LMFDB - Embedded newform 231.4.i.a.100.2

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			100.2
Root			$2.32362 + 4.02463i$ of defining polynomial
Character	$\chi$	$=$	231.100
Dual form			231.4.i.a.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.82362 + 3.15860i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.65118 - 4.59197i) q^{4} +(1.62425 - 2.81329i) q^{5} -10.9417 q^{6} +(-2.33065 - 18.3730i) q^{7} -9.83896 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.92404 + 10.2607i) q^{10} +(-5.50000 - 9.52628i) q^{11} +(7.95353 - 13.7759i) q^{12} +40.9617 q^{13} +(62.2833 + 26.1438i) q^{14} +9.74551 q^{15} +(39.1519 - 67.8131i) q^{16} +(-47.6051 - 82.4545i) q^{17} +(-16.4126 - 28.4274i) q^{18} +(41.0011 - 71.0160i) q^{19} -17.2247 q^{20} +(44.2386 - 33.6147i) q^{21} +40.1196 q^{22} +(28.1656 - 48.7843i) q^{23} +(-14.7584 - 25.5624i) q^{24} +(57.2236 + 99.1142i) q^{25} +(-74.6986 + 129.382i) q^{26} -27.0000 q^{27} +(-78.1895 + 59.4124i) q^{28} +12.0038 q^{29} +(-17.7721 + 30.7822i) q^{30} +(-101.602 - 175.980i) q^{31} +(103.441 + 179.164i) q^{32} +(16.5000 - 28.5788i) q^{33} +347.255 q^{34} +(-55.4741 - 23.2856i) q^{35} +47.7212 q^{36} +(74.4813 - 129.005i) q^{37} +(149.541 + 259.012i) q^{38} +(61.4426 + 106.422i) q^{39} +(-15.9809 + 27.6798i) q^{40} -30.5005 q^{41} +(25.5013 + 201.032i) q^{42} +269.054 q^{43} +(-29.1630 + 50.5117i) q^{44} +(14.6183 + 25.3196i) q^{45} +(102.727 + 177.928i) q^{46} +(-94.9465 + 164.452i) q^{47} +234.912 q^{48} +(-332.136 + 85.6421i) q^{49} -417.416 q^{50} +(142.815 - 247.364i) q^{51} +(-108.597 - 188.095i) q^{52} +(226.954 + 393.097i) q^{53} +(49.2377 - 85.2823i) q^{54} -35.7335 q^{55} +(22.9311 + 180.771i) q^{56} +246.007 q^{57} +(-21.8903 + 37.9152i) q^{58} +(188.094 + 325.789i) q^{59} +(-25.8371 - 44.7511i) q^{60} +(119.191 - 206.444i) q^{61} +741.134 q^{62} +(153.691 + 64.5130i) q^{63} -128.115 q^{64} +(66.5322 - 115.237i) q^{65} +(60.1794 + 104.234i) q^{66} +(-173.761 - 300.964i) q^{67} +(-252.419 + 437.203i) q^{68} +168.994 q^{69} +(174.714 - 132.757i) q^{70} -769.107 q^{71} +(44.2753 - 76.6871i) q^{72} +(-300.412 - 520.328i) q^{73} +(271.651 + 470.513i) q^{74} +(-171.671 + 297.343i) q^{75} -434.805 q^{76} +(-162.208 + 123.254i) q^{77} -448.192 q^{78} +(616.171 - 1067.24i) q^{79} +(-127.185 - 220.291i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(55.6214 - 96.3391i) q^{82} -351.925 q^{83} +(-271.642 - 114.024i) q^{84} -309.291 q^{85} +(-490.653 + 849.835i) q^{86} +(18.0057 + 31.1867i) q^{87} +(54.1143 + 93.7287i) q^{88} +(378.743 - 656.002i) q^{89} -106.633 q^{90} +(-95.4673 - 752.591i) q^{91} -298.688 q^{92} +(304.806 - 527.939i) q^{93} +(-346.293 - 599.796i) q^{94} +(-133.192 - 230.696i) q^{95} +(-310.322 + 537.493i) q^{96} -818.178 q^{97} +(335.181 - 1205.26i) 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 $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.82362	+	3.15860i	−0.644747	+	1.11673i	0.339613	+	0.940565i	$0.389704\pi$
$2$	−1.82362	+	3.15860i	−0.644747	+	1.11673i	−0.984360	+	0.176169i	$0.943629\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.65118	−	4.59197i	−0.331397	−	0.573997i
$5$	1.62425	−	2.81329i	0.145277	−	0.251628i	−0.784199	−	0.620509i	$-0.786926\pi$
$5$	1.62425	−	2.81329i	0.145277	−	0.251628i	0.929476	+	0.368881i	$0.120259\pi$
$6$	−10.9417			−0.744490
$7$	−2.33065	−	18.3730i	−0.125843	−	0.992050i
$7$	−2.33065	−	18.3730i	−0.125843	−	0.992050i
$8$	−9.83896			−0.434825
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	5.92404	+	10.2607i	0.187334	+	0.324473i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$12$	7.95353	−	13.7759i	0.191332	−	0.331397i
$13$	40.9617			0.873903			0.436952	−	0.899485i	$-0.356058\pi$
$13$	40.9617			0.873903			0.436952	+	0.899485i	$0.356058\pi$
$14$	62.2833	+	26.1438i	1.18899	+	0.499088i
$15$	9.74551			0.167752
$16$	39.1519	−	67.8131i	0.611749	−	1.05958i
$17$	−47.6051	−	82.4545i	−0.679173	−	1.17636i	−0.975230	−	0.221192i	$-0.929005\pi$
$17$	−47.6051	−	82.4545i	−0.679173	−	1.17636i	0.296057	−	0.955170i	$-0.404328\pi$
$18$	−16.4126	−	28.4274i	−0.214916	−	0.372245i
$19$	41.0011	−	71.0160i	0.495068	−	0.857483i	−0.504916	−	0.863169i	$-0.668476\pi$
$19$	41.0011	−	71.0160i	0.495068	−	0.857483i	0.999984	+	0.00568549i	$0.00180976\pi$
$20$	−17.2247			−0.192578
$21$	44.2386	−	33.6147i	0.459697	−	0.349302i
$22$	40.1196			0.388797
$23$	28.1656	−	48.7843i	0.255345	−	0.442271i	−0.709644	−	0.704560i	$-0.751144\pi$
$23$	28.1656	−	48.7843i	0.255345	−	0.442271i	0.964989	+	0.262290i	$0.0844776\pi$
$24$	−14.7584	−	25.5624i	−0.125523	−	0.217412i
$25$	57.2236	+	99.1142i	0.457789	+	0.792914i
$26$	−74.6986	+	129.382i	−0.563446	+	0.975918i
$27$	−27.0000			−0.192450
$28$	−78.1895	+	59.4124i	−0.527729	+	0.400996i
$29$	12.0038			0.0768637			0.0384318	−	0.999261i	$-0.487764\pi$
$29$	12.0038			0.0768637			0.0384318	+	0.999261i	$0.487764\pi$
$30$	−17.7721	+	30.7822i	−0.108158	+	0.187334i
$31$	−101.602	−	175.980i	−0.588653	−	1.01958i	−0.994409	−	0.105596i	$-0.966325\pi$
$31$	−101.602	−	175.980i	−0.588653	−	1.01958i	0.405756	−	0.913982i	$-0.367008\pi$
$32$	103.441	+	179.164i	0.571434	+	0.989753i
$33$	16.5000	−	28.5788i	0.0870388	−	0.150756i
$34$	347.255			1.75158
$35$	−55.4741	−	23.2856i	−0.267910	−	0.112457i
$36$	47.7212			0.220931
$37$	74.4813	−	129.005i	0.330936	−	0.573199i	−0.651759	−	0.758426i	$-0.725969\pi$
$37$	74.4813	−	129.005i	0.330936	−	0.573199i	0.982696	+	0.185227i	$0.0593021\pi$
$38$	149.541	+	259.012i	0.638387	+	1.10572i
$39$	61.4426	+	106.422i	0.252274	+	0.436952i
$40$	−15.9809	+	27.6798i	−0.0631702	+	0.109414i
$41$	−30.5005			−0.116180			−0.0580900	−	0.998311i	$-0.518501\pi$
$41$	−30.5005			−0.116180			−0.0580900	+	0.998311i	$0.518501\pi$
$42$	25.5013	+	201.032i	0.0936889	+	0.738571i
$43$	269.054			0.954195			0.477098	−	0.878850i	$-0.341689\pi$
$43$	269.054			0.954195			0.477098	+	0.878850i	$0.341689\pi$
$44$	−29.1630	+	50.5117i	−0.0999200	+	0.173067i
$45$	14.6183	+	25.3196i	0.0484258	+	0.0838760i
$46$	102.727	+	177.928i	0.329266	+	0.570305i
$47$	−94.9465	+	164.452i	−0.294667	+	0.510379i	−0.974907	−	0.222610i	$-0.928542\pi$
$47$	−94.9465	+	164.452i	−0.294667	+	0.510379i	0.680240	+	0.732989i	$0.261876\pi$
$48$	234.912			0.706387
$49$	−332.136	+	85.6421i	−0.968327	+	0.249685i
$50$	−417.416			−1.18063
$51$	142.815	−	247.364i	0.392121	−	0.679173i
$52$	−108.597	−	188.095i	−0.289609	−	0.501618i
$53$	226.954	+	393.097i	0.588200	+	1.01879i	0.994468	+	0.105038i	$0.0334965\pi$
$53$	226.954	+	393.097i	0.588200	+	1.01879i	−0.406268	+	0.913754i	$0.633170\pi$
$54$	49.2377	−	85.2823i	0.124082	−	0.214916i
$55$	−35.7335			−0.0876056
$56$	22.9311	+	180.771i	0.0547197	+	0.431368i
$57$	246.007			0.571655
$58$	−21.8903	+	37.9152i	−0.0495576	+	0.0858363i
$59$	188.094	+	325.789i	0.415048	+	0.718884i	0.995433	−	0.0954580i	$-0.0304315\pi$
$59$	188.094	+	325.789i	0.415048	+	0.718884i	−0.580386	+	0.814342i	$0.697098\pi$
$60$	−25.8371	−	44.7511i	−0.0555925	−	0.0962891i
$61$	119.191	−	206.444i	0.250177	−	0.433319i	−0.713397	−	0.700760i	$-0.752845\pi$
$61$	119.191	−	206.444i	0.250177	−	0.433319i	0.963574	+	0.267440i	$0.0861779\pi$
$62$	741.134			1.51813
$63$	153.691	+	64.5130i	0.307354	+	0.129014i
$64$	−128.115			−0.250224
$65$	66.5322	−	115.237i	0.126958	−	0.219898i
$66$	60.1794	+	104.234i	0.112236	+	0.194399i
$67$	−173.761	−	300.964i	−0.316841	−	0.548784i	0.662986	−	0.748632i	$-0.269289\pi$
$67$	−173.761	−	300.964i	−0.316841	−	0.548784i	−0.979827	+	0.199847i	$0.935955\pi$
$68$	−252.419	+	437.203i	−0.450152	+	0.779686i
$69$	168.994			0.294847
$70$	174.714	−	132.757i	0.298319	−	0.226678i
$71$	−769.107			−1.28558			−0.642790	−	0.766042i	$-0.722223\pi$
$71$	−769.107			−1.28558			−0.642790	+	0.766042i	$0.722223\pi$
$72$	44.2753	−	76.6871i	0.0724708	−	0.125523i
$73$	−300.412	−	520.328i	−0.481651	−	0.834244i	0.518127	−	0.855304i	$-0.326629\pi$
$73$	−300.412	−	520.328i	−0.481651	−	0.834244i	−0.999778	+	0.0210595i	$0.993296\pi$
$74$	271.651	+	470.513i	0.426740	+	0.739136i
$75$	−171.671	+	297.343i	−0.264305	+	0.457789i
$76$	−434.805			−0.656257
$77$	−162.208	+	123.254i	−0.240069	+	0.182417i
$78$	−448.192			−0.650612
$79$	616.171	−	1067.24i	0.877528	−	1.51992i	0.0234819	−	0.999724i	$-0.492525\pi$
$79$	616.171	−	1067.24i	0.877528	−	1.51992i	0.854046	−	0.520198i	$-0.174142\pi$
$80$	−127.185	−	220.291i	−0.177747	−	0.307866i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	55.6214	−	96.3391i	0.0749068	−	0.129742i
$83$	−351.925			−0.465407			−0.232703	−	0.972548i	$-0.574757\pi$
$83$	−351.925			−0.465407			−0.232703	+	0.972548i	$0.574757\pi$
$84$	−271.642	−	114.024i	−0.352840	−	0.148107i
$85$	−309.291			−0.394674
$86$	−490.653	+	849.835i	−0.615214	+	1.06558i
$87$	18.0057	+	31.1867i	0.0221886	+	0.0384318i
$88$	54.1143	+	93.7287i	0.0655523	+	0.113540i
$89$	378.743	−	656.002i	0.451087	−	0.781305i	−0.547367	−	0.836892i	$-0.684370\pi$
$89$	378.743	−	656.002i	0.451087	−	0.781305i	0.998454	+	0.0555877i	$0.0177032\pi$
$90$	−106.633			−0.124890
$91$	−95.4673	−	752.591i	−0.109975	−	0.866956i
$92$	−298.688			−0.338482
$93$	304.806	−	527.939i	0.339859	−	0.588653i
$94$	−346.293	−	599.796i	−0.379972	−	0.658130i
$95$	−133.192	−	230.696i	−0.143845	−	0.249146i
$96$	−310.322	+	537.493i	−0.329918	+	0.571434i
$97$	−818.178			−0.856427			−0.428214	−	0.903678i	$-0.640857\pi$
$97$	−818.178			−0.856427			−0.428214	+	0.903678i	$0.640857\pi$
$98$	335.181	−	1205.26i	0.345494	−	1.24235i
$99$	99.0000			0.100504
$100$	303.420	−	525.539i	0.303420	−	0.525539i
$101$	−276.823	−	479.472i	−0.272722	−	0.472369i	0.696836	−	0.717231i	$-0.254591\pi$
$101$	−276.823	−	479.472i	−0.272722	−	0.472369i	−0.969558	+	0.244862i	$0.921257\pi$
$102$	520.882	+	902.194i	0.505637	+	0.875790i
$103$	766.610	−	1327.81i	0.733363	−	1.27022i	−0.222075	−	0.975030i	$-0.571283\pi$
$103$	766.610	−	1327.81i	0.733363	−	1.27022i	0.955438	−	0.295192i	$-0.0953837\pi$
$104$	−403.021			−0.379995
$105$	−22.7133	−	179.055i	−0.0211104	−	0.166418i
$106$	−1655.51			−1.51696
$107$	165.019	−	285.821i	0.149093	−	0.258237i	−0.781799	−	0.623530i	$-0.785698\pi$
$107$	165.019	−	285.821i	0.149093	−	0.258237i	0.930893	+	0.365293i	$0.119031\pi$
$108$	71.5818	+	123.983i	0.0637774	+	0.110466i
$109$	733.204	+	1269.95i	0.644296	+	1.11595i	0.984464	+	0.175588i	$0.0561827\pi$
$109$	733.204	+	1269.95i	0.644296	+	1.11595i	−0.340168	+	0.940365i	$0.610484\pi$
$110$	65.1644	−	112.868i	0.0564835	−	0.0978322i
$111$	446.888			0.382132
$112$	−1337.18	−	561.291i	−1.12814	−	0.473545i
$113$	−1082.09			−0.900836			−0.450418	−	0.892818i	$-0.648725\pi$
$113$	−1082.09			−0.900836			−0.450418	+	0.892818i	$0.648725\pi$
$114$	−448.622	+	777.037i	−0.368573	+	0.638387i
$115$	−91.4961	−	158.476i	−0.0741918	−	0.128504i
$116$	−31.8242	−	55.1211i	−0.0254724	−	0.0441195i
$117$	−184.328	+	319.265i	−0.145651	+	0.252274i
$118$	−1372.05			−1.07040
$119$	−1403.99	+	1066.82i	−1.08154	+	0.821811i
$120$	−95.8857			−0.0729427
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$	434.717	+	752.951i	0.322602	+	0.558762i
$123$	−45.7508	−	79.2427i	−0.0335383	−	0.0580900i
$124$	−538.730	+	933.107i	−0.390156	+	0.675770i
$125$	777.845			0.556581
$126$	−484.046	+	367.803i	−0.342240	+	0.260052i
$127$	−1047.31			−0.731760			−0.365880	−	0.930662i	$-0.619232\pi$
$127$	−1047.31			−0.731760			−0.365880	+	0.930662i	$0.619232\pi$
$128$	−593.893	+	1028.65i	−0.410103	+	0.710320i
$129$	403.581	+	699.023i	0.275452	+	0.477098i
$130$	242.659	+	420.297i	0.163712	+	0.283558i
$131$	1278.45	−	2214.35i	0.852664	−	1.47686i	−0.0261305	−	0.999659i	$-0.508319\pi$
$131$	1278.45	−	2214.35i	0.852664	−	1.47686i	0.878795	−	0.477200i	$-0.158348\pi$
$132$	−174.978			−0.115378
$133$	−1400.34	−	587.801i	−0.912967	−	0.383224i
$134$	1267.50			0.817129
$135$	−43.8548	+	75.9587i	−0.0279587	+	0.0484258i
$136$	468.385	+	811.267i	0.295321	+	0.511511i
$137$	−348.765	−	604.079i	−0.217497	−	0.376715i	0.736545	−	0.676388i	$-0.236456\pi$
$137$	−348.765	−	604.079i	−0.217497	−	0.376715i	−0.954042	+	0.299673i	$0.903122\pi$
$138$	−308.180	+	533.784i	−0.190102	+	0.329266i
$139$	99.4507			0.0606856			0.0303428	−	0.999540i	$-0.490340\pi$
$139$	99.4507			0.0606856			0.0303428	+	0.999540i	$0.490340\pi$
$140$	40.1447	+	316.470i	0.0242346	+	0.191047i
$141$	−569.679			−0.340253
$142$	1402.56	−	2429.30i	0.828874	−	1.43565i
$143$	−225.290	−	390.213i	−0.131746	−	0.228190i
$144$	352.367	+	610.318i	0.203916	+	0.353193i
$145$	19.4972	−	33.7701i	0.0111666	−	0.0193411i
$146$	2191.35			1.24217
$147$	−720.709	−	734.452i	−0.404375	−	0.412086i
$148$	−789.852			−0.438686
$149$	1624.22	−	2813.24i	0.893030	−	1.54677i	0.0568062	−	0.998385i	$-0.481908\pi$
$149$	1624.22	−	2813.24i	0.893030	−	1.54677i	0.836224	−	0.548388i	$-0.184758\pi$
$150$	−626.125	−	1084.48i	−0.340819	−	0.590316i
$151$	1236.10	+	2140.98i	0.666173	+	1.15385i	0.978966	+	0.204024i	$0.0654022\pi$
$151$	1236.10	+	2140.98i	0.666173	+	1.15385i	−0.312793	+	0.949821i	$0.601264\pi$
$152$	−403.408	+	698.723i	−0.215268	+	0.372855i
$153$	856.893			0.452782
$154$	−93.5047	−	737.119i	−0.0489274	−	0.385706i
$155$	−660.109			−0.342072
$156$	325.790	−	564.286i	0.167206	−	0.289609i
$157$	308.665	+	534.623i	0.156905	+	0.271768i	0.933751	−	0.357923i	$-0.116515\pi$
$157$	308.665	+	534.623i	0.156905	+	0.271768i	−0.776846	+	0.629691i	$0.783182\pi$
$158$	2247.32	+	3892.48i	1.13157	+	1.95993i
$159$	−680.863	+	1179.29i	−0.339597	+	0.588200i
$160$	672.055			0.332066
$161$	−961.959	−	403.789i	−0.470888	−	0.197658i
$162$	295.426			0.143277
$163$	−1337.14	+	2316.00i	−0.642535	+	1.11290i	0.342330	+	0.939580i	$0.388784\pi$
$163$	−1337.14	+	2316.00i	−0.642535	+	1.11290i	−0.984865	+	0.173324i	$0.944549\pi$
$164$	80.8623	+	140.058i	0.0385018	+	0.0666870i
$165$	−53.6003	−	92.8385i	−0.0252896	−	0.0438028i
$166$	641.777	−	1111.59i	0.300070	−	0.519736i
$167$	2747.54			1.27312			0.636560	−	0.771227i	$-0.280357\pi$
$167$	2747.54			1.27312			0.636560	+	0.771227i	$0.280357\pi$
$168$	−435.261	+	330.734i	−0.199888	+	0.151885i
$169$	−519.137			−0.236293
$170$	564.029	−	976.927i	0.254465	−	0.440746i
$171$	369.010	+	639.144i	0.165023	+	0.285828i
$172$	−713.310	−	1235.49i	−0.316218	−	0.547705i
$173$	253.067	−	438.324i	0.111216	−	0.192631i	−0.805045	−	0.593214i	$-0.797859\pi$
$173$	253.067	−	438.324i	0.111216	−	0.192631i	0.916261	+	0.400583i	$0.131192\pi$
$174$	−131.342			−0.0572242
$175$	1687.66	−	1282.37i	0.729001	−	0.553932i
$176$	−861.343			−0.368899
$177$	−564.283	+	977.368i	−0.239628	+	0.415048i
$178$	1381.37	+	2392.60i	0.581673	+	1.00749i
$179$	−303.730	−	526.075i	−0.126826	−	0.219669i	0.795619	−	0.605797i	$-0.207146\pi$
$179$	−303.730	−	526.075i	−0.126826	−	0.219669i	−0.922445	+	0.386128i	$0.873812\pi$
$180$	77.5112	−	134.253i	0.0320964	−	0.0555925i
$181$	2546.22			1.04563			0.522815	−	0.852446i	$-0.324882\pi$
$181$	2546.22			1.04563			0.522815	+	0.852446i	$0.324882\pi$
$182$	2551.23	+	1070.90i	1.03907	+	0.436155i
$183$	715.144			0.288879
$184$	−277.120	+	479.986i	−0.111030	+	0.192310i
$185$	−241.953	−	419.074i	−0.0961552	−	0.166546i
$186$	1111.70	+	1925.52i	0.438246	+	0.759065i
$187$	−523.657	+	907.000i	−0.204778	+	0.354687i
$188$	1006.88			0.390608
$189$	62.9275	+	496.072i	0.0242185	+	0.190920i
$190$	971.568			0.370973
$191$	−1189.08	+	2059.55i	−0.450465	+	0.780229i	−0.998415	−	0.0562824i	$-0.982075\pi$
$191$	−1189.08	+	2059.55i	−0.450465	+	0.780229i	0.547949	+	0.836511i	$0.315409\pi$
$192$	−192.172	−	332.852i	−0.0722334	−	0.125112i
$193$	−1207.72	−	2091.84i	−0.450434	−	0.780175i	0.547979	−	0.836492i	$-0.315397\pi$
$193$	−1207.72	−	2091.84i	−0.450434	−	0.780175i	−0.998413	+	0.0563175i	$0.982064\pi$
$194$	1492.05	−	2584.30i	0.552179	−	0.956402i
$195$	399.193			0.146599
$196$	1273.82	+	1298.11i	0.464219	+	0.473072i
$197$	−3381.10			−1.22281			−0.611404	−	0.791318i	$-0.709395\pi$
$197$	−3381.10			−1.22281			−0.611404	+	0.791318i	$0.709395\pi$
$198$	−180.538	+	312.702i	−0.0647995	+	0.112236i
$199$	2393.84	+	4146.25i	0.852738	+	1.47699i	0.878728	+	0.477323i	$0.158393\pi$
$199$	2393.84	+	4146.25i	0.852738	+	1.47699i	−0.0259903	+	0.999662i	$0.508274\pi$
$200$	−563.021	−	975.181i	−0.199058	−	0.344778i
$201$	521.284	−	902.891i	0.182928	−	0.316841i
$202$	2019.28			0.703348
$203$	−27.9766	−	220.546i	−0.00967276	−	0.0762526i
$204$	−1514.52			−0.519791
$205$	−49.5406	+	85.8068i	−0.0168784	+	0.0292342i
$206$	2796.01	+	4842.83i	0.945667	+	1.63794i
$207$	253.490	+	439.058i	0.0851150	+	0.147424i
$208$	1603.73	−	2777.74i	0.534609	−	0.925971i
$209$	−902.024			−0.298537
$210$	606.982	+	254.785i	0.199456	+	0.0837230i
$211$	2580.29			0.841870			0.420935	−	0.907091i	$-0.361702\pi$
$211$	2580.29			0.841870			0.420935	+	0.907091i	$0.361702\pi$
$212$	1203.39	−	2084.34i	0.389856	−	0.675250i
$213$	−1153.66	−	1998.20i	−0.371115	−	0.642790i
$214$	601.863	+	1042.46i	0.192255	+	0.332995i
$215$	437.012	−	756.927i	0.138623	−	0.240102i
$216$	265.652			0.0836820
$217$	−2996.48	+	2276.88i	−0.937394	+	0.712281i
$218$	−5348.34			−1.66163
$219$	901.235	−	1560.98i	0.278081	−	0.481651i
$220$	94.7360	+	164.087i	0.0290323	+	0.0502853i
$221$	−1949.99	−	3377.48i	−0.593532	−	1.02803i
$222$	−814.953	+	1411.54i	−0.246379	+	0.426740i
$223$	−3554.80			−1.06747			−0.533737	−	0.845650i	$-0.679213\pi$
$223$	−3554.80			−1.06747			−0.533737	+	0.845650i	$0.679213\pi$
$224$	3050.71	−	2318.09i	0.909974	−	0.691445i
$225$	−1030.03			−0.305193
$226$	1973.32	−	3417.89i	0.580811	−	1.00599i
$227$	2437.58	+	4222.02i	0.712723	+	1.23447i	0.963831	+	0.266513i	$0.0858717\pi$
$227$	2437.58	+	4222.02i	0.712723	+	1.23447i	−0.251108	+	0.967959i	$0.580795\pi$
$228$	−652.207	−	1129.66i	−0.189445	−	0.328128i
$229$	−3151.69	+	5458.89i	−0.909475	+	1.57526i	−0.0946791	+	0.995508i	$0.530182\pi$
$229$	−3151.69	+	5458.89i	−0.909475	+	1.57526i	−0.814796	+	0.579748i	$0.803151\pi$
$230$	667.416			0.191340
$231$	−563.535	−	236.548i	−0.160510	−	0.0673753i
$232$	−118.105			−0.0334222
$233$	−1952.53	+	3381.88i	−0.548989	+	0.950877i	0.449355	+	0.893353i	$0.351654\pi$
$233$	−1952.53	+	3381.88i	−0.548989	+	0.950877i	−0.998344	+	0.0575238i	$0.981679\pi$
$234$	−672.288	−	1164.44i	−0.187815	−	0.325306i
$235$	308.434	+	534.223i	0.0856171	+	0.148293i
$236$	997.344	−	1727.45i	0.275091	−	0.476472i
$237$	3697.03			1.01328
$238$	−809.328	−	6380.12i	−0.220424	−	1.73765i
$239$	−3569.46			−0.966063			−0.483032	−	0.875603i	$-0.660464\pi$
$239$	−3569.46			−0.966063			−0.483032	+	0.875603i	$0.660464\pi$
$240$	381.556	−	660.874i	0.102622	−	0.177747i
$241$	−2226.61	−	3856.60i	−0.595139	−	1.03081i	−0.993527	−	0.113594i	$-0.963764\pi$
$241$	−2226.61	−	3856.60i	−0.595139	−	1.03081i	0.398388	−	0.917217i	$-0.369570\pi$
$242$	−220.658	−	382.191i	−0.0586134	−	0.101521i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−1263.98			−0.331632
$245$	−298.537	+	1073.50i	−0.0778483	+	0.279932i
$246$	333.728			0.0864949
$247$	1679.48	−	2908.94i	0.432642	−	0.749357i
$248$	999.658	+	1731.46i	0.255961	+	0.443337i
$249$	−527.887	−	914.327i	−0.134351	−	0.232703i
$250$	−1418.49	+	2456.90i	−0.358854	+	0.621553i
$251$	5783.13			1.45429			0.727147	−	0.686482i	$-0.240846\pi$
$251$	5783.13			1.45429			0.727147	+	0.686482i	$0.240846\pi$
$252$	−111.221	−	876.783i	−0.0278027	−	0.219175i
$253$	−619.643			−0.153979
$254$	1909.89	−	3308.03i	0.471800	−	0.817181i
$255$	−463.936	−	803.562i	−0.113933	−	0.197337i
$256$	−2678.53	−	4639.35i	−0.653937	−	1.13265i
$257$	−1296.56	+	2245.71i	−0.314698	+	0.545072i	−0.979373	−	0.202060i	$-0.935236\pi$
$257$	−1296.56	+	2245.71i	−0.314698	+	0.545072i	0.664676	+	0.747132i	$0.268570\pi$
$258$	−2943.92			−0.710388
$259$	−2543.81	−	1067.78i	−0.610288	−	0.256172i
$260$	−705.554			−0.168295
$261$	−54.0170	+	93.5602i	−0.0128106	+	0.0221886i
$262$	4662.83	+	8076.25i	1.09951	+	1.90440i
$263$	−4143.48	−	7176.71i	−0.971474	−	1.68264i	−0.691110	−	0.722749i	$-0.742878\pi$
$263$	−4143.48	−	7176.71i	−0.971474	−	1.68264i	−0.280364	−	0.959894i	$-0.590455\pi$
$264$	−162.343	+	281.186i	−0.0378466	+	0.0655523i
$265$	1474.52			0.341809
$266$	4410.31	−	3351.18i	1.01659	−	0.772459i
$267$	2272.46			0.520870
$268$	−921.345	+	1595.82i	−0.210000	+	0.363731i
$269$	−945.714	−	1638.02i	−0.214354	−	0.371272i	0.738719	−	0.674014i	$-0.235431\pi$
$269$	−945.714	−	1638.02i	−0.214354	−	0.371272i	−0.953073	+	0.302742i	$0.902098\pi$
$270$	−159.949	−	277.040i	−0.0360525	−	0.0624448i
$271$	734.668	−	1272.48i	0.164679	−	0.285232i	−0.771862	−	0.635790i	$-0.780675\pi$
$271$	734.668	−	1272.48i	0.164679	−	0.285232i	0.936541	+	0.350558i	$0.114008\pi$
$272$	−7455.33			−1.66193
$273$	1812.09	−	1376.92i	0.401731	−	0.305256i
$274$	2544.06			0.560921
$275$	629.460	−	1090.26i	0.138029	−	0.239072i
$276$	−448.032	−	776.014i	−0.0977115	−	0.169241i
$277$	3214.90	+	5568.37i	0.697346	+	1.20784i	0.969384	+	0.245551i	$0.0789690\pi$
$277$	3214.90	+	5568.37i	0.697346	+	1.20784i	−0.272038	+	0.962286i	$0.587698\pi$
$278$	−181.360	+	314.125i	−0.0391269	+	0.0677697i
$279$	1828.84			0.392436
$280$	545.808	+	229.106i	0.116494	+	0.0488990i
$281$	−210.954			−0.0447846			−0.0223923	−	0.999749i	$-0.507128\pi$
$281$	−210.954			−0.0447846			−0.0223923	+	0.999749i	$0.507128\pi$
$282$	1038.88	−	1799.39i	0.219377	−	0.379972i
$283$	−463.018	−	801.971i	−0.0972564	−	0.168453i	0.813292	−	0.581856i	$-0.197673\pi$
$283$	−463.018	−	801.971i	−0.0972564	−	0.168453i	−0.910548	+	0.413403i	$0.864340\pi$
$284$	2039.04	+	3531.72i	0.426038	+	0.737919i
$285$	399.577	−	692.087i	0.0830487	−	0.143845i
$286$	1643.37			0.339771
$287$	71.0860	+	560.387i	0.0146205	+	0.115256i
$288$	−1861.93			−0.380956
$289$	−2076.00	+	3595.74i	−0.422552	+	0.731882i
$290$	71.1108	+	123.168i	0.0143992	+	0.0249402i
$291$	−1227.27	−	2125.69i	−0.247229	−	0.428214i
$292$	−1592.89	+	2758.97i	−0.319236	+	0.552932i
$293$	−1290.46			−0.257303			−0.128651	−	0.991690i	$-0.541065\pi$
$293$	−1290.46			−0.257303			−0.128651	+	0.991690i	$0.541065\pi$
$294$	3634.14	−	937.071i	0.720909	−	0.185888i
$295$	1222.05			0.241188
$296$	−732.818	+	1269.28i	−0.143899	+	0.249241i
$297$	148.500	+	257.210i	0.0290129	+	0.0502519i
$298$	5923.93	+	10260.5i	1.15156	+	1.99455i
$299$	1153.71	−	1998.29i	0.223147	−	0.386502i
$300$	1820.52			0.350359
$301$	−627.070	−	4943.34i	−0.120079	−	0.946609i
$302$	−9016.68			−1.71805
$303$	830.470	−	1438.42i	0.157456	−	0.272722i
$304$	−3210.54	−	5560.83i	−0.605715	−	1.04913i
$305$	−387.191	−	670.635i	−0.0726902	−	0.125903i
$306$	−1562.65	+	2706.58i	−0.291930	+	0.505637i
$307$	−3882.39			−0.721757			−0.360879	−	0.932613i	$-0.617523\pi$
$307$	−3882.39			−0.721757			−0.360879	+	0.932613i	$0.617523\pi$
$308$	996.022	+	418.087i	0.184265	+	0.0773464i
$309$	4599.66			0.846814
$310$	1203.79	−	2085.02i	0.220550	−	0.382004i
$311$	3274.24	+	5671.15i	0.596994	+	1.03402i	0.993262	+	0.115889i	$0.0369716\pi$
$311$	3274.24	+	5671.15i	0.596994	+	1.03402i	−0.396269	+	0.918135i	$0.629695\pi$
$312$	−604.531	−	1047.08i	−0.109695	−	0.189997i
$313$	−191.406	+	331.525i	−0.0345652	+	0.0598687i	−0.882791	−	0.469767i	$-0.844338\pi$
$313$	−191.406	+	331.525i	−0.0345652	+	0.0598687i	0.848225	+	0.529636i	$0.177671\pi$
$314$	−2251.55			−0.404657
$315$	431.127	−	327.593i	0.0771151	−	0.0585961i
$316$	−6534.32			−1.16324
$317$	−4329.97	+	7499.73i	−0.767178	+	1.32879i	0.171909	+	0.985113i	$0.445007\pi$
$317$	−4329.97	+	7499.73i	−0.767178	+	1.32879i	−0.939087	+	0.343679i	$0.888327\pi$
$318$	−2483.27	−	4301.15i	−0.437909	−	0.758480i
$319$	−66.0208	−	114.351i	−0.0115876	−	0.0200704i
$320$	−208.090	+	360.423i	−0.0363519	+	0.0629633i
$321$	990.112			0.172158
$322$	3029.65	−	2302.09i	0.524336	−	0.398417i
$323$	−7807.45			−1.34495
$324$	−214.745	+	371.950i	−0.0368219	+	0.0637774i
$325$	2343.98	+	4059.89i	0.400063	+	0.692930i
$326$	−4876.88	−	8447.01i	−0.828545	−	1.43508i
$327$	−2199.61	+	3809.84i	−0.371984	+	0.644296i
$328$	300.094			0.0505180
$329$	3242.77	+	1361.17i	0.543403	+	0.228097i
$330$	390.986			0.0652215
$331$	5298.30	−	9176.92i	0.879821	−	1.52390i	0.0282850	−	0.999600i	$-0.490995\pi$
$331$	5298.30	−	9176.92i	0.879821	−	1.52390i	0.851536	−	0.524295i	$-0.175671\pi$
$332$	933.015	+	1616.03i	0.154234	+	0.267142i
$333$	670.332	+	1161.05i	0.110312	+	0.191066i
$334$	−5010.47	+	8678.38i	−0.820840	+	1.42174i
$335$	−1128.93			−0.184119
$336$	−547.496	−	4316.04i	−0.0888939	−	0.700771i
$337$	−3561.41			−0.575675			−0.287838	−	0.957679i	$-0.592936\pi$
$337$	−3561.41			−0.575675			−0.287838	+	0.957679i	$0.592936\pi$
$338$	946.708	−	1639.75i	0.152349	−	0.263877i
$339$	−1623.13	−	2811.35i	−0.260049	−	0.450418i
$340$	819.985	+	1420.26i	0.130794	+	0.226542i
$341$	−1117.62	+	1935.78i	−0.177486	+	0.307414i
$342$	−2691.73			−0.425592
$343$	2347.60	+	5902.75i	0.369558	+	0.929208i
$344$	−2647.21			−0.414907
$345$	274.488	−	475.428i	0.0428346	−	0.0741918i
$346$	922.995	+	1598.67i	0.143412	+	0.248397i
$347$	97.6127	+	169.070i	0.0151012	+	0.0261561i	0.873477	−	0.486865i	$-0.161860\pi$
$347$	97.6127	+	169.070i	0.0151012	+	0.0261561i	−0.858376	+	0.513021i	$0.828526\pi$
$348$	95.4725	−	165.363i	0.0147065	−	0.0254724i
$349$	−614.409			−0.0942366			−0.0471183	−	0.998889i	$-0.515004\pi$
$349$	−614.409			−0.0942366			−0.0471183	+	0.998889i	$0.515004\pi$
$350$	972.850	+	7669.20i	0.148574	+	1.17125i
$351$	−1105.97			−0.168183
$352$	1137.85	−	1970.81i	0.172294	−	0.298422i
$353$	772.956	+	1338.80i	0.116545	+	0.201861i	0.918396	−	0.395662i	$-0.129485\pi$
$353$	772.956	+	1338.80i	0.116545	+	0.201861i	−0.801851	+	0.597523i	$0.796151\pi$
$354$	−2058.08	−	3564.69i	−0.308999	−	0.535201i
$355$	−1249.22	+	2163.72i	−0.186766	+	0.323488i
$356$	−4016.46			−0.597955
$357$	−4877.67	−	2047.43i	−0.723120	−	0.303534i
$358$	2215.55			0.327082
$359$	−1362.00	+	2359.06i	−0.200233	+	0.346814i	−0.948603	−	0.316467i	$-0.897503\pi$
$359$	−1362.00	+	2359.06i	−0.200233	+	0.346814i	0.748370	+	0.663281i	$0.230837\pi$
$360$	−143.829	−	249.118i	−0.0210567	−	0.0364714i
$361$	67.3215	+	116.604i	0.00981507	+	0.0170002i
$362$	−4643.34	+	8042.50i	−0.674167	+	1.16769i
$363$	−363.000			−0.0524864
$364$	−3202.78	+	2433.64i	−0.461184	+	0.350432i
$365$	−1951.78			−0.279892
$366$	−1304.15	+	2258.85i	−0.186254	+	0.322602i
$367$	4779.56	+	8278.44i	0.679812	+	1.17747i	0.975037	+	0.222042i	$0.0712721\pi$
$367$	4779.56	+	8278.44i	0.679812	+	1.17747i	−0.295225	+	0.955428i	$0.595395\pi$
$368$	−2205.48	−	3820.00i	−0.312414	−	0.541117i
$369$	137.252	−	237.728i	0.0193633	−	0.0335383i
$370$	1764.92			0.247983
$371$	6693.42	−	5086.01i	0.936672	−	0.711732i
$372$	−3232.38			−0.450514
$373$	−3634.77	+	6295.61i	−0.504561	+	0.873926i	0.495425	+	0.868651i	$0.335012\pi$
$373$	−3634.77	+	6295.61i	−0.504561	+	0.873926i	−0.999986	+	0.00527489i	$0.998321\pi$
$374$	−1909.90	−	3308.05i	−0.264061	−	0.457366i
$375$	1166.77	+	2020.90i	0.160671	+	0.278290i
$376$	934.174	−	1618.04i	0.128129	−	0.221925i
$377$	491.696			0.0671714
$378$	−1681.65	−	705.883i	−0.228822	−	0.0960495i
$379$	12989.3			1.76047			0.880234	−	0.474540i	$-0.157385\pi$
$379$	12989.3			1.76047			0.880234	+	0.474540i	$0.157385\pi$
$380$	−706.232	+	1223.23i	−0.0953393	+	0.165133i
$381$	−1570.96	−	2720.98i	−0.211241	−	0.365880i
$382$	−4336.86	−	7511.67i	−0.580872	−	1.00610i
$383$	1154.46	−	1999.59i	0.154021	−	0.266773i	−0.778681	−	0.627420i	$-0.784111\pi$
$383$	1154.46	−	1999.59i	0.154021	−	0.266773i	0.932702	+	0.360647i	$0.117444\pi$
$384$	−3563.36			−0.473546
$385$	83.2823	+	656.533i	0.0110246	+	0.0869092i
$386$	8809.71			1.16166
$387$	−1210.74	+	2097.07i	−0.159033	+	0.275452i
$388$	2169.14	+	3757.05i	0.283817	+	0.491586i
$389$	2635.09	+	4564.11i	0.343456	+	0.594883i	0.985072	−	0.172143i	$-0.0550690\pi$
$389$	2635.09	+	4564.11i	0.343456	+	0.594883i	−0.641616	+	0.767026i	$0.721736\pi$
$390$	−727.976	+	1260.89i	−0.0945192	+	0.163712i
$391$	−5363.31			−0.693694
$392$	3267.87	−	842.629i	0.421052	−	0.108569i
$393$	7670.72			0.984572
$394$	6165.84	−	10679.5i	0.788402	−	1.36555i
$395$	−2001.63	−	3466.93i	−0.254970	−	0.441621i
$396$	−262.467	−	454.605i	−0.0333067	−	0.0576888i
$397$	−6373.42	+	11039.1i	−0.805724	+	1.39556i	0.110077	+	0.993923i	$0.464890\pi$
$397$	−6373.42	+	11039.1i	−0.805724	+	1.39556i	−0.915801	+	0.401632i	$0.868443\pi$
$398$	−17461.8			−2.19920
$399$	−573.354	−	4519.88i	−0.0719389	−	0.567111i
$400$	8961.66			1.12021
$401$	3001.53	−	5198.81i	0.373789	−	0.647421i	−0.616356	−	0.787468i	$-0.711392\pi$
$401$	3001.53	−	5198.81i	0.373789	−	0.647421i	0.990145	+	0.140046i	$0.0447251\pi$
$402$	1901.25	+	3293.06i	0.235885	+	0.408564i
$403$	−4161.79	−	7208.44i	−0.514426	−	0.891012i
$404$	−1467.82	+	2542.33i	−0.180759	+	0.313084i
$405$	−263.129			−0.0322839
$406$	747.635	+	313.825i	0.0913904	+	0.0383617i
$407$	−1638.59			−0.199562
$408$	−1405.16	+	2433.80i	−0.170504	+	0.295321i
$409$	4110.19	+	7119.05i	0.496909	+	0.860671i	0.999994	−	0.00356568i	$-0.00113499\pi$
$409$	4110.19	+	7119.05i	0.496909	+	0.860671i	−0.503085	+	0.864237i	$0.667802\pi$
$410$	−180.686	−	312.958i	−0.0217645	−	0.0376973i
$411$	1046.30	−	1812.24i	0.125572	−	0.217497i
$412$	−8129.68			−0.972137
$413$	5547.35	−	4215.16i	0.660938	−	0.502215i
$414$	−1849.08			−0.219511
$415$	−571.614	+	990.065i	−0.0676131	+	0.117109i
$416$	4237.11	+	7338.89i	0.499378	+	0.864948i
$417$	149.176	+	258.381i	0.0175184	+	0.0303428i
$418$	1644.95	−	2849.13i	0.192481	−	0.333387i
$419$	−2847.79			−0.332037			−0.166019	−	0.986123i	$-0.553091\pi$
$419$	−2847.79			−0.332037			−0.166019	+	0.986123i	$0.553091\pi$
$420$	−761.997	+	579.004i	−0.0885277	+	0.0672679i
$421$	−1481.78			−0.171538			−0.0857688	−	0.996315i	$-0.527335\pi$
$421$	−1481.78			−0.171538			−0.0857688	+	0.996315i	$0.527335\pi$
$422$	−4705.47	+	8150.12i	−0.542793	+	0.940146i
$423$	−854.518	−	1480.07i	−0.0982225	−	0.170126i
$424$	−2233.00	−	3867.66i	−0.255764	−	0.442996i
$425$	5448.28	−	9436.69i	0.621836	−	1.07705i
$426$	8415.35			0.957101
$427$	−4070.80	−	1708.74i	−0.461357	−	0.193658i
$428$	−1749.98			−0.197636
$429$	675.869	−	1170.64i	0.0760635	−	0.131746i
$430$	1593.89	+	2760.69i	0.178754	+	0.309610i
$431$	−489.376	−	847.624i	−0.0546924	−	0.0947299i	0.837383	−	0.546617i	$-0.184084\pi$
$431$	−489.376	−	847.624i	−0.0546924	−	0.0947299i	−0.892075	+	0.451887i	$0.850751\pi$
$432$	−1057.10	+	1830.95i	−0.117731	+	0.203916i
$433$	15417.0			1.71108			0.855538	−	0.517740i	$-0.173226\pi$
$433$	15417.0			1.71108			0.855538	+	0.517740i	$0.173226\pi$
$434$	−1727.32	−	13616.9i	−0.191046	−	1.50606i
$435$	116.983			0.0128940
$436$	3887.71	−	6733.71i	0.427035	−	0.739647i
$437$	−2309.64	−	4000.42i	−0.252826	−	0.437908i
$438$	3287.02	+	5693.29i	0.358584	+	0.621086i
$439$	2859.61	−	4952.99i	0.310893	−	0.538482i	−0.667663	−	0.744463i	$-0.732705\pi$
$439$	2859.61	−	4952.99i	0.310893	−	0.538482i	0.978556	+	0.205982i	$0.0660387\pi$
$440$	351.581			0.0380931
$441$	827.099	−	2974.13i	0.0893099	−	0.321146i
$442$	14224.2			1.53071
$443$	4677.64	−	8101.92i	0.501674	−	0.868925i	−0.498324	−	0.866991i	$-0.666051\pi$
$443$	4677.64	−	8101.92i	0.501674	−	0.868925i	0.999998	−	0.00193389i	$-0.000615577\pi$
$444$	−1184.78	−	2052.10i	−0.126638	−	0.219343i
$445$	−1230.35	−	2131.03i	−0.131065	−	0.227012i
$446$	6482.60	−	11228.2i	0.688251	−	1.19209i
$447$	9745.33			1.03118
$448$	298.590	+	2353.85i	0.0314889	+	0.248235i
$449$	8588.44			0.902703			0.451351	−	0.892346i	$-0.350942\pi$
$449$	8588.44			0.902703			0.451351	+	0.892346i	$0.350942\pi$
$450$	1878.37	−	3253.44i	0.196772	−	0.340819i
$451$	167.753	+	290.557i	0.0175148	+	0.0303365i
$452$	2868.81	+	4968.93i	0.298534	+	0.517077i
$453$	−3708.29	+	6422.95i	−0.384615	+	0.666173i
$454$	−17780.9			−1.83810
$455$	−2272.32	−	953.820i	−0.234127	−	0.0982764i
$456$	−2420.45			−0.248570
$457$	−6552.95	+	11350.0i	−0.670753	+	1.16178i	0.306938	+	0.951729i	$0.400695\pi$
$457$	−6552.95	+	11350.0i	−0.670753	+	1.16178i	−0.977691	+	0.210048i	$0.932638\pi$
$458$	−11495.0	−	19909.9i	−1.17276	−	2.03128i
$459$	1285.34	+	2226.27i	0.130707	+	0.226391i
$460$	−485.145	+	840.295i	−0.0491739	+	0.0851717i
$461$	3602.92			0.364002			0.182001	−	0.983298i	$-0.441743\pi$
$461$	3602.92			0.364002			0.182001	+	0.983298i	$0.441743\pi$
$462$	1774.83	−	1348.61i	0.178729	−	0.135807i
$463$	−12636.3			−1.26838			−0.634190	−	0.773177i	$-0.718667\pi$
$463$	−12636.3			−1.26838			−0.634190	+	0.773177i	$0.718667\pi$
$464$	469.971	−	814.014i	0.0470213	−	0.0814433i
$465$	−990.163	−	1715.01i	−0.0987478	−	0.171036i
$466$	−7121.34	−	12334.5i	−0.707918	−	1.22615i
$467$	7013.66	−	12148.0i	0.694976	−	1.20373i	−0.275213	−	0.961383i	$-0.588748\pi$
$467$	7013.66	−	12148.0i	0.694976	−	1.20373i	0.970189	−	0.242350i	$-0.0779182\pi$
$468$	1954.74			0.193073
$469$	−5124.64	+	3893.96i	−0.504549	+	0.383383i
$470$	−2249.87			−0.220805
$471$	−925.994	+	1603.87i	−0.0905893	+	0.156905i
$472$	−1850.65	−	3205.43i	−0.180473	−	0.312588i
$473$	−1479.80	−	2563.09i	−0.143850	−	0.249156i
$474$	−6741.97	+	11677.4i	−0.653310	+	1.13157i
$475$	9384.92			0.906547
$476$	8621.05	+	3618.74i	0.830137	+	0.348455i
$477$	−4085.18			−0.392133
$478$	6509.33	−	11274.5i	0.622866	−	1.07884i
$479$	5141.84	+	8905.93i	0.490473	+	0.849524i	0.999940	−	0.0109659i	$-0.00349063\pi$
$479$	5141.84	+	8905.93i	0.490473	+	0.849524i	−0.509467	+	0.860490i	$0.670157\pi$
$480$	1008.08	+	1746.05i	0.0958592	+	0.166033i
$481$	3050.88	−	5284.28i	0.289206	−	0.500920i
$482$	16241.9			1.53486
$483$	−393.865	−	3104.92i	−0.0371045	−	0.292503i
$484$	641.585			0.0602540
$485$	−1328.93	+	2301.77i	−0.124420	+	0.215501i
$486$	443.140	+	767.540i	0.0413605	+	0.0716385i
$487$	−2801.03	−	4851.53i	−0.260630	−	0.451425i	0.705779	−	0.708432i	$-0.250597\pi$
$487$	−2801.03	−	4851.53i	−0.260630	−	0.451425i	−0.966410	+	0.257007i	$0.917264\pi$
$488$	−1172.71	+	2031.20i	−0.108783	+	0.188418i
$489$	−8022.87			−0.741936
$490$	−2846.34	−	2900.61i	−0.262417	−	0.267421i
$491$	17867.1			1.64222			0.821109	−	0.570772i	$-0.193356\pi$
$491$	17867.1			1.64222			0.821109	+	0.570772i	$0.193356\pi$
$492$	−242.587	+	420.173i	−0.0222290	+	0.0385018i
$493$	−571.442	−	989.766i	−0.0522038	−	0.0904196i
$494$	6125.45	+	10609.6i	0.557889	+	0.966291i
$495$	160.801	−	278.515i	0.0146009	−	0.0252896i
$496$	−15911.7			−1.44043
$497$	1792.52	+	14130.8i	0.161781	+	1.27536i
$498$	3850.66			0.346490
$499$	2155.31	−	3733.10i	0.193356	−	0.334903i	−0.753004	−	0.658016i	$-0.771396\pi$
$499$	2155.31	−	3733.10i	0.193356	−	0.334903i	0.946360	+	0.323113i	$0.104729\pi$
$500$	−2062.21	−	3571.84i	−0.184449	−	0.319476i
$501$	4121.31	+	7138.32i	0.367518	+	0.636560i
$502$	−10546.2	+	18266.6i	−0.937652	+	1.62406i
$503$	21922.9			1.94333			0.971664	−	0.236368i	$-0.0759570\pi$
$503$	21922.9			1.94333			0.971664	+	0.236368i	$0.0759570\pi$
$504$	−1512.16	−	634.741i	−0.133645	−	0.0560984i
$505$	−1798.52			−0.158482
$506$	1129.99	−	1957.21i	0.0992774	−	0.171953i
$507$	−778.705	−	1348.76i	−0.0682120	−	0.118147i
$508$	2776.60	+	4809.21i	0.242503	+	0.420028i
$509$	207.297	−	359.050i	0.0180517	−	0.0312664i	−0.856858	−	0.515552i	$-0.827587\pi$
$509$	207.297	−	359.050i	0.0180517	−	0.0312664i	0.874910	+	0.484285i	$0.160920\pi$
$510$	3384.17			0.293831
$511$	−8859.85	+	6732.17i	−0.767000	+	0.582806i
$512$	10036.2			0.866290
$513$	−1107.03	+	1917.43i	−0.0952759	+	0.165023i
$514$	−4728.87	−	8190.64i	−0.405801	−	0.702867i
$515$	−2490.34	−	4313.39i	−0.213082	−	0.369069i
$516$	2139.93	−	3706.47i	0.182568	−	0.316218i
$517$	2088.82			0.177691
$518$	8011.63	−	6087.65i	0.679558	−	0.516363i
$519$	1518.40			0.128421
$520$	−654.607	+	1133.81i	−0.0552047	+	0.0956173i
$521$	6318.50	+	10944.0i	0.531322	+	0.920276i	0.999332	+	0.0365530i	$0.0116378\pi$
$521$	6318.50	+	10944.0i	0.531322	+	0.920276i	−0.468010	+	0.883723i	$0.655029\pi$
$522$	−197.013	−	341.237i	−0.0165192	−	0.0286121i
$523$	−4311.01	+	7466.89i	−0.360435	+	0.624291i	−0.988032	−	0.154246i	$-0.950705\pi$
$523$	−4311.01	+	7466.89i	−0.360435	+	0.624291i	0.627598	+	0.778538i	$0.284038\pi$
$524$	−13557.6			−1.13028
$525$	5863.19	+	2461.11i	0.487410	+	0.204594i
$526$	30224.5			2.50542
$527$	−9673.56	+	16755.1i	−0.799595	+	1.38494i
$528$	−1292.01	−	2237.83i	−0.106492	−	0.184449i
$529$	4496.90	+	7788.85i	0.369598	+	0.640162i
$530$	−2688.97	+	4657.44i	−0.220380	+	0.381710i
$531$	−3385.70			−0.276698
$532$	1013.38	+	7988.68i	0.0825854	+	0.651040i
$533$	−1249.35			−0.101530
$534$	−4144.10	+	7177.79i	−0.335829	+	0.581673i
$535$	−536.064	−	928.490i	−0.0433198	−	0.0750320i
$536$	1709.63	+	2961.17i	0.137770	+	0.238625i
$537$	911.189	−	1578.23i	0.0732229	−	0.126826i
$538$	6898.49			0.552816
$539$	2642.60	+	2692.99i	0.211178	+	0.215205i
$540$	465.067			0.0370617
$541$	−3015.28	+	5222.62i	−0.239625	+	0.415042i	−0.960607	−	0.277912i	$-0.910358\pi$
$541$	−3015.28	+	5222.62i	−0.239625	+	0.415042i	0.720982	+	0.692954i	$0.243691\pi$
$542$	2679.51	+	4641.05i	0.212352	+	0.367805i
$543$	3819.33	+	6615.28i	0.301848	+	0.522815i
$544$	9848.61	−	17058.3i	0.776206	−	1.34443i
$545$	4763.63			0.374407
$546$	1044.58	+	8234.64i	0.0818750	+	0.645439i
$547$	−4459.63			−0.348593			−0.174296	−	0.984693i	$-0.555765\pi$
$547$	−4459.63			−0.348593			−0.174296	+	0.984693i	$0.555765\pi$
$548$	−1849.28	+	3203.04i	−0.144156	+	0.249685i
$549$	1072.72	+	1858.00i	0.0833923	+	0.144440i
$550$	2295.79	+	3976.43i	0.177987	+	0.308282i
$551$	492.168	−	852.460i	0.0380528	−	0.0659093i
$552$	−1662.72			−0.128207
$553$	−21044.5	−	8833.57i	−1.61827	−	0.679280i
$554$	−23451.0			−1.79845
$555$	725.858	−	1257.22i	0.0555153	−	0.0961552i
$556$	−263.662	−	456.675i	−0.0201110	−	0.0348334i
$557$	4131.98	+	7156.80i	0.314323	+	0.544423i	0.979293	−	0.202447i	$-0.0648893\pi$
$557$	4131.98	+	7156.80i	0.314323	+	0.544423i	−0.664971	+	0.746869i	$0.731556\pi$
$558$	−3335.10	+	5776.56i	−0.253022	+	0.438246i
$559$	11020.9			0.833874
$560$	−3750.99	+	2850.20i	−0.283051	+	0.215077i
$561$	−3141.94			−0.236458
$562$	384.700	−	666.320i	0.0288747	−	0.0500125i
$563$	−5679.00	−	9836.31i	−0.425118	−	0.736325i	0.571314	−	0.820732i	$-0.306434\pi$
$563$	−5679.00	−	9836.31i	−0.425118	−	0.736325i	−0.996431	+	0.0844065i	$0.973101\pi$
$564$	1510.32	+	2615.95i	0.112759	+	0.195304i
$565$	−1757.59	+	3044.23i	−0.130871	+	0.226676i
$566$	3377.48			0.250823
$567$	−1194.44	+	907.598i	−0.0884688	+	0.0672232i
$568$	7567.21			0.559002
$569$	4938.58	−	8553.88i	0.363860	−	0.630224i	−0.624733	−	0.780839i	$-0.714792\pi$
$569$	4938.58	−	8553.88i	0.363860	−	0.630224i	0.988592	+	0.150615i	$0.0481254\pi$
$570$	1457.35	+	2524.21i	0.107091	+	0.185487i
$571$	−2632.59	−	4559.78i	−0.192943	−	0.334187i	0.753281	−	0.657699i	$-0.228470\pi$
$571$	−2632.59	−	4559.78i	−0.192943	−	0.334187i	−0.946224	+	0.323511i	$0.895137\pi$
$572$	−1194.56	+	2069.05i	−0.0873204	+	0.151243i
$573$	−7134.49			−0.520153
$574$	−1899.67	−	797.401i	−0.138137	−	0.0579841i
$575$	6446.95			0.467576
$576$	576.516	−	998.555i	0.0417040	−	0.0722334i
$577$	9596.53	+	16621.7i	0.692390	+	1.19925i	0.971053	+	0.238865i	$0.0767755\pi$
$577$	9596.53	+	16621.7i	0.692390	+	1.19925i	−0.278663	+	0.960389i	$0.589891\pi$
$578$	−7571.67	−	13114.5i	−0.544879	−	0.943758i
$579$	3623.17	−	6275.51i	0.260058	−	0.450434i
$580$	−206.762			−0.0148023
$581$	820.212	+	6465.92i	0.0585682	+	0.461707i
$582$	8952.28			0.637601
$583$	2496.50	−	4324.06i	0.177349	−	0.307177i
$584$	2955.74	+	5119.49i	0.209434	+	0.362750i
$585$	598.789	+	1037.13i	0.0423195	+	0.0732995i
$586$	2353.31	−	4076.06i	0.165895	−	0.287339i
$587$	21860.1			1.53708			0.768538	−	0.639805i	$-0.220985\pi$
$587$	21860.1			1.53708			0.768538	+	0.639805i	$0.220985\pi$
$588$	−1461.86	+	5256.64i	−0.102527	+	0.368674i
$589$	−16663.2			−1.16569
$590$	−2228.56	+	3859.97i	−0.155505	+	0.269343i
$591$	−5071.65	−	8784.35i	−0.352994	−	0.611404i
$592$	−5832.17	−	10101.6i	−0.404900	−	0.701308i
$593$	−2857.79	+	4949.84i	−0.197901	+	0.342775i	−0.947848	−	0.318723i	$-0.896746\pi$
$593$	−2857.79	+	4949.84i	−0.197901	+	0.342775i	0.749946	+	0.661499i	$0.230079\pi$
$594$	−1083.23			−0.0748240
$595$	720.848	+	5682.61i	0.0496670	+	0.391537i
$596$	−17224.4			−1.18379
$597$	−7181.52	+	12438.8i	−0.492328	+	0.852738i
$598$	4207.86	+	7288.23i	0.287746	+	0.498391i
$599$	−7340.57	−	12714.2i	−0.500714	−	0.867262i	−1.00000		0.000824549i	$-0.999738\pi$
$599$	−7340.57	−	12714.2i	−0.500714	−	0.867262i	0.499286	−	0.866437i	$-0.333596\pi$
$600$	1689.06	−	2925.54i	0.114926	−	0.199058i
$601$	−12450.1			−0.845011			−0.422505	−	0.906360i	$-0.638849\pi$
$601$	−12450.1			−0.845011			−0.422505	+	0.906360i	$0.638849\pi$
$602$	16757.6	+	7034.11i	1.13453	+	0.476227i
$603$	3127.71			0.211227
$604$	6554.22	−	11352.3i	0.441536	−	0.764762i
$605$	196.534	+	340.408i	0.0132070	+	0.0228753i
$606$	3028.92	+	5246.25i	0.203039	+	0.351674i
$607$	4760.50	−	8245.43i	0.318324	−	0.551354i	−0.661814	−	0.749668i	$-0.730213\pi$
$607$	4760.50	−	8245.43i	0.318324	−	0.551354i	0.980139	+	0.198314i	$0.0635466\pi$
$608$	16964.7			1.13160
$609$	531.030	−	403.504i	0.0353340	−	0.0268486i
$610$	2824.36			0.187467
$611$	−3889.17	+	6736.24i	−0.257511	+	0.446022i
$612$	−2271.77	−	3934.83i	−0.150051	−	0.259895i
$613$	14.7694	+	25.5813i	0.000973133	+	0.00168551i	0.866512	−	0.499157i	$-0.166357\pi$
$613$	14.7694	+	25.5813i	0.000973133	+	0.00168551i	−0.865538	+	0.500843i	$0.833024\pi$
$614$	7080.00	−	12262.9i	0.465351	−	0.806011i
$615$	−297.243			−0.0194894
$616$	1595.96	−	1212.69i	0.104388	−	0.0793194i
$617$	−13875.2			−0.905342			−0.452671	−	0.891678i	$-0.649529\pi$
$617$	−13875.2			−0.905342			−0.452671	+	0.891678i	$0.649529\pi$
$618$	−8388.04	+	14528.5i	−0.545981	+	0.945667i
$619$	−5183.58	−	8978.23i	−0.336584	−	0.582981i	0.647203	−	0.762317i	$-0.275938\pi$
$619$	−5183.58	−	8978.23i	−0.336584	−	0.582981i	−0.983788	+	0.179336i	$0.942605\pi$
$620$	1750.07	+	3031.20i	0.113362	+	0.196348i
$621$	−760.471	+	1317.18i	−0.0491412	+	0.0851150i
$622$	−23883.9			−1.53964
$623$	−12935.5	−	5429.75i	−0.831860	−	0.349179i
$624$	9622.39			0.617314
$625$	−5889.54	+	10201.0i	−0.376930	+	0.652862i
$626$	−698.104	−	1209.15i	−0.0445716	−	0.0772003i
$627$	−1353.04	−	2343.53i	−0.0861803	−	0.149269i
$628$	1636.65	−	2834.76i	0.103996	−	0.180126i
$629$	−14182.8			−0.899053
$630$	248.523	+	1959.16i	0.0157165	+	0.123897i
$631$	5081.22			0.320571			0.160285	−	0.987071i	$-0.448759\pi$
$631$	5081.22			0.320571			0.160285	+	0.987071i	$0.448759\pi$
$632$	−6062.48	+	10500.5i	−0.381571	+	0.660900i
$633$	3870.44	+	6703.80i	0.243027	+	0.420935i
$634$	−15792.4	−	27353.3i	−0.989272	−	1.71347i
$635$	−1701.09	+	2946.37i	−0.106308	+	0.184131i
$636$	7220.36			0.450166
$637$	−13604.9	+	3508.05i	−0.846224	+	0.218201i
$638$	481.587			0.0298844
$639$	3460.98	−	5994.60i	0.214263	−	0.371115i
$640$	1929.26	+	3341.58i	0.119158	+	0.206387i
$641$	−4860.33	−	8418.33i	−0.299487	−	0.518727i	0.676531	−	0.736414i	$-0.263482\pi$
$641$	−4860.33	−	8418.33i	−0.299487	−	0.518727i	−0.976019	+	0.217687i	$0.930149\pi$
$642$	−1805.59	+	3127.37i	−0.110998	+	0.192255i
$643$	22740.9			1.39473			0.697365	−	0.716716i	$-0.254355\pi$
$643$	22740.9			1.39473			0.697365	+	0.716716i	$0.254355\pi$
$644$	696.136	+	5487.80i	0.0425957	+	0.335792i
$645$	2622.07			0.160068
$646$	14237.8	−	24660.6i	0.867151	−	1.50195i
$647$	−13931.4	−	24129.8i	−0.846520	−	1.46622i	−0.884295	−	0.466929i	$-0.845360\pi$
$647$	−13931.4	−	24129.8i	−0.846520	−	1.46622i	0.0377747	−	0.999286i	$-0.487973\pi$
$648$	398.478	+	690.184i	0.0241569	+	0.0418410i
$649$	2069.04	−	3583.68i	0.125142	−	0.216752i
$650$	−17098.1			−1.03176
$651$	−10410.2	−	4369.77i	−0.626743	−	0.263079i
$652$	14180.0			0.851737
$653$	−13055.6	+	22613.0i	−0.782399	+	1.35515i	0.148142	+	0.988966i	$0.452671\pi$
$653$	−13055.6	+	22613.0i	−0.782399	+	1.35515i	−0.930541	+	0.366188i	$0.880663\pi$
$654$	−8022.51	−	13895.4i	−0.479671	−	0.830815i
$655$	−4153.06	−	7193.31i	−0.247746	−	0.429109i
$656$	−1194.16	+	2068.34i	−0.0710731	+	0.123102i
$657$	5407.41			0.321101
$658$	−10213.0	+	7760.36i	−0.605082	+	0.459772i
$659$	−22590.4			−1.33535			−0.667676	−	0.744452i	$-0.732711\pi$
$659$	−22590.4			−1.33535			−0.667676	+	0.744452i	$0.732711\pi$
$660$	−284.208	+	492.262i	−0.0167618	+	0.0290323i
$661$	−15089.2	−	26135.2i	−0.887899	−	1.53789i	−0.842355	−	0.538924i	$-0.818831\pi$
$661$	−15089.2	−	26135.2i	−0.887899	−	1.53789i	−0.0455444	−	0.998962i	$-0.514502\pi$
$662$	19324.2	+	33470.4i	1.13452	+	1.96505i
$663$	5849.97	−	10132.4i	0.342676	−	0.593532i
$664$	3462.57			0.202370
$665$	−3928.15	+	2984.81i	−0.229064	+	0.174054i
$666$	−4889.72			−0.284494
$667$	338.094	−	585.596i	0.0196268	−	0.0339945i
$668$	−7284.22	−	12616.6i	−0.421908	−	0.730767i
$669$	−5332.19	−	9235.63i	−0.308153	−	0.533737i
$670$	2058.74	−	3565.84i	0.118710	−	0.205612i
$671$	−2622.19			−0.150862
$672$	10598.6	+	4448.85i	0.608409	+	0.255384i
$673$	3391.09			0.194230			0.0971151	−	0.995273i	$-0.469038\pi$
$673$	3391.09			0.194230			0.0971151	+	0.995273i	$0.469038\pi$
$674$	6494.67	−	11249.1i	0.371165	−	0.642877i
$675$	−1545.04	−	2676.08i	−0.0881015	−	0.152596i
$676$	1376.32	+	2383.86i	0.0783070	+	0.135632i
$677$	−1635.66	+	2833.04i	−0.0928559	+	0.160831i	−0.908712	−	0.417424i	$-0.862933\pi$
$677$	−1635.66	+	2833.04i	−0.0928559	+	0.160831i	0.815856	+	0.578255i	$0.196266\pi$
$678$	11839.9			0.670663
$679$	1906.88	+	15032.4i	0.107775	+	0.849619i
$680$	3043.10			0.171614
$681$	−7312.75	+	12666.1i	−0.411491	+	0.712723i
$682$	−4076.23	−	7060.25i	−0.228867	−	0.396409i
$683$	15970.7	+	27662.1i	0.894734	+	1.54972i	0.834134	+	0.551562i	$0.185968\pi$
$683$	15970.7	+	27662.1i	0.894734	+	1.54972i	0.0606000	+	0.998162i	$0.480699\pi$
$684$	1956.62	−	3388.97i	0.109376	−	0.189445i
$685$	−2265.93			−0.126389
$686$	−22925.5	−	3349.24i	−1.27595	−	0.186406i
$687$	−18910.2			−1.05017
$688$	10534.0	−	18245.4i	0.583728	−	1.01105i
$689$	9296.45	+	16101.9i	0.514030	+	0.890326i
$690$	1001.12	+	1734.00i	0.0552350	+	0.0956698i
$691$	6405.55	−	11094.7i	0.352646	−	0.610801i	−0.634066	−	0.773279i	$-0.718615\pi$
$691$	6405.55	−	11094.7i	0.352646	−	0.610801i	0.986712	+	0.162478i	$0.0519486\pi$
$692$	−2683.70			−0.147426
$693$	−230.734	−	1818.93i	−0.0126477	−	0.0997048i
$694$	−712.034			−0.0389459
$695$	161.533	−	279.783i	0.00881626	−	0.0152702i
$696$	−177.157	−	306.845i	−0.00964817	−	0.0167111i
$697$	1451.98	+	2514.91i	0.0789064	+	0.136670i
$698$	1120.45	−	1940.67i	0.0607588	−	0.105237i
$699$	−11715.2			−0.633918
$700$	−10362.9	−	4349.90i	−0.559544	−	0.234872i
$701$	17225.0			0.928076			0.464038	−	0.885815i	$-0.346400\pi$
$701$	17225.0			0.928076			0.464038	+	0.885815i	$0.346400\pi$
$702$	2016.86	−	3493.31i	0.108435	−	0.187815i
$703$	−6107.63	−	10578.7i	−0.327672	−	0.567545i
$704$	704.630	+	1220.46i	0.0377227	+	0.0653376i
$705$	−925.302	+	1602.67i	−0.0494310	+	0.0856171i
$706$	−5638.31			−0.300568
$707$	−8164.18	+	6203.57i	−0.434294	+	0.329999i
$708$	5984.06			0.317648
$709$	1411.05	−	2444.01i	0.0747434	−	0.129459i	−0.826231	−	0.563331i	$-0.809520\pi$
$709$	1411.05	−	2444.01i	0.0747434	−	0.129459i	0.900975	+	0.433872i	$0.142853\pi$
$710$	−4556.22	−	7891.60i	−0.240834	−	0.417136i
$711$	5545.54	+	9605.16i	0.292509	+	0.506641i
$712$	−3726.44	+	6454.38i	−0.196144	+	0.339731i
$713$	−11446.7			−0.601239
$714$	15362.0	−	11672.9i	0.805196	−	0.611830i
$715$	−1463.71			−0.0765588
$716$	−1610.48	+	2789.44i	−0.0840595	+	0.145595i
$717$	−5354.19	−	9273.73i	−0.278878	−	0.483032i
$718$	−4967.55	−	8604.04i	−0.258199	−	0.447214i
$719$	15464.9	−	26786.0i	0.802147	−	1.38936i	−0.116054	−	0.993243i	$-0.537024\pi$
$719$	15464.9	−	26786.0i	0.802147	−	1.38936i	0.918200	−	0.396116i	$-0.129642\pi$
$720$	2289.33			0.118498
$721$	−26182.6	−	10990.3i	−1.35241	−	0.567684i
$722$	−491.076			−0.0253129
$723$	6679.83	−	11569.8i	0.343604	−	0.595139i
$724$	−6750.49	−	11692.2i	−0.346519	−	0.600189i
$725$	686.900	+	1189.75i	0.0351873	+	0.0609463i
$726$	661.974	−	1146.57i	0.0338404	−	0.0586134i
$727$	−8100.81			−0.413263			−0.206632	−	0.978419i	$-0.566250\pi$
$727$	−8100.81			−0.413263			−0.206632	+	0.978419i	$0.566250\pi$
$728$	939.299	+	7404.71i	0.0478197	+	0.376974i
$729$	729.000			0.0370370
$730$	3559.30	−	6164.89i	0.180460	−	0.312565i
$731$	−12808.4	−	22184.7i	−0.648064	−	1.12248i
$732$	−1895.97	−	3283.92i	−0.0957338	−	0.165816i
$733$	15747.1	−	27274.7i	0.793494	−	1.37437i	−0.130297	−	0.991475i	$-0.541593\pi$
$733$	15747.1	−	27274.7i	0.793494	−	1.37437i	0.923791	−	0.382897i	$-0.125074\pi$
$734$	−34864.4			−1.75323
$735$	−3236.84	+	834.626i	−0.162439	+	0.0418852i
$736$	11653.9			0.583652
$737$	−1911.38	+	3310.60i	−0.0955311	+	0.165465i
$738$	500.592	+	867.052i	0.0249689	+	0.0432474i
$739$	12424.2	+	21519.3i	0.618444	+	1.07118i	0.989770	+	0.142674i	$0.0455700\pi$
$739$	12424.2	+	21519.3i	0.618444	+	1.07118i	−0.371326	+	0.928503i	$0.621097\pi$
$740$	−1282.92	+	2222.08i	−0.0637311	+	0.110386i
$741$	10076.9			0.499571
$742$	3858.42	+	30416.8i	0.190899	+	1.50490i
$743$	−16842.2			−0.831600			−0.415800	−	0.909456i	$-0.636498\pi$
$743$	−16842.2			−0.831600			−0.415800	+	0.909456i	$0.636498\pi$
$744$	−2998.97	+	5194.37i	−0.147779	+	0.255961i
$745$	−5276.29	−	9138.81i	−0.259474	−	0.449423i
$746$	−13256.9	−	22961.6i	−0.650629	−	1.12692i
$747$	1583.66	−	2742.98i	0.0775678	−	0.134351i
$748$	5553.23			0.271452
$749$	−5635.99	−	2365.75i	−0.274946	−	0.115411i
$750$	−8510.96			−0.414369
$751$	−8040.32	+	13926.2i	−0.390673	+	0.676666i	−0.992538	−	0.121932i	$-0.961091\pi$
$751$	−8040.32	+	13926.2i	−0.390673	+	0.676666i	0.601865	+	0.798598i	$0.294424\pi$
$752$	7434.68	+	12877.2i	0.360525	+	0.624448i
$753$	8674.69	+	15025.0i	0.419819	+	0.727147i
$754$	−896.666	+	1553.07i	−0.0433086	+	0.0750126i
$755$	8030.93			0.387120
$756$	2111.12	−	1604.14i	0.101562	−	0.0771717i
$757$	−19231.4			−0.923351			−0.461675	−	0.887049i	$-0.652751\pi$
$757$	−19231.4			−0.923351			−0.461675	+	0.887049i	$0.652751\pi$
$758$	−23687.6	+	41028.1i	−1.13506	+	1.96598i
$759$	−929.465	−	1609.88i	−0.0444499	−	0.0769894i
$760$	1310.47	+	2269.80i	0.0625471	+	0.108335i
$761$	5701.35	−	9875.03i	0.271582	−	0.470394i	−0.697685	−	0.716404i	$-0.745787\pi$
$761$	5701.35	−	9875.03i	0.271582	−	0.470394i	0.969267	+	0.246011i	$0.0791199\pi$
$762$	11459.3			0.544787
$763$	21623.9	−	16431.0i	1.02600	−	0.779608i
$764$	12609.9			0.597132
$765$	1391.81	−	2410.68i	0.0657791	−	0.113933i
$766$	4210.60	+	7292.97i	0.198610	+	0.344002i
$767$	7704.68	+	13344.9i	0.362711	+	0.628235i
$768$	8035.58	−	13918.0i	0.377551	−	0.653937i
$769$	−35970.1			−1.68675			−0.843377	−	0.537322i	$-0.819436\pi$
$769$	−35970.1			−1.68675			−0.843377	+	0.537322i	$0.819436\pi$
$770$	−2225.60	−	934.211i	−0.104163	−	0.0437229i
$771$	−7779.37			−0.363381
$772$	−6403.77	+	11091.7i	−0.298545	+	0.517095i
$773$	−9159.08	−	15864.0i	−0.426170	−	0.738148i	0.570359	−	0.821395i	$-0.306804\pi$
$773$	−9159.08	−	15864.0i	−0.426170	−	0.738148i	−0.996529	+	0.0832478i	$0.973471\pi$
$774$	−4415.87	−	7648.52i	−0.205071	−	0.355194i
$775$	11628.1	−	20140.4i	0.538958	−	0.933503i
$776$	8050.02			0.372396
$777$	−1041.54	−	8210.68i	−0.0480887	−	0.379095i
$778$	−19221.6			−0.885769
$779$	−1250.56	+	2166.03i	−0.0575171	+	0.0996225i
$780$	−1058.33	−	1833.08i	−0.0485825	−	0.0841473i
$781$	4230.09	+	7326.73i	0.193809	+	0.335686i
$782$	9780.64	−	16940.6i	0.447257	−	0.774672i
$783$	−324.102			−0.0147924
$784$	−7196.12	+	25876.3i	−0.327811	+	1.17877i
$785$	2005.40			0.0911792
$786$	−13988.5	+	24228.8i	−0.634800	+	1.09951i
$787$	16707.0	+	28937.5i	0.756724	+	1.31068i	0.944513	+	0.328475i	$0.106535\pi$
$787$	16707.0	+	28937.5i	0.756724	+	1.31068i	−0.187789	+	0.982209i	$0.560132\pi$
$788$	8963.89	+	15525.9i	0.405235	+	0.701888i
$789$	12430.4	−	21530.1i	0.560881	−	0.971474i
$790$	14600.9			0.657565
$791$	2521.97	+	19881.3i	0.113364	+	0.893674i
$792$	−974.057			−0.0437015
$793$	4882.25	−	8456.31i	0.218630	−	0.378679i
$794$	−23245.4	−	40262.2i	−1.03898	−	1.79956i
$795$	2211.79	+	3830.93i	0.0986717	+	0.170904i
$796$	12693.0	−	21984.9i	0.565190	−	0.978937i
$797$	24235.5			1.07712			0.538560	−	0.842587i	$-0.318968\pi$
$797$	24235.5			1.07712			0.538560	+	0.842587i	$0.318968\pi$
$798$	15322.1	+	6431.55i	0.679695	+	0.285306i
$799$	18079.8			0.800521
$800$	−11838.5	+	20504.9i	−0.523193	+	0.906196i
$801$	3408.69	+	5904.02i	0.150362	+	0.260435i
$802$	10947.3	+	18961.3i	0.481999	+	0.834846i
$803$	−3304.53	+	5723.61i	−0.145223	+	0.251534i
$804$	−5528.07			−0.242487
$805$	−2698.44	+	2050.41i	−0.118146	+	0.0897733i
$806$	30358.1			1.32670
$807$	2837.14	−	4914.07i	0.123757	−	0.214354i
$808$	2723.65	+	4717.51i	0.118586	+	0.205398i
$809$	12399.9	+	21477.2i	0.538883	+	0.933373i	0.998965	+	0.0454959i	$0.0144868\pi$
$809$	12399.9	+	21477.2i	0.538883	+	0.933373i	−0.460082	+	0.887877i	$0.652180\pi$
$810$	479.847	−	831.119i	0.0208149	−	0.0360525i
$811$	−32827.3			−1.42136			−0.710680	−	0.703515i	$-0.751613\pi$
$811$	−32827.3			−1.42136			−0.710680	+	0.703515i	$0.751613\pi$
$812$	−938.570	+	713.174i	−0.0405632	+	0.0308220i
$813$	4408.01			0.190155
$814$	2988.16	−	5175.65i	0.128667	−	0.222858i
$815$	4343.72	+	7523.54i	0.186692	+	0.323360i
$816$	−11183.0	−	19369.5i	−0.479759	−	0.830967i
$817$	11031.5	−	19107.1i	0.472392	−	0.818206i
$818$	−29981.7			−1.28152
$819$	6295.47	+	2642.57i	0.268598	+	0.112746i
$820$	525.363			0.0223738
$821$	−6280.27	+	10877.8i	−0.266971	+	0.462407i	−0.968078	−	0.250649i	$-0.919356\pi$
$821$	−6280.27	+	10877.8i	−0.266971	+	0.462407i	0.701107	+	0.713056i	$0.252689\pi$
$822$	3816.09	+	6609.67i	0.161924	+	0.280461i
$823$	1527.35	+	2645.45i	0.0646902	+	0.112047i	0.896557	−	0.442929i	$-0.146061\pi$
$823$	1527.35	+	2645.45i	0.0646902	+	0.112047i	−0.831866	+	0.554976i	$0.812727\pi$
$824$	−7542.65	+	13064.3i	−0.318884	+	0.552324i
$825$	3776.76			0.159382
$826$	3197.77	+	25208.7i	0.134703	+	1.06189i
$827$	34363.5			1.44491			0.722453	−	0.691420i	$-0.243015\pi$
$827$	34363.5			1.44491			0.722453	+	0.691420i	$0.243015\pi$
$828$	1344.10	−	2328.04i	0.0564137	−	0.0977115i
$829$	10121.6	+	17531.2i	0.424051	+	0.734479i	0.996331	−	0.0855797i	$-0.0272742\pi$
$829$	10121.6	+	17531.2i	0.424051	+	0.734479i	−0.572280	+	0.820058i	$0.693941\pi$
$830$	−2084.81	−	3611.00i	−0.0871867	−	0.151012i
$831$	−9644.70	+	16705.1i	−0.402613	+	0.697346i
$832$	−5247.80			−0.218671
$833$	22873.0	+	23309.1i	0.951382	+	0.969524i
$834$	−1088.16			−0.0451798
$835$	4462.70	−	7729.62i	0.184956	−	0.320353i
$836$	2391.43	+	4142.07i	0.0989344	+	0.171359i
$837$	2743.25	+	4751.46i	0.113286	+	0.196218i
$838$	5193.28	−	8995.03i	0.214080	−	0.370797i
$839$	29046.6			1.19523			0.597616	−	0.801782i	$-0.296115\pi$
$839$	29046.6			1.19523			0.597616	+	0.801782i	$0.296115\pi$
$840$	223.476	+	1761.71i	0.00917934	+	0.0723628i
$841$	−24244.9			−0.994092
$842$	2702.20	−	4680.34i	0.110598	−	0.191562i
$843$	−316.431	−	548.075i	−0.0129282	−	0.0223923i
$844$	−6840.81	−	11848.6i	−0.278993	−	0.483231i
$845$	−843.209	+	1460.48i	−0.0343281	+	0.0594580i
$846$	6233.27			0.253315
$847$	2066.30	+	867.342i	0.0838238	+	0.0351856i
$848$	35542.8			1.43932
$849$	1389.05	−	2405.91i	0.0561510	−	0.0972564i
$850$	19871.2	+	34417.9i	0.801854	+	1.38885i
$851$	−4195.62	−	7267.03i	−0.169006	−	0.292727i
$852$	−6117.12	+	10595.2i	−0.245973	+	0.426038i
$853$	−13618.2			−0.546635			−0.273317	−	0.961924i	$-0.588121\pi$
$853$	−13618.2			−0.546635			−0.273317	+	0.961924i	$0.588121\pi$
$854$	12820.8	−	9741.93i	0.513723	−	0.390353i
$855$	2397.46			0.0958963
$856$	−1623.61	+	2812.18i	−0.0648294	+	0.112288i
$857$	−9107.46	−	15774.6i	−0.363016	−	0.628763i	0.625439	−	0.780273i	$-0.284920\pi$
$857$	−9107.46	−	15774.6i	−0.363016	−	0.628763i	−0.988456	+	0.151510i	$0.951586\pi$
$858$	2465.05	+	4269.60i	0.0980834	+	0.169885i
$859$	−6237.03	+	10802.9i	−0.247736	+	0.429091i	−0.962897	−	0.269869i	$-0.913020\pi$
$859$	−6237.03	+	10802.9i	−0.247736	+	0.429091i	0.715162	+	0.698959i	$0.246353\pi$
$860$	−4634.38			−0.183757
$861$	−1349.30	+	1025.27i	−0.0534077	+	0.0405819i
$862$	3569.74			0.141051
$863$	16244.0	−	28135.5i	0.640734	−	1.10978i	−0.344535	−	0.938774i	$-0.611963\pi$
$863$	16244.0	−	28135.5i	0.640734	−	1.10978i	0.985269	−	0.171011i	$-0.0547033\pi$
$864$	−2792.90	−	4837.44i	−0.109973	−	0.190478i
$865$	−822.088	−	1423.90i	−0.0323143	−	0.0559699i
$866$	−28114.8	+	48696.3i	−1.10321	+	1.91082i
$867$	−12456.0			−0.487921
$868$	18399.6	+	7723.35i	0.719497	+	0.302013i
$869$	−13555.8			−0.529169
$870$	−213.333	+	369.503i	−0.00831339	+	0.0143992i
$871$	−7117.57	−	12328.0i	−0.276888	−	0.479584i
$872$	−7213.96	−	12495.0i	−0.280156	−	0.485244i
$873$	3681.80	−	6377.07i	0.142738	−	0.247229i
$874$	16847.6			0.652036
$875$	−1812.88	−	14291.4i	−0.0700418	−	0.552156i
$876$	−9557.34			−0.368622
$877$	15910.0	−	27557.0i	0.612592	−	1.06104i	−0.378210	−	0.925720i	$-0.623460\pi$
$877$	15910.0	−	27557.0i	0.612592	−	1.06104i	0.990802	−	0.135320i	$-0.0432064\pi$
$878$	10429.7	+	18064.8i	0.400894	+	0.694369i
$879$	−1935.69	−	3352.72i	−0.0742769	−	0.128651i
$880$	−1399.04	+	2423.20i	−0.0535927	+	0.0928252i
$881$	32871.3			1.25705			0.628525	−	0.777789i	$-0.283659\pi$
$881$	32871.3			1.25705			0.628525	+	0.777789i	$0.283659\pi$
$882$	7885.79	+	8036.17i	0.301053	+	0.306793i
$883$	11692.0			0.445603			0.222802	−	0.974864i	$-0.428480\pi$
$883$	11692.0			0.445603			0.222802	+	0.974864i	$0.428480\pi$
$884$	−10339.5	+	17908.6i	−0.393389	+	0.681370i
$885$	1833.08	+	3174.98i	0.0696251	+	0.120594i
$886$	17060.5	+	29549.6i	0.646905	+	1.12047i
$887$	−3348.60	+	5799.95i	−0.126759	+	0.219553i	−0.922419	−	0.386190i	$-0.873791\pi$
$887$	−3348.60	+	5799.95i	−0.126759	+	0.219553i	0.795660	+	0.605743i	$0.207124\pi$
$888$	−4396.91			−0.166161
$889$	2440.90	+	19242.2i	0.0920869	+	0.725942i
$890$	8974.75			0.338016
$891$	−445.500	+	771.629i	−0.0167506	+	0.0290129i
$892$	9424.40	+	16323.5i	0.353758	+	0.612727i
$893$	7785.82	+	13485.4i	0.291761	+	0.505345i
$894$	−17771.8	+	30781.6i	−0.664852	+	1.15156i
$895$	−1973.33			−0.0736998
$896$	20283.6	+	8514.18i	0.756281	+	0.317454i
$897$	6922.27			0.257668
$898$	−15662.0	+	27127.5i	−0.582015	+	1.00808i
$899$	−1219.61	−	2112.42i	−0.0452461	−	0.0783685i
$900$	2730.78	+	4729.85i	0.101140	+	0.175180i
$901$	21608.4	−	37426.9i	0.798979	−	1.38387i
$902$	−1223.67			−0.0451705
$903$	11902.6	−	9044.19i	0.438641	−	0.333302i
$904$	10646.6			0.391706
$905$	4135.71	−	7163.25i	0.151907	−	0.263110i
$906$	−13525.0	−	23426.0i	−0.495959	−	0.859026i
$907$	13043.5	+	22591.9i	0.477509	+	0.827070i	0.999668	−	0.0257781i	$-0.00820634\pi$
$907$	13043.5	+	22591.9i	0.477509	+	0.827070i	−0.522158	+	0.852849i	$0.674873\pi$
$908$	12924.9	−	22386.6i	0.472389	−	0.818201i
$909$	4982.82			0.181815
$910$	7156.58	−	5437.94i	0.260701	−	0.198094i
$911$	−15265.3			−0.555174			−0.277587	−	0.960701i	$-0.589535\pi$
$911$	−15265.3			−0.555174			−0.277587	+	0.960701i	$0.589535\pi$
$912$	9631.63	−	16682.5i	0.349710	−	0.605715i
$913$	1935.59	+	3352.53i	0.0701627	+	0.121525i
$914$	−23900.2	−	41396.3i	−0.864931	−	1.49811i
$915$	1161.57	−	2011.90i	0.0419677	−	0.0726902i
$916$	33422.8			1.20559
$917$	−43663.9	−	18328.2i	−1.57242	−	0.660033i
$918$	−9375.88			−0.337092
$919$	969.683	−	1679.54i	0.0348062	−	0.0602861i	−0.848098	−	0.529840i	$-0.822252\pi$
$919$	969.683	−	1679.54i	0.0348062	−	0.0602861i	0.882904	+	0.469554i	$0.155585\pi$
$920$	900.226	+	1559.24i	0.0322604	+	0.0558767i
$921$	−5823.58	−	10086.7i	−0.208353	−	0.360879i
$922$	−6570.36	+	11380.2i	−0.234689	+	0.406493i
$923$	−31504.0			−1.12347
$924$	407.811	+	3214.87i	0.0145195	+	0.114460i
$925$	17048.4			0.605996
$926$	23043.9	−	39913.2i	0.817785	−	1.41644i
$927$	6899.49	+	11950.3i	0.244454	+	0.423407i
$928$	1241.68	+	2150.65i	0.0439225	+	0.0760761i
$929$	3178.23	−	5504.86i	0.112244	−	0.194412i	−0.804431	−	0.594046i	$-0.797530\pi$
$929$	3178.23	−	5504.86i	0.112244	−	0.194412i	0.916675	+	0.399634i	$0.130863\pi$
$930$	7222.73			0.254669
$931$	−7535.99	+	27098.4i	−0.265287	+	0.953935i
$932$	20706.0			0.727734
$933$	−9822.71	+	17013.4i	−0.344674	+	0.596994i
$934$	25580.5	+	44306.7i	0.896167	+	1.55221i
$935$	1701.10	+	2946.39i	0.0594994	+	0.103056i
$936$	1813.59	−	3141.24i	0.0633324	−	0.109695i
$937$	−11467.9			−0.399828			−0.199914	−	0.979813i	$-0.564066\pi$
$937$	−11467.9			−0.399828			−0.199914	+	0.979813i	$0.564066\pi$
$938$	−2954.09	−	23287.8i	−0.102830	−	0.810633i
$939$	−1148.44			−0.0399125
$940$	1635.43	−	2832.64i	0.0567465	−	0.0982879i
$941$	−18795.0	−	32554.0i	−0.651117	−	1.12777i	−0.982852	−	0.184395i	$-0.940967\pi$
$941$	−18795.0	−	32554.0i	−0.651117	−	1.12777i	0.331735	−	0.943372i	$-0.392366\pi$
$942$	−3377.32	−	5849.69i	−0.116814	−	0.202328i
$943$	−859.066	+	1487.95i	−0.0296660	+	0.0513830i
$944$	29457.1			1.01562
$945$	1497.80	+	628.712i	0.0515593	+	0.0216423i
$946$	10794.4			0.370988
$947$	25694.1	−	44503.5i	0.881674	−	1.52710i	0.0321960	−	0.999482i	$-0.489750\pi$
$947$	25694.1	−	44503.5i	0.881674	−	1.52710i	0.849478	−	0.527623i	$-0.176917\pi$
$948$	−9801.47	−	16976.7i	−0.335799	−	0.581620i
$949$	−12305.4	−	21313.5i	−0.420916	−	0.729049i
$950$	−17114.5	+	29643.2i	−0.584493	+	1.01237i
$951$	−25979.8			−0.885861
$952$	13813.8	−	10496.4i	0.470281	−	0.357344i
$953$	18421.2			0.626151			0.313075	−	0.949728i	$-0.398641\pi$
$953$	18421.2			0.626151			0.313075	+	0.949728i	$0.398641\pi$
$954$	7449.82	−	12903.5i	0.252827	−	0.437909i
$955$	3862.74	+	6690.45i	0.130885	+	0.226699i
$956$	9463.27	+	16390.9i	0.320151	+	0.554517i
$957$	198.062	−	343.054i	0.00669013	−	0.0115876i
$958$	−37507.0			−1.26492
$959$	−10285.9	+	7815.77i	−0.346350	+	0.263175i
$960$	−1248.54			−0.0419756
$961$	−5750.43	+	9960.04i	−0.193026	+	0.334330i
$962$	11127.3	+	19273.0i	0.372930	+	0.645933i
$963$	1485.17	+	2572.39i	0.0496977	+	0.0860790i
$964$	−11806.3	+	20449.1i	−0.394455	+	0.683216i
$965$	−7846.58			−0.261752
$966$	10525.5	+	4418.14i	0.350571	+	0.147155i
$967$	24037.9			0.799386			0.399693	−	0.916649i	$-0.369117\pi$
$967$	24037.9			0.799386			0.399693	+	0.916649i	$0.369117\pi$
$968$	595.257	−	1031.02i	0.0197648	−	0.0342336i
$969$	−11711.2	−	20284.4i	−0.388253	−	0.672474i
$970$	−4846.92	−	8395.11i	−0.160438	−	0.277887i
$971$	−12501.6	+	21653.4i	−0.413177	+	0.715644i	−0.995235	−	0.0975032i	$-0.968914\pi$
$971$	−12501.6	+	21653.4i	−0.413177	+	0.715644i	0.582058	+	0.813147i	$0.302248\pi$
$972$	−1288.47			−0.0425183
$973$	−231.785	−	1827.21i	−0.00763687	−	0.0602032i
$974$	20432.1			0.672162
$975$	−7031.93	+	12179.7i	−0.230977	+	0.400063i
$976$	−9333.09	−	16165.4i	−0.306091	−	0.530165i
$977$	−6010.27	−	10410.1i	−0.196812	−	0.340889i	0.750681	−	0.660665i	$-0.229726\pi$
$977$	−6010.27	−	10410.1i	−0.196812	−	0.340889i	−0.947493	+	0.319776i	$0.896392\pi$
$978$	14630.7	−	25341.0i	0.478361	−	0.828545i
$979$	−8332.35			−0.272015
$980$	5720.95	−	1475.16i	0.186479	−	0.0480840i
$981$	−13197.7			−0.429530
$982$	−32582.7	+	56434.9i	−1.05881	+	1.83392i
$983$	−19943.5	−	34543.2i	−0.647100	−	1.12081i	−0.983812	−	0.179202i	$-0.942648\pi$
$983$	−19943.5	−	34543.2i	−0.647100	−	1.12081i	0.336712	−	0.941608i	$-0.390685\pi$
$984$	450.140	+	779.666i	0.0145833	+	0.0252590i
$985$	−5491.75	+	9512.00i	−0.177647	+	0.307693i
$986$	4168.37			0.134633
$987$	1327.72	+	10466.7i	0.0428184	+	0.337548i
$988$	−17810.3			−0.573505
$989$	7578.08	−	13125.6i	0.243649	−	0.422012i
$990$	586.479	+	1015.81i	0.0188278	+	0.0326107i
$991$	−14152.3	−	24512.5i	−0.453645	−	0.785735i	0.544965	−	0.838459i	$-0.316543\pi$
$991$	−14152.3	−	24512.5i	−0.453645	−	0.785735i	−0.998609	+	0.0527236i	$0.983210\pi$
$992$	21019.6	−	36406.9i	0.672753	−	1.16524i
$993$	31789.8			1.01593
$994$	−47902.5	−	20107.4i	−1.52855	−	0.641618i
$995$	15552.8			0.495534
$996$	−2799.04	+	4848.09i	−0.0890473	+	0.154234i
$997$	16912.8	+	29293.8i	0.537244	+	0.930534i	0.999051	+	0.0435536i	$0.0138679\pi$
$997$	16912.8	+	29293.8i	0.537244	+	0.930534i	−0.461807	+	0.886980i	$0.652799\pi$
$998$	7860.92	+	13615.5i	0.249332	+	0.431855i
$999$	−2010.99	+	3483.15i	−0.0636887	+	0.110312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.i.a.100.2	yes	16
7.2	even	3		1617.4.a.u.1.7		8
7.4	even	3	inner	231.4.i.a.67.2	✓	16
7.5	odd	6		1617.4.a.v.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.i.a.67.2	✓	16	7.4	even	3	inner
231.4.i.a.100.2	yes	16	1.1	even	1	trivial
1617.4.a.u.1.7		8	7.2	even	3
1617.4.a.v.1.7		8	7.5	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+(-1.82362 + 3.15860i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.65118 - 4.59197i) q^{4} +(1.62425 - 2.81329i) q^{5} -10.9417 q^{6} +(-2.33065 - 18.3730i) q^{7} -9.83896 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.92404 + 10.2607i) q^{10} +(-5.50000 - 9.52628i) q^{11} +(7.95353 - 13.7759i) q^{12} +40.9617 q^{13} +(62.2833 + 26.1438i) q^{14} +9.74551 q^{15} +(39.1519 - 67.8131i) q^{16} +(-47.6051 - 82.4545i) q^{17} +(-16.4126 - 28.4274i) q^{18} +(41.0011 - 71.0160i) q^{19} -17.2247 q^{20} +(44.2386 - 33.6147i) q^{21} +40.1196 q^{22} +(28.1656 - 48.7843i) q^{23} +(-14.7584 - 25.5624i) q^{24} +(57.2236 + 99.1142i) q^{25} +(-74.6986 + 129.382i) q^{26} -27.0000 q^{27} +(-78.1895 + 59.4124i) q^{28} +12.0038 q^{29} +(-17.7721 + 30.7822i) q^{30} +(-101.602 - 175.980i) q^{31} +(103.441 + 179.164i) q^{32} +(16.5000 - 28.5788i) q^{33} +347.255 q^{34} +(-55.4741 - 23.2856i) q^{35} +47.7212 q^{36} +(74.4813 - 129.005i) q^{37} +(149.541 + 259.012i) q^{38} +(61.4426 + 106.422i) q^{39} +(-15.9809 + 27.6798i) q^{40} -30.5005 q^{41} +(25.5013 + 201.032i) q^{42} +269.054 q^{43} +(-29.1630 + 50.5117i) q^{44} +(14.6183 + 25.3196i) q^{45} +(102.727 + 177.928i) q^{46} +(-94.9465 + 164.452i) q^{47} +234.912 q^{48} +(-332.136 + 85.6421i) q^{49} -417.416 q^{50} +(142.815 - 247.364i) q^{51} +(-108.597 - 188.095i) q^{52} +(226.954 + 393.097i) q^{53} +(49.2377 - 85.2823i) q^{54} -35.7335 q^{55} +(22.9311 + 180.771i) q^{56} +246.007 q^{57} +(-21.8903 + 37.9152i) q^{58} +(188.094 + 325.789i) q^{59} +(-25.8371 - 44.7511i) q^{60} +(119.191 - 206.444i) q^{61} +741.134 q^{62} +(153.691 + 64.5130i) q^{63} -128.115 q^{64} +(66.5322 - 115.237i) q^{65} +(60.1794 + 104.234i) q^{66} +(-173.761 - 300.964i) q^{67} +(-252.419 + 437.203i) q^{68} +168.994 q^{69} +(174.714 - 132.757i) q^{70} -769.107 q^{71} +(44.2753 - 76.6871i) q^{72} +(-300.412 - 520.328i) q^{73} +(271.651 + 470.513i) q^{74} +(-171.671 + 297.343i) q^{75} -434.805 q^{76} +(-162.208 + 123.254i) q^{77} -448.192 q^{78} +(616.171 - 1067.24i) q^{79} +(-127.185 - 220.291i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(55.6214 - 96.3391i) q^{82} -351.925 q^{83} +(-271.642 - 114.024i) q^{84} -309.291 q^{85} +(-490.653 + 849.835i) q^{86} +(18.0057 + 31.1867i) q^{87} +(54.1143 + 93.7287i) q^{88} +(378.743 - 656.002i) q^{89} -106.633 q^{90} +(-95.4673 - 752.591i) q^{91} -298.688 q^{92} +(304.806 - 527.939i) q^{93} +(-346.293 - 599.796i) q^{94} +(-133.192 - 230.696i) q^{95} +(-310.322 + 537.493i) q^{96} -818.178 q^{97} +(335.181 - 1205.26i) 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

Related objects

Downloads

Learn more