LMFDB - Embedded newform 273.2.bz.b.73.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (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			73.9
Character	$\chi$	$=$	273.73
Dual form			273.2.bz.b.187.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587020 - 2.19079i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72291 - 1.57208i) q^{4} +(-1.78371 - 0.477944i) q^{5} +(-1.60377 + 1.60377i) q^{6} +(-2.58471 - 0.565048i) q^{7} +(-1.83495 + 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.587020 - 2.19079i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72291 - 1.57208i) q^{4} +(-1.78371 - 0.477944i) q^{5} +(-1.60377 + 1.60377i) q^{6} +(-2.58471 - 0.565048i) q^{7} +(-1.83495 + 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.09415 + 3.62718i) q^{10} +(0.733638 + 2.73797i) q^{11} +(1.57208 + 2.72291i) q^{12} +(1.91891 - 3.05250i) q^{13} +(-2.75518 + 5.33086i) q^{14} +(1.30577 + 1.30577i) q^{15} +(-0.201308 - 0.348677i) q^{16} +(-1.30569 + 2.26152i) q^{17} +(2.19079 - 0.587020i) q^{18} +(-7.68035 - 2.05794i) q^{19} +(4.10553 + 4.10553i) q^{20} +(1.95590 + 1.78170i) q^{21} +6.42899 q^{22} +(6.09364 - 3.51816i) q^{23} +(2.50659 - 0.671640i) q^{24} +(-1.37693 - 0.794969i) q^{25} +(-5.56095 - 5.99582i) q^{26} -1.00000i q^{27} +(6.14964 + 5.60193i) q^{28} -2.00830 q^{29} +(3.62718 - 2.09415i) q^{30} +(-2.15228 - 8.03240i) q^{31} +(-5.89524 + 1.57962i) q^{32} +(0.733638 - 2.73797i) q^{33} +(4.18805 + 4.18805i) q^{34} +(4.34032 + 2.24323i) q^{35} -3.14415i q^{36} +(5.55896 + 1.48952i) q^{37} +(-9.01704 + 15.6180i) q^{38} +(-3.18808 + 1.68409i) q^{39} +(4.15004 - 2.39602i) q^{40} +(4.97086 - 4.97086i) q^{41} +(5.05148 - 3.23907i) q^{42} -5.75547i q^{43} +(2.30667 - 8.60860i) q^{44} +(-0.477944 - 1.78371i) q^{45} +(-4.13047 - 15.4151i) q^{46} +(-2.23820 + 8.35306i) q^{47} +0.402617i q^{48} +(6.36144 + 2.92097i) q^{49} +(-2.54989 + 2.54989i) q^{50} +(2.26152 - 1.30569i) q^{51} +(-10.0238 + 5.29503i) q^{52} +(4.51283 - 7.81645i) q^{53} +(-2.19079 - 0.587020i) q^{54} -5.23440i q^{55} +(5.77966 - 3.70599i) q^{56} +(5.62240 + 5.62240i) q^{57} +(-1.17891 + 4.39975i) q^{58} +(-1.16093 + 0.311071i) q^{59} +(-1.50273 - 5.60826i) q^{60} +(1.80598 - 1.04268i) q^{61} -18.8607 q^{62} +(-0.803009 - 2.52095i) q^{63} +13.0373i q^{64} +(-4.88172 + 4.52765i) q^{65} +(-5.56767 - 3.21449i) q^{66} +(0.0372433 - 0.00997932i) q^{67} +(7.11057 - 4.10529i) q^{68} -7.03633 q^{69} +(7.46230 - 8.19190i) q^{70} +(-1.50379 - 1.50379i) q^{71} +(-2.50659 - 0.671640i) q^{72} +(-2.83190 + 0.758806i) q^{73} +(6.52644 - 11.3041i) q^{74} +(0.794969 + 1.37693i) q^{75} +(17.6777 + 17.6777i) q^{76} +(-0.349154 - 7.49141i) q^{77} +(1.81802 + 7.97300i) q^{78} +(1.66248 + 2.87950i) q^{79} +(0.192429 + 0.718153i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.97211 - 13.8081i) q^{82} +(-5.45368 + 5.45368i) q^{83} +(-2.52478 - 7.92624i) q^{84} +(3.40986 - 3.40986i) q^{85} +(-12.6090 - 3.37858i) q^{86} +(1.73924 + 1.00415i) q^{87} +(-6.37025 - 3.67786i) q^{88} +(0.808673 - 3.01801i) q^{89} -4.18830 q^{90} +(-6.68464 + 6.80555i) q^{91} -22.1233 q^{92} +(-2.15228 + 8.03240i) q^{93} +(16.9859 + 9.80684i) q^{94} +(12.7160 + 7.34156i) q^{95} +(5.89524 + 1.57962i) q^{96} +(7.47680 - 7.47680i) q^{97} +(10.1335 - 12.2219i) q^{98} +(-2.00434 + 2.00434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 + 18 * q^9	$ 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.587020	−	2.19079i	0.415086	−	1.54912i	−0.369577	−	0.929200i	$-0.620498\pi$
$2$	0.587020	−	2.19079i	0.415086	−	1.54912i	0.784663	−	0.619922i	$-0.212836\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−2.72291	−	1.57208i	−1.36146	−	0.786038i
$5$	−1.78371	−	0.477944i	−0.797701	−	0.213743i	−0.163126	−	0.986605i	$-0.552158\pi$
$5$	−1.78371	−	0.477944i	−0.797701	−	0.213743i	−0.634574	+	0.772862i	$0.718825\pi$
$6$	−1.60377	+	1.60377i	−0.654736	+	0.654736i
$7$	−2.58471	−	0.565048i	−0.976928	−	0.213568i
$7$	−2.58471	−	0.565048i	−0.976928	−	0.213568i
$8$	−1.83495	+	1.83495i	−0.648754	+	0.648754i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.09415	+	3.62718i	−0.662229	+	1.14701i
$11$	0.733638	+	2.73797i	0.221200	+	0.825530i	0.983891	+	0.178768i	$0.0572110\pi$
$11$	0.733638	+	2.73797i	0.221200	+	0.825530i	−0.762691	+	0.646763i	$0.776122\pi$
$12$	1.57208	+	2.72291i	0.453819	+	0.786038i
$13$	1.91891	−	3.05250i	0.532211	−	0.846612i
$13$	1.91891	−	3.05250i	0.532211	−	0.846612i
$14$	−2.75518	+	5.33086i	−0.736352	+	1.42473i
$15$	1.30577	+	1.30577i	0.337148	+	0.337148i
$16$	−0.201308	−	0.348677i	−0.0503271	−	0.0871691i
$17$	−1.30569	+	2.26152i	−0.316677	+	0.548500i	−0.979792	−	0.200017i	$-0.935900\pi$
$17$	−1.30569	+	2.26152i	−0.316677	+	0.548500i	0.663116	+	0.748517i	$0.269234\pi$
$18$	2.19079	−	0.587020i	0.516374	−	0.138362i
$19$	−7.68035	−	2.05794i	−1.76199	−	0.472124i	−0.774874	−	0.632116i	$-0.782187\pi$
$19$	−7.68035	−	2.05794i	−1.76199	−	0.472124i	−0.987118	+	0.159991i	$0.948853\pi$
$20$	4.10553	+	4.10553i	0.918025	+	0.918025i
$21$	1.95590	+	1.78170i	0.426812	+	0.388799i
$22$	6.42899			1.37066
$23$	6.09364	−	3.51816i	1.27061	−	0.733588i	0.295508	−	0.955340i	$-0.404511\pi$
$23$	6.09364	−	3.51816i	1.27061	−	0.733588i	0.975103	+	0.221753i	$0.0711778\pi$
$24$	2.50659	−	0.671640i	0.511656	−	0.137098i
$25$	−1.37693	−	0.794969i	−0.275385	−	0.158994i
$26$	−5.56095	−	5.99582i	−1.09059	−	1.17588i
$27$		−	1.00000i		−	0.192450i
$28$	6.14964	+	5.60193i	1.16217	+	1.05867i
$29$	−2.00830			−0.372931			−0.186466	−	0.982461i	$-0.559703\pi$
$29$	−2.00830			−0.372931			−0.186466	+	0.982461i	$0.559703\pi$
$30$	3.62718	−	2.09415i	0.662229	−	0.382338i
$31$	−2.15228	−	8.03240i	−0.386560	−	1.44266i	−0.835693	−	0.549197i	$-0.814934\pi$
$31$	−2.15228	−	8.03240i	−0.386560	−	1.44266i	0.449133	−	0.893465i	$-0.351733\pi$
$32$	−5.89524	+	1.57962i	−1.04214	+	0.279241i
$33$	0.733638	−	2.73797i	0.127710	−	0.476620i
$34$	4.18805	+	4.18805i	0.718245	+	0.718245i
$35$	4.34032	+	2.24323i	0.733648	+	0.379175i
$36$		−	3.14415i		−	0.524025i
$37$	5.55896	+	1.48952i	0.913887	+	0.244875i	0.684970	−	0.728571i	$-0.259815\pi$
$37$	5.55896	+	1.48952i	0.913887	+	0.244875i	0.228916	+	0.973446i	$0.426482\pi$
$38$	−9.01704	+	15.6180i	−1.46276	+	2.53357i
$39$	−3.18808	+	1.68409i	−0.510501	+	0.269670i
$40$	4.15004	−	2.39602i	0.656178	−	0.378845i
$41$	4.97086	−	4.97086i	0.776317	−	0.776317i	−0.202885	−	0.979203i	$-0.565032\pi$
$41$	4.97086	−	4.97086i	0.776317	−	0.776317i	0.979203	+	0.202885i	$0.0650318\pi$
$42$	5.05148	−	3.23907i	0.779461	−	0.499799i
$43$		−	5.75547i		−	0.877701i	−0.898560	−	0.438850i	$-0.855386\pi$
$43$		−	5.75547i		−	0.877701i	0.898560	−	0.438850i	$-0.144614\pi$
$44$	2.30667	−	8.60860i	0.347743	−	1.29780i
$45$	−0.477944	−	1.78371i	−0.0712477	−	0.265900i
$46$	−4.13047	−	15.4151i	−0.609004	−	2.27283i
$47$	−2.23820	+	8.35306i	−0.326475	+	1.21842i	0.586347	+	0.810060i	$0.300566\pi$
$47$	−2.23820	+	8.35306i	−0.326475	+	1.21842i	−0.912821	+	0.408359i	$0.866101\pi$
$48$			0.402617i			0.0581128i
$49$	6.36144	+	2.92097i	0.908777	+	0.417281i
$50$	−2.54989	+	2.54989i	−0.360609	+	0.360609i
$51$	2.26152	−	1.30569i	0.316677	−	0.182833i
$52$	−10.0238	+	5.29503i	−1.39005	+	0.734288i
$53$	4.51283	−	7.81645i	0.619885	−	1.07367i	−0.369621	−	0.929182i	$-0.620513\pi$
$53$	4.51283	−	7.81645i	0.619885	−	1.07367i	0.989506	−	0.144490i	$-0.0461540\pi$
$54$	−2.19079	−	0.587020i	−0.298129	−	0.0798833i
$55$		−	5.23440i		−	0.705806i
$56$	5.77966	−	3.70599i	0.772339	−	0.495233i
$57$	5.62240	+	5.62240i	0.744706	+	0.744706i
$58$	−1.17891	+	4.39975i	−0.154799	+	0.577716i
$59$	−1.16093	+	0.311071i	−0.151141	+	0.0404980i	−0.333596	−	0.942716i	$-0.608262\pi$
$59$	−1.16093	+	0.311071i	−0.151141	+	0.0404980i	0.182455	+	0.983214i	$0.441595\pi$
$60$	−1.50273	−	5.60826i	−0.194002	−	0.724024i
$61$	1.80598	−	1.04268i	0.231232	−	0.133502i	−0.379908	−	0.925024i	$-0.624044\pi$
$61$	1.80598	−	1.04268i	0.231232	−	0.133502i	0.611140	+	0.791522i	$0.290711\pi$
$62$	−18.8607			−2.39532
$63$	−0.803009	−	2.52095i	−0.101170	−	0.317610i
$64$			13.0373i			1.62966i
$65$	−4.88172	+	4.52765i	−0.605502	+	0.561586i
$66$	−5.56767	−	3.21449i	−0.685332	−	0.395677i
$67$	0.0372433	−	0.00997932i	0.00455000	−	0.00121917i	−0.256543	−	0.966533i	$-0.582584\pi$
$67$	0.0372433	−	0.00997932i	0.00455000	−	0.00121917i	0.261093	+	0.965314i	$0.415917\pi$
$68$	7.11057	−	4.10529i	0.862283	−	0.497840i
$69$	−7.03633			−0.847074
$70$	7.46230	−	8.19190i	0.891915	−	0.979119i
$71$	−1.50379	−	1.50379i	−0.178467	−	0.178467i	0.612220	−	0.790687i	$-0.290277\pi$
$71$	−1.50379	−	1.50379i	−0.178467	−	0.178467i	−0.790687	+	0.612220i	$0.790277\pi$
$72$	−2.50659	−	0.671640i	−0.295405	−	0.0791535i
$73$	−2.83190	+	0.758806i	−0.331449	+	0.0888116i	−0.420706	−	0.907197i	$-0.638218\pi$
$73$	−2.83190	+	0.758806i	−0.331449	+	0.0888116i	0.0892566	+	0.996009i	$0.471551\pi$
$74$	6.52644	−	11.3041i	0.758683	−	1.31408i
$75$	0.794969	+	1.37693i	0.0917951	+	0.158994i
$76$	17.6777	+	17.6777i	2.02777	+	2.02777i
$77$	−0.349154	−	7.49141i	−0.0397898	−	0.853725i
$78$	1.81802	+	7.97300i	0.205850	+	0.902765i
$79$	1.66248	+	2.87950i	0.187044	+	0.323969i	0.944263	−	0.329191i	$-0.106776\pi$
$79$	1.66248	+	2.87950i	0.187044	+	0.323969i	−0.757220	+	0.653160i	$0.773443\pi$
$80$	0.192429	+	0.718153i	0.0215142	+	0.0802920i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.97211	−	13.8081i	−0.880372	−	1.52485i
$83$	−5.45368	+	5.45368i	−0.598619	+	0.598619i	−0.939945	−	0.341326i	$-0.889124\pi$
$83$	−5.45368	+	5.45368i	−0.598619	+	0.598619i	0.341326	+	0.939945i	$0.389124\pi$
$84$	−2.52478	−	7.92624i	−0.275476	−	0.864824i
$85$	3.40986	−	3.40986i	0.369851	−	0.369851i
$86$	−12.6090	−	3.37858i	−1.35967	−	0.364321i
$87$	1.73924	+	1.00415i	0.186466	+	0.107656i
$88$	−6.37025	−	3.67786i	−0.679071	−	0.392062i
$89$	0.808673	−	3.01801i	0.0857192	−	0.319908i	−0.909730	−	0.415200i	$-0.863712\pi$
$89$	0.808673	−	3.01801i	0.0857192	−	0.319908i	0.995449	+	0.0952915i	$0.0303783\pi$
$90$	−4.18830			−0.441486
$91$	−6.68464	+	6.80555i	−0.700741	+	0.713416i
$92$	−22.1233			−2.30651
$93$	−2.15228	+	8.03240i	−0.223181	+	0.832921i
$94$	16.9859	+	9.80684i	1.75197	+	1.01150i
$95$	12.7160	+	7.34156i	1.30463	+	0.753228i
$96$	5.89524	+	1.57962i	0.601680	+	0.161220i
$97$	7.47680	−	7.47680i	0.759154	−	0.759154i	−0.217015	−	0.976168i	$-0.569632\pi$
$97$	7.47680	−	7.47680i	0.759154	−	0.759154i	0.976168	+	0.217015i	$0.0696319\pi$
$98$	10.1335	−	12.2219i	1.02364	−	1.23460i
$99$	−2.00434	+	2.00434i	−0.201443	+	0.201443i
$100$	2.49950	+	4.32926i	0.249950	+	0.432926i
$101$	4.03973	−	6.99701i	0.401968	−	0.696229i	−0.591996	−	0.805941i	$-0.701660\pi$
$101$	4.03973	−	6.99701i	0.401968	−	0.696229i	0.993963	+	0.109713i	$0.0349931\pi$
$102$	−1.53293	−	5.72099i	−0.151783	−	0.566462i
$103$	6.70232	+	11.6088i	0.660399	+	1.14385i	0.980511	+	0.196465i	$0.0629464\pi$
$103$	6.70232	+	11.6088i	0.660399	+	1.14385i	−0.320111	+	0.947380i	$0.603720\pi$
$104$	2.08008	+	9.12232i	0.203969	+	0.894517i
$105$	−2.63721	−	4.11285i	−0.257365	−	0.401373i
$106$	−14.4751	−	14.4751i	−1.40594	−	1.40594i
$107$	−1.72357	−	2.98531i	−0.166624	−	0.288601i	0.770607	−	0.637311i	$-0.219953\pi$
$107$	−1.72357	−	2.98531i	−0.166624	−	0.288601i	−0.937231	+	0.348710i	$0.886620\pi$
$108$	−1.57208	+	2.72291i	−0.151273	+	0.262013i
$109$	−9.96024	+	2.66884i	−0.954018	+	0.255628i	−0.702066	−	0.712112i	$-0.747739\pi$
$109$	−9.96024	+	2.66884i	−0.954018	+	0.255628i	−0.251951	+	0.967740i	$0.581072\pi$
$110$	−11.4675	−	3.07270i	−1.09338	−	0.292970i
$111$	−4.06944	−	4.06944i	−0.386254	−	0.386254i
$112$	0.323305	+	1.01498i	0.0305494	+	0.0959062i
$113$	16.0087			1.50598			0.752988	−	0.658034i	$-0.228612\pi$
$113$	16.0087			1.50598			0.752988	+	0.658034i	$0.228612\pi$
$114$	15.6180	−	9.01704i	1.46276	−	0.844523i
$115$	−12.5508	+	3.36297i	−1.17037	+	0.313599i
$116$	5.46842	+	3.15719i	0.507730	+	0.293138i
$117$	3.60300	+	0.135576i	0.333098	+	0.0125340i
$118$			2.72597i			0.250945i
$119$	4.65270	−	5.10760i	0.426512	−	0.468213i
$120$	−4.79205			−0.437452
$121$	2.56800	−	1.48264i	0.233455	−	0.134785i
$122$	−1.22415	−	4.56861i	−0.110830	−	0.413622i
$123$	−6.79032	+	1.81946i	−0.612262	+	0.164055i
$124$	−6.76708	+	25.2551i	−0.607702	+	2.26797i
$125$	8.60493	+	8.60493i	0.769649	+	0.769649i
$126$	−5.99425	+	0.279376i	−0.534010	+	0.0248888i
$127$			1.01584i			0.0901411i	0.998984	+	0.0450705i	$0.0143513\pi$
$127$			1.01584i			0.0901411i	−0.998984	+	0.0450705i	$0.985649\pi$
$128$	16.7714	+	4.49389i	1.48240	+	0.397207i
$129$	−2.87773	+	4.98438i	−0.253370	+	0.438850i
$130$	7.05347	+	13.3526i	0.618630	+	1.17110i
$131$	9.02400	−	5.21001i	0.788430	−	0.455200i	−0.0509795	−	0.998700i	$-0.516234\pi$
$131$	9.02400	−	5.21001i	0.788430	−	0.455200i	0.839410	+	0.543499i	$0.182901\pi$
$132$	−6.30194	+	6.30194i	−0.548513	+	0.548513i
$133$	18.6886	+	9.65895i	1.62051	+	0.837537i
$134$		−	0.0874503i		−	0.00755456i
$135$	−0.477944	+	1.78371i	−0.0411349	+	0.153518i
$136$	−1.75391	−	6.54567i	−0.150396	−	0.561287i
$137$	4.11154	+	15.3445i	0.351272	+	1.31097i	0.885111	+	0.465380i	$0.154082\pi$
$137$	4.11154	+	15.3445i	0.351272	+	1.31097i	−0.533839	+	0.845586i	$0.679251\pi$
$138$	−4.13047	+	15.4151i	−0.351609	+	1.31222i
$139$			1.97133i			0.167206i	0.996499	+	0.0836029i	$0.0266427\pi$
$139$			1.97133i			0.167206i	−0.996499	+	0.0836029i	$0.973357\pi$
$140$	−8.29179	−	12.9314i	−0.700784	−	1.09291i
$141$	6.11487	−	6.11487i	0.514965	−	0.514965i
$142$	−4.17725	+	2.41174i	−0.350547	+	0.202389i
$143$	9.76546	+	3.01450i	0.816629	+	0.252085i
$144$	0.201308	−	0.348677i	0.0167757	−	0.0290564i
$145$	3.58222	+	0.959854i	0.297487	+	0.0797115i
$146$			6.64954i			0.550320i
$147$	−4.04869	−	5.71035i	−0.333930	−	0.470982i
$148$	−12.7949	−	12.7949i	−1.05174	−	1.05174i
$149$	−2.79087	+	10.4157i	−0.228637	+	0.853286i	0.752277	+	0.658847i	$0.228955\pi$
$149$	−2.79087	+	10.4157i	−0.228637	+	0.853286i	−0.980915	+	0.194439i	$0.937711\pi$
$150$	3.48322	−	0.933326i	0.284404	−	0.0762057i
$151$	−3.13005	−	11.6815i	−0.254720	−	0.950627i	−0.968246	−	0.249999i	$-0.919570\pi$
$151$	−3.13005	−	11.6815i	−0.254720	−	0.950627i	0.713526	−	0.700628i	$-0.247097\pi$
$152$	17.8693	−	10.3169i	1.44939	−	0.836807i
$153$	−2.61138			−0.211118
$154$	−16.6171	−	3.63268i	−1.33904	−	0.292730i
$155$			15.3562i			1.23344i
$156$	11.3284	+	0.426272i	0.906996	+	0.0341291i
$157$	7.20193	+	4.15804i	0.574777	+	0.331848i	0.759055	−	0.651027i	$-0.225661\pi$
$157$	7.20193	+	4.15804i	0.574777	+	0.331848i	−0.184278	+	0.982874i	$0.558995\pi$
$158$	7.28428	−	1.95182i	0.579506	−	0.155278i
$159$	−7.81645	+	4.51283i	−0.619885	+	0.357891i
$160$	11.2704			0.891002
$161$	−17.7382	+	5.65023i	−1.39797	+	0.445301i
$162$	1.60377	+	1.60377i	0.126004	+	0.126004i
$163$	−18.2705	−	4.89558i	−1.43106	−	0.383451i	−0.541666	−	0.840594i	$-0.682206\pi$
$163$	−18.2705	−	4.89558i	−1.43106	−	0.383451i	−0.889393	+	0.457142i	$0.848873\pi$
$164$	−21.3498	+	5.72066i	−1.66714	+	0.446708i
$165$	−2.61720	+	4.53312i	−0.203749	+	0.352903i
$166$	8.74644	+	15.1493i	0.678856	+	1.17581i
$167$	−6.63924	−	6.63924i	−0.513760	−	0.513760i	0.401917	−	0.915676i	$-0.368344\pi$
$167$	−6.63924	−	6.63924i	−0.513760	−	0.513760i	−0.915676	+	0.401917i	$0.868344\pi$
$168$	−6.85832	+	0.319648i	−0.529131	+	0.0246614i
$169$	−5.63554	−	11.7150i	−0.433503	−	0.901152i
$170$	−5.46863	−	9.47194i	−0.419425	−	0.726465i
$171$	−2.05794	−	7.68035i	−0.157375	−	0.587331i
$172$	−9.04803	+	15.6716i	−0.689906	+	1.19495i
$173$	9.93427	+	17.2067i	0.755289	+	1.30820i	0.945231	+	0.326403i	$0.105837\pi$
$173$	9.93427	+	17.2067i	0.755289	+	1.30820i	−0.189942	+	0.981795i	$0.560830\pi$
$174$	3.22084	−	3.22084i	0.244172	−	0.244172i
$175$	3.10976	+	2.83279i	0.235076	+	0.214139i
$176$	0.806980	−	0.806980i	0.0608284	−	0.0608284i
$177$	1.16093	+	0.311071i	0.0872611	+	0.0233815i
$178$	−6.13712	−	3.54327i	−0.459996	−	0.265579i
$179$	−19.3888	−	11.1941i	−1.44919	−	0.836687i	−0.450752	−	0.892649i	$-0.648844\pi$
$179$	−19.3888	−	11.1941i	−1.44919	−	0.836687i	−0.998433	+	0.0559616i	$0.982178\pi$
$180$	−1.50273	+	5.60826i	−0.112007	+	0.418015i
$181$	−2.06190			−0.153260			−0.0766300	−	0.997060i	$-0.524416\pi$
$181$	−2.06190			−0.153260			−0.0766300	+	0.997060i	$0.524416\pi$
$182$	10.9855	+	18.6396i	0.814300	+	1.38166i
$183$	−2.08537			−0.154155
$184$	−4.72588	+	17.6372i	−0.348396	+	1.30023i
$185$	−9.20367	−	5.31374i	−0.676668	−	0.390674i
$186$	16.3339	+	9.43037i	1.19766	+	0.691468i
$187$	−7.14990	−	1.91581i	−0.522852	−	0.140098i
$188$	19.2261	−	19.2261i	1.40220	−	1.40220i
$189$	−0.565048	+	2.58471i	−0.0411012	+	0.188010i
$190$	23.5483	−	23.5483i	1.70838	−	1.70838i
$191$	0.185230	+	0.320827i	0.0134028	+	0.0232143i	0.872649	−	0.488348i	$-0.162400\pi$
$191$	0.185230	+	0.320827i	0.0134028	+	0.0232143i	−0.859246	+	0.511562i	$0.829067\pi$
$192$	6.51863	−	11.2906i	0.470442	−	0.814829i
$193$	−6.28942	−	23.4725i	−0.452723	−	1.68958i	−0.694698	−	0.719302i	$-0.744462\pi$
$193$	−6.28942	−	23.4725i	−0.452723	−	1.68958i	0.241975	−	0.970282i	$-0.422205\pi$
$194$	−11.9911	−	20.7691i	−0.860908	−	1.49114i
$195$	6.49152	−	1.48021i	0.464867	−	0.106000i
$196$	−12.7297	−	17.9542i	−0.909263	−	1.28244i
$197$	0.745688	+	0.745688i	0.0531281	+	0.0531281i	0.733172	−	0.680044i	$-0.238039\pi$
$197$	0.745688	+	0.745688i	0.0531281	+	0.0531281i	−0.680044	+	0.733172i	$0.738039\pi$
$198$	3.21449	+	5.56767i	0.228444	+	0.395677i
$199$	2.17610	−	3.76911i	0.154259	−	0.267185i	−0.778530	−	0.627608i	$-0.784034\pi$
$199$	2.17610	−	3.76911i	0.154259	−	0.267185i	0.932789	+	0.360423i	$0.117368\pi$
$200$	3.98533	−	1.06787i	0.281805	−	0.0755095i
$201$	−0.0372433	−	0.00997932i	−0.00262694	−	0.000703887i
$202$	−12.9576	−	12.9576i	−0.911692	−	0.911692i
$203$	5.19086	+	1.13478i	0.364327	+	0.0796462i
$204$	−8.21058			−0.574856
$205$	−11.2424	+	6.49079i	−0.785202	+	0.453336i
$206$	29.3668	−	7.86880i	2.04608	−	0.548245i
$207$	6.09364	+	3.51816i	0.423537	+	0.244529i
$208$	−1.45063	−	0.0545853i	−0.100583	−	0.00378481i
$209$		−	22.5384i		−	1.55901i
$210$	−10.5585	+	3.36324i	−0.728605	+	0.232086i
$211$	−27.3690			−1.88416			−0.942079	−	0.335391i	$-0.891132\pi$
$211$	−27.3690			−1.88416			−0.942079	+	0.335391i	$0.891132\pi$
$212$	−24.5761	+	14.1890i	−1.68789	+	0.974506i
$213$	0.550427	+	2.05422i	0.0377146	+	0.140753i
$214$	−7.55197	+	2.02354i	−0.516242	+	0.138327i
$215$	−2.75079	+	10.2661i	−0.187603	+	0.700142i
$216$	1.83495	+	1.83495i	0.124853	+	0.124853i
$217$	1.02432	+	21.9776i	0.0695350	+	1.49193i
$218$			23.3874i			1.58400i
$219$	2.83190	+	0.758806i	0.191362	+	0.0512754i
$220$	−8.22887	+	14.2528i	−0.554790	+	0.960925i
$221$	4.39780	+	8.32529i	0.295828	+	0.560020i
$222$	−11.3041	+	6.52644i	−0.758683	+	0.438026i
$223$	15.0854	−	15.0854i	1.01020	−	1.01020i	0.0102479	−	0.999947i	$-0.496738\pi$
$223$	15.0854	−	15.0854i	1.01020	−	1.01020i	0.999947	−	0.0102479i	$-0.00326208\pi$
$224$	16.1300	−	0.751778i	1.07773	−	0.0502302i
$225$		−	1.58994i		−	0.105996i
$226$	9.39746	−	35.0718i	0.625110	−	2.33294i
$227$	−6.35934	−	23.7334i	−0.422084	−	1.57524i	−0.770209	−	0.637791i	$-0.779848\pi$
$227$	−6.35934	−	23.7334i	−0.422084	−	1.57524i	0.348125	−	0.937448i	$-0.386818\pi$
$228$	−6.47048	−	24.1482i	−0.428518	−	1.59925i
$229$	2.22239	−	8.29409i	0.146860	−	0.548089i	−0.852806	−	0.522229i	$-0.825101\pi$
$229$	2.22239	−	8.29409i	0.146860	−	0.548089i	0.999666	−	0.0258603i	$-0.00823252\pi$
$230$			29.4703i			1.94321i
$231$	−3.44333	+	6.66233i	−0.226554	+	0.438349i
$232$	3.68513	−	3.68513i	0.241941	−	0.241941i
$233$	−2.66410	+	1.53812i	−0.174531	+	0.100765i	−0.584720	−	0.811235i	$-0.698796\pi$
$233$	−2.66410	+	1.53812i	−0.174531	+	0.100765i	0.410190	+	0.912000i	$0.365462\pi$
$234$	2.41205	−	7.81383i	0.157681	−	0.510806i
$235$	7.98460	−	13.8297i	0.520858	−	0.902152i
$236$	3.65015	+	0.978055i	0.237604	+	0.0636659i
$237$		−	3.32496i		−	0.215979i
$238$	−8.45845	−	13.1914i	−0.548280	−	0.855068i
$239$	15.2980	+	15.2980i	0.989543	+	0.989543i	0.999946	−	0.0104032i	$-0.00331150\pi$
$239$	15.2980	+	15.2980i	0.989543	+	0.989543i	−0.0104032	+	0.999946i	$0.503311\pi$
$240$	0.192429	−	0.718153i	0.0124212	−	0.0463566i
$241$	2.71134	−	0.726501i	0.174653	−	0.0467980i	−0.170433	−	0.985369i	$-0.554517\pi$
$241$	2.71134	−	0.726501i	0.174653	−	0.0467980i	0.345085	+	0.938571i	$0.387850\pi$
$242$	−1.74067	−	6.49628i	−0.111895	−	0.417597i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−6.55672			−0.419751
$245$	−9.95093	−	8.25058i	−0.635741	−	0.527111i
$246$			15.9442i			1.01657i
$247$	−21.0198	+	19.4953i	−1.33746	+	1.24045i
$248$	18.6884	+	10.7898i	1.18672	+	0.685151i
$249$	7.44986	−	1.99619i	0.472116	−	0.126503i
$250$	23.9029	−	13.8003i	1.51175	−	0.872809i
$251$	−2.52209			−0.159193			−0.0795964	−	0.996827i	$-0.525363\pi$
$251$	−2.52209			−0.159193			−0.0795964	+	0.996827i	$0.525363\pi$
$252$	−1.77660	+	8.12672i	−0.111915	+	0.511935i
$253$	14.1032	+	14.1032i	0.886658	+	0.886658i
$254$	2.22549	+	0.596318i	0.139639	+	0.0374163i
$255$	−4.65796	+	1.24810i	−0.291693	+	0.0781588i
$256$	6.65306	−	11.5234i	0.415816	−	0.720215i
$257$	4.19417	+	7.26452i	0.261625	+	0.453148i	0.966674	−	0.256011i	$-0.0824082\pi$
$257$	4.19417	+	7.26452i	0.261625	+	0.453148i	−0.705049	+	0.709159i	$0.749075\pi$
$258$	9.23044	+	9.23044i	0.574662	+	0.574662i
$259$	−13.5266	−	6.99105i	−0.840504	−	0.434402i
$260$	20.4103	−	4.65399i	1.26579	−	0.288628i
$261$	−1.00415	−	1.73924i	−0.0621552	−	0.107656i
$262$	−6.11676	−	22.8281i	−0.377895	−	1.41032i
$263$	−10.4150	+	18.0393i	−0.642215	+	1.11235i	0.342723	+	0.939437i	$0.388651\pi$
$263$	−10.4150	+	18.0393i	−0.642215	+	1.11235i	−0.984937	+	0.172912i	$0.944683\pi$
$264$	3.67786	+	6.37025i	0.226357	+	0.392062i
$265$	−11.7854	+	11.7854i	−0.723973	+	0.723973i
$266$	32.1313	−	35.2728i	1.97010	−	2.16272i
$267$	−2.20934	+	2.20934i	−0.135209	+	0.135209i
$268$	−0.117099	−	0.0313765i	−0.00715294	−	0.00191662i
$269$	−20.7771	−	11.9956i	−1.26680	−	0.731387i	−0.292419	−	0.956290i	$-0.594460\pi$
$269$	−20.7771	−	11.9956i	−1.26680	−	0.731387i	−0.974381	+	0.224903i	$0.927793\pi$
$270$	3.62718	+	2.09415i	0.220743	+	0.127446i
$271$	−4.78503	+	17.8580i	−0.290670	+	1.08480i	0.653926	+	0.756559i	$0.273121\pi$
$271$	−4.78503	+	17.8580i	−0.290670	+	1.08480i	−0.944596	+	0.328236i	$0.893546\pi$
$272$	1.05139			0.0637497
$273$	9.19185	−	2.55146i	0.556316	−	0.154421i
$274$	36.0301			2.17666
$275$	1.16644	−	4.35321i	0.0703389	−	0.262508i
$276$	19.1593	+	11.0616i	1.15326	+	0.665832i
$277$	13.4967	+	7.79230i	0.810936	+	0.468194i	0.847281	−	0.531145i	$-0.178238\pi$
$277$	13.4967	+	7.79230i	0.810936	+	0.468194i	−0.0363448	+	0.999339i	$0.511571\pi$
$278$	4.31877	+	1.15721i	0.259022	+	0.0694048i
$279$	5.88013	−	5.88013i	0.352034	−	0.352034i
$280$	−12.0805	+	3.84806i	−0.721948	+	0.229965i
$281$	10.9101	−	10.9101i	0.650839	−	0.650839i	−0.302356	−	0.953195i	$-0.597773\pi$
$281$	10.9101	−	10.9101i	0.650839	−	0.650839i	0.953195	+	0.302356i	$0.0977731\pi$
$282$	−9.80684	−	16.9859i	−0.583989	−	1.01150i
$283$	9.96595	−	17.2615i	0.592414	−	1.02609i	−0.401492	−	0.915863i	$-0.631508\pi$
$283$	9.96595	−	17.2615i	0.592414	−	1.02609i	0.993906	−	0.110229i	$-0.0351584\pi$
$284$	1.73062	+	6.45878i	0.102694	+	0.383258i
$285$	−7.34156	−	12.7160i	−0.434876	−	0.753228i
$286$	12.3367	−	19.6245i	0.729482	−	1.16042i
$287$	−15.6570	+	10.0394i	−0.924203	+	0.592610i
$288$	−4.31561	−	4.31561i	−0.254300	−	0.254300i
$289$	5.09034	+	8.81673i	0.299432	+	0.518631i
$290$	4.20568	−	7.28444i	0.246966	−	0.427757i
$291$	−10.2135	+	2.73670i	−0.598726	+	0.160428i
$292$	8.90393	+	2.38580i	0.521063	+	0.139618i
$293$	−0.636307	−	0.636307i	−0.0371734	−	0.0371734i	0.688276	−	0.725449i	$-0.258368\pi$
$293$	−0.636307	−	0.636307i	−0.0371734	−	0.0371734i	−0.725449	+	0.688276i	$0.758368\pi$
$294$	−14.8868	+	5.51773i	−0.868218	+	0.321800i
$295$	2.21945			0.129221
$296$	−12.9336	+	7.46723i	−0.751752	+	0.434024i
$297$	2.73797	−	0.733638i	0.158873	−	0.0425700i
$298$	21.1803	+	12.2284i	1.22694	+	0.708374i
$299$	0.953958	−	25.3519i	0.0551688	−	1.46614i
$300$		−	4.99900i		−	0.288618i
$301$	−3.25211	+	14.8762i	−0.187449	+	0.857451i
$302$	−27.4291			−1.57837
$303$	−6.99701	+	4.03973i	−0.401968	+	0.232076i
$304$	0.828563	+	3.09224i	0.0475213	+	0.177352i
$305$	−3.71970	+	0.996691i	−0.212989	+	0.0570703i
$306$	−1.53293	+	5.72099i	−0.0876320	+	0.327047i
$307$	6.68446	+	6.68446i	0.381502	+	0.381502i	0.871643	−	0.490141i	$-0.163055\pi$
$307$	6.68446	+	6.68446i	0.381502	+	0.381502i	−0.490141	+	0.871643i	$0.663055\pi$
$308$	−10.8263	+	20.9474i	−0.616888	+	1.19359i
$309$		−	13.4046i		−	0.762564i
$310$	33.6421	+	9.01438i	1.91074	+	0.511983i
$311$	5.07819	−	8.79569i	0.287958	−	0.498758i	−0.685364	−	0.728200i	$-0.740357\pi$
$311$	5.07819	−	8.79569i	0.287958	−	0.498758i	0.973322	+	0.229443i	$0.0736903\pi$
$312$	2.75975	−	8.94020i	0.156240	−	0.506139i
$313$	−17.7955	+	10.2743i	−1.00586	+	0.580736i	−0.909978	−	0.414657i	$-0.863902\pi$
$313$	−17.7955	+	10.2743i	−1.00586	+	0.580736i	−0.0958859	+	0.995392i	$0.530568\pi$
$314$	13.3371	−	13.3371i	0.752654	−	0.752654i
$315$	0.227464	+	4.88044i	0.0128162	+	0.274982i
$316$		−	10.4542i		−	0.588093i
$317$	7.35161	−	27.4366i	0.412908	−	1.54099i	−0.376082	−	0.926586i	$-0.622729\pi$
$317$	7.35161	−	27.4366i	0.412908	−	1.54099i	0.788990	−	0.614406i	$-0.210604\pi$
$318$	5.29825	+	19.7733i	0.297111	+	1.10883i
$319$	−1.47336	−	5.49866i	−0.0824925	−	0.307866i
$320$	6.23108	−	23.2547i	0.348328	−	1.29998i
$321$			3.44714i			0.192401i
$322$	1.96578	+	42.1775i	0.109549	+	2.35046i
$323$	14.6822	−	14.6822i	0.816942	−	0.816942i
$324$	2.72291	−	1.57208i	0.151273	−	0.0873375i
$325$	−5.06885	+	2.67760i	−0.281169	+	0.148526i
$326$	−21.4504	+	37.1531i	−1.18803	+	2.05772i
$327$	9.96024	+	2.66884i	0.550802	+	0.147587i
$328$			18.2426i			1.00728i
$329$	10.5050	−	20.3256i	0.579158	−	1.12058i
$330$	8.39477	+	8.39477i	0.462117	+	0.462117i
$331$	−3.37737	+	12.6045i	−0.185637	+	0.692807i	0.808856	+	0.588007i	$0.200087\pi$
$331$	−3.37737	+	12.6045i	−0.185637	+	0.692807i	−0.994493	+	0.104801i	$0.966580\pi$
$332$	23.4235	−	6.27631i	1.28553	−	0.344457i
$333$	1.48952	+	5.55896i	0.0816251	+	0.304629i
$334$	−18.4425	+	10.6478i	−1.00913	+	0.582622i
$335$	−0.0712009			−0.00389012
$336$	0.227498	−	1.04065i	0.0124110	−	0.0567720i
$337$		−	24.2904i		−	1.32318i	−0.749865	−	0.661591i	$-0.769882\pi$
$337$		−	24.2904i		−	1.32318i	0.749865	−	0.661591i	$-0.230118\pi$
$338$	−28.9732	+	5.46936i	−1.57594	+	0.297494i
$339$	−13.8640	−	8.00437i	−0.752988	−	0.434738i
$340$	−14.6453	+	3.92420i	−0.794254	+	0.212820i
$341$	20.4135	−	11.7858i	1.10545	−	0.638234i
$342$	−18.0341			−0.975171
$343$	−14.7920	−	11.1444i	−0.798692	−	0.601740i
$344$	10.5610	+	10.5610i	0.569412	+	0.569412i
$345$	12.5508	+	3.36297i	0.675711	+	0.181056i
$346$	43.5278	−	11.6632i	2.34007	−	0.627020i
$347$	−10.7828	+	18.6764i	−0.578852	+	1.00260i	0.416760	+	0.909017i	$0.363166\pi$
$347$	−10.7828	+	18.6764i	−0.578852	+	1.00260i	−0.995611	+	0.0935838i	$0.970168\pi$
$348$	−3.15719	−	5.46842i	−0.169243	−	0.293138i
$349$	−19.0403	−	19.0403i	−1.01920	−	1.01920i	−0.999812	−	0.0193924i	$-0.993827\pi$
$349$	−19.0403	−	19.0403i	−1.01920	−	1.01920i	−0.0193924	−	0.999812i	$-0.506173\pi$
$350$	8.03154	−	5.14992i	0.429304	−	0.275275i
$351$	−3.05250	−	1.91891i	−0.162931	−	0.102424i
$352$	−8.64994	−	14.9821i	−0.461043	−	0.798550i
$353$	0.124255	+	0.463726i	0.00661342	+	0.0246816i	0.969154	−	0.246457i	$-0.0792664\pi$
$353$	0.124255	+	0.463726i	0.00661342	+	0.0246816i	−0.962540	+	0.271139i	$0.912600\pi$
$354$	1.36298	−	2.36076i	0.0724417	−	0.125473i
$355$	1.96361	+	3.40107i	0.104217	+	0.180510i
$356$	−6.94649	+	6.94649i	−0.368163	+	0.368163i
$357$	−6.58316	+	2.09696i	−0.348418	+	0.110983i
$358$	−35.9056	+	35.9056i	−1.89767	+	1.89767i
$359$	0.909775	+	0.243774i	0.0480161	+	0.0128659i	0.282747	−	0.959194i	$-0.408754\pi$
$359$	0.909775	+	0.243774i	0.0480161	+	0.0128659i	−0.234731	+	0.972060i	$0.575421\pi$
$360$	4.15004	+	2.39602i	0.218726	+	0.126282i
$361$	38.2981	+	22.1114i	2.01569	+	1.16376i
$362$	−1.21038	+	4.51719i	−0.0636160	+	0.237418i
$363$	−2.96527			−0.155636
$364$	28.9006	−	8.02218i	1.51480	−	0.420476i
$365$	5.41397			0.283380
$366$	−1.22415	+	4.56861i	−0.0639876	+	0.238805i
$367$	10.2125	+	5.89618i	0.533087	+	0.307778i	0.742273	−	0.670098i	$-0.233748\pi$
$367$	10.2125	+	5.89618i	0.533087	+	0.307778i	−0.209186	+	0.977876i	$0.567081\pi$
$368$	−2.45340	−	1.41647i	−0.127892	−	0.0738387i
$369$	6.79032	+	1.81946i	0.353490	+	0.0947173i
$370$	−17.0440	+	17.0440i	−0.886077	+	0.886077i
$371$	−16.0810	+	17.6533i	−0.834885	+	0.916513i
$372$	18.4880	−	18.4880i	0.958559	−	0.958559i
$373$	−0.518872	−	0.898712i	−0.0268662	−	0.0465336i	0.852280	−	0.523086i	$-0.175219\pi$
$373$	−0.518872	−	0.898712i	−0.0268662	−	0.0465336i	−0.879146	+	0.476553i	$0.841886\pi$
$374$	−8.39427	+	14.5393i	−0.434057	+	0.751809i
$375$	−3.14962	−	11.7546i	−0.162646	−	0.607003i
$376$	−11.2205	−	19.4345i	−0.578653	−	1.00226i
$377$	−3.85375	+	6.13033i	−0.198478	+	0.315728i
$378$	5.33086	+	2.75518i	0.274190	+	0.141711i
$379$	14.2069	+	14.2069i	0.729757	+	0.729757i	0.970571	−	0.240814i	$-0.0774145\pi$
$379$	14.2069	+	14.2069i	0.729757	+	0.729757i	−0.240814	+	0.970571i	$0.577414\pi$
$380$	−23.0830	−	39.9809i	−1.18413	−	2.05098i
$381$	0.507919	−	0.879742i	0.0260215	−	0.0450705i
$382$	0.811599	−	0.217467i	0.0415250	−	0.0111266i
$383$	2.32371	+	0.622635i	0.118736	+	0.0318152i	0.317698	−	0.948192i	$-0.397090\pi$
$383$	2.32371	+	0.622635i	0.118736	+	0.0318152i	−0.198962	+	0.980007i	$0.563757\pi$
$384$	−12.2775	−	12.2775i	−0.626535	−	0.626535i
$385$	−2.95769	+	13.5294i	−0.150738	+	0.689522i
$386$	−55.1152			−2.80529
$387$	4.98438	−	2.87773i	0.253370	−	0.146283i
$388$	−32.1128	+	8.60459i	−1.63028	+	0.436832i
$389$	1.37773	+	0.795431i	0.0698535	+	0.0403299i	0.534520	−	0.845156i	$-0.320492\pi$
$389$	1.37773	+	0.795431i	0.0698535	+	0.0403299i	−0.464666	+	0.885486i	$0.653826\pi$
$390$	0.567834	−	15.0905i	0.0287534	−	0.764135i
$391$			18.3745i			0.929240i
$392$	−17.0328	+	6.31311i	−0.860286	+	0.318860i
$393$	−10.4200			−0.525620
$394$	2.07138	−	1.19591i	0.104355	−	0.0602492i
$395$	−1.58915	−	5.93077i	−0.0799586	−	0.298409i
$396$	8.60860	−	2.30667i	0.432599	−	0.115914i
$397$	1.30201	−	4.85916i	0.0653459	−	0.243874i	−0.925525	−	0.378685i	$-0.876376\pi$
$397$	1.30201	−	4.85916i	0.0653459	−	0.243874i	0.990871	+	0.134811i	$0.0430429\pi$
$398$	−6.97991	−	6.97991i	−0.349871	−	0.349871i
$399$	−11.3554	−	17.7092i	−0.568479	−	0.886569i
$400$			0.640136i			0.0320068i
$401$	−24.9893	−	6.69585i	−1.24790	−	0.334375i	−0.426378	−	0.904545i	$-0.640211\pi$
$401$	−24.9893	−	6.69585i	−1.24790	−	0.334375i	−0.821526	+	0.570170i	$0.806877\pi$
$402$	−0.0437252	+	0.0757342i	−0.00218081	+	0.00377728i
$403$	−28.6490	−	8.84366i	−1.42711	−	0.440534i
$404$	−21.9997	+	12.7015i	−1.09452	+	0.631924i
$405$	1.30577	−	1.30577i	0.0648842	−	0.0648842i
$406$	5.53321	−	10.7059i	0.274609	−	0.531327i
$407$			16.3130i			0.808608i
$408$	−1.75391	+	6.54567i	−0.0868314	+	0.324059i
$409$	10.4140	+	38.8658i	0.514942	+	1.92179i	0.355936	+	0.934511i	$0.384162\pi$
$409$	10.4140	+	38.8658i	0.514942	+	1.92179i	0.159006	+	0.987278i	$0.449171\pi$
$410$	7.62045	+	28.4399i	0.376347	+	1.40455i
$411$	4.11154	−	15.3445i	0.202807	−	0.756887i
$412$		−	42.1462i		−	2.07640i
$413$	3.17644	−	0.148046i	0.156303	−	0.00728485i
$414$	11.2846	−	11.2846i	0.554610	−	0.554610i
$415$	12.3344	−	7.12124i	0.605470	−	0.349568i
$416$	−6.49064	+	21.0264i	−0.318230	+	1.03090i
$417$	0.985664	−	1.70722i	0.0482682	−	0.0836029i
$418$	−49.3768	−	13.2305i	−2.41510	−	0.647124i
$419$		−	10.8704i		−	0.531056i	−0.964103	−	0.265528i	$-0.914454\pi$
$419$		−	10.8704i		−	0.531056i	0.964103	−	0.265528i	$-0.0855462\pi$
$420$	0.715182	+	15.3448i	0.0348973	+	0.748752i
$421$	−23.2762	−	23.2762i	−1.13441	−	1.13441i	−0.989435	−	0.144977i	$-0.953689\pi$
$421$	−23.2762	−	23.2762i	−1.13441	−	1.13441i	−0.144977	−	0.989435i	$-0.546311\pi$
$422$	−16.0661	+	59.9597i	−0.782088	+	2.91879i
$423$	−8.35306	+	2.23820i	−0.406140	+	0.108825i
$424$	6.06199	+	22.6237i	0.294396	+	1.09870i
$425$	3.59568	−	2.07597i	0.174416	−	0.100699i
$426$	4.82348			0.233698
$427$	−5.25711	+	1.67457i	−0.254409	+	0.0810381i
$428$			10.8383i			0.523891i
$429$	−6.94989	−	7.49337i	−0.335544	−	0.361783i
$430$	20.8761	+	12.0528i	1.00673	+	0.581239i
$431$	12.0222	−	3.22133i	0.579088	−	0.155166i	0.0426265	−	0.999091i	$-0.486427\pi$
$431$	12.0222	−	3.22133i	0.579088	−	0.155166i	0.536461	+	0.843925i	$0.319761\pi$
$432$	−0.348677	+	0.201308i	−0.0167757	+	0.00968546i
$433$	18.0375			0.866828			0.433414	−	0.901195i	$-0.357309\pi$
$433$	18.0375			0.866828			0.433414	+	0.901195i	$0.357309\pi$
$434$	48.7495	+	10.6572i	2.34005	+	0.511563i
$435$	−2.62237	−	2.62237i	−0.125733	−	0.125733i
$436$	31.3165	+	8.39123i	1.49979	+	0.401867i
$437$	−54.0414	+	14.4804i	−2.58515	+	0.692689i
$438$	3.32477	−	5.75867i	0.158864	−	0.275160i
$439$	7.62316	+	13.2037i	0.363834	+	0.630178i	0.988588	−	0.150643i	$-0.0481343\pi$
$439$	7.62316	+	13.2037i	0.363834	+	0.630178i	−0.624755	+	0.780821i	$0.714801\pi$
$440$	9.60488	+	9.60488i	0.457895	+	0.457895i
$441$	0.651088	+	6.96965i	0.0310042	+	0.331888i
$442$	20.8206	−	4.74753i	0.990333	−	0.225817i
$443$	14.4921	+	25.1010i	0.688540	+	1.19259i	0.972310	+	0.233694i	$0.0750813\pi$
$443$	14.4921	+	25.1010i	0.688540	+	1.19259i	−0.283770	+	0.958892i	$0.591585\pi$
$444$	4.68327	+	17.4782i	0.222258	+	0.829479i
$445$	−2.88488	+	4.99676i	−0.136756	+	0.236869i
$446$	−24.1936	−	41.9045i	−1.14560	−	1.98423i
$447$	7.62481	−	7.62481i	0.360641	−	0.360641i
$448$	7.36667	−	33.6975i	0.348043	−	1.59206i
$449$	−2.92167	+	2.92167i	−0.137882	+	0.137882i	−0.772679	−	0.634797i	$-0.781084\pi$
$449$	−2.92167	+	2.92167i	−0.137882	+	0.137882i	0.634797	+	0.772679i	$0.281084\pi$
$450$	−3.48322	−	0.933326i	−0.164200	−	0.0439974i
$451$	17.2569	+	9.96327i	0.812595	+	0.469152i
$452$	−43.5904	−	25.1670i	−2.05032	−	1.18375i
$453$	−3.13005	+	11.6815i	−0.147063	+	0.548845i
$454$	−55.7279			−2.61544
$455$	15.1762	−	8.94427i	0.711469	−	0.419314i
$456$	−20.6337			−0.966262
$457$	−0.111468	+	0.416004i	−0.00521425	+	0.0194599i	−0.968484	−	0.249076i	$-0.919873\pi$
$457$	−0.111468	+	0.416004i	−0.00521425	+	0.0194599i	0.963270	+	0.268536i	$0.0865398\pi$
$458$	−16.8660	−	9.73760i	−0.788097	−	0.455008i
$459$	2.26152	+	1.30569i	0.105559	+	0.0609444i
$460$	39.4616	+	10.5737i	1.83990	+	0.493001i
$461$	−17.3315	+	17.3315i	−0.807210	+	0.807210i	−0.984211	−	0.177001i	$-0.943360\pi$
$461$	−17.3315	+	17.3315i	−0.807210	+	0.807210i	0.177001	+	0.984211i	$0.443360\pi$
$462$	12.5745	+	11.4545i	0.585016	+	0.532913i
$463$	−0.666087	+	0.666087i	−0.0309557	+	0.0309557i	−0.722415	−	0.691460i	$-0.756968\pi$
$463$	−0.666087	+	0.666087i	−0.0309557	+	0.0309557i	0.691460	+	0.722415i	$0.256968\pi$
$464$	0.404287	+	0.700246i	0.0187686	+	0.0325081i
$465$	7.67808	−	13.2988i	0.356063	−	0.616719i
$466$	1.80581	+	6.73938i	0.0836526	+	0.312196i
$467$	−13.2451	−	22.9412i	−0.612910	−	1.06159i	−0.990747	−	0.135719i	$-0.956665\pi$
$467$	−13.2451	−	22.9412i	−0.612910	−	1.06159i	0.377837	−	0.925872i	$-0.376668\pi$
$468$	−9.59753	−	6.03335i	−0.443646	−	0.278892i
$469$	−0.101902	+	0.00474938i	−0.00470539	+	0.000219306i
$470$	−25.6109	−	25.6109i	−1.18134	−	1.18134i
$471$	−4.15804	−	7.20193i	−0.191592	−	0.331848i
$472$	1.55946	−	2.70106i	0.0717799	−	0.124326i
$473$	15.7583	−	4.22243i	0.724569	−	0.194148i
$474$	−7.28428	−	1.95182i	−0.334578	−	0.0896500i
$475$	8.93927	+	8.93927i	0.410162	+	0.410162i
$476$	−20.6984	+	6.59317i	−0.948712	+	0.302197i
$477$	9.02566			0.413257
$478$	42.4948	−	24.5344i	1.94367	−	1.12218i
$479$	23.2818	−	6.23835i	1.06377	−	0.285038i	0.315842	−	0.948812i	$-0.397713\pi$
$479$	23.2818	−	6.23835i	1.06377	−	0.285038i	0.747933	+	0.663774i	$0.231046\pi$
$480$	−9.76044	−	5.63519i	−0.445501	−	0.257210i
$481$	15.2139	−	14.1105i	0.693695	−	0.643382i
$482$		−	6.36644i		−	0.289983i
$483$	18.1869	+	3.97586i	0.827530	+	0.180908i
$484$	−9.32326			−0.423784
$485$	−16.9100	+	9.76297i	−0.767841	+	0.443313i
$486$	−0.587020	−	2.19079i	−0.0266278	−	0.0993762i
$487$	35.5651	−	9.52963i	1.61161	−	0.431829i	0.663086	−	0.748543i	$-0.269246\pi$
$487$	35.5651	−	9.52963i	1.61161	−	0.431829i	0.948521	+	0.316714i	$0.102580\pi$
$488$	−1.40062	+	5.22717i	−0.0634030	+	0.236623i
$489$	13.3750	+	13.3750i	0.604837	+	0.604837i
$490$	−23.9167	+	16.9571i	−1.08045	+	0.766045i
$491$		−	0.407582i		−	0.0183939i	−0.999958	−	0.00919695i	$-0.997072\pi$
$491$		−	0.407582i		−	0.0183939i	0.999958	−	0.00919695i	$-0.00292752\pi$
$492$	21.3498	+	5.72066i	0.962522	+	0.257907i
$493$	2.62221	−	4.54181i	0.118099	−	0.204553i
$494$	30.3710	+	57.4941i	1.36645	+	2.58678i
$495$	4.53312	−	2.61720i	0.203749	−	0.117634i
$496$	−2.36744	+	2.36744i	−0.106301	+	0.106301i
$497$	3.03715	+	4.73658i	0.136235	+	0.212465i
$498$		−	17.4929i		−	0.783875i
$499$	8.45163	−	31.5419i	0.378347	−	1.41201i	−0.470045	−	0.882642i	$-0.655762\pi$
$499$	8.45163	−	31.5419i	0.378347	−	1.41201i	0.848392	−	0.529368i	$-0.177571\pi$
$500$	−9.90289	−	36.9581i	−0.442871	−	1.65282i
$501$	2.43013	+	9.06937i	0.108570	+	0.405189i
$502$	−1.48052	+	5.52536i	−0.0660787	+	0.246609i
$503$			43.4769i			1.93854i	0.246005	+	0.969269i	$0.420882\pi$
$503$			43.4769i			1.93854i	−0.246005	+	0.969269i	$0.579118\pi$
$504$	6.09931	+	3.15234i	0.271685	+	0.140416i
$505$	−10.5499	+	10.5499i	−0.469464	+	0.469464i
$506$	39.1759	−	22.6182i	1.74158	−	1.00550i
$507$	−0.976962	+	12.9632i	−0.0433884	+	0.575718i
$508$	1.59697	−	2.76604i	0.0708543	−	0.122723i
$509$	−16.4789	−	4.41551i	−0.730415	−	0.195714i	−0.125601	−	0.992081i	$-0.540086\pi$
$509$	−16.4789	−	4.41551i	−0.730415	−	0.195714i	−0.604814	+	0.796367i	$0.706752\pi$
$510$			10.9373i			0.484310i
$511$	7.74841	−	0.361133i	0.342769	−	0.0159756i
$512$	3.21511	+	3.21511i	0.142089	+	0.142089i
$513$	−2.05794	+	7.68035i	−0.0908604	+	0.339096i
$514$	18.3771	−	4.92413i	0.810579	−	0.217194i
$515$	−6.40668	−	23.9100i	−0.282312	−	1.05360i
$516$	15.6716	−	9.04803i	0.689906	−	0.398317i
$517$	−24.5125			−1.07806
$518$	−23.2563	+	25.5301i	−1.02182	+	1.12173i
$519$		−	19.8685i		−	0.872132i
$520$	0.649688	−	17.2658i	0.0284907	−	0.757154i
$521$	14.8357	+	8.56541i	0.649965	+	0.375257i	0.788443	−	0.615108i	$-0.210888\pi$
$521$	14.8357	+	8.56541i	0.649965	+	0.375257i	−0.138478	+	0.990366i	$0.544221\pi$
$522$	−4.39975	+	1.17891i	−0.192572	+	0.0515995i
$523$	33.3673	−	19.2646i	1.45905	−	0.842384i	0.460086	−	0.887874i	$-0.347818\pi$
$523$	33.3673	−	19.2646i	1.45905	−	0.842384i	0.998965	+	0.0454905i	$0.0144851\pi$
$524$	−32.7621			−1.43122
$525$	−1.27673	−	4.00815i	−0.0557212	−	0.174930i
$526$	33.4064	+	33.4064i	1.45659	+	1.45659i
$527$	20.9757	+	5.62042i	0.913715	+	0.244829i
$528$	−1.10236	+	0.295375i	−0.0479738	+	0.0128546i
$529$	13.2549	−	22.9582i	0.576302	−	0.998184i
$530$	18.9011	+	32.7377i	0.821011	+	1.42203i
$531$	−0.849862	−	0.849862i	−0.0368809	−	0.0368809i
$532$	−35.7029	−	55.6804i	−1.54792	−	2.41405i
$533$	−5.63491	−	24.7122i	−0.244075	−	1.07040i
$534$	3.54327	+	6.13712i	0.153332	+	0.265579i
$535$	1.64754	+	6.14872i	0.0712295	+	0.265832i
$536$	−0.0500282	+	0.0866514i	−0.00216089	+	0.00374277i
$537$	11.1941	+	19.3888i	0.483062	+	0.836687i
$538$	−38.4765	+	38.4765i	−1.65884	+	1.65884i
$539$	−3.33054	+	19.5604i	−0.143457	+	0.842526i
$540$	4.10553	−	4.10553i	0.176674	−	0.176674i
$541$	19.3047	+	5.17267i	0.829972	+	0.222390i	0.648701	−	0.761043i	$-0.275312\pi$
$541$	19.3047	+	5.17267i	0.829972	+	0.222390i	0.181270	+	0.983433i	$0.441979\pi$
$542$	36.3142	+	20.9660i	1.55983	+	0.900567i
$543$	1.78566	+	1.03095i	0.0766300	+	0.0442423i
$544$	4.12500	−	15.3947i	0.176858	−	0.660043i
$545$	19.0418			0.815659
$546$	−0.193914	−	21.6352i	−0.00829876	−	0.925899i
$547$	−13.3946			−0.572711			−0.286355	−	0.958123i	$-0.592444\pi$
$547$	−13.3946			−0.572711			−0.286355	+	0.958123i	$0.592444\pi$
$548$	12.9273	−	48.2453i	0.552227	−	2.06094i
$549$	1.80598	+	1.04268i	0.0770775	+	0.0445007i
$550$	−8.85224	−	5.11084i	−0.377461	−	0.217927i
$551$	15.4244	+	4.13296i	0.657102	+	0.176070i
$552$	12.9113	−	12.9113i	0.549543	−	0.549543i
$553$	−2.66997	−	8.38204i	−0.113539	−	0.356441i
$554$	24.9941	−	24.9941i	1.06190	−	1.06190i
$555$	5.31374	+	9.20367i	0.225556	+	0.390674i
$556$	3.09908	−	5.36776i	0.131430	−	0.227644i
$557$	8.90050	+	33.2171i	0.377126	+	1.40745i	0.850213	+	0.526439i	$0.176473\pi$
$557$	8.90050	+	33.2171i	0.377126	+	1.40745i	−0.473087	+	0.881016i	$0.656860\pi$
$558$	−9.43037	−	16.3339i	−0.399219	−	0.691468i
$559$	−17.5686	−	11.0442i	−0.743072	−	0.467122i
$560$	−0.0915810	−	1.96495i	−0.00387000	−	0.0830342i
$561$	5.23409	+	5.23409i	0.220983	+	0.220983i
$562$	−17.4972	−	30.3060i	−0.738075	−	1.27838i
$563$	0.632829	−	1.09609i	0.0266705	−	0.0461947i	−0.852382	−	0.522920i	$-0.824843\pi$
$563$	0.632829	−	1.09609i	0.0266705	−	0.0461947i	0.879053	+	0.476725i	$0.158176\pi$
$564$	−26.2633	+	7.03723i	−1.10588	+	0.296321i
$565$	−28.5550	−	7.65129i	−1.20132	−	0.321892i
$566$	−31.9662	−	31.9662i	−1.34364	−	1.34364i
$567$	1.78170	−	1.95590i	0.0748244	−	0.0821401i
$568$	5.51878			0.231563
$569$	25.4078	−	14.6692i	1.06515	−	0.614965i	0.138298	−	0.990391i	$-0.455837\pi$
$569$	25.4078	−	14.6692i	1.06515	−	0.614965i	0.926853	+	0.375425i	$0.122503\pi$
$570$	−32.1676	+	8.61929i	−1.34735	+	0.361022i
$571$	16.5675	+	9.56528i	0.693330	+	0.400294i	0.804858	−	0.593467i	$-0.202241\pi$
$571$	16.5675	+	9.56528i	0.693330	+	0.400294i	−0.111528	+	0.993761i	$0.535575\pi$
$572$	−21.8515	−	23.5603i	−0.913657	−	0.985105i
$573$		−	0.370460i		−	0.0154762i
$574$	12.8033	+	40.1945i	0.534401	+	1.67769i
$575$	−11.1873			−0.466543
$576$	−11.2906	+	6.51863i	−0.470442	+	0.271610i
$577$	2.41298	+	9.00535i	0.100454	+	0.374898i	0.997790	−	0.0664499i	$-0.0211673\pi$
$577$	2.41298	+	9.00535i	0.100454	+	0.374898i	−0.897336	+	0.441348i	$0.854501\pi$
$578$	22.3037	−	5.97627i	0.927713	−	0.248580i
$579$	−6.28942	+	23.4725i	−0.261380	+	0.975482i
$580$	−8.24513	−	8.24513i	−0.342360	−	0.342360i
$581$	17.1778	−	11.0146i	0.712654	−	0.456962i
$582$			23.9821i			0.994091i
$583$	24.7120	+	6.62157i	1.02347	+	0.274237i
$584$	3.80404	−	6.58879i	0.157412	−	0.272646i
$585$	−6.36192	−	1.96386i	−0.263033	−	0.0811958i
$586$	−1.76754	+	1.02049i	−0.0730164	+	0.0421560i
$587$	14.3009	−	14.3009i	0.590262	−	0.590262i	−0.347440	−	0.937702i	$-0.612949\pi$
$587$	14.3009	−	14.3009i	0.590262	−	0.590262i	0.937702	+	0.347440i	$0.112949\pi$
$588$	2.04712	+	21.9136i	0.0844218	+	0.903704i
$589$			66.1209i			2.72446i
$590$	1.30286	−	4.86234i	0.0536379	−	0.200179i
$591$	−0.272941	−	1.01863i	−0.0112273	−	0.0419008i
$592$	−0.599705	−	2.23813i	−0.0246477	−	0.0919866i
$593$	−6.29003	+	23.4747i	−0.258300	+	0.963990i	0.707924	+	0.706289i	$0.249632\pi$
$593$	−6.29003	+	23.4747i	−0.258300	+	0.963990i	−0.966225	+	0.257702i	$0.917035\pi$
$594$		−	6.42899i		−	0.263784i
$595$	−10.7402	+	6.88676i	−0.440307	+	0.282330i
$596$	23.9736	−	23.9736i	0.981995	−	0.981995i
$597$	−3.76911	+	2.17610i	−0.154259	+	0.0890616i
$598$	−54.9807	−	16.9720i	−2.24833	−	0.694036i
$599$	19.8737	−	34.4222i	0.812016	−	1.40645i	−0.0994342	−	0.995044i	$-0.531703\pi$
$599$	19.8737	−	34.4222i	0.812016	−	1.40645i	0.911451	−	0.411410i	$-0.134963\pi$
$600$	−3.98533	−	1.06787i	−0.162700	−	0.0435954i
$601$		−	17.6143i		−	0.718502i	−0.933241	−	0.359251i	$-0.883032\pi$
$601$		−	17.6143i		−	0.718502i	0.933241	−	0.359251i	$-0.116968\pi$
$602$	30.6816	+	15.8573i	1.25049	+	0.646297i
$603$	0.0272640	+	0.0272640i	0.00111028	+	0.00111028i
$604$	−9.84135	+	36.7284i	−0.400439	+	1.49446i
$605$	−5.28919	+	1.41723i	−0.215036	+	0.0576188i
$606$	4.74280	+	17.7004i	0.192663	+	0.719029i
$607$	13.1007	−	7.56369i	0.531741	−	0.307001i	−0.209984	−	0.977705i	$-0.567341\pi$
$607$	13.1007	−	7.56369i	0.531741	−	0.307001i	0.741725	+	0.670704i	$0.234008\pi$
$608$	48.5282			1.96808
$609$	−3.92803	−	3.57818i	−0.159172	−	0.144995i
$610$			8.73416i			0.353636i
$611$	21.2028	+	22.8609i	0.857775	+	0.924853i
$612$	7.11057	+	4.10529i	0.287428	+	0.165947i
$613$	−14.4822	+	3.88050i	−0.584932	+	0.156732i	−0.539136	−	0.842219i	$-0.681249\pi$
$613$	−14.4822	+	3.88050i	−0.584932	+	0.156732i	−0.0457959	+	0.998951i	$0.514582\pi$
$614$	18.5682	−	10.7203i	0.749350	−	0.432637i
$615$	12.9816			0.523468
$616$	14.3871	+	13.1057i	0.579672	+	0.528044i
$617$	6.81851	+	6.81851i	0.274503	+	0.274503i	0.830910	−	0.556407i	$-0.187820\pi$
$617$	6.81851	+	6.81851i	0.274503	+	0.274503i	−0.556407	+	0.830910i	$0.687820\pi$
$618$	−29.3668	−	7.86880i	−1.18130	−	0.316529i
$619$	7.00446	−	1.87684i	0.281533	−	0.0754365i	−0.115289	−	0.993332i	$-0.536780\pi$
$619$	7.00446	−	1.87684i	0.281533	−	0.0754365i	0.396822	+	0.917895i	$0.370113\pi$
$620$	24.1411	−	41.8135i	0.969528	−	1.67927i
$621$	−3.51816	−	6.09364i	−0.141179	−	0.244529i
$622$	−16.2885	−	16.2885i	−0.653109	−	0.653109i
$623$	−3.79550	+	7.34374i	−0.152064	+	0.294221i
$624$	1.22899	+	0.772587i	0.0491990	+	0.0309282i
$625$	−7.26121	−	12.5768i	−0.290448	−	0.503071i
$626$	12.0624	+	45.0175i	0.482111	+	1.79926i
$627$	−11.2692	+	19.5188i	−0.450048	+	0.779506i
$628$	−13.0735	−	22.6440i	−0.521689	−	0.903593i
$629$	−10.6269	+	10.6269i	−0.423721	+	0.423721i
$630$	10.8255	+	2.36659i	0.431300	+	0.0942872i
$631$	−17.8111	+	17.8111i	−0.709049	+	0.709049i	−0.966335	−	0.257286i	$-0.917172\pi$
$631$	−17.8111	+	17.8111i	−0.709049	+	0.709049i	0.257286	+	0.966335i	$0.417172\pi$
$632$	−8.33432	−	2.23317i	−0.331521	−	0.0888309i
$633$	23.7022	+	13.6845i	0.942079	+	0.543910i
$634$	−55.7923	−	32.2117i	−2.21579	−	1.27929i
$635$	0.485514	−	1.81196i	0.0192670	−	0.0719056i
$636$	28.3780			1.12526
$637$	21.1233	−	13.8132i	0.836936	−	0.547300i
$638$	−12.9113			−0.511164
$639$	0.550427	−	2.05422i	0.0217745	−	0.0812637i
$640$	−27.7676	−	16.0316i	−1.09761	−	0.633705i
$641$	−25.8518	−	14.9255i	−1.02108	−	0.589523i	−0.106666	−	0.994295i	$-0.534018\pi$
$641$	−25.8518	−	14.9255i	−1.02108	−	0.589523i	−0.914418	+	0.404772i	$0.867351\pi$
$642$	7.55197	+	2.02354i	0.298052	+	0.0798629i
$643$	11.6589	−	11.6589i	0.459783	−	0.459783i	−0.438801	−	0.898584i	$-0.644597\pi$
$643$	11.6589	−	11.6589i	0.459783	−	0.459783i	0.898584	+	0.438801i	$0.144597\pi$
$644$	57.1822	+	12.5007i	2.25329	+	0.492597i
$645$	7.51531	−	7.51531i	0.295915	−	0.295915i
$646$	−23.5469	−	40.7845i	−0.926442	−	1.60464i
$647$	−10.3019	+	17.8434i	−0.405010	+	0.701498i	−0.994323	−	0.106407i	$-0.966065\pi$
$647$	−10.3019	+	17.8434i	−0.405010	+	0.701498i	0.589313	+	0.807905i	$0.299399\pi$
$648$	−0.671640	−	2.50659i	−0.0263845	−	0.0984683i
$649$	−1.70341	−	2.95039i	−0.0668647	−	0.115813i
$650$	2.89053	+	12.6766i	0.113376	+	0.497216i
$651$	10.1017	−	19.5453i	0.395917	−	0.766040i
$652$	42.0529	+	42.0529i	1.64692	+	1.64692i
$653$	−7.50527	−	12.9995i	−0.293704	−	0.508710i	0.680979	−	0.732303i	$-0.261555\pi$
$653$	−7.50527	−	12.9995i	−0.293704	−	0.508710i	−0.974683	+	0.223593i	$0.928221\pi$
$654$	11.6937	−	20.2541i	0.457261	−	0.791999i
$655$	−18.5863	+	4.98019i	−0.726227	+	0.194592i
$656$	−2.73390	−	0.732545i	−0.106741	−	0.0286011i
$657$	−2.07310	−	2.07310i	−0.0808792	−	0.0808792i
$658$	−38.3624	−	34.9457i	−1.49552	−	1.36232i
$659$	−38.4365			−1.49727			−0.748637	−	0.662980i	$-0.769292\pi$
$659$	−38.4365			−1.49727			−0.748637	+	0.662980i	$0.769292\pi$
$660$	14.2528	−	8.22887i	0.554790	−	0.320308i
$661$	31.8115	−	8.52385i	1.23732	−	0.331539i	0.419896	−	0.907572i	$-0.362067\pi$
$661$	31.8115	−	8.52385i	1.23732	−	0.331539i	0.817427	+	0.576033i	$0.195400\pi$
$662$	25.6313	+	14.7982i	0.996187	+	0.575149i
$663$	0.354041	−	9.40881i	0.0137498	−	0.365408i
$664$		−	20.0145i		−	0.776713i
$665$	−28.7187	−	26.1609i	−1.11366	−	1.01448i
$666$	13.0529			0.505789
$667$	−12.2378	+	7.06551i	−0.473851	+	0.273578i
$668$	7.64069	+	28.5155i	0.295627	+	1.10330i
$669$	−20.6071	+	5.52165i	−0.796716	+	0.213479i
$670$	−0.0417964	+	0.155986i	−0.00161474	+	0.00602628i
$671$	4.17978	+	4.17978i	0.161359	+	0.161359i
$672$	−14.3449	−	7.41396i	−0.553367	−	0.286000i
$673$		−	16.4905i		−	0.635663i	−0.948147	−	0.317832i	$-0.897045\pi$
$673$		−	16.4905i		−	0.635663i	0.948147	−	0.317832i	$-0.102955\pi$
$674$	−53.2151	−	14.2590i	−2.04977	−	0.549234i
$675$	−0.794969	+	1.37693i	−0.0305984	+	0.0529979i
$676$	−3.07172	+	40.7584i	−0.118143	+	1.56763i
$677$	16.9952	−	9.81217i	0.653178	−	0.377112i	−0.136495	−	0.990641i	$-0.543584\pi$
$677$	16.9952	−	9.81217i	0.653178	−	0.377112i	0.789673	+	0.613528i	$0.210250\pi$
$678$	−25.6743	+	25.6743i	−0.986017	+	0.986017i
$679$	−23.5501	+	15.1006i	−0.903770	+	0.579508i
$680$			12.5139i			0.479885i
$681$	−6.35934	+	23.7334i	−0.243690	+	0.909465i
$682$	−13.8370	−	51.6402i	−0.529844	−	1.97741i
$683$	−12.3880	−	46.2326i	−0.474013	−	1.76904i	−0.625125	−	0.780525i	$-0.714952\pi$
$683$	−12.3880	−	46.2326i	−0.474013	−	1.76904i	0.151112	−	0.988517i	$-0.451715\pi$
$684$	−6.47048	+	24.1482i	−0.247405	+	0.923328i
$685$		−	29.3352i		−	1.12084i
$686$	−33.0982	+	25.8642i	−1.26369	+	0.987498i
$687$	−6.07169	+	6.07169i	−0.231650	+	0.231650i
$688$	−2.00680	+	1.15862i	−0.0765084	+	0.0441722i
$689$	−15.2000	−	28.7745i	−0.579074	−	1.09622i
$690$	14.7351	−	25.5220i	0.560957	−	0.971606i
$691$	−5.68894	−	1.52435i	−0.216417	−	0.0579889i	0.148981	−	0.988840i	$-0.452401\pi$
$691$	−5.68894	−	1.52435i	−0.216417	−	0.0579889i	−0.365399	+	0.930851i	$0.619067\pi$
$692$		−	62.4697i		−	2.37474i
$693$	6.31317	−	4.04808i	0.239818	−	0.153774i
$694$	34.5863	+	34.5863i	1.31288	+	1.31288i
$695$	0.942185	−	3.51628i	0.0357391	−	0.133380i
$696$	−5.03398	+	1.34885i	−0.190813	+	0.0511281i
$697$	4.75131	+	17.7321i	0.179969	+	0.671652i
$698$	−52.8904	+	30.5363i	−2.00193	+	1.15581i
$699$	3.07623			0.116354
$700$	−4.01424	−	12.6022i	−0.151724	−	0.476319i
$701$			1.40309i			0.0529939i	0.999649	+	0.0264970i	$0.00843523\pi$
$701$			1.40309i			0.0529939i	−0.999649	+	0.0264970i	$0.991565\pi$
$702$	−5.99582	+	5.56095i	−0.226297	+	0.209885i
$703$	−39.6294	−	22.8800i	−1.49465	−	0.862936i
$704$	−35.6957	+	9.56463i	−1.34533	+	0.360481i
$705$	−13.8297	+	7.98460i	−0.520858	+	0.300717i
$706$	1.08887			0.0409800
$707$	−14.3952	+	15.8026i	−0.541386	+	0.594318i
$708$	−2.67209	−	2.67209i	−0.100423	−	0.100423i
$709$	−7.71800	−	2.06803i	−0.289855	−	0.0776665i	0.110961	−	0.993825i	$-0.464607\pi$
$709$	−7.71800	−	2.06803i	−0.289855	−	0.0776665i	−0.400817	+	0.916158i	$0.631274\pi$
$710$	8.60369	−	2.30535i	0.322891	−	0.0865184i
$711$	−1.66248	+	2.87950i	−0.0623478	+	0.107990i
$712$	4.05403	+	7.02179i	0.151931	+	0.263153i
$713$	−41.3745	−	41.3745i	−1.54949	−	1.54949i
$714$	0.729557	+	15.6533i	0.0273030	+	0.585809i
$715$	−15.9780	−	10.0444i	−0.597544	−	0.375638i
$716$	35.1960	+	60.9612i	1.31534	+	2.27823i
$717$	−5.59944	−	20.8974i	−0.209115	−	0.780428i
$718$	1.06811	−	1.85003i	0.0398616	−	0.0690424i
$719$	−5.50575	−	9.53625i	−0.205330	−	0.355642i	0.744908	−	0.667167i	$-0.232493\pi$
$719$	−5.50575	−	9.53625i	−0.205330	−	0.355642i	−0.950238	+	0.311525i	$0.899160\pi$
$720$	−0.525725	+	0.525725i	−0.0195926	+	0.0195926i
$721$	−10.7640	−	33.7924i	−0.400874	−	1.25850i
$722$	70.9232	−	70.9232i	2.63949	−	2.63949i
$723$	−2.71134	−	0.726501i	−0.100836	−	0.0270188i
$724$	5.61438	+	3.24146i	0.208657	+	0.120468i
$725$	2.76528	+	1.59653i	0.102700	+	0.0592937i
$726$	−1.74067	+	6.49628i	−0.0646025	+	0.241100i
$727$	41.0098			1.52097			0.760484	−	0.649357i	$-0.224962\pi$
$727$	41.0098			1.52097			0.760484	+	0.649357i	$0.224962\pi$
$728$	−0.221867	−	24.7539i	−0.00822294	−	0.917440i
$729$	−1.00000			−0.0370370
$730$	3.17811	−	11.8609i	0.117627	−	0.438991i
$731$	13.0161	+	7.51486i	0.481419	+	0.277947i
$732$	5.67828	+	3.27836i	0.209875	+	0.121172i
$733$	11.7325	+	3.14371i	0.433349	+	0.116115i	0.468898	−	0.883252i	$-0.344651\pi$
$733$	11.7325	+	3.14371i	0.433349	+	0.116115i	−0.0355489	+	0.999368i	$0.511318\pi$
$734$	18.9122	−	18.9122i	0.698062	−	0.698062i
$735$	4.49246	+	12.1207i	0.165707	+	0.447078i
$736$	−30.3661	+	30.3661i	−1.11931	+	1.11931i
$737$	0.0546462	+	0.0946501i	0.00201292	+	0.00348648i
$738$	7.97211	−	13.8081i	0.293457	−	0.508283i
$739$	−2.34691	−	8.75877i	−0.0863323	−	0.322197i	0.909231	−	0.416292i	$-0.136671\pi$
$739$	−2.34691	−	8.75877i	−0.0863323	−	0.322197i	−0.995563	+	0.0940957i	$0.970004\pi$
$740$	16.7072	+	28.9377i	0.614169	+	1.06377i
$741$	27.9513	−	6.37350i	1.02682	−	0.234136i
$742$	29.2347	+	45.5930i	1.07324	+	1.67377i
$743$	9.19856	+	9.19856i	0.337462	+	0.337462i	0.855411	−	0.517949i	$-0.173304\pi$
$743$	9.19856	+	9.19856i	0.337462	+	0.337462i	−0.517949	+	0.855411i	$0.673304\pi$
$744$	−10.7898	−	18.6884i	−0.395572	−	0.685151i
$745$	9.95624	−	17.2447i	0.364768	−	0.631797i
$746$	−2.27348	+	0.609176i	−0.0832379	+	0.0223035i
$747$	−7.44986	−	1.99619i	−0.272576	−	0.0730366i
$748$	16.4568	+	16.4568i	0.601719	+	0.601719i
$749$	2.76809	+	8.69007i	0.101144	+	0.317528i
$750$	−27.6007			−1.00783
$751$	4.97790	−	2.87399i	0.181646	−	0.104873i	−0.406420	−	0.913686i	$-0.633223\pi$
$751$	4.97790	−	2.87399i	0.181646	−	0.104873i	0.588066	+	0.808813i	$0.299890\pi$
$752$	3.36309	−	0.901136i	0.122639	−	0.0328610i
$753$	2.18419	+	1.26104i	0.0795964	+	0.0459550i
$754$	11.1680	+	12.0414i	0.406716	+	0.438521i
$755$			22.3324i			0.812761i
$756$	5.60193	−	6.14964i	0.203740	−	0.223660i
$757$	−6.78438			−0.246583			−0.123291	−	0.992371i	$-0.539345\pi$
$757$	−6.78438			−0.246583			−0.123291	+	0.992371i	$0.539345\pi$
$758$	39.4639	−	22.7845i	1.43339	−	0.827571i
$759$	−5.16212	−	19.2653i	−0.187373	−	0.699285i
$760$	−36.8046	+	9.86176i	−1.33504	+	0.357724i
$761$	0.500800	−	1.86901i	0.0181540	−	0.0677516i	−0.956255	−	0.292536i	$-0.905501\pi$
$761$	0.500800	−	1.86901i	0.0181540	−	0.0677516i	0.974409	+	0.224784i	$0.0721677\pi$
$762$	−1.62917	−	1.62917i	−0.0590186	−	0.0590186i
$763$	27.2523	−	1.27016i	0.986601	−	0.0459828i
$764$		−	1.16478i		−	0.0421403i
$765$	4.65796	+	1.24810i	0.168409	+	0.0451250i
$766$	2.72812	−	4.72525i	0.0985712	−	0.170730i
$767$	−1.27818	+	4.14067i	−0.0461526	+	0.149511i
$768$	−11.5234	+	6.65306i	−0.415816	+	0.240072i
$769$	1.49568	−	1.49568i	0.0539356	−	0.0539356i	−0.679625	−	0.733560i	$-0.737857\pi$
$769$	1.49568	−	1.49568i	0.0539356	−	0.0539356i	0.733560	+	0.679625i	$0.237857\pi$
$770$	27.9038	+	14.4217i	1.00558	+	0.519722i
$771$		−	8.38834i		−	0.302099i
$772$	−19.7749	+	73.8009i	−0.711714	+	2.65615i
$773$	3.23742	+	12.0822i	0.116442	+	0.434567i	0.999391	−	0.0349020i	$-0.0111119\pi$
$773$	3.23742	+	12.0822i	0.116442	+	0.434567i	−0.882949	+	0.469469i	$0.844445\pi$
$774$	−3.37858	−	12.6090i	−0.121440	−	0.453222i
$775$	−3.42198	+	12.7710i	−0.122921	+	0.458749i
$776$			27.4392i			0.985008i
$777$	8.21889	+	12.8177i	0.294851	+	0.459834i
$778$	2.55137	−	2.55137i	0.0914712	−	0.0914712i
$779$	−48.4076	+	27.9482i	−1.73438	+	1.00135i
$780$	−20.0028	−	6.17468i	−0.716217	−	0.221089i
$781$	3.01411	−	5.22059i	0.107853	−	0.186807i
$782$	40.2547	+	10.7862i	1.43951	+	0.385715i
$783$			2.00830i			0.0717706i
$784$	−0.262139	−	2.80610i	−0.00936211	−	0.100218i
$785$	−10.8589	−	10.8589i	−0.387570	−	0.387570i
$786$	−6.11676	+	22.8281i	−0.218178	+	0.814250i
$787$	44.0357	−	11.7993i	1.56970	−	0.420601i	0.633984	−	0.773346i	$-0.281418\pi$
$787$	44.0357	−	11.7993i	1.56970	−	0.420601i	0.935719	+	0.352745i	$0.114752\pi$
$788$	−0.858167	−	3.20272i	−0.0305709	−	0.114092i
$789$	18.0393	−	10.4150i	0.642215	−	0.370783i
$790$	−13.9259			−0.495462
$791$	−41.3779	−	9.04571i	−1.47123	−	0.321628i
$792$		−	7.35573i		−	0.261374i
$793$	0.282726	−	7.51359i	0.0100399	−	0.266815i
$794$	−9.88108	−	5.70485i	−0.350667	−	0.202457i
$795$	16.0992	−	4.31376i	0.570979	−	0.152993i
$796$	−11.8506	+	6.84197i	−0.420035	+	0.242507i
$797$	−4.01929			−0.142371			−0.0711853	−	0.997463i	$-0.522678\pi$
$797$	−4.01929			−0.142371			−0.0711853	+	0.997463i	$0.522678\pi$
$798$	−45.4630	+	14.4815i	−1.60937	+	0.512640i
$799$	−15.9683	−	15.9683i	−0.564916	−	0.564916i
$800$	9.37306	+	2.51150i	0.331388	+	0.0887951i
$801$	3.01801	−	0.808673i	0.106636	−	0.0285731i
$802$	−29.3384	+	50.8156i	−1.03597	+	1.79436i
$803$	−4.15519	−	7.19699i	−0.146633	−	0.253976i
$804$	0.0857221	+	0.0857221i	0.00302319	+	0.00302319i
$805$	34.3404	−	1.60051i	1.21034	−	0.0564106i
$806$	−36.1921	+	57.5724i	−1.27481	+	2.02790i
$807$	11.9956	+	20.7771i	0.422267	+	0.731387i
$808$	5.42648	+	20.2519i	0.190903	+	0.712459i
$809$	−21.6566	+	37.5104i	−0.761406	+	1.31879i	0.180720	+	0.983535i	$0.442157\pi$
$809$	−21.6566	+	37.5104i	−0.761406	+	1.31879i	−0.942126	+	0.335259i	$0.891176\pi$
$810$	−2.09415	−	3.62718i	−0.0735810	−	0.127446i
$811$	−24.4994	+	24.4994i	−0.860289	+	0.860289i	−0.991371	−	0.131083i	$-0.958155\pi$
$811$	−24.4994	+	24.4994i	−0.860289	+	0.860289i	0.131083	+	0.991371i	$0.458155\pi$
$812$	−12.3503	−	11.2503i	−0.433411	−	0.394810i
$813$	13.0730	−	13.0730i	0.458488	−	0.458488i
$814$	35.7384	+	9.57609i	1.25263	+	0.335642i
$815$	30.2496	+	17.4646i	1.05960	+	0.611759i
$816$	−0.910528	−	0.525693i	−0.0318748	−	0.0184030i
$817$	−11.8444	+	44.2040i	−0.414384	+	1.54650i
$818$	91.2600			3.19083
$819$	−9.23610	−	2.38629i	−0.322736	−	0.0833838i
$820$	40.8160			1.42536
$821$	−2.81490	+	10.5054i	−0.0982407	+	0.366639i	−0.997491	−	0.0707954i	$-0.977446\pi$
$821$	−2.81490	+	10.5054i	−0.0982407	+	0.366639i	0.899250	+	0.437435i	$0.144113\pi$
$822$	−31.2029	−	18.0150i	−1.08833	−	0.628346i
$823$	24.2246	+	13.9861i	0.844416	+	0.487524i	0.858763	−	0.512373i	$-0.171233\pi$
$823$	24.2246	+	13.9861i	0.844416	+	0.487524i	−0.0143466	+	0.999897i	$0.504567\pi$
$824$	−33.6000	−	9.00309i	−1.17051	−	0.313638i
$825$	−3.18677	+	3.18677i	−0.110949	+	0.110949i
$826$	1.54030	−	7.04583i	0.0535939	−	0.245156i
$827$	−3.42803	+	3.42803i	−0.119204	+	0.119204i	−0.764193	−	0.644988i	$-0.776862\pi$
$827$	−3.42803	+	3.42803i	−0.119204	+	0.119204i	0.644988	+	0.764193i	$0.276862\pi$
$828$	−11.0616	−	19.1593i	−0.384418	−	0.665832i
$829$	10.7071	−	18.5452i	0.371871	−	0.644100i	−0.617982	−	0.786192i	$-0.712050\pi$
$829$	10.7071	−	18.5452i	0.371871	−	0.644100i	0.989853	+	0.142092i	$0.0453829\pi$
$830$	−8.36063	−	31.2023i	−0.290202	−	1.08305i
$831$	−7.79230	−	13.4967i	−0.270312	−	0.468194i
$832$	39.7963	+	25.0174i	1.37969	+	0.867321i
$833$	−14.9119	+	10.5727i	−0.516667	+	0.366321i
$834$	−3.16156	−	3.16156i	−0.109476	−	0.109476i
$835$	8.66931	+	15.0157i	0.300014	+	0.519639i
$836$	−35.4320	+	61.3701i	−1.22544	+	2.12253i
$837$	−8.03240	+	2.15228i	−0.277640	+	0.0743935i
$838$	−23.8148	−	6.38117i	−0.822670	−	0.220434i
$839$	34.4914	+	34.4914i	1.19078	+	1.19078i	0.976850	+	0.213927i	$0.0686255\pi$
$839$	34.4914	+	34.4914i	1.19078	+	1.19078i	0.213927	+	0.976850i	$0.431375\pi$
$840$	12.3861	+	2.70774i	0.427359	+	0.0934258i
$841$	−24.9667			−0.860922
$842$	−64.6568	+	37.3296i	−2.22822	+	1.28646i
$843$	−14.9034	+	3.99336i	−0.513301	+	0.137539i
$844$	74.5234	+	43.0261i	2.56520	+	1.48102i
$845$	4.45309	+	23.5896i	0.153191	+	0.811508i
$846$			19.6137i			0.674332i
$847$	−7.47529	+	2.38114i	−0.256854	+	0.0818169i
$848$	−3.63388			−0.124788
$849$	−17.2615	+	9.96595i	−0.592414	+	0.342031i
$850$	−2.43727	−	9.09602i	−0.0835977	−	0.311991i
$851$	39.1146	−	10.4807i	1.34083	−	0.359275i
$852$	1.73062	−	6.45878i	0.0592902	−	0.221274i
$853$	−2.96642	−	2.96642i	−0.101568	−	0.101568i	0.654497	−	0.756065i	$-0.272881\pi$
$853$	−2.96642	−	2.96642i	−0.101568	−	0.101568i	−0.756065	+	0.654497i	$0.772881\pi$
$854$	0.582602	+	12.5002i	0.0199362	+	0.427749i
$855$			14.6831i			0.502152i
$856$	8.64059	+	2.31524i	0.295329	+	0.0791332i
$857$	−4.40555	+	7.63063i	−0.150491	+	0.260657i	−0.931408	−	0.363977i	$-0.881419\pi$
$857$	−4.40555	+	7.63063i	−0.150491	+	0.260657i	0.780917	+	0.624634i	$0.214752\pi$
$858$	−20.4961	+	10.8270i	−0.699726	+	0.369627i
$859$	−23.1214	+	13.3491i	−0.788891	+	0.455466i	−0.839572	−	0.543249i	$-0.817194\pi$
$859$	−23.1214	+	13.3491i	−0.788891	+	0.455466i	0.0506813	+	0.998715i	$0.483861\pi$
$860$	23.6293	−	23.6293i	0.805751	−	0.805751i
$861$	18.5791	−	0.865921i	0.633173	−	0.0295105i
$862$		−	28.2290i		−	0.961485i
$863$	3.49278	−	13.0352i	0.118896	−	0.443724i	−0.880653	−	0.473761i	$-0.842896\pi$
$863$	3.49278	−	13.0352i	0.118896	−	0.443724i	0.999549	+	0.0300371i	$0.00956256\pi$
$864$	1.57962	+	5.89524i	0.0537399	+	0.200560i
$865$	−9.49606	−	35.4398i	−0.322876	−	1.20499i
$866$	10.5884	−	39.5164i	0.359808	−	1.34282i
$867$		−	10.1807i		−	0.345754i
$868$	31.7613	−	61.4533i	1.07805	−	2.08586i
$869$	−6.66433	+	6.66433i	−0.226072	+	0.226072i
$870$	−7.28444	+	4.20568i	−0.246966	+	0.142586i
$871$	0.0410048	−	0.132835i	0.00138939	−	0.00450093i
$872$	13.3794	−	23.1738i	0.453083	−	0.784763i
$873$	10.2135	+	2.73670i	0.345674	+	0.0926232i
$874$			126.894i			4.29224i
$875$	−17.3790	−	27.1034i	−0.587519	−	0.916264i
$876$	−6.51813	−	6.51813i	−0.220227	−	0.220227i
$877$	8.54398	−	31.8866i	0.288510	−	1.07673i	−0.657726	−	0.753257i	$-0.728482\pi$
$877$	8.54398	−	31.8866i	0.288510	−	1.07673i	0.946236	−	0.323476i	$-0.104852\pi$
$878$	33.4015	−	8.94990i	1.12725	−	0.302045i
$879$	0.232904	+	0.869211i	0.00785567	+	0.0293178i
$880$	−1.82511	+	1.05373i	−0.0615245	+	0.0355212i
$881$	−10.7473			−0.362086			−0.181043	−	0.983475i	$-0.557947\pi$
$881$	−10.7473			−0.362086			−0.181043	+	0.983475i	$0.557947\pi$
$882$	15.6512	+	2.66493i	0.527005	+	0.0897329i
$883$		−	28.8826i		−	0.971978i	−0.873965	−	0.485989i	$-0.838459\pi$
$883$		−	28.8826i		−	0.971978i	0.873965	−	0.485989i	$-0.161541\pi$
$884$	1.11316	−	29.5827i	0.0374396	−	0.994975i
$885$	−1.92210	−	1.10972i	−0.0646106	−	0.0373029i
$886$	63.4982	−	17.0143i	2.13326	−	0.571607i
$887$	5.86683	−	3.38722i	0.196989	−	0.113732i	−0.398261	−	0.917272i	$-0.630386\pi$
$887$	5.86683	−	3.38722i	0.196989	−	0.113732i	0.595250	+	0.803540i	$0.297053\pi$
$888$	14.9345			0.501168
$889$	0.573997	−	2.62565i	0.0192512	−	0.0880613i
$890$	9.25337	+	9.25337i	0.310174	+	0.310174i
$891$	−2.73797	−	0.733638i	−0.0917256	−	0.0245778i
$892$	−64.7918	+	17.3609i	−2.16939	+	0.581286i
$893$	34.3803	−	59.5483i	1.15049	−	1.99271i
$894$	−12.2284	−	21.1803i	−0.408980	−	0.708374i
$895$	29.2338	+	29.2338i	0.977180	+	0.977180i
$896$	−40.8100	−	21.0920i	−1.36337	−	0.704636i
$897$	−13.5021	+	21.4784i	−0.450822	+	0.717143i
$898$	4.68568	+	8.11584i	0.156363	+	0.270829i
$899$	4.32241	+	16.1314i	0.144160	+	0.538014i
$900$	−2.49950	+	4.32926i	−0.0833167	+	0.144309i
$901$	11.7847	+	20.4117i	0.392606	+	0.680014i
$902$	31.9576	−	31.9576i	1.06407	−	1.06407i
$903$	10.2545	−	11.2571i	0.341249	−	0.374613i
$904$	−29.3753	+	29.3753i	−0.977008	+	0.977008i
$905$	3.67784	+	0.985474i	0.122256	+	0.0327583i
$906$	23.7543	+	13.7146i	0.789184	+	0.455636i
$907$	−18.5360	−	10.7018i	−0.615478	−	0.355347i	0.159628	−	0.987177i	$-0.448970\pi$
$907$	−18.5360	−	10.7018i	−0.615478	−	0.355347i	−0.775106	+	0.631831i	$0.782304\pi$
$908$	−19.9947	+	74.6213i	−0.663548	+	2.47640i
$909$	8.07945			0.267979
$910$	−10.6863	−	38.4982i	−0.354247	−	1.27620i
$911$	31.0273			1.02798			0.513990	−	0.857796i	$-0.328167\pi$
$911$	31.0273			1.02798			0.513990	+	0.857796i	$0.328167\pi$
$912$	0.828563	−	3.09224i	0.0274365	−	0.102394i
$913$	−18.9331	−	10.9310i	−0.626593	−	0.361764i
$914$	0.845944	+	0.488406i	0.0279813	+	0.0161550i
$915$	3.71970	+	0.996691i	0.122969	+	0.0329496i
$916$	−19.0903	+	19.0903i	−0.630762	+	0.630762i
$917$	−26.2683	+	8.36736i	−0.867456	+	0.276315i
$918$	4.18805	−	4.18805i	0.138226	−	0.138226i
$919$	−12.8898	−	22.3258i	−0.425195	−	0.736459i	0.571244	−	0.820780i	$-0.306461\pi$
$919$	−12.8898	−	22.3258i	−0.425195	−	0.736459i	−0.996439	+	0.0843215i	$0.973128\pi$
$920$	16.8592	−	29.2010i	0.555832	−	0.962729i
$921$	−2.44668	−	9.13114i	−0.0806209	−	0.300881i
$922$	27.7958	+	48.1437i	0.915405	+	1.58553i
$923$	−7.47598	+	1.70468i	−0.246075	+	0.0561104i
$924$	19.8496	−	12.7278i	0.653003	−	0.418713i
$925$	−6.47015	−	6.47015i	−0.212737	−	0.212737i
$926$	1.06825	+	1.85026i	0.0351049	+	0.0608034i
$927$	−6.70232	+	11.6088i	−0.220133	+	0.381282i
$928$	11.8394	−	3.17235i	0.388647	−	0.104138i
$929$	−9.63049	−	2.58048i	−0.315966	−	0.0846629i	0.0973506	−	0.995250i	$-0.468963\pi$
$929$	−9.63049	−	2.58048i	−0.315966	−	0.0846629i	−0.413317	+	0.910587i	$0.635630\pi$
$930$	−24.6277	−	24.6277i	−0.807576	−	0.807576i
$931$	−42.8469	−	35.5255i	−1.40425	−	1.16430i
$932$	9.67214			0.316821
$933$	−8.79569	+	5.07819i	−0.287958	+	0.166253i
$934$	−58.0344	+	15.5503i	−1.89895	+	0.508821i
$935$	11.8377	+	6.83451i	0.387135	+	0.223512i
$936$	−6.86012	+	6.36257i	−0.224230	+	0.207967i
$937$			21.1625i			0.691349i	0.938354	+	0.345675i	$0.112350\pi$
$937$			21.1625i			0.691349i	−0.938354	+	0.345675i	$0.887650\pi$
$938$	−0.0494136	+	0.226034i	−0.00161341	+	0.00738026i
$939$	20.5485			0.670576
$940$	−43.4828	+	25.1048i	−1.41825	+	0.818828i
$941$	−5.84488	−	21.8134i	−0.190538	−	0.711096i	−0.993377	−	0.114901i	$-0.963345\pi$
$941$	−5.84488	−	21.8134i	−0.190538	−	0.711096i	0.802839	−	0.596195i	$-0.203322\pi$
$942$	−18.2188	+	4.88171i	−0.593600	+	0.159055i
$943$	12.8023	−	47.7789i	0.416901	−	1.55589i
$944$	0.342169	+	0.342169i	0.0111366	+	0.0111366i
$945$	2.24323	−	4.34032i	0.0729723	−	0.141191i
$946$		−	37.0018i		−	1.20303i
$947$	38.2495	+	10.2489i	1.24294	+	0.333045i	0.819606	−	0.572928i	$-0.194192\pi$
$947$	38.2495	+	10.2489i	1.24294	+	0.333045i	0.423336	+	0.905973i	$0.360859\pi$
$948$	−5.22708	+	9.05358i	−0.169768	+	0.294046i
$949$	−3.11792	+	10.1005i	−0.101212	+	0.327875i
$950$	24.8316	−	14.3365i	0.805643	−	0.465138i
$951$	−20.0850	+	20.0850i	−0.651300	+	0.651300i
$952$	0.834723	+	17.9097i	0.0270535	+	0.580457i
$953$		−	37.4474i		−	1.21304i	−0.795069	−	0.606520i	$-0.792565\pi$
$953$		−	37.4474i		−	1.21304i	0.795069	−	0.606520i	$-0.207435\pi$
$954$	5.29825	−	19.7733i	0.171537	−	0.640185i
$955$	−0.177059	−	0.660794i	−0.00572950	−	0.0213828i
$956$	−17.6055	−	65.7046i	−0.569402	−	2.12504i
$957$	−1.47336	+	5.49866i	−0.0476270	+	0.177747i
$958$		−	54.6677i		−	1.76623i
$959$	−1.95677	−	41.9842i	−0.0631874	−	1.35574i
$960$	−17.0236	+	17.0236i	−0.549436	+	0.549436i
$961$	−33.0404	+	19.0759i	−1.06582	+	0.615352i
$962$	−21.9822	−	41.6136i	−0.708735	−	1.34168i
$963$	1.72357	−	2.98531i	0.0555413	−	0.0962004i
$964$	−8.52485	−	2.28423i	−0.274567	−	0.0735700i
$965$			44.8741i			1.44455i
$966$	19.3863	−	37.5097i	0.623745	−	1.20685i
$967$	−17.5939	−	17.5939i	−0.565781	−	0.565781i	0.365163	−	0.930944i	$-0.381013\pi$
$967$	−17.5939	−	17.5939i	−0.565781	−	0.565781i	−0.930944	+	0.365163i	$0.881013\pi$
$968$	−1.99159	+	7.43273i	−0.0640122	+	0.238897i
$969$	−20.0563	+	5.37408i	−0.644302	+	0.172640i
$970$	11.4621	+	42.7772i	0.368026	+	1.37349i
$971$	26.2328	−	15.1455i	0.841851	−	0.486043i	−0.0160417	−	0.999871i	$-0.505106\pi$
$971$	26.2328	−	15.1455i	0.841851	−	0.486043i	0.857893	+	0.513828i	$0.171773\pi$
$972$	−3.14415			−0.100849
$973$	1.11389	−	5.09531i	0.0357098	−	0.163348i
$974$		−	83.5097i		−	2.67582i
$975$	5.72855	+	0.215558i	0.183460	+	0.00690337i
$976$	−0.727119	−	0.419803i	−0.0232745	−	0.0134376i
$977$	0.0786069	−	0.0210627i	0.00251486	−	0.000673854i	−0.257561	−	0.966262i	$-0.582919\pi$
$977$	0.0786069	−	0.0210627i	0.00251486	−	0.000673854i	0.260076	+	0.965588i	$0.416252\pi$
$978$	37.1531	−	21.4504i	1.18803	−	0.685907i
$979$	8.85651			0.283055
$980$	14.1250	+	38.1092i	0.451206	+	1.21736i
$981$	−7.29140	−	7.29140i	−0.232796	−	0.232796i
$982$	−0.892925	−	0.239259i	−0.0284944	−	0.00763505i
$983$	−14.4178	+	3.86323i	−0.459856	+	0.123218i	−0.481307	−	0.876552i	$-0.659838\pi$
$983$	−14.4178	+	3.86323i	−0.459856	+	0.123218i	0.0214516	+	0.999770i	$0.493171\pi$
$984$	9.12129	−	15.7985i	0.290776	−	0.503639i
$985$	−0.973696	−	1.68649i	−0.0310245	−	0.0537361i
$986$	−8.41085	−	8.41085i	−0.267856	−	0.267856i
$987$	−19.2603	+	12.3500i	−0.613064	+	0.393104i
$988$	87.8831	−	20.0392i	2.79593	−	0.637533i
$989$	−20.2487	−	35.0717i	−0.643870	−	1.11522i
$990$	−3.07270	−	11.4675i	−0.0976567	−	0.364460i
$991$	17.0275	−	29.4925i	0.540897	−	0.936861i	−0.457956	−	0.888975i	$-0.651418\pi$
$991$	17.0275	−	29.4925i	0.540897	−	0.936861i	0.998853	−	0.0478864i	$-0.0152485\pi$
$992$	25.3764	+	43.9531i	0.805700	+	1.39551i
$993$	9.22715	−	9.22715i	0.292815	−	0.292815i
$994$	12.1597	−	3.87329i	0.385683	−	0.122853i
$995$	−5.68295	+	5.68295i	−0.180162	+	0.180162i
$996$	−23.4235	−	6.27631i	−0.742202	−	0.198872i
$997$	0.957007	+	0.552528i	0.0303087	+	0.0174987i	0.515078	−	0.857143i	$-0.327763\pi$
$997$	0.957007	+	0.552528i	0.0303087	+	0.0174987i	−0.484769	+	0.874642i	$0.661096\pi$
$998$	−64.1404	−	37.0315i	−2.03033	−	1.17221i
$999$	1.48952	−	5.55896i	0.0471263	−	0.175878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.b.73.9	yes	36
3.2	odd	2		819.2.fn.g.73.1		36
7.5	odd	6		273.2.bz.a.229.1	yes	36
13.5	odd	4		273.2.bz.a.31.1	✓	36
21.5	even	6		819.2.fn.f.775.9		36
39.5	even	4		819.2.fn.f.577.9		36
91.5	even	12	inner	273.2.bz.b.187.9	yes	36
273.5	odd	12		819.2.fn.g.460.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.31.1	✓	36	13.5	odd	4
273.2.bz.a.229.1	yes	36	7.5	odd	6
273.2.bz.b.73.9	yes	36	1.1	even	1	trivial
273.2.bz.b.187.9	yes	36	91.5	even	12	inner
819.2.fn.f.577.9		36	39.5	even	4
819.2.fn.f.775.9		36	21.5	even	6
819.2.fn.g.73.1		36	3.2	odd	2
819.2.fn.g.460.1		36	273.5	odd	12

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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587020 - 2.19079i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72291 - 1.57208i) q^{4} +(-1.78371 - 0.477944i) q^{5} +(-1.60377 + 1.60377i) q^{6} +(-2.58471 - 0.565048i) q^{7} +(-1.83495 + 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.587020 - 2.19079i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.72291 - 1.57208i) q^{4} +(-1.78371 - 0.477944i) q^{5} +(-1.60377 + 1.60377i) q^{6} +(-2.58471 - 0.565048i) q^{7} +(-1.83495 + 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.09415 + 3.62718i) q^{10} +(0.733638 + 2.73797i) q^{11} +(1.57208 + 2.72291i) q^{12} +(1.91891 - 3.05250i) q^{13} +(-2.75518 + 5.33086i) q^{14} +(1.30577 + 1.30577i) q^{15} +(-0.201308 - 0.348677i) q^{16} +(-1.30569 + 2.26152i) q^{17} +(2.19079 - 0.587020i) q^{18} +(-7.68035 - 2.05794i) q^{19} +(4.10553 + 4.10553i) q^{20} +(1.95590 + 1.78170i) q^{21} +6.42899 q^{22} +(6.09364 - 3.51816i) q^{23} +(2.50659 - 0.671640i) q^{24} +(-1.37693 - 0.794969i) q^{25} +(-5.56095 - 5.99582i) q^{26} -1.00000i q^{27} +(6.14964 + 5.60193i) q^{28} -2.00830 q^{29} +(3.62718 - 2.09415i) q^{30} +(-2.15228 - 8.03240i) q^{31} +(-5.89524 + 1.57962i) q^{32} +(0.733638 - 2.73797i) q^{33} +(4.18805 + 4.18805i) q^{34} +(4.34032 + 2.24323i) q^{35} -3.14415i q^{36} +(5.55896 + 1.48952i) q^{37} +(-9.01704 + 15.6180i) q^{38} +(-3.18808 + 1.68409i) q^{39} +(4.15004 - 2.39602i) q^{40} +(4.97086 - 4.97086i) q^{41} +(5.05148 - 3.23907i) q^{42} -5.75547i q^{43} +(2.30667 - 8.60860i) q^{44} +(-0.477944 - 1.78371i) q^{45} +(-4.13047 - 15.4151i) q^{46} +(-2.23820 + 8.35306i) q^{47} +0.402617i q^{48} +(6.36144 + 2.92097i) q^{49} +(-2.54989 + 2.54989i) q^{50} +(2.26152 - 1.30569i) q^{51} +(-10.0238 + 5.29503i) q^{52} +(4.51283 - 7.81645i) q^{53} +(-2.19079 - 0.587020i) q^{54} -5.23440i q^{55} +(5.77966 - 3.70599i) q^{56} +(5.62240 + 5.62240i) q^{57} +(-1.17891 + 4.39975i) q^{58} +(-1.16093 + 0.311071i) q^{59} +(-1.50273 - 5.60826i) q^{60} +(1.80598 - 1.04268i) q^{61} -18.8607 q^{62} +(-0.803009 - 2.52095i) q^{63} +13.0373i q^{64} +(-4.88172 + 4.52765i) q^{65} +(-5.56767 - 3.21449i) q^{66} +(0.0372433 - 0.00997932i) q^{67} +(7.11057 - 4.10529i) q^{68} -7.03633 q^{69} +(7.46230 - 8.19190i) q^{70} +(-1.50379 - 1.50379i) q^{71} +(-2.50659 - 0.671640i) q^{72} +(-2.83190 + 0.758806i) q^{73} +(6.52644 - 11.3041i) q^{74} +(0.794969 + 1.37693i) q^{75} +(17.6777 + 17.6777i) q^{76} +(-0.349154 - 7.49141i) q^{77} +(1.81802 + 7.97300i) q^{78} +(1.66248 + 2.87950i) q^{79} +(0.192429 + 0.718153i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.97211 - 13.8081i) q^{82} +(-5.45368 + 5.45368i) q^{83} +(-2.52478 - 7.92624i) q^{84} +(3.40986 - 3.40986i) q^{85} +(-12.6090 - 3.37858i) q^{86} +(1.73924 + 1.00415i) q^{87} +(-6.37025 - 3.67786i) q^{88} +(0.808673 - 3.01801i) q^{89} -4.18830 q^{90} +(-6.68464 + 6.80555i) q^{91} -22.1233 q^{92} +(-2.15228 + 8.03240i) q^{93} +(16.9859 + 9.80684i) q^{94} +(12.7160 + 7.34156i) q^{95} +(5.89524 + 1.57962i) q^{96} +(7.47680 - 7.47680i) q^{97} +(10.1335 - 12.2219i) q^{98} +(-2.00434 + 2.00434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 + 18 * q^9	\( 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

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