LMFDB - Embedded newform 825.2.bi.h.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(101,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("825.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bi (of order $10$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.664572 + 2.04534i) q^{2} +(-1.37038 + 1.05927i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(-1.25585 - 3.50686i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(1.08756 - 0.790156i) q^{8} +(0.755895 - 2.90321i) q^{9} +O(q^{10})$	\(q+(-0.664572 + 2.04534i) q^{2} +(-1.37038 + 1.05927i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(-1.25585 - 3.50686i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(1.08756 - 0.790156i) q^{8} +(0.755895 - 2.90321i) q^{9} +(-1.78718 + 2.79392i) q^{11} +(4.54476 - 0.135131i) q^{12} +(-0.117164 - 0.0380688i) q^{13} +(-2.46148 - 3.38794i) q^{14} +(-0.729008 - 2.24366i) q^{16} +(-1.05363 - 3.24273i) q^{17} +(5.43571 + 3.47545i) q^{18} +(-4.19337 - 5.77168i) q^{19} +(-0.100238 - 3.37122i) q^{21} +(-4.52681 - 5.51216i) q^{22} +2.50155i q^{23} +(-0.653380 + 2.23483i) q^{24} +(0.155728 - 0.214341i) q^{26} +(2.03942 + 4.77920i) q^{27} +(4.86146 - 1.57958i) q^{28} +(5.07427 + 3.68667i) q^{29} +(0.480284 - 1.47816i) q^{31} +7.76211 q^{32} +(-0.510392 - 5.72184i) q^{33} +7.33270 q^{34} +(-6.08492 + 4.99931i) q^{36} +(-6.03482 - 4.38456i) q^{37} +(14.5918 - 4.74118i) q^{38} +(0.200884 - 0.0719392i) q^{39} +(4.03282 - 2.93001i) q^{41} +(6.96191 + 2.03540i) q^{42} -8.66147i q^{43} +(8.10647 - 3.17595i) q^{44} +(-5.11652 - 1.66246i) q^{46} +(0.202715 + 0.279013i) q^{47} +(3.37566 + 2.30245i) q^{48} +(0.991413 + 3.05126i) q^{49} +(4.87879 + 3.32770i) q^{51} +(0.190085 + 0.261630i) q^{52} +(3.52839 + 1.14644i) q^{53} +(-11.1304 + 0.995182i) q^{54} +2.61765i q^{56} +(11.8603 + 3.46749i) q^{57} +(-10.9127 + 7.92855i) q^{58} +(-6.52040 + 8.97456i) q^{59} +(9.07864 - 2.94983i) q^{61} +(2.70416 + 1.96469i) q^{62} +(3.70839 + 4.51368i) q^{63} +(-3.70046 + 11.3889i) q^{64} +(12.0423 + 2.75865i) q^{66} -7.76130 q^{67} +(-2.76585 + 8.51242i) q^{68} +(-2.64981 - 3.42808i) q^{69} +(-7.62506 + 2.47753i) q^{71} +(-1.47191 - 3.75468i) q^{72} +(-2.65271 + 3.65114i) q^{73} +(12.9785 - 9.42942i) q^{74} +18.7278i q^{76} +(-2.35586 - 6.01322i) q^{77} +(0.0136383 + 0.458686i) q^{78} +(4.54966 + 1.47827i) q^{79} +(-7.85725 - 4.38904i) q^{81} +(3.31278 + 10.1957i) q^{82} +(-0.0277937 - 0.0855401i) q^{83} +(-4.98885 + 7.31423i) q^{84} +(17.7157 + 5.75617i) q^{86} +(-10.8589 + 0.322870i) q^{87} +(0.263971 + 4.45070i) q^{88} -7.03271i q^{89} +(0.194072 - 0.141002i) q^{91} +(3.85984 - 5.31262i) q^{92} +(0.907600 + 2.53440i) q^{93} +(-0.705397 + 0.229197i) q^{94} +(-10.6371 + 8.22217i) q^{96} +(5.30569 - 16.3292i) q^{97} -6.89973 q^{98} +(6.76041 + 7.30047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	−0.664572	+	2.04534i	−0.469923	+	1.44628i	0.382761	+	0.923848i	$0.374973\pi$
$2$	−0.664572	+	2.04534i	−0.469923	+	1.44628i	−0.852684	+	0.522427i	$0.825027\pi$
$3$	−1.37038	+	1.05927i	−0.791191	+	0.611570i
$3$	−1.37038	+	1.05927i	−0.791191	+	0.611570i
$4$	−2.12373	−	1.54298i	−1.06187	−	0.771491i
$5$		0			0
$5$		0			0
$6$	−1.25585	−	3.50686i	−0.512699	−	1.43167i
$7$	−1.14456	+	1.57535i	−0.432601	+	0.595424i	−0.968548	−	0.248827i	$-0.919955\pi$
$7$	−1.14456	+	1.57535i	−0.432601	+	0.595424i	0.535947	+	0.844252i	$0.319955\pi$
$8$	1.08756	−	0.790156i	0.384509	−	0.279362i
$9$	0.755895	−	2.90321i	0.251965	−	0.967736i
$10$		0			0
$11$	−1.78718	+	2.79392i	−0.538856	+	0.842398i
$11$	−1.78718	+	2.79392i	−0.538856	+	0.842398i
$12$	4.54476	−	0.135131i	1.31196	−	0.0390089i
$13$	−0.117164	−	0.0380688i	−0.0324954	−	0.0105584i	0.292724	−	0.956197i	$-0.405438\pi$
$13$	−0.117164	−	0.0380688i	−0.0324954	−	0.0105584i	−0.325220	+	0.945639i	$0.605438\pi$
$14$	−2.46148	−	3.38794i	−0.657858	−	0.905464i
$15$		0			0
$16$	−0.729008	−	2.24366i	−0.182252	−	0.560914i
$17$	−1.05363	−	3.24273i	−0.255542	−	0.786477i	−0.993722	−	0.111874i	$-0.964315\pi$
$17$	−1.05363	−	3.24273i	−0.255542	−	0.786477i	0.738181	−	0.674603i	$-0.235685\pi$
$18$	5.43571	+	3.47545i	1.28121	+	0.819172i
$19$	−4.19337	−	5.77168i	−0.962025	−	1.32411i	−0.945974	−	0.324242i	$-0.894891\pi$
$19$	−4.19337	−	5.77168i	−0.962025	−	1.32411i	−0.0160504	−	0.999871i	$-0.505109\pi$
$20$		0			0
$21$	−0.100238	−	3.37122i	−0.0218736	−	0.735660i
$22$	−4.52681	−	5.51216i	−0.965119	−	1.17520i
$23$			2.50155i			0.521609i	0.965392	+	0.260804i	$0.0839877\pi$
$23$			2.50155i			0.521609i	−0.965392	+	0.260804i	$0.916012\pi$
$24$	−0.653380	+	2.23483i	−0.133371	+	0.456183i
$25$		0			0
$26$	0.155728	−	0.214341i	0.0305407	−	0.0420356i
$27$	2.03942	+	4.77920i	0.392486	+	0.919758i
$28$	4.86146	−	1.57958i	0.918730	−	0.298513i
$29$	5.07427	+	3.68667i	0.942268	+	0.684597i	0.948965	−	0.315380i	$-0.102132\pi$
$29$	5.07427	+	3.68667i	0.942268	+	0.684597i	−0.00669788	+	0.999978i	$0.502132\pi$
$30$		0			0
$31$	0.480284	−	1.47816i	0.0862615	−	0.265486i	−0.898616	−	0.438735i	$-0.855427\pi$
$31$	0.480284	−	1.47816i	0.0862615	−	0.265486i	0.984878	+	0.173249i	$0.0554267\pi$
$32$	7.76211			1.37216
$33$	−0.510392	−	5.72184i	−0.0888478	−	0.996045i
$34$	7.33270			1.25755
$35$		0			0
$36$	−6.08492	+	4.99931i	−1.01415	+	0.833218i
$37$	−6.03482	−	4.38456i	−0.992119	−	0.720817i	−0.0317348	−	0.999496i	$-0.510103\pi$
$37$	−6.03482	−	4.38456i	−0.992119	−	0.720817i	−0.960384	+	0.278680i	$0.910103\pi$
$38$	14.5918	−	4.74118i	2.36711	−	0.769121i
$39$	0.200884	−	0.0719392i	0.0321672	−	0.0115195i
$40$		0			0
$41$	4.03282	−	2.93001i	0.629821	−	0.457591i	−0.226518	−	0.974007i	$-0.572734\pi$
$41$	4.03282	−	2.93001i	0.629821	−	0.457591i	0.856338	+	0.516416i	$0.172734\pi$
$42$	6.96191	+	2.03540i	1.07425	+	0.314068i
$43$		−	8.66147i		−	1.32086i	−0.750887	−	0.660431i	$-0.770374\pi$
$43$		−	8.66147i		−	1.32086i	0.750887	−	0.660431i	$-0.229626\pi$
$44$	8.10647	−	3.17595i	1.22210	−	0.478792i
$45$		0			0
$46$	−5.11652	−	1.66246i	−0.754390	−	0.245116i
$47$	0.202715	+	0.279013i	0.0295690	+	0.0406983i	0.823546	−	0.567250i	$-0.191993\pi$
$47$	0.202715	+	0.279013i	0.0295690	+	0.0406983i	−0.793977	+	0.607948i	$0.791993\pi$
$48$	3.37566	+	2.30245i	0.487234	+	0.332330i
$49$	0.991413	+	3.05126i	0.141630	+	0.435894i
$50$		0			0
$51$	4.87879	+	3.32770i	0.683168	+	0.465971i
$52$	0.190085	+	0.261630i	0.0263601	+	0.0362815i
$53$	3.52839	+	1.14644i	0.484662	+	0.157476i	0.541148	−	0.840927i	$-0.317990\pi$
$53$	3.52839	+	1.14644i	0.484662	+	0.157476i	−0.0564863	+	0.998403i	$0.517990\pi$
$54$	−11.1304	+	0.995182i	−1.51466	+	0.135427i
$55$		0			0
$56$			2.61765i			0.349799i
$57$	11.8603	+	3.46749i	1.57093	+	0.459281i
$58$	−10.9127	+	7.92855i	−1.43291	+	1.04107i
$59$	−6.52040	+	8.97456i	−0.848884	+	1.16839i	0.135223	+	0.990815i	$0.456825\pi$
$59$	−6.52040	+	8.97456i	−0.848884	+	1.16839i	−0.984108	+	0.177574i	$0.943175\pi$
$60$		0			0
$61$	9.07864	−	2.94983i	1.16240	−	0.377687i	0.336599	−	0.941648i	$-0.390723\pi$
$61$	9.07864	−	2.94983i	1.16240	−	0.377687i	0.825801	+	0.563961i	$0.190723\pi$
$62$	2.70416	+	1.96469i	0.343429	+	0.249516i
$63$	3.70839	+	4.51368i	0.467214	+	0.568670i
$64$	−3.70046	+	11.3889i	−0.462558	+	1.42361i
$65$		0			0
$66$	12.0423	+	2.75865i	1.48231	+	0.339566i
$67$	−7.76130			−0.948193			−0.474097	−	0.880473i	$-0.657225\pi$
$67$	−7.76130			−0.948193			−0.474097	+	0.880473i	$0.657225\pi$
$68$	−2.76585	+	8.51242i	−0.335409	+	1.03228i
$69$	−2.64981	−	3.42808i	−0.319000	−	0.412692i
$70$		0			0
$71$	−7.62506	+	2.47753i	−0.904928	+	0.294029i	−0.724270	−	0.689517i	$-0.757823\pi$
$71$	−7.62506	+	2.47753i	−0.904928	+	0.294029i	−0.180659	+	0.983546i	$0.557823\pi$
$72$	−1.47191	−	3.75468i	−0.173466	−	0.442493i
$73$	−2.65271	+	3.65114i	−0.310476	+	0.427333i	−0.935530	−	0.353249i	$-0.885077\pi$
$73$	−2.65271	+	3.65114i	−0.310476	+	0.427333i	0.625054	+	0.780582i	$0.285077\pi$
$74$	12.9785	−	9.42942i	1.50872	−	1.09615i
$75$		0			0
$76$			18.7278i			2.14823i
$77$	−2.35586	−	6.01322i	−0.268475	−	0.685270i
$78$	0.0136383	+	0.458686i	0.00154423	+	0.0519360i
$79$	4.54966	+	1.47827i	0.511877	+	0.166319i	0.553556	−	0.832812i	$-0.313271\pi$
$79$	4.54966	+	1.47827i	0.511877	+	0.166319i	−0.0416787	+	0.999131i	$0.513271\pi$
$80$		0			0
$81$	−7.85725	−	4.38904i	−0.873027	−	0.487671i
$82$	3.31278	+	10.1957i	0.365836	+	1.12593i
$83$	−0.0277937	−	0.0855401i	−0.00305075	−	0.00938925i	0.949520	−	0.313708i	$-0.101571\pi$
$83$	−0.0277937	−	0.0855401i	−0.00305075	−	0.00938925i	−0.952570	+	0.304319i	$0.901571\pi$
$84$	−4.98885	+	7.31423i	−0.544328	+	0.798048i
$85$		0			0
$86$	17.7157	+	5.75617i	1.91033	+	0.620703i
$87$	−10.8589	+	0.322870i	−1.16419	+	0.0346153i
$88$	0.263971	+	4.45070i	0.0281394	+	0.474446i
$89$		−	7.03271i		−	0.745465i	−0.927939	−	0.372733i	$-0.878421\pi$
$89$		−	7.03271i		−	0.745465i	0.927939	−	0.372733i	$-0.121579\pi$
$90$		0			0
$91$	0.194072	−	0.141002i	0.0203443	−	0.0147810i
$92$	3.85984	−	5.31262i	0.402417	−	0.553879i
$93$	0.907600	+	2.53440i	0.0941137	+	0.262805i
$94$	−0.705397	+	0.229197i	−0.0727561	+	0.0236399i
$95$		0			0
$96$	−10.6371	+	8.22217i	−1.08564	+	0.839172i
$97$	5.30569	−	16.3292i	0.538711	−	1.65798i	−0.196779	−	0.980448i	$-0.563048\pi$
$97$	5.30569	−	16.3292i	0.538711	−	1.65798i	0.735491	−	0.677535i	$-0.236952\pi$
$98$	−6.89973			−0.696978
$99$	6.76041	+	7.30047i	0.679447	+	0.733725i
$100$		0			0
$101$	3.66734	−	11.2869i	0.364914	−	1.12309i	−0.585122	−	0.810946i	$-0.698953\pi$
$101$	3.66734	−	11.2869i	0.364914	−	1.12309i	0.950035	−	0.312143i	$-0.101047\pi$
$102$	−10.0486	+	7.76730i	−0.994959	+	0.769078i
$103$	−4.34359	−	3.15580i	−0.427986	−	0.310950i	0.352857	−	0.935677i	$-0.385210\pi$
$103$	−4.34359	−	3.15580i	−0.427986	−	0.310950i	−0.780843	+	0.624727i	$0.785210\pi$
$104$	−0.157503	+	0.0511757i	−0.0154444	+	0.00501819i
$105$		0			0
$106$	−4.68974	+	6.45488i	−0.455508	+	0.626953i
$107$	−12.1803	+	8.84951i	−1.17751	+	0.855514i	−0.991889	−	0.127106i	$-0.959431\pi$
$107$	−12.1803	+	8.84951i	−1.17751	+	0.855514i	−0.185625	+	0.982621i	$0.559431\pi$
$108$	3.04305	−	13.2965i	0.292817	−	1.27946i
$109$			8.38022i			0.802680i	0.915929	+	0.401340i	$0.131455\pi$
$109$			8.38022i			0.802680i	−0.915929	+	0.401340i	$0.868545\pi$
$110$		0			0
$111$	12.9144	−	0.383989i	1.22578	−	0.0364467i
$112$	4.36892	+	1.41955i	0.412824	+	0.134135i
$113$	−7.19519	−	9.90333i	−0.676866	−	0.931627i	0.323025	−	0.946391i	$-0.395300\pi$
$113$	−7.19519	−	9.90333i	−0.676866	−	0.931627i	−0.999891	+	0.0147639i	$0.995300\pi$
$114$	−14.9742	+	21.9539i	−1.40246	+	2.05617i
$115$		0			0
$116$	−5.08792	−	15.6590i	−0.472402	−	1.45390i
$117$	−0.199085	+	0.311375i	−0.0184054	+	0.0287866i
$118$	−14.0228	−	19.3007i	−1.29090	−	1.77677i
$119$	6.31435	+	2.05166i	0.578835	+	0.188075i
$120$		0			0
$121$	−4.61196	−	9.98648i	−0.419269	−	0.907862i
$122$			20.5293i			1.85863i
$123$	−2.42283	+	8.28708i	−0.218459	+	0.747221i
$124$	−3.30077	+	2.39815i	−0.296418	+	0.215360i
$125$		0			0
$126$	−11.6965	+	4.58527i	−1.04201	+	0.408488i
$127$	9.95189	−	3.23356i	0.883087	−	0.286932i	0.167849	−	0.985813i	$-0.446318\pi$
$127$	9.95189	−	3.23356i	0.883087	−	0.286932i	0.715239	+	0.698880i	$0.246318\pi$
$128$	−8.27552	−	6.01252i	−0.731460	−	0.531436i
$129$	9.17483	+	11.8695i	0.807799	+	1.04505i
$130$		0			0
$131$	3.24512			0.283527			0.141764	−	0.989901i	$-0.454723\pi$
$131$	3.24512			0.283527			0.141764	+	0.989901i	$0.454723\pi$
$132$	−7.74477	+	12.9392i	−0.674096	+	1.12621i
$133$	13.8919			1.20458
$134$	5.15794	−	15.8745i	0.445578	−	1.37135i
$135$		0			0
$136$	−3.70814	−	2.69412i	−0.317970	−	0.231019i
$137$	−0.702012	+	0.228097i	−0.0599769	+	0.0194877i	−0.338852	−	0.940840i	$-0.610039\pi$
$137$	−0.702012	+	0.228097i	−0.0599769	+	0.0194877i	0.278875	+	0.960327i	$0.410039\pi$
$138$	8.77258	−	3.14157i	0.746771	−	0.267428i
$139$	8.28287	−	11.4004i	0.702544	−	0.966969i	−0.297381	−	0.954759i	$-0.596113\pi$
$139$	8.28287	−	11.4004i	0.702544	−	0.966969i	0.999925	−	0.0122104i	$-0.00388677\pi$
$140$		0			0
$141$	−0.573348	−	0.167625i	−0.0482846	−	0.0141166i
$142$		−	17.2424i		−	1.44695i
$143$	0.315754	−	0.259310i	0.0264047	−	0.0216846i
$144$	−7.06485	+	0.420495i	−0.588738	+	0.0350413i
$145$		0			0
$146$	−5.70491	−	7.85213i	−0.472142	−	0.649847i
$147$	−4.59072	−	3.13121i	−0.378636	−	0.258258i
$148$	6.05106	+	18.6233i	0.497394	+	1.53082i
$149$	−3.17871	−	9.78306i	−0.260410	−	0.801460i	−0.992715	−	0.120483i	$-0.961556\pi$
$149$	−3.17871	−	9.78306i	−0.260410	−	0.801460i	0.732305	−	0.680976i	$-0.238444\pi$
$150$		0			0
$151$	0.973453	+	1.33984i	0.0792185	+	0.109035i	0.846787	−	0.531932i	$-0.178534\pi$
$151$	0.973453	+	1.33984i	0.0792185	+	0.109035i	−0.767569	+	0.640967i	$0.778534\pi$
$152$	−9.12105	−	2.96361i	−0.739815	−	0.240380i
$153$	−10.2107	+	0.607736i	−0.825490	+	0.0491326i
$154$	13.8647	−	0.822317i	1.11725	−	0.0662642i
$155$		0			0
$156$	−0.537626	−	0.157181i	−0.0430445	−	0.0125846i
$157$	−13.6623	+	9.92625i	−1.09037	+	0.792201i	−0.979462	−	0.201629i	$-0.935376\pi$
$157$	−13.6623	+	9.92625i	−1.09037	+	0.792201i	−0.110910	+	0.993830i	$0.535376\pi$
$158$	−6.04715	+	8.32319i	−0.481086	+	0.662158i
$159$	−6.04964	+	2.16645i	−0.479768	+	0.171811i
$160$		0			0
$161$	−3.94080	−	2.86316i	−0.310579	−	0.225649i
$162$	14.1988	−	13.1539i	1.11556	−	1.03347i
$163$	1.45923	−	4.49104i	0.114295	−	0.351765i	−0.877504	−	0.479569i	$-0.840793\pi$
$163$	1.45923	−	4.49104i	0.114295	−	0.351765i	0.991799	+	0.127804i	$0.0407929\pi$
$164$	−13.0856			−1.02181
$165$		0			0
$166$	0.193430			0.0150130
$167$	7.20408	−	22.1719i	0.557468	−	1.71571i	−0.131866	−	0.991268i	$-0.542097\pi$
$167$	7.20408	−	22.1719i	0.557468	−	1.71571i	0.689334	−	0.724444i	$-0.257903\pi$
$168$	−2.77280	−	3.58719i	−0.213926	−	0.276757i
$169$	−10.5049	−	7.63229i	−0.808073	−	0.587099i
$170$		0			0
$171$	−19.9261	+	7.81145i	−1.52379	+	0.597356i
$172$	−13.3645	+	18.3946i	−1.01903	+	1.40258i
$173$	−7.08409	+	5.14689i	−0.538593	+	0.391311i	−0.823562	−	0.567226i	$-0.808017\pi$
$173$	−7.08409	+	5.14689i	−0.538593	+	0.391311i	0.284969	+	0.958537i	$0.408017\pi$
$174$	6.55611	−	22.4247i	0.497018	−	1.70001i
$175$		0			0
$176$	7.57146	+	1.97303i	0.570720	+	0.148723i
$177$	−0.571042	−	19.2054i	−0.0429221	−	1.44357i
$178$	14.3843	+	4.67374i	1.07815	+	0.350311i
$179$	−13.1171	−	18.0542i	−0.980419	−	1.34943i	−0.936603	−	0.350392i	$-0.886048\pi$
$179$	−13.1171	−	18.0542i	−0.980419	−	1.34943i	−0.0438163	−	0.999040i	$-0.513952\pi$
$180$		0			0
$181$	−3.69344	−	11.3672i	−0.274531	−	0.844921i	−0.989343	−	0.145604i	$-0.953488\pi$
$181$	−3.69344	−	11.3672i	−0.274531	−	0.844921i	0.714812	−	0.699317i	$-0.246512\pi$
$182$	0.159422	+	0.490649i	0.0118171	+	0.0363693i
$183$	−9.31654	+	13.6591i	−0.688698	+	1.00971i
$184$	1.97661	+	2.72057i	0.145718	+	0.200563i
$185$		0			0
$186$	−5.78687	+	0.172063i	−0.424314	+	0.0126163i
$187$	10.9429	+	2.85160i	0.800227	+	0.208529i
$188$		−	0.905336i		−	0.0660284i
$189$	−9.86312	−	2.25727i	−0.717436	−	0.164193i
$190$		0			0
$191$	−10.4191	+	14.3406i	−0.753897	+	1.03765i	0.243800	+	0.969826i	$0.421606\pi$
$191$	−10.4191	+	14.3406i	−0.753897	+	1.03765i	−0.997697	+	0.0678249i	$0.978394\pi$
$192$	−6.99282	−	19.5269i	−0.504663	−	1.40923i
$193$	−5.50924	+	1.79006i	−0.396564	+	0.128851i	−0.500508	−	0.865732i	$-0.666853\pi$
$193$	−5.50924	+	1.79006i	−0.396564	+	0.128851i	0.103945	+	0.994583i	$0.466853\pi$
$194$	29.8729	+	21.7039i	2.14475	+	1.55825i
$195$		0			0
$196$	2.60254	−	8.00979i	0.185896	−	0.572128i
$197$	−0.928915			−0.0661824			−0.0330912	−	0.999452i	$-0.510535\pi$
$197$	−0.928915			−0.0661824			−0.0330912	+	0.999452i	$0.510535\pi$
$198$	−19.4247	+	8.97566i	−1.38046	+	0.637872i
$199$	−6.36009			−0.450855			−0.225427	−	0.974260i	$-0.572378\pi$
$199$	−6.36009			−0.450855			−0.225427	+	0.974260i	$0.572378\pi$
$200$		0			0
$201$	10.6359	−	8.22131i	0.750202	−	0.579886i
$202$	20.6484	+	15.0019i	1.45281	+	1.05553i
$203$	−11.6156	+	3.77412i	−0.815252	+	0.264891i
$204$	−5.22667	−	14.5950i	−0.365940	−	1.02186i
$205$		0			0
$206$	9.34131	−	6.78686i	0.650840	−	0.472863i
$207$	7.26251	+	1.89091i	0.504780	+	0.131427i
$208$			0.290628i			0.0201514i
$209$	23.6199	−	1.40090i	1.63382	−	0.0969020i
$210$		0			0
$211$	−5.76987	−	1.87474i	−0.397214	−	0.129063i	0.103597	−	0.994619i	$-0.466965\pi$
$211$	−5.76987	−	1.87474i	−0.397214	−	0.129063i	−0.500811	+	0.865557i	$0.666965\pi$
$212$	−5.72442	−	7.87899i	−0.393155	−	0.541131i
$213$	7.82487	−	11.4722i	0.536151	−	0.786060i
$214$	−10.0056	−	30.7940i	−0.683968	−	2.10504i
$215$		0			0
$216$	5.99430	+	3.58620i	0.407860	+	0.244010i
$217$	1.77890	+	2.44845i	0.120760	+	0.166212i
$218$	−17.1404	−	5.56926i	−1.16090	−	0.377198i
$219$	−0.232318	−	7.81338i	−0.0156986	−	0.527979i
$220$		0			0
$221$			0.420041i			0.0282550i
$222$	−7.79719	+	26.6696i	−0.523313	+	1.78995i
$223$	8.34144	−	6.06041i	0.558584	−	0.405835i	−0.272356	−	0.962196i	$-0.587803\pi$
$223$	8.34144	−	6.06041i	0.558584	−	0.405835i	0.830940	+	0.556361i	$0.187803\pi$
$224$	−8.88416	+	12.2280i	−0.593598	+	0.817018i
$225$		0			0
$226$	25.0374	−	8.13515i	1.66546	−	0.541142i
$227$	−11.4477	−	8.31726i	−0.759812	−	0.552036i	0.139040	−	0.990287i	$-0.455598\pi$
$227$	−11.4477	−	8.31726i	−0.759812	−	0.552036i	−0.898853	+	0.438251i	$0.855598\pi$
$228$	−19.8378	−	25.6642i	−1.31379	−	1.69966i
$229$	−2.24944	+	6.92305i	−0.148647	+	0.457488i	−0.997462	−	0.0712018i	$-0.977317\pi$
$229$	−2.24944	+	6.92305i	−0.148647	+	0.457488i	0.848815	+	0.528690i	$0.177317\pi$
$230$		0			0
$231$	9.59805	+	5.74492i	0.631505	+	0.377988i
$232$	8.43160			0.553561
$233$	4.76389	−	14.6617i	0.312093	−	0.960522i	−0.664842	−	0.746984i	$-0.731501\pi$
$233$	4.76389	−	14.6617i	0.312093	−	0.960522i	0.976935	−	0.213538i	$-0.0684988\pi$
$234$	−0.504562	−	0.614128i	−0.0329842	−	0.0401468i
$235$		0			0
$236$	27.6952	−	8.99871i	1.80280	−	0.585766i
$237$	−7.80067	+	2.79352i	−0.506708	+	0.181459i
$238$	−8.39268	+	11.5515i	−0.544016	+	0.748774i
$239$	1.57556	−	1.14471i	0.101915	−	0.0740453i	−0.535661	−	0.844433i	$-0.679937\pi$
$239$	1.57556	−	1.14471i	0.101915	−	0.0740453i	0.637575	+	0.770388i	$0.279937\pi$
$240$		0			0
$241$			19.3437i			1.24604i	0.782207	+	0.623019i	$0.214094\pi$
$241$			19.3437i			1.24604i	−0.782207	+	0.623019i	$0.785906\pi$
$242$	23.4907	−	2.79631i	1.51004	−	0.179753i
$243$	15.4166	−	2.30828i	0.988976	−	0.148076i
$244$	−23.8321	−	7.74353i	−1.52570	−	0.495729i
$245$		0			0
$246$	−15.3398	−	10.4629i	−0.978028	−	0.667088i
$247$	0.271590	+	0.835868i	0.0172809	+	0.0531850i
$248$	−0.645643	−	1.98708i	−0.0409984	−	0.126180i
$249$	0.128698	+	0.0877816i	0.00815590	+	0.00556294i
$250$		0			0
$251$	−19.6517	−	6.38523i	−1.24041	−	0.403032i	−0.385932	−	0.922527i	$-0.626120\pi$
$251$	−19.6517	−	6.38523i	−1.24041	−	0.403032i	−0.854474	+	0.519495i	$0.826120\pi$
$252$	−0.911111	−	15.3078i	−0.0573946	−	0.964303i
$253$	−6.98912	−	4.47072i	−0.439402	−	0.281072i
$254$			22.5040i			1.41202i
$255$		0			0
$256$	−1.57855	+	1.14688i	−0.0986591	+	0.0716801i
$257$	−10.7937	+	14.8562i	−0.673291	+	0.926706i	−0.999829	−	0.0184780i	$-0.994118\pi$
$257$	−10.7937	+	14.8562i	−0.673291	+	0.926706i	0.326538	+	0.945184i	$0.394118\pi$
$258$	−30.3746	+	10.8775i	−1.89104	+	0.677205i
$259$	13.8144	−	4.48856i	0.858384	−	0.278906i
$260$		0			0
$261$	14.5388	−	11.9449i	0.899928	−	0.739372i
$262$	−2.15661	+	6.63737i	−0.133236	+	0.410058i
$263$	22.0290			1.35837			0.679184	−	0.733968i	$-0.262334\pi$
$263$	22.0290			1.35837			0.679184	+	0.733968i	$0.262334\pi$
$264$	−5.07623	−	5.81954i	−0.312420	−	0.358168i
$265$		0			0
$266$	−9.23218	+	28.4137i	−0.566061	+	1.74216i
$267$	7.44953	+	9.63749i	0.455904	+	0.589805i
$268$	16.4829	+	11.9755i	1.00685	+	0.731523i
$269$	−24.1801	+	7.85660i	−1.47429	+	0.479025i	−0.932401	−	0.361426i	$-0.882290\pi$
$269$	−24.1801	+	7.85660i	−1.47429	+	0.479025i	−0.541888	+	0.840451i	$0.682290\pi$
$270$		0			0
$271$	−0.701540	+	0.965587i	−0.0426155	+	0.0586552i	−0.829793	−	0.558071i	$-0.811542\pi$
$271$	−0.701540	+	0.965587i	−0.0426155	+	0.0586552i	0.787177	+	0.616727i	$0.211542\pi$
$272$	−6.50746	+	4.72795i	−0.394573	+	0.286674i
$273$	−0.116594	+	0.398801i	−0.00705659	+	0.0241365i
$274$		−	1.58744i		−	0.0959008i
$275$		0			0
$276$	0.338036	+	11.3689i	0.0203474	+	0.684329i
$277$	−8.19364	−	2.66227i	−0.492308	−	0.159961i	0.0523333	−	0.998630i	$-0.483334\pi$
$277$	−8.19364	−	2.66227i	−0.492308	−	0.159961i	−0.544641	+	0.838669i	$0.683334\pi$
$278$	17.8131	+	24.5177i	1.06836	+	1.47047i
$279$	−3.92837	−	2.51170i	−0.235185	−	0.150372i
$280$		0			0
$281$	−0.0245556	−	0.0755745i	−0.00146487	−	0.00450840i	0.950321	−	0.311270i	$-0.100754\pi$
$281$	−0.0245556	−	0.0755745i	−0.00146487	−	0.00450840i	−0.951786	+	0.306762i	$0.900754\pi$
$282$	0.723881	−	1.06129i	0.0431065	−	0.0631991i
$283$	−9.09567	−	12.5191i	−0.540681	−	0.744184i	0.448030	−	0.894019i	$-0.352126\pi$
$283$	−9.09567	−	12.5191i	−0.540681	−	0.744184i	−0.988711	+	0.149835i	$0.952126\pi$
$284$	20.0164	+	6.50372i	1.18775	+	0.385925i
$285$		0			0
$286$	0.320537	+	0.818155i	0.0189537	+	0.0483785i
$287$			9.70665i			0.572965i
$288$	5.86734	−	22.5350i	0.345736	−	1.32789i
$289$	4.34813	−	3.15910i	0.255773	−	0.185830i
$290$		0			0
$291$	10.0262	+	27.9975i	0.587749	+	1.64124i
$292$	11.2673	−	3.66096i	0.659368	−	0.214242i
$293$	−15.2756	−	11.0984i	−0.892413	−	0.648376i	0.0440932	−	0.999027i	$-0.485960\pi$
$293$	−15.2756	−	11.0984i	−0.892413	−	0.648376i	−0.936506	+	0.350652i	$0.885960\pi$
$294$	9.45526	−	7.30867i	0.551442	−	0.426251i
$295$		0			0
$296$	−10.0277			−0.582848
$297$	−16.9975	−	2.84334i	−0.986296	−	0.164987i
$298$	22.1222			1.28150
$299$	0.0952310	−	0.293091i	0.00550735	−	0.0169499i
$300$		0			0
$301$	13.6448	+	9.91353i	0.786473	+	0.571406i
$302$	−3.38737	+	1.10062i	−0.194921	+	0.0633337i
$303$	6.93022	+	19.3521i	0.398131	+	1.11175i
$304$	−9.89265	+	13.6161i	−0.567383	+	0.780935i
$305$		0			0
$306$	5.54275	−	21.2884i	0.316858	−	1.21697i
$307$			13.5048i			0.770762i	0.922758	+	0.385381i	$0.125930\pi$
$307$			13.5048i			0.770762i	−0.922758	+	0.385381i	$0.874070\pi$
$308$	−4.27508	+	16.4055i	−0.243595	+	0.934792i
$309$	9.29522	−	0.276378i	0.528786	−	0.0157226i
$310$		0			0
$311$	9.93791	+	13.6784i	0.563527	+	0.775628i	0.991770	−	0.128035i	$-0.0408671\pi$
$311$	9.93791	+	13.6784i	0.563527	+	0.775628i	−0.428243	+	0.903664i	$0.640867\pi$
$312$	0.161630	−	0.236968i	0.00915049	−	0.0134157i
$313$	−0.512595	−	1.57760i	−0.0289736	−	0.0891715i	0.935524	−	0.353263i	$-0.114928\pi$
$313$	−0.512595	−	1.57760i	−0.0289736	−	0.0891715i	−0.964498	+	0.264092i	$0.914928\pi$
$314$	−11.2230	−	34.5408i	−0.633350	−	1.94925i
$315$		0			0
$316$	−7.38132	−	10.1595i	−0.415231	−	0.571517i
$317$	−9.54434	−	3.10114i	−0.536064	−	0.174178i	0.0284595	−	0.999595i	$-0.490940\pi$
$317$	−9.54434	−	3.10114i	−0.536064	−	0.174178i	−0.564523	+	0.825417i	$0.690940\pi$
$318$	−0.410717	−	13.8134i	−0.0230319	−	0.774614i
$319$	−19.3689	+	7.58834i	−1.08445	+	0.424865i
$320$		0			0
$321$	7.31765	−	25.0294i	0.408432	−	1.39701i
$322$	8.47508	−	6.15751i	0.472298	−	0.343145i
$323$	−14.2977	+	19.6791i	−0.795547	+	1.09498i
$324$	9.91448	+	21.4447i	0.550805	+	1.19137i
$325$		0			0
$326$	8.21595	+	5.96923i	0.455039	+	0.330605i
$327$	−8.87692	−	11.4841i	−0.490895	−	0.635073i
$328$	2.07075	−	6.37311i	0.114338	−	0.351896i
$329$	−0.671561			−0.0370244
$330$		0			0
$331$	−9.03657			−0.496695			−0.248348	−	0.968671i	$-0.579887\pi$
$331$	−9.03657			−0.496695			−0.248348	+	0.968671i	$0.579887\pi$
$332$	−0.0729606	+	0.224549i	−0.00400423	+	0.0123238i
$333$	−17.2910	+	14.2061i	−0.947540	+	0.778489i
$334$	40.5614	+	29.4696i	2.21942	+	1.61251i
$335$		0			0
$336$	−7.49078	+	2.68254i	−0.408655	+	0.146345i
$337$	4.61320	−	6.34953i	0.251297	−	0.345881i	−0.664668	−	0.747139i	$-0.731427\pi$
$337$	4.61320	−	6.34953i	0.251297	−	0.345881i	0.915965	+	0.401258i	$0.131427\pi$
$338$	22.5919	−	16.4140i	1.22884	−	0.892804i
$339$	20.3505	+	5.94970i	1.10528	+	0.323143i
$340$		0			0
$341$	3.27151	+	3.98362i	0.177162	+	0.215725i
$342$	−2.73473	−	45.9470i	−0.147877	−	2.48453i
$343$	−18.9050	−	6.14261i	−1.02077	−	0.331670i
$344$	−6.84391	−	9.41984i	−0.368999	−	0.507884i
$345$		0			0
$346$	−5.81926	−	17.9099i	−0.312846	−	0.962840i
$347$	5.06410	+	15.5857i	0.271855	+	0.836684i	0.990034	+	0.140826i	$0.0449757\pi$
$347$	5.06410	+	15.5857i	0.271855	+	0.836684i	−0.718179	+	0.695858i	$0.755024\pi$
$348$	23.5595	+	16.0693i	1.26292	+	0.861407i
$349$	−1.73563	−	2.38889i	−0.0929063	−	0.127874i	0.760033	−	0.649884i	$-0.225183\pi$
$349$	−1.73563	−	2.38889i	−0.0929063	−	0.127874i	−0.852940	+	0.522010i	$0.825183\pi$
$350$		0			0
$351$	−0.0570073	−	0.637588i	−0.00304282	−	0.0340319i
$352$	−13.8723	+	21.6867i	−0.739396	+	1.15591i
$353$		−	14.9894i		−	0.797806i	−0.916993	−	0.398903i	$-0.869391\pi$
$353$		−	14.9894i		−	0.797806i	0.916993	−	0.398903i	$-0.130609\pi$
$354$	39.6612	+	11.5954i	2.10797	+	0.616290i
$355$		0			0
$356$	−10.8513	+	14.9356i	−0.575120	+	0.791585i
$357$	−10.8263	+	3.87705i	−0.572990	+	0.205195i
$358$	45.6442	−	14.8307i	2.41237	−	0.783827i
$359$	−10.3639	−	7.52980i	−0.546985	−	0.397408i	0.279688	−	0.960091i	$-0.409769\pi$
$359$	−10.3639	−	7.52980i	−0.546985	−	0.397408i	−0.826673	+	0.562683i	$0.809769\pi$
$360$		0			0
$361$	−9.85658	+	30.3354i	−0.518768	+	1.59660i
$362$	25.7045			1.35100
$363$	16.8985	+	8.79998i	0.886943	+	0.461879i
$364$	−0.629720			−0.0330063
$365$		0			0
$366$	−21.7461	−	28.1330i	−1.13668	−	1.47053i
$367$	5.36573	+	3.89843i	0.280089	+	0.203496i	0.718956	−	0.695055i	$-0.244620\pi$
$367$	5.36573	+	3.89843i	0.280089	+	0.203496i	−0.438867	+	0.898552i	$0.644620\pi$
$368$	5.61261	−	1.82365i	0.292578	−	0.0950642i
$369$	−5.45806	−	13.9229i	−0.284135	−	0.724797i
$370$		0			0
$371$	−5.84449	+	4.24627i	−0.303431	+	0.220455i
$372$	1.98303	−	6.78279i	0.102815	−	0.351672i
$373$			0.119429i			0.00618378i	0.999995	+	0.00309189i	$0.000984181\pi$
$373$			0.119429i			0.00618378i	−0.999995	+	0.00309189i	$0.999016\pi$
$374$	−13.1049	+	20.4870i	−0.677636	+	1.05936i
$375$		0			0
$376$	0.440928	+	0.143266i	0.0227391	+	0.00738840i
$377$	−0.454173	−	0.625116i	−0.0233911	−	0.0321951i
$378$	11.1716	−	18.6733i	0.574608	−	0.960452i
$379$	8.32626	+	25.6256i	0.427691	+	1.31630i	0.900394	+	0.435076i	$0.143278\pi$
$379$	8.32626	+	25.6256i	0.427691	+	1.31630i	−0.472703	+	0.881222i	$0.656722\pi$
$380$		0			0
$381$	−10.2127	+	14.9730i	−0.523211	+	0.767088i
$382$	−22.4072	−	30.8409i	−1.14645	−	1.57796i
$383$	15.2646	+	4.95979i	0.779987	+	0.253433i	0.671835	−	0.740701i	$-0.265507\pi$
$383$	15.2646	+	4.95979i	0.779987	+	0.253433i	0.108152	+	0.994134i	$0.465507\pi$
$384$	17.7095	−	0.526563i	0.903734	−	0.0268710i
$385$		0			0
$386$		−	12.4579i		−	0.634090i
$387$	−25.1460	−	6.54716i	−1.27825	−	0.332811i
$388$	−36.4636	+	26.4924i	−1.85116	+	1.34495i
$389$	−6.83231	+	9.40387i	−0.346412	+	0.476795i	−0.946300	−	0.323289i	$-0.895212\pi$
$389$	−6.83231	+	9.40387i	−0.346412	+	0.476795i	0.599889	+	0.800084i	$0.295212\pi$
$390$		0			0
$391$	8.11184	−	2.63570i	0.410233	−	0.133293i
$392$	3.48919	+	2.53504i	0.176231	+	0.128039i
$393$	−4.44705	+	3.43745i	−0.224324	+	0.173397i
$394$	0.617330	−	1.89995i	0.0311007	−	0.0957180i
$395$		0			0
$396$	−3.09281	−	25.9354i	−0.155419	−	1.30331i
$397$	27.4437			1.37736			0.688681	−	0.725064i	$-0.258190\pi$
$397$	27.4437			1.37736			0.688681	+	0.725064i	$0.258190\pi$
$398$	4.22674	−	13.0086i	0.211867	−	0.652060i
$399$	−19.0372	+	14.7153i	−0.953054	+	0.736686i
$400$		0			0
$401$	−29.2593	+	9.50692i	−1.46114	+	0.474753i	−0.928418	−	0.371538i	$-0.878831\pi$
$401$	−29.2593	+	9.50692i	−1.46114	+	0.474753i	−0.532721	+	0.846291i	$0.678831\pi$
$402$	9.74704	+	27.2178i	0.486138	+	1.35750i
$403$	−0.112544	+	0.154903i	−0.00560620	+	0.00771628i
$404$	−25.2039	+	18.3117i	−1.25394	+	0.911043i
$405$		0			0
$406$		−	26.2660i		−	1.30356i
$407$	23.0354	−	9.02481i	1.14182	−	0.447343i
$408$	7.93537	−	0.235945i	0.392859	−	0.0116810i
$409$	−2.58614	−	0.840288i	−0.127876	−	0.0415496i	0.244380	−	0.969680i	$-0.421416\pi$
$409$	−2.58614	−	0.840288i	−0.127876	−	0.0415496i	−0.372256	+	0.928130i	$0.621416\pi$
$410$		0			0
$411$	0.720407	−	1.05620i	0.0355351	−	0.0520985i
$412$	4.35527	+	13.4042i	0.214569	+	0.660375i
$413$	−6.67508	−	20.5438i	−0.328459	−	1.01089i
$414$	−8.69401	+	13.5977i	−0.427287	+	0.668290i
$415$		0			0
$416$	−0.909438	−	0.295494i	−0.0445889	−	0.0144878i
$417$	0.725395	+	24.3967i	0.0355228	+	1.19471i
$418$	−12.8318	+	49.2418i	−0.627624	+	2.40849i
$419$		−	1.95260i		−	0.0953907i	−0.998862	−	0.0476954i	$-0.984812\pi$
$419$		−	1.95260i		−	0.0953907i	0.998862	−	0.0476954i	$-0.0151877\pi$
$420$		0			0
$421$	−24.0128	+	17.4463i	−1.17031	+	0.850281i	−0.991046	−	0.133519i	$-0.957372\pi$
$421$	−24.0128	+	17.4463i	−1.17031	+	0.850281i	−0.179266	+	0.983801i	$0.557372\pi$
$422$	7.66899	−	10.5555i	0.373320	−	0.513831i
$423$	0.963266	−	0.377620i	0.0468356	−	0.0183605i
$424$	4.74320	−	1.54116i	0.230350	−	0.0748453i
$425$		0			0
$426$	18.2643	+	23.6286i	0.884908	+	1.14481i
$427$	−5.74400	+	17.6782i	−0.277972	+	0.855509i
$428$	39.5224			1.91039
$429$	−0.158024	+	0.689823i	−0.00762949	+	0.0333050i
$430$		0			0
$431$	8.62224	−	26.5365i	0.415319	−	1.27822i	−0.496647	−	0.867953i	$-0.665435\pi$
$431$	8.62224	−	26.5365i	0.415319	−	1.27822i	0.911965	−	0.410267i	$-0.134565\pi$
$432$	9.23613	−	8.05983i	0.444374	−	0.387779i
$433$	11.3140	+	8.22011i	0.543717	+	0.395033i	0.825464	−	0.564455i	$-0.190914\pi$
$433$	11.3140	+	8.22011i	0.543717	+	0.395033i	−0.281747	+	0.959489i	$0.590914\pi$
$434$	−6.19013	+	2.01129i	−0.297136	+	0.0965452i
$435$		0			0
$436$	12.9305	−	17.7974i	0.619260	−	0.852339i
$437$	14.4381	−	10.4899i	0.690669	−	0.501800i
$438$	16.1354	+	4.71738i	0.770981	+	0.225405i
$439$			26.8917i			1.28347i	0.766926	+	0.641736i	$0.221786\pi$
$439$			26.8917i			1.28347i	−0.766926	+	0.641736i	$0.778214\pi$
$440$		0			0
$441$	9.60784	−	0.571852i	0.457516	−	0.0272310i
$442$	−0.859127	−	0.279147i	−0.0408645	−	0.0132777i
$443$	12.8649	+	17.7071i	0.611231	+	0.841288i	0.996678	−	0.0814422i	$-0.0259526\pi$
$443$	12.8649	+	17.7071i	0.611231	+	0.841288i	−0.385447	+	0.922730i	$0.625953\pi$
$444$	−28.0193	−	19.1113i	−1.32974	−	0.906981i
$445$		0			0
$446$	6.85212	+	21.0887i	0.324457	+	0.998577i
$447$	14.7189	+	10.0394i	0.696182	+	0.474848i
$448$	−13.7060	−	18.8647i	−0.647547	−	0.891272i
$449$	−4.43555	−	1.44120i	−0.209326	−	0.0680143i	0.202477	−	0.979287i	$-0.435101\pi$
$449$	−4.43555	−	1.44120i	−0.209326	−	0.0680143i	−0.411803	+	0.911273i	$0.635101\pi$
$450$		0			0
$451$	0.978842	+	16.5038i	0.0460919	+	0.777135i
$452$			32.1341i			1.51146i
$453$	−2.75326	−	0.804948i	−0.129359	−	0.0378197i
$454$	24.6195	−	17.8871i	1.15545	−	0.839483i
$455$		0			0
$456$	15.6386	−	5.60038i	0.732344	−	0.262262i
$457$	1.25776	−	0.408670i	0.0588354	−	0.0191168i	−0.279451	−	0.960160i	$-0.590153\pi$
$457$	1.25776	−	0.408670i	0.0588354	−	0.0191168i	0.338287	+	0.941043i	$0.390153\pi$
$458$	−12.6651	−	9.20173i	−0.591801	−	0.429969i
$459$	13.3489	−	11.6488i	0.623072	−	0.543718i
$460$		0			0
$461$	−17.8605			−0.831848			−0.415924	−	0.909399i	$-0.636542\pi$
$461$	−17.8605			−0.831848			−0.415924	+	0.909399i	$0.636542\pi$
$462$	−18.1289	+	15.8134i	−0.843434	+	0.735705i
$463$	−7.47799			−0.347532			−0.173766	−	0.984787i	$-0.555594\pi$
$463$	−7.47799			−0.347532			−0.173766	+	0.984787i	$0.555594\pi$
$464$	4.57244	−	14.0725i	0.212270	−	0.653300i
$465$		0			0
$466$	26.8223	+	19.4875i	1.24252	+	0.902743i
$467$	21.4793	−	6.97904i	0.993943	−	0.322952i	0.233500	−	0.972357i	$-0.424982\pi$
$467$	21.4793	−	6.97904i	0.993943	−	0.322952i	0.760443	+	0.649405i	$0.224982\pi$
$468$	0.903250	−	0.354092i	0.0417528	−	0.0163679i
$469$	8.88323	−	12.2267i	0.410190	−	0.564578i
$470$		0			0
$471$	8.20801	−	28.0748i	0.378205	−	1.29362i
$472$			14.9125i			0.686403i
$473$	24.1994	+	15.4796i	1.11269	+	0.711753i
$474$	−0.529596	−	17.8115i	−0.0243251	−	0.818110i
$475$		0			0
$476$	−10.2443	−	14.1001i	−0.469548	−	0.646277i
$477$	5.99546	−	9.37707i	0.274513	−	0.429347i
$478$	1.29425	+	3.98330i	0.0591978	+	0.182192i
$479$	5.96037	+	18.3441i	0.272336	+	0.838165i	0.989912	+	0.141685i	$0.0452519\pi$
$479$	5.96037	+	18.3441i	0.272336	+	0.838165i	−0.717575	+	0.696481i	$0.754748\pi$
$480$		0			0
$481$	0.540148	+	0.743450i	0.0246286	+	0.0338984i
$482$	−39.5645	−	12.8553i	−1.80211	−	0.585542i
$483$	8.43326	−	0.250749i	0.383727	−	0.0114095i
$484$	−5.61439	+	28.3248i	−0.255199	+	1.28749i
$485$		0			0
$486$	−5.52422	+	33.0663i	−0.250584	+	1.49992i
$487$	22.0394	−	16.0126i	0.998702	−	0.725599i	0.0368921	−	0.999319i	$-0.488254\pi$
$487$	22.0394	−	16.0126i	0.998702	−	0.725599i	0.961809	+	0.273720i	$0.0882542\pi$
$488$	7.54271	−	10.3816i	0.341442	−	0.469955i
$489$	2.75752	+	7.70015i	0.124699	+	0.348213i
$490$		0			0
$491$	−1.11853	−	0.812661i	−0.0504786	−	0.0366749i	0.562260	−	0.826961i	$-0.309932\pi$
$491$	−1.11853	−	0.812661i	−0.0504786	−	0.0366749i	−0.612738	+	0.790286i	$0.709932\pi$
$492$	17.9323	−	13.8612i	0.808449	−	0.624910i
$493$	6.60849	−	20.3388i	0.297631	−	0.916015i
$494$	−1.89013			−0.0850408
$495$		0			0
$496$	−3.66662			−0.164636
$497$	4.82433	−	14.8478i	0.216401	−	0.666014i
$498$	−0.265073	+	0.204894i	−0.0118782	+	0.00918153i
$499$	−5.90653	−	4.29135i	−0.264413	−	0.192107i	0.447677	−	0.894195i	$-0.352251\pi$
$499$	−5.90653	−	4.29135i	−0.264413	−	0.192107i	−0.712090	+	0.702088i	$0.752251\pi$
$500$		0			0
$501$	13.6137	+	38.0150i	0.608213	+	1.69839i
$502$	26.1200	−	35.9510i	1.16579	−	1.60457i
$503$	1.17583	−	0.854293i	0.0524278	−	0.0380910i	−0.561263	−	0.827638i	$-0.689684\pi$
$503$	1.17583	−	0.854293i	0.0524278	−	0.0380910i	0.613691	+	0.789547i	$0.289684\pi$
$504$	7.59960	+	1.97867i	0.338513	+	0.0881370i
$505$		0			0
$506$	13.7889	−	11.3240i	0.612992	−	0.503414i
$507$	22.4804	−	0.668418i	0.998391	−	0.0296855i
$508$	−26.1245	−	8.48836i	−1.15909	−	0.376610i
$509$	21.5451	+	29.6543i	0.954970	+	1.31440i	0.949284	+	0.314419i	$0.101810\pi$
$509$	21.5451	+	29.6543i	0.954970	+	1.31440i	0.00568571	+	0.999984i	$0.498190\pi$
$510$		0			0
$511$	−2.71563	−	8.35785i	−0.120132	−	0.369730i
$512$	−7.61864	−	23.4478i	−0.336700	−	1.03625i
$513$	19.0320	−	31.8118i	0.840282	−	1.40453i
$514$	−23.2129	−	31.9498i	−1.02388	−	1.40925i
$515$		0			0
$516$	−1.17043	−	39.3643i	−0.0515254	−	1.73292i
$517$	−1.14183	+	0.0677219i	−0.0502176	+	0.00297840i
$518$			31.2381i			1.37252i
$519$	4.25596	−	14.5572i	0.186816	−	0.638989i
$520$		0			0
$521$	0.239887	−	0.330177i	0.0105097	−	0.0144653i	−0.803730	−	0.594994i	$-0.797154\pi$
$521$	0.239887	−	0.330177i	0.0105097	−	0.0144653i	0.814239	+	0.580529i	$0.197154\pi$
$522$	14.7694	+	37.6750i	0.646438	+	1.64899i
$523$	6.15416	−	1.99961i	0.269102	−	0.0874367i	−0.171358	−	0.985209i	$-0.554815\pi$
$523$	6.15416	−	1.99961i	0.269102	−	0.0874367i	0.440460	+	0.897772i	$0.354815\pi$
$524$	−6.89176	−	5.00716i	−0.301068	−	0.218739i
$525$		0			0
$526$	−14.6399	+	45.0569i	−0.638328	+	1.96457i
$527$	−5.29932			−0.230842
$528$	−12.4658	+	5.31641i	−0.542503	+	0.231367i
$529$	16.7423			0.727924
$530$		0			0
$531$	21.1263	+	25.7139i	0.916803	+	1.11589i
$532$	−29.5027	−	21.4350i	−1.27911	−	0.929325i
$533$	−0.584043	+	0.189767i	−0.0252977	+	0.00821972i
$534$	−24.6627	+	8.83203i	−1.06726	+	0.382199i
$535$		0			0
$536$	−8.44085	+	6.13264i	−0.364589	+	0.264890i
$537$	37.0997	+	10.8465i	1.60097	+	0.468063i
$538$		−	54.6779i		−	2.35733i
$539$	−10.2968	−	2.68322i	−0.443515	−	0.115575i
$540$		0			0
$541$	15.7416	+	5.11476i	0.676784	+	0.219901i	0.627187	−	0.778869i	$-0.284206\pi$
$541$	15.7416	+	5.11476i	0.676784	+	0.219901i	0.0495974	+	0.998769i	$0.484206\pi$
$542$	−1.50873	−	2.07659i	−0.0648056	−	0.0891972i
$543$	17.1024	+	11.6651i	0.733935	+	0.500598i
$544$	−8.17836	−	25.1704i	−0.350644	−	1.07917i
$545$		0			0
$546$	−0.738198	−	0.503506i	−0.0315920	−	0.0215481i
$547$	−8.96505	−	12.3393i	−0.383318	−	0.527592i	0.573142	−	0.819456i	$-0.305724\pi$
$547$	−8.96505	−	12.3393i	−0.383318	−	0.527592i	−0.956460	+	0.291864i	$0.905724\pi$
$548$	1.84284	+	0.598774i	0.0787220	+	0.0255783i
$549$	−1.70147	−	28.5869i	−0.0726172	−	1.22006i
$550$		0			0
$551$		−	44.7466i		−	1.90627i
$552$	−5.59054	−	1.63446i	−0.237949	−	0.0695672i
$553$	−7.53613	+	5.47532i	−0.320469	+	0.232834i
$554$	10.8905	−	14.9895i	0.462694	−	0.636844i
$555$		0			0
$556$	−35.1812	+	11.4311i	−1.49202	+	0.484786i
$557$	−6.11022	−	4.43933i	−0.258898	−	0.188101i	0.450763	−	0.892644i	$-0.351152\pi$
$557$	−6.11022	−	4.43933i	−0.258898	−	0.188101i	−0.709661	+	0.704543i	$0.751152\pi$
$558$	7.74797	−	6.36565i	0.327998	−	0.269480i
$559$	−0.329732	+	1.01481i	−0.0139462	+	0.0429219i
$560$		0			0
$561$	−18.0166	+	7.68375i	−0.760662	+	0.324408i
$562$	0.170895			0.00720876
$563$	−5.72266	+	17.6125i	−0.241181	+	0.742279i	0.755060	+	0.655656i	$0.227608\pi$
$563$	−5.72266	+	17.6125i	−0.241181	+	0.742279i	−0.996241	+	0.0866235i	$0.972392\pi$
$564$	0.958995	+	1.24066i	0.0403810	+	0.0522411i
$565$		0			0
$566$	31.6506	−	10.2839i	1.33037	−	0.432264i
$567$	15.9073	−	7.35438i	0.668044	−	0.308855i
$568$	−6.33505	+	8.71945i	−0.265813	+	0.365860i
$569$	−0.551284	+	0.400531i	−0.0231110	+	0.0167911i	−0.599281	−	0.800539i	$-0.704547\pi$
$569$	−0.551284	+	0.400531i	−0.0231110	+	0.0167911i	0.576170	+	0.817330i	$0.304547\pi$
$570$		0			0
$571$		−	23.0233i		−	0.963497i	−0.876310	−	0.481748i	$-0.840002\pi$
$571$		−	23.0233i		−	0.963497i	0.876310	−	0.481748i	$-0.159998\pi$
$572$	−1.07069	+	0.0635025i	−0.0447677	+	0.00265517i
$573$	−0.912478	−	30.6887i	−0.0381193	−	1.28204i
$574$	−19.8534	−	6.45076i	−0.828665	−	0.269250i
$575$		0			0
$576$	30.2671	+	19.3520i	1.26113	+	0.806333i
$577$	−7.21572	−	22.2077i	−0.300394	−	0.924519i	−0.981356	−	0.192199i	$-0.938438\pi$
$577$	−7.21572	−	22.2077i	−0.300394	−	0.924519i	0.680962	−	0.732319i	$-0.261562\pi$
$578$	3.57180	+	10.9929i	0.148567	+	0.457243i
$579$	5.65360	−	8.28883i	0.234956	−	0.344472i
$580$		0			0
$581$	0.166567	+	0.0541208i	0.00691034	+	0.00224531i
$582$	−63.9275	+	1.90078i	−2.64988	+	0.0787898i
$583$	−9.50895	+	7.80914i	−0.393821	+	0.323422i
$584$			6.06687i			0.251049i
$585$		0			0
$586$	32.8518	−	23.8682i	1.35710	−	0.985987i
$587$	−19.9289	+	27.4297i	−0.822553	+	1.13215i	0.166711	+	0.986006i	$0.446685\pi$
$587$	−19.9289	+	27.4297i	−0.822553	+	1.13215i	−0.989264	+	0.146141i	$0.953315\pi$
$588$	4.91806	+	13.7333i	0.202817	+	0.566350i
$589$	−10.5455	+	3.42643i	−0.434519	+	0.141184i
$590$		0			0
$591$	1.27297	−	0.983971i	0.0523629	−	0.0404752i
$592$	−5.43800	+	16.7364i	−0.223500	+	0.687864i
$593$	−30.0564			−1.23427			−0.617135	−	0.786857i	$-0.711707\pi$
$593$	−30.0564			−1.23427			−0.617135	+	0.786857i	$0.711707\pi$
$594$	17.1117	−	32.8761i	0.702100	−	1.34892i
$595$		0			0
$596$	−8.34436	+	25.6813i	−0.341798	+	1.05195i
$597$	8.71576	−	6.73705i	0.356712	−	0.275729i
$598$	0.536183	+	0.389560i	0.0219262	+	0.0159303i
$599$	−23.9088	+	7.76845i	−0.976888	+	0.317410i	−0.753593	−	0.657341i	$-0.771681\pi$
$599$	−23.9088	+	7.76845i	−0.976888	+	0.317410i	−0.223295	+	0.974751i	$0.571681\pi$
$600$		0			0
$601$	23.1361	−	31.8441i	0.943742	−	1.29895i	−0.0105099	−	0.999945i	$-0.503345\pi$
$601$	23.1361	−	31.8441i	0.943742	−	1.29895i	0.954252	−	0.299004i	$-0.0966545\pi$
$602$	−29.3445	+	21.3200i	−1.19599	+	0.868939i
$603$	−5.86672	+	22.5327i	−0.238911	+	0.917601i
$604$		−	4.34749i		−	0.176897i
$605$		0			0
$606$	−44.1872	+	1.31383i	−1.79498	+	0.0533708i
$607$	−38.8536	−	12.6243i	−1.57702	−	0.512405i	−0.615734	−	0.787954i	$-0.711140\pi$
$607$	−38.8536	−	12.6243i	−1.57702	−	0.512405i	−0.961287	+	0.275549i	$0.911140\pi$
$608$	−32.5494	−	44.8004i	−1.32005	−	1.81690i
$609$	11.9199	−	17.4760i	0.483020	−	0.708163i
$610$		0			0
$611$	−0.0131292	−	0.0404074i	−0.000531149	−	0.00163471i
$612$	22.6226	+	14.4643i	0.914466	+	0.584686i
$613$	−4.87815	−	6.71420i	−0.197027	−	0.271184i	0.699060	−	0.715063i	$-0.253602\pi$
$613$	−4.87815	−	6.71420i	−0.197027	−	0.271184i	−0.896087	+	0.443879i	$0.853602\pi$
$614$	−27.6220	−	8.97493i	−1.11473	−	0.362199i
$615$		0			0
$616$	−7.31351	−	4.67822i	−0.294670	−	0.188491i
$617$			25.3263i			1.01960i	0.860294	+	0.509799i	$0.170280\pi$
$617$			25.3263i			1.01960i	−0.860294	+	0.509799i	$0.829720\pi$
$618$	−5.61205	+	19.1956i	−0.225750	+	0.772159i
$619$	19.8164	−	14.3975i	0.796488	−	0.578682i	−0.113394	−	0.993550i	$-0.536172\pi$
$619$	19.8164	−	14.3975i	0.796488	−	0.578682i	0.909882	+	0.414868i	$0.136172\pi$
$620$		0			0
$621$	−11.9554	+	5.10170i	−0.479754	+	0.204724i
$622$	−34.5814	+	11.2362i	−1.38659	+	0.450529i
$623$	11.0789	+	8.04932i	0.443868	+	0.322489i
$624$	−0.307853	−	0.398271i	−0.0123240	−	0.0159436i
$625$		0			0
$626$	3.56740			0.142582
$627$	−30.8844	+	26.9396i	−1.23340	+	1.07586i
$628$	44.3312			1.76901
$629$	−7.85947	+	24.1890i	−0.313378	+	0.964478i
$630$		0			0
$631$	−34.8044	−	25.2869i	−1.38554	−	1.00666i	−0.996338	−	0.0855048i	$-0.972750\pi$
$631$	−34.8044	−	25.2869i	−1.38554	−	1.00666i	−0.389205	−	0.921151i	$-0.627250\pi$
$632$	6.11608	−	1.98724i	0.243285	−	0.0790480i
$633$	9.89279	−	3.54273i	0.393203	−	0.140811i
$634$	12.6858	−	17.4605i	0.503817	−	0.693445i
$635$		0			0
$636$	16.1906	+	4.73352i	0.642000	+	0.187696i
$637$		−	0.395239i		−	0.0156599i
$638$	−2.64872	−	44.6590i	−0.104864	−	1.76807i
$639$	1.42905	+	24.0099i	0.0565324	+	0.949817i
$640$		0			0
$641$	10.2049	+	14.0459i	0.403070	+	0.554778i	0.961511	−	0.274766i	$-0.0886004\pi$
$641$	10.2049	+	14.0459i	0.403070	+	0.554778i	−0.558441	+	0.829544i	$0.688600\pi$
$642$	46.3307	+	31.6010i	1.82853	+	1.24719i
$643$	2.75376	+	8.47520i	0.108598	+	0.334229i	0.990558	−	0.137094i	$-0.0437763\pi$
$643$	2.75376	+	8.47520i	0.108598	+	0.334229i	−0.881960	+	0.471324i	$0.843776\pi$
$644$	3.95140	+	12.1612i	0.155707	+	0.479217i
$645$		0			0
$646$	−30.7487	−	42.3219i	−1.20979	−	1.66513i
$647$	0.289752	+	0.0941460i	0.0113913	+	0.00370126i	0.314707	−	0.949189i	$-0.398094\pi$
$647$	0.289752	+	0.0941460i	0.0113913	+	0.00370126i	−0.303316	+	0.952890i	$0.598094\pi$
$648$	−12.0132	+	1.43512i	−0.471924	+	0.0563769i
$649$	−13.4211	−	34.2567i	−0.526823	−	1.34469i
$650$		0			0
$651$	−5.03135	−	1.47097i	−0.197194	−	0.0576520i
$652$	−10.0286	+	7.28620i	−0.392750	+	0.285350i
$653$	17.0754	−	23.5022i	0.668210	−	0.919712i	−0.331508	−	0.943452i	$-0.607557\pi$
$653$	17.0754	−	23.5022i	0.668210	−	0.919712i	0.999718	+	0.0237401i	$0.00755742\pi$
$654$	29.3883	−	10.5243i	1.14917	−	0.411533i
$655$		0			0
$656$	−9.51390	−	6.91225i	−0.371455	−	0.269878i
$657$	8.59485	+	10.4612i	0.335317	+	0.408132i
$658$	0.446301	−	1.37357i	0.0173986	−	0.0535474i
$659$	13.8565			0.539773			0.269886	−	0.962892i	$-0.413014\pi$
$659$	13.8565			0.539773			0.269886	+	0.962892i	$0.413014\pi$
$660$		0			0
$661$	−23.8607			−0.928075			−0.464038	−	0.885816i	$-0.653600\pi$
$661$	−23.8607			−0.928075			−0.464038	+	0.885816i	$0.653600\pi$
$662$	6.00545	−	18.4829i	0.233409	−	0.718358i
$663$	−0.444936	−	0.575616i	−0.0172799	−	0.0223551i
$664$	−0.0978172	−	0.0710684i	−0.00379604	−	0.00275799i
$665$		0			0
$666$	−17.5652	−	44.8069i	−0.680638	−	1.73623i
$667$	−9.22238	+	12.6935i	−0.357092	+	0.491495i
$668$	−49.5104	+	35.9714i	−1.91561	+	1.39177i
$669$	−5.01135	+	17.1409i	−0.193750	+	0.662706i
$670$		0			0
$671$	−7.98359	+	30.6369i	−0.308203	+	1.18272i
$672$	−0.778055	−	26.1678i	−0.0300141	−	1.00944i
$673$	5.32191	+	1.72919i	0.205145	+	0.0666555i	0.409787	−	0.912181i	$-0.365603\pi$
$673$	5.32191	+	1.72919i	0.205145	+	0.0666555i	−0.204642	+	0.978837i	$0.565603\pi$
$674$	9.92116	+	13.6553i	0.382149	+	0.525982i
$675$		0			0
$676$	10.5332	+	32.4179i	0.405123	+	1.24684i
$677$	4.11639	+	12.6690i	0.158206	+	0.486907i	0.998472	−	0.0552673i	$-0.0176011\pi$
$677$	4.11639	+	12.6690i	0.158206	+	0.486907i	−0.840266	+	0.542175i	$0.817601\pi$
$678$	−25.6935	+	37.6696i	−0.986753	+	1.44669i
$679$	19.6515	+	27.0480i	0.754156	+	1.03801i
$680$		0			0
$681$	24.4980	−	0.728407i	0.938765	−	0.0279126i
$682$	−10.3220	+	4.04395i	−0.395250	+	0.154851i
$683$			47.2151i			1.80664i	0.428971	+	0.903318i	$0.358876\pi$
$683$			47.2151i			1.80664i	−0.428971	+	0.903318i	$0.641124\pi$
$684$	54.3707	+	14.1562i	2.07892	+	0.541277i
$685$		0			0
$686$	25.1275	−	34.5850i	0.959372	−	1.32046i
$687$	−4.25079	−	11.8700i	−0.162178	−	0.452868i
$688$	−19.4333	+	6.31428i	−0.740889	+	0.240730i
$689$	−0.369756	−	0.268644i	−0.0140866	−	0.0102345i
$690$		0			0
$691$	−0.213838	+	0.658126i	−0.00813478	+	0.0250363i	−0.955042	−	0.296472i	$-0.904190\pi$
$691$	−0.213838	+	0.658126i	−0.00813478	+	0.0250363i	0.946907	+	0.321508i	$0.104190\pi$
$692$	22.9863			0.873807
$693$	−19.2384	+	2.29419i	−0.730807	+	0.0871489i
$694$	−35.2435			−1.33783
$695$		0			0
$696$	−11.5545	+	8.93134i	−0.437973	+	0.338541i
$697$	−13.7503	−	9.99019i	−0.520831	−	0.378406i
$698$	6.03955	−	1.96237i	0.228600	−	0.0742768i
$699$	9.00239	+	25.1384i	0.340502	+	0.950822i
$700$		0			0
$701$	12.4038	−	9.01192i	0.468487	−	0.340376i	−0.328364	−	0.944551i	$-0.606497\pi$
$701$	12.4038	−	9.01192i	0.468487	−	0.340376i	0.796851	+	0.604175i	$0.206497\pi$
$702$	1.34197	+	0.307124i	0.0506494	+	0.0115916i
$703$			53.2171i			2.00712i
$704$	−25.2061	−	30.6927i	−0.949992	−	1.15678i
$705$		0			0
$706$	30.6585	+	9.96154i	1.15385	+	0.374907i
$707$	13.5833	+	18.6958i	0.510852	+	0.703128i
$708$	−28.4209	+	41.6684i	−1.06812	+	1.56599i
$709$	−7.80063	−	24.0079i	−0.292959	−	0.901635i	−0.983899	−	0.178723i	$-0.942803\pi$
$709$	−7.80063	−	24.0079i	−0.292959	−	0.901635i	0.690941	−	0.722912i	$-0.257197\pi$
$710$		0			0
$711$	7.73081	−	12.0912i	0.289928	−	0.453455i
$712$	−5.55694	−	7.64847i	−0.208255	−	0.286638i
$713$	3.69769	+	1.20145i	0.138480	+	0.0449948i
$714$	−0.735011	−	24.7201i	−0.0275071	−	0.925127i
$715$		0			0
$716$			58.5817i			2.18930i
$717$	−0.946562	+	3.23764i	−0.0353500	+	0.120912i
$718$	22.2886	−	16.1936i	0.831802	−	0.604339i
$719$	16.7090	−	22.9980i	0.623142	−	0.857681i	−0.374435	−	0.927253i	$-0.622163\pi$
$719$	16.7090	−	22.9980i	0.623142	−	0.857681i	0.997577	+	0.0695719i	$0.0221633\pi$
$720$		0			0
$721$	9.94295	−	3.23066i	0.370295	−	0.120316i
$722$	−55.4959	−	40.3202i	−2.06535	−	1.50056i
$723$	−20.4902	−	26.5083i	−0.762039	−	0.985854i
$724$	−9.69558	+	29.8399i	−0.360333	+	1.10899i
$725$		0			0
$726$	−29.2293	+	28.7150i	−1.08480	+	1.06572i
$727$	16.2689			0.603379			0.301689	−	0.953406i	$-0.402449\pi$
$727$	16.2689			0.603379			0.301689	+	0.953406i	$0.402449\pi$
$728$	0.0996510	−	0.306694i	0.00369331	−	0.0113668i
$729$	−18.6816	+	19.4936i	−0.691909	+	0.721984i
$730$		0			0
$731$	−28.0868	+	9.12595i	−1.03883	+	0.337535i
$732$	40.8616	−	14.6331i	1.51029	−	0.540854i
$733$	−6.77262	+	9.32172i	−0.250153	+	0.344305i	−0.915565	−	0.402171i	$-0.868256\pi$
$733$	−6.77262	+	9.32172i	−0.250153	+	0.344305i	0.665412	+	0.746476i	$0.268256\pi$
$734$	−11.5395	+	8.38397i	−0.425932	+	0.309458i
$735$		0			0
$736$			19.4173i			0.715730i
$737$	13.8708	−	21.6844i	0.510939	−	0.798756i
$738$	32.1044	−	1.91083i	1.18178	−	0.0703386i
$739$	−24.9958	−	8.12164i	−0.919487	−	0.298759i	−0.189231	−	0.981933i	$-0.560599\pi$
$739$	−24.9958	−	8.12164i	−0.919487	−	0.298759i	−0.730256	+	0.683173i	$0.760599\pi$
$740$		0			0
$741$	−1.25759	−	0.857772i	−0.0461988	−	0.0315110i
$742$	−4.80099	−	14.7759i	−0.176250	−	0.542441i
$743$	−5.20821	−	16.0292i	−0.191071	−	0.588056i	−1.00000		0.000149450i	$-0.999952\pi$
$743$	−5.20821	−	16.0292i	−0.191071	−	0.588056i	0.808929	−	0.587906i	$-0.200048\pi$
$744$	2.98964	+	2.03915i	0.109605	+	0.0747590i
$745$		0			0
$746$	−0.244272	−	0.0793689i	−0.00894345	−	0.00290590i
$747$	−0.269350	+	0.0160315i	−0.00985500	+	0.000586562i
$748$	−18.8399	−	22.9408i	−0.688856	−	0.838799i
$749$		−	29.3169i		−	1.07122i
$750$		0			0
$751$	21.4570	−	15.5894i	0.782977	−	0.568866i	−0.122894	−	0.992420i	$-0.539218\pi$
$751$	21.4570	−	15.5894i	0.782977	−	0.568866i	0.905871	+	0.423554i	$0.139218\pi$
$752$	0.478229	−	0.658226i	0.0174392	−	0.0240030i
$753$	33.6941	−	12.0663i	1.22788	−	0.439719i
$754$	1.58041	−	0.513505i	0.0575550	−	0.0187007i
$755$		0			0
$756$	17.4637	+	20.0125i	0.635149	+	0.727847i
$757$	−0.197044	+	0.606440i	−0.00716169	+	0.0220414i	−0.954574	−	0.297976i	$-0.903689\pi$
$757$	−0.197044	+	0.606440i	−0.00716169	+	0.0220414i	0.947412	+	0.320017i	$0.103689\pi$
$758$	−57.9465			−2.10471
$759$	14.3135	−	1.27677i	0.519546	−	0.0463438i
$760$		0			0
$761$	−1.19848	+	3.68855i	−0.0434450	+	0.133710i	−0.970426	−	0.241398i	$-0.922394\pi$
$761$	−1.19848	+	3.68855i	−0.0434450	+	0.133710i	0.926981	+	0.375108i	$0.122394\pi$
$762$	−23.8378	−	30.8390i	−0.863551	−	1.11718i
$763$	−13.2017	−	9.59163i	−0.477935	−	0.347240i
$764$	44.2546	−	14.3792i	1.60108	−	0.520221i
$765$		0			0
$766$	−20.2889	+	27.9253i	−0.733068	+	1.00898i
$767$	1.10561	−	0.803270i	0.0399211	−	0.0290044i
$768$	0.948355	−	3.24377i	0.0342208	−	0.117050i
$769$		−	15.5441i		−	0.560534i	−0.959922	−	0.280267i	$-0.909577\pi$
$769$		−	15.5441i		−	0.560534i	0.959922	−	0.280267i	$-0.0904230\pi$
$770$		0			0
$771$	−0.945286	−	31.7921i	−0.0340436	−	1.14497i
$772$	14.4622	+	4.69905i	0.520505	+	0.169122i
$773$	−5.50984	−	7.58365i	−0.198175	−	0.272765i	0.698351	−	0.715756i	$-0.253918\pi$
$773$	−5.50984	−	7.58365i	−0.198175	−	0.272765i	−0.896526	+	0.442991i	$0.853918\pi$
$774$	30.1025	−	47.0812i	1.08201	−	1.69230i
$775$		0			0
$776$	−7.13241	−	21.9513i	−0.256039	−	0.788006i
$777$	−14.1764	+	20.7842i	−0.508575	+	0.745629i
$778$	−14.6936	−	20.2240i	−0.526790	−	0.725064i
$779$	−33.8222	−	10.9895i	−1.21181	−	0.393740i
$780$		0			0
$781$	6.70534	−	25.7316i	0.239936	−	0.920749i
$782$			18.3431i			0.655947i
$783$	−7.27080	+	31.7696i	−0.259837	+	1.13535i
$784$	6.12322	−	4.44878i	0.218686	−	0.158885i
$785$		0			0
$786$	−4.07538	−	11.3802i	−0.145364	−	0.405917i
$787$	−2.37869	+	0.772884i	−0.0847913	+	0.0275503i	−0.351105	−	0.936336i	$-0.614194\pi$
$787$	−2.37869	+	0.772884i	−0.0847913	+	0.0275503i	0.266314	+	0.963886i	$0.414194\pi$
$788$	1.97277	+	1.43330i	0.0702769	+	0.0510592i
$789$	−30.1882	+	23.3347i	−1.07473	+	0.830736i
$790$		0			0
$791$	23.8364			0.847527
$792$	13.1208	+	2.59790i	0.466229	+	0.0923122i
$793$	−1.17598			−0.0417604
$794$	−18.2383	+	56.1318i	−0.647254	+	1.99204i
$795$		0			0
$796$	13.5071	+	9.81351i	0.478748	+	0.347831i
$797$	24.9196	−	8.09685i	0.882696	−	0.286805i	0.167620	−	0.985852i	$-0.446392\pi$
$797$	24.9196	−	8.09685i	0.882696	−	0.286805i	0.715076	+	0.699046i	$0.246392\pi$
$798$	−17.4462	−	48.7170i	−0.617588	−	1.72456i
$799$	0.691179	−	0.951326i	0.0244521	−	0.0336555i
$800$		0			0
$801$	−20.4174	−	5.31598i	−0.721414	−	0.187831i
$802$		−	66.1633i		−	2.33631i
$803$	−5.46011	−	13.9367i	−0.192683	−	0.491815i
$804$	−35.2732	+	1.04879i	−1.24399	+	0.0369880i
$805$		0			0
$806$	−0.242037	−	0.333135i	−0.00852538	−	0.0117342i
$807$	24.8138	−	36.3798i	0.873486	−	1.28063i
$808$	−4.92998	−	15.1729i	−0.173436	−	0.533781i
$809$	11.3391	+	34.8982i	0.398662	+	1.22695i	0.926073	+	0.377344i	$0.123163\pi$
$809$	11.3391	+	34.8982i	0.398662	+	1.22695i	−0.527412	+	0.849610i	$0.676837\pi$
$810$		0			0
$811$	16.4779	+	22.6799i	0.578617	+	0.796399i	0.993543	−	0.113457i	$-0.0361924\pi$
$811$	16.4779	+	22.6799i	0.578617	+	0.796399i	−0.414926	+	0.909855i	$0.636192\pi$
$812$	30.4917	+	9.90737i	1.07005	+	0.347680i
$813$	−0.0614393	−	2.06634i	−0.00215477	−	0.0724698i
$814$	3.15013	+	53.1129i	0.110412	+	1.86161i
$815$		0			0
$816$	3.90954	−	13.3723i	0.136861	−	0.468123i
$817$	−49.9912	+	36.3207i	−1.74897	+	1.27070i
$818$	3.43735	−	4.73111i	0.120184	−	0.165419i
$819$	−0.262659	−	0.670014i	−0.00917805	−	0.0234122i
$820$		0			0
$821$	−19.7438	−	14.3447i	−0.689065	−	0.500635i	0.187288	−	0.982305i	$-0.440030\pi$
$821$	−19.7438	−	14.3447i	−0.689065	−	0.500635i	−0.876353	+	0.481670i	$0.840030\pi$
$822$	1.68153	+	2.17540i	0.0586500	+	0.0758758i
$823$	7.03794	−	21.6605i	0.245327	−	0.755039i	−0.750255	−	0.661148i	$-0.770070\pi$
$823$	7.03794	−	21.6605i	0.245327	−	0.755039i	0.995582	−	0.0938909i	$-0.0299305\pi$
$824$	−7.21747			−0.251433
$825$		0			0
$826$	46.4551			1.61638
$827$	−14.1132	+	43.4361i	−0.490765	+	1.51042i	0.332689	+	0.943037i	$0.392044\pi$
$827$	−14.1132	+	43.4361i	−0.490765	+	1.51042i	−0.823454	+	0.567383i	$0.807956\pi$
$828$	−12.5060	−	15.2217i	−0.434614	−	0.528991i
$829$	26.6279	+	19.3463i	0.924824	+	0.671924i	0.944720	−	0.327878i	$-0.106334\pi$
$829$	26.6279	+	19.3463i	0.924824	+	0.671924i	−0.0198961	+	0.999802i	$0.506334\pi$
$830$		0			0
$831$	14.0485	−	5.03094i	0.487336	−	0.174521i
$832$	0.867121	−	1.19349i	0.0300620	−	0.0413768i
$833$	8.84982	−	6.42977i	0.306628	−	0.222778i
$834$	−50.3817	−	14.7297i	−1.74457	−	0.510047i
$835$		0			0
$836$	−52.3239	−	33.4700i	−1.80966	−	1.15758i
$837$	8.04393	−	0.719215i	0.278039	−	0.0248597i
$838$	3.99373	+	1.29764i	0.137961	+	0.0448263i
$839$	−17.9017	−	24.6396i	−0.618035	−	0.850653i	0.379173	−	0.925326i	$-0.376209\pi$
$839$	−17.9017	−	24.6396i	−0.618035	−	0.850653i	−0.997208	+	0.0746733i	$0.976209\pi$
$840$		0			0
$841$	3.19515	+	9.83365i	0.110177	+	0.339091i
$842$	−19.7255	−	60.7087i	−0.679784	−	2.09216i
$843$	0.113704	+	0.0775549i	0.00391619	+	0.00267113i
$844$	9.36097	+	12.8843i	0.322218	+	0.443495i
$845$		0			0
$846$	0.132202	+	2.22116i	0.00454520	+	0.0763651i
$847$	21.0108	+	4.16465i	0.721940	+	0.143099i
$848$		−	8.75227i		−	0.300554i
$849$	25.7257	+	7.52120i	0.882902	+	0.258127i
$850$		0			0
$851$	10.9682	−	15.0964i	0.375984	−	0.517498i
$852$	−34.3193	+	12.2902i	−1.17576	+	0.421054i
$853$	40.5237	−	13.1670i	1.38751	−	0.450828i	0.482376	−	0.875964i	$-0.339774\pi$
$853$	40.5237	−	13.1670i	1.38751	−	0.450828i	0.905129	+	0.425136i	$0.139774\pi$
$854$	−32.3407	−	23.4969i	−1.10668	−	0.804047i
$855$		0			0
$856$	−6.25428	+	19.2487i	−0.213767	+	0.657907i
$857$	33.8986			1.15796			0.578978	−	0.815343i	$-0.303452\pi$
$857$	33.8986			1.15796			0.578978	+	0.815343i	$0.303452\pi$
$858$	−1.30591	−	0.781651i	−0.0445829	−	0.0266851i
$859$	7.18762			0.245238			0.122619	−	0.992454i	$-0.460871\pi$
$859$	7.18762			0.245238			0.122619	+	0.992454i	$0.460871\pi$
$860$		0			0
$861$	−10.2820	−	13.3018i	−0.350408	−	0.453325i
$862$	48.5462	+	35.2709i	1.65349	+	1.20133i
$863$	14.4234	−	4.68646i	0.490979	−	0.159529i	−0.0530553	−	0.998592i	$-0.516896\pi$
$863$	14.4234	−	4.68646i	0.490979	−	0.159529i	0.544035	+	0.839063i	$0.316896\pi$
$864$	15.8302	+	37.0967i	0.538554	+	1.26206i
$865$		0			0
$866$	−24.3319	+	17.6782i	−0.826832	+	0.600729i
$867$	−2.61226	+	8.93503i	−0.0887171	+	0.303449i
$868$		−	7.94467i		−	0.269660i
$869$	−12.2613	+	10.0694i	−0.415934	+	0.341582i
$870$		0			0
$871$	0.909343	+	0.295463i	0.0308119	+	0.0100114i
$872$	6.62169	+	9.11397i	0.224239	+	0.308638i
$873$	−43.3966	−	27.7467i	−1.46875	−	0.939084i
$874$	11.8603	+	36.5022i	0.401180	+	1.23470i
$875$		0			0
$876$	−11.5625	+	16.9520i	−0.390662	+	0.572755i
$877$	15.5443	+	21.3949i	0.524894	+	0.722455i	0.986342	−	0.164713i	$-0.0526696\pi$
$877$	15.5443	+	21.3949i	0.524894	+	0.722455i	−0.461447	+	0.887168i	$0.652670\pi$
$878$	−55.0028	−	17.8715i	−1.85625	−	0.603133i
$879$	32.6897	−	0.971973i	1.10260	−	0.0327838i
$880$		0			0
$881$			34.8870i			1.17537i	0.809088	+	0.587687i	$0.199961\pi$
$881$			34.8870i			1.17537i	−0.809088	+	0.587687i	$0.800039\pi$
$882$	−5.21547	+	20.0314i	−0.175614	+	0.674491i
$883$	1.93185	−	1.40357i	0.0650119	−	0.0472339i	−0.554805	−	0.831981i	$-0.687207\pi$
$883$	1.93185	−	1.40357i	0.0650119	−	0.0472339i	0.619817	+	0.784747i	$0.287207\pi$
$884$	0.648115	−	0.892054i	0.0217985	−	0.0300030i
$885$		0			0
$886$	−44.7667	+	14.5456i	−1.50397	+	0.488668i
$887$	15.0279	+	10.9184i	0.504586	+	0.366603i	0.810766	−	0.585370i	$-0.199051\pi$
$887$	15.0279	+	10.9184i	0.504586	+	0.366603i	−0.306180	+	0.951974i	$0.599051\pi$
$888$	13.7418	−	10.6220i	0.461144	−	0.356452i
$889$	−6.29651	+	19.3787i	−0.211178	+	0.649939i
$890$		0			0
$891$	26.3049	−	14.1085i	0.881249	−	0.472652i
$892$	−27.0661			−0.906240
$893$	0.760316	−	2.34001i	0.0254430	−	0.0783055i
$894$	−30.3158	+	23.4334i	−1.01391	+	0.783729i
$895$		0			0
$896$	18.9436	−	6.15514i	0.632861	−	0.205629i
$897$	0.179959	+	0.502522i	0.00600867	+	0.0167787i
$898$	5.89548	−	8.11443i	0.196735	−	0.270782i
$899$	7.88658	−	5.72994i	0.263032	−	0.191104i
$900$		0			0
$901$		−	12.6495i		−	0.421417i
$902$	−34.4065	−	8.96592i	−1.14561	−	0.298532i
$903$	−29.1997	+	0.868204i	−0.971705	+	0.0288920i
$904$	−15.6504	−	5.08511i	−0.520523	−	0.169128i
$905$		0			0
$906$	3.47613	−	5.09641i	0.115487	−	0.169317i
$907$	−8.69186	−	26.7508i	−0.288608	−	0.888245i	−0.985294	−	0.170868i	$-0.945343\pi$
$907$	−8.69186	−	26.7508i	−0.288608	−	0.888245i	0.696686	−	0.717377i	$-0.254657\pi$
$908$	11.4785	+	35.3273i	0.380928	+	1.17238i
$909$	−29.9961	−	19.1787i	−0.994908	−	0.636119i
$910$		0			0
$911$	−24.3697	−	7.91820i	−0.807405	−	0.262342i	−0.123907	−	0.992294i	$-0.539542\pi$
$911$	−24.3697	−	7.91820i	−0.807405	−	0.262342i	−0.683498	+	0.729952i	$0.739542\pi$
$912$	−0.866376	−	29.1382i	−0.0286886	−	0.964863i
$913$	0.288664	+	0.0752225i	0.00955340	+	0.00248950i
$914$			2.84413i			0.0940755i
$915$		0			0
$916$	15.4594	−	11.2319i	0.510791	−	0.371112i
$917$	−3.71421	+	5.11218i	−0.122654	+	0.168819i
$918$	14.9544	+	35.0444i	0.493570	+	1.15664i
$919$	−21.2077	+	6.89080i	−0.699578	+	0.227307i	−0.637147	−	0.770743i	$-0.719885\pi$
$919$	−21.2077	+	6.89080i	−0.699578	+	0.227307i	−0.0624313	+	0.998049i	$0.519885\pi$
$920$		0			0
$921$	−14.3053	−	18.5068i	−0.471375	−	0.609819i
$922$	11.8696	−	36.5309i	0.390905	−	1.20308i
$923$	0.987698			0.0325105
$924$	−11.5194	−	27.0103i	−0.378960	−	0.888574i
$925$		0			0
$926$	4.96966	−	15.2950i	0.163313	−	0.502626i
$927$	−12.4452	+	10.2249i	−0.408755	+	0.335829i
$928$	39.3870	+	28.6163i	1.29294	+	0.939377i
$929$	54.3549	−	17.6610i	1.78333	−	0.579438i	0.784172	−	0.620544i	$-0.213088\pi$
$929$	54.3549	−	17.6610i	1.78333	−	0.579438i	0.999155	+	0.0411063i	$0.0130882\pi$
$930$		0			0
$931$	13.4535	−	18.5172i	0.440921	−	0.606875i
$932$	−32.7400	+	23.7870i	−1.07243	+	0.779170i
$933$	−28.1078	−	8.21765i	−0.920208	−	0.269034i
$934$			48.5706i			1.58928i
$935$		0			0
$936$	0.0295184	+	0.495946i	0.000964838	+	0.0162105i
$937$	21.2504	+	6.90467i	0.694220	+	0.225566i	0.634810	−	0.772668i	$-0.281078\pi$
$937$	21.2504	+	6.90467i	0.694220	+	0.225566i	0.0594094	+	0.998234i	$0.481078\pi$
$938$	19.1043	+	26.2948i	0.623777	+	0.858555i
$939$	2.37356	+	1.61894i	0.0774582	+	0.0528323i
$940$		0			0
$941$	13.3303	+	41.0263i	0.434554	+	1.33742i	0.893543	+	0.448978i	$0.148212\pi$
$941$	13.3303	+	41.0263i	0.434554	+	1.33742i	−0.458989	+	0.888442i	$0.651788\pi$
$942$	51.9678	+	35.4459i	1.69320	+	1.15489i
$943$	7.32957	+	10.0883i	0.238684	+	0.328520i
$944$	24.8893	+	8.08701i	0.810076	+	0.263210i
$945$		0			0
$946$	−47.7434	+	39.2088i	−1.55227	+	1.27479i
$947$			7.60444i			0.247111i	0.992338	+	0.123555i	$0.0394297\pi$
$947$			7.60444i			0.247111i	−0.992338	+	0.123555i	$0.960570\pi$
$948$	20.8769	+	6.10361i	0.678050	+	0.198236i
$949$	0.449795	−	0.326796i	0.0146010	−	0.0106082i
$950$		0			0
$951$	16.3643	−	5.86028i	0.530650	−	0.190033i
$952$	8.48834	−	2.75803i	0.275109	−	0.0893882i
$953$	3.54873	+	2.57831i	0.114955	+	0.0835195i	0.643777	−	0.765213i	$-0.277366\pi$
$953$	3.54873	+	2.57831i	0.114955	+	0.0835195i	−0.528823	+	0.848732i	$0.677366\pi$
$954$	15.1949	+	18.4945i	0.491953	+	0.598782i
$955$		0			0
$956$	−5.11234			−0.165345
$957$	18.5047	−	30.9158i	0.598172	−	0.999366i
$958$	−41.4811			−1.34020
$959$	0.444159	−	1.36698i	0.0143426	−	0.0441421i
$960$		0			0
$961$	23.1252	+	16.8015i	0.745975	+	0.541983i
$962$	−1.87958	+	0.610711i	−0.0606000	+	0.0196901i
$963$	16.4850	+	42.0513i	0.531220	+	1.35508i
$964$	29.8470	−	41.0809i	0.961308	−	1.32313i
$965$		0			0
$966$	−5.09164	+	17.4155i	−0.163821	+	0.560336i
$967$			33.6482i			1.08205i	0.841006	+	0.541026i	$0.181964\pi$
$967$			33.6482i			1.08205i	−0.841006	+	0.541026i	$0.818036\pi$
$968$	−12.9067	−	7.21669i	−0.414835	−	0.231953i
$969$	−1.25216	−	42.1131i	−0.0402253	−	1.35287i
$970$		0			0
$971$	−0.0580491	−	0.0798977i	−0.00186288	−	0.00256404i	0.808085	−	0.589067i	$-0.200504\pi$
$971$	−0.0580491	−	0.0798977i	−0.00186288	−	0.00256404i	−0.809947	+	0.586502i	$0.800504\pi$
$972$	−36.3024	−	18.8854i	−1.16440	−	0.605749i
$973$	8.47935	+	26.0968i	0.271836	+	0.836624i
$974$	18.1044	+	55.7197i	0.580103	+	1.78537i
$975$		0			0
$976$	−13.2368	−	18.2189i	−0.423700	−	0.583172i
$977$	−44.4018	−	14.4270i	−1.42054	−	0.461561i	−0.504766	−	0.863256i	$-0.668421\pi$
$977$	−44.4018	−	14.4270i	−1.42054	−	0.461561i	−0.915774	+	0.401695i	$0.868421\pi$
$978$	−17.5820	+	0.522772i	−0.562211	+	0.0167164i
$979$	19.6488	+	12.5687i	0.627979	+	0.401698i
$980$		0			0
$981$	24.3295	+	6.33457i	0.776782	+	0.202247i
$982$	2.40551	−	1.74771i	0.0767630	−	0.0557716i
$983$	−30.8531	+	42.4656i	−0.984061	+	1.35444i	−0.0494483	+	0.998777i	$0.515746\pi$
$983$	−30.8531	+	42.4656i	−0.984061	+	1.35444i	−0.934613	+	0.355667i	$0.884254\pi$
$984$	3.91313	+	10.9271i	0.124746	+	0.348343i
$985$		0			0
$986$	37.2081	+	27.0332i	1.18495	+	0.860914i
$987$	0.920295	−	0.711364i	0.0292933	−	0.0226430i
$988$	0.712945	−	2.19422i	0.0226818	−	0.0698074i
$989$	21.6671			0.688973
$990$		0			0
$991$	2.51390			0.0798565			0.0399283	−	0.999203i	$-0.487287\pi$
$991$	2.51390			0.0798565			0.0399283	+	0.999203i	$0.487287\pi$
$992$	3.72802	−	11.4737i	0.118365	−	0.364289i
$993$	12.3836	−	9.57217i	0.392980	−	0.303764i
$994$	27.1627	+	19.7348i	0.861547	+	0.625951i
$995$		0			0
$996$	−0.137875	−	0.385004i	−0.00436873	−	0.0121993i
$997$	−20.4772	+	28.1845i	−0.648520	+	0.892611i	−0.999034	−	0.0439466i	$-0.986007\pi$
$997$	−20.4772	+	28.1845i	−0.648520	+	0.892611i	0.350514	+	0.936557i	$0.386007\pi$
$998$	12.7026	−	9.22897i	0.402093	−	0.292138i
$999$	8.64716	−	37.7836i	0.273584	−	1.19542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bi.h.101.3		80
3.2	odd	2	inner	825.2.bi.h.101.17		80
5.2	odd	4		165.2.r.a.134.4	yes	80
5.3	odd	4		165.2.r.a.134.17	yes	80
5.4	even	2	inner	825.2.bi.h.101.18		80
11.6	odd	10	inner	825.2.bi.h.776.17		80
15.2	even	4		165.2.r.a.134.18	yes	80
15.8	even	4		165.2.r.a.134.3	✓	80
15.14	odd	2	inner	825.2.bi.h.101.4		80
33.17	even	10	inner	825.2.bi.h.776.3		80
55.17	even	20		165.2.r.a.149.3	yes	80
55.28	even	20		165.2.r.a.149.18	yes	80
55.39	odd	10	inner	825.2.bi.h.776.4		80
165.17	odd	20		165.2.r.a.149.17	yes	80
165.83	odd	20		165.2.r.a.149.4	yes	80
165.149	even	10	inner	825.2.bi.h.776.18		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.r.a.134.3	✓	80	15.8	even	4
165.2.r.a.134.4	yes	80	5.2	odd	4
165.2.r.a.134.17	yes	80	5.3	odd	4
165.2.r.a.134.18	yes	80	15.2	even	4
165.2.r.a.149.3	yes	80	55.17	even	20
165.2.r.a.149.4	yes	80	165.83	odd	20
165.2.r.a.149.17	yes	80	165.17	odd	20
165.2.r.a.149.18	yes	80	55.28	even	20
825.2.bi.h.101.3		80	1.1	even	1	trivial
825.2.bi.h.101.4		80	15.14	odd	2	inner
825.2.bi.h.101.17		80	3.2	odd	2	inner
825.2.bi.h.101.18		80	5.4	even	2	inner
825.2.bi.h.776.3		80	33.17	even	10	inner
825.2.bi.h.776.4		80	55.39	odd	10	inner
825.2.bi.h.776.17		80	11.6	odd	10	inner
825.2.bi.h.776.18		80	165.149	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.664572 + 2.04534i) q^{2} +(-1.37038 + 1.05927i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(-1.25585 - 3.50686i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(1.08756 - 0.790156i) q^{8} +(0.755895 - 2.90321i) q^{9} +O(q^{10})\)	\(q+(-0.664572 + 2.04534i) q^{2} +(-1.37038 + 1.05927i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(-1.25585 - 3.50686i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(1.08756 - 0.790156i) q^{8} +(0.755895 - 2.90321i) q^{9} +(-1.78718 + 2.79392i) q^{11} +(4.54476 - 0.135131i) q^{12} +(-0.117164 - 0.0380688i) q^{13} +(-2.46148 - 3.38794i) q^{14} +(-0.729008 - 2.24366i) q^{16} +(-1.05363 - 3.24273i) q^{17} +(5.43571 + 3.47545i) q^{18} +(-4.19337 - 5.77168i) q^{19} +(-0.100238 - 3.37122i) q^{21} +(-4.52681 - 5.51216i) q^{22} +2.50155i q^{23} +(-0.653380 + 2.23483i) q^{24} +(0.155728 - 0.214341i) q^{26} +(2.03942 + 4.77920i) q^{27} +(4.86146 - 1.57958i) q^{28} +(5.07427 + 3.68667i) q^{29} +(0.480284 - 1.47816i) q^{31} +7.76211 q^{32} +(-0.510392 - 5.72184i) q^{33} +7.33270 q^{34} +(-6.08492 + 4.99931i) q^{36} +(-6.03482 - 4.38456i) q^{37} +(14.5918 - 4.74118i) q^{38} +(0.200884 - 0.0719392i) q^{39} +(4.03282 - 2.93001i) q^{41} +(6.96191 + 2.03540i) q^{42} -8.66147i q^{43} +(8.10647 - 3.17595i) q^{44} +(-5.11652 - 1.66246i) q^{46} +(0.202715 + 0.279013i) q^{47} +(3.37566 + 2.30245i) q^{48} +(0.991413 + 3.05126i) q^{49} +(4.87879 + 3.32770i) q^{51} +(0.190085 + 0.261630i) q^{52} +(3.52839 + 1.14644i) q^{53} +(-11.1304 + 0.995182i) q^{54} +2.61765i q^{56} +(11.8603 + 3.46749i) q^{57} +(-10.9127 + 7.92855i) q^{58} +(-6.52040 + 8.97456i) q^{59} +(9.07864 - 2.94983i) q^{61} +(2.70416 + 1.96469i) q^{62} +(3.70839 + 4.51368i) q^{63} +(-3.70046 + 11.3889i) q^{64} +(12.0423 + 2.75865i) q^{66} -7.76130 q^{67} +(-2.76585 + 8.51242i) q^{68} +(-2.64981 - 3.42808i) q^{69} +(-7.62506 + 2.47753i) q^{71} +(-1.47191 - 3.75468i) q^{72} +(-2.65271 + 3.65114i) q^{73} +(12.9785 - 9.42942i) q^{74} +18.7278i q^{76} +(-2.35586 - 6.01322i) q^{77} +(0.0136383 + 0.458686i) q^{78} +(4.54966 + 1.47827i) q^{79} +(-7.85725 - 4.38904i) q^{81} +(3.31278 + 10.1957i) q^{82} +(-0.0277937 - 0.0855401i) q^{83} +(-4.98885 + 7.31423i) q^{84} +(17.7157 + 5.75617i) q^{86} +(-10.8589 + 0.322870i) q^{87} +(0.263971 + 4.45070i) q^{88} -7.03271i q^{89} +(0.194072 - 0.141002i) q^{91} +(3.85984 - 5.31262i) q^{92} +(0.907600 + 2.53440i) q^{93} +(-0.705397 + 0.229197i) q^{94} +(-10.6371 + 8.22217i) q^{96} +(5.30569 - 16.3292i) q^{97} -6.89973 q^{98} +(6.76041 + 7.30047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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