LMFDB - Embedded newform 504.2.cc.b.293.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.12
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30669 + 0.540891i) q^{2} +(0.0157202 - 1.73198i) q^{3} +(1.41487 - 1.41355i) q^{4} +(1.10228 + 0.636400i) q^{5} +(0.916271 + 2.27166i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(-1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +O(q^{10})$	\(q+(-1.30669 + 0.540891i) q^{2} +(0.0157202 - 1.73198i) q^{3} +(1.41487 - 1.41355i) q^{4} +(1.10228 + 0.636400i) q^{5} +(0.916271 + 2.27166i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(-1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +(-1.78456 - 0.235365i) q^{10} +(-3.13927 - 5.43737i) q^{11} +(-2.42600 - 2.47275i) q^{12} +(-1.74580 + 3.02381i) q^{13} +(1.18240 - 3.54992i) q^{14} +(1.11956 - 1.89912i) q^{15} +(0.00373360 - 4.00000i) q^{16} -4.69263 q^{17} +(3.94888 - 1.55125i) q^{18} +3.31331 q^{19} +(2.45917 - 0.657702i) q^{20} +(3.43593 + 3.03222i) q^{21} +(7.04307 + 5.40695i) q^{22} +(-3.77266 - 2.17814i) q^{23} +(4.50752 + 1.91892i) q^{24} +(-1.68999 - 2.92715i) q^{25} +(0.645662 - 4.89546i) q^{26} +(-0.141466 + 5.19423i) q^{27} +(0.375089 + 5.27819i) q^{28} +(-1.85192 - 3.20761i) q^{29} +(-0.435701 + 3.08712i) q^{30} +(-1.65681 - 0.956557i) q^{31} +(2.15869 + 5.22877i) q^{32} +(-9.46676 + 5.35167i) q^{33} +(6.13181 - 2.53820i) q^{34} +(-3.18229 + 1.10144i) q^{35} +(-4.32089 + 4.16292i) q^{36} +5.75725i q^{37} +(-4.32946 + 1.79214i) q^{38} +(5.20973 + 3.07122i) q^{39} +(-2.85762 + 2.18955i) q^{40} +(-4.50957 + 7.81080i) q^{41} +(-6.12980 - 2.10370i) q^{42} +(3.03629 - 1.75300i) q^{43} +(-12.1277 - 3.25567i) q^{44} +(-3.27163 - 1.96891i) q^{45} +(6.10783 + 0.805561i) q^{46} +(-4.04334 - 7.00327i) q^{47} +(-6.92786 - 0.0693474i) q^{48} +(-0.996363 - 6.92873i) q^{49} +(3.79156 + 2.91077i) q^{50} +(-0.0737691 + 8.12753i) q^{51} +(1.80423 + 6.74608i) q^{52} +5.64307 q^{53} +(-2.62466 - 6.86376i) q^{54} -7.99132i q^{55} +(-3.34505 - 6.69407i) q^{56} +(0.0520859 - 5.73858i) q^{57} +(4.15485 + 3.18967i) q^{58} +(-6.06444 - 3.50131i) q^{59} +(-1.10047 - 4.26957i) q^{60} +(-0.973767 - 1.68661i) q^{61} +(2.68232 + 0.353771i) q^{62} +(5.30575 - 5.90330i) q^{63} +(-5.64893 - 5.66477i) q^{64} +(-3.84870 + 2.22205i) q^{65} +(9.47544 - 12.1135i) q^{66} +(-4.62684 - 2.67131i) q^{67} +(-6.63947 + 6.63328i) q^{68} +(-3.83181 + 6.49992i) q^{69} +(3.56250 - 3.16051i) q^{70} +8.38003i q^{71} +(3.39438 - 7.77677i) q^{72} +10.4345i q^{73} +(-3.11404 - 7.52293i) q^{74} +(-5.09633 + 2.88101i) q^{75} +(4.68791 - 4.68354i) q^{76} +(16.3113 + 3.14355i) q^{77} +(-8.46869 - 1.19523i) q^{78} +(-2.27516 - 3.94070i) q^{79} +(2.54971 - 4.40673i) q^{80} +(8.99407 + 0.326671i) q^{81} +(1.66781 - 12.6455i) q^{82} +(7.47660 - 4.31662i) q^{83} +(9.14762 - 0.566672i) q^{84} +(-5.17258 - 2.98639i) q^{85} +(-3.01931 + 3.93294i) q^{86} +(-5.58463 + 3.15706i) q^{87} +(17.6081 - 2.30561i) q^{88} +8.19765 q^{89} +(5.33997 + 0.803155i) q^{90} +(-3.02152 - 8.72978i) q^{91} +(-8.41676 + 2.25105i) q^{92} +(-1.68278 + 2.85452i) q^{93} +(9.07140 + 6.96409i) q^{94} +(3.65218 + 2.10859i) q^{95} +(9.09006 - 3.65660i) q^{96} +(-5.08552 + 2.93613i) q^{97} +(5.04962 + 8.51477i) q^{98} +(9.12016 + 16.4804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.30669	+	0.540891i	−0.923969	+	0.382468i
$2$	−1.30669	+	0.540891i	−0.923969	+	0.382468i
$3$	0.0157202	−	1.73198i	0.00907607	−	0.999959i
$3$	0.0157202	−	1.73198i	0.00907607	−	0.999959i
$4$	1.41487	−	1.41355i	0.707437	−	0.706777i
$5$	1.10228	+	0.636400i	0.492953	+	0.284607i	0.725799	−	0.687907i	$-0.241470\pi$
$5$	1.10228	+	0.636400i	0.492953	+	0.284607i	−0.232846	+	0.972514i	$0.574804\pi$
$6$	0.916271	+	2.27166i	0.374066	+	0.927402i
$7$	−1.73258	+	1.99955i	−0.654852	+	0.755757i
$7$	−1.73258	+	1.99955i	−0.654852	+	0.755757i
$8$	−1.08422	+	2.61237i	−0.383330	+	0.923611i
$9$	−2.99951	−	0.0544542i	−0.999835	−	0.0181514i
$10$	−1.78456	−	0.235365i	−0.564326	−	0.0744289i
$11$	−3.13927	−	5.43737i	−0.946524	−	1.63943i	−0.752670	−	0.658398i	$-0.771234\pi$
$11$	−3.13927	−	5.43737i	−0.946524	−	1.63943i	−0.193854	−	0.981030i	$-0.562099\pi$
$12$	−2.42600	−	2.47275i	−0.700327	−	0.713822i
$13$	−1.74580	+	3.02381i	−0.484197	+	0.838653i	−0.999835	−	0.0181528i	$-0.994221\pi$
$13$	−1.74580	+	3.02381i	−0.484197	+	0.838653i	0.515638	+	0.856806i	$0.327555\pi$
$14$	1.18240	−	3.54992i	0.316010	−	0.948756i
$15$	1.11956	−	1.89912i	0.289069	−	0.490350i
$16$	0.00373360	−	4.00000i	0.000933400	−	1.00000i
$17$	−4.69263			−1.13813			−0.569065	−	0.822293i	$-0.692695\pi$
$17$	−4.69263			−1.13813			−0.569065	+	0.822293i	$0.692695\pi$
$18$	3.94888	−	1.55125i	0.930759	−	0.365634i
$19$	3.31331			0.760125			0.380062	−	0.924961i	$-0.375903\pi$
$19$	3.31331			0.760125			0.380062	+	0.924961i	$0.375903\pi$
$20$	2.45917	−	0.657702i	0.549887	−	0.147067i
$21$	3.43593	+	3.03222i	0.749782	+	0.661684i
$22$	7.04307	+	5.40695i	1.50159	+	1.15277i
$23$	−3.77266	−	2.17814i	−0.786653	−	0.454175i	0.0521296	−	0.998640i	$-0.483399\pi$
$23$	−3.77266	−	2.17814i	−0.786653	−	0.454175i	−0.838783	+	0.544466i	$0.816732\pi$
$24$	4.50752	+	1.91892i	0.920094	+	0.391697i
$25$	−1.68999	−	2.92715i	−0.337998	−	0.585430i
$26$	0.645662	−	4.89546i	0.126625	−	0.960079i
$27$	−0.141466	+	5.19423i	−0.0272252	+	0.999629i
$28$	0.375089	+	5.27819i	0.0708851	+	0.997484i
$29$	−1.85192	−	3.20761i	−0.343892	−	0.595639i	0.641260	−	0.767324i	$-0.278412\pi$
$29$	−1.85192	−	3.20761i	−0.343892	−	0.595639i	−0.985152	+	0.171685i	$0.945079\pi$
$30$	−0.435701	+	3.08712i	−0.0795477	+	0.563628i
$31$	−1.65681	−	0.956557i	−0.297571	−	0.171803i	0.343780	−	0.939050i	$-0.388293\pi$
$31$	−1.65681	−	0.956557i	−0.297571	−	0.171803i	−0.641351	+	0.767247i	$0.721626\pi$
$32$	2.15869	+	5.22877i	0.381605	+	0.924325i
$33$	−9.46676	+	5.35167i	−1.64795	+	0.931606i
$34$	6.13181	−	2.53820i	1.05160	−	0.435298i
$35$	−3.18229	+	1.10144i	−0.537905	+	0.186178i
$36$	−4.32089	+	4.16292i	−0.720149	+	0.693819i
$37$			5.75725i			0.946486i	0.880932	+	0.473243i	$0.156917\pi$
$37$			5.75725i			0.946486i	−0.880932	+	0.473243i	$0.843083\pi$
$38$	−4.32946	+	1.79214i	−0.702332	+	0.290723i
$39$	5.20973	+	3.07122i	0.834224	+	0.491789i
$40$	−2.85762	+	2.18955i	−0.451830	+	0.346199i
$41$	−4.50957	+	7.81080i	−0.704276	+	1.21984i	0.262676	+	0.964884i	$0.415395\pi$
$41$	−4.50957	+	7.81080i	−0.704276	+	1.21984i	−0.966952	+	0.254958i	$0.917938\pi$
$42$	−6.12980	−	2.10370i	−0.945849	−	0.324608i
$43$	3.03629	−	1.75300i	0.463030	−	0.267331i	−0.250287	−	0.968172i	$-0.580525\pi$
$43$	3.03629	−	1.75300i	0.463030	−	0.267331i	0.713318	+	0.700841i	$0.247192\pi$
$44$	−12.1277	−	3.25567i	−1.82832	−	0.490810i
$45$	−3.27163	−	1.96891i	−0.487706	−	0.293508i
$46$	6.10783	+	0.805561i	0.900550	+	0.118774i
$47$	−4.04334	−	7.00327i	−0.589782	−	1.02153i	−0.994261	−	0.106985i	$-0.965880\pi$
$47$	−4.04334	−	7.00327i	−0.589782	−	1.02153i	0.404479	−	0.914547i	$-0.367453\pi$
$48$	−6.92786	−	0.0693474i	−0.999950	−	0.0100094i
$49$	−0.996363	−	6.92873i	−0.142338	−	0.989818i
$50$	3.79156	+	2.91077i	0.536208	+	0.411645i
$51$	−0.0737691	+	8.12753i	−0.0103297	+	1.13808i
$52$	1.80423	+	6.74608i	0.250202	+	0.935513i
$53$	5.64307			0.775136			0.387568	−	0.921841i	$-0.373315\pi$
$53$	5.64307			0.775136			0.387568	+	0.921841i	$0.373315\pi$
$54$	−2.62466	−	6.86376i	−0.357171	−	0.934039i
$55$		−	7.99132i		−	1.07755i
$56$	−3.34505	−	6.69407i	−0.447001	−	0.894533i
$57$	0.0520859	−	5.73858i	0.00689895	−	0.760093i
$58$	4.15485	+	3.18967i	0.545558	+	0.418824i
$59$	−6.06444	−	3.50131i	−0.789523	−	0.455831i	0.0502716	−	0.998736i	$-0.483991\pi$
$59$	−6.06444	−	3.50131i	−0.789523	−	0.455831i	−0.839795	+	0.542904i	$0.817325\pi$
$60$	−1.10047	−	4.26957i	−0.142070	−	0.551199i
$61$	−0.973767	−	1.68661i	−0.124678	−	0.215949i	0.796929	−	0.604073i	$-0.206456\pi$
$61$	−0.973767	−	1.68661i	−0.124678	−	0.215949i	−0.921607	+	0.388124i	$0.873123\pi$
$62$	2.68232	+	0.353771i	0.340655	+	0.0449290i
$63$	5.30575	−	5.90330i	0.668462	−	0.743746i
$64$	−5.64893	−	5.66477i	−0.706116	−	0.708096i
$65$	−3.84870	+	2.22205i	−0.477373	+	0.275611i
$66$	9.47544	−	12.1135i	1.16635	−	1.49106i
$67$	−4.62684	−	2.67131i	−0.565258	−	0.326352i	0.189995	−	0.981785i	$-0.439153\pi$
$67$	−4.62684	−	2.67131i	−0.565258	−	0.326352i	−0.755253	+	0.655433i	$0.772486\pi$
$68$	−6.63947	+	6.63328i	−0.805155	+	0.804403i
$69$	−3.83181	+	6.49992i	−0.461296	+	0.782499i
$70$	3.56250	−	3.16051i	0.425800	−	0.377754i
$71$			8.38003i			0.994527i	0.867600	+	0.497263i	$0.165662\pi$
$71$			8.38003i			0.994527i	−0.867600	+	0.497263i	$0.834338\pi$
$72$	3.39438	−	7.77677i	0.400032	−	0.916501i
$73$			10.4345i			1.22126i	0.791915	+	0.610631i	$0.209084\pi$
$73$			10.4345i			1.22126i	−0.791915	+	0.610631i	$0.790916\pi$
$74$	−3.11404	−	7.52293i	−0.362000	−	0.874523i
$75$	−5.09633	+	2.88101i	−0.588473	+	0.332671i
$76$	4.68791	−	4.68354i	0.537740	−	0.537238i
$77$	16.3113	+	3.14355i	1.85884	+	0.358241i
$78$	−8.46869	−	1.19523i	−0.958891	−	0.135333i
$79$	−2.27516	−	3.94070i	−0.255976	−	0.443363i	0.709184	−	0.705023i	$-0.249063\pi$
$79$	−2.27516	−	3.94070i	−0.255976	−	0.443363i	−0.965160	+	0.261660i	$0.915730\pi$
$80$	2.54971	−	4.40673i	0.285067	−	0.492687i
$81$	8.99407	+	0.326671i	0.999341	+	0.0362968i
$82$	1.66781	−	12.6455i	0.184179	−	1.39646i
$83$	7.47660	−	4.31662i	0.820663	−	0.473810i	−0.0299820	−	0.999550i	$-0.509545\pi$
$83$	7.47660	−	4.31662i	0.820663	−	0.473810i	0.850645	+	0.525740i	$0.176212\pi$
$84$	9.14762	−	0.566672i	0.998087	−	0.0618289i
$85$	−5.17258	−	2.98639i	−0.561045	−	0.323919i
$86$	−3.01931	+	3.93294i	−0.325580	+	0.424099i
$87$	−5.58463	+	3.15706i	−0.598735	+	0.338472i
$88$	17.6081	−	2.30561i	1.87703	−	0.245778i
$89$	8.19765			0.868950			0.434475	−	0.900684i	$-0.356934\pi$
$89$	8.19765			0.868950			0.434475	+	0.900684i	$0.356934\pi$
$90$	5.33997	+	0.803155i	0.562882	+	0.0846600i
$91$	−3.02152	−	8.72978i	−0.316741	−	0.915129i
$92$	−8.41676	+	2.25105i	−0.877508	+	0.234689i
$93$	−1.68278	+	2.85452i	−0.174496	+	0.296000i
$94$	9.07140	+	6.96409i	0.935643	+	0.718291i
$95$	3.65218	+	2.10859i	0.374706	+	0.216337i
$96$	9.09006	−	3.65660i	0.927751	−	0.373200i
$97$	−5.08552	+	2.93613i	−0.516357	+	0.298119i	−0.735443	−	0.677587i	$-0.763026\pi$
$97$	−5.08552	+	2.93613i	−0.516357	+	0.298119i	0.219086	+	0.975706i	$0.429692\pi$
$98$	5.04962	+	8.51477i	0.510089	+	0.860122i
$99$	9.12016	+	16.4804i	0.916610	+	1.65634i
$100$	−6.52880	−	1.75265i	−0.652880	−	0.175265i
$101$	−4.24754	+	2.45232i	−0.422646	+	0.244015i	−0.696209	−	0.717840i	$-0.745131\pi$
$101$	−4.24754	+	2.45232i	−0.422646	+	0.244015i	0.273563	+	0.961854i	$0.411798\pi$
$102$	−4.29972	−	10.6601i	−0.425736	−	1.05550i
$103$	13.4323	+	7.75514i	1.32352	+	0.764137i	0.984289	−	0.176565i	$-0.0564986\pi$
$103$	13.4323	+	7.75514i	1.32352	+	0.764137i	0.339235	+	0.940702i	$0.389832\pi$
$104$	−6.00647	−	7.83914i	−0.588983	−	0.768691i
$105$	1.85765	+	5.52897i	0.181288	+	0.539573i
$106$	−7.37374	+	3.05229i	−0.716201	+	0.296465i
$107$	−0.101350			−0.00979788			−0.00489894	−	0.999988i	$-0.501559\pi$
$107$	−0.101350			−0.00979788			−0.00489894	+	0.999988i	$0.501559\pi$
$108$	7.14216	+	7.54914i	0.687255	+	0.726417i
$109$		−	0.947778i		−	0.0907807i	−0.998969	−	0.0453904i	$-0.985547\pi$
$109$		−	0.947778i		−	0.0907807i	0.998969	−	0.0453904i	$-0.0144532\pi$
$110$	4.32243	+	10.4422i	0.412128	+	0.995621i
$111$	9.97143	+	0.0905052i	0.946447	+	0.00859037i
$112$	7.99171	+	6.93777i	0.755146	+	0.655557i
$113$	−14.5062	−	8.37517i	−1.36463	−	0.787870i	−0.374394	−	0.927270i	$-0.622149\pi$
$113$	−14.5062	−	8.37517i	−1.36463	−	0.787870i	−0.990236	+	0.139400i	$0.955483\pi$
$114$	3.03589	+	7.52671i	0.284337	+	0.704941i
$115$	−2.77234	−	4.80184i	−0.258522	−	0.447774i
$116$	−7.15436	−	1.92058i	−0.664266	−	0.178322i
$117$	5.40119	−	8.97486i	0.499340	−	0.829726i
$118$	9.81817	+	1.29492i	0.903835	+	0.119207i
$119$	8.13033	−	9.38312i	0.745306	−	0.860149i
$120$	3.74734	+	4.98376i	0.342084	+	0.454953i
$121$	−14.2100	+	24.6124i	−1.29182	+	2.23749i
$122$	2.18469	+	1.67718i	0.197792	+	0.151845i
$123$	13.4573	+	7.93327i	1.21340	+	0.715319i
$124$	−3.69632	+	0.988576i	−0.331939	+	0.0887767i
$125$		−	10.6660i		−	0.953999i
$126$	−3.73993	+	10.5836i	−0.333179	+	0.942863i
$127$	−3.07181			−0.272579			−0.136290	−	0.990669i	$-0.543518\pi$
$127$	−3.07181			−0.272579			−0.136290	+	0.990669i	$0.543518\pi$
$128$	10.4454	+	4.34664i	0.923253	+	0.384192i
$129$	−2.98844	−	5.28636i	−0.263117	−	0.465438i
$130$	3.82717	−	4.98526i	0.335665	−	0.437236i
$131$	4.00339	+	2.31136i	0.349778	+	0.201944i	0.664587	−	0.747210i	$-0.268607\pi$
$131$	4.00339	+	2.31136i	0.349778	+	0.201944i	−0.314809	+	0.949155i	$0.601941\pi$
$132$	−5.82940	+	20.9537i	−0.507384	+	1.82379i
$133$	−5.74056	+	6.62511i	−0.497769	+	0.574470i
$134$	7.49073	+	0.987951i	0.647100	+	0.0853460i
$135$	−3.46154	+	5.63545i	−0.297922	+	0.485022i
$136$	5.08785	−	12.2589i	0.436279	−	1.05119i
$137$	6.29625	−	3.63514i	0.537925	−	0.310571i	−0.206312	−	0.978486i	$-0.566146\pi$
$137$	6.29625	−	3.63514i	0.537925	−	0.310571i	0.744238	+	0.667915i	$0.232813\pi$
$138$	1.49123	−	10.5660i	0.126942	−	0.899435i
$139$	5.40059	−	9.35409i	0.458072	−	0.793403i	−0.540787	−	0.841159i	$-0.681874\pi$
$139$	5.40059	−	9.35409i	0.458072	−	0.793403i	0.998859	+	0.0477559i	$0.0152070\pi$
$140$	−2.94559	+	6.05674i	−0.248948	+	0.511888i
$141$	−12.1931	+	6.89289i	−1.02684	+	0.580486i
$142$	−4.53269	−	10.9501i	−0.380374	−	0.918912i
$143$	21.9221			1.83322
$144$	−0.229016	+	11.9978i	−0.0190846	+	0.999818i
$145$		−	4.71424i		−	0.391496i
$146$	−5.64391	−	13.6346i	−0.467093	−	1.12841i
$147$	−12.0161	+	1.61676i	−0.991069	+	0.133348i
$148$	8.13818	+	8.14578i	0.668954	+	0.669579i
$149$	11.0512	−	19.1412i	0.905347	−	1.56811i	0.0848967	−	0.996390i	$-0.472944\pi$
$149$	11.0512	−	19.1412i	0.905347	−	1.56811i	0.820450	−	0.571718i	$-0.193723\pi$
$150$	5.10100	−	6.52115i	0.416495	−	0.532450i
$151$	4.55315	+	7.88628i	0.370530	+	0.641777i	0.989647	−	0.143522i	$-0.0458428\pi$
$151$	4.55315	+	7.88628i	0.370530	+	0.641777i	−0.619117	+	0.785299i	$0.712509\pi$
$152$	−3.59236	+	8.65558i	−0.291379	+	0.702060i
$153$	14.0756	+	0.255533i	1.13794	+	0.0206586i
$154$	−23.0141	+	4.71499i	−1.85453	+	0.379945i
$155$	−1.21751	−	2.10878i	−0.0977924	−	0.169381i
$156$	11.7124	−	3.01885i	0.937746	−	0.241701i
$157$	11.6887	−	20.2454i	0.932860	−	1.61576i	0.154454	−	0.988000i	$-0.450638\pi$
$157$	11.6887	−	20.2454i	0.932860	−	1.61576i	0.778406	−	0.627761i	$-0.216028\pi$
$158$	5.10442	+	3.91865i	0.406086	+	0.311751i
$159$	0.0887104	−	9.77369i	0.00703519	−	0.775104i
$160$	−0.948122	+	7.13734i	−0.0749557	+	0.564257i
$161$	10.8917	−	3.76980i	0.858387	−	0.297102i
$162$	−11.9291	+	4.43796i	−0.937242	+	0.348679i
$163$		−	13.7674i		−	1.07835i	−0.842194	−	0.539175i	$-0.818736\pi$
$163$		−	13.7674i		−	1.07835i	0.842194	−	0.539175i	$-0.181264\pi$
$164$	4.66052	+	17.4258i	0.363925	+	1.36073i
$165$	−13.8408	−	0.125625i	−1.07750	−	0.00977991i
$166$	−7.43477	+	9.68450i	−0.577050	+	0.751663i
$167$	−0.0915189	+	0.158515i	−0.00708195	+	0.0122663i	−0.869545	−	0.493854i	$-0.835588\pi$
$167$	−0.0915189	+	0.158515i	−0.00708195	+	0.0122663i	0.862463	+	0.506121i	$0.168921\pi$
$168$	−11.6466	+	5.68833i	−0.898553	+	0.438864i
$169$	0.404390	+	0.700424i	0.0311069	+	0.0538788i
$170$	8.37426	+	1.10448i	0.642276	+	0.0847098i
$171$	−9.93828	−	0.180423i	−0.760000	−	0.0137973i
$172$	1.81800	−	6.77224i	0.138622	−	0.516379i
$173$	−9.34311	+	5.39425i	−0.710343	+	0.410117i	−0.811188	−	0.584785i	$-0.801179\pi$
$173$	−9.34311	+	5.39425i	−0.710343	+	0.410117i	0.100845	+	0.994902i	$0.467845\pi$
$174$	5.58975	−	7.14597i	0.423758	−	0.541735i
$175$	8.78100	+	1.69230i	0.663781	+	0.127925i
$176$	−21.7612	+	12.5368i	−1.64031	+	0.944994i
$177$	−6.15953	+	10.4484i	−0.462978	+	0.785353i
$178$	−10.7118	+	4.43404i	−0.802882	+	0.332345i
$179$	2.16504			0.161822			0.0809112	−	0.996721i	$-0.474217\pi$
$179$	2.16504			0.161822			0.0809112	+	0.996721i	$0.474217\pi$
$180$	−7.41210	+	1.83887i	−0.552466	+	0.137061i
$181$	−13.5557			−1.00759			−0.503793	−	0.863824i	$-0.668063\pi$
$181$	−13.5557			−1.00759			−0.503793	+	0.863824i	$0.668063\pi$
$182$	8.67004	+	9.77279i	0.642666	+	0.724408i
$183$	−2.93649	+	1.66003i	−0.217072	+	0.122713i
$184$	9.78051	−	7.49398i	0.721029	−	0.552463i
$185$	−3.66391	+	6.34608i	−0.269376	+	0.466573i
$186$	0.654892	−	4.64017i	0.0480190	−	0.340234i
$187$	14.7314	+	25.5155i	1.07727	+	1.86588i
$188$	−15.6203	−	4.19327i	−1.13923	−	0.305825i
$189$	−10.1410	−	9.28226i	−0.737648	−	0.675185i
$190$	−5.91278	−	0.779836i	−0.428958	−	0.0565753i
$191$	−4.82469	+	2.78554i	−0.349103	+	0.201555i	−0.664290	−	0.747475i	$-0.731266\pi$
$191$	−4.82469	+	2.78554i	−0.349103	+	0.201555i	0.315187	+	0.949029i	$0.397933\pi$
$192$	−9.90007	+	9.69478i	−0.714476	+	0.699660i
$193$	10.2386	−	17.7338i	0.736990	−	1.27650i	−0.216854	−	0.976204i	$-0.569580\pi$
$193$	10.2386	−	17.7338i	0.736990	−	1.27650i	0.953845	−	0.300301i	$-0.0970870\pi$
$194$	5.05707	−	6.58732i	0.363077	−	0.472942i
$195$	3.78804	+	6.70080i	0.271267	+	0.479855i
$196$	−11.2039	−	8.39486i	−0.800275	−	0.599633i
$197$	25.8582			1.84232			0.921161	−	0.389183i	$-0.127242\pi$
$197$	25.8582			1.84232			0.921161	+	0.389183i	$0.127242\pi$
$198$	−20.8313	−	16.6017i	−1.48042	−	1.17983i
$199$		−	25.8157i		−	1.83003i	−0.403423	−	0.915013i	$-0.632180\pi$
$199$		−	25.8157i		−	1.83003i	0.403423	−	0.915013i	$-0.367820\pi$
$200$	9.47911	−	1.24120i	0.670274	−	0.0877660i
$201$	−4.69938	+	7.97160i	−0.331469	+	0.562273i
$202$	4.22377	−	5.50187i	0.297184	−	0.387110i
$203$	9.62235	+	1.85444i	0.675357	+	0.130156i
$204$	11.3843	+	11.6037i	0.797063	+	0.812422i
$205$	−9.94159	+	5.73978i	−0.694351	+	0.400883i
$206$	−21.7465	−	2.86815i	−1.51515	−	0.199833i
$207$	11.1975	+	6.73880i	0.778280	+	0.468379i
$208$	12.0887	+	6.99447i	0.838201	+	0.484979i
$209$	−10.4014	−	18.0157i	−0.719477	−	1.24617i
$210$	−5.41794	−	6.21987i	−0.373874	−	0.429211i
$211$	−17.9224	−	10.3475i	−1.23383	−	0.712351i	−0.266003	−	0.963972i	$-0.585703\pi$
$211$	−17.9224	−	10.3475i	−1.23383	−	0.712351i	−0.967826	+	0.251621i	$0.919036\pi$
$212$	7.98424	−	7.97679i	0.548360	−	0.547848i
$213$	14.5140	+	0.131736i	0.994486	+	0.00902640i
$214$	0.132433	−	0.0548194i	0.00905294	−	0.00374737i
$215$	4.46245			0.304336
$216$	−13.4158	−	6.00125i	−0.912833	−	0.408334i
$217$	4.78322	−	1.65555i	0.324706	−	0.112386i
$218$	0.512645	+	1.23845i	0.0347207	+	0.0838785i
$219$	18.0723	+	0.164032i	1.22121	+	0.0110843i
$220$	−11.2962	−	11.3067i	−0.761586	−	0.762298i
$221$	8.19237	−	14.1896i	0.551079	−	0.954496i
$222$	−13.0785	+	5.27520i	−0.877773	+	0.354048i
$223$	−13.2687	+	7.66067i	−0.888536	+	0.512996i	−0.873463	−	0.486890i	$-0.838131\pi$
$223$	−13.2687	+	7.66067i	−0.888536	+	0.512996i	−0.0150725	+	0.999886i	$0.504798\pi$
$224$	−14.1953	−	4.74286i	−0.948460	−	0.316896i
$225$	4.90974	+	8.87203i	0.327316	+	0.591468i
$226$	23.4852	+	3.09746i	1.56221	+	0.206040i
$227$	−18.4876	+	10.6738i	−1.22706	+	0.708446i	−0.966415	−	0.256987i	$-0.917270\pi$
$227$	−18.4876	+	10.6738i	−1.22706	+	0.708446i	−0.260650	+	0.965433i	$0.583937\pi$
$228$	−8.03809	−	8.19299i	−0.532336	−	0.542594i
$229$	−4.11091	+	7.12030i	−0.271656	+	0.470523i	−0.969286	−	0.245936i	$-0.920905\pi$
$229$	−4.11091	+	7.12030i	−0.271656	+	0.470523i	0.697630	+	0.716458i	$0.254238\pi$
$230$	6.21986	+	4.77497i	0.410126	+	0.314852i
$231$	5.70098	−	28.2014i	0.375097	−	1.85551i
$232$	10.3874	−	1.36012i	0.681963	−	0.0892965i
$233$			10.1986i			0.668134i	0.942549	+	0.334067i	$0.108421\pi$
$233$			10.1986i			0.668134i	−0.942549	+	0.334067i	$0.891579\pi$
$234$	−2.20325	+	14.6488i	−0.144031	+	0.957623i
$235$		−	10.2927i		−	0.671424i
$236$	−13.5297	+	3.61851i	−0.880709	+	0.235545i
$237$	−6.86097	+	3.87859i	−0.445668	+	0.251941i
$238$	−5.54857	+	16.6584i	−0.359660	+	1.07981i
$239$	−1.81305	−	1.04676i	−0.117276	−	0.0677096i	0.440214	−	0.897893i	$-0.354902\pi$
$239$	−1.81305	−	1.04676i	−0.117276	−	0.0677096i	−0.557491	+	0.830183i	$0.688236\pi$
$240$	−7.59228	−	4.48533i	−0.490080	−	0.289527i
$241$	2.96166	−	1.70991i	0.190777	−	0.110145i	−0.401569	−	0.915829i	$-0.631535\pi$
$241$	2.96166	−	1.70991i	0.190777	−	0.110145i	0.592346	+	0.805683i	$0.298202\pi$
$242$	5.25539	−	39.8468i	0.337830	−	2.56145i
$243$	0.707177	−	15.5724i	0.0453654	−	0.998970i
$244$	−3.76188	−	1.00987i	−0.240830	−	0.0646506i
$245$	3.31117	−	8.27146i	0.211543	−	0.528444i
$246$	−21.8755	−	3.08740i	−1.39473	−	0.196846i
$247$	−5.78436	+	10.0188i	−0.368050	+	0.637481i
$248$	4.29522	−	3.29107i	0.272747	−	0.208983i
$249$	−7.35875	−	13.0172i	−0.466342	−	0.824930i
$250$	5.76917	+	13.9372i	0.364874	+	0.881466i
$251$		−	15.4144i		−	0.972948i	−0.873695	−	0.486474i	$-0.838283\pi$
$251$		−	15.4144i		−	0.972948i	0.873695	−	0.486474i	$-0.161717\pi$
$252$	−0.837661	−	15.8524i	−0.0527677	−	0.998607i
$253$			27.3511i			1.71955i
$254$	4.01390	−	1.66151i	0.251855	−	0.104253i
$255$	−5.25368	+	8.91185i	−0.328998	+	0.558082i
$256$	−16.0000	−	0.0298688i	−0.999998	−	0.00186680i
$257$	0.288031	−	0.498884i	0.0179669	−	0.0311195i	−0.856902	−	0.515479i	$-0.827614\pi$
$257$	0.288031	−	0.498884i	0.0179669	−	0.0311195i	0.874869	+	0.484360i	$0.160947\pi$
$258$	6.76430	+	5.29120i	0.421127	+	0.329416i
$259$	−11.5119	−	9.97487i	−0.715313	−	0.619808i
$260$	−2.30444	+	8.58427i	−0.142915	+	0.532374i
$261$	5.38016	+	9.72210i	0.333024	+	0.601783i
$262$	−6.48138	−	0.854829i	−0.400421	−	0.0528115i
$263$	−20.8885	+	12.0600i	−1.28804	+	0.743651i	−0.978305	−	0.207171i	$-0.933574\pi$
$263$	−20.8885	+	12.0600i	−1.28804	+	0.743651i	−0.309737	+	0.950822i	$0.600241\pi$
$264$	−3.71646	−	30.5330i	−0.228732	−	1.87918i
$265$	6.22023	+	3.59125i	0.382106	+	0.220609i
$266$	3.91766	−	11.7620i	0.240207	−	0.721173i
$267$	0.128869	−	14.1982i	0.00788665	−	0.868914i
$268$	−10.3224	+	2.76072i	−0.630543	+	0.168638i
$269$			26.4734i			1.61411i	0.590476	+	0.807055i	$0.298940\pi$
$269$			26.4734i			1.61411i	−0.590476	+	0.807055i	$0.701060\pi$
$270$	1.47499	−	9.23609i	0.0897653	−	0.562091i
$271$		−	10.0266i		−	0.609074i	−0.952500	−	0.304537i	$-0.901498\pi$
$271$		−	10.0266i		−	0.609074i	0.952500	−	0.304537i	$-0.0985018\pi$
$272$	−0.0175204	+	18.7705i	−0.00106233	+	1.13813i
$273$	−15.1673	+	5.09597i	−0.917966	+	0.308422i
$274$	−6.26103	+	8.15559i	−0.378243	+	0.492697i
$275$	−10.6107	+	18.3782i	−0.639847	+	1.10825i
$276$	3.76647	+	14.6130i	0.226715	+	0.879601i
$277$	−20.3678	+	11.7593i	−1.22378	+	0.706550i	−0.965722	−	0.259579i	$-0.916416\pi$
$277$	−20.3678	+	11.7593i	−1.22378	+	0.706550i	−0.258059	+	0.966129i	$0.583083\pi$
$278$	−1.99734	+	15.1440i	−0.119793	+	0.908278i
$279$	4.91751	+	2.95942i	0.294404	+	0.177176i
$280$	0.572935	−	9.50752i	0.0342394	−	0.568183i
$281$	11.6875	−	6.74780i	0.697220	−	0.402540i	−0.109091	−	0.994032i	$-0.534794\pi$
$281$	11.6875	−	6.74780i	0.697220	−	0.402540i	0.806311	+	0.591492i	$0.201461\pi$
$282$	12.2043	−	15.6020i	0.726754	−	0.929086i
$283$	7.03951	−	12.1928i	0.418455	−	0.724786i	−0.577329	−	0.816512i	$-0.695905\pi$
$283$	7.03951	−	12.1928i	0.418455	−	0.724786i	0.995784	+	0.0917258i	$0.0292383\pi$
$284$	11.8456	+	11.8567i	0.702908	+	0.703565i
$285$	3.70944	−	6.29236i	0.219729	−	0.372727i
$286$	−28.6453	+	11.8575i	−1.69383	+	0.701146i
$287$	−7.80488	−	22.5499i	−0.460708	−	1.33108i
$288$	−6.19026	−	15.8013i	−0.364765	−	0.931100i
$289$	5.02075			0.295339
$290$	2.54989	+	6.16004i	0.149735	+	0.361730i
$291$	5.00537	+	8.85418i	0.293420	+	0.519041i
$292$	14.7497	+	14.7634i	0.863159	+	0.863965i
$293$	−7.36385	−	4.25152i	−0.430200	−	0.248376i	0.269232	−	0.963075i	$-0.413230\pi$
$293$	−7.36385	−	4.25152i	−0.430200	−	0.248376i	−0.699432	+	0.714699i	$0.746564\pi$
$294$	14.8268	−	8.61199i	0.864716	−	0.502262i
$295$	−4.45646	−	7.71882i	−0.259465	−	0.449407i
$296$	−15.0400	−	6.24213i	−0.874185	−	0.362816i
$297$	28.6870	−	15.5369i	1.66459	−	0.901540i
$298$	−4.08714	+	30.9891i	−0.236762	+	1.79515i
$299$	13.1726	−	7.60520i	0.761790	−	0.439820i
$300$	−3.13819	+	11.2802i	−0.181184	+	0.651263i
$301$	−1.75540	+	9.10842i	−0.101179	+	0.525001i
$302$	−10.2152	−	7.84216i	−0.587817	−	0.451266i
$303$	4.18059	+	7.39519i	0.240169	+	0.424843i
$304$	0.0123706	−	13.2532i	0.000709500	−	0.760124i
$305$		−	2.47882i		−	0.141937i
$306$	−18.5306	+	7.27945i	−1.05932	+	0.416138i
$307$	−14.7932			−0.844292			−0.422146	−	0.906528i	$-0.638723\pi$
$307$	−14.7932			−0.844292			−0.422146	+	0.906528i	$0.638723\pi$
$308$	27.5220	−	18.6091i	1.56821	−	1.06035i
$309$	13.6429	−	23.1426i	0.776118	−	1.31653i
$310$	2.73152	+	2.09698i	0.155140	+	0.119101i
$311$	−9.69605	+	16.7940i	−0.549812	+	0.952303i	0.448475	+	0.893796i	$0.351967\pi$
$311$	−9.69605	+	16.7940i	−0.549812	+	0.952303i	−0.998287	+	0.0585073i	$0.981366\pi$
$312$	−13.6717	+	10.2798i	−0.774005	+	0.581982i
$313$	10.7235	−	6.19124i	0.606131	−	0.349950i	−0.165319	−	0.986240i	$-0.552865\pi$
$313$	10.7235	−	6.19124i	0.606131	−	0.349950i	0.771450	+	0.636290i	$0.219532\pi$
$314$	−4.32293	+	32.7768i	−0.243957	+	1.84970i
$315$	9.60527	−	3.13049i	0.541196	−	0.176383i
$316$	−8.78945	−	2.35952i	−0.494445	−	0.132734i
$317$	15.2671	+	26.4434i	0.857485	+	1.48521i	0.874321	+	0.485349i	$0.161307\pi$
$317$	15.2671	+	26.4434i	0.857485	+	1.48521i	−0.0168358	+	0.999858i	$0.505359\pi$
$318$	5.17059	+	12.8192i	0.289952	+	0.718863i
$319$	−11.6273	+	20.1391i	−0.651005	+	1.12757i
$320$	−2.62163	−	9.83912i	−0.146553	−	0.550024i
$321$	−0.00159325	+	0.175536i	−8.89263e−5	+	0.00979748i
$322$	−12.1930	+	10.8172i	−0.679491	+	0.602818i
$323$	−15.5481			−0.865120
$324$	13.1872	−	12.2514i	0.732624	−	0.680633i
$325$	11.8015			0.654630
$326$	7.44669	+	17.9898i	0.412434	+	0.996361i
$327$	−1.64153	−	0.0148993i	−0.0907770	−	0.000823932i
$328$	−15.5153	−	20.2493i	−0.856690	−	1.11808i
$329$	21.0088	+	4.04886i	1.15825	+	0.223221i
$330$	18.1536	−	7.32221i	0.999321	−	0.403074i
$331$	0.609148	−	0.351692i	0.0334818	−	0.0193307i	−0.483166	−	0.875529i	$-0.660513\pi$
$331$	0.609148	−	0.351692i	0.0334818	−	0.0193307i	0.516647	+	0.856198i	$0.327180\pi$
$332$	4.47667	−	16.6760i	0.245689	−	0.915216i
$333$	0.313506	−	17.2689i	0.0171800	−	0.946330i
$334$	0.0338472	−	0.256632i	0.00185204	−	0.0140423i
$335$	−3.40004	−	5.88904i	−0.185764	−	0.321753i
$336$	12.1417	−	13.7324i	0.662384	−	0.749165i
$337$	4.19417	−	7.26452i	0.228471	−	0.395724i	−0.728884	−	0.684637i	$-0.759961\pi$
$337$	4.19417	−	7.26452i	0.228471	−	0.395724i	0.957355	+	0.288914i	$0.0932940\pi$
$338$	−0.907265	−	0.696505i	−0.0493487	−	0.0378849i
$339$	−14.7337	+	24.9928i	−0.800223	+	1.35742i
$340$	−11.5400	+	3.08635i	−0.625842	+	0.167381i
$341$			12.0116i			0.650462i
$342$	13.0838	−	5.13977i	0.707493	−	0.277927i
$343$	15.5806	+	10.0123i	0.841272	+	0.540612i
$344$	1.28748	+	9.83256i	0.0694162	+	0.530136i
$345$	−8.36027	+	4.72615i	−0.450102	+	0.254448i
$346$	9.29084	−	12.1022i	0.499479	−	0.650619i
$347$	−10.0003	+	17.3210i	−0.536843	+	0.929839i	0.462229	+	0.886761i	$0.347050\pi$
$347$	−10.0003	+	17.3210i	−0.536843	+	0.929839i	−0.999072	+	0.0430784i	$0.986283\pi$
$348$	−3.43888	+	12.3610i	−0.184343	+	0.662620i
$349$	−12.6341	−	21.8830i	−0.676290	−	1.17137i	−0.976090	−	0.217367i	$-0.930253\pi$
$349$	−12.6341	−	21.8830i	−0.676290	−	1.17137i	0.299800	−	0.954002i	$-0.403080\pi$
$350$	−12.3894	+	2.53826i	−0.662241	+	0.135676i
$351$	−15.4594	−	9.49583i	−0.825160	−	0.506850i
$352$	21.6541	−	28.1521i	1.15417	−	1.50051i
$353$	−3.69854	−	6.40606i	−0.196854	−	0.340960i	0.750653	−	0.660697i	$-0.229739\pi$
$353$	−3.69854	−	6.40606i	−0.196854	−	0.340960i	−0.947507	+	0.319736i	$0.896406\pi$
$354$	2.39711	−	16.9845i	0.127405	−	0.902716i
$355$	−5.33305	+	9.23712i	−0.283049	+	0.490255i
$356$	11.5986	−	11.5878i	0.614727	−	0.614153i
$357$	−16.1236	−	14.2291i	−0.853349	−	0.753082i
$358$	−2.82903	+	1.17105i	−0.149519	+	0.0618919i
$359$		−	0.116139i		−	0.00612960i	−0.999995	−	0.00306480i	$-0.999024\pi$
$359$		−	0.116139i		−	0.00612960i	0.999995	−	0.00306480i	$-0.000975558\pi$
$360$	8.69069	−	6.41197i	0.458039	−	0.337941i
$361$	−8.02200			−0.422210
$362$	17.7131	−	7.33215i	0.930978	−	0.385369i
$363$	42.4048	+	24.9983i	2.22568	+	1.31207i
$364$	−16.6151	−	8.08045i	−0.870866	−	0.423531i
$365$	−6.64049	+	11.5017i	−0.347579	+	0.602025i
$366$	2.93918	−	3.75747i	0.153634	−	0.196406i
$367$	−17.2380	+	9.95237i	−0.899817	+	0.519510i	−0.877141	−	0.480233i	$-0.840552\pi$
$367$	−17.2380	+	9.95237i	−0.899817	+	0.519510i	−0.0226761	+	0.999743i	$0.507219\pi$
$368$	−8.72666	+	15.0825i	−0.454909	+	0.786229i
$369$	13.9518	−	23.1830i	0.726302	−	1.20686i
$370$	1.35505	−	10.2741i	0.0704459	−	0.534127i
$371$	−9.77705	+	11.2836i	−0.507599	+	0.585814i
$372$	1.65409	+	6.41748i	0.0857604	+	0.332731i
$373$	14.7253	+	8.50167i	0.762448	+	0.440200i	0.830174	−	0.557504i	$-0.188241\pi$
$373$	14.7253	+	8.50167i	0.762448	+	0.440200i	−0.0677258	+	0.997704i	$0.521574\pi$
$374$	−33.0505	−	25.3728i	−1.70900	−	1.31200i
$375$	−18.4734	−	0.167672i	−0.953960	−	0.00865857i
$376$	22.6790	−	2.96960i	1.16958	−	0.153145i
$377$	12.9323			0.666046
$378$	18.2718	+	6.64386i	0.939801	+	0.341723i
$379$			2.01228i			0.103364i	0.998664	+	0.0516821i	$0.0164582\pi$
$379$			2.01228i			0.103364i	−0.998664	+	0.0516821i	$0.983542\pi$
$380$	8.14798	−	2.17917i	0.417982	−	0.111789i
$381$	−0.0482895	+	5.32031i	−0.00247395	+	0.272568i
$382$	4.79770	−	6.24947i	0.245472	−	0.319751i
$383$	−15.6332	+	27.0775i	−0.798819	+	1.38359i	0.121567	+	0.992583i	$0.461208\pi$
$383$	−15.6332	+	27.0775i	−0.798819	+	1.38359i	−0.920386	+	0.391012i	$0.872125\pi$
$384$	7.69249	−	18.0229i	0.392556	−	0.919728i
$385$	15.9790	+	13.8456i	0.814365	+	0.705635i
$386$	−3.78662	+	28.7105i	−0.192734	+	1.46133i
$387$	−9.20284	+	5.09281i	−0.467807	+	0.258882i
$388$	−3.04500	+	11.3429i	−0.154586	+	0.575849i
$389$	6.77013	+	11.7262i	0.343259	+	0.594543i	0.985036	−	0.172349i	$-0.0551357\pi$
$389$	6.77013	+	11.7262i	0.343259	+	0.594543i	−0.641777	+	0.766892i	$0.721802\pi$
$390$	−8.57420	−	6.70695i	−0.434171	−	0.339620i
$391$	17.7037	+	10.2212i	0.895313	+	0.516909i
$392$	19.1807	+	4.90941i	0.968770	+	0.247963i
$393$	4.06616	−	6.89746i	0.205111	−	0.347931i
$394$	−33.7886	+	13.9865i	−1.70225	+	0.704629i
$395$		−	5.79165i		−	0.291410i
$396$	36.1997	+	10.4258i	1.81911	+	0.523916i
$397$	−23.5302			−1.18094			−0.590472	−	0.807058i	$-0.701059\pi$
$397$	−23.5302			−1.18094			−0.590472	+	0.807058i	$0.701059\pi$
$398$	13.9635	+	33.7331i	0.699926	+	1.69089i
$399$	11.3843	+	10.0467i	0.569928	+	0.502963i
$400$	−11.7149	+	6.74903i	−0.585745	+	0.337451i
$401$	6.25180	+	3.60948i	0.312200	+	0.180249i	0.647911	−	0.761716i	$-0.275643\pi$
$401$	6.25180	+	3.60948i	0.312200	+	0.180249i	−0.335710	+	0.941965i	$0.608976\pi$
$402$	1.82887	−	12.9583i	0.0912156	−	0.646299i
$403$	5.78489	−	3.33991i	0.288166	−	0.166373i
$404$	−2.54325	+	9.47383i	−0.126531	+	0.471341i
$405$	9.70606	+	6.08391i	0.482298	+	0.302312i
$406$	−13.5765	+	2.78147i	−0.673789	+	0.138042i
$407$	31.3043	−	18.0735i	1.55170	−	0.895872i
$408$	−21.1521	−	9.00476i	−1.04719	−	0.445802i
$409$	−14.5844	−	8.42031i	−0.721152	−	0.416357i	0.0940245	−	0.995570i	$-0.470027\pi$
$409$	−14.5844	−	8.42031i	−0.721152	−	0.416357i	−0.815177	+	0.579213i	$0.803360\pi$
$410$	9.88597	−	12.8774i	0.488233	−	0.635971i
$411$	−6.19702	−	10.9621i	−0.305676	−	0.540722i
$412$	29.9673	−	8.01473i	1.47638	−	0.394857i
$413$	17.5081	−	6.05985i	0.861519	−	0.298186i
$414$	−18.2766	−	2.74888i	−0.898246	−	0.135100i
$415$	10.9884			0.539398
$416$	−19.5794	−	2.60093i	−0.959961	−	0.127521i
$417$	−16.1162	−	9.50075i	−0.789213	−	0.465254i
$418$	23.3359	+	17.9149i	1.14139	+	0.876246i
$419$	−6.87675	−	3.97029i	−0.335951	−	0.193961i	0.322529	−	0.946560i	$-0.395467\pi$
$419$	−6.87675	−	3.97029i	−0.335951	−	0.193961i	−0.658480	+	0.752598i	$0.728800\pi$
$420$	10.4438	+	5.19691i	0.509607	+	0.253583i
$421$	2.79460	−	1.61346i	0.136200	−	0.0786353i	−0.430352	−	0.902661i	$-0.641610\pi$
$421$	2.79460	−	1.61346i	0.136200	−	0.0786353i	0.566552	+	0.824026i	$0.308277\pi$
$422$	29.0159	+	3.82690i	1.41247	+	0.186291i
$423$	11.7467	+	21.2265i	0.571143	+	1.03207i
$424$	−6.11834	+	14.7418i	−0.297133	+	0.715924i
$425$	7.93049	+	13.7360i	0.384686	+	0.666295i
$426$	−19.0366	+	7.67838i	−0.922326	+	0.372019i
$427$	5.05959	+	0.975095i	0.244851	+	0.0471882i
$428$	−0.143398	+	0.143264i	−0.00693138	+	0.00692492i
$429$	0.344620	−	37.9686i	0.0166384	−	1.83314i
$430$	−5.83103	+	2.41370i	−0.281197	+	0.116399i
$431$			27.6928i			1.33391i	0.745096	+	0.666957i	$0.232404\pi$
$431$			27.6928i			1.33391i	−0.745096	+	0.666957i	$0.767596\pi$
$432$	20.7764	+	0.585259i	0.999603	+	0.0281583i
$433$			15.8572i			0.762048i	0.924565	+	0.381024i	$0.124428\pi$
$433$			15.8572i			0.762048i	−0.924565	+	0.381024i	$0.875572\pi$
$434$	−5.35471	+	4.75049i	−0.257034	+	0.228031i
$435$	−8.16496	−	0.0741088i	−0.391480	−	0.00355325i
$436$	−1.33974	−	1.34099i	−0.0641617	−	0.0642216i
$437$	−12.5000	−	7.21686i	−0.597955	−	0.345229i
$438$	−23.7036	+	9.56080i	−1.13260	+	0.456833i
$439$	−13.3461	+	7.70535i	−0.636972	+	0.367756i	−0.783447	−	0.621458i	$-0.786541\pi$
$439$	−13.3461	+	7.70535i	−0.636972	+	0.367756i	0.146475	+	0.989214i	$0.453207\pi$
$440$	20.8763	+	8.66435i	0.995236	+	0.413057i
$441$	2.61130	+	20.8370i	0.124347	+	0.992239i
$442$	−3.02985	+	22.9726i	−0.144115	+	1.09269i
$443$	−14.5960	−	25.2810i	−0.693478	−	1.20114i	−0.970691	−	0.240330i	$-0.922744\pi$
$443$	−14.5960	−	25.2810i	−0.693478	−	1.20114i	0.277214	−	0.960808i	$-0.410589\pi$
$444$	14.2363	−	13.9671i	0.675623	−	0.662849i
$445$	9.03609	+	5.21699i	0.428352	+	0.247309i
$446$	13.1944	−	17.1870i	0.624775	−	0.813829i
$447$	−32.9784	−	19.4413i	−1.55983	−	0.919542i
$448$	21.1142	−	1.48065i	0.997550	−	0.0699540i
$449$		−	9.59739i		−	0.452929i	−0.974019	−	0.226464i	$-0.927283\pi$
$449$		−	9.59739i		−	0.452929i	0.974019	−	0.226464i	$-0.0727167\pi$
$450$	−11.2143	−	8.93735i	−0.528647	−	0.421311i
$451$	56.6269			2.66646
$452$	−32.3632	+	8.65551i	−1.52224	+	0.407121i
$453$	13.7305	−	7.76198i	0.645113	−	0.364690i
$454$	18.3842	−	23.9471i	0.862811	−	1.12389i
$455$	2.22508	−	11.5455i	0.104313	−	0.541263i
$456$	14.9348	+	6.35796i	0.699386	+	0.297739i
$457$	6.21748	+	10.7690i	0.290841	+	0.503752i	0.974009	−	0.226510i	$-0.0727315\pi$
$457$	6.21748	+	10.7690i	0.290841	+	0.503752i	−0.683168	+	0.730262i	$0.739398\pi$
$458$	1.52037	−	11.5276i	0.0710422	−	0.538648i
$459$	0.663849	−	24.3746i	0.0309858	−	1.13771i
$460$	−10.7102	−	2.87514i	−0.499364	−	0.134054i
$461$	32.3857	−	18.6979i	1.50835	−	0.870849i	0.508401	−	0.861120i	$-0.330237\pi$
$461$	32.3857	−	18.6979i	1.50835	−	0.870849i	0.999953	−	0.00972827i	$-0.00309665\pi$
$462$	7.80448	+	39.9341i	0.363097	+	1.85790i
$463$	10.6499	−	18.4461i	0.494941	−	0.857263i	−0.505042	−	0.863095i	$-0.668523\pi$
$463$	10.6499	−	18.4461i	0.494941	−	0.857263i	0.999983	+	0.00583150i	$0.00185623\pi$
$464$	−12.8374	+	7.39569i	−0.595959	+	0.343336i
$465$	−3.67151	+	2.07554i	−0.170262	+	0.0962511i
$466$	−5.51634	−	13.3264i	−0.255540	−	0.617335i
$467$		−	25.5216i		−	1.18100i	−0.807038	−	0.590499i	$-0.798931\pi$
$467$		−	25.5216i		−	1.18100i	0.807038	−	0.590499i	$-0.201069\pi$
$468$	−5.04446	−	20.3332i	−0.233180	−	0.939901i
$469$	13.3578	−	4.62333i	0.616804	−	0.213486i
$470$	5.56725	+	13.4494i	0.256798	+	0.620374i
$471$	−34.8809	−	20.5629i	−1.60723	−	0.947486i
$472$	15.7219	−	12.0464i	0.723659	−	0.554479i
$473$	−19.0635	−	11.0063i	−0.876539	−	0.506070i
$474$	6.86727	−	8.77915i	0.315424	−	0.403240i
$475$	−5.59946	−	9.69854i	−0.256921	−	0.445000i
$476$	−1.76015	−	24.7686i	−0.0806764	−	1.13527i
$477$	−16.9264	−	0.307289i	−0.775008	−	0.0140698i
$478$	2.93528	+	0.387133i	0.134256	+	0.0177071i
$479$	3.66280	+	6.34415i	0.167358	+	0.289872i	0.937490	−	0.348012i	$-0.113143\pi$
$479$	3.66280	+	6.34415i	0.167358	+	0.289872i	−0.770132	+	0.637884i	$0.779810\pi$
$480$	12.3468	+	1.75433i	0.563553	+	0.0800738i
$481$	−17.4088	−	10.0510i	−0.793773	−	0.458285i
$482$	−2.94509	+	3.83626i	−0.134145	+	0.174737i
$483$	−6.35799	−	18.9235i	−0.289299	−	0.861049i
$484$	14.6856	+	54.9100i	0.667529	+	2.49591i
$485$	−7.47421			−0.339386
$486$	7.49892	+	20.7308i	0.340158	+	0.940368i
$487$	−13.3475			−0.604832			−0.302416	−	0.953176i	$-0.597793\pi$
$487$	−13.3475			−0.604832			−0.302416	+	0.953176i	$0.597793\pi$
$488$	5.46184	−	0.715175i	0.247246	−	0.0323744i
$489$	−23.8449	−	0.216427i	−1.07830	−	0.00978717i
$490$	0.147286	+	12.5992i	0.00665369	+	0.569175i
$491$	−2.61391	+	4.52742i	−0.117964	+	0.204320i	−0.918961	−	0.394349i	$-0.870970\pi$
$491$	−2.61391	+	4.52742i	−0.117964	+	0.204320i	0.800997	+	0.598669i	$0.204303\pi$
$492$	30.2544	−	7.79798i	1.36397	−	0.351560i
$493$	8.69035	+	15.0521i	0.391394	+	0.677914i
$494$	2.13928	−	16.2202i	0.0962506	−	0.729780i
$495$	−0.435161	+	23.9700i	−0.0195590	+	1.07737i
$496$	−3.83241	+	6.62365i	−0.172080	+	0.297411i
$497$	−16.7563	−	14.5190i	−0.751621	−	0.651268i
$498$	16.6565	+	13.0291i	0.746395	+	0.583848i
$499$	1.06064	+	0.612360i	0.0474807	+	0.0274130i	0.523552	−	0.851993i	$-0.324606\pi$
$499$	1.06064	+	0.612360i	0.0474807	+	0.0274130i	−0.476072	+	0.879406i	$0.657940\pi$
$500$	−15.0770	−	15.0911i	−0.674265	−	0.674894i
$501$	0.273107	+	0.161001i	0.0122015	+	0.00719298i
$502$	8.33751	+	20.1418i	0.372121	+	0.898974i
$503$	−4.83778			−0.215706			−0.107853	−	0.994167i	$-0.534398\pi$
$503$	−4.83778			−0.215706			−0.107853	+	0.994167i	$0.534398\pi$
$504$	9.66898	+	20.2611i	0.430691	+	0.902500i
$505$	−6.24261			−0.277793
$506$	−14.7940	−	35.7394i	−0.657672	−	1.58881i
$507$	1.21948	−	0.689384i	0.0541589	−	0.0306166i
$508$	−4.34622	+	4.34217i	−0.192832	+	0.192653i
$509$	9.42023	+	5.43877i	0.417544	+	0.241069i	0.694026	−	0.719950i	$-0.255835\pi$
$509$	9.42023	+	5.43877i	0.417544	+	0.241069i	−0.276482	+	0.961019i	$0.589169\pi$
$510$	2.04458	−	14.4867i	0.0905356	−	0.641481i
$511$	−20.8642	−	18.0785i	−0.922977	−	0.799746i
$512$	20.9231	−	8.61521i	0.924681	−	0.380742i
$513$	−0.468722	+	17.2101i	−0.0206946	+	0.759843i
$514$	−0.106525	+	0.807680i	−0.00469861	+	0.0356252i
$515$	9.87074	+	17.0966i	0.434957	+	0.753368i
$516$	−11.7008	−	3.25521i	−0.515099	−	0.143303i
$517$	−25.3862	+	43.9703i	−1.11649	+	1.93381i
$518$	20.4378	+	6.80738i	0.897984	+	0.299099i
$519$	9.19585	+	16.2669i	0.403653	+	0.714036i
$520$	−1.63196	−	12.4634i	−0.0715664	−	0.546557i
$521$	26.7321			1.17116			0.585578	−	0.810616i	$-0.300868\pi$
$521$	26.7321			1.17116			0.585578	+	0.810616i	$0.300868\pi$
$522$	−12.2888	−	9.79368i	−0.537866	−	0.428658i
$523$	−33.0841			−1.44667			−0.723334	−	0.690499i	$-0.757391\pi$
$523$	−33.0841			−1.44667			−0.723334	+	0.690499i	$0.757391\pi$
$524$	8.93152	−	2.38873i	0.390175	−	0.104352i
$525$	3.06906	−	15.1819i	0.133945	−	0.662593i
$526$	20.7717	−	27.0571i	0.905688	−	1.17974i
$527$	7.77477	+	4.48877i	0.338674	+	0.195534i
$528$	21.3713	+	37.8870i	0.930067	+	1.64882i
$529$	−2.01137	−	3.48379i	−0.0874509	−	0.151469i
$530$	−10.0704	−	1.32818i	−0.437430	−	0.0576926i
$531$	17.9997	+	10.8324i	0.781119	+	0.470087i
$532$	1.24278	+	17.4883i	0.0538815	+	0.758213i
$533$	−15.7456	−	27.2721i	−0.682017	−	1.18129i
$534$	7.51127	+	18.6223i	0.325045	+	0.805866i
$535$	−0.111716	−	0.0644992i	−0.00482990	−	0.00278854i
$536$	11.9950	−	9.19072i	0.518103	−	0.396979i
$537$	0.0340349	−	3.74980i	0.00146871	−	0.161816i
$538$	−14.3192	−	34.5925i	−0.617345	−	1.49139i
$539$	−34.5462	+	27.1687i	−1.48801	+	1.17024i
$540$	3.06836	+	12.8665i	0.132041	+	0.553687i
$541$		−	2.90649i		−	0.124960i	−0.998046	−	0.0624798i	$-0.980099\pi$
$541$		−	2.90649i		−	0.124960i	0.998046	−	0.0624798i	$-0.0199009\pi$
$542$	5.42332	+	13.1017i	0.232951	+	0.562766i
$543$	−0.213098	+	23.4782i	−0.00914492	+	1.00754i
$544$	−10.1299	−	24.5367i	−0.434316	−	1.05200i
$545$	0.603166	−	1.04471i	0.0258368	−	0.0447506i
$546$	17.0626	−	14.8627i	0.730211	−	0.636065i
$547$	26.5965	−	15.3555i	1.13719	−	0.656554i	0.191453	−	0.981502i	$-0.438680\pi$
$547$	26.5965	−	15.3555i	1.13719	−	0.656554i	0.945732	+	0.324948i	$0.105347\pi$
$548$	3.76993	−	14.0434i	0.161044	−	0.599903i
$549$	2.82898	+	5.11204i	0.120738	+	0.218176i
$550$	3.92423	−	29.7538i	0.167330	−	1.26871i
$551$	−6.13597	−	10.6278i	−0.261401	−	0.452760i
$552$	−12.8257	−	17.0575i	−0.545896	−	0.726013i
$553$	11.8215	+	2.27827i	0.502701	+	0.0968817i
$554$	20.2538	−	26.3825i	0.860502	−	1.12089i
$555$	10.9337	+	6.44558i	0.464109	+	0.273600i
$556$	−5.58136	−	20.8689i	−0.236702	−	0.885037i
$557$	−16.5412			−0.700871			−0.350436	−	0.936587i	$-0.613966\pi$
$557$	−16.5412			−0.700871			−0.350436	+	0.936587i	$0.613966\pi$
$558$	−8.02638	−	1.20720i	−0.339784	−	0.0511050i
$559$			12.2416i			0.517763i
$560$	4.39388	+	12.7333i	0.185675	+	0.538079i
$561$	44.4240	−	25.1134i	1.87558	−	1.06029i
$562$	−11.6221	+	15.1390i	−0.490251	+	0.638599i
$563$	0.986336	+	0.569461i	0.0415691	+	0.0239999i	0.520641	−	0.853776i	$-0.325693\pi$
$563$	0.986336	+	0.569461i	0.0415691	+	0.0239999i	−0.479071	+	0.877776i	$0.659027\pi$
$564$	−7.50820	+	26.9881i	−0.316152	+	1.13641i
$565$	−10.6599	−	18.4635i	−0.448466	−	0.776766i
$566$	−2.60348	+	19.7398i	−0.109432	+	0.829725i
$567$	−16.2361	+	17.4181i	−0.681852	+	0.731490i
$568$	−21.8917	−	9.08581i	−0.918556	−	0.381232i
$569$	−30.6460	+	17.6935i	−1.28475	+	0.741748i	−0.977712	−	0.209950i	$-0.932670\pi$
$569$	−30.6460	+	17.6935i	−1.28475	+	0.741748i	−0.307034	+	0.951699i	$0.599336\pi$
$570$	−1.44361	+	10.2286i	−0.0604662	+	0.428427i
$571$	25.6297	+	14.7973i	1.07257	+	0.619249i	0.928883	−	0.370373i	$-0.120770\pi$
$571$	25.6297	+	14.7973i	1.07257	+	0.619249i	0.143689	+	0.989623i	$0.454104\pi$
$572$	31.0170	−	30.9880i	1.29688	−	1.29567i
$573$	4.74865	+	8.40006i	0.198378	+	0.350918i
$574$	22.3956	+	25.2441i	0.934774	+	1.05367i
$575$			14.7242i			0.614041i
$576$	16.6355	+	17.2991i	0.693147	+	0.720796i
$577$		−	29.8808i		−	1.24395i	−0.783035	−	0.621977i	$-0.786330\pi$
$577$		−	29.8808i		−	1.24395i	0.783035	−	0.621977i	$-0.213670\pi$
$578$	−6.56057	+	2.71568i	−0.272884	+	0.112957i
$579$	−30.5536	−	18.0118i	−1.26976	−	0.748546i
$580$	−6.66383	−	6.67005i	−0.276700	−	0.276959i
$581$	−4.32250	+	22.4287i	−0.179328	+	0.930497i
$582$	−11.3296	−	8.86230i	−0.469627	−	0.367354i
$583$	−17.7151	−	30.6835i	−0.733685	−	1.27078i
$584$	−27.2587	−	11.3133i	−1.12797	−	0.468146i
$585$	11.6652	−	6.45547i	0.482297	−	0.266901i
$586$	11.9219	+	1.57237i	0.492488	+	0.0649542i
$587$	−10.1592	+	5.86540i	−0.419314	+	0.242091i	−0.694784	−	0.719219i	$-0.744500\pi$
$587$	−10.1592	+	5.86540i	−0.419314	+	0.242091i	0.275470	+	0.961310i	$0.411167\pi$
$588$	−14.7159	+	19.2729i	−0.606872	+	0.794800i
$589$	−5.48951	−	3.16937i	−0.226191	−	0.130592i
$590$	9.99825	+	7.67564i	0.411622	+	0.316001i
$591$	0.406497	−	44.7859i	0.0167210	−	1.84225i
$592$	23.0290	+	0.0214953i	0.946485	+	0.000883450i
$593$	−16.6383			−0.683252			−0.341626	−	0.939836i	$-0.610978\pi$
$593$	−16.6383			−0.683252			−0.341626	+	0.939836i	$0.610978\pi$
$594$	−29.0813	+	35.8184i	−1.19322	+	1.46965i
$595$	14.9333	−	5.16866i	0.612206	−	0.211894i
$596$	−11.4211	−	42.7038i	−0.467826	−	1.74921i
$597$	−44.7123	−	0.405828i	−1.82995	−	0.0166095i
$598$	−13.0989	+	17.0626i	−0.535653	+	0.697740i
$599$	−13.8777	−	8.01229i	−0.567027	−	0.327373i	0.188934	−	0.981990i	$-0.439497\pi$
$599$	−13.8777	−	8.01229i	−0.567027	−	0.327373i	−0.755961	+	0.654616i	$0.772830\pi$
$600$	−2.00072	−	16.4371i	−0.0816789	−	0.671043i
$601$	24.7145	−	14.2689i	1.00812	−	0.582041i	0.0974826	−	0.995237i	$-0.468921\pi$
$601$	24.7145	−	14.2689i	1.00812	−	0.582041i	0.910642	+	0.413196i	$0.135588\pi$
$602$	−2.63291	−	12.8514i	−0.107309	−	0.523782i
$603$	13.7328	+	8.26455i	0.559242	+	0.336559i
$604$	17.5898	+	4.72197i	0.715719	+	0.192134i
$605$	−31.3267	+	18.0865i	−1.27361	+	0.735319i
$606$	−9.46273	−	7.40198i	−0.384397	−	0.300685i
$607$	−6.42574	−	3.70991i	−0.260813	−	0.150580i	0.363892	−	0.931441i	$-0.381448\pi$
$607$	−6.42574	−	3.70991i	−0.260813	−	0.150580i	−0.624705	+	0.780861i	$0.714781\pi$
$608$	7.15239	+	17.3245i	0.290068	+	0.702603i
$609$	3.36312	−	16.6366i	0.136281	−	0.674148i
$610$	1.34077	+	3.23905i	0.0542863	+	0.131145i
$611$	28.2354			1.14228
$612$	20.2764	−	19.5350i	0.819623	−	0.789656i
$613$			28.4394i			1.14866i	0.818625	+	0.574328i	$0.194737\pi$
$613$			28.4394i			1.14866i	−0.818625	+	0.574328i	$0.805263\pi$
$614$	19.3301	−	8.00151i	0.780099	−	0.322914i
$615$	9.78489	+	17.3089i	0.394565	+	0.697960i
$616$	−25.8971	+	39.2028i	−1.04343	+	1.57952i
$617$	1.24160	+	0.716841i	0.0499851	+	0.0288589i	0.524784	−	0.851235i	$-0.324146\pi$
$617$	1.24160	+	0.716841i	0.0499851	+	0.0288589i	−0.474799	+	0.880094i	$0.657479\pi$
$618$	−5.30943	+	37.6195i	−0.213577	+	1.51328i
$619$	6.94630	+	12.0313i	0.279195	+	0.483581i	0.971185	−	0.238327i	$-0.0765990\pi$
$619$	6.94630	+	12.0313i	0.279195	+	0.483581i	−0.691990	+	0.721907i	$0.743266\pi$
$620$	−4.70349	−	1.26265i	−0.188897	−	0.0507093i
$621$	11.8475	−	19.2879i	0.475423	−	0.773997i
$622$	3.58597	−	27.1891i	0.143784	−	1.09018i
$623$	−14.2031	+	16.3916i	−0.569033	+	0.656715i
$624$	12.3043	−	20.8274i	0.492567	−	0.833765i
$625$	−1.66208	+	2.87882i	−0.0664834	+	0.115153i
$626$	−10.6636	+	13.8903i	−0.426201	+	0.555168i
$627$	−31.3663	+	17.7317i	−1.25265	+	0.708137i
$628$	−12.0800	−	45.1673i	−0.482043	−	1.80237i
$629$		−	27.0166i		−	1.07722i
$630$	−10.8578	+	9.28599i	−0.432587	+	0.369963i
$631$	3.67771			0.146407			0.0732037	−	0.997317i	$-0.476678\pi$
$631$	3.67771			0.146407			0.0732037	+	0.997317i	$0.476678\pi$
$632$	12.7613	−	1.67097i	0.507618	−	0.0664678i
$633$	−18.2034	+	30.8786i	−0.723520	+	1.22731i
$634$	−34.2523	−	26.2954i	−1.36033	−	1.04432i
$635$	−3.38599	−	1.95490i	−0.134369	−	0.0775778i
$636$	−13.6901	−	13.9539i	−0.542848	−	0.553309i
$637$	22.6906	+	9.08334i	0.899034	+	0.359895i
$638$	4.30022	−	32.6047i	0.170248	−	1.29083i
$639$	0.456328	−	25.1360i	0.0180520	−	0.994363i
$640$	8.74754	+	11.4387i	0.345777	+	0.452153i
$641$	29.1479	−	16.8285i	1.15127	−	0.664687i	0.202075	−	0.979370i	$-0.435231\pi$
$641$	29.1479	−	16.8285i	1.15127	−	0.664687i	0.949197	+	0.314683i	$0.101898\pi$
$642$	−0.0928641	−	0.230233i	−0.00366506	−	0.00908658i
$643$	−14.1784	+	24.5578i	−0.559143	+	0.968464i	0.438425	+	0.898768i	$0.355536\pi$
$643$	−14.1784	+	24.5578i	−0.559143	+	0.968464i	−0.997568	+	0.0696966i	$0.977797\pi$
$644$	10.0816	−	20.7298i	0.397270	−	0.816869i
$645$	0.0701507	−	7.72887i	0.00276218	−	0.304324i
$646$	20.3166	−	8.40984i	0.799344	−	0.330881i
$647$	−49.2414			−1.93588			−0.967939	−	0.251185i	$-0.919180\pi$
$647$	−49.2414			−1.93588			−0.967939	+	0.251185i	$0.919180\pi$
$648$	−10.6049	+	23.1416i	−0.416602	+	0.909089i
$649$			43.9661i			1.72582i
$650$	−15.4209	+	6.38334i	−0.604858	+	0.250375i
$651$	−2.79219	−	8.31047i	−0.109434	−	0.325713i
$652$	−19.4610	−	19.4792i	−0.762152	−	0.762864i
$653$	−2.44370	+	4.23260i	−0.0956292	+	0.165635i	−0.909871	−	0.414891i	$-0.863820\pi$
$653$	−2.44370	+	4.23260i	−0.0956292	+	0.165635i	0.814242	+	0.580526i	$0.197153\pi$
$654$	2.15303	−	0.868422i	0.0841902	−	0.0339580i
$655$	2.94190	+	5.09552i	0.114949	+	0.199098i
$656$	31.2264	+	18.0674i	1.21918	+	0.705415i
$657$	0.568200	−	31.2982i	0.0221676	−	1.22106i
$658$	−29.6419	+	6.07285i	−1.15556	+	0.236745i
$659$	12.2863	+	21.2805i	0.478605	+	0.828969i	0.999699	−	0.0245308i	$-0.00780917\pi$
$659$	12.2863	+	21.2805i	0.478605	+	0.828969i	−0.521094	+	0.853499i	$0.674476\pi$
$660$	−19.7605	+	19.3870i	−0.769178	+	0.754636i
$661$	18.3991	−	31.8681i	0.715640	−	1.23953i	−0.247072	−	0.968997i	$-0.579468\pi$
$661$	18.3991	−	31.8681i	0.715640	−	1.23953i	0.962712	−	0.270528i	$-0.0871984\pi$
$662$	−0.605740	+	0.789035i	−0.0235428	+	0.0306667i
$663$	−24.4473	−	14.4121i	−0.949455	−	0.559719i
$664$	3.17030	+	24.2118i	0.123032	+	0.939599i
$665$	−10.5439	+	3.64941i	−0.408875	+	0.141518i
$666$	8.93094	+	22.7347i	0.346067	+	0.880950i
$667$			16.1350i			0.624748i
$668$	0.0945823	+	0.353646i	0.00365950	+	0.0136830i
$669$	13.0595	+	23.1015i	0.504911	+	0.893155i
$670$	7.62813	+	5.85610i	0.294700	+	0.226241i
$671$	−6.11383	+	10.5895i	−0.236022	+	0.408802i
$672$	−8.43769	+	24.5113i	−0.325491	+	0.945545i
$673$	4.12350	+	7.14211i	0.158949	+	0.275308i	0.934490	−	0.355989i	$-0.115856\pi$
$673$	4.12350	+	7.14211i	0.158949	+	0.275308i	−0.775541	+	0.631297i	$0.782523\pi$
$674$	−1.55116	+	11.7611i	−0.0597486	+	0.453019i
$675$	15.4434	−	8.36410i	0.594415	−	0.321934i
$676$	1.56225	+	0.419384i	0.0600864	+	0.0161302i
$677$	−16.8817	+	9.74663i	−0.648815	+	0.374593i	−0.788002	−	0.615673i	$-0.788884\pi$
$677$	−16.8817	+	9.74663i	−0.648815	+	0.374593i	0.139187	+	0.990266i	$0.455551\pi$
$678$	5.73393	−	40.6272i	0.220210	−	1.56028i
$679$	2.94013	−	15.2558i	0.112832	−	0.585464i
$680$	13.4098	−	10.2748i	0.514241	−	0.394019i
$681$	18.1962	+	32.1879i	0.697280	+	1.23344i
$682$	−6.49694	−	15.6954i	−0.248781	−	0.601007i
$683$	−19.5324			−0.747385			−0.373692	−	0.927553i	$-0.621908\pi$
$683$	−19.5324			−0.747385			−0.373692	+	0.927553i	$0.621908\pi$
$684$	−14.3165	+	13.7930i	−0.547403	+	0.527389i
$685$	9.25362			0.353563
$686$	−25.7745	−	4.65553i	−0.984076	−	0.177749i
$687$	12.2676	+	7.23194i	0.468038	+	0.275916i
$688$	−7.00068	−	12.1517i	−0.266898	−	0.463280i
$689$	−9.85166	+	17.0636i	−0.375318	+	0.650070i
$690$	8.36794	−	10.6976i	0.318562	−	0.407251i
$691$	15.0696	+	26.1013i	0.573275	+	0.992942i	0.996227	+	0.0867893i	$0.0276607\pi$
$691$	15.0696	+	26.1013i	0.573275	+	0.992942i	−0.422952	+	0.906152i	$0.639006\pi$
$692$	−5.59426	+	20.8392i	−0.212662	+	0.792186i
$693$	−48.7546	−	10.3173i	−1.85203	−	0.391922i
$694$	3.69848	−	28.0422i	0.140393	−	1.06447i
$695$	11.9059	−	6.87386i	0.451616	−	0.260741i
$696$	−2.19241	−	18.0121i	−0.0831033	−	0.682745i
$697$	21.1617	−	36.6532i	0.801557	−	1.38834i
$698$	28.3452	+	21.7605i	1.07288	+	0.823649i
$699$	17.6638	+	0.160324i	0.668106	+	0.00606403i
$700$	14.8162	−	10.0180i	0.559998	−	0.378646i
$701$	−14.1730			−0.535308			−0.267654	−	0.963515i	$-0.586248\pi$
$701$	−14.1730			−0.535308			−0.267654	+	0.963515i	$0.586248\pi$
$702$	25.3368	+	4.04626i	0.956276	+	0.152716i
$703$			19.0755i			0.719447i
$704$	−13.0679	+	48.4985i	−0.492517	+	1.82786i
$705$	−17.8268	−	0.161804i	−0.671396	−	0.00609389i
$706$	8.29783	+	6.37023i	0.312293	+	0.239747i
$707$	2.45566	−	12.7420i	0.0923546	−	0.479211i
$708$	6.05449	+	23.4900i	0.227542	+	0.882810i
$709$	23.1267	−	13.3522i	0.868541	−	0.501452i	0.00167799	−	0.999999i	$-0.499466\pi$
$709$	23.1267	−	13.3522i	0.868541	−	0.501452i	0.866863	+	0.498546i	$0.166133\pi$
$710$	1.97237	−	14.9546i	0.0740216	−	0.561238i
$711$	6.60978	+	11.9440i	0.247886	+	0.447936i
$712$	−8.88807	+	21.4153i	−0.333095	+	0.802572i
$713$	4.16704	+	7.21753i	0.156057	+	0.270298i
$714$	28.7649	+	9.87188i	1.07650	+	0.369446i
$715$	24.1642	+	13.9512i	0.903690	+	0.521746i
$716$	3.06325	−	3.06040i	0.114479	−	0.114372i
$717$	−1.84148	+	3.12371i	−0.0687712	+	0.116657i
$718$	0.0628188	+	0.151758i	0.00234438	+	0.00566356i
$719$	19.7874			0.737945			0.368973	−	0.929440i	$-0.379710\pi$
$719$	19.7874			0.737945			0.368973	+	0.929440i	$0.379710\pi$
$720$	−7.88785	+	13.0792i	−0.293963	+	0.487432i
$721$	−38.7792	+	13.4221i	−1.44421	+	0.499866i
$722$	10.4823	−	4.33903i	0.390109	−	0.161482i
$723$	−2.91498	−	5.15641i	−0.108409	−	0.191769i
$724$	−19.1796	+	19.1617i	−0.712803	+	0.712138i
$725$	−6.25944	+	10.8417i	−0.232470	+	0.402649i
$726$	−68.9313	−	9.72864i	−2.55828	−	0.361064i
$727$	−10.2124	+	5.89615i	−0.378758	+	0.218676i	−0.677278	−	0.735727i	$-0.736840\pi$
$727$	−10.2124	+	5.89615i	−0.378758	+	0.218676i	0.298520	+	0.954403i	$0.403507\pi$
$728$	26.0814	+	1.57170i	0.966640	+	0.0582509i
$729$	−26.9600	−	1.46962i	−0.998518	−	0.0544303i
$730$	2.45591	−	18.6209i	0.0908972	−	0.689190i
$731$	−14.2482	+	8.22620i	−0.526988	+	0.304257i
$732$	−1.80822	+	6.49962i	−0.0668337	+	0.240233i
$733$	5.16168	−	8.94030i	0.190651	−	0.330217i	−0.754815	−	0.655938i	$-0.772273\pi$
$733$	5.16168	−	8.94030i	0.190651	−	0.330217i	0.945466	+	0.325720i	$0.105607\pi$
$734$	17.1416	−	22.3285i	0.632707	−	0.824162i
$735$	−14.2740	−	5.86491i	−0.526503	−	0.216331i
$736$	3.24505	−	24.4283i	0.119614	−	0.900439i
$737$			33.5438i			1.23560i
$738$	−5.69121	+	37.8394i	−0.209496	+	1.39289i
$739$		−	16.8945i		−	0.621473i	−0.950496	−	0.310737i	$-0.899424\pi$
$739$		−	16.8945i		−	0.621473i	0.950496	−	0.310737i	$-0.100576\pi$
$740$	3.78655	+	14.1580i	0.139196	+	0.520460i
$741$	17.2614	+	10.1759i	0.634115	+	0.373821i
$742$	6.67238	−	20.0325i	0.244951	−	0.735415i
$743$	−4.99429	−	2.88345i	−0.183223	−	0.105784i	0.405583	−	0.914058i	$-0.367068\pi$
$743$	−4.99429	−	2.88345i	−0.183223	−	0.105784i	−0.588806	+	0.808274i	$0.700402\pi$
$744$	−5.63254	−	7.49097i	−0.206499	−	0.274632i
$745$	24.3629	−	14.0659i	0.892588	−	0.515336i
$746$	−23.8399	−	3.14424i	−0.872841	−	0.115119i
$747$	−22.6612	+	12.5406i	−0.829128	+	0.458836i
$748$	56.9107	+	15.2776i	2.08086	+	0.558606i
$749$	0.175597	−	0.202654i	0.00641616	−	0.00740482i
$750$	24.2296	−	9.77298i	0.884741	−	0.356859i
$751$	−1.28939	+	2.23329i	−0.0470505	+	0.0814938i	−0.888592	−	0.458699i	$-0.848315\pi$
$751$	−1.28939	+	2.23329i	−0.0470505	+	0.0814938i	0.841541	+	0.540193i	$0.181649\pi$
$752$	−28.0282	+	16.1472i	−1.02208	+	0.588828i
$753$	−26.6974	−	0.242318i	−0.972908	−	0.00883054i
$754$	−16.8985	+	6.99495i	−0.615406	+	0.254741i
$755$			11.5905i			0.421821i
$756$	−27.4692	+	1.20161i	−0.999045	+	0.0437021i
$757$		−	34.1200i		−	1.24011i	−0.784558	−	0.620056i	$-0.787110\pi$
$757$		−	34.1200i		−	1.24011i	0.784558	−	0.620056i	$-0.212890\pi$
$758$	−1.08843	−	2.62943i	−0.0395334	−	0.0955052i
$759$	47.3716	+	0.429965i	1.71948	+	0.0156068i
$760$	−9.46818	+	7.25467i	−0.343447	+	0.263154i
$761$	6.52600	−	11.3034i	0.236567	−	0.409747i	−0.723160	−	0.690681i	$-0.757311\pi$
$761$	6.52600	−	11.3034i	0.236567	−	0.409747i	0.959727	+	0.280934i	$0.0906442\pi$
$762$	−2.81461	−	6.97811i	−0.101963	−	0.252790i
$763$	1.89513	+	1.64210i	0.0686082	+	0.0594479i
$764$	−2.88882	+	10.7611i	−0.104514	+	0.389325i
$765$	15.3525	+	9.23936i	0.555073	+	0.334050i
$766$	5.78175	−	43.8377i	0.208903	−	1.58392i
$767$	21.1746	−	12.2251i	0.764569	−	0.441424i
$768$	−0.303255	+	27.7112i	−0.0109428	+	0.999940i
$769$	−29.2410	−	16.8823i	−1.05446	−	0.608791i	−0.130563	−	0.991440i	$-0.541679\pi$
$769$	−29.2410	−	16.8823i	−1.05446	−	0.608791i	−0.923894	+	0.382649i	$0.875012\pi$
$770$	−28.3685	−	9.44894i	−1.02233	−	0.340516i
$771$	−0.859529	−	0.506706i	−0.0309552	−	0.0182486i
$772$	−10.5813	−	39.5638i	−0.380830	−	1.42393i
$773$		−	9.10747i		−	0.327573i	−0.986496	−	0.163786i	$-0.947629\pi$
$773$		−	9.10747i		−	0.327573i	0.986496	−	0.163786i	$-0.0523708\pi$
$774$	9.27059	−	11.6325i	0.333225	−	0.418120i
$775$			6.46629i			0.232276i
$776$	−2.15641	−	16.4687i	−0.0774107	−	0.591191i
$777$	−17.4572	+	19.7815i	−0.626275	+	0.709658i
$778$	−15.1891	−	11.6606i	−0.544554	−	0.418053i
$779$	−14.9416	+	25.8796i	−0.535338	+	0.927232i
$780$	14.8315	+	4.12619i	0.531054	+	0.147741i
$781$	45.5653	−	26.3071i	1.63046	−	0.941344i
$782$	−28.6618	−	3.78020i	−1.02494	−	0.135180i
$783$	16.9231	−	9.16550i	0.604780	−	0.327548i
$784$	−27.7186	+	3.95958i	−0.989951	+	0.141414i
$785$	25.7684	−	14.8774i	0.919713	−	0.530996i
$786$	−1.58244	+	11.2122i	−0.0564436	+	0.399925i
$787$	9.98641	−	17.2970i	0.355977	−	0.616570i	−0.631308	−	0.775532i	$-0.717481\pi$
$787$	9.98641	−	17.2970i	0.355977	−	0.616570i	0.987285	+	0.158962i	$0.0508148\pi$
$788$	36.5861	−	36.5520i	1.30333	−	1.30211i
$789$	20.5593	+	36.3681i	0.731930	+	1.29474i
$790$	3.13265	+	7.56789i	0.111455	+	0.269254i
$791$	41.8797	−	14.4952i	1.48907	−	0.515391i
$792$	−52.9410	+	5.95685i	−1.88118	+	0.211667i
$793$	6.80000			0.241475
$794$	30.7466	−	12.7273i	1.09116	−	0.451673i
$795$	6.31776	−	10.7169i	0.224068	−	0.380088i
$796$	−36.4919	−	36.5260i	−1.29342	−	1.29463i
$797$	−10.3053	−	5.94979i	−0.365034	−	0.210753i	0.306253	−	0.951950i	$-0.400925\pi$
$797$	−10.3053	−	5.94979i	−0.365034	−	0.210753i	−0.671287	+	0.741198i	$0.734258\pi$
$798$	−20.3099	−	6.97021i	−0.718963	−	0.246743i
$799$	18.9739	+	32.8638i	0.671248	+	1.16264i
$800$	11.6572	−	15.1554i	0.412146	−	0.535823i
$801$	−24.5889	−	0.446397i	−0.868806	−	0.0157726i
$802$	−10.1215	−	1.33492i	−0.357403	−	0.0471378i
$803$	56.7360	−	32.7566i	2.00217	−	1.15595i
$804$	4.61925	+	17.9216i	0.162908	+	0.632047i
$805$	14.4048	+	2.77612i	0.507702	+	0.0978455i
$806$	−5.75253	+	7.49322i	−0.202624	+	0.263937i
$807$	45.8513	+	0.416167i	1.61404	+	0.0146498i
$808$	−1.80108	−	13.7550i	−0.0633618	−	0.483898i
$809$		−	13.9299i		−	0.489749i	−0.969555	−	0.244874i	$-0.921253\pi$
$809$		−	13.9299i		−	0.489749i	0.969555	−	0.244874i	$-0.0787468\pi$
$810$	−15.9735	−	2.69985i	−0.561253	−	0.0948631i
$811$	−50.8542			−1.78573			−0.892867	−	0.450321i	$-0.851309\pi$
$811$	−50.8542			−1.78573			−0.892867	+	0.450321i	$0.851309\pi$
$812$	16.2358	−	10.9779i	0.569764	−	0.385249i
$813$	−17.3659	−	0.157621i	−0.609049	−	0.00552800i
$814$	−31.1291	+	40.5487i	−1.09108	+	1.42123i
$815$	8.76160	−	15.1755i	0.306905	−	0.531576i
$816$	32.5098	+	0.325421i	1.13807	+	0.0113920i
$817$	10.0602	−	5.80824i	0.351961	−	0.203205i
$818$	23.6117	+	3.11415i	0.825565	+	0.108884i
$819$	8.58768	+	26.3495i	0.300078	+	0.920728i
$820$	−5.95260	+	22.1740i	−0.207874	+	0.774350i
$821$	−4.59857	−	7.96496i	−0.160491	−	0.277979i	0.774554	−	0.632508i	$-0.217975\pi$
$821$	−4.59857	−	7.96496i	−0.160491	−	0.277979i	−0.935045	+	0.354529i	$0.884641\pi$
$822$	14.0269	+	10.9722i	0.489244	+	0.382699i
$823$	−28.1429	+	48.7450i	−0.981001	+	1.69914i	−0.322488	+	0.946574i	$0.604519\pi$
$823$	−28.1429	+	48.7450i	−0.981001	+	1.69914i	−0.658513	+	0.752569i	$0.728814\pi$
$824$	−34.8229	+	26.6818i	−1.21311	+	0.929505i
$825$	31.6639	+	18.6664i	1.10239	+	0.649879i
$826$	−19.6000	+	17.3883i	−0.681970	+	0.605017i
$827$	−19.2776			−0.670347			−0.335174	−	0.942156i	$-0.608795\pi$
$827$	−19.2776			−0.670347			−0.335174	+	0.942156i	$0.608795\pi$
$828$	25.3687	−	6.29372i	0.881623	−	0.218722i
$829$	24.4426			0.848928			0.424464	−	0.905445i	$-0.360463\pi$
$829$	24.4426			0.848928			0.424464	+	0.905445i	$0.360463\pi$
$830$	−14.3584	+	5.94352i	−0.498387	+	0.206302i
$831$	20.0467	+	35.4614i	0.695414	+	1.23014i
$832$	26.9911	−	7.19174i	0.935746	−	0.249329i
$833$	4.67556	+	32.5139i	0.161999	+	1.12654i
$834$	26.1977	+	3.69742i	0.907153	+	0.128031i
$835$	−0.201758	+	0.116485i	−0.00698214	+	0.00403114i
$836$	−40.1827	−	10.7870i	−1.38975	−	0.373077i
$837$	5.20296	−	8.47050i	0.179841	−	0.292783i
$838$	11.1333	+	1.46837i	0.384592	+	0.0507238i
$839$	−3.60473	−	6.24357i	−0.124449	−	0.215552i	0.797068	−	0.603889i	$-0.206383\pi$
$839$	−3.60473	−	6.24357i	−0.124449	−	0.215552i	−0.921517	+	0.388337i	$0.873050\pi$
$840$	−16.4578	−	1.14177i	−0.567849	−	0.0393948i
$841$	7.64081	−	13.2343i	0.263476	−	0.456354i
$842$	−2.77896	+	3.61987i	−0.0957694	+	0.124749i
$843$	−11.5033	−	20.3486i	−0.396195	−	0.700845i
$844$	−39.9847	+	10.6939i	−1.37633	+	0.368098i
$845$			1.02941i			0.0354129i
$846$	−26.8305	−	21.3828i	−0.922451	−	0.735156i
$847$	−24.5938	−	71.0564i	−0.845052	−	2.44153i
$848$	0.0210690	−	22.5723i	0.000723512	−	0.775136i
$849$	−21.0070	−	12.3840i	−0.720958	−	0.425016i
$850$	−17.7924	−	13.6592i	−0.610274	−	0.468506i
$851$	12.5401	−	21.7201i	0.429870	−	0.744556i
$852$	20.7217	−	20.3300i	0.709915	−	0.696494i
$853$	25.2367	+	43.7112i	0.864087	+	1.49664i	0.867951	+	0.496649i	$0.165437\pi$
$853$	25.2367	+	43.7112i	0.864087	+	1.49664i	−0.00386463	+	0.999993i	$0.501230\pi$
$854$	−7.13873	+	1.46254i	−0.244282	+	0.0500471i
$855$	−10.8399	−	6.52360i	−0.370717	−	0.223102i
$856$	0.109886	−	0.264764i	0.00375582	−	0.00904944i
$857$	17.1805	+	29.7575i	0.586874	+	1.01650i	0.994639	+	0.103408i	$0.0329748\pi$
$857$	17.1805	+	29.7575i	0.586874	+	1.01650i	−0.407765	+	0.913087i	$0.633692\pi$
$858$	20.0866	+	49.7995i	0.685744	+	1.70013i
$859$	−17.9017	+	31.0066i	−0.610798	+	1.05793i	0.380309	+	0.924860i	$0.375818\pi$
$859$	−17.9017	+	31.0066i	−0.610798	+	1.05793i	−0.991106	+	0.133073i	$0.957516\pi$
$860$	6.31380	−	6.30791i	0.215299	−	0.215098i
$861$	−39.1786	+	13.1634i	−1.33520	+	0.448608i
$862$	−14.9788	−	36.1859i	−0.510180	−	1.23250i
$863$		−	31.3395i		−	1.06681i	−0.845861	−	0.533404i	$-0.820913\pi$
$863$		−	31.3395i		−	1.06681i	0.845861	−	0.533404i	$-0.179087\pi$
$864$	−27.4648	+	10.4730i	−0.934372	+	0.356299i
$865$	−13.7316			−0.466888
$866$	−8.57701	−	20.7204i	−0.291459	−	0.704108i
$867$	0.0789274	−	8.69584i	0.00268051	−	0.295326i
$868$	4.42744	−	9.10373i	0.150277	−	0.309001i
$869$	−14.2847	+	24.7418i	−0.484575	+	0.839308i
$870$	10.7092	−	4.31952i	0.363074	−	0.146445i
$871$	16.1550	−	9.32712i	0.547393	−	0.316037i
$872$	2.47595	+	1.02760i	0.0838461	+	0.0347990i
$873$	15.4139	−	8.53000i	0.521683	−	0.288697i
$874$	20.2371	+	2.66907i	0.684531	+	0.0902827i
$875$	21.3272	+	18.4797i	0.720992	+	0.624729i
$876$	25.8019	−	25.3140i	0.871764	−	0.855282i
$877$	7.35227	+	4.24484i	0.248269	+	0.143338i	0.618971	−	0.785414i	$-0.287550\pi$
$877$	7.35227	+	4.24484i	0.248269	+	0.143338i	−0.370703	+	0.928752i	$0.620883\pi$
$878$	13.2714	−	17.2873i	0.447888	−	0.583417i
$879$	−7.47930	+	12.6872i	−0.252271	+	0.427928i
$880$	−31.9652	−	0.0298364i	−1.07755	−	0.00100578i
$881$	−21.8272			−0.735377			−0.367689	−	0.929949i	$-0.619851\pi$
$881$	−21.8272			−0.735377			−0.367689	+	0.929949i	$0.619851\pi$
$882$	−14.6827	−	25.8151i	−0.494393	−	0.869239i
$883$		−	4.68838i		−	0.157776i	−0.996883	−	0.0788882i	$-0.974863\pi$
$883$		−	4.68838i		−	0.157776i	0.996883	−	0.0788882i	$-0.0251370\pi$
$884$	−8.46659	−	31.6569i	−0.284762	−	1.06474i
$885$	−13.4389	+	7.59716i	−0.451744	+	0.255376i
$886$	32.7467	+	25.1396i	1.10015	+	0.844582i
$887$	26.4358	−	45.7881i	0.887626	−	1.53741i	0.0449523	−	0.998989i	$-0.485686\pi$
$887$	26.4358	−	45.7881i	0.887626	−	1.53741i	0.842674	−	0.538424i	$-0.180980\pi$
$888$	−11.0477	+	25.9509i	−0.370736	+	0.870856i
$889$	5.32214	−	6.14222i	0.178499	−	0.206004i
$890$	−14.6292	−	1.92944i	−0.490371	−	0.0646750i
$891$	−26.4585	−	49.9296i	−0.886395	−	1.67270i
$892$	−7.94472	+	29.5948i	−0.266009	+	0.990909i
$893$	−13.3968	−	23.2040i	−0.448308	−	0.776492i
$894$	53.6082	+	7.56601i	1.79293	+	0.253045i
$895$	2.38647	+	1.37783i	0.0797709	+	0.0460558i
$896$	−26.7888	+	13.3552i	−0.894950	+	0.446166i
$897$	−12.9650	−	22.9342i	−0.432888	−	0.765751i
$898$	5.19114	+	12.5408i	0.173231	+	0.418492i
$899$			7.08586i			0.236326i
$900$	19.4877	+	5.61262i	0.649591	+	0.187087i
$901$	−26.4808			−0.882205
$902$	−73.9938	+	30.6290i	−2.46372	+	1.01983i
$903$	15.7480	+	3.18350i	0.524061	+	0.105940i
$904$	37.6070	−	28.8150i	1.25079	−	0.958374i
$905$	−14.9421	−	8.62684i	−0.496693	−	0.286766i
$906$	−13.7431	+	17.5692i	−0.456582	+	0.583697i
$907$	7.97257	−	4.60297i	0.264725	−	0.152839i	−0.361763	−	0.932270i	$-0.617825\pi$
$907$	7.97257	−	4.60297i	0.264725	−	0.152839i	0.626488	+	0.779431i	$0.284492\pi$
$908$	−11.0696	+	41.2353i	−0.367357	+	1.36844i
$909$	12.8740	−	7.12444i	0.427005	−	0.236303i
$910$	3.33738	+	16.2899i	0.110633	+	0.540006i
$911$	−21.6571	+	12.5037i	−0.717531	+	0.414267i	−0.813843	−	0.581085i	$-0.802629\pi$
$911$	−21.6571	+	12.5037i	−0.717531	+	0.414267i	0.0963123	+	0.995351i	$0.469295\pi$
$912$	−22.9541	−	0.229769i	−0.760087	−	0.00760841i
$913$	−46.9421	−	27.1020i	−1.55356	−	0.896946i
$914$	−13.9492	−	10.7087i	−0.461397	−	0.354214i
$915$	−4.29327	−	0.0389676i	−0.141931	−	0.00128823i
$916$	4.24851	+	15.8853i	0.140375	+	0.524865i
$917$	−11.5578	+	4.00036i	−0.381674	+	0.132103i
$918$	12.3165	+	32.2091i	0.406507	+	1.06306i
$919$	21.7406			0.717155			0.358578	−	0.933500i	$-0.383262\pi$
$919$	21.7406			0.717155			0.358578	+	0.933500i	$0.383262\pi$
$920$	15.5500	−	2.03612i	0.512668	−	0.0671290i
$921$	−0.232552	+	25.6215i	−0.00766285	+	0.844257i
$922$	−32.2046	+	41.9495i	−1.06060	+	1.38153i
$923$	−25.3396	−	14.6298i	−0.834063	−	0.481547i
$924$	−31.7980	−	47.9600i	−1.04608	−	1.57777i
$925$	16.8523	−	9.72969i	0.554101	−	0.319910i
$926$	−3.93873	+	29.8638i	−0.129435	+	0.981384i
$927$	−39.8680	−	23.9930i	−1.30944	−	0.788035i
$928$	12.7742	−	16.6075i	0.419333	−	0.545167i
$929$	−26.2799	−	45.5181i	−0.862216	−	1.49340i	−0.869785	−	0.493430i	$-0.835743\pi$
$929$	−26.2799	−	45.5181i	−0.862216	−	1.49340i	0.00756952	−	0.999971i	$-0.497591\pi$
$930$	3.67487	−	4.69798i	0.120504	−	0.154053i
$931$	−3.30126	−	22.9570i	−0.108194	−	0.752385i
$932$	14.4163	+	14.4298i	0.472221	+	0.472662i
$933$	28.9345	+	17.0574i	0.947274	+	0.558433i
$934$	13.8044	+	33.3488i	0.451694	+	1.09121i
$935$			37.5003i			1.22639i
$936$	17.5896	+	23.8406i	0.574933	+	0.779255i
$937$			31.9676i			1.04433i	0.852843	+	0.522167i	$0.174876\pi$
$937$			31.9676i			1.04433i	−0.852843	+	0.522167i	$0.825124\pi$
$938$	−14.9537	+	13.2664i	−0.488256	+	0.433162i
$939$	−10.5545	−	18.6703i	−0.344434	−	0.609282i
$940$	−14.5493	−	14.5629i	−0.474547	−	0.474990i
$941$	−14.8170	−	8.55458i	−0.483019	−	0.278871i	0.238655	−	0.971105i	$-0.423294\pi$
$941$	−14.8170	−	8.55458i	−0.483019	−	0.278871i	−0.721674	+	0.692233i	$0.756627\pi$
$942$	56.7008	+	8.00248i	1.84741	+	0.260735i
$943$	34.0261	−	19.6450i	1.10804	−	0.639729i
$944$	−14.0279	+	24.2447i	−0.456568	+	0.789097i
$945$	−5.27095	−	16.6853i	−0.171464	−	0.542774i
$946$	30.8632	+	4.07055i	1.00345	+	0.132345i
$947$	−2.26136	−	3.91679i	−0.0734842	−	0.127278i	0.826942	−	0.562287i	$-0.190079\pi$
$947$	−2.26136	−	3.91679i	−0.0734842	−	0.127278i	−0.900426	+	0.435009i	$0.856745\pi$
$948$	−4.22482	+	15.1861i	−0.137216	+	0.493220i
$949$	−31.5518	−	18.2165i	−1.02422	−	0.591331i
$950$	12.5626	+	9.64428i	0.407585	+	0.312902i
$951$	46.0394	−	26.0266i	1.49293	−	0.843970i
$952$	15.6971	+	31.4128i	0.508745	+	1.01809i
$953$			23.7679i			0.769919i	0.922934	+	0.384959i	$0.125785\pi$
$953$			23.7679i			0.769919i	−0.922934	+	0.384959i	$0.874215\pi$
$954$	22.2838	−	8.75383i	0.721465	−	0.283416i
$955$	−7.09087			−0.229455
$956$	−4.04489	+	1.08180i	−0.130821	+	0.0349880i
$957$	34.6977	+	20.4549i	1.12162	+	0.661212i
$958$	−8.21764	−	6.30866i	−0.265500	−	0.203824i
$959$	−3.64010	+	18.8878i	−0.117545	+	0.609919i
$960$	−17.0824	+	4.38593i	−0.551331	+	0.141555i
$961$	−13.6700	−	23.6771i	−0.440968	−	0.763778i
$962$	28.1844	+	3.71724i	0.908701	+	0.119849i
$963$	0.304000	+	0.00551894i	0.00979627	+	0.000177845i
$964$	1.77332	−	6.60577i	0.0571147	−	0.212758i
$965$	22.5715	−	13.0317i	0.726604	−	0.419505i
$966$	18.5435	+	21.2881i	0.596626	+	0.684934i
$967$	17.9107	−	31.0222i	0.575968	−	0.997607i	−0.419967	−	0.907539i	$-0.637958\pi$
$967$	17.9107	−	31.0222i	0.575968	−	0.997607i	0.995936	−	0.0900673i	$-0.0287082\pi$
$968$	−48.8899	−	63.8070i	−1.57138	−	2.05083i
$969$	−0.244420	+	26.9290i	−0.00785189	+	0.865085i
$970$	9.76646	−	4.04273i	0.313582	−	0.129804i
$971$		−	40.8117i		−	1.30971i	−0.755754	−	0.654856i	$-0.772729\pi$
$971$		−	40.8117i		−	1.30971i	0.755754	−	0.654856i	$-0.227271\pi$
$972$	−21.0119	−	23.0326i	−0.673956	−	0.738772i
$973$	9.34700	+	27.0054i	0.299651	+	0.865753i
$974$	17.4410	−	7.21954i	0.558846	−	0.231329i
$975$	0.185522	−	20.4400i	0.00594147	−	0.654603i
$976$	−6.75009	+	3.88877i	−0.216065	+	0.124477i
$977$	5.98473	+	3.45529i	0.191469	+	0.110544i	0.592670	−	0.805445i	$-0.298074\pi$
$977$	5.98473	+	3.45529i	0.191469	+	0.110544i	−0.401201	+	0.915990i	$0.631407\pi$
$978$	31.2750	−	12.6147i	1.00006	−	0.403374i
$979$	−25.7346	−	44.5737i	−0.822482	−	1.42458i
$980$	−7.00726	−	16.3836i	−0.223839	−	0.523355i
$981$	−0.0516105	+	2.84287i	−0.00164780	+	0.0907658i
$982$	0.966723	−	7.32977i	0.0308494	−	0.233902i
$983$	−8.95933	−	15.5180i	−0.285758	−	0.494948i	0.687034	−	0.726625i	$-0.258912\pi$
$983$	−8.95933	−	15.5180i	−0.285758	−	0.494948i	−0.972793	+	0.231677i	$0.925579\pi$
$984$	−35.3153	+	26.5539i	−1.12581	+	0.846507i
$985$	28.5029	+	16.4562i	0.908178	+	0.524337i
$986$	−19.4972	−	14.9679i	−0.620916	−	0.476676i
$987$	7.34280	−	36.3231i	0.233724	−	1.15618i
$988$	5.97798	+	22.3518i	0.190185	+	0.711107i
$989$	−15.2732			−0.485659
$990$	−12.3965	−	31.5567i	−0.393988	−	1.00294i
$991$	50.5900			1.60704			0.803522	−	0.595276i	$-0.202957\pi$
$991$	50.5900			1.60704			0.803522	+	0.595276i	$0.202957\pi$
$992$	1.42510	−	10.7280i	0.0452470	−	0.340613i
$993$	−0.599547	−	1.06056i	−0.0190260	−	0.0336559i
$994$	29.7484	+	9.90856i	0.943563	+	0.314281i
$995$	16.4291	−	28.4561i	0.520838	−	0.902118i
$996$	−28.8122	−	8.01565i	−0.912949	−	0.253986i
$997$	−27.8729	−	48.2773i	−0.882744	−	1.52896i	−0.848278	−	0.529552i	$-0.822360\pi$
$997$	−27.8729	−	48.2773i	−0.882744	−	1.52896i	−0.0344663	−	0.999406i	$-0.510973\pi$
$998$	−1.71715	−	0.226474i	−0.0543553	−	0.00716891i
$999$	−29.9044	−	0.814457i	−0.946135	−	0.0257683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.12	yes	168
7.6	odd	2	inner	504.2.cc.b.293.11	✓	168
8.5	even	2	inner	504.2.cc.b.293.17	yes	168
9.2	odd	6	inner	504.2.cc.b.461.18	yes	168
56.13	odd	2	inner	504.2.cc.b.293.18	yes	168
63.20	even	6	inner	504.2.cc.b.461.17	yes	168
72.29	odd	6	inner	504.2.cc.b.461.11	yes	168
504.461	even	6	inner	504.2.cc.b.461.12	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.11	✓	168	7.6	odd	2	inner
504.2.cc.b.293.12	yes	168	1.1	even	1	trivial
504.2.cc.b.293.17	yes	168	8.5	even	2	inner
504.2.cc.b.293.18	yes	168	56.13	odd	2	inner
504.2.cc.b.461.11	yes	168	72.29	odd	6	inner
504.2.cc.b.461.12	yes	168	504.461	even	6	inner
504.2.cc.b.461.17	yes	168	63.20	even	6	inner
504.2.cc.b.461.18	yes	168	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30669 + 0.540891i) q^{2} +(0.0157202 - 1.73198i) q^{3} +(1.41487 - 1.41355i) q^{4} +(1.10228 + 0.636400i) q^{5} +(0.916271 + 2.27166i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(-1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +O(q^{10})\)	\(q+(-1.30669 + 0.540891i) q^{2} +(0.0157202 - 1.73198i) q^{3} +(1.41487 - 1.41355i) q^{4} +(1.10228 + 0.636400i) q^{5} +(0.916271 + 2.27166i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(-1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +(-1.78456 - 0.235365i) q^{10} +(-3.13927 - 5.43737i) q^{11} +(-2.42600 - 2.47275i) q^{12} +(-1.74580 + 3.02381i) q^{13} +(1.18240 - 3.54992i) q^{14} +(1.11956 - 1.89912i) q^{15} +(0.00373360 - 4.00000i) q^{16} -4.69263 q^{17} +(3.94888 - 1.55125i) q^{18} +3.31331 q^{19} +(2.45917 - 0.657702i) q^{20} +(3.43593 + 3.03222i) q^{21} +(7.04307 + 5.40695i) q^{22} +(-3.77266 - 2.17814i) q^{23} +(4.50752 + 1.91892i) q^{24} +(-1.68999 - 2.92715i) q^{25} +(0.645662 - 4.89546i) q^{26} +(-0.141466 + 5.19423i) q^{27} +(0.375089 + 5.27819i) q^{28} +(-1.85192 - 3.20761i) q^{29} +(-0.435701 + 3.08712i) q^{30} +(-1.65681 - 0.956557i) q^{31} +(2.15869 + 5.22877i) q^{32} +(-9.46676 + 5.35167i) q^{33} +(6.13181 - 2.53820i) q^{34} +(-3.18229 + 1.10144i) q^{35} +(-4.32089 + 4.16292i) q^{36} +5.75725i q^{37} +(-4.32946 + 1.79214i) q^{38} +(5.20973 + 3.07122i) q^{39} +(-2.85762 + 2.18955i) q^{40} +(-4.50957 + 7.81080i) q^{41} +(-6.12980 - 2.10370i) q^{42} +(3.03629 - 1.75300i) q^{43} +(-12.1277 - 3.25567i) q^{44} +(-3.27163 - 1.96891i) q^{45} +(6.10783 + 0.805561i) q^{46} +(-4.04334 - 7.00327i) q^{47} +(-6.92786 - 0.0693474i) q^{48} +(-0.996363 - 6.92873i) q^{49} +(3.79156 + 2.91077i) q^{50} +(-0.0737691 + 8.12753i) q^{51} +(1.80423 + 6.74608i) q^{52} +5.64307 q^{53} +(-2.62466 - 6.86376i) q^{54} -7.99132i q^{55} +(-3.34505 - 6.69407i) q^{56} +(0.0520859 - 5.73858i) q^{57} +(4.15485 + 3.18967i) q^{58} +(-6.06444 - 3.50131i) q^{59} +(-1.10047 - 4.26957i) q^{60} +(-0.973767 - 1.68661i) q^{61} +(2.68232 + 0.353771i) q^{62} +(5.30575 - 5.90330i) q^{63} +(-5.64893 - 5.66477i) q^{64} +(-3.84870 + 2.22205i) q^{65} +(9.47544 - 12.1135i) q^{66} +(-4.62684 - 2.67131i) q^{67} +(-6.63947 + 6.63328i) q^{68} +(-3.83181 + 6.49992i) q^{69} +(3.56250 - 3.16051i) q^{70} +8.38003i q^{71} +(3.39438 - 7.77677i) q^{72} +10.4345i q^{73} +(-3.11404 - 7.52293i) q^{74} +(-5.09633 + 2.88101i) q^{75} +(4.68791 - 4.68354i) q^{76} +(16.3113 + 3.14355i) q^{77} +(-8.46869 - 1.19523i) q^{78} +(-2.27516 - 3.94070i) q^{79} +(2.54971 - 4.40673i) q^{80} +(8.99407 + 0.326671i) q^{81} +(1.66781 - 12.6455i) q^{82} +(7.47660 - 4.31662i) q^{83} +(9.14762 - 0.566672i) q^{84} +(-5.17258 - 2.98639i) q^{85} +(-3.01931 + 3.93294i) q^{86} +(-5.58463 + 3.15706i) q^{87} +(17.6081 - 2.30561i) q^{88} +8.19765 q^{89} +(5.33997 + 0.803155i) q^{90} +(-3.02152 - 8.72978i) q^{91} +(-8.41676 + 2.25105i) q^{92} +(-1.68278 + 2.85452i) q^{93} +(9.07140 + 6.96409i) q^{94} +(3.65218 + 2.10859i) q^{95} +(9.09006 - 3.65660i) q^{96} +(-5.08552 + 2.93613i) q^{97} +(5.04962 + 8.51477i) q^{98} +(9.12016 + 16.4804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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