LMFDB - Embedded newform 105.3.n.b.31.1

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			31.1
Root			$0.500000 + 0.0182799i$ of defining polynomial
Character	$\chi$	$=$	105.31
Dual form			105.3.n.b.61.1

$q$-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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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	−0.581179	−	0.813776i	$-0.697408\pi$
$2$	−1.99068	−	3.44796i	−0.995340	−	1.72398i	−0.414161	−	0.910204i	$-0.635925\pi$
$3$	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	−0.933938	−	0.357436i	$-0.883651\pi$
$11$	−1.73163	+	2.99927i	−0.157421	+	0.272661i	0.776517	+	0.630096i	$0.216985\pi$
$12$	−17.7768	+	10.2635i	−1.48140	+	0.855289i
$13$			11.3934i			0.876413i	0.898874	+	0.438207i	$0.144386\pi$
$13$			11.3934i			0.876413i	−0.898874	+	0.438207i	$0.855614\pi$
$14$	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	0.616868	−	0.787067i	$-0.288401\pi$
$17$	4.14259	+	2.39172i	0.243682	+	0.140690i	−0.373186	+	0.927757i	$0.621735\pi$
$18$	5.97204	−	10.3439i	0.331780	−	0.574660i
$19$	−1.06215	+	0.613231i	−0.0559025	+	0.0322753i	−0.527691	−	0.849437i	$-0.676942\pi$
$19$	−1.06215	+	0.613231i	−0.0559025	+	0.0322753i	0.471788	+	0.881712i	$0.343609\pi$
$20$		−	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	0.977920	−	0.208978i	$-0.0670138\pi$
$23$	7.08353	+	12.2690i	0.307980	+	0.533436i	−0.669941	+	0.742415i	$0.733680\pi$
$24$	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	0.943484	−	0.331417i	$-0.107527\pi$
$31$	34.9746	+	20.1926i	1.12821	+	0.651373i	0.184727	+	0.982790i	$0.440860\pi$
$32$	−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	0.983929	−	0.178558i	$-0.0571433\pi$
$37$	12.4812	+	21.6180i	0.337329	+	0.584270i	−0.646601	+	0.762829i	$0.723810\pi$
$38$	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	$-0.952898\pi$
$41$		−	12.0897i		−	0.294871i	0.989072	−	0.147436i	$-0.0471019\pi$
$42$	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	0.0857797	−	0.996314i	$-0.472662\pi$
$47$	46.6006	−	26.9049i	0.991503	−	0.572444i	0.905723	+	0.423870i	$0.139329\pi$
$48$		−	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	−0.718331	−	0.695701i	$-0.755094\pi$
$53$	12.8965	−	22.3373i	0.243330	−	0.421459i	0.961661	+	0.274242i	$0.0884270\pi$
$54$	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	−0.391846	−	0.920031i	$-0.628163\pi$
$59$	−81.6878	−	47.1625i	−1.38454	−	0.799364i	−0.992693	+	0.120667i	$0.961497\pi$
$60$	22.9498	−	39.7502i	0.382497	−	0.662504i
$61$	44.0700	−	25.4438i	0.722458	−	0.417112i	−0.0931984	−	0.995648i	$-0.529709\pi$
$61$	44.0700	−	25.4438i	0.722458	−	0.417112i	0.815657	+	0.578536i	$0.196376\pi$
$62$		−	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	−0.856734	−	0.515758i	$-0.827510\pi$
$67$	1.22557	−	2.12275i	0.0182921	−	0.0316828i	0.875027	+	0.484075i	$0.160844\pi$
$68$	−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	0.452074	−	0.891980i	$-0.350684\pi$
$73$	−6.88877	−	3.97723i	−0.0943667	−	0.0544826i	−0.546441	+	0.837498i	$0.684018\pi$
$74$	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	−0.979877	−	0.199601i	$-0.936035\pi$
$79$	−52.3611	−	90.6921i	−0.662799	−	1.14800i	0.317079	−	0.948399i	$-0.397298\pi$
$80$	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	$-0.887450\pi$
$83$		−	57.4797i		−	0.692527i	0.938137	−	0.346263i	$-0.112550\pi$
$84$	−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	−0.234043	−	0.972226i	$-0.575196\pi$
$89$	43.6908	−	25.2249i	0.490907	−	0.283425i	0.724951	+	0.688801i	$0.241862\pi$
$90$			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	$0.0843186\pi$
$97$			50.7907i			0.523615i	−0.965120	+	0.261808i	$0.915681\pi$
$98$	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	0.782902	−	0.622145i	$-0.213738\pi$
$101$	64.1916	+	37.0610i	0.635560	+	0.366941i	−0.147342	+	0.989086i	$0.547072\pi$
$102$	16.4931	−	28.5669i	0.161697	−	0.280068i
$103$	157.758	−	91.0815i	1.53163	−	0.884286i	0.532342	−	0.846529i	$-0.321312\pi$
$103$	157.758	−	91.0815i	1.53163	−	0.884286i	0.999287	−	0.0377568i	$-0.0120212\pi$
$104$			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	0.994022	−	0.109179i	$-0.0348223\pi$
$107$	43.0631	+	74.5875i	0.402459	+	0.697079i	−0.591563	+	0.806259i	$0.701489\pi$
$108$	−53.3305	−	30.7904i	−0.493801	−	0.285096i
$109$	−1.27150	+	2.20230i	−0.0116651	+	0.0202046i	−0.871799	−	0.489864i	$-0.837047\pi$
$109$	−1.27150	+	2.20230i	−0.0116651	+	0.0202046i	0.860134	+	0.510068i	$0.170380\pi$
$110$	−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	−0.376112	−	0.926574i	$-0.622739\pi$
$131$	31.2132	−	18.0209i	0.238269	−	0.137564i	0.614381	+	0.789010i	$0.289406\pi$
$132$		−	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	−0.973542	−	0.228506i	$-0.926616\pi$
$137$	−39.5764	+	68.5484i	−0.288879	+	0.500353i	0.684663	+	0.728859i	$0.259949\pi$
$138$	84.6063	−	48.8475i	0.613089	−	0.353967i
$139$		−	260.590i		−	1.87475i	−0.348322	−	0.937375i	$-0.613248\pi$
$139$		−	260.590i		−	1.87475i	0.348322	−	0.937375i	$-0.386752\pi$
$140$	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	0.999201	−	0.0399554i	$-0.0127216\pi$
$149$	69.2848	+	120.005i	0.464998	+	0.805401i	−0.534203	+	0.845356i	$0.679388\pi$
$150$	−29.8602	−	17.2398i	−0.199068	−	0.114932i
$151$	66.6000	−	115.355i	0.441060	−	0.763938i	−0.556709	−	0.830708i	$-0.687936\pi$
$151$	66.6000	−	115.355i	0.441060	−	0.763938i	0.997768	+	0.0667699i	$0.0212693\pi$
$152$	−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	0.903037	−	0.429562i	$-0.141332\pi$
$157$	154.260	+	89.0618i	0.982545	+	0.567273i	0.0795073	+	0.996834i	$0.474665\pi$
$158$	−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	0.747523	−	0.664236i	$-0.231243\pi$
$163$	−32.8419	−	56.8839i	−0.201484	−	0.348981i	−0.949007	+	0.315255i	$0.897910\pi$
$164$	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	$-0.839980\pi$
$167$		−	160.924i		−	0.963620i	0.876276	−	0.481810i	$-0.160020\pi$
$168$	−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	−0.411212	−	0.911540i	$-0.634894\pi$
$173$	29.8595	−	17.2394i	0.172598	−	0.0996496i	0.583810	+	0.811890i	$0.301561\pi$
$174$			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	0.200256	+	0.979744i	$0.435822\pi$
$179$	−133.955	+	232.018i	−0.748355	+	1.29619i	−0.948611	+	0.316445i	$0.897511\pi$
$180$	68.8494	−	39.7502i	0.382497	−	0.220835i
$181$			59.5598i			0.329060i	0.986372	+	0.164530i	$0.0526107\pi$
$181$			59.5598i			0.329060i	−0.986372	+	0.164530i	$0.947389\pi$
$182$	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	0.885385	+	0.464858i	$0.153895\pi$
$191$	161.447	+	279.634i	0.845272	+	1.46405i	−0.0401133	+	0.999195i	$0.512772\pi$
$192$	622.937	+	359.653i	3.24446	+	1.87319i
$193$	10.6139	−	18.3839i	0.0549945	−	0.0952533i	−0.837218	−	0.546870i	$-0.815819\pi$
$193$	10.6139	−	18.3839i	0.0549945	−	0.0952533i	0.892212	+	0.451617i	$0.149153\pi$
$194$	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	−0.217311	−	0.976102i	$-0.569729\pi$
$199$	−233.088	−	134.573i	−1.17130	−	0.676248i	−0.953985	+	0.299854i	$0.903062\pi$
$200$	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	$-0.766195\pi$
$223$		−	298.923i		−	1.34046i	0.742153	−	0.670230i	$-0.233805\pi$
$224$	−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	0.521290	−	0.853379i	$-0.325451\pi$
$227$	9.73538	+	5.62073i	0.0428871	+	0.0247609i	−0.478403	+	0.878140i	$0.658784\pi$
$228$	12.5878	−	21.8026i	0.0552095	−	0.0956256i
$229$	257.902	−	148.900i	1.12621	−	0.650218i	0.183232	−	0.983070i	$-0.441344\pi$
$229$	257.902	−	148.900i	1.12621	−	0.650218i	0.942979	+	0.332852i	$0.108011\pi$
$230$			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	0.981408	−	0.191933i	$-0.0614756\pi$
$233$	75.6050	+	130.952i	0.324485	+	0.562025i	−0.656923	+	0.753958i	$0.728142\pi$
$234$	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	0.910315	−	0.413917i	$-0.135840\pi$
$241$	242.689	+	140.117i	1.00701	+	0.581397i	0.0966949	+	0.995314i	$0.469173\pi$
$242$	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	$-0.881376\pi$
$251$		−	182.780i		−	0.728206i	0.931359	−	0.364103i	$-0.118624\pi$
$252$	−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	−0.721147	−	0.692782i	$-0.756385\pi$
$257$	−123.811	+	71.4823i	−0.481754	+	0.278141i	0.239393	+	0.970923i	$0.423052\pi$
$258$		−	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	−0.999643	−	0.0267172i	$-0.991495\pi$
$263$	−125.368	+	217.143i	−0.476684	+	0.825640i	0.522959	+	0.852358i	$0.324828\pi$
$264$	−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	0.998831	+	0.0483369i	$0.0153921\pi$
$269$	414.289	+	239.190i	1.54011	+	0.889182i	0.541277	+	0.840845i	$0.317941\pi$
$270$	−23.1296	+	40.0617i	−0.0856652	+	0.148377i
$271$	−74.5415	+	43.0365i	−0.275061	+	0.158806i	−0.631185	−	0.775632i	$-0.717431\pi$
$271$	−74.5415	+	43.0365i	−0.275061	+	0.158806i	0.356124	+	0.934439i	$0.384098\pi$
$272$		−	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	−0.931612	−	0.363455i	$-0.881597\pi$
$277$	−41.8394	+	72.4680i	−0.151045	+	0.261617i	0.780567	+	0.625072i	$0.214930\pi$
$278$	−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	−0.274687	−	0.961534i	$-0.588574\pi$
$283$	−352.262	−	203.379i	−1.24474	−	0.718653i	−0.970056	+	0.242881i	$0.921907\pi$
$284$	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	$-0.749472\pi$
$293$		−	415.051i		−	1.41656i	0.705933	−	0.708279i	$-0.250528\pi$
$294$	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	$0.160668\pi$
$307$			296.925i			0.967184i	−0.875294	+	0.483592i	$0.839332\pi$
$308$	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	0.859473	−	0.511181i	$-0.170792\pi$
$311$	263.266	+	151.997i	0.846514	+	0.488735i	−0.0129592	+	0.999916i	$0.504125\pi$
$312$	−308.427	+	534.211i	−0.988547	+	1.71221i
$313$	−357.904	+	206.636i	−1.14346	+	0.660179i	−0.947286	−	0.320389i	$-0.896186\pi$
$313$	−357.904	+	206.636i	−1.14346	+	0.660179i	−0.196178	+	0.980568i	$0.562853\pi$
$314$		−	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	−0.998485	−	0.0550197i	$-0.982478\pi$
$317$	−173.364	−	300.276i	−0.546891	−	0.947243i	0.451594	−	0.892223i	$-0.350856\pi$
$318$	−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	−0.999270	−	0.0382075i	$-0.987835\pi$
$331$	−176.332	−	305.415i	−0.532724	−	0.922704i	0.466546	−	0.884497i	$-0.345498\pi$
$332$	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	−0.725245	−	0.688491i	$-0.758274\pi$
$347$	81.0689	−	140.415i	0.233628	−	0.404655i	0.958873	+	0.283835i	$0.0916069\pi$
$348$	522.352	−	301.580i	1.50101	−	0.866610i
$349$			369.302i			1.05817i	0.848568	+	0.529086i	$0.177465\pi$
$349$			369.302i			1.05817i	−0.848568	+	0.529086i	$0.822535\pi$
$350$	−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	0.539475	−	0.842002i	$-0.318623\pi$
$353$	28.2461	+	16.3079i	0.0800174	+	0.0461980i	−0.459457	+	0.888200i	$0.651956\pi$
$354$	−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	0.996369	+	0.0851420i	$0.0271344\pi$
$359$	205.319	+	355.623i	0.571920	+	0.990594i	−0.424449	+	0.905452i	$0.639532\pi$
$360$	−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	0.980899	−	0.194520i	$-0.0623149\pi$
$367$	478.160	+	276.066i	1.30289	+	0.752223i	0.321990	+	0.946743i	$0.395648\pi$
$368$	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	0.639661	−	0.768657i	$-0.279075\pi$
$373$	−129.001	−	223.436i	−0.345846	−	0.599023i	−0.985507	+	0.169634i	$0.945741\pi$
$374$	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	−0.358504	−	0.933528i	$-0.616713\pi$
$383$	103.680	−	59.8595i	0.270704	−	0.156291i	0.629208	+	0.777237i	$0.283380\pi$
$384$		−	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	−0.978729	−	0.205159i	$-0.934229\pi$
$389$	−121.248	+	210.008i	−0.311692	+	0.539866i	0.667037	+	0.745024i	$0.267562\pi$
$390$	−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	−0.921953	−	0.387303i	$-0.873407\pi$
$397$	−415.863	+	240.099i	−1.04751	+	0.604783i	−0.125562	+	0.992086i	$0.540073\pi$
$398$			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	0.580376	−	0.814349i	$-0.302906\pi$
$401$	−166.439	−	288.280i	−0.415059	−	0.718903i	−0.995435	+	0.0954459i	$0.969572\pi$
$402$	−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	0.811923	−	0.583765i	$-0.198421\pi$
$409$	291.343	+	168.207i	0.712329	+	0.411263i	−0.0995937	+	0.995028i	$0.531754\pi$
$410$	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	$-0.983514\pi$
$419$		−	43.3827i		−	0.103539i	0.998659	−	0.0517693i	$-0.0164861\pi$
$420$	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	−0.121925	−	0.992539i	$-0.538907\pi$
$431$	344.197	−	596.168i	0.798602	−	1.38322i	0.920527	−	0.390680i	$-0.127760\pi$
$432$	346.710	−	200.173i	0.802569	−	0.463364i
$433$			670.156i			1.54770i	0.633367	+	0.773852i	$0.281673\pi$
$433$			670.156i			1.54770i	−0.633367	+	0.773852i	$0.718327\pi$
$434$	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	0.395364	−	0.918524i	$-0.370618\pi$
$439$	609.557	−	351.928i	1.38851	−	0.801658i	0.993148	+	0.116867i	$0.0372851\pi$
$440$		−	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	0.938715	−	0.344693i	$-0.112017\pi$
$443$	75.6841	+	131.089i	0.170845	+	0.295911i	−0.767871	+	0.640605i	$0.778684\pi$
$444$	−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	−0.987792	−	0.155780i	$-0.950211\pi$
$457$	−287.364	−	497.729i	−0.628805	−	1.08912i	0.358987	−	0.933343i	$-0.383122\pi$
$458$	−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	$-0.614156\pi$
$461$		−	863.340i		−	1.87276i	0.350994	−	0.936378i	$-0.385844\pi$
$462$	−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	−0.570222	−	0.821491i	$-0.693143\pi$
$467$	−67.2019	+	38.7991i	−0.143901	+	0.0830815i	0.426321	+	0.904572i	$0.359810\pi$
$468$		−	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	0.291347	−	0.956618i	$-0.405897\pi$
$479$	−187.498	−	108.252i	−0.391435	−	0.225995i	−0.682782	+	0.730622i	$0.739230\pi$
$480$	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	−0.940011	−	0.341143i	$-0.889186\pi$
$487$	−85.0142	+	147.249i	−0.174567	+	0.302359i	0.765444	+	0.643502i	$0.222519\pi$
$488$	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	0.560153	−	0.828389i	$-0.310742\pi$
$499$	−218.228	−	377.981i	−0.437330	−	0.757477i	−0.997483	+	0.0709120i	$0.977409\pi$
$500$	−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	$-0.871290\pi$
$503$		−	395.785i		−	0.786849i	0.919357	−	0.393424i	$-0.128710\pi$
$504$	−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	−0.856381	−	0.516345i	$-0.827292\pi$
$509$	−426.239	+	246.089i	−0.837404	+	0.483475i	0.0189771	+	0.999820i	$0.493959\pi$
$510$			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	0.887187	−	0.461411i	$-0.152657\pi$
$521$	485.148	+	280.100i	0.931187	+	0.537621i	0.0440000	+	0.999032i	$0.485990\pi$
$522$	−175.482	+	303.943i	−0.336172	+	0.582266i
$523$	−60.8040	+	35.1052i	−0.116260	+	0.0671227i	−0.557002	−	0.830511i	$-0.688049\pi$
$523$	−60.8040	+	35.1052i	−0.116260	+	0.0671227i	0.440742	+	0.897634i	$0.354715\pi$
$524$			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	−0.999060	−	0.0433513i	$-0.986197\pi$
$541$	−290.557	−	503.259i	−0.537073	−	0.930238i	0.461987	−	0.886887i	$-0.347137\pi$
$542$	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	−0.787242	−	0.616644i	$-0.788492\pi$
$557$	78.2077	−	135.460i	0.140409	−	0.243195i	0.927651	+	0.373449i	$0.121825\pi$
$558$	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	−0.0537158	−	0.998556i	$-0.517106\pi$
$563$	−532.231	−	307.284i	−0.945349	−	0.545797i	−0.891633	+	0.452759i	$0.850440\pi$
$564$	−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	−0.958737	−	0.284295i	$-0.908241\pi$
$569$	−412.852	−	715.081i	−0.725575	−	1.25673i	0.233162	−	0.972438i	$-0.425093\pi$
$570$	−16.3780	−	9.45587i	−0.0287334	−	0.0165892i
$571$	92.3654	−	159.982i	0.161761	−	0.280178i	−0.773739	−	0.633504i	$-0.781616\pi$
$571$	92.3654	−	159.982i	0.161761	−	0.280178i	0.935500	+	0.353326i	$0.114949\pi$
$572$	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	0.456324	−	0.889814i	$-0.349166\pi$
$577$	−49.6890	−	28.6880i	−0.0861161	−	0.0497192i	−0.542440	+	0.840095i	$0.682499\pi$
$578$	−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	$0.190904\pi$
$587$			662.641i			1.12886i	−0.825481	+	0.564430i	$0.809096\pi$
$588$	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	−0.299651	−	0.954049i	$-0.596870\pi$
$593$	223.415	−	128.989i	0.376754	−	0.217519i	0.676405	+	0.736530i	$0.263537\pi$
$594$			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	−0.962550	−	0.271103i	$-0.912612\pi$
$599$	−147.649	+	255.736i	−0.246493	+	0.426938i	0.716057	+	0.698041i	$0.245945\pi$
$600$	234.439	−	135.354i	0.390732	−	0.225589i
$601$		−	283.545i		−	0.471789i	−0.971779	−	0.235895i	$-0.924198\pi$
$601$		−	283.545i		−	0.471789i	0.971779	−	0.235895i	$-0.0758020\pi$
$602$	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	0.206096	−	0.978532i	$-0.433924\pi$
$607$	702.042	−	405.324i	1.15658	−	0.667750i	0.950481	+	0.310782i	$0.100591\pi$
$608$		−	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	−0.309231	+	0.950987i	$0.600071\pi$
$613$	−599.633	+	1038.59i	−0.978194	+	1.69428i	−0.668964	+	0.743295i	$0.733262\pi$
$614$	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	−0.170266	−	0.985398i	$-0.554463\pi$
$619$	−686.334	−	396.255i	−1.10878	−	0.640153i	−0.938513	+	0.345245i	$0.887796\pi$
$620$	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	−0.251639	−	0.967821i	$-0.580970\pi$
$641$	456.609	−	790.870i	0.712338	−	1.23381i	0.963977	−	0.265985i	$-0.0856971\pi$
$642$	514.349	−	296.960i	0.801167	−	0.462554i
$643$			782.798i			1.21742i	0.793394	+	0.608708i	$0.208312\pi$
$643$			782.798i			1.21742i	−0.793394	+	0.608708i	$0.791688\pi$
$644$	−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	0.921403	−	0.388609i	$-0.127044\pi$
$647$	676.477	+	390.564i	1.04556	+	0.603654i	0.124156	+	0.992263i	$0.460378\pi$
$648$	−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	0.990308	+	0.138885i	$0.0443520\pi$
$653$	401.877	+	696.072i	0.615433	+	1.06596i	−0.374876	+	0.927075i	$0.622315\pi$
$654$	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	0.910841	−	0.412758i	$-0.135435\pi$
$661$	666.818	+	384.987i	1.00880	+	0.582432i	0.0979611	+	0.995190i	$0.468768\pi$
$662$	−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	−0.717031	−	0.697041i	$-0.754499\pi$
$677$	−319.470	+	184.446i	−0.471891	+	0.272446i	0.245140	+	0.969488i	$0.421166\pi$
$678$		−	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	0.398347	+	0.917235i	$0.369584\pi$
$683$	−406.505	+	704.087i	−0.595175	+	1.03087i	−0.993522	+	0.113639i	$0.963749\pi$
$684$	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	−0.337773	−	0.941228i	$-0.609674\pi$
$691$	213.151	−	123.063i	0.308468	−	0.178094i	0.646241	+	0.763134i	$0.276340\pi$
$692$			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	0.984514	+	0.175309i	$0.0560924\pi$
$709$	456.652	+	790.944i	0.644079	+	1.11558i	−0.340435	+	0.940268i	$0.610574\pi$
$710$	−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	−0.877899	−	0.478846i	$-0.841055\pi$
$719$	−648.650	+	374.498i	−0.902156	+	0.520860i	−0.0242571	+	0.999706i	$0.507722\pi$
$720$			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	$0.0539443\pi$
$727$			245.233i			0.337322i	−0.985674	+	0.168661i	$0.946056\pi$
$728$	−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	−0.421283	−	0.906929i	$-0.638420\pi$
$733$	112.515	−	64.9604i	0.153499	−	0.0886226i	0.574782	+	0.818307i	$0.305087\pi$
$734$		−	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	−0.856715	−	0.515790i	$-0.827499\pi$
$739$	13.5453	−	23.4612i	0.0183293	−	0.0317472i	0.875045	+	0.484042i	$0.160832\pi$
$740$	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	0.670237	−	0.742147i	$-0.266192\pi$
$751$	−231.007	−	400.117i	−0.307600	−	0.532778i	−0.977837	+	0.209369i	$0.932859\pi$
$752$	−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	−0.981948	−	0.189150i	$-0.939427\pi$
$761$	−996.236	+	575.177i	−1.30911	+	0.755817i	−0.327166	+	0.944967i	$0.606094\pi$
$762$		−	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	$-0.928565\pi$
$769$		−	342.266i		−	0.445079i	0.974924	−	0.222539i	$-0.0714346\pi$
$770$	−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	0.475549	−	0.879689i	$-0.342249\pi$
$773$	−37.4974	−	21.6492i	−0.0485090	−	0.0280067i	−0.524058	+	0.851682i	$0.675583\pi$
$774$	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	0.00701626	−	0.999975i	$-0.497767\pi$
$787$	−673.263	−	388.708i	−0.855480	−	0.493911i	−0.862496	+	0.506064i	$0.831100\pi$
$788$	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	$0.335556\pi$
$797$			1385.98i			1.73899i	−0.493942	+	0.869495i	$0.664444\pi$
$798$	−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	−0.902975	−	0.429692i	$-0.858622\pi$
$809$	−64.2049	+	111.206i	−0.0793633	+	0.137461i	0.823612	+	0.567153i	$0.191955\pi$
$810$	−69.3888	+	40.0617i	−0.0856652	+	0.0494588i
$811$		−	550.689i		−	0.679024i	−0.940602	−	0.339512i	$-0.889738\pi$
$811$		−	550.689i		−	0.679024i	0.940602	−	0.339512i	$-0.110262\pi$
$812$	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	0.787948	−	0.615742i	$-0.211143\pi$
$821$	−114.344	−	198.049i	−0.139274	−	0.241229i	−0.927222	+	0.374512i	$0.877810\pi$
$822$	472.704	+	272.916i	0.575066	+	0.332014i
$823$	203.552	−	352.562i	0.247329	−	0.428387i	−0.715455	−	0.698659i	$-0.753780\pi$
$823$	203.552	−	352.562i	0.247329	−	0.428387i	0.962784	+	0.270273i	$0.0871138\pi$
$824$	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	−0.151787	−	0.988413i	$-0.548503\pi$
$829$	−898.364	−	518.671i	−1.08367	−	0.625658i	−0.931885	+	0.362755i	$0.881836\pi$
$830$	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	$-0.930276\pi$
$839$		−	364.625i		−	0.434595i	0.976105	−	0.217297i	$-0.0697241\pi$
$840$	−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	$0.164744\pi$
$853$			844.062i			0.989522i	−0.869029	+	0.494761i	$0.835256\pi$
$854$	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	0.531020	−	0.847360i	$-0.321809\pi$
$857$	53.7291	+	31.0205i	0.0626944	+	0.0361966i	−0.468325	+	0.883556i	$0.655142\pi$
$858$	−136.050	+	235.646i	−0.158566	+	0.274645i
$859$	767.453	−	443.089i	0.893426	−	0.515820i	0.0183642	−	0.999831i	$-0.494154\pi$
$859$	767.453	−	443.089i	0.893426	−	0.515820i	0.875061	+	0.484012i	$0.160821\pi$
$860$		−	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	0.999042	−	0.0437590i	$-0.0139334\pi$
$863$	398.382	+	690.018i	0.461625	+	0.799557i	−0.537417	+	0.843316i	$0.680600\pi$
$864$	−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	−0.854237	−	0.519883i	$-0.825976\pi$
$877$	−769.437	−	1332.70i	−0.877351	−	1.51962i	−0.0231132	−	0.999733i	$-0.507358\pi$
$878$	−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	$-0.764273\pi$
$881$		−	1188.82i		−	1.34940i	0.738092	−	0.674700i	$-0.235727\pi$
$882$	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	0.0291599	−	0.999575i	$-0.490717\pi$
$887$	806.635	−	465.711i	0.909397	−	0.525041i	0.880237	+	0.474534i	$0.157383\pi$
$888$			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	−0.0734628	−	0.997298i	$-0.523405\pi$
$907$	750.047	−	1299.12i	0.826954	−	1.43233i	0.900417	−	0.435028i	$-0.143262\pi$
$908$	−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	0.963566	−	0.267470i	$-0.0861875\pi$
$919$	229.886	+	398.174i	0.250148	+	0.433268i	−0.713419	+	0.700738i	$0.752854\pi$
$920$	−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	−0.855067	−	0.518518i	$-0.826484\pi$
$929$	−774.369	+	447.082i	−0.833551	+	0.481251i	0.0215159	+	0.999769i	$0.493151\pi$
$930$			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	$-0.862607\pi$
$937$		−	783.995i		−	0.836707i	0.908284	−	0.418354i	$-0.137393\pi$
$938$	−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	0.185815	−	0.982585i	$-0.440507\pi$
$941$	−538.460	−	310.880i	−0.572221	−	0.330372i	−0.758036	+	0.652213i	$0.773841\pi$
$942$	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	0.739407	−	0.673259i	$-0.235106\pi$
$947$	−202.048	−	349.958i	−0.213356	−	0.369544i	−0.952763	+	0.303715i	$0.901773\pi$
$948$	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	−0.357339	−	0.933975i	$-0.616316\pi$
$971$	264.925	−	152.954i	0.272837	−	0.157523i	0.630176	+	0.776452i	$0.282983\pi$
$972$		−	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	−0.573542	−	0.819176i	$-0.694431\pi$
$977$	412.936	−	715.226i	0.422657	−	0.732063i	0.996198	+	0.0871133i	$0.0277642\pi$
$978$	−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	−0.984786	−	0.173770i	$-0.944405\pi$
$983$	−1600.00	−	923.759i	−1.62767	−	0.939735i	−0.642882	−	0.765965i	$-0.722261\pi$
$984$	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	−0.860695	−	0.509121i	$-0.829970\pi$
$991$	10.4697	−	18.1341i	0.0105648	−	0.0182988i	0.871259	+	0.490823i	$0.163304\pi$
$992$	−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	−0.119466	−	0.992838i	$-0.538118\pi$
$997$	−1035.91	−	598.080i	−1.03902	−	0.599880i	−0.919556	+	0.392958i	$0.871452\pi$
$998$	−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.31.1	✓	12
3.2	odd	2		315.3.w.b.136.6		12
5.2	odd	4		525.3.s.j.199.12		24
5.3	odd	4		525.3.s.j.199.1		24
5.4	even	2		525.3.o.m.451.6		12
7.3	odd	6		735.3.h.b.391.12		12
7.4	even	3		735.3.h.b.391.11		12
7.5	odd	6	inner	105.3.n.b.61.1	yes	12
21.5	even	6		315.3.w.b.271.6		12
35.12	even	12		525.3.s.j.124.1		24
35.19	odd	6		525.3.o.m.376.6		12
35.33	even	12		525.3.s.j.124.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.b.31.1	✓	12	1.1	even	1	trivial
105.3.n.b.61.1	yes	12	7.5	odd	6	inner
315.3.w.b.136.6		12	3.2	odd	2
315.3.w.b.271.6		12	21.5	even	6
525.3.o.m.376.6		12	35.19	odd	6
525.3.o.m.451.6		12	5.4	even	2
525.3.s.j.124.1		24	35.12	even	12
525.3.s.j.124.12		24	35.33	even	12
525.3.s.j.199.1		24	5.3	odd	4
525.3.s.j.199.12		24	5.2	odd	4
735.3.h.b.391.11		12	7.4	even	3
735.3.h.b.391.12		12	7.3	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
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

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