LMFDB - Embedded newform 361.3.f.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(116,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("361.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not 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:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.7659539263855005696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2197x^{6} + 4826809 $ x^12 - 2197*x^6 + 4826809
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.2
Root			$2.31760 + 2.76201i$ of defining polynomial
Character	$\chi$	$=$	361.127
Dual form			361.3.f.d.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.31760 + 2.76201i) q^{2} +(-1.23317 + 3.38811i) q^{3} +(-1.56283 + 8.86327i) q^{4} +(0.694593 + 3.93923i) q^{5} +(-12.2160 + 4.44626i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(-3.06418 - 2.57115i) q^{9} +O(q^{10})$	\(q+(2.31760 + 2.76201i) q^{2} +(-1.23317 + 3.38811i) q^{3} +(-1.56283 + 8.86327i) q^{4} +(0.694593 + 3.93923i) q^{5} +(-12.2160 + 4.44626i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(-3.06418 - 2.57115i) q^{9} +(-9.27041 + 11.0481i) q^{10} +(5.00000 + 8.66025i) q^{11} +(-28.1025 - 16.2250i) q^{12} +(-1.23317 - 3.38811i) q^{13} +(17.7539 - 3.13049i) q^{14} +(-14.2031 - 2.50439i) q^{15} +(-27.2511 - 9.91858i) q^{16} +(11.4907 - 9.64181i) q^{17} -14.4222i q^{18} -36.0000 q^{20} +(11.5880 + 13.8101i) q^{21} +(-12.3317 + 33.8811i) q^{22} +(6.07769 - 34.4683i) q^{23} +(-11.2871 - 64.0125i) q^{24} +(8.45723 - 3.07818i) q^{25} +(6.50000 - 11.2583i) q^{26} +(-15.6125 + 9.01388i) q^{27} +(34.4720 + 28.9254i) q^{28} +(-11.5880 + 13.8101i) q^{29} +(-26.0000 - 45.0333i) q^{30} +(31.2250 + 18.0278i) q^{31} +(-11.0985 - 30.4930i) q^{32} +(-35.5077 + 6.26097i) q^{33} +(53.2616 + 9.39146i) q^{34} +(18.7939 + 6.84040i) q^{35} +(27.5776 - 23.1404i) q^{36} -21.6333i q^{37} +13.0000 q^{39} +(-46.3521 - 55.2403i) q^{40} +(12.3317 - 33.8811i) q^{41} +(-11.2871 + 64.0125i) q^{42} +(-3.47296 - 19.6962i) q^{43} +(-84.5723 + 30.7818i) q^{44} +(8.00000 - 13.8564i) q^{45} +(109.287 - 63.0971i) q^{46} +(7.66044 + 6.42788i) q^{47} +(67.2105 - 80.0984i) q^{48} +(12.0000 + 20.7846i) q^{49} +(28.1025 + 16.2250i) q^{50} +(18.4976 + 50.8216i) q^{51} +(31.9570 - 5.63488i) q^{52} +(-74.5663 - 13.1480i) q^{53} +(-61.0800 - 22.2313i) q^{54} +(-30.6418 + 25.7115i) q^{55} +90.1388i q^{56} -65.0000 q^{58} +(11.5880 + 13.8101i) q^{59} +(44.3942 - 121.972i) q^{60} +(-6.94593 + 39.3923i) q^{61} +(22.5743 + 128.025i) q^{62} +(-18.7939 + 6.84040i) q^{63} +(0.500000 - 0.866025i) q^{64} +(12.4900 - 7.21110i) q^{65} +(-99.5858 - 83.5624i) q^{66} +(-25.4936 + 30.3821i) q^{67} +(67.5000 + 116.913i) q^{68} +(109.287 + 63.0971i) q^{69} +(24.6634 + 67.7622i) q^{70} +(-106.523 + 18.7829i) q^{71} +(71.0155 + 12.5219i) q^{72} +(-98.6677 - 35.9121i) q^{73} +(59.7515 - 50.1374i) q^{74} +32.4500i q^{75} +50.0000 q^{77} +(30.1288 + 35.9062i) q^{78} +(-12.3317 + 33.8811i) q^{79} +(20.1432 - 114.238i) q^{80} +(-17.5385 - 99.4656i) q^{81} +(122.160 - 44.4626i) q^{82} +(20.0000 - 34.6410i) q^{83} +(-140.512 + 81.1249i) q^{84} +(45.9627 + 38.5673i) q^{85} +(46.3521 - 55.2403i) q^{86} +(-32.5000 - 56.2917i) q^{87} +(-156.125 - 90.1388i) q^{88} +(56.8124 - 10.0176i) q^{90} +(-17.7539 - 3.13049i) q^{91} +(296.003 + 107.736i) q^{92} +(-99.5858 + 83.5624i) q^{93} +36.0555i q^{94} +117.000 q^{96} +(78.7985 + 93.9084i) q^{97} +(-29.5961 + 81.3146i) q^{98} +(6.94593 - 39.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 30 q^{7}+O(q^{10}) $ 12 * q + 30 * q^7	$ 12 q + 30 q^{7} + 60 q^{11} - 432 q^{20} + 78 q^{26} - 312 q^{30} + 156 q^{39} + 96 q^{45} + 144 q^{49} - 780 q^{58} + 6 q^{64} + 810 q^{68} + 600 q^{77} + 240 q^{83} - 390 q^{87} + 1404 q^{96}+O(q^{100}) $ 12 * q + 30 * q^7 + 60 * q^11 - 432 * q^20 + 78 * q^26 - 312 * q^30 + 156 * q^39 + 96 * q^45 + 144 * q^49 - 780 * q^58 + 6 * q^64 + 810 * q^68 + 600 * q^77 + 240 * q^83 - 390 * q^87 + 1404 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	2.31760	+	2.76201i	1.15880	+	1.38101i	0.911108	+	0.412168i	$0.135228\pi$
$2$	2.31760	+	2.76201i	1.15880	+	1.38101i	0.247694	+	0.968838i	$0.420327\pi$
$3$	−1.23317	+	3.38811i	−0.411057	+	1.12937i	0.545573	+	0.838063i	$0.316312\pi$
$3$	−1.23317	+	3.38811i	−0.411057	+	1.12937i	−0.956630	+	0.291306i	$0.905910\pi$
$4$	−1.56283	+	8.86327i	−0.390708	+	2.21582i
$5$	0.694593	+	3.93923i	0.138919	+	0.787846i	0.972050	+	0.234772i	$0.0754343\pi$
$5$	0.694593	+	3.93923i	0.138919	+	0.787846i	−0.833132	+	0.553074i	$0.813455\pi$
$6$	−12.2160	+	4.44626i	−2.03600	+	0.741044i
$7$	2.50000	−	4.33013i	0.357143	−	0.618590i	−0.630339	−	0.776320i	$-0.717084\pi$
$7$	2.50000	−	4.33013i	0.357143	−	0.618590i	0.987482	+	0.157730i	$0.0504176\pi$
$8$	−15.6125	+	9.01388i	−1.95156	+	1.12673i
$9$	−3.06418	−	2.57115i	−0.340464	−	0.285683i
$10$	−9.27041	+	11.0481i	−0.927041	+	1.10481i
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	0.998662	−	0.0517139i	$-0.0164684\pi$
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	−0.544116	+	0.839010i	$0.683135\pi$
$12$	−28.1025	−	16.2250i	−2.34187	−	1.35208i
$13$	−1.23317	−	3.38811i	−0.0948593	−	0.260624i	0.883184	−	0.469027i	$-0.155395\pi$
$13$	−1.23317	−	3.38811i	−0.0948593	−	0.260624i	−0.978043	+	0.208404i	$0.933173\pi$
$14$	17.7539	−	3.13049i	1.26813	−	0.223606i
$15$	−14.2031	−	2.50439i	−0.946873	−	0.166959i
$16$	−27.2511	−	9.91858i	−1.70319	−	0.619912i
$17$	11.4907	−	9.64181i	0.675922	−	0.567166i	−0.238890	−	0.971047i	$-0.576784\pi$
$17$	11.4907	−	9.64181i	0.675922	−	0.567166i	0.914811	+	0.403881i	$0.132339\pi$
$18$		−	14.4222i		−	0.801234i
$19$		0			0
$19$		0			0
$20$	−36.0000			−1.80000
$21$	11.5880	+	13.8101i	0.551810	+	0.657622i
$22$	−12.3317	+	33.8811i	−0.560532	+	1.54005i
$23$	6.07769	−	34.4683i	0.264247	−	1.49862i	−0.506923	−	0.861991i	$-0.669217\pi$
$23$	6.07769	−	34.4683i	0.264247	−	1.49862i	0.771170	−	0.636629i	$-0.219672\pi$
$24$	−11.2871	−	64.0125i	−0.470297	−	2.66719i
$25$	8.45723	−	3.07818i	0.338289	−	0.123127i
$26$	6.50000	−	11.2583i	0.250000	−	0.433013i
$27$	−15.6125	+	9.01388i	−0.578241	+	0.333847i
$28$	34.4720	+	28.9254i	1.23114	+	1.03305i
$29$	−11.5880	+	13.8101i	−0.399587	+	0.476209i	−0.927894	−	0.372844i	$-0.878383\pi$
$29$	−11.5880	+	13.8101i	−0.399587	+	0.476209i	0.528307	+	0.849053i	$0.322827\pi$
$30$	−26.0000	−	45.0333i	−0.866667	−	1.50111i
$31$	31.2250	+	18.0278i	1.00726	+	0.581541i	0.910388	−	0.413756i	$-0.135784\pi$
$31$	31.2250	+	18.0278i	1.00726	+	0.581541i	0.0968702	+	0.995297i	$0.469117\pi$
$32$	−11.0985	−	30.4930i	−0.346829	−	0.952906i
$33$	−35.5077	+	6.26097i	−1.07599	+	0.189726i
$34$	53.2616	+	9.39146i	1.56652	+	0.276219i
$35$	18.7939	+	6.84040i	0.536967	+	0.195440i
$36$	27.5776	−	23.1404i	0.766044	−	0.642788i
$37$		−	21.6333i		−	0.584684i	−0.956314	−	0.292342i	$-0.905565\pi$
$37$		−	21.6333i		−	0.584684i	0.956314	−	0.292342i	$-0.0944346\pi$
$38$		0			0
$39$	13.0000			0.333333
$40$	−46.3521	−	55.2403i	−1.15880	−	1.38101i
$41$	12.3317	−	33.8811i	0.300773	−	0.826368i	−0.693593	−	0.720367i	$-0.743973\pi$
$41$	12.3317	−	33.8811i	0.300773	−	0.826368i	0.994366	−	0.106001i	$-0.0338046\pi$
$42$	−11.2871	+	64.0125i	−0.268741	+	1.52411i
$43$	−3.47296	−	19.6962i	−0.0807666	−	0.458050i	−0.998190	−	0.0601379i	$-0.980846\pi$
$43$	−3.47296	−	19.6962i	−0.0807666	−	0.458050i	0.917423	−	0.397912i	$-0.130265\pi$
$44$	−84.5723	+	30.7818i	−1.92210	+	0.699587i
$45$	8.00000	−	13.8564i	0.177778	−	0.307920i
$46$	109.287	−	63.0971i	2.37581	−	1.37168i
$47$	7.66044	+	6.42788i	0.162988	+	0.136763i	0.720634	−	0.693316i	$-0.243851\pi$
$47$	7.66044	+	6.42788i	0.162988	+	0.136763i	−0.557646	+	0.830079i	$0.688295\pi$
$48$	67.2105	−	80.0984i	1.40022	−	1.66872i
$49$	12.0000	+	20.7846i	0.244898	+	0.424176i
$50$	28.1025	+	16.2250i	0.562050	+	0.324500i
$51$	18.4976	+	50.8216i	0.362697	+	0.996503i
$52$	31.9570	−	5.63488i	0.614557	−	0.108363i
$53$	−74.5663	−	13.1480i	−1.40691	−	0.248076i	−0.581931	−	0.813238i	$-0.697703\pi$
$53$	−74.5663	−	13.1480i	−1.40691	−	0.248076i	−0.824980	+	0.565162i	$0.808814\pi$
$54$	−61.0800	−	22.2313i	−1.13111	−	0.411691i
$55$	−30.6418	+	25.7115i	−0.557123	+	0.467482i
$56$			90.1388i			1.60962i
$57$		0			0
$58$	−65.0000			−1.12069
$59$	11.5880	+	13.8101i	0.196407	+	0.234069i	0.855255	−	0.518207i	$-0.173400\pi$
$59$	11.5880	+	13.8101i	0.196407	+	0.234069i	−0.658848	+	0.752276i	$0.728956\pi$
$60$	44.3942	−	121.972i	0.739903	−	2.03287i
$61$	−6.94593	+	39.3923i	−0.113868	+	0.645776i	0.873437	+	0.486937i	$0.161886\pi$
$61$	−6.94593	+	39.3923i	−0.113868	+	0.645776i	−0.987305	+	0.158838i	$0.949225\pi$
$62$	22.5743	+	128.025i	0.364101	+	2.06492i
$63$	−18.7939	+	6.84040i	−0.298315	+	0.108578i
$64$	0.500000	−	0.866025i	0.00781250	−	0.0135316i
$65$	12.4900	−	7.21110i	0.192154	−	0.110940i
$66$	−99.5858	−	83.5624i	−1.50888	−	1.26610i
$67$	−25.4936	+	30.3821i	−0.380502	+	0.453465i	−0.921973	−	0.387255i	$-0.873423\pi$
$67$	−25.4936	+	30.3821i	−0.380502	+	0.453465i	0.541471	+	0.840720i	$0.317868\pi$
$68$	67.5000	+	116.913i	0.992647	+	1.71932i
$69$	109.287	+	63.0971i	1.58388	+	0.914451i
$70$	24.6634	+	67.7622i	0.352335	+	0.968031i
$71$	−106.523	+	18.7829i	−1.50033	+	0.264548i	−0.862668	−	0.505770i	$-0.831208\pi$
$71$	−106.523	+	18.7829i	−1.50033	+	0.264548i	−0.637659	+	0.770319i	$0.720097\pi$
$72$	71.0155	+	12.5219i	0.986326	+	0.173916i
$73$	−98.6677	−	35.9121i	−1.35161	−	0.491947i	−0.438162	−	0.898896i	$-0.644370\pi$
$73$	−98.6677	−	35.9121i	−1.35161	−	0.491947i	−0.913451	+	0.406949i	$0.866593\pi$
$74$	59.7515	−	50.1374i	0.807452	−	0.677533i
$75$			32.4500i			0.432666i
$76$		0			0
$77$	50.0000			0.649351
$78$	30.1288	+	35.9062i	0.386267	+	0.460335i
$79$	−12.3317	+	33.8811i	−0.156098	+	0.428875i	−0.992947	−	0.118558i	$-0.962173\pi$
$79$	−12.3317	+	33.8811i	−0.156098	+	0.428875i	0.836849	+	0.547433i	$0.184395\pi$
$80$	20.1432	−	114.238i	0.251790	−	1.42797i
$81$	−17.5385	−	99.4656i	−0.216524	−	1.22797i
$82$	122.160	−	44.4626i	1.48976	−	0.542227i
$83$	20.0000	−	34.6410i	0.240964	−	0.417362i	−0.720025	−	0.693948i	$-0.755870\pi$
$83$	20.0000	−	34.6410i	0.240964	−	0.417362i	0.960989	+	0.276586i	$0.0892031\pi$
$84$	−140.512	+	81.1249i	−1.67277	+	0.965773i
$85$	45.9627	+	38.5673i	0.540737	+	0.453732i
$86$	46.3521	−	55.2403i	0.538978	−	0.642328i
$87$	−32.5000	−	56.2917i	−0.373563	−	0.647030i
$88$	−156.125	−	90.1388i	−1.77415	−	1.02430i
$89$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$89$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$90$	56.8124	−	10.0176i	0.631249	−	0.111306i
$91$	−17.7539	−	3.13049i	−0.195098	−	0.0344010i
$92$	296.003	+	107.736i	3.21743	+	1.17105i
$93$	−99.5858	+	83.5624i	−1.07081	+	0.898520i
$94$			36.0555i			0.383569i
$95$		0			0
$96$	117.000			1.21875
$97$	78.7985	+	93.9084i	0.812356	+	0.968128i	0.999900	−	0.0141281i	$-0.00449725\pi$
$97$	78.7985	+	93.9084i	0.812356	+	0.968128i	−0.187544	+	0.982256i	$0.560053\pi$
$98$	−29.5961	+	81.3146i	−0.302001	+	0.829741i
$99$	6.94593	−	39.3923i	0.0701609	−	0.397902i
$100$	14.0655	+	79.7694i	0.140655	+	0.797694i
$101$	46.9846	−	17.1010i	0.465194	−	0.169317i	−0.0987798	−	0.995109i	$-0.531494\pi$
$101$	46.9846	−	17.1010i	0.465194	−	0.169317i	0.563974	+	0.825792i	$0.309272\pi$
$102$	−97.5000	+	168.875i	−0.955882	+	1.65564i
$103$	49.9600	−	28.8444i	0.485048	−	0.280043i	−0.237470	−	0.971395i	$-0.576318\pi$
$103$	49.9600	−	28.8444i	0.485048	−	0.280043i	0.722518	+	0.691352i	$0.242985\pi$
$104$	49.7929	+	41.7812i	0.478778	+	0.401742i
$105$	−46.3521	+	55.2403i	−0.441448	+	0.526098i
$106$	−136.500	−	236.425i	−1.28774	−	2.23042i
$107$	−65.5725	−	37.8583i	−0.612827	−	0.353816i	0.161244	−	0.986915i	$-0.448449\pi$
$107$	−65.5725	−	37.8583i	−0.612827	−	0.353816i	−0.774071	+	0.633099i	$0.781783\pi$
$108$	−55.4927	−	152.465i	−0.513821	−	1.41171i
$109$	195.293	−	34.4354i	1.79168	−	0.315921i	0.823711	−	0.567009i	$-0.191900\pi$
$109$	195.293	−	34.4354i	1.79168	−	0.315921i	0.967964	+	0.251089i	$0.0807886\pi$
$110$	−142.031	−	25.0439i	−1.29119	−	0.227672i
$111$	73.2960	+	26.6776i	0.660325	+	0.240338i
$112$	−111.076	+	93.2042i	−0.991754	+	0.832180i
$113$		−	122.589i		−	1.08486i	−0.840102	−	0.542428i	$-0.817505\pi$
$113$		−	122.589i		−	1.08486i	0.840102	−	0.542428i	$-0.182495\pi$
$114$		0			0
$115$	140.000			1.21739
$116$	−104.292	−	124.291i	−0.899070	−	1.07147i
$117$	−4.93268	+	13.5524i	−0.0421597	+	0.115833i
$118$	−11.2871	+	64.0125i	−0.0956537	+	0.542479i
$119$	−13.0236	−	73.8606i	−0.109442	−	0.620677i
$120$	244.320	−	88.9252i	2.03600	−	0.741044i
$121$	10.5000	−	18.1865i	0.0867769	−	0.150302i
$122$	−124.900	+	72.1110i	−1.02377	+	0.591074i
$123$	99.5858	+	83.5624i	0.809640	+	0.679369i
$124$	−208.584	+	248.581i	−1.68213	+	2.00469i
$125$	68.0000	+	117.779i	0.544000	+	0.942236i
$126$	−62.4500	−	36.0555i	−0.495635	−	0.286155i
$127$	44.3942	+	121.972i	0.349560	+	0.960409i	0.982509	+	0.186215i	$0.0596222\pi$
$127$	44.3942	+	121.972i	0.349560	+	0.960409i	−0.632949	+	0.774194i	$0.718156\pi$
$128$	−124.277	+	21.9134i	−0.970915	+	0.171199i
$129$	71.0155	+	12.5219i	0.550508	+	0.0970694i
$130$	48.8640	+	17.7850i	0.375877	+	0.136808i
$131$	85.7970	−	71.9922i	0.654939	−	0.549559i	−0.253626	−	0.967302i	$-0.581623\pi$
$131$	85.7970	−	71.9922i	0.654939	−	0.549559i	0.908565	+	0.417743i	$0.137179\pi$
$132$		−	324.500i		−	2.45833i
$133$		0			0
$134$	−143.000			−1.06716
$135$	−46.3521	−	55.2403i	−0.343349	−	0.409187i
$136$	−92.4878	+	254.108i	−0.680058	+	1.86844i
$137$	21.7060	−	123.101i	0.158438	−	0.898547i	−0.797137	−	0.603799i	$-0.793653\pi$
$137$	21.7060	−	123.101i	0.158438	−	0.898547i	0.955575	−	0.294748i	$-0.0952358\pi$
$138$	79.0099	+	448.088i	0.572536	+	3.24701i
$139$	−46.9846	+	17.1010i	−0.338019	+	0.123029i	−0.505452	−	0.862855i	$-0.668674\pi$
$139$	−46.9846	+	17.1010i	−0.338019	+	0.123029i	0.167433	+	0.985883i	$0.446452\pi$
$140$	−90.0000	+	155.885i	−0.642857	+	1.11346i
$141$	−31.2250	+	18.0278i	−0.221454	+	0.127856i
$142$	−298.757	−	250.687i	−2.10392	−	1.76540i
$143$	23.1760	−	27.6201i	0.162070	−	0.193148i
$144$	58.0000	+	100.459i	0.402778	+	0.697632i
$145$	−62.4500	−	36.0555i	−0.430690	−	0.248659i
$146$	−129.483	−	355.752i	−0.886870	−	2.43665i
$147$	−85.2186	+	15.0263i	−0.579718	+	0.102220i
$148$	191.742	+	33.8093i	1.29555	+	0.228441i
$149$	−65.7785	−	23.9414i	−0.441466	−	0.160681i	0.111717	−	0.993740i	$-0.464365\pi$
$149$	−65.7785	−	23.9414i	−0.441466	−	0.160681i	−0.553183	+	0.833059i	$0.686587\pi$
$150$	−89.6272	+	75.2062i	−0.597515	+	0.501374i
$151$			36.0555i			0.238778i	0.992848	+	0.119389i	$0.0380936\pi$
$151$			36.0555i			0.238778i	−0.992848	+	0.119389i	$0.961906\pi$
$152$		0			0
$153$	−60.0000			−0.392157
$154$	115.880	+	138.101i	0.752469	+	0.896757i
$155$	−49.3268	+	135.524i	−0.318238	+	0.874351i
$156$	−20.3168	+	115.223i	−0.130236	+	0.738606i
$157$	1.73648	+	9.84808i	0.0110604	+	0.0627266i	0.989838	−	0.142197i	$-0.0454166\pi$
$157$	1.73648	+	9.84808i	0.0110604	+	0.0627266i	−0.978778	+	0.204923i	$0.934305\pi$
$158$	−122.160	+	44.4626i	−0.773165	+	0.281409i
$159$	136.500	−	236.425i	0.858491	−	1.48695i
$160$	112.410	−	64.8999i	0.702562	−	0.405625i
$161$	−134.058	−	112.488i	−0.832657	−	0.698682i
$162$	234.078	−	278.963i	1.44493	−	1.72200i
$163$	135.000	+	233.827i	0.828221	+	1.43452i	0.899433	+	0.437059i	$0.143980\pi$
$163$	135.000	+	233.827i	0.828221	+	1.43452i	−0.0712118	+	0.997461i	$0.522687\pi$
$164$	281.025	+	162.250i	1.71357	+	0.989328i
$165$	−49.3268	−	135.524i	−0.298951	−	0.821360i
$166$	142.031	−	25.0439i	0.855608	−	0.150867i
$167$	120.726	+	21.2873i	0.722912	+	0.127469i	0.522985	−	0.852342i	$-0.324818\pi$
$167$	120.726	+	21.2873i	0.722912	+	0.127469i	0.199927	+	0.979811i	$0.435929\pi$
$168$	−305.400	−	111.157i	−1.81786	−	0.661646i
$169$	119.503	−	100.275i	0.707118	−	0.593342i
$170$			216.333i			1.27255i
$171$		0			0
$172$	180.000			1.04651
$173$	−78.7985	−	93.9084i	−0.455483	−	0.542823i	0.488610	−	0.872502i	$-0.337504\pi$
$173$	−78.7985	−	93.9084i	−0.455483	−	0.542823i	−0.944093	+	0.329679i	$0.893060\pi$
$174$	80.1561	−	220.227i	0.460667	−	1.26567i
$175$	7.81417	−	44.3163i	0.0446524	−	0.253236i
$176$	−50.3580	−	285.594i	−0.286125	−	1.62269i
$177$	−61.0800	+	22.2313i	−0.345085	+	0.125601i
$178$		0			0
$179$	31.2250	−	18.0278i	0.174441	−	0.100714i	−0.410237	−	0.911979i	$-0.634554\pi$
$179$	31.2250	−	18.0278i	0.174441	−	0.100714i	0.584678	+	0.811265i	$0.301221\pi$
$180$	110.310	+	92.5614i	0.612836	+	0.514230i
$181$	−69.5281	+	82.8604i	−0.384133	+	0.457792i	−0.923114	−	0.384526i	$-0.874365\pi$
$181$	−69.5281	+	82.8604i	−0.384133	+	0.457792i	0.538981	+	0.842318i	$0.318809\pi$
$182$	−32.5000	−	56.2917i	−0.178571	−	0.309295i
$183$	−124.900	−	72.1110i	−0.682513	−	0.394049i
$184$	215.805	+	592.919i	1.17285	+	3.22239i
$185$	85.2186	−	15.0263i	0.460641	−	0.0812234i
$186$	−461.601	−	81.3927i	−2.48172	−	0.437595i
$187$	140.954	+	51.3030i	0.753764	+	0.274348i
$188$	−68.9440	+	57.8509i	−0.366723	+	0.307717i
$189$			90.1388i			0.476925i
$190$		0			0
$191$	193.000			1.01047			0.505236	−	0.862981i	$-0.331406\pi$
$191$	193.000			1.01047			0.505236	+	0.862981i	$0.331406\pi$
$192$	2.31760	+	2.76201i	0.0120709	+	0.0143855i
$193$	91.2547	−	250.720i	0.472822	−	1.29907i	−0.442653	−	0.896693i	$-0.645963\pi$
$193$	91.2547	−	250.720i	0.472822	−	1.29907i	0.915475	−	0.402375i	$-0.131815\pi$
$194$	−76.7525	+	435.285i	−0.395631	+	2.24374i
$195$	9.02971	+	51.2100i	0.0463062	+	0.262615i
$196$	−202.974	+	73.8764i	−1.03558	+	0.376920i
$197$	−45.0000	+	77.9423i	−0.228426	+	0.395646i	−0.957342	−	0.288958i	$-0.906691\pi$
$197$	−45.0000	+	77.9423i	−0.228426	+	0.395646i	0.728916	+	0.684604i	$0.240025\pi$
$198$	124.900	−	72.1110i	0.630808	−	0.364197i
$199$	94.2235	+	79.0629i	0.473485	+	0.397301i	0.848064	−	0.529894i	$-0.177768\pi$
$199$	94.2235	+	79.0629i	0.473485	+	0.397301i	−0.374579	+	0.927195i	$0.622213\pi$
$200$	−104.292	+	124.291i	−0.521461	+	0.621453i
$201$	−71.5000	−	123.842i	−0.355721	−	0.616128i
$202$	156.125	+	90.1388i	0.772896	+	0.446232i
$203$	30.8293	+	84.7027i	0.151868	+	0.417255i
$204$	−479.355	+	84.5232i	−2.34978	+	0.414329i
$205$	142.031	+	25.0439i	0.692834	+	0.122165i
$206$	195.456	+	71.1402i	0.948816	+	0.345341i
$207$	−107.246	+	89.9903i	−0.518098	+	0.434736i
$208$			104.561i			0.502697i
$209$		0			0
$210$	−260.000			−1.23810
$211$	−150.644	−	179.531i	−0.713954	−	0.850857i	0.280075	−	0.959978i	$-0.409641\pi$
$211$	−150.644	−	179.531i	−0.713954	−	0.850857i	−0.994028	+	0.109121i	$0.965196\pi$
$212$	233.069	−	640.353i	1.09938	−	3.02053i
$213$	67.7228	−	384.075i	0.317947	−	1.80317i
$214$	−47.4060	−	268.853i	−0.221523	−	1.25632i
$215$	75.1754	−	27.3616i	0.349653	−	0.127263i
$216$	162.500	−	281.458i	0.752315	−	1.30305i
$217$	156.125	−	90.1388i	0.719470	−	0.415386i
$218$	547.722	+	459.593i	2.51249	+	2.10823i
$219$	243.348	−	290.011i	1.11118	−	1.32425i
$220$	−180.000	−	311.769i	−0.818182	−	1.41713i
$221$	−46.8375	−	27.0416i	−0.211934	−	0.122360i
$222$	96.1874	+	264.273i	0.433276	+	1.19042i
$223$	198.843	−	35.0615i	0.891674	−	0.157226i	0.291003	−	0.956722i	$-0.406011\pi$
$223$	198.843	−	35.0615i	0.891674	−	0.157226i	0.600672	+	0.799496i	$0.294900\pi$
$224$	−159.785	−	28.1744i	−0.713325	−	0.125778i
$225$	−33.8289	−	12.3127i	−0.150351	−	0.0547232i
$226$	338.592	−	284.112i	1.49819	−	1.25713i
$227$			255.994i			1.12773i	0.825868	+	0.563864i	$0.190686\pi$
$227$			255.994i			1.12773i	−0.825868	+	0.563864i	$0.809314\pi$
$228$		0			0
$229$	−160.000			−0.698690			−0.349345	−	0.936994i	$-0.613596\pi$
$229$	−160.000			−0.698690			−0.349345	+	0.936994i	$0.613596\pi$
$230$	324.465	+	386.682i	1.41072	+	1.68123i
$231$	−61.6586	+	169.405i	−0.266920	+	0.733357i
$232$	56.4357	−	320.063i	0.243257	−	1.37958i
$233$	−46.8850	−	265.898i	−0.201223	−	1.14119i	−0.903273	−	0.429066i	$-0.858843\pi$
$233$	−46.8850	−	265.898i	−0.201223	−	1.14119i	0.702050	−	0.712128i	$-0.252268\pi$
$234$	−48.8640	+	17.7850i	−0.208821	+	0.0760045i
$235$	−20.0000	+	34.6410i	−0.0851064	+	0.147409i
$236$	−140.512	+	81.1249i	−0.595392	+	0.343750i
$237$	−99.5858	−	83.5624i	−0.420193	−	0.352584i
$238$	173.820	−	207.151i	0.730337	−	0.870382i
$239$	−98.5000	−	170.607i	−0.412134	−	0.713837i	0.582989	−	0.812480i	$-0.301883\pi$
$239$	−98.5000	−	170.607i	−0.412134	−	0.713837i	−0.995123	+	0.0986432i	$0.968550\pi$
$240$	362.210	+	209.122i	1.50921	+	0.871342i
$241$	−135.649	−	372.692i	−0.562858	−	1.54644i	−0.815426	−	0.578861i	$-0.803497\pi$
$241$	−135.649	−	372.692i	−0.562858	−	1.54644i	0.252568	−	0.967579i	$-0.418725\pi$
$242$	74.5663	−	13.1480i	0.308125	−	0.0543308i
$243$	198.843	+	35.0615i	0.818286	+	0.144286i
$244$	−338.289	−	123.127i	−1.38643	−	0.504620i
$245$	−73.5403	+	61.7076i	−0.300164	+	0.251868i
$246$			468.722i			1.90537i
$247$		0			0
$248$	−650.000			−2.62097
$249$	92.7041	+	110.481i	0.372306	+	0.443697i
$250$	−167.711	+	460.783i	−0.670845	+	1.84313i
$251$	−69.8066	+	395.893i	−0.278114	+	1.57726i	0.450780	+	0.892635i	$0.351146\pi$
$251$	−69.8066	+	395.893i	−0.278114	+	1.57726i	−0.728894	+	0.684627i	$0.759965\pi$
$252$	−31.2567	−	177.265i	−0.124034	−	0.703434i
$253$	328.892	−	119.707i	1.29997	−	0.473150i
$254$	−234.000	+	405.300i	−0.921260	+	1.59567i
$255$	−187.350	+	108.167i	−0.734706	+	0.424183i
$256$	−351.614	−	295.040i	−1.37349	−	1.15250i
$257$	268.842	−	320.393i	1.04608	−	1.24667i	0.0777533	−	0.996973i	$-0.475225\pi$
$257$	268.842	−	320.393i	1.04608	−	1.24667i	0.968325	−	0.249694i	$-0.0803302\pi$
$258$	130.000	+	225.167i	0.503876	+	0.872739i
$259$	−93.6750	−	54.0833i	−0.361679	−	0.208816i
$260$	44.3942	+	121.972i	0.170747	+	0.469123i
$261$	71.0155	−	12.5219i	0.272090	−	0.0479768i
$262$	397.687	+	70.1229i	1.51789	+	0.267645i
$263$	−291.305	−	106.026i	−1.10762	−	0.403142i	−0.277502	−	0.960725i	$-0.589506\pi$
$263$	−291.305	−	106.026i	−1.10762	−	0.403142i	−0.830121	+	0.557584i	$0.811729\pi$
$264$	497.929	−	417.812i	1.88609	−	1.58262i
$265$		−	302.866i		−	1.14289i
$266$		0			0
$267$		0			0
$268$	−229.443	−	273.439i	−0.856130	−	1.02030i
$269$	36.9951	−	101.643i	0.137528	−	0.377856i	−0.851740	−	0.523964i	$-0.824453\pi$
$269$	36.9951	−	101.643i	0.137528	−	0.377856i	0.989269	+	0.146108i	$0.0466748\pi$
$270$	45.1485	−	256.050i	0.167217	−	0.948333i
$271$	18.2331	+	103.405i	0.0672807	+	0.381568i	0.999791	+	0.0204253i	$0.00650202\pi$
$271$	18.2331	+	103.405i	0.0672807	+	0.381568i	−0.932511	+	0.361142i	$0.882387\pi$
$272$	−408.766	+	148.779i	−1.50282	+	0.546981i
$273$	32.5000	−	56.2917i	0.119048	−	0.206197i
$274$	390.312	−	225.347i	1.42450	−	0.822434i
$275$	68.9440	+	57.8509i	0.250705	+	0.210367i
$276$	−730.045	+	870.034i	−2.64509	+	3.15230i
$277$	25.0000	+	43.3013i	0.0902527	+	0.156322i	0.907617	−	0.419798i	$-0.137899\pi$
$277$	25.0000	+	43.3013i	0.0902527	+	0.156322i	−0.817365	+	0.576121i	$0.804566\pi$
$278$	−156.125	−	90.1388i	−0.561601	−	0.324240i
$279$	−49.3268	−	135.524i	−0.176799	−	0.485751i
$280$	−355.077	+	62.6097i	−1.26813	+	0.223606i
$281$	−284.062	−	50.0878i	−1.01090	−	0.178248i	−0.356416	−	0.934327i	$-0.616001\pi$
$281$	−284.062	−	50.0878i	−1.01090	−	0.178248i	−0.654480	+	0.756079i	$0.727113\pi$
$282$	−122.160	−	44.4626i	−0.433192	−	0.157669i
$283$	−245.134	+	205.692i	−0.866199	+	0.726827i	−0.963294	−	0.268448i	$-0.913489\pi$
$283$	−245.134	+	205.692i	−0.866199	+	0.726827i	0.0970955	+	0.995275i	$0.469045\pi$
$284$		−	973.499i		−	3.42781i
$285$		0			0
$286$	130.000			0.454545
$287$	−115.880	−	138.101i	−0.403764	−	0.481187i
$288$	−44.3942	+	121.972i	−0.154146	+	0.423514i
$289$	−11.1135	+	63.0277i	−0.0384550	+	0.218089i
$290$	−45.1485	−	256.050i	−0.155685	−	0.882931i
$291$	−415.344	+	151.173i	−1.42730	+	0.519495i
$292$	472.500	−	818.394i	1.61815	−	2.80272i
$293$	−190.472	+	109.969i	−0.650077	+	0.375322i	−0.788486	−	0.615053i	$-0.789134\pi$
$293$	−190.472	+	109.969i	−0.650077	+	0.375322i	0.138409	+	0.990375i	$0.455801\pi$
$294$	−239.006	−	200.550i	−0.812945	−	0.682142i
$295$	−46.3521	+	55.2403i	−0.157126	+	0.187255i
$296$	195.000	+	337.750i	0.658784	+	1.14105i
$297$	−156.125	−	90.1388i	−0.525673	−	0.303498i
$298$	−86.3220	−	237.168i	−0.289671	−	0.795865i
$299$	−124.277	+	21.9134i	−0.415643	+	0.0732890i
$300$	−287.613	−	50.7139i	−0.958709	−	0.169046i
$301$	−93.9693	−	34.2020i	−0.312190	−	0.113628i
$302$	−99.5858	+	83.5624i	−0.329754	+	0.276697i
$303$			180.278i			0.594975i
$304$		0			0
$305$	−160.000			−0.524590
$306$	−139.056	−	165.721i	−0.454432	−	0.541571i
$307$	81.3893	−	223.615i	0.265112	−	0.728388i	−0.733692	−	0.679483i	$-0.762204\pi$
$307$	81.3893	−	223.615i	0.265112	−	0.728388i	0.998803	−	0.0489059i	$-0.0155734\pi$
$308$	−78.1417	+	443.163i	−0.253707	+	1.43884i
$309$	36.1188	+	204.840i	0.116889	+	0.662913i
$310$	−488.640	+	177.850i	−1.57626	+	0.573711i
$311$	−197.500	+	342.080i	−0.635048	+	1.09994i	0.351457	+	0.936204i	$0.385686\pi$
$311$	−197.500	+	342.080i	−0.635048	+	1.09994i	−0.986505	+	0.163732i	$0.947647\pi$
$312$	−202.962	+	117.180i	−0.650521	+	0.375578i
$313$	95.7556	+	80.3485i	0.305928	+	0.256704i	0.782807	−	0.622265i	$-0.213787\pi$
$313$	95.7556	+	80.3485i	0.305928	+	0.256704i	−0.476878	+	0.878969i	$0.658232\pi$
$314$	−23.1760	+	27.6201i	−0.0738090	+	0.0879622i
$315$	−40.0000	−	69.2820i	−0.126984	−	0.219943i
$316$	−281.025	−	162.250i	−0.889319	−	0.513449i
$317$	−1.23317	−	3.38811i	−0.00389013	−	0.0106880i	0.937732	−	0.347359i	$-0.112921\pi$
$317$	−1.23317	−	3.38811i	−0.00389013	−	0.0106880i	−0.941622	+	0.336671i	$0.890699\pi$
$318$	969.362	−	170.925i	3.04831	−	0.537499i
$319$	−177.539	−	31.3049i	−0.556548	−	0.0981344i
$320$	3.75877	+	1.36808i	0.0117462	+	0.00427525i
$321$	209.130	−	175.481i	0.651496	−	0.546670i
$322$		−	630.971i		−	1.95954i
$323$		0			0
$324$	909.000			2.80556
$325$	−20.8584	−	24.8581i	−0.0641798	−	0.0764865i
$326$	−332.956	+	914.790i	−1.02134	+	2.80610i
$327$	−124.158	+	704.138i	−0.379689	+	2.15333i
$328$	112.871	+	640.125i	0.344120	+	1.95160i
$329$	46.9846	−	17.1010i	0.142810	−	0.0519787i
$330$	260.000	−	450.333i	0.787879	−	1.36465i
$331$	−171.737	+	99.1527i	−0.518844	+	0.299555i	−0.736462	−	0.676479i	$-0.763505\pi$
$331$	−171.737	+	99.1527i	−0.518844	+	0.299555i	0.217617	+	0.976034i	$0.430171\pi$
$332$	275.776	+	231.404i	0.830651	+	0.696999i
$333$	−55.6225	+	66.2883i	−0.167034	+	0.199064i
$334$	221.000	+	382.783i	0.661677	+	1.14606i
$335$	−137.390	−	79.3221i	−0.410119	−	0.236782i
$336$	−178.810	−	491.276i	−0.532172	−	1.46213i
$337$	−56.8124	+	10.0176i	−0.168583	+	0.0297257i	−0.257302	−	0.966331i	$-0.582834\pi$
$337$	−56.8124	+	10.0176i	−0.168583	+	0.0297257i	0.0887195	+	0.996057i	$0.471723\pi$
$338$	553.921	+	97.6712i	1.63882	+	0.288968i
$339$	415.344	+	151.173i	1.22520	+	0.445938i
$340$	−413.664	+	347.105i	−1.21666	+	1.02090i
$341$			360.555i			1.05735i
$342$		0			0
$343$	365.000			1.06414
$344$	231.760	+	276.201i	0.673722	+	0.802911i
$345$	−172.644	+	474.335i	−0.500417	+	1.37489i
$346$	76.7525	−	435.285i	0.221828	−	1.25805i
$347$	−6.94593	−	39.3923i	−0.0200171	−	0.113523i	0.973162	−	0.230121i	$-0.0739121\pi$
$347$	−6.94593	−	39.3923i	−0.0200171	−	0.113523i	−0.993179	+	0.116598i	$0.962801\pi$
$348$	549.720	−	200.082i	1.57966	−	0.574948i
$349$	−49.0000	+	84.8705i	−0.140401	+	0.243182i	−0.927648	−	0.373456i	$-0.878173\pi$
$349$	−49.0000	+	84.8705i	−0.140401	+	0.243182i	0.787247	+	0.616638i	$0.211506\pi$
$350$	140.512	−	81.1249i	0.401464	−	0.231785i
$351$	49.7929	+	41.7812i	0.141860	+	0.119035i
$352$	208.584	−	248.581i	0.592569	−	0.706196i
$353$	92.5000	+	160.215i	0.262040	+	0.453866i	0.966784	−	0.255596i	$-0.0822715\pi$
$353$	92.5000	+	160.215i	0.262040	+	0.453866i	−0.704744	+	0.709462i	$0.748938\pi$
$354$	−202.962	−	117.180i	−0.573340	−	0.331018i
$355$	−147.981	−	406.573i	−0.416847	−	1.14528i
$356$		0			0
$357$	266.308	+	46.9573i	0.745961	+	0.131533i
$358$	122.160	+	44.4626i	0.341229	+	0.124197i
$359$	−172.360	+	144.627i	−0.480111	+	0.402861i	−0.850467	−	0.526029i	$-0.823680\pi$
$359$	−172.360	+	144.627i	−0.480111	+	0.402861i	0.370355	+	0.928890i	$0.379236\pi$
$360$			288.444i			0.801234i
$361$		0			0
$362$	−390.000			−1.07735
$363$	48.6697	+	58.0023i	0.134076	+	0.159786i
$364$	55.4927	−	152.465i	0.152452	−	0.418860i
$365$	72.9322	−	413.619i	0.199814	−	1.13320i
$366$	−90.2971	−	512.100i	−0.246713	−	1.39918i
$367$	−46.9846	+	17.1010i	−0.128024	+	0.0465967i	−0.405237	−	0.914211i	$-0.632811\pi$
$367$	−46.9846	+	17.1010i	−0.128024	+	0.0465967i	0.277214	+	0.960808i	$0.410589\pi$
$368$	−507.500	+	879.016i	−1.37908	+	2.38863i
$369$	−124.900	+	72.1110i	−0.338482	+	0.195423i
$370$	239.006	+	200.550i	0.645962	+	0.542026i
$371$	−243.348	+	290.011i	−0.655926	+	0.781702i
$372$	−585.000	−	1013.25i	−1.57258	−	2.72379i
$373$	377.822	+	218.136i	1.01293	+	0.584815i	0.912048	−	0.410084i	$-0.134501\pi$
$373$	377.822	+	218.136i	1.01293	+	0.584815i	0.100881	+	0.994899i	$0.467834\pi$
$374$	184.976	+	508.216i	0.494587	+	1.35887i
$375$	−482.905	+	85.1492i	−1.28775	+	0.227065i
$376$	−177.539	−	31.3049i	−0.472178	−	0.0832576i
$377$	61.0800	+	22.2313i	0.162016	+	0.0589690i
$378$	−248.964	+	208.906i	−0.658636	+	0.552661i
$379$		−	486.749i		−	1.28430i	−0.766579	−	0.642150i	$-0.778043\pi$
$379$		−	486.749i		−	1.28430i	0.766579	−	0.642150i	$-0.221957\pi$
$380$		0			0
$381$	−468.000			−1.22835
$382$	447.298	+	533.068i	1.17094	+	1.39547i
$383$	69.0576	−	189.734i	0.180307	−	0.495389i	−0.816306	−	0.577619i	$-0.803982\pi$
$383$	69.0576	−	189.734i	0.180307	−	0.495389i	0.996613	+	0.0822297i	$0.0262041\pi$
$384$	79.0099	−	448.088i	0.205755	−	1.16689i
$385$	34.7296	+	196.962i	0.0902068	+	0.511588i
$386$	903.984	−	329.023i	2.34193	−	0.852392i
$387$	−40.0000	+	69.2820i	−0.103359	+	0.179023i
$388$	−955.485	+	551.649i	−2.46259	+	1.42178i
$389$	−366.169	−	307.252i	−0.941309	−	0.789852i	0.0365035	−	0.999334i	$-0.488378\pi$
$389$	−366.169	−	307.252i	−0.941309	−	0.789852i	−0.977813	+	0.209481i	$0.932822\pi$
$390$	−120.515	+	143.625i	−0.309014	+	0.368268i
$391$	−262.500	−	454.663i	−0.671355	−	1.16282i
$392$	−374.700	−	216.333i	−0.955867	−	0.551870i
$393$	138.115	+	379.468i	0.351438	+	0.965568i
$394$	−319.570	+	56.3488i	−0.811091	+	0.143017i
$395$	−142.031	−	25.0439i	−0.359572	−	0.0634023i
$396$	338.289	+	123.127i	0.854266	+	0.310927i
$397$	574.533	−	482.091i	1.44719	−	1.21433i	0.512587	−	0.858636i	$-0.328687\pi$
$397$	574.533	−	482.091i	1.44719	−	1.21433i	0.934601	−	0.355699i	$-0.115757\pi$
$398$			443.483i			1.11428i
$399$		0			0
$400$	−261.000			−0.652500
$401$	−185.408	−	220.961i	−0.462365	−	0.551025i	0.483602	−	0.875288i	$-0.339328\pi$
$401$	−185.408	−	220.961i	−0.462365	−	0.551025i	−0.945967	+	0.324263i	$0.894884\pi$
$402$	176.343	−	484.500i	0.438665	−	1.20522i
$403$	22.5743	−	128.025i	0.0560155	−	0.317680i
$404$	78.1417	+	443.163i	0.193420	+	1.09694i
$405$	379.636	−	138.176i	0.937372	−	0.341176i
$406$	−162.500	+	281.458i	−0.400246	+	0.693247i
$407$	187.350	−	108.167i	0.460319	−	0.265765i
$408$	−746.893	−	626.718i	−1.83062	−	1.53607i
$409$	23.1760	−	27.6201i	0.0566651	−	0.0675309i	−0.736967	−	0.675928i	$-0.763743\pi$
$409$	23.1760	−	27.6201i	0.0566651	−	0.0675309i	0.793632	+	0.608397i	$0.208187\pi$
$410$	260.000	+	450.333i	0.634146	+	1.09837i
$411$	390.312	+	225.347i	0.949665	+	0.548289i
$412$	177.577	+	487.888i	0.431011	+	1.18419i
$413$	88.7694	−	15.6524i	0.214938	−	0.0378994i
$414$	−497.108	−	87.6536i	−1.20075	−	0.211724i
$415$	150.351	+	54.7232i	0.362291	+	0.131863i
$416$	−89.6272	+	75.2062i	−0.215450	+	0.180784i
$417$		−	180.278i		−	0.432320i
$418$		0			0
$419$	112.000			0.267303			0.133652	−	0.991028i	$-0.457330\pi$
$419$	112.000			0.267303			0.133652	+	0.991028i	$0.457330\pi$
$420$	−417.169	−	497.162i	−0.993259	−	1.18372i
$421$	215.805	−	592.919i	0.512601	−	1.40836i	−0.365916	−	0.930648i	$-0.619244\pi$
$421$	215.805	−	592.919i	0.512601	−	1.40836i	0.878517	−	0.477711i	$-0.158534\pi$
$422$	146.733	−	832.163i	0.347708	−	1.97195i
$423$	−6.94593	−	39.3923i	−0.0164206	−	0.0931260i
$424$	1282.68	−	466.857i	3.02519	−	1.10108i
$425$	67.5000	−	116.913i	0.158824	−	0.275090i
$426$	1217.77	−	703.082i	2.85863	−	1.65043i
$427$	153.209	+	128.558i	0.358803	+	0.301071i
$428$	438.027	−	522.020i	1.02343	−	1.21967i
$429$	65.0000	+	112.583i	0.151515	+	0.262432i
$430$	249.800	+	144.222i	0.580930	+	0.335400i
$431$	147.981	+	406.573i	0.343342	+	0.943325i	0.984417	+	0.175847i	$0.0562665\pi$
$431$	147.981	+	406.573i	0.343342	+	0.943325i	−0.641075	+	0.767478i	$0.721511\pi$
$432$	514.862	−	90.7841i	1.19181	−	0.210148i
$433$	−724.358	−	127.724i	−1.67288	−	0.294974i	−0.744783	−	0.667307i	$-0.767447\pi$
$433$	−724.358	−	127.724i	−1.67288	−	0.294974i	−0.928099	+	0.372332i	$0.878558\pi$
$434$	610.800	+	222.313i	1.40737	+	0.512242i
$435$	199.172	−	167.125i	0.457866	−	0.384195i
$436$			1784.75i			4.09346i
$437$		0			0
$438$	1365.00			3.11644
$439$	509.873	+	607.643i	1.16144	+	1.38415i	0.909133	+	0.416505i	$0.136745\pi$
$439$	509.873	+	607.643i	1.16144	+	1.38415i	0.252308	+	0.967647i	$0.418810\pi$
$440$	246.634	−	677.622i	0.560532	−	1.54005i
$441$	16.6702	−	94.5415i	0.0378010	−	0.214380i
$442$	−33.8614	−	192.038i	−0.0766095	−	0.434474i
$443$	−629.594	+	229.153i	−1.42121	+	0.517277i	−0.934397	−	0.356232i	$-0.884061\pi$
$443$	−629.594	+	229.153i	−1.42121	+	0.517277i	−0.486808	+	0.873509i	$0.661839\pi$
$444$	−351.000	+	607.950i	−0.790541	+	1.36926i
$445$		0			0
$446$	557.680	+	467.949i	1.25040	+	1.04921i
$447$	162.232	−	193.341i	0.362936	−	0.432530i
$448$	−2.50000	−	4.33013i	−0.00558036	−	0.00966546i
$449$	31.2250	+	18.0278i	0.0695434	+	0.0401509i	0.534369	−	0.845252i	$-0.320549\pi$
$449$	31.2250	+	18.0278i	0.0695434	+	0.0401509i	−0.464825	+	0.885403i	$0.653883\pi$
$450$	−44.3942	−	121.972i	−0.0986537	−	0.271049i
$451$	355.077	−	62.6097i	0.787311	−	0.138824i
$452$	1086.54	+	191.586i	2.40384	+	0.423862i
$453$	−122.160	−	44.4626i	−0.269669	−	0.0981515i
$454$	−707.059	+	593.293i	−1.55740	+	1.30681i
$455$		−	72.1110i		−	0.158486i
$456$		0			0
$457$	−755.000			−1.65208			−0.826039	−	0.563612i	$-0.809411\pi$
$457$	−755.000			−1.65208			−0.826039	+	0.563612i	$0.809411\pi$
$458$	−370.817	−	441.922i	−0.809643	−	0.964895i
$459$	−92.4878	+	254.108i	−0.201499	+	0.553613i
$460$	−218.797	+	1240.86i	−0.475645	+	2.69752i
$461$	134.056	+	760.272i	0.290795	+	1.64918i	0.683819	+	0.729651i	$0.260318\pi$
$461$	134.056	+	760.272i	0.290795	+	1.64918i	−0.393025	+	0.919528i	$0.628571\pi$
$462$	−610.800	+	222.313i	−1.32208	+	0.481197i
$463$	175.000	−	303.109i	0.377970	−	0.654663i	−0.612797	−	0.790240i	$-0.709956\pi$
$463$	175.000	−	303.109i	0.377970	−	0.654663i	0.990767	+	0.135578i	$0.0432890\pi$
$464$	452.762	−	261.402i	0.975781	−	0.563367i
$465$	−398.343	−	334.250i	−0.856652	−	0.718816i
$466$	625.753	−	745.743i	1.34282	−	1.60031i
$467$	−35.0000	−	60.6218i	−0.0749465	−	0.129811i	0.826117	−	0.563499i	$-0.190545\pi$
$467$	−35.0000	−	60.6218i	−0.0749465	−	0.129811i	−0.901063	+	0.433688i	$0.857212\pi$
$468$	−112.410	−	64.8999i	−0.240192	−	0.138675i
$469$	67.8244	+	186.346i	0.144615	+	0.397326i
$470$	−142.031	+	25.0439i	−0.302194	+	0.0532849i
$471$	−35.5077	−	6.26097i	−0.0753880	−	0.0132929i
$472$	−305.400	−	111.157i	−0.647034	−	0.235501i
$473$	153.209	−	128.558i	0.323909	−	0.271792i
$474$		−	468.722i		−	0.988864i
$475$		0			0
$476$	675.000			1.41807
$477$	194.679	+	232.009i	0.408131	+	0.486392i
$478$	242.935	−	667.458i	0.508232	−	1.39635i
$479$	−64.2498	+	364.379i	−0.134133	+	0.760707i	0.841326	+	0.540528i	$0.181775\pi$
$479$	−64.2498	+	364.379i	−0.134133	+	0.760707i	−0.975459	+	0.220180i	$0.929336\pi$
$480$	81.2673	+	460.890i	0.169307	+	0.960188i
$481$	−73.2960	+	26.6776i	−0.152383	+	0.0554627i
$482$	715.000	−	1238.42i	1.48340	−	2.56933i
$483$	546.437	−	315.486i	1.13134	−	0.653180i
$484$	144.782	+	121.487i	0.299137	+	0.251006i
$485$	−315.194	+	375.634i	−0.649885	+	0.774502i
$486$	364.000	+	630.466i	0.748971	+	1.29726i
$487$	449.640	+	259.600i	0.923285	+	0.533059i	0.884682	−	0.466196i	$-0.154376\pi$
$487$	449.640	+	259.600i	0.923285	+	0.533059i	0.0386035	+	0.999255i	$0.487709\pi$
$488$	−246.634	−	677.622i	−0.505398	−	1.38857i
$489$	−958.709	+	169.046i	−1.96055	+	0.345698i
$490$	−340.874	−	60.1054i	−0.695662	−	0.122664i
$491$	593.886	+	216.157i	1.20954	+	0.440238i	0.866545	−	0.499098i	$-0.166335\pi$
$491$	593.886	+	216.157i	1.20954	+	0.440238i	0.342998	+	0.939336i	$0.388558\pi$
$492$	−896.272	+	752.062i	−1.82169	+	1.52858i
$493$			270.416i			0.548512i
$494$		0			0
$495$	160.000			0.323232
$496$	−672.105	−	800.984i	−1.35505	−	1.61489i
$497$	−184.976	+	508.216i	−0.372184	+	1.02257i
$498$	−90.2971	+	512.100i	−0.181319	+	1.02831i
$499$	65.9863	+	374.227i	0.132237	+	0.749954i	0.976744	+	0.214409i	$0.0687826\pi$
$499$	65.9863	+	374.227i	0.132237	+	0.749954i	−0.844507	+	0.535545i	$0.820106\pi$
$500$	−1150.18	+	418.633i	−2.30037	+	0.837265i
$501$	−221.000	+	382.783i	−0.441118	+	0.764038i
$502$	−1255.24	+	724.716i	−2.50049	+	1.44366i
$503$	−34.4720	−	28.9254i	−0.0685328	−	0.0575058i	0.607878	−	0.794031i	$-0.292021\pi$
$503$	−34.4720	−	28.9254i	−0.0685328	−	0.0575058i	−0.676411	+	0.736525i	$0.736465\pi$
$504$	231.760	−	276.201i	0.459842	−	0.548018i
$505$	100.000	+	173.205i	0.198020	+	0.342980i
$506$	1092.87	+	630.971i	2.15983	+	1.24698i
$507$	192.375	+	528.545i	0.379437	+	1.04250i
$508$	−1150.45	+	202.856i	−2.26467	+	0.399322i
$509$	816.678	+	144.002i	1.60448	+	0.282912i	0.902955	−	0.429736i	$-0.141393\pi$
$509$	816.678	+	144.002i	1.60448	+	0.282912i	0.701521	+	0.712648i	$0.252505\pi$
$510$	−732.960	−	266.776i	−1.43718	−	0.523090i
$511$	−402.173	+	337.463i	−0.787032	+	0.660398i
$512$		−	1150.17i		−	2.24643i
$513$		0			0
$514$	1508.00			2.93385
$515$	148.327	+	176.769i	0.288013	+	0.343240i
$516$	−221.971	+	609.860i	−0.430176	+	1.18190i
$517$	−17.3648	+	98.4808i	−0.0335877	+	0.190485i
$518$	−67.7228	−	384.075i	−0.130739	−	0.741458i
$519$	415.344	−	151.173i	0.800278	−	0.291277i
$520$	−130.000	+	225.167i	−0.250000	+	0.433013i
$521$	530.825	−	306.472i	1.01886	−	0.588238i	0.105085	−	0.994463i	$-0.466489\pi$
$521$	530.825	−	306.472i	1.01886	−	0.588238i	0.913773	+	0.406226i	$0.133155\pi$
$522$	199.172	+	167.125i	0.381555	+	0.320162i
$523$	−298.971	+	356.300i	−0.571646	+	0.681261i	−0.971968	−	0.235113i	$-0.924454\pi$
$523$	−298.971	+	356.300i	−0.571646	+	0.681261i	0.400322	+	0.916375i	$0.368898\pi$
$524$	504.000	+	872.954i	0.961832	+	1.66594i
$525$	140.512	+	81.1249i	0.267643	+	0.154524i
$526$	−382.283	−	1050.31i	−0.726774	−	1.99679i
$527$	532.616	−	93.9146i	1.01066	−	0.178206i
$528$	1029.72	+	181.568i	1.95024	+	0.343879i
$529$	−654.026	−	238.046i	−1.23634	−	0.449992i
$530$	836.521	−	701.924i	1.57834	−	1.32439i
$531$		−	72.1110i		−	0.135802i
$532$		0			0
$533$	−130.000			−0.243902
$534$		0			0
$535$	103.586	−	284.601i	0.193619	−	0.531965i
$536$	124.158	−	704.138i	0.231639	−	1.31369i
$537$	22.5743	+	128.025i	0.0420377	+	0.238408i
$538$	366.480	−	133.388i	0.681190	−	0.247933i
$539$	−120.000	+	207.846i	−0.222635	+	0.385614i
$540$	562.050	−	324.500i	1.04083	−	0.600925i
$541$	−459.627	−	385.673i	−0.849587	−	0.712888i	0.110112	−	0.993919i	$-0.464879\pi$
$541$	−459.627	−	385.673i	−0.849587	−	0.712888i	−0.959699	+	0.281031i	$0.909324\pi$
$542$	−243.348	+	290.011i	−0.448982	+	0.535076i
$543$	−195.000	−	337.750i	−0.359116	−	0.622007i
$544$	−421.537	−	243.375i	−0.774885	−	0.447380i
$545$	271.298	+	745.384i	0.497794	+	1.36768i
$546$	230.800	−	40.6963i	0.422711	−	0.0745354i
$547$	−589.429	−	103.932i	−1.07757	−	0.190004i	−0.393427	−	0.919356i	$-0.628711\pi$
$547$	−589.429	−	103.932i	−1.07757	−	0.190004i	−0.684139	+	0.729352i	$0.739822\pi$
$548$	1057.15	+	384.773i	1.92911	+	0.702140i
$549$	122.567	−	102.846i	0.223255	−	0.187333i
$550$			324.500i			0.589999i
$551$		0			0
$552$	−2275.00			−4.12138
$553$	115.880	+	138.101i	0.209548	+	0.249730i
$554$	−61.6586	+	169.405i	−0.111297	+	0.305786i
$555$	−54.1782	+	307.260i	−0.0976184	+	0.553622i
$556$	−78.1417	−	443.163i	−0.140543	−	0.797057i
$557$	−357.083	+	129.968i	−0.641083	+	0.233335i	−0.642048	−	0.766664i	$-0.721915\pi$
$557$	−357.083	+	129.968i	−0.641083	+	0.233335i	0.000965080		1.00000i	$0.499693\pi$
$558$	260.000	−	450.333i	0.465950	−	0.807049i
$559$	−62.4500	+	36.0555i	−0.111717	+	0.0645000i
$560$	−444.306	−	372.817i	−0.793403	−	0.665744i
$561$	−347.641	+	414.302i	−0.619680	+	0.738506i
$562$	−520.000	−	900.666i	−0.925267	−	1.60261i
$563$	−106.165	−	61.2944i	−0.188570	−	0.108871i	0.402743	−	0.915313i	$-0.368057\pi$
$563$	−106.165	−	61.2944i	−0.188570	−	0.108871i	−0.591313	+	0.806442i	$0.701390\pi$
$564$	−110.985	−	304.930i	−0.196783	−	0.540656i
$565$	482.905	−	85.1492i	0.854700	−	0.150707i
$566$	−1136.25	−	200.351i	−2.00751	−	0.353977i
$567$	−474.545	−	172.720i	−0.836940	−	0.304621i
$568$	1493.79	−	1253.44i	2.62991	−	2.20675i
$569$			36.0555i			0.0633665i	0.999498	+	0.0316832i	$0.0100868\pi$
$569$			36.0555i			0.0633665i	−0.999498	+	0.0316832i	$0.989913\pi$
$570$		0			0
$571$	−790.000			−1.38354			−0.691769	−	0.722119i	$-0.743168\pi$
$571$	−790.000			−1.38354			−0.691769	+	0.722119i	$0.743168\pi$
$572$	208.584	+	248.581i	0.364658	+	0.434582i
$573$	−238.002	+	653.905i	−0.415361	+	1.14120i
$574$	112.871	−	640.125i	0.196640	−	1.11520i
$575$	−54.6992	−	310.214i	−0.0951290	−	0.539503i
$576$	−3.75877	+	1.36808i	−0.00652564	+	0.00237514i
$577$	−337.500	+	584.567i	−0.584922	+	1.01311i	0.409963	+	0.912102i	$0.365542\pi$
$577$	−337.500	+	584.567i	−0.584922	+	1.01311i	−0.994885	+	0.101013i	$0.967792\pi$
$578$	−199.840	+	115.378i	−0.345744	+	0.199615i
$579$	736.935	+	618.362i	1.27277	+	1.06798i
$580$	417.169	−	497.162i	0.719256	−	0.857176i
$581$	−100.000	−	173.205i	−0.172117	−	0.298115i
$582$	−1380.14	−	796.827i	−2.37138	−	1.36912i
$583$	−258.966	−	711.503i	−0.444195	−	1.22042i
$584$	1864.16	−	328.701i	3.19205	−	0.562844i
$585$	−56.8124	−	10.0176i	−0.0971152	−	0.0171240i
$586$	−745.176	−	271.222i	−1.27163	−	0.462836i
$587$	−214.492	+	179.981i	−0.365405	+	0.306611i	−0.806940	−	0.590633i	$-0.798878\pi$
$587$	−214.492	+	179.981i	−0.365405	+	0.306611i	0.441536	+	0.897244i	$0.354434\pi$
$588$		−	778.799i		−	1.32449i
$589$		0			0
$590$	−260.000			−0.440678
$591$	−208.584	−	248.581i	−0.352935	−	0.420611i
$592$	−214.572	+	589.531i	−0.362452	+	0.995830i
$593$	130.236	−	738.606i	0.219622	−	1.24554i	−0.653080	−	0.757289i	$-0.726524\pi$
$593$	130.236	−	738.606i	0.219622	−	1.24554i	0.872703	−	0.488252i	$-0.162365\pi$
$594$	−112.871	−	640.125i	−0.190019	−	1.07765i
$595$	281.908	−	102.606i	0.473795	−	0.172447i
$596$	315.000	−	545.596i	0.528523	−	0.915430i
$597$	−384.067	+	221.741i	−0.643329	+	0.371426i
$598$	−348.550	−	292.468i	−0.582860	−	0.489078i
$599$	−324.465	+	386.682i	−0.541677	+	0.645545i	−0.965563	−	0.260170i	$-0.916221\pi$
$599$	−324.465	+	386.682i	−0.541677	+	0.645545i	0.423886	+	0.905716i	$0.360666\pi$
$600$	−292.500	−	506.625i	−0.487500	−	0.844375i
$601$	−530.825	−	306.472i	−0.883236	−	0.509937i	−0.0115120	−	0.999934i	$-0.503664\pi$
$601$	−530.825	−	306.472i	−0.883236	−	0.509937i	−0.871724	+	0.489997i	$0.836998\pi$
$602$	−123.317	−	338.811i	−0.204846	−	0.562809i
$603$	156.234	−	27.5483i	0.259095	−	0.0456854i
$604$	−319.570	−	56.3488i	−0.529089	−	0.0932927i
$605$	78.9342	+	28.7297i	0.130470	+	0.0474871i
$606$	−497.929	+	417.812i	−0.821665	+	0.689459i
$607$		−	987.921i		−	1.62755i	−0.581182	−	0.813774i	$-0.697410\pi$
$607$		−	987.921i		−	1.62755i	0.581182	−	0.813774i	$-0.302590\pi$
$608$		0			0
$609$	−325.000			−0.533662
$610$	−370.817	−	441.922i	−0.607896	−	0.724462i
$611$	12.3317	−	33.8811i	0.0201828	−	0.0554519i
$612$	93.7700	−	531.796i	0.153219	−	0.868948i
$613$	−208.378	−	1181.77i	−0.339931	−	1.92785i	−0.371706	−	0.928350i	$-0.621227\pi$
$613$	−208.378	−	1181.77i	−0.339931	−	1.92785i	0.0317749	−	0.999495i	$-0.489884\pi$
$614$	806.256	−	293.453i	1.31312	−	0.477937i
$615$	−260.000	+	450.333i	−0.422764	+	0.732249i
$616$	−780.625	+	450.694i	−1.26725	+	0.731646i
$617$	−268.116	−	224.976i	−0.434547	−	0.364628i	0.399117	−	0.916900i	$-0.369317\pi$
$617$	−268.116	−	224.976i	−0.434547	−	0.364628i	−0.833664	+	0.552272i	$0.813761\pi$
$618$	−482.062	+	574.499i	−0.780035	+	0.929609i
$619$	−280.000	−	484.974i	−0.452342	−	0.783480i	0.546189	−	0.837662i	$-0.316078\pi$
$619$	−280.000	−	484.974i	−0.452342	−	0.783480i	−0.998531	+	0.0541821i	$0.982745\pi$
$620$	−1124.10	−	648.999i	−1.81306	−	1.04677i
$621$	215.805	+	592.919i	0.347512	+	0.954781i
$622$	−1402.56	+	247.308i	−2.25491	+	0.397602i
$623$		0			0
$624$	−354.264	−	128.942i	−0.567731	−	0.206637i
$625$	−244.368	+	205.049i	−0.390989	+	0.328079i
$626$			450.694i			0.719958i
$627$		0			0
$628$	−90.0000			−0.143312
$629$	−208.584	−	248.581i	−0.331613	−	0.395201i
$630$	98.6537	−	271.049i	0.156593	−	0.430236i
$631$	−182.331	+	1034.05i	−0.288955	+	1.63875i	0.401851	+	0.915705i	$0.368367\pi$
$631$	−182.331	+	1034.05i	−0.288955	+	1.63875i	−0.690806	+	0.723040i	$0.742744\pi$
$632$	−112.871	−	640.125i	−0.178594	−	1.01286i
$633$	794.040	−	289.007i	1.25441	−	0.456567i
$634$	6.50000	−	11.2583i	0.0102524	−	0.0177576i
$635$	−449.640	+	259.600i	−0.708094	+	0.408818i
$636$	1882.17	+	1579.33i	2.95939	+	2.48322i
$637$	55.6225	−	66.2883i	0.0873194	−	0.104063i
$638$	−325.000	−	562.917i	−0.509404	−	0.882314i
$639$	374.700	+	216.333i	0.586385	+	0.338549i
$640$	−172.644	−	474.335i	−0.269756	−	0.741149i
$641$	−1207.26	+	212.873i	−1.88341	+	0.332095i	−0.992515	−	0.122121i	$-0.961030\pi$
$641$	−1207.26	+	212.873i	−1.88341	+	0.332095i	−0.890891	+	0.454217i	$0.849919\pi$
$642$	969.362	+	170.925i	1.50991	+	0.266238i
$643$	967.883	+	352.281i	1.50526	+	0.547871i	0.957417	−	0.288709i	$-0.0932261\pi$
$643$	967.883	+	352.281i	1.50526	+	0.547871i	0.547845	+	0.836580i	$0.315448\pi$
$644$	1206.52	−	1012.39i	1.87348	−	1.57203i
$645$			288.444i			0.447200i
$646$		0			0
$647$	555.000			0.857805			0.428903	−	0.903351i	$-0.358900\pi$
$647$	555.000			0.857805			0.428903	+	0.903351i	$0.358900\pi$
$648$	1170.39	+	1394.82i	1.80616	+	2.15249i
$649$	−61.6586	+	169.405i	−0.0950055	+	0.261025i
$650$	20.3168	−	115.223i	0.0312567	−	0.177265i
$651$	112.871	+	640.125i	0.173381	+	0.983295i
$652$	−2283.45	+	831.109i	−3.50223	+	1.27471i
$653$	−25.0000	+	43.3013i	−0.0382848	+	0.0663113i	−0.884533	−	0.466478i	$-0.845523\pi$
$653$	−25.0000	+	43.3013i	−0.0382848	+	0.0663113i	0.846248	+	0.532789i	$0.178856\pi$
$654$	−2232.59	+	1288.98i	−3.41374	+	1.97092i
$655$	343.188	+	287.969i	0.523951	+	0.439647i
$656$	−672.105	+	800.984i	−1.02455	+	1.22101i
$657$	210.000	+	363.731i	0.319635	+	0.553624i
$658$	156.125	+	90.1388i	0.237272	+	0.136989i
$659$	−67.8244	−	186.346i	−0.102920	−	0.282771i	0.877535	−	0.479512i	$-0.159186\pi$
$659$	−67.8244	−	186.346i	−0.102920	−	0.282771i	−0.980455	+	0.196741i	$0.936964\pi$
$660$	1278.28	−	225.395i	1.93679	−	0.341508i
$661$	195.293	+	34.4354i	0.295450	+	0.0520959i	0.319409	−	0.947617i	$-0.396516\pi$
$661$	195.293	+	34.4354i	0.295450	+	0.0520959i	−0.0239583	+	0.999713i	$0.507627\pi$
$662$	−671.880	−	244.544i	−1.01492	−	0.369402i
$663$	149.379	−	125.344i	0.225307	−	0.189055i
$664$			721.110i			1.08601i
$665$		0			0
$666$	−312.000			−0.468468
$667$	405.581	+	483.352i	0.608067	+	0.724666i
$668$	−377.350	+	1036.76i	−0.564896	+	1.55204i
$669$	−126.416	+	716.940i	−0.188962	+	1.07166i
$670$	−99.3268	−	563.310i	−0.148249	−	0.840761i
$671$	−375.877	+	136.808i	−0.560174	+	0.203887i
$672$	292.500	−	506.625i	0.435268	−	0.753906i
$673$	518.335	−	299.261i	0.770185	−	0.444667i	−0.0627553	−	0.998029i	$-0.519989\pi$
$673$	518.335	−	299.261i	0.770185	−	0.444667i	0.832941	+	0.553362i	$0.186655\pi$
$674$	−159.337	−	133.700i	−0.236405	−	0.198368i
$675$	−104.292	+	124.291i	−0.154507	+	0.184134i
$676$	702.000	+	1215.90i	1.03846	+	1.79867i
$677$	−59.3275	−	34.2527i	−0.0876329	−	0.0505949i	0.455543	−	0.890214i	$-0.349445\pi$
$677$	−59.3275	−	34.2527i	−0.0876329	−	0.0505949i	−0.543176	+	0.839619i	$0.682778\pi$
$678$	545.062	+	1497.54i	0.803926	+	2.20877i
$679$	603.632	−	106.437i	0.889001	−	0.156755i
$680$	−1065.23	−	187.829i	−1.56652	−	0.276219i
$681$	−867.336	−	315.685i	−1.27362	−	0.463560i
$682$	−995.858	+	835.624i	−1.46020	+	1.22525i
$683$		−	237.966i		−	0.348413i	−0.984709	−	0.174207i	$-0.944264\pi$
$683$		−	237.966i		−	0.348413i	0.984709	−	0.174207i	$-0.0557361\pi$
$684$		0			0
$685$	500.000			0.729927
$686$	845.925	+	1008.13i	1.23313	+	1.46958i
$687$	197.307	−	542.098i	0.287201	−	0.789079i
$688$	−100.716	+	571.188i	−0.146389	+	0.830216i
$689$	47.4060	+	268.853i	0.0688040	+	0.390207i
$690$	−1710.24	+	622.477i	−2.47861	+	0.902140i
$691$	410.000	−	710.141i	0.593343	−	1.02770i	−0.400435	−	0.916325i	$-0.631141\pi$
$691$	410.000	−	710.141i	0.593343	−	1.02770i	0.993778	−	0.111375i	$-0.0355255\pi$
$692$	955.485	−	551.649i	1.38076	−	0.797181i
$693$	−153.209	−	128.558i	−0.221081	−	0.185509i
$694$	92.7041	−	110.481i	0.133579	−	0.159194i
$695$	−100.000	−	173.205i	−0.143885	−	0.249216i
$696$	1014.81	+	585.902i	1.45806	+	0.841813i
$697$	−184.976	−	508.216i	−0.265388	−	0.729148i
$698$	−347.976	+	61.3575i	−0.498533	+	0.0879048i
$699$	958.709	+	169.046i	1.37154	+	0.241840i
$700$	380.576	+	138.518i	0.543679	+	0.197883i
$701$	−413.664	+	347.105i	−0.590106	+	0.495157i	−0.888248	−	0.459364i	$-0.848077\pi$
$701$	−413.664	+	347.105i	−0.590106	+	0.495157i	0.298143	+	0.954521i	$0.403633\pi$
$702$			234.361i			0.333847i
$703$		0			0
$704$	10.0000			0.0142045
$705$	−92.7041	−	110.481i	−0.131495	−	0.156710i
$706$	−228.137	+	626.800i	−0.323140	+	0.887819i
$707$	43.4120	−	246.202i	0.0614032	−	0.348235i
$708$	−101.584	−	576.113i	−0.143480	−	0.813718i
$709$	−251.838	+	91.6614i	−0.355201	+	0.129283i	−0.513457	−	0.858116i	$-0.671635\pi$
$709$	−251.838	+	91.6614i	−0.355201	+	0.129283i	0.158255	+	0.987398i	$0.449413\pi$
$710$	780.000	−	1351.00i	1.09859	−	1.90282i
$711$	124.900	−	72.1110i	0.175668	−	0.101422i
$712$		0			0
$713$	811.161	−	966.704i	1.13767	−	1.35583i
$714$	487.500	+	844.375i	0.682773	+	1.18260i
$715$	124.900	+	72.1110i	0.174685	+	0.100855i
$716$	110.985	+	304.930i	0.155008	+	0.425880i
$717$	699.503	−	123.341i	0.975596	−	0.172024i
$718$	−798.924	−	140.872i	−1.11271	−	0.196200i
$719$	−98.6677	−	35.9121i	−0.137229	−	0.0499473i	0.272493	−	0.962158i	$-0.412152\pi$
$719$	−98.6677	−	35.9121i	−0.137229	−	0.0499473i	−0.409722	+	0.912211i	$0.634374\pi$
$720$	−355.445	+	298.253i	−0.493673	+	0.414241i
$721$		−	288.444i		−	0.400061i
$722$		0			0
$723$	1430.00			1.97787
$724$	−625.753	−	745.743i	−0.864300	−	1.03003i
$725$	−55.4927	+	152.465i	−0.0765417	+	0.210296i
$726$	−47.4060	+	268.853i	−0.0652975	+	0.370320i
$727$	120.685	+	684.441i	0.166005	+	0.941460i	0.948022	+	0.318204i	$0.103080\pi$
$727$	120.685	+	684.441i	0.166005	+	0.941460i	−0.782018	+	0.623256i	$0.785809\pi$
$728$	305.400	−	111.157i	0.419506	−	0.152688i
$729$	90.5000	−	156.751i	0.124143	−	0.215021i
$730$	1311.45	−	757.166i	1.79651	−	1.03721i
$731$	−229.813	−	192.836i	−0.314382	−	0.263798i
$732$	834.337	−	994.325i	1.13981	−	1.35837i
$733$	−80.0000	−	138.564i	−0.109141	−	0.189037i	0.806282	−	0.591532i	$-0.201477\pi$
$733$	−80.0000	−	138.564i	−0.109141	−	0.189037i	−0.915422	+	0.402495i	$0.868143\pi$
$734$	−156.125	−	90.1388i	−0.212704	−	0.122805i
$735$	−118.384	−	325.259i	−0.161067	−	0.442529i
$736$	−1118.49	+	197.221i	−1.51969	+	0.267963i
$737$	−390.585	−	68.8707i	−0.529966	−	0.0934474i
$738$	−488.640	−	177.850i	−0.662114	−	0.240990i
$739$	787.494	−	660.786i	1.06562	−	0.894162i	0.0709721	−	0.997478i	$-0.477390\pi$
$739$	787.494	−	660.786i	1.06562	−	0.894162i	0.994649	+	0.103316i	$0.0329454\pi$
$740$			778.799i			1.05243i
$741$		0			0
$742$	−1365.00			−1.83962
$743$	−338.370	−	403.254i	−0.455411	−	0.542737i	0.488663	−	0.872473i	$-0.337485\pi$
$743$	−338.370	−	403.254i	−0.455411	−	0.542737i	−0.944073	+	0.329735i	$0.893040\pi$
$744$	801.561	−	2202.27i	1.07737	−	2.96004i
$745$	48.6215	−	275.746i	0.0652637	−	0.370129i
$746$	273.149	+	1549.10i	0.366151	+	2.07655i
$747$	−150.351	+	54.7232i	−0.201273	+	0.0732573i
$748$	−675.000	+	1169.13i	−0.902406	+	1.56301i
$749$	−327.862	+	189.291i	−0.437734	+	0.252726i
$750$	−1354.37	−	1136.45i	−1.80582	−	1.51526i
$751$	−23.1760	+	27.6201i	−0.0308602	+	0.0367778i	−0.781254	−	0.624213i	$-0.785420\pi$
$751$	−23.1760	+	27.6201i	−0.0308602	+	0.0367778i	0.750394	+	0.660991i	$0.229864\pi$
$752$	−145.000	−	251.147i	−0.192819	−	0.333973i
$753$	−1255.24	−	724.716i	−1.66699	−	0.962438i
$754$	80.1561	+	220.227i	0.106308	+	0.292078i
$755$	−142.031	+	25.0439i	−0.188121	+	0.0331707i
$756$	−798.924	−	140.872i	−1.05678	−	0.186339i
$757$	−56.3816	−	20.5212i	−0.0744803	−	0.0271086i	0.304511	−	0.952509i	$-0.401507\pi$
$757$	−56.3816	−	20.5212i	−0.0744803	−	0.0271086i	−0.378992	+	0.925400i	$0.623729\pi$
$758$	1344.41	−	1128.09i	1.77363	−	1.48825i
$759$			1261.94i			1.66264i
$760$		0			0
$761$	−655.000			−0.860710			−0.430355	−	0.902660i	$-0.641612\pi$
$761$	−655.000			−0.860710			−0.430355	+	0.902660i	$0.641612\pi$
$762$	−1084.64	−	1292.62i	−1.42341	−	1.69635i
$763$	339.122	−	931.730i	0.444459	−	1.22114i
$764$	−301.627	+	1710.61i	−0.394800	+	2.23902i
$765$	−41.6756	−	236.354i	−0.0544779	−	0.308959i
$766$	684.096	−	248.991i	0.893076	−	0.325053i
$767$	32.5000	−	56.2917i	0.0423729	−	0.0733920i
$768$	1433.23	−	827.474i	1.86618	−	1.07744i
$769$	−141.718	−	118.916i	−0.184289	−	0.154637i	0.545976	−	0.837801i	$-0.316159\pi$
$769$	−141.718	−	118.916i	−0.184289	−	0.154637i	−0.730265	+	0.683164i	$0.760603\pi$
$770$	−463.521	+	552.403i	−0.601975	+	0.717406i
$771$	754.000	+	1305.97i	0.977951	+	1.69386i
$772$	2079.58	+	1200.65i	2.69376	+	1.55524i
$773$	109.752	+	301.542i	0.141982	+	0.390093i	0.990219	−	0.139525i	$-0.0445576\pi$
$773$	109.752	+	301.542i	0.141982	+	0.390093i	−0.848236	+	0.529618i	$0.822335\pi$
$774$	−284.062	+	50.0878i	−0.367005	+	0.0647129i
$775$	319.570	+	56.3488i	0.412348	+	0.0727081i
$776$	−2076.72	−	755.865i	−2.67619	−	0.974052i
$777$	298.757	−	250.687i	0.384501	−	0.322635i
$778$		−	1723.45i		−	2.21524i
$779$		0			0
$780$	−468.000			−0.600000
$781$	−695.281	−	828.604i	−0.890245	−	1.06095i
$782$	647.415	−	1778.76i	0.827896	−	2.27463i
$783$	56.4357	−	320.063i	0.0720762	−	0.408764i
$784$	−120.859	−	685.426i	−0.154157	−	0.874268i
$785$	−37.5877	+	13.6808i	−0.0478824	+	0.0174278i
$786$	−728.000	+	1260.93i	−0.926209	+	1.60424i
$787$	59.3275	−	34.2527i	0.0753843	−	0.0435232i	−0.461834	−	0.886966i	$-0.652808\pi$
$787$	59.3275	−	34.2527i	0.0753843	−	0.0435232i	0.537218	+	0.843443i	$0.319475\pi$
$788$	−620.496	−	520.658i	−0.787431	−	0.660733i
$789$	718.457	−	856.224i	0.910592	−	1.08520i
$790$	−260.000	−	450.333i	−0.329114	−	0.570042i
$791$	−530.825	−	306.472i	−0.671081	−	0.387449i
$792$	246.634	+	677.622i	0.311407	+	0.855583i
$793$	142.031	−	25.0439i	0.179106	−	0.0315812i
$794$	2663.08	+	469.573i	3.35401	+	0.591402i
$795$	1026.14	+	373.486i	1.29075	+	0.469794i
$796$	−848.011	+	711.566i	−1.06534	+	0.893927i
$797$			1258.34i			1.57884i	0.613852	+	0.789421i	$0.289619\pi$
$797$			1258.34i			1.57884i	−0.613852	+	0.789421i	$0.710381\pi$
$798$		0			0
$799$	150.000			0.187735
$800$	−187.726	−	223.723i	−0.234657	−	0.279654i
$801$		0			0
$802$	180.594	−	1024.20i	0.225180	−	1.27706i
$803$	−182.331	−	1034.05i	−0.227062	−	1.28773i
$804$	1209.38	−	440.180i	1.50421	−	0.547487i
$805$	350.000	−	606.218i	0.434783	−	0.753066i
$806$	405.925	−	234.361i	0.503629	−	0.290770i
$807$	298.757	+	250.687i	0.370207	+	0.310641i
$808$	−579.401	+	690.503i	−0.717080	+	0.854583i
$809$	3.50000	+	6.06218i	0.00432633	+	0.00749342i	0.868180	−	0.496249i	$-0.165290\pi$
$809$	3.50000	+	6.06218i	0.00432633	+	0.00749342i	−0.863854	+	0.503742i	$0.831956\pi$
$810$	1261.49	+	728.321i	1.55739	+	0.899162i
$811$	−351.454	−	965.611i	−0.433359	−	1.19064i	−0.943738	−	0.330694i	$-0.892717\pi$
$811$	−351.454	−	965.611i	−0.433359	−	1.19064i	0.510380	−	0.859949i	$-0.329505\pi$
$812$	−798.924	+	140.872i	−0.983897	+	0.173488i
$813$	−372.831	−	65.7402i	−0.458587	−	0.0808613i
$814$	732.960	+	266.776i	0.900443	+	0.327734i
$815$	−827.328	+	694.211i	−1.01513	+	0.851792i
$816$		−	1568.41i		−	1.92208i
$817$		0			0
$818$	130.000			0.158924
$819$	46.3521	+	55.2403i	0.0565959	+	0.0674484i
$820$	−443.942	+	1219.72i	−0.541392	+	1.48746i
$821$	146.212	−	829.208i	0.178090	−	1.01000i	−0.756427	−	0.654078i	$-0.773057\pi$
$821$	146.212	−	829.208i	0.178090	−	1.01000i	0.934517	−	0.355919i	$-0.115832\pi$
$822$	282.178	+	1600.31i	0.343283	+	1.94685i
$823$	−728.262	+	265.066i	−0.884887	+	0.322072i	−0.744180	−	0.667979i	$-0.767160\pi$
$823$	−728.262	+	265.066i	−0.884887	+	0.322072i	−0.140707	+	0.990051i	$0.544937\pi$
$824$	−520.000	+	900.666i	−0.631068	+	1.09304i
$825$	−281.025	+	162.250i	−0.340636	+	0.196666i
$826$	248.964	+	208.906i	0.301410	+	0.252913i
$827$	813.479	−	969.466i	0.983650	−	1.17227i	−0.00139937	−	0.999999i	$-0.500445\pi$
$827$	813.479	−	969.466i	0.983650	−	1.17227i	0.985050	−	0.172270i	$-0.0551101\pi$
$828$	−630.000	−	1091.19i	−0.760870	−	1.31786i
$829$	1358.29	+	784.207i	1.63846	+	0.945968i	0.981362	+	0.192166i	$0.0615513\pi$
$829$	1358.29	+	784.207i	1.63846	+	0.945968i	0.657102	+	0.753802i	$0.271782\pi$
$830$	197.307	+	542.098i	0.237720	+	0.653130i
$831$	−177.539	+	31.3049i	−0.213645	+	0.0376713i
$832$	−3.55077	−	0.626097i	−0.00426776	−	0.000752521i
$833$	338.289	+	123.127i	0.406110	+	0.147812i
$834$	497.929	−	417.812i	0.597037	−	0.500974i
$835$			490.355i			0.587251i
$836$		0			0
$837$	−650.000			−0.776583
$838$	259.572	+	309.345i	0.309751	+	0.369147i
$839$	−394.615	+	1084.20i	−0.470339	+	1.29225i	0.447140	+	0.894464i	$0.352443\pi$
$839$	−394.615	+	1084.20i	−0.470339	+	1.29225i	−0.917480	+	0.397783i	$0.869780\pi$
$840$	225.743	−	1280.25i	0.268741	−	1.52411i
$841$	89.6025	+	508.161i	0.106543	+	0.604234i
$842$	2137.80	−	778.096i	2.53896	−	0.924104i
$843$	520.000	−	900.666i	0.616845	−	1.06841i
$844$	1826.66	−	1054.62i	2.16429	−	1.24955i
$845$	478.012	+	401.099i	0.565694	+	0.474674i
$846$	92.7041	−	110.481i	0.109579	−	0.130592i
$847$	−52.5000	−	90.9327i	−0.0619835	−	0.107359i
$848$	1901.60	+	1097.89i	2.24246	+	1.29468i
$849$	−394.615	−	1084.20i	−0.464799	−	1.27703i
$850$	479.355	−	84.5232i	0.563947	−	0.0994390i
$851$	−745.663	−	131.480i	−0.876219	−	0.154501i
$852$	3298.32	+	1200.49i	3.87127	+	1.40903i
$853$	306.418	−	257.115i	0.359224	−	0.301424i	−0.445258	−	0.895403i	$-0.646888\pi$
$853$	306.418	−	257.115i	0.359224	−	0.301424i	0.804481	+	0.593978i	$0.202443\pi$
$854$			721.110i			0.844391i
$855$		0			0
$856$	1365.00			1.59463
$857$	101.975	+	121.529i	0.118990	+	0.141807i	0.822251	−	0.569125i	$-0.192718\pi$
$857$	101.975	+	121.529i	0.118990	+	0.141807i	−0.703261	+	0.710932i	$0.748273\pi$
$858$	−160.312	+	440.454i	−0.186844	+	0.513350i
$859$	248.664	−	1410.24i	0.289481	−	1.64173i	−0.399344	−	0.916801i	$-0.630762\pi$
$859$	248.664	−	1410.24i	0.289481	−	1.64173i	0.688825	−	0.724927i	$-0.258127\pi$
$860$	125.027	+	709.062i	0.145380	+	0.824490i
$861$	610.800	−	222.313i	0.709408	−	0.258203i
$862$	−780.000	+	1351.00i	−0.904872	+	1.56728i
$863$	−112.410	+	64.8999i	−0.130255	+	0.0752027i	−0.563712	−	0.825972i	$-0.690627\pi$
$863$	−112.410	+	64.8999i	−0.130255	+	0.0752027i	0.433457	+	0.901174i	$0.357294\pi$
$864$	448.136	+	376.031i	0.518676	+	0.435221i
$865$	315.194	−	375.634i	0.364386	−	0.434259i
$866$	−1326.00	−	2296.70i	−1.53118	−	2.65208i
$867$	−199.840	−	115.378i	−0.230496	−	0.133077i
$868$	554.927	+	1524.65i	0.639317	+	1.75651i
$869$	−355.077	+	62.6097i	−0.408605	+	0.0720480i
$870$	923.201	+	162.785i	1.06115	+	0.187110i
$871$	134.376	+	48.9089i	0.154278	+	0.0561526i
$872$	−2738.61	+	2297.97i	−3.14061	+	2.63528i
$873$		−	490.355i		−	0.561690i
$874$		0			0
$875$	680.000			0.777143
$876$	2190.14	+	2610.10i	2.50015	+	2.97957i
$877$	134.416	−	369.304i	0.153268	−	0.421099i	−0.839167	−	0.543874i	$-0.816957\pi$
$877$	134.416	−	369.304i	0.153268	−	0.421099i	0.992435	+	0.122775i	$0.0391792\pi$
$878$	−496.634	+	2816.55i	−0.565642	+	3.20792i
$879$	−137.703	−	780.953i	−0.156659	−	0.888456i
$880$	1090.04	−	396.743i	1.23869	−	0.450845i
$881$	−375.000	+	649.519i	−0.425653	+	0.737252i	−0.996481	−	0.0838173i	$-0.973289\pi$
$881$	−375.000	+	649.519i	−0.425653	+	0.737252i	0.570828	+	0.821069i	$0.306622\pi$
$882$	299.760	−	173.066i	0.339864	−	0.196220i
$883$	91.9253	+	77.1345i	0.104106	+	0.0873551i	0.693355	−	0.720596i	$-0.256132\pi$
$883$	91.9253	+	77.1345i	0.104106	+	0.0873551i	−0.589249	+	0.807951i	$0.700576\pi$
$884$	312.876	−	372.872i	0.353933	−	0.421801i
$885$	−130.000	−	225.167i	−0.146893	−	0.254426i
$886$	−2092.07	−	1207.86i	−2.36126	−	1.36327i
$887$	−291.028	−	799.594i	−0.328104	−	0.901459i	−0.988591	−	0.150622i	$-0.951872\pi$
$887$	−291.028	−	799.594i	−0.328104	−	0.901459i	0.660487	−	0.750837i	$-0.270350\pi$
$888$	−1384.80	+	244.178i	−1.55946	+	0.274975i
$889$	639.139	+	112.698i	0.718942	+	0.126769i
$890$		0			0
$891$	773.705	−	649.215i	0.868356	−	0.728637i
$892$			1817.20i			2.03722i
$893$		0			0
$894$	910.000			1.01790
$895$	92.7041	+	110.481i	0.103580	+	0.123442i
$896$	−215.805	+	592.919i	−0.240854	+	0.661740i
$897$	79.0099	−	448.088i	0.0880824	−	0.499540i
$898$	22.5743	+	128.025i	0.0251384	+	0.142567i
$899$	−610.800	+	222.313i	−0.679422	+	0.247289i
$900$	162.000	−	280.592i	0.180000	−	0.311769i
$901$	−983.587	+	567.874i	−1.09166	+	0.630271i
$902$	995.858	+	835.624i	1.10406	+	0.926412i
$903$	231.760	−	276.201i	0.256656	−	0.305871i
$904$	1105.00	+	1913.92i	1.22235	+	2.11716i
$905$	−374.700	−	216.333i	−0.414033	−	0.239042i
$906$	−160.312	−	440.454i	−0.176945	−	0.486153i
$907$	635.589	−	112.071i	0.700759	−	0.123563i	0.188094	−	0.982151i	$-0.439769\pi$
$907$	635.589	−	112.071i	0.700759	−	0.123563i	0.512666	+	0.858588i	$0.328658\pi$
$908$	−2268.95	−	400.076i	−2.49884	−	0.440613i
$909$	−187.939	−	68.4040i	−0.206753	−	0.0752520i
$910$	199.172	−	167.125i	0.218870	−	0.183654i
$911$		−	1225.89i		−	1.34565i	−0.739802	−	0.672825i	$-0.765081\pi$
$911$		−	1225.89i		−	1.34565i	0.739802	−	0.672825i	$-0.234919\pi$
$912$		0			0
$913$	400.000			0.438116
$914$	−1749.79	−	2085.32i	−1.91443	−	2.28153i
$915$	197.307	−	542.098i	0.215636	−	0.592456i
$916$	250.053	−	1418.12i	0.272984	−	1.54817i
$917$	−97.2430	−	551.492i	−0.106045	−	0.601409i
$918$	−916.200	+	333.470i	−0.998040	+	0.363257i
$919$	256.500	−	444.271i	0.279108	−	0.483429i	−0.692056	−	0.721844i	$-0.743295\pi$
$919$	256.500	−	444.271i	0.279108	−	0.483429i	0.971163	+	0.238416i	$0.0766280\pi$
$920$	−2185.75	+	1261.94i	−2.37581	+	1.37168i
$921$	657.266	+	551.512i	0.713644	+	0.598818i
$922$	−1789.19	+	2132.27i	−1.94055	+	2.31266i
$923$	195.000	+	337.750i	0.211268	+	0.365926i
$924$	−1405.12	−	811.249i	−1.52070	−	0.877975i
$925$	−66.5912	−	182.958i	−0.0719905	−	0.197792i
$926$	1242.77	−	219.134i	1.34209	−	0.236646i
$927$	−227.250	−	40.0702i	−0.245145	−	0.0432257i
$928$	549.720	+	200.082i	0.592371	+	0.215605i
$929$	−932.276	+	782.273i	−1.00353	+	0.842059i	−0.987469	−	0.157812i	$-0.949556\pi$
$929$	−932.276	+	782.273i	−1.00353	+	0.842059i	−0.0160574	+	0.999871i	$0.505111\pi$
$930$		−	1874.89i		−	2.01601i
$931$		0			0
$932$	2430.00			2.60730
$933$	−915.453	−	1090.99i	−0.981193	−	1.16934i
$934$	86.3220	−	237.168i	0.0924218	−	0.253927i
$935$	−104.189	+	590.885i	−0.111432	+	0.631962i
$936$	−45.1485	−	256.050i	−0.0482356	−	0.273558i
$937$	1028.96	−	374.512i	1.09815	−	0.399693i	0.271514	−	0.962435i	$-0.412476\pi$
$937$	1028.96	−	374.512i	1.09815	−	0.399693i	0.826633	+	0.562742i	$0.190253\pi$
$938$	−357.500	+	619.208i	−0.381130	+	0.660137i
$939$	−390.312	+	225.347i	−0.415668	+	0.239986i
$940$	−275.776	−	231.404i	−0.293379	−	0.246174i
$941$	−706.869	+	842.414i	−0.751189	+	0.895233i	−0.997257	−	0.0740202i	$-0.976417\pi$
$941$	−706.869	+	842.414i	−0.751189	+	0.895233i	0.246067	+	0.969253i	$0.420862\pi$
$942$	−65.0000	−	112.583i	−0.0690021	−	0.119515i
$943$	−1092.87	−	630.971i	−1.15893	−	0.669111i
$944$	−178.810	−	491.276i	−0.189417	−	0.520419i
$945$	−355.077	+	62.6097i	−0.375743	+	0.0662537i
$946$	710.155	+	125.219i	0.750692	+	0.132367i
$947$	−601.403	−	218.893i	−0.635062	−	0.231143i	0.00437131	−	0.999990i	$-0.498609\pi$
$947$	−601.403	−	218.893i	−0.635062	−	0.231143i	−0.639433	+	0.768847i	$0.720831\pi$
$948$	896.272	−	752.062i	0.945435	−	0.793314i
$949$			378.583i			0.398928i
$950$		0			0
$951$	13.0000			0.0136698
$952$	869.101	+	1035.75i	0.912922	+	1.08798i
$953$	399.547	−	1097.75i	0.419252	−	1.15189i	−0.532878	−	0.846192i	$-0.678889\pi$
$953$	399.547	−	1097.75i	0.419252	−	1.15189i	0.952130	−	0.305694i	$-0.0988884\pi$
$954$	−189.624	+	1075.41i	−0.198767	+	1.12726i
$955$	134.056	+	760.272i	0.140373	+	0.796096i
$956$	1666.08	−	606.402i	1.74276	−	0.634311i
$957$	325.000	−	562.917i	0.339603	−	0.588210i
$958$	−1155.32	+	667.027i	−1.20598	+	0.696270i
$959$	−478.778	−	401.742i	−0.499247	−	0.418918i
$960$	−9.27041	+	11.0481i	−0.00965668	+	0.0115084i
$961$	169.500	+	293.583i	0.176379	+	0.305497i
$962$	−243.555	−	140.616i	−0.253176	−	0.146171i
$963$	103.586	+	284.601i	0.107566	+	0.295536i
$964$	3515.27	−	619.836i	3.64654	−	0.642984i
$965$	1051.03	+	185.325i	1.08915	+	0.192046i
$966$	2137.80	+	778.096i	2.21304	+	0.805482i
$967$	−773.705	+	649.215i	−0.800108	+	0.671371i	−0.948225	−	0.317599i	$-0.897123\pi$
$967$	−773.705	+	649.215i	−0.800108	+	0.671371i	0.148117	+	0.988970i	$0.452679\pi$
$968$			378.583i			0.391098i
$969$		0			0
$970$	−1768.00			−1.82268
$971$	−486.697	−	580.023i	−0.501233	−	0.597346i	0.454805	−	0.890591i	$-0.349709\pi$
$971$	−486.697	−	580.023i	−0.501233	−	0.597346i	−0.956037	+	0.293246i	$0.905265\pi$
$972$	−621.518	+	1707.61i	−0.639422	+	1.75680i
$973$	−43.4120	+	246.202i	−0.0446167	+	0.253034i
$974$	325.069	+	1843.56i	0.333747	+	1.89277i
$975$	109.944	−	40.0164i	0.112763	−	0.0410424i
$976$	580.000	−	1004.59i	0.594262	−	1.02929i
$977$	518.335	−	299.261i	0.530537	−	0.306306i	−0.210698	−	0.977551i	$-0.567574\pi$
$977$	518.335	−	299.261i	0.530537	−	0.306306i	0.741235	+	0.671245i	$0.234240\pi$
$978$	−2688.82	−	2256.18i	−2.74930	−	2.30694i
$979$		0			0
$980$	−432.000	−	748.246i	−0.440816	−	0.763516i
$981$	−686.950	−	396.611i	−0.700255	−	0.404292i
$982$	779.364	+	2141.29i	0.793650	+	2.18054i
$983$	−56.8124	+	10.0176i	−0.0577949	+	0.0101908i	−0.202471	−	0.979288i	$-0.564897\pi$
$983$	−56.8124	+	10.0176i	−0.0577949	+	0.0101908i	0.144676	+	0.989479i	$0.453786\pi$
$984$	−2308.00	−	406.963i	−2.34553	−	0.413581i
$985$	−338.289	−	123.127i	−0.343441	−	0.125002i
$986$	−746.893	+	626.718i	−0.757498	+	0.635617i
$987$			180.278i			0.182652i
$988$		0			0
$989$	−700.000			−0.707786
$990$	370.817	+	441.922i	0.374562	+	0.446386i
$991$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$991$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$992$	203.168	−	1152.23i	0.204807	−	1.16152i
$993$	−124.158	−	704.138i	−0.125034	−	0.709101i
$994$	−1832.40	+	666.939i	−1.84346	+	0.670965i
$995$	−246.000	+	426.084i	−0.247236	+	0.428226i
$996$	−1124.10	+	648.999i	−1.12861	+	0.651606i
$997$	−130.228	−	109.274i	−0.130619	−	0.109603i	0.575138	−	0.818057i	$-0.304949\pi$
$997$	−130.228	−	109.274i	−0.130619	−	0.109603i	−0.705757	+	0.708454i	$0.749393\pi$
$998$	−880.689	+	1049.56i	−0.882454	+	1.05167i
$999$	195.000	+	337.750i	0.195195	+	0.338088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.d.127.2		12
19.2	odd	18	inner	361.3.f.d.299.2		12
19.3	odd	18	inner	361.3.f.d.307.2		12
19.4	even	9		19.3.b.b.18.2	yes	2
19.5	even	9	inner	361.3.f.d.116.2		12
19.6	even	9		361.3.d.b.69.2		4
19.7	even	3	inner	361.3.f.d.333.1		12
19.8	odd	6	inner	361.3.f.d.262.1		12
19.9	even	9		361.3.d.b.293.1		4
19.10	odd	18		361.3.d.b.293.2		4
19.11	even	3	inner	361.3.f.d.262.2		12
19.12	odd	6	inner	361.3.f.d.333.2		12
19.13	odd	18		361.3.d.b.69.1		4
19.14	odd	18	inner	361.3.f.d.116.1		12
19.15	odd	18		19.3.b.b.18.1	✓	2
19.16	even	9	inner	361.3.f.d.307.1		12
19.17	even	9	inner	361.3.f.d.299.1		12
19.18	odd	2	inner	361.3.f.d.127.1		12
57.23	odd	18		171.3.c.b.37.1		2
57.53	even	18		171.3.c.b.37.2		2
76.15	even	18		304.3.e.d.113.1		2
76.23	odd	18		304.3.e.d.113.2		2
95.4	even	18		475.3.c.b.151.1		2
95.23	odd	36		475.3.d.b.474.4		4
95.34	odd	18		475.3.c.b.151.2		2
95.42	odd	36		475.3.d.b.474.1		4
95.53	even	36		475.3.d.b.474.2		4
95.72	even	36		475.3.d.b.474.3		4
152.53	odd	18		1216.3.e.g.1025.1		2
152.61	even	18		1216.3.e.g.1025.2		2
152.91	even	18		1216.3.e.h.1025.2		2
152.99	odd	18		1216.3.e.h.1025.1		2
228.23	even	18		2736.3.o.d.721.2		2
228.167	odd	18		2736.3.o.d.721.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.b.b.18.1	✓	2	19.15	odd	18
19.3.b.b.18.2	yes	2	19.4	even	9
171.3.c.b.37.1		2	57.23	odd	18
171.3.c.b.37.2		2	57.53	even	18
304.3.e.d.113.1		2	76.15	even	18
304.3.e.d.113.2		2	76.23	odd	18
361.3.d.b.69.1		4	19.13	odd	18
361.3.d.b.69.2		4	19.6	even	9
361.3.d.b.293.1		4	19.9	even	9
361.3.d.b.293.2		4	19.10	odd	18
361.3.f.d.116.1		12	19.14	odd	18	inner
361.3.f.d.116.2		12	19.5	even	9	inner
361.3.f.d.127.1		12	19.18	odd	2	inner
361.3.f.d.127.2		12	1.1	even	1	trivial
361.3.f.d.262.1		12	19.8	odd	6	inner
361.3.f.d.262.2		12	19.11	even	3	inner
361.3.f.d.299.1		12	19.17	even	9	inner
361.3.f.d.299.2		12	19.2	odd	18	inner
361.3.f.d.307.1		12	19.16	even	9	inner
361.3.f.d.307.2		12	19.3	odd	18	inner
361.3.f.d.333.1		12	19.7	even	3	inner
361.3.f.d.333.2		12	19.12	odd	6	inner
475.3.c.b.151.1		2	95.4	even	18
475.3.c.b.151.2		2	95.34	odd	18
475.3.d.b.474.1		4	95.42	odd	36
475.3.d.b.474.2		4	95.53	even	36
475.3.d.b.474.3		4	95.72	even	36
475.3.d.b.474.4		4	95.23	odd	36
1216.3.e.g.1025.1		2	152.53	odd	18
1216.3.e.g.1025.2		2	152.61	even	18
1216.3.e.h.1025.1		2	152.99	odd	18
1216.3.e.h.1025.2		2	152.91	even	18
2736.3.o.d.721.1		2	228.167	odd	18
2736.3.o.d.721.2		2	228.23	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.31760 + 2.76201i) q^{2} +(-1.23317 + 3.38811i) q^{3} +(-1.56283 + 8.86327i) q^{4} +(0.694593 + 3.93923i) q^{5} +(-12.2160 + 4.44626i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(-3.06418 - 2.57115i) q^{9} +O(q^{10})\)	\(q+(2.31760 + 2.76201i) q^{2} +(-1.23317 + 3.38811i) q^{3} +(-1.56283 + 8.86327i) q^{4} +(0.694593 + 3.93923i) q^{5} +(-12.2160 + 4.44626i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(-3.06418 - 2.57115i) q^{9} +(-9.27041 + 11.0481i) q^{10} +(5.00000 + 8.66025i) q^{11} +(-28.1025 - 16.2250i) q^{12} +(-1.23317 - 3.38811i) q^{13} +(17.7539 - 3.13049i) q^{14} +(-14.2031 - 2.50439i) q^{15} +(-27.2511 - 9.91858i) q^{16} +(11.4907 - 9.64181i) q^{17} -14.4222i q^{18} -36.0000 q^{20} +(11.5880 + 13.8101i) q^{21} +(-12.3317 + 33.8811i) q^{22} +(6.07769 - 34.4683i) q^{23} +(-11.2871 - 64.0125i) q^{24} +(8.45723 - 3.07818i) q^{25} +(6.50000 - 11.2583i) q^{26} +(-15.6125 + 9.01388i) q^{27} +(34.4720 + 28.9254i) q^{28} +(-11.5880 + 13.8101i) q^{29} +(-26.0000 - 45.0333i) q^{30} +(31.2250 + 18.0278i) q^{31} +(-11.0985 - 30.4930i) q^{32} +(-35.5077 + 6.26097i) q^{33} +(53.2616 + 9.39146i) q^{34} +(18.7939 + 6.84040i) q^{35} +(27.5776 - 23.1404i) q^{36} -21.6333i q^{37} +13.0000 q^{39} +(-46.3521 - 55.2403i) q^{40} +(12.3317 - 33.8811i) q^{41} +(-11.2871 + 64.0125i) q^{42} +(-3.47296 - 19.6962i) q^{43} +(-84.5723 + 30.7818i) q^{44} +(8.00000 - 13.8564i) q^{45} +(109.287 - 63.0971i) q^{46} +(7.66044 + 6.42788i) q^{47} +(67.2105 - 80.0984i) q^{48} +(12.0000 + 20.7846i) q^{49} +(28.1025 + 16.2250i) q^{50} +(18.4976 + 50.8216i) q^{51} +(31.9570 - 5.63488i) q^{52} +(-74.5663 - 13.1480i) q^{53} +(-61.0800 - 22.2313i) q^{54} +(-30.6418 + 25.7115i) q^{55} +90.1388i q^{56} -65.0000 q^{58} +(11.5880 + 13.8101i) q^{59} +(44.3942 - 121.972i) q^{60} +(-6.94593 + 39.3923i) q^{61} +(22.5743 + 128.025i) q^{62} +(-18.7939 + 6.84040i) q^{63} +(0.500000 - 0.866025i) q^{64} +(12.4900 - 7.21110i) q^{65} +(-99.5858 - 83.5624i) q^{66} +(-25.4936 + 30.3821i) q^{67} +(67.5000 + 116.913i) q^{68} +(109.287 + 63.0971i) q^{69} +(24.6634 + 67.7622i) q^{70} +(-106.523 + 18.7829i) q^{71} +(71.0155 + 12.5219i) q^{72} +(-98.6677 - 35.9121i) q^{73} +(59.7515 - 50.1374i) q^{74} +32.4500i q^{75} +50.0000 q^{77} +(30.1288 + 35.9062i) q^{78} +(-12.3317 + 33.8811i) q^{79} +(20.1432 - 114.238i) q^{80} +(-17.5385 - 99.4656i) q^{81} +(122.160 - 44.4626i) q^{82} +(20.0000 - 34.6410i) q^{83} +(-140.512 + 81.1249i) q^{84} +(45.9627 + 38.5673i) q^{85} +(46.3521 - 55.2403i) q^{86} +(-32.5000 - 56.2917i) q^{87} +(-156.125 - 90.1388i) q^{88} +(56.8124 - 10.0176i) q^{90} +(-17.7539 - 3.13049i) q^{91} +(296.003 + 107.736i) q^{92} +(-99.5858 + 83.5624i) q^{93} +36.0555i q^{94} +117.000 q^{96} +(78.7985 + 93.9084i) q^{97} +(-29.5961 + 81.3146i) q^{98} +(6.94593 - 39.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{7}+O(q^{10}) \) 12 * q + 30 * q^7	\( 12 q + 30 q^{7} + 60 q^{11} - 432 q^{20} + 78 q^{26} - 312 q^{30} + 156 q^{39} + 96 q^{45} + 144 q^{49} - 780 q^{58} + 6 q^{64} + 810 q^{68} + 600 q^{77} + 240 q^{83} - 390 q^{87} + 1404 q^{96}+O(q^{100}) \) 12 * q + 30 * q^7 + 60 * q^11 - 432 * q^20 + 78 * q^26 - 312 * q^30 + 156 * q^39 + 96 * q^45 + 144 * q^49 - 780 * q^58 + 6 * q^64 + 810 * q^68 + 600 * q^77 + 240 * q^83 - 390 * q^87 + 1404 * q^96

Introduction

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