LMFDB - Embedded newform 224.2.u.c.85.6

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			85.6
Character	$\chi$	$=$	224.85
Dual form			224.2.u.c.29.6

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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	0.184646	−	0.982805i	$-0.440886\pi$
$3$	1.74965	−	0.724727i	1.01016	−	0.418421i	0.825512	+	0.564384i	$0.190886\pi$
$4$	−0.934745	+	1.76812i	−0.467372	+	0.884061i
$5$	1.44353	−	3.48498i	0.645565	−	1.55853i	−0.173502	−	0.984833i	$-0.555508\pi$
$5$	1.44353	−	3.48498i	0.645565	−	1.55853i	0.819067	−	0.573698i	$-0.194492\pi$
$6$	−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	−0.0514204	−	0.998677i	$-0.516375\pi$
$11$	−2.63324	−	1.09072i	−0.793951	−	0.328865i	−0.742531	+	0.669812i	$0.766375\pi$
$12$	−0.354067	+	3.77102i	−0.102210	+	1.08860i
$13$	2.43617	+	5.88144i	0.675672	+	1.63122i	0.771813	+	0.635849i	$0.219350\pi$
$13$	2.43617	+	5.88144i	0.675672	+	1.63122i	−0.0961412	+	0.995368i	$0.530650\pi$
$14$	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	$-0.710847\pi$
$17$		−	6.50231i		−	1.57704i	0.615007	−	0.788521i	$-0.289153\pi$
$18$	−0.805018	−	0.199698i	−0.189745	−	0.0470693i
$19$	0.581888	+	1.40480i	0.133494	+	0.322284i	0.976465	−	0.215676i	$-0.0691954\pi$
$19$	0.581888	+	1.40480i	0.133494	+	0.322284i	−0.842971	+	0.537959i	$0.819195\pi$
$20$	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	−0.952529	−	0.304448i	$-0.901528\pi$
$23$	−3.10808	+	3.10808i	−0.648080	+	0.648080i	0.304448	+	0.952529i	$0.401528\pi$
$24$	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	−0.665192	−	0.746672i	$-0.731650\pi$
$29$	−3.27190	+	1.35527i	−0.607577	+	0.251667i	0.0576150	+	0.998339i	$0.481650\pi$
$30$	−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	−0.887265	−	0.461260i	$-0.847398\pi$
$37$	0.403202	−	0.973415i	0.0662860	−	0.160028i	0.953551	+	0.301231i	$0.0973976\pi$
$38$	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	−0.188849	−	0.982006i	$-0.560476\pi$
$41$	5.07868	−	5.07868i	0.793157	−	0.793157i	0.982006	+	0.188849i	$0.0604758\pi$
$42$	−0.399016	−	2.64835i	−0.0615695	−	0.408649i
$43$	4.48831	+	1.85912i	0.684462	+	0.283513i	0.697691	−	0.716399i	$-0.254211\pi$
$43$	4.48831	+	1.85912i	0.684462	+	0.283513i	−0.0132290	+	0.999912i	$0.504211\pi$
$44$	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	$0.240491\pi$
$47$			9.40146i			1.37134i	−0.727911	+	0.685672i	$0.759509\pi$
$48$	−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	0.616409	−	0.787426i	$-0.288587\pi$
$53$	3.60715	+	1.49413i	0.495481	+	0.205235i	−0.120928	+	0.992661i	$0.538587\pi$
$54$	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	0.544313	+	0.838882i	$0.316790\pi$
$59$	−3.33172	+	8.04349i	−0.433754	+	1.04717i	−0.978067	+	0.208292i	$0.933210\pi$
$60$	12.6308	+	6.67748i	1.63063	+	0.862059i
$61$	2.34669	−	0.972032i	0.300463	−	0.124456i	−0.227358	−	0.973811i	$-0.573009\pi$
$61$	2.34669	−	0.972032i	0.300463	−	0.124456i	0.527822	+	0.849355i	$0.323009\pi$
$62$	−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	−0.438872	−	0.898550i	$-0.644622\pi$
$67$	−0.931743	+	0.385940i	−0.113830	+	0.0471501i	0.325041	+	0.945700i	$0.394622\pi$
$68$	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	0.989602	−	0.143831i	$-0.0459421\pi$
$71$	7.12660	+	7.12660i	0.845771	+	0.845771i	−0.143831	+	0.989602i	$0.545942\pi$
$72$	1.10558	−	1.23670i	0.130293	−	0.145747i
$73$	3.38133	−	3.38133i	0.395755	−	0.395755i	−0.480978	−	0.876733i	$-0.659718\pi$
$73$	3.38133	−	3.38133i	0.395755	−	0.395755i	0.876733	+	0.480978i	$0.159718\pi$
$74$	−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	$-0.975707\pi$
$79$		−	1.35534i		−	0.152487i	0.997089	−	0.0762436i	$-0.0242927\pi$
$80$	−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	0.807909	−	0.589307i	$-0.200599\pi$
$83$	−1.64053	−	3.96059i	−0.180072	−	0.434731i	−0.987981	+	0.154575i	$0.950599\pi$
$84$	−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	0.0455735	−	0.998961i	$-0.485488\pi$
$89$	−8.99424	−	8.99424i	−0.953387	−	0.953387i	−0.998961	+	0.0455735i	$0.985488\pi$
$90$	−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	0.401276	+	0.915957i	$0.368567\pi$
$101$	−5.32793	+	12.8628i	−0.530148	+	1.27989i	−0.931425	+	0.363934i	$0.881433\pi$
$102$	−10.3421	+	14.0113i	−1.02402	+	1.38732i
$103$	−12.5880	−	12.5880i	−1.24033	−	1.24033i	−0.959864	−	0.280466i	$-0.909511\pi$
$103$	−12.5880	−	12.5880i	−1.24033	−	1.24033i	−0.280466	−	0.959864i	$-0.590489\pi$
$104$	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	−0.112013	−	0.993707i	$-0.535730\pi$
$107$	−9.24632	−	3.82995i	−0.893875	−	0.370255i	−0.781862	+	0.623451i	$0.785730\pi$
$108$	−5.83141	−	7.03992i	−0.561128	−	0.677417i
$109$	−2.26472	−	5.46751i	−0.216921	−	0.523693i	0.777536	−	0.628838i	$-0.216469\pi$
$109$	−2.26472	−	5.46751i	−0.216921	−	0.523693i	−0.994457	+	0.105145i	$0.966469\pi$
$110$	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	$-0.852304\pi$
$113$		−	9.51463i		−	0.895061i	0.894269	−	0.447530i	$-0.147696\pi$
$114$	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	−0.712077	−	0.702101i	$-0.752245\pi$
$131$	−8.23083	+	3.40932i	−0.719131	+	0.297874i	−0.00705412	+	0.999975i	$0.502245\pi$
$132$	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	−0.996323	−	0.0856733i	$-0.972696\pi$
$137$	−10.6589	+	10.6589i	−0.910650	+	0.910650i	0.0856733	+	0.996323i	$0.472696\pi$
$138$	11.6408	−	1.75387i	0.990932	−	0.149299i
$139$	−3.55792	−	1.47374i	−0.301779	−	0.125001i	0.226656	−	0.973975i	$-0.427221\pi$
$139$	−3.55792	−	1.47374i	−0.301779	−	0.125001i	−0.528435	+	0.848974i	$0.677221\pi$
$140$	−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	0.534957	−	0.844879i	$-0.320328\pi$
$149$	3.85494	+	1.59677i	0.315809	+	0.130812i	−0.219148	+	0.975692i	$0.570328\pi$
$150$	3.68246	+	24.4413i	0.300672	+	1.99562i
$151$	7.19011	−	7.19011i	0.585123	−	0.585123i	−0.351184	−	0.936307i	$-0.614221\pi$
$151$	7.19011	−	7.19011i	0.585123	−	0.585123i	0.936307	+	0.351184i	$0.114221\pi$
$152$	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	0.286323	−	0.958133i	$-0.407567\pi$
$157$	14.6135	−	6.05312i	1.16629	−	0.483092i	0.879963	+	0.475042i	$0.157567\pi$
$158$	−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	−0.612104	−	0.790777i	$-0.709677\pi$
$163$	−6.20182	+	2.56888i	−0.485764	+	0.201210i	0.126341	+	0.991987i	$0.459677\pi$
$164$	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	0.325825	−	0.945430i	$-0.394358\pi$
$167$	−8.00706	−	8.00706i	−0.619605	−	0.619605i	−0.945430	+	0.325825i	$0.894358\pi$
$168$	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	−0.987852	−	0.155399i	$-0.950334\pi$
$173$	−5.25090	−	12.6768i	−0.399218	−	0.963799i	0.588633	−	0.808400i	$-0.299666\pi$
$174$	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	0.773257	−	0.634093i	$-0.218626\pi$
$179$	−2.96868	−	7.16702i	−0.221889	−	0.535689i	−0.995147	+	0.0984041i	$0.968626\pi$
$180$	4.40522	+	0.413613i	0.328345	+	0.0308289i
$181$	−6.16090	−	2.55193i	−0.457936	−	0.189683i	0.141777	−	0.989899i	$-0.454719\pi$
$181$	−6.16090	−	2.55193i	−0.457936	−	0.189683i	−0.599713	+	0.800215i	$0.704719\pi$
$182$	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	−0.999752	−	0.0222601i	$-0.992914\pi$
$197$	−3.88901	+	9.38890i	−0.277080	+	0.668931i	0.722672	+	0.691191i	$0.242914\pi$
$198$	1.90199	+	1.40390i	0.135168	+	0.0997711i
$199$	8.28449	+	8.28449i	0.587272	+	0.587272i	0.936892	−	0.349620i	$-0.113689\pi$
$199$	8.28449	+	8.28449i	0.587272	+	0.587272i	−0.349620	+	0.936892i	$0.613689\pi$
$200$	−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	0.843367	−	0.537337i	$-0.180570\pi$
$211$	−1.93104	−	4.66194i	−0.132938	−	0.320941i	−0.976306	+	0.216396i	$0.930570\pi$
$212$	−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	−0.799799	−	0.600268i	$-0.795060\pi$
$227$	−14.1759	+	5.87185i	−0.940888	+	0.389728i	−0.141089	+	0.989997i	$0.545060\pi$
$228$	−5.50356	+	1.69692i	−0.364482	+	0.112381i
$229$	−5.83040	+	14.0758i	−0.385284	+	0.930157i	0.605641	+	0.795738i	$0.292917\pi$
$229$	−5.83040	+	14.0758i	−0.385284	+	0.930157i	−0.990925	+	0.134419i	$0.957083\pi$
$230$	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	−0.110265	−	0.993902i	$-0.535170\pi$
$233$	13.4881	−	13.4881i	0.883638	−	0.883638i	0.993902	+	0.110265i	$0.0351698\pi$
$234$	−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	$-0.745695\pi$
$239$		−	22.1569i		−	1.43321i	0.697478	−	0.716606i	$-0.254305\pi$
$240$	−23.6132	+	16.0911i	−1.52423	+	1.03868i
$241$		−	1.85041i		−	0.119195i	−0.998222	−	0.0595976i	$-0.981018\pi$
$241$		−	1.85041i		−	0.119195i	0.998222	−	0.0595976i	$-0.0189818\pi$
$242$	−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	−0.893889	−	0.448288i	$-0.852034\pi$
$251$	0.874117	−	2.11031i	0.0551738	−	0.133201i	0.949063	+	0.315087i	$0.102034\pi$
$252$	−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	0.250084	−	0.968224i	$-0.419542\pi$
$263$	−11.6463	−	11.6463i	−0.718141	−	0.718141i	−0.968224	+	0.250084i	$0.919542\pi$
$264$	−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	0.989062	+	0.147501i	$0.0471229\pi$
$269$	6.46189	+	15.6004i	0.393988	+	0.951172i	−0.595074	+	0.803671i	$0.702877\pi$
$270$	5.87063	−	23.6656i	0.357275	−	1.44024i
$271$			11.9824i			0.727881i	0.931422	+	0.363940i	$0.118569\pi$
$271$			11.9824i			0.727881i	−0.931422	+	0.363940i	$0.881431\pi$
$272$	−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	0.733573	−	0.679611i	$-0.237851\pi$
$277$	12.8441	+	5.32021i	0.771729	+	0.319661i	0.0381566	+	0.999272i	$0.487851\pi$
$278$	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	0.765535	−	0.643394i	$-0.222474\pi$
$281$	2.04746	+	2.04746i	0.122141	+	0.122141i	−0.643394	+	0.765535i	$0.722474\pi$
$282$	14.9532	−	20.2584i	0.890450	−	1.20637i
$283$	6.07132	−	14.6575i	0.360902	−	0.871295i	−0.634266	−	0.773115i	$-0.718698\pi$
$283$	6.07132	−	14.6575i	0.360902	−	0.871295i	0.995169	−	0.0981806i	$-0.0313023\pi$
$284$	−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	−0.987177	−	0.159627i	$-0.948971\pi$
$293$	−3.01716	+	7.28406i	−0.176264	+	0.425539i	0.810913	+	0.585166i	$0.198971\pi$
$294$	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	0.998978	−	0.0451968i	$-0.0143915\pi$
$307$	4.56669	+	11.0250i	0.260635	+	0.629228i	−0.738343	+	0.674425i	$0.764391\pi$
$308$	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	−0.964587	−	0.263765i	$-0.915036\pi$
$311$	−12.3591	+	12.3591i	−0.700822	+	0.700822i	0.263765	+	0.964587i	$0.415036\pi$
$312$	25.4220	+	22.7265i	1.43924	+	1.28664i
$313$	2.27228	+	2.27228i	0.128437	+	0.128437i	0.768403	−	0.639966i	$-0.221052\pi$
$313$	2.27228	+	2.27228i	0.128437	+	0.128437i	−0.639966	+	0.768403i	$0.721052\pi$
$314$	−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	−0.830368	−	0.557216i	$-0.811870\pi$
$317$	−18.2232	+	7.54829i	−1.02352	+	0.423954i	−0.193148	+	0.981170i	$0.561870\pi$
$318$	−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	0.525565	−	0.850753i	$-0.323854\pi$
$331$	5.37837	+	2.22779i	0.295622	+	0.122451i	−0.229943	+	0.973204i	$0.573854\pi$
$332$	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	$-0.983358\pi$
$337$		−	1.91866i		−	0.104516i	0.998634	−	0.0522582i	$-0.0166419\pi$
$338$	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	−0.500880	−	0.865516i	$-0.666990\pi$
$347$	8.66773	−	20.9257i	0.465308	−	1.12335i	0.966189	−	0.257837i	$-0.0830096\pi$
$348$	−3.95226	−	12.8183i	−0.211864	−	0.687131i
$349$	−13.9558	+	5.78067i	−0.747035	+	0.309432i	−0.723531	−	0.690292i	$-0.757482\pi$
$349$	−13.9558	+	5.78067i	−0.747035	+	0.309432i	−0.0235038	+	0.999724i	$0.507482\pi$
$350$	−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	0.260589	−	0.965450i	$-0.416083\pi$
$359$	−13.3552	−	13.3552i	−0.704861	−	0.704861i	−0.965450	+	0.260589i	$0.916083\pi$
$360$	−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	$-0.836020\pi$
$367$		−	18.8765i		−	0.985344i	0.870215	−	0.492672i	$-0.163980\pi$
$368$	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	0.143117	−	0.989706i	$-0.454287\pi$
$373$	−8.79738	−	3.64399i	−0.455511	−	0.188679i	−0.598628	+	0.801027i	$0.704287\pi$
$374$	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	0.679581	+	0.733600i	$0.262162\pi$
$379$	−6.22368	+	15.0253i	−0.319689	+	0.771798i	−0.999270	+	0.0381974i	$0.987838\pi$
$380$	−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	0.337085	+	0.941474i	$0.390559\pi$
$389$	−11.1828	+	26.9978i	−0.566993	+	1.36884i	−0.904078	+	0.427368i	$0.859441\pi$
$390$	−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	0.998558	+	0.0536868i	$0.0170973\pi$
$397$	6.58383	+	15.8948i	0.330433	+	0.797736i	−0.668125	+	0.744049i	$0.732903\pi$
$398$	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	$0.208132\pi$
$401$			24.3608i			1.21652i	−0.793737	+	0.608261i	$0.791868\pi$
$402$	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	0.989314	−	0.145803i	$-0.0465766\pi$
$409$	17.0589	+	17.0589i	0.843511	+	0.843511i	−0.145803	+	0.989314i	$0.546577\pi$
$410$	−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	0.801970	−	0.597364i	$-0.203785\pi$
$419$	36.6700	−	15.1892i	1.79145	−	0.742043i	0.989479	−	0.144679i	$-0.0462149\pi$
$420$	4.20965	+	13.6530i	0.205410	+	0.666200i
$421$	10.1569	−	24.5210i	0.495018	−	1.19508i	−0.457119	−	0.889406i	$-0.651118\pi$
$421$	10.1569	−	24.5210i	0.495018	−	1.19508i	0.952136	−	0.305673i	$-0.0988815\pi$
$422$	−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	$-0.711182\pi$
$431$		−	32.7133i		−	1.57575i	0.615838	−	0.787873i	$-0.288818\pi$
$432$	17.8983	−	3.73011i	0.861133	−	0.179465i
$433$		−	21.4556i		−	1.03109i	−0.856862	−	0.515546i	$-0.827589\pi$
$433$		−	21.4556i		−	1.03109i	0.856862	−	0.515546i	$-0.172411\pi$
$434$	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	−0.890934	−	0.454132i	$-0.849949\pi$
$439$	−9.15202	+	9.15202i	−0.436802	+	0.436802i	0.454132	+	0.890934i	$0.349949\pi$
$440$	−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	0.237961	+	0.971275i	$0.423521\pi$
$443$	−12.9884	+	31.3568i	−0.617098	+	1.48981i	−0.855059	+	0.518531i	$0.826479\pi$
$444$	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	−0.207464	−	0.978243i	$-0.566521\pi$
$457$	16.4774	−	16.4774i	0.770779	−	0.770779i	0.978243	+	0.207464i	$0.0665210\pi$
$458$	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	0.980205	+	0.197987i	$0.0634403\pi$
$461$	9.17008	+	22.1385i	0.427093	+	1.03109i	−0.553112	+	0.833107i	$0.686560\pi$
$462$	−1.83791	+	7.40896i	−0.0855075	+	0.344696i
$463$			8.92132i			0.414609i	0.978276	+	0.207304i	$0.0664690\pi$
$463$			8.92132i			0.414609i	−0.978276	+	0.207304i	$0.933531\pi$
$464$	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	0.863726	−	0.503962i	$-0.168125\pi$
$467$	−2.23397	−	5.39328i	−0.103376	−	0.249571i	−0.967101	+	0.254391i	$0.918125\pi$
$468$	−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	−0.843826	−	0.536618i	$-0.819702\pi$
$487$	−30.4637	−	30.4637i	−1.38044	−	1.38044i	−0.536618	−	0.843826i	$-0.680298\pi$
$488$	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	0.847515	−	0.530772i	$-0.178098\pi$
$491$	23.7425	+	9.83448i	1.07149	+	0.443824i	0.223971	+	0.974596i	$0.428098\pi$
$492$	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	−0.950361	−	0.311150i	$-0.899286\pi$
$499$	−11.1328	−	26.8768i	−0.498370	−	1.20317i	0.451990	−	0.892023i	$-0.350714\pi$
$500$	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	−0.532779	−	0.846255i	$-0.678852\pi$
$503$	7.03053	−	7.03053i	0.313476	−	0.313476i	0.846255	+	0.532779i	$0.178852\pi$
$504$	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	0.367602	−	0.929983i	$-0.380179\pi$
$509$	28.9939	−	12.0097i	1.28513	−	0.532319i	0.917531	+	0.397664i	$0.130179\pi$
$510$	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	−0.618766	−	0.785575i	$-0.712367\pi$
$521$	3.80750	−	3.80750i	0.166810	−	0.166810i	0.785575	+	0.618766i	$0.212367\pi$
$522$	2.90458	−	0.437621i	0.127130	−	0.0191542i
$523$	37.8891	+	15.6942i	1.65678	+	0.686259i	0.997825	−	0.0659260i	$-0.0210001\pi$
$523$	37.8891	+	15.6942i	1.65678	+	0.686259i	0.658952	+	0.752185i	$0.271000\pi$
$524$	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	0.0667503	−	0.997770i	$-0.478737\pi$
$541$	19.0606	−	7.89516i	0.819480	−	0.339440i	0.752729	+	0.658330i	$0.228737\pi$
$542$	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	−0.978522	−	0.206142i	$-0.933909\pi$
$547$	−35.6592	+	14.7705i	−1.52468	+	0.631542i	−0.546155	+	0.837684i	$0.683909\pi$
$548$	−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	0.825831	−	0.563917i	$-0.190706\pi$
$557$	−3.70225	−	8.93802i	−0.156869	−	0.378716i	−0.982701	+	0.185201i	$0.940706\pi$
$558$	−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	0.877153	−	0.480212i	$-0.159440\pi$
$563$	−1.96106	−	4.73442i	−0.0826489	−	0.199532i	−0.959802	+	0.280680i	$0.909440\pi$
$564$	−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	0.236399	−	0.971656i	$-0.424033\pi$
$569$	−17.5386	−	17.5386i	−0.735257	−	0.735257i	−0.971656	+	0.236399i	$0.924033\pi$
$570$	−12.3593	−	9.12271i	−0.517675	−	0.382108i
$571$	3.64399	−	8.79737i	0.152496	−	0.368158i	−0.829107	−	0.559090i	$-0.811151\pi$
$571$	3.64399	−	8.79737i	0.152496	−	0.368158i	0.981603	+	0.190931i	$0.0611508\pi$
$572$	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	0.534120	−	0.845409i	$-0.320643\pi$
$587$	7.60776	+	3.15124i	0.314006	+	0.130066i	−0.220114	+	0.975474i	$0.570643\pi$
$588$	−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	$-0.705968\pi$
$593$		−	38.8581i		−	1.59571i	0.602849	−	0.797856i	$-0.294032\pi$
$594$	−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	−0.700140	−	0.714006i	$-0.746879\pi$
$599$	0.339367	−	0.339367i	0.0138662	−	0.0138662i	0.714006	+	0.700140i	$0.246879\pi$
$600$	−46.6573	−	16.3353i	−1.90478	−	0.666886i
$601$	−4.77407	−	4.77407i	−0.194738	−	0.194738i	0.603002	−	0.797740i	$-0.293971\pi$
$601$	−4.77407	−	4.77407i	−0.194738	−	0.194738i	−0.797740	+	0.603002i	$0.793971\pi$
$602$	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	−0.974811	−	0.223033i	$-0.928404\pi$
$613$	−3.16436	+	7.63944i	−0.127807	+	0.308554i	0.847004	+	0.531587i	$0.178404\pi$
$614$	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	−0.669241	−	0.743046i	$-0.733380\pi$
$617$	1.83328	−	1.83328i	0.0738050	−	0.0738050i	0.743046	+	0.669241i	$0.233380\pi$
$618$	7.10331	+	47.1461i	0.285737	+	1.89650i
$619$	13.9279	+	5.76910i	0.559808	+	0.231880i	0.644602	−	0.764519i	$-0.277023\pi$
$619$	13.9279	+	5.76910i	0.559808	+	0.231880i	−0.0847941	+	0.996398i	$0.527023\pi$
$620$	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	0.412288	−	0.911054i	$-0.364730\pi$
$631$	33.2420	−	33.2420i	1.32334	−	1.32334i	0.911054	−	0.412288i	$-0.135270\pi$
$632$	−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	−0.466875	−	0.884323i	$-0.654620\pi$
$643$	−4.35374	+	1.80338i	−0.171695	+	0.0711184i	0.295180	+	0.955442i	$0.404620\pi$
$644$	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	0.933191	−	0.359382i	$-0.117012\pi$
$647$	14.5955	+	14.5955i	0.573809	+	0.573809i	−0.359382	+	0.933191i	$0.617012\pi$
$648$	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	0.958261	−	0.285895i	$-0.0922908\pi$
$653$	2.00624	+	4.84348i	0.0785101	+	0.189540i	−0.879751	+	0.475435i	$0.842291\pi$
$654$	−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	−0.999539	−	0.0303479i	$-0.990338\pi$
$659$	−8.06628	−	19.4737i	−0.314218	−	0.758588i	0.685322	−	0.728240i	$-0.259662\pi$
$660$	−25.9767	−	31.3601i	−1.01114	−	1.22069i
$661$	−15.5918	−	6.45832i	−0.606449	−	0.251199i	0.0582603	−	0.998301i	$-0.481445\pi$
$661$	−15.5918	−	6.45832i	−0.606449	−	0.251199i	−0.664709	+	0.747102i	$0.731445\pi$
$662$	−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	−0.665500	−	0.746398i	$-0.731782\pi$
$677$	8.66082	−	20.9091i	0.332863	−	0.803601i	0.998363	−	0.0572034i	$-0.0182184\pi$
$678$	−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	0.985565	−	0.169295i	$-0.0541490\pi$
$683$	40.8415	+	16.9171i	1.56276	+	0.647315i	0.577190	+	0.816610i	$0.304149\pi$
$684$	−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	0.896509	+	0.443025i	$0.146095\pi$
$691$	15.1372	+	36.5445i	0.575847	+	1.39022i	−0.320662	+	0.947194i	$0.603905\pi$
$692$	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	−0.332925	−	0.942953i	$-0.608036\pi$
$701$	2.60607	−	1.07947i	0.0984300	−	0.0407710i	0.431355	+	0.902182i	$0.358036\pi$
$702$	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	−0.802068	−	0.597233i	$-0.796267\pi$
$709$	4.98958	−	12.0459i	0.187387	−	0.452393i	0.989455	+	0.144840i	$0.0462667\pi$
$710$	−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	$0.306803\pi$
$719$			44.0500i			1.64279i	−0.570361	+	0.821394i	$0.693197\pi$
$720$	−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	−0.999996	−	0.00271192i	$-0.999137\pi$
$727$	−26.8897	+	26.8897i	−0.997284	+	0.997284i	0.00271192	+	0.999996i	$0.499137\pi$
$728$	−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	−0.986190	−	0.165619i	$-0.947038\pi$
$733$	−42.4092	+	17.5665i	−1.56642	+	0.648833i	−0.580231	+	0.814452i	$0.697038\pi$
$734$	−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	0.169192	−	0.985583i	$-0.445884\pi$
$739$	26.7969	−	11.0996i	0.985741	−	0.408307i	0.816549	+	0.577276i	$0.195884\pi$
$740$	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	0.383601	−	0.923499i	$-0.374684\pi$
$743$	−14.7166	−	14.7166i	−0.539898	−	0.539898i	−0.923499	+	0.383601i	$0.874684\pi$
$744$	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	$-0.819891\pi$
$751$		−	29.3838i		−	1.07223i	0.844145	−	0.536115i	$-0.180109\pi$
$752$	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	0.233643	−	0.972322i	$-0.424935\pi$
$757$	−7.94268	−	3.28997i	−0.288682	−	0.119576i	−0.522325	+	0.852746i	$0.674935\pi$
$758$	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	0.898534	+	0.438904i	$0.144633\pi$
$761$	36.8949	+	36.8949i	1.33744	+	1.33744i	0.438904	+	0.898534i	$0.355367\pi$
$762$	−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	0.106850	+	0.994275i	$0.465923\pi$
$773$	−18.6769	+	45.0901i	−0.671763	+	1.62178i	−0.778613	+	0.627504i	$0.784077\pi$
$774$	−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	−0.974603	−	0.223940i	$-0.928108\pi$
$787$	−12.4503	−	30.0576i	−0.443804	−	1.07144i	0.530798	−	0.847498i	$-0.321892\pi$
$788$	−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	−0.715302	−	0.698815i	$-0.753711\pi$
$797$	−20.5229	+	8.50088i	−0.726960	+	0.301117i	−0.0116578	+	0.999932i	$0.503711\pi$
$798$	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	−0.258395	−	0.966039i	$-0.583194\pi$
$809$	20.1275	−	20.1275i	0.707644	−	0.707644i	0.966039	+	0.258395i	$0.0831937\pi$
$810$	−8.27790	−	54.9422i	−0.290856	−	1.93047i
$811$	33.3517	+	13.8147i	1.17114	+	0.485101i	0.881569	−	0.472056i	$-0.156488\pi$
$811$	33.3517	+	13.8147i	1.17114	+	0.485101i	0.289569	+	0.957157i	$0.406488\pi$
$812$	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	0.811061	−	0.584962i	$-0.198890\pi$
$821$	27.8204	+	11.5236i	0.970937	+	0.402175i	0.159876	+	0.987137i	$0.448890\pi$
$822$	39.9211	−	6.01474i	1.39241	−	0.209788i
$823$	−0.438124	+	0.438124i	−0.0152720	+	0.0152720i	−0.714702	−	0.699430i	$-0.753437\pi$
$823$	−0.438124	+	0.438124i	−0.0152720	+	0.0152720i	0.699430	+	0.714702i	$0.253437\pi$
$824$	−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	0.428644	+	0.903474i	$0.358992\pi$
$827$	−14.7614	+	35.6373i	−0.513306	+	1.23923i	−0.941949	+	0.335756i	$0.891008\pi$
$828$	−4.55804	−	2.40968i	−0.158403	−	0.0837421i
$829$	−50.4450	+	20.8950i	−1.75203	+	0.725713i	−0.754433	+	0.656377i	$0.772088\pi$
$829$	−50.4450	+	20.8950i	−1.75203	+	0.725713i	−0.997593	+	0.0693355i	$0.977912\pi$
$830$	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	0.883427	−	0.468568i	$-0.155230\pi$
$839$	12.0166	+	12.0166i	0.414859	+	0.414859i	−0.468568	+	0.883427i	$0.655230\pi$
$840$	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	0.249653	−	0.968335i	$-0.419683\pi$
$853$	−7.55073	−	3.12762i	−0.258532	−	0.107088i	−0.508185	+	0.861248i	$0.669683\pi$
$854$	−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	0.839102	−	0.543975i	$-0.183081\pi$
$857$	8.63970	+	8.63970i	0.295127	+	0.295127i	−0.543975	+	0.839102i	$0.683081\pi$
$858$	−28.8591	+	39.0978i	−0.985232	+	1.33478i
$859$	9.41900	−	22.7395i	0.321372	−	0.775861i	−0.677803	−	0.735244i	$-0.737068\pi$
$859$	9.41900	−	22.7395i	0.321372	−	0.775861i	0.999175	−	0.0406170i	$-0.0129324\pi$
$860$	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	0.946426	+	0.322921i	$0.104665\pi$
$877$	14.9712	+	36.1436i	0.505541	+	1.22048i	−0.440885	+	0.897564i	$0.645335\pi$
$878$	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	$-0.937757\pi$
$881$		−	11.5342i		−	0.388596i	0.980943	−	0.194298i	$-0.0622428\pi$
$882$	0.199698	−	0.805018i	0.00672418	−	0.0271064i
$883$	−11.7901	−	28.4639i	−0.396769	−	0.957885i	−0.988427	−	0.151696i	$-0.951526\pi$
$883$	−11.7901	−	28.4639i	−0.396769	−	0.957885i	0.591658	−	0.806189i	$-0.298474\pi$
$884$	−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	−0.725062	−	0.688683i	$-0.758189\pi$
$887$	−1.08345	+	1.08345i	−0.0363789	+	0.0363789i	0.688683	+	0.725062i	$0.258189\pi$
$888$	−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	−0.517510	−	0.855677i	$-0.673141\pi$
$907$	−44.8283	−	18.5685i	−1.48850	−	0.616557i	−0.970990	+	0.239120i	$0.923141\pi$
$908$	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	$0.171126\pi$
$911$			30.9122i			1.02417i	−0.858935	+	0.512084i	$0.828874\pi$
$912$	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	−0.465345	−	0.885129i	$-0.654070\pi$
$919$	12.7258	−	12.7258i	0.419785	−	0.419785i	0.885129	+	0.465345i	$0.154070\pi$
$920$	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	−0.774390	−	0.632709i	$-0.781943\pi$
$937$	−4.33693	+	4.33693i	−0.141681	+	0.141681i	0.632709	+	0.774390i	$0.281943\pi$
$938$	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	0.896689	−	0.442661i	$-0.145966\pi$
$941$	−1.54528	−	3.73063i	−0.0503746	−	0.121615i	−0.947064	+	0.321046i	$0.895966\pi$
$942$	−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	0.738602	−	0.674142i	$-0.235486\pi$
$947$	−8.01211	−	19.3429i	−0.260359	−	0.628561i	−0.998961	+	0.0455804i	$0.985486\pi$
$948$	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	0.330190	−	0.943915i	$-0.392887\pi$
$953$	−18.9461	−	18.9461i	−0.613725	−	0.613725i	−0.943915	+	0.330190i	$0.892887\pi$
$954$	−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	−0.949095	−	0.314989i	$-0.897999\pi$
$967$	−39.3087	−	39.3087i	−1.26408	−	1.26408i	−0.314989	−	0.949095i	$-0.602001\pi$
$968$	−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	−0.393902	−	0.919152i	$-0.628875\pi$
$971$	−41.2063	−	17.0682i	−1.32237	−	0.547744i	−0.928470	+	0.371408i	$0.878875\pi$
$972$	−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	$0.0762394\pi$
$977$			14.8302i			0.474460i	−0.971454	+	0.237230i	$0.923761\pi$
$978$	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	−0.731218	−	0.682144i	$-0.761048\pi$
$983$	−1.53859	+	1.53859i	−0.0490735	+	0.0490735i	0.682144	+	0.731218i	$0.261048\pi$
$984$	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	0.702822	+	0.711365i	$0.251923\pi$
$997$	−9.38290	+	22.6523i	−0.297159	+	0.717406i	−0.999982	+	0.00604089i	$0.998077\pi$
$998$	−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.85.6	yes	52
4.3	odd	2		896.2.u.c.561.4		52
32.3	odd	8		896.2.u.c.337.4		52
32.29	even	8	inner	224.2.u.c.29.6	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.6	✓	52	32.29	even	8	inner
224.2.u.c.85.6	yes	52	1.1	even	1	trivial
896.2.u.c.337.4		52	32.3	odd	8
896.2.u.c.561.4		52	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
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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