LMFDB - Embedded newform 96.2.n.a.61.3

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			61.3
Character	$\chi$	$=$	96.61
Dual form			96.2.n.a.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.947612 + 1.04978i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-0.204063 - 1.98956i) q^{4} +(-1.48656 - 3.58888i) q^{5} +(1.27721 - 0.607232i) q^{6} +(1.03821 - 1.03821i) q^{7} +(2.28197 + 1.67111i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.947612 + 1.04978i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-0.204063 - 1.98956i) q^{4} +(-1.48656 - 3.58888i) q^{5} +(1.27721 - 0.607232i) q^{6} +(1.03821 - 1.03821i) q^{7} +(2.28197 + 1.67111i) q^{8} +(0.707107 + 0.707107i) q^{9} +(5.17620 + 1.84030i) q^{10} +(-2.98911 + 1.23813i) q^{11} +(-0.572843 + 1.91621i) q^{12} +(1.33971 - 3.23434i) q^{13} +(0.106069 + 2.07371i) q^{14} +3.88457i q^{15} +(-3.91672 + 0.811991i) q^{16} -5.31367i q^{17} +(-1.41237 + 0.0722414i) q^{18} +(-0.339726 + 0.820171i) q^{19} +(-6.83694 + 3.68996i) q^{20} +(-1.35649 + 0.561876i) q^{21} +(1.53276 - 4.31117i) q^{22} +(4.32186 + 4.32186i) q^{23} +(-1.46876 - 2.41718i) q^{24} +(-7.13463 + 7.13463i) q^{25} +(2.12581 + 4.47129i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(-2.27745 - 1.85373i) q^{28} +(5.78209 + 2.39502i) q^{29} +(-4.07793 - 3.68107i) q^{30} -1.42287 q^{31} +(2.85912 - 4.88113i) q^{32} +3.23539 q^{33} +(5.57817 + 5.03530i) q^{34} +(-5.26938 - 2.18265i) q^{35} +(1.26254 - 1.55113i) q^{36} +(0.646238 + 1.56016i) q^{37} +(-0.539068 - 1.13384i) q^{38} +(-2.47546 + 2.47546i) q^{39} +(2.60513 - 10.6739i) q^{40} +(3.42644 + 3.42644i) q^{41} +(0.695581 - 1.95645i) q^{42} +(6.50505 - 2.69448i) q^{43} +(3.07331 + 5.69437i) q^{44} +(1.48656 - 3.58888i) q^{45} +(-8.63244 + 0.441542i) q^{46} -10.5764i q^{47} +(3.92931 + 0.748681i) q^{48} +4.84423i q^{49} +(-0.728907 - 14.2506i) q^{50} +(-2.03345 + 4.90919i) q^{51} +(-6.70831 - 2.00542i) q^{52} +(6.63468 - 2.74817i) q^{53} +(1.33250 + 0.473747i) q^{54} +(8.88700 + 8.88700i) q^{55} +(4.10414 - 0.634197i) q^{56} +(0.627732 - 0.627732i) q^{57} +(-7.99342 + 3.80036i) q^{58} +(-0.185450 - 0.447716i) q^{59} +(7.72860 - 0.792696i) q^{60} +(-3.16624 - 1.31150i) q^{61} +(1.34833 - 1.49369i) q^{62} +1.46825 q^{63} +(2.41476 + 7.62686i) q^{64} -13.5992 q^{65} +(-3.06590 + 3.39644i) q^{66} +(-6.09277 - 2.52371i) q^{67} +(-10.5719 + 1.08432i) q^{68} +(-2.33898 - 5.64679i) q^{69} +(7.28462 - 3.46337i) q^{70} +(2.91549 - 2.91549i) q^{71} +(0.431940 + 2.79525i) q^{72} +(1.02065 + 1.02065i) q^{73} +(-2.25020 - 0.800018i) q^{74} +(9.32184 - 3.86123i) q^{75} +(1.70111 + 0.508540i) q^{76} +(-1.81789 + 4.38878i) q^{77} +(-0.252904 - 4.94445i) q^{78} -12.8099i q^{79} +(8.73657 + 12.8495i) q^{80} +1.00000i q^{81} +(-6.84393 + 0.350061i) q^{82} +(-6.41532 + 15.4879i) q^{83} +(1.39470 + 2.58416i) q^{84} +(-19.0701 + 7.89910i) q^{85} +(-3.33566 + 9.38217i) q^{86} +(-4.42542 - 4.42542i) q^{87} +(-8.89012 - 2.16977i) q^{88} +(-0.991462 + 0.991462i) q^{89} +(2.35883 + 4.96142i) q^{90} +(-1.96703 - 4.74883i) q^{91} +(7.71668 - 9.48055i) q^{92} +(1.31456 + 0.544508i) q^{93} +(11.1029 + 10.0224i) q^{94} +3.44851 q^{95} +(-4.50941 + 3.41544i) q^{96} +14.5301 q^{97} +(-5.08536 - 4.59045i) q^{98} +(-2.98911 - 1.23813i) 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 $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	−0.947612	+	1.04978i	−0.670063	+	0.742304i
$2$	−0.947612	+	1.04978i	−0.670063	+	0.742304i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$	−0.204063	−	1.98956i	−0.102031	−	0.994781i
$5$	−1.48656	−	3.58888i	−0.664810	−	1.60499i	−0.790174	−	0.612883i	$-0.790010\pi$
$5$	−1.48656	−	3.58888i	−0.664810	−	1.60499i	0.125364	−	0.992111i	$-0.459990\pi$
$6$	1.27721	−	0.607232i	0.521419	−	0.247901i
$7$	1.03821	−	1.03821i	0.392407	−	0.392407i	−0.483137	−	0.875545i	$-0.660503\pi$
$7$	1.03821	−	1.03821i	0.392407	−	0.392407i	0.875545	+	0.483137i	$0.160503\pi$
$8$	2.28197	+	1.67111i	0.806798	+	0.590828i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	5.17620	+	1.84030i	1.63686	+	0.581955i
$11$	−2.98911	+	1.23813i	−0.901252	+	0.373311i	−0.784701	−	0.619874i	$-0.787184\pi$
$11$	−2.98911	+	1.23813i	−0.901252	+	0.373311i	−0.116550	+	0.993185i	$0.537184\pi$
$12$	−0.572843	+	1.91621i	−0.165366	+	0.553161i
$13$	1.33971	−	3.23434i	0.371568	−	0.897045i	−0.621917	−	0.783083i	$-0.713646\pi$
$13$	1.33971	−	3.23434i	0.371568	−	0.897045i	0.993485	−	0.113962i	$-0.0363541\pi$
$14$	0.106069	+	2.07371i	0.0283480	+	0.554223i
$15$			3.88457i			1.00299i
$16$	−3.91672	+	0.811991i	−0.979179	+	0.202998i
$17$		−	5.31367i		−	1.28876i	−0.764708	−	0.644378i	$-0.777117\pi$
$17$		−	5.31367i		−	1.28876i	0.764708	−	0.644378i	$-0.222883\pi$
$18$	−1.41237	+	0.0722414i	−0.332898	+	0.0170275i
$19$	−0.339726	+	0.820171i	−0.0779385	+	0.188160i	−0.958046	−	0.286614i	$-0.907470\pi$
$19$	−0.339726	+	0.820171i	−0.0779385	+	0.188160i	0.880108	+	0.474774i	$0.157470\pi$
$20$	−6.83694	+	3.68996i	−1.52879	+	0.825100i
$21$	−1.35649	+	0.561876i	−0.296010	+	0.122611i
$22$	1.53276	−	4.31117i	0.326785	−	0.919145i
$23$	4.32186	+	4.32186i	0.901171	+	0.901171i	0.995537	−	0.0943668i	$-0.0300826\pi$
$23$	4.32186	+	4.32186i	0.901171	+	0.901171i	−0.0943668	+	0.995537i	$0.530083\pi$
$24$	−1.46876	−	2.41718i	−0.299809	−	0.493405i
$25$	−7.13463	+	7.13463i	−1.42693	+	1.42693i
$26$	2.12581	+	4.47129i	0.416906	+	0.876893i
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$	−2.27745	−	1.85373i	−0.430397	−	0.350321i
$29$	5.78209	+	2.39502i	1.07371	+	0.444744i	0.848298	−	0.529520i	$-0.177628\pi$
$29$	5.78209	+	2.39502i	1.07371	+	0.444744i	0.225410	+	0.974264i	$0.427628\pi$
$30$	−4.07793	−	3.68107i	−0.744525	−	0.672068i
$31$	−1.42287			−0.255555			−0.127777	−	0.991803i	$-0.540784\pi$
$31$	−1.42287			−0.255555			−0.127777	+	0.991803i	$0.540784\pi$
$32$	2.85912	−	4.88113i	0.505426	−	0.862870i
$33$	3.23539			0.563210
$34$	5.57817	+	5.03530i	0.956648	+	0.863547i
$35$	−5.26938	−	2.18265i	−0.890687	−	0.368935i
$36$	1.26254	−	1.55113i	0.210423	−	0.258521i
$37$	0.646238	+	1.56016i	0.106241	+	0.256488i	0.968056	−	0.250735i	$-0.0806721\pi$
$37$	0.646238	+	1.56016i	0.106241	+	0.256488i	−0.861815	+	0.507223i	$0.830672\pi$
$38$	−0.539068	−	1.13384i	−0.0874484	−	0.183933i
$39$	−2.47546	+	2.47546i	−0.396390	+	0.396390i
$40$	2.60513	−	10.6739i	0.411907	−	1.68769i
$41$	3.42644	+	3.42644i	0.535120	+	0.535120i	0.922092	−	0.386972i	$-0.126479\pi$
$41$	3.42644	+	3.42644i	0.535120	+	0.535120i	−0.386972	+	0.922092i	$0.626479\pi$
$42$	0.695581	−	1.95645i	0.107330	−	0.301887i
$43$	6.50505	−	2.69448i	0.992010	−	0.410904i	0.173149	−	0.984896i	$-0.444606\pi$
$43$	6.50505	−	2.69448i	0.992010	−	0.410904i	0.818861	+	0.573991i	$0.194606\pi$
$44$	3.07331	+	5.69437i	0.463318	+	0.858459i
$45$	1.48656	−	3.58888i	0.221603	−	0.534998i
$46$	−8.63244	+	0.441542i	−1.27278	+	0.0651018i
$47$		−	10.5764i		−	1.54273i	−0.636391	−	0.771366i	$-0.719574\pi$
$47$		−	10.5764i		−	1.54273i	0.636391	−	0.771366i	$-0.280426\pi$
$48$	3.92931	+	0.748681i	0.567147	+	0.108063i
$49$			4.84423i			0.692033i
$50$	−0.728907	−	14.2506i	−0.103083	−	2.01534i
$51$	−2.03345	+	4.90919i	−0.284741	+	0.687425i
$52$	−6.70831	−	2.00542i	−0.930275	−	0.278102i
$53$	6.63468	−	2.74817i	0.911344	−	0.377491i	0.122773	−	0.992435i	$-0.460821\pi$
$53$	6.63468	−	2.74817i	0.911344	−	0.377491i	0.788571	+	0.614944i	$0.210821\pi$
$54$	1.33250	+	0.473747i	0.181331	+	0.0644688i
$55$	8.88700	+	8.88700i	1.19832	+	1.19832i
$56$	4.10414	−	0.634197i	0.548438	−	0.0847482i
$57$	0.627732	−	0.627732i	0.0831451	−	0.0831451i
$58$	−7.99342	+	3.80036i	−1.04959	+	0.499011i
$59$	−0.185450	−	0.447716i	−0.0241435	−	0.0582877i	0.911348	−	0.411637i	$-0.135043\pi$
$59$	−0.185450	−	0.447716i	−0.0241435	−	0.0582877i	−0.935492	+	0.353349i	$0.885043\pi$
$60$	7.72860	−	0.792696i	0.997757	−	0.102337i
$61$	−3.16624	−	1.31150i	−0.405396	−	0.167920i	0.170662	−	0.985330i	$-0.445410\pi$
$61$	−3.16624	−	1.31150i	−0.405396	−	0.167920i	−0.576057	+	0.817409i	$0.695410\pi$
$62$	1.34833	−	1.49369i	0.171238	−	0.189699i
$63$	1.46825			0.184983
$64$	2.41476	+	7.62686i	0.301845	+	0.953357i
$65$	−13.5992			−1.68677
$66$	−3.06590	+	3.39644i	−0.377386	+	0.418073i
$67$	−6.09277	−	2.52371i	−0.744350	−	0.308320i	−0.0219162	−	0.999760i	$-0.506977\pi$
$67$	−6.09277	−	2.52371i	−0.744350	−	0.308320i	−0.722434	+	0.691440i	$0.756977\pi$
$68$	−10.5719	+	1.08432i	−1.28203	+	0.131493i
$69$	−2.33898	−	5.64679i	−0.281580	−	0.679793i
$70$	7.28462	−	3.46337i	0.870679	−	0.413952i
$71$	2.91549	−	2.91549i	0.346005	−	0.346005i	−0.512614	−	0.858619i	$-0.671323\pi$
$71$	2.91549	−	2.91549i	0.346005	−	0.346005i	0.858619	+	0.512614i	$0.171323\pi$
$72$	0.431940	+	2.79525i	0.0509046	+	0.329423i
$73$	1.02065	+	1.02065i	0.119458	+	0.119458i	0.764309	−	0.644851i	$-0.223080\pi$
$73$	1.02065	+	1.02065i	0.119458	+	0.119458i	−0.644851	+	0.764309i	$0.723080\pi$
$74$	−2.25020	−	0.800018i	−0.261580	−	0.0930002i
$75$	9.32184	−	3.86123i	1.07639	−	0.445857i
$76$	1.70111	+	0.508540i	0.195130	+	0.0583335i
$77$	−1.81789	+	4.38878i	−0.207168	+	0.500147i
$78$	−0.252904	−	4.94445i	−0.0286358	−	0.559849i
$79$		−	12.8099i		−	1.44122i	−0.693338	−	0.720612i	$-0.743861\pi$
$79$		−	12.8099i		−	1.44122i	0.693338	−	0.720612i	$-0.256139\pi$
$80$	8.73657	+	12.8495i	0.976778	+	1.43662i
$81$			1.00000i			0.111111i
$82$	−6.84393	+	0.350061i	−0.755786	+	0.0386578i
$83$	−6.41532	+	15.4879i	−0.704173	+	1.70002i	0.00989955	+	0.999951i	$0.496849\pi$
$83$	−6.41532	+	15.4879i	−0.704173	+	1.70002i	−0.714072	+	0.700072i	$0.753151\pi$
$84$	1.39470	+	2.58416i	0.152174	+	0.281955i
$85$	−19.0701	+	7.89910i	−2.06844	+	0.856778i
$86$	−3.33566	+	9.38217i	−0.359693	+	1.01171i
$87$	−4.42542	−	4.42542i	−0.474455	−	0.474455i
$88$	−8.89012	−	2.16977i	−0.947690	−	0.231298i
$89$	−0.991462	+	0.991462i	−0.105095	+	0.105095i	−0.757699	−	0.652604i	$-0.773676\pi$
$89$	−0.991462	+	0.991462i	−0.105095	+	0.105095i	0.652604	+	0.757699i	$0.273676\pi$
$90$	2.35883	+	4.96142i	0.248643	+	0.522979i
$91$	−1.96703	−	4.74883i	−0.206201	−	0.497813i
$92$	7.71668	−	9.48055i	0.804520	−	0.988415i
$93$	1.31456	+	0.544508i	0.136313	+	0.0564628i
$94$	11.1029	+	10.0224i	1.14518	+	1.03373i
$95$	3.44851			0.353810
$96$	−4.50941	+	3.41544i	−0.460240	+	0.348587i
$97$	14.5301			1.47530			0.737652	−	0.675182i	$-0.235935\pi$
$97$	14.5301			1.47530			0.737652	+	0.675182i	$0.235935\pi$
$98$	−5.08536	−	4.59045i	−0.513699	−	0.463706i
$99$	−2.98911	−	1.23813i	−0.300417	−	0.124437i
$100$	15.6507	+	12.7389i	1.56507	+	1.27389i
$101$	0.742560	+	1.79270i	0.0738875	+	0.178380i	0.956508	−	0.291706i	$-0.0942229\pi$
$101$	0.742560	+	1.79270i	0.0738875	+	0.178380i	−0.882621	+	0.470086i	$0.844223\pi$
$102$	−3.22663	−	6.78669i	−0.319484	−	0.671982i
$103$	−2.11500	+	2.11500i	−0.208397	+	0.208397i	−0.803586	−	0.595189i	$-0.797077\pi$
$103$	−2.11500	+	2.11500i	−0.208397	+	0.208397i	0.595189	+	0.803586i	$0.297077\pi$
$104$	8.46212	−	5.14186i	0.829779	−	0.504201i
$105$	4.03301	+	4.03301i	0.393581	+	0.393581i
$106$	−3.40213	+	9.56914i	−0.330444	+	0.929437i
$107$	4.62290	−	1.91487i	0.446913	−	0.185117i	−0.147865	−	0.989008i	$-0.547240\pi$
$107$	4.62290	−	1.91487i	0.446913	−	0.185117i	0.594778	+	0.803890i	$0.297240\pi$
$108$	−1.76002	+	0.949902i	−0.169358	+	0.0914044i
$109$	0.135885	−	0.328056i	0.0130155	−	0.0314221i	−0.917238	−	0.398339i	$-0.869587\pi$
$109$	0.135885	−	0.328056i	0.0130155	−	0.0314221i	0.930254	+	0.366917i	$0.119587\pi$
$110$	−17.7508	+	0.907938i	−1.69247	+	0.0865685i
$111$		−	1.68870i		−	0.160284i
$112$	−3.22336	+	4.90940i	−0.304579	+	0.463895i
$113$		−	2.38693i		−	0.224543i	−0.993678	−	0.112272i	$-0.964187\pi$
$113$		−	2.38693i		−	0.224543i	0.993678	−	0.112272i	$-0.0358127\pi$
$114$	0.0641320	+	1.25382i	0.00600651	+	0.117431i
$115$	9.08591	−	21.9353i	0.847266	−	2.04548i
$116$	3.58514	−	11.9926i	0.332871	−	1.11348i
$117$	3.23434	−	1.33971i	0.299015	−	0.123856i
$118$	0.645737	+	0.229580i	0.0594449	+	0.0211346i
$119$	−5.51672	−	5.51672i	−0.505717	−	0.505717i
$120$	−6.49156	+	8.86447i	−0.592595	+	0.809212i
$121$	−0.376343	+	0.376343i	−0.0342130	+	0.0342130i
$122$	4.37715	−	2.08105i	0.396289	−	0.188410i
$123$	−1.85438	−	4.47686i	−0.167203	−	0.403665i
$124$	0.290354	+	2.83088i	0.0260746	+	0.254221i
$125$	18.2670	+	7.56643i	1.63385	+	0.676762i
$126$	−1.39133	+	1.54134i	−0.123950	+	0.137313i
$127$	−13.4220			−1.19101			−0.595507	−	0.803350i	$-0.703049\pi$
$127$	−13.4220			−1.19101			−0.595507	+	0.803350i	$0.703049\pi$
$128$	−10.2948	−	4.69234i	−0.909936	−	0.414748i
$129$	−7.04101			−0.619927
$130$	12.8868	−	14.2761i	1.13024	−	1.25210i
$131$	7.38818	+	3.06028i	0.645508	+	0.267378i	0.681326	−	0.731980i	$-0.261404\pi$
$131$	7.38818	+	3.06028i	0.645508	+	0.267378i	−0.0358180	+	0.999358i	$0.511404\pi$
$132$	−0.660223	−	6.43702i	−0.0574650	−	0.560270i
$133$	0.498804	+	1.20422i	0.0432518	+	0.104419i
$134$	8.42291	−	4.00455i	0.727629	−	0.345941i
$135$	−2.74681	+	2.74681i	−0.236407	+	0.236407i
$136$	8.87975	−	12.1256i	0.761432	−	1.03976i
$137$	−10.6802	−	10.6802i	−0.912474	−	0.912474i	0.0839927	−	0.996466i	$-0.473233\pi$
$137$	−10.6802	−	10.6802i	−0.912474	−	0.912474i	−0.996466	+	0.0839927i	$0.973233\pi$
$138$	8.14431	+	2.89556i	0.693289	+	0.246486i
$139$	−4.00214	+	1.65774i	−0.339457	+	0.140608i	−0.545899	−	0.837851i	$-0.683812\pi$
$139$	−4.00214	+	1.65774i	−0.339457	+	0.140608i	0.206441	+	0.978459i	$0.433812\pi$
$140$	−3.26723	+	10.9292i	−0.276131	+	0.923682i
$141$	−4.04743	+	9.77136i	−0.340855	+	0.822897i
$142$	0.297860	+	5.82337i	0.0249959	+	0.488687i
$143$			11.3265i			0.947173i
$144$	−3.34370	−	2.19537i	−0.278642	−	0.182948i
$145$		−	24.3116i		−	2.01896i
$146$	−2.03864	+	0.104275i	−0.168719	+	0.00862982i
$147$	1.85381	−	4.47549i	0.152899	−	0.369132i
$148$	2.97216	−	1.60410i	0.244310	−	0.131856i
$149$	−17.5080	+	7.25206i	−1.43431	+	0.594112i	−0.958412	−	0.285387i	$-0.907878\pi$
$149$	−17.5080	+	7.25206i	−1.43431	+	0.594112i	−0.475901	+	0.879499i	$0.657878\pi$
$150$	−4.78006	+	13.4448i	−0.390290	+	1.09776i
$151$	1.13128	+	1.13128i	0.0920621	+	0.0920621i	0.751638	−	0.659576i	$-0.229264\pi$
$151$	1.13128	+	1.13128i	0.0920621	+	0.0920621i	−0.659576	+	0.751638i	$0.729264\pi$
$152$	−2.14584	+	1.30388i	−0.174051	+	0.105759i
$153$	3.75733	−	3.75733i	0.303762	−	0.303762i
$154$	−2.88458	−	6.06724i	−0.232446	−	0.488912i
$155$	2.11518	+	5.10649i	0.169895	+	0.410163i
$156$	5.43022	+	4.41993i	0.434766	+	0.353877i
$157$	1.69192	+	0.700815i	0.135030	+	0.0559311i	0.449175	−	0.893444i	$-0.351718\pi$
$157$	1.69192	+	0.700815i	0.135030	+	0.0559311i	−0.314145	+	0.949375i	$0.601718\pi$
$158$	13.4475	+	12.1388i	1.06983	+	0.965711i
$159$	−7.18133			−0.569516
$160$	−21.7680	−	3.00492i	−1.72091	−	0.237560i
$161$	8.97402			0.707252
$162$	−1.04978	−	0.947612i	−0.0824783	−	0.0744514i
$163$	20.1880	+	8.36212i	1.58124	+	0.654972i	0.988610	−	0.150501i	$-0.0480887\pi$
$163$	20.1880	+	8.36212i	1.58124	+	0.654972i	0.592632	+	0.805473i	$0.298089\pi$
$164$	6.11791	−	7.51632i	0.477728	−	0.586926i
$165$	−4.80961	−	11.6114i	−0.374428	−	0.903948i
$166$	−10.1797	−	21.4112i	−0.790094	−	1.66183i
$167$	−2.40472	+	2.40472i	−0.186083	+	0.186083i	−0.794000	−	0.607917i	$-0.792005\pi$
$167$	−2.40472	+	2.40472i	−0.186083	+	0.186083i	0.607917	+	0.794000i	$0.292005\pi$
$168$	−4.03442	−	0.984663i	−0.311263	−	0.0759684i
$169$	0.526247	+	0.526247i	0.0404805	+	0.0404805i
$170$	9.77878	−	27.5046i	0.749998	−	2.10951i
$171$	−0.820171	+	0.339726i	−0.0627200	+	0.0259795i
$172$	−6.68827	−	12.3924i	−0.509976	−	0.944908i
$173$	−3.78491	+	9.13758i	−0.287761	+	0.694717i	−0.999974	−	0.00724669i	$-0.997693\pi$
$173$	−3.78491	+	9.13758i	−0.287761	+	0.694717i	0.712212	+	0.701964i	$0.247693\pi$
$174$	8.83929	−	0.452122i	0.670105	−	0.0342753i
$175$			14.8145i			1.11987i
$176$	10.7022	−	7.27654i	0.806706	−	0.548490i
$177$			0.484604i			0.0364251i
$178$	−0.101292	−	1.98033i	−0.00759219	−	0.148432i
$179$	−7.05680	+	17.0366i	−0.527450	+	1.27338i	0.405738	+	0.913989i	$0.367015\pi$
$179$	−7.05680	+	17.0366i	−0.527450	+	1.27338i	−0.933188	+	0.359388i	$0.882985\pi$
$180$	−7.44364	−	2.22525i	−0.554816	−	0.165860i
$181$	17.3885	−	7.20257i	1.29248	−	0.535363i	0.372757	−	0.927929i	$-0.378413\pi$
$181$	17.3885	−	7.20257i	1.29248	−	0.535363i	0.919724	+	0.392566i	$0.128413\pi$
$182$	6.84919	+	2.43511i	0.507696	+	0.180502i
$183$	2.42334	+	2.42334i	0.179138	+	0.179138i
$184$	2.64003	+	17.0847i	0.194626	+	1.25950i
$185$	4.63854	−	4.63854i	0.341032	−	0.341032i
$186$	−1.81730	+	0.864010i	−0.133251	+	0.0633523i
$187$	6.57903	+	15.8832i	0.481106	+	1.16149i
$188$	−21.0425	+	2.15826i	−1.53468	+	0.157407i
$189$	−1.35649	−	0.561876i	−0.0986701	−	0.0408705i
$190$	−3.26785	+	3.62017i	−0.237075	+	0.262635i
$191$	9.91467			0.717400			0.358700	−	0.933453i	$-0.383220\pi$
$191$	9.91467			0.717400			0.358700	+	0.933453i	$0.383220\pi$
$192$	0.687722	−	7.97039i	0.0496321	−	0.575213i
$193$	9.84834			0.708899			0.354450	−	0.935075i	$-0.384668\pi$
$193$	9.84834			0.708899			0.354450	+	0.935075i	$0.384668\pi$
$194$	−13.7689	+	15.2533i	−0.988546	+	1.09512i
$195$	12.5640	+	5.20419i	0.899728	+	0.372680i
$196$	9.63790	−	0.988527i	0.688422	−	0.0706091i
$197$	5.46439	+	13.1922i	0.389322	+	0.939905i	0.990084	+	0.140478i	$0.0448638\pi$
$197$	5.46439	+	13.1922i	0.389322	+	0.939905i	−0.600762	+	0.799428i	$0.705136\pi$
$198$	4.13228	−	1.96463i	0.293669	−	0.139620i
$199$	−6.14473	+	6.14473i	−0.435588	+	0.435588i	−0.890524	−	0.454936i	$-0.849662\pi$
$199$	−6.14473	+	6.14473i	−0.435588	+	0.435588i	0.454936	+	0.890524i	$0.349662\pi$
$200$	−28.2038	+	4.35823i	−1.99431	+	0.308173i
$201$	4.66320	+	4.66320i	0.328917	+	0.328917i
$202$	−2.58559	−	0.919261i	−0.181922	−	0.0646790i
$203$	8.48958	−	3.51650i	0.595852	−	0.246810i
$204$	10.1821	+	3.04390i	0.712890	+	0.213116i
$205$	7.20345	−	17.3907i	0.503111	−	1.21462i
$206$	−0.216078	−	4.22447i	−0.0150549	−	0.294333i
$207$			6.11204i			0.424816i
$208$	−2.62100	+	13.7558i	−0.181734	+	0.953795i
$209$		−	2.87221i		−	0.198675i
$210$	−8.05548	+	0.412031i	−0.555881	+	0.0284328i
$211$	−4.14085	+	9.99689i	−0.285068	+	0.688214i	−0.999939	−	0.0110418i	$-0.996485\pi$
$211$	−4.14085	+	9.99689i	−0.285068	+	0.688214i	0.714871	+	0.699256i	$0.246485\pi$
$212$	−6.82156	−	12.6393i	−0.468506	−	0.868071i
$213$	−3.80927	+	1.57785i	−0.261007	+	0.108113i
$214$	−2.37053	+	6.66757i	−0.162046	+	0.455786i
$215$	−19.3403	−	19.3403i	−1.31900	−	1.31900i
$216$	0.670636	−	2.74777i	0.0456310	−	0.186962i
$217$	−1.47724	+	1.47724i	−0.100281	+	0.100281i
$218$	0.215619	+	0.453520i	0.0146036	+	0.0307162i
$219$	−0.552372	−	1.33355i	−0.0373259	−	0.0901126i
$220$	15.8677	−	19.4947i	1.06980	−	1.31434i
$221$	−17.1862	−	7.11877i	−1.15607	−	0.478860i
$222$	1.77276	+	1.60023i	0.118980	+	0.107401i
$223$	−14.1199			−0.945540			−0.472770	−	0.881186i	$-0.656746\pi$
$223$	−14.1199			−0.945540			−0.472770	+	0.881186i	$0.656746\pi$
$224$	−2.09928	−	8.03602i	−0.140264	−	0.536929i
$225$	−10.0899			−0.672659
$226$	2.50574	+	2.26188i	0.166679	+	0.150458i
$227$	−16.8836	−	6.99343i	−1.12061	−	0.464170i	−0.256029	−	0.966669i	$-0.582414\pi$
$227$	−16.8836	−	6.99343i	−1.12061	−	0.464170i	−0.864578	+	0.502499i	$0.832414\pi$
$228$	−1.37701	−	1.12081i	−0.0911946	−	0.0742278i
$229$	3.92011	+	9.46398i	0.259048	+	0.625397i	0.998876	−	0.0473987i	$-0.0150931\pi$
$229$	3.92011	+	9.46398i	0.259048	+	0.625397i	−0.739828	+	0.672796i	$0.765093\pi$
$230$	14.4173	+	30.3244i	0.950648	+	1.99953i
$231$	3.35902	−	3.35902i	0.221008	−	0.221008i
$232$	9.19220	+	15.1279i	0.603498	+	0.993195i
$233$	3.06027	+	3.06027i	0.200485	+	0.200485i	0.800208	−	0.599723i	$-0.204722\pi$
$233$	3.06027	+	3.06027i	0.200485	+	0.200485i	−0.599723	+	0.800208i	$0.704722\pi$
$234$	−1.65851	+	4.66486i	−0.108420	+	0.304951i
$235$	−37.9575	+	15.7225i	−2.47608	+	1.02562i
$236$	−0.852916	+	0.460327i	−0.0555201	+	0.0299647i
$237$	−4.90213	+	11.8348i	−0.318428	+	0.768752i
$238$	11.0190	−	0.563614i	0.714258	−	0.0365337i
$239$		−	0.210325i		−	0.0136048i	−0.999977	−	0.00680240i	$-0.997835\pi$
$239$		−	0.210325i		−	0.0136048i	0.999977	−	0.00680240i	$-0.00216529\pi$
$240$	−3.15424	−	15.2148i	−0.203605	−	0.982109i
$241$			13.0724i			0.842068i	0.907045	+	0.421034i	$0.138333\pi$
$241$			13.0724i			0.842068i	−0.907045	+	0.421034i	$0.861667\pi$
$242$	−0.0384489	−	0.751702i	−0.00247159	−	0.0483213i
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$	−1.96320	+	6.56707i	−0.125681	+	0.420413i
$245$	17.3853	−	7.20125i	1.11071	−	0.460071i
$246$	6.45693	+	2.29565i	0.411679	+	0.146365i
$247$	2.19758	+	2.19758i	0.139829	+	0.139829i
$248$	−3.24694	−	2.37777i	−0.206181	−	0.150989i
$249$	11.8540	−	11.8540i	0.751214	−	0.751214i
$250$	−25.2531	+	12.0062i	−1.59714	+	0.759339i
$251$	−1.21528	−	2.93395i	−0.0767079	−	0.185189i	0.880874	−	0.473351i	$-0.156956\pi$
$251$	−1.21528	−	2.93395i	−0.0767079	−	0.185189i	−0.957582	+	0.288162i	$0.906956\pi$
$252$	−0.299616	−	2.92118i	−0.0188740	−	0.184017i
$253$	−18.2696	−	7.56751i	−1.14860	−	0.475765i
$254$	12.7189	−	14.0902i	0.798054	−	0.884095i
$255$	20.6413			1.29261
$256$	14.6813	−	6.36068i	0.917584	−	0.397542i
$257$	2.57305			0.160502			0.0802512	−	0.996775i	$-0.474428\pi$
$257$	2.57305			0.160502			0.0802512	+	0.996775i	$0.474428\pi$
$258$	6.67215	−	7.39149i	0.415390	−	0.460174i
$259$	2.29071	+	0.948841i	0.142338	+	0.0589581i
$260$	2.77509	+	27.0565i	0.172104	+	1.67797i
$261$	2.39502	+	5.78209i	0.148248	+	0.357903i
$262$	−10.2137	+	4.85598i	−0.631007	+	0.300003i
$263$	12.8467	−	12.8467i	0.792159	−	0.792159i	−0.189686	−	0.981845i	$-0.560747\pi$
$263$	12.8467	−	12.8467i	0.792159	−	0.792159i	0.981845	+	0.189686i	$0.0607469\pi$
$264$	7.38307	+	5.40671i	0.454396	+	0.332760i
$265$	−19.7257	−	19.7257i	−1.21174	−	1.21174i
$266$	−1.73683	−	0.617500i	−0.106492	−	0.0378613i
$267$	1.29541	−	0.536575i	0.0792776	−	0.0328379i
$268$	−3.77777	+	12.6369i	−0.230764	+	0.771924i
$269$	3.18478	−	7.68874i	0.194180	−	0.468791i	−0.796561	−	0.604558i	$-0.793350\pi$
$269$	3.18478	−	7.68874i	0.194180	−	0.468791i	0.990741	+	0.135767i	$0.0433499\pi$
$270$	−0.280627	−	5.48644i	−0.0170784	−	0.333894i
$271$		−	29.7589i		−	1.80772i	−0.427823	−	0.903862i	$-0.640719\pi$
$271$		−	29.7589i		−	1.80772i	0.427823	−	0.903862i	$-0.359281\pi$
$272$	4.31465	+	20.8122i	0.261614	+	1.26192i
$273$			5.14010i			0.311093i
$274$	21.3326	−	1.09114i	1.28875	−	0.0659183i
$275$	12.4926	−	30.1598i	0.753333	−	1.81871i
$276$	−10.7573	+	5.80584i	−0.647515	+	0.349470i
$277$	13.4191	−	5.55836i	0.806274	−	0.333970i	0.0588078	−	0.998269i	$-0.481270\pi$
$277$	13.4191	−	5.55836i	0.806274	−	0.333970i	0.747466	+	0.664300i	$0.231270\pi$
$278$	2.05222	−	5.77225i	0.123084	−	0.346197i
$279$	−1.00612	−	1.00612i	−0.0602348	−	0.0602348i
$280$	−8.37710	−	13.7865i	−0.500628	−	0.823899i
$281$	0.428981	−	0.428981i	0.0255909	−	0.0255909i	−0.694196	−	0.719786i	$-0.744240\pi$
$281$	0.428981	−	0.428981i	0.0255909	−	0.0255909i	0.719786	+	0.694196i	$0.244240\pi$
$282$	−6.42235	−	13.5084i	−0.382446	−	0.804411i
$283$	10.2786	+	24.8146i	0.610997	+	1.47508i	0.861907	+	0.507067i	$0.169270\pi$
$283$	10.2786	+	24.8146i	0.610997	+	1.47508i	−0.250910	+	0.968010i	$0.580730\pi$
$284$	−6.39550	−	5.20561i	−0.379503	−	0.308896i
$285$	−3.18601	−	1.31969i	−0.188723	−	0.0781716i
$286$	−11.8903	−	10.7332i	−0.703091	−	0.634666i
$287$	7.11474			0.419970
$288$	5.47318	−	1.42978i	0.322510	−	0.0842505i
$289$	−11.2351			−0.660890
$290$	25.5217	+	23.0379i	1.49869	+	1.35283i
$291$	−13.4240	−	5.56041i	−0.786930	−	0.325957i
$292$	1.82237	−	2.23893i	0.106646	−	0.131023i
$293$	−4.95811	−	11.9699i	−0.289656	−	0.699292i	0.710333	−	0.703865i	$-0.248544\pi$
$293$	−4.95811	−	11.9699i	−0.289656	−	0.699292i	−0.999990	+	0.00457366i	$0.998544\pi$
$294$	2.94157	+	6.18711i	0.171556	+	0.360840i
$295$	−1.33111	+	1.33111i	−0.0775005	+	0.0775005i
$296$	−1.13250	+	4.64017i	−0.0658254	+	0.269704i
$297$	2.28777	+	2.28777i	0.132750	+	0.132750i
$298$	8.97777	−	25.2517i	0.520068	−	1.46279i
$299$	19.7684	−	8.18834i	1.14324	−	0.473544i
$300$	−9.58440	−	17.7585i	−0.553356	−	1.02528i
$301$	3.95618	−	9.55106i	0.228030	−	0.550514i
$302$	−2.25960	+	0.115577i	−0.130025	+	0.00665069i
$303$		−	1.94040i		−	0.111473i
$304$	0.664639	−	3.48823i	0.0381197	−	0.200064i
$305$			13.3129i			0.762293i
$306$	0.383867	+	7.50486i	0.0219442	+	0.429024i
$307$	8.37498	−	20.2190i	0.477985	−	1.15396i	−0.482567	−	0.875859i	$-0.660296\pi$
$307$	8.37498	−	20.2190i	0.477985	−	1.15396i	0.960552	−	0.278099i	$-0.0897044\pi$
$308$	9.10271	+	2.72122i	0.518675	+	0.155056i
$309$	2.76338	−	1.14463i	0.157203	−	0.0651157i
$310$	−7.36505	−	2.61851i	−0.418307	−	0.148721i
$311$	5.71820	+	5.71820i	0.324249	+	0.324249i	0.850395	−	0.526145i	$-0.176363\pi$
$311$	5.71820	+	5.71820i	0.324249	+	0.324249i	−0.526145	+	0.850395i	$0.676363\pi$
$312$	−9.78568	+	1.51215i	−0.554005	+	0.0856084i
$313$	11.6027	−	11.6027i	0.655823	−	0.655823i	−0.298566	−	0.954389i	$-0.596508\pi$
$313$	11.6027	−	11.6027i	0.655823	−	0.655823i	0.954389	+	0.298566i	$0.0965083\pi$
$314$	−2.33898	+	1.11203i	−0.131996	+	0.0627557i
$315$	−2.18265	−	5.26938i	−0.122978	−	0.296896i
$316$	−25.4861	+	2.61402i	−1.43370	+	0.147050i
$317$	−19.5616	−	8.10268i	−1.09869	−	0.455092i	−0.241660	−	0.970361i	$-0.577692\pi$
$317$	−19.5616	−	8.10268i	−1.09869	−	0.455092i	−0.857028	+	0.515269i	$0.827692\pi$
$318$	6.80511	−	7.53879i	0.381612	−	0.422754i
$319$	−20.2487			−1.13371
$320$	23.7821	−	20.0041i	1.32946	−	1.11826i
$321$	−5.00379			−0.279284
$322$	−8.50389	+	9.42072i	−0.473903	+	0.524996i
$323$	4.35812	+	1.80519i	0.242492	+	0.100444i
$324$	1.98956	−	0.204063i	0.110531	−	0.0113368i
$325$	13.5175	+	32.6341i	0.749816	+	1.81022i
$326$	−27.9087	+	13.2688i	−1.54572	+	0.734890i
$327$	−0.251083	+	0.251083i	−0.0138849	+	0.0138849i
$328$	2.09306	+	13.5450i	0.115570	+	0.747897i
$329$	−10.9806	−	10.9806i	−0.605379	−	0.605379i
$330$	16.7470	+	5.95411i	0.921895	+	0.327763i
$331$	0.922294	−	0.382027i	0.0506939	−	0.0209981i	−0.357192	−	0.934031i	$-0.616266\pi$
$331$	0.922294	−	0.382027i	0.0506939	−	0.0209981i	0.407886	+	0.913033i	$0.366266\pi$
$332$	32.1234	+	9.60316i	1.76300	+	0.527042i
$333$	−0.646238	+	1.56016i	−0.0354136	+	0.0854961i
$334$	−0.245678	−	4.80316i	−0.0134429	−	0.262817i
$335$			25.6178i			1.39965i
$336$	4.85675	−	3.30217i	0.264957	−	0.180148i
$337$			32.5245i			1.77172i	0.463949	+	0.885862i	$0.346432\pi$
$337$			32.5245i			1.77172i	−0.463949	+	0.885862i	$0.653568\pi$
$338$	−1.05112	+	0.0537639i	−0.0571734	+	0.00292437i
$339$	−0.913437	+	2.20523i	−0.0496111	+	0.119772i
$340$	19.6072	+	36.3293i	1.06335	+	1.97023i
$341$	4.25311	−	1.76170i	0.230319	−	0.0954012i
$342$	0.420567	−	1.18292i	0.0227417	−	0.0639652i
$343$	12.2968	+	12.2968i	0.663966	+	0.663966i
$344$	19.3471	+	4.72195i	1.04313	+	0.254591i
$345$	−16.7886	+	16.7886i	−0.903867	+	0.903867i
$346$	−6.00579	−	12.6322i	−0.322873	−	0.679111i
$347$	−11.0057	−	26.5700i	−0.590815	−	1.42635i	−0.882717	−	0.469906i	$-0.844288\pi$
$347$	−11.0057	−	26.5700i	−0.590815	−	1.42635i	0.291901	−	0.956448i	$-0.405712\pi$
$348$	−7.90159	+	9.70772i	−0.423570	+	0.520388i
$349$	−6.12429	−	2.53676i	−0.327826	−	0.135790i	0.212700	−	0.977118i	$-0.431774\pi$
$349$	−6.12429	−	2.53676i	−0.327826	−	0.135790i	−0.540525	+	0.841328i	$0.681774\pi$
$350$	−15.5519	−	14.0384i	−0.831286	−	0.750385i
$351$	−3.50082			−0.186860
$352$	−2.50275	+	18.1302i	−0.133397	+	0.966344i
$353$	−27.1372			−1.44437			−0.722185	−	0.691700i	$-0.756862\pi$
$353$	−27.1372			−1.44437			−0.722185	+	0.691700i	$0.756862\pi$
$354$	−0.508726	−	0.459217i	−0.0270385	−	0.0244071i
$355$	−14.7974	−	6.12928i	−0.785364	−	0.325309i
$356$	2.17490	+	1.77025i	0.115269	+	0.0938233i
$357$	2.98563	+	7.20794i	0.158016	+	0.381485i
$358$	−11.1975	−	23.5522i	−0.591809	−	1.24477i
$359$	−6.86522	+	6.86522i	−0.362332	+	0.362332i	−0.864671	−	0.502339i	$-0.832473\pi$
$359$	−6.86522	+	6.86522i	−0.362332	+	0.362332i	0.502339	+	0.864671i	$0.332473\pi$
$360$	9.38970	−	5.70549i	0.494881	−	0.300706i
$361$	12.8778	+	12.8778i	0.677777	+	0.677777i
$362$	−8.91650	+	25.0793i	−0.468641	+	1.31814i
$363$	0.491715	−	0.203675i	0.0258084	−	0.0106902i
$364$	−9.04670	+	4.88259i	−0.474176	+	0.255917i
$365$	2.14573	−	5.18025i	0.112313	−	0.271147i
$366$	−4.84035	+	0.247580i	−0.253009	+	0.0129412i
$367$			32.3050i			1.68631i	0.537671	+	0.843154i	$0.319304\pi$
$367$			32.3050i			1.68631i	−0.537671	+	0.843154i	$0.680696\pi$
$368$	−20.4368	−	13.4182i	−1.06534	−	0.699472i
$369$			4.84572i			0.252258i
$370$	0.473895	+	9.26496i	0.0246366	+	0.481662i
$371$	4.03502	−	9.74139i	0.209488	−	0.505748i
$372$	0.815080	−	2.72651i	0.0422599	−	0.141363i
$373$	1.12962	−	0.467902i	0.0584893	−	0.0242271i	−0.353247	−	0.935530i	$-0.614922\pi$
$373$	1.12962	−	0.467902i	0.0584893	−	0.0242271i	0.411736	+	0.911303i	$0.364922\pi$
$374$	−22.9082	−	8.14458i	−1.18455	−	0.421146i
$375$	−13.9809	−	13.9809i	−0.721973	−	0.721973i
$376$	17.6744	−	24.1351i	0.911489	−	1.24467i
$377$	15.4926	−	15.4926i	0.797911	−	0.797911i
$378$	1.87527	−	0.891570i	0.0964535	−	0.0458574i
$379$	−12.6694	−	30.5866i	−0.650783	−	1.57113i	−0.811644	−	0.584152i	$-0.801427\pi$
$379$	−12.6694	−	30.5866i	−0.650783	−	1.57113i	0.160861	−	0.986977i	$-0.448573\pi$
$380$	−0.703713	−	6.86103i	−0.0360997	−	0.351964i
$381$	12.4004	+	5.13640i	0.635289	+	0.263145i
$382$	−9.39526	+	10.4082i	−0.480703	+	0.532529i
$383$	9.01248			0.460516			0.230258	−	0.973130i	$-0.426043\pi$
$383$	9.01248			0.460516			0.230258	+	0.973130i	$0.426043\pi$
$384$	7.71543	+	8.27479i	0.393726	+	0.422271i
$385$	18.4532			0.940461
$386$	−9.33241	+	10.3386i	−0.475007	+	0.526219i
$387$	6.50505	+	2.69448i	0.330670	+	0.136968i
$388$	−2.96504	−	28.9084i	−0.150527	−	1.46760i
$389$	−0.147171	−	0.355303i	−0.00746188	−	0.0180146i	0.920105	−	0.391673i	$-0.128103\pi$
$389$	−0.147171	−	0.355303i	−0.00746188	−	0.0180146i	−0.927567	+	0.373658i	$0.878103\pi$
$390$	−17.3691	+	8.25787i	−0.879516	+	0.418153i
$391$	22.9650	−	22.9650i	1.16139	−	1.16139i
$392$	−8.09526	+	11.0544i	−0.408872	+	0.558331i
$393$	−5.65467	−	5.65467i	−0.285240	−	0.285240i
$394$	−19.0270	−	6.76470i	−0.958566	−	0.340801i
$395$	−45.9731	+	19.0427i	−2.31316	+	0.958141i
$396$	−1.85337	+	6.19968i	−0.0931355	+	0.311546i
$397$	−10.7013	+	25.8353i	−0.537084	+	1.29664i	0.389666	+	0.920956i	$0.372591\pi$
$397$	−10.7013	+	25.8353i	−0.537084	+	1.29664i	−0.926750	+	0.375679i	$0.877409\pi$
$398$	−0.627774	−	12.2734i	−0.0314675	−	0.615210i
$399$		−	1.30344i		−	0.0652535i
$400$	22.1511	−	33.7376i	1.10755	−	1.68688i
$401$			39.5351i			1.97429i	0.159825	+	0.987145i	$0.448907\pi$
$401$			39.5351i			1.97429i	−0.159825	+	0.987145i	$0.551093\pi$
$402$	−9.31423	+	0.476415i	−0.464552	+	0.0237614i
$403$	−1.90623	+	4.60204i	−0.0949559	+	0.229244i
$404$	3.41516	−	1.84319i	0.169910	−	0.0917023i
$405$	3.58888	−	1.48656i	0.178333	−	0.0738678i
$406$	−4.35329	+	12.2444i	−0.216050	+	0.607681i
$407$	−3.86336	−	3.86336i	−0.191500	−	0.191500i
$408$	−12.8441	+	7.80449i	−0.635878	+	0.386380i
$409$	−16.6530	+	16.6530i	−0.823439	+	0.823439i	−0.986600	−	0.163160i	$-0.947831\pi$
$409$	−16.6530	+	16.6530i	−0.823439	+	0.823439i	0.163160	+	0.986600i	$0.447831\pi$
$410$	11.4302	+	24.0416i	0.564500	+	1.18733i
$411$	5.78010	+	13.9544i	0.285111	+	0.688319i
$412$	4.63951	+	3.77633i	0.228572	+	0.186046i
$413$	−0.657361	−	0.272288i	−0.0323466	−	0.0133984i
$414$	−6.41627	−	5.79184i	−0.315343	−	0.284653i
$415$	65.1211			3.19667
$416$	−11.9569	−	15.7867i	−0.586233	−	0.774004i
$417$	4.33189			0.212133
$418$	3.01518	+	2.72174i	0.147477	+	0.133125i
$419$	30.2809	+	12.5428i	1.47932	+	0.612754i	0.968962	−	0.247210i	$-0.0795136\pi$
$419$	30.2809	+	12.5428i	1.47932	+	0.612754i	0.510356	+	0.859963i	$0.329514\pi$
$420$	7.20093	−	8.84691i	0.351370	−	0.431685i
$421$	−14.0297	−	33.8706i	−0.683764	−	1.65075i	−0.756981	−	0.653436i	$-0.773327\pi$
$421$	−14.0297	−	33.8706i	−0.683764	−	1.65075i	0.0732174	−	0.997316i	$-0.476673\pi$
$422$	−6.57058	−	13.8201i	−0.319851	−	0.672754i
$423$	7.47867	−	7.47867i	0.363626	−	0.363626i
$424$	19.7326	+	4.81605i	0.958302	+	0.233888i
$425$	37.9111	+	37.9111i	1.83896	+	1.83896i
$426$	1.95332	−	5.49408i	0.0946387	−	0.266189i
$427$	−4.64885	+	1.92561i	−0.224973	+	0.0931870i
$428$	−4.75311	−	8.80680i	−0.229750	−	0.425693i
$429$	4.33448	−	10.4644i	0.209271	−	0.505224i
$430$	38.6301	−	1.97590i	1.86291	−	0.0952862i
$431$		−	11.0244i		−	0.531027i	−0.964107	−	0.265513i	$-0.914459\pi$
$431$		−	11.0244i		−	0.531027i	0.964107	−	0.265513i	$-0.0855414\pi$
$432$	2.24904	+	3.30784i	0.108207	+	0.159148i
$433$		−	26.0973i		−	1.25416i	−0.778956	−	0.627079i	$-0.784250\pi$
$433$		−	26.0973i		−	1.25416i	0.778956	−	0.627079i	$-0.215750\pi$
$434$	−0.150922	−	2.95062i	−0.00724447	−	0.141634i
$435$	−9.30363	+	22.4609i	−0.446075	+	1.07692i
$436$	−0.680418	−	0.203408i	−0.0325861	−	0.00974150i
$437$	−5.01291	+	2.07642i	−0.239800	+	0.0993285i
$438$	1.92336	+	0.683816i	0.0919017	+	0.0326740i
$439$	−9.89316	−	9.89316i	−0.472175	−	0.472175i	0.430443	−	0.902618i	$-0.358357\pi$
$439$	−9.89316	−	9.89316i	−0.472175	−	0.472175i	−0.902618	+	0.430443i	$0.858357\pi$
$440$	5.42867	+	35.1310i	0.258802	+	1.67481i
$441$	−3.42539	+	3.42539i	−0.163114	+	0.163114i
$442$	23.7590	−	11.2959i	1.13010	−	0.537290i
$443$	7.29919	+	17.6218i	0.346795	+	0.837237i	0.996994	+	0.0774732i	$0.0246852\pi$
$443$	7.29919	+	17.6218i	0.346795	+	0.837237i	−0.650200	+	0.759763i	$0.725315\pi$
$444$	−3.35978	+	0.344601i	−0.159448	+	0.0163540i
$445$	5.03210	+	2.08436i	0.238544	+	0.0988083i
$446$	13.3802	−	14.8228i	0.633571	−	0.701879i
$447$	18.9505			0.896330
$448$	10.4253	+	5.41126i	0.492550	+	0.255658i
$449$	7.16414			0.338096			0.169048	−	0.985608i	$-0.445931\pi$
$449$	7.16414			0.338096			0.169048	+	0.985608i	$0.445931\pi$
$450$	9.56130	−	10.5921i	0.450724	−	0.499318i
$451$	−14.4844	−	5.99964i	−0.682044	−	0.282512i
$452$	−4.74894	+	0.487083i	−0.223371	+	0.0229104i
$453$	−0.612243	−	1.47809i	−0.0287657	−	0.0694465i
$454$	23.3407	−	11.0970i	1.09543	−	0.520808i
$455$	−14.1189	+	14.1189i	−0.661902	+	0.661902i
$456$	2.48147	−	0.383453i	0.116206	−	0.0179568i
$457$	−15.2704	−	15.2704i	−0.714317	−	0.714317i	0.253118	−	0.967435i	$-0.418544\pi$
$457$	−15.2704	−	15.2704i	−0.714317	−	0.714317i	−0.967435	+	0.253118i	$0.918544\pi$
$458$	−13.6498	−	4.85294i	−0.637814	−	0.226763i
$459$	−4.90919	+	2.03345i	−0.229142	+	0.0949135i
$460$	−45.4958	−	13.6008i	−2.12125	−	0.634141i
$461$	−5.40240	+	13.0425i	−0.251615	+	0.607452i	−0.998335	−	0.0576867i	$-0.981628\pi$
$461$	−5.40240	+	13.0425i	−0.251615	+	0.607452i	0.746720	+	0.665139i	$0.231628\pi$
$462$	0.343174	+	6.70928i	0.0159659	+	0.312144i
$463$			13.5410i			0.629305i	0.949207	+	0.314652i	$0.101888\pi$
$463$			13.5410i			0.629305i	−0.949207	+	0.314652i	$0.898112\pi$
$464$	−24.5916	−	4.68561i	−1.14163	−	0.217524i
$465$		−	5.52723i		−	0.256319i
$466$	−6.11255	+	0.312652i	−0.283159	+	0.0144833i
$467$	6.18122	−	14.9228i	0.286033	−	0.690544i	−0.713920	−	0.700227i	$-0.753082\pi$
$467$	6.18122	−	14.9228i	0.286033	−	0.690544i	0.999953	+	0.00968289i	$0.00308221\pi$
$468$	−3.32544	−	6.16154i	−0.153719	−	0.284817i
$469$	−8.94573	+	3.70544i	−0.413075	+	0.171101i
$470$	19.4639	−	54.7458i	0.897802	−	2.52524i
$471$	−1.29494	−	1.29494i	−0.0596676	−	0.0596676i
$472$	0.324993	−	1.33158i	0.0149590	−	0.0612910i
$473$	−16.1082	+	16.1082i	−0.740656	+	0.740656i
$474$	−7.77857	−	16.3609i	−0.357282	−	0.751483i
$475$	−3.42780	−	8.27543i	−0.157278	−	0.379703i
$476$	−9.85010	+	12.1016i	−0.451479	+	0.554676i
$477$	6.63468	+	2.74817i	0.303781	+	0.125830i
$478$	0.220794	+	0.199307i	0.0100989	+	0.00911607i
$479$	−6.44443			−0.294453			−0.147227	−	0.989103i	$-0.547035\pi$
$479$	−6.44443			−0.294453			−0.147227	+	0.989103i	$0.547035\pi$
$480$	18.9611	+	11.1065i	0.865452	+	0.506938i
$481$	5.91185			0.269557
$482$	−13.7231	−	12.3876i	−0.625070	−	0.564238i
$483$	−8.29091	−	3.43421i	−0.377250	−	0.156262i
$484$	0.825555	+	0.671960i	0.0375252	+	0.0305436i
$485$	−21.5998	−	52.1465i	−0.980797	−	2.36785i
$486$	0.607232	+	1.27721i	0.0275446	+	0.0579355i
$487$	4.42962	−	4.42962i	0.200725	−	0.200725i	−0.599585	−	0.800311i	$-0.704668\pi$
$487$	4.42962	−	4.42962i	0.200725	−	0.200725i	0.800311	+	0.599585i	$0.204668\pi$
$488$	−5.03360	−	8.28395i	−0.227860	−	0.374997i
$489$	−15.4512	−	15.4512i	−0.698727	−	0.698727i
$490$	−8.91486	+	25.0747i	−0.402732	+	1.13276i
$491$	−11.7801	+	4.87947i	−0.531628	+	0.220207i	−0.632316	−	0.774711i	$-0.717896\pi$
$491$	−11.7801	+	4.87947i	−0.531628	+	0.220207i	0.100688	+	0.994918i	$0.467896\pi$
$492$	−8.52858	+	4.60296i	−0.384498	+	0.207517i
$493$	12.7264	−	30.7242i	0.573167	−	1.38375i
$494$	−4.38942	+	0.224515i	−0.197489	+	0.0101014i
$495$			12.5681i			0.564895i
$496$	5.57297	−	1.15536i	0.250234	−	0.0518770i
$497$		−	6.05380i		−	0.271550i
$498$	1.21106	+	23.6770i	0.0542687	+	1.06099i
$499$	2.23679	−	5.40009i	0.100132	−	0.241741i	−0.865873	−	0.500265i	$-0.833236\pi$
$499$	2.23679	−	5.40009i	0.100132	−	0.241741i	0.966005	+	0.258524i	$0.0832360\pi$
$500$	11.3263	−	37.8873i	0.506526	−	1.69437i
$501$	3.14192	−	1.30143i	0.140371	−	0.0581434i
$502$	4.23161	+	1.50447i	0.188866	+	0.0671478i
$503$	2.89565	+	2.89565i	0.129111	+	0.129111i	0.768709	−	0.639598i	$-0.220899\pi$
$503$	2.89565	+	2.89565i	0.129111	+	0.129111i	−0.639598	+	0.768709i	$0.720899\pi$
$504$	3.35051	+	2.45362i	0.149243	+	0.109293i
$505$	5.32991	−	5.32991i	0.237178	−	0.237178i
$506$	25.2567	−	12.0079i	1.12280	−	0.533817i
$507$	−0.284803	−	0.687575i	−0.0126485	−	0.0305363i
$508$	2.73894	+	26.7040i	0.121521	+	1.18480i
$509$	5.36042	+	2.22036i	0.237596	+	0.0984156i	0.498305	−	0.867002i	$-0.333956\pi$
$509$	5.36042	+	2.22036i	0.237596	+	0.0984156i	−0.260708	+	0.965418i	$0.583956\pi$
$510$	−19.5600	+	21.6688i	−0.866131	+	0.959511i
$511$	2.11930			0.0937525
$512$	−7.23493	+	21.4396i	−0.319742	+	0.947505i
$513$	0.887747			0.0391950
$514$	−2.43825	+	2.70113i	−0.107547	+	0.119142i
$515$	10.7345	+	4.44639i	0.473020	+	0.195931i
$516$	1.43681	+	14.0085i	0.0632519	+	0.616691i
$517$	13.0950	+	31.6142i	0.575919	+	1.39039i
$518$	−3.16677	+	1.50560i	−0.139140	+	0.0661521i
$519$	6.99360	−	6.99360i	0.306985	−	0.306985i
$520$	−31.0330	−	22.7258i	−1.36088	−	0.996592i
$521$	18.2831	+	18.2831i	0.800998	+	0.800998i	0.983252	−	0.182254i	$-0.0583392\pi$
$521$	18.2831	+	18.2831i	0.800998	+	0.800998i	−0.182254	+	0.983252i	$0.558339\pi$
$522$	−8.33946	−	2.96494i	−0.365008	−	0.129772i
$523$	−5.66441	+	2.34627i	−0.247687	+	0.102595i	−0.503073	−	0.864244i	$-0.667797\pi$
$523$	−5.66441	+	2.34627i	−0.247687	+	0.102595i	0.255386	+	0.966839i	$0.417797\pi$
$524$	4.58097	−	15.3237i	0.200121	−	0.669420i
$525$	5.66927	−	13.6868i	0.247427	−	0.597342i
$526$	1.31248	+	25.6598i	0.0572267	+	1.11882i
$527$			7.56065i			0.329347i
$528$	−12.6721	+	2.62711i	−0.551483	+	0.114330i
$529$			14.3570i			0.624217i
$530$	39.3999	−	2.01527i	1.71142	−	0.0875378i
$531$	0.185450	−	0.447716i	0.00804785	−	0.0194292i
$532$	2.29408	−	1.23814i	0.0994610	−	0.0536800i
$533$	15.6727	−	6.49185i	0.678860	−	0.281193i
$534$	−0.664259	+	1.86835i	−0.0287453	+	0.0808516i
$535$	−13.7445	−	13.7445i	−0.594224	−	0.594224i
$536$	−9.68611	−	15.9407i	−0.418376	−	0.688535i
$537$	13.0393	−	13.0393i	0.562686	−	0.562686i
$538$	5.05352	+	10.6293i	0.217873	+	0.458260i
$539$	−5.99780	−	14.4800i	−0.258343	−	0.623696i
$540$	6.02546	+	4.90442i	0.259295	+	0.211053i
$541$	5.96613	+	2.47125i	0.256504	+	0.106247i	0.507230	−	0.861811i	$-0.330669\pi$
$541$	5.96613	+	2.47125i	0.256504	+	0.106247i	−0.250726	+	0.968058i	$0.580669\pi$
$542$	31.2402	+	28.1999i	1.34188	+	1.21129i
$543$	−18.8212			−0.807696
$544$	−25.9367	−	15.1924i	−1.11203	−	0.651370i
$545$	−1.37936			−0.0590851
$546$	−5.39596	−	4.87082i	−0.230926	−	0.208452i
$547$	32.5453	+	13.4807i	1.39154	+	0.576393i	0.947541	−	0.319635i	$-0.103560\pi$
$547$	32.5453	+	13.4807i	1.39154	+	0.576393i	0.443996	+	0.896029i	$0.353560\pi$
$548$	−19.0695	+	23.4284i	−0.814611	+	1.00081i
$549$	−1.31150	−	3.16624i	−0.0559735	−	0.135132i
$550$	19.8229	+	41.6943i	0.845253	+	1.77785i
$551$	−3.92865	+	3.92865i	−0.167366	+	0.167366i
$552$	4.09895	−	16.7945i	0.174463	−	0.714821i
$553$	−13.2994	−	13.2994i	−0.565547	−	0.565547i
$554$	−6.88104	+	19.3542i	−0.292347	+	0.822282i
$555$	−6.06054	+	2.51036i	−0.257256	+	0.106559i
$556$	4.11487	+	7.62423i	0.174509	+	0.323339i
$557$	−6.30768	+	15.2281i	−0.267265	+	0.645235i	−0.999353	−	0.0359756i	$-0.988546\pi$
$557$	−6.30768	+	15.2281i	−0.267265	+	0.645235i	0.732088	+	0.681210i	$0.238546\pi$
$558$	2.00961	−	0.102790i	0.0850736	−	0.00435144i
$559$		−	24.6494i		−	1.04256i
$560$	22.4110	+	4.27013i	0.947036	+	0.180446i
$561$		−	17.1918i		−	0.725839i
$562$	0.0438267	+	0.856842i	0.00184872	+	0.0361437i
$563$	−3.06528	+	7.40024i	−0.129186	+	0.311883i	−0.975217	−	0.221251i	$-0.928986\pi$
$563$	−3.06528	+	7.40024i	−0.129186	+	0.311883i	0.846031	+	0.533134i	$0.178986\pi$
$564$	20.2667	+	6.05864i	0.853380	+	0.255115i
$565$	−8.56638	+	3.54831i	−0.360390	+	0.149279i
$566$	−35.7899	−	12.7245i	−1.50436	−	0.534849i
$567$	1.03821	+	1.03821i	0.0436008	+	0.0436008i
$568$	11.5252	−	1.78094i	0.483586	−	0.0747268i
$569$	17.9001	−	17.9001i	0.750410	−	0.750410i	−0.224146	−	0.974556i	$-0.571959\pi$
$569$	17.9001	−	17.9001i	0.750410	−	0.750410i	0.974556	+	0.224146i	$0.0719591\pi$
$570$	4.40448	−	2.09405i	0.184483	−	0.0877100i
$571$	−2.41948	−	5.84113i	−0.101252	−	0.244444i	0.865133	−	0.501542i	$-0.167234\pi$
$571$	−2.41948	−	5.84113i	−0.101252	−	0.244444i	−0.966385	+	0.257098i	$0.917234\pi$
$572$	22.5349	−	2.31133i	0.942230	−	0.0966414i
$573$	−9.15996	−	3.79418i	−0.382663	−	0.158504i
$574$	−6.74201	+	7.46889i	−0.281406	+	0.311745i
$575$	−61.6698			−2.57181
$576$	−3.68551	+	7.10050i	−0.153563	+	0.295854i
$577$	−24.5768			−1.02314			−0.511572	−	0.859240i	$-0.670937\pi$
$577$	−24.5768			−1.02314			−0.511572	+	0.859240i	$0.670937\pi$
$578$	10.6465	−	11.7944i	0.442838	−	0.490581i
$579$	−9.09868	−	3.76880i	−0.378128	−	0.156626i
$580$	−48.3694	+	4.96108i	−2.00843	+	0.205998i
$581$	9.41931	+	22.7402i	0.390779	+	0.943424i
$582$	18.5580	−	8.82311i	0.769252	−	0.365730i
$583$	−16.4292	+	16.4292i	−0.680429	+	0.680429i
$584$	0.623471	+	4.03472i	0.0257994	+	0.166958i
$585$	−9.61609	−	9.61609i	−0.397576	−	0.397576i
$586$	17.2641	+	6.13795i	0.713175	+	0.253556i
$587$	29.2268	−	12.1061i	1.20632	−	0.499674i	0.313284	−	0.949659i	$-0.398571\pi$
$587$	29.2268	−	12.1061i	1.20632	−	0.499674i	0.893036	+	0.449985i	$0.148571\pi$
$588$	−9.28255	−	2.77499i	−0.382806	−	0.114438i
$589$	0.483385	−	1.16699i	0.0199175	−	0.0480852i
$590$	−0.135993	−	2.65875i	−0.00559874	−	0.109459i
$591$		−	14.2791i		−	0.587365i
$592$	−3.79797	−	5.58595i	−0.156095	−	0.229581i
$593$		−	20.8403i		−	0.855810i	−0.903824	−	0.427905i	$-0.859252\pi$
$593$		−	20.8403i		−	0.855810i	0.903824	−	0.427905i	$-0.140748\pi$
$594$	−4.56956	+	0.233729i	−0.187491	+	0.00959003i
$595$	−11.5979	+	27.9998i	−0.475467	+	1.14788i
$596$	18.0012	+	33.3534i	0.737356	+	1.36621i
$597$	8.02847	−	3.32550i	0.328584	−	0.136104i
$598$	−10.1369	+	28.5118i	−0.414527	+	1.16593i
$599$	31.6901	+	31.6901i	1.29482	+	1.29482i	0.931768	+	0.363053i	$0.118266\pi$
$599$	31.6901	+	31.6901i	1.29482	+	1.29482i	0.363053	+	0.931768i	$0.381734\pi$
$600$	27.7247	+	6.76664i	1.13186	+	0.276247i
$601$	−12.9864	+	12.9864i	−0.529726	+	0.529726i	−0.920491	−	0.390764i	$-0.872211\pi$
$601$	−12.9864	+	12.9864i	−0.529726	+	0.529726i	0.390764	+	0.920491i	$0.372211\pi$
$602$	6.27756	+	13.2038i	0.255854	+	0.538147i
$603$	−2.52371	−	6.09277i	−0.102773	−	0.248117i
$604$	2.01990	−	2.48160i	0.0821884	−	0.100975i
$605$	1.91010	+	0.791190i	0.0776567	+	0.0321665i
$606$	2.03699	+	1.83875i	0.0827471	+	0.0746941i
$607$	−7.55886			−0.306805			−0.153402	−	0.988164i	$-0.549023\pi$
$607$	−7.55886			−0.306805			−0.153402	+	0.988164i	$0.549023\pi$
$608$	3.03204	+	4.00321i	0.122966	+	0.162352i
$609$	−9.18905			−0.372359
$610$	−13.9755	−	12.6154i	−0.565853	−	0.510784i
$611$	−34.2078	−	14.1693i	−1.38390	−	0.573230i
$612$	−8.24218	−	6.70872i	−0.333170	−	0.271184i
$613$	−5.16053	−	12.4586i	−0.208432	−	0.503199i	0.784745	−	0.619819i	$-0.212794\pi$
$613$	−5.16053	−	12.4586i	−0.208432	−	0.503199i	−0.993177	+	0.116620i	$0.962794\pi$
$614$	13.2892	+	27.9516i	0.536308	+	1.12804i
$615$	−13.3102	+	13.3102i	−0.536721	+	0.536721i
$616$	−11.4825	+	6.97715i	−0.462644	+	0.281117i
$617$	−23.7425	−	23.7425i	−0.955835	−	0.955835i	0.0432297	−	0.999065i	$-0.486235\pi$
$617$	−23.7425	−	23.7425i	−0.955835	−	0.955835i	−0.999065	+	0.0432297i	$0.986235\pi$
$618$	−1.41701	+	3.98560i	−0.0570003	+	0.160324i
$619$	37.9338	−	15.7127i	1.52469	−	0.631547i	0.546165	−	0.837678i	$-0.316087\pi$
$619$	37.9338	−	15.7127i	1.52469	−	0.631547i	0.978524	+	0.206131i	$0.0660872\pi$
$620$	9.72806	−	5.25033i	0.390688	−	0.210858i
$621$	2.33898	−	5.64679i	0.0938598	−	0.226598i
$622$	−11.4215	+	0.584198i	−0.457959	+	0.0234242i
$623$			2.05869i			0.0824798i
$624$	7.68562	−	11.7057i	0.307671	−	0.468604i
$625$		−	26.3564i		−	1.05426i
$626$	1.18539	+	23.1751i	0.0473775	+	0.926263i
$627$	−1.09915	+	2.65358i	−0.0438957	+	0.105974i
$628$	1.04906	−	3.50918i	0.0418620	−	0.140032i
$629$	8.29016	−	3.43390i	0.330551	−	0.136919i
$630$	7.59997	+	2.70203i	0.302790	+	0.107652i
$631$	−5.63001	−	5.63001i	−0.224127	−	0.224127i	0.586107	−	0.810234i	$-0.300660\pi$
$631$	−5.63001	−	5.63001i	−0.224127	−	0.224127i	−0.810234	+	0.586107i	$0.800660\pi$
$632$	21.4068	−	29.2318i	0.851516	−	1.16278i
$633$	7.65129	−	7.65129i	0.304111	−	0.304111i
$634$	27.0428	−	12.8571i	1.07401	−	0.510621i
$635$	19.9527	+	48.1701i	0.791798	+	1.91157i
$636$	1.46544	+	14.2877i	0.0581085	+	0.566544i
$637$	15.6679	+	6.48986i	0.620785	+	0.257137i
$638$	19.1879	−	21.2566i	0.759656	−	0.841557i
$639$	4.12313			0.163108
$640$	−1.53644	+	43.9220i	−0.0607333	+	1.73617i
$641$	36.4242			1.43867			0.719334	−	0.694664i	$-0.244447\pi$
$641$	36.4242			1.43867			0.719334	+	0.694664i	$0.244447\pi$
$642$	4.74165	−	5.25287i	0.187138	−	0.207314i
$643$	−22.9769	−	9.51734i	−0.906120	−	0.375327i	−0.119550	−	0.992828i	$-0.538145\pi$
$643$	−22.9769	−	9.51734i	−0.906120	−	0.375327i	−0.786570	+	0.617501i	$0.788145\pi$
$644$	−1.83126	−	17.8544i	−0.0721618	−	0.703561i
$645$	10.4669	+	25.2693i	0.412133	+	0.994978i
$646$	−6.02486	+	2.86443i	−0.237045	+	0.112700i
$647$	−34.0895	+	34.0895i	−1.34020	+	1.34020i	−0.444336	+	0.895860i	$0.646560\pi$
$647$	−34.0895	+	34.0895i	−1.34020	+	1.34020i	−0.895860	+	0.444336i	$0.853440\pi$
$648$	−1.67111	+	2.28197i	−0.0656475	+	0.0896442i
$649$	1.10866	+	1.10866i	0.0435188	+	0.0435188i
$650$	−47.0679	−	16.7341i	−1.84616	−	0.656367i
$651$	1.93010	−	0.799475i	0.0756468	−	0.0313339i
$652$	12.5174	−	41.8716i	0.490218	−	1.63982i
$653$	11.4288	−	27.5915i	0.447243	−	1.07974i	−0.526108	−	0.850418i	$-0.676349\pi$
$653$	11.4288	−	27.5915i	0.447243	−	1.07974i	0.973351	−	0.229322i	$-0.0736508\pi$
$654$	−0.0256519	−	0.501511i	−0.00100307	−	0.0196106i
$655$		−	31.0645i		−	1.21379i
$656$	−16.2026	−	10.6382i	−0.632607	−	0.415350i
$657$			1.44342i			0.0563131i
$658$	21.9325	−	1.12183i	0.855018	−	0.0437334i
$659$	−4.60322	+	11.1132i	−0.179316	+	0.432907i	−0.987824	−	0.155579i	$-0.950276\pi$
$659$	−4.60322	+	11.1132i	−0.179316	+	0.432907i	0.808507	+	0.588486i	$0.200276\pi$
$660$	−22.1202	+	11.9385i	−0.861027	+	0.464705i
$661$	−18.8580	+	7.81122i	−0.733490	+	0.303821i	−0.717985	−	0.696058i	$-0.754935\pi$
$661$	−18.8580	+	7.81122i	−0.733490	+	0.303821i	−0.0155046	+	0.999880i	$0.504935\pi$
$662$	−0.472934	+	1.33022i	−0.0183811	+	0.0517003i
$663$	13.1538	+	13.1538i	0.510850	+	0.510850i
$664$	−40.5217	+	24.6223i	−1.57255	+	0.955530i
$665$	3.58029	−	3.58029i	0.138838	−	0.138838i
$666$	−1.02543	−	2.15683i	−0.0397347	−	0.0835754i
$667$	14.6385	+	35.3404i	0.566803	+	1.36838i
$668$	5.27506	+	4.29363i	0.204098	+	0.166125i
$669$	13.0451	+	5.40346i	0.504353	+	0.208910i
$670$	−26.8930	−	24.2758i	−1.03897	−	0.937855i
$671$	11.0881			0.428050
$672$	−1.13577	+	8.22767i	−0.0438134	+	0.317389i
$673$	−46.7689			−1.80281			−0.901404	−	0.432979i	$-0.857463\pi$
$673$	−46.7689			−1.80281			−0.901404	+	0.432979i	$0.857463\pi$
$674$	−34.1435	−	30.8206i	−1.31516	−	1.18717i
$675$	9.32184	+	3.86123i	0.358798	+	0.148619i
$676$	0.939614	−	1.15439i	0.0361390	−	0.0443996i
$677$	−7.05433	−	17.0307i	−0.271120	−	0.654541i	0.728412	−	0.685140i	$-0.240259\pi$
$677$	−7.05433	−	17.0307i	−0.271120	−	0.654541i	−0.999532	+	0.0305981i	$0.990259\pi$
$678$	−1.44942	−	3.04861i	−0.0556646	−	0.117081i
$679$	15.0853	−	15.0853i	0.578920	−	0.578920i
$680$	−56.7177	−	13.8428i	−2.17502	−	0.530848i
$681$	12.9222	+	12.9222i	0.495179	+	0.495179i
$682$	−2.18091	+	6.13422i	−0.0835115	+	0.234892i
$683$	36.1287	−	14.9650i	1.38243	−	0.572620i	0.437297	−	0.899317i	$-0.355936\pi$
$683$	36.1287	−	14.9650i	1.38243	−	0.572620i	0.945129	+	0.326697i	$0.105936\pi$
$684$	0.843272	+	1.56246i	0.0322433	+	0.0597420i
$685$	−22.4532	+	54.2068i	−0.857893	+	2.07114i
$686$	−24.5615	+	1.25630i	−0.937764	+	0.0479658i
$687$		−	10.2437i		−	0.390823i
$688$	−23.2905	+	15.8355i	−0.887943	+	0.603725i
$689$		−	25.1406i		−	0.957779i
$690$	−1.71520	−	33.5333i	−0.0652966	−	1.27659i
$691$	−11.2605	+	27.1853i	−0.428371	+	1.03418i	0.551434	+	0.834219i	$0.314081\pi$
$691$	−11.2605	+	27.1853i	−0.428371	+	1.03418i	−0.979804	+	0.199959i	$0.935919\pi$
$692$	18.9521	+	5.66567i	0.720452	+	0.215377i
$693$	−4.38878	+	1.81789i	−0.166716	+	0.0690560i
$694$	38.3217	+	13.6246i	1.45467	+	0.517182i
$695$	11.8989	+	11.8989i	0.451349	+	0.451349i
$696$	−2.70329	−	17.4941i	−0.102468	−	0.663111i
$697$	18.2070	−	18.2070i	0.689639	−	0.689639i
$698$	8.46648	−	4.02527i	0.320461	−	0.152359i
$699$	−1.65621	−	3.99844i	−0.0626435	−	0.151235i
$700$	29.4744	−	3.02309i	1.11403	−	0.114262i
$701$	−21.0746	−	8.72940i	−0.795978	−	0.329705i	−0.0526339	−	0.998614i	$-0.516762\pi$
$701$	−21.0746	−	8.72940i	−0.795978	−	0.329705i	−0.743344	+	0.668909i	$0.766762\pi$
$702$	3.31742	−	3.67508i	0.125208	−	0.138707i
$703$	−1.49914			−0.0565411
$704$	−16.6610	−	19.8077i	−0.627937	−	0.746533i
$705$	41.0849			1.54735
$706$	25.7156	−	28.4881i	0.967819	−	1.07216i
$707$	2.63214	+	1.09027i	0.0989917	+	0.0410037i
$708$	0.964151	−	0.0988897i	0.0362350	−	0.00371650i
$709$	0.617186	+	1.49002i	0.0231789	+	0.0559588i	0.935045	−	0.354528i	$-0.115359\pi$
$709$	0.617186	+	1.49002i	0.0231789	+	0.0559588i	−0.911866	+	0.410487i	$0.865359\pi$
$710$	20.4566	−	9.72578i	0.767721	−	0.365002i
$711$	9.05796	−	9.05796i	0.339700	−	0.339700i
$712$	−3.91933	+	0.605640i	−0.146883	+	0.0226973i
$713$	−6.14944	−	6.14944i	−0.230298	−	0.230298i
$714$	−10.3959	−	3.69609i	−0.389058	−	0.138323i
$715$	40.6496	−	16.8376i	1.52021	−	0.629691i
$716$	35.3355	+	10.5634i	1.32055	+	0.394773i
$717$	−0.0804880	+	0.194315i	−0.00300588	+	0.00725683i
$718$	−0.701383	−	13.7125i	−0.0261754	−	0.511746i
$719$			11.8288i			0.441140i	0.975371	+	0.220570i	$0.0707917\pi$
$719$			11.8288i			0.441140i	−0.975371	+	0.220570i	$0.929208\pi$
$720$	−2.90830	+	15.2637i	−0.108386	+	0.568844i
$721$			4.39163i			0.163553i
$722$	−25.7219	+	1.31565i	−0.957270	+	0.0489635i
$723$	5.00259	−	12.0773i	0.186048	−	0.449161i
$724$	−17.8783	−	33.1258i	−0.664442	−	1.23111i
$725$	−58.3407	+	24.1655i	−2.16672	+	0.897484i
$726$	−0.252142	+	0.709196i	−0.00935786	+	0.0263207i
$727$	−12.9471	−	12.9471i	−0.480182	−	0.480182i	0.425008	−	0.905190i	$-0.360271\pi$
$727$	−12.9471	−	12.9471i	−0.480182	−	0.480182i	−0.905190	+	0.425008i	$0.860271\pi$
$728$	3.44713	−	14.1238i	0.127759	−	0.523463i
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$	3.40479	+	7.16141i	0.126017	+	0.265056i
$731$	−14.3176	−	34.5657i	−0.529555	−	1.27846i
$732$	4.32687	−	5.31589i	0.159926	−	0.196481i
$733$	8.82183	+	3.65412i	0.325842	+	0.134968i	0.539607	−	0.841917i	$-0.318573\pi$
$733$	8.82183	+	3.65412i	0.325842	+	0.134968i	−0.213765	+	0.976885i	$0.568573\pi$
$734$	−33.9131	−	30.6126i	−1.25175	−	1.12993i
$735$	−18.8178			−0.694104
$736$	33.4523	−	8.73886i	1.23307	−	0.322119i
$737$	21.3367			0.785946
$738$	−5.08692	−	4.59186i	−0.187252	−	0.169029i
$739$	2.54866	+	1.05569i	0.0937540	+	0.0388342i	0.429068	−	0.903272i	$-0.358842\pi$
$739$	2.54866	+	1.05569i	0.0937540	+	0.0388342i	−0.335313	+	0.942107i	$0.608842\pi$
$740$	−10.1752	−	8.28211i	−0.374048	−	0.304456i
$741$	−1.18932	−	2.87127i	−0.0436908	−	0.105479i
$742$	6.40266	+	13.4669i	0.235049	+	0.494386i
$743$	14.0090	−	14.0090i	0.513942	−	0.513942i	−0.401790	−	0.915732i	$-0.631612\pi$
$743$	14.0090	−	14.0090i	0.513942	−	0.513942i	0.915732	+	0.401790i	$0.131612\pi$
$744$	2.08985	+	3.43933i	0.0766175	+	0.126092i
$745$	52.0535	+	52.0535i	1.90709	+	1.90709i
$746$	−0.579245	+	1.62923i	−0.0212077	+	0.0596505i
$747$	−15.4879	+	6.41532i	−0.566674	+	0.234724i
$748$	30.2580	−	16.3305i	1.10634	−	0.597104i
$749$	2.81151	−	6.78759i	0.102730	−	0.248013i
$750$	27.9254	−	1.42836i	1.01969	−	0.0521563i
$751$		−	1.69567i		−	0.0618757i	−0.999521	−	0.0309379i	$-0.990151\pi$
$751$		−	1.69567i		−	0.0618757i	0.999521	−	0.0309379i	$-0.00984940\pi$
$752$	8.58797	+	41.4249i	0.313171	+	1.51061i
$753$			3.17568i			0.115728i
$754$	1.58280	+	30.9448i	0.0576422	+	1.12694i
$755$	2.37830	−	5.74173i	0.0865553	−	0.208963i
$756$	−0.841079	+	2.81348i	−0.0305897	+	0.102325i
$757$	21.3707	−	8.85204i	0.776731	−	0.321733i	0.0411358	−	0.999154i	$-0.486902\pi$
$757$	21.3707	−	8.85204i	0.776731	−	0.321733i	0.735596	+	0.677421i	$0.236902\pi$
$758$	44.1148	+	15.6842i	1.60232	+	0.569676i
$759$	13.9829	+	13.9829i	0.507548	+	0.507548i
$760$	7.86940	+	5.76286i	0.285453	+	0.209041i
$761$	−16.4756	+	16.4756i	−0.597239	+	0.597239i	−0.939577	−	0.342338i	$-0.888781\pi$
$761$	−16.4756	+	16.4756i	−0.597239	+	0.597239i	0.342338	+	0.939577i	$0.388781\pi$
$762$	−17.1428	+	8.15029i	−0.621018	+	0.295254i
$763$	−0.199514	−	0.481670i	−0.00722290	−	0.0174376i
$764$	−2.02321	−	19.7258i	−0.0731973	−	0.713656i
$765$	−19.0701	−	7.89910i	−0.689481	−	0.285593i
$766$	−8.54034	+	9.46109i	−0.308575	+	0.341843i
$767$	−1.69652			−0.0612576
$768$	−15.9979	+	0.258192i	−0.577275	+	0.00931670i
$769$	−10.8924			−0.392791			−0.196395	−	0.980525i	$-0.562924\pi$
$769$	−10.8924			−0.392791			−0.196395	+	0.980525i	$0.562924\pi$
$770$	−17.4865	+	19.3717i	−0.630168	+	0.698108i
$771$	−2.37719	−	0.984663i	−0.0856123	−	0.0354618i
$772$	−2.00968	−	19.5939i	−0.0723299	−	0.705200i
$773$	19.5101	+	47.1015i	0.701728	+	1.69412i	0.719701	+	0.694284i	$0.244279\pi$
$773$	19.5101	+	47.1015i	0.701728	+	1.69412i	−0.0179727	+	0.999838i	$0.505721\pi$
$774$	−8.99286	+	4.27553i	−0.323242	+	0.153681i
$775$	10.1516	−	10.1516i	0.364657	−	0.364657i
$776$	33.1571	+	24.2814i	1.19027	+	0.871650i
$777$	−1.75323	−	1.75323i	−0.0628968	−	0.0628968i
$778$	0.512450	+	0.182192i	0.0183722	+	0.00653191i
$779$	−3.97432	+	1.64622i	−0.142395	+	0.0589818i
$780$	7.79021	−	26.0589i	0.278934	−	0.933058i
$781$	−5.10498	+	12.3245i	−0.182670	+	0.441005i
$782$	2.34621	+	45.8700i	0.0839003	+	1.64031i
$783$		−	6.25849i		−	0.223660i
$784$	−3.93347	−	18.9735i	−0.140481	−	0.677625i
$785$		−	7.11388i		−	0.253905i
$786$	11.2946	−	0.577707i	0.402864	−	0.0206061i
$787$	10.4222	−	25.1613i	0.371510	−	0.896905i	−0.621985	−	0.783029i	$-0.713673\pi$
$787$	10.4222	−	25.1613i	0.371510	−	0.896905i	0.993495	−	0.113876i	$-0.0363266\pi$
$788$	25.1316	−	13.5638i	0.895277	−	0.483190i
$789$	−16.7850	+	6.95257i	−0.597561	+	0.247518i
$790$	23.5741	−	66.3065i	0.838729	−	2.35908i
$791$	−2.47814	−	2.47814i	−0.0881124	−	0.0881124i
$792$	−4.75201	−	7.82052i	−0.168855	−	0.277890i
$793$	−8.48368	+	8.48368i	−0.301264	+	0.301264i
$794$	−16.9806	−	35.7158i	−0.602618	−	1.26751i
$795$	10.6755	+	25.7729i	0.378620	+	0.914070i
$796$	13.4792	+	10.9714i	0.477759	+	0.388871i
$797$	11.4090	+	4.72576i	0.404128	+	0.167395i	0.575482	−	0.817814i	$-0.304814\pi$
$797$	11.4090	+	4.72576i	0.404128	+	0.167395i	−0.171355	+	0.985209i	$0.554814\pi$
$798$	1.36832	+	1.23515i	0.0484379	+	0.0437239i
$799$	−56.1998			−1.98820
$800$	14.4263	+	55.2238i	0.510047	+	1.95246i
$801$	−1.40214			−0.0495421
$802$	−41.5031	−	37.4640i	−1.46552	−	1.32290i
$803$	−4.31454	−	1.78714i	−0.152257	−	0.0630669i
$804$	8.32615	−	10.2293i	0.293641	−	0.360760i
$805$	−13.3404	−	32.2066i	−0.470188	−	1.13513i
$806$	−3.02475	−	6.36206i	−0.106542	−	0.224094i
$807$	−5.88471	+	5.88471i	−0.207152	+	0.207152i
$808$	−1.30130	+	5.33179i	−0.0457797	+	0.187572i
$809$	15.5322	+	15.5322i	0.546082	+	0.546082i	0.925305	−	0.379223i	$-0.123809\pi$
$809$	15.5322	+	15.5322i	0.546082	+	0.546082i	−0.379223	+	0.925305i	$0.623809\pi$
$810$	−1.84030	+	5.17620i	−0.0646617	+	0.181873i
$811$	−10.1946	+	4.22272i	−0.357979	+	0.148280i	−0.554423	−	0.832235i	$-0.687061\pi$
$811$	−10.1946	+	4.22272i	−0.357979	+	0.148280i	0.196443	+	0.980515i	$0.437061\pi$
$812$	−8.72870	−	16.1730i	−0.306317	−	0.567560i
$813$	−11.3882	+	27.4936i	−0.399403	+	0.964244i
$814$	7.71663	−	0.394699i	0.270468	−	0.0138342i
$815$		−	84.8828i		−	2.97332i
$816$	3.97825	−	20.8791i	0.139266	−	0.730914i
$817$			6.25063i			0.218682i
$818$	−1.70135	−	33.2626i	−0.0594864	−	1.16300i
$819$	1.96703	−	4.74883i	0.0687336	−	0.165938i
$820$	−36.0698	−	10.7829i	−1.25961	−	0.376556i
$821$	−26.9571	+	11.1660i	−0.940808	+	0.389695i	−0.799768	−	0.600309i	$-0.795044\pi$
$821$	−26.9571	+	11.1660i	−0.940808	+	0.389695i	−0.141039	+	0.990004i	$0.545044\pi$
$822$	−20.1263	−	7.15554i	−0.701985	−	0.249578i
$823$	14.3701	+	14.3701i	0.500911	+	0.500911i	0.911721	−	0.410810i	$-0.134754\pi$
$823$	14.3701	+	14.3701i	0.500911	+	0.500911i	−0.410810	+	0.911721i	$0.634754\pi$
$824$	−8.36076	+	1.29196i	−0.291261	+	0.0450075i
$825$	−23.0833	+	23.0833i	−0.803658	+	0.803658i
$826$	0.908764	−	0.432059i	0.0316199	−	0.0150332i
$827$	−1.27090	−	3.06822i	−0.0441935	−	0.106693i	0.900241	−	0.435391i	$-0.143390\pi$
$827$	−1.27090	−	3.06822i	−0.0441935	−	0.106693i	−0.944435	+	0.328699i	$0.893390\pi$
$828$	12.1603	−	1.24724i	0.422599	−	0.0433445i
$829$	44.8916	+	18.5947i	1.55915	+	0.645821i	0.984941	−	0.172889i	$-0.0553103\pi$
$829$	44.8916	+	18.5947i	1.55915	+	0.645821i	0.574207	+	0.818710i	$0.305310\pi$
$830$	−61.7095	+	68.3626i	−2.14197	+	2.37290i
$831$	−14.5247			−0.503856
$832$	27.9029	+	2.40759i	0.967360	+	0.0834683i
$833$	25.7407			0.891861
$834$	−4.10495	+	4.54752i	−0.142143	+	0.157468i
$835$	12.2050	+	5.05548i	0.422372	+	0.174952i
$836$	−5.71444	+	0.586111i	−0.197638	+	0.0202711i
$837$	0.544508	+	1.31456i	0.0188209	+	0.0454378i
$838$	−41.8616	+	19.9025i	−1.44609	+	0.687521i
$839$	1.80010	−	1.80010i	0.0621465	−	0.0621465i	−0.675350	−	0.737497i	$-0.736008\pi$
$839$	1.80010	−	1.80010i	0.0621465	−	0.0621465i	0.737497	+	0.675350i	$0.236008\pi$
$840$	2.46358	+	15.9428i	0.0850018	+	0.550079i
$841$	7.19038	+	7.19038i	0.247944	+	0.247944i
$842$	48.8513	+	17.3682i	1.68353	+	0.598547i
$843$	−0.560491	+	0.232163i	−0.0193043	+	0.00799612i
$844$	20.7344	+	6.19848i	0.713708	+	0.213361i
$845$	1.10634	−	2.67093i	0.0380591	−	0.0918829i
$846$	0.764057	+	14.9378i	0.0262688	+	0.513573i
$847$			0.781447i			0.0268508i
$848$	−23.7547	+	16.1511i	−0.815739	+	0.554632i
$849$		−	26.8592i		−	0.921804i
$850$	−75.7232	+	3.87318i	−2.59728	+	0.132849i
$851$	−3.94983	+	9.53574i	−0.135398	+	0.326881i
$852$	3.91657	+	7.25681i	0.134179	+	0.248614i
$853$	−13.8932	+	5.75474i	−0.475693	+	0.197039i	−0.607631	−	0.794219i	$-0.707880\pi$
$853$	−13.8932	+	5.75474i	−0.475693	+	0.197039i	0.131938	+	0.991258i	$0.457880\pi$
$854$	2.38384	−	6.70499i	0.0815732	−	0.229440i
$855$	2.43847	+	2.43847i	0.0833938	+	0.0833938i
$856$	13.7493	+	3.35572i	0.469941	+	0.114696i
$857$	−31.5080	+	31.5080i	−1.07629	+	1.07629i	−0.0794556	+	0.996838i	$0.525318\pi$
$857$	−31.5080	+	31.5080i	−1.07629	+	1.07629i	−0.996838	+	0.0794556i	$0.974682\pi$
$858$	6.87784	+	14.4664i	0.234806	+	0.493875i
$859$	−7.59894	−	18.3455i	−0.259272	−	0.625939i	0.739618	−	0.673027i	$-0.235006\pi$
$859$	−7.59894	−	18.3455i	−0.259272	−	0.625939i	−0.998891	+	0.0470875i	$0.985006\pi$
$860$	−34.5321	+	42.4254i	−1.17753	+	1.44669i
$861$	−6.57316	−	2.72269i	−0.224013	−	0.0927891i
$862$	11.5732	+	10.4469i	0.394183	+	0.355821i
$863$	1.95965			0.0667073			0.0333537	−	0.999444i	$-0.489381\pi$
$863$	1.95965			0.0667073			0.0333537	+	0.999444i	$0.489381\pi$
$864$	−5.60371	−	0.773554i	−0.190642	−	0.0263168i
$865$	38.4201			1.30632
$866$	27.3964	+	24.7301i	0.930967	+	0.840365i
$867$	10.3799	+	4.29950i	0.352520	+	0.146019i
$868$	3.24051	+	2.63761i	0.109990	+	0.0895262i
$869$	15.8603	+	38.2902i	0.538025	+	1.29891i
$870$	−14.7628	−	31.0510i	−0.500504	−	1.05273i
$871$	−16.3251	+	16.3251i	−0.553154	+	0.553154i
$872$	0.858306	−	0.521535i	0.0290659	−	0.0176614i
$873$	10.2743	+	10.2743i	0.347732	+	0.347732i
$874$	2.57052	−	7.23008i	0.0869493	−	0.244561i
$875$	26.8205	−	11.1094i	0.906700	−	0.375567i
$876$	−2.54045	+	1.37111i	−0.0858339	+	0.0463254i
$877$	−8.40988	+	20.3033i	−0.283982	+	0.685592i	−0.999921	−	0.0125703i	$-0.995999\pi$
$877$	−8.40988	+	20.3033i	−0.283982	+	0.685592i	0.715939	+	0.698162i	$0.245999\pi$
$878$	19.7605	−	1.01073i	0.666884	−	0.0341105i
$879$			12.9562i			0.437001i
$880$	−42.0240	−	27.5917i	−1.41663	−	0.930116i
$881$		−	8.86541i		−	0.298683i	−0.988786	−	0.149342i	$-0.952285\pi$
$881$		−	8.86541i		−	0.298683i	0.988786	−	0.149342i	$-0.0477154\pi$
$882$	−0.349954	−	6.84184i	−0.0117836	−	0.230377i
$883$	−9.81319	+	23.6911i	−0.330240	+	0.797270i	0.668333	+	0.743863i	$0.267008\pi$
$883$	−9.81319	+	23.6911i	−0.330240	+	0.797270i	−0.998573	+	0.0534078i	$0.982992\pi$
$884$	−10.6562	+	35.6457i	−0.358406	+	1.19890i
$885$	1.73918	−	0.720394i	0.0584621	−	0.0242158i
$886$	−25.4157	−	9.03611i	−0.853859	−	0.303574i
$887$	−40.7094	−	40.7094i	−1.36689	−	1.36689i	−0.864839	−	0.502050i	$-0.832579\pi$
$887$	−40.7094	−	40.7094i	−1.36689	−	1.36689i	−0.502050	−	0.864839i	$-0.667421\pi$
$888$	2.82201	−	3.85356i	0.0947005	−	0.129317i
$889$	−13.9349	+	13.9349i	−0.467362	+	0.467362i
$890$	−6.95660	+	3.30741i	−0.233186	+	0.110865i
$891$	−1.23813	−	2.98911i	−0.0414790	−	0.100139i
$892$	2.88135	+	28.0925i	0.0964747	+	0.940606i
$893$	8.67449	+	3.59309i	0.290281	+	0.120238i
$894$	−17.9578	+	19.8938i	−0.600598	+	0.665350i
$895$	71.6327			2.39442
$896$	−15.5598	+	5.81649i	−0.519816	+	0.194315i
$897$	−21.3972			−0.714431
$898$	−6.78882	+	7.52074i	−0.226546	+	0.250970i
$899$	−8.22715	−	3.40780i	−0.274391	−	0.113656i
$900$	2.05897	+	20.0745i	0.0686323	+	0.669149i
$901$	−14.6029	−	35.2545i	−0.486493	−	1.17450i
$902$	20.0239	−	9.52006i	0.666722	−	0.316983i
$903$	−7.31006	+	7.31006i	−0.243264	+	0.243264i
$904$	3.98882	−	5.44689i	0.132666	−	0.181161i
$905$	−51.6983	−	51.6983i	−1.71851	−	1.71851i
$906$	2.13183	+	0.757933i	0.0708253	+	0.0251806i
$907$	20.7020	−	8.57503i	0.687397	−	0.284729i	−0.0115180	−	0.999934i	$-0.503666\pi$
$907$	20.7020	−	8.57503i	0.687397	−	0.284729i	0.698915	+	0.715204i	$0.253666\pi$
$908$	−10.4685	+	35.0182i	−0.347411	+	1.16212i
$909$	−0.742560	+	1.79270i	−0.0246292	+	0.0594601i
$910$	−1.44245	−	28.2008i	−0.0478167	−	0.934849i
$911$			49.0914i			1.62647i	0.581935	+	0.813235i	$0.302296\pi$
$911$			49.0914i			1.62647i	−0.581935	+	0.813235i	$0.697704\pi$
$912$	−1.94893	+	2.96836i	−0.0645357	+	0.0982922i
$913$		−	54.2382i		−	1.79502i
$914$	30.5008	−	1.56009i	1.00888	−	0.0516033i
$915$	5.09462	−	12.2995i	0.168423	−	0.406609i
$916$	18.0292	−	9.73054i	0.595702	−	0.321506i
$917$	10.8477	−	4.49327i	0.358223	−	0.148381i
$918$	2.51734	−	7.08048i	0.0830845	−	0.233691i
$919$	26.2568	+	26.2568i	0.866131	+	0.866131i	0.992042	−	0.125910i	$-0.0401852\pi$
$919$	26.2568	+	26.2568i	0.866131	+	0.866131i	−0.125910	+	0.992042i	$0.540185\pi$
$920$	57.3902	−	34.8722i	1.89210	−	1.14970i
$921$	−15.4749	+	15.4749i	−0.509917	+	0.509917i
$922$	−8.57238	−	18.0306i	−0.282316	−	0.593806i
$923$	−5.52379	−	13.3356i	−0.181818	−	0.438947i
$924$	−7.36844	−	5.99754i	−0.242404	−	0.197304i
$925$	−15.7418	−	6.52047i	−0.517588	−	0.214392i
$926$	−14.2151	−	12.8316i	−0.467136	−	0.421674i
$927$	−2.99106			−0.0982393
$928$	28.2221	−	21.3755i	0.926436	−	0.701685i
$929$	9.33360			0.306225			0.153113	−	0.988209i	$-0.451070\pi$
$929$	9.33360			0.306225			0.153113	+	0.988209i	$0.451070\pi$
$930$	5.80236	+	5.23767i	0.190267	+	0.171750i
$931$	−3.97310	−	1.64571i	−0.130213	−	0.0539360i
$932$	5.46411	−	6.71309i	0.178983	−	0.219895i
$933$	−3.09467	−	7.47119i	−0.101315	−	0.244596i
$934$	9.80819	+	20.6299i	0.320934	+	0.675031i
$935$	47.2226	−	47.2226i	1.54434	−	1.54434i
$936$	9.61947	+	2.34778i	0.314422	+	0.0767395i
$937$	−26.9828	−	26.9828i	−0.881491	−	0.881491i	0.112195	−	0.993686i	$-0.464212\pi$
$937$	−26.9828	−	26.9828i	−0.881491	−	0.881491i	−0.993686	+	0.112195i	$0.964212\pi$
$938$	4.58719	−	12.9023i	0.149777	−	0.421276i
$939$	−15.1596	+	6.27933i	−0.494716	+	0.204918i
$940$	39.0267	+	72.3105i	1.27291	+	2.35851i
$941$	20.9573	−	50.5954i	0.683188	−	1.64936i	−0.0748852	−	0.997192i	$-0.523859\pi$
$941$	20.9573	−	50.5954i	0.683188	−	1.64936i	0.758073	−	0.652169i	$-0.226141\pi$
$942$	2.58649	−	0.132297i	0.0842725	−	0.00431047i
$943$			29.6172i			0.964469i
$944$	1.08990	+	1.60299i	0.0354731	+	0.0521730i
$945$			5.70353i			0.185536i
$946$	−1.64569	−	32.1744i	−0.0535060	−	1.04608i
$947$	7.14980	−	17.2611i	0.232337	−	0.560912i	−0.764114	−	0.645081i	$-0.776824\pi$
$947$	7.14980	−	17.2611i	0.232337	−	0.560912i	0.996451	+	0.0841692i	$0.0268236\pi$
$948$	24.5464	+	7.33806i	0.797230	+	0.238329i
$949$	4.66851	−	1.93376i	0.151546	−	0.0627725i
$950$	11.9356	+	4.24348i	0.387241	+	0.137677i
$951$	14.9718	+	14.9718i	0.485494	+	0.485494i
$952$	−3.36992	−	21.8080i	−0.109220	−	0.706803i
$953$	−18.0649	+	18.0649i	−0.585181	+	0.585181i	−0.936322	−	0.351142i	$-0.885794\pi$
$953$	−18.0649	+	18.0649i	−0.585181	+	0.585181i	0.351142	+	0.936322i	$0.385794\pi$
$954$	−9.17207	+	4.36073i	−0.296957	+	0.141184i
$955$	−14.7388	−	35.5825i	−0.476935	−	1.15142i
$956$	−0.418455	+	0.0429195i	−0.0135338	+	0.00138812i
$957$	18.7073	+	7.74884i	0.604723	+	0.250484i
$958$	6.10682	−	6.76521i	0.197302	−	0.218574i
$959$	−22.1767			−0.716122
$960$	−29.6271	+	9.38031i	−0.956209	+	0.302748i
$961$	−28.9754			−0.934692
$962$	−5.60214	+	6.20612i	−0.180620	+	0.200093i
$963$	4.62290	+	1.91487i	0.148971	+	0.0617058i
$964$	26.0084	−	2.66759i	0.837673	−	0.0859173i
$965$	−14.6402	−	35.3445i	−0.471283	−	1.13778i
$966$	11.4617	−	5.44931i	0.368775	−	0.175329i
$967$	−35.9715	+	35.9715i	−1.15677	+	1.15677i	−0.171599	+	0.985167i	$0.554893\pi$
$967$	−35.9715	+	35.9715i	−1.15677	+	1.15677i	−0.985167	+	0.171599i	$0.945107\pi$
$968$	−1.48771	+	0.229891i	−0.0478169	+	0.00738898i
$969$	−3.33556	−	3.33556i	−0.107154	−	0.107154i
$970$	75.2105	+	26.7397i	2.41486	+	0.858561i
$971$	−21.1238	+	8.74978i	−0.677896	+	0.280794i	−0.694947	−	0.719061i	$-0.744572\pi$
$971$	−21.1238	+	8.74978i	−0.677896	+	0.280794i	0.0170508	+	0.999855i	$0.494572\pi$
$972$	−1.91621	−	0.572843i	−0.0614624	−	0.0183740i
$973$	−2.43398	+	5.87616i	−0.0780300	+	0.188381i
$974$	0.452551	+	8.84768i	0.0145007	+	0.283498i
$975$		−	35.3229i		−	1.13124i
$976$	13.4662	+	2.56582i	0.431043	+	0.0821298i
$977$		−	14.2027i		−	0.454386i	−0.973850	−	0.227193i	$-0.927045\pi$
$977$		−	14.2027i		−	0.454386i	0.973850	−	0.227193i	$-0.0729548\pi$
$978$	30.8620	−	1.57857i	0.986859	−	0.0504770i
$979$	1.73603	−	4.19115i	0.0554838	−	0.133950i
$980$	−17.8750	−	33.1197i	−0.570997	−	1.05797i
$981$	0.328056	−	0.135885i	0.0104740	−	0.00433849i
$982$	6.04060	−	16.9903i	0.192763	−	0.542183i
$983$	−25.7336	−	25.7336i	−0.820775	−	0.820775i	0.165444	−	0.986219i	$-0.447094\pi$
$983$	−25.7336	−	25.7336i	−0.820775	−	0.820775i	−0.986219	+	0.165444i	$0.947094\pi$
$984$	3.24971	−	13.3149i	0.103597	−	0.424464i
$985$	39.2220	−	39.2220i	1.24972	−	1.24972i
$986$	20.1939	+	42.4744i	0.643103	+	1.35266i
$987$	5.94265	+	14.3468i	0.189157	+	0.456665i
$988$	3.92378	−	4.82066i	0.124832	−	0.153366i
$989$	39.7591	+	16.4688i	1.26427	+	0.523676i
$990$	−13.1937	−	11.9097i	−0.419324	−	0.378515i
$991$	−13.6553			−0.433776			−0.216888	−	0.976197i	$-0.569591\pi$
$991$	−13.6553			−0.433776			−0.216888	+	0.976197i	$0.569591\pi$
$992$	−4.06815	+	6.94520i	−0.129164	+	0.220510i
$993$	−0.998284			−0.0316796
$994$	6.35514	+	5.73665i	0.201573	+	0.181956i
$995$	31.1872	+	12.9181i	0.988700	+	0.409533i
$996$	−26.0031	−	21.1652i	−0.823941	−	0.670646i
$997$	−8.35787	−	20.1777i	−0.264696	−	0.639033i	0.734521	−	0.678586i	$-0.237407\pi$
$997$	−8.35787	−	20.1777i	−0.264696	−	0.639033i	−0.999218	+	0.0395523i	$0.987407\pi$
$998$	3.54928	+	7.46531i	0.112350	+	0.236310i
$999$	1.19409	−	1.19409i	0.0377794	−	0.0377794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.61.3	✓	32
3.2	odd	2		288.2.v.d.253.6		32
4.3	odd	2		384.2.n.a.337.5		32
8.3	odd	2		768.2.n.b.673.4		32
8.5	even	2		768.2.n.a.673.8		32
12.11	even	2		1152.2.v.c.721.8		32
32.5	even	8		768.2.n.a.97.8		32
32.11	odd	8		384.2.n.a.49.5		32
32.21	even	8	inner	96.2.n.a.85.3	yes	32
32.27	odd	8		768.2.n.b.97.4		32
96.11	even	8		1152.2.v.c.433.8		32
96.53	odd	8		288.2.v.d.181.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.3	✓	32	1.1	even	1	trivial
96.2.n.a.85.3	yes	32	32.21	even	8	inner
288.2.v.d.181.6		32	96.53	odd	8
288.2.v.d.253.6		32	3.2	odd	2
384.2.n.a.49.5		32	32.11	odd	8
384.2.n.a.337.5		32	4.3	odd	2
768.2.n.a.97.8		32	32.5	even	8
768.2.n.a.673.8		32	8.5	even	2
768.2.n.b.97.4		32	32.27	odd	8
768.2.n.b.673.4		32	8.3	odd	2
1152.2.v.c.433.8		32	96.11	even	8
1152.2.v.c.721.8		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.947612 + 1.04978i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-0.204063 - 1.98956i) q^{4} +(-1.48656 - 3.58888i) q^{5} +(1.27721 - 0.607232i) q^{6} +(1.03821 - 1.03821i) q^{7} +(2.28197 + 1.67111i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.947612 + 1.04978i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-0.204063 - 1.98956i) q^{4} +(-1.48656 - 3.58888i) q^{5} +(1.27721 - 0.607232i) q^{6} +(1.03821 - 1.03821i) q^{7} +(2.28197 + 1.67111i) q^{8} +(0.707107 + 0.707107i) q^{9} +(5.17620 + 1.84030i) q^{10} +(-2.98911 + 1.23813i) q^{11} +(-0.572843 + 1.91621i) q^{12} +(1.33971 - 3.23434i) q^{13} +(0.106069 + 2.07371i) q^{14} +3.88457i q^{15} +(-3.91672 + 0.811991i) q^{16} -5.31367i q^{17} +(-1.41237 + 0.0722414i) q^{18} +(-0.339726 + 0.820171i) q^{19} +(-6.83694 + 3.68996i) q^{20} +(-1.35649 + 0.561876i) q^{21} +(1.53276 - 4.31117i) q^{22} +(4.32186 + 4.32186i) q^{23} +(-1.46876 - 2.41718i) q^{24} +(-7.13463 + 7.13463i) q^{25} +(2.12581 + 4.47129i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(-2.27745 - 1.85373i) q^{28} +(5.78209 + 2.39502i) q^{29} +(-4.07793 - 3.68107i) q^{30} -1.42287 q^{31} +(2.85912 - 4.88113i) q^{32} +3.23539 q^{33} +(5.57817 + 5.03530i) q^{34} +(-5.26938 - 2.18265i) q^{35} +(1.26254 - 1.55113i) q^{36} +(0.646238 + 1.56016i) q^{37} +(-0.539068 - 1.13384i) q^{38} +(-2.47546 + 2.47546i) q^{39} +(2.60513 - 10.6739i) q^{40} +(3.42644 + 3.42644i) q^{41} +(0.695581 - 1.95645i) q^{42} +(6.50505 - 2.69448i) q^{43} +(3.07331 + 5.69437i) q^{44} +(1.48656 - 3.58888i) q^{45} +(-8.63244 + 0.441542i) q^{46} -10.5764i q^{47} +(3.92931 + 0.748681i) q^{48} +4.84423i q^{49} +(-0.728907 - 14.2506i) q^{50} +(-2.03345 + 4.90919i) q^{51} +(-6.70831 - 2.00542i) q^{52} +(6.63468 - 2.74817i) q^{53} +(1.33250 + 0.473747i) q^{54} +(8.88700 + 8.88700i) q^{55} +(4.10414 - 0.634197i) q^{56} +(0.627732 - 0.627732i) q^{57} +(-7.99342 + 3.80036i) q^{58} +(-0.185450 - 0.447716i) q^{59} +(7.72860 - 0.792696i) q^{60} +(-3.16624 - 1.31150i) q^{61} +(1.34833 - 1.49369i) q^{62} +1.46825 q^{63} +(2.41476 + 7.62686i) q^{64} -13.5992 q^{65} +(-3.06590 + 3.39644i) q^{66} +(-6.09277 - 2.52371i) q^{67} +(-10.5719 + 1.08432i) q^{68} +(-2.33898 - 5.64679i) q^{69} +(7.28462 - 3.46337i) q^{70} +(2.91549 - 2.91549i) q^{71} +(0.431940 + 2.79525i) q^{72} +(1.02065 + 1.02065i) q^{73} +(-2.25020 - 0.800018i) q^{74} +(9.32184 - 3.86123i) q^{75} +(1.70111 + 0.508540i) q^{76} +(-1.81789 + 4.38878i) q^{77} +(-0.252904 - 4.94445i) q^{78} -12.8099i q^{79} +(8.73657 + 12.8495i) q^{80} +1.00000i q^{81} +(-6.84393 + 0.350061i) q^{82} +(-6.41532 + 15.4879i) q^{83} +(1.39470 + 2.58416i) q^{84} +(-19.0701 + 7.89910i) q^{85} +(-3.33566 + 9.38217i) q^{86} +(-4.42542 - 4.42542i) q^{87} +(-8.89012 - 2.16977i) q^{88} +(-0.991462 + 0.991462i) q^{89} +(2.35883 + 4.96142i) q^{90} +(-1.96703 - 4.74883i) q^{91} +(7.71668 - 9.48055i) q^{92} +(1.31456 + 0.544508i) q^{93} +(11.1029 + 10.0224i) q^{94} +3.44851 q^{95} +(-4.50941 + 3.41544i) q^{96} +14.5301 q^{97} +(-5.08536 - 4.59045i) q^{98} +(-2.98911 - 1.23813i) 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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