LMFDB - Embedded newform 273.3.bo.c.160.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(160,273)]

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([0, 3, 1]))

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

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

chi := DirichletCharacter("273.160");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	273.bo (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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			160.18
Character	$\chi$	$=$	273.160
Dual form			273.3.bo.c.244.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.26818 + 1.88688i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(5.12066 + 8.86924i) q^{4} +3.17854 q^{5} +(-3.26818 - 5.66065i) q^{6} +(6.65578 - 2.16809i) q^{7} +23.5533i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(3.26818 + 1.88688i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(5.12066 + 8.86924i) q^{4} +3.17854 q^{5} +(-3.26818 - 5.66065i) q^{6} +(6.65578 - 2.16809i) q^{7} +23.5533i q^{8} +(1.50000 + 2.59808i) q^{9} +(10.3880 + 5.99754i) q^{10} +(-6.15750 - 3.55504i) q^{11} -17.7385i q^{12} +(6.68635 - 11.1487i) q^{13} +(25.8432 + 5.47296i) q^{14} +(-4.76781 - 2.75270i) q^{15} +(-23.9596 + 41.4993i) q^{16} +(-26.7605 + 15.4502i) q^{17} +11.3213i q^{18} +(7.54483 + 13.0680i) q^{19} +(16.2762 + 28.1912i) q^{20} +(-11.8613 - 2.51193i) q^{21} +(-13.4159 - 23.2370i) q^{22} +(-1.77472 + 3.07391i) q^{23} +(20.3977 - 35.3299i) q^{24} -14.8969 q^{25} +(42.8884 - 23.8195i) q^{26} -5.19615i q^{27} +(53.3113 + 47.9296i) q^{28} +(21.9060 - 37.9423i) q^{29} +(-10.3880 - 17.9926i) q^{30} +10.4085 q^{31} +(-75.0178 + 43.3116i) q^{32} +(6.15750 + 10.6651i) q^{33} -116.611 q^{34} +(21.1557 - 6.89138i) q^{35} +(-15.3620 + 26.6077i) q^{36} +(-6.73830 - 3.89036i) q^{37} +56.9449i q^{38} +(-19.6846 + 10.9325i) q^{39} +74.8650i q^{40} +(17.0048 - 29.4531i) q^{41} +(-34.0251 - 30.5903i) q^{42} +(-17.2636 - 29.9014i) q^{43} -72.8165i q^{44} +(4.76781 + 8.25809i) q^{45} +(-11.6002 + 6.69739i) q^{46} -56.0600 q^{47} +(71.8789 - 41.4993i) q^{48} +(39.5987 - 28.8607i) q^{49} +(-48.6856 - 28.1087i) q^{50} +53.5210 q^{51} +(133.119 + 2.21432i) q^{52} +47.4276 q^{53} +(9.80453 - 16.9820i) q^{54} +(-19.5719 - 11.2998i) q^{55} +(51.0657 + 156.765i) q^{56} -26.1361i q^{57} +(143.186 - 82.6682i) q^{58} +(-54.2307 - 93.9304i) q^{59} -56.3825i q^{60} +(-0.722790 + 0.417303i) q^{61} +(34.0170 + 19.6397i) q^{62} +(15.6165 + 14.0401i) q^{63} -135.218 q^{64} +(21.2528 - 35.4365i) q^{65} +46.4740i q^{66} +(-25.1044 - 14.4940i) q^{67} +(-274.063 - 158.230i) q^{68} +(5.32417 - 3.07391i) q^{69} +(82.1437 + 17.3960i) q^{70} +(-105.878 + 61.1286i) q^{71} +(-61.1932 + 35.3299i) q^{72} +121.814 q^{73} +(-14.6813 - 25.4288i) q^{74} +(22.3453 + 12.9011i) q^{75} +(-77.2690 + 133.834i) q^{76} +(-48.6906 - 10.3115i) q^{77} +(-84.9609 - 1.41326i) q^{78} -7.63503 q^{79} +(-76.1567 + 131.907i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(111.149 - 64.1721i) q^{82} +31.7944 q^{83} +(-38.4587 - 118.063i) q^{84} +(-85.0594 + 49.1091i) q^{85} -130.298i q^{86} +(-65.7181 + 37.9423i) q^{87} +(83.7327 - 145.029i) q^{88} +(-42.7821 + 74.1007i) q^{89} +35.9852i q^{90} +(20.3315 - 88.6997i) q^{91} -36.3510 q^{92} +(-15.6128 - 9.01407i) q^{93} +(-183.214 - 105.779i) q^{94} +(23.9816 + 41.5373i) q^{95} +150.036 q^{96} +(-35.0376 - 60.6869i) q^{97} +(183.872 - 19.6037i) q^{98} -21.3302i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.26818	+	1.88688i	1.63409	+	0.943442i	0.982814	+	0.184600i	$0.0590990\pi$
$2$	3.26818	+	1.88688i	1.63409	+	0.943442i	0.651275	+	0.758842i	$0.274234\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	5.12066	+	8.86924i	1.28016	+	2.21731i
$5$	3.17854			0.635708			0.317854	−	0.948140i	$-0.397038\pi$
$5$	3.17854			0.635708			0.317854	+	0.948140i	$0.397038\pi$
$6$	−3.26818	−	5.66065i	−0.544696	−	0.943442i
$7$	6.65578	−	2.16809i	0.950825	−	0.309728i
$7$	6.65578	−	2.16809i	0.950825	−	0.309728i
$8$			23.5533i			2.94416i
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	10.3880	+	5.99754i	1.03880	+	0.599754i
$11$	−6.15750	−	3.55504i	−0.559773	−	0.323185i	0.193281	−	0.981143i	$-0.438087\pi$
$11$	−6.15750	−	3.55504i	−0.559773	−	0.323185i	−0.753054	+	0.657958i	$0.771420\pi$
$12$		−	17.7385i		−	1.47821i
$13$	6.68635	−	11.1487i	0.514334	−	0.857590i
$13$	6.68635	−	11.1487i	0.514334	−	0.857590i
$14$	25.8432	+	5.47296i	1.84594	+	0.390925i
$15$	−4.76781	−	2.75270i	−0.317854	−	0.183513i
$16$	−23.9596	+	41.4993i	−1.49748	+	2.59371i
$17$	−26.7605	+	15.4502i	−1.57415	+	0.908835i	−0.578495	+	0.815686i	$0.696360\pi$
$17$	−26.7605	+	15.4502i	−1.57415	+	0.908835i	−0.995652	+	0.0931489i	$0.970307\pi$
$18$			11.3213i			0.628961i
$19$	7.54483	+	13.0680i	0.397097	+	0.687791i	0.993366	−	0.114993i	$-0.0366845\pi$
$19$	7.54483	+	13.0680i	0.397097	+	0.687791i	−0.596270	+	0.802784i	$0.703351\pi$
$20$	16.2762	+	28.1912i	0.813811	+	1.40956i
$21$	−11.8613	−	2.51193i	−0.564823	−	0.119616i
$22$	−13.4159	−	23.2370i	−0.609813	−	1.05623i
$23$	−1.77472	+	3.07391i	−0.0771618	+	0.133648i	−0.902024	−	0.431685i	$-0.857919\pi$
$23$	−1.77472	+	3.07391i	−0.0771618	+	0.133648i	0.824863	+	0.565333i	$0.191252\pi$
$24$	20.3977	−	35.3299i	0.849905	−	1.47208i
$25$	−14.8969			−0.595875
$26$	42.8884	−	23.8195i	1.64955	−	0.916133i
$27$		−	5.19615i		−	0.192450i
$28$	53.3113	+	47.9296i	1.90398	+	1.71177i
$29$	21.9060	−	37.9423i	0.755380	−	1.30836i	−0.189805	−	0.981822i	$-0.560786\pi$
$29$	21.9060	−	37.9423i	0.755380	−	1.30836i	0.945185	−	0.326535i	$-0.105881\pi$
$30$	−10.3880	−	17.9926i	−0.346268	−	0.599754i
$31$	10.4085			0.335760			0.167880	−	0.985807i	$-0.446308\pi$
$31$	10.4085			0.335760			0.167880	+	0.985807i	$0.446308\pi$
$32$	−75.0178	+	43.3116i	−2.34431	+	1.35349i
$33$	6.15750	+	10.6651i	0.186591	+	0.323185i
$34$	−116.611			−3.42973
$35$	21.1557	−	6.89138i	0.604447	−	0.196897i
$36$	−15.3620	+	26.6077i	−0.426721	+	0.739103i
$37$	−6.73830	−	3.89036i	−0.182116	−	0.105145i	0.406170	−	0.913797i	$-0.366864\pi$
$37$	−6.73830	−	3.89036i	−0.182116	−	0.105145i	−0.588287	+	0.808653i	$0.700197\pi$
$38$			56.9449i			1.49855i
$39$	−19.6846	+	10.9325i	−0.504732	+	0.280319i
$40$			74.8650i			1.87163i
$41$	17.0048	−	29.4531i	0.414751	−	0.718369i	−0.580652	−	0.814152i	$-0.697202\pi$
$41$	17.0048	−	29.4531i	0.414751	−	0.718369i	0.995402	+	0.0957830i	$0.0305355\pi$
$42$	−34.0251	−	30.5903i	−0.810121	−	0.728341i
$43$	−17.2636	−	29.9014i	−0.401479	−	0.695382i	0.592425	−	0.805625i	$-0.298170\pi$
$43$	−17.2636	−	29.9014i	−0.401479	−	0.695382i	−0.993905	+	0.110243i	$0.964837\pi$
$44$		−	72.8165i		−	1.65492i
$45$	4.76781	+	8.25809i	0.105951	+	0.183513i
$46$	−11.6002	+	6.69739i	−0.252179	+	0.145595i
$47$	−56.0600			−1.19277			−0.596384	−	0.802700i	$-0.703396\pi$
$47$	−56.0600			−1.19277			−0.596384	+	0.802700i	$0.703396\pi$
$48$	71.8789	−	41.4993i	1.49748	−	0.864569i
$49$	39.5987	−	28.8607i	0.808137	−	0.588994i
$50$	−48.6856	−	28.1087i	−0.973713	−	0.562173i
$51$	53.5210			1.04943
$52$	133.119	+	2.21432i	2.55997	+	0.0425831i
$53$	47.4276			0.894860			0.447430	−	0.894319i	$-0.352339\pi$
$53$	47.4276			0.894860			0.447430	+	0.894319i	$0.352339\pi$
$54$	9.80453	−	16.9820i	0.181565	−	0.314481i
$55$	−19.5719	−	11.2998i	−0.355852	−	0.205451i
$56$	51.0657	+	156.765i	0.911888	+	2.79938i
$57$		−	26.1361i		−	0.458528i
$58$	143.186	−	82.6682i	2.46872	−	1.42531i
$59$	−54.2307	−	93.9304i	−0.919165	−	1.59204i	−0.800686	−	0.599084i	$-0.795532\pi$
$59$	−54.2307	−	93.9304i	−0.919165	−	1.59204i	−0.118479	−	0.992957i	$-0.537802\pi$
$60$		−	56.3825i		−	0.939708i
$61$	−0.722790	+	0.417303i	−0.0118490	+	0.00684103i	−0.505913	−	0.862585i	$-0.668844\pi$
$61$	−0.722790	+	0.417303i	−0.0118490	+	0.00684103i	0.494064	+	0.869426i	$0.335511\pi$
$62$	34.0170	+	19.6397i	0.548661	+	0.316770i
$63$	15.6165	+	14.0401i	0.247882	+	0.222858i
$64$	−135.218			−2.11279
$65$	21.2528	−	35.4365i	0.326967	−	0.545177i
$66$			46.4740i			0.704151i
$67$	−25.1044	−	14.4940i	−0.374692	−	0.216329i	0.300814	−	0.953683i	$-0.402742\pi$
$67$	−25.1044	−	14.4940i	−0.374692	−	0.216329i	−0.675506	+	0.737354i	$0.736075\pi$
$68$	−274.063	−	158.230i	−4.03034	−	2.32692i
$69$	5.32417	−	3.07391i	0.0771618	−	0.0445494i
$70$	82.1437	+	17.3960i	1.17348	+	0.248515i
$71$	−105.878	+	61.1286i	−1.49124	+	0.860966i	−0.999950	−	0.0100314i	$-0.996807\pi$
$71$	−105.878	+	61.1286i	−1.49124	+	0.860966i	−0.491287	+	0.870998i	$0.663474\pi$
$72$	−61.1932	+	35.3299i	−0.849905	+	0.490693i
$73$	121.814			1.66869			0.834345	−	0.551242i	$-0.185846\pi$
$73$	121.814			1.66869			0.834345	+	0.551242i	$0.185846\pi$
$74$	−14.6813	−	25.4288i	−0.198396	−	0.343632i
$75$	22.3453	+	12.9011i	0.297938	+	0.172014i
$76$	−77.2690	+	133.834i	−1.01670	+	1.76097i
$77$	−48.6906	−	10.3115i	−0.632346	−	0.133915i
$78$	−84.9609	−	1.41326i	−1.08924	−	0.0181187i
$79$	−7.63503			−0.0966460			−0.0483230	−	0.998832i	$-0.515388\pi$
$79$	−7.63503			−0.0966460			−0.0483230	+	0.998832i	$0.515388\pi$
$80$	−76.1567	+	131.907i	−0.951959	+	1.64884i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	111.149	−	64.1721i	1.35548	−	0.782586i
$83$	31.7944			0.383066			0.191533	−	0.981486i	$-0.438654\pi$
$83$	31.7944			0.383066			0.191533	+	0.981486i	$0.438654\pi$
$84$	−38.4587	−	118.063i	−0.457842	−	1.40552i
$85$	−85.0594	+	49.1091i	−1.00070	+	0.577754i
$86$		−	130.298i		−	1.51509i
$87$	−65.7181	+	37.9423i	−0.755380	+	0.436119i
$88$	83.7327	−	145.029i	0.951508	−	1.64806i
$89$	−42.7821	+	74.1007i	−0.480697	+	0.832592i	−0.999755	−	0.0221472i	$-0.992950\pi$
$89$	−42.7821	+	74.1007i	−0.480697	+	0.832592i	0.519057	+	0.854739i	$0.326283\pi$
$90$			35.9852i			0.399836i
$91$	20.3315	−	88.6997i	0.223423	−	0.974722i
$92$	−36.3510			−0.395119
$93$	−15.6128	−	9.01407i	−0.167880	−	0.0969254i
$94$	−183.214	−	105.779i	−1.94909	−	1.12531i
$95$	23.9816	+	41.5373i	0.252438	+	0.437235i
$96$	150.036			1.56287
$97$	−35.0376	−	60.6869i	−0.361213	−	0.625639i	0.626948	−	0.779061i	$-0.284304\pi$
$97$	−35.0376	−	60.6869i	−0.361213	−	0.625639i	−0.988161	+	0.153422i	$0.950970\pi$
$98$	183.872	−	19.6037i	1.87625	−	0.200038i
$99$		−	21.3302i		−	0.215457i
$100$	−76.2818	−	132.124i	−0.762818	−	1.32124i
$101$	140.279	+	80.9903i	1.38890	+	0.801884i	0.993192	−	0.116490i	$-0.0371643\pi$
$101$	140.279	+	80.9903i	1.38890	+	0.801884i	0.395713	+	0.918374i	$0.370498\pi$
$102$	174.916	+	100.988i	1.71486	+	0.990078i
$103$			118.506i			1.15054i	0.817964	+	0.575270i	$0.195103\pi$
$103$			118.506i			1.15054i	−0.817964	+	0.575270i	$0.804897\pi$
$104$	262.588	+	157.485i	2.52488	+	1.51428i
$105$	−37.7016	−	7.98427i	−0.359063	−	0.0760407i
$106$	155.002	+	89.4903i	1.46228	+	0.844248i
$107$	−38.8983	+	67.3738i	−0.363535	+	0.629661i	−0.988540	−	0.150960i	$-0.951764\pi$
$107$	−38.8983	+	67.3738i	−0.363535	+	0.629661i	0.625005	+	0.780621i	$0.285097\pi$
$108$	46.0859	−	26.6077i	0.426721	−	0.246368i
$109$			179.552i			1.64727i	0.567121	+	0.823634i	$0.308057\pi$
$109$			179.552i			1.64727i	−0.567121	+	0.823634i	$0.691943\pi$
$110$	−42.6429	−	73.8597i	−0.387663	−	0.671452i
$111$	6.73830	+	11.6711i	0.0607054	+	0.105145i
$112$	−69.4956	+	328.157i	−0.620496	+	2.92997i
$113$	42.6427	+	73.8594i	0.377369	+	0.653623i	0.990679	−	0.136220i	$-0.0434954\pi$
$113$	42.6427	+	73.8594i	0.377369	+	0.653623i	−0.613309	+	0.789843i	$0.710162\pi$
$114$	49.3157	−	85.4173i	0.432594	−	0.749275i
$115$	−5.64103	+	9.77055i	−0.0490524	+	0.0849613i
$116$	448.693			3.86804
$117$	38.9946	+	0.648644i	0.333287	+	0.00554396i
$118$		−	409.308i		−	3.46871i
$119$	−144.615	+	160.852i	−1.21525	+	1.35170i
$120$	64.8350	−	112.298i	0.540292	−	0.935813i
$121$	−35.2234	−	61.0088i	−0.291103	−	0.504205i
$122$	−3.14961			−0.0258165
$123$	−51.0143	+	29.4531i	−0.414751	+	0.239456i
$124$	53.2986	+	92.3159i	0.429827	+	0.744483i
$125$	−126.814			−1.01451
$126$	24.5456	+	75.3520i	0.194807	+	0.598032i
$127$	53.5242	−	92.7066i	0.421450	−	0.729973i	−0.574632	−	0.818412i	$-0.694855\pi$
$127$	53.5242	−	92.7066i	0.421450	−	0.729973i	0.996082	+	0.0884394i	$0.0281880\pi$
$128$	−141.846	−	81.8950i	−1.10817	−	0.639805i
$129$			59.8029i			0.463588i
$130$	136.323	−	75.7111i	1.04864	−	0.582393i
$131$		−	24.1468i		−	0.184327i	−0.995744	−	0.0921635i	$-0.970622\pi$
$131$		−	24.1468i		−	0.184327i	0.995744	−	0.0921635i	$-0.0293783\pi$
$132$	−63.0609	+	109.225i	−0.477734	+	0.827460i
$133$	78.5495	+	70.6200i	0.590598	+	0.530978i
$134$	−54.6970	−	94.7380i	−0.408187	−	0.707000i
$135$		−	16.5162i		−	0.122342i
$136$	−363.902	−	630.297i	−2.67575	−	4.63454i
$137$	−7.63138	+	4.40598i	−0.0557035	+	0.0321604i	−0.527593	−	0.849497i	$-0.676905\pi$
$137$	−7.63138	+	4.40598i	−0.0557035	+	0.0321604i	0.471890	+	0.881658i	$0.343572\pi$
$138$	23.2004			0.168119
$139$	137.110	−	79.1607i	0.986405	−	0.569501i	0.0822072	−	0.996615i	$-0.473803\pi$
$139$	137.110	−	79.1607i	0.986405	−	0.569501i	0.904198	+	0.427114i	$0.140470\pi$
$140$	169.452	+	152.346i	1.21037	+	1.08819i
$141$	84.0901	+	48.5494i	0.596384	+	0.344322i
$142$	−461.370			−3.24909
$143$	−80.8051	+	44.8777i	−0.565071	+	0.313830i
$144$	−143.758			−0.998318
$145$	69.6292	−	120.601i	0.480201	−	0.831733i
$146$	398.111	+	229.850i	2.72679	+	1.57431i
$147$	−84.3922	+	8.99755i	−0.574097	+	0.0612078i
$148$		−	79.6847i		−	0.538410i
$149$	−112.134	+	64.7405i	−0.752577	+	0.434500i	−0.826624	−	0.562754i	$-0.809742\pi$
$149$	−112.134	+	64.7405i	−0.752577	+	0.434500i	0.0740476	+	0.997255i	$0.476408\pi$
$150$	48.6856	+	84.3260i	0.324571	+	0.562173i
$151$			29.5268i			0.195541i	0.995209	+	0.0977707i	$0.0311712\pi$
$151$			29.5268i			0.195541i	−0.995209	+	0.0977707i	$0.968829\pi$
$152$	−307.795	+	177.706i	−2.02497	+	1.16912i
$153$	−80.2815	−	46.3506i	−0.524716	−	0.302945i
$154$	−139.673	−	125.573i	−0.906968	−	0.815411i
$155$	33.0840			0.213445
$156$	−197.760	−	118.606i	−1.26769	−	0.760293i
$157$			16.2513i			0.103511i	0.998660	+	0.0517556i	$0.0164817\pi$
$157$			16.2513i			0.103511i	−0.998660	+	0.0517556i	$0.983518\pi$
$158$	−24.9526	−	14.4064i	−0.157928	−	0.0911798i
$159$	−71.1414	−	41.0735i	−0.447430	−	0.258324i
$160$	−238.447	+	137.668i	−1.49030	+	0.860422i
$161$	−5.14763	+	24.3070i	−0.0319729	+	0.150975i
$162$	−29.4136	+	16.9820i	−0.181565	+	0.104827i
$163$	−102.978	+	59.4546i	−0.631769	+	0.364752i	−0.781437	−	0.623984i	$-0.785513\pi$
$163$	−102.978	+	59.4546i	−0.631769	+	0.364752i	0.149668	+	0.988736i	$0.452180\pi$
$164$	348.303			2.12380
$165$	19.5719	+	33.8995i	0.118617	+	0.205451i
$166$	103.910	+	59.9924i	0.625963	+	0.361400i
$167$	−62.3293	+	107.958i	−0.373229	+	0.646452i	−0.990060	−	0.140643i	$-0.955083\pi$
$167$	−62.3293	+	107.958i	−0.373229	+	0.646452i	0.616831	+	0.787096i	$0.288416\pi$
$168$	59.1642	−	279.372i	0.352168	−	1.66293i
$169$	−79.5855	−	149.088i	−0.470920	−	0.882176i
$170$	−370.652			−2.18031
$171$	−22.6345	+	39.2041i	−0.132366	+	0.229264i
$172$	176.802	−	306.230i	1.02792	−	1.78041i
$173$	−103.241	+	59.6062i	−0.596769	+	0.344544i	−0.767769	−	0.640726i	$-0.778633\pi$
$173$	−103.241	+	59.6062i	−0.596769	+	0.344544i	0.171001	+	0.985271i	$0.445300\pi$
$174$	−286.371			−1.64581
$175$	−99.1503	+	32.2978i	−0.566573	+	0.184559i
$176$	295.063	−	170.355i	1.67650	−	0.967925i
$177$			187.861i			1.06136i
$178$	−279.639	+	161.450i	−1.57100	+	0.907020i
$179$	−135.664	+	234.977i	−0.757899	+	1.31272i	0.186020	+	0.982546i	$0.440441\pi$
$179$	−135.664	+	234.977i	−0.757899	+	1.31272i	−0.943920	+	0.330174i	$0.892892\pi$
$180$	−48.8287	+	84.5737i	−0.271270	+	0.469854i
$181$		−	71.9902i		−	0.397736i	−0.980026	−	0.198868i	$-0.936273\pi$
$181$		−	71.9902i		−	0.397736i	0.980026	−	0.198868i	$-0.0637265\pi$
$182$	233.813	−	251.523i	1.28469	−	1.38200i
$183$	1.44558			0.00789934
$184$	−72.4006	−	41.8005i	−0.393482	−	0.227177i
$185$	−21.4180	−	12.3657i	−0.115773	−	0.0668414i
$186$	−34.0170	−	58.9191i	−0.182887	−	0.316770i
$187$	219.704			1.17489
$188$	−287.064	−	497.210i	−1.52694	−	2.64473i
$189$	−11.2657	−	34.5844i	−0.0596071	−	0.182986i
$190$			181.002i			0.952640i
$191$	−158.594	−	274.693i	−0.830336	−	1.43818i	−0.897772	−	0.440461i	$-0.854815\pi$
$191$	−158.594	−	274.693i	−0.830336	−	1.43818i	0.0674359	−	0.997724i	$-0.478518\pi$
$192$	202.828	+	117.103i	1.05639	+	0.609909i
$193$	172.432	+	99.5539i	0.893432	+	0.515823i	0.875064	−	0.484008i	$-0.160819\pi$
$193$	172.432	+	99.5539i	0.893432	+	0.515823i	0.0183686	+	0.999831i	$0.494153\pi$
$194$		−	264.448i		−	1.36313i
$195$	−62.5681	+	34.7492i	−0.320862	+	0.178201i
$196$	458.744	+	203.425i	2.34053	+	1.03788i
$197$	128.217	+	74.0263i	0.650850	+	0.375768i	0.788782	−	0.614674i	$-0.210712\pi$
$197$	128.217	+	74.0263i	0.650850	+	0.375768i	−0.137932	+	0.990442i	$0.544046\pi$
$198$	40.2476	−	69.7110i	0.203271	−	0.352076i
$199$	205.362	−	118.566i	1.03197	−	0.595809i	0.114423	−	0.993432i	$-0.463498\pi$
$199$	205.362	−	118.566i	1.03197	−	0.595809i	0.917549	+	0.397623i	$0.130165\pi$
$200$		−	350.870i		−	1.75435i
$201$	25.1044	+	43.4820i	0.124897	+	0.216329i
$202$	305.639	+	529.382i	1.51306	+	2.62070i
$203$	63.5390	−	300.030i	0.313000	−	1.47798i
$204$	274.063	+	474.691i	1.34345	+	2.32692i
$205$	54.0504	−	93.6180i	0.263660	−	0.456673i
$206$	−223.606	+	387.297i	−1.08547	+	1.88008i
$207$	−10.6483			−0.0514412
$208$	302.460	+	544.597i	1.45413	+	2.61825i
$209$		−	107.289i		−	0.513343i
$210$	−108.150	−	97.2325i	−0.515001	−	0.463012i
$211$	−124.741	+	216.059i	−0.591192	+	1.02397i	0.402880	+	0.915253i	$0.368009\pi$
$211$	−124.741	+	216.059i	−0.591192	+	1.02397i	−0.994072	+	0.108722i	$0.965324\pi$
$212$	242.860	+	420.647i	1.14557	+	1.98418i
$213$	211.756			0.994158
$214$	−254.253	+	146.793i	−1.18810	+	0.685948i
$215$	−54.8731	−	95.0430i	−0.255224	−	0.442060i
$216$	122.386			0.566604
$217$	69.2770	−	22.5667i	0.319249	−	0.103994i
$218$	−338.794	+	586.809i	−1.55410	+	2.69178i
$219$	−182.722	−	105.494i	−0.834345	−	0.481709i
$220$		−	231.450i		−	1.05205i
$221$	−6.68111	+	401.649i	−0.0302313	+	1.81742i
$222$			50.8575i			0.229088i
$223$	19.1656	−	33.1958i	0.0859443	−	0.148860i	−0.819849	−	0.572580i	$-0.805943\pi$
$223$	19.1656	−	33.1958i	0.0859443	−	0.148860i	0.905793	+	0.423720i	$0.139276\pi$
$224$	−405.398	+	450.918i	−1.80981	+	2.01303i
$225$	−22.3453	−	38.7032i	−0.0993125	−	0.172014i
$226$			321.847i			1.42410i
$227$	−56.7575	−	98.3069i	−0.250033	−	0.433070i	0.713501	−	0.700654i	$-0.247108\pi$
$227$	−56.7575	−	98.3069i	−0.250033	−	0.433070i	−0.963535	+	0.267583i	$0.913775\pi$
$228$	231.807	−	133.834i	1.01670	−	0.586991i
$229$	230.843			1.00805			0.504023	−	0.863690i	$-0.331853\pi$
$229$	230.843			1.00805			0.504023	+	0.863690i	$0.331853\pi$
$230$	−36.8718	+	21.2879i	−0.160312	+	0.0925562i
$231$	64.1059	+	57.6345i	0.277515	+	0.249500i
$232$	893.666	+	515.959i	3.85201	+	2.22396i
$233$	321.747			1.38089			0.690444	−	0.723386i	$-0.257415\pi$
$233$	321.747			1.38089			0.690444	+	0.723386i	$0.257415\pi$
$234$	126.217	+	75.6982i	0.539391	+	0.323496i
$235$	−178.189			−0.758252
$236$	555.394	−	961.971i	2.35336	−	4.07615i
$237$	11.4525	+	6.61213i	0.0483230	+	0.0278993i
$238$	−776.136	+	252.823i	−3.26107	+	1.06228i
$239$		−	84.4617i		−	0.353396i	−0.984265	−	0.176698i	$-0.943458\pi$
$239$		−	84.4617i		−	0.353396i	0.984265	−	0.176698i	$-0.0565416\pi$
$240$	228.470	−	131.907i	0.951959	−	0.549614i
$241$	−62.2386	−	107.800i	−0.258251	−	0.447305i	0.707522	−	0.706691i	$-0.249813\pi$
$241$	−62.2386	−	107.800i	−0.258251	−	0.447305i	−0.965774	+	0.259387i	$0.916480\pi$
$242$		−	265.850i		−	1.09855i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	−7.40232	−	4.27373i	−0.0303374	−	0.0175153i
$245$	125.866	−	91.7349i	0.513740	−	0.374428i
$246$	−222.299			−0.903653
$247$	196.139	+	3.26261i	0.794083	+	0.0132089i
$248$			245.155i			0.988530i
$249$	−47.6917	−	27.5348i	−0.191533	−	0.110582i
$250$	−414.450	−	239.283i	−1.65780	−	0.957132i
$251$	−240.000	+	138.564i	−0.956177	+	0.552049i	−0.894994	−	0.446078i	$-0.852820\pi$
$251$	−240.000	+	138.564i	−0.956177	+	0.552049i	−0.0611824	+	0.998127i	$0.519487\pi$
$252$	−44.5578	+	210.401i	−0.176817	+	0.834926i
$253$	21.8557	−	12.6184i	0.0863862	−	0.0498751i
$254$	349.853	−	201.988i	1.37737	−	0.795227i
$255$	170.119			0.667132
$256$	−38.6159	−	66.8847i	−0.150843	−	0.261268i
$257$	−339.052	−	195.752i	−1.31927	−	0.761680i	−0.335658	−	0.941984i	$-0.608959\pi$
$257$	−339.052	−	195.752i	−1.31927	−	0.761680i	−0.983611	+	0.180304i	$0.942292\pi$
$258$	−112.841	+	195.446i	−0.437369	+	0.757545i
$259$	−53.2833	−	11.2841i	−0.205727	−	0.0435679i
$260$	423.123	+	7.03831i	1.62740	+	0.0270704i
$261$	131.436			0.503587
$262$	45.5623	−	78.9162i	0.173902	−	0.301207i
$263$	40.9087	−	70.8559i	0.155546	−	0.269414i	−0.777712	−	0.628621i	$-0.783620\pi$
$263$	40.9087	−	70.8559i	0.155546	−	0.269414i	0.933258	+	0.359207i	$0.116953\pi$
$264$	−251.198	+	145.029i	−0.951508	+	0.549354i
$265$	150.751			0.568870
$266$	123.462	+	379.012i	0.464143	+	1.42486i
$267$	128.346	−	74.1007i	0.480697	−	0.277531i
$268$		−	296.876i		−	1.10774i
$269$	−74.1992	+	42.8389i	−0.275834	+	0.159253i	−0.631536	−	0.775347i	$-0.717575\pi$
$269$	−74.1992	+	42.8389i	−0.275834	+	0.159253i	0.355702	+	0.934599i	$0.384242\pi$
$270$	31.1641	−	53.9778i	0.115423	−	0.199918i
$271$	−215.728	+	373.652i	−0.796044	+	1.37879i	0.126131	+	0.992014i	$0.459744\pi$
$271$	−215.728	+	373.652i	−0.796044	+	1.37879i	−0.922174	+	0.386774i	$0.873589\pi$
$272$		−	1480.72i		−	5.44384i
$273$	−107.313	+	115.442i	−0.393089	+	0.422864i
$274$	−33.2543			−0.121366
$275$	91.7276	+	52.9589i	0.333555	+	0.192578i
$276$	54.5265	+	31.4809i	0.197560	+	0.114061i
$277$	160.383	+	277.791i	0.579000	+	1.00286i	0.995594	+	0.0937647i	$0.0298901\pi$
$277$	160.383	+	277.791i	0.579000	+	1.00286i	−0.416595	+	0.909092i	$0.636777\pi$
$278$	597.468			2.14916
$279$	15.6128	+	27.0422i	0.0559599	+	0.0969254i
$280$	162.314	+	498.285i	0.579695	+	1.77959i
$281$			251.286i			0.894254i	0.894470	+	0.447127i	$0.147553\pi$
$281$			251.286i			0.894254i	−0.894470	+	0.447127i	$0.852447\pi$
$282$	183.214	+	317.336i	0.649696	+	1.12531i
$283$	−407.646	−	235.355i	−1.44045	−	0.831642i	−0.442567	−	0.896735i	$-0.645932\pi$
$283$	−407.646	−	235.355i	−1.44045	−	0.831642i	−0.997879	+	0.0650932i	$0.979266\pi$
$284$	−1084.33	−	626.037i	−3.81806	−	2.20436i
$285$		−	83.0746i		−	0.291490i
$286$	−348.765	−	5.80142i	−1.21946	−	0.0202847i
$287$	49.3228	−	232.901i	0.171856	−	0.811503i
$288$	−225.053	−	129.935i	−0.781436	−	0.451162i
$289$	332.917	−	576.628i	1.15196	−	1.99525i
$290$	455.121	−	262.764i	1.56938	−	0.906084i
$291$			121.374i			0.417092i
$292$	623.770	+	1080.40i	2.13620	+	3.70000i
$293$	204.557	+	354.304i	0.698148	+	1.20923i	0.969108	+	0.246638i	$0.0793258\pi$
$293$	204.557	+	354.304i	0.698148	+	1.20923i	−0.270959	+	0.962591i	$0.587341\pi$
$294$	−292.786	−	129.833i	−0.995871	−	0.441608i
$295$	−172.375	−	298.562i	−0.584321	−	1.01207i
$296$	91.6306	−	158.709i	0.309563	−	0.536179i
$297$	−18.4725	+	31.9953i	−0.0621970	+	0.107728i
$298$	−488.631			−1.63970
$299$	22.4036	+	40.3390i	0.0749283	+	0.134913i
$300$			264.248i			0.880826i
$301$	−179.732	−	161.588i	−0.597116	−	0.536838i
$302$	−55.7136	+	96.4987i	−0.184482	+	0.319532i
$303$	−140.279	−	242.971i	−0.462968	−	0.801884i
$304$	−723.086			−2.37857
$305$	−2.29742	+	1.32641i	−0.00753251	+	0.00434890i
$306$	−174.916	−	302.964i	−0.571622	−	0.990078i
$307$	235.086			0.765753			0.382877	−	0.923800i	$-0.374933\pi$
$307$	235.086			0.765753			0.382877	+	0.923800i	$0.374933\pi$
$308$	−157.873	−	484.650i	−0.512575	−	1.57354i
$309$	102.629	−	177.758i	0.332132	−	0.575270i
$310$	108.124	+	62.4256i	0.348788	+	0.201373i
$311$			103.693i			0.333417i	0.986006	+	0.166709i	$0.0533139\pi$
$311$			103.693i			0.333417i	−0.986006	+	0.166709i	$0.946686\pi$
$312$	−257.495	−	463.636i	−0.825304	−	1.48601i
$313$			236.229i			0.754725i	0.926066	+	0.377362i	$0.123169\pi$
$313$			236.229i			0.754725i	−0.926066	+	0.377362i	$0.876831\pi$
$314$	−30.6643	+	53.1120i	−0.0976568	+	0.169147i
$315$	49.6378	+	44.6270i	0.157580	+	0.141673i
$316$	−39.0964	−	67.7169i	−0.123723	−	0.214294i
$317$		−	102.703i		−	0.323985i	−0.986792	−	0.161993i	$-0.948208\pi$
$317$		−	102.703i		−	0.323985i	0.986792	−	0.161993i	$-0.0517921\pi$
$318$	−155.002	−	268.471i	−0.487427	−	0.844248i
$319$	−269.773	+	155.753i	−0.845683	+	0.488255i
$320$	−429.797			−1.34312
$321$	116.695	−	67.3738i	0.363535	−	0.209887i
$322$	−62.6879	+	69.7267i	−0.194683	+	0.216542i
$323$	−403.807	−	233.138i	−1.25018	−	0.721790i
$324$	−92.1718			−0.284481
$325$	−99.6057	+	166.080i	−0.306479	+	0.511016i
$326$	−448.735			−1.37649
$327$	155.497	−	269.328i	0.475526	−	0.823634i
$328$	693.718	+	400.518i	2.11499	+	1.22109i
$329$	−373.123	+	121.543i	−1.13411	+	0.369433i
$330$			147.719i			0.447635i
$331$	223.367	−	128.961i	0.674824	−	0.389610i	−0.123078	−	0.992397i	$-0.539276\pi$
$331$	223.367	−	128.961i	0.674824	−	0.389610i	0.797902	+	0.602787i	$0.205943\pi$
$332$	162.808	+	281.993i	0.490387	+	0.849375i
$333$		−	23.3421i		−	0.0700965i
$334$	−407.406	+	235.216i	−1.21978	+	0.704240i
$335$	−79.7953	−	46.0698i	−0.238195	−	0.137522i
$336$	388.436	−	432.051i	1.15606	−	1.28586i
$337$	565.284			1.67740			0.838700	−	0.544594i	$-0.183316\pi$
$337$	565.284			1.67740			0.838700	+	0.544594i	$0.183316\pi$
$338$	21.2116	−	637.414i	0.0627562	−	1.88584i
$339$		−	147.719i		−	0.435749i
$340$	−871.120	−	502.941i	−2.56212	−	1.47924i
$341$	−64.0907	−	37.0028i	−0.187949	−	0.108513i
$342$	−147.947	+	85.4173i	−0.432594	+	0.249758i
$343$	200.988	−	277.944i	0.585970	−	0.810333i
$344$	704.277	−	406.614i	2.04732	−	1.18202i
$345$	16.9231	−	9.77055i	0.0490524	−	0.0283204i
$346$	−449.880			−1.30023
$347$	74.4978	+	129.034i	0.214691	+	0.371856i	0.953177	−	0.302413i	$-0.0977922\pi$
$347$	74.4978	+	129.034i	0.214691	+	0.371856i	−0.738486	+	0.674269i	$0.764459\pi$
$348$	−673.040	−	388.580i	−1.93402	−	1.11661i
$349$	127.402	−	220.666i	0.365048	−	0.632281i	−0.623736	−	0.781635i	$-0.714386\pi$
$349$	127.402	−	220.666i	0.365048	−	0.632281i	0.988784	+	0.149354i	$0.0477194\pi$
$350$	−384.983	−	81.5300i	−1.09995	−	0.232943i
$351$	−57.9302	−	34.7433i	−0.165043	−	0.0989837i
$352$	615.897			1.74971
$353$	1.41693	−	2.45420i	0.00401398	−	0.00695241i	−0.864011	−	0.503472i	$-0.832056\pi$
$353$	1.41693	−	2.45420i	0.00401398	−	0.00695241i	0.868025	+	0.496520i	$0.165389\pi$
$354$	−354.471	+	613.962i	−1.00133	+	1.73436i
$355$	−336.537	+	194.300i	−0.947992	+	0.547323i
$356$	−876.289			−2.46149
$357$	356.224	−	116.039i	0.997826	−	0.325038i
$358$	−886.748	+	511.964i	−2.47695	+	1.43007i
$359$		−	293.040i		−	0.816268i	−0.912922	−	0.408134i	$-0.866180\pi$
$359$		−	293.040i		−	0.816268i	0.912922	−	0.408134i	$-0.133820\pi$
$360$	−194.505	+	112.298i	−0.540292	+	0.311938i
$361$	66.6510	−	115.443i	0.184629	−	0.319786i
$362$	135.837	−	235.277i	0.375241	−	0.649936i
$363$			122.018i			0.336136i
$364$	890.809	−	273.876i	2.44728	−	0.752406i
$365$	387.192			1.06080
$366$	4.72441	+	2.72764i	0.0129082	+	0.00745257i
$367$	390.672	+	225.555i	1.06450	+	0.614590i	0.926674	−	0.375866i	$-0.122655\pi$
$367$	390.672	+	225.555i	1.06450	+	0.614590i	0.137828	+	0.990456i	$0.455988\pi$
$368$	−85.0434	−	147.300i	−0.231096	−	0.400270i
$369$	102.029			0.276500
$370$	−46.6651	−	80.8263i	−0.126122	−	0.218450i
$371$	315.667	−	102.827i	0.850855	−	0.277163i
$372$		−	184.632i		−	0.496322i
$373$	79.2270	+	137.225i	0.212405	+	0.367896i	0.952467	−	0.304643i	$-0.0985372\pi$
$373$	79.2270	+	137.225i	0.212405	+	0.367896i	−0.740062	+	0.672539i	$0.765204\pi$
$374$	718.032	+	414.556i	1.91987	+	1.10844i
$375$	190.221	+	109.824i	0.507255	+	0.292864i
$376$		−	1320.40i		−	3.51170i
$377$	−276.535	−	497.919i	−0.733515	−	1.32074i
$378$	28.4383	−	134.285i	0.0752336	−	0.355252i
$379$	603.346	+	348.342i	1.59194	+	0.919108i	0.992974	+	0.118336i	$0.0377561\pi$
$379$	603.346	+	348.342i	1.59194	+	0.919108i	0.598969	+	0.800772i	$0.295577\pi$
$380$	−245.603	+	425.396i	−0.646323	+	1.11946i
$381$	−160.572	+	92.7066i	−0.421450	+	0.243324i
$382$		−	1196.99i		−	3.13349i
$383$	90.8982	+	157.440i	0.237332	+	0.411071i	0.959948	−	0.280179i	$-0.0903937\pi$
$383$	90.8982	+	157.440i	0.237332	+	0.411071i	−0.722616	+	0.691250i	$0.757060\pi$
$384$	141.846	+	245.685i	0.369391	+	0.639805i
$385$	−154.765	−	32.7755i	−0.401987	−	0.0851311i
$386$	375.693	+	650.720i	0.973298	+	1.68580i
$387$	51.7908	−	89.7043i	0.133826	−	0.231794i
$388$	358.831	−	621.514i	0.924823	−	1.60184i
$389$	67.1678			0.172668			0.0863340	−	0.996266i	$-0.472485\pi$
$389$	67.1678			0.172668			0.0863340	+	0.996266i	$0.472485\pi$
$390$	−270.052	−	4.49209i	−0.692440	−	0.0115182i
$391$		−	109.679i		−	0.280509i
$392$	679.764	+	932.680i	1.73409	+	2.37928i
$393$	−20.9118	+	36.2203i	−0.0532106	+	0.0921635i
$394$	279.358	+	483.862i	0.709031	+	1.22808i
$395$	−24.2683			−0.0614386
$396$	189.183	−	109.225i	0.477734	−	0.275820i
$397$	56.2646	+	97.4532i	0.141725	+	0.245474i	0.928146	−	0.372216i	$-0.121402\pi$
$397$	56.2646	+	97.4532i	0.141725	+	0.245474i	−0.786422	+	0.617690i	$0.788069\pi$
$398$	894.881			2.24844
$399$	−56.6655	−	173.956i	−0.142019	−	0.435980i
$400$	356.924	−	618.210i	0.892310	−	1.54553i
$401$	−16.6482	−	9.61183i	−0.0415166	−	0.0239696i	0.479098	−	0.877761i	$-0.340964\pi$
$401$	−16.6482	−	9.61183i	−0.0415166	−	0.0239696i	−0.520615	+	0.853792i	$0.674297\pi$
$402$			189.476i			0.471334i
$403$	69.5952	−	116.041i	0.172693	−	0.287944i
$404$			1658.89i			4.10618i
$405$	−14.3034	+	24.7743i	−0.0353171	+	0.0611711i
$406$	773.779	−	860.661i	1.90586	−	2.11985i
$407$	27.6607	+	47.9098i	0.0679625	+	0.117714i
$408$			1260.59i			3.08969i
$409$	−375.446	−	650.291i	−0.917960	−	1.58995i	−0.802508	−	0.596641i	$-0.796502\pi$
$409$	−375.446	−	650.291i	−0.917960	−	1.58995i	−0.115452	−	0.993313i	$-0.536832\pi$
$410$	353.292	−	203.974i	0.861689	−	0.497496i
$411$	15.2628			0.0371357
$412$	−1051.05	+	606.826i	−2.55110	+	1.47288i
$413$	−564.598	−	507.602i	−1.36706	−	1.22906i
$414$	−34.8006	−	20.0922i	−0.0840595	−	0.0485318i
$415$	101.060			0.243518
$416$	−18.7292	+	1125.94i	−0.0450221	+	2.70660i
$417$	−274.221			−0.657603
$418$	202.441	−	350.638i	0.484309	−	0.838848i
$419$	541.068	+	312.386i	1.29133	+	0.745551i	0.978890	−	0.204386i	$-0.0655197\pi$
$419$	541.068	+	312.386i	1.29133	+	0.745551i	0.312442	+	0.949937i	$0.398853\pi$
$420$	−122.243	−	375.269i	−0.291054	−	0.893498i
$421$		−	257.224i		−	0.610984i	−0.952195	−	0.305492i	$-0.901179\pi$
$421$		−	257.224i		−	0.610984i	0.952195	−	0.305492i	$-0.0988209\pi$
$422$	−815.355	+	470.745i	−1.93212	+	1.11551i
$423$	−84.0901	−	145.648i	−0.198795	−	0.344322i
$424$			1117.07i			2.63461i
$425$	398.648	−	230.160i	0.937995	−	0.541552i
$426$	692.055	+	399.558i	1.62454	+	0.937930i
$427$	−3.90598	+	4.34455i	−0.00914748	+	0.0101746i
$428$	−796.739			−1.86154
$429$	160.073	+	2.66268i	0.373130	+	0.00620672i
$430$		−	414.156i		−	0.963155i
$431$	−40.6844	−	23.4891i	−0.0943953	−	0.0544991i	0.452059	−	0.891988i	$-0.350690\pi$
$431$	−40.6844	−	23.4891i	−0.0943953	−	0.0544991i	−0.546455	+	0.837489i	$0.684023\pi$
$432$	215.637	+	124.498i	0.499159	+	0.288190i
$433$	−460.412	+	265.819i	−1.06331	+	0.613901i	−0.926345	−	0.376675i	$-0.877067\pi$
$433$	−460.412	+	265.819i	−1.06331	+	0.613901i	−0.136963	+	0.990576i	$0.543734\pi$
$434$	268.990	+	56.9655i	0.619793	+	0.131257i
$435$	−208.888	+	120.601i	−0.480201	+	0.277244i
$436$	−1592.49	+	919.426i	−3.65251	+	2.10878i
$437$	−53.5599			−0.122563
$438$	−398.111	−	689.549i	−0.908930	−	1.57431i
$439$	−337.211	−	194.689i	−0.768134	−	0.443483i	0.0640743	−	0.997945i	$-0.479591\pi$
$439$	−337.211	−	194.689i	−0.768134	−	0.443483i	−0.832209	+	0.554463i	$0.812924\pi$
$440$	266.148	−	460.982i	0.604882	−	1.04769i
$441$	134.380	+	59.5895i	0.304717	+	0.135123i
$442$	−779.700	+	1300.05i	−1.76403	+	2.94130i
$443$	−51.5064			−0.116267			−0.0581337	−	0.998309i	$-0.518515\pi$
$443$	−51.5064			−0.116267			−0.0581337	+	0.998309i	$0.518515\pi$
$444$	−69.0090	+	119.527i	−0.155426	+	0.269205i
$445$	−135.985	+	235.532i	−0.305583	+	0.529286i
$446$	125.273	−	72.3265i	0.280881	−	0.162167i
$447$	224.268			0.501718
$448$	−899.983	+	293.166i	−2.00889	+	0.654389i
$449$	617.708	−	356.634i	1.37574	−	0.794285i	0.384098	−	0.923292i	$-0.374512\pi$
$449$	617.708	−	356.634i	1.37574	−	0.794285i	0.991644	+	0.129007i	$0.0411791\pi$
$450$		−	168.652i		−	0.374782i
$451$	−209.414	+	120.905i	−0.464332	+	0.268082i
$452$	−436.718	+	756.417i	−0.966190	+	1.67349i
$453$	25.5709	−	44.2901i	0.0564480	−	0.0977707i
$454$		−	428.379i		−	0.943567i
$455$	64.6244	−	281.936i	0.142032	−	0.619639i
$456$	615.590			1.34998
$457$	−308.729	−	178.245i	−0.675556	−	0.390032i	0.122623	−	0.992453i	$-0.460870\pi$
$457$	−308.729	−	178.245i	−0.675556	−	0.390032i	−0.798179	+	0.602421i	$0.794203\pi$
$458$	754.435	+	435.573i	1.64724	+	0.951033i
$459$	80.2815	+	139.052i	0.174905	+	0.302945i
$460$	−115.543			−0.251181
$461$	−111.827	−	193.689i	−0.242574	−	0.420151i	0.718873	−	0.695142i	$-0.244658\pi$
$461$	−111.827	−	193.689i	−0.242574	−	0.420151i	−0.961447	+	0.274991i	$0.911325\pi$
$462$	100.760	+	309.320i	0.218095	+	0.669525i
$463$		−	449.289i		−	0.970387i	−0.874407	−	0.485193i	$-0.838749\pi$
$463$		−	449.289i		−	0.970387i	0.874407	−	0.485193i	$-0.161251\pi$
$464$	1049.72	+	1818.17i	2.26233	+	3.91847i
$465$	−49.6260	−	28.6516i	−0.106723	−	0.0616163i
$466$	1051.53	+	607.098i	2.25649	+	1.30279i
$467$			556.408i			1.19145i	0.803188	+	0.595726i	$0.203136\pi$
$467$			556.408i			1.19145i	−0.803188	+	0.595726i	$0.796864\pi$
$468$	193.925	+	349.174i	0.414370	+	0.746098i
$469$	−198.513	−	42.0403i	−0.423270	−	0.0896381i
$470$	−582.354	−	336.222i	−1.23905	−	0.715366i
$471$	14.0740	−	24.3769i	0.0298811	−	0.0517556i
$472$	2212.37	−	1277.31i	4.68722	−	2.70617i
$473$			245.491i			0.519009i
$474$	24.9526	+	43.2192i	0.0526427	+	0.0911798i
$475$	−112.394	−	194.673i	−0.236620	−	0.409838i
$476$	−2167.16	−	458.951i	−4.55286	−	0.964183i
$477$	71.1414	+	123.220i	0.149143	+	0.258324i
$478$	159.369	−	276.036i	0.333409	−	0.577481i
$479$	−64.1114	+	111.044i	−0.133844	+	0.231825i	−0.925155	−	0.379589i	$-0.876066\pi$
$479$	−64.1114	+	111.044i	−0.133844	+	0.231825i	0.791311	+	0.611414i	$0.209399\pi$
$480$	476.894			0.993530
$481$	−88.4269	+	49.1107i	−0.183840	+	0.102101i
$482$		−	469.748i		−	0.974581i
$483$	28.7719	−	32.0025i	0.0595692	−	0.0662579i
$484$	360.734	−	624.810i	0.745319	−	1.29093i
$485$	−111.369	−	192.896i	−0.229626	−	0.397724i
$486$	58.8272			0.121044
$487$	−531.957	+	307.125i	−1.09231	+	0.630647i	−0.934191	−	0.356772i	$-0.883877\pi$
$487$	−531.957	+	307.125i	−1.09231	+	0.630647i	−0.158122	+	0.987420i	$0.550544\pi$
$488$	−9.82885	−	17.0241i	−0.0201411	−	0.0348854i
$489$	205.957			0.421179
$490$	584.446	−	62.3113i	1.19275	−	0.127166i
$491$	262.022	−	453.835i	0.533649	−	0.924307i	−0.465578	−	0.885007i	$-0.654154\pi$
$491$	262.022	−	453.835i	0.533649	−	0.924307i	0.999227	−	0.0393006i	$-0.0125130\pi$
$492$	−522.454	−	301.639i	−1.06190	−	0.613087i
$493$			1353.81i			2.74606i
$494$	634.860	+	380.753i	1.28514	+	0.770756i
$495$		−	67.7990i		−	0.136968i
$496$	−249.385	+	431.948i	−0.502792	+	0.870862i
$497$	−572.167	+	636.411i	−1.15124	+	1.28051i
$498$	−103.910	−	179.977i	−0.208654	−	0.361400i
$499$		−	789.236i		−	1.58163i	−0.612052	−	0.790817i	$-0.709656\pi$
$499$		−	789.236i		−	1.58163i	0.612052	−	0.790817i	$-0.290344\pi$
$500$	−649.370	−	1124.74i	−1.29874	−	2.24949i
$501$	186.988	−	107.958i	0.373229	−	0.215484i
$502$	−1045.82			−2.08330
$503$	−510.911	+	294.975i	−1.01573	+	0.586431i	−0.912864	−	0.408264i	$-0.866134\pi$
$503$	−510.911	+	294.975i	−1.01573	+	0.586431i	−0.102864	+	0.994695i	$0.532801\pi$
$504$	−330.690	+	367.821i	−0.656130	+	0.729803i
$505$	445.884	+	257.431i	0.882938	+	0.509764i
$506$	95.2378			0.188217
$507$	−9.73551	+	292.555i	−0.0192022	+	0.577031i
$508$	1096.32			2.15810
$509$	263.123	−	455.742i	0.516940	−	0.895367i	−0.482866	−	0.875694i	$-0.660404\pi$
$509$	263.123	−	455.742i	0.516940	−	0.895367i	0.999806	−	0.0196725i	$-0.00626235\pi$
$510$	555.978	+	320.994i	1.09015	+	0.629400i
$511$	810.770	−	264.105i	1.58663	−	0.516840i
$512$			363.705i			0.710362i
$513$	67.9035	−	39.2041i	0.132366	−	0.0764213i
$514$	−738.722	−	1279.50i	−1.43720	−	2.48931i
$515$			376.675i			0.731407i
$516$	−530.406	+	306.230i	−1.02792	+	0.593469i
$517$	345.190	+	199.296i	0.667679	+	0.385485i
$518$	−152.847	−	137.418i	−0.295072	−	0.265285i
$519$	206.482			0.397846
$520$	834.645	+	500.574i	1.60509	+	0.962642i
$521$		−	755.993i		−	1.45104i	−0.688200	−	0.725521i	$-0.741599\pi$
$521$		−	755.993i		−	1.45104i	0.688200	−	0.725521i	$-0.258401\pi$
$522$	429.557	+	248.005i	0.822906	+	0.475105i
$523$	−357.618	−	206.471i	−0.683783	−	0.394782i	0.117496	−	0.993073i	$-0.462513\pi$
$523$	−357.618	−	206.471i	−0.683783	−	0.394782i	−0.801279	+	0.598291i	$0.795847\pi$
$524$	214.164	−	123.648i	0.408710	−	0.235969i
$525$	176.696	+	37.4199i	0.336564	+	0.0712760i
$526$	267.394	−	154.380i	0.508353	−	0.293498i
$527$	−278.538	+	160.814i	−0.528535	+	0.305150i
$528$	−590.126			−1.11766
$529$	258.201	+	447.217i	0.488092	+	0.845400i
$530$	492.679	+	284.449i	0.929584	+	0.536696i
$531$	162.692	−	281.791i	0.306388	−	0.530680i
$532$	−224.121	+	1058.30i	−0.421280	+	1.98928i
$533$	−214.663	−	386.514i	−0.402745	−	0.725168i
$534$	559.278			1.04734
$535$	−123.640	+	214.150i	−0.231102	+	0.400281i
$536$	341.381	−	591.290i	0.636906	−	1.10315i
$537$	406.992	−	234.977i	0.757899	−	0.437573i
$538$	−323.328			−0.600982
$539$	−346.430	+	36.9350i	−0.642728	+	0.0685250i
$540$	146.486	−	84.5737i	0.271270	−	0.156618i
$541$			413.536i			0.764391i	0.924081	+	0.382196i	$0.124832\pi$
$541$			413.536i			0.764391i	−0.924081	+	0.382196i	$0.875168\pi$
$542$	−1410.07	+	814.107i	−2.60161	+	1.50204i
$543$	−62.3454	+	107.985i	−0.114817	+	0.198868i
$544$	1338.34	−	2318.08i	2.46019	−	4.26117i
$545$			570.714i			1.04718i
$546$	−568.545	+	174.797i	−1.04129	+	0.320141i
$547$	−894.896			−1.63601			−0.818003	−	0.575213i	$-0.804919\pi$
$547$	−894.896			−1.63601			−0.818003	+	0.575213i	$0.804919\pi$
$548$	−78.1554	−	45.1230i	−0.142619	−	0.0823413i
$549$	−2.16837	−	1.25191i	−0.00394967	−	0.00228034i
$550$	199.855	+	346.158i	0.363372	+	0.629379i
$551$	661.109			1.19984
$552$	72.4006	+	125.402i	0.131161	+	0.227177i
$553$	−50.8171	+	16.5535i	−0.0918934	+	0.0299339i
$554$			1210.50i			2.18501i
$555$	21.4180	+	37.0970i	0.0385909	+	0.0668414i
$556$	1404.19	+	810.709i	2.52552	+	1.45811i
$557$	−153.668	−	88.7205i	−0.275886	−	0.159283i	0.355674	−	0.934610i	$-0.384251\pi$
$557$	−153.668	−	88.7205i	−0.275886	−	0.159283i	−0.631559	+	0.775327i	$0.717585\pi$
$558$			117.838i			0.211180i
$559$	−448.792	−	7.46529i	−0.802847	−	0.0133547i
$560$	−220.895	+	1043.06i	−0.394455	+	1.86261i
$561$	−329.556	−	190.269i	−0.587444	−	0.339161i
$562$	−474.146	+	821.246i	−0.843677	+	1.46129i
$563$	615.714	−	355.483i	1.09363	−	0.631408i	0.159090	−	0.987264i	$-0.449144\pi$
$563$	615.714	−	355.483i	1.09363	−	0.631408i	0.934541	+	0.355856i	$0.115811\pi$
$564$			994.420i			1.76316i
$565$	135.542	+	234.765i	0.239897	+	0.415513i
$566$	−888.174	−	1538.36i	−1.56921	−	2.71795i
$567$	−13.0524	+	61.6331i	−0.0230201	+	0.108700i
$568$	−1439.78	−	2493.77i	−2.53482	−	4.39044i
$569$	113.487	−	196.565i	0.199449	−	0.345456i	−0.748901	−	0.662682i	$-0.769418\pi$
$569$	113.487	−	196.565i	0.199449	−	0.345456i	0.948350	+	0.317226i	$0.102751\pi$
$570$	156.752	−	271.503i	0.275004	−	0.476320i
$571$	−294.874			−0.516417			−0.258209	−	0.966089i	$-0.583132\pi$
$571$	−294.874			−0.516417			−0.258209	+	0.966089i	$0.583132\pi$
$572$	−811.807	−	486.877i	−1.41924	−	0.851183i
$573$			549.386i			0.958790i
$574$	600.654	−	668.097i	1.04643	−	1.16393i
$575$	26.4378	−	45.7916i	0.0459788	−	0.0796376i
$576$	−202.828	−	351.308i	−0.352131	−	0.609909i
$577$	−112.647			−0.195229			−0.0976146	−	0.995224i	$-0.531121\pi$
$577$	−112.647			−0.195229			−0.0976146	+	0.995224i	$0.531121\pi$
$578$	2176.06	−	1256.35i	3.76481	−	2.17361i
$579$	−172.432	−	298.662i	−0.297811	−	0.515823i
$580$	1426.19			2.45895
$581$	211.617	−	68.9334i	0.364228	−	0.118646i
$582$	−229.018	+	396.671i	−0.393502	+	0.681566i
$583$	−292.036	−	168.607i	−0.500919	−	0.289205i
$584$			2869.13i			4.91289i
$585$	123.946	+	2.06174i	0.211873	+	0.00352434i
$586$			1543.90i			2.63465i
$587$	22.5449	−	39.0490i	0.0384070	−	0.0665230i	−0.846183	−	0.532893i	$-0.821105\pi$
$587$	22.5449	−	39.0490i	0.0384070	−	0.0665230i	0.884590	+	0.466370i	$0.154438\pi$
$588$	−511.945	−	702.421i	−0.870655	−	1.19459i
$589$	78.5308	+	136.019i	0.133329	+	0.230933i
$590$		−	1301.00i		−	2.20509i
$591$	−128.217	−	222.079i	−0.216950	−	0.375768i
$592$	322.894	−	186.423i	0.545430	−	0.314904i
$593$	450.813			0.760224			0.380112	−	0.924941i	$-0.375886\pi$
$593$	450.813			0.760224			0.380112	+	0.924941i	$0.375886\pi$
$594$	−120.743	+	69.7110i	−0.203271	+	0.117359i
$595$	−459.663	+	511.276i	−0.772543	+	0.859287i
$596$	−1148.40	−	663.028i	−1.92684	−	1.11246i
$597$	−410.725			−0.687981
$598$	−2.89615	+	174.108i	−0.00484305	+	0.291150i
$599$	659.272			1.10062			0.550310	−	0.834960i	$-0.314509\pi$
$599$	659.272			1.10062			0.550310	+	0.834960i	$0.314509\pi$
$600$	−303.862	+	526.305i	−0.506437	+	0.877175i
$601$	177.713	+	102.602i	0.295695	+	0.170720i	0.640507	−	0.767952i	$-0.278724\pi$
$601$	177.713	+	102.602i	0.295695	+	0.170720i	−0.344812	+	0.938672i	$0.612057\pi$
$602$	−282.498	−	867.232i	−0.469265	−	1.44059i
$603$		−	86.9641i		−	0.144219i
$604$	−261.880	+	151.196i	−0.433576	+	0.250325i
$605$	−111.959	−	193.919i	−0.185056	−	0.320527i
$606$		−	1058.76i		−	1.74713i
$607$	−487.381	+	281.389i	−0.802934	+	0.463574i	−0.844496	−	0.535562i	$-0.820100\pi$
$607$	−487.381	+	281.389i	−0.802934	+	0.463574i	0.0415623	+	0.999136i	$0.486767\pi$
$608$	−1131.99	−	653.557i	−1.86183	−	1.07493i
$609$	−355.142	+	395.019i	−0.583156	+	0.648635i
$610$	−10.0112			−0.0164117
$611$	−374.837	+	624.995i	−0.613481	+	1.02290i
$612$		−	949.381i		−	1.55128i
$613$	665.394	+	384.166i	1.08547	+	0.626698i	0.932367	−	0.361512i	$-0.117739\pi$
$613$	665.394	+	384.166i	1.08547	+	0.626698i	0.153105	+	0.988210i	$0.451073\pi$
$614$	768.304	+	443.580i	1.25131	+	0.722443i
$615$	−162.151	+	93.6180i	−0.263660	+	0.152224i
$616$	242.869	−	1146.82i	0.394268	−	1.86173i
$617$	−439.927	+	253.992i	−0.713010	+	0.411656i	−0.812174	−	0.583415i	$-0.801716\pi$
$617$	−439.927	+	253.992i	−0.713010	+	0.411656i	0.0991646	+	0.995071i	$0.468383\pi$
$618$	670.818	−	387.297i	1.08547	−	0.626695i
$619$	−54.4556			−0.0879735			−0.0439867	−	0.999032i	$-0.514006\pi$
$619$	−54.4556			−0.0879735			−0.0439867	+	0.999032i	$0.514006\pi$
$620$	169.412	+	293.430i	0.273245	+	0.473274i
$621$	15.9725	+	9.22173i	0.0257206	+	0.0148498i
$622$	−195.656	+	338.886i	−0.314560	+	0.544833i
$623$	−124.091	+	585.953i	−0.199182	+	0.940535i
$624$	17.9455	−	1078.83i	0.0287588	−	1.72890i
$625$	−30.6611			−0.0490578
$626$	−445.736	+	772.038i	−0.712039	+	1.23329i
$627$	−92.9147	+	160.933i	−0.148189	+	0.256671i
$628$	−144.136	+	83.2172i	−0.229517	+	0.132511i
$629$	240.427			0.382237
$630$	78.0194	+	239.510i	0.123840	+	0.380174i
$631$	222.405	−	128.406i	0.352465	−	0.203496i	−0.313306	−	0.949652i	$-0.601436\pi$
$631$	222.405	−	128.406i	0.352465	−	0.203496i	0.665770	+	0.746157i	$0.268103\pi$
$632$		−	179.830i		−	0.284541i
$633$	374.224	−	216.059i	0.591192	−	0.341325i
$634$	193.789	−	335.653i	0.305661	−	0.529421i
$635$	170.129	−	294.672i	0.267919	−	0.464050i
$636$		−	841.293i		−	1.32279i
$637$	−56.9875	−	634.446i	−0.0894623	−	0.995990i
$638$	−1175.55			−1.84256
$639$	−317.633	−	183.386i	−0.497079	−	0.286989i
$640$	−450.864	−	260.307i	−0.704475	−	0.406729i
$641$	62.2913	+	107.892i	0.0971784	+	0.168318i	0.910516	−	0.413475i	$-0.135685\pi$
$641$	62.2913	+	107.892i	0.0971784	+	0.168318i	−0.813337	+	0.581792i	$0.802352\pi$
$642$	508.506			0.792065
$643$	−448.521	−	776.862i	−0.697545	−	1.20818i	−0.969315	−	0.245821i	$-0.920942\pi$
$643$	−448.521	−	776.862i	−0.697545	−	1.20818i	0.271770	−	0.962362i	$-0.412391\pi$
$644$	−241.944	+	78.8124i	−0.375689	+	0.122379i
$645$			190.086i			0.294707i
$646$	−879.809	−	1523.87i	−1.36193	−	2.35894i
$647$	385.136	+	222.358i	0.595264	+	0.343676i	0.767176	−	0.641437i	$-0.221661\pi$
$647$	385.136	+	222.358i	0.595264	+	0.343676i	−0.171912	+	0.985112i	$0.554995\pi$
$648$	−183.580	−	105.990i	−0.283302	−	0.163564i
$649$			771.169i			1.18824i
$650$	−638.903	+	354.836i	−0.982928	+	0.545901i
$651$	−123.459	−	26.1455i	−0.189645	−	0.0401621i
$652$	−1054.63	−	608.893i	−1.61754	−	0.933885i
$653$	234.314	−	405.843i	0.358827	−	0.621506i	−0.628938	−	0.777455i	$-0.716510\pi$
$653$	234.314	−	405.843i	0.358827	−	0.621506i	0.987765	+	0.155949i	$0.0498436\pi$
$654$	1016.38	−	586.809i	1.55410	−	0.897261i
$655$		−	76.7517i		−	0.117178i
$656$	814.857	+	1411.37i	1.24216	+	2.15148i
$657$	182.722	+	316.483i	0.278115	+	0.481709i
$658$	−1448.77	−	306.814i	−2.20178	−	0.466283i
$659$	−8.80049	−	15.2429i	−0.0133543	−	0.0231303i	0.859271	−	0.511521i	$-0.170918\pi$
$659$	−8.80049	−	15.2429i	−0.0133543	−	0.0231303i	−0.872625	+	0.488390i	$0.837584\pi$
$660$	−200.442	+	347.175i	−0.303700	+	0.526023i
$661$	−144.600	+	250.454i	−0.218759	+	0.378901i	−0.954429	−	0.298439i	$-0.903534\pi$
$661$	−144.600	+	250.454i	−0.218759	+	0.378901i	0.735670	+	0.677340i	$0.236867\pi$
$662$	973.337			1.47030
$663$	357.860	−	596.688i	0.539759	−	0.899982i
$664$			748.863i			1.12781i
$665$	249.673	+	224.469i	0.375448	+	0.337547i
$666$	44.0439	−	76.2863i	0.0661320	−	0.114544i
$667$	77.7542	+	134.674i	0.116573	+	0.201910i
$668$	−1276.67			−1.91118
$669$	−57.4968	+	33.1958i	−0.0859443	+	0.0496200i
$670$	−173.857	−	301.129i	−0.259488	−	0.449446i
$671$	5.93411			0.00884368
$672$	998.604	−	325.291i	1.48602	−	0.484065i
$673$	−569.722	+	986.787i	−0.846541	+	1.46625i	0.0377361	+	0.999288i	$0.487985\pi$
$673$	−569.722	+	986.787i	−0.846541	+	1.46625i	−0.884277	+	0.466963i	$0.845348\pi$
$674$	1847.45	+	1066.62i	2.74102	+	1.58253i
$675$			77.4064i			0.114676i
$676$	914.765	−	1469.29i	1.35320	−	2.17351i
$677$		−	226.465i		−	0.334512i	−0.985913	−	0.167256i	$-0.946509\pi$
$677$		−	226.465i		−	0.334512i	0.985913	−	0.167256i	$-0.0534907\pi$
$678$	278.728	−	482.771i	0.411103	−	0.712052i
$679$	−364.778	−	327.954i	−0.537228	−	0.482995i
$680$	−1156.68	−	2003.43i	−1.70100	−	2.94622i
$681$			196.614i			0.288714i
$682$	−139.640	−	241.863i	−0.204750	−	0.354638i
$683$	−1139.80	+	658.065i	−1.66882	+	0.963492i	−0.700541	+	0.713612i	$0.747058\pi$
$683$	−1139.80	+	658.065i	−1.66882	+	0.963492i	−0.968277	+	0.249880i	$0.919609\pi$
$684$	−463.614			−0.677799
$685$	−24.2566	+	14.0046i	−0.0354112	+	0.0204446i
$686$	1181.31	−	529.131i	1.72203	−	0.771328i
$687$	−346.264	−	199.916i	−0.504023	−	0.290998i
$688$	1654.52			2.40482
$689$	317.117	−	528.754i	0.460257	−	0.767423i
$690$	73.7435			0.106875
$691$	−211.396	+	366.149i	−0.305928	+	0.529883i	−0.977468	−	0.211086i	$-0.932300\pi$
$691$	−211.396	+	366.149i	−0.305928	+	0.529883i	0.671539	+	0.740969i	$0.265633\pi$
$692$	−1057.32	−	610.446i	−1.52792	−	0.882147i
$693$	−46.2459	−	141.969i	−0.0667329	−	0.204862i
$694$			562.275i			0.810194i
$695$	435.811	−	251.615i	0.627066	−	0.362037i
$696$	−893.666	−	1547.88i	−1.28400	−	2.22396i
$697$			1050.91i			1.50776i
$698$	832.742	−	480.784i	1.19304	−	0.688802i
$699$	−482.620	−	278.641i	−0.690444	−	0.398628i
$700$	−794.172	−	714.001i	−1.13453	−	1.02000i
$701$	−70.1515			−0.100073			−0.0500367	−	0.998747i	$-0.515934\pi$
$701$	−70.1515			−0.100073			−0.0500367	+	0.998747i	$0.515934\pi$
$702$	−123.770	−	222.855i	−0.176310	−	0.317457i
$703$		−	117.408i		−	0.167011i
$704$	832.607	+	480.706i	1.18268	+	0.682821i
$705$	267.284	+	154.316i	0.379126	+	0.218888i
$706$	9.26159	−	5.34718i	0.0131184	−	0.00757391i
$707$	1109.26	+	234.915i	1.56897	+	0.332270i
$708$	−1666.18	+	961.971i	−2.35336	+	1.35872i
$709$	−430.533	+	248.568i	−0.607240	+	0.350590i	−0.771884	−	0.635763i	$-0.780686\pi$
$709$	−430.533	+	248.568i	−0.607240	+	0.350590i	0.164645	+	0.986353i	$0.447352\pi$
$710$	−1466.48			−2.06547
$711$	−11.4525	−	19.8364i	−0.0161077	−	0.0278993i
$712$	−1745.31	−	1007.66i	−2.45128	−	1.41525i
$713$	−18.4723	+	31.9949i	−0.0259078	+	0.0448737i
$714$	1383.15	+	292.918i	1.93719	+	0.410250i
$715$	−256.842	+	142.646i	−0.359220	+	0.199505i
$716$	−2778.76			−3.88094
$717$	−73.1460	+	126.693i	−0.102017	+	0.176698i
$718$	552.933	−	957.708i	0.770102	−	1.33386i
$719$	−1123.33	+	648.553i	−1.56235	+	0.902021i	−0.565326	+	0.824868i	$0.691250\pi$
$719$	−1123.33	+	648.553i	−1.56235	+	0.902021i	−0.997019	+	0.0771530i	$0.975417\pi$
$720$	−456.940			−0.634639
$721$	256.931	+	788.746i	0.356354	+	1.09396i
$722$	435.654	−	251.525i	0.603399	−	0.348373i
$723$			215.601i			0.298203i
$724$	638.499	−	368.637i	0.881904	−	0.509168i
$725$	−326.331	+	565.222i	−0.450112	+	0.779617i
$726$	−230.233	+	398.775i	−0.317125	+	0.549277i
$727$			38.6647i			0.0531839i	0.999646	+	0.0265920i	$0.00846549\pi$
$727$			38.6647i			0.0531839i	−0.999646	+	0.0265920i	$0.991535\pi$
$728$	2089.17	+	478.873i	2.86974	+	0.657792i
$729$	−27.0000			−0.0370370
$730$	1265.41	+	730.586i	1.73344	+	1.00080i
$731$	923.966	+	533.452i	1.26398	+	0.729756i
$732$	7.40232	+	12.8212i	0.0101125	+	0.0175153i
$733$	8.73859			0.0119217			0.00596084	−	0.999982i	$-0.498103\pi$
$733$	8.73859			0.0119217			0.00596084	+	0.999982i	$0.498103\pi$
$734$	851.191	+	1474.31i	1.15966	+	2.00859i
$735$	−268.244	+	28.5991i	−0.364958	+	0.0389103i
$736$		−	307.464i		−	0.417750i
$737$	103.054	+	178.494i	0.139828	+	0.242190i
$738$	333.448	+	192.516i	0.451826	+	0.260862i
$739$	−532.423	−	307.394i	−0.720464	−	0.415960i	0.0944597	−	0.995529i	$-0.469888\pi$
$739$	−532.423	−	307.394i	−0.720464	−	0.415960i	−0.814923	+	0.579569i	$0.803221\pi$
$740$		−	253.281i		−	0.342272i
$741$	−291.382	−	174.755i	−0.393229	−	0.235837i
$742$	1225.68	+	259.569i	1.65186	+	0.349824i
$743$	−454.505	−	262.409i	−0.611716	−	0.353175i	0.161921	−	0.986804i	$-0.448231\pi$
$743$	−454.505	−	262.409i	−0.611716	−	0.353175i	−0.773637	+	0.633629i	$0.781564\pi$
$744$	212.311	−	367.733i	0.285364	−	0.494265i
$745$	−356.422	+	205.780i	−0.478419	+	0.276215i
$746$			597.968i			0.801566i
$747$	47.6917	+	82.6044i	0.0638443	+	0.110582i
$748$	1125.03	+	1948.61i	1.50405	+	2.60509i
$749$	−112.825	+	532.760i	−0.150635	+	0.711295i
$750$	414.450	+	717.849i	0.552600	+	0.957132i
$751$	−120.728	+	209.107i	−0.160756	+	0.278438i	−0.935140	−	0.354278i	$-0.884727\pi$
$751$	−120.728	+	209.107i	−0.160756	+	0.278438i	0.774384	+	0.632716i	$0.218060\pi$
$752$	1343.18	−	2326.45i	1.78614	−	3.09369i
$753$	480.001			0.637451
$754$	35.7481	−	2149.08i	0.0474113	−	2.85023i
$755$			93.8520i			0.124307i
$756$	249.050	−	277.014i	0.329431	−	0.366420i
$757$	258.019	−	446.901i	0.340844	−	0.590359i	−0.643746	−	0.765239i	$-0.722621\pi$
$757$	258.019	−	446.901i	0.340844	−	0.590359i	0.984590	+	0.174881i	$0.0559540\pi$
$758$	1314.56	+	2276.89i	1.73425	+	3.00381i
$759$	−43.7114			−0.0575908
$760$	−978.339	+	564.844i	−1.28729	+	0.743216i
$761$	7.55430	+	13.0844i	0.00992680	+	0.0171937i	0.870946	−	0.491378i	$-0.163507\pi$
$761$	7.55430	+	13.0844i	0.00992680	+	0.0171937i	−0.861019	+	0.508572i	$0.830173\pi$
$762$	−699.706			−0.918249
$763$	389.286	+	1195.06i	0.510205	+	1.56626i
$764$	1624.21	−	2813.22i	2.12593	−	3.68222i
$765$	−255.178	−	147.327i	−0.333566	−	0.192585i
$766$			686.057i			0.895636i
$767$	−1409.80	−	23.4509i	−1.83808	−	0.0305749i
$768$			133.769i			0.174179i
$769$	608.849	−	1054.56i	0.791741	−	1.37134i	−0.133147	−	0.991096i	$-0.542508\pi$
$769$	608.849	−	1054.56i	0.791741	−	1.37134i	0.924888	−	0.380240i	$-0.124159\pi$
$770$	−443.957	−	399.140i	−0.576567	−	0.518363i
$771$	339.052	+	587.256i	0.439756	+	0.761680i
$772$			2039.13i			2.64135i
$773$	−429.441	−	743.814i	−0.555551	−	0.962243i	−0.997860	−	0.0653803i	$-0.979174\pi$
$773$	−429.441	−	743.814i	−0.555551	−	0.962243i	0.442309	−	0.896863i	$-0.354159\pi$
$774$	338.523	−	195.446i	0.437369	−	0.252515i
$775$	−155.055			−0.200071
$776$	1429.38	−	825.251i	1.84198	−	1.06347i
$777$	70.1526	+	63.0708i	0.0902865	+	0.0811722i
$778$	219.516	+	126.738i	0.282155	+	0.162902i
$779$	513.193			0.658784
$780$	−628.589	−	376.993i	−0.805884	−	0.483324i
$781$	869.258			1.11301
$782$	206.952	−	358.451i	0.264644	−	0.458377i
$783$	−197.154	−	113.827i	−0.251793	−	0.145373i
$784$	248.928	+	2334.81i	0.317510	+	2.97808i
$785$			51.6553i			0.0658030i
$786$	−136.687	+	78.9162i	−0.173902	+	0.100402i
$787$	684.552	+	1185.68i	0.869825	+	1.50658i	0.862175	+	0.506610i	$0.169102\pi$
$787$	684.552	+	1185.68i	0.869825	+	1.50658i	0.00764984	+	0.999971i	$0.497565\pi$
$788$			1516.25i			1.92418i
$789$	−122.726	+	70.8559i	−0.155546	+	0.0898046i
$790$	−79.3130	−	45.7914i	−0.100396	−	0.0579638i
$791$	443.955	+	399.138i	0.561257	+	0.504599i
$792$	502.396			0.634339
$793$	−0.180454	+	10.8484i	−0.000227559	+	0.0136802i
$794$			424.659i			0.534835i
$795$	−226.126	−	130.554i	−0.284435	−	0.164219i
$796$	2103.18	+	1214.27i	2.64219	+	1.52547i
$797$	343.900	−	198.551i	0.431493	−	0.249123i	−0.268490	−	0.963283i	$-0.586524\pi$
$797$	343.900	−	198.551i	0.431493	−	0.249123i	0.699982	+	0.714160i	$0.253191\pi$
$798$	143.042	−	675.440i	0.179250	−	0.846416i
$799$	1500.20	−	866.138i	1.87759	−	1.08403i
$800$	1117.53	−	645.207i	1.39691	−	0.806509i
$801$	−256.692			−0.320465
$802$	−36.2728	−	62.8263i	−0.0452279	−	0.0783370i
$803$	−750.073	−	433.055i	−0.934088	−	0.539296i
$804$	−257.102	+	445.313i	−0.319778	+	0.553872i
$805$	−16.3620	+	77.2609i	−0.0203254	+	0.0959762i
$806$	446.406	−	247.926i	0.553854	−	0.307601i
$807$	148.398			0.183889
$808$	−1907.59	+	3304.04i	−2.36087	+	4.08916i
$809$	−101.488	+	175.783i	−0.125449	+	0.217284i	−0.921908	−	0.387408i	$-0.873370\pi$
$809$	−101.488	+	175.783i	−0.125449	+	0.217284i	0.796459	+	0.604692i	$0.206704\pi$
$810$	−93.4923	+	53.9778i	−0.115423	+	0.0666393i
$811$	1174.49			1.44820			0.724099	−	0.689696i	$-0.242256\pi$
$811$	1174.49			1.44820			0.724099	+	0.689696i	$0.242256\pi$
$812$	2986.40	−	972.809i	3.67783	−	1.19804i
$813$	647.183	−	373.652i	0.796044	−	0.459596i
$814$			208.770i			0.256474i
$815$	−327.321	+	188.979i	−0.401621	+	0.231876i
$816$	−1282.34	+	2221.09i	−1.57150	+	2.72192i
$817$	260.502	−	451.203i	0.318852	−	0.552268i
$818$		−	2833.69i		−	3.46417i
$819$	260.946	−	80.2268i	0.318615	−	0.0979570i
$820$	1107.09			1.35011
$821$	−762.118	−	440.009i	−0.928281	−	0.535943i	−0.0420133	−	0.999117i	$-0.513377\pi$
$821$	−762.118	−	440.009i	−0.928281	−	0.535943i	−0.886267	+	0.463174i	$0.846711\pi$
$822$	49.8814	+	28.7990i	0.0606830	+	0.0350353i
$823$	−729.427	−	1263.40i	−0.886302	−	1.53512i	−0.844214	−	0.536006i	$-0.819932\pi$
$823$	−729.427	−	1263.40i	−0.886302	−	1.53512i	−0.0420883	−	0.999114i	$-0.513401\pi$
$824$	−2791.19			−3.38737
$825$	−91.7276	−	158.877i	−0.111185	−	0.192578i
$826$	−887.419	−	2724.26i	−1.07436	−	3.29814i
$827$		−	439.745i		−	0.531735i	−0.964010	−	0.265868i	$-0.914342\pi$
$827$		−	439.745i		−	0.531735i	0.964010	−	0.265868i	$-0.0856584\pi$
$828$	−54.5265	−	94.4426i	−0.0658532	−	0.114061i
$829$	−278.840	−	160.988i	−0.336357	−	0.194196i	0.322303	−	0.946637i	$-0.395543\pi$
$829$	−278.840	−	160.988i	−0.336357	−	0.194196i	−0.658660	+	0.752441i	$0.728876\pi$
$830$	330.282	+	190.688i	0.397930	+	0.229745i
$831$		−	555.583i		−	0.668571i
$832$	−904.117	+	1507.50i	−1.08668	+	1.81190i
$833$	−613.779	+	1384.14i	−0.736829	+	1.66163i
$834$	−896.202	−	517.422i	−1.07458	−	0.620410i
$835$	−198.116	+	343.147i	−0.237265	+	0.410955i
$836$	951.569	−	549.388i	1.13824	−	0.657163i
$837$		−	54.0844i		−	0.0646170i
$838$	1178.87	+	2041.87i	1.40677	+	2.43659i
$839$	130.148	+	225.423i	0.155123	+	0.268681i	0.933104	−	0.359607i	$-0.117089\pi$
$839$	130.148	+	225.423i	0.155123	+	0.268681i	−0.777981	+	0.628288i	$0.783756\pi$
$840$	188.056	−	887.996i	0.223876	−	1.05714i
$841$	−539.248	−	934.005i	−0.641198	−	1.11059i
$842$	485.352	−	840.654i	0.576428	−	0.998402i
$843$	217.620	−	376.928i	0.258149	−	0.447127i
$844$	−2555.03			−3.02729
$845$	−252.966	−	473.881i	−0.299368	−	0.560806i
$846$		−	634.673i		−	0.750204i
$847$	−366.712	−	329.693i	−0.432954	−	0.389248i
$848$	−1136.35	+	1968.21i	−1.34003	+	2.32101i
$849$	407.646	+	706.064i	0.480149	+	0.831642i
$850$	1737.14			2.04369
$851$	23.9172	−	13.8086i	0.0281048	−	0.0162263i
$852$	1084.33	+	1878.11i	1.27269	+	2.20436i
$853$	872.005			1.02228			0.511140	−	0.859498i	$-0.329223\pi$
$853$	872.005			1.02228			0.511140	+	0.859498i	$0.329223\pi$
$854$	−20.9631	+	6.82865i	−0.0245469	+	0.00799607i
$855$	−71.9447	+	124.612i	−0.0841458	+	0.145745i
$856$	−1586.87	−	916.181i	−1.85382	−	1.07031i
$857$		−	743.591i		−	0.867668i	−0.900993	−	0.433834i	$-0.857160\pi$
$857$		−	743.591i		−	0.867668i	0.900993	−	0.433834i	$-0.142840\pi$
$858$	518.123	+	310.741i	0.603873	+	0.362169i
$859$		−	688.625i		−	0.801659i	−0.916153	−	0.400830i	$-0.868722\pi$
$859$		−	688.625i		−	0.801659i	0.916153	−	0.400830i	$-0.131278\pi$
$860$	561.973	−	973.365i	0.653457	−	1.13182i
$861$	−275.683	+	306.637i	−0.320189	+	0.356141i
$862$	−88.6425	−	153.533i	−0.102834	−	0.178113i
$863$		−	329.151i		−	0.381404i	−0.981648	−	0.190702i	$-0.938924\pi$
$863$		−	329.151i		−	0.381404i	0.981648	−	0.190702i	$-0.0610764\pi$
$864$	225.053	+	389.804i	0.260479	+	0.451162i
$865$	−328.156	+	189.461i	−0.379371	+	0.219030i
$866$	−2006.28			−2.31672
$867$	−998.750	+	576.628i	−1.15196	+	0.665085i
$868$	554.893	+	498.878i	0.639278	+	0.574744i
$869$	47.0127	+	27.1428i	0.0540998	+	0.0312345i
$870$	−910.242			−1.04626
$871$	−329.445	+	182.968i	−0.378238	+	0.210067i
$872$	−4229.04			−4.84982
$873$	105.113	−	182.061i	0.120404	−	0.208546i
$874$	−175.043	−	101.061i	−0.200279	−	0.115631i
$875$	−844.045	+	274.944i	−0.964623	+	0.314222i
$876$		−	2160.80i		−	2.46667i
$877$	195.750	−	113.016i	0.223204	−	0.128867i	−0.384229	−	0.923238i	$-0.625533\pi$
$877$	195.750	−	113.016i	0.223204	−	0.128867i	0.607433	+	0.794371i	$0.292199\pi$
$878$	−734.710	−	1272.56i	−0.836800	−	1.44938i
$879$		−	708.608i		−	0.806152i
$880$	937.870	−	541.480i	1.06576	−	0.615318i
$881$	−1018.76	−	588.178i	−1.15636	−	0.667626i	−0.205933	−	0.978566i	$-0.566023\pi$
$881$	−1018.76	−	588.178i	−1.15636	−	0.667626i	−0.950429	+	0.310940i	$0.899356\pi$
$882$	326.741	+	448.309i	0.370454	+	0.508287i
$883$	−1196.78			−1.35536			−0.677681	−	0.735356i	$-0.737015\pi$
$883$	−1196.78			−1.35536			−0.677681	+	0.735356i	$0.737015\pi$
$884$	−3596.54	+	1997.45i	−4.06848	+	2.25956i
$885$			597.123i			0.674715i
$886$	−168.332	−	97.1866i	−0.189991	−	0.109691i
$887$	51.0430	+	29.4697i	0.0575457	+	0.0332240i	0.528497	−	0.848935i	$-0.322756\pi$
$887$	51.0430	+	29.4697i	0.0575457	+	0.0332240i	−0.470951	+	0.882159i	$0.656089\pi$
$888$	−274.892	+	158.709i	−0.309563	+	0.178726i
$889$	155.248	−	733.080i	0.174632	−	0.824611i
$890$	−888.843	+	513.174i	−0.998700	+	0.576600i
$891$	55.4175	−	31.9953i	0.0621970	−	0.0359095i
$892$	392.562			0.440092
$893$	−422.964	−	732.595i	−0.473644	−	0.820375i
$894$	732.947	+	423.167i	0.819851	+	0.473341i
$895$	−431.214	+	746.884i	−0.481803	+	0.834507i
$896$	−1121.65	−	237.539i	−1.25185	−	0.265110i
$897$	1.32925	−	79.9106i	0.00148188	−	0.0890865i
$898$	2691.71			2.99745
$899$	228.010	−	394.925i	0.253626	−	0.439293i
$900$	228.845	−	396.372i	0.254273	−	0.440413i
$901$	−1269.19	+	732.765i	−1.40864	+	0.813280i
$902$	−912.536			−1.01168
$903$	129.658	+	398.035i	0.143586	+	0.440791i
$904$	−1739.63	+	1004.38i	−1.92437	+	1.11104i
$905$		−	228.824i		−	0.252844i
$906$	167.141	−	96.4987i	0.184482	−	0.106511i
$907$	−92.4454	+	160.120i	−0.101924	+	0.176538i	−0.912477	−	0.409127i	$-0.865833\pi$
$907$	−92.4454	+	160.120i	−0.101924	+	0.176538i	0.810553	+	0.585665i	$0.199167\pi$
$908$	581.272	−	1006.79i	0.640167	−	1.10880i
$909$			485.942i			0.534590i
$910$	743.184	−	799.477i	0.816685	−	0.878546i
$911$	1155.12			1.26797			0.633986	−	0.773344i	$-0.281418\pi$
$911$	1155.12			1.26797			0.633986	+	0.773344i	$0.281418\pi$
$912$	1084.63	+	626.211i	1.18929	+	0.686635i
$913$	−195.774	−	113.030i	−0.214430	−	0.123801i
$914$	−672.654	−	1165.07i	−0.735946	−	1.27470i
$915$	4.59483			0.00502168
$916$	1182.07	+	2047.40i	1.29047	+	2.23515i
$917$	−52.3526	−	160.716i	−0.0570912	−	0.175263i
$918$			605.928i			0.660052i
$919$	−409.789	−	709.776i	−0.445908	−	0.772335i	0.552207	−	0.833707i	$-0.313786\pi$
$919$	−409.789	−	709.776i	−0.445908	−	0.772335i	−0.998115	+	0.0613722i	$0.980452\pi$
$920$	−230.128	−	132.865i	−0.250139	−	0.144418i
$921$	−352.629	−	203.591i	−0.382877	−	0.221054i
$922$		−	844.015i		−	0.915418i
$923$	−26.4338	+	1589.12i	−0.0286390	+	1.72169i
$924$	−182.910	+	863.698i	−0.197955	+	0.934738i
$925$	100.380	+	57.9542i	0.108518	+	0.0626532i
$926$	847.756	−	1468.36i	0.915503	−	1.58570i
$927$	−307.886	+	177.758i	−0.332132	+	0.191757i
$928$			3795.14i			4.08959i
$929$	−550.860	−	954.118i	−0.592960	−	1.02704i	−0.993831	−	0.110903i	$-0.964626\pi$
$929$	−550.860	−	954.118i	−0.592960	−	1.02704i	0.400871	−	0.916135i	$-0.368708\pi$
$930$	−108.124	−	187.277i	−0.116263	−	0.201373i
$931$	675.919	+	299.728i	0.726014	+	0.321942i
$932$	1647.55	+	2853.65i	1.76776	+	3.06185i
$933$	89.8005	−	155.539i	0.0962492	−	0.166709i
$934$	−1049.88	+	1818.44i	−1.12407	+	1.94694i
$935$	698.338			0.746885
$936$	−15.2777	+	918.450i	−0.0163223	+	0.981251i
$937$		−	1157.34i		−	1.23515i	−0.786511	−	0.617576i	$-0.788115\pi$
$937$		−	1157.34i		−	1.23515i	0.786511	−	0.617576i	$-0.211885\pi$
$938$	−569.452	−	511.967i	−0.607092	−	0.545807i
$939$	204.580	−	354.343i	0.217870	−	0.377362i
$940$	−912.446	−	1580.40i	−0.970687	−	1.68128i
$941$	1370.66			1.45660			0.728299	−	0.685260i	$-0.240311\pi$
$941$	1370.66			1.45660			0.728299	+	0.685260i	$0.240311\pi$
$942$	91.9928	−	53.1120i	0.0976568	−	0.0563822i
$943$	60.3575	+	104.542i	0.0640058	+	0.110861i
$944$	5197.40			5.50572
$945$	−35.8086	−	109.928i	−0.0378927	−	0.116326i
$946$	−463.213	+	802.308i	−0.489654	+	0.848106i
$947$	649.530	+	375.007i	0.685882	+	0.395994i	0.802068	−	0.597233i	$-0.203733\pi$
$947$	649.530	+	375.007i	0.685882	+	0.395994i	−0.116185	+	0.993228i	$0.537067\pi$
$948$			135.434i			0.142863i
$949$	814.494	−	1358.07i	0.858265	−	1.43105i
$950$		−	848.301i		−	0.892948i
$951$	−88.9437	+	154.055i	−0.0935265	+	0.161993i
$952$	−3788.60	−	3406.14i	−3.97962	−	3.57788i
$953$	189.848	+	328.827i	0.199211	+	0.345044i	0.948273	−	0.317456i	$-0.102829\pi$
$953$	189.848	+	328.827i	0.199211	+	0.345044i	−0.749062	+	0.662500i	$0.769495\pi$
$954$			536.942i			0.562832i
$955$	−504.098	−	873.124i	−0.527851	−	0.914266i
$956$	749.111	−	432.499i	0.783589	−	0.452405i
$957$	539.546			0.563789
$958$	−419.055	+	241.941i	−0.437427	+	0.252549i
$959$	−41.2402	+	45.8708i	−0.0430033	+	0.0478319i
$960$	644.696	+	372.215i	0.671558	+	0.387724i
$961$	−852.662			−0.887265
$962$	−381.661	−	6.34862i	−0.396737	−	0.00659940i
$963$	−233.390			−0.242357
$964$	637.405	−	1104.02i	0.661209	−	1.14525i
$965$	548.083	+	316.436i	0.567962	+	0.327913i
$966$	154.417	−	50.3007i	0.159852	−	0.0520711i
$967$			1053.89i			1.08985i	0.838483	+	0.544927i	$0.183443\pi$
$967$			1053.89i			1.08985i	−0.838483	+	0.544927i	$0.816557\pi$
$968$	1436.96	−	829.627i	1.48446	−	0.857053i
$969$	403.807	+	699.415i	0.416726	+	0.721790i
$970$		−	840.558i		−	0.866554i
$971$	1177.03	−	679.561i	1.21219	−	0.699857i	0.248953	−	0.968516i	$-0.419914\pi$
$971$	1177.03	−	679.561i	1.21219	−	0.699857i	0.963236	+	0.268658i	$0.0865802\pi$
$972$	138.258	+	79.8232i	0.142240	+	0.0821226i
$973$	740.948	−	824.144i	0.761508	−	0.847013i
$974$	−2318.04			−2.37992
$975$	293.238	−	162.859i	0.300757	−	0.167035i
$976$		−	39.9937i		−	0.0409772i
$977$	−604.174	−	348.820i	−0.618397	−	0.357032i	0.157848	−	0.987463i	$-0.449545\pi$
$977$	−604.174	−	348.820i	−0.618397	−	0.357032i	−0.776245	+	0.630432i	$0.782878\pi$
$978$	673.103	+	388.616i	0.688245	+	0.397358i
$979$	526.861	−	304.184i	0.538163	−	0.310708i
$980$	1458.14	+	646.594i	1.48789	+	0.659790i
$981$	−466.491	+	269.328i	−0.475526	+	0.274545i
$982$	1712.67	−	988.809i	1.74406	−	1.00693i
$983$	914.350			0.930163			0.465081	−	0.885268i	$-0.346025\pi$
$983$	914.350			0.930163			0.465081	+	0.885268i	$0.346025\pi$
$984$	−693.718	−	1201.55i	−0.704998	−	1.22109i
$985$	407.544	+	235.296i	0.413750	+	0.238879i
$986$	−2554.48	+	4424.49i	−2.59075	+	4.48731i
$987$	664.945	+	140.819i	0.673703	+	0.142674i
$988$	975.422	+	1756.31i	0.987269	+	1.77764i
$989$	122.552			0.123916
$990$	127.929	−	221.579i	0.129221	−	0.223817i
$991$	31.4663	−	54.5013i	0.0317521	−	0.0549962i	−0.849713	−	0.527246i	$-0.823225\pi$
$991$	31.4663	−	54.5013i	0.0317521	−	0.0549962i	0.881465	+	0.472250i	$0.156558\pi$
$992$	−780.827	+	450.810i	−0.787124	+	0.454446i
$993$	−446.734			−0.449883
$994$	−3070.78	+	1000.29i	−3.08931	+	1.00633i
$995$	652.752	−	376.867i	0.656033	−	0.378761i
$996$		−	563.985i		−	0.566250i
$997$	−792.593	+	457.604i	−0.794978	+	0.458981i	−0.841712	−	0.539927i	$-0.818452\pi$
$997$	−792.593	+	457.604i	−0.794978	+	0.458981i	0.0467343	+	0.998907i	$0.485119\pi$
$998$	1489.20	−	2579.36i	1.49218	−	2.58453i
$999$	−20.2149	+	35.0132i	−0.0202351	+	0.0350483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.bo.c.160.18	✓	36
7.6	odd	2		273.3.bo.d.160.18	yes	36
13.10	even	6		273.3.bo.d.244.18	yes	36
91.62	odd	6	inner	273.3.bo.c.244.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.bo.c.160.18	✓	36	1.1	even	1	trivial
273.3.bo.c.244.18	yes	36	91.62	odd	6	inner
273.3.bo.d.160.18	yes	36	7.6	odd	2
273.3.bo.d.244.18	yes	36	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(3.26818 + 1.88688i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(5.12066 + 8.86924i) q^{4} +3.17854 q^{5} +(-3.26818 - 5.66065i) q^{6} +(6.65578 - 2.16809i) q^{7} +23.5533i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(3.26818 + 1.88688i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(5.12066 + 8.86924i) q^{4} +3.17854 q^{5} +(-3.26818 - 5.66065i) q^{6} +(6.65578 - 2.16809i) q^{7} +23.5533i q^{8} +(1.50000 + 2.59808i) q^{9} +(10.3880 + 5.99754i) q^{10} +(-6.15750 - 3.55504i) q^{11} -17.7385i q^{12} +(6.68635 - 11.1487i) q^{13} +(25.8432 + 5.47296i) q^{14} +(-4.76781 - 2.75270i) q^{15} +(-23.9596 + 41.4993i) q^{16} +(-26.7605 + 15.4502i) q^{17} +11.3213i q^{18} +(7.54483 + 13.0680i) q^{19} +(16.2762 + 28.1912i) q^{20} +(-11.8613 - 2.51193i) q^{21} +(-13.4159 - 23.2370i) q^{22} +(-1.77472 + 3.07391i) q^{23} +(20.3977 - 35.3299i) q^{24} -14.8969 q^{25} +(42.8884 - 23.8195i) q^{26} -5.19615i q^{27} +(53.3113 + 47.9296i) q^{28} +(21.9060 - 37.9423i) q^{29} +(-10.3880 - 17.9926i) q^{30} +10.4085 q^{31} +(-75.0178 + 43.3116i) q^{32} +(6.15750 + 10.6651i) q^{33} -116.611 q^{34} +(21.1557 - 6.89138i) q^{35} +(-15.3620 + 26.6077i) q^{36} +(-6.73830 - 3.89036i) q^{37} +56.9449i q^{38} +(-19.6846 + 10.9325i) q^{39} +74.8650i q^{40} +(17.0048 - 29.4531i) q^{41} +(-34.0251 - 30.5903i) q^{42} +(-17.2636 - 29.9014i) q^{43} -72.8165i q^{44} +(4.76781 + 8.25809i) q^{45} +(-11.6002 + 6.69739i) q^{46} -56.0600 q^{47} +(71.8789 - 41.4993i) q^{48} +(39.5987 - 28.8607i) q^{49} +(-48.6856 - 28.1087i) q^{50} +53.5210 q^{51} +(133.119 + 2.21432i) q^{52} +47.4276 q^{53} +(9.80453 - 16.9820i) q^{54} +(-19.5719 - 11.2998i) q^{55} +(51.0657 + 156.765i) q^{56} -26.1361i q^{57} +(143.186 - 82.6682i) q^{58} +(-54.2307 - 93.9304i) q^{59} -56.3825i q^{60} +(-0.722790 + 0.417303i) q^{61} +(34.0170 + 19.6397i) q^{62} +(15.6165 + 14.0401i) q^{63} -135.218 q^{64} +(21.2528 - 35.4365i) q^{65} +46.4740i q^{66} +(-25.1044 - 14.4940i) q^{67} +(-274.063 - 158.230i) q^{68} +(5.32417 - 3.07391i) q^{69} +(82.1437 + 17.3960i) q^{70} +(-105.878 + 61.1286i) q^{71} +(-61.1932 + 35.3299i) q^{72} +121.814 q^{73} +(-14.6813 - 25.4288i) q^{74} +(22.3453 + 12.9011i) q^{75} +(-77.2690 + 133.834i) q^{76} +(-48.6906 - 10.3115i) q^{77} +(-84.9609 - 1.41326i) q^{78} -7.63503 q^{79} +(-76.1567 + 131.907i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(111.149 - 64.1721i) q^{82} +31.7944 q^{83} +(-38.4587 - 118.063i) q^{84} +(-85.0594 + 49.1091i) q^{85} -130.298i q^{86} +(-65.7181 + 37.9423i) q^{87} +(83.7327 - 145.029i) q^{88} +(-42.7821 + 74.1007i) q^{89} +35.9852i q^{90} +(20.3315 - 88.6997i) q^{91} -36.3510 q^{92} +(-15.6128 - 9.01407i) q^{93} +(-183.214 - 105.779i) q^{94} +(23.9816 + 41.5373i) q^{95} +150.036 q^{96} +(-35.0376 - 60.6869i) q^{97} +(183.872 - 19.6037i) q^{98} -21.3302i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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