LMFDB - Embedded newform 19.3.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,3,Mod(8,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

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("19.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.d (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:	$0.517712502285$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.1
Root			$1.56632 - 2.71294i$ of defining polynomial
Character	$\chi$	$=$	19.8
Dual form			19.3.d.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.90671 - 1.67819i) q^{2} +(-3.29225 - 1.90078i) q^{3} +(3.63264 + 6.29191i) q^{4} +(3.47303 - 6.01546i) q^{5} +(6.37974 + 11.0500i) q^{6} -1.22892 q^{7} -10.9595i q^{8} +(2.72593 + 4.72145i) q^{9} +O(q^{10})$	\(q+(-2.90671 - 1.67819i) q^{2} +(-3.29225 - 1.90078i) q^{3} +(3.63264 + 6.29191i) q^{4} +(3.47303 - 6.01546i) q^{5} +(6.37974 + 11.0500i) q^{6} -1.22892 q^{7} -10.9595i q^{8} +(2.72593 + 4.72145i) q^{9} +(-20.1902 + 11.6568i) q^{10} -0.0363521 q^{11} -27.6194i q^{12} +(14.6268 - 8.44481i) q^{13} +(3.57212 + 2.06236i) q^{14} +(-22.8681 + 13.2029i) q^{15} +(-3.86156 + 6.68842i) q^{16} +(-4.59329 + 7.95581i) q^{17} -18.2985i q^{18} +(12.7864 + 14.0537i) q^{19} +50.4650 q^{20} +(4.04592 + 2.33591i) q^{21} +(0.105665 + 0.0610058i) q^{22} +(-4.87974 - 8.45195i) q^{23} +(-20.8316 + 36.0814i) q^{24} +(-11.6238 - 20.1331i) q^{25} -56.6879 q^{26} +13.4885i q^{27} +(-4.46423 - 7.73228i) q^{28} +(4.50339 - 2.60003i) q^{29} +88.6280 q^{30} -44.3727i q^{31} +(-15.5160 + 8.95814i) q^{32} +(0.119680 + 0.0690974i) q^{33} +(26.7027 - 15.4168i) q^{34} +(-4.26808 + 7.39254i) q^{35} +(-19.8046 + 34.3026i) q^{36} +45.5661i q^{37} +(-13.5817 - 62.3081i) q^{38} -64.2069 q^{39} +(-65.9264 - 38.0626i) q^{40} +(50.0829 + 28.9153i) q^{41} +(-7.84020 - 13.5796i) q^{42} +(15.1574 - 26.2534i) q^{43} +(-0.132054 - 0.228724i) q^{44} +37.8689 q^{45} +32.7565i q^{46} +(25.5066 + 44.1787i) q^{47} +(25.4264 - 14.6800i) q^{48} -47.4897 q^{49} +78.0280i q^{50} +(30.2445 - 17.4617i) q^{51} +(106.268 + 61.3538i) q^{52} +(10.0847 - 5.82239i) q^{53} +(22.6362 - 39.2071i) q^{54} +(-0.126252 + 0.218675i) q^{55} +13.4684i q^{56} +(-15.3831 - 70.5725i) q^{57} -17.4534 q^{58} +(-17.7409 - 10.2427i) q^{59} +(-166.143 - 95.9229i) q^{60} +(-8.23849 - 14.2695i) q^{61} +(-74.4658 + 128.978i) q^{62} +(-3.34996 - 5.80229i) q^{63} +91.0263 q^{64} -117.316i q^{65} +(-0.231917 - 0.401692i) q^{66} +(-1.83276 + 1.05814i) q^{67} -66.7430 q^{68} +37.1012i q^{69} +(24.8121 - 14.3253i) q^{70} +(-33.7958 - 19.5120i) q^{71} +(51.7447 - 29.8748i) q^{72} +(-28.1064 + 48.6818i) q^{73} +(76.4686 - 132.447i) q^{74} +88.3775i q^{75} +(-41.9762 + 131.503i) q^{76} +0.0446740 q^{77} +(186.631 + 107.751i) q^{78} +(39.8385 + 23.0008i) q^{79} +(26.8226 + 46.4581i) q^{80} +(50.1720 - 86.9004i) q^{81} +(-97.0508 - 168.097i) q^{82} +65.3332 q^{83} +33.9421i q^{84} +(31.9053 + 55.2615i) q^{85} +(-88.1162 + 50.8739i) q^{86} -19.7684 q^{87} +0.398401i q^{88} +(-134.435 + 77.6163i) q^{89} +(-110.074 - 63.5512i) q^{90} +(-17.9753 + 10.3780i) q^{91} +(35.4526 - 61.4058i) q^{92} +(-84.3427 + 146.086i) q^{93} -171.219i q^{94} +(128.947 - 28.1074i) q^{95} +68.1098 q^{96} +(-98.8107 - 57.0484i) q^{97} +(138.039 + 79.6968i) q^{98} +(-0.0990933 - 0.171635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23} - 83 q^{24} - 17 q^{25} - 148 q^{26} + 32 q^{28} - 12 q^{29} + 304 q^{30} + 51 q^{32} + 123 q^{33} - 6 q^{34} - 38 q^{35} - 54 q^{36} - 14 q^{38} - 44 q^{39} - 96 q^{40} + 63 q^{41} - 92 q^{42} - 34 q^{43} - 69 q^{44} - 28 q^{45} + 58 q^{47} - 147 q^{48} + 18 q^{49} + 132 q^{51} + 162 q^{52} - 12 q^{53} + 29 q^{54} - 28 q^{55} - 16 q^{57} + 172 q^{58} - 147 q^{59} - 222 q^{60} + 58 q^{61} - 116 q^{62} + 86 q^{63} + 166 q^{64} + 11 q^{66} + 201 q^{67} - 84 q^{68} - 198 q^{70} - 102 q^{71} + 210 q^{72} + 7 q^{73} + 174 q^{74} - 173 q^{76} - 376 q^{77} + 450 q^{78} + 134 q^{80} + 253 q^{81} - 145 q^{82} + 146 q^{83} - 90 q^{85} - 270 q^{86} - 568 q^{87} - 72 q^{89} - 438 q^{90} - 216 q^{91} + 72 q^{92} - 160 q^{93} + 558 q^{95} + 126 q^{96} + 21 q^{97} + 411 q^{98} - 56 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.90671	−	1.67819i	−1.45335	−	0.839095i	−0.454684	−	0.890653i	$-0.650248\pi$
$2$	−2.90671	−	1.67819i	−1.45335	−	0.839095i	−0.998670	+	0.0515581i	$0.983581\pi$
$3$	−3.29225	−	1.90078i	−1.09742	−	0.633593i	−0.161875	−	0.986811i	$-0.551754\pi$
$3$	−3.29225	−	1.90078i	−1.09742	−	0.633593i	−0.935541	+	0.353218i	$0.885087\pi$
$4$	3.63264	+	6.29191i	0.908159	+	1.57298i
$5$	3.47303	−	6.01546i	0.694606	−	1.20309i	−0.275708	−	0.961241i	$-0.588912\pi$
$5$	3.47303	−	6.01546i	0.694606	−	1.20309i	0.970313	−	0.241851i	$-0.0777544\pi$
$6$	6.37974	+	11.0500i	1.06329	+	1.84167i
$7$	−1.22892			−0.175560			−0.0877802	−	0.996140i	$-0.527977\pi$
$7$	−1.22892			−0.175560			−0.0877802	+	0.996140i	$0.527977\pi$
$8$		−	10.9595i		−	1.36994i
$9$	2.72593	+	4.72145i	0.302881	+	0.524605i
$10$	−20.1902	+	11.6568i	−2.01902	+	1.16568i
$11$	−0.0363521			−0.00330474			−0.00165237	−	0.999999i	$-0.500526\pi$
$11$	−0.0363521			−0.00330474			−0.00165237	+	0.999999i	$0.500526\pi$
$12$		−	27.6194i		−	2.30161i
$13$	14.6268	−	8.44481i	1.12514	−	0.649601i	0.182433	−	0.983218i	$-0.441603\pi$
$13$	14.6268	−	8.44481i	1.12514	−	0.649601i	0.942708	+	0.333618i	$0.108269\pi$
$14$	3.57212	+	2.06236i	0.255151	+	0.147312i
$15$	−22.8681	+	13.2029i	−1.52454	+	0.880195i
$16$	−3.86156	+	6.68842i	−0.241348	+	0.418026i
$17$	−4.59329	+	7.95581i	−0.270194	+	0.467989i	−0.968911	−	0.247408i	$-0.920421\pi$
$17$	−4.59329	+	7.95581i	−0.270194	+	0.467989i	0.698718	+	0.715398i	$0.253754\pi$
$18$		−	18.2985i		−	1.01658i
$19$	12.7864	+	14.0537i	0.672971	+	0.739669i
$19$	12.7864	+	14.0537i	0.672971	+	0.739669i
$20$	50.4650			2.52325
$21$	4.04592	+	2.33591i	0.192663	+	0.111234i
$22$	0.105665	+	0.0610058i	0.00480296	+	0.00277299i
$23$	−4.87974	−	8.45195i	−0.212162	−	0.367476i	0.740229	−	0.672355i	$-0.234717\pi$
$23$	−4.87974	−	8.45195i	−0.212162	−	0.367476i	−0.952391	+	0.304879i	$0.901384\pi$
$24$	−20.8316	+	36.0814i	−0.867983	+	1.50339i
$25$	−11.6238	−	20.1331i	−0.464954	−	0.805323i
$26$	−56.6879			−2.18031
$27$			13.4885i			0.499573i
$28$	−4.46423	−	7.73228i	−0.159437	−	0.276153i
$29$	4.50339	−	2.60003i	0.155289	−	0.0896564i	−0.420342	−	0.907366i	$-0.638090\pi$
$29$	4.50339	−	2.60003i	0.155289	−	0.0896564i	0.575631	+	0.817710i	$0.304756\pi$
$30$	88.6280			2.95427
$31$		−	44.3727i		−	1.43138i	−0.698420	−	0.715689i	$-0.746113\pi$
$31$		−	44.3727i		−	1.43138i	0.698420	−	0.715689i	$-0.253887\pi$
$32$	−15.5160	+	8.95814i	−0.484873	+	0.279942i
$33$	0.119680	+	0.0690974i	0.00362667	+	0.00209386i
$34$	26.7027	−	15.4168i	0.785374	−	0.453436i
$35$	−4.26808	+	7.39254i	−0.121945	+	0.211215i
$36$	−19.8046	+	34.3026i	−0.550128	+	0.952850i
$37$			45.5661i			1.23152i	0.787935	+	0.615758i	$0.211150\pi$
$37$			45.5661i			1.23152i	−0.787935	+	0.615758i	$0.788850\pi$
$38$	−13.5817	−	62.3081i	−0.357413	−	1.63969i
$39$	−64.2069			−1.64633
$40$	−65.9264	−	38.0626i	−1.64816	−	0.951566i
$41$	50.0829	+	28.9153i	1.22153	+	0.705252i	0.965245	−	0.261348i	$-0.0841670\pi$
$41$	50.0829	+	28.9153i	1.22153	+	0.705252i	0.256288	+	0.966600i	$0.417500\pi$
$42$	−7.84020	−	13.5796i	−0.186672	−	0.323325i
$43$	15.1574	−	26.2534i	0.352497	−	0.610543i	−0.634189	−	0.773178i	$-0.718666\pi$
$43$	15.1574	−	26.2534i	0.352497	−	0.610543i	0.986686	+	0.162635i	$0.0519992\pi$
$44$	−0.132054	−	0.228724i	−0.00300123	−	0.00519828i
$45$	37.8689			0.841531
$46$			32.7565i			0.712097i
$47$	25.5066	+	44.1787i	0.542693	+	0.939972i	0.998748	+	0.0500204i	$0.0159286\pi$
$47$	25.5066	+	44.1787i	0.542693	+	0.939972i	−0.456055	+	0.889951i	$0.650738\pi$
$48$	25.4264	−	14.6800i	0.529717	−	0.305832i
$49$	−47.4897			−0.969179
$50$			78.0280i			1.56056i
$51$	30.2445	−	17.4617i	0.593029	−	0.342386i
$52$	106.268	+	61.3538i	2.04362	+	1.17988i
$53$	10.0847	−	5.82239i	0.190277	−	0.109856i	−0.401835	−	0.915712i	$-0.631628\pi$
$53$	10.0847	−	5.82239i	0.190277	−	0.109856i	0.592112	+	0.805856i	$0.298294\pi$
$54$	22.6362	−	39.2071i	0.419189	−	0.726057i
$55$	−0.126252	+	0.218675i	−0.00229549	+	0.00397591i
$56$			13.4684i			0.240507i
$57$	−15.3831	−	70.5725i	−0.269879	−	1.23811i
$58$	−17.4534			−0.300921
$59$	−17.7409	−	10.2427i	−0.300694	−	0.173606i	0.342061	−	0.939678i	$-0.388875\pi$
$59$	−17.7409	−	10.2427i	−0.300694	−	0.173606i	−0.642754	+	0.766072i	$0.722208\pi$
$60$	−166.143	−	95.9229i	−2.76905	−	1.59871i
$61$	−8.23849	−	14.2695i	−0.135057	−	0.233926i	0.790562	−	0.612382i	$-0.209788\pi$
$61$	−8.23849	−	14.2695i	−0.135057	−	0.233926i	−0.925619	+	0.378456i	$0.876455\pi$
$62$	−74.4658	+	128.978i	−1.20106	+	2.08030i
$63$	−3.34996	−	5.80229i	−0.0531739	−	0.0920999i
$64$	91.0263			1.42229
$65$		−	117.316i		−	1.80486i
$66$	−0.231917	−	0.401692i	−0.00351389	−	0.00608624i
$67$	−1.83276	+	1.05814i	−0.0273546	+	0.0157932i	−0.513615	−	0.858021i	$-0.671694\pi$
$67$	−1.83276	+	1.05814i	−0.0273546	+	0.0157932i	0.486260	+	0.873814i	$0.338361\pi$
$68$	−66.7430			−0.981515
$69$			37.1012i			0.537699i
$70$	24.8121	−	14.3253i	0.354459	−	0.204647i
$71$	−33.7958	−	19.5120i	−0.475998	−	0.274817i	0.242749	−	0.970089i	$-0.421951\pi$
$71$	−33.7958	−	19.5120i	−0.475998	−	0.274817i	−0.718747	+	0.695272i	$0.755284\pi$
$72$	51.7447	−	29.8748i	0.718676	−	0.414928i
$73$	−28.1064	+	48.6818i	−0.385020	+	0.666874i	−0.991772	−	0.128017i	$-0.959139\pi$
$73$	−28.1064	+	48.6818i	−0.385020	+	0.666874i	0.606752	+	0.794891i	$0.292472\pi$
$74$	76.4686	−	132.447i	1.03336	−	1.78983i
$75$			88.3775i			1.17837i
$76$	−41.9762	+	131.503i	−0.552319	+	1.73031i
$77$	0.0446740			0.000580181
$78$	186.631	+	107.751i	2.39270	+	1.38143i
$79$	39.8385	+	23.0008i	0.504285	+	0.291149i	0.730481	−	0.682933i	$-0.239296\pi$
$79$	39.8385	+	23.0008i	0.504285	+	0.291149i	−0.226196	+	0.974082i	$0.572629\pi$
$80$	26.8226	+	46.4581i	0.335283	+	0.580727i
$81$	50.1720	−	86.9004i	0.619407	−	1.07284i
$82$	−97.0508	−	168.097i	−1.18355	−	2.04996i
$83$	65.3332			0.787146			0.393573	−	0.919293i	$-0.371239\pi$
$83$	65.3332			0.787146			0.393573	+	0.919293i	$0.371239\pi$
$84$			33.9421i			0.404072i
$85$	31.9053	+	55.2615i	0.375356	+	0.650136i
$86$	−88.1162	+	50.8739i	−1.02461	+	0.591557i
$87$	−19.7684			−0.227223
$88$			0.398401i			0.00452729i
$89$	−134.435	+	77.6163i	−1.51051	+	0.872093i	−0.510585	+	0.859828i	$0.670571\pi$
$89$	−134.435	+	77.6163i	−1.51051	+	0.872093i	−0.999925	+	0.0122654i	$0.996096\pi$
$90$	−110.074	−	63.5512i	−1.22304	−	0.706124i
$91$	−17.9753	+	10.3780i	−0.197530	+	0.114044i
$92$	35.4526	−	61.4058i	0.385355	−	0.667454i
$93$	−84.3427	+	146.086i	−0.906911	+	1.57082i
$94$		−	171.219i		−	1.82148i
$95$	128.947	−	28.1074i	1.35734	−	0.295868i
$96$	68.1098			0.709477
$97$	−98.8107	−	57.0484i	−1.01867	−	0.588128i	−0.104949	−	0.994478i	$-0.533468\pi$
$97$	−98.8107	−	57.0484i	−1.01867	−	0.588128i	−0.913718	+	0.406350i	$0.866801\pi$
$98$	138.039	+	79.6968i	1.40856	+	0.813232i
$99$	−0.0990933	−	0.171635i	−0.00100094	−	0.00173368i
$100$	84.4504	−	146.272i	0.844504	−	1.46272i
$101$	85.7095	+	148.453i	0.848609	+	1.46983i	0.882450	+	0.470406i	$0.155893\pi$
$101$	85.7095	+	148.453i	0.848609	+	1.46983i	−0.0338413	+	0.999427i	$0.510774\pi$
$102$	−117.216			−1.14918
$103$			121.297i			1.17764i	0.808264	+	0.588820i	$0.200407\pi$
$103$			121.297i			1.17764i	−0.808264	+	0.588820i	$0.799593\pi$
$104$	−92.5508	−	160.303i	−0.889912	−	1.54137i
$105$	28.1032	−	16.2254i	0.267649	−	0.154527i
$106$	−39.0843			−0.368720
$107$		−	56.0566i		−	0.523893i	−0.965082	−	0.261947i	$-0.915636\pi$
$107$		−	56.0566i		−	0.523893i	0.965082	−	0.261947i	$-0.0843644\pi$
$108$	−84.8683	+	48.9987i	−0.785818	+	0.453692i
$109$	−46.0431	−	26.5830i	−0.422414	−	0.243881i	0.273696	−	0.961816i	$-0.411754\pi$
$109$	−46.0431	−	26.5830i	−0.422414	−	0.243881i	−0.696109	+	0.717936i	$0.745087\pi$
$110$	0.733955	−	0.423749i	0.00667232	−	0.00385227i
$111$	86.6112	−	150.015i	0.780281	−	1.35149i
$112$	4.74556	−	8.21955i	0.0423711	−	0.0733888i
$113$		−	136.946i		−	1.21191i	−0.795497	−	0.605957i	$-0.792790\pi$
$113$		−	136.946i		−	1.21191i	0.795497	−	0.605957i	$-0.207210\pi$
$114$	−73.7198	+	230.950i	−0.646665	+	2.02587i
$115$	−67.7898			−0.589477
$116$	32.7184	+	18.8900i	0.282055	+	0.162845i
$117$	79.7434	+	46.0399i	0.681568	+	0.393503i
$118$	34.3785	+	59.5453i	0.291343	+	0.504621i
$119$	5.64480	−	9.77708i	0.0474353	−	0.0821603i
$120$	144.697	+	250.623i	1.20581	+	2.08853i
$121$	−120.999			−0.999989
$122$			55.3030i			0.453303i
$123$	−109.923	−	190.393i	−0.893686	−	1.54791i
$124$	279.189	−	161.190i	2.25153	−	1.29992i
$125$	12.1717			0.0973736
$126$			22.4874i			0.178472i
$127$	136.758	−	78.9573i	1.07684	−	0.621711i	0.146794	−	0.989167i	$-0.453104\pi$
$127$	136.758	−	78.9573i	1.07684	−	0.621711i	0.930041	+	0.367456i	$0.119771\pi$
$128$	−202.523	−	116.927i	−1.58221	−	0.913490i
$129$	−99.8037	+	57.6217i	−0.773672	+	0.446680i
$130$	−196.879	+	341.004i	−1.51445	+	2.62311i
$131$	38.5396	−	66.7525i	0.294195	−	0.509561i	−0.680602	−	0.732653i	$-0.738282\pi$
$131$	38.5396	−	66.7525i	0.294195	−	0.509561i	0.974797	+	0.223092i	$0.0716151\pi$
$132$			1.00402i			0.00760624i
$133$	−15.7136	−	17.2709i	−0.118147	−	0.129857i
$134$	7.10307			0.0530080
$135$	81.1394	+	46.8459i	0.601033	+	0.347006i
$136$	87.1917	+	50.3402i	0.641116	+	0.370148i
$137$	45.3969	+	78.6298i	0.331364	+	0.573940i	0.982780	−	0.184781i	$-0.0591577\pi$
$137$	45.3969	+	78.6298i	0.331364	+	0.573940i	−0.651415	+	0.758721i	$0.725824\pi$
$138$	62.2629	−	107.842i	0.451180	−	0.781467i
$139$	45.7773	+	79.2886i	0.329333	+	0.570421i	0.982380	−	0.186896i	$-0.0598428\pi$
$139$	45.7773	+	79.2886i	0.329333	+	0.570421i	−0.653047	+	0.757318i	$0.726509\pi$
$140$	−62.0176			−0.442983
$141$		−	193.930i		−	1.37539i
$142$	65.4897	+	113.432i	0.461195	+	0.798814i
$143$	−0.531717	+	0.306987i	−0.00371830	+	0.00214676i
$144$	−42.1054			−0.292398
$145$		−	36.1200i		−	0.249103i
$146$	163.394	−	94.3358i	1.11914	−	0.646136i
$147$	156.348	+	90.2676i	1.06359	+	0.614065i
$148$	−286.698	+	165.525i	−1.93715	+	1.11841i
$149$	−12.0587	+	20.8863i	−0.0809308	+	0.140176i	−0.903650	−	0.428272i	$-0.859123\pi$
$149$	−12.0587	+	20.8863i	−0.0809308	+	0.140176i	0.822719	+	0.568448i	$0.192456\pi$
$150$	148.314	−	256.888i	0.988761	−	1.71258i
$151$			251.451i			1.66524i	0.553848	+	0.832618i	$0.313159\pi$
$151$			251.451i			1.66524i	−0.553848	+	0.832618i	$0.686841\pi$
$152$	154.022	−	140.133i	1.01330	−	0.921928i
$153$	−50.0839			−0.327346
$154$	−0.129854	−	0.0749714i	−0.000843209	−	0.000486827i
$155$	−266.922	−	154.108i	−1.72208	−	0.994242i
$156$	−233.240	−	403.984i	−1.49513	−	2.58964i
$157$	44.0172	−	76.2401i	0.280364	−	0.485605i	−0.691110	−	0.722750i	$-0.742878\pi$
$157$	44.0172	−	76.2401i	0.280364	−	0.485605i	0.971474	+	0.237144i	$0.0762113\pi$
$158$	−77.1994	−	133.713i	−0.488604	−	0.846286i
$159$	−44.2684			−0.278417
$160$			124.447i			0.777797i
$161$	5.99682	+	10.3868i	0.0372473	+	0.0645143i
$162$	−291.671	+	168.396i	−1.80044	+	1.03948i
$163$	−28.3608			−0.173992			−0.0869962	−	0.996209i	$-0.527727\pi$
$163$	−28.3608			−0.173992			−0.0869962	+	0.996209i	$0.527727\pi$
$164$			420.156i			2.56193i
$165$	0.831305	−	0.479954i	0.00503821	−	0.00290881i
$166$	−189.904	−	109.641i	−1.14400	−	0.660490i
$167$	−52.1162	+	30.0893i	−0.312073	+	0.180176i	−0.647854	−	0.761765i	$-0.724333\pi$
$167$	−52.1162	+	30.0893i	−0.312073	+	0.180176i	0.335781	+	0.941940i	$0.391000\pi$
$168$	25.6004	−	44.3412i	0.152383	−	0.263936i
$169$	58.1295	−	100.683i	0.343962	−	0.595759i
$170$		−	214.172i		−	1.25984i
$171$	−31.4989	+	98.6799i	−0.184204	+	0.577076i
$172$	220.245			1.28050
$173$	152.888	+	88.2699i	0.883745	+	0.510230i	0.871891	−	0.489699i	$-0.162893\pi$
$173$	152.888	+	88.2699i	0.883745	+	0.510230i	0.0118536	+	0.999930i	$0.496227\pi$
$174$	57.4609	+	33.1751i	0.330235	+	0.190661i
$175$	14.2848	+	24.7420i	0.0816275	+	0.141383i
$176$	0.140376	−	0.243138i	0.000797591	−	0.00138147i
$177$	38.9383	+	67.4432i	0.219991	+	0.381035i
$178$	521.019			2.92707
$179$		−	0.226943i		−	0.00126784i	−1.00000		0.000633920i	$-0.999798\pi$
$179$		−	0.226943i		−	0.00126784i	1.00000		0.000633920i	$-0.000201783\pi$
$180$	137.564	+	238.268i	0.764244	+	1.32371i
$181$	129.410	−	74.7148i	0.714971	−	0.412789i	−0.0979279	−	0.995194i	$-0.531221\pi$
$181$	129.410	−	74.7148i	0.714971	−	0.412789i	0.812899	+	0.582405i	$0.197888\pi$
$182$	69.6651			0.382775
$183$			62.6382i			0.342285i
$184$	−92.6291	+	53.4795i	−0.503419	+	0.290649i
$185$	274.101	+	158.252i	1.48163	+	0.855418i
$186$	490.319	−	283.086i	2.63613	−	1.52197i
$187$	0.166976	−	0.289211i	0.000892919	−	0.00154658i
$188$	−185.312	+	320.970i	−0.985703	+	1.70729i
$189$		−	16.5763i		−	0.0877053i
$190$	−421.982	−	134.698i	−2.22096	−	0.708935i
$191$	−251.306			−1.31574			−0.657870	−	0.753132i	$-0.728542\pi$
$191$	−251.306			−1.31574			−0.657870	+	0.753132i	$0.728542\pi$
$192$	−299.681	−	173.021i	−1.56084	−	0.901151i
$193$	−109.795	−	63.3899i	−0.568884	−	0.328445i	0.187820	−	0.982204i	$-0.439858\pi$
$193$	−109.795	−	63.3899i	−0.568884	−	0.328445i	−0.756703	+	0.653758i	$0.773191\pi$
$194$	191.476	+	331.646i	0.986989	+	1.70952i
$195$	−222.992	+	386.234i	−1.14355	+	1.98069i
$196$	−172.513	−	298.801i	−0.880169	−	1.52450i
$197$	−285.803			−1.45077			−0.725387	−	0.688341i	$-0.758339\pi$
$197$	−285.803			−1.45077			−0.725387	+	0.688341i	$0.758339\pi$
$198$			0.665189i			0.00335954i
$199$	−77.0371	−	133.432i	−0.387121	−	0.670514i	0.604940	−	0.796271i	$-0.293197\pi$
$199$	−77.0371	−	133.432i	−0.387121	−	0.670514i	−0.992061	+	0.125757i	$0.959864\pi$
$200$	−220.648	+	127.391i	−1.10324	+	0.636957i
$201$	8.04520			0.0400259
$202$		−	575.347i		−	2.84825i
$203$	−5.53432	+	3.19524i	−0.0272627	+	0.0157401i
$204$	219.735	+	126.864i	1.07713	+	0.621882i
$205$	347.878	−	200.848i	1.69697	−	0.979744i
$206$	203.559	−	352.575i	0.988151	−	1.71153i
$207$	26.6036	−	46.0788i	0.128520	−	0.222603i
$208$			130.441i			0.627118i
$209$	−0.464815	−	0.510882i	−0.00222399	−	0.00244441i
$210$	−108.917			−0.518652
$211$	−138.091	−	79.7266i	−0.654458	−	0.377851i	0.135704	−	0.990749i	$-0.456670\pi$
$211$	−138.091	−	79.7266i	−0.654458	−	0.377851i	−0.790162	+	0.612898i	$0.790004\pi$
$212$	73.2680	+	42.3013i	0.345604	+	0.199534i
$213$	74.1761	+	128.477i	0.348245	+	0.603178i
$214$	−94.0735	+	162.940i	−0.439596	+	0.761402i
$215$	−105.284	−	182.357i	−0.489693	−	0.848173i
$216$	147.827			0.684384
$217$			54.5306i			0.251293i
$218$	89.2226	+	154.538i	0.409278	+	0.708890i
$219$	185.067	−	106.848i	0.845053	−	0.487892i
$220$	−1.83451			−0.00833868
$221$			155.158i			0.702072i
$222$	−503.507	+	290.700i	−2.26805	+	1.30946i
$223$	−161.907	−	93.4771i	−0.726041	−	0.419180i	0.0909314	−	0.995857i	$-0.471016\pi$
$223$	−161.907	−	93.4771i	−0.726041	−	0.419180i	−0.816972	+	0.576677i	$0.804349\pi$
$224$	19.0679	−	11.0089i	0.0851246	−	0.0491467i
$225$	63.3715	−	109.763i	0.281651	−	0.487834i
$226$	−229.822	+	398.063i	−1.01691	+	1.76134i
$227$			8.87518i			0.0390977i	0.999809	+	0.0195489i	$0.00622299\pi$
$227$			8.87518i			0.0390977i	−0.999809	+	0.0195489i	$0.993777\pi$
$228$	388.155	−	353.154i	1.70243	−	1.54892i
$229$	265.920			1.16122			0.580611	−	0.814181i	$-0.302814\pi$
$229$	265.920			1.16122			0.580611	+	0.814181i	$0.302814\pi$
$230$	197.045	+	113.764i	0.856719	+	0.494627i
$231$	−0.147078	−	0.0849154i	−0.000636700	−	0.000367599i
$232$	−28.4951	−	49.3549i	−0.122824	−	0.212737i
$233$	4.52199	−	7.83232i	0.0194077	−	0.0336151i	−0.856158	−	0.516713i	$-0.827155\pi$
$233$	4.52199	−	7.83232i	0.0194077	−	0.0336151i	0.875566	+	0.483098i	$0.160489\pi$
$234$	−154.527	−	267.649i	−0.660373	−	1.14380i
$235$	354.340			1.50783
$236$		−	148.832i		−	0.630646i
$237$	−87.4389	−	151.449i	−0.368940	−	0.639024i
$238$	−32.8156	+	18.9461i	−0.137881	+	0.0796054i
$239$	−48.3793			−0.202424			−0.101212	−	0.994865i	$-0.532272\pi$
$239$	−48.3793			−0.202424			−0.101212	+	0.994865i	$0.532272\pi$
$240$		−	203.936i		−	0.849731i
$241$	−120.431	+	69.5306i	−0.499712	+	0.288509i	−0.728594	−	0.684945i	$-0.759826\pi$
$241$	−120.431	+	69.5306i	−0.499712	+	0.288509i	0.228883	+	0.973454i	$0.426493\pi$
$242$	351.708	+	203.059i	1.45334	+	0.839085i
$243$	−225.225	+	130.034i	−0.926851	+	0.535118i
$244$	59.8549	−	103.672i	0.245307	−	0.424884i
$245$	−164.933	+	285.673i	−0.673197	+	1.16601i
$246$			737.889i			2.99955i
$247$	305.706	+	97.5823i	1.23768	+	0.395070i
$248$	−486.302			−1.96090
$249$	−215.093	−	124.184i	−0.863827	−	0.498731i
$250$	−35.3796	−	20.4264i	−0.141518	−	0.0817056i
$251$	−109.025	−	188.837i	−0.434363	−	0.752340i	0.562880	−	0.826539i	$-0.309693\pi$
$251$	−109.025	−	188.837i	−0.434363	−	0.752340i	−0.997243	+	0.0741991i	$0.976360\pi$
$252$	24.3384	−	42.1553i	0.0965808	−	0.167283i
$253$	0.177389	+	0.307246i	0.000701142	+	0.00121441i
$254$	−530.021			−2.08670
$255$		−	242.579i		−	0.951292i
$256$	210.398	+	364.420i	0.821867	+	1.42352i
$257$	192.080	−	110.898i	0.747394	−	0.431508i	−0.0773578	−	0.997003i	$-0.524648\pi$
$257$	192.080	−	110.898i	0.747394	−	0.431508i	0.824751	+	0.565495i	$0.191315\pi$
$258$	386.800			1.49923
$259$		−	55.9973i		−	0.216206i
$260$	738.143	−	426.167i	2.83901	−	1.63910i
$261$	24.5518	+	14.1750i	0.0940684	+	0.0543104i
$262$	−224.047	+	129.353i	−0.855139	+	0.493715i
$263$	−160.691	+	278.326i	−0.610994	+	1.05827i	0.380079	+	0.924954i	$0.375897\pi$
$263$	−160.691	+	278.326i	−0.610994	+	1.05827i	−0.991073	+	0.133319i	$0.957437\pi$
$264$	0.757273	−	1.31164i	0.00286846	−	0.00496832i
$265$		−	80.8853i		−	0.305228i
$266$	16.6908	+	76.5719i	0.0627475	+	0.287864i
$267$	590.126			2.21021
$268$	−13.3155	−	7.68771i	−0.0496847	−	0.0286855i
$269$	−137.447	−	79.3552i	−0.510956	−	0.295001i	0.222270	−	0.974985i	$-0.428653\pi$
$269$	−137.447	−	79.3552i	−0.510956	−	0.295001i	−0.733227	+	0.679984i	$0.761987\pi$
$270$	−157.232	−	272.335i	−0.582342	−	1.00865i
$271$	−244.649	+	423.745i	−0.902765	+	1.56364i	−0.0788765	+	0.996884i	$0.525133\pi$
$271$	−244.649	+	423.745i	−0.902765	+	1.56364i	−0.823889	+	0.566751i	$0.808200\pi$
$272$	−35.4745	−	61.4437i	−0.130421	−	0.225896i
$273$	78.9053			0.289030
$274$		−	304.739i		−	1.11218i
$275$	0.422551	+	0.731881i	0.00153655	+	0.00266138i
$276$	−233.438	+	134.775i	−0.845789	+	0.488316i
$277$	−183.051			−0.660835			−0.330417	−	0.943835i	$-0.607189\pi$
$277$	−183.051			−0.660835			−0.330417	+	0.943835i	$0.607189\pi$
$278$		−	307.292i		−	1.10537i
$279$	209.503	−	120.957i	0.750908	−	0.433537i
$280$	81.0185	+	46.7760i	0.289352	+	0.167057i
$281$	230.908	−	133.315i	0.821736	−	0.474430i	−0.0292787	−	0.999571i	$-0.509321\pi$
$281$	230.908	−	133.315i	0.821736	−	0.474430i	0.851015	+	0.525142i	$0.175988\pi$
$282$	−325.450	+	563.697i	−1.15408	+	1.99892i
$283$	178.014	−	308.329i	0.629025	−	1.08950i	−0.358723	−	0.933444i	$-0.616788\pi$
$283$	178.014	−	308.329i	0.629025	−	1.08950i	0.987748	−	0.156059i	$-0.0498789\pi$
$284$		−	283.521i		−	0.998312i
$285$	−477.952	−	152.564i	−1.67703	−	0.535311i
$286$	2.06073			0.00720534
$287$	−61.5480	−	35.5347i	−0.214453	−	0.123814i
$288$	−84.5908	−	48.8385i	−0.293718	−	0.169578i
$289$	102.303	+	177.195i	0.353991	+	0.613130i
$290$	−60.6161	+	104.990i	−0.209021	+	0.362035i
$291$	216.873	+	375.635i	0.745267	+	1.29084i
$292$	−408.402			−1.39864
$293$			357.755i			1.22101i	0.792014	+	0.610503i	$0.209033\pi$
$293$			357.755i			1.22101i	−0.792014	+	0.610503i	$0.790967\pi$
$294$	−302.972	−	524.763i	−1.03052	−	1.78491i
$295$	−123.229	+	71.1465i	−0.417727	+	0.241175i
$296$	499.382			1.68710
$297$		−	0.490335i		−	0.00165096i
$298$	70.1022	−	40.4735i	0.235242	−	0.135817i
$299$	−142.750	−	82.4169i	−0.477425	−	0.275642i
$300$	−556.063	+	321.043i	−1.85354	+	1.07014i
$301$	−18.6273	+	32.2634i	−0.0618846	+	0.107187i
$302$	421.982	−	730.894i	1.39729	−	2.42018i
$303$		−	651.659i		−	2.15069i
$304$	−143.373	+	31.2518i	−0.471621	+	0.102802i
$305$	−114.450			−0.375246
$306$	145.579	+	84.0503i	0.475750	+	0.274674i
$307$	125.866	+	72.6688i	0.409987	+	0.236706i	0.690784	−	0.723061i	$-0.257265\pi$
$307$	125.866	+	72.6688i	0.409987	+	0.236706i	−0.280797	+	0.959767i	$0.590599\pi$
$308$	0.162284	+	0.281085i	0.000526897	+	0.000912613i
$309$	230.559	−	399.339i	0.746145	−	1.29236i
$310$	517.243	+	895.892i	1.66853	+	2.88997i
$311$	−191.291			−0.615084			−0.307542	−	0.951534i	$-0.599506\pi$
$311$	−191.291			−0.615084			−0.307542	+	0.951534i	$0.599506\pi$
$312$			703.675i			2.25537i
$313$	156.376	+	270.851i	0.499603	+	0.865337i	1.00000		0.000458751i	$-0.000146025\pi$
$313$	156.376	+	270.851i	0.499603	+	0.865337i	−0.500397	+	0.865796i	$0.666813\pi$
$314$	−255.890	+	147.738i	−0.814938	+	0.470505i
$315$	−46.5380			−0.147740
$316$			334.214i			1.05764i
$317$	78.3676	−	45.2456i	0.247217	−	0.142731i	−0.371273	−	0.928524i	$-0.621078\pi$
$317$	78.3676	−	45.2456i	0.247217	−	0.142731i	0.618489	+	0.785793i	$0.287745\pi$
$318$	128.675	+	74.2907i	0.404639	+	0.233618i
$319$	−0.163708	+	0.0945168i	−0.000513191	+	0.000296291i
$320$	316.137	−	547.565i	0.987928	−	1.71114i
$321$	−106.551	+	184.552i	−0.331935	+	0.574928i
$322$		−	40.2552i		−	0.125016i
$323$	−170.541	+	37.1738i	−0.527989	+	0.115089i
$324$	729.027			2.25008
$325$	−340.040	−	196.322i	−1.04628	−	0.604068i
$326$	82.4365	+	47.5947i	0.252873	+	0.145996i
$327$	101.057	+	175.036i	0.309042	+	0.535277i
$328$	316.898	−	548.883i	0.966152	−	1.67342i
$329$	−31.3456	−	54.2922i	−0.0952754	−	0.165022i
$330$	−3.22182			−0.00976308
$331$		−	251.295i		−	0.759199i	−0.925151	−	0.379599i	$-0.876062\pi$
$331$		−	251.295i		−	0.759199i	0.925151	−	0.379599i	$-0.123938\pi$
$332$	237.332	+	411.071i	0.714854	+	1.23816i
$333$	−215.138	+	124.210i	−0.646060	+	0.373003i
$334$	201.982			0.604737
$335$			14.6999i			0.0438802i
$336$	−31.2471	+	18.0405i	−0.0929974	+	0.0536921i
$337$	−225.749	−	130.336i	−0.669879	−	0.386755i	0.126152	−	0.992011i	$-0.459737\pi$
$337$	−225.749	−	130.336i	−0.669879	−	0.386755i	−0.796031	+	0.605256i	$0.793071\pi$
$338$	−337.931	+	195.105i	−0.999797	+	0.577233i
$339$	−260.305	+	450.861i	−0.767861	+	1.32997i
$340$	−231.800	+	401.490i	−0.681766	+	1.18085i
$341$			1.61304i			0.00473033i
$342$	257.162	−	233.973i	0.751935	−	0.684131i
$343$	118.578			0.345710
$344$	−287.724	−	166.117i	−0.836406	−	0.482899i
$345$	223.181	+	128.854i	0.646901	+	0.373489i
$346$	−296.267	−	513.150i	−0.856263	−	1.48309i
$347$	169.713	−	293.952i	0.489088	−	0.847125i	−0.510833	−	0.859680i	$-0.670663\pi$
$347$	169.713	−	293.952i	0.489088	−	0.847125i	0.999921	+	0.0125549i	$0.00399646\pi$
$348$	−71.8113	−	124.381i	−0.206354	−	0.357416i
$349$	−76.4095			−0.218938			−0.109469	−	0.993990i	$-0.534915\pi$
$349$	−76.4095			−0.218938			−0.109469	+	0.993990i	$0.534915\pi$
$350$		−	95.8904i		−	0.273973i
$351$	113.908	+	197.294i	0.324523	+	0.562090i
$352$	0.564038	−	0.325647i	0.00160238	−	0.000925135i
$353$	635.437			1.80010			0.900052	−	0.435783i	$-0.143528\pi$
$353$	635.437			1.80010			0.900052	+	0.435783i	$0.143528\pi$
$354$		−	261.384i		−	0.738372i
$355$	−234.748	+	135.532i	−0.661261	+	0.381779i
$356$	−976.710	−	563.904i	−2.74357	−	1.58400i
$357$	−37.1682	+	21.4590i	−0.104112	+	0.0601094i
$358$	−0.380854	+	0.659658i	−0.00106384	+	0.00184262i
$359$	−2.43138	+	4.21127i	−0.00677264	+	0.0117306i	−0.869392	−	0.494123i	$-0.835489\pi$
$359$	−2.43138	+	4.21127i	−0.00677264	+	0.0117306i	0.862619	+	0.505854i	$0.168822\pi$
$360$		−	415.024i		−	1.15284i
$361$	−34.0136	+	359.394i	−0.0942206	+	0.995551i
$362$	−501.542			−1.38548
$363$	398.358	+	229.992i	1.09740	+	0.633586i
$364$	−130.595	−	75.3991i	−0.358778	−	0.207141i
$365$	195.229	+	338.146i	0.534874	+	0.926428i
$366$	105.119	−	182.071i	0.287210	−	0.497462i
$367$	−149.568	−	259.060i	−0.407542	−	0.705884i	0.587071	−	0.809535i	$-0.300281\pi$
$367$	−149.568	−	259.060i	−0.407542	−	0.705884i	−0.994614	+	0.103651i	$0.966948\pi$
$368$	75.3736			0.204820
$369$			315.285i			0.854430i
$370$	−531.155	−	919.987i	−1.43555	−	2.48645i
$371$	−12.3933	+	7.15527i	−0.0334051	+	0.0192864i
$372$	−1225.55			−3.29448
$373$		−	286.394i		−	0.767813i	−0.923372	−	0.383907i	$-0.874578\pi$
$373$		−	286.394i		−	0.767813i	0.923372	−	0.383907i	$-0.125422\pi$
$374$	−0.970701	+	0.560434i	−0.00259546	+	0.00149849i
$375$	−40.0722	−	23.1357i	−0.106859	−	0.0616952i
$376$	484.176	−	279.539i	1.28770	−	0.743455i
$377$	43.9136	−	76.0605i	0.116482	−	0.201752i
$378$	−27.8182	+	48.1825i	−0.0735930	+	0.127467i
$379$			638.486i			1.68466i	0.538962	+	0.842330i	$0.318817\pi$
$379$			638.486i			1.68466i	−0.538962	+	0.842330i	$0.681183\pi$
$380$	645.268	+	709.221i	1.69807	+	1.86637i
$381$	−600.322			−1.57565
$382$	730.474	+	421.739i	1.91224	+	1.10403i
$383$	297.246	+	171.615i	0.776100	+	0.448082i	0.835046	−	0.550180i	$-0.185441\pi$
$383$	297.246	+	171.615i	0.776100	+	0.448082i	−0.0589464	+	0.998261i	$0.518774\pi$
$384$	444.504	+	769.904i	1.15756	+	2.00496i
$385$	0.155154	−	0.268734i	0.000402997	−	0.000698012i
$386$	212.761	+	368.512i	0.551193	+	0.954694i
$387$	165.272			0.427059
$388$		−	828.944i		−	2.13645i
$389$	−176.043	−	304.915i	−0.452552	−	0.783843i	0.545992	−	0.837791i	$-0.316153\pi$
$389$	−176.043	−	304.915i	−0.452552	−	0.783843i	−0.998544	+	0.0539474i	$0.982820\pi$
$390$	1296.35	−	748.446i	3.32397	−	1.91909i
$391$	89.6562			0.229300
$392$			520.464i			1.32771i
$393$	−253.764	+	146.510i	−0.645709	+	0.372800i
$394$	830.745	+	479.631i	2.10849	+	1.21734i
$395$	276.721	−	159.765i	0.700559	−	0.404468i
$396$	0.719940	−	1.24697i	0.00181803	−	0.00314892i
$397$	205.686	−	356.259i	0.518101	−	0.897378i	−0.481678	−	0.876349i	$-0.659972\pi$
$397$	205.686	−	356.259i	0.518101	−	0.897378i	0.999779	−	0.0210293i	$-0.00669432\pi$
$398$			517.132i			1.29933i
$399$	18.9047	+	86.7282i	0.0473801	+	0.217364i
$400$	179.545			0.448862
$401$	−26.8409	−	15.4966i	−0.0669349	−	0.0386449i	0.466159	−	0.884701i	$-0.345637\pi$
$401$	−26.8409	−	15.4966i	−0.0669349	−	0.0386449i	−0.533094	+	0.846056i	$0.678971\pi$
$402$	−23.3851	−	13.5014i	−0.0581718	−	0.0335855i
$403$	−374.719	−	649.032i	−0.929823	−	1.61050i
$404$	−622.703	+	1078.55i	−1.54134	+	2.66969i
$405$	−348.497	−	603.615i	−0.860487	−	1.49041i
$406$	21.4489			0.0528297
$407$		−	1.65643i		−	0.00406984i
$408$	−191.371	−	331.465i	−0.469047	−	0.812413i
$409$	−336.926	+	194.525i	−0.823781	+	0.475610i	−0.851719	−	0.524000i	$-0.824439\pi$
$409$	−336.926	+	194.525i	−0.823781	+	0.475610i	0.0279377	+	0.999610i	$0.491106\pi$
$410$	−1348.24			−3.28839
$411$		−	345.158i		−	0.839801i
$412$	−763.190	+	440.628i	−1.85240	+	1.06948i
$413$	21.8022	+	12.5875i	0.0527899	+	0.0304783i
$414$	−154.658	+	89.2918i	−0.373570	+	0.215681i
$415$	226.904	−	393.009i	0.546756	−	0.947010i
$416$	−151.300	+	262.058i	−0.363701	+	0.629948i
$417$		−	348.050i		−	0.834653i
$418$	0.493723	+	2.26503i	0.00118116	+	0.00541874i
$419$	455.941			1.08817			0.544083	−	0.839032i	$-0.316878\pi$
$419$	455.941			1.08817			0.544083	+	0.839032i	$0.316878\pi$
$420$	204.177	+	117.882i	0.486136	+	0.280671i
$421$	−176.502	−	101.903i	−0.419244	−	0.242051i	0.275510	−	0.961298i	$-0.411153\pi$
$421$	−176.502	−	101.903i	−0.419244	−	0.242051i	−0.694754	+	0.719248i	$0.744487\pi$
$422$	267.593	+	463.484i	0.634106	+	1.09830i
$423$	−139.058	+	240.856i	−0.328743	+	0.569399i
$424$	−63.8105	−	110.523i	−0.150496	−	0.260668i
$425$	213.567			0.502510
$426$		−	497.926i		−	1.16884i
$427$	10.1245	+	17.5361i	0.0237107	+	0.0410681i
$428$	352.703	−	203.633i	0.824072	−	0.475778i
$429$	2.33406			0.00544069
$430$			706.746i			1.64360i
$431$	609.299	−	351.779i	1.41369	−	0.816193i	0.417954	−	0.908468i	$-0.362747\pi$
$431$	609.299	−	351.779i	1.41369	−	0.816193i	0.995734	+	0.0922756i	$0.0294141\pi$
$432$	−90.2166	−	52.0866i	−0.208835	−	0.120571i
$433$	−164.941	+	95.2288i	−0.380927	+	0.219928i	−0.678221	−	0.734858i	$-0.737249\pi$
$433$	−164.941	+	95.2288i	−0.380927	+	0.219928i	0.297295	+	0.954786i	$0.403916\pi$
$434$	91.5127	−	158.505i	0.210859	−	0.365218i
$435$	−68.6561	+	118.916i	−0.157830	+	0.273370i
$436$		−	386.265i		−	0.885930i
$437$	56.3868	−	176.649i	0.129032	−	0.404231i
$438$	−717.247			−1.63755
$439$	415.097	+	239.656i	0.945551	+	0.545914i	0.891696	−	0.452634i	$-0.149516\pi$
$439$	415.097	+	239.656i	0.945551	+	0.545914i	0.0538552	+	0.998549i	$0.482849\pi$
$440$	2.39657	+	1.38366i	0.00544674	+	0.00314468i
$441$	−129.454	−	224.220i	−0.293546	−	0.508436i
$442$	260.384	−	450.999i	0.589105	−	1.02036i
$443$	−383.888	−	664.914i	−0.866565	−	1.50094i	−0.865484	−	0.500936i	$-0.832989\pi$
$443$	−383.888	−	664.914i	−0.866565	−	1.50094i	−0.00108097	−	0.999999i	$-0.500344\pi$
$444$	1258.51			2.83448
$445$			1078.25i			2.42304i
$446$	313.744	+	543.421i	0.703463	+	1.21843i
$447$	79.4004	−	45.8418i	0.177629	−	0.102554i
$448$	−111.864			−0.249697
$449$			392.421i			0.873988i	0.899464	+	0.436994i	$0.143957\pi$
$449$			392.421i			0.873988i	−0.899464	+	0.436994i	$0.856043\pi$
$450$	−368.405	+	212.699i	−0.818678	+	0.472664i
$451$	−1.82062	−	1.05113i	−0.00403685	−	0.00233068i
$452$	861.654	−	497.476i	1.90631	−	1.10061i
$453$	477.952	−	827.837i	1.05508	−	1.82746i
$454$	14.8942	−	25.7976i	0.0328067	−	0.0568228i
$455$			144.173i			0.316863i
$456$	−773.439	+	168.591i	−1.69614	+	0.369718i
$457$	−695.090			−1.52099			−0.760493	−	0.649347i	$-0.775042\pi$
$457$	−695.090			−1.52099			−0.760493	+	0.649347i	$0.775042\pi$
$458$	−772.952	−	446.264i	−1.68767	−	0.974376i
$459$	−107.312	−	61.9565i	−0.233795	−	0.134981i
$460$	−246.256	−	426.528i	−0.535339	−	0.927234i
$461$	351.150	−	608.210i	0.761714	−	1.31933i	−0.180253	−	0.983620i	$-0.557692\pi$
$461$	351.150	−	608.210i	0.761714	−	1.31933i	0.941967	−	0.335707i	$-0.108975\pi$
$462$	0.285008	+	0.493649i	0.000616901	+	0.00106850i
$463$	−14.4955			−0.0313077			−0.0156538	−	0.999877i	$-0.504983\pi$
$463$	−14.4955			−0.0313077			−0.0156538	+	0.999877i	$0.504983\pi$
$464$			40.1608i			0.0865534i
$465$	585.849	+	1014.72i	1.25989	+	2.18219i
$466$	−26.2882	+	15.1775i	−0.0564125	+	0.0325698i
$467$	−863.890			−1.84987			−0.924935	−	0.380124i	$-0.875881\pi$
$467$	−863.890			−1.84987			−0.924935	+	0.380124i	$0.875881\pi$
$468$			668.985i			1.42945i
$469$	2.25232	−	1.30038i	0.00480239	−	0.00277266i
$470$	−1029.96	−	594.650i	−2.19141	−	1.26521i
$471$	−289.831	+	167.334i	−0.615353	+	0.355274i
$472$	−112.255	+	194.432i	−0.237829	+	0.411931i
$473$	−0.551003	+	0.954366i	−0.00116491	+	0.00201769i
$474$			586.956i			1.23830i
$475$	134.317	−	420.789i	0.282773	−	0.885871i
$476$	82.0221			0.172315
$477$	54.9802	+	31.7429i	0.115263	+	0.0665469i
$478$	140.625	+	81.1897i	0.294194	+	0.169853i
$479$	−198.015	−	342.972i	−0.413393	−	0.716017i	0.581866	−	0.813285i	$-0.302323\pi$
$479$	−198.015	−	342.972i	−0.413393	−	0.716017i	−0.995258	+	0.0972678i	$0.968990\pi$
$480$	236.547	−	409.712i	0.492807	−	0.853566i
$481$	384.797	+	666.488i	0.799994	+	1.38563i
$482$	466.742			0.968344
$483$		−	45.5945i		−	0.0943986i
$484$	−439.544	−	761.313i	−0.908149	−	1.57296i
$485$	−686.345	+	396.261i	−1.41514	+	0.817033i
$486$	872.884			1.79606
$487$			872.905i			1.79241i	0.443636	+	0.896207i	$0.353688\pi$
$487$			872.905i			1.79241i	−0.443636	+	0.896207i	$0.646312\pi$
$488$	−156.386	+	90.2897i	−0.320464	+	0.185020i
$489$	93.3707	+	53.9076i	0.190942	+	0.110240i
$490$	958.826	−	553.578i	1.95679	−	1.12975i
$491$	−350.193	+	606.552i	−0.713224	+	1.23534i	0.250417	+	0.968138i	$0.419432\pi$
$491$	−350.193	+	606.552i	−0.713224	+	1.23534i	−0.963641	+	0.267201i	$0.913901\pi$
$492$	798.624	−	1383.26i	1.62322	−	2.81150i
$493$			47.7709i			0.0968983i
$494$	−724.837	−	796.676i	−1.46728	−	1.61270i
$495$	−1.37662			−0.00278104
$496$	296.783	+	171.348i	0.598353	+	0.345459i
$497$	41.5325	+	23.9788i	0.0835663	+	0.0482470i
$498$	416.808	+	721.933i	0.836965	+	1.44967i
$499$	−76.5488	+	132.586i	−0.153404	+	0.265704i	−0.932477	−	0.361230i	$-0.882357\pi$
$499$	−76.5488	+	132.586i	−0.153404	+	0.265704i	0.779073	+	0.626934i	$0.215690\pi$
$500$	44.2154	+	76.5832i	0.0884307	+	0.153166i
$501$	228.773			0.456632
$502$			731.860i			1.45789i
$503$	203.824	+	353.033i	0.405216	+	0.701855i	0.994347	−	0.106183i	$-0.0338628\pi$
$503$	203.824	+	353.033i	0.405216	+	0.701855i	−0.589130	+	0.808038i	$0.700530\pi$
$504$	−63.5902	+	36.7138i	−0.126171	+	0.0728449i
$505$	1190.69			2.35779
$506$		−	1.19077i		−	0.00235330i
$507$	−382.754	+	220.983i	−0.754938	+	0.435864i
$508$	993.585	+	573.647i	1.95588	+	1.12923i
$509$	−171.070	+	98.7673i	−0.336090	+	0.194042i	−0.658542	−	0.752544i	$-0.728826\pi$
$509$	−171.070	+	98.7673i	−0.336090	+	0.194042i	0.322452	+	0.946586i	$0.395493\pi$
$510$	−407.094	+	705.108i	−0.798224	+	1.38256i
$511$	34.5406	−	59.8261i	0.0675942	−	0.117077i
$512$		−	476.936i		−	0.931515i
$513$	−189.563	+	172.470i	−0.369519	+	0.336198i
$514$	−744.428			−1.44830
$515$	729.657	+	421.268i	1.41681	+	0.817995i
$516$	−725.102	−	418.638i	−1.40524	−	0.811313i
$517$	−0.927218	−	1.60599i	−0.00179346	−	0.00310636i
$518$	−93.9740	+	162.768i	−0.181417	+	0.314223i
$519$	−335.563	−	581.212i	−0.646557	−	1.11987i
$520$	−1285.73			−2.47255
$521$		−	698.844i		−	1.34135i	−0.741751	−	0.670676i	$-0.766004\pi$
$521$		−	698.844i		−	1.34135i	0.741751	−	0.670676i	$-0.233996\pi$
$522$	−47.5767	−	82.4053i	−0.0911431	−	0.157865i
$523$	−381.571	+	220.300i	−0.729582	+	0.421224i	−0.818269	−	0.574835i	$-0.805066\pi$
$523$	−381.571	+	220.300i	−0.729582	+	0.421224i	0.0886874	+	0.996060i	$0.471733\pi$
$524$	560.001			1.06870
$525$		−	108.609i		−	0.206874i
$526$	934.166	−	539.341i	1.77598	−	1.02536i
$527$	353.021	+	203.817i	0.669869	+	0.386749i
$528$	−0.924305	+	0.533648i	−0.00175058	+	0.00101070i
$529$	216.876	−	375.641i	0.409974	−	0.710096i
$530$	−135.741	+	235.110i	−0.256115	+	0.443604i
$531$		−	111.684i		−	0.210327i
$532$	51.5855	−	161.607i	0.0969653	−	0.303773i
$533$	976.738			1.83253
$534$	−1715.32	−	990.343i	−3.21222	−	1.85457i
$535$	−337.206	−	194.686i	−0.630292	−	0.363899i
$536$	11.5967	+	20.0861i	0.0216357	+	0.0374741i
$537$	−0.431369	+	0.747153i	−0.000803295	+	0.00139135i
$538$	266.346	+	461.325i	0.495067	+	0.857481i
$539$	1.72635			0.00320288
$540$			680.696i			1.26055i
$541$	−442.696	−	766.772i	−0.818292	−	1.41732i	−0.906940	−	0.421260i	$-0.861588\pi$
$541$	−442.696	−	766.772i	−0.818292	−	1.41732i	0.0886479	−	0.996063i	$-0.471745\pi$
$542$	1422.25	−	821.136i	2.62408	−	1.51501i
$543$	−568.065			−1.04616
$544$		−	164.589i		−	0.302554i
$545$	−319.818	+	184.647i	−0.586822	+	0.338802i
$546$	−229.355	−	132.418i	−0.420064	−	0.242524i
$547$	−801.617	+	462.814i	−1.46548	+	0.846095i	−0.999256	−	0.0385725i	$-0.987719\pi$
$547$	−801.617	+	462.814i	−1.46548	+	0.846095i	−0.466223	+	0.884667i	$0.654386\pi$
$548$	−329.821	+	571.267i	−0.601863	+	1.04246i
$549$	44.9151	−	77.7952i	0.0818125	−	0.141703i
$550$		−	2.83648i		−	0.00515725i
$551$	94.1225	+	30.0442i	0.170821	+	0.0545266i
$552$	406.611			0.736614
$553$	−48.9585	−	28.2662i	−0.0885325	−	0.0511143i
$554$	532.077	+	307.195i	0.960427	+	0.554503i
$555$	−601.606	−	1042.01i	−1.08397	−	1.87750i
$556$	−332.585	+	576.053i	−0.598174	+	1.03607i
$557$	176.665	+	305.992i	0.317172	+	0.549358i	0.979897	−	0.199505i	$-0.0639335\pi$
$557$	176.665	+	305.992i	0.317172	+	0.549358i	−0.662725	+	0.748863i	$0.730600\pi$
$558$	−811.954			−1.45511
$559$		−	512.005i		−	0.915930i
$560$	−32.9629	−	57.0935i	−0.0588624	−	0.101953i
$561$	−1.09945	+	0.634769i	−0.00195981	+	0.00113150i
$562$	−894.909			−1.59236
$563$			21.4065i			0.0380221i	0.999819	+	0.0190111i	$0.00605177\pi$
$563$			21.4065i			0.0380221i	−0.999819	+	0.0190111i	$0.993948\pi$
$564$	1220.19	−	704.476i	2.16345	−	1.24907i
$565$	−823.795	−	475.618i	−1.45804	−	0.841802i
$566$	−1034.87	+	597.482i	−1.82839	+	1.05562i
$567$	−61.6575	+	106.794i	−0.108743	+	0.188349i
$568$	−213.842	+	370.385i	−0.376482	+	0.652087i
$569$		−	378.852i		−	0.665821i	−0.942958	−	0.332911i	$-0.891969\pi$
$569$		−	378.852i		−	0.665821i	0.942958	−	0.332911i	$-0.108031\pi$
$570$	1133.24	+	1245.55i	1.98814	+	2.18518i
$571$	−38.5842			−0.0675730			−0.0337865	−	0.999429i	$-0.510757\pi$
$571$	−38.5842			−0.0675730			−0.0337865	+	0.999429i	$0.510757\pi$
$572$	−3.86307	−	2.23034i	−0.00675362	−	0.00389920i
$573$	827.362	+	477.678i	1.44391	+	0.833644i
$574$	119.268	+	206.578i	0.207784	+	0.359892i
$575$	−113.443	+	196.488i	−0.197291	+	0.341719i
$576$	248.131	+	429.776i	0.430783	+	0.746139i
$577$	399.348			0.692112			0.346056	−	0.938214i	$-0.387521\pi$
$577$	399.348			0.692112			0.346056	+	0.938214i	$0.387521\pi$
$578$		−	686.737i		−	1.18813i
$579$	240.981	+	417.391i	0.416201	+	0.720882i
$580$	227.264	−	131.211i	0.391834	−	0.226225i
$581$	−80.2894			−0.138192
$582$		−	1455.81i		−	2.50140i
$583$	−0.366600	+	0.211656i	−0.000628816	+	0.000363047i
$584$	533.528	+	308.032i	0.913575	+	0.527453i
$585$	553.902	−	319.796i	0.946841	−	0.546659i
$586$	600.380	−	1039.89i	1.02454	−	1.77455i
$587$	−247.769	+	429.148i	−0.422093	+	0.731087i	−0.996144	−	0.0877330i	$-0.972038\pi$
$587$	−247.769	+	429.148i	−0.422093	+	0.731087i	0.574051	+	0.818820i	$0.305371\pi$
$588$			1311.64i			2.23068i
$589$	623.601	−	567.369i	1.05875	−	0.963275i
$590$	477.589			0.809474
$591$	940.933	+	543.248i	1.59210	+	0.919201i
$592$	−304.765	−	175.956i	−0.514806	−	0.297224i
$593$	−114.717	−	198.696i	−0.193452	−	0.335069i	0.752940	−	0.658089i	$-0.228635\pi$
$593$	−114.717	−	198.696i	−0.193452	−	0.335069i	−0.946392	+	0.323020i	$0.895302\pi$
$594$	−0.822875	+	1.42526i	−0.00138531	+	0.00239943i
$595$	−39.2091	−	67.9121i	−0.0658976	−	0.114138i
$596$	−175.219			−0.293992
$597$			585.723i			0.981110i
$598$	276.622	+	479.124i	0.462579	+	0.801210i
$599$	−26.4546	+	15.2736i	−0.0441646	+	0.0254984i	−0.521920	−	0.852995i	$-0.674784\pi$
$599$	−26.4546	+	15.2736i	−0.0441646	+	0.0254984i	0.477755	+	0.878493i	$0.341451\pi$
$600$	968.573			1.61429
$601$		−	962.490i		−	1.60148i	−0.599012	−	0.800740i	$-0.704440\pi$
$601$		−	962.490i		−	1.60148i	0.599012	−	0.800740i	$-0.295560\pi$
$602$	108.288	−	62.5201i	0.179880	−	0.103854i
$603$	−9.99195	−	5.76885i	−0.0165704	−	0.00956692i
$604$	−1582.10	+	913.429i	−2.61938	+	1.51230i
$605$	−420.232	+	727.863i	−0.694598	+	1.20308i
$606$	−1093.61	+	1894.18i	−1.80463	+	3.12572i
$607$		−	249.770i		−	0.411483i	−0.978606	−	0.205741i	$-0.934039\pi$
$607$		−	249.770i		−	0.411483i	0.978606	−	0.205741i	$-0.0659606\pi$
$608$	−324.289	−	103.514i	−0.533370	−	0.170253i
$609$	24.2938			0.0398913
$610$	332.673	+	192.069i	0.545365	+	0.314867i
$611$	746.161	+	430.796i	1.22121	+	0.705067i
$612$	−181.937	−	315.124i	−0.297282	−	0.514908i
$613$	−189.015	+	327.384i	−0.308345	+	0.534069i	−0.978000	−	0.208603i	$-0.933108\pi$
$613$	−189.015	+	327.384i	−0.308345	+	0.534069i	0.669655	+	0.742672i	$0.266442\pi$
$614$	−243.904	−	422.454i	−0.397238	−	0.688036i
$615$	−1527.07			−2.48304
$616$		−	0.489604i		−	0.000794812i
$617$	−259.371	−	449.243i	−0.420374	−	0.728109i	0.575602	−	0.817730i	$-0.304768\pi$
$617$	−259.371	−	449.243i	−0.420374	−	0.728109i	−0.995976	+	0.0896208i	$0.971434\pi$
$618$	−1340.33	+	773.842i	−2.16883	+	1.25217i
$619$	1035.34			1.67261			0.836303	−	0.548267i	$-0.184712\pi$
$619$	1035.34			1.67261			0.836303	+	0.548267i	$0.184712\pi$
$620$		−	2239.27i		−	3.61172i
$621$	114.004	−	65.8202i	0.183581	−	0.105991i
$622$	556.028	+	321.023i	0.893935	+	0.516114i
$623$	165.211	−	95.3844i	0.265186	−	0.153105i
$624$	247.939	−	429.443i	0.397338	−	0.688209i
$625$	332.869	−	576.545i	0.532590	−	0.922473i
$626$		−	1049.71i		−	1.67686i
$627$	0.559210	+	2.56546i	0.000891881	+	0.00409165i
$628$	639.594			1.01846
$629$	−362.516	−	209.298i	−0.576336	−	0.332748i
$630$	135.272	+	78.0995i	0.214718	+	0.123967i
$631$	528.945	+	916.160i	0.838265	+	1.45192i	0.891344	+	0.453327i	$0.149763\pi$
$631$	528.945	+	916.160i	0.838265	+	1.45192i	−0.0530794	+	0.998590i	$0.516904\pi$
$632$	252.077	−	436.610i	0.398856	−	0.690839i
$633$	303.086	+	524.960i	0.478808	+	0.829320i
$634$	−303.723			−0.479058
$635$		−	1096.88i		−	1.72738i
$636$	−160.811	−	278.533i	−0.252847	−	0.437944i
$637$	−694.625	+	401.042i	−1.09046	+	0.629579i
$638$	0.634468			0.000994464
$639$		−	212.754i		−	0.332948i
$640$	−1406.74	+	812.180i	−2.19803	+	1.26903i
$641$	−560.504	−	323.607i	−0.874421	−	0.504847i	−0.00560636	−	0.999984i	$-0.501785\pi$
$641$	−560.504	−	323.607i	−0.874421	−	0.504847i	−0.868815	+	0.495137i	$0.835118\pi$
$642$	619.426	−	357.626i	0.964839	−	0.557050i
$643$	157.333	−	272.508i	0.244685	−	0.423807i	−0.717358	−	0.696705i	$-0.754649\pi$
$643$	157.333	−	272.508i	0.244685	−	0.423807i	0.962043	+	0.272898i	$0.0879820\pi$
$644$	−43.5685	+	75.4629i	−0.0676530	+	0.117178i
$645$			800.487i			1.24107i
$646$	558.096	+	178.146i	0.863926	+	0.275768i
$647$	−320.116			−0.494769			−0.247384	−	0.968917i	$-0.579571\pi$
$647$	−320.116			−0.494769			−0.247384	+	0.968917i	$0.579571\pi$
$648$	−952.385	−	549.860i	−1.46973	−	0.848549i
$649$	0.644920	+	0.372345i	0.000993714	+	0.000573721i
$650$	658.932	+	1141.30i	1.01374	+	1.75585i
$651$	103.651	−	179.528i	0.159218	−	0.275773i
$652$	−103.024	−	178.443i	−0.158013	−	0.273686i
$653$	131.969			0.202097			0.101049	−	0.994881i	$-0.467780\pi$
$653$	131.969			0.202097			0.101049	+	0.994881i	$0.467780\pi$
$654$		−	678.370i		−	1.03726i
$655$	−267.698	−	463.666i	−0.408699	−	0.707888i
$656$	−386.796	+	223.317i	−0.589628	+	0.340422i
$657$	−306.465			−0.466460
$658$			210.415i			0.319780i
$659$	−635.205	+	366.736i	−0.963892	+	0.556503i	−0.897369	−	0.441281i	$-0.854524\pi$
$659$	−635.205	+	366.736i	−0.963892	+	0.556503i	−0.0665235	+	0.997785i	$0.521191\pi$
$660$	6.03966	+	3.48700i	0.00915100	+	0.00528333i
$661$	590.038	−	340.659i	0.892644	−	0.515368i	0.0178378	−	0.999841i	$-0.494322\pi$
$661$	590.038	−	340.659i	0.892644	−	0.515368i	0.874807	+	0.484472i	$0.160988\pi$
$662$	−421.720	+	730.441i	−0.637040	+	1.10338i
$663$	294.921	−	510.818i	0.444828	−	0.770465i
$664$		−	716.019i		−	1.07834i
$665$	−158.466	+	34.5419i	−0.238295	+	0.0519426i
$666$	833.792			1.25194
$667$	−43.9507	−	25.3750i	−0.0658931	−	0.0380434i
$668$	−378.639	−	218.607i	−0.566824	−	0.327256i
$669$	355.359	+	615.499i	0.531179	+	0.920029i
$670$	24.6692	−	42.7282i	0.0368196	−	0.0637735i
$671$	0.299487	+	0.518726i	0.000446329	+	0.000773064i
$672$	−83.7017			−0.124556
$673$			710.831i			1.05621i	0.849178	+	0.528107i	$0.177098\pi$
$673$			710.831i			1.05621i	−0.849178	+	0.528107i	$0.822902\pi$
$674$	437.458	+	757.700i	0.649048	+	1.12418i
$675$	271.565	−	156.788i	0.402318	−	0.232278i
$676$	844.654			1.24949
$677$			493.970i			0.729645i	0.931077	+	0.364823i	$0.118870\pi$
$677$			493.970i			0.729645i	−0.931077	+	0.364823i	$0.881130\pi$
$678$	1513.26	−	873.681i	2.23195	−	1.28862i
$679$	121.431	+	70.1081i	0.178838	+	0.103252i
$680$	605.639	−	349.666i	0.890645	−	0.514214i
$681$	16.8698	−	29.2193i	0.0247721	−	0.0429065i
$682$	2.70699	−	4.68864i	0.00396919	−	0.00687484i
$683$		−	442.962i		−	0.648553i	−0.945962	−	0.324276i	$-0.894879\pi$
$683$		−	442.962i		−	0.648553i	0.945962	−	0.324276i	$-0.105121\pi$
$684$	−735.310	+	160.280i	−1.07501	+	0.234327i
$685$	630.659			0.920670
$686$	−344.673	−	198.997i	−0.502439	−	0.290083i
$687$	−875.474	−	505.455i	−1.27434	−	0.735743i
$688$	117.062	+	202.758i	0.170149	+	0.294706i
$689$	98.3380	−	170.326i	0.142726	−	0.247208i
$690$	−432.481	−	749.080i	−0.626784	−	1.08562i
$691$	924.711			1.33822			0.669110	−	0.743163i	$-0.266675\pi$
$691$	924.711			1.33822			0.669110	+	0.743163i	$0.266675\pi$
$692$			1282.61i			1.85348i
$693$	0.121778	+	0.210926i	0.000175726	+	0.000304366i
$694$	−986.615	+	569.622i	−1.42164	+	0.820782i
$695$	635.943			0.915026
$696$			216.651i			0.311281i
$697$	−460.090	+	265.633i	−0.660101	+	0.381109i
$698$	222.100	+	128.230i	0.318195	+	0.183710i
$699$	−29.7750	+	17.1906i	−0.0425966	+	0.0245932i
$700$	−103.783	+	179.757i	−0.148261	+	0.256796i
$701$	−277.112	+	479.973i	−0.395310	+	0.684697i	−0.993141	−	0.116925i	$-0.962696\pi$
$701$	−277.112	+	479.973i	−0.395310	+	0.684697i	0.597831	+	0.801622i	$0.296030\pi$
$702$		−	764.634i		−	1.08922i
$703$	−640.373	+	582.629i	−0.910915	+	0.828775i
$704$	−3.30900			−0.00470028
$705$	−1166.58	−	673.523i	−1.65472	−	0.955351i
$706$	−1847.03	−	1066.38i	−2.61619	−	1.51046i
$707$	−105.330	−	182.437i	−0.148982	−	0.258045i
$708$	−282.898	+	489.993i	−0.399573	+	0.692081i
$709$	249.802	+	432.670i	0.352331	+	0.610254i	0.986657	−	0.162811i	$-0.0520560\pi$
$709$	249.802	+	432.670i	0.352331	+	0.610254i	−0.634327	+	0.773065i	$0.718723\pi$
$710$	909.791			1.28140
$711$			250.794i			0.352734i
$712$	850.635	+	1473.34i	1.19471	+	2.06930i
$713$	−375.036	+	216.527i	−0.525997	+	0.303684i
$714$	144.049			0.201750
$715$			4.26469i			0.00596461i
$716$	1.42791	−	0.824403i	0.00199428	−	0.00115140i
$717$	159.277	+	91.9584i	0.222143	+	0.128254i
$718$	14.1346	−	8.16063i	0.0196861	−	0.0113658i
$719$	174.396	−	302.062i	0.242553	−	0.420114i	−0.718888	−	0.695126i	$-0.755348\pi$
$719$	174.396	−	302.062i	0.242553	−	0.420114i	0.961441	+	0.275012i	$0.0886818\pi$
$720$	−146.233	+	253.283i	−0.203101	+	0.351782i
$721$		−	149.065i		−	0.206747i
$722$	701.999	−	987.573i	0.972298	−	1.36783i
$723$	528.649			0.731189
$724$	940.198	+	542.823i	1.29862	+	0.749756i
$725$	−104.693	−	60.4448i	−0.144405	−	0.0833721i
$726$	−771.940	−	1337.04i	−1.06328	−	1.84165i
$727$	41.3116	−	71.5538i	0.0568247	−	0.0984233i	−0.836214	−	0.548404i	$-0.815236\pi$
$727$	41.3116	−	71.5538i	0.0568247	−	0.0984233i	0.893038	+	0.449980i	$0.148569\pi$
$728$	113.738	+	197.000i	0.156233	+	0.270604i
$729$	85.5657			0.117374
$730$		−	1310.52i		−	1.79524i
$731$	139.245	+	241.179i	0.190485	+	0.329930i
$732$	−394.114	+	227.542i	−0.538407	+	0.310850i
$733$	−981.828			−1.33947			−0.669733	−	0.742602i	$-0.733591\pi$
$733$	−981.828			−1.33947			−0.669733	+	0.742602i	$0.733591\pi$
$734$			1004.01i			1.36787i
$735$	1086.00	−	627.003i	1.47755	−	0.853066i
$736$	151.428	+	87.4267i	0.205744	+	0.118786i
$737$	0.0666248	−	0.0384658i	9.03999e−5	−	5.21924e-5i
$738$	529.107	−	916.441i	0.716948	−	1.24179i
$739$	−64.8765	+	112.369i	−0.0877895	+	0.152056i	−0.906576	−	0.422042i	$-0.861314\pi$
$739$	−64.8765	+	112.369i	−0.0877895	+	0.152056i	0.818787	+	0.574097i	$0.194647\pi$
$740$			2299.49i			3.10743i
$741$	−820.978	−	902.345i	−1.10793	−	1.21774i
$742$	48.0316			0.0647326
$743$	−450.862	−	260.306i	−0.606814	−	0.350344i	0.164904	−	0.986310i	$-0.447269\pi$
$743$	−450.862	−	260.306i	−0.606814	−	0.350344i	−0.771717	+	0.635966i	$0.780602\pi$
$744$	1601.03	+	924.354i	2.15192	+	1.24241i
$745$	83.7603	+	145.077i	0.112430	+	0.194734i
$746$	−480.624	+	832.465i	−0.644268	+	1.11590i
$747$	178.094	+	308.467i	0.238412	+	0.412941i
$748$	2.42625			0.00324365
$749$			68.8892i			0.0919749i
$750$	77.6522	+	134.498i	0.103536	+	0.179330i
$751$	880.913	−	508.595i	1.17299	−	0.677224i	0.218605	−	0.975813i	$-0.429849\pi$
$751$	880.913	−	508.595i	1.17299	−	0.677224i	0.954382	+	0.298590i	$0.0965161\pi$
$752$	−393.981			−0.523910
$753$			828.932i			1.10084i
$754$	−255.288	+	147.391i	−0.338578	+	0.195478i
$755$	1512.59	+	873.295i	2.00343	+	1.15668i
$756$	104.297	−	60.2157i	0.137958	−	0.0796504i
$757$	155.490	−	269.317i	0.205403	−	0.355768i	−0.744858	−	0.667223i	$-0.767483\pi$
$757$	155.490	−	269.317i	0.205403	−	0.355768i	0.950261	+	0.311455i	$0.100816\pi$
$758$	1071.50	−	1855.89i	1.41359	−	2.44841i
$759$		−	1.34871i		−	0.00177695i
$760$	−308.043	−	1413.20i	−0.405320	−	1.85947i
$761$	−1402.51			−1.84298			−0.921489	−	0.388404i	$-0.873027\pi$
$761$	−1402.51			−1.84298			−0.921489	+	0.388404i	$0.873027\pi$
$762$	1744.96	+	1007.45i	2.28998	+	1.32212i
$763$	56.5834	+	32.6684i	0.0741591	+	0.0428158i
$764$	−912.904	−	1581.20i	−1.19490	−	2.06963i
$765$	−173.943	+	301.278i	−0.227376	+	0.393827i
$766$	−576.006	−	997.671i	−0.751966	−	1.30244i
$767$	−345.991			−0.451097
$768$		−	1599.68i		−	2.08292i
$769$	196.711	+	340.714i	0.255802	+	0.443061i	0.965113	−	0.261834i	$-0.0843273\pi$
$769$	196.711	+	340.714i	0.255802	+	0.443061i	−0.709311	+	0.704895i	$0.750994\pi$
$770$	−0.901975	+	0.520755i	−0.00117140	+	0.000676306i
$771$	−843.167			−1.09360
$772$		−	921.090i		−	1.19312i
$773$	201.825	−	116.524i	0.261093	−	0.150742i	−0.363740	−	0.931501i	$-0.618500\pi$
$773$	201.825	−	116.524i	0.261093	−	0.150742i	0.624833	+	0.780758i	$0.285167\pi$
$774$	−480.397	−	277.357i	−0.620668	−	0.358343i
$775$	−893.359	+	515.781i	−1.15272	+	0.665524i
$776$	−625.222	+	1082.92i	−0.805698	+	1.39551i
$777$	−106.438	+	184.357i	−0.136986	+	0.237267i
$778$			1181.73i			1.51894i
$779$	234.014	+	1073.57i	0.300403	+	1.37814i
$780$	−3240.20			−4.15410
$781$	1.22855	+	0.709304i	0.00157305	+	0.000908200i
$782$	−260.604	−	150.460i	−0.333254	−	0.192404i
$783$	35.0705	+	60.7439i	0.0447899	+	0.0775784i
$784$	183.385	−	317.631i	0.233909	−	0.405142i
$785$	−305.746	−	529.568i	−0.389485	−	0.674609i
$786$	983.489			1.25126
$787$			193.205i			0.245495i	0.992438	+	0.122748i	$0.0391706\pi$
$787$			193.205i			0.245495i	−0.992438	+	0.122748i	$0.960829\pi$
$788$	−1038.22	−	1798.25i	−1.31753	−	2.28204i
$789$	1058.07	−	610.878i	1.34103	−	0.774243i
$790$	−1072.46			−1.35755
$791$			168.296i			0.212764i
$792$	−1.88103	+	1.08601i	−0.00237504	+	0.00137123i
$793$	−241.006	−	139.145i	−0.303917	−	0.175466i
$794$	−1195.74	+	690.361i	−1.50597	+	0.869472i
$795$	−153.745	+	266.295i	−0.193390	+	0.334962i
$796$	559.696	−	969.422i	0.703136	−	1.21787i
$797$		−	255.622i		−	0.320730i	−0.987058	−	0.160365i	$-0.948733\pi$
$797$		−	255.622i		−	0.320730i	0.987058	−	0.160365i	$-0.0512672\pi$
$798$	90.5959	−	283.819i	0.113529	−	0.355663i
$799$	−468.636			−0.586529
$800$	360.710	+	208.256i	0.450887	+	0.260320i
$801$	−732.922	−	423.153i	−0.915009	−	0.528281i
$802$	52.0124	+	90.0882i	0.0648534	+	0.112329i
$803$	1.02173	−	1.76969i	0.00127239	−	0.00220384i
$804$	29.2253	+	50.6197i	0.0363499	+	0.0629598i
$805$	83.3085			0.103489
$806$			2515.40i			3.12084i
$807$	301.674	+	522.514i	0.373821	+	0.647477i
$808$	1626.97	−	939.333i	2.01358	−	1.16254i
$809$	478.346			0.591281			0.295641	−	0.955299i	$-0.404467\pi$
$809$	478.346			0.591281			0.295641	+	0.955299i	$0.404467\pi$
$810$			2339.38i			2.88812i
$811$	810.296	−	467.825i	0.999132	−	0.576849i	0.0911409	−	0.995838i	$-0.470949\pi$
$811$	810.296	−	467.825i	0.999132	−	0.576849i	0.907991	+	0.418989i	$0.137615\pi$
$812$	−40.2084	−	23.2143i	−0.0495177	−	0.0285890i
$813$	1610.89	−	930.049i	1.98142	−	1.14397i
$814$	−2.77980	+	4.81475i	−0.00341498	+	0.00591492i
$815$	−98.4977	+	170.603i	−0.120856	+	0.209329i
$816$			269.717i			0.330536i
$817$	562.766	−	122.670i	0.688820	−	0.150146i
$818$	1305.80			1.59633
$819$	−97.9985	−	56.5795i	−0.119656	−	0.0690836i
$820$	2527.43	+	1459.21i	3.08223	+	1.77953i
$821$	207.851	+	360.008i	0.253168	+	0.438500i	0.964396	−	0.264461i	$-0.0851941\pi$
$821$	207.851	+	360.008i	0.253168	+	0.438500i	−0.711228	+	0.702961i	$0.751861\pi$
$822$	−579.241	+	1003.27i	−0.704673	+	1.22053i
$823$	−571.455	−	989.790i	−0.694356	−	1.20266i	−0.970397	−	0.241515i	$-0.922356\pi$
$823$	−571.455	−	989.790i	−0.694356	−	1.20266i	0.276041	−	0.961146i	$-0.410978\pi$
$824$	1329.35			1.61329
$825$		−	3.21271i		−	0.00389419i
$826$	−42.2485	−	73.1765i	−0.0511483	−	0.0885914i
$827$	943.619	−	544.799i	1.14101	−	0.658765i	0.194333	−	0.980936i	$-0.437746\pi$
$827$	943.619	−	544.799i	1.14101	−	0.658765i	0.946682	+	0.322170i	$0.104412\pi$
$828$	386.565			0.466866
$829$			242.265i			0.292237i	0.989267	+	0.146119i	$0.0466781\pi$
$829$			242.265i			0.292237i	−0.989267	+	0.146119i	$0.953322\pi$
$830$	−1319.09	+	761.575i	−1.58926	+	0.917560i
$831$	602.650	+	347.940i	0.725210	+	0.418700i
$832$	1331.43	−	768.699i	1.60027	−	0.923918i
$833$	218.134	−	377.820i	0.261866	−	0.453565i
$834$	−584.094	+	1011.68i	−0.700352	+	1.21305i
$835$			418.004i			0.500604i
$836$	1.52592	−	4.78042i	0.00182527	−	0.00571821i
$837$	598.520			0.715078
$838$	−1325.29	−	765.156i	−1.58149	−	0.913074i
$839$	−1272.95	−	734.939i	−1.51723	−	0.875971i	−0.999795	−	0.0202457i	$-0.993555\pi$
$839$	−1272.95	−	734.939i	−1.51723	−	0.875971i	−0.517431	−	0.855725i	$-0.673112\pi$
$840$	−177.822	−	307.997i	−0.211693	−	0.366663i
$841$	−406.980	+	704.909i	−0.483923	+	0.838180i
$842$	342.026	+	592.407i	0.406207	+	0.703571i
$843$	−1013.61			−1.20238
$844$		−	1158.47i		−	1.37260i
$845$	−403.771	−	699.352i	−0.477836	−	0.827635i
$846$	808.403	−	466.732i	0.955560	−	0.551693i
$847$	148.698			0.175558
$848$			89.9341i			0.106054i
$849$	−1172.13	+	676.731i	−1.38060	+	0.797092i
$850$	−620.776	−	358.405i	−0.730325	−	0.421653i
$851$	385.123	−	222.351i	0.452553	−	0.261282i
$852$	−538.910	+	933.420i	−0.632524	+	1.09556i
$853$	−493.706	+	855.124i	−0.578788	+	1.00249i	0.416831	+	0.908984i	$0.363141\pi$
$853$	−493.706	+	855.124i	−0.578788	+	1.00249i	−0.995619	+	0.0935062i	$0.970192\pi$
$854$		−	67.9631i		−	0.0795821i
$855$	484.209	+	532.199i	0.566326	+	0.622455i
$856$	−614.352			−0.717701
$857$	−1279.05	−	738.461i	−1.49248	−	0.861681i	−0.492513	−	0.870305i	$-0.663922\pi$
$857$	−1279.05	−	738.461i	−1.49248	−	0.861681i	−0.999963	+	0.00862354i	$0.997255\pi$
$858$	−6.78442	−	3.91699i	−0.00790726	−	0.00456526i
$859$	466.025	+	807.179i	0.542520	+	0.939673i	0.998758	+	0.0498150i	$0.0158632\pi$
$859$	466.025	+	807.179i	0.542520	+	0.939673i	−0.456238	+	0.889858i	$0.650803\pi$
$860$	764.917	−	1324.88i	0.889439	−	1.54055i
$861$	135.087	+	233.978i	0.156896	+	0.271752i
$862$	−2361.41			−2.73945
$863$			1088.87i			1.26172i	0.775896	+	0.630861i	$0.217298\pi$
$863$			1088.87i			1.26172i	−0.775896	+	0.630861i	$0.782702\pi$
$864$	−120.832	−	209.287i	−0.139851	−	0.242230i
$865$	1061.97	−	613.127i	1.22771	−	0.708818i
$866$	639.248			0.738162
$867$		−	777.825i		−	0.897145i
$868$	−343.102	+	198.090i	−0.395279	+	0.228214i
$869$	−1.44822	−	0.836128i	−0.00166653	−	0.000962172i
$870$	399.127	−	230.436i	0.458766	−	0.264869i
$871$	−17.8717	+	30.9546i	−0.0205185	+	0.0355392i
$872$	−291.336	+	504.609i	−0.334101	+	0.578680i
$873$		−	622.039i		−	0.712531i
$874$	−460.350	+	418.839i	−0.526716	+	0.479221i
$875$	−14.9581			−0.0170949
$876$	1344.56	+	776.282i	1.53489	+	0.886167i
$877$	−202.296	−	116.796i	−0.230669	−	0.133177i	0.380212	−	0.924899i	$-0.375851\pi$
$877$	−202.296	−	116.796i	−0.230669	−	0.133177i	−0.610881	+	0.791723i	$0.709184\pi$
$878$	−804.378	−	1393.22i	−0.916148	−	1.58681i
$879$	680.013	−	1177.82i	0.773621	−	1.33995i
$880$	−0.975059	−	1.68885i	−0.00110802	−	0.00191915i
$881$	488.267			0.554220			0.277110	−	0.960838i	$-0.410623\pi$
$881$	488.267			0.554220			0.277110	+	0.960838i	$0.410623\pi$
$882$			868.991i			0.985251i
$883$	−833.774	−	1444.14i	−0.944252	−	1.63549i	−0.757243	−	0.653134i	$-0.773454\pi$
$883$	−833.774	−	1444.14i	−0.944252	−	1.63549i	−0.187009	−	0.982358i	$-0.559879\pi$
$884$	−976.240	+	563.632i	−1.10434	+	0.637593i
$885$	540.936			0.611227
$886$			2576.95i			2.90852i
$887$	544.718	−	314.493i	0.614113	−	0.354558i	−0.160460	−	0.987042i	$-0.551298\pi$
$887$	544.718	−	314.493i	0.614113	−	0.354558i	0.774573	+	0.632484i	$0.217965\pi$
$888$	−1644.09	−	949.215i	−1.85145	−	1.06894i
$889$	−168.065	+	97.0325i	−0.189050	+	0.109148i
$890$	1809.51	−	3134.17i	2.03316	−	3.52154i
$891$	−1.82386	+	3.15902i	−0.00204698	+	0.00354547i
$892$		−	1358.27i		−	1.52273i
$893$	−294.736	+	923.350i	−0.330052	+	1.03399i
$894$	−307.725			−0.344211
$895$	−1.36517	−	0.788180i	−0.00152533	−	0.000880648i
$896$	248.885	+	143.694i	0.277774	+	0.160373i
$897$	313.313	+	542.673i	0.349289	+	0.604987i
$898$	658.556	−	1140.65i	0.733359	−	1.27021i
$899$	−115.371	−	199.828i	−0.128332	−	0.222278i
$900$	920.823			1.02314
$901$			106.976i			0.118730i
$902$	3.52801	+	6.11068i	0.00391131	+	0.00677460i
$903$	122.651	−	70.8126i	0.135826	−	0.0784193i
$904$	−1500.86			−1.66025
$905$		−	1037.95i		−	1.14690i
$906$	−2778.54	+	1604.19i	−3.06682	+	1.77063i
$907$	−1402.39	−	809.670i	−1.54619	−	0.892690i	−0.998428	−	0.0560533i	$-0.982148\pi$
$907$	−1402.39	−	809.670i	−1.54619	−	0.892690i	−0.547757	−	0.836637i	$-0.684518\pi$
$908$	−55.8419	+	32.2403i	−0.0614999	+	0.0355070i
$909$	−467.276	+	809.346i	−0.514055	+	0.890369i
$910$	241.949	−	419.068i	0.265878	−	0.460514i
$911$			895.922i			0.983449i	0.870751	+	0.491725i	$0.163633\pi$
$911$			895.922i			0.983449i	−0.870751	+	0.491725i	$0.836367\pi$
$912$	531.421	+	169.631i	0.582699	+	0.185999i
$913$	−2.37500			−0.00260131
$914$	2020.42	+	1166.49i	2.21053	+	1.27625i
$915$	376.798	+	217.544i	0.411801	+	0.237753i
$916$	965.991	+	1673.15i	1.05458	+	1.82658i
$917$	−47.3621	+	82.0336i	−0.0516490	+	0.0894587i
$918$	207.949	+	360.179i	0.226524	+	0.392352i
$919$	741.588			0.806951			0.403476	−	0.914990i	$-0.367802\pi$
$919$	741.588			0.806951			0.403476	+	0.914990i	$0.367802\pi$
$920$			742.943i			0.807546i
$921$	−276.255	−	478.487i	−0.299951	−	0.519530i
$922$	−2041.38	+	1178.59i	−2.21408	+	1.27830i
$923$	−659.101			−0.714086
$924$		−	1.23387i		−	0.00133535i
$925$	917.387	−	529.653i	0.991769	−	0.572598i
$926$	42.1341	+	24.3261i	0.0455012	+	0.0262701i
$927$	−572.697	+	330.647i	−0.617796	+	0.356685i
$928$	−46.5829	+	80.6840i	−0.0501971	+	0.0869440i
$929$	657.059	−	1138.06i	0.707275	−	1.22504i	−0.258589	−	0.965988i	$-0.583257\pi$
$929$	657.059	−	1138.06i	0.707275	−	1.22504i	0.965864	−	0.259049i	$-0.0834093\pi$
$930$		−	3932.66i		−	4.22867i
$931$	−607.225	−	667.407i	−0.652229	−	0.716871i
$932$	65.7070			0.0705011
$933$	629.778	+	363.602i	0.675003	+	0.389713i
$934$	2511.08	+	1449.77i	2.68852	+	1.55222i
$935$	−1.15982	−	2.00887i	−0.00124045	−	0.00214853i
$936$	504.574	−	873.948i	0.539075	−	0.933705i
$937$	392.873	+	680.475i	0.419288	+	0.726228i	0.995868	−	0.0908128i	$-0.0289465\pi$
$937$	392.873	+	680.475i	0.419288	+	0.726228i	−0.576580	+	0.817041i	$0.695613\pi$
$938$	−8.72912			−0.00930610
$939$		−	1188.94i		−	1.26618i
$940$	1287.19	+	2229.48i	1.36935	+	2.37178i
$941$	−224.279	+	129.487i	−0.238341	+	0.137606i	−0.614414	−	0.788984i	$-0.710608\pi$
$941$	−224.279	+	129.487i	−0.238341	+	0.137606i	0.376073	+	0.926590i	$0.377274\pi$
$942$	1123.27			1.19243
$943$		−	564.397i		−	0.598512i
$944$	137.015	−	79.1058i	0.145143	−	0.0837985i
$945$	−99.7141	−	57.5699i	−0.105518	−	0.0609206i
$946$	3.20321	−	1.84938i	0.00338606	−	0.00195494i
$947$	−211.830	+	366.901i	−0.223686	+	0.387435i	−0.955924	−	0.293613i	$-0.905142\pi$
$947$	−211.830	+	366.901i	−0.223686	+	0.387435i	0.732239	+	0.681048i	$0.238476\pi$
$948$	635.268	−	1100.32i	0.670113	−	1.16067i
$949$			949.414i			1.00044i
$950$	−1096.58	+	997.701i	−1.15430	+	1.05021i
$951$	−344.008			−0.361732
$952$	−107.152	−	61.8642i	−0.112555	−	0.0649834i
$953$	1077.21	+	621.927i	1.13034	+	0.652599i	0.944019	−	0.329891i	$-0.107012\pi$
$953$	1077.21	+	621.927i	1.13034	+	0.652599i	0.186316	+	0.982490i	$0.440345\pi$
$954$	−106.541	−	184.534i	−0.111678	−	0.193432i
$955$	−872.794	+	1511.72i	−0.913920	+	1.58296i
$956$	−175.745	−	304.398i	−0.183833	−	0.318408i
$957$	0.718623			0.000750912
$958$			1329.23i			1.38750i
$959$	−55.7893	−	96.6299i	−0.0581745	−	0.100761i
$960$	−2081.60	+	1201.81i	−2.16833	+	1.25189i
$961$	−1007.94			−1.04884
$962$		−	2583.05i		−	2.68508i
$963$	264.668	−	152.806i	0.274837	−	0.158677i
$964$	−874.961	−	505.159i	−0.907636	−	0.524024i
$965$	−762.639	+	440.310i	−0.790300	+	0.456280i
$966$	−76.5163	+	132.530i	−0.0792094	+	0.137195i
$967$	120.498	−	208.709i	0.124610	−	0.215832i	−0.796970	−	0.604019i	$-0.793565\pi$
$967$	120.498	−	208.709i	0.124610	−	0.215832i	0.921581	+	0.388187i	$0.126899\pi$
$968$			1326.08i			1.36992i
$969$	632.121	+	201.775i	0.652344	+	0.208230i
$970$	2660.00			2.74227
$971$	94.1758	+	54.3724i	0.0969885	+	0.0559963i	0.547710	−	0.836668i	$-0.315500\pi$
$971$	94.1758	+	54.3724i	0.0969885	+	0.0559963i	−0.450721	+	0.892665i	$0.648833\pi$
$972$	−1636.32	−	944.730i	−1.68346	−	0.971945i
$973$	−56.2567	−	97.4395i	−0.0578178	−	0.100143i
$974$	1464.90	−	2537.28i	1.50400	−	2.60501i
$975$	746.331	+	1292.68i	0.765467	+	1.32583i
$976$	127.254			0.130383
$977$		−	1730.59i		−	1.77133i	−0.464323	−	0.885666i	$-0.653702\pi$
$977$		−	1730.59i		−	1.77133i	0.464323	−	0.885666i	$-0.346298\pi$
$978$	−180.934	−	313.387i	−0.185004	−	0.320437i
$979$	4.88701	−	2.82152i	0.00499184	−	0.00288204i
$980$	−2396.57			−2.44548
$981$		−	289.853i		−	0.295467i
$982$	2035.82	−	1175.38i	2.07313	−	1.19692i
$983$	1505.59	+	869.256i	1.53163	+	0.884288i	0.999287	+	0.0377615i	$0.0120227\pi$
$983$	1505.59	+	869.256i	1.53163	+	0.884288i	0.532346	+	0.846527i	$0.321311\pi$
$984$	−2086.61	+	1204.71i	−2.12054	+	1.22429i
$985$	−992.600	+	1719.23i	−1.00772	+	1.74542i
$986$	80.1685	−	138.856i	0.0813068	−	0.140828i
$987$			238.324i			0.241463i
$988$	496.540	+	2277.96i	0.502571	+	2.30562i
$989$	−295.856			−0.299147
$990$	4.00142	+	2.31022i	0.00404184	+	0.00233356i
$991$	−273.421	−	157.860i	−0.275904	−	0.159293i	0.355663	−	0.934614i	$-0.384255\pi$
$991$	−273.421	−	157.860i	−0.275904	−	0.159293i	−0.631568	+	0.775321i	$0.717588\pi$
$992$	397.497	+	688.485i	0.400702	+	0.694037i
$993$	−477.656	+	827.325i	−0.481023	+	0.833157i
$994$	−80.4818	−	139.399i	−0.0809677	−	0.140240i
$995$	−1070.21			−1.07559
$996$		−	1804.46i		−	1.81171i
$997$	637.836	+	1104.76i	0.639755	+	1.10809i	0.985486	+	0.169755i	$0.0542976\pi$
$997$	637.836	+	1104.76i	0.639755	+	1.10809i	−0.345731	+	0.938334i	$0.612369\pi$
$998$	445.010	−	256.927i	0.445902	−	0.257442i
$999$	−614.618			−0.615233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.d.a.8.1	✓	6
3.2	odd	2		171.3.p.d.46.3		6
4.3	odd	2		304.3.r.b.65.2		6
19.2	odd	18		361.3.f.i.127.1		18
19.3	odd	18		361.3.f.i.262.1		18
19.4	even	9		361.3.f.i.299.1		18
19.5	even	9		361.3.f.h.333.1		18
19.6	even	9		361.3.f.i.307.1		18
19.7	even	3		361.3.d.c.69.3		6
19.8	odd	6		361.3.b.b.360.1		6
19.9	even	9		361.3.f.i.116.3		18
19.10	odd	18		361.3.f.h.116.1		18
19.11	even	3		361.3.b.b.360.6		6
19.12	odd	6	inner	19.3.d.a.12.1	yes	6
19.13	odd	18		361.3.f.h.307.3		18
19.14	odd	18		361.3.f.i.333.3		18
19.15	odd	18		361.3.f.h.299.3		18
19.16	even	9		361.3.f.h.262.3		18
19.17	even	9		361.3.f.h.127.3		18
19.18	odd	2		361.3.d.c.293.3		6
57.50	even	6		171.3.p.d.145.3		6
76.31	even	6		304.3.r.b.145.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.1	✓	6	1.1	even	1	trivial
19.3.d.a.12.1	yes	6	19.12	odd	6	inner
171.3.p.d.46.3		6	3.2	odd	2
171.3.p.d.145.3		6	57.50	even	6
304.3.r.b.65.2		6	4.3	odd	2
304.3.r.b.145.2		6	76.31	even	6
361.3.b.b.360.1		6	19.8	odd	6
361.3.b.b.360.6		6	19.11	even	3
361.3.d.c.69.3		6	19.7	even	3
361.3.d.c.293.3		6	19.18	odd	2
361.3.f.h.116.1		18	19.10	odd	18
361.3.f.h.127.3		18	19.17	even	9
361.3.f.h.262.3		18	19.16	even	9
361.3.f.h.299.3		18	19.15	odd	18
361.3.f.h.307.3		18	19.13	odd	18
361.3.f.h.333.1		18	19.5	even	9
361.3.f.i.116.3		18	19.9	even	9
361.3.f.i.127.1		18	19.2	odd	18
361.3.f.i.262.1		18	19.3	odd	18
361.3.f.i.299.1		18	19.4	even	9
361.3.f.i.307.1		18	19.6	even	9
361.3.f.i.333.3		18	19.14	odd	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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.90671 - 1.67819i) q^{2} +(-3.29225 - 1.90078i) q^{3} +(3.63264 + 6.29191i) q^{4} +(3.47303 - 6.01546i) q^{5} +(6.37974 + 11.0500i) q^{6} -1.22892 q^{7} -10.9595i q^{8} +(2.72593 + 4.72145i) q^{9} +O(q^{10})\)	\(q+(-2.90671 - 1.67819i) q^{2} +(-3.29225 - 1.90078i) q^{3} +(3.63264 + 6.29191i) q^{4} +(3.47303 - 6.01546i) q^{5} +(6.37974 + 11.0500i) q^{6} -1.22892 q^{7} -10.9595i q^{8} +(2.72593 + 4.72145i) q^{9} +(-20.1902 + 11.6568i) q^{10} -0.0363521 q^{11} -27.6194i q^{12} +(14.6268 - 8.44481i) q^{13} +(3.57212 + 2.06236i) q^{14} +(-22.8681 + 13.2029i) q^{15} +(-3.86156 + 6.68842i) q^{16} +(-4.59329 + 7.95581i) q^{17} -18.2985i q^{18} +(12.7864 + 14.0537i) q^{19} +50.4650 q^{20} +(4.04592 + 2.33591i) q^{21} +(0.105665 + 0.0610058i) q^{22} +(-4.87974 - 8.45195i) q^{23} +(-20.8316 + 36.0814i) q^{24} +(-11.6238 - 20.1331i) q^{25} -56.6879 q^{26} +13.4885i q^{27} +(-4.46423 - 7.73228i) q^{28} +(4.50339 - 2.60003i) q^{29} +88.6280 q^{30} -44.3727i q^{31} +(-15.5160 + 8.95814i) q^{32} +(0.119680 + 0.0690974i) q^{33} +(26.7027 - 15.4168i) q^{34} +(-4.26808 + 7.39254i) q^{35} +(-19.8046 + 34.3026i) q^{36} +45.5661i q^{37} +(-13.5817 - 62.3081i) q^{38} -64.2069 q^{39} +(-65.9264 - 38.0626i) q^{40} +(50.0829 + 28.9153i) q^{41} +(-7.84020 - 13.5796i) q^{42} +(15.1574 - 26.2534i) q^{43} +(-0.132054 - 0.228724i) q^{44} +37.8689 q^{45} +32.7565i q^{46} +(25.5066 + 44.1787i) q^{47} +(25.4264 - 14.6800i) q^{48} -47.4897 q^{49} +78.0280i q^{50} +(30.2445 - 17.4617i) q^{51} +(106.268 + 61.3538i) q^{52} +(10.0847 - 5.82239i) q^{53} +(22.6362 - 39.2071i) q^{54} +(-0.126252 + 0.218675i) q^{55} +13.4684i q^{56} +(-15.3831 - 70.5725i) q^{57} -17.4534 q^{58} +(-17.7409 - 10.2427i) q^{59} +(-166.143 - 95.9229i) q^{60} +(-8.23849 - 14.2695i) q^{61} +(-74.4658 + 128.978i) q^{62} +(-3.34996 - 5.80229i) q^{63} +91.0263 q^{64} -117.316i q^{65} +(-0.231917 - 0.401692i) q^{66} +(-1.83276 + 1.05814i) q^{67} -66.7430 q^{68} +37.1012i q^{69} +(24.8121 - 14.3253i) q^{70} +(-33.7958 - 19.5120i) q^{71} +(51.7447 - 29.8748i) q^{72} +(-28.1064 + 48.6818i) q^{73} +(76.4686 - 132.447i) q^{74} +88.3775i q^{75} +(-41.9762 + 131.503i) q^{76} +0.0446740 q^{77} +(186.631 + 107.751i) q^{78} +(39.8385 + 23.0008i) q^{79} +(26.8226 + 46.4581i) q^{80} +(50.1720 - 86.9004i) q^{81} +(-97.0508 - 168.097i) q^{82} +65.3332 q^{83} +33.9421i q^{84} +(31.9053 + 55.2615i) q^{85} +(-88.1162 + 50.8739i) q^{86} -19.7684 q^{87} +0.398401i q^{88} +(-134.435 + 77.6163i) q^{89} +(-110.074 - 63.5512i) q^{90} +(-17.9753 + 10.3780i) q^{91} +(35.4526 - 61.4058i) q^{92} +(-84.3427 + 146.086i) q^{93} -171.219i q^{94} +(128.947 - 28.1074i) q^{95} +68.1098 q^{96} +(-98.8107 - 57.0484i) q^{97} +(138.039 + 79.6968i) q^{98} +(-0.0990933 - 0.171635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23} - 83 q^{24} - 17 q^{25} - 148 q^{26} + 32 q^{28} - 12 q^{29} + 304 q^{30} + 51 q^{32} + 123 q^{33} - 6 q^{34} - 38 q^{35} - 54 q^{36} - 14 q^{38} - 44 q^{39} - 96 q^{40} + 63 q^{41} - 92 q^{42} - 34 q^{43} - 69 q^{44} - 28 q^{45} + 58 q^{47} - 147 q^{48} + 18 q^{49} + 132 q^{51} + 162 q^{52} - 12 q^{53} + 29 q^{54} - 28 q^{55} - 16 q^{57} + 172 q^{58} - 147 q^{59} - 222 q^{60} + 58 q^{61} - 116 q^{62} + 86 q^{63} + 166 q^{64} + 11 q^{66} + 201 q^{67} - 84 q^{68} - 198 q^{70} - 102 q^{71} + 210 q^{72} + 7 q^{73} + 174 q^{74} - 173 q^{76} - 376 q^{77} + 450 q^{78} + 134 q^{80} + 253 q^{81} - 145 q^{82} + 146 q^{83} - 90 q^{85} - 270 q^{86} - 568 q^{87} - 72 q^{89} - 438 q^{90} - 216 q^{91} + 72 q^{92} - 160 q^{93} + 558 q^{95} + 126 q^{96} + 21 q^{97} + 411 q^{98} - 56 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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