LMFDB - Embedded newform 231.4.i.a.67.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [231,4,Mod(67,231)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("231.67"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(231, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 55 x^{14} - 108 x^{13} + 1559 x^{12} - 2354 x^{11} + 27458 x^{10} - 12372 x^{9} + \cdots + 7225344 $ x^16 - 4x^15 + 55x^14 - 108x^13 + 1559x^12 - 2354x^11 + 27458x^10 - 12372x^9 + 283834x^8 - 22636x^7 + 1962928x^6 + 1329492x^5 + 5746308x^4 + 2322624x^3 + 8808192x^2 + 4386816*x + 7225344
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$1.74221 - 3.01759i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.4.i.a.100.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24221 - 2.15156i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.913847 - 1.58283i) q^{4} +(2.47926 + 4.29420i) q^{5} -7.45324 q^{6} +(5.11112 - 17.8010i) q^{7} -24.4160 q^{8} +(-4.50000 - 7.79423i) q^{9} +(6.15950 - 10.6686i) q^{10} +(-5.50000 + 9.52628i) q^{11} +(-2.74154 - 4.74849i) q^{12} -15.2217 q^{13} +(-44.6491 + 11.1156i) q^{14} +14.8756 q^{15} +(23.0190 + 39.8701i) q^{16} +(0.586100 - 1.01516i) q^{17} +(-11.1799 + 19.3641i) q^{18} +(-67.1398 - 116.290i) q^{19} +9.06266 q^{20} +(-38.5817 - 39.9806i) q^{21} +27.3285 q^{22} +(-42.5332 - 73.6697i) q^{23} +(-36.6241 + 63.4348i) q^{24} +(50.2065 - 86.9603i) q^{25} +(18.9084 + 32.7504i) q^{26} -27.0000 q^{27} +(-23.5052 - 24.3575i) q^{28} +44.5084 q^{29} +(-18.4785 - 32.0057i) q^{30} +(-132.686 + 229.818i) q^{31} +(-40.4755 + 70.1057i) q^{32} +(16.5000 + 28.5788i) q^{33} -2.91223 q^{34} +(89.1130 - 22.1852i) q^{35} -16.4493 q^{36} +(8.69454 + 15.0594i) q^{37} +(-166.803 + 288.911i) q^{38} +(-22.8325 + 39.5470i) q^{39} +(-60.5337 - 104.847i) q^{40} +79.0547 q^{41} +(-38.0944 + 132.675i) q^{42} -323.538 q^{43} +(10.0523 + 17.4111i) q^{44} +(22.3133 - 38.6478i) q^{45} +(-105.670 + 183.026i) q^{46} +(239.778 + 415.308i) q^{47} +138.114 q^{48} +(-290.753 - 181.966i) q^{49} -249.468 q^{50} +(-1.75830 - 3.04547i) q^{51} +(-13.9103 + 24.0933i) q^{52} +(46.1456 - 79.9266i) q^{53} +(33.5396 + 58.0922i) q^{54} -54.5437 q^{55} +(-124.793 + 434.631i) q^{56} -402.839 q^{57} +(-55.2886 - 95.7626i) q^{58} +(-118.898 + 205.937i) q^{59} +(13.5940 - 23.5455i) q^{60} +(-170.461 - 295.248i) q^{61} +659.292 q^{62} +(-161.745 + 40.2673i) q^{63} +569.420 q^{64} +(-37.7385 - 65.3649i) q^{65} +(40.9928 - 71.0016i) q^{66} +(366.559 - 634.898i) q^{67} +(-1.07121 - 1.85539i) q^{68} -255.199 q^{69} +(-158.430 - 164.174i) q^{70} -327.228 q^{71} +(109.872 + 190.304i) q^{72} +(370.181 - 641.172i) q^{73} +(21.6008 - 37.4137i) q^{74} +(-150.620 - 260.881i) q^{75} -245.422 q^{76} +(141.466 + 146.596i) q^{77} +113.451 q^{78} +(34.5321 + 59.8113i) q^{79} +(-114.140 + 197.696i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-98.2022 - 170.091i) q^{82} +423.586 q^{83} +(-98.5403 + 24.5321i) q^{84} +5.81238 q^{85} +(401.900 + 696.112i) q^{86} +(66.7625 - 115.636i) q^{87} +(134.288 - 232.594i) q^{88} +(-66.0794 - 114.453i) q^{89} -110.871 q^{90} +(-77.7998 + 270.961i) q^{91} -155.475 q^{92} +(398.057 + 689.455i) q^{93} +(595.709 - 1031.80i) q^{94} +(332.914 - 576.624i) q^{95} +(121.427 + 210.317i) q^{96} +1117.29 q^{97} +(-30.3375 + 851.613i) q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 24 q^{3} - 30 q^{4} - 20 q^{5} + 24 q^{6} + 18 q^{7} - 156 q^{8} - 72 q^{9} - 94 q^{10} - 88 q^{11} + 90 q^{12} - 188 q^{13} + 52 q^{14} - 120 q^{15} + 10 q^{16} - 144 q^{17} + 36 q^{18}+ \cdots + 1584 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 24 * q^3 - 30 * q^4 - 20 * q^5 + 24 * q^6 + 18 * q^7 - 156 * q^8 - 72 * q^9 - 94 * q^10 - 88 * q^11 + 90 * q^12 - 188 * q^13 + 52 * q^14 - 120 * q^15 + 10 * q^16 - 144 * q^17 + 36 * q^18 + 8 * q^19 - 288 * q^20 - 36 * q^21 - 88 * q^22 + 286 * q^23 - 234 * q^24 + 206 * q^25 - 132 * q^26 - 432 * q^27 + 14 * q^28 + 40 * q^29 + 282 * q^30 - 192 * q^31 + 948 * q^32 + 264 * q^33 - 972 * q^34 - 112 * q^35 + 540 * q^36 + 666 * q^37 - 200 * q^38 - 282 * q^39 - 486 * q^40 + 120 * q^41 - 660 * q^42 - 492 * q^43 - 330 * q^44 - 180 * q^45 - 454 * q^46 - 922 * q^47 + 60 * q^48 - 386 * q^49 + 2972 * q^50 + 432 * q^51 + 1714 * q^52 + 1064 * q^53 - 108 * q^54 + 440 * q^55 + 1176 * q^56 + 48 * q^57 + 1832 * q^58 - 50 * q^59 - 432 * q^60 - 1174 * q^61 - 1388 * q^62 - 270 * q^63 + 3204 * q^64 + 1840 * q^65 - 132 * q^66 + 766 * q^67 - 2806 * q^68 + 1716 * q^69 - 2584 * q^70 - 1572 * q^71 + 702 * q^72 + 398 * q^73 + 1504 * q^74 - 618 * q^75 - 3036 * q^76 + 132 * q^77 - 792 * q^78 + 1886 * q^79 + 504 * q^80 - 648 * q^81 - 2738 * q^82 - 1564 * q^83 - 132 * q^84 - 3284 * q^85 + 356 * q^86 + 60 * q^87 + 858 * q^88 - 2380 * q^89 + 1692 * q^90 + 2240 * q^91 - 4512 * q^92 + 576 * q^93 + 2588 * q^94 - 58 * q^95 - 2844 * q^96 - 504 * q^97 + 1132 * q^98 + 1584 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.24221	−	2.15156i	−0.439186	−	0.760693i	0.558441	−	0.829544i	$-0.311400\pi$
$2$	−1.24221	−	2.15156i	−0.439186	−	0.760693i	−0.997627	+	0.0688516i	$0.978067\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	0.913847	−	1.58283i	0.114231	−	0.197854i
$5$	2.47926	+	4.29420i	0.221752	+	0.384085i	0.955340	−	0.295509i	$-0.0954892\pi$
$5$	2.47926	+	4.29420i	0.221752	+	0.384085i	−0.733588	+	0.679594i	$0.762156\pi$
$6$	−7.45324			−0.507129
$7$	5.11112	−	17.8010i	0.275975	−	0.961165i
$7$	5.11112	−	17.8010i	0.275975	−	0.961165i
$8$	−24.4160			−1.07905
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	6.15950	−	10.6686i	0.194781	−	0.337370i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	−2.74154	−	4.74849i	−0.0659513	−	0.114231i
$13$	−15.2217			−0.324748			−0.162374	−	0.986729i	$-0.551915\pi$
$13$	−15.2217			−0.324748			−0.162374	+	0.986729i	$0.551915\pi$
$14$	−44.6491	+	11.1156i	−0.852356	+	0.212198i
$15$	14.8756			0.256057
$16$	23.0190	+	39.8701i	0.359672	+	0.622970i
$17$	0.586100	−	1.01516i	0.00836178	−	0.0144830i	−0.861814	−	0.507224i	$-0.830672\pi$
$17$	0.586100	−	1.01516i	0.00836178	−	0.0144830i	0.870176	+	0.492741i	$0.164005\pi$
$18$	−11.1799	+	19.3641i	−0.146395	+	0.253564i
$19$	−67.1398	−	116.290i	−0.810680	−	1.40414i	−0.912389	−	0.409325i	$-0.865764\pi$
$19$	−67.1398	−	116.290i	−0.810680	−	1.40414i	0.101709	−	0.994814i	$-0.467569\pi$
$20$	9.06266			0.101324
$21$	−38.5817	−	39.9806i	−0.400915	−	0.415452i
$22$	27.3285			0.264839
$23$	−42.5332	−	73.6697i	−0.385600	−	0.667878i	0.606253	−	0.795272i	$-0.292672\pi$
$23$	−42.5332	−	73.6697i	−0.385600	−	0.667878i	−0.991852	+	0.127394i	$0.959339\pi$
$24$	−36.6241	+	63.4348i	−0.311494	+	0.539524i
$25$	50.2065	−	86.9603i	0.401652	−	0.695682i
$26$	18.9084	+	32.7504i	0.142625	+	0.247034i
$27$	−27.0000			−0.192450
$28$	−23.5052	−	24.3575i	−0.158645	−	0.164397i
$29$	44.5084			0.285000			0.142500	−	0.989795i	$-0.454486\pi$
$29$	44.5084			0.285000			0.142500	+	0.989795i	$0.454486\pi$
$30$	−18.4785	−	32.0057i	−0.112457	−	0.194781i
$31$	−132.686	+	229.818i	−0.768744	+	1.33150i	0.169500	+	0.985530i	$0.445785\pi$
$31$	−132.686	+	229.818i	−0.768744	+	1.33150i	−0.938244	+	0.345974i	$0.887549\pi$
$32$	−40.4755	+	70.1057i	−0.223598	+	0.387283i
$33$	16.5000	+	28.5788i	0.0870388	+	0.150756i
$34$	−2.91223			−0.0146895
$35$	89.1130	−	22.1852i	0.430367	−	0.107142i
$36$	−16.4493			−0.0761540
$37$	8.69454	+	15.0594i	0.0386317	+	0.0669121i	0.884695	−	0.466171i	$-0.154367\pi$
$37$	8.69454	+	15.0594i	0.0386317	+	0.0669121i	−0.846063	+	0.533083i	$0.821033\pi$
$38$	−166.803	+	288.911i	−0.712079	+	1.23336i
$39$	−22.8325	+	39.5470i	−0.0937468	+	0.162374i
$40$	−60.5337	−	104.847i	−0.239281	−	0.414446i
$41$	79.0547			0.301129			0.150564	−	0.988600i	$-0.451891\pi$
$41$	79.0547			0.301129			0.150564	+	0.988600i	$0.451891\pi$
$42$	−38.0944	+	132.675i	−0.139955	+	0.487434i
$43$	−323.538			−1.14742			−0.573710	−	0.819059i	$-0.694496\pi$
$43$	−323.538			−1.14742			−0.573710	+	0.819059i	$0.694496\pi$
$44$	10.0523	+	17.4111i	0.0344419	+	0.0596552i
$45$	22.3133	−	38.6478i	0.0739172	−	0.128028i
$46$	−105.670	+	183.026i	−0.338700	+	0.586646i
$47$	239.778	+	415.308i	0.744155	+	1.28891i	0.950589	+	0.310453i	$0.100481\pi$
$47$	239.778	+	415.308i	0.744155	+	1.28891i	−0.206434	+	0.978461i	$0.566186\pi$
$48$	138.114			0.415313
$49$	−290.753	−	181.966i	−0.847676	−	0.530514i
$50$	−249.468			−0.705601
$51$	−1.75830	−	3.04547i	−0.00482767	−	0.00836178i
$52$	−13.9103	+	24.0933i	−0.0370963	+	0.0642527i
$53$	46.1456	−	79.9266i	0.119596	−	0.207146i	−0.800012	−	0.599985i	$-0.795173\pi$
$53$	46.1456	−	79.9266i	0.119596	−	0.207146i	0.919608	+	0.392838i	$0.128507\pi$
$54$	33.5396	+	58.0922i	0.0845214	+	0.146395i
$55$	−54.5437			−0.133721
$56$	−124.793	+	434.631i	−0.297790	+	1.03714i
$57$	−402.839			−0.936093
$58$	−55.2886	−	95.7626i	−0.125168	−	0.216797i
$59$	−118.898	+	205.937i	−0.262359	+	0.454420i	−0.966868	−	0.255275i	$-0.917834\pi$
$59$	−118.898	+	205.937i	−0.262359	+	0.454420i	0.704509	+	0.709695i	$0.251167\pi$
$60$	13.5940	−	23.5455i	0.0292496	−	0.0506618i
$61$	−170.461	−	295.248i	−0.357793	−	0.619715i	0.629799	−	0.776758i	$-0.283137\pi$
$61$	−170.461	−	295.248i	−0.357793	−	0.619715i	−0.987592	+	0.157043i	$0.949804\pi$
$62$	659.292			1.35049
$63$	−161.745	+	40.2673i	−0.323460	+	0.0805271i
$64$	569.420			1.11215
$65$	−37.7385	−	65.3649i	−0.0720135	−	0.124731i
$66$	40.9928	−	71.0016i	0.0764525	−	0.132420i
$67$	366.559	−	634.898i	0.668392	−	1.15769i	−0.309961	−	0.950749i	$-0.600316\pi$
$67$	366.559	−	634.898i	0.668392	−	1.15769i	0.978354	−	0.206940i	$-0.0663505\pi$
$68$	−1.07121	−	1.85539i	−0.00191035	−	0.00330882i
$69$	−255.199			−0.445252
$70$	−158.430	−	164.174i	−0.270514	−	0.280322i
$71$	−327.228			−0.546969			−0.273484	−	0.961876i	$-0.588176\pi$
$71$	−327.228			−0.546969			−0.273484	+	0.961876i	$0.588176\pi$
$72$	109.872	+	190.304i	0.179841	+	0.311494i
$73$	370.181	−	641.172i	0.593512	−	1.02799i	−0.400243	−	0.916409i	$-0.631074\pi$
$73$	370.181	−	641.172i	0.593512	−	1.02799i	0.993755	−	0.111584i	$-0.0355923\pi$
$74$	21.6008	−	37.4137i	0.0339330	−	0.0587737i
$75$	−150.620	−	260.881i	−0.231894	−	0.401652i
$76$	−245.422			−0.370419
$77$	141.466	+	146.596i	0.209371	+	0.216963i
$78$	113.451			0.164689
$79$	34.5321	+	59.8113i	0.0491793	+	0.0851810i	0.889567	−	0.456804i	$-0.151006\pi$
$79$	34.5321	+	59.8113i	0.0491793	+	0.0851810i	−0.840388	+	0.541986i	$0.817673\pi$
$80$	−114.140	+	197.696i	−0.159516	+	0.276289i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−98.2022	−	170.091i	−0.132252	−	0.229066i
$83$	423.586			0.560177			0.280088	−	0.959974i	$-0.409636\pi$
$83$	423.586			0.560177			0.280088	+	0.959974i	$0.409636\pi$
$84$	−98.5403	+	24.5321i	−0.127996	+	0.0318652i
$85$	5.81238			0.00741696
$86$	401.900	+	696.112i	0.503931	+	0.872833i
$87$	66.7625	−	115.636i	0.0822724	−	0.142500i
$88$	134.288	−	232.594i	0.162672	−	0.281757i
$89$	−66.0794	−	114.453i	−0.0787012	−	0.136314i	0.823989	−	0.566606i	$-0.191744\pi$
$89$	−66.0794	−	114.453i	−0.0787012	−	0.136314i	−0.902690	+	0.430292i	$0.858411\pi$
$90$	−110.871			−0.129854
$91$	−77.7998	+	270.961i	−0.0896224	+	0.312137i
$92$	−155.475			−0.176190
$93$	398.057	+	689.455i	0.443835	+	0.768744i
$94$	595.709	−	1031.80i	0.653645	−	1.13215i
$95$	332.914	−	576.624i	0.359539	−	0.622741i
$96$	121.427	+	210.317i	0.129094	+	0.223598i
$97$	1117.29			1.16952			0.584760	−	0.811206i	$-0.301189\pi$
$97$	1117.29			1.16952			0.584760	+	0.811206i	$0.301189\pi$
$98$	−30.3375	+	851.613i	−0.0312709	+	0.877816i
$99$	99.0000			0.100504
$100$	−91.7622	−	158.937i	−0.0917622	−	0.158937i
$101$	651.125	−	1127.78i	0.641479	−	1.11107i	−0.343624	−	0.939107i	$-0.611654\pi$
$101$	651.125	−	1127.78i	0.641479	−	1.11107i	0.985103	−	0.171967i	$-0.0550122\pi$
$102$	−4.36835	+	7.56620i	−0.00424050	+	0.00734476i
$103$	−86.5588	−	149.924i	−0.0828048	−	0.143422i	0.821649	−	0.569994i	$-0.193054\pi$
$103$	−86.5588	−	149.924i	−0.0828048	−	0.143422i	−0.904454	+	0.426572i	$0.859721\pi$
$104$	371.653			0.350419
$105$	76.0308	−	264.800i	0.0706652	−	0.246113i
$106$	−229.290			−0.210100
$107$	−32.6773	−	56.5987i	−0.0295237	−	0.0511365i	0.850886	−	0.525350i	$-0.176066\pi$
$107$	−32.6773	−	56.5987i	−0.0295237	−	0.0511365i	−0.880410	+	0.474214i	$0.842732\pi$
$108$	−24.6739	+	42.7364i	−0.0219838	+	0.0380770i
$109$	1115.81	−	1932.64i	0.980506	−	1.69829i	0.320086	−	0.947388i	$-0.396288\pi$
$109$	1115.81	−	1932.64i	0.980506	−	1.69829i	0.660419	−	0.750897i	$-0.270379\pi$
$110$	67.7545	+	117.354i	0.0587286	+	0.101721i
$111$	52.1672			0.0446081
$112$	827.381	−	205.981i	0.698037	−	0.173780i
$113$	−264.433			−0.220140			−0.110070	−	0.993924i	$-0.535107\pi$
$113$	−264.433			−0.220140			−0.110070	+	0.993924i	$0.535107\pi$
$114$	500.409	+	866.733i	0.411119	+	0.712079i
$115$	210.902	−	365.293i	0.171015	−	0.296206i
$116$	40.6739	−	70.4492i	0.0325558	−	0.0563883i
$117$	68.4975	+	118.641i	0.0541247	+	0.0937468i
$118$	590.784			0.460899
$119$	−15.0752	−	15.6218i	−0.0116129	−	0.0120340i
$120$	−363.202			−0.276297
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	−423.496	+	733.517i	−0.314275	+	0.544340i
$123$	118.582	−	205.390i	0.0869283	−	0.150564i
$124$	242.509	+	420.038i	0.175629	+	0.304198i
$125$	1117.72			0.799772
$126$	287.559	+	297.985i	0.203316	+	0.210687i
$127$	−649.675			−0.453932			−0.226966	−	0.973903i	$-0.572881\pi$
$127$	−649.675			−0.453932			−0.226966	+	0.973903i	$0.572881\pi$
$128$	−383.532	−	664.297i	−0.264842	−	0.458720i
$129$	−485.306	+	840.575i	−0.331231	+	0.573710i
$130$	−93.7579	+	162.393i	−0.0632547	+	0.109560i
$131$	−1020.94	−	1768.31i	−0.680913	−	1.17938i	−0.974703	−	0.223506i	$-0.928250\pi$
$131$	−1020.94	−	1768.31i	−0.680913	−	1.17938i	0.293789	−	0.955870i	$-0.405084\pi$
$132$	60.3139			0.0397701
$133$	−2413.23	+	600.787i	−1.57334	+	0.391690i
$134$	−1821.37			−1.17419
$135$	−66.9400	−	115.944i	−0.0426761	−	0.0739172i
$136$	−14.3103	+	24.7861i	−0.00902275	+	0.0156279i
$137$	1408.41	−	2439.44i	0.878310	−	1.52128i	0.0251165	−	0.999685i	$-0.492004\pi$
$137$	1408.41	−	2439.44i	0.878310	−	1.52128i	0.853194	−	0.521594i	$-0.174662\pi$
$138$	317.010	+	549.078i	0.195549	+	0.338700i
$139$	1643.67			1.00298			0.501490	−	0.865163i	$-0.332785\pi$
$139$	1643.67			1.00298			0.501490	+	0.865163i	$0.332785\pi$
$140$	46.3204	−	161.325i	0.0279628	−	0.0973887i
$141$	1438.67			0.859276
$142$	406.484	+	704.052i	0.240221	+	0.416075i
$143$	83.7192	−	145.006i	0.0489577	−	0.0847972i
$144$	207.171	−	358.830i	0.119891	−	0.207657i
$145$	110.348	+	191.128i	0.0631992	+	0.109464i
$146$	−1839.36			−1.04265
$147$	−908.892	+	482.448i	−0.509960	+	0.270692i
$148$	31.7819			0.0176517
$149$	188.362	+	326.252i	0.103565	+	0.179380i	0.913151	−	0.407621i	$-0.133642\pi$
$149$	188.362	+	326.252i	0.103565	+	0.179380i	−0.809586	+	0.587001i	$0.800308\pi$
$150$	−374.201	+	648.136i	−0.203689	+	0.352800i
$151$	−76.6136	+	132.699i	−0.0412896	+	0.0715156i	−0.885932	−	0.463816i	$-0.846480\pi$
$151$	−76.6136	+	132.699i	−0.0412896	+	0.0715156i	0.844642	+	0.535331i	$0.179813\pi$
$152$	1639.29	+	2839.33i	0.874762	+	1.51513i
$153$	−10.5498			−0.00557452
$154$	139.680	−	486.476i	0.0730889	−	0.254554i
$155$	−1315.85			−0.681881
$156$	41.7308	+	72.2799i	0.0214176	+	0.0370963i
$157$	1445.27	−	2503.28i	0.734683	−	1.27251i	−0.220179	−	0.975459i	$-0.570664\pi$
$157$	1445.27	−	2503.28i	0.734683	−	1.27251i	0.954862	−	0.297049i	$-0.0960025\pi$
$158$	85.7920	−	148.596i	0.0431977	−	0.0748207i
$159$	−138.437	−	239.780i	−0.0690488	−	0.119596i
$160$	−401.397			−0.198333
$161$	−1528.79	+	380.600i	−0.748357	+	0.186307i
$162$	201.237			0.0975969
$163$	1645.50	+	2850.09i	0.790708	+	1.36955i	0.925529	+	0.378677i	$0.123621\pi$
$163$	1645.50	+	2850.09i	0.790708	+	1.36955i	−0.134821	+	0.990870i	$0.543046\pi$
$164$	72.2439	−	125.130i	0.0343982	−	0.0595794i
$165$	−81.8156	+	141.709i	−0.0386020	+	0.0668607i
$166$	−526.182	−	911.373i	−0.246022	−	0.426122i
$167$	−1959.51			−0.907973			−0.453987	−	0.891009i	$-0.649999\pi$
$167$	−1959.51			−0.907973			−0.453987	+	0.891009i	$0.649999\pi$
$168$	942.013	+	976.169i	0.432607	+	0.448292i
$169$	−1965.30			−0.894538
$170$	−7.22018	−	12.5057i	−0.00325742	−	0.00564203i
$171$	−604.258	+	1046.61i	−0.270227	+	0.468046i
$172$	−295.664	+	512.105i	−0.131071	+	0.227021i
$173$	1973.73	+	3418.60i	0.867397	+	1.50238i	0.864647	+	0.502380i	$0.167542\pi$
$173$	1973.73	+	3418.60i	0.867397	+	1.50238i	0.00275021	+	0.999996i	$0.499125\pi$
$174$	−331.731			−0.144532
$175$	−1291.37	−	1338.19i	−0.557819	−	0.578045i
$176$	−506.418			−0.216890
$177$	356.694	+	617.812i	0.151473	+	0.262359i
$178$	−164.169	+	284.348i	−0.0691289	+	0.119735i
$179$	−2167.93	+	3754.96i	−0.905243	+	1.56793i	−0.0846530	+	0.996410i	$0.526978\pi$
$179$	−2167.93	+	3754.96i	−0.905243	+	1.56793i	−0.820590	+	0.571517i	$0.806355\pi$
$180$	−40.7820	−	70.6365i	−0.0168873	−	0.0292496i
$181$	−1512.91			−0.621293			−0.310647	−	0.950525i	$-0.600546\pi$
$181$	−1512.91			−0.621293			−0.310647	+	0.950525i	$0.600546\pi$
$182$	679.634	−	169.198i	0.276801	−	0.0689111i
$183$	−1022.77			−0.413143
$184$	1038.49	+	1798.72i	0.416080	+	0.720672i
$185$	−43.1120	+	74.6722i	−0.0171333	+	0.0296757i
$186$	988.938	−	1712.89i	0.389852	−	0.675244i
$187$	6.44710	+	11.1667i	0.00252117	+	0.00436680i
$188$	876.484			0.340022
$189$	−138.000	+	480.628i	−0.0531114	+	0.184976i
$190$	−1654.19			−0.631619
$191$	−528.274	−	914.997i	−0.200128	−	0.346633i	0.748441	−	0.663201i	$-0.230803\pi$
$191$	−528.274	−	914.997i	−0.200128	−	0.346633i	−0.948570	+	0.316568i	$0.897469\pi$
$192$	854.129	−	1479.40i	0.321049	−	0.556074i
$193$	1059.36	−	1834.87i	0.395101	−	0.684335i	−0.598013	−	0.801486i	$-0.704043\pi$
$193$	1059.36	−	1834.87i	0.395101	−	0.684335i	0.993114	+	0.117151i	$0.0373763\pi$
$194$	−1387.90	−	2403.92i	−0.513637	−	0.889645i
$195$	−226.431			−0.0831541
$196$	−553.726	+	293.923i	−0.201795	+	0.107115i
$197$	−1262.14			−0.456465			−0.228232	−	0.973607i	$-0.573295\pi$
$197$	−1262.14			−0.456465			−0.228232	+	0.973607i	$0.573295\pi$
$198$	−122.978	−	213.005i	−0.0441399	−	0.0764525i
$199$	−791.323	+	1370.61i	−0.281887	+	0.488242i	−0.971849	−	0.235603i	$-0.924294\pi$
$199$	−791.323	+	1370.61i	−0.281887	+	0.488242i	0.689963	+	0.723845i	$0.257627\pi$
$200$	−1225.85	+	2123.23i	−0.433402	+	0.750674i
$201$	−1099.68	−	1904.69i	−0.385896	−	0.668392i
$202$	−3235.33			−1.12692
$203$	227.488	−	792.294i	0.0786527	−	0.273932i
$204$	−6.42728			−0.00220588
$205$	195.997	+	339.477i	0.0667758	+	0.115659i
$206$	−215.048	+	372.474i	−0.0727334	+	0.125978i
$207$	−382.799	+	663.027i	−0.128533	+	0.222626i
$208$	−350.387	−	606.889i	−0.116803	−	0.202308i
$209$	1477.08			0.488858
$210$	−664.181	+	165.351i	−0.218251	+	0.0543349i
$211$	114.417			0.0373306			0.0186653	−	0.999826i	$-0.494058\pi$
$211$	114.417			0.0373306			0.0186653	+	0.999826i	$0.494058\pi$
$212$	−84.3401	−	146.081i	−0.0273231	−	0.0473250i
$213$	−490.842	+	850.163i	−0.157896	+	0.273484i
$214$	−81.1838	+	140.615i	−0.0259328	+	0.0449169i
$215$	−802.134	−	1389.34i	−0.254442	−	0.440707i
$216$	659.233			0.207663
$217$	3412.83	+	3536.57i	1.06764	+	1.10635i
$218$	−5544.26			−1.72250
$219$	−1110.54	−	1923.52i	−0.342664	−	0.593512i
$220$	−49.8446	+	86.3334i	−0.0152751	+	0.0264573i
$221$	−8.92142	+	15.4524i	−0.00271547	+	0.00470334i
$222$	−64.8025	−	112.241i	−0.0195912	−	0.0339330i
$223$	2891.63			0.868332			0.434166	−	0.900833i	$-0.357043\pi$
$223$	2891.63			0.868332			0.434166	+	0.900833i	$0.357043\pi$
$224$	1041.08	+	1078.82i	0.310535	+	0.321795i
$225$	−903.718			−0.267768
$226$	328.481	+	568.945i	0.0966823	+	0.167459i
$227$	2988.15	−	5175.62i	0.873702	−	1.51330i	0.0155620	−	0.999879i	$-0.495046\pi$
$227$	2988.15	−	5175.62i	0.873702	−	1.51330i	0.858140	−	0.513417i	$-0.171620\pi$
$228$	−368.133	+	637.625i	−0.106931	+	0.185209i
$229$	318.269	+	551.259i	0.0918421	+	0.159075i	0.908286	−	0.418349i	$-0.137391\pi$
$229$	318.269	+	551.259i	0.0918421	+	0.159075i	−0.816444	+	0.577424i	$0.804058\pi$
$230$	−1047.93			−0.300429
$231$	593.066	−	147.647i	0.168922	−	0.0420539i
$232$	−1086.72			−0.307528
$233$	−1090.71	−	1889.16i	−0.306672	−	0.531171i	0.670960	−	0.741493i	$-0.265882\pi$
$233$	−1090.71	−	1889.16i	−0.306672	−	0.531171i	−0.977632	+	0.210322i	$0.932549\pi$
$234$	170.176	−	294.754i	0.0475417	−	0.0823446i
$235$	−1188.95	+	2059.32i	−0.330035	+	0.571638i
$236$	217.309	+	376.391i	0.0599391	+	0.103818i
$237$	207.193			0.0567874
$238$	−14.8848	+	51.8407i	−0.00405393	+	0.0141190i
$239$	−1678.75			−0.454349			−0.227175	−	0.973854i	$-0.572949\pi$
$239$	−1678.75			−0.454349			−0.227175	+	0.973854i	$0.572949\pi$
$240$	342.420	+	593.089i	0.0920964	+	0.159516i
$241$	504.512	−	873.841i	0.134849	−	0.233565i	−0.790691	−	0.612215i	$-0.790279\pi$
$241$	504.512	−	873.841i	0.134849	−	0.233565i	0.925540	+	0.378651i	$0.123612\pi$
$242$	−150.307	+	260.339i	−0.0399260	+	0.0691539i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−623.103			−0.163484
$245$	60.5491	−	1699.69i	0.0157892	−	0.443222i
$246$	−589.213			−0.152711
$247$	1021.98	+	1770.12i	0.263267	+	0.455992i
$248$	3239.66	−	5611.26i	0.829511	−	1.43676i
$249$	635.380	−	1100.51i	0.161709	−	0.280088i
$250$	−1388.43	−	2404.84i	−0.351249	−	0.608381i
$251$	6785.33			1.70632			0.853160	−	0.521649i	$-0.174683\pi$
$251$	6785.33			1.70632			0.853160	+	0.521649i	$0.174683\pi$
$252$	−84.0742	+	292.814i	−0.0210166	+	0.0731965i
$253$	935.731			0.232525
$254$	807.031	+	1397.82i	0.199361	+	0.345303i
$255$	8.71857	−	15.1010i	0.00214109	−	0.00370848i
$256$	1324.83	−	2294.67i	0.323444	−	0.560221i
$257$	2270.39	+	3932.43i	0.551063	+	0.954468i	0.998198	+	0.0600022i	$0.0191108\pi$
$257$	2270.39	+	3932.43i	0.551063	+	0.954468i	−0.447136	+	0.894466i	$0.647556\pi$
$258$	2411.40			0.581889
$259$	312.511	−	77.8013i	0.0749749	−	0.0186654i
$260$	−137.949			−0.0329047
$261$	−200.288	−	346.908i	−0.0475000	−	0.0822724i
$262$	−2536.43	+	4393.22i	−0.598095	+	1.03593i
$263$	518.827	−	898.634i	0.121643	−	0.210693i	−0.798772	−	0.601633i	$-0.794517\pi$
$263$	518.827	−	898.634i	0.121643	−	0.210693i	0.920416	+	0.390941i	$0.127850\pi$
$264$	−402.865	−	697.782i	−0.0939190	−	0.162672i
$265$	457.628			0.106082
$266$	4290.36	+	4445.92i	0.988944	+	1.02480i
$267$	−396.476			−0.0908763
$268$	−669.957	−	1160.40i	−0.152702	−	0.264488i
$269$	1495.73	−	2590.68i	0.339019	−	0.587199i	−0.645229	−	0.763989i	$-0.723238\pi$
$269$	1495.73	−	2590.68i	0.339019	−	0.587199i	0.984249	+	0.176790i	$0.0565714\pi$
$270$	−166.307	+	288.052i	−0.0374855	+	0.0649269i
$271$	−2220.49	−	3846.00i	−0.497732	−	0.862096i	0.502265	−	0.864714i	$-0.332500\pi$
$271$	−2220.49	−	3846.00i	−0.497732	−	0.862096i	−0.999997	+	0.00261742i	$0.999167\pi$
$272$	53.9657			0.0120300
$273$	587.278	+	608.572i	0.130197	+	0.134917i
$274$	−6998.14			−1.54297
$275$	552.272	+	956.563i	0.121103	+	0.209756i
$276$	−233.213	+	403.937i	−0.0508616	+	0.0880948i
$277$	−3693.72	+	6397.72i	−0.801207	+	1.38773i	0.117615	+	0.993059i	$0.462475\pi$
$277$	−3693.72	+	6397.72i	−0.801207	+	1.38773i	−0.918822	+	0.394672i	$0.870858\pi$
$278$	−2041.78	−	3536.46i	−0.440495	−	0.762960i
$279$	2388.34			0.512496
$280$	−2175.79	+	541.674i	−0.464386	+	0.115611i
$281$	−5581.14			−1.18485			−0.592425	−	0.805626i	$-0.701829\pi$
$281$	−5581.14			−1.18485			−0.592425	+	0.805626i	$0.701829\pi$
$282$	−1787.13	−	3095.39i	−0.377382	−	0.653645i
$283$	2122.12	−	3675.61i	0.445748	−	0.772058i	−0.552356	−	0.833608i	$-0.686271\pi$
$283$	2122.12	−	3675.61i	0.445748	−	0.772058i	0.998104	+	0.0615502i	$0.0196044\pi$
$284$	−299.036	+	517.946i	−0.0624808	+	0.108220i
$285$	−998.742	−	1729.87i	−0.207580	−	0.359539i
$286$	−415.986			−0.0860061
$287$	404.058	−	1407.25i	0.0831039	−	0.289434i
$288$	728.560			0.149065
$289$	2455.81	+	4253.59i	0.499860	+	0.865783i
$290$	274.149	−	474.841i	0.0555124	−	0.0961504i
$291$	1675.93	−	2902.80i	0.337611	−	0.584760i
$292$	−676.577	−	1171.87i	−0.135595	−	0.234857i
$293$	−168.835			−0.0336637			−0.0168319	−	0.999858i	$-0.505358\pi$
$293$	−168.835			−0.0336637			−0.0168319	+	0.999858i	$0.505358\pi$
$294$	2167.05	+	1356.24i	0.429881	+	0.269039i
$295$	−1179.12			−0.232715
$296$	−212.286	−	367.691i	−0.0416854	−	0.0722013i
$297$	148.500	−	257.210i	0.0290129	−	0.0502519i
$298$	467.969	−	810.545i	0.0909688	−	0.157563i
$299$	647.426	+	1121.38i	0.125223	+	0.216892i
$300$	−550.573			−0.105958
$301$	−1653.64	+	5759.30i	−0.316659	+	1.10286i
$302$	380.680			0.0725353
$303$	−1953.38	−	3383.35i	−0.370358	−	0.641479i
$304$	3090.98	−	5353.73i	0.583157	−	1.01006i
$305$	845.236	−	1463.99i	0.158682	−	0.274846i
$306$	13.1050	+	22.6986i	0.00244825	+	0.00424050i
$307$	941.743			0.175075			0.0875376	−	0.996161i	$-0.472100\pi$
$307$	941.743			0.175075			0.0875376	+	0.996161i	$0.472100\pi$
$308$	361.315	−	89.9512i	0.0668435	−	0.0166411i
$309$	−519.353			−0.0956147
$310$	1634.56	+	2831.14i	0.299473	+	0.518702i
$311$	1323.73	−	2292.77i	0.241357	−	0.418043i	−0.719744	−	0.694240i	$-0.755741\pi$
$311$	1323.73	−	2292.77i	0.241357	−	0.418043i	0.961101	+	0.276197i	$0.0890742\pi$
$312$	557.479	−	965.583i	0.101157	−	0.175209i
$313$	692.157	+	1198.85i	0.124994	+	0.216495i	0.921730	−	0.387831i	$-0.126776\pi$
$313$	692.157	+	1198.85i	0.124994	+	0.216495i	−0.796737	+	0.604326i	$0.793442\pi$
$314$	−7181.30			−1.29065
$315$	−573.925	−	594.734i	−0.102657	−	0.106379i
$316$	126.228			0.0224712
$317$	4285.77	+	7423.16i	0.759346	+	1.31523i	0.943185	+	0.332269i	$0.107814\pi$
$317$	4285.77	+	7423.16i	0.759346	+	1.31523i	−0.183839	+	0.982956i	$0.558853\pi$
$318$	−343.934	+	595.712i	−0.0606506	+	0.105050i
$319$	−244.796	+	423.999i	−0.0429653	+	0.0744182i
$320$	1411.74	+	2445.20i	0.246621	+	0.427160i
$321$	−196.064			−0.0340910
$322$	2717.96	+	2816.50i	0.470391	+	0.487446i
$323$	−157.403			−0.0271149
$324$	74.0216	+	128.209i	0.0126923	+	0.0219838i
$325$	−764.227	+	1323.68i	−0.130436	+	0.225922i
$326$	4088.10	−	7080.79i	0.694536	−	1.20297i
$327$	−3347.43	−	5797.91i	−0.566095	−	0.980506i
$328$	−1930.20			−0.324932
$329$	8618.45	−	2145.61i	1.44423	−	0.359548i
$330$	406.527			0.0678139
$331$	3341.45	+	5787.56i	0.554872	+	0.961066i	0.997913	+	0.0645653i	$0.0205661\pi$
$331$	3341.45	+	5787.56i	0.554872	+	0.961066i	−0.443042	+	0.896501i	$0.646101\pi$
$332$	387.093	−	670.465i	0.0639895	−	0.110833i
$333$	78.2508	−	135.534i	0.0128772	−	0.0223040i
$334$	2434.12	+	4216.01i	0.398769	+	0.690689i
$335$	3635.18			0.592869
$336$	705.917	−	2458.57i	0.114616	−	0.399184i
$337$	6780.34			1.09599			0.547995	−	0.836482i	$-0.315391\pi$
$337$	6780.34			1.09599			0.547995	+	0.836482i	$0.315391\pi$
$338$	2441.31	+	4228.47i	0.392869	+	0.680469i
$339$	−396.650	+	687.018i	−0.0635488	+	0.110070i
$340$	5.31163	−	9.20001i	0.000847246	−	0.00146747i
$341$	−1459.54	−	2528.00i	−0.231785	−	0.401463i
$342$	3002.45			0.474719
$343$	−4725.26	+	4245.65i	−0.743849	+	0.668348i
$344$	7899.51			1.23812
$345$	−632.705	−	1095.88i	−0.0987354	−	0.171015i
$346$	4903.55	−	8493.20i	0.761898	−	1.31965i
$347$	−6092.05	+	10551.7i	−0.942474	+	1.63241i	−0.181744	+	0.983346i	$0.558174\pi$
$347$	−6092.05	+	10551.7i	−0.942474	+	1.63241i	−0.760731	+	0.649068i	$0.775159\pi$
$348$	−122.022	−	211.348i	−0.0187961	−	0.0325558i
$349$	3464.32			0.531350			0.265675	−	0.964063i	$-0.414405\pi$
$349$	3464.32			0.531350			0.265675	+	0.964063i	$0.414405\pi$
$350$	−1275.06	+	4440.78i	−0.194728	+	0.678199i
$351$	410.985			0.0624979
$352$	−445.231	−	771.162i	−0.0674173	−	0.116770i
$353$	1014.41	−	1757.02i	0.152951	−	0.264920i	−0.779360	−	0.626577i	$-0.784456\pi$
$353$	1014.41	−	1757.02i	0.152951	−	0.264920i	0.932311	+	0.361657i	$0.117789\pi$
$354$	886.176	−	1534.90i	0.133050	−	0.230449i
$355$	−811.283	−	1405.18i	−0.121291	−	0.210083i
$356$	−241.546			−0.0359604
$357$	−63.1993	+	15.7338i	−0.00936936	+	0.00233255i
$358$	10772.1			1.59028
$359$	−2963.72	−	5133.32i	−0.435708	−	0.754669i	0.561645	−	0.827378i	$-0.310169\pi$
$359$	−2963.72	−	5133.32i	−0.435708	−	0.754669i	−0.997353	+	0.0727096i	$0.976835\pi$
$360$	−544.804	+	943.627i	−0.0797602	+	0.138149i
$361$	−5586.00	+	9675.24i	−0.814404	+	1.41059i
$362$	1879.35	+	3255.13i	0.272863	+	0.472613i
$363$	−363.000			−0.0524864
$364$	357.788	+	370.761i	0.0515198	+	0.0533878i
$365$	3671.10			0.526449
$366$	1270.49	+	2200.55i	0.181447	+	0.314275i
$367$	−312.369	+	541.039i	−0.0444292	+	0.0769537i	−0.887385	−	0.461029i	$-0.847480\pi$
$367$	−312.369	+	541.039i	−0.0444292	+	0.0769537i	0.842956	+	0.537983i	$0.180814\pi$
$368$	1958.14	−	3391.60i	0.277378	−	0.480434i
$369$	−355.746	−	616.170i	−0.0501881	−	0.0869283i
$370$	214.216			0.0300988
$371$	−1186.92	−	1229.95i	−0.166096	−	0.172119i
$372$	1455.05			0.202799
$373$	−3877.28	−	6715.65i	−0.538225	−	0.932233i	−0.999000	−	0.0447162i	$-0.985762\pi$
$373$	−3877.28	−	6715.65i	−0.538225	−	0.932233i	0.460774	−	0.887517i	$-0.347572\pi$
$374$	16.0173	−	27.7427i	0.00221453	−	0.00383567i
$375$	1676.57	−	2903.91i	0.230874	−	0.399886i
$376$	−5854.44	−	10140.2i	−0.802978	−	1.39080i
$377$	−677.491			−0.0925533
$378$	1205.53	−	300.122i	0.164036	−	0.0408376i
$379$	−9904.96			−1.34244			−0.671219	−	0.741259i	$-0.734229\pi$
$379$	−9904.96			−1.34244			−0.671219	+	0.741259i	$0.734229\pi$
$380$	−608.465	−	1053.89i	−0.0821410	−	0.142272i
$381$	−974.513	+	1687.91i	−0.131039	+	0.226966i
$382$	−1312.45	+	2273.23i	−0.175787	+	0.304473i
$383$	735.224	+	1273.44i	0.0980892	+	0.169896i	0.910894	−	0.412641i	$-0.135394\pi$
$383$	735.224	+	1273.44i	0.0980892	+	0.169896i	−0.812804	+	0.582537i	$0.802060\pi$
$384$	−2301.19			−0.305813
$385$	−278.780	+	970.934i	−0.0369037	+	0.128528i
$386$	−5263.78			−0.694091
$387$	1455.92	+	2521.73i	0.191237	+	0.331231i
$388$	1021.03	−	1768.48i	0.133595	−	0.231394i
$389$	−1212.48	+	2100.08i	−0.158034	+	0.273724i	−0.934160	−	0.356855i	$-0.883849\pi$
$389$	−1212.48	+	2100.08i	−0.158034	+	0.273724i	0.776125	+	0.630579i	$0.217182\pi$
$390$	281.274	+	487.180i	0.0365201	+	0.0632547i
$391$	−99.7150			−0.0128972
$392$	7099.04	+	4442.90i	0.914682	+	0.572450i
$393$	−6125.62			−0.786251
$394$	1567.83	+	2715.57i	0.200473	+	0.347229i
$395$	−171.228	+	296.576i	−0.0218112	+	0.0377781i
$396$	90.4709	−	156.700i	0.0114806	−	0.0198851i
$397$	5476.05	+	9484.80i	0.692280	+	1.19906i	0.971089	+	0.238718i	$0.0767270\pi$
$397$	5476.05	+	9484.80i	0.692280	+	1.19906i	−0.278809	+	0.960347i	$0.589940\pi$
$398$	3931.95			0.495203
$399$	−2058.96	+	7170.94i	−0.258338	+	0.899739i
$400$	4622.81			0.577852
$401$	−7916.44	−	13711.7i	−0.985856	−	1.70755i	−0.638070	−	0.769978i	$-0.720267\pi$
$401$	−7916.44	−	13711.7i	−0.985856	−	1.70755i	−0.347786	−	0.937574i	$-0.613066\pi$
$402$	−2732.05	+	4732.05i	−0.338961	+	0.587097i
$403$	2019.70	−	3498.22i	0.249648	−	0.432404i
$404$	−1190.06	−	2061.24i	−0.146553	−	0.253838i
$405$	−401.640			−0.0492782
$406$	−1987.26	+	494.739i	−0.242921	+	0.0604765i
$407$	−191.280			−0.0232958
$408$	42.9308	+	74.3583i	0.00520929	+	0.00902275i
$409$	−870.547	+	1507.83i	−0.105246	+	0.182292i	−0.913839	−	0.406077i	$-0.866896\pi$
$409$	−870.547	+	1507.83i	−0.105246	+	0.182292i	0.808592	+	0.588369i	$0.200230\pi$
$410$	486.938	−	843.401i	0.0586540	−	0.101592i
$411$	−4225.23	−	7318.31i	−0.507093	−	0.878310i
$412$	−316.406			−0.0378355
$413$	3058.20	+	3169.08i	0.364368	+	0.377579i
$414$	1902.06			0.225800
$415$	1050.18	+	1818.97i	0.124220	+	0.215156i
$416$	616.105	−	1067.13i	0.0726131	−	0.125770i
$417$	2465.50	−	4270.38i	0.289535	−	0.501490i
$418$	−1834.83	−	3178.02i	−0.214700	−	0.371871i
$419$	−12573.1			−1.46596			−0.732980	−	0.680250i	$-0.761871\pi$
$419$	−12573.1			−1.46596			−0.732980	+	0.680250i	$0.761871\pi$
$420$	−349.653	−	362.331i	−0.0406222	−	0.0420951i
$421$	15134.3			1.75202			0.876008	−	0.482297i	$-0.160198\pi$
$421$	15134.3			1.75202			0.876008	+	0.482297i	$0.160198\pi$
$422$	−142.129	−	246.175i	−0.0163951	−	0.0283971i
$423$	2158.01	−	3737.78i	0.248052	−	0.429638i
$424$	−1126.69	+	1951.49i	−0.129050	+	0.223521i
$425$	−58.8521	−	101.935i	−0.00671706	−	0.0116343i
$426$	2438.91			0.277384
$427$	−6126.96	+	1525.34i	−0.694390	+	0.172872i
$428$	−119.448			−0.0134901
$429$	−251.157	−	435.017i	−0.0282657	−	0.0489577i
$430$	−1992.83	+	3451.68i	−0.223495	+	0.387105i
$431$	−133.274	+	230.838i	−0.0148946	+	0.0257983i	−0.873377	−	0.487045i	$-0.838075\pi$
$431$	−133.274	+	230.838i	−0.0148946	+	0.0257983i	0.858482	+	0.512844i	$0.171408\pi$
$432$	−621.513	−	1076.49i	−0.0692188	−	0.119891i
$433$	5174.52			0.574299			0.287150	−	0.957886i	$-0.407292\pi$
$433$	5174.52			0.574299			0.287150	+	0.957886i	$0.407292\pi$
$434$	3369.72	−	11736.1i	0.372700	−	1.29804i
$435$	662.087			0.0729762
$436$	−2039.36	−	3532.27i	−0.224008	−	0.387993i
$437$	−5711.34	+	9892.34i	−0.625196	+	1.08287i
$438$	−2759.04	+	4778.80i	−0.300987	+	0.521324i
$439$	3271.67	+	5666.69i	0.355691	+	0.616074i	0.987236	−	0.159265i	$-0.0509124\pi$
$439$	3271.67	+	5666.69i	0.355691	+	0.616074i	−0.631545	+	0.775339i	$0.717579\pi$
$440$	1331.74			0.144292
$441$	−109.900	+	3085.04i	−0.0118670	+	0.333122i
$442$	44.3290			0.00477040
$443$	−3719.69	−	6442.69i	−0.398934	−	0.690974i	0.594661	−	0.803977i	$-0.297286\pi$
$443$	−3719.69	−	6442.69i	−0.398934	−	0.690974i	−0.993595	+	0.113003i	$0.963953\pi$
$444$	47.6729	−	82.5719i	0.00509562	−	0.00882587i
$445$	327.656	−	567.517i	0.0349042	−	0.0604559i
$446$	−3592.01	−	6221.54i	−0.381360	−	0.660534i
$447$	1130.17			0.119587
$448$	2910.37	−	10136.3i	0.306925	−	1.06896i
$449$	−17134.3			−1.80093			−0.900466	−	0.434927i	$-0.856774\pi$
$449$	−17134.3			−1.80093			−0.900466	+	0.434927i	$0.856774\pi$
$450$	1122.60	+	1944.41i	0.117600	+	0.203689i
$451$	−434.801	+	753.097i	−0.0453968	+	0.0786296i
$452$	−241.652	+	418.553i	−0.0251468	+	0.0435555i
$453$	229.841	+	398.096i	0.0238385	+	0.0412896i
$454$	−14847.6			−1.53487
$455$	−1356.45	+	337.695i	−0.139761	+	0.0347943i
$456$	9835.73			1.01009
$457$	2421.96	+	4194.96i	0.247909	+	0.429392i	0.962946	−	0.269696i	$-0.0869231\pi$
$457$	2421.96	+	4194.96i	0.247909	+	0.429392i	−0.715036	+	0.699087i	$0.753590\pi$
$458$	790.713	−	1369.55i	0.0806716	−	0.139727i
$459$	−15.8247	+	27.4092i	−0.00160922	+	0.00278726i
$460$	−385.464	−	667.644i	−0.0390703	−	0.0676718i
$461$	10300.6			1.04066			0.520330	−	0.853965i	$-0.325809\pi$
$461$	10300.6			1.04066			0.520330	+	0.853965i	$0.325809\pi$
$462$	−1054.38	−	1092.61i	−0.106178	−	0.110028i
$463$	6748.75			0.677410			0.338705	−	0.940893i	$-0.390011\pi$
$463$	6748.75			0.677410			0.338705	+	0.940893i	$0.390011\pi$
$464$	1024.54	+	1774.55i	0.102506	+	0.177546i
$465$	−1973.77	+	3418.68i	−0.196842	+	0.340941i
$466$	−2709.76	+	4693.45i	−0.269372	+	0.466566i
$467$	−469.629	−	813.420i	−0.0465349	−	0.0806009i	0.841820	−	0.539759i	$-0.181485\pi$
$467$	−469.629	−	813.420i	−0.0465349	−	0.0806009i	−0.888355	+	0.459158i	$0.848151\pi$
$468$	250.385			0.0247309
$469$	−9428.31	−	9770.16i	−0.928271	−	0.961928i
$470$	5907.67			0.579788
$471$	−4335.82	−	7509.85i	−0.424170	−	0.734683i
$472$	2903.02	−	5028.18i	0.283098	−	0.490341i
$473$	1779.46	−	3082.11i	0.172980	−	0.299610i
$474$	−257.376	−	445.788i	−0.0249402	−	0.0431977i
$475$	−13483.4			−1.30245
$476$	−38.5030	+	9.58553i	−0.00370753	+	0.000923009i
$477$	−830.621			−0.0797307
$478$	2085.36	+	3611.94i	0.199544	+	0.345620i
$479$	5380.23	−	9318.82i	0.513212	−	0.888910i	−0.486670	−	0.873586i	$-0.661789\pi$
$479$	5380.23	−	9318.82i	0.513212	−	0.888910i	0.999883	−	0.0153242i	$-0.00487805\pi$
$480$	−602.096	+	1042.86i	−0.0572538	+	0.0991664i
$481$	−132.345	−	229.229i	−0.0125456	−	0.0217296i
$482$	−2506.83			−0.236894
$483$	−1304.36	+	4542.81i	−0.122878	+	0.427961i
$484$	−221.151			−0.0207693
$485$	2770.05	+	4797.86i	0.259343	+	0.449195i
$486$	301.856	−	522.830i	0.0281738	−	0.0487985i
$487$	−3841.41	+	6653.52i	−0.357435	+	0.619096i	−0.987532	−	0.157421i	$-0.949682\pi$
$487$	−3841.41	+	6653.52i	−0.357435	+	0.619096i	0.630096	+	0.776517i	$0.283015\pi$
$488$	4161.99	+	7208.78i	0.386075	+	0.668702i
$489$	9872.99			0.913031
$490$	−3732.22	+	1981.10i	−0.344090	+	0.182646i
$491$	−12080.6			−1.11037			−0.555185	−	0.831727i	$-0.687353\pi$
$491$	−12080.6			−1.11037			−0.555185	+	0.831727i	$0.687353\pi$
$492$	−216.732	−	375.391i	−0.0198598	−	0.0343982i
$493$	26.0864	−	45.1829i	0.00238311	−	0.00412766i
$494$	2539.02	−	4397.71i	0.231247	−	0.400531i
$495$	245.447	+	425.126i	0.0222869	+	0.0386020i
$496$	−12217.2			−1.10598
$497$	−1672.50	+	5824.99i	−0.150950	+	0.525727i
$498$	−3157.09			−0.284082
$499$	473.811	+	820.665i	0.0425064	+	0.0736233i	0.886496	−	0.462736i	$-0.153132\pi$
$499$	473.811	+	820.665i	0.0425064	+	0.0736233i	−0.843989	+	0.536360i	$0.819799\pi$
$500$	1021.42	−	1769.15i	0.0913587	−	0.158238i
$501$	−2939.27	+	5090.96i	−0.262109	+	0.453987i
$502$	−8428.78	−	14599.1i	−0.749393	−	1.29799i
$503$	−12353.5			−1.09506			−0.547532	−	0.836785i	$-0.684433\pi$
$503$	−12353.5			−1.09506			−0.547532	+	0.836785i	$0.684433\pi$
$504$	3949.18	−	983.169i	0.349029	−	0.0868925i
$505$	6457.24			0.568996
$506$	−1162.37	−	2013.29i	−0.102122	−	0.176880i
$507$	−2947.95	+	5106.00i	−0.258231	+	0.447269i
$508$	−593.704	+	1028.33i	−0.0518531	+	0.0898122i
$509$	−5333.38	−	9237.69i	−0.464436	−	0.804427i	0.534740	−	0.845017i	$-0.320410\pi$
$509$	−5333.38	−	9237.69i	−0.464436	−	0.804427i	−0.999176	+	0.0405896i	$0.987076\pi$
$510$	−43.3211			−0.00376135
$511$	−9521.47	−	9866.70i	−0.824276	−	0.854163i
$512$	−12719.3			−1.09789
$513$	1812.77	+	3139.82i	0.156015	+	0.270227i
$514$	5640.59	−	9769.78i	0.484038	−	0.838379i
$515$	429.204	−	743.402i	0.0367242	−	0.0636082i
$516$	886.992	+	1536.32i	0.0756737	+	0.131071i
$517$	−5275.13			−0.448742
$518$	−555.598	−	575.743i	−0.0471266	−	0.0488353i
$519$	11842.4			1.00158
$520$	921.424	+	1595.95i	0.0777060	+	0.134591i
$521$	−10208.3	+	17681.3i	−0.858416	+	1.48682i	0.0150228	+	0.999887i	$0.495218\pi$
$521$	−10208.3	+	17681.3i	−0.858416	+	1.48682i	−0.873439	+	0.486933i	$0.838115\pi$
$522$	−497.597	+	861.863i	−0.0417227	+	0.0722658i
$523$	3645.26	+	6313.77i	0.304772	+	0.527881i	0.977211	−	0.212272i	$-0.0680862\pi$
$523$	3645.26	+	6313.77i	0.304772	+	0.527881i	−0.672438	+	0.740153i	$0.734753\pi$
$524$	−3731.92			−0.311125
$525$	−5413.78	+	1347.79i	−0.450051	+	0.112043i
$526$	−2577.96			−0.213696
$527$	155.534	+	269.393i	0.0128561	+	0.0222675i
$528$	−759.627	+	1315.71i	−0.0626108	+	0.108445i
$529$	2465.35	−	4270.11i	0.202626	−	0.350958i
$530$	−568.468	−	984.616i	−0.0465900	−	0.0806962i
$531$	2140.17			0.174906
$532$	−1254.38	+	4368.76i	−0.102226	+	0.356034i
$533$	−1203.34			−0.0977910
$534$	492.506	+	853.045i	0.0399116	+	0.0691289i
$535$	162.031	−	280.646i	0.0130938	−	0.0226792i
$536$	−8949.92	+	15501.7i	−0.721227	+	1.24920i
$537$	6503.78	+	11264.9i	0.522642	+	0.905243i
$538$	−7432.02			−0.595571
$539$	3332.60	−	1768.98i	0.266318	−	0.141364i
$540$	−244.692			−0.0194997
$541$	8510.19	+	14740.1i	0.676306	+	1.17140i	0.976085	+	0.217388i	$0.0697538\pi$
$541$	8510.19	+	14740.1i	0.676306	+	1.17140i	−0.299779	+	0.954009i	$0.596913\pi$
$542$	−5516.62	+	9555.06i	−0.437194	+	0.757242i
$543$	−2269.37	+	3930.67i	−0.179352	+	0.310647i
$544$	47.4455	+	82.1779i	0.00373935	+	0.00647675i
$545$	11065.5			0.869715
$546$	579.860	−	2019.54i	0.0454501	−	0.158294i
$547$	−3900.40			−0.304879			−0.152440	−	0.988313i	$-0.548713\pi$
$547$	−3900.40			−0.304879			−0.152440	+	0.988313i	$0.548713\pi$
$548$	−2574.14	−	4458.55i	−0.200660	−	0.347554i
$549$	−1534.15	+	2657.23i	−0.119264	+	0.206572i
$550$	1372.07	−	2376.50i	0.106373	−	0.184244i
$551$	−2988.28	−	5175.86i	−0.231044	−	0.400179i
$552$	6230.96			0.480448
$553$	1241.20	−	309.003i	0.0954453	−	0.0237616i
$554$	18353.5			1.40752
$555$	129.336	+	224.017i	0.00989191	+	0.0171333i
$556$	1502.06	−	2601.65i	0.114571	−	0.198443i
$557$	−8033.51	+	13914.4i	−0.611114	+	1.05848i	0.379939	+	0.925012i	$0.375945\pi$
$557$	−8033.51	+	13914.4i	−0.611114	+	1.05848i	−0.991053	+	0.133469i	$0.957388\pi$
$558$	−2966.82	−	5138.67i	−0.225081	−	0.389852i
$559$	4924.78			0.372623
$560$	2935.82	+	3042.26i	0.221537	+	0.229570i
$561$	38.6826			0.00291120
$562$	6932.92	+	12008.2i	0.520370	+	0.901306i
$563$	−10095.3	+	17485.5i	−0.755710	+	1.30893i	0.189311	+	0.981917i	$0.439375\pi$
$563$	−10095.3	+	17485.5i	−0.755710	+	1.30893i	−0.945021	+	0.327010i	$0.893959\pi$
$564$	1314.73	−	2277.17i	0.0981559	−	0.170011i
$565$	−655.599	−	1135.53i	−0.0488164	−	0.0845524i
$566$	−10544.4			−0.783065
$567$	1041.71	+	1079.48i	0.0771562	+	0.0799537i
$568$	7989.61			0.590205
$569$	−4469.12	−	7740.75i	−0.329271	−	0.570315i	0.653096	−	0.757275i	$-0.273470\pi$
$569$	−4469.12	−	7740.75i	−0.329271	−	0.570315i	−0.982367	+	0.186960i	$0.940136\pi$
$570$	−2481.29	+	4297.71i	−0.182333	+	0.315810i
$571$	8306.16	−	14386.7i	0.608760	−	1.05440i	−0.382685	−	0.923879i	$-0.625001\pi$
$571$	8306.16	−	14386.7i	0.608760	−	1.05440i	0.991445	−	0.130524i	$-0.0416661\pi$
$572$	−153.013	−	265.026i	−0.0111850	−	0.0193729i
$573$	−3169.64			−0.231088
$574$	−3529.72	+	878.743i	−0.256669	+	0.0638990i
$575$	−8541.78			−0.619508
$576$	−2562.39	−	4438.19i	−0.185358	−	0.321049i
$577$	1960.68	−	3395.99i	0.141463	−	0.245021i	−0.786585	−	0.617482i	$-0.788153\pi$
$577$	1960.68	−	3395.99i	0.141463	−	0.245021i	0.928048	+	0.372461i	$0.121486\pi$
$578$	6101.25	−	10567.7i	0.439063	−	0.760480i
$579$	−3178.08	−	5504.60i	−0.228112	−	0.395101i
$580$	403.364			0.0288772
$581$	2165.00	−	7540.27i	0.154595	−	0.538422i
$582$	−8327.41			−0.593097
$583$	507.602	+	879.192i	0.0360596	+	0.0624570i
$584$	−9038.35	+	15654.9i	−0.640427	+	1.10925i
$585$	−339.646	+	588.284i	−0.0240045	+	0.0415770i
$586$	209.728	+	363.260i	0.0147846	+	0.0256077i
$587$	19646.6			1.38144			0.690719	−	0.723123i	$-0.257294\pi$
$587$	19646.6			1.38144			0.690719	+	0.723123i	$0.257294\pi$
$588$	−66.9547	+	1879.51i	−0.00469586	+	0.131819i
$589$	35634.0			2.49282
$590$	1464.71	+	2536.95i	0.102205	+	0.177024i
$591$	−1893.20	+	3279.13i	−0.131770	+	0.228232i
$592$	−400.279	+	693.303i	−0.0277895	+	0.0481328i
$593$	12017.4	+	20814.8i	0.832202	+	1.44142i	0.896288	+	0.443472i	$0.146254\pi$
$593$	12017.4	+	20814.8i	0.832202	+	1.44142i	−0.0640857	+	0.997944i	$0.520413\pi$
$594$	−737.870			−0.0509683
$595$	29.7078	−	103.466i	0.00204689	−	0.00712892i
$596$	688.536			0.0473214
$597$	2373.97	+	4111.84i	0.162747	+	0.281887i
$598$	1608.47	−	2785.96i	0.109992	−	0.190512i
$599$	1125.73	−	1949.82i	0.0767881	−	0.133001i	−0.825074	−	0.565024i	$-0.808867\pi$
$599$	1125.73	−	1949.82i	0.0767881	−	0.133001i	0.901862	+	0.432023i	$0.142200\pi$
$600$	3677.54	+	6369.68i	0.250225	+	0.433402i
$601$	22743.7			1.54365			0.771826	−	0.635833i	$-0.219343\pi$
$601$	22743.7			1.54365			0.771826	+	0.635833i	$0.219343\pi$
$602$	14445.7	−	3596.32i	0.978009	−	0.243480i
$603$	−6598.06			−0.445595
$604$	140.026	+	242.533i	0.00943309	+	0.0163386i
$605$	299.990	−	519.599i	0.0201592	−	0.0349168i
$606$	−4852.99	+	8405.63i	−0.325312	+	0.563458i
$607$	9673.75	+	16755.4i	0.646862	+	1.12040i	0.983868	+	0.178896i	$0.0572525\pi$
$607$	9673.75	+	16755.4i	0.646862	+	1.12040i	−0.337006	+	0.941503i	$0.609414\pi$
$608$	10870.1			0.725065
$609$	−1717.21	−	1779.47i	−0.114261	−	0.118404i
$610$	−4199.83			−0.278764
$611$	−3649.83	−	6321.69i	−0.241663	−	0.418573i
$612$	−9.64091	+	16.6986i	−0.000636782	+	0.00110294i
$613$	3901.55	−	6757.69i	0.257067	−	0.445253i	−0.708388	−	0.705823i	$-0.750577\pi$
$613$	3901.55	−	6757.69i	0.257067	−	0.445253i	0.965455	+	0.260570i	$0.0839105\pi$
$614$	−1169.84	−	2026.22i	−0.0768906	−	0.133178i
$615$	1175.98			0.0771060
$616$	−3454.05	−	3579.29i	−0.225921	−	0.234113i
$617$	−1122.39			−0.0732345			−0.0366172	−	0.999329i	$-0.511658\pi$
$617$	−1122.39			−0.0732345			−0.0366172	+	0.999329i	$0.511658\pi$
$618$	645.143	+	1117.42i	0.0419927	+	0.0727334i
$619$	10410.9	−	18032.2i	0.676010	−	1.17088i	−0.300163	−	0.953888i	$-0.597041\pi$
$619$	10410.9	−	18032.2i	0.676010	−	1.17088i	0.976173	−	0.216995i	$-0.0696255\pi$
$620$	−1202.49	+	2082.77i	−0.0778919	+	0.134913i
$621$	1148.40	+	1989.08i	0.0742087	+	0.128533i
$622$	−6577.40			−0.424003
$623$	−2375.12	+	591.298i	−0.152740	+	0.0380255i
$624$	−2102.32			−0.134872
$625$	−3504.71	−	6070.34i	−0.224302	−	0.388502i
$626$	1719.60	−	2978.44i	0.109791	−	0.190164i
$627$	2215.61	−	3837.55i	0.141121	−	0.244429i
$628$	−2641.52	−	4575.24i	−0.167847	−	0.290720i
$629$	20.3835			0.00129212
$630$	−566.676	+	1973.62i	−0.0358363	+	0.124811i
$631$	−24051.6			−1.51740			−0.758700	−	0.651440i	$-0.774165\pi$
$631$	−24051.6			−1.51740			−0.758700	+	0.651440i	$0.774165\pi$
$632$	−843.137	−	1460.36i	−0.0530668	−	0.0919143i
$633$	171.625	−	297.263i	0.0107764	−	0.0186653i
$634$	10647.6	−	18442.2i	0.666988	−	1.15526i
$635$	−1610.71	−	2789.84i	−0.100660	−	0.174349i
$636$	−506.041			−0.0315500
$637$	4425.74	+	2769.83i	0.275281	+	0.172284i
$638$	1216.35			0.0754791
$639$	1472.53	+	2550.49i	0.0911615	+	0.157896i
$640$	1901.75	−	3293.93i	0.117458	−	0.203444i
$641$	−1013.35	+	1755.17i	−0.0624414	+	0.108152i	−0.895556	−	0.444948i	$-0.853222\pi$
$641$	−1013.35	+	1755.17i	−0.0624414	+	0.108152i	0.833115	+	0.553100i	$0.186555\pi$
$642$	243.552	+	421.844i	0.0149723	+	0.0259328i
$643$	−10457.5			−0.641375			−0.320688	−	0.947185i	$-0.603914\pi$
$643$	−10457.5			−0.641375			−0.320688	+	0.947185i	$0.603914\pi$
$644$	−794.654	+	2767.62i	−0.0486239	+	0.169347i
$645$	−4812.80			−0.293805
$646$	195.526	+	338.662i	0.0119085	+	0.0206261i
$647$	−3390.93	+	5873.27i	−0.206045	+	0.356881i	−0.950465	−	0.310831i	$-0.899393\pi$
$647$	−3390.93	+	5873.27i	−0.206045	+	0.356881i	0.744420	+	0.667712i	$0.232726\pi$
$648$	988.850	−	1712.74i	0.0599471	−	0.103831i
$649$	−1307.88	−	2265.31i	−0.0791044	−	0.137013i
$650$	3797.31			0.229143
$651$	14307.5	−	3561.94i	0.861377	−	0.214444i
$652$	6014.94			0.361293
$653$	−5607.44	−	9712.37i	−0.336043	−	0.582043i	0.647642	−	0.761945i	$-0.275755\pi$
$653$	−5607.44	−	9712.37i	−0.336043	−	0.582043i	−0.983685	+	0.179902i	$0.942422\pi$
$654$	−8316.39	+	14404.4i	−0.497242	+	0.861249i
$655$	5062.33	−	8768.22i	0.301987	−	0.523058i
$656$	1819.76	+	3151.92i	0.108307	+	0.187594i
$657$	−6663.25			−0.395675
$658$	−15322.3	−	15877.9i	−0.907790	−	0.940705i
$659$	17393.9			1.02818			0.514089	−	0.857737i	$-0.328130\pi$
$659$	17393.9			1.02818			0.514089	+	0.857737i	$0.328130\pi$
$660$	149.534	+	259.000i	0.00881909	+	0.0152751i
$661$	7123.47	−	12338.2i	0.419169	−	0.726022i	−0.576687	−	0.816965i	$-0.695655\pi$
$661$	7123.47	−	12338.2i	0.419169	−	0.726022i	0.995856	+	0.0909428i	$0.0289881\pi$
$662$	8301.54	−	14378.7i	0.487384	−	0.844174i
$663$	26.7643	+	46.3571i	0.00156778	+	0.00271547i
$664$	−10342.3			−0.604457
$665$	−8562.93	−	8873.40i	−0.499333	−	0.517437i
$666$	−388.815			−0.0226220
$667$	−1893.08	−	3278.92i	−0.109896	−	0.190345i
$668$	−1790.69	+	3101.57i	−0.103719	+	0.179646i
$669$	4337.45	−	7512.68i	0.250666	−	0.434166i
$670$	−4515.64	−	7821.32i	−0.260380	−	0.450991i
$671$	3750.15			0.215757
$672$	4364.48	−	1086.56i	0.250541	−	0.0623735i
$673$	−21886.3			−1.25357			−0.626785	−	0.779192i	$-0.715630\pi$
$673$	−21886.3			−1.25357			−0.626785	+	0.779192i	$0.715630\pi$
$674$	−8422.58	−	14588.3i	−0.481343	−	0.833711i
$675$	−1355.58	+	2347.93i	−0.0772980	+	0.133884i
$676$	−1795.99	+	3110.74i	−0.102184	+	0.176988i
$677$	13678.8	+	23692.3i	0.776540	+	1.34501i	0.933925	+	0.357469i	$0.116360\pi$
$677$	13678.8	+	23692.3i	0.776540	+	1.34501i	−0.157385	+	0.987537i	$0.550306\pi$
$678$	1970.88			0.111639
$679$	5710.60	−	19888.9i	0.322758	−	1.12410i
$680$	−141.915			−0.00800324
$681$	−8964.44	−	15526.9i	−0.504432	−	0.873702i
$682$	−3626.11	+	6280.60i	−0.203594	+	0.352634i
$683$	15691.2	−	27177.9i	0.879073	−	1.52260i	0.0267131	−	0.999643i	$-0.491496\pi$
$683$	15691.2	−	27177.9i	0.879073	−	1.52260i	0.852360	−	0.522956i	$-0.175171\pi$
$684$	1104.40	+	1912.88i	0.0617365	+	0.106931i
$685$	13967.3			0.779067
$686$	15004.5	+	4892.74i	0.835096	+	0.272311i
$687$	1909.62			0.106050
$688$	−7447.51	−	12899.5i	−0.412694	−	0.714807i
$689$	−702.413	+	1216.62i	−0.0388386	+	0.0672705i
$690$	−1571.90	+	2722.61i	−0.0867265	+	0.150215i
$691$	−5615.64	−	9726.57i	−0.309159	−	0.535479i	0.669020	−	0.743245i	$-0.266714\pi$
$691$	−5615.64	−	9726.57i	−0.309159	−	0.535479i	−0.978179	+	0.207766i	$0.933381\pi$
$692$	7214.74			0.396334
$693$	506.001	−	1762.30i	0.0277365	−	0.0966007i
$694$	30270.4			1.65569
$695$	4075.08	+	7058.25i	0.222413	+	0.385230i
$696$	−1630.08	+	2823.38i	−0.0887758	+	0.153764i
$697$	46.3340	−	80.2528i	0.00251797	−	0.00436125i
$698$	−4303.40	−	7453.72i	−0.233361	−	0.404194i
$699$	−6544.23			−0.354114
$700$	−3298.25	+	821.116i	−0.178089	+	0.0443361i
$701$	2836.65			0.152837			0.0764185	−	0.997076i	$-0.475651\pi$
$701$	2836.65			0.152837			0.0764185	+	0.997076i	$0.475651\pi$
$702$	−510.528	−	884.261i	−0.0274482	−	0.0475417i
$703$	1167.50	−	2022.17i	0.0626359	−	0.108489i
$704$	−3131.81	+	5424.45i	−0.167663	+	0.290400i
$705$	3566.84	+	6177.95i	0.190546	+	0.330035i
$706$	−5040.45			−0.268697
$707$	−16747.7	−	17354.9i	−0.890894	−	0.923196i
$708$	1303.86			0.0692118
$709$	1612.32	+	2792.63i	0.0854049	+	0.147926i	0.905564	−	0.424210i	$-0.139448\pi$
$709$	1612.32	+	2792.63i	0.0854049	+	0.147926i	−0.820159	+	0.572136i	$0.806115\pi$
$710$	−2015.56	+	3491.05i	−0.106539	+	0.184531i
$711$	310.789	−	538.302i	0.0163931	−	0.0283937i
$712$	1613.40	+	2794.49i	0.0849223	+	0.147090i
$713$	22574.2			1.18571
$714$	112.359	+	116.433i	0.00588925	+	0.00610278i
$715$	830.246			0.0434258
$716$	3962.31	+	6862.92i	0.206814	+	0.358212i
$717$	−2518.13	+	4361.53i	−0.131159	+	0.227175i
$718$	−7363.11	+	12753.3i	−0.382714	+	0.662880i
$719$	8419.13	+	14582.4i	0.436691	+	0.756371i	0.997432	−	0.0716204i	$-0.0228170\pi$
$719$	8419.13	+	14582.4i	0.436691	+	0.756371i	−0.560741	+	0.827991i	$0.689484\pi$
$720$	2054.52			0.106344
$721$	−3111.22	+	774.554i	−0.160704	+	0.0400082i
$722$	27755.9			1.43070
$723$	−1513.54	−	2621.52i	−0.0778548	−	0.134849i
$724$	−1382.57	+	2394.69i	−0.0709709	+	0.122925i
$725$	2234.61	−	3870.46i	0.114471	−	0.198269i
$726$	450.921	+	781.018i	0.0230513	+	0.0399260i
$727$	7433.04			0.379197			0.189598	−	0.981862i	$-0.439281\pi$
$727$	7433.04			0.379197			0.189598	+	0.981862i	$0.439281\pi$
$728$	1899.56	−	6615.80i	0.0967067	−	0.336810i
$729$	729.000			0.0370370
$730$	−4560.26	−	7898.60i	−0.231209	−	0.400466i
$731$	−189.626	+	328.441i	−0.00959446	+	0.0166181i
$732$	−934.654	+	1618.87i	−0.0471937	+	0.0817420i
$733$	11509.2	+	19934.4i	0.579946	+	1.00450i	0.995485	+	0.0949203i	$0.0302596\pi$
$733$	11509.2	+	19934.4i	0.579946	+	1.00450i	−0.415539	+	0.909575i	$0.636407\pi$
$734$	1552.11			0.0780508
$735$	−4325.11	−	2706.85i	−0.217053	−	0.135842i
$736$	6886.22			0.344877
$737$	4032.15	+	6983.88i	0.201528	+	0.349056i
$738$	−883.820	+	1530.82i	−0.0440838	+	0.0763554i
$739$	9115.95	−	15789.3i	0.453769	−	0.785952i	−0.544847	−	0.838535i	$-0.683412\pi$
$739$	9115.95	−	15789.3i	0.453769	−	0.785952i	0.998617	+	0.0525837i	$0.0167456\pi$
$740$	78.7956	+	136.478i	0.00391430	+	0.00677977i
$741$	6131.88			0.303995
$742$	−1171.93	+	4081.59i	−0.0579822	+	0.201940i
$743$	−11383.5			−0.562072			−0.281036	−	0.959697i	$-0.590678\pi$
$743$	−11383.5			−0.562072			−0.281036	+	0.959697i	$0.590678\pi$
$744$	−9718.98	−	16833.8i	−0.478918	−	0.829511i
$745$	−933.996	+	1617.73i	−0.0459315	+	0.0795557i
$746$	−9632.77	+	16684.4i	−0.472762	+	0.818848i
$747$	−1906.14	−	3301.53i	−0.0933628	−	0.161709i
$748$	23.5667			0.00115198
$749$	−1174.53	+	292.406i	−0.0572984	+	0.0142647i
$750$	−8330.60			−0.405587
$751$	−13747.1	−	23810.6i	−0.667960	−	1.15694i	−0.978474	−	0.206372i	$-0.933834\pi$
$751$	−13747.1	−	23810.6i	−0.667960	−	1.15694i	0.310513	−	0.950569i	$-0.399499\pi$
$752$	−11038.9	+	19120.0i	−0.535303	+	0.927172i
$753$	10178.0	−	17628.8i	0.492572	−	0.853160i
$754$	841.584	+	1457.67i	0.0406481	+	0.0704046i
$755$	−759.780			−0.0366241
$756$	634.641	+	657.651i	0.0305313	+	0.0316383i
$757$	36682.7			1.76124			0.880618	−	0.473827i	$-0.157128\pi$
$757$	36682.7			1.76124			0.880618	+	0.473827i	$0.157128\pi$
$758$	12304.0	+	21311.2i	0.589580	+	1.02118i
$759$	1403.60	−	2431.10i	0.0671243	−	0.116263i
$760$	−8128.44	+	14078.9i	−0.387960	+	0.671966i
$761$	18028.8	+	31226.8i	0.858795	+	1.48748i	0.873079	+	0.487579i	$0.162120\pi$
$761$	18028.8	+	31226.8i	0.858795	+	1.48748i	−0.0142838	+	0.999898i	$0.504547\pi$
$762$	4842.19			0.230202
$763$	−28699.9	−	29740.5i	−1.36174	−	1.41111i
$764$	−1931.05			−0.0914434
$765$	−26.1557	−	45.3030i	−0.00123616	−	0.00214109i
$766$	1826.60	−	3163.76i	0.0861589	−	0.149232i
$767$	1809.83	−	3134.71i	0.0852008	−	0.147572i
$768$	−3974.48	−	6884.00i	−0.186740	−	0.323444i
$769$	−18923.0			−0.887363			−0.443682	−	0.896185i	$-0.646328\pi$
$769$	−18923.0			−0.887363			−0.443682	+	0.896185i	$0.646328\pi$
$770$	2435.33	−	606.288i	0.113978	−	0.0283755i
$771$	13622.3			0.636312
$772$	−1936.19	−	3353.58i	−0.0902655	−	0.156344i
$773$	−4638.28	+	8033.74i	−0.215818	+	0.373808i	−0.953525	−	0.301313i	$-0.902575\pi$
$773$	−4638.28	+	8033.74i	−0.215818	+	0.373808i	0.737707	+	0.675121i	$0.235908\pi$
$774$	3617.10	−	6265.01i	0.167977	−	0.290944i
$775$	13323.4	+	23076.8i	0.617536	+	1.06960i
$776$	−27279.8			−1.26197
$777$	266.633	−	928.630i	0.0123107	−	0.0428757i
$778$	6024.62			0.277626
$779$	−5307.72	−	9193.23i	−0.244119	−	0.422826i
$780$	−206.923	+	358.401i	−0.00949877	+	0.0164523i
$781$	1799.75	−	3117.26i	0.0824587	−	0.142823i
$782$	123.867	+	214.543i	0.00566427	+	0.00981080i
$783$	−1201.73			−0.0548482
$784$	562.176	−	15781.0i	0.0256093	−	0.718887i
$785$	14332.8			0.651669
$786$	7609.28	+	13179.7i	0.345311	+	0.598095i
$787$	6893.45	−	11939.8i	0.312230	−	0.540798i	−0.666615	−	0.745402i	$-0.732257\pi$
$787$	6893.45	−	11939.8i	0.312230	−	0.540798i	0.978845	+	0.204604i	$0.0655908\pi$
$788$	−1153.40	+	1997.75i	−0.0521424	+	0.0903132i
$789$	−1556.48	−	2695.90i	−0.0702309	−	0.121643i
$790$	850.802			0.0383167
$791$	−1351.55	+	4707.18i	−0.0607530	+	0.211591i
$792$	−2417.19			−0.108448
$793$	2594.71	+	4494.16i	0.116193	+	0.201251i
$794$	13604.8	−	23564.2i	0.608080	−	1.05322i
$795$	686.442	−	1188.95i	0.0306234	−	0.0530412i
$796$	1446.30	+	2505.06i	0.0644003	+	0.111545i
$797$	−11360.1			−0.504887			−0.252444	−	0.967612i	$-0.581234\pi$
$797$	−11360.1			−0.504887			−0.252444	+	0.967612i	$0.581234\pi$
$798$	17986.4	−	4477.81i	0.797884	−	0.198637i
$799$	562.137			0.0248898
$800$	4064.27	+	7039.53i	0.179617	+	0.311106i
$801$	−594.715	+	1030.08i	−0.0262337	+	0.0454381i
$802$	−19667.7	+	34065.5i	−0.865949	+	1.49987i
$803$	4071.99	+	7052.89i	0.178951	+	0.309951i
$804$	−4019.74			−0.176325
$805$	−5424.64	−	5621.32i	−0.237507	−	0.246119i
$806$	−10035.5			−0.438569
$807$	−4487.19	−	7772.04i	−0.195733	−	0.339019i
$808$	−15897.9	+	27536.0i	−0.692186	+	1.19890i
$809$	−2919.33	+	5056.43i	−0.126870	+	0.219746i	−0.922463	−	0.386087i	$-0.873827\pi$
$809$	−2919.33	+	5056.43i	−0.126870	+	0.219746i	0.795592	+	0.605833i	$0.207160\pi$
$810$	498.920	+	864.155i	0.0216423	+	0.0374855i
$811$	−40805.7			−1.76681			−0.883403	−	0.468613i	$-0.844754\pi$
$811$	−40805.7			−1.76681			−0.883403	+	0.468613i	$0.844754\pi$
$812$	−1046.18	−	1084.11i	−0.0452139	−	0.0468532i
$813$	−13322.9			−0.574731
$814$	237.609	+	411.551i	0.0102312	+	0.0177209i
$815$	−8159.24	+	14132.2i	−0.350682	+	0.607399i
$816$	80.9486	−	140.207i	0.00347276	−	0.00601499i
$817$	21722.2	+	37624.0i	0.930190	+	1.61114i
$818$	4325.60			0.184891
$819$	2462.03	−	612.936i	0.105043	−	0.0261511i
$820$	716.446			0.0305114
$821$	−17069.0	−	29564.3i	−0.725592	−	1.25676i	−0.958730	−	0.284319i	$-0.908232\pi$
$821$	−17069.0	−	29564.3i	−0.725592	−	1.25676i	0.233137	−	0.972444i	$-0.425101\pi$
$822$	−10497.2	+	18181.7i	−0.445416	+	0.771484i
$823$	−541.969	+	938.718i	−0.0229549	+	0.0397590i	−0.877275	−	0.479989i	$-0.840641\pi$
$823$	−541.969	+	938.718i	−0.0229549	+	0.0397590i	0.854320	+	0.519748i	$0.173974\pi$
$824$	2113.42	+	3660.56i	0.0893502	+	0.154759i
$825$	3313.63			0.139837
$826$	3019.57	−	10516.6i	0.127196	−	0.443000i
$827$	−12650.5			−0.531922			−0.265961	−	0.963984i	$-0.585689\pi$
$827$	−12650.5			−0.531922			−0.265961	+	0.963984i	$0.585689\pi$
$828$	699.640	+	1211.81i	0.0293649	+	0.0508616i
$829$	8386.54	−	14525.9i	0.351359	−	0.608571i	−0.635129	−	0.772406i	$-0.719053\pi$
$829$	8386.54	−	14525.9i	0.351359	−	0.608571i	0.986488	+	0.163835i	$0.0523864\pi$
$830$	2609.08	−	4519.06i	0.109112	−	0.188987i
$831$	11081.2	+	19193.2i	0.462577	+	0.801207i
$832$	−8667.51			−0.361168
$833$	−355.135	+	188.509i	−0.0147715	+	0.00784087i
$834$	−12250.7			−0.508640
$835$	−4858.14	−	8414.54i	−0.201345	−	0.348739i
$836$	1349.82	−	2337.96i	0.0558428	−	0.0967225i
$837$	3582.52	−	6205.10i	0.147945	−	0.256248i
$838$	15618.4	+	27051.9i	0.643830	+	1.11515i
$839$	12587.5			0.517960			0.258980	−	0.965883i	$-0.416614\pi$
$839$	12587.5			0.517960			0.258980	+	0.965883i	$0.416614\pi$
$840$	−1856.37	+	6465.37i	−0.0762511	+	0.265567i
$841$	−22408.0			−0.918775
$842$	−18799.9	−	32562.3i	−0.769461	−	1.33275i
$843$	−8371.70	+	14500.2i	−0.342037	+	0.592425i
$844$	104.559	−	181.102i	0.00426431	−	0.00738600i
$845$	−4872.49	−	8439.40i	−0.198365	−	0.343579i
$846$	−10722.8			−0.435763
$847$	−2174.58	+	541.372i	−0.0882164	+	0.0219619i
$848$	4248.90			0.172061
$849$	−6366.35	−	11026.8i	−0.257353	−	0.445748i
$850$	−146.213	+	253.248i	−0.00590008	+	0.0102192i
$851$	739.613	−	1281.05i	0.0297927	−	0.0516025i
$852$	897.109	+	1553.84i	0.0360733	+	0.0624808i
$853$	3697.77			0.148428			0.0742140	−	0.997242i	$-0.476355\pi$
$853$	3697.77			0.148428			0.0742140	+	0.997242i	$0.476355\pi$
$854$	10892.8	+	11287.8i	0.436469	+	0.452294i
$855$	−5992.45			−0.239693
$856$	797.850	+	1381.92i	0.0318574	+	0.0551787i
$857$	−17659.4	+	30587.0i	−0.703889	+	1.21917i	0.263201	+	0.964741i	$0.415222\pi$
$857$	−17659.4	+	30587.0i	−0.703889	+	1.21917i	−0.967091	+	0.254431i	$0.918112\pi$
$858$	−623.979	+	1080.76i	−0.0248278	+	0.0430031i
$859$	−5408.41	−	9367.64i	−0.214822	−	0.372083i	0.738395	−	0.674368i	$-0.235584\pi$
$859$	−5408.41	−	9367.64i	−0.214822	−	0.372083i	−0.953218	+	0.302285i	$0.902251\pi$
$860$	−2932.11			−0.116261
$861$	−3050.07	−	3160.66i	−0.120727	−	0.125104i
$862$	662.216			0.0261661
$863$	3901.17	+	6757.02i	0.153879	+	0.266526i	0.932650	−	0.360782i	$-0.117490\pi$
$863$	3901.17	+	6757.02i	0.153879	+	0.266526i	−0.778772	+	0.627308i	$0.784157\pi$
$864$	1092.84	−	1892.85i	0.0430314	−	0.0745326i
$865$	−9786.77	+	16951.2i	−0.384694	+	0.666309i
$866$	−6427.82	−	11133.3i	−0.252224	−	0.436865i
$867$	14734.9			0.577189
$868$	8716.60	−	2170.04i	0.340853	−	0.0848572i
$869$	−759.706			−0.0296562
$870$	−822.448	−	1424.52i	−0.0320501	−	0.0555124i
$871$	−5579.63	+	9664.21i	−0.217059	+	0.375958i
$872$	−27243.6	+	47187.4i	−1.05801	+	1.83253i
$873$	−5027.80	−	8708.40i	−0.194920	−	0.337611i
$874$	28378.7			1.09831
$875$	5712.78	−	19896.5i	0.220717	−	0.768713i
$876$	−4059.46			−0.156571
$877$	21962.3	+	38039.9i	0.845627	+	1.46467i	0.885076	+	0.465447i	$0.154106\pi$
$877$	21962.3	+	38039.9i	0.845627	+	1.46467i	−0.0394487	+	0.999222i	$0.512560\pi$
$878$	8128.17	−	14078.4i	0.312429	−	0.541143i
$879$	−253.253	+	438.647i	−0.00971787	+	0.0168319i
$880$	−1255.54	−	2174.66i	−0.0480958	−	0.0833043i
$881$	−31311.8			−1.19741			−0.598706	−	0.800969i	$-0.704318\pi$
$881$	−31311.8			−1.19741			−0.598706	+	0.800969i	$0.704318\pi$
$882$	6774.19	−	3595.80i	0.258615	−	0.137275i
$883$	−25960.6			−0.989404			−0.494702	−	0.869063i	$-0.664723\pi$
$883$	−25960.6			−0.989404			−0.494702	+	0.869063i	$0.664723\pi$
$884$	16.3056	+	28.2422i	0.000620382	+	0.00107453i
$885$	−1768.68	+	3063.44i	−0.0671789	+	0.116357i
$886$	−9241.24	+	16006.3i	−0.350413	+	0.606932i
$887$	−5292.29	−	9166.52i	−0.200336	−	0.346992i	0.748301	−	0.663360i	$-0.230870\pi$
$887$	−5292.29	−	9166.52i	−0.200336	−	0.346992i	−0.948637	+	0.316368i	$0.897537\pi$
$888$	−1273.72			−0.0481342
$889$	−3320.57	+	11564.9i	−0.125274	+	0.436304i
$890$	−1628.07			−0.0613178
$891$	−445.500	−	771.629i	−0.0167506	−	0.0290129i
$892$	2642.51	−	4576.96i	0.0991904	−	0.171803i
$893$	32197.3	−	55767.4i	1.20654	−	2.08979i
$894$	−1403.91	−	2431.64i	−0.0525208	−	0.0909688i
$895$	−21499.4			−0.802957
$896$	−13785.5	+	3431.96i	−0.513995	+	0.127962i
$897$	3884.56			0.144595
$898$	21284.4	+	36865.6i	0.790944	+	1.36996i
$899$	−5905.63	+	10228.8i	−0.219092	+	0.379478i
$900$	−825.860	+	1430.43i	−0.0305874	+	0.0529790i
$901$	−54.0919	−	93.6900i	−0.00200007	−	0.00346422i
$902$	2160.45			0.0797507
$903$	12482.6	+	12935.2i	0.460018	+	0.476697i
$904$	6456.41			0.237541
$905$	−3750.91	−	6496.77i	−0.137773	−	0.238630i
$906$	571.019	−	989.035i	0.0209391	−	0.0362676i
$907$	−13351.8	+	23126.0i	−0.488798	+	0.846624i	−0.999917	−	0.0128866i	$-0.995898\pi$
$907$	−13351.8	+	23126.0i	−0.488798	+	0.846624i	0.511119	+	0.859510i	$0.329231\pi$
$908$	−5461.42	−	9459.46i	−0.199607	−	0.345730i
$909$	−11720.3			−0.427653
$910$	2411.56	+	2499.00i	0.0878489	+	0.0910341i
$911$	40608.6			1.47686			0.738432	−	0.674328i	$-0.235567\pi$
$911$	40608.6			1.47686			0.738432	+	0.674328i	$0.235567\pi$
$912$	−9272.94	−	16061.2i	−0.336686	−	0.583157i
$913$	−2329.73	+	4035.20i	−0.0844498	+	0.146271i
$914$	6017.15	−	10422.0i	0.217757	−	0.377166i
$915$	−2535.71	−	4391.98i	−0.0916152	−	0.158682i
$916$	1163.40			0.0419648
$917$	−36695.9	+	9135.64i	−1.32149	+	0.328992i
$918$	78.6302			0.00282700
$919$	14772.9	+	25587.4i	0.530265	+	0.918446i	0.999377	+	0.0353071i	$0.0112409\pi$
$919$	14772.9	+	25587.4i	0.530265	+	0.918446i	−0.469111	+	0.883139i	$0.655426\pi$
$920$	−5149.39	+	8919.00i	−0.184533	+	0.319620i
$921$	1412.61	−	2446.72i	0.0505399	−	0.0875376i
$922$	−12795.4	−	22162.3i	−0.457044	−	0.791623i
$923$	4980.95			0.177627
$924$	308.272	−	1073.65i	0.0109755	−	0.0382256i
$925$	1746.09			0.0620661
$926$	−8383.33	−	14520.4i	−0.297509	−	0.515301i
$927$	−779.029	+	1349.32i	−0.0276016	+	0.0478074i
$928$	−1801.50	+	3120.29i	−0.0637253	+	0.110376i
$929$	−22402.8	−	38802.8i	−0.791186	−	1.37038i	−0.925233	−	0.379400i	$-0.876130\pi$
$929$	−22402.8	−	38802.8i	−0.791186	−	1.37038i	0.134046	−	0.990975i	$-0.457203\pi$
$930$	9807.34			0.345801
$931$	−1639.71	+	46028.7i	−0.0577220	+	1.62033i
$932$	−3986.95			−0.140126
$933$	−3971.20	−	6878.32i	−0.139348	−	0.241357i
$934$	−1166.75	+	2020.87i	−0.0408750	+	0.0707976i
$935$	−31.9681	+	55.3704i	−0.00111815	+	0.00193669i
$936$	−1672.44	−	2896.75i	−0.0584031	−	0.101157i
$937$	−46926.5			−1.63610			−0.818048	−	0.575150i	$-0.804944\pi$
$937$	−46926.5			−1.63610			−0.818048	+	0.575150i	$0.804944\pi$
$938$	−9309.23	+	32422.2i	−0.324048	+	1.12859i
$939$	4152.94			0.144330
$940$	2173.03	+	3763.80i	0.0754005	+	0.130597i
$941$	−5626.52	+	9745.42i	−0.194920	+	0.337611i	−0.946874	−	0.321604i	$-0.895778\pi$
$941$	−5626.52	+	9745.42i	−0.194920	+	0.337611i	0.751955	+	0.659215i	$0.229111\pi$
$942$	−10772.0	+	18657.6i	−0.372579	+	0.645325i
$943$	−3362.45	−	5823.94i	−0.116115	−	0.201117i
$944$	−10947.7			−0.377453
$945$	−2406.05	+	598.999i	−0.0828242	+	0.0206195i
$946$	−8841.81			−0.303882
$947$	−18412.1	−	31890.6i	−0.631797	−	1.09430i	−0.987184	−	0.159585i	$-0.948984\pi$
$947$	−18412.1	−	31890.6i	−0.631797	−	1.09430i	0.355387	−	0.934719i	$-0.384349\pi$
$948$	189.342	−	327.951i	0.00648687	−	0.0112356i
$949$	−5634.77	+	9759.70i	−0.192742	+	0.333839i
$950$	16749.2	+	29010.5i	0.572016	+	0.990762i
$951$	25714.6			0.876817
$952$	368.076	+	381.422i	0.0125309	+	0.0129852i
$953$	18571.8			0.631268			0.315634	−	0.948881i	$-0.397783\pi$
$953$	18571.8			0.631268			0.315634	+	0.948881i	$0.397783\pi$
$954$	1031.80	+	1787.13i	0.0350166	+	0.0606506i
$955$	2619.46	−	4537.03i	0.0887577	−	0.153733i
$956$	−1534.12	+	2657.18i	−0.0519007	+	0.0898947i
$957$	734.388	+	1272.00i	0.0248061	+	0.0429653i
$958$	−26733.4			−0.901583
$959$	−36225.9	−	37539.4i	−1.21981	−	1.26404i
$960$	8470.44			0.284773
$961$	−20315.5	−	35187.5i	−0.681935	−	1.18115i
$962$	−328.800	+	569.499i	−0.0110197	+	0.0190867i
$963$	−294.095	+	509.388i	−0.00984122	+	0.0170455i
$964$	−922.095	−	1597.11i	−0.0308077	−	0.0533606i
$965$	10505.7			0.350457
$966$	11394.4	−	2836.70i	0.379513	−	0.0944818i
$967$	8548.12			0.284270			0.142135	−	0.989847i	$-0.454603\pi$
$967$	8548.12			0.284270			0.142135	+	0.989847i	$0.454603\pi$
$968$	1477.17	+	2558.53i	0.0490476	+	0.0849529i
$969$	−236.104	+	408.944i	−0.00782740	+	0.0135575i
$970$	6881.94	−	11919.9i	0.227800	−	0.394561i
$971$	−11494.7	−	19909.5i	−0.379901	−	0.658007i	0.611147	−	0.791517i	$-0.290708\pi$
$971$	−11494.7	−	19909.5i	−0.379901	−	0.658007i	−0.991047	+	0.133510i	$0.957375\pi$
$972$	444.130			0.0146558
$973$	8400.99	−	29259.0i	0.276797	−	0.964029i
$974$	19087.3			0.627923
$975$	2292.68	+	3971.04i	0.0753072	+	0.130436i
$976$	7847.70	−	13592.6i	0.257376	−	0.445788i
$977$	−5502.20	+	9530.09i	−0.180175	+	0.312072i	−0.941940	−	0.335781i	$-0.891000\pi$
$977$	−5502.20	+	9530.09i	−0.180175	+	0.312072i	0.761765	+	0.647853i	$0.224333\pi$
$978$	−12264.3	−	21242.4i	−0.400991	−	0.694536i
$979$	1453.75			0.0474586
$980$	−2634.99	−	1649.10i	−0.0858896	−	0.0537536i
$981$	−20084.6			−0.653670
$982$	15006.7	+	25992.3i	0.487660	+	0.844651i
$983$	25143.5	−	43549.8i	0.815822	−	1.41305i	−0.0929141	−	0.995674i	$-0.529618\pi$
$983$	25143.5	−	43549.8i	0.815822	−	1.41305i	0.908736	−	0.417371i	$-0.137048\pi$
$984$	−2895.31	+	5014.82i	−0.0937998	+	0.162466i
$985$	−3129.16	−	5419.87i	−0.101222	−	0.175321i
$986$	−129.619			−0.00418651
$987$	7353.22	−	25609.8i	0.237138	−	0.825906i
$988$	3735.73			0.120293
$989$	13761.1	+	23834.9i	0.442444	+	0.766336i
$990$	609.791	−	1056.19i	0.0195762	−	0.0339070i
$991$	5719.62	−	9906.67i	0.183340	−	0.317554i	−0.759676	−	0.650302i	$-0.774642\pi$
$991$	5719.62	−	9906.67i	0.183340	−	0.317554i	0.943016	+	0.332748i	$0.107976\pi$
$992$	−10741.1	−	18604.0i	−0.343779	−	0.595443i
$993$	20048.7			0.640711
$994$	14610.4	−	3637.34i	0.466212	−	0.116066i
$995$	−7847.58			−0.250035
$996$	−1161.28	−	2011.40i	−0.0369443	−	0.0639895i
$997$	11537.5	−	19983.5i	0.366495	−	0.634787i	−0.622520	−	0.782604i	$-0.713891\pi$
$997$	11537.5	−	19983.5i	0.366495	−	0.634787i	0.989015	+	0.147816i	$0.0472245\pi$
$998$	1177.14	−	2038.87i	0.0373365	−	0.0646686i
$999$	−234.753	−	406.603i	−0.00743468	−	0.0128772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.i.a.67.3	✓	16
7.2	even	3	inner	231.4.i.a.100.3	yes	16
7.3	odd	6		1617.4.a.v.1.6		8
7.4	even	3		1617.4.a.u.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.i.a.67.3	✓	16	1.1	even	1	trivial
231.4.i.a.100.3	yes	16	7.2	even	3	inner
1617.4.a.u.1.6		8	7.4	even	3
1617.4.a.v.1.6		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24221 - 2.15156i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.913847 - 1.58283i) q^{4} +(2.47926 + 4.29420i) q^{5} -7.45324 q^{6} +(5.11112 - 17.8010i) q^{7} -24.4160 q^{8} +(-4.50000 - 7.79423i) q^{9} +(6.15950 - 10.6686i) q^{10} +(-5.50000 + 9.52628i) q^{11} +(-2.74154 - 4.74849i) q^{12} -15.2217 q^{13} +(-44.6491 + 11.1156i) q^{14} +14.8756 q^{15} +(23.0190 + 39.8701i) q^{16} +(0.586100 - 1.01516i) q^{17} +(-11.1799 + 19.3641i) q^{18} +(-67.1398 - 116.290i) q^{19} +9.06266 q^{20} +(-38.5817 - 39.9806i) q^{21} +27.3285 q^{22} +(-42.5332 - 73.6697i) q^{23} +(-36.6241 + 63.4348i) q^{24} +(50.2065 - 86.9603i) q^{25} +(18.9084 + 32.7504i) q^{26} -27.0000 q^{27} +(-23.5052 - 24.3575i) q^{28} +44.5084 q^{29} +(-18.4785 - 32.0057i) q^{30} +(-132.686 + 229.818i) q^{31} +(-40.4755 + 70.1057i) q^{32} +(16.5000 + 28.5788i) q^{33} -2.91223 q^{34} +(89.1130 - 22.1852i) q^{35} -16.4493 q^{36} +(8.69454 + 15.0594i) q^{37} +(-166.803 + 288.911i) q^{38} +(-22.8325 + 39.5470i) q^{39} +(-60.5337 - 104.847i) q^{40} +79.0547 q^{41} +(-38.0944 + 132.675i) q^{42} -323.538 q^{43} +(10.0523 + 17.4111i) q^{44} +(22.3133 - 38.6478i) q^{45} +(-105.670 + 183.026i) q^{46} +(239.778 + 415.308i) q^{47} +138.114 q^{48} +(-290.753 - 181.966i) q^{49} -249.468 q^{50} +(-1.75830 - 3.04547i) q^{51} +(-13.9103 + 24.0933i) q^{52} +(46.1456 - 79.9266i) q^{53} +(33.5396 + 58.0922i) q^{54} -54.5437 q^{55} +(-124.793 + 434.631i) q^{56} -402.839 q^{57} +(-55.2886 - 95.7626i) q^{58} +(-118.898 + 205.937i) q^{59} +(13.5940 - 23.5455i) q^{60} +(-170.461 - 295.248i) q^{61} +659.292 q^{62} +(-161.745 + 40.2673i) q^{63} +569.420 q^{64} +(-37.7385 - 65.3649i) q^{65} +(40.9928 - 71.0016i) q^{66} +(366.559 - 634.898i) q^{67} +(-1.07121 - 1.85539i) q^{68} -255.199 q^{69} +(-158.430 - 164.174i) q^{70} -327.228 q^{71} +(109.872 + 190.304i) q^{72} +(370.181 - 641.172i) q^{73} +(21.6008 - 37.4137i) q^{74} +(-150.620 - 260.881i) q^{75} -245.422 q^{76} +(141.466 + 146.596i) q^{77} +113.451 q^{78} +(34.5321 + 59.8113i) q^{79} +(-114.140 + 197.696i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-98.2022 - 170.091i) q^{82} +423.586 q^{83} +(-98.5403 + 24.5321i) q^{84} +5.81238 q^{85} +(401.900 + 696.112i) q^{86} +(66.7625 - 115.636i) q^{87} +(134.288 - 232.594i) q^{88} +(-66.0794 - 114.453i) q^{89} -110.871 q^{90} +(-77.7998 + 270.961i) q^{91} -155.475 q^{92} +(398.057 + 689.455i) q^{93} +(595.709 - 1031.80i) q^{94} +(332.914 - 576.624i) q^{95} +(121.427 + 210.317i) q^{96} +1117.29 q^{97} +(-30.3375 + 851.613i) q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 24 q^{3} - 30 q^{4} - 20 q^{5} + 24 q^{6} + 18 q^{7} - 156 q^{8} - 72 q^{9} - 94 q^{10} - 88 q^{11} + 90 q^{12} - 188 q^{13} + 52 q^{14} - 120 q^{15} + 10 q^{16} - 144 q^{17} + 36 q^{18}+ \cdots + 1584 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 24 * q^3 - 30 * q^4 - 20 * q^5 + 24 * q^6 + 18 * q^7 - 156 * q^8 - 72 * q^9 - 94 * q^10 - 88 * q^11 + 90 * q^12 - 188 * q^13 + 52 * q^14 - 120 * q^15 + 10 * q^16 - 144 * q^17 + 36 * q^18 + 8 * q^19 - 288 * q^20 - 36 * q^21 - 88 * q^22 + 286 * q^23 - 234 * q^24 + 206 * q^25 - 132 * q^26 - 432 * q^27 + 14 * q^28 + 40 * q^29 + 282 * q^30 - 192 * q^31 + 948 * q^32 + 264 * q^33 - 972 * q^34 - 112 * q^35 + 540 * q^36 + 666 * q^37 - 200 * q^38 - 282 * q^39 - 486 * q^40 + 120 * q^41 - 660 * q^42 - 492 * q^43 - 330 * q^44 - 180 * q^45 - 454 * q^46 - 922 * q^47 + 60 * q^48 - 386 * q^49 + 2972 * q^50 + 432 * q^51 + 1714 * q^52 + 1064 * q^53 - 108 * q^54 + 440 * q^55 + 1176 * q^56 + 48 * q^57 + 1832 * q^58 - 50 * q^59 - 432 * q^60 - 1174 * q^61 - 1388 * q^62 - 270 * q^63 + 3204 * q^64 + 1840 * q^65 - 132 * q^66 + 766 * q^67 - 2806 * q^68 + 1716 * q^69 - 2584 * q^70 - 1572 * q^71 + 702 * q^72 + 398 * q^73 + 1504 * q^74 - 618 * q^75 - 3036 * q^76 + 132 * q^77 - 792 * q^78 + 1886 * q^79 + 504 * q^80 - 648 * q^81 - 2738 * q^82 - 1564 * q^83 - 132 * q^84 - 3284 * q^85 + 356 * q^86 + 60 * q^87 + 858 * q^88 - 2380 * q^89 + 1692 * q^90 + 2240 * q^91 - 4512 * q^92 + 576 * q^93 + 2588 * q^94 - 58 * q^95 - 2844 * q^96 - 504 * q^97 + 1132 * q^98 + 1584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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