LMFDB - Embedded newform 825.2.bi.h.101.17

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			101.17
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.664572 - 2.04534i) q^{2} +(-1.43090 + 0.975979i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(1.04528 + 3.57528i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(-1.08756 + 0.790156i) q^{8} +(1.09493 - 2.79305i) q^{9} +O(q^{10})$	\(q+(0.664572 - 2.04534i) q^{2} +(-1.43090 + 0.975979i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(1.04528 + 3.57528i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(-1.08756 + 0.790156i) q^{8} +(1.09493 - 2.79305i) 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} +(-4.98508 - 4.09569i) q^{18} +(-4.19337 - 5.77168i) q^{19} +(0.100238 - 3.37122i) q^{21} +(-4.52681 - 5.51216i) q^{22} -2.50155i q^{23} +(0.785006 - 2.19206i) q^{24} +(-0.155728 + 0.214341i) q^{26} +(1.15922 + 5.06520i) q^{27} +(4.86146 - 1.57958i) q^{28} +(-5.07427 - 3.68667i) q^{29} +(0.480284 - 1.47816i) q^{31} -7.76211 q^{32} +(0.169532 + 5.74206i) q^{33} +7.33270 q^{34} +(-6.63497 + 4.24223i) q^{36} +(-6.03482 - 4.38456i) q^{37} +(-14.5918 + 4.74118i) q^{38} +(0.204804 - 0.0598768i) q^{39} +(-4.03282 + 2.93001i) q^{41} +(-6.82868 - 2.44544i) q^{42} -8.66147i q^{43} +(-8.10647 + 3.17595i) q^{44} +(-5.11652 - 1.66246i) q^{46} +(-0.202715 - 0.279013i) q^{47} +(3.23289 + 2.49894i) q^{48} +(0.991413 + 3.05126i) q^{49} +(-4.67246 - 3.61169i) q^{51} +(0.190085 + 0.261630i) q^{52} +(-3.52839 - 1.14644i) q^{53} +(11.1304 + 0.995182i) q^{54} -2.61765i q^{56} +(11.6333 + 4.16604i) 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} +(3.14681 + 4.92169i) q^{63} +(-3.70046 + 11.3889i) q^{64} +(11.8571 + 3.46926i) q^{66} -7.76130 q^{67} +(2.76585 - 8.51242i) q^{68} +(2.44146 + 3.57946i) q^{69} +(7.62506 - 2.47753i) q^{71} +(1.01614 + 3.90277i) 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} +(-6.60225 - 6.11640i) q^{81} +(3.31278 + 10.1957i) q^{82} +(0.0277937 + 0.0855401i) q^{83} +(-5.41461 + 7.00490i) 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} +(0.755418 + 2.58384i) q^{93} +(-0.705397 + 0.229197i) q^{94} +(11.1068 - 7.57565i) q^{96} +(5.30569 - 16.3292i) q^{97} +6.89973 q^{98} +(-5.84671 - 8.05084i) 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	$-0.625027\pi$
$2$	0.664572	−	2.04534i	0.469923	−	1.44628i	0.852684	−	0.522427i	$-0.174973\pi$
$3$	−1.43090	+	0.975979i	−0.826129	+	0.563481i
$3$	−1.43090	+	0.975979i	−0.826129	+	0.563481i
$4$	−2.12373	−	1.54298i	−1.06187	−	0.771491i
$5$		0			0
$5$		0			0
$6$	1.04528	+	3.57528i	0.426732	+	1.45960i
$7$	−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
$9$	1.09493	−	2.79305i	0.364977	−	0.931016i
$10$		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	$0.0356852\pi$
$17$	1.05363	+	3.24273i	0.255542	+	0.786477i	−0.738181	+	0.674603i	$0.764315\pi$
$18$	−4.98508	−	4.09569i	−1.17499	−	0.965364i
$19$	−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	$-0.916012\pi$
$23$		−	2.50155i		−	0.521609i	0.965392	−	0.260804i	$-0.0839877\pi$
$24$	0.785006	−	2.19206i	0.160239	−	0.447453i
$25$		0			0
$26$	−0.155728	+	0.214341i	−0.0305407	+	0.0420356i
$27$	1.15922	+	5.06520i	0.223092	+	0.974797i
$28$	4.86146	−	1.57958i	0.918730	−	0.298513i
$29$	−5.07427	−	3.68667i	−0.942268	−	0.684597i	0.00669788	−	0.999978i	$-0.497868\pi$
$29$	−5.07427	−	3.68667i	−0.942268	−	0.684597i	−0.948965	+	0.315380i	$0.897868\pi$
$30$		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
$33$	0.169532	+	5.74206i	0.0295117	+	0.999564i
$34$	7.33270			1.25755
$35$		0			0
$36$	−6.63497	+	4.24223i	−1.10583	+	0.707038i
$37$	−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
$39$	0.204804	−	0.0598768i	0.0327948	−	0.00958796i
$40$		0			0
$41$	−4.03282	+	2.93001i	−0.629821	+	0.457591i	−0.856338	−	0.516416i	$-0.827266\pi$
$41$	−4.03282	+	2.93001i	−0.629821	+	0.457591i	0.226518	+	0.974007i	$0.427266\pi$
$42$	−6.82868	−	2.44544i	−1.05369	−	0.377339i
$43$		−	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	0.793977	−	0.607948i	$-0.208007\pi$
$47$	−0.202715	−	0.279013i	−0.0295690	−	0.0406983i	−0.823546	+	0.567250i	$0.808007\pi$
$48$	3.23289	+	2.49894i	0.466628	+	0.360691i
$49$	0.991413	+	3.05126i	0.141630	+	0.435894i
$50$		0			0
$51$	−4.67246	−	3.61169i	−0.654276	−	0.505738i
$52$	0.190085	+	0.261630i	0.0263601	+	0.0362815i
$53$	−3.52839	−	1.14644i	−0.484662	−	0.157476i	0.0564863	−	0.998403i	$-0.482010\pi$
$53$	−3.52839	−	1.14644i	−0.484662	−	0.157476i	−0.541148	+	0.840927i	$0.682010\pi$
$54$	11.1304	+	0.995182i	1.51466	+	0.135427i
$55$		0			0
$56$		−	2.61765i		−	0.349799i
$57$	11.6333	+	4.16604i	1.54087	+	0.551805i
$58$	−10.9127	+	7.92855i	−1.43291	+	1.04107i
$59$	6.52040	−	8.97456i	0.848884	−	1.16839i	−0.135223	−	0.990815i	$-0.543175\pi$
$59$	6.52040	−	8.97456i	0.848884	−	1.16839i	0.984108	−	0.177574i	$-0.0568248\pi$
$60$		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
$63$	3.14681	+	4.92169i	0.396460	+	0.620075i
$64$	−3.70046	+	11.3889i	−0.462558	+	1.42361i
$65$		0			0
$66$	11.8571	+	3.46926i	1.45951	+	0.427037i
$67$	−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
$69$	2.44146	+	3.57946i	0.293917	+	0.430916i
$70$		0			0
$71$	7.62506	−	2.47753i	0.904928	−	0.294029i	0.180659	−	0.983546i	$-0.442177\pi$
$71$	7.62506	−	2.47753i	0.904928	−	0.294029i	0.724270	+	0.689517i	$0.242177\pi$
$72$	1.01614	+	3.90277i	0.119754	+	0.459945i
$73$	−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
$81$	−6.60225	−	6.11640i	−0.733583	−	0.679600i
$82$	3.31278	+	10.1957i	0.365836	+	1.12593i
$83$	0.0277937	+	0.0855401i	0.00305075	+	0.00938925i	0.952570	−	0.304319i	$-0.0984287\pi$
$83$	0.0277937	+	0.0855401i	0.00305075	+	0.00938925i	−0.949520	+	0.313708i	$0.898429\pi$
$84$	−5.41461	+	7.00490i	−0.590782	+	0.764298i
$85$		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	$0.121579\pi$
$89$			7.03271i			0.745465i	−0.927939	+	0.372733i	$0.878421\pi$
$90$		0			0
$91$	0.194072	−	0.141002i	0.0203443	−	0.0147810i
$92$	−3.85984	+	5.31262i	−0.402417	+	0.553879i
$93$	0.755418	+	2.58384i	0.0783331	+	0.267932i
$94$	−0.705397	+	0.229197i	−0.0727561	+	0.0236399i
$95$		0			0
$96$	11.1068	−	7.57565i	1.13358	−	0.773187i
$97$	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
$99$	−5.84671	−	8.05084i	−0.587616	−	0.809140i
$100$		0			0
$101$	−3.66734	+	11.2869i	−0.364914	+	1.12309i	0.585122	+	0.810946i	$0.301047\pi$
$101$	−3.66734	+	11.2869i	−0.364914	+	1.12309i	−0.950035	+	0.312143i	$0.898953\pi$
$102$	−10.4923	+	7.15655i	−1.03890	+	0.708604i
$103$	−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	0.185625	−	0.982621i	$-0.440569\pi$
$107$	12.1803	−	8.84951i	1.17751	−	0.855514i	0.991889	+	0.127106i	$0.0405689\pi$
$108$	5.35363	−	12.5458i	0.515153	−	1.20722i
$109$			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	0.999891	−	0.0147639i	$-0.00469967\pi$
$113$	7.19519	+	9.90333i	0.676866	+	0.931627i	−0.323025	+	0.946391i	$0.604700\pi$
$114$	16.2521	−	21.0255i	1.52215	−	1.96921i
$115$		0			0
$116$	5.08792	+	15.6590i	0.472402	+	1.45390i
$117$	−0.234614	+	0.285561i	−0.0216901	+	0.0264002i
$118$	−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
$123$	2.91092	−	8.12849i	0.262469	−	0.732922i
$124$	−3.30077	+	2.39815i	−0.296418	+	0.215360i
$125$		0			0
$126$	12.1578	−	3.16548i	1.08311	−	0.282003i
$127$	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
$129$	8.45341	+	12.3937i	0.744281	+	1.09120i
$130$		0			0
$131$	−3.24512			−0.283527			−0.141764	−	0.989901i	$-0.545277\pi$
$131$	−3.24512			−0.283527			−0.141764	+	0.989901i	$0.545277\pi$
$132$	8.49986	−	12.4562i	0.739818	−	1.08417i
$133$	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	−0.278875	−	0.960327i	$-0.589961\pi$
$137$	0.702012	−	0.228097i	0.0599769	−	0.0194877i	0.338852	+	0.940840i	$0.389961\pi$
$138$	8.94373	−	2.61481i	0.761341	−	0.222587i
$139$	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
$141$	0.562376	+	0.201394i	0.0473606	+	0.0169604i
$142$		−	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
$147$	−4.39657	−	3.39844i	−0.362623	−	0.280298i
$148$	6.05106	+	18.6233i	0.497394	+	1.53082i
$149$	3.17871	+	9.78306i	0.260410	+	0.801460i	0.992715	+	0.120483i	$0.0384444\pi$
$149$	3.17871	+	9.78306i	0.260410	+	0.801460i	−0.732305	+	0.680976i	$0.761556\pi$
$150$		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
$156$	−0.527337	−	0.188846i	−0.0422208	−	0.0151198i
$157$	−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
$159$	6.16767	−	1.80319i	0.489128	−	0.143002i
$160$		0			0
$161$	3.94080	+	2.86316i	0.310579	+	0.225649i
$162$	−16.8978	+	9.43907i	−1.32762	+	0.741603i
$163$	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	$0.457903\pi$
$167$	−7.20408	+	22.1719i	−0.557468	+	1.71571i	−0.689334	+	0.724444i	$0.742097\pi$
$168$	2.55477	+	3.74559i	0.197105	+	0.288979i
$169$	−10.5049	−	7.63229i	−0.808073	−	0.587099i
$170$		0			0
$171$	−20.7120	+	5.39269i	−1.58389	+	0.412389i
$172$	−13.3645	+	18.3946i	−1.01903	+	1.40258i
$173$	7.08409	−	5.14689i	0.538593	−	0.391311i	−0.284969	−	0.958537i	$-0.591983\pi$
$173$	7.08409	−	5.14689i	0.538593	−	0.391311i	0.823562	+	0.567226i	$0.191983\pi$
$174$	7.87687	−	21.9955i	0.597144	−	1.66748i
$175$		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	$0.113952\pi$
$179$	13.1171	+	18.0542i	0.980419	+	1.34943i	0.0438163	+	0.999040i	$0.486048\pi$
$180$		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
$183$	−10.1116	+	13.0815i	−0.747473	+	0.967009i
$184$	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
$189$	−9.30622	−	3.97122i	−0.676928	−	0.288864i
$190$		0			0
$191$	10.4191	−	14.3406i	0.753897	−	1.03765i	−0.243800	−	0.969826i	$-0.578394\pi$
$191$	10.4191	−	14.3406i	0.753897	−	1.03765i	0.997697	−	0.0678249i	$-0.0216059\pi$
$192$	−5.82030	−	19.9078i	−0.420044	−	1.43673i
$193$	−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	$-0.489465\pi$
$197$	0.928915			0.0661824			0.0330912	+	0.999452i	$0.489465\pi$
$198$	−20.3523	+	6.60816i	−1.44637	+	0.469622i
$199$	−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
$201$	11.1056	−	7.57486i	0.783330	−	0.534289i
$202$	20.6484	+	15.0019i	1.45281	+	1.05553i
$203$	11.6156	−	3.77412i	0.815252	−	0.264891i
$204$	4.35029	+	14.8798i	0.304581	+	1.04179i
$205$		0			0
$206$	−9.34131	+	6.78686i	−0.650840	+	0.472863i
$207$	−6.98694	−	2.73902i	−0.485626	−	0.190375i
$208$			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
$213$	−8.49266	+	10.9870i	−0.581907	+	0.752816i
$214$	−10.0056	−	30.7940i	−0.683968	−	2.10504i
$215$		0			0
$216$	−5.26301	−	4.59272i	−0.358103	−	0.312495i
$217$	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
$222$	9.36797	−	26.1593i	0.628737	−	1.75569i
$223$	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	0.898853	−	0.438251i	$-0.144402\pi$
$227$	11.4477	+	8.31726i	0.759812	+	0.552036i	−0.139040	+	0.990287i	$0.544402\pi$
$228$	−18.2779	−	26.7975i	−1.21049	−	1.77471i
$229$	−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
$231$	−9.23977	−	6.30503i	−0.607932	−	0.414841i
$232$	8.43160			0.553561
$233$	−4.76389	+	14.6617i	−0.312093	+	0.960522i	0.664842	+	0.746984i	$0.268499\pi$
$233$	−4.76389	+	14.6617i	−0.312093	+	0.960522i	−0.976935	+	0.213538i	$0.931501\pi$
$234$	0.428153	+	0.669643i	0.0279892	+	0.0437759i
$235$		0			0
$236$	−27.6952	+	8.99871i	−1.80280	+	0.585766i
$237$	−7.95286	+	2.32511i	−0.516594	+	0.151032i
$238$	−8.39268	+	11.5515i	−0.544016	+	0.748774i
$239$	−1.57556	+	1.14471i	−0.101915	+	0.0740453i	−0.637575	−	0.770388i	$-0.720063\pi$
$239$	−1.57556	+	1.14471i	−0.101915	+	0.0740453i	0.535661	+	0.844433i	$0.320063\pi$
$240$		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
$246$	−14.6910	−	11.3558i	−0.936666	−	0.724019i
$247$	0.271590	+	0.835868i	0.0172809	+	0.0531850i
$248$	0.645643	+	1.98708i	0.0409984	+	0.126180i
$249$	−0.123255	−	0.0952730i	−0.00781098	−	0.00603768i
$250$		0			0
$251$	19.6517	+	6.38523i	1.24041	+	0.403032i	0.854474	−	0.519495i	$-0.173880\pi$
$251$	19.6517	+	6.38523i	1.24041	+	0.403032i	0.385932	+	0.922527i	$0.373880\pi$
$252$	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	−0.326538	−	0.945184i	$-0.605882\pi$
$257$	10.7937	−	14.8562i	0.673291	−	0.926706i	0.999829	+	0.0184780i	$0.00588207\pi$
$258$	30.9672	−	9.05362i	1.92793	−	0.563654i
$259$	13.8144	−	4.48856i	0.858384	−	0.278906i
$260$		0			0
$261$	−15.8530	+	10.1360i	−0.981278	+	0.627404i
$262$	−2.15661	+	6.63737i	−0.133236	+	0.410058i
$263$	−22.0290			−1.35837			−0.679184	−	0.733968i	$-0.737666\pi$
$263$	−22.0290			−1.35837			−0.679184	+	0.733968i	$0.737666\pi$
$264$	−4.72150	−	6.11086i	−0.290588	−	0.376097i
$265$		0			0
$266$	9.23218	−	28.4137i	0.566061	−	1.74216i
$267$	−6.86377	−	10.0631i	−0.420056	−	0.615850i
$268$	16.4829	+	11.9755i	1.00685	+	0.731523i
$269$	24.1801	−	7.85660i	1.47429	−	0.479025i	0.541888	−	0.840451i	$-0.317710\pi$
$269$	24.1801	−	7.85660i	1.47429	−	0.479025i	0.932401	+	0.361426i	$0.117710\pi$
$270$		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
$273$	−0.140082	+	0.391169i	−0.00847818	+	0.0236746i
$274$		−	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
$279$	−3.60270	−	2.95994i	−0.215688	−	0.177207i
$280$		0			0
$281$	0.0245556	+	0.0755745i	0.00146487	+	0.00450840i	0.951786	−	0.306762i	$-0.0992455\pi$
$281$	0.0245556	+	0.0755745i	0.00146487	+	0.00450840i	−0.950321	+	0.311270i	$0.899246\pi$
$282$	0.785658	−	1.01641i	0.0467853	−	0.0605263i
$283$	−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
$288$	−8.49898	+	21.6800i	−0.500807	+	1.27750i
$289$	4.34813	−	3.15910i	0.255773	−	0.185830i
$290$		0			0
$291$	8.34509	+	28.5437i	0.489198	+	1.67326i
$292$	11.2673	−	3.66096i	0.659368	−	0.214242i
$293$	15.2756	+	11.0984i	0.892413	+	0.648376i	0.936506	−	0.350652i	$-0.114040\pi$
$293$	15.2756	+	11.0984i	0.892413	+	0.648376i	−0.0440932	+	0.999027i	$0.514040\pi$
$294$	−9.87280	+	6.73399i	−0.575793	+	0.392734i
$295$		0			0
$296$	10.0277			0.582848
$297$	16.2235	+	5.81365i	0.941382	+	0.337342i
$298$	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
$303$	−5.76819	−	19.7296i	−0.331374	−	1.13344i
$304$	−9.89265	+	13.6161i	−0.567383	+	0.780935i
$305$		0			0
$306$	8.02880	−	20.4806i	0.458976	−	1.17080i
$307$			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	0.428243	−	0.903664i	$-0.359133\pi$
$311$	−9.93791	−	13.6784i	−0.563527	−	0.775628i	−0.991770	+	0.128035i	$0.959133\pi$
$312$	−0.175424	+	0.226946i	−0.00993140	+	0.0128483i
$313$	−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	0.564523	−	0.825417i	$-0.309060\pi$
$317$	9.54434	+	3.10114i	0.536064	+	0.174178i	−0.0284595	+	0.999595i	$0.509060\pi$
$318$	0.410717	−	13.8134i	0.0230319	−	0.774614i
$319$	−19.3689	+	7.58834i	−1.08445	+	0.424865i
$320$		0			0
$321$	−8.79183	+	24.5505i	−0.490712	+	1.37027i
$322$	8.47508	−	6.15751i	0.472298	−	0.343145i
$323$	14.2977	−	19.6791i	0.795547	−	1.09498i
$324$	4.58392	+	23.1768i	0.254662	+	1.28760i
$325$		0			0
$326$	−8.21595	−	5.96923i	−0.455039	−	0.330605i
$327$	−8.17892	−	11.9912i	−0.452295	−	0.663117i
$328$	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
$333$	−18.8540	+	12.0548i	−1.03319	+	0.660597i
$334$	40.5614	+	29.4696i	2.21942	+	1.61251i
$335$		0			0
$336$	−7.63693	+	2.23275i	−0.416628	+	0.121806i
$337$	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
$339$	−19.9610	−	7.14829i	−1.08413	−	0.388242i
$340$		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	$-0.955024\pi$
$347$	−5.06410	−	15.5857i	−0.271855	−	0.836684i	0.718179	−	0.695858i	$-0.244976\pi$
$348$	−22.5631	−	17.4407i	−1.20951	−	0.934921i
$349$	−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	$0.130609\pi$
$353$			14.9894i			0.797806i	−0.916993	+	0.398903i	$0.869391\pi$
$354$	38.9022	+	13.9314i	2.06763	+	0.740444i
$355$		0			0
$356$	10.8513	−	14.9356i	0.575120	−	0.791585i
$357$	11.0376	−	3.22696i	0.584169	−	0.170789i
$358$	45.6442	−	14.8307i	2.41237	−	0.783827i
$359$	10.3639	+	7.52980i	0.546985	+	0.397408i	0.826673	−	0.562683i	$-0.190231\pi$
$359$	10.3639	+	7.52980i	0.546985	+	0.397408i	−0.279688	+	0.960091i	$0.590231\pi$
$360$		0			0
$361$	−9.85658	+	30.3354i	−0.518768	+	1.59660i
$362$	−25.7045			−1.35100
$363$	16.3458	+	9.78845i	0.857934	+	0.513760i
$364$	−0.629720			−0.0330063
$365$		0			0
$366$	20.0361	+	29.3753i	1.04731	+	1.53547i
$367$	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
$369$	3.76801	+	14.4720i	0.196155	+	0.753384i
$370$		0			0
$371$	5.84449	−	4.24627i	0.303431	−	0.220455i
$372$	2.38252	−	6.65299i	0.123528	−	0.344942i
$373$			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
$378$	−14.3072	+	16.3952i	−0.735881	+	0.843280i
$379$	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
$381$	−11.0842	+	14.3397i	−0.567863	+	0.734647i
$382$	−22.4072	−	30.8409i	−1.14645	−	1.57796i
$383$	−15.2646	−	4.95979i	−0.779987	−	0.253433i	−0.108152	−	0.994134i	$-0.534493\pi$
$383$	−15.2646	−	4.95979i	−0.779987	−	0.253433i	−0.671835	+	0.740701i	$0.734493\pi$
$384$	−17.7095	−	0.526563i	−0.903734	−	0.0268710i
$385$		0			0
$386$			12.4579i			0.634090i
$387$	−24.1919	−	9.48372i	−1.22974	−	0.482084i
$388$	−36.4636	+	26.4924i	−1.85116	+	1.34495i
$389$	6.83231	−	9.40387i	0.346412	−	0.476795i	−0.599889	−	0.800084i	$-0.704788\pi$
$389$	6.83231	−	9.40387i	0.346412	−	0.476795i	0.946300	+	0.323289i	$0.104788\pi$
$390$		0			0
$391$	8.11184	−	2.63570i	0.410233	−	0.133293i
$392$	−3.48919	−	2.53504i	−0.176231	−	0.128039i
$393$	4.64343	−	3.16716i	0.234230	−	0.159762i
$394$	0.617330	−	1.89995i	0.0311007	−	0.0957180i
$395$		0			0
$396$	−0.00544821	+	26.1192i	−0.000273783	+	1.31254i
$397$	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
$399$	−19.8779	+	13.5582i	−0.995140	+	0.678760i
$400$		0			0
$401$	29.2593	−	9.50692i	1.46114	−	0.474753i	0.532721	−	0.846291i	$-0.321169\pi$
$401$	29.2593	−	9.50692i	1.46114	−	0.474753i	0.928418	+	0.371538i	$0.121169\pi$
$402$	−8.11270	−	27.7488i	−0.404625	−	1.38399i
$403$	−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
$411$	−0.781888	+	1.01153i	−0.0385677	+	0.0498952i
$412$	4.35527	+	13.4042i	0.214569	+	0.660375i
$413$	6.67508	+	20.5438i	0.328459	+	1.01089i
$414$	−10.2456	+	12.4704i	−0.503542	+	0.612887i
$415$		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	$0.0151877\pi$
$419$			1.95260i			0.0953907i	−0.998862	+	0.0476954i	$0.984812\pi$
$420$		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
$423$	−1.00126	+	0.260693i	−0.0486828	+	0.0126753i
$424$	4.74320	−	1.54116i	0.230350	−	0.0748453i
$425$		0			0
$426$	16.8282	+	24.6720i	0.815327	+	1.19536i
$427$	−5.74400	+	17.6782i	−0.277972	+	0.855509i
$428$	−39.5224			−1.91039
$429$	0.198730	−	0.679215i	0.00959480	−	0.0327928i
$430$		0			0
$431$	−8.62224	+	26.5365i	−0.415319	+	1.27822i	0.496647	+	0.867953i	$0.334565\pi$
$431$	−8.62224	+	26.5365i	−0.415319	+	1.27822i	−0.911965	+	0.410267i	$0.865435\pi$
$432$	10.5195	−	6.29346i	0.506118	−	0.302794i
$433$	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
$438$	−15.8266	−	5.66772i	−0.756226	−	0.270814i
$439$			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	0.385447	−	0.922730i	$-0.374047\pi$
$443$	−12.8649	−	17.7071i	−0.611231	−	0.841288i	−0.996678	+	0.0814422i	$0.974047\pi$
$444$	−26.8343	−	20.7423i	−1.27350	−	0.984384i
$445$		0			0
$446$	−6.85212	−	21.0887i	−0.324457	−	0.998577i
$447$	−14.0965	−	10.8962i	−0.666740	−	0.515373i
$448$	−13.7060	−	18.8647i	−0.647547	−	0.891272i
$449$	4.43555	+	1.44120i	0.209326	+	0.0680143i	0.411803	−	0.911273i	$-0.364899\pi$
$449$	4.43555	+	1.44120i	0.209326	+	0.0680143i	−0.202477	+	0.979287i	$0.564899\pi$
$450$		0			0
$451$	0.978842	+	16.5038i	0.0460919	+	0.777135i
$452$		−	32.1341i		−	1.51146i
$453$	−2.70057	−	0.967108i	−0.126884	−	0.0454387i
$454$	24.6195	−	17.8871i	1.15545	−	0.839483i
$455$		0			0
$456$	−15.9437	+	4.66133i	−0.746632	+	0.218287i
$457$	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
$459$	−15.2037	+	9.09586i	−0.709646	+	0.424558i
$460$		0			0
$461$	17.8605			0.831848			0.415924	−	0.909399i	$-0.363458\pi$
$461$	17.8605			0.831848			0.415924	+	0.909399i	$0.363458\pi$
$462$	−19.0364	+	14.7083i	−0.885655	+	0.684293i
$463$	−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	−0.760443	−	0.649405i	$-0.775018\pi$
$467$	−21.4793	+	6.97904i	−0.993943	+	0.322952i	−0.233500	+	0.972357i	$0.575018\pi$
$468$	0.938875	−	0.244450i	0.0433995	−	0.0112997i
$469$	8.88323	−	12.2267i	0.410190	−	0.564578i
$470$		0			0
$471$	9.86156	−	27.5376i	0.454396	−	1.26886i
$472$			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
$477$	−7.06543	+	8.59970i	−0.323504	+	0.393753i
$478$	1.29425	+	3.98330i	0.0591978	+	0.182192i
$479$	−5.96037	−	18.3441i	−0.272336	−	0.838165i	−0.989912	−	0.141685i	$-0.954748\pi$
$479$	−5.96037	−	18.3441i	−0.272336	−	0.838165i	0.717575	−	0.696481i	$-0.245252\pi$
$480$		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
$486$	14.9667	−	29.9982i	0.678902	−	1.36075i
$487$	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
$489$	2.29515	+	7.85039i	0.103790	+	0.355007i
$490$		0			0
$491$	1.11853	+	0.812661i	0.0504786	+	0.0366749i	0.612738	−	0.790286i	$-0.290068\pi$
$491$	1.11853	+	0.812661i	0.0504786	+	0.0366749i	−0.562260	+	0.826961i	$0.690068\pi$
$492$	−18.7241	+	12.7713i	−0.844149	+	0.575773i
$493$	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
$498$	−0.276778	+	0.188783i	−0.0124027	+	0.00845958i
$499$	−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
$501$	−11.3310	−	38.7567i	−0.506231	−	1.73152i
$502$	26.1200	−	35.9510i	1.16579	−	1.60457i
$503$	−1.17583	+	0.854293i	−0.0524278	+	0.0380910i	−0.613691	−	0.789547i	$-0.710316\pi$
$503$	−1.17583	+	0.854293i	−0.0524278	+	0.0380910i	0.561263	+	0.827638i	$0.310316\pi$
$504$	−7.31124	−	2.86615i	−0.325668	−	0.127669i
$505$		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	$-0.898190\pi$
$509$	−21.5451	−	29.6543i	−0.954970	−	1.31440i	−0.00568571	−	0.999984i	$-0.501810\pi$
$510$		0			0
$511$	−2.71563	−	8.35785i	−0.120132	−	0.369730i
$512$	7.61864	+	23.4478i	0.336700	+	1.03625i
$513$	24.3736	−	27.9309i	1.07612	−	1.23318i
$514$	−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
$519$	−5.11334	+	14.2786i	−0.224451	+	0.626760i
$520$		0			0
$521$	−0.239887	+	0.330177i	−0.0105097	+	0.0144653i	−0.814239	−	0.580529i	$-0.802846\pi$
$521$	−0.239887	+	0.330177i	−0.0105097	+	0.0144653i	0.803730	+	0.594994i	$0.202846\pi$
$522$	10.1962	+	39.1610i	0.446274	+	1.71403i
$523$	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
$528$	12.7596	−	4.56638i	0.555291	−	0.198726i
$529$	16.7423			0.727924
$530$		0			0
$531$	−17.9270	−	28.0383i	−0.777966	−	1.21676i
$532$	−29.5027	−	21.4350i	−1.27911	−	0.929325i
$533$	0.584043	−	0.189767i	0.0252977	−	0.00821972i
$534$	−25.1439	+	7.35112i	−1.08808	+	0.318114i
$535$		0			0
$536$	8.44085	−	6.13264i	0.364589	−	0.264890i
$537$	−36.3897	−	13.0316i	−1.57033	−	0.562356i
$538$		−	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
$543$	16.3791	+	12.6606i	0.702896	+	0.543320i
$544$	−8.17836	−	25.1704i	−0.350644	−	1.07917i
$545$		0			0
$546$	0.706979	+	0.546476i	0.0302559	+	0.0233870i
$547$	−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
$552$	−5.48355	−	1.96373i	−0.233395	−	0.0835819i
$553$	−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	0.709661	−	0.704543i	$-0.248848\pi$
$557$	6.11022	+	4.43933i	0.258898	+	0.188101i	−0.450763	+	0.892644i	$0.648848\pi$
$558$	−8.44835	+	5.40166i	−0.357647	+	0.228671i
$559$	−0.329732	+	1.01481i	−0.0139462	+	0.0429219i
$560$		0			0
$561$	−18.4413	+	6.59973i	−0.778593	+	0.278641i
$562$	0.170895			0.00720876
$563$	5.72266	−	17.6125i	0.241181	−	0.742279i	−0.755060	−	0.655656i	$-0.772392\pi$
$563$	5.72266	−	17.6125i	0.241181	−	0.742279i	0.996241	−	0.0866235i	$-0.0276077\pi$
$564$	−0.883588	−	1.29544i	−0.0372058	−	0.0545480i
$565$		0			0
$566$	−31.6506	+	10.2839i	−1.33037	+	0.432264i
$567$	17.1921	−	3.40027i	0.721999	−	0.142798i
$568$	−6.33505	+	8.71945i	−0.265813	+	0.365860i
$569$	0.551284	−	0.400531i	0.0231110	−	0.0167911i	−0.576170	−	0.817330i	$-0.695453\pi$
$569$	0.551284	−	0.400531i	0.0231110	−	0.0167911i	0.599281	+	0.800539i	$0.295453\pi$
$570$		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
$576$	27.7579	+	22.8056i	1.15658	+	0.950233i
$577$	−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
$579$	6.13609	−	7.93829i	0.255007	−	0.329904i
$580$		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	$-0.553315\pi$
$587$	19.9289	−	27.4297i	0.822553	−	1.13215i	0.989264	−	0.146141i	$-0.0466852\pi$
$588$	4.09342	+	14.0012i	0.168810	+	0.577400i
$589$	−10.5455	+	3.42643i	−0.434519	+	0.141184i
$590$		0			0
$591$	−1.32918	+	0.906601i	−0.0546752	+	0.0372926i
$592$	−5.43800	+	16.7364i	−0.223500	+	0.687864i
$593$	30.0564			1.23427			0.617135	−	0.786857i	$-0.288293\pi$
$593$	30.0564			1.23427			0.617135	+	0.786857i	$0.288293\pi$
$594$	22.6726	−	29.3190i	0.930267	−	1.20297i
$595$		0			0
$596$	8.34436	−	25.6813i	0.341798	−	1.05195i
$597$	9.10064	−	6.20731i	0.372464	−	0.254048i
$598$	0.536183	+	0.389560i	0.0219262	+	0.0159303i
$599$	23.9088	−	7.76845i	0.976888	−	0.317410i	0.223295	−	0.974751i	$-0.428319\pi$
$599$	23.9088	−	7.76845i	0.976888	−	0.317410i	0.753593	+	0.657341i	$0.228319\pi$
$600$		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
$603$	−8.49809	+	21.6777i	−0.346069	+	0.882784i
$604$		−	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
$609$	−12.9372	+	16.7369i	−0.524242	+	0.678214i
$610$		0			0
$611$	0.0131292	+	0.0404074i	0.000531149	+	0.00163471i
$612$	−20.7472	−	17.0457i	−0.838655	−	0.689031i
$613$	−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	$-0.829720\pi$
$617$		−	25.3263i		−	1.01960i	0.860294	−	0.509799i	$-0.170280\pi$
$618$	6.74263	−	18.8282i	0.271228	−	0.757382i
$619$	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
$621$	12.6708	−	2.89985i	0.508463	−	0.116367i
$622$	−34.5814	+	11.2362i	−1.38659	+	0.450529i
$623$	−11.0789	−	8.04932i	−0.443868	−	0.322489i
$624$	−0.283646	−	0.415858i	−0.0113549	−	0.0166477i
$625$		0			0
$626$	−3.56740			−0.142582
$627$	32.4304	−	25.0571i	1.29515	−	1.00068i
$628$	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
$633$	10.0858	−	2.94870i	0.400875	−	0.117200i
$634$	12.6858	−	17.4605i	0.503817	−	0.693445i
$635$		0			0
$636$	−15.8808	−	5.68711i	−0.629714	−	0.225509i
$637$		−	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	0.558441	−	0.829544i	$-0.311400\pi$
$641$	−10.2049	−	14.0459i	−0.403070	−	0.554778i	−0.961511	+	0.274766i	$0.911400\pi$
$642$	44.3713	+	34.2978i	1.75119	+	1.35363i
$643$	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	0.303316	−	0.952890i	$-0.401906\pi$
$647$	−0.289752	−	0.0941460i	−0.0113913	−	0.00370126i	−0.314707	+	0.949189i	$0.601906\pi$
$648$	12.0132	+	1.43512i	0.471924	+	0.0563769i
$649$	−13.4211	−	34.2567i	−0.526823	−	1.34469i
$650$		0			0
$651$	−4.93506	−	1.76731i	−0.193420	−	0.0692663i
$652$	−10.0286	+	7.28620i	−0.392750	+	0.285350i
$653$	−17.0754	+	23.5022i	−0.668210	+	0.919712i	−0.999718	−	0.0237401i	$-0.992443\pi$
$653$	−17.0754	+	23.5022i	−0.668210	+	0.919712i	0.331508	+	0.943452i	$0.392443\pi$
$654$	−29.9617	+	8.75965i	−1.17159	+	0.342529i
$655$		0			0
$656$	9.51390	+	6.91225i	0.371455	+	0.269878i
$657$	7.29327	+	11.4069i	0.284538	+	0.445025i
$658$	0.446301	−	1.37357i	0.0173986	−	0.0535474i
$659$	−13.8565			−0.539773			−0.269886	−	0.962892i	$-0.586986\pi$
$659$	−13.8565			−0.539773			−0.269886	+	0.962892i	$0.586986\pi$
$660$		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
$663$	0.409951	+	0.601035i	0.0159212	+	0.0233423i
$664$	−0.0978172	−	0.0710684i	−0.00379604	−	0.00275799i
$665$		0			0
$666$	12.1263	+	46.5741i	0.469884	+	1.80471i
$667$	−9.22238	+	12.6935i	−0.357092	+	0.491495i
$668$	49.5104	−	35.9714i	1.91561	−	1.39177i
$669$	−6.02091	+	16.8129i	−0.232782	+	0.650024i
$670$		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	0.840266	−	0.542175i	$-0.182399\pi$
$677$	−4.11639	−	12.6690i	−0.158206	−	0.486907i	−0.998472	+	0.0552673i	$0.982399\pi$
$678$	−27.8862	+	36.0765i	−1.07096	+	1.38551i
$679$	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	$-0.641124\pi$
$683$		−	47.2151i		−	1.80664i	0.428971	−	0.903318i	$-0.358876\pi$
$684$	52.3076	+	20.5057i	2.00003	+	0.784053i
$685$		0			0
$686$	−25.1275	+	34.5850i	−0.959372	+	1.32046i
$687$	−3.53804	−	12.1016i	−0.134985	−	0.461704i
$688$	−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
$693$	19.3747	+	0.00404138i	0.735985	+	0.000153519i
$694$	−35.2435			−1.33783
$695$		0			0
$696$	−12.0647	+	8.22906i	−0.457313	+	0.311922i
$697$	−13.7503	−	9.99019i	−0.520831	−	0.378406i
$698$	−6.03955	+	1.96237i	−0.228600	+	0.0742768i
$699$	−7.49291	−	25.6289i	−0.283408	−	0.969373i
$700$		0			0
$701$	−12.4038	+	9.01192i	−0.468487	+	0.340376i	−0.796851	−	0.604175i	$-0.793503\pi$
$701$	−12.4038	+	9.01192i	−0.468487	+	0.340376i	0.328364	+	0.944551i	$0.393503\pi$
$702$	−1.26620	−	0.540322i	−0.0477896	−	0.0203931i
$703$			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
$708$	30.8464	−	39.9061i	1.15928	−	1.49976i
$709$	−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
$711$	9.11046	−	11.0888i	0.341669	−	0.415863i
$712$	−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
$717$	1.13725	−	3.17568i	0.0424714	−	0.118598i
$718$	22.2886	−	16.1936i	0.831802	−	0.604339i
$719$	−16.7090	+	22.9980i	−0.623142	+	0.857681i	−0.997577	−	0.0695719i	$-0.977837\pi$
$719$	−16.7090	+	22.9980i	−0.623142	+	0.857681i	0.374435	+	0.927253i	$0.377837\pi$
$720$		0			0
$721$	9.94295	−	3.23066i	0.370295	−	0.120316i
$722$	55.4959	+	40.3202i	2.06535	+	1.50056i
$723$	−18.8791	−	27.6789i	−0.702119	−	1.02939i
$724$	−9.69558	+	29.8399i	−0.360333	+	1.10899i
$725$		0			0
$726$	30.8837	−	26.9277i	1.14620	−	0.999380i
$727$	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
$729$	−24.3124	+	11.7434i	−0.900460	+	0.434939i
$730$		0			0
$731$	28.0868	−	9.12595i	1.03883	−	0.337535i
$732$	41.6588	−	12.1795i	1.53976	−	0.450166i
$733$	−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
$741$	−1.20441	−	0.930975i	−0.0442450	−	0.0342002i
$742$	−4.80099	−	14.7759i	−0.176250	−	0.542441i
$743$	5.20821	+	16.0292i	0.191071	+	0.588056i	1.00000		0.000149450i	$4.75713e-5\pi$
$743$	5.20821	+	16.0292i	0.191071	+	0.588056i	−0.808929	+	0.587906i	$0.799952\pi$
$744$	−2.86320	−	2.21318i	−0.104970	−	0.0811391i
$745$		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
$753$	−34.3514	+	10.0431i	−1.25184	+	0.365989i
$754$	1.58041	−	0.513505i	0.0575550	−	0.0187007i
$755$		0			0
$756$	13.6364	+	22.7932i	0.495951	+	0.828979i
$757$	−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
$759$	14.3640	−	0.424092i	0.521381	−	0.0153936i
$760$		0			0
$761$	1.19848	−	3.68855i	0.0434450	−	0.133710i	−0.926981	−	0.375108i	$-0.877606\pi$
$761$	1.19848	−	3.68855i	0.0434450	−	0.133710i	0.970426	+	0.241398i	$0.0776058\pi$
$762$	21.9634	+	32.2008i	0.795649	+	1.16651i
$763$	−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
$768$	1.13941	−	3.18170i	0.0411148	−	0.114810i
$769$		−	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	0.896526	−	0.442991i	$-0.146082\pi$
$773$	5.50984	+	7.58365i	0.198175	+	0.272765i	−0.698351	+	0.715756i	$0.746082\pi$
$774$	−35.4747	+	43.1781i	−1.27511	+	1.55200i
$775$		0			0
$776$	7.13241	+	21.9513i	0.256039	+	0.788006i
$777$	−15.3862	+	19.9052i	−0.551977	+	0.714095i
$778$	−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
$783$	12.7915	−	29.9758i	0.457131	−	1.07125i
$784$	6.12322	−	4.44878i	0.218686	−	0.158885i
$785$		0			0
$786$	−3.39204	−	11.6022i	−0.120990	−	0.413837i
$787$	−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
$789$	31.5213	−	21.4998i	1.12219	−	0.765415i
$790$		0			0
$791$	−23.8364			−0.847527
$792$	12.7200	+	4.13593i	0.451987	+	0.146964i
$793$	−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	−0.715076	−	0.699046i	$-0.753608\pi$
$797$	−24.9196	+	8.09685i	−0.882696	+	0.286805i	−0.167620	+	0.985852i	$0.553608\pi$
$798$	14.5209	+	49.6675i	0.514034	+	1.75821i
$799$	0.691179	−	0.951326i	0.0244521	−	0.0336555i
$800$		0			0
$801$	19.6427	+	7.70033i	0.694040	+	0.272078i
$802$		−	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
$807$	−26.9314	+	34.8413i	−0.948030	+	1.22647i
$808$	−4.92998	−	15.1729i	−0.173436	−	0.533781i
$809$	−11.3391	−	34.8982i	−0.398662	−	1.22695i	−0.926073	−	0.377344i	$-0.876837\pi$
$809$	−11.3391	−	34.8982i	−0.398662	−	1.22695i	0.527412	−	0.849610i	$-0.323163\pi$
$810$		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
$816$	−4.69713	+	13.1164i	−0.164433	+	0.459164i
$817$	−49.9912	+	36.3207i	−1.74897	+	1.27070i
$818$	−3.43735	+	4.73111i	−0.120184	+	0.165419i
$819$	−0.181329	−	0.696440i	−0.00633614	−	0.0243356i
$820$		0			0
$821$	19.7438	+	14.3447i	0.689065	+	0.500635i	0.876353	−	0.481670i	$-0.159970\pi$
$821$	19.7438	+	14.3447i	0.689065	+	0.500635i	−0.187288	+	0.982305i	$0.559970\pi$
$822$	1.54931	+	2.27146i	0.0540383	+	0.0792264i
$823$	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	$-0.607956\pi$
$827$	14.1132	−	43.4361i	0.490765	−	1.51042i	0.823454	−	0.567383i	$-0.192044\pi$
$828$	10.6121	+	16.5977i	0.368797	+	0.576810i
$829$	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
$831$	14.3226	−	4.18737i	0.496845	−	0.145258i
$832$	0.867121	−	1.19349i	0.0300620	−	0.0413768i
$833$	−8.84982	+	6.42977i	−0.306628	+	0.222778i
$834$	49.4175	+	17.6970i	1.71119	+	0.612798i
$835$		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	0.997208	−	0.0746733i	$-0.0237914\pi$
$839$	17.9017	+	24.6396i	0.618035	+	0.850653i	−0.379173	+	0.925326i	$0.623791\pi$
$840$		0			0
$841$	3.19515	+	9.83365i	0.110177	+	0.339091i
$842$	19.7255	+	60.7087i	0.679784	+	2.09216i
$843$	−0.108896	−	0.0841735i	−0.00375057	−	0.00289909i
$844$	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
$849$	25.2333	+	9.03638i	0.866006	+	0.310128i
$850$		0			0
$851$	−10.9682	+	15.0964i	−0.375984	+	0.517498i
$852$	34.9889	−	10.2294i	1.19870	−	0.350454i
$853$	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	$-0.696548\pi$
$857$	−33.8986			−1.15796			−0.578978	+	0.815343i	$0.696548\pi$
$858$	−1.25716	−	0.857859i	−0.0429186	−	0.0292868i
$859$	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
$861$	9.47348	+	13.8892i	0.322855	+	0.473343i
$862$	48.5462	+	35.2709i	1.65349	+	1.20133i
$863$	−14.4234	+	4.68646i	−0.490979	+	0.159529i	−0.544035	−	0.839063i	$-0.683104\pi$
$863$	−14.4234	+	4.68646i	−0.490979	+	0.159529i	0.0530553	+	0.998592i	$0.483104\pi$
$864$	−8.99800	−	39.3166i	−0.306118	−	1.33758i
$865$		0			0
$866$	24.3319	−	17.6782i	0.826832	−	0.600729i
$867$	−3.13851	+	8.76404i	−0.106590	+	0.297642i
$868$		−	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
$873$	−39.7990	−	32.6985i	−1.34699	−	1.10668i
$874$	11.8603	+	36.5022i	0.401180	+	1.23470i
$875$		0			0
$876$	−12.5493	+	16.2351i	−0.424001	+	0.548532i
$877$	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	$-0.800039\pi$
$881$		−	34.8870i		−	1.17537i	0.809088	−	0.587687i	$-0.199961\pi$
$882$	7.55473	−	19.2713i	0.254381	−	0.648898i
$883$	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	0.306180	−	0.951974i	$-0.400949\pi$
$887$	−15.0279	−	10.9184i	−0.504586	−	0.366603i	−0.810766	+	0.585370i	$0.800949\pi$
$888$	−14.3486	+	9.78682i	−0.481508	+	0.328424i
$889$	−6.29651	+	19.3787i	−0.211178	+	0.649939i
$890$		0			0
$891$	−28.8881	+	7.51503i	−0.967789	+	0.251763i
$892$	−27.0661			−0.906240
$893$	−0.760316	+	2.34001i	−0.0254430	+	0.0783055i
$894$	−31.6546	+	21.5908i	−1.05869	+	0.722104i
$895$		0			0
$896$	−18.9436	+	6.15514i	−0.632861	+	0.205629i
$897$	−0.149785	−	0.512326i	−0.00500116	−	0.0171061i
$898$	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
$906$	−3.77279	+	4.88087i	−0.125343	+	0.162156i
$907$	−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
$909$	27.5094	+	22.6014i	0.912429	+	0.749642i
$910$		0			0
$911$	24.3697	+	7.91820i	0.807405	+	0.262342i	0.683498	−	0.729952i	$-0.260458\pi$
$911$	24.3697	+	7.91820i	0.807405	+	0.262342i	0.123907	+	0.992294i	$0.460458\pi$
$912$	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
$918$	8.50022	+	37.1415i	0.280549	+	1.22585i
$919$	−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
$921$	−13.1804	−	19.3240i	−0.434310	−	0.636748i
$922$	11.8696	−	36.5309i	0.390905	−	1.20308i
$923$	−0.987698			−0.0325105
$924$	9.89424	+	27.6470i	0.325497	+	0.909520i
$925$		0			0
$926$	−4.96966	+	15.2950i	−0.163313	+	0.502626i
$927$	−13.5702	+	8.67646i	−0.445705	+	0.284972i
$928$	39.3870	+	28.6163i	1.29294	+	0.939377i
$929$	−54.3549	+	17.6610i	−1.78333	+	0.579438i	−0.999155	−	0.0411063i	$-0.986912\pi$
$929$	−54.3549	+	17.6610i	−1.78333	+	0.579438i	−0.784172	+	0.620544i	$0.786912\pi$
$930$		0			0
$931$	13.4535	−	18.5172i	0.440921	−	0.606875i
$932$	32.7400	−	23.7870i	1.07243	−	0.779170i
$933$	27.5699	+	9.87313i	0.902598	+	0.323232i
$934$			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
$939$	2.27318	+	1.75711i	0.0741824	+	0.0573410i
$940$		0			0
$941$	−13.3303	−	41.0263i	−0.434554	−	1.33742i	−0.893543	−	0.448978i	$-0.851788\pi$
$941$	−13.3303	−	41.0263i	−0.434554	−	1.33742i	0.458989	−	0.888442i	$-0.348212\pi$
$942$	−49.7700	−	38.4709i	−1.62160	−	1.25345i
$943$	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	$-0.960570\pi$
$947$		−	7.60444i		−	0.247111i	0.992338	−	0.123555i	$-0.0394297\pi$
$948$	20.4774	+	7.33321i	0.665074	+	0.238171i
$949$	0.449795	−	0.326796i	0.0146010	−	0.0106082i
$950$		0			0
$951$	−16.6836	+	4.87765i	−0.541003	+	0.158169i
$952$	8.48834	−	2.75803i	0.275109	−	0.0893882i
$953$	−3.54873	−	2.57831i	−0.114955	−	0.0835195i	0.528823	−	0.848732i	$-0.322634\pi$
$953$	−3.54873	−	2.57831i	−0.114955	−	0.0835195i	−0.643777	+	0.765213i	$0.722634\pi$
$954$	12.8938	+	20.1663i	0.417453	+	0.652909i
$955$		0			0
$956$	5.11234			0.165345
$957$	20.3088	−	29.7618i	0.656491	−	0.962061i
$958$	−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
$963$	−11.3805	−	43.7098i	−0.366732	−	1.40853i
$964$	29.8470	−	41.0809i	0.961308	−	1.32313i
$965$		0			0
$966$	−6.11737	+	17.0823i	−0.196823	+	0.549613i
$967$			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	0.809947	−	0.586502i	$-0.199496\pi$
$971$	0.0580491	+	0.0798977i	0.00186288	+	0.00256404i	−0.808085	+	0.589067i	$0.799496\pi$
$972$	−29.1791	−	28.6897i	−0.935921	−	0.920224i
$973$	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	0.915774	−	0.401695i	$-0.131579\pi$
$977$	44.4018	+	14.4270i	1.42054	+	0.461561i	0.504766	+	0.863256i	$0.331579\pi$
$978$	17.5820	+	0.522772i	0.562211	+	0.0167164i
$979$	19.6488	+	12.5687i	0.627979	+	0.401698i
$980$		0			0
$981$	23.4064	+	9.17577i	0.747308	+	0.292960i
$982$	2.40551	−	1.74771i	0.0767630	−	0.0557716i
$983$	30.8531	−	42.4656i	0.984061	−	1.35444i	0.0494483	−	0.998777i	$-0.484254\pi$
$983$	30.8531	−	42.4656i	0.984061	−	1.35444i	0.934613	−	0.355667i	$-0.115746\pi$
$984$	3.25699	+	11.1403i	0.103829	+	0.355139i
$985$		0			0
$986$	−37.2081	−	27.0332i	−1.18495	−	0.860914i
$987$	−0.960935	+	0.655429i	−0.0305869	+	0.0208625i
$988$	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
$993$	12.9304	−	8.81950i	0.410334	−	0.279878i
$994$	27.1627	+	19.7348i	0.861547	+	0.625951i
$995$		0			0
$996$	0.114756	+	0.392515i	0.00363620	+	0.0124373i
$997$	−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
$999$	15.2129	−	35.6502i	0.481316	−	1.12792i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.664572 - 2.04534i) q^{2} +(-1.43090 + 0.975979i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(1.04528 + 3.57528i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(-1.08756 + 0.790156i) q^{8} +(1.09493 - 2.79305i) q^{9} +O(q^{10})\)	\(q+(0.664572 - 2.04534i) q^{2} +(-1.43090 + 0.975979i) q^{3} +(-2.12373 - 1.54298i) q^{4} +(1.04528 + 3.57528i) q^{6} +(-1.14456 + 1.57535i) q^{7} +(-1.08756 + 0.790156i) q^{8} +(1.09493 - 2.79305i) 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} +(-4.98508 - 4.09569i) q^{18} +(-4.19337 - 5.77168i) q^{19} +(0.100238 - 3.37122i) q^{21} +(-4.52681 - 5.51216i) q^{22} -2.50155i q^{23} +(0.785006 - 2.19206i) q^{24} +(-0.155728 + 0.214341i) q^{26} +(1.15922 + 5.06520i) q^{27} +(4.86146 - 1.57958i) q^{28} +(-5.07427 - 3.68667i) q^{29} +(0.480284 - 1.47816i) q^{31} -7.76211 q^{32} +(0.169532 + 5.74206i) q^{33} +7.33270 q^{34} +(-6.63497 + 4.24223i) q^{36} +(-6.03482 - 4.38456i) q^{37} +(-14.5918 + 4.74118i) q^{38} +(0.204804 - 0.0598768i) q^{39} +(-4.03282 + 2.93001i) q^{41} +(-6.82868 - 2.44544i) q^{42} -8.66147i q^{43} +(-8.10647 + 3.17595i) q^{44} +(-5.11652 - 1.66246i) q^{46} +(-0.202715 - 0.279013i) q^{47} +(3.23289 + 2.49894i) q^{48} +(0.991413 + 3.05126i) q^{49} +(-4.67246 - 3.61169i) q^{51} +(0.190085 + 0.261630i) q^{52} +(-3.52839 - 1.14644i) q^{53} +(11.1304 + 0.995182i) q^{54} -2.61765i q^{56} +(11.6333 + 4.16604i) 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} +(3.14681 + 4.92169i) q^{63} +(-3.70046 + 11.3889i) q^{64} +(11.8571 + 3.46926i) q^{66} -7.76130 q^{67} +(2.76585 - 8.51242i) q^{68} +(2.44146 + 3.57946i) q^{69} +(7.62506 - 2.47753i) q^{71} +(1.01614 + 3.90277i) 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} +(-6.60225 - 6.11640i) q^{81} +(3.31278 + 10.1957i) q^{82} +(0.0277937 + 0.0855401i) q^{83} +(-5.41461 + 7.00490i) 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} +(0.755418 + 2.58384i) q^{93} +(-0.705397 + 0.229197i) q^{94} +(11.1068 - 7.57565i) q^{96} +(5.30569 - 16.3292i) q^{97} +6.89973 q^{98} +(-5.84671 - 8.05084i) 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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