LMFDB - Embedded newform 273.2.cd.e.44.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			44.7
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87036 + 0.501163i) q^{2} +(1.45895 + 0.933521i) q^{3} +(1.51505 - 0.874714i) q^{4} +(-1.33892 + 0.358762i) q^{5} +(-3.19662 - 1.01485i) q^{6} +(1.90555 - 1.83545i) q^{7} +(0.343083 - 0.343083i) q^{8} +(1.25708 + 2.72392i) q^{9} +O(q^{10})$	\(q+(-1.87036 + 0.501163i) q^{2} +(1.45895 + 0.933521i) q^{3} +(1.51505 - 0.874714i) q^{4} +(-1.33892 + 0.358762i) q^{5} +(-3.19662 - 1.01485i) q^{6} +(1.90555 - 1.83545i) q^{7} +(0.343083 - 0.343083i) q^{8} +(1.25708 + 2.72392i) q^{9} +(2.32447 - 1.34203i) q^{10} +(2.28763 + 0.612968i) q^{11} +(3.02695 + 0.138165i) q^{12} +(2.20676 + 2.85135i) q^{13} +(-2.64421 + 4.38795i) q^{14} +(-2.28833 - 0.726491i) q^{15} +(-2.21918 + 3.84373i) q^{16} +(1.10119 + 1.90732i) q^{17} +(-3.71632 - 4.46473i) q^{18} +(-1.11846 - 4.17416i) q^{19} +(-1.71471 + 1.71471i) q^{20} +(4.49354 - 0.898964i) q^{21} -4.58590 q^{22} +(-0.362760 + 0.628318i) q^{23} +(0.820816 - 0.180266i) q^{24} +(-2.66614 + 1.53929i) q^{25} +(-5.55644 - 4.22712i) q^{26} +(-0.708822 + 5.14758i) q^{27} +(1.28151 - 4.44761i) q^{28} +4.61440i q^{29} +(4.64410 + 0.211979i) q^{30} +(5.52871 + 1.48141i) q^{31} +(1.97318 - 7.36403i) q^{32} +(2.76532 + 3.02984i) q^{33} +(-3.01551 - 3.01551i) q^{34} +(-1.89288 + 3.14116i) q^{35} +(4.28719 + 3.02729i) q^{36} +(-4.96920 + 1.33149i) q^{37} +(4.18386 + 7.24666i) q^{38} +(0.557758 + 6.22004i) q^{39} +(-0.336275 + 0.582445i) q^{40} +(6.19631 + 6.19631i) q^{41} +(-7.95402 + 3.93338i) q^{42} -1.48686i q^{43} +(4.00204 - 1.07234i) q^{44} +(-2.66036 - 3.19612i) q^{45} +(0.363603 - 1.35699i) q^{46} +(-1.11365 - 4.15620i) q^{47} +(-6.82587 + 3.53617i) q^{48} +(0.262239 - 6.99509i) q^{49} +(4.21521 - 4.21521i) q^{50} +(-0.173938 + 3.81068i) q^{51} +(5.83747 + 2.38966i) q^{52} +(10.3415 - 5.97064i) q^{53} +(-1.25402 - 9.98309i) q^{54} -3.28286 q^{55} +(0.0240496 - 1.28347i) q^{56} +(2.26488 - 7.13400i) q^{57} +(-2.31257 - 8.63061i) q^{58} +(-7.06192 - 1.89224i) q^{59} +(-4.10240 + 0.900963i) q^{60} +(4.17980 - 7.23963i) q^{61} -11.0831 q^{62} +(7.39505 + 2.88326i) q^{63} +5.88559i q^{64} +(-3.97763 - 3.02603i) q^{65} +(-6.69060 - 4.28103i) q^{66} +(0.579944 + 0.155395i) q^{67} +(3.33672 + 1.92646i) q^{68} +(-1.11580 + 0.578042i) q^{69} +(1.96615 - 6.82375i) q^{70} +(-10.8703 - 10.8703i) q^{71} +(1.36581 + 0.503249i) q^{72} +(-2.05058 + 7.65287i) q^{73} +(8.62693 - 4.98076i) q^{74} +(-5.32673 - 0.243137i) q^{75} +(-5.34572 - 5.34572i) q^{76} +(5.48426 - 3.03079i) q^{77} +(-4.16046 - 11.3542i) q^{78} +(3.29571 - 5.70834i) q^{79} +(1.59231 - 5.94260i) q^{80} +(-5.83951 + 6.84837i) q^{81} +(-14.6947 - 8.48400i) q^{82} +(-1.03740 - 1.03740i) q^{83} +(6.02159 - 5.29253i) q^{84} +(-2.15868 - 2.15868i) q^{85} +(0.745157 + 2.78097i) q^{86} +(-4.30764 + 6.73219i) q^{87} +(0.995145 - 0.574547i) q^{88} +(-2.90393 - 10.8376i) q^{89} +(6.57763 + 4.64463i) q^{90} +(9.43861 + 1.38300i) q^{91} +1.26924i q^{92} +(6.68319 + 7.32247i) q^{93} +(4.16587 + 7.21549i) q^{94} +(2.99506 + 5.18759i) q^{95} +(9.75325 - 8.90175i) q^{96} +(-0.431627 + 0.431627i) q^{97} +(3.01519 + 13.2148i) q^{98} +(1.20605 + 7.00187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.87036	+	0.501163i	−1.32255	+	0.354376i	−0.849932	−	0.526893i	$-0.823357\pi$
$2$	−1.87036	+	0.501163i	−1.32255	+	0.354376i	−0.472616	+	0.881268i	$0.656690\pi$
$3$	1.45895	+	0.933521i	0.842326	+	0.538968i
$3$	1.45895	+	0.933521i	0.842326	+	0.538968i
$4$	1.51505	−	0.874714i	0.757525	−	0.437357i
$5$	−1.33892	+	0.358762i	−0.598782	+	0.160443i	−0.545464	−	0.838134i	$-0.683647\pi$
$5$	−1.33892	+	0.358762i	−0.598782	+	0.160443i	−0.0533184	+	0.998578i	$0.516980\pi$
$6$	−3.19662	−	1.01485i	−1.30501	−	0.414312i
$7$	1.90555	−	1.83545i	0.720230	−	0.693735i
$7$	1.90555	−	1.83545i	0.720230	−	0.693735i
$8$	0.343083	−	0.343083i	0.121298	−	0.121298i
$9$	1.25708	+	2.72392i	0.419026	+	0.907974i
$10$	2.32447	−	1.34203i	0.735061	−	0.424388i
$11$	2.28763	+	0.612968i	0.689746	+	0.184817i	0.586633	−	0.809853i	$-0.300453\pi$
$11$	2.28763	+	0.612968i	0.689746	+	0.184817i	0.103113	+	0.994670i	$0.467120\pi$
$12$	3.02695	+	0.138165i	0.873805	+	0.0398847i
$13$	2.20676	+	2.85135i	0.612045	+	0.790823i
$13$	2.20676	+	2.85135i	0.612045	+	0.790823i
$14$	−2.64421	+	4.38795i	−0.706696	+	1.17273i
$15$	−2.28833	−	0.726491i	−0.590844	−	0.187579i
$16$	−2.21918	+	3.84373i	−0.554795	+	0.960932i
$17$	1.10119	+	1.90732i	0.267078	+	0.462593i	0.968106	−	0.250541i	$-0.0806084\pi$
$17$	1.10119	+	1.90732i	0.267078	+	0.462593i	−0.701028	+	0.713134i	$0.747275\pi$
$18$	−3.71632	−	4.46473i	−0.875946	−	1.05235i
$19$	−1.11846	−	4.17416i	−0.256593	−	0.957617i	−0.967197	−	0.254026i	$-0.918245\pi$
$19$	−1.11846	−	4.17416i	−0.256593	−	0.957617i	0.710605	−	0.703591i	$-0.248421\pi$
$20$	−1.71471	+	1.71471i	−0.383421	+	0.383421i
$21$	4.49354	−	0.898964i	0.980570	−	0.196170i
$22$	−4.58590			−0.977716
$23$	−0.362760	+	0.628318i	−0.0756406	+	0.131013i	−0.901365	−	0.433061i	$-0.857434\pi$
$23$	−0.362760	+	0.628318i	−0.0756406	+	0.131013i	0.825724	+	0.564074i	$0.190767\pi$
$24$	0.820816	−	0.180266i	0.167548	−	0.0367967i
$25$	−2.66614	+	1.53929i	−0.533227	+	0.307859i
$26$	−5.55644	−	4.22712i	−1.08971	−	0.829007i
$27$	−0.708822	+	5.14758i	−0.136413	+	0.990652i
$28$	1.28151	−	4.44761i	0.242182	−	0.840519i
$29$			4.61440i			0.856873i	0.903572	+	0.428436i	$0.140935\pi$
$29$			4.61440i			0.856873i	−0.903572	+	0.428436i	$0.859065\pi$
$30$	4.64410	+	0.211979i	0.847893	+	0.0387019i
$31$	5.52871	+	1.48141i	0.992985	+	0.266070i	0.718504	−	0.695523i	$-0.244827\pi$
$31$	5.52871	+	1.48141i	0.992985	+	0.266070i	0.274481	+	0.961592i	$0.411494\pi$
$32$	1.97318	−	7.36403i	0.348813	−	1.30179i
$33$	2.76532	+	3.02984i	0.481380	+	0.527427i
$34$	−3.01551	−	3.01551i	−0.517156	−	0.517156i
$35$	−1.89288	+	3.14116i	−0.319956	+	0.530952i
$36$	4.28719	+	3.02729i	0.714532	+	0.504549i
$37$	−4.96920	+	1.33149i	−0.816932	+	0.218896i	−0.643005	−	0.765862i	$-0.722312\pi$
$37$	−4.96920	+	1.33149i	−0.816932	+	0.218896i	−0.173927	+	0.984758i	$0.555646\pi$
$38$	4.18386	+	7.24666i	0.678712	+	1.17556i
$39$	0.557758	+	6.22004i	0.0893127	+	0.996004i
$40$	−0.336275	+	0.582445i	−0.0531697	+	0.0920926i
$41$	6.19631	+	6.19631i	0.967701	+	0.967701i	0.999494	−	0.0317931i	$-0.0101218\pi$
$41$	6.19631	+	6.19631i	0.967701	+	0.967701i	−0.0317931	+	0.999494i	$0.510122\pi$
$42$	−7.95402	+	3.93338i	−1.22733	+	0.606934i
$43$		−	1.48686i		−	0.226744i	−0.993553	−	0.113372i	$-0.963835\pi$
$43$		−	1.48686i		−	0.226744i	0.993553	−	0.113372i	$-0.0361651\pi$
$44$	4.00204	−	1.07234i	0.603331	−	0.161662i
$45$	−2.66036	−	3.19612i	−0.396584	−	0.476449i
$46$	0.363603	−	1.35699i	0.0536104	−	0.200077i
$47$	−1.11365	−	4.15620i	−0.162443	−	0.606244i	−0.998353	−	0.0573775i	$-0.981726\pi$
$47$	−1.11365	−	4.15620i	−0.162443	−	0.606244i	0.835910	−	0.548867i	$-0.184941\pi$
$48$	−6.82587	+	3.53617i	−0.985230	+	0.510402i
$49$	0.262239	−	6.99509i	0.0374627	−	0.999298i
$50$	4.21521	−	4.21521i	0.596121	−	0.596121i
$51$	−0.173938	+	3.81068i	−0.0243561	+	0.533601i
$52$	5.83747	+	2.38966i	0.809511	+	0.331386i
$53$	10.3415	−	5.97064i	1.42051	−	0.820130i	0.424166	−	0.905585i	$-0.360567\pi$
$53$	10.3415	−	5.97064i	1.42051	−	0.820130i	0.996342	+	0.0854542i	$0.0272341\pi$
$54$	−1.25402	−	9.98309i	−0.170650	−	1.35853i
$55$	−3.28286			−0.442660
$56$	0.0240496	−	1.28347i	0.00321377	−	0.171511i
$57$	2.26488	−	7.13400i	0.299991	−	0.944921i
$58$	−2.31257	−	8.63061i	−0.303655	−	1.13326i
$59$	−7.06192	−	1.89224i	−0.919384	−	0.246348i	−0.232062	−	0.972701i	$-0.574547\pi$
$59$	−7.06192	−	1.89224i	−0.919384	−	0.246348i	−0.687322	+	0.726353i	$0.741214\pi$
$60$	−4.10240	+	0.900963i	−0.529618	+	0.116314i
$61$	4.17980	−	7.23963i	0.535169	−	0.926939i	−0.463987	−	0.885842i	$-0.653581\pi$
$61$	4.17980	−	7.23963i	0.535169	−	0.926939i	0.999155	−	0.0410969i	$-0.0130852\pi$
$62$	−11.0831			−1.40756
$63$	7.39505	+	2.88326i	0.931689	+	0.363257i
$64$			5.88559i			0.735699i
$65$	−3.97763	−	3.02603i	−0.493364	−	0.375332i
$66$	−6.69060	−	4.28103i	−0.823556	−	0.526958i
$67$	0.579944	+	0.155395i	0.0708514	+	0.0189846i	0.294071	−	0.955784i	$-0.404990\pi$
$67$	0.579944	+	0.155395i	0.0708514	+	0.0189846i	−0.223219	+	0.974768i	$0.571657\pi$
$68$	3.33672	+	1.92646i	0.404637	+	0.233617i
$69$	−1.11580	+	0.578042i	−0.134326	+	0.0695881i
$70$	1.96615	−	6.82375i	0.235000	−	0.815595i
$71$	−10.8703	−	10.8703i	−1.29007	−	1.29007i	−0.934743	−	0.355324i	$-0.884371\pi$
$71$	−10.8703	−	10.8703i	−1.29007	−	1.29007i	−0.355324	−	0.934743i	$-0.615629\pi$
$72$	1.36581	+	0.503249i	0.160963	+	0.0593085i
$73$	−2.05058	+	7.65287i	−0.240002	+	0.895701i	0.735828	+	0.677169i	$0.236793\pi$
$73$	−2.05058	+	7.65287i	−0.240002	+	0.895701i	−0.975830	+	0.218532i	$0.929873\pi$
$74$	8.62693	−	4.98076i	1.00286	−	0.579002i
$75$	−5.32673	−	0.243137i	−0.615077	−	0.0280751i
$76$	−5.34572	−	5.34572i	−0.613196	−	0.613196i
$77$	5.48426	−	3.03079i	0.624990	−	0.345390i
$78$	−4.16046	−	11.3542i	−0.471080	−	1.28561i
$79$	3.29571	−	5.70834i	0.370797	−	0.642239i	−0.618892	−	0.785476i	$-0.712418\pi$
$79$	3.29571	−	5.70834i	0.370797	−	0.642239i	0.989688	+	0.143238i	$0.0457513\pi$
$80$	1.59231	−	5.94260i	0.178026	−	0.664402i
$81$	−5.83951	+	6.84837i	−0.648834	+	0.760930i
$82$	−14.6947	−	8.48400i	−1.62276	−	0.936901i
$83$	−1.03740	−	1.03740i	−0.113869	−	0.113869i	0.647876	−	0.761746i	$-0.275657\pi$
$83$	−1.03740	−	1.03740i	−0.113869	−	0.113869i	−0.761746	+	0.647876i	$0.775657\pi$
$84$	6.02159	−	5.29253i	0.657010	−	0.577463i
$85$	−2.15868	−	2.15868i	−0.234142	−	0.234142i
$86$	0.745157	+	2.78097i	0.0803524	+	0.299879i
$87$	−4.30764	+	6.73219i	−0.461827	+	0.721766i
$88$	0.995145	−	0.574547i	0.106083	−	0.0612469i
$89$	−2.90393	−	10.8376i	−0.307816	−	1.14879i	−0.930494	−	0.366308i	$-0.880622\pi$
$89$	−2.90393	−	10.8376i	−0.307816	−	1.14879i	0.622677	−	0.782479i	$-0.286045\pi$
$90$	6.57763	+	4.64463i	0.693343	+	0.489587i
$91$	9.43861	+	1.38300i	0.989435	+	0.144977i
$92$			1.26924i			0.132328i
$93$	6.68319	+	7.32247i	0.693014	+	0.759305i
$94$	4.16587	+	7.21549i	0.429676	+	0.744221i
$95$	2.99506	+	5.18759i	0.307286	+	0.532236i
$96$	9.75325	−	8.90175i	0.995437	−	0.908531i
$97$	−0.431627	+	0.431627i	−0.0438250	+	0.0438250i	−0.728680	−	0.684855i	$-0.759866\pi$
$97$	−0.431627	+	0.431627i	−0.0438250	+	0.0438250i	0.684855	+	0.728680i	$0.259866\pi$
$98$	3.01519	+	13.2148i	0.304581	+	1.33490i
$99$	1.20605	+	7.00187i	0.121213	+	0.703715i
$100$	−2.69289	+	4.66421i	−0.269289	+	0.466421i
$101$	−9.65337	−	16.7201i	−0.960546	−	1.66371i	−0.721133	−	0.692797i	$-0.756378\pi$
$101$	−9.65337	−	16.7201i	−0.960546	−	1.66371i	−0.239413	−	0.970918i	$-0.576955\pi$
$102$	−1.58444	−	7.21453i	−0.156883	−	0.714344i
$103$	16.9974	+	9.81345i	1.67480	+	0.966948i	0.964888	+	0.262662i	$0.0846003\pi$
$103$	16.9974	+	9.81345i	1.67480	+	0.966948i	0.709916	+	0.704287i	$0.248733\pi$
$104$	1.73535	+	0.221149i	0.170165	+	0.0216854i
$105$	−5.69396	+	2.81575i	−0.555674	+	0.274789i
$106$	−16.3500	+	16.3500i	−1.58805	+	1.58805i
$107$	−4.79758	−	2.76988i	−0.463800	−	0.267775i	0.249841	−	0.968287i	$-0.419622\pi$
$107$	−4.79758	−	2.76988i	−0.463800	−	0.267775i	−0.713641	+	0.700512i	$0.752955\pi$
$108$	3.42876	+	8.41885i	0.329933	+	0.810105i
$109$	−11.6405	−	3.11906i	−1.11496	−	0.298752i	−0.346117	−	0.938192i	$-0.612500\pi$
$109$	−11.6405	−	3.11906i	−1.11496	−	0.298752i	−0.768842	+	0.639439i	$0.779167\pi$
$110$	6.14014	−	1.64525i	0.585439	−	0.156868i
$111$	−8.49281	−	2.69627i	−0.806101	−	0.255919i
$112$	2.82622	+	11.3976i	0.267053	+	1.07697i
$113$			13.5251i			1.27234i	0.771549	+	0.636169i	$0.219482\pi$
$113$			13.5251i			1.27234i	−0.771549	+	0.636169i	$0.780518\pi$
$114$	−0.660857	+	14.4783i	−0.0618950	+	1.35601i
$115$	0.260289	−	0.971411i	0.0242721	−	0.0905846i
$116$	4.03628	+	6.99105i	0.374759	+	0.649102i
$117$	−4.99280	+	9.59542i	−0.461584	+	0.887096i
$118$	14.1567			1.30323
$119$	5.59917	+	1.61331i	0.513275	+	0.147892i
$120$	−1.03433	+	0.535839i	−0.0944212	+	0.0489152i
$121$	−4.66877	−	2.69551i	−0.424433	−	0.245047i
$122$	−4.18952	+	15.6355i	−0.379301	+	1.41557i
$123$	3.25573	+	14.8245i	0.293560	+	1.33668i
$124$	9.67208	−	2.59163i	0.868579	−	0.232735i
$125$	7.91828	−	7.91828i	0.708232	−	0.708232i
$126$	−15.2764	−	1.68663i	−1.36093	−	0.150257i
$127$			4.52614i			0.401630i	0.979629	+	0.200815i	$0.0643590\pi$
$127$			4.52614i			0.401630i	−0.979629	+	0.200815i	$0.935641\pi$
$128$	0.996732	+	3.71985i	0.0880995	+	0.328792i
$129$	1.38801	−	2.16925i	0.122208	−	0.190992i
$130$	8.95615	+	3.66633i	0.785506	+	0.321559i
$131$	9.71563	+	5.60932i	0.848859	+	0.490089i	0.860266	−	0.509846i	$-0.170298\pi$
$131$	9.71563	+	5.60932i	0.848859	+	0.490089i	−0.0114069	+	0.999935i	$0.503631\pi$
$132$	6.83984	+	2.17149i	0.595332	+	0.189004i
$133$	−9.79274	−	5.90118i	−0.849139	−	0.511697i
$134$	−1.16258			−0.100432
$135$	−0.897701	−	7.14649i	−0.0772618	−	0.615072i
$136$	1.03217	+	0.276569i	0.0885078	+	0.0237156i
$137$	−9.90799	−	2.65484i	−0.846497	−	0.226818i	−0.190599	−	0.981668i	$-0.561043\pi$
$137$	−9.90799	−	2.65484i	−0.846497	−	0.226818i	−0.655898	+	0.754850i	$0.727710\pi$
$138$	1.79725	−	1.64035i	0.152992	−	0.139636i
$139$	−1.90381			−0.161479			−0.0807397	−	0.996735i	$-0.525728\pi$
$139$	−1.90381			−0.161479			−0.0807397	+	0.996735i	$0.525728\pi$
$140$	−0.120199	+	6.41474i	−0.0101587	+	0.542145i
$141$	2.25514	−	7.10331i	0.189917	−	0.598207i
$142$	25.7792	+	14.8836i	2.16334	+	1.24901i
$143$	3.30046	+	7.87551i	0.275998	+	0.658583i
$144$	−13.2597	−	1.21300i	−1.10498	−	0.101083i
$145$	−1.65547	−	6.17831i	−0.137479	−	0.513080i
$146$		−	15.3413i		−	1.26966i
$147$	6.91265	−	9.96069i	0.570146	−	0.821543i
$148$	−6.36391	+	6.36391i	−0.523111	+	0.523111i
$149$	−0.697277	+	0.186835i	−0.0571231	+	0.0153061i	−0.287267	−	0.957850i	$-0.592747\pi$
$149$	−0.697277	+	0.186835i	−0.0571231	+	0.0153061i	0.230144	+	0.973157i	$0.426080\pi$
$150$	10.0848	−	2.21480i	0.823418	−	0.180838i
$151$	4.72655	−	17.6397i	0.384641	−	1.43550i	−0.454090	−	0.890956i	$-0.650035\pi$
$151$	4.72655	−	17.6397i	0.384641	−	1.43550i	0.838731	−	0.544545i	$-0.183298\pi$
$152$	−1.81581	−	1.04836i	−0.147281	−	0.0850329i
$153$	−3.81111	+	5.39722i	−0.308110	+	0.436339i
$154$	−8.73865	+	8.41719i	−0.704181	+	0.678276i
$155$	−7.93396			−0.637271
$156$	6.28579	+	8.93579i	0.503266	+	0.715436i
$157$	−4.40329	−	7.62673i	−0.351421	−	0.608679i	0.635078	−	0.772448i	$-0.280968\pi$
$157$	−4.40329	−	7.62673i	−0.351421	−	0.608679i	−0.986499	+	0.163769i	$0.947635\pi$
$158$	−3.30338	+	12.3284i	−0.262803	+	0.980793i
$159$	20.6614	+	0.943086i	1.63855	+	0.0747916i
$160$			10.5677i			0.835453i
$161$	0.461991	+	1.86312i	0.0364100	+	0.146834i
$162$	7.48986	−	15.7355i	0.588459	−	1.23630i
$163$	−8.96152	+	2.40123i	−0.701921	+	0.188079i	−0.592091	−	0.805871i	$-0.701697\pi$
$163$	−8.96152	+	2.40123i	−0.701921	+	0.188079i	−0.109830	+	0.993950i	$0.535031\pi$
$164$	14.8077	+	3.96772i	1.15629	+	0.309827i
$165$	−4.78953	−	3.06461i	−0.372864	−	0.238580i
$166$	2.46022	+	1.42041i	0.190950	+	0.110245i
$167$	5.66815	−	5.66815i	0.438614	−	0.438614i	−0.452931	−	0.891545i	$-0.649622\pi$
$167$	5.66815	−	5.66815i	0.438614	−	0.438614i	0.891545	+	0.452931i	$0.149622\pi$
$168$	1.23324	−	1.85007i	0.0951462	−	0.142736i
$169$	−3.26043	+	12.5845i	−0.250802	+	0.968038i
$170$	5.11937	+	2.95567i	0.392638	+	0.226690i
$171$	9.96408	−	8.29384i	0.761973	−	0.634246i
$172$	−1.30058	−	2.25266i	−0.0991679	−	0.171764i
$173$	−5.32380	+	9.22110i	−0.404761	+	0.701067i	−0.994294	−	0.106678i	$-0.965979\pi$
$173$	−5.32380	+	9.22110i	−0.404761	+	0.701067i	0.589532	+	0.807745i	$0.299312\pi$
$174$	4.68294	−	14.7505i	0.355012	−	1.11823i
$175$	−2.25515	+	7.82676i	−0.170474	+	0.591648i
$176$	−7.43274	+	7.43274i	−0.560264	+	0.560264i
$177$	−8.53656	−	9.35313i	−0.641647	−	0.703024i
$178$	10.8628	+	18.8150i	0.814204	+	1.41024i
$179$	−6.40516	−	11.0941i	−0.478744	−	0.829210i	0.520959	−	0.853582i	$-0.325575\pi$
$179$	−6.40516	−	11.0941i	−0.478744	−	0.829210i	−0.999703	+	0.0243724i	$0.992241\pi$
$180$	−6.82627	−	2.51522i	−0.508800	−	0.187473i
$181$		−	3.09288i		−	0.229892i	−0.993372	−	0.114946i	$-0.963330\pi$
$181$		−	3.09288i		−	0.229892i	0.993372	−	0.114946i	$-0.0366695\pi$
$182$	−18.3467	+	2.14357i	−1.35995	+	0.158892i
$183$	12.8565	−	6.66033i	0.950377	−	0.492346i
$184$	0.0911086	+	0.340022i	0.00671661	+	0.0250667i
$185$	6.17567	−	3.56552i	0.454044	−	0.262143i
$186$	−16.1698	−	10.3463i	−1.18562	−	0.758630i
$187$	1.34999	+	5.03824i	0.0987212	+	0.368433i
$188$	−5.32272	−	5.32272i	−0.388200	−	0.388200i
$189$	8.09743	+	11.1100i	0.589002	+	0.808132i
$190$	−8.20168	−	8.20168i	−0.595012	−	0.595012i
$191$	−10.7534	−	6.20849i	−0.778091	−	0.449231i	0.0576626	−	0.998336i	$-0.481635\pi$
$191$	−10.7534	−	6.20849i	−0.778091	−	0.449231i	−0.835753	+	0.549105i	$0.814969\pi$
$192$	−5.49432	+	8.58679i	−0.396518	+	0.619698i
$193$	−5.49136	+	20.4940i	−0.395277	+	1.47519i	0.426032	+	0.904708i	$0.359911\pi$
$193$	−5.49136	+	20.4940i	−0.395277	+	1.47519i	−0.821309	+	0.570484i	$0.806756\pi$
$194$	0.590984	−	1.02361i	0.0424302	−	0.0734912i
$195$	−2.97831	−	8.12802i	−0.213281	−	0.582060i
$196$	−5.72140	−	10.8273i	−0.408671	−	0.773378i
$197$	−5.64266	−	5.64266i	−0.402023	−	0.402023i	0.476922	−	0.878945i	$-0.341752\pi$
$197$	−5.64266	−	5.64266i	−0.402023	−	0.402023i	−0.878945	+	0.476922i	$0.841752\pi$
$198$	−5.76483	−	12.4916i	−0.409689	−	0.887741i
$199$	12.3618	−	7.13709i	0.876305	−	0.505935i	0.00686693	−	0.999976i	$-0.497814\pi$
$199$	12.3618	−	7.13709i	0.876305	−	0.505935i	0.869438	+	0.494041i	$0.164481\pi$
$200$	−0.386600	+	1.44281i	−0.0273367	+	0.102022i
$201$	0.701045	+	0.768104i	0.0494479	+	0.0541779i
$202$	26.4348	+	26.4348i	1.85995	+	1.85995i
$203$	8.46951	+	8.79297i	0.594443	+	0.617146i
$204$	3.06973	+	5.92551i	0.214924	+	0.414869i
$205$	−10.5194	−	6.07335i	−0.734704	−	0.424181i
$206$	−36.7095	−	9.83627i	−2.55767	−	0.685326i
$207$	−2.16751	−	0.198284i	−0.150652	−	0.0137817i
$208$	−15.8570	+	2.15453i	−1.09949	+	0.149389i
$209$		−	10.2345i		−	0.707935i
$210$	9.23864	−	8.12008i	0.637527	−	0.560339i
$211$	−28.0505			−1.93108			−0.965538	−	0.260260i	$-0.916192\pi$
$211$	−28.0505			−1.93108			−0.965538	+	0.260260i	$0.916192\pi$
$212$	10.4452	−	18.0916i	0.717380	−	1.24254i
$213$	−5.71159	−	26.0069i	−0.391352	−	1.78196i
$214$	10.3614	+	2.77633i	0.708290	+	0.189786i
$215$	0.533428	+	1.99078i	0.0363795	+	0.135770i
$216$	1.52286	+	2.00923i	0.103618	+	0.136711i
$217$	13.2543	−	7.32477i	0.899760	−	0.497238i
$218$	23.3351			1.58046
$219$	−10.1358	+	9.25091i	−0.684915	+	0.625118i
$220$	−4.97369	+	2.87156i	−0.335326	+	0.193601i
$221$	−3.00838	+	7.34889i	−0.202366	+	0.494340i
$222$	17.2359	+	0.786730i	1.15680	+	0.0528019i
$223$	11.4761	−	11.4761i	0.768500	−	0.768500i	−0.209343	−	0.977842i	$-0.567132\pi$
$223$	11.4761	−	11.4761i	0.768500	−	0.768500i	0.977842	+	0.209343i	$0.0671324\pi$
$224$	−9.75631	−	17.6542i	−0.651871	−	1.17957i
$225$	−7.54446	−	5.32733i	−0.502964	−	0.355156i
$226$	−6.77830	−	25.2970i	−0.450886	−	1.68273i
$227$	−5.05250	+	18.8562i	−0.335346	+	1.25153i	0.568147	+	0.822927i	$0.307661\pi$
$227$	−5.05250	+	18.8562i	−0.335346	+	1.25153i	−0.903493	+	0.428602i	$0.859006\pi$
$228$	−2.80880	−	12.7895i	−0.186018	−	0.847004i
$229$	−1.05919	+	0.283809i	−0.0699932	+	0.0187546i	−0.293646	−	0.955914i	$-0.594869\pi$
$229$	−1.05919	+	0.283809i	−0.0699932	+	0.0187546i	0.223652	+	0.974669i	$0.428202\pi$
$230$			1.94734i			0.128404i
$231$	10.8306	+	0.697899i	0.712600	+	0.0459184i
$232$	1.58312	+	1.58312i	0.103937	+	0.103937i
$233$	−9.18559	+	15.9099i	−0.601768	+	1.04229i	0.390785	+	0.920482i	$0.372204\pi$
$233$	−9.18559	+	15.9099i	−0.601768	+	1.04229i	−0.992553	+	0.121811i	$0.961130\pi$
$234$	4.52948	−	20.4491i	0.296102	−	1.33680i
$235$	2.98217	+	5.16528i	0.194536	+	0.336946i
$236$	−12.3543	+	3.31033i	−0.804198	+	0.215484i
$237$	10.1371	−	5.25158i	0.658478	−	0.341127i
$238$	−11.2810	−	0.211383i	−0.731240	−	0.0137019i
$239$	19.7676	+	19.7676i	1.27866	+	1.27866i	0.941418	+	0.337242i	$0.109494\pi$
$239$	19.7676	+	19.7676i	1.27866	+	1.27866i	0.337242	+	0.941418i	$0.390506\pi$
$240$	7.87064	−	7.18350i	0.508048	−	0.463693i
$241$	1.80299	−	6.72886i	0.116141	−	0.433444i	−0.883229	−	0.468942i	$-0.844635\pi$
$241$	1.80299	−	6.72886i	0.116141	−	0.433444i	0.999370	+	0.0354985i	$0.0113019\pi$
$242$	10.0832	+	2.70178i	0.648172	+	0.173677i
$243$	−14.9127	+	4.54013i	−0.956647	+	0.291250i
$244$		−	14.6245i		−	0.936239i
$245$	2.15845	+	9.45993i	0.137899	+	0.604373i
$246$	−13.5189	−	26.0956i	−0.861933	−	1.66379i
$247$	9.43382	−	12.4005i	0.600259	−	0.789024i
$248$	2.40505	−	1.38856i	0.152721	−	0.0881735i
$249$	−0.545081	−	2.48195i	−0.0345431	−	0.157287i
$250$	−10.8417	+	18.7784i	−0.685691	+	1.18765i
$251$	12.8536			0.811313			0.405657	−	0.914026i	$-0.367043\pi$
$251$	12.8536			0.811313			0.405657	+	0.914026i	$0.367043\pi$
$252$	13.7259	−	2.10027i	0.864651	−	0.132305i
$253$	−1.21500	+	1.21500i	−0.0763863	+	0.0763863i
$254$	−2.26833	−	8.46553i	−0.142328	−	0.531175i
$255$	−1.13424	−	5.16458i	−0.0710287	−	0.323419i
$256$	−9.61409	−	16.6521i	−0.600881	−	1.04076i
$257$	5.02416	−	8.70211i	0.313399	−	0.542822i	−0.665697	−	0.746222i	$-0.731866\pi$
$257$	5.02416	−	8.70211i	0.313399	−	0.542822i	0.979096	+	0.203400i	$0.0651991\pi$
$258$	−1.50894	+	4.75291i	−0.0939425	+	0.295903i
$259$	−7.02517	+	11.6580i	−0.436523	+	0.724390i
$260$	−8.67321	−	1.10529i	−0.537890	−	0.0685474i
$261$	−12.5693	+	5.80066i	−0.778018	+	0.359052i
$262$	−20.9830	−	5.62237i	−1.29633	−	0.347351i
$263$	10.5483	−	6.09009i	0.650439	−	0.375531i	−0.138186	−	0.990406i	$-0.544127\pi$
$263$	10.5483	−	6.09009i	0.650439	−	0.375531i	0.788624	+	0.614875i	$0.210794\pi$
$264$	1.98822	+	0.0907520i	0.122366	+	0.00558540i
$265$	−11.7043	+	11.7043i	−0.718991	+	0.718991i
$266$	21.2735	+	6.12960i	1.30436	+	0.375830i
$267$	5.88045	−	18.5225i	0.359878	−	1.13356i
$268$	1.01457	−	0.271853i	0.0619747	−	0.0166061i
$269$	2.20753	−	1.27452i	0.134596	−	0.0777088i	−0.431190	−	0.902261i	$-0.641906\pi$
$269$	2.20753	−	1.27452i	0.134596	−	0.0777088i	0.565786	+	0.824552i	$0.308573\pi$
$270$	5.26058	+	12.9166i	0.320149	+	0.786082i
$271$	−14.0283	+	3.75888i	−0.852161	+	0.228336i	−0.658358	−	0.752705i	$-0.728749\pi$
$271$	−14.0283	+	3.75888i	−0.852161	+	0.228336i	−0.193802	+	0.981041i	$0.562082\pi$
$272$	−9.77497			−0.592695
$273$	12.4794	+	10.8289i	0.755289	+	0.655392i
$274$	19.8621			1.19991
$275$	−7.04267	+	1.88708i	−0.424689	+	0.113795i
$276$	−1.18487	+	1.85177i	−0.0713206	+	0.111463i
$277$	−10.7355	+	6.19815i	−0.645035	+	0.372411i	−0.786551	−	0.617525i	$-0.788135\pi$
$277$	−10.7355	+	6.19815i	−0.645035	+	0.372411i	0.141517	+	0.989936i	$0.454802\pi$
$278$	3.56083	−	0.954121i	0.213564	−	0.0572244i
$279$	2.91477	+	16.9220i	0.174502	+	1.01310i
$280$	0.428261	+	1.72709i	0.0255935	+	0.103214i
$281$	−7.15435	+	7.15435i	−0.426793	+	0.426793i	−0.887534	−	0.460742i	$-0.847583\pi$
$281$	−7.15435	+	7.15435i	−0.426793	+	0.426793i	0.460742	+	0.887534i	$0.347583\pi$
$282$	−0.658015	+	14.4160i	−0.0391842	+	0.858459i
$283$	18.9127	−	10.9192i	1.12424	−	0.649081i	0.181761	−	0.983343i	$-0.441820\pi$
$283$	18.9127	−	10.9192i	1.12424	−	0.649081i	0.942480	+	0.334262i	$0.108487\pi$
$284$	−25.9774	−	6.96064i	−1.54148	−	0.413038i
$285$	−0.473081	+	10.3644i	−0.0280229	+	0.613934i
$286$	−10.1200	−	13.0760i	−0.598406	−	0.773201i
$287$	23.1804	+	0.434353i	1.36830	+	0.0256390i
$288$	22.5395	−	3.88235i	1.32815	−	0.228770i
$289$	6.07475	−	10.5218i	0.357338	−	0.618928i
$290$	6.19267	+	10.7260i	0.363646	+	0.629854i
$291$	−1.03265	+	0.226790i	−0.0605353	+	0.0132947i
$292$	3.58734	+	13.3882i	0.209933	+	0.783482i
$293$	5.41525	−	5.41525i	0.316362	−	0.316362i	−0.531006	−	0.847368i	$-0.678186\pi$
$293$	5.41525	−	5.41525i	0.316362	−	0.316362i	0.847368	+	0.531006i	$0.178186\pi$
$294$	−7.93726	+	22.0945i	−0.462910	+	1.28858i
$295$	10.1342			0.590036
$296$	−1.24804	+	2.16166i	−0.0725406	+	0.125644i
$297$	−4.77682	+	11.3413i	−0.277179	+	0.658087i
$298$	1.21053	−	0.698898i	0.0701239	−	0.0404861i
$299$	−2.59208	+	0.352191i	−0.149904	+	0.0203677i
$300$	−8.28293	+	4.29100i	−0.478215	+	0.247741i
$301$	−2.72905	−	2.83328i	−0.157300	−	0.163308i
$302$			35.3615i			2.03483i
$303$	1.52479	−	33.4055i	0.0875967	−	1.91909i
$304$	18.5264	+	4.96413i	1.06256	+	0.284713i
$305$	−2.99911	+	11.1928i	−0.171728	+	0.640899i
$306$	4.42328	−	12.0048i	0.252862	−	0.686266i
$307$	−8.74360	−	8.74360i	−0.499024	−	0.499024i	0.412110	−	0.911134i	$-0.364792\pi$
$307$	−8.74360	−	8.74360i	−0.499024	−	0.499024i	−0.911134	+	0.412110i	$0.864792\pi$
$308$	5.65786	−	9.38896i	0.322386	−	0.534986i
$309$	15.6373	+	30.1848i	0.889576	+	1.71715i
$310$	14.8394	−	3.97621i	0.842822	−	0.225833i
$311$	2.78775	+	4.82853i	0.158079	+	0.273801i	0.934176	−	0.356813i	$-0.116137\pi$
$311$	2.78775	+	4.82853i	0.158079	+	0.273801i	−0.776097	+	0.630614i	$0.782803\pi$
$312$	2.32535	+	1.94263i	0.131647	+	0.109980i
$313$	−4.96467	+	8.59906i	−0.280620	+	0.486048i	−0.971538	−	0.236886i	$-0.923873\pi$
$313$	−4.96467	+	8.59906i	−0.280620	+	0.486048i	0.690918	+	0.722933i	$0.257207\pi$
$314$	12.0580	+	12.0580i	0.680472	+	0.680472i
$315$	−10.9358	−	1.20739i	−0.616161	−	0.0680288i
$316$		−	11.5312i		−	0.648682i
$317$	−10.9373	+	2.93063i	−0.614297	+	0.164600i	−0.552534	−	0.833490i	$-0.686339\pi$
$317$	−10.9373	+	2.93063i	−0.614297	+	0.164600i	−0.0617632	+	0.998091i	$0.519672\pi$
$318$	−39.1170	+	8.59080i	−2.19357	+	0.481748i
$319$	−2.82848	+	10.5560i	−0.158365	+	0.591025i
$320$	−2.11153	−	7.88032i	−0.118038	−	0.440523i
$321$	−4.41369	−	8.51977i	−0.246348	−	0.475527i
$322$	−1.79782	−	3.25318i	−0.100188	−	0.181293i
$323$	6.72982	−	6.72982i	0.374457	−	0.374457i
$324$	−2.85678	+	15.4835i	−0.158710	+	0.860195i
$325$	−10.2726	−	4.20524i	−0.569821	−	0.233265i
$326$	15.5579	−	8.98236i	0.861673	−	0.497487i
$327$	−14.0712	−	15.4172i	−0.778140	−	0.852574i
$328$	4.25170			0.234761
$329$	−9.75062	−	5.87580i	−0.537569	−	0.323943i
$330$	10.4940	+	3.33161i	0.577678	+	0.183399i
$331$	0.208395	+	0.777741i	0.0114544	+	0.0427485i	0.971417	−	0.237381i	$-0.0762891\pi$
$331$	0.208395	+	0.777741i	0.0114544	+	0.0427485i	−0.959962	+	0.280130i	$0.909622\pi$
$332$	−2.47914	−	0.664283i	−0.136060	−	0.0364573i
$333$	−9.87357	−	11.8619i	−0.541068	−	0.650030i
$334$	−7.76084	+	13.4422i	−0.424654	+	0.735523i
$335$	−0.832247			−0.0454705
$336$	−6.51658	+	19.2669i	−0.355509	+	1.05110i
$337$		−	12.9314i		−	0.704420i	−0.935921	−	0.352210i	$-0.885430\pi$
$337$		−	12.9314i		−	0.704420i	0.935921	−	0.352210i	$-0.114570\pi$
$338$	−0.208695	−	25.1716i	−0.0113515	−	1.36916i
$339$	−12.6260	+	19.7325i	−0.685750	+	1.07172i
$340$	−5.15874	−	1.38228i	−0.279772	−	0.0749647i
$341$	11.7396	+	6.77785i	0.635734	+	0.367041i
$342$	−14.4799	+	20.5061i	−0.782984	+	1.10885i
$343$	−12.3394	−	13.8108i	−0.666267	−	0.745714i
$344$	−0.510115	−	0.510115i	−0.0275036	−	0.0275036i
$345$	1.28658	−	1.17426i	0.0692672	−	0.0632199i
$346$	5.33619	−	19.9149i	0.286875	−	1.07063i
$347$	5.66698	−	3.27183i	0.304219	−	0.175641i	−0.340118	−	0.940383i	$-0.610467\pi$
$347$	5.66698	−	3.27183i	0.304219	−	0.175641i	0.644337	+	0.764742i	$0.277134\pi$
$348$	−0.637547	+	13.9676i	−0.0341761	+	0.748739i
$349$	−16.8430	−	16.8430i	−0.901585	−	0.901585i	0.0939883	−	0.995573i	$-0.470038\pi$
$349$	−16.8430	−	16.8430i	−0.901585	−	0.901585i	−0.995573	+	0.0939883i	$0.970038\pi$
$350$	0.295480	−	15.7691i	0.0157941	−	0.842894i
$351$	−16.2418	+	9.33837i	−0.866921	+	0.498445i
$352$	9.02783	−	15.6367i	0.481185	−	0.833437i
$353$	8.07679	−	30.1430i	0.429884	−	1.60435i	−0.323137	−	0.946352i	$-0.604737\pi$
$353$	8.07679	−	30.1430i	0.429884	−	1.60435i	0.753021	−	0.657997i	$-0.228596\pi$
$354$	20.6539	+	13.2156i	1.09774	+	0.702399i
$355$	18.4543	+	10.6546i	0.979452	+	0.565487i
$356$	−13.8794	−	13.8794i	−0.735608	−	0.735608i
$357$	6.66286	+	7.58069i	0.352636	+	0.401212i
$358$	17.5399	+	17.5399i	0.927014	+	0.927014i
$359$	5.21338	+	19.4566i	0.275152	+	1.02688i	0.955740	+	0.294213i	$0.0950576\pi$
$359$	5.21338	+	19.4566i	0.275152	+	1.02688i	−0.680588	+	0.732666i	$0.738276\pi$
$360$	−2.00926	−	0.183807i	−0.105897	−	0.00968750i
$361$	0.281861	−	0.162733i	0.0148348	−	0.00856488i
$362$	1.55004	+	5.78482i	0.0814682	+	0.304043i
$363$	−4.29518	−	8.29101i	−0.225439	−	0.435165i
$364$	15.5097	−	6.16078i	0.812928	−	0.322913i
$365$		−	10.9822i		−	0.574837i
$366$	−20.7084	+	18.9004i	−1.08244	+	0.987941i
$367$	9.40991	+	16.2984i	0.491193	+	0.850772i	0.999949	−	0.0101393i	$-0.00322751\pi$
$367$	9.40991	+	16.2984i	0.491193	+	0.850772i	−0.508755	+	0.860911i	$0.669894\pi$
$368$	−1.61006	−	2.78870i	−0.0839300	−	0.145371i
$369$	−9.08902	+	24.6675i	−0.473156	+	1.28414i
$370$	−9.76385	+	9.76385i	−0.507598	+	0.507598i
$371$	8.74733	−	30.3586i	0.454139	−	1.57614i
$372$	16.5304	+	5.24803i	0.857063	+	0.272098i
$373$	−3.91334	+	6.77811i	−0.202625	+	0.350957i	−0.949374	−	0.314150i	$-0.898281\pi$
$373$	−3.91334	+	6.77811i	−0.202625	+	0.350957i	0.746748	+	0.665107i	$0.231614\pi$
$374$	−5.04996	−	8.74678i	−0.261127	−	0.452285i
$375$	18.9443	−	4.16051i	0.978277	−	0.214848i
$376$	−1.80800	−	1.04385i	−0.0932403	−	0.0538323i
$377$	−13.1573	+	10.1829i	−0.677635	+	0.524445i
$378$	−20.7131	−	16.7216i	−1.06536	−	0.860065i
$379$	7.03400	−	7.03400i	0.361312	−	0.361312i	−0.502984	−	0.864296i	$-0.667764\pi$
$379$	7.03400	−	7.03400i	0.361312	−	0.361312i	0.864296	+	0.502984i	$0.167764\pi$
$380$	9.07532	+	5.23964i	0.465554	+	0.268788i
$381$	−4.22525	+	6.60342i	−0.216466	+	0.338303i
$382$	23.2243	+	6.22293i	1.18826	+	0.318393i
$383$	−16.4146	+	4.39829i	−0.838749	+	0.224742i	−0.652527	−	0.757766i	$-0.726291\pi$
$383$	−16.4146	+	4.39829i	−0.838749	+	0.224742i	−0.186222	+	0.982508i	$0.559624\pi$
$384$	−2.01838	+	6.35756i	−0.103000	+	0.324433i
$385$	−6.25565	+	6.02552i	−0.318817	+	0.307089i
$386$		−	41.0834i		−	2.09109i
$387$	4.05008	−	1.86910i	0.205877	−	0.0950115i
$388$	−0.276386	+	1.03149i	−0.0140314	+	0.0523658i
$389$	−17.6555	−	30.5803i	−0.895170	−	1.55048i	−0.833594	−	0.552378i	$-0.813721\pi$
$389$	−17.6555	−	30.5803i	−0.895170	−	1.55048i	−0.0615764	−	0.998102i	$-0.519613\pi$
$390$	9.64398	+	13.7098i	0.488342	+	0.694220i
$391$	−1.59787			−0.0808080
$392$	−2.30992	−	2.48986i	−0.116669	−	0.125757i
$393$	8.93822	+	17.2535i	0.450873	+	0.870323i
$394$	13.3817	+	7.72595i	0.674162	+	0.389228i
$395$	−2.36475	+	8.82538i	−0.118984	+	0.444053i
$396$	7.95186	+	9.55323i	0.399596	+	0.480068i
$397$	16.8391	−	4.51203i	0.845132	−	0.226452i	0.189828	−	0.981817i	$-0.439207\pi$
$397$	16.8391	−	4.51203i	0.845132	−	0.226452i	0.655304	+	0.755365i	$0.272540\pi$
$398$	−19.5442	+	19.5442i	−0.979665	+	0.979665i
$399$	−8.77826	−	17.7513i	−0.439463	−	0.888675i
$400$		−	13.6639i		−	0.683194i
$401$	9.39391	+	35.0585i	0.469109	+	1.75074i	0.642893	+	0.765956i	$0.277734\pi$
$401$	9.39391	+	35.0585i	0.469109	+	1.75074i	−0.173784	+	0.984784i	$0.555599\pi$
$402$	−1.69615	−	1.08530i	−0.0845965	−	0.0541297i
$403$	7.97650	+	19.0334i	0.397338	+	0.948122i
$404$	−29.2507	−	16.8879i	−1.45527	−	0.840203i
$405$	5.36169	−	11.2644i	0.266424	−	0.559732i
$406$	−20.2478	−	12.2015i	−1.00488	−	0.605548i
$407$	−12.1839			−0.603931
$408$	1.24770	+	1.36705i	0.0617705	+	0.0676792i
$409$	−22.9709	−	6.15503i	−1.13584	−	0.304347i	−0.358561	−	0.933506i	$-0.616732\pi$
$409$	−22.9709	−	6.15503i	−1.13584	−	0.304347i	−0.777276	+	0.629160i	$0.783399\pi$
$410$	22.7188	+	6.08748i	1.12200	+	0.300639i
$411$	−11.9769	−	13.1226i	−0.590778	−	0.647290i
$412$	34.3359			1.69161
$413$	−16.9299	+	9.35606i	−0.833068	+	0.460382i
$414$	4.15340	−	0.715411i	0.204129	−	0.0351605i
$415$	1.76117	+	1.01681i	0.0864525	+	0.0499133i
$416$	25.3518	−	10.6244i	1.24297	−	0.520903i
$417$	−2.77757	−	1.77725i	−0.136018	−	0.0870323i
$418$	5.12915	+	19.1422i	0.250875	+	0.936278i
$419$		−	17.4455i		−	0.852269i	−0.904660	−	0.426134i	$-0.859875\pi$
$419$		−	17.4455i		−	0.852269i	0.904660	−	0.426134i	$-0.140125\pi$
$420$	−6.16366	+	9.24659i	−0.300756	+	0.451187i
$421$	0.682835	−	0.682835i	0.0332793	−	0.0332793i	−0.690271	−	0.723551i	$-0.742509\pi$
$421$	0.682835	−	0.682835i	0.0332793	−	0.0332793i	0.723551	+	0.690271i	$0.242509\pi$
$422$	52.4647	−	14.0579i	2.55394	−	0.684326i
$423$	9.92122	−	8.25817i	0.482386	−	0.401526i
$424$	1.49955	−	5.59640i	0.0728246	−	0.271785i
$425$	−5.87186	−	3.39012i	−0.284827	−	0.164445i
$426$	23.7164	+	45.7799i	1.14907	+	2.21804i
$427$	−5.32316	−	21.4673i	−0.257606	−	1.03887i
$428$	−9.69143			−0.468453
$429$	−2.53674	+	14.5710i	−0.122475	+	0.703496i
$430$	−1.99541	−	3.45615i	−0.0962272	−	0.166670i
$431$	0.151236	−	0.564422i	0.00728480	−	0.0271872i	−0.962188	−	0.272387i	$-0.912187\pi$
$431$	0.151236	−	0.564422i	0.00728480	−	0.0271872i	0.969473	+	0.245200i	$0.0788536\pi$
$432$	−18.2129	−	14.1479i	−0.876269	−	0.680692i
$433$		−	24.1411i		−	1.16015i	−0.814564	−	0.580074i	$-0.803024\pi$
$433$		−	24.1411i		−	1.16015i	0.814564	−	0.580074i	$-0.196976\pi$
$434$	−21.1195	+	20.3425i	−1.01377	+	0.976473i
$435$	3.35232	−	10.5593i	0.160732	−	0.506278i
$436$	−20.3642	+	5.45658i	−0.975270	+	0.261323i
$437$	3.02843	+	0.811466i	0.144870	+	0.0388177i
$438$	14.3215	−	22.3823i	0.684306	−	1.06947i
$439$	32.3732	+	18.6907i	1.54509	+	0.892056i	0.998506	+	0.0546506i	$0.0174045\pi$
$439$	32.3732	+	18.6907i	1.54509	+	0.892056i	0.546582	+	0.837406i	$0.315929\pi$
$440$	−1.12629	+	1.12629i	−0.0536939	+	0.0536939i
$441$	19.3837	−	8.07905i	0.923035	−	0.384717i
$442$	1.94378	−	15.2528i	0.0924561	−	0.725501i
$443$	13.3228	+	7.69193i	0.632986	+	0.365455i	0.781908	−	0.623394i	$-0.214247\pi$
$443$	13.3228	+	7.69193i	0.632986	+	0.365455i	−0.148922	+	0.988849i	$0.547580\pi$
$444$	−15.2255	+	3.34380i	−0.722570	+	0.158690i
$445$	7.77626	+	13.4689i	0.368630	+	0.638486i
$446$	−15.7132	+	27.2160i	−0.744040	+	1.28871i
$447$	−1.19171	−	0.378339i	−0.0563658	−	0.0178948i
$448$	10.8027	+	11.2153i	0.510380	+	0.529872i
$449$	24.2044	−	24.2044i	1.14228	−	1.14228i	0.154243	−	0.988033i	$-0.450706\pi$
$449$	24.2044	−	24.2044i	1.14228	−	1.14228i	0.988033	−	0.154243i	$-0.0492938\pi$
$450$	16.7808	+	6.18306i	0.791052	+	0.291472i
$451$	10.3767	+	17.9730i	0.488621	+	0.846316i
$452$	11.8306	+	20.4913i	0.556466	+	0.963828i
$453$	23.3629	−	21.3232i	1.09768	−	1.00185i
$454$		−	37.8001i		−	1.77405i
$455$	−13.1337	+	1.53450i	−0.615717	+	0.0719383i
$456$	−1.67051	−	3.22459i	−0.0782288	−	0.151005i
$457$	6.02561	+	22.4879i	0.281866	+	1.05194i	0.951099	+	0.308886i	$0.0999563\pi$
$457$	6.02561	+	22.4879i	0.281866	+	1.05194i	−0.669233	+	0.743053i	$0.733377\pi$
$458$	1.83884	−	1.06165i	0.0859232	−	0.0496078i
$459$	−10.5986	+	4.31653i	−0.494702	+	0.201478i
$460$	−0.455357	−	1.69941i	−0.0212311	−	0.0792356i
$461$	24.0178	+	24.0178i	1.11862	+	1.11862i	0.991944	+	0.126677i	$0.0404310\pi$
$461$	24.0178	+	24.0178i	1.11862	+	1.11862i	0.126677	+	0.991944i	$0.459569\pi$
$462$	−20.6069	+	4.12256i	−0.958719	+	0.191799i
$463$	−6.56142	−	6.56142i	−0.304935	−	0.304935i	0.538006	−	0.842941i	$-0.319178\pi$
$463$	−6.56142	−	6.56142i	−0.304935	−	0.304935i	−0.842941	+	0.538006i	$0.819178\pi$
$464$	−17.7365	−	10.2402i	−0.823397	−	0.475388i
$465$	−11.5753	−	7.40652i	−0.536790	−	0.343469i
$466$	9.20696	−	34.3608i	0.426504	−	1.59173i
$467$	−13.3120	+	23.0571i	−0.616006	+	1.06695i	0.374201	+	0.927347i	$0.377917\pi$
$467$	−13.3120	+	23.0571i	−0.616006	+	1.06695i	−0.990207	+	0.139606i	$0.955416\pi$
$468$	0.828914	+	18.9048i	0.0383166	+	0.873875i
$469$	1.39033	−	0.768345i	0.0641996	−	0.0354789i
$470$	−8.16640	−	8.16640i	−0.376688	−	0.376688i
$471$	0.695517	−	15.2376i	0.0320477	−	0.702111i
$472$	−3.07202	+	1.77363i	−0.141401	+	0.0816379i
$473$	0.911396	−	3.40138i	0.0419060	−	0.156395i
$474$	−16.3283	+	14.9027i	−0.749982	+	0.684505i
$475$	9.40722	+	9.40722i	0.431633	+	0.431633i
$476$	9.89421	−	2.45343i	0.453500	−	0.112453i
$477$	29.2636	+	20.6638i	1.33989	+	0.946128i
$478$	−46.8794	−	27.0658i	−2.14421	−	1.23796i
$479$	−13.2078	−	3.53902i	−0.603479	−	0.161702i	−0.0558729	−	0.998438i	$-0.517794\pi$
$479$	−13.2078	−	3.53902i	−0.603479	−	0.161702i	−0.547606	+	0.836736i	$0.684461\pi$
$480$	−9.86520	+	15.4178i	−0.450283	+	0.703723i
$481$	−14.7624	−	11.2307i	−0.673107	−	0.512074i
$482$			13.4890i			0.614407i
$483$	−1.06524	+	3.14948i	−0.0484700	+	0.143306i
$484$	−9.43121			−0.428692
$485$	0.423061	−	0.732764i	0.0192102	−	0.0332731i
$486$	25.6168	−	15.9654i	1.16200	−	0.724204i
$487$	−0.828582	−	0.222018i	−0.0375466	−	0.0100606i	0.239997	−	0.970774i	$-0.422854\pi$
$487$	−0.828582	−	0.222018i	−0.0375466	−	0.0100606i	−0.277543	+	0.960713i	$0.589520\pi$
$488$	−1.04977	−	3.91781i	−0.0475210	−	0.177351i
$489$	−15.3160	−	4.86249i	−0.692615	−	0.219889i
$490$	−8.77806	−	16.6118i	−0.396552	−	0.750444i
$491$	2.60011			0.117342			0.0586708	−	0.998277i	$-0.481314\pi$
$491$	2.60011			0.117342			0.0586708	+	0.998277i	$0.481314\pi$
$492$	17.8998	+	19.6120i	0.806985	+	0.884178i
$493$	−8.80115	+	5.08135i	−0.396384	+	0.228852i
$494$	−11.4300	+	27.9213i	−0.514261	+	1.25624i
$495$	−4.12681	−	8.94225i	−0.185486	−	0.401924i
$496$	−17.9633	+	17.9633i	−0.806578	+	0.806578i
$497$	−40.6658	−	0.761993i	−1.82411	−	0.0341800i
$498$	2.26336	+	4.36897i	0.101424	+	0.195778i
$499$	1.43469	+	5.35433i	0.0642254	+	0.239693i	0.990575	−	0.136973i	$-0.0437373\pi$
$499$	1.43469	+	5.35433i	0.0642254	+	0.239693i	−0.926349	+	0.376665i	$0.877071\pi$
$500$	5.07035	−	18.9228i	0.226753	−	0.846254i
$501$	13.5609	−	2.97822i	0.605855	−	0.133057i
$502$	−24.0410	+	6.44175i	−1.07300	+	0.287510i
$503$			39.5365i			1.76284i	0.472329	+	0.881422i	$0.343413\pi$
$503$			39.5365i			1.76284i	−0.472329	+	0.881422i	$0.656587\pi$
$504$	3.52631	−	1.54792i	0.157074	−	0.0689497i
$505$	18.9236	+	18.9236i	0.842090	+	0.842090i
$506$	1.66358	−	2.88140i	0.0739551	−	0.128094i
$507$	−16.5047	+	15.3165i	−0.732999	+	0.680230i
$508$	3.95908	+	6.85733i	0.175656	+	0.304245i
$509$	19.8987	−	5.33184i	0.881994	−	0.236330i	0.210727	−	0.977545i	$-0.432417\pi$
$509$	19.8987	−	5.33184i	0.881994	−	0.236330i	0.671267	+	0.741215i	$0.265750\pi$
$510$	4.70974	+	9.09122i	0.208551	+	0.402566i
$511$	10.1390	+	18.3467i	0.448522	+	0.811609i
$512$	20.8810	+	20.8810i	0.922820	+	0.922820i
$513$	22.2796	−	2.79864i	0.983668	−	0.123563i
$514$	−5.03585	+	18.7940i	−0.222122	+	0.828969i
$515$	−26.2788	−	7.04139i	−1.15798	−	0.310281i
$516$	0.205431	−	4.50064i	0.00904359	−	0.198130i
$517$		−	10.1905i		−	0.448177i
$518$	7.29710	−	25.3254i	0.320616	−	1.11273i
$519$	−16.3753	+	8.48326i	−0.718794	+	0.372374i
$520$	−2.40283	+	0.326478i	−0.105371	+	0.0143170i
$521$	−8.86791	+	5.11989i	−0.388510	+	0.224307i	−0.681514	−	0.731805i	$-0.738678\pi$
$521$	−8.86791	+	5.11989i	−0.388510	+	0.224307i	0.293004	+	0.956111i	$0.405345\pi$
$522$	20.6020	−	17.1486i	0.901727	−	0.750574i
$523$	6.10685	−	10.5774i	0.267034	−	0.462516i	−0.701061	−	0.713102i	$-0.747290\pi$
$523$	6.10685	−	10.5774i	0.267034	−	0.462516i	0.968095	+	0.250585i	$0.0806231\pi$
$524$	19.6262			0.857375
$525$	−10.5966	+	9.31363i	−0.462474	+	0.406480i
$526$	−16.6771	+	16.6771i	−0.727157	+	0.727157i
$527$	3.26264	+	12.1763i	0.142123	+	0.530410i
$528$	−17.7826	+	3.90539i	−0.773889	+	0.169960i
$529$	11.2368	+	19.4627i	0.488557	+	0.846206i
$530$	16.0256	−	27.7571i	0.696107	−	1.20569i
$531$	−3.72308	−	21.6148i	−0.161568	−	0.938003i
$532$	−19.9983	−	0.374727i	−0.867038	−	0.0162465i
$533$	−3.99410	+	31.3416i	−0.173004	+	1.35756i
$534$	−1.71583	+	37.5908i	−0.0742511	+	1.62671i
$535$	7.41730	+	1.98746i	0.320678	+	0.0859253i
$536$	0.252282	−	0.145655i	0.0108969	−	0.00629135i
$537$	1.01172	−	22.1651i	0.0436590	−	0.956493i
$538$	−3.49015	+	3.49015i	−0.150471	+	0.150471i
$539$	4.88767	−	15.8414i	0.210527	−	0.682338i
$540$	−7.61119	−	10.0420i	−0.327534	−	0.432141i
$541$	−8.53926	+	2.28809i	−0.367132	+	0.0983726i	−0.437668	−	0.899137i	$-0.644196\pi$
$541$	−8.53926	+	2.28809i	−0.367132	+	0.0983726i	0.0705366	+	0.997509i	$0.477529\pi$
$542$	24.3543	−	14.0610i	1.04611	−	0.603970i
$543$	2.88727	−	4.51237i	0.123905	−	0.193644i
$544$	16.2184	−	4.34571i	0.695359	−	0.186321i
$545$	16.7047			0.715550
$546$	−28.7681	−	13.9997i	−1.23116	−	0.599132i
$547$	10.7037			0.457659			0.228830	−	0.973466i	$-0.426510\pi$
$547$	10.7037			0.457659			0.228830	+	0.973466i	$0.426510\pi$
$548$	−17.3333	+	4.64445i	−0.740443	+	0.198401i
$549$	24.9745	+	2.28468i	1.06589	+	0.0975076i
$550$	12.2266	−	7.05904i	0.521345	−	0.300999i
$551$	19.2612	−	5.16103i	0.820556	−	0.219867i
$552$	−0.184494	+	0.581127i	−0.00785261	+	0.0247344i
$553$	−4.19724	−	16.9267i	−0.178485	−	0.719794i
$554$	16.9730	−	16.9730i	0.721116	−	0.721116i
$555$	12.3385	+	0.563188i	0.523740	+	0.0239060i
$556$	−2.88437	+	1.66529i	−0.122325	+	0.0706242i
$557$	8.70078	+	2.33137i	0.368664	+	0.0987831i	0.438394	−	0.898783i	$-0.355547\pi$
$557$	8.70078	+	2.33137i	0.368664	+	0.0987831i	−0.0697307	+	0.997566i	$0.522214\pi$
$558$	−13.9324	−	30.1896i	−0.589804	−	1.27803i
$559$	4.23955	−	3.28114i	0.179314	−	0.138777i
$560$	−7.87311	−	14.2465i	−0.332700	−	0.602026i
$561$	−2.73373	+	8.61079i	−0.115418	+	0.363548i
$562$	9.79575	−	16.9667i	0.413209	−	0.715698i
$563$	6.65130	+	11.5204i	0.280319	+	0.485527i	0.971463	−	0.237190i	$-0.0762264\pi$
$563$	6.65130	+	11.5204i	0.280319	+	0.485527i	−0.691144	+	0.722717i	$0.742893\pi$
$564$	−2.79672	−	12.7345i	−0.117763	−	0.536218i
$565$	−4.85231	−	18.1091i	−0.204138	−	0.761854i
$566$	−29.9013	+	29.9013i	−1.25684	+	1.25684i
$567$	1.44237	+	23.7680i	0.0605739	+	0.998164i
$568$	−7.45883			−0.312965
$569$	11.2617	−	19.5058i	0.472115	−	0.817727i	−0.527376	−	0.849632i	$-0.676824\pi$
$569$	11.2617	−	19.5058i	0.472115	−	0.817727i	0.999491	+	0.0319049i	$0.0101574\pi$
$570$	−4.30941	−	19.6223i	−0.180501	−	0.821887i
$571$	−30.7521	+	17.7548i	−1.28694	+	0.743013i	−0.978107	−	0.208104i	$-0.933271\pi$
$571$	−30.7521	+	17.7548i	−1.28694	+	0.743013i	−0.308830	+	0.951117i	$0.599937\pi$
$572$	11.8892	+	9.04483i	0.497111	+	0.378183i
$573$	−9.89297	−	19.0964i	−0.413285	−	0.797765i
$574$	−43.5735	+	10.8048i	−1.81872	+	0.450982i
$575$		−	2.23358i		−	0.0931466i
$576$	−16.0319	+	7.39865i	−0.667995	+	0.308277i
$577$	−18.4532	−	4.94452i	−0.768218	−	0.205843i	−0.146634	−	0.989191i	$-0.546844\pi$
$577$	−18.4532	−	4.94452i	−0.768218	−	0.205843i	−0.621584	+	0.783348i	$0.713511\pi$
$578$	−6.08888	+	22.7240i	−0.253264	+	0.945194i
$579$	−27.1432	+	24.7735i	−1.12803	+	1.02955i
$580$	−7.91237	−	7.91237i	−0.328543	−	0.328543i
$581$	−3.88091	−	0.0727202i	−0.161007	−	0.00301694i
$582$	1.81778	−	0.941708i	0.0753495	−	0.0390350i
$583$	27.3172	−	7.31963i	1.13136	−	0.303148i
$584$	1.92205	+	3.32909i	0.0795350	+	0.137759i
$585$	3.24247	−	14.6387i	0.134060	−	0.605236i
$586$	−7.41457	+	12.8424i	−0.306293	+	0.530515i
$587$	5.45570	+	5.45570i	0.225181	+	0.225181i	0.810676	−	0.585495i	$-0.199100\pi$
$587$	5.45570	+	5.45570i	0.225181	+	0.225181i	−0.585495	+	0.810676i	$0.699100\pi$
$588$	1.76026	−	21.1375i	0.0725917	−	0.871697i
$589$		−	24.7346i		−	1.01917i
$590$	−18.9546	+	5.07888i	−0.780350	+	0.209094i
$591$	−2.96483	−	13.4999i	−0.121957	−	0.555312i
$592$	5.90965	−	22.0551i	0.242885	−	0.906459i
$593$	−1.37797	−	5.14265i	−0.0565864	−	0.211183i	0.931844	−	0.362860i	$-0.118200\pi$
$593$	−1.37797	−	5.14265i	−0.0565864	−	0.211183i	−0.988430	+	0.151676i	$0.951533\pi$
$594$	3.25058	−	23.6063i	0.133373	−	0.968577i
$595$	−8.07563	−	0.151321i	−0.331068	−	0.00620354i
$596$	−0.892982	+	0.892982i	−0.0365779	+	0.0365779i
$597$	24.6979	+	1.12733i	1.01082	+	0.0461386i
$598$	4.67163	−	1.95778i	0.191037	−	0.0800596i
$599$	−27.4491	+	15.8477i	−1.12154	+	0.647521i	−0.941793	−	0.336193i	$-0.890861\pi$
$599$	−27.4491	+	15.8477i	−1.12154	+	0.647521i	−0.179745	+	0.983713i	$0.557527\pi$
$600$	−1.91092	+	1.74409i	−0.0780132	+	0.0712022i
$601$	29.8604			1.21803			0.609016	−	0.793158i	$-0.291565\pi$
$601$	29.8604			1.21803			0.609016	+	0.793158i	$0.291565\pi$
$602$	6.52426	+	3.93157i	0.265909	+	0.160239i
$603$	0.305749	+	1.77507i	0.0124511	+	0.0722863i
$604$	−8.26877	−	30.8595i	−0.336451	−	1.25565i
$605$	7.21814	+	1.93410i	0.293459	+	0.0786321i
$606$	13.8897	+	63.2446i	0.564229	+	2.56914i
$607$	18.0891	−	31.3312i	0.734214	−	1.27170i	−0.220854	−	0.975307i	$-0.570884\pi$
$607$	18.0891	−	31.3312i	0.734214	−	1.27170i	0.955068	−	0.296388i	$-0.0957822\pi$
$608$	−32.9455			−1.33612
$609$	4.14818	+	20.7350i	0.168093	+	0.840224i
$610$		−	22.4377i		−	0.908476i
$611$	9.39324	−	12.3471i	0.380010	−	0.499512i
$612$	−1.05300	+	11.5107i	−0.0425650	+	0.465292i
$613$	38.7241	+	10.3761i	1.56405	+	0.419086i	0.933943	−	0.357421i	$-0.116344\pi$
$613$	38.7241	+	10.3761i	1.56405	+	0.419086i	0.630108	+	0.776507i	$0.283010\pi$
$614$	20.7357	+	11.9718i	0.836824	+	0.483141i
$615$	−9.67763	−	18.6808i	−0.390240	−	0.753281i
$616$	0.841745	−	2.92137i	0.0339149	−	0.117705i
$617$	−33.0811	−	33.0811i	−1.33180	−	1.33180i	−0.903763	−	0.428034i	$-0.859206\pi$
$617$	−33.0811	−	33.0811i	−1.33180	−	1.33180i	−0.428034	−	0.903763i	$-0.640794\pi$
$618$	−44.3750	−	48.6197i	−1.78502	−	1.95577i
$619$	2.13272	−	7.95941i	0.0857212	−	0.319916i	−0.909729	−	0.415203i	$-0.863710\pi$
$619$	2.13272	−	7.95941i	0.0857212	−	0.319916i	0.995450	+	0.0952876i	$0.0303771\pi$
$620$	−12.0203	+	6.93995i	−0.482749	+	0.278715i
$621$	−2.97719	−	2.31270i	−0.119470	−	0.0928055i
$622$	−7.63399	−	7.63399i	−0.306095	−	0.306095i
$623$	−25.4255	−	15.3216i	−1.01865	−	0.613847i
$624$	−25.1459	−	11.6595i	−1.00664	−	0.466754i
$625$	−0.0646763	+	0.112023i	−0.00258705	+	0.00448091i
$626$	4.97622	−	18.5715i	0.198890	−	0.742266i
$627$	9.55412	−	14.9316i	0.381555	−	0.596312i
$628$	−13.3424	−	7.70325i	−0.532420	−	0.307393i
$629$	−8.01164	−	8.01164i	−0.319445	−	0.319445i
$630$	21.0590	−	3.22234i	0.839010	−	0.128381i
$631$	18.8858	+	18.8858i	0.751833	+	0.751833i	0.974821	−	0.222988i	$-0.0715811\pi$
$631$	18.8858	+	18.8858i	0.751833	+	0.751833i	−0.222988	+	0.974821i	$0.571581\pi$
$632$	−0.827732	−	3.08914i	−0.0329254	−	0.122879i
$633$	−40.9243	−	26.1857i	−1.62660	−	1.04079i
$634$	18.9879	−	10.9627i	0.754107	−	0.435384i
$635$	−1.62381	−	6.06013i	−0.0644388	−	0.240489i
$636$	32.1280	−	16.6440i	1.27396	−	0.659977i
$637$	20.5242	−	14.6887i	0.813197	−	0.581989i
$638$		−	21.1612i		−	0.837779i
$639$	15.9450	−	43.2747i	0.630776	−	1.71192i
$640$	−2.66908	−	4.62299i	−0.105505	−	0.182740i
$641$	18.8454	+	32.6411i	0.744347	+	1.28925i	0.950499	+	0.310727i	$0.100573\pi$
$641$	18.8454	+	32.6411i	0.744347	+	1.28925i	−0.206152	+	0.978520i	$0.566094\pi$
$642$	12.5250	+	13.7231i	0.494323	+	0.541607i
$643$	−26.5007	+	26.5007i	−1.04508	+	1.04508i	−0.0461500	+	0.998935i	$0.514695\pi$
$643$	−26.5007	+	26.5007i	−1.04508	+	1.04508i	−0.998935	+	0.0461500i	$0.985305\pi$
$644$	2.32964	+	2.41861i	0.0918005	+	0.0953065i
$645$	−1.08019	+	3.40242i	−0.0425324	+	0.133970i
$646$	−9.21448	+	15.9599i	−0.362539	+	0.627936i
$647$	9.44143	+	16.3530i	0.371181	+	0.642904i	0.989748	−	0.142828i	$-0.0456196\pi$
$647$	9.44143	+	16.3530i	0.371181	+	0.642904i	−0.618566	+	0.785732i	$0.712286\pi$
$648$	0.346122	+	4.35299i	0.0135970	+	0.171002i
$649$	−14.9952	−	8.65746i	−0.588612	−	0.339835i
$650$	21.3210	+	2.71710i	0.836279	+	0.106573i
$651$	26.1752	+	1.68667i	1.02589	+	0.0661059i
$652$	−11.4768	+	11.4768i	−0.449465	+	0.449465i
$653$	−27.2368	−	15.7252i	−1.06586	−	0.615373i	−0.138811	−	0.990319i	$-0.544328\pi$
$653$	−27.2368	−	15.7252i	−1.06586	−	0.615373i	−0.927047	+	0.374945i	$0.877661\pi$
$654$	34.0448	+	21.7838i	1.33126	+	0.851816i
$655$	−15.0208	−	4.02482i	−0.586913	−	0.157263i
$656$	−37.5677	+	10.0662i	−1.46677	+	0.393020i
$657$	−23.4236	+	4.03463i	−0.913840	+	0.157406i
$658$	21.1819	+	6.10323i	0.825758	+	0.237929i
$659$			2.46575i			0.0960519i	0.998846	+	0.0480259i	$0.0152930\pi$
$659$			2.46575i			0.0960519i	−0.998846	+	0.0480259i	$0.984707\pi$
$660$	−9.93704	−	0.453574i	−0.386799	−	0.0176554i
$661$	4.51394	−	16.8462i	0.175572	−	0.655243i	−0.820882	−	0.571098i	$-0.806518\pi$
$661$	4.51394	−	16.8462i	0.175572	−	0.655243i	0.996454	−	0.0841448i	$-0.0268158\pi$
$662$	−0.779550	−	1.35022i	−0.0302981	−	0.0524778i
$663$	−11.2494	+	7.91329i	−0.436891	+	0.307327i
$664$	−0.711827			−0.0276242
$665$	15.2288	+	4.38793i	0.590548	+	0.170157i
$666$	24.4119	+	17.2379i	0.945943	+	0.667954i
$667$	−2.89931	−	1.67392i	−0.112262	−	0.0648144i
$668$	3.62951	−	13.5455i	0.140430	−	0.524092i
$669$	27.4564	−	6.02992i	1.06152	−	0.233130i
$670$	1.55661	−	0.417091i	0.0601369	−	0.0161136i
$671$	13.9995	−	13.9995i	0.540444	−	0.540444i
$672$	2.24658	−	34.8643i	0.0866639	−	1.34492i
$673$		−	11.2854i		−	0.435020i	−0.976058	−	0.217510i	$-0.930207\pi$
$673$		−	11.2854i		−	0.435020i	0.976058	−	0.217510i	$-0.0697934\pi$
$674$	6.48075	+	24.1865i	0.249629	+	0.931629i
$675$	−6.03382	−	14.8152i	−0.232242	−	0.570238i
$676$	6.06813	+	21.9181i	0.233390	+	0.843003i
$677$	8.62267	+	4.97830i	0.331396	+	0.191332i	0.656461	−	0.754360i	$-0.272053\pi$
$677$	8.62267	+	4.97830i	0.331396	+	0.191332i	−0.325065	+	0.945692i	$0.605386\pi$
$678$	13.7260	−	43.2347i	0.527145	−	1.66042i
$679$	−0.0302564	+	1.61472i	−0.00116113	+	0.0619671i
$680$	−1.48121			−0.0568019
$681$	−24.9740	+	22.7937i	−0.957006	+	0.873455i
$682$	−25.3541	−	6.79361i	−0.970858	−	0.260141i
$683$	−39.8038	−	10.6654i	−1.52305	−	0.408100i	−0.602305	−	0.798266i	$-0.705751\pi$
$683$	−39.8038	−	10.6654i	−1.52305	−	0.408100i	−0.920745	+	0.390166i	$0.872418\pi$
$684$	7.84134	−	21.2813i	0.299821	−	0.813711i
$685$	14.2184			0.543259
$686$	30.0007	+	19.6472i	1.14543	+	0.750133i
$687$	−1.81025	−	0.574712i	−0.0690653	−	0.0219266i
$688$	5.71508	+	3.29960i	0.217885	+	0.125796i
$689$	39.8455	+	16.3114i	1.51799	+	0.621413i
$690$	−1.81788	+	2.84108i	−0.0692056	+	0.108158i
$691$	4.87743	+	18.2028i	0.185546	+	0.692467i	0.994513	+	0.104613i	$0.0333604\pi$
$691$	4.87743	+	18.2028i	0.185546	+	0.692467i	−0.808967	+	0.587854i	$0.799973\pi$
$692$			18.6272i			0.708101i
$693$	15.1498	+	11.1288i	0.575493	+	0.422747i
$694$	−8.95959	+	8.95959i	−0.340101	+	0.340101i
$695$	2.54905	−	0.683016i	0.0966910	−	0.0259083i
$696$	0.831821	+	3.78758i	0.0315301	+	0.143568i
$697$	−4.99503	+	18.6417i	−0.189200	+	0.706104i
$698$	39.9436	+	23.0615i	1.51189	+	0.872889i
$699$	−28.2536	+	14.6369i	−1.06865	+	0.553617i
$700$	3.42951	+	13.8306i	0.129623	+	0.522746i
$701$	38.6302			1.45904			0.729522	−	0.683957i	$-0.239743\pi$
$701$	38.6302			1.45904			0.729522	+	0.683957i	$0.239743\pi$
$702$	25.6980	−	25.6059i	0.969908	−	0.966433i
$703$	11.1157	+	19.2530i	0.419238	+	0.726141i
$704$	−3.60768	+	13.4640i	−0.135970	+	0.507445i
$705$	−0.471046	+	10.3198i	−0.0177406	+	0.388666i
$706$			60.4262i			2.27417i
$707$	−49.0839	−	14.1427i	−1.84599	−	0.531893i
$708$	−21.1146	−	6.70340i	−0.793536	−	0.251929i
$709$	−30.8334	+	8.26177i	−1.15797	+	0.310277i	−0.786155	−	0.618029i	$-0.787931\pi$
$709$	−30.8334	+	8.26177i	−1.15797	+	0.310277i	−0.371816	+	0.928307i	$0.621265\pi$
$710$	−39.8559	−	10.6794i	−1.49577	−	0.400789i
$711$	19.6921	+	1.80143i	0.738510	+	0.0675591i
$712$	−4.71449	−	2.72191i	−0.176683	−	0.102008i
$713$	−2.93639	+	2.93639i	−0.109969	+	0.109969i
$714$	−16.2611	−	10.8395i	−0.608558	−	0.405657i
$715$	−7.24448	−	9.36058i	−0.270928	−	0.350066i
$716$	−19.4083	−	11.2054i	−0.725322	−	0.418765i
$717$	10.3865	+	47.2934i	0.387891	+	1.76621i
$718$	−19.5018	−	33.7782i	−0.727802	−	1.26059i
$719$	10.6104	−	18.3777i	0.395700	−	0.685373i	−0.597490	−	0.801876i	$-0.703835\pi$
$719$	10.6104	−	18.3777i	0.395700	−	0.685373i	0.993190	+	0.116503i	$0.0371686\pi$
$720$	18.1888	−	3.13297i	0.677858	−	0.116759i
$721$	50.4015	−	12.4979i	1.87705	−	0.465445i
$722$	−0.445628	+	0.445628i	−0.0165846	+	0.0165846i
$723$	8.91200	−	8.13394i	0.331441	−	0.302505i
$724$	−2.70539	−	4.68587i	−0.100545	−	0.174149i
$725$	−7.10292	−	12.3026i	−0.263796	−	0.456908i
$726$	12.1887	+	13.3546i	0.452365	+	0.495637i
$727$			22.5796i			0.837432i	0.908117	+	0.418716i	$0.137520\pi$
$727$			22.5796i			0.837432i	−0.908117	+	0.418716i	$0.862480\pi$
$728$	3.71271	−	2.76374i	0.137602	−	0.102431i
$729$	−25.9951	−	7.29744i	−0.962783	−	0.270275i
$730$	5.50389	+	20.5408i	0.203708	+	0.760249i
$731$	2.83591	−	1.63732i	0.104890	−	0.0605583i
$732$	13.6523	−	21.3365i	0.504603	−	0.788619i
$733$	7.49980	+	27.9896i	0.277011	+	1.03382i	0.954482	+	0.298270i	$0.0964096\pi$
$733$	7.49980	+	27.9896i	0.277011	+	1.03382i	−0.677470	+	0.735550i	$0.736924\pi$
$734$	−25.7681	−	25.7681i	−0.951119	−	0.951119i
$735$	−5.68196	+	15.8165i	−0.209582	+	0.583402i
$736$	3.91116	+	3.91116i	0.144167	+	0.144167i
$737$	1.23144	+	0.710974i	0.0453608	+	0.0261891i
$738$	4.63735	−	50.6923i	0.170703	−	1.86601i
$739$	−11.8341	+	44.1656i	−0.435326	+	1.62466i	0.304959	+	0.952366i	$0.401357\pi$
$739$	−11.8341	+	44.1656i	−0.435326	+	1.62466i	−0.740285	+	0.672293i	$0.765309\pi$
$740$	6.23763	−	10.8039i	0.229300	−	0.397159i
$741$	25.3396	−	9.28505i	0.930873	−	0.341095i
$742$	−1.14611	+	61.1655i	−0.0420752	+	2.24545i
$743$	−12.5735	−	12.5735i	−0.461277	−	0.461277i	0.437797	−	0.899074i	$-0.355759\pi$
$743$	−12.5735	−	12.5735i	−0.461277	−	0.461277i	−0.899074	+	0.437797i	$0.855759\pi$
$744$	4.80510	+	0.219328i	0.176164	+	0.00804096i
$745$	0.866567	−	0.500313i	0.0317486	−	0.0183300i
$746$	3.92244	−	14.6388i	0.143611	−	0.535963i
$747$	1.52170	−	4.12988i	0.0556762	−	0.151105i
$748$	6.45233	+	6.45233i	0.235920	+	0.235920i
$749$	−14.2260	+	3.52757i	−0.519807	+	0.128895i
$750$	−33.3476	+	17.2758i	−1.21768	+	0.630824i
$751$	−12.0283	−	6.94455i	−0.438919	−	0.253410i	0.264220	−	0.964462i	$-0.414886\pi$
$751$	−12.0283	−	6.94455i	−0.438919	−	0.253410i	−0.703139	+	0.711052i	$0.748219\pi$
$752$	18.4467	+	4.94278i	0.672682	+	0.180245i
$753$	18.7528	+	11.9991i	0.683390	+	0.437272i
$754$	19.5057	−	25.6396i	0.710354	−	0.933740i
$755$			25.3139i			0.921266i
$756$	21.9861	+	9.74922i	0.799626	+	0.354576i
$757$	−42.8297			−1.55667			−0.778336	−	0.627848i	$-0.783936\pi$
$757$	−42.8297			−1.55667			−0.778336	+	0.627848i	$0.783936\pi$
$758$	−9.63097	+	16.6813i	−0.349812	+	0.605893i
$759$	−2.90685	+	0.638398i	−0.105512	+	0.0231724i
$760$	2.80733	+	0.752221i	0.101832	+	0.0272859i
$761$	2.47352	+	9.23131i	0.0896651	+	0.334635i	0.996157	−	0.0875891i	$-0.0279163\pi$
$761$	2.47352	+	9.23131i	0.0896651	+	0.334635i	−0.906492	+	0.422224i	$0.861250\pi$
$762$	4.59336	−	14.4683i	0.166400	−	0.524133i
$763$	−27.9064	+	15.4220i	−1.01028	+	0.558316i
$764$	−21.7226			−0.785897
$765$	3.16645	−	8.59371i	0.114483	−	0.310706i
$766$	28.4971	−	16.4528i	1.02964	−	0.594464i
$767$	−10.1885	−	24.3117i	−0.367886	−	0.877846i
$768$	1.51858	−	33.2696i	0.0547972	−	1.20051i
$769$	−1.62419	+	1.62419i	−0.0585700	+	0.0585700i	−0.735785	−	0.677215i	$-0.763187\pi$
$769$	−1.62419	+	1.62419i	−0.0585700	+	0.0585700i	0.677215	+	0.735785i	$0.263187\pi$
$770$	8.68057	−	14.4050i	0.312826	−	0.519121i
$771$	15.4536	−	8.00579i	0.556548	−	0.288321i
$772$	9.60674	+	35.8528i	0.345754	+	1.29037i
$773$	−6.79603	+	25.3631i	−0.244436	+	0.912249i	0.729230	+	0.684269i	$0.239879\pi$
$773$	−6.79603	+	25.3631i	−0.244436	+	0.912249i	−0.973666	+	0.227980i	$0.926788\pi$
$774$	−6.63841	+	5.52564i	−0.238613	+	0.198615i
$775$	−17.0206	+	4.56066i	−0.611399	+	0.163824i
$776$			0.296167i			0.0106318i
$777$	−21.1323	+	10.4503i	−0.758118	+	0.374901i
$778$	48.3479	+	48.3479i	1.73336	+	1.73336i
$779$	18.9340	−	32.7947i	0.678382	−	1.17499i
$780$	−11.6220	−	9.70919i	−0.416134	−	0.347645i
$781$	−18.2041	−	31.5304i	−0.651392	−	1.12824i
$782$	2.98861	−	0.800795i	0.106872	−	0.0286364i
$783$	−23.7530	−	3.27079i	−0.848863	−	0.116888i
$784$	26.3053	+	16.5313i	0.939474	+	0.590404i
$785$	8.63183	+	8.63183i	0.308083	+	0.308083i
$786$	−25.3645	−	27.7908i	−0.904723	−	0.991265i
$787$	−3.26894	+	12.1998i	−0.116525	+	0.434878i	−0.999396	−	0.0347373i	$-0.988941\pi$
$787$	−3.26894	+	12.1998i	−0.116525	+	0.434878i	0.882871	+	0.469615i	$0.155607\pi$
$788$	−13.4846	−	3.61320i	−0.480370	−	0.128715i
$789$	21.0747	+	0.961953i	0.750281	+	0.0342464i
$790$		−	17.6918i		−	0.629446i
$791$	24.8247	+	25.7728i	0.882666	+	0.916377i
$792$	2.81600	+	1.98845i	0.100062	+	0.0706564i
$793$	29.8665	−	4.05803i	1.06059	−	0.144105i
$794$	−29.2341	+	16.8783i	−1.03748	+	0.598988i
$795$	−28.0023	+	6.14981i	−0.993138	+	0.218111i
$796$	12.4858	−	21.6261i	0.442549	−	0.766517i
$797$	−18.7237			−0.663228			−0.331614	−	0.943415i	$-0.607593\pi$
$797$	−18.7237			−0.663228			−0.331614	+	0.943415i	$0.607593\pi$
$798$	25.3148	+	28.8020i	0.896135	+	1.01958i
$799$	6.70087	−	6.70087i	0.237060	−	0.237060i
$800$	6.07462	+	22.6708i	0.214770	+	0.801534i
$801$	25.8704	−	21.5338i	0.914085	−	0.760861i
$802$	−35.1401	−	60.8644i	−1.24084	−	2.14920i
$803$	−9.38193	+	16.2500i	−0.331081	+	0.573450i
$804$	1.73399	+	0.550502i	0.0611531	+	0.0194147i
$805$	−1.28698	−	2.32882i	−0.0453602	−	0.0820801i
$806$	−24.4578	−	31.6019i	−0.861489	−	1.11313i
$807$	4.41047	+	0.201315i	0.155256	+	0.00708663i
$808$	−9.04829	−	2.42448i	−0.318318	−	0.0852930i
$809$	4.85170	−	2.80113i	0.170577	−	0.0984824i	−0.412281	−	0.911057i	$-0.635268\pi$
$809$	4.85170	−	2.80113i	0.170577	−	0.0984824i	0.582858	+	0.812574i	$0.301935\pi$
$810$	−4.38302	+	23.7556i	−0.154004	+	0.834687i
$811$	−21.3504	+	21.3504i	−0.749714	+	0.749714i	−0.974425	−	0.224711i	$-0.927856\pi$
$811$	−21.3504	+	21.3504i	−0.749714	+	0.749714i	0.224711	+	0.974425i	$0.427856\pi$
$812$	20.5231	+	5.91339i	0.720218	+	0.207519i
$813$	−23.9757	−	7.61172i	−0.840863	−	0.266955i
$814$	22.7883	−	6.10610i	0.798728	−	0.214019i
$815$	11.1373	−	6.43011i	0.390122	−	0.225237i
$816$	−14.2612	−	9.12514i	−0.499242	−	0.319444i
$817$	−6.20637	+	1.66299i	−0.217134	+	0.0581807i
$818$	46.0486			1.61005
$819$	8.09790	+	27.4486i	0.282963	+	0.959131i
$820$	−21.2498			−0.742075
$821$	−42.0255	+	11.2607i	−1.46670	+	0.393002i	−0.901799	−	0.432156i	$-0.857753\pi$
$821$	−42.0255	+	11.2607i	−1.46670	+	0.393002i	−0.564903	+	0.825157i	$0.691086\pi$
$822$	28.9778	+	18.5416i	1.01072	+	0.646714i
$823$	13.1887	−	7.61452i	0.459730	−	0.265425i	−0.252201	−	0.967675i	$-0.581154\pi$
$823$	13.1887	−	7.61452i	0.459730	−	0.265425i	0.711931	+	0.702250i	$0.247821\pi$
$824$	9.19834	−	2.46469i	0.320440	−	0.0858615i
$825$	−12.0365	−	3.82132i	−0.419058	−	0.133041i
$826$	26.9763	−	25.9839i	0.938624	−	0.904095i
$827$	30.5539	−	30.5539i	1.06246	−	1.06246i	0.0645489	−	0.997915i	$-0.479439\pi$
$827$	30.5539	−	30.5539i	1.06246	−	1.06246i	0.997915	−	0.0645489i	$-0.0205609\pi$
$828$	−3.45732	+	1.59554i	−0.120150	+	0.0554488i
$829$	−33.1940	+	19.1646i	−1.15288	+	0.665613i	−0.949586	−	0.313506i	$-0.898497\pi$
$829$	−33.1940	+	19.1646i	−1.15288	+	0.665613i	−0.203289	+	0.979119i	$0.565163\pi$
$830$	−3.80362	−	1.01918i	−0.132026	−	0.0353761i
$831$	−21.4487	−	0.979022i	−0.744047	−	0.0339619i
$832$	−16.7819	+	12.9881i	−0.581807	+	0.450281i
$833$	13.6307	−	7.20276i	0.472274	−	0.249561i
$834$	6.08577	+	1.93209i	0.210733	+	0.0669028i
$835$	−5.55567	+	9.62270i	−0.192262	+	0.333007i
$836$	−8.95226	−	15.5058i	−0.309621	−	0.536278i
$837$	−11.5446	+	27.4094i	−0.399038	+	0.947408i
$838$	8.74304	+	32.6295i	0.302023	+	1.12717i
$839$	16.9198	−	16.9198i	0.584135	−	0.584135i	−0.351902	−	0.936037i	$-0.614465\pi$
$839$	16.9198	−	16.9198i	0.584135	−	0.584135i	0.936037	+	0.351902i	$0.114465\pi$
$840$	−0.987466	+	2.91954i	−0.0340708	+	0.100734i
$841$	7.70730			0.265769
$842$	−0.934939	+	1.61936i	−0.0322201	+	0.0558069i
$843$	−17.1166	+	3.75911i	−0.589526	+	0.129471i
$844$	−42.4979	+	24.5362i	−1.46284	+	0.844570i
$845$	−0.149396	−	18.0193i	−0.00513939	−	0.619884i
$846$	−14.4176	+	20.4179i	−0.495688	+	0.701983i
$847$	−13.8440	+	3.43286i	−0.475687	+	0.117954i
$848$			52.9997i			1.82002i
$849$	37.7860	+	1.72474i	1.29681	+	0.0591928i
$850$	12.6815	+	3.39800i	0.434973	+	0.116551i
$851$	0.966025	−	3.60526i	0.0331149	−	0.123587i
$852$	−31.4019	−	34.4057i	−1.07581	−	1.17872i
$853$	19.3817	+	19.3817i	0.663616	+	0.663616i	0.956230	−	0.292615i	$-0.0945254\pi$
$853$	19.3817	+	19.3817i	0.663616	+	0.663616i	−0.292615	+	0.956230i	$0.594525\pi$
$854$	20.7149	+	37.4839i	0.708848	+	1.28267i
$855$	−10.3656	+	14.6795i	−0.354495	+	0.502029i
$856$	−2.59627	+	0.695668i	−0.0887386	+	0.0237774i
$857$	19.1028	+	33.0871i	0.652540	+	1.13023i	0.982504	+	0.186240i	$0.0596301\pi$
$857$	19.1028	+	33.0871i	0.652540	+	1.13023i	−0.329964	+	0.943994i	$0.607037\pi$
$858$	−2.55782	−	28.5245i	−0.0873225	−	0.973809i
$859$	−2.59214	+	4.48971i	−0.0884425	+	0.153187i	−0.906853	−	0.421447i	$-0.861522\pi$
$859$	−2.59214	+	4.48971i	−0.0884425	+	0.153187i	0.818410	+	0.574634i	$0.194856\pi$
$860$	2.54953	+	2.54953i	0.0869384	+	0.0869384i
$861$	33.4136	+	22.2731i	1.13873	+	0.759065i
$862$			1.13147i			0.0385380i
$863$	43.4506	−	11.6425i	1.47908	−	0.396317i	0.573043	−	0.819525i	$-0.305763\pi$
$863$	43.4506	−	11.6425i	1.47908	−	0.396317i	0.906032	+	0.423208i	$0.139096\pi$
$864$	36.5083	+	15.3769i	1.24204	+	0.523133i
$865$	3.81996	−	14.2563i	0.129882	−	0.484728i
$866$	12.0986	+	45.1527i	0.411128	+	1.53435i
$867$	18.6851	−	9.67985i	0.634578	−	0.328745i
$868$	13.6738	−	22.6911i	0.464120	−	0.770186i
$869$	11.0384	−	11.0384i	0.374452	−	0.374452i
$870$	−0.978157	+	21.4297i	−0.0331626	+	0.726536i
$871$	0.836709	+	1.99654i	0.0283508	+	0.0676503i
$872$	−5.06375	+	2.92356i	−0.171480	+	0.0990042i
$873$	−1.71831	−	0.633129i	−0.0581558	−	0.0214282i
$874$	−6.07095			−0.205353
$875$	0.555060	−	29.6223i	0.0187645	−	1.00142i
$876$	−7.26436	+	22.8815i	−0.245440	+	0.773095i
$877$	5.89384	+	21.9961i	0.199021	+	0.742756i	0.991189	+	0.132453i	$0.0422854\pi$
$877$	5.89384	+	21.9961i	0.199021	+	0.742756i	−0.792168	+	0.610302i	$0.791048\pi$
$878$	−69.9167	−	18.7341i	−2.35957	−	0.632246i
$879$	12.9558	−	2.84534i	0.436989	−	0.0959709i
$880$	7.28524	−	12.6184i	0.245586	−	0.425367i
$881$	−4.86242			−0.163819			−0.0819095	−	0.996640i	$-0.526102\pi$
$881$	−4.86242			−0.163819			−0.0819095	+	0.996640i	$0.526102\pi$
$882$	−32.2057	+	24.8252i	−1.08442	+	0.835907i
$883$			23.4032i			0.787582i	0.919200	+	0.393791i	$0.128837\pi$
$883$			23.4032i			0.787582i	−0.919200	+	0.393791i	$0.871163\pi$
$884$	1.87033	+	13.7654i	0.0629061	+	0.462981i
$885$	14.7853	+	9.46048i	0.497002	+	0.318011i
$886$	−28.7734	−	7.70982i	−0.966662	−	0.259016i
$887$	11.0699	+	6.39123i	0.371692	+	0.214596i	0.674197	−	0.738551i	$-0.264490\pi$
$887$	11.0699	+	6.39123i	0.371692	+	0.214596i	−0.302506	+	0.953148i	$0.597823\pi$
$888$	−3.83878	+	1.98869i	−0.128821	+	0.0667361i
$889$	8.30751	+	8.62479i	0.278625	+	0.289266i
$890$	−21.2945	−	21.2945i	−0.713795	−	0.713795i
$891$	−17.5565	+	12.0871i	−0.588163	+	0.404933i
$892$	7.34858	−	27.4253i	0.246049	−	0.918266i
$893$	−16.1031	+	9.29710i	−0.538868	+	0.311116i
$894$	2.41854	+	0.110394i	0.0808879	+	0.00369212i
$895$	12.5561	+	12.5561i	0.419705	+	0.419705i
$896$	8.72693	+	5.25891i	0.291546	+	0.175688i
$897$	−4.11050	−	1.90593i	−0.137246	−	0.0636372i
$898$	−33.1407	+	57.4014i	−1.10592	+	1.91551i
$899$	−6.83584	+	25.5117i	−0.227988	+	0.850862i
$900$	−16.0901	−	1.47193i	−0.536338	−	0.0490643i
$901$	22.7759	+	13.1497i	0.758774	+	0.438078i
$902$	−28.4156	−	28.4156i	−0.946138	−	0.946138i
$903$	−1.33663	−	6.68125i	−0.0444803	−	0.222338i
$904$	4.64025	+	4.64025i	0.154332	+	0.154332i
$905$	1.10961	+	4.14112i	0.0368847	+	0.137655i
$906$	−33.0107	+	51.5907i	−1.09671	+	1.71399i
$907$	17.2026	−	9.93191i	0.571202	−	0.329784i	−0.186427	−	0.982469i	$-0.559691\pi$
$907$	17.2026	−	9.93191i	0.571202	−	0.329784i	0.757629	+	0.652685i	$0.226358\pi$
$908$	8.83899	+	32.9876i	0.293332	+	1.09473i
$909$	33.4093	−	47.3135i	1.10812	−	1.56929i
$910$	23.7958	−	9.45218i	0.788822	−	0.313337i
$911$			22.4777i			0.744718i	0.928089	+	0.372359i	$0.121451\pi$
$911$			22.4777i			0.744718i	−0.928089	+	0.372359i	$0.878549\pi$
$912$	22.3950	+	24.5372i	0.741572	+	0.812508i
$913$	−1.73729	−	3.00907i	−0.0574959	−	0.0995858i
$914$	−22.5402	−	39.0408i	−0.745563	−	1.29135i
$915$	−14.8243	+	13.5301i	−0.490076	+	0.447290i
$916$	−1.35647	+	1.35647i	−0.0448191	+	0.0448191i
$917$	28.8093	−	7.14372i	0.951365	−	0.235907i
$918$	17.6600	−	13.3851i	0.582868	−	0.441775i
$919$	−7.41584	+	12.8446i	−0.244626	+	0.423705i	−0.962026	−	0.272956i	$-0.911999\pi$
$919$	−7.41584	+	12.8446i	−0.244626	+	0.423705i	0.717400	+	0.696661i	$0.245332\pi$
$920$	−0.243974	−	0.422575i	−0.00804358	−	0.0139319i
$921$	−4.59415	−	20.9188i	−0.151383	−	0.689298i
$922$	−56.9589	−	32.8852i	−1.87584	−	1.08302i
$923$	7.00692	−	54.9832i	0.230636	−	1.80979i
$924$	17.0193	−	8.41631i	0.559895	−	0.276876i
$925$	11.1990	−	11.1990i	0.368221	−	0.368221i
$926$	15.5606	+	8.98390i	0.511352	+	0.295229i
$927$	−5.36403	+	58.6359i	−0.176178	+	1.92586i
$928$	33.9806	+	9.10507i	1.11547	+	0.298889i
$929$	16.3271	−	4.37484i	0.535676	−	0.143534i	0.0191680	−	0.999816i	$-0.493898\pi$
$929$	16.3271	−	4.37484i	0.535676	−	0.143534i	0.516508	+	0.856282i	$0.327232\pi$
$930$	25.3618	+	8.05180i	0.831648	+	0.264029i
$931$	−29.4919	+	6.72911i	−0.966557	+	0.220538i
$932$			32.1391i			1.05275i
$933$	−0.440336	+	9.64701i	−0.0144160	+	0.315829i
$934$	13.3430	−	49.7966i	0.436595	−	1.62939i
$935$	−3.61506	−	6.26146i	−0.118225	−	0.204772i
$936$	1.57908	+	5.00496i	0.0516138	+	0.163592i
$937$	44.2646			1.44606			0.723032	−	0.690815i	$-0.242748\pi$
$937$	44.2646			1.44606			0.723032	+	0.690815i	$0.242748\pi$
$938$	−2.21536	+	2.13387i	−0.0723342	+	0.0696732i
$939$	−15.2706	+	7.91099i	−0.498338	+	0.258165i
$940$	9.03628	+	5.21710i	0.294731	+	0.170163i
$941$	10.5873	−	39.5125i	0.345137	−	1.28807i	−0.547314	−	0.836927i	$-0.684350\pi$
$941$	10.5873	−	39.5125i	0.345137	−	1.28807i	0.892452	−	0.451143i	$-0.148984\pi$
$942$	6.33564	+	28.8484i	0.206426	+	0.939932i
$943$	−6.14103	+	1.64548i	−0.199979	+	0.0535843i
$944$	22.9449	−	22.9449i	0.746793	−	0.746793i
$945$	−14.8276	−	11.9703i	−0.482343	−	0.389394i
$946$			6.81857i			0.221691i
$947$	−2.00548	−	7.48455i	−0.0651693	−	0.243215i	0.925656	−	0.378367i	$-0.123514\pi$
$947$	−2.00548	−	7.48455i	−0.0651693	−	0.243215i	−0.990825	+	0.135152i	$0.956848\pi$
$948$	10.7646	−	16.8235i	0.349619	−	0.546402i
$949$	−26.3462	+	11.0411i	−0.855233	+	0.358410i
$950$	−22.3095	−	12.8804i	−0.723816	−	0.417895i
$951$	−18.6927	−	5.93451i	−0.606153	−	0.192440i
$952$	2.47448	−	1.36748i	0.0801983	−	0.0443203i
$953$	−19.1400			−0.620005			−0.310002	−	0.950736i	$-0.600330\pi$
$953$	−19.1400			−0.620005			−0.310002	+	0.950736i	$0.600330\pi$
$954$	−65.0895	−	23.9829i	−2.10735	−	0.776476i
$955$	16.6253	+	4.45474i	0.537983	+	0.144152i
$956$	47.2399	+	12.6579i	1.52785	+	0.409386i
$957$	−13.9809	+	12.7603i	−0.451938	+	0.412482i
$958$	26.4770			0.855433
$959$	−23.7530	+	13.1267i	−0.767024	+	0.423883i
$960$	4.27583	−	13.4682i	0.138002	−	0.434683i
$961$	1.52525	+	0.880605i	0.0492017	+	0.0284066i
$962$	33.2395	+	13.6071i	1.07168	+	0.438710i
$963$	1.51402	−	16.5502i	0.0487885	−	0.533323i
$964$	−3.15421	−	11.7717i	−0.101590	−	0.379139i
$965$		−	29.4099i		−	0.946738i
$966$	0.413983	−	6.42453i	0.0133197	−	0.206706i
$967$	−12.5566	+	12.5566i	−0.403793	+	0.403793i	−0.879568	−	0.475774i	$-0.842168\pi$
$967$	−12.5566	+	12.5566i	−0.403793	+	0.403793i	0.475774	+	0.879568i	$0.342168\pi$
$968$	−2.52656	+	0.676989i	−0.0812066	+	0.0217593i
$969$	16.1009	−	3.53605i	0.517235	−	0.113594i
$970$	−0.424045	+	1.58256i	−0.0136153	+	0.0508129i
$971$	−6.51008	−	3.75860i	−0.208918	−	0.120619i	0.391890	−	0.920012i	$-0.371821\pi$
$971$	−6.51008	−	3.75860i	−0.208918	−	0.120619i	−0.600809	+	0.799393i	$0.705155\pi$
$972$	−18.6221	+	19.9228i	−0.597304	+	0.639025i
$973$	−3.62781	+	3.49436i	−0.116302	+	0.112024i
$974$	1.66102			0.0532224
$975$	−11.0615	−	15.7249i	−0.354252	−	0.503600i
$976$	18.5514	+	32.1320i	0.593817	+	1.02852i
$977$	−0.881124	+	3.28840i	−0.0281897	+	0.105205i	−0.978587	−	0.205832i	$-0.934010\pi$
$977$	−0.881124	+	3.28840i	−0.0281897	+	0.105205i	0.950398	+	0.311038i	$0.100677\pi$
$978$	31.0835	+	1.41880i	0.993939	+	0.0453682i
$979$		−	26.5725i		−	0.849260i
$980$	11.5449	+	12.4442i	0.368788	+	0.397516i
$981$	−6.13694	−	35.6287i	−0.195937	−	1.13754i
$982$	−4.86316	+	1.30308i	−0.155190	+	0.0415830i
$983$	−0.621219	−	0.166455i	−0.0198138	−	0.00530909i	0.248899	−	0.968530i	$-0.419931\pi$
$983$	−0.621219	−	0.166455i	−0.0198138	−	0.00530909i	−0.268712	+	0.963220i	$0.586598\pi$
$984$	6.20302	+	3.96905i	0.197745	+	0.126529i
$985$	9.57944	+	5.53069i	0.305226	+	0.176222i
$986$	13.9148	−	13.9148i	0.443137	−	0.443137i
$987$	−8.74050	−	17.6749i	−0.278213	−	0.562598i
$988$	3.44582	−	27.0392i	0.109626	−	0.860233i
$989$	0.934220	+	0.539372i	0.0297065	+	0.0171510i
$990$	12.2002	+	14.6571i	0.387746	+	0.465832i
$991$	−27.6263	−	47.8502i	−0.877579	−	1.52001i	−0.853990	−	0.520289i	$-0.825824\pi$
$991$	−27.6263	−	47.8502i	−0.877579	−	1.52001i	−0.0235887	−	0.999722i	$-0.507509\pi$
$992$	21.8183	−	37.7905i	0.692733	−	1.19985i
$993$	−0.421999	+	1.32923i	−0.0133917	+	0.0421818i
$994$	76.4418	−	18.9550i	2.42459	−	0.601215i
$995$	−13.9909	+	13.9909i	−0.443542	+	0.443542i
$996$	−2.99682	−	3.28348i	−0.0949578	−	0.104041i
$997$	4.61783	+	7.99832i	0.146248	+	0.253309i	0.929838	−	0.367969i	$-0.119947\pi$
$997$	4.61783	+	7.99832i	0.146248	+	0.253309i	−0.783590	+	0.621279i	$0.786614\pi$
$998$	−5.36678	−	9.29553i	−0.169882	−	0.294245i
$999$	−3.33169	−	26.5232i	−0.105410	−	0.839156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.44.7	✓	112
3.2	odd	2	inner	273.2.cd.e.44.22	yes	112
7.4	even	3	inner	273.2.cd.e.200.22	yes	112
13.8	odd	4	inner	273.2.cd.e.86.7	yes	112
21.11	odd	6	inner	273.2.cd.e.200.7	yes	112
39.8	even	4	inner	273.2.cd.e.86.22	yes	112
91.60	odd	12	inner	273.2.cd.e.242.22	yes	112
273.242	even	12	inner	273.2.cd.e.242.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.7	✓	112	1.1	even	1	trivial
273.2.cd.e.44.22	yes	112	3.2	odd	2	inner
273.2.cd.e.86.7	yes	112	13.8	odd	4	inner
273.2.cd.e.86.22	yes	112	39.8	even	4	inner
273.2.cd.e.200.7	yes	112	21.11	odd	6	inner
273.2.cd.e.200.22	yes	112	7.4	even	3	inner
273.2.cd.e.242.7	yes	112	273.242	even	12	inner
273.2.cd.e.242.22	yes	112	91.60	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.87036 + 0.501163i) q^{2} +(1.45895 + 0.933521i) q^{3} +(1.51505 - 0.874714i) q^{4} +(-1.33892 + 0.358762i) q^{5} +(-3.19662 - 1.01485i) q^{6} +(1.90555 - 1.83545i) q^{7} +(0.343083 - 0.343083i) q^{8} +(1.25708 + 2.72392i) q^{9} +O(q^{10})\)	\(q+(-1.87036 + 0.501163i) q^{2} +(1.45895 + 0.933521i) q^{3} +(1.51505 - 0.874714i) q^{4} +(-1.33892 + 0.358762i) q^{5} +(-3.19662 - 1.01485i) q^{6} +(1.90555 - 1.83545i) q^{7} +(0.343083 - 0.343083i) q^{8} +(1.25708 + 2.72392i) q^{9} +(2.32447 - 1.34203i) q^{10} +(2.28763 + 0.612968i) q^{11} +(3.02695 + 0.138165i) q^{12} +(2.20676 + 2.85135i) q^{13} +(-2.64421 + 4.38795i) q^{14} +(-2.28833 - 0.726491i) q^{15} +(-2.21918 + 3.84373i) q^{16} +(1.10119 + 1.90732i) q^{17} +(-3.71632 - 4.46473i) q^{18} +(-1.11846 - 4.17416i) q^{19} +(-1.71471 + 1.71471i) q^{20} +(4.49354 - 0.898964i) q^{21} -4.58590 q^{22} +(-0.362760 + 0.628318i) q^{23} +(0.820816 - 0.180266i) q^{24} +(-2.66614 + 1.53929i) q^{25} +(-5.55644 - 4.22712i) q^{26} +(-0.708822 + 5.14758i) q^{27} +(1.28151 - 4.44761i) q^{28} +4.61440i q^{29} +(4.64410 + 0.211979i) q^{30} +(5.52871 + 1.48141i) q^{31} +(1.97318 - 7.36403i) q^{32} +(2.76532 + 3.02984i) q^{33} +(-3.01551 - 3.01551i) q^{34} +(-1.89288 + 3.14116i) q^{35} +(4.28719 + 3.02729i) q^{36} +(-4.96920 + 1.33149i) q^{37} +(4.18386 + 7.24666i) q^{38} +(0.557758 + 6.22004i) q^{39} +(-0.336275 + 0.582445i) q^{40} +(6.19631 + 6.19631i) q^{41} +(-7.95402 + 3.93338i) q^{42} -1.48686i q^{43} +(4.00204 - 1.07234i) q^{44} +(-2.66036 - 3.19612i) q^{45} +(0.363603 - 1.35699i) q^{46} +(-1.11365 - 4.15620i) q^{47} +(-6.82587 + 3.53617i) q^{48} +(0.262239 - 6.99509i) q^{49} +(4.21521 - 4.21521i) q^{50} +(-0.173938 + 3.81068i) q^{51} +(5.83747 + 2.38966i) q^{52} +(10.3415 - 5.97064i) q^{53} +(-1.25402 - 9.98309i) q^{54} -3.28286 q^{55} +(0.0240496 - 1.28347i) q^{56} +(2.26488 - 7.13400i) q^{57} +(-2.31257 - 8.63061i) q^{58} +(-7.06192 - 1.89224i) q^{59} +(-4.10240 + 0.900963i) q^{60} +(4.17980 - 7.23963i) q^{61} -11.0831 q^{62} +(7.39505 + 2.88326i) q^{63} +5.88559i q^{64} +(-3.97763 - 3.02603i) q^{65} +(-6.69060 - 4.28103i) q^{66} +(0.579944 + 0.155395i) q^{67} +(3.33672 + 1.92646i) q^{68} +(-1.11580 + 0.578042i) q^{69} +(1.96615 - 6.82375i) q^{70} +(-10.8703 - 10.8703i) q^{71} +(1.36581 + 0.503249i) q^{72} +(-2.05058 + 7.65287i) q^{73} +(8.62693 - 4.98076i) q^{74} +(-5.32673 - 0.243137i) q^{75} +(-5.34572 - 5.34572i) q^{76} +(5.48426 - 3.03079i) q^{77} +(-4.16046 - 11.3542i) q^{78} +(3.29571 - 5.70834i) q^{79} +(1.59231 - 5.94260i) q^{80} +(-5.83951 + 6.84837i) q^{81} +(-14.6947 - 8.48400i) q^{82} +(-1.03740 - 1.03740i) q^{83} +(6.02159 - 5.29253i) q^{84} +(-2.15868 - 2.15868i) q^{85} +(0.745157 + 2.78097i) q^{86} +(-4.30764 + 6.73219i) q^{87} +(0.995145 - 0.574547i) q^{88} +(-2.90393 - 10.8376i) q^{89} +(6.57763 + 4.64463i) q^{90} +(9.43861 + 1.38300i) q^{91} +1.26924i q^{92} +(6.68319 + 7.32247i) q^{93} +(4.16587 + 7.21549i) q^{94} +(2.99506 + 5.18759i) q^{95} +(9.75325 - 8.90175i) q^{96} +(-0.431627 + 0.431627i) q^{97} +(3.01519 + 13.2148i) q^{98} +(1.20605 + 7.00187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more