LMFDB - Embedded newform 43.4.c.a.6.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.c (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:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 $ x^20 - x^19 + 60x^18 - 25x^17 + 2336x^16 - 645x^15 + 52478x^14 - 2415x^13 + 850704x^12 - 4147x^11 + 8670544x^10 + 873865x^9 + 62344097x^8 + 3655316x^7 + 215661012x^6 + 43840208x^5 + 507687824x^4 - 3907840x^3 + 17517568x^2 + 245760x + 589824
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.5
Root			$0.0954556 - 0.165334i$ of defining polynomial
Character	$\chi$	$=$	43.6
Dual form			43.4.c.a.36.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.190911 q^{2} +(-0.719182 + 1.24566i) q^{3} -7.96355 q^{4} +(-8.17312 + 14.1563i) q^{5} +(0.137300 - 0.237810i) q^{6} +(-3.11997 - 5.40394i) q^{7} +3.04762 q^{8} +(12.4656 + 21.5910i) q^{9} +O(q^{10})$	\(q-0.190911 q^{2} +(-0.719182 + 1.24566i) q^{3} -7.96355 q^{4} +(-8.17312 + 14.1563i) q^{5} +(0.137300 - 0.237810i) q^{6} +(-3.11997 - 5.40394i) q^{7} +3.04762 q^{8} +(12.4656 + 21.5910i) q^{9} +(1.56034 - 2.70259i) q^{10} -29.4459 q^{11} +(5.72724 - 9.91987i) q^{12} +(-11.1187 - 19.2582i) q^{13} +(0.595637 + 1.03167i) q^{14} +(-11.7559 - 20.3618i) q^{15} +63.1266 q^{16} +(30.1880 + 52.2872i) q^{17} +(-2.37981 - 4.12196i) q^{18} +(5.01887 - 8.69294i) q^{19} +(65.0871 - 112.734i) q^{20} +8.97530 q^{21} +5.62155 q^{22} +(20.3168 - 35.1897i) q^{23} +(-2.19179 + 3.79630i) q^{24} +(-71.0999 - 123.149i) q^{25} +(2.12269 + 3.67660i) q^{26} -74.6958 q^{27} +(24.8460 + 43.0346i) q^{28} +(97.8503 + 169.482i) q^{29} +(2.24434 + 3.88731i) q^{30} +(-120.424 + 208.581i) q^{31} -36.4326 q^{32} +(21.1769 - 36.6795i) q^{33} +(-5.76323 - 9.98221i) q^{34} +102.000 q^{35} +(-99.2701 - 171.941i) q^{36} +(-121.507 + 210.457i) q^{37} +(-0.958159 + 1.65958i) q^{38} +31.9855 q^{39} +(-24.9086 + 43.1429i) q^{40} -172.596 q^{41} -1.71349 q^{42} +(-281.883 - 6.99017i) q^{43} +234.494 q^{44} -407.530 q^{45} +(-3.87870 + 6.71810i) q^{46} +583.708 q^{47} +(-45.3995 + 78.6342i) q^{48} +(152.032 - 263.326i) q^{49} +(13.5738 + 23.5104i) q^{50} -86.8427 q^{51} +(88.5444 + 153.363i) q^{52} +(-185.144 + 320.679i) q^{53} +14.2603 q^{54} +(240.665 - 416.843i) q^{55} +(-9.50848 - 16.4692i) q^{56} +(7.21896 + 12.5036i) q^{57} +(-18.6807 - 32.3559i) q^{58} +714.277 q^{59} +(93.6189 + 162.153i) q^{60} +(-353.918 - 613.004i) q^{61} +(22.9903 - 39.8204i) q^{62} +(77.7843 - 134.726i) q^{63} -498.057 q^{64} +363.498 q^{65} +(-4.04291 + 7.00253i) q^{66} +(188.790 - 326.993i) q^{67} +(-240.404 - 416.392i) q^{68} +(29.2229 + 50.6155i) q^{69} -19.4729 q^{70} +(23.7165 + 41.0783i) q^{71} +(37.9903 + 65.8011i) q^{72} +(345.757 + 598.868i) q^{73} +(23.1971 - 40.1786i) q^{74} +204.535 q^{75} +(-39.9681 + 69.2267i) q^{76} +(91.8701 + 159.124i) q^{77} -6.10639 q^{78} +(-144.391 - 250.093i) q^{79} +(-515.941 + 893.637i) q^{80} +(-282.850 + 489.911i) q^{81} +32.9505 q^{82} +(416.911 - 722.112i) q^{83} -71.4753 q^{84} -986.922 q^{85} +(53.8147 + 1.33450i) q^{86} -281.488 q^{87} -89.7398 q^{88} +(-343.605 + 595.141i) q^{89} +77.8021 q^{90} +(-69.3801 + 120.170i) q^{91} +(-161.794 + 280.235i) q^{92} +(-173.214 - 300.015i) q^{93} -111.436 q^{94} +(82.0397 + 142.097i) q^{95} +(26.2016 - 45.3825i) q^{96} +1131.96 q^{97} +(-29.0245 + 50.2720i) q^{98} +(-367.059 - 635.765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.190911			−0.0674973			−0.0337487	−	0.999430i	$-0.510745\pi$
$2$	−0.190911			−0.0674973			−0.0337487	+	0.999430i	$0.510745\pi$
$3$	−0.719182	+	1.24566i	−0.138407	+	0.239727i	−0.926894	−	0.375324i	$-0.877531\pi$
$3$	−0.719182	+	1.24566i	−0.138407	+	0.239727i	0.788487	+	0.615051i	$0.210865\pi$
$4$	−7.96355			−0.995444
$5$	−8.17312	+	14.1563i	−0.731026	+	1.26617i	0.225419	+	0.974262i	$0.427625\pi$
$5$	−8.17312	+	14.1563i	−0.731026	+	1.26617i	−0.956445	+	0.291913i	$0.905708\pi$
$6$	0.137300	−	0.237810i	0.00934207	−	0.0161809i
$7$	−3.11997	−	5.40394i	−0.168462	−	0.291786i	0.769417	−	0.638747i	$-0.220547\pi$
$7$	−3.11997	−	5.40394i	−0.168462	−	0.291786i	−0.937879	+	0.346961i	$0.887214\pi$
$8$	3.04762			0.134687
$9$	12.4656	+	21.5910i	0.461687	+	0.799666i
$10$	1.56034	−	2.70259i	0.0493423	−	0.0854634i
$11$	−29.4459			−0.807115			−0.403557	−	0.914954i	$-0.632226\pi$
$11$	−29.4459			−0.807115			−0.403557	+	0.914954i	$0.632226\pi$
$12$	5.72724	−	9.91987i	0.137776	−	0.238635i
$13$	−11.1187	−	19.2582i	−0.237214	−	0.410866i	0.722700	−	0.691162i	$-0.242901\pi$
$13$	−11.1187	−	19.2582i	−0.237214	−	0.410866i	−0.959914	+	0.280296i	$0.909567\pi$
$14$	0.595637	+	1.03167i	0.0113708	+	0.0196947i
$15$	−11.7559	−	20.3618i	−0.202358	−	0.350494i
$16$	63.1266			0.986353
$17$	30.1880	+	52.2872i	0.430687	+	0.745971i	0.996933	−	0.0782653i	$-0.0249381\pi$
$17$	30.1880	+	52.2872i	0.430687	+	0.745971i	−0.566246	+	0.824236i	$0.691605\pi$
$18$	−2.37981	−	4.12196i	−0.0311627	−	0.0539753i
$19$	5.01887	−	8.69294i	0.0606004	−	0.104963i	−0.834134	−	0.551563i	$-0.814032\pi$
$19$	5.01887	−	8.69294i	0.0606004	−	0.104963i	0.894734	+	0.446600i	$0.147365\pi$
$20$	65.0871	−	112.734i	0.727696	−	1.26041i
$21$	8.97530			0.0932653
$22$	5.62155			0.0544781
$23$	20.3168	−	35.1897i	0.184189	−	0.319024i	−0.759114	−	0.650957i	$-0.774368\pi$
$23$	20.3168	−	35.1897i	0.184189	−	0.319024i	0.943303	+	0.331933i	$0.107701\pi$
$24$	−2.19179	+	3.79630i	−0.0186416	+	0.0322882i
$25$	−71.0999	−	123.149i	−0.568799	−	0.985189i
$26$	2.12269	+	3.67660i	0.0160113	+	0.0277323i
$27$	−74.6958			−0.532415
$28$	24.8460	+	43.0346i	0.167695	+	0.290456i
$29$	97.8503	+	169.482i	0.626563	+	1.08524i	0.988236	+	0.152935i	$0.0488724\pi$
$29$	97.8503	+	169.482i	0.626563	+	1.08524i	−0.361673	+	0.932305i	$0.617794\pi$
$30$	2.24434	+	3.88731i	0.0136586	+	0.0236574i
$31$	−120.424	+	208.581i	−0.697704	+	1.20846i	0.271557	+	0.962422i	$0.412462\pi$
$31$	−120.424	+	208.581i	−0.697704	+	1.20846i	−0.969261	+	0.246036i	$0.920872\pi$
$32$	−36.4326			−0.201263
$33$	21.1769	−	36.6795i	0.111710	−	0.193487i
$34$	−5.76323	−	9.98221i	−0.0290702	−	0.0503510i
$35$	102.000			0.492602
$36$	−99.2701	−	171.941i	−0.459584	−	0.796023i
$37$	−121.507	+	210.457i	−0.539883	+	0.935105i	0.459026	+	0.888423i	$0.348198\pi$
$37$	−121.507	+	210.457i	−0.539883	+	0.935105i	−0.998910	+	0.0466828i	$0.985135\pi$
$38$	−0.958159	+	1.65958i	−0.00409037	+	0.00708472i
$39$	31.9855			0.131328
$40$	−24.9086	+	43.1429i	−0.0984598	+	0.170537i
$41$	−172.596			−0.657439			−0.328719	−	0.944428i	$-0.606617\pi$
$41$	−172.596			−0.657439			−0.328719	+	0.944428i	$0.606617\pi$
$42$	−1.71349			−0.00629515
$43$	−281.883	−	6.99017i	−0.999693	−	0.0247905i
$43$	−281.883	−	6.99017i	−0.999693	−	0.0247905i
$44$	234.494			0.803437
$45$	−407.530			−1.35002
$46$	−3.87870	+	6.71810i	−0.0124322	+	0.0215333i
$47$	583.708			1.81154			0.905772	−	0.423766i	$-0.139292\pi$
$47$	583.708			1.81154			0.905772	+	0.423766i	$0.139292\pi$
$48$	−45.3995	+	78.6342i	−0.136518	+	0.236456i
$49$	152.032	−	263.326i	0.443241	−	0.767716i
$50$	13.5738	+	23.5104i	0.0383924	+	0.0664976i
$51$	−86.8427			−0.238439
$52$	88.5444	+	153.363i	0.236133	+	0.408994i
$53$	−185.144	+	320.679i	−0.479839	+	0.831106i	−0.999733	−	0.0231250i	$-0.992638\pi$
$53$	−185.144	+	320.679i	−0.479839	+	0.831106i	0.519893	+	0.854231i	$0.325972\pi$
$54$	14.2603			0.0359366
$55$	240.665	−	416.843i	0.590022	−	1.02195i
$56$	−9.50848	−	16.4692i	−0.0226897	−	0.0392998i
$57$	7.21896	+	12.5036i	0.0167750	+	0.0290552i
$58$	−18.6807	−	32.3559i	−0.0422913	−	0.0732508i
$59$	714.277			1.57612			0.788059	−	0.615599i	$-0.211086\pi$
$59$	714.277			1.57612			0.788059	+	0.615599i	$0.211086\pi$
$60$	93.6189	+	162.153i	0.201436	+	0.348897i
$61$	−353.918	−	613.004i	−0.742862	−	1.28667i	−0.951187	−	0.308615i	$-0.900135\pi$
$61$	−353.918	−	613.004i	−0.742862	−	1.28667i	0.208325	−	0.978060i	$-0.433199\pi$
$62$	22.9903	−	39.8204i	0.0470931	−	0.0815677i
$63$	77.7843	−	134.726i	0.155554	−	0.269427i
$64$	−498.057			−0.972768
$65$	363.498			0.693637
$66$	−4.04291	+	7.00253i	−0.00754012	+	0.0130599i
$67$	188.790	−	326.993i	0.344244	−	0.596248i	−0.640972	−	0.767564i	$-0.721469\pi$
$67$	188.790	−	326.993i	0.344244	−	0.596248i	0.985216	+	0.171316i	$0.0548020\pi$
$68$	−240.404	−	416.392i	−0.428724	−	0.742572i
$69$	29.2229	+	50.6155i	0.0509858	+	0.0883100i
$70$	−19.4729			−0.0332493
$71$	23.7165	+	41.0783i	0.0396428	+	0.0686633i	0.885166	−	0.465275i	$-0.154045\pi$
$71$	23.7165	+	41.0783i	0.0396428	+	0.0686633i	−0.845523	+	0.533939i	$0.820711\pi$
$72$	37.9903	+	65.8011i	0.0621833	+	0.107705i
$73$	345.757	+	598.868i	0.554353	+	0.960167i	0.997954	+	0.0639425i	$0.0203674\pi$
$73$	345.757	+	598.868i	0.554353	+	0.960167i	−0.443601	+	0.896224i	$0.646299\pi$
$74$	23.1971	−	40.1786i	0.0364407	−	0.0631171i
$75$	204.535			0.314902
$76$	−39.9681	+	69.2267i	−0.0603244	+	0.104485i
$77$	91.8701	+	159.124i	0.135969	+	0.235504i
$78$	−6.10639			−0.00886426
$79$	−144.391	−	250.093i	−0.205637	−	0.356173i	0.744699	−	0.667401i	$-0.232593\pi$
$79$	−144.391	−	250.093i	−0.205637	−	0.356173i	−0.950335	+	0.311228i	$0.899260\pi$
$80$	−515.941	+	893.637i	−0.721050	+	1.24890i
$81$	−282.850	+	489.911i	−0.387997	+	0.672031i
$82$	32.9505			0.0443753
$83$	416.911	−	722.112i	0.551349	−	0.954965i	−0.446829	−	0.894620i	$-0.647447\pi$
$83$	416.911	−	722.112i	0.551349	−	0.954965i	0.998178	−	0.0603450i	$-0.0192201\pi$
$84$	−71.4753			−0.0928403
$85$	−986.922			−1.25937
$86$	53.8147	+	1.33450i	0.0674766	+	0.00167329i
$87$	−281.488			−0.346882
$88$	−89.7398			−0.108708
$89$	−343.605	+	595.141i	−0.409236	+	0.708818i	−0.994804	−	0.101805i	$-0.967538\pi$
$89$	−343.605	+	595.141i	−0.409236	+	0.708818i	0.585568	+	0.810623i	$0.300871\pi$
$90$	77.8021			0.0911229
$91$	−69.3801	+	120.170i	−0.0799232	+	0.138431i
$92$	−161.794	+	280.235i	−0.183349	+	0.317571i
$93$	−173.214	−	300.015i	−0.193134	−	0.334517i
$94$	−111.436			−0.122274
$95$	82.0397	+	142.097i	0.0886010	+	0.153461i
$96$	26.2016	−	45.3825i	0.0278562	−	0.0482483i
$97$	1131.96			1.18488			0.592439	−	0.805615i	$-0.298165\pi$
$97$	1131.96			1.18488			0.592439	+	0.805615i	$0.298165\pi$
$98$	−29.0245	+	50.2720i	−0.0299176	+	0.0518187i
$99$	−367.059	−	635.765i	−0.372634	−	0.645422i
$100$	566.207	+	980.700i	0.566207	+	0.980700i
$101$	−417.630	−	723.357i	−0.411443	−	0.712641i	0.583604	−	0.812038i	$-0.301642\pi$
$101$	−417.630	−	723.357i	−0.411443	−	0.712641i	−0.995048	+	0.0993973i	$0.968309\pi$
$102$	16.5792			0.0160940
$103$	193.524	+	335.194i	0.185131	+	0.320657i	0.943621	−	0.331029i	$-0.107396\pi$
$103$	193.524	+	335.194i	0.185131	+	0.320657i	−0.758490	+	0.651685i	$0.774062\pi$
$104$	−33.8856	−	58.6916i	−0.0319496	−	0.0553383i
$105$	−73.3562	+	127.057i	−0.0681794	+	0.118090i
$106$	35.3461	−	61.2212i	0.0323879	−	0.0560974i
$107$	−797.155			−0.720224			−0.360112	−	0.932909i	$-0.617261\pi$
$107$	−797.155			−0.720224			−0.360112	+	0.932909i	$0.617261\pi$
$108$	594.844			0.529990
$109$	−644.331	+	1116.01i	−0.566199	+	0.980686i	0.430738	+	0.902477i	$0.358253\pi$
$109$	−644.331	+	1116.01i	−0.566199	+	0.980686i	−0.996937	+	0.0782089i	$0.975080\pi$
$110$	−45.9456	+	79.5801i	−0.0398249	+	0.0689787i
$111$	−174.772	−	302.713i	−0.149447	−	0.258849i
$112$	−196.953	−	341.133i	−0.166163	−	0.287804i
$113$	1133.47			0.943607			0.471804	−	0.881704i	$-0.343603\pi$
$113$	1133.47			0.943607			0.471804	+	0.881704i	$0.343603\pi$
$114$	−1.37818	−	2.38708i	−0.00113227	−	0.00196114i
$115$	332.103	+	575.219i	0.269293	+	0.466430i
$116$	−779.236	−	1349.68i	−0.623709	−	1.08030i
$117$	277.202	−	480.128i	0.219037	−	0.379383i
$118$	−136.364			−0.106384
$119$	188.371	−	326.269i	0.145109	−	0.251336i
$120$	−35.8276	−	62.0552i	−0.0272550	−	0.0472070i
$121$	−463.942			−0.348566
$122$	67.5670	+	117.029i	0.0501412	+	0.0868471i
$123$	124.128	−	214.996i	0.0909938	−	0.157606i
$124$	959.004	−	1661.04i	0.694525	−	1.20295i
$125$	281.151			0.201175
$126$	−14.8499	+	25.7208i	−0.0104995	+	0.0181856i
$127$	1984.05			1.38627			0.693133	−	0.720810i	$-0.256230\pi$
$127$	1984.05			1.38627			0.693133	+	0.720810i	$0.256230\pi$
$128$	386.545			0.266923
$129$	211.433	−	346.103i	0.144307	−	0.236222i
$130$	−69.3959			−0.0468187
$131$	−479.419			−0.319748			−0.159874	−	0.987137i	$-0.551109\pi$
$131$	−479.419			−0.319748			−0.159874	+	0.987137i	$0.551109\pi$
$132$	−168.644	+	292.099i	−0.111201	+	0.192606i
$133$	−62.6349			−0.0408356
$134$	−36.0421	+	62.4267i	−0.0232355	+	0.0402451i
$135$	610.498	−	1057.41i	0.389210	−	0.674131i
$136$	92.0017	+	159.352i	0.0580079	+	0.100473i
$137$	2598.71			1.62060			0.810302	−	0.586013i	$-0.199303\pi$
$137$	2598.71			1.62060			0.810302	+	0.586013i	$0.199303\pi$
$138$	−5.57898	−	9.66307i	−0.00344141	−	0.00596069i
$139$	408.535	−	707.603i	0.249291	−	0.431785i	−0.714038	−	0.700107i	$-0.753136\pi$
$139$	408.535	−	707.603i	0.249291	−	0.431785i	0.963329	+	0.268322i	$0.0864691\pi$
$140$	−812.279			−0.490358
$141$	−419.792	+	727.101i	−0.250730	+	0.434276i
$142$	−4.52775	−	7.84230i	−0.00267578	−	0.00463459i
$143$	327.400	+	567.073i	0.191458	+	0.331616i
$144$	786.908	+	1362.96i	0.455387	+	0.788753i
$145$	−3198.97			−1.83214
$146$	−66.0088	−	114.331i	−0.0374173	−	0.0648087i
$147$	218.677	+	378.759i	0.122695	+	0.212514i
$148$	967.630	−	1675.98i	0.537424	−	0.930845i
$149$	−1778.60	+	3080.63i	−0.977911	+	1.69379i	−0.307939	+	0.951406i	$0.599639\pi$
$149$	−1778.60	+	3080.63i	−0.977911	+	1.69379i	−0.669972	+	0.742386i	$0.733694\pi$
$150$	−39.0480			−0.0212550
$151$	−3401.24			−1.83304			−0.916520	−	0.399989i	$-0.869014\pi$
$151$	−3401.24			−1.83304			−0.916520	+	0.399989i	$0.869014\pi$
$152$	15.2956	−	26.4928i	0.00816210	−	0.0141372i
$153$	−752.621	+	1303.58i	−0.397685	+	0.688811i
$154$	−17.5390	−	30.3785i	−0.00917751	−	0.0158959i
$155$	−1968.48	−	3409.51i	−1.02008	−	1.76683i
$156$	−254.718			−0.130729
$157$	456.696	+	791.021i	0.232155	+	0.402104i	0.958442	−	0.285287i	$-0.0920891\pi$
$157$	456.696	+	791.021i	0.232155	+	0.402104i	−0.726287	+	0.687391i	$0.758756\pi$
$158$	27.5659	+	47.7456i	0.0138799	+	0.0240407i
$159$	−266.304	−	461.253i	−0.132826	−	0.230061i
$160$	297.768	−	515.749i	0.147129	−	0.254835i
$161$	−253.551			−0.124115
$162$	53.9993	−	93.5295i	0.0261888	−	0.0453603i
$163$	1860.90	+	3223.17i	0.894213	+	1.54882i	0.834776	+	0.550590i	$0.185597\pi$
$163$	1860.90	+	3223.17i	0.894213	+	1.54882i	0.0594365	+	0.998232i	$0.481070\pi$
$164$	1374.48			0.654443
$165$	346.163	+	599.572i	0.163326	+	0.282889i
$166$	−79.5931	+	137.859i	−0.0372146	+	0.0644576i
$167$	−930.163	+	1611.09i	−0.431007	+	0.746526i	−0.996960	−	0.0779115i	$-0.975175\pi$
$167$	−930.163	+	1611.09i	−0.431007	+	0.746526i	0.565953	+	0.824437i	$0.308508\pi$
$168$	27.3533			0.0125616
$169$	851.249	−	1474.41i	0.387459	−	0.671100i
$170$	188.414			0.0850043
$171$	250.252			0.111914
$172$	2244.79	+	55.6666i	0.995138	+	0.0246775i
$173$	−2169.88			−0.953601			−0.476801	−	0.879011i	$-0.658204\pi$
$173$	−2169.88			−0.953601			−0.476801	+	0.879011i	$0.658204\pi$
$174$	53.7393			0.0234136
$175$	−443.659	+	768.439i	−0.191643	+	0.331935i
$176$	−1858.82			−0.796100
$177$	−513.695	+	889.746i	−0.218145	+	0.377839i
$178$	65.5980	−	113.619i	0.0276223	−	0.0478433i
$179$	1012.37	+	1753.48i	0.422728	+	0.732186i	0.996205	−	0.0870351i	$-0.0277392\pi$
$179$	1012.37	+	1753.48i	0.422728	+	0.732186i	−0.573477	+	0.819221i	$0.694406\pi$
$180$	3245.39			1.34387
$181$	−456.514	−	790.705i	−0.187472	−	0.324711i	0.756935	−	0.653490i	$-0.226696\pi$
$181$	−456.514	−	790.705i	−0.187472	−	0.324711i	−0.944407	+	0.328780i	$0.893363\pi$
$182$	13.2454	−	22.9418i	0.00539460	−	0.00934372i
$183$	1018.13			0.411268
$184$	61.9178	−	107.245i	0.0248078	−	0.0429684i
$185$	−1986.19	−	3440.18i	−0.789338	−	1.36717i
$186$	33.0684	+	57.2762i	0.0130360	+	0.0225790i
$187$	−888.912	−	1539.64i	−0.347613	−	0.602084i
$188$	−4648.39			−1.80329
$189$	233.049	+	403.652i	0.0896920	+	0.155351i
$190$	−15.6623	−	27.1279i	−0.00598033	−	0.0103582i
$191$	−100.085	+	173.352i	−0.0379156	+	0.0656717i	−0.884360	−	0.466805i	$-0.845405\pi$
$191$	−100.085	+	173.352i	−0.0379156	+	0.0656717i	0.846445	+	0.532476i	$0.178738\pi$
$192$	358.194	−	620.410i	0.134638	−	0.233199i
$193$	601.137			0.224201			0.112100	−	0.993697i	$-0.464242\pi$
$193$	601.137			0.224201			0.112100	+	0.993697i	$0.464242\pi$
$194$	−216.104			−0.0799761
$195$	−261.421	+	452.795i	−0.0960040	+	0.166284i
$196$	−1210.71	+	2097.01i	−0.441221	+	0.764218i
$197$	243.611	+	421.946i	0.0881043	+	0.152601i	0.906710	−	0.421755i	$-0.138586\pi$
$197$	243.611	+	421.946i	0.0881043	+	0.152601i	−0.818606	+	0.574356i	$0.805252\pi$
$198$	70.0757	+	121.375i	0.0251518	+	0.0435642i
$199$	2852.48			1.01612			0.508058	−	0.861323i	$-0.330364\pi$
$199$	2852.48			1.01612			0.508058	+	0.861323i	$0.330364\pi$
$200$	−216.685	−	375.310i	−0.0766099	−	0.132692i
$201$	271.548	+	470.335i	0.0952912	+	0.165049i
$202$	79.7303	+	138.097i	0.0277713	+	0.0481013i
$203$	610.579	−	1057.55i	0.211105	−	0.365644i
$204$	691.576			0.237353
$205$	1410.65	−	2443.32i	0.480605	−	0.832432i
$206$	−36.9460	−	63.9923i	−0.0124959	−	0.0216435i
$207$	1013.04			0.340150
$208$	−701.886	−	1215.70i	−0.233976	−	0.405259i
$209$	−147.785	+	255.971i	−0.0489115	+	0.0847172i
$210$	14.0045	−	24.2565i	0.00460192	−	0.00797077i
$211$	4622.59			1.50821			0.754104	−	0.656755i	$-0.228071\pi$
$211$	4622.59			1.50821			0.754104	+	0.656755i	$0.228071\pi$
$212$	1474.40	−	2553.74i	0.477653	−	0.827320i
$213$	−68.2260			−0.0219473
$214$	152.186			0.0486132
$215$	2402.82	−	3933.28i	0.762191	−	1.24766i
$216$	−227.645			−0.0717095
$217$	1502.88			0.470148
$218$	123.010	−	213.060i	0.0382169	−	0.0661937i
$219$	−994.647			−0.306904
$220$	−1916.55	+	3319.55i	−0.587334	+	1.01729i
$221$	671.304	−	1162.73i	0.204329	−	0.353909i
$222$	33.3659	+	57.7914i	0.0100873	+	0.0174716i
$223$	1600.61			0.480648			0.240324	−	0.970693i	$-0.422746\pi$
$223$	1600.61			0.480648			0.240324	+	0.970693i	$0.422746\pi$
$224$	113.668	+	196.879i	0.0339053	+	0.0587257i
$225$	1772.60	−	3070.23i	0.525214	−	0.909698i
$226$	−216.392			−0.0636909
$227$	−1682.39	+	2913.98i	−0.491912	+	0.852017i	−0.999957	−	0.00931415i	$-0.997035\pi$
$227$	−1682.39	+	2913.98i	−0.491912	+	0.852017i	0.508045	+	0.861331i	$0.330369\pi$
$228$	−57.4886	−	99.5732i	−0.0166986	−	0.0289228i
$229$	−875.663	−	1516.69i	−0.252688	−	0.437668i	0.711577	−	0.702608i	$-0.247981\pi$
$229$	−875.663	−	1516.69i	−0.252688	−	0.437668i	−0.964265	+	0.264940i	$0.914648\pi$
$230$	−63.4022	−	109.816i	−0.0181766	−	0.0314828i
$231$	−264.285			−0.0752757
$232$	298.211	+	516.516i	0.0843900	+	0.146168i
$233$	243.565	+	421.867i	0.0684828	+	0.118616i	0.898234	−	0.439518i	$-0.144851\pi$
$233$	243.565	+	421.867i	0.0684828	+	0.118616i	−0.829751	+	0.558134i	$0.811518\pi$
$234$	−52.9209	+	91.6618i	−0.0147844	+	0.0256073i
$235$	−4770.72	+	8263.12i	−1.32429	+	2.29373i
$236$	−5688.19			−1.56894
$237$	415.374			0.113846
$238$	−35.9622	+	62.2884i	−0.00979447	+	0.0169645i
$239$	522.021	−	904.167i	0.141283	−	0.244710i	−0.786697	−	0.617340i	$-0.788210\pi$
$239$	522.021	−	904.167i	0.141283	−	0.244710i	0.927980	+	0.372630i	$0.121544\pi$
$240$	−742.111	−	1285.37i	−0.199596	−	0.345711i
$241$	−2784.31	−	4822.56i	−0.744203	−	1.28900i	−0.950566	−	0.310522i	$-0.899496\pi$
$241$	−2784.31	−	4822.56i	−0.744203	−	1.28900i	0.206363	−	0.978475i	$-0.433837\pi$
$242$	88.5717			0.0235273
$243$	−1415.23	−	2451.26i	−0.373610	−	0.647112i
$244$	2818.45	+	4881.69i	0.739478	+	1.28081i
$245$	2485.15	+	4304.40i	0.648041	+	1.12244i
$246$	−23.6974	+	41.0451i	−0.00614184	+	0.0106380i
$247$	−223.214			−0.0575010
$248$	−367.007	+	635.675i	−0.0939717	+	0.162764i
$249$	599.670	+	1038.66i	0.152621	+	0.264347i
$250$	−53.6748			−0.0135788
$251$	−2161.54	−	3743.89i	−0.543566	−	0.941483i	−0.998696	−	0.0510582i	$-0.983741\pi$
$251$	−2161.54	−	3743.89i	−0.543566	−	0.941483i	0.455130	−	0.890425i	$-0.349593\pi$
$252$	−619.439	+	1072.90i	−0.154845	+	0.268200i
$253$	−598.244	+	1036.19i	−0.148661	+	0.257489i
$254$	−378.777			−0.0935692
$255$	709.776	−	1229.37i	0.174305	−	0.301906i
$256$	3910.66			0.954752
$257$	2098.48			0.509336			0.254668	−	0.967029i	$-0.418034\pi$
$257$	2098.48			0.509336			0.254668	+	0.967029i	$0.418034\pi$
$258$	−40.3649	+	66.0750i	−0.00974033	+	0.0159444i
$259$	1516.40			0.363800
$260$	−2894.74			−0.690477
$261$	−2439.52	+	4225.37i	−0.578553	+	1.00208i
$262$	91.5265			0.0215822
$263$	−2026.84	+	3510.60i	−0.475211	+	0.823090i	−0.999597	−	0.0283906i	$-0.990962\pi$
$263$	−2026.84	+	3510.60i	−0.475211	+	0.823090i	0.524385	+	0.851481i	$0.324295\pi$
$264$	64.5392	−	111.785i	0.0150459	−	0.0260603i
$265$	−3026.41	−	5241.90i	−0.701550	−	1.21512i
$266$	11.9577			0.00275629
$267$	−494.228	−	856.028i	−0.113282	−	0.196210i
$268$	−1503.44	+	2604.03i	−0.342676	+	0.593531i
$269$	6316.81			1.43176			0.715879	−	0.698225i	$-0.246026\pi$
$269$	6316.81			1.43176			0.715879	+	0.698225i	$0.246026\pi$
$270$	−116.551	+	201.872i	−0.0262706	+	0.0455020i
$271$	−1337.76	−	2317.08i	−0.299865	−	0.519381i	0.676240	−	0.736682i	$-0.263608\pi$
$271$	−1337.76	−	2317.08i	−0.299865	−	0.519381i	−0.976105	+	0.217300i	$0.930275\pi$
$272$	1905.67	+	3300.71i	0.424809	+	0.735791i
$273$	−99.7937	−	172.848i	−0.0221238	−	0.0383195i
$274$	−496.123			−0.109386
$275$	2093.60	+	3626.21i	0.459086	+	0.795160i
$276$	−232.718	−	403.079i	−0.0507535	−	0.0879077i
$277$	−643.898	+	1115.26i	−0.139668	+	0.241912i	−0.927371	−	0.374143i	$-0.877937\pi$
$277$	−643.898	+	1115.26i	−0.139668	+	0.241912i	0.787703	+	0.616055i	$0.211270\pi$
$278$	−77.9938	+	135.089i	−0.0168265	+	0.0291443i
$279$	−6004.62			−1.28848
$280$	310.856			0.0663471
$281$	302.910	−	524.656i	0.0643065	−	0.111382i	−0.832080	−	0.554656i	$-0.812850\pi$
$281$	302.910	−	524.656i	0.0643065	−	0.111382i	0.896386	+	0.443274i	$0.146183\pi$
$282$	80.1430	−	138.812i	0.0169236	−	0.0293125i
$283$	−4042.59	−	7001.98i	−0.849142	−	1.47076i	−0.881975	−	0.471297i	$-0.843786\pi$
$283$	−4042.59	−	7001.98i	−0.849142	−	1.47076i	0.0328324	−	0.999461i	$-0.489547\pi$
$284$	−188.868	−	327.129i	−0.0394621	−	0.0683504i
$285$	−236.006			−0.0490519
$286$	−62.5043	−	108.261i	−0.0129229	−	0.0223832i
$287$	538.494	+	932.700i	0.110754	+	0.191831i
$288$	−454.152	−	786.614i	−0.0929207	−	0.160943i
$289$	633.867	−	1097.89i	0.129018	−	0.223466i
$290$	610.719			0.123664
$291$	−814.085	+	1410.04i	−0.163995	+	0.284048i
$292$	−2753.45	−	4769.12i	−0.551827	−	0.955792i
$293$	8460.67			1.68695			0.843477	−	0.537165i	$-0.180505\pi$
$293$	8460.67			1.68695			0.843477	+	0.537165i	$0.180505\pi$
$294$	−41.7478	−	72.3094i	−0.00828158	−	0.0143441i
$295$	−5837.88	+	10111.5i	−1.15218	+	1.99564i
$296$	−370.308	+	641.393i	−0.0727153	+	0.125947i
$297$	2199.48			0.429720
$298$	339.555	−	588.127i	0.0660064	−	0.114326i
$299$	−903.585			−0.174768
$300$	−1628.82			−0.313467
$301$	841.692	+	1545.09i	0.161177	+	0.295872i
$302$	649.335			0.123725
$303$	1201.41			0.227786
$304$	316.824	−	548.756i	0.0597734	−	0.103531i
$305$	11570.5			2.17221
$306$	143.684	−	248.868i	0.0268427	−	0.0464929i
$307$	3017.66	−	5226.74i	0.561000	−	0.971680i	−0.436410	−	0.899748i	$-0.643750\pi$
$307$	3017.66	−	5226.74i	0.561000	−	0.971680i	0.997410	−	0.0719323i	$-0.0229166\pi$
$308$	−731.613	−	1267.19i	−0.135349	−	0.234431i
$309$	−556.716			−0.102493
$310$	375.806	+	650.914i	0.0688526	+	0.119256i
$311$	−365.189	+	632.526i	−0.0665851	+	0.115329i	−0.897396	−	0.441226i	$-0.854544\pi$
$311$	−365.189	+	632.526i	−0.0665851	+	0.115329i	0.830811	+	0.556555i	$0.187877\pi$
$312$	97.4797			0.0176881
$313$	4111.36	−	7121.09i	0.742453	−	1.28597i	−0.208922	−	0.977932i	$-0.566995\pi$
$313$	4111.36	−	7121.09i	0.742453	−	1.28597i	0.951375	−	0.308034i	$-0.0996712\pi$
$314$	−87.1884	−	151.015i	−0.0156698	−	0.0271409i
$315$	1271.48	+	2202.27i	0.227428	+	0.393917i
$316$	1149.87	+	1991.63i	0.204700	+	0.354550i
$317$	−810.334			−0.143574			−0.0717869	−	0.997420i	$-0.522870\pi$
$317$	−810.334			−0.143574			−0.0717869	+	0.997420i	$0.522870\pi$
$318$	50.8405	+	88.0583i	0.00896539	+	0.0155285i
$319$	−2881.28	−	4990.53i	−0.505708	−	0.875913i
$320$	4070.68	−	7050.63i	0.711119	−	1.23169i
$321$	573.300	−	992.984i	0.0996837	−	0.172657i
$322$	48.4057			0.00837746
$323$	606.039			0.104399
$324$	2252.49	−	3901.43i	0.386230	−	0.668970i
$325$	−1581.08	+	2738.51i	−0.269854	+	0.467400i
$326$	−355.266	−	615.339i	−0.0603570	−	0.104541i
$327$	−926.782	−	1605.23i	−0.156731	−	0.271467i
$328$	−526.008			−0.0885485
$329$	−1821.15	−	3154.32i	−0.305177	−	0.528582i
$330$	−66.0864	−	114.465i	−0.0110241	−	0.0190942i
$331$	1912.97	+	3313.36i	0.317662	+	0.550207i	0.980000	−	0.198998i	$-0.0637688\pi$
$331$	1912.97	+	3313.36i	0.317662	+	0.550207i	−0.662337	+	0.749206i	$0.730435\pi$
$332$	−3320.10	+	5750.58i	−0.548837	+	0.950614i
$333$	−6058.63			−0.997029
$334$	177.578	−	307.575i	0.0290918	−	0.0503885i
$335$	3086.00	+	5345.11i	0.503303	+	0.871746i
$336$	566.580			0.0919925
$337$	−5448.00	−	9436.20i	−0.880627	−	1.52529i	−0.850645	−	0.525740i	$-0.823789\pi$
$337$	−5448.00	−	9436.20i	−0.880627	−	1.52529i	−0.0299814	−	0.999550i	$-0.509545\pi$
$338$	−162.513	+	281.481i	−0.0261525	+	0.0452974i
$339$	−815.169	+	1411.91i	−0.130601	+	0.226208i
$340$	7859.40			1.25364
$341$	3545.99	−	6141.84i	0.563127	−	0.975364i
$342$	−47.7760			−0.00755388
$343$	−4037.63			−0.635603
$344$	−859.073	−	21.3034i	−0.134646	−	0.00333896i
$345$	−955.369			−0.149088
$346$	414.255			0.0643655
$347$	−5152.95	+	8925.17i	−0.797189	+	1.38077i	0.124250	+	0.992251i	$0.460347\pi$
$347$	−5152.95	+	8925.17i	−0.797189	+	1.38077i	−0.921440	+	0.388521i	$0.872986\pi$
$348$	2241.65			0.345302
$349$	−2891.82	+	5008.77i	−0.443540	+	0.768233i	−0.997949	−	0.0640108i	$-0.979611\pi$
$349$	−2891.82	+	5008.77i	−0.443540	+	0.768233i	0.554410	+	0.832244i	$0.312944\pi$
$350$	84.6994	−	146.704i	0.0129354	−	0.0224047i
$351$	830.521	+	1438.50i	0.126296	+	0.218751i
$352$	1072.79			0.162443
$353$	5004.42	+	8667.90i	0.754556	+	1.30693i	0.945595	+	0.325347i	$0.105481\pi$
$353$	5004.42	+	8667.90i	0.754556	+	1.30693i	−0.191039	+	0.981582i	$0.561186\pi$
$354$	98.0702	−	169.863i	0.0147242	−	0.0255031i
$355$	−775.353			−0.115920
$356$	2736.31	−	4739.43i	0.407372	−	0.705588i
$357$	270.946	+	469.293i	0.0401681	+	0.0695732i
$358$	−193.273	−	334.759i	−0.0285330	−	0.0494206i
$359$	−2512.42	−	4351.64i	−0.369360	−	0.639751i	0.620105	−	0.784519i	$-0.287090\pi$
$359$	−2512.42	−	4351.64i	−0.369360	−	0.639751i	−0.989466	+	0.144768i	$0.953757\pi$
$360$	−1242.00			−0.181831
$361$	3379.12	+	5852.81i	0.492655	+	0.853304i
$362$	87.1536	+	150.954i	0.0126538	+	0.0219171i
$363$	333.658	−	577.913i	0.0482438	−	0.0835608i
$364$	552.512	−	956.979i	0.0795590	−	0.137800i
$365$	−11303.6			−1.62099
$366$	−194.372			−0.0277595
$367$	−4009.86	+	6945.29i	−0.570335	+	0.987850i	0.426196	+	0.904631i	$0.359853\pi$
$367$	−4009.86	+	6945.29i	−0.570335	+	0.987850i	−0.996531	+	0.0832191i	$0.973480\pi$
$368$	1282.53	−	2221.40i	0.181675	−	0.314670i
$369$	−2151.51	−	3726.52i	−0.303531	−	0.525731i
$370$	379.186	+	656.769i	0.0532782	+	0.0922805i
$371$	2310.57			0.323340
$372$	1379.40	+	2389.18i	0.192254	+	0.332993i
$373$	5161.82	+	8940.53i	0.716539	+	1.24108i	0.962363	+	0.271767i	$0.0876080\pi$
$373$	5161.82	+	8940.53i	0.716539	+	1.24108i	−0.245824	+	0.969314i	$0.579059\pi$
$374$	169.703	+	293.935i	0.0234630	+	0.0406391i
$375$	−202.198	+	350.218i	−0.0278440	+	0.0482271i
$376$	1778.92			0.243992
$377$	2175.94	−	3768.83i	0.297259	−	0.514867i
$378$	−44.4916	−	77.0617i	−0.00605397	−	0.0104858i
$379$	−2810.62			−0.380928			−0.190464	−	0.981694i	$-0.560999\pi$
$379$	−2810.62			−0.380928			−0.190464	+	0.981694i	$0.560999\pi$
$380$	−653.328	−	1131.60i	−0.0881974	−	0.152762i
$381$	−1426.89	+	2471.45i	−0.191868	+	0.332326i
$382$	19.1073	−	33.0948i	0.00255920	−	0.00443266i
$383$	−6097.28			−0.813463			−0.406731	−	0.913548i	$-0.633332\pi$
$383$	−6097.28			−0.813463			−0.406731	+	0.913548i	$0.633332\pi$
$384$	−277.996	+	481.504i	−0.0369438	+	0.0639886i
$385$	−3003.46			−0.397586
$386$	−114.764			−0.0151330
$387$	−3362.91	−	6173.27i	−0.441721	−	0.810865i
$388$	−9014.43			−1.17948
$389$	−8231.65			−1.07291			−0.536454	−	0.843930i	$-0.680236\pi$
$389$	−8231.65			−1.07291			−0.536454	+	0.843930i	$0.680236\pi$
$390$	49.9083	−	86.4437i	0.00648001	−	0.0112237i
$391$	2453.29			0.317310
$392$	463.335	−	802.519i	0.0596988	−	0.103401i
$393$	344.789	−	597.193i	0.0442553	−	0.0766524i
$394$	−46.5080	−	80.5542i	−0.00594680	−	0.0103002i
$395$	4720.51			0.601303
$396$	2923.09	+	5062.95i	0.370937	+	0.642481i
$397$	−2592.65	+	4490.60i	−0.327761	+	0.567699i	−0.982067	−	0.188531i	$-0.939628\pi$
$397$	−2592.65	+	4490.60i	−0.327761	+	0.567699i	0.654306	+	0.756230i	$0.272961\pi$
$398$	−544.571			−0.0685851
$399$	45.0459	−	78.0217i	0.00565192	−	0.00978941i
$400$	−4488.29	−	7773.95i	−0.561037	−	0.971744i
$401$	3340.64	+	5786.17i	0.416020	+	0.720567i	0.995535	−	0.0943944i	$-0.0300915\pi$
$401$	3340.64	+	5786.17i	0.416020	+	0.720567i	−0.579515	+	0.814961i	$0.696758\pi$
$402$	−51.8416	−	89.7923i	−0.00643190	−	0.0111404i
$403$	5355.85			0.662019
$404$	3325.82	+	5760.49i	0.409569	+	0.709394i
$405$	−4623.54	−	8008.20i	−0.567273	−	0.982545i
$406$	−116.566	+	201.899i	−0.0142490	+	0.0246800i
$407$	3577.89	−	6197.08i	0.435748	−	0.754737i
$408$	−264.664			−0.0321147
$409$	−1375.67			−0.166315			−0.0831573	−	0.996536i	$-0.526500\pi$
$409$	−1375.67			−0.166315			−0.0831573	+	0.996536i	$0.526500\pi$
$410$	−269.309	+	466.456i	−0.0324395	+	0.0561869i
$411$	−1868.94	+	3237.11i	−0.224302	+	0.388503i
$412$	−1541.14	−	2669.33i	−0.184288	−	0.319196i
$413$	−2228.52	−	3859.92i	−0.265517	−	0.459889i
$414$	−193.401			−0.0229592
$415$	6814.94	+	11803.8i	0.806101	+	1.39621i
$416$	405.083	+	701.624i	0.0477424	+	0.0826922i
$417$	587.621	+	1017.79i	0.0690070	+	0.119524i
$418$	28.2138	−	48.8678i	0.00330139	−	0.00571818i
$419$	3509.28			0.409164			0.204582	−	0.978849i	$-0.434416\pi$
$419$	3509.28			0.409164			0.204582	+	0.978849i	$0.434416\pi$
$420$	584.176	−	1011.82i	0.0678687	−	0.117552i
$421$	−1031.58	−	1786.74i	−0.119420	−	0.206842i	0.800118	−	0.599843i	$-0.204770\pi$
$421$	−1031.58	−	1786.74i	−0.119420	−	0.206842i	−0.919538	+	0.393001i	$0.871437\pi$
$422$	−882.504			−0.101800
$423$	7276.24	+	12602.8i	0.836367	+	1.44863i
$424$	−564.249	+	977.308i	−0.0646282	+	0.111939i
$425$	4292.73	−	7435.22i	0.489948	−	0.848615i
$426$	13.0251			0.00148138
$427$	−2208.43	+	3825.11i	−0.250289	+	0.433513i
$428$	6348.19			0.716942
$429$	−941.840			−0.105996
$430$	−458.725	+	750.908i	−0.0514458	+	0.0842139i
$431$	9348.39			1.04477			0.522385	−	0.852710i	$-0.325042\pi$
$431$	9348.39			1.04477			0.522385	+	0.852710i	$0.325042\pi$
$432$	−4715.29			−0.525150
$433$	4060.57	−	7033.11i	0.450666	−	0.780577i	−0.547761	−	0.836635i	$-0.684520\pi$
$433$	4060.57	−	7033.11i	0.450666	−	0.780577i	0.998428	+	0.0560576i	$0.0178531\pi$
$434$	−286.916			−0.0317337
$435$	2300.64	−	3984.82i	0.253580	−	0.439213i
$436$	5131.17	−	8887.44i	0.563620	−	0.976218i
$437$	−203.934	−	353.225i	−0.0223238	−	0.0386660i
$438$	189.889			0.0207152
$439$	−7116.17	−	12325.6i	−0.773659	−	1.34002i	−0.935545	−	0.353207i	$-0.885091\pi$
$439$	−7116.17	−	12325.6i	−0.773659	−	1.34002i	0.161886	−	0.986809i	$-0.448242\pi$
$440$	733.455	−	1270.38i	0.0794684	−	0.137643i
$441$	7580.63			0.818554
$442$	−128.159	+	221.979i	−0.0137917	+	0.0238879i
$443$	−2761.05	−	4782.27i	−0.296120	−	0.512895i	0.679125	−	0.734023i	$-0.262360\pi$
$443$	−2761.05	−	4782.27i	−0.296120	−	0.512895i	−0.975245	+	0.221128i	$0.929026\pi$
$444$	1391.80	+	2410.67i	0.148766	+	0.257670i
$445$	−5616.64	−	9728.31i	−0.598325	−	1.03633i
$446$	−305.574			−0.0324425
$447$	−2558.28	−	4431.07i	−0.270699	−	0.468864i
$448$	1553.92	+	2691.47i	0.163875	+	0.283840i
$449$	−5820.18	+	10080.8i	−0.611740	+	1.05956i	0.379207	+	0.925312i	$0.376197\pi$
$449$	−5820.18	+	10080.8i	−0.611740	+	1.05956i	−0.990947	+	0.134253i	$0.957137\pi$
$450$	−338.409	+	586.142i	−0.0354506	+	0.0614022i
$451$	5082.24			0.530628
$452$	−9026.42			−0.939308
$453$	2446.11	−	4236.79i	0.253705	−	0.439430i
$454$	321.187	−	556.312i	0.0332027	−	0.0575088i
$455$	−1134.10	−	1964.32i	−0.116852	−	0.202393i
$456$	22.0007	+	38.1063i	0.00225938	+	0.00391335i
$457$	11485.5			1.17564			0.587820	−	0.808992i	$-0.299987\pi$
$457$	11485.5			1.17564			0.587820	+	0.808992i	$0.299987\pi$
$458$	167.174	+	289.554i	0.0170557	+	0.0295414i
$459$	−2254.92	−	3905.63i	−0.229304	−	0.397166i
$460$	−2644.72	−	4580.79i	−0.268067	−	0.464305i
$461$	1759.52	−	3047.58i	0.177764	−	0.307896i	−0.763351	−	0.645985i	$-0.776447\pi$
$461$	1759.52	−	3047.58i	0.177764	−	0.307896i	0.941114	+	0.338089i	$0.109780\pi$
$462$	50.4550			0.00508091
$463$	1170.94	−	2028.12i	0.117533	−	0.203574i	−0.801256	−	0.598321i	$-0.795835\pi$
$463$	1170.94	−	2028.12i	0.117533	−	0.203574i	0.918790	+	0.394747i	$0.129168\pi$
$464$	6176.95	+	10698.8i	0.618013	+	1.07043i
$465$	5662.79			0.564743
$466$	−46.4993	−	80.5392i	−0.00462240	−	0.00800624i
$467$	1057.40	−	1831.47i	0.104777	−	0.181479i	−0.808870	−	0.587987i	$-0.799921\pi$
$467$	1057.40	−	1831.47i	0.104777	−	0.181479i	0.913647	+	0.406509i	$0.133254\pi$
$468$	−2207.51	+	3823.52i	−0.218039	+	0.377655i
$469$	−2356.07			−0.231969
$470$	910.783	−	1577.52i	0.0893858	−	0.154821i
$471$	−1313.79			−0.128527
$472$	2176.85			0.212283
$473$	8300.29	+	205.831i	0.806866	+	0.0200087i
$474$	−79.2996			−0.00768429
$475$	−1427.36			−0.137878
$476$	−1500.11	+	2598.26i	−0.144448	+	0.250191i
$477$	−9231.69			−0.886143
$478$	−99.6597	+	172.616i	−0.00953625	+	0.0165173i
$479$	−3212.30	+	5563.86i	−0.306417	+	0.530729i	−0.977576	−	0.210584i	$-0.932463\pi$
$479$	−3212.30	+	5563.86i	−0.306417	+	0.530729i	0.671159	+	0.741313i	$0.265797\pi$
$480$	428.298	+	741.834i	0.0407272	+	0.0705415i
$481$	5404.02			0.512271
$482$	531.555	+	920.681i	0.0502317	+	0.0870039i
$483$	182.349	−	315.838i	0.0171784	−	0.0297539i
$484$	3694.62			0.346978
$485$	−9251.65	+	16024.3i	−0.866177	+	1.50026i
$486$	270.184	+	467.973i	0.0252177	+	0.0436783i
$487$	−2018.97	−	3496.96i	−0.187861	−	0.325385i	0.756676	−	0.653790i	$-0.226822\pi$
$487$	−2018.97	−	3496.96i	−0.187861	−	0.325385i	−0.944537	+	0.328405i	$0.893489\pi$
$488$	−1078.61	−	1868.21i	−0.100054	−	0.173299i
$489$	−5353.29			−0.495060
$490$	−474.442	−	821.758i	−0.0437411	−	0.0757617i
$491$	−572.362	−	991.359i	−0.0526076	−	0.0911190i	0.838522	−	0.544867i	$-0.183420\pi$
$491$	−572.362	−	991.359i	−0.0526076	−	0.0911190i	−0.891130	+	0.453748i	$0.850087\pi$
$492$	−988.500	+	1712.13i	−0.0905793	+	0.156888i
$493$	−5907.81	+	10232.6i	−0.539705	+	0.934796i
$494$	42.6140			0.00388116
$495$	12000.1			1.08962
$496$	−7601.97	+	13167.0i	−0.688182	+	1.19197i
$497$	147.990	−	256.326i	0.0133566	−	0.0231344i
$498$	−114.484	−	198.292i	−0.0103015	−	0.0178427i
$499$	−2377.61	−	4118.14i	−0.213300	−	0.369446i	0.739446	−	0.673216i	$-0.235088\pi$
$499$	−2377.61	−	4118.14i	−0.213300	−	0.369446i	−0.952745	+	0.303771i	$0.901754\pi$
$500$	−2238.96			−0.200259
$501$	−1337.91	−	2317.33i	−0.119308	−	0.206648i
$502$	412.662	+	714.751i	0.0366892	+	0.0635476i
$503$	−7594.91	−	13154.8i	−0.673241	−	1.16609i	−0.976980	−	0.213333i	$-0.931568\pi$
$503$	−7594.91	−	13154.8i	−0.673241	−	1.16609i	0.303738	−	0.952756i	$-0.401765\pi$
$504$	237.057	−	410.595i	0.0209511	−	0.0362884i
$505$	13653.4			1.20310
$506$	114.212	−	197.820i	0.0100342	−	0.0173798i
$507$	1224.40	+	2120.73i	0.107254	+	0.185769i
$508$	−15800.1			−1.37995
$509$	1197.00	+	2073.27i	0.104236	+	0.180542i	0.913426	−	0.407005i	$-0.133427\pi$
$509$	1197.00	+	2073.27i	0.104236	+	0.180542i	−0.809190	+	0.587547i	$0.800094\pi$
$510$	−135.504	+	234.700i	−0.0117652	+	0.0203778i
$511$	2157.50	−	3736.90i	0.186775	−	0.323504i
$512$	−3838.95			−0.331366
$513$	−374.889	+	649.326i	−0.0322646	+	0.0558839i
$514$	−400.623			−0.0343788
$515$	−6326.79			−0.541343
$516$	−1683.75	+	2756.21i	−0.143650	+	0.235146i
$517$	−17187.8			−1.46212
$518$	−289.497			−0.0245555
$519$	1560.54	−	2702.93i	0.131985	−	0.228604i
$520$	1107.81			0.0934240
$521$	4591.27	−	7952.32i	0.386079	−	0.668709i	−0.605839	−	0.795587i	$-0.707162\pi$
$521$	4591.27	−	7952.32i	0.386079	−	0.668709i	0.991918	+	0.126878i	$0.0404958\pi$
$522$	465.731	−	806.670i	0.0390507	−	0.0676379i
$523$	8160.82	+	14135.0i	0.682310	+	1.18179i	0.974274	+	0.225366i	$0.0723577\pi$
$523$	8160.82	+	14135.0i	0.682310	+	1.18179i	−0.291965	+	0.956429i	$0.594309\pi$
$524$	3817.88			0.318292
$525$	−638.142	−	1105.29i	−0.0530492	−	0.0918839i
$526$	386.947	−	670.213i	0.0320755	−	0.0555564i
$527$	−14541.5			−1.20197
$528$	1336.83	−	2315.45i	0.110185	−	0.190847i
$529$	5257.96	+	9107.05i	0.432149	+	0.748504i
$530$	577.776	+	1000.74i	0.0473528	+	0.0820174i
$531$	8903.87	+	15421.9i	0.727674	+	1.26037i
$532$	498.796			0.0406496
$533$	1919.05	+	3323.89i	0.155953	+	0.270119i
$534$	94.3537	+	163.425i	0.00764623	+	0.0132437i
$535$	6515.25	−	11284.7i	0.526502	−	0.911929i
$536$	575.360	−	996.552i	0.0463652	−	0.0803069i
$537$	−2912.32			−0.234033
$538$	−1205.95			−0.0966398
$539$	−4476.70	+	7753.87i	−0.357746	+	0.619634i
$540$	−4861.73	+	8420.77i	−0.387436	+	0.671060i
$541$	11319.3	+	19605.6i	0.899549	+	1.55806i	0.828072	+	0.560622i	$0.189438\pi$
$541$	11319.3	+	19605.6i	0.899549	+	1.55806i	0.0714765	+	0.997442i	$0.477229\pi$
$542$	255.394	+	442.356i	0.0202401	+	0.0350569i
$543$	1313.27			0.103789
$544$	−1099.83	−	1904.96i	−0.0866814	−	0.150137i
$545$	−10532.4	−	18242.6i	−0.827813	−	1.43381i
$546$	19.0517	+	32.9986i	0.00149330	+	0.00258646i
$547$	11746.8	−	20346.1i	0.918206	−	1.59038i	0.116068	−	0.993241i	$-0.462971\pi$
$547$	11746.8	−	20346.1i	0.918206	−	1.59038i	0.802138	−	0.597139i	$-0.203696\pi$
$548$	−20695.0			−1.61322
$549$	8823.57	−	15282.9i	0.685940	−	1.18808i
$550$	−399.691	−	692.285i	−0.0309871	−	0.0536712i
$551$	1964.39			0.151880
$552$	89.0603	+	154.257i	0.00686713	+	0.0118942i
$553$	−900.993	+	1560.57i	−0.0692841	+	0.120004i
$554$	122.927	−	212.916i	0.00942723	−	0.0163284i
$555$	5713.72			0.436998
$556$	−3253.39	+	5635.03i	−0.248155	+	0.429818i
$557$	−2071.07			−0.157547			−0.0787737	−	0.996893i	$-0.525100\pi$
$557$	−2071.07			−0.157547			−0.0787737	+	0.996893i	$0.525100\pi$
$558$	1146.35			0.0869692
$559$	2999.56	+	5506.28i	0.226955	+	0.416620i
$560$	6438.88			0.485879
$561$	2557.16			0.192448
$562$	−57.8290	+	100.163i	−0.00434051	+	0.00751799i
$563$	−7675.72			−0.574588			−0.287294	−	0.957842i	$-0.592756\pi$
$563$	−7675.72			−0.574588			−0.287294	+	0.957842i	$0.592756\pi$
$564$	3343.04	−	5790.31i	0.249587	−	0.432298i
$565$	−9263.96	+	16045.7i	−0.689802	+	1.19477i
$566$	771.777	+	1336.76i	0.0573148	+	0.0992722i
$567$	3529.93			0.261452
$568$	72.2790	+	125.191i	0.00533937	+	0.00924806i
$569$	−3958.68	+	6856.64i	−0.291664	+	0.505176i	−0.974203	−	0.225672i	$-0.927542\pi$
$569$	−3958.68	+	6856.64i	−0.291664	+	0.505176i	0.682540	+	0.730849i	$0.260875\pi$
$570$	45.0562			0.00331087
$571$	3187.11	−	5520.24i	0.233584	−	0.404579i	−0.725276	−	0.688458i	$-0.758288\pi$
$571$	3187.11	−	5520.24i	0.233584	−	0.404579i	0.958860	+	0.283879i	$0.0916213\pi$
$572$	−2607.27	−	4515.92i	−0.190586	−	0.330105i
$573$	−143.958	−	249.343i	−0.0104955	−	0.0181788i
$574$	−102.805	−	178.063i	−0.00747558	−	0.0129481i
$575$	−5778.08			−0.419065
$576$	−6208.56	−	10753.5i	−0.449115	−	0.777890i
$577$	−422.965	−	732.597i	−0.0305169	−	0.0528569i	0.850364	−	0.526196i	$-0.176382\pi$
$577$	−422.965	−	732.597i	−0.0305169	−	0.0528569i	−0.880881	+	0.473339i	$0.843049\pi$
$578$	−121.012	+	209.599i	−0.00870839	+	0.0150834i
$579$	−432.326	+	748.811i	−0.0310309	+	0.0537470i
$580$	25475.2			1.82379
$581$	−5203.00			−0.371527
$582$	155.418	−	269.192i	0.0110692	−	0.0191725i
$583$	5451.72	−	9442.66i	0.387285	−	0.670798i
$584$	1053.74	+	1825.12i	0.0746642	+	0.129322i
$585$	4531.21	+	7848.28i	0.320243	+	0.554678i
$586$	−1615.24			−0.113865
$587$	−5651.54	−	9788.75i	−0.397383	−	0.688288i	0.596019	−	0.802970i	$-0.296748\pi$
$587$	−5651.54	−	9788.75i	−0.397383	−	0.688288i	−0.993402	+	0.114682i	$0.963415\pi$
$588$	−1741.44	−	3016.27i	−0.122136	−	0.211546i
$589$	1208.79	+	2093.68i	0.0845623	+	0.146466i
$590$	1114.52	−	1930.40i	0.0777693	−	0.134700i
$591$	−700.801			−0.0487768
$592$	−7670.35	+	13285.4i	−0.532516	+	0.922344i
$593$	−8136.87	−	14093.5i	−0.563476	−	0.975968i	−0.997190	−	0.0749179i	$-0.976131\pi$
$593$	−8136.87	−	14093.5i	−0.563476	−	0.975968i	0.433714	−	0.901051i	$-0.357203\pi$
$594$	−419.906			−0.0290050
$595$	3079.16	+	5333.27i	0.212157	+	0.367467i
$596$	14164.0	−	24532.8i	0.973456	−	1.68608i
$597$	−2051.45	+	3553.22i	−0.140637	+	0.243591i
$598$	172.505			0.0117964
$599$	10342.8	−	17914.2i	0.705499	−	1.22196i	−0.261012	−	0.965335i	$-0.584056\pi$
$599$	10342.8	−	17914.2i	0.705499	−	1.22196i	0.966511	−	0.256624i	$-0.0826103\pi$
$600$	623.345			0.0424132
$601$	3962.98			0.268974			0.134487	−	0.990915i	$-0.457061\pi$
$601$	3962.98			0.268974			0.134487	+	0.990915i	$0.457061\pi$
$602$	−160.689	−	294.975i	−0.0108790	−	0.0199706i
$603$	9413.48			0.635732
$604$	27086.0			1.82469
$605$	3791.85	−	6567.68i	0.254811	−	0.441346i
$606$	−229.362			−0.0153749
$607$	−4021.06	+	6964.69i	−0.268880	+	0.465713i	−0.968573	−	0.248730i	$-0.919987\pi$
$607$	−4021.06	+	6964.69i	−0.268880	+	0.465713i	0.699693	+	0.714443i	$0.253320\pi$
$608$	−182.850	+	316.706i	−0.0121966	+	0.0211252i
$609$	878.235	+	1521.15i	0.0584366	+	0.101215i
$610$	−2208.93			−0.146618
$611$	−6490.08	−	11241.1i	−0.429723	−	0.744301i
$612$	5993.54	−	10381.1i	0.395873	−	0.685672i
$613$	2499.78			0.164707			0.0823533	−	0.996603i	$-0.473756\pi$
$613$	2499.78			0.164707			0.0823533	+	0.996603i	$0.473756\pi$
$614$	−576.105	+	997.844i	−0.0378660	+	0.0655858i
$615$	2029.03	+	3514.38i	0.133038	+	0.230428i
$616$	279.985	+	484.949i	0.0183132	+	0.0317194i
$617$	7133.27	+	12355.2i	0.465437	+	0.806160i	0.999221	−	0.0394603i	$-0.0125639\pi$
$617$	7133.27	+	12355.2i	0.465437	+	0.806160i	−0.533784	+	0.845621i	$0.679231\pi$
$618$	106.283			0.00691804
$619$	−9276.31	−	16067.0i	−0.602336	−	1.04328i	−0.992466	−	0.122517i	$-0.960903\pi$
$619$	−9276.31	−	16067.0i	−0.602336	−	1.04328i	0.390130	−	0.920760i	$-0.372430\pi$
$620$	15676.1	+	27151.8i	1.01543	+	1.75878i
$621$	−1517.58	+	2628.52i	−0.0980648	+	0.169853i
$622$	69.7187	−	120.756i	0.00449432	−	0.00778438i
$623$	4288.14			0.275764
$624$	2019.14			0.129535
$625$	6589.60	−	11413.5i	0.421735	−	0.730466i
$626$	−784.905	+	1359.50i	−0.0501136	+	0.0867993i
$627$	−212.569	−	368.180i	−0.0135393	−	0.0234508i
$628$	−3636.92	−	6299.34i	−0.231097	−	0.400272i
$629$	−14672.3			−0.930082
$630$	−242.740	−	420.438i	−0.0153508	−	0.0265883i
$631$	2890.77	+	5006.96i	0.182377	+	0.315886i	0.942689	−	0.333671i	$-0.108288\pi$
$631$	2890.77	+	5006.96i	0.182377	+	0.315886i	−0.760313	+	0.649557i	$0.774954\pi$
$632$	−440.050	−	762.189i	−0.0276966	−	0.0479719i
$633$	−3324.48	+	5758.17i	−0.208746	+	0.361559i
$634$	154.702			0.00969084
$635$	−16215.9	+	28086.7i	−1.01340	+	1.75525i
$636$	2120.73	+	3673.21i	0.132221	+	0.229013i
$637$	−6761.58			−0.420571
$638$	550.070	+	952.749i	0.0341340	+	0.0591218i
$639$	−591.280	+	1024.13i	−0.0366051	+	0.0634019i
$640$	−3159.28	+	5472.04i	−0.195127	+	0.337971i
$641$	−11652.1			−0.717988			−0.358994	−	0.933340i	$-0.616880\pi$
$641$	−11652.1			−0.717988			−0.358994	+	0.933340i	$0.616880\pi$
$642$	−109.449	+	189.572i	−0.00672838	+	0.0116539i
$643$	16276.0			0.998232			0.499116	−	0.866535i	$-0.333658\pi$
$643$	16276.0			0.998232			0.499116	+	0.866535i	$0.333658\pi$
$644$	2019.16			0.123550
$645$	3171.46	+	5821.84i	0.193607	+	0.355403i
$646$	−115.700			−0.00704666
$647$	−8989.81			−0.546253			−0.273127	−	0.961978i	$-0.588058\pi$
$647$	−8989.81			−0.546253			−0.273127	+	0.961978i	$0.588058\pi$
$648$	−862.020	+	1493.06i	−0.0522583	+	0.0905140i
$649$	−21032.5			−1.27211
$650$	301.845	−	522.812i	0.0182144	−	0.0315483i
$651$	−1080.84	+	1872.07i	−0.0650715	+	0.112707i
$652$	−14819.3	−	25667.9i	−0.890139	−	1.54177i
$653$	−21403.8			−1.28269			−0.641345	−	0.767253i	$-0.721623\pi$
$653$	−21403.8			−1.28269			−0.641345	+	0.767253i	$0.721623\pi$
$654$	176.933	+	306.457i	0.0105790	+	0.0183233i
$655$	3918.35	−	6786.78i	0.233744	−	0.404857i
$656$	−10895.4			−0.648467
$657$	−8620.09	+	14930.4i	−0.511875	+	0.886594i
$658$	347.678	+	602.196i	0.0205986	+	0.0356779i
$659$	−1684.03	−	2916.82i	−0.0995453	−	0.172418i	0.811951	−	0.583725i	$-0.198405\pi$
$659$	−1684.03	−	2916.82i	−0.0995453	−	0.172418i	−0.911497	+	0.411308i	$0.865072\pi$
$660$	−2756.69	−	4774.72i	−0.162582	−	0.281600i
$661$	−2486.31			−0.146303			−0.0731516	−	0.997321i	$-0.523306\pi$
$661$	−2486.31			−0.146303			−0.0731516	+	0.997321i	$0.523306\pi$
$662$	−365.207	−	632.557i	−0.0214414	−	0.0371375i
$663$	965.579	+	1672.43i	0.0565610	+	0.0979666i
$664$	1270.59	−	2200.72i	0.0742596	−	0.128621i
$665$	511.923	−	886.676i	0.0298519	−	0.0517050i
$666$	1156.66			0.0672968
$667$	7952.00			0.461623
$668$	7407.40	−	12830.0i	0.429043	−	0.743125i
$669$	−1151.13	+	1993.81i	−0.0665249	+	0.115224i
$670$	−589.153	−	1020.44i	−0.0339716	−	0.0588405i
$671$	10421.4	+	18050.4i	0.599575	+	1.03849i
$672$	−326.993			−0.0187709
$673$	657.095	+	1138.12i	0.0376362	+	0.0651878i	0.884230	−	0.467052i	$-0.154684\pi$
$673$	657.095	+	1138.12i	0.0376362	+	0.0651878i	−0.846594	+	0.532240i	$0.821351\pi$
$674$	1040.08	+	1801.48i	0.0594399	+	0.102953i
$675$	5310.86	+	9198.68i	0.302837	+	0.524529i
$676$	−6778.96	+	11741.5i	−0.385694	+	0.668042i
$677$	22015.0			1.24978			0.624892	−	0.780711i	$-0.285143\pi$
$677$	22015.0			1.24978			0.624892	+	0.780711i	$0.285143\pi$
$678$	155.625	−	269.550i	0.00881525	−	0.0152685i
$679$	−3531.68	−	6117.05i	−0.199608	−	0.345730i
$680$	−3007.76			−0.169621
$681$	−2419.89	−	4191.36i	−0.136168	−	0.235849i
$682$	−676.970	+	1172.55i	−0.0380096	+	0.0658345i
$683$	890.777	−	1542.87i	0.0499043	−	0.0864368i	−0.839994	−	0.542595i	$-0.817442\pi$
$683$	890.777	−	1542.87i	0.0499043	−	0.0864368i	0.889898	+	0.456159i	$0.150775\pi$
$684$	−1992.90			−0.111404
$685$	−21239.6	+	36788.0i	−1.18470	+	2.05197i
$686$	770.830			0.0429015
$687$	2519.04			0.139895
$688$	−17794.3	−	441.265i	−0.986050	−	0.0244522i
$689$	8234.25			0.455298
$690$	182.391			0.0100630
$691$	8950.02	−	15501.9i	0.492728	−	0.853429i	−0.507237	−	0.861806i	$-0.669333\pi$
$691$	8950.02	−	15501.9i	0.492728	−	0.853429i	0.999965	+	0.00837716i	$0.00266657\pi$
$692$	17280.0			0.949257
$693$	−2290.42	+	3967.13i	−0.125550	+	0.217459i
$694$	983.756	−	1703.91i	0.0538081	−	0.0931984i
$695$	6678.01	+	11566.6i	0.364477	+	0.631292i
$696$	−857.870			−0.0467205
$697$	−5210.33	−	9024.56i	−0.283150	−	0.490430i
$698$	552.080	−	956.231i	0.0299377	−	0.0518537i
$699$	−700.671			−0.0379139
$700$	3533.10	−	6119.51i	0.190769	−	0.330422i
$701$	10927.0	+	18926.0i	0.588738	+	1.01972i	0.994398	+	0.105701i	$0.0337085\pi$
$701$	10927.0	+	18926.0i	0.588738	+	1.01972i	−0.405660	+	0.914024i	$0.632958\pi$
$702$	−158.556	−	274.627i	−0.00852465	−	0.0147651i
$703$	1219.66	+	2112.51i	0.0654343	+	0.113336i
$704$	14665.7			0.785135
$705$	−6862.02	−	11885.4i	−0.366580	−	0.634935i
$706$	−955.399	−	1654.80i	−0.0509305	−	0.0882142i
$707$	−2605.99	+	4513.70i	−0.138626	+	0.240106i
$708$	4090.84	−	7085.54i	0.217151	−	0.376117i
$709$	−6023.38			−0.319059			−0.159529	−	0.987193i	$-0.550998\pi$
$709$	−6023.38			−0.319059			−0.159529	+	0.987193i	$0.550998\pi$
$710$	148.024			0.00782426
$711$	3599.84	−	6235.10i	0.189880	−	0.328881i
$712$	−1047.18	+	1813.76i	−0.0551188	+	0.0954686i
$713$	4893.26	+	8475.37i	0.257018	+	0.445169i
$714$	−51.7267	−	89.5933i	−0.00271124	−	0.00469600i
$715$	−10703.5			−0.559845
$716$	−8062.09	−	13963.9i	−0.420802	−	0.728851i
$717$	750.856	+	1300.52i	0.0391091	+	0.0677390i
$718$	479.649	+	830.777i	0.0249308	+	0.0431815i
$719$	−16356.0	+	28329.5i	−0.848369	+	1.46942i	0.0342938	+	0.999412i	$0.489082\pi$
$719$	−16356.0	+	28329.5i	−0.848369	+	1.46942i	−0.882663	+	0.470007i	$0.844252\pi$
$720$	−25726.0			−1.33160
$721$	1207.58	−	2091.59i	0.0623753	−	0.108037i
$722$	−645.112	−	1117.37i	−0.0332529	−	0.0575957i
$723$	8009.69			0.412010
$724$	3635.47	+	6296.82i	0.186618	+	0.323231i
$725$	13914.3	−	24100.2i	0.712777	−	1.23457i
$726$	−63.6991	+	110.330i	−0.00325633	+	0.00564013i
$727$	1159.22			0.0591379			0.0295690	−	0.999563i	$-0.490587\pi$
$727$	1159.22			0.0591379			0.0295690	+	0.999563i	$0.490587\pi$
$728$	−211.444	+	366.232i	−0.0107646	+	0.0186449i
$729$	−11202.7			−0.569154
$730$	2157.99			0.109412
$731$	−8144.00	−	14949.9i	−0.412061	−	0.756419i
$732$	−8107.90			−0.409394
$733$	13950.0			0.702938			0.351469	−	0.936199i	$-0.385682\pi$
$733$	13950.0			0.702938			0.351469	+	0.936199i	$0.385682\pi$
$734$	765.528	−	1325.93i	0.0384961	−	0.0666772i
$735$	−7149.08			−0.358773
$736$	−740.191	+	1282.05i	−0.0370704	+	0.0642078i
$737$	−5559.08	+	9628.60i	−0.277844	+	0.481240i
$738$	410.747	+	711.434i	0.0204875	+	0.0354854i
$739$	−39671.7			−1.97476			−0.987381	−	0.158366i	$-0.949378\pi$
$739$	−39671.7			−1.97476			−0.987381	+	0.158366i	$0.949378\pi$
$740$	15817.1	+	27396.1i	0.785742	+	1.36094i
$741$	160.531	−	278.048i	0.00795851	−	0.0137846i
$742$	−441.115			−0.0218246
$743$	−3181.91	+	5511.23i	−0.157110	+	0.272123i	−0.933825	−	0.357729i	$-0.883551\pi$
$743$	−3181.91	+	5511.23i	−0.157110	+	0.272123i	0.776715	+	0.629852i	$0.216884\pi$
$744$	−527.890	−	914.332i	−0.0260126	−	0.0450552i
$745$	−29073.5	−	50356.7i	−1.42976	−	2.47641i
$746$	−985.449	−	1706.85i	−0.0483644	−	0.0837697i
$747$	20788.1			1.01820
$748$	7078.90	+	12261.0i	0.346030	+	0.599341i
$749$	2487.10	+	4307.78i	0.121331	+	0.210151i
$750$	38.6020	−	66.8606i	0.00187939	−	0.00325520i
$751$	14192.3	−	24581.8i	0.689593	−	1.19441i	−0.282377	−	0.959304i	$-0.591123\pi$
$751$	14192.3	−	24581.8i	0.689593	−	1.19441i	0.971970	−	0.235106i	$-0.0755439\pi$
$752$	36847.5			1.78682
$753$	6218.15			0.300932
$754$	−415.411	+	719.513i	−0.0200642	+	0.0347521i
$755$	27798.8	−	48148.8i	1.34000	−	2.32095i
$756$	−1855.89	−	3214.50i	−0.0892834	−	0.154643i
$757$	15444.3	+	26750.2i	0.741520	+	1.28435i	0.951803	+	0.306710i	$0.0992283\pi$
$757$	15444.3	+	26750.2i	0.741520	+	1.28435i	−0.210282	+	0.977641i	$0.567438\pi$
$758$	536.579			0.0257117
$759$	−860.493	−	1490.42i	−0.0411514	−	0.0712763i
$760$	250.026	+	433.058i	0.0119334	+	0.0206693i
$761$	11412.2	+	19766.5i	0.543615	+	0.941569i	0.998693	+	0.0511175i	$0.0162783\pi$
$761$	11412.2	+	19766.5i	0.543615	+	0.941569i	−0.455077	+	0.890452i	$0.650388\pi$
$762$	272.409	−	471.827i	0.0129506	−	0.0224311i
$763$	8041.17			0.381533
$764$	797.030	−	1380.50i	0.0377428	−	0.0653725i
$765$	−12302.5	−	21308.6i	−0.581436	−	1.00708i
$766$	1164.04			0.0549066
$767$	−7941.85	−	13755.7i	−0.373877	−	0.647573i
$768$	−2812.48	+	4871.35i	−0.132144	+	0.228880i
$769$	3645.94	−	6314.95i	0.170970	−	0.296129i	−0.767789	−	0.640702i	$-0.778643\pi$
$769$	3645.94	−	6314.95i	0.170970	−	0.296129i	0.938759	+	0.344574i	$0.111977\pi$
$770$	573.395			0.0268360
$771$	−1509.19	+	2613.99i	−0.0704954	+	0.122102i
$772$	−4787.18			−0.223179
$773$	24056.6			1.11935			0.559674	−	0.828713i	$-0.310926\pi$
$773$	24056.6			1.11935			0.559674	+	0.828713i	$0.310926\pi$
$774$	642.017	+	1178.55i	0.0298150	+	0.0547312i
$775$	34248.6			1.58741
$776$	3449.79			0.159588
$777$	−1090.56	+	1888.91i	−0.0503524	+	0.0872128i
$778$	1571.51			0.0724184
$779$	−866.238	+	1500.37i	−0.0398411	+	0.0690068i
$780$	2081.84	−	3605.86i	0.0955666	−	0.165526i
$781$	−698.354	−	1209.58i	−0.0319962	−	0.0554191i
$782$	−468.361			−0.0214176
$783$	−7309.00	−	12659.6i	−0.333592	−	0.577798i
$784$	9597.24	−	16622.9i	0.437192	−	0.757239i
$785$	−14930.5			−0.678845
$786$	−65.8242	+	114.011i	−0.00298711	+	0.00517383i
$787$	17548.6	+	30395.1i	0.794843	+	1.37671i	0.922939	+	0.384947i	$0.125780\pi$
$787$	17548.6	+	30395.1i	0.794843	+	1.37671i	−0.128095	+	0.991762i	$0.540886\pi$
$788$	−1940.01	−	3360.19i	−0.0877029	−	0.151906i
$789$	−2915.34	−	5049.52i	−0.131545	−	0.227842i
$790$	−901.199			−0.0405863
$791$	−3536.38	−	6125.19i	−0.158962	−	0.275331i
$792$	−1118.66	−	1937.57i	−0.0501891	−	0.0869300i
$793$	−7870.23	+	13631.6i	−0.352434	+	0.610433i
$794$	494.966	−	857.306i	0.0221230	−	0.0383182i
$795$	8706.15			0.388397
$796$	−22715.9			−1.01149
$797$	19618.6	−	33980.5i	0.871930	−	1.51023i	0.0119316	−	0.999929i	$-0.496202\pi$
$797$	19618.6	−	33980.5i	0.871930	−	1.51023i	0.859998	−	0.510297i	$-0.170465\pi$
$798$	−8.59976	+	14.8952i	−0.000381489	+	0.000660759i
$799$	17621.0	+	30520.4i	0.780207	+	1.35136i
$800$	2590.35	+	4486.62i	0.114478	+	0.198282i
$801$	−17132.9			−0.755756
$802$	−637.767	−	1104.64i	−0.0280802	−	0.0486363i
$803$	−10181.1	−	17634.2i	−0.447426	−	0.774965i
$804$	−2162.49	−	3745.54i	−0.0948571	−	0.164297i
$805$	2072.30	−	3589.33i	0.0907317	−	0.157152i
$806$	−1022.49			−0.0446845
$807$	−4542.94	+	7868.59i	−0.198165	+	0.343231i
$808$	−1272.78	−	2204.52i	−0.0554161	−	0.0959835i
$809$	21145.2			0.918945			0.459473	−	0.888192i	$-0.348038\pi$
$809$	21145.2			0.918945			0.459473	+	0.888192i	$0.348038\pi$
$810$	882.685	+	1528.86i	0.0382894	+	0.0663192i
$811$	−14302.0	+	24771.8i	−0.619250	+	1.07257i	0.370373	+	0.928883i	$0.379230\pi$
$811$	−14302.0	+	24771.8i	−0.619250	+	1.07257i	−0.989623	+	0.143689i	$0.954104\pi$
$812$	−4862.38	+	8421.89i	−0.210143	+	0.363978i
$813$	3848.38			0.166013
$814$	−683.059	+	1183.09i	−0.0294118	+	0.0509427i
$815$	−60837.3			−2.61477
$816$	−5482.08			−0.235185
$817$	−1475.50	+	2415.31i	−0.0631839	+	0.103428i
$818$	262.632			0.0112258
$819$	−3459.44			−0.147598
$820$	−11233.8	+	19457.5i	−0.478415	+	0.828640i
$821$	1010.47			0.0429547			0.0214773	−	0.999769i	$-0.493163\pi$
$821$	1010.47			0.0429547			0.0214773	+	0.999769i	$0.493163\pi$
$822$	356.802	−	618.000i	0.0151398	−	0.0262229i
$823$	−10776.2	+	18664.9i	−0.456420	+	0.790543i	−0.998769	−	0.0496107i	$-0.984202\pi$
$823$	−10776.2	+	18664.9i	−0.456420	+	0.790543i	0.542348	+	0.840154i	$0.317535\pi$
$824$	589.789	+	1021.54i	0.0249348	+	0.0431883i
$825$	−6022.70			−0.254162
$826$	425.450	+	736.901i	0.0179217	+	0.0310413i
$827$	−13263.9	+	22973.7i	−0.557716	+	0.965992i	0.439971	+	0.898012i	$0.354989\pi$
$827$	−13263.9	+	22973.7i	−0.557716	+	0.965992i	−0.997687	+	0.0679801i	$0.978345\pi$
$828$	−8067.39			−0.338600
$829$	21810.5	−	37776.9i	0.913763	−	1.58268i	0.105060	−	0.994466i	$-0.466496\pi$
$829$	21810.5	−	37776.9i	0.913763	−	1.58268i	0.808702	−	0.588218i	$-0.200170\pi$
$830$	−1301.05	−	2253.48i	−0.0544097	−	0.0942403i
$831$	−926.159	−	1604.15i	−0.0386620	−	0.0669645i
$832$	5537.76	+	9591.68i	0.230754	+	0.399677i
$833$	18358.1			0.763591
$834$	−112.183	−	194.307i	−0.00465779	−	0.00806753i
$835$	−15204.7	−	26335.3i	−0.630155	−	1.09146i
$836$	1176.89	−	2038.44i	0.0486887	−	0.0843312i
$837$	8995.18	−	15580.1i	0.371468	−	0.643402i
$838$	−669.962			−0.0276175
$839$	15663.1			0.644517			0.322259	−	0.946652i	$-0.395558\pi$
$839$	15663.1			0.644517			0.322259	+	0.946652i	$0.395558\pi$
$840$	−223.562	+	387.221i	−0.00918288	+	0.0159052i
$841$	−6954.85	+	12046.1i	−0.285163	+	0.493917i
$842$	196.940	+	341.109i	0.00806055	+	0.0139613i
$843$	435.695	+	754.646i	0.0178009	+	0.0308320i
$844$	−36812.2			−1.50134
$845$	13914.7	+	24101.0i	0.566486	+	0.981183i
$846$	−1389.12	−	2406.02i	−0.0564525	−	0.0977786i
$847$	1447.48	+	2507.11i	0.0587203	+	0.101707i
$848$	−11687.5	+	20243.4i	−0.473291	+	0.819764i
$849$	11629.4			0.470108
$850$	−819.530	+	1419.47i	−0.0330702	+	0.0572792i
$851$	4937.27	+	8551.61i	0.198881	+	0.344472i
$852$	543.321			0.0218473
$853$	9459.36	+	16384.1i	0.379698	+	0.657656i	0.991018	−	0.133727i	$-0.0426947\pi$
$853$	9459.36	+	16384.1i	0.379698	+	0.657656i	−0.611320	+	0.791383i	$0.709361\pi$
$854$	421.614	−	730.256i	0.0168938	−	0.0292609i
$855$	−2045.34	+	3542.64i	−0.0818119	+	0.141702i
$856$	−2429.43			−0.0970049
$857$	−7840.30	+	13579.8i	−0.312508	+	0.541280i	−0.978905	−	0.204318i	$-0.934502\pi$
$857$	−7840.30	+	13579.8i	−0.312508	+	0.541280i	0.666397	+	0.745598i	$0.267836\pi$
$858$	179.808			0.00715448
$859$	−5297.64			−0.210423			−0.105211	−	0.994450i	$-0.533552\pi$
$859$	−5297.64			−0.210423			−0.105211	+	0.994450i	$0.533552\pi$
$860$	−19135.0	+	31322.9i	−0.758718	+	1.24198i
$861$	−1549.10			−0.0613162
$862$	−1784.71			−0.0705192
$863$	22417.3	−	38827.9i	0.884234	−	1.53154i	0.0376458	−	0.999291i	$-0.488014\pi$
$863$	22417.3	−	38827.9i	0.884234	−	1.53154i	0.846589	−	0.532248i	$-0.178653\pi$
$864$	2721.36			0.107156
$865$	17734.7	−	30717.4i	0.697108	−	1.20743i
$866$	−775.209	+	1342.70i	−0.0304188	+	0.0526869i
$867$	911.731	+	1579.16i	0.0357139	+	0.0618584i
$868$	−11968.3			−0.468006
$869$	4251.73	+	7364.20i	0.165972	+	0.287472i
$870$	−439.218	+	760.748i	−0.0171160	+	0.0296457i
$871$	−8396.40			−0.326637
$872$	−1963.68	+	3401.19i	−0.0762598	+	0.132086i
$873$	14110.5	+	24440.1i	0.547043	+	0.947507i
$874$	38.9334	+	67.4346i	0.00150680	+	0.00260985i
$875$	−877.181	−	1519.32i	−0.0338905	−	0.0587000i
$876$	7920.92			0.305506
$877$	−2061.67	−	3570.92i	−0.0793816	−	0.137493i	0.823602	−	0.567169i	$-0.191961\pi$
$877$	−2061.67	−	3570.92i	−0.0793816	−	0.137493i	−0.902983	+	0.429676i	$0.858628\pi$
$878$	1358.56	+	2353.09i	0.0522199	+	0.0904475i
$879$	−6084.76	+	10539.1i	−0.233486	+	0.404409i
$880$	15192.3	−	26313.9i	0.581970	−	1.00800i
$881$	−16577.6			−0.633954			−0.316977	−	0.948433i	$-0.602668\pi$
$881$	−16577.6			−0.633954			−0.316977	+	0.948433i	$0.602668\pi$
$882$	−1447.23			−0.0552502
$883$	−5146.06	+	8913.23i	−0.196125	+	0.339699i	−0.947269	−	0.320440i	$-0.896169\pi$
$883$	−5146.06	+	8913.23i	−0.196125	+	0.339699i	0.751144	+	0.660139i	$0.229503\pi$
$884$	−5345.96	+	9259.48i	−0.203398	+	0.352296i
$885$	−8396.99	−	14544.0i	−0.318940	−	0.552420i
$886$	527.115	+	912.989i	0.0199873	+	0.0346190i
$887$	36360.5			1.37640			0.688200	−	0.725521i	$-0.258401\pi$
$887$	36360.5			1.37640			0.688200	+	0.725521i	$0.258401\pi$
$888$	−532.638	−	922.556i	−0.0201286	−	0.0348637i
$889$	−6190.17	−	10721.7i	−0.233534	−	0.404492i
$890$	1072.28	+	1857.24i	0.0403853	+	0.0699494i
$891$	8328.76	−	14425.8i	0.313158	−	0.542406i
$892$	−12746.5			−0.478458
$893$	2929.56	−	5074.14i	0.109780	−	0.190145i
$894$	488.404	+	845.940i	0.0182714	+	0.0316471i
$895$	−33097.0			−1.23610
$896$	−1206.01	−	2088.87i	−0.0449664	−	0.0778842i
$897$	649.842	−	1125.56i	0.0241891	−	0.0418967i
$898$	1111.14	−	1924.55i	0.0412908	−	0.0715178i
$899$	−47134.1			−1.74862
$900$	−14116.2	+	24449.9i	−0.522822	+	0.905553i
$901$	−22356.5			−0.826641
$902$	−970.257			−0.0358160
$903$	−2529.99	−	62.7388i	−0.0932366	−	0.00231209i
$904$	3454.38			0.127092
$905$	14924.6			0.548187
$906$	−466.990	+	808.850i	−0.0171244	+	0.0296603i
$907$	7338.83			0.268668			0.134334	−	0.990936i	$-0.457111\pi$
$907$	7338.83			0.268668			0.134334	+	0.990936i	$0.457111\pi$
$908$	13397.8	−	23205.6i	0.489671	−	0.848135i
$909$	10412.0	−	18034.1i	0.379916	−	0.658034i
$910$	216.513	+	375.012i	0.00788719	+	0.0136610i
$911$	−30551.5			−1.11111			−0.555553	−	0.831481i	$-0.687493\pi$
$911$	−30551.5			−1.11111			−0.555553	+	0.831481i	$0.687493\pi$
$912$	455.709	+	789.310i	0.0165461	+	0.0286586i
$913$	−12276.3	+	21263.2i	−0.445002	+	0.770766i
$914$	−2192.70			−0.0793525
$915$	−8321.27	+	14412.9i	−0.300648	+	0.520737i
$916$	6973.39	+	12078.3i	0.251536	+	0.435674i
$917$	1495.77	+	2590.75i	0.0538656	+	0.0932979i
$918$	430.489	+	745.629i	0.0154774	+	0.0268077i
$919$	36007.4			1.29246			0.646232	−	0.763141i	$-0.276344\pi$
$919$	36007.4			1.29246			0.646232	+	0.763141i	$0.276344\pi$
$920$	1012.12	+	1753.05i	0.0362704	+	0.0628221i
$921$	4340.49	+	7517.95i	0.155292	+	0.268974i
$922$	−335.912	+	581.817i	−0.0119986	+	0.0207821i
$923$	527.395	−	913.474i	0.0188076	−	0.0325757i
$924$	2104.65			0.0749328
$925$	34556.6			1.22834
$926$	−223.545	+	387.191i	−0.00793319	+	0.0137407i
$927$	−4824.77	+	8356.76i	−0.170945	+	0.296086i
$928$	−3564.93	−	6174.65i	−0.126104	−	0.218419i
$929$	16240.6	+	28129.6i	0.573560	+	0.993435i	0.996196	+	0.0871361i	$0.0277715\pi$
$929$	16240.6	+	28129.6i	0.573560	+	0.993435i	−0.422636	+	0.906299i	$0.638895\pi$
$930$	−1081.09			−0.0381186
$931$	−1526.05	−	2643.20i	−0.0537212	−	0.0930478i
$932$	−1939.64	−	3359.56i	−0.0681708	−	0.118075i
$933$	−525.274	−	909.802i	−0.0184316	−	0.0319245i
$934$	−201.870	+	349.649i	−0.00707215	+	0.0122493i
$935$	29060.8			1.01646
$936$	844.806	−	1463.25i	0.0295015	−	0.0510980i
$937$	−8410.69	−	14567.7i	−0.293239	−	0.507905i	0.681335	−	0.731972i	$-0.261400\pi$
$937$	−8410.69	−	14567.7i	−0.293239	−	0.507905i	−0.974574	+	0.224067i	$0.928067\pi$
$938$	449.801			0.0156573
$939$	5913.63	+	10242.7i	0.205521	+	0.355973i
$940$	37991.9	−	65803.8i	1.31825	−	2.28328i
$941$	13740.7	−	23799.5i	0.476018	−	0.824488i	−0.523604	−	0.851962i	$-0.675413\pi$
$941$	13740.7	−	23799.5i	0.476018	−	0.824488i	0.999623	+	0.0274738i	$0.00874627\pi$
$942$	250.817			0.00867523
$943$	−3506.59	+	6073.60i	−0.121093	+	0.209739i
$944$	45089.9			1.55461
$945$	−7618.94			−0.262269
$946$	−1584.62	−	39.2955i	−0.0544613	−	0.00135054i
$947$	108.644			0.00372806			0.00186403	−	0.999998i	$-0.499407\pi$
$947$	108.644			0.00372806			0.00186403	+	0.999998i	$0.499407\pi$
$948$	−3307.86			−0.113327
$949$	7688.73	−	13317.3i	0.263000	−	0.455529i
$950$	272.500			0.00930639
$951$	582.777	−	1009.40i	0.0198716	−	0.0344185i
$952$	574.085	−	994.344i	0.0195443	−	0.0338518i
$953$	−14099.0	−	24420.1i	−0.479234	−	0.830058i	0.520482	−	0.853873i	$-0.325752\pi$
$953$	−14099.0	−	24420.1i	−0.479234	−	0.830058i	−0.999716	+	0.0238146i	$0.992419\pi$
$954$	1762.43			0.0598123
$955$	−1636.01	−	2833.65i	−0.0554346	−	0.0960155i
$956$	−4157.14	+	7200.38i	−0.140640	+	0.243595i
$957$	8288.67			0.279973
$958$	613.264	−	1062.20i	0.0206823	−	0.0358228i
$959$	−8107.89	−	14043.3i	−0.273011	−	0.472869i
$960$	5855.12	+	10141.4i	0.196847	+	0.340949i
$961$	−14108.5	−	24436.6i	−0.473581	−	0.820267i
$962$	−1031.69			−0.0345769
$963$	−9936.99	−	17211.4i	−0.332518	−	0.575938i
$964$	22173.0	+	38404.7i	0.740813	+	1.28312i
$965$	−4913.16	+	8509.85i	−0.163897	+	0.283877i
$966$	−34.8125	+	60.2970i	−0.00115950	+	0.00200831i
$967$	29918.6			0.994950			0.497475	−	0.867478i	$-0.334261\pi$
$967$	29918.6			0.994950			0.497475	+	0.867478i	$0.334261\pi$
$968$	−1413.92			−0.0469474
$969$	−435.852	+	754.919i	−0.0144495	+	0.0250273i
$970$	1766.24	−	3059.23i	0.0584646	−	0.101264i
$971$	10448.3	+	18097.0i	0.345316	+	0.598105i	0.985411	−	0.170191i	$-0.0544384\pi$
$971$	10448.3	+	18097.0i	0.345316	+	0.598105i	−0.640095	+	0.768296i	$0.721105\pi$
$972$	11270.3	+	19520.7i	0.371908	+	0.644164i
$973$	−5098.46			−0.167985
$974$	385.444	+	667.609i	0.0126801	+	0.0219626i
$975$	−2274.16	−	3938.97i	−0.0746990	−	0.129382i
$976$	−22341.6	−	38696.9i	−0.732724	−	1.26912i
$977$	17945.7	−	31082.9i	0.587650	−	1.01784i	−0.406889	−	0.913477i	$-0.633387\pi$
$977$	17945.7	−	31082.9i	0.587650	−	1.01784i	0.994539	−	0.104362i	$-0.0332801\pi$
$978$	1022.00			0.0334152
$979$	10117.7	−	17524.4i	0.330300	−	0.572097i
$980$	−19790.6	−	34278.3i	−0.645089	−	1.11733i
$981$	−32127.8			−1.04563
$982$	109.270	+	189.262i	0.00355087	+	0.00615029i
$983$	−1738.54	+	3011.24i	−0.0564098	+	0.0977047i	−0.892851	−	0.450352i	$-0.851299\pi$
$983$	−1738.54	+	3011.24i	−0.0564098	+	0.0977047i	0.836442	+	0.548056i	$0.184632\pi$
$984$	378.295	−	655.226i	0.0122557	−	0.0212275i
$985$	−7964.24			−0.257626
$986$	1127.87	−	1953.52i	0.0364286	−	0.0630962i
$987$	5238.95			0.168954
$988$	1777.57			0.0572390
$989$	−5972.94	+	9777.36i	−0.192041	+	0.314360i
$990$	−2290.95			−0.0735466
$991$	−33877.8			−1.08594			−0.542968	−	0.839753i	$-0.682700\pi$
$991$	−33877.8			−1.08594			−0.542968	+	0.839753i	$0.682700\pi$
$992$	4387.36	−	7599.13i	0.140422	−	0.243218i
$993$	−5503.09			−0.175866
$994$	−28.2529	+	48.9355i	−0.000901537	+	0.00156151i
$995$	−23313.7	+	40380.5i	−0.742807	+	1.28658i
$996$	−4775.50	−	8271.42i	−0.151925	−	0.263142i
$997$	15043.0			0.477850			0.238925	−	0.971038i	$-0.423205\pi$
$997$	15043.0			0.477850			0.238925	+	0.971038i	$0.423205\pi$
$998$	453.913	+	786.200i	0.0143971	+	0.0249366i
$999$	9076.09	−	15720.2i	0.287442	−	0.497864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.6.5	✓	20
43.6	even	3		1849.4.a.d.1.5		10
43.36	even	3	inner	43.4.c.a.36.5	yes	20
43.37	odd	6		1849.4.a.f.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.5	✓	20	1.1	even	1	trivial
43.4.c.a.36.5	yes	20	43.36	even	3	inner
1849.4.a.d.1.5		10	43.6	even	3
1849.4.a.f.1.6		10	43.37	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.190911 q^{2} +(-0.719182 + 1.24566i) q^{3} -7.96355 q^{4} +(-8.17312 + 14.1563i) q^{5} +(0.137300 - 0.237810i) q^{6} +(-3.11997 - 5.40394i) q^{7} +3.04762 q^{8} +(12.4656 + 21.5910i) q^{9} +O(q^{10})\)	\(q-0.190911 q^{2} +(-0.719182 + 1.24566i) q^{3} -7.96355 q^{4} +(-8.17312 + 14.1563i) q^{5} +(0.137300 - 0.237810i) q^{6} +(-3.11997 - 5.40394i) q^{7} +3.04762 q^{8} +(12.4656 + 21.5910i) q^{9} +(1.56034 - 2.70259i) q^{10} -29.4459 q^{11} +(5.72724 - 9.91987i) q^{12} +(-11.1187 - 19.2582i) q^{13} +(0.595637 + 1.03167i) q^{14} +(-11.7559 - 20.3618i) q^{15} +63.1266 q^{16} +(30.1880 + 52.2872i) q^{17} +(-2.37981 - 4.12196i) q^{18} +(5.01887 - 8.69294i) q^{19} +(65.0871 - 112.734i) q^{20} +8.97530 q^{21} +5.62155 q^{22} +(20.3168 - 35.1897i) q^{23} +(-2.19179 + 3.79630i) q^{24} +(-71.0999 - 123.149i) q^{25} +(2.12269 + 3.67660i) q^{26} -74.6958 q^{27} +(24.8460 + 43.0346i) q^{28} +(97.8503 + 169.482i) q^{29} +(2.24434 + 3.88731i) q^{30} +(-120.424 + 208.581i) q^{31} -36.4326 q^{32} +(21.1769 - 36.6795i) q^{33} +(-5.76323 - 9.98221i) q^{34} +102.000 q^{35} +(-99.2701 - 171.941i) q^{36} +(-121.507 + 210.457i) q^{37} +(-0.958159 + 1.65958i) q^{38} +31.9855 q^{39} +(-24.9086 + 43.1429i) q^{40} -172.596 q^{41} -1.71349 q^{42} +(-281.883 - 6.99017i) q^{43} +234.494 q^{44} -407.530 q^{45} +(-3.87870 + 6.71810i) q^{46} +583.708 q^{47} +(-45.3995 + 78.6342i) q^{48} +(152.032 - 263.326i) q^{49} +(13.5738 + 23.5104i) q^{50} -86.8427 q^{51} +(88.5444 + 153.363i) q^{52} +(-185.144 + 320.679i) q^{53} +14.2603 q^{54} +(240.665 - 416.843i) q^{55} +(-9.50848 - 16.4692i) q^{56} +(7.21896 + 12.5036i) q^{57} +(-18.6807 - 32.3559i) q^{58} +714.277 q^{59} +(93.6189 + 162.153i) q^{60} +(-353.918 - 613.004i) q^{61} +(22.9903 - 39.8204i) q^{62} +(77.7843 - 134.726i) q^{63} -498.057 q^{64} +363.498 q^{65} +(-4.04291 + 7.00253i) q^{66} +(188.790 - 326.993i) q^{67} +(-240.404 - 416.392i) q^{68} +(29.2229 + 50.6155i) q^{69} -19.4729 q^{70} +(23.7165 + 41.0783i) q^{71} +(37.9903 + 65.8011i) q^{72} +(345.757 + 598.868i) q^{73} +(23.1971 - 40.1786i) q^{74} +204.535 q^{75} +(-39.9681 + 69.2267i) q^{76} +(91.8701 + 159.124i) q^{77} -6.10639 q^{78} +(-144.391 - 250.093i) q^{79} +(-515.941 + 893.637i) q^{80} +(-282.850 + 489.911i) q^{81} +32.9505 q^{82} +(416.911 - 722.112i) q^{83} -71.4753 q^{84} -986.922 q^{85} +(53.8147 + 1.33450i) q^{86} -281.488 q^{87} -89.7398 q^{88} +(-343.605 + 595.141i) q^{89} +77.8021 q^{90} +(-69.3801 + 120.170i) q^{91} +(-161.794 + 280.235i) q^{92} +(-173.214 - 300.015i) q^{93} -111.436 q^{94} +(82.0397 + 142.097i) q^{95} +(26.2016 - 45.3825i) q^{96} +1131.96 q^{97} +(-29.0245 + 50.2720i) q^{98} +(-367.059 - 635.765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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