LMFDB - Embedded newform 273.3.w.c.116.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(116,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("273.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	273.w (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:	$7.43871121704$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16 x^{14} - 176 x^{13} + 344 x^{12} + 4576 x^{11} + 11040 x^{10} - 37664 x^{9} + \cdots + 97900608 $ x^16 - 16x^14 - 176x^13 + 344x^12 + 4576x^11 + 11040x^10 - 37664x^9 - 313120x^8 - 230912x^7 + 2040576x^6 + 9332224x^5 + 33838912x^4 + 73579264x^3 + 95390464x^2 + 117266688x + 97900608
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.3
Root			$4.54639 + 2.26426i$ of defining polynomial
Character	$\chi$	$=$	273.116
Dual form			273.3.w.c.233.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.759866 - 1.31613i) q^{2} +(-0.447581 - 2.96642i) q^{3} +(0.845208 - 1.46394i) q^{4} +(-0.681452 - 1.18031i) q^{5} +(-3.56409 + 2.84316i) q^{6} +(0.736052 + 6.96119i) q^{7} -8.64790 q^{8} +(-8.59934 + 2.65543i) q^{9} +O(q^{10})$	\(q+(-0.759866 - 1.31613i) q^{2} +(-0.447581 - 2.96642i) q^{3} +(0.845208 - 1.46394i) q^{4} +(-0.681452 - 1.18031i) q^{5} +(-3.56409 + 2.84316i) q^{6} +(0.736052 + 6.96119i) q^{7} -8.64790 q^{8} +(-8.59934 + 2.65543i) q^{9} +(-1.03562 + 1.79375i) q^{10} +(-2.96105 + 5.12869i) q^{11} +(-4.72097 - 1.85201i) q^{12} -13.0000 q^{13} +(8.60251 - 6.25831i) q^{14} +(-3.19629 + 2.54976i) q^{15} +(3.19042 + 5.52596i) q^{16} +(-8.60251 - 4.96666i) q^{17} +(10.0292 + 9.30005i) q^{18} +(-7.13265 + 4.11804i) q^{19} -2.30387 q^{20} +(20.3204 - 5.29914i) q^{21} +9.00000 q^{22} +(-2.23720 + 1.29165i) q^{23} +(3.87064 + 25.6534i) q^{24} +(11.5712 - 20.0420i) q^{25} +(9.87826 + 17.1096i) q^{26} +(11.7260 + 24.3208i) q^{27} +(10.8129 + 4.80612i) q^{28} -21.1583i q^{29} +(5.78456 + 2.26925i) q^{30} +(-9.34080 - 5.39292i) q^{31} +(-12.4472 + 21.5592i) q^{32} +(16.5392 + 6.48822i) q^{33} +15.0960i q^{34} +(7.71478 - 5.61249i) q^{35} +(-3.38083 + 14.8333i) q^{36} +(-28.5306 + 16.4721i) q^{37} +(10.8397 + 6.25831i) q^{38} +(5.81856 + 38.5635i) q^{39} +(5.89313 + 10.2072i) q^{40} +16.9822 q^{41} +(-22.4151 - 22.7176i) q^{42} -3.30958 q^{43} +(5.00540 + 8.66961i) q^{44} +(8.99427 + 8.34033i) q^{45} +(3.39995 + 1.96296i) q^{46} +(-32.9393 - 57.0526i) q^{47} +(14.9644 - 11.9374i) q^{48} +(-47.9165 + 10.2476i) q^{49} -35.1704 q^{50} +(-10.8829 + 27.7417i) q^{51} +(-10.9877 + 19.0313i) q^{52} +(58.6730 + 33.8749i) q^{53} +(23.0990 - 33.9135i) q^{54} +8.07125 q^{55} +(-6.36531 - 60.1997i) q^{56} +(15.4083 + 19.3153i) q^{57} +(-27.8470 + 16.0775i) q^{58} +(8.56949 - 14.8428i) q^{59} +(1.03117 + 6.83426i) q^{60} +(-9.60687 - 16.6396i) q^{61} +16.3916i q^{62} +(-24.8145 - 57.9072i) q^{63} +63.3562 q^{64} +(8.85887 + 15.3440i) q^{65} +(-4.02823 - 26.6978i) q^{66} +(-88.3081 - 50.9847i) q^{67} +(-14.5418 + 8.39572i) q^{68} +(4.83291 + 6.05837i) q^{69} +(-13.2489 - 5.88888i) q^{70} +27.8257 q^{71} +(74.3663 - 22.9639i) q^{72} +(-87.1163 - 50.2966i) q^{73} +(43.3588 + 25.0332i) q^{74} +(-64.6321 - 25.3548i) q^{75} +13.9224i q^{76} +(-37.8813 - 16.8375i) q^{77} +(46.3331 - 36.9610i) q^{78} +(28.4521 + 49.2804i) q^{79} +(4.34823 - 7.53135i) q^{80} +(66.8974 - 45.6699i) q^{81} +(-12.9042 - 22.3507i) q^{82} +104.294 q^{83} +(9.41733 - 34.2268i) q^{84} +13.5382i q^{85} +(2.51484 + 4.35583i) q^{86} +(-62.7645 + 9.47006i) q^{87} +(25.6069 - 44.3524i) q^{88} +(-43.7586 - 75.7921i) q^{89} +(4.14249 - 18.1751i) q^{90} +(-9.56867 - 90.4955i) q^{91} +4.36685i q^{92} +(-11.8169 + 30.1226i) q^{93} +(-50.0589 + 86.7046i) q^{94} +(9.72111 + 5.61249i) q^{95} +(69.5250 + 27.2743i) q^{96} +27.8448i q^{97} +(49.8972 + 55.2773i) q^{98} +(11.8442 - 51.9662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 24 * q^4 - 16 * q^9	$ 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) $ 16 * q - 24 * q^4 - 16 * q^9 + 96 * q^10 - 88 * q^12 - 208 * q^13 - 24 * q^16 + 144 * q^22 - 40 * q^25 + 264 * q^30 + 96 * q^36 + 432 * q^40 - 448 * q^42 - 128 * q^43 + 352 * q^48 - 504 * q^49 + 280 * q^51 + 312 * q^52 - 96 * q^55 + 184 * q^61 - 112 * q^64 - 448 * q^69 - 528 * q^75 + 80 * q^79 + 584 * q^81 + 544 * q^82 - 448 * q^87 + 72 * q^88 - 384 * q^90 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.759866	−	1.31613i	−0.379933	−	0.658063i	0.611119	−	0.791539i	$-0.290720\pi$
$2$	−0.759866	−	1.31613i	−0.379933	−	0.658063i	−0.991052	+	0.133475i	$0.957386\pi$
$3$	−0.447581	−	2.96642i	−0.149194	−	0.988808i
$3$	−0.447581	−	2.96642i	−0.149194	−	0.988808i
$4$	0.845208	−	1.46394i	0.211302	−	0.365986i
$5$	−0.681452	−	1.18031i	−0.136290	−	0.236062i	0.789799	−	0.613365i	$-0.210185\pi$
$5$	−0.681452	−	1.18031i	−0.136290	−	0.236062i	−0.926090	+	0.377304i	$0.876851\pi$
$6$	−3.56409	+	2.84316i	−0.594014	+	0.473860i
$7$	0.736052	+	6.96119i	0.105150	+	0.994456i
$7$	0.736052	+	6.96119i	0.105150	+	0.994456i
$8$	−8.64790			−1.08099
$9$	−8.59934	+	2.65543i	−0.955482	+	0.295048i
$10$	−1.03562	+	1.79375i	−0.103562	+	0.179375i
$11$	−2.96105	+	5.12869i	−0.269186	+	0.466244i	−0.968652	−	0.248422i	$-0.920088\pi$
$11$	−2.96105	+	5.12869i	−0.269186	+	0.466244i	0.699466	+	0.714666i	$0.253421\pi$
$12$	−4.72097	−	1.85201i	−0.393415	−	0.154334i
$13$	−13.0000			−1.00000
$13$	−13.0000			−1.00000
$14$	8.60251	−	6.25831i	0.614465	−	0.447022i
$15$	−3.19629	+	2.54976i	−0.213086	+	0.169984i
$16$	3.19042	+	5.52596i	0.199401	+	0.345373i
$17$	−8.60251	−	4.96666i	−0.506030	−	0.292157i	0.225170	−	0.974319i	$-0.427706\pi$
$17$	−8.60251	−	4.96666i	−0.506030	−	0.292157i	−0.731200	+	0.682163i	$0.761039\pi$
$18$	10.0292	+	9.30005i	0.557179	+	0.516669i
$19$	−7.13265	+	4.11804i	−0.375403	+	0.216739i	−0.675816	−	0.737070i	$-0.736209\pi$
$19$	−7.13265	+	4.11804i	−0.375403	+	0.216739i	0.300414	+	0.953809i	$0.402875\pi$
$20$	−2.30387			−0.115194
$21$	20.3204	−	5.29914i	0.967639	−	0.252340i
$22$	9.00000			0.409091
$23$	−2.23720	+	1.29165i	−0.0972697	+	0.0561587i	−0.547846	−	0.836579i	$-0.684552\pi$
$23$	−2.23720	+	1.29165i	−0.0972697	+	0.0561587i	0.450576	+	0.892738i	$0.351219\pi$
$24$	3.87064	+	25.6534i	0.161277	+	1.06889i
$25$	11.5712	−	20.0420i	0.462850	−	0.801680i
$26$	9.87826	+	17.1096i	0.379933	+	0.658063i
$27$	11.7260	+	24.3208i	0.434298	+	0.900769i
$28$	10.8129	+	4.80612i	0.386175	+	0.171647i
$29$		−	21.1583i		−	0.729596i	−0.931087	−	0.364798i	$-0.881138\pi$
$29$		−	21.1583i		−	0.729596i	0.931087	−	0.364798i	$-0.118862\pi$
$30$	5.78456	+	2.26925i	0.192819	+	0.0756416i
$31$	−9.34080	−	5.39292i	−0.301316	−	0.173965i	0.341718	−	0.939803i	$-0.388991\pi$
$31$	−9.34080	−	5.39292i	−0.301316	−	0.173965i	−0.643034	+	0.765838i	$0.722325\pi$
$32$	−12.4472	+	21.5592i	−0.388976	+	0.673726i
$33$	16.5392	+	6.48822i	0.501187	+	0.196613i
$34$			15.0960i			0.444000i
$35$	7.71478	−	5.61249i	0.220422	−	0.160357i
$36$	−3.38083	+	14.8333i	−0.0939120	+	0.412037i
$37$	−28.5306	+	16.4721i	−0.771097	+	0.445193i	−0.833266	−	0.552872i	$-0.813532\pi$
$37$	−28.5306	+	16.4721i	−0.771097	+	0.445193i	0.0621687	+	0.998066i	$0.480198\pi$
$38$	10.8397	+	6.25831i	0.285256	+	0.164692i
$39$	5.81856	+	38.5635i	0.149194	+	0.988808i
$40$	5.89313	+	10.2072i	0.147328	+	0.255180i
$41$	16.9822			0.414199			0.207099	−	0.978320i	$-0.433598\pi$
$41$	16.9822			0.414199			0.207099	+	0.978320i	$0.433598\pi$
$42$	−22.4151	−	22.7176i	−0.533693	−	0.540895i
$43$	−3.30958			−0.0769671			−0.0384835	−	0.999259i	$-0.512253\pi$
$43$	−3.30958			−0.0769671			−0.0384835	+	0.999259i	$0.512253\pi$
$44$	5.00540	+	8.66961i	0.113759	+	0.197037i
$45$	8.99427	+	8.34033i	0.199873	+	0.185341i
$46$	3.39995	+	1.96296i	0.0739119	+	0.0426731i
$47$	−32.9393	−	57.0526i	−0.700837	−	1.21389i	−0.968173	−	0.250282i	$-0.919477\pi$
$47$	−32.9393	−	57.0526i	−0.700837	−	1.21389i	0.267336	−	0.963603i	$-0.413857\pi$
$48$	14.9644	−	11.9374i	0.311758	−	0.248697i
$49$	−47.9165	+	10.2476i	−0.977887	+	0.209135i
$50$	−35.1704			−0.703408
$51$	−10.8829	+	27.7417i	−0.213390	+	0.543954i
$52$	−10.9877	+	19.0313i	−0.211302	+	0.365986i
$53$	58.6730	+	33.8749i	1.10704	+	0.639148i	0.938060	−	0.346472i	$-0.112620\pi$
$53$	58.6730	+	33.8749i	1.10704	+	0.639148i	0.168977	+	0.985620i	$0.445954\pi$
$54$	23.0990	−	33.9135i	0.427759	−	0.628027i
$55$	8.07125			0.146750
$56$	−6.36531	−	60.1997i	−0.113666	−	1.07500i
$57$	15.4083	+	19.3153i	0.270321	+	0.338865i
$58$	−27.8470	+	16.0775i	−0.480120	+	0.277198i
$59$	8.56949	−	14.8428i	0.145246	−	0.251573i	−0.784219	−	0.620484i	$-0.786936\pi$
$59$	8.56949	−	14.8428i	0.145246	−	0.251573i	0.929465	+	0.368911i	$0.120269\pi$
$60$	1.03117	+	6.83426i	0.0171862	+	0.113904i
$61$	−9.60687	−	16.6396i	−0.157490	−	0.272780i	0.776473	−	0.630150i	$-0.217007\pi$
$61$	−9.60687	−	16.6396i	−0.157490	−	0.272780i	−0.933963	+	0.357370i	$0.883673\pi$
$62$			16.3916i			0.264380i
$63$	−24.8145	−	57.9072i	−0.393882	−	0.919161i
$64$	63.3562			0.989941
$65$	8.85887	+	15.3440i	0.136290	+	0.236062i
$66$	−4.02823	−	26.6978i	−0.0610338	−	0.404512i
$67$	−88.3081	−	50.9847i	−1.31803	−	0.760966i	−0.334620	−	0.942353i	$-0.608608\pi$
$67$	−88.3081	−	50.9847i	−1.31803	−	0.760966i	−0.983412	+	0.181387i	$0.941941\pi$
$68$	−14.5418	+	8.39572i	−0.213850	+	0.123467i
$69$	4.83291	+	6.05837i	0.0700422	+	0.0878025i
$70$	−13.2489	−	5.88888i	−0.189270	−	0.0841269i
$71$	27.8257			0.391911			0.195955	−	0.980613i	$-0.437219\pi$
$71$	27.8257			0.391911			0.195955	+	0.980613i	$0.437219\pi$
$72$	74.3663	−	22.9639i	1.03287	−	0.318943i
$73$	−87.1163	−	50.2966i	−1.19337	−	0.688995i	−0.234304	−	0.972163i	$-0.575281\pi$
$73$	−87.1163	−	50.2966i	−1.19337	−	0.688995i	−0.959070	+	0.283168i	$0.908615\pi$
$74$	43.3588	+	25.0332i	0.585930	+	0.338287i
$75$	−64.6321	−	25.3548i	−0.861761	−	0.338064i
$76$			13.9224i			0.183189i
$77$	−37.8813	−	16.8375i	−0.491965	−	0.218668i
$78$	46.3331	−	36.9610i	0.594014	−	0.473860i
$79$	28.4521	+	49.2804i	0.360153	+	0.623803i	0.987986	−	0.154545i	$-0.0493912\pi$
$79$	28.4521	+	49.2804i	0.360153	+	0.623803i	−0.627833	+	0.778348i	$0.716058\pi$
$80$	4.34823	−	7.53135i	0.0543529	−	0.0941419i
$81$	66.8974	−	45.6699i	0.825893	−	0.563826i
$82$	−12.9042	−	22.3507i	−0.157368	−	0.272569i
$83$	104.294			1.25655			0.628276	−	0.777990i	$-0.283761\pi$
$83$	104.294			1.25655			0.628276	+	0.777990i	$0.283761\pi$
$84$	9.41733	−	34.2268i	0.112111	−	0.407462i
$85$			13.5382i			0.159272i
$86$	2.51484	+	4.35583i	0.0292423	+	0.0506492i
$87$	−62.7645	+	9.47006i	−0.721431	+	0.108851i
$88$	25.6069	−	44.3524i	0.290987	−	0.504005i
$89$	−43.7586	−	75.7921i	−0.491669	−	0.851596i	0.508285	−	0.861189i	$-0.330280\pi$
$89$	−43.7586	−	75.7921i	−0.491669	−	0.851596i	−0.999954	+	0.00959299i	$0.996946\pi$
$90$	4.14249	−	18.1751i	0.0460277	−	0.201946i
$91$	−9.56867	−	90.4955i	−0.105150	−	0.994456i
$92$			4.36685i			0.0474658i
$93$	−11.8169	+	30.1226i	−0.127064	+	0.323898i
$94$	−50.0589	+	86.7046i	−0.532542	+	0.922390i
$95$	9.72111	+	5.61249i	0.102327	+	0.0590788i
$96$	69.5250	+	27.2743i	0.724219	+	0.284107i
$97$			27.8448i			0.287060i	0.989646	+	0.143530i	$0.0458453\pi$
$97$			27.8448i			0.287060i	−0.989646	+	0.143530i	$0.954155\pi$
$98$	49.8972	+	55.2773i	0.509155	+	0.564054i
$99$	11.8442	−	51.9662i	0.119638	−	0.524911i
$100$	−19.5602	−	33.8793i	−0.195602	−	0.338793i
$101$	−145.044	−	83.7414i	−1.43608	−	0.829123i	−0.438508	−	0.898727i	$-0.644493\pi$
$101$	−145.044	−	83.7414i	−1.43608	−	0.829123i	−0.997575	+	0.0696044i	$0.977826\pi$
$102$	44.7811	−	6.75668i	0.439030	−	0.0662420i
$103$	−68.0356	−	117.841i	−0.660540	−	1.14409i	−0.980474	−	0.196649i	$-0.936994\pi$
$103$	−68.0356	−	117.841i	−0.660540	−	1.14409i	0.319934	−	0.947440i	$-0.396339\pi$
$104$	112.423			1.08099
$105$	−20.1020	−	20.3733i	−0.191448	−	0.194031i
$106$		−	102.961i		−	0.971334i
$107$	−103.923	+	59.9998i	−0.971240	+	0.560746i	−0.899614	−	0.436686i	$-0.856152\pi$
$107$	−103.923	+	59.9998i	−0.971240	+	0.560746i	−0.0716262	+	0.997432i	$0.522819\pi$
$108$	45.5152	+	3.38986i	0.421437	+	0.0313876i
$109$	−98.3325	−	56.7723i	−0.902133	−	0.520847i	−0.0242417	−	0.999706i	$-0.507717\pi$
$109$	−98.3325	−	56.7723i	−0.902133	−	0.520847i	−0.877892	+	0.478859i	$0.841050\pi$
$110$	−6.13306	−	10.6228i	−0.0557551	−	0.0965707i
$111$	61.6331	+	77.2612i	0.555253	+	0.696047i
$112$	−36.1190	+	26.2765i	−0.322491	+	0.234612i
$113$			82.4498i			0.729644i	0.931077	+	0.364822i	$0.118870\pi$
$113$			82.4498i			0.729644i	−0.931077	+	0.364822i	$0.881130\pi$
$114$	13.7132	−	34.9563i	0.120291	−	0.306634i
$115$	3.04909	+	1.76039i	0.0265138	+	0.0153078i
$116$	−30.9745	−	17.8832i	−0.267022	−	0.154165i
$117$	111.791	−	34.5206i	0.955482	−	0.295048i
$118$	−26.0467			−0.220734
$119$	28.2420	−	63.5395i	0.237328	−	0.533945i
$120$	27.6412	−	22.0501i	0.230344	−	0.183751i
$121$	42.9644	+	74.4165i	0.355077	+	0.615012i
$122$	−14.5999	+	25.2877i	−0.119671	+	0.207276i
$123$	−7.60089	−	50.3763i	−0.0617959	−	0.409563i
$124$	−15.7898	+	9.11627i	−0.127337	+	0.0735183i
$125$	−65.6136			−0.524909
$126$	−57.3574	+	76.6607i	−0.455218	+	0.608418i
$127$	143.118			1.12691			0.563456	−	0.826146i	$-0.309471\pi$
$127$	143.118			1.12691			0.563456	+	0.826146i	$0.309471\pi$
$128$	1.64670	+	2.85216i	0.0128648	+	0.0222825i
$129$	1.48131	+	9.81763i	0.0114830	+	0.0761057i
$130$	13.4631	−	23.3188i	0.103562	−	0.179375i
$131$	146.509	−	84.5872i	1.11839	−	0.645704i	0.177402	−	0.984139i	$-0.443231\pi$
$131$	146.509	−	84.5872i	1.11839	−	0.645704i	0.940990	+	0.338435i	$0.109898\pi$
$132$	23.4774	−	18.7285i	0.177859	−	0.141883i
$133$	−33.9165	−	46.6207i	−0.255011	−	0.350531i
$134$			154.966i			1.15646i
$135$	20.7153	−	30.4138i	0.153447	−	0.225287i
$136$	74.3937	+	42.9512i	0.547012	+	0.315818i
$137$	−113.201	+	196.070i	−0.826287	+	1.43117i	0.0746447	+	0.997210i	$0.476218\pi$
$137$	−113.201	+	196.070i	−0.826287	+	1.43117i	−0.900932	+	0.433961i	$0.857116\pi$
$138$	4.30122	−	10.9643i	0.0311683	−	0.0794512i
$139$	24.8821			0.179008			0.0895040	−	0.995986i	$-0.471472\pi$
$139$	24.8821			0.179008			0.0895040	+	0.995986i	$0.471472\pi$
$140$	−1.69577	−	16.0377i	−0.0121126	−	0.114555i
$141$	−154.499	+	123.248i	−1.09574	+	0.874097i
$142$	−21.1438	−	36.6221i	−0.148900	−	0.257902i
$143$	38.4936	−	66.6729i	0.269186	−	0.466244i
$144$	−42.1093	−	39.0477i	−0.292426	−	0.271165i
$145$	−24.9733	+	14.4184i	−0.172230	+	0.0994369i
$146$			152.875i			1.04709i
$147$	51.8452	+	137.554i	0.352689	+	0.935741i
$148$			55.6896i			0.376281i
$149$	−13.3098	−	23.0532i	−0.0893274	−	0.154720i	0.817900	−	0.575361i	$-0.195138\pi$
$149$	−13.3098	−	23.0532i	−0.0893274	−	0.154720i	−0.907227	+	0.420641i	$0.861805\pi$
$150$	15.7416	+	104.330i	0.104944	+	0.695535i
$151$	5.60810	+	3.23784i	0.0371398	+	0.0214426i	0.518455	−	0.855105i	$-0.326507\pi$
$151$	5.60810	+	3.23784i	0.0371398	+	0.0214426i	−0.481315	+	0.876548i	$0.659841\pi$
$152$	61.6825	−	35.6124i	0.405806	−	0.234292i
$153$	87.1646	+	19.8666i	0.569703	+	0.129847i
$154$	6.62447	+	62.6507i	0.0430160	+	0.406823i
$155$			14.7000i			0.0948390i
$156$	61.3727	+	24.0761i	0.393415	+	0.154334i
$157$	−110.262	+	190.979i	−0.702304	+	1.21643i	0.265352	+	0.964152i	$0.414512\pi$
$157$	−110.262	+	190.979i	−0.702304	+	1.21643i	−0.967656	+	0.252274i	$0.918822\pi$
$158$	43.2395	−	74.8931i	0.273668	−	0.474007i
$159$	74.2263	−	189.211i	0.466832	−	1.19000i
$160$	33.9288			0.212055
$161$	−10.6381	−	14.6229i	−0.0660753	−	0.0908254i
$162$	−110.940	−	53.3424i	−0.684817	−	0.329274i
$163$	−24.4470	+	14.1145i	−0.149982	+	0.0865920i	−0.573113	−	0.819476i	$-0.694264\pi$
$163$	−24.4470	+	14.1145i	−0.149982	+	0.0865920i	0.423131	+	0.906069i	$0.360931\pi$
$164$	14.3534	−	24.8609i	0.0875210	−	0.151591i
$165$	−3.61254	−	23.9427i	−0.0218942	−	0.145108i
$166$	−79.2494	−	137.264i	−0.477406	−	0.826891i
$167$	−262.828			−1.57382			−0.786909	−	0.617069i	$-0.788320\pi$
$167$	−262.828			−1.57382			−0.786909	+	0.617069i	$0.788320\pi$
$168$	−175.729	+	45.8265i	−1.04601	+	0.272777i
$169$	169.000			1.00000
$170$	17.8179	−	10.2872i	0.104811	−	0.0605128i
$171$	50.4009	−	54.3527i	0.294742	−	0.317852i
$172$	−2.79729	+	4.84504i	−0.0162633	+	0.0281689i
$173$	97.5574	−	56.3248i	0.563916	−	0.325577i	−0.190800	−	0.981629i	$-0.561108\pi$
$173$	97.5574	−	56.3248i	0.563916	−	0.325577i	0.754716	+	0.656052i	$0.227775\pi$
$174$	60.1564	+	75.4100i	0.345726	+	0.433391i
$175$	148.033	+	65.7978i	0.845904	+	0.375987i
$176$	−37.7879			−0.214704
$177$	−47.8656	−	18.7774i	−0.270427	−	0.106087i
$178$	−66.5013	+	115.184i	−0.373603	+	0.647099i
$179$	−128.612	−	74.2540i	−0.718501	−	0.414827i	0.0956998	−	0.995410i	$-0.469491\pi$
$179$	−128.612	−	74.2540i	−0.718501	−	0.414827i	−0.814201	+	0.580584i	$0.802824\pi$
$180$	19.8118	−	6.11778i	0.110066	−	0.0339877i
$181$	−42.0467			−0.232302			−0.116151	−	0.993232i	$-0.537056\pi$
$181$	−42.0467			−0.232302			−0.116151	+	0.993232i	$0.537056\pi$
$182$	−111.833	+	81.3580i	−0.614465	+	0.447022i
$183$	−45.0602	+	35.9456i	−0.246231	+	0.196424i
$184$	19.3471	−	11.1701i	0.105147	−	0.0607069i
$185$	38.8844	+	22.4499i	0.210186	+	0.121351i
$186$	48.6243	−	7.33656i	0.261421	−	0.0394439i
$187$	50.9449	−	29.4131i	0.272433	−	0.157289i
$188$	−111.362			−0.592353
$189$	−160.671	+	99.5286i	−0.850109	+	0.526606i
$190$		−	17.0589i		−	0.0897839i
$191$	112.872	−	65.1664i	0.590950	−	0.341185i	−0.174523	−	0.984653i	$-0.555838\pi$
$191$	112.872	−	65.1664i	0.590950	−	0.341185i	0.765473	+	0.643468i	$0.222505\pi$
$192$	−28.3571	−	187.941i	−0.147693	−	0.978862i
$193$	245.910	+	141.976i	1.27415	+	0.735628i	0.975765	−	0.218819i	$-0.0702205\pi$
$193$	245.910	+	141.976i	1.27415	+	0.735628i	0.298380	+	0.954447i	$0.403554\pi$
$194$	36.6472	−	21.1583i	0.188903	−	0.109063i
$195$	41.5518	−	33.1469i	0.213086	−	0.169984i
$196$	−25.4975	+	78.8083i	−0.130089	+	0.402083i
$197$	11.8442			0.0601228			0.0300614	−	0.999548i	$-0.490430\pi$
$197$	11.8442			0.0601228			0.0300614	+	0.999548i	$0.490430\pi$
$198$	−77.3941	+	23.8989i	−0.390879	+	0.120701i
$199$	−46.4987	+	80.5382i	−0.233662	+	0.404714i	−0.958883	−	0.283802i	$-0.908404\pi$
$199$	−46.4987	+	80.5382i	−0.233662	+	0.404714i	0.725221	+	0.688516i	$0.241738\pi$
$200$	−100.067	+	173.321i	−0.500335	+	0.866606i
$201$	−111.717	+	284.779i	−0.555807	+	1.41681i
$202$			254.529i			1.26004i
$203$	147.287	−	15.5736i	0.725552	−	0.0767173i
$204$	31.4139	+	39.3794i	0.153990	+	0.193036i
$205$	−11.5725	−	20.0442i	−0.0564513	−	0.0977765i
$206$	−103.396	+	179.087i	−0.501922	+	0.869354i
$207$	15.8086	−	17.0481i	0.0763700	−	0.0823579i
$208$	−41.4754	−	71.8375i	−0.199401	−	0.345373i
$209$		−	48.7748i		−	0.233372i
$210$	−11.5389	+	41.9377i	−0.0549474	+	0.199703i
$211$	189.047			0.895956			0.447978	−	0.894045i	$-0.352144\pi$
$211$	189.047			0.895956			0.447978	+	0.894045i	$0.352144\pi$
$212$	99.1817	−	57.2626i	0.467838	−	0.270107i
$213$	−12.4542	−	82.5427i	−0.0584706	−	0.387524i
$214$	157.935	+	91.1836i	0.738012	+	0.426092i
$215$	2.25532	+	3.90633i	0.0104899	+	0.0181690i
$216$	−101.406	−	210.324i	−0.469471	−	0.973721i
$217$	30.6658	−	68.9926i	0.141317	−	0.317938i
$218$			172.557i			0.791548i
$219$	−110.210	+	280.936i	−0.503240	+	1.28281i
$220$	6.82188	−	11.8158i	0.0310086	−	0.0537084i
$221$	111.833	+	64.5666i	0.506030	+	0.292157i
$222$	54.8526	−	139.825i	0.247084	−	0.629843i
$223$		−	265.517i		−	1.19066i	−0.803481	−	0.595330i	$-0.797021\pi$
$223$		−	265.517i		−	1.19066i	0.803481	−	0.595330i	$-0.202979\pi$
$224$	−159.240	−	70.7789i	−0.710892	−	0.315977i
$225$	−46.2850	+	203.075i	−0.205711	+	0.902554i
$226$	108.514	−	62.6507i	0.480152	−	0.277216i
$227$	−20.7516	+	35.9429i	−0.0914168	+	0.158339i	−0.908108	−	0.418737i	$-0.862473\pi$
$227$	−20.7516	+	35.9429i	−0.0914168	+	0.158339i	0.816691	+	0.577076i	$0.195806\pi$
$228$	41.2997	−	6.23140i	0.181139	−	0.0273307i
$229$	18.5243	−	10.6950i	0.0808921	−	0.0467031i	−0.459008	−	0.888432i	$-0.651795\pi$
$229$	18.5243	−	10.6950i	0.0808921	−	0.0467031i	0.539900	+	0.841729i	$0.318462\pi$
$230$		−	5.35065i		−	0.0232637i
$231$	−32.9921	+	119.908i	−0.142823	+	0.519082i
$232$			182.975i			0.788685i
$233$	−324.073	+	187.104i	−1.39087	+	0.803019i	−0.993412	−	0.114601i	$-0.963441\pi$
$233$	−324.073	+	187.104i	−1.39087	+	0.803019i	−0.397459	+	0.917620i	$0.630108\pi$
$234$	−130.380	−	120.901i	−0.557179	−	0.516669i
$235$	−44.8931	+	77.7572i	−0.191035	+	0.330882i
$236$	−14.4860	−	25.0905i	−0.0613814	−	0.106316i
$237$	133.452	−	106.458i	0.563089	−	0.449190i
$238$	−105.086	+	11.1114i	−0.441538	+	0.0466867i
$239$	301.411			1.26113			0.630567	−	0.776135i	$-0.282823\pi$
$239$	301.411			1.26113			0.630567	+	0.776135i	$0.282823\pi$
$240$	−24.2874	−	9.52780i	−0.101197	−	0.0396992i
$241$	373.439	+	215.605i	1.54954	+	0.894626i	0.998177	+	0.0603596i	$0.0192248\pi$
$241$	373.439	+	215.605i	1.54954	+	0.894626i	0.551361	+	0.834267i	$0.314109\pi$
$242$	65.2943	−	113.093i	0.269811	−	0.467327i
$243$	−165.418	−	178.005i	−0.680734	−	0.732531i
$244$	−32.4792			−0.133112
$245$	44.7481	+	49.5730i	0.182645	+	0.202339i
$246$	−60.5259	+	48.2829i	−0.246040	+	0.196272i
$247$	92.7244	−	53.5345i	0.375403	−	0.216739i
$248$	80.7784	+	46.6374i	0.325719	+	0.188054i
$249$	−46.6800	−	309.380i	−0.187470	−	1.24249i
$250$	49.8575	+	86.3557i	0.199430	+	0.345423i
$251$		−	344.407i		−	1.37214i	−0.727536	−	0.686070i	$-0.759334\pi$
$251$		−	344.407i		−	1.37214i	0.727536	−	0.686070i	$-0.240666\pi$
$252$	−105.746	−	12.6165i	−0.419628	−	0.0500655i
$253$		−	15.2986i		−	0.0604686i
$254$	−108.750	−	188.361i	−0.428151	−	0.741580i
$255$	40.1599	−	6.05943i	0.157490	−	0.0237625i
$256$	129.215	−	223.807i	0.504746	−	0.874246i
$257$	180.999	−	104.500i	0.704276	−	0.406614i	−0.104662	−	0.994508i	$-0.533376\pi$
$257$	180.999	−	104.500i	0.704276	−	0.406614i	0.808938	+	0.587894i	$0.200043\pi$
$258$	11.7956	−	9.40967i	0.0457196	−	0.0364716i
$259$	−135.666	−	186.483i	−0.523806	−	0.720010i
$260$	29.9504			0.115194
$261$	56.1844	+	181.947i	0.215266	+	0.697117i
$262$	−222.655	−	128.550i	−0.849827	−	0.490648i
$263$	−144.352	−	83.3415i	−0.548866	−	0.316888i	0.199798	−	0.979837i	$-0.435971\pi$
$263$	−144.352	−	83.3415i	−0.548866	−	0.316888i	−0.748665	+	0.662949i	$0.769305\pi$
$264$	−143.029	−	56.1095i	−0.541777	−	0.212536i
$265$		−	92.3363i		−	0.348439i
$266$	−35.5867	+	80.0638i	−0.133785	+	0.300992i
$267$	−205.246	+	163.730i	−0.768711	+	0.613219i
$268$	−149.277	+	86.1854i	−0.557005	+	0.321587i
$269$	−330.092	−	190.579i	−1.22711	−	0.708471i	−0.260683	−	0.965424i	$-0.583948\pi$
$269$	−330.092	−	190.579i	−1.22711	−	0.708471i	−0.966424	+	0.256954i	$0.917281\pi$
$270$	−55.7692	−	4.15355i	−0.206553	−	0.0153835i
$271$	315.379	−	182.084i	1.16376	−	0.671898i	0.211558	−	0.977365i	$-0.432146\pi$
$271$	315.379	−	182.084i	1.16376	−	0.671898i	0.952202	+	0.305468i	$0.0988128\pi$
$272$		−	63.3829i		−	0.233025i
$273$	−264.165	+	68.8888i	−0.967639	+	0.252340i
$274$	344.071			1.25573
$275$	68.5261	+	118.691i	0.249186	+	0.431602i
$276$	12.9539	−	1.95452i	0.0469345	−	0.00708159i
$277$	3.36853	−	5.83447i	0.0121608	−	0.0210631i	−0.859881	−	0.510495i	$-0.829462\pi$
$277$	3.36853	−	5.83447i	0.0121608	−	0.0210631i	0.872042	+	0.489431i	$0.162796\pi$
$278$	−18.9071	−	32.7480i	−0.0680110	−	0.117799i
$279$	94.6453	+	21.5717i	0.339230	+	0.0773178i
$280$	−66.7166	+	48.5362i	−0.238274	+	0.173344i
$281$	394.126			1.40258			0.701291	−	0.712875i	$-0.252607\pi$
$281$	394.126			1.40258			0.701291	+	0.712875i	$0.252607\pi$
$282$	279.608	+	109.689i	0.991518	+	0.388967i
$283$	−23.7973	+	41.2181i	−0.0840894	+	0.145647i	−0.905003	−	0.425406i	$-0.860131\pi$
$283$	−23.7973	+	41.2181i	−0.0840894	+	0.145647i	0.820913	+	0.571053i	$0.193465\pi$
$284$	23.5185	−	40.7352i	0.0828115	−	0.143434i
$285$	12.2980	−	31.3490i	0.0431510	−	0.109996i
$286$	−117.000			−0.409091
$287$	12.4997	+	118.216i	0.0435531	+	0.411903i
$288$	49.7889	−	218.448i	0.172878	−	0.758500i
$289$	−95.1646	−	164.830i	−0.329289	−	0.570345i
$290$	37.9527	+	21.9120i	0.130872	+	0.0755587i
$291$	82.5994	−	12.4628i	0.283847	−	0.0428275i
$292$	−147.263	+	85.0222i	−0.504325	+	0.291172i
$293$	−440.042			−1.50185			−0.750926	−	0.660387i	$-0.770392\pi$
$293$	−440.042			−1.50185			−0.750926	+	0.660387i	$0.770392\pi$
$294$	141.643	−	172.757i	0.481778	−	0.587610i
$295$	−23.3588			−0.0791823
$296$	246.730	−	142.450i	0.833547	−	0.481249i
$297$	−159.455	−	11.8758i	−0.536886	−	0.0399859i
$298$	−20.2273	+	35.0347i	−0.0678769	+	0.117566i
$299$	29.0836	−	16.7914i	0.0972697	−	0.0561587i
$300$	−91.7456	+	73.1876i	−0.305819	+	0.243959i
$301$	−2.43603	−	23.0387i	−0.00809311	−	0.0765404i
$302$		−	9.84130i		−	0.0325871i
$303$	−183.493	+	467.744i	−0.605589	+	1.54371i
$304$	−45.5122	−	26.2765i	−0.149711	−	0.0864359i
$305$	−13.0932	+	22.6782i	−0.0429286	+	0.0743546i
$306$	−40.0864	−	129.816i	−0.131001	−	0.424234i
$307$		−	506.508i		−	1.64986i	−0.565232	−	0.824932i	$-0.691213\pi$
$307$		−	506.508i		−	1.64986i	0.565232	−	0.824932i	$-0.308787\pi$
$308$	−56.6666	+	41.2249i	−0.183983	+	0.133847i
$309$	−319.115	+	254.566i	−1.03274	+	0.823838i
$310$	19.3471	−	11.1701i	0.0624101	−	0.0360325i
$311$	261.698	+	151.091i	0.841472	+	0.485824i	0.857764	−	0.514043i	$-0.171853\pi$
$311$	261.698	+	151.091i	0.841472	+	0.485824i	−0.0162925	+	0.999867i	$0.505186\pi$
$312$	−50.3183	−	333.494i	−0.161277	−	1.06889i
$313$	−138.858	−	240.508i	−0.443634	−	0.768397i	0.554322	−	0.832302i	$-0.312978\pi$
$313$	−138.858	−	240.508i	−0.443634	−	0.768397i	−0.997956	+	0.0639055i	$0.979644\pi$
$314$	335.136			1.06731
$315$	−51.4384	+	68.7497i	−0.163297	+	0.218253i
$316$	96.1917			0.304404
$317$	−243.071	−	421.012i	−0.766786	−	1.32811i	−0.939297	−	0.343105i	$-0.888521\pi$
$317$	−243.071	−	421.012i	−0.766786	−	1.32811i	0.172511	−	0.985008i	$-0.444812\pi$
$318$	−305.427	+	46.0836i	−0.960463	+	0.144917i
$319$	108.514	+	62.6507i	0.340170	+	0.196397i
$320$	−43.1742	−	74.7799i	−0.134919	−	0.233687i
$321$	224.499	+	281.424i	0.699373	+	0.876710i
$322$	−11.1620	+	25.1125i	−0.0346646	+	0.0779893i
$323$	81.8116			0.253287
$324$	−10.3160	−	136.535i	−0.0318395	−	0.421403i
$325$	−150.426	+	260.546i	−0.462850	+	0.801680i
$326$	37.1529	+	21.4503i	0.113966	+	0.0657983i
$327$	−124.399	+	317.106i	−0.380425	+	0.969744i
$328$	−146.860			−0.447744
$329$	372.909	−	271.291i	1.13346	−	0.824592i
$330$	−28.7666	+	22.9478i	−0.0871716	+	0.0695389i
$331$	496.394	−	286.593i	1.49968	−	0.865840i	0.499679	−	0.866211i	$-0.333451\pi$
$331$	496.394	−	286.593i	1.49968	−	0.865840i	1.00000		0.000370819i	$0.000118035\pi$
$332$	88.1500	−	152.680i	0.265512	−	0.459880i
$333$	201.604	−	217.411i	0.605417	−	0.652885i
$334$	199.714	+	345.914i	0.597945	+	1.03567i
$335$			138.974i			0.414849i
$336$	94.1134	+	95.3834i	0.280099	+	0.283879i
$337$	290.118			0.860884			0.430442	−	0.902618i	$-0.358358\pi$
$337$	290.118			0.860884			0.430442	+	0.902618i	$0.358358\pi$
$338$	−128.417	−	222.425i	−0.379933	−	0.658063i
$339$	244.581	−	36.9030i	0.721478	−	0.108858i
$340$	19.8191	+	11.4426i	0.0582914	+	0.0336546i
$341$	55.3172	−	31.9374i	0.162220	−	0.0936580i
$342$	−109.833	−	25.0332i	−0.321149	−	0.0731966i
$343$	−106.605	−	326.013i	−0.310800	−	0.950475i
$344$	28.6210			0.0832005
$345$	3.85736	−	9.83282i	0.0111807	−	0.0285009i
$346$	−148.261	−	85.5986i	−0.428500	−	0.247395i
$347$	248.115	+	143.249i	0.715029	+	0.412822i	0.812920	−	0.582375i	$-0.197876\pi$
$347$	248.115	+	143.249i	0.715029	+	0.412822i	−0.0978913	+	0.995197i	$0.531210\pi$
$348$	−39.1854	+	99.8878i	−0.112602	+	0.287034i
$349$			372.586i			1.06758i	0.845616	+	0.533791i	$0.179233\pi$
$349$			372.586i			1.06758i	−0.845616	+	0.533791i	$0.820767\pi$
$350$	−25.8872	−	244.828i	−0.0739635	−	0.699508i
$351$	−152.439	−	316.170i	−0.434298	−	0.900769i
$352$	−73.7137	−	127.676i	−0.209414	−	0.362716i
$353$	185.062	−	320.536i	0.524254	−	0.908035i	−0.475347	−	0.879798i	$-0.657677\pi$
$353$	185.062	−	320.536i	0.524254	−	0.908035i	0.999601	−	0.0282368i	$-0.00898925\pi$
$354$	11.6580	+	77.2654i	0.0329322	+	0.218264i
$355$	−18.9618	−	32.8429i	−0.0534136	−	0.0925151i
$356$	−147.940			−0.415563
$357$	−201.126	−	55.3387i	−0.563377	−	0.155010i
$358$			225.692i			0.630425i
$359$	218.798	+	378.970i	0.609466	+	1.05563i	0.991328	+	0.131407i	$0.0419496\pi$
$359$	218.798	+	378.970i	0.609466	+	1.05563i	−0.381862	+	0.924219i	$0.624717\pi$
$360$	−77.7815	−	72.1264i	−0.216060	−	0.200351i
$361$	−146.584	+	253.890i	−0.406049	+	0.703297i
$362$	31.9498	+	55.3387i	0.0882592	+	0.152869i
$363$	201.521	−	160.758i	0.555154	−	0.442859i
$364$	−140.568	−	62.4795i	−0.386175	−	0.171647i
$365$			137.099i			0.375613i
$366$	81.5487	+	31.9911i	0.222811	+	0.0874073i
$367$	37.2604	−	64.5369i	0.101527	−	0.175850i	−0.810787	−	0.585341i	$-0.800961\pi$
$367$	37.2604	−	64.5369i	0.101527	−	0.175850i	0.912314	+	0.409491i	$0.134294\pi$
$368$	−14.2752	−	8.24180i	−0.0387913	−	0.0223962i
$369$	−146.035	+	45.0949i	−0.395760	+	0.122209i
$370$		−	68.2358i		−	0.184421i
$371$	−192.623	+	433.368i	−0.519200	+	1.16811i
$372$	34.1100	+	42.7591i	0.0916934	+	0.114944i
$373$	−75.7137	−	131.140i	−0.202986	−	0.351582i	0.746503	−	0.665382i	$-0.231731\pi$
$373$	−75.7137	−	131.140i	−0.202986	−	0.351582i	−0.949489	+	0.313800i	$0.898398\pi$
$374$	−77.4226	−	44.7000i	−0.207012	−	0.119519i
$375$	29.3674	+	194.638i	0.0783131	+	0.519034i
$376$	284.856	+	493.385i	0.757596	+	1.31220i
$377$			275.058i			0.729596i
$378$	253.080	+	135.834i	0.669525	+	0.359350i
$379$		−	726.940i		−	1.91805i	−0.283326	−	0.959024i	$-0.591438\pi$
$379$		−	726.940i		−	1.91805i	0.283326	−	0.959024i	$-0.408562\pi$
$380$	16.4327	−	9.48743i	0.0432440	−	0.0249669i
$381$	−64.0569	−	424.548i	−0.168128	−	1.11430i
$382$	−171.534	−	99.0355i	−0.449043	−	0.259255i
$383$	115.240	+	199.602i	0.300888	+	0.521153i	0.976337	−	0.216253i	$-0.0693836\pi$
$383$	115.240	+	199.602i	0.300888	+	0.521153i	−0.675449	+	0.737406i	$0.736050\pi$
$384$	7.72370	−	6.16138i	0.0201138	−	0.0160453i
$385$	5.94086	+	56.1855i	0.0154308	+	0.145936i
$386$		−	431.531i		−	1.11796i
$387$	28.4602	−	8.78837i	0.0735407	−	0.0227090i
$388$	40.7632	+	23.5346i	0.105060	+	0.0606563i
$389$	−42.2402	−	24.3874i	−0.108587	−	0.0626926i	0.444723	−	0.895668i	$-0.353302\pi$
$389$	−42.2402	−	24.3874i	−0.108587	−	0.0626926i	−0.553310	+	0.832976i	$0.686635\pi$
$390$	−75.1992	−	29.5002i	−0.192819	−	0.0756416i
$391$	25.6607			0.0656285
$392$	414.377	−	88.6203i	1.05708	−	0.226072i
$393$	−316.496	−	396.749i	−0.805334	−	1.00954i
$394$	−9.00000	−	15.5885i	−0.0228426	−	0.0395646i
$395$	38.7774	−	67.1645i	0.0981707	−	0.170037i
$396$	−66.0647	−	61.2615i	−0.166830	−	0.154701i
$397$	−425.769	+	245.818i	−1.07247	+	0.619188i	−0.928854	−	0.370446i	$-0.879205\pi$
$397$	−425.769	+	245.818i	−1.07247	+	0.619188i	−0.143612	+	0.989634i	$0.545872\pi$
$398$	141.331			0.355103
$399$	−123.116	+	121.477i	−0.308562	+	0.304454i
$400$	147.668			0.369171
$401$	234.688	+	406.492i	0.585258	+	1.01370i	0.994843	+	0.101424i	$0.0323400\pi$
$401$	234.688	+	406.492i	0.585258	+	1.01370i	−0.409586	+	0.912272i	$0.634327\pi$
$402$	459.695	−	69.3600i	1.14352	−	0.172537i
$403$	121.430	+	70.1079i	0.301316	+	0.173965i
$404$	−245.185	+	141.558i	−0.606894	+	0.350391i
$405$	−99.4919	−	47.8377i	−0.245659	−	0.118118i
$406$	−132.415	−	182.014i	−0.326146	−	0.448311i
$407$		−	195.099i		−	0.479360i
$408$	94.1143	−	239.907i	0.230672	−	0.588008i
$409$	481.463	+	277.973i	1.17717	+	0.679640i	0.955358	−	0.295449i	$-0.0954694\pi$
$409$	481.463	+	277.973i	1.17717	+	0.679640i	0.221812	+	0.975089i	$0.428803\pi$
$410$	−17.5871	+	30.4618i	−0.0428954	+	0.0742970i
$411$	632.295	+	248.046i	1.53843	+	0.603517i
$412$	−230.017			−0.558294
$413$	109.631	+	48.7288i	0.265451	+	0.117987i
$414$	−34.4498	−	7.85184i	−0.0832121	−	0.0189658i
$415$	−71.0712	−	123.099i	−0.171256	−	0.296624i
$416$	161.814	−	280.270i	0.388976	−	0.673726i
$417$	−11.1368	−	73.8109i	−0.0267069	−	0.177004i
$418$	−64.1938	+	37.0623i	−0.153574	+	0.0886659i
$419$			452.382i			1.07967i	0.841771	+	0.539835i	$0.181513\pi$
$419$			452.382i			1.07967i	−0.841771	+	0.539835i	$0.818487\pi$
$420$	−46.8157	+	12.2086i	−0.111466	+	0.0290680i
$421$			502.198i			1.19287i	0.802662	+	0.596435i	$0.203416\pi$
$421$			502.198i			1.19287i	−0.802662	+	0.596435i	$0.796584\pi$
$422$	−143.650	−	248.809i	−0.340403	−	0.589595i
$423$	434.756	+	403.147i	1.02779	+	0.953065i
$424$	−507.398	−	292.947i	−1.19669	−	0.690912i
$425$	−199.084	+	114.941i	−0.468432	+	0.270449i
$426$	−99.1730	+	79.1127i	−0.232801	+	0.185711i
$427$	108.760	−	79.1229i	0.254708	−	0.185300i
$428$			202.849i			0.473947i
$429$	−215.009	−	84.3469i	−0.501187	−	0.196613i
$430$	3.42748	−	5.93658i	0.00797089	−	0.0138060i
$431$	−177.101	+	306.748i	−0.410907	+	0.711712i	−0.994989	−	0.0999827i	$-0.968121\pi$
$431$	−177.101	+	306.748i	−0.410907	+	0.711712i	0.584082	+	0.811695i	$0.301455\pi$
$432$	−96.9847	+	142.391i	−0.224502	+	0.329609i
$433$	−102.479			−0.236673			−0.118336	−	0.992974i	$-0.537756\pi$
$433$	−102.479			−0.236673			−0.118336	+	0.992974i	$0.537756\pi$
$434$	−114.105	+	12.0650i	−0.262915	+	0.0277996i
$435$	53.9485	+	67.6281i	0.124020	+	0.155467i
$436$	−166.223	+	95.9688i	−0.381245	+	0.220112i
$437$	10.6381	−	18.4258i	0.0243435	−	0.0421642i
$438$	453.491	−	68.4239i	1.03537	−	0.156219i
$439$	56.2960	+	97.5076i	0.128237	+	0.222113i	0.922994	−	0.384815i	$-0.125735\pi$
$439$	56.2960	+	97.5076i	0.128237	+	0.222113i	−0.794757	+	0.606928i	$0.792402\pi$
$440$	−69.7994			−0.158635
$441$	384.838	−	215.361i	0.872649	−	0.488348i
$442$		−	196.248i		−	0.444000i
$443$	−695.206	+	401.378i	−1.56931	+	0.906044i	−0.573066	+	0.819509i	$0.694246\pi$
$443$	−695.206	+	401.378i	−1.56931	+	0.906044i	−0.996249	+	0.0865352i	$0.972420\pi$
$444$	165.199	−	24.9256i	0.372069	−	0.0561387i
$445$	−59.6387	+	103.297i	−0.134020	+	0.232129i
$446$	−349.454	+	201.758i	−0.783530	+	0.452371i
$447$	−62.4284	+	49.8007i	−0.139661	+	0.111411i
$448$	46.6335	+	441.035i	0.104093	+	0.984453i
$449$	−784.854			−1.74800			−0.874002	−	0.485923i	$-0.838484\pi$
$449$	−784.854			−1.74800			−0.874002	+	0.485923i	$0.838484\pi$
$450$	302.442	−	93.3925i	0.672094	−	0.207539i
$451$	−50.2850	+	87.0962i	−0.111497	+	0.193118i
$452$	120.702	+	69.6872i	0.267039	+	0.154175i
$453$	7.09472	−	18.0852i	0.0156616	−	0.0399232i
$454$	63.0738			0.138929
$455$	−100.292	+	72.9623i	−0.220422	+	0.160357i
$456$	−133.249	−	167.037i	−0.292214	−	0.366309i
$457$	−197.681	+	114.131i	−0.432563	+	0.249741i	−0.700438	−	0.713713i	$-0.747012\pi$
$457$	−197.681	+	114.131i	−0.432563	+	0.249741i	0.267875	+	0.963454i	$0.413679\pi$
$458$	−28.1519	−	16.2535i	−0.0614671	−	0.0354881i
$459$	19.9197	−	267.459i	0.0433980	−	0.582699i
$460$	5.15423	−	2.97580i	0.0112049	−	0.00646912i
$461$	−398.928			−0.865353			−0.432676	−	0.901549i	$-0.642431\pi$
$461$	−398.928			−0.865353			−0.432676	+	0.901549i	$0.642431\pi$
$462$	182.884	−	47.6923i	0.395852	−	0.103230i
$463$			44.0935i			0.0952342i	0.998866	+	0.0476171i	$0.0151627\pi$
$463$			44.0935i			0.0952342i	−0.998866	+	0.0476171i	$0.984837\pi$
$464$	116.920	−	67.5038i	0.251983	−	0.145482i
$465$	43.6066	−	6.57947i	0.0937776	−	0.0141494i
$466$	492.504	+	284.347i	1.05687	+	0.610187i
$467$	−399.258	+	230.512i	−0.854943	+	0.493601i	−0.862315	−	0.506372i	$-0.830986\pi$
$467$	−399.258	+	230.512i	−0.854943	+	0.493601i	0.00737290	+	0.999973i	$0.497653\pi$
$468$	43.9508	−	192.833i	0.0939120	−	0.412037i
$469$	289.915	−	652.257i	0.618156	−	1.39074i
$470$	136.451			0.290321
$471$	615.875	+	241.604i	1.30759	+	0.512960i
$472$	−74.1081	+	128.359i	−0.157009	+	0.271947i
$473$	9.79984	−	16.9738i	0.0207185	−	0.0358855i
$474$	−241.518	−	94.7460i	−0.509531	−	0.199886i
$475$			190.603i			0.401270i
$476$	−69.1478	−	95.0487i	−0.145268	−	0.199682i
$477$	−594.501	−	135.499i	−1.24633	−	0.284066i
$478$	−229.032	−	396.695i	−0.479146	−	0.829905i
$479$	−144.978	+	251.108i	−0.302667	+	0.524235i	−0.976739	−	0.214431i	$-0.931210\pi$
$479$	−144.978	+	251.108i	−0.302667	+	0.524235i	0.674072	+	0.738666i	$0.264544\pi$
$480$	−15.1859	−	100.647i	−0.0316372	−	0.209681i
$481$	370.898	−	214.138i	0.771097	−	0.445193i
$482$		−	655.323i		−	1.35959i
$483$	−38.6162	+	38.1021i	−0.0799508	+	0.0788863i
$484$	145.255			0.300114
$485$	32.8654	−	18.9749i	0.0677638	−	0.0391234i
$486$	−108.581	+	352.971i	−0.223418	+	0.726278i
$487$	−46.1777	−	26.6607i	−0.0948208	−	0.0547448i	0.451840	−	0.892099i	$-0.350768\pi$
$487$	−46.1777	−	26.6607i	−0.0948208	−	0.0547448i	−0.546661	+	0.837354i	$0.684101\pi$
$488$	83.0793	+	143.898i	0.170244	+	0.294872i
$489$	52.8116	+	66.2029i	0.107999	+	0.135384i
$490$	31.2418	−	96.5629i	0.0637587	−	0.197067i
$491$		−	604.181i		−	1.23051i	−0.788328	−	0.615255i	$-0.789053\pi$
$491$		−	604.181i		−	1.23051i	0.788328	−	0.615255i	$-0.210947\pi$
$492$	−80.1723	−	31.4511i	−0.162952	−	0.0639251i
$493$	−105.086	+	182.014i	−0.213156	+	0.369198i
$494$	−140.916	−	81.3580i	−0.285256	−	0.164692i
$495$	−69.4074	+	21.4326i	−0.140217	+	0.0432983i
$496$		−	68.8226i		−	0.138755i
$497$	20.4811	+	193.700i	0.0412095	+	0.389738i
$498$	−371.712	+	296.524i	−0.746411	+	0.595430i
$499$	−211.439	+	122.074i	−0.423725	+	0.244637i	−0.696670	−	0.717392i	$-0.745336\pi$
$499$	−211.439	+	122.074i	−0.423725	+	0.244637i	0.272945	+	0.962030i	$0.412002\pi$
$500$	−55.4571	+	96.0545i	−0.110914	+	0.192109i
$501$	117.637	+	779.658i	0.234804	+	1.55620i
$502$	−453.283	+	261.703i	−0.902954	+	0.521321i
$503$			424.673i			0.844281i	0.906530	+	0.422141i	$0.138721\pi$
$503$			424.673i			0.844281i	−0.906530	+	0.422141i	$0.861279\pi$
$504$	214.594	+	500.776i	0.425781	+	0.993602i
$505$			228.263i			0.452006i
$506$	−20.1348	+	11.6248i	−0.0397921	+	0.0229740i
$507$	−75.6412	−	501.326i	−0.149194	−	0.988808i
$508$	120.964	−	209.516i	0.238119	−	0.412434i
$509$	−444.742	−	770.315i	−0.873756	−	1.51339i	−0.858082	−	0.513512i	$-0.828344\pi$
$509$	−444.742	−	770.315i	−0.873756	−	1.51339i	−0.0156736	−	0.999877i	$-0.504989\pi$
$510$	−38.4911	−	48.2512i	−0.0754728	−	0.0946101i
$511$	286.003	−	643.455i	0.559692	−	1.25921i
$512$	−379.571			−0.741349
$513$	−183.792	−	125.183i	−0.358268	−	0.244022i
$514$	−275.070	−	158.812i	−0.535155	−	0.308972i
$515$	−92.7260	+	160.606i	−0.180050	+	0.311857i
$516$	15.6245	+	6.12939i	0.0302800	+	0.0118787i
$517$	390.140			0.754623
$518$	−142.347	+	320.255i	−0.274801	+	0.618253i
$519$	−210.748	−	264.187i	−0.406066	−	0.509030i
$520$	−76.6107	−	132.694i	−0.147328	−	0.255180i
$521$	−265.480	−	153.275i	−0.509558	−	0.294193i	0.223094	−	0.974797i	$-0.428384\pi$
$521$	−265.480	−	153.275i	−0.509558	−	0.294193i	−0.732652	+	0.680604i	$0.761718\pi$
$522$	196.773	−	212.201i	0.376960	−	0.406516i
$523$	292.129	+	505.982i	0.558564	+	0.967461i	0.997617	+	0.0689998i	$0.0219808\pi$
$523$	292.129	+	505.982i	0.558564	+	0.967461i	−0.439053	+	0.898461i	$0.644686\pi$
$524$		−	285.975i		−	0.545754i
$525$	128.927	−	468.579i	0.245576	−	0.892532i
$526$			253.314i			0.481585i
$527$	53.5696	+	92.7852i	0.101650	+	0.176063i
$528$	16.9132	+	112.095i	0.0320325	+	0.212301i
$529$	−261.163	+	452.348i	−0.493692	+	0.855100i
$530$	−121.526	+	70.1632i	−0.229295	+	0.132383i
$531$	−34.2780	+	150.394i	−0.0645536	+	0.283228i
$532$	−96.9165	+	10.2476i	−0.182174	+	0.0192624i
$533$	−220.768			−0.414199
$534$	371.448	+	145.717i	0.695596	+	0.272878i
$535$	141.637	+	81.7739i	0.264741	+	0.152848i
$536$	763.680	+	440.911i	1.42478	+	0.822595i
$537$	−162.705	+	414.751i	−0.302988	+	0.772349i
$538$			579.257i			1.07669i
$539$	89.3262	−	276.092i	0.165726	−	0.512230i
$540$	−27.0153	−	56.0320i	−0.0500283	−	0.103763i
$541$	−222.619	+	128.529i	−0.411495	+	0.237577i	−0.691432	−	0.722442i	$-0.743020\pi$
$541$	−222.619	+	128.529i	−0.411495	+	0.237577i	0.279937	+	0.960018i	$0.409686\pi$
$542$	−479.292	−	276.719i	−0.884302	−	0.510552i
$543$	18.8193	+	124.728i	0.0346580	+	0.229702i
$544$	214.155	−	123.642i	0.393667	−	0.227284i
$545$			154.750i			0.283946i
$546$	291.397	+	295.329i	0.533693	+	0.540895i
$547$	−356.044			−0.650903			−0.325452	−	0.945559i	$-0.605516\pi$
$547$	−356.044			−0.650903			−0.325452	+	0.945559i	$0.605516\pi$
$548$	191.357	+	331.441i	0.349192	+	0.604819i
$549$	126.798	+	117.579i	0.230962	+	0.214170i
$550$	104.141	−	180.378i	0.189348	−	0.327960i
$551$	87.1306	+	150.915i	0.158132	+	0.273892i
$552$	−41.7945	−	52.3922i	−0.0757148	−	0.0949135i
$553$	−322.109	+	234.333i	−0.582475	+	0.423749i
$554$	−10.2385			−0.0184811
$555$	49.1921	−	125.396i	0.0886344	−	0.225939i
$556$	21.0305	−	36.4260i	0.0378247	−	0.0655143i
$557$	254.710	−	441.171i	0.457289	−	0.792048i	−0.541528	−	0.840683i	$-0.682154\pi$
$557$	254.710	−	441.171i	0.457289	−	0.792048i	0.998817	+	0.0486352i	$0.0154872\pi$
$558$	−43.5267	−	140.957i	−0.0780048	−	0.252611i
$559$	43.0246			0.0769671
$560$	55.6277	+	24.7254i	0.0993352	+	0.0441525i
$561$	−110.054	−	137.959i	−0.196174	−	0.245917i
$562$	−299.483	−	518.719i	−0.532887	−	0.922988i
$563$	711.106	+	410.557i	1.26307	+	0.729231i	0.973666	−	0.227977i	$-0.0732111\pi$
$563$	711.106	+	410.557i	1.26307	+	0.729231i	0.289399	+	0.957208i	$0.406544\pi$
$564$	49.8437	+	330.348i	0.0883753	+	0.585723i
$565$	97.3162	−	56.1855i	0.172241	−	0.0994434i
$566$	72.3310			0.127793
$567$	367.157	+	432.070i	0.647544	+	0.762028i
$568$	−240.634			−0.423651
$569$	967.744	−	558.727i	1.70078	−	0.981946i	0.755809	−	0.654792i	$-0.227244\pi$
$569$	967.744	−	558.727i	1.70078	−	0.981946i	0.944971	−	0.327154i	$-0.106090\pi$
$570$	−50.6041	+	7.63526i	−0.0887791	+	0.0133952i
$571$	−480.817	+	832.799i	−0.842061	+	1.45849i	0.0460884	+	0.998937i	$0.485324\pi$
$571$	−480.817	+	832.799i	−0.842061	+	1.45849i	−0.888149	+	0.459555i	$0.848009\pi$
$572$	−65.0703	−	112.705i	−0.113759	−	0.197037i
$573$	−243.830	−	305.658i	−0.425533	−	0.533434i
$574$	146.089	−	106.280i	0.254511	−	0.185156i
$575$			59.7840i			0.103972i
$576$	−544.822	+	168.238i	−0.945871	+	0.292080i
$577$	−856.777	−	494.660i	−1.48488	−	0.857297i	−0.485030	−	0.874498i	$-0.661191\pi$
$577$	−856.777	−	494.660i	−1.48488	−	0.857297i	−0.999852	+	0.0172005i	$0.994525\pi$
$578$	−144.625	+	250.497i	−0.250216	+	0.433386i
$579$	311.097	−	793.019i	0.537300	−	1.36964i
$580$			48.7460i			0.0840449i
$581$	76.7657	+	726.010i	0.132127	+	1.24959i
$582$	−79.1671	−	99.2412i	−0.136026	−	0.170518i
$583$	−347.467	+	200.610i	−0.595998	+	0.344100i
$584$	753.374	+	434.961i	1.29002	+	0.744795i
$585$	−116.925	−	108.424i	−0.199873	−	0.185341i
$586$	334.373	+	579.151i	0.570603	+	0.988313i
$587$	725.629			1.23616			0.618082	−	0.786113i	$-0.287910\pi$
$587$	725.629			1.23616			0.618082	+	0.786113i	$0.287910\pi$
$588$	245.191	+	40.3632i	0.416992	+	0.0686448i
$589$	88.8329			0.150820
$590$	17.7495	+	30.7431i	0.0300840	+	0.0521069i
$591$	−5.30124	−	35.1349i	−0.00896995	−	0.0594499i
$592$	−182.049	−	105.106i	−0.307515	−	0.177544i
$593$	−54.7757	−	94.8742i	−0.0923704	−	0.159990i	0.816138	−	0.577857i	$-0.196111\pi$
$593$	−54.7757	−	94.8742i	−0.0923704	−	0.159990i	−0.908508	+	0.417867i	$0.862778\pi$
$594$	105.534	+	218.887i	0.177667	+	0.368497i
$595$	−94.2418	+	9.96479i	−0.158389	+	0.0167475i
$596$	−44.9982			−0.0755003
$597$	259.722	+	101.888i	0.435046	+	0.170666i
$598$	−44.1993	−	25.5185i	−0.0739119	−	0.0426731i
$599$	−519.534	−	299.953i	−0.867335	−	0.500756i	−0.000873542	−	1.00000i	$-0.500278\pi$
$599$	−519.534	−	299.953i	−0.867335	−	0.500756i	−0.866462	+	0.499243i	$0.833611\pi$
$600$	558.932	+	219.266i	0.931554	+	0.365443i
$601$	322.830			0.537155			0.268578	−	0.963258i	$-0.413446\pi$
$601$	322.830			0.537155			0.268578	+	0.963258i	$0.413446\pi$
$602$	−28.4707	+	20.7124i	−0.0472936	+	0.0344060i
$603$	894.778	+	203.939i	1.48388	+	0.338207i
$604$	9.48003	−	5.47330i	0.0156954	−	0.00906175i
$605$	58.5563	−	101.422i	0.0967873	−	0.167640i
$606$	755.041	−	113.922i	1.24594	−	0.187991i
$607$	112.203	+	194.341i	0.184848	+	0.320166i	0.943525	−	0.331301i	$-0.107487\pi$
$607$	112.203	+	194.341i	0.184848	+	0.320166i	−0.758677	+	0.651467i	$0.774154\pi$
$608$		−	205.033i		−	0.337225i
$609$	−112.121	−	429.945i	−0.184106	−	0.705986i
$610$	39.7964			0.0652400
$611$	428.211	+	741.684i	0.700837	+	1.21389i
$612$	102.756	−	110.812i	0.167902	−	0.181066i
$613$	−485.335	−	280.208i	−0.791737	−	0.457110i	0.0488367	−	0.998807i	$-0.484449\pi$
$613$	−485.335	−	280.208i	−0.791737	−	0.457110i	−0.840574	+	0.541697i	$0.817782\pi$
$614$	−666.629	+	384.878i	−1.08571	+	0.626837i
$615$	−54.2799	+	43.3004i	−0.0882600	+	0.0704071i
$616$	327.594	+	145.609i	0.531808	+	0.236378i
$617$	610.674			0.989748			0.494874	−	0.868965i	$-0.335214\pi$
$617$	610.674			0.989748			0.494874	+	0.868965i	$0.335214\pi$
$618$	577.526	+	226.560i	0.934508	+	0.366602i
$619$	−634.279	−	366.201i	−1.02468	−	0.591602i	−0.109227	−	0.994017i	$-0.534837\pi$
$619$	−634.279	−	366.201i	−1.02468	−	0.591602i	−0.915457	+	0.402415i	$0.868171\pi$
$620$	21.5200	+	12.4246i	0.0347097	+	0.0200397i
$621$	−57.6474	−	39.2646i	−0.0928300	−	0.0632280i
$622$		−	459.236i		−	0.738322i
$623$	495.395	−	360.399i	0.795176	−	0.578489i
$624$	−194.537	+	155.187i	−0.311758	+	0.248697i
$625$	−244.569	−	423.605i	−0.391310	−	0.677769i
$626$	−211.026	+	365.508i	−0.337102	+	0.583879i
$627$	−144.687	+	21.8307i	−0.230761	+	0.0348177i
$628$	186.388	+	322.834i	0.296796	+	0.514066i
$629$	327.246			0.520264
$630$	129.570	+	15.4589i	0.205666	+	0.0245379i
$631$		−	806.507i		−	1.27814i	−0.769148	−	0.639070i	$-0.779319\pi$
$631$		−	806.507i		−	1.27814i	0.769148	−	0.639070i	$-0.220681\pi$
$632$	−246.051	−	426.173i	−0.389321	−	0.674324i
$633$	−84.6137	−	560.793i	−0.133671	−	0.885928i
$634$	−369.403	+	639.825i	−0.582654	+	1.00919i
$635$	−97.5279	−	168.923i	−0.153587	−	0.266021i
$636$	−214.257	−	268.585i	−0.336882	−	0.422304i
$637$	622.914	−	133.219i	0.977887	−	0.209135i
$638$		−	190.425i		−	0.298471i
$639$	−239.282	+	73.8891i	−0.374464	+	0.115632i
$640$	2.24429	−	3.88722i	0.00350670	−	0.00607379i
$641$	−406.049	−	234.433i	−0.633462	−	0.365730i	0.148629	−	0.988893i	$-0.452514\pi$
$641$	−406.049	−	234.433i	−0.633462	−	0.365730i	−0.782092	+	0.623163i	$0.785847\pi$
$642$	199.801	−	509.313i	0.311216	−	0.793323i
$643$		−	183.967i		−	0.286107i	−0.989715	−	0.143054i	$-0.954308\pi$
$643$		−	183.967i		−	0.286107i	0.989715	−	0.143054i	$-0.0456921\pi$
$644$	−30.3985	+	3.21423i	−0.0472026	+	0.00499104i
$645$	10.5784	−	8.43864i	0.0164006	−	0.0130832i
$646$	−62.1658	−	107.674i	−0.0962319	−	0.166679i
$647$	557.646	+	321.957i	0.861895	+	0.497615i	0.864646	−	0.502381i	$-0.167542\pi$
$647$	557.646	+	321.957i	0.861895	+	0.497615i	−0.00275144	+	0.999996i	$0.500876\pi$
$648$	−578.522	+	394.949i	−0.892781	+	0.609489i
$649$	50.7494	+	87.9005i	0.0781962	+	0.135440i
$650$	457.215			0.703408
$651$	−218.387	−	60.0880i	−0.335464	−	0.0923011i
$652$			47.7188i			0.0731883i
$653$	349.801	−	201.957i	0.535682	−	0.309276i	−0.207645	−	0.978204i	$-0.566580\pi$
$653$	349.801	−	201.957i	0.535682	−	0.309276i	0.743327	+	0.668928i	$0.233247\pi$
$654$	511.878	−	77.2334i	0.782689	−	0.118094i
$655$	−199.678	−	115.284i	−0.304852	−	0.176006i
$656$	54.1801	+	93.8427i	0.0825917	+	0.143053i
$657$	882.702	+	201.187i	1.34353	+	0.306220i
$658$	−640.414	−	284.651i	−0.973273	−	0.432600i
$659$		−	970.422i		−	1.47257i	−0.676673	−	0.736284i	$-0.736579\pi$
$659$		−	970.422i		−	1.47257i	0.676673	−	0.736284i	$-0.263421\pi$
$660$	−38.1042	−	14.9480i	−0.0577336	−	0.0226485i
$661$	364.763	+	210.596i	0.551836	+	0.318602i	0.749862	−	0.661594i	$-0.230120\pi$
$661$	364.763	+	210.596i	0.551836	+	0.318602i	−0.198026	+	0.980197i	$0.563453\pi$
$662$	−754.385	−	435.544i	−1.13955	−	0.657922i
$663$	141.478	−	360.642i	0.213390	−	0.543954i
$664$	−901.924			−1.35832
$665$	−31.9144	+	71.8016i	−0.0479915	+	0.107972i
$666$	−439.332	−	100.133i	−0.659657	−	0.150350i
$667$	27.3291	+	47.3354i	0.0409732	+	0.0709676i
$668$	−222.144	+	384.765i	−0.332551	+	0.575995i
$669$	−787.637	+	118.841i	−1.17733	+	0.177639i
$670$	182.908	−	105.602i	0.272997	−	0.157615i
$671$	113.786			0.169576
$672$	−138.687	+	504.052i	−0.206380	+	0.750078i
$673$	441.956			0.656695			0.328348	−	0.944557i	$-0.393508\pi$
$673$	441.956			0.656695			0.328348	+	0.944557i	$0.393508\pi$
$674$	−220.451	−	381.832i	−0.327078	−	0.566516i
$675$	623.122	+	46.4085i	0.923143	+	0.0687534i
$676$	142.840	−	247.406i	0.211302	−	0.365986i
$677$	−84.1342	+	48.5749i	−0.124275	+	0.0717502i	−0.560849	−	0.827918i	$-0.689525\pi$
$677$	−84.1342	+	48.5749i	−0.124275	+	0.0717502i	0.436574	+	0.899668i	$0.356192\pi$
$678$	−234.418	−	293.858i	−0.345749	−	0.433419i
$679$	−193.833	+	20.4952i	−0.285468	+	0.0301844i
$680$		−	117.077i		−	0.172172i
$681$	115.910	+	45.4708i	0.170205	+	0.0667706i
$682$	−84.0672	−	48.5362i	−0.123266	−	0.0711675i
$683$	581.988	−	1008.03i	0.852105	−	1.47589i	−0.0271990	−	0.999630i	$-0.508659\pi$
$683$	581.988	−	1008.03i	0.852105	−	1.47589i	0.879305	−	0.476260i	$-0.158008\pi$
$684$	−36.9699	−	119.723i	−0.0540496	−	0.175034i
$685$	308.565			0.450460
$686$	−348.069	+	388.031i	−0.507389	+	0.565643i
$687$	−40.0170	−	50.1640i	−0.0582489	−	0.0730189i
$688$	−10.5589	−	18.2886i	−0.0153473	−	0.0265823i
$689$	−762.749	−	440.373i	−1.10704	−	0.639148i
$690$	−15.8723	+	2.39485i	−0.0230033	+	0.00347080i
$691$	−50.1221	+	28.9380i	−0.0725356	+	0.0418784i	−0.535829	−	0.844326i	$-0.680001\pi$
$691$	−50.1221	+	28.9380i	−0.0725356	+	0.0418784i	0.463294	+	0.886205i	$0.346668\pi$
$692$		−	190.425i		−	0.275180i
$693$	370.465	+	44.1999i	0.534581	+	0.0637806i
$694$		−	435.401i		−	0.627379i
$695$	−16.9559	−	29.3686i	−0.0243970	−	0.0422569i
$696$	542.781	−	81.8961i	0.779858	−	0.117667i
$697$	−146.089	−	84.3446i	−0.209597	−	0.121011i
$698$	490.371	−	283.116i	0.702537	−	0.405610i
$699$	700.077	+	877.593i	1.00154	+	1.25550i
$700$	221.443	−	161.099i	0.316347	−	0.230142i
$701$			920.879i			1.31367i	0.754036	+	0.656833i	$0.228104\pi$
$701$			920.879i			1.31367i	−0.754036	+	0.656833i	$0.771896\pi$
$702$	−300.287	+	440.875i	−0.427759	+	0.628027i
$703$	135.666	−	234.980i	0.192981	−	0.334253i
$704$	−187.601	+	324.934i	−0.266479	+	0.461554i
$705$	250.754	+	98.3694i	0.355680	+	0.139531i
$706$	−562.489			−0.796726
$707$	476.180	−	1071.32i	0.673522	−	1.51530i
$708$	−67.9454	+	54.2017i	−0.0959680	+	0.0765560i
$709$	−518.790	+	299.523i	−0.731721	+	0.422459i	−0.819051	−	0.573720i	$-0.805500\pi$
$709$	−518.790	+	299.523i	−0.731721	+	0.422459i	0.0873307	+	0.996179i	$0.472166\pi$
$710$	−28.8169	+	49.9123i	−0.0405872	+	0.0702991i
$711$	−375.530	−	348.227i	−0.528172	−	0.489771i
$712$	378.420	+	655.442i	0.531489	+	0.920565i
$713$	27.8630			0.0390786
$714$	79.9958	+	306.757i	0.112039	+	0.429631i
$715$	−104.926			−0.146750
$716$	−217.407	+	125.520i	−0.303641	+	0.175307i
$717$	−134.906	−	894.112i	−0.188153	−	1.24702i
$718$	332.515	−	575.933i	0.463113	−	0.802135i
$719$	453.270	−	261.695i	0.630417	−	0.363971i	−0.150497	−	0.988611i	$-0.548087\pi$
$719$	453.270	−	261.695i	0.630417	−	0.363971i	0.780914	+	0.624639i	$0.214754\pi$
$720$	−17.3929	+	76.3111i	−0.0241568	+	0.105988i
$721$	770.237	−	560.346i	1.06829	−	0.777179i
$722$	445.535			0.617085
$723$	472.431	−	1204.28i	0.653432	−	1.66567i
$724$	−35.5382	+	61.5539i	−0.0490859	+	0.0850192i
$725$	−424.054	−	244.828i	−0.584902	−	0.337694i
$726$	−364.707	−	143.072i	−0.502351	−	0.197069i
$727$	−554.641			−0.762918			−0.381459	−	0.924386i	$-0.624578\pi$
$727$	−554.641			−0.762918			−0.381459	+	0.924386i	$0.624578\pi$
$728$	82.7490	+	782.597i	0.113666	+	1.07500i
$729$	−454.000	+	570.373i	−0.622771	+	0.782404i
$730$	180.439	−	104.177i	0.247177	−	0.142708i
$731$	28.4707	+	16.4376i	0.0389476	+	0.0224864i
$732$	14.5371	+	96.3471i	0.0198594	+	0.131622i
$733$	−640.607	+	369.855i	−0.873953	+	0.504577i	−0.868660	−	0.495409i	$-0.835018\pi$
$733$	−640.607	+	369.855i	−0.873953	+	0.504577i	−0.00529302	+	0.999986i	$0.501685\pi$
$734$	−113.252			−0.154294
$735$	127.026	−	154.930i	0.172825	−	0.210789i
$736$		−	64.3099i		−	0.0873775i
$737$	522.969	−	301.937i	0.709592	−	0.409683i
$738$	170.318	+	157.935i	0.230783	+	0.214004i
$739$	−587.454	−	339.167i	−0.794931	−	0.458954i	0.0467643	−	0.998906i	$-0.485109\pi$
$739$	−587.454	−	339.167i	−0.794931	−	0.458954i	−0.841696	+	0.539952i	$0.818442\pi$
$740$	65.7309	−	37.9497i	0.0888255	−	0.0512834i
$741$	−200.308	−	251.099i	−0.270321	−	0.338865i
$742$	716.734	−	75.7849i	0.965949	−	0.102136i
$743$	−891.716			−1.20016			−0.600078	−	0.799941i	$-0.704864\pi$
$743$	−891.716			−1.20016			−0.600078	+	0.799941i	$0.704864\pi$
$744$	102.191	−	260.497i	0.137354	−	0.350130i
$745$	−18.1400	+	31.4193i	−0.0243489	+	0.0421736i
$746$	−115.065	+	199.298i	−0.154242	+	0.267155i
$747$	−896.859	+	276.945i	−1.20061	+	0.370743i
$748$		−	99.4406i		−	0.132942i
$749$	−494.163	−	679.263i	−0.659763	−	0.906894i
$750$	233.852	−	186.550i	0.311803	−	0.248733i
$751$	−439.436	−	761.125i	−0.585134	−	1.01348i	−0.994859	−	0.101273i	$-0.967708\pi$
$751$	−439.436	−	761.125i	−0.585134	−	1.01348i	0.409724	−	0.912209i	$-0.365625\pi$
$752$	210.180	−	364.043i	0.279495	−	0.484100i
$753$	−1021.66	+	154.150i	−1.35678	+	0.204715i
$754$	362.011	−	209.007i	0.480120	−	0.277198i
$755$		−	8.82573i		−	0.0116897i
$756$	9.90408	+	319.335i	0.0131006	+	0.422401i
$757$	−262.211			−0.346382			−0.173191	−	0.984888i	$-0.555408\pi$
$757$	−262.211			−0.346382			−0.173191	+	0.984888i	$0.555408\pi$
$758$	−956.745	+	552.377i	−1.26220	+	0.728729i
$759$	−45.3820	+	6.84734i	−0.0597918	+	0.00902153i
$760$	−84.0672	−	48.5362i	−0.110615	−	0.0638635i
$761$	286.792	+	496.739i	0.376862	+	0.652745i	0.990604	−	0.136762i	$-0.0436696\pi$
$761$	286.792	+	496.739i	0.376862	+	0.652745i	−0.613741	+	0.789507i	$0.710336\pi$
$762$	−510.085	+	406.907i	−0.669402	+	0.533998i
$763$	322.825	−	726.299i	0.423100	−	0.951899i
$764$		−	220.317i		−	0.288373i
$765$	−35.9497	−	116.419i	−0.0469930	−	0.152182i
$766$	175.134	−	303.341i	0.228634	−	0.396007i
$767$	−111.403	+	192.956i	−0.145246	+	0.251573i
$768$	−721.741	−	283.135i	−0.939766	−	0.368665i
$769$			951.682i			1.23756i	0.785565	+	0.618779i	$0.212372\pi$
$769$			951.682i			1.23756i	−0.785565	+	0.618779i	$0.787628\pi$
$770$	69.4330	−	50.5124i	0.0901727	−	0.0656005i
$771$	−391.003	−	490.148i	−0.507137	−	0.635730i
$772$	415.690	−	239.999i	0.538459	−	0.310879i
$773$	−82.4071	+	142.733i	−0.106607	+	0.184648i	−0.914394	−	0.404826i	$-0.867332\pi$
$773$	−82.4071	+	142.733i	−0.106607	+	0.184648i	0.807787	+	0.589475i	$0.200665\pi$
$774$	−33.1926	−	30.7793i	−0.0428845	−	0.0397665i
$775$	−216.170	+	124.806i	−0.278928	+	0.161039i
$776$		−	240.799i		−	0.310308i
$777$	−492.465	+	485.908i	−0.633803	+	0.625365i
$778$			74.1247i			0.0952759i
$779$	−121.128	+	69.9331i	−0.155491	+	0.0897730i
$780$	−13.4052	−	88.8454i	−0.0171862	−	0.113904i
$781$	−82.3931	+	142.709i	−0.105497	+	0.182726i
$782$	−19.4987	−	33.7728i	−0.0249344	−	0.0431877i
$783$	514.586	−	248.103i	0.657198	−	0.316862i
$784$	−209.501	−	232.090i	−0.267221	−	0.296034i
$785$	300.552			0.382869
$786$	−281.677	+	718.025i	−0.358368	+	0.913518i
$787$	−656.573	−	379.072i	−0.834273	−	0.481668i	0.0210406	−	0.999779i	$-0.493302\pi$
$787$	−656.573	−	379.072i	−0.834273	−	0.481668i	−0.855313	+	0.518111i	$0.826635\pi$
$788$	10.0108	−	17.3392i	0.0127041	−	0.0220041i
$789$	−182.617	+	465.511i	−0.231454	+	0.590001i
$790$	−117.863			−0.149193
$791$	−573.949	+	60.6873i	−0.725599	+	0.0767222i
$792$	−102.427	+	449.399i	−0.129328	+	0.567423i
$793$	124.889	+	216.315i	0.157490	+	0.272780i
$794$	647.054	+	373.577i	0.814930	+	0.470500i
$795$	−273.909	+	41.3280i	−0.344539	+	0.0519849i
$796$	78.6022	+	136.143i	0.0987465	+	0.171034i
$797$		−	329.799i		−	0.413801i	−0.978362	−	0.206900i	$-0.933662\pi$
$797$		−	329.799i		−	0.413801i	0.978362	−	0.206900i	$-0.0663376\pi$
$798$	253.431	+	69.7303i	0.317583	+	0.0873813i
$799$			654.394i			0.819016i
$800$	288.060	+	498.935i	0.360075	+	0.623668i
$801$	577.555	+	535.564i	0.721043	+	0.668619i
$802$	356.663	−	617.759i	0.444717	−	0.770273i
$803$	515.911	−	297.862i	0.642480	−	0.370936i
$804$	322.476	+	404.245i	0.401090	+	0.502793i
$805$	−10.0102	+	22.5211i	−0.0124350	+	0.0279765i
$806$		−	213.090i		−	0.264380i
$807$	−417.594	+	1064.49i	−0.517465	+	1.31907i
$808$	1254.33	+	724.188i	1.55239	+	0.896272i
$809$	−1032.17	−	595.923i	−1.27586	−	0.736617i	−0.299774	−	0.954010i	$-0.596911\pi$
$809$	−1032.17	−	595.923i	−1.27586	−	0.736617i	−0.976084	+	0.217393i	$0.930245\pi$
$810$	12.6401	+	167.294i	0.0156050	+	0.206536i
$811$		−	906.597i		−	1.11788i	−0.829210	−	0.558938i	$-0.811209\pi$
$811$		−	906.597i		−	1.11788i	0.829210	−	0.558938i	$-0.188791\pi$
$812$	101.689	−	228.783i	0.125233	−	0.281752i
$813$	−681.297	−	854.051i	−0.838004	−	1.05049i
$814$	−256.775	+	148.249i	−0.315449	+	0.182124i
$815$	33.3189	+	19.2367i	0.0408821	+	0.0236033i
$816$	−188.020	+	28.3690i	−0.230417	+	0.0347659i
$817$	23.6061	−	13.6290i	0.0288936	−	0.0166818i
$818$		−	844.888i		−	1.03287i
$819$	322.589	+	752.793i	0.393882	+	0.919161i
$820$	−39.1247			−0.0477131
$821$	−234.515	−	406.191i	−0.285645	−	0.494752i	0.687120	−	0.726544i	$-0.258875\pi$
$821$	−234.515	−	406.191i	−0.285645	−	0.494752i	−0.972765	+	0.231792i	$0.925541\pi$
$822$	−154.000	−	1020.66i	−0.187348	−	1.24168i
$823$	−386.069	+	668.691i	−0.469099	+	0.812504i	−0.999376	−	0.0353208i	$-0.988755\pi$
$823$	−386.069	+	668.691i	−0.469099	+	0.812504i	0.530277	+	0.847825i	$0.322088\pi$
$824$	588.366	+	1019.08i	0.714036	+	1.23675i
$825$	321.416	−	256.401i	0.389595	−	0.310789i
$826$	−19.1717	−	181.316i	−0.0232103	−	0.219511i
$827$	−248.971			−0.301053			−0.150527	−	0.988606i	$-0.548097\pi$
$827$	−248.971			−0.301053			−0.150527	+	0.988606i	$0.548097\pi$
$828$	−11.5959	−	37.5520i	−0.0140047	−	0.0453527i
$829$	14.0148	−	24.2744i	0.0169057	−	0.0292816i	−0.857449	−	0.514569i	$-0.827952\pi$
$829$	14.0148	−	24.2744i	0.0169057	−	0.0292816i	0.874354	+	0.485288i	$0.161285\pi$
$830$	−108.009	+	187.077i	−0.130132	+	0.225395i
$831$	−18.8152	−	7.38110i	−0.0226416	−	0.00888219i
$832$	−823.631			−0.989941
$833$	463.098	+	149.830i	0.555940	+	0.179868i
$834$	−88.6820	+	70.7437i	−0.106333	+	0.0848246i
$835$	179.104	+	310.218i	0.214496	+	0.371518i
$836$	−71.4036	−	41.2249i	−0.0854110	−	0.0493121i
$837$	21.6292	−	290.413i	0.0258414	−	0.346969i
$838$	595.392	−	343.750i	0.710491	−	0.410202i
$839$	11.5043			0.0137120			0.00685598	−	0.999976i	$-0.497818\pi$
$839$	11.5043			0.0137120			0.00685598	+	0.999976i	$0.497818\pi$
$840$	173.840	+	176.186i	0.206953	+	0.209745i
$841$	393.327			0.467689
$842$	660.956	−	381.603i	0.784983	−	0.453210i
$843$	−176.403	−	1169.14i	−0.209257	−	1.38688i
$844$	159.784	−	276.754i	0.189317	−	0.327907i
$845$	−115.165	−	199.472i	−0.136290	−	0.236062i
$846$	200.236	−	878.531i	0.236685	−	1.03845i
$847$	−486.404	+	353.858i	−0.574266	+	0.417778i
$848$			432.299i			0.509787i
$849$	132.922	+	52.1444i	0.156563	+	0.0614186i
$850$	302.554	+	174.679i	0.355945	+	0.205505i
$851$	42.5525	−	73.7031i	0.0500029	−	0.0866076i
$852$	−131.364	−	51.5334i	−0.154183	−	0.0604852i
$853$			1165.82i			1.36673i	0.730077	+	0.683365i	$0.239484\pi$
$853$			1165.82i			1.36673i	−0.730077	+	0.683365i	$0.760516\pi$
$854$	−186.779	−	83.0194i	−0.218711	−	0.0972125i
$855$	−98.4987	−	22.4499i	−0.115203	−	0.0262572i
$856$	898.714	−	518.873i	1.04990	−	0.606160i
$857$	656.668	+	379.128i	0.766241	+	0.442389i	0.831532	−	0.555477i	$-0.187464\pi$
$857$	656.668	+	379.128i	0.766241	+	0.442389i	−0.0652912	+	0.997866i	$0.520798\pi$
$858$	52.3670	+	347.072i	0.0610338	+	0.404512i
$859$	−59.6904	−	103.387i	−0.0694883	−	0.120357i	0.829188	−	0.558970i	$-0.188803\pi$
$859$	−59.6904	−	103.387i	−0.0694883	−	0.120357i	−0.898676	+	0.438613i	$0.855470\pi$
$860$	7.62486			0.00886612
$861$	345.084	−	89.9908i	0.400795	−	0.104519i
$862$	538.292			0.624468
$863$	30.3293	+	52.5319i	0.0351441	+	0.0608713i	0.883062	−	0.469255i	$-0.155478\pi$
$863$	30.3293	+	52.5319i	0.0351441	+	0.0608713i	−0.847918	+	0.530127i	$0.822144\pi$
$864$	−670.294	−	49.9218i	−0.775803	−	0.0577799i
$865$	−132.961	−	76.7653i	−0.153713	−	0.0887460i
$866$	77.8705	+	134.876i	0.0899197	+	0.155745i
$867$	−446.361	+	356.073i	−0.514834	+	0.410696i
$868$	−75.0823	−	103.206i	−0.0865003	−	0.118901i
$869$	−336.992			−0.387793
$870$	48.0134	−	122.391i	0.0551879	−	0.140680i
$871$	1148.01	+	662.801i	1.31803	+	0.760966i
$872$	850.370	+	490.962i	0.975195	+	0.563029i
$873$	−73.9399	−	239.447i	−0.0846963	−	0.274280i
$874$	−32.3342			−0.0369956
$875$	−48.2950	−	456.749i	−0.0551943	−	0.521999i
$876$	318.124	+	398.790i	0.363155	+	0.455239i
$877$	1059.35	−	611.614i	1.20792	−	0.697393i	0.245616	−	0.969367i	$-0.421010\pi$
$877$	1059.35	−	611.614i	1.20792	−	0.697393i	0.962305	+	0.271974i	$0.0876764\pi$
$878$	85.5548	−	148.185i	0.0974429	−	0.168776i
$879$	196.955	+	1305.35i	0.224067	+	1.48504i
$880$	25.7506	+	44.6014i	0.0292621	+	0.0506834i
$881$			913.498i			1.03689i	0.855112	+	0.518444i	$0.173488\pi$
$881$			913.498i			1.03689i	−0.855112	+	0.518444i	$0.826512\pi$
$882$	−575.868	−	342.850i	−0.652912	−	0.388719i
$883$	299.052			0.338677			0.169338	−	0.985558i	$-0.445837\pi$
$883$	299.052			0.338677			0.169338	+	0.985558i	$0.445837\pi$
$884$	189.044	−	109.144i	0.213850	−	0.123467i
$885$	10.4549	+	69.2920i	0.0118135	+	0.0782961i
$886$	1056.53	+	609.986i	1.19247	+	0.688472i
$887$	−527.257	+	304.412i	−0.594427	+	0.343193i	−0.766846	−	0.641831i	$-0.778175\pi$
$887$	−527.257	+	304.412i	−0.594427	+	0.343193i	0.172419	+	0.985024i	$0.444842\pi$
$888$	−532.997	−	668.148i	−0.600222	−	0.752419i
$889$	105.342	+	996.272i	0.118495	+	1.12067i
$890$	181.270			0.203674
$891$	36.1404	+	478.327i	0.0405616	+	0.536842i
$892$	−388.702	−	224.417i	−0.435765	−	0.251589i
$893$	469.889	+	271.291i	0.526192	+	0.303797i
$894$	112.981	+	44.3219i	0.126377	+	0.0495771i
$895$			202.402i			0.226147i
$896$	−18.6424	+	13.5623i	−0.0208063	+	0.0151365i
$897$	−62.8278	−	78.7589i	−0.0700422	−	0.0878025i
$898$	596.383	+	1032.97i	0.664124	+	1.15030i
$899$	−114.105	+	197.636i	−0.126924	+	0.219839i
$900$	258.169	+	239.399i	0.286855	+	0.265999i
$901$	−336.490	−	582.818i	−0.373463	−	0.646856i
$902$	152.839			0.169445
$903$	−67.2521	+	17.5380i	−0.0744763	+	0.0194219i
$904$		−	713.018i		−	0.788736i
$905$	28.6528	+	49.6280i	0.0316605	+	0.0548376i
$906$	−29.1935	+	4.40478i	−0.0322224	+	0.00486179i
$907$	−393.512	+	681.583i	−0.433861	+	0.751470i	−0.997202	−	0.0747548i	$-0.976183\pi$
$907$	−393.512	+	681.583i	−0.433861	+	0.751470i	0.563341	+	0.826225i	$0.309516\pi$
$908$	35.0789	+	60.7584i	0.0386331	+	0.0669145i
$909$	1469.66	+	334.966i	1.61678	+	0.368499i
$910$	172.236	+	76.5555i	0.189270	+	0.0841269i
$911$			551.623i			0.605514i	0.953068	+	0.302757i	$0.0979070\pi$
$911$			551.623i			0.605514i	−0.953068	+	0.302757i	$0.902093\pi$
$912$	−57.5768	+	146.769i	−0.0631325	+	0.160931i
$913$	−308.819	+	534.891i	−0.338247	+	0.585861i
$914$	300.423	+	173.449i	0.328690	+	0.189769i
$915$	73.1333	+	28.6898i	0.0799271	+	0.0313549i
$916$		−	36.1580i		−	0.0394738i
$917$	696.666	+	957.619i	0.759723	+	1.04430i
$918$	−367.146	+	177.016i	−0.399941	+	0.192828i
$919$	13.0331	+	22.5740i	0.0141818	+	0.0245636i	0.873029	−	0.487668i	$-0.162152\pi$
$919$	13.0331	+	22.5740i	0.0141818	+	0.0245636i	−0.858847	+	0.512232i	$0.828819\pi$
$920$	−26.3682	−	15.2237i	−0.0286611	−	0.0165475i
$921$	−1502.52	+	226.704i	−1.63140	+	0.246149i
$922$	303.131	+	525.039i	0.328776	+	0.569457i
$923$	−361.734			−0.391911
$924$	147.653	+	149.646i	0.159798	+	0.161954i
$925$			762.413i			0.824230i
$926$	58.0326	−	33.5051i	0.0626701	−	0.0361826i
$927$	897.981	+	832.692i	0.968695	+	0.898266i
$928$	456.157	+	263.362i	0.491548	+	0.283796i
$929$	371.444	+	643.359i	0.399832	+	0.692529i	0.993705	−	0.112030i	$-0.0357353\pi$
$929$	371.444	+	643.359i	0.399832	+	0.692529i	−0.593873	+	0.804559i	$0.702402\pi$
$930$	−41.7945	−	52.3922i	−0.0449404	−	0.0563357i
$931$	299.571	−	270.414i	0.321774	−	0.290456i
$932$			632.565i			0.678718i
$933$	331.070	−	843.932i	0.354844	−	0.904536i
$934$	606.765	+	350.316i	0.649642	+	0.375071i
$935$	−69.4330	−	40.0872i	−0.0742599	−	0.0428740i
$936$	−966.762	+	298.531i	−1.03287	+	0.318943i
$937$	−621.718			−0.663519			−0.331760	−	0.943364i	$-0.607642\pi$
$937$	−621.718			−0.663519			−0.331760	+	0.943364i	$0.607642\pi$
$938$	−1078.75	+	114.063i	−1.15005	+	0.121603i
$939$	−651.299	+	519.557i	−0.693610	+	0.553309i
$940$	75.8881	+	131.442i	0.0807320	+	0.139832i
$941$	−833.188	+	1443.12i	−0.885428	+	1.53361i	−0.0402064	+	0.999191i	$0.512802\pi$
$941$	−833.188	+	1443.12i	−0.885428	+	1.53361i	−0.845222	+	0.534415i	$0.820532\pi$
$942$	−150.001	−	994.156i	−0.159236	−	1.05537i
$943$	−37.9925	+	21.9350i	−0.0402890	+	0.0232609i
$944$	109.361			0.115848
$945$	226.964	+	121.817i	0.240173	+	0.128907i
$946$	−29.7863			−0.0314865
$947$	−720.823	−	1248.50i	−0.761165	−	1.31838i	−0.942251	−	0.334909i	$-0.891294\pi$
$947$	−720.823	−	1248.50i	−0.761165	−	1.31838i	0.181086	−	0.983467i	$-0.442039\pi$
$948$	−43.0536	−	285.345i	−0.0454152	−	0.300997i
$949$	1132.51	+	653.856i	1.19337	+	0.688995i
$950$	250.858	−	144.833i	0.264061	−	0.152456i
$951$	−1140.10	+	909.489i	−1.19885	+	0.956350i
$952$	−244.234	+	549.483i	−0.256548	+	0.577188i
$953$		−	705.606i		−	0.740405i	−0.928951	−	0.370202i	$-0.879288\pi$
$953$		−	705.606i		−	0.740405i	0.928951	−	0.370202i	$-0.120712\pi$
$954$	273.407	+	885.400i	0.286590	+	0.928092i
$955$	−153.833	−	88.8155i	−0.161082	−	0.0930005i
$956$	254.755	−	441.248i	0.266480	−	0.461557i
$957$	137.280	−	349.941i	0.143448	−	0.365664i
$958$	440.654			0.459973
$959$	−1448.21	−	643.698i	−1.51012	−	0.671218i
$960$	−202.505	+	161.543i	−0.210943	+	0.168274i
$961$	−422.333	−	731.502i	−0.439472	−	0.761188i
$962$	−563.665	−	325.432i	−0.585930	−	0.338287i
$963$	734.342	−	791.919i	0.762556	−	0.822345i
$964$	631.267	−	364.462i	0.654841	−	0.378073i
$965$		−	387.000i		−	0.401036i
$966$	79.4903	+	21.8714i	0.0822881	+	0.0226412i
$967$			1131.68i			1.17030i	0.810925	+	0.585151i	$0.198965\pi$
$967$			1131.68i			1.17030i	−0.810925	+	0.585151i	$0.801035\pi$
$968$	−371.552	−	643.547i	−0.383835	−	0.664821i
$969$	−36.6173	−	242.688i	−0.0377888	−	0.250452i
$970$	−49.9466	−	28.8367i	−0.0514914	−	0.0297286i
$971$	−137.401	+	79.3285i	−0.141505	+	0.0816978i	−0.569081	−	0.822282i	$-0.692701\pi$
$971$	−137.401	+	79.3285i	−0.141505	+	0.0816978i	0.427576	+	0.903979i	$0.359368\pi$
$972$	−400.402	+	91.7119i	−0.411936	+	0.0943538i
$973$	18.3145	+	173.209i	0.0188227	+	0.178016i
$974$			81.0343i			0.0831974i
$975$	840.217	+	329.612i	0.861761	+	0.338064i
$976$	61.2998	−	106.174i	0.0628072	−	0.108785i
$977$	313.438	−	542.891i	0.320817	−	0.555671i	−0.659840	−	0.751406i	$-0.729376\pi$
$977$	313.438	−	542.891i	0.320817	−	0.555671i	0.980657	+	0.195735i	$0.0627093\pi$
$978$	47.0016	−	119.812i	0.0480589	−	0.122507i
$979$	518.285			0.529402
$980$	110.393	−	23.6092i	0.112646	−	0.0240910i
$981$	996.350	+	227.089i	1.01565	+	0.231488i
$982$	−795.178	+	459.096i	−0.809754	+	0.467512i
$983$	−587.356	+	1017.33i	−0.597513	+	1.03492i	0.395674	+	0.918391i	$0.370511\pi$
$983$	−587.356	+	1017.33i	−0.597513	+	1.03492i	−0.993187	+	0.116532i	$0.962822\pi$
$984$	65.7318	+	435.649i	0.0668006	+	0.442733i
$985$	−8.07125	−	13.9798i	−0.00819416	−	0.0141927i
$986$	319.405			0.323940
$987$	−971.671	−	984.782i	−0.984469	−	0.997753i
$988$		−	180.991i		−	0.183189i
$989$	7.40421	−	4.27482i	0.00748656	−	0.00432237i
$990$	80.9484	+	75.0630i	0.0817660	+	0.0758212i
$991$	−242.964	+	420.827i	−0.245171	+	0.424648i	−0.962180	−	0.272416i	$-0.912177\pi$
$991$	−242.964	+	420.827i	−0.245171	+	0.424648i	0.717009	+	0.697064i	$0.245511\pi$
$992$	232.534	−	134.254i	0.234410	−	0.135336i
$993$	−1072.33	−	1344.24i	−1.07989	−	1.35372i
$994$	239.370	−	174.142i	0.240815	−	0.175193i
$995$	126.747			0.127383
$996$	−492.369	−	193.153i	−0.494346	−	0.193929i
$997$	−568.005	+	983.813i	−0.569714	+	0.986773i	0.426880	+	0.904308i	$0.359613\pi$
$997$	−568.005	+	983.813i	−0.569714	+	0.986773i	−0.996594	+	0.0824651i	$0.973721\pi$
$998$	321.330	+	185.520i	0.321974	+	0.185892i
$999$	−735.166	−	500.733i	−0.735902	−	0.501234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.w.c.116.3	✓	16
3.2	odd	2	inner	273.3.w.c.116.6	yes	16
7.2	even	3	inner	273.3.w.c.233.4	yes	16
13.12	even	2	inner	273.3.w.c.116.5	yes	16
21.2	odd	6	inner	273.3.w.c.233.5	yes	16
39.38	odd	2	inner	273.3.w.c.116.4	yes	16
91.51	even	6	inner	273.3.w.c.233.6	yes	16
273.233	odd	6	inner	273.3.w.c.233.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.w.c.116.3	✓	16	1.1	even	1	trivial
273.3.w.c.116.4	yes	16	39.38	odd	2	inner
273.3.w.c.116.5	yes	16	13.12	even	2	inner
273.3.w.c.116.6	yes	16	3.2	odd	2	inner
273.3.w.c.233.3	yes	16	273.233	odd	6	inner
273.3.w.c.233.4	yes	16	7.2	even	3	inner
273.3.w.c.233.5	yes	16	21.2	odd	6	inner
273.3.w.c.233.6	yes	16	91.51	even	6	inner

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.759866 - 1.31613i) q^{2} +(-0.447581 - 2.96642i) q^{3} +(0.845208 - 1.46394i) q^{4} +(-0.681452 - 1.18031i) q^{5} +(-3.56409 + 2.84316i) q^{6} +(0.736052 + 6.96119i) q^{7} -8.64790 q^{8} +(-8.59934 + 2.65543i) q^{9} +O(q^{10})\)	\(q+(-0.759866 - 1.31613i) q^{2} +(-0.447581 - 2.96642i) q^{3} +(0.845208 - 1.46394i) q^{4} +(-0.681452 - 1.18031i) q^{5} +(-3.56409 + 2.84316i) q^{6} +(0.736052 + 6.96119i) q^{7} -8.64790 q^{8} +(-8.59934 + 2.65543i) q^{9} +(-1.03562 + 1.79375i) q^{10} +(-2.96105 + 5.12869i) q^{11} +(-4.72097 - 1.85201i) q^{12} -13.0000 q^{13} +(8.60251 - 6.25831i) q^{14} +(-3.19629 + 2.54976i) q^{15} +(3.19042 + 5.52596i) q^{16} +(-8.60251 - 4.96666i) q^{17} +(10.0292 + 9.30005i) q^{18} +(-7.13265 + 4.11804i) q^{19} -2.30387 q^{20} +(20.3204 - 5.29914i) q^{21} +9.00000 q^{22} +(-2.23720 + 1.29165i) q^{23} +(3.87064 + 25.6534i) q^{24} +(11.5712 - 20.0420i) q^{25} +(9.87826 + 17.1096i) q^{26} +(11.7260 + 24.3208i) q^{27} +(10.8129 + 4.80612i) q^{28} -21.1583i q^{29} +(5.78456 + 2.26925i) q^{30} +(-9.34080 - 5.39292i) q^{31} +(-12.4472 + 21.5592i) q^{32} +(16.5392 + 6.48822i) q^{33} +15.0960i q^{34} +(7.71478 - 5.61249i) q^{35} +(-3.38083 + 14.8333i) q^{36} +(-28.5306 + 16.4721i) q^{37} +(10.8397 + 6.25831i) q^{38} +(5.81856 + 38.5635i) q^{39} +(5.89313 + 10.2072i) q^{40} +16.9822 q^{41} +(-22.4151 - 22.7176i) q^{42} -3.30958 q^{43} +(5.00540 + 8.66961i) q^{44} +(8.99427 + 8.34033i) q^{45} +(3.39995 + 1.96296i) q^{46} +(-32.9393 - 57.0526i) q^{47} +(14.9644 - 11.9374i) q^{48} +(-47.9165 + 10.2476i) q^{49} -35.1704 q^{50} +(-10.8829 + 27.7417i) q^{51} +(-10.9877 + 19.0313i) q^{52} +(58.6730 + 33.8749i) q^{53} +(23.0990 - 33.9135i) q^{54} +8.07125 q^{55} +(-6.36531 - 60.1997i) q^{56} +(15.4083 + 19.3153i) q^{57} +(-27.8470 + 16.0775i) q^{58} +(8.56949 - 14.8428i) q^{59} +(1.03117 + 6.83426i) q^{60} +(-9.60687 - 16.6396i) q^{61} +16.3916i q^{62} +(-24.8145 - 57.9072i) q^{63} +63.3562 q^{64} +(8.85887 + 15.3440i) q^{65} +(-4.02823 - 26.6978i) q^{66} +(-88.3081 - 50.9847i) q^{67} +(-14.5418 + 8.39572i) q^{68} +(4.83291 + 6.05837i) q^{69} +(-13.2489 - 5.88888i) q^{70} +27.8257 q^{71} +(74.3663 - 22.9639i) q^{72} +(-87.1163 - 50.2966i) q^{73} +(43.3588 + 25.0332i) q^{74} +(-64.6321 - 25.3548i) q^{75} +13.9224i q^{76} +(-37.8813 - 16.8375i) q^{77} +(46.3331 - 36.9610i) q^{78} +(28.4521 + 49.2804i) q^{79} +(4.34823 - 7.53135i) q^{80} +(66.8974 - 45.6699i) q^{81} +(-12.9042 - 22.3507i) q^{82} +104.294 q^{83} +(9.41733 - 34.2268i) q^{84} +13.5382i q^{85} +(2.51484 + 4.35583i) q^{86} +(-62.7645 + 9.47006i) q^{87} +(25.6069 - 44.3524i) q^{88} +(-43.7586 - 75.7921i) q^{89} +(4.14249 - 18.1751i) q^{90} +(-9.56867 - 90.4955i) q^{91} +4.36685i q^{92} +(-11.8169 + 30.1226i) q^{93} +(-50.0589 + 86.7046i) q^{94} +(9.72111 + 5.61249i) q^{95} +(69.5250 + 27.2743i) q^{96} +27.8448i q^{97} +(49.8972 + 55.2773i) q^{98} +(11.8442 - 51.9662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 24 * q^4 - 16 * q^9	\( 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) \) 16 * q - 24 * q^4 - 16 * q^9 + 96 * q^10 - 88 * q^12 - 208 * q^13 - 24 * q^16 + 144 * q^22 - 40 * q^25 + 264 * q^30 + 96 * q^36 + 432 * q^40 - 448 * q^42 - 128 * q^43 + 352 * q^48 - 504 * q^49 + 280 * q^51 + 312 * q^52 - 96 * q^55 + 184 * q^61 - 112 * q^64 - 448 * q^69 - 528 * q^75 + 80 * q^79 + 584 * q^81 + 544 * q^82 - 448 * q^87 + 72 * q^88 - 384 * q^90 - 88 * q^94

Introduction

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