LMFDB - Embedded newform 43.4.c.a.36.5

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			36.5
Root			$0.0954556 + 0.165334i$ of defining polynomial
Character	$\chi$	$=$	43.36
Dual form			43.4.c.a.6.5

$q$-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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

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	0.788487	−	0.615051i	$-0.210865\pi$
$3$	−0.719182	−	1.24566i	−0.138407	−	0.239727i	−0.926894	+	0.375324i	$0.877531\pi$
$4$	−7.96355			−0.995444
$5$	−8.17312	−	14.1563i	−0.731026	−	1.26617i	−0.956445	−	0.291913i	$-0.905708\pi$
$5$	−8.17312	−	14.1563i	−0.731026	−	1.26617i	0.225419	−	0.974262i	$-0.427625\pi$
$6$	0.137300	+	0.237810i	0.00934207	+	0.0161809i
$7$	−3.11997	+	5.40394i	−0.168462	+	0.291786i	−0.937879	−	0.346961i	$-0.887214\pi$
$7$	−3.11997	+	5.40394i	−0.168462	+	0.291786i	0.769417	+	0.638747i	$0.220547\pi$
$8$	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	−0.959914	−	0.280296i	$-0.909567\pi$
$13$	−11.1187	+	19.2582i	−0.237214	+	0.410866i	0.722700	+	0.691162i	$0.242901\pi$
$14$	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	−0.566246	−	0.824236i	$-0.691605\pi$
$17$	30.1880	−	52.2872i	0.430687	−	0.745971i	0.996933	+	0.0782653i	$0.0249381\pi$
$18$	−2.37981	+	4.12196i	−0.0311627	+	0.0539753i
$19$	5.01887	+	8.69294i	0.0606004	+	0.104963i	0.894734	−	0.446600i	$-0.147365\pi$
$19$	5.01887	+	8.69294i	0.0606004	+	0.104963i	−0.834134	+	0.551563i	$0.814032\pi$
$20$	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	0.943303	−	0.331933i	$-0.107701\pi$
$23$	20.3168	+	35.1897i	0.184189	+	0.319024i	−0.759114	+	0.650957i	$0.774368\pi$
$24$	−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	−0.361673	−	0.932305i	$-0.617794\pi$
$29$	97.8503	−	169.482i	0.626563	−	1.08524i	0.988236	−	0.152935i	$-0.0488724\pi$
$30$	2.24434	−	3.88731i	0.0136586	−	0.0236574i
$31$	−120.424	−	208.581i	−0.697704	−	1.20846i	−0.969261	−	0.246036i	$-0.920872\pi$
$31$	−120.424	−	208.581i	−0.697704	−	1.20846i	0.271557	−	0.962422i	$-0.412462\pi$
$32$	−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	−0.998910	−	0.0466828i	$-0.985135\pi$
$37$	−121.507	−	210.457i	−0.539883	−	0.935105i	0.459026	−	0.888423i	$-0.348198\pi$
$38$	−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	0.519893	−	0.854231i	$-0.325972\pi$
$53$	−185.144	−	320.679i	−0.479839	−	0.831106i	−0.999733	+	0.0231250i	$0.992638\pi$
$54$	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	0.208325	+	0.978060i	$0.433199\pi$
$61$	−353.918	+	613.004i	−0.742862	+	1.28667i	−0.951187	+	0.308615i	$0.900135\pi$
$62$	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	0.985216	−	0.171316i	$-0.0548020\pi$
$67$	188.790	+	326.993i	0.344244	+	0.596248i	−0.640972	+	0.767564i	$0.721469\pi$
$68$	−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	−0.845523	−	0.533939i	$-0.820711\pi$
$71$	23.7165	−	41.0783i	0.0396428	−	0.0686633i	0.885166	+	0.465275i	$0.154045\pi$
$72$	37.9903	−	65.8011i	0.0621833	−	0.107705i
$73$	345.757	−	598.868i	0.554353	−	0.960167i	−0.443601	−	0.896224i	$-0.646299\pi$
$73$	345.757	−	598.868i	0.554353	−	0.960167i	0.997954	−	0.0639425i	$-0.0203674\pi$
$74$	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	−0.950335	−	0.311228i	$-0.899260\pi$
$79$	−144.391	+	250.093i	−0.205637	+	0.356173i	0.744699	+	0.667401i	$0.232593\pi$
$80$	−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	0.998178	+	0.0603450i	$0.0192201\pi$
$83$	416.911	+	722.112i	0.551349	+	0.954965i	−0.446829	+	0.894620i	$0.647447\pi$
$84$	−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	0.585568	−	0.810623i	$-0.300871\pi$
$89$	−343.605	−	595.141i	−0.409236	−	0.708818i	−0.994804	+	0.101805i	$0.967538\pi$
$90$	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	−0.995048	−	0.0993973i	$-0.968309\pi$
$101$	−417.630	+	723.357i	−0.411443	+	0.712641i	0.583604	+	0.812038i	$0.301642\pi$
$102$	16.5792			0.0160940
$103$	193.524	−	335.194i	0.185131	−	0.320657i	−0.758490	−	0.651685i	$-0.774062\pi$
$103$	193.524	−	335.194i	0.185131	−	0.320657i	0.943621	+	0.331029i	$0.107396\pi$
$104$	−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	−0.996937	−	0.0782089i	$-0.975080\pi$
$109$	−644.331	−	1116.01i	−0.566199	−	0.980686i	0.430738	−	0.902477i	$-0.358253\pi$
$110$	−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	0.963329	−	0.268322i	$-0.0864691\pi$
$139$	408.535	+	707.603i	0.249291	+	0.431785i	−0.714038	+	0.700107i	$0.753136\pi$
$140$	−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	−0.669972	−	0.742386i	$-0.733694\pi$
$149$	−1778.60	−	3080.63i	−0.977911	−	1.69379i	−0.307939	−	0.951406i	$-0.599639\pi$
$150$	−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	−0.726287	−	0.687391i	$-0.758756\pi$
$157$	456.696	−	791.021i	0.232155	−	0.402104i	0.958442	+	0.285287i	$0.0920891\pi$
$158$	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	0.0594365	−	0.998232i	$-0.481070\pi$
$163$	1860.90	−	3223.17i	0.894213	−	1.54882i	0.834776	−	0.550590i	$-0.185597\pi$
$164$	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	0.565953	−	0.824437i	$-0.308508\pi$
$167$	−930.163	−	1611.09i	−0.431007	−	0.746526i	−0.996960	+	0.0779115i	$0.975175\pi$
$168$	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	−0.573477	−	0.819221i	$-0.694406\pi$
$179$	1012.37	−	1753.48i	0.422728	−	0.732186i	0.996205	+	0.0870351i	$0.0277392\pi$
$180$	3245.39			1.34387
$181$	−456.514	+	790.705i	−0.187472	+	0.324711i	−0.944407	−	0.328780i	$-0.893363\pi$
$181$	−456.514	+	790.705i	−0.187472	+	0.324711i	0.756935	+	0.653490i	$0.226696\pi$
$182$	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	0.846445	−	0.532476i	$-0.178738\pi$
$191$	−100.085	−	173.352i	−0.0379156	−	0.0656717i	−0.884360	+	0.466805i	$0.845405\pi$
$192$	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	−0.818606	−	0.574356i	$-0.805252\pi$
$197$	243.611	−	421.946i	0.0881043	−	0.152601i	0.906710	+	0.421755i	$0.138586\pi$
$198$	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	0.508045	−	0.861331i	$-0.330369\pi$
$227$	−1682.39	−	2913.98i	−0.491912	−	0.852017i	−0.999957	+	0.00931415i	$0.997035\pi$
$228$	−57.4886	+	99.5732i	−0.0166986	+	0.0289228i
$229$	−875.663	+	1516.69i	−0.252688	+	0.437668i	−0.964265	−	0.264940i	$-0.914648\pi$
$229$	−875.663	+	1516.69i	−0.252688	+	0.437668i	0.711577	+	0.702608i	$0.247981\pi$
$230$	−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	−0.829751	−	0.558134i	$-0.811518\pi$
$233$	243.565	−	421.867i	0.0684828	−	0.118616i	0.898234	+	0.439518i	$0.144851\pi$
$234$	−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	0.927980	−	0.372630i	$-0.121544\pi$
$239$	522.021	+	904.167i	0.141283	+	0.244710i	−0.786697	+	0.617340i	$0.788210\pi$
$240$	−742.111	+	1285.37i	−0.199596	+	0.345711i
$241$	−2784.31	+	4822.56i	−0.744203	+	1.28900i	0.206363	+	0.978475i	$0.433837\pi$
$241$	−2784.31	+	4822.56i	−0.744203	+	1.28900i	−0.950566	+	0.310522i	$0.899496\pi$
$242$	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	0.455130	+	0.890425i	$0.349593\pi$
$251$	−2161.54	+	3743.89i	−0.543566	+	0.941483i	−0.998696	+	0.0510582i	$0.983741\pi$
$252$	−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	0.524385	−	0.851481i	$-0.324295\pi$
$263$	−2026.84	−	3510.60i	−0.475211	−	0.823090i	−0.999597	+	0.0283906i	$0.990962\pi$
$264$	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	−0.976105	−	0.217300i	$-0.930275\pi$
$271$	−1337.76	+	2317.08i	−0.299865	+	0.519381i	0.676240	+	0.736682i	$0.263608\pi$
$272$	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	0.787703	−	0.616055i	$-0.211270\pi$
$277$	−643.898	−	1115.26i	−0.139668	−	0.241912i	−0.927371	+	0.374143i	$0.877937\pi$
$278$	−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	0.896386	−	0.443274i	$-0.146183\pi$
$281$	302.910	+	524.656i	0.0643065	+	0.111382i	−0.832080	+	0.554656i	$0.812850\pi$
$282$	80.1430	+	138.812i	0.0169236	+	0.0293125i
$283$	−4042.59	+	7001.98i	−0.849142	+	1.47076i	0.0328324	+	0.999461i	$0.489547\pi$
$283$	−4042.59	+	7001.98i	−0.849142	+	1.47076i	−0.881975	+	0.471297i	$0.843786\pi$
$284$	−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	0.997410	+	0.0719323i	$0.0229166\pi$
$307$	3017.66	+	5226.74i	0.561000	+	0.971680i	−0.436410	+	0.899748i	$0.643750\pi$
$308$	−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	0.830811	−	0.556555i	$-0.187877\pi$
$311$	−365.189	−	632.526i	−0.0665851	−	0.115329i	−0.897396	+	0.441226i	$0.854544\pi$
$312$	97.4797			0.0176881
$313$	4111.36	+	7121.09i	0.742453	+	1.28597i	0.951375	+	0.308034i	$0.0996712\pi$
$313$	4111.36	+	7121.09i	0.742453	+	1.28597i	−0.208922	+	0.977932i	$0.566995\pi$
$314$	−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	−0.662337	−	0.749206i	$-0.730435\pi$
$331$	1912.97	−	3313.36i	0.317662	−	0.550207i	0.980000	+	0.198998i	$0.0637688\pi$
$332$	−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	−0.0299814	+	0.999550i	$0.509545\pi$
$337$	−5448.00	+	9436.20i	−0.880627	+	1.52529i	−0.850645	+	0.525740i	$0.823789\pi$
$338$	−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	−0.921440	−	0.388521i	$-0.872986\pi$
$347$	−5152.95	−	8925.17i	−0.797189	−	1.38077i	0.124250	−	0.992251i	$-0.460347\pi$
$348$	2241.65			0.345302
$349$	−2891.82	−	5008.77i	−0.443540	−	0.768233i	0.554410	−	0.832244i	$-0.312944\pi$
$349$	−2891.82	−	5008.77i	−0.443540	−	0.768233i	−0.997949	+	0.0640108i	$0.979611\pi$
$350$	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	−0.191039	−	0.981582i	$-0.561186\pi$
$353$	5004.42	−	8667.90i	0.754556	−	1.30693i	0.945595	−	0.325347i	$-0.105481\pi$
$354$	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	−0.989466	−	0.144768i	$-0.953757\pi$
$359$	−2512.42	+	4351.64i	−0.369360	+	0.639751i	0.620105	+	0.784519i	$0.287090\pi$
$360$	−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	−0.996531	−	0.0832191i	$-0.973480\pi$
$367$	−4009.86	−	6945.29i	−0.570335	−	0.987850i	0.426196	−	0.904631i	$-0.359853\pi$
$368$	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	−0.245824	−	0.969314i	$-0.579059\pi$
$373$	5161.82	−	8940.53i	0.716539	−	1.24108i	0.962363	−	0.271767i	$-0.0876080\pi$
$374$	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	0.654306	−	0.756230i	$-0.272961\pi$
$397$	−2592.65	−	4490.60i	−0.327761	−	0.567699i	−0.982067	+	0.188531i	$0.939628\pi$
$398$	−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	−0.579515	−	0.814961i	$-0.696758\pi$
$401$	3340.64	−	5786.17i	0.416020	−	0.720567i	0.995535	+	0.0943944i	$0.0300915\pi$
$402$	−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	−0.919538	−	0.393001i	$-0.871437\pi$
$421$	−1031.58	+	1786.74i	−0.119420	+	0.206842i	0.800118	+	0.599843i	$0.204770\pi$
$422$	−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	0.998428	−	0.0560576i	$-0.0178531\pi$
$433$	4060.57	+	7033.11i	0.450666	+	0.780577i	−0.547761	+	0.836635i	$0.684520\pi$
$434$	−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	0.161886	+	0.986809i	$0.448242\pi$
$439$	−7116.17	+	12325.6i	−0.773659	+	1.34002i	−0.935545	+	0.353207i	$0.885091\pi$
$440$	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	−0.975245	−	0.221128i	$-0.929026\pi$
$443$	−2761.05	+	4782.27i	−0.296120	+	0.512895i	0.679125	+	0.734023i	$0.262360\pi$
$444$	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	−0.990947	−	0.134253i	$-0.957137\pi$
$449$	−5820.18	−	10080.8i	−0.611740	−	1.05956i	0.379207	−	0.925312i	$-0.376197\pi$
$450$	−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	0.941114	−	0.338089i	$-0.109780\pi$
$461$	1759.52	+	3047.58i	0.177764	+	0.307896i	−0.763351	+	0.645985i	$0.776447\pi$
$462$	50.4550			0.00508091
$463$	1170.94	+	2028.12i	0.117533	+	0.203574i	0.918790	−	0.394747i	$-0.129168\pi$
$463$	1170.94	+	2028.12i	0.117533	+	0.203574i	−0.801256	+	0.598321i	$0.795835\pi$
$464$	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	0.913647	−	0.406509i	$-0.133254\pi$
$467$	1057.40	+	1831.47i	0.104777	+	0.181479i	−0.808870	+	0.587987i	$0.799921\pi$
$468$	−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	0.671159	−	0.741313i	$-0.265797\pi$
$479$	−3212.30	−	5563.86i	−0.306417	−	0.530729i	−0.977576	+	0.210584i	$0.932463\pi$
$480$	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	−0.944537	−	0.328405i	$-0.893489\pi$
$487$	−2018.97	+	3496.96i	−0.187861	+	0.325385i	0.756676	+	0.653790i	$0.226822\pi$
$488$	−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	−0.891130	−	0.453748i	$-0.850087\pi$
$491$	−572.362	+	991.359i	−0.0526076	+	0.0911190i	0.838522	+	0.544867i	$0.183420\pi$
$492$	−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	−0.952745	−	0.303771i	$-0.901754\pi$
$499$	−2377.61	+	4118.14i	−0.213300	+	0.369446i	0.739446	+	0.673216i	$0.235088\pi$
$500$	−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	0.303738	+	0.952756i	$0.401765\pi$
$503$	−7594.91	+	13154.8i	−0.673241	+	1.16609i	−0.976980	+	0.213333i	$0.931568\pi$
$504$	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	−0.809190	−	0.587547i	$-0.800094\pi$
$509$	1197.00	−	2073.27i	0.104236	−	0.180542i	0.913426	+	0.407005i	$0.133427\pi$
$510$	−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	0.991918	−	0.126878i	$-0.0404958\pi$
$521$	4591.27	+	7952.32i	0.386079	+	0.668709i	−0.605839	+	0.795587i	$0.707162\pi$
$522$	465.731	+	806.670i	0.0390507	+	0.0676379i
$523$	8160.82	−	14135.0i	0.682310	−	1.18179i	−0.291965	−	0.956429i	$-0.594309\pi$
$523$	8160.82	−	14135.0i	0.682310	−	1.18179i	0.974274	−	0.225366i	$-0.0723577\pi$
$524$	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	0.0714765	−	0.997442i	$-0.477229\pi$
$541$	11319.3	−	19605.6i	0.899549	−	1.55806i	0.828072	−	0.560622i	$-0.189438\pi$
$542$	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	0.802138	+	0.597139i	$0.203696\pi$
$547$	11746.8	+	20346.1i	0.918206	+	1.59038i	0.116068	+	0.993241i	$0.462971\pi$
$548$	−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	0.682540	−	0.730849i	$-0.260875\pi$
$569$	−3958.68	−	6856.64i	−0.291664	−	0.505176i	−0.974203	+	0.225672i	$0.927542\pi$
$570$	45.0562			0.00331087
$571$	3187.11	+	5520.24i	0.233584	+	0.404579i	0.958860	−	0.283879i	$-0.0916213\pi$
$571$	3187.11	+	5520.24i	0.233584	+	0.404579i	−0.725276	+	0.688458i	$0.758288\pi$
$572$	−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	−0.880881	−	0.473339i	$-0.843049\pi$
$577$	−422.965	+	732.597i	−0.0305169	+	0.0528569i	0.850364	+	0.526196i	$0.176382\pi$
$578$	−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	−0.993402	−	0.114682i	$-0.963415\pi$
$587$	−5651.54	+	9788.75i	−0.397383	+	0.688288i	0.596019	+	0.802970i	$0.296748\pi$
$588$	−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	0.433714	+	0.901051i	$0.357203\pi$
$593$	−8136.87	+	14093.5i	−0.563476	+	0.975968i	−0.997190	+	0.0749179i	$0.976131\pi$
$594$	−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	0.966511	+	0.256624i	$0.0826103\pi$
$599$	10342.8	+	17914.2i	0.705499	+	1.22196i	−0.261012	+	0.965335i	$0.584056\pi$
$600$	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	0.699693	−	0.714443i	$-0.253320\pi$
$607$	−4021.06	−	6964.69i	−0.268880	−	0.465713i	−0.968573	+	0.248730i	$0.919987\pi$
$608$	−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	−0.533784	−	0.845621i	$-0.679231\pi$
$617$	7133.27	−	12355.2i	0.465437	−	0.806160i	0.999221	+	0.0394603i	$0.0125639\pi$
$618$	106.283			0.00691804
$619$	−9276.31	+	16067.0i	−0.602336	+	1.04328i	0.390130	+	0.920760i	$0.372430\pi$
$619$	−9276.31	+	16067.0i	−0.602336	+	1.04328i	−0.992466	+	0.122517i	$0.960903\pi$
$620$	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	−0.760313	−	0.649557i	$-0.774954\pi$
$631$	2890.77	−	5006.96i	0.182377	−	0.315886i	0.942689	+	0.333671i	$0.108288\pi$
$632$	−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	−0.911497	−	0.411308i	$-0.865072\pi$
$659$	−1684.03	+	2916.82i	−0.0995453	+	0.172418i	0.811951	+	0.583725i	$0.198405\pi$
$660$	−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	−0.846594	−	0.532240i	$-0.821351\pi$
$673$	657.095	−	1138.12i	0.0376362	−	0.0651878i	0.884230	+	0.467052i	$0.154684\pi$
$674$	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	0.889898	−	0.456159i	$-0.150775\pi$
$683$	890.777	+	1542.87i	0.0499043	+	0.0864368i	−0.839994	+	0.542595i	$0.817442\pi$
$684$	−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	0.999965	−	0.00837716i	$-0.00266657\pi$
$691$	8950.02	+	15501.9i	0.492728	+	0.853429i	−0.507237	+	0.861806i	$0.669333\pi$
$692$	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	−0.405660	−	0.914024i	$-0.632958\pi$
$701$	10927.0	−	18926.0i	0.588738	−	1.01972i	0.994398	−	0.105701i	$-0.0337085\pi$
$702$	−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	−0.882663	−	0.470007i	$-0.844252\pi$
$719$	−16356.0	−	28329.5i	−0.848369	−	1.46942i	0.0342938	−	0.999412i	$-0.489082\pi$
$720$	−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	0.776715	−	0.629852i	$-0.216884\pi$
$743$	−3181.91	−	5511.23i	−0.157110	−	0.272123i	−0.933825	+	0.357729i	$0.883551\pi$
$744$	−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	0.971970	+	0.235106i	$0.0755439\pi$
$751$	14192.3	+	24581.8i	0.689593	+	1.19441i	−0.282377	+	0.959304i	$0.591123\pi$
$752$	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	−0.210282	−	0.977641i	$-0.567438\pi$
$757$	15444.3	−	26750.2i	0.741520	−	1.28435i	0.951803	−	0.306710i	$-0.0992283\pi$
$758$	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	−0.455077	−	0.890452i	$-0.650388\pi$
$761$	11412.2	−	19766.5i	0.543615	−	0.941569i	0.998693	−	0.0511175i	$-0.0162783\pi$
$762$	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	0.938759	−	0.344574i	$-0.111977\pi$
$769$	3645.94	+	6314.95i	0.170970	+	0.296129i	−0.767789	+	0.640702i	$0.778643\pi$
$770$	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	−0.128095	−	0.991762i	$-0.540886\pi$
$787$	17548.6	−	30395.1i	0.794843	−	1.37671i	0.922939	−	0.384947i	$-0.125780\pi$
$788$	−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	0.859998	+	0.510297i	$0.170465\pi$
$797$	19618.6	+	33980.5i	0.871930	+	1.51023i	0.0119316	+	0.999929i	$0.496202\pi$
$798$	−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	−0.989623	−	0.143689i	$-0.954104\pi$
$811$	−14302.0	−	24771.8i	−0.619250	−	1.07257i	0.370373	−	0.928883i	$-0.379230\pi$
$812$	−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	0.542348	−	0.840154i	$-0.317535\pi$
$823$	−10776.2	−	18664.9i	−0.456420	−	0.790543i	−0.998769	+	0.0496107i	$0.984202\pi$
$824$	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	−0.997687	−	0.0679801i	$-0.978345\pi$
$827$	−13263.9	−	22973.7i	−0.557716	−	0.965992i	0.439971	−	0.898012i	$-0.354989\pi$
$828$	−8067.39			−0.338600
$829$	21810.5	+	37776.9i	0.913763	+	1.58268i	0.808702	+	0.588218i	$0.200170\pi$
$829$	21810.5	+	37776.9i	0.913763	+	1.58268i	0.105060	+	0.994466i	$0.466496\pi$
$830$	−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	−0.611320	−	0.791383i	$-0.709361\pi$
$853$	9459.36	−	16384.1i	0.379698	−	0.657656i	0.991018	+	0.133727i	$0.0426947\pi$
$854$	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	0.666397	−	0.745598i	$-0.267836\pi$
$857$	−7840.30	−	13579.8i	−0.312508	−	0.541280i	−0.978905	+	0.204318i	$0.934502\pi$
$858$	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	0.846589	+	0.532248i	$0.178653\pi$
$863$	22417.3	+	38827.9i	0.884234	+	1.53154i	0.0376458	+	0.999291i	$0.488014\pi$
$864$	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	−0.902983	−	0.429676i	$-0.858628\pi$
$877$	−2061.67	+	3570.92i	−0.0793816	+	0.137493i	0.823602	+	0.567169i	$0.191961\pi$
$878$	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	0.751144	−	0.660139i	$-0.229503\pi$
$883$	−5146.06	−	8913.23i	−0.196125	−	0.339699i	−0.947269	+	0.320440i	$0.896169\pi$
$884$	−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	−0.422636	−	0.906299i	$-0.638895\pi$
$929$	16240.6	−	28129.6i	0.573560	−	0.993435i	0.996196	−	0.0871361i	$-0.0277715\pi$
$930$	−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	−0.974574	−	0.224067i	$-0.928067\pi$
$937$	−8410.69	+	14567.7i	−0.293239	+	0.507905i	0.681335	+	0.731972i	$0.261400\pi$
$938$	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	0.999623	−	0.0274738i	$-0.00874627\pi$
$941$	13740.7	+	23799.5i	0.476018	+	0.824488i	−0.523604	+	0.851962i	$0.675413\pi$
$942$	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	−0.999716	−	0.0238146i	$-0.992419\pi$
$953$	−14099.0	+	24420.1i	−0.479234	+	0.830058i	0.520482	+	0.853873i	$0.325752\pi$
$954$	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	−0.640095	−	0.768296i	$-0.721105\pi$
$971$	10448.3	−	18097.0i	0.345316	−	0.598105i	0.985411	+	0.170191i	$0.0544384\pi$
$972$	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	0.994539	+	0.104362i	$0.0332801\pi$
$977$	17945.7	+	31082.9i	0.587650	+	1.01784i	−0.406889	+	0.913477i	$0.633387\pi$
$978$	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	0.836442	−	0.548056i	$-0.184632\pi$
$983$	−1738.54	−	3011.24i	−0.0564098	−	0.0977047i	−0.892851	+	0.450352i	$0.851299\pi$
$984$	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.36.5	yes	20
43.6	even	3	inner	43.4.c.a.6.5	✓	20
43.7	odd	6		1849.4.a.f.1.6		10
43.36	even	3		1849.4.a.d.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.5	✓	20	43.6	even	3	inner
43.4.c.a.36.5	yes	20	1.1	even	1	trivial
1849.4.a.d.1.5		10	43.36	even	3
1849.4.a.f.1.6		10	43.7	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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