LMFDB - Embedded newform 240.2.bk.b.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(11,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("240.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.983055 - 1.01666i) q^{2} +(-1.40626 - 1.01116i) q^{3} +(-0.0672039 + 1.99887i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.354421 + 2.42371i) q^{6} +4.53819 q^{7} +(2.09824 - 1.89668i) q^{8} +(0.955115 + 2.84390i) q^{9} +O(q^{10})$	\(q+(-0.983055 - 1.01666i) q^{2} +(-1.40626 - 1.01116i) q^{3} +(-0.0672039 + 1.99887i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.354421 + 2.42371i) q^{6} +4.53819 q^{7} +(2.09824 - 1.89668i) q^{8} +(0.955115 + 2.84390i) q^{9} +(-1.41401 - 0.0237635i) q^{10} +(-2.95298 - 2.95298i) q^{11} +(2.11568 - 2.74297i) q^{12} +(1.65071 - 1.65071i) q^{13} +(-4.46129 - 4.61381i) q^{14} +(-1.70937 + 0.279376i) q^{15} +(-3.99097 - 0.268664i) q^{16} +0.996523i q^{17} +(1.95235 - 3.76674i) q^{18} +(-2.53663 - 2.53663i) q^{19} +(1.36589 + 1.46094i) q^{20} +(-6.38186 - 4.58883i) q^{21} +(-0.0992398 + 5.90512i) q^{22} -5.82394i q^{23} +(-4.86851 + 0.545558i) q^{24} -1.00000i q^{25} +(-3.30094 - 0.0554748i) q^{26} +(1.53250 - 4.96502i) q^{27} +(-0.304984 + 9.07126i) q^{28} +(7.18333 + 7.18333i) q^{29} +(1.96444 + 1.46321i) q^{30} -2.56764i q^{31} +(3.65020 + 4.32158i) q^{32} +(1.16671 + 7.13857i) q^{33} +(1.01313 - 0.979637i) q^{34} +(3.20899 - 3.20899i) q^{35} +(-5.74877 + 1.71803i) q^{36} +(-4.34078 - 4.34078i) q^{37} +(-0.0852478 + 5.07254i) q^{38} +(-3.99044 + 0.652189i) q^{39} +(0.142528 - 2.82483i) q^{40} -0.184329 q^{41} +(1.60843 + 10.9993i) q^{42} +(2.08594 - 2.08594i) q^{43} +(6.10107 - 5.70416i) q^{44} +(2.68631 + 1.33557i) q^{45} +(-5.92098 + 5.72526i) q^{46} -3.21485 q^{47} +(5.34066 + 4.41331i) q^{48} +13.5952 q^{49} +(-1.01666 + 0.983055i) q^{50} +(1.00764 - 1.40137i) q^{51} +(3.18861 + 3.41048i) q^{52} +(3.52871 - 3.52871i) q^{53} +(-6.55428 + 3.32286i) q^{54} -4.17614 q^{55} +(9.52222 - 8.60748i) q^{56} +(1.00222 + 6.13209i) q^{57} +(0.241408 - 14.3646i) q^{58} +(5.11138 + 5.11138i) q^{59} +(-0.443560 - 3.43559i) q^{60} +(-7.75362 + 7.75362i) q^{61} +(-2.61042 + 2.52413i) q^{62} +(4.33449 + 12.9062i) q^{63} +(0.805233 - 7.95937i) q^{64} -2.33445i q^{65} +(6.11057 - 8.20376i) q^{66} +(6.85036 + 6.85036i) q^{67} +(-1.99192 - 0.0669703i) q^{68} +(-5.88893 + 8.18995i) q^{69} +(-6.41707 - 0.107843i) q^{70} +11.4005i q^{71} +(7.39802 + 4.15564i) q^{72} -4.00109i q^{73} +(-0.145879 + 8.68033i) q^{74} +(-1.01116 + 1.40626i) q^{75} +(5.24086 - 4.89992i) q^{76} +(-13.4012 - 13.4012i) q^{77} +(4.58588 + 3.41579i) q^{78} +2.78657i q^{79} +(-3.01201 + 2.63207i) q^{80} +(-7.17551 + 5.43250i) q^{81} +(0.181206 + 0.187401i) q^{82} +(-9.66719 + 9.66719i) q^{83} +(9.60137 - 12.4481i) q^{84} +(0.704648 + 0.704648i) q^{85} +(-4.17130 - 0.0701017i) q^{86} +(-2.83811 - 17.3651i) q^{87} +(-11.7969 - 0.595215i) q^{88} -0.120080 q^{89} +(-1.28296 - 4.04401i) q^{90} +(7.49122 - 7.49122i) q^{91} +(11.6413 + 0.391392i) q^{92} +(-2.59629 + 3.61076i) q^{93} +(3.16038 + 3.26842i) q^{94} -3.58733 q^{95} +(-0.763318 - 9.76818i) q^{96} +6.44188 q^{97} +(-13.3648 - 13.8217i) q^{98} +(5.57753 - 11.2184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.983055	−	1.01666i	−0.695125	−	0.718889i
$2$	−0.983055	−	1.01666i	−0.695125	−	0.718889i
$3$	−1.40626	−	1.01116i	−0.811903	−	0.583793i
$3$	−1.40626	−	1.01116i	−0.811903	−	0.583793i
$4$	−0.0672039	+	1.99887i	−0.0336020	+	0.999435i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.354421	+	2.42371i	0.144692	+	0.989477i
$7$	4.53819			1.71528			0.857638	−	0.514255i	$-0.171931\pi$
$7$	4.53819			1.71528			0.857638	+	0.514255i	$0.171931\pi$
$8$	2.09824	−	1.89668i	0.741840	−	0.670577i
$9$	0.955115	+	2.84390i	0.318372	+	0.947966i
$10$	−1.41401	−	0.0237635i	−0.447150	−	0.00751469i
$11$	−2.95298	−	2.95298i	−0.890356	−	0.890356i	0.104201	−	0.994556i	$-0.466772\pi$
$11$	−2.95298	−	2.95298i	−0.890356	−	0.890356i	−0.994556	+	0.104201i	$0.966772\pi$
$12$	2.11568	−	2.74297i	0.610745	−	0.791827i
$13$	1.65071	−	1.65071i	0.457823	−	0.457823i	−0.440117	−	0.897940i	$-0.645063\pi$
$13$	1.65071	−	1.65071i	0.457823	−	0.457823i	0.897940	+	0.440117i	$0.145063\pi$
$14$	−4.46129	−	4.61381i	−1.19233	−	1.23309i
$15$	−1.70937	+	0.279376i	−0.441358	+	0.0721346i
$16$	−3.99097	−	0.268664i	−0.997742	−	0.0671660i
$17$			0.996523i			0.241692i	0.992671	+	0.120846i	$0.0385608\pi$
$17$			0.996523i			0.241692i	−0.992671	+	0.120846i	$0.961439\pi$
$18$	1.95235	−	3.76674i	0.460174	−	0.887829i
$19$	−2.53663	−	2.53663i	−0.581943	−	0.581943i	0.353494	−	0.935437i	$-0.384993\pi$
$19$	−2.53663	−	2.53663i	−0.581943	−	0.581943i	−0.935437	+	0.353494i	$0.884993\pi$
$20$	1.36589	+	1.46094i	0.305423	+	0.326675i
$21$	−6.38186	−	4.58883i	−1.39264	−	1.00137i
$22$	−0.0992398	+	5.90512i	−0.0211580	+	1.25898i
$23$		−	5.82394i		−	1.21438i	−0.794558	−	0.607188i	$-0.792298\pi$
$23$		−	5.82394i		−	1.21438i	0.794558	−	0.607188i	$-0.207702\pi$
$24$	−4.86851	+	0.545558i	−0.993780	+	0.111362i
$25$		−	1.00000i		−	0.200000i
$26$	−3.30094	−	0.0554748i	−0.647368	−	0.0108795i
$27$	1.53250	−	4.96502i	0.294929	−	0.955519i
$28$	−0.304984	+	9.07126i	−0.0576366	+	1.71431i
$29$	7.18333	+	7.18333i	1.33391	+	1.33391i	0.901840	+	0.432070i	$0.142217\pi$
$29$	7.18333	+	7.18333i	1.33391	+	1.33391i	0.432070	+	0.901840i	$0.357783\pi$
$30$	1.96444	+	1.46321i	0.358656	+	0.267144i
$31$		−	2.56764i		−	0.461162i	−0.973053	−	0.230581i	$-0.925937\pi$
$31$		−	2.56764i		−	0.461162i	0.973053	−	0.230581i	$-0.0740627\pi$
$32$	3.65020	+	4.32158i	0.645271	+	0.763954i
$33$	1.16671	+	7.13857i	0.203099	+	1.24267i
$34$	1.01313	−	0.979637i	0.173750	−	0.168006i
$35$	3.20899	−	3.20899i	0.542418	−	0.542418i
$36$	−5.74877	+	1.71803i	−0.958129	+	0.286338i
$37$	−4.34078	−	4.34078i	−0.713620	−	0.713620i	0.253671	−	0.967291i	$-0.418362\pi$
$37$	−4.34078	−	4.34078i	−0.713620	−	0.713620i	−0.967291	+	0.253671i	$0.918362\pi$
$38$	−0.0852478	+	5.07254i	−0.0138290	+	0.822875i
$39$	−3.99044	+	0.652189i	−0.638982	+	0.104434i
$40$	0.142528	−	2.82483i	0.0225356	−	0.446645i
$41$	−0.184329			−0.0287874			−0.0143937	−	0.999896i	$-0.504582\pi$
$41$	−0.184329			−0.0287874			−0.0143937	+	0.999896i	$0.504582\pi$
$42$	1.60843	+	10.9993i	0.248186	+	1.69722i
$43$	2.08594	−	2.08594i	0.318103	−	0.318103i	−0.529935	−	0.848038i	$-0.677784\pi$
$43$	2.08594	−	2.08594i	0.318103	−	0.318103i	0.848038	+	0.529935i	$0.177784\pi$
$44$	6.10107	−	5.70416i	0.919770	−	0.859935i
$45$	2.68631	+	1.33557i	0.400451	+	0.199095i
$46$	−5.92098	+	5.72526i	−0.873001	+	0.844143i
$47$	−3.21485			−0.468934			−0.234467	−	0.972124i	$-0.575335\pi$
$47$	−3.21485			−0.468934			−0.234467	+	0.972124i	$0.575335\pi$
$48$	5.34066	+	4.41331i	0.770858	+	0.637007i
$49$	13.5952			1.94217
$50$	−1.01666	+	0.983055i	−0.143778	+	0.139025i
$51$	1.00764	−	1.40137i	0.141098	−	0.196231i
$52$	3.18861	+	3.41048i	0.442181	+	0.472949i
$53$	3.52871	−	3.52871i	0.484706	−	0.484706i	−0.421925	−	0.906631i	$-0.638645\pi$
$53$	3.52871	−	3.52871i	0.484706	−	0.484706i	0.906631	+	0.421925i	$0.138645\pi$
$54$	−6.55428	+	3.32286i	−0.891925	+	0.452184i
$55$	−4.17614			−0.563110
$56$	9.52222	−	8.60748i	1.27246	−	1.15022i
$57$	1.00222	+	6.13209i	0.132747	+	0.812215i
$58$	0.241408	−	14.3646i	0.0316984	−	1.88617i
$59$	5.11138	+	5.11138i	0.665445	+	0.665445i	0.956658	−	0.291213i	$-0.0940588\pi$
$59$	5.11138	+	5.11138i	0.665445	+	0.665445i	−0.291213	+	0.956658i	$0.594059\pi$
$60$	−0.443560	−	3.43559i	−0.0572634	−	0.443532i
$61$	−7.75362	+	7.75362i	−0.992750	+	0.992750i	−0.999974	−	0.00722402i	$-0.997701\pi$
$61$	−7.75362	+	7.75362i	−0.992750	+	0.992750i	0.00722402	+	0.999974i	$0.497701\pi$
$62$	−2.61042	+	2.52413i	−0.331524	+	0.320565i
$63$	4.33449	+	12.9062i	0.546095	+	1.62602i
$64$	0.805233	−	7.95937i	0.100654	−	0.994921i
$65$		−	2.33445i		−	0.289553i
$66$	6.11057	−	8.20376i	0.752159	−	1.00981i
$67$	6.85036	+	6.85036i	0.836905	+	0.836905i	0.988450	−	0.151546i	$-0.0484251\pi$
$67$	6.85036	+	6.85036i	0.836905	+	0.836905i	−0.151546	+	0.988450i	$0.548425\pi$
$68$	−1.99192	−	0.0669703i	−0.241556	−	0.00812134i
$69$	−5.88893	+	8.18995i	−0.708944	+	0.985955i
$70$	−6.41707	−	0.107843i	−0.766986	−	0.0128898i
$71$			11.4005i			1.35299i	0.736448	+	0.676494i	$0.236502\pi$
$71$			11.4005i			1.35299i	−0.736448	+	0.676494i	$0.763498\pi$
$72$	7.39802	+	4.15564i	0.871865	+	0.489747i
$73$		−	4.00109i		−	0.468292i	−0.972201	−	0.234146i	$-0.924771\pi$
$73$		−	4.00109i		−	0.468292i	0.972201	−	0.234146i	$-0.0752293\pi$
$74$	−0.145879	+	8.68033i	−0.0169581	+	1.00907i
$75$	−1.01116	+	1.40626i	−0.116759	+	0.162381i
$76$	5.24086	−	4.89992i	0.601168	−	0.562060i
$77$	−13.4012	−	13.4012i	−1.52720	−	1.52720i
$78$	4.58588	+	3.41579i	0.519249	+	0.386762i
$79$			2.78657i			0.313513i	0.987637	+	0.156757i	$0.0501038\pi$
$79$			2.78657i			0.313513i	−0.987637	+	0.156757i	$0.949896\pi$
$80$	−3.01201	+	2.63207i	−0.336753	+	0.294274i
$81$	−7.17551	+	5.43250i	−0.797279	+	0.603611i
$82$	0.181206	+	0.187401i	0.0200108	+	0.0206949i
$83$	−9.66719	+	9.66719i	−1.06111	+	1.06111i	−0.0631053	+	0.998007i	$0.520100\pi$
$83$	−9.66719	+	9.66719i	−1.06111	+	1.06111i	−0.998007	+	0.0631053i	$0.979900\pi$
$84$	9.60137	−	12.4481i	1.04760	−	1.35820i
$85$	0.704648	+	0.704648i	0.0764298	+	0.0764298i
$86$	−4.17130	−	0.0701017i	−0.449803	−	0.00755926i
$87$	−2.83811	−	17.3651i	−0.304278	−	1.86173i
$88$	−11.7969	−	0.595215i	−1.25755	−	0.0634501i
$89$	−0.120080			−0.0127284			−0.00636422	−	0.999980i	$-0.502026\pi$
$89$	−0.120080			−0.0127284			−0.00636422	+	0.999980i	$0.502026\pi$
$90$	−1.28296	−	4.04401i	−0.135236	−	0.426276i
$91$	7.49122	−	7.49122i	0.785293	−	0.785293i
$92$	11.6413	+	0.391392i	1.21369	+	0.0408054i
$93$	−2.59629	+	3.61076i	−0.269223	+	0.374419i
$94$	3.16038	+	3.26842i	0.325968	+	0.337112i
$95$	−3.58733			−0.368053
$96$	−0.763318	−	9.76818i	−0.0779058	−	0.996961i
$97$	6.44188			0.654073			0.327037	−	0.945012i	$-0.393950\pi$
$97$	6.44188			0.654073			0.327037	+	0.945012i	$0.393950\pi$
$98$	−13.3648	−	13.8217i	−1.35005	−	1.39620i
$99$	5.57753	−	11.2184i	0.560563	−	1.12749i
$100$	1.99887	+	0.0672039i	0.199887	+	0.00672039i
$101$	3.18989	−	3.18989i	0.317406	−	0.317406i	−0.530364	−	0.847770i	$-0.677945\pi$
$101$	3.18989	−	3.18989i	0.317406	−	0.317406i	0.847770	+	0.530364i	$0.177945\pi$
$102$	−2.41529	+	0.353188i	−0.239149	+	0.0349709i
$103$	−2.48706			−0.245057			−0.122528	−	0.992465i	$-0.539100\pi$
$103$	−2.48706			−0.245057			−0.122528	+	0.992465i	$0.539100\pi$
$104$	0.332723	−	6.59443i	0.0326262	−	0.646637i
$105$	−7.75745	+	1.26786i	−0.757050	+	0.123731i
$106$	−7.05643	−	0.118588i	−0.685381	−	0.0115183i
$107$	−3.31294	−	3.31294i	−0.320274	−	0.320274i	0.528598	−	0.848872i	$-0.322718\pi$
$107$	−3.31294	−	3.31294i	−0.320274	−	0.320274i	−0.848872	+	0.528598i	$0.822718\pi$
$108$	9.82145	+	3.39693i	0.945069	+	0.326870i
$109$	−5.05003	+	5.05003i	−0.483706	+	0.483706i	−0.906313	−	0.422607i	$-0.861115\pi$
$109$	−5.05003	+	5.05003i	−0.483706	+	0.483706i	0.422607	+	0.906313i	$0.361115\pi$
$110$	4.10538	+	4.24572i	0.391432	+	0.404814i
$111$	1.71503	+	10.4935i	0.162783	+	0.995996i
$112$	−18.1118	−	1.21925i	−1.71140	−	0.115208i
$113$			3.64034i			0.342454i	0.985232	+	0.171227i	$0.0547731\pi$
$113$			3.64034i			0.342454i	−0.985232	+	0.171227i	$0.945227\pi$
$114$	5.24903	−	7.04710i	0.491616	−	0.660021i
$115$	−4.11815	−	4.11815i	−0.384019	−	0.384019i
$116$	−14.8413	+	13.8758i	−1.37798	+	1.28833i
$117$	6.27105	+	3.11782i	0.579759	+	0.288243i
$118$	0.171777	−	10.2213i	0.0158133	−	0.940949i
$119$			4.52241i			0.414569i
$120$	−3.05679	+	3.82832i	−0.279045	+	0.349476i
$121$			6.44013i			0.585466i
$122$	15.5051	+	0.260574i	1.40376	+	0.0235913i
$123$	0.259214	+	0.186386i	0.0233726	+	0.0168059i
$124$	5.13238	+	0.172556i	0.460902	+	0.0154960i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	8.86015	−	17.0942i	0.789325	−	1.52287i
$127$			11.5387i			1.02389i	0.859017	+	0.511946i	$0.171075\pi$
$127$			11.5387i			1.02389i	−0.859017	+	0.511946i	$0.828925\pi$
$128$	−8.88358	+	7.00585i	−0.785205	+	0.619236i
$129$	−5.04259	+	0.824151i	−0.443976	+	0.0725624i
$130$	−2.37335	+	2.29489i	−0.208156	+	0.201275i
$131$	9.11090	−	9.11090i	0.796023	−	0.796023i	−0.186443	−	0.982466i	$-0.559696\pi$
$131$	9.11090	−	9.11090i	0.796023	−	0.796023i	0.982466	+	0.186443i	$0.0596959\pi$
$132$	−14.3475	+	1.85237i	−1.24879	+	0.161228i
$133$	−11.5117	−	11.5117i	−0.998192	−	0.998192i
$134$	0.230218	−	13.6988i	0.0198878	−	1.18339i
$135$	−2.42716	−	4.59444i	−0.208897	−	0.395426i
$136$	1.89008	+	2.09094i	0.162073	+	0.179297i
$137$	15.3240			1.30922			0.654609	−	0.755968i	$-0.272833\pi$
$137$	15.3240			1.30922			0.654609	+	0.755968i	$0.272833\pi$
$138$	14.1156	−	2.06413i	1.20160	−	0.175710i
$139$	1.80541	−	1.80541i	0.153133	−	0.153133i	−0.626383	−	0.779516i	$-0.715465\pi$
$139$	1.80541	−	1.80541i	0.153133	−	0.153133i	0.779516	+	0.626383i	$0.215465\pi$
$140$	6.19869	+	6.63000i	0.523885	+	0.560338i
$141$	4.52091	+	3.25073i	0.380729	+	0.273761i
$142$	11.5904	−	11.2073i	0.972648	−	0.940496i
$143$	−9.74898			−0.815251
$144$	−3.04778	−	11.6065i	−0.253981	−	0.967209i
$145$	10.1588			0.843639
$146$	−4.06775	+	3.93329i	−0.336650	+	0.325521i
$147$	−19.1183	−	13.7469i	−1.57685	−	1.13382i
$148$	8.96837	−	8.38494i	0.737196	−	0.689238i
$149$	3.02715	−	3.02715i	0.247994	−	0.247994i	−0.572153	−	0.820147i	$-0.693892\pi$
$149$	3.02715	−	3.02715i	0.247994	−	0.247994i	0.820147	+	0.572153i	$0.193892\pi$
$150$	2.42371	−	0.354421i	0.197895	−	0.0289383i
$151$	−3.79486			−0.308821			−0.154410	−	0.988007i	$-0.549348\pi$
$151$	−3.79486			−0.308821			−0.154410	+	0.988007i	$0.549348\pi$
$152$	−10.1336	−	0.511294i	−0.821946	−	0.0414714i
$153$	−2.83401	+	0.951793i	−0.229116	+	0.0769479i
$154$	−0.450369	+	26.7986i	−0.0362918	+	2.15949i
$155$	−1.81560	−	1.81560i	−0.145832	−	0.145832i
$156$	−1.03547	−	8.02020i	−0.0829038	−	0.642130i
$157$	0.786850	−	0.786850i	0.0627975	−	0.0627975i	−0.675011	−	0.737808i	$-0.735861\pi$
$157$	0.786850	−	0.786850i	0.0627975	−	0.0627975i	0.737808	+	0.675011i	$0.235861\pi$
$158$	2.83300	−	2.73935i	0.225381	−	0.217931i
$159$	−8.53036	+	1.39418i	−0.676502	+	0.110566i
$160$	5.63690	+	0.474734i	0.445636	+	0.0375310i
$161$		−	26.4302i		−	2.08299i
$162$	12.5769	+	1.95463i	0.988138	+	0.153570i
$163$	8.42495	+	8.42495i	0.659893	+	0.659893i	0.955355	−	0.295461i	$-0.0954733\pi$
$163$	8.42495	+	8.42495i	0.659893	+	0.659893i	−0.295461	+	0.955355i	$0.595473\pi$
$164$	0.0123877	−	0.368450i	0.000967314	−	0.0287711i
$165$	5.87272	+	4.22274i	0.457191	+	0.328740i
$166$	19.3317	+	0.324883i	1.50043	+	0.0252158i
$167$			12.8064i			0.990992i	0.868610	+	0.495496i	$0.165014\pi$
$167$			12.8064i			0.990992i	−0.868610	+	0.495496i	$0.834986\pi$
$168$	−22.0942	+	2.47585i	−1.70461	+	0.191016i
$169$			7.55034i			0.580796i
$170$	0.0236809	−	1.40910i	0.00181624	−	0.108073i
$171$	4.79114	−	9.63668i	0.366388	−	0.736936i
$172$	4.02935	+	4.30972i	0.307235	+	0.328613i
$173$	5.38409	+	5.38409i	0.409345	+	0.409345i	0.881510	−	0.472165i	$-0.156527\pi$
$173$	5.38409	+	5.38409i	0.409345	+	0.409345i	−0.472165	+	0.881510i	$0.656527\pi$
$174$	−14.8644	+	19.9562i	−1.12687	+	1.51288i
$175$		−	4.53819i		−	0.343055i
$176$	10.9919	+	12.5786i	0.828543	+	0.948147i
$177$	−2.01949	−	12.3563i	−0.151794	−	0.928759i
$178$	0.118045	+	0.122081i	0.00884786	+	0.00915033i
$179$	−17.8800	+	17.8800i	−1.33641	+	1.33641i	−0.436906	+	0.899507i	$0.643926\pi$
$179$	−17.8800	+	17.8800i	−1.33641	+	1.33641i	−0.899507	+	0.436906i	$0.856074\pi$
$180$	−2.85017	+	5.27983i	−0.212439	+	0.393535i
$181$	−1.39734	−	1.39734i	−0.103864	−	0.103864i	0.653265	−	0.757129i	$-0.273399\pi$
$181$	−1.39734	−	1.39734i	−0.103864	−	0.103864i	−0.757129	+	0.653265i	$0.773399\pi$
$182$	−14.9803	−	0.251755i	−1.11042	−	0.0186613i
$183$	18.7437	−	3.06344i	1.38558	−	0.226456i
$184$	−11.0461	−	12.2200i	−0.814332	−	0.900873i
$185$	−6.13879			−0.451333
$186$	6.22323	−	0.910026i	0.456309	−	0.0667263i
$187$	2.94271	−	2.94271i	0.215192	−	0.215192i
$188$	0.216051	−	6.42607i	0.0157571	−	0.468670i
$189$	6.95477	−	22.5322i	0.505885	−	1.63898i
$190$	3.52655	+	3.64711i	0.255843	+	0.264589i
$191$	3.32647			0.240695			0.120348	−	0.992732i	$-0.461599\pi$
$191$	3.32647			0.240695			0.120348	+	0.992732i	$0.461599\pi$
$192$	−9.18056	+	10.3787i	−0.662550	+	0.749018i
$193$	−7.35780			−0.529626			−0.264813	−	0.964300i	$-0.585310\pi$
$193$	−7.35780			−0.529626			−0.264813	+	0.964300i	$0.585310\pi$
$194$	−6.33272	−	6.54921i	−0.454663	−	0.470206i
$195$	−2.36050	+	3.28284i	−0.169039	+	0.235089i
$196$	−0.913650	+	27.1750i	−0.0652607	+	1.94107i
$197$	−12.2757	+	12.2757i	−0.874605	+	0.874605i	−0.992970	−	0.118365i	$-0.962235\pi$
$197$	−12.2757	+	12.2757i	−0.874605	+	0.874605i	0.118365	+	0.992970i	$0.462235\pi$
$198$	−16.8883	+	5.35784i	−1.20020	+	0.380765i
$199$	−25.5014			−1.80774			−0.903872	−	0.427802i	$-0.859288\pi$
$199$	−25.5014			−1.80774			−0.903872	+	0.427802i	$0.859288\pi$
$200$	−1.89668	−	2.09824i	−0.134115	−	0.148368i
$201$	−2.70656	−	16.5602i	−0.190906	−	1.16806i
$202$	−6.37888	−	0.107202i	−0.448816	−	0.00754269i
$203$	32.5993	+	32.5993i	2.28802	+	2.28802i
$204$	2.73343	+	2.10833i	0.191379	+	0.147612i
$205$	−0.130341	+	0.130341i	−0.00910338	+	0.00910338i
$206$	2.44491	+	2.52850i	0.170345	+	0.176169i
$207$	16.5627	−	5.56253i	1.15119	−	0.386623i
$208$	−7.03140	+	6.14443i	−0.487540	+	0.426039i
$209$			14.9812i			1.03627i
$210$	8.91499	+	6.64033i	0.615193	+	0.458226i
$211$	18.3902	+	18.3902i	1.26603	+	1.26603i	0.948119	+	0.317914i	$0.102982\pi$
$211$	18.3902	+	18.3902i	1.26603	+	1.26603i	0.317914	+	0.948119i	$0.397018\pi$
$212$	6.81629	+	7.29058i	0.468145	+	0.500719i
$213$	11.5277	−	16.0320i	0.789865	−	1.09849i
$214$	−0.111337	+	6.62494i	−0.00761083	+	0.452871i
$215$		−	2.94997i		−	0.201186i
$216$	−6.20149	−	13.3245i	−0.421958	−	0.906615i
$217$		−	11.6524i		−	0.791020i
$218$	10.0986	+	0.169715i	0.683966	+	0.0114946i
$219$	−4.04573	+	5.62655i	−0.273385	+	0.380207i
$220$	0.280653	−	8.34756i	0.0189216	−	0.562792i
$221$	1.64497	+	1.64497i	0.110652	+	0.110652i
$222$	8.98234	−	12.0593i	0.602855	−	0.809365i
$223$		−	18.4536i		−	1.23575i	−0.786278	−	0.617873i	$-0.787994\pi$
$223$		−	18.4536i		−	1.23575i	0.786278	−	0.617873i	$-0.212006\pi$
$224$	16.5653	+	19.6121i	1.10682	+	1.31039i
$225$	2.84390	−	0.955115i	0.189593	−	0.0636743i
$226$	3.70099	−	3.57865i	0.246186	−	0.238048i
$227$	−2.65639	+	2.65639i	−0.176311	+	0.176311i	−0.789745	−	0.613435i	$-0.789787\pi$
$227$	−2.65639	+	2.65639i	−0.176311	+	0.176311i	0.613435	+	0.789745i	$0.289787\pi$
$228$	−12.3246	+	1.59120i	−0.816217	+	0.105380i
$229$	10.8007	+	10.8007i	0.713731	+	0.713731i	0.967314	−	0.253583i	$-0.0816091\pi$
$229$	10.8007	+	10.8007i	0.713731	+	0.713731i	−0.253583	+	0.967314i	$0.581609\pi$
$230$	−0.138397	+	8.23513i	−0.00912566	+	0.543009i
$231$	5.29477	+	32.3962i	0.348370	+	2.13151i
$232$	28.6968	+	1.44790i	1.88404	+	0.0950595i
$233$	−23.6828			−1.55151			−0.775756	−	0.631033i	$-0.782631\pi$
$233$	−23.6828			−1.55151			−0.775756	+	0.631033i	$0.782631\pi$
$234$	−2.99502	−	9.44053i	−0.195790	−	0.617147i
$235$	−2.27324	+	2.27324i	−0.148290	+	0.148290i
$236$	−10.5605	+	9.87349i	−0.687430	+	0.642709i
$237$	2.81766	−	3.91863i	0.183027	−	0.254542i
$238$	4.59776	−	4.44578i	0.298029	−	0.288177i
$239$	24.5124			1.58558			0.792789	−	0.609496i	$-0.208628\pi$
$239$	24.5124			1.58558			0.792789	+	0.609496i	$0.208628\pi$
$240$	6.89710	−	0.655734i	0.445206	−	0.0423275i
$241$	11.4229			0.735816			0.367908	−	0.929862i	$-0.380074\pi$
$241$	11.4229			0.735816			0.367908	+	0.929862i	$0.380074\pi$
$242$	6.54743	−	6.33100i	0.420885	−	0.406972i
$243$	15.5837	−	0.383899i	0.999697	−	0.0246271i
$244$	−14.9774	−	16.0196i	−0.958831	−	1.02555i
$245$	9.61325	−	9.61325i	0.614168	−	0.614168i
$246$	−0.0653302	−	0.446761i	−0.00416530	−	0.0284845i
$247$	−8.37445			−0.532854
$248$	−4.86999	−	5.38753i	−0.309244	−	0.342109i
$249$	23.3696	−	3.81948i	1.48099	−	0.242050i
$250$	−0.0237635	+	1.41401i	−0.00150294	+	0.0894301i
$251$	−10.6487	−	10.6487i	−0.672138	−	0.672138i	0.286071	−	0.958208i	$-0.407651\pi$
$251$	−10.6487	−	10.6487i	−0.672138	−	0.672138i	−0.958208	+	0.286071i	$0.907651\pi$
$252$	−26.0890	+	7.79675i	−1.64345	+	0.491149i
$253$	−17.1980	+	17.1980i	−1.08123	+	1.08123i
$254$	11.7309	−	11.3432i	0.736065	−	0.711734i
$255$	−0.278405	−	1.70343i	−0.0174344	−	0.106673i
$256$	15.8556	+	2.14446i	0.990977	+	0.134029i
$257$		−	8.24255i		−	0.514156i	−0.966391	−	0.257078i	$-0.917240\pi$
$257$		−	8.24255i		−	0.514156i	0.966391	−	0.257078i	$-0.0827597\pi$
$258$	5.79503	+	4.31643i	0.360783	+	0.268729i
$259$	−19.6993	−	19.6993i	−1.22405	−	1.22405i
$260$	4.66626	+	0.156884i	0.289389	+	0.00972955i
$261$	−13.5677	+	27.2895i	−0.839823	+	1.68918i
$262$	−18.2192	−	0.306187i	−1.12559	−	0.0189163i
$263$		−	9.18657i		−	0.566468i	−0.959051	−	0.283234i	$-0.908593\pi$
$263$		−	9.18657i		−	0.566468i	0.959051	−	0.283234i	$-0.0914074\pi$
$264$	15.9876	+	12.7656i	0.983969	+	0.785666i
$265$		−	4.99035i		−	0.306555i
$266$	−0.386871	+	23.0202i	−0.0237206	+	1.41146i
$267$	0.168863	+	0.121420i	0.0103343	+	0.00743077i
$268$	−14.1534	+	13.2326i	−0.864554	+	0.808310i
$269$	−20.2167	−	20.2167i	−1.23263	−	1.23263i	−0.962950	−	0.269681i	$-0.913082\pi$
$269$	−20.2167	−	20.2167i	−1.23263	−	1.23263i	−0.269681	−	0.962950i	$-0.586918\pi$
$270$	−2.28496	+	6.98419i	−0.139058	+	0.425044i
$271$			4.57076i			0.277654i	0.990317	+	0.138827i	$0.0443332\pi$
$271$			4.57076i			0.277654i	−0.990317	+	0.138827i	$0.955667\pi$
$272$	0.267730	−	3.97709i	0.0162335	−	0.241146i
$273$	−18.1094	+	2.95976i	−1.09603	+	0.179133i
$274$	−15.0643	−	15.5793i	−0.910070	−	0.941182i
$275$	−2.95298	+	2.95298i	−0.178071	+	0.178071i
$276$	−15.9749	−	12.3216i	−0.961576	−	0.741674i
$277$	−11.7763	−	11.7763i	−0.707570	−	0.707570i	0.258454	−	0.966024i	$-0.416787\pi$
$277$	−11.7763	−	11.7763i	−0.707570	−	0.707570i	−0.966024	+	0.258454i	$0.916787\pi$
$278$	−3.61031	−	0.0606740i	−0.216532	−	0.00363898i
$279$	7.30211	−	2.45239i	0.437166	−	0.146821i
$280$	0.646817	−	12.8196i	0.0386547	−	0.766120i
$281$	15.8206			0.943780			0.471890	−	0.881657i	$-0.343572\pi$
$281$	15.8206			0.943780			0.471890	+	0.881657i	$0.343572\pi$
$282$	−1.13941	−	7.79188i	−0.0678509	−	0.464000i
$283$	−7.75700	+	7.75700i	−0.461106	+	0.461106i	−0.899018	−	0.437912i	$-0.855718\pi$
$283$	−7.75700	+	7.75700i	−0.461106	+	0.461106i	0.437912	+	0.899018i	$0.355718\pi$
$284$	−22.7881	−	0.766158i	−1.35222	−	0.0454631i
$285$	5.04471	+	3.62737i	0.298823	+	0.214867i
$286$	9.58379	+	9.91142i	0.566702	+	0.586075i
$287$	−0.836522			−0.0493783
$288$	−8.80376	+	14.5084i	−0.518767	+	0.854916i
$289$	16.0069			0.941585
$290$	−9.98662	−	10.3280i	−0.586435	−	0.606482i
$291$	−9.05893	−	6.51376i	−0.531044	−	0.381843i
$292$	7.99765	+	0.268889i	0.468027	+	0.0157355i
$293$	12.3582	−	12.3582i	0.721971	−	0.721971i	−0.247035	−	0.969007i	$-0.579456\pi$
$293$	12.3582	−	12.3582i	0.721971	−	0.721971i	0.969007	+	0.247035i	$0.0794563\pi$
$294$	4.81842	+	32.9508i	0.281016	+	1.92173i
$295$	7.22859			0.420865
$296$	−17.3411	−	0.874946i	−1.00793	−	0.0508552i
$297$	−19.1870	+	10.1362i	−1.11334	+	0.588160i
$298$	−6.05345	−	0.101733i	−0.350667	−	0.00589322i
$299$	−9.61361	−	9.61361i	−0.555969	−	0.555969i
$300$	−2.74297	−	2.11568i	−0.158365	−	0.122149i
$301$	9.46641	−	9.46641i	0.545635	−	0.545635i
$302$	3.73055	+	3.85809i	0.214669	+	0.222008i
$303$	−7.71129	+	1.26032i	−0.443002	+	0.0724033i
$304$	9.44210	+	10.8051i	0.541542	+	0.619715i
$305$			10.9653i			0.627870i
$306$	3.75364	+	1.94556i	0.214581	+	0.111220i
$307$	8.10636	+	8.10636i	0.462655	+	0.462655i	0.899525	−	0.436870i	$-0.143913\pi$
$307$	8.10636	+	8.10636i	0.462655	+	0.462655i	−0.436870	+	0.899525i	$0.643913\pi$
$308$	27.6878	−	25.8866i	1.57766	−	1.47503i
$309$	3.49744	+	2.51481i	0.198962	+	0.143062i
$310$	−0.0610162	+	3.63068i	−0.00346549	+	0.206209i
$311$			7.41277i			0.420339i	0.977665	+	0.210170i	$0.0674017\pi$
$311$			7.41277i			0.420339i	−0.977665	+	0.210170i	$0.932598\pi$
$312$	−7.13592	+	8.93703i	−0.403992	+	0.505960i
$313$		−	13.5102i		−	0.763643i	−0.924236	−	0.381821i	$-0.875297\pi$
$313$		−	13.5102i		−	0.763643i	0.924236	−	0.381821i	$-0.124703\pi$
$314$	−1.57348	−	0.0264435i	−0.0887965	−	0.00149229i
$315$	12.1910	+	6.06108i	0.686884	+	0.341503i
$316$	−5.56999	−	0.187268i	−0.313336	−	0.0105347i
$317$	4.22773	+	4.22773i	0.237453	+	0.237453i	0.815795	−	0.578342i	$-0.196300\pi$
$317$	4.22773	+	4.22773i	0.237453	+	0.237453i	−0.578342	+	0.815795i	$0.696300\pi$
$318$	9.80323	+	7.30194i	0.549738	+	0.409472i
$319$		−	42.4244i		−	2.37531i
$320$	−5.05874	−	6.19751i	−0.282792	−	0.346451i
$321$	1.30893	+	8.00874i	0.0730575	+	0.447004i
$322$	−26.8705	+	25.9823i	−1.49744	+	1.44794i
$323$	2.52781	−	2.52781i	0.140651	−	0.140651i
$324$	−10.3766	−	14.7080i	−0.576480	−	0.817111i
$325$	−1.65071	−	1.65071i	−0.0915647	−	0.0915647i
$326$	0.283135	−	16.8475i	0.0156814	−	0.933098i
$327$	12.2080	−	1.99526i	0.675106	−	0.110338i
$328$	−0.386767	+	0.349613i	−0.0213557	+	0.0193042i
$329$	−14.5896			−0.804351
$330$	−1.48011	−	10.1218i	−0.0814774	−	0.557185i
$331$	−21.5620	+	21.5620i	−1.18516	+	1.18516i	−0.206766	+	0.978390i	$0.566294\pi$
$331$	−21.5620	+	21.5620i	−1.18516	+	1.18516i	−0.978390	+	0.206766i	$0.933706\pi$
$332$	−18.6738	−	19.9731i	−1.02486	−	1.09617i
$333$	8.19879	−	16.4907i	0.449291	−	0.903683i
$334$	13.0198	−	12.5894i	0.712413	−	0.688863i
$335$	9.68787			0.529305
$336$	24.2369	+	20.0285i	1.32223	+	1.09264i
$337$	−22.1368			−1.20587			−0.602935	−	0.797791i	$-0.706002\pi$
$337$	−22.1368			−1.20587			−0.602935	+	0.797791i	$0.706002\pi$
$338$	7.67615	−	7.42241i	0.417527	−	0.403726i
$339$	3.68096	−	5.11925i	0.199922	−	0.278039i
$340$	−1.45586	+	1.36114i	−0.0789548	+	0.0738184i
$341$	−7.58218	+	7.58218i	−0.410598	+	0.410598i
$342$	−14.5072	+	4.60242i	−0.784460	+	0.248870i
$343$	29.9302			1.61608
$344$	0.420452	−	8.33317i	0.0226693	−	0.449295i
$345$	1.62707	+	9.95528i	0.0875985	+	0.535974i
$346$	0.180942	−	10.7667i	0.00972749	−	0.578820i
$347$	−7.05990	−	7.05990i	−0.378995	−	0.378995i	0.491744	−	0.870740i	$-0.336359\pi$
$347$	−7.05990	−	7.05990i	−0.378995	−	0.378995i	−0.870740	+	0.491744i	$0.836359\pi$
$348$	34.9013	−	4.50602i	1.87091	−	0.241548i
$349$	4.68415	−	4.68415i	0.250737	−	0.250737i	−0.570536	−	0.821273i	$-0.693264\pi$
$349$	4.68415	−	4.68415i	0.250737	−	0.250737i	0.821273	+	0.570536i	$0.193264\pi$
$350$	−4.61381	+	4.46129i	−0.246618	+	0.238466i
$351$	−5.66609	−	10.7255i	−0.302433	−	0.572484i
$352$	1.98256	−	23.5405i	0.105671	−	1.25471i
$353$		−	26.6528i		−	1.41859i	−0.704913	−	0.709293i	$-0.749014\pi$
$353$		−	26.6528i		−	1.41859i	0.704913	−	0.709293i	$-0.250986\pi$
$354$	−10.5769	+	14.2001i	−0.562158	+	0.754727i
$355$	8.06136	+	8.06136i	0.427853	+	0.427853i
$356$	0.00806984	−	0.240024i	0.000427701	−	0.0127213i
$357$	4.57288	−	6.35967i	0.242022	−	0.336589i
$358$	35.7549	+	0.600888i	1.88971	+	0.0317579i
$359$		−	16.4555i		−	0.868486i	−0.900796	−	0.434243i	$-0.857016\pi$
$359$		−	16.4555i		−	0.868486i	0.900796	−	0.434243i	$-0.142984\pi$
$360$	8.16967	−	2.29271i	0.430579	−	0.120836i
$361$		−	6.13103i		−	0.322686i
$362$	−0.0469602	+	2.79429i	−0.00246817	+	0.146865i
$363$	6.51199	−	9.05647i	0.341791	−	0.475341i
$364$	14.4705	+	15.4774i	0.758462	+	0.811237i
$365$	−2.82919	−	2.82919i	−0.148087	−	0.148087i
$366$	−21.5406	−	16.0445i	−1.12595	−	0.838660i
$367$		−	14.8577i		−	0.775566i	−0.921751	−	0.387783i	$-0.873241\pi$
$367$		−	14.8577i		−	0.775566i	0.921751	−	0.387783i	$-0.126759\pi$
$368$	−1.56468	+	23.2432i	−0.0815647	+	1.21163i
$369$	−0.176056	−	0.524214i	−0.00916509	−	0.0272895i
$370$	6.03477	+	6.24107i	0.313733	+	0.324458i
$371$	16.0140	−	16.0140i	0.831404	−	0.831404i
$372$	−7.04297	−	5.43231i	−0.365161	−	0.281652i
$373$	7.38244	+	7.38244i	0.382248	+	0.382248i	0.871912	−	0.489663i	$-0.162880\pi$
$373$	7.38244	+	7.38244i	0.382248	+	0.382248i	−0.489663	+	0.871912i	$0.662880\pi$
$374$	−5.88458	−	0.0988947i	−0.304285	−	0.00511372i
$375$	0.279376	+	1.70937i	0.0144269	+	0.0882715i
$376$	−6.74554	+	6.09754i	−0.347874	+	0.314456i
$377$	23.7151			1.22139
$378$	−29.7446	+	15.0798i	−1.52990	+	0.775620i
$379$	−23.4398	+	23.4398i	−1.20402	+	1.20402i	−0.231089	+	0.972933i	$0.574229\pi$
$379$	−23.4398	+	23.4398i	−1.20402	+	1.20402i	−0.972933	+	0.231089i	$0.925771\pi$
$380$	0.241083	−	7.17062i	0.0123673	−	0.367845i
$381$	11.6674	−	16.2264i	0.597742	−	0.831301i
$382$	−3.27011	−	3.38190i	−0.167313	−	0.173033i
$383$	−23.9285			−1.22269			−0.611345	−	0.791364i	$-0.709371\pi$
$383$	−23.9285			−1.22269			−0.611345	+	0.791364i	$0.709371\pi$
$384$	19.5766	−	0.869313i	0.999016	−	0.0443619i
$385$	−18.9521			−0.965889
$386$	7.23313	+	7.48040i	0.368156	+	0.380742i
$387$	7.92453	+	3.93990i	0.402826	+	0.200276i
$388$	−0.432920	+	12.8765i	−0.0219782	+	0.653704i
$389$	2.00876	−	2.00876i	0.101848	−	0.101848i	−0.654347	−	0.756195i	$-0.727056\pi$
$389$	2.00876	−	2.00876i	0.101848	−	0.101848i	0.756195	+	0.654347i	$0.227056\pi$
$390$	5.65804	−	0.827378i	0.286506	−	0.0418959i
$391$	5.80369			0.293505
$392$	28.5260	−	25.7857i	1.44078	−	1.30237i
$393$	−22.0248	+	3.59969i	−1.11101	+	0.181580i
$394$	24.5479	+	0.412545i	1.23670	+	0.0207837i
$395$	1.97040	+	1.97040i	0.0991416	+	0.0991416i
$396$	22.0493	+	11.9027i	1.10802	+	0.598132i
$397$	−9.72041	+	9.72041i	−0.487853	+	0.487853i	−0.907628	−	0.419775i	$-0.862109\pi$
$397$	−9.72041	+	9.72041i	−0.487853	+	0.487853i	0.419775	+	0.907628i	$0.362109\pi$
$398$	25.0693	+	25.9263i	1.25661	+	1.29957i
$399$	4.54825	+	27.8286i	0.227697	+	1.39317i
$400$	−0.268664	+	3.99097i	−0.0134332	+	0.199548i
$401$		−	5.95792i		−	0.297524i	−0.988873	−	0.148762i	$-0.952471\pi$
$401$		−	5.95792i		−	0.297524i	0.988873	−	0.148762i	$-0.0475289\pi$
$402$	−14.1754	+	19.0312i	−0.707004	+	0.949191i
$403$	−4.23842	−	4.23842i	−0.211131	−	0.211131i
$404$	6.16180	+	6.59055i	0.306561	+	0.327892i
$405$	−1.23250	+	8.91521i	−0.0612433	+	0.443000i
$406$	1.09556	−	65.1894i	0.0543715	−	3.23530i
$407$			25.6364i			1.27075i
$408$	−0.543661	−	4.85158i	−0.0269152	−	0.240189i
$409$			23.4196i			1.15802i	0.815319	+	0.579012i	$0.196562\pi$
$409$			23.4196i			1.15802i	−0.815319	+	0.579012i	$0.803438\pi$
$410$	0.260644	+	0.00438032i	0.0128723	+	0.000216328i
$411$	−21.5495	−	15.4950i	−1.06296	−	0.764312i
$412$	0.167140	−	4.97130i	0.00823439	−	0.244918i
$413$	23.1964	+	23.1964i	1.14142	+	1.14142i
$414$	−21.9373	−	11.3704i	−1.07816	−	0.558824i
$415$			13.6715i			0.671106i
$416$	13.1591	+	1.10824i	0.645176	+	0.0543361i
$417$	−4.36443	+	0.713314i	−0.213727	+	0.0349311i
$418$	15.2308	−	14.7274i	0.744964	−	0.720338i
$419$	6.81995	−	6.81995i	0.333176	−	0.333176i	−0.520615	−	0.853791i	$-0.674297\pi$
$419$	6.81995	−	6.81995i	0.333176	−	0.333176i	0.853791	+	0.520615i	$0.174297\pi$
$420$	−2.01296	−	15.5913i	−0.0982224	−	0.760780i
$421$	−1.76572	−	1.76572i	−0.0860558	−	0.0860558i	0.662769	−	0.748824i	$-0.269381\pi$
$421$	−1.76572	−	1.76572i	−0.0860558	−	0.0860558i	−0.748824	+	0.662769i	$0.769381\pi$
$422$	0.618034	−	36.7752i	0.0300854	−	1.79019i
$423$	−3.07055	−	9.14271i	−0.149295	−	0.444534i
$424$	0.711263	−	14.0969i	0.0345420	−	0.684607i
$425$	0.996523			0.0483384
$426$	−27.6315	+	4.04057i	−1.33875	+	0.195766i
$427$	−35.1874	+	35.1874i	−1.70284	+	1.70284i
$428$	6.84477	−	6.39949i	0.330855	−	0.309331i
$429$	13.7096	+	9.85777i	0.661904	+	0.475938i
$430$	−2.99912	+	2.89998i	−0.144631	+	0.139850i
$431$	−5.09224			−0.245285			−0.122642	−	0.992451i	$-0.539137\pi$
$431$	−5.09224			−0.245285			−0.122642	+	0.992451i	$0.539137\pi$
$432$	−7.45007	+	19.4035i	−0.358442	+	0.933552i
$433$	−20.4411			−0.982338			−0.491169	−	0.871064i	$-0.663430\pi$
$433$	−20.4411			−0.982338			−0.491169	+	0.871064i	$0.663430\pi$
$434$	−11.8466	+	11.4550i	−0.568655	+	0.549858i
$435$	−14.2858	−	10.2721i	−0.684953	−	0.492510i
$436$	−9.75498	−	10.4337i	−0.467179	−	0.499686i
$437$	−14.7732	+	14.7732i	−0.706697	+	0.706697i
$438$	9.69748	−	1.41807i	0.463364	−	0.0677579i
$439$	−3.07645			−0.146831			−0.0734154	−	0.997301i	$-0.523390\pi$
$439$	−3.07645			−0.146831			−0.0734154	+	0.997301i	$0.523390\pi$
$440$	−8.76254	+	7.92078i	−0.417738	+	0.377609i
$441$	12.9850	+	38.6633i	0.618331	+	1.84111i
$442$	0.0552819	−	3.28947i	0.00262949	−	0.156464i
$443$	−5.61677	−	5.61677i	−0.266861	−	0.266861i	0.560973	−	0.827834i	$-0.310427\pi$
$443$	−5.61677	−	5.61677i	−0.266861	−	0.266861i	−0.827834	+	0.560973i	$0.810427\pi$
$444$	−21.0903	+	2.72292i	−1.00090	+	0.129224i
$445$	−0.0849093	+	0.0849093i	−0.00402509	+	0.00402509i
$446$	−18.7611	+	18.1409i	−0.888364	+	0.858998i
$447$	−7.31789	+	1.19602i	−0.346124	+	0.0565698i
$448$	3.65430	−	36.1212i	0.172650	−	1.70656i
$449$			11.0672i			0.522294i	0.965299	+	0.261147i	$0.0841007\pi$
$449$			11.0672i			0.522294i	−0.965299	+	0.261147i	$0.915899\pi$
$450$	−3.76674	−	1.95235i	−0.177566	−	0.0920348i
$451$	0.544320	+	0.544320i	0.0256310	+	0.0256310i
$452$	−7.27656	−	0.244645i	−0.342261	−	0.0115071i
$453$	5.33654	+	3.83720i	0.250733	+	0.180288i
$454$	5.31203	+	0.0892725i	0.249306	+	0.00418977i
$455$		−	10.5942i		−	0.496663i
$456$	13.7335	+	10.9657i	0.643129	+	0.513517i
$457$		−	8.00185i		−	0.374311i	−0.982330	−	0.187155i	$-0.940073\pi$
$457$		−	8.00185i		−	0.374311i	0.982330	−	0.187155i	$-0.0599268\pi$
$458$	0.362976	−	21.5984i	0.0169608	−	1.00923i
$459$	4.94776	+	1.52717i	0.230942	+	0.0712821i
$460$	8.50840	−	7.95489i	0.396706	−	0.370899i
$461$	−13.2743	−	13.2743i	−0.618247	−	0.618247i	0.326835	−	0.945082i	$-0.394018\pi$
$461$	−13.2743	−	13.2743i	−0.618247	−	0.618247i	−0.945082	+	0.326835i	$0.894018\pi$
$462$	27.7309	−	37.2302i	1.29016	−	1.73211i
$463$		−	7.17773i		−	0.333577i	−0.985993	−	0.166789i	$-0.946660\pi$
$463$		−	7.17773i		−	0.333577i	0.985993	−	0.166789i	$-0.0533397\pi$
$464$	−26.7385	−	30.5983i	−1.24130	−	1.42049i
$465$	0.717337	+	4.38905i	0.0332657	+	0.203537i
$466$	23.2815	+	24.0774i	1.07849	+	1.11536i
$467$	3.05937	−	3.05937i	0.141571	−	0.141571i	−0.632770	−	0.774340i	$-0.718082\pi$
$467$	3.05937	−	3.05937i	0.141571	−	0.141571i	0.774340	+	0.632770i	$0.218082\pi$
$468$	−6.65357	+	12.3255i	−0.307561	+	0.569746i
$469$	31.0882	+	31.0882i	1.43552	+	1.43552i
$470$	4.54585	+	0.0763963i	0.209684	+	0.00352390i
$471$	−1.90214	+	0.310883i	−0.0876462	+	0.0143247i
$472$	20.4196	+	1.03027i	0.939886	+	0.0474221i
$473$	−12.3195			−0.566450
$474$	−6.75384	+	0.987617i	−0.310214	+	0.0453628i
$475$	−2.53663	+	2.53663i	−0.116389	+	0.116389i
$476$	−9.03971	−	0.303924i	−0.414335	−	0.0139303i
$477$	13.4056	+	6.66497i	0.613801	+	0.305168i
$478$	−24.0971	−	24.9209i	−1.10218	−	1.13985i
$479$	3.68548			0.168394			0.0841969	−	0.996449i	$-0.473168\pi$
$479$	3.68548			0.168394			0.0841969	+	0.996449i	$0.473168\pi$
$480$	−7.44689	−	6.36740i	−0.339903	−	0.290631i
$481$	−14.3307			−0.653423
$482$	−11.2294	−	11.6133i	−0.511484	−	0.528970i
$483$	−26.7251	+	37.1676i	−1.21603	+	1.69118i
$484$	−12.8730	−	0.432802i	−0.585135	−	0.0196728i
$485$	4.55509	−	4.55509i	0.206836	−	0.206836i
$486$	−15.7100	−	15.4660i	−0.712619	−	0.701552i
$487$	16.0525			0.727408			0.363704	−	0.931515i	$-0.381512\pi$
$487$	16.0525			0.727408			0.363704	+	0.931515i	$0.381512\pi$
$488$	−1.56285	+	30.9751i	−0.0707471	+	1.40218i
$489$	−3.32868	−	20.3666i	−0.150528	−	0.921010i
$490$	−19.2238	−	0.323070i	−0.868442	−	0.0145948i
$491$	−9.07282	−	9.07282i	−0.409451	−	0.409451i	0.472096	−	0.881547i	$-0.343497\pi$
$491$	−9.07282	−	9.07282i	−0.409451	−	0.409451i	−0.881547	+	0.472096i	$0.843497\pi$
$492$	−0.389982	+	0.505610i	−0.0175818	+	0.0227947i
$493$	−7.15835	+	7.15835i	−0.322396	+	0.322396i
$494$	8.23255	+	8.51399i	0.370400	+	0.383063i
$495$	−3.98869	−	11.8765i	−0.179278	−	0.533809i
$496$	−0.689833	+	10.2474i	−0.0309744	+	0.460121i
$497$			51.7376i			2.32075i
$498$	−26.8568	−	20.0042i	−1.20348	−	0.896412i
$499$	18.2451	+	18.2451i	0.816764	+	0.816764i	0.985638	−	0.168874i	$-0.0540131\pi$
$499$	18.2451	+	18.2451i	0.816764	+	0.816764i	−0.168874	+	0.985638i	$0.554013\pi$
$500$	1.46094	−	1.36589i	0.0653350	−	0.0610847i
$501$	12.9493	−	18.0091i	0.578534	−	0.804589i
$502$	−0.357867	+	21.2943i	−0.0159724	+	0.950412i
$503$		−	43.1853i		−	1.92554i	−0.270323	−	0.962770i	$-0.587131\pi$
$503$		−	43.1853i		−	1.92554i	0.270323	−	0.962770i	$-0.412869\pi$
$504$	33.5736	+	18.8591i	1.49549	+	0.840051i
$505$		−	4.51119i		−	0.200745i
$506$	34.3911	+	0.577967i	1.52887	+	0.0256938i
$507$	7.63460	−	10.6177i	0.339064	−	0.471549i
$508$	−23.0643	−	0.775445i	−1.02331	−	0.0344048i
$509$	17.8184	+	17.8184i	0.789785	+	0.789785i	0.981459	−	0.191674i	$-0.0613916\pi$
$509$	17.8184	+	17.8184i	0.789785	+	0.789785i	−0.191674	+	0.981459i	$0.561392\pi$
$510$	−1.45812	+	1.95761i	−0.0645668	+	0.0866843i
$511$		−	18.1577i		−	0.803249i
$512$	−13.4068	−	18.2280i	−0.592502	−	0.805569i
$513$	−16.4818	+	8.70704i	−0.727689	+	0.384425i
$514$	−8.37989	+	8.10288i	−0.369621	+	0.357403i
$515$	−1.75861	+	1.75861i	−0.0774938	+	0.0774938i
$516$	−1.30849	−	10.1349i	−0.0576030	−	0.446163i
$517$	9.49338	+	9.49338i	0.417518	+	0.417518i
$518$	−0.662028	+	39.3930i	−0.0290879	+	1.73083i
$519$	−2.12724	−	13.0156i	−0.0933755	−	0.571321i
$520$	−4.42770	−	4.89824i	−0.194167	−	0.214802i
$521$	37.3760			1.63747			0.818737	−	0.574168i	$-0.194675\pi$
$521$	37.3760			1.63747			0.818737	+	0.574168i	$0.194675\pi$
$522$	41.0821	−	13.0333i	1.79811	−	0.570453i
$523$	16.8160	−	16.8160i	0.735313	−	0.735313i	−0.236354	−	0.971667i	$-0.575953\pi$
$523$	16.8160	−	16.8160i	0.735313	−	0.735313i	0.971667	+	0.236354i	$0.0759525\pi$
$524$	17.5992	+	18.8238i	0.768826	+	0.822322i
$525$	−4.58883	+	6.38186i	−0.200273	+	0.278527i
$526$	−9.33964	+	9.03091i	−0.407228	+	0.393766i
$527$	2.55871			0.111459
$528$	−2.73844	−	28.8032i	−0.119175	−	1.25350i
$529$	−10.9183			−0.474708
$530$	−5.07350	+	4.90579i	−0.220379	+	0.213094i
$531$	−9.65429	+	19.4182i	−0.418961	+	0.842678i
$532$	23.7840	−	22.2368i	1.03117	−	0.964087i
$533$	−0.304273	+	0.304273i	−0.0131795	+	0.0131795i
$534$	−0.0425588	−	0.291039i	−0.00184170	−	0.0125945i
$535$	−4.68520			−0.202559
$536$	27.3666	+	1.38079i	1.18206	+	0.0596410i
$537$	43.2234	−	7.06434i	1.86523	−	0.304849i
$538$	−0.679415	+	40.4276i	−0.0292917	+	1.74296i
$539$	−40.1462	−	40.1462i	−1.72922	−	1.72922i
$540$	9.34681	−	4.54282i	0.402223	−	0.195492i
$541$	−19.8065	+	19.8065i	−0.851550	+	0.851550i	−0.990324	−	0.138774i	$-0.955684\pi$
$541$	−19.8065	+	19.8065i	−0.851550	+	0.851550i	0.138774	+	0.990324i	$0.455684\pi$
$542$	4.64692	−	4.49331i	0.199602	−	0.193004i
$543$	0.552087	+	3.37796i	0.0236923	+	0.144962i
$544$	−4.30655	+	3.63751i	−0.184642	+	0.155957i
$545$			7.14183i			0.305922i
$546$	20.8116	+	15.5015i	0.890654	+	0.663404i
$547$	12.1897	+	12.1897i	0.521194	+	0.521194i	0.917932	−	0.396738i	$-0.129858\pi$
$547$	12.1897	+	12.1897i	0.521194	+	0.521194i	−0.396738	+	0.917932i	$0.629858\pi$
$548$	−1.02983	+	30.6307i	−0.0439923	+	1.30848i
$549$	−29.4561	−	14.6449i	−1.25716	−	0.625030i
$550$	5.90512	+	0.0992398i	0.251795	+	0.00423160i
$551$		−	36.4429i		−	1.55252i
$552$	3.17730	+	28.3539i	0.135235	+	1.20682i
$553$			12.6460i			0.537761i
$554$	−0.395763	+	23.5493i	−0.0168144	+	1.00051i
$555$	8.63271	+	6.20729i	0.366438	+	0.263485i
$556$	3.48745	+	3.73012i	0.147901	+	0.158192i
$557$	27.6342	+	27.6342i	1.17090	+	1.17090i	0.981996	+	0.188901i	$0.0604926\pi$
$557$	27.6342	+	27.6342i	1.17090	+	1.17090i	0.188901	+	0.981996i	$0.439507\pi$
$558$	−9.67163	−	5.01294i	−0.409433	−	0.212215i
$559$		−	6.88656i		−	0.291270i
$560$	−13.6691	+	11.9448i	−0.577625	+	0.504761i
$561$	−7.11375	+	1.16266i	−0.300343	+	0.0490874i
$562$	−15.5526	−	16.0843i	−0.656046	−	0.678473i
$563$	11.6633	−	11.6633i	0.491548	−	0.491548i	−0.417245	−	0.908794i	$-0.637004\pi$
$563$	11.6633	−	11.6633i	0.491548	−	0.491548i	0.908794	+	0.417245i	$0.137004\pi$
$564$	−6.80161	+	8.81825i	−0.286399	+	0.371315i
$565$	2.57411	+	2.57411i	0.108293	+	0.108293i
$566$	15.5118	+	0.260687i	0.652010	+	0.0109575i
$567$	−32.5638	+	24.6537i	−1.36755	+	1.03536i
$568$	21.6230	+	23.9210i	0.907282	+	1.00370i
$569$	−1.67359			−0.0701606			−0.0350803	−	0.999384i	$-0.511169\pi$
$569$	−1.67359			−0.0701606			−0.0350803	+	0.999384i	$0.511169\pi$
$570$	−1.27143	−	8.69467i	−0.0532542	−	0.364180i
$571$	12.3559	−	12.3559i	0.517080	−	0.517080i	−0.399606	−	0.916687i	$-0.630853\pi$
$571$	12.3559	−	12.3559i	0.517080	−	0.517080i	0.916687	+	0.399606i	$0.130853\pi$
$572$	0.655170	−	19.4870i	0.0273940	−	0.814791i
$573$	−4.67788	−	3.36359i	−0.195421	−	0.140516i
$574$	0.822347	+	0.850460i	0.0343241	+	0.0354975i
$575$	−5.82394			−0.242875
$576$	23.4047	−	5.31211i	0.975197	−	0.221338i
$577$	22.2591			0.926658			0.463329	−	0.886186i	$-0.346655\pi$
$577$	22.2591			0.926658			0.463329	+	0.886186i	$0.346655\pi$
$578$	−15.7357	−	16.2737i	−0.654519	−	0.676895i
$579$	10.3470	+	7.43991i	0.430005	+	0.309192i
$580$	−0.682709	+	20.3060i	−0.0283479	+	0.843162i
$581$	−43.8716	+	43.8716i	−1.82010	+	1.82010i
$582$	2.28314	+	15.6133i	0.0946390	+	0.647190i
$583$	−20.8404			−0.863121
$584$	−7.58877	−	8.39524i	−0.314025	−	0.347398i
$585$	6.63894	−	2.22967i	0.274486	−	0.0921854i
$586$	−24.7128	−	0.415317i	−1.02088	−	0.0171566i
$587$	13.5459	+	13.5459i	0.559100	+	0.559100i	0.929051	−	0.369951i	$-0.120626\pi$
$587$	13.5459	+	13.5459i	0.559100	+	0.559100i	−0.369951	+	0.929051i	$0.620626\pi$
$588$	28.7631	−	37.2912i	1.18617	−	1.53786i
$589$	−6.51315	+	6.51315i	−0.268370	+	0.268370i
$590$	−7.10610	−	7.34903i	−0.292554	−	0.302555i
$591$	29.6754	−	4.85008i	1.22068	−	0.199506i
$592$	16.1577	+	18.4901i	0.664077	+	0.759939i
$593$			32.6688i			1.34155i	0.741663	+	0.670773i	$0.234037\pi$
$593$			32.6688i			1.34155i	−0.741663	+	0.670773i	$0.765963\pi$
$594$	29.1670	+	9.54230i	1.19673	+	0.391525i
$595$	3.19783	+	3.19783i	0.131098	+	0.131098i
$596$	5.84745	+	6.25433i	0.239521	+	0.256187i
$597$	35.8615	+	25.7860i	1.46771	+	1.05535i
$598$	−0.323082	+	19.2245i	−0.0132118	+	0.786148i
$599$			26.7287i			1.09211i	0.837751	+	0.546053i	$0.183870\pi$
$599$			26.7287i			1.09211i	−0.837751	+	0.546053i	$0.816130\pi$
$600$	0.545558	+	4.86851i	0.0222723	+	0.198756i
$601$		−	40.3275i		−	1.64499i	−0.568771	−	0.822496i	$-0.692581\pi$
$601$		−	40.3275i		−	1.64499i	0.568771	−	0.822496i	$-0.307419\pi$
$602$	−18.9302	−	0.318135i	−0.771535	−	0.0129662i
$603$	−12.9388	+	26.0246i	−0.526910	+	1.05980i
$604$	0.255029	−	7.58543i	0.0103770	−	0.308647i
$605$	4.55386	+	4.55386i	0.185141	+	0.185141i
$606$	8.86194	+	6.60082i	0.359992	+	0.268140i
$607$			11.9863i			0.486510i	0.969962	+	0.243255i	$0.0782151\pi$
$607$			11.9863i			0.486510i	−0.969962	+	0.243255i	$0.921785\pi$
$608$	1.70303	−	20.2214i	0.0690670	−	0.820088i
$609$	−12.8799	−	78.8061i	−0.521920	−	3.19338i
$610$	11.1480	−	10.7795i	0.451369	−	0.436448i
$611$	−5.30677	+	5.30677i	−0.214689	+	0.214689i
$612$	−1.71206	−	5.72878i	−0.0692057	−	0.231572i
$613$	28.5787	+	28.5787i	1.15428	+	1.15428i	0.985685	+	0.168597i	$0.0539235\pi$
$613$	28.5787	+	28.5787i	1.15428	+	1.15428i	0.168597	+	0.985685i	$0.446076\pi$
$614$	0.272428	−	16.2104i	0.0109943	−	0.654200i
$615$	0.315087	−	0.0514972i	0.0127055	−	0.00207657i
$616$	−53.5366	−	2.70120i	−2.15705	−	0.108834i
$617$	−38.3951			−1.54573			−0.772864	−	0.634572i	$-0.781176\pi$
$617$	−38.3951			−1.54573			−0.772864	+	0.634572i	$0.781176\pi$
$618$	−0.881464	−	6.02791i	−0.0354577	−	0.242478i
$619$	30.8621	−	30.8621i	1.24045	−	1.24045i	0.280638	−	0.959814i	$-0.409454\pi$
$619$	30.8621	−	30.8621i	1.24045	−	1.24045i	0.959814	−	0.280638i	$-0.0905460\pi$
$620$	3.75116	−	3.50713i	0.150650	−	0.140850i
$621$	−28.9160	−	8.92517i	−1.16036	−	0.358155i
$622$	7.53628	−	7.28716i	0.302177	−	0.292189i
$623$	−0.544945			−0.0218328
$624$	16.1009	−	1.53078i	0.644553	−	0.0612802i
$625$	−1.00000			−0.0400000
$626$	−13.7353	+	13.2813i	−0.548974	+	0.530827i
$627$	15.1484	−	21.0674i	0.604968	−	0.841352i
$628$	1.51993	+	1.62569i	0.0606519	+	0.0648722i
$629$	4.32568	−	4.32568i	0.172476	−	0.172476i
$630$	−5.82234	−	18.3525i	−0.231967	−	0.731180i
$631$	−14.3917			−0.572923			−0.286462	−	0.958092i	$-0.592479\pi$
$631$	−14.3917			−0.572923			−0.286462	+	0.958092i	$0.592479\pi$
$632$	5.28522	+	5.84689i	0.210235	+	0.232577i
$633$	−7.26592	−	44.4568i	−0.288794	−	1.76700i
$634$	0.142080	−	8.45427i	0.00564272	−	0.335762i
$635$	8.15908	+	8.15908i	0.323783	+	0.323783i
$636$	−2.21352	−	17.1448i	−0.0877718	−	0.679835i
$637$	22.4416	−	22.4416i	0.889170	−	0.889170i
$638$	−43.1313	+	41.7055i	−1.70758	+	1.65114i
$639$	−32.4218	+	10.8888i	−1.28259	+	0.430753i
$640$	−1.32775	+	11.2355i	−0.0524841	+	0.444123i
$641$		−	3.83398i		−	0.151433i	−0.997129	−	0.0757165i	$-0.975876\pi$
$641$		−	3.83398i		−	0.151433i	0.997129	−	0.0757165i	$-0.0241244\pi$
$642$	6.85543	−	9.20378i	0.270562	−	0.363244i
$643$	−1.27757	−	1.27757i	−0.0503826	−	0.0503826i	0.681467	−	0.731849i	$-0.261342\pi$
$643$	−1.27757	−	1.27757i	−0.0503826	−	0.0503826i	−0.731849	+	0.681467i	$0.761342\pi$
$644$	52.8305	+	1.77621i	2.08181	+	0.0699925i
$645$	−2.98289	+	4.14841i	−0.117451	+	0.163344i
$646$	−5.05490	−	0.0849513i	−0.198882	−	0.00334237i
$647$			12.3417i			0.485201i	0.970126	+	0.242600i	$0.0780004\pi$
$647$			12.3417i			0.485201i	−0.970126	+	0.242600i	$0.922000\pi$
$648$	−4.75227	+	25.0083i	−0.186687	+	0.982420i
$649$		−	30.1876i		−	1.18497i
$650$	−0.0554748	+	3.30094i	−0.00217590	+	0.129474i
$651$	−11.7825	+	16.3863i	−0.461792	+	0.642231i
$652$	−17.4066	+	16.2742i	−0.681694	+	0.637347i
$653$	−17.7323	−	17.7323i	−0.693919	−	0.693919i	0.269173	−	0.963092i	$-0.413250\pi$
$653$	−17.7323	−	17.7323i	−0.693919	−	0.693919i	−0.963092	+	0.269173i	$0.913250\pi$
$654$	−14.0297	−	10.4500i	−0.548604	−	0.408627i
$655$		−	12.8848i		−	0.503449i
$656$	0.735652	+	0.0495227i	0.0287224	+	0.00193353i
$657$	11.3787	−	3.82149i	0.443925	−	0.149091i
$658$	14.3424	+	14.8327i	0.559125	+	0.578239i
$659$	12.7018	−	12.7018i	0.494794	−	0.494794i	−0.415019	−	0.909813i	$-0.636225\pi$
$659$	12.7018	−	12.7018i	0.494794	−	0.494794i	0.909813	+	0.415019i	$0.136225\pi$
$660$	−8.83538	+	11.4550i	−0.343917	+	0.445886i
$661$	−16.6430	−	16.6430i	−0.647336	−	0.647336i	0.305012	−	0.952348i	$-0.401339\pi$
$661$	−16.6430	−	16.6430i	−0.647336	−	0.647336i	−0.952348	+	0.305012i	$0.901339\pi$
$662$	43.1180	+	0.724629i	1.67583	+	0.0281635i
$663$	−0.649921	−	3.97656i	−0.0252409	−	0.154437i
$664$	−1.94856	+	38.6196i	−0.0756189	+	1.49873i
$665$	−16.2800			−0.631312
$666$	−24.8253	+	7.87585i	−0.961961	+	0.305183i
$667$	41.8353	−	41.8353i	1.61987	−	1.61987i
$668$	−25.5984	−	0.860643i	−0.990432	−	0.0332993i
$669$	−18.6596	+	25.9505i	−0.721420	+	1.00331i
$670$	−9.52371	−	9.84929i	−0.367933	−	0.380511i
$671$	45.7925			1.76780
$672$	−3.46408	−	44.3299i	−0.133630	−	1.71006i
$673$	50.0697			1.93004			0.965022	−	0.262169i	$-0.0844379\pi$
$673$	50.0697			1.93004			0.965022	+	0.262169i	$0.0844379\pi$
$674$	21.7617	+	22.5057i	0.838230	+	0.866886i
$675$	−4.96502	−	1.53250i	−0.191104	−	0.0589859i
$676$	−15.0922	−	0.507413i	−0.580468	−	0.0195159i
$677$	−13.1312	+	13.1312i	−0.504673	+	0.504673i	−0.912887	−	0.408213i	$-0.866152\pi$
$677$	−13.1312	+	13.1312i	−0.504673	+	0.504673i	0.408213	+	0.912887i	$0.366152\pi$
$678$	−8.82313	+	1.29021i	−0.338850	+	0.0495503i
$679$	29.2345			1.12192
$680$	2.81501	+	0.142032i	0.107951	+	0.00544668i
$681$	6.42160	−	1.04953i	0.246076	−	0.0402182i
$682$	15.1622	+	0.254812i	0.580592	+	0.00975727i
$683$	17.3816	+	17.3816i	0.665088	+	0.665088i	0.956575	−	0.291487i	$-0.0941500\pi$
$683$	17.3816	+	17.3816i	0.665088	+	0.665088i	−0.291487	+	0.956575i	$0.594150\pi$
$684$	18.9405	+	10.2245i	0.724208	+	0.390943i
$685$	10.8357	−	10.8357i	0.414011	−	0.414011i
$686$	−29.4230	−	30.4289i	−1.12338	−	1.16178i
$687$	−4.26733	−	26.1098i	−0.162809	−	0.996151i
$688$	−8.88535	+	7.76452i	−0.338751	+	0.296019i
$689$		−	11.6497i		−	0.443819i
$690$	8.52165	−	11.4408i	0.324414	−	0.435543i
$691$	−27.8125	−	27.8125i	−1.05804	−	1.05804i	−0.998209	−	0.0598304i	$-0.980944\pi$
$691$	−27.8125	−	27.8125i	−1.05804	−	1.05804i	−0.0598304	−	0.998209i	$-0.519056\pi$
$692$	−11.1239	+	10.4003i	−0.422869	+	0.395359i
$693$	25.3119	−	50.9112i	0.961520	−	1.93396i
$694$	−0.237260	+	14.1178i	−0.00900626	+	0.535904i
$695$		−	2.55324i		−	0.0968499i
$696$	−38.8910	−	31.0532i	−1.47416	−	1.17707i
$697$		−	0.183688i		−	0.00695769i
$698$	−9.36697	−	0.157419i	−0.354545	−	0.00595839i
$699$	33.3041	+	23.9471i	1.25968	+	0.905761i
$700$	9.07126	+	0.304984i	0.342861	+	0.0115273i
$701$	−3.23625	−	3.23625i	−0.122231	−	0.122231i	0.643345	−	0.765576i	$-0.277546\pi$
$701$	−3.23625	−	3.23625i	−0.122231	−	0.122231i	−0.765576	+	0.643345i	$0.777546\pi$
$702$	−5.33412	+	16.3043i	−0.201323	+	0.615364i
$703$			22.0219i			0.830571i
$704$	−25.8817	+	21.1260i	−0.975452	+	0.796216i
$705$	5.49537	−	0.898153i	0.206968	−	0.0338264i
$706$	−27.0969	+	26.2012i	−1.01981	+	0.986095i
$707$	14.4763	−	14.4763i	0.544439	−	0.544439i
$708$	24.8344	−	3.20631i	0.933335	−	0.120501i
$709$	−31.9710	−	31.9710i	−1.20069	−	1.20069i	−0.973956	−	0.226739i	$-0.927194\pi$
$709$	−31.9710	−	31.9710i	−1.20069	−	1.20069i	−0.226739	−	0.973956i	$-0.572806\pi$
$710$	0.270916	−	16.1204i	0.0101673	−	0.604989i
$711$	−7.92471	+	2.66149i	−0.297200	+	0.0998137i
$712$	−0.251957	+	0.227753i	−0.00944247	+	0.00853539i
$713$	−14.9538			−0.560024
$714$	−10.9610	+	1.60284i	−0.410206	+	0.0599847i
$715$	−6.89357	+	6.89357i	−0.257805	+	0.257805i
$716$	−34.5382	−	36.9414i	−1.29075	−	1.38056i
$717$	−34.4708	−	24.7860i	−1.28733	−	0.925649i
$718$	−16.7296	+	16.1766i	−0.624345	+	0.603707i
$719$	−38.3720			−1.43103			−0.715516	−	0.698596i	$-0.753809\pi$
$719$	−38.3720			−1.43103			−0.715516	+	0.698596i	$0.753809\pi$
$720$	−10.3621	−	6.05194i	−0.386174	−	0.225542i
$721$	−11.2867			−0.420340
$722$	−6.23318	+	6.02714i	−0.231975	+	0.224307i
$723$	−16.0636	−	11.5504i	−0.597411	−	0.429564i
$724$	2.88702	−	2.69920i	0.107295	−	0.100315i
$725$	7.18333	−	7.18333i	0.266782	−	0.266782i
$726$	−15.6090	+	2.28252i	−0.579305	+	0.0847121i
$727$	−16.1634			−0.599467			−0.299733	−	0.954023i	$-0.596898\pi$
$727$	−16.1634			−0.599467			−0.299733	+	0.954023i	$0.596898\pi$
$728$	1.50996	−	29.9268i	0.0559629	−	1.10916i
$729$	−22.3029	−	15.2178i	−0.826033	−	0.563621i
$730$	−0.0950799	+	5.65759i	−0.00351907	+	0.209397i
$731$	2.07869	+	2.07869i	0.0768831	+	0.0768831i
$732$	4.86376	+	37.6722i	0.179770	+	1.39240i
$733$	21.5127	−	21.5127i	0.794589	−	0.794589i	−0.187648	−	0.982236i	$-0.560086\pi$
$733$	21.5127	−	21.5127i	0.794589	−	0.794589i	0.982236	+	0.187648i	$0.0600863\pi$
$734$	−15.1053	+	14.6059i	−0.557546	+	0.539115i
$735$	−23.2392	+	3.79817i	−0.857191	+	0.140098i
$736$	25.1686	−	21.2586i	0.927727	−	0.783601i
$737$		−	40.4579i		−	1.49029i
$738$	−0.359876	+	0.694320i	−0.0132472	+	0.0255583i
$739$	−0.450522	−	0.450522i	−0.0165727	−	0.0165727i	0.698772	−	0.715345i	$-0.253730\pi$
$739$	−0.450522	−	0.450522i	−0.0165727	−	0.0165727i	−0.715345	+	0.698772i	$0.753730\pi$
$740$	0.412551	−	12.2706i	0.0151657	−	0.451078i
$741$	11.7766	+	8.46790i	0.432625	+	0.311076i
$742$	−32.0234	−	0.538177i	−1.17562	−	0.0197571i
$743$		−	24.6877i		−	0.905705i	−0.891586	−	0.452852i	$-0.850406\pi$
$743$		−	24.6877i		−	0.905705i	0.891586	−	0.452852i	$-0.149594\pi$
$744$	1.40080	+	12.5006i	0.0513558	+	0.458294i
$745$		−	4.28104i		−	0.156845i
$746$	0.248100	−	14.7628i	0.00908357	−	0.540504i
$747$	−36.7258	−	18.2592i	−1.34373	−	0.668070i
$748$	5.68433	+	6.07985i	0.207840	+	0.222301i
$749$	−15.0347	−	15.0347i	−0.549357	−	0.549357i
$750$	1.46321	−	1.96444i	0.0534289	−	0.0717311i
$751$			27.5362i			1.00481i	0.864633	+	0.502405i	$0.167551\pi$
$751$			27.5362i			1.00481i	−0.864633	+	0.502405i	$0.832449\pi$
$752$	12.8304	+	0.863715i	0.467875	+	0.0314964i
$753$	4.20726	+	25.7422i	0.153321	+	0.938099i
$754$	−23.3133	−	24.1103i	−0.849019	−	0.878044i
$755$	−2.68337	+	2.68337i	−0.0976578	+	0.0976578i
$756$	44.5716	+	15.4159i	1.62105	+	0.560672i
$757$	−11.7825	−	11.7825i	−0.428240	−	0.428240i	0.459788	−	0.888029i	$-0.347925\pi$
$757$	−11.7825	−	11.7825i	−0.428240	−	0.428240i	−0.888029	+	0.459788i	$0.847925\pi$
$758$	46.8730	+	0.787735i	1.70250	+	0.0286118i
$759$	41.5746	−	6.79487i	1.50906	−	0.246638i
$760$	−7.52709	+	6.80402i	−0.273036	+	0.246808i
$761$	36.4550			1.32149			0.660747	−	0.750609i	$-0.270240\pi$
$761$	36.4550			1.32149			0.660747	+	0.750609i	$0.270240\pi$
$762$	−27.9665	+	4.08955i	−1.01312	+	0.148149i
$763$	−22.9180	+	22.9180i	−0.829688	+	0.829688i
$764$	−0.223552	+	6.64919i	−0.00808783	+	0.240559i
$765$	−1.33093	+	2.67697i	−0.0481198	+	0.0967859i
$766$	23.5231	+	24.3272i	0.849923	+	0.878978i
$767$	16.8748			0.609313
$768$	−20.1287	−	19.0482i	−0.726332	−	0.687344i
$769$	−7.98721			−0.288026			−0.144013	−	0.989576i	$-0.546001\pi$
$769$	−7.98721			−0.288026			−0.144013	+	0.989576i	$0.546001\pi$
$770$	18.6310	+	19.2679i	0.671414	+	0.694367i
$771$	−8.33453	+	11.5911i	−0.300161	+	0.417445i
$772$	0.494473	−	14.7073i	0.0177965	−	0.529327i
$773$	−4.69086	+	4.69086i	−0.168719	+	0.168719i	−0.786416	−	0.617697i	$-0.788066\pi$
$773$	−4.69086	+	4.69086i	−0.168719	+	0.168719i	0.617697	+	0.786416i	$0.288066\pi$
$774$	−3.78471	−	11.9297i	−0.136038	−	0.428804i
$775$	−2.56764			−0.0922324
$776$	13.5166	−	12.2182i	0.485218	−	0.438606i
$777$	7.78314	+	47.6214i	0.279218	+	1.70841i
$778$	−4.01694	−	0.0675077i	−0.144014	−	0.00242027i
$779$	0.467575	+	0.467575i	0.0167526	+	0.0167526i
$780$	−6.40333	−	4.93895i	−0.229276	−	0.176843i
$781$	33.6654	−	33.6654i	1.20464	−	1.20464i
$782$	−5.70535	−	5.90039i	−0.204023	−	0.210998i
$783$	46.6738	−	24.6570i	1.66799	−	0.881168i
$784$	−54.2579	−	3.65254i	−1.93778	−	0.130448i
$785$		−	1.11277i		−	0.0397166i
$786$	25.3113	+	18.8531i	0.902824	+	0.672468i
$787$	0.865648	+	0.865648i	0.0308570	+	0.0308570i	0.722367	−	0.691510i	$-0.243054\pi$
$787$	0.865648	+	0.865648i	0.0308570	+	0.0308570i	−0.691510	+	0.722367i	$0.743054\pi$
$788$	−23.7125	−	25.3624i	−0.844723	−	0.903499i
$789$	−9.28909	+	12.9187i	−0.330700	+	0.459917i
$790$	0.0662187	−	3.94024i	0.00235596	−	0.140188i
$791$			16.5205i			0.587403i
$792$	−9.57466	−	34.1177i	−0.340221	−	1.21232i
$793$			25.5979i			0.909008i
$794$	19.4381	+	0.326671i	0.689831	+	0.0115931i
$795$	−5.04604	+	7.01771i	−0.178965	+	0.248893i
$796$	1.71379	−	50.9740i	0.0607438	−	1.80672i
$797$	11.7478	+	11.7478i	0.416130	+	0.416130i	0.883867	−	0.467737i	$-0.154931\pi$
$797$	11.7478	+	11.7478i	0.416130	+	0.416130i	−0.467737	+	0.883867i	$0.654931\pi$
$798$	23.8211	−	31.9811i	0.843257	−	1.13212i
$799$		−	3.20367i		−	0.113338i
$800$	4.32158	−	3.65020i	0.152791	−	0.129054i
$801$	−0.114690	−	0.341495i	−0.00405237	−	0.0120661i
$802$	−6.05720	+	5.85697i	−0.213887	+	0.206817i
$803$	−11.8151	+	11.8151i	−0.416946	+	0.416946i
$804$	33.2835	−	4.29715i	1.17382	−	0.151549i
$805$	−18.6889	−	18.6889i	−0.658699	−	0.658699i
$806$	−0.142439	+	8.47564i	−0.00501721	+	0.298542i
$807$	7.98755	+	48.8720i	0.281175	+	1.72038i
$808$	0.642968	−	12.7434i	0.0226195	−	0.448310i
$809$	−17.1344			−0.602413			−0.301206	−	0.953559i	$-0.597389\pi$
$809$	−17.1344			−0.602413			−0.301206	+	0.953559i	$0.597389\pi$
$810$	10.2754	−	7.51111i	0.361040	−	0.263914i
$811$	27.9871	−	27.9871i	0.982762	−	0.982762i	−0.0170924	−	0.999854i	$-0.505441\pi$
$811$	27.9871	−	27.9871i	0.982762	−	0.982762i	0.999854	+	0.0170924i	$0.00544095\pi$
$812$	−67.3526	+	62.9710i	−2.36361	+	2.20985i
$813$	4.62176	−	6.42766i	0.162092	−	0.225428i
$814$	26.0636	−	25.2020i	0.913528	−	0.883331i
$815$	11.9147			0.417353
$816$	−4.39797	+	5.32209i	−0.153960	+	0.186310i
$817$	−10.5825			−0.370236
$818$	23.8098	−	23.0228i	0.832491	−	0.804972i
$819$	28.4592	+	14.1493i	0.994446	+	0.494416i
$820$	−0.251774	−	0.269293i	−0.00879234	−	0.00940413i
$821$	14.6930	−	14.6930i	0.512789	−	0.512789i	−0.402591	−	0.915380i	$-0.631890\pi$
$821$	14.6930	−	14.6930i	0.512789	−	0.512789i	0.915380	+	0.402591i	$0.131890\pi$
$822$	5.43114	+	37.1410i	0.189433	+	1.29544i
$823$	−5.78654			−0.201706			−0.100853	−	0.994901i	$-0.532157\pi$
$823$	−5.78654			−0.201706			−0.100853	+	0.994901i	$0.532157\pi$
$824$	−5.21844	+	4.71714i	−0.181793	+	0.164329i
$825$	7.13857	−	1.16671i	0.248533	−	0.0406197i
$826$	0.779556	−	46.3863i	0.0271242	−	1.61399i
$827$	10.2958	+	10.2958i	0.358019	+	0.358019i	0.863082	−	0.505064i	$-0.168531\pi$
$827$	10.2958	+	10.2958i	0.358019	+	0.358019i	−0.505064	+	0.863082i	$0.668531\pi$
$828$	10.0057	+	33.4805i	0.347722	+	1.16353i
$829$	14.4304	−	14.4304i	0.501189	−	0.501189i	−0.410619	−	0.911807i	$-0.634687\pi$
$829$	14.4304	−	14.4304i	0.501189	−	0.501189i	0.911807	+	0.410619i	$0.134687\pi$
$830$	13.8993	−	13.4398i	0.482451	−	0.466503i
$831$	4.65279	+	28.4682i	0.161404	+	0.987552i
$832$	−11.8094	−	14.4678i	−0.409416	−	0.501580i
$833$			13.5479i			0.469407i
$834$	5.01568	+	3.73593i	0.173679	+	0.129365i
$835$	9.05552	+	9.05552i	0.313379	+	0.313379i
$836$	−29.9455	−	1.00680i	−1.03569	−	0.0348208i
$837$	−12.7484	−	3.93490i	−0.440649	−	0.136010i
$838$	−13.6380	−	0.229196i	−0.471116	−	0.00791745i
$839$			32.1643i			1.11043i	0.831705	+	0.555217i	$0.187365\pi$
$839$			32.1643i			1.11043i	−0.831705	+	0.555217i	$0.812635\pi$
$840$	−13.8723	+	17.3737i	−0.478639	+	0.599448i
$841$			74.2004i			2.55863i
$842$	−0.0593399	+	3.53093i	−0.00204499	+	0.121684i
$843$	−22.2479	−	15.9972i	−0.766258	−	0.550972i
$844$	−37.9955	+	35.5237i	−1.30786	+	1.22278i
$845$	5.33890	+	5.33890i	0.183664	+	0.183664i
$846$	−6.27653	+	12.1095i	−0.215791	+	0.416333i
$847$			29.2265i			1.00424i
$848$	−15.0310	+	13.1349i	−0.516167	+	0.451055i
$849$	18.7519	−	3.06477i	0.643564	−	0.105183i
$850$	−0.979637	−	1.01313i	−0.0336013	−	0.0347500i
$851$	−25.2804	+	25.2804i	−0.866602	+	0.866602i
$852$	31.2712	+	24.1198i	1.07133	+	0.826331i
$853$	−9.48972	−	9.48972i	−0.324922	−	0.324922i	0.525730	−	0.850652i	$-0.323792\pi$
$853$	−9.48972	−	9.48972i	−0.324922	−	0.324922i	−0.850652	+	0.525730i	$0.823792\pi$
$854$	70.3649	+	1.18253i	2.40784	+	0.0404655i
$855$	−3.42632	−	10.2020i	−0.117178	−	0.348902i
$856$	−13.2349	−	0.667770i	−0.452360	−	0.0228239i
$857$	−40.7849			−1.39318			−0.696592	−	0.717467i	$-0.745301\pi$
$857$	−40.7849			−1.39318			−0.696592	+	0.717467i	$0.745301\pi$
$858$	−3.45524	−	23.6287i	−0.117960	−	0.806672i
$859$	17.0728	−	17.0728i	0.582515	−	0.582515i	−0.353079	−	0.935594i	$-0.614865\pi$
$859$	17.0728	−	17.0728i	0.582515	−	0.582515i	0.935594	+	0.353079i	$0.114865\pi$
$860$	5.89661	+	0.198250i	0.201073	+	0.00676026i
$861$	1.17636	+	0.845857i	0.0400904	+	0.0288267i
$862$	5.00596	+	5.17709i	0.170504	+	0.176332i
$863$	−9.27301			−0.315657			−0.157828	−	0.987467i	$-0.550449\pi$
$863$	−9.27301			−0.315657			−0.157828	+	0.987467i	$0.550449\pi$
$864$	27.0507	−	11.5005i	0.920282	−	0.391256i
$865$	7.61426			0.258893
$866$	20.0948	+	20.7817i	0.682848	+	0.706191i
$867$	−22.5099	−	16.1856i	−0.764475	−	0.549691i
$868$	23.2917	+	0.783091i	0.790573	+	0.0265798i
$869$	8.22866	−	8.22866i	0.279138	−	0.279138i
$870$	3.60048	+	24.6219i	0.122068	+	0.834761i
$871$	22.6158			0.766309
$872$	−1.01791	+	20.1745i	−0.0344707	+	0.683194i
$873$	6.15273	+	18.3200i	0.208238	+	0.620039i
$874$	29.5422	+	0.496478i	0.999279	+	0.0167936i
$875$	−3.20899	−	3.20899i	−0.108484	−	0.108484i
$876$	−10.9749	−	8.46502i	−0.370806	−	0.286007i
$877$	−12.4222	+	12.4222i	−0.419467	+	0.419467i	−0.885020	−	0.465553i	$-0.845855\pi$
$877$	−12.4222	+	12.4222i	−0.419467	+	0.419467i	0.465553	+	0.885020i	$0.345855\pi$
$878$	3.02432	+	3.12771i	0.102066	+	0.105555i
$879$	−29.8748	+	4.88268i	−1.00765	+	0.164689i
$880$	16.6668	+	1.12198i	0.561839	+	0.0378219i
$881$			15.4799i			0.521530i	0.965402	+	0.260765i	$0.0839747\pi$
$881$			15.4799i			0.521530i	−0.965402	+	0.260765i	$0.916025\pi$
$882$	26.5426	−	51.2095i	0.893736	−	1.72431i
$883$	−24.5840	−	24.5840i	−0.827318	−	0.827318i	0.159827	−	0.987145i	$-0.448906\pi$
$883$	−24.5840	−	24.5840i	−0.827318	−	0.827318i	−0.987145	+	0.159827i	$0.948906\pi$
$884$	−3.39862	+	3.17752i	−0.114308	+	0.106872i
$885$	−10.1652	−	7.30925i	−0.341701	−	0.245698i
$886$	−0.188761	+	11.2320i	−0.00634156	+	0.377345i
$887$		−	22.3287i		−	0.749726i	−0.927080	−	0.374863i	$-0.877690\pi$
$887$		−	22.3287i		−	0.749726i	0.927080	−	0.374863i	$-0.122310\pi$
$888$	23.5013	+	18.7650i	0.788651	+	0.629711i
$889$			52.3648i			1.75626i
$890$	0.169795	+	0.00285352i	0.00569153	+	9.56503e-5i
$891$	37.2311	+	5.14708i	1.24729	+	0.172434i
$892$	36.8864	+	1.24016i	1.23505	+	0.0415235i
$893$	8.15489	+	8.15489i	0.272893	+	0.272893i
$894$	8.40984	+	6.26407i	0.281267	+	0.209502i
$895$			25.2861i			0.845222i
$896$	−40.3154	+	31.7939i	−1.34684	+	1.06216i
$897$	3.79831	+	23.2401i	0.126822	+	0.775964i
$898$	11.2516	−	10.8797i	0.375471	−	0.363059i
$899$	18.4442	−	18.4442i	0.615149	−	0.615149i
$900$	1.71803	+	5.74877i	0.0572676	+	0.191626i
$901$	3.51644	+	3.51644i	0.117150	+	0.117150i
$902$	0.0182928	−	1.08849i	0.000609084	−	0.0362426i
$903$	−22.8843	+	3.74015i	−0.761540	+	0.124465i
$904$	6.90454	+	7.63830i	0.229642	+	0.254046i
$905$	−1.97614			−0.0656892
$906$	−1.34498	−	9.19764i	−0.0446838	−	0.305571i
$907$	−0.368071	+	0.368071i	−0.0122216	+	0.0122216i	−0.713191	−	0.700970i	$-0.752751\pi$
$907$	−0.368071	+	0.368071i	−0.0122216	+	0.0122216i	0.700970	+	0.713191i	$0.252751\pi$
$908$	−5.13126	−	5.48830i	−0.170287	−	0.182136i
$909$	12.1184	+	6.02501i	0.401943	+	0.199837i
$910$	−10.7707	+	10.4147i	−0.357045	+	0.345243i
$911$	−46.5893			−1.54357			−0.771787	−	0.635881i	$-0.780637\pi$
$911$	−46.5893			−1.54357			−0.771787	+	0.635881i	$0.780637\pi$
$912$	−2.35234	−	24.7422i	−0.0778937	−	0.819297i
$913$	57.0940			1.88953
$914$	−8.13518	+	7.86626i	−0.269088	+	0.260193i
$915$	11.0876	−	15.4200i	0.366546	−	0.509769i
$916$	−22.3151	+	20.8634i	−0.737310	+	0.689345i
$917$	41.3470	−	41.3470i	1.36540	−	1.36540i
$918$	−3.31131	−	6.53149i	−0.109289	−	0.215571i
$919$	−27.3662			−0.902727			−0.451364	−	0.892340i	$-0.649062\pi$
$919$	−27.3662			−0.902727			−0.451364	+	0.892340i	$0.649062\pi$
$920$	−16.4517	−	0.830072i	−0.542395	−	0.0273667i
$921$	−3.20280	−	19.5964i	−0.105536	−	0.645725i
$922$	−0.446106	+	26.5449i	−0.0146917	+	0.874210i
$923$	18.8188	+	18.8188i	0.619430	+	0.619430i
$924$	−65.1116	+	8.40640i	−2.14202	+	0.276550i
$925$	−4.34078	+	4.34078i	−0.142724	+	0.142724i
$926$	−7.29732	+	7.05610i	−0.239805	+	0.231878i
$927$	−2.37542	−	7.07293i	−0.0780191	−	0.232306i
$928$	−4.82271	+	57.2639i	−0.158313	+	1.87978i
$929$			36.2614i			1.18970i	0.803838	+	0.594848i	$0.202788\pi$
$929$			36.2614i			1.18970i	−0.803838	+	0.594848i	$0.797212\pi$
$930$	3.75700	−	5.04397i	0.123197	−	0.165398i
$931$	−34.4859	−	34.4859i	−1.13023	−	1.13023i
$932$	1.59158	−	47.3388i	0.0521338	−	1.55064i
$933$	7.49549	−	10.4243i	0.245391	−	0.341275i
$934$	−6.11787	−	0.102815i	−0.200183	−	0.00336422i
$935$		−	4.16162i		−	0.136099i
$936$	19.0717	−	5.35221i	0.623377	−	0.174942i
$937$		−	55.1658i		−	1.80219i	−0.433625	−	0.901093i	$-0.642766\pi$
$937$		−	55.1658i		−	1.80219i	0.433625	−	0.901093i	$-0.357234\pi$
$938$	1.04477	−	62.1677i	0.0341131	−	2.02985i
$939$	−13.6610	+	18.9988i	−0.445809	+	0.620003i
$940$	−4.39115	−	4.69669i	−0.143223	−	0.153189i
$941$	−33.6697	−	33.6697i	−1.09760	−	1.09760i	−0.994690	−	0.102912i	$-0.967184\pi$
$941$	−33.6697	−	33.6697i	−1.09760	−	1.09760i	−0.102912	−	0.994690i	$-0.532816\pi$
$942$	2.18598	+	1.62822i	0.0712229	+	0.0530504i
$943$			1.07352i			0.0349587i
$944$	−19.0261	−	21.7726i	−0.619247	−	0.708638i
$945$	−11.0149	−	20.8505i	−0.358316	−	0.678265i
$946$	12.1107	+	12.5248i	0.393754	+	0.407215i
$947$	−20.8503	+	20.8503i	−0.677542	+	0.677542i	−0.959443	−	0.281901i	$-0.909035\pi$
$947$	−20.8503	+	20.8503i	−0.677542	+	0.677542i	0.281901	+	0.959443i	$0.409035\pi$
$948$	7.64347	+	5.89549i	0.248248	+	0.191477i
$949$	−6.60461	−	6.60461i	−0.214395	−	0.214395i
$950$	5.07254	+	0.0852478i	0.164575	+	0.00276580i
$951$	−1.67037	−	10.2202i	−0.0541653	−	0.331412i
$952$	8.57755	+	9.48911i	0.278000	+	0.307544i
$953$	58.5221			1.89572			0.947858	−	0.318694i	$-0.103244\pi$
$953$	58.5221			1.89572			0.947858	+	0.318694i	$0.103244\pi$
$954$	−6.40244	−	20.1810i	−0.207287	−	0.653385i
$955$	2.35217	−	2.35217i	0.0761145	−	0.0761145i
$956$	−1.64733	+	48.9972i	−0.0532785	+	1.58468i
$957$	−42.8978	+	59.6595i	−1.38669	+	1.92852i
$958$	−3.62303	−	3.74689i	−0.117055	−	0.121056i
$959$	69.5432			2.24567
$960$	0.847215	+	13.8305i	0.0273438	+	0.446377i
$961$	24.4072			0.787330
$962$	14.0879	+	14.5695i	0.454211	+	0.469739i
$963$	6.25742	−	12.5859i	0.201642	−	0.405574i
$964$	−0.767666	+	22.8330i	−0.0247249	+	0.735401i
$965$	−5.20275	+	5.20275i	−0.167482	+	0.167482i
$966$	64.0591	−	9.36740i	2.06107	−	0.301391i
$967$	31.1740			1.00249			0.501245	−	0.865306i	$-0.332876\pi$
$967$	31.1740			1.00249			0.501245	+	0.865306i	$0.332876\pi$
$968$	12.2148	+	13.5129i	0.392600	+	0.434322i
$969$	−6.11076	+	0.998730i	−0.196306	+	0.0320838i
$970$	−9.10890	−	0.153082i	−0.292469	−	0.00491516i
$971$	6.14097	+	6.14097i	0.197073	+	0.197073i	0.798744	−	0.601671i	$-0.205498\pi$
$971$	6.14097	+	6.14097i	0.197073	+	0.197073i	−0.601671	+	0.798744i	$0.705498\pi$
$972$	−0.279923	+	31.1757i	−0.00897854	+	0.999960i
$973$	8.19331	−	8.19331i	0.262665	−	0.262665i
$974$	−15.7805	−	16.3200i	−0.505640	−	0.522925i
$975$	0.652189	+	3.99044i	0.0208868	+	0.127796i
$976$	33.0276	−	28.8613i	1.05719	−	0.923829i
$977$		−	49.0247i		−	1.56844i	−0.620484	−	0.784219i	$-0.713064\pi$
$977$		−	49.0247i		−	1.56844i	0.620484	−	0.784219i	$-0.286936\pi$
$978$	−17.4337	+	23.4057i	−0.557468	+	0.748430i
$979$	0.354593	+	0.354593i	0.0113328	+	0.0113328i
$980$	18.5696	+	19.8617i	0.593184	+	0.634458i
$981$	−19.1851	−	9.53842i	−0.612534	−	0.304538i
$982$	−0.304908	+	18.1431i	−0.00973000	+	0.578969i
$983$			45.4654i			1.45012i	0.688685	+	0.725061i	$0.258188\pi$
$983$			45.4654i			1.45012i	−0.688685	+	0.725061i	$0.741812\pi$
$984$	0.897409	−	0.100562i	0.0286083	−	0.00320581i
$985$			17.3604i			0.553149i
$986$	14.3147	+	0.240569i	0.455872	+	0.00766126i
$987$	20.5167	+	14.7524i	0.653055	+	0.469575i
$988$	0.562796	−	16.7394i	0.0179049	−	0.532553i
$989$	−12.1484	−	12.1484i	−0.386297	−	0.386297i
$990$	−8.15330	+	15.7304i	−0.259129	+	0.499946i
$991$		−	21.9826i		−	0.698301i	−0.937067	−	0.349151i	$-0.886470\pi$
$991$		−	21.9826i		−	0.698301i	0.937067	−	0.349151i	$-0.113530\pi$
$992$	11.0963	−	9.37241i	0.352307	−	0.297574i
$993$	52.1244	−	8.51910i	1.65412	−	0.270346i
$994$	52.5996	−	50.8609i	1.66836	−	1.61321i
$995$	−18.0322	+	18.0322i	−0.571659	+	0.571659i
$996$	6.06412	+	46.9695i	0.192149	+	1.48829i
$997$	−37.0366	−	37.0366i	−1.17296	−	1.17296i	−0.981500	−	0.191461i	$-0.938677\pi$
$997$	−37.0366	−	37.0366i	−1.17296	−	1.17296i	−0.191461	−	0.981500i	$-0.561323\pi$
$998$	0.613159	−	36.4851i	0.0194092	−	1.15492i
$999$	−28.2043	+	14.8998i	−0.892344	+	0.471410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.11.9	✓	60
3.2	odd	2	inner	240.2.bk.b.11.22	yes	60
4.3	odd	2		960.2.bk.b.911.24		60
12.11	even	2		960.2.bk.b.911.22		60
16.3	odd	4	inner	240.2.bk.b.131.22	yes	60
16.13	even	4		960.2.bk.b.431.22		60
48.29	odd	4		960.2.bk.b.431.24		60
48.35	even	4	inner	240.2.bk.b.131.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.9	✓	60	1.1	even	1	trivial
240.2.bk.b.11.22	yes	60	3.2	odd	2	inner
240.2.bk.b.131.9	yes	60	48.35	even	4	inner
240.2.bk.b.131.22	yes	60	16.3	odd	4	inner
960.2.bk.b.431.22		60	16.13	even	4
960.2.bk.b.431.24		60	48.29	odd	4
960.2.bk.b.911.22		60	12.11	even	2
960.2.bk.b.911.24		60	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.983055 - 1.01666i) q^{2} +(-1.40626 - 1.01116i) q^{3} +(-0.0672039 + 1.99887i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.354421 + 2.42371i) q^{6} +4.53819 q^{7} +(2.09824 - 1.89668i) q^{8} +(0.955115 + 2.84390i) q^{9} +O(q^{10})\)	\(q+(-0.983055 - 1.01666i) q^{2} +(-1.40626 - 1.01116i) q^{3} +(-0.0672039 + 1.99887i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.354421 + 2.42371i) q^{6} +4.53819 q^{7} +(2.09824 - 1.89668i) q^{8} +(0.955115 + 2.84390i) q^{9} +(-1.41401 - 0.0237635i) q^{10} +(-2.95298 - 2.95298i) q^{11} +(2.11568 - 2.74297i) q^{12} +(1.65071 - 1.65071i) q^{13} +(-4.46129 - 4.61381i) q^{14} +(-1.70937 + 0.279376i) q^{15} +(-3.99097 - 0.268664i) q^{16} +0.996523i q^{17} +(1.95235 - 3.76674i) q^{18} +(-2.53663 - 2.53663i) q^{19} +(1.36589 + 1.46094i) q^{20} +(-6.38186 - 4.58883i) q^{21} +(-0.0992398 + 5.90512i) q^{22} -5.82394i q^{23} +(-4.86851 + 0.545558i) q^{24} -1.00000i q^{25} +(-3.30094 - 0.0554748i) q^{26} +(1.53250 - 4.96502i) q^{27} +(-0.304984 + 9.07126i) q^{28} +(7.18333 + 7.18333i) q^{29} +(1.96444 + 1.46321i) q^{30} -2.56764i q^{31} +(3.65020 + 4.32158i) q^{32} +(1.16671 + 7.13857i) q^{33} +(1.01313 - 0.979637i) q^{34} +(3.20899 - 3.20899i) q^{35} +(-5.74877 + 1.71803i) q^{36} +(-4.34078 - 4.34078i) q^{37} +(-0.0852478 + 5.07254i) q^{38} +(-3.99044 + 0.652189i) q^{39} +(0.142528 - 2.82483i) q^{40} -0.184329 q^{41} +(1.60843 + 10.9993i) q^{42} +(2.08594 - 2.08594i) q^{43} +(6.10107 - 5.70416i) q^{44} +(2.68631 + 1.33557i) q^{45} +(-5.92098 + 5.72526i) q^{46} -3.21485 q^{47} +(5.34066 + 4.41331i) q^{48} +13.5952 q^{49} +(-1.01666 + 0.983055i) q^{50} +(1.00764 - 1.40137i) q^{51} +(3.18861 + 3.41048i) q^{52} +(3.52871 - 3.52871i) q^{53} +(-6.55428 + 3.32286i) q^{54} -4.17614 q^{55} +(9.52222 - 8.60748i) q^{56} +(1.00222 + 6.13209i) q^{57} +(0.241408 - 14.3646i) q^{58} +(5.11138 + 5.11138i) q^{59} +(-0.443560 - 3.43559i) q^{60} +(-7.75362 + 7.75362i) q^{61} +(-2.61042 + 2.52413i) q^{62} +(4.33449 + 12.9062i) q^{63} +(0.805233 - 7.95937i) q^{64} -2.33445i q^{65} +(6.11057 - 8.20376i) q^{66} +(6.85036 + 6.85036i) q^{67} +(-1.99192 - 0.0669703i) q^{68} +(-5.88893 + 8.18995i) q^{69} +(-6.41707 - 0.107843i) q^{70} +11.4005i q^{71} +(7.39802 + 4.15564i) q^{72} -4.00109i q^{73} +(-0.145879 + 8.68033i) q^{74} +(-1.01116 + 1.40626i) q^{75} +(5.24086 - 4.89992i) q^{76} +(-13.4012 - 13.4012i) q^{77} +(4.58588 + 3.41579i) q^{78} +2.78657i q^{79} +(-3.01201 + 2.63207i) q^{80} +(-7.17551 + 5.43250i) q^{81} +(0.181206 + 0.187401i) q^{82} +(-9.66719 + 9.66719i) q^{83} +(9.60137 - 12.4481i) q^{84} +(0.704648 + 0.704648i) q^{85} +(-4.17130 - 0.0701017i) q^{86} +(-2.83811 - 17.3651i) q^{87} +(-11.7969 - 0.595215i) q^{88} -0.120080 q^{89} +(-1.28296 - 4.04401i) q^{90} +(7.49122 - 7.49122i) q^{91} +(11.6413 + 0.391392i) q^{92} +(-2.59629 + 3.61076i) q^{93} +(3.16038 + 3.26842i) q^{94} -3.58733 q^{95} +(-0.763318 - 9.76818i) q^{96} +6.44188 q^{97} +(-13.3648 - 13.8217i) q^{98} +(5.57753 - 11.2184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more