LMFDB - Embedded newform 105.3.n.b.31.4

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			31.4
Root			$0.500000 + 2.68684i$ of defining polynomial
Character	$\chi$	$=$	105.31
Dual form			105.3.n.b.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.687692 + 1.19112i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.05416 - 1.82586i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.38224i q^{6} +(6.56639 + 2.42539i) q^{7} +8.40129 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.687692 + 1.19112i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.05416 - 1.82586i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.38224i q^{6} +(6.56639 + 2.42539i) q^{7} +8.40129 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.66342 - 1.53773i) q^{10} +(-5.31788 + 9.21084i) q^{11} +(3.16247 - 1.82586i) q^{12} -7.84307i q^{13} +(1.62673 + 9.48927i) q^{14} -3.87298 q^{15} +(1.56087 + 2.70350i) q^{16} +(-23.2862 - 13.4443i) q^{17} +(-2.06308 + 3.57335i) q^{18} +(2.69290 - 1.55475i) q^{19} +4.71434i q^{20} +(7.74913 + 9.32475i) q^{21} -14.6283 q^{22} +(2.29447 + 3.97414i) q^{23} +(12.6019 + 7.27573i) q^{24} +(2.50000 - 4.33013i) q^{25} +(9.34203 - 5.39362i) q^{26} +5.19615i q^{27} +(11.3504 - 9.43253i) q^{28} +11.4716 q^{29} +(-2.66342 - 4.61318i) q^{30} +(-40.1586 - 23.1856i) q^{31} +(14.6558 - 25.3846i) q^{32} +(-15.9536 + 9.21084i) q^{33} -36.9822i q^{34} +(-15.4274 + 2.64469i) q^{35} +6.32495 q^{36} +(-30.4528 - 52.7458i) q^{37} +(3.70378 + 2.13838i) q^{38} +(6.79230 - 11.7646i) q^{39} +(-16.2690 + 9.39292i) q^{40} +16.5328i q^{41} +(-5.77786 + 15.6427i) q^{42} +35.8074 q^{43} +(11.2118 + 19.4194i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-3.15578 + 5.46597i) q^{46} +(-52.2811 + 30.1845i) q^{47} +5.40700i q^{48} +(37.2349 + 31.8521i) q^{49} +6.87692 q^{50} +(-23.2862 - 40.3329i) q^{51} +(-14.3203 - 8.26784i) q^{52} +(-2.45862 + 4.25845i) q^{53} +(-6.18923 + 3.57335i) q^{54} -23.7823i q^{55} +(55.1661 + 20.3764i) q^{56} +5.38580 q^{57} +(7.88891 + 13.6640i) q^{58} +(25.7432 + 14.8629i) q^{59} +(-4.08274 + 7.07151i) q^{60} +(-36.9450 + 21.3302i) q^{61} -63.7782i q^{62} +(3.54823 + 20.6981i) q^{63} +52.8016 q^{64} +(8.76882 + 15.1880i) q^{65} +(-21.9424 - 12.6684i) q^{66} +(-38.3684 + 66.4560i) q^{67} +(-49.0948 + 28.3449i) q^{68} +7.94828i q^{69} +(-13.7595 - 16.5572i) q^{70} +84.8719 q^{71} +(12.6019 + 21.8272i) q^{72} +(37.0605 + 21.3969i) q^{73} +(41.8843 - 72.5458i) q^{74} +(7.50000 - 4.33013i) q^{75} -6.55580i q^{76} +(-57.2592 + 47.5840i) q^{77} +18.6841 q^{78} +(62.6367 + 108.490i) q^{79} +(-6.04521 - 3.49021i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-19.6925 + 11.3695i) q^{82} -132.554i q^{83} +(25.1945 - 4.31904i) q^{84} +60.1248 q^{85} +(24.6245 + 42.6509i) q^{86} +(17.2074 + 9.93467i) q^{87} +(-44.6770 + 77.3829i) q^{88} +(-82.9234 + 47.8758i) q^{89} -9.22636i q^{90} +(19.0225 - 51.5007i) q^{91} +9.67494 q^{92} +(-40.1586 - 69.5567i) q^{93} +(-71.9066 - 41.5153i) q^{94} +(-3.47652 + 6.02151i) q^{95} +(43.9673 - 25.3846i) q^{96} +105.841i q^{97} +(-12.3335 + 66.2557i) q^{98} -31.9073 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 $

$2$	0.687692	+	1.19112i	0.343846	+	0.595559i	0.985143	−	0.171733i	$-0.0549368\pi$
$2$	0.687692	+	1.19112i	0.343846	+	0.595559i	−0.641297	+	0.767293i	$0.721603\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	1.05416	−	1.82586i	0.263540	−	0.456464i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$			2.38224i			0.397039i
$7$	6.56639	+	2.42539i	0.938056	+	0.346485i
$7$	6.56639	+	2.42539i	0.938056	+	0.346485i
$8$	8.40129			1.05016
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−2.66342	−	1.53773i	−0.266342	−	0.153773i
$11$	−5.31788	+	9.21084i	−0.483444	+	0.837349i	−0.999819	−	0.0190134i	$-0.993947\pi$
$11$	−5.31788	+	9.21084i	−0.483444	+	0.837349i	0.516376	+	0.856362i	$0.327281\pi$
$12$	3.16247	−	1.82586i	0.263540	−	0.152155i
$13$		−	7.84307i		−	0.603313i	−0.953417	−	0.301657i	$-0.902460\pi$
$13$		−	7.84307i		−	0.603313i	0.953417	−	0.301657i	$-0.0975396\pi$
$14$	1.62673	+	9.48927i	0.116195	+	0.677805i
$15$	−3.87298			−0.258199
$16$	1.56087	+	2.70350i	0.0975542	+	0.168969i
$17$	−23.2862	−	13.4443i	−1.36978	−	0.790842i	−0.378879	−	0.925446i	$-0.623690\pi$
$17$	−23.2862	−	13.4443i	−1.36978	−	0.790842i	−0.990899	+	0.134604i	$0.957024\pi$
$18$	−2.06308	+	3.57335i	−0.114615	+	0.198520i
$19$	2.69290	−	1.55475i	0.141732	−	0.0818288i	−0.427457	−	0.904036i	$-0.640591\pi$
$19$	2.69290	−	1.55475i	0.141732	−	0.0818288i	0.569189	+	0.822207i	$0.307257\pi$
$20$			4.71434i			0.235717i
$21$	7.74913	+	9.32475i	0.369006	+	0.444036i
$22$	−14.6283			−0.664921
$23$	2.29447	+	3.97414i	0.0997595	+	0.172789i	0.911585	−	0.411111i	$-0.134859\pi$
$23$	2.29447	+	3.97414i	0.0997595	+	0.172789i	−0.811826	+	0.583900i	$0.801526\pi$
$24$	12.6019	+	7.27573i	0.525080	+	0.303155i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	9.34203	−	5.39362i	0.359309	−	0.207447i
$27$			5.19615i			0.192450i
$28$	11.3504	−	9.43253i	0.405373	−	0.336876i
$29$	11.4716			0.395571			0.197786	−	0.980245i	$-0.436625\pi$
$29$	11.4716			0.395571			0.197786	+	0.980245i	$0.436625\pi$
$30$	−2.66342	−	4.61318i	−0.0887807	−	0.153773i
$31$	−40.1586	−	23.1856i	−1.29544	−	0.747921i	−0.315825	−	0.948817i	$-0.602281\pi$
$31$	−40.1586	−	23.1856i	−1.29544	−	0.747921i	−0.979613	+	0.200896i	$0.935615\pi$
$32$	14.6558	−	25.3846i	0.457993	−	0.793267i
$33$	−15.9536	+	9.21084i	−0.483444	+	0.279116i
$34$		−	36.9822i		−	1.08771i
$35$	−15.4274	+	2.64469i	−0.440784	+	0.0755627i
$36$	6.32495			0.175693
$37$	−30.4528	−	52.7458i	−0.823049	−	1.42556i	−0.903401	−	0.428796i	$-0.858938\pi$
$37$	−30.4528	−	52.7458i	−0.823049	−	1.42556i	0.0803520	−	0.996767i	$-0.474396\pi$
$38$	3.70378	+	2.13838i	0.0974678	+	0.0562731i
$39$	6.79230	−	11.7646i	0.174162	−	0.301657i
$40$	−16.2690	+	9.39292i	−0.406726	+	0.234823i
$41$			16.5328i			0.403238i	0.979464	+	0.201619i	$0.0646203\pi$
$41$			16.5328i			0.403238i	−0.979464	+	0.201619i	$0.935380\pi$
$42$	−5.77786	+	15.6427i	−0.137568	+	0.372445i
$43$	35.8074			0.832731			0.416366	−	0.909197i	$-0.363304\pi$
$43$	35.8074			0.832731			0.416366	+	0.909197i	$0.363304\pi$
$44$	11.2118	+	19.4194i	0.254813	+	0.441349i
$45$	−5.80948	−	3.35410i	−0.129099	−	0.0745356i
$46$	−3.15578	+	5.46597i	−0.0686039	+	0.118825i
$47$	−52.2811	+	30.1845i	−1.11236	+	0.642223i	−0.939440	−	0.342712i	$-0.888654\pi$
$47$	−52.2811	+	30.1845i	−1.11236	+	0.642223i	−0.172923	+	0.984935i	$0.555321\pi$
$48$			5.40700i			0.112646i
$49$	37.2349	+	31.8521i	0.759897	+	0.650044i
$50$	6.87692			0.137538
$51$	−23.2862	−	40.3329i	−0.456593	−	0.790842i
$52$	−14.3203	−	8.26784i	−0.275391	−	0.158997i
$53$	−2.45862	+	4.25845i	−0.0463890	+	0.0803481i	−0.888288	−	0.459288i	$-0.848105\pi$
$53$	−2.45862	+	4.25845i	−0.0463890	+	0.0803481i	0.841899	+	0.539636i	$0.181438\pi$
$54$	−6.18923	+	3.57335i	−0.114615	+	0.0661732i
$55$		−	23.7823i		−	0.432405i
$56$	55.1661	+	20.3764i	0.985109	+	0.363865i
$57$	5.38580			0.0944878
$58$	7.88891	+	13.6640i	0.136016	+	0.235586i
$59$	25.7432	+	14.8629i	0.436326	+	0.251913i	0.702038	−	0.712140i	$-0.252274\pi$
$59$	25.7432	+	14.8629i	0.436326	+	0.251913i	−0.265712	+	0.964052i	$0.585607\pi$
$60$	−4.08274	+	7.07151i	−0.0680456	+	0.117858i
$61$	−36.9450	+	21.3302i	−0.605656	+	0.349676i	−0.771264	−	0.636516i	$-0.780375\pi$
$61$	−36.9450	+	21.3302i	−0.605656	+	0.349676i	0.165607	+	0.986192i	$0.447042\pi$
$62$		−	63.7782i		−	1.02868i
$63$	3.54823	+	20.6981i	0.0563211	+	0.328541i
$64$	52.8016			0.825025
$65$	8.76882	+	15.1880i	0.134905	+	0.233662i
$66$	−21.9424	−	12.6684i	−0.332460	−	0.191946i
$67$	−38.3684	+	66.4560i	−0.572662	+	0.991880i	0.423629	+	0.905836i	$0.360756\pi$
$67$	−38.3684	+	66.4560i	−0.572662	+	0.991880i	−0.996291	+	0.0860443i	$0.972577\pi$
$68$	−49.0948	+	28.3449i	−0.721982	+	0.416836i
$69$			7.94828i			0.115192i
$70$	−13.7595	−	16.5572i	−0.196564	−	0.236531i
$71$	84.8719			1.19538			0.597689	−	0.801728i	$-0.296086\pi$
$71$	84.8719			1.19538			0.597689	+	0.801728i	$0.296086\pi$
$72$	12.6019	+	21.8272i	0.175027	+	0.303155i
$73$	37.0605	+	21.3969i	0.507678	+	0.293108i	0.731879	−	0.681435i	$-0.238644\pi$
$73$	37.0605	+	21.3969i	0.507678	+	0.293108i	−0.224201	+	0.974543i	$0.571977\pi$
$74$	41.8843	−	72.5458i	0.566005	−	0.980349i
$75$	7.50000	−	4.33013i	0.100000	−	0.0577350i
$76$		−	6.55580i		−	0.0862605i
$77$	−57.2592	+	47.5840i	−0.743625	+	0.617974i
$78$	18.6841			0.239539
$79$	62.6367	+	108.490i	0.792869	+	1.37329i	0.924183	+	0.381949i	$0.124747\pi$
$79$	62.6367	+	108.490i	0.792869	+	1.37329i	−0.131314	+	0.991341i	$0.541920\pi$
$80$	−6.04521	−	3.49021i	−0.0755652	−	0.0436276i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−19.6925	+	11.3695i	−0.240152	+	0.138652i
$83$		−	132.554i		−	1.59704i	−0.601968	−	0.798520i	$-0.705616\pi$
$83$		−	132.554i		−	1.59704i	0.601968	−	0.798520i	$-0.294384\pi$
$84$	25.1945	−	4.31904i	0.299934	−	0.0514171i
$85$	60.1248			0.707351
$86$	24.6245	+	42.6509i	0.286332	+	0.495941i
$87$	17.2074	+	9.93467i	0.197786	+	0.114192i
$88$	−44.6770	+	77.3829i	−0.507693	+	0.879351i
$89$	−82.9234	+	47.8758i	−0.931723	+	0.537931i	−0.887356	−	0.461085i	$-0.847460\pi$
$89$	−82.9234	+	47.8758i	−0.931723	+	0.537931i	−0.0443671	+	0.999015i	$0.514127\pi$
$90$		−	9.22636i		−	0.102515i
$91$	19.0225	−	51.5007i	0.209039	−	0.565941i
$92$	9.67494			0.105162
$93$	−40.1586	−	69.5567i	−0.431813	−	0.747921i
$94$	−71.9066	−	41.5153i	−0.764964	−	0.441652i
$95$	−3.47652	+	6.02151i	−0.0365950	+	0.0633843i
$96$	43.9673	−	25.3846i	0.457993	−	0.264422i
$97$			105.841i			1.09114i	0.838064	+	0.545572i	$0.183687\pi$
$97$			105.841i			1.09114i	−0.838064	+	0.545572i	$0.816313\pi$
$98$	−12.3335	+	66.2557i	−0.125852	+	0.676079i
$99$	−31.9073			−0.322296
$100$	−5.27079	−	9.12928i	−0.0527079	−	0.0912928i
$101$	83.5961	+	48.2642i	0.827684	+	0.477864i	0.853059	−	0.521814i	$-0.174745\pi$
$101$	83.5961	+	48.2642i	0.827684	+	0.477864i	−0.0253749	+	0.999678i	$0.508078\pi$
$102$	32.0275	−	55.4733i	0.313995	−	0.543856i
$103$	164.541	−	94.9975i	1.59748	−	0.922306i	0.605510	−	0.795838i	$-0.292969\pi$
$103$	164.541	−	94.9975i	1.59748	−	0.922306i	0.991971	−	0.126468i	$-0.0403641\pi$
$104$		−	65.8919i		−	0.633576i
$105$	−25.4315	−	9.39351i	−0.242205	−	0.0894620i
$106$	−6.76309			−0.0638027
$107$	−80.1546	−	138.832i	−0.749108	−	1.29749i	−0.948251	−	0.317523i	$-0.897149\pi$
$107$	−80.1546	−	138.832i	−0.749108	−	1.29749i	0.199142	−	0.979971i	$-0.436184\pi$
$108$	9.48742	+	5.47757i	0.0878465	+	0.0507182i
$109$	−71.8518	+	124.451i	−0.659191	+	1.14175i	0.321634	+	0.946864i	$0.395768\pi$
$109$	−71.8518	+	124.451i	−0.659191	+	1.14175i	−0.980825	+	0.194888i	$0.937566\pi$
$110$	28.3275	−	16.3549i	0.257523	−	0.148681i
$111$		−	105.492i		−	0.950375i
$112$	3.69221	+	21.5380i	0.0329662	+	0.192303i
$113$	−87.8570			−0.777495			−0.388748	−	0.921344i	$-0.627092\pi$
$113$	−87.8570			−0.777495			−0.388748	+	0.921344i	$0.627092\pi$
$114$	3.70378	+	6.41513i	0.0324893	+	0.0562731i
$115$	−8.88644	−	5.13059i	−0.0772734	−	0.0446138i
$116$	12.0928	−	20.9454i	0.104249	−	0.180564i
$117$	20.3769	−	11.7646i	0.174162	−	0.100552i
$118$			40.8843i			0.346477i
$119$	−120.299	−	144.759i	−1.01091	−	1.21646i
$120$	−32.5380			−0.271150
$121$	3.94034	+	6.82486i	0.0325648	+	0.0564038i
$122$	−50.8136	−	29.3373i	−0.416505	−	0.240469i
$123$	−14.3178	+	24.7992i	−0.116405	+	0.201619i
$124$	−84.6670	+	48.8825i	−0.682798	+	0.394214i
$125$			11.1803i			0.0894427i
$126$	−22.2138	+	18.4603i	−0.176300	+	0.146510i
$127$	216.354			1.70357			0.851787	−	0.523888i	$-0.175519\pi$
$127$	216.354			1.70357			0.851787	+	0.523888i	$0.175519\pi$
$128$	−22.3118	−	38.6452i	−0.174311	−	0.301916i
$129$	53.7112	+	31.0102i	0.416366	+	0.240389i
$130$	−12.0605	+	20.8894i	−0.0927731	+	0.160688i
$131$	−83.9226	+	48.4528i	−0.640631	+	0.369868i	−0.784857	−	0.619676i	$-0.787264\pi$
$131$	−83.9226	+	48.4528i	−0.640631	+	0.369868i	0.144227	+	0.989545i	$0.453931\pi$
$132$			38.8387i			0.294233i
$133$	21.4535	−	3.67773i	0.161305	−	0.0276521i
$134$	−105.543			−0.787631
$135$	−5.80948	−	10.0623i	−0.0430331	−	0.0745356i
$136$	−195.634	−	112.950i	−1.43849	−	0.830511i
$137$	76.5114	−	132.522i	0.558478	−	0.967311i	−0.439146	−	0.898416i	$-0.644719\pi$
$137$	76.5114	−	132.522i	0.558478	−	0.967311i	0.997624	−	0.0688959i	$-0.0219476\pi$
$138$	−9.46734	+	5.46597i	−0.0686039	+	0.0396085i
$139$		−	205.564i		−	1.47888i	−0.673224	−	0.739439i	$-0.735091\pi$
$139$		−	205.564i		−	1.47888i	0.673224	−	0.739439i	$-0.264909\pi$
$140$	−11.4341	+	30.9562i	−0.0816723	+	0.221116i
$141$	−104.562			−0.741576
$142$	58.3657	+	101.092i	0.411026	+	0.711918i
$143$	72.2412	+	41.7085i	0.505184	+	0.291668i
$144$	−4.68260	+	8.11051i	−0.0325181	+	0.0563230i
$145$	−22.2146	+	12.8256i	−0.153204	+	0.0884524i
$146$			58.8579i			0.403136i
$147$	28.2676	+	80.0246i	0.192297	+	0.544385i
$148$	−128.408			−0.867624
$149$	12.2896	+	21.2862i	0.0824804	+	0.142860i	0.904315	−	0.426866i	$-0.140382\pi$
$149$	12.2896	+	21.2862i	0.0824804	+	0.142860i	−0.821834	+	0.569726i	$0.807049\pi$
$150$	10.3154	+	5.95559i	0.0687692	+	0.0397039i
$151$	−41.9754	+	72.7036i	−0.277983	+	0.481481i	−0.970883	−	0.239553i	$-0.922999\pi$
$151$	−41.9754	+	72.7036i	−0.277983	+	0.481481i	0.692900	+	0.721033i	$0.256333\pi$
$152$	22.6238	−	13.0619i	0.148841	−	0.0859334i
$153$		−	80.6659i		−	0.527228i
$154$	−96.0548	−	35.4793i	−0.623733	−	0.230385i
$155$	103.689			0.668961
$156$	−14.3203	−	24.8035i	−0.0917969	−	0.158997i
$157$	91.9961	+	53.1139i	0.585962	+	0.338305i	0.763499	−	0.645809i	$-0.223480\pi$
$157$	91.9961	+	53.1139i	0.585962	+	0.338305i	−0.177537	+	0.984114i	$0.556813\pi$
$158$	−86.1495	+	149.215i	−0.545250	+	0.944401i
$159$	−7.37585	+	4.25845i	−0.0463890	+	0.0267827i
$160$			65.5426i			0.409641i
$161$	5.42754	+	31.6607i	0.0337114	+	0.196650i
$162$	−12.3785			−0.0764103
$163$	−105.113	−	182.061i	−0.644865	−	1.11694i	−0.984333	−	0.176322i	$-0.943580\pi$
$163$	−105.113	−	182.061i	−0.644865	−	1.11694i	0.339467	−	0.940618i	$-0.389753\pi$
$164$	30.1865	+	17.4282i	0.184064	+	0.106269i
$165$	20.5961	−	35.6734i	0.124825	−	0.216203i
$166$	157.888	−	91.1566i	0.951132	−	0.549136i
$167$			121.596i			0.728119i	0.931376	+	0.364059i	$0.118609\pi$
$167$			121.596i			0.728119i	−0.931376	+	0.364059i	$0.881391\pi$
$168$	65.1027	+	78.3399i	0.387516	+	0.466309i
$169$	107.486			0.636013
$170$	41.3474	+	71.6157i	0.243220	+	0.421269i
$171$	8.07871	+	4.66424i	0.0472439	+	0.0272763i
$172$	37.7467	−	65.3792i	0.219458	−	0.380112i
$173$	257.612	−	148.732i	1.48909	−	0.859724i	0.489164	−	0.872192i	$-0.337302\pi$
$173$	257.612	−	148.732i	1.48909	−	0.859724i	0.999922	+	0.0124675i	$0.00396864\pi$
$174$			27.3280i			0.157057i
$175$	26.9182	−	22.3698i	0.153818	−	0.127828i
$176$	−33.2020			−0.188648
$177$	25.7432	+	44.5886i	0.145442	+	0.251913i
$178$	−114.052	−	65.8477i	−0.640739	−	0.369931i
$179$	72.7870	−	126.071i	0.406631	−	0.704306i	−0.587879	−	0.808949i	$-0.700037\pi$
$179$	72.7870	−	126.071i	0.406631	−	0.704306i	0.994510	+	0.104643i	$0.0333700\pi$
$180$	−12.2482	+	7.07151i	−0.0680456	+	0.0392862i
$181$			155.877i			0.861200i	0.902543	+	0.430600i	$0.141698\pi$
$181$			155.877i			0.861200i	−0.902543	+	0.430600i	$0.858302\pi$
$182$	74.4250	−	12.7585i	0.408929	−	0.0701018i
$183$	−73.8901			−0.403771
$184$	19.2765	+	33.3879i	0.104764	+	0.181456i
$185$	117.943	+	68.0946i	0.637531	+	0.368079i
$186$	55.2335	−	95.6672i	0.296954	−	0.514340i
$187$	247.667	−	142.990i	1.32442	−	0.764655i
$188$			127.277i			0.677005i
$189$	−12.6027	+	34.1200i	−0.0666810	+	0.180529i
$190$	−9.56311			−0.0503322
$191$	57.2259	+	99.1181i	0.299612	+	0.518943i	0.976047	−	0.217559i	$-0.0698095\pi$
$191$	57.2259	+	99.1181i	0.299612	+	0.518943i	−0.676435	+	0.736502i	$0.736476\pi$
$192$	79.2024	+	45.7275i	0.412513	+	0.238164i
$193$	−140.168	+	242.779i	−0.726261	+	1.25792i	0.232192	+	0.972670i	$0.425410\pi$
$193$	−140.168	+	242.779i	−0.726261	+	1.25792i	−0.958453	+	0.285251i	$0.907923\pi$
$194$	−126.069	+	72.7860i	−0.649840	+	0.375185i
$195$			30.3761i			0.155775i
$196$	97.4089	−	34.4084i	0.496984	−	0.175553i
$197$	76.0092			0.385834			0.192917	−	0.981215i	$-0.438205\pi$
$197$	76.0092			0.385834			0.192917	+	0.981215i	$0.438205\pi$
$198$	−21.9424	−	38.0053i	−0.110820	−	0.191946i
$199$	39.5702	+	22.8459i	0.198845	+	0.114803i	0.596117	−	0.802898i	$-0.296710\pi$
$199$	39.5702	+	22.8459i	0.198845	+	0.114803i	−0.397271	+	0.917701i	$0.630043\pi$
$200$	21.0032	−	36.3786i	0.105016	−	0.181893i
$201$	−115.105	+	66.4560i	−0.572662	+	0.330627i
$202$			132.764i			0.657246i
$203$	75.3268	+	27.8231i	0.371068	+	0.137059i
$204$	−98.1895			−0.481321
$205$	−18.4842	−	32.0156i	−0.0901668	−	0.156174i
$206$	226.307	+	130.658i	1.09858	+	0.634263i
$207$	−6.88341	+	11.9224i	−0.0332532	+	0.0575962i
$208$	21.2038	−	12.2420i	0.101941	−	0.0588558i
$209$			33.0718i			0.158238i
$210$	−6.30029	−	36.7518i	−0.0300014	−	0.175009i
$211$	−213.994			−1.01419			−0.507095	−	0.861890i	$-0.669281\pi$
$211$	−213.994			−1.01419			−0.507095	+	0.861890i	$0.669281\pi$
$212$	5.18354	+	8.97816i	0.0244507	+	0.0423498i
$213$	127.308	+	73.5012i	0.597689	+	0.345076i
$214$	110.243	−	190.947i	0.515156	−	0.892277i
$215$	−69.3408	+	40.0339i	−0.322515	+	0.186204i
$216$			43.6544i			0.202104i
$217$	−207.463	−	249.646i	−0.956050	−	1.15044i
$218$	−197.648			−0.906641
$219$	37.0605	+	64.1907i	0.169226	+	0.293108i
$220$	−43.4230	−	25.0703i	−0.197377	−	0.113956i
$221$	−105.445	+	182.636i	−0.477125	+	0.826405i
$222$	125.653	−	72.5458i	0.566005	−	0.326783i
$223$			83.5421i			0.374628i	0.982300	+	0.187314i	$0.0599782\pi$
$223$			83.5421i			0.374628i	−0.982300	+	0.187314i	$0.940022\pi$
$224$	157.803	−	131.139i	0.704478	−	0.585441i
$225$	15.0000			0.0666667
$226$	−60.4186	−	104.648i	−0.267339	−	0.463044i
$227$	4.41656	+	2.54990i	0.0194562	+	0.0112330i	0.509697	−	0.860354i	$-0.329758\pi$
$227$	4.41656	+	2.54990i	0.0194562	+	0.0112330i	−0.490240	+	0.871587i	$0.663091\pi$
$228$	5.67749	−	9.83370i	0.0249013	−	0.0431303i
$229$	−243.421	+	140.539i	−1.06297	+	0.613708i	−0.926253	−	0.376902i	$-0.876989\pi$
$229$	−243.421	+	140.539i	−1.06297	+	0.613708i	−0.136720	+	0.990610i	$0.543656\pi$
$230$		−	14.1131i		−	0.0613612i
$231$	−127.098	+	21.7881i	−0.550206	+	0.0943208i
$232$	96.3759			0.415414
$233$	−56.1219	−	97.2060i	−0.240866	−	0.417193i	0.720095	−	0.693876i	$-0.244098\pi$
$233$	−56.1219	−	97.2060i	−0.240866	−	0.417193i	−0.960961	+	0.276683i	$0.910765\pi$
$234$	28.0261	+	16.1809i	0.119770	+	0.0691490i
$235$	67.4946	−	116.904i	0.287211	−	0.497464i
$236$	54.2749	−	31.3356i	0.229978	−	0.132778i
$237$			216.980i			0.915527i
$238$	89.6964	−	242.840i	0.376876	−	1.02033i
$239$	−470.655			−1.96927			−0.984635	−	0.174627i	$-0.944128\pi$
$239$	−470.655			−1.96927			−0.984635	+	0.174627i	$0.944128\pi$
$240$	−6.04521	−	10.4706i	−0.0251884	−	0.0436276i
$241$	−231.772	−	133.814i	−0.961711	−	0.555244i	−0.0650115	−	0.997885i	$-0.520708\pi$
$241$	−231.772	−	133.814i	−0.961711	−	0.555244i	−0.896699	+	0.442641i	$0.854042\pi$
$242$	−5.41948	+	9.38681i	−0.0223945	+	0.0387885i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			89.9417i			0.368614i
$245$	−107.717	−	20.0515i	−0.439661	−	0.0818428i
$246$	−39.3850			−0.160102
$247$	−12.1940	−	21.1206i	−0.0493684	−	0.0855086i
$248$	−337.384	−	194.789i	−1.36042	−	0.785438i
$249$	114.795	−	198.832i	0.461026	−	0.798520i
$250$	−13.3171	+	7.68864i	−0.0532684	+	0.0307545i
$251$			63.3872i			0.252539i	0.991996	+	0.126269i	$0.0403003\pi$
$251$			63.3872i			0.252539i	−0.991996	+	0.126269i	$0.959700\pi$
$252$	41.5321	+	15.3405i	0.164810	+	0.0608749i
$253$	−48.8068			−0.192912
$254$	148.785	+	257.703i	0.585768	+	1.01458i
$255$	90.1872	+	52.0696i	0.353675	+	0.204195i
$256$	136.291	−	236.062i	0.532385	−	0.922118i
$257$	−93.9827	+	54.2610i	−0.365692	+	0.211132i	−0.671575	−	0.740937i	$-0.734382\pi$
$257$	−93.9827	+	54.2610i	−0.365692	+	0.211132i	0.305883	+	0.952069i	$0.401048\pi$
$258$			85.3018i			0.330627i
$259$	−72.0357	−	420.210i	−0.278130	−	1.62243i
$260$	36.9749			0.142211
$261$	17.2074	+	29.8040i	0.0659286	+	0.114192i
$262$	−115.426	−	66.6412i	−0.440557	−	0.254356i
$263$	140.864	−	243.984i	0.535605	−	0.927696i	−0.463528	−	0.886082i	$-0.653417\pi$
$263$	140.864	−	243.984i	0.535605	−	0.927696i	0.999134	−	0.0416136i	$-0.0132498\pi$
$264$	−134.031	+	77.3829i	−0.507693	+	0.293117i
$265$		−	10.9953i		−	0.0414916i
$266$	19.1340	+	23.0245i	0.0719325	+	0.0865584i
$267$	−165.847			−0.621149
$268$	80.8927	+	140.110i	0.301838	+	0.522799i
$269$	66.6805	+	38.4980i	0.247883	+	0.143115i	0.618794	−	0.785553i	$-0.287621\pi$
$269$	66.6805	+	38.4980i	0.247883	+	0.143115i	−0.370912	+	0.928668i	$0.620955\pi$
$270$	7.99026	−	13.8395i	0.0295936	−	0.0512576i
$271$	317.165	−	183.116i	1.17035	−	0.675703i	0.216589	−	0.976263i	$-0.430507\pi$
$271$	317.165	−	183.116i	1.17035	−	0.675703i	0.953763	+	0.300560i	$0.0971735\pi$
$272$		−	83.9392i		−	0.308600i
$273$	73.1347	−	60.7770i	0.267893	−	0.222626i
$274$	210.465			0.768122
$275$	26.5894	+	46.0542i	0.0966887	+	0.167470i
$276$	14.5124	+	8.37874i	0.0525812	+	0.0303578i
$277$	−150.176	+	260.112i	−0.542151	+	0.939034i	0.456629	+	0.889657i	$0.349057\pi$
$277$	−150.176	+	260.112i	−0.542151	+	0.939034i	−0.998780	+	0.0493766i	$0.984277\pi$
$278$	244.851	−	141.365i	0.880759	−	0.508506i
$279$		−	139.113i		−	0.498614i
$280$	−129.610	+	22.2188i	−0.462894	+	0.0793530i
$281$	−157.928			−0.562020			−0.281010	−	0.959705i	$-0.590669\pi$
$281$	−157.928			−0.562020			−0.281010	+	0.959705i	$0.590669\pi$
$282$	−71.9066	−	124.546i	−0.254988	−	0.441652i
$283$	−136.966	−	79.0774i	−0.483979	−	0.279425i	0.238094	−	0.971242i	$-0.423477\pi$
$283$	−136.966	−	79.0774i	−0.483979	−	0.279425i	−0.722073	+	0.691817i	$0.756811\pi$
$284$	89.4684	−	154.964i	0.315029	−	0.545647i
$285$	−10.4296	+	6.02151i	−0.0365950	+	0.0211281i
$286$			114.730i			0.401156i
$287$	−40.0985	+	108.561i	−0.139716	+	0.378260i
$288$	87.9347			0.305329
$289$	216.999	+	375.853i	0.750862	+	1.30053i
$290$	−30.5536	−	17.6401i	−0.105357	−	0.0608281i
$291$	−91.6609	+	158.761i	−0.314986	+	0.545572i
$292$	78.1352	−	45.1114i	0.267586	−	0.154491i
$293$			174.804i			0.596602i	0.954472	+	0.298301i	$0.0964199\pi$
$293$			174.804i			0.596602i	−0.954472	+	0.298301i	$0.903580\pi$
$294$	−75.8793	+	88.7024i	−0.258093	+	0.301709i
$295$	−66.4687			−0.225318
$296$	−255.843	−	443.133i	−0.864334	−	1.49707i
$297$	−47.8609	−	27.6325i	−0.161148	−	0.0930387i
$298$	−16.9029	+	29.2767i	−0.0567211	+	0.0982439i
$299$	31.1694	−	17.9957i	0.104246	−	0.0601863i
$300$		−	18.2586i		−	0.0608619i
$301$	235.126	+	86.8471i	0.781148	+	0.288529i
$302$	−115.465			−0.382334
$303$	83.5961	+	144.793i	0.275895	+	0.477864i
$304$	8.40653	+	4.85351i	0.0276531	+	0.0159655i
$305$	47.6958	−	82.6116i	0.156380	−	0.270858i
$306$	96.0826	−	55.4733i	0.313995	−	0.181285i
$307$		−	11.6570i		−	0.0379708i	−0.999820	−	0.0189854i	$-0.993956\pi$
$307$		−	11.6570i		−	0.0379708i	0.999820	−	0.0189854i	$-0.00604360\pi$
$308$	26.5213	+	154.708i	0.0861081	+	0.502299i
$309$	329.081			1.06499
$310$	71.3061	+	123.506i	0.230020	+	0.398406i
$311$	111.296	+	64.2566i	0.357864	+	0.206613i	0.668143	−	0.744032i	$-0.267089\pi$
$311$	111.296	+	64.2566i	0.357864	+	0.206613i	−0.310279	+	0.950645i	$0.600423\pi$
$312$	57.0640	−	98.8378i	0.182898	−	0.316788i
$313$	−111.325	+	64.2732i	−0.355669	+	0.205346i	−0.667179	−	0.744897i	$-0.732499\pi$
$313$	−111.325	+	64.2732i	−0.355669	+	0.205346i	0.311510	+	0.950243i	$0.399165\pi$
$314$			146.104i			0.465300i
$315$	−30.0123	−	36.1146i	−0.0952770	−	0.114650i
$316$	264.116			0.835810
$317$	−180.266	−	312.229i	−0.568661	−	0.984950i	−0.996699	−	0.0811893i	$-0.974128\pi$
$317$	−180.266	−	312.229i	−0.568661	−	0.984950i	0.428037	−	0.903761i	$-0.359205\pi$
$318$	−10.1446	−	5.85701i	−0.0319014	−	0.0184183i
$319$	−61.0044	+	105.663i	−0.191236	+	0.331231i
$320$	−102.250	+	59.0340i	−0.319531	+	0.184481i
$321$		−	277.664i		−	0.864996i
$322$	−33.9792	+	28.2377i	−0.105525	+	0.0876947i
$323$	−83.6101			−0.258855
$324$	9.48742	+	16.4327i	0.0292822	+	0.0507182i
$325$	−33.9615	−	19.6077i	−0.104497	−	0.0603313i
$326$	144.571	−	250.404i	0.443469	−	0.768111i
$327$	−215.555	+	124.451i	−0.659191	+	0.380584i
$328$			138.897i			0.423465i
$329$	−416.507	+	71.4010i	−1.26598	+	0.217024i
$330$	56.6550			0.171682
$331$	49.4928	+	85.7241i	0.149525	+	0.258985i	0.931052	−	0.364886i	$-0.118892\pi$
$331$	49.4928	+	85.7241i	0.149525	+	0.258985i	−0.781527	+	0.623872i	$0.785559\pi$
$332$	−242.025	−	139.733i	−0.728991	−	0.420883i
$333$	91.3585	−	158.237i	0.274350	−	0.475188i
$334$	−144.835	+	83.6205i	−0.433638	+	0.250361i
$335$		−	171.589i		−	0.512205i
$336$	−13.1141	+	35.5045i	−0.0390301	+	0.105668i
$337$	−409.551			−1.21528			−0.607642	−	0.794211i	$-0.707884\pi$
$337$	−409.551			−1.21528			−0.607642	+	0.794211i	$0.707884\pi$
$338$	73.9175	+	128.029i	0.218691	+	0.378783i
$339$	−131.785	−	76.0864i	−0.388748	−	0.224444i
$340$	63.3810	−	109.779i	0.186415	−	0.322880i
$341$	427.117	−	246.596i	1.25254	−	0.723156i
$342$			12.8303i			0.0375154i
$343$	167.245	+	299.463i	0.487595	+	0.873070i
$344$	300.829			0.874502
$345$	−8.88644	−	15.3918i	−0.0257578	−	0.0446138i
$346$	354.316	+	204.564i	1.02403	+	0.591226i
$347$	−184.699	+	319.908i	−0.532274	+	0.921925i	0.467016	+	0.884249i	$0.345329\pi$
$347$	−184.699	+	319.908i	−0.532274	+	0.921925i	−0.999290	+	0.0376765i	$0.988004\pi$
$348$	36.2785	−	20.9454i	0.104249	−	0.0601880i
$349$		−	126.187i		−	0.361568i	−0.983523	−	0.180784i	$-0.942137\pi$
$349$		−	126.187i		−	0.361568i	0.983523	−	0.180784i	$-0.0578635\pi$
$350$	45.1566	+	16.6792i	0.129019	+	0.0476550i
$351$	40.7538			0.116108
$352$	155.875	+	269.984i	0.442828	+	0.767000i
$353$	437.641	+	252.672i	1.23977	+	0.715784i	0.969048	−	0.246872i	$-0.0794027\pi$
$353$	437.641	+	252.672i	1.23977	+	0.715784i	0.270727	+	0.962656i	$0.412736\pi$
$354$	−35.4068	+	61.3265i	−0.100019	+	0.173239i
$355$	−164.354	+	94.8896i	−0.462968	+	0.267295i
$356$			201.875i			0.567064i
$357$	−55.0833	−	321.320i	−0.154295	−	0.900056i
$358$	200.220			0.559275
$359$	200.469	+	347.222i	0.558408	+	0.967192i	0.997630	+	0.0688127i	$0.0219211\pi$
$359$	200.469	+	347.222i	0.558408	+	0.967192i	−0.439221	+	0.898379i	$0.644746\pi$
$360$	−48.8071	−	28.1788i	−0.135575	−	0.0782744i
$361$	−175.666	+	304.262i	−0.486608	+	0.842830i
$362$	−185.668	+	107.196i	−0.512896	+	0.296121i
$363$			13.6497i			0.0376025i
$364$	−73.9800	−	89.0222i	−0.203242	−	0.244567i
$365$	−95.6898			−0.262164
$366$	−50.8136	−	88.0118i	−0.138835	−	0.240469i
$367$	−80.3967	−	46.4171i	−0.219065	−	0.126477i	0.386452	−	0.922309i	$-0.373700\pi$
$367$	−80.3967	−	46.4171i	−0.219065	−	0.126477i	−0.605517	+	0.795832i	$0.707034\pi$
$368$	−7.16273	+	12.4062i	−0.0194639	+	0.0337125i
$369$	−42.9534	+	24.7992i	−0.116405	+	0.0672064i
$370$			187.312i			0.506250i
$371$	−26.4727	+	21.9995i	−0.0713549	+	0.0592979i
$372$	−169.334			−0.455199
$373$	−145.541	−	252.084i	−0.390190	−	0.675829i	0.602284	−	0.798282i	$-0.294257\pi$
$373$	−145.541	−	252.084i	−0.390190	−	0.675829i	−0.992474	+	0.122453i	$0.960924\pi$
$374$	340.637	+	196.667i	0.910794	+	0.525847i
$375$	−9.68246	+	16.7705i	−0.0258199	+	0.0447214i
$376$	−439.228	+	253.589i	−1.16816	+	0.674438i
$377$		−	89.9723i		−	0.238653i
$378$	−49.3077	+	8.45272i	−0.130444	+	0.0223617i
$379$	206.257			0.544212			0.272106	−	0.962267i	$-0.412280\pi$
$379$	206.257			0.544212			0.272106	+	0.962267i	$0.412280\pi$
$380$	7.32961	+	12.6953i	0.0192884	+	0.0334086i
$381$	324.531	+	187.368i	0.851787	+	0.491780i
$382$	−78.7076	+	136.326i	−0.206041	+	0.356873i
$383$	448.377	−	258.870i	1.17070	−	0.675902i	0.216852	−	0.976204i	$-0.430421\pi$
$383$	448.377	−	258.870i	1.17070	−	0.675902i	0.953844	+	0.300303i	$0.0970878\pi$
$384$		−	77.2905i		−	0.201277i
$385$	57.6814	−	156.164i	0.149822	−	0.405620i
$386$	−385.571			−0.998888
$387$	53.7112	+	93.0305i	0.138789	+	0.240389i
$388$	193.250	+	111.573i	0.498067	+	0.287559i
$389$	64.1734	−	111.152i	0.164970	−	0.285737i	−0.771675	−	0.636018i	$-0.780581\pi$
$389$	64.1734	−	111.152i	0.164970	−	0.285737i	0.936645	+	0.350281i	$0.113914\pi$
$390$	−36.1815	+	20.8894i	−0.0927731	+	0.0535626i
$391$		−	123.390i		−	0.315576i
$392$	312.821	+	267.599i	0.798014	+	0.682650i
$393$	−167.845			−0.427087
$394$	52.2710	+	90.5360i	0.132667	+	0.229787i
$395$	−242.591	−	140.060i	−0.614154	−	0.354582i
$396$	−33.6353	+	58.2581i	−0.0849377	+	0.147116i
$397$	255.551	−	147.542i	0.643705	−	0.371643i	−0.142335	−	0.989819i	$-0.545461\pi$
$397$	255.551	−	147.542i	0.643705	−	0.371643i	0.786040	+	0.618175i	$0.212128\pi$
$398$			62.8437i			0.157899i
$399$	35.3653	+	13.0627i	0.0886348	+	0.0327386i
$400$	15.6087			0.0390217
$401$	−308.227	−	533.865i	−0.768646	−	1.33133i	−0.938297	−	0.345829i	$-0.887598\pi$
$401$	−308.227	−	533.865i	−0.768646	−	1.33133i	0.169652	−	0.985504i	$-0.445736\pi$
$402$	−158.314	−	91.4025i	−0.393815	−	0.227369i
$403$	−181.846	+	314.967i	−0.451231	+	0.781555i
$404$	176.247	−	101.756i	0.436255	−	0.251872i
$405$		−	20.1246i		−	0.0496904i
$406$	18.6611	+	108.857i	0.0459633	+	0.268120i
$407$	647.778			1.59159
$408$	−195.634	−	338.849i	−0.479496	−	0.830511i
$409$	386.812	+	223.326i	0.945751	+	0.546029i	0.891758	−	0.452512i	$-0.149472\pi$
$409$	386.812	+	223.326i	0.945751	+	0.546029i	0.0539922	+	0.998541i	$0.482805\pi$
$410$	25.4229	−	44.0337i	0.0620070	−	0.107399i
$411$	229.534	−	132.522i	0.558478	−	0.322437i
$412$		−	400.570i		−	0.972256i
$413$	132.992	+	160.033i	0.322014	+	0.387489i
$414$	−18.9347			−0.0457359
$415$	148.200	+	256.690i	0.357109	+	0.618531i
$416$	−199.093	−	114.946i	−0.478589	−	0.276313i
$417$	178.024	−	308.346i	0.426915	−	0.739439i
$418$	−39.3925	+	22.7433i	−0.0942404	+	0.0544097i
$419$		−	117.725i		−	0.280966i	−0.990083	−	0.140483i	$-0.955134\pi$
$419$		−	117.725i		−	0.280966i	0.990083	−	0.140483i	$-0.0448656\pi$
$420$	−43.9600	+	36.5320i	−0.104667	+	0.0869810i
$421$	−3.34256			−0.00793957			−0.00396979	−	0.999992i	$-0.501264\pi$
$421$	−3.34256			−0.00793957			−0.00396979	+	0.999992i	$0.501264\pi$
$422$	−147.162	−	254.892i	−0.348725	−	0.604010i
$423$	−156.843	−	90.5535i	−0.370788	−	0.214074i
$424$	−20.6555	+	35.7765i	−0.0487159	+	0.0843784i
$425$	−116.431	+	67.2216i	−0.273956	+	0.158168i
$426$			202.185i			0.474612i
$427$	−294.330	+	50.4564i	−0.689297	+	0.118165i
$428$	−337.983			−0.789679
$429$	72.2412	+	125.126i	0.168395	+	0.291668i
$430$	−95.3703	−	55.0621i	−0.221791	−	0.128051i
$431$	−339.544	+	588.108i	−0.787805	+	1.36452i	0.139504	+	0.990222i	$0.455449\pi$
$431$	−339.544	+	588.108i	−0.787805	+	1.36452i	−0.927309	+	0.374297i	$0.877884\pi$
$432$	−14.0478	+	8.11051i	−0.0325181	+	0.0187743i
$433$		−	452.002i		−	1.04389i	−0.852981	−	0.521943i	$-0.825207\pi$
$433$		−	452.002i		−	1.04389i	0.852981	−	0.521943i	$-0.174793\pi$
$434$	154.687	−	418.792i	0.356422	−	0.964959i
$435$	−44.4292			−0.102136
$436$	151.486	+	262.382i	0.347446	+	0.601794i
$437$	12.3576	+	7.13464i	0.0282782	+	0.0163264i
$438$	−50.9724	+	88.2869i	−0.116375	+	0.201568i
$439$	303.623	−	175.297i	0.691625	−	0.399310i	−0.112596	−	0.993641i	$-0.535916\pi$
$439$	303.623	−	175.297i	0.691625	−	0.399310i	0.804220	+	0.594331i	$0.202583\pi$
$440$		−	199.802i		−	0.454095i
$441$	−26.9019	+	144.517i	−0.0610020	+	0.327704i
$442$	−290.054			−0.656231
$443$	−173.403	−	300.343i	−0.391430	−	0.677976i	0.601209	−	0.799092i	$-0.294686\pi$
$443$	−173.403	−	300.343i	−0.391430	−	0.677976i	−0.992638	+	0.121116i	$0.961353\pi$
$444$	−192.613	−	111.205i	−0.433812	−	0.250461i
$445$	107.054	−	185.422i	0.240570	−	0.416679i
$446$	−99.5085	+	57.4513i	−0.223113	+	0.128815i
$447$			42.5723i			0.0952402i
$448$	346.716	+	128.065i	0.773920	+	0.285859i
$449$	783.377			1.74471			0.872357	−	0.488869i	$-0.162590\pi$
$449$	783.377			1.74471			0.872357	+	0.488869i	$0.162590\pi$
$450$	10.3154	+	17.8668i	0.0229231	+	0.0397039i
$451$	−152.281	−	87.9193i	−0.337651	−	0.194943i
$452$	−92.6151	+	160.414i	−0.204901	+	0.354899i
$453$	−125.926	+	72.7036i	−0.277983	+	0.160494i
$454$			7.01419i			0.0154498i
$455$	20.7425	+	120.998i	0.0455880	+	0.265931i
$456$	45.2477			0.0992274
$457$	−320.271	−	554.725i	−0.700811	−	1.21384i	−0.968182	−	0.250247i	$-0.919488\pi$
$457$	−320.271	−	554.725i	−0.700811	−	1.21384i	0.267371	−	0.963594i	$-0.413845\pi$
$458$	−334.797	−	193.295i	−0.730999	−	0.422042i
$459$	69.8587	−	120.999i	0.152198	−	0.263614i
$460$	−18.7354	+	10.8169i	−0.0407292	+	0.0235150i
$461$		−	758.376i		−	1.64507i	−0.568716	−	0.822534i	$-0.692560\pi$
$461$		−	758.376i		−	1.64507i	0.568716	−	0.822534i	$-0.307440\pi$
$462$	−113.356	−	136.405i	−0.245360	−	0.295249i
$463$	151.903			0.328084			0.164042	−	0.986453i	$-0.447547\pi$
$463$	151.903			0.328084			0.164042	+	0.986453i	$0.447547\pi$
$464$	17.9056	+	31.0134i	0.0385897	+	0.0668393i
$465$	155.533	+	89.7973i	0.334481	+	0.193112i
$466$	77.1892	−	133.696i	0.165642	−	0.286900i
$467$	−312.205	+	180.251i	−0.668533	+	0.385977i	−0.795520	−	0.605927i	$-0.792802\pi$
$467$	−312.205	+	180.251i	−0.668533	+	0.385977i	0.126988	+	0.991904i	$0.459469\pi$
$468$		−	49.6070i		−	0.105998i
$469$	−413.123	+	343.317i	−0.880860	+	0.732020i
$470$	185.662			0.395026
$471$	91.9961	+	159.342i	0.195321	+	0.338305i
$472$	216.276	+	124.867i	0.458212	+	0.264549i
$473$	−190.420	+	329.817i	−0.402579	+	0.697286i
$474$	−258.449	+	149.215i	−0.545250	+	0.314800i
$475$		−	15.5475i		−	0.0327315i
$476$	−391.123	+	67.0494i	−0.821686	+	0.140860i
$477$	−14.7517			−0.0309260
$478$	−323.666	−	560.606i	−0.677126	−	1.17282i
$479$	−463.427	−	267.560i	−0.967489	−	0.558580i	−0.0690193	−	0.997615i	$-0.521987\pi$
$479$	−463.427	−	267.560i	−0.967489	−	0.558580i	−0.898470	+	0.439035i	$0.855320\pi$
$480$	−56.7616	+	98.3139i	−0.118253	+	0.204821i
$481$	−413.689	+	238.844i	−0.860061	+	0.496556i
$482$		−	368.091i		−	0.763674i
$483$	−19.2777	+	52.1915i	−0.0399124	+	0.108057i
$484$	16.6150			0.0343284
$485$	−118.334	−	204.960i	−0.243987	−	0.422598i
$486$	−18.5677	−	10.7201i	−0.0382051	−	0.0220577i
$487$	−163.431	+	283.070i	−0.335586	+	0.581253i	−0.983597	−	0.180378i	$-0.942268\pi$
$487$	−163.431	+	283.070i	−0.335586	+	0.581253i	0.648011	+	0.761631i	$0.275601\pi$
$488$	−310.386	+	179.201i	−0.636037	+	0.367216i
$489$		−	364.122i		−	0.744626i
$490$	−50.1924	−	142.093i	−0.102434	−	0.289985i
$491$	238.455			0.485652			0.242826	−	0.970070i	$-0.421926\pi$
$491$	238.455			0.485652			0.242826	+	0.970070i	$0.421926\pi$
$492$	30.1865	+	52.2845i	0.0613546	+	0.106269i
$493$	−267.130	−	154.227i	−0.541845	−	0.312834i
$494$	16.7714	−	29.0490i	0.0339503	−	0.0588036i
$495$	61.7882	−	35.6734i	0.124825	−	0.0720675i
$496$		−	144.758i		−	0.291852i
$497$	557.302	+	205.848i	1.12133	+	0.414180i
$498$	315.776			0.634088
$499$	−229.401	−	397.334i	−0.459722	−	0.796261i	0.539224	−	0.842162i	$-0.318717\pi$
$499$	−229.401	−	397.334i	−0.459722	−	0.796261i	−0.998946	+	0.0459009i	$0.985384\pi$
$500$	20.4137	+	11.7858i	0.0408274	+	0.0235717i
$501$	−105.305	+	182.394i	−0.210190	+	0.364059i
$502$	−75.5016	+	43.5909i	−0.150402	+	0.0868344i
$503$			724.087i			1.43954i	0.694215	+	0.719768i	$0.255752\pi$
$503$			724.087i			1.43954i	−0.694215	+	0.719768i	$0.744248\pi$
$504$	29.8097	+	173.890i	0.0591462	+	0.345021i
$505$	−215.844			−0.427414
$506$	−33.5641	−	58.1347i	−0.0663322	−	0.114891i
$507$	161.229	+	93.0858i	0.318007	+	0.183601i
$508$	228.071	−	395.031i	0.448959	−	0.777620i
$509$	−382.635	+	220.914i	−0.751738	+	0.434016i	−0.826321	−	0.563199i	$-0.809571\pi$
$509$	−382.635	+	220.914i	−0.751738	+	0.434016i	0.0745837	+	0.997215i	$0.476237\pi$
$510$			143.231i			0.280846i
$511$	191.458	+	230.387i	0.374673	+	0.450854i
$512$	196.409			0.383612
$513$	8.07871	+	13.9927i	0.0157480	+	0.0272763i
$514$	−129.262	−	74.6297i	−0.251483	−	0.145194i
$515$	−212.421	+	367.924i	−0.412468	+	0.714415i
$516$	113.240	−	65.3792i	0.219458	−	0.126704i
$517$		−	642.070i		−	1.24191i
$518$	450.981	−	374.778i	0.870620	−	0.723510i
$519$	515.224			0.992724
$520$	73.6694	+	127.599i	0.141672	+	0.245383i
$521$	−73.9438	−	42.6915i	−0.141927	−	0.0819415i	0.427355	−	0.904084i	$-0.359445\pi$
$521$	−73.9438	−	42.6915i	−0.141927	−	0.0819415i	−0.569282	+	0.822142i	$0.692779\pi$
$522$	−23.6667	+	40.9920i	−0.0453386	+	0.0785287i
$523$	211.920	−	122.352i	0.405201	−	0.233943i	−0.283525	−	0.958965i	$-0.591504\pi$
$523$	211.920	−	122.352i	0.405201	−	0.233943i	0.688726	+	0.725022i	$0.258171\pi$
$524$			204.307i			0.389900i
$525$	59.7502	−	10.2429i	0.113810	−	0.0195102i
$526$	387.485			0.736663
$527$	623.428	+	1079.81i	1.18298	+	2.04897i
$528$	−49.8030	−	28.7538i	−0.0943239	−	0.0544579i
$529$	253.971	−	439.890i	0.480096	−	0.831551i
$530$	13.0967	−	7.56136i	0.0247107	−	0.0142667i
$531$			89.1772i			0.167942i
$532$	15.9004	−	43.0479i	0.0298879	−	0.0809172i
$533$	129.668			0.243279
$534$	−114.052	−	197.543i	−0.213580	−	0.369931i
$535$	310.437	+	179.231i	0.580257	+	0.335011i
$536$	−322.344	+	558.316i	−0.601387	+	1.04163i
$537$	218.361	−	126.071i	0.406631	−	0.234769i
$538$			105.899i			0.196838i
$539$	−491.396	+	173.579i	−0.911680	+	0.322039i
$540$	−24.4964			−0.0453637
$541$	10.9532	+	18.9715i	0.0202462	+	0.0350675i	0.875971	−	0.482364i	$-0.160222\pi$
$541$	10.9532	+	18.9715i	0.0202462	+	0.0350675i	−0.855725	+	0.517431i	$0.826888\pi$
$542$	436.225	+	251.854i	0.804842	+	0.464676i
$543$	−134.994	+	233.816i	−0.248607	+	0.430600i
$544$	−682.556	+	394.074i	−1.25470	+	0.724400i
$545$		−	321.331i		−	0.589598i
$546$	122.687	+	45.3162i	0.224701	+	0.0829966i
$547$	−59.9613			−0.109618			−0.0548092	−	0.998497i	$-0.517455\pi$
$547$	−59.9613			−0.109618			−0.0548092	+	0.998497i	$0.517455\pi$
$548$	−161.310	−	279.398i	−0.294362	−	0.509850i
$549$	−110.835	−	63.9907i	−0.201885	−	0.116559i
$550$	−36.5706	+	63.3422i	−0.0664921	+	0.115168i
$551$	30.8918	−	17.8354i	0.0560650	−	0.0323691i
$552$			66.7757i			0.120971i
$553$	148.166	+	864.306i	0.267932	+	1.56294i
$554$	−413.099			−0.745667
$555$	117.943	+	204.284i	0.212510	+	0.368079i
$556$	−375.330	−	216.697i	−0.675054	−	0.389743i
$557$	112.551	−	194.944i	0.202066	−	0.349989i	−0.747128	−	0.664680i	$-0.768568\pi$
$557$	112.551	−	194.944i	0.202066	−	0.349989i	0.949194	+	0.314692i	$0.101901\pi$
$558$	165.700	−	95.6672i	0.296954	−	0.171447i
$559$		−	280.840i		−	0.502398i
$560$	−31.2301	−	37.5801i	−0.0557681	−	0.0671073i
$561$	495.333			0.882947
$562$	−108.606	−	188.111i	−0.193249	−	0.334716i
$563$	−333.356	−	192.463i	−0.592106	−	0.341853i	0.173824	−	0.984777i	$-0.444388\pi$
$563$	−333.356	−	192.463i	−0.592106	−	0.341853i	−0.765930	+	0.642924i	$0.777721\pi$
$564$	−110.225	+	190.915i	−0.195435	+	0.338502i
$565$	170.134	−	98.2271i	0.301123	−	0.173853i
$566$		−	217.524i		−	0.384317i
$567$	−48.4528	+	40.2657i	−0.0854547	+	0.0710153i
$568$	713.033			1.25534
$569$	66.0920	+	114.475i	0.116155	+	0.201186i	0.918241	−	0.396023i	$-0.129610\pi$
$569$	66.0920	+	114.475i	0.116155	+	0.201186i	−0.802086	+	0.597208i	$0.796277\pi$
$570$	−14.3447	−	8.28190i	−0.0251661	−	0.0145296i
$571$	410.880	−	711.665i	0.719580	−	1.24635i	−0.241587	−	0.970379i	$-0.577668\pi$
$571$	410.880	−	711.665i	0.719580	−	1.24635i	0.961166	−	0.275970i	$-0.0889989\pi$
$572$	152.307	−	87.9347i	0.266272	−	0.153732i
$573$			198.236i			0.345962i
$574$	−156.884	+	26.8943i	−0.273317	+	0.0468542i
$575$	22.9447			0.0399038
$576$	79.2024	+	137.183i	0.137504	+	0.238164i
$577$	650.829	+	375.756i	1.12795	+	0.651224i	0.943419	−	0.331602i	$-0.107589\pi$
$577$	650.829	+	375.756i	1.12795	+	0.651224i	0.184534	+	0.982826i	$0.440922\pi$
$578$	−298.457	+	516.943i	−0.516362	+	0.894365i
$579$	−420.505	+	242.779i	−0.726261	+	0.419307i
$580$			54.0809i			0.0932429i
$581$	321.496	−	870.404i	0.553350	−	1.49811i
$582$	−252.138			−0.433227
$583$	−26.1493	−	45.2918i	−0.0448529	−	0.0776875i
$584$	311.356	+	179.761i	0.533143	+	0.307811i
$585$	−26.3065	+	45.5641i	−0.0449683	+	0.0778874i
$586$	−208.213	+	120.212i	−0.355312	+	0.205139i
$587$		−	193.435i		−	0.329531i	−0.986333	−	0.164766i	$-0.947313\pi$
$587$		−	193.435i		−	0.329531i	0.986333	−	0.164766i	$-0.0526868\pi$
$588$	175.912	+	32.7460i	0.299170	+	0.0556904i
$589$	−144.191			−0.244806
$590$	−45.7100	−	79.1721i	−0.0774747	−	0.134190i
$591$	114.014	+	65.8259i	0.192917	+	0.111381i
$592$	95.0656	−	164.659i	0.160584	−	0.278139i
$593$	172.012	−	99.3113i	0.290071	−	0.167473i	−0.347903	−	0.937531i	$-0.613106\pi$
$593$	172.012	−	99.3113i	0.290071	−	0.167473i	0.637974	+	0.770058i	$0.279773\pi$
$594$		−	76.0107i		−	0.127964i
$595$	394.803	+	145.826i	0.663534	+	0.245086i
$596$	51.8206			0.0869474
$597$	39.5702	+	68.5376i	0.0662818	+	0.114803i
$598$	42.8700	+	24.7510i	0.0716889	+	0.0413896i
$599$	409.817	−	709.823i	0.684168	−	1.18501i	−0.289530	−	0.957169i	$-0.593499\pi$
$599$	409.817	−	709.823i	0.684168	−	1.18501i	0.973698	−	0.227845i	$-0.0731678\pi$
$600$	63.0096	−	36.3786i	0.105016	−	0.0606311i
$601$			531.115i			0.883719i	0.897084	+	0.441860i	$0.145681\pi$
$601$			531.115i			0.883719i	−0.897084	+	0.441860i	$0.854319\pi$
$602$	58.2489	+	339.787i	0.0967590	+	0.564429i
$603$	−230.210			−0.381775
$604$	88.4975	+	153.282i	0.146519	+	0.253778i
$605$	−15.2609	−	8.81086i	−0.0252246	−	0.0145634i
$606$	−114.977	+	199.146i	−0.189731	+	0.328623i
$607$	205.349	−	118.558i	0.338302	−	0.195319i	−0.321219	−	0.947005i	$-0.604093\pi$
$607$	205.349	−	118.558i	0.338302	−	0.195319i	0.659521	+	0.751686i	$0.270759\pi$
$608$		−	91.1441i		−	0.149908i
$609$	88.8947	+	106.970i	0.145968	+	0.175648i
$610$	131.200			0.215082
$611$	236.739	+	410.044i	0.387462	+	0.671104i
$612$	−147.284	−	85.0346i	−0.240661	−	0.138945i
$613$	140.546	−	243.432i	0.229275	−	0.397116i	−0.728318	−	0.685239i	$-0.759698\pi$
$613$	140.546	−	243.432i	0.229275	−	0.397116i	0.957594	+	0.288123i	$0.0930311\pi$
$614$	13.8849	−	8.01646i	0.0226139	−	0.0130561i
$615$		−	64.0311i		−	0.104116i
$616$	−481.051	+	399.767i	−0.780926	+	0.648972i
$617$	1022.97			1.65798			0.828988	−	0.559267i	$-0.188917\pi$
$617$	1022.97			1.65798			0.828988	+	0.559267i	$0.188917\pi$
$618$	226.307	+	391.974i	0.366192	+	0.634263i
$619$	−420.023	−	242.500i	−0.678551	−	0.391761i	0.120758	−	0.992682i	$-0.461467\pi$
$619$	−420.023	−	242.500i	−0.678551	−	0.391761i	−0.799309	+	0.600921i	$0.794801\pi$
$620$	109.305	−	189.321i	0.176298	−	0.305357i
$621$	−20.6502	+	11.9224i	−0.0332532	+	0.0191987i
$622$			176.755i			0.284172i
$623$	−660.625	+	113.250i	−1.06039	+	0.181781i
$624$	42.4075			0.0679608
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−153.114	−	88.4005i	−0.244591	−	0.141215i
$627$	−28.6411	+	49.6078i	−0.0456795	+	0.0791192i
$628$	193.957	−	111.981i	0.308848	−	0.178314i
$629$			1637.67i			2.60361i
$630$	22.3776	−	60.5839i	0.0355199	−	0.0961649i
$631$	−563.866			−0.893607			−0.446804	−	0.894632i	$-0.647438\pi$
$631$	−563.866			−0.893607			−0.446804	+	0.894632i	$0.647438\pi$
$632$	526.229	+	911.455i	0.832640	+	1.44218i
$633$	−320.991	−	185.324i	−0.507095	−	0.292771i
$634$	247.935	−	429.435i	0.391064	−	0.677343i
$635$	−418.968	+	241.891i	−0.659792	+	0.380931i
$636$			17.9563i			0.0282332i
$637$	249.819	−	292.036i	0.392180	−	0.458456i
$638$	−167.809			−0.263024
$639$	127.308	+	220.504i	0.199230	+	0.345076i
$640$	86.4134	+	49.8908i	0.135021	+	0.0779544i
$641$	401.202	−	694.902i	0.625900	−	1.08409i	−0.362466	−	0.931997i	$-0.618065\pi$
$641$	401.202	−	694.902i	0.625900	−	1.08409i	0.988366	−	0.152093i	$-0.0486015\pi$
$642$	330.730	−	190.947i	0.515156	−	0.297426i
$643$		−	297.581i		−	0.462801i	−0.972859	−	0.231401i	$-0.925669\pi$
$643$		−	297.581i		−	0.462801i	0.972859	−	0.231401i	$-0.0743308\pi$
$644$	63.5294	+	23.4655i	0.0986481	+	0.0364371i
$645$	−138.682			−0.215010
$646$	−57.4980	−	99.5895i	−0.0890062	−	0.154163i
$647$	−339.308	−	195.900i	−0.524433	−	0.302782i	0.214313	−	0.976765i	$-0.431249\pi$
$647$	−339.308	−	195.900i	−0.524433	−	0.302782i	−0.738747	+	0.673983i	$0.764582\pi$
$648$	−37.8058	+	65.4815i	−0.0583423	+	0.101052i
$649$	−273.799	+	158.078i	−0.421878	+	0.243571i
$650$		−	53.9362i		−	0.0829788i
$651$	−94.9946	−	554.137i	−0.145921	−	0.851208i
$652$	−443.223			−0.679790
$653$	119.502	+	206.983i	0.183004	+	0.316972i	0.942902	−	0.333070i	$-0.108084\pi$
$653$	119.502	+	206.983i	0.183004	+	0.316972i	−0.759898	+	0.650042i	$0.774751\pi$
$654$	−296.472	−	171.168i	−0.453321	−	0.261725i
$655$	108.344	−	187.657i	0.165410	−	0.286499i
$656$	−44.6964	+	25.8055i	−0.0681347	+	0.0393376i
$657$			128.381i			0.195405i
$658$	−371.476	−	447.007i	−0.564553	−	0.679342i
$659$	−773.060			−1.17308			−0.586540	−	0.809920i	$-0.699510\pi$
$659$	−773.060			−1.17308			−0.586540	+	0.809920i	$0.699510\pi$
$660$	−43.4230	−	75.2108i	−0.0657924	−	0.113956i
$661$	−415.385	−	239.823i	−0.628419	−	0.362818i	0.151721	−	0.988423i	$-0.451519\pi$
$661$	−415.385	−	239.823i	−0.628419	−	0.362818i	−0.780139	+	0.625606i	$0.784852\pi$
$662$	−68.0717	+	117.904i	−0.102827	+	0.178102i
$663$	−316.334	+	182.636i	−0.477125	+	0.275468i
$664$		−	1113.63i		−	1.67715i
$665$	−37.4327	+	31.1077i	−0.0562898	+	0.0467784i
$666$	251.306			0.377336
$667$	26.3212	+	45.5896i	0.0394620	+	0.0683502i
$668$	222.016	+	128.181i	0.332360	+	0.191888i
$669$	−72.3496	+	125.313i	−0.108146	+	0.187314i
$670$	204.382	−	118.000i	0.305048	−	0.176120i
$671$		−	453.726i		−	0.676194i
$672$	350.274	−	60.0468i	0.521241	−	0.0893554i
$673$	−925.495			−1.37518			−0.687589	−	0.726100i	$-0.741331\pi$
$673$	−925.495			−1.37518			−0.687589	+	0.726100i	$0.741331\pi$
$674$	−281.645	−	487.823i	−0.417871	−	0.723773i
$675$	22.5000	+	12.9904i	0.0333333	+	0.0192450i
$676$	113.307	−	196.254i	0.167615	−	0.290317i
$677$	−898.188	+	518.569i	−1.32672	+	0.765981i	−0.984791	−	0.173745i	$-0.944413\pi$
$677$	−898.188	+	518.569i	−1.32672	+	0.765981i	−0.341928	+	0.939726i	$0.611080\pi$
$678$		−	209.296i		−	0.308696i
$679$	−256.706	+	694.992i	−0.378064	+	1.02355i
$680$	505.126			0.742832
$681$	4.41656	+	7.64970i	0.00648540	+	0.0112330i
$682$	587.450	+	339.164i	0.861364	+	0.497309i
$683$	428.777	−	742.663i	0.627785	−	1.08735i	−0.360211	−	0.932871i	$-0.617295\pi$
$683$	428.777	−	742.663i	0.627785	−	1.08735i	0.987995	−	0.154484i	$-0.0493715\pi$
$684$	17.0325	−	9.83370i	0.0249013	−	0.0143768i
$685$			342.169i			0.499517i
$686$	−241.683	+	405.147i	−0.352307	+	0.590594i
$687$	−486.842			−0.708649
$688$	55.8907	+	96.8055i	0.0812365	+	0.140706i
$689$	33.3993	+	19.2831i	0.0484751	+	0.0279871i
$690$	12.2223	−	21.1696i	0.0177134	−	0.0306806i
$691$	679.984	−	392.589i	0.984058	−	0.568146i	0.0805652	−	0.996749i	$-0.474327\pi$
$691$	679.984	−	392.589i	0.984058	−	0.568146i	0.903493	+	0.428603i	$0.140994\pi$
$692$		−	627.150i		−	0.906285i
$693$	−209.516	−	77.3877i	−0.302331	−	0.111671i
$694$	−508.064			−0.732081
$695$	229.828	+	398.073i	0.330687	+	0.572767i
$696$	144.564	+	83.4640i	0.207707	+	0.119920i
$697$	222.272	−	384.986i	0.318898	−	0.552347i
$698$	150.304	−	86.7780i	0.215335	−	0.124324i
$699$		−	194.412i		−	0.278129i
$700$	−12.4680	−	72.7301i	−0.0178114	−	0.103900i
$701$	425.572			0.607093			0.303546	−	0.952817i	$-0.401829\pi$
$701$	425.572			0.607093			0.303546	+	0.952817i	$0.401829\pi$
$702$	28.0261	+	48.5426i	0.0399232	+	0.0691490i
$703$	−164.013	−	94.6929i	−0.233304	−	0.134698i
$704$	−280.793	+	486.347i	−0.398853	+	0.690834i
$705$	202.484	−	116.904i	0.287211	−	0.165821i
$706$			695.042i			0.984479i
$707$	431.865	+	519.675i	0.610841	+	0.735043i
$708$	108.550			0.153319
$709$	−628.376	−	1088.38i	−0.886284	−	1.53509i	−0.844234	−	0.535974i	$-0.819944\pi$
$709$	−628.376	−	1088.38i	−0.886284	−	1.53509i	−0.0420501	−	0.999116i	$-0.513389\pi$
$710$	−226.050	−	130.510i	−0.318380	−	0.183817i
$711$	−187.910	+	325.470i	−0.264290	+	0.457763i
$712$	−696.663	+	402.219i	−0.978459	+	0.564914i
$713$		−	212.794i		−	0.298449i
$714$	344.850	−	286.580i	0.482983	−	0.401373i
$715$	−186.526			−0.260876
$716$	−153.458	−	265.797i	−0.214327	−	0.371225i
$717$	−705.983	−	407.599i	−0.984635	−	0.568479i
$718$	−275.721	+	477.564i	−0.384013	+	0.665130i
$719$	339.594	−	196.065i	0.472314	−	0.272691i	−0.244894	−	0.969550i	$-0.578753\pi$
$719$	339.594	−	196.065i	0.472314	−	0.272691i	0.717208	+	0.696859i	$0.245420\pi$
$720$		−	20.9412i		−	0.0290851i
$721$	1310.84	−	224.715i	1.81809	−	0.311672i
$722$	−483.215			−0.669273
$723$	−231.772	−	401.441i	−0.320570	−	0.555244i
$724$	284.609	+	164.319i	0.393107	+	0.226960i
$725$	28.6789	−	49.6734i	0.0395571	−	0.0685150i
$726$	−16.2584	+	9.38681i	−0.0223945	+	0.0129295i
$727$			1227.13i			1.68794i	0.536388	+	0.843971i	$0.319788\pi$
$727$			1227.13i			1.68794i	−0.536388	+	0.843971i	$0.680212\pi$
$728$	159.814	−	432.672i	0.219524	−	0.594329i
$729$	−27.0000			−0.0370370
$730$	−65.8051	−	113.978i	−0.0901440	−	0.156134i
$731$	−833.821	−	481.407i	−1.14066	−	0.658559i
$732$	−77.8918	+	134.913i	−0.106410	+	0.184307i
$733$	−373.772	+	215.797i	−0.509921	+	0.294403i	−0.732801	−	0.680443i	$-0.761787\pi$
$733$	−373.772	+	215.797i	−0.509921	+	0.294403i	0.222880	+	0.974846i	$0.428454\pi$
$734$		−	127.683i		−	0.173955i
$735$	−144.210	−	123.363i	−0.196205	−	0.167841i
$736$	134.509			0.182757
$737$	−408.077	−	706.809i	−0.553700	−	0.959036i
$738$	−59.0775	−	34.1084i	−0.0800508	−	0.0462173i
$739$	−264.829	+	458.698i	−0.358362	+	0.620701i	−0.987687	−	0.156441i	$-0.949998\pi$
$739$	−264.829	+	458.698i	−0.358362	+	0.620701i	0.629326	+	0.777142i	$0.283331\pi$
$740$	248.662	−	143.565i	0.336029	−	0.194007i
$741$		−	42.2412i		−	0.0570057i
$742$	−44.4091	−	16.4031i	−0.0598505	−	0.0221067i
$743$	−11.8268			−0.0159176			−0.00795878	−	0.999968i	$-0.502533\pi$
$743$	−11.8268			−0.0159176			−0.00795878	+	0.999968i	$0.502533\pi$
$744$	−337.384	−	584.366i	−0.453473	−	0.785438i
$745$	−47.5973	−	27.4803i	−0.0638890	−	0.0368864i
$746$	200.175	−	346.713i	0.268331	−	0.464762i
$747$	344.386	−	198.832i	0.461026	−	0.266173i
$748$		−	602.938i		−	0.806067i
$749$	−189.605	−	1106.03i	−0.253144	−	1.47668i
$750$	−26.6342			−0.0355123
$751$	−90.5156	−	156.778i	−0.120527	−	0.208759i	0.799449	−	0.600734i	$-0.205125\pi$
$751$	−90.5156	−	156.778i	−0.120527	−	0.208759i	−0.919976	+	0.391976i	$0.871792\pi$
$752$	−163.208	−	94.2280i	−0.217032	−	0.125303i
$753$	−54.8949	+	95.0808i	−0.0729016	+	0.126269i
$754$	107.168	−	61.8733i	0.142132	−	0.0820601i
$755$		−	187.720i		−	0.248636i
$756$	49.0129	+	58.9786i	0.0648318	+	0.0780140i
$757$	−600.909			−0.793803			−0.396902	−	0.917861i	$-0.629915\pi$
$757$	−600.909			−0.793803			−0.396902	+	0.917861i	$0.629915\pi$
$758$	141.841	+	245.676i	0.187125	+	0.324111i
$759$	−73.2103	−	42.2680i	−0.0964562	−	0.0556890i
$760$	−29.2073	+	50.5884i	−0.0384306	+	0.0665637i
$761$	−163.630	+	94.4716i	−0.215019	+	0.124141i	−0.603642	−	0.797256i	$-0.706284\pi$
$761$	−163.630	+	94.4716i	−0.215019	+	0.124141i	0.388623	+	0.921397i	$0.372951\pi$
$762$			515.406i			0.676386i
$763$	−773.650	+	642.925i	−1.01396	+	0.842628i
$764$	241.301			0.315838
$765$	90.1872	+	156.209i	0.117892	+	0.204195i
$766$	616.690	+	356.046i	0.805079	+	0.464812i
$767$	116.570	−	201.906i	0.151982	−	0.263241i
$768$	408.872	−	236.062i	0.532385	−	0.307373i
$769$			1154.26i			1.50099i	0.660877	+	0.750494i	$0.270184\pi$
$769$			1154.26i			1.50099i	−0.660877	+	0.750494i	$0.729816\pi$
$770$	225.676	−	38.6873i	0.293086	−	0.0502432i
$771$	−187.965			−0.243794
$772$	295.519	+	511.854i	0.382797	+	0.663024i
$773$	533.785	+	308.181i	0.690537	+	0.398682i	0.803813	−	0.594882i	$-0.202801\pi$
$773$	533.785	+	308.181i	0.690537	+	0.398682i	−0.113276	+	0.993564i	$0.536135\pi$
$774$	−73.8735	+	127.953i	−0.0954438	+	0.165314i
$775$	−200.793	+	115.928i	−0.259088	+	0.149584i
$776$			889.200i			1.14588i
$777$	255.859	−	692.699i	0.329290	−	0.891505i
$778$	176.526			0.226897
$779$	25.7043	+	44.5211i	0.0329965	+	0.0571516i
$780$	55.4623	+	32.0212i	0.0711056	+	0.0410528i
$781$	−451.338	+	781.741i	−0.577898	+	1.00095i
$782$	146.972	−	84.8546i	0.187944	−	0.108510i
$783$			59.6080i			0.0761277i
$784$	−27.9935	+	150.382i	−0.0357060	+	0.191813i
$785$	−237.533			−0.302590
$786$	−115.426	−	199.924i	−0.146852	−	0.254356i
$787$	707.577	+	408.520i	0.899081	+	0.519085i	0.876902	−	0.480669i	$-0.159606\pi$
$787$	707.577	+	408.520i	0.899081	+	0.519085i	0.0221791	+	0.999754i	$0.492940\pi$
$788$	80.1258	−	138.782i	0.101682	−	0.176119i
$789$	422.593	−	243.984i	0.535605	−	0.309232i
$790$		−	385.272i		−	0.487687i
$791$	−576.903	−	213.088i	−0.729334	−	0.269390i
$792$	−268.062			−0.338462
$793$	167.295	+	289.763i	0.210964	+	0.365400i
$794$	351.481	+	202.928i	0.442671	+	0.255576i
$795$	9.52218	−	16.4929i	0.0119776	−	0.0207458i
$796$	83.4265	−	48.1663i	0.104807	−	0.0605105i
$797$		−	951.327i		−	1.19364i	−0.802377	−	0.596818i	$-0.796432\pi$
$797$		−	951.327i		−	1.19364i	0.802377	−	0.596818i	$-0.203568\pi$
$798$	8.76123	+	51.1073i	0.0109790	+	0.0640443i
$799$	1623.24			2.03159
$800$	−73.2789	−	126.923i	−0.0915986	−	0.158653i
$801$	−248.770	−	143.627i	−0.310574	−	0.179310i
$802$	423.931	−	734.269i	0.528592	−	0.915548i
$803$	−394.166	+	227.572i	−0.490867	+	0.283402i
$804$			280.220i			0.348533i
$805$	−45.9081	−	55.2426i	−0.0570288	−	0.0686243i
$806$	−500.217			−0.620616
$807$	66.6805	+	115.494i	0.0826276	+	0.143115i
$808$	702.315	+	405.482i	0.869201	+	0.501834i
$809$	−196.405	+	340.183i	−0.242775	+	0.420498i	−0.961504	−	0.274792i	$-0.911391\pi$
$809$	−196.405	+	340.183i	−0.242775	+	0.420498i	0.718729	+	0.695290i	$0.244724\pi$
$810$	23.9708	−	13.8395i	0.0295936	−	0.0170859i
$811$			58.5439i			0.0721872i	0.999348	+	0.0360936i	$0.0114915\pi$
$811$			58.5439i			0.0721872i	−0.999348	+	0.0360936i	$0.988509\pi$
$812$	130.207	−	108.206i	0.160354	−	0.133259i
$813$	634.331			0.780235
$814$	445.472	+	771.580i	0.547263	+	0.947887i
$815$	407.101	+	235.040i	0.499511	+	0.288393i
$816$	72.6935	−	125.909i	0.0890851	−	0.154300i
$817$	96.4259	−	55.6715i	0.118024	−	0.0681414i
$818$			614.318i			0.751000i
$819$	162.336	−	27.8290i	0.198213	−	0.0339793i
$820$	−77.9411			−0.0950501
$821$	599.338	+	1038.08i	0.730010	+	1.26441i	0.956878	+	0.290489i	$0.0938179\pi$
$821$	599.338	+	1038.08i	0.730010	+	1.26441i	−0.226869	+	0.973925i	$0.572849\pi$
$822$	315.698	+	182.268i	0.384061	+	0.221738i
$823$	487.238	−	843.921i	0.592027	−	1.02542i	−0.401933	−	0.915669i	$-0.631661\pi$
$823$	487.238	−	843.921i	0.592027	−	1.02542i	0.993959	−	0.109751i	$-0.0350053\pi$
$824$	1382.35	−	798.101i	1.67761	−	0.968569i
$825$			92.1084i			0.111646i
$826$	−99.1605	+	268.462i	−0.120049	+	0.325015i
$827$	556.448			0.672851			0.336426	−	0.941710i	$-0.390782\pi$
$827$	556.448			0.672851			0.336426	+	0.941710i	$0.390782\pi$
$828$	14.5124	+	25.1362i	0.0175271	+	0.0303578i
$829$	663.387	+	383.007i	0.800225	+	0.462010i	0.843550	−	0.537051i	$-0.180462\pi$
$829$	663.387	+	383.007i	0.800225	+	0.462010i	−0.0433247	+	0.999061i	$0.513795\pi$
$830$	−203.832	+	353.048i	−0.245581	+	0.425359i
$831$	−450.528	+	260.112i	−0.542151	+	0.313011i
$832$		−	414.127i		−	0.497749i
$833$	−438.831	−	1242.31i	−0.526808	−	1.49137i
$834$	489.702			0.587173
$835$	−135.948	−	235.469i	−0.162812	−	0.281999i
$836$	60.3844	+	34.8629i	0.0722301	+	0.0417021i
$837$	120.476	−	208.670i	0.143938	−	0.249307i
$838$	140.224	−	80.9585i	0.167332	−	0.0966092i
$839$			1045.06i			1.24560i	0.782380	+	0.622801i	$0.214006\pi$
$839$			1045.06i			1.24560i	−0.782380	+	0.622801i	$0.785994\pi$
$840$	−213.657	−	78.9175i	−0.254354	−	0.0939494i
$841$	−709.403			−0.843523
$842$	−2.29865	−	3.98138i	−0.00272999	−	0.00472849i
$843$	−236.892	−	136.769i	−0.281010	−	0.162241i
$844$	−225.584	+	390.722i	−0.267279	+	0.462941i
$845$	−208.146	+	120.173i	−0.246327	+	0.142217i
$846$		−	249.092i		−	0.294435i
$847$	9.32081	+	54.3716i	0.0110045	+	0.0641931i
$848$	−15.3503			−0.0181018
$849$	−136.966	−	237.232i	−0.161326	−	0.279425i
$850$	−160.138	−	92.4555i	−0.188397	−	0.108771i
$851$	139.746	−	242.047i	0.164214	−	0.284427i
$852$	268.405	−	154.964i	0.315029	−	0.181882i
$853$			1525.75i			1.78869i	0.447379	+	0.894344i	$0.352358\pi$
$853$			1525.75i			1.78869i	−0.447379	+	0.894344i	$0.647642\pi$
$854$	−262.508	−	315.883i	−0.307386	−	0.369886i
$855$	−20.8591			−0.0243966
$856$	−673.402	−	1166.37i	−0.786684	−	1.36258i
$857$	−1388.21	−	801.483i	−1.61985	−	0.935219i	−0.986958	−	0.160976i	$-0.948536\pi$
$857$	−1388.21	−	801.483i	−1.61985	−	0.935219i	−0.632888	−	0.774243i	$-0.718131\pi$
$858$	−99.3595	+	172.096i	−0.115804	+	0.200578i
$859$	1083.23	−	625.402i	1.26103	−	0.728058i	0.287758	−	0.957703i	$-0.407090\pi$
$859$	1083.23	−	625.402i	1.26103	−	0.728058i	0.973274	+	0.229645i	$0.0737566\pi$
$860$			168.808i			0.196289i
$861$	−154.164	+	128.115i	−0.179052	+	0.148797i
$862$	−934.007			−1.08354
$863$	341.394	+	591.311i	0.395589	+	0.685181i	0.993176	−	0.116623i	$-0.0372071\pi$
$863$	341.394	+	591.311i	0.395589	+	0.685181i	−0.597587	+	0.801804i	$0.703874\pi$
$864$	131.902	+	76.1537i	0.152664	+	0.0881408i
$865$	−332.576	+	576.038i	−0.384480	+	0.665940i
$866$	538.388	−	310.839i	0.621695	−	0.358936i
$867$			751.707i			0.867021i
$868$	−674.516	+	115.631i	−0.777092	+	0.133215i
$869$	−1332.38			−1.53323
$870$	−30.5536	−	52.9204i	−0.0351191	−	0.0608281i
$871$	521.219	+	300.926i	0.598414	+	0.345495i
$872$	−603.648	+	1045.55i	−0.692256	+	1.19902i
$873$	−274.983	+	158.761i	−0.314986	+	0.181857i
$874$			19.6258i			0.0224551i
$875$	−27.1167	+	73.4145i	−0.0309905	+	0.0839022i
$876$	156.270			0.178391
$877$	−375.466	−	650.327i	−0.428126	−	0.741536i	0.568581	−	0.822627i	$-0.307493\pi$
$877$	−375.466	−	650.327i	−0.428126	−	0.741536i	−0.996707	+	0.0810918i	$0.974159\pi$
$878$	417.599	+	241.101i	0.475625	+	0.274602i
$879$	−151.385	+	262.206i	−0.172224	+	0.298301i
$880$	64.2954	−	37.1210i	0.0730630	−	0.0421829i
$881$			1010.05i			1.14648i	0.819388	+	0.573240i	$0.194314\pi$
$881$			1010.05i			1.14648i	−0.819388	+	0.573240i	$0.805686\pi$
$882$	−190.638	+	67.3402i	−0.216142	+	0.0763495i
$883$	−834.105			−0.944627			−0.472313	−	0.881431i	$-0.656581\pi$
$883$	−834.105			−0.944627			−0.472313	+	0.881431i	$0.656581\pi$
$884$	222.311	+	385.054i	0.251483	+	0.435581i
$885$	−99.7031	−	57.5636i	−0.112659	−	0.0650436i
$886$	238.496	−	413.088i	0.269183	−	0.466239i
$887$	473.928	−	273.622i	0.534304	−	0.308481i	−0.208463	−	0.978030i	$-0.566846\pi$
$887$	473.928	−	273.622i	0.534304	−	0.308481i	0.742767	+	0.669549i	$0.233513\pi$
$888$		−	886.266i		−	0.998047i
$889$	1420.66	+	524.743i	1.59805	+	0.590263i
$890$	294.480			0.330876
$891$	−47.8609	−	82.8975i	−0.0537159	−	0.0930387i
$892$	152.536	+	88.0666i	0.171004	+	0.0987294i
$893$	−93.8585	+	162.568i	−0.105105	+	0.182047i
$894$	−50.7087	+	29.2767i	−0.0567211	+	0.0327480i
$895$			325.513i			0.363702i
$896$	−52.7784	−	307.875i	−0.0589044	−	0.343610i
$897$	62.3389			0.0694971
$898$	538.722	+	933.095i	0.599914	+	1.03908i
$899$	−460.682	−	265.975i	−0.512438	−	0.295856i
$900$	15.8124	−	27.3878i	0.0175693	−	0.0304309i
$901$	114.504	−	66.1088i	0.127085	−	0.0733727i
$902$		−	241.846i		−	0.268122i
$903$	277.477	+	333.895i	0.307283	+	0.369762i
$904$	−738.111			−0.816495
$905$	−174.276	−	301.855i	−0.192570	−	0.333542i
$906$	−173.197	−	99.9954i	−0.191167	−	0.110370i
$907$	−245.672	+	425.516i	−0.270862	+	0.469147i	−0.969083	−	0.246736i	$-0.920642\pi$
$907$	−245.672	+	425.516i	−0.270862	+	0.469147i	0.698221	+	0.715882i	$0.253975\pi$
$908$	9.31150	−	5.37600i	0.0102550	−	0.00592070i
$909$			289.585i			0.318576i
$910$	−129.859	+	107.917i	−0.142702	+	0.118590i
$911$	−1000.27			−1.09800			−0.548998	−	0.835824i	$-0.684991\pi$
$911$	−1000.27			−1.09800			−0.548998	+	0.835824i	$0.684991\pi$
$912$	8.40653	+	14.5605i	0.00921768	+	0.0159655i
$913$	1220.94	+	704.908i	1.33728	+	0.772079i
$914$	440.496	−	762.961i	0.481943	−	0.834749i
$915$	143.088	−	82.6116i	0.156380	−	0.0902859i
$916$			592.602i			0.646945i
$917$	−668.586	+	114.614i	−0.729101	+	0.124988i
$918$	192.165			0.209330
$919$	−144.233	−	249.819i	−0.156946	−	0.271838i	0.776820	−	0.629723i	$-0.216831\pi$
$919$	−144.233	−	249.819i	−0.156946	−	0.271838i	−0.933766	+	0.357884i	$0.883498\pi$
$920$	−74.6575	−	43.1036i	−0.0811495	−	0.0468517i
$921$	10.0953	−	17.4856i	0.0109612	−	0.0189854i
$922$	903.316	−	521.530i	0.979735	−	0.565650i
$923$		−	665.656i		−	0.721188i
$924$	−94.1991	+	255.030i	−0.101947	+	0.276007i
$925$	−304.528			−0.329220
$926$	104.463	+	180.934i	0.112811	+	0.195394i
$927$	493.622	+	284.993i	0.532494	+	0.307435i
$928$	168.125	−	291.201i	0.181169	−	0.313794i
$929$	274.999	−	158.771i	0.296016	−	0.170905i	−0.344636	−	0.938737i	$-0.611998\pi$
$929$	274.999	−	158.771i	0.296016	−	0.170905i	0.640652	+	0.767831i	$0.278664\pi$
$930$			247.012i			0.265604i
$931$	149.792	+	27.8838i	0.160894	+	0.0299503i
$932$	−236.645			−0.253911
$933$	111.296	+	192.770i	0.119288	+	0.206613i
$934$	−429.402	−	247.915i	−0.459745	−	0.265434i
$935$	−319.736	+	553.800i	−0.341964	+	0.592299i
$936$	171.192	−	98.8378i	0.182898	−	0.105596i
$937$			198.412i			0.211753i	0.994379	+	0.105876i	$0.0337648\pi$
$937$			198.412i			0.211753i	−0.994379	+	0.105876i	$0.966235\pi$
$938$	−693.033	−	255.982i	−0.738842	−	0.272902i
$939$	−222.649			−0.237113
$940$	−142.300	−	246.471i	−0.151383	−	0.262203i
$941$	1199.22	+	692.373i	1.27442	+	0.735784i	0.975816	−	0.218595i	$-0.0701472\pi$
$941$	1199.22	+	692.373i	1.27442	+	0.735784i	0.298599	+	0.954379i	$0.403481\pi$
$942$	−126.530	+	219.156i	−0.134321	+	0.232650i
$943$	−65.7035	+	37.9339i	−0.0696750	+	0.0402269i
$944$			92.7958i			0.0983007i
$945$	−13.7422	−	80.1633i	−0.0145420	−	0.0848289i
$946$	−523.801			−0.553700
$947$	−691.402	−	1197.54i	−0.730097	−	1.26457i	−0.956841	−	0.290611i	$-0.906141\pi$
$947$	−691.402	−	1197.54i	−0.730097	−	1.26457i	0.226744	−	0.973954i	$-0.427192\pi$
$948$	396.174	+	228.731i	0.417905	+	0.241277i
$949$	167.817	−	290.668i	0.176836	−	0.306289i
$950$	18.5189	−	10.6919i	0.0194936	−	0.0112546i
$951$		−	624.458i		−	0.656634i
$952$	−1010.66	−	1216.16i	−1.06162	−	1.27748i
$953$	730.736			0.766774			0.383387	−	0.923588i	$-0.374758\pi$
$953$	730.736			0.766774			0.383387	+	0.923588i	$0.374758\pi$
$954$	−10.1446	−	17.5710i	−0.0106338	−	0.0184183i
$955$	−221.635	−	127.961i	−0.232078	−	0.133991i
$956$	−496.145	+	859.349i	−0.518980	+	0.898900i
$957$	−183.013	+	105.663i	−0.191236	+	0.110410i
$958$		−	735.996i		−	0.768263i
$959$	823.821	−	684.619i	0.859042	−	0.713888i
$960$	−204.500			−0.213021
$961$	594.641	+	1029.95i	0.618773	+	1.07175i
$962$	−568.982	−	328.502i	−0.591457	−	0.341478i
$963$	240.464	−	416.496i	0.249703	−	0.432498i
$964$	−488.649	+	282.122i	−0.506898	+	0.292657i
$965$		−	626.852i		−	0.649588i
$966$	−75.4233	+	12.9297i	−0.0780780	+	0.0133848i
$967$	−176.021			−0.182028			−0.0910138	−	0.995850i	$-0.529011\pi$
$967$	−176.021			−0.182028			−0.0910138	+	0.995850i	$0.529011\pi$
$968$	33.1039	+	57.3376i	0.0341982	+	0.0592331i
$969$	−125.415	−	72.4084i	−0.129427	−	0.0747249i
$970$	162.754	−	281.899i	0.167788	−	0.290617i
$971$	281.978	−	162.800i	0.290399	−	0.167662i	−0.347723	−	0.937597i	$-0.613045\pi$
$971$	281.978	−	162.800i	0.290399	−	0.167662i	0.638122	+	0.769935i	$0.279712\pi$
$972$			32.8654i			0.0338121i
$973$	498.573	−	1349.81i	0.512408	−	1.38727i
$974$	−449.560			−0.461560
$975$	−33.9615	−	58.8230i	−0.0348323	−	0.0603313i
$976$	−115.333	−	66.5873i	−0.118169	−	0.0682247i
$977$	103.657	−	179.540i	0.106098	−	0.183766i	−0.808089	−	0.589061i	$-0.799498\pi$
$977$	103.657	−	179.540i	0.106098	−	0.183766i	0.914186	+	0.405295i	$0.132831\pi$
$978$	433.713	−	250.404i	0.443469	−	0.256037i
$979$		−	1018.39i		−	1.04024i
$980$	−150.162	+	175.538i	−0.153226	+	0.179121i
$981$	−431.111			−0.439461
$982$	163.984	+	284.028i	0.166990	+	0.289234i
$983$	1020.36	+	589.104i	1.03800	+	0.599292i	0.919267	−	0.393634i	$-0.128782\pi$
$983$	1020.36	+	589.104i	1.03800	+	0.599292i	0.118737	+	0.992926i	$0.462115\pi$
$984$	−120.288	+	208.345i	−0.122244	+	0.211733i
$985$	−147.191	+	84.9809i	−0.149433	+	0.0862750i
$986$		−	424.244i		−	0.430268i
$987$	−686.596	−	253.604i	−0.695639	−	0.256945i
$988$	−51.4176			−0.0520421
$989$	82.1591	+	142.304i	0.0830729	+	0.143886i
$990$	84.9825	+	49.0647i	0.0858409	+	0.0495603i
$991$	981.182	−	1699.46i	0.990093	−	1.71489i	0.373446	−	0.927652i	$-0.378176\pi$
$991$	981.182	−	1699.46i	0.990093	−	1.71489i	0.616647	−	0.787240i	$-0.288491\pi$
$992$	−1177.11	+	679.605i	−1.18660	+	0.685086i
$993$			171.448i			0.172657i
$994$	138.063	+	805.372i	0.138897	+	0.810233i
$995$	−102.170			−0.102683
$996$	−242.025	−	419.200i	−0.242997	−	0.420883i
$997$	−314.648	−	181.662i	−0.315594	−	0.182209i	0.333833	−	0.942632i	$-0.391658\pi$
$997$	−314.648	−	181.662i	−0.315594	−	0.182209i	−0.649427	+	0.760424i	$0.724991\pi$
$998$	315.515	−	546.488i	0.316147	−	0.547583i
$999$	274.075	−	158.237i	0.274350	−	0.158396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.b.31.4	✓	12
3.2	odd	2		315.3.w.b.136.3		12
5.2	odd	4		525.3.s.j.199.5		24
5.3	odd	4		525.3.s.j.199.8		24
5.4	even	2		525.3.o.m.451.3		12
7.3	odd	6		735.3.h.b.391.6		12
7.4	even	3		735.3.h.b.391.5		12
7.5	odd	6	inner	105.3.n.b.61.4	yes	12
21.5	even	6		315.3.w.b.271.3		12
35.12	even	12		525.3.s.j.124.8		24
35.19	odd	6		525.3.o.m.376.3		12
35.33	even	12		525.3.s.j.124.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.b.31.4	✓	12	1.1	even	1	trivial
105.3.n.b.61.4	yes	12	7.5	odd	6	inner
315.3.w.b.136.3		12	3.2	odd	2
315.3.w.b.271.3		12	21.5	even	6
525.3.o.m.376.3		12	35.19	odd	6
525.3.o.m.451.3		12	5.4	even	2
525.3.s.j.124.5		24	35.33	even	12
525.3.s.j.124.8		24	35.12	even	12
525.3.s.j.199.5		24	5.2	odd	4
525.3.s.j.199.8		24	5.3	odd	4
735.3.h.b.391.5		12	7.4	even	3
735.3.h.b.391.6		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)

\(f(q)\)	\(=\)	\(q+(0.687692 + 1.19112i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.05416 - 1.82586i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.38224i q^{6} +(6.56639 + 2.42539i) q^{7} +8.40129 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.687692 + 1.19112i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.05416 - 1.82586i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.38224i q^{6} +(6.56639 + 2.42539i) q^{7} +8.40129 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.66342 - 1.53773i) q^{10} +(-5.31788 + 9.21084i) q^{11} +(3.16247 - 1.82586i) q^{12} -7.84307i q^{13} +(1.62673 + 9.48927i) q^{14} -3.87298 q^{15} +(1.56087 + 2.70350i) q^{16} +(-23.2862 - 13.4443i) q^{17} +(-2.06308 + 3.57335i) q^{18} +(2.69290 - 1.55475i) q^{19} +4.71434i q^{20} +(7.74913 + 9.32475i) q^{21} -14.6283 q^{22} +(2.29447 + 3.97414i) q^{23} +(12.6019 + 7.27573i) q^{24} +(2.50000 - 4.33013i) q^{25} +(9.34203 - 5.39362i) q^{26} +5.19615i q^{27} +(11.3504 - 9.43253i) q^{28} +11.4716 q^{29} +(-2.66342 - 4.61318i) q^{30} +(-40.1586 - 23.1856i) q^{31} +(14.6558 - 25.3846i) q^{32} +(-15.9536 + 9.21084i) q^{33} -36.9822i q^{34} +(-15.4274 + 2.64469i) q^{35} +6.32495 q^{36} +(-30.4528 - 52.7458i) q^{37} +(3.70378 + 2.13838i) q^{38} +(6.79230 - 11.7646i) q^{39} +(-16.2690 + 9.39292i) q^{40} +16.5328i q^{41} +(-5.77786 + 15.6427i) q^{42} +35.8074 q^{43} +(11.2118 + 19.4194i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-3.15578 + 5.46597i) q^{46} +(-52.2811 + 30.1845i) q^{47} +5.40700i q^{48} +(37.2349 + 31.8521i) q^{49} +6.87692 q^{50} +(-23.2862 - 40.3329i) q^{51} +(-14.3203 - 8.26784i) q^{52} +(-2.45862 + 4.25845i) q^{53} +(-6.18923 + 3.57335i) q^{54} -23.7823i q^{55} +(55.1661 + 20.3764i) q^{56} +5.38580 q^{57} +(7.88891 + 13.6640i) q^{58} +(25.7432 + 14.8629i) q^{59} +(-4.08274 + 7.07151i) q^{60} +(-36.9450 + 21.3302i) q^{61} -63.7782i q^{62} +(3.54823 + 20.6981i) q^{63} +52.8016 q^{64} +(8.76882 + 15.1880i) q^{65} +(-21.9424 - 12.6684i) q^{66} +(-38.3684 + 66.4560i) q^{67} +(-49.0948 + 28.3449i) q^{68} +7.94828i q^{69} +(-13.7595 - 16.5572i) q^{70} +84.8719 q^{71} +(12.6019 + 21.8272i) q^{72} +(37.0605 + 21.3969i) q^{73} +(41.8843 - 72.5458i) q^{74} +(7.50000 - 4.33013i) q^{75} -6.55580i q^{76} +(-57.2592 + 47.5840i) q^{77} +18.6841 q^{78} +(62.6367 + 108.490i) q^{79} +(-6.04521 - 3.49021i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-19.6925 + 11.3695i) q^{82} -132.554i q^{83} +(25.1945 - 4.31904i) q^{84} +60.1248 q^{85} +(24.6245 + 42.6509i) q^{86} +(17.2074 + 9.93467i) q^{87} +(-44.6770 + 77.3829i) q^{88} +(-82.9234 + 47.8758i) q^{89} -9.22636i q^{90} +(19.0225 - 51.5007i) q^{91} +9.67494 q^{92} +(-40.1586 - 69.5567i) q^{93} +(-71.9066 - 41.5153i) q^{94} +(-3.47652 + 6.02151i) q^{95} +(43.9673 - 25.3846i) q^{96} +105.841i q^{97} +(-12.3335 + 66.2557i) q^{98} -31.9073 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

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