LMFDB - Embedded newform 273.2.cg.a.124.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.9
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.a.262.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.705851 - 2.63427i) q^{2} +1.00000i q^{3} +(-4.70911 - 2.71881i) q^{4} +(-0.914933 - 3.41458i) q^{5} +(2.63427 + 0.705851i) q^{6} +(2.62078 + 0.362619i) q^{7} +(-6.62917 + 6.62917i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.705851 - 2.63427i) q^{2} +1.00000i q^{3} +(-4.70911 - 2.71881i) q^{4} +(-0.914933 - 3.41458i) q^{5} +(2.63427 + 0.705851i) q^{6} +(2.62078 + 0.362619i) q^{7} +(-6.62917 + 6.62917i) q^{8} -1.00000 q^{9} -9.64073 q^{10} +(0.312538 - 0.312538i) q^{11} +(2.71881 - 4.70911i) q^{12} +(-3.60449 - 0.0874303i) q^{13} +(2.80512 - 6.64790i) q^{14} +(3.41458 - 0.914933i) q^{15} +(7.34621 + 12.7240i) q^{16} +(0.715520 - 1.23932i) q^{17} +(-0.705851 + 2.63427i) q^{18} +(-0.931473 + 0.931473i) q^{19} +(-4.97505 + 18.5671i) q^{20} +(-0.362619 + 2.62078i) q^{21} +(-0.602706 - 1.04392i) q^{22} +(6.22490 - 3.59395i) q^{23} +(-6.62917 - 6.62917i) q^{24} +(-6.49210 + 3.74822i) q^{25} +(-2.77455 + 9.43350i) q^{26} -1.00000i q^{27} +(-11.3557 - 8.83302i) q^{28} +(3.82097 - 6.61812i) q^{29} -9.64073i q^{30} +(0.698697 + 0.187215i) q^{31} +(20.5926 - 5.51778i) q^{32} +(0.312538 + 0.312538i) q^{33} +(-2.75965 - 2.75965i) q^{34} +(-1.15965 - 9.28064i) q^{35} +(4.70911 + 2.71881i) q^{36} +(-0.982321 - 0.263212i) q^{37} +(1.79627 + 3.11123i) q^{38} +(0.0874303 - 3.60449i) q^{39} +(28.7010 + 16.5706i) q^{40} +(0.748673 + 2.79409i) q^{41} +(6.64790 + 2.80512i) q^{42} +(7.20261 - 4.15843i) q^{43} +(-2.32151 + 0.622047i) q^{44} +(0.914933 + 3.41458i) q^{45} +(-5.07358 - 18.9349i) q^{46} +(0.906290 - 0.242840i) q^{47} +(-12.7240 + 7.34621i) q^{48} +(6.73701 + 1.90069i) q^{49} +(5.29136 + 19.7476i) q^{50} +(1.23932 + 0.715520i) q^{51} +(16.7362 + 10.2116i) q^{52} +(2.48381 + 4.30208i) q^{53} +(-2.63427 - 0.705851i) q^{54} +(-1.35314 - 0.781234i) q^{55} +(-19.7775 + 14.9698i) q^{56} +(-0.931473 - 0.931473i) q^{57} +(-14.7369 - 14.7369i) q^{58} +(-3.14180 + 0.841844i) q^{59} +(-18.5671 - 4.97505i) q^{60} -13.0177i q^{61} +(0.986352 - 1.70841i) q^{62} +(-2.62078 - 0.362619i) q^{63} -28.7565i q^{64} +(2.99933 + 12.3878i) q^{65} +(1.04392 - 0.602706i) q^{66} +(4.49370 + 4.49370i) q^{67} +(-6.73893 + 3.89072i) q^{68} +(3.59395 + 6.22490i) q^{69} +(-25.2663 - 3.49591i) q^{70} +(0.487730 - 1.82023i) q^{71} +(6.62917 - 6.62917i) q^{72} +(-3.29282 + 12.2890i) q^{73} +(-1.38674 + 2.40191i) q^{74} +(-3.74822 - 6.49210i) q^{75} +(6.91890 - 1.85391i) q^{76} +(0.932428 - 0.705763i) q^{77} +(-9.43350 - 2.77455i) q^{78} +(-1.77054 + 3.06666i) q^{79} +(36.7258 - 36.7258i) q^{80} +1.00000 q^{81} +7.88884 q^{82} +(-2.33307 + 2.33307i) q^{83} +(8.83302 - 11.3557i) q^{84} +(-4.88639 - 1.30931i) q^{85} +(-5.87046 - 21.9089i) q^{86} +(6.61812 + 3.82097i) q^{87} +4.14374i q^{88} +(-2.70782 + 10.1057i) q^{89} +9.64073 q^{90} +(-9.41489 - 1.53619i) q^{91} -39.0850 q^{92} +(-0.187215 + 0.698697i) q^{93} -2.55882i q^{94} +(4.03282 + 2.32835i) q^{95} +(5.51778 + 20.5926i) q^{96} +(2.51514 + 0.673929i) q^{97} +(9.76227 - 16.4055i) q^{98} +(-0.312538 + 0.312538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.705851	−	2.63427i	0.499112	−	1.86271i	−0.00654752	−	0.999979i	$-0.502084\pi$
$2$	0.705851	−	2.63427i	0.499112	−	1.86271i	0.505660	−	0.862733i	$-0.331249\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−4.70911	−	2.71881i	−2.35456	−	1.35940i
$5$	−0.914933	−	3.41458i	−0.409170	−	1.52704i	−0.796232	−	0.604991i	$-0.793177\pi$
$5$	−0.914933	−	3.41458i	−0.409170	−	1.52704i	0.387062	−	0.922054i	$-0.373490\pi$
$6$	2.63427	+	0.705851i	1.07544	+	0.288162i
$7$	2.62078	+	0.362619i	0.990563	+	0.137057i
$7$	2.62078	+	0.362619i	0.990563	+	0.137057i
$8$	−6.62917	+	6.62917i	−2.34377	+	2.34377i
$9$	−1.00000			−0.333333
$10$	−9.64073			−3.04867
$11$	0.312538	−	0.312538i	0.0942339	−	0.0942339i	−0.658418	−	0.752652i	$-0.728774\pi$
$11$	0.312538	−	0.312538i	0.0942339	−	0.0942339i	0.752652	+	0.658418i	$0.228774\pi$
$12$	2.71881	−	4.70911i	0.784852	−	1.35940i
$13$	−3.60449	−	0.0874303i	−0.999706	−	0.0242488i
$13$	−3.60449	−	0.0874303i	−0.999706	−	0.0242488i
$14$	2.80512	−	6.64790i	0.749700	−	1.77673i
$15$	3.41458	−	0.914933i	0.881640	−	0.236235i
$16$	7.34621	+	12.7240i	1.83655	+	3.18100i
$17$	0.715520	−	1.23932i	0.173539	−	0.300578i	−0.766116	−	0.642703i	$-0.777813\pi$
$17$	0.715520	−	1.23932i	0.173539	−	0.300578i	0.939655	+	0.342124i	$0.111146\pi$
$18$	−0.705851	+	2.63427i	−0.166371	+	0.620904i
$19$	−0.931473	+	0.931473i	−0.213694	+	0.213694i	−0.805835	−	0.592140i	$-0.798283\pi$
$19$	−0.931473	+	0.931473i	−0.213694	+	0.213694i	0.592140	+	0.805835i	$0.298283\pi$
$20$	−4.97505	+	18.5671i	−1.11246	+	4.15174i
$21$	−0.362619	+	2.62078i	−0.0791300	+	0.571902i
$22$	−0.602706	−	1.04392i	−0.128497	−	0.222564i
$23$	6.22490	−	3.59395i	1.29798	−	0.749390i	0.317926	−	0.948115i	$-0.397013\pi$
$23$	6.22490	−	3.59395i	1.29798	−	0.749390i	0.980055	+	0.198725i	$0.0636801\pi$
$24$	−6.62917	−	6.62917i	−1.35317	−	1.35317i
$25$	−6.49210	+	3.74822i	−1.29842	+	0.749643i
$26$	−2.77455	+	9.43350i	−0.544134	+	1.85006i
$27$		−	1.00000i		−	0.192450i
$28$	−11.3557	−	8.83302i	−2.14602	−	1.66928i
$29$	3.82097	−	6.61812i	0.709537	−	1.22895i	−0.255492	−	0.966811i	$-0.582238\pi$
$29$	3.82097	−	6.61812i	0.709537	−	1.22895i	0.965029	−	0.262143i	$-0.0844291\pi$
$30$		−	9.64073i		−	1.76015i
$31$	0.698697	+	0.187215i	0.125490	+	0.0336249i	0.321017	−	0.947073i	$-0.395975\pi$
$31$	0.698697	+	0.187215i	0.125490	+	0.0336249i	−0.195528	+	0.980698i	$0.562642\pi$
$32$	20.5926	−	5.51778i	3.64030	−	0.975414i
$33$	0.312538	+	0.312538i	0.0544060	+	0.0544060i
$34$	−2.75965	−	2.75965i	−0.473276	−	0.473276i
$35$	−1.15965	−	9.28064i	−0.196017	−	1.56871i
$36$	4.70911	+	2.71881i	0.784852	+	0.453135i
$37$	−0.982321	−	0.263212i	−0.161493	−	0.0432718i	0.177167	−	0.984181i	$-0.443307\pi$
$37$	−0.982321	−	0.263212i	−0.161493	−	0.0432718i	−0.338659	+	0.940909i	$0.609973\pi$
$38$	1.79627	+	3.11123i	0.291394	+	0.504709i
$39$	0.0874303	−	3.60449i	0.0140001	−	0.577181i
$40$	28.7010	+	16.5706i	4.53803	+	2.62003i
$41$	0.748673	+	2.79409i	0.116923	+	0.436363i	0.999424	−	0.0339485i	$-0.0108082\pi$
$41$	0.748673	+	2.79409i	0.116923	+	0.436363i	−0.882500	+	0.470312i	$0.844142\pi$
$42$	6.64790	+	2.80512i	1.02579	+	0.432840i
$43$	7.20261	−	4.15843i	1.09839	−	0.634155i	0.162591	−	0.986694i	$-0.448015\pi$
$43$	7.20261	−	4.15843i	1.09839	−	0.634155i	0.935797	+	0.352539i	$0.114682\pi$
$44$	−2.32151	+	0.622047i	−0.349981	+	0.0937771i
$45$	0.914933	+	3.41458i	0.136390	+	0.509015i
$46$	−5.07358	−	18.9349i	−0.748059	−	2.79180i
$47$	0.906290	−	0.242840i	0.132196	−	0.0354218i	−0.192114	−	0.981373i	$-0.561534\pi$
$47$	0.906290	−	0.242840i	0.132196	−	0.0354218i	0.324310	+	0.945951i	$0.394868\pi$
$48$	−12.7240	+	7.34621i	−1.83655	+	1.06033i
$49$	6.73701	+	1.90069i	0.962431	+	0.271528i
$50$	5.29136	+	19.7476i	0.748312	+	2.79274i
$51$	1.23932	+	0.715520i	0.173539	+	0.100193i
$52$	16.7362	+	10.2116i	2.32090	+	1.41610i
$53$	2.48381	+	4.30208i	0.341177	+	0.590936i	0.984652	−	0.174531i	$-0.0558411\pi$
$53$	2.48381	+	4.30208i	0.341177	+	0.590936i	−0.643474	+	0.765468i	$0.722508\pi$
$54$	−2.63427	−	0.705851i	−0.358479	−	0.0960542i
$55$	−1.35314	−	0.781234i	−0.182457	−	0.105342i
$56$	−19.7775	+	14.9698i	−2.64288	+	2.00042i
$57$	−0.931473	−	0.931473i	−0.123377	−	0.123377i
$58$	−14.7369	−	14.7369i	−1.93505	−	1.93505i
$59$	−3.14180	+	0.841844i	−0.409028	+	0.109599i	−0.457465	−	0.889227i	$-0.651243\pi$
$59$	−3.14180	+	0.841844i	−0.409028	+	0.109599i	0.0484372	+	0.998826i	$0.484576\pi$
$60$	−18.5671	−	4.97505i	−2.39701	−	0.642277i
$61$		−	13.0177i		−	1.66674i	−0.552715	−	0.833370i	$-0.686408\pi$
$61$		−	13.0177i		−	1.66674i	0.552715	−	0.833370i	$-0.313592\pi$
$62$	0.986352	−	1.70841i	0.125267	−	0.216969i
$63$	−2.62078	−	0.362619i	−0.330188	−	0.0456857i
$64$		−	28.7565i		−	3.59456i
$65$	2.99933	+	12.3878i	0.372021	+	1.53652i
$66$	1.04392	−	0.602706i	0.128497	−	0.0741879i
$67$	4.49370	+	4.49370i	0.548993	+	0.548993i	0.926150	−	0.377156i	$-0.123098\pi$
$67$	4.49370	+	4.49370i	0.548993	+	0.548993i	−0.377156	+	0.926150i	$0.623098\pi$
$68$	−6.73893	+	3.89072i	−0.817215	+	0.471819i
$69$	3.59395	+	6.22490i	0.432661	+	0.749390i
$70$	−25.2663	−	3.49591i	−3.01990	−	0.417842i
$71$	0.487730	−	1.82023i	0.0578829	−	0.216022i	−0.930926	−	0.365207i	$-0.880998\pi$
$71$	0.487730	−	1.82023i	0.0578829	−	0.216022i	0.988809	+	0.149185i	$0.0476649\pi$
$72$	6.62917	−	6.62917i	0.781255	−	0.781255i
$73$	−3.29282	+	12.2890i	−0.385396	+	1.43832i	0.452146	+	0.891944i	$0.350659\pi$
$73$	−3.29282	+	12.2890i	−0.385396	+	1.43832i	−0.837542	+	0.546373i	$0.816008\pi$
$74$	−1.38674	+	2.40191i	−0.161206	+	0.279217i
$75$	−3.74822	−	6.49210i	−0.432807	−	0.749643i
$76$	6.91890	−	1.85391i	0.793653	−	0.212659i
$77$	0.932428	−	0.705763i	0.106260	−	0.0804292i
$78$	−9.43350	−	2.77455i	−1.06813	−	0.314156i
$79$	−1.77054	+	3.06666i	−0.199201	+	0.345026i	−0.948270	−	0.317466i	$-0.897168\pi$
$79$	−1.77054	+	3.06666i	−0.199201	+	0.345026i	0.749069	+	0.662493i	$0.230501\pi$
$80$	36.7258	−	36.7258i	4.10607	−	4.10607i
$81$	1.00000			0.111111
$82$	7.88884			0.871176
$83$	−2.33307	+	2.33307i	−0.256087	+	0.256087i	−0.823461	−	0.567373i	$-0.807960\pi$
$83$	−2.33307	+	2.33307i	−0.256087	+	0.256087i	0.567373	+	0.823461i	$0.307960\pi$
$84$	8.83302	−	11.3557i	0.963762	−	1.23901i
$85$	−4.88639	−	1.30931i	−0.530004	−	0.142014i
$86$	−5.87046	−	21.9089i	−0.633028	−	2.36249i
$87$	6.61812	+	3.82097i	0.709537	+	0.409651i
$88$			4.14374i			0.441724i
$89$	−2.70782	+	10.1057i	−0.287028	+	1.07120i	0.660317	+	0.750987i	$0.270422\pi$
$89$	−2.70782	+	10.1057i	−0.287028	+	1.07120i	−0.947345	+	0.320216i	$0.896245\pi$
$90$	9.64073			1.01622
$91$	−9.41489	−	1.53619i	−0.986948	−	0.161037i
$92$	−39.0850			−4.07489
$93$	−0.187215	+	0.698697i	−0.0194133	+	0.0724515i
$94$		−	2.55882i		−	0.263922i
$95$	4.03282	+	2.32835i	0.413758	+	0.238884i
$96$	5.51778	+	20.5926i	0.563156	+	2.10173i
$97$	2.51514	+	0.673929i	0.255373	+	0.0684271i	0.384234	−	0.923236i	$-0.374465\pi$
$97$	2.51514	+	0.673929i	0.255373	+	0.0684271i	−0.128861	+	0.991663i	$0.541132\pi$
$98$	9.76227	−	16.4055i	0.986138	−	1.65721i
$99$	−0.312538	+	0.312538i	−0.0314113	+	0.0314113i
$100$	40.7627			4.07627
$101$	1.44573			0.143856			0.0719279	−	0.997410i	$-0.477085\pi$
$101$	1.44573			0.143856			0.0719279	+	0.997410i	$0.477085\pi$
$102$	2.75965	−	2.75965i	0.273246	−	0.273246i
$103$	−6.70272	+	11.6095i	−0.660439	+	1.14391i	0.320061	+	0.947397i	$0.396296\pi$
$103$	−6.70272	+	11.6095i	−0.660439	+	1.14391i	−0.980500	+	0.196517i	$0.937037\pi$
$104$	24.4744	−	23.3152i	2.39991	−	2.28624i
$105$	9.28064	−	1.15965i	0.905697	−	0.113170i
$106$	13.0860	−	3.50640i	1.27103	−	0.340571i
$107$	−0.944877	−	1.63658i	−0.0913447	−	0.158214i	0.816732	−	0.577017i	$-0.195783\pi$
$107$	−0.944877	−	1.63658i	−0.0913447	−	0.158214i	−0.908077	+	0.418803i	$0.862450\pi$
$108$	−2.71881	+	4.70911i	−0.261617	+	0.453135i
$109$	−1.90898	+	7.12442i	−0.182847	+	0.682396i	0.812234	+	0.583332i	$0.198251\pi$
$109$	−1.90898	+	7.12442i	−0.182847	+	0.682396i	−0.995081	+	0.0990637i	$0.968415\pi$
$110$	−3.01310	+	3.01310i	−0.287288	+	0.287288i
$111$	0.263212	−	0.982321i	0.0249830	−	0.0932378i
$112$	14.6389	+	36.0108i	1.38324	+	3.40270i
$113$	−3.09382	−	5.35865i	−0.291042	−	0.504100i	0.683014	−	0.730405i	$-0.260669\pi$
$113$	−3.09382	−	5.35865i	−0.291042	−	0.504100i	−0.974056	+	0.226305i	$0.927335\pi$
$114$	−3.11123	+	1.79627i	−0.291394	+	0.168236i
$115$	−17.9672	−	17.9672i	−1.67545	−	1.67545i
$116$	−35.9868	+	20.7770i	−3.34129	+	1.92909i
$117$	3.60449	+	0.0874303i	0.333235	+	0.00808293i
$118$			8.87058i			0.816603i
$119$	2.32462	−	2.98852i	0.213098	−	0.273957i
$120$	−16.5706	+	28.7010i	−1.51268	+	2.62003i
$121$			10.8046i			0.982240i
$122$	−34.2921	−	9.18853i	−3.10466	−	0.831890i
$123$	−2.79409	+	0.748673i	−0.251934	+	0.0675056i
$124$	−2.78124	−	2.78124i	−0.249763	−	0.249763i
$125$	6.24018	+	6.24018i	0.558139	+	0.558139i
$126$	−2.80512	+	6.64790i	−0.249900	+	0.592242i
$127$	5.90231	+	3.40770i	0.523745	+	0.302384i	0.738466	−	0.674291i	$-0.235551\pi$
$127$	5.90231	+	3.40770i	0.523745	+	0.302384i	−0.214721	+	0.976676i	$0.568884\pi$
$128$	−34.5671	−	9.26222i	−3.05533	−	0.818672i
$129$	4.15843	+	7.20261i	0.366129	+	0.634155i
$130$	34.7499	+	0.842892i	3.04777	+	0.0739265i
$131$	−3.17967	−	1.83578i	−0.277809	−	0.160393i	0.354622	−	0.935010i	$-0.384610\pi$
$131$	−3.17967	−	1.83578i	−0.277809	−	0.160393i	−0.632431	+	0.774617i	$0.717943\pi$
$132$	−0.622047	−	2.32151i	−0.0541422	−	0.202062i
$133$	−2.77896	+	2.10342i	−0.240966	+	0.182389i
$134$	15.0095	−	8.66575i	1.29662	−	0.748607i
$135$	−3.41458	+	0.914933i	−0.293880	+	0.0787449i
$136$	3.47234	+	12.9589i	0.297751	+	1.11122i
$137$	−2.04025	−	7.61433i	−0.174311	−	0.650536i	−0.996668	−	0.0815648i	$-0.974008\pi$
$137$	−2.04025	−	7.61433i	−0.174311	−	0.650536i	0.822357	−	0.568971i	$-0.192658\pi$
$138$	18.9349	−	5.07358i	1.61184	−	0.431892i
$139$	−10.3222	+	5.95952i	−0.875517	+	0.505480i	−0.869178	−	0.494500i	$-0.835351\pi$
$139$	−10.3222	+	5.95952i	−0.875517	+	0.505480i	−0.00633943	+	0.999980i	$0.502018\pi$
$140$	−19.7713	+	46.8564i	−1.67098	+	3.96009i
$141$	0.242840	+	0.906290i	0.0204508	+	0.0763234i
$142$	−4.45073	−	2.56963i	−0.373497	−	0.215638i
$143$	−1.15387	+	1.09922i	−0.0964912	+	0.0919211i
$144$	−7.34621	−	12.7240i	−0.612184	−	1.06033i
$145$	−26.0940	−	6.99187i	−2.16699	−	0.580643i
$146$	30.0483	+	17.3484i	2.48681	+	1.43576i
$147$	−1.90069	+	6.73701i	−0.156767	+	0.555660i
$148$	3.91024	+	3.91024i	0.321420	+	0.321420i
$149$	15.3953	+	15.3953i	1.26123	+	1.26123i	0.950497	+	0.310735i	$0.100575\pi$
$149$	15.3953	+	15.3953i	1.26123	+	1.26123i	0.310735	+	0.950497i	$0.399425\pi$
$150$	−19.7476	+	5.29136i	−1.61239	+	0.432038i
$151$	13.4854	+	3.61340i	1.09742	+	0.294054i	0.761715	−	0.647912i	$-0.224357\pi$
$151$	13.4854	+	3.61340i	1.09742	+	0.294054i	0.335709	+	0.941966i	$0.391024\pi$
$152$		−	12.3498i		−	1.00170i
$153$	−0.715520	+	1.23932i	−0.0578464	+	0.100193i
$154$	−1.20102	−	2.95443i	−0.0967807	−	0.238075i
$155$		−	2.55704i		−	0.205387i
$156$	−10.2116	+	16.7362i	−0.817585	+	1.33997i
$157$	12.9689	−	7.48759i	1.03503	−	0.597574i	0.116608	−	0.993178i	$-0.462798\pi$
$157$	12.9689	−	7.48759i	1.03503	−	0.597574i	0.918421	+	0.395604i	$0.129465\pi$
$158$	6.82869	+	6.82869i	0.543261	+	0.543261i
$159$	−4.30208	+	2.48381i	−0.341177	+	0.196979i
$160$	−37.6817	−	65.2667i	−2.97900	−	5.15978i
$161$	17.6174	−	7.16169i	1.38844	−	0.564420i
$162$	0.705851	−	2.63427i	0.0554569	−	0.206968i
$163$	−6.25479	+	6.25479i	−0.489913	+	0.489913i	−0.908279	−	0.418366i	$-0.862603\pi$
$163$	−6.25479	+	6.25479i	−0.489913	+	0.489913i	0.418366	+	0.908279i	$0.362603\pi$
$164$	4.07100	−	15.1932i	0.317891	−	1.18639i
$165$	0.781234	−	1.35314i	0.0608190	−	0.105342i
$166$	4.49914	+	7.79273i	0.349201	+	0.604833i
$167$	0.331336	−	0.0887813i	0.0256396	−	0.00687010i	−0.245976	−	0.969276i	$-0.579109\pi$
$167$	0.331336	−	0.0887813i	0.0256396	−	0.00687010i	0.271616	+	0.962406i	$0.412442\pi$
$168$	−14.9698	−	19.7775i	−1.15494	−	1.52587i
$169$	12.9847	+	0.630284i	0.998824	+	0.0484833i
$170$	−6.89813	+	11.9479i	−0.529063	+	0.916363i
$171$	0.931473	−	0.931473i	0.0712315	−	0.0712315i
$172$	−45.2239			−3.44829
$173$	9.25073			0.703320			0.351660	−	0.936128i	$-0.385617\pi$
$173$	9.25073			0.703320			0.351660	+	0.936128i	$0.385617\pi$
$174$	14.7369	−	14.7369i	1.11720	−	1.11720i
$175$	−18.3736	+	7.46910i	−1.38891	+	0.564611i
$176$	6.27272	+	1.68077i	0.472824	+	0.126693i
$177$	−0.841844	−	3.14180i	−0.0632769	−	0.236152i
$178$	24.7099	+	14.2663i	1.85208	+	1.06930i
$179$		−	14.6054i		−	1.09166i	−0.837897	−	0.545829i	$-0.816215\pi$
$179$		−	14.6054i		−	1.09166i	0.837897	−	0.545829i	$-0.183785\pi$
$180$	4.97505	−	18.5671i	0.370819	−	1.38391i
$181$	8.63806			0.642062			0.321031	−	0.947069i	$-0.395971\pi$
$181$	8.63806			0.642062			0.321031	+	0.947069i	$0.395971\pi$
$182$	−10.6923	+	23.7171i	−0.792563	+	1.75802i
$183$	13.0177			0.962293
$184$	−17.4410	+	65.0908i	−1.28577	+	4.79856i
$185$			3.59503i			0.264312i
$186$	1.70841	+	0.986352i	0.125267	+	0.0723228i
$187$	−0.163707	−	0.610962i	−0.0119714	−	0.0446779i
$188$	−4.92806	−	1.32047i	−0.359415	−	0.0963051i
$189$	0.362619	−	2.62078i	0.0263767	−	0.190634i
$190$	8.98007	−	8.98007i	0.651483	−	0.651483i
$191$	−7.04823			−0.509992			−0.254996	−	0.966942i	$-0.582074\pi$
$191$	−7.04823			−0.509992			−0.254996	+	0.966942i	$0.582074\pi$
$192$	28.7565			2.07532
$193$	16.3420	−	16.3420i	1.17633	−	1.17633i	0.195652	−	0.980673i	$-0.437318\pi$
$193$	16.3420	−	16.3420i	1.17633	−	1.17633i	0.980673	−	0.195652i	$-0.0626822\pi$
$194$	3.55062	−	6.14986i	0.254920	−	0.441534i
$195$	−12.3878	+	2.99933i	−0.887109	+	0.214786i
$196$	−26.5577	−	27.2672i	−1.89698	−	1.94766i
$197$	−18.7705	+	5.02954i	−1.33734	+	0.358340i	−0.855448	−	0.517889i	$-0.826718\pi$
$197$	−18.7705	+	5.02954i	−1.33734	+	0.358340i	−0.481895	+	0.876229i	$0.660051\pi$
$198$	0.602706	+	1.04392i	0.0428324	+	0.0741879i
$199$	8.90538	−	15.4246i	0.631285	−	1.09342i	−0.356004	−	0.934485i	$-0.615861\pi$
$199$	8.90538	−	15.4246i	0.631285	−	1.09342i	0.987289	−	0.158934i	$-0.0508057\pi$
$200$	18.1897	−	67.8848i	1.28620	−	4.80018i
$201$	−4.49370	+	4.49370i	−0.316961	+	0.316961i
$202$	1.02047	−	3.80846i	0.0718002	−	0.267962i
$203$	12.4138	−	15.9591i	0.871278	−	1.12011i
$204$	−3.89072	−	6.73893i	−0.272405	−	0.471819i
$205$	8.85563	−	5.11280i	0.618504	−	0.357094i
$206$	25.8513	+	25.8513i	1.80115	+	1.80115i
$207$	−6.22490	+	3.59395i	−0.432661	+	0.249797i
$208$	−25.3669	−	46.5059i	−1.75888	−	3.22460i
$209$			0.582242i			0.0402745i
$210$	3.49591	−	25.2663i	0.241241	−	1.74354i
$211$	−5.03848	+	8.72690i	−0.346863	+	0.600785i	−0.985690	−	0.168565i	$-0.946087\pi$
$211$	−5.03848	+	8.72690i	−0.346863	+	0.600785i	0.638827	+	0.769350i	$0.279420\pi$
$212$		−	27.0120i		−	1.85519i
$213$	1.82023	+	0.487730i	0.124720	+	0.0334187i
$214$	−4.97813	+	1.33388i	−0.340298	+	0.0911825i
$215$	−20.7892	−	20.7892i	−1.41781	−	1.41781i
$216$	6.62917	+	6.62917i	0.451058	+	0.451058i
$217$	1.76325	+	0.744012i	0.119697	+	0.0505068i
$218$	17.4202	+	10.0576i	1.17985	+	0.681184i
$219$	−12.2890	−	3.29282i	−0.830413	−	0.222508i
$220$	4.24805	+	7.35784i	0.286404	+	0.496066i
$221$	−2.68744	+	4.40455i	−0.180777	+	0.296282i
$222$	−2.40191	−	1.38674i	−0.161206	−	0.0930722i
$223$	−0.246185	−	0.918774i	−0.0164857	−	0.0615256i	0.957193	−	0.289451i	$-0.0934726\pi$
$223$	−0.246185	−	0.918774i	−0.0164857	−	0.0615256i	−0.973679	+	0.227925i	$0.926806\pi$
$224$	55.9697	−	6.99362i	3.73963	−	0.467281i
$225$	6.49210	−	3.74822i	0.432807	−	0.249881i
$226$	−16.2999	+	4.36755i	−1.08425	+	0.290525i
$227$	−6.34800	−	23.6911i	−0.421331	−	1.57243i	−0.771806	−	0.635858i	$-0.780646\pi$
$227$	−6.34800	−	23.6911i	−0.421331	−	1.57243i	0.350475	−	0.936572i	$-0.386020\pi$
$228$	1.85391	+	6.91890i	0.122779	+	0.458216i
$229$	−19.9283	+	5.33978i	−1.31690	+	0.352863i	−0.847816	−	0.530290i	$-0.822083\pi$
$229$	−19.9283	+	5.33978i	−1.31690	+	0.352863i	−0.469085	+	0.883153i	$0.655416\pi$
$230$	−60.0126	+	34.6483i	−3.95711	+	2.28464i
$231$	0.705763	+	0.932428i	0.0464358	+	0.0613493i
$232$	18.5428	+	69.2025i	1.21739	+	4.54337i
$233$	−19.6906	−	11.3684i	−1.28998	−	0.744768i	−0.311326	−	0.950303i	$-0.600773\pi$
$233$	−19.6906	−	11.3684i	−1.28998	−	0.744768i	−0.978650	+	0.205536i	$0.934106\pi$
$234$	2.77455	−	9.43350i	0.181378	−	0.616687i
$235$	−1.65839	−	2.87241i	−0.108181	−	0.187376i
$236$	17.0839	+	4.57762i	1.11207	+	0.297978i
$237$	−3.06666	−	1.77054i	−0.199201	−	0.115009i
$238$	−6.23174	−	8.23314i	−0.403944	−	0.533675i
$239$	20.7640	+	20.7640i	1.34311	+	1.34311i	0.892943	+	0.450171i	$0.148637\pi$
$239$	20.7640	+	20.7640i	1.34311	+	1.34311i	0.450171	+	0.892943i	$0.351363\pi$
$240$	36.7258	+	36.7258i	2.37064	+	2.37064i
$241$	−6.55065	+	1.75524i	−0.421965	+	0.113065i	−0.463552	−	0.886070i	$-0.653425\pi$
$241$	−6.55065	+	1.75524i	−0.421965	+	0.113065i	0.0415872	+	0.999135i	$0.486759\pi$
$242$	28.4624	+	7.62647i	1.82963	+	0.490248i
$243$			1.00000i			0.0641500i
$244$	−35.3925	+	61.3016i	−2.26577	+	3.92443i
$245$	0.326147	−	24.7431i	0.0208367	−	1.58078i
$246$			7.88884i			0.502974i
$247$	3.43892	−	3.27605i	0.218813	−	0.208450i
$248$	−5.87286	+	3.39070i	−0.372927	+	0.215310i
$249$	−2.33307	−	2.33307i	−0.147852	−	0.147852i
$250$	20.8430	−	12.0337i	1.31823	−	0.761078i
$251$	−2.83547	−	4.91118i	−0.178973	−	0.309991i	0.762556	−	0.646922i	$-0.223944\pi$
$251$	−2.83547	−	4.91118i	−0.178973	−	0.309991i	−0.941529	+	0.336932i	$0.890611\pi$
$252$	11.3557	+	8.83302i	0.715340	+	0.556428i
$253$	0.822274	−	3.06877i	0.0516959	−	0.192932i
$254$	13.1430	−	13.1430i	0.824662	−	0.824662i
$255$	1.30931	−	4.88639i	0.0819919	−	0.305998i
$256$	−20.0419	+	34.7137i	−1.25262	+	2.16960i
$257$	0.596987	+	1.03401i	0.0372390	+	0.0644999i	0.884044	−	0.467403i	$-0.154810\pi$
$257$	0.596987	+	1.03401i	0.0372390	+	0.0644999i	−0.846805	+	0.531903i	$0.821477\pi$
$258$	21.9089	−	5.87046i	1.36399	−	0.365479i
$259$	−2.47901	−	1.04603i	−0.154038	−	0.0649972i
$260$	19.5559	−	66.4902i	1.21280	−	4.12354i
$261$	−3.82097	+	6.61812i	−0.236512	+	0.409651i
$262$	−7.08033	+	7.08033i	−0.437424	+	0.437424i
$263$	−24.1173			−1.48714			−0.743569	−	0.668660i	$-0.766868\pi$
$263$	−24.1173			−1.48714			−0.743569	+	0.668660i	$0.766868\pi$
$264$	−4.14374			−0.255030
$265$	12.4173	−	12.4173i	0.762786	−	0.762786i
$266$	3.57945	+	8.80523i	0.219470	+	0.539883i
$267$	−10.1057	−	2.70782i	−0.618459	−	0.165716i
$268$	−8.94384	−	33.3789i	−0.546332	−	2.03894i
$269$	15.9791	+	9.22552i	0.974261	+	0.562490i	0.900533	−	0.434788i	$-0.143177\pi$
$269$	15.9791	+	9.22552i	0.974261	+	0.562490i	0.0737284	+	0.997278i	$0.476510\pi$
$270$			9.64073i			0.586716i
$271$	−0.254418	+	0.949503i	−0.0154548	+	0.0576782i	−0.973223	−	0.229865i	$-0.926172\pi$
$271$	−0.254418	+	0.949503i	−0.0154548	+	0.0576782i	0.957768	+	0.287543i	$0.0928383\pi$
$272$	21.0254			1.27486
$273$	1.53619	−	9.41489i	0.0929747	−	0.569815i
$274$	−21.4983			−1.29876
$275$	−0.857569	+	3.20049i	−0.0517134	+	0.192997i
$276$		−	39.0850i		−	2.35264i
$277$	−15.6299	−	9.02390i	−0.939107	−	0.542194i	−0.0494268	−	0.998778i	$-0.515739\pi$
$277$	−15.6299	−	9.02390i	−0.939107	−	0.542194i	−0.889680	+	0.456584i	$0.849073\pi$
$278$	8.41307	+	31.3980i	0.504582	+	1.88313i
$279$	−0.698697	−	0.187215i	−0.0418299	−	0.0112083i
$280$	69.2104	+	53.8354i	4.13611	+	3.21728i
$281$	15.4188	−	15.4188i	0.919807	−	0.919807i	−0.0772077	−	0.997015i	$-0.524600\pi$
$281$	15.4188	−	15.4188i	0.919807	−	0.919807i	0.997015	+	0.0772077i	$0.0246005\pi$
$282$	2.55882			0.152376
$283$	−27.4720			−1.63304			−0.816521	−	0.577316i	$-0.804100\pi$
$283$	−27.4720			−1.63304			−0.816521	+	0.577316i	$0.804100\pi$
$284$	−7.24564	+	7.24564i	−0.429950	+	0.429950i
$285$	−2.32835	+	4.03282i	−0.137919	+	0.238884i
$286$	2.08118	+	3.81548i	0.123063	+	0.225614i
$287$	0.948921	+	7.59418i	0.0560130	+	0.448270i
$288$	−20.5926	+	5.51778i	−1.21343	+	0.325138i
$289$	7.47606	+	12.9489i	0.439768	+	0.761701i
$290$	−36.8370	+	63.8035i	−2.16314	+	3.74667i
$291$	−0.673929	+	2.51514i	−0.0395064	+	0.147440i
$292$	48.9177	−	48.9177i	2.86269	−	2.86269i
$293$	−2.03171	+	7.58244i	−0.118694	+	0.442971i	−0.999537	−	0.0304377i	$-0.990310\pi$
$293$	−2.03171	+	7.58244i	−0.118694	+	0.442971i	0.880843	+	0.473409i	$0.156977\pi$
$294$	16.4055	+	9.76227i	0.956790	+	0.569347i
$295$	5.74908	+	9.95770i	0.334724	+	0.579760i
$296$	8.25685	−	4.76709i	0.479920	−	0.277082i
$297$	−0.312538	−	0.312538i	−0.0181353	−	0.0181353i
$298$	51.4222	−	29.6886i	2.97881	−	1.71982i
$299$	−22.7518	+	12.4101i	−1.31577	+	0.717695i
$300$			40.7627i			2.35344i
$301$	20.3844	−	8.28654i	1.17494	−	0.477628i
$302$	19.0373	−	32.9736i	1.09548	−	1.89742i
$303$			1.44573i			0.0830552i
$304$	−18.6949	−	5.00927i	−1.07222	−	0.287302i
$305$	−44.4498	+	11.9103i	−2.54519	+	0.681981i
$306$	2.75965	+	2.75965i	0.157759	+	0.157759i
$307$	16.1223	+	16.1223i	0.920147	+	0.920147i	0.997039	−	0.0768923i	$-0.0244998\pi$
$307$	16.1223	+	16.1223i	0.920147	+	0.920147i	−0.0768923	+	0.997039i	$0.524500\pi$
$308$	−6.30974	+	0.788426i	−0.359531	+	0.0449247i
$309$	−11.6095	−	6.70272i	−0.660439	−	0.381305i
$310$	−6.73595	−	1.80489i	−0.382576	−	0.102511i
$311$	2.75580	+	4.77319i	0.156267	+	0.270663i	0.933520	−	0.358526i	$-0.116721\pi$
$311$	2.75580	+	4.77319i	0.156267	+	0.270663i	−0.777253	+	0.629189i	$0.783387\pi$
$312$	23.3152	+	24.4744i	1.31996	+	1.38559i
$313$	16.8101	+	9.70534i	0.950165	+	0.548578i	0.893132	−	0.449794i	$-0.148503\pi$
$313$	16.8101	+	9.70534i	0.950165	+	0.548578i	0.0570329	+	0.998372i	$0.481836\pi$
$314$	−10.5702	−	39.4487i	−0.596513	−	2.22622i
$315$	1.15965	+	9.28064i	0.0653389	+	0.522905i
$316$	16.6753	−	9.62750i	0.938060	−	0.541589i
$317$	−27.1214	+	7.26716i	−1.52329	+	0.408164i	−0.920823	−	0.389980i	$-0.872482\pi$
$317$	−27.1214	+	7.26716i	−1.52329	+	0.408164i	−0.602467	+	0.798144i	$0.705815\pi$
$318$	3.50640	+	13.0860i	0.196629	+	0.733829i
$319$	−0.874216	−	3.26262i	−0.0489467	−	0.182671i
$320$	−98.1911	+	26.3102i	−5.48905	+	1.47079i
$321$	1.63658	−	0.944877i	0.0913447	−	0.0527379i
$322$	−6.43062	−	51.4640i	−0.358364	−	2.86798i
$323$	0.487902	+	1.82088i	0.0271476	+	0.101316i
$324$	−4.70911	−	2.71881i	−0.261617	−	0.151045i
$325$	23.7284	−	12.9428i	1.31622	−	0.717937i
$326$	12.0619	+	20.8918i	0.668045	+	1.15709i
$327$	−7.12442	−	1.90898i	−0.393981	−	0.105567i
$328$	−23.4856	−	13.5594i	−1.29677	−	0.748692i
$329$	2.46325	−	0.307792i	0.135803	−	0.0169691i
$330$	−3.01310	−	3.01310i	−0.165866	−	0.165866i
$331$	5.36907	+	5.36907i	0.295111	+	0.295111i	0.839095	−	0.543985i	$-0.183085\pi$
$331$	5.36907	+	5.36907i	0.295111	+	0.295111i	−0.543985	+	0.839095i	$0.683085\pi$
$332$	17.3298	−	4.64352i	0.951098	−	0.254846i
$333$	0.982321	+	0.263212i	0.0538309	+	0.0144239i
$334$		−	0.935496i		−	0.0511881i
$335$	11.2327	−	19.4555i	0.613705	−	1.06297i
$336$	−36.0108	+	14.6389i	−1.96455	+	0.798615i
$337$		−	3.26189i		−	0.177686i	−0.996046	−	0.0888431i	$-0.971683\pi$
$337$		−	3.26189i		−	0.177686i	0.996046	−	0.0888431i	$-0.0283170\pi$
$338$	10.8256	−	33.7604i	0.588836	−	1.83632i
$339$	5.35865	−	3.09382i	0.291042	−	0.168033i
$340$	19.4508	+	19.4508i	1.05487	+	1.05487i
$341$	0.276882	−	0.159858i	0.0149940	−	0.00865678i
$342$	−1.79627	−	3.11123i	−0.0971312	−	0.168236i
$343$	16.9670	+	7.42428i	0.916133	+	0.400873i
$344$	−20.1804	+	75.3143i	−1.08805	+	4.06067i
$345$	17.9672	−	17.9672i	0.967320	−	0.967320i
$346$	6.52964	−	24.3689i	0.351035	−	1.31008i
$347$	15.4833	−	26.8178i	0.831185	−	1.43965i	−0.0659143	−	0.997825i	$-0.520996\pi$
$347$	15.4833	−	26.8178i	0.831185	−	1.43965i	0.897099	−	0.441829i	$-0.145670\pi$
$348$	−20.7770	−	35.9868i	−1.11376	−	1.92909i
$349$	11.7105	−	3.13781i	0.626847	−	0.167963i	0.0686086	−	0.997644i	$-0.478144\pi$
$349$	11.7105	−	3.13781i	0.626847	−	0.167963i	0.558239	+	0.829680i	$0.311477\pi$
$350$	6.70664	+	53.6730i	0.358485	+	2.86894i
$351$	−0.0874303	+	3.60449i	−0.00466668	+	0.192394i
$352$	4.71147	−	8.16050i	0.251122	−	0.434956i
$353$	−20.7922	+	20.7922i	−1.10665	+	1.10665i	−0.113068	+	0.993587i	$0.536068\pi$
$353$	−20.7922	+	20.7922i	−1.10665	+	1.10665i	−0.993587	+	0.113068i	$0.963932\pi$
$354$	−8.87058			−0.471466
$355$	−6.66157			−0.353559
$356$	40.2269	−	40.2269i	2.13202	−	2.13202i
$357$	2.98852	+	2.32462i	0.158169	+	0.123032i
$358$	−38.4746	−	10.3092i	−2.03344	−	0.544860i
$359$	−2.40975	−	8.99331i	−0.127182	−	0.474649i	0.872726	−	0.488210i	$-0.162350\pi$
$359$	−2.40975	−	8.99331i	−0.127182	−	0.474649i	−0.999908	+	0.0135610i	$0.995683\pi$
$360$	−28.7010	−	16.5706i	−1.51268	−	0.873345i
$361$			17.2647i			0.908669i
$362$	6.09719	−	22.7550i	0.320461	−	1.19598i
$363$	−10.8046			−0.567097
$364$	40.1592	+	32.8314i	2.10491	+	1.72083i
$365$	44.9744			2.35407
$366$	9.18853	−	34.2921i	0.480292	−	1.79247i
$367$		−	25.2235i		−	1.31666i	−0.752731	−	0.658329i	$-0.771264\pi$
$367$		−	25.2235i		−	1.31666i	0.752731	−	0.658329i	$-0.228736\pi$
$368$	91.4589	+	52.8038i	4.76763	+	2.75259i
$369$	−0.748673	−	2.79409i	−0.0389744	−	0.145454i
$370$	9.47029	+	2.53756i	0.492337	+	0.131921i
$371$	4.94950	+	12.1755i	0.256965	+	0.632120i
$372$	2.78124	−	2.78124i	0.144201	−	0.144201i
$373$	−1.04834			−0.0542808			−0.0271404	−	0.999632i	$-0.508640\pi$
$373$	−1.04834			−0.0542808			−0.0271404	+	0.999632i	$0.508640\pi$
$374$	−1.72499			−0.0891972
$375$	−6.24018	+	6.24018i	−0.322242	+	0.322242i
$376$	−4.39812	+	7.61777i	−0.226816	+	0.392857i
$377$	−14.3513	+	23.5209i	−0.739129	+	1.21139i
$378$	−6.64790	−	2.80512i	−0.341931	−	0.144280i
$379$	−15.3006	+	4.09979i	−0.785941	+	0.210592i	−0.629402	−	0.777080i	$-0.716700\pi$
$379$	−15.3006	+	4.09979i	−0.785941	+	0.210592i	−0.156539	+	0.987672i	$0.550034\pi$
$380$	−12.6607	−	21.9289i	−0.649478	−	1.12493i
$381$	−3.40770	+	5.90231i	−0.174582	+	0.302384i
$382$	−4.97500	+	18.5669i	−0.254543	+	0.949968i
$383$	18.3682	−	18.3682i	0.938571	−	0.938571i	−0.0596485	−	0.998219i	$-0.518998\pi$
$383$	18.3682	−	18.3682i	0.938571	−	0.938571i	0.998219	+	0.0596485i	$0.0189980\pi$
$384$	9.26222	−	34.5671i	0.472661	−	1.76399i
$385$	−3.26299	−	2.53812i	−0.166297	−	0.129355i
$386$	−31.5143	−	54.5844i	−1.60404	−	2.77827i
$387$	−7.20261	+	4.15843i	−0.366129	+	0.211385i
$388$	−10.0118	−	10.0118i	−0.508271	−	0.508271i
$389$	−20.0494	+	11.5755i	−1.01655	+	0.586903i	−0.913102	−	0.407732i	$-0.866320\pi$
$389$	−20.0494	+	11.5755i	−1.01655	+	0.586903i	−0.103444	+	0.994635i	$0.532986\pi$
$390$	−0.842892	+	34.7499i	−0.0426815	+	1.75963i
$391$		−	10.2862i		−	0.520194i
$392$	−57.2608	+	32.0608i	−2.89211	+	1.61931i
$393$	1.83578	−	3.17967i	0.0926031	−	0.160393i
$394$			52.9967i			2.66994i
$395$	12.0913	+	3.23985i	0.608378	+	0.163014i
$396$	2.32151	−	0.622047i	0.116660	−	0.0312590i
$397$	−8.35961	−	8.35961i	−0.419557	−	0.419557i	0.465494	−	0.885051i	$-0.345877\pi$
$397$	−8.35961	−	8.35961i	−0.419557	−	0.419557i	−0.885051	+	0.465494i	$0.845877\pi$
$398$	−34.3466	−	34.3466i	−1.72164	−	1.72164i
$399$	−2.10342	−	2.77896i	−0.105303	−	0.139122i
$400$	−95.3847	−	55.0704i	−4.76923	−	2.75352i
$401$	−20.1219	−	5.39164i	−1.00484	−	0.269245i	−0.281367	−	0.959600i	$-0.590788\pi$
$401$	−20.1219	−	5.39164i	−1.00484	−	0.269245i	−0.723471	+	0.690355i	$0.757454\pi$
$402$	8.66575	+	15.0095i	0.432208	+	0.748607i
$403$	−2.50208	−	0.735903i	−0.124637	−	0.0366580i
$404$	−6.80812	−	3.93067i	−0.338717	−	0.195558i
$405$	−0.914933	−	3.41458i	−0.0454634	−	0.169672i
$406$	−33.2783	−	43.9661i	−1.65158	−	2.18200i
$407$	−0.389277	+	0.224749i	−0.0192957	+	0.0111404i
$408$	−12.9589	+	3.47234i	−0.641563	+	0.171906i
$409$	4.11554	+	15.3594i	0.203501	+	0.759474i	0.989901	+	0.141758i	$0.0452754\pi$
$409$	4.11554	+	15.3594i	0.203501	+	0.759474i	−0.786401	+	0.617717i	$0.788058\pi$
$410$	−7.21775	−	26.9370i	−0.356459	−	1.33032i
$411$	7.61433	−	2.04025i	0.375587	−	0.100638i
$412$	63.1278	−	36.4468i	3.11008	−	1.79561i
$413$	−8.53926	+	1.06701i	−0.420189	+	0.0525042i
$414$	5.07358	+	18.9349i	0.249353	+	0.930598i
$415$	10.1010	+	5.83183i	0.495840	+	0.286274i
$416$	−74.7084	+	18.0884i	−3.66288	+	0.886855i
$417$	−5.95952	−	10.3222i	−0.291839	−	0.505480i
$418$	1.53378	+	0.410976i	0.0750198	+	0.0201015i
$419$	4.29128	+	2.47757i	0.209643	+	0.121037i	0.601145	−	0.799140i	$-0.294711\pi$
$419$	4.29128	+	2.47757i	0.209643	+	0.121037i	−0.391503	+	0.920177i	$0.628045\pi$
$420$	−46.8564	−	19.7713i	−2.28636	−	0.964743i
$421$	0.811225	+	0.811225i	0.0395367	+	0.0395367i	0.726599	−	0.687062i	$-0.241100\pi$
$421$	0.811225	+	0.811225i	0.0395367	+	0.0395367i	−0.687062	+	0.726599i	$0.741100\pi$
$422$	19.4326	+	19.4326i	0.945965	+	0.945965i
$423$	−0.906290	+	0.242840i	−0.0440653	+	0.0118073i
$424$	−44.9848	−	12.0536i	−2.18465	−	0.585376i
$425$			10.7277i			0.520369i
$426$	2.56963	−	4.45073i	0.124499	−	0.215638i
$427$	4.72045	−	34.1165i	0.228439	−	1.65101i
$428$			10.2758i			0.496697i
$429$	−1.09922	−	1.15387i	−0.0530707	−	0.0557092i
$430$	−69.4384	+	40.0903i	−3.34862	+	1.93333i
$431$	−14.4954	−	14.4954i	−0.698217	−	0.698217i	0.265809	−	0.964026i	$-0.414361\pi$
$431$	−14.4954	−	14.4954i	−0.698217	−	0.698217i	−0.964026	+	0.265809i	$0.914361\pi$
$432$	12.7240	−	7.34621i	0.612184	−	0.353445i
$433$	0.246122	+	0.426295i	0.0118279	+	0.0204864i	0.871879	−	0.489722i	$-0.162902\pi$
$433$	0.246122	+	0.426295i	0.0118279	+	0.0204864i	−0.860051	+	0.510208i	$0.829568\pi$
$434$	3.20452	−	4.11971i	0.153822	−	0.197752i
$435$	6.99187	−	26.0940i	0.335234	−	1.25111i
$436$	28.3596	−	28.3596i	1.35818	−	1.35818i
$437$	−2.45066	+	9.14599i	−0.117231	+	0.437512i
$438$	−17.3484	+	30.0483i	−0.828938	+	1.43576i
$439$	11.1891	+	19.3801i	0.534028	+	0.924963i	0.999210	+	0.0397478i	$0.0126555\pi$
$439$	11.1891	+	19.3801i	0.534028	+	0.924963i	−0.465182	+	0.885215i	$0.654011\pi$
$440$	14.1491	−	3.79124i	0.674533	−	0.180740i
$441$	−6.73701	−	1.90069i	−0.320810	−	0.0905092i
$442$	9.70585	+	10.1884i	0.461660	+	0.484613i
$443$	4.77420	−	8.26916i	0.226829	−	0.392880i	−0.730038	−	0.683407i	$-0.760497\pi$
$443$	4.77420	−	8.26916i	0.226829	−	0.392880i	0.956867	+	0.290527i	$0.0938308\pi$
$444$	−3.91024	+	3.91024i	−0.185572	+	0.185572i
$445$	36.9842			1.75322
$446$	−2.59407			−0.122833
$447$	−15.3953	+	15.3953i	−0.728172	+	0.728172i
$448$	10.4276	−	75.3644i	0.492660	−	3.56064i
$449$	−17.1874	−	4.60535i	−0.811124	−	0.217340i	−0.170662	−	0.985330i	$-0.554591\pi$
$449$	−17.1874	−	4.60535i	−0.811124	−	0.217340i	−0.640462	+	0.767990i	$0.721257\pi$
$450$	−5.29136	−	19.7476i	−0.249437	−	0.930913i
$451$	1.10725	+	0.639270i	0.0521383	+	0.0301021i
$452$			33.6460i			1.58257i
$453$	−3.61340	+	13.4854i	−0.169772	+	0.633598i
$454$	−66.8894			−3.13928
$455$	3.36854	+	33.5534i	0.157920	+	1.57301i
$456$	12.3498			0.578331
$457$	−7.13005	+	26.6097i	−0.333530	+	1.24475i	0.571925	+	0.820306i	$0.306197\pi$
$457$	−7.13005	+	26.6097i	−0.333530	+	1.24475i	−0.905455	+	0.424443i	$0.860470\pi$
$458$			56.2658i			2.62913i
$459$	−1.23932	−	0.715520i	−0.0578464	−	0.0333976i
$460$	35.7602	+	133.459i	1.66733	+	6.22255i
$461$	10.0918	+	2.70408i	0.470021	+	0.125942i	0.486052	−	0.873930i	$-0.338437\pi$
$461$	10.0918	+	2.70408i	0.470021	+	0.125942i	−0.0160314	+	0.999871i	$0.505103\pi$
$462$	2.95443	−	1.20102i	0.137453	−	0.0558764i
$463$	−10.7292	+	10.7292i	−0.498628	+	0.498628i	−0.911011	−	0.412382i	$-0.864697\pi$
$463$	−10.7292	+	10.7292i	−0.498628	+	0.498628i	0.412382	+	0.911011i	$0.364697\pi$
$464$	112.279			5.21241
$465$	2.55704			0.118580
$466$	−43.8461	+	43.8461i	−2.03113	+	2.03113i
$467$	7.08987	−	12.2800i	0.328080	−	0.568251i	−0.654051	−	0.756451i	$-0.726932\pi$
$467$	7.08987	−	12.2800i	0.328080	−	0.568251i	0.982131	+	0.188199i	$0.0602651\pi$
$468$	−16.7362	−	10.2116i	−0.773633	−	0.472033i
$469$	10.1475	+	13.4065i	0.468569	+	0.619056i
$470$	−8.73729	+	2.34115i	−0.403021	+	0.107989i
$471$	7.48759	+	12.9689i	0.345010	+	0.597574i
$472$	15.2468	−	26.4083i	0.701792	−	1.21554i
$473$	0.951424	−	3.55076i	0.0437465	−	0.163264i
$474$	−6.82869	+	6.82869i	−0.313652	+	0.313652i
$475$	2.55585	−	9.53857i	0.117271	−	0.437660i
$476$	−19.0721	+	7.75308i	−0.874169	+	0.355362i
$477$	−2.48381	−	4.30208i	−0.113726	−	0.196979i
$478$	69.3544	−	40.0418i	3.17220	−	1.83147i
$479$	17.7459	+	17.7459i	0.810829	+	0.810829i	0.984758	−	0.173929i	$-0.0556463\pi$
$479$	17.7459	+	17.7459i	0.810829	+	0.810829i	−0.173929	+	0.984758i	$0.555646\pi$
$480$	65.2667	−	37.6817i	2.97900	−	1.71993i
$481$	3.51775	+	1.03463i	0.160396	+	0.0471751i
$482$			18.4951i			0.842431i
$483$	7.16169	+	17.6174i	0.325868	+	0.801617i
$484$	29.3757	−	50.8803i	1.33526	−	2.31274i
$485$		−	9.20473i		−	0.417965i
$486$	2.63427	+	0.705851i	0.119493	+	0.0320181i
$487$	23.4418	−	6.28121i	1.06225	−	0.284629i	0.314944	−	0.949110i	$-0.398014\pi$
$487$	23.4418	−	6.28121i	1.06225	−	0.284629i	0.747305	+	0.664481i	$0.231347\pi$
$488$	86.2963	+	86.2963i	3.90645	+	3.90645i
$489$	−6.25479	−	6.25479i	−0.282851	−	0.282851i
$490$	−64.9497	−	18.3241i	−2.93413	−	0.827797i
$491$	−9.68019	−	5.58886i	−0.436861	−	0.252222i	0.265404	−	0.964137i	$-0.414495\pi$
$491$	−9.68019	−	5.58886i	−0.436861	−	0.252222i	−0.702265	+	0.711915i	$0.747828\pi$
$492$	15.1932	+	4.07100i	0.684961	+	0.183535i
$493$	−5.46796	−	9.47079i	−0.246265	−	0.426543i
$494$	−6.20263	−	11.3715i	−0.279069	−	0.511626i
$495$	1.35314	+	0.781234i	0.0608190	+	0.0351139i
$496$	2.75065	+	10.2656i	0.123508	+	0.460937i
$497$	1.93829	−	4.59358i	0.0869441	−	0.206050i
$498$	−7.79273	+	4.49914i	−0.349201	+	0.201611i
$499$	38.1144	−	10.2127i	1.70623	−	0.457184i	0.731737	−	0.681587i	$-0.238710\pi$
$499$	38.1144	−	10.2127i	1.70623	−	0.457184i	0.974496	+	0.224403i	$0.0720431\pi$
$500$	−12.4199	−	46.3516i	−0.555434	−	2.07291i
$501$	0.0887813	+	0.331336i	0.00396645	+	0.0148030i
$502$	−14.9388	+	4.00284i	−0.666751	+	0.178655i
$503$	7.48538	−	4.32169i	0.333757	−	0.192694i	−0.323751	−	0.946142i	$-0.604944\pi$
$503$	7.48538	−	4.32169i	0.333757	−	0.192694i	0.657508	+	0.753448i	$0.271611\pi$
$504$	19.7775	−	14.9698i	0.880959	−	0.666806i
$505$	−1.32275	−	4.93657i	−0.0588616	−	0.219674i
$506$	−7.50357	−	4.33219i	−0.333574	−	0.192589i
$507$	−0.630284	+	12.9847i	−0.0279919	+	0.576671i
$508$	−18.5297	−	32.0945i	−0.822125	−	1.42396i
$509$	5.40390	+	1.44797i	0.239524	+	0.0641801i	0.376584	−	0.926383i	$-0.377099\pi$
$509$	5.40390	+	1.44797i	0.239524	+	0.0641801i	−0.137060	+	0.990563i	$0.543765\pi$
$510$	−11.9479	−	6.89813i	−0.529063	−	0.305454i
$511$	−13.0860	+	31.0127i	−0.578891	+	1.37192i
$512$	26.6889	+	26.6889i	1.17950	+	1.17950i
$513$	0.931473	+	0.931473i	0.0411255	+	0.0411255i
$514$	3.14525	−	0.842768i	0.138731	−	0.0371729i
$515$	45.7739	+	12.2651i	2.01704	+	0.540464i
$516$		−	45.2239i		−	1.99087i
$517$	0.207354	−	0.359147i	0.00911940	−	0.0157953i
$518$	−4.50534	+	5.79203i	−0.197953	+	0.254487i
$519$			9.25073i			0.406062i
$520$	−102.004	−	62.2378i	−4.47317	−	2.72931i
$521$	5.55782	−	3.20881i	0.243493	−	0.140581i	−0.373288	−	0.927715i	$-0.621770\pi$
$521$	5.55782	−	3.20881i	0.243493	−	0.140581i	0.616781	+	0.787135i	$0.288436\pi$
$522$	14.7369	+	14.7369i	0.645016	+	0.645016i
$523$	27.3972	−	15.8178i	1.19799	−	0.691663i	0.237887	−	0.971293i	$-0.423545\pi$
$523$	27.3972	−	15.8178i	1.19799	−	0.691663i	0.960108	+	0.279630i	$0.0902119\pi$
$524$	9.98229	+	17.2898i	0.436078	+	0.755310i
$525$	−7.46910	−	18.3736i	−0.325978	−	0.801888i
$526$	−17.0232	+	63.5316i	−0.742248	+	2.77011i
$527$	0.731951	−	0.731951i	0.0318843	−	0.0318843i
$528$	−1.68077	+	6.27272i	−0.0731461	+	0.272985i
$529$	14.3329	−	24.8254i	0.623171	−	1.07936i
$530$	−23.9457	−	41.4752i	−1.04014	−	1.80157i
$531$	3.14180	−	0.841844i	0.136343	−	0.0365329i
$532$	18.8052	−	2.34978i	0.815310	−	0.101876i
$533$	−2.45430	−	10.1367i	−0.106307	−	0.439070i
$534$	−14.2663	+	24.7099i	−0.617361	+	1.06930i
$535$	−4.72371	+	4.72371i	−0.204224	+	0.204224i
$536$	−59.5790			−2.57342
$537$	14.6054			0.630269
$538$	35.5814	−	35.5814i	1.53402	−	1.53402i
$539$	2.69962	−	1.51154i	0.116281	−	0.0651065i
$540$	18.5671	+	4.97505i	0.799003	+	0.214092i
$541$	4.90078	+	18.2900i	0.210701	+	0.786347i	0.987636	+	0.156766i	$0.0501068\pi$
$541$	4.90078	+	18.2900i	0.210701	+	0.786347i	−0.776935	+	0.629581i	$0.783227\pi$
$542$	2.32167	+	1.34041i	0.0997241	+	0.0575758i
$543$			8.63806i			0.370695i
$544$	7.89616	−	29.4689i	0.338545	−	1.26347i
$545$	26.0735			1.11686
$546$	−23.7171	−	10.6923i	−1.01500	−	0.457587i
$547$	−13.7543			−0.588091			−0.294046	−	0.955791i	$-0.595002\pi$
$547$	−13.7543			−0.588091			−0.294046	+	0.955791i	$0.595002\pi$
$548$	−11.0941	+	41.4038i	−0.473917	+	1.76868i
$549$			13.0177i			0.555580i
$550$	7.82565	+	4.51814i	0.333687	+	0.192654i
$551$	2.60546	+	9.72373i	0.110997	+	0.414245i
$552$	−65.0908	−	17.4410i	−2.77045	−	0.742340i
$553$	−5.75223	+	7.39503i	−0.244610	+	0.314468i
$554$	−34.8038	+	34.8038i	−1.47867	+	1.47867i
$555$	−3.59503			−0.152601
$556$	64.8112			2.74861
$557$	−12.1953	+	12.1953i	−0.516731	+	0.516731i	−0.916581	−	0.399850i	$-0.869062\pi$
$557$	−12.1953	+	12.1953i	−0.516731	+	0.516731i	0.399850	+	0.916581i	$0.369062\pi$
$558$	−0.986352	+	1.70841i	−0.0417556	+	0.0723228i
$559$	−26.3253	+	14.3593i	−1.11344	+	0.607334i
$560$	109.568	−	82.9329i	4.63009	−	3.50456i
$561$	0.610962	−	0.163707i	0.0257948	−	0.00691170i
$562$	−29.7339	−	51.5006i	−1.25425	−	2.17242i
$563$	16.5277	−	28.6268i	0.696559	−	1.20648i	−0.273093	−	0.961988i	$-0.588047\pi$
$563$	16.5277	−	28.6268i	0.696559	−	1.20648i	0.969652	−	0.244488i	$-0.0786200\pi$
$564$	1.32047	−	4.92806i	0.0556017	−	0.207509i
$565$	−15.4669	+	15.4669i	−0.650697	+	0.650697i
$566$	−19.3912	+	72.3688i	−0.815071	+	3.04189i
$567$	2.62078	+	0.362619i	0.110063	+	0.0152286i
$568$	8.83340	+	15.2999i	0.370641	+	0.641969i
$569$	−28.5293	+	16.4714i	−1.19601	+	0.690518i	−0.959664	−	0.281151i	$-0.909284\pi$
$569$	−28.5293	+	16.4714i	−1.19601	+	0.690518i	−0.236348	+	0.971669i	$0.575950\pi$
$570$	8.98007	+	8.98007i	0.376134	+	0.376134i
$571$	−6.40074	+	3.69547i	−0.267862	+	0.154650i	−0.627916	−	0.778281i	$-0.716092\pi$
$571$	−6.40074	+	3.69547i	−0.267862	+	0.154650i	0.360053	+	0.932932i	$0.382758\pi$
$572$	8.42225	−	2.03919i	0.352152	−	0.0852629i
$573$		−	7.04823i		−	0.294444i
$574$	20.6749	+	2.86064i	0.862955	+	0.119401i
$575$	−26.9418	+	46.6645i	−1.12355	+	1.94605i
$576$			28.7565i			1.19819i
$577$	−37.8634	−	10.1455i	−1.57627	−	0.422362i	−0.638505	−	0.769618i	$-0.720447\pi$
$577$	−37.8634	−	10.1455i	−1.57627	−	0.422362i	−0.937770	+	0.347257i	$0.887113\pi$
$578$	39.3880	−	10.5540i	1.63832	−	0.438987i
$579$	16.3420	+	16.3420i	0.679152	+	0.679152i
$580$	103.870	+	103.870i	4.31297	+	4.31297i
$581$	−6.96048	+	5.26845i	−0.288769	+	0.218572i
$582$	6.14986	+	3.55062i	0.254920	+	0.147178i
$583$	2.12085	+	0.568280i	0.0878367	+	0.0235358i
$584$	−59.6371	−	103.294i	−2.46780	−	4.27435i
$585$	−2.99933	−	12.3878i	−0.124007	−	0.512173i
$586$	18.5401	+	10.7041i	0.765886	+	0.442184i
$587$	−5.58839	−	20.8562i	−0.230658	−	0.860826i	−0.980058	−	0.198709i	$-0.936325\pi$
$587$	−5.58839	−	20.8562i	−0.230658	−	0.860826i	0.749401	−	0.662117i	$-0.230342\pi$
$588$	27.2672	−	26.5577i	1.12448	−	1.09522i
$589$	−0.825203	+	0.476431i	−0.0340019	+	0.0196310i
$590$	30.2893	−	8.11599i	1.24699	−	0.334130i
$591$	−5.02954	−	18.7705i	−0.206888	−	0.772116i
$592$	−3.86723	−	14.4327i	−0.158942	−	0.593180i
$593$	−29.2070	+	7.82600i	−1.19939	+	0.321375i	−0.802591	−	0.596530i	$-0.796546\pi$
$593$	−29.2070	+	7.82600i	−1.19939	+	0.321375i	−0.396799	+	0.917906i	$0.629879\pi$
$594$	−1.04392	+	0.602706i	−0.0428324	+	0.0247293i
$595$	−12.3314	−	5.20331i	−0.505538	−	0.213315i
$596$	−30.6413	−	114.355i	−1.25512	−	4.68416i
$597$	15.4246	+	8.90538i	0.631285	+	0.364473i
$598$	16.6322	+	68.6942i	0.680142	+	2.80911i
$599$	9.06280	+	15.6972i	0.370296	+	0.641371i	0.989611	−	0.143771i	$-0.0459230\pi$
$599$	9.06280	+	15.6972i	0.370296	+	0.641371i	−0.619315	+	0.785143i	$0.712590\pi$
$600$	67.8848	+	18.1897i	2.77138	+	0.742590i
$601$	30.9648	+	17.8775i	1.26308	+	0.729240i	0.973669	−	0.227965i	$-0.0732073\pi$
$601$	30.9648	+	17.8775i	1.26308	+	0.729240i	0.289411	+	0.957205i	$0.406541\pi$
$602$	−7.44064	−	59.5472i	−0.303258	−	2.42696i
$603$	−4.49370	−	4.49370i	−0.182998	−	0.182998i
$604$	−53.6800	−	53.6800i	−2.18421	−	2.18421i
$605$	36.8933	−	9.88552i	1.49992	−	0.401904i
$606$	3.80846	+	1.02047i	0.154708	+	0.0414539i
$607$			3.81356i			0.154787i	0.997001	+	0.0773937i	$0.0246598\pi$
$607$			3.81356i			0.154787i	−0.997001	+	0.0773937i	$0.975340\pi$
$608$	−14.0418	+	24.3211i	−0.569470	+	0.986352i
$609$	15.9591	+	12.4138i	0.646695	+	0.503033i
$610$			125.500i			5.08133i
$611$	−3.28795	+	0.796076i	−0.133016	+	0.0322058i
$612$	6.73893	−	3.89072i	0.272405	−	0.157273i
$613$	2.91437	+	2.91437i	0.117710	+	0.117710i	0.763508	−	0.645798i	$-0.223475\pi$
$613$	2.91437	+	2.91437i	0.117710	+	0.117710i	−0.645798	+	0.763508i	$0.723475\pi$
$614$	53.8504	−	31.0905i	2.17323	−	1.25471i
$615$	5.11280	+	8.85563i	0.206168	+	0.357094i
$616$	−1.50260	+	10.8598i	−0.0605415	+	0.437556i
$617$	4.26184	−	15.9054i	0.171575	−	0.640327i	−0.825535	−	0.564351i	$-0.809126\pi$
$617$	4.26184	−	15.9054i	0.171575	−	0.640327i	0.997110	−	0.0759754i	$-0.0242070\pi$
$618$	−25.8513	+	25.8513i	−1.03989	+	1.03989i
$619$	2.63282	−	9.82581i	0.105822	−	0.394933i	−0.892615	−	0.450819i	$-0.851132\pi$
$619$	2.63282	−	9.82581i	0.105822	−	0.394933i	0.998437	+	0.0558866i	$0.0177985\pi$
$620$	−6.95211	+	12.0414i	−0.279203	+	0.483595i
$621$	−3.59395	−	6.22490i	−0.144220	−	0.249797i
$622$	14.5191	−	3.89037i	0.582161	−	0.155990i
$623$	−10.7611	+	25.5030i	−0.431135	+	1.02176i
$624$	46.5059	−	25.3669i	1.86173	−	1.01549i
$625$	−3.14284	+	5.44356i	−0.125714	+	0.217743i
$626$	37.4320	−	37.4320i	1.49608	−	1.49608i
$627$	−0.582242			−0.0232525
$628$	−81.4292			−3.24938
$629$	−1.02907	+	1.02907i	−0.0410318	+	0.0410318i
$630$	25.2663	+	3.49591i	1.00663	+	0.139281i
$631$	−35.7618	−	9.58236i	−1.42366	−	0.381468i	−0.536877	−	0.843661i	$-0.680396\pi$
$631$	−35.7618	−	9.58236i	−1.42366	−	0.381468i	−0.886779	+	0.462193i	$0.847063\pi$
$632$	−8.59222	−	32.0666i	−0.341780	−	1.27554i
$633$	−8.72690	−	5.03848i	−0.346863	−	0.200262i
$634$			76.5747i			3.04117i
$635$	6.23563	−	23.2717i	0.247453	−	0.923509i
$636$	27.0120			1.07109
$637$	−24.1173	−	7.44005i	−0.955563	−	0.294786i
$638$	−9.21169			−0.364694
$639$	−0.487730	+	1.82023i	−0.0192943	+	0.0720074i
$640$			126.506i			5.00060i
$641$	−26.1041	−	15.0712i	−1.03105	−	0.595278i	−0.113766	−	0.993508i	$-0.536291\pi$
$641$	−26.1041	−	15.0712i	−1.03105	−	0.595278i	−0.917286	+	0.398230i	$0.869625\pi$
$642$	−1.33388	−	4.97813i	−0.0526442	−	0.196471i
$643$	−36.7921	−	9.85840i	−1.45094	−	0.388778i	−0.554588	−	0.832125i	$-0.687124\pi$
$643$	−36.7921	−	9.85840i	−1.45094	−	0.388778i	−0.896350	+	0.443348i	$0.853791\pi$
$644$	−102.433	−	14.1730i	−4.03644	−	0.558494i
$645$	20.7892	−	20.7892i	0.818573	−	0.818573i
$646$	5.14107			0.202273
$647$	−38.7803			−1.52461			−0.762305	−	0.647218i	$-0.775933\pi$
$647$	−38.7803			−1.52461			−0.762305	+	0.647218i	$0.775933\pi$
$648$	−6.62917	+	6.62917i	−0.260418	+	0.260418i
$649$	−0.718826	+	1.24504i	−0.0282164	+	0.0488722i
$650$	−17.3461	−	71.6428i	−0.680371	−	2.81006i
$651$	−0.744012	+	1.76325i	−0.0291601	+	0.0691071i
$652$	46.4600	−	12.4489i	1.81952	−	0.487538i
$653$	6.50852	+	11.2731i	0.254698	+	0.441150i	0.964813	−	0.262935i	$-0.0846906\pi$
$653$	6.50852	+	11.2731i	0.254698	+	0.441150i	−0.710115	+	0.704085i	$0.751357\pi$
$654$	−10.0576	+	17.4202i	−0.393282	+	0.681184i
$655$	−3.35924	+	12.5368i	−0.131256	+	0.489855i
$656$	−30.0521	+	30.0521i	−1.17334	+	1.17334i
$657$	3.29282	−	12.2890i	0.128465	−	0.479439i
$658$	0.927878	−	6.70612i	0.0361725	−	0.261432i
$659$	25.0015	+	43.3039i	0.973921	+	1.68688i	0.683451	+	0.729996i	$0.260478\pi$
$659$	25.0015	+	43.3039i	0.973921	+	1.68688i	0.290470	+	0.956884i	$0.406188\pi$
$660$	−7.35784	+	4.24805i	−0.286404	+	0.165355i
$661$	−9.11369	−	9.11369i	−0.354481	−	0.354481i	0.507292	−	0.861774i	$-0.330646\pi$
$661$	−9.11369	−	9.11369i	−0.354481	−	0.354481i	−0.861774	+	0.507292i	$0.830646\pi$
$662$	17.9333	−	10.3538i	0.696999	−	0.402413i
$663$	−4.40455	−	2.68744i	−0.171058	−	0.104371i
$664$		−	30.9326i		−	1.20042i
$665$	9.72484	+	7.56448i	0.377113	+	0.293338i
$666$	1.38674	−	2.40191i	0.0537353	−	0.0930722i
$667$		−	54.9295i		−	2.12688i
$668$	−1.80168	−	0.482758i	−0.0697090	−	0.0186785i
$669$	0.918774	−	0.246185i	0.0355218	−	0.00951805i
$670$	−43.3226	−	43.3226i	−1.67370	−	1.67370i
$671$	−4.06852	−	4.06852i	−0.157063	−	0.157063i
$672$	6.99362	+	55.9697i	0.269785	+	2.15908i
$673$	34.5128	+	19.9259i	1.33037	+	0.768089i	0.985356	−	0.170509i	$-0.0545413\pi$
$673$	34.5128	+	19.9259i	1.33037	+	0.768089i	0.345013	+	0.938598i	$0.387875\pi$
$674$	−8.59270	−	2.30241i	−0.330978	−	0.0886854i
$675$	3.74822	+	6.49210i	0.144269	+	0.249881i
$676$	−59.4329	−	38.2710i	−2.28588	−	1.47196i
$677$	−3.61272	−	2.08580i	−0.138848	−	0.0801640i	0.428967	−	0.903320i	$-0.358878\pi$
$677$	−3.61272	−	2.08580i	−0.138848	−	0.0801640i	−0.567815	+	0.823156i	$0.692211\pi$
$678$	−4.36755	−	16.2999i	−0.167735	−	0.625995i
$679$	6.34725	+	2.67826i	0.243585	+	0.102782i
$680$	41.0723	−	23.7131i	1.57505	−	0.909357i
$681$	23.6911	−	6.34800i	0.907843	−	0.243256i
$682$	−0.225671	−	0.842217i	−0.00864141	−	0.0322502i
$683$	1.82696	+	6.81833i	0.0699069	+	0.260896i	0.992030	−	0.126000i	$-0.0402139\pi$
$683$	1.82696	+	6.81833i	0.0699069	+	0.260896i	−0.922123	+	0.386896i	$0.873547\pi$
$684$	−6.91890	+	1.85391i	−0.264551	+	0.0708862i
$685$	−24.1330	+	13.9332i	−0.922075	+	0.532360i
$686$	31.5338	−	39.4553i	1.20396	−	1.50641i
$687$	−5.33978	−	19.9283i	−0.203725	−	0.760314i
$688$	105.824	+	61.0974i	4.03450	+	2.32932i
$689$	−8.57673	−	15.7240i	−0.326747	−	0.599036i
$690$	−34.6483	−	60.0126i	−1.31904	−	2.28464i
$691$	−21.8060	−	5.84290i	−0.829539	−	0.222274i	−0.181026	−	0.983478i	$-0.557942\pi$
$691$	−21.8060	−	5.84290i	−0.829539	−	0.222274i	−0.648512	+	0.761204i	$0.724609\pi$
$692$	−43.5627	−	25.1510i	−1.65601	−	0.956096i
$693$	−0.932428	+	0.705763i	−0.0354200	+	0.0268097i
$694$	−59.7165	−	59.7165i	−2.26681	−	2.26681i
$695$	29.7934	+	29.7934i	1.13013	+	1.13013i
$696$	−69.2025	+	18.5428i	−2.62311	+	0.702861i
$697$	3.99845	+	1.07138i	0.151452	+	0.0405815i
$698$		−	33.0634i		−	1.25147i
$699$	11.3684	−	19.6906i	0.429992	−	0.744768i
$700$	106.830	+	14.7813i	4.03780	+	0.558682i
$701$			38.0674i			1.43779i	0.695120	+	0.718894i	$0.255351\pi$
$701$			38.0674i			1.43779i	−0.695120	+	0.718894i	$0.744649\pi$
$702$	9.43350	+	2.77455i	0.356044	+	0.104719i
$703$	1.16018	−	0.669830i	0.0437570	−	0.0252631i
$704$	−8.98750	−	8.98750i	−0.338729	−	0.338729i
$705$	2.87241	−	1.65839i	0.108181	−	0.0624585i
$706$	40.0960	+	69.4484i	1.50903	+	2.61372i
$707$	3.78896	+	0.524251i	0.142498	+	0.0197165i
$708$	−4.57762	+	17.0839i	−0.172038	+	0.642053i
$709$	−1.28394	+	1.28394i	−0.0482195	+	0.0482195i	−0.730805	−	0.682586i	$-0.760855\pi$
$709$	−1.28394	+	1.28394i	−0.0482195	+	0.0482195i	0.682586	+	0.730805i	$0.260855\pi$
$710$	−4.70208	+	17.5484i	−0.176466	+	0.658579i
$711$	1.77054	−	3.06666i	0.0664004	−	0.115009i
$712$	−49.0419	−	84.9430i	−1.83792	−	3.18337i
$713$	5.02216	−	1.34568i	0.188081	−	0.0503963i
$714$	8.23314	−	6.23174i	0.308118	−	0.233217i
$715$	4.80907	+	2.93426i	0.179849	+	0.109735i
$716$	−39.7092	+	68.7784i	−1.48400	+	2.57037i
$717$	−20.7640	+	20.7640i	−0.775447	+	0.775447i
$718$	−25.3918			−0.947612
$719$	27.5916			1.02899			0.514496	−	0.857493i	$-0.327979\pi$
$719$	27.5916			1.02899			0.514496	+	0.857493i	$0.327979\pi$
$720$	−36.7258	+	36.7258i	−1.36869	+	1.36869i
$721$	−21.7762	+	27.9953i	−0.810988	+	1.04260i
$722$	45.4800	+	12.1863i	1.69259	+	0.453528i
$723$	−1.75524	−	6.55065i	−0.0652781	−	0.243621i
$724$	−40.6776	−	23.4852i	−1.51177	−	0.872822i
$725$			57.2873i			2.12760i
$726$	−7.62647	+	28.4624i	−0.283045	+	1.05634i
$727$	−1.57479			−0.0584058			−0.0292029	−	0.999574i	$-0.509297\pi$
$727$	−1.57479			−0.0584058			−0.0292029	+	0.999574i	$0.509297\pi$
$728$	72.5966	−	52.2292i	2.69061	−	1.93574i
$729$	−1.00000			−0.0370370
$730$	31.7452	−	118.475i	1.17494	−	4.38495i
$731$		−	11.9018i		−	0.440202i
$732$	−61.3016	−	35.3925i	−2.26577	−	1.30814i
$733$	−10.0600	−	37.5443i	−0.371574	−	1.38673i	−0.858287	−	0.513170i	$-0.828471\pi$
$733$	−10.0600	−	37.5443i	−0.371574	−	1.38673i	0.486713	−	0.873562i	$-0.338196\pi$
$734$	−66.4456	−	17.8040i	−2.45255	−	0.657159i
$735$	24.7431	+	0.326147i	0.912661	+	0.0120301i
$736$	108.356	−	108.356i	3.99407	−	3.99407i
$737$	2.80891			0.103467
$738$	−7.88884			−0.290392
$739$	30.9642	−	30.9642i	1.13904	−	1.13904i	0.150414	−	0.988623i	$-0.451939\pi$
$739$	30.9642	−	30.9642i	1.13904	−	1.13904i	0.988623	−	0.150414i	$-0.0480607\pi$
$740$	9.77420	−	16.9294i	0.359307	−	0.622337i
$741$	3.27605	+	3.43892i	0.120349	+	0.126332i
$742$	35.5672	−	4.44425i	1.30571	−	0.163154i
$743$	18.3147	−	4.90740i	0.671900	−	0.180035i	0.0932893	−	0.995639i	$-0.470262\pi$
$743$	18.3147	−	4.90740i	0.671900	−	0.180035i	0.578610	+	0.815604i	$0.303595\pi$
$744$	−3.39070	−	5.87286i	−0.124309	−	0.215310i
$745$	38.4827	−	66.6541i	1.40990	−	2.44202i
$746$	−0.739970	+	2.76160i	−0.0270922	+	0.101110i
$747$	2.33307	−	2.33307i	0.0853625	−	0.0853625i
$748$	−0.890174	+	3.32217i	−0.0325480	+	0.121471i
$749$	−1.88286	−	4.63174i	−0.0687984	−	0.169240i
$750$	12.0337	+	20.8430i	0.439409	+	0.761078i
$751$	9.94670	−	5.74273i	0.362960	−	0.209555i	−0.307418	−	0.951574i	$-0.599465\pi$
$751$	9.94670	−	5.74273i	0.362960	−	0.209555i	0.670378	+	0.742019i	$0.266132\pi$
$752$	9.74769	+	9.74769i	0.355462	+	0.355462i
$753$	4.91118	−	2.83547i	0.178973	−	0.103330i
$754$	51.8305	+	54.4074i	1.88756	+	1.98140i
$755$		−	49.3529i		−	1.79613i
$756$	−8.83302	+	11.3557i	−0.321254	+	0.413002i
$757$	0.505532	−	0.875607i	0.0183739	−	0.0318245i	−0.856692	−	0.515828i	$-0.827484\pi$
$757$	0.505532	−	0.875607i	0.0183739	−	0.0318245i	0.875066	+	0.484003i	$0.160818\pi$
$758$			43.1999i			1.56909i
$759$	3.06877	+	0.822274i	0.111389	+	0.0298467i
$760$	−42.1693	+	11.2992i	−1.52964	+	0.409866i
$761$	32.8804	+	32.8804i	1.19191	+	1.19191i	0.976530	+	0.215383i	$0.0691001\pi$
$761$	32.8804	+	32.8804i	1.19191	+	1.19191i	0.215383	+	0.976530i	$0.430900\pi$
$762$	13.1430	+	13.1430i	0.476119	+	0.476119i
$763$	−7.58649	+	17.9793i	−0.274649	+	0.650896i
$764$	33.1909	+	19.1628i	1.20080	+	0.693285i
$765$	4.88639	+	1.30931i	0.176668	+	0.0473380i
$766$	−35.4216	−	61.3520i	−1.27983	−	2.21674i
$767$	11.3982	−	2.75973i	0.411565	−	0.0996481i
$768$	−34.7137	−	20.0419i	−1.25262	−	0.723202i
$769$	−10.0112	−	37.3624i	−0.361014	−	1.34732i	−0.872745	−	0.488177i	$-0.837662\pi$
$769$	−10.0112	−	37.3624i	−0.361014	−	1.34732i	0.511730	−	0.859146i	$-0.329005\pi$
$770$	−8.98929	+	6.80407i	−0.323951	+	0.245202i
$771$	−1.03401	+	0.596987i	−0.0372390	+	0.0215000i
$772$	−121.387	+	32.5256i	−4.36882	+	1.17062i
$773$	7.72212	+	28.8193i	0.277745	+	1.03656i	0.953979	+	0.299872i	$0.0969441\pi$
$773$	7.72212	+	28.8193i	0.277745	+	1.03656i	−0.676234	+	0.736687i	$0.736389\pi$
$774$	5.87046	+	21.9089i	0.211009	+	0.787498i
$775$	−5.23773	+	1.40345i	−0.188145	+	0.0504133i
$776$	−21.1409	+	12.2057i	−0.758913	+	0.438158i
$777$	1.04603	−	2.47901i	0.0375261	−	0.0889338i
$778$	16.3412	+	60.9862i	0.585861	+	2.18646i
$779$	−3.29998	−	1.90525i	−0.118234	−	0.0682625i
$780$	66.4902	+	19.5559i	2.38073	+	0.700212i
$781$	−0.416459	−	0.721328i	−0.0149021	−	0.0258111i
$782$	−27.0966	−	7.26050i	−0.968971	−	0.259635i
$783$	−6.61812	−	3.82097i	−0.236512	−	0.136550i
$784$	25.3071	+	99.6848i	0.903825	+	3.56017i
$785$	−37.4326	−	37.4326i	−1.33603	−	1.33603i
$786$	−7.08033	−	7.08033i	−0.252547	−	0.252547i
$787$	4.27040	−	1.14425i	0.152223	−	0.0407881i	−0.181903	−	0.983317i	$-0.558226\pi$
$787$	4.27040	−	1.14425i	0.152223	−	0.0407881i	0.334126	+	0.942528i	$0.391559\pi$
$788$	102.067	+	27.3487i	3.63598	+	0.974258i
$789$		−	24.1173i		−	0.858599i
$790$	17.0693	−	29.5649i	0.607298	−	1.05187i
$791$	−6.16508	−	15.1657i	−0.219205	−	0.539232i
$792$		−	4.14374i		−	0.147241i
$793$	−1.13814	+	46.9220i	−0.0404165	+	1.66625i
$794$	−27.9221	+	16.1209i	−0.990920	+	0.572108i
$795$	12.4173	+	12.4173i	0.440395	+	0.440395i
$796$	−83.8729	+	48.4240i	−2.97279	+	1.71634i
$797$	8.62284	+	14.9352i	0.305437	+	0.529032i	0.977358	−	0.211590i	$-0.0678642\pi$
$797$	8.62284	+	14.9352i	0.305437	+	0.529032i	−0.671922	+	0.740622i	$0.734531\pi$
$798$	−8.80523	+	3.57945i	−0.311702	+	0.126711i
$799$	0.347513	−	1.29694i	0.0122941	−	0.0458823i
$800$	−113.008	+	113.008i	−3.99542	+	3.99542i
$801$	2.70782	−	10.1057i	0.0956760	−	0.357068i
$802$	−28.4061	+	49.2008i	−1.00305	+	1.73734i
$803$	2.81165	+	4.86991i	0.0992208	+	0.171856i
$804$	33.3789	−	8.94384i	1.17718	−	0.315425i
$805$	−40.5728	−	53.6033i	−1.43000	−	1.88927i
$806$	−3.70466	+	6.07172i	−0.130491	+	0.213867i
$807$	−9.22552	+	15.9791i	−0.324754	+	0.562490i
$808$	−9.58401	+	9.58401i	−0.337164	+	0.337164i
$809$	23.5998			0.829724			0.414862	−	0.909884i	$-0.363830\pi$
$809$	23.5998			0.829724			0.414862	+	0.909884i	$0.363830\pi$
$810$	−9.64073			−0.338741
$811$	−16.8186	+	16.8186i	−0.590582	+	0.590582i	−0.937789	−	0.347207i	$-0.887130\pi$
$811$	−16.8186	+	16.8186i	−0.590582	+	0.590582i	0.347207	+	0.937789i	$0.387130\pi$
$812$	−101.848	+	41.4025i	−3.57415	+	1.45294i
$813$	−0.949503	−	0.254418i	−0.0333005	−	0.00892285i
$814$	0.317279	+	1.18410i	0.0111206	+	0.0415027i
$815$	27.0801	+	15.6347i	0.948576	+	0.547661i
$816$			21.0254i			0.736038i
$817$	−2.83557	+	10.5825i	−0.0992041	+	0.370235i
$818$	43.3659			1.51625
$819$	9.41489	+	1.53619i	0.328983	+	0.0536790i
$820$	−55.6029			−1.94174
$821$	4.64880	−	17.3495i	0.162244	−	0.605503i	−0.836132	−	0.548529i	$-0.815188\pi$
$821$	4.64880	−	17.3495i	0.162244	−	0.605503i	0.998376	−	0.0569742i	$-0.0181453\pi$
$822$		−	21.4983i		−	0.749840i
$823$	24.0752	+	13.8998i	0.839209	+	0.484518i	0.856995	−	0.515324i	$-0.172329\pi$
$823$	24.0752	+	13.8998i	0.839209	+	0.484518i	−0.0177863	+	0.999842i	$0.505662\pi$
$824$	−32.5276	−	121.395i	−1.13315	−	4.22898i
$825$	−3.20049	−	0.857569i	−0.111427	−	0.0298567i
$826$	−3.21665	+	23.2479i	−0.111921	+	0.808897i
$827$	−19.2095	+	19.2095i	−0.667980	+	0.667980i	−0.957248	−	0.289268i	$-0.906588\pi$
$827$	−19.2095	+	19.2095i	−0.667980	+	0.667980i	0.289268	+	0.957248i	$0.406588\pi$
$828$	39.0850			1.35830
$829$	40.3767			1.40234			0.701170	−	0.712994i	$-0.252661\pi$
$829$	40.3767			1.40234			0.701170	+	0.712994i	$0.252661\pi$
$830$	22.4925	−	22.4925i	0.780725	−	0.780725i
$831$	9.02390	−	15.6299i	0.313036	−	0.542194i
$832$	−2.51419	+	103.652i	−0.0871637	+	3.59350i
$833$	7.17603	−	6.98931i	0.248635	−	0.242165i
$834$	−31.3980	+	8.41307i	−1.08722	+	0.291321i
$835$	−0.606301	−	1.05014i	−0.0209819	−	0.0363417i
$836$	1.58300	−	2.74184i	0.0547493	−	0.0948286i
$837$	0.187215	−	0.698697i	0.00647111	−	0.0241505i
$838$	9.55559	−	9.55559i	0.330092	−	0.330092i
$839$	3.20470	−	11.9601i	0.110638	−	0.412908i	−0.888285	−	0.459292i	$-0.848103\pi$
$839$	3.20470	−	11.9601i	0.110638	−	0.412908i	0.998924	+	0.0463840i	$0.0147698\pi$
$840$	−53.8354	+	69.2104i	−1.85750	+	2.38799i
$841$	−14.6997	−	25.4606i	−0.506885	−	0.877951i
$842$	2.70959	−	1.56438i	0.0933787	−	0.0539122i
$843$	15.4188	+	15.4188i	0.531051	+	0.531051i
$844$	47.4535	−	27.3973i	1.63342	−	0.943055i
$845$	−9.72799	−	44.9140i	−0.334653	−	1.54509i
$846$			2.55882i			0.0879741i
$847$	−3.91797	+	28.3166i	−0.134623	+	0.972971i
$848$	−36.4932	+	63.2080i	−1.25318	+	2.17057i
$849$		−	27.4720i		−	0.942837i
$850$	28.2597	+	7.57215i	0.969298	+	0.259723i
$851$	−7.06082	+	1.89194i	−0.242042	+	0.0648549i
$852$	−7.24564	−	7.24564i	−0.248232	−	0.248232i
$853$	−30.9345	−	30.9345i	−1.05918	−	1.05918i	−0.998135	−	0.0610421i	$-0.980558\pi$
$853$	−30.9345	−	30.9345i	−1.05918	−	1.05918i	−0.0610421	−	0.998135i	$-0.519442\pi$
$854$	−86.5401	−	36.5161i	−2.96134	−	1.24956i
$855$	−4.03282	−	2.32835i	−0.137919	−	0.0796279i
$856$	17.1129	+	4.58538i	0.584906	+	0.156725i
$857$	−4.46536	−	7.73423i	−0.152534	−	0.264196i	0.779624	−	0.626247i	$-0.215410\pi$
$857$	−4.46536	−	7.73423i	−0.152534	−	0.264196i	−0.932158	+	0.362051i	$0.882077\pi$
$858$	−3.81548	+	2.08118i	−0.130258	+	0.0710502i
$859$	21.5650	+	12.4506i	0.735789	+	0.424808i	0.820536	−	0.571594i	$-0.193675\pi$
$859$	21.5650	+	12.4506i	0.735789	+	0.424808i	−0.0847471	+	0.996402i	$0.527008\pi$
$860$	41.3768	+	154.420i	1.41094	+	5.26569i
$861$	−7.59418	+	0.948921i	−0.258809	+	0.0323391i
$862$	−48.4163	+	27.9532i	−1.64907	+	0.952089i
$863$	−17.0923	+	4.57987i	−0.581829	+	0.155900i	−0.537716	−	0.843126i	$-0.680713\pi$
$863$	−17.0923	+	4.57987i	−0.581829	+	0.155900i	−0.0441126	+	0.999027i	$0.514046\pi$
$864$	−5.51778	−	20.5926i	−0.187719	−	0.700575i
$865$	−8.46380	−	31.5873i	−0.287778	−	1.07400i
$866$	1.29670	−	0.347450i	0.0440638	−	0.0118068i
$867$	−12.9489	+	7.47606i	−0.439768	+	0.253900i
$868$	−6.28050	−	8.29756i	−0.213174	−	0.281638i
$869$	0.405088	+	1.51181i	0.0137417	+	0.0512847i
$870$	−63.8035	−	36.8370i	−2.16314	−	1.24889i
$871$	−15.8046	−	16.5904i	−0.535519	−	0.562144i
$872$	−34.5740	−	59.8840i	−1.17082	−	2.02793i
$873$	−2.51514	−	0.673929i	−0.0851245	−	0.0228090i
$874$	22.3632	+	12.9114i	0.756447	+	0.436735i
$875$	14.0914	+	18.6170i	0.476375	+	0.629369i
$876$	48.9177	+	48.9177i	1.65277	+	1.65277i
$877$	1.82577	+	1.82577i	0.0616519	+	0.0616519i	0.737260	−	0.675609i	$-0.236119\pi$
$877$	1.82577	+	1.82577i	0.0616519	+	0.0616519i	−0.675609	+	0.737260i	$0.736119\pi$
$878$	58.9504	−	15.7957i	1.98948	−	0.533079i
$879$	−7.58244	−	2.03171i	−0.255749	−	0.0685278i
$880$		−	22.9565i		−	0.773862i
$881$	5.24887	−	9.09131i	0.176839	−	0.306294i	−0.763957	−	0.645267i	$-0.776746\pi$
$881$	5.24887	−	9.09131i	0.176839	−	0.306294i	0.940796	+	0.338973i	$0.110079\pi$
$882$	−9.76227	+	16.4055i	−0.328713	+	0.552403i
$883$		−	0.987737i		−	0.0332400i	−0.999862	−	0.0166200i	$-0.994709\pi$
$883$		−	0.987737i		−	0.0332400i	0.999862	−	0.0166200i	$-0.00529056\pi$
$884$	24.6306	−	13.4349i	0.828416	−	0.451864i
$885$	−9.95770	+	5.74908i	−0.334724	+	0.193253i
$886$	−18.4133	−	18.4133i	−0.618608	−	0.618608i
$887$	−34.5253	+	19.9332i	−1.15925	+	0.669291i	−0.951123	−	0.308812i	$-0.900069\pi$
$887$	−34.5253	+	19.9332i	−1.15925	+	0.669291i	−0.208122	+	0.978103i	$0.566735\pi$
$888$	4.76709	+	8.25685i	0.159973	+	0.277082i
$889$	14.2330	+	11.0711i	0.477358	+	0.371314i
$890$	26.1053	−	97.4264i	0.875052	−	3.26574i
$891$	0.312538	−	0.312538i	0.0104704	−	0.0104704i
$892$	−1.33866	+	4.99594i	−0.0448216	+	0.167276i
$893$	−0.617986	+	1.07038i	−0.0206801	+	0.0358190i
$894$	29.6886	+	51.4222i	0.992936	+	1.71982i
$895$	−49.8712	+	13.3629i	−1.66701	+	0.446674i
$896$	−87.2341	−	36.8090i	−2.91429	−	1.22970i
$897$	−12.4101	−	22.7518i	−0.414362	−	0.759661i
$898$	−24.2635	+	42.0256i	−0.809684	+	1.40241i
$899$	3.90872	−	3.90872i	0.130363	−	0.130363i
$900$	−40.7627			−1.35876
$901$	7.10885			0.236830
$902$	2.46556	−	2.46556i	0.0820943	−	0.0820943i
$903$	8.28654	+	20.3844i	0.275759	+	0.678351i
$904$	56.0329	+	15.0140i	1.86362	+	0.499357i
$905$	−7.90325	−	29.4953i	−0.262713	−	0.980458i
$906$	32.9736	+	19.0373i	1.09548	+	0.632473i
$907$			9.12416i			0.302963i	0.988460	+	0.151481i	$0.0484044\pi$
$907$			9.12416i			0.302963i	−0.988460	+	0.151481i	$0.951596\pi$
$908$	−34.5180	+	128.823i	−1.14552	+	4.27514i
$909$	−1.44573			−0.0479520
$910$	90.7664	+	14.8100i	3.00888	+	0.490948i
$911$	28.0053			0.927856			0.463928	−	0.885873i	$-0.346440\pi$
$911$	28.0053			0.927856			0.463928	+	0.885873i	$0.346440\pi$
$912$	5.00927	−	18.6949i	0.165874	−	0.619049i
$913$			1.45835i			0.0482642i
$914$	65.0644	+	37.5650i	2.15214	+	1.24254i
$915$	−11.9103	−	44.4498i	−0.393742	−	1.46946i
$916$	108.363	+	29.0357i	3.58040	+	0.959366i
$917$	−7.66754	−	5.96420i	−0.253204	−	0.196955i
$918$	−2.75965	+	2.75965i	−0.0910819	+	0.0910819i
$919$	12.5006			0.412356			0.206178	−	0.978515i	$-0.433897\pi$
$919$	12.5006			0.412356			0.206178	+	0.978515i	$0.433897\pi$
$920$	238.215			7.85371
$921$	−16.1223	+	16.1223i	−0.531247	+	0.531247i
$922$	14.2466	−	24.6758i	0.469186	−	0.812654i
$923$	−1.91716	+	6.51838i	−0.0631042	+	0.214555i
$924$	−0.788426	−	6.30974i	−0.0259373	−	0.207575i
$925$	7.36390	−	1.97315i	0.242124	−	0.0648768i
$926$	20.6904	+	35.8369i	0.679929	+	1.17767i
$927$	6.70272	−	11.6095i	0.220146	−	0.381305i
$928$	42.1666	−	157.368i	1.38418	−	5.16585i
$929$	17.9287	−	17.9287i	0.588221	−	0.588221i	−0.348928	−	0.937149i	$-0.613454\pi$
$929$	17.9287	−	17.9287i	0.588221	−	0.588221i	0.937149	+	0.348928i	$0.113454\pi$
$930$	1.80489	−	6.73595i	0.0591847	−	0.220880i
$931$	−8.04579	+	4.50490i	−0.263690	+	0.147642i
$932$	61.8169	+	107.070i	2.02488	+	3.50719i
$933$	−4.77319	+	2.75580i	−0.156267	+	0.0902208i
$934$	−27.3445	−	27.3445i	−0.894739	−	0.894739i
$935$	−1.93639	+	1.11798i	−0.0633269	+	0.0365618i
$936$	−24.4744	+	23.3152i	−0.799970	+	0.762081i
$937$		−	27.8676i		−	0.910396i	−0.890390	−	0.455198i	$-0.849569\pi$
$937$		−	27.8676i		−	0.910396i	0.890390	−	0.455198i	$-0.150431\pi$
$938$	42.4791	−	17.2683i	1.38699	−	0.563830i
$939$	−9.70534	+	16.8101i	−0.316722	+	0.548578i
$940$			18.0354i			0.588249i
$941$	−13.9004	−	3.72461i	−0.453141	−	0.121419i	0.0250276	−	0.999687i	$-0.492033\pi$
$941$	−13.9004	−	3.72461i	−0.453141	−	0.121419i	−0.478169	+	0.878268i	$0.658699\pi$
$942$	39.4487	−	10.5702i	1.28531	−	0.344397i
$943$	14.7022	+	14.7022i	0.478770	+	0.478770i
$944$	−33.7920	−	33.7920i	−1.09984	−	1.09984i
$945$	−9.28064	+	1.15965i	−0.301899	+	0.0377234i
$946$	−8.68211	−	5.01262i	−0.282280	−	0.162974i
$947$	12.4758	+	3.34288i	0.405409	+	0.108629i	0.455760	−	0.890103i	$-0.349367\pi$
$947$	12.4758	+	3.34288i	0.405409	+	0.108629i	−0.0503512	+	0.998732i	$0.516034\pi$
$948$	9.62750	+	16.6753i	0.312687	+	0.541589i
$949$	12.9434	−	44.0076i	0.420160	−	1.42855i
$950$	−23.3231	−	13.4656i	−0.756703	−	0.436882i
$951$	−7.26716	−	27.1214i	−0.235654	−	0.879472i
$952$	4.40108	+	35.2217i	0.142640	+	1.14154i
$953$	−52.8130	+	30.4916i	−1.71078	+	0.987720i	−0.777275	+	0.629161i	$0.783399\pi$
$953$	−52.8130	+	30.4916i	−1.71078	+	0.987720i	−0.933507	+	0.358559i	$0.883268\pi$
$954$	−13.0860	+	3.50640i	−0.423676	+	0.113524i
$955$	6.44865	+	24.0667i	0.208674	+	0.778780i
$956$	−41.3267	−	154.234i	−1.33660	−	4.98827i
$957$	3.26262	−	0.874216i	0.105465	−	0.0282594i
$958$	59.2734	−	34.2215i	1.91504	−	1.10565i
$959$	−2.58596	−	20.6953i	−0.0835050	−	0.668288i
$960$	−26.3102	−	98.1911i	−0.849159	−	3.16910i
$961$	−26.3937	−	15.2384i	−0.851408	−	0.491561i
$962$	5.20851	−	8.53643i	0.167929	−	0.275225i
$963$	0.944877	+	1.63658i	0.0304482	+	0.0527379i
$964$	35.6199	+	9.54433i	1.14724	+	0.307402i
$965$	−70.7530	−	40.8492i	−2.27762	−	1.31498i
$966$	51.4640	−	6.43062i	1.65583	−	0.206902i
$967$	33.5388	+	33.5388i	1.07853	+	1.07853i	0.996641	+	0.0818928i	$0.0260965\pi$
$967$	33.5388	+	33.5388i	1.07853	+	1.07853i	0.0818928	+	0.996641i	$0.473903\pi$
$968$	−71.6258	−	71.6258i	−2.30214	−	2.30214i
$969$	−1.82088	+	0.487902i	−0.0584950	+	0.0156737i
$970$	−24.2478	−	6.49717i	−0.778548	−	0.208611i
$971$			13.6543i			0.438187i	0.975704	+	0.219094i	$0.0703100\pi$
$971$			13.6543i			0.438187i	−0.975704	+	0.219094i	$0.929690\pi$
$972$	2.71881	−	4.70911i	0.0872058	−	0.151045i
$973$	−29.2133	+	11.8756i	−0.936535	+	0.380714i
$974$		−	66.1857i		−	2.12073i
$975$	12.9428	+	23.7284i	0.414501	+	0.759918i
$976$	165.637	−	95.6305i	5.30191	−	3.06106i
$977$	−21.5324	−	21.5324i	−0.688883	−	0.688883i	0.273102	−	0.961985i	$-0.411950\pi$
$977$	−21.5324	−	21.5324i	−0.688883	−	0.688883i	−0.961985	+	0.273102i	$0.911950\pi$
$978$	−20.8918	+	12.0619i	−0.668045	+	0.385696i
$979$	2.31213	+	4.00472i	0.0738959	+	0.127991i
$980$	−68.8075	+	115.631i	−2.19797	+	3.69370i
$981$	1.90898	−	7.12442i	0.0609491	−	0.227465i
$982$	−21.5554	+	21.5554i	−0.687859	+	0.687859i
$983$	−0.901257	+	3.36354i	−0.0287456	+	0.107280i	−0.978808	−	0.204780i	$-0.934352\pi$
$983$	−0.901257	+	3.36354i	−0.0287456	+	0.107280i	0.950062	+	0.312060i	$0.101019\pi$
$984$	13.5594	−	23.4856i	0.432258	−	0.748692i
$985$	34.3475	+	59.4916i	1.09440	+	1.89556i
$986$	−28.8082	+	7.71914i	−0.917440	+	0.245827i
$987$	0.307792	+	2.46325i	0.00979713	+	0.0784060i
$988$	−25.1012	+	6.07750i	−0.798576	+	0.193351i
$989$	29.8904	−	51.7716i	0.950458	−	1.64624i
$990$	3.01310	−	3.01310i	0.0957625	−	0.0957625i
$991$	−27.0123			−0.858073			−0.429036	−	0.903287i	$-0.641147\pi$
$991$	−27.0123			−0.858073			−0.429036	+	0.903287i	$0.641147\pi$
$992$	15.4210			0.489618
$993$	−5.36907	+	5.36907i	−0.170382	+	0.170382i
$994$	−10.7326	−	8.34836i	−0.340417	−	0.264794i
$995$	−60.8162	−	16.2956i	−1.92800	−	0.516607i
$996$	4.64352	+	17.3298i	0.147135	+	0.549117i
$997$	−18.1168	−	10.4597i	−0.573764	−	0.331263i	0.184887	−	0.982760i	$-0.440808\pi$
$997$	−18.1168	−	10.4597i	−0.573764	−	0.331263i	−0.758651	+	0.651497i	$0.774141\pi$
$998$		−	107.612i		−	3.40641i
$999$	−0.263212	+	0.982321i	−0.00832766	+	0.0310793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.124.9	yes	36
3.2	odd	2		819.2.gh.c.397.1		36
7.3	odd	6		273.2.bt.a.241.9	yes	36
13.2	odd	12		273.2.bt.a.145.9	✓	36
21.17	even	6		819.2.et.c.514.1		36
39.2	even	12		819.2.et.c.145.1		36
91.80	even	12	inner	273.2.cg.a.262.9	yes	36
273.80	odd	12		819.2.gh.c.262.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.9	✓	36	13.2	odd	12
273.2.bt.a.241.9	yes	36	7.3	odd	6
273.2.cg.a.124.9	yes	36	1.1	even	1	trivial
273.2.cg.a.262.9	yes	36	91.80	even	12	inner
819.2.et.c.145.1		36	39.2	even	12
819.2.et.c.514.1		36	21.17	even	6
819.2.gh.c.262.1		36	273.80	odd	12
819.2.gh.c.397.1		36	3.2	odd	2

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.705851 - 2.63427i) q^{2} +1.00000i q^{3} +(-4.70911 - 2.71881i) q^{4} +(-0.914933 - 3.41458i) q^{5} +(2.63427 + 0.705851i) q^{6} +(2.62078 + 0.362619i) q^{7} +(-6.62917 + 6.62917i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.705851 - 2.63427i) q^{2} +1.00000i q^{3} +(-4.70911 - 2.71881i) q^{4} +(-0.914933 - 3.41458i) q^{5} +(2.63427 + 0.705851i) q^{6} +(2.62078 + 0.362619i) q^{7} +(-6.62917 + 6.62917i) q^{8} -1.00000 q^{9} -9.64073 q^{10} +(0.312538 - 0.312538i) q^{11} +(2.71881 - 4.70911i) q^{12} +(-3.60449 - 0.0874303i) q^{13} +(2.80512 - 6.64790i) q^{14} +(3.41458 - 0.914933i) q^{15} +(7.34621 + 12.7240i) q^{16} +(0.715520 - 1.23932i) q^{17} +(-0.705851 + 2.63427i) q^{18} +(-0.931473 + 0.931473i) q^{19} +(-4.97505 + 18.5671i) q^{20} +(-0.362619 + 2.62078i) q^{21} +(-0.602706 - 1.04392i) q^{22} +(6.22490 - 3.59395i) q^{23} +(-6.62917 - 6.62917i) q^{24} +(-6.49210 + 3.74822i) q^{25} +(-2.77455 + 9.43350i) q^{26} -1.00000i q^{27} +(-11.3557 - 8.83302i) q^{28} +(3.82097 - 6.61812i) q^{29} -9.64073i q^{30} +(0.698697 + 0.187215i) q^{31} +(20.5926 - 5.51778i) q^{32} +(0.312538 + 0.312538i) q^{33} +(-2.75965 - 2.75965i) q^{34} +(-1.15965 - 9.28064i) q^{35} +(4.70911 + 2.71881i) q^{36} +(-0.982321 - 0.263212i) q^{37} +(1.79627 + 3.11123i) q^{38} +(0.0874303 - 3.60449i) q^{39} +(28.7010 + 16.5706i) q^{40} +(0.748673 + 2.79409i) q^{41} +(6.64790 + 2.80512i) q^{42} +(7.20261 - 4.15843i) q^{43} +(-2.32151 + 0.622047i) q^{44} +(0.914933 + 3.41458i) q^{45} +(-5.07358 - 18.9349i) q^{46} +(0.906290 - 0.242840i) q^{47} +(-12.7240 + 7.34621i) q^{48} +(6.73701 + 1.90069i) q^{49} +(5.29136 + 19.7476i) q^{50} +(1.23932 + 0.715520i) q^{51} +(16.7362 + 10.2116i) q^{52} +(2.48381 + 4.30208i) q^{53} +(-2.63427 - 0.705851i) q^{54} +(-1.35314 - 0.781234i) q^{55} +(-19.7775 + 14.9698i) q^{56} +(-0.931473 - 0.931473i) q^{57} +(-14.7369 - 14.7369i) q^{58} +(-3.14180 + 0.841844i) q^{59} +(-18.5671 - 4.97505i) q^{60} -13.0177i q^{61} +(0.986352 - 1.70841i) q^{62} +(-2.62078 - 0.362619i) q^{63} -28.7565i q^{64} +(2.99933 + 12.3878i) q^{65} +(1.04392 - 0.602706i) q^{66} +(4.49370 + 4.49370i) q^{67} +(-6.73893 + 3.89072i) q^{68} +(3.59395 + 6.22490i) q^{69} +(-25.2663 - 3.49591i) q^{70} +(0.487730 - 1.82023i) q^{71} +(6.62917 - 6.62917i) q^{72} +(-3.29282 + 12.2890i) q^{73} +(-1.38674 + 2.40191i) q^{74} +(-3.74822 - 6.49210i) q^{75} +(6.91890 - 1.85391i) q^{76} +(0.932428 - 0.705763i) q^{77} +(-9.43350 - 2.77455i) q^{78} +(-1.77054 + 3.06666i) q^{79} +(36.7258 - 36.7258i) q^{80} +1.00000 q^{81} +7.88884 q^{82} +(-2.33307 + 2.33307i) q^{83} +(8.83302 - 11.3557i) q^{84} +(-4.88639 - 1.30931i) q^{85} +(-5.87046 - 21.9089i) q^{86} +(6.61812 + 3.82097i) q^{87} +4.14374i q^{88} +(-2.70782 + 10.1057i) q^{89} +9.64073 q^{90} +(-9.41489 - 1.53619i) q^{91} -39.0850 q^{92} +(-0.187215 + 0.698697i) q^{93} -2.55882i q^{94} +(4.03282 + 2.32835i) q^{95} +(5.51778 + 20.5926i) q^{96} +(2.51514 + 0.673929i) q^{97} +(9.76227 - 16.4055i) q^{98} +(-0.312538 + 0.312538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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