$	694.137			0.952177
$82$	413.653	+	413.653i	0.557077	+	0.557077i
$83$	−819.532	−	819.532i	−1.08380	−	1.08380i	−0.996152	−	0.0876480i	$-0.972065\pi$
$83$	−819.532	−	819.532i	−1.08380	−	1.08380i	−0.0876480	−	0.996152i	$-0.527935\pi$
$84$	467.966			0.607849
$85$	655.461	−	587.053i	0.836409	−	0.749116i
$86$			835.215i			1.04725i
$87$	−1054.06	−	1054.06i	−1.29893	−	1.29893i
$88$	195.366	+	195.366i	0.236661	+	0.236661i
$89$	−394.478			−0.469827			−0.234914	−	0.972016i	$-0.575481\pi$
$89$	−394.478			−0.469827			−0.234914	+	0.972016i	$0.575481\pi$
$90$	20.5670	−	18.4205i	0.0240884	−	0.0215744i
$91$			769.184i			0.886070i
$92$	62.1294	−	436.820i	0.0704069	−	0.495018i
$93$	913.292	−	913.292i	1.01832	−	1.01832i
$94$		−	784.455i		−	0.860748i
$95$	−324.716	−	17.8776i	−0.350685	−	0.0193074i
$96$	−162.430			−0.172687
$97$	−587.067	+	587.067i	−0.614512	+	0.614512i	−0.944118	−	0.329606i	$-0.893084\pi$
$97$	−587.067	+	587.067i	−0.614512	+	0.614512i	0.329606	+	0.944118i	$0.393084\pi$
$98$	−266.184	+	266.184i	−0.274374	+	0.274374i
$99$	−42.6441			−0.0432918
$100$	−54.8898	+	496.978i	−0.0548898	+	0.496978i
$101$	−1486.26			−1.46424			−0.732120	−	0.681176i	$-0.761469\pi$
$101$	−1486.26			−1.46424			−0.732120	+	0.681176i	$0.761469\pi$
$102$	564.964	−	564.964i	0.548429	−	0.548429i
$103$	−296.856	−	296.856i	−0.283981	−	0.283981i	0.550713	−	0.834695i	$-0.314356\pi$
$103$	−296.856	−	296.856i	−0.283981	−	0.283981i	−0.834695	+	0.550713i	$0.814356\pi$
$104$		−	266.982i		−	0.251729i
$105$	71.9048	−	1306.03i	0.0668304	−	1.21386i
$106$			525.500i			0.481519i
$107$	496.586	−	496.586i	0.448662	−	0.448662i	−0.446248	−	0.894909i	$-0.647240\pi$
$107$	496.586	−	496.586i	0.448662	−	0.448662i	0.894909	+	0.446248i	$0.147240\pi$
$108$	405.365	−	405.365i	0.361169	−	0.361169i
$109$	1517.89			1.33383			0.666915	−	0.745133i	$-0.267614\pi$
$109$	1517.89			1.33383			0.666915	+	0.745133i	$0.267614\pi$
$110$	575.259	−	515.221i	0.498625	−	0.446586i
$111$		−	593.192i		−	0.507237i
$112$	260.761	−	260.761i	0.219996	−	0.219996i
$113$	425.791	+	425.791i	0.354469	+	0.354469i	0.861769	−	0.507300i	$-0.169356\pi$
$113$	425.791	+	425.791i	0.354469	+	0.354469i	−0.507300	+	0.861769i	$0.669356\pi$
$114$	−295.293			−0.242602
$115$	−1209.56	−	240.513i	−0.980798	−	0.195026i
$116$	−1174.69			−0.940232
$117$	29.1381	+	29.1381i	0.0230241	+	0.0230241i
$118$	36.9026	−	36.9026i	0.0287895	−	0.0287895i
$119$			1813.95i			1.39735i
$120$	−24.9580	+	453.320i	−0.0189862	+	0.344852i
$121$	138.249			0.103868
$122$	−271.293	+	271.293i	−0.201326	+	0.201326i
$123$	1049.84	−	1049.84i	0.769601	−	0.769601i
$124$		−	1017.81i		−	0.737115i
$125$	1378.56	+	229.552i	0.986418	+	0.164254i
$126$			56.9182i			0.0402434i
$127$	1967.47	+	1967.47i	1.37468	+	1.37468i	0.853363	+	0.521317i	$0.174559\pi$
$127$	1967.47	+	1967.47i	1.37468	+	1.37468i	0.521317	+	0.853363i	$0.325441\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	2119.75			1.44677
$130$	−745.110	−	41.0229i	−0.502696	−	0.0276765i
$131$	2260.95			1.50794			0.753971	−	0.656908i	$-0.228136\pi$
$131$	2260.95			1.50794			0.753971	+	0.656908i	$0.228136\pi$
$132$	495.835	−	495.835i	0.326946	−	0.326946i
$133$	474.054	−	474.054i	0.309065	−	0.309065i
$134$	267.633			0.172537
$135$	−1069.03	−	1193.60i	−0.681537	−	0.760955i
$136$		−	629.620i		−	0.396982i
$137$	1431.87	−	1431.87i	0.892940	−	0.892940i	−0.101858	−	0.994799i	$-0.532479\pi$
$137$	1431.87	−	1431.87i	0.892940	−	0.892940i	0.994799	+	0.101858i	$0.0324789\pi$
$138$	−1108.64	−	157.683i	−0.683866	−	0.0972670i
$139$			2049.70i			1.25074i	0.780328	+	0.625371i	$0.215052\pi$
$139$			2049.70i			1.25074i	−0.780328	+	0.625371i	$0.784948\pi$
$140$	−687.680	−	767.813i	−0.415140	−	0.463515i
$141$	−1990.93			−1.18912
$142$	−25.4544	−	25.4544i	−0.0150429	−	0.0150429i
$143$	814.991	+	814.991i	0.476594	+	0.476594i
$144$		−	19.7562i		−	0.0114330i
$145$	−180.495	+	3278.38i	−0.103375	+	1.87762i
$146$	771.156			0.437132
$147$	675.567	+	675.567i	0.379047	+	0.379047i
$148$	−330.540	−	330.540i	−0.183582	−	0.183582i
$149$	−2654.25			−1.45936			−0.729679	−	0.683790i	$-0.760330\pi$
$149$	−2654.25			−1.45936			−0.729679	+	0.683790i	$0.760330\pi$
$150$	1261.32	+	139.309i	0.686574	+	0.0758301i
$151$	−340.342			−0.183422			−0.0917108	−	0.995786i	$-0.529234\pi$
$151$	−340.342			−0.183422			−0.0917108	+	0.995786i	$0.529234\pi$
$152$	−164.543	+	164.543i	−0.0878041	+	0.0878041i
$153$	68.7159	+	68.7159i	0.0363095	+	0.0363095i
$154$			1592.00i			0.833031i
$155$	−2840.57	−	156.391i	−1.47200	−	0.0810427i
$156$	−677.594			−0.347763
$157$	−2167.14	+	2167.14i	−1.10163	+	1.10163i	−0.107419	+	0.994214i	$0.534259\pi$
$157$	−2167.14	+	2167.14i	−1.10163	+	1.10163i	−0.994214	+	0.107419i	$0.965741\pi$
$158$	−1463.28	−	1463.28i	−0.736788	−	0.736788i
$159$	1333.70			0.665218
$160$	238.693	+	266.507i	0.117939	+	0.131683i
$161$	2032.91	−	1526.64i	0.995131	−	0.747303i
$162$	−981.658	−	981.658i	−0.476088	−	0.476088i
$163$	932.254	−	932.254i	0.447974	−	0.447974i	−0.446707	−	0.894681i	$-0.647403\pi$
$163$	932.254	−	932.254i	0.447974	−	0.447974i	0.894681	+	0.446707i	$0.147403\pi$
$164$		−	1169.99i		−	0.557077i
$165$	−1307.62	−	1459.99i	−0.616957	−	0.688850i
$166$			2317.99i			1.08380i
$167$	−1559.83	−	1559.83i	−0.722774	−	0.722774i	0.246395	−	0.969169i	$-0.420754\pi$
$167$	−1559.83	−	1559.83i	−0.722774	−	0.722774i	−0.969169	+	0.246395i	$0.920754\pi$
$168$	−661.804	−	661.804i	−0.303924	−	0.303924i
$169$			1083.26i			0.493062i
$170$	−1757.18	−	96.7436i	−0.792763	−	0.0436464i
$171$		−	35.9161i		−	0.0160618i
$172$	1181.17	−	1181.17i	0.523626	−	0.523626i
$173$	782.352	−	782.352i	0.343821	−	0.343821i	−0.513980	−	0.857802i	$-0.671830\pi$
$173$	782.352	−	782.352i	0.343821	−	0.343821i	0.857802	+	0.513980i	$0.171830\pi$
$174$			2981.32i			1.29893i
$175$	−2248.52	+	1801.24i	−0.971271	+	0.778062i
$176$		−	552.580i		−	0.236661i
$177$	−93.6577	−	93.6577i	−0.0397726	−	0.0397726i
$178$	557.877	+	557.877i	0.234914	+	0.234914i
$179$			3066.88i			1.28061i	0.768120	+	0.640306i	$0.221193\pi$
$179$			3066.88i			1.28061i	−0.768120	+	0.640306i	$0.778807\pi$
$180$	−55.1368	−	3.03562i	−0.0228314	−	0.00125701i
$181$			1873.27i			0.769276i	0.923068	+	0.384638i	$0.125674\pi$
$181$			1873.27i			0.769276i	−0.923068	+	0.384638i	$0.874326\pi$
$182$	1087.79	−	1087.79i	0.443035	−	0.443035i
$183$	688.535	+	688.535i	0.278131	+	0.278131i
$184$	−705.621	+	529.893i	−0.282712	+	0.212306i
$185$	−973.278	+	871.700i	−0.386794	+	0.346425i
$186$	−2583.18			−1.01832
$187$	1921.98	+	1921.98i	0.751599	+	0.751599i
$188$	−1109.39	+	1109.39i	−0.430374	+	0.430374i
$189$	3303.23			1.27129
$190$	433.935	+	484.500i	0.165689	+	0.184996i
$191$		−	1899.87i		−	0.719736i	−0.933003	−	0.359868i	$-0.882822\pi$
$191$		−	1899.87i		−	0.719736i	0.933003	−	0.359868i	$-0.117178\pi$
$192$	229.711	+	229.711i	0.0863436	+	0.0863436i
$193$	−522.001	+	522.001i	−0.194686	+	0.194686i	−0.797718	−	0.603031i	$-0.793959\pi$
$193$	−522.001	+	522.001i	−0.194686	+	0.194686i	0.603031	+	0.797718i	$0.293959\pi$
$194$	1660.48			0.614512
$195$	−104.115	+	1891.07i	−0.0382350	+	0.694473i
$196$	752.881			0.274374
$197$	591.134	+	591.134i	0.213789	+	0.213789i	0.805875	−	0.592086i	$-0.201695\pi$
$197$	591.134	+	591.134i	0.213789	+	0.213789i	−0.592086	+	0.805875i	$0.701695\pi$
$198$	60.3078	+	60.3078i	0.0216459	+	0.0216459i
$199$	−670.246			−0.238756			−0.119378	−	0.992849i	$-0.538090\pi$
$199$	−670.246			−0.238756			−0.119378	+	0.992849i	$0.538090\pi$
$200$	780.459	−	625.207i	0.275934	−	0.221044i
$201$		−	679.247i		−	0.238360i
$202$	2101.89	+	2101.89i	0.732120	+	0.732120i
$203$	−4786.13	−	4786.13i	−1.65478	−	1.65478i
$204$	−1597.96			−0.548429
$205$	−3265.27	−	179.773i	−1.11247	−	0.0612483i
$206$			839.635i			0.283981i
$207$	19.1788	−	134.842i	0.00643969	−	0.0452763i
$208$	−377.570	+	377.570i	−0.125864	+	0.125864i
$209$		−	1004.57i		−	0.332476i
$210$	−1948.69	+	1745.31i	−0.640345	+	0.573514i
$211$	−14.5641			−0.00475181			−0.00237591	−	0.999997i	$-0.500756\pi$
$211$	−14.5641			−0.00475181			−0.00237591	+	0.999997i	$0.500756\pi$
$212$	743.169	−	743.169i	0.240760	−	0.240760i
$213$	−64.6026	+	64.6026i	−0.0207817	+	0.0207817i
$214$	−1404.56			−0.448662
$215$	−3114.99	−	3477.98i	−0.988097	−	1.10324i
$216$	−1146.55			−0.361169
$217$	4146.96	−	4146.96i	1.29730	−	1.29730i
$218$	−2146.62	−	2146.62i	−0.666915	−	0.666915i
$219$		−	1957.17i		−	0.603897i
$220$	−1542.17	−	84.9060i	−0.472605	−	0.0260198i
$221$		−	2626.52i		−	0.799453i
$222$	−838.901	+	838.901i	−0.253619	+	0.253619i
$223$	−1741.84	+	1741.84i	−0.523059	+	0.523059i	−0.918494	−	0.395435i	$-0.870594\pi$
$223$	−1741.84	+	1741.84i	−0.523059	+	0.523059i	0.395435	+	0.918494i	$0.370594\pi$
$224$	−737.543			−0.219996
$225$	−16.9440	+	153.412i	−0.00502043	+	0.0454555i
$226$		−	1204.32i		−	0.354469i
$227$	−1293.57	+	1293.57i	−0.378226	+	0.378226i	−0.870462	−	0.492236i	$-0.836180\pi$
$227$	−1293.57	+	1293.57i	−0.378226	+	0.378226i	0.492236	+	0.870462i	$0.336180\pi$
$228$	417.607	+	417.607i	0.121301	+	0.121301i
$229$	773.785			0.223289			0.111644	−	0.993748i	$-0.464388\pi$
$229$	773.785			0.223289			0.111644	+	0.993748i	$0.464388\pi$
$230$	1370.43	+	2050.71i	0.392886	+	0.587912i
$231$	4040.45			1.15083
$232$	1661.26	+	1661.26i	0.470116	+	0.470116i
$233$	−3928.73	+	3928.73i	−1.10463	+	1.10463i	−0.110790	+	0.993844i	$0.535338\pi$
$233$	−3928.73	+	3928.73i	−1.10463	+	1.10463i	−0.993844	+	0.110790i	$0.964662\pi$
$234$		−	82.4150i		−	0.0230241i
$235$	2925.68	+	3266.60i	0.812129	+	0.906764i
$236$	−104.376			−0.0287895
$237$	−3713.77	+	3713.77i	−1.01787	+	1.01787i
$238$	2565.32	−	2565.32i	0.698676	−	0.698676i
$239$			3050.20i			0.825528i	0.910838	+	0.412764i	$0.135437\pi$
$239$			3050.20i			0.825528i	−0.910838	+	0.412764i	$0.864563\pi$
$240$	676.387	−	605.795i	0.181919	−	0.162933i
$241$		−	6098.11i		−	1.62993i	−0.579509	−	0.814966i	$-0.696756\pi$
$241$		−	6098.11i		−	1.62993i	0.579509	−	0.814966i	$-0.303244\pi$
$242$	−195.513	−	195.513i	−0.0519342	−	0.0519342i
$243$	244.792	−	244.792i	0.0646232	−	0.0646232i
$244$	767.333			0.201326
$245$	115.683	−	2101.19i	0.0301662	−	0.547918i
$246$	−2969.40			−0.769601
$247$	−686.409	+	686.409i	−0.176823	+	0.176823i
$248$	−1439.40	+	1439.40i	−0.368557	+	0.368557i
$249$	5882.99			1.49727
$250$	−1624.94	−	2274.22i	−0.411082	−	0.575336i
$251$			6237.25i			1.56849i	0.620450	+	0.784246i	$0.286950\pi$
$251$			6237.25i			1.56849i	−0.620450	+	0.784246i	$0.713050\pi$
$252$	80.4944	−	80.4944i	0.0201217	−	0.0201217i
$253$	536.429	−	3771.53i	0.133300	−	0.937210i
$254$		−	5564.83i		−	1.37468i
$255$	−245.533	+	4459.68i	−0.0602975	+	1.09520i
$256$	256.000			0.0625000
$257$	−3221.28	−	3221.28i	−0.781861	−	0.781861i	0.198284	−	0.980145i	$-0.436463\pi$
$257$	−3221.28	−	3221.28i	−0.781861	−	0.781861i	−0.980145	+	0.198284i	$0.936463\pi$
$258$	−2997.79	−	2997.79i	−0.723387	−	0.723387i
$259$		−	2693.49i		−	0.646199i
$260$	995.730	+	1111.76i	0.237510	+	0.265186i
$261$	−362.615			−0.0859973
$262$	−3197.47	−	3197.47i	−0.753971	−	0.753971i
$263$	4700.24	+	4700.24i	1.10201	+	1.10201i	0.994168	+	0.107844i	$0.0343946\pi$
$263$	4700.24	+	4700.24i	1.10201	+	1.10201i	0.107844	+	0.994168i	$0.465605\pi$
$264$	−1402.43			−0.326946
$265$	−1959.89	−	2188.27i	−0.454321	−	0.507262i
$266$	−1340.83			−0.309065
$267$	1415.88	−	1415.88i	0.324533	−	0.324533i
$268$	−378.491	−	378.491i	−0.0862687	−	0.0862687i
$269$		−	5566.29i		−	1.26165i	−0.775927	−	0.630823i	$-0.782717\pi$
$269$		−	5566.29i		−	1.26165i	0.775927	−	0.630823i	$-0.217283\pi$
$270$	−176.171	+	3199.85i	−0.0397090	+	0.721246i
$271$	1543.04			0.345878			0.172939	−	0.984933i	$-0.444674\pi$
$271$	1543.04			0.345878			0.172939	+	0.984933i	$0.444674\pi$
$272$	−890.418	+	890.418i	−0.198491	+	0.198491i
$273$	−2760.78	−	2760.78i	−0.612052	−	0.612052i
$274$	−4049.94			−0.892940
$275$	−473.921	+	4290.94i	−0.103922	+	0.940921i
$276$	1344.85	+	1790.85i	0.293300	+	0.390567i
$277$	4150.38	+	4150.38i	0.900261	+	0.900261i	0.995458	−	0.0951970i	$-0.0303481\pi$
$277$	4150.38	+	4150.38i	0.900261	+	0.900261i	−0.0951970	+	0.995458i	$0.530348\pi$
$278$	2898.71	−	2898.71i	0.625371	−	0.625371i
$279$		−	314.189i		−	0.0674194i
$280$	−113.326	+	2058.38i	−0.0241877	+	0.439327i
$281$			6344.83i			1.34698i	0.739197	+	0.673489i	$0.235205\pi$
$281$			6344.83i			1.34698i	−0.739197	+	0.673489i	$0.764795\pi$
$282$	2815.59	+	2815.59i	0.594561	+	0.594561i
$283$	1755.93	+	1755.93i	0.368832	+	0.368832i	0.867051	−	0.498219i	$-0.166013\pi$
$283$	1755.93	+	1755.93i	0.368832	+	0.368832i	−0.498219	+	0.867051i	$0.666013\pi$
$284$			71.9960i			0.0150429i
$285$	1229.65	−	1101.31i	0.255572	−	0.228899i
$286$		−	2305.14i		−	0.476594i
$287$	4766.98	−	4766.98i	0.980440	−	0.980440i
$288$	−27.9395	+	27.9395i	−0.00571649	+	0.00571649i
$289$		−	1281.09i		−	0.260755i
$290$	4891.59	−	4381.08i	0.990497	−	0.887123i
$291$		−	4214.25i		−	0.848947i
$292$	−1090.58	−	1090.58i	−0.218566	−	0.218566i
$293$	3749.98	+	3749.98i	0.747701	+	0.747701i	0.974047	−	0.226346i	$-0.0726781\pi$
$293$	3749.98	+	3749.98i	0.747701	+	0.747701i	−0.226346	+	0.974047i	$0.572678\pi$
$294$		−	1910.79i		−	0.379047i
$295$	−16.0378	+	291.299i	−0.00316528	+	0.0574919i
$296$			934.907i			0.183582i
$297$	3499.94	−	3499.94i	0.683796	−	0.683796i
$298$	3753.67	+	3753.67i	0.729679	+	0.729679i
$299$	−2943.57	+	2210.50i	−0.569335	+	0.427547i
$300$	−1586.76	−	1980.78i	−0.305372	−	0.381202i
$301$	9625.11			1.84313
$302$	481.317	+	481.317i	0.0917108	+	0.0917108i
$303$	5334.53	−	5334.53i	1.01142	−	1.01142i
$304$	465.399			0.0878041
$305$	117.904	−	2141.52i	0.0221349	−	0.402043i
$306$		−	194.358i		−	0.0363095i
$307$	4887.74	+	4887.74i	0.908658	+	0.908658i	0.996164	−	0.0875063i	$-0.0278898\pi$
$307$	4887.74	+	4887.74i	0.908658	+	0.908658i	−0.0875063	+	0.996164i	$0.527890\pi$
$308$	2251.42	−	2251.42i	0.416516	−	0.416516i
$309$	2130.97			0.392319
$310$	3796.00	+	4238.34i	0.695479	+	0.776522i
$311$	−5917.47			−1.07894			−0.539468	−	0.842006i	$-0.681374\pi$
$311$	−5917.47			−1.07894			−0.539468	+	0.842006i	$0.681374\pi$
$312$	958.263	+	958.263i	0.173881	+	0.173881i
$313$	4814.96	+	4814.96i	0.869512	+	0.869512i	0.992418	−	0.122906i	$-0.0392213\pi$
$313$	4814.96	+	4814.96i	0.869512	+	0.869512i	−0.122906	+	0.992418i	$0.539221\pi$
$314$	6129.59			1.10163
$315$	−212.280	−	237.017i	−0.0379703	−	0.0423949i
$316$			4138.79i			0.736788i
$317$	−4131.17	−	4131.17i	−0.731954	−	0.731954i	0.239053	−	0.971007i	$-0.423163\pi$
$317$	−4131.17	−	4131.17i	−0.731954	−	0.731954i	−0.971007	+	0.239053i	$0.923163\pi$
$318$	−1886.14	−	1886.14i	−0.332609	−	0.332609i
$319$	−10142.3			−1.78013
$320$	39.3354	−	714.460i	0.00687161	−	0.124811i
$321$			3564.73i			0.619825i
$322$	−5033.96	−	715.986i	−0.871217	−	0.123914i
$323$	−1618.75	+	1618.75i	−0.278853	+	0.278853i
$324$			2776.55i			0.476088i
$325$	3255.76	−	2608.11i	0.555684	−	0.445145i
$326$	−2636.81			−0.447974
$327$	−5448.07	+	5448.07i	−0.921342	+	0.921342i
$328$	−1654.61	+	1654.61i	−0.278539	+	0.278539i
$329$	−9040.14			−1.51489
$330$	−215.489	+	3913.99i	−0.0359463	+	0.652903i
$331$	8484.07			1.40884			0.704421	−	0.709783i	$-0.251207\pi$
$331$	8484.07			1.40884			0.704421	+	0.709783i	$0.251207\pi$
$332$	3278.13	−	3278.13i	0.541900	−	0.541900i
$333$	−102.034	−	102.034i	−0.0167912	−	0.0167912i
$334$			4411.87i			0.722774i
$335$	−1114.47	+	998.158i	−0.181761	+	0.162792i
$336$			1871.86i			0.303924i
$337$	−942.042	+	942.042i	−0.152274	+	0.152274i	−0.779133	−	0.626859i	$-0.784340\pi$
$337$	−942.042	+	942.042i	−0.152274	+	0.152274i	0.626859	+	0.779133i	$0.284340\pi$
$338$	1531.96	−	1531.96i	0.246531	−	0.246531i
$339$	−3056.53			−0.489699
$340$	2348.21	+	2621.85i	0.374558	+	0.418205i
$341$		−	8787.85i		−	1.39557i
$342$	−50.7930	+	50.7930i	−0.00803091	+	0.00803091i
$343$	−2522.53	−	2522.53i	−0.397096	−	0.397096i
$344$	−3340.86			−0.523626
$345$	5204.65	−	3478.13i	0.812199	−	0.542771i
$346$	−2212.83			−0.343821
$347$	−853.519	−	853.519i	−0.132044	−	0.132044i	0.637996	−	0.770040i	$-0.279764\pi$
$347$	−853.519	−	853.519i	−0.132044	−	0.132044i	−0.770040	+	0.637996i	$0.779764\pi$
$348$	4216.23	−	4216.23i	0.649464	−	0.649464i
$349$			3838.94i			0.588807i	0.955681	+	0.294403i	$0.0951209\pi$
$349$			3838.94i			0.588807i	−0.955681	+	0.294403i	$0.904879\pi$
$350$	5727.23	+	632.556i	0.874666	+	0.0966043i
$351$	−4782.93			−0.727333
$352$	−781.466	+	781.466i	−0.118330	+	0.118330i
$353$	−1305.24	+	1305.24i	−0.196802	+	0.196802i	−0.798628	−	0.601826i	$-0.794440\pi$
$353$	−1305.24	+	1305.24i	−0.196802	+	0.196802i	0.601826	+	0.798628i	$0.294440\pi$
$354$			264.904i			0.0397726i
$355$	200.931	+	11.0625i	0.0300402	+	0.00165390i
$356$		−	1577.91i		−	0.234914i
$357$	−6510.71	−	6510.71i	−0.965219	−	0.965219i
$358$	4337.23	−	4337.23i	0.640306	−	0.640306i
$359$	10264.1			1.50897			0.754483	−	0.656319i	$-0.227888\pi$
$359$	10264.1			1.50897			0.754483	+	0.656319i	$0.227888\pi$
$360$	73.6822	+	82.2682i	0.0107872	+	0.0120442i
$361$	−6012.92			−0.876647
$362$	2649.20	−	2649.20i	0.384638	−	0.384638i
$363$	−496.207	+	496.207i	−0.0717469	+	0.0717469i
$364$	−3076.73			−0.443035
$365$	−3211.22	+	2876.08i	−0.460501	+	0.412441i
$366$		−	1947.47i		−	0.278131i
$367$	6029.58	−	6029.58i	0.857606	−	0.857606i	−0.133449	−	0.991056i	$-0.542605\pi$
$367$	6029.58	−	6029.58i	0.857606	−	0.857606i	0.991056	+	0.133449i	$0.0426053\pi$
$368$	1747.28	+	248.518i	0.247509	+	0.0352035i
$369$		−	361.164i		−	0.0509525i
$370$	2609.19	+	143.652i	0.366609	+	0.0201841i
$371$	6055.92			0.847460
$372$	3653.17	+	3653.17i	0.509161	+	0.509161i
$373$	4977.72	+	4977.72i	0.690983	+	0.690983i	0.962448	−	0.271465i	$-0.0875081\pi$
$373$	4977.72	+	4977.72i	0.690983	+	0.690983i	−0.271465	+	0.962448i	$0.587508\pi$
$374$		−	5436.18i		−	0.751599i
$375$	−5771.90	+	4124.07i	−0.794826	+	0.567909i
$376$	3137.82			0.430374
$377$	6930.10	+	6930.10i	0.946733	+	0.946733i
$378$	−4671.47	−	4671.47i	−0.635647	−	0.635647i
$379$	6705.13			0.908758			0.454379	−	0.890809i	$-0.349861\pi$
$379$	6705.13			0.908758			0.454379	+	0.890809i	$0.349861\pi$
$380$	71.5104	−	1298.86i	0.00965369	−	0.175343i
$381$	−14123.4			−1.89912
$382$	−2686.82	+	2686.82i	−0.359868	+	0.359868i
$383$	−3134.02	−	3134.02i	−0.418122	−	0.418122i	0.466434	−	0.884556i	$-0.345539\pi$
$383$	−3134.02	−	3134.02i	−0.418122	−	0.418122i	−0.884556	+	0.466434i	$0.845539\pi$
$384$		−	649.721i		−	0.0863436i
$385$	−5937.47	−	6629.35i	−0.785977	−	0.877566i
$386$	1476.44			0.194686
$387$	364.617	−	364.617i	0.0478928	−	0.0478928i
$388$	−2348.27	−	2348.27i	−0.307256	−	0.307256i
$389$	2699.41			0.351839			0.175920	−	0.984405i	$-0.443710\pi$
$389$	2699.41			0.351839			0.175920	+	0.984405i	$0.443710\pi$
$390$	2821.62	−	2527.14i	0.366354	−	0.328119i
$391$	−6941.77	+	5212.99i	−0.897853	+	0.674251i
$392$	−1064.74	−	1064.74i	−0.137187	−	0.137187i
$393$	−8115.10	+	8115.10i	−1.04161	+	1.04161i
$394$		−	1671.98i		−	0.213789i
$395$	11550.8	+	635.941i	1.47135	+	0.0810068i
$396$		−	170.576i		−	0.0216459i
$397$	−826.019	−	826.019i	−0.104425	−	0.104425i	0.652964	−	0.757389i	$-0.273525\pi$
$397$	−826.019	−	826.019i	−0.104425	−	0.104425i	−0.757389	+	0.652964i	$0.773525\pi$
$398$	947.871	+	947.871i	0.119378	+	0.119378i
$399$			3402.98i			0.426973i
$400$	−1987.91	−	219.559i	−0.248489	−	0.0274449i
$401$		−	2012.63i		−	0.250638i	−0.992116	−	0.125319i	$-0.960005\pi$
$401$		−	2012.63i		−	0.250638i	0.992116	−	0.125319i	$-0.0399954\pi$
$402$	−960.600	+	960.600i	−0.119180	+	0.119180i
$403$	−6004.62	+	6004.62i	−0.742212	+	0.742212i
$404$		−	5945.03i		−	0.732120i
$405$	7748.95	+	426.627i	0.950737	+	0.0523439i
$406$			13537.2i			1.65478i
$407$	−2853.90	−	2853.90i	−0.347574	−	0.347574i
$408$	2259.86	+	2259.86i	0.274215	+	0.274215i
$409$		−	12168.8i		−	1.47117i	−0.677430	−	0.735587i	$-0.736906\pi$
$409$		−	12168.8i		−	1.47117i	0.677430	−	0.735587i	$-0.263094\pi$
$410$	4363.55	+	4872.03i	0.525611	+	0.586859i
$411$			10278.6i			1.23360i
$412$	1187.42	−	1187.42i	0.141991	−	0.141991i
$413$	−425.269	−	425.269i	−0.0506686	−	0.0506686i
$414$	−217.819	+	163.573i	−0.0258580	+	0.0194183i
$415$	−8645.10	−	9652.49i	−1.02258	−	1.14174i
$416$	1067.93			0.125864
$417$	−7356.85	−	7356.85i	−0.863949	−	0.863949i
$418$	−1420.68	+	1420.68i	−0.166238	+	0.166238i
$419$	6572.45			0.766313			0.383157	−	0.923683i	$-0.374837\pi$
$419$	6572.45			0.766313			0.383157	+	0.923683i	$0.374837\pi$
$420$	5224.11	+	287.619i	0.606930	+	0.0334152i
$421$		−	2258.85i		−	0.261495i	−0.991416	−	0.130748i	$-0.958262\pi$
$421$		−	2258.85i		−	0.261495i	0.991416	−	0.130748i	$-0.0417378\pi$
$422$	20.5967	+	20.5967i	0.00237591	+	0.00237591i
$423$	−342.457	+	342.457i	−0.0393637	+	0.0393637i
$424$	−2102.00			−0.240760
$425$	7678.01	−	6150.67i	0.876325	−	0.702004i
$426$	182.724			0.0207817
$427$	3126.41	+	3126.41i	0.354327	+	0.354327i
$428$	1986.35	+	1986.35i	0.224331	+	0.224331i
$429$	−5850.39			−0.658414
$430$	−513.336	+	9323.87i	−0.0575704	+	1.04567i
$431$		−	5226.87i		−	0.584151i	−0.956395	−	0.292076i	$-0.905654\pi$
$431$		−	5226.87i		−	0.584151i	0.956395	−	0.292076i	$-0.0943459\pi$
$432$	1621.46	+	1621.46i	0.180585	+	0.180585i
$433$	−3549.16	−	3549.16i	−0.393907	−	0.393907i	0.482170	−	0.876077i	$-0.339849\pi$
$433$	−3549.16	−	3549.16i	−0.393907	−	0.393907i	−0.876077	+	0.482170i	$0.839849\pi$
$434$	−11729.4			−1.29730
$435$	−11119.1	−	12414.7i	−1.22556	−	1.36837i
$436$			6071.56i			0.666915i
$437$	3176.50	+	451.796i	0.347717	+	0.0494562i
$438$	−2767.86	+	2767.86i	−0.301949	+	0.301949i
$439$		−	2774.35i		−	0.301624i	−0.988562	−	0.150812i	$-0.951811\pi$
$439$		−	2774.35i		−	0.301624i	0.988562	−	0.150812i	$-0.0481887\pi$
$440$	2060.88	+	2301.04i	0.223293	+	0.249313i
$441$	232.407			0.0250953
$442$	−3714.47	+	3714.47i	−0.399727	+	0.399727i
$443$	−10016.0	+	10016.0i	−1.07420	+	1.07420i	−0.0771876	+	0.997017i	$0.524594\pi$
$443$	−10016.0	+	10016.0i	−1.07420	+	1.07420i	−0.997017	+	0.0771876i	$0.975406\pi$
$444$	2372.77			0.253619
$445$	−4403.73	−	242.452i	−0.469117	−	0.0258277i
$446$	4926.66			0.523059
$447$	9526.71	−	9526.71i	1.00805	−	1.00805i
$448$	1043.04	+	1043.04i	0.109998	+	0.109998i
$449$			2708.96i			0.284730i	0.989814	+	0.142365i	$0.0454707\pi$
$449$			2708.96i			0.284730i	−0.989814	+	0.142365i	$0.954529\pi$
$450$	240.920	−	192.996i	0.0252380	−	0.0202176i
$451$		−	10101.7i		−	1.05471i
$452$	−1703.16	+	1703.16i	−0.177235	+	0.177235i
$453$	1221.57	−	1221.57i	0.126698	−	0.126698i
$454$	3658.77			0.378226
$455$	−472.752	+	8586.73i	−0.0487098	+	0.884730i
$456$		−	1181.17i		−	0.121301i
$457$	−9791.54	+	9791.54i	−1.00225	+	1.00225i	−0.00225395	+	0.999997i	$0.500717\pi$
$457$	−9791.54	+	9791.54i	−1.00225	+	1.00225i	−0.999997	+	0.00225395i	$0.999283\pi$
$458$	−1094.30	−	1094.30i	−0.111644	−	0.111644i
$459$	−11279.5			−1.14702
$460$	962.054	−	4838.23i	0.0975130	−	0.490399i
$461$	2971.05			0.300163			0.150082	−	0.988674i	$-0.452046\pi$
$461$	2971.05			0.300163			0.150082	+	0.988674i	$0.452046\pi$
$462$	−5714.05	−	5714.05i	−0.575415	−	0.575415i
$463$	3578.43	−	3578.43i	0.359188	−	0.359188i	−0.504326	−	0.863513i	$-0.668259\pi$
$463$	3578.43	−	3578.43i	0.359188	−	0.359188i	0.863513	+	0.504326i	$0.168259\pi$
$464$		−	4698.75i		−	0.470116i
$465$	10756.8	−	9634.15i	1.07276	−	0.960803i
$466$	11112.1			1.10463
$467$	−10004.2	+	10004.2i	−0.991303	+	0.991303i	−0.999963	−	0.00865908i	$-0.997244\pi$
$467$	−10004.2	+	10004.2i	−0.991303	+	0.991303i	0.00865908	+	0.999963i	$0.497244\pi$
$468$	−116.552	+	116.552i	−0.0115120	+	0.0115120i
$469$		−	3084.24i		−	0.303661i
$470$	482.138	−	8757.21i	0.0473178	−	0.859447i
$471$		−	15556.7i		−	1.52190i
$472$	147.610	+	147.610i	0.0143947	+	0.0143947i
$473$	10198.3	−	10198.3i	0.991372	−	0.991372i
$474$	10504.1			1.01787
$475$	−3613.95	−	399.151i	−0.349094	−	0.0385564i
$476$	−7255.81			−0.698676
$477$	229.409	−	229.409i	0.0220208	−	0.0220208i
$478$	4313.64	−	4313.64i	0.412764	−	0.412764i
$479$	−5421.54			−0.517154			−0.258577	−	0.965991i	$-0.583253\pi$
$479$	−5421.54			−0.517154			−0.258577	+	0.965991i	$0.583253\pi$
$480$	−1813.28	−	99.8322i	−0.172426	−	0.00949311i
$481$			3900.06i			0.369703i
$482$	−8624.02	+	8624.02i	−0.814966	+	0.814966i
$483$	−1817.15	+	12776.1i	−0.171187	+	1.20358i
$484$			552.995i			0.0519342i
$485$	−6914.51	+	6192.87i	−0.647364	+	0.579801i
$486$	−692.378			−0.0646232
$487$	4796.89	+	4796.89i	0.446340	+	0.446340i	0.894136	−	0.447796i	$-0.147791\pi$
$487$	4796.89	+	4796.89i	0.446340	+	0.446340i	−0.447796	+	0.894136i	$0.647791\pi$
$488$	−1085.17	−	1085.17i	−0.100663	−	0.100663i
$489$			6692.16i			0.618875i
$490$	−3135.13	+	2807.92i	−0.289042	+	0.258876i
$491$	−1256.47			−0.115487			−0.0577433	−	0.998331i	$-0.518390\pi$
$491$	−1256.47			−0.115487			−0.0577433	+	0.998331i	$0.518390\pi$
$492$	4199.36	+	4199.36i	0.384801	+	0.384801i
$493$	16343.1	+	16343.1i	1.49302	+	1.49302i
$494$	1941.46			0.176823
$495$	−476.054	−	26.2097i	−0.0432263	−	0.00237988i
$496$	4071.25			0.368557
$497$	−293.339	+	293.339i	−0.0264750	+	0.0264750i
$498$	−8319.81	−	8319.81i	−0.748633	−	0.748633i
$499$			18315.4i			1.64311i	0.570131	+	0.821554i	$0.306892\pi$
$499$			18315.4i			1.64311i	−0.570131	+	0.821554i	$0.693108\pi$
$500$	−918.209	+	5514.24i	−0.0821271	+	0.493209i
$501$	11197.2			0.998511
$502$	8820.80	−	8820.80i	0.784246	−	0.784246i
$503$	4577.23	+	4577.23i	0.405743	+	0.405743i	0.880251	−	0.474508i	$-0.157374\pi$
$503$	4577.23	+	4577.23i	0.405743	+	0.405743i	−0.474508	+	0.880251i	$0.657374\pi$
$504$	−227.673			−0.0201217
$505$	−16591.7	−	913.477i	−1.46203	−	0.0804935i
$506$	−6092.38	+	4575.13i	−0.535255	+	0.401955i
$507$	−3888.06	−	3888.06i	−0.340582	−	0.340582i
$508$	−7869.86	+	7869.86i	−0.687340	+	0.687340i
$509$			167.537i			0.0145893i	0.999973	+	0.00729464i	$0.00232198\pi$
$509$			167.537i			0.0145893i	−0.999973	+	0.00729464i	$0.997678\pi$
$510$	6654.17	−	5959.70i	0.577749	−	0.517451i
$511$		−	8886.88i		−	0.769339i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	2947.76	+	2947.76i	0.253697	+	0.253697i
$514$			9111.17i			0.781861i
$515$	−3131.48	−	3496.38i	−0.267941	−	0.299163i
$516$			8479.02i			0.723387i
$517$	−9578.51	+	9578.51i	−0.814821	+	0.814821i
$518$	−3809.17	+	3809.17i	−0.323099	+	0.323099i
$519$			5616.09i			0.474989i
$520$	164.092	−	2980.44i	0.0138382	−	0.251348i
$521$		−	9958.29i		−	0.837391i	−0.908127	−	0.418695i	$-0.862488\pi$
$521$		−	9958.29i		−	0.837391i	0.908127	−	0.418695i	$-0.137512\pi$
$522$	512.815	+	512.815i	0.0429986	+	0.0429986i
$523$	4106.92	+	4106.92i	0.343371	+	0.343371i	0.857633	−	0.514262i	$-0.171934\pi$
$523$	4106.92	+	4106.92i	0.343371	+	0.343371i	−0.514262	+	0.857633i	$0.671934\pi$
$524$			9043.81i			0.753971i
$525$	1605.41	−	14535.6i	0.133459	−	1.20835i
$526$		−	13294.3i		−	1.10201i
$527$	−14160.6	+	14160.6i	−1.17048	+	1.17048i
$528$	1983.34	+	1983.34i	0.163473	+	0.163473i
$529$	11684.5	+	3392.42i	0.960343	+	0.278822i
$530$	−322.980	+	5866.38i	−0.0264705	+	0.480791i
$531$	−32.2200			−0.00263320
$532$	1896.22	+	1896.22i	0.154533	+	0.154533i
$533$	−6902.38	+	6902.38i	−0.560929	+	0.560929i
$534$	−4004.70			−0.324533
$535$	5848.82	−	5238.40i	0.472648	−	0.423319i
$536$			1070.53i			0.0862687i
$537$	−11007.8	−	11007.8i	−0.884582	−	0.884582i
$538$	−7871.93	+	7871.93i	−0.630823	+	0.630823i
$539$	6500.42			0.519468
$540$	4774.41	−	4276.12i	0.380477	−	0.340768i
$541$	10610.8			0.843239			0.421619	−	0.906773i	$-0.361462\pi$
$541$	10610.8			0.843239			0.421619	+	0.906773i	$0.361462\pi$
$542$	−2182.18	−	2182.18i	−0.172939	−	0.172939i
$543$	−6723.60	−	6723.60i	−0.531376	−	0.531376i
$544$	2518.48			0.198491
$545$	16944.9	+	932.919i	1.33181	+	0.0733245i
$546$			7808.67i			0.612052i
$547$	−831.075	−	831.075i	−0.0649619	−	0.0649619i	0.673879	−	0.738841i	$-0.264627\pi$
$547$	−831.075	−	831.075i	−0.0649619	−	0.0649619i	−0.738841	+	0.673879i	$0.764627\pi$
$548$	5727.48	+	5727.48i	0.446470	+	0.446470i
$549$	236.869			0.0184140
$550$	6738.53	−	5398.07i	0.522421	−	0.418499i
$551$		−	8542.15i		−	0.660450i
$552$	630.731	−	4434.55i	0.0486335	−	0.341933i
$553$	−16863.0	+	16863.0i	−1.29673	+	1.29673i
$554$		−	11739.1i		−	0.900261i
$555$	364.585	−	6622.06i	0.0278843	−	0.506470i
$556$	−8198.79			−0.625371
$557$	−12274.3	+	12274.3i	−0.933712	+	0.933712i	−0.997936	−	0.0642239i	$-0.979543\pi$
$557$	−12274.3	+	12274.3i	−0.933712	+	0.933712i	0.0642239	+	0.997936i	$0.479543\pi$
$558$	−444.331	+	444.331i	−0.0337097	+	0.0337097i
$559$	−13936.7			−1.05449
$560$	3071.25	−	2750.72i	0.231757	−	0.207570i
$561$	−13796.9			−1.03833
$562$	8972.94	−	8972.94i	0.673489	−	0.673489i
$563$	893.267	+	893.267i	0.0668680	+	0.0668680i	0.739750	−	0.672882i	$-0.234944\pi$
$563$	893.267	+	893.267i	0.0668680	+	0.0668680i	−0.672882	+	0.739750i	$0.734944\pi$
$564$		−	7963.70i		−	0.594561i
$565$	4491.59	+	5014.98i	0.334447	+	0.373419i
$566$		−	4966.53i		−	0.368832i
$567$	−11312.7	+	11312.7i	−0.837901	+	0.837901i
$568$	101.818	−	101.818i	0.00752143	−	0.00752143i
$569$	−21107.7			−1.55515			−0.777575	−	0.628790i	$-0.783550\pi$
$569$	−21107.7			−1.55515			−0.777575	+	0.628790i	$0.783550\pi$
$570$	−3296.48	−	181.491i	−0.242236	−	0.0133366i
$571$		−	5737.00i		−	0.420466i	−0.977651	−	0.210233i	$-0.932578\pi$
$571$		−	5737.00i		−	0.420466i	0.977651	−	0.210233i	$-0.0674222\pi$
$572$	−3259.96	+	3259.96i	−0.238297	+	0.238297i
$573$	6819.07	+	6819.07i	0.497157	+	0.497157i
$574$	−13483.1			−0.980440
$575$	−13355.0	−	3428.37i	−0.968594	−	0.248648i
$576$	79.0248			0.00571649
$577$	−13830.6	−	13830.6i	−0.997879	−	0.997879i	0.00211866	−	0.999998i	$-0.499326\pi$
$577$	−13830.6	−	13830.6i	−0.997879	−	0.997879i	−0.999998	+	0.00211866i	$0.999326\pi$
$578$	−1811.74	+	1811.74i	−0.130378	+	0.130378i
$579$		−	3747.17i		−	0.268959i
$580$	−13113.5	−	721.980i	−0.938810	−	0.0516873i
$581$	26712.7			1.90745
$582$	−5959.85	+	5959.85i	−0.424473	+	0.424473i
$583$	6416.56	−	6416.56i	0.455827	−	0.455827i
$584$			3084.62i			0.218566i
$585$	307.372	+	343.190i	0.0217236	+	0.0242550i
$586$		−	10606.6i		−	0.747701i
$587$	1687.96	+	1687.96i	0.118687	+	0.118687i	0.763956	−	0.645269i	$-0.223255\pi$
$587$	1687.96	+	1687.96i	0.118687	+	0.118687i	−0.645269	+	0.763956i	$0.723255\pi$
$588$	−2702.27	+	2702.27i	−0.189523	+	0.189523i
$589$	7401.39			0.517774
$590$	434.640	−	389.278i	0.0303286	−	0.0271633i
$591$	−4243.44			−0.295350
$592$	1322.16	−	1322.16i	0.0917912	−	0.0917912i
$593$	−8965.67	+	8965.67i	−0.620870	+	0.620870i	−0.945754	−	0.324884i	$-0.894675\pi$
$593$	−8965.67	+	8965.67i	−0.620870	+	0.620870i	0.324884	+	0.945754i	$0.394675\pi$
$594$	−9899.34			−0.683796
$595$	−1114.88	+	20249.9i	−0.0768164	+	1.39524i
$596$		−	10617.0i		−	0.729679i
$597$	2405.67	−	2405.67i	0.164921	−	0.164921i
$598$	7288.96	+	1036.72i	0.498441	+	0.0708937i
$599$		−	5282.85i		−	0.360353i	−0.983634	−	0.180177i	$-0.942333\pi$
$599$		−	5282.85i		−	0.360353i	0.983634	−	0.180177i	$-0.0576669\pi$
$600$	−557.235	+	5045.27i	−0.0379150	+	0.343287i
$601$	5315.70			0.360785			0.180393	−	0.983595i	$-0.442263\pi$
$601$	5315.70			0.360785			0.180393	+	0.983595i	$0.442263\pi$
$602$	−13612.0	−	13612.0i	−0.921565	−	0.921565i
$603$	−116.837	−	116.837i	−0.00789047	−	0.00789047i
$604$		−	1361.37i		−	0.0917108i
$605$	1543.33	+	84.9698i	0.103711	+	0.00570994i
$606$	−15088.3			−1.01142
$607$	−6202.81	−	6202.81i	−0.414768	−	0.414768i	0.468628	−	0.883396i	$-0.344749\pi$
$607$	−6202.81	−	6202.81i	−0.414768	−	0.414768i	−0.883396	+	0.468628i	$0.844749\pi$
$608$	−658.174	−	658.174i	−0.0439021	−	0.0439021i
$609$	34357.1			2.28607
$610$	−3195.31	+	2861.82i	−0.212089	+	0.189954i
$611$	13089.7			0.866700
$612$	−274.864	+	274.864i	−0.0181547	+	0.0181547i
$613$	1307.70	+	1307.70i	0.0861624	+	0.0861624i	0.748874	−	0.662712i	$-0.230595\pi$
$613$	1307.70	+	1307.70i	0.0861624	+	0.0861624i	−0.662712	+	0.748874i	$0.730595\pi$
$614$		−	13824.6i		−	0.908658i
$615$	12365.1	−	11074.6i	0.810745	−	0.726130i
$616$	−6367.99			−0.416516
$617$	−9160.28	+	9160.28i	−0.597697	+	0.597697i	−0.939699	−	0.342002i	$-0.888895\pi$
$617$	−9160.28	+	9160.28i	−0.597697	+	0.597697i	0.342002	+	0.939699i	$0.388895\pi$
$618$	−3013.65	−	3013.65i	−0.196160	−	0.196160i
$619$	18119.3			1.17654			0.588269	−	0.808665i	$-0.299810\pi$
$619$	18119.3			1.17654			0.588269	+	0.808665i	$0.299810\pi$
$620$	625.563	−	11362.3i	0.0405213	−	0.736000i
$621$	9492.91	+	12641.0i	0.613426	+	0.816856i
$622$	8368.57	+	8368.57i	0.539468	+	0.539468i
$623$	6429.03	−	6429.03i	0.413441	−	0.413441i
$624$		−	2710.38i		−	0.173881i
$625$	15248.4	+	3409.87i	0.975897	+	0.218232i
$626$		−	13618.8i		−	0.869512i
$627$	3605.64	+	3605.64i	0.229658	+	0.229658i
$628$	−8668.55	−	8668.55i	−0.550816	−	0.550816i
$629$			9197.45i			0.583030i
$630$	−34.9828	+	635.402i	−0.00221230	+	0.0401826i
$631$		−	14142.0i		−	0.892209i	−0.894981	−	0.446104i	$-0.852811\pi$
$631$		−	14142.0i		−	0.892209i	0.894981	−	0.446104i	$-0.147189\pi$
$632$	5853.13	−	5853.13i	0.368394	−	0.368394i
$633$	52.2739	−	52.2739i	0.00328231	−	0.00328231i
$634$			11684.7i			0.731954i
$635$	20754.4	+	23172.9i	1.29703	+	1.44817i
$636$			5334.82i			0.332609i
$637$	−4441.65	−	4441.65i	−0.276271	−	0.276271i
$638$	14343.4	+	14343.4i	0.890063	+	0.890063i
$639$			22.2245i			0.00137588i
$640$	−1066.03	+	954.770i	−0.0658413	+	0.0589697i
$641$			8264.69i			0.509260i	0.967039	+	0.254630i	$0.0819536\pi$
$641$			8264.69i			0.509260i	−0.967039	+	0.254630i	$0.918046\pi$
$642$	5041.29	−	5041.29i	0.309913	−	0.309913i
$643$	−13951.1	−	13951.1i	−0.855643	−	0.855643i	0.135178	−	0.990821i	$-0.456839\pi$
$643$	−13951.1	−	13951.1i	−0.855643	−	0.855643i	−0.990821	+	0.135178i	$0.956839\pi$
$644$	6106.54	+	8131.66i	0.373651	+	0.497566i
$645$	23663.7	+	1302.83i	1.44459	+	0.0795334i
$646$	4578.51			0.278853
$647$	17400.6	+	17400.6i	1.05732	+	1.05732i	0.998254	+	0.0590664i	$0.0188124\pi$
$647$	17400.6	+	17400.6i	1.05732	+	1.05732i	0.0590664	+	0.998254i	$0.481188\pi$
$648$	3926.63	−	3926.63i	0.238044	−	0.238044i
$649$	−901.190			−0.0545066
$650$	−8292.77	−	915.912i	−0.500414	−	0.0552693i
$651$			29768.9i			1.79222i
$652$	3729.02	+	3729.02i	0.223987	+	0.223987i
$653$	21138.5	−	21138.5i	1.26679	−	1.26679i	0.319055	−	0.947736i	$-0.396635\pi$
$653$	21138.5	−	21138.5i	1.26679	−	1.26679i	0.947736	−	0.319055i	$-0.103365\pi$
$654$	15409.5			0.921342
$655$	25240.0	+	1389.62i	1.50566	+	0.0828959i
$656$	4679.95			0.278539
$657$	−336.651	−	336.651i	−0.0199909	−	0.0199909i
$658$	12784.7	+	12784.7i	0.757446	+	0.757446i
$659$	−27312.0			−1.61445			−0.807225	−	0.590244i	$-0.799032\pi$
$659$	−27312.0			−1.61445			−0.807225	+	0.590244i	$0.799032\pi$
$660$	5839.97	−	5230.47i	0.344425	−	0.308479i
$661$		−	2264.49i		−	0.133250i	−0.997778	−	0.0666250i	$-0.978777\pi$
$661$		−	2264.49i		−	0.133250i	0.997778	−	0.0666250i	$-0.0212231\pi$
$662$	−11998.3	−	11998.3i	−0.704421	−	0.704421i
$663$	9427.22	+	9427.22i	0.552221	+	0.552221i
$664$	−9271.95			−0.541900
$665$	5583.43	−	5000.71i	0.325588	−	0.291608i
$666$			288.597i			0.0167912i
$667$	4561.41	−	32070.4i	0.264795	−	1.86173i
$668$	6239.32	−	6239.32i	0.361387	−	0.361387i
$669$		−	12503.7i		−	0.722605i
$670$	2987.71	+	164.492i	0.172276	+	0.00948488i
$671$	6625.20			0.381167
$672$	2647.22	−	2647.22i	0.151962	−	0.151962i
$673$	2657.89	−	2657.89i	0.152235	−	0.152235i	−0.626880	−	0.779115i	$-0.715669\pi$
$673$	2657.89	−	2657.89i	0.152235	−	0.152235i	0.779115	+	0.626880i	$0.215669\pi$
$674$	2664.50			0.152274
$675$	−11200.4	−	13981.7i	−0.638674	−	0.797270i
$676$	−4333.02			−0.246531
$677$	19494.0	−	19494.0i	1.10667	−	1.10667i	0.113082	−	0.993586i	$-0.463928\pi$
$677$	19494.0	−	19494.0i	1.10667	−	1.10667i	0.993586	−	0.113082i	$-0.0360723\pi$
$678$	4322.58	+	4322.58i	0.244849	+	0.244849i
$679$		−	19135.5i		−	1.08152i
$680$	386.974	−	7028.73i	0.0218232	−	0.396381i
$681$		−	9285.87i		−	0.522519i
$682$	−12427.9	+	12427.9i	−0.697784	+	0.697784i
$683$	6638.10	−	6638.10i	0.371889	−	0.371889i	−0.496276	−	0.868165i	$-0.665300\pi$
$683$	6638.10	−	6638.10i	0.371889	−	0.371889i	0.868165	+	0.496276i	$0.165300\pi$
$684$	143.664			0.00803091
$685$	16864.6	−	15104.5i	0.940678	−	0.842503i
$686$			7134.79i			0.397096i
$687$	−2777.30	+	2777.30i	−0.154237	+	0.154237i
$688$	4724.69	+	4724.69i	0.261813	+	0.261813i
$689$	−8768.70			−0.484849
$690$	−12279.3	−	2441.67i	−0.677485	−	0.134714i
$691$	18671.1			1.02791			0.513953	−	0.857818i	$-0.328181\pi$
$691$	18671.1			1.02791			0.513953	+	0.857818i	$0.328181\pi$
$692$	3129.41	+	3129.41i	0.171911	+	0.171911i
$693$	694.994	−	694.994i	0.0380961	−	0.0380961i
$694$			2414.12i			0.132044i
$695$	−1259.78	+	22881.7i	−0.0687569	+	1.24885i
$696$	−11925.3			−0.649464
$697$	−16277.8	+	16277.8i	−0.884598	+	0.884598i
$698$	5429.07	−	5429.07i	0.294403	−	0.294403i
$699$		−	28202.3i		−	1.52605i
$700$	−7204.96	−	8994.09i	−0.389031	−	0.485635i
$701$			16896.1i			0.910353i	0.890401	+	0.455177i	$0.150424\pi$
$701$			16896.1i			0.910353i	−0.890401	+	0.455177i	$0.849576\pi$
$702$	6764.08	+	6764.08i	0.363666	+	0.363666i
$703$	2403.64	−	2403.64i	0.128954	−	0.128954i
$704$	2210.32			0.118330
$705$	−22225.6	−	1223.65i	−1.18732	−	0.0653694i
$706$	3691.78			0.196802
$707$	24222.4	−	24222.4i	1.28851	−	1.28851i
$708$	374.631	−	374.631i	0.0198863	−	0.0198863i
$709$	7468.97			0.395632			0.197816	−	0.980239i	$-0.436615\pi$
$709$	7468.97			0.395632			0.197816	+	0.980239i	$0.436615\pi$
$710$	−268.514	−	299.803i	−0.0141932	−	0.0158471i
$711$			1277.61i			0.0673895i
$712$	−2231.51	+	2231.51i	−0.117457	+	0.117457i
$713$	27787.6	+	3952.25i	1.45954	+	0.207592i
$714$			18415.1i			0.965219i
$715$	8597.19	+	9599.00i	0.449674	+	0.502073i
$716$	−12267.5			−0.640306
$717$	−10947.9	−	10947.9i	−0.570233	−	0.570233i
$718$	−14515.6	−	14515.6i	−0.754483	−	0.754483i
$719$		−	35163.3i		−	1.82388i	−0.410326	−	0.911939i	$-0.634585\pi$
$719$		−	35163.3i		−	1.82388i	0.410326	−	0.911939i	$-0.365415\pi$
$720$	12.1425	−	220.547i	0.000628504	−	0.0114157i
$721$	9676.05			0.499799
$722$	8503.55	+	8503.55i	0.438323	+	0.438323i
$723$	21887.5	+	21887.5i	1.12587	+	1.12587i
$724$	−7493.07			−0.384638
$725$	−4029.89	+	36487.1i	−0.206436	+	1.86910i
$726$	1403.49			0.0717469
$727$	−1878.64	+	1878.64i	−0.0958387	+	0.0958387i	−0.753401	−	0.657562i	$-0.771588\pi$
$727$	−1878.64	+	1878.64i	−0.0958387	+	0.0958387i	0.657562	+	0.753401i	$0.271588\pi$
$728$	4351.16	+	4351.16i	0.221517	+	0.221517i
$729$			20498.9i			1.04145i
$730$	8608.74	+	473.964i	0.436471	+	0.0240304i
$731$	−32866.8			−1.66296
$732$	−2754.14	+	2754.14i	−0.139066	+	0.139066i
$733$	11088.0	+	11088.0i	0.558725	+	0.558725i	0.928944	−	0.370220i	$-0.120718\pi$
$733$	11088.0	+	11088.0i	0.558725	+	0.558725i	−0.370220	+	0.928944i	$0.620718\pi$
$734$	−17054.2			−0.857606
$735$	7126.44	+	7956.87i	0.357636	+	0.399311i
$736$	−2119.57	−	2822.49i	−0.106153	−	0.141356i
$737$	−3267.91	−	3267.91i	−0.163331	−	0.163331i
$738$	−510.763	+	510.763i	−0.0254762	+	0.0254762i
$739$		−	18426.7i		−	0.917234i	−0.888634	−	0.458617i	$-0.848345\pi$
$739$		−	18426.7i		−	0.917234i	0.888634	−	0.458617i	$-0.151655\pi$
$740$	−3486.80	−	3893.11i	−0.173213	−	0.193397i
$741$		−	4927.37i		−	0.244280i
$742$	−8564.36	−	8564.36i	−0.423730	−	0.423730i
$743$	−15733.1	−	15733.1i	−0.776837	−	0.776837i	0.202455	−	0.979292i	$-0.435108\pi$
$743$	−15733.1	−	15733.1i	−0.776837	−	0.776837i	−0.979292	+	0.202455i	$0.935108\pi$
$744$		−	10332.7i		−	0.509161i
$745$	−29630.5	−	1631.34i	−1.45715	−	0.0802251i
$746$		−	14079.1i		−	0.690983i
$747$	1011.93	−	1011.93i	0.0495643	−	0.0495643i
$748$	−7687.92	+	7687.92i	−0.375800	+	0.375800i
$749$			16186.3i			0.789631i
$750$	13995.0	+	2330.39i	0.681367	+	0.113458i
$751$			4794.47i			0.232960i	0.993193	+	0.116480i	$0.0371611\pi$
$751$			4794.47i			0.232960i	−0.993193	+	0.116480i	$0.962839\pi$
$752$	−4437.55	−	4437.55i	−0.215187	−	0.215187i
$753$	−22387.0	−	22387.0i	−1.08343	−	1.08343i
$754$		−	19601.3i		−	0.946733i
$755$	−3799.39	−	209.180i	−0.183144	−	0.0100832i
$756$			13212.9i			0.635647i
$757$	8896.21	−	8896.21i	0.427131	−	0.427131i	−0.460519	−	0.887650i	$-0.652337\pi$
$757$	8896.21	−	8896.21i	0.427131	−	0.427131i	0.887650	+	0.460519i	$0.152337\pi$
$758$	−9482.48	−	9482.48i	−0.454379	−	0.454379i
$759$	11611.5	+	15462.3i	0.555300	+	0.739454i
$760$	−1938.00	+	1735.74i	−0.0924982	+	0.0828445i
$761$	−25854.0			−1.23155			−0.615773	−	0.787924i	$-0.711156\pi$
$761$	−25854.0			−1.23155			−0.615773	+	0.787924i	$0.711156\pi$
$762$	19973.5	+	19973.5i	0.949559	+	0.949559i
$763$	−24737.9	+	24737.9i	−1.17375	+	1.17375i
$764$	7599.47			0.359868
$765$	724.872	+	809.339i	0.0342585	+	0.0382506i
$766$			8864.33i			0.418122i
$767$	615.771	+	615.771i	0.0289885	+	0.0289885i
$768$	−918.845	+	918.845i	−0.0431718	+	0.0431718i
$769$	−22072.6			−1.03506			−0.517528	−	0.855666i	$-0.673148\pi$
$769$	−22072.6			−1.03506			−0.517528	+	0.855666i	$0.673148\pi$
$770$	−978.466	+	17772.2i	−0.0457941	+	0.831771i
$771$	23123.9			1.08014
$772$	−2088.01	−	2088.01i	−0.0973432	−	0.0973432i
$773$	−21974.2	−	21974.2i	−1.02245	−	1.02245i	−0.999742	−	0.0227116i	$-0.992770\pi$
$773$	−21974.2	−	21974.2i	−1.02245	−	1.02245i	−0.0227116	−	0.999742i	$-0.507230\pi$
$774$	−1031.29			−0.0478928
$775$	−31614.4	−	3491.72i	−1.46532	−	0.161840i
$776$			6641.91i			0.307256i
$777$	9667.58	+	9667.58i	0.446361	+	0.446361i
$778$	−3817.54	−	3817.54i	−0.175920	−	0.175920i
$779$	8507.99			0.391310
$780$	−7564.28	−	416.460i	−0.347237	−	0.0191175i
$781$			621.617i			0.0284804i
$782$	17189.4	+	2444.87i	0.786052	+	0.111801i
$783$	29761.0	−	29761.0i	1.35833	−	1.35833i
$784$			3011.53i			0.137187i
$785$	−25524.6	+	22860.7i	−1.16053	+	1.03941i
$786$	22953.0			1.04161
$787$	22171.3	−	22171.3i	1.00422	−	1.00422i	0.00423164	−	0.999991i	$-0.498653\pi$
$787$	22171.3	−	22171.3i	1.00422	−	1.00422i	0.999991	−	0.00423164i	$-0.00134698\pi$
$788$	−2364.53	+	2364.53i	−0.106895	+	0.106895i
$789$	−33740.5			−1.52243
$790$	−15435.9	−	17234.6i	−0.695171	−	0.776178i
$791$	−13878.7			−0.623855
$792$	−241.231	+	241.231i	−0.0108230	+	0.0108230i
$793$	−4526.91	−	4526.91i	−0.202718	−	0.202718i
$794$			2336.34i			0.104425i
$795$	14888.7	+	819.715i	0.664212	+	0.0365689i
$796$		−	2680.99i		−	0.119378i
$797$	−18583.3	+	18583.3i	−0.825916	+	0.825916i	−0.986949	−	0.161033i	$-0.948517\pi$
$797$	−18583.3	+	18583.3i	−0.825916	+	0.825916i	0.161033	+	0.986949i	$0.448517\pi$
$798$	4812.55	−	4812.55i	0.213487	−	0.213487i
$799$	30869.3			1.36680
$800$	2500.83	+	3121.84i	0.110522	+	0.137967i
$801$		−	487.087i		−	0.0214861i
$802$	−2846.29	+	2846.29i	−0.125319	+	0.125319i
$803$	−9416.12	−	9416.12i	−0.413808	−	0.413808i
$804$	2716.99			0.119180
$805$	23632.6	−	15793.0i	1.03471	−	0.691468i
$806$	16983.6			0.742212
$807$	19978.7	+	19978.7i	0.871481	+	0.871481i
$808$	−8407.55	+	8407.55i	−0.366060	+	0.366060i
$809$		−	3348.92i		−	0.145540i	−0.997349	−	0.0727700i	$-0.976816\pi$
$809$		−	3348.92i		−	0.145540i	0.997349	−	0.0727700i	$-0.0231839\pi$
$810$	−10355.3	−	11562.0i	−0.449196	−	0.501540i
$811$	−10843.3			−0.469493			−0.234747	−	0.972057i	$-0.575426\pi$
$811$	−10843.3			−0.469493			−0.234747	+	0.972057i	$0.575426\pi$
$812$	19144.5	−	19144.5i	0.827390	−	0.827390i
$813$	−5538.33	+	5538.33i	−0.238915	+	0.238915i
$814$			8072.04i			0.347574i
$815$	10980.1	−	9834.18i	0.471923	−	0.422670i
$816$		−	6391.84i		−	0.274215i
$817$	8589.32	+	8589.32i	0.367812	+	0.367812i
$818$	−17209.3	+	17209.3i	−0.735587	+	0.735587i
$819$	−949.759			−0.0405217
$820$	719.093	−	13061.1i	0.0306242	−	0.556235i
$821$	28815.9			1.22495			0.612473	−	0.790491i	$-0.290175\pi$
$821$	28815.9			1.22495			0.612473	+	0.790491i	$0.290175\pi$
$822$	14536.2	−	14536.2i	0.616798	−	0.616798i
$823$	−13149.8	+	13149.8i	−0.556954	+	0.556954i	−0.928439	−	0.371485i	$-0.878849\pi$
$823$	−13149.8	+	13149.8i	−0.556954	+	0.556954i	0.371485	+	0.928439i	$0.378849\pi$
$824$	−3358.54			−0.141991
$825$	−13700.2	−	17102.2i	−0.578156	−	0.721724i
$826$			1202.84i			0.0506686i
$827$	−20215.0	+	20215.0i	−0.849992	+	0.849992i	−0.990132	−	0.140140i	$-0.955245\pi$
$827$	−20215.0	+	20215.0i	−0.849992	+	0.849992i	0.140140	+	0.990132i	$0.455245\pi$
$828$	539.369	+	76.7150i	0.0226381	+	0.00321985i
$829$		−	5028.77i		−	0.210683i	−0.994436	−	0.105342i	$-0.966406\pi$
$829$		−	5028.77i		−	0.210683i	0.994436	−	0.105342i	$-0.0335936\pi$
$830$	−1424.67	+	25876.7i	−0.0595796	+	1.08216i
$831$	−29793.4			−1.24371
$832$	−1510.28	−	1510.28i	−0.0629322	−	0.0629322i
$833$	−10474.7	−	10474.7i	−0.435685	−	0.435685i
$834$			20808.3i			0.863949i
$835$	−16454.4	−	18371.8i	−0.681948	−	0.761414i
$836$	4018.28			0.166238
$837$	25786.6	+	25786.6i	1.06489	+	1.06489i
$838$	−9294.85	−	9294.85i	−0.383157	−	0.383157i
$839$	36780.3			1.51347			0.756733	−	0.653724i	$-0.226794\pi$
$839$	36780.3			1.51347			0.756733	+	0.653724i	$0.226794\pi$
$840$	−6981.25	−	7794.76i	−0.286757	−	0.320172i
$841$	−61854.0			−2.53614
$842$	−3194.50	+	3194.50i	−0.130748	+	0.130748i
$843$	−22773.1	−	22773.1i	−0.930423	−	0.930423i
$844$		−	58.2563i		−	0.00237591i
$845$	−665.786	+	12092.9i	−0.0271050	+	0.492316i
$846$	968.615			0.0393637
$847$	−2253.12	+	2253.12i	−0.0914026	+	0.0914026i
$848$	2972.68	+	2972.68i	0.120380	+	0.120380i
$849$	−12604.9			−0.509540
$850$	−19556.7	−	2159.98i	−0.789165	−	0.0871609i
$851$	10307.7	−	7740.63i	0.415208	−	0.311804i
$852$	−258.410	−	258.410i	−0.0103908	−	0.0103908i
$853$	−13283.5	+	13283.5i	−0.533197	+	0.533197i	−0.921522	−	0.388325i	$-0.873054\pi$
$853$	−13283.5	+	13283.5i	−0.533197	+	0.533197i	0.388325	+	0.921522i	$0.373054\pi$
$854$		−	8842.83i		−	0.354327i
$855$	22.0746	−	400.947i	0.000882965	−	0.0160375i
$856$		−	5618.23i		−	0.224331i
$857$	5653.76	+	5653.76i	0.225355	+	0.225355i	0.810749	−	0.585394i	$-0.199060\pi$
$857$	5653.76	+	5653.76i	0.225355	+	0.225355i	−0.585394	+	0.810749i	$0.699060\pi$
$858$	8273.70	+	8273.70i	0.329207	+	0.329207i
$859$			12916.6i			0.513047i	0.966538	+	0.256524i	$0.0825772\pi$
$859$			12916.6i			0.513047i	−0.966538	+	0.256524i	$0.917423\pi$
$860$	13911.9	−	12460.0i	0.551619	−	0.494049i
$861$			34219.7i			1.35448i
$862$	−7391.90	+	7391.90i	−0.292076	+	0.292076i
$863$	18172.2	−	18172.2i	0.716788	−	0.716788i	−0.251158	−	0.967946i	$-0.580811\pi$
$863$	18172.2	−	18172.2i	0.716788	−	0.716788i	0.967946	+	0.251158i	$0.0808113\pi$
$864$		−	4586.18i		−	0.180585i
$865$	9214.58	−	8252.89i	0.362202	−	0.324401i
$866$			10038.5i			0.393907i
$867$	4598.14	+	4598.14i	0.180116	+	0.180116i
$868$	16587.8	+	16587.8i	0.648650	+	0.648650i
$869$			35734.6i			1.39495i
$870$	−1832.37	+	33281.8i	−0.0714058	+	1.29696i
$871$			4465.84i			0.173730i
$872$	8586.49	−	8586.49i	0.333458	−	0.333458i
$873$	−724.889	−	724.889i	−0.0281028	−	0.0281028i
$874$	−3853.31	−	5131.18i	−0.149130	−	0.198587i
$875$	−26208.3	+	18726.0i	−1.01257	+	0.723492i
$876$	7828.69			0.301949
$877$	17689.5	+	17689.5i	0.681109	+	0.681109i	0.960250	−	0.279141i	$-0.0900498\pi$
$877$	17689.5	+	17689.5i	0.681109	+	0.681109i	−0.279141	+	0.960250i	$0.590050\pi$
$878$	−3923.53	+	3923.53i	−0.150812	+	0.150812i
$879$	−26919.1			−1.03295
$880$	339.624	−	6168.69i	0.0130099	−	0.236303i
$881$		−	13916.2i		−	0.532177i	−0.963949	−	0.266089i	$-0.914269\pi$
$881$		−	13916.2i		−	0.532177i	0.963949	−	0.266089i	$-0.0857314\pi$
$882$	−328.674	−	328.674i	−0.0125476	−	0.0125476i
$883$	−2950.43	+	2950.43i	−0.112446	+	0.112446i	−0.761091	−	0.648645i	$-0.775336\pi$
$883$	−2950.43	+	2950.43i	−0.112446	+	0.112446i	0.648645	+	0.761091i	$0.275336\pi$
$884$	10506.1			0.399727
$885$	−987.978	−	1103.11i	−0.0375260	−	0.0418988i
$886$	28329.4			1.07420
$887$	19546.3	+	19546.3i	0.739909	+	0.739909i	0.972560	−	0.232652i	$-0.0747402\pi$
$887$	19546.3	+	19546.3i	0.739909	+	0.739909i	−0.232652	+	0.972560i	$0.574740\pi$
$888$	−3355.60	−	3355.60i	−0.126809	−	0.126809i
$889$	−64129.8			−2.41940
$890$	5884.94	+	6570.70i	0.221644	+	0.247472i
$891$			23972.9i			0.901371i
$892$	−6967.36	−	6967.36i	−0.261530	−	0.261530i
$893$	−8067.30	−	8067.30i	−0.302309	−	0.302309i
$894$	−26945.6			−1.00805
$895$	−1884.95	+	34237.0i	−0.0703990	+	1.27868i
$896$		−	2950.17i		−	0.109998i
$897$	2631.16	−	18499.2i	0.0979396	−	0.688595i
$898$	3831.05	−	3831.05i	0.142365	−	0.142365i
$899$		−	74725.6i		−	2.77224i
$900$	−613.650	−	67.7758i	−0.0227278	−	0.00251022i
$901$	−20679.1			−0.764617
$902$	−14286.0	+	14286.0i	−0.527353	+	0.527353i
$903$	−34546.8	+	34546.8i	−1.27314	+	1.27314i
$904$	4817.27			0.177235
$905$	−1151.34	+	20912.1i	−0.0422893	+	0.768113i
$906$	−3455.12			−0.126698
$907$	26736.7	−	26736.7i	0.978805	−	0.978805i	−0.0209745	−	0.999780i	$-0.506677\pi$
$907$	26736.7	−	26736.7i	0.978805	−	0.978805i	0.999780	+	0.0209745i	$0.00667689\pi$
$908$	−5174.29	−	5174.29i	−0.189113	−	0.189113i
$909$		−	1835.18i		−	0.0669625i
$910$	12812.0	−	11474.9i	0.466720	−	0.418010i
$911$		−	18077.7i		−	0.657455i	−0.944425	−	0.328727i	$-0.893380\pi$
$911$		−	18077.7i		−	0.657455i	0.944425	−	0.328727i	$-0.106620\pi$
$912$	−1670.43	+	1670.43i	−0.0606506	+	0.0606506i
$913$	28303.6	−	28303.6i	1.02597	−	1.02597i
$914$	27694.7			1.00225
$915$	7263.23	+	8109.60i	0.262421	+	0.293000i
$916$			3095.14i			0.111644i
$917$	−36848.0	+	36848.0i	−1.32697	+	1.32697i
$918$	15951.6	+	15951.6i	0.573510	+	0.573510i
$919$	−21950.3			−0.787894			−0.393947	−	0.919133i	$-0.628891\pi$
$919$	−21950.3			−0.787894			−0.393947	+	0.919133i	$0.628891\pi$
$920$	−8202.84	+	5481.74i	−0.293956	+	0.196443i
$921$	−35086.5			−1.25531
$922$	−4201.69	−	4201.69i	−0.150082	−	0.150082i
$923$	424.743	−	424.743i	0.0151469	−	0.0151469i
$924$			16161.8i			0.575415i
$925$	−11400.9	+	9132.98i	−0.405253	+	0.324638i
$926$	−10121.3			−0.359188
$927$	366.546	−	366.546i	0.0129870	−	0.0129870i
$928$	−6645.03	+	6645.03i	−0.235058	+	0.235058i
$929$			50841.4i			1.79553i	0.440470	+	0.897767i	$0.354812\pi$
$929$			50841.4i			1.79553i	−0.440470	+	0.897767i	$0.645188\pi$
$930$	−28837.2	−	1587.66i	−1.01678	−	0.0559801i
$931$			5474.85i			0.192729i
$932$	−15714.9	−	15714.9i	−0.552317	−	0.552317i
$933$	21239.2	−	21239.2i	0.745273	−	0.745273i
$934$	28296.1			0.991303
$935$	20274.6	+	22637.2i	0.709145	+	0.791780i
$936$	329.660			0.0115120
$937$	22341.3	−	22341.3i	0.778932	−	0.778932i	−0.200717	−	0.979649i	$-0.564327\pi$
$937$	22341.3	−	22341.3i	0.778932	−	0.778932i	0.979649	+	0.200717i	$0.0643271\pi$
$938$	−4361.77	+	4361.77i	−0.151830	+	0.151830i
$939$	−34564.0			−1.20123
$940$	−13066.4	+	11702.7i	−0.453382	+	0.406064i
$941$			36032.4i			1.24827i	0.781317	+	0.624135i	$0.214548\pi$
$941$			36032.4i			1.24827i	−0.781317	+	0.624135i	$0.785452\pi$
$942$	−22000.5	+	22000.5i	−0.760951	+	0.760951i
$943$	31942.1	+	4543.16i	1.10305	+	0.156888i
$944$		−	417.505i		−	0.0143947i
$945$	36875.4	+	2030.22i	1.26937	+	0.0698867i
$946$	−28845.2			−0.991372
$947$	−18091.0	−	18091.0i	−0.620780	−	0.620780i	0.324951	−	0.945731i	$-0.394652\pi$
$947$	−18091.0	−	18091.0i	−0.620780	−	0.620780i	−0.945731	+	0.324951i	$0.894652\pi$
$948$	−14855.1	−	14855.1i	−0.508936	−	0.508936i
$949$			12867.8i			0.440155i
$950$	4546.42	+	5675.39i	0.155269	+	0.193825i
$951$	29655.5			1.01119
$952$	10261.3	+	10261.3i	0.349338	+	0.349338i
$953$	−15084.4	−	15084.4i	−0.512730	−	0.512730i	0.402632	−	0.915362i	$-0.368095\pi$
$953$	−15084.4	−	15084.4i	−0.512730	−	0.512730i	−0.915362	+	0.402632i	$0.868095\pi$
$954$	−648.867			−0.0220208
$955$	1167.69	−	21209.0i	0.0395660	−	0.718648i
$956$	−12200.8			−0.412764
$957$	36403.2	−	36403.2i	1.22962	−	1.22962i
$958$	7667.22	+	7667.22i	0.258577	+	0.258577i
$959$			46671.9i			1.57155i
$960$	2423.18	+	2705.55i	0.0814665	+	0.0909596i
$961$	34955.4			1.17335
$962$	5515.52	−	5515.52i	0.184852	−	0.184852i
$963$	613.166	+	613.166i	0.0205182	+	0.0205182i
$964$	24392.4			0.814966
$965$	−6148.16	+	5506.50i	−0.205094	+	0.183690i
$966$	20637.9	−	15498.2i	0.687386	−	0.516199i
$967$	−34559.9	−	34559.9i	−1.14930	−	1.14930i	−0.986691	−	0.162608i	$-0.948009\pi$
$967$	−34559.9	−	34559.9i	−1.14930	−	1.14930i	−0.162608	−	0.986691i	$-0.551991\pi$
$968$	782.053	−	782.053i	0.0259671	−	0.0259671i
$969$		−	11620.1i		−	0.385235i
$970$	18536.6	+	1020.56i	0.613583	+	0.0337815i
$971$		−	40057.3i		−	1.32389i	−0.749551	−	0.661947i	$-0.769730\pi$
$971$		−	40057.3i		−	1.32389i	0.749551	−	0.661947i	$-0.230270\pi$
$972$	979.170	+	979.170i	0.0323116	+	0.0323116i
$973$	−33405.1	−	33405.1i	−1.10063	−	1.10063i
$974$		−	13567.6i		−	0.446340i
$975$	−2324.56	+	21046.8i	−0.0763544	+	0.691321i
$976$			3069.33i			0.100663i
$977$	15511.6	−	15511.6i	0.507942	−	0.507942i	−0.405952	−	0.913894i	$-0.633060\pi$
$977$	15511.6	−	15511.6i	0.507942	−	0.507942i	0.913894	+	0.405952i	$0.133060\pi$
$978$	9464.14	−	9464.14i	0.309438	−	0.309438i
$979$		−	13623.8i		−	0.444758i
$980$	8404.74	+	462.733i	0.273959	+	0.0150831i
$981$			1874.23i			0.0609987i
$982$	1776.92	+	1776.92i	0.0577433	+	0.0577433i
$983$	−16036.2	−	16036.2i	−0.520320	−	0.520320i	0.397348	−	0.917668i	$-0.369931\pi$
$983$	−16036.2	−	16036.2i	−0.520320	−	0.520320i	−0.917668	+	0.397348i	$0.869931\pi$
$984$		−	11877.6i		−	0.384801i
$985$	6235.76	+	6962.40i	0.201714	+	0.225219i
$986$		−	46225.4i		−	1.49302i
$987$	32447.2	−	32447.2i	1.04641	−	1.04641i
$988$	−2745.64	−	2745.64i	−0.0884113	−	0.0884113i
$989$	27660.9	+	36834.1i	0.889349	+	1.18428i
$990$	636.176	+	710.308i	0.0204232	+	0.0228031i
$991$	13807.0			0.442576			0.221288	−	0.975208i	$-0.428974\pi$
$991$	13807.0			0.442576			0.221288	+	0.975208i	$0.428974\pi$
$992$	−5757.62	−	5757.62i	−0.184279	−	0.184279i
$993$	−30451.3	+	30451.3i	−0.973156	+	0.973156i
$994$	829.689			0.0264750
$995$	−7482.25	−	411.944i	−0.238395	−	0.0131251i
$996$			23532.0i			0.748633i
$997$	26167.7	+	26167.7i	0.831234	+	0.831234i	0.987686	−	0.156451i	$-0.0500054\pi$
$997$	26167.7	+	26167.7i	0.831234	+	0.831234i	−0.156451	+	0.987686i	$0.550005\pi$
$998$	25901.9	−	25901.9i	0.821554	−	0.821554i
$999$	16748.6			0.530434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.e.a.137.6	yes	72
5.3	odd	4	inner	230.4.e.a.183.5	yes	72
23.22	odd	2	inner	230.4.e.a.137.5	✓	72
115.68	even	4	inner	230.4.e.a.183.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.e.a.137.5	✓	72	23.22	odd	2	inner
230.4.e.a.137.6	yes	72	1.1	even	1	trivial
230.4.e.a.183.5	yes	72	5.3	odd	4	inner
230.4.e.a.183.6	yes	72	115.68	even	4	inner

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

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-3.58924 + 3.58924i) q^{3} +4.00000i q^{4} +(11.1634 + 0.614616i) q^{5} +10.1519 q^{6} +(-16.2976 + 16.2976i) q^{7} +(5.65685 - 5.65685i) q^{8} +1.23476i q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-3.58924 + 3.58924i) q^{3} +4.00000i q^{4} +(11.1634 + 0.614616i) q^{5} +10.1519 q^{6} +(-16.2976 + 16.2976i) q^{7} +(5.65685 - 5.65685i) q^{8} +1.23476i q^{9} +(-14.9183 - 16.6567i) q^{10} +34.5362i q^{11} +(-14.3569 - 14.3569i) q^{12} +(23.5981 - 23.5981i) q^{13} +46.0964 q^{14} +(-42.2742 + 37.8622i) q^{15} -16.0000 q^{16} +(55.6511 - 55.6511i) q^{17} +(1.74622 - 1.74622i) q^{18} -29.0874 q^{19} +(-2.45846 + 44.6537i) q^{20} -116.992i q^{21} +(48.8416 - 48.8416i) q^{22} +(-109.205 - 15.5323i) q^{23} +40.6076i q^{24} +(124.244 + 13.7224i) q^{25} -66.7456 q^{26} +(-101.341 - 101.341i) q^{27} +(-65.1902 - 65.1902i) q^{28} +293.672i q^{29} +(113.330 + 6.23951i) q^{30} -254.453 q^{31} +(22.6274 + 22.6274i) q^{32} +(-123.959 - 123.959i) q^{33} -157.405 q^{34} +(-191.953 + 171.920i) q^{35} -4.93905 q^{36} +(-82.6349 + 82.6349i) q^{37} +(41.1358 + 41.1358i) q^{38} +169.399i q^{39} +(66.6267 - 59.6731i) q^{40} -292.497 q^{41} +(-165.451 + 165.451i) q^{42} +(-295.293 - 295.293i) q^{43} -138.145 q^{44} +(-0.758904 + 13.7842i) q^{45} +(132.473 + 176.405i) q^{46} +(277.347 + 277.347i) q^{47} +(57.4278 - 57.4278i) q^{48} -188.220i q^{49} +(-156.302 - 195.115i) q^{50} +399.490i q^{51} +(94.3925 + 94.3925i) q^{52} +(-185.792 - 185.792i) q^{53} +286.636i q^{54} +(-21.2265 + 385.543i) q^{55} +184.386i q^{56} +(104.402 - 104.402i) q^{57} +(415.314 - 415.314i) q^{58} +26.0941i q^{59} +(-151.449 - 169.097i) q^{60} -191.833i q^{61} +(359.851 + 359.851i) q^{62} +(-20.1236 - 20.1236i) q^{63} -64.0000i q^{64} +(277.940 - 248.932i) q^{65} +350.608i q^{66} +(-94.6227 + 94.6227i) q^{67} +(222.604 + 222.604i) q^{68} +(447.712 - 336.214i) q^{69} +(514.595 + 28.3316i) q^{70} +17.9990 q^{71} +(6.98487 + 6.98487i) q^{72} +(-272.645 + 272.645i) q^{73} +233.727 q^{74} +(-495.196 + 396.690i) q^{75} -116.350i q^{76} +(-562.856 - 562.856i) q^{77} +(239.566 - 239.566i) q^{78} +1034.70 q^{79} +(-178.615 - 9.83385i) q^{80} +694.137 q^{81} +(413.653 + 413.653i) q^{82} +(-819.532 - 819.532i) q^{83} +467.966 q^{84} +(655.461 - 587.053i) q^{85} +835.215i q^{86} +(-1054.06 - 1054.06i) q^{87} +(195.366 + 195.366i) q^{88} -394.478 q^{89} +(20.5670 - 18.4205i) q^{90} +769.184i q^{91} +(62.1294 - 436.820i) q^{92} +(913.292 - 913.292i) q^{93} -784.455i q^{94} +(-324.716 - 17.8776i) q^{95} -162.430 q^{96} +(-587.067 + 587.067i) q^{97} +(-266.184 + 266.184i) q^{98} -42.6441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) \) 72 * q - 16 * q^3 - 16 * q^6	\( 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) \) 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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