LMFDB - Embedded newform 96.2.n.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (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:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	96.13
Dual form			96.2.n.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.333592 - 1.37431i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.77743 - 0.916914i) q^{4} +(-1.20409 + 0.498752i) q^{5} +(-1.14203 - 0.834122i) q^{6} +(2.59422 - 2.59422i) q^{7} +(-1.85306 + 2.13686i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(0.333592 - 1.37431i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.77743 - 0.916914i) q^{4} +(-1.20409 + 0.498752i) q^{5} +(-1.14203 - 0.834122i) q^{6} +(2.59422 - 2.59422i) q^{7} +(-1.85306 + 2.13686i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(0.283762 + 1.82117i) q^{10} +(2.14608 + 5.18109i) q^{11} +(-1.52731 + 1.29125i) q^{12} +(-0.984096 - 0.407626i) q^{13} +(-2.69984 - 4.43066i) q^{14} +1.30330i q^{15} +(2.31854 + 3.25951i) q^{16} -0.979053i q^{17} +(-1.20767 + 0.735896i) q^{18} +(5.68961 + 2.35671i) q^{19} +(2.59751 + 0.217551i) q^{20} +(-1.40398 - 3.38951i) q^{21} +(7.83631 - 1.22100i) q^{22} +(-3.70206 - 3.70206i) q^{23} +(1.26507 + 2.52974i) q^{24} +(-2.33445 + 2.33445i) q^{25} +(-0.888489 + 1.21647i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-6.98973 + 2.23238i) q^{28} +(-1.17302 + 2.83193i) q^{29} +(1.79113 + 0.434770i) q^{30} +1.54469 q^{31} +(5.25300 - 2.09904i) q^{32} +5.60797 q^{33} +(-1.34552 - 0.326604i) q^{34} +(-1.82981 + 4.41756i) q^{35} +(0.608479 + 1.90519i) q^{36} +(-8.23352 + 3.41044i) q^{37} +(5.13685 - 7.03308i) q^{38} +(-0.753195 + 0.753195i) q^{39} +(1.16549 - 3.49720i) q^{40} +(-1.10862 - 1.10862i) q^{41} +(-5.12659 + 0.798789i) q^{42} +(-3.47106 - 8.37989i) q^{43} +(0.936101 - 11.1768i) q^{44} +(1.20409 + 0.498752i) q^{45} +(-6.32273 + 3.85278i) q^{46} +3.15582i q^{47} +(3.89866 - 0.894692i) q^{48} -6.45997i q^{49} +(2.42949 + 3.98700i) q^{50} +(-0.904527 - 0.374667i) q^{51} +(1.37541 + 1.62686i) q^{52} +(-2.55252 - 6.16232i) q^{53} +(0.217726 + 1.39735i) q^{54} +(-5.16815 - 5.16815i) q^{55} +(0.736256 + 10.3507i) q^{56} +(4.35464 - 4.35464i) q^{57} +(3.50063 + 2.55680i) q^{58} +(-8.95423 + 3.70896i) q^{59} +(1.19501 - 2.31653i) q^{60} +(-2.00717 + 4.84573i) q^{61} +(0.515295 - 2.12287i) q^{62} -3.66878 q^{63} +(-1.13236 - 7.91945i) q^{64} +1.38825 q^{65} +(1.87077 - 7.70706i) q^{66} +(1.14380 - 2.76138i) q^{67} +(-0.897707 + 1.74020i) q^{68} +(-4.83697 + 2.00354i) q^{69} +(5.46066 + 3.98838i) q^{70} +(10.0373 - 10.0373i) q^{71} +(2.82130 - 0.200681i) q^{72} +(8.11103 + 8.11103i) q^{73} +(1.94035 + 12.4531i) q^{74} +(1.26339 + 3.05010i) q^{75} +(-7.95200 - 9.40578i) q^{76} +(19.0083 + 7.87349i) q^{77} +(0.783860 + 1.28638i) q^{78} +0.155459i q^{79} +(-4.41742 - 2.76837i) q^{80} +1.00000i q^{81} +(-1.89342 + 1.15376i) q^{82} +(5.13862 + 2.12849i) q^{83} +(-0.612406 + 7.31197i) q^{84} +(0.488304 + 1.17887i) q^{85} +(-12.6745 + 1.97484i) q^{86} +(2.16747 + 2.16747i) q^{87} +(-15.0481 - 5.01498i) q^{88} +(-6.15303 + 6.15303i) q^{89} +(1.08711 - 1.48841i) q^{90} +(-3.61044 + 1.49549i) q^{91} +(3.18569 + 9.97462i) q^{92} +(0.591127 - 1.42711i) q^{93} +(4.33707 + 1.05276i) q^{94} -8.02623 q^{95} +(0.0709783 - 5.65641i) q^{96} +14.3852 q^{97} +(-8.87798 - 2.15499i) q^{98} +(2.14608 - 5.18109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	0.333592	−	1.37431i	0.235885	−	0.971781i
$2$	0.333592	−	1.37431i	0.235885	−	0.971781i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$	−1.77743	−	0.916914i	−0.888717	−	0.458457i
$5$	−1.20409	+	0.498752i	−0.538487	+	0.223048i	−0.635316	−	0.772253i	$-0.719130\pi$
$5$	−1.20409	+	0.498752i	−0.538487	+	0.223048i	0.0968290	+	0.995301i	$0.469130\pi$
$6$	−1.14203	−	0.834122i	−0.466233	−	0.340529i
$7$	2.59422	−	2.59422i	0.980524	−	0.980524i	−0.0192902	−	0.999814i	$-0.506141\pi$
$7$	2.59422	−	2.59422i	0.980524	−	0.980524i	0.999814	+	0.0192902i	$0.00614065\pi$
$8$	−1.85306	+	2.13686i	−0.655154	+	0.755495i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	0.283762	+	1.82117i	0.0897334	+	0.575905i
$11$	2.14608	+	5.18109i	0.647066	+	1.56216i	0.816960	+	0.576694i	$0.195658\pi$
$11$	2.14608	+	5.18109i	0.647066	+	1.56216i	−0.169894	+	0.985462i	$0.554342\pi$
$12$	−1.52731	+	1.29125i	−0.440897	+	0.372751i
$13$	−0.984096	−	0.407626i	−0.272939	−	0.113055i	0.242016	−	0.970272i	$-0.422191\pi$
$13$	−0.984096	−	0.407626i	−0.272939	−	0.113055i	−0.514955	+	0.857217i	$0.672191\pi$
$14$	−2.69984	−	4.43066i	−0.721564	−	1.18414i
$15$			1.30330i			0.336511i
$16$	2.31854	+	3.25951i	0.579635	+	0.814876i
$17$		−	0.979053i		−	0.237455i	−0.992927	−	0.118728i	$-0.962118\pi$
$17$		−	0.979053i		−	0.237455i	0.992927	−	0.118728i	$-0.0378815\pi$
$18$	−1.20767	+	0.735896i	−0.284650	+	0.173452i
$19$	5.68961	+	2.35671i	1.30529	+	0.540667i	0.923505	−	0.383586i	$-0.125311\pi$
$19$	5.68961	+	2.35671i	1.30529	+	0.540667i	0.381781	+	0.924253i	$0.375311\pi$
$20$	2.59751	+	0.217551i	0.580820	+	0.0486459i
$21$	−1.40398	−	3.38951i	−0.306374	−	0.739653i
$22$	7.83631	−	1.22100i	1.67071	−	0.260318i
$23$	−3.70206	−	3.70206i	−0.771932	−	0.771932i	0.206512	−	0.978444i	$-0.433789\pi$
$23$	−3.70206	−	3.70206i	−0.771932	−	0.771932i	−0.978444	+	0.206512i	$0.933789\pi$
$24$	1.26507	+	2.52974i	0.258231	+	0.516382i
$25$	−2.33445	+	2.33445i	−0.466890	+	0.466890i
$26$	−0.888489	+	1.21647i	−0.174247	+	0.238569i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	−6.98973	+	2.23238i	−1.32094	+	0.421880i
$29$	−1.17302	+	2.83193i	−0.217825	+	0.525876i	−0.994586	−	0.103920i	$-0.966861\pi$
$29$	−1.17302	+	2.83193i	−0.217825	+	0.525876i	0.776761	+	0.629796i	$0.216861\pi$
$30$	1.79113	+	0.434770i	0.327015	+	0.0793778i
$31$	1.54469			0.277434			0.138717	−	0.990332i	$-0.455702\pi$
$31$	1.54469			0.277434			0.138717	+	0.990332i	$0.455702\pi$
$32$	5.25300	−	2.09904i	0.928608	−	0.371061i
$33$	5.60797			0.976222
$34$	−1.34552	−	0.326604i	−0.230755	−	0.0560121i
$35$	−1.82981	+	4.41756i	−0.309295	+	0.746703i
$36$	0.608479	+	1.90519i	0.101413	+	0.317532i
$37$	−8.23352	+	3.41044i	−1.35358	+	0.560672i	−0.937288	−	0.348557i	$-0.886672\pi$
$37$	−8.23352	+	3.41044i	−1.35358	+	0.560672i	−0.416295	+	0.909229i	$0.636672\pi$
$38$	5.13685	−	7.03308i	0.833307	−	1.14092i
$39$	−0.753195	+	0.753195i	−0.120608	+	0.120608i
$40$	1.16549	−	3.49720i	0.184280	−	0.552955i
$41$	−1.10862	−	1.10862i	−0.173138	−	0.173138i	0.615219	−	0.788357i	$-0.289068\pi$
$41$	−1.10862	−	1.10862i	−0.173138	−	0.173138i	−0.788357	+	0.615219i	$0.789068\pi$
$42$	−5.12659	+	0.798789i	−0.791049	+	0.123256i
$43$	−3.47106	−	8.37989i	−0.529332	−	1.27792i	−0.931961	−	0.362558i	$-0.881903\pi$
$43$	−3.47106	−	8.37989i	−0.529332	−	1.27792i	0.402629	−	0.915363i	$-0.368097\pi$
$44$	0.936101	−	11.1768i	0.141123	−	1.68497i
$45$	1.20409	+	0.498752i	0.179496	+	0.0743495i
$46$	−6.32273	+	3.85278i	−0.932236	+	0.568062i
$47$			3.15582i			0.460324i	0.973152	+	0.230162i	$0.0739256\pi$
$47$			3.15582i			0.460324i	−0.973152	+	0.230162i	$0.926074\pi$
$48$	3.89866	−	0.894692i	0.562723	−	0.129138i
$49$		−	6.45997i		−	0.922853i
$50$	2.42949	+	3.98700i	0.343582	+	0.563847i
$51$	−0.904527	−	0.374667i	−0.126659	−	0.0524639i
$52$	1.37541	+	1.62686i	0.190735	+	0.225605i
$53$	−2.55252	−	6.16232i	−0.350615	−	0.846460i	−0.996544	−	0.0830627i	$-0.973530\pi$
$53$	−2.55252	−	6.16232i	−0.350615	−	0.846460i	0.645929	−	0.763397i	$-0.276470\pi$
$54$	0.217726	+	1.39735i	0.0296287	+	0.190156i
$55$	−5.16815	−	5.16815i	−0.696873	−	0.696873i
$56$	0.736256	+	10.3507i	0.0983864	+	1.38318i
$57$	4.35464	−	4.35464i	0.576786	−	0.576786i
$58$	3.50063	+	2.55680i	0.459655	+	0.335724i
$59$	−8.95423	+	3.70896i	−1.16574	+	0.482866i	−0.879783	−	0.475376i	$-0.842312\pi$
$59$	−8.95423	+	3.70896i	−1.16574	+	0.482866i	−0.285958	+	0.958242i	$0.592312\pi$
$60$	1.19501	−	2.31653i	0.154276	−	0.299063i
$61$	−2.00717	+	4.84573i	−0.256991	+	0.620432i	−0.998737	−	0.0502499i	$-0.983998\pi$
$61$	−2.00717	+	4.84573i	−0.256991	+	0.620432i	0.741746	+	0.670681i	$0.233998\pi$
$62$	0.515295	−	2.12287i	0.0654425	−	0.269605i
$63$	−3.66878			−0.462223
$64$	−1.13236	−	7.91945i	−0.141545	−	0.989932i
$65$	1.38825			0.172191
$66$	1.87077	−	7.70706i	0.230276	−	0.948674i
$67$	1.14380	−	2.76138i	0.139738	−	0.337357i	−0.838482	−	0.544930i	$-0.816556\pi$
$67$	1.14380	−	2.76138i	0.139738	−	0.337357i	0.978220	+	0.207573i	$0.0665564\pi$
$68$	−0.897707	+	1.74020i	−0.108863	+	0.211030i
$69$	−4.83697	+	2.00354i	−0.582303	+	0.241198i
$70$	5.46066	+	3.98838i	0.652674	+	0.476703i
$71$	10.0373	−	10.0373i	1.19120	−	1.19120i	0.214474	−	0.976730i	$-0.431196\pi$
$71$	10.0373	−	10.0373i	1.19120	−	1.19120i	0.976730	−	0.214474i	$-0.0688038\pi$
$72$	2.82130	−	0.200681i	0.332493	−	0.0236505i
$73$	8.11103	+	8.11103i	0.949324	+	0.949324i	0.998776	−	0.0494525i	$-0.0157476\pi$
$73$	8.11103	+	8.11103i	0.949324	+	0.949324i	−0.0494525	+	0.998776i	$0.515748\pi$
$74$	1.94035	+	12.4531i	0.225561	+	1.44764i
$75$	1.26339	+	3.05010i	0.145884	+	0.352196i
$76$	−7.95200	−	9.40578i	−0.912157	−	1.07892i
$77$	19.0083	+	7.87349i	2.16620	+	0.897268i
$78$	0.783860	+	1.28638i	0.0887547	+	0.145654i
$79$			0.155459i			0.0174905i	0.999962	+	0.00874523i	$0.00278373\pi$
$79$			0.155459i			0.0174905i	−0.999962	+	0.00874523i	$0.997216\pi$
$80$	−4.41742	−	2.76837i	−0.493883	−	0.309513i
$81$			1.00000i			0.111111i
$82$	−1.89342	+	1.15376i	−0.209093	+	0.127412i
$83$	5.13862	+	2.12849i	0.564037	+	0.233632i	0.646437	−	0.762968i	$-0.276258\pi$
$83$	5.13862	+	2.12849i	0.564037	+	0.233632i	−0.0823997	+	0.996599i	$0.526258\pi$
$84$	−0.612406	+	7.31197i	−0.0668189	+	0.797801i
$85$	0.488304	+	1.17887i	0.0529640	+	0.127866i
$86$	−12.6745	+	1.97484i	−1.36672	+	0.212953i
$87$	2.16747	+	2.16747i	0.232377	+	0.232377i
$88$	−15.0481	−	5.01498i	−1.60413	−	0.534598i
$89$	−6.15303	+	6.15303i	−0.652220	+	0.652220i	−0.953527	−	0.301307i	$-0.902577\pi$
$89$	−6.15303	+	6.15303i	−0.652220	+	0.652220i	0.301307	+	0.953527i	$0.402577\pi$
$90$	1.08711	−	1.48841i	0.114592	−	0.156892i
$91$	−3.61044	+	1.49549i	−0.378477	+	0.156770i
$92$	3.18569	+	9.97462i	0.332131	+	1.03993i
$93$	0.591127	−	1.42711i	0.0612970	−	0.147984i
$94$	4.33707	+	1.05276i	0.447334	+	0.108583i
$95$	−8.02623			−0.823474
$96$	0.0709783	−	5.65641i	0.00724420	−	0.577305i
$97$	14.3852			1.46059			0.730296	−	0.683131i	$-0.239382\pi$
$97$	14.3852			1.46059			0.730296	+	0.683131i	$0.239382\pi$
$98$	−8.87798	−	2.15499i	−0.896811	−	0.217687i
$99$	2.14608	−	5.18109i	0.215689	−	0.520719i
$100$	6.28981	−	2.00884i	0.628981	−	0.200884i
$101$	12.1198	−	5.02020i	1.20597	−	0.499528i	0.313045	−	0.949738i	$-0.398651\pi$
$101$	12.1198	−	5.02020i	1.20597	−	0.499528i	0.892923	+	0.450210i	$0.148651\pi$
$102$	−0.816650	+	1.11811i	−0.0808604	+	0.110709i
$103$	−10.3057	+	10.3057i	−1.01545	+	1.01545i	−0.0155752	+	0.999879i	$0.504958\pi$
$103$	−10.3057	+	10.3057i	−1.01545	+	1.01545i	−0.999879	+	0.0155752i	$0.995042\pi$
$104$	2.69463	−	1.34752i	0.264230	−	0.132136i
$105$	3.38105	+	3.38105i	0.329957	+	0.329957i
$106$	−9.32041	+	1.45224i	−0.905279	+	0.141054i
$107$	−0.576841	−	1.39262i	−0.0557653	−	0.134629i	0.893541	−	0.448981i	$-0.148213\pi$
$107$	−0.576841	−	1.39262i	−0.0557653	−	0.134629i	−0.949307	+	0.314352i	$0.898213\pi$
$108$	1.99302	+	0.166923i	0.191779	+	0.0160622i
$109$	−11.0738	−	4.58693i	−1.06068	−	0.439348i	−0.216987	−	0.976174i	$-0.569623\pi$
$109$	−11.0738	−	4.58693i	−1.06068	−	0.439348i	−0.843693	+	0.536826i	$0.819623\pi$
$110$	−8.82667	+	5.37857i	−0.841590	+	0.512826i
$111$			8.91190i			0.845880i
$112$	14.4707	+	2.44108i	1.36735	+	0.230660i
$113$		−	9.41139i		−	0.885349i	−0.896682	−	0.442675i	$-0.854030\pi$
$113$		−	9.41139i		−	0.885349i	0.896682	−	0.442675i	$-0.145970\pi$
$114$	−4.53193	−	7.43727i	−0.424455	−	0.696565i
$115$	6.30402	+	2.61121i	0.587853	+	0.243497i
$116$	4.68161	−	3.95801i	0.434676	−	0.367492i
$117$	0.407626	+	0.984096i	0.0376850	+	0.0909797i
$118$	2.11019	+	13.5431i	0.194259	+	1.24675i
$119$	−2.53988	−	2.53988i	−0.232831	−	0.232831i
$120$	−2.78497	−	2.41509i	−0.254232	−	0.220466i
$121$	−14.4598	+	14.4598i	−1.31453	+	1.31453i
$122$	5.98994	+	4.37495i	0.542303	+	0.396090i
$123$	−1.44849	+	0.599983i	−0.130606	+	0.0540986i
$124$	−2.74558	−	1.41635i	−0.246560	−	0.127192i
$125$	4.14034	−	9.99566i	0.370323	−	0.894039i
$126$	−1.22388	+	5.04203i	−0.109031	+	0.449180i
$127$	16.0219			1.42171			0.710855	−	0.703338i	$-0.248308\pi$
$127$	16.0219			1.42171			0.710855	+	0.703338i	$0.248308\pi$
$128$	−11.2615	−	1.08565i	−0.995385	−	0.0959586i
$129$	−9.07033			−0.798598
$130$	0.463107	−	1.90788i	0.0406172	−	0.167332i
$131$	2.18619	−	5.27794i	0.191009	−	0.461135i	−0.799142	−	0.601142i	$-0.794712\pi$
$131$	2.18619	−	5.27794i	0.191009	−	0.461135i	0.990151	+	0.140007i	$0.0447125\pi$
$132$	−9.96779	−	5.14202i	−0.867585	−	0.447556i
$133$	20.8739	−	8.64627i	1.81000	−	0.749727i
$134$	−3.41342	−	2.49311i	−0.294875	−	0.215372i
$135$	0.921573	−	0.921573i	0.0793163	−	0.0793163i
$136$	2.09210	+	1.81424i	0.179396	+	0.155570i
$137$	−8.63573	−	8.63573i	−0.737801	−	0.737801i	0.234351	−	0.972152i	$-0.424703\pi$
$137$	−8.63573	−	8.63573i	−0.737801	−	0.737801i	−0.972152	+	0.234351i	$0.924703\pi$
$138$	1.13990	+	7.31584i	0.0970349	+	0.622765i
$139$	−4.05369	−	9.78647i	−0.343829	−	0.830078i	−0.997321	−	0.0731441i	$-0.976697\pi$
$139$	−4.05369	−	9.78647i	−0.343829	−	0.830078i	0.653492	−	0.756933i	$-0.273303\pi$
$140$	7.30288	−	6.17413i	0.617206	−	0.521809i
$141$	2.91560	+	1.20768i	0.245538	+	0.101705i
$142$	−10.4459	−	17.1426i	−0.876602	−	1.43858i
$143$		−	5.97348i		−	0.499528i
$144$	0.665364	−	3.94427i	0.0554470	−	0.328689i
$145$		−	3.99495i		−	0.331763i
$146$	13.8528	−	8.44126i	1.14647	−	0.698604i
$147$	−5.96824	−	2.47213i	−0.492252	−	0.203897i
$148$	17.7616	+	1.48760i	1.46000	+	0.122280i
$149$	1.10547	+	2.66884i	0.0905637	+	0.218640i	0.962671	−	0.270675i	$-0.0872468\pi$
$149$	1.10547	+	2.66884i	0.0905637	+	0.218640i	−0.872107	+	0.489315i	$0.837247\pi$
$150$	4.61323	−	0.718801i	0.376669	−	0.0586899i
$151$	6.40487	+	6.40487i	0.521221	+	0.521221i	0.917940	−	0.396719i	$-0.129851\pi$
$151$	6.40487	+	6.40487i	0.521221	+	0.521221i	−0.396719	+	0.917940i	$0.629851\pi$
$152$	−15.5791	+	7.79079i	−1.26363	+	0.631916i
$153$	−0.692295	+	0.692295i	−0.0559687	+	0.0559687i
$154$	17.1616	−	23.4967i	1.38292	−	1.89342i
$155$	−1.85995	+	0.770416i	−0.149395	+	0.0618813i
$156$	2.02937	−	0.648139i	0.162479	−	0.0518926i
$157$	−2.85724	+	6.89798i	−0.228032	+	0.550519i	−0.995938	−	0.0900446i	$-0.971299\pi$
$157$	−2.85724	+	6.89798i	−0.228032	+	0.550519i	0.767905	+	0.640563i	$0.221299\pi$
$158$	0.213648	+	0.0518597i	0.0169969	+	0.00412573i
$159$	−6.67005			−0.528969
$160$	−5.27820	+	5.14738i	−0.417279	+	0.406936i
$161$	−19.2079			−1.51379
$162$	1.37431	+	0.333592i	0.107976	+	0.0262094i
$163$	0.958379	−	2.31373i	0.0750661	−	0.181225i	−0.881892	−	0.471451i	$-0.843730\pi$
$163$	0.958379	−	2.31373i	0.0750661	−	0.181225i	0.956958	+	0.290226i	$0.0937304\pi$
$164$	0.953993	+	2.98702i	0.0744943	+	0.233247i
$165$	−6.75251	+	2.79698i	−0.525683	+	0.217745i
$166$	4.63939	−	6.35199i	0.360087	−	0.493010i
$167$	3.60896	−	3.60896i	0.279270	−	0.279270i	−0.553548	−	0.832817i	$-0.686726\pi$
$167$	3.60896	−	3.60896i	0.279270	−	0.279270i	0.832817	+	0.553548i	$0.186726\pi$
$168$	9.84459	+	3.28084i	0.759526	+	0.253123i
$169$	−8.39010	−	8.39010i	−0.645392	−	0.645392i
$170$	1.78302	−	0.277818i	0.136752	−	0.0213077i
$171$	−2.35671	−	5.68961i	−0.180222	−	0.435095i
$172$	−1.51405	+	18.0774i	−0.115445	+	1.37839i
$173$	−2.16959	−	0.898673i	−0.164951	−	0.0683248i	0.298680	−	0.954353i	$-0.403454\pi$
$173$	−2.16959	−	0.898673i	−0.164951	−	0.0683248i	−0.463631	+	0.886028i	$0.653454\pi$
$174$	3.70181	−	2.25571i	0.280633	−	0.171005i
$175$			12.1122i			0.915593i
$176$	−11.9120	+	19.0077i	−0.897902	+	1.43276i
$177$			9.69199i			0.728494i
$178$	6.40354	+	10.5087i	0.479966	+	0.787663i
$179$	−2.66481	−	1.10380i	−0.199177	−	0.0825020i	0.280865	−	0.959747i	$-0.409379\pi$
$179$	−2.66481	−	1.10380i	−0.199177	−	0.0825020i	−0.480042	+	0.877245i	$0.659379\pi$
$180$	−1.68288	−	1.99055i	−0.125435	−	0.148367i
$181$	−1.10884	−	2.67697i	−0.0824191	−	0.198977i	0.877298	−	0.479947i	$-0.159344\pi$
$181$	−1.10884	−	2.67697i	−0.0824191	−	0.198977i	−0.959717	+	0.280969i	$0.909344\pi$
$182$	0.850852	+	5.46073i	0.0630693	+	0.404776i
$183$	3.70876	+	3.70876i	0.274159	+	0.274159i
$184$	14.7709	−	1.05067i	1.08893	−	0.0774562i
$185$	8.21296	−	8.21296i	0.603829	−	0.603829i
$186$	−1.76409	−	1.28846i	−0.129349	−	0.0944744i
$187$	5.07256	−	2.10112i	0.370942	−	0.153649i
$188$	2.89362	−	5.60927i	0.211039	−	0.409098i
$189$	−1.40398	+	3.38951i	−0.102125	+	0.246551i
$190$	−2.67748	+	11.0305i	−0.194245	+	0.800236i
$191$	8.35300			0.604402			0.302201	−	0.953244i	$-0.402279\pi$
$191$	8.35300			0.604402			0.302201	+	0.953244i	$0.402279\pi$
$192$	−7.74996	−	1.98448i	−0.559305	−	0.143217i
$193$	−12.3350			−0.887894			−0.443947	−	0.896053i	$-0.646422\pi$
$193$	−12.3350			−0.887894			−0.443947	+	0.896053i	$0.646422\pi$
$194$	4.79877	−	19.7696i	0.344532	−	1.41938i
$195$	0.531259	−	1.28257i	0.0380443	−	0.0918470i
$196$	−5.92324	+	11.4822i	−0.423088	+	0.820155i
$197$	−21.5154	+	8.91197i	−1.53291	+	0.634952i	−0.980126	−	0.198374i	$-0.936434\pi$
$197$	−21.5154	+	8.91197i	−1.53291	+	0.634952i	−0.552782	+	0.833326i	$0.686434\pi$
$198$	−6.40449	−	4.67773i	−0.455147	−	0.332432i
$199$	−17.0334	+	17.0334i	−1.20746	+	1.20746i	−0.235616	+	0.971846i	$0.575711\pi$
$199$	−17.0334	+	17.0334i	−1.20746	+	1.20746i	−0.971846	+	0.235616i	$0.924289\pi$
$200$	−0.662531	−	9.31426i	−0.0468480	−	0.658617i
$201$	−2.11347	−	2.11347i	−0.149073	−	0.149073i
$202$	−2.85622	−	18.3310i	−0.200963	−	1.28977i
$203$	4.30357	+	10.3897i	0.302051	+	0.729217i
$204$	1.26420	+	1.49532i	0.0885116	+	0.104693i
$205$	1.88781	+	0.781958i	0.131851	+	0.0546143i
$206$	10.7253	+	17.6011i	0.747269	+	1.22633i
$207$			5.23550i			0.363892i
$208$	−0.953006	−	4.15276i	−0.0660791	−	0.287942i
$209$			34.5360i			2.38891i
$210$	5.77449	−	3.51871i	0.398478	−	0.242814i
$211$	−8.86549	−	3.67221i	−0.610325	−	0.252805i	0.0560422	−	0.998428i	$-0.482152\pi$
$211$	−8.86549	−	3.67221i	−0.610325	−	0.252805i	−0.666368	+	0.745623i	$0.732152\pi$
$212$	−1.11339	+	13.2936i	−0.0764677	+	0.913005i
$213$	−5.43213	−	13.1143i	−0.372203	−	0.898578i
$214$	−2.10631	+	0.328191i	−0.143984	+	0.0224347i
$215$	8.35897	+	8.35897i	0.570077	+	0.570077i
$216$	0.894259	−	2.68334i	0.0608466	−	0.182578i
$217$	4.00726	−	4.00726i	0.272031	−	0.272031i
$218$	−9.99798	+	13.6887i	−0.677149	+	0.927113i
$219$	10.5976	−	4.38966i	0.716117	−	0.296626i
$220$	4.44730	+	13.9248i	0.299837	+	0.938809i
$221$	−0.399087	+	0.963482i	−0.0268455	+	0.0648108i
$222$	12.2477	+	2.97293i	0.822010	+	0.199530i
$223$	6.90976			0.462712			0.231356	−	0.972869i	$-0.425684\pi$
$223$	6.90976			0.462712			0.231356	+	0.972869i	$0.425684\pi$
$224$	8.18208	−	19.0728i	0.546688	−	1.27436i
$225$	3.30141			0.220094
$226$	−12.9341	−	3.13956i	−0.860365	−	0.208840i
$227$	1.65113	−	3.98617i	0.109589	−	0.264572i	−0.859565	−	0.511026i	$-0.829266\pi$
$227$	1.65113	−	3.98617i	0.109589	−	0.264572i	0.969154	+	0.246454i	$0.0792656\pi$
$228$	−11.7329	+	3.74725i	−0.777031	+	0.248168i
$229$	7.09073	−	2.93708i	0.468568	−	0.194087i	−0.135890	−	0.990724i	$-0.543389\pi$
$229$	7.09073	−	2.93708i	0.468568	−	0.194087i	0.604459	+	0.796636i	$0.293389\pi$
$230$	5.69157	−	7.79258i	0.375291	−	0.513827i
$231$	14.5483	−	14.5483i	0.957209	−	0.957209i
$232$	−3.87777	−	7.75432i	−0.254588	−	0.509096i
$233$	−1.49412	−	1.49412i	−0.0978831	−	0.0978831i	0.656470	−	0.754353i	$-0.272049\pi$
$233$	−1.49412	−	1.49412i	−0.0978831	−	0.0978831i	−0.754353	+	0.656470i	$0.772049\pi$
$234$	1.48843	−	0.231917i	0.0973017	−	0.0151609i
$235$	−1.57397	−	3.79990i	−0.102675	−	0.247878i
$236$	19.3163	+	1.61782i	1.25739	+	0.105311i
$237$	0.143625	+	0.0594914i	0.00932945	+	0.00386438i
$238$	−4.33786	+	2.64329i	−0.281181	+	0.171339i
$239$		−	5.41212i		−	0.350081i	−0.984561	−	0.175041i	$-0.943994\pi$
$239$		−	5.41212i		−	0.350081i	0.984561	−	0.175041i	$-0.0560057\pi$
$240$	−4.24812	+	3.02175i	−0.274215	+	0.195053i
$241$		−	19.6684i		−	1.26695i	−0.773762	−	0.633476i	$-0.781628\pi$
$241$		−	19.6684i		−	1.26695i	0.773762	−	0.633476i	$-0.218372\pi$
$242$	15.0486	+	24.6959i	0.967359	+	1.58752i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	8.01071	−	6.77256i	0.512833	−	0.433569i
$245$	3.22192	+	7.77841i	0.205841	+	0.496944i
$246$	0.341357	+	2.19081i	0.0217641	+	0.139681i
$247$	−4.63846	−	4.63846i	−0.295138	−	0.295138i
$248$	−2.86239	+	3.30079i	−0.181762	+	0.209600i
$249$	3.93293	−	3.93293i	0.249239	−	0.249239i
$250$	−12.3559	−	9.02456i	−0.781457	−	0.570763i
$251$	23.6647	−	9.80223i	1.49370	−	0.618711i	0.521582	−	0.853201i	$-0.325342\pi$
$251$	23.6647	−	9.80223i	1.49370	−	0.618711i	0.972119	+	0.234490i	$0.0753419\pi$
$252$	6.52102	+	3.36396i	0.410786	+	0.211909i
$253$	11.2358	−	27.1256i	0.706387	−	1.70537i
$254$	5.34476	−	22.0189i	0.335360	−	1.38159i
$255$	1.27600			0.0799062
$256$	−5.24875	+	15.1146i	−0.328047	+	0.944661i
$257$	−9.44245			−0.589004			−0.294502	−	0.955651i	$-0.595154\pi$
$257$	−9.44245			−0.589004			−0.294502	+	0.955651i	$0.595154\pi$
$258$	−3.02579	+	12.4654i	−0.188377	+	0.776062i
$259$	−12.5122	+	30.2070i	−0.777468	+	1.87697i
$260$	−2.46752	−	1.27290i	−0.153029	−	0.0789421i
$261$	2.83193	−	1.17302i	0.175292	−	0.0726084i
$262$	−6.52420	−	4.76517i	−0.403067	−	0.294393i
$263$	−8.38788	+	8.38788i	−0.517219	+	0.517219i	−0.916729	−	0.399510i	$-0.869180\pi$
$263$	−8.38788	+	8.38788i	−0.517219	+	0.517219i	0.399510	+	0.916729i	$0.369180\pi$
$264$	−10.3919	+	11.9835i	−0.639576	+	0.737531i
$265$	6.14694	+	6.14694i	0.377603	+	0.377603i
$266$	−4.91925	−	31.5715i	−0.301619	−	1.93577i
$267$	3.32999	+	8.03932i	0.203792	+	0.491998i
$268$	−4.56498	+	3.85941i	−0.278851	+	0.235751i
$269$	0.0655084	+	0.0271345i	0.00399412	+	0.00165442i	0.384680	−	0.923050i	$-0.374312\pi$
$269$	0.0655084	+	0.0271345i	0.00399412	+	0.00165442i	−0.380685	+	0.924705i	$0.624312\pi$
$270$	−0.959094	−	1.57395i	−0.0583686	−	0.0957876i
$271$		−	14.4877i		−	0.880062i	−0.897982	−	0.440031i	$-0.854967\pi$
$271$		−	14.4877i		−	0.880062i	0.897982	−	0.440031i	$-0.145033\pi$
$272$	3.19123	−	2.26997i	0.193497	−	0.137637i
$273$			3.90791i			0.236517i
$274$	−14.7489	+	8.98733i	−0.891017	+	0.542945i
$275$	−17.1049	−	7.08507i	−1.03146	−	0.427246i
$276$	10.4345	+	0.873927i	0.628081	+	0.0526042i
$277$	8.16981	+	19.7237i	0.490876	+	1.18508i	0.954275	+	0.298931i	$0.0966299\pi$
$277$	8.16981	+	19.7237i	0.490876	+	1.18508i	−0.463398	+	0.886150i	$0.653370\pi$
$278$	−14.8019	+	2.30632i	−0.887758	+	0.138324i
$279$	−1.09226	−	1.09226i	−0.0653919	−	0.0653919i
$280$	−6.04897	−	12.0960i	−0.361495	−	0.722876i
$281$	2.76272	−	2.76272i	0.164810	−	0.164810i	−0.619884	−	0.784694i	$-0.712820\pi$
$281$	2.76272	−	2.76272i	0.164810	−	0.164810i	0.784694	+	0.619884i	$0.212820\pi$
$282$	2.63234	−	3.60406i	0.156754	−	0.214618i
$283$	−5.86879	+	2.43093i	−0.348864	+	0.144504i	−0.550233	−	0.835011i	$-0.685461\pi$
$283$	−5.86879	+	2.43093i	−0.348864	+	0.144504i	0.201369	+	0.979515i	$0.435461\pi$
$284$	−27.0439	+	8.63726i	−1.60476	+	0.512527i
$285$	−3.07151	+	7.41527i	−0.181940	+	0.439243i
$286$	−8.20940	−	1.99270i	−0.485432	−	0.117831i
$287$	−5.75203			−0.339532
$288$	−5.19868	−	2.23019i	−0.306335	−	0.131415i
$289$	16.0415			0.943615
$290$	−5.49029	−	1.33268i	−0.322401	−	0.0782578i
$291$	5.50497	−	13.2902i	0.322707	−	0.779083i
$292$	−6.97970	−	21.8539i	−0.408456	−	1.27890i
$293$	4.51526	−	1.87028i	0.263784	−	0.109263i	−0.246872	−	0.969048i	$-0.579403\pi$
$293$	4.51526	−	1.87028i	0.263784	−	0.109263i	0.510656	+	0.859785i	$0.329403\pi$
$294$	−5.38841	+	7.37750i	−0.314258	+	0.430265i
$295$	8.93187	−	8.93187i	0.520034	−	0.520034i
$296$	7.96955	−	23.9136i	0.463221	−	1.38995i
$297$	−3.96543	−	3.96543i	−0.230098	−	0.230098i
$298$	4.03658	−	0.628952i	0.233833	−	0.0364342i
$299$	2.13412	+	5.15223i	0.123420	+	0.297961i
$300$	0.551082	−	6.57978i	0.0318167	−	0.379884i
$301$	−30.7440	−	12.7346i	−1.77206	−	0.734009i
$302$	10.9389	−	6.66564i	0.629461	−	0.383564i
$303$		−	13.1184i		−	0.753633i
$304$	5.50986	+	24.0094i	0.316012	+	1.37704i
$305$		−	6.83578i		−	0.391416i
$306$	0.720481	+	1.18237i	0.0411872	+	0.0675915i
$307$	8.44200	+	3.49679i	0.481810	+	0.199572i	0.610350	−	0.792132i	$-0.291029\pi$
$307$	8.44200	+	3.49679i	0.481810	+	0.199572i	−0.128539	+	0.991704i	$0.541029\pi$
$308$	−26.5667	−	31.4236i	−1.51378	−	1.79052i
$309$	5.57742	+	13.4651i	0.317288	+	0.766002i
$310$	0.438324	+	2.81314i	0.0248951	+	0.159776i
$311$	20.8439	+	20.8439i	1.18195	+	1.18195i	0.979239	+	0.202710i	$0.0649748\pi$
$311$	20.8439	+	20.8439i	1.18195	+	1.18195i	0.202710	+	0.979239i	$0.435025\pi$
$312$	−0.213761	−	3.00519i	−0.0121019	−	0.170135i
$313$	14.1026	−	14.1026i	0.797124	−	0.797124i	−0.185517	−	0.982641i	$-0.559396\pi$
$313$	14.1026	−	14.1026i	0.797124	−	0.797124i	0.982641	+	0.185517i	$0.0593959\pi$
$314$	8.52678	+	6.22782i	0.481194	+	0.351456i
$315$	4.41756	−	1.82981i	0.248901	−	0.103098i
$316$	0.142542	−	0.276317i	0.00801862	−	0.0155441i
$317$	1.07307	−	2.59063i	0.0602698	−	0.145504i	−0.890876	−	0.454247i	$-0.849908\pi$
$317$	1.07307	−	2.59063i	0.0602698	−	0.145504i	0.951145	+	0.308743i	$0.0999083\pi$
$318$	−2.22507	+	9.16669i	−0.124776	+	0.514042i
$319$	−17.1899			−0.962448
$320$	5.31331	+	8.97099i	0.297023	+	0.501494i
$321$	−1.50736			−0.0841325
$322$	−6.40759	+	26.3975i	−0.357081	+	1.47108i
$323$	2.30735	−	5.57043i	0.128384	−	0.309947i
$324$	0.916914	−	1.77743i	0.0509396	−	0.0987463i
$325$	3.24890	−	1.34574i	0.180217	−	0.0746482i
$326$	−2.86007	−	2.08895i	−0.158405	−	0.115696i
$327$	−8.47554	+	8.47554i	−0.468698	+	0.468698i
$328$	4.42332	−	0.314634i	0.244237	−	0.0173728i
$329$	8.18691	+	8.18691i	0.451359	+	0.451359i
$330$	1.59133	+	10.2131i	0.0875998	+	0.562211i
$331$	−1.37795	−	3.32667i	−0.0757390	−	0.182850i	0.881475	−	0.472230i	$-0.156551\pi$
$331$	−1.37795	−	3.32667i	−0.0757390	−	0.182850i	−0.957214	+	0.289380i	$0.906551\pi$
$332$	−7.18192	−	8.49492i	−0.394159	−	0.466219i
$333$	8.23352	+	3.41044i	0.451194	+	0.186891i
$334$	−3.75590	−	6.16374i	−0.205514	−	0.337265i
$335$			3.89544i			0.212830i
$336$	7.79295	−	12.4350i	0.425140	−	0.678385i
$337$			0.473748i			0.0258067i	0.999917	+	0.0129034i	$0.00410738\pi$
$337$			0.473748i			0.0258067i	−0.999917	+	0.0129034i	$0.995893\pi$
$338$	−14.3294	+	8.73170i	−0.779418	+	0.474942i
$339$	−8.69499	−	3.60158i	−0.472247	−	0.195611i
$340$	0.212994	−	2.54310i	0.0115512	−	0.137919i
$341$	3.31502	+	8.00317i	0.179518	+	0.433396i
$342$	−8.60544	+	1.34084i	−0.465329	+	0.0725043i
$343$	1.40095	+	1.40095i	0.0756440	+	0.0756440i
$344$	24.3388	+	8.11122i	1.31226	+	0.437328i
$345$	4.82489	−	4.82489i	0.259763	−	0.259763i
$346$	−1.95881	+	2.68189i	−0.105306	+	0.144179i
$347$	−9.36785	+	3.88029i	−0.502893	+	0.208305i	−0.619684	−	0.784852i	$-0.712739\pi$
$347$	−9.36785	+	3.88029i	−0.502893	+	0.208305i	0.116791	+	0.993156i	$0.462739\pi$
$348$	−1.86515	−	5.83990i	−0.0999824	−	0.313052i
$349$	−2.04231	+	4.93057i	−0.109322	+	0.263928i	−0.969068	−	0.246796i	$-0.920622\pi$
$349$	−2.04231	+	4.93057i	−0.109322	+	0.263928i	0.859745	+	0.510723i	$0.170622\pi$
$350$	16.6458	+	4.04051i	0.889755	+	0.215974i
$351$	1.06518			0.0568550
$352$	22.1486	+	22.7116i	1.18053	+	1.21053i
$353$	34.7185			1.84788			0.923939	−	0.382539i	$-0.124950\pi$
$353$	34.7185			1.84788			0.923939	+	0.382539i	$0.124950\pi$
$354$	13.3198	+	3.23316i	0.707937	+	0.171841i
$355$	−7.07969	+	17.0919i	−0.375751	+	0.907144i
$356$	16.5784	−	5.29480i	0.878653	−	0.280624i
$357$	−3.31851	+	1.37457i	−0.175634	+	0.0727502i
$358$	−2.40592	+	3.29405i	−0.127157	+	0.174096i
$359$	−4.06394	+	4.06394i	−0.214486	+	0.214486i	−0.806170	−	0.591684i	$-0.798463\pi$
$359$	−4.06394	+	4.06394i	−0.214486	+	0.214486i	0.591684	+	0.806170i	$0.298463\pi$
$360$	−3.29702	+	1.64877i	−0.173768	+	0.0868976i
$361$	13.3825	+	13.3825i	0.704343	+	0.704343i
$362$	−4.04887	+	0.630867i	−0.212804	+	0.0331576i
$363$	7.82561	+	18.8927i	0.410738	+	0.991610i
$364$	7.78855	+	0.652321i	0.408231	+	0.0341909i
$365$	−13.8118	−	5.72104i	−0.722944	−	0.299453i
$366$	6.33418	−	3.85976i	0.331093	−	0.201753i
$367$		−	30.2747i		−	1.58033i	−0.612896	−	0.790164i	$-0.709996\pi$
$367$		−	30.2747i		−	1.58033i	0.612896	−	0.790164i	$-0.290004\pi$
$368$	3.48351	−	20.6502i	0.181591	−	1.07647i
$369$			1.56783i			0.0816180i
$370$	−8.54735	−	14.0269i	−0.444356	−	0.729224i
$371$	−22.6082	−	9.36463i	−1.17376	−	0.486188i
$372$	−2.35922	+	1.99457i	−0.122320	+	0.103414i
$373$	8.46231	+	20.4298i	0.438162	+	1.05782i	0.976583	+	0.215141i	$0.0690210\pi$
$373$	8.46231	+	20.4298i	0.438162	+	1.05782i	−0.538421	+	0.842676i	$0.680979\pi$
$374$	−1.19542	−	7.67217i	−0.0618139	−	0.396718i
$375$	−7.65035	−	7.65035i	−0.395062	−	0.395062i
$376$	−6.74356	−	5.84792i	−0.347773	−	0.301583i
$377$	2.30874	−	2.30874i	0.118906	−	0.118906i
$378$	4.18987	+	3.06021i	0.215504	+	0.157400i
$379$	21.3128	−	8.82807i	1.09477	−	0.453467i	0.239100	−	0.970995i	$-0.423147\pi$
$379$	21.3128	−	8.82807i	1.09477	−	0.453467i	0.855667	+	0.517527i	$0.173147\pi$
$380$	14.2661	+	7.35936i	0.731835	+	0.377527i
$381$	6.13130	−	14.8023i	0.314116	−	0.758343i
$382$	2.78649	−	11.4796i	0.142569	−	0.587346i
$383$	−25.5734			−1.30674			−0.653370	−	0.757039i	$-0.726645\pi$
$383$	−25.5734			−1.30674			−0.653370	+	0.757039i	$0.726645\pi$
$384$	−5.31260	+	9.98881i	−0.271107	+	0.509739i
$385$	−26.8147			−1.36660
$386$	−4.11486	+	16.9521i	−0.209441	+	0.862839i
$387$	−3.47106	+	8.37989i	−0.176444	+	0.425974i
$388$	−25.5687	−	13.1900i	−1.29805	−	0.669619i
$389$	−1.19642	+	0.495572i	−0.0606608	+	0.0251265i	−0.412808	−	0.910818i	$-0.635452\pi$
$389$	−1.19642	+	0.495572i	−0.0606608	+	0.0251265i	0.352147	+	0.935945i	$0.385452\pi$
$390$	−1.58542	−	1.15797i	−0.0802811	−	0.0586360i
$391$	−3.62451	+	3.62451i	−0.183299	+	0.183299i
$392$	13.8041	+	11.9707i	0.697211	+	0.604611i
$393$	−4.03956	−	4.03956i	−0.203769	−	0.203769i
$394$	5.07042	+	32.5417i	0.255444	+	1.63943i
$395$	−0.0775352	−	0.187187i	−0.00390122	−	0.00941838i
$396$	−8.56512	+	7.24127i	−0.430413	+	0.363888i
$397$	5.47211	+	2.26662i	0.274637	+	0.113758i	0.515751	−	0.856738i	$-0.327513\pi$
$397$	5.47211	+	2.26662i	0.274637	+	0.113758i	−0.241114	+	0.970497i	$0.577513\pi$
$398$	17.7269	+	29.0912i	0.888567	+	1.45821i
$399$		−	22.5938i		−	1.13110i
$400$	−13.0217	−	2.19664i	−0.651083	−	0.109832i
$401$			33.2794i			1.66189i	0.556352	+	0.830947i	$0.312201\pi$
$401$			33.2794i			1.66189i	−0.556352	+	0.830947i	$0.687799\pi$
$402$	−3.60959	+	2.19952i	−0.180030	+	0.109702i
$403$	−1.52012	−	0.629655i	−0.0757227	−	0.0313654i
$404$	−26.1453	−	2.18977i	−1.30078	−	0.108945i
$405$	−0.498752	−	1.20409i	−0.0247832	−	0.0598318i
$406$	15.7143	−	2.44849i	0.779888	−	0.121517i
$407$	−35.3395	−	35.3395i	−1.75172	−	1.75172i
$408$	2.47675	−	1.23857i	0.122618	−	0.0613184i
$409$	7.40530	−	7.40530i	0.366168	−	0.366168i	−0.499909	−	0.866078i	$-0.666633\pi$
$409$	7.40530	−	7.40530i	0.366168	−	0.366168i	0.866078	+	0.499909i	$0.166633\pi$
$410$	1.70441	−	2.33358i	0.0841747	−	0.115247i
$411$	−11.2831	+	4.67363i	−0.556556	+	0.230533i
$412$	27.7672	−	8.86829i	1.36799	−	0.436909i
$413$	−13.6074	+	32.8511i	−0.669575	+	1.61650i
$414$	7.19517	+	1.74652i	0.353623	+	0.0858366i
$415$	−7.24896			−0.355838
$416$	−6.02508	−	0.0756046i	−0.295404	−	0.00370682i
$417$	−10.5928			−0.518732
$418$	47.4631	+	11.5209i	2.32150	+	0.563507i
$419$	−6.43037	+	15.5243i	−0.314144	+	0.758411i	0.685399	+	0.728168i	$0.259628\pi$
$419$	−6.43037	+	15.5243i	−0.314144	+	0.758411i	−0.999543	+	0.0302425i	$0.990372\pi$
$420$	−2.90946	−	9.10972i	−0.141967	−	0.444509i
$421$	5.60807	−	2.32294i	0.273321	−	0.113213i	−0.241813	−	0.970323i	$-0.577742\pi$
$421$	5.60807	−	2.32294i	0.273321	−	0.113213i	0.515134	+	0.857110i	$0.327742\pi$
$422$	−8.00419	+	10.9589i	−0.389638	+	0.533470i
$423$	2.23150	−	2.23150i	0.108499	−	0.108499i
$424$	17.8980	+	5.96475i	0.869204	+	0.289674i
$425$	2.28555	+	2.28555i	0.110865	+	0.110865i
$426$	−19.8352	+	3.09058i	−0.961018	+	0.149739i
$427$	7.36385	+	17.7779i	0.356362	+	0.860334i
$428$	−0.251613	+	3.00420i	−0.0121622	+	0.145213i
$429$	−5.51878	−	2.28595i	−0.266449	−	0.110367i
$430$	14.2763	−	8.69930i	0.688462	−	0.419517i
$431$		−	0.297166i		−	0.0143140i	−0.999974	−	0.00715698i	$-0.997722\pi$
$431$		−	0.297166i		−	0.0143140i	0.999974	−	0.00715698i	$-0.00227816\pi$
$432$	−3.38941	−	2.12412i	−0.163073	−	0.102197i
$433$			15.4119i			0.740649i	0.928902	+	0.370325i	$0.120754\pi$
$433$			15.4119i			0.740649i	−0.928902	+	0.370325i	$0.879246\pi$
$434$	−4.17042	−	6.84400i	−0.200186	−	0.328522i
$435$	−3.69086	−	1.52880i	−0.176963	−	0.0733005i
$436$	15.4772	+	18.3067i	0.741222	+	0.876732i
$437$	−12.3386	−	29.7879i	−0.590233	−	1.42495i
$438$	−2.49747	−	16.0287i	−0.119334	−	0.765879i
$439$	−3.15252	−	3.15252i	−0.150462	−	0.150462i	0.627863	−	0.778324i	$-0.283930\pi$
$439$	−3.15252	−	3.15252i	−0.150462	−	0.150462i	−0.778324	+	0.627863i	$0.783930\pi$
$440$	20.6205	−	1.46675i	0.983044	−	0.0699247i
$441$	−4.56789	+	4.56789i	−0.217519	+	0.217519i
$442$	1.19099	+	0.869878i	0.0566495	+	0.0413759i
$443$	2.80647	−	1.16248i	0.133339	−	0.0552310i	−0.315016	−	0.949086i	$-0.602010\pi$
$443$	2.80647	−	1.16248i	0.133339	−	0.0552310i	0.448355	+	0.893855i	$0.352010\pi$
$444$	8.17144	−	15.8403i	0.387800	−	0.751748i
$445$	4.33998	−	10.4776i	0.205735	−	0.496688i
$446$	2.30504	−	9.49612i	0.109147	−	0.449654i
$447$	2.88874			0.136632
$448$	−23.4824	−	17.6072i	−1.10944	−	0.831863i
$449$	−3.57715			−0.168816			−0.0844080	−	0.996431i	$-0.526900\pi$
$449$	−3.57715			−0.168816			−0.0844080	+	0.996431i	$0.526900\pi$
$450$	1.10132	−	4.53714i	0.0519168	−	0.213883i
$451$	3.36469	−	8.12307i	0.158437	−	0.382500i
$452$	−8.62943	+	16.7281i	−0.405894	+	0.786825i
$453$	8.36836	−	3.46629i	0.393180	−	0.162860i
$454$	−4.92742	−	3.59891i	−0.231255	−	0.168905i
$455$	3.60142	−	3.60142i	0.168837	−	0.168837i
$456$	1.23587	+	17.3747i	0.0578751	+	0.813643i
$457$	−8.97857	−	8.97857i	−0.420000	−	0.420000i	0.465204	−	0.885204i	$-0.345981\pi$
$457$	−8.97857	−	8.97857i	−0.420000	−	0.420000i	−0.885204	+	0.465204i	$0.845981\pi$
$458$	−1.67103	−	10.7246i	−0.0780823	−	0.501128i
$459$	0.374667	+	0.904527i	0.0174880	+	0.0422197i
$460$	−8.81073	−	10.4215i	−0.410802	−	0.485905i
$461$	−26.0500	−	10.7903i	−1.21327	−	0.502553i	−0.318006	−	0.948089i	$-0.603013\pi$
$461$	−26.0500	−	10.7903i	−1.21327	−	0.502553i	−0.895264	+	0.445536i	$0.853013\pi$
$462$	−15.1406	−	24.8470i	−0.704406	−	1.15599i
$463$		−	10.9782i		−	0.510199i	−0.966915	−	0.255100i	$-0.917892\pi$
$463$		−	10.9782i		−	0.510199i	0.966915	−	0.255100i	$-0.0821083\pi$
$464$	−11.9504	+	2.74246i	−0.554783	+	0.127316i
$465$			2.01319i			0.0933596i
$466$	−2.55180	+	1.55495i	−0.118210	+	0.0720318i
$467$	38.5388	+	15.9633i	1.78336	+	0.738694i	0.991829	+	0.127571i	$0.0407180\pi$
$467$	38.5388	+	15.9633i	1.78336	+	0.738694i	0.791535	+	0.611123i	$0.209282\pi$
$468$	0.177803	−	2.12292i	0.00821895	−	0.0981322i
$469$	−4.19636	−	10.1309i	−0.193770	−	0.467802i
$470$	−5.74730	+	0.895503i	−0.265103	+	0.0413065i
$471$	5.27948	+	5.27948i	0.243266	+	0.243266i
$472$	8.66714	−	26.0069i	0.398938	−	1.19706i
$473$	35.9678	−	35.9678i	1.65380	−	1.65380i
$474$	0.129672	−	0.177539i	0.00595601	−	0.00815463i
$475$	−18.7837	+	7.78047i	−0.861856	+	0.356992i
$476$	2.18562	+	6.84332i	0.100178	+	0.313663i
$477$	−2.55252	+	6.16232i	−0.116872	+	0.282153i
$478$	−7.43791	−	1.80544i	−0.340202	−	0.0825788i
$479$	20.8426			0.952324			0.476162	−	0.879357i	$-0.342027\pi$
$479$	20.8426			0.952324			0.476162	+	0.879357i	$0.342027\pi$
$480$	2.73568	+	6.84624i	0.124866	+	0.312487i
$481$	9.49276			0.432833
$482$	−27.0304	−	6.56121i	−1.23120	−	0.298855i
$483$	−7.35055	+	17.7458i	−0.334461	+	0.807461i
$484$	38.9599	−	12.4430i	1.77090	−	0.565590i
$485$	−17.3211	+	7.17462i	−0.786510	+	0.325783i
$486$	0.834122	−	1.14203i	0.0378366	−	0.0518037i
$487$	−16.3086	+	16.3086i	−0.739014	+	0.739014i	−0.972387	−	0.233373i	$-0.925024\pi$
$487$	−16.3086	+	16.3086i	−0.739014	+	0.739014i	0.233373	+	0.972387i	$0.425024\pi$
$488$	−6.63526	−	13.2684i	−0.300364	−	0.600634i
$489$	−1.77085	−	1.77085i	−0.0800808	−	0.0800808i
$490$	11.7647	−	1.83310i	0.531476	−	0.0828108i
$491$	−2.22643	−	5.37508i	−0.100477	−	0.242574i	0.865645	−	0.500658i	$-0.166909\pi$
$491$	−2.22643	−	5.37508i	−0.100477	−	0.242574i	−0.966122	+	0.258084i	$0.916909\pi$
$492$	3.12472	+	0.261708i	0.140873	+	0.0117987i
$493$	2.77261	+	1.14845i	0.124872	+	0.0517237i
$494$	−7.92202	+	4.82732i	−0.356429	+	0.217191i
$495$			7.30887i			0.328509i
$496$	3.58142	+	5.03492i	0.160811	+	0.226075i
$497$		−	52.0778i		−	2.33601i
$498$	−4.09306	−	6.71704i	−0.183414	−	0.300998i
$499$	9.39859	+	3.89302i	0.420739	+	0.174276i	0.583000	−	0.812472i	$-0.301879\pi$
$499$	9.39859	+	3.89302i	0.420739	+	0.174276i	−0.162261	+	0.986748i	$0.551879\pi$
$500$	−16.5243	+	13.9703i	−0.738991	+	0.624771i
$501$	−1.95316	−	4.71534i	−0.0872606	−	0.210666i
$502$	−5.57693	−	35.7924i	−0.248910	−	1.59749i
$503$	21.5760	+	21.5760i	0.962027	+	0.962027i	0.999305	−	0.0372777i	$-0.0118686\pi$
$503$	21.5760	+	21.5760i	0.962027	+	0.962027i	−0.0372777	+	0.999305i	$0.511869\pi$
$504$	6.79846	−	7.83969i	0.302828	−	0.349207i
$505$	−12.0896	+	12.0896i	−0.537979	+	0.537979i
$506$	−33.5307	−	24.4903i	−1.49062	−	1.08872i
$507$	−10.9622	+	4.54069i	−0.486848	+	0.201659i
$508$	−28.4778	−	14.6907i	−1.26350	−	0.651793i
$509$	1.30560	−	3.15200i	0.0578697	−	0.139710i	−0.892300	−	0.451443i	$-0.850909\pi$
$509$	1.30560	−	3.15200i	0.0578697	−	0.139710i	0.950170	+	0.311733i	$0.100909\pi$
$510$	0.425663	−	1.75361i	0.0188487	−	0.0776514i
$511$	42.0836			1.86167
$512$	19.0211	+	12.2555i	0.840623	+	0.541621i
$513$	−6.15839			−0.271899
$514$	−3.14992	+	12.9768i	−0.138937	+	0.572383i
$515$	7.26906	−	17.5491i	0.320313	−	0.773304i
$516$	16.1219	+	8.31671i	0.709727	+	0.366123i
$517$	−16.3506	+	6.77264i	−0.719099	+	0.297860i
$518$	37.3397	+	27.2723i	1.64061	+	1.19828i
$519$	−1.66053	+	1.66053i	−0.0728892	+	0.0728892i
$520$	−2.57250	+	2.96649i	−0.112812	+	0.130089i
$521$	7.58009	+	7.58009i	0.332090	+	0.332090i	0.853380	−	0.521290i	$-0.174549\pi$
$521$	7.58009	+	7.58009i	0.332090	+	0.332090i	−0.521290	+	0.853380i	$0.674549\pi$
$522$	−0.667386	−	4.28325i	−0.0292107	−	0.187473i
$523$	−5.67736	−	13.7064i	−0.248254	−	0.599337i	0.749802	−	0.661662i	$-0.230149\pi$
$523$	−5.67736	−	13.7064i	−0.248254	−	0.599337i	−0.998056	+	0.0623246i	$0.980149\pi$
$524$	−8.72522	+	7.37663i	−0.381163	+	0.322250i
$525$	11.1902	+	4.63512i	0.488379	+	0.202293i
$526$	8.72939	+	14.3256i	0.380619	+	0.624628i
$527$		−	1.51233i		−	0.0658782i
$528$	13.0023	+	18.2792i	0.565852	+	0.795500i
$529$			4.41042i			0.191758i
$530$	10.4983	−	6.39720i	0.456019	−	0.277877i
$531$	8.95423	+	3.70896i	0.388580	+	0.160955i
$532$	−45.0299	−	3.77143i	−1.95229	−	0.163512i
$533$	0.639089	+	1.54290i	0.0276820	+	0.0668303i
$534$	12.1593	−	1.89458i	0.526186	−	0.0819866i
$535$	1.38914	+	1.38914i	0.0600578	+	0.0600578i
$536$	3.78117	+	7.56115i	0.163322	+	0.326592i
$537$	−2.03956	+	2.03956i	−0.0880135	+	0.0880135i
$538$	0.0591441	−	0.0809768i	0.00254988	−	0.00349116i
$539$	33.4697	−	13.8636i	1.44164	−	0.597148i
$540$	−2.48304	+	0.793032i	−0.106853	+	0.0341266i
$541$	−14.0508	+	33.9216i	−0.604090	+	1.45840i	0.265247	+	0.964181i	$0.414547\pi$
$541$	−14.0508	+	33.9216i	−0.604090	+	1.45840i	−0.869336	+	0.494221i	$0.835453\pi$
$542$	−19.9105	−	4.83296i	−0.855228	−	0.207593i
$543$	−2.89753			−0.124345
$544$	−2.05507	−	5.14297i	−0.0881104	−	0.220503i
$545$	15.6217			0.669158
$546$	5.37066	+	1.30364i	0.229843	+	0.0557908i
$547$	7.85438	−	18.9622i	0.335829	−	0.810763i	−0.662278	−	0.749258i	$-0.730410\pi$
$547$	7.85438	−	18.9622i	0.335829	−	0.810763i	0.998107	−	0.0615046i	$-0.0195899\pi$
$548$	7.43122	+	23.2677i	0.317446	+	0.993945i
$549$	4.84573	−	2.00717i	0.206811	−	0.0856637i
$550$	−15.4431	+	21.1438i	−0.658496	+	0.901576i
$551$	−13.3481	+	13.3481i	−0.568648	+	0.568648i
$552$	4.68189	−	14.0486i	0.199274	−	0.597948i
$553$	0.403294	+	0.403294i	0.0171498	+	0.0171498i
$554$	29.8317	−	4.64817i	1.26743	−	0.197482i
$555$	−4.44482	−	10.7308i	−0.188672	−	0.455495i
$556$	−1.76819	+	21.1117i	−0.0749878	+	0.895335i
$557$	−20.1683	−	8.35400i	−0.854560	−	0.353970i	−0.0879825	−	0.996122i	$-0.528042\pi$
$557$	−20.1683	−	8.35400i	−0.854560	−	0.353970i	−0.766578	+	0.642152i	$0.778042\pi$
$558$	−1.86547	+	1.13673i	−0.0789715	+	0.0481216i
$559$			9.66152i			0.408639i
$560$	−18.6415	+	4.27799i	−0.787749	+	0.180778i
$561$		−	5.49050i		−	0.231809i
$562$	−2.87520	−	4.71843i	−0.121283	−	0.199035i
$563$	−21.3521	−	8.84433i	−0.899884	−	0.372744i	−0.115708	−	0.993283i	$-0.536914\pi$
$563$	−21.3521	−	8.84433i	−0.899884	−	0.372744i	−0.784175	+	0.620539i	$0.786914\pi$
$564$	−4.07495	−	4.81993i	−0.171586	−	0.202956i
$565$	4.69395	+	11.3322i	0.197476	+	0.476749i
$566$	1.38307	+	8.87646i	0.0581346	+	0.373105i
$567$	2.59422	+	2.59422i	0.108947	+	0.108947i
$568$	2.84864	+	40.0479i	0.119526	+	1.68037i
$569$	−7.60582	+	7.60582i	−0.318853	+	0.318853i	−0.848326	−	0.529474i	$-0.822389\pi$
$569$	−7.60582	+	7.60582i	−0.318853	+	0.318853i	0.529474	+	0.848326i	$0.322389\pi$
$570$	9.16622	+	6.69486i	0.383931	+	0.280417i
$571$	0.616329	−	0.255292i	0.0257926	−	0.0106836i	−0.369750	−	0.929131i	$-0.620557\pi$
$571$	0.616329	−	0.255292i	0.0257926	−	0.0106836i	0.395542	+	0.918448i	$0.370557\pi$
$572$	−5.47717	+	10.6175i	−0.229012	+	0.443939i
$573$	3.19656	−	7.71717i	0.133538	−	0.322389i
$574$	−1.91883	+	7.90505i	−0.0800904	+	0.329950i
$575$	17.2845			0.720814
$576$	−4.79920	+	6.40060i	−0.199967	+	0.266692i
$577$	−8.78481			−0.365716			−0.182858	−	0.983139i	$-0.558535\pi$
$577$	−8.78481			−0.365716			−0.182858	+	0.983139i	$0.558535\pi$
$578$	5.35129	−	22.0459i	0.222584	−	0.916987i
$579$	−4.72041	+	11.3961i	−0.196173	+	0.473605i
$580$	−3.66303	+	7.10076i	−0.152099	+	0.294843i
$581$	18.8525	−	7.80896i	0.782133	−	0.323970i
$582$	−16.4283	−	11.9990i	−0.680977	−	0.497374i
$583$	26.4496	−	26.4496i	1.09543	−	1.09543i
$584$	−32.3623	+	2.30196i	−1.33916	+	0.0952558i
$585$	−0.981639	−	0.981639i	−0.0405858	−	0.0405858i
$586$	−1.06409	−	6.82925i	−0.0439570	−	0.282114i
$587$	−10.5345	−	25.4324i	−0.434803	−	1.04971i	−0.977718	−	0.209921i	$-0.932679\pi$
$587$	−10.5345	−	25.4324i	−0.434803	−	1.04971i	0.542915	−	0.839788i	$-0.317321\pi$
$588$	8.34142	+	9.86640i	0.343994	+	0.406883i
$589$	8.78867	+	3.64039i	0.362131	+	0.150000i
$590$	−9.29552	−	15.2547i	−0.382691	−	0.628027i
$591$			23.2881i			0.957944i
$592$	−30.2061	−	18.9300i	−1.24146	−	0.778018i
$593$		−	12.6478i		−	0.519384i	−0.965691	−	0.259692i	$-0.916379\pi$
$593$		−	12.6478i		−	0.519384i	0.965691	−	0.259692i	$-0.0836211\pi$
$594$	−6.77255	+	4.12688i	−0.277881	+	0.169328i
$595$	4.32502	+	1.79148i	0.177309	+	0.0734436i
$596$	0.482197	−	5.75731i	0.0197516	−	0.235829i
$597$	9.21839	+	22.2552i	0.377283	+	0.910843i
$598$	7.79267	−	1.21420i	0.318666	−	0.0496523i
$599$	10.2749	+	10.2749i	0.419820	+	0.419820i	0.885142	−	0.465322i	$-0.154061\pi$
$599$	10.2749	+	10.2749i	0.419820	+	0.419820i	−0.465322	+	0.885142i	$0.654061\pi$
$600$	−8.85879	−	2.95231i	−0.361659	−	0.120528i
$601$	−34.4571	+	34.4571i	−1.40554	+	1.40554i	−0.624552	+	0.780983i	$0.714719\pi$
$601$	−34.4571	+	34.4571i	−1.40554	+	1.40554i	−0.780983	+	0.624552i	$0.785281\pi$
$602$	−27.7572	+	38.0035i	−1.13130	+	1.54891i
$603$	−2.76138	+	1.14380i	−0.112452	+	0.0465792i
$604$	−5.51152	−	17.2569i	−0.224260	−	0.702175i
$605$	10.1991	−	24.6229i	0.414653	−	1.00106i
$606$	−18.0287	−	4.37619i	−0.732366	−	0.177771i
$607$	5.97427			0.242488			0.121244	−	0.992623i	$-0.461312\pi$
$607$	5.97427			0.242488			0.121244	+	0.992623i	$0.461312\pi$
$608$	34.8344	+	0.437112i	1.41272	+	0.0177272i
$609$	11.2458			0.455702
$610$	−9.39445	−	2.28036i	−0.380370	−	0.0923290i
$611$	1.28640	−	3.10563i	0.0520420	−	0.125641i
$612$	1.86528	−	0.595734i	0.0753996	−	0.0240811i
$613$	1.37874	−	0.571093i	0.0556868	−	0.0230662i	−0.354666	−	0.934993i	$-0.615405\pi$
$613$	1.37874	−	0.571093i	0.0556868	−	0.0230662i	0.410353	+	0.911927i	$0.365405\pi$
$614$	7.62184	−	10.4354i	0.307592	−	0.421138i
$615$	1.44487	−	1.44487i	0.0582628	−	0.0582628i
$616$	−52.0480	+	26.0281i	−2.09707	+	1.04870i
$617$	20.4851	+	20.4851i	0.824698	+	0.824698i	0.986778	−	0.162080i	$-0.0518203\pi$
$617$	20.4851	+	20.4851i	0.824698	+	0.824698i	−0.162080	+	0.986778i	$0.551820\pi$
$618$	20.3657	−	3.17324i	0.819230	−	0.127647i
$619$	13.2969	+	32.1015i	0.534447	+	1.29027i	0.928552	+	0.371203i	$0.121055\pi$
$619$	13.2969	+	32.1015i	0.534447	+	1.29027i	−0.394105	+	0.919065i	$0.628945\pi$
$620$	4.01234	+	0.336049i	0.161139	+	0.0134961i
$621$	4.83697	+	2.00354i	0.194101	+	0.0803992i
$622$	35.5992	−	21.6925i	1.42740	−	0.869792i
$623$			31.9246i			1.27903i
$624$	−4.20135	−	0.708731i	−0.168189	−	0.0283719i
$625$		−	2.40633i		−	0.0962532i
$626$	−14.6767	−	24.0857i	−0.586601	−	0.962660i
$627$	31.9071	+	13.2164i	1.27425	+	0.527811i
$628$	11.4034	−	9.64086i	0.455045	−	0.384712i
$629$	3.33900	+	8.06106i	0.133135	+	0.321415i
$630$	−1.04106	−	6.68148i	−0.0414769	−	0.266197i
$631$	2.04327	+	2.04327i	0.0813412	+	0.0813412i	0.746607	−	0.665266i	$-0.231682\pi$
$631$	2.04327	+	2.04327i	0.0813412	+	0.0813412i	−0.665266	+	0.746607i	$0.731682\pi$
$632$	−0.332194	−	0.288074i	−0.0132140	−	0.0114590i
$633$	−6.78535	+	6.78535i	−0.269694	+	0.269694i
$634$	−3.20235	−	2.33894i	−0.127181	−	0.0928912i
$635$	−19.2918	+	7.99093i	−0.765572	+	0.317110i
$636$	11.8556	+	6.11586i	0.470104	+	0.242510i
$637$	−2.63325	+	6.35724i	−0.104333	+	0.251883i
$638$	−5.73440	+	23.6242i	−0.227027	+	0.935289i
$639$	−14.1948			−0.561539
$640$	14.1014	−	4.30947i	0.557405	−	0.170347i
$641$	−20.3790			−0.804922			−0.402461	−	0.915437i	$-0.631845\pi$
$641$	−20.3790			−0.804922			−0.402461	+	0.915437i	$0.631845\pi$
$642$	−0.502842	+	2.07157i	−0.0198456	+	0.0817584i
$643$	4.75816	−	11.4872i	0.187644	−	0.453012i	−0.801861	−	0.597510i	$-0.796157\pi$
$643$	4.75816	−	11.4872i	0.187644	−	0.453012i	0.989505	+	0.144498i	$0.0461568\pi$
$644$	34.1408	+	17.6120i	1.34533	+	0.694010i
$645$	10.9215	−	4.52384i	0.430034	−	0.178126i
$646$	−6.88576	−	5.02925i	−0.270917	−	0.197873i
$647$	8.97597	−	8.97597i	0.352882	−	0.352882i	−0.508299	−	0.861181i	$-0.669726\pi$
$647$	8.97597	−	8.97597i	0.352882	−	0.352882i	0.861181	+	0.508299i	$0.169726\pi$
$648$	−2.13686	−	1.85306i	−0.0839439	−	0.0727949i
$649$	−38.4329	−	38.4329i	−1.50862	−	1.50862i
$650$	−0.765651	−	4.91391i	−0.0300313	−	0.192740i
$651$	−2.16872	−	5.23574i	−0.0849987	−	0.205205i
$652$	−3.82495	+	3.23375i	−0.149797	+	0.126644i
$653$	42.2027	+	17.4809i	1.65152	+	0.684082i	0.997383	−	0.0722952i	$-0.0230324\pi$
$653$	42.2027	+	17.4809i	1.65152	+	0.684082i	0.654136	+	0.756377i	$0.273032\pi$
$654$	8.82062	+	14.4754i	0.344913	+	0.566031i
$655$			7.44549i			0.290919i
$656$	1.04318	−	6.18395i	0.0407293	−	0.241443i
$657$		−	11.4707i		−	0.447516i
$658$	13.9824	−	8.52023i	0.545091	−	0.332153i
$659$	5.50356	+	2.27965i	0.214388	+	0.0888025i	0.487293	−	0.873239i	$-0.337984\pi$
$659$	5.50356	+	2.27965i	0.214388	+	0.0888025i	−0.272905	+	0.962041i	$0.587984\pi$
$660$	14.5667	+	1.22002i	0.567009	+	0.0474892i
$661$	−17.5581	−	42.3890i	−0.682931	−	1.64874i	−0.758557	−	0.651606i	$-0.774095\pi$
$661$	−17.5581	−	42.3890i	−0.682931	−	1.64874i	0.0756260	−	0.997136i	$-0.475905\pi$
$662$	−5.03153	+	0.783978i	−0.195556	+	0.0304702i
$663$	0.737417	+	0.737417i	0.0286389	+	0.0286389i
$664$	−14.0704	+	7.03632i	−0.546039	+	0.273062i
$665$	−20.8218	+	20.8218i	−0.807436	+	0.807436i
$666$	7.43362	−	10.1777i	0.288047	−	0.394377i
$667$	14.8266	−	6.14136i	0.574087	−	0.237795i
$668$	−9.72379	+	3.10558i	−0.376225	+	0.120159i
$669$	2.64425	−	6.38378i	0.102233	−	0.246811i
$670$	5.35352	+	1.29948i	0.206824	+	0.0502034i
$671$	−29.4137			−1.13550
$672$	−14.4898	−	14.8581i	−0.558958	−	0.573164i
$673$	−14.4979			−0.558853			−0.279427	−	0.960167i	$-0.590144\pi$
$673$	−14.4979			−0.558853			−0.279427	+	0.960167i	$0.590144\pi$
$674$	0.651075	+	0.158038i	0.0250785	+	0.00608741i
$675$	1.26339	−	3.05010i	0.0486281	−	0.117399i
$676$	7.21985	+	22.6058i	0.277687	+	0.869456i
$677$	−11.0022	+	4.55726i	−0.422849	+	0.175150i	−0.583953	−	0.811788i	$-0.698495\pi$
$677$	−11.0022	+	4.55726i	−0.422849	+	0.175150i	0.161104	+	0.986937i	$0.448495\pi$
$678$	−7.85025	+	10.7481i	−0.301487	+	0.412779i
$679$	37.3183	−	37.3183i	1.43215	−	1.43215i
$680$	−3.42394	−	1.14107i	−0.131302	−	0.0437582i
$681$	−3.05088	−	3.05088i	−0.116910	−	0.116910i
$682$	12.1047	−	1.88606i	0.463511	−	0.0722211i
$683$	−3.03396	−	7.32464i	−0.116091	−	0.280269i	0.855144	−	0.518390i	$-0.173469\pi$
$683$	−3.03396	−	7.32464i	−0.116091	−	0.280269i	−0.971236	+	0.238121i	$0.923469\pi$
$684$	−1.02798	+	12.2738i	−0.0393057	+	0.469301i
$685$	14.7053	+	6.09114i	0.561861	+	0.232730i
$686$	2.39267	−	1.45799i	0.0913527	−	0.0556662i
$687$		−	7.67495i		−	0.292818i
$688$	19.2665	−	30.7431i	0.734529	−	1.17207i
$689$			7.10479i			0.270671i
$690$	−5.02133	−	8.24042i	−0.191159	−	0.313707i
$691$	−21.8871	−	9.06592i	−0.832623	−	0.344884i	−0.0746825	−	0.997207i	$-0.523794\pi$
$691$	−21.8871	−	9.06592i	−0.832623	−	0.344884i	−0.757941	+	0.652324i	$0.773794\pi$
$692$	3.03229	+	3.58666i	0.115270	+	0.136344i
$693$	−7.87349	−	19.0083i	−0.299089	−	0.722065i
$694$	2.20767	+	14.1687i	0.0838021	+	0.537837i
$695$	9.76203	+	9.76203i	0.370295	+	0.370295i
$696$	−8.64801	+	0.615140i	−0.327802	+	0.0233168i
$697$	−1.08540	+	1.08540i	−0.0411125	+	0.0411125i
$698$	6.09482	+	4.45156i	0.230692	+	0.168494i
$699$	−1.95216	+	0.808612i	−0.0738376	+	0.0305845i
$700$	11.1058	−	21.5285i	0.419760	−	0.813702i
$701$	18.8146	−	45.4224i	0.710617	−	1.71558i	0.0121647	−	0.999926i	$-0.496128\pi$
$701$	18.8146	−	45.4224i	0.710617	−	1.71558i	0.698453	−	0.715656i	$-0.253872\pi$
$702$	0.355334	−	1.46388i	0.0134112	−	0.0552506i
$703$	−54.8829			−2.06995
$704$	38.6012	−	22.8626i	1.45484	−	0.861668i
$705$	−4.11299			−0.154904
$706$	11.5818	−	47.7138i	0.435886	−	1.79573i
$707$	18.4180	−	44.4650i	0.692681	−	1.67228i
$708$	8.88671	−	17.2269i	0.333983	−	0.647425i
$709$	−22.5420	+	9.33718i	−0.846581	+	0.350665i	−0.763445	−	0.645873i	$-0.776494\pi$
$709$	−22.5420	+	9.33718i	−0.846581	+	0.350665i	−0.0831359	+	0.996538i	$0.526494\pi$
$710$	21.1278	+	15.4314i	0.792911	+	0.579129i
$711$	0.109926	−	0.109926i	0.00412254	−	0.00412254i
$712$	−1.74627	−	24.5501i	−0.0654442	−	0.920053i
$713$	−5.71852	−	5.71852i	−0.214160	−	0.214160i
$714$	0.782056	+	5.01920i	0.0292677	+	0.187839i
$715$	2.97928	+	7.19263i	0.111419	+	0.268989i
$716$	3.72444	+	4.40534i	0.139189	+	0.164635i
$717$	−5.00015	−	2.07113i	−0.186734	−	0.0773478i
$718$	4.22940	+	6.94078i	0.157840	+	0.259028i
$719$			38.2799i			1.42760i	0.700350	+	0.713800i	$0.253027\pi$
$719$			38.2799i			1.42760i	−0.700350	+	0.713800i	$0.746973\pi$
$720$	1.16605	+	5.08112i	0.0434562	+	0.189362i
$721$			53.4707i			1.99135i
$722$	22.8560	−	13.9274i	0.850611	−	0.518323i
$723$	−18.1712	−	7.52676i	−0.675795	−	0.279923i
$724$	−0.483665	+	5.77484i	−0.0179753	+	0.214620i
$725$	−3.87263	−	9.34936i	−0.143826	−	0.347226i
$726$	28.5749	−	4.45234i	1.06051	−	0.165242i
$727$	−2.75063	−	2.75063i	−0.102015	−	0.102015i	0.654257	−	0.756272i	$-0.272981\pi$
$727$	−2.75063	−	2.75063i	−0.102015	−	0.102015i	−0.756272	+	0.654257i	$0.772981\pi$
$728$	3.49468	−	10.4862i	0.129522	−	0.388646i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	−12.4700	+	17.0732i	−0.461534	+	0.631906i
$731$	−8.20436	+	3.39836i	−0.303449	+	0.125693i
$732$	−3.19146	−	9.99268i	−0.117960	−	0.369340i
$733$	−6.75290	+	16.3029i	−0.249424	+	0.602163i	−0.998155	−	0.0607106i	$-0.980663\pi$
$733$	−6.75290	+	16.3029i	−0.249424	+	0.602163i	0.748731	+	0.662874i	$0.230663\pi$
$734$	−41.6067	−	10.0994i	−1.53573	−	0.372775i
$735$	8.41929			0.310550
$736$	−27.2177	−	11.6761i	−1.00326	−	0.430389i
$737$	16.7617			0.617424
$738$	2.15468	+	0.523015i	0.0793148	+	0.0192524i
$739$	9.62421	−	23.2349i	0.354032	−	0.854709i	−0.642082	−	0.766636i	$-0.721929\pi$
$739$	9.62421	−	23.2349i	0.354032	−	0.854709i	0.996114	−	0.0880732i	$-0.0280709\pi$
$740$	−22.1286	+	7.06742i	−0.813463	+	0.259803i
$741$	−6.06045	+	2.51032i	−0.222636	+	0.0922189i
$742$	−20.4118	+	27.9467i	−0.749340	+	1.02595i
$743$	−32.2711	+	32.2711i	−1.18391	+	1.18391i	−0.205192	+	0.978722i	$0.565782\pi$
$743$	−32.2711	+	32.2711i	−1.18391	+	1.18391i	−0.978722	+	0.205192i	$0.934218\pi$
$744$	1.95414	+	3.90766i	0.0716422	+	0.143262i
$745$	−2.66218	−	2.66218i	−0.0975347	−	0.0975347i
$746$	30.8998	−	4.81459i	1.13132	−	0.176275i
$747$	−2.12849	−	5.13862i	−0.0778773	−	0.188012i
$748$	−10.9427	−	0.916493i	−0.400104	−	0.0335103i
$749$	−5.10921	−	2.11630i	−0.186687	−	0.0773281i
$750$	−13.0660	+	7.96183i	−0.477103	+	0.290725i
$751$			2.67256i			0.0975231i	0.998810	+	0.0487616i	$0.0155274\pi$
$751$			2.67256i			0.0975231i	−0.998810	+	0.0487616i	$0.984473\pi$
$752$	−10.2864	+	7.31690i	−0.375107	+	0.266820i
$753$		−	25.6145i		−	0.933443i
$754$	−2.40274	−	3.94309i	−0.0875025	−	0.143599i
$755$	−10.9065	−	4.51762i	−0.396928	−	0.164413i
$756$	5.60338	−	4.73730i	0.203793	−	0.172294i
$757$	−9.38519	−	22.6579i	−0.341111	−	0.823514i	−0.997604	−	0.0691822i	$-0.977961\pi$
$757$	−9.38519	−	22.6579i	−0.341111	−	0.823514i	0.656493	−	0.754332i	$-0.272039\pi$
$758$	−5.02268	−	32.2353i	−0.182432	−	1.17084i
$759$	−20.7610	−	20.7610i	−0.753577	−	0.753577i
$760$	14.8731	−	17.1510i	0.539502	−	0.622130i
$761$	−12.8473	+	12.8473i	−0.465714	+	0.465714i	−0.900523	−	0.434809i	$-0.856816\pi$
$761$	−12.8473	+	12.8473i	−0.465714	+	0.465714i	0.434809	+	0.900523i	$0.356816\pi$
$762$	−18.2975	−	13.3642i	−0.662848	−	0.484134i
$763$	−40.6275	+	16.8285i	−1.47081	+	0.609231i
$764$	−14.8469	−	7.65898i	−0.537142	−	0.277092i
$765$	0.488304	−	1.17887i	0.0176547	−	0.0426222i
$766$	−8.53106	+	35.1457i	−0.308240	+	1.26986i
$767$	10.3237			0.372767
$768$	11.9554	+	10.6333i	0.431405	+	0.383697i
$769$	15.9481			0.575102			0.287551	−	0.957765i	$-0.407159\pi$
$769$	15.9481			0.575102			0.287551	+	0.957765i	$0.407159\pi$
$770$	−8.94514	+	36.8515i	−0.322361	+	1.32804i
$771$	−3.61347	+	8.72369i	−0.130136	+	0.314176i
$772$	21.9247	+	11.3101i	0.789086	+	0.407061i
$773$	4.77420	−	1.97754i	0.171716	−	0.0711271i	−0.295169	−	0.955445i	$-0.595376\pi$
$773$	4.77420	−	1.97754i	0.171716	−	0.0711271i	0.466885	+	0.884318i	$0.345376\pi$
$774$	10.3586	+	7.56577i	0.372333	+	0.271946i
$775$	−3.60599	+	3.60599i	−0.129531	+	0.129531i
$776$	−26.6565	+	30.7391i	−0.956914	+	1.10347i
$777$	23.1194	+	23.1194i	0.829406	+	0.829406i
$778$	0.281953	+	1.80956i	0.0101085	+	0.0648760i
$779$	−3.69493	−	8.92034i	−0.132385	−	0.319604i
$780$	−2.12029	+	1.79257i	−0.0759184	+	0.0641843i
$781$	73.5447	+	30.4632i	2.63164	+	1.09006i
$782$	3.77208	+	6.19029i	0.134889	+	0.221364i
$783$		−	3.06526i		−	0.109543i
$784$	21.0563	−	14.9777i	0.752011	−	0.534918i
$785$		−	9.73086i		−	0.347309i
$786$	−6.89915	+	4.20402i	−0.246084	+	0.149953i
$787$	−14.1033	−	5.84179i	−0.502730	−	0.208237i	0.116882	−	0.993146i	$-0.462710\pi$
$787$	−14.1033	−	5.84179i	−0.502730	−	0.208237i	−0.619612	+	0.784908i	$0.712710\pi$
$788$	46.4137	+	3.88733i	1.65342	+	0.138480i
$789$	4.53949	+	10.9593i	0.161610	+	0.390161i
$790$	−0.283117	+	0.0441133i	−0.0100728	+	0.00156948i
$791$	−24.4152	−	24.4152i	−0.868106	−	0.868106i
$792$	7.09447	+	14.1867i	0.252091	+	0.504103i
$793$	3.95049	−	3.95049i	0.140286	−	0.140286i
$794$	4.94048	−	6.76422i	0.175331	−	0.240053i
$795$	8.03136	−	3.32670i	0.284843	−	0.117986i
$796$	45.8938	−	14.6575i	1.62666	−	0.519523i
$797$	−15.7714	+	38.0755i	−0.558652	+	1.34870i	0.352182	+	0.935931i	$0.385440\pi$
$797$	−15.7714	+	38.0755i	−0.558652	+	1.34870i	−0.910834	+	0.412773i	$0.864560\pi$
$798$	−31.0508	−	7.53710i	−1.09919	−	0.266810i
$799$	3.08972			0.109306
$800$	−7.36276	+	17.1630i	−0.260313	+	0.606802i
$801$	8.70170			0.307459
$802$	45.7361	+	11.1017i	1.61500	+	0.392015i
$803$	−24.6171	+	59.4308i	−0.868717	+	2.09727i
$804$	1.81868	+	5.69443i	0.0641400	+	0.200827i
$805$	23.1281	−	9.57997i	0.815158	−	0.337650i
$806$	−1.37244	+	1.87907i	−0.0483421	+	0.0661872i
$807$	0.0501380	−	0.0501380i	0.00176494	−	0.00176494i
$808$	−11.7313	+	35.2011i	−0.412704	+	1.23837i
$809$	−22.3087	−	22.3087i	−0.784333	−	0.784333i	0.196226	−	0.980559i	$-0.437131\pi$
$809$	−22.3087	−	22.3087i	−0.784333	−	0.784333i	−0.980559	+	0.196226i	$0.937131\pi$
$810$	−1.82117	+	0.283762i	−0.0639894	+	0.00997038i
$811$	−17.0179	−	41.0848i	−0.597579	−	1.44268i	−0.876041	−	0.482236i	$-0.839825\pi$
$811$	−17.0179	−	41.0848i	−0.597579	−	1.44268i	0.278462	−	0.960447i	$-0.410175\pi$
$812$	1.87718	−	22.4131i	0.0658762	−	0.786545i
$813$	−13.3848	−	5.54419i	−0.469427	−	0.194443i
$814$	−60.3563	+	36.7784i	−2.11549	+	1.28908i
$815$			3.26394i			0.114331i
$816$	−0.875951	−	3.81699i	−0.0306644	−	0.133621i
$817$		−	55.8586i		−	1.95425i
$818$	−7.70680	−	12.6475i	−0.269462	−	0.442209i
$819$	3.61044	+	1.49549i	0.126159	+	0.0522567i
$820$	−2.63848	−	3.12084i	−0.0921395	−	0.108984i
$821$	4.17316	+	10.0749i	0.145644	+	0.351616i	0.979820	−	0.199883i	$-0.0640561\pi$
$821$	4.17316	+	10.0749i	0.145644	+	0.351616i	−0.834176	+	0.551499i	$0.814056\pi$
$822$	2.65903	+	17.0656i	0.0927445	+	0.595230i
$823$	−21.0647	−	21.0647i	−0.734269	−	0.734269i	0.237194	−	0.971462i	$-0.423772\pi$
$823$	−21.0647	−	21.0647i	−0.734269	−	0.734269i	−0.971462	+	0.237194i	$0.923772\pi$
$824$	−2.92483	−	41.1190i	−0.101891	−	1.43245i
$825$	−13.0915	+	13.0915i	−0.455788	+	0.455788i
$826$	40.6082	+	29.6596i	1.41294	+	1.03199i
$827$	−51.5584	+	21.3562i	−1.79286	+	0.742627i	−0.803840	+	0.594845i	$0.797213\pi$
$827$	−51.5584	+	21.3562i	−1.79286	+	0.742627i	−0.989020	+	0.147782i	$0.952787\pi$
$828$	4.80050	−	9.30575i	0.166829	−	0.323397i
$829$	12.1450	−	29.3206i	0.421813	−	1.01835i	−0.560000	−	0.828493i	$-0.689199\pi$
$829$	12.1450	−	29.3206i	0.421813	−	1.01835i	0.981812	−	0.189853i	$-0.0608013\pi$
$830$	−2.41819	+	9.96229i	−0.0839367	+	0.345796i
$831$	21.3487			0.740580
$832$	−2.11382	+	8.25508i	−0.0732835	+	0.286194i
$833$	−6.32466			−0.219136
$834$	−3.53367	+	14.5577i	−0.122361	+	0.504094i
$835$	−2.54555	+	6.14550i	−0.0880924	+	0.212674i
$836$	31.6666	−	61.3855i	1.09521	−	2.12306i
$837$	−1.42711	+	0.591127i	−0.0493280	+	0.0204323i
$838$	19.1900	+	14.0161i	0.662907	+	0.484177i
$839$	21.1653	−	21.1653i	0.730706	−	0.730706i	−0.240054	−	0.970760i	$-0.577165\pi$
$839$	21.1653	−	21.1653i	0.730706	−	0.730706i	0.970760	+	0.240054i	$0.0771651\pi$
$840$	−13.4901	+	0.959563i	−0.465453	+	0.0331081i
$841$	13.8623	+	13.8623i	0.478009	+	0.478009i
$842$	−1.32162	−	8.48212i	−0.0455462	−	0.292313i
$843$	−1.49517	−	3.60966i	−0.0514964	−	0.124323i
$844$	12.3907	+	14.6560i	0.426506	+	0.504480i
$845$	14.2870	+	5.91788i	0.491489	+	0.203581i
$846$	−2.32236	−	3.81118i	−0.0798443	−	0.131031i
$847$			75.0241i			2.57786i
$848$	14.1680	−	22.6075i	0.486532	−	0.776346i
$849$			6.35234i			0.218012i
$850$	3.90348	−	2.37860i	0.133888	−	0.0815854i
$851$	43.1066	+	17.8553i	1.47767	+	0.612073i
$852$	−2.36945	+	28.2906i	−0.0811760	+	0.969220i
$853$	6.84996	+	16.5373i	0.234538	+	0.566225i	0.996701	−	0.0811601i	$-0.0258625\pi$
$853$	6.84996	+	16.5373i	0.234538	+	0.566225i	−0.762163	+	0.647385i	$0.775863\pi$
$854$	26.8888	−	4.18963i	0.920116	−	0.143366i
$855$	5.67540	+	5.67540i	0.194095	+	0.194095i
$856$	4.04475	+	1.34797i	0.138247	+	0.0460726i
$857$	−33.6370	+	33.6370i	−1.14902	+	1.14902i	−0.162272	+	0.986746i	$0.551882\pi$
$857$	−33.6370	+	33.6370i	−1.14902	+	1.14902i	−0.986746	+	0.162272i	$0.948118\pi$
$858$	−4.98262	+	6.82192i	−0.170104	+	0.232896i
$859$	35.7350	−	14.8019i	1.21926	−	0.505035i	0.322088	−	0.946710i	$-0.395615\pi$
$859$	35.7350	−	14.8019i	1.21926	−	0.505035i	0.897175	+	0.441674i	$0.145615\pi$
$860$	−7.19306	−	22.5220i	−0.245281	−	0.767992i
$861$	−2.20121	+	5.31418i	−0.0750169	+	0.181107i
$862$	−0.408396	−	0.0991319i	−0.0139100	−	0.00337645i
$863$	44.4296			1.51240			0.756201	−	0.654340i	$-0.227053\pi$
$863$	44.4296			1.51240			0.756201	+	0.654340i	$0.227053\pi$
$864$	−4.04987	+	3.94950i	−0.137780	+	0.134365i
$865$	3.06060			0.104064
$866$	21.1807	+	5.14128i	0.719749	+	0.174708i
$867$	6.13880	−	14.8204i	0.208485	−	0.503326i
$868$	−10.7970	+	3.44833i	−0.366473	+	0.117044i
$869$	−0.805445	+	0.333626i	−0.0273228	+	0.0113175i
$870$	−3.33228	+	4.56237i	−0.112975	+	0.154679i
$871$	−2.25122	+	2.25122i	−0.0762798	+	0.0762798i
$872$	30.3221	−	15.1634i	1.02683	−	0.513498i
$873$	−10.1718	−	10.1718i	−0.344265	−	0.344265i
$874$	−45.0538	+	7.01996i	−1.52397	+	0.237454i
$875$	−15.1900	−	36.6719i	−0.513516	−	1.23974i
$876$	−22.8614	−	1.91473i	−0.772415	−	0.0646928i
$877$	31.7336	+	13.1445i	1.07157	+	0.443857i	0.847543	−	0.530727i	$-0.178081\pi$
$877$	31.7336	+	13.1445i	1.07157	+	0.443857i	0.224023	+	0.974584i	$0.428081\pi$
$878$	−5.38418	+	3.28087i	−0.181707	+	0.110724i
$879$		−	4.88728i		−	0.164844i
$880$	4.86306	−	28.8282i	0.163934	−	0.971798i
$881$			42.6814i			1.43797i	0.695023	+	0.718987i	$0.255394\pi$
$881$			42.6814i			1.43797i	−0.695023	+	0.718987i	$0.744606\pi$
$882$	4.75387	+	7.80149i	0.160071	+	0.262690i
$883$	22.4520	+	9.29994i	0.755571	+	0.312968i	0.727012	−	0.686624i	$-0.240908\pi$
$883$	22.4520	+	9.29994i	0.755571	+	0.312968i	0.0285587	+	0.999592i	$0.490908\pi$
$884$	1.59278	−	1.34660i	0.0535710	−	0.0452910i
$885$	−4.83389	−	11.6700i	−0.162490	−	0.392284i
$886$	−0.661386	−	4.24474i	−0.0222197	−	0.142605i
$887$	−25.1413	−	25.1413i	−0.844161	−	0.844161i	0.145236	−	0.989397i	$-0.453606\pi$
$887$	−25.1413	−	25.1413i	−0.844161	−	0.844161i	−0.989397	+	0.145236i	$0.953606\pi$
$888$	−19.0435	−	16.5143i	−0.639058	−	0.554182i
$889$	41.5643	−	41.5643i	1.39402	−	1.39402i
$890$	−12.9517	−	9.45972i	−0.434142	−	0.317091i
$891$	−5.18109	+	2.14608i	−0.173573	+	0.0718963i
$892$	−12.2816	−	6.33565i	−0.411220	−	0.212133i
$893$	−7.43737	+	17.9554i	−0.248882	+	0.600855i
$894$	0.963658	−	3.97001i	0.0322295	−	0.132777i
$895$	3.75920			0.125656
$896$	−32.0312	+	26.3984i	−1.07009	+	0.881909i
$897$	5.57674			0.186202
$898$	−1.19331	+	4.91609i	−0.0398211	+	0.164052i
$899$	−1.81196	+	4.37445i	−0.0604321	+	0.145896i
$900$	−5.86803	−	3.02711i	−0.195601	−	0.100904i
$901$	−6.03324	+	2.49905i	−0.200996	+	0.0832554i
$902$	−10.0412	−	7.33389i	−0.334334	−	0.244192i
$903$	−23.5304	+	23.5304i	−0.783044	+	0.783044i
$904$	20.1108	+	17.4398i	0.668877	+	0.580040i
$905$	2.67028	+	2.67028i	0.0887632	+	0.0887632i
$906$	−1.97213	−	12.6570i	−0.0655195	−	0.420501i
$907$	14.9664	+	36.1321i	0.496951	+	1.19975i	0.951118	+	0.308829i	$0.0999371\pi$
$907$	14.9664	+	36.1321i	0.496951	+	1.19975i	−0.454167	+	0.890917i	$0.650063\pi$
$908$	−6.58974	+	5.57121i	−0.218688	+	0.184887i
$909$	−12.1198	−	5.02020i	−0.401989	−	0.166509i
$910$	−3.74805	−	6.15086i	−0.124247	−	0.203899i
$911$		−	23.3974i		−	0.775190i	−0.921830	−	0.387595i	$-0.873306\pi$
$911$		−	23.3974i		−	0.775190i	0.921830	−	0.387595i	$-0.126694\pi$
$912$	24.2904	+	4.09757i	0.804334	+	0.135684i
$913$			31.1915i			1.03229i
$914$	−15.3345	+	9.34413i	−0.507220	+	0.309076i
$915$	−6.31544	−	2.61594i	−0.208782	−	0.0864803i
$916$	−15.2963	−	1.28113i	−0.505405	−	0.0423297i
$917$	−8.02067	−	19.3636i	−0.264866	−	0.639442i
$918$	1.36808	−	0.213165i	0.0451535	−	0.00703550i
$919$	20.8473	+	20.8473i	0.687689	+	0.687689i	0.961721	−	0.274032i	$-0.0883574\pi$
$919$	20.8473	+	20.8473i	0.687689	+	0.687689i	−0.274032	+	0.961721i	$0.588357\pi$
$920$	−17.2615	+	8.63211i	−0.569095	+	0.284592i
$921$	6.46123	−	6.46123i	0.212905	−	0.212905i
$922$	−23.5192	+	32.2011i	−0.774563	+	1.06049i
$923$	−13.9691	+	5.78618i	−0.459798	+	0.190455i
$924$	−39.1982	+	12.5191i	−1.28953	+	0.411849i
$925$	11.2592	−	27.1822i	0.370202	−	0.893746i
$926$	−15.0874	−	3.66223i	−0.495802	−	0.120348i
$927$	14.5745			0.478690
$928$	−0.217567	+	17.3384i	−0.00714199	+	0.569160i
$929$	55.9215			1.83472			0.917362	−	0.398055i	$-0.130315\pi$
$929$	55.9215			1.83472			0.917362	+	0.398055i	$0.130315\pi$
$930$	2.76674	+	0.671584i	0.0907251	+	0.0220221i
$931$	15.2243	−	36.7547i	0.498956	−	1.20459i
$932$	1.28572	+	4.02568i	0.0421152	+	0.131865i
$933$	27.2339	−	11.2806i	0.891596	−	0.369311i
$934$	34.7947	−	47.6389i	1.13852	−	1.55879i
$935$	−5.05989	+	5.05989i	−0.165476	+	0.165476i
$936$	−2.85823	−	0.952545i	−0.0934242	−	0.0311349i
$937$	31.6178	+	31.6178i	1.03291	+	1.03291i	0.999440	+	0.0334692i	$0.0106556\pi$
$937$	31.6178	+	31.6178i	1.03291	+	1.03291i	0.0334692	+	0.999440i	$0.489344\pi$
$938$	−15.3229	+	2.38750i	−0.500309	+	0.0779546i
$939$	−7.63226	−	18.4259i	−0.249069	−	0.601306i
$940$	−0.686554	+	8.19727i	−0.0223929	+	0.267366i
$941$	23.4212	+	9.70137i	0.763509	+	0.316256i	0.730240	−	0.683191i	$-0.239408\pi$
$941$	23.4212	+	9.70137i	0.763509	+	0.316256i	0.0332688	+	0.999446i	$0.489408\pi$
$942$	9.01682	−	5.49444i	0.293784	−	0.179018i
$943$			8.20837i			0.267301i
$944$	−32.8501	−	20.5870i	−1.06918	−	0.670049i
$945$		−	4.78153i		−	0.155543i
$946$	−37.4322	−	61.4293i	−1.21703	−	1.99724i
$947$	30.2016	+	12.5099i	0.981419	+	0.406517i	0.814951	−	0.579530i	$-0.196764\pi$
$947$	30.2016	+	12.5099i	0.981419	+	0.406517i	0.166468	+	0.986047i	$0.446764\pi$
$948$	−0.200735	−	0.237434i	−0.00651958	−	0.00771149i
$949$	−4.67577	−	11.2883i	−0.151782	−	0.366434i
$950$	4.42666	+	28.4101i	0.143620	+	0.921744i
$951$	−1.98278	−	1.98278i	−0.0642961	−	0.0642961i
$952$	10.1339	−	0.720834i	0.328442	−	0.0233624i
$953$	−17.7752	+	17.7752i	−0.575795	+	0.575795i	−0.933742	−	0.357947i	$-0.883477\pi$
$953$	−17.7752	+	17.7752i	−0.575795	+	0.575795i	0.357947	+	0.933742i	$0.383477\pi$
$954$	7.61742	+	5.56364i	0.246623	+	0.180129i
$955$	−10.0578	+	4.16607i	−0.325462	+	0.134811i
$956$	−4.96245	+	9.61969i	−0.160497	+	0.311123i
$957$	−6.57828	+	15.8814i	−0.212646	+	0.513372i
$958$	6.95293	−	28.6442i	0.224639	−	0.925451i
$959$	−44.8060			−1.44686
$960$	10.3214	−	1.47581i	0.333123	−	0.0476316i
$961$	−28.6139			−0.923030
$962$	3.16670	−	13.0460i	0.102099	−	0.420619i
$963$	−0.576841	+	1.39262i	−0.0185884	+	0.0448765i
$964$	−18.0342	+	34.9592i	−0.580843	+	1.12596i
$965$	14.8525	−	6.15211i	0.478119	−	0.198043i
$966$	21.9361	+	16.0217i	0.705781	+	0.515491i
$967$	5.23073	−	5.23073i	0.168209	−	0.168209i	−0.617983	−	0.786192i	$-0.712050\pi$
$967$	5.23073	−	5.23073i	0.168209	−	0.168209i	0.786192	+	0.617983i	$0.212050\pi$
$968$	−4.10380	−	57.6936i	−0.131901	−	1.85434i
$969$	−4.26342	−	4.26342i	−0.136961	−	0.136961i
$970$	4.08197	+	26.1979i	0.131064	+	0.841162i
$971$	6.01158	+	14.5132i	0.192921	+	0.465752i	0.990509	−	0.137451i	$-0.0438910\pi$
$971$	6.01158	+	14.5132i	0.192921	+	0.465752i	−0.797588	+	0.603203i	$0.793891\pi$
$972$	−1.29125	−	1.52731i	−0.0414168	−	0.0489886i
$973$	−35.9044	−	14.8721i	−1.15104	−	0.476778i
$974$	16.9726	+	27.8535i	0.543838	+	0.892482i
$975$		−	3.51659i		−	0.112621i
$976$	−20.4484	+	4.69264i	−0.654536	+	0.150208i
$977$		−	48.6725i		−	1.55717i	−0.627539	−	0.778585i	$-0.715938\pi$
$977$		−	48.6725i		−	1.55717i	0.627539	−	0.778585i	$-0.284062\pi$
$978$	−3.02444	+	1.84295i	−0.0967108	+	0.0589311i
$979$	−45.0842	−	18.6745i	−1.44090	−	0.596840i
$980$	1.40538	−	16.7798i	0.0448931	−	0.536012i
$981$	4.58693	+	11.0738i	0.146449	+	0.353560i
$982$	−8.12973	+	1.26672i	−0.259430	+	0.0404226i
$983$	7.17484	+	7.17484i	0.228842	+	0.228842i	0.812209	−	0.583367i	$-0.198265\pi$
$983$	7.17484	+	7.17484i	0.228842	+	0.228842i	−0.583367	+	0.812209i	$0.698265\pi$
$984$	1.40205	−	4.20702i	0.0446956	−	0.134115i
$985$	21.4617	−	21.4617i	0.683826	−	0.683826i
$986$	2.50324	−	3.42730i	0.0797195	−	0.109147i
$987$	10.6967	−	4.43072i	0.340480	−	0.141031i
$988$	3.99149	+	12.4976i	0.126986	+	0.397603i
$989$	−18.1727	+	43.8729i	−0.577860	+	1.39508i
$990$	10.0446	+	2.43818i	0.319239	+	0.0774903i
$991$	−20.8957			−0.663774			−0.331887	−	0.943319i	$-0.607685\pi$
$991$	−20.8957			−0.663774			−0.331887	+	0.943319i	$0.607685\pi$
$992$	8.11425	−	3.24236i	0.257628	−	0.102945i
$993$	−3.60076			−0.114267
$994$	−71.5708	−	17.3727i	−2.27009	−	0.551029i
$995$	12.0143	−	29.0051i	0.380880	−	0.919525i
$996$	−10.5967	+	3.38436i	−0.335769	+	0.107238i
$997$	−48.3465	+	20.0258i	−1.53115	+	0.634223i	−0.979787	−	0.200042i	$-0.935892\pi$
$997$	−48.3465	+	20.0258i	−1.53115	+	0.634223i	−0.551363	+	0.834266i	$0.685892\pi$
$998$	8.48550	−	11.6179i	0.268604	−	0.367757i
$999$	6.30167	−	6.30167i	0.199376	−	0.199376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.13.4	✓	32
3.2	odd	2		288.2.v.d.109.5		32
4.3	odd	2		384.2.n.a.145.2		32
8.3	odd	2		768.2.n.b.289.7		32
8.5	even	2		768.2.n.a.289.3		32
12.11	even	2		1152.2.v.c.145.5		32
32.5	even	8	inner	96.2.n.a.37.4	yes	32
32.11	odd	8		768.2.n.b.481.7		32
32.21	even	8		768.2.n.a.481.3		32
32.27	odd	8		384.2.n.a.241.2		32
96.5	odd	8		288.2.v.d.37.5		32
96.59	even	8		1152.2.v.c.1009.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.4	✓	32	1.1	even	1	trivial
96.2.n.a.37.4	yes	32	32.5	even	8	inner
288.2.v.d.37.5		32	96.5	odd	8
288.2.v.d.109.5		32	3.2	odd	2
384.2.n.a.145.2		32	4.3	odd	2
384.2.n.a.241.2		32	32.27	odd	8
768.2.n.a.289.3		32	8.5	even	2
768.2.n.a.481.3		32	32.21	even	8
768.2.n.b.289.7		32	8.3	odd	2
768.2.n.b.481.7		32	32.11	odd	8
1152.2.v.c.145.5		32	12.11	even	2
1152.2.v.c.1009.5		32	96.59	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.333592 - 1.37431i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.77743 - 0.916914i) q^{4} +(-1.20409 + 0.498752i) q^{5} +(-1.14203 - 0.834122i) q^{6} +(2.59422 - 2.59422i) q^{7} +(-1.85306 + 2.13686i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.333592 - 1.37431i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.77743 - 0.916914i) q^{4} +(-1.20409 + 0.498752i) q^{5} +(-1.14203 - 0.834122i) q^{6} +(2.59422 - 2.59422i) q^{7} +(-1.85306 + 2.13686i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(0.283762 + 1.82117i) q^{10} +(2.14608 + 5.18109i) q^{11} +(-1.52731 + 1.29125i) q^{12} +(-0.984096 - 0.407626i) q^{13} +(-2.69984 - 4.43066i) q^{14} +1.30330i q^{15} +(2.31854 + 3.25951i) q^{16} -0.979053i q^{17} +(-1.20767 + 0.735896i) q^{18} +(5.68961 + 2.35671i) q^{19} +(2.59751 + 0.217551i) q^{20} +(-1.40398 - 3.38951i) q^{21} +(7.83631 - 1.22100i) q^{22} +(-3.70206 - 3.70206i) q^{23} +(1.26507 + 2.52974i) q^{24} +(-2.33445 + 2.33445i) q^{25} +(-0.888489 + 1.21647i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-6.98973 + 2.23238i) q^{28} +(-1.17302 + 2.83193i) q^{29} +(1.79113 + 0.434770i) q^{30} +1.54469 q^{31} +(5.25300 - 2.09904i) q^{32} +5.60797 q^{33} +(-1.34552 - 0.326604i) q^{34} +(-1.82981 + 4.41756i) q^{35} +(0.608479 + 1.90519i) q^{36} +(-8.23352 + 3.41044i) q^{37} +(5.13685 - 7.03308i) q^{38} +(-0.753195 + 0.753195i) q^{39} +(1.16549 - 3.49720i) q^{40} +(-1.10862 - 1.10862i) q^{41} +(-5.12659 + 0.798789i) q^{42} +(-3.47106 - 8.37989i) q^{43} +(0.936101 - 11.1768i) q^{44} +(1.20409 + 0.498752i) q^{45} +(-6.32273 + 3.85278i) q^{46} +3.15582i q^{47} +(3.89866 - 0.894692i) q^{48} -6.45997i q^{49} +(2.42949 + 3.98700i) q^{50} +(-0.904527 - 0.374667i) q^{51} +(1.37541 + 1.62686i) q^{52} +(-2.55252 - 6.16232i) q^{53} +(0.217726 + 1.39735i) q^{54} +(-5.16815 - 5.16815i) q^{55} +(0.736256 + 10.3507i) q^{56} +(4.35464 - 4.35464i) q^{57} +(3.50063 + 2.55680i) q^{58} +(-8.95423 + 3.70896i) q^{59} +(1.19501 - 2.31653i) q^{60} +(-2.00717 + 4.84573i) q^{61} +(0.515295 - 2.12287i) q^{62} -3.66878 q^{63} +(-1.13236 - 7.91945i) q^{64} +1.38825 q^{65} +(1.87077 - 7.70706i) q^{66} +(1.14380 - 2.76138i) q^{67} +(-0.897707 + 1.74020i) q^{68} +(-4.83697 + 2.00354i) q^{69} +(5.46066 + 3.98838i) q^{70} +(10.0373 - 10.0373i) q^{71} +(2.82130 - 0.200681i) q^{72} +(8.11103 + 8.11103i) q^{73} +(1.94035 + 12.4531i) q^{74} +(1.26339 + 3.05010i) q^{75} +(-7.95200 - 9.40578i) q^{76} +(19.0083 + 7.87349i) q^{77} +(0.783860 + 1.28638i) q^{78} +0.155459i q^{79} +(-4.41742 - 2.76837i) q^{80} +1.00000i q^{81} +(-1.89342 + 1.15376i) q^{82} +(5.13862 + 2.12849i) q^{83} +(-0.612406 + 7.31197i) q^{84} +(0.488304 + 1.17887i) q^{85} +(-12.6745 + 1.97484i) q^{86} +(2.16747 + 2.16747i) q^{87} +(-15.0481 - 5.01498i) q^{88} +(-6.15303 + 6.15303i) q^{89} +(1.08711 - 1.48841i) q^{90} +(-3.61044 + 1.49549i) q^{91} +(3.18569 + 9.97462i) q^{92} +(0.591127 - 1.42711i) q^{93} +(4.33707 + 1.05276i) q^{94} -8.02623 q^{95} +(0.0709783 - 5.65641i) q^{96} +14.3852 q^{97} +(-8.87798 - 2.15499i) q^{98} +(2.14608 - 5.18109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

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