LMFDB - Embedded newform 105.4.i.d.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} + \cdots + 7056 $ x^10 - 2x^9 + 34x^8 + 16x^7 + 791x^6 - 132x^5 + 4906x^4 - 1674x^3 + 25257x^2 - 12852*x + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$-2.05285 + 3.55565i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.4.i.d.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55285 + 4.42167i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.03412 - 15.6476i) q^{4} +(-2.50000 + 4.33013i) q^{5} +15.3171 q^{6} +(-2.74187 - 18.3162i) q^{7} +51.4055 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.55285 + 4.42167i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.03412 - 15.6476i) q^{4} +(-2.50000 + 4.33013i) q^{5} +15.3171 q^{6} +(-2.74187 - 18.3162i) q^{7} +51.4055 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-12.7643 - 22.1084i) q^{10} +(20.3677 + 35.2779i) q^{11} +(-27.1024 + 46.9427i) q^{12} +70.9263 q^{13} +(87.9877 + 34.6349i) q^{14} +15.0000 q^{15} +(-58.9577 + 102.118i) q^{16} +(-11.3350 - 19.6329i) q^{17} +(-22.9757 - 39.7950i) q^{18} +(-38.8294 + 67.2545i) q^{19} +90.3412 q^{20} +(-43.4740 + 34.5978i) q^{21} -207.983 q^{22} +(45.0311 - 77.9962i) q^{23} +(-77.1083 - 133.555i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-181.064 + 313.613i) q^{26} +27.0000 q^{27} +(-261.833 + 208.374i) q^{28} +213.332 q^{29} +(-38.2928 + 66.3251i) q^{30} +(87.8644 + 152.186i) q^{31} +(-95.3990 - 165.236i) q^{32} +(61.1031 - 105.834i) q^{33} +115.747 q^{34} +(86.1660 + 33.9178i) q^{35} +162.614 q^{36} +(177.466 - 307.381i) q^{37} +(-198.251 - 343.382i) q^{38} +(-106.389 - 184.272i) q^{39} +(-128.514 + 222.592i) q^{40} +249.001 q^{41} +(-41.9975 - 280.551i) q^{42} +297.920 q^{43} +(368.009 - 637.410i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(229.916 + 398.226i) q^{46} +(-84.3854 + 146.160i) q^{47} +353.746 q^{48} +(-327.964 + 100.441i) q^{49} +127.643 q^{50} +(-34.0051 + 58.8986i) q^{51} +(-640.757 - 1109.82i) q^{52} +(51.2366 + 88.7444i) q^{53} +(-68.9270 + 119.385i) q^{54} -203.677 q^{55} +(-140.947 - 941.552i) q^{56} +232.976 q^{57} +(-544.605 + 943.284i) q^{58} +(11.7399 + 20.3340i) q^{59} +(-135.512 - 234.713i) q^{60} +(437.314 - 757.450i) q^{61} -897.220 q^{62} +(155.099 + 61.0521i) q^{63} +30.8343 q^{64} +(-177.316 + 307.120i) q^{65} +(311.975 + 540.356i) q^{66} +(405.386 + 702.149i) q^{67} +(-204.804 + 354.731i) q^{68} -270.187 q^{69} +(-369.943 + 294.411i) q^{70} -632.487 q^{71} +(-231.325 + 400.666i) q^{72} +(-457.436 - 792.302i) q^{73} +(906.091 + 1569.40i) q^{74} +(-37.5000 + 64.9519i) q^{75} +1403.16 q^{76} +(590.311 - 469.786i) q^{77} +1086.39 q^{78} +(260.443 - 451.101i) q^{79} +(-294.789 - 510.589i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-635.664 + 1101.00i) q^{82} -1027.67 q^{83} +(934.121 + 367.701i) q^{84} +113.350 q^{85} +(-760.546 + 1317.30i) q^{86} +(-319.998 - 554.253i) q^{87} +(1047.01 + 1813.48i) q^{88} +(-501.875 + 869.273i) q^{89} +229.757 q^{90} +(-194.470 - 1299.10i) q^{91} -1627.27 q^{92} +(263.593 - 456.557i) q^{93} +(-430.847 - 746.249i) q^{94} +(-194.147 - 336.272i) q^{95} +(-286.197 + 495.708i) q^{96} -639.620 q^{97} +(393.128 - 1706.56i) q^{98} -366.619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9	\( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9} - 15 q^{10} - 43 q^{11} - 75 q^{12} + 246 q^{13} - 23 q^{14} + 150 q^{15} - 161 q^{16} - 124 q^{17} - 27 q^{18} - 37 q^{19} + 250 q^{20} + 3 q^{21} - 442 q^{22} - 77 q^{23} - 63 q^{24} - 125 q^{25} + 79 q^{26} + 270 q^{27} - 71 q^{28} + 720 q^{29} - 45 q^{30} - 314 q^{31} + 59 q^{32} - 129 q^{33} + 352 q^{34} + 155 q^{35} + 450 q^{36} - 225 q^{37} - 759 q^{38} - 369 q^{39} - 105 q^{40} + 682 q^{41} + 354 q^{42} + 64 q^{43} - 679 q^{44} - 225 q^{45} + 331 q^{46} - 25 q^{47} + 966 q^{48} + 710 q^{49} + 150 q^{50} - 372 q^{51} - 2299 q^{52} + 317 q^{53} - 81 q^{54} + 430 q^{55} + 1884 q^{56} + 222 q^{57} - 8 q^{58} - 676 q^{59} - 375 q^{60} + 188 q^{61} - 696 q^{62} + 279 q^{63} - 2206 q^{64} - 615 q^{65} + 663 q^{66} + 1776 q^{67} - 1280 q^{68} + 462 q^{69} - 475 q^{70} - 12 q^{71} - 189 q^{72} - 2006 q^{73} + 2729 q^{74} - 375 q^{75} + 2834 q^{76} + 3731 q^{77} - 474 q^{78} - 200 q^{79} - 805 q^{80} - 405 q^{81} + 539 q^{82} - 664 q^{83} + 1821 q^{84} + 1240 q^{85} - 4262 q^{86} - 1080 q^{87} + 4529 q^{88} - 894 q^{89} + 270 q^{90} + 2016 q^{91} - 7374 q^{92} - 942 q^{93} - 4233 q^{94} - 185 q^{95} + 177 q^{96} - 1152 q^{97} + 2539 q^{98} + 774 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9 - 15 * q^10 - 43 * q^11 - 75 * q^12 + 246 * q^13 - 23 * q^14 + 150 * q^15 - 161 * q^16 - 124 * q^17 - 27 * q^18 - 37 * q^19 + 250 * q^20 + 3 * q^21 - 442 * q^22 - 77 * q^23 - 63 * q^24 - 125 * q^25 + 79 * q^26 + 270 * q^27 - 71 * q^28 + 720 * q^29 - 45 * q^30 - 314 * q^31 + 59 * q^32 - 129 * q^33 + 352 * q^34 + 155 * q^35 + 450 * q^36 - 225 * q^37 - 759 * q^38 - 369 * q^39 - 105 * q^40 + 682 * q^41 + 354 * q^42 + 64 * q^43 - 679 * q^44 - 225 * q^45 + 331 * q^46 - 25 * q^47 + 966 * q^48 + 710 * q^49 + 150 * q^50 - 372 * q^51 - 2299 * q^52 + 317 * q^53 - 81 * q^54 + 430 * q^55 + 1884 * q^56 + 222 * q^57 - 8 * q^58 - 676 * q^59 - 375 * q^60 + 188 * q^61 - 696 * q^62 + 279 * q^63 - 2206 * q^64 - 615 * q^65 + 663 * q^66 + 1776 * q^67 - 1280 * q^68 + 462 * q^69 - 475 * q^70 - 12 * q^71 - 189 * q^72 - 2006 * q^73 + 2729 * q^74 - 375 * q^75 + 2834 * q^76 + 3731 * q^77 - 474 * q^78 - 200 * q^79 - 805 * q^80 - 405 * q^81 + 539 * q^82 - 664 * q^83 + 1821 * q^84 + 1240 * q^85 - 4262 * q^86 - 1080 * q^87 + 4529 * q^88 - 894 * q^89 + 270 * q^90 + 2016 * q^91 - 7374 * q^92 - 942 * q^93 - 4233 * q^94 - 185 * q^95 + 177 * q^96 - 1152 * q^97 + 2539 * q^98 + 774 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−2.55285	+	4.42167i	−0.902570	+	1.56330i	−0.0784237	+	0.996920i	$0.524989\pi$
$2$	−2.55285	+	4.42167i	−0.902570	+	1.56330i	−0.824146	+	0.566377i	$0.808345\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−9.03412	−	15.6476i	−1.12927	−	1.95594i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	15.3171			1.04220
$7$	−2.74187	−	18.3162i	−0.148047	−	0.988980i
$7$	−2.74187	−	18.3162i	−0.148047	−	0.988980i
$8$	51.4055			2.27182
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−12.7643	−	22.1084i	−0.403642	−	0.699128i
$11$	20.3677	+	35.2779i	0.558281	+	0.966972i	0.997640	+	0.0686601i	$0.0218724\pi$
$11$	20.3677	+	35.2779i	0.558281	+	0.966972i	−0.439359	+	0.898312i	$0.644794\pi$
$12$	−27.1024	+	46.9427i	−0.651982	+	1.12927i
$13$	70.9263			1.51319			0.756593	−	0.653887i	$-0.226863\pi$
$13$	70.9263			1.51319			0.756593	+	0.653887i	$0.226863\pi$
$14$	87.9877	+	34.6349i	1.67969	+	0.661183i
$15$	15.0000			0.258199
$16$	−58.9577	+	102.118i	−0.921215	+	1.59559i
$17$	−11.3350	−	19.6329i	−0.161715	−	0.280098i	0.773769	−	0.633468i	$-0.218369\pi$
$17$	−11.3350	−	19.6329i	−0.161715	−	0.280098i	−0.935484	+	0.353370i	$0.885036\pi$
$18$	−22.9757	−	39.7950i	−0.300857	−	0.521099i
$19$	−38.8294	+	67.2545i	−0.468846	+	0.812065i	−0.999366	−	0.0356075i	$-0.988663\pi$
$19$	−38.8294	+	67.2545i	−0.468846	+	0.812065i	0.530520	+	0.847672i	$0.321997\pi$
$20$	90.3412			1.01005
$21$	−43.4740	+	34.5978i	−0.451753	+	0.359517i
$22$	−207.983			−2.01555
$23$	45.0311	−	77.9962i	0.408245	−	0.707101i	−0.586448	−	0.809987i	$-0.699474\pi$
$23$	45.0311	−	77.9962i	0.408245	−	0.707101i	0.994693	+	0.102886i	$0.0328076\pi$
$24$	−77.1083	−	133.555i	−0.655819	−	1.13591i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−181.064	+	313.613i	−1.36576	+	2.36556i
$27$	27.0000			0.192450
$28$	−261.833	+	208.374i	−1.76721	+	1.40639i
$29$	213.332			1.36603			0.683013	−	0.730406i	$-0.260669\pi$
$29$	213.332			1.36603			0.683013	+	0.730406i	$0.260669\pi$
$30$	−38.2928	+	66.3251i	−0.233043	+	0.403642i
$31$	87.8644	+	152.186i	0.509062	+	0.881721i	0.999945	+	0.0104956i	$0.00334091\pi$
$31$	87.8644	+	152.186i	0.509062	+	0.881721i	−0.490883	+	0.871225i	$0.663326\pi$
$32$	−95.3990	−	165.236i	−0.527010	−	0.912808i
$33$	61.1031	−	105.834i	0.322324	−	0.558281i
$34$	115.747			0.583836
$35$	86.1660	+	33.9178i	0.416135	+	0.163804i
$36$	162.614			0.752844
$37$	177.466	−	307.381i	0.788521	−	1.36576i	−0.138351	−	0.990383i	$-0.544180\pi$
$37$	177.466	−	307.381i	0.788521	−	1.36576i	0.926873	−	0.375376i	$-0.122486\pi$
$38$	−198.251	−	343.382i	−0.846333	−	1.46589i
$39$	−106.389	−	184.272i	−0.436819	−	0.756593i
$40$	−128.514	+	222.592i	−0.507995	+	0.879874i
$41$	249.001			0.948475			0.474238	−	0.880397i	$-0.342724\pi$
$41$	249.001			0.948475			0.474238	+	0.880397i	$0.342724\pi$
$42$	−41.9975	−	280.551i	−0.154294	−	1.03071i
$43$	297.920			1.05657			0.528284	−	0.849068i	$-0.322836\pi$
$43$	297.920			1.05657			0.528284	+	0.849068i	$0.322836\pi$
$44$	368.009	−	637.410i	1.26090	−	2.18394i
$45$	−22.5000	−	38.9711i	−0.0745356	−	0.129099i
$46$	229.916	+	398.226i	0.736939	+	1.27642i
$47$	−84.3854	+	146.160i	−0.261891	+	0.453608i	−0.966744	−	0.255745i	$-0.917679\pi$
$47$	−84.3854	+	146.160i	−0.261891	+	0.453608i	0.704853	+	0.709353i	$0.251013\pi$
$48$	353.746			1.06373
$49$	−327.964	+	100.441i	−0.956164	+	0.292831i
$50$	127.643			0.361028
$51$	−34.0051	+	58.8986i	−0.0933661	+	0.161715i
$52$	−640.757	−	1109.82i	−1.70879	−	2.95971i
$53$	51.2366	+	88.7444i	0.132790	+	0.230000i	0.924751	−	0.380572i	$-0.124273\pi$
$53$	51.2366	+	88.7444i	0.132790	+	0.230000i	−0.791961	+	0.610572i	$0.790940\pi$
$54$	−68.9270	+	119.385i	−0.173700	+	0.300857i
$55$	−203.677			−0.499342
$56$	−140.947	−	941.552i	−0.336336	−	2.24679i
$57$	232.976			0.541377
$58$	−544.605	+	943.284i	−1.23293	+	2.13551i
$59$	11.7399	+	20.3340i	0.0259051	+	0.0448689i	0.878687	−	0.477398i	$-0.158420\pi$
$59$	11.7399	+	20.3340i	0.0259051	+	0.0448689i	−0.852782	+	0.522267i	$0.825087\pi$
$60$	−135.512	−	234.713i	−0.291575	−	0.505023i
$61$	437.314	−	757.450i	0.917907	−	1.58986i	0.115318	−	0.993329i	$-0.463211\pi$
$61$	437.314	−	757.450i	0.917907	−	1.58986i	0.802589	−	0.596533i	$-0.203455\pi$
$62$	−897.220			−1.83786
$63$	155.099	+	61.0521i	0.310169	+	0.122093i
$64$	30.8343			0.0602232
$65$	−177.316	+	307.120i	−0.338358	+	0.586054i
$66$	311.975	+	540.356i	0.581840	+	1.00778i
$67$	405.386	+	702.149i	0.739190	+	1.28032i	0.952860	+	0.303409i	$0.0981249\pi$
$67$	405.386	+	702.149i	0.739190	+	1.28032i	−0.213670	+	0.976906i	$0.568542\pi$
$68$	−204.804	+	354.731i	−0.365238	+	0.632610i
$69$	−270.187			−0.471401
$70$	−369.943	+	294.411i	−0.631666	+	0.502697i
$71$	−632.487			−1.05722			−0.528608	−	0.848866i	$-0.677286\pi$
$71$	−632.487			−1.05722			−0.528608	+	0.848866i	$0.677286\pi$
$72$	−231.325	+	400.666i	−0.378637	+	0.655819i
$73$	−457.436	−	792.302i	−0.733409	−	1.27030i	−0.955418	−	0.295256i	$-0.904595\pi$
$73$	−457.436	−	792.302i	−0.733409	−	1.27030i	0.222010	−	0.975045i	$-0.428738\pi$
$74$	906.091	+	1569.40i	1.42339	+	2.46539i
$75$	−37.5000	+	64.9519i	−0.0577350	+	0.100000i
$76$	1403.16			2.11781
$77$	590.311	−	469.786i	0.873664	−	0.695286i
$78$	1086.39			1.57704
$79$	260.443	−	451.101i	0.370913	−	0.642441i	−0.618793	−	0.785554i	$-0.712378\pi$
$79$	260.443	−	451.101i	0.370913	−	0.642441i	0.989706	+	0.143113i	$0.0457114\pi$
$80$	−294.789	−	510.589i	−0.411980	−	0.713570i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−635.664	+	1101.00i	−0.856065	+	1.48275i
$83$	−1027.67			−1.35905			−0.679527	−	0.733651i	$-0.737815\pi$
$83$	−1027.67			−1.35905			−0.679527	+	0.733651i	$0.737815\pi$
$84$	934.121	+	367.701i	1.21334	+	0.477613i
$85$	113.350			0.144642
$86$	−760.546	+	1317.30i	−0.953626	+	1.65173i
$87$	−319.998	−	554.253i	−0.394338	−	0.683013i
$88$	1047.01	+	1813.48i	1.26832	+	2.19679i
$89$	−501.875	+	869.273i	−0.597738	+	1.03531i	0.395416	+	0.918502i	$0.370600\pi$
$89$	−501.875	+	869.273i	−0.597738	+	1.03531i	−0.993154	+	0.116810i	$0.962733\pi$
$90$	229.757			0.269094
$91$	−194.470	−	1299.10i	−0.224022	−	1.49651i
$92$	−1627.27			−1.84407
$93$	263.593	−	456.557i	0.293907	−	0.509062i
$94$	−430.847	−	746.249i	−0.472750	−	0.818827i
$95$	−194.147	−	336.272i	−0.209674	−	0.363166i
$96$	−286.197	+	495.708i	−0.304269	+	0.527010i
$97$	−639.620			−0.669522			−0.334761	−	0.942303i	$-0.608656\pi$
$97$	−639.620			−0.669522			−0.334761	+	0.942303i	$0.608656\pi$
$98$	393.128	−	1706.56i	0.405224	−	1.75907i
$99$	−366.619			−0.372188
$100$	−225.853	+	391.189i	−0.225853	+	0.391189i
$101$	316.935	+	548.947i	0.312239	+	0.540814i	0.978847	−	0.204595i	$-0.0655876\pi$
$101$	316.935	+	548.947i	0.312239	+	0.540814i	−0.666608	+	0.745409i	$0.732254\pi$
$102$	−173.620	−	300.719i	−0.168539	−	0.291918i
$103$	193.789	−	335.653i	0.185385	−	0.321096i	−0.758321	−	0.651881i	$-0.773980\pi$
$103$	193.789	−	335.653i	0.185385	−	0.321096i	0.943706	+	0.330785i	$0.107314\pi$
$104$	3646.00			3.43769
$105$	−41.1280	−	274.743i	−0.0382255	−	0.255354i
$106$	−523.198			−0.479410
$107$	−69.3650	+	120.144i	−0.0626707	+	0.108549i	−0.895658	−	0.444743i	$-0.853295\pi$
$107$	−69.3650	+	120.144i	−0.0626707	+	0.108549i	0.832988	+	0.553292i	$0.186628\pi$
$108$	−243.921	−	422.484i	−0.217327	−	0.376422i
$109$	856.485	+	1483.48i	0.752628	+	1.30359i	0.946545	+	0.322571i	$0.104547\pi$
$109$	856.485	+	1483.48i	0.752628	+	1.30359i	−0.193918	+	0.981018i	$0.562119\pi$
$110$	519.958	−	900.593i	0.450691	−	0.780620i
$111$	−1064.80			−0.910506
$112$	2032.06	+	799.887i	1.71439	+	0.674841i
$113$	2083.35			1.73438			0.867192	−	0.497975i	$-0.165923\pi$
$113$	2083.35			1.73438			0.867192	+	0.497975i	$0.165923\pi$
$114$	−594.754	+	1030.14i	−0.488630	+	0.846333i
$115$	225.156	+	389.981i	0.182573	+	0.316225i
$116$	−1927.27	−	3338.13i	−1.54261	−	2.67187i
$117$	−319.168	+	552.816i	−0.252198	+	0.436819i
$118$	−119.881			−0.0935246
$119$	−328.520	+	261.445i	−0.253070	+	0.201400i
$120$	771.083			0.586582
$121$	−164.187	+	284.381i	−0.123356	+	0.213660i
$122$	2232.80	+	3867.32i	1.65695	+	2.86992i
$123$	−373.502	−	646.925i	−0.273801	−	0.474238i
$124$	1587.56	−	2749.73i	1.14973	−	1.99139i
$125$	125.000			0.0894427
$126$	−665.897	+	529.939i	−0.470816	+	0.374688i
$127$	432.085			0.301900			0.150950	−	0.988541i	$-0.451767\pi$
$127$	432.085			0.301900			0.150950	+	0.988541i	$0.451767\pi$
$128$	684.476	−	1185.55i	0.472654	−	0.818661i
$129$	−446.880	−	774.019i	−0.305005	−	0.528284i
$130$	−905.322	−	1568.06i	−0.610784	−	1.05791i
$131$	328.750	−	569.411i	0.219259	−	0.379769i	−0.735322	−	0.677718i	$-0.762969\pi$
$131$	328.750	−	569.411i	0.219259	−	0.379769i	0.954582	+	0.297949i	$0.0963025\pi$
$132$	−2208.05			−1.45596
$133$	1338.31	+	526.803i	0.872527	+	0.343456i
$134$	−4139.56			−2.66868
$135$	−67.5000	+	116.913i	−0.0430331	+	0.0745356i
$136$	−582.683	−	1009.24i	−0.367387	−	0.636334i
$137$	−146.258	−	253.326i	−0.0912090	−	0.157979i	0.816811	−	0.576905i	$-0.195740\pi$
$137$	−146.258	−	253.326i	−0.0912090	−	0.157979i	−0.908020	+	0.418927i	$0.862406\pi$
$138$	689.747	−	1194.68i	0.425472	−	0.736939i
$139$	−1673.02			−1.02089			−0.510445	−	0.859910i	$-0.670519\pi$
$139$	−1673.02			−1.02089			−0.510445	+	0.859910i	$0.670519\pi$
$140$	−247.703	−	1654.71i	−0.149534	−	0.998915i
$141$	506.312			0.302406
$142$	1614.65	−	2796.65i	0.954212	−	1.65274i
$143$	1444.61	+	2502.13i	0.844783	+	1.46321i
$144$	−530.620	−	919.060i	−0.307072	−	0.531864i
$145$	−533.330	+	923.755i	−0.305453	+	0.529060i
$146$	4671.07			2.64781
$147$	752.900	+	701.415i	0.422436	+	0.393549i
$148$	−6413.01			−3.56180
$149$	−1260.50	+	2183.26i	−0.693050	+	1.20040i	0.277784	+	0.960644i	$0.410400\pi$
$149$	−1260.50	+	2183.26i	−0.693050	+	1.20040i	−0.970834	+	0.239754i	$0.922933\pi$
$150$	−191.464	−	331.625i	−0.104220	−	0.180514i
$151$	−689.660	−	1194.53i	−0.371680	−	0.643769i	0.618144	−	0.786065i	$-0.287885\pi$
$151$	−689.660	−	1194.53i	−0.371680	−	0.643769i	−0.989824	+	0.142296i	$0.954552\pi$
$152$	−1996.04	+	3457.25i	−1.06514	+	1.84487i
$153$	204.031			0.107810
$154$	570.262	+	3809.45i	0.298396	+	1.99334i
$155$	−878.644			−0.455319
$156$	−1922.27	+	3329.47i	−0.986569	+	1.70879i
$157$	−996.365	−	1725.76i	−0.506488	−	0.877263i	−0.999972	−	0.00750789i	$-0.997610\pi$
$157$	−996.365	−	1725.76i	−0.506488	−	0.877263i	0.493484	−	0.869755i	$-0.335723\pi$
$158$	1329.75	+	2303.19i	0.669550	+	1.15970i
$159$	153.710	−	266.233i	0.0766666	−	0.132790i
$160$	953.990			0.471372
$161$	−1552.06	−	610.943i	−0.759749	−	0.299062i
$162$	413.562			0.200571
$163$	−951.472	+	1648.00i	−0.457209	+	0.791909i	−0.998812	−	0.0487253i	$-0.984484\pi$
$163$	−951.472	+	1648.00i	−0.457209	+	0.791909i	0.541603	+	0.840634i	$0.317817\pi$
$164$	−2249.51	−	3896.26i	−1.07108	−	1.85516i
$165$	305.516	+	529.169i	0.144148	+	0.249671i
$166$	2623.49	−	4544.02i	1.22664	−	2.12460i
$167$	−378.184			−0.175238			−0.0876189	−	0.996154i	$-0.527926\pi$
$167$	−378.184			−0.175238			−0.0876189	+	0.996154i	$0.527926\pi$
$168$	−2234.80	+	1778.52i	−1.02630	+	0.816760i
$169$	2833.54			1.28973
$170$	−289.367	+	501.198i	−0.130550	+	0.226119i
$171$	−349.464	−	605.290i	−0.156282	−	0.270688i
$172$	−2691.45	−	4661.72i	−1.19314	−	2.06659i
$173$	332.018	−	575.073i	0.145913	−	0.252728i	−0.783800	−	0.621013i	$-0.786722\pi$
$173$	332.018	−	575.073i	0.145913	−	0.252728i	0.929713	+	0.368285i	$0.120055\pi$
$174$	3267.63			1.42367
$175$	−362.283	+	288.315i	−0.156492	+	0.124540i
$176$	−4803.34			−2.05719
$177$	35.2196	−	61.0021i	0.0149563	−	0.0259051i
$178$	−2562.43	−	4438.26i	−1.07900	−	1.86888i
$179$	167.500	+	290.118i	0.0699414	+	0.121142i	0.898875	−	0.438204i	$-0.144385\pi$
$179$	167.500	+	290.118i	0.0699414	+	0.121142i	−0.828934	+	0.559347i	$0.811052\pi$
$180$	−406.535	+	704.140i	−0.168341	+	0.291575i
$181$	1225.58			0.503298			0.251649	−	0.967819i	$-0.419027\pi$
$181$	1225.58			0.503298			0.251649	+	0.967819i	$0.419027\pi$
$182$	6240.64	+	2456.52i	2.54169	+	1.00049i
$183$	−2623.88			−1.05991
$184$	2314.85	−	4009.43i	0.927461	−	1.60641i
$185$	887.332	+	1536.90i	0.352637	+	0.610786i
$186$	1345.83	+	2331.05i	0.530543	+	0.918928i
$187$	461.738	−	799.753i	0.180565	−	0.312747i
$188$	3049.39			1.18298
$189$	−74.0304	−	494.537i	−0.0284916	−	0.190329i
$190$	1982.51			0.756983
$191$	790.698	−	1369.53i	0.299544	−	0.518826i	−0.676488	−	0.736454i	$-0.736499\pi$
$191$	790.698	−	1369.53i	0.299544	−	0.518826i	0.976032	+	0.217628i	$0.0698321\pi$
$192$	−46.2515	−	80.1099i	−0.0173850	−	0.0301116i
$193$	1947.31	+	3372.85i	0.726273	+	1.25794i	0.958448	+	0.285268i	$0.0920825\pi$
$193$	1947.31	+	3372.85i	0.726273	+	1.25794i	−0.232175	+	0.972674i	$0.574584\pi$
$194$	1632.86	−	2828.19i	0.604290	−	1.04666i
$195$	1063.89			0.390703
$196$	4534.53	+	4224.45i	1.65252	+	1.53952i
$197$	993.858			0.359439			0.179719	−	0.983718i	$-0.442481\pi$
$197$	993.858			0.359439			0.179719	+	0.983718i	$0.442481\pi$
$198$	935.924	−	1621.07i	0.335925	−	0.581840i
$199$	1539.94	+	2667.26i	0.548560	+	0.950134i	0.998374	+	0.0570118i	$0.0181572\pi$
$199$	1539.94	+	2667.26i	0.548560	+	0.950134i	−0.449813	+	0.893123i	$0.648509\pi$
$200$	−642.569	−	1112.96i	−0.227182	−	0.393491i
$201$	1216.16	−	2106.45i	0.426772	−	0.739190i
$202$	−3236.35			−1.12727
$203$	−584.928	−	3907.43i	−0.202236	−	1.35097i
$204$	1228.83			0.421740
$205$	−622.503	+	1078.21i	−0.212085	+	0.367343i
$206$	989.431	+	1713.74i	0.334645	+	0.579622i
$207$	405.280	+	701.966i	0.136082	+	0.235700i
$208$	−4181.65	+	7242.83i	−1.39397	+	2.41442i
$209$	−3163.46			−1.04699
$210$	1319.82	+	519.523i	0.433695	+	0.170717i
$211$	2114.72			0.689968			0.344984	−	0.938609i	$-0.387884\pi$
$211$	2114.72			0.689968			0.344984	+	0.938609i	$0.387884\pi$
$212$	925.756	−	1603.46i	0.299911	−	0.519461i
$213$	948.730	+	1643.25i	0.305192	+	0.528608i
$214$	−354.157	−	613.419i	−0.113129	−	0.195946i
$215$	−744.800	+	1290.03i	−0.236256	+	0.409207i
$216$	1387.95			0.437213
$217$	2546.55	−	2026.61i	0.796640	−	0.633988i
$218$	−8745.92			−2.71720
$219$	−1372.31	+	2376.91i	−0.423434	+	0.733409i
$220$	1840.04	+	3187.05i	0.563890	+	0.976686i
$221$	−803.952	−	1392.49i	−0.244704	−	0.423840i
$222$	2718.27	−	4708.19i	0.821795	−	1.42339i
$223$	2578.44			0.774282			0.387141	−	0.922021i	$-0.373463\pi$
$223$	2578.44			0.774282			0.387141	+	0.922021i	$0.373463\pi$
$224$	−2764.92	+	2200.40i	−0.824727	+	0.656341i
$225$	225.000			0.0666667
$226$	−5318.49	+	9211.90i	−1.56540	+	2.71136i
$227$	−1462.96	−	2533.93i	−0.427754	−	0.740892i	0.568919	−	0.822394i	$-0.307362\pi$
$227$	−1462.96	−	2533.93i	−0.427754	−	0.740892i	−0.996673	+	0.0815014i	$0.974028\pi$
$228$	−2104.74	−	3645.51i	−0.611358	−	1.05890i
$229$	523.938	−	907.488i	0.151191	−	0.261871i	−0.780474	−	0.625188i	$-0.785022\pi$
$229$	523.938	−	907.488i	0.151191	−	0.261871i	0.931666	+	0.363317i	$0.118356\pi$
$230$	−2299.16			−0.659139
$231$	−2106.01	−	828.994i	−0.599848	−	0.236120i
$232$	10966.4			3.10337
$233$	1934.99	−	3351.51i	0.544058	−	0.942337i	−0.454607	−	0.890692i	$-0.650220\pi$
$233$	1934.99	−	3351.51i	0.544058	−	0.942337i	0.998666	−	0.0516447i	$-0.0164463\pi$
$234$	−1629.58	−	2822.51i	−0.455252	−	0.788519i
$235$	−421.927	−	730.799i	−0.117121	−	0.202860i
$236$	212.119	−	367.400i	0.0585074	−	0.101338i
$237$	−1562.66			−0.428294
$238$	−317.362	−	2120.04i	−0.0864350	−	0.577402i
$239$	−6060.77			−1.64033			−0.820164	−	0.572128i	$-0.806118\pi$
$239$	−6060.77			−1.64033			−0.820164	+	0.572128i	$0.806118\pi$
$240$	−884.366	+	1531.77i	−0.237857	+	0.411980i
$241$	2092.06	+	3623.55i	0.559176	+	0.968521i	0.997565	+	0.0697357i	$0.0222156\pi$
$241$	2092.06	+	3623.55i	0.559176	+	0.968521i	−0.438390	+	0.898785i	$0.644451\pi$
$242$	−838.292	−	1451.97i	−0.222676	−	0.385685i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−15803.0			−4.14624
$245$	384.989	−	1671.23i	0.100392	−	0.435800i
$246$	3813.98			0.988499
$247$	−2754.02	+	4770.11i	−0.709451	+	1.22880i
$248$	4516.72	+	7823.18i	1.15650	+	2.00311i
$249$	1541.50	+	2669.96i	0.392325	+	0.679527i
$250$	−319.107	+	552.709i	−0.0807283	+	0.139826i
$251$	−2631.65			−0.661786			−0.330893	−	0.943668i	$-0.607350\pi$
$251$	−2631.65			−0.661786			−0.330893	+	0.943668i	$0.607350\pi$
$252$	−445.866	−	2978.47i	−0.111456	−	0.744547i
$253$	3668.72			0.911663
$254$	−1103.05	+	1910.54i	−0.272486	+	0.471959i
$255$	−170.026	−	294.493i	−0.0417546	−	0.0723210i
$256$	3618.07	+	6266.68i	0.883318	+	1.52995i
$257$	−1644.38	+	2848.15i	−0.399120	+	0.691296i	−0.993618	−	0.112802i	$-0.964018\pi$
$257$	−1644.38	+	2848.15i	−0.399120	+	0.691296i	0.594498	+	0.804097i	$0.297351\pi$
$258$	4563.28			1.10115
$259$	−6116.63	−	2407.71i	−1.46745	−	0.577636i
$260$	6407.57			1.52839
$261$	−959.994	+	1662.76i	−0.227671	+	0.394338i
$262$	1678.50	+	2907.25i	0.395794	+	0.685535i
$263$	2704.45	+	4684.24i	0.634081	+	1.09826i	0.986709	+	0.162498i	$0.0519550\pi$
$263$	2704.45	+	4684.24i	0.634081	+	1.09826i	−0.352627	+	0.935764i	$0.614712\pi$
$264$	3141.04	−	5440.44i	0.732263	−	1.26832i
$265$	−512.366			−0.118771
$266$	−5745.86	+	4572.71i	−1.32444	+	1.05403i
$267$	3011.25			0.690208
$268$	7324.61	−	12686.6i	1.66948	−	2.89163i
$269$	−269.894	−	467.470i	−0.0611738	−	0.105956i	0.833817	−	0.552042i	$-0.186151\pi$
$269$	−269.894	−	467.470i	−0.0611738	−	0.105956i	−0.894990	+	0.446086i	$0.852818\pi$
$270$	−344.635	−	596.926i	−0.0776809	−	0.134547i
$271$	−2045.57	+	3543.03i	−0.458522	+	0.794184i	−0.998883	−	0.0472494i	$-0.984954\pi$
$271$	−2045.57	+	3543.03i	−0.458522	+	0.794184i	0.540361	+	0.841433i	$0.318288\pi$
$272$	2673.15			0.595896
$273$	−3083.45	+	2453.90i	−0.683586	+	0.544016i
$274$	1493.50			0.329290
$275$	509.193	−	881.948i	0.111656	−	0.193394i
$276$	2440.90	+	4227.76i	0.532336	+	0.922034i
$277$	−1545.67	−	2677.18i	−0.335271	−	0.580707i	0.648265	−	0.761414i	$-0.275495\pi$
$277$	−1545.67	−	2677.18i	−0.335271	−	0.580707i	−0.983537	+	0.180707i	$0.942161\pi$
$278$	4270.97	−	7397.55i	0.921425	−	1.59595i
$279$	−1581.56			−0.339375
$280$	4429.41	+	1743.56i	0.945385	+	0.372135i
$281$	7215.73			1.53187			0.765933	−	0.642920i	$-0.222277\pi$
$281$	7215.73			1.53187			0.765933	+	0.642920i	$0.222277\pi$
$282$	−1292.54	+	2238.75i	−0.272942	+	0.472750i
$283$	−1482.36	−	2567.52i	−0.311368	−	0.539305i	0.667291	−	0.744797i	$-0.267454\pi$
$283$	−1482.36	−	2567.52i	−0.311368	−	0.539305i	−0.978659	+	0.205492i	$0.934120\pi$
$284$	5713.96	+	9896.87i	1.19388	+	2.06786i
$285$	−582.441	+	1008.82i	−0.121055	+	0.209674i
$286$	−14751.5			−3.04990
$287$	−682.728	−	4560.75i	−0.140419	−	0.938023i
$288$	1717.18			0.351340
$289$	2199.53	−	3809.70i	0.447697	−	0.775433i
$290$	−2723.03	−	4716.42i	−0.551385	−	0.955027i
$291$	959.430	+	1661.78i	0.193274	+	0.334761i
$292$	−8265.06	+	14315.5i	−1.65643	+	2.86901i
$293$	−7924.10			−1.57997			−0.789984	−	0.613127i	$-0.789911\pi$
$293$	−7924.10			−1.57997			−0.789984	+	0.613127i	$0.789911\pi$
$294$	−5023.47	+	1538.47i	−0.996513	+	0.305188i
$295$	−117.399			−0.0231702
$296$	9122.75	−	15801.1i	1.79138	−	3.10276i
$297$	549.928	+	952.504i	0.107441	+	0.186094i
$298$	−6435.76	−	11147.1i	−1.25105	−	2.16689i
$299$	3193.89	−	5531.98i	0.617750	−	1.06997i
$300$	1355.12			0.260793
$301$	−816.857	−	5456.76i	−0.156421	−	1.04492i
$302$	7042.41			1.34187
$303$	950.804	−	1646.84i	0.180271	−	0.312239i
$304$	−4578.59	−	7930.34i	−0.863816	−	1.49617i
$305$	2186.57	+	3787.25i	0.410500	+	0.711008i
$306$	−520.861	+	902.157i	−0.0973059	+	0.168539i
$307$	−4067.00			−0.756079			−0.378039	−	0.925790i	$-0.623402\pi$
$307$	−4067.00			−0.756079			−0.378039	+	0.925790i	$0.623402\pi$
$308$	−12683.9	−	4992.82i	−2.34654	−	0.923676i
$309$	−1162.73			−0.214064
$310$	2243.05	−	3885.08i	0.410957	−	0.711799i
$311$	−3826.29	−	6627.33i	−0.697650	−	1.20836i	−0.969279	−	0.245963i	$-0.920896\pi$
$311$	−3826.29	−	6627.33i	−0.697650	−	1.20836i	0.271630	−	0.962402i	$-0.412437\pi$
$312$	−5469.00	−	9472.59i	−0.992376	−	1.71884i
$313$	−911.061	+	1578.00i	−0.164525	+	0.284965i	−0.936486	−	0.350704i	$-0.885942\pi$
$313$	−911.061	+	1578.00i	−0.164525	+	0.284965i	0.771962	+	0.635669i	$0.219276\pi$
$314$	10174.3			1.82856
$315$	−652.110	+	518.968i	−0.116642	+	0.0928270i
$316$	−9411.50			−1.67544
$317$	−1574.43	+	2726.99i	−0.278955	+	0.483164i	−0.971125	−	0.238570i	$-0.923321\pi$
$317$	−1574.43	+	2726.99i	−0.278955	+	0.483164i	0.692170	+	0.721734i	$0.256655\pi$
$318$	784.797	+	1359.31i	0.138394	+	0.239705i
$319$	4345.09	+	7525.91i	0.762627	+	1.32091i
$320$	−77.0858	+	133.516i	−0.0134663	+	0.0233244i
$321$	416.190			0.0723659
$322$	6663.57	−	5303.06i	1.15325	−	0.917788i
$323$	1760.53			0.303277
$324$	−731.764	+	1267.45i	−0.125474	+	0.217327i
$325$	−886.578	−	1535.60i	−0.151319	−	0.262091i
$326$	−4857.94	−	8414.19i	−0.825326	−	1.42951i
$327$	2569.46	−	4450.43i	0.434530	−	0.752628i
$328$	12800.0			2.15477
$329$	2908.46	+	1144.87i	0.487382	+	0.191850i
$330$	−3119.75			−0.520413
$331$	2928.06	−	5071.55i	0.486226	−	0.842168i	−0.513649	−	0.858001i	$-0.671707\pi$
$331$	2928.06	−	5071.55i	0.486226	−	0.842168i	0.999875	+	0.0158326i	$0.00503989\pi$
$332$	9284.10	+	16080.5i	1.53473	+	2.65823i
$333$	1597.20	+	2766.43i	0.262840	+	0.455253i
$334$	965.447	−	1672.20i	0.158164	−	0.273949i
$335$	−4053.86			−0.661152
$336$	−969.925	−	6479.28i	−0.157481	−	1.05201i
$337$	−7065.69			−1.14212			−0.571058	−	0.820910i	$-0.693467\pi$
$337$	−7065.69			−1.14212			−0.571058	+	0.820910i	$0.693467\pi$
$338$	−7233.60	+	12529.0i	−1.16407	+	2.01623i
$339$	−3125.03	−	5412.71i	−0.500673	−	0.867192i
$340$	−1024.02	−	1773.66i	−0.163339	−	0.282912i
$341$	−3579.20	+	6199.35i	−0.568400	+	0.984497i
$342$	3568.53			0.564222
$343$	2738.93	+	5731.66i	0.431161	+	0.902275i
$344$	15314.7			2.40033
$345$	675.467	−	1169.94i	0.105408	−	0.182573i
$346$	1695.19	+	2936.15i	0.263393	+	0.456210i
$347$	−4948.72	−	8571.44i	−0.765595	−	1.32605i	−0.939932	−	0.341363i	$-0.889111\pi$
$347$	−4948.72	−	8571.44i	−0.765595	−	1.32605i	0.174337	−	0.984686i	$-0.444222\pi$
$348$	−5781.80	+	10014.4i	−0.890624	+	1.54261i
$349$	11832.6			1.81486			0.907431	−	0.420201i	$-0.138040\pi$
$349$	11832.6			1.81486			0.907431	+	0.420201i	$0.138040\pi$
$350$	−349.979	−	2337.93i	−0.0534490	−	0.357050i
$351$	1915.01			0.291213
$352$	3886.12	−	6730.95i	0.588440	−	1.01921i
$353$	−3503.69	−	6068.57i	−0.528279	−	0.915007i	−0.999456	−	0.0329681i	$-0.989504\pi$
$353$	−3503.69	−	6068.57i	−0.528279	−	0.915007i	0.471177	−	0.882039i	$-0.343829\pi$
$354$	179.821	+	311.459i	0.0269982	+	0.0467623i
$355$	1581.22	−	2738.75i	0.236401	−	0.409458i
$356$	18136.0			2.70002
$357$	1172.03	+	461.352i	0.173755	+	0.0683959i
$358$	−1710.41			−0.252508
$359$	−1407.19	+	2437.33i	−0.206877	+	0.358322i	−0.950729	−	0.310023i	$-0.899663\pi$
$359$	−1407.19	+	2437.33i	−0.206877	+	0.358322i	0.743852	+	0.668344i	$0.232997\pi$
$360$	−1156.62	−	2003.33i	−0.169332	−	0.293291i
$361$	414.057	+	717.169i	0.0603670	+	0.104559i
$362$	−3128.73	+	5419.13i	−0.454261	+	0.786804i
$363$	985.124			0.142440
$364$	−18570.8	+	14779.2i	−2.67411	+	2.12813i
$365$	4574.36			0.655981
$366$	6698.39	−	11602.0i	0.956641	−	1.65695i
$367$	−1174.93	−	2035.03i	−0.167114	−	0.289449i	0.770290	−	0.637694i	$-0.220111\pi$
$367$	−1174.93	−	2035.03i	−0.167114	−	0.289449i	−0.937404	+	0.348244i	$0.886778\pi$
$368$	5309.87	+	9196.96i	0.752163	+	1.30278i
$369$	−1120.51	+	1940.77i	−0.158079	+	0.273801i
$370$	−9060.91			−1.27312
$371$	1484.97	−	1181.78i	0.207806	−	0.165378i
$372$	−9525.34			−1.32760
$373$	829.650	−	1437.00i	0.115168	−	0.199477i	−0.802679	−	0.596411i	$-0.796593\pi$
$373$	829.650	−	1437.00i	0.115168	−	0.199477i	0.917847	+	0.396935i	$0.129926\pi$
$374$	2357.50	+	4083.31i	0.325945	+	0.564553i
$375$	−187.500	−	324.760i	−0.0258199	−	0.0447214i
$376$	−4337.87	+	7513.42i	−0.594970	+	1.03052i
$377$	15130.8			2.06705
$378$	2375.67	+	935.142i	0.323257	+	0.127245i
$379$	5327.80			0.722087			0.361043	−	0.932549i	$-0.382421\pi$
$379$	5327.80			0.722087			0.361043	+	0.932549i	$0.382421\pi$
$380$	−3507.89	+	6075.85i	−0.473556	+	0.820223i
$381$	−648.127	−	1122.59i	−0.0871510	−	0.150950i
$382$	4037.07	+	6992.42i	0.540719	+	0.936553i
$383$	−3119.88	+	5403.78i	−0.416235	+	0.720941i	−0.995557	−	0.0941580i	$-0.969984\pi$
$383$	−3119.88	+	5403.78i	−0.416235	+	0.720941i	0.579322	+	0.815099i	$0.303317\pi$
$384$	−4106.86			−0.545774
$385$	558.455	+	3730.59i	0.0739260	+	0.493840i
$386$	−19884.8			−2.62205
$387$	−1340.64	+	2322.06i	−0.176095	+	0.305005i
$388$	5778.41	+	10008.5i	0.756067	+	1.30955i
$389$	−4742.61	−	8214.43i	−0.618148	−	1.07066i	−0.989823	−	0.142301i	$-0.954550\pi$
$389$	−4742.61	−	8214.43i	−0.618148	−	1.07066i	0.371675	−	0.928363i	$-0.378784\pi$
$390$	−2715.97	+	4704.19i	−0.352637	+	0.610784i
$391$	−2041.72			−0.264077
$392$	−16859.2	+	5163.22i	−2.17224	+	0.665260i
$393$	−1972.50			−0.253179
$394$	−2537.17	+	4394.51i	−0.324419	+	0.561910i
$395$	1302.22	+	2255.50i	0.165877	+	0.287308i
$396$	3312.08	+	5736.69i	0.420299	+	0.727978i
$397$	−3946.37	+	6835.31i	−0.498898	+	0.864117i	−0.999999	−	0.00127185i	$-0.999595\pi$
$397$	−3946.37	+	6835.31i	−0.498898	+	0.864117i	0.501101	+	0.865389i	$0.332928\pi$
$398$	−15725.0			−1.98046
$399$	−638.790	−	4267.23i	−0.0801491	−	0.535411i
$400$	2947.89			0.368486
$401$	6229.83	−	10790.4i	0.775817	−	1.34375i	−0.158517	−	0.987356i	$-0.550671\pi$
$401$	6229.83	−	10790.4i	0.775817	−	1.34375i	0.934334	−	0.356398i	$-0.115995\pi$
$402$	6209.34	+	10754.9i	0.770383	+	1.33434i
$403$	6231.90	+	10794.0i	0.770305	+	1.33421i
$404$	5726.45	−	9918.50i	0.705202	−	1.22145i
$405$	405.000			0.0496904
$406$	18770.6	+	7388.73i	2.29450	+	0.903193i
$407$	14458.3			1.76087
$408$	−1748.05	+	3027.71i	−0.212111	+	0.367387i
$409$	−1701.81	−	2947.62i	−0.205744	−	0.356358i	0.744626	−	0.667482i	$-0.232628\pi$
$409$	−1701.81	−	2947.62i	−0.205744	−	0.356358i	−0.950369	+	0.311124i	$0.899295\pi$
$410$	−3178.32	−	5505.01i	−0.382844	−	0.663105i
$411$	−438.773	+	759.977i	−0.0526595	+	0.0912090i
$412$	−7002.86			−0.837393
$413$	340.253	−	270.783i	0.0405393	−	0.0322623i
$414$	−4138.48			−0.491293
$415$	2569.17	−	4449.94i	0.303894	−	0.526359i
$416$	−6766.29	−	11719.6i	−0.797463	−	1.38125i
$417$	2509.53	+	4346.63i	0.294706	+	0.510445i
$418$	8075.86	−	13987.8i	0.944983	−	1.63676i
$419$	−1376.83			−0.160532			−0.0802658	−	0.996773i	$-0.525577\pi$
$419$	−1376.83			−0.160532			−0.0802658	+	0.996773i	$0.525577\pi$
$420$	−3927.50	+	3125.61i	−0.456291	+	0.363129i
$421$	−15757.3			−1.82414			−0.912069	−	0.410036i	$-0.865516\pi$
$421$	−15757.3			−1.82414			−0.912069	+	0.410036i	$0.865516\pi$
$422$	−5398.57	+	9350.60i	−0.622745	+	1.07863i
$423$	−759.469	−	1315.44i	−0.0872970	−	0.151203i
$424$	2633.84	+	4561.95i	0.301676	+	0.522519i
$425$	−283.376	+	490.822i	−0.0323430	+	0.0560196i
$426$	−9687.88			−1.10183
$427$	−15072.6	−	5933.09i	−1.70823	−	0.672418i
$428$	2506.61			0.283088
$429$	4333.82	−	7506.39i	0.487736	−	0.844783i
$430$	−3802.73	−	6586.52i	−0.426474	−	0.738675i
$431$	−2541.85	−	4402.62i	−0.284076	−	0.492034i	0.688309	−	0.725418i	$-0.258353\pi$
$431$	−2541.85	−	4402.62i	−0.284076	−	0.492034i	−0.972385	+	0.233384i	$0.925020\pi$
$432$	−1591.86	+	2757.18i	−0.177288	+	0.307072i
$433$	4631.44			0.514025			0.257013	−	0.966408i	$-0.417262\pi$
$433$	4631.44			0.514025			0.257013	+	0.966408i	$0.417262\pi$
$434$	2460.06	+	16433.6i	0.272089	+	1.81760i
$435$	3199.98			0.352706
$436$	15475.2	−	26803.8i	1.69983	−	2.94420i
$437$	3497.06	+	6057.09i	0.382808	+	0.663043i
$438$	−7006.60	−	12135.8i	−0.764357	−	1.32391i
$439$	1169.44	−	2025.52i	0.127139	−	0.220212i	−0.795428	−	0.606048i	$-0.792754\pi$
$439$	1169.44	−	2025.52i	0.127139	−	0.220212i	0.922567	+	0.385837i	$0.126087\pi$
$440$	−10470.1			−1.13442
$441$	692.980	−	3008.21i	0.0748277	−	0.324826i
$442$	8209.49			0.883451
$443$	−5905.74	+	10229.0i	−0.633387	+	1.09706i	0.353468	+	0.935447i	$0.385002\pi$
$443$	−5905.74	+	10229.0i	−0.633387	+	1.09706i	−0.986854	+	0.161612i	$0.948331\pi$
$444$	9619.52	+	16661.5i	1.02820	+	1.78090i
$445$	−2509.38	−	4346.37i	−0.267316	−	0.463006i
$446$	−6582.37	+	11401.0i	−0.698844	+	1.21043i
$447$	7563.02			0.800265
$448$	−84.5435	−	564.766i	−0.00891586	−	0.0595596i
$449$	9582.29			1.00716			0.503582	−	0.863948i	$-0.332015\pi$
$449$	9582.29			1.00716			0.503582	+	0.863948i	$0.332015\pi$
$450$	−574.392	+	994.876i	−0.0601713	+	0.104220i
$451$	5071.59	+	8784.25i	0.529516	+	0.917149i
$452$	−18821.3	−	32599.4i	−1.95858	−	3.39236i
$453$	−2068.98	+	3583.58i	−0.214590	+	0.371680i
$454$	14938.9			1.54431
$455$	6111.43	+	2405.66i	0.629689	+	0.247866i
$456$	11976.3			1.22991
$457$	3285.97	−	5691.47i	0.336349	−	0.582573i	−0.647394	−	0.762155i	$-0.724141\pi$
$457$	3285.97	−	5691.47i	0.336349	−	0.582573i	0.983743	+	0.179582i	$0.0574746\pi$
$458$	2675.08	+	4633.37i	0.272922	+	0.472714i
$459$	−306.046	−	530.087i	−0.0311220	−	0.0539049i
$460$	4068.17	−	7046.27i	0.412346	−	0.714204i
$461$	−4197.59			−0.424081			−0.212041	−	0.977261i	$-0.568011\pi$
$461$	−4197.59			−0.424081			−0.212041	+	0.977261i	$0.568011\pi$
$462$	9041.86	−	7195.77i	0.910531	−	0.724626i
$463$	−6125.75			−0.614876			−0.307438	−	0.951568i	$-0.599472\pi$
$463$	−6125.75			−0.614876			−0.307438	+	0.951568i	$0.599472\pi$
$464$	−12577.6	+	21785.0i	−1.25840	+	2.17962i
$465$	1317.97	+	2282.79i	0.131439	+	0.227659i
$466$	9879.51	+	17111.8i	0.982101	+	1.70105i
$467$	−1614.04	+	2795.60i	−0.159934	+	0.277013i	−0.934845	−	0.355057i	$-0.884461\pi$
$467$	−1614.04	+	2795.60i	−0.159934	+	0.277013i	0.774911	+	0.632070i	$0.217795\pi$
$468$	11533.6			1.13919
$469$	11749.2	−	9350.31i	1.15677	−	0.920591i
$470$	4308.47			0.422840
$471$	−2989.10	+	5177.27i	−0.292421	+	0.506488i
$472$	603.494	+	1045.28i	0.0588518	+	0.101934i
$473$	6067.95	+	10510.0i	0.589862	+	1.02167i
$474$	3989.24	−	6909.57i	0.386565	−	0.669550i
$475$	1941.47			0.187538
$476$	7058.87	+	2778.60i	0.679711	+	0.267557i
$477$	−922.259			−0.0885269
$478$	15472.3	−	26798.7i	1.48051	−	2.56432i
$479$	−1563.15	−	2707.46i	−0.149107	−	0.258261i	0.781791	−	0.623541i	$-0.214307\pi$
$479$	−1563.15	−	2707.46i	−0.149107	−	0.258261i	−0.930898	+	0.365280i	$0.880973\pi$
$480$	−1430.98	−	2478.54i	−0.136073	−	0.235686i
$481$	12587.0	−	21801.4i	1.19318	−	2.06665i
$482$	−21362.9			−2.01878
$483$	740.815	+	4948.79i	0.0697894	+	0.466206i
$484$	5933.15			0.557208
$485$	1599.05	−	2769.64i	0.149710	−	0.259305i
$486$	−620.343	−	1074.47i	−0.0578999	−	0.100286i
$487$	434.519	+	752.609i	0.0404311	+	0.0700286i	0.885533	−	0.464577i	$-0.153794\pi$
$487$	434.519	+	752.609i	0.0404311	+	0.0700286i	−0.845102	+	0.534605i	$0.820460\pi$
$488$	22480.3	−	38937.1i	2.08532	−	3.61188i
$489$	5708.83			0.527939
$490$	6406.81	+	5968.70i	0.590674	+	0.550282i
$491$	6617.71			0.608254			0.304127	−	0.952631i	$-0.401635\pi$
$491$	6617.71			0.608254			0.304127	+	0.952631i	$0.401635\pi$
$492$	−6748.53	+	11688.8i	−0.618388	+	1.07108i
$493$	−2418.13	−	4188.32i	−0.220907	−	0.382622i
$494$	−14061.2	−	24354.8i	−1.28066	−	2.21816i
$495$	916.547	−	1587.51i	0.0832237	−	0.144148i
$496$	−20721.2			−1.87582
$497$	1734.19	+	11584.7i	0.156518	+	1.04557i
$498$	−15740.9			−1.41640
$499$	444.077	−	769.164i	0.0398389	−	0.0690030i	−0.845418	−	0.534105i	$-0.820649\pi$
$499$	444.077	−	769.164i	0.0398389	−	0.0690030i	0.885257	+	0.465102i	$0.153982\pi$
$500$	−1129.27	−	1955.94i	−0.101005	−	0.174945i
$501$	567.275	+	982.550i	0.0505868	+	0.0876189i
$502$	6718.21	−	11636.3i	0.597308	−	1.03457i
$503$	−10757.4			−0.953572			−0.476786	−	0.879019i	$-0.658198\pi$
$503$	−10757.4			−0.953572			−0.476786	+	0.879019i	$0.658198\pi$
$504$	7972.93	+	3138.41i	0.704648	+	0.277373i
$505$	−3169.35			−0.279275
$506$	−9365.71	+	16221.9i	−0.822839	+	1.42520i
$507$	−4250.30	−	7361.74i	−0.372313	−	0.644865i
$508$	−3903.50	−	6761.07i	−0.340925	−	0.590500i
$509$	−4430.01	+	7673.01i	−0.385770	+	0.668173i	−0.991876	−	0.127211i	$-0.959397\pi$
$509$	−4430.01	+	7673.01i	−0.385770	+	0.668173i	0.606106	+	0.795384i	$0.292731\pi$
$510$	1736.20			0.150746
$511$	−13257.7	+	10550.9i	−1.14772	+	0.913391i
$512$	−25994.0			−2.24372
$513$	−1048.39	+	1815.87i	−0.0902294	+	0.156282i
$514$	−8395.74	−	14541.8i	−0.720467	−	1.24789i
$515$	968.946	+	1678.26i	0.0829065	+	0.143598i
$516$	−8074.34	+	13985.2i	−0.688862	+	1.19314i
$517$	−6874.95			−0.584835
$518$	26261.0	−	20899.2i	2.22749	−	1.77270i
$519$	−1992.11			−0.168485
$520$	−9115.00	+	15787.6i	−0.768691	+	1.33141i
$521$	37.6937	+	65.2875i	0.00316966	+	0.00549001i	0.867606	−	0.497252i	$-0.165658\pi$
$521$	37.6937	+	65.2875i	0.00316966	+	0.00549001i	−0.864436	+	0.502742i	$0.832324\pi$
$522$	−4901.45	−	8489.56i	−0.410978	−	0.711835i
$523$	−4333.30	+	7505.49i	−0.362298	+	0.627518i	−0.988339	−	0.152272i	$-0.951341\pi$
$523$	−4333.30	+	7505.49i	−0.362298	+	0.627518i	0.626041	+	0.779790i	$0.284674\pi$
$524$	−11879.9			−0.990408
$525$	1292.49	+	508.767i	0.107446	+	0.0422941i
$526$	−27616.2			−2.28921
$527$	1991.89	−	3450.06i	0.164646	−	0.285175i
$528$	7205.01	+	12479.4i	0.593859	+	1.02859i
$529$	2027.90	+	3512.42i	0.166672	+	0.288684i
$530$	1308.00	−	2265.51i	0.107199	−	0.185675i
$531$	−211.318			−0.0172701
$532$	−3847.27	−	25700.5i	−0.313534	−	2.09447i
$533$	17660.7			1.43522
$534$	−7687.28	+	13314.8i	−0.622961	+	1.07900i
$535$	−346.825	−	600.719i	−0.0280272	−	0.0485445i
$536$	20839.1	+	36094.3i	1.67931	+	2.90865i
$537$	502.499	−	870.354i	0.0403807	−	0.0699414i
$538$	2756.00			0.220854
$539$	−10223.2	−	9524.14i	−0.816968	−	0.761102i
$540$	2439.21			0.194383
$541$	−6142.38	+	10638.9i	−0.488136	+	0.845477i	−0.999907	−	0.0136455i	$-0.995656\pi$
$541$	−6142.38	+	10638.9i	−0.488136	+	0.845477i	0.511771	+	0.859122i	$0.328990\pi$
$542$	−10444.1	−	18089.7i	−0.827697	−	1.43361i
$543$	−1838.37	−	3184.16i	−0.145290	−	0.251649i
$544$	−2162.70	+	3745.91i	−0.170451	+	0.295229i
$545$	−8564.85			−0.673171
$546$	−2978.72	−	19898.4i	−0.233476	−	1.55966i
$547$	−2906.85			−0.227218			−0.113609	−	0.993526i	$-0.536241\pi$
$547$	−2906.85			−0.227218			−0.113609	+	0.993526i	$0.536241\pi$
$548$	−2642.62	+	4577.15i	−0.205998	+	0.356800i
$549$	3935.83	+	6817.05i	0.305969	+	0.529954i
$550$	2599.79	+	4502.97i	0.201555	+	0.349104i
$551$	−8283.55	+	14347.5i	−0.640456	+	1.10930i
$552$	−13889.1			−1.07094
$553$	−8976.54	−	3533.46i	−0.690274	−	0.271715i
$554$	15783.5			1.21042
$555$	2662.00	−	4610.71i	0.203595	−	0.352637i
$556$	15114.3	+	26178.7i	1.15286	+	1.99680i
$557$	−1936.91	−	3354.83i	−0.147342	−	0.255204i	0.782902	−	0.622145i	$-0.213738\pi$
$557$	−1936.91	−	3354.83i	−0.147342	−	0.255204i	−0.930244	+	0.366941i	$0.880405\pi$
$558$	4037.49	−	6993.14i	0.306309	−	0.530543i
$559$	21130.4			1.59878
$560$	−8543.77	+	6799.37i	−0.644714	+	0.513082i
$561$	−2770.43			−0.208498
$562$	−18420.7	+	31905.6i	−1.38262	+	2.39476i
$563$	2730.54	+	4729.44i	0.204403	+	0.354036i	0.949942	−	0.312426i	$-0.101141\pi$
$563$	2730.54	+	4729.44i	0.204403	+	0.354036i	−0.745540	+	0.666461i	$0.767808\pi$
$564$	−4574.09	−	7922.55i	−0.341496	−	0.591489i
$565$	−5208.38	+	9021.18i	−0.387820	+	0.671724i
$566$	15137.0			1.12412
$567$	−1173.80	+	934.142i	−0.0869399	+	0.0691892i
$568$	−32513.3			−2.40181
$569$	−6552.48	+	11349.2i	−0.482767	+	0.836177i	−0.999804	−	0.0197860i	$-0.993701\pi$
$569$	−6552.48	+	11349.2i	−0.482767	+	0.836177i	0.517037	+	0.855963i	$0.327035\pi$
$570$	−2973.77	−	5150.72i	−0.218522	−	0.378491i
$571$	−1719.63	−	2978.49i	−0.126032	−	0.218294i	0.796104	−	0.605160i	$-0.206891\pi$
$571$	−1719.63	−	2978.49i	−0.126032	−	0.218294i	−0.922136	+	0.386866i	$0.873558\pi$
$572$	26101.5	−	45209.1i	1.90797	−	3.30470i
$573$	−4744.19			−0.345884
$574$	21909.1	+	8624.13i	1.59315	+	0.627115i
$575$	−2251.56			−0.163298
$576$	−138.754	+	240.330i	−0.0100372	+	0.0173850i
$577$	−8896.09	−	15408.5i	−0.641853	−	1.11172i	−0.985019	−	0.172447i	$-0.944833\pi$
$577$	−8896.09	−	15408.5i	−0.641853	−	1.11172i	0.343166	−	0.939275i	$-0.388501\pi$
$578$	11230.2	+	19451.2i	0.808155	+	1.39977i
$579$	5841.94	−	10118.5i	0.419314	−	0.726273i
$580$	19272.7			1.37975
$581$	2817.73	+	18823.0i	0.201204	+	1.34408i
$582$	−9797.14			−0.697774
$583$	−2087.15	+	3615.04i	−0.148269	+	0.256809i
$584$	−23514.7	−	40728.7i	−1.66617	−	2.88590i
$585$	−1595.84	−	2764.08i	−0.112786	−	0.195351i
$586$	20229.1	−	35037.8i	1.42603	−	2.46996i
$587$	14416.6			1.01369			0.506846	−	0.862037i	$-0.330811\pi$
$587$	14416.6			1.01369			0.506846	+	0.862037i	$0.330811\pi$
$588$	4173.64	−	18117.7i	0.292718	−	1.27068i
$589$	−13646.9			−0.954686
$590$	299.702	−	519.098i	0.0209127	−	0.0362219i
$591$	−1490.79	−	2582.12i	−0.103761	−	0.179719i
$592$	20926.0	+	36245.0i	1.45280	+	2.51631i
$593$	−4086.02	+	7077.19i	−0.282955	+	0.490093i	−0.972111	−	0.234520i	$-0.924648\pi$
$593$	−4086.02	+	7077.19i	−0.282955	+	0.490093i	0.689156	+	0.724613i	$0.257982\pi$
$594$	−5615.54			−0.387893
$595$	−310.792	−	2076.15i	−0.0214138	−	0.143048i
$596$	45550.2			3.13055
$597$	4619.82	−	8001.77i	0.316711	−	0.548560i
$598$	16307.1	+	28244.7i	1.11513	+	1.93145i
$599$	1246.09	+	2158.29i	0.0849980	+	0.147221i	0.905390	−	0.424580i	$-0.139578\pi$
$599$	1246.09	+	2158.29i	0.0849980	+	0.147221i	−0.820392	+	0.571801i	$0.806245\pi$
$600$	−1927.71	+	3338.89i	−0.131164	+	0.227182i
$601$	−13835.4			−0.939031			−0.469516	−	0.882924i	$-0.655571\pi$
$601$	−13835.4			−0.939031			−0.469516	+	0.882924i	$0.655571\pi$
$602$	26213.3	+	10318.4i	1.77471	+	0.698584i
$603$	−7296.94			−0.492794
$604$	−12460.9	+	21583.0i	−0.839452	+	1.45397i
$605$	−820.937	−	1421.90i	−0.0551666	−	0.0955514i
$606$	4854.52	+	8408.28i	0.325415	+	0.563636i
$607$	−3667.95	+	6353.08i	−0.245268	+	0.424816i	−0.962207	−	0.272320i	$-0.912209\pi$
$607$	−3667.95	+	6353.08i	−0.245268	+	0.424816i	0.716939	+	0.697136i	$0.245543\pi$
$608$	14817.1			0.988345
$609$	−9274.40	+	7380.83i	−0.617106	+	0.491110i
$610$	−22328.0			−1.48202
$611$	−5985.14	+	10366.6i	−0.396289	+	0.686394i
$612$	−1843.24	−	3192.58i	−0.121746	−	0.210870i
$613$	−3006.02	−	5206.58i	−0.198062	−	0.343054i	0.749838	−	0.661622i	$-0.230131\pi$
$613$	−3006.02	−	5206.58i	−0.198062	−	0.343054i	−0.947900	+	0.318568i	$0.896798\pi$
$614$	10382.5	−	17983.0i	0.682414	−	1.18198i
$615$	3735.02			0.244895
$616$	30345.2	−	24149.6i	1.98481	−	1.57957i
$617$	−22927.4			−1.49598			−0.747991	−	0.663708i	$-0.768982\pi$
$617$	−22927.4			−1.49598			−0.747991	+	0.663708i	$0.768982\pi$
$618$	2968.29	−	5141.23i	0.193207	−	0.334645i
$619$	−8960.76	−	15520.5i	−0.581847	−	1.00779i	−0.995260	−	0.0972452i	$-0.968997\pi$
$619$	−8960.76	−	15520.5i	−0.581847	−	1.00779i	0.413413	−	0.910543i	$-0.364336\pi$
$620$	7937.78	+	13748.6i	0.514176	+	0.890578i
$621$	1215.84	−	2105.90i	0.0785668	−	0.136082i
$622$	39071.8			2.51871
$623$	17297.8	+	6809.00i	1.11240	+	0.437876i
$624$	25089.9			1.60962
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−4651.61	−	8056.82i	−0.296990	−	0.514402i
$627$	4745.19	+	8218.92i	0.302241	+	0.523496i
$628$	−18002.6	+	31181.4i	−1.14392	+	1.98132i
$629$	−8046.35			−0.510062
$630$	−629.962	−	4208.27i	−0.0398386	−	0.266129i
$631$	19270.7			1.21578			0.607888	−	0.794023i	$-0.292017\pi$
$631$	19270.7			1.21578			0.607888	+	0.794023i	$0.292017\pi$
$632$	13388.2	−	23189.1i	0.842650	−	1.45951i
$633$	−3172.08	−	5494.20i	−0.199177	−	0.344984i
$634$	−8038.57	−	13923.2i	−0.503553	−	0.872179i
$635$	−1080.21	+	1870.98i	−0.0675069	+	0.116925i
$636$	−5554.53			−0.346308
$637$	−23261.3	+	7123.90i	−1.44685	+	0.443107i
$638$	−44369.5			−2.75330
$639$	2846.19	−	4929.75i	0.176203	−	0.305192i
$640$	3422.38	+	5927.74i	0.211377	+	0.366116i
$641$	−14119.3	−	24455.3i	−0.870013	−	1.50691i	−0.861982	−	0.506939i	$-0.830777\pi$
$641$	−14119.3	−	24455.3i	−0.870013	−	1.50691i	−0.00803063	−	0.999968i	$-0.502556\pi$
$642$	−1062.47	+	1840.26i	−0.0653153	+	0.113129i
$643$	−19055.3			−1.16869			−0.584346	−	0.811505i	$-0.698649\pi$
$643$	−19055.3			−1.16869			−0.584346	+	0.811505i	$0.698649\pi$
$644$	4461.74	+	29805.3i	0.273008	+	1.82375i
$645$	4468.80			0.272804
$646$	−4494.38	+	7784.49i	−0.273729	+	0.474112i
$647$	8105.65	+	14039.4i	0.492529	+	0.853084i	0.999963	−	0.00860593i	$-0.00273939\pi$
$647$	8105.65	+	14039.4i	0.492529	+	0.853084i	−0.507434	+	0.861690i	$0.669406\pi$
$648$	−2081.92	−	3606.00i	−0.126212	−	0.218606i
$649$	−478.228	+	828.316i	−0.0289247	+	0.0500990i
$650$	9053.22			0.546302
$651$	−9085.11	−	3576.20i	−0.546964	−	0.215303i
$652$	34382.9			2.06524
$653$	13266.0	−	22977.4i	0.795007	−	1.37699i	−0.127827	−	0.991796i	$-0.540800\pi$
$653$	13266.0	−	22977.4i	0.795007	−	1.37699i	0.922834	−	0.385197i	$-0.125866\pi$
$654$	13118.9	+	22722.6i	0.784387	+	1.35860i
$655$	1643.75	+	2847.06i	0.0980558	+	0.169838i
$656$	−14680.6	+	25427.5i	−0.873749	+	1.51338i
$657$	8233.85			0.488939
$658$	−12487.1	+	9937.58i	−0.739814	+	0.588765i
$659$	1883.19			0.111318			0.0556592	−	0.998450i	$-0.482274\pi$
$659$	1883.19			0.111318			0.0556592	+	0.998450i	$0.482274\pi$
$660$	5520.13	−	9561.15i	0.325562	−	0.563890i
$661$	−2337.13	−	4048.03i	−0.137525	−	0.238200i	0.789034	−	0.614349i	$-0.210581\pi$
$661$	−2337.13	−	4048.03i	−0.137525	−	0.238200i	−0.926559	+	0.376149i	$0.877248\pi$
$662$	14949.8	+	25893.8i	0.877706	+	1.52023i
$663$	−2411.86	+	4177.46i	−0.141280	+	0.244704i
$664$	−52827.9			−3.08753
$665$	−5626.90	+	4478.04i	−0.328123	+	0.261129i
$666$	−16309.6			−0.948928
$667$	9606.58	−	16639.1i	0.557673	−	0.965919i
$668$	3416.56	+	5917.65i	0.197890	+	0.342756i
$669$	−3867.65	−	6698.97i	−0.223516	−	0.387141i
$670$	10348.9	−	17924.8i	0.596736	−	1.03358i
$671$	35628.3			2.04980
$672$	9864.18	+	3882.87i	0.566248	+	0.222894i
$673$	−23344.3			−1.33709			−0.668543	−	0.743674i	$-0.733082\pi$
$673$	−23344.3			−1.33709			−0.668543	+	0.743674i	$0.733082\pi$
$674$	18037.7	−	31242.2i	1.03084	−	1.78547i
$675$	−337.500	−	584.567i	−0.0192450	−	0.0333333i
$676$	−25598.5	−	44337.9i	−1.45645	−	2.52264i
$677$	−699.747	+	1212.00i	−0.0397245	+	0.0688048i	−0.885204	−	0.465203i	$-0.845981\pi$
$677$	−699.747	+	1212.00i	−0.0397245	+	0.0688048i	0.845480	+	0.534008i	$0.179315\pi$
$678$	31911.0			1.80757
$679$	1753.75	+	11715.4i	0.0991205	+	0.662144i
$680$	5826.83			0.328601
$681$	−4388.89	+	7601.78i	−0.246964	+	0.427754i
$682$	−18274.3	−	31652.1i	−1.02604	−	1.77716i
$683$	−16510.3	−	28596.8i	−0.924964	−	1.60209i	−0.791618	−	0.611016i	$-0.790761\pi$
$683$	−16510.3	−	28596.8i	−0.924964	−	1.60209i	−0.133346	−	0.991070i	$-0.542572\pi$
$684$	−6314.21	+	10936.5i	−0.352968	+	0.611358i
$685$	1462.58			0.0815798
$686$	−32335.6	−	2521.44i	−1.79968	−	0.140334i
$687$	−3143.63			−0.174581
$688$	−17564.7	+	30422.9i	−0.973325	+	1.68585i
$689$	3634.02	+	6294.31i	0.200936	+	0.348032i
$690$	3448.73	+	5973.38i	0.190277	+	0.329569i
$691$	−360.088	+	623.691i	−0.0198240	+	0.0343362i	−0.875767	−	0.482734i	$-0.839644\pi$
$691$	−360.088	+	623.691i	−0.0198240	+	0.0343362i	0.855943	+	0.517070i	$0.172977\pi$
$692$	−11998.0			−0.659096
$693$	1005.22	+	6715.05i	0.0551012	+	0.368086i
$694$	50533.5			2.76401
$695$	4182.55	−	7244.39i	0.228278	−	0.395389i
$696$	−16449.7	−	28491.6i	−0.895866	−	1.55169i
$697$	−2822.44	−	4888.61i	−0.153382	−	0.265666i
$698$	−30207.0	+	52320.1i	−1.63804	+	2.83717i
$699$	−11610.0			−0.628224
$700$	7784.34	+	3064.18i	0.420315	+	0.165450i
$701$	11675.1			0.629048			0.314524	−	0.949249i	$-0.398155\pi$
$701$	11675.1			0.629048			0.314524	+	0.949249i	$0.398155\pi$
$702$	−4888.74	+	8467.54i	−0.262840	+	0.455252i
$703$	13781.8	+	23870.8i	0.739390	+	1.28066i
$704$	628.024	+	1087.77i	0.0336215	+	0.0582342i
$705$	−1265.78	+	2192.40i	−0.0676200	+	0.117121i
$706$	35777.6			1.90724
$707$	9185.61	−	7310.17i	0.488629	−	0.388864i
$708$	−1272.71			−0.0675586
$709$	13385.9	−	23185.0i	0.709050	−	1.22811i	−0.256159	−	0.966635i	$-0.582457\pi$
$709$	13385.9	−	23185.0i	0.709050	−	1.22811i	0.965210	−	0.261477i	$-0.0842095\pi$
$710$	8073.23	+	13983.2i	0.426736	+	0.739129i
$711$	2343.99	+	4059.91i	0.123638	+	0.214147i
$712$	−25799.1	+	44685.4i	−1.35796	+	2.35205i
$713$	15826.5			0.831288
$714$	−5031.98	+	4004.59i	−0.263749	+	0.209899i
$715$	−14446.1			−0.755597
$716$	3026.43	−	5241.92i	0.157965	−	0.273603i
$717$	9091.15	+	15746.3i	0.473522	+	0.820164i
$718$	−7184.72	−	12444.3i	−0.373442	−	0.646821i
$719$	−17391.7	+	30123.4i	−0.902089	+	1.56246i	−0.0773114	+	0.997007i	$0.524634\pi$
$719$	−17391.7	+	30123.4i	−0.902089	+	1.56246i	−0.824778	+	0.565457i	$0.808700\pi$
$720$	5306.20			0.274653
$721$	−6679.22	−	2629.16i	−0.345003	−	0.135805i
$722$	−4228.11			−0.217942
$723$	6276.18	−	10870.7i	0.322840	−	0.559176i
$724$	−11072.1	−	19177.4i	−0.568357	−	0.984422i
$725$	−2666.65	−	4618.77i	−0.136603	−	0.236603i
$726$	−2514.88	+	4355.90i	−0.128562	+	0.222676i
$727$	25368.1			1.29415			0.647077	−	0.762425i	$-0.275991\pi$
$727$	25368.1			1.29415			0.647077	+	0.762425i	$0.275991\pi$
$728$	−9996.84	−	66780.8i	−0.508939	−	3.39981i
$729$	729.000			0.0370370
$730$	−11677.7	+	20226.3i	−0.592068	+	1.02549i
$731$	−3376.94	−	5849.02i	−0.170863	−	0.295943i
$732$	23704.5	+	41057.4i	1.19692	+	2.07312i
$733$	−15845.8	+	27445.7i	−0.798468	+	1.38299i	0.122146	+	0.992512i	$0.461022\pi$
$733$	−15845.8	+	27445.7i	−0.798468	+	1.38299i	−0.920614	+	0.390474i	$0.872311\pi$
$734$	11997.7			0.603327
$735$	−4919.47	+	1506.61i	−0.246881	+	0.0756086i
$736$	−17183.7			−0.860596
$737$	−16513.6	+	28602.3i	−0.825352	+	1.42955i
$738$	−5720.98	−	9909.02i	−0.285355	−	0.494249i
$739$	6597.98	+	11428.0i	0.328431	+	0.568860i	0.982201	−	0.187834i	$-0.0601467\pi$
$739$	6597.98	+	11428.0i	0.328431	+	0.568860i	−0.653770	+	0.756694i	$0.726813\pi$
$740$	16032.5	−	27769.2i	0.796443	−	1.37948i
$741$	16524.1			0.819203
$742$	1434.54	+	9582.99i	0.0709752	+	0.474128i
$743$	8244.34			0.407073			0.203537	−	0.979067i	$-0.434756\pi$
$743$	8244.34			0.407073			0.203537	+	0.979067i	$0.434756\pi$
$744$	13550.1	−	23469.5i	0.667705	−	1.15650i
$745$	−6302.52	−	10916.3i	−0.309941	−	0.536834i
$746$	4235.95	+	7336.88i	0.207894	+	0.360083i
$747$	4624.51	−	8009.89i	0.226509	−	0.392325i
$748$	−16685.6			−0.815622
$749$	2390.76	+	941.084i	0.116631	+	0.0459098i
$750$	1914.64			0.0932170
$751$	−15884.9	+	27513.4i	−0.771834	+	1.33686i	0.164722	+	0.986340i	$0.447327\pi$
$751$	−15884.9	+	27513.4i	−0.771834	+	1.33686i	−0.936557	+	0.350516i	$0.886006\pi$
$752$	−9950.35	−	17234.5i	−0.482516	−	0.835742i
$753$	3947.47	+	6837.22i	0.191041	+	0.330893i
$754$	−38626.8	+	66903.6i	−1.86566	+	3.23141i
$755$	6896.60			0.332441
$756$	−7069.49	+	5626.10i	−0.340099	+	0.270660i
$757$	−3019.09			−0.144954			−0.0724772	−	0.997370i	$-0.523090\pi$
$757$	−3019.09			−0.144954			−0.0724772	+	0.997370i	$0.523090\pi$
$758$	−13601.1	+	23557.8i	−0.651734	+	1.12884i
$759$	−5503.08	−	9531.62i	−0.263174	−	0.455831i
$760$	−9980.22	−	17286.2i	−0.476343	−	0.825050i
$761$	−12048.2	+	20868.0i	−0.573910	+	0.994041i	0.422249	+	0.906480i	$0.361241\pi$
$761$	−12048.2	+	20868.0i	−0.573910	+	0.994041i	−0.996159	+	0.0875612i	$0.972093\pi$
$762$	6618.29			0.314640
$763$	24823.2	−	19755.0i	1.17780	−	0.937326i
$764$	−28573.1			−1.35306
$765$	−510.077	+	883.479i	−0.0241070	+	0.0417546i
$766$	−15929.2	−	27590.1i	−0.751363	−	1.30140i
$767$	832.665	+	1442.22i	0.0391992	+	0.0678950i
$768$	10854.2	−	18800.1i	0.509984	−	0.883318i
$769$	7954.16			0.372996			0.186498	−	0.982455i	$-0.440286\pi$
$769$	7954.16			0.372996			0.186498	+	0.982455i	$0.440286\pi$
$770$	−17921.1	−	7054.33i	−0.838741	−	0.330156i
$771$	9866.30			0.460864
$772$	35184.5	−	60941.4i	1.64031	−	2.84110i
$773$	−18119.7	−	31384.2i	−0.843105	−	1.46030i	−0.887257	−	0.461275i	$-0.847392\pi$
$773$	−18119.7	−	31384.2i	−0.843105	−	1.46030i	0.0441523	−	0.999025i	$-0.485941\pi$
$774$	−6844.92	−	11855.7i	−0.317875	−	0.550576i
$775$	2196.61	−	3804.64i	0.101812	−	0.176344i
$776$	−32880.0			−1.52104
$777$	2919.53	+	19503.0i	0.134798	+	0.900473i
$778$	48428.7			2.23169
$779$	−9668.57	+	16746.5i	−0.444689	+	0.770223i
$780$	−9611.35	−	16647.3i	−0.441207	−	0.764193i
$781$	−12882.3	−	22312.8i	−0.590224	−	1.02230i
$782$	5212.21	−	9027.81i	0.238348	−	0.412831i
$783$	5759.96			0.262892
$784$	9079.23	−	39412.8i	0.413595	−	1.79541i
$785$	9963.65			0.453017
$786$	5035.50	−	8721.74i	0.228512	−	0.395794i
$787$	4842.06	+	8386.70i	0.219315	+	0.379865i	0.954599	−	0.297895i	$-0.0962844\pi$
$787$	4842.06	+	8386.70i	0.219315	+	0.379865i	−0.735284	+	0.677759i	$0.762951\pi$
$788$	−8978.63	−	15551.4i	−0.405902	−	0.703042i
$789$	8113.34	−	14052.7i	0.366087	−	0.634081i
$790$	−13297.5			−0.598864
$791$	−5712.27	−	38159.0i	−0.256770	−	1.71527i
$792$	−18846.2			−0.845545
$793$	31017.0	−	53723.1i	1.38896	−	2.40575i
$794$	−20149.0	−	34899.1i	−0.900581	−	1.55985i
$795$	768.549	+	1331.17i	0.0342863	+	0.0593857i
$796$	27824.0	−	48192.6i	1.23894	−	2.14591i
$797$	6717.98			0.298573			0.149287	−	0.988794i	$-0.452302\pi$
$797$	6717.98			0.298573			0.149287	+	0.988794i	$0.452302\pi$
$798$	20499.0	+	8069.11i	0.909346	+	0.357949i
$799$	3826.05			0.169407
$800$	−2384.97	+	4130.90i	−0.105402	+	0.182562i
$801$	−4516.88	−	7823.46i	−0.199246	−	0.345104i
$802$	31807.7	+	55092.5i	1.40046	+	2.42567i
$803$	18633.8	−	32274.8i	0.818897	−	1.41837i
$804$	−43947.7			−1.92775
$805$	6525.61	−	5193.26i	0.285711	−	0.227377i
$806$	−63636.5			−2.78102
$807$	−809.683	+	1402.41i	−0.0353187	+	0.0611738i
$808$	16292.2	+	28218.9i	0.709353	+	1.22863i
$809$	605.364	+	1048.52i	0.0263083	+	0.0455674i	0.878880	−	0.477043i	$-0.158291\pi$
$809$	605.364	+	1048.52i	0.0263083	+	0.0455674i	−0.852571	+	0.522611i	$0.824958\pi$
$810$	−1033.91	+	1790.78i	−0.0448491	+	0.0776809i
$811$	34825.1			1.50786			0.753930	−	0.656955i	$-0.228156\pi$
$811$	34825.1			1.50786			0.753930	+	0.656955i	$0.228156\pi$
$812$	−55857.4	+	44452.9i	−2.41405	+	1.92117i
$813$	12273.4			0.529456
$814$	−36910.0	+	63930.0i	−1.58931	+	2.75276i
$815$	−4757.36	−	8239.99i	−0.204470	−	0.354152i
$816$	−4009.73	−	6945.06i	−0.172020	−	0.297948i
$817$	−11568.1	+	20036.5i	−0.495367	+	0.858001i
$818$	17377.9			0.742792
$819$	11000.6	+	4330.19i	0.469342	+	0.184749i
$820$	22495.1			0.958003
$821$	−15084.8	+	26127.7i	−0.641247	+	1.11067i	0.343908	+	0.939003i	$0.388249\pi$
$821$	−15084.8	+	26127.7i	−0.641247	+	1.11067i	−0.985155	+	0.171669i	$0.945084\pi$
$822$	−2240.25	−	3880.22i	−0.0950579	−	0.164645i
$823$	13008.2	+	22530.8i	0.550956	+	0.954284i	0.998206	+	0.0598746i	$0.0190701\pi$
$823$	13008.2	+	22530.8i	0.550956	+	0.954284i	−0.447250	+	0.894409i	$0.647597\pi$
$824$	9961.83	−	17254.4i	0.421161	−	0.729472i
$825$	−3055.16			−0.128930
$826$	328.696	+	2195.75i	0.0138460	+	0.0924940i
$827$	15602.4			0.656045			0.328022	−	0.944670i	$-0.393618\pi$
$827$	15602.4			0.656045			0.328022	+	0.944670i	$0.393618\pi$
$828$	7322.70	−	12683.3i	0.307345	−	0.532336i
$829$	9753.00	+	16892.7i	0.408607	+	0.707729i	0.994734	−	0.102491i	$-0.0326812\pi$
$829$	9753.00	+	16892.7i	0.408607	+	0.707729i	−0.586126	+	0.810220i	$0.699348\pi$
$830$	13117.5	+	22720.1i	0.548570	+	0.950152i
$831$	−4637.00	+	8031.53i	−0.193569	+	0.335271i
$832$	2186.96			0.0911289
$833$	5689.43	+	5300.38i	0.236647	+	0.220465i
$834$	−25625.8			−1.06397
$835$	945.459	−	1637.58i	0.0391844	−	0.0678693i
$836$	28579.1	+	49500.5i	1.18233	+	2.04786i
$837$	2372.34	+	4109.01i	0.0979690	+	0.169687i
$838$	3514.86	−	6087.91i	0.144891	−	0.250959i
$839$	−12231.2			−0.503300			−0.251650	−	0.967818i	$-0.580973\pi$
$839$	−12231.2			−0.503300			−0.251650	+	0.967818i	$0.580973\pi$
$840$	−2114.20	−	14123.3i	−0.0868417	−	0.580118i
$841$	21121.6			0.866028
$842$	40226.0	−	69673.5i	1.64641	−	2.85167i
$843$	−10823.6	−	18747.0i	−0.442212	−	0.765933i
$844$	−19104.6	−	33090.2i	−0.779157	−	1.34954i
$845$	−7083.84	+	12269.6i	−0.288392	+	0.499510i
$846$	7755.25			0.315167
$847$	5658.95	+	2227.55i	0.229568	+	0.0903654i
$848$	−12083.2			−0.489314
$849$	−4447.07	+	7702.56i	−0.179768	+	0.311368i
$850$	−1446.83	−	2505.99i	−0.0583836	−	0.101123i
$851$	−15983.0	−	27683.4i	−0.643820	−	1.11513i
$852$	17141.9	−	29690.6i	0.689286	−	1.19388i
$853$	1234.83			0.0495660			0.0247830	−	0.999693i	$-0.492111\pi$
$853$	1234.83			0.0495660			0.0247830	+	0.999693i	$0.492111\pi$
$854$	64712.4	−	51500.0i	2.59299	−	2.06357i
$855$	3494.64			0.139783
$856$	−3565.74	+	6176.05i	−0.142377	+	0.246604i
$857$	−12050.7	−	20872.4i	−0.480331	−	0.831958i	0.519414	−	0.854523i	$-0.326150\pi$
$857$	−12050.7	−	20872.4i	−0.480331	−	0.831958i	−0.999745	+	0.0225648i	$0.992817\pi$
$858$	22127.2	+	38325.4i	0.880431	+	1.52495i
$859$	−6681.47	+	11572.6i	−0.265389	+	0.459666i	−0.967665	−	0.252238i	$-0.918834\pi$
$859$	−6681.47	+	11572.6i	−0.265389	+	0.459666i	0.702277	+	0.711904i	$0.252167\pi$
$860$	26914.5			1.06718
$861$	−10825.1	+	8614.91i	−0.428476	+	0.340993i
$862$	25955.9			1.02559
$863$	10967.0	−	18995.5i	0.432587	−	0.749262i	−0.564508	−	0.825427i	$-0.690934\pi$
$863$	10967.0	−	18995.5i	0.432587	−	0.749262i	0.997095	+	0.0761649i	$0.0242675\pi$
$864$	−2575.77	−	4461.37i	−0.101423	−	0.175670i
$865$	1660.09	+	2875.36i	0.0652541	+	0.113023i
$866$	−11823.4	+	20478.7i	−0.463944	+	0.803574i
$867$	−13197.2			−0.516956
$868$	−54717.4	−	21538.6i	−2.13966	−	0.842243i
$869$	21218.5			0.828296
$870$	−8169.08	+	14149.3i	−0.318342	+	0.551385i
$871$	28752.5	+	49800.8i	1.11853	+	1.93735i
$872$	44028.1	+	76258.8i	1.70984	+	2.96152i
$873$	2878.29	−	4985.35i	0.111587	−	0.193274i
$874$	−35709.9			−1.38204
$875$	−342.733	−	2289.52i	−0.0132417	−	0.0884571i
$876$	49590.4			1.91268
$877$	385.159	−	667.115i	0.0148300	−	0.0256863i	−0.858515	−	0.512788i	$-0.828613\pi$
$877$	385.159	−	667.115i	0.0148300	−	0.0256863i	0.873345	+	0.487102i	$0.161946\pi$
$878$	5970.80	+	10341.7i	0.229504	+	0.397513i
$879$	11886.1	+	20587.4i	0.456097	+	0.789984i
$880$	12008.3	−	20799.1i	0.460001	−	0.796746i
$881$	17887.9			0.684064			0.342032	−	0.939688i	$-0.388885\pi$
$881$	17887.9			0.684064			0.342032	+	0.939688i	$0.388885\pi$
$882$	11532.3	+	10743.7i	0.440262	+	0.410156i
$883$	583.389			0.0222340			0.0111170	−	0.999938i	$-0.496461\pi$
$883$	583.389			0.0222340			0.0111170	+	0.999938i	$0.496461\pi$
$884$	−14526.0	+	25159.8i	−0.552672	+	0.957257i
$885$	176.098	+	305.011i	0.00668866	+	0.0115851i
$886$	−30153.0	−	52226.5i	−1.14335	−	1.98034i
$887$	21221.9	−	36757.4i	0.803340	−	1.39143i	−0.114067	−	0.993473i	$-0.536388\pi$
$887$	21221.9	−	36757.4i	0.803340	−	1.39143i	0.917406	−	0.397952i	$-0.130279\pi$
$888$	−54736.5			−2.06851
$889$	−1184.72	−	7914.14i	−0.0446953	−	0.298573i
$890$	25624.3			0.965087
$891$	1649.78	−	2857.51i	0.0620313	−	0.107441i
$892$	−23293.9	−	40346.2i	−0.874370	−	1.51445i
$893$	−6553.27	−	11350.6i	−0.245573	−	0.425345i
$894$	−19307.3	+	33441.2i	−0.722295	+	1.25105i
$895$	−1675.00			−0.0625575
$896$	−23591.4	−	9286.37i	−0.879614	−	0.346245i
$897$	−19163.3			−0.713317
$898$	−24462.2	+	42369.8i	−0.909036	+	1.57450i
$899$	18744.3	+	32466.1i	0.695392	+	1.20445i
$900$	−2032.68	−	3520.70i	−0.0752844	−	0.130396i
$901$	1161.54	−	2011.84i	0.0429483	−	0.0743887i
$902$	−51788.1			−1.91170
$903$	−12951.8	+	10307.4i	−0.477307	+	0.379854i
$904$	107096.			3.94021
$905$	−3063.96	+	5306.93i	−0.112541	+	0.194926i
$906$	−10563.6	−	18296.7i	−0.387365	−	0.670935i
$907$	13858.9	+	24004.3i	0.507362	+	0.878777i	0.999964	+	0.00852197i	$0.00271266\pi$
$907$	13858.9	+	24004.3i	0.507362	+	0.878777i	−0.492602	+	0.870255i	$0.663954\pi$
$908$	−26433.2	+	45783.6i	−0.966096	+	1.67333i
$909$	−5704.82			−0.208160
$910$	−26238.6	+	20881.4i	−0.955827	+	0.760674i
$911$	20446.7			0.743609			0.371805	−	0.928311i	$-0.378739\pi$
$911$	20446.7			0.743609			0.371805	+	0.928311i	$0.378739\pi$
$912$	−13735.8	+	23791.0i	−0.498724	+	0.863816i
$913$	−20931.3	−	36254.0i	−0.758734	−	1.31417i
$914$	16777.2	+	29059.0i	0.607156	+	1.05163i
$915$	6559.71	−	11361.8i	0.237003	−	0.410500i
$916$	−18933.3			−0.682941
$917$	−11330.8	−	4460.19i	−0.408044	−	0.160620i
$918$	3125.16			0.112359
$919$	−8727.76	+	15116.9i	−0.313278	+	0.542613i	−0.979070	−	0.203524i	$-0.934760\pi$
$919$	−8727.76	+	15116.9i	−0.313278	+	0.542613i	0.665792	+	0.746137i	$0.268094\pi$
$920$	11574.2	+	20047.2i	0.414773	+	0.718408i
$921$	6100.50	+	10566.4i	0.218261	+	0.378039i
$922$	10715.8	−	18560.4i	0.382763	−	0.662965i
$923$	−44859.9			−1.59976
$924$	6054.18	+	40443.1i	0.215550	+	1.43991i
$925$	−8873.32			−0.315409
$926$	15638.1	−	27086.0i	0.554969	−	0.961234i
$927$	1744.10	+	3020.87i	0.0617949	+	0.107032i
$928$	−20351.7	−	35250.1i	−0.719909	−	1.24692i
$929$	−10374.4	+	17969.0i	−0.366387	+	0.634600i	−0.988998	−	0.147931i	$-0.952739\pi$
$929$	−10374.4	+	17969.0i	−0.366387	+	0.634600i	0.622611	+	0.782531i	$0.286072\pi$
$930$	−13458.3			−0.474532
$931$	5979.55	−	25957.1i	0.210496	−	0.913760i
$932$	−69923.8			−2.45754
$933$	−11478.9	+	19882.0i	−0.402788	+	0.697650i
$934$	−8240.83	−	14273.5i	−0.288702	−	0.500047i
$935$	2308.69	+	3998.77i	0.0807510	+	0.139865i
$936$	−16407.0	+	28417.8i	−0.572948	+	0.992376i
$937$	12135.5			0.423106			0.211553	−	0.977366i	$-0.432148\pi$
$937$	12135.5			0.423106			0.211553	+	0.977366i	$0.432148\pi$
$938$	11350.1	+	75820.9i	0.395090	+	2.63928i
$939$	5466.36			0.189977
$940$	−7623.48	+	13204.3i	−0.264522	+	0.458165i
$941$	12633.0	+	21881.0i	0.437646	+	0.758025i	0.997507	−	0.0705612i	$-0.0224790\pi$
$941$	12633.0	+	21881.0i	0.437646	+	0.758025i	−0.559862	+	0.828586i	$0.689146\pi$
$942$	−15261.4	−	26433.6i	−0.527861	−	0.914282i
$943$	11212.8	−	19421.2i	0.387210	−	0.670668i
$944$	−2768.62			−0.0954566
$945$	2326.48	+	915.781i	0.0800852	+	0.0315242i
$946$	−61962.3			−2.12957
$947$	21384.4	−	37038.8i	0.733789	−	1.27096i	−0.221464	−	0.975169i	$-0.571083\pi$
$947$	21384.4	−	37038.8i	0.733789	−	1.27096i	0.955253	−	0.295791i	$-0.0955832\pi$
$948$	14117.3	+	24451.8i	0.483657	+	0.837719i
$949$	−32444.2	−	56195.0i	−1.10978	−	1.92220i
$950$	−4956.29	+	8584.54i	−0.169267	+	0.293178i
$951$	9446.57			0.322110
$952$	−16887.7	+	13439.7i	−0.574931	+	0.457546i
$953$	−25855.5			−0.878846			−0.439423	−	0.898280i	$-0.644817\pi$
$953$	−25855.5			−0.878846			−0.439423	+	0.898280i	$0.644817\pi$
$954$	2354.39	−	4077.93i	0.0799017	−	0.138394i
$955$	3953.49	+	6847.65i	0.133960	+	0.232026i
$956$	54753.7	+	94836.2i	1.85237	+	3.20839i
$957$	13035.3	−	22577.7i	0.440303	−	0.762627i
$958$	15962.0			0.538318
$959$	−4238.94	+	3373.47i	−0.142735	+	0.113592i
$960$	462.515			0.0155496
$961$	−544.820	+	943.655i	−0.0182881	+	0.0316758i
$962$	64265.7	+	111311.i	2.15385	+	3.73059i
$963$	−624.285	−	1081.29i	−0.0208902	−	0.0361830i
$964$	37799.8	−	65471.2i	1.26292	−	2.18743i
$965$	−19473.1			−0.649598
$966$	−23773.1	−	9357.88i	−0.791808	−	0.311682i
$967$	−20336.0			−0.676278			−0.338139	−	0.941096i	$-0.609797\pi$
$967$	−20336.0			−0.676278			−0.338139	+	0.941096i	$0.609797\pi$
$968$	−8440.13	+	14618.7i	−0.280244	+	0.485397i
$969$	−2640.80	−	4573.99i	−0.0875486	−	0.151639i
$970$	8164.28	+	14141.0i	0.270247	+	0.468081i
$971$	15561.9	−	26953.9i	0.514319	−	0.890827i	−0.485543	−	0.874213i	$-0.661378\pi$
$971$	15561.9	−	26953.9i	0.514319	−	0.890827i	0.999862	−	0.0166139i	$-0.00528862\pi$
$972$	4390.58			0.144885
$973$	4587.20	+	30643.3i	0.151140	+	1.00964i
$974$	−4437.05			−0.145967
$975$	−2659.73	+	4606.80i	−0.0873638	+	0.151319i
$976$	51566.1	+	89315.1i	1.69118	+	2.92921i
$977$	−15658.7	−	27121.6i	−0.512758	−	0.888123i	−0.999891	−	0.0147951i	$-0.995290\pi$
$977$	−15658.7	−	27121.6i	−0.512758	−	0.888123i	0.487132	−	0.873328i	$-0.338043\pi$
$978$	−14573.8	+	25242.6i	−0.476502	+	0.825326i
$979$	−40888.2			−1.33482
$980$	−29628.7	+	9073.96i	−0.965769	+	0.295772i
$981$	−15416.7			−0.501752
$982$	−16894.0	+	29261.3i	−0.548992	+	0.950882i
$983$	2001.06	+	3465.94i	0.0649277	+	0.112458i	0.896662	−	0.442716i	$-0.145985\pi$
$983$	2001.06	+	3465.94i	0.0649277	+	0.112458i	−0.831734	+	0.555174i	$0.812652\pi$
$984$	−19200.1	−	33255.5i	−0.622028	−	1.07738i
$985$	−2484.64	+	4303.53i	−0.0803729	+	0.139210i
$986$	24692.5			0.797535
$987$	−1388.24	−	9273.70i	−0.0447702	−	0.299073i
$988$	99520.7			3.20463
$989$	13415.7	−	23236.6i	0.431338	−	0.747100i
$990$	4679.62	+	8105.34i	0.150230	+	0.260207i
$991$	−5021.23	−	8697.02i	−0.160953	−	0.278779i	0.774258	−	0.632871i	$-0.218123\pi$
$991$	−5021.23	−	8697.02i	−0.160953	−	0.278779i	−0.935211	+	0.354091i	$0.884790\pi$
$992$	16764.4	−	29036.7i	0.536561	−	0.929351i
$993$	−17568.4			−0.561445
$994$	−55651.0	−	21906.1i	−1.77580	−	0.699013i
$995$	−15399.4			−0.490647
$996$	27852.3	−	48241.6i	0.886078	−	1.53473i
$997$	4703.72	+	8147.08i	0.149417	+	0.258797i	0.931012	−	0.364989i	$-0.118927\pi$
$997$	4703.72	+	8147.08i	0.149417	+	0.258797i	−0.781595	+	0.623786i	$0.785594\pi$
$998$	2267.33	+	3927.13i	0.0719148	+	0.124560i
$999$	4791.59	−	8299.28i	0.151751	−	0.262840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.d.16.1	✓	10
3.2	odd	2		315.4.j.h.226.5		10
7.2	even	3		735.4.a.ba.1.5		5
7.4	even	3	inner	105.4.i.d.46.1	yes	10
7.5	odd	6		735.4.a.z.1.5		5
21.2	odd	6		2205.4.a.br.1.1		5
21.5	even	6		2205.4.a.bs.1.1		5
21.11	odd	6		315.4.j.h.46.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.d.16.1	✓	10	1.1	even	1	trivial
105.4.i.d.46.1	yes	10	7.4	even	3	inner
315.4.j.h.46.5		10	21.11	odd	6
315.4.j.h.226.5		10	3.2	odd	2
735.4.a.z.1.5		5	7.5	odd	6
735.4.a.ba.1.5		5	7.2	even	3
2205.4.a.br.1.1		5	21.2	odd	6
2205.4.a.bs.1.1		5	21.5	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55285 + 4.42167i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.03412 - 15.6476i) q^{4} +(-2.50000 + 4.33013i) q^{5} +15.3171 q^{6} +(-2.74187 - 18.3162i) q^{7} +51.4055 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.55285 + 4.42167i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.03412 - 15.6476i) q^{4} +(-2.50000 + 4.33013i) q^{5} +15.3171 q^{6} +(-2.74187 - 18.3162i) q^{7} +51.4055 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-12.7643 - 22.1084i) q^{10} +(20.3677 + 35.2779i) q^{11} +(-27.1024 + 46.9427i) q^{12} +70.9263 q^{13} +(87.9877 + 34.6349i) q^{14} +15.0000 q^{15} +(-58.9577 + 102.118i) q^{16} +(-11.3350 - 19.6329i) q^{17} +(-22.9757 - 39.7950i) q^{18} +(-38.8294 + 67.2545i) q^{19} +90.3412 q^{20} +(-43.4740 + 34.5978i) q^{21} -207.983 q^{22} +(45.0311 - 77.9962i) q^{23} +(-77.1083 - 133.555i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-181.064 + 313.613i) q^{26} +27.0000 q^{27} +(-261.833 + 208.374i) q^{28} +213.332 q^{29} +(-38.2928 + 66.3251i) q^{30} +(87.8644 + 152.186i) q^{31} +(-95.3990 - 165.236i) q^{32} +(61.1031 - 105.834i) q^{33} +115.747 q^{34} +(86.1660 + 33.9178i) q^{35} +162.614 q^{36} +(177.466 - 307.381i) q^{37} +(-198.251 - 343.382i) q^{38} +(-106.389 - 184.272i) q^{39} +(-128.514 + 222.592i) q^{40} +249.001 q^{41} +(-41.9975 - 280.551i) q^{42} +297.920 q^{43} +(368.009 - 637.410i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(229.916 + 398.226i) q^{46} +(-84.3854 + 146.160i) q^{47} +353.746 q^{48} +(-327.964 + 100.441i) q^{49} +127.643 q^{50} +(-34.0051 + 58.8986i) q^{51} +(-640.757 - 1109.82i) q^{52} +(51.2366 + 88.7444i) q^{53} +(-68.9270 + 119.385i) q^{54} -203.677 q^{55} +(-140.947 - 941.552i) q^{56} +232.976 q^{57} +(-544.605 + 943.284i) q^{58} +(11.7399 + 20.3340i) q^{59} +(-135.512 - 234.713i) q^{60} +(437.314 - 757.450i) q^{61} -897.220 q^{62} +(155.099 + 61.0521i) q^{63} +30.8343 q^{64} +(-177.316 + 307.120i) q^{65} +(311.975 + 540.356i) q^{66} +(405.386 + 702.149i) q^{67} +(-204.804 + 354.731i) q^{68} -270.187 q^{69} +(-369.943 + 294.411i) q^{70} -632.487 q^{71} +(-231.325 + 400.666i) q^{72} +(-457.436 - 792.302i) q^{73} +(906.091 + 1569.40i) q^{74} +(-37.5000 + 64.9519i) q^{75} +1403.16 q^{76} +(590.311 - 469.786i) q^{77} +1086.39 q^{78} +(260.443 - 451.101i) q^{79} +(-294.789 - 510.589i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-635.664 + 1101.00i) q^{82} -1027.67 q^{83} +(934.121 + 367.701i) q^{84} +113.350 q^{85} +(-760.546 + 1317.30i) q^{86} +(-319.998 - 554.253i) q^{87} +(1047.01 + 1813.48i) q^{88} +(-501.875 + 869.273i) q^{89} +229.757 q^{90} +(-194.470 - 1299.10i) q^{91} -1627.27 q^{92} +(263.593 - 456.557i) q^{93} +(-430.847 - 746.249i) q^{94} +(-194.147 - 336.272i) q^{95} +(-286.197 + 495.708i) q^{96} -639.620 q^{97} +(393.128 - 1706.56i) q^{98} -366.619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9	\( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9} - 15 q^{10} - 43 q^{11} - 75 q^{12} + 246 q^{13} - 23 q^{14} + 150 q^{15} - 161 q^{16} - 124 q^{17} - 27 q^{18} - 37 q^{19} + 250 q^{20} + 3 q^{21} - 442 q^{22} - 77 q^{23} - 63 q^{24} - 125 q^{25} + 79 q^{26} + 270 q^{27} - 71 q^{28} + 720 q^{29} - 45 q^{30} - 314 q^{31} + 59 q^{32} - 129 q^{33} + 352 q^{34} + 155 q^{35} + 450 q^{36} - 225 q^{37} - 759 q^{38} - 369 q^{39} - 105 q^{40} + 682 q^{41} + 354 q^{42} + 64 q^{43} - 679 q^{44} - 225 q^{45} + 331 q^{46} - 25 q^{47} + 966 q^{48} + 710 q^{49} + 150 q^{50} - 372 q^{51} - 2299 q^{52} + 317 q^{53} - 81 q^{54} + 430 q^{55} + 1884 q^{56} + 222 q^{57} - 8 q^{58} - 676 q^{59} - 375 q^{60} + 188 q^{61} - 696 q^{62} + 279 q^{63} - 2206 q^{64} - 615 q^{65} + 663 q^{66} + 1776 q^{67} - 1280 q^{68} + 462 q^{69} - 475 q^{70} - 12 q^{71} - 189 q^{72} - 2006 q^{73} + 2729 q^{74} - 375 q^{75} + 2834 q^{76} + 3731 q^{77} - 474 q^{78} - 200 q^{79} - 805 q^{80} - 405 q^{81} + 539 q^{82} - 664 q^{83} + 1821 q^{84} + 1240 q^{85} - 4262 q^{86} - 1080 q^{87} + 4529 q^{88} - 894 q^{89} + 270 q^{90} + 2016 q^{91} - 7374 q^{92} - 942 q^{93} - 4233 q^{94} - 185 q^{95} + 177 q^{96} - 1152 q^{97} + 2539 q^{98} + 774 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9 - 15 * q^10 - 43 * q^11 - 75 * q^12 + 246 * q^13 - 23 * q^14 + 150 * q^15 - 161 * q^16 - 124 * q^17 - 27 * q^18 - 37 * q^19 + 250 * q^20 + 3 * q^21 - 442 * q^22 - 77 * q^23 - 63 * q^24 - 125 * q^25 + 79 * q^26 + 270 * q^27 - 71 * q^28 + 720 * q^29 - 45 * q^30 - 314 * q^31 + 59 * q^32 - 129 * q^33 + 352 * q^34 + 155 * q^35 + 450 * q^36 - 225 * q^37 - 759 * q^38 - 369 * q^39 - 105 * q^40 + 682 * q^41 + 354 * q^42 + 64 * q^43 - 679 * q^44 - 225 * q^45 + 331 * q^46 - 25 * q^47 + 966 * q^48 + 710 * q^49 + 150 * q^50 - 372 * q^51 - 2299 * q^52 + 317 * q^53 - 81 * q^54 + 430 * q^55 + 1884 * q^56 + 222 * q^57 - 8 * q^58 - 676 * q^59 - 375 * q^60 + 188 * q^61 - 696 * q^62 + 279 * q^63 - 2206 * q^64 - 615 * q^65 + 663 * q^66 + 1776 * q^67 - 1280 * q^68 + 462 * q^69 - 475 * q^70 - 12 * q^71 - 189 * q^72 - 2006 * q^73 + 2729 * q^74 - 375 * q^75 + 2834 * q^76 + 3731 * q^77 - 474 * q^78 - 200 * q^79 - 805 * q^80 - 405 * q^81 + 539 * q^82 - 664 * q^83 + 1821 * q^84 + 1240 * q^85 - 4262 * q^86 - 1080 * q^87 + 4529 * q^88 - 894 * q^89 + 270 * q^90 + 2016 * q^91 - 7374 * q^92 - 942 * q^93 - 4233 * q^94 - 185 * q^95 + 177 * q^96 - 1152 * q^97 + 2539 * q^98 + 774 * q^99

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