LMFDB - Embedded newform 105.3.n.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(31,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.n (of order $6$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 456 x^{8} - 1050 x^{7} + 1999 x^{6} - 2844 x^{5} + 2949 x^{4} + \cdots + 36 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 456x^8 - 1050x^7 + 1999x^6 - 2844x^5 + 2949x^4 - 2136x^3 + 1020x^2 - 288*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.1
Root			$0.500000 - 0.0182799i$ of defining polynomial
Character	$\chi$	$=$	105.61
Dual form			105.3.n.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99068 + 3.44796i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-5.92561 - 10.2635i) q^{4} +(-1.93649 - 1.11803i) q^{5} +6.89592i q^{6} +(2.28451 - 6.61672i) q^{7} +31.2586 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.99068 + 3.44796i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-5.92561 - 10.2635i) q^{4} +(-1.93649 - 1.11803i) q^{5} +6.89592i q^{6} +(2.28451 - 6.61672i) q^{7} +31.2586 q^{8} +(1.50000 - 2.59808i) q^{9} +(7.70987 - 4.45130i) q^{10} +(-1.73163 - 2.99927i) q^{11} +(-17.7768 - 10.2635i) q^{12} -11.3934i q^{13} +(18.2665 + 21.0487i) q^{14} -3.87298 q^{15} +(-38.5233 + 66.7244i) q^{16} +(4.14259 - 2.39172i) q^{17} +(5.97204 + 10.3439i) q^{18} +(-1.06215 - 0.613231i) q^{19} +26.5001i q^{20} +(-2.30348 - 11.9035i) q^{21} +13.7885 q^{22} +(7.08353 - 12.2690i) q^{23} +(46.8878 - 27.0707i) q^{24} +(2.50000 + 4.33013i) q^{25} +(39.2839 + 22.6806i) q^{26} -5.19615i q^{27} +(-81.4476 + 15.7611i) q^{28} -29.3839 q^{29} +(7.70987 - 13.3539i) q^{30} +(34.9746 - 20.1926i) q^{31} +(-90.8581 - 157.371i) q^{32} +(-5.19488 - 2.99927i) q^{33} +19.0446i q^{34} +(-11.8217 + 10.2591i) q^{35} -35.5537 q^{36} +(12.4812 - 21.6180i) q^{37} +(4.22879 - 2.44150i) q^{38} +(-9.86695 - 17.0901i) q^{39} +(-60.5319 - 34.9481i) q^{40} +12.0897i q^{41} +(45.6284 + 15.7538i) q^{42} +4.34737 q^{43} +(-20.5219 + 35.5450i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(28.2021 + 48.8475i) q^{46} +(46.6006 + 26.9049i) q^{47} +133.449i q^{48} +(-38.5620 - 30.2320i) q^{49} -19.9068 q^{50} +(4.14259 - 7.17517i) q^{51} +(-116.935 + 67.5127i) q^{52} +(12.8965 + 22.3373i) q^{53} +(17.9161 + 10.3439i) q^{54} +7.74407i q^{55} +(71.4105 - 206.829i) q^{56} -2.12430 q^{57} +(58.4939 - 101.314i) q^{58} +(-81.6878 + 47.1625i) q^{59} +(22.9498 + 39.7502i) q^{60} +(44.0700 + 25.4438i) q^{61} +160.788i q^{62} +(-13.7640 - 15.8604i) q^{63} +415.291 q^{64} +(-12.7382 + 22.0632i) q^{65} +(20.6827 - 11.9412i) q^{66} +(1.22557 + 2.12275i) q^{67} +(-49.0948 - 28.3449i) q^{68} -24.5381i q^{69} +(-11.8397 - 61.1831i) q^{70} -96.9398 q^{71} +(46.8878 - 81.2121i) q^{72} +(-6.88877 + 3.97723i) q^{73} +(49.6920 + 86.0690i) q^{74} +(7.50000 + 4.33013i) q^{75} +14.5351i q^{76} +(-23.8012 + 4.60584i) q^{77} +78.5677 q^{78} +(-52.3611 + 90.6921i) q^{79} +(149.200 - 86.1408i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-41.6848 - 24.0668i) q^{82} +57.4797i q^{83} +(-108.522 + 94.1774i) q^{84} -10.6961 q^{85} +(-8.65423 + 14.9896i) q^{86} +(-44.0758 + 25.4472i) q^{87} +(-54.1282 - 93.7527i) q^{88} +(43.6908 + 25.2249i) q^{89} -26.7078i q^{90} +(-75.3868 - 26.0283i) q^{91} -167.897 q^{92} +(34.9746 - 60.5777i) q^{93} +(-185.534 + 107.118i) q^{94} +(1.37123 + 2.37504i) q^{95} +(-272.574 - 157.371i) q^{96} -50.7907i q^{97} +(181.003 - 72.7781i) q^{98} -10.3898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9	$ 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9} + 20 q^{11} - 66 q^{12} + 32 q^{14} - 82 q^{16} - 78 q^{17} - 6 q^{18} - 6 q^{19} + 36 q^{21} + 56 q^{22} + 2 q^{23} + 60 q^{24} + 30 q^{25} + 36 q^{26} - 128 q^{28} - 100 q^{29} + 108 q^{31} - 108 q^{32} + 60 q^{33} - 60 q^{35} - 132 q^{36} - 34 q^{37} + 126 q^{38} - 42 q^{39} - 90 q^{40} + 114 q^{42} - 124 q^{43} + 234 q^{44} + 278 q^{46} + 96 q^{47} - 60 q^{49} + 20 q^{50} - 78 q^{51} - 444 q^{52} - 76 q^{53} - 18 q^{54} + 112 q^{56} - 12 q^{57} - 52 q^{58} - 270 q^{59} + 60 q^{60} - 60 q^{61} + 42 q^{63} + 700 q^{64} - 60 q^{65} + 84 q^{66} - 18 q^{67} + 108 q^{68} - 300 q^{70} - 628 q^{71} + 60 q^{72} + 234 q^{73} + 244 q^{74} + 90 q^{75} - 196 q^{77} + 72 q^{78} + 108 q^{79} + 480 q^{80} - 54 q^{81} + 480 q^{82} - 192 q^{84} - 60 q^{85} + 130 q^{86} - 150 q^{87} - 668 q^{88} - 186 q^{89} + 444 q^{91} + 456 q^{92} + 108 q^{93} + 30 q^{94} - 324 q^{96} + 416 q^{98} + 120 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9 + 20 * q^11 - 66 * q^12 + 32 * q^14 - 82 * q^16 - 78 * q^17 - 6 * q^18 - 6 * q^19 + 36 * q^21 + 56 * q^22 + 2 * q^23 + 60 * q^24 + 30 * q^25 + 36 * q^26 - 128 * q^28 - 100 * q^29 + 108 * q^31 - 108 * q^32 + 60 * q^33 - 60 * q^35 - 132 * q^36 - 34 * q^37 + 126 * q^38 - 42 * q^39 - 90 * q^40 + 114 * q^42 - 124 * q^43 + 234 * q^44 + 278 * q^46 + 96 * q^47 - 60 * q^49 + 20 * q^50 - 78 * q^51 - 444 * q^52 - 76 * q^53 - 18 * q^54 + 112 * q^56 - 12 * q^57 - 52 * q^58 - 270 * q^59 + 60 * q^60 - 60 * q^61 + 42 * q^63 + 700 * q^64 - 60 * q^65 + 84 * q^66 - 18 * q^67 + 108 * q^68 - 300 * q^70 - 628 * q^71 + 60 * q^72 + 234 * q^73 + 244 * q^74 + 90 * q^75 - 196 * q^77 + 72 * q^78 + 108 * q^79 + 480 * q^80 - 54 * q^81 + 480 * q^82 - 192 * q^84 - 60 * q^85 + 130 * q^86 - 150 * q^87 - 668 * q^88 - 186 * q^89 + 444 * q^91 + 456 * q^92 + 108 * q^93 + 30 * q^94 - 324 * q^96 + 416 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.99068	+	3.44796i	−0.995340	+	1.72398i	−0.414161	+	0.910204i	$0.635925\pi$
$2$	−1.99068	+	3.44796i	−0.995340	+	1.72398i	−0.581179	+	0.813776i	$0.697408\pi$
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−5.92561	−	10.2635i	−1.48140	−	2.56587i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$6$			6.89592i			1.14932i
$7$	2.28451	−	6.61672i	0.326359	−	0.945246i
$7$	2.28451	−	6.61672i	0.326359	−	0.945246i
$8$	31.2586			3.90732
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	7.70987	−	4.45130i	0.770987	−	0.445130i
$11$	−1.73163	−	2.99927i	−0.157421	−	0.272661i	0.776517	−	0.630096i	$-0.216985\pi$
$11$	−1.73163	−	2.99927i	−0.157421	−	0.272661i	−0.933938	+	0.357436i	$0.883651\pi$
$12$	−17.7768	−	10.2635i	−1.48140	−	0.855289i
$13$		−	11.3934i		−	0.876413i	−0.898874	−	0.438207i	$-0.855614\pi$
$13$		−	11.3934i		−	0.876413i	0.898874	−	0.438207i	$-0.144386\pi$
$14$	18.2665	+	21.0487i	1.30475	+	1.50348i
$15$	−3.87298			−0.258199
$16$	−38.5233	+	66.7244i	−2.40771	+	4.17027i
$17$	4.14259	−	2.39172i	0.243682	−	0.140690i	−0.373186	−	0.927757i	$-0.621735\pi$
$17$	4.14259	−	2.39172i	0.243682	−	0.140690i	0.616868	+	0.787067i	$0.288401\pi$
$18$	5.97204	+	10.3439i	0.331780	+	0.574660i
$19$	−1.06215	−	0.613231i	−0.0559025	−	0.0322753i	0.471788	−	0.881712i	$-0.343609\pi$
$19$	−1.06215	−	0.613231i	−0.0559025	−	0.0322753i	−0.527691	+	0.849437i	$0.676942\pi$
$20$			26.5001i			1.32501i
$21$	−2.30348	−	11.9035i	−0.109690	−	0.566835i
$22$	13.7885			0.626748
$23$	7.08353	−	12.2690i	0.307980	−	0.533436i	−0.669941	−	0.742415i	$-0.733680\pi$
$23$	7.08353	−	12.2690i	0.307980	−	0.533436i	0.977920	+	0.208978i	$0.0670138\pi$
$24$	46.8878	−	27.0707i	1.95366	−	1.12795i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	39.2839	+	22.6806i	1.51092	+	0.872329i
$27$		−	5.19615i		−	0.192450i
$28$	−81.4476	+	15.7611i	−2.90884	+	0.562898i
$29$	−29.3839			−1.01324			−0.506618	−	0.862170i	$-0.669105\pi$
$29$	−29.3839			−1.01324			−0.506618	+	0.862170i	$0.669105\pi$
$30$	7.70987	−	13.3539i	0.256996	−	0.445130i
$31$	34.9746	−	20.1926i	1.12821	−	0.651373i	0.184727	−	0.982790i	$-0.440860\pi$
$31$	34.9746	−	20.1926i	1.12821	−	0.651373i	0.943484	+	0.331417i	$0.107527\pi$
$32$	−90.8581	−	157.371i	−2.83932	−	4.91784i
$33$	−5.19488	−	2.99927i	−0.157421	−	0.0908868i
$34$			19.0446i			0.560136i
$35$	−11.8217	+	10.2591i	−0.337762	+	0.293116i
$36$	−35.5537			−0.987602
$37$	12.4812	−	21.6180i	0.337329	−	0.584270i	−0.646601	−	0.762829i	$-0.723810\pi$
$37$	12.4812	−	21.6180i	0.337329	−	0.584270i	0.983929	+	0.178558i	$0.0571433\pi$
$38$	4.22879	−	2.44150i	0.111284	−	0.0642499i
$39$	−9.86695	−	17.0901i	−0.252999	−	0.438207i
$40$	−60.5319	−	34.9481i	−1.51330	−	0.873703i
$41$			12.0897i			0.294871i	0.989072	+	0.147436i	$0.0471019\pi$
$41$			12.0897i			0.294871i	−0.989072	+	0.147436i	$0.952898\pi$
$42$	45.6284	+	15.7538i	1.08639	+	0.375091i
$43$	4.34737			0.101102			0.0505508	−	0.998721i	$-0.483902\pi$
$43$	4.34737			0.101102			0.0505508	+	0.998721i	$0.483902\pi$
$44$	−20.5219	+	35.5450i	−0.466407	+	0.807840i
$45$	−5.80948	+	3.35410i	−0.129099	+	0.0745356i
$46$	28.2021	+	48.8475i	0.613089	+	1.06190i
$47$	46.6006	+	26.9049i	0.991503	+	0.572444i	0.905723	−	0.423870i	$-0.139329\pi$
$47$	46.6006	+	26.9049i	0.991503	+	0.572444i	0.0857797	+	0.996314i	$0.472662\pi$
$48$			133.449i			2.78018i
$49$	−38.5620	−	30.2320i	−0.786980	−	0.616979i
$50$	−19.9068			−0.398136
$51$	4.14259	−	7.17517i	0.0812272	−	0.140690i
$52$	−116.935	+	67.5127i	−2.24876	+	1.29832i
$53$	12.8965	+	22.3373i	0.243330	+	0.421459i	0.961661	−	0.274242i	$-0.0884270\pi$
$53$	12.8965	+	22.3373i	0.243330	+	0.421459i	−0.718331	+	0.695701i	$0.755094\pi$
$54$	17.9161	+	10.3439i	0.331780	+	0.191553i
$55$			7.74407i			0.140801i
$56$	71.4105	−	206.829i	1.27519	−	3.69338i
$57$	−2.12430			−0.0372684
$58$	58.4939	−	101.314i	1.00852	−	1.74680i
$59$	−81.6878	+	47.1625i	−1.38454	+	0.799364i	−0.992693	−	0.120667i	$-0.961497\pi$
$59$	−81.6878	+	47.1625i	−1.38454	+	0.799364i	−0.391846	+	0.920031i	$0.628163\pi$
$60$	22.9498	+	39.7502i	0.382497	+	0.662504i
$61$	44.0700	+	25.4438i	0.722458	+	0.417112i	0.815657	−	0.578536i	$-0.196376\pi$
$61$	44.0700	+	25.4438i	0.722458	+	0.417112i	−0.0931984	+	0.995648i	$0.529709\pi$
$62$			160.788i			2.59335i
$63$	−13.7640	−	15.8604i	−0.218476	−	0.251753i
$64$	415.291			6.48893
$65$	−12.7382	+	22.0632i	−0.195972	+	0.339433i
$66$	20.6827	−	11.9412i	0.313374	−	0.180927i
$67$	1.22557	+	2.12275i	0.0182921	+	0.0316828i	0.875027	−	0.484075i	$-0.160844\pi$
$67$	1.22557	+	2.12275i	0.0182921	+	0.0316828i	−0.856734	+	0.515758i	$0.827510\pi$
$68$	−49.0948	−	28.3449i	−0.721982	−	0.416836i
$69$		−	24.5381i		−	0.355624i
$70$	−11.8397	−	61.1831i	−0.169139	−	0.874044i
$71$	−96.9398			−1.36535			−0.682675	−	0.730722i	$-0.739183\pi$
$71$	−96.9398			−1.36535			−0.682675	+	0.730722i	$0.739183\pi$
$72$	46.8878	−	81.2121i	0.651220	−	1.12795i
$73$	−6.88877	+	3.97723i	−0.0943667	+	0.0544826i	−0.546441	−	0.837498i	$-0.684018\pi$
$73$	−6.88877	+	3.97723i	−0.0943667	+	0.0544826i	0.452074	+	0.891980i	$0.350684\pi$
$74$	49.6920	+	86.0690i	0.671513	+	1.16310i
$75$	7.50000	+	4.33013i	0.100000	+	0.0577350i
$76$			14.5351i			0.191251i
$77$	−23.8012	+	4.60584i	−0.309107	+	0.0598161i
$78$	78.5677			1.00728
$79$	−52.3611	+	90.6921i	−0.662799	+	1.14800i	0.317079	+	0.948399i	$0.397298\pi$
$79$	−52.3611	+	90.6921i	−0.662799	+	1.14800i	−0.979877	+	0.199601i	$0.936035\pi$
$80$	149.200	−	86.1408i	1.86500	−	1.07676i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−41.6848	−	24.0668i	−0.508352	−	0.293497i
$83$			57.4797i			0.692527i	0.938137	+	0.346263i	$0.112550\pi$
$83$			57.4797i			0.692527i	−0.938137	+	0.346263i	$0.887450\pi$
$84$	−108.522	+	94.1774i	−1.29193	+	1.12116i
$85$	−10.6961			−0.125837
$86$	−8.65423	+	14.9896i	−0.100631	+	0.174297i
$87$	−44.0758	+	25.4472i	−0.506618	+	0.292496i
$88$	−54.1282	−	93.7527i	−0.615093	−	1.06537i
$89$	43.6908	+	25.2249i	0.490907	+	0.283425i	0.724951	−	0.688801i	$-0.241862\pi$
$89$	43.6908	+	25.2249i	0.490907	+	0.283425i	−0.234043	+	0.972226i	$0.575196\pi$
$90$		−	26.7078i		−	0.296753i
$91$	−75.3868	−	26.0283i	−0.828426	−	0.286025i
$92$	−167.897			−1.82497
$93$	34.9746	−	60.5777i	0.376070	−	0.651373i
$94$	−185.534	+	107.118i	−1.97377	+	1.13955i
$95$	1.37123	+	2.37504i	0.0144340	+	0.0250004i
$96$	−272.574	−	157.371i	−2.83932	−	1.63928i
$97$		−	50.7907i		−	0.523615i	−0.965120	−	0.261808i	$-0.915681\pi$
$97$		−	50.7907i		−	0.523615i	0.965120	−	0.261808i	$-0.0843186\pi$
$98$	181.003	−	72.7781i	1.84697	−	0.742634i
$99$	−10.3898			−0.104947
$100$	29.6281	−	51.3173i	0.296281	−	0.513173i
$101$	64.1916	−	37.0610i	0.635560	−	0.366941i	−0.147342	−	0.989086i	$-0.547072\pi$
$101$	64.1916	−	37.0610i	0.635560	−	0.366941i	0.782902	+	0.622145i	$0.213738\pi$
$102$	16.4931	+	28.5669i	0.161697	+	0.280068i
$103$	157.758	+	91.0815i	1.53163	+	0.884286i	0.999287	+	0.0377568i	$0.0120212\pi$
$103$	157.758	+	91.0815i	1.53163	+	0.884286i	0.532342	+	0.846529i	$0.321312\pi$
$104$		−	356.140i		−	3.42443i
$105$	−8.84787	+	25.6265i	−0.0842655	+	0.244061i
$106$	−102.691			−0.968783
$107$	43.0631	−	74.5875i	0.402459	−	0.697079i	−0.591563	−	0.806259i	$-0.701489\pi$
$107$	43.0631	−	74.5875i	0.402459	−	0.697079i	0.994022	+	0.109179i	$0.0348223\pi$
$108$	−53.3305	+	30.7904i	−0.493801	+	0.285096i
$109$	−1.27150	−	2.20230i	−0.0116651	−	0.0202046i	0.860134	−	0.510068i	$-0.170380\pi$
$109$	−1.27150	−	2.20230i	−0.0116651	−	0.0202046i	−0.871799	+	0.489864i	$0.837047\pi$
$110$	−26.7012	−	15.4160i	−0.242739	−	0.140145i
$111$		−	43.2360i		−	0.389513i
$112$	353.490	+	407.331i	3.15616	+	3.63688i
$113$	130.311			1.15319			0.576596	−	0.817029i	$-0.304381\pi$
$113$	130.311			1.15319			0.576596	+	0.817029i	$0.304381\pi$
$114$	4.22879	−	7.32449i	0.0370947	−	0.0642499i
$115$	−27.4344	+	15.8393i	−0.238560	+	0.137733i
$116$	174.117	+	301.580i	1.50101	+	2.59983i
$117$	−29.6008	−	17.0901i	−0.252999	−	0.146069i
$118$		−	375.542i		−	3.18256i
$119$	−6.36159	−	32.8743i	−0.0534587	−	0.276254i
$120$	−121.064			−1.00887
$121$	54.5029	−	94.4019i	0.450437	−	0.780181i
$122$	−175.458	+	101.301i	−1.43818	+	0.830336i
$123$	10.4700	+	18.1346i	0.0851220	+	0.147436i
$124$	−414.491	−	239.307i	−3.34267	−	1.92989i
$125$		−	11.1803i		−	0.0894427i
$126$	82.0857	−	15.8846i	0.651474	−	0.126068i
$127$	95.7961			0.754300			0.377150	−	0.926152i	$-0.376904\pi$
$127$	95.7961			0.754300			0.377150	+	0.926152i	$0.376904\pi$
$128$	−463.279	+	802.424i	−3.61937	+	6.26893i
$129$	6.52106	−	3.76494i	0.0505508	−	0.0291855i
$130$	−50.7153	−	87.8414i	−0.390117	−	0.675703i
$131$	31.2132	+	18.0209i	0.238269	+	0.137564i	0.614381	−	0.789010i	$-0.289406\pi$
$131$	31.2132	+	18.0209i	0.238269	+	0.137564i	−0.376112	+	0.926574i	$0.622739\pi$
$132$			71.0900i			0.538560i
$133$	−6.48407	+	5.62700i	−0.0487524	+	0.0423083i
$134$	−9.75887			−0.0728274
$135$	−5.80948	+	10.0623i	−0.0430331	+	0.0745356i
$136$	129.491	−	74.7619i	0.952142	−	0.549720i
$137$	−39.5764	−	68.5484i	−0.288879	−	0.500353i	0.684663	−	0.728859i	$-0.259949\pi$
$137$	−39.5764	−	68.5484i	−0.288879	−	0.500353i	−0.973542	+	0.228506i	$0.926616\pi$
$138$	84.6063	+	48.8475i	0.613089	+	0.353967i
$139$			260.590i			1.87475i	0.348322	+	0.937375i	$0.386752\pi$
$139$			260.590i			1.87475i	−0.348322	+	0.937375i	$0.613248\pi$
$140$	175.344	+	60.5399i	1.25246	+	0.432428i
$141$	93.2013			0.661002
$142$	192.976	−	334.244i	1.35899	−	2.35383i
$143$	−34.1717	+	19.7291i	−0.238963	+	0.137965i
$144$	115.570	+	200.173i	0.802569	+	1.39009i
$145$	56.9016	+	32.8522i	0.392425	+	0.226567i
$146$		−	31.6696i		−	0.216915i
$147$	−84.0247	−	11.9522i	−0.571596	−	0.0813078i
$148$	−295.834			−1.99888
$149$	69.2848	−	120.005i	0.464998	−	0.805401i	−0.534203	−	0.845356i	$-0.679388\pi$
$149$	69.2848	−	120.005i	0.464998	−	0.805401i	0.999201	+	0.0399554i	$0.0127216\pi$
$150$	−29.8602	+	17.2398i	−0.199068	+	0.114932i
$151$	66.6000	+	115.355i	0.441060	+	0.763938i	0.997768	−	0.0667699i	$-0.0212693\pi$
$151$	66.6000	+	115.355i	0.441060	+	0.763938i	−0.556709	+	0.830708i	$0.687936\pi$
$152$	−33.2012	−	19.1687i	−0.218429	−	0.126110i
$153$		−	14.3503i		−	0.0937931i
$154$	31.4999	−	91.2344i	0.204545	−	0.592431i
$155$	−90.3039			−0.582606
$156$	−116.935	+	202.538i	−0.749586	+	1.29832i
$157$	154.260	−	89.0618i	0.982545	−	0.567273i	0.0795073	−	0.996834i	$-0.474665\pi$
$157$	154.260	−	89.0618i	0.982545	−	0.567273i	0.903037	+	0.429562i	$0.141332\pi$
$158$	−208.468	−	361.078i	−1.31942	−	2.28530i
$159$	38.6894	+	22.3373i	0.243330	+	0.140486i
$160$			406.330i			2.53956i
$161$	−64.9984	−	74.8985i	−0.403717	−	0.465208i
$162$	35.8322			0.221187
$163$	−32.8419	+	56.8839i	−0.201484	+	0.348981i	−0.949007	−	0.315255i	$-0.897910\pi$
$163$	−32.8419	+	56.8839i	−0.201484	+	0.348981i	0.747523	+	0.664236i	$0.231243\pi$
$164$	124.082	−	71.6390i	0.756600	−	0.436823i
$165$	6.70656	+	11.6161i	0.0406458	+	0.0704006i
$166$	−198.188	−	114.424i	−1.19390	−	0.689299i
$167$			160.924i			0.963620i	0.876276	+	0.481810i	$0.160020\pi$
$167$			160.924i			0.963620i	−0.876276	+	0.481810i	$0.839980\pi$
$168$	−72.0035	−	372.087i	−0.428592	−	2.21480i
$169$	39.1911			0.231900
$170$	21.2925	−	36.8798i	0.125250	−	0.216940i
$171$	−3.18644	+	1.83969i	−0.0186342	+	0.0107584i
$172$	−25.7609	−	44.6191i	−0.149772	−	0.259413i
$173$	29.8595	+	17.2394i	0.172598	+	0.0996496i	0.583810	−	0.811890i	$-0.301561\pi$
$173$	29.8595	+	17.2394i	0.172598	+	0.0996496i	−0.411212	+	0.911540i	$0.634894\pi$
$174$		−	202.629i		−	1.16453i
$175$	34.3625	−	6.64958i	0.196357	−	0.0379976i
$176$	266.832			1.51609
$177$	−81.6878	+	141.487i	−0.461513	+	0.799364i
$178$	−173.949	+	100.429i	−0.977239	+	0.564209i
$179$	−133.955	−	232.018i	−0.748355	−	1.29619i	−0.948611	−	0.316445i	$-0.897511\pi$
$179$	−133.955	−	232.018i	−0.748355	−	1.29619i	0.200256	−	0.979744i	$-0.435822\pi$
$180$	68.8494	+	39.7502i	0.382497	+	0.220835i
$181$		−	59.5598i		−	0.329060i	−0.986372	−	0.164530i	$-0.947389\pi$
$181$		−	59.5598i		−	0.329060i	0.986372	−	0.164530i	$-0.0526107\pi$
$182$	239.815	−	208.116i	1.31767	−	1.14350i
$183$	88.1399			0.481639
$184$	221.421	−	383.512i	1.20338	−	2.08431i
$185$	−48.3393	+	27.9087i	−0.261294	+	0.150858i
$186$	139.246	+	241.182i	0.748636	+	1.29668i
$187$	−14.3468	−	8.28315i	−0.0767210	−	0.0442949i
$188$		−	637.712i		−	3.39208i
$189$	−34.3815	−	11.8707i	−0.181913	−	0.0628078i
$190$	−10.9187			−0.0574668
$191$	161.447	−	279.634i	0.845272	−	1.46405i	−0.0401133	−	0.999195i	$-0.512772\pi$
$191$	161.447	−	279.634i	0.845272	−	1.46405i	0.885385	−	0.464858i	$-0.153895\pi$
$192$	622.937	−	359.653i	3.24446	−	1.87319i
$193$	10.6139	+	18.3839i	0.0549945	+	0.0952533i	0.892212	−	0.451617i	$-0.149153\pi$
$193$	10.6139	+	18.3839i	0.0549945	+	0.0952533i	−0.837218	+	0.546870i	$0.815819\pi$
$194$	175.124	+	101.108i	0.902702	+	0.521175i
$195$			44.1263i			0.226289i
$196$	−81.7809	+	574.923i	−0.417250	+	2.93328i
$197$	−97.0569			−0.492675			−0.246337	−	0.969184i	$-0.579227\pi$
$197$	−97.0569			−0.492675			−0.246337	+	0.969184i	$0.579227\pi$
$198$	20.6827	−	35.8235i	0.104458	−	0.180927i
$199$	−233.088	+	134.573i	−1.17130	+	0.676248i	−0.953985	−	0.299854i	$-0.903062\pi$
$199$	−233.088	+	134.573i	−1.17130	+	0.676248i	−0.217311	+	0.976102i	$0.569729\pi$
$200$	78.1464	+	135.354i	0.390732	+	0.676768i
$201$	3.67671	+	2.12275i	0.0182921	+	0.0105609i
$202$			295.107i			1.46092i
$203$	−67.1278	+	194.425i	−0.330679	+	0.957758i
$204$	−98.1895			−0.481321
$205$	13.5167	−	23.4116i	0.0659352	−	0.114203i
$206$	−628.090	+	362.628i	−3.04898	+	1.76033i
$207$	−21.2506	−	36.8071i	−0.102660	−	0.177812i
$208$	760.216	+	438.911i	3.65488	+	2.11015i
$209$			4.24755i			0.0203232i
$210$	−70.7457	−	81.5212i	−0.336884	−	0.388196i
$211$	−120.629			−0.571703			−0.285852	−	0.958274i	$-0.592276\pi$
$211$	−120.629			−0.571703			−0.285852	+	0.958274i	$0.592276\pi$
$212$	152.839	−	264.725i	0.720939	−	1.24870i
$213$	−145.410	+	83.9523i	−0.682675	+	0.394142i
$214$	171.450	+	296.960i	0.801167	+	1.38766i
$215$	−8.41865	−	4.86051i	−0.0391565	−	0.0226070i
$216$		−	162.424i		−	0.751964i
$217$	−53.7088	−	277.547i	−0.247506	−	1.27902i
$218$	10.1246			0.0464431
$219$	−6.88877	+	11.9317i	−0.0314556	+	0.0544826i
$220$	79.4810	−	45.8884i	0.361277	−	0.208583i
$221$	−27.2498	−	47.1980i	−0.123302	−	0.213566i
$222$	149.076	+	86.0690i	0.671513	+	0.387698i
$223$			298.923i			1.34046i	0.742153	+	0.670230i	$0.233805\pi$
$223$			298.923i			1.34046i	−0.742153	+	0.670230i	$0.766195\pi$
$224$	−1248.85	+	241.667i	−5.57521	+	1.07887i
$225$	15.0000			0.0666667
$226$	−259.407	+	449.306i	−1.14782	+	1.98808i
$227$	9.73538	−	5.62073i	0.0428871	−	0.0247609i	−0.478403	−	0.878140i	$-0.658784\pi$
$227$	9.73538	−	5.62073i	0.0428871	−	0.0247609i	0.521290	+	0.853379i	$0.325451\pi$
$228$	12.5878	+	21.8026i	0.0552095	+	0.0956256i
$229$	257.902	+	148.900i	1.12621	+	0.650218i	0.942979	−	0.332852i	$-0.108011\pi$
$229$	257.902	+	148.900i	1.12621	+	0.650218i	0.183232	+	0.983070i	$0.441344\pi$
$230$		−	126.124i		−	0.548363i
$231$	−31.7131	+	27.5212i	−0.137286	+	0.119139i
$232$	−918.497			−3.95904
$233$	75.6050	−	130.952i	0.324485	−	0.562025i	−0.656923	−	0.753958i	$-0.728142\pi$
$233$	75.6050	−	130.952i	0.324485	−	0.562025i	0.981408	+	0.191933i	$0.0614756\pi$
$234$	117.852	−	68.0417i	0.503639	−	0.290776i
$235$	−60.1612	−	104.202i	−0.256005	−	0.443414i
$236$	968.101	+	558.933i	4.10212	+	2.36836i
$237$			181.384i			0.765334i
$238$	126.013	+	43.5077i	0.529466	+	0.182805i
$239$	−7.05698			−0.0295271			−0.0147636	−	0.999891i	$-0.504700\pi$
$239$	−7.05698			−0.0295271			−0.0147636	+	0.999891i	$0.504700\pi$
$240$	149.200	−	258.422i	0.621668	−	1.07676i
$241$	242.689	−	140.117i	1.00701	−	0.581397i	0.0966949	−	0.995314i	$-0.469173\pi$
$241$	242.689	−	140.117i	1.00701	−	0.581397i	0.910315	+	0.413917i	$0.135840\pi$
$242$	216.996	+	375.848i	0.896677	+	1.55309i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		−	603.081i		−	2.47164i
$245$	40.8747	+	101.658i	0.166835	+	0.414929i
$246$	−83.3697			−0.338901
$247$	−6.98677	+	12.1014i	−0.0282865	+	0.0489937i
$248$	1093.25	−	631.191i	4.40828	−	2.54512i
$249$	49.7789	+	86.2196i	0.199915	+	0.346263i
$250$	38.5494	+	22.2565i	0.154197	+	0.0890259i
$251$			182.780i			0.728206i	0.931359	+	0.364103i	$0.118624\pi$
$251$			182.780i			0.728206i	−0.931359	+	0.364103i	$0.881376\pi$
$252$	−81.2228	+	235.249i	−0.322313	+	0.933527i
$253$	−49.0641			−0.193929
$254$	−190.699	+	330.301i	−0.750785	+	1.30040i
$255$	−16.0442	+	9.26311i	−0.0629183	+	0.0363259i
$256$	−1013.90	−	1756.13i	−3.96055	−	6.85987i
$257$	−123.811	−	71.4823i	−0.481754	−	0.278141i	0.239393	−	0.970923i	$-0.423052\pi$
$257$	−123.811	−	71.4823i	−0.481754	−	0.278141i	−0.721147	+	0.692782i	$0.756385\pi$
$258$			29.9791i			0.116198i
$259$	−114.527	−	131.971i	−0.442189	−	0.509540i
$260$	301.926			1.16125
$261$	−44.0758	+	76.3415i	−0.168873	+	0.292496i
$262$	−124.271	+	71.7478i	−0.474316	+	0.273847i
$263$	−125.368	−	217.143i	−0.476684	−	0.825640i	0.522959	−	0.852358i	$-0.324828\pi$
$263$	−125.368	−	217.143i	−0.476684	−	0.825640i	−0.999643	+	0.0267172i	$0.991495\pi$
$264$	−162.384	−	93.7527i	−0.615093	−	0.355124i
$265$		−	57.6748i		−	0.217641i
$266$	−6.49397	−	33.5584i	−0.0244134	−	0.126159i
$267$	87.3815			0.327272
$268$	14.5245	−	25.1572i	0.0541959	−	0.0938701i
$269$	414.289	−	239.190i	1.54011	−	0.889182i	0.541277	−	0.840845i	$-0.317941\pi$
$269$	414.289	−	239.190i	1.54011	−	0.889182i	0.998831	−	0.0483369i	$-0.0153921\pi$
$270$	−23.1296	−	40.0617i	−0.0856652	−	0.148377i
$271$	−74.5415	−	43.0365i	−0.275061	−	0.158806i	0.356124	−	0.934439i	$-0.384098\pi$
$271$	−74.5415	−	43.0365i	−0.275061	−	0.158806i	−0.631185	+	0.775632i	$0.717431\pi$
$272$			368.549i			1.35496i
$273$	−135.621	+	26.2444i	−0.496781	+	0.0961334i
$274$	315.136			1.15013
$275$	8.65813	−	14.9963i	0.0314841	−	0.0545321i
$276$	−251.846	+	145.403i	−0.912484	+	0.526823i
$277$	−41.8394	−	72.4680i	−0.151045	−	0.261617i	0.780567	−	0.625072i	$-0.214930\pi$
$277$	−41.8394	−	72.4680i	−0.151045	−	0.261617i	−0.931612	+	0.363455i	$0.881597\pi$
$278$	−898.504	−	518.752i	−3.23203	−	1.86601i
$279$		−	121.155i		−	0.434249i
$280$	−369.528	+	320.684i	−1.31974	+	1.14530i
$281$	−381.543			−1.35780			−0.678901	−	0.734230i	$-0.737544\pi$
$281$	−381.543			−1.35780			−0.678901	+	0.734230i	$0.737544\pi$
$282$	−185.534	+	321.354i	−0.657922	+	1.13955i
$283$	−352.262	+	203.379i	−1.24474	+	0.718653i	−0.970056	−	0.242881i	$-0.921907\pi$
$283$	−352.262	+	203.379i	−1.24474	+	0.718653i	−0.274687	+	0.961534i	$0.588574\pi$
$284$	574.428	+	994.938i	2.02263	+	3.50330i
$285$	4.11368	+	2.37504i	0.0144340	+	0.00833346i
$286$		−	157.097i		−	0.549290i
$287$	79.9943	+	27.6191i	0.278726	+	0.0962338i
$288$	−545.149			−1.89288
$289$	−133.059	+	230.465i	−0.460413	+	0.797458i
$290$	−226.546	+	130.796i	−0.781192	+	0.451022i
$291$	−43.9860	−	76.1860i	−0.151155	−	0.261808i
$292$	81.6403	+	47.1351i	0.279590	+	0.161421i
$293$			415.051i			1.41656i	0.705933	+	0.708279i	$0.250528\pi$
$293$			415.051i			1.41656i	−0.705933	+	0.708279i	$0.749472\pi$
$294$	208.477	−	265.920i	0.709106	−	0.904491i
$295$	210.917			0.714973
$296$	390.143	−	675.748i	1.31805	−	2.28293i
$297$	−15.5846	+	8.99780i	−0.0524735	+	0.0302956i
$298$	275.848	+	477.782i	0.925663	+	1.60330i
$299$	−139.786	−	80.7053i	−0.467511	−	0.269917i
$300$		−	102.635i		−	0.342115i
$301$	9.93162	−	28.7654i	0.0329954	−	0.0955660i
$302$	−530.317			−1.75602
$303$	64.1916	−	111.183i	0.211853	−	0.366941i
$304$	81.8350	−	47.2474i	0.269194	−	0.155419i
$305$	−56.8941	−	98.5434i	−0.186538	−	0.323093i
$306$	49.4794	+	28.5669i	0.161697	+	0.0933560i
$307$		−	296.925i		−	0.967184i	−0.875294	−	0.483592i	$-0.839332\pi$
$307$		−	296.925i		−	0.967184i	0.875294	−	0.483592i	$-0.160668\pi$
$308$	188.309	+	216.991i	0.611392	+	0.704515i
$309$	315.516			1.02109
$310$	179.766	−	311.364i	0.579891	−	1.00440i
$311$	263.266	−	151.997i	0.846514	−	0.488735i	−0.0129592	−	0.999916i	$-0.504125\pi$
$311$	263.266	−	151.997i	0.846514	−	0.488735i	0.859473	+	0.511181i	$0.170792\pi$
$312$	−308.427	−	534.211i	−0.988547	−	1.71221i
$313$	−357.904	−	206.636i	−1.14346	−	0.660179i	−0.196178	−	0.980568i	$-0.562853\pi$
$313$	−357.904	−	206.636i	−1.14346	−	0.660179i	−0.947286	+	0.320389i	$0.896186\pi$
$314$			709.174i			2.25852i
$315$	8.92135	+	46.1022i	0.0283217	+	0.146356i
$316$	1241.09			3.92749
$317$	−173.364	+	300.276i	−0.546891	+	0.947243i	0.451594	+	0.892223i	$0.350856\pi$
$317$	−173.364	+	300.276i	−0.546891	+	0.947243i	−0.998485	+	0.0550197i	$0.982478\pi$
$318$	−154.036	+	88.9330i	−0.484391	+	0.279663i
$319$	50.8819	+	88.1300i	0.159504	+	0.276270i
$320$	−804.208	−	464.310i	−2.51315	−	1.45097i
$321$		−	149.175i		−	0.464719i
$322$	387.638	−	75.0128i	1.20384	−	0.232959i
$323$	−5.86672			−0.0181632
$324$	−53.3305	+	92.3712i	−0.164600	+	0.285096i
$325$	49.3347	−	28.4834i	0.151799	−	0.0876413i
$326$	−130.755	−	226.475i	−0.401090	−	0.694709i
$327$	−3.81450	−	2.20230i	−0.0116651	−	0.00673487i
$328$			377.907i			1.15216i
$329$	284.482	−	246.879i	0.864687	−	0.750392i
$330$	−53.4025			−0.161826
$331$	−176.332	+	305.415i	−0.532724	+	0.922704i	0.466546	+	0.884497i	$0.345498\pi$
$331$	−176.332	+	305.415i	−0.532724	+	0.922704i	−0.999270	+	0.0382075i	$0.987835\pi$
$332$	589.941	−	340.603i	1.77693	−	1.02591i
$333$	−37.4435	−	64.8540i	−0.112443	−	0.194757i
$334$	−554.861	−	320.349i	−1.66126	−	0.959129i
$335$		−	5.48092i		−	0.0163609i
$336$	882.993	+	304.865i	2.62796	+	0.907337i
$337$	203.772			0.604664			0.302332	−	0.953203i	$-0.402235\pi$
$337$	203.772			0.604664			0.302332	+	0.953203i	$0.402235\pi$
$338$	−78.0169	+	135.129i	−0.230819	+	0.399791i
$339$	195.466	−	112.852i	0.576596	−	0.332898i
$340$	63.3810	+	109.779i	0.186415	+	0.322880i
$341$	−121.126	−	69.9320i	−0.355207	−	0.205079i
$342$		−	14.6490i		−	0.0428332i
$343$	−288.132	+	186.089i	−0.840034	+	0.542533i
$344$	135.893			0.395037
$345$	−27.4344	+	47.5178i	−0.0795200	+	0.137733i
$346$	−118.881	+	68.6362i	−0.343588	+	0.198370i
$347$	81.0689	+	140.415i	0.233628	+	0.404655i	0.958873	−	0.283835i	$-0.0916069\pi$
$347$	81.0689	+	140.415i	0.233628	+	0.404655i	−0.725245	+	0.688491i	$0.758274\pi$
$348$	522.352	+	301.580i	1.50101	+	0.866610i
$349$		−	369.302i		−	1.05817i	−0.848568	−	0.529086i	$-0.822535\pi$
$349$		−	369.302i		−	1.05817i	0.848568	−	0.529086i	$-0.177465\pi$
$350$	−45.4773	+	131.718i	−0.129935	+	0.376336i
$351$	−59.2017			−0.168666
$352$	−314.665	+	545.015i	−0.893934	+	1.54834i
$353$	28.2461	−	16.3079i	0.0800174	−	0.0461980i	−0.459457	−	0.888200i	$-0.651956\pi$
$353$	28.2461	−	16.3079i	0.0800174	−	0.0461980i	0.539475	+	0.842002i	$0.318623\pi$
$354$	−325.229	−	563.312i	−0.918725	−	1.59128i
$355$	187.723	+	108.382i	0.528798	+	0.305301i
$356$		−	597.891i		−	1.67947i
$357$	−38.0123	−	43.8021i	−0.106477	−	0.122695i
$358$	1066.65			2.97947
$359$	205.319	−	355.623i	0.571920	−	0.990594i	−0.424449	−	0.905452i	$-0.639532\pi$
$359$	205.319	−	355.623i	0.571920	−	0.990594i	0.996369	−	0.0851420i	$-0.0271344\pi$
$360$	−181.596	+	104.844i	−0.504433	+	0.291234i
$361$	−179.748	−	311.332i	−0.497917	−	0.862417i
$362$	205.360	+	118.564i	0.567292	+	0.327526i
$363$		−	188.804i		−	0.520120i
$364$	179.572	+	927.963i	0.493331	+	2.54935i
$365$	17.7867			0.0487307
$366$	−175.458	+	303.903i	−0.479394	+	0.830336i
$367$	478.160	−	276.066i	1.30289	−	0.752223i	0.321990	−	0.946743i	$-0.395648\pi$
$367$	478.160	−	276.066i	1.30289	−	0.752223i	0.980899	+	0.194520i	$0.0623149\pi$
$368$	545.763	+	945.289i	1.48305	+	2.56872i
$369$	31.4100	+	18.1346i	0.0851220	+	0.0491452i
$370$		−	222.229i		−	0.600620i
$371$	177.262	−	34.3024i	0.477795	−	0.0924594i
$372$	−828.983			−2.22845
$373$	−129.001	+	223.436i	−0.345846	+	0.599023i	−0.985507	−	0.169634i	$-0.945741\pi$
$373$	−129.001	+	223.436i	−0.345846	+	0.599023i	0.639661	+	0.768657i	$0.279075\pi$
$374$	57.1199	−	32.9782i	0.152727	−	0.0881770i
$375$	−9.68246	−	16.7705i	−0.0258199	−	0.0447214i
$376$	1456.67	+	841.008i	3.87412	+	2.23672i
$377$			334.781i			0.888014i
$378$	109.372	−	94.9153i	0.289344	−	0.251099i
$379$	−421.167			−1.11126			−0.555629	−	0.831430i	$-0.687523\pi$
$379$	−421.167			−1.11126			−0.555629	+	0.831430i	$0.687523\pi$
$380$	16.2507	−	28.1471i	0.0427651	−	0.0740713i
$381$	143.694	−	82.9619i	0.377150	−	0.217748i
$382$	642.778	+	1113.32i	1.68267	+	2.91446i
$383$	103.680	+	59.8595i	0.270704	+	0.156291i	0.629208	−	0.777237i	$-0.283380\pi$
$383$	103.680	+	59.8595i	0.270704	+	0.156291i	−0.358504	+	0.933528i	$0.616713\pi$
$384$			1604.85i			4.17929i
$385$	51.2404	+	17.6914i	0.133092	+	0.0459517i
$386$	−84.5158			−0.218953
$387$	6.52106	−	11.2948i	0.0168503	−	0.0291855i
$388$	−521.288	+	300.966i	−1.34353	+	0.775685i
$389$	−121.248	−	210.008i	−0.311692	−	0.539866i	0.667037	−	0.745024i	$-0.267562\pi$
$389$	−121.248	−	210.008i	−0.311692	−	0.539866i	−0.978729	+	0.205159i	$0.934229\pi$
$390$	−152.146	−	87.8414i	−0.390117	−	0.225234i
$391$		−	67.7674i		−	0.173318i
$392$	−1205.39	−	945.007i	−3.07498	−	2.41073i
$393$	62.4263			0.158846
$394$	193.209	−	334.648i	0.490379	−	0.849361i
$395$	202.794	−	117.083i	0.513402	−	0.296413i
$396$	61.5657	+	106.635i	0.155469	+	0.269280i
$397$	−415.863	−	240.099i	−1.04751	−	0.604783i	−0.125562	−	0.992086i	$-0.540073\pi$
$397$	−415.863	−	240.099i	−1.04751	−	0.604783i	−0.921953	+	0.387303i	$0.873407\pi$
$398$		−	1071.57i		−	2.69239i
$399$	−4.85298	+	14.0559i	−0.0121629	+	0.0352278i
$400$	−385.233			−0.963083
$401$	−166.439	+	288.280i	−0.415059	+	0.718903i	−0.995435	−	0.0954459i	$-0.969572\pi$
$401$	−166.439	+	288.280i	−0.415059	+	0.718903i	0.580376	+	0.814349i	$0.302906\pi$
$402$	−14.6383	+	8.45143i	−0.0364137	+	0.0210235i
$403$	−230.061	−	398.478i	−0.570872	−	0.988779i
$404$	−760.749	−	439.219i	−1.88304	−	1.08717i
$405$			20.1246i			0.0496904i
$406$	−536.739	−	618.491i	−1.32202	−	1.52338i
$407$	−86.4508			−0.212410
$408$	129.491	−	224.286i	0.317381	−	0.549720i
$409$	291.343	−	168.207i	0.712329	−	0.411263i	−0.0995937	−	0.995028i	$-0.531754\pi$
$409$	291.343	−	168.207i	0.712329	−	0.411263i	0.811923	+	0.583765i	$0.198421\pi$
$410$	53.8149	+	93.2102i	0.131256	+	0.227342i
$411$	−118.729	−	68.5484i	−0.288879	−	0.166784i
$412$		−	2158.85i		−	5.23994i
$413$	125.444	+	648.249i	0.303739	+	1.56961i
$414$	169.213			0.408726
$415$	64.2643	−	111.309i	0.154854	−	0.268214i
$416$	−1792.99	+	1035.18i	−4.31006	+	2.48841i
$417$	225.678	+	390.885i	0.541194	+	0.937375i
$418$	−14.6454	−	8.45552i	−0.0350368	−	0.0202285i
$419$			43.3827i			0.103539i	0.998659	+	0.0517693i	$0.0164861\pi$
$419$			43.3827i			0.103539i	−0.998659	+	0.0517693i	$0.983514\pi$
$420$	315.445	−	61.0426i	0.751060	−	0.145340i
$421$	−463.793			−1.10165			−0.550823	−	0.834622i	$-0.685686\pi$
$421$	−463.793			−1.10165			−0.550823	+	0.834622i	$0.685686\pi$
$422$	240.135	−	415.925i	0.569039	−	0.985605i
$423$	139.802	−	80.7147i	0.330501	−	0.190815i
$424$	403.125	+	698.233i	0.950767	+	1.64678i
$425$	20.7129	+	11.9586i	0.0487363	+	0.0281379i
$426$		−	668.489i		−	1.56922i
$427$	269.033	−	233.472i	0.630054	−	0.546773i
$428$	−1020.70			−2.38482
$429$	−34.1717	+	59.1872i	−0.0796544	+	0.137965i
$430$	33.5177	−	19.3514i	0.0779481	−	0.0450034i
$431$	344.197	+	596.168i	0.798602	+	1.38322i	0.920527	+	0.390680i	$0.127760\pi$
$431$	344.197	+	596.168i	0.798602	+	1.38322i	−0.121925	+	0.992539i	$0.538907\pi$
$432$	346.710	+	200.173i	0.802569	+	0.463364i
$433$		−	670.156i		−	1.54770i	−0.633367	−	0.773852i	$-0.718327\pi$
$433$		−	670.156i		−	1.54770i	0.633367	−	0.773852i	$-0.281673\pi$
$434$	1063.89	+	367.321i	2.45135	+	0.846363i
$435$	113.803			0.261617
$436$	−15.0688	+	26.1000i	−0.0345615	+	0.0598624i
$437$	−15.0475	+	8.68769i	−0.0344337	+	0.0198803i
$438$	−27.4267	−	47.5044i	−0.0626179	−	0.108457i
$439$	609.557	+	351.928i	1.38851	+	0.801658i	0.993148	−	0.116867i	$-0.0372851\pi$
$439$	609.557	+	351.928i	1.38851	+	0.801658i	0.395364	+	0.918524i	$0.370618\pi$
$440$			242.068i			0.550156i
$441$	−136.388	+	54.8391i	−0.309270	+	0.124352i
$442$	216.983			0.490911
$443$	75.6841	−	131.089i	0.170845	−	0.295911i	−0.767871	−	0.640605i	$-0.778684\pi$
$443$	75.6841	−	131.089i	0.170845	−	0.295911i	0.938715	+	0.344693i	$0.112017\pi$
$444$	−443.751	+	256.200i	−0.999439	+	0.577027i
$445$	−56.4045	−	97.6955i	−0.126752	−	0.219540i
$446$	−1030.67	−	595.060i	−2.31093	−	1.33421i
$447$		−	240.009i		−	0.536934i
$448$	948.738	−	2747.87i	2.11772	−	6.13363i
$449$	151.643			0.337735			0.168868	−	0.985639i	$-0.445989\pi$
$449$	151.643			0.337735			0.168868	+	0.985639i	$0.445989\pi$
$450$	−29.8602	+	51.7194i	−0.0663560	+	0.114932i
$451$	36.2603	−	20.9349i	0.0803997	−	0.0464188i
$452$	−772.171	−	1337.44i	−1.70834	−	2.95894i
$453$	199.800	+	115.355i	0.441060	+	0.254646i
$454$			44.7563i			0.0985821i
$455$	116.885	+	134.689i	0.256891	+	0.296019i
$456$	−66.4024			−0.145619
$457$	−287.364	+	497.729i	−0.628805	+	1.08912i	0.358987	+	0.933343i	$0.383122\pi$
$457$	−287.364	+	497.729i	−0.628805	+	1.08912i	−0.987792	+	0.155780i	$0.950211\pi$
$458$	−1026.80	+	592.824i	−2.24193	+	1.29438i
$459$	−12.4278	−	21.5255i	−0.0270757	−	0.0468966i
$460$	325.131	+	187.715i	0.706807	+	0.408075i
$461$			863.340i			1.87276i	0.350994	+	0.936378i	$0.385844\pi$
$461$			863.340i			1.87276i	−0.350994	+	0.936378i	$0.614156\pi$
$462$	−31.7615	−	164.131i	−0.0687478	−	0.355263i
$463$	669.975			1.44703			0.723516	−	0.690308i	$-0.242525\pi$
$463$	669.975			1.44703			0.723516	+	0.690308i	$0.242525\pi$
$464$	1131.96	−	1960.62i	2.43958	−	4.22547i
$465$	−135.456	+	78.2055i	−0.291303	+	0.168184i
$466$	301.011	+	521.366i	0.645946	+	1.11881i
$467$	−67.2019	−	38.7991i	−0.143901	−	0.0830815i	0.426321	−	0.904572i	$-0.359810\pi$
$467$	−67.2019	−	38.7991i	−0.143901	−	0.0830815i	−0.570222	+	0.821491i	$0.693143\pi$
$468$			405.076i			0.865548i
$469$	16.8455	−	3.25981i	0.0359178	−	0.00695056i
$470$	479.046			1.01925
$471$	154.260	−	267.185i	0.327515	−	0.567273i
$472$	−2553.44	+	1474.23i	−5.40984	+	3.12337i
$473$	−7.52803	−	13.0389i	−0.0159155	−	0.0275664i
$474$	−625.405	−	361.078i	−1.31942	−	0.761767i
$475$		−	6.13231i		−	0.0129101i
$476$	−299.708	+	260.092i	−0.629638	+	0.546412i
$477$	77.3788			0.162220
$478$	14.0482	−	24.3322i	0.0293895	−	0.0509042i
$479$	−187.498	+	108.252i	−0.391435	+	0.225995i	−0.682782	−	0.730622i	$-0.739230\pi$
$479$	−187.498	+	108.252i	−0.391435	+	0.225995i	0.291347	+	0.956618i	$0.405897\pi$
$480$	351.892	+	609.495i	0.733109	+	1.26978i
$481$	−246.302	−	142.202i	−0.512062	−	0.295639i
$482$			1115.71i			2.31475i
$483$	−162.362	−	56.0575i	−0.336152	−	0.116061i
$484$	−1291.85			−2.66912
$485$	−56.7857	+	98.3557i	−0.117084	+	0.202795i
$486$	53.7484	−	31.0316i	0.110593	−	0.0638511i
$487$	−85.0142	−	147.249i	−0.174567	−	0.302359i	0.765444	−	0.643502i	$-0.222519\pi$
$487$	−85.0142	−	147.249i	−0.174567	−	0.302359i	−0.940011	+	0.341143i	$0.889186\pi$
$488$	1377.56	+	795.337i	2.82288	+	1.62979i
$489$			113.768i			0.232654i
$490$	−431.880	−	61.4335i	−0.881387	−	0.125374i
$491$	−292.423			−0.595567			−0.297784	−	0.954633i	$-0.596247\pi$
$491$	−292.423			−0.595567			−0.297784	+	0.954633i	$0.596247\pi$
$492$	124.082	−	214.917i	0.252200	−	0.436823i
$493$	−121.725	+	70.2781i	−0.246907	+	0.142552i
$494$	−27.8169	−	48.1802i	−0.0563094	−	0.0975308i
$495$	20.1197	+	11.6161i	0.0406458	+	0.0234669i
$496$			3111.54i			6.27327i
$497$	−221.460	+	641.424i	−0.445594	+	1.29059i
$498$	−396.375			−0.795934
$499$	−218.228	+	377.981i	−0.437330	+	0.757477i	−0.997483	−	0.0709120i	$-0.977409\pi$
$499$	−218.228	+	377.981i	−0.437330	+	0.757477i	0.560153	+	0.828389i	$0.310742\pi$
$500$	−114.749	+	66.2504i	−0.229498	+	0.132501i
$501$	139.365	+	241.387i	0.278173	+	0.481810i
$502$	−630.217	−	363.856i	−1.25541	−	0.724813i
$503$			395.785i			0.786849i	0.919357	+	0.393424i	$0.128710\pi$
$503$			395.785i			0.786849i	−0.919357	+	0.393424i	$0.871290\pi$
$504$	−430.242	−	495.774i	−0.853655	−	0.983678i
$505$	−165.742			−0.328202
$506$	97.6710	−	169.171i	0.193026	−	0.334330i
$507$	58.7867	−	33.9405i	0.115950	−	0.0669438i
$508$	−567.651	−	983.200i	−1.11742	−	1.93543i
$509$	−426.239	−	246.089i	−0.837404	−	0.483475i	0.0189771	−	0.999820i	$-0.493959\pi$
$509$	−426.239	−	246.089i	−0.837404	−	0.483475i	−0.856381	+	0.516345i	$0.827292\pi$
$510$		−	73.7595i		−	0.144627i
$511$	10.5788	+	54.6671i	0.0207021	+	0.106981i
$512$	4367.16			8.52962
$513$	−3.18644	+	5.51908i	−0.00621139	+	0.0107584i
$514$	492.936	−	284.597i	0.959019	−	0.553690i
$515$	−203.664	−	352.757i	−0.395465	−	0.684965i
$516$	−77.2826	−	44.6191i	−0.149772	−	0.0864711i
$517$		−	186.357i		−	0.360458i
$518$	683.017	−	132.172i	1.31857	−	0.255159i
$519$	59.7190			0.115065
$520$	−398.177	+	689.663i	−0.765725	+	1.32627i
$521$	485.148	−	280.100i	0.931187	−	0.537621i	0.0440000	−	0.999032i	$-0.485990\pi$
$521$	485.148	−	280.100i	0.931187	−	0.537621i	0.887187	+	0.461411i	$0.152657\pi$
$522$	−175.482	−	303.943i	−0.336172	−	0.582266i
$523$	−60.8040	−	35.1052i	−0.116260	−	0.0671227i	0.440742	−	0.897634i	$-0.354715\pi$
$523$	−60.8040	−	35.1052i	−0.116260	−	0.0671227i	−0.557002	+	0.830511i	$0.688049\pi$
$524$		−	427.140i		−	0.815153i
$525$	45.7851	−	39.7332i	0.0872097	−	0.0756823i
$526$	998.269			1.89785
$527$	96.5901	−	167.299i	0.183283	−	0.317455i
$528$	400.248	−	231.083i	0.758046	−	0.437658i
$529$	164.147	+	284.311i	0.310297	+	0.537450i
$530$	198.860	+	114.812i	0.375208	+	0.216626i
$531$			282.975i			0.532909i
$532$	96.1747	+	33.2056i	0.180779	+	0.0624165i
$533$	137.743			0.258429
$534$	−173.949	+	301.288i	−0.325746	+	0.564209i
$535$	−166.783	+	96.2920i	−0.311743	+	0.179985i
$536$	38.3096	+	66.3541i	0.0714730	+	0.123795i
$537$	−401.866	−	232.018i	−0.748355	−	0.432063i
$538$			1904.60i			3.54015i
$539$	−23.8986	+	168.008i	−0.0443388	+	0.311703i
$540$	137.699			0.254998
$541$	−290.557	+	503.259i	−0.537073	+	0.930238i	0.461987	+	0.886887i	$0.347137\pi$
$541$	−290.557	+	503.259i	−0.537073	+	0.930238i	−0.999060	+	0.0433513i	$0.986197\pi$
$542$	296.776	−	171.344i	0.547558	−	0.316133i
$543$	−51.5803	−	89.3397i	−0.0949913	−	0.164530i
$544$	−752.776	−	434.615i	−1.38378	−	0.798925i
$545$			5.68632i			0.0104336i
$546$	179.489	−	519.861i	0.328734	−	0.952126i
$547$	364.423			0.666221			0.333110	−	0.942888i	$-0.391902\pi$
$547$	364.423			0.666221			0.333110	+	0.942888i	$0.391902\pi$
$548$	−469.029	+	812.383i	−0.855893	+	1.48245i
$549$	132.210	−	76.3314i	0.240819	−	0.139037i
$550$	34.4711	+	59.7058i	0.0626748	+	0.108556i
$551$	31.2100	+	18.0191i	0.0566425	+	0.0327026i
$552$		−	767.025i		−	1.38954i
$553$	480.465	+	553.646i	0.868833	+	1.00117i
$554$	333.155			0.601364
$555$	−48.3393	+	83.7261i	−0.0870979	+	0.150858i
$556$	2674.56	−	1544.16i	4.81036	−	2.77726i
$557$	78.2077	+	135.460i	0.140409	+	0.243195i	0.927651	−	0.373449i	$-0.121825\pi$
$557$	78.2077	+	135.460i	0.140409	+	0.243195i	−0.787242	+	0.616644i	$0.788492\pi$
$558$	417.739	+	241.182i	0.748636	+	0.432225i
$559$		−	49.5312i		−	0.0886069i
$560$	−229.120	−	1184.01i	−0.409143	−	2.11430i
$561$	−28.6937			−0.0511474
$562$	759.529	−	1315.54i	1.35148	−	2.34082i
$563$	−532.231	+	307.284i	−0.945349	+	0.545797i	−0.891633	−	0.452759i	$-0.850440\pi$
$563$	−532.231	+	307.284i	−0.945349	+	0.545797i	−0.0537158	+	0.998556i	$0.517106\pi$
$564$	−552.275	−	956.568i	−0.979211	−	1.69604i
$565$	−252.346	−	145.692i	−0.446629	−	0.257862i
$566$		−	1619.45i		−	2.86121i
$567$	−61.8525	+	11.9692i	−0.109087	+	0.0211098i
$568$	−3030.20			−5.33486
$569$	−412.852	+	715.081i	−0.725575	+	1.25673i	0.233162	+	0.972438i	$0.425093\pi$
$569$	−412.852	+	715.081i	−0.725575	+	1.25673i	−0.958737	+	0.284295i	$0.908241\pi$
$570$	−16.3780	+	9.45587i	−0.0287334	+	0.0165892i
$571$	92.3654	+	159.982i	0.161761	+	0.280178i	0.935500	−	0.353326i	$-0.114949\pi$
$571$	92.3654	+	159.982i	0.161761	+	0.280178i	−0.773739	+	0.633504i	$0.781616\pi$
$572$	404.977	+	233.814i	0.708002	+	0.408765i
$573$		−	559.268i		−	0.976036i
$574$	−254.473	+	220.836i	−0.443332	+	0.384732i
$575$	70.8353			0.123192
$576$	622.937	−	1078.96i	1.08149	−	1.87319i
$577$	−49.6890	+	28.6880i	−0.0861161	+	0.0497192i	−0.542440	−	0.840095i	$-0.682499\pi$
$577$	−49.6890	+	28.6880i	−0.0861161	+	0.0497192i	0.456324	+	0.889814i	$0.349166\pi$
$578$	−529.757	−	917.566i	−0.916535	−	1.58748i
$579$	31.8418	+	18.3839i	0.0549945	+	0.0317511i
$580$		−	778.677i		−	1.34255i
$581$	380.327	+	131.313i	0.654608	+	0.226012i
$582$	350.248			0.601801
$583$	44.6637	−	77.3599i	0.0766102	−	0.132693i
$584$	−215.333	+	124.323i	−0.368721	+	0.212881i
$585$	38.2145	+	66.1895i	0.0653240	+	0.113144i
$586$	−1431.08	−	826.234i	−2.44212	−	1.40996i
$587$		−	662.641i		−	1.12886i	−0.825481	−	0.564430i	$-0.809096\pi$
$587$		−	662.641i		−	1.12886i	0.825481	−	0.564430i	$-0.190904\pi$
$588$	375.226	+	933.208i	0.638140	+	1.58709i
$589$	−49.5309			−0.0840932
$590$	−419.868	+	727.233i	−0.711641	+	1.23260i
$591$	−145.585	+	84.0537i	−0.246337	+	0.142223i
$592$	961.632	+	1665.59i	1.62438	+	2.81350i
$593$	223.415	+	128.989i	0.376754	+	0.217519i	0.676405	−	0.736530i	$-0.263537\pi$
$593$	223.415	+	128.989i	0.376754	+	0.217519i	−0.299651	+	0.954049i	$0.596870\pi$
$594$		−	71.6469i		−	0.120618i
$595$	−24.4354	+	70.7732i	−0.0410679	+	0.118947i
$596$	−1642.22			−2.75540
$597$	−233.088	+	403.720i	−0.390432	+	0.676248i
$598$	556.537	−	321.317i	0.930664	−	0.537319i
$599$	−147.649	−	255.736i	−0.246493	−	0.426938i	0.716057	−	0.698041i	$-0.245945\pi$
$599$	−147.649	−	255.736i	−0.246493	−	0.426938i	−0.962550	+	0.271103i	$0.912612\pi$
$600$	234.439	+	135.354i	0.390732	+	0.225589i
$601$			283.545i			0.471789i	0.971779	+	0.235895i	$0.0758020\pi$
$601$			283.545i			0.471789i	−0.971779	+	0.235895i	$0.924198\pi$
$602$	79.4111	+	91.5064i	0.131912	+	0.152004i
$603$	7.35342			0.0121947
$604$	789.292	−	1367.09i	1.30677	−	2.26340i
$605$	−211.089	+	121.872i	−0.348907	+	0.201442i
$606$	255.570	+	442.660i	0.421732	+	0.730462i
$607$	702.042	+	405.324i	1.15658	+	0.667750i	0.950481	−	0.310782i	$-0.100591\pi$
$607$	702.042	+	405.324i	1.15658	+	0.667750i	0.206096	+	0.978532i	$0.433924\pi$
$608$			222.868i			0.366560i
$609$	67.6852	+	349.772i	0.111142	+	0.574338i
$610$	453.032			0.742675
$611$	306.537	−	530.938i	0.501698	−	0.868966i
$612$	−147.284	+	85.0346i	−0.240661	+	0.138945i
$613$	−599.633	−	1038.59i	−0.978194	−	1.69428i	−0.668964	−	0.743295i	$-0.733262\pi$
$613$	−599.633	−	1038.59i	−0.978194	−	1.69428i	−0.309231	−	0.950987i	$-0.600071\pi$
$614$	1023.79	+	591.084i	1.66741	+	0.962677i
$615$		−	46.8233i		−	0.0761354i
$616$	−743.992	+	143.972i	−1.20778	+	0.233720i
$617$	−265.361			−0.430082			−0.215041	−	0.976605i	$-0.568989\pi$
$617$	−265.361			−0.430082			−0.215041	+	0.976605i	$0.568989\pi$
$618$	−628.090	+	1087.88i	−1.01633	+	1.76033i
$619$	−686.334	+	396.255i	−1.10878	+	0.640153i	−0.938513	−	0.345245i	$-0.887796\pi$
$619$	−686.334	+	396.255i	−1.10878	+	0.640153i	−0.170266	+	0.985398i	$0.554463\pi$
$620$	535.106	+	926.831i	0.863074	+	1.49489i
$621$	−63.7518	−	36.8071i	−0.102660	−	0.0592707i
$622$			1210.31i			1.94583i
$623$	266.718	−	231.463i	0.428119	−	0.371530i
$624$	1520.43			2.43659
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	1424.94	−	822.692i	2.27627	−	1.31420i
$627$	3.67849	+	6.37133i	0.00586681	+	0.0101616i
$628$	−1828.16	−	1055.49i	−2.91109	−	1.68072i
$629$		−	119.406i		−	0.189835i
$630$	−176.718	−	61.0142i	−0.280505	−	0.0968480i
$631$	−285.152			−0.451905			−0.225953	−	0.974138i	$-0.572549\pi$
$631$	−285.152			−0.451905			−0.225953	+	0.974138i	$0.572549\pi$
$632$	−1636.73	+	2834.90i	−2.58977	+	4.48561i
$633$	−180.944	+	104.468i	−0.285852	+	0.165037i
$634$	−690.226	−	1195.51i	−1.08869	−	1.88566i
$635$	−185.508	−	107.103i	−0.292139	−	0.168667i
$636$		−	529.450i		−	0.832468i
$637$	−344.444	+	439.351i	−0.540728	+	0.689720i
$638$	−405.158			−0.635044
$639$	−145.410	+	251.857i	−0.227558	+	0.394142i
$640$	1794.27	−	1035.92i	2.80355	−	1.61863i
$641$	456.609	+	790.870i	0.712338	+	1.23381i	0.963977	+	0.265985i	$0.0856971\pi$
$641$	456.609	+	790.870i	0.712338	+	1.23381i	−0.251639	+	0.967821i	$0.580970\pi$
$642$	514.349	+	296.960i	0.801167	+	0.462554i
$643$		−	782.798i		−	1.21742i	−0.793394	−	0.608708i	$-0.791688\pi$
$643$		−	782.798i		−	1.21742i	0.793394	−	0.608708i	$-0.208312\pi$
$644$	−383.563	+	1110.93i	−0.595594	+	1.72504i
$645$	−16.8373			−0.0261043
$646$	11.6788	−	20.2282i	0.0180786	−	0.0313130i
$647$	676.477	−	390.564i	1.04556	−	0.603654i	0.124156	−	0.992263i	$-0.460378\pi$
$647$	676.477	−	390.564i	1.04556	−	0.603654i	0.921403	+	0.388609i	$0.127044\pi$
$648$	−140.664	−	243.636i	−0.217073	−	0.375982i
$649$	282.906	+	163.336i	0.435910	+	0.251673i
$650$			226.806i			0.348932i
$651$	−320.926	−	369.807i	−0.492974	−	0.568060i
$652$	778.434			1.19392
$653$	401.877	−	696.072i	0.615433	−	1.06596i	−0.374876	−	0.927075i	$-0.622315\pi$
$653$	401.877	−	696.072i	0.615433	−	1.06596i	0.990308	−	0.138885i	$-0.0443520\pi$
$654$	15.1869	−	8.76816i	0.0232216	−	0.0134070i
$655$	−40.2960	−	69.7948i	−0.0615207	−	0.106557i
$656$	−806.679	−	465.736i	−1.22969	−	0.709964i
$657$			23.8634i			0.0363217i
$658$	284.916	+	1472.34i	0.433003	+	2.23760i
$659$	−560.925			−0.851176			−0.425588	−	0.904917i	$-0.639933\pi$
$659$	−560.925			−0.851176			−0.425588	+	0.904917i	$0.639933\pi$
$660$	79.4810	−	137.665i	0.120426	−	0.208583i
$661$	666.818	−	384.987i	1.00880	−	0.582432i	0.0979611	−	0.995190i	$-0.468768\pi$
$661$	666.818	−	384.987i	1.00880	−	0.582432i	0.910841	+	0.412758i	$0.135435\pi$
$662$	−702.039	−	1215.97i	−1.06048	−	1.83681i
$663$	−81.7494	−	47.1980i	−0.123302	−	0.0711886i
$664$			1796.73i			2.70592i
$665$	18.8475	−	3.64723i	0.0283422	−	0.00548456i
$666$	298.152			0.447675
$667$	−208.142	+	360.512i	−0.312056	+	0.540497i
$668$	1651.64	−	953.576i	2.47252	−	1.42751i
$669$	258.875	+	448.384i	0.386958	+	0.670230i
$670$	18.8980	+	10.9107i	0.0282059	+	0.0162847i
$671$		−	176.237i		−	0.262648i
$672$	−1663.98	+	1444.03i	−2.47616	+	2.14886i
$673$	1013.31			1.50566			0.752829	−	0.658216i	$-0.228689\pi$
$673$	1013.31			1.50566			0.752829	+	0.658216i	$0.228689\pi$
$674$	−405.644	+	702.597i	−0.601846	+	1.04243i
$675$	22.5000	−	12.9904i	0.0333333	−	0.0192450i
$676$	−232.231	−	402.236i	−0.343537	−	0.595024i
$677$	−319.470	−	184.446i	−0.471891	−	0.272446i	0.245140	−	0.969488i	$-0.421166\pi$
$677$	−319.470	−	184.446i	−0.471891	−	0.272446i	−0.717031	+	0.697041i	$0.754499\pi$
$678$			898.612i			1.32539i
$679$	−336.068	−	116.032i	−0.494945	−	0.170886i
$680$	−334.345			−0.491684
$681$	9.73538	−	16.8622i	0.0142957	−	0.0247609i
$682$	482.245	−	278.424i	0.707104	−	0.408247i
$683$	−406.505	−	704.087i	−0.595175	−	1.03087i	−0.993522	−	0.113639i	$-0.963749\pi$
$683$	−406.505	−	704.087i	−0.595175	−	1.03087i	0.398347	−	0.917235i	$-0.369584\pi$
$684$	37.7633	+	21.8026i	0.0552095	+	0.0318752i
$685$			176.991i			0.258381i
$686$	−68.0487	−	1363.91i	−0.0991964	−	1.98821i
$687$	515.804			0.750807
$688$	−167.475	+	290.076i	−0.243423	+	0.421622i
$689$	254.498	−	146.934i	0.369372	−	0.213257i
$690$	−109.226	−	189.185i	−0.158299	−	0.274182i
$691$	213.151	+	123.063i	0.308468	+	0.178094i	0.646241	−	0.763134i	$-0.276340\pi$
$691$	213.151	+	123.063i	0.308468	+	0.178094i	−0.337773	+	0.941228i	$0.609674\pi$
$692$		−	408.616i		−	0.590485i
$693$	−23.7355	+	68.7462i	−0.0342504	+	0.0992008i
$694$	−645.529			−0.930157
$695$	291.349	−	504.631i	0.419207	−	0.726088i
$696$	−1377.75	+	795.442i	−1.97952	+	1.14288i
$697$	28.9153	+	50.0827i	0.0414853	+	0.0718547i
$698$	1273.34	+	735.163i	1.82427	+	1.05324i
$699$		−	261.904i		−	0.374683i
$700$	−271.867	−	313.276i	−0.388381	−	0.447537i
$701$	141.681			0.202113			0.101056	−	0.994881i	$-0.467778\pi$
$701$	141.681			0.202113			0.101056	+	0.994881i	$0.467778\pi$
$702$	117.852	−	204.125i	0.167880	−	0.290776i
$703$	−26.5137	+	15.3077i	−0.0377150	+	0.0217748i
$704$	−719.129	−	1245.57i	−1.02149	−	1.76927i
$705$	−180.483	−	104.202i	−0.256005	−	0.147805i
$706$			129.855i			0.183931i
$707$	−98.5761	−	509.404i	−0.139429	−	0.720515i
$708$	1936.20			2.73475
$709$	456.652	−	790.944i	0.644079	−	1.11558i	−0.340435	−	0.940268i	$-0.610574\pi$
$709$	456.652	−	790.944i	0.644079	−	1.11558i	0.984514	−	0.175309i	$-0.0560924\pi$
$710$	−747.393	+	431.508i	−1.05267	+	0.607757i
$711$	157.083	+	272.076i	0.220933	+	0.382667i
$712$	1365.71	+	788.493i	1.91813	+	1.10743i
$713$		−	572.139i		−	0.802439i
$714$	226.698	−	43.8690i	0.317505	−	0.0614411i
$715$	88.2311			0.123400
$716$	−1587.54	+	2749.69i	−2.21723	+	3.84035i
$717$	−10.5855	+	6.11153i	−0.0147636	+	0.00852375i
$718$	817.449	+	1415.86i	1.13851	+	1.97196i
$719$	−648.650	−	374.498i	−0.902156	−	0.520860i	−0.0242571	−	0.999706i	$-0.507722\pi$
$719$	−648.650	−	374.498i	−0.902156	−	0.520860i	−0.877899	+	0.478846i	$0.841055\pi$
$720$		−	516.845i		−	0.717840i
$721$	963.060	−	835.763i	1.33573	−	1.15917i
$722$	1431.28			1.98239
$723$	242.689	−	420.350i	0.335670	−	0.581397i
$724$	−611.290	+	352.928i	−0.844323	+	0.487470i
$725$	−73.4597	−	127.236i	−0.101324	−	0.175498i
$726$	650.987	+	375.848i	0.896677	+	0.517697i
$727$		−	245.233i		−	0.337322i	−0.985674	−	0.168661i	$-0.946056\pi$
$727$		−	245.233i		−	0.337322i	0.985674	−	0.168661i	$-0.0539443\pi$
$728$	−2356.48	−	813.607i	−3.23693	−	1.11759i
$729$	−27.0000			−0.0370370
$730$	−35.4077	+	61.3279i	−0.0485037	+	0.0840108i
$731$	18.0094	−	10.3977i	0.0246366	−	0.0142240i
$732$	−522.283	−	904.621i	−0.713502	−	1.23582i
$733$	112.515	+	64.9604i	0.153499	+	0.0886226i	0.574782	−	0.818307i	$-0.305087\pi$
$733$	112.515	+	64.9604i	0.153499	+	0.0886226i	−0.421283	+	0.906929i	$0.638420\pi$
$734$			2198.24i			2.99487i
$735$	149.350	+	117.088i	0.203197	+	0.159303i
$736$	−2574.39			−3.49781
$737$	4.24446	−	7.35162i	0.00575910	−	0.00997506i
$738$	−125.055	+	72.2003i	−0.169451	+	0.0978324i
$739$	13.5453	+	23.4612i	0.0183293	+	0.0317472i	0.875045	−	0.484042i	$-0.160832\pi$
$739$	13.5453	+	23.4612i	0.0183293	+	0.0317472i	−0.856715	+	0.515790i	$0.827499\pi$
$740$	572.880	+	330.753i	0.774162	+	0.446963i
$741$			24.2029i			0.0326625i
$742$	−234.599	+	679.478i	−0.316171	+	0.915738i
$743$	1190.70			1.60255			0.801277	−	0.598293i	$-0.204154\pi$
$743$	1190.70			1.60255			0.801277	+	0.598293i	$0.204154\pi$
$744$	1093.25	−	1893.57i	1.46943	−	2.54512i
$745$	−268.339	+	154.925i	−0.360186	+	0.207954i
$746$	−513.598	−	889.577i	−0.688469	−	1.19246i
$747$	149.337	+	86.2196i	0.199915	+	0.115421i
$748$			196.331i			0.262474i
$749$	−395.146	−	455.332i	−0.527565	−	0.607921i
$750$	77.0987			0.102798
$751$	−231.007	+	400.117i	−0.307600	+	0.532778i	−0.977837	−	0.209369i	$-0.932859\pi$
$751$	−231.007	+	400.117i	−0.307600	+	0.532778i	0.670237	+	0.742147i	$0.266192\pi$
$752$	−3590.42	+	2072.93i	−4.77450	+	2.75656i
$753$	158.292	+	274.170i	0.210215	+	0.364103i
$754$	−1154.31	−	666.442i	−1.53092	−	0.883876i
$755$		−	297.844i		−	0.394496i
$756$	81.8973	+	423.214i	0.108330	+	0.559807i
$757$	−702.589			−0.928122			−0.464061	−	0.885803i	$-0.653608\pi$
$757$	−702.589			−0.928122			−0.464061	+	0.885803i	$0.653608\pi$
$758$	838.409	−	1452.17i	1.10608	−	1.91579i
$759$	−73.5962	+	42.4908i	−0.0969647	+	0.0559826i
$760$	42.8626	+	74.2402i	0.0563981	+	0.0976845i
$761$	−996.236	−	575.177i	−1.30911	−	0.755817i	−0.327166	−	0.944967i	$-0.606094\pi$
$761$	−996.236	−	575.177i	−1.30911	−	0.755817i	−0.981948	+	0.189150i	$0.939427\pi$
$762$			660.602i			0.866932i
$763$	−17.4768	+	3.38198i	−0.0229053	+	0.00443247i
$764$	−3826.69			−5.00875
$765$	−16.0442	+	27.7893i	−0.0209728	+	0.0363259i
$766$	−412.786	+	238.322i	−0.538885	+	0.311125i
$767$	537.340	+	930.699i	0.700573	+	1.21343i
$768$	−3041.70	−	1756.13i	−3.96055	−	2.28662i
$769$			342.266i			0.445079i	0.974924	+	0.222539i	$0.0714346\pi$
$769$			342.266i			0.445079i	−0.974924	+	0.222539i	$0.928565\pi$
$770$	−163.002	+	141.457i	−0.211691	+	0.183710i
$771$	−247.622			−0.321170
$772$	125.788	−	217.872i	0.162938	−	0.282217i
$773$	−37.4974	+	21.6492i	−0.0485090	+	0.0280067i	−0.524058	−	0.851682i	$-0.675583\pi$
$773$	−37.4974	+	21.6492i	−0.0485090	+	0.0280067i	0.475549	+	0.879689i	$0.342249\pi$
$774$	25.9627	+	44.9687i	0.0335435	+	0.0580991i
$775$	174.873	+	100.963i	0.225642	+	0.130275i
$776$		−	1587.64i		−	2.04593i
$777$	−286.081	−	98.7731i	−0.368186	−	0.127121i
$778$	965.464			1.24096
$779$	7.41380	−	12.8411i	0.00951707	−	0.0164840i
$780$	452.889	−	261.476i	0.580627	−	0.335225i
$781$	167.864	+	290.748i	0.214934	+	0.372277i
$782$	233.659	+	134.903i	0.298797	+	0.172511i
$783$			152.683i			0.194998i
$784$	3502.75	−	1408.39i	4.46779	−	1.79642i
$785$	−398.296			−0.507384
$786$	−124.271	+	215.243i	−0.158105	+	0.273847i
$787$	−673.263	+	388.708i	−0.855480	+	0.493911i	−0.862496	−	0.506064i	$-0.831100\pi$
$787$	−673.263	+	388.708i	−0.855480	+	0.493911i	0.00701626	+	0.999975i	$0.497767\pi$
$788$	575.122	+	996.140i	0.729850	+	1.26414i
$789$	−376.103	−	217.143i	−0.476684	−	0.275213i
$790$			932.299i			1.18012i
$791$	297.696	−	862.230i	0.376354	−	1.09005i
$792$	−324.769			−0.410062
$793$	289.891	−	502.105i	0.365562	−	0.633172i
$794$	1655.70	−	955.920i	2.08527	−	1.20393i
$795$	−49.9478	−	86.5121i	−0.0628274	−	0.108820i
$796$	2762.38	+	1594.86i	3.47032	+	2.00359i
$797$		−	1385.98i		−	1.73899i	−0.493942	−	0.869495i	$-0.664444\pi$
$797$		−	1385.98i		−	1.73899i	0.493942	−	0.869495i	$-0.335556\pi$
$798$	−38.8034	−	44.7136i	−0.0486258	−	0.0560321i
$799$	257.396			0.322148
$800$	454.291	−	786.855i	0.567863	−	0.983568i
$801$	131.072	−	75.6746i	0.163636	−	0.0944752i
$802$	−662.652	−	1147.75i	−0.826249	−	1.43111i
$803$	23.8575	+	13.7742i	0.0297105	+	0.0171534i
$804$		−	50.3144i		−	0.0625801i
$805$	42.1298	+	217.711i	0.0523351	+	0.270448i
$806$	1831.91			2.27285
$807$	414.289	−	717.569i	0.513369	−	0.889182i
$808$	2006.54	−	1158.47i	2.48334	−	1.43376i
$809$	−64.2049	−	111.206i	−0.0793633	−	0.137461i	0.823612	−	0.567153i	$-0.191955\pi$
$809$	−64.2049	−	111.206i	−0.0793633	−	0.137461i	−0.902975	+	0.429692i	$0.858622\pi$
$810$	−69.3888	−	40.0617i	−0.0856652	−	0.0494588i
$811$			550.689i			0.679024i	0.940602	+	0.339512i	$0.110262\pi$
$811$			550.689i			0.679024i	−0.940602	+	0.339512i	$0.889738\pi$
$812$	2393.25	−	463.123i	2.94735	−	0.570349i
$813$	−149.083			−0.183374
$814$	172.096	−	298.079i	0.211420	−	0.366190i
$815$	127.196	−	73.4368i	0.156069	−	0.0901065i
$816$	319.173	+	552.823i	0.391143	+	0.677479i
$817$	−4.61755	−	2.66595i	−0.00565184	−	0.00326309i
$818$			1339.38i			1.63739i
$819$	−180.704	+	156.818i	−0.220639	+	0.191475i
$820$	−320.379			−0.390706
$821$	−114.344	+	198.049i	−0.139274	+	0.241229i	−0.927222	−	0.374512i	$-0.877810\pi$
$821$	−114.344	+	198.049i	−0.139274	+	0.241229i	0.787948	+	0.615742i	$0.211143\pi$
$822$	472.704	−	272.916i	0.575066	−	0.332014i
$823$	203.552	+	352.562i	0.247329	+	0.428387i	0.962784	−	0.270273i	$-0.0871138\pi$
$823$	203.552	+	352.562i	0.247329	+	0.428387i	−0.715455	+	0.698659i	$0.753780\pi$
$824$	4931.28	+	2847.08i	5.98456	+	3.45519i
$825$		−	29.9927i		−	0.0363547i
$826$	−2484.85	−	857.929i	−3.00830	−	1.03865i
$827$	−493.469			−0.596697			−0.298349	−	0.954457i	$-0.596436\pi$
$827$	−493.469			−0.596697			−0.298349	+	0.954457i	$0.596436\pi$
$828$	−251.846	+	436.209i	−0.304161	+	0.526823i
$829$	−898.364	+	518.671i	−1.08367	+	0.625658i	−0.931885	−	0.362755i	$-0.881836\pi$
$829$	−898.364	+	518.671i	−1.08367	+	0.625658i	−0.151787	+	0.988413i	$0.548503\pi$
$830$	255.859	+	443.161i	0.308264	+	0.533929i
$831$	−125.518	−	72.4680i	−0.151045	−	0.0872057i
$832$		−	4731.57i		−	5.68698i
$833$	−232.053	−	33.0088i	−0.278575	−	0.0396264i
$834$	−1797.01			−2.15469
$835$	179.919	−	311.629i	0.215472	−	0.373208i
$836$	43.5946	−	25.1694i	0.0521466	−	0.0301069i
$837$	−104.924	−	181.733i	−0.125357	−	0.217124i
$838$	−149.582	−	86.3611i	−0.178499	−	0.103056i
$839$			364.625i			0.434595i	0.976105	+	0.217297i	$0.0697241\pi$
$839$			364.625i			0.434595i	−0.976105	+	0.217297i	$0.930276\pi$
$840$	−276.572	+	801.046i	−0.329252	+	0.953626i
$841$	22.4116			0.0266487
$842$	923.263	−	1599.14i	1.09651	−	1.89922i
$843$	−572.314	+	330.426i	−0.678901	+	0.391964i
$844$	714.803	+	1238.08i	0.846923	+	1.46691i
$845$	−75.8932	−	43.8170i	−0.0898145	−	0.0518544i
$846$			642.708i			0.759703i
$847$	−500.118	−	576.293i	−0.590458	−	0.680393i
$848$	−1987.26			−2.34347
$849$	−352.262	+	610.136i	−0.414914	+	0.718653i
$850$	−82.4657	+	47.6116i	−0.0970184	+	0.0560136i
$851$	−176.821	−	306.264i	−0.207781	−	0.359887i
$852$	1723.28	+	994.938i	2.02263	+	1.16777i
$853$		−	844.062i		−	0.989522i	−0.869029	−	0.494761i	$-0.835256\pi$
$853$		−	844.062i		−	0.989522i	0.869029	−	0.494761i	$-0.164744\pi$
$854$	269.444	+	1392.38i	0.315508	+	1.63042i
$855$	8.22736			0.00962265
$856$	1346.09	−	2331.50i	1.57254	−	2.72371i
$857$	53.7291	−	31.0205i	0.0626944	−	0.0361966i	−0.468325	−	0.883556i	$-0.655142\pi$
$857$	53.7291	−	31.0205i	0.0626944	−	0.0361966i	0.531020	+	0.847360i	$0.321809\pi$
$858$	−136.050	−	235.646i	−0.158566	−	0.274645i
$859$	767.453	+	443.089i	0.893426	+	0.515820i	0.875061	−	0.484012i	$-0.160821\pi$
$859$	767.453	+	443.089i	0.893426	+	0.515820i	0.0183642	+	0.999831i	$0.494154\pi$
$860$			115.206i			0.133960i
$861$	143.910	−	27.8485i	0.167143	−	0.0323443i
$862$	−2740.75			−3.17952
$863$	398.382	−	690.018i	0.461625	−	0.799557i	−0.537417	−	0.843316i	$-0.680600\pi$
$863$	398.382	−	690.018i	0.461625	−	0.799557i	0.999042	+	0.0437590i	$0.0139334\pi$
$864$	−817.723	+	472.113i	−0.946439	+	0.546427i
$865$	−38.5484	−	66.7678i	−0.0445647	−	0.0771883i
$866$	2310.67	+	1334.07i	2.66821	+	1.54049i
$867$			460.931i			0.531639i
$868$	−2530.34	+	2195.88i	−2.91513	+	2.52981i
$869$	362.679			0.417353
$870$	−226.546	+	392.389i	−0.260397	+	0.451022i
$871$	24.1853	−	13.9634i	0.0277672	−	0.0160314i
$872$	−39.7453	−	68.8408i	−0.0455794	−	0.0789459i
$873$	−131.958	−	76.1860i	−0.151155	−	0.0872692i
$874$		−	69.1776i		−	0.0791506i
$875$	−73.9772	−	25.5416i	−0.0845454	−	0.0291904i
$876$	163.281			0.186393
$877$	−769.437	+	1332.70i	−0.877351	+	1.51962i	−0.0231132	+	0.999733i	$0.507358\pi$
$877$	−769.437	+	1332.70i	−0.877351	+	1.51962i	−0.854237	+	0.519883i	$0.825976\pi$
$878$	−2426.86	+	1401.15i	−2.76408	+	1.59584i
$879$	359.445	+	622.577i	0.408925	+	0.708279i
$880$	−516.718	−	298.327i	−0.587180	−	0.339008i
$881$			1188.82i			1.34940i	0.738092	+	0.674700i	$0.235727\pi$
$881$			1188.82i			1.34940i	−0.738092	+	0.674700i	$0.764273\pi$
$882$	82.4217	−	579.427i	0.0934486	−	0.656947i
$883$	−684.581			−0.775290			−0.387645	−	0.921809i	$-0.626711\pi$
$883$	−684.581			−0.775290			−0.387645	+	0.921809i	$0.626711\pi$
$884$	−322.944	+	559.355i	−0.365321	+	0.632754i
$885$	316.375	−	182.659i	0.357486	−	0.206395i
$886$	301.326	+	521.911i	0.340097	+	0.589065i
$887$	806.635	+	465.711i	0.909397	+	0.525041i	0.880237	−	0.474534i	$-0.157383\pi$
$887$	806.635	+	465.711i	0.909397	+	0.525041i	0.0291599	+	0.999575i	$0.490717\pi$
$888$		−	1351.50i		−	1.52195i
$889$	218.847	−	633.856i	0.246173	−	0.712999i
$890$	449.133			0.504644
$891$	−15.5846	+	26.9934i	−0.0174912	+	0.0302956i
$892$	3067.98	−	1771.30i	3.43944	−	1.98576i
$893$	−32.9979	−	57.1540i	−0.0369517	−	0.0640022i
$894$	827.543	+	477.782i	0.925663	+	0.534432i
$895$			599.067i			0.669349i
$896$	4251.05	+	4898.54i	4.74447	+	5.46712i
$897$	−279.571			−0.311674
$898$	−301.873	+	522.860i	−0.336162	+	0.582249i
$899$	−1027.69	+	593.336i	−1.14315	+	0.659995i
$900$	−88.8842	−	153.952i	−0.0987602	−	0.171058i
$901$	106.850	+	61.6896i	0.118590	+	0.0684679i
$902$			166.699i			0.184810i
$903$	−10.0141	−	51.7491i	−0.0110898	−	0.0573079i
$904$	4073.33			4.50589
$905$	−66.5899	+	115.337i	−0.0735799	+	0.127444i
$906$	−795.476	+	459.268i	−0.878009	+	0.506919i
$907$	750.047	+	1299.12i	0.826954	+	1.43233i	0.900417	+	0.435028i	$0.143262\pi$
$907$	750.047	+	1299.12i	0.826954	+	1.43233i	−0.0734628	+	0.997298i	$0.523405\pi$
$908$	−115.376	−	66.6125i	−0.127066	−	0.0733618i
$909$		−	222.366i		−	0.244627i
$910$	−697.082	+	134.894i	−0.766024	+	0.148235i
$911$	−1154.90			−1.26773			−0.633866	−	0.773443i	$-0.718533\pi$
$911$	−1154.90			−1.26773			−0.633866	+	0.773443i	$0.718533\pi$
$912$	81.8350	−	141.742i	0.0897313	−	0.155419i
$913$	172.397	−	99.5334i	0.188825	−	0.109018i
$914$	−1144.10	−	1981.64i	−1.25175	−	2.16809i
$915$	−170.682	−	98.5434i	−0.186538	−	0.107698i
$916$		−	3529.29i		−	3.85294i
$917$	190.546	−	165.360i	0.207793	−	0.180327i
$918$	98.9588			0.107798
$919$	229.886	−	398.174i	0.250148	−	0.433268i	−0.713419	−	0.700738i	$-0.752854\pi$
$919$	229.886	−	398.174i	0.250148	−	0.433268i	0.963566	+	0.267470i	$0.0861875\pi$
$920$	−857.560	+	495.112i	−0.932130	+	0.538166i
$921$	−257.145	−	445.388i	−0.279202	−	0.483592i
$922$	−2976.76	−	1718.63i	−3.22859	−	1.86403i
$923$			1104.47i			1.19661i
$924$	470.382	+	162.406i	0.509072	+	0.175764i
$925$	124.812			0.134931
$926$	−1333.71	+	2310.05i	−1.44029	+	2.49465i
$927$	473.273	−	273.244i	0.510543	−	0.294762i
$928$	2669.76	+	4624.17i	2.87690	+	4.98294i
$929$	−774.369	−	447.082i	−0.833551	−	0.481251i	0.0215159	−	0.999769i	$-0.493151\pi$
$929$	−774.369	−	447.082i	−0.833551	−	0.481251i	−0.855067	+	0.518518i	$0.826484\pi$
$930$		−	622.728i		−	0.669600i
$931$	22.4194	+	55.7583i	0.0240810	+	0.0598907i
$932$	−1792.03			−1.92277
$933$	263.266	−	455.990i	0.282171	−	0.488735i
$934$	267.555	−	154.473i	0.286462	−	0.165389i
$935$	18.5217	+	32.0805i	0.0198093	+	0.0343107i
$936$	−925.280	−	534.211i	−0.988547	−	0.570738i
$937$			783.995i			0.836707i	0.908284	+	0.418354i	$0.137393\pi$
$937$			783.995i			0.836707i	−0.908284	+	0.418354i	$0.862607\pi$
$938$	−22.2942	+	64.5717i	−0.0237679	+	0.0688398i
$939$	−715.808			−0.762309
$940$	−712.984	+	1234.92i	−0.758493	+	1.31375i
$941$	−538.460	+	310.880i	−0.572221	+	0.330372i	−0.758036	−	0.652213i	$-0.773841\pi$
$941$	−538.460	+	310.880i	−0.572221	+	0.330372i	0.185815	+	0.982585i	$0.440507\pi$
$942$	614.163	+	1063.76i	0.651977	+	1.12926i
$943$	148.329	+	85.6379i	0.157295	+	0.0908143i
$944$		−	7267.42i		−	7.69854i
$945$	53.3077	+	61.4271i	0.0564102	+	0.0650023i
$946$	59.9436			0.0633653
$947$	−202.048	+	349.958i	−0.213356	+	0.369544i	−0.952763	−	0.303715i	$-0.901773\pi$
$947$	−202.048	+	349.958i	−0.213356	+	0.369544i	0.739407	+	0.673259i	$0.235106\pi$
$948$	1861.63	−	1074.81i	1.96374	−	1.13377i
$949$	45.3141	+	78.4863i	0.0477493	+	0.0827042i
$950$	21.1440	+	12.2075i	0.0222568	+	0.0128500i
$951$			600.552i			0.631495i
$952$	−198.854	−	1027.60i	−0.208880	−	1.07941i
$953$	531.482			0.557693			0.278847	−	0.960336i	$-0.410048\pi$
$953$	531.482			0.557693			0.278847	+	0.960336i	$0.410048\pi$
$954$	−154.036	+	266.799i	−0.161464	+	0.279663i
$955$	−625.281	+	361.006i	−0.654745	+	0.378017i
$956$	41.8170	+	72.4291i	0.0437416	+	0.0757626i
$957$	152.646	+	88.1300i	0.159504	+	0.0920899i
$958$		−	861.978i		−	0.899769i
$959$	−543.979	+	105.267i	−0.567235	+	0.109767i
$960$	−1608.42			−1.67543
$961$	334.980	−	580.202i	0.348574	−	0.603748i
$962$	980.616	−	566.159i	1.01935	−	0.588523i
$963$	−129.189	−	223.762i	−0.134153	−	0.232360i
$964$	−2876.17	−	1660.56i	−2.98357	−	1.72257i
$965$		−	47.4670i		−	0.0491886i
$966$	516.494	−	448.224i	0.534673	−	0.464000i
$967$	315.842			0.326620			0.163310	−	0.986575i	$-0.447783\pi$
$967$	315.842			0.326620			0.163310	+	0.986575i	$0.447783\pi$
$968$	1703.68	−	2950.87i	1.76000	−	3.04842i
$969$	−8.80008	+	5.08073i	−0.00908161	+	0.00524327i
$970$	−226.084	−	391.590i	−0.233077	−	0.403701i
$971$	264.925	+	152.954i	0.272837	+	0.157523i	0.630176	−	0.776452i	$-0.282983\pi$
$971$	264.925	+	152.954i	0.272837	+	0.157523i	−0.357339	+	0.933975i	$0.616316\pi$
$972$			184.742i			0.190064i
$973$	1724.25	+	595.321i	1.77210	+	0.611841i
$974$	676.944			0.695014
$975$	49.3347	−	85.4503i	0.0505997	−	0.0876413i
$976$	−3395.44	+	1960.36i	−3.47894	+	2.00857i
$977$	412.936	+	715.226i	0.422657	+	0.732063i	0.996198	−	0.0871133i	$-0.0277642\pi$
$977$	412.936	+	715.226i	0.422657	+	0.732063i	−0.573542	+	0.819176i	$0.694431\pi$
$978$	−392.266	−	226.475i	−0.401090	−	0.231570i
$979$		−	174.720i		−	0.178468i
$980$	801.151	−	1021.90i	0.817501	−	1.04275i
$981$	−7.62900			−0.00777676
$982$	582.122	−	1008.26i	0.592792	−	1.02675i
$983$	−1600.00	+	923.759i	−1.62767	+	0.939735i	−0.642882	+	0.765965i	$0.722261\pi$
$983$	−1600.00	+	923.759i	−1.62767	+	0.939735i	−0.984786	+	0.173770i	$0.944405\pi$
$984$	327.277	+	566.861i	0.332599	+	0.576078i
$985$	187.950	+	108.513i	0.190812	+	0.110165i
$986$		−	559.605i		−	0.567551i
$987$	212.919	−	616.687i	0.215724	−	0.624809i
$988$	165.604			0.167615
$989$	30.7948	−	53.3381i	0.0311373	−	0.0539313i
$990$	−80.1037	+	46.2479i	−0.0809128	+	0.0467150i
$991$	10.4697	+	18.1341i	0.0105648	+	0.0182988i	0.871259	−	0.490823i	$-0.163304\pi$
$991$	10.4697	+	18.1341i	0.0105648	+	0.0182988i	−0.860695	+	0.509121i	$0.829970\pi$
$992$	−6355.45	−	3669.32i	−6.40670	−	3.69891i
$993$			610.830i			0.615136i
$994$	−1770.75	−	2040.45i	−1.78143	−	2.05277i
$995$	601.830			0.604855
$996$	589.941	−	1021.81i	0.592310	−	1.02591i
$997$	−1035.91	+	598.080i	−1.03902	+	0.599880i	−0.919556	−	0.392958i	$-0.871452\pi$
$997$	−1035.91	+	598.080i	−1.03902	+	0.599880i	−0.119466	+	0.992838i	$0.538118\pi$
$998$	−868.842	−	1504.88i	−0.870583	−	1.50789i
$999$	−112.330	−	64.8540i	−0.112443	−	0.0649189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.b.61.1	yes	12
3.2	odd	2		315.3.w.b.271.6		12
5.2	odd	4		525.3.s.j.124.1		24
5.3	odd	4		525.3.s.j.124.12		24
5.4	even	2		525.3.o.m.376.6		12
7.2	even	3		735.3.h.b.391.12		12
7.3	odd	6	inner	105.3.n.b.31.1	✓	12
7.5	odd	6		735.3.h.b.391.11		12
21.17	even	6		315.3.w.b.136.6		12
35.3	even	12		525.3.s.j.199.1		24
35.17	even	12		525.3.s.j.199.12		24
35.24	odd	6		525.3.o.m.451.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.b.31.1	✓	12	7.3	odd	6	inner
105.3.n.b.61.1	yes	12	1.1	even	1	trivial
315.3.w.b.136.6		12	21.17	even	6
315.3.w.b.271.6		12	3.2	odd	2
525.3.o.m.376.6		12	5.4	even	2
525.3.o.m.451.6		12	35.24	odd	6
525.3.s.j.124.1		24	5.2	odd	4
525.3.s.j.124.12		24	5.3	odd	4
525.3.s.j.199.1		24	35.3	even	12
525.3.s.j.199.12		24	35.17	even	12
735.3.h.b.391.11		12	7.5	odd	6
735.3.h.b.391.12		12	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99068 + 3.44796i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-5.92561 - 10.2635i) q^{4} +(-1.93649 - 1.11803i) q^{5} +6.89592i q^{6} +(2.28451 - 6.61672i) q^{7} +31.2586 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.99068 + 3.44796i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-5.92561 - 10.2635i) q^{4} +(-1.93649 - 1.11803i) q^{5} +6.89592i q^{6} +(2.28451 - 6.61672i) q^{7} +31.2586 q^{8} +(1.50000 - 2.59808i) q^{9} +(7.70987 - 4.45130i) q^{10} +(-1.73163 - 2.99927i) q^{11} +(-17.7768 - 10.2635i) q^{12} -11.3934i q^{13} +(18.2665 + 21.0487i) q^{14} -3.87298 q^{15} +(-38.5233 + 66.7244i) q^{16} +(4.14259 - 2.39172i) q^{17} +(5.97204 + 10.3439i) q^{18} +(-1.06215 - 0.613231i) q^{19} +26.5001i q^{20} +(-2.30348 - 11.9035i) q^{21} +13.7885 q^{22} +(7.08353 - 12.2690i) q^{23} +(46.8878 - 27.0707i) q^{24} +(2.50000 + 4.33013i) q^{25} +(39.2839 + 22.6806i) q^{26} -5.19615i q^{27} +(-81.4476 + 15.7611i) q^{28} -29.3839 q^{29} +(7.70987 - 13.3539i) q^{30} +(34.9746 - 20.1926i) q^{31} +(-90.8581 - 157.371i) q^{32} +(-5.19488 - 2.99927i) q^{33} +19.0446i q^{34} +(-11.8217 + 10.2591i) q^{35} -35.5537 q^{36} +(12.4812 - 21.6180i) q^{37} +(4.22879 - 2.44150i) q^{38} +(-9.86695 - 17.0901i) q^{39} +(-60.5319 - 34.9481i) q^{40} +12.0897i q^{41} +(45.6284 + 15.7538i) q^{42} +4.34737 q^{43} +(-20.5219 + 35.5450i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(28.2021 + 48.8475i) q^{46} +(46.6006 + 26.9049i) q^{47} +133.449i q^{48} +(-38.5620 - 30.2320i) q^{49} -19.9068 q^{50} +(4.14259 - 7.17517i) q^{51} +(-116.935 + 67.5127i) q^{52} +(12.8965 + 22.3373i) q^{53} +(17.9161 + 10.3439i) q^{54} +7.74407i q^{55} +(71.4105 - 206.829i) q^{56} -2.12430 q^{57} +(58.4939 - 101.314i) q^{58} +(-81.6878 + 47.1625i) q^{59} +(22.9498 + 39.7502i) q^{60} +(44.0700 + 25.4438i) q^{61} +160.788i q^{62} +(-13.7640 - 15.8604i) q^{63} +415.291 q^{64} +(-12.7382 + 22.0632i) q^{65} +(20.6827 - 11.9412i) q^{66} +(1.22557 + 2.12275i) q^{67} +(-49.0948 - 28.3449i) q^{68} -24.5381i q^{69} +(-11.8397 - 61.1831i) q^{70} -96.9398 q^{71} +(46.8878 - 81.2121i) q^{72} +(-6.88877 + 3.97723i) q^{73} +(49.6920 + 86.0690i) q^{74} +(7.50000 + 4.33013i) q^{75} +14.5351i q^{76} +(-23.8012 + 4.60584i) q^{77} +78.5677 q^{78} +(-52.3611 + 90.6921i) q^{79} +(149.200 - 86.1408i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-41.6848 - 24.0668i) q^{82} +57.4797i q^{83} +(-108.522 + 94.1774i) q^{84} -10.6961 q^{85} +(-8.65423 + 14.9896i) q^{86} +(-44.0758 + 25.4472i) q^{87} +(-54.1282 - 93.7527i) q^{88} +(43.6908 + 25.2249i) q^{89} -26.7078i q^{90} +(-75.3868 - 26.0283i) q^{91} -167.897 q^{92} +(34.9746 - 60.5777i) q^{93} +(-185.534 + 107.118i) q^{94} +(1.37123 + 2.37504i) q^{95} +(-272.574 - 157.371i) q^{96} -50.7907i q^{97} +(181.003 - 72.7781i) q^{98} -10.3898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9	\( 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9} + 20 q^{11} - 66 q^{12} + 32 q^{14} - 82 q^{16} - 78 q^{17} - 6 q^{18} - 6 q^{19} + 36 q^{21} + 56 q^{22} + 2 q^{23} + 60 q^{24} + 30 q^{25} + 36 q^{26} - 128 q^{28} - 100 q^{29} + 108 q^{31} - 108 q^{32} + 60 q^{33} - 60 q^{35} - 132 q^{36} - 34 q^{37} + 126 q^{38} - 42 q^{39} - 90 q^{40} + 114 q^{42} - 124 q^{43} + 234 q^{44} + 278 q^{46} + 96 q^{47} - 60 q^{49} + 20 q^{50} - 78 q^{51} - 444 q^{52} - 76 q^{53} - 18 q^{54} + 112 q^{56} - 12 q^{57} - 52 q^{58} - 270 q^{59} + 60 q^{60} - 60 q^{61} + 42 q^{63} + 700 q^{64} - 60 q^{65} + 84 q^{66} - 18 q^{67} + 108 q^{68} - 300 q^{70} - 628 q^{71} + 60 q^{72} + 234 q^{73} + 244 q^{74} + 90 q^{75} - 196 q^{77} + 72 q^{78} + 108 q^{79} + 480 q^{80} - 54 q^{81} + 480 q^{82} - 192 q^{84} - 60 q^{85} + 130 q^{86} - 150 q^{87} - 668 q^{88} - 186 q^{89} + 444 q^{91} + 456 q^{92} + 108 q^{93} + 30 q^{94} - 324 q^{96} + 416 q^{98} + 120 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9 + 20 * q^11 - 66 * q^12 + 32 * q^14 - 82 * q^16 - 78 * q^17 - 6 * q^18 - 6 * q^19 + 36 * q^21 + 56 * q^22 + 2 * q^23 + 60 * q^24 + 30 * q^25 + 36 * q^26 - 128 * q^28 - 100 * q^29 + 108 * q^31 - 108 * q^32 + 60 * q^33 - 60 * q^35 - 132 * q^36 - 34 * q^37 + 126 * q^38 - 42 * q^39 - 90 * q^40 + 114 * q^42 - 124 * q^43 + 234 * q^44 + 278 * q^46 + 96 * q^47 - 60 * q^49 + 20 * q^50 - 78 * q^51 - 444 * q^52 - 76 * q^53 - 18 * q^54 + 112 * q^56 - 12 * q^57 - 52 * q^58 - 270 * q^59 + 60 * q^60 - 60 * q^61 + 42 * q^63 + 700 * q^64 - 60 * q^65 + 84 * q^66 - 18 * q^67 + 108 * q^68 - 300 * q^70 - 628 * q^71 + 60 * q^72 + 234 * q^73 + 244 * q^74 + 90 * q^75 - 196 * q^77 + 72 * q^78 + 108 * q^79 + 480 * q^80 - 54 * q^81 + 480 * q^82 - 192 * q^84 - 60 * q^85 + 130 * q^86 - 150 * q^87 - 668 * q^88 - 186 * q^89 + 444 * q^91 + 456 * q^92 + 108 * q^93 + 30 * q^94 - 324 * q^96 + 416 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more