LMFDB - Embedded newform 845.2.m.j.361.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.14
Character	$\chi$	$=$	845.361
Dual form			845.2.m.j.316.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.91007 - 1.10278i) q^{2} +(0.00652833 + 0.0113074i) q^{3} +(1.43225 - 2.48072i) q^{4} +1.00000i q^{5} +(0.0249391 + 0.0143986i) q^{6} +(3.99148 + 2.30448i) q^{7} -1.90669i q^{8} +(1.49991 - 2.59793i) q^{9} +(1.10278 + 1.91007i) q^{10} +(-2.53946 + 1.46616i) q^{11} +0.0374007 q^{12} +10.1654 q^{14} +(-0.0113074 + 0.00652833i) q^{15} +(0.761834 + 1.31954i) q^{16} +(-1.67603 + 2.90297i) q^{17} -6.61630i q^{18} +(2.13060 + 1.23010i) q^{19} +(2.48072 + 1.43225i) q^{20} +0.0601778i q^{21} +(-3.23370 + 5.60094i) q^{22} +(-0.791645 - 1.37117i) q^{23} +(0.0215597 - 0.0124475i) q^{24} -1.00000 q^{25} +0.0783378 q^{27} +(11.4336 - 6.60118i) q^{28} +(-4.13161 - 7.15616i) q^{29} +(-0.0143986 + 0.0249391i) q^{30} -9.77959i q^{31} +(6.21280 + 3.58696i) q^{32} +(-0.0331569 - 0.0191432i) q^{33} +7.39317i q^{34} +(-2.30448 + 3.99148i) q^{35} +(-4.29649 - 7.44175i) q^{36} +(-3.57597 + 2.06458i) q^{37} +5.42613 q^{38} +1.90669 q^{40} +(6.29175 - 3.63254i) q^{41} +(0.0663628 + 0.114944i) q^{42} +(-0.352665 + 0.610833i) q^{43} +8.39961i q^{44} +(2.59793 + 1.49991i) q^{45} +(-3.02419 - 1.74602i) q^{46} -8.57322i q^{47} +(-0.00994701 + 0.0172287i) q^{48} +(7.12130 + 12.3344i) q^{49} +(-1.91007 + 1.10278i) q^{50} -0.0437667 q^{51} -12.4639 q^{53} +(0.149631 - 0.0863893i) q^{54} +(-1.46616 - 2.53946i) q^{55} +(4.39394 - 7.61052i) q^{56} +0.0321221i q^{57} +(-15.7833 - 9.11251i) q^{58} +(-4.61977 - 2.66723i) q^{59} +0.0374007i q^{60} +(-0.960460 + 1.66357i) q^{61} +(-10.7847 - 18.6797i) q^{62} +(11.9738 - 6.91306i) q^{63} +12.7752 q^{64} -0.0844427 q^{66} +(-6.32019 + 3.64896i) q^{67} +(4.80097 + 8.31553i) q^{68} +(0.0103362 - 0.0179029i) q^{69} +10.1654i q^{70} +(5.78577 + 3.34041i) q^{71} +(-4.95344 - 2.85987i) q^{72} +12.4541i q^{73} +(-4.55356 + 7.88700i) q^{74} +(-0.00652833 - 0.0113074i) q^{75} +(6.10309 - 3.52362i) q^{76} -13.5150 q^{77} +0.984840 q^{79} +(-1.31954 + 0.761834i) q^{80} +(-4.49923 - 7.79290i) q^{81} +(8.01179 - 13.8768i) q^{82} -7.84405i q^{83} +(0.149284 + 0.0861894i) q^{84} +(-2.90297 - 1.67603i) q^{85} +1.55565i q^{86} +(0.0539450 - 0.0934356i) q^{87} +(2.79551 + 4.84197i) q^{88} +(0.357525 - 0.206417i) q^{89} +6.61630 q^{90} -4.53532 q^{92} +(0.110582 - 0.0638444i) q^{93} +(-9.45437 - 16.3755i) q^{94} +(-1.23010 + 2.13060i) q^{95} +0.0936675i q^{96} +(2.93077 + 1.69208i) q^{97} +(27.2044 + 15.7064i) q^{98} +8.79646i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{3} + 34 q^{4} - 32 q^{9} + 6 q^{10} - 48 q^{12} - 8 q^{14} - 74 q^{16} - 2 q^{17} - 24 q^{22} + 28 q^{23} - 36 q^{25} + 88 q^{27} - 24 q^{29} - 4 q^{30} - 14 q^{35} + 6 q^{36} + 188 q^{38}+ \cdots - 8 q^{95}+O(q^{100}) $ 36 * q - 14 * q^3 + 34 * q^4 - 32 * q^9 + 6 * q^10 - 48 * q^12 - 8 * q^14 - 74 * q^16 - 2 * q^17 - 24 * q^22 + 28 * q^23 - 36 * q^25 + 88 * q^27 - 24 * q^29 - 4 * q^30 - 14 * q^35 + 6 * q^36 + 188 * q^38 + 48 * q^40 + 22 * q^42 + 78 * q^43 + 6 * q^48 + 32 * q^49 - 172 * q^51 - 32 * q^53 + 18 * q^55 - 58 * q^56 + 6 * q^61 - 20 * q^62 - 136 * q^64 - 196 * q^66 + 40 * q^68 - 26 * q^69 + 30 * q^74 + 14 * q^75 + 16 * q^77 + 156 * q^79 - 58 * q^81 - 8 * q^82 - 32 * q^87 + 84 * q^88 + 40 * q^90 - 108 * q^92 - 32 * q^94 - 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.91007	−	1.10278i	1.35062	−	0.779783i	0.362287	−	0.932067i	$-0.381996\pi$
$2$	1.91007	−	1.10278i	1.35062	−	0.779783i	0.988337	+	0.152284i	$0.0486627\pi$
$3$	0.00652833	+	0.0113074i	0.00376913	+	0.00652833i	0.867904	−	0.496732i	$-0.165467\pi$
$3$	0.00652833	+	0.0113074i	0.00376913	+	0.00652833i	−0.864135	+	0.503261i	$0.832134\pi$
$4$	1.43225	−	2.48072i	0.716123	−	1.24036i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.0249391	+	0.0143986i	0.0101814	+	0.00587821i
$7$	3.99148	+	2.30448i	1.50864	+	0.871013i	0.999949	+	0.0100635i	$0.00320335\pi$
$7$	3.99148	+	2.30448i	1.50864	+	0.871013i	0.508690	+	0.860950i	$0.330130\pi$
$8$		−	1.90669i		−	0.674116i
$9$	1.49991	−	2.59793i	0.499972	−	0.865976i
$10$	1.10278	+	1.91007i	0.348730	+	0.604017i
$11$	−2.53946	+	1.46616i	−0.765677	+	0.442064i	−0.831330	−	0.555779i	$-0.812420\pi$
$11$	−2.53946	+	1.46616i	−0.765677	+	0.442064i	0.0656533	+	0.997842i	$0.479087\pi$
$12$	0.0374007			0.0107967
$13$		0			0
$13$		0			0
$14$	10.1654			2.71681
$15$	−0.0113074	+	0.00652833i	−0.00291956	+	0.00168561i
$16$	0.761834	+	1.31954i	0.190459	+	0.329884i
$17$	−1.67603	+	2.90297i	−0.406497	+	0.704073i	−0.994494	−	0.104789i	$-0.966583\pi$
$17$	−1.67603	+	2.90297i	−0.406497	+	0.704073i	0.587997	+	0.808863i	$0.299916\pi$
$18$		−	6.61630i		−	1.55948i
$19$	2.13060	+	1.23010i	0.488793	+	0.282205i	0.724074	−	0.689723i	$-0.242267\pi$
$19$	2.13060	+	1.23010i	0.488793	+	0.282205i	−0.235280	+	0.971928i	$0.575601\pi$
$20$	2.48072	+	1.43225i	0.554707	+	0.320260i
$21$			0.0601778i			0.0131319i
$22$	−3.23370	+	5.60094i	−0.689428	+	1.19412i
$23$	−0.791645	−	1.37117i	−0.165069	−	0.285908i	0.771611	−	0.636095i	$-0.219451\pi$
$23$	−0.791645	−	1.37117i	−0.165069	−	0.285908i	−0.936680	+	0.350187i	$0.886118\pi$
$24$	0.0215597	−	0.0124475i	0.00440085	−	0.00254083i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	0.0783378			0.0150761
$28$	11.4336	−	6.60118i	2.16074	−	1.24751i
$29$	−4.13161	−	7.15616i	−0.767221	−	1.32887i	−0.939064	−	0.343741i	$-0.888306\pi$
$29$	−4.13161	−	7.15616i	−0.767221	−	1.32887i	0.171844	−	0.985124i	$-0.445028\pi$
$30$	−0.0143986	+	0.0249391i	−0.00262882	+	0.00455324i
$31$		−	9.77959i		−	1.75647i	−0.478233	−	0.878233i	$-0.658723\pi$
$31$		−	9.77959i		−	1.75647i	0.478233	−	0.878233i	$-0.341277\pi$
$32$	6.21280	+	3.58696i	1.09828	+	0.634091i
$33$	−0.0331569	−	0.0191432i	−0.00577188	−	0.00333240i
$34$			7.39317i			1.26792i
$35$	−2.30448	+	3.99148i	−0.389529	+	0.674684i
$36$	−4.29649	−	7.44175i	−0.716082	−	1.24029i
$37$	−3.57597	+	2.06458i	−0.587885	+	0.339416i	−0.764261	−	0.644907i	$-0.776896\pi$
$37$	−3.57597	+	2.06458i	−0.587885	+	0.339416i	0.176376	+	0.984323i	$0.443563\pi$
$38$	5.42613			0.880235
$39$		0			0
$40$	1.90669			0.301474
$41$	6.29175	−	3.63254i	0.982606	−	0.567308i	0.0795500	−	0.996831i	$-0.474652\pi$
$41$	6.29175	−	3.63254i	0.982606	−	0.567308i	0.903056	+	0.429523i	$0.141318\pi$
$42$	0.0663628	+	0.114944i	0.0102400	+	0.0177362i
$43$	−0.352665	+	0.610833i	−0.0537809	+	0.0931512i	−0.891662	−	0.452701i	$-0.850461\pi$
$43$	−0.352665	+	0.610833i	−0.0537809	+	0.0931512i	0.837882	+	0.545852i	$0.183794\pi$
$44$			8.39961i			1.26629i
$45$	2.59793	+	1.49991i	0.387276	+	0.223594i
$46$	−3.02419	−	1.74602i	−0.445893	−	0.257437i
$47$		−	8.57322i		−	1.25053i	−0.780411	−	0.625266i	$-0.784990\pi$
$47$		−	8.57322i		−	1.25053i	0.780411	−	0.625266i	$-0.215010\pi$
$48$	−0.00994701	+	0.0172287i	−0.00143573	+	0.00248675i
$49$	7.12130	+	12.3344i	1.01733	+	1.76206i
$50$	−1.91007	+	1.10278i	−0.270125	+	0.155957i
$51$	−0.0437667			−0.00612857
$52$		0			0
$53$	−12.4639			−1.71204			−0.856022	−	0.516940i	$-0.827071\pi$
$53$	−12.4639			−1.71204			−0.856022	+	0.516940i	$0.827071\pi$
$54$	0.149631	−	0.0863893i	0.0203621	−	0.0117561i
$55$	−1.46616	−	2.53946i	−0.197697	−	0.342421i
$56$	4.39394	−	7.61052i	0.587164	−	1.01700i
$57$			0.0321221i			0.00425467i
$58$	−15.7833	−	9.11251i	−2.07245	−	1.19653i
$59$	−4.61977	−	2.66723i	−0.601443	−	0.347243i	0.168166	−	0.985759i	$-0.446216\pi$
$59$	−4.61977	−	2.66723i	−0.601443	−	0.347243i	−0.769609	+	0.638515i	$0.779549\pi$
$60$			0.0374007i			0.00482841i
$61$	−0.960460	+	1.66357i	−0.122974	+	0.212998i	−0.920939	−	0.389706i	$-0.872577\pi$
$61$	−0.960460	+	1.66357i	−0.122974	+	0.212998i	0.797965	+	0.602704i	$0.205910\pi$
$62$	−10.7847	−	18.6797i	−1.36966	−	2.37232i
$63$	11.9738	−	6.91306i	1.50855	−	0.870964i
$64$	12.7752			1.59690
$65$		0			0
$66$	−0.0844427			−0.0103942
$67$	−6.32019	+	3.64896i	−0.772134	+	0.445792i	−0.833635	−	0.552315i	$-0.813745\pi$
$67$	−6.32019	+	3.64896i	−0.772134	+	0.445792i	0.0615011	+	0.998107i	$0.480411\pi$
$68$	4.80097	+	8.31553i	0.582204	+	1.00841i
$69$	0.0103362	−	0.0179029i	0.00124434	−	0.00215525i
$70$			10.1654i			1.21499i
$71$	5.78577	+	3.34041i	0.686644	+	0.396434i	0.802354	−	0.596849i	$-0.203581\pi$
$71$	5.78577	+	3.34041i	0.686644	+	0.396434i	−0.115710	+	0.993283i	$0.536914\pi$
$72$	−4.95344	−	2.85987i	−0.583769	−	0.337039i
$73$			12.4541i			1.45765i	0.684702	+	0.728824i	$0.259933\pi$
$73$			12.4541i			1.45765i	−0.684702	+	0.728824i	$0.740067\pi$
$74$	−4.55356	+	7.88700i	−0.529341	+	0.916846i
$75$	−0.00652833	−	0.0113074i	−0.000753827	−	0.00130567i
$76$	6.10309	−	3.52362i	0.700073	−	0.404187i
$77$	−13.5150			−1.54017
$78$		0			0
$79$	0.984840			0.110803			0.0554016	−	0.998464i	$-0.482356\pi$
$79$	0.984840			0.110803			0.0554016	+	0.998464i	$0.482356\pi$
$80$	−1.31954	+	0.761834i	−0.147529	+	0.0851757i
$81$	−4.49923	−	7.79290i	−0.499915	−	0.865878i
$82$	8.01179	−	13.8768i	0.884754	−	1.53244i
$83$		−	7.84405i		−	0.860997i	−0.902591	−	0.430498i	$-0.858338\pi$
$83$		−	7.84405i		−	0.860997i	0.902591	−	0.430498i	$-0.141662\pi$
$84$	0.149284	+	0.0861894i	0.0162883	+	0.00940403i
$85$	−2.90297	−	1.67603i	−0.314871	−	0.181791i
$86$			1.55565i			0.167750i
$87$	0.0539450	−	0.0934356i	0.00578352	−	0.0100173i
$88$	2.79551	+	4.84197i	0.298002	+	0.516155i
$89$	0.357525	−	0.206417i	0.0378976	−	0.0218802i	−0.480932	−	0.876758i	$-0.659701\pi$
$89$	0.357525	−	0.206417i	0.0378976	−	0.0218802i	0.518829	+	0.854878i	$0.326368\pi$
$90$	6.61630			0.697419
$91$		0			0
$92$	−4.53532			−0.472840
$93$	0.110582	−	0.0638444i	0.0114668	−	0.00662035i
$94$	−9.45437	−	16.3755i	−0.975144	−	1.68900i
$95$	−1.23010	+	2.13060i	−0.126206	+	0.218595i
$96$			0.0936675i			0.00955989i
$97$	2.93077	+	1.69208i	0.297574	+	0.171805i	0.641353	−	0.767246i	$-0.278374\pi$
$97$	2.93077	+	1.69208i	0.297574	+	0.171805i	−0.343778	+	0.939051i	$0.611707\pi$
$98$	27.2044	+	15.7064i	2.74806	+	1.58659i
$99$			8.79646i			0.884077i
$100$	−1.43225	+	2.48072i	−0.143225	+	0.248072i
$101$	−5.27162	−	9.13071i	−0.524545	−	0.908539i	−0.999592	−	0.0285783i	$-0.990902\pi$
$101$	−5.27162	−	9.13071i	−0.524545	−	0.908539i	0.475046	−	0.879961i	$-0.342431\pi$
$102$	−0.0835975	+	0.0482650i	−0.00827739	+	0.00477895i
$103$	−14.1152			−1.39081			−0.695404	−	0.718619i	$-0.744774\pi$
$103$	−14.1152			−1.39081			−0.695404	+	0.718619i	$0.744774\pi$
$104$		0			0
$105$	−0.0601778			−0.00587275
$106$	−23.8069	+	13.7449i	−2.31233	+	1.33502i
$107$	1.98582	+	3.43955i	0.191977	+	0.332514i	0.945905	−	0.324443i	$-0.105177\pi$
$107$	1.98582	+	3.43955i	0.191977	+	0.332514i	−0.753928	+	0.656957i	$0.771844\pi$
$108$	0.112199	−	0.194334i	0.0107963	−	0.0186998i
$109$			10.1737i			0.974460i	0.873274	+	0.487230i	$0.161993\pi$
$109$			10.1737i			0.974460i	−0.873274	+	0.487230i	$0.838007\pi$
$110$	−5.60094	−	3.23370i	−0.534028	−	0.308321i
$111$	−0.0466902	−	0.0269566i	−0.00443164	−	0.00255861i
$112$			7.02254i			0.663568i
$113$	1.29992	−	2.25152i	0.122286	−	0.211806i	−0.798383	−	0.602150i	$-0.794311\pi$
$113$	1.29992	−	2.25152i	0.122286	−	0.211806i	0.920669	+	0.390345i	$0.127644\pi$
$114$	0.0354236	+	0.0613555i	0.00331772	+	0.00574646i
$115$	1.37117	−	0.791645i	0.127862	−	0.0738212i
$116$	−23.6699			−2.19770
$117$		0			0
$118$	−11.7655			−1.08310
$119$	−13.3797	+	7.72477i	−1.22651	+	0.708128i
$120$	0.0124475	+	0.0215597i	0.00113630	+	0.00196812i
$121$	−1.20075	+	2.07976i	−0.109159	+	0.189069i
$122$			4.23670i			0.383573i
$123$	0.0821492	+	0.0474289i	0.00740715	+	0.00427652i
$124$	−24.2604	−	14.0068i	−2.17865	−	1.25785i
$125$		−	1.00000i		−	0.0894427i
$126$	15.2472	−	26.4089i	1.35833	−	2.35269i
$127$	9.98595	+	17.2962i	0.886109	+	1.53479i	0.844437	+	0.535655i	$0.179935\pi$
$127$	9.98595	+	17.2962i	0.886109	+	1.53479i	0.0416726	+	0.999131i	$0.486731\pi$
$128$	11.9759	−	6.91428i	1.05853	−	0.611142i
$129$	−0.00920925			−0.000810829
$130$		0			0
$131$	−11.4400			−0.999514			−0.499757	−	0.866166i	$-0.666577\pi$
$131$	−11.4400			−0.999514			−0.499757	+	0.866166i	$0.666577\pi$
$132$	−0.0949777	+	0.0548354i	−0.00826675	+	0.00477281i
$133$	5.66951	+	9.81988i	0.491609	+	0.851491i
$134$	−8.04801	+	13.9396i	−0.695242	+	1.20419i
$135$			0.0783378i			0.00674224i
$136$	5.53506	+	3.19567i	0.474627	+	0.274026i
$137$	2.70650	+	1.56260i	0.231232	+	0.133502i	0.611140	−	0.791522i	$-0.290711\pi$
$137$	2.70650	+	1.56260i	0.231232	+	0.133502i	−0.379908	+	0.925024i	$0.624044\pi$
$138$		−	0.0455944i		−	0.00388125i
$139$	−3.04763	+	5.27865i	−0.258497	+	0.447729i	−0.965839	−	0.259142i	$-0.916560\pi$
$139$	−3.04763	+	5.27865i	−0.258497	+	0.447729i	0.707343	+	0.706871i	$0.249894\pi$
$140$	6.60118	+	11.4336i	0.557901	+	0.966314i
$141$	0.0969409	−	0.0559688i	0.00816389	−	0.00471343i
$142$	14.7350			1.23653
$143$		0			0
$144$	4.57075			0.380896
$145$	7.15616	−	4.13161i	0.594287	−	0.343112i
$146$	13.7342	+	23.7883i	1.13665	+	1.96873i
$147$	−0.0929804	+	0.161047i	−0.00766889	+	0.0132829i
$148$			11.8280i			0.972253i
$149$	12.6610	+	7.30982i	1.03723	+	0.598844i	0.919047	−	0.394148i	$-0.128960\pi$
$149$	12.6610	+	7.30982i	1.03723	+	0.598844i	0.118181	+	0.992992i	$0.462294\pi$
$150$	−0.0249391	−	0.0143986i	−0.00203627	−	0.00117564i
$151$		−	12.2510i		−	0.996973i	−0.866897	−	0.498487i	$-0.833889\pi$
$151$		−	12.2510i		−	0.996973i	0.866897	−	0.498487i	$-0.166111\pi$
$152$	2.34542	−	4.06239i	0.190239	−	0.329504i
$153$	5.02780	+	8.70841i	0.406474	+	0.704033i
$154$	−25.8145	+	14.9040i	−2.08020	+	1.20100i
$155$	9.77959			0.785515
$156$		0			0
$157$	7.13991			0.569827			0.284914	−	0.958553i	$-0.408035\pi$
$157$	7.13991			0.569827			0.284914	+	0.958553i	$0.408035\pi$
$158$	1.88111	−	1.08606i	0.149653	−	0.0864024i
$159$	−0.0813682	−	0.140934i	−0.00645292	−	0.0111768i
$160$	−3.58696	+	6.21280i	−0.283574	+	0.491165i
$161$		−	7.29733i		−	0.575110i
$162$	−17.1877	−	9.92333i	−1.35039	−	0.779650i
$163$	2.06982	+	1.19501i	0.162121	+	0.0936004i	0.578865	−	0.815423i	$-0.303496\pi$
$163$	2.06982	+	1.19501i	0.162121	+	0.0936004i	−0.416745	+	0.909024i	$0.636829\pi$
$164$		−	20.8108i		−	1.62505i
$165$	0.0191432	−	0.0331569i	0.00149029	−	0.00258126i
$166$	−8.65026	−	14.9827i	−0.671391	−	1.16288i
$167$	6.44185	−	3.71920i	0.498485	−	0.287801i	−0.229603	−	0.973284i	$-0.573743\pi$
$167$	6.44185	−	3.71920i	0.498485	−	0.287801i	0.728088	+	0.685484i	$0.240409\pi$
$168$	0.114740			0.00885240
$169$		0			0
$170$	−7.39317			−0.567030
$171$	6.39144	−	3.69010i	0.488766	−	0.282189i
$172$	1.01021	+	1.74973i	0.0770274	+	0.133415i
$173$	1.27059	−	2.20073i	0.0966015	−	0.167319i	−0.813674	−	0.581321i	$-0.802536\pi$
$173$	1.27059	−	2.20073i	0.0966015	−	0.167319i	0.910276	+	0.414002i	$0.135869\pi$
$174$		−	0.237958i		−	0.0180396i
$175$	−3.99148	−	2.30448i	−0.301728	−	0.174203i
$176$	−3.86930	−	2.23394i	−0.291660	−	0.168390i
$177$		−	0.0696502i		−	0.00523523i
$178$	0.455265	−	0.788543i	0.0341236	−	0.0591038i
$179$	−5.34565	−	9.25894i	−0.399553	−	0.692045i	0.594118	−	0.804378i	$-0.297501\pi$
$179$	−5.34565	−	9.25894i	−0.399553	−	0.692045i	−0.993671	+	0.112332i	$0.964168\pi$
$180$	7.44175	−	4.29649i	0.554675	−	0.320242i
$181$	11.7908			0.876402			0.438201	−	0.898877i	$-0.355616\pi$
$181$	11.7908			0.876402			0.438201	+	0.898877i	$0.355616\pi$
$182$		0			0
$183$	−0.0250808			−0.00185403
$184$	−2.61439	+	1.50942i	−0.192736	+	0.111276i
$185$	−2.06458	−	3.57597i	−0.151791	−	0.262910i
$186$	0.140813	−	0.243895i	0.0103249	−	0.0178832i
$187$		−	9.82931i		−	0.718790i
$188$	−21.2678	−	12.2790i	−1.55111	−	0.895535i
$189$	0.312684	+	0.180528i	0.0227444	+	0.0131315i
$190$			5.42613i			0.393653i
$191$	−6.73731	+	11.6694i	−0.487495	+	0.844366i	−0.999897	−	0.0143798i	$-0.995423\pi$
$191$	−6.73731	+	11.6694i	−0.487495	+	0.844366i	0.512402	+	0.858746i	$0.328756\pi$
$192$	0.0834005	+	0.144454i	0.00601892	+	0.0104251i
$193$	−6.05124	+	3.49368i	−0.435578	+	0.251481i	−0.701720	−	0.712453i	$-0.747584\pi$
$193$	−6.05124	+	3.49368i	−0.435578	+	0.251481i	0.266142	+	0.963934i	$0.414251\pi$
$194$	7.46397			0.535882
$195$		0			0
$196$	40.7978			2.91413
$197$	1.24530	−	0.718974i	0.0887240	−	0.0512248i	−0.454982	−	0.890501i	$-0.650354\pi$
$197$	1.24530	−	0.718974i	0.0887240	−	0.0512248i	0.543706	+	0.839276i	$0.317021\pi$
$198$	9.70056	+	16.8019i	0.689389	+	1.19406i
$199$	−1.21426	+	2.10316i	−0.0860765	+	0.149089i	−0.905849	−	0.423600i	$-0.860766\pi$
$199$	−1.21426	+	2.10316i	−0.0860765	+	0.149089i	0.819773	+	0.572689i	$0.194100\pi$
$200$			1.90669i			0.134823i
$201$	−0.0825206	−	0.0476433i	−0.00582056	−	0.00336050i
$202$	−20.1383	−	11.6269i	−1.41693	−	0.818063i
$203$		−	38.0849i		−	2.67304i
$204$	−0.0626847	+	0.108573i	−0.00438881	+	0.00760164i
$205$	3.63254	+	6.29175i	0.253708	+	0.439435i
$206$	−26.9609	+	15.5659i	−1.87846	+	1.08453i
$207$	−4.74960			−0.330120
$208$		0			0
$209$	−7.21411			−0.499011
$210$	−0.114944	+	0.0663628i	−0.00793187	+	0.00457947i
$211$	−9.13202	−	15.8171i	−0.628674	−	1.08890i	−0.987818	−	0.155613i	$-0.950265\pi$
$211$	−9.13202	−	15.8171i	−0.628674	−	1.08890i	0.359144	−	0.933282i	$-0.383069\pi$
$212$	−17.8513	+	30.9194i	−1.22603	+	2.12355i
$213$			0.0872293i			0.00597685i
$214$	7.58612	+	4.37985i	0.518577	+	0.299400i
$215$	−0.610833	−	0.352665i	−0.0416585	−	0.0240515i
$216$		−	0.149366i		−	0.0101631i
$217$	22.5369	−	39.0351i	1.52990	−	2.64987i
$218$	11.2193	+	19.4324i	0.759867	+	1.31613i
$219$	−0.140824	+	0.0813048i	−0.00951600	+	0.00549407i
$220$	−8.39961			−0.566301
$221$		0			0
$222$	−0.118909			−0.00798063
$223$	13.4962	−	7.79204i	0.903773	−	0.521793i	0.0253505	−	0.999679i	$-0.491930\pi$
$223$	13.4962	−	7.79204i	0.903773	−	0.521793i	0.878422	+	0.477885i	$0.158596\pi$
$224$	16.5322	+	28.6346i	1.10460	+	1.91323i
$225$	−1.49991	+	2.59793i	−0.0999943	+	0.173195i
$226$		−	5.73409i		−	0.381426i
$227$	3.49338	+	2.01690i	0.231863	+	0.133866i	0.611431	−	0.791297i	$-0.290594\pi$
$227$	3.49338	+	2.01690i	0.231863	+	0.133866i	−0.379568	+	0.925164i	$0.623927\pi$
$228$	0.0796860	+	0.0460067i	0.00527733	+	0.00304687i
$229$		−	22.5147i		−	1.48781i	−0.668284	−	0.743906i	$-0.732971\pi$
$229$		−	22.5147i		−	1.48781i	0.668284	−	0.743906i	$-0.267029\pi$
$230$	1.74602	−	3.02419i	0.115129	−	0.199409i
$231$	−0.0882302	−	0.152819i	−0.00580512	−	0.0100548i
$232$	−13.6446	+	7.87770i	−0.895810	+	0.517196i
$233$	7.69759			0.504286			0.252143	−	0.967690i	$-0.418865\pi$
$233$	7.69759			0.504286			0.252143	+	0.967690i	$0.418865\pi$
$234$		0			0
$235$	8.57322			0.559255
$236$	−13.2333	+	7.64025i	−0.861414	+	0.497338i
$237$	0.00642936	+	0.0111360i	0.000417632	+	0.000723360i
$238$	−17.0374	+	29.5097i	−1.10437	+	1.91283i
$239$			18.7203i			1.21092i	0.795877	+	0.605459i	$0.207010\pi$
$239$			18.7203i			1.21092i	−0.795877	+	0.605459i	$0.792990\pi$
$240$	−0.0172287	−	0.00994701i	−0.00111211	−	0.000642077i
$241$	−19.5880	−	11.3091i	−1.26177	−	0.728486i	−0.288357	−	0.957523i	$-0.593109\pi$
$241$	−19.5880	−	11.3091i	−1.26177	−	0.728486i	−0.973418	+	0.229037i	$0.926442\pi$
$242$			5.29665i			0.340482i
$243$	0.176252	−	0.305277i	0.0113065	−	0.0195835i
$244$	2.75123	+	4.76527i	0.176130	+	0.305065i
$245$	−12.3344	+	7.12130i	−0.788019	+	0.454963i
$246$	0.209214			0.0133390
$247$		0			0
$248$	−18.6466			−1.18406
$249$	0.0886959	−	0.0512086i	0.00562087	−	0.00324521i
$250$	−1.10278	−	1.91007i	−0.0697459	−	0.120803i
$251$	0.892059	−	1.54509i	0.0563062	−	0.0975253i	−0.836498	−	0.547969i	$-0.815401\pi$
$251$	0.892059	−	1.54509i	0.0563062	−	0.0975253i	0.892805	+	0.450444i	$0.148734\pi$
$252$		−	39.6048i		−	2.49487i
$253$	4.02071	+	2.32136i	0.252780	+	0.145942i
$254$	38.1477	+	22.0246i	2.39360	+	1.38195i
$255$		−	0.0437667i		−	0.00274078i
$256$	2.47468	−	4.28627i	0.154667	−	0.267892i
$257$	−2.29924	−	3.98240i	−0.143422	−	0.248415i	0.785361	−	0.619038i	$-0.212477\pi$
$257$	−2.29924	−	3.98240i	−0.143422	−	0.248415i	−0.928783	+	0.370623i	$0.879144\pi$
$258$	−0.0175903	+	0.0101558i	−0.00109513	+	0.000632271i
$259$	−19.0312			−1.18254
$260$		0			0
$261$	−24.7883			−1.53435
$262$	−21.8511	+	12.6158i	−1.34997	+	0.779404i
$263$	−9.40637	−	16.2923i	−0.580022	−	1.00463i	−0.995476	−	0.0950132i	$-0.969711\pi$
$263$	−9.40637	−	16.2923i	−0.580022	−	1.00463i	0.415454	−	0.909614i	$-0.363623\pi$
$264$	−0.0365000	+	0.0632199i	−0.00224642	+	0.00389092i
$265$		−	12.4639i		−	0.765649i
$266$	21.6583	+	12.5044i	1.32796	+	0.766696i
$267$	0.00466808	+	0.00269512i	0.000285682	+	0.000164939i
$268$			20.9049i			1.27697i
$269$	−0.927060	+	1.60571i	−0.0565238	+	0.0979022i	−0.892903	−	0.450250i	$-0.851335\pi$
$269$	−0.927060	+	1.60571i	−0.0565238	+	0.0979022i	0.836379	+	0.548152i	$0.184668\pi$
$270$	0.0863893	+	0.149631i	0.00525748	+	0.00910623i
$271$	−0.129642	+	0.0748491i	−0.00787522	+	0.00454676i	−0.503932	−	0.863743i	$-0.668114\pi$
$271$	−0.129642	+	0.0748491i	−0.00787522	+	0.00454676i	0.496057	+	0.868290i	$0.334781\pi$
$272$	−5.10743			−0.309683
$273$		0			0
$274$	6.89281			0.416410
$275$	2.53946	−	1.46616i	0.153135	−	0.0884128i
$276$	−0.0296081	−	0.0512827i	−0.00178220	−	0.00308686i
$277$	11.0092	−	19.0685i	0.661478	−	1.14571i	−0.318749	−	0.947839i	$-0.603263\pi$
$277$	11.0092	−	19.0685i	0.661478	−	1.14571i	0.980227	−	0.197874i	$-0.0634038\pi$
$278$			13.4435i			0.806285i
$279$	−25.4067	−	14.6685i	−1.52106	−	0.878183i
$280$	7.61052	+	4.39394i	0.454815	+	0.262588i
$281$			0.438029i			0.0261306i	0.999915	+	0.0130653i	$0.00415894\pi$
$281$			0.438029i			0.0261306i	−0.999915	+	0.0130653i	$0.995841\pi$
$282$	0.123443	−	0.213809i	0.00735090	−	0.0127321i
$283$	6.91451	+	11.9763i	0.411025	+	0.711916i	0.995002	−	0.0998543i	$-0.0318377\pi$
$283$	6.91451	+	11.9763i	0.411025	+	0.711916i	−0.583977	+	0.811770i	$0.698504\pi$
$284$	16.5733	−	9.56859i	0.983443	−	0.567791i
$285$	−0.0321221			−0.00190275
$286$		0			0
$287$	33.4845			1.97653
$288$	18.6373	−	10.7603i	1.09822	−	0.634055i
$289$	2.88185	+	4.99151i	0.169520	+	0.293618i
$290$	9.11251	−	15.7833i	0.535105	−	0.926829i
$291$			0.0441858i			0.00259022i
$292$	30.8953	+	17.8374i	1.80801	+	1.04385i
$293$	12.6141	+	7.28278i	0.736926	+	0.425464i	0.820951	−	0.570999i	$-0.193444\pi$
$293$	12.6141	+	7.28278i	0.736926	+	0.425464i	−0.0840245	+	0.996464i	$0.526777\pi$
$294$			0.410148i			0.0239203i
$295$	2.66723	−	4.61977i	0.155292	−	0.268974i
$296$	3.93652	+	6.81825i	0.228806	+	0.396303i
$297$	−0.198936	+	0.114856i	−0.0115434	+	0.00666460i
$298$	32.2445			1.86787
$299$		0			0
$300$	−0.0374007			−0.00215933
$301$	−2.81531	+	1.62542i	−0.162272	+	0.0936877i
$302$	−13.5102	−	23.4003i	−0.777423	−	1.34654i
$303$	0.0688297	−	0.119217i	0.00395416	−	0.00684881i
$304$			3.74854i			0.214994i
$305$	−1.66357	−	0.960460i	−0.0952555	−	0.0549958i
$306$	19.2069	+	11.0891i	1.09799	+	0.633923i
$307$			9.05062i			0.516546i	0.966072	+	0.258273i	$0.0831535\pi$
$307$			9.05062i			0.516546i	−0.966072	+	0.258273i	$0.916847\pi$
$308$	−19.3568	+	33.5269i	−1.10295	+	1.91037i
$309$	−0.0921484	−	0.159606i	−0.00524214	−	0.00907965i
$310$	18.6797	−	10.7847i	1.06094	−	0.612531i
$311$	−7.28812			−0.413272			−0.206636	−	0.978418i	$-0.566252\pi$
$311$	−7.28812			−0.413272			−0.206636	+	0.978418i	$0.566252\pi$
$312$		0			0
$313$	12.9725			0.733250			0.366625	−	0.930369i	$-0.380513\pi$
$313$	12.9725			0.733250			0.366625	+	0.930369i	$0.380513\pi$
$314$	13.6377	−	7.87375i	0.769622	−	0.444342i
$315$	6.91306	+	11.9738i	0.389507	+	0.674646i
$316$	1.41053	−	2.44312i	0.0793487	−	0.137436i
$317$			15.5048i			0.870838i	0.900228	+	0.435419i	$0.143400\pi$
$317$			15.5048i			0.870838i	−0.900228	+	0.435419i	$0.856600\pi$
$318$	−0.310838	−	0.179462i	−0.0174309	−	0.0100638i
$319$	20.9841	+	12.1152i	1.17489	+	0.678321i
$320$			12.7752i			0.714154i
$321$	−0.0259282	+	0.0449090i	−0.00144717	+	0.00250658i
$322$	−8.04735	−	13.9384i	−0.448461	−	0.776758i
$323$	−7.14190	+	4.12338i	−0.397386	+	0.229431i
$324$	−25.7760			−1.43200
$325$		0			0
$326$	5.27133			0.291952
$327$	−0.115038	+	0.0664170i	−0.00636160	+	0.00367287i
$328$	−6.92613	−	11.9964i	−0.382431	−	0.662391i
$329$	19.7569	−	34.2199i	1.08923	−	1.88660i
$330$		−	0.0844427i		−	0.00464842i
$331$	−22.5906	−	13.0427i	−1.24169	−	0.716890i	−0.272252	−	0.962226i	$-0.587768\pi$
$331$	−22.5906	−	13.0427i	−1.24169	−	0.716890i	−0.969438	+	0.245336i	$0.921102\pi$
$332$	−19.4589	−	11.2346i	−1.06795	−	0.616580i
$333$			12.3868i			0.678793i
$334$	8.20292	−	14.2079i	0.448844	−	0.777420i
$335$	−3.64896	−	6.32019i	−0.199364	−	0.345309i
$336$	−0.0794067	+	0.0458455i	−0.00433199	+	0.00250108i
$337$	14.4785			0.788697			0.394348	−	0.918961i	$-0.370970\pi$
$337$	14.4785			0.788697			0.394348	+	0.918961i	$0.370970\pi$
$338$		0			0
$339$	0.0339452			0.00184365
$340$	−8.31553	+	4.80097i	−0.450973	+	0.260369i
$341$	14.3384	+	24.8349i	0.776470	+	1.34489i
$342$	8.13874	−	14.0967i	0.440092	−	0.762262i
$343$			33.3809i			1.80240i
$344$	1.16467	+	0.672422i	0.0627947	+	0.0362546i
$345$	0.0179029	+	0.0103362i	0.000963859	+	0.000556484i
$346$		−	5.60474i		−	0.301313i
$347$	−3.40706	+	5.90120i	−0.182901	+	0.316793i	−0.942867	−	0.333169i	$-0.891882\pi$
$347$	−3.40706	+	5.90120i	−0.182901	+	0.316793i	0.759967	+	0.649962i	$0.225215\pi$
$348$	−0.154525	−	0.267645i	−0.00828342	−	0.0143473i
$349$	29.2160	−	16.8679i	1.56390	−	0.902915i	0.567039	−	0.823691i	$-0.308089\pi$
$349$	29.2160	−	16.8679i	1.56390	−	0.902915i	0.996857	−	0.0792242i	$-0.0252443\pi$
$350$	−10.1654			−0.543361
$351$		0			0
$352$	−21.0362			−1.12123
$353$	−16.2133	+	9.36077i	−0.862948	+	0.498223i	−0.864998	−	0.501775i	$-0.832681\pi$
$353$	−16.2133	+	9.36077i	−0.862948	+	0.498223i	0.00205026	+	0.999998i	$0.499347\pi$
$354$	−0.0768088	−	0.133037i	−0.00408234	−	0.00707082i
$355$	−3.34041	+	5.78577i	−0.177291	+	0.307077i
$356$		−	1.18256i		−	0.0626756i
$357$	−0.174694	−	0.100860i	−0.00924579	−	0.00533806i
$358$	−20.4211	−	11.7901i	−1.07929	−	0.623129i
$359$			27.9262i			1.47389i	0.675952	+	0.736945i	$0.263732\pi$
$359$			27.9262i			1.47389i	−0.675952	+	0.736945i	$0.736268\pi$
$360$	2.85987	−	4.95344i	0.150728	−	0.261069i
$361$	−6.47369	−	11.2128i	−0.340721	−	0.590145i
$362$	22.5212	−	13.0026i	1.18369	−	0.683404i
$363$	−0.0313556			−0.00164574
$364$		0			0
$365$	−12.4541			−0.651880
$366$	−0.0479061	+	0.0276586i	−0.00250409	+	0.00144574i
$367$	−1.25494	−	2.17362i	−0.0655074	−	0.113462i	0.831412	−	0.555657i	$-0.187533\pi$
$367$	−1.25494	−	2.17362i	−0.0655074	−	0.113462i	−0.896919	+	0.442195i	$0.854200\pi$
$368$	1.20620	−	2.08921i	0.0628777	−	0.108907i
$369$		−	21.7940i		−	1.13455i
$370$	−7.88700	−	4.55356i	−0.410026	−	0.236729i
$371$	−49.7493	−	28.7228i	−2.58286	−	1.49121i
$372$		−	0.365763i		−	0.0189640i
$373$	−11.0890	+	19.2067i	−0.574165	+	0.994483i	0.421967	+	0.906611i	$0.361340\pi$
$373$	−11.0890	+	19.2067i	−0.574165	+	0.994483i	−0.996132	+	0.0878719i	$0.971993\pi$
$374$	−10.8396	−	18.7747i	−0.560501	−	0.970815i
$375$	0.0113074	−	0.00652833i	0.000583912	−	0.000337122i
$376$	−16.3465			−0.843005
$377$		0			0
$378$	0.796331			0.0409589
$379$	−1.23076	+	0.710581i	−0.0632200	+	0.0365001i	−0.531277	−	0.847198i	$-0.678288\pi$
$379$	−1.23076	+	0.710581i	−0.0632200	+	0.0365001i	0.468057	+	0.883698i	$0.344954\pi$
$380$	3.52362	+	6.10309i	0.180758	+	0.313082i
$381$	−0.130383	+	0.225830i	−0.00667973	+	0.0115696i
$382$			29.7191i			1.52056i
$383$	−18.2500	−	10.5366i	−0.932531	−	0.538397i	−0.0449197	−	0.998991i	$-0.514303\pi$
$383$	−18.2500	−	10.5366i	−0.932531	−	0.538397i	−0.887611	+	0.460594i	$0.847637\pi$
$384$	0.156365	+	0.0902774i	0.00797947	+	0.00460695i
$385$		−	13.5150i		−	0.688787i
$386$	−7.70553	+	13.3464i	−0.392201	+	0.679312i
$387$	1.05793	+	1.83240i	0.0537778	+	0.0931459i
$388$	8.39516	−	4.84695i	0.426200	−	0.246067i
$389$	−13.4713			−0.683021			−0.341511	−	0.939878i	$-0.610939\pi$
$389$	−13.4713			−0.683021			−0.341511	+	0.939878i	$0.610939\pi$
$390$		0			0
$391$	5.30728			0.268401
$392$	23.5180	−	13.5781i	1.18784	−	0.685798i
$393$	−0.0746839	−	0.129356i	−0.00376730	−	0.00652516i
$394$	1.58574	−	2.74658i	0.0798885	−	0.138371i
$395$			0.984840i			0.0495527i
$396$	21.8216	+	12.5987i	1.09658	+	0.633108i
$397$	23.5437	+	13.5929i	1.18162	+	0.682210i	0.956390	−	0.292094i	$-0.0943521\pi$
$397$	23.5437	+	13.5929i	1.18162	+	0.682210i	0.225234	+	0.974305i	$0.427685\pi$
$398$			5.35624i			0.268484i
$399$	−0.0740249	+	0.128215i	−0.00370588	+	0.00641877i
$400$	−0.761834	−	1.31954i	−0.0380917	−	0.0659768i
$401$	2.83641	−	1.63760i	0.141643	−	0.0817779i	−0.427504	−	0.904014i	$-0.640607\pi$
$401$	2.83641	−	1.63760i	0.141643	−	0.0817779i	0.569147	+	0.822236i	$0.307274\pi$
$402$	−0.210160			−0.0104818
$403$		0			0
$404$	−30.2010			−1.50256
$405$	7.79290	−	4.49923i	0.387232	−	0.223569i
$406$	−41.9993	−	72.7449i	−2.08439	−	3.61027i
$407$	6.05402	−	10.4859i	0.300087	−	0.519765i
$408$			0.0834495i			0.00413137i
$409$	16.5997	+	9.58386i	0.820804	+	0.473891i	0.850694	−	0.525662i	$-0.176182\pi$
$409$	16.5997	+	9.58386i	0.820804	+	0.473891i	−0.0298899	+	0.999553i	$0.509516\pi$
$410$	13.8768	+	8.01179i	0.685327	+	0.395674i
$411$			0.0408047i			0.00201275i
$412$	−20.2164	+	35.0158i	−0.995989	+	1.72510i
$413$	−12.2932	−	21.2924i	−0.604907	−	1.04773i
$414$	−9.07207	+	5.23776i	−0.445868	+	0.257422i
$415$	7.84405			0.385049
$416$		0			0
$417$	−0.0795837			−0.00389723
$418$	−13.7795	+	7.95558i	−0.673976	+	0.389120i
$419$	−0.196231	−	0.339883i	−0.00958653	−	0.0166044i	0.861192	−	0.508279i	$-0.169718\pi$
$419$	−0.196231	−	0.339883i	−0.00958653	−	0.0166044i	−0.870779	+	0.491675i	$0.836385\pi$
$420$	−0.0861894	+	0.149284i	−0.00420561	+	0.00728433i
$421$			35.1816i			1.71465i	0.514779	+	0.857323i	$0.327874\pi$
$421$			35.1816i			1.71465i	−0.514779	+	0.857323i	$0.672126\pi$
$422$	−34.8856	−	20.1412i	−1.69820	−	0.980458i
$423$	−22.2726	−	12.8591i	−1.08293	−	0.625231i
$424$			23.7647i			1.15412i
$425$	1.67603	−	2.90297i	0.0812994	−	0.140815i
$426$	0.0961947	+	0.166614i	0.00466065	+	0.00807248i
$427$	−7.66732	+	4.42673i	−0.371048	+	0.214225i
$428$	11.3768			0.549916
$429$		0			0
$430$	−1.55565			−0.0750199
$431$	1.96981	−	1.13727i	0.0948823	−	0.0547803i	−0.451808	−	0.892115i	$-0.649221\pi$
$431$	1.96981	−	1.13727i	0.0948823	−	0.0547803i	0.546690	+	0.837335i	$0.315887\pi$
$432$	0.0596804	+	0.103369i	0.00287137	+	0.00497337i
$433$	5.94137	−	10.2908i	0.285524	−	0.494542i	−0.687212	−	0.726457i	$-0.741166\pi$
$433$	5.94137	−	10.2908i	0.285524	−	0.494542i	0.972736	+	0.231915i	$0.0744990\pi$
$434$		−	99.4130i		−	4.77197i
$435$	0.0934356	+	0.0539450i	0.00447989	+	0.00258647i
$436$	25.2380	+	14.5712i	1.20868	+	0.697833i
$437$		−	3.89522i		−	0.186334i
$438$	−0.179322	+	0.310596i	−0.00856836	+	0.0148408i
$439$	−17.8636	−	30.9407i	−0.852585	−	1.47672i	−0.878867	−	0.477067i	$-0.841700\pi$
$439$	−17.8636	−	30.9407i	−0.852585	−	1.47672i	0.0262818	−	0.999655i	$-0.491633\pi$
$440$	−4.84197	+	2.79551i	−0.230832	+	0.133271i
$441$	42.7254			2.03454
$442$		0			0
$443$	4.98904			0.237036			0.118518	−	0.992952i	$-0.462186\pi$
$443$	4.98904			0.237036			0.118518	+	0.992952i	$0.462186\pi$
$444$	−0.133744	+	0.0772169i	−0.00634719	+	0.00366455i
$445$	0.206417	+	0.357525i	0.00978511	+	0.0169483i
$446$	17.1858	−	29.7667i	0.813771	−	1.40949i
$447$			0.190884i			0.00902849i
$448$	50.9919	+	29.4402i	2.40914	+	1.39092i
$449$	−20.3417	−	11.7443i	−0.959985	−	0.554248i	−0.0638165	−	0.997962i	$-0.520327\pi$
$449$	−20.3417	−	11.7443i	−0.959985	−	0.554248i	−0.896168	+	0.443714i	$0.853661\pi$
$450$			6.61630i			0.311895i
$451$	−10.6518	+	18.4494i	−0.501572	+	0.868749i
$452$	−3.72361	−	6.44947i	−0.175144	−	0.303358i
$453$	0.138527	−	0.0799787i	0.00650857	−	0.00375773i
$454$	8.89679			0.417547
$455$		0			0
$456$	0.0612468			0.00286815
$457$	34.8584	−	20.1255i	1.63061	−	0.941430i	0.646699	−	0.762746i	$-0.276149\pi$
$457$	34.8584	−	20.1255i	1.63061	−	0.941430i	0.983906	−	0.178685i	$-0.0571842\pi$
$458$	−24.8287	−	43.0046i	−1.16017	−	2.00947i
$459$	−0.131296	+	0.227412i	−0.00612839	+	0.0106147i
$460$		−	4.53532i		−	0.211460i
$461$	27.0321	+	15.6070i	1.25901	+	0.726890i	0.972882	−	0.231302i	$-0.0742985\pi$
$461$	27.0321	+	15.6070i	1.25901	+	0.726890i	0.286128	+	0.958191i	$0.407632\pi$
$462$	−0.337052	−	0.194597i	−0.0156811	−	0.00905347i
$463$			17.7491i			0.824872i	0.910987	+	0.412436i	$0.135322\pi$
$463$			17.7491i			0.824872i	−0.910987	+	0.412436i	$0.864678\pi$
$464$	6.29521	−	10.9036i	0.292248	−	0.506188i
$465$	0.0638444	+	0.110582i	0.00296071	+	0.00512810i
$466$	14.7029	−	8.48875i	0.681101	−	0.393234i
$467$	−26.6645			−1.23389			−0.616944	−	0.787007i	$-0.711630\pi$
$467$	−26.6645			−1.23389			−0.616944	+	0.787007i	$0.711630\pi$
$468$		0			0
$469$	−33.6359			−1.55316
$470$	16.3755	−	9.45437i	0.755344	−	0.436098i
$471$	0.0466117	+	0.0807339i	0.00214775	+	0.00372002i
$472$	−5.08557	+	8.80847i	−0.234082	+	0.405443i
$473$		−	2.06825i		−	0.0950983i
$474$	0.0245611	+	0.0141803i	0.00112813	+	0.000651325i
$475$	−2.13060	−	1.23010i	−0.0977587	−	0.0564410i
$476$			44.2551i			2.02843i
$477$	−18.6947	+	32.3802i	−0.855973	+	1.48259i
$478$	20.6444	+	35.7572i	0.944253	+	1.63549i
$479$	17.7215	−	10.2315i	0.809716	−	0.467490i	−0.0371410	−	0.999310i	$-0.511825\pi$
$479$	17.7215	−	10.2315i	0.809716	−	0.467490i	0.846857	+	0.531820i	$0.178492\pi$
$480$	−0.0936675			−0.00427531
$481$		0			0
$482$	−49.8860			−2.27224
$483$	0.0825139	−	0.0476394i	0.00375451	−	0.00216767i
$484$	3.43954	+	5.95746i	0.156343	+	0.270794i
$485$	−1.69208	+	2.93077i	−0.0768334	+	0.133079i
$486$		−	0.777467i		−	0.0352666i
$487$	7.03030	+	4.05895i	0.318573	+	0.183928i	0.650757	−	0.759286i	$-0.274452\pi$
$487$	7.03030	+	4.05895i	0.318573	+	0.183928i	−0.332183	+	0.943215i	$0.607785\pi$
$488$	3.17190	+	1.83130i	0.143585	+	0.0828990i
$489$			0.0312057i			0.00141117i
$490$	−15.7064	+	27.2044i	−0.709545	+	1.22897i
$491$	1.63498	+	2.83187i	0.0737857	+	0.127801i	0.900558	−	0.434737i	$-0.143159\pi$
$491$	1.63498	+	2.83187i	0.0737857	+	0.127801i	−0.826772	+	0.562537i	$0.809825\pi$
$492$	0.235316	−	0.135860i	0.0106089	−	0.00612503i
$493$	27.6988			1.24749
$494$		0			0
$495$	−8.79646			−0.395371
$496$	12.9045	−	7.45042i	0.579430	−	0.334534i
$497$	15.3959	+	26.6664i	0.690599	+	1.19615i
$498$	0.112944	−	0.195624i	0.00506112	−	0.00876612i
$499$		−	8.89340i		−	0.398123i	−0.979987	−	0.199062i	$-0.936211\pi$
$499$		−	8.89340i		−	0.398123i	0.979987	−	0.199062i	$-0.0637894\pi$
$500$	−2.48072	−	1.43225i	−0.110941	−	0.0640520i
$501$	0.0841090	+	0.0485604i	0.00375771	+	0.00216952i
$502$		−	3.93498i		−	0.175627i
$503$	11.8987	−	20.6092i	0.530537	−	0.918917i	−0.468828	−	0.883289i	$-0.655324\pi$
$503$	11.8987	−	20.6092i	0.530537	−	0.918917i	0.999365	−	0.0356275i	$-0.0113430\pi$
$504$	−13.1811	−	22.8303i	−0.587131	−	1.01694i
$505$	9.13071	−	5.27162i	0.406311	−	0.234584i
$506$	10.2398			0.455213
$507$		0			0
$508$	57.2093			2.53825
$509$	1.09786	−	0.633850i	0.0486618	−	0.0280949i	−0.475472	−	0.879731i	$-0.657723\pi$
$509$	1.09786	−	0.633850i	0.0486618	−	0.0280949i	0.524134	+	0.851636i	$0.324389\pi$
$510$	−0.0482650	−	0.0835975i	−0.00213721	−	0.00370176i
$511$	−28.7004	+	49.7105i	−1.26963	+	2.19906i
$512$			16.7410i			0.739855i
$513$	0.166907	+	0.0963635i	0.00736910	+	0.00425455i
$514$	−8.78341	−	5.07110i	−0.387420	−	0.223677i
$515$		−	14.1152i		−	0.621988i
$516$	−0.0131899	+	0.0228456i	−0.000580653	+	0.00100572i
$517$	12.5697	+	21.7714i	0.552815	+	0.957504i
$518$	−36.3510	+	20.9872i	−1.59717	+	0.922126i
$519$	0.0331794			0.00145642
$520$		0			0
$521$	14.3916			0.630506			0.315253	−	0.949008i	$-0.397911\pi$
$521$	14.3916			0.630506			0.315253	+	0.949008i	$0.397911\pi$
$522$	−47.3473	+	27.3360i	−2.07234	+	1.19646i
$523$	−9.50927	−	16.4705i	−0.415811	−	0.720206i	0.579702	−	0.814829i	$-0.303169\pi$
$523$	−9.50927	−	16.4705i	−0.415811	−	0.720206i	−0.995513	+	0.0946225i	$0.969836\pi$
$524$	−16.3848	+	28.3794i	−0.715775	+	1.23976i
$525$		−	0.0601778i		−	0.00262637i
$526$	−35.9337	−	20.7463i	−1.56678	−	0.904582i
$527$	28.3898	+	16.3909i	1.23668	+	0.713998i
$528$		−	0.0583357i		−	0.00253873i
$529$	10.2466	−	17.7476i	0.445504	−	0.771636i
$530$	−13.7449	−	23.8069i	−0.597040	−	1.03410i
$531$	−13.8585	+	8.00122i	−0.601409	+	0.347224i
$532$	32.4805			1.40821
$533$		0			0
$534$	0.0118885			0.000514465
$535$	−3.43955	+	1.98582i	−0.148705	+	0.0858546i
$536$	6.95744	+	12.0506i	0.300516	+	0.520508i
$537$	0.0697963	−	0.120891i	0.00301193	−	0.00521682i
$538$			4.08937i			0.176305i
$539$	−36.1685	−	20.8819i	−1.55789	−	0.899448i
$540$	0.194334	+	0.112199i	0.00836282	+	0.00482827i
$541$		−	13.8969i		−	0.597475i	−0.954335	−	0.298738i	$-0.903434\pi$
$541$		−	13.8969i		−	0.597475i	0.954335	−	0.298738i	$-0.0965656\pi$
$542$	−0.165084	+	0.285934i	−0.00709097	+	0.0122819i
$543$	0.0769742	+	0.133323i	0.00330328	+	0.00572145i
$544$	−20.8257	+	12.0237i	−0.892893	+	0.515512i
$545$	−10.1737			−0.435792
$546$		0			0
$547$	37.0840			1.58560			0.792798	−	0.609484i	$-0.208623\pi$
$547$	37.0840			1.58560			0.792798	+	0.609484i	$0.208623\pi$
$548$	7.75275	−	4.47605i	0.331181	−	0.191208i
$549$	2.88122	+	4.99041i	0.122967	+	0.212986i
$550$	3.23370	−	5.60094i	0.137886	−	0.238825i
$551$		−	20.3292i		−	0.866054i
$552$	−0.0341352	−	0.0197080i	−0.00145289	−	0.000838828i
$553$	3.93097	+	2.26955i	0.167162	+	0.0965110i
$554$		−	48.5628i		−	2.06324i
$555$	0.0269566	−	0.0466902i	0.00114424	−	0.00198189i
$556$	8.72991	+	15.1206i	0.370231	+	0.641258i
$557$	−27.5452	+	15.9033i	−1.16713	+	0.673842i	−0.953002	−	0.302963i	$-0.902024\pi$
$557$	−27.5452	+	15.9033i	−1.16713	+	0.673842i	−0.214127	+	0.976806i	$0.568691\pi$
$558$	−64.7047			−2.73917
$559$		0			0
$560$	−7.02254			−0.296757
$561$	0.111144	−	0.0641690i	0.00469250	−	0.00270922i
$562$	0.483050	+	0.836667i	0.0203762	+	0.0352927i
$563$	13.1798	−	22.8280i	0.555461	−	0.962086i	−0.442407	−	0.896814i	$-0.645875\pi$
$563$	13.1798	−	22.8280i	0.555461	−	0.962086i	0.997868	−	0.0652715i	$-0.0207913\pi$
$564$		−	0.320645i		−	0.0135016i
$565$	2.25152	+	1.29992i	0.0947223	+	0.0546880i
$566$	26.4144	+	15.2504i	1.11028	+	0.641020i
$567$		−	41.4736i		−	1.74173i
$568$	6.36913	−	11.0317i	0.267243	−	0.462878i
$569$	8.89230	+	15.4019i	0.372785	+	0.645682i	0.989993	−	0.141118i	$-0.0450697\pi$
$569$	8.89230	+	15.4019i	0.372785	+	0.645682i	−0.617208	+	0.786800i	$0.711736\pi$
$570$	−0.0613555	+	0.0354236i	−0.00256990	+	0.00148373i
$571$	−19.6399			−0.821903			−0.410952	−	0.911657i	$-0.634804\pi$
$571$	−19.6399			−0.821903			−0.410952	+	0.911657i	$0.634804\pi$
$572$		0			0
$573$	−0.175934			−0.00734974
$574$	63.9578	−	36.9261i	2.66955	−	1.54126i
$575$	0.791645	+	1.37117i	0.0330139	+	0.0571817i
$576$	19.1617	−	33.1890i	0.798403	−	1.38287i
$577$			18.1454i			0.755403i	0.925927	+	0.377701i	$0.123285\pi$
$577$			18.1454i			0.755403i	−0.925927	+	0.377701i	$0.876715\pi$
$578$	11.0091	+	6.35609i	0.457917	+	0.264378i
$579$	−0.0790090	−	0.0456159i	−0.00328350	−	0.00189573i
$580$		−	23.6699i		−	0.982840i
$581$	18.0765	−	31.3094i	0.749940	−	1.29893i
$582$	0.0487273	+	0.0843981i	0.00201981	+	0.00349841i
$583$	31.6515	−	18.2740i	1.31087	−	0.756832i
$584$	23.7462			0.982624
$585$		0			0
$586$	32.1252			1.32708
$587$	−0.367059	+	0.211922i	−0.0151501	+	0.00874694i	−0.507556	−	0.861619i	$-0.669451\pi$
$587$	−0.367059	+	0.211922i	−0.0151501	+	0.00874694i	0.492406	+	0.870366i	$0.336118\pi$
$588$	0.266342	+	0.461317i	0.0109837	+	0.0190244i
$589$	12.0299	−	20.8364i	0.495683	−	0.858549i
$590$		−	11.7655i		−	0.484376i
$591$	0.0162595	+	0.00938741i	0.000668825	+	0.000386146i
$592$	−5.44859	−	3.14574i	−0.223936	−	0.129289i
$593$			47.5064i			1.95085i	0.220327	+	0.975426i	$0.429288\pi$
$593$			47.5064i			1.95085i	−0.220327	+	0.975426i	$0.570712\pi$
$594$	−0.253321	+	0.438765i	−0.0103939	+	0.0180027i
$595$	−7.72477	−	13.3797i	−0.316685	−	0.548514i
$596$	36.2673	−	20.9389i	1.48557	−	0.857692i
$597$	−0.0317083			−0.00129774
$598$		0			0
$599$	25.7871			1.05363			0.526816	−	0.849979i	$-0.323386\pi$
$599$	25.7871			1.05363			0.526816	+	0.849979i	$0.323386\pi$
$600$	−0.0215597	+	0.0124475i	−0.000880171	+	0.000508167i
$601$	6.33880	+	10.9791i	0.258565	+	0.447848i	0.965858	−	0.259073i	$-0.0834171\pi$
$601$	6.33880	+	10.9791i	0.258565	+	0.447848i	−0.707293	+	0.706921i	$0.750084\pi$
$602$	−3.58496	+	6.20934i	−0.146112	+	0.253074i
$603$			21.8925i			0.891533i
$604$	−30.3914	−	17.5465i	−1.23661	−	0.713955i
$605$	−2.07976	−	1.20075i	−0.0845543	−	0.0488175i
$606$		−	0.303616i		−	0.0123336i
$607$	2.20224	−	3.81439i	0.0893862	−	0.154821i	−0.817866	−	0.575409i	$-0.804843\pi$
$607$	2.20224	−	3.81439i	0.0893862	−	0.154821i	0.907252	+	0.420588i	$0.138176\pi$
$608$	8.82466	+	15.2848i	0.357887	+	0.619879i
$609$	0.430642	−	0.248631i	0.0174505	−	0.0100750i
$610$	−4.23670			−0.171539
$611$		0			0
$612$	28.8042			1.16434
$613$	−28.8905	+	16.6799i	−1.16688	+	0.673696i	−0.952942	−	0.303152i	$-0.901961\pi$
$613$	−28.8905	+	16.6799i	−1.16688	+	0.673696i	−0.213934	+	0.976848i	$0.568628\pi$
$614$	9.98084	+	17.2873i	0.402794	+	0.697660i
$615$	−0.0474289	+	0.0821492i	−0.00191252	+	0.00331258i
$616$			25.7688i			1.03826i
$617$	28.1921	+	16.2767i	1.13497	+	0.655277i	0.945181	−	0.326547i	$-0.105885\pi$
$617$	28.1921	+	16.2767i	1.13497	+	0.655277i	0.189792	+	0.981824i	$0.439219\pi$
$618$	−0.352020	−	0.203239i	−0.0141603	−	0.00817546i
$619$			35.5813i			1.43013i	0.699056	+	0.715067i	$0.253604\pi$
$619$			35.5813i			1.43013i	−0.699056	+	0.715067i	$0.746396\pi$
$620$	14.0068	−	24.2604i	0.562526	−	0.974323i
$621$	−0.0620157	−	0.107414i	−0.00248860	−	0.00431039i
$622$	−13.9208	+	8.03719i	−0.558174	+	0.322262i
$623$	1.90274			0.0762317
$624$		0			0
$625$	1.00000			0.0400000
$626$	24.7784	−	14.3058i	0.990344	−	0.571776i
$627$	−0.0470961	−	0.0815729i	−0.00188084	−	0.00325771i
$628$	10.2261	−	17.7121i	0.408066	−	0.706792i
$629$		−	13.8412i		−	0.551886i
$630$	26.4089	+	15.2472i	1.05215	+	0.607462i
$631$	22.0072	+	12.7058i	0.876091	+	0.505812i	0.869368	−	0.494166i	$-0.164526\pi$
$631$	22.0072	+	12.7058i	0.876091	+	0.505812i	0.00672365	+	0.999977i	$0.497860\pi$
$632$		−	1.87778i		−	0.0746942i
$633$	0.119234	−	0.206519i	0.00473911	−	0.00820838i
$634$	17.0984	+	29.6153i	0.679064	+	1.17617i
$635$	−17.2962	+	9.98595i	−0.686377	+	0.396280i
$636$	−0.466157			−0.0184843
$637$		0			0
$638$	53.4416			2.11577
$639$	17.3563	−	10.0207i	0.686605	−	0.396412i
$640$	6.91428	+	11.9759i	0.273311	+	0.473388i
$641$	−5.07393	+	8.78831i	−0.200408	+	0.347117i	−0.948660	−	0.316298i	$-0.897560\pi$
$641$	−5.07393	+	8.78831i	−0.200408	+	0.347117i	0.748252	+	0.663415i	$0.230894\pi$
$642$			0.114372i			0.00451392i
$643$	−1.60595	−	0.927193i	−0.0633323	−	0.0365649i	0.467999	−	0.883729i	$-0.344975\pi$
$643$	−1.60595	−	0.927193i	−0.0633323	−	0.0365649i	−0.531332	+	0.847164i	$0.678308\pi$
$644$	−18.1027	−	10.4516i	−0.713345	−	0.411850i
$645$		−	0.00920925i		−	0.000362614i
$646$	−9.09436	+	15.7519i	−0.357813	+	0.619750i
$647$	−14.8017	−	25.6373i	−0.581914	−	1.00790i	−0.995252	−	0.0973272i	$-0.968971\pi$
$647$	−14.8017	−	25.6373i	−0.581914	−	1.00790i	0.413338	−	0.910577i	$-0.364363\pi$
$648$	−14.8586	+	8.57864i	−0.583702	+	0.337001i
$649$	15.6423			0.614015
$650$		0			0
$651$	0.588514			0.0230657
$652$	5.92898	−	3.42310i	0.232197	−	0.134059i
$653$	−3.39441	−	5.87929i	−0.132834	−	0.230075i	0.791934	−	0.610606i	$-0.209074\pi$
$653$	−3.39441	−	5.87929i	−0.132834	−	0.230075i	−0.924768	+	0.380532i	$0.875741\pi$
$654$	−0.146487	+	0.253722i	−0.00572808	+	0.00992133i
$655$		−	11.4400i		−	0.446996i
$656$	9.58654	+	5.53479i	0.374291	+	0.216097i
$657$	32.3550	+	18.6802i	1.26229	+	0.728782i
$658$		−	87.1498i		−	3.39745i
$659$	−3.97479	+	6.88455i	−0.154836	+	0.268184i	−0.932999	−	0.359878i	$-0.882818\pi$
$659$	−3.97479	+	6.88455i	−0.154836	+	0.268184i	0.778163	+	0.628062i	$0.216152\pi$
$660$	−0.0548354	−	0.0949777i	−0.00213447	−	0.00369700i
$661$	−34.9728	+	20.1916i	−1.36029	+	0.785361i	−0.989662	−	0.143422i	$-0.954189\pi$
$661$	−34.9728	+	20.1916i	−1.36029	+	0.785361i	−0.370624	+	0.928783i	$0.620856\pi$
$662$	−57.5328			−2.23607
$663$		0			0
$664$	−14.9562			−0.580412
$665$	−9.81988	+	5.66951i	−0.380798	+	0.219854i
$666$	13.6599	+	23.6597i	0.529311	+	0.916794i
$667$	−6.54154	+	11.3303i	−0.253289	+	0.438710i
$668$		−	21.3073i		−	0.824402i
$669$	0.176215	+	0.101738i	0.00681288	+	0.00393342i
$670$	−13.9396	−	8.04801i	−0.538532	−	0.310922i
$671$		−	5.63275i		−	0.217450i
$672$	−0.215855	+	0.373872i	−0.00832680	+	0.0144224i
$673$	4.81960	+	8.34779i	0.185782	+	0.321784i	0.943840	−	0.330404i	$-0.107185\pi$
$673$	4.81960	+	8.34779i	0.185782	+	0.321784i	−0.758058	+	0.652187i	$0.773852\pi$
$674$	27.6550	−	15.9666i	1.06523	−	0.615012i
$675$	−0.0783378			−0.00301522
$676$		0			0
$677$	51.1565			1.96610			0.983051	−	0.183330i	$-0.0586878\pi$
$677$	51.1565			1.96610			0.983051	+	0.183330i	$0.0586878\pi$
$678$	0.0648377	−	0.0374341i	0.00249008	−	0.00143765i
$679$	7.79875	+	13.5078i	0.299288	+	0.518383i
$680$	−3.19567	+	5.53506i	−0.122548	+	0.212260i
$681$			0.0526680i			0.00201824i
$682$	54.7748	+	31.6243i	2.09744	+	1.21096i
$683$	−7.22700	−	4.17251i	−0.276533	−	0.159657i	0.355320	−	0.934745i	$-0.384372\pi$
$683$	−7.22700	−	4.17251i	−0.276533	−	0.159657i	−0.631853	+	0.775088i	$0.717705\pi$
$684$		−	21.1405i		−	0.808328i
$685$	−1.56260	+	2.70650i	−0.0597039	+	0.103410i
$686$	36.8118	+	63.7599i	1.40548	+	2.43436i
$687$	0.254583	−	0.146983i	0.00971293	−	0.00560776i
$688$	−1.07469			−0.0409721
$689$		0			0
$690$	0.0455944			0.00173575
$691$	−31.2846	+	18.0622i	−1.19012	+	0.687117i	−0.958334	−	0.285649i	$-0.907791\pi$
$691$	−31.2846	+	18.0622i	−1.19012	+	0.687117i	−0.231788	+	0.972766i	$0.574457\pi$
$692$	−3.63961	−	6.30398i	−0.138357	−	0.239641i
$693$	−20.2713	+	35.1109i	−0.770043	+	1.33375i
$694$			15.0289i			0.570491i
$695$	−5.27865	−	3.04763i	−0.200231	−	0.115603i
$696$	−0.178153	−	0.102856i	−0.00675286	−	0.00389876i
$697$			24.3530i			0.922435i
$698$	37.2030	−	64.4376i	1.40816	−	2.43900i
$699$	0.0502524	+	0.0870398i	0.00190072	+	0.00329215i
$700$	−11.4336	+	6.60118i	−0.432149	+	0.249501i
$701$	45.9823			1.73673			0.868364	−	0.495928i	$-0.165172\pi$
$701$	45.9823			1.73673			0.868364	+	0.495928i	$0.165172\pi$
$702$		0			0
$703$	−10.1586			−0.383139
$704$	−32.4421	+	18.7304i	−1.22271	+	0.705930i
$705$	0.0559688	+	0.0969409i	0.00210791	+	0.00365100i
$706$	−20.6457	+	35.7595i	−0.777012	+	1.34582i
$707$		−	48.5934i		−	1.82754i
$708$	−0.172783	−	0.0997562i	−0.00649357	−	0.00374907i
$709$	32.9912	+	19.0475i	1.23901	+	0.715343i	0.968892	−	0.247484i	$-0.0796039\pi$
$709$	32.9912	+	19.0475i	1.23901	+	0.715343i	0.270118	+	0.962827i	$0.412937\pi$
$710$			14.7350i			0.552993i
$711$	1.47718	−	2.55854i	0.0553984	−	0.0959529i
$712$	−0.393573	−	0.681689i	−0.0147498	−	0.0255474i
$713$	−13.4095	+	7.74196i	−0.502188	+	0.289939i
$714$	−0.444904			−0.0166501
$715$		0			0
$716$	−30.6251			−1.14452
$717$	−0.211678	+	0.122213i	−0.00790527	+	0.00456411i
$718$	30.7965	+	53.3411i	1.14931	+	1.99067i
$719$	−13.9336	+	24.1337i	−0.519635	+	0.900035i	0.480104	+	0.877212i	$0.340599\pi$
$719$	−13.9336	+	24.1337i	−0.519635	+	0.900035i	−0.999740	+	0.0228234i	$0.992734\pi$
$720$			4.57075i			0.170342i
$721$	−56.3404	−	32.5281i	−2.09823	−	1.21141i
$722$	−24.7304	−	14.2781i	−0.920371	−	0.531376i
$723$		−	0.295319i		−	0.0109830i
$724$	16.8873	−	29.2497i	0.627612	−	1.08706i
$725$	4.13161	+	7.15616i	0.153444	+	0.265773i
$726$	−0.0598914	+	0.0345783i	−0.00222278	+	0.00128332i
$727$	13.7750			0.510885			0.255443	−	0.966824i	$-0.417779\pi$
$727$	13.7750			0.510885			0.255443	+	0.966824i	$0.417779\pi$
$728$		0			0
$729$	−26.9908			−0.999659
$730$	−23.7883	+	13.7342i	−0.880444	+	0.508325i
$731$	−1.18215	−	2.04755i	−0.0437235	−	0.0757313i
$732$	−0.0359219	+	0.0622185i	−0.00132771	+	0.00229966i
$733$		−	6.58392i		−	0.243183i	−0.992580	−	0.121591i	$-0.961200\pi$
$733$		−	6.58392i		−	0.243183i	0.992580	−	0.121591i	$-0.0387997\pi$
$734$	−4.79406	−	2.76785i	−0.176952	−	0.102163i
$735$	−0.161047	−	0.0929804i	−0.00594030	−	0.00342963i
$736$		−	11.3584i		−	0.418676i
$737$	10.6999	−	18.5328i	0.394137	−	0.682665i
$738$	−24.0340	−	41.6281i	−0.884704	−	1.53235i
$739$	−4.74150	+	2.73750i	−0.174419	+	0.100701i	−0.584668	−	0.811273i	$-0.698775\pi$
$739$	−4.74150	+	2.73750i	−0.174419	+	0.100701i	0.410249	+	0.911974i	$0.365442\pi$
$740$	−11.8280			−0.434805
$741$		0			0
$742$	−126.700			−4.65129
$743$	−23.0981	+	13.3357i	−0.847387	+	0.489239i	−0.859769	−	0.510684i	$-0.829392\pi$
$743$	−23.0981	+	13.3357i	−0.847387	+	0.489239i	0.0123810	+	0.999923i	$0.496059\pi$
$744$	−0.121731	−	0.210845i	−0.00446289	−	0.00772995i
$745$	−7.30982	+	12.6610i	−0.267811	+	0.463862i
$746$			48.9148i			1.79090i
$747$	−20.3783	−	11.7654i	−0.745603	−	0.430474i
$748$	−24.3838	−	14.0780i	−0.891560	−	0.514742i
$749$			18.3052i			0.668857i
$750$	0.0143986	−	0.0249391i	0.000525763	−	0.000910649i
$751$	10.9034	+	18.8852i	0.397870	+	0.689131i	0.993463	−	0.114156i	$-0.0364162\pi$
$751$	10.9034	+	18.8852i	0.397870	+	0.689131i	−0.595593	+	0.803286i	$0.703083\pi$
$752$	11.3127	−	6.53137i	0.412531	−	0.238175i
$753$	0.0232946			0.000848903
$754$		0			0
$755$	12.2510			0.445860
$756$	0.895681	−	0.517121i	0.0325756	−	0.0188075i
$757$	4.16711	+	7.21764i	0.151456	+	0.262330i	0.931763	−	0.363067i	$-0.118270\pi$
$757$	4.16711	+	7.21764i	0.151456	+	0.262330i	−0.780307	+	0.625397i	$0.784937\pi$
$758$	−1.56723	+	2.71452i	−0.0569243	+	0.0985957i
$759$			0.0606183i			0.00220031i
$760$	4.06239	+	2.34542i	0.147359	+	0.0850775i
$761$	−6.34880	−	3.66548i	−0.230144	−	0.132874i	0.380495	−	0.924783i	$-0.375754\pi$
$761$	−6.34880	−	3.66548i	−0.230144	−	0.132874i	−0.610638	+	0.791910i	$0.709087\pi$
$762$			0.575135i			0.0208350i
$763$	−23.4450	+	40.6080i	−0.848767	+	1.47011i
$764$	19.2990	+	33.4268i	0.698213	+	1.20934i
$765$	−8.70841	+	5.02780i	−0.314853	+	0.181781i
$766$	−46.4783			−1.67933
$767$		0			0
$768$	0.0646221			0.00233185
$769$	−19.3423	+	11.1673i	−0.697503	+	0.402703i	−0.806417	−	0.591348i	$-0.798596\pi$
$769$	−19.3423	+	11.1673i	−0.697503	+	0.402703i	0.108914	+	0.994051i	$0.465263\pi$
$770$	−14.9040	−	25.8145i	−0.537104	−	0.930292i
$771$	0.0300204	−	0.0519968i	0.00108116	−	0.00187262i
$772$			20.0153i			0.720365i
$773$	23.5204	+	13.5795i	0.845971	+	0.488422i	0.859290	−	0.511490i	$-0.170906\pi$
$773$	23.5204	+	13.5795i	0.845971	+	0.488422i	−0.0133182	+	0.999911i	$0.504239\pi$
$774$	4.04146	+	2.33334i	0.145267	+	0.0838700i
$775$			9.77959i			0.351293i
$776$	3.22627	−	5.58806i	0.115816	−	0.200600i
$777$	−0.124242	−	0.215194i	−0.00445716	−	0.00772003i
$778$	−25.7311	+	14.8559i	−0.922505	+	0.532608i
$779$	17.8736			0.640388
$780$		0			0
$781$	−19.5903			−0.700997
$782$	10.1373	−	5.85276i	0.362508	−	0.209294i
$783$	−0.323661	−	0.560597i	−0.0115667	−	0.0200341i
$784$	−10.8505	+	18.7936i	−0.387518	+	0.671201i
$785$			7.13991i			0.254834i
$786$	−0.285303	−	0.164720i	−0.0101764	−	0.00587536i
$787$	10.0291	+	5.79032i	0.357500	+	0.206403i	0.667983	−	0.744176i	$-0.267158\pi$
$787$	10.0291	+	5.79032i	0.357500	+	0.206403i	−0.310484	+	0.950579i	$0.600491\pi$
$788$		−	4.11899i		−	0.146733i
$789$	0.122816	−	0.212723i	0.00437236	−	0.00757315i
$790$	1.08606	+	1.88111i	0.0386403	+	0.0669270i
$791$	10.3772	−	5.99128i	0.368971	−	0.213025i
$792$	16.7721			0.595971
$793$		0			0
$794$	59.9601			2.12790
$795$	0.140934	−	0.0813682i	0.00499841	−	0.00288583i
$796$	3.47824	+	6.02448i	0.123283	+	0.213532i
$797$	−23.8502	+	41.3097i	−0.844817	+	1.46327i	0.0409626	+	0.999161i	$0.486958\pi$
$797$	−23.8502	+	41.3097i	−0.844817	+	1.46327i	−0.885780	+	0.464106i	$0.846376\pi$
$798$			0.326532i			0.0115591i
$799$	24.8878	+	14.3690i	0.880467	+	0.508338i
$800$	−6.21280	−	3.58696i	−0.219656	−	0.126818i
$801$		−	1.23843i		−	0.0437579i
$802$	3.61183	−	6.25587i	0.127538	−	0.220902i
$803$	−18.2598	−	31.6268i	−0.644373	−	1.11609i
$804$	−0.236380	+	0.136474i	−0.00833647	+	0.00481306i
$805$	7.29733			0.257197
$806$		0			0
$807$	−0.0242086			−0.000852184
$808$	−17.4094	+	10.0513i	−0.612461	+	0.353605i
$809$	−18.1955	−	31.5155i	−0.639720	−	1.10803i	−0.985494	−	0.169709i	$-0.945717\pi$
$809$	−18.1955	−	31.5155i	−0.639720	−	1.10803i	0.345774	−	0.938318i	$-0.387616\pi$
$810$	9.92333	−	17.1877i	0.348670	−	0.603914i
$811$		−	36.8088i		−	1.29253i	−0.763112	−	0.646266i	$-0.776330\pi$
$811$		−	36.8088i		−	1.29253i	0.763112	−	0.646266i	$-0.223670\pi$
$812$	−94.4782	−	54.5470i	−3.31553	−	1.91422i
$813$	−0.00169270		0.000977280i	−5.93655e−5		3.42747e-5i
$814$		−	26.7050i		−	0.936010i
$815$	−1.19501	+	2.06982i	−0.0418594	+	0.0725026i
$816$	−0.0333430	−	0.0577517i	−0.00116724	−	0.00202172i
$817$	−1.50278	+	0.867628i	−0.0525755	+	0.0303545i
$818$	42.2755			1.47813
$819$		0			0
$820$	20.8108			0.726744
$821$	29.1563	−	16.8334i	1.01756	−	0.587491i	0.104166	−	0.994560i	$-0.466783\pi$
$821$	29.1563	−	16.8334i	1.01756	−	0.587491i	0.913397	+	0.407069i	$0.133449\pi$
$822$	0.0449986	+	0.0779398i	0.00156951	+	0.00271846i
$823$	15.9404	−	27.6096i	0.555649	−	0.962412i	−0.442204	−	0.896914i	$-0.645803\pi$
$823$	15.9404	−	27.6096i	0.555649	−	0.962412i	0.997853	−	0.0654973i	$-0.0208634\pi$
$824$			26.9132i			0.937566i
$825$	0.0331569	+	0.0191432i	0.00115438	+	0.000666479i
$826$	−46.9616	−	27.1133i	−1.63400	−	0.943392i
$827$			18.4625i			0.642003i	0.947079	+	0.321002i	$0.104019\pi$
$827$			18.4625i			0.642003i	−0.947079	+	0.321002i	$0.895981\pi$
$828$	−6.80259	+	11.7824i	−0.236406	+	0.409468i
$829$	−17.4831	−	30.2817i	−0.607214	−	1.05173i	−0.991697	−	0.128594i	$-0.958954\pi$
$829$	−17.4831	−	30.2817i	−0.607214	−	1.05173i	0.384483	−	0.923132i	$-0.374380\pi$
$830$	14.9827	−	8.65026i	0.520057	−	0.300255i
$831$	0.287487			0.00997280
$832$		0			0
$833$	−47.7420			−1.65416
$834$	−0.152011	+	0.0877633i	−0.00526369	+	0.00303900i
$835$	3.71920	+	6.44185i	0.128708	+	0.222929i
$836$	−10.3324	+	17.8962i	−0.357353	+	0.618954i
$837$		−	0.766111i		−	0.0264807i
$838$	−0.749632	−	0.432800i	−0.0258956	−	0.0149508i
$839$	−24.8752	−	14.3617i	−0.858786	−	0.495820i	0.00481947	−	0.999988i	$-0.498466\pi$
$839$	−24.8752	−	14.3617i	−0.858786	−	0.495820i	−0.863606	+	0.504168i	$0.831799\pi$
$840$			0.114740i			0.00395892i
$841$	−19.6404	+	34.0182i	−0.677256	+	1.17304i
$842$	38.7975	+	67.1993i	1.33705	+	2.31584i
$843$	−0.00495297	+	0.00285960i	−0.000170589	+	9.84899e-5i
$844$	−52.3172			−1.80083
$845$		0			0
$846$	−56.7230			−1.95018
$847$	−9.58555	+	5.53422i	−0.329364	+	0.190158i
$848$	−9.49540	−	16.4465i	−0.326073	−	0.564776i
$849$	−0.0902804	+	0.156370i	−0.00309841	+	0.00536661i
$850$		−	7.39317i		−	0.253584i
$851$	5.66179	+	3.26884i	0.194084	+	0.112054i
$852$	0.216392	+	0.124934i	0.00741346	+	0.00428016i
$853$			13.7453i			0.470629i	0.971919	+	0.235315i	$0.0756121\pi$
$853$			13.7453i			0.470629i	−0.971919	+	0.235315i	$0.924388\pi$
$854$	−9.76342	+	16.9107i	−0.334097	+	0.578674i
$855$	3.69010	+	6.39144i	0.126199	+	0.218583i
$856$	6.55815	−	3.78635i	0.224153	−	0.129415i
$857$	12.6495			0.432099			0.216049	−	0.976382i	$-0.430683\pi$
$857$	12.6495			0.432099			0.216049	+	0.976382i	$0.430683\pi$
$858$		0			0
$859$	−11.0929			−0.378485			−0.189243	−	0.981930i	$-0.560603\pi$
$859$	−11.0929			−0.378485			−0.189243	+	0.981930i	$0.560603\pi$
$860$	−1.74973	+	1.01021i	−0.0596652	+	0.0344477i
$861$	0.218598	+	0.378623i	0.00744981	+	0.0129034i
$862$	2.50832	−	4.34453i	0.0854336	−	0.147975i
$863$		−	33.0295i		−	1.12434i	−0.827022	−	0.562169i	$-0.809967\pi$
$863$		−	33.0295i		−	1.12434i	0.827022	−	0.562169i	$-0.190033\pi$
$864$	0.486697	+	0.280994i	0.0165578	+	0.00955962i
$865$	2.20073	+	1.27059i	0.0748272	+	0.0432015i
$866$		−	26.2081i		−	0.890587i
$867$	−0.0376273	+	0.0651724i	−0.00127789	+	0.00221337i
$868$	−64.5568	−	111.816i	−2.19120	−	3.79527i
$869$	−2.50096	+	1.44393i	−0.0848394	+	0.0489821i
$870$	0.237958			0.00806753
$871$		0			0
$872$	19.3980			0.656899
$873$	8.79181	−	5.07595i	0.297558	−	0.171795i
$874$	−4.29557	−	7.44014i	−0.145300	−	0.251667i
$875$	2.30448	−	3.99148i	0.0779058	−	0.134937i
$876$			0.465794i			0.0157377i
$877$	−13.3712	−	7.71986i	−0.451513	−	0.260681i	0.256956	−	0.966423i	$-0.417280\pi$
$877$	−13.3712	−	7.71986i	−0.451513	−	0.260681i	−0.708469	+	0.705742i	$0.750614\pi$
$878$	−68.2417	−	39.3993i	−2.30304	−	1.32966i
$879$			0.190178i			0.00641453i
$880$	2.23394	−	3.86930i	0.0753062	−	0.130434i
$881$	−8.31299	−	14.3985i	−0.280072	−	0.485098i	0.691331	−	0.722539i	$-0.257025\pi$
$881$	−8.31299	−	14.3985i	−0.280072	−	0.485098i	−0.971402	+	0.237440i	$0.923692\pi$
$882$	81.6084	−	47.1167i	2.74790	−	1.58650i
$883$	−57.2845			−1.92778			−0.963888	−	0.266309i	$-0.914196\pi$
$883$	−57.2845			−1.92778			−0.963888	+	0.266309i	$0.914196\pi$
$884$		0			0
$885$	0.0696502			0.00234126
$886$	9.52942	−	5.50181i	0.320147	−	0.184837i
$887$	−9.23286	−	15.9918i	−0.310009	−	0.536952i	0.668355	−	0.743843i	$-0.266999\pi$
$887$	−9.23286	−	15.9918i	−0.310009	−	0.536952i	−0.978364	+	0.206891i	$0.933665\pi$
$888$	−0.0513978	+	0.0890236i	−0.00172480	+	0.00298744i
$889$			92.0498i			3.08725i
$890$	0.788543	+	0.455265i	0.0264320	+	0.0152605i
$891$	22.8513	+	13.1932i	0.765546	+	0.441988i
$892$		−	44.6405i		−	1.49467i
$893$	10.5459	−	18.2661i	0.352907	−	0.611252i
$894$	0.210503	+	0.364601i	0.00704026	+	0.0121941i
$895$	9.25894	−	5.34565i	0.309492	−	0.178685i
$896$	63.7354			2.12925
$897$		0			0
$898$	−51.8055			−1.72877
$899$	−69.9843	+	40.4054i	−2.33411	+	1.34760i
$900$	4.29649	+	7.44175i	0.143216	+	0.248058i
$901$	20.8898	−	36.1822i	0.695940	−	1.20540i
$902$			46.9862i			1.56447i
$903$	−0.0367586	−	0.0212226i	−0.00122325	−	0.000706243i
$904$	−4.29296	−	2.47854i	−0.142782	−	0.0824350i
$905$			11.7908i			0.391939i
$906$	0.176398	−	0.305530i	0.00586042	−	0.0101505i
$907$	22.4744	+	38.9269i	0.746251	+	1.29255i	0.949608	+	0.313440i	$0.101482\pi$
$907$	22.4744	+	38.9269i	0.746251	+	1.29255i	−0.203357	+	0.979105i	$0.565185\pi$
$908$	10.0067	−	5.77740i	0.332086	−	0.191730i
$909$	−31.6279			−1.04903
$910$		0			0
$911$	−44.3728			−1.47014			−0.735069	−	0.677992i	$-0.762850\pi$
$911$	−44.3728			−1.47014			−0.735069	+	0.677992i	$0.762850\pi$
$912$	−0.0423862	+	0.0244717i	−0.00140355	+	0.000810339i
$913$	11.5006	+	19.9197i	0.380616	+	0.659245i
$914$	44.3879	−	76.8822i	1.46822	−	2.54304i
$915$		−	0.0250808i		−	0.000829146i
$916$	−55.8527	−	32.2466i	−1.84542	−	1.06546i
$917$	−45.6624	−	26.3632i	−1.50791	−	0.870590i
$918$			0.579164i			0.0191153i
$919$	−12.5840	+	21.7961i	−0.415108	+	0.718989i	−0.995440	−	0.0953917i	$-0.969590\pi$
$919$	−12.5840	+	21.7961i	−0.415108	+	0.718989i	0.580332	+	0.814380i	$0.302923\pi$
$920$	−1.50942	−	2.61439i	−0.0497641	−	0.0861940i
$921$	−0.102339	+	0.0590855i	−0.00337219	+	0.00194693i
$922$	68.8443			2.26726
$923$		0			0
$924$	−0.505469			−0.0166287
$925$	3.57597	−	2.06458i	0.117577	−	0.0678831i
$926$	19.5734	+	33.9021i	0.643221	+	1.11409i
$927$	−21.1715	+	36.6702i	−0.695364	+	1.20441i
$928$		−	59.2797i		−	1.94595i
$929$	32.5280	+	18.7800i	1.06721	+	0.616153i	0.927417	−	0.374028i	$-0.122024\pi$
$929$	32.5280	+	18.7800i	1.06721	+	0.616153i	0.139791	+	0.990181i	$0.455357\pi$
$930$	0.243895	+	0.140813i	0.00799762	+	0.00461743i
$931$			35.0397i			1.14838i
$932$	11.0248	−	19.0956i	0.361131	−	0.625497i
$933$	−0.0475793	−	0.0824097i	−0.00155768	−	0.00269797i
$934$	−50.9312	+	29.4051i	−1.66652	+	0.962165i
$935$	9.82931			0.321453
$936$		0			0
$937$	−17.1212			−0.559326			−0.279663	−	0.960098i	$-0.590223\pi$
$937$	−17.1212			−0.559326			−0.279663	+	0.960098i	$0.590223\pi$
$938$	−64.2470	+	37.0930i	−2.09774	+	1.21113i
$939$	0.0846889	+	0.146685i	0.00276372	+	0.00478690i
$940$	12.2790	−	21.2678i	0.400496	−	0.693679i
$941$			0.208568i			0.00679913i	0.999994	+	0.00339956i	$0.00108212\pi$
$941$			0.208568i			0.00679913i	−0.999994	+	0.00339956i	$0.998918\pi$
$942$	0.178063	+	0.102805i	0.00580162	+	0.00334957i
$943$	−9.96166	−	5.75137i	−0.324396	−	0.187290i
$944$		−	8.12794i		−	0.264542i
$945$	−0.180528	+	0.312684i	−0.00587258	+	0.0101716i
$946$	−2.28083	−	3.95051i	−0.0741560	−	0.128442i
$947$	0.358585	−	0.207029i	0.0116525	−	0.00672755i	−0.494162	−	0.869370i	$-0.664525\pi$
$947$	0.358585	−	0.207029i	0.0116525	−	0.00672755i	0.505815	+	0.862642i	$0.331192\pi$
$948$	0.0368337			0.00119630
$949$		0			0
$950$	−5.42613			−0.176047
$951$	−0.175319	+	0.101221i	−0.00568512	+	0.00328230i
$952$	14.7287	+	25.5109i	0.477361	+	0.826813i
$953$	−16.9296	+	29.3230i	−0.548404	+	0.949864i	0.449980	+	0.893039i	$0.351431\pi$
$953$	−16.9296	+	29.3230i	−0.548404	+	0.949864i	−0.998384	+	0.0568255i	$0.981902\pi$
$954$			82.4647i			2.66989i
$955$	−11.6694	−	6.73731i	−0.377612	−	0.218014i
$956$	46.4400	+	26.8121i	1.50198	+	0.867166i
$957$			0.316368i			0.0102267i
$958$	22.5662	−	39.0858i	0.729081	−	1.26281i
$959$	7.20197	+	12.4742i	0.232564	+	0.402812i
$960$	−0.144454	+	0.0834005i	−0.00466223	+	0.00269174i
$961$	−64.6403			−2.08517
$962$		0			0
$963$	11.9143			0.383932
$964$	−56.1097	+	32.3949i	−1.80717	+	1.04337i
$965$	−3.49368	−	6.05124i	−0.112466	−	0.194796i
$966$	0.105072	−	0.181989i	0.00338062	−	0.00585541i
$967$		−	13.2125i		−	0.424885i	−0.977174	−	0.212442i	$-0.931858\pi$
$967$		−	13.2125i		−	0.424885i	0.977174	−	0.212442i	$-0.0681417\pi$
$968$	3.96546	+	2.28946i	0.127455	+	0.0735860i
$969$	−0.0932494	−	0.0538376i	−0.00299560	−	0.00172951i
$970$			7.46397i			0.239654i
$971$	8.80095	−	15.2437i	0.282436	−	0.489193i	−0.689548	−	0.724240i	$-0.742191\pi$
$971$	8.80095	−	15.2437i	0.282436	−	0.489193i	0.971984	+	0.235046i	$0.0755242\pi$
$972$	−0.504871	−	0.874463i	−0.0161938	−	0.0280484i
$973$	−24.3291	+	14.0464i	−0.779956	+	0.450308i
$974$	17.9045			0.573697
$975$		0			0
$976$	−2.92685			−0.0936861
$977$	10.2028	−	5.89059i	0.326416	−	0.188457i	−0.327833	−	0.944736i	$-0.606318\pi$
$977$	10.2028	−	5.89059i	0.326416	−	0.188457i	0.654249	+	0.756279i	$0.272985\pi$
$978$	0.0344130	+	0.0596051i	0.00110041	+	0.00190596i
$979$	−0.605281	+	1.04838i	−0.0193449	+	0.0335063i
$980$			40.7978i			1.30324i
$981$	26.4304	+	15.2596i	0.843859	+	0.487202i
$982$	6.24586	+	3.60605i	0.199314	+	0.115074i
$983$		−	45.4985i		−	1.45118i	−0.688128	−	0.725589i	$-0.741567\pi$
$983$		−	45.4985i		−	1.45118i	0.688128	−	0.725589i	$-0.258433\pi$
$984$	0.0904321	−	0.156633i	0.00288287	−	0.00499328i
$985$	0.718974	+	1.24530i	0.0229084	+	0.0396786i
$986$	52.9067	−	30.5457i	1.68489	−	0.972773i
$987$	0.515917			0.0164218
$988$		0			0
$989$	1.11674			0.0355103
$990$	−16.8019	+	9.70056i	−0.533998	+	0.308304i
$991$	−16.6343	−	28.8114i	−0.528405	−	0.915224i	−0.999452	−	0.0331155i	$-0.989457\pi$
$991$	−16.6343	−	28.8114i	−0.528405	−	0.915224i	0.471047	−	0.882108i	$-0.343876\pi$
$992$	35.0790	−	60.7586i	1.11376	−	1.92909i
$993$		−	0.340588i		−	0.0108082i
$994$	58.8144	+	33.9565i	1.86548	+	1.07703i
$995$	−2.10316	−	1.21426i	−0.0666746	−	0.0384946i
$996$		−	0.293373i		−	0.00929589i
$997$	19.8935	−	34.4566i	0.630033	−	1.09125i	−0.357511	−	0.933909i	$-0.616375\pi$
$997$	19.8935	−	34.4566i	0.630033	−	1.09125i	0.987544	−	0.157341i	$-0.0502922\pi$
$998$	−9.80746	−	16.9870i	−0.310450	−	0.537715i
$999$	−0.280133	+	0.161735i	−0.00886302	+	0.00511707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.j.361.14		36
13.2	odd	12		845.2.a.o.1.7	yes	9
13.3	even	3		845.2.c.h.506.14		18
13.4	even	6	inner	845.2.m.j.316.14		36
13.5	odd	4		845.2.e.o.146.3		18
13.6	odd	12		845.2.e.o.191.3		18
13.7	odd	12		845.2.e.p.191.7		18
13.8	odd	4		845.2.e.p.146.7		18
13.9	even	3	inner	845.2.m.j.316.5		36
13.10	even	6		845.2.c.h.506.5		18
13.11	odd	12		845.2.a.n.1.3	✓	9
13.12	even	2	inner	845.2.m.j.361.5		36
39.2	even	12		7605.2.a.cp.1.3		9
39.11	even	12		7605.2.a.cs.1.7		9
65.24	odd	12		4225.2.a.bt.1.7		9
65.54	odd	12		4225.2.a.bs.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.3	✓	9	13.11	odd	12
845.2.a.o.1.7	yes	9	13.2	odd	12
845.2.c.h.506.5		18	13.10	even	6
845.2.c.h.506.14		18	13.3	even	3
845.2.e.o.146.3		18	13.5	odd	4
845.2.e.o.191.3		18	13.6	odd	12
845.2.e.p.146.7		18	13.8	odd	4
845.2.e.p.191.7		18	13.7	odd	12
845.2.m.j.316.5		36	13.9	even	3	inner
845.2.m.j.316.14		36	13.4	even	6	inner
845.2.m.j.361.5		36	13.12	even	2	inner
845.2.m.j.361.14		36	1.1	even	1	trivial
4225.2.a.bs.1.3		9	65.54	odd	12
4225.2.a.bt.1.7		9	65.24	odd	12
7605.2.a.cp.1.3		9	39.2	even	12
7605.2.a.cs.1.7		9	39.11	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.91007 - 1.10278i) q^{2} +(0.00652833 + 0.0113074i) q^{3} +(1.43225 - 2.48072i) q^{4} +1.00000i q^{5} +(0.0249391 + 0.0143986i) q^{6} +(3.99148 + 2.30448i) q^{7} -1.90669i q^{8} +(1.49991 - 2.59793i) q^{9} +(1.10278 + 1.91007i) q^{10} +(-2.53946 + 1.46616i) q^{11} +0.0374007 q^{12} +10.1654 q^{14} +(-0.0113074 + 0.00652833i) q^{15} +(0.761834 + 1.31954i) q^{16} +(-1.67603 + 2.90297i) q^{17} -6.61630i q^{18} +(2.13060 + 1.23010i) q^{19} +(2.48072 + 1.43225i) q^{20} +0.0601778i q^{21} +(-3.23370 + 5.60094i) q^{22} +(-0.791645 - 1.37117i) q^{23} +(0.0215597 - 0.0124475i) q^{24} -1.00000 q^{25} +0.0783378 q^{27} +(11.4336 - 6.60118i) q^{28} +(-4.13161 - 7.15616i) q^{29} +(-0.0143986 + 0.0249391i) q^{30} -9.77959i q^{31} +(6.21280 + 3.58696i) q^{32} +(-0.0331569 - 0.0191432i) q^{33} +7.39317i q^{34} +(-2.30448 + 3.99148i) q^{35} +(-4.29649 - 7.44175i) q^{36} +(-3.57597 + 2.06458i) q^{37} +5.42613 q^{38} +1.90669 q^{40} +(6.29175 - 3.63254i) q^{41} +(0.0663628 + 0.114944i) q^{42} +(-0.352665 + 0.610833i) q^{43} +8.39961i q^{44} +(2.59793 + 1.49991i) q^{45} +(-3.02419 - 1.74602i) q^{46} -8.57322i q^{47} +(-0.00994701 + 0.0172287i) q^{48} +(7.12130 + 12.3344i) q^{49} +(-1.91007 + 1.10278i) q^{50} -0.0437667 q^{51} -12.4639 q^{53} +(0.149631 - 0.0863893i) q^{54} +(-1.46616 - 2.53946i) q^{55} +(4.39394 - 7.61052i) q^{56} +0.0321221i q^{57} +(-15.7833 - 9.11251i) q^{58} +(-4.61977 - 2.66723i) q^{59} +0.0374007i q^{60} +(-0.960460 + 1.66357i) q^{61} +(-10.7847 - 18.6797i) q^{62} +(11.9738 - 6.91306i) q^{63} +12.7752 q^{64} -0.0844427 q^{66} +(-6.32019 + 3.64896i) q^{67} +(4.80097 + 8.31553i) q^{68} +(0.0103362 - 0.0179029i) q^{69} +10.1654i q^{70} +(5.78577 + 3.34041i) q^{71} +(-4.95344 - 2.85987i) q^{72} +12.4541i q^{73} +(-4.55356 + 7.88700i) q^{74} +(-0.00652833 - 0.0113074i) q^{75} +(6.10309 - 3.52362i) q^{76} -13.5150 q^{77} +0.984840 q^{79} +(-1.31954 + 0.761834i) q^{80} +(-4.49923 - 7.79290i) q^{81} +(8.01179 - 13.8768i) q^{82} -7.84405i q^{83} +(0.149284 + 0.0861894i) q^{84} +(-2.90297 - 1.67603i) q^{85} +1.55565i q^{86} +(0.0539450 - 0.0934356i) q^{87} +(2.79551 + 4.84197i) q^{88} +(0.357525 - 0.206417i) q^{89} +6.61630 q^{90} -4.53532 q^{92} +(0.110582 - 0.0638444i) q^{93} +(-9.45437 - 16.3755i) q^{94} +(-1.23010 + 2.13060i) q^{95} +0.0936675i q^{96} +(2.93077 + 1.69208i) q^{97} +(27.2044 + 15.7064i) q^{98} +8.79646i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{3} + 34 q^{4} - 32 q^{9} + 6 q^{10} - 48 q^{12} - 8 q^{14} - 74 q^{16} - 2 q^{17} - 24 q^{22} + 28 q^{23} - 36 q^{25} + 88 q^{27} - 24 q^{29} - 4 q^{30} - 14 q^{35} + 6 q^{36} + 188 q^{38}+ \cdots - 8 q^{95}+O(q^{100}) \) 36 * q - 14 * q^3 + 34 * q^4 - 32 * q^9 + 6 * q^10 - 48 * q^12 - 8 * q^14 - 74 * q^16 - 2 * q^17 - 24 * q^22 + 28 * q^23 - 36 * q^25 + 88 * q^27 - 24 * q^29 - 4 * q^30 - 14 * q^35 + 6 * q^36 + 188 * q^38 + 48 * q^40 + 22 * q^42 + 78 * q^43 + 6 * q^48 + 32 * q^49 - 172 * q^51 - 32 * q^53 + 18 * q^55 - 58 * q^56 + 6 * q^61 - 20 * q^62 - 136 * q^64 - 196 * q^66 + 40 * q^68 - 26 * q^69 + 30 * q^74 + 14 * q^75 + 16 * q^77 + 156 * q^79 - 58 * q^81 - 8 * q^82 - 32 * q^87 + 84 * q^88 + 40 * q^90 - 108 * q^92 - 32 * q^94 - 8 * q^95

Introduction

L-functions

Modular forms

Varieties

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