LMFDB - Embedded newform 240.2.bb.a.173.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

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([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (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:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.10
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06890 - 0.925990i) q^{2} +(0.847085 + 1.51078i) q^{3} +(0.285084 + 1.97958i) q^{4} +(2.22651 + 0.206476i) q^{5} +(0.493518 - 2.39926i) q^{6} +(0.209149 + 0.209149i) q^{7} +(1.52834 - 2.37995i) q^{8} +(-1.56489 + 2.55951i) q^{9} +O(q^{10})$	\(q+(-1.06890 - 0.925990i) q^{2} +(0.847085 + 1.51078i) q^{3} +(0.285084 + 1.97958i) q^{4} +(2.22651 + 0.206476i) q^{5} +(0.493518 - 2.39926i) q^{6} +(0.209149 + 0.209149i) q^{7} +(1.52834 - 2.37995i) q^{8} +(-1.56489 + 2.55951i) q^{9} +(-2.18872 - 2.28243i) q^{10} +(-1.98621 - 1.98621i) q^{11} +(-2.74921 + 2.10757i) q^{12} +5.12987i q^{13} +(-0.0298889 - 0.417229i) q^{14} +(1.57411 + 3.53867i) q^{15} +(-3.83745 + 1.12869i) q^{16} +(3.10607 + 3.10607i) q^{17} +(4.04280 - 1.28678i) q^{18} +(3.67937 - 3.67937i) q^{19} +(0.226008 + 4.46642i) q^{20} +(-0.138810 + 0.493145i) q^{21} +(0.283843 + 3.96226i) q^{22} +(-2.11409 - 2.11409i) q^{23} +(4.89021 + 0.292966i) q^{24} +(4.91474 + 0.919443i) q^{25} +(4.75021 - 5.48331i) q^{26} +(-5.19245 - 0.196079i) q^{27} +(-0.354402 + 0.473652i) q^{28} +(-5.11906 - 5.11906i) q^{29} +(1.59421 - 5.24008i) q^{30} +2.71509 q^{31} +(5.14700 + 2.34699i) q^{32} +(1.31823 - 4.68320i) q^{33} +(-0.443880 - 6.19627i) q^{34} +(0.422489 + 0.508858i) q^{35} +(-5.51288 - 2.36815i) q^{36} +5.52487i q^{37} +(-7.33993 + 0.525809i) q^{38} +(-7.75009 + 4.34544i) q^{39} +(3.89428 - 4.98343i) q^{40} +5.15202 q^{41} +(0.605021 - 0.398584i) q^{42} +5.45696 q^{43} +(3.36561 - 4.49808i) q^{44} +(-4.01274 + 5.37568i) q^{45} +(0.302119 + 4.21738i) q^{46} +(-4.76275 - 4.76275i) q^{47} +(-4.95585 - 4.84144i) q^{48} -6.91251i q^{49} +(-4.40195 - 5.53379i) q^{50} +(-2.06148 + 7.32369i) q^{51} +(-10.1550 + 1.46244i) q^{52} -0.554732i q^{53} +(5.36863 + 5.01775i) q^{54} +(-4.01221 - 4.83242i) q^{55} +(0.817416 - 0.178113i) q^{56} +(8.67545 + 2.44197i) q^{57} +(0.731550 + 10.2119i) q^{58} +(-3.04667 + 3.04667i) q^{59} +(-6.55632 + 4.12489i) q^{60} +(-9.01463 - 9.01463i) q^{61} +(-2.90215 - 2.51414i) q^{62} +(-0.862616 + 0.208024i) q^{63} +(-3.32833 - 7.27477i) q^{64} +(-1.05920 + 11.4217i) q^{65} +(-5.74565 + 3.78519i) q^{66} -10.9329 q^{67} +(-5.26322 + 7.03420i) q^{68} +(1.40311 - 4.98474i) q^{69} +(0.0195996 - 0.935138i) q^{70} -7.59933 q^{71} +(3.69982 + 7.63619i) q^{72} +(4.26347 - 4.26347i) q^{73} +(5.11598 - 5.90552i) q^{74} +(2.77413 + 8.20392i) q^{75} +(8.33253 + 6.23467i) q^{76} -0.830826i q^{77} +(12.3079 + 2.53168i) q^{78} -12.6207i q^{79} +(-8.77720 + 1.72071i) q^{80} +(-4.10222 - 8.01073i) q^{81} +(-5.50699 - 4.77072i) q^{82} +6.66265 q^{83} +(-1.01579 - 0.134199i) q^{84} +(6.27439 + 7.55705i) q^{85} +(-5.83294 - 5.05310i) q^{86} +(3.39748 - 12.0700i) q^{87} +(-7.76268 + 1.69146i) q^{88} -5.00655i q^{89} +(9.26703 - 2.03030i) q^{90} +(-1.07291 + 1.07291i) q^{91} +(3.58232 - 4.78771i) q^{92} +(2.29991 + 4.10189i) q^{93} +(0.680631 + 9.50115i) q^{94} +(8.95188 - 7.43247i) q^{95} +(0.814170 + 9.76407i) q^{96} +(9.37084 - 9.37084i) q^{97} +(-6.40092 + 7.38877i) q^{98} +(8.19192 - 1.97552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.06890	−	0.925990i	−0.755825	−	0.654774i
$2$	−1.06890	−	0.925990i	−0.755825	−	0.654774i
$3$	0.847085	+	1.51078i	0.489065	+	0.872247i
$3$	0.847085	+	1.51078i	0.489065	+	0.872247i
$4$	0.285084	+	1.97958i	0.142542	+	0.989789i
$5$	2.22651	+	0.206476i	0.995728	+	0.0923388i
$5$	2.22651	+	0.206476i	0.995728	+	0.0923388i
$6$	0.493518	−	2.39926i	0.201478	−	0.979493i
$7$	0.209149	+	0.209149i	0.0790509	+	0.0790509i	0.745527	−	0.666476i	$-0.232198\pi$
$7$	0.209149	+	0.209149i	0.0790509	+	0.0790509i	−0.666476	+	0.745527i	$0.732198\pi$
$8$	1.52834	−	2.37995i	0.540351	−	0.841440i
$9$	−1.56489	+	2.55951i	−0.521631	+	0.853171i
$10$	−2.18872	−	2.28243i	−0.692134	−	0.721769i
$11$	−1.98621	−	1.98621i	−0.598863	−	0.598863i	0.341147	−	0.940010i	$-0.389185\pi$
$11$	−1.98621	−	1.98621i	−0.598863	−	0.598863i	−0.940010	+	0.341147i	$0.889185\pi$
$12$	−2.74921	+	2.10757i	−0.793628	+	0.608403i
$13$			5.12987i			1.42277i	0.702802	+	0.711385i	$0.251932\pi$
$13$			5.12987i			1.42277i	−0.702802	+	0.711385i	$0.748068\pi$
$14$	−0.0298889	−	0.417229i	−0.00798814	−	0.111509i
$15$	1.57411	+	3.53867i	0.406433	+	0.913681i
$16$	−3.83745	+	1.12869i	−0.959364	+	0.282173i
$17$	3.10607	+	3.10607i	0.753333	+	0.753333i	0.975100	−	0.221766i	$-0.0711822\pi$
$17$	3.10607	+	3.10607i	0.753333	+	0.753333i	−0.221766	+	0.975100i	$0.571182\pi$
$18$	4.04280	−	1.28678i	0.952896	−	0.303297i
$19$	3.67937	−	3.67937i	0.844106	−	0.844106i	−0.145284	−	0.989390i	$-0.546410\pi$
$19$	3.67937	−	3.67937i	0.844106	−	0.844106i	0.989390	+	0.145284i	$0.0464097\pi$
$20$	0.226008	+	4.46642i	0.0505370	+	0.998722i
$21$	−0.138810	+	0.493145i	−0.0302909	+	0.107613i
$22$	0.283843	+	3.96226i	0.0605155	+	0.844756i
$23$	−2.11409	−	2.11409i	−0.440819	−	0.440819i	0.451468	−	0.892287i	$-0.350900\pi$
$23$	−2.11409	−	2.11409i	−0.440819	−	0.440819i	−0.892287	+	0.451468i	$0.850900\pi$
$24$	4.89021	+	0.292966i	0.998210	+	0.0598015i
$25$	4.91474	+	0.919443i	0.982947	+	0.183889i
$26$	4.75021	−	5.48331i	0.931593	−	1.07537i
$27$	−5.19245	−	0.196079i	−0.999288	−	0.0377354i
$28$	−0.354402	+	0.473652i	−0.0669756	+	0.0895118i
$29$	−5.11906	−	5.11906i	−0.950585	−	0.950585i	0.0482501	−	0.998835i	$-0.484636\pi$
$29$	−5.11906	−	5.11906i	−0.950585	−	0.950585i	−0.998835	+	0.0482501i	$0.984636\pi$
$30$	1.59421	−	5.24008i	0.291062	−	0.956704i
$31$	2.71509			0.487644			0.243822	−	0.969820i	$-0.421599\pi$
$31$	2.71509			0.487644			0.243822	+	0.969820i	$0.421599\pi$
$32$	5.14700	+	2.34699i	0.909870	+	0.414893i
$33$	1.31823	−	4.68320i	0.229474	−	0.815240i
$34$	−0.443880	−	6.19627i	−0.0761248	−	1.06265i
$35$	0.422489	+	0.508858i	0.0714137	+	0.0860126i
$36$	−5.51288	−	2.36815i	−0.918813	−	0.394692i
$37$			5.52487i			0.908283i	0.890930	+	0.454142i	$0.150054\pi$
$37$			5.52487i			0.908283i	−0.890930	+	0.454142i	$0.849946\pi$
$38$	−7.33993	+	0.525809i	−1.19069	+	0.0852974i
$39$	−7.75009	+	4.34544i	−1.24101	+	0.695827i
$40$	3.89428	−	4.98343i	0.615740	−	0.787949i
$41$	5.15202			0.804611			0.402306	−	0.915505i	$-0.368209\pi$
$41$	5.15202			0.804611			0.402306	+	0.915505i	$0.368209\pi$
$42$	0.605021	−	0.398584i	0.0933568	−	0.0615028i
$43$	5.45696			0.832179			0.416090	−	0.909324i	$-0.363400\pi$
$43$	5.45696			0.832179			0.416090	+	0.909324i	$0.363400\pi$
$44$	3.36561	−	4.49808i	0.507385	−	0.678111i
$45$	−4.01274	+	5.37568i	−0.598183	+	0.801359i
$46$	0.302119	+	4.21738i	0.0445450	+	0.621819i
$47$	−4.76275	−	4.76275i	−0.694719	−	0.694719i	0.268548	−	0.963266i	$-0.413456\pi$
$47$	−4.76275	−	4.76275i	−0.694719	−	0.694719i	−0.963266	+	0.268548i	$0.913456\pi$
$48$	−4.95585	−	4.84144i	−0.715315	−	0.698802i
$49$		−	6.91251i		−	0.987502i
$50$	−4.40195	−	5.53379i	−0.622530	−	0.782596i
$51$	−2.06148	+	7.32369i	−0.288664	+	1.02552i
$52$	−10.1550	+	1.46244i	−1.40824	+	0.202804i
$53$		−	0.554732i		−	0.0761983i	−0.999274	−	0.0380991i	$-0.987870\pi$
$53$		−	0.554732i		−	0.0761983i	0.999274	−	0.0380991i	$-0.0121303\pi$
$54$	5.36863	+	5.01775i	0.730578	+	0.682829i
$55$	−4.01221	−	4.83242i	−0.541007	−	0.651603i
$56$	0.817416	−	0.178113i	0.109232	−	0.0238013i
$57$	8.67545	+	2.44197i	1.14909	+	0.323447i
$58$	0.731550	+	10.2119i	0.0960572	+	1.34089i
$59$	−3.04667	+	3.04667i	−0.396643	+	0.396643i	−0.877047	−	0.480404i	$-0.840490\pi$
$59$	−3.04667	+	3.04667i	−0.396643	+	0.396643i	0.480404	+	0.877047i	$0.340490\pi$
$60$	−6.55632	+	4.12489i	−0.846417	+	0.532521i
$61$	−9.01463	−	9.01463i	−1.15421	−	1.15421i	−0.985701	−	0.168504i	$-0.946106\pi$
$61$	−9.01463	−	9.01463i	−1.15421	−	1.15421i	−0.168504	−	0.985701i	$-0.553894\pi$
$62$	−2.90215	−	2.51414i	−0.368573	−	0.319297i
$63$	−0.862616	+	0.208024i	−0.108679	+	0.0262085i
$64$	−3.32833	−	7.27477i	−0.416041	−	0.909346i
$65$	−1.05920	+	11.4217i	−0.131377	+	1.41669i
$66$	−5.74565	+	3.78519i	−0.707240	+	0.465925i
$67$	−10.9329			−1.33567			−0.667834	−	0.744310i	$-0.732779\pi$
$67$	−10.9329			−1.33567			−0.667834	+	0.744310i	$0.732779\pi$
$68$	−5.26322	+	7.03420i	−0.638259	+	0.853023i
$69$	1.40311	−	4.98474i	0.168914	−	0.600092i
$70$	0.0195996	−	0.935138i	0.00234260	−	0.111770i
$71$	−7.59933			−0.901875			−0.450937	−	0.892556i	$-0.648910\pi$
$71$	−7.59933			−0.901875			−0.450937	+	0.892556i	$0.648910\pi$
$72$	3.69982	+	7.63619i	0.436028	+	0.899933i
$73$	4.26347	−	4.26347i	0.499001	−	0.499001i	−0.412126	−	0.911127i	$-0.635214\pi$
$73$	4.26347	−	4.26347i	0.499001	−	0.499001i	0.911127	+	0.412126i	$0.135214\pi$
$74$	5.11598	−	5.90552i	0.594720	−	0.686503i
$75$	2.77413	+	8.20392i	0.320328	+	0.947307i
$76$	8.33253	+	6.23467i	0.955807	+	0.715166i
$77$		−	0.830826i		−	0.0946814i
$78$	12.3079	+	2.53168i	1.39359	+	0.286657i
$79$		−	12.6207i		−	1.41994i	−0.704231	−	0.709971i	$-0.748708\pi$
$79$		−	12.6207i		−	1.41994i	0.704231	−	0.709971i	$-0.251292\pi$
$80$	−8.77720	+	1.72071i	−0.981320	+	0.192381i
$81$	−4.10222	−	8.01073i	−0.455802	−	0.890081i
$82$	−5.50699	−	4.77072i	−0.608145	−	0.526838i
$83$	6.66265			0.731321			0.365660	−	0.930748i	$-0.380843\pi$
$83$	6.66265			0.731321			0.365660	+	0.930748i	$0.380843\pi$
$84$	−1.01579	−	0.134199i	−0.110832	−	0.0146423i
$85$	6.27439	+	7.55705i	0.680553	+	0.819677i
$86$	−5.83294	−	5.05310i	−0.628982	−	0.544889i
$87$	3.39748	−	12.0700i	0.364248	−	1.29404i
$88$	−7.76268	+	1.69146i	−0.827504	+	0.180311i
$89$		−	5.00655i		−	0.530693i	−0.964153	−	0.265346i	$-0.914514\pi$
$89$		−	5.00655i		−	0.530693i	0.964153	−	0.265346i	$-0.0854863\pi$
$90$	9.26703	−	2.03030i	0.976831	−	0.214012i
$91$	−1.07291	+	1.07291i	−0.112471	+	0.112471i
$92$	3.58232	−	4.78771i	0.373482	−	0.499153i
$93$	2.29991	+	4.10189i	0.238489	+	0.425346i
$94$	0.680631	+	9.50115i	0.0702018	+	0.979969i
$95$	8.95188	−	7.43247i	0.918443	−	0.762556i
$96$	0.814170	+	9.76407i	0.0830959	+	0.996542i
$97$	9.37084	−	9.37084i	0.951465	−	0.951465i	−0.0474109	−	0.998875i	$-0.515097\pi$
$97$	9.37084	−	9.37084i	0.951465	−	0.951465i	0.998875	+	0.0474109i	$0.0150970\pi$
$98$	−6.40092	+	7.38877i	−0.646591	+	0.746378i
$99$	8.19192	−	1.97552i	0.823319	−	0.198547i
$100$	−0.418998	+	9.99122i	−0.0418998	+	0.999122i
$101$	8.41531	+	8.41531i	0.837355	+	0.837355i	0.988510	−	0.151155i	$-0.0482993\pi$
$101$	8.41531	+	8.41531i	0.837355	+	0.837355i	−0.151155	+	0.988510i	$0.548299\pi$
$102$	8.98517	−	5.91937i	0.889665	−	0.586105i
$103$	0.857056	−	0.857056i	0.0844483	−	0.0844483i	−0.663621	−	0.748069i	$-0.730981\pi$
$103$	0.857056	−	0.857056i	0.0844483	−	0.0844483i	0.748069	+	0.663621i	$0.230981\pi$
$104$	12.2088	+	7.84021i	1.19718	+	0.768796i
$105$	−0.410886	+	1.06933i	−0.0400984	+	0.104356i
$106$	−0.513676	+	0.592952i	−0.0498927	+	0.0575926i
$107$	−10.0388			−0.970486			−0.485243	−	0.874379i	$-0.661269\pi$
$107$	−10.0388			−0.970486			−0.485243	+	0.874379i	$0.661269\pi$
$108$	−1.09213	−	10.3348i	−0.105090	−	0.994463i
$109$	−3.30841	+	3.30841i	−0.316888	+	0.316888i	−0.847571	−	0.530683i	$-0.821936\pi$
$109$	−3.30841	+	3.30841i	−0.316888	+	0.316888i	0.530683	+	0.847571i	$0.321936\pi$
$110$	−0.186130	+	8.88063i	−0.0177468	+	0.846735i
$111$	−8.34685	+	4.68004i	−0.792248	+	0.444209i
$112$	−1.03866	−	0.566535i	−0.0981446	−	0.0535325i
$113$	5.35259	−	5.35259i	0.503529	−	0.503529i	−0.409004	−	0.912533i	$-0.634124\pi$
$113$	5.35259	−	5.35259i	0.503529	−	0.503529i	0.912533	+	0.409004i	$0.134124\pi$
$114$	−7.01193	−	10.6436i	−0.656727	−	0.996864i
$115$	−4.27055	−	5.14357i	−0.398231	−	0.479640i
$116$	8.67421	−	11.5929i	0.805380	−	1.07638i
$117$	−13.1300	−	8.02770i	−1.21387	−	0.742162i
$118$	6.07777	−	0.435391i	0.559504	−	0.0400810i
$119$			1.29926i			0.119103i
$120$	10.8276	+	1.66201i	0.988424	+	0.151720i
$121$		−	3.10998i		−	0.282725i
$122$	1.28826	+	17.9832i	0.116633	+	1.62812i
$123$	4.36420	+	7.78356i	0.393507	+	0.701820i
$124$	0.774027	+	5.37472i	0.0695097	+	0.482664i
$125$	10.7529	+	3.06193i	0.961768	+	0.273867i
$126$	1.11468	+	0.576418i	0.0993032	+	0.0513514i
$127$	−2.33195	+	2.33195i	−0.206927	+	0.206927i	−0.802960	−	0.596033i	$-0.796743\pi$
$127$	−2.33195	+	2.33195i	−0.206927	+	0.206927i	0.596033	+	0.802960i	$0.296743\pi$
$128$	−3.17872	+	10.8580i	−0.280962	+	0.959719i
$129$	4.62251	+	8.24426i	0.406990	+	0.725866i
$130$	11.7086	−	11.2279i	1.02691	−	0.984749i
$131$	4.62439	−	4.62439i	0.404035	−	0.404035i	−0.475617	−	0.879652i	$-0.657775\pi$
$131$	4.62439	−	4.62439i	0.404035	−	0.404035i	0.879652	+	0.475617i	$0.157775\pi$
$132$	9.64656	+	1.27443i	0.839625	+	0.110925i
$133$	1.53907			0.133455
$134$	11.6862	+	10.1238i	1.00953	+	0.874561i
$135$	−11.5206	−	1.50869i	−0.991534	−	0.129847i
$136$	12.1395	−	2.64515i	1.04095	−	0.226820i
$137$	−8.93752	+	8.93752i	−0.763584	+	0.763584i	−0.976968	−	0.213384i	$-0.931551\pi$
$137$	−8.93752	+	8.93752i	−0.763584	+	0.763584i	0.213384	+	0.976968i	$0.431551\pi$
$138$	−6.11560	+	4.02891i	−0.520594	+	0.342964i
$139$	15.9309	+	15.9309i	1.35124	+	1.35124i	0.884276	+	0.466965i	$0.154652\pi$
$139$	15.9309	+	15.9309i	1.35124	+	1.35124i	0.466965	+	0.884276i	$0.345348\pi$
$140$	−0.886878	+	0.981417i	−0.0749549	+	0.0829449i
$141$	3.16100	−	11.2299i	0.266204	−	0.945729i
$142$	8.12291	+	7.03691i	0.681659	+	0.590524i
$143$	10.1890	−	10.1890i	0.852045	−	0.852045i
$144$	3.11631	−	11.5883i	0.259692	−	0.965691i
$145$	−10.3407	−	12.4546i	−0.858748	−	1.03430i
$146$	−8.50514	+	0.609280i	−0.703891	+	0.0504244i
$147$	10.4433	−	5.85549i	0.861346	−	0.482952i
$148$	−10.9369	+	1.57505i	−0.899008	+	0.129468i
$149$	−8.50390	+	8.50390i	−0.696667	+	0.696667i	−0.963690	−	0.267023i	$-0.913960\pi$
$149$	−8.50390	+	8.50390i	−0.696667	+	0.696667i	0.267023	+	0.963690i	$0.413960\pi$
$150$	4.63149	−	11.3380i	0.378160	−	0.925740i
$151$			19.9160i			1.62074i	0.585916	+	0.810372i	$0.300735\pi$
$151$			19.9160i			1.62074i	−0.585916	+	0.810372i	$0.699265\pi$
$152$	−3.13338	−	14.3801i	−0.254150	−	1.16638i
$153$	−12.8107	+	3.08936i	−1.03568	+	0.249760i
$154$	−0.769337	+	0.888068i	−0.0619949	+	0.0715625i
$155$	6.04518	+	0.560600i	0.485560	+	0.0450285i
$156$	−10.8116	−	14.1031i	−0.865618	−	1.12915i
$157$	−12.2759			−0.979726			−0.489863	−	0.871800i	$-0.662953\pi$
$157$	−12.2759			−0.979726			−0.489863	+	0.871800i	$0.662953\pi$
$158$	−11.6867	+	13.4903i	−0.929741	+	1.07323i
$159$	0.838076	−	0.469905i	0.0664638	−	0.0372659i
$160$	10.9753	+	6.28834i	0.867672	+	0.497137i
$161$		−	0.884321i		−	0.0696943i
$162$	−3.03301	+	12.3613i	−0.238296	+	0.971193i
$163$			0.402051i			0.0314911i	0.999876	+	0.0157455i	$0.00501216\pi$
$163$			0.402051i			0.0314911i	−0.999876	+	0.0157455i	$0.994988\pi$
$164$	1.46876	+	10.1988i	0.114691	+	0.796395i
$165$	3.90202	−	10.1550i	0.303772	−	0.790568i
$166$	−7.12169	−	6.16955i	−0.552750	−	0.478850i
$167$	11.5587	−	11.5587i	0.894440	−	0.894440i	−0.100497	−	0.994937i	$-0.532043\pi$
$167$	11.5587	−	11.5587i	0.894440	−	0.894440i	0.994937	+	0.100497i	$0.0320434\pi$
$168$	0.961509	+	1.08406i	0.0741821	+	0.0836368i
$169$	−13.3156			−1.02428
$170$	0.291074	−	13.8877i	0.0223244	−	1.06514i
$171$	3.65958	+	15.1752i	0.279855	+	1.16048i
$172$	1.55569	+	10.8025i	0.118620	+	0.823682i
$173$	−5.19971			−0.395327			−0.197663	−	0.980270i	$-0.563335\pi$
$173$	−5.19971			−0.395327			−0.197663	+	0.980270i	$0.563335\pi$
$174$	−14.8083	+	9.75560i	−1.12261	+	0.739570i
$175$	0.835611	+	1.22021i	0.0631663	+	0.0922394i
$176$	9.86378	+	5.38016i	0.743511	+	0.405545i
$177$	−7.18363	−	2.02205i	−0.539955	−	0.151987i
$178$	−4.63601	+	5.35148i	−0.347484	+	0.401111i
$179$	−9.96688	−	9.96688i	−0.744960	−	0.744960i	0.228568	−	0.973528i	$-0.426596\pi$
$179$	−9.96688	−	9.96688i	−0.744960	−	0.744960i	−0.973528	+	0.228568i	$0.926596\pi$
$180$	−11.7855	−	6.41100i	−0.878443	−	0.477848i
$181$	−8.78238	+	8.78238i	−0.652789	+	0.652789i	−0.953664	−	0.300875i	$-0.902721\pi$
$181$	−8.78238	+	8.78238i	−0.652789	+	0.652789i	0.300875	+	0.953664i	$0.402721\pi$
$182$	2.14033	−	0.153326i	0.158652	−	0.0113653i
$183$	5.98293	−	21.2553i	0.442271	−	1.57123i
$184$	−8.26250	+	1.80038i	−0.609120	+	0.132725i
$185$	−1.14075	+	12.3012i	−0.0838698	+	0.904403i
$186$	1.33994	−	6.51419i	0.0982493	−	0.477644i
$187$		−	12.3386i		−	0.902288i
$188$	8.07045	−	10.7860i	0.588598	−	0.786651i
$189$	−1.04499	−	1.12701i	−0.0760116	−	0.0819776i
$190$	−16.4510	−	0.344799i	−1.19348	−	0.0250143i
$191$			18.9762i			1.37307i	0.727096	+	0.686536i	$0.240870\pi$
$191$			18.9762i			1.37307i	−0.727096	+	0.686536i	$0.759130\pi$
$192$	8.17117	−	11.1907i	0.589704	−	0.807620i
$193$	8.44228	+	8.44228i	0.607689	+	0.607689i	0.942341	−	0.334653i	$-0.108619\pi$
$193$	8.44228	+	8.44228i	0.607689	+	0.607689i	−0.334653	+	0.942341i	$0.608619\pi$
$194$	−18.6938	+	1.33916i	−1.34213	+	0.0961461i
$195$	−18.1529	+	8.07498i	−1.29996	+	0.578261i
$196$	13.6839	−	1.97065i	0.977418	−	0.140760i
$197$	−7.67131			−0.546558			−0.273279	−	0.961935i	$-0.588108\pi$
$197$	−7.67131			−0.546558			−0.273279	+	0.961935i	$0.588108\pi$
$198$	−10.5856	−	5.47401i	−0.752288	−	0.389021i
$199$	3.64353			0.258283			0.129141	−	0.991626i	$-0.458778\pi$
$199$	3.64353			0.258283			0.129141	+	0.991626i	$0.458778\pi$
$200$	9.69964	−	10.2916i	0.685868	−	0.727726i
$201$	−9.26111	−	16.5172i	−0.653229	−	1.16503i
$202$	−1.20261	−	16.7876i	−0.0846152	−	1.18117i
$203$		−	2.14129i		−	0.150289i
$204$	−15.0855	−	1.99298i	−1.05620	−	0.139537i
$205$	11.4711	+	1.06377i	0.801173	+	0.0742968i
$206$	−1.70973	+	0.122480i	−0.119123	+	0.00853355i
$207$	8.71938	−	2.10272i	0.606039	−	0.146149i
$208$	−5.79004	−	19.6857i	−0.401467	−	1.36495i
$209$	−14.6160			−1.01101
$210$	1.42939	−	0.762530i	0.0986371	−	0.0526196i
$211$	8.05418	+	8.05418i	0.554473	+	0.554473i	0.927728	−	0.373256i	$-0.121759\pi$
$211$	8.05418	+	8.05418i	0.554473	+	0.554473i	−0.373256	+	0.927728i	$0.621759\pi$
$212$	1.09813	−	0.158145i	0.0754202	−	0.0108615i
$213$	−6.43728	−	11.4809i	−0.441075	−	0.786658i
$214$	10.7304	+	9.29582i	0.733517	+	0.635449i
$215$	12.1500	+	1.12673i	0.828624	+	0.0768425i
$216$	−8.40251	+	12.0581i	−0.571719	+	0.820450i
$217$	0.567858	+	0.567858i	0.0385487	+	0.0385487i
$218$	6.59990	−	0.472795i	0.447002	−	0.0320217i
$219$	10.0527	+	2.82963i	0.679297	+	0.191209i
$220$	8.42233	−	9.32013i	0.567833	−	0.628363i
$221$	−15.9338	+	15.9338i	−1.07182	+	1.07182i
$222$	13.2556	+	2.72662i	0.889657	+	0.182999i
$223$	1.76936	+	1.76936i	0.118485	+	0.118485i	0.763863	−	0.645378i	$-0.223300\pi$
$223$	1.76936	+	1.76936i	0.118485	+	0.118485i	−0.645378	+	0.763863i	$0.723300\pi$
$224$	0.585620	+	1.56736i	0.0391284	+	0.104724i
$225$	−10.0444	+	11.1405i	−0.669624	+	0.742700i
$226$	−10.6778	+	0.764923i	−0.710278	+	0.0508819i
$227$			25.1549i			1.66959i	0.550562	+	0.834794i	$0.314413\pi$
$227$			25.1549i			1.66959i	−0.550562	+	0.834794i	$0.685587\pi$
$228$	−2.36083	+	17.8699i	−0.156350	+	1.18346i
$229$	−2.05939	−	2.05939i	−0.136088	−	0.136088i	0.635781	−	0.771869i	$-0.280678\pi$
$229$	−2.05939	−	2.05939i	−0.136088	−	0.136088i	−0.771869	+	0.635781i	$0.780678\pi$
$230$	−0.198114	+	9.45244i	−0.0130633	+	0.623275i
$231$	1.25519	−	0.703780i	0.0825856	−	0.0463053i
$232$	−20.0068	+	4.35942i	−1.31351	+	0.286210i
$233$	−6.88397	−	6.88397i	−0.450984	−	0.450984i	0.444697	−	0.895681i	$-0.353311\pi$
$233$	−6.88397	−	6.88397i	−0.450984	−	0.450984i	−0.895681	+	0.444697i	$0.853311\pi$
$234$	6.60102	+	20.7390i	0.431522	+	1.35575i
$235$	−9.62094	−	11.5877i	−0.627601	−	0.755900i
$236$	−6.89968	−	5.16257i	−0.449131	−	0.336055i
$237$	19.0671	−	10.6908i	1.23854	−	0.694444i
$238$	1.20311	−	1.38878i	0.0779858	−	0.0900213i
$239$	−5.82803			−0.376984			−0.188492	−	0.982075i	$-0.560360\pi$
$239$	−5.82803			−0.376984			−0.188492	+	0.982075i	$0.560360\pi$
$240$	−10.0346	−	11.8028i	−0.647733	−	0.761868i
$241$	30.2391			1.94787			0.973936	−	0.226824i	$-0.0728343\pi$
$241$	30.2391			1.94787			0.973936	+	0.226824i	$0.0728343\pi$
$242$	−2.87981	+	3.32425i	−0.185121	+	0.213691i
$243$	8.62750	−	12.9833i	0.553454	−	0.832879i
$244$	15.2752	−	20.4151i	0.977897	−	1.30694i
$245$	1.42727	−	15.3908i	0.0911848	−	0.983283i
$246$	2.54261	−	12.3610i	0.162111	−	0.788111i
$247$	18.8747	+	18.8747i	1.20097	+	1.20097i
$248$	4.14959	−	6.46177i	0.263499	−	0.410323i
$249$	5.64383	+	10.0658i	0.357663	+	0.637893i
$250$	−8.65842	−	13.2300i	−0.547606	−	0.836736i
$251$	−5.26950	−	5.26950i	−0.332608	−	0.332608i	0.520968	−	0.853576i	$-0.325571\pi$
$251$	−5.26950	−	5.26950i	−0.332608	−	0.332608i	−0.853576	+	0.520968i	$0.825571\pi$
$252$	−0.657717	−	1.64831i	−0.0414323	−	0.103834i
$253$			8.39805i			0.527981i
$254$	4.65198	−	0.333252i	0.291891	−	0.0209101i
$255$	−6.10207	+	15.8807i	−0.382127	+	0.994486i
$256$	13.4521	−	8.66260i	0.840757	−	0.541413i
$257$	13.6464	+	13.6464i	0.851240	+	0.851240i	0.990286	−	0.139046i	$-0.0444035\pi$
$257$	13.6464	+	13.6464i	0.851240	+	0.851240i	−0.139046	+	0.990286i	$0.544404\pi$
$258$	2.69311	−	13.0927i	0.167666	−	0.815114i
$259$	−1.15552	+	1.15552i	−0.0718006	+	0.0718006i
$260$	−22.9122	+	1.15939i	−1.42095	+	0.0719025i
$261$	21.1131	−	5.09152i	1.30687	−	0.315157i
$262$	−9.22514	+	0.660859i	−0.569931	+	0.0408280i
$263$	1.97332	+	1.97332i	0.121680	+	0.121680i	0.765325	−	0.643645i	$-0.222578\pi$
$263$	1.97332	+	1.97332i	0.121680	+	0.121680i	−0.643645	+	0.765325i	$0.722578\pi$
$264$	−9.13107	−	10.2949i	−0.561979	−	0.633605i
$265$	0.114539	−	1.23512i	0.00703606	−	0.0758728i
$266$	−1.64511	−	1.42517i	−0.100868	−	0.0873826i
$267$	7.56377	−	4.24097i	0.462895	−	0.259543i
$268$	−3.11680	−	21.6426i	−0.190389	−	1.32203i
$269$	−5.36810	−	5.36810i	−0.327299	−	0.327299i	0.524260	−	0.851558i	$-0.324342\pi$
$269$	−5.36810	−	5.36810i	−0.327299	−	0.327299i	−0.851558	+	0.524260i	$0.824342\pi$
$270$	10.9173	+	12.2806i	0.664405	+	0.747373i
$271$	5.80725			0.352766			0.176383	−	0.984322i	$-0.443560\pi$
$271$	5.80725			0.352766			0.176383	+	0.984322i	$0.443560\pi$
$272$	−15.4252	−	8.41362i	−0.935291	−	0.510151i
$273$	−2.52977	−	0.712080i	−0.153109	−	0.0430970i
$274$	17.8294	−	1.27724i	1.07711	−	0.0771607i
$275$	−7.93547	−	11.5879i	−0.478527	−	0.698775i
$276$	10.2677	+	1.35649i	0.618042	+	0.0816510i
$277$		−	17.7589i		−	1.06703i	−0.845791	−	0.533515i	$-0.820871\pi$
$277$		−	17.7589i		−	1.06703i	0.845791	−	0.533515i	$-0.179129\pi$
$278$	−2.27664	−	31.7803i	−0.136544	−	1.90606i
$279$	−4.24882	+	6.94930i	−0.254370	+	0.416044i
$280$	1.85676	−	0.227794i	0.110963	−	0.0136133i
$281$	9.74352			0.581250			0.290625	−	0.956837i	$-0.406137\pi$
$281$	9.74352			0.581250			0.290625	+	0.956837i	$0.406137\pi$
$282$	−13.7776	+	9.07657i	−0.820442	+	0.540502i
$283$	−28.1213			−1.67164			−0.835820	−	0.549003i	$-0.815007\pi$
$283$	−28.1213			−1.67164			−0.835820	+	0.549003i	$0.815007\pi$
$284$	−2.16645	−	15.0435i	−0.128555	−	0.892665i
$285$	18.8118	+	7.22835i	1.11432	+	0.428170i
$286$	−20.3259	+	1.45608i	−1.20189	+	0.0860997i
$287$	1.07754	+	1.07754i	0.0636052	+	0.0636052i
$288$	−14.0617	+	9.50103i	−0.828592	+	0.559854i
$289$			2.29539i			0.135023i
$290$	−0.479714	+	22.8881i	−0.0281698	+	1.34404i
$291$	22.0951	+	6.21935i	1.29524	+	0.364585i
$292$	9.65531	+	7.22442i	0.565035	+	0.422777i
$293$			19.2112i			1.12233i	0.827703	+	0.561166i	$0.189647\pi$
$293$			19.2112i			1.12233i	−0.827703	+	0.561166i	$0.810353\pi$
$294$	−16.5849	−	3.41145i	−0.967251	−	0.198960i
$295$	−7.41253	+	6.15440i	−0.431574	+	0.358323i
$296$	13.1489	+	8.44390i	0.764265	+	0.490792i
$297$	9.92382	+	10.7027i	0.575839	+	0.621035i
$298$	16.9643	−	1.21527i	0.982717	−	0.0703986i
$299$	10.8450	−	10.8450i	0.627184	−	0.627184i
$300$	−15.4494	+	7.83040i	−0.891973	+	0.452088i
$301$	1.14132	+	1.14132i	0.0657845	+	0.0657845i
$302$	18.4421	−	21.2882i	1.06122	−	1.22500i
$303$	−5.58517	+	19.8421i	−0.320860	+	1.13990i
$304$	−9.96655	+	18.2723i	−0.571621	+	1.04799i
$305$	−18.2099	−	21.9325i	−1.04270	−	1.25585i
$306$	16.5541	+	8.56038i	0.946332	+	0.489364i
$307$	−26.4923			−1.51200			−0.755998	−	0.654574i	$-0.772848\pi$
$307$	−26.4923			−1.51200			−0.755998	+	0.654574i	$0.772848\pi$
$308$	1.64468	−	0.236855i	0.0937146	−	0.0134961i
$309$	2.02082	+	0.568821i	0.114960	+	0.0323591i
$310$	−5.94257	−	6.19700i	−0.337515	−	0.351966i
$311$	−16.4372			−0.932066			−0.466033	−	0.884767i	$-0.654317\pi$
$311$	−16.4372			−0.932066			−0.466033	+	0.884767i	$0.654317\pi$
$312$	−1.50288	+	25.0862i	−0.0850839	+	1.42022i
$313$	−8.65723	+	8.65723i	−0.489335	+	0.489335i	−0.908096	−	0.418761i	$-0.862465\pi$
$313$	−8.65723	+	8.65723i	−0.489335	+	0.489335i	0.418761	+	0.908096i	$0.362465\pi$
$314$	13.1217	+	11.3674i	0.740501	+	0.641499i
$315$	−1.96358	+	0.285059i	−0.110635	+	0.0160612i
$316$	24.9837	−	3.59796i	1.40544	−	0.202401i
$317$			12.4547i			0.699523i	0.936839	+	0.349762i	$0.113737\pi$
$317$			12.4547i			0.699523i	−0.936839	+	0.349762i	$0.886263\pi$
$318$	−1.33095	−	0.273770i	−0.0746357	−	0.0153523i
$319$			20.3350i			1.13854i
$320$	−5.90851	−	16.8846i	−0.330296	−	0.943878i
$321$	−8.50371	−	15.1664i	−0.474631	−	0.846504i
$322$	−0.818873	+	0.945249i	−0.0456340	+	0.0526767i
$323$	22.8568			1.27179
$324$	14.6884	−	10.4044i	0.816022	−	0.578021i
$325$	−4.71663	+	25.2120i	−0.261631	+	1.39851i
$326$	0.372295	−	0.429751i	0.0206195	−	0.0238017i
$327$	−7.80077	−	2.19576i	−0.431384	−	0.121426i
$328$	7.87407	−	12.2616i	0.434773	−	0.677032i
$329$		−	1.99225i		−	0.109836i
$330$	−13.5743	+	7.24145i	−0.747242	+	0.398629i
$331$	6.63929	−	6.63929i	0.364928	−	0.364928i	−0.500695	−	0.865624i	$-0.666922\pi$
$331$	6.63929	−	6.63929i	0.364928	−	0.364928i	0.865624	+	0.500695i	$0.166922\pi$
$332$	1.89941	+	13.1892i	0.104244	+	0.723853i
$333$	−14.1410	−	8.64583i	−0.774921	−	0.473789i
$334$	−23.0583	+	1.65182i	−1.26170	+	0.0903837i
$335$	−24.3423	−	2.25738i	−1.32996	−	0.123334i
$336$	−0.0239290	−	2.04909i	−0.00130543	−	0.111787i
$337$	−10.1322	+	10.1322i	−0.551938	+	0.551938i	−0.927000	−	0.375062i	$-0.877621\pi$
$337$	−10.1322	+	10.1322i	−0.551938	+	0.551938i	0.375062	+	0.927000i	$0.377621\pi$
$338$	14.2330	+	12.3301i	0.774174	+	0.670670i
$339$	12.6207	+	3.55247i	0.685460	+	0.192944i
$340$	−13.1710	+	14.5750i	−0.714300	+	0.790442i
$341$	−5.39272	−	5.39272i	−0.292032	−	0.292032i
$342$	10.1404	−	19.6095i	0.548330	−	1.06036i
$343$	2.90979	−	2.90979i	0.157114	−	0.157114i
$344$	8.34012	−	12.9873i	0.449669	−	0.700228i
$345$	4.15327	−	10.8089i	0.223604	−	0.581931i
$346$	5.55796	+	4.81488i	0.298798	+	0.258850i
$347$	12.0143			0.644960			0.322480	−	0.946576i	$-0.395483\pi$
$347$	12.0143			0.644960			0.322480	+	0.946576i	$0.395483\pi$
$348$	24.8621	+	3.28460i	1.33275	+	0.176073i
$349$	−4.40984	+	4.40984i	−0.236053	+	0.236053i	−0.815214	−	0.579160i	$-0.803381\pi$
$349$	−4.40984	+	4.40984i	−0.236053	+	0.236053i	0.579160	+	0.815214i	$0.303381\pi$
$350$	0.236722	−	2.07805i	0.0126533	−	0.111076i
$351$	1.00586	−	26.6366i	0.0536889	−	1.42176i
$352$	−5.56140	−	14.8846i	−0.296424	−	0.793352i
$353$	5.49644	−	5.49644i	0.292546	−	0.292546i	−0.545539	−	0.838085i	$-0.683675\pi$
$353$	5.49644	−	5.49644i	0.292546	−	0.292546i	0.838085	+	0.545539i	$0.183675\pi$
$354$	5.80617	+	8.81334i	0.308594	+	0.468424i
$355$	−16.9200	−	1.56908i	−0.898022	−	0.0832781i
$356$	9.91085	−	1.42729i	0.525274	−	0.0756460i
$357$	−1.96290	+	1.10059i	−0.103888	+	0.0582493i
$358$	1.42434	+	19.8828i	0.0752787	+	1.05084i
$359$			28.4808i			1.50316i	0.659642	+	0.751580i	$0.270708\pi$
$359$			28.4808i			1.50316i	−0.659642	+	0.751580i	$0.729292\pi$
$360$	6.66101	+	17.7660i	0.351066	+	0.936351i
$361$		−	8.07555i		−	0.425029i
$362$	17.5199	−	1.25506i	0.920823	−	0.0659647i
$363$	4.69848	−	2.63442i	0.246606	−	0.138271i
$364$	−2.42977	−	1.81804i	−0.127355	−	0.0952910i
$365$	10.3730	−	8.61237i	0.542947	−	0.450792i
$366$	−26.0773	+	17.1795i	−1.36308	+	0.897989i
$367$	5.29634	−	5.29634i	0.276467	−	0.276467i	−0.555230	−	0.831697i	$-0.687370\pi$
$367$	5.29634	−	5.29634i	0.276467	−	0.276467i	0.831697	+	0.555230i	$0.187370\pi$
$368$	10.4989	+	5.72658i	0.547293	+	0.298519i
$369$	−8.06237	+	13.1867i	−0.419710	+	0.686471i
$370$	12.6101	−	12.0924i	0.655570	−	0.628654i
$371$	0.116022	−	0.116022i	0.00602354	−	0.00602354i
$372$	−7.46434	+	5.72223i	−0.387008	+	0.296684i
$373$	−6.11480			−0.316613			−0.158306	−	0.987390i	$-0.550603\pi$
$373$	−6.11480			−0.316613			−0.158306	+	0.987390i	$0.550603\pi$
$374$	−11.4254	+	13.1887i	−0.590795	+	0.681971i
$375$	4.48272	+	18.8389i	0.231487	+	0.972838i
$376$	−18.6142	+	4.05599i	−0.959956	+	0.209172i
$377$	26.2601	−	26.2601i	1.35246	−	1.35246i
$378$	0.0733868	+	2.17230i	0.00377461	+	0.111731i
$379$	−18.0034	−	18.0034i	−0.924775	−	0.924775i	0.0725875	−	0.997362i	$-0.476874\pi$
$379$	−18.0034	−	18.0034i	−0.924775	−	0.924775i	−0.997362	+	0.0725875i	$0.976874\pi$
$380$	17.2652	+	15.6021i	0.885686	+	0.800369i
$381$	−5.49841	−	1.54769i	−0.281692	−	0.0792908i
$382$	17.5718	−	20.2836i	0.899052	−	1.03780i
$383$	−4.27897	+	4.27897i	−0.218645	+	0.218645i	−0.807927	−	0.589282i	$-0.799411\pi$
$383$	−4.27897	+	4.27897i	−0.218645	+	0.218645i	0.589282	+	0.807927i	$0.299411\pi$
$384$	−19.0966	+	4.39529i	−0.974521	+	0.224296i
$385$	0.171546	−	1.84985i	0.00874277	−	0.0942769i
$386$	−1.20646	−	16.8414i	−0.0614073	−	0.857205i
$387$	−8.53957	+	13.9672i	−0.434091	+	0.709991i
$388$	21.2218	+	15.8788i	1.07737	+	0.806125i
$389$	27.5892	−	27.5892i	1.39883	−	1.39883i	0.595395	−	0.803433i	$-0.296996\pi$
$389$	27.5892	−	27.5892i	1.39883	−	1.39883i	0.803433	−	0.595395i	$-0.203004\pi$
$390$	26.8810	+	8.17811i	1.36117	+	0.414115i
$391$		−	13.1331i		−	0.664167i
$392$	−16.4514	−	10.5647i	−0.830923	−	0.533598i
$393$	10.9037	+	3.06917i	0.550018	+	0.154819i
$394$	8.19984	+	7.10356i	0.413102	+	0.357872i
$395$	2.60588	−	28.1002i	0.131116	−	1.41388i
$396$	6.24608	+	15.6533i	0.313877	+	0.786610i
$397$	11.3368			0.568978			0.284489	−	0.958679i	$-0.408176\pi$
$397$	11.3368			0.568978			0.284489	+	0.958679i	$0.408176\pi$
$398$	−3.89456	−	3.37387i	−0.195216	−	0.169117i
$399$	1.30373	+	2.32520i	0.0652680	+	0.116405i
$400$	−19.8978	+	2.01890i	−0.994892	+	0.100945i
$401$		−	1.76226i		−	0.0880033i	−0.999031	−	0.0440017i	$-0.985989\pi$
$401$		−	1.76226i		−	0.0880033i	0.999031	−	0.0440017i	$-0.0140107\pi$
$402$	−5.39559	+	26.2309i	−0.269107	+	1.30828i
$403$			13.9280i			0.693805i
$404$	−14.2597	+	19.0578i	−0.709446	+	0.948163i
$405$	−7.47962	−	18.6830i	−0.371665	−	0.928367i
$406$	−1.98282	+	2.28882i	−0.0984055	+	0.113592i
$407$	10.9735	−	10.9735i	0.543938	−	0.543938i
$408$	14.2794	+	16.0993i	0.706935	+	0.797036i
$409$	−18.4672			−0.913145			−0.456572	−	0.889686i	$-0.650923\pi$
$409$	−18.4672			−0.913145			−0.456572	+	0.889686i	$0.650923\pi$
$410$	−11.2763	−	11.7591i	−0.556899	−	0.580743i
$411$	−21.0734	−	5.93176i	−1.03948	−	0.292592i
$412$	1.94094	+	1.45228i	0.0956234	+	0.0715485i
$413$	−1.27442			−0.0627100
$414$	−11.2672	−	5.82647i	−0.553754	−	0.286355i
$415$	14.8345	+	1.37568i	0.728196	+	0.0675293i
$416$	−12.0398	+	26.4035i	−0.590298	+	1.29454i
$417$	−10.5732	+	37.5628i	−0.517772	+	1.83946i
$418$	15.6230	+	13.5343i	0.764145	+	0.661982i
$419$	−21.5295	−	21.5295i	−1.05179	−	1.05179i	−0.998584	−	0.0532015i	$-0.983057\pi$
$419$	−21.5295	−	21.5295i	−1.05179	−	1.05179i	−0.0532015	−	0.998584i	$-0.516943\pi$
$420$	−2.23396	−	0.508531i	−0.109006	−	0.0248138i
$421$	−7.35125	+	7.35125i	−0.358278	+	0.358278i	−0.863178	−	0.504900i	$-0.831529\pi$
$421$	−7.35125	+	7.35125i	−0.358278	+	0.358278i	0.504900	+	0.863178i	$0.331529\pi$
$422$	−1.15100	−	16.0672i	−0.0560298	−	0.782138i
$423$	19.6435	−	4.73713i	0.955101	−	0.230327i
$424$	−1.32023	−	0.847821i	−0.0641163	−	0.0411738i
$425$	12.4097	+	18.1214i	0.601957	+	0.879016i
$426$	−3.75040	+	18.2328i	−0.181708	+	0.883380i
$427$		−	3.77080i		−	0.182482i
$428$	−2.86190	−	19.8726i	−0.138335	−	0.960576i
$429$	24.0242	+	6.76234i	1.15990	+	0.326489i
$430$	−11.9438	−	12.4552i	−0.575980	−	0.600641i
$431$		−	3.27016i		−	0.157518i	−0.996894	−	0.0787590i	$-0.974904\pi$
$431$		−	3.27016i		−	0.157518i	0.996894	−	0.0787590i	$-0.0250958\pi$
$432$	20.1471	−	5.10823i	0.969328	−	0.245770i
$433$	13.2739	+	13.2739i	0.637901	+	0.637901i	0.950037	−	0.312136i	$-0.101045\pi$
$433$	13.2739	+	13.2739i	0.637901	+	0.637901i	−0.312136	+	0.950037i	$0.601045\pi$
$434$	−0.0811509	−	1.13281i	−0.00389537	−	0.0543767i
$435$	10.0567	−	26.1726i	0.482182	−	1.25488i
$436$	−7.49242	−	5.60608i	−0.358822	−	0.268482i
$437$	−15.5571			−0.744196
$438$	−8.12507	−	12.3333i	−0.388231	−	0.589306i
$439$	31.6152			1.50891			0.754456	−	0.656351i	$-0.227901\pi$
$439$	31.6152			1.50891			0.754456	+	0.656351i	$0.227901\pi$
$440$	−17.6330	+	2.16327i	−0.840618	+	0.103130i
$441$	17.6927	+	10.8173i	0.842508	+	0.515112i
$442$	31.7861	−	2.27705i	1.51191	−	0.108308i
$443$			17.8636i			0.848727i	0.905492	+	0.424364i	$0.139502\pi$
$443$			17.8636i			0.848727i	−0.905492	+	0.424364i	$0.860498\pi$
$444$	−11.6440	−	15.1890i	−0.552602	−	0.720839i
$445$	1.03373	−	11.1471i	0.0490036	−	0.528425i
$446$	−0.252855	−	3.52968i	−0.0119730	−	0.167135i
$447$	−20.0510	−	5.64397i	−0.948381	−	0.266950i
$448$	0.825394	−	2.21763i	0.0389962	−	0.104773i
$449$	−1.61654			−0.0762893			−0.0381447	−	0.999272i	$-0.512145\pi$
$449$	−1.61654			−0.0762893			−0.0381447	+	0.999272i	$0.512145\pi$
$450$	21.0524	−	2.60707i	0.992419	−	0.122898i
$451$	−10.2330	−	10.2330i	−0.481852	−	0.481852i
$452$	12.1218	+	9.06993i	0.570162	+	0.426613i
$453$	−30.0887	+	16.8706i	−1.41369	+	0.792649i
$454$	23.2932	−	26.8880i	1.09320	−	1.26192i
$455$	−2.61037	+	2.16732i	−0.122376	+	0.101605i
$456$	19.0708	−	16.9150i	0.893074	−	0.792116i
$457$	−14.2221	−	14.2221i	−0.665282	−	0.665282i	0.291338	−	0.956620i	$-0.405900\pi$
$457$	−14.2221	−	14.2221i	−0.665282	−	0.665282i	−0.956620	+	0.291338i	$0.905900\pi$
$458$	0.294301	+	4.10824i	0.0137518	+	0.191966i
$459$	−15.5191	−	16.7372i	−0.724370	−	0.781224i
$460$	8.96463	−	9.92024i	0.417978	−	0.462533i
$461$	9.61119	−	9.61119i	0.447638	−	0.447638i	−0.446931	−	0.894569i	$-0.647483\pi$
$461$	9.61119	−	9.61119i	0.447638	−	0.447638i	0.894569	+	0.446931i	$0.147483\pi$
$462$	−1.99337	−	0.410027i	−0.0927398	−	0.0190762i
$463$	−28.0146	−	28.0146i	−1.30195	−	1.30195i	−0.927076	−	0.374873i	$-0.877686\pi$
$463$	−28.0146	−	28.0146i	−1.30195	−	1.30195i	−0.374873	−	0.927076i	$-0.622314\pi$
$464$	25.4220	+	13.8663i	1.18019	+	0.643728i
$465$	4.27384	+	9.60779i	0.198195	+	0.445551i
$466$	0.983769	+	13.7327i	0.0455722	+	0.636157i
$467$			23.1084i			1.06933i	0.845064	+	0.534665i	$0.179562\pi$
$467$			23.1084i			1.06933i	−0.845064	+	0.534665i	$0.820438\pi$
$468$	12.1483	−	28.2804i	0.561556	−	1.30726i
$469$	−2.28661	−	2.28661i	−0.105586	−	0.105586i
$470$	−0.446324	+	21.2950i	−0.0205874	+	0.982265i
$471$	−10.3988	−	18.5462i	−0.479149	−	0.854563i
$472$	2.59457	+	11.9073i	0.119425	+	0.548078i
$473$	−10.8387	−	10.8387i	−0.498362	−	0.498362i
$474$	−30.2804	−	6.22855i	−1.39082	−	0.286087i
$475$	21.4661	−	14.7002i	0.984933	−	0.674490i
$476$	−2.57199	+	0.370399i	−0.117887	+	0.0169772i
$477$	1.41984	+	0.868096i	0.0650102	+	0.0397474i
$478$	6.22957	+	5.39670i	0.284934	+	0.246839i
$479$	7.67282			0.350580			0.175290	−	0.984517i	$-0.443914\pi$
$479$	7.67282			0.350580			0.175290	+	0.984517i	$0.443914\pi$
$480$	−0.203283	+	21.9080i	−0.00927858	+	0.999957i
$481$	−28.3419			−1.29228
$482$	−32.3225	−	28.0011i	−1.47225	−	1.27542i
$483$	1.33601	−	0.749095i	0.0607907	−	0.0340850i
$484$	6.15644	−	0.886604i	0.279838	−	0.0403002i
$485$	22.7992	−	18.9295i	1.03526	−	0.859542i
$486$	−21.2443	+	5.88884i	−0.963662	+	0.267123i
$487$	20.5657	+	20.5657i	0.931919	+	0.931919i	0.997826	−	0.0659067i	$-0.0209940\pi$
$487$	20.5657	+	20.5657i	0.931919	+	0.931919i	−0.0659067	+	0.997826i	$0.520994\pi$
$488$	−35.2318	+	7.67691i	−1.59487	+	0.347518i
$489$	−0.607409	+	0.340571i	−0.0274680	+	0.0154012i
$490$	−15.7773	+	15.1296i	−0.712748	+	0.683484i
$491$	14.4415	+	14.4415i	0.651734	+	0.651734i	0.953410	−	0.301676i	$-0.0975461\pi$
$491$	14.4415	+	14.4415i	0.651734	+	0.651734i	−0.301676	+	0.953410i	$0.597546\pi$
$492$	−14.1640	+	10.8582i	−0.638562	+	0.489528i
$493$		−	31.8003i		−	1.43222i
$494$	−2.69733	−	37.6529i	−0.121359	−	1.69409i
$495$	18.6473	−	2.70709i	0.838135	−	0.121675i
$496$	−10.4190	+	3.06449i	−0.467828	+	0.137600i
$497$	−1.58939	−	1.58939i	−0.0712940	−	0.0712940i
$498$	3.28813	−	15.9854i	0.147345	−	0.716324i
$499$	0.719966	−	0.719966i	0.0322301	−	0.0322301i	−0.690808	−	0.723038i	$-0.742745\pi$
$499$	0.719966	−	0.719966i	0.0322301	−	0.0322301i	0.723038	+	0.690808i	$0.242745\pi$
$500$	−2.99585	+	22.1591i	−0.133979	+	0.990984i
$501$	27.2538	+	7.67142i	1.21761	+	0.342734i
$502$	0.753050	+	10.5121i	0.0336103	+	0.469176i
$503$	3.53441	+	3.53441i	0.157592	+	0.157592i	0.781499	−	0.623907i	$-0.214456\pi$
$503$	3.53441	+	3.53441i	0.157592	+	0.157592i	−0.623907	+	0.781499i	$0.714456\pi$
$504$	−0.823287	+	2.37091i	−0.0366721	+	0.105609i
$505$	16.9993	+	20.4744i	0.756457	+	0.911098i
$506$	7.77651	−	8.97665i	0.345708	−	0.399061i
$507$	−11.2794	−	20.1169i	−0.500938	−	0.893423i
$508$	−5.28107	−	3.95147i	−0.234310	−	0.175318i
$509$	23.4794	+	23.4794i	1.04071	+	1.04071i	0.999136	+	0.0415716i	$0.0132365\pi$
$509$	23.4794	+	23.4794i	1.04071	+	1.04071i	0.0415716	+	0.999136i	$0.486764\pi$
$510$	21.2278	−	11.3243i	0.939984	−	0.501450i
$511$	1.78340			0.0788930
$512$	−22.4004	−	3.19709i	−0.989968	−	0.141293i
$513$	−19.8264	+	18.3835i	−0.875357	+	0.811652i
$514$	−1.95017	−	27.2231i	−0.0860184	−	1.20076i
$515$	2.08521	−	1.73129i	0.0918853	−	0.0762896i
$516$	−15.0023	+	11.5009i	−0.660441	+	0.506300i
$517$			18.9196i			0.832083i
$518$	2.30514	−	0.165132i	0.101282	−	0.00725550i
$519$	−4.40460	−	7.85560i	−0.193340	−	0.344823i
$520$	25.5644	+	19.9772i	1.12107	+	0.876057i
$521$	−29.7915			−1.30519			−0.652595	−	0.757707i	$-0.726320\pi$
$521$	−29.7915			−1.30519			−0.652595	+	0.757707i	$0.726320\pi$
$522$	−27.2824	−	14.1082i	−1.19412	−	0.617499i
$523$	−4.27696			−0.187019			−0.0935093	−	0.995618i	$-0.529808\pi$
$523$	−4.27696			−0.187019			−0.0935093	+	0.995618i	$0.529808\pi$
$524$	10.4727	+	7.83600i	0.457501	+	0.342317i
$525$	−1.13564	+	2.29605i	−0.0495632	+	0.100208i
$526$	−0.282001	−	3.93655i	−0.0122958	−	0.171642i
$527$	8.43326	+	8.43326i	0.367358	+	0.367358i
$528$	0.227244	+	19.4594i	0.00988953	+	0.846863i
$529$		−	14.0612i		−	0.611357i
$530$	−1.26614	+	1.21415i	−0.0549975	+	0.0527395i
$531$	−3.03028	−	12.5657i	−0.131503	−	0.545306i
$532$	0.438765	+	3.04672i	0.0190229	+	0.132092i
$533$			26.4292i			1.14478i
$534$	−12.0120	−	2.47082i	−0.519810	−	0.106923i
$535$	−22.3515	−	2.07277i	−0.966340	−	0.0896136i
$536$	−16.7093	+	26.0198i	−0.721730	+	1.12388i
$537$	6.61494	−	23.5005i	0.285456	−	1.01412i
$538$	0.767140	+	10.7088i	0.0330737	+	0.461687i
$539$	−13.7297	+	13.7297i	−0.591379	+	0.591379i
$540$	−0.297765	−	23.2360i	−0.0128138	−	0.999918i
$541$	−2.44200	−	2.44200i	−0.104990	−	0.104990i	0.652661	−	0.757650i	$-0.273653\pi$
$541$	−2.44200	−	2.44200i	−0.104990	−	0.104990i	−0.757650	+	0.652661i	$0.773653\pi$
$542$	−6.20736	−	5.37746i	−0.266629	−	0.230982i
$543$	−20.7076	−	5.82879i	−0.888649	−	0.250137i
$544$	8.69704	+	23.2769i	0.372883	+	0.997989i
$545$	−8.04932	+	6.68311i	−0.344795	+	0.286273i
$546$	2.04468	+	3.10368i	0.0875044	+	0.132825i
$547$	12.2209			0.522526			0.261263	−	0.965268i	$-0.415861\pi$
$547$	12.2209			0.522526			0.261263	+	0.965268i	$0.415861\pi$
$548$	−20.2405	−	15.1446i	−0.864630	−	0.646944i
$549$	37.1800	−	8.96613i	1.58680	−	0.382665i
$550$	−2.24806	+	19.7344i	−0.0958575	+	0.841479i
$551$	−37.6698			−1.60479
$552$	−9.71901	−	10.9577i	−0.413668	−	0.466392i
$553$	2.63961	−	2.63961i	0.112248	−	0.112248i
$554$	−16.4446	+	18.9825i	−0.698664	+	0.806488i
$555$	−19.5507	+	8.69675i	−0.829881	+	0.369156i
$556$	−26.9948	+	36.0781i	−1.14483	+	1.53005i
$557$		−	35.8116i		−	1.51739i	−0.651448	−	0.758694i	$-0.725838\pi$
$557$		−	35.8116i		−	1.51739i	0.651448	−	0.758694i	$-0.274162\pi$
$558$	10.9765	−	3.49372i	0.464674	−	0.147901i
$559$			27.9935i			1.18400i
$560$	−2.19563	−	1.47586i	−0.0927821	−	0.0623664i
$561$	18.6409	−	10.4518i	0.787018	−	0.441277i
$562$	−10.4148	−	9.02241i	−0.439323	−	0.380587i
$563$	−39.8938			−1.68132			−0.840661	−	0.541562i	$-0.817833\pi$
$563$	−39.8938			−1.68132			−0.840661	+	0.541562i	$0.817833\pi$
$564$	23.1316	+	3.05598i	0.974017	+	0.128680i
$565$	13.0228	−	10.8124i	0.547873	−	0.454883i
$566$	30.0588	+	26.0401i	1.26347	+	1.09455i
$567$	0.817462	−	2.53341i	0.0343302	−	0.106393i
$568$	−11.6144	+	18.0860i	−0.487329	+	0.758873i
$569$		−	26.1233i		−	1.09515i	−0.836758	−	0.547573i	$-0.815552\pi$
$569$		−	26.1233i		−	1.09515i	0.836758	−	0.547573i	$-0.184448\pi$
$570$	−13.4145	−	25.1459i	−0.561872	−	1.05325i
$571$	0.486665	−	0.486665i	0.0203663	−	0.0203663i	−0.696850	−	0.717217i	$-0.745416\pi$
$571$	0.486665	−	0.486665i	0.0203663	−	0.0203663i	0.717217	+	0.696850i	$0.245416\pi$
$572$	23.0746	+	17.2652i	0.964797	+	0.721893i
$573$	−28.6689	+	16.0745i	−1.19766	+	0.671521i
$574$	−0.153988	−	2.14957i	−0.00642735	−	0.0897215i
$575$	−8.44642	−	12.3340i	−0.352240	−	0.514363i
$576$	23.8283	+	2.86534i	0.992848	+	0.119389i
$577$	−15.6322	+	15.6322i	−0.650779	+	0.650779i	−0.953181	−	0.302402i	$-0.902212\pi$
$577$	−15.6322	+	15.6322i	−0.650779	+	0.650779i	0.302402	+	0.953181i	$0.402212\pi$
$578$	2.12551	−	2.45353i	0.0884094	−	0.102053i
$579$	−5.60307	+	19.9057i	−0.232856	+	0.827254i
$580$	21.7069	−	24.0208i	0.901331	−	0.997410i
$581$	1.39349	+	1.39349i	0.0578116	+	0.0578116i
$582$	−17.8584	−	27.1077i	−0.740254	−	1.12365i
$583$	−1.10181	+	1.10181i	−0.0456324	+	0.0456324i
$584$	−3.63080	−	16.6629i	−0.150243	−	0.689516i
$585$	−27.5766	−	20.5848i	−1.14015	−	0.851078i
$586$	17.7894	−	20.5348i	0.734874	−	0.848287i
$587$	−20.2496			−0.835789			−0.417894	−	0.908496i	$-0.637232\pi$
$587$	−20.2496			−0.835789			−0.417894	+	0.908496i	$0.637232\pi$
$588$	14.5686	+	19.0039i	0.600799	+	0.783710i
$589$	9.98981	−	9.98981i	0.411623	−	0.411623i
$590$	13.6221	+	0.285508i	0.560815	+	0.0117542i
$591$	−6.49825	−	11.5896i	−0.267302	−	0.476734i
$592$	−6.23587	−	21.2014i	−0.256293	−	0.871374i
$593$	4.83605	−	4.83605i	0.198593	−	0.198593i	−0.600804	−	0.799397i	$-0.705153\pi$
$593$	4.83605	−	4.83605i	0.198593	−	0.198593i	0.799397	+	0.600804i	$0.205153\pi$
$594$	−0.696925	−	20.6295i	−0.0285952	−	0.846438i
$595$	−0.268267	+	2.89283i	−0.0109979	+	0.118595i
$596$	−19.2585	−	14.4098i	−0.788857	−	0.590249i
$597$	3.08638	+	5.50455i	0.126317	+	0.225286i
$598$	−21.6346	+	1.54983i	−0.884705	+	0.0633774i
$599$		−	9.00019i		−	0.367738i	−0.982951	−	0.183869i	$-0.941138\pi$
$599$		−	9.00019i		−	0.367738i	0.982951	−	0.183869i	$-0.0588622\pi$
$600$	23.7647	+	5.93613i	0.970191	+	0.242341i
$601$		−	9.45079i		−	0.385506i	−0.981247	−	0.192753i	$-0.938258\pi$
$601$		−	9.45079i		−	0.385506i	0.981247	−	0.192753i	$-0.0617416\pi$
$602$	−0.163103	−	2.27680i	−0.00664757	−	0.0927956i
$603$	17.1089	−	27.9830i	0.696726	−	1.13955i
$604$	−39.4253	+	5.67774i	−1.60419	+	0.231024i
$605$	0.642135	−	6.92441i	0.0261065	−	0.281517i
$606$	24.3436	−	16.0374i	0.988892	−	0.651475i
$607$	−5.58614	+	5.58614i	−0.226734	+	0.226734i	−0.811327	−	0.584593i	$-0.801254\pi$
$607$	−5.58614	+	5.58614i	−0.226734	+	0.226734i	0.584593	+	0.811327i	$0.301254\pi$
$608$	27.5732	−	10.3023i	1.11824	−	0.417813i
$609$	3.23501	−	1.81386i	0.131089	−	0.0735012i
$610$	−0.844773	+	40.3058i	−0.0342038	+	1.63193i
$611$	24.4323	−	24.4323i	0.988425	−	0.988425i
$612$	−9.76776	−	24.4791i	−0.394838	−	0.989508i
$613$	6.85897			0.277031			0.138516	−	0.990360i	$-0.455767\pi$
$613$	6.85897			0.277031			0.138516	+	0.990360i	$0.455767\pi$
$614$	28.3176	+	24.5316i	1.14280	+	0.990015i
$615$	8.10985	+	18.2313i	0.327021	+	0.735157i
$616$	−1.97732	−	1.26979i	−0.0796687	−	0.0511612i
$617$	−25.2500	+	25.2500i	−1.01653	+	1.01653i	−0.0166666	+	0.999861i	$0.505305\pi$
$617$	−25.2500	+	25.2500i	−1.01653	+	1.01653i	−0.999861	+	0.0166666i	$0.994695\pi$
$618$	−1.63333	−	2.47927i	−0.0657021	−	0.0997309i
$619$	−6.09246	−	6.09246i	−0.244877	−	0.244877i	0.573987	−	0.818864i	$-0.305396\pi$
$619$	−6.09246	−	6.09246i	−0.244877	−	0.244877i	−0.818864	+	0.573987i	$0.805396\pi$
$620$	0.613632	+	12.1267i	0.0246440	+	0.487021i
$621$	10.5628	+	11.3919i	0.423871	+	0.457140i
$622$	17.5696	+	15.2207i	0.704479	+	0.610293i
$623$	1.04711	−	1.04711i	0.0419517	−	0.0419517i
$624$	24.8360	−	25.4229i	0.994235	−	1.01773i
$625$	23.3092	+	9.03764i	0.932370	+	0.361506i
$626$	17.2702	−	1.23718i	0.690256	−	0.0494477i
$627$	−12.3810	−	22.0815i	−0.494448	−	0.881849i
$628$	−3.49967	−	24.3012i	−0.139652	−	0.969722i
$629$	−17.1607	+	17.1607i	−0.684240	+	0.684240i
$630$	2.36283	+	1.51356i	0.0941372	+	0.0603015i
$631$		−	12.6389i		−	0.503145i	−0.967838	−	0.251573i	$-0.919052\pi$
$631$		−	12.6389i		−	0.503145i	0.967838	−	0.251573i	$-0.0809477\pi$
$632$	−30.0367	−	19.2888i	−1.19480	−	0.767268i
$633$	−5.34549	+	18.9906i	−0.212464	+	0.754810i
$634$	11.5329	−	13.3128i	0.458030	−	0.528717i
$635$	−5.67361	+	4.71063i	−0.225150	+	0.186935i
$636$	1.16914	+	1.52507i	0.0463593	+	0.0604731i
$637$	35.4603			1.40499
$638$	18.8300	−	21.7360i	0.745487	−	0.860538i
$639$	11.8921	−	19.4506i	0.470446	−	0.769453i
$640$	−9.31938	+	23.5191i	−0.368381	+	0.929675i
$641$		−	3.85715i		−	0.152348i	−0.997095	−	0.0761740i	$-0.975730\pi$
$641$		−	3.85715i		−	0.152348i	0.997095	−	0.0761740i	$-0.0242705\pi$
$642$	−4.95432	+	24.0856i	−0.195531	+	0.950585i
$643$		−	3.85299i		−	0.151947i	−0.997110	−	0.0759736i	$-0.975794\pi$
$643$		−	3.85299i		−	0.151947i	0.997110	−	0.0759736i	$-0.0242065\pi$
$644$	1.75058	−	0.252106i	0.0689826	−	0.00993436i
$645$	8.58985	+	19.3104i	0.338225	+	0.760346i
$646$	−24.4316	−	21.1652i	−0.961247	−	0.832733i
$647$	−17.0921	+	17.0921i	−0.671960	+	0.671960i	−0.958168	−	0.286207i	$-0.907605\pi$
$647$	−17.0921	+	17.0921i	−0.671960	+	0.671960i	0.286207	+	0.958168i	$0.407605\pi$
$648$	−25.3347	−	2.48008i	−0.995243	−	0.0974268i
$649$	12.1026			0.475070
$650$	28.3876	−	22.5815i	1.11345	−	0.885718i
$651$	−0.376882	+	1.33893i	−0.0147712	+	0.0524768i
$652$	−0.795891	+	0.114618i	−0.0311695	+	0.00448880i
$653$	34.9451			1.36751			0.683754	−	0.729713i	$-0.260346\pi$
$653$	34.9451			1.36751			0.683754	+	0.729713i	$0.260346\pi$
$654$	6.30497	+	9.57048i	0.246544	+	0.374235i
$655$	11.2511	−	9.34145i	0.439617	−	0.365001i
$656$	−19.7707	+	5.81504i	−0.771915	+	0.227039i
$657$	4.24053	+	17.5843i	0.165439	+	0.686028i
$658$	−1.84480	+	2.12951i	−0.0719179	+	0.0830170i
$659$	19.6923	+	19.6923i	0.767101	+	0.767101i	0.977595	−	0.210494i	$-0.0675072\pi$
$659$	19.6923	+	19.6923i	0.767101	+	0.767101i	−0.210494	+	0.977595i	$0.567507\pi$
$660$	21.2151	+	4.82932i	0.825795	+	0.187981i
$661$	−7.54566	+	7.54566i	−0.293492	+	0.293492i	−0.838458	−	0.544966i	$-0.816543\pi$
$661$	−7.54566	+	7.54566i	−0.293492	+	0.293492i	0.544966	+	0.838458i	$0.316543\pi$
$662$	−13.2446	+	0.948802i	−0.514768	+	0.0368763i
$663$	−37.5696	−	10.5751i	−1.45908	−	0.410703i
$664$	10.1828	−	15.8568i	0.395170	−	0.615362i
$665$	3.42677	+	0.317782i	0.132884	+	0.0123230i
$666$	7.10930	+	22.3359i	0.275480	+	0.865499i
$667$			21.6443i			0.838072i
$668$	26.1766	+	19.5862i	1.01280	+	0.757811i
$669$	−1.17431	+	4.17191i	−0.0454015	+	0.161295i
$670$	23.9291	+	24.9537i	0.924462	+	0.964044i
$671$			35.8098i			1.38242i
$672$	−1.87186	+	2.21243i	−0.0722087	+	0.0853463i
$673$	1.84927	+	1.84927i	0.0712841	+	0.0712841i	0.741850	−	0.670566i	$-0.233949\pi$
$673$	1.84927	+	1.84927i	0.0712841	+	0.0712841i	−0.670566	+	0.741850i	$0.733949\pi$
$674$	20.2127	−	1.44797i	0.778563	−	0.0557737i
$675$	−25.3392	−	5.73784i	−0.975308	−	0.220850i
$676$	−3.79606	−	26.3593i	−0.146002	−	1.01382i
$677$	1.91201			0.0734846			0.0367423	−	0.999325i	$-0.488302\pi$
$677$	1.91201			0.0734846			0.0367423	+	0.999325i	$0.488302\pi$
$678$	−10.2006	−	15.4838i	−0.391753	−	0.594653i
$679$	3.91980			0.150428
$680$	27.5748	−	3.38296i	1.05745	−	0.129731i
$681$	−38.0034	+	21.3083i	−1.45629	+	0.816537i
$682$	0.770658	+	10.7579i	0.0295100	+	0.411940i
$683$			45.8402i			1.75403i	0.480468	+	0.877013i	$0.340467\pi$
$683$			45.8402i			1.75403i	−0.480468	+	0.877013i	$0.659533\pi$
$684$	−28.9972	+	11.5706i	−1.10874	+	0.442414i
$685$	−21.7449	+	18.0541i	−0.830830	+	0.689813i
$686$	−5.80470	+	0.415830i	−0.221625	+	0.0158765i
$687$	1.36680	−	4.85575i	0.0521465	−	0.185258i
$688$	−20.9409	+	6.15923i	−0.798362	+	0.234818i
$689$	2.84570			0.108413
$690$	−14.4483	+	7.70771i	−0.550039	+	0.293428i
$691$	17.5456	+	17.5456i	0.667466	+	0.667466i	0.957129	−	0.289663i	$-0.0935431\pi$
$691$	17.5456	+	17.5456i	0.667466	+	0.667466i	−0.289663	+	0.957129i	$0.593543\pi$
$692$	−1.48235	−	10.2932i	−0.0563506	−	0.391290i
$693$	2.12651	+	1.30015i	0.0807794	+	0.0493888i
$694$	−12.8420	−	11.1251i	−0.487477	−	0.422303i
$695$	32.1810	+	38.7597i	1.22070	+	1.47024i
$696$	−23.5336	−	26.5330i	−0.892037	−	1.00573i
$697$	16.0026	+	16.0026i	0.606140	+	0.606140i
$698$	8.79714	−	0.630198i	0.332977	−	0.0238534i
$699$	4.56883	−	16.2314i	0.172809	−	0.613930i
$700$	−2.17729	+	2.00202i	−0.0822937	+	0.0756693i
$701$	1.30739	−	1.30739i	0.0493793	−	0.0493793i	−0.681986	−	0.731365i	$-0.738884\pi$
$701$	1.30739	−	1.30739i	0.0493793	−	0.0493793i	0.731365	+	0.681986i	$0.238884\pi$
$702$	−25.7404	+	27.5404i	−0.971509	+	1.03945i
$703$	20.3281	+	20.3281i	0.766687	+	0.766687i
$704$	−7.83844	+	21.0599i	−0.295422	+	0.793726i
$705$	9.35671	−	24.3509i	0.352394	−	0.917107i
$706$	−10.9648	+	0.785481i	−0.412665	+	0.0295620i
$707$			3.52011i			0.132387i
$708$	1.95487	−	14.7970i	0.0734685	−	0.556106i
$709$	−0.856472	−	0.856472i	−0.0321655	−	0.0321655i	0.690841	−	0.723007i	$-0.257240\pi$
$709$	−0.856472	−	0.856472i	−0.0321655	−	0.0321655i	−0.723007	+	0.690841i	$0.757240\pi$
$710$	16.6328	+	17.3450i	0.624219	+	0.650945i
$711$	32.3029	+	19.7501i	1.21145	+	0.740686i
$712$	−11.9153	−	7.65173i	−0.446546	−	0.286761i
$713$	−5.73995	−	5.73995i	−0.214963	−	0.214963i
$714$	3.11727	+	0.641210i	0.116661	+	0.0239967i
$715$	24.7897	−	20.5821i	0.927082	−	0.769728i
$716$	16.8888	−	22.5716i	0.631165	−	0.843541i
$717$	−4.93684	−	8.80486i	−0.184370	−	0.328823i
$718$	26.3730	−	30.4431i	0.984230	−	1.13613i
$719$	32.7512			1.22142			0.610708	−	0.791856i	$-0.290885\pi$
$719$	32.7512			1.22142			0.610708	+	0.791856i	$0.290885\pi$
$720$	9.33121	−	25.1581i	0.347754	−	0.937586i
$721$	0.358505			0.0133514
$722$	−7.47788	+	8.63193i	−0.278298	+	0.321247i
$723$	25.6151	+	45.6845i	0.952635	+	1.69903i
$724$	−19.8891	−	14.8817i	−0.739173	−	0.553073i
$725$	−20.4521	−	29.8655i	−0.759573	−	1.10918i
$726$	−7.46164	−	1.53483i	−0.276927	−	0.0569628i
$727$	−24.9562	−	24.9562i	−0.925575	−	0.925575i	0.0718407	−	0.997416i	$-0.477113\pi$
$727$	−24.9562	−	24.9562i	−0.925575	−	0.925575i	−0.997416	+	0.0718407i	$0.977113\pi$
$728$	0.913695	+	4.19324i	0.0338638	+	0.155412i
$729$	26.9231	+	2.03626i	0.997152	+	0.0754171i
$730$	−19.0626	−	0.399535i	−0.705540	−	0.0147875i
$731$	16.9497	+	16.9497i	0.626908	+	0.626908i
$732$	43.7821	+	5.78415i	1.61823	+	0.213789i
$733$		−	25.0888i		−	0.926677i	−0.886181	−	0.463338i	$-0.846651\pi$
$733$		−	25.0888i		−	0.926677i	0.886181	−	0.463338i	$-0.153349\pi$
$734$	−10.5656	+	0.756885i	−0.389984	+	0.0279371i
$735$	24.4611	−	10.8810i	0.902261	−	0.401353i
$736$	−5.91949	−	15.8430i	−0.218195	−	0.583981i
$737$	21.7150	+	21.7150i	0.799883	+	0.799883i
$738$	20.8286	−	6.62953i	0.766711	−	0.244036i
$739$	4.09647	−	4.09647i	0.150691	−	0.150691i	−0.627736	−	0.778427i	$-0.716018\pi$
$739$	4.09647	−	4.09647i	0.150691	−	0.150691i	0.778427	+	0.627736i	$0.216018\pi$
$740$	−24.6764	+	1.24867i	−0.907123	+	0.0459019i
$741$	−12.5270	+	44.5040i	−0.460190	+	1.63489i
$742$	−0.231450	+	0.0165803i	−0.00849680	+	0.000608683i
$743$	−11.2904	−	11.2904i	−0.414206	−	0.414206i	0.468995	−	0.883201i	$-0.344616\pi$
$743$	−11.2904	−	11.2904i	−0.414206	−	0.414206i	−0.883201	+	0.468995i	$0.844616\pi$
$744$	13.2773	+	0.795429i	0.486771	+	0.0291618i
$745$	−20.6899	+	17.1782i	−0.758020	+	0.629361i
$746$	6.53610	+	5.66225i	0.239304	+	0.207310i
$747$	−10.4263	+	17.0531i	−0.381480	+	0.623942i
$748$	24.4252	−	3.51754i	0.893074	−	0.128614i
$749$	−2.09960	−	2.09960i	−0.0767178	−	0.0767178i
$750$	12.6531	−	24.2878i	0.462026	−	0.886867i
$751$	−12.5652			−0.458510			−0.229255	−	0.973366i	$-0.573629\pi$
$751$	−12.5652			−0.458510			−0.229255	+	0.973366i	$0.573629\pi$
$752$	23.6525	+	12.9012i	0.862518	+	0.470457i
$753$	3.49732	−	12.4248i	0.127450	−	0.452783i
$754$	−52.3860	+	3.75276i	−1.90779	+	0.136667i
$755$	−4.11218	+	44.3433i	−0.149658	+	1.61382i
$756$	1.93309	−	2.38992i	0.0703057	−	0.0869207i
$757$		−	49.9626i		−	1.81592i	−0.419055	−	0.907961i	$-0.637639\pi$
$757$		−	49.9626i		−	1.81592i	0.419055	−	0.907961i	$-0.362361\pi$
$758$	2.57282	+	35.9148i	0.0934491	+	1.30449i
$759$	−12.6876	+	7.11386i	−0.460530	+	0.258217i
$760$	−4.00737	−	32.6644i	−0.145363	−	1.18486i
$761$	38.8563			1.40854			0.704271	−	0.709932i	$-0.251274\pi$
$761$	38.8563			1.40854			0.704271	+	0.709932i	$0.251274\pi$
$762$	4.44409	+	6.74580i	0.160992	+	0.244375i
$763$	−1.38390			−0.0501006
$764$	−37.5649	+	5.40982i	−1.35905	+	0.195720i
$765$	−29.1611	+	4.23341i	−1.05432	+	0.153059i
$766$	8.53607	−	0.611496i	0.308421	−	0.0220942i
$767$	−15.6290	−	15.6290i	−0.564332	−	0.564332i
$768$	24.4823	+	12.9852i	0.883430	+	0.468562i
$769$		−	4.11329i		−	0.148329i	−0.997246	−	0.0741644i	$-0.976371\pi$
$769$		−	4.11329i		−	0.148329i	0.997246	−	0.0741644i	$-0.0236290\pi$
$770$	−1.89630	+	1.81845i	−0.0683381	+	0.0655323i
$771$	−9.05701	+	32.1764i	−0.326180	+	1.15880i
$772$	−14.3054	+	19.1189i	−0.514862	+	0.688104i
$773$		−	15.4328i		−	0.555078i	−0.960714	−	0.277539i	$-0.910481\pi$
$773$		−	15.4328i		−	0.555078i	0.960714	−	0.277539i	$-0.0895187\pi$
$774$	22.0614	−	7.02192i	0.792980	−	0.252398i
$775$	13.3439	+	2.49637i	0.479328	+	0.0896722i
$776$	−7.98026	−	36.6240i	−0.286475	−	1.31472i
$777$	−2.72456	−	0.766910i	−0.0977430	−	0.0275127i
$778$	−55.0374	+	3.94270i	−1.97319	+	0.141352i
$779$	18.9562	−	18.9562i	0.679177	−	0.679177i
$780$	−21.1601	−	33.6331i	−0.757655	−	1.20426i
$781$	15.0938	+	15.0938i	0.540100	+	0.540100i
$782$	−12.1611	+	14.0379i	−0.434880	+	0.501994i
$783$	25.5767	+	27.5842i	0.914037	+	0.985779i
$784$	7.80209	+	26.5265i	0.278646	+	0.947373i
$785$	−27.3325	−	2.53468i	−0.975540	−	0.0904667i
$786$	−8.81289	−	13.3773i	−0.314345	−	0.477154i
$787$	3.52648			0.125705			0.0628527	−	0.998023i	$-0.479980\pi$
$787$	3.52648			0.125705			0.0628527	+	0.998023i	$0.479980\pi$
$788$	−2.18697	−	15.1859i	−0.0779074	−	0.540977i
$789$	−1.30967	+	4.65281i	−0.0466256	+	0.165644i
$790$	−28.8059	+	27.6232i	−1.02487	+	0.982791i
$791$	2.23898			0.0796089
$792$	7.81843	−	22.5156i	0.277816	−	0.800058i
$793$	46.2439	−	46.2439i	1.64217	−	1.64217i
$794$	−12.1179	−	10.4978i	−0.430048	−	0.372552i
$795$	1.96301	−	0.873208i	0.0696209	−	0.0309695i
$796$	1.03871	+	7.21264i	0.0368161	+	0.255645i
$797$			33.2526i			1.17787i	0.808181	+	0.588934i	$0.200452\pi$
$797$			33.2526i			1.17787i	−0.808181	+	0.588934i	$0.799548\pi$
$798$	0.759560	−	3.69264i	0.0268881	−	0.130718i
$799$		−	29.5869i		−	1.04671i
$800$	23.1382	+	16.2672i	0.818060	+	0.575133i
$801$	12.8143	+	7.83471i	0.452772	+	0.276826i
$802$	−1.63184	+	1.88368i	−0.0576223	+	0.0665151i
$803$	−16.9363			−0.597667
$804$	30.0569	−	23.0419i	1.06002	−	0.812624i
$805$	0.182591	−	1.96895i	0.00643549	−	0.0693965i
$806$	12.8972	−	14.8877i	0.454286	−	0.524395i
$807$	3.56276	−	12.6572i	0.125415	−	0.445556i
$808$	32.8895	−	7.16653i	1.15705	−	0.252118i
$809$			5.42562i			0.190755i	0.995441	+	0.0953774i	$0.0304058\pi$
$809$			5.42562i			0.190755i	−0.995441	+	0.0953774i	$0.969594\pi$
$810$	−9.30535	+	26.8963i	−0.326956	+	0.945039i
$811$	−12.6278	+	12.6278i	−0.443422	+	0.443422i	−0.893160	−	0.449738i	$-0.851517\pi$
$811$	−12.6278	+	12.6278i	−0.443422	+	0.443422i	0.449738	+	0.893160i	$0.351517\pi$
$812$	4.23885	−	0.610448i	0.148755	−	0.0214225i
$813$	4.91924	+	8.77347i	0.172525	+	0.307699i
$814$	−21.8910	+	1.56820i	−0.767278	+	0.0549652i
$815$	−0.0830138	+	0.895172i	−0.00290785	+	0.0313565i
$816$	−0.355370	−	30.4311i	−0.0124404	−	1.06530i
$817$	20.0782	−	20.0782i	0.702447	−	0.702447i
$818$	19.7396	+	17.1005i	0.690177	+	0.597904i
$819$	−1.06714	−	4.42511i	−0.0372887	−	0.154626i
$820$	1.16440	+	23.0111i	0.0406626	+	0.803583i
$821$	−38.3154	−	38.3154i	−1.33722	−	1.33722i	−0.898746	−	0.438469i	$-0.855521\pi$
$821$	−38.3154	−	38.3154i	−1.33722	−	1.33722i	−0.438469	−	0.898746i	$-0.644479\pi$
$822$	17.0326	+	25.8542i	0.594080	+	0.901770i
$823$	−25.9737	+	25.9737i	−0.905386	+	0.905386i	−0.995896	−	0.0905092i	$-0.971151\pi$
$823$	−25.9737	+	25.9737i	−0.905386	+	0.905386i	0.0905092	+	0.995896i	$0.471151\pi$
$824$	−0.729874	−	3.34963i	−0.0254264	−	0.116690i
$825$	10.7847	−	21.8046i	0.375474	−	0.759140i
$826$	1.36222	+	1.18010i	0.0473978	+	0.0410609i
$827$	47.5048			1.65190			0.825951	−	0.563742i	$-0.190639\pi$
$827$	47.5048			1.65190			0.825951	+	0.563742i	$0.190639\pi$
$828$	6.64825	+	16.6612i	0.231043	+	0.579018i
$829$	−36.6881	+	36.6881i	−1.27423	+	1.27423i	−0.330383	+	0.943847i	$0.607178\pi$
$829$	−36.6881	+	36.6881i	−1.27423	+	1.27423i	−0.943847	+	0.330383i	$0.892822\pi$
$830$	−14.5827	−	15.2070i	−0.506172	−	0.527844i
$831$	26.8298	−	15.0433i	0.930714	−	0.521847i
$832$	37.3186	−	17.0739i	1.29379	−	0.591931i
$833$	21.4708	−	21.4708i	0.743918	−	0.743918i
$834$	46.0845	−	30.3602i	1.59578	−	1.05129i
$835$	28.1222	−	23.3490i	0.973210	−	0.808027i
$836$	−4.16678	−	28.9335i	−0.144111	−	1.00068i
$837$	−14.0980	−	0.532372i	−0.487296	−	0.0184015i
$838$	3.07672	+	42.9490i	0.106284	+	1.48365i
$839$		−	45.1166i		−	1.55760i	−0.627273	−	0.778799i	$-0.715829\pi$
$839$		−	45.1166i		−	1.55760i	0.627273	−	0.778799i	$-0.284171\pi$
$840$	1.91698	+	2.61220i	0.0661422	+	0.0901293i
$841$			23.4095i			0.807224i
$842$	14.6649	−	1.05055i	0.505386	−	0.0362042i
$843$	8.25359	+	14.7203i	0.284269	+	0.506994i
$844$	−13.6478	+	18.2400i	−0.469775	+	0.627846i
$845$	−29.6474	−	2.74935i	−1.01990	−	0.0945805i
$846$	−25.3834	−	13.1262i	−0.872701	−	0.451288i
$847$	0.650449	−	0.650449i	0.0223497	−	0.0223497i
$848$	0.626121	+	2.12876i	0.0215011	+	0.0731019i
$849$	−23.8212	−	42.4851i	−0.817540	−	1.45808i
$850$	3.51556	−	30.8611i	0.120583	−	1.05853i
$851$	11.6801	−	11.6801i	0.400388	−	0.400388i
$852$	20.8922	−	16.0161i	0.715753	−	0.548703i
$853$	40.5114			1.38708			0.693542	−	0.720416i	$-0.256049\pi$
$853$	40.5114			1.38708			0.693542	+	0.720416i	$0.256049\pi$
$854$	−3.49173	+	4.03060i	−0.119484	+	0.137924i
$855$	5.01478	+	34.5435i	0.171502	+	1.18136i
$856$	−15.3427	+	23.8918i	−0.524404	+	0.816606i
$857$	−14.1574	+	14.1574i	−0.483608	+	0.483608i	−0.906282	−	0.422674i	$-0.861092\pi$
$857$	−14.1574	+	14.1574i	−0.483608	+	0.483608i	0.422674	+	0.906282i	$0.361092\pi$
$858$	−19.4176	−	29.4744i	−0.662904	−	1.00624i
$859$	38.2626	+	38.2626i	1.30550	+	1.30550i	0.924626	+	0.380875i	$0.124377\pi$
$859$	38.2626	+	38.2626i	1.30550	+	1.30550i	0.380875	+	0.924626i	$0.375623\pi$
$860$	1.23332	+	24.3731i	0.0420558	+	0.831116i
$861$	−0.715155	+	2.54069i	−0.0243724	+	0.0865866i
$862$	−3.02814	+	3.49547i	−0.103139	+	0.119056i
$863$	−24.1592	+	24.1592i	−0.822388	+	0.822388i	−0.986450	−	0.164062i	$-0.947540\pi$
$863$	−24.1592	+	24.1592i	−0.822388	+	0.822388i	0.164062	+	0.986450i	$0.447540\pi$
$864$	−26.2654	−	13.1959i	−0.893566	−	0.448932i
$865$	−11.5772	−	1.07361i	−0.393638	−	0.0365040i
$866$	−1.89693	−	26.4799i	−0.0644603	−	0.899822i
$867$	−3.46782	+	1.94439i	−0.117773	+	0.0660349i
$868$	−0.962231	+	1.28601i	−0.0326602	+	0.0436499i
$869$	−25.0673	+	25.0673i	−0.850351	+	0.850351i
$870$	−34.9852	+	18.6634i	−1.18611	+	0.632749i
$871$		−	56.0845i		−	1.90035i
$872$	2.81746	+	12.9302i	0.0954112	+	0.437873i
$873$	9.32042	+	38.6492i	0.315449	+	1.30808i
$874$	16.6289	+	14.4057i	0.562481	+	0.487280i
$875$	1.60856	+	2.88936i	0.0543791	+	0.0976780i
$876$	−2.73562	+	20.7067i	−0.0924279	+	0.699615i
$877$	−27.3111			−0.922231			−0.461115	−	0.887340i	$-0.652551\pi$
$877$	−27.3111			−0.922231			−0.461115	+	0.887340i	$0.652551\pi$
$878$	−33.7934	−	29.2754i	−1.14047	−	0.987996i
$879$	−29.0239	+	16.2736i	−0.978952	+	0.548893i
$880$	20.8510	+	14.0156i	0.702887	+	0.472467i
$881$		−	26.1087i		−	0.879623i	−0.898090	−	0.439812i	$-0.855045\pi$
$881$		−	26.1087i		−	0.879623i	0.898090	−	0.439812i	$-0.144955\pi$
$882$	−8.89489	−	27.9459i	−0.299507	−	0.940987i
$883$		−	29.0554i		−	0.977791i	−0.872342	−	0.488896i	$-0.837400\pi$
$883$		−	29.0554i		−	0.977791i	0.872342	−	0.488896i	$-0.162600\pi$
$884$	−36.0846	−	26.9997i	−1.21366	−	0.908097i
$885$	−15.5770	−	5.98538i	−0.523614	−	0.201196i
$886$	16.5416	−	19.0944i	0.555725	−	0.641489i
$887$	40.5736	−	40.5736i	1.36233	−	1.36233i	0.491385	−	0.870943i	$-0.336491\pi$
$887$	40.5736	−	40.5736i	1.36233	−	1.36233i	0.870943	−	0.491385i	$-0.163509\pi$
$888$	−1.61860	+	27.0178i	−0.0543167	+	0.906658i
$889$	−0.975449			−0.0327155
$890$	−11.4271	+	10.9579i	−0.383037	+	0.367311i
$891$	−7.76311	+	24.0588i	−0.260074	+	0.806000i
$892$	−2.99817	+	4.00701i	−0.100386	+	0.134165i
$893$	−35.0479			−1.17283
$894$	16.2062	+	24.5999i	0.542017	+	0.822743i
$895$	−20.1335	−	24.2493i	−0.672988	−	0.810566i
$896$	−2.93576	+	1.60611i	−0.0980769	+	0.0536563i
$897$	25.5711	+	7.19776i	0.853794	+	0.240326i
$898$	1.72792	+	1.49690i	0.0576614	+	0.0499523i
$899$	−13.8987	−	13.8987i	−0.463547	−	0.463547i
$900$	−24.9170	−	16.7076i	−0.830566	−	0.556921i
$901$	1.72304	−	1.72304i	0.0574027	−	0.0574027i
$902$	1.46237	+	20.4136i	0.0486915	+	0.679700i
$903$	−0.757484	+	2.69107i	−0.0252075	+	0.0895533i
$904$	−4.55830	−	20.9195i	−0.151607	−	0.695772i
$905$	−21.3674	+	17.7407i	−0.710278	+	0.589722i
$906$	47.7837	+	9.82891i	1.58751	+	0.326544i
$907$			49.1451i			1.63184i	0.578167	+	0.815918i	$0.303768\pi$
$907$			49.1451i			1.63184i	−0.578167	+	0.815918i	$0.696232\pi$
$908$	−49.7960	+	7.17125i	−1.65254	+	0.237986i
$909$	−34.7082	+	8.37004i	−1.15120	+	0.277617i
$910$	4.79714	+	0.100544i	0.159024	+	0.00333299i
$911$			6.01797i			0.199384i	0.995018	+	0.0996921i	$0.0317858\pi$
$911$			6.01797i			0.199384i	−0.995018	+	0.0996921i	$0.968214\pi$
$912$	−36.0479	+	0.420961i	−1.19366	+	0.0139394i
$913$	−13.2334	−	13.2334i	−0.437961	−	0.437961i
$914$	2.03244	+	28.3715i	0.0672272	+	0.938446i
$915$	17.7098	−	46.0898i	0.585468	−	1.52368i
$916$	3.48961	−	4.66381i	0.115300	−	0.154097i
$917$	1.93437			0.0638787
$918$	1.08987	+	32.2609i	0.0359710	+	1.06477i
$919$	−15.5196			−0.511943			−0.255972	−	0.966684i	$-0.582395\pi$
$919$	−15.5196			−0.511943			−0.255972	+	0.966684i	$0.582395\pi$
$920$	−18.7683	+	2.30255i	−0.618773	+	0.0759130i
$921$	−22.4412	−	40.0240i	−0.739464	−	1.31883i
$922$	−19.1733	+	1.37351i	−0.631437	+	0.0452341i
$923$		−	38.9836i		−	1.28316i
$924$	1.75102	+	2.28411i	0.0576044	+	0.0751418i
$925$	−5.07981	+	27.1533i	−0.167023	+	0.892794i
$926$	4.00349	+	55.8860i	0.131563	+	1.83653i
$927$	0.852445	+	3.53485i	0.0279980	+	0.116100i
$928$	−14.3334	−	38.3622i	−0.470518	−	1.25930i
$929$	1.94538			0.0638258			0.0319129	−	0.999491i	$-0.489840\pi$
$929$	1.94538			0.0638258			0.0319129	+	0.999491i	$0.489840\pi$
$930$	4.32843	−	14.2273i	0.141935	−	0.466531i
$931$	−25.4337	−	25.4337i	−0.833556	−	0.833556i
$932$	11.6648	−	15.5899i	0.382095	−	0.510663i
$933$	−13.9237	−	24.8329i	−0.455841	−	0.812992i
$934$	21.3982	−	24.7005i	0.700169	−	0.808226i
$935$	2.54762	−	27.4721i	0.0833162	−	0.898433i
$936$	−39.1727	+	18.9796i	−1.28040	+	0.620368i
$937$	−20.7507	−	20.7507i	−0.677895	−	0.677895i	0.281628	−	0.959524i	$-0.409126\pi$
$937$	−20.7507	−	20.7507i	−0.677895	−	0.677895i	−0.959524	+	0.281628i	$0.909126\pi$
$938$	0.326773	+	4.56153i	0.0106695	+	0.148939i
$939$	−20.4125	−	5.74573i	−0.666138	−	0.187505i
$940$	20.1960	−	22.3489i	0.658722	−	0.728940i
$941$	−9.06568	+	9.06568i	−0.295533	+	0.295533i	−0.839261	−	0.543729i	$-0.817012\pi$
$941$	−9.06568	+	9.06568i	−0.295533	+	0.295533i	0.543729	+	0.839261i	$0.317012\pi$
$942$	−6.05839	+	29.4531i	−0.197393	+	0.959635i
$943$	−10.8919	−	10.8919i	−0.354688	−	0.354688i
$944$	8.25272	−	15.1302i	0.268603	−	0.492447i
$945$	−2.09398	−	2.72506i	−0.0681171	−	0.0886462i
$946$	1.54892	+	21.6219i	0.0503598	+	0.702988i
$947$			4.61234i			0.149881i	0.997188	+	0.0749405i	$0.0238767\pi$
$947$			4.61234i			0.149881i	−0.997188	+	0.0749405i	$0.976123\pi$
$948$	26.5990	+	34.6970i	0.863897	+	1.12691i
$949$	21.8711	+	21.8711i	0.709965	+	0.709965i
$950$	−36.5573	−	4.16444i	−1.18607	−	0.135112i
$951$	−18.8162	+	10.5502i	−0.610157	+	0.342112i
$952$	3.09219	+	1.98572i	0.100218	+	0.0643577i
$953$	7.76778	+	7.76778i	0.251623	+	0.251623i	0.821636	−	0.570013i	$-0.193062\pi$
$953$	7.76778	+	7.76778i	0.251623	+	0.251623i	−0.570013	+	0.821636i	$0.693062\pi$
$954$	−0.713819	−	2.24267i	−0.0231107	−	0.0726091i
$955$	−3.91813	+	42.2509i	−0.126788	+	1.36721i
$956$	−1.66148	−	11.5370i	−0.0537360	−	0.373135i
$957$	−30.7216	+	17.2255i	−0.993090	+	0.556821i
$958$	−8.20145	−	7.10495i	−0.264977	−	0.229551i
$959$	−3.73855			−0.120724
$960$	20.5038	−	23.2291i	0.661759	−	0.749717i
$961$	−23.6283			−0.762204
$962$	30.2946	+	26.2443i	0.976736	+	0.846151i
$963$	15.7096	−	25.6944i	0.506236	−	0.827991i
$964$	8.62068	+	59.8606i	0.277653	+	1.92798i
$965$	17.0537	+	20.5400i	0.548979	+	0.661206i
$966$	−2.12172	−	0.436428i	−0.0682651	−	0.0140418i
$967$	16.1803	+	16.1803i	0.520325	+	0.520325i	0.917669	−	0.397345i	$-0.130068\pi$
$967$	16.1803	+	16.1803i	0.520325	+	0.520325i	−0.397345	+	0.917669i	$0.630068\pi$
$968$	−7.40159	−	4.75312i	−0.237896	−	0.152771i
$969$	19.3617	+	34.5315i	0.621986	+	1.10931i
$970$	−41.8985	−	0.878154i	−1.34528	−	0.0281958i
$971$	−20.5784	−	20.5784i	−0.660393	−	0.660393i	0.295080	−	0.955473i	$-0.404654\pi$
$971$	−20.5784	−	20.5784i	−0.660393	−	0.660393i	−0.955473	+	0.295080i	$0.904654\pi$
$972$	28.1610	+	13.3775i	0.903265	+	0.429083i
$973$			6.66386i			0.213634i
$974$	−2.93898	−	41.0262i	−0.0941710	−	1.31456i
$975$	−42.0850	+	14.2309i	−1.34780	+	0.455754i
$976$	44.7680	+	24.4185i	1.43299	+	0.781617i
$977$	−16.3734	−	16.3734i	−0.523833	−	0.523833i	0.394894	−	0.918727i	$-0.370781\pi$
$977$	−16.3734	−	16.3734i	−0.523833	−	0.523833i	−0.918727	+	0.394894i	$0.870781\pi$
$978$	0.964624	+	0.198419i	0.0308453	+	0.00634475i
$979$	−9.94403	+	9.94403i	−0.317813	+	0.317813i
$980$	30.8742	−	1.56229i	0.986240	−	0.0499054i
$981$	−3.29061	−	13.6452i	−0.105061	−	0.435658i
$982$	−2.06379	−	28.8091i	−0.0658582	−	0.919336i
$983$	7.10524	+	7.10524i	0.226622	+	0.226622i	0.811280	−	0.584658i	$-0.198771\pi$
$983$	7.10524	+	7.10524i	0.226622	+	0.226622i	−0.584658	+	0.811280i	$0.698771\pi$
$984$	25.1945	+	1.50937i	0.803171	+	0.0481170i
$985$	−17.0803	−	1.58394i	−0.544223	−	0.0504685i
$986$	−29.4468	+	33.9913i	−0.937777	+	1.08250i
$987$	3.00984	−	1.68760i	0.0958044	−	0.0537171i
$988$	−31.9831	+	42.7448i	−1.01752	+	1.35989i
$989$	−11.5365	−	11.5365i	−0.366840	−	0.366840i
$990$	−22.4388	−	14.3736i	−0.713152	−	0.456824i
$991$	−13.6881			−0.434817			−0.217408	−	0.976081i	$-0.569760\pi$
$991$	−13.6881			−0.434817			−0.217408	+	0.976081i	$0.569760\pi$
$992$	13.9746	+	6.37228i	0.443693	+	0.202320i
$993$	15.6545	+	4.40644i	0.496782	+	0.139834i
$994$	0.227136	+	3.17066i	0.00720431	+	0.100567i
$995$	8.11236	+	0.752300i	0.257179	+	0.0238495i
$996$	−18.3170	+	14.0420i	−0.580397	+	0.444938i
$997$		−	31.7776i		−	1.00641i	−0.864168	−	0.503203i	$-0.832155\pi$
$997$		−	31.7776i		−	1.00641i	0.864168	−	0.503203i	$-0.167845\pi$
$998$	−1.43625	+	0.102888i	−0.0454638	+	0.00325687i
$999$	1.08331	−	28.6876i	0.0342745	−	0.907636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.10	✓	88
3.2	odd	2	inner	240.2.bb.a.173.35	yes	88
4.3	odd	2		960.2.bb.a.593.16		88
5.2	odd	4		240.2.bf.a.77.32	yes	88
12.11	even	2		960.2.bb.a.593.29		88
15.2	even	4		240.2.bf.a.77.13	yes	88
16.5	even	4		240.2.bf.a.53.13	yes	88
16.11	odd	4		960.2.bf.a.113.8		88
20.7	even	4		960.2.bf.a.17.8		88
48.5	odd	4		240.2.bf.a.53.32	yes	88
48.11	even	4		960.2.bf.a.113.7		88
60.47	odd	4		960.2.bf.a.17.7		88
80.27	even	4		960.2.bb.a.497.29		88
80.37	odd	4	inner	240.2.bb.a.197.35	yes	88
240.107	odd	4		960.2.bb.a.497.16		88
240.197	even	4	inner	240.2.bb.a.197.10	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.10	✓	88	1.1	even	1	trivial
240.2.bb.a.173.35	yes	88	3.2	odd	2	inner
240.2.bb.a.197.10	yes	88	240.197	even	4	inner
240.2.bb.a.197.35	yes	88	80.37	odd	4	inner
240.2.bf.a.53.13	yes	88	16.5	even	4
240.2.bf.a.53.32	yes	88	48.5	odd	4
240.2.bf.a.77.13	yes	88	15.2	even	4
240.2.bf.a.77.32	yes	88	5.2	odd	4
960.2.bb.a.497.16		88	240.107	odd	4
960.2.bb.a.497.29		88	80.27	even	4
960.2.bb.a.593.16		88	4.3	odd	2
960.2.bb.a.593.29		88	12.11	even	2
960.2.bf.a.17.7		88	60.47	odd	4
960.2.bf.a.17.8		88	20.7	even	4
960.2.bf.a.113.7		88	48.11	even	4
960.2.bf.a.113.8		88	16.11	odd	4

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.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06890 - 0.925990i) q^{2} +(0.847085 + 1.51078i) q^{3} +(0.285084 + 1.97958i) q^{4} +(2.22651 + 0.206476i) q^{5} +(0.493518 - 2.39926i) q^{6} +(0.209149 + 0.209149i) q^{7} +(1.52834 - 2.37995i) q^{8} +(-1.56489 + 2.55951i) q^{9} +O(q^{10})\)	\(q+(-1.06890 - 0.925990i) q^{2} +(0.847085 + 1.51078i) q^{3} +(0.285084 + 1.97958i) q^{4} +(2.22651 + 0.206476i) q^{5} +(0.493518 - 2.39926i) q^{6} +(0.209149 + 0.209149i) q^{7} +(1.52834 - 2.37995i) q^{8} +(-1.56489 + 2.55951i) q^{9} +(-2.18872 - 2.28243i) q^{10} +(-1.98621 - 1.98621i) q^{11} +(-2.74921 + 2.10757i) q^{12} +5.12987i q^{13} +(-0.0298889 - 0.417229i) q^{14} +(1.57411 + 3.53867i) q^{15} +(-3.83745 + 1.12869i) q^{16} +(3.10607 + 3.10607i) q^{17} +(4.04280 - 1.28678i) q^{18} +(3.67937 - 3.67937i) q^{19} +(0.226008 + 4.46642i) q^{20} +(-0.138810 + 0.493145i) q^{21} +(0.283843 + 3.96226i) q^{22} +(-2.11409 - 2.11409i) q^{23} +(4.89021 + 0.292966i) q^{24} +(4.91474 + 0.919443i) q^{25} +(4.75021 - 5.48331i) q^{26} +(-5.19245 - 0.196079i) q^{27} +(-0.354402 + 0.473652i) q^{28} +(-5.11906 - 5.11906i) q^{29} +(1.59421 - 5.24008i) q^{30} +2.71509 q^{31} +(5.14700 + 2.34699i) q^{32} +(1.31823 - 4.68320i) q^{33} +(-0.443880 - 6.19627i) q^{34} +(0.422489 + 0.508858i) q^{35} +(-5.51288 - 2.36815i) q^{36} +5.52487i q^{37} +(-7.33993 + 0.525809i) q^{38} +(-7.75009 + 4.34544i) q^{39} +(3.89428 - 4.98343i) q^{40} +5.15202 q^{41} +(0.605021 - 0.398584i) q^{42} +5.45696 q^{43} +(3.36561 - 4.49808i) q^{44} +(-4.01274 + 5.37568i) q^{45} +(0.302119 + 4.21738i) q^{46} +(-4.76275 - 4.76275i) q^{47} +(-4.95585 - 4.84144i) q^{48} -6.91251i q^{49} +(-4.40195 - 5.53379i) q^{50} +(-2.06148 + 7.32369i) q^{51} +(-10.1550 + 1.46244i) q^{52} -0.554732i q^{53} +(5.36863 + 5.01775i) q^{54} +(-4.01221 - 4.83242i) q^{55} +(0.817416 - 0.178113i) q^{56} +(8.67545 + 2.44197i) q^{57} +(0.731550 + 10.2119i) q^{58} +(-3.04667 + 3.04667i) q^{59} +(-6.55632 + 4.12489i) q^{60} +(-9.01463 - 9.01463i) q^{61} +(-2.90215 - 2.51414i) q^{62} +(-0.862616 + 0.208024i) q^{63} +(-3.32833 - 7.27477i) q^{64} +(-1.05920 + 11.4217i) q^{65} +(-5.74565 + 3.78519i) q^{66} -10.9329 q^{67} +(-5.26322 + 7.03420i) q^{68} +(1.40311 - 4.98474i) q^{69} +(0.0195996 - 0.935138i) q^{70} -7.59933 q^{71} +(3.69982 + 7.63619i) q^{72} +(4.26347 - 4.26347i) q^{73} +(5.11598 - 5.90552i) q^{74} +(2.77413 + 8.20392i) q^{75} +(8.33253 + 6.23467i) q^{76} -0.830826i q^{77} +(12.3079 + 2.53168i) q^{78} -12.6207i q^{79} +(-8.77720 + 1.72071i) q^{80} +(-4.10222 - 8.01073i) q^{81} +(-5.50699 - 4.77072i) q^{82} +6.66265 q^{83} +(-1.01579 - 0.134199i) q^{84} +(6.27439 + 7.55705i) q^{85} +(-5.83294 - 5.05310i) q^{86} +(3.39748 - 12.0700i) q^{87} +(-7.76268 + 1.69146i) q^{88} -5.00655i q^{89} +(9.26703 - 2.03030i) q^{90} +(-1.07291 + 1.07291i) q^{91} +(3.58232 - 4.78771i) q^{92} +(2.29991 + 4.10189i) q^{93} +(0.680631 + 9.50115i) q^{94} +(8.95188 - 7.43247i) q^{95} +(0.814170 + 9.76407i) q^{96} +(9.37084 - 9.37084i) q^{97} +(-6.40092 + 7.38877i) q^{98} +(8.19192 - 1.97552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

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