LMFDB - Embedded newform 224.2.u.c.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.729813 + 1.21135i) q^{2} +(1.74965 + 0.724727i) q^{3} +(-0.934745 - 1.76812i) q^{4} +(1.44353 + 3.48498i) q^{5} +(-2.15481 + 1.59052i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.82401 + 0.158094i) q^{8} +(0.414709 + 0.414709i) q^{9} +O(q^{10})$	\(q+(-0.729813 + 1.21135i) q^{2} +(1.74965 + 0.724727i) q^{3} +(-0.934745 - 1.76812i) q^{4} +(1.44353 + 3.48498i) q^{5} +(-2.15481 + 1.59052i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.82401 + 0.158094i) q^{8} +(0.414709 + 0.414709i) q^{9} +(-5.27504 - 0.794768i) q^{10} +(-2.63324 + 1.09072i) q^{11} +(-0.354067 - 3.77102i) q^{12} +(2.43617 - 5.88144i) q^{13} +(0.340499 + 1.37261i) q^{14} +7.14364i q^{15} +(-2.25250 + 3.30548i) q^{16} +6.50231i q^{17} +(-0.805018 + 0.199698i) q^{18} +(0.581888 - 1.40480i) q^{19} +(4.81254 - 5.80990i) q^{20} +(1.74965 - 0.724727i) q^{21} +(0.600524 - 3.98580i) q^{22} +(-3.10808 - 3.10808i) q^{23} +(4.82643 + 2.32324i) q^{24} +(-6.52579 + 6.52579i) q^{25} +(5.34654 + 7.24341i) q^{26} +(-1.74914 - 4.22279i) q^{27} +(-1.91121 - 0.589286i) q^{28} +(-3.27190 - 1.35527i) q^{29} +(-8.65346 - 5.21353i) q^{30} +3.10839 q^{31} +(-2.36019 - 5.14096i) q^{32} -5.39771 q^{33} +(-7.87659 - 4.74548i) q^{34} +(3.48498 + 1.44353i) q^{35} +(0.345608 - 1.12090i) q^{36} +(0.403202 + 0.973415i) q^{37} +(1.27704 + 1.73011i) q^{38} +(8.52487 - 8.52487i) q^{39} +(3.52557 + 10.0698i) q^{40} +(5.07868 + 5.07868i) q^{41} +(-0.399016 + 2.64835i) q^{42} +(4.48831 - 1.85912i) q^{43} +(4.38994 + 3.63634i) q^{44} +(-0.846609 + 2.04389i) q^{45} +(6.03331 - 1.49666i) q^{46} -9.40146i q^{47} +(-6.33666 + 4.15097i) q^{48} -1.00000i q^{49} +(-3.14242 - 12.6676i) q^{50} +(-4.71240 + 11.3767i) q^{51} +(-12.6763 + 1.19020i) q^{52} +(3.60715 - 1.49413i) q^{53} +(6.39183 + 0.963030i) q^{54} +(-7.60230 - 7.60230i) q^{55} +(2.10866 - 1.88508i) q^{56} +(2.03619 - 2.03619i) q^{57} +(4.02958 - 2.97433i) q^{58} +(-3.33172 - 8.04349i) q^{59} +(12.6308 - 6.67748i) q^{60} +(2.34669 + 0.972032i) q^{61} +(-2.26854 + 3.76535i) q^{62} +0.586487 q^{63} +(7.95001 + 0.892918i) q^{64} +24.0134 q^{65} +(3.93932 - 6.53852i) q^{66} +(-0.931743 - 0.385940i) q^{67} +(11.4969 - 6.07800i) q^{68} +(-3.18553 - 7.69056i) q^{69} +(-4.29200 + 3.16803i) q^{70} +(7.12660 - 7.12660i) q^{71} +(1.10558 + 1.23670i) q^{72} +(3.38133 + 3.38133i) q^{73} +(-1.47341 - 0.221992i) q^{74} +(-16.1472 + 6.68841i) q^{75} +(-3.02778 + 0.284283i) q^{76} +(-1.09072 + 2.63324i) q^{77} +(4.10505 + 16.5482i) q^{78} +1.35534i q^{79} +(-14.7711 - 3.07838i) q^{80} -10.4155i q^{81} +(-9.85856 + 2.44558i) q^{82} +(-1.64053 + 3.96059i) q^{83} +(-2.91688 - 2.41615i) q^{84} +(-22.6604 + 9.38626i) q^{85} +(-1.02358 + 6.79374i) q^{86} +(-4.74247 - 4.74247i) q^{87} +(-7.60872 + 2.66391i) q^{88} +(-8.99424 + 8.99424i) q^{89} +(-1.85801 - 2.51720i) q^{90} +(-2.43617 - 5.88144i) q^{91} +(-2.59020 + 8.40074i) q^{92} +(5.43858 + 2.25273i) q^{93} +(11.3885 + 6.86131i) q^{94} +5.73568 q^{95} +(-0.403711 - 10.7054i) q^{96} +1.01105 q^{97} +(1.21135 + 0.729813i) q^{98} +(-1.54436 - 0.639695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.729813	+	1.21135i	−0.516056	+	0.856555i
$2$	−0.729813	+	1.21135i	−0.516056	+	0.856555i
$3$	1.74965	+	0.724727i	1.01016	+	0.418421i	0.825512	−	0.564384i	$-0.190886\pi$
$3$	1.74965	+	0.724727i	1.01016	+	0.418421i	0.184646	+	0.982805i	$0.440886\pi$
$4$	−0.934745	−	1.76812i	−0.467372	−	0.884061i
$5$	1.44353	+	3.48498i	0.645565	+	1.55853i	0.819067	+	0.573698i	$0.194492\pi$
$5$	1.44353	+	3.48498i	0.645565	+	1.55853i	−0.173502	+	0.984833i	$0.555508\pi$
$6$	−2.15481	+	1.59052i	−0.879699	+	0.649327i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	2.82401	+	0.158094i	0.998437	+	0.0558947i
$9$	0.414709	+	0.414709i	0.138236	+	0.138236i
$10$	−5.27504	−	0.794768i	−1.66811	−	0.251328i
$11$	−2.63324	+	1.09072i	−0.793951	+	0.328865i	−0.742531	−	0.669812i	$-0.766375\pi$
$11$	−2.63324	+	1.09072i	−0.793951	+	0.328865i	−0.0514204	+	0.998677i	$0.516375\pi$
$12$	−0.354067	−	3.77102i	−0.102210	−	1.08860i
$13$	2.43617	−	5.88144i	0.675672	−	1.63122i	−0.0961412	−	0.995368i	$-0.530650\pi$
$13$	2.43617	−	5.88144i	0.675672	−	1.63122i	0.771813	−	0.635849i	$-0.219350\pi$
$14$	0.340499	+	1.37261i	0.0910021	+	0.366846i
$15$			7.14364i			1.84448i
$16$	−2.25250	+	3.30548i	−0.563126	+	0.826371i
$17$			6.50231i			1.57704i	0.615007	+	0.788521i	$0.289153\pi$
$17$			6.50231i			1.57704i	−0.615007	+	0.788521i	$0.710847\pi$
$18$	−0.805018	+	0.199698i	−0.189745	+	0.0470693i
$19$	0.581888	−	1.40480i	0.133494	−	0.322284i	−0.842971	−	0.537959i	$-0.819195\pi$
$19$	0.581888	−	1.40480i	0.133494	−	0.322284i	0.976465	+	0.215676i	$0.0691954\pi$
$20$	4.81254	−	5.80990i	1.07612	−	1.29913i
$21$	1.74965	−	0.724727i	0.381804	−	0.158148i
$22$	0.600524	−	3.98580i	0.128032	−	0.849776i
$23$	−3.10808	−	3.10808i	−0.648080	−	0.648080i	0.304448	−	0.952529i	$-0.401528\pi$
$23$	−3.10808	−	3.10808i	−0.648080	−	0.648080i	−0.952529	+	0.304448i	$0.901528\pi$
$24$	4.82643	+	2.32324i	0.985191	+	0.474230i
$25$	−6.52579	+	6.52579i	−1.30516	+	1.30516i
$26$	5.34654	+	7.24341i	1.04854	+	1.42055i
$27$	−1.74914	−	4.22279i	−0.336622	−	0.812677i
$28$	−1.91121	−	0.589286i	−0.361186	−	0.111365i
$29$	−3.27190	−	1.35527i	−0.607577	−	0.251667i	0.0576150	−	0.998339i	$-0.481650\pi$
$29$	−3.27190	−	1.35527i	−0.607577	−	0.251667i	−0.665192	+	0.746672i	$0.731650\pi$
$30$	−8.65346	−	5.21353i	−1.57990	−	0.951855i
$31$	3.10839			0.558283			0.279142	−	0.960250i	$-0.409950\pi$
$31$	3.10839			0.558283			0.279142	+	0.960250i	$0.409950\pi$
$32$	−2.36019	−	5.14096i	−0.417227	−	0.908802i
$33$	−5.39771			−0.939621
$34$	−7.87659	−	4.74548i	−1.35082	−	0.813842i
$35$	3.48498	+	1.44353i	0.589069	+	0.244001i
$36$	0.345608	−	1.12090i	0.0576014	−	0.186817i
$37$	0.403202	+	0.973415i	0.0662860	+	0.160028i	0.953551	−	0.301231i	$-0.0973976\pi$
$37$	0.403202	+	0.973415i	0.0662860	+	0.160028i	−0.887265	+	0.461260i	$0.847398\pi$
$38$	1.27704	+	1.73011i	0.207163	+	0.280661i
$39$	8.52487	−	8.52487i	1.36507	−	1.36507i
$40$	3.52557	+	10.0698i	0.557442	+	1.59218i
$41$	5.07868	+	5.07868i	0.793157	+	0.793157i	0.982006	−	0.188849i	$-0.0604758\pi$
$41$	5.07868	+	5.07868i	0.793157	+	0.793157i	−0.188849	+	0.982006i	$0.560476\pi$
$42$	−0.399016	+	2.64835i	−0.0615695	+	0.408649i
$43$	4.48831	−	1.85912i	0.684462	−	0.283513i	−0.0132290	−	0.999912i	$-0.504211\pi$
$43$	4.48831	−	1.85912i	0.684462	−	0.283513i	0.697691	+	0.716399i	$0.254211\pi$
$44$	4.38994	+	3.63634i	0.661808	+	0.548199i
$45$	−0.846609	+	2.04389i	−0.126205	+	0.304686i
$46$	6.03331	−	1.49666i	0.889562	−	0.220671i
$47$		−	9.40146i		−	1.37134i	−0.727911	−	0.685672i	$-0.759509\pi$
$47$		−	9.40146i		−	1.37134i	0.727911	−	0.685672i	$-0.240491\pi$
$48$	−6.33666	+	4.15097i	−0.914618	+	0.599141i
$49$		−	1.00000i		−	0.142857i
$50$	−3.14242	−	12.6676i	−0.444405	−	1.79147i
$51$	−4.71240	+	11.3767i	−0.659868	+	1.59306i
$52$	−12.6763	+	1.19020i	−1.75788	+	0.165051i
$53$	3.60715	−	1.49413i	0.495481	−	0.205235i	−0.120928	−	0.992661i	$-0.538587\pi$
$53$	3.60715	−	1.49413i	0.495481	−	0.205235i	0.616409	+	0.787426i	$0.288587\pi$
$54$	6.39183	+	0.963030i	0.869818	+	0.131052i
$55$	−7.60230	−	7.60230i	−1.02509	−	1.02509i
$56$	2.10866	−	1.88508i	0.281782	−	0.251905i
$57$	2.03619	−	2.03619i	0.269700	−	0.269700i
$58$	4.02958	−	2.97433i	0.529110	−	0.390549i
$59$	−3.33172	−	8.04349i	−0.433754	−	1.04717i	−0.978067	−	0.208292i	$-0.933210\pi$
$59$	−3.33172	−	8.04349i	−0.433754	−	1.04717i	0.544313	−	0.838882i	$-0.316790\pi$
$60$	12.6308	−	6.67748i	1.63063	−	0.862059i
$61$	2.34669	+	0.972032i	0.300463	+	0.124456i	0.527822	−	0.849355i	$-0.323009\pi$
$61$	2.34669	+	0.972032i	0.300463	+	0.124456i	−0.227358	+	0.973811i	$0.573009\pi$
$62$	−2.26854	+	3.76535i	−0.288105	+	0.478200i
$63$	0.586487			0.0738904
$64$	7.95001	+	0.892918i	0.993752	+	0.111615i
$65$	24.0134			2.97849
$66$	3.93932	−	6.53852i	0.484897	−	0.804837i
$67$	−0.931743	−	0.385940i	−0.113830	−	0.0471501i	0.325041	−	0.945700i	$-0.394622\pi$
$67$	−0.931743	−	0.385940i	−0.113830	−	0.0471501i	−0.438872	+	0.898550i	$0.644622\pi$
$68$	11.4969	−	6.07800i	1.39420	−	0.737066i
$69$	−3.18553	−	7.69056i	−0.383493	−	0.925834i
$70$	−4.29200	+	3.16803i	−0.512993	+	0.378652i
$71$	7.12660	−	7.12660i	0.845771	−	0.845771i	−0.143831	−	0.989602i	$-0.545942\pi$
$71$	7.12660	−	7.12660i	0.845771	−	0.845771i	0.989602	+	0.143831i	$0.0459421\pi$
$72$	1.10558	+	1.23670i	0.130293	+	0.145747i
$73$	3.38133	+	3.38133i	0.395755	+	0.395755i	0.876733	−	0.480978i	$-0.159718\pi$
$73$	3.38133	+	3.38133i	0.395755	+	0.395755i	−0.480978	+	0.876733i	$0.659718\pi$
$74$	−1.47341	−	0.221992i	−0.171280	−	0.0258061i
$75$	−16.1472	+	6.68841i	−1.86452	+	0.772311i
$76$	−3.02778	+	0.284283i	−0.347310	+	0.0326094i
$77$	−1.09072	+	2.63324i	−0.124299	+	0.300085i
$78$	4.10505	+	16.5482i	0.464805	+	1.87371i
$79$			1.35534i			0.152487i	0.997089	+	0.0762436i	$0.0242927\pi$
$79$			1.35534i			0.152487i	−0.997089	+	0.0762436i	$0.975707\pi$
$80$	−14.7711	−	3.07838i	−1.65146	−	0.344174i
$81$		−	10.4155i		−	1.15728i
$82$	−9.85856	+	2.44558i	−1.08870	+	0.270069i
$83$	−1.64053	+	3.96059i	−0.180072	+	0.434731i	−0.987981	−	0.154575i	$-0.950599\pi$
$83$	−1.64053	+	3.96059i	−0.180072	+	0.434731i	0.807909	+	0.589307i	$0.200599\pi$
$84$	−2.91688	−	2.41615i	−0.318257	−	0.263624i
$85$	−22.6604	+	9.38626i	−2.45787	+	1.01808i
$86$	−1.02358	+	6.79374i	−0.110376	+	0.732588i
$87$	−4.74247	−	4.74247i	−0.508446	−	0.508446i
$88$	−7.60872	+	2.66391i	−0.811092	+	0.283974i
$89$	−8.99424	+	8.99424i	−0.953387	+	0.953387i	−0.998961	−	0.0455735i	$-0.985488\pi$
$89$	−8.99424	+	8.99424i	−0.953387	+	0.953387i	0.0455735	+	0.998961i	$0.485488\pi$
$90$	−1.85801	−	2.51720i	−0.195851	−	0.265336i
$91$	−2.43617	−	5.88144i	−0.255380	−	0.616542i
$92$	−2.59020	+	8.40074i	−0.270047	+	0.875837i
$93$	5.43858	+	2.25273i	0.563954	+	0.233598i
$94$	11.3885	+	6.86131i	1.17463	+	0.707690i
$95$	5.73568			0.588468
$96$	−0.403711	−	10.7054i	−0.0412035	−	1.09261i
$97$	1.01105			0.102657			0.0513283	−	0.998682i	$-0.483655\pi$
$97$	1.01105			0.102657			0.0513283	+	0.998682i	$0.483655\pi$
$98$	1.21135	+	0.729813i	0.122365	+	0.0737223i
$99$	−1.54436	−	0.639695i	−0.155214	−	0.0642917i
$100$	17.6383	+	5.43844i	1.76383	+	0.543844i
$101$	−5.32793	−	12.8628i	−0.530148	−	1.27989i	−0.931425	−	0.363934i	$-0.881433\pi$
$101$	−5.32793	−	12.8628i	−0.530148	−	1.27989i	0.401276	−	0.915957i	$-0.368567\pi$
$102$	−10.3421	−	14.0113i	−1.02402	−	1.38732i
$103$	−12.5880	+	12.5880i	−1.24033	+	1.24033i	−0.280466	+	0.959864i	$0.590489\pi$
$103$	−12.5880	+	12.5880i	−1.24033	+	1.24033i	−0.959864	+	0.280466i	$0.909511\pi$
$104$	7.80958	−	16.2241i	0.765792	−	1.59090i
$105$	5.05132	+	5.05132i	0.492958	+	0.492958i
$106$	−0.822630	+	5.45997i	−0.0799009	+	0.530319i
$107$	−9.24632	+	3.82995i	−0.893875	+	0.370255i	−0.781862	−	0.623451i	$-0.785730\pi$
$107$	−9.24632	+	3.82995i	−0.893875	+	0.370255i	−0.112013	+	0.993707i	$0.535730\pi$
$108$	−5.83141	+	7.03992i	−0.561128	+	0.677417i
$109$	−2.26472	+	5.46751i	−0.216921	+	0.523693i	−0.994457	−	0.105145i	$-0.966469\pi$
$109$	−2.26472	+	5.46751i	−0.216921	+	0.523693i	0.777536	+	0.628838i	$0.216469\pi$
$110$	14.7573	−	3.66080i	1.40706	−	0.349043i
$111$			1.99534i			0.189390i
$112$	0.744569	+	3.93009i	0.0703551	+	0.371359i
$113$			9.51463i			0.895061i	0.894269	+	0.447530i	$0.147696\pi$
$113$			9.51463i			0.895061i	−0.894269	+	0.447530i	$0.852304\pi$
$114$	0.980505	+	3.95259i	0.0918327	+	0.370194i
$115$	6.34501	−	15.3182i	0.591676	−	1.42843i
$116$	0.662119	+	7.05195i	0.0614762	+	0.654757i
$117$	3.44938	−	1.42878i	0.318896	−	0.132091i
$118$	12.1750	+	1.83436i	1.12080	+	0.168867i
$119$	4.59783	+	4.59783i	0.421482	+	0.421482i
$120$	−1.12937	+	20.1737i	−0.103097	+	1.84160i
$121$	−2.03390	+	2.03390i	−0.184900	+	0.184900i
$122$	−2.89012	+	2.13327i	−0.261659	+	0.193137i
$123$	5.20523	+	12.5665i	0.469340	+	1.13309i
$124$	−2.90555	−	5.49601i	−0.260926	−	0.493556i
$125$	−14.7375	−	6.10448i	−1.31816	−	0.546001i
$126$	−0.428026	+	0.710441i	−0.0381316	+	0.0632911i
$127$	6.58940			0.584715			0.292357	−	0.956309i	$-0.405560\pi$
$127$	6.58940			0.584715			0.292357	+	0.956309i	$0.405560\pi$
$128$	−6.88366	+	8.97860i	−0.608436	+	0.793603i
$129$	9.20031			0.810042
$130$	−17.5253	+	29.0886i	−1.53707	+	2.55124i
$131$	−8.23083	−	3.40932i	−0.719131	−	0.297874i	−0.00705412	−	0.999975i	$-0.502245\pi$
$131$	−8.23083	−	3.40932i	−0.719131	−	0.297874i	−0.712077	+	0.702101i	$0.752245\pi$
$132$	5.04548	+	9.54381i	0.439153	+	0.830682i
$133$	−0.581888	−	1.40480i	−0.0504561	−	0.121812i
$134$	1.14751	−	0.847003i	0.0991296	−	0.0731699i
$135$	12.1914	−	12.1914i	1.04927	−	1.04927i
$136$	−1.02798	+	18.3626i	−0.0881484	+	1.57458i
$137$	−10.6589	−	10.6589i	−0.910650	−	0.910650i	0.0856733	−	0.996323i	$-0.472696\pi$
$137$	−10.6589	−	10.6589i	−0.910650	−	0.910650i	−0.996323	+	0.0856733i	$0.972696\pi$
$138$	11.6408	+	1.75387i	0.990932	+	0.149299i
$139$	−3.55792	+	1.47374i	−0.301779	+	0.125001i	−0.528435	−	0.848974i	$-0.677221\pi$
$139$	−3.55792	+	1.47374i	−0.301779	+	0.125001i	0.226656	+	0.973975i	$0.427221\pi$
$140$	−0.705238	−	7.51120i	−0.0596035	−	0.634812i
$141$	6.81349	−	16.4492i	0.573799	−	1.38527i
$142$	3.43173	+	13.8339i	0.287984	+	1.16092i
$143$			18.1444i			1.51731i
$144$	−2.30495	+	0.436679i	−0.192079	+	0.0363900i
$145$		−	13.3589i		−	1.10940i
$146$	−6.56373	+	1.62824i	−0.543218	+	0.134754i
$147$	0.724727	−	1.74965i	0.0597745	−	0.144308i
$148$	1.34423	−	1.62280i	0.110495	−	0.133394i
$149$	3.85494	−	1.59677i	0.315809	−	0.130812i	−0.219148	−	0.975692i	$-0.570328\pi$
$149$	3.85494	−	1.59677i	0.315809	−	0.130812i	0.534957	+	0.844879i	$0.320328\pi$
$150$	3.68246	−	24.4413i	0.300672	−	1.99562i
$151$	7.19011	+	7.19011i	0.585123	+	0.585123i	0.936307	−	0.351184i	$-0.114221\pi$
$151$	7.19011	+	7.19011i	0.585123	+	0.585123i	−0.351184	+	0.936307i	$0.614221\pi$
$152$	1.86535	−	3.87517i	0.151299	−	0.314318i
$153$	−2.69657	+	2.69657i	−0.218004	+	0.218004i
$154$	−2.39375	−	3.24302i	−0.192894	−	0.261330i
$155$	4.48704	+	10.8327i	0.360408	+	0.870102i
$156$	−23.0416	−	7.10442i	−1.84480	−	0.568809i
$157$	14.6135	+	6.05312i	1.16629	+	0.483092i	0.879963	−	0.475042i	$-0.157567\pi$
$157$	14.6135	+	6.05312i	1.16629	+	0.483092i	0.286323	+	0.958133i	$0.407567\pi$
$158$	−1.64179	−	0.989142i	−0.130614	−	0.0786919i
$159$	7.39408			0.586388
$160$	14.5092	−	15.6463i	1.14705	−	1.23695i
$161$	−4.39550			−0.346414
$162$	12.6168	+	7.60137i	0.991271	+	0.597220i
$163$	−6.20182	−	2.56888i	−0.485764	−	0.201210i	0.126341	−	0.991987i	$-0.459677\pi$
$163$	−6.20182	−	2.56888i	−0.485764	−	0.201210i	−0.612104	+	0.790777i	$0.709677\pi$
$164$	4.23245	−	13.7270i	0.330499	−	1.07190i
$165$	−7.79174	−	18.8109i	−0.606586	−	1.46443i
$166$	−3.60039	−	4.87775i	−0.279444	−	0.378587i
$167$	−8.00706	+	8.00706i	−0.619605	+	0.619605i	−0.945430	−	0.325825i	$-0.894358\pi$
$167$	−8.00706	+	8.00706i	−0.619605	+	0.619605i	0.325825	+	0.945430i	$0.394358\pi$
$168$	5.05558	−	1.77002i	0.390047	−	0.136560i
$169$	−19.4640	−	19.4640i	−1.49723	−	1.49723i
$170$	5.16783	−	34.3000i	0.396355	−	2.63069i
$171$	0.823897	−	0.341269i	0.0630050	−	0.0260975i
$172$	−7.48258	−	6.19808i	−0.570541	−	0.472599i
$173$	−5.25090	+	12.6768i	−0.399218	+	0.963799i	0.588633	+	0.808400i	$0.299666\pi$
$173$	−5.25090	+	12.6768i	−0.399218	+	0.963799i	−0.987852	+	0.155399i	$0.950334\pi$
$174$	9.20592	−	2.28368i	0.697899	−	0.173125i
$175$			9.22887i			0.697637i
$176$	2.32602	−	11.1610i	0.175330	−	0.841291i
$177$		−	16.4878i		−	1.23930i
$178$	−4.33107	−	17.4593i	−0.324627	−	1.30863i
$179$	−2.96868	+	7.16702i	−0.221889	+	0.535689i	−0.995147	−	0.0984041i	$-0.968626\pi$
$179$	−2.96868	+	7.16702i	−0.221889	+	0.535689i	0.773257	+	0.634093i	$0.218626\pi$
$180$	4.40522	−	0.413613i	0.328345	−	0.0308289i
$181$	−6.16090	+	2.55193i	−0.457936	+	0.189683i	−0.599713	−	0.800215i	$-0.704719\pi$
$181$	−6.16090	+	2.55193i	−0.457936	+	0.189683i	0.141777	+	0.989899i	$0.454719\pi$
$182$	8.90244	+	1.34129i	0.659892	+	0.0994232i
$183$	3.40142	+	3.40142i	0.251440	+	0.251440i
$184$	−8.28588	−	9.26862i	−0.610843	−	0.683292i
$185$	−2.81030	+	2.81030i	−0.206618	+	0.206618i
$186$	−6.69800	+	4.94395i	−0.491121	+	0.362508i
$187$	−7.09223	−	17.1221i	−0.518635	−	1.25210i
$188$	−16.6229	+	8.78796i	−1.21235	+	0.640928i
$189$	−4.22279	−	1.74914i	−0.307163	−	0.127231i
$190$	−4.18597	+	6.94792i	−0.303682	+	0.504055i
$191$	17.5840			1.27233			0.636167	−	0.771552i	$-0.280519\pi$
$191$	17.5840			1.27233			0.636167	+	0.771552i	$0.280519\pi$
$192$	13.2626	+	7.32388i	0.957144	+	0.528555i
$193$	0.448251			0.0322658			0.0161329	−	0.999870i	$-0.494865\pi$
$193$	0.448251			0.0322658			0.0161329	+	0.999870i	$0.494865\pi$
$194$	−0.737878	+	1.22474i	−0.0529765	+	0.0879309i
$195$	42.0149	+	17.4031i	3.00875	+	1.24626i
$196$	−1.76812	+	0.934745i	−0.126294	+	0.0667675i
$197$	−3.88901	−	9.38890i	−0.277080	−	0.668931i	0.722672	−	0.691191i	$-0.242914\pi$
$197$	−3.88901	−	9.38890i	−0.277080	−	0.668931i	−0.999752	+	0.0222601i	$0.992914\pi$
$198$	1.90199	−	1.40390i	0.135168	−	0.0997711i
$199$	8.28449	−	8.28449i	0.587272	−	0.587272i	−0.349620	−	0.936892i	$-0.613689\pi$
$199$	8.28449	−	8.28449i	0.587272	−	0.587272i	0.936892	+	0.349620i	$0.113689\pi$
$200$	−19.4606	+	17.3972i	−1.37607	+	1.23017i
$201$	−1.35052	−	1.35052i	−0.0952582	−	0.0952582i
$202$	19.4697	+	2.93342i	1.36988	+	0.206395i
$203$	−3.27190	+	1.35527i	−0.229643	+	0.0951211i
$204$	24.5203	−	2.30225i	1.71677	−	0.161190i
$205$	−10.3679	+	25.0303i	−0.724125	+	1.74819i
$206$	−6.06159	−	24.4353i	−0.422331	−	1.70249i
$207$		−	2.57790i		−	0.179176i
$208$	13.9535	+	21.3007i	0.967502	+	1.47694i
$209$			4.33386i			0.299779i
$210$	−9.80544	+	2.43240i	−0.676640	+	0.167852i
$211$	−1.93104	+	4.66194i	−0.132938	+	0.320941i	−0.976306	−	0.216396i	$-0.930570\pi$
$211$	−1.93104	+	4.66194i	−0.132938	+	0.320941i	0.843367	+	0.537337i	$0.180570\pi$
$212$	−6.01358	−	4.98125i	−0.413014	−	0.342114i
$213$	17.6338	−	7.30418i	1.20825	−	0.500474i
$214$	2.10867	−	13.9957i	0.144146	−	0.956726i
$215$	12.9580	+	12.9580i	0.883729	+	0.883729i
$216$	−4.27198	−	12.2017i	−0.290671	−	0.830222i
$217$	2.19796	−	2.19796i	0.149207	−	0.149207i
$218$	−4.97026	−	6.73363i	−0.336628	−	0.456059i
$219$	3.46559	+	8.36668i	0.234183	+	0.565368i
$220$	−6.33558	+	20.5480i	−0.427145	+	1.38535i
$221$	38.2429	+	15.8407i	2.57250	+	1.06556i
$222$	−2.41706	−	1.45623i	−0.162223	−	0.0977356i
$223$	−22.5689			−1.51133			−0.755664	−	0.654959i	$-0.772686\pi$
$223$	−22.5689			−1.51133			−0.755664	+	0.654959i	$0.772686\pi$
$224$	−5.30412	−	1.96630i	−0.354396	−	0.131379i
$225$	−5.41261			−0.360840
$226$	−11.5256	−	6.94390i	−0.766669	−	0.461902i
$227$	−14.1759	−	5.87185i	−0.940888	−	0.389728i	−0.141089	−	0.989997i	$-0.545060\pi$
$227$	−14.1759	−	5.87185i	−0.940888	−	0.389728i	−0.799799	+	0.600268i	$0.795060\pi$
$228$	−5.50356	−	1.69692i	−0.364482	−	0.112381i
$229$	−5.83040	−	14.0758i	−0.385284	−	0.930157i	−0.990925	−	0.134419i	$-0.957083\pi$
$229$	−5.83040	−	14.0758i	−0.385284	−	0.930157i	0.605641	−	0.795738i	$-0.292917\pi$
$230$	13.9251	+	18.8655i	0.918192	+	1.24395i
$231$	−3.81676	+	3.81676i	−0.251124	+	0.251124i
$232$	−9.02561	−	4.34455i	−0.592561	−	0.285234i
$233$	13.4881	+	13.4881i	0.883638	+	0.883638i	0.993902	−	0.110265i	$-0.0351698\pi$
$233$	13.4881	+	13.4881i	0.883638	+	0.883638i	−0.110265	+	0.993902i	$0.535170\pi$
$234$	−0.786650	+	5.22116i	−0.0514249	+	0.341318i
$235$	32.7639	−	13.5713i	2.13728	−	0.885291i
$236$	−11.1076	+	13.4095i	−0.723041	+	0.872884i
$237$	−0.982248	+	2.37136i	−0.0638038	+	0.154036i
$238$	−8.92515	+	2.21403i	−0.578531	+	0.143514i
$239$			22.1569i			1.43321i	0.697478	+	0.716606i	$0.254305\pi$
$239$			22.1569i			1.43321i	−0.697478	+	0.716606i	$0.745695\pi$
$240$	−23.6132	−	16.0911i	−1.52423	−	1.03868i
$241$			1.85041i			0.119195i	0.998222	+	0.0595976i	$0.0189818\pi$
$241$			1.85041i			0.119195i	−0.998222	+	0.0595976i	$0.981018\pi$
$242$	−0.979402	−	3.94814i	−0.0629583	−	0.253796i
$243$	2.30097	−	5.55504i	0.147607	−	0.356356i
$244$	−0.474889	−	5.05784i	−0.0304016	−	0.323795i
$245$	3.48498	−	1.44353i	0.222647	−	0.0922235i
$246$	−19.0213	−	2.86587i	−1.21276	−	0.182721i
$247$	−6.84467	−	6.84467i	−0.435516	−	0.435516i
$248$	8.77811	+	0.491418i	0.557410	+	0.0312051i
$249$	−5.74069	+	5.74069i	−0.363801	+	0.363801i
$250$	18.1503	−	13.3972i	1.14793	−	0.847312i
$251$	0.874117	+	2.11031i	0.0551738	+	0.133201i	0.949063	−	0.315087i	$-0.102034\pi$
$251$	0.874117	+	2.11031i	0.0551738	+	0.133201i	−0.893889	+	0.448288i	$0.852034\pi$
$252$	−0.548215	−	1.03698i	−0.0345343	−	0.0653236i
$253$	11.5744	+	4.79427i	0.727676	+	0.301413i
$254$	−4.80903	+	7.98208i	−0.301746	+	0.500840i
$255$	−46.4502			−2.90882
$256$	−5.85245	−	14.8912i	−0.365778	−	0.930702i
$257$	24.8369			1.54928			0.774642	−	0.632399i	$-0.217930\pi$
$257$	24.8369			1.54928			0.774642	+	0.632399i	$0.217930\pi$
$258$	−6.71451	+	11.1448i	−0.418027	+	0.693846i
$259$	0.973415	+	0.403202i	0.0604851	+	0.0250537i
$260$	−22.4464	−	42.4586i	−1.39206	−	2.63317i
$261$	−0.794846	−	1.91893i	−0.0491997	−	0.118779i
$262$	10.1369	−	7.48226i	0.626257	−	0.462256i
$263$	−11.6463	+	11.6463i	−0.718141	+	0.718141i	−0.968224	−	0.250084i	$-0.919542\pi$
$263$	−11.6463	+	11.6463i	−0.718141	+	0.718141i	0.250084	+	0.968224i	$0.419542\pi$
$264$	−15.2432	−	0.853347i	−0.938152	−	0.0525199i
$265$	10.4140	+	10.4140i	0.639730	+	0.639730i
$266$	2.12638	+	0.320372i	0.130377	+	0.0196433i
$267$	−22.2551	+	9.21836i	−1.36199	+	0.564155i
$268$	0.188552	+	2.00819i	0.0115176	+	0.122670i
$269$	6.46189	−	15.6004i	0.393988	−	0.951172i	−0.595074	−	0.803671i	$-0.702877\pi$
$269$	6.46189	−	15.6004i	0.393988	−	0.951172i	0.989062	−	0.147501i	$-0.0471229\pi$
$270$	5.87063	+	23.6656i	0.357275	+	1.44024i
$271$		−	11.9824i		−	0.727881i	−0.931422	−	0.363940i	$-0.881431\pi$
$271$		−	11.9824i		−	0.727881i	0.931422	−	0.363940i	$-0.118569\pi$
$272$	−21.4933	−	14.6465i	−1.30322	−	0.888074i
$273$		−	12.0560i		−	0.729661i
$274$	20.6907	−	5.13266i	1.24997	−	0.310075i
$275$	10.0661	−	24.3018i	0.607011	−	1.46545i
$276$	−10.6202	+	12.8211i	−0.639259	+	0.771740i
$277$	12.8441	−	5.32021i	0.771729	−	0.319661i	0.0381566	−	0.999272i	$-0.487851\pi$
$277$	12.8441	−	5.32021i	0.771729	−	0.319661i	0.733573	+	0.679611i	$0.237851\pi$
$278$	0.811402	−	5.38545i	0.0486647	−	0.322998i
$279$	1.28908	+	1.28908i	0.0771750	+	0.0771750i
$280$	9.61339	+	4.62748i	0.574510	+	0.276545i
$281$	2.04746	−	2.04746i	0.122141	−	0.122141i	−0.643394	−	0.765535i	$-0.722474\pi$
$281$	2.04746	−	2.04746i	0.122141	−	0.122141i	0.765535	+	0.643394i	$0.222474\pi$
$282$	14.9532	+	20.2584i	0.890450	+	1.20637i
$283$	6.07132	+	14.6575i	0.360902	+	0.871295i	0.995169	+	0.0981806i	$0.0313023\pi$
$283$	6.07132	+	14.6575i	0.360902	+	0.871295i	−0.634266	+	0.773115i	$0.718698\pi$
$284$	−19.2622	−	5.93914i	−1.14300	−	0.352423i
$285$	10.0354	+	4.15680i	0.594446	+	0.246227i
$286$	−21.9793	−	13.2420i	−1.29966	−	0.783018i
$287$	7.18234			0.423960
$288$	1.15321	−	3.11079i	0.0679534	−	0.183305i
$289$	−25.2801			−1.48706
$290$	16.1823	+	9.74950i	0.950258	+	0.572510i
$291$	1.76898	+	0.732735i	0.103699	+	0.0429537i
$292$	2.81792	−	9.13929i	0.164907	−	0.534837i
$293$	−3.01716	−	7.28406i	−0.176264	−	0.425539i	0.810913	−	0.585166i	$-0.198971\pi$
$293$	−3.01716	−	7.28406i	−0.176264	−	0.425539i	−0.987177	+	0.159627i	$0.948971\pi$
$294$	1.59052	+	2.15481i	0.0927610	+	0.125671i
$295$	23.2220	−	23.2220i	1.35204	−	1.35204i
$296$	0.984753	+	2.81267i	0.0572376	+	0.163483i
$297$	9.21180	+	9.21180i	0.534523	+	0.534523i
$298$	−0.879139	+	5.83503i	−0.0509271	+	0.338014i
$299$	−25.8518	+	10.7082i	−1.49505	+	0.619270i
$300$	26.9195	+	22.2983i	1.55420	+	1.28739i
$301$	1.85912	−	4.48831i	0.107158	−	0.258702i
$302$	−13.9572	+	3.46231i	−0.803146	+	0.199234i
$303$		−	26.3665i		−	1.51472i
$304$	3.33284	+	5.08774i	0.191152	+	0.291802i
$305$			9.58134i			0.548626i
$306$	−1.29850	−	5.23448i	−0.0742302	−	0.299235i
$307$	4.56669	−	11.0250i	0.260635	−	0.629228i	−0.738343	−	0.674425i	$-0.764391\pi$
$307$	4.56669	−	11.0250i	0.260635	−	0.629228i	0.998978	+	0.0451968i	$0.0143915\pi$
$308$	5.67543	−	0.532875i	0.323388	−	0.0303634i
$309$	−31.1473	+	12.9016i	−1.77191	+	0.733949i
$310$	−16.3969	−	2.47045i	−0.931281	−	0.140312i
$311$	−12.3591	−	12.3591i	−0.700822	−	0.700822i	0.263765	−	0.964587i	$-0.415036\pi$
$311$	−12.3591	−	12.3591i	−0.700822	−	0.700822i	−0.964587	+	0.263765i	$0.915036\pi$
$312$	25.4220	−	22.7265i	1.43924	−	1.28664i
$313$	2.27228	−	2.27228i	0.128437	−	0.128437i	−0.639966	−	0.768403i	$-0.721052\pi$
$313$	2.27228	−	2.27228i	0.128437	−	0.128437i	0.768403	+	0.639966i	$0.221052\pi$
$314$	−17.9976	+	13.2845i	−1.01566	+	0.749686i
$315$	0.846609	+	2.04389i	0.0477010	+	0.115160i
$316$	2.39640	−	1.26689i	0.134808	−	0.0712683i
$317$	−18.2232	−	7.54829i	−1.02352	−	0.423954i	−0.193148	−	0.981170i	$-0.561870\pi$
$317$	−18.2232	−	7.54829i	−1.02352	−	0.423954i	−0.830368	+	0.557216i	$0.811870\pi$
$318$	−5.39630	+	8.95683i	−0.302609	+	0.502274i
$319$	10.0939			0.565151
$320$	8.36425	+	28.9946i	0.467576	+	1.62085i
$321$	−18.9534			−1.05788
$322$	3.20789	−	5.32449i	0.178769	−	0.296722i
$323$	9.13446	+	3.78362i	0.508255	+	0.210526i
$324$	−18.4159	+	9.73583i	−1.02310	+	0.540879i
$325$	22.4831	+	54.2790i	1.24714	+	3.01086i
$326$	7.63798	−	5.63778i	0.423029	−	0.312248i
$327$	−7.92490	+	7.92490i	−0.438248	+	0.438248i
$328$	13.5393	+	15.1451i	0.747583	+	0.836250i
$329$	−6.64784	−	6.64784i	−0.366507	−	0.366507i
$330$	28.4732	+	4.28993i	1.56740	+	0.236153i
$331$	5.37837	−	2.22779i	0.295622	−	0.122451i	−0.229943	−	0.973204i	$-0.573854\pi$
$331$	5.37837	−	2.22779i	0.295622	−	0.122451i	0.525565	+	0.850753i	$0.323854\pi$
$332$	8.53628	−	0.801485i	0.468489	−	0.0439872i
$333$	−0.236472	+	0.570895i	−0.0129586	+	0.0312849i
$334$	−3.85570	−	15.5430i	−0.210975	−	0.850476i
$335$		−	3.80422i		−	0.207847i
$336$	−1.54551	+	7.41587i	−0.0843146	+	0.404569i
$337$			1.91866i			0.104516i	0.998634	+	0.0522582i	$0.0166419\pi$
$337$			1.91866i			0.104516i	−0.998634	+	0.0522582i	$0.983358\pi$
$338$	37.7828	−	9.37264i	2.05511	−	0.509805i
$339$	−6.89550	+	16.6472i	−0.374512	+	0.904153i
$340$	37.7778	+	31.2927i	2.04879	+	1.69708i
$341$	−8.18513	+	3.39039i	−0.443250	+	0.183600i
$342$	−0.187894	+	1.24709i	−0.0101601	+	0.0674350i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	12.9689	−	4.54059i	0.699238	−	0.244812i
$345$	22.2030	−	22.2030i	1.19537	−	1.19537i
$346$	−11.5239	−	15.6124i	−0.619527	−	0.839327i
$347$	8.66773	+	20.9257i	0.465308	+	1.12335i	0.966189	+	0.257837i	$0.0830096\pi$
$347$	8.66773	+	20.9257i	0.465308	+	1.12335i	−0.500880	+	0.865516i	$0.666990\pi$
$348$	−3.95226	+	12.8183i	−0.211864	+	0.687131i
$349$	−13.9558	−	5.78067i	−0.747035	−	0.309432i	−0.0235038	−	0.999724i	$-0.507482\pi$
$349$	−13.9558	−	5.78067i	−0.747035	−	0.309432i	−0.723531	+	0.690292i	$0.757482\pi$
$350$	−11.1794	−	6.73535i	−0.597564	−	0.360020i
$351$	−29.0973			−1.55310
$352$	11.8223	+	10.9631i	0.630132	+	0.584333i
$353$	−17.8712			−0.951186			−0.475593	−	0.879665i	$-0.657766\pi$
$353$	−17.8712			−0.951186			−0.475593	+	0.879665i	$0.657766\pi$
$354$	19.9726	+	12.0331i	1.06153	+	0.639550i
$355$	35.1235	+	14.5486i	1.86416	+	0.772161i
$356$	24.3102	+	7.49559i	1.28844	+	0.397265i
$357$	4.71240	+	11.3767i	0.249407	+	0.602121i
$358$	−6.51520	−	8.82670i	−0.344339	−	0.466506i
$359$	−13.3552	+	13.3552i	−0.704861	+	0.704861i	−0.965450	−	0.260589i	$-0.916083\pi$
$359$	−13.3552	+	13.3552i	−0.704861	+	0.704861i	0.260589	+	0.965450i	$0.416083\pi$
$360$	−2.71396	+	5.63813i	−0.143038	+	0.297155i
$361$	11.8002	+	11.8002i	0.621061	+	0.621061i
$362$	1.40503	−	9.32545i	0.0738465	−	0.490135i
$363$	−5.03263	+	2.08459i	−0.264145	+	0.109412i
$364$	−8.12189	+	9.80509i	−0.425703	+	0.513926i
$365$	−6.90284	+	16.6649i	−0.361311	+	0.872283i
$366$	−6.60272	+	1.63791i	−0.345130	+	0.0856152i
$367$			18.8765i			0.985344i	0.870215	+	0.492672i	$0.163980\pi$
$367$			18.8765i			0.985344i	−0.870215	+	0.492672i	$0.836020\pi$
$368$	17.2747	−	3.27275i	0.900506	−	0.170604i
$369$			4.21235i			0.219286i
$370$	−1.35327	−	5.45526i	−0.0703530	−	0.283605i
$371$	1.49413	−	3.60715i	0.0775715	−	0.187274i
$372$	−1.10058	−	11.7218i	−0.0570623	−	0.607747i
$373$	−8.79738	+	3.64399i	−0.455511	+	0.188679i	−0.598628	−	0.801027i	$-0.704287\pi$
$373$	−8.79738	+	3.64399i	−0.455511	+	0.188679i	0.143117	+	0.989706i	$0.454287\pi$
$374$	25.9169	+	3.90480i	1.34013	+	0.201912i
$375$	−21.3613	−	21.3613i	−1.10310	−	1.10310i
$376$	1.48632	−	26.5498i	0.0766509	−	1.36920i
$377$	−15.9418	+	15.9418i	−0.821046	+	0.821046i
$378$	5.20067	−	3.83874i	0.267494	−	0.197444i
$379$	−6.22368	−	15.0253i	−0.319689	−	0.771798i	−0.999270	−	0.0381974i	$-0.987838\pi$
$379$	−6.22368	−	15.0253i	−0.319689	−	0.771798i	0.679581	−	0.733600i	$-0.262162\pi$
$380$	−5.36139	−	10.1414i	−0.275034	−	0.520241i
$381$	11.5291	+	4.77551i	0.590654	+	0.244657i
$382$	−12.8330	+	21.3004i	−0.656595	+	1.08982i
$383$	−9.20639			−0.470425			−0.235212	−	0.971944i	$-0.575579\pi$
$383$	−9.20639			−0.470425			−0.235212	+	0.971944i	$0.575579\pi$
$384$	−18.5510	+	10.7206i	−0.946676	+	0.547082i
$385$	−10.7513			−0.547936
$386$	−0.327140	+	0.542990i	−0.0166510	+	0.0276374i
$387$	2.63234	+	1.09035i	0.133809	+	0.0554256i
$388$	−0.945073	−	1.78766i	−0.0479788	−	0.0907546i
$389$	−11.1828	−	26.9978i	−0.566993	−	1.36884i	−0.904078	−	0.427368i	$-0.859441\pi$
$389$	−11.1828	−	26.9978i	−0.566993	−	1.36884i	0.337085	−	0.941474i	$-0.390559\pi$
$390$	−51.7443	+	38.1937i	−2.62018	+	1.93402i
$391$	20.2097	−	20.2097i	1.02205	−	1.02205i
$392$	0.158094	−	2.82401i	0.00798496	−	0.142634i
$393$	−11.9302	−	11.9302i	−0.601800	−	0.601800i
$394$	14.2115	+	2.14119i	0.715965	+	0.107871i
$395$	−4.72332	+	1.95646i	−0.237656	+	0.0984403i
$396$	0.312524	+	3.32857i	0.0157049	+	0.167267i
$397$	6.58383	−	15.8948i	0.330433	−	0.797736i	−0.668125	−	0.744049i	$-0.732903\pi$
$397$	6.58383	−	15.8948i	0.330433	−	0.797736i	0.998558	−	0.0536868i	$-0.0170973\pi$
$398$	3.98930	+	16.0816i	0.199965	+	0.806096i
$399$		−	2.87961i		−	0.144161i
$400$	−6.87152	−	36.2703i	−0.343576	−	1.81351i
$401$		−	24.3608i		−	1.21652i	−0.793737	−	0.608261i	$-0.791868\pi$
$401$		−	24.3608i		−	1.21652i	0.793737	−	0.608261i	$-0.208132\pi$
$402$	2.62158	−	0.650326i	0.130752	−	0.0324353i
$403$	7.57257	−	18.2818i	0.377216	−	0.910681i
$404$	−17.7627	+	21.4438i	−0.883725	+	1.06687i
$405$	36.2978	−	15.0350i	1.80365	−	0.747097i
$406$	0.746175	−	4.95252i	0.0370320	−	0.245789i
$407$	−2.12345	−	2.12345i	−0.105256	−	0.105256i
$408$	−15.1064	+	31.3830i	−0.747880	+	1.55369i
$409$	17.0589	−	17.0589i	0.843511	−	0.843511i	−0.145803	−	0.989314i	$-0.546577\pi$
$409$	17.0589	−	17.0589i	0.843511	−	0.843511i	0.989314	+	0.145803i	$0.0465766\pi$
$410$	−22.7539	−	30.8266i	−1.12373	−	1.52242i
$411$	−10.9245	−	26.3740i	−0.538865	−	1.30094i
$412$	34.0236	+	10.4905i	1.67622	+	0.516831i
$413$	−8.04349	−	3.33172i	−0.395794	−	0.163943i
$414$	3.12274	+	1.88139i	0.153474	+	0.0924650i
$415$	−16.1707			−0.793790
$416$	−35.9861	+	1.35707i	−1.76436	+	0.0665360i
$417$	−7.29316			−0.357147
$418$	−5.24982	−	3.16291i	−0.256777	−	0.154703i
$419$	36.6700	+	15.1892i	1.79145	+	0.742043i	0.989479	+	0.144679i	$0.0462149\pi$
$419$	36.6700	+	15.1892i	1.79145	+	0.742043i	0.801970	+	0.597364i	$0.203785\pi$
$420$	4.20965	−	13.6530i	0.205410	−	0.666200i
$421$	10.1569	+	24.5210i	0.495018	+	1.19508i	0.952136	+	0.305673i	$0.0988815\pi$
$421$	10.1569	+	24.5210i	0.495018	+	1.19508i	−0.457119	+	0.889406i	$0.651118\pi$
$422$	−4.23795	−	5.74152i	−0.206300	−	0.279493i
$423$	3.89887	−	3.89887i	0.189569	−	0.189569i
$424$	10.4228	−	3.64917i	0.506178	−	0.177219i
$425$	−42.4328	−	42.4328i	−2.05829	−	2.05829i
$426$	−4.02149	+	26.6915i	−0.194842	+	1.29321i
$427$	2.34669	−	0.972032i	0.113564	−	0.0470399i
$428$	15.4148	+	12.7686i	0.745101	+	0.617193i
$429$	−13.1497	+	31.7463i	−0.634876	+	1.53273i
$430$	−25.1536	+	6.23977i	−1.21302	+	0.300909i
$431$			32.7133i			1.57575i	0.615838	+	0.787873i	$0.288818\pi$
$431$			32.7133i			1.57575i	−0.615838	+	0.787873i	$0.711182\pi$
$432$	17.8983	+	3.73011i	0.861133	+	0.179465i
$433$			21.4556i			1.03109i	0.856862	+	0.515546i	$0.172411\pi$
$433$			21.4556i			1.03109i	−0.856862	+	0.515546i	$0.827589\pi$
$434$	1.05840	+	4.26661i	0.0508050	+	0.204804i
$435$	9.68154	−	23.3733i	0.464194	−	1.12066i
$436$	11.7842	−	1.10643i	0.564359	−	0.0529885i
$437$	−6.17480	+	2.55769i	−0.295381	+	0.122351i
$438$	−12.6642	−	1.90806i	−0.605120	−	0.0911709i
$439$	−9.15202	−	9.15202i	−0.436802	−	0.436802i	0.454132	−	0.890934i	$-0.349949\pi$
$439$	−9.15202	−	9.15202i	−0.436802	−	0.436802i	−0.890934	+	0.454132i	$0.849949\pi$
$440$	−20.2671	−	22.6708i	−0.966194	−	1.08079i
$441$	0.414709	−	0.414709i	0.0197480	−	0.0197480i
$442$	−47.0989	+	34.7649i	−2.24027	+	1.65360i
$443$	−12.9884	−	31.3568i	−0.617098	−	1.48981i	−0.855059	−	0.518531i	$-0.826479\pi$
$443$	−12.9884	−	31.3568i	−0.617098	−	1.48981i	0.237961	−	0.971275i	$-0.423521\pi$
$444$	3.52801	−	1.86514i	0.167432	−	0.0885154i
$445$	−44.3282	−	18.3613i	−2.10136	−	0.870411i
$446$	16.4711	−	27.3389i	0.779930	−	1.29454i
$447$	7.90199			0.373751
$448$	6.25290	−	4.99012i	0.295422	−	0.235761i
$449$	26.1852			1.23576			0.617878	−	0.786274i	$-0.287993\pi$
$449$	26.1852			1.23576			0.617878	+	0.786274i	$0.287993\pi$
$450$	3.95019	−	6.55657i	0.186214	−	0.309080i
$451$	−18.9128	−	7.83394i	−0.890570	−	0.368886i
$452$	16.8230	−	8.89375i	0.791288	−	0.418327i
$453$	7.36928	+	17.7910i	0.346239	+	0.835894i
$454$	17.4586	−	12.8866i	0.819375	−	0.604800i
$455$	16.9800	−	16.9800i	0.796036	−	0.796036i
$456$	6.07213	−	5.42831i	0.284354	−	0.254204i
$457$	16.4774	+	16.4774i	0.770779	+	0.770779i	0.978243	−	0.207464i	$-0.0665210\pi$
$457$	16.4774	+	16.4774i	0.770779	+	0.770779i	−0.207464	+	0.978243i	$0.566521\pi$
$458$	21.3059	+	3.21007i	0.995558	+	0.149997i
$459$	27.4579	−	11.3734i	1.28163	−	0.530867i
$460$	−33.0154	+	3.09987i	−1.53935	+	0.144532i
$461$	9.17008	−	22.1385i	0.427093	−	1.03109i	−0.553112	−	0.833107i	$-0.686560\pi$
$461$	9.17008	−	22.1385i	0.427093	−	1.03109i	0.980205	−	0.197987i	$-0.0634403\pi$
$462$	−1.83791	−	7.40896i	−0.0855075	−	0.344696i
$463$		−	8.92132i		−	0.414609i	−0.978276	−	0.207304i	$-0.933531\pi$
$463$		−	8.92132i		−	0.414609i	0.978276	−	0.207304i	$-0.0664690\pi$
$464$	11.8498	−	7.76248i	0.550113	−	0.360364i
$465$			22.2052i			1.02974i
$466$	−26.1827	+	6.49505i	−1.21289	+	0.300878i
$467$	−2.23397	+	5.39328i	−0.103376	+	0.249571i	−0.967101	−	0.254391i	$-0.918125\pi$
$467$	−2.23397	+	5.39328i	−0.103376	+	0.249571i	0.863726	+	0.503962i	$0.168125\pi$
$468$	−5.75055	−	4.76338i	−0.265819	−	0.220187i
$469$	−0.931743	+	0.385940i	−0.0430239	+	0.0178211i
$470$	−7.47198	+	49.5931i	−0.344657	+	2.28756i
$471$	21.1816	+	21.1816i	0.975998	+	0.975998i
$472$	−8.13718	−	23.2416i	−0.374544	−	1.06978i
$473$	−9.79102	+	9.79102i	−0.450192	+	0.450192i
$474$	−2.15569	−	2.92049i	−0.0990140	−	0.134143i
$475$	5.37016	+	12.9647i	0.246400	+	0.594862i
$476$	3.83172	−	12.4273i	0.175627	−	0.569605i
$477$	2.11555	+	0.876288i	0.0968643	+	0.0401225i
$478$	−26.8398	−	16.1704i	−1.22762	−	0.739618i
$479$	20.8530			0.952798			0.476399	−	0.879229i	$-0.341942\pi$
$479$	20.8530			0.952798			0.476399	+	0.879229i	$0.341942\pi$
$480$	36.7252	−	16.8604i	1.67627	−	0.769568i
$481$	6.70735			0.305829
$482$	−2.24149	−	1.35045i	−0.102097	−	0.0615114i
$483$	−7.69056	−	3.18553i	−0.349932	−	0.144947i
$484$	5.49737	+	1.69501i	0.249880	+	0.0770458i
$485$	1.45948	+	3.52349i	0.0662714	+	0.159993i
$486$	5.04983	+	6.84143i	0.229065	+	0.310334i
$487$	−30.4637	+	30.4637i	−1.38044	+	1.38044i	−0.536618	+	0.843826i	$0.680298\pi$
$487$	−30.4637	+	30.4637i	−1.38044	+	1.38044i	−0.843826	+	0.536618i	$0.819702\pi$
$488$	6.47340	+	3.11602i	0.293037	+	0.141056i
$489$	−8.98924	−	8.98924i	−0.406508	−	0.406508i
$490$	−0.794768	+	5.27504i	−0.0359040	+	0.238302i
$491$	23.7425	−	9.83448i	1.07149	−	0.443824i	0.223971	−	0.974596i	$-0.428098\pi$
$491$	23.7425	−	9.83448i	1.07149	−	0.443824i	0.847515	+	0.530772i	$0.178098\pi$
$492$	17.3536	−	20.9500i	0.782361	−	0.944499i
$493$	8.81237	−	21.2749i	0.396889	−	0.958175i
$494$	13.2866	−	3.29597i	0.597794	−	0.148293i
$495$		−	6.30548i		−	0.283410i
$496$	−7.00166	+	10.2747i	−0.314384	+	0.461349i
$497$		−	10.0785i		−	0.452084i
$498$	−2.76436	−	11.1436i	−0.123874	−	0.499358i
$499$	−11.1328	+	26.8768i	−0.498370	+	1.20317i	0.451990	+	0.892023i	$0.350714\pi$
$499$	−11.1328	+	26.8768i	−0.498370	+	1.20317i	−0.950361	+	0.311150i	$0.899286\pi$
$500$	2.98236	+	31.7638i	0.133375	+	1.42052i
$501$	−19.8124	+	8.20658i	−0.885155	+	0.366643i
$502$	−3.19426	−	0.481266i	−0.142567	−	0.0214800i
$503$	7.03053	+	7.03053i	0.313476	+	0.313476i	0.846255	−	0.532779i	$-0.178852\pi$
$503$	7.03053	+	7.03053i	0.313476	+	0.313476i	−0.532779	+	0.846255i	$0.678852\pi$
$504$	1.65624	+	0.0927201i	0.0737748	+	0.00413008i
$505$	37.1354	−	37.1354i	1.65251	−	1.65251i
$506$	−14.2547	+	10.5217i	−0.633698	+	0.467748i
$507$	−19.9490	−	48.1611i	−0.885965	−	2.13891i
$508$	−6.15941	−	11.6509i	−0.273279	−	0.516923i
$509$	28.9939	+	12.0097i	1.28513	+	0.532319i	0.917531	−	0.397664i	$-0.130179\pi$
$509$	28.9939	+	12.0097i	1.28513	+	0.532319i	0.367602	+	0.929983i	$0.380179\pi$
$510$	33.9000	−	56.2675i	1.50112	−	2.49157i
$511$	4.78193			0.211540
$512$	22.3097	+	3.77845i	0.985959	+	0.166986i
$513$	−6.94999			−0.306849
$514$	−18.1263	+	30.0862i	−0.799518	+	1.32705i
$515$	−62.0399	−	25.6978i	−2.73381	−	1.13238i
$516$	−8.59994	−	16.2673i	−0.378591	−	0.716126i
$517$	10.2544	+	24.7563i	0.450988	+	1.08878i
$518$	−1.19883	+	0.884886i	−0.0526736	+	0.0388797i
$519$	−18.3744	+	18.3744i	−0.806548	+	0.806548i
$520$	67.8139	+	3.79637i	2.97384	+	0.166482i
$521$	3.80750	+	3.80750i	0.166810	+	0.166810i	0.785575	−	0.618766i	$-0.212367\pi$
$521$	3.80750	+	3.80750i	0.166810	+	0.166810i	−0.618766	+	0.785575i	$0.712367\pi$
$522$	2.90458	+	0.437621i	0.127130	+	0.0191542i
$523$	37.8891	−	15.6942i	1.65678	−	0.686259i	0.658952	−	0.752185i	$-0.271000\pi$
$523$	37.8891	−	15.6942i	1.65678	−	0.686259i	0.997825	+	0.0659260i	$0.0210001\pi$
$524$	1.66563	+	17.7400i	0.0727635	+	0.774974i
$525$	−6.68841	+	16.1472i	−0.291906	+	0.704723i
$526$	−5.60813	−	22.6074i	−0.244526	−	0.985728i
$527$			20.2117i			0.880436i
$528$	12.1584	−	17.8420i	0.529125	−	0.776475i
$529$		−	3.67962i		−	0.159983i
$530$	−20.2154	+	5.01476i	−0.878100	+	0.217827i
$531$	1.95401	−	4.71740i	0.0847969	−	0.204718i
$532$	−1.93994	+	2.34198i	−0.0841072	+	0.101538i
$533$	42.2425	−	17.4974i	1.82972	−	0.757897i
$534$	5.07539	−	33.6864i	0.219634	−	1.45775i
$535$	−26.6946	−	26.6946i	−1.15411	−	1.15411i
$536$	−2.57023	−	1.23720i	−0.111017	−	0.0534389i
$537$	−10.3883	+	10.3883i	−0.448287	+	0.448287i
$538$	14.1816	+	19.2130i	0.611411	+	0.828331i
$539$	1.09072	+	2.63324i	0.0469808	+	0.113422i
$540$	−32.9518	−	10.1600i	−1.41802	−	0.437219i
$541$	19.0606	+	7.89516i	0.819480	+	0.339440i	0.752729	−	0.658330i	$-0.228737\pi$
$541$	19.0606	+	7.89516i	0.819480	+	0.339440i	0.0667503	+	0.997770i	$0.478737\pi$
$542$	14.5149	+	8.74494i	0.623470	+	0.375627i
$543$	−12.6288			−0.541956
$544$	33.4281	−	15.3467i	1.43322	−	0.657985i
$545$	−22.3234			−0.956228
$546$	14.6040	+	8.79862i	0.624995	+	0.376546i
$547$	−35.6592	−	14.7705i	−1.52468	−	0.631542i	−0.546155	−	0.837684i	$-0.683909\pi$
$547$	−35.6592	−	14.7705i	−1.52468	−	0.631542i	−0.978522	+	0.206142i	$0.933909\pi$
$548$	−8.88286	+	28.8095i	−0.379457	+	1.23068i
$549$	0.570084	+	1.37630i	0.0243306	+	0.0587392i
$550$	22.0916	+	29.9294i	0.941990	+	1.27619i
$551$	−3.80776	+	3.80776i	−0.162216	+	0.162216i
$552$	−7.78013	−	22.2218i	−0.331144	−	0.945822i
$553$	0.958367	+	0.958367i	0.0407539	+	0.0407539i
$554$	−2.92917	+	19.4415i	−0.124449	+	0.825991i
$555$	−6.95373	+	2.88033i	−0.295169	+	0.122263i
$556$	5.93150	+	4.91326i	0.251551	+	0.208369i
$557$	−3.70225	+	8.93802i	−0.156869	+	0.378716i	−0.982701	−	0.185201i	$-0.940706\pi$
$557$	−3.70225	+	8.93802i	−0.156869	+	0.378716i	0.825831	+	0.563917i	$0.190706\pi$
$558$	−2.50231	+	0.620739i	−0.105931	+	0.0262780i
$559$		−	30.9269i		−	1.30807i
$560$	−12.6215	+	8.26800i	−0.533355	+	0.349387i
$561$		−	35.0976i		−	1.48182i
$562$	0.985929	+	3.97445i	0.0415889	+	0.167652i
$563$	−1.96106	+	4.73442i	−0.0826489	+	0.199532i	−0.959802	−	0.280680i	$-0.909440\pi$
$563$	−1.96106	+	4.73442i	−0.0826489	+	0.199532i	0.877153	+	0.480212i	$0.159440\pi$
$564$	−35.4531	+	3.32874i	−1.49284	+	0.140165i
$565$	−33.1583	+	13.7346i	−1.39498	+	0.577820i
$566$	−22.1863	−	3.34271i	−0.932558	−	0.140505i
$567$	−7.36487	−	7.36487i	−0.309295	−	0.309295i
$568$	21.2522	−	18.9989i	0.891723	−	0.797175i
$569$	−17.5386	+	17.5386i	−0.735257	+	0.735257i	−0.971656	−	0.236399i	$-0.924033\pi$
$569$	−17.5386	+	17.5386i	−0.735257	+	0.735257i	0.236399	+	0.971656i	$0.424033\pi$
$570$	−12.3593	+	9.12271i	−0.517675	+	0.382108i
$571$	3.64399	+	8.79737i	0.152496	+	0.368158i	0.981603	−	0.190931i	$-0.0611508\pi$
$571$	3.64399	+	8.79737i	0.152496	+	0.368158i	−0.829107	+	0.559090i	$0.811151\pi$
$572$	32.0815	−	16.9604i	1.34140	−	0.709150i
$573$	30.7658	+	12.7436i	1.28526	+	0.532371i
$574$	−5.24177	+	8.70034i	−0.218787	+	0.363145i
$575$	40.5654			1.69170
$576$	2.92664	+	3.66724i	0.121943	+	0.152802i
$577$	−6.47657			−0.269623			−0.134812	−	0.990871i	$-0.543043\pi$
$577$	−6.47657			−0.269623			−0.134812	+	0.990871i	$0.543043\pi$
$578$	18.4497	−	30.6231i	0.767408	−	1.27375i
$579$	0.784280	+	0.324860i	0.0325936	+	0.0135007i
$580$	−23.6201	+	12.4871i	−0.980773	+	0.518501i
$581$	1.64053	+	3.96059i	0.0680607	+	0.164313i
$582$	−2.17862	+	1.60809i	−0.0903068	+	0.0666577i
$583$	−7.86882	+	7.86882i	−0.325893	+	0.325893i
$584$	9.01434	+	10.0835i	0.373016	+	0.417257i
$585$	9.95855	+	9.95855i	0.411735	+	0.411735i
$586$	11.0255	+	1.66117i	0.455460	+	0.0686222i
$587$	7.60776	−	3.15124i	0.314006	−	0.130066i	−0.220114	−	0.975474i	$-0.570643\pi$
$587$	7.60776	−	3.15124i	0.314006	−	0.130066i	0.534120	+	0.845409i	$0.320643\pi$
$588$	−3.77102	+	0.354067i	−0.155514	+	0.0146015i
$589$	1.80873	−	4.36667i	0.0745276	−	0.179925i
$590$	11.1823	+	45.0777i	0.460367	+	1.85582i
$591$		−	19.2457i		−	0.791663i
$592$	−4.12582	−	0.859845i	−0.169570	−	0.0353394i
$593$			38.8581i			1.59571i	0.602849	+	0.797856i	$0.294032\pi$
$593$			38.8581i			1.59571i	−0.602849	+	0.797856i	$0.705968\pi$
$594$	−17.8816	+	4.43583i	−0.733692	+	0.182004i
$595$	−9.38626	+	22.6604i	−0.384799	+	0.928988i
$596$	−6.42666	−	5.32343i	−0.263246	−	0.218056i
$597$	20.4989	−	8.49092i	0.838964	−	0.347510i
$598$	5.89564	−	39.1306i	0.241091	−	1.60017i
$599$	0.339367	+	0.339367i	0.0138662	+	0.0138662i	0.714006	−	0.700140i	$-0.246879\pi$
$599$	0.339367	+	0.339367i	0.0138662	+	0.0138662i	−0.700140	+	0.714006i	$0.746879\pi$
$600$	−46.6573	+	16.3353i	−1.90478	+	0.666886i
$601$	−4.77407	+	4.77407i	−0.194738	+	0.194738i	−0.797740	−	0.603002i	$-0.793971\pi$
$601$	−4.77407	+	4.77407i	−0.194738	+	0.194738i	0.603002	+	0.797740i	$0.293971\pi$
$602$	4.08012	+	5.52768i	0.166293	+	0.225291i
$603$	−0.226349	−	0.546455i	−0.00921764	−	0.0222533i
$604$	5.99207	−	19.4339i	0.243814	−	0.790754i
$605$	−10.0241	−	4.15212i	−0.407538	−	0.168808i
$606$	31.9391	+	19.2427i	1.29744	+	0.781679i
$607$	31.9217			1.29566			0.647832	−	0.761783i	$-0.275676\pi$
$607$	31.9217			1.29566			0.647832	+	0.761783i	$0.275676\pi$
$608$	−8.59540	+	0.324142i	−0.348589	+	0.0131457i
$609$	−6.70687			−0.271776
$610$	−11.6064	−	6.99259i	−0.469928	−	0.283122i
$611$	−55.2941	−	22.9036i	−2.23696	−	0.926579i
$612$	7.28846	+	2.24725i	0.294618	+	0.0908399i
$613$	−3.16436	−	7.63944i	−0.127807	−	0.308554i	0.847004	−	0.531587i	$-0.178404\pi$
$613$	−3.16436	−	7.63944i	−0.127807	−	0.308554i	−0.974811	+	0.223033i	$0.928404\pi$
$614$	10.0223	+	13.5780i	0.404466	+	0.547965i
$615$	−36.2803	+	36.2803i	−1.46296	+	1.46296i
$616$	−3.49651	+	7.26384i	−0.140878	+	0.292669i
$617$	1.83328	+	1.83328i	0.0738050	+	0.0738050i	0.743046	−	0.669241i	$-0.233380\pi$
$617$	1.83328	+	1.83328i	0.0738050	+	0.0738050i	−0.669241	+	0.743046i	$0.733380\pi$
$618$	7.10331	−	47.1461i	0.285737	−	1.89650i
$619$	13.9279	−	5.76910i	0.559808	−	0.231880i	−0.0847941	−	0.996398i	$-0.527023\pi$
$619$	13.9279	−	5.76910i	0.559808	−	0.231880i	0.644602	+	0.764519i	$0.277023\pi$
$620$	14.9593	−	18.0594i	0.600778	−	0.725284i
$621$	−7.68833	+	18.5613i	−0.308522	+	0.744838i
$622$	23.9911	−	5.95139i	0.961956	−	0.238629i
$623$			12.7198i			0.509607i
$624$	8.97651	+	47.3811i	0.359348	+	1.89676i
$625$		−	14.0276i		−	0.561105i
$626$	1.09419	+	4.41088i	0.0437326	+	0.176294i
$627$	−3.14086	+	7.58271i	−0.125434	+	0.302824i
$628$	−2.95727	−	31.4966i	−0.118008	−	1.25685i
$629$	−6.32945	+	2.62174i	−0.252372	+	0.104536i
$630$	−3.09374	−	0.466121i	−0.123258	−	0.0185707i
$631$	33.2420	+	33.2420i	1.32334	+	1.32334i	0.911054	+	0.412288i	$0.135270\pi$
$631$	33.2420	+	33.2420i	1.32334	+	1.32334i	0.412288	+	0.911054i	$0.364730\pi$
$632$	−0.214271	+	3.82747i	−0.00852323	+	0.152249i
$633$	−6.75727	+	6.75727i	−0.268577	+	0.268577i
$634$	22.4431	−	16.5658i	0.891331	−	0.657913i
$635$	9.51197	+	22.9639i	0.377471	+	0.911296i
$636$	−6.91157	−	13.0736i	−0.274062	−	0.518403i
$637$	−5.88144	−	2.43617i	−0.233031	−	0.0965246i
$638$	−7.36668	+	12.2273i	−0.291650	+	0.484083i
$639$	5.91092			0.233832
$640$	−41.2270	−	11.0286i	−1.62964	−	0.435944i
$641$	44.2904			1.74936			0.874682	−	0.484696i	$-0.161070\pi$
$641$	44.2904			1.74936			0.874682	+	0.484696i	$0.161070\pi$
$642$	13.8325	−	22.9593i	0.545924	−	0.906131i
$643$	−4.35374	−	1.80338i	−0.171695	−	0.0711184i	0.295180	−	0.955442i	$-0.404620\pi$
$643$	−4.35374	−	1.80338i	−0.171695	−	0.0711184i	−0.466875	+	0.884323i	$0.654620\pi$
$644$	4.10867	+	7.77177i	0.161904	+	0.306251i
$645$	13.2809	+	32.0629i	0.522935	+	1.26248i
$646$	−11.2497	+	8.30371i	−0.442615	+	0.326705i
$647$	14.5955	−	14.5955i	0.573809	−	0.573809i	−0.359382	−	0.933191i	$-0.617012\pi$
$647$	14.5955	−	14.5955i	0.573809	−	0.573809i	0.933191	+	0.359382i	$0.117012\pi$
$648$	1.64663	−	29.4134i	0.0646857	−	1.15547i
$649$	17.5465	+	17.5465i	0.688759	+	0.688759i
$650$	−82.1594	−	12.3786i	−3.22256	−	0.485529i
$651$	5.43858	−	2.25273i	0.213155	−	0.0882916i
$652$	1.25503	+	13.3668i	0.0491508	+	0.523485i
$653$	2.00624	−	4.84348i	0.0785101	−	0.189540i	−0.879751	−	0.475435i	$-0.842291\pi$
$653$	2.00624	−	4.84348i	0.0785101	−	0.189540i	0.958261	+	0.285895i	$0.0922908\pi$
$654$	−3.81614	−	15.3835i	−0.149223	−	0.601544i
$655$		−	33.6058i		−	1.31309i
$656$	−28.2272	+	5.34774i	−1.10209	+	0.208794i
$657$			2.80454i			0.109415i
$658$	12.9045	−	3.20119i	0.503072	−	0.124795i
$659$	−8.06628	+	19.4737i	−0.314218	+	0.758588i	0.685322	+	0.728240i	$0.259662\pi$
$659$	−8.06628	+	19.4737i	−0.314218	+	0.758588i	−0.999539	+	0.0303479i	$0.990338\pi$
$660$	−25.9767	+	31.3601i	−1.01114	+	1.22069i
$661$	−15.5918	+	6.45832i	−0.606449	+	0.251199i	−0.664709	−	0.747102i	$-0.731445\pi$
$661$	−15.5918	+	6.45832i	−0.606449	+	0.251199i	0.0582603	+	0.998301i	$0.481445\pi$
$662$	−1.22657	+	8.14097i	−0.0476718	+	0.316408i
$663$	55.4314	+	55.4314i	2.15278	+	2.15278i
$664$	−5.25901	+	10.9254i	−0.204089	+	0.423987i
$665$	4.05574	−	4.05574i	0.157275	−	0.157275i
$666$	−0.518974	−	0.703098i	−0.0201098	−	0.0272445i
$667$	5.95707	+	14.3816i	0.230659	+	0.556859i
$668$	21.6420	+	6.67290i	0.837355	+	0.258182i
$669$	−39.4876	−	16.3563i	−1.52668	−	0.632372i
$670$	4.60825	+	2.77637i	0.178032	+	0.107261i
$671$	−7.23962			−0.279483
$672$	−7.85529	−	7.28436i	−0.303025	−	0.281000i
$673$	6.90473			0.266158			0.133079	−	0.991105i	$-0.457514\pi$
$673$	6.90473			0.266158			0.133079	+	0.991105i	$0.457514\pi$
$674$	−2.32418	−	1.40027i	−0.0895240	−	0.0539363i
$675$	38.9716	+	16.1426i	1.50002	+	0.621327i
$676$	−16.2208	+	52.6085i	−0.623878	+	2.02340i
$677$	8.66082	+	20.9091i	0.332863	+	0.803601i	0.998363	+	0.0572034i	$0.0182184\pi$
$677$	8.66082	+	20.9091i	0.332863	+	0.803601i	−0.665500	+	0.746398i	$0.731782\pi$
$678$	−15.1332	−	20.5022i	−0.581187	−	0.787384i
$679$	0.714920	−	0.714920i	0.0274361	−	0.0274361i
$680$	−65.4771	+	22.9244i	−2.51093	+	0.879110i
$681$	−20.5473	−	20.5473i	−0.787375	−	0.787375i
$682$	1.86666	−	12.3894i	0.0714782	−	0.474416i
$683$	40.8415	−	16.9171i	1.56276	−	0.647315i	0.577190	−	0.816610i	$-0.304149\pi$
$683$	40.8415	−	16.9171i	1.56276	−	0.647315i	0.985565	+	0.169295i	$0.0541490\pi$
$684$	−1.37354	−	1.13775i	−0.0525186	−	0.0435030i
$685$	21.7596	−	52.5324i	0.831393	−	2.00716i
$686$	1.37261	−	0.340499i	0.0524065	−	0.0130003i
$687$		−	28.8531i		−	1.10082i
$688$	−3.96466	+	19.0237i	−0.151151	+	0.725273i
$689$		−	24.8552i		−	0.946908i
$690$	10.6916	+	43.0998i	0.407023	+	1.64078i
$691$	15.1372	−	36.5445i	0.575847	−	1.39022i	−0.320662	−	0.947194i	$-0.603905\pi$
$691$	15.1372	−	36.5445i	0.575847	−	1.39022i	0.896509	−	0.443025i	$-0.146095\pi$
$692$	27.3224	−	2.56534i	1.03864	−	0.0975195i
$693$	−1.54436	+	0.639695i	−0.0586654	+	0.0243000i
$694$	−31.6743	−	4.77223i	−1.20234	−	0.181151i
$695$	−10.2719	−	10.2719i	−0.389636	−	0.389636i
$696$	−12.6430	−	14.1425i	−0.479232	−	0.536071i
$697$	−33.0232	+	33.0232i	−1.25084	+	1.25084i
$698$	17.1875	−	12.6865i	0.650557	−	0.480192i
$699$	13.8242	+	33.3747i	0.522881	+	1.26235i
$700$	16.3178	−	8.62663i	0.616753	−	0.326056i
$701$	2.60607	+	1.07947i	0.0984300	+	0.0407710i	0.431355	−	0.902182i	$-0.358036\pi$
$701$	2.60607	+	1.07947i	0.0984300	+	0.0407710i	−0.332925	+	0.942953i	$0.608036\pi$
$702$	21.2356	−	35.2470i	0.801485	−	1.33031i
$703$	1.60207			0.0604233
$704$	−21.9082	+	6.32000i	−0.825697	+	0.238194i
$705$	67.1607			2.52942
$706$	13.0426	−	21.6483i	0.490865	−	0.814743i
$707$	−12.8628	−	5.32793i	−0.483754	−	0.200377i
$708$	−29.1525	+	15.4119i	−1.09562	+	0.579216i
$709$	4.98958	+	12.0459i	0.187387	+	0.452393i	0.989455	−	0.144840i	$-0.0462667\pi$
$709$	4.98958	+	12.0459i	0.187387	+	0.452393i	−0.802068	+	0.597233i	$0.796267\pi$
$710$	−43.2571	+	31.9291i	−1.62341	+	1.19828i
$711$	−0.562069	+	0.562069i	−0.0210792	+	0.0210792i
$712$	−26.8217	+	23.9778i	−1.00519	+	0.898608i
$713$	−9.66114	−	9.66114i	−0.361812	−	0.361812i
$714$	−17.2204	−	2.59453i	−0.644457	−	0.0970977i
$715$	−63.2330	+	26.1919i	−2.36478	+	0.979523i
$716$	15.4471	−	1.45035i	0.577286	−	0.0542023i
$717$	−16.0577	+	38.7668i	−0.599686	+	1.44777i
$718$	−6.43104	−	25.9247i	−0.240004	−	0.967500i
$719$		−	44.0500i		−	1.64279i	−0.570361	−	0.821394i	$-0.693197\pi$
$719$		−	44.0500i		−	1.64279i	0.570361	−	0.821394i	$-0.306803\pi$
$720$	−4.84907	−	7.40233i	−0.180714	−	0.275869i
$721$			17.8021i			0.662984i
$722$	−22.9060	+	5.68222i	−0.852475	+	0.211470i
$723$	−1.34104	+	3.23756i	−0.0498738	+	0.120406i
$724$	10.2710	+	8.50782i	0.381718	+	0.316191i
$725$	30.1960	−	12.5076i	1.12145	−	0.464520i
$726$	1.14772	−	7.61765i	0.0425958	−	0.282717i
$727$	−26.8897	−	26.8897i	−0.997284	−	0.997284i	0.00271192	−	0.999996i	$-0.499137\pi$
$727$	−26.8897	−	26.8897i	−0.997284	−	0.997284i	−0.999996	+	0.00271192i	$0.999137\pi$
$728$	−5.94994	−	16.9944i	−0.220519	−	0.629853i
$729$	−14.0428	+	14.0428i	−0.520105	+	0.520105i
$730$	−15.1493	−	20.5241i	−0.560701	−	0.759630i
$731$	12.0886	+	29.1844i	0.447113	+	1.07943i
$732$	2.83467	−	9.19359i	0.104772	−	0.339805i
$733$	−42.4092	−	17.5665i	−1.56642	−	0.648833i	−0.580231	−	0.814452i	$-0.697038\pi$
$733$	−42.4092	−	17.5665i	−1.56642	−	0.648833i	−0.986190	+	0.165619i	$0.947038\pi$
$734$	−22.8660	−	13.7763i	−0.844001	−	0.508493i
$735$	7.14364			0.263497
$736$	−8.64286	+	23.3142i	−0.318580	+	0.859374i
$737$	2.87446			0.105882
$738$	−5.10263	−	3.07423i	−0.187830	−	0.113164i
$739$	26.7969	+	11.0996i	0.985741	+	0.408307i	0.816549	−	0.577276i	$-0.195884\pi$
$739$	26.7969	+	11.0996i	0.985741	+	0.408307i	0.169192	+	0.985583i	$0.445884\pi$
$740$	7.59587	+	2.34204i	0.279230	+	0.0860951i
$741$	−7.01523	−	16.9363i	−0.257711	−	0.622169i
$742$	3.27909	+	4.44247i	0.120379	+	0.163088i
$743$	−14.7166	+	14.7166i	−0.539898	+	0.539898i	−0.923499	−	0.383601i	$-0.874684\pi$
$743$	−14.7166	+	14.7166i	−0.539898	+	0.539898i	0.383601	+	0.923499i	$0.374684\pi$
$744$	15.0024	+	7.22154i	0.550016	+	0.264754i
$745$	11.1294	+	11.1294i	0.407750	+	0.407750i
$746$	2.00629	−	13.3162i	0.0734555	−	0.487539i
$747$	−2.32283	+	0.962149i	−0.0849880	+	0.0352032i
$748$	−23.6446	+	28.5448i	−0.864533	+	1.04370i
$749$	−3.82995	+	9.24632i	−0.139943	+	0.337853i
$750$	41.4659	−	10.2863i	1.51412	−	0.375603i
$751$			29.3838i			1.07223i	0.844145	+	0.536115i	$0.180109\pi$
$751$			29.3838i			1.07223i	−0.844145	+	0.536115i	$0.819891\pi$
$752$	31.0764	+	21.1768i	1.13324	+	0.772240i
$753$			4.32578i			0.157640i
$754$	−7.67660	−	30.9457i	−0.279565	−	1.12698i
$755$	−14.6783	+	35.4365i	−0.534198	+	1.28967i
$756$	0.854545	+	9.10140i	0.0310795	+	0.331015i
$757$	−7.94268	+	3.28997i	−0.288682	+	0.119576i	−0.522325	−	0.852746i	$-0.674935\pi$
$757$	−7.94268	+	3.28997i	−0.288682	+	0.119576i	0.233643	+	0.972322i	$0.424935\pi$
$758$	22.7430	+	3.42660i	0.826065	+	0.124460i
$759$	16.7765	+	16.7765i	0.608950	+	0.608950i
$760$	16.1976	+	0.906777i	0.587548	+	0.0328923i
$761$	36.8949	−	36.8949i	1.33744	−	1.33744i	0.438904	−	0.898534i	$-0.355367\pi$
$761$	36.8949	−	36.8949i	1.33744	−	1.33744i	0.898534	−	0.438904i	$-0.144633\pi$
$762$	−14.1989	+	10.4806i	−0.514373	+	0.379671i
$763$	2.26472	+	5.46751i	0.0819883	+	0.197937i
$764$	−16.4365	−	31.0906i	−0.594653	−	1.12482i
$765$	−13.2900	−	5.50492i	−0.480503	−	0.199031i
$766$	6.71895	−	11.1522i	0.242766	−	0.402945i
$767$	−55.4239			−2.00124
$768$	0.552373	−	30.2958i	0.0199321	−	1.09321i
$769$	−1.28218			−0.0462366			−0.0231183	−	0.999733i	$-0.507359\pi$
$769$	−1.28218			−0.0462366			−0.0231183	+	0.999733i	$0.507359\pi$
$770$	7.84643	−	13.0236i	0.282766	−	0.469337i
$771$	43.4558	+	18.0000i	1.56502	+	0.648254i
$772$	−0.419000	−	0.792562i	−0.0150802	−	0.0285249i
$773$	−18.6769	−	45.0901i	−0.671763	−	1.62178i	−0.778613	−	0.627504i	$-0.784077\pi$
$773$	−18.6769	−	45.0901i	−0.671763	−	1.62178i	0.106850	−	0.994275i	$-0.465923\pi$
$774$	−3.24191	+	2.39293i	−0.116528	+	0.0860122i
$775$	−20.2847	+	20.2847i	−0.728648	+	0.728648i
$776$	2.85521	+	0.159841i	0.102496	+	0.00573796i
$777$	1.41092	+	1.41092i	0.0506165	+	0.0506165i
$778$	40.8652	+	6.15698i	1.46509	+	0.220739i
$779$	10.0898	−	4.17931i	0.361503	−	0.149739i
$780$	−8.50234	−	90.5549i	−0.304433	−	3.24238i
$781$	−10.9929	+	26.5392i	−0.393356	+	0.949646i
$782$	9.73176	+	39.2304i	0.348007	+	1.40288i
$783$			16.1871i			0.578480i
$784$	3.30548	+	2.25250i	0.118053	+	0.0804466i
$785$			59.6657i			2.12956i
$786$	23.1585	−	5.74485i	0.826037	−	0.204912i
$787$	−12.4503	+	30.0576i	−0.443804	+	1.07144i	0.530798	+	0.847498i	$0.321892\pi$
$787$	−12.4503	+	30.0576i	−0.443804	+	1.07144i	−0.974603	+	0.223940i	$0.928108\pi$
$788$	−12.9655	+	15.6525i	−0.461876	+	0.557596i
$789$	−28.8172	+	11.9365i	−1.02592	+	0.424950i
$790$	1.07718	−	7.14945i	0.0383243	−	0.254366i
$791$	6.72786	+	6.72786i	0.239215	+	0.239215i
$792$	−4.26015	−	2.05066i	−0.151378	−	0.0728669i
$793$	11.4339	−	11.4339i	0.406029	−	0.406029i
$794$	14.4492	+	19.5756i	0.512783	+	0.694711i
$795$	10.6735	+	25.7682i	0.378552	+	0.913905i
$796$	−22.3919	−	6.90410i	−0.793658	−	0.244709i
$797$	−20.5229	−	8.50088i	−0.726960	−	0.301117i	−0.0116578	−	0.999932i	$-0.503711\pi$
$797$	−20.5229	−	8.50088i	−0.726960	−	0.301117i	−0.715302	+	0.698815i	$0.753711\pi$
$798$	3.48822	+	2.10158i	0.123482	+	0.0743951i
$799$	61.1312			2.16267
$800$	48.9510	+	18.1467i	1.73068	+	0.641583i
$801$	−7.45998			−0.263585
$802$	29.5095	+	17.7789i	1.04202	+	0.627793i
$803$	−12.5920	−	5.21576i	−0.444361	−	0.184060i
$804$	−1.12549	+	3.65027i	−0.0396930	+	0.128735i
$805$	−6.34501	−	15.3182i	−0.223632	−	0.539896i
$806$	16.6191	+	22.5153i	0.585383	+	0.793069i
$807$	22.6120	−	22.6120i	0.795981	−	0.795981i
$808$	−13.0126	−	37.1668i	−0.457780	−	1.30752i
$809$	20.1275	+	20.1275i	0.707644	+	0.707644i	0.966039	−	0.258395i	$-0.0831937\pi$
$809$	20.1275	+	20.1275i	0.707644	+	0.707644i	−0.258395	+	0.966039i	$0.583194\pi$
$810$	−8.27790	+	54.9422i	−0.290856	+	1.93047i
$811$	33.3517	−	13.8147i	1.17114	−	0.485101i	0.289569	−	0.957157i	$-0.406488\pi$
$811$	33.3517	−	13.8147i	1.17114	−	0.485101i	0.881569	+	0.472056i	$0.156488\pi$
$812$	5.45467	+	4.51829i	0.191421	+	0.158561i
$813$	8.68399	−	20.9650i	0.304561	−	0.735275i
$814$	4.12197	−	1.02252i	0.144475	−	0.0358394i
$815$		−	25.3215i		−	0.886972i
$816$	−26.9909	−	41.2029i	−0.944872	−	1.44239i
$817$		−	7.38699i		−	0.258438i
$818$	8.21453	+	33.1142i	0.287214	+	1.15781i
$819$	1.42878	−	3.44938i	0.0499257	−	0.120531i
$820$	53.9480	−	5.06526i	1.88394	−	0.176887i
$821$	27.8204	−	11.5236i	0.970937	−	0.402175i	0.159876	−	0.987137i	$-0.448890\pi$
$821$	27.8204	−	11.5236i	0.970937	−	0.402175i	0.811061	+	0.584962i	$0.198890\pi$
$822$	39.9211	+	6.01474i	1.39241	+	0.209788i
$823$	−0.438124	−	0.438124i	−0.0152720	−	0.0152720i	0.699430	−	0.714702i	$-0.253437\pi$
$823$	−0.438124	−	0.438124i	−0.0152720	−	0.0152720i	−0.714702	+	0.699430i	$0.753437\pi$
$824$	−37.5386	+	33.5584i	−1.30772	+	1.16906i
$825$	35.2243	−	35.2243i	1.22635	−	1.22635i
$826$	9.90614	−	7.31196i	0.344679	−	0.254416i
$827$	−14.7614	−	35.6373i	−0.513306	−	1.23923i	−0.941949	−	0.335756i	$-0.891008\pi$
$827$	−14.7614	−	35.6373i	−0.513306	−	1.23923i	0.428644	−	0.903474i	$-0.358992\pi$
$828$	−4.55804	+	2.40968i	−0.158403	+	0.0837421i
$829$	−50.4450	−	20.8950i	−1.75203	−	0.725713i	−0.997593	−	0.0693355i	$-0.977912\pi$
$829$	−50.4450	−	20.8950i	−1.75203	−	0.725713i	−0.754433	−	0.656377i	$-0.772088\pi$
$830$	11.8016	−	19.5884i	0.409640	−	0.679925i
$831$	26.3284			0.913321
$832$	24.6192	−	44.5822i	0.853518	−	1.54561i
$833$	6.50231			0.225292
$834$	5.32264	−	8.83457i	0.184308	−	0.305916i
$835$	−39.4629	−	16.3461i	−1.36567	−	0.565678i
$836$	7.66278	−	4.05105i	0.265023	−	0.140108i
$837$	−5.43700	−	13.1261i	−0.187930	−	0.453704i
$838$	−45.1618	+	33.3350i	−1.56009	+	1.15154i
$839$	12.0166	−	12.0166i	0.414859	−	0.414859i	−0.468568	−	0.883427i	$-0.655230\pi$
$839$	12.0166	−	12.0166i	0.414859	−	0.414859i	0.883427	+	0.468568i	$0.155230\pi$
$840$	13.4664	+	15.0635i	0.464634	+	0.519741i
$841$	−11.6375	−	11.6375i	−0.401293	−	0.401293i
$842$	−37.1162	−	5.59214i	−1.27911	−	0.192718i
$843$	5.06617	−	2.09848i	0.174488	−	0.0722754i
$844$	10.0479	−	0.943414i	0.345863	−	0.0324736i
$845$	39.7348	−	95.9284i	1.36692	−	3.30004i
$846$	1.87745	+	7.56834i	0.0645481	+	0.260205i
$847$			2.87637i			0.0988334i
$848$	−3.18630	+	15.2889i	−0.109418	+	0.525024i
$849$			30.0454i			1.03116i
$850$	82.3690	−	20.4330i	2.82523	−	0.700846i
$851$	1.77227	−	4.27864i	0.0607527	−	0.146670i
$852$	−29.3978	−	24.3512i	−1.00715	−	0.834260i
$853$	−7.55073	+	3.12762i	−0.258532	+	0.107088i	−0.508185	−	0.861248i	$-0.669683\pi$
$853$	−7.55073	+	3.12762i	−0.258532	+	0.107088i	0.249653	+	0.968335i	$0.419683\pi$
$854$	−0.535176	+	3.55207i	−0.0183133	+	0.121549i
$855$	2.37863	+	2.37863i	0.0813476	+	0.0813476i
$856$	−26.7171	+	9.35401i	−0.913173	+	0.319714i
$857$	8.63970	−	8.63970i	0.295127	−	0.295127i	−0.543975	−	0.839102i	$-0.683081\pi$
$857$	8.63970	−	8.63970i	0.295127	−	0.295127i	0.839102	+	0.543975i	$0.183081\pi$
$858$	−28.8591	−	39.0978i	−0.985232	−	1.33478i
$859$	9.41900	+	22.7395i	0.321372	+	0.775861i	0.999175	+	0.0406170i	$0.0129324\pi$
$859$	9.41900	+	22.7395i	0.321372	+	0.775861i	−0.677803	+	0.735244i	$0.737068\pi$
$860$	10.7989	−	35.0237i	0.368239	−	1.19430i
$861$	12.5665	+	5.20523i	0.428267	+	0.177394i
$862$	−39.6273	−	23.8746i	−1.34971	−	0.813173i
$863$	8.06187			0.274429			0.137215	−	0.990541i	$-0.456185\pi$
$863$	8.06187			0.274429			0.137215	+	0.990541i	$0.456185\pi$
$864$	−17.5809	+	18.9589i	−0.598115	+	0.644993i
$865$	−51.7582			−1.75983
$866$	−25.9903	−	15.6586i	−0.883187	−	0.532101i
$867$	−44.2312	−	18.3212i	−1.50217	−	0.622219i
$868$	−5.94080	−	1.83173i	−0.201644	−	0.0621730i
$869$	−1.47830	−	3.56892i	−0.0501477	−	0.121067i
$870$	21.2476	+	28.7859i	0.720360	+	0.975934i
$871$	−4.53977	+	4.53977i	−0.153824	+	0.153824i
$872$	−7.25996	+	15.0822i	−0.245853	+	0.510749i
$873$	0.419291	+	0.419291i	0.0141908	+	0.0141908i
$874$	1.40819	−	9.34648i	0.0476329	−	0.316150i
$875$	−14.7375	+	6.10448i	−0.498219	+	0.206369i
$876$	11.5539	−	13.9483i	0.390369	−	0.471269i
$877$	14.9712	−	36.1436i	0.505541	−	1.22048i	−0.440885	−	0.897564i	$-0.645335\pi$
$877$	14.9712	−	36.1436i	0.505541	−	1.22048i	0.946426	−	0.322921i	$-0.104665\pi$
$878$	17.7656	−	4.40705i	0.599559	−	0.148731i
$879$		−	14.9311i		−	0.503615i
$880$	42.2535	−	8.00506i	1.42437	−	0.269851i
$881$			11.5342i			0.388596i	0.980943	+	0.194298i	$0.0622428\pi$
$881$			11.5342i			0.388596i	−0.980943	+	0.194298i	$0.937757\pi$
$882$	0.199698	+	0.805018i	0.00672418	+	0.0271064i
$883$	−11.7901	+	28.4639i	−0.396769	+	0.957885i	0.591658	+	0.806189i	$0.298474\pi$
$883$	−11.7901	+	28.4639i	−0.396769	+	0.957885i	−0.988427	+	0.151696i	$0.951526\pi$
$884$	−7.73903	−	82.4252i	−0.260292	−	2.77226i
$885$	57.4599	−	23.8006i	1.93149	−	0.800050i
$886$	47.4632	+	7.15108i	1.59456	+	0.240245i
$887$	−1.08345	−	1.08345i	−0.0363789	−	0.0363789i	0.688683	−	0.725062i	$-0.258189\pi$
$887$	−1.08345	−	1.08345i	−0.0363789	−	0.0363789i	−0.725062	+	0.688683i	$0.758189\pi$
$888$	−0.315452	+	5.63486i	−0.0105859	+	0.189093i
$889$	4.65941	−	4.65941i	0.156272	−	0.156272i
$890$	54.5933	−	40.2967i	1.82997	−	1.35075i
$891$	11.3604	+	27.4265i	0.380588	+	0.918822i
$892$	21.0962	+	39.9046i	0.706353	+	1.33611i
$893$	−13.2072	−	5.47059i	−0.441961	−	0.183066i
$894$	−5.76698	+	9.57209i	−0.192877	+	0.320139i
$895$	−29.2623			−0.978131
$896$	1.48134	+	11.2163i	0.0494881	+	0.374711i
$897$	−52.9920			−1.76935
$898$	−19.1103	+	31.7195i	−0.637719	+	1.05849i
$899$	−10.1704	−	4.21270i	−0.339200	−	0.140501i
$900$	5.05940	+	9.57014i	0.168647	+	0.319005i
$901$	9.71532	+	23.4548i	0.323664	+	0.781394i
$902$	23.2925	−	17.1927i	0.775555	−	0.572456i
$903$	6.50560	−	6.50560i	0.216493	−	0.216493i
$904$	−1.50421	+	26.8694i	−0.0500292	+	0.893662i
$905$	−17.7869	−	17.7869i	−0.591255	−	0.591255i
$906$	−26.9294	−	4.05733i	−0.894668	−	0.134796i
$907$	−44.8283	+	18.5685i	−1.48850	+	0.616557i	−0.970990	−	0.239120i	$-0.923141\pi$
$907$	−44.8283	+	18.5685i	−1.48850	+	0.616557i	−0.517510	+	0.855677i	$0.673141\pi$
$908$	2.86871	+	30.5534i	0.0952013	+	1.01395i
$909$	3.12476	−	7.54383i	0.103642	−	0.250213i
$910$	8.17652	+	32.9610i	0.271049	+	1.09265i
$911$		−	30.9122i		−	1.02417i	−0.858935	−	0.512084i	$-0.828874\pi$
$911$		−	30.9122i		−	1.02417i	0.858935	−	0.512084i	$-0.171126\pi$
$912$	2.14407	+	11.3171i	0.0709972	+	0.374748i
$913$		−	12.2185i		−	0.404375i
$914$	−31.9853	+	7.93448i	−1.05798	+	0.262449i
$915$	−6.94385	+	16.7639i	−0.229557	+	0.554199i
$916$	−19.4378	+	23.4662i	−0.642244	+	0.775344i
$917$	−8.23083	+	3.40932i	−0.271806	+	0.112586i
$918$	−6.26192	+	41.5617i	−0.206674	+	1.37174i
$919$	12.7258	+	12.7258i	0.419785	+	0.419785i	0.885129	−	0.465345i	$-0.154070\pi$
$919$	12.7258	+	12.7258i	0.419785	+	0.419785i	−0.465345	+	0.885129i	$0.654070\pi$
$920$	20.3401	−	42.2556i	0.670593	−	1.39313i
$921$	15.9802	−	15.9802i	0.526565	−	0.526565i
$922$	20.1251	+	27.2652i	0.662784	+	0.897931i
$923$	−24.5530	−	59.2762i	−0.808172	−	1.95110i
$924$	10.3162	+	3.18080i	0.339378	+	0.104640i
$925$	−8.98352	−	3.72110i	−0.295376	−	0.122349i
$926$	10.8069	+	6.51090i	0.355135	+	0.213961i
$927$	−10.4407			−0.342917
$928$	0.754954	+	20.0194i	0.0247826	+	0.657170i
$929$	−22.3642			−0.733747			−0.366874	−	0.930271i	$-0.619572\pi$
$929$	−22.3642			−0.733747			−0.366874	+	0.930271i	$0.619572\pi$
$930$	−26.8983	−	16.2057i	−0.882031	−	0.531405i
$931$	−1.40480	−	0.581888i	−0.0460405	−	0.0190706i
$932$	11.2407	−	36.4566i	0.368201	−	1.19418i
$933$	−12.6671	−	30.5811i	−0.414702	−	1.00118i
$934$	−4.90278	−	6.64221i	−0.160424	−	0.217340i
$935$	49.4326	−	49.4326i	1.61662	−	1.61662i
$936$	9.96696	−	3.48956i	0.325780	−	0.114060i
$937$	−4.33693	−	4.33693i	−0.141681	−	0.141681i	0.632709	−	0.774390i	$-0.281943\pi$
$937$	−4.33693	−	4.33693i	−0.141681	−	0.141681i	−0.774390	+	0.632709i	$0.781943\pi$
$938$	0.212489	−	1.41033i	0.00693800	−	0.0460490i
$939$	5.62247	−	2.32890i	0.183482	−	0.0760009i
$940$	−54.6215	−	45.2449i	−1.78156	−	1.47573i
$941$	−1.54528	+	3.73063i	−0.0503746	+	0.121615i	−0.947064	−	0.321046i	$-0.895966\pi$
$941$	−1.54528	+	3.73063i	−0.0503746	+	0.121615i	0.896689	+	0.442661i	$0.145966\pi$
$942$	−41.1170	+	10.1998i	−1.33966	+	0.332326i
$943$		−	31.5699i		−	1.02806i
$944$	34.0924	+	7.10505i	1.10961	+	0.231250i
$945$		−	17.2413i		−	0.560859i
$946$	−4.71475	−	19.0060i	−0.153290	−	0.617938i
$947$	−8.01211	+	19.3429i	−0.260359	+	0.628561i	−0.998961	−	0.0455804i	$-0.985486\pi$
$947$	−8.01211	+	19.3429i	−0.260359	+	0.628561i	0.738602	+	0.674142i	$0.235486\pi$
$948$	5.11099	−	0.479879i	0.165997	−	0.0155858i
$949$	28.1246	−	11.6496i	0.912963	−	0.378162i
$950$	−19.6241	−	2.95667i	−0.636688	−	0.0959271i
$951$	−26.4136	−	26.4136i	−0.856521	−	0.856521i
$952$	12.2574	+	13.7112i	0.397265	+	0.444382i
$953$	−18.9461	+	18.9461i	−0.613725	+	0.613725i	−0.943915	−	0.330190i	$-0.892887\pi$
$953$	−18.9461	+	18.9461i	−0.613725	+	0.613725i	0.330190	+	0.943915i	$0.392887\pi$
$954$	−2.60545	+	1.92314i	−0.0843545	+	0.0622641i
$955$	25.3830	+	61.2799i	0.821374	+	1.98297i
$956$	39.1761	−	20.7111i	1.26705	−	0.669844i
$957$	17.6608	+	7.31534i	0.570892	+	0.236471i
$958$	−15.2188	+	25.2603i	−0.491697	+	0.816124i
$959$	−15.0739			−0.486763
$960$	−6.37868	+	56.7921i	−0.205871	+	1.83296i
$961$	−21.3379			−0.688320
$962$	−4.89511	+	8.12496i	−0.157825	+	0.261959i
$963$	−5.42284	−	2.24621i	−0.174749	−	0.0723832i
$964$	3.27174	−	1.72966i	0.105376	−	0.0557085i
$965$	0.647062	+	1.56215i	0.0208297	+	0.0502873i
$966$	9.47147	−	6.99112i	0.304740	−	0.224936i
$967$	−39.3087	+	39.3087i	−1.26408	+	1.26408i	−0.314989	+	0.949095i	$0.602001\pi$
$967$	−39.3087	+	39.3087i	−1.26408	+	1.26408i	−0.949095	+	0.314989i	$0.897999\pi$
$968$	−6.06530	+	5.42221i	−0.194946	+	0.174276i
$969$	13.2400	+	13.2400i	0.425329	+	0.425329i
$970$	−5.33333	−	0.803550i	−0.171243	−	0.0258004i
$971$	−41.2063	+	17.0682i	−1.32237	+	0.547744i	−0.928470	−	0.371408i	$-0.878875\pi$
$971$	−41.2063	+	17.0682i	−1.32237	+	0.547744i	−0.393902	+	0.919152i	$0.628875\pi$
$972$	−11.9728	+	1.12415i	−0.384028	+	0.0360570i
$973$	−1.47374	+	3.55792i	−0.0472459	+	0.114062i
$974$	−14.6694	−	59.1351i	−0.470039	−	1.89481i
$975$			111.263i			3.56327i
$976$	−8.49898	+	5.56745i	−0.272046	+	0.178210i
$977$		−	14.8302i		−	0.474460i	−0.971454	−	0.237230i	$-0.923761\pi$
$977$		−	14.8302i		−	0.474460i	0.971454	−	0.237230i	$-0.0762394\pi$
$978$	17.4496	−	4.32866i	0.557977	−	0.138415i
$979$	13.8738	−	33.4942i	0.443407	−	1.07048i
$980$	−5.80990	−	4.81254i	−0.185590	−	0.153731i
$981$	−3.20662	+	1.32823i	−0.102380	+	0.0424070i
$982$	−5.41461	+	35.9379i	−0.172787	+	1.14682i
$983$	−1.53859	−	1.53859i	−0.0490735	−	0.0490735i	0.682144	−	0.731218i	$-0.261048\pi$
$983$	−1.53859	−	1.53859i	−0.0490735	−	0.0490735i	−0.731218	+	0.682144i	$0.761048\pi$
$984$	12.7129	+	36.3109i	0.405273	+	1.15755i
$985$	27.1062	−	27.1062i	0.863677	−	0.863677i
$986$	19.3400	+	26.2016i	0.615913	+	0.834430i
$987$	−6.81349	−	16.4492i	−0.216876	−	0.523584i
$988$	−5.70419	+	18.5002i	−0.181474	+	0.588571i
$989$	−19.7284	−	8.17176i	−0.627326	−	0.259847i
$990$	7.63815	+	4.60182i	0.242756	+	0.146256i
$991$	16.0590			0.510132			0.255066	−	0.966924i	$-0.417903\pi$
$991$	16.0590			0.510132			0.255066	+	0.966924i	$0.417903\pi$
$992$	−7.33640	−	15.9801i	−0.232931	−	0.507369i
$993$	11.0248			0.349861
$994$	12.2086	+	7.35545i	0.387235	+	0.233301i
$995$	40.8302	+	16.9124i	1.29440	+	0.536159i
$996$	15.5163	+	4.78416i	0.491653	+	0.151592i
$997$	−9.38290	−	22.6523i	−0.297159	−	0.717406i	−0.999982	−	0.00604089i	$-0.998077\pi$
$997$	−9.38290	−	22.6523i	−0.297159	−	0.717406i	0.702822	−	0.711365i	$-0.251923\pi$
$998$	−24.4325	−	33.1008i	−0.773396	−	1.04779i
$999$	3.40527	−	3.40527i	0.107738	−	0.107738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.29.6	✓	52
4.3	odd	2		896.2.u.c.337.4		52
32.11	odd	8		896.2.u.c.561.4		52
32.21	even	8	inner	224.2.u.c.85.6	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.6	✓	52	1.1	even	1	trivial
224.2.u.c.85.6	yes	52	32.21	even	8	inner
896.2.u.c.337.4		52	4.3	odd	2
896.2.u.c.561.4		52	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.729813 + 1.21135i) q^{2} +(1.74965 + 0.724727i) q^{3} +(-0.934745 - 1.76812i) q^{4} +(1.44353 + 3.48498i) q^{5} +(-2.15481 + 1.59052i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.82401 + 0.158094i) q^{8} +(0.414709 + 0.414709i) q^{9} +O(q^{10})\)	\(q+(-0.729813 + 1.21135i) q^{2} +(1.74965 + 0.724727i) q^{3} +(-0.934745 - 1.76812i) q^{4} +(1.44353 + 3.48498i) q^{5} +(-2.15481 + 1.59052i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.82401 + 0.158094i) q^{8} +(0.414709 + 0.414709i) q^{9} +(-5.27504 - 0.794768i) q^{10} +(-2.63324 + 1.09072i) q^{11} +(-0.354067 - 3.77102i) q^{12} +(2.43617 - 5.88144i) q^{13} +(0.340499 + 1.37261i) q^{14} +7.14364i q^{15} +(-2.25250 + 3.30548i) q^{16} +6.50231i q^{17} +(-0.805018 + 0.199698i) q^{18} +(0.581888 - 1.40480i) q^{19} +(4.81254 - 5.80990i) q^{20} +(1.74965 - 0.724727i) q^{21} +(0.600524 - 3.98580i) q^{22} +(-3.10808 - 3.10808i) q^{23} +(4.82643 + 2.32324i) q^{24} +(-6.52579 + 6.52579i) q^{25} +(5.34654 + 7.24341i) q^{26} +(-1.74914 - 4.22279i) q^{27} +(-1.91121 - 0.589286i) q^{28} +(-3.27190 - 1.35527i) q^{29} +(-8.65346 - 5.21353i) q^{30} +3.10839 q^{31} +(-2.36019 - 5.14096i) q^{32} -5.39771 q^{33} +(-7.87659 - 4.74548i) q^{34} +(3.48498 + 1.44353i) q^{35} +(0.345608 - 1.12090i) q^{36} +(0.403202 + 0.973415i) q^{37} +(1.27704 + 1.73011i) q^{38} +(8.52487 - 8.52487i) q^{39} +(3.52557 + 10.0698i) q^{40} +(5.07868 + 5.07868i) q^{41} +(-0.399016 + 2.64835i) q^{42} +(4.48831 - 1.85912i) q^{43} +(4.38994 + 3.63634i) q^{44} +(-0.846609 + 2.04389i) q^{45} +(6.03331 - 1.49666i) q^{46} -9.40146i q^{47} +(-6.33666 + 4.15097i) q^{48} -1.00000i q^{49} +(-3.14242 - 12.6676i) q^{50} +(-4.71240 + 11.3767i) q^{51} +(-12.6763 + 1.19020i) q^{52} +(3.60715 - 1.49413i) q^{53} +(6.39183 + 0.963030i) q^{54} +(-7.60230 - 7.60230i) q^{55} +(2.10866 - 1.88508i) q^{56} +(2.03619 - 2.03619i) q^{57} +(4.02958 - 2.97433i) q^{58} +(-3.33172 - 8.04349i) q^{59} +(12.6308 - 6.67748i) q^{60} +(2.34669 + 0.972032i) q^{61} +(-2.26854 + 3.76535i) q^{62} +0.586487 q^{63} +(7.95001 + 0.892918i) q^{64} +24.0134 q^{65} +(3.93932 - 6.53852i) q^{66} +(-0.931743 - 0.385940i) q^{67} +(11.4969 - 6.07800i) q^{68} +(-3.18553 - 7.69056i) q^{69} +(-4.29200 + 3.16803i) q^{70} +(7.12660 - 7.12660i) q^{71} +(1.10558 + 1.23670i) q^{72} +(3.38133 + 3.38133i) q^{73} +(-1.47341 - 0.221992i) q^{74} +(-16.1472 + 6.68841i) q^{75} +(-3.02778 + 0.284283i) q^{76} +(-1.09072 + 2.63324i) q^{77} +(4.10505 + 16.5482i) q^{78} +1.35534i q^{79} +(-14.7711 - 3.07838i) q^{80} -10.4155i q^{81} +(-9.85856 + 2.44558i) q^{82} +(-1.64053 + 3.96059i) q^{83} +(-2.91688 - 2.41615i) q^{84} +(-22.6604 + 9.38626i) q^{85} +(-1.02358 + 6.79374i) q^{86} +(-4.74247 - 4.74247i) q^{87} +(-7.60872 + 2.66391i) q^{88} +(-8.99424 + 8.99424i) q^{89} +(-1.85801 - 2.51720i) q^{90} +(-2.43617 - 5.88144i) q^{91} +(-2.59020 + 8.40074i) q^{92} +(5.43858 + 2.25273i) q^{93} +(11.3885 + 6.86131i) q^{94} +5.73568 q^{95} +(-0.403711 - 10.7054i) q^{96} +1.01105 q^{97} +(1.21135 + 0.729813i) q^{98} +(-1.54436 - 0.639695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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