LMFDB - Embedded newform 648.2.t.a.181.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(37,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("648.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			181.24
Character	$\chi$	$=$	648.181
Dual form			648.2.t.a.469.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.907362 - 1.08476i) q^{2} +(-0.353388 - 1.96853i) q^{4} +(3.55522 - 0.626880i) q^{5} +(0.197520 + 0.165739i) q^{7} +(-2.45603 - 1.40283i) q^{8} +O(q^{10})$	\(q+(0.907362 - 1.08476i) q^{2} +(-0.353388 - 1.96853i) q^{4} +(3.55522 - 0.626880i) q^{5} +(0.197520 + 0.165739i) q^{7} +(-2.45603 - 1.40283i) q^{8} +(2.54586 - 4.42535i) q^{10} +(-4.72909 - 0.833866i) q^{11} +(2.06615 - 5.67671i) q^{13} +(0.359008 - 0.0638755i) q^{14} +(-3.75023 + 1.39131i) q^{16} +(2.76368 + 4.78684i) q^{17} +(1.75645 + 1.01409i) q^{19} +(-2.49040 - 6.77702i) q^{20} +(-5.19554 + 4.37328i) q^{22} +(0.164150 - 0.137738i) q^{23} +(7.54812 - 2.74729i) q^{25} +(-4.28309 - 7.39210i) q^{26} +(0.256461 - 0.447394i) q^{28} +(0.455110 + 1.25040i) q^{29} +(-0.00197394 + 0.00165633i) q^{31} +(-1.89359 + 5.33051i) q^{32} +(7.70020 + 1.34548i) q^{34} +(0.806124 + 0.465416i) q^{35} +(0.995752 - 0.574898i) q^{37} +(2.69377 - 0.985173i) q^{38} +(-9.61111 - 3.44774i) q^{40} +(-4.72689 - 1.72045i) q^{41} +(4.99819 + 0.881316i) q^{43} +(0.0297094 + 9.60404i) q^{44} +(-0.000468717 - 0.303041i) q^{46} +(1.18349 + 0.993067i) q^{47} +(-1.20399 - 6.82818i) q^{49} +(3.86874 - 10.6806i) q^{50} +(-11.9049 - 2.06121i) q^{52} +12.4496i q^{53} -17.3357 q^{55} +(-0.252610 - 0.684146i) q^{56} +(1.76933 + 0.640886i) q^{58} +(-10.3154 + 1.81887i) q^{59} +(-5.31333 + 6.33218i) q^{61} +(5.63643e-6 + 0.00364414i) q^{62} +(4.06412 + 6.89078i) q^{64} +(3.78700 - 21.4771i) q^{65} +(1.10004 - 3.02234i) q^{67} +(8.44639 - 7.13200i) q^{68} +(1.23631 - 0.452146i) q^{70} +(3.40904 + 5.90464i) q^{71} +(1.51096 - 2.61705i) q^{73} +(0.279884 - 1.60179i) q^{74} +(1.37555 - 3.81599i) q^{76} +(-0.795884 - 0.948498i) q^{77} +(10.1554 - 3.69627i) q^{79} +(-12.4607 + 7.29735i) q^{80} +(-6.15527 + 3.56645i) q^{82} +(2.84189 + 7.80804i) q^{83} +(12.8263 + 15.2857i) q^{85} +(5.49118 - 4.62214i) q^{86} +(10.4450 + 8.68211i) q^{88} +(0.381609 - 0.660965i) q^{89} +(1.34896 - 0.778820i) q^{91} +(-0.329150 - 0.274459i) q^{92} +(2.15109 - 0.382727i) q^{94} +(6.88026 + 2.50421i) q^{95} +(-0.902281 + 5.11709i) q^{97} +(-8.49936 - 4.88960i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40} + 24 q^{41} - 21 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} + 99 q^{50} - 33 q^{52} - 24 q^{55} - 99 q^{56} + 21 q^{58} + 36 q^{62} - 3 q^{64} + 12 q^{65} - 75 q^{68} + 9 q^{70} + 90 q^{71} - 6 q^{73} - 9 q^{74} - 18 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} + 30 q^{86} - 30 q^{88} + 6 q^{89} - 111 q^{92} - 33 q^{94} + 42 q^{95} - 12 q^{97} - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.907362	−	1.08476i	0.641602	−	0.767038i
$2$	0.907362	−	1.08476i	0.641602	−	0.767038i
$3$		0			0
$3$		0			0
$4$	−0.353388	−	1.96853i	−0.176694	−	0.984266i
$5$	3.55522	−	0.626880i	1.58994	−	0.280349i	0.692478	−	0.721439i	$-0.256519\pi$
$5$	3.55522	−	0.626880i	1.58994	−	0.280349i	0.897463	+	0.441090i	$0.145408\pi$
$6$		0			0
$7$	0.197520	+	0.165739i	0.0746554	+	0.0626434i	0.679352	−	0.733813i	$-0.262261\pi$
$7$	0.197520	+	0.165739i	0.0746554	+	0.0626434i	−0.604696	+	0.796456i	$0.706706\pi$
$8$	−2.45603	−	1.40283i	−0.868336	−	0.495976i
$9$		0			0
$10$	2.54586	−	4.42535i	0.805071	−	1.39942i
$11$	−4.72909	−	0.833866i	−1.42587	−	0.251420i	−0.593143	−	0.805097i	$-0.702113\pi$
$11$	−4.72909	−	0.833866i	−1.42587	−	0.251420i	−0.832731	+	0.553677i	$0.813224\pi$
$12$		0			0
$13$	2.06615	−	5.67671i	0.573047	−	1.57443i	−0.226615	−	0.973984i	$-0.572766\pi$
$13$	2.06615	−	5.67671i	0.573047	−	1.57443i	0.799662	−	0.600450i	$-0.205012\pi$
$14$	0.359008	−	0.0638755i	0.0959489	−	0.0170714i
$15$		0			0
$16$	−3.75023	+	1.39131i	−0.937559	+	0.347827i
$17$	2.76368	+	4.78684i	0.670291	+	1.16098i	0.977822	+	0.209440i	$0.0671641\pi$
$17$	2.76368	+	4.78684i	0.670291	+	1.16098i	−0.307530	+	0.951538i	$0.599503\pi$
$18$		0			0
$19$	1.75645	+	1.01409i	0.402957	+	0.232647i	0.687759	−	0.725939i	$-0.258595\pi$
$19$	1.75645	+	1.01409i	0.402957	+	0.232647i	−0.284802	+	0.958586i	$0.591928\pi$
$20$	−2.49040	−	6.77702i	−0.556871	−	1.51539i
$21$		0			0
$22$	−5.19554	+	4.37328i	−1.10769	+	0.932387i
$23$	0.164150	−	0.137738i	0.0342276	−	0.0287204i	−0.625513	−	0.780213i	$-0.715110\pi$
$23$	0.164150	−	0.137738i	0.0342276	−	0.0287204i	0.659741	+	0.751493i	$0.270666\pi$
$24$		0			0
$25$	7.54812	−	2.74729i	1.50962	−	0.549458i
$26$	−4.28309	−	7.39210i	−0.839982	−	1.44971i
$27$		0			0
$28$	0.256461	−	0.447394i	0.0484666	−	0.0845495i
$29$	0.455110	+	1.25040i	0.0845117	+	0.232194i	0.974749	−	0.223303i	$-0.0716839\pi$
$29$	0.455110	+	1.25040i	0.0845117	+	0.232194i	−0.890237	+	0.455497i	$0.849462\pi$
$30$		0			0
$31$	−0.00197394	+	0.00165633i	−0.000354531	+	0.000297486i	−0.642965	−	0.765896i	$-0.722296\pi$
$31$	−0.00197394	+	0.00165633i	−0.000354531	+	0.000297486i	0.642610	+	0.766193i	$0.277851\pi$
$32$	−1.89359	+	5.33051i	−0.334743	+	0.942310i
$33$		0			0
$34$	7.70020	+	1.34548i	1.32057	+	0.230747i
$35$	0.806124	+	0.465416i	0.136260	+	0.0786696i
$36$		0			0
$37$	0.995752	−	0.574898i	0.163701	−	0.0945126i	−0.415912	−	0.909405i	$-0.636537\pi$
$37$	0.995752	−	0.574898i	0.163701	−	0.0945126i	0.579612	+	0.814892i	$0.303204\pi$
$38$	2.69377	−	0.985173i	0.436987	−	0.159816i
$39$		0			0
$40$	−9.61111	−	3.44774i	−1.51965	−	0.545135i
$41$	−4.72689	−	1.72045i	−0.738217	−	0.268689i	−0.0545779	−	0.998510i	$-0.517381\pi$
$41$	−4.72689	−	1.72045i	−0.738217	−	0.268689i	−0.683639	+	0.729821i	$0.739604\pi$
$42$		0			0
$43$	4.99819	+	0.881316i	0.762217	+	0.134399i	0.541227	−	0.840877i	$-0.317960\pi$
$43$	4.99819	+	0.881316i	0.762217	+	0.134399i	0.220990	+	0.975276i	$0.429071\pi$
$44$	0.0297094	+	9.60404i	0.00447886	+	1.44786i
$45$		0			0
$46$	−0.000468717	−	0.303041i	−6.91085e−5	−	0.0446809i
$47$	1.18349	+	0.993067i	0.172630	+	0.144854i	0.725009	−	0.688739i	$-0.241835\pi$
$47$	1.18349	+	0.993067i	0.172630	+	0.144854i	−0.552379	+	0.833593i	$0.686280\pi$
$48$		0			0
$49$	−1.20399	−	6.82818i	−0.171999	−	0.975454i
$50$	3.86874	−	10.6806i	0.547122	−	1.51047i
$51$		0			0
$52$	−11.9049	−	2.06121i	−1.65092	−	0.285838i
$53$			12.4496i			1.71008i	0.518560	+	0.855041i	$0.326468\pi$
$53$			12.4496i			1.71008i	−0.518560	+	0.855041i	$0.673532\pi$
$54$		0			0
$55$	−17.3357			−2.33754
$56$	−0.252610	−	0.684146i	−0.0337564	−	0.0914228i
$57$		0			0
$58$	1.76933	+	0.640886i	0.232324	+	0.0841525i
$59$	−10.3154	+	1.81887i	−1.34294	+	0.236797i	−0.798497	−	0.601998i	$-0.794371\pi$
$59$	−10.3154	+	1.81887i	−1.34294	+	0.236797i	−0.544447	+	0.838795i	$0.683260\pi$
$60$		0			0
$61$	−5.31333	+	6.33218i	−0.680303	+	0.810753i	−0.990147	−	0.140034i	$-0.955279\pi$
$61$	−5.31333	+	6.33218i	−0.680303	+	0.810753i	0.309844	+	0.950787i	$0.399723\pi$
$62$	5.63643e−6		0.00364414i	7.15827e−7		0.000462806i
$63$		0			0
$64$	4.06412	+	6.89078i	0.508015	+	0.861348i
$65$	3.78700	−	21.4771i	0.469720	−	2.66391i
$66$		0			0
$67$	1.10004	−	3.02234i	0.134392	−	0.369238i	−0.854182	−	0.519973i	$-0.825942\pi$
$67$	1.10004	−	3.02234i	0.134392	−	0.369238i	0.988574	+	0.150735i	$0.0481641\pi$
$68$	8.44639	−	7.13200i	1.02427	−	0.864882i
$69$		0			0
$70$	1.23631	−	0.452146i	0.147767	−	0.0540418i
$71$	3.40904	+	5.90464i	0.404579	+	0.700751i	0.994272	−	0.106876i	$-0.0340847\pi$
$71$	3.40904	+	5.90464i	0.404579	+	0.700751i	−0.589693	+	0.807627i	$0.700751\pi$
$72$		0			0
$73$	1.51096	−	2.61705i	0.176844	−	0.306303i	−0.763954	−	0.645271i	$-0.776744\pi$
$73$	1.51096	−	2.61705i	0.176844	−	0.306303i	0.940798	+	0.338968i	$0.110078\pi$
$74$	0.279884	−	1.60179i	0.0325359	−	0.186204i
$75$		0			0
$76$	1.37555	−	3.81599i	0.157787	−	0.437724i
$77$	−0.795884	−	0.948498i	−0.0906995	−	0.108091i
$78$		0			0
$79$	10.1554	−	3.69627i	1.14257	−	0.415863i	0.299732	−	0.954023i	$-0.403103\pi$
$79$	10.1554	−	3.69627i	1.14257	−	0.415863i	0.842843	+	0.538160i	$0.180880\pi$
$80$	−12.4607	+	7.29735i	−1.39315	+	0.815869i
$81$		0			0
$82$	−6.15527	+	3.56645i	−0.679736	+	0.393849i
$83$	2.84189	+	7.80804i	0.311938	+	0.857044i	0.992265	+	0.124135i	$0.0396156\pi$
$83$	2.84189	+	7.80804i	0.311938	+	0.857044i	−0.680327	+	0.732909i	$0.738162\pi$
$84$		0			0
$85$	12.8263	+	15.2857i	1.39120	+	1.65797i
$86$	5.49118	−	4.62214i	0.592129	−	0.498418i
$87$		0			0
$88$	10.4450	+	8.68211i	1.11344	+	0.925517i
$89$	0.381609	−	0.660965i	0.0404504	−	0.0700622i	−0.845091	−	0.534622i	$-0.820454\pi$
$89$	0.381609	−	0.660965i	0.0404504	−	0.0700622i	0.885542	+	0.464560i	$0.153787\pi$
$90$		0			0
$91$	1.34896	−	0.778820i	0.141409	−	0.0816425i
$92$	−0.329150	−	0.274459i	−0.0343163	−	0.0286144i
$93$		0			0
$94$	2.15109	−	0.382727i	0.221868	−	0.0394752i
$95$	6.88026	+	2.50421i	0.705900	+	0.256927i
$96$		0			0
$97$	−0.902281	+	5.11709i	−0.0916127	+	0.519562i	0.904120	+	0.427278i	$0.140528\pi$
$97$	−0.902281	+	5.11709i	−0.0916127	+	0.519562i	−0.995733	+	0.0922832i	$0.970584\pi$
$98$	−8.49936	−	4.88960i	−0.858565	−	0.493924i
$99$		0			0
$100$	−8.07554	−	13.8879i	−0.807554	−	1.38879i
$101$	4.68417	−	5.58238i	0.466092	−	0.555467i	−0.480878	−	0.876787i	$-0.659682\pi$
$101$	4.68417	−	5.58238i	0.466092	−	0.555467i	0.946971	+	0.321320i	$0.104127\pi$
$102$		0			0
$103$	0.771419	+	4.37493i	0.0760102	+	0.431075i	0.998937	+	0.0460994i	$0.0146791\pi$
$103$	0.771419	+	4.37493i	0.0760102	+	0.431075i	−0.922927	+	0.384976i	$0.874210\pi$
$104$	−13.0380	+	11.0437i	−1.27848	+	1.08292i
$105$		0			0
$106$	13.5048	+	11.2963i	1.31170	+	1.09719i
$107$		−	9.51271i		−	0.919629i	−0.888015	−	0.459814i	$-0.847916\pi$
$107$		−	9.51271i		−	0.919629i	0.888015	−	0.459814i	$-0.152084\pi$
$108$		0			0
$109$			7.93890i			0.760409i	0.924903	+	0.380204i	$0.124146\pi$
$109$			7.93890i			0.760409i	−0.924903	+	0.380204i	$0.875854\pi$
$110$	−15.7297	+	18.8050i	−1.49977	+	1.79298i
$111$		0			0
$112$	−0.971339	−	0.346748i	−0.0917829	−	0.0327646i
$113$	1.23440	+	7.00061i	0.116122	+	0.658562i	0.986188	+	0.165627i	$0.0529648\pi$
$113$	1.23440	+	7.00061i	0.116122	+	0.658562i	−0.870066	+	0.492935i	$0.835924\pi$
$114$		0			0
$115$	0.497243	−	0.592591i	0.0463682	−	0.0552594i
$116$	2.30063	−	1.33777i	0.213608	−	0.124209i
$117$		0			0
$118$	−7.38673	+	12.8400i	−0.680003	+	1.18202i
$119$	−0.247483	+	1.40354i	−0.0226867	+	0.128663i
$120$		0			0
$121$	11.3323	+	4.12463i	1.03021	+	0.374966i
$122$	2.04775	+	11.5092i	0.185395	+	1.04200i
$123$		0			0
$124$	0.00395811	+	0.00330044i	0.000355449	+	0.000296388i
$125$	9.48095	−	5.47383i	0.848002	−	0.489594i
$126$		0			0
$127$	−8.72390	+	15.1102i	−0.774121	+	1.34082i	0.161167	+	0.986927i	$0.448474\pi$
$127$	−8.72390	+	15.1102i	−0.774121	+	1.34082i	−0.935287	+	0.353889i	$0.884859\pi$
$128$	11.1624	+	1.84386i	0.986630	+	0.162976i
$129$		0			0
$130$	−19.8613	−	23.5955i	−1.74195	−	2.06946i
$131$	9.50899	+	11.3324i	0.830805	+	0.990114i	0.999990	+	0.00453015i	$0.00144200\pi$
$131$	9.50899	+	11.3324i	0.830805	+	0.990114i	−0.169185	+	0.985584i	$0.554114\pi$
$132$		0			0
$133$	0.178860	+	0.491413i	0.0155091	+	0.0426109i
$134$	−2.28037	−	3.93564i	−0.196994	−	0.339987i
$135$		0			0
$136$	−0.0725423	−	15.6336i	−0.00622045	−	1.34057i
$137$	11.3732	−	4.13951i	0.971678	−	0.353662i	0.193079	−	0.981183i	$-0.438153\pi$
$137$	11.3732	−	4.13951i	0.971678	−	0.353662i	0.778599	+	0.627521i	$0.215930\pi$
$138$		0			0
$139$	−6.31955	−	7.53135i	−0.536017	−	0.638801i	0.428272	−	0.903650i	$-0.359122\pi$
$139$	−6.31955	−	7.53135i	−0.536017	−	0.638801i	−0.964290	+	0.264849i	$0.914678\pi$
$140$	0.631312	−	1.75135i	0.0533556	−	0.148016i
$141$		0			0
$142$	9.49832	+	1.65967i	0.797082	+	0.139276i
$143$	−14.5046	+	25.1227i	−1.21294	+	2.10087i
$144$		0			0
$145$	2.40187	+	4.16015i	0.199464	+	0.345482i
$146$	−1.46788	−	4.01363i	−0.121482	−	0.332171i
$147$		0			0
$148$	−1.48359	−	1.75701i	−0.121950	−	0.144425i
$149$	−5.68507	+	15.6196i	−0.465739	+	1.27961i	0.455370	+	0.890302i	$0.349507\pi$
$149$	−5.68507	+	15.6196i	−0.465739	+	1.27961i	−0.921109	+	0.389305i	$0.872715\pi$
$150$		0			0
$151$	0.796354	−	4.51635i	0.0648064	−	0.367535i	−0.935107	−	0.354366i	$-0.884697\pi$
$151$	0.796354	−	4.51635i	0.0648064	−	0.367535i	0.999913	−	0.0131695i	$-0.00419209\pi$
$152$	−2.89129	−	4.95462i	−0.234514	−	0.401873i
$153$		0			0
$154$	−1.75104	+	0.00270836i	−0.141103	+	0.000218246i
$155$	−0.00597947	+	0.00712605i	−0.000480282	+	0.000572378i
$156$		0			0
$157$	1.68663	−	0.297399i	0.134608	−	0.0237350i	−0.105938	−	0.994373i	$-0.533785\pi$
$157$	1.68663	−	0.297399i	0.134608	−	0.0237350i	0.240546	+	0.970638i	$0.422673\pi$
$158$	5.20510	−	14.3700i	0.414096	−	1.14322i
$159$		0			0
$160$	−3.39054	+	20.1382i	−0.268045	+	1.59206i
$161$	0.0552514			0.00435442
$162$		0			0
$163$			12.9384i			1.01341i	0.862119	+	0.506705i	$0.169137\pi$
$163$			12.9384i			1.01341i	−0.862119	+	0.506705i	$0.830863\pi$
$164$	−1.71633	+	9.91302i	−0.134023	+	0.774077i
$165$		0			0
$166$	11.0484	+	4.00196i	0.857525	+	0.310612i
$167$	−2.50837	−	14.2257i	−0.194103	−	1.10082i	−0.913690	−	0.406412i	$-0.866780\pi$
$167$	−2.50837	−	14.2257i	−0.194103	−	1.10082i	0.719586	−	0.694403i	$-0.244332\pi$
$168$		0			0
$169$	−17.9974	−	15.1016i	−1.38442	−	1.16166i
$170$	28.2193	−	0.0436472i	2.16432	−	0.00334758i
$171$		0			0
$172$	−0.0314000	−	10.1505i	−0.00239423	−	0.773972i
$173$	−11.9612	−	2.10908i	−0.909391	−	0.160350i	−0.300664	−	0.953730i	$-0.597208\pi$
$173$	−11.9612	−	2.10908i	−0.909391	−	0.160350i	−0.608727	+	0.793380i	$0.708320\pi$
$174$		0			0
$175$	1.94623	+	0.708372i	0.147122	+	0.0535479i
$176$	18.8954	−	3.45243i	1.42429	−	0.260237i
$177$		0			0
$178$	−0.370728	−	1.01369i	−0.0277873	−	0.0759790i
$179$	16.4151	−	9.47728i	1.22692	−	0.708365i	0.260539	−	0.965463i	$-0.416100\pi$
$179$	16.4151	−	9.47728i	1.22692	−	0.708365i	0.966385	+	0.257098i	$0.0827664\pi$
$180$		0			0
$181$	2.91223	+	1.68138i	0.216465	+	0.124976i	0.604312	−	0.796748i	$-0.293448\pi$
$181$	2.91223	+	1.68138i	0.216465	+	0.124976i	−0.387848	+	0.921723i	$0.626781\pi$
$182$	0.379163	−	2.16996i	0.0281054	−	0.160848i
$183$		0			0
$184$	−0.596380	+	0.108014i	−0.0439657	+	0.00796286i
$185$	3.17972	−	2.66810i	0.233778	−	0.196163i
$186$		0			0
$187$	−9.07811	−	24.9419i	−0.663857	−	1.82393i
$188$	1.53665	−	2.68068i	0.112072	−	0.195509i
$189$		0			0
$190$	8.95935	−	5.19117i	0.649979	−	0.376607i
$191$	−5.49500	+	2.00002i	−0.397604	+	0.144716i	−0.533081	−	0.846064i	$-0.678966\pi$
$191$	−5.49500	+	2.00002i	−0.397604	+	0.144716i	0.135476	+	0.990781i	$0.456744\pi$
$192$		0			0
$193$	5.79233	−	4.86034i	0.416941	−	0.349855i	−0.410057	−	0.912060i	$-0.634491\pi$
$193$	5.79233	−	4.86034i	0.416941	−	0.349855i	0.826998	+	0.562205i	$0.190047\pi$
$194$	4.73209	+	5.62181i	0.339744	+	0.403622i
$195$		0			0
$196$	−13.0160	+	4.78309i	−0.929715	+	0.341649i
$197$	−10.5090	−	6.06740i	−0.748739	−	0.432284i	0.0764994	−	0.997070i	$-0.475626\pi$
$197$	−10.5090	−	6.06740i	−0.748739	−	0.432284i	−0.825238	+	0.564785i	$0.808959\pi$
$198$		0			0
$199$	−6.35656	−	11.0099i	−0.450605	−	0.780470i	0.547819	−	0.836597i	$-0.315458\pi$
$199$	−6.35656	−	11.0099i	−0.450605	−	0.780470i	−0.998424	+	0.0561267i	$0.982125\pi$
$200$	−22.3924	−	3.84133i	−1.58338	−	0.271623i
$201$		0			0
$202$	−1.80527	−	10.1464i	−0.127019	−	0.713899i
$203$	−0.117347	+	0.322409i	−0.00823616	+	0.0226287i
$204$		0			0
$205$	−17.8836	−	3.15337i	−1.24905	−	0.220241i
$206$	5.44569	+	3.13285i	0.379419	+	0.218276i
$207$		0			0
$208$	0.149498	+	24.1636i	0.0103658	+	1.67545i
$209$	−7.46079	−	6.26034i	−0.516073	−	0.433037i
$210$		0			0
$211$	−25.8007	+	4.54936i	−1.77619	+	0.313191i	−0.963140	−	0.269000i	$-0.913307\pi$
$211$	−25.8007	+	4.54936i	−1.77619	+	0.313191i	−0.813052	+	0.582191i	$0.802196\pi$
$212$	24.5074	−	4.39953i	1.68318	−	0.302161i
$213$		0			0
$214$	−10.3190	−	8.63148i	−0.705390	−	0.590036i
$215$	18.3221			1.24956
$216$		0			0
$217$	−0.000664411	0		−4.51032e−5	0
$218$	8.61176	+	7.20346i	0.583262	+	0.487880i
$219$		0			0
$220$	6.12621	+	34.1258i	0.413029	+	2.30076i
$221$	32.8836	−	5.79827i	2.21199	−	0.390034i
$222$		0			0
$223$	3.37847	+	2.83488i	0.226239	+	0.189837i	0.748860	−	0.662728i	$-0.230601\pi$
$223$	3.37847	+	2.83488i	0.226239	+	0.189837i	−0.522621	+	0.852565i	$0.675046\pi$
$224$	−1.25749	+	0.739039i	−0.0840198	+	0.0493791i
$225$		0			0
$226$	8.71399	+	5.01307i	0.579646	+	0.333465i
$227$	4.31991	+	0.761717i	0.286723	+	0.0505569i	0.315160	−	0.949039i	$-0.397942\pi$
$227$	4.31991	+	0.761717i	0.286723	+	0.0505569i	−0.0284371	+	0.999596i	$0.509053\pi$
$228$		0			0
$229$	3.02517	−	8.31159i	0.199909	−	0.549246i	−0.798714	−	0.601711i	$-0.794486\pi$
$229$	3.02517	−	8.31159i	0.199909	−	0.549246i	0.998623	+	0.0524657i	$0.0167080\pi$
$230$	−0.191637	−	1.07708i	−0.0126362	−	0.0710207i
$231$		0			0
$232$	0.636346	−	3.70946i	0.0417781	−	0.243538i
$233$	−12.1136	−	20.9814i	−0.793589	−	1.37454i	−0.923731	−	0.383042i	$-0.874877\pi$
$233$	−12.1136	−	20.9814i	−0.793589	−	1.37454i	0.130142	−	0.991495i	$-0.458457\pi$
$234$		0			0
$235$	4.83010	+	2.78866i	0.315081	+	0.181912i
$236$	7.22583	+	19.6633i	0.470361	+	1.27997i
$237$		0			0
$238$	1.29794	+	1.54198i	0.0841333	+	0.0999518i
$239$	−16.6186	+	13.9446i	−1.07497	+	0.902004i	−0.995493	−	0.0948328i	$-0.969768\pi$
$239$	−16.6186	+	13.9446i	−1.07497	+	0.902004i	−0.0794735	+	0.996837i	$0.525324\pi$
$240$		0			0
$241$	17.1009	−	6.22423i	1.10157	−	0.400938i	0.273674	−	0.961823i	$-0.411761\pi$
$241$	17.1009	−	6.22423i	1.10157	−	0.400938i	0.827894	+	0.560885i	$0.189539\pi$
$242$	14.7567	−	8.55027i	0.948599	−	0.549632i
$243$		0			0
$244$	14.3428	+	8.22175i	0.918202	+	0.526344i
$245$	−8.56091	−	23.5209i	−0.546936	−	1.50270i
$246$		0			0
$247$	9.38575	−	7.87558i	0.597201	−	0.501111i
$248$	0.00717161	−	0.00129889i	0.000455398	−	8.24795e-5i
$249$		0			0
$250$	2.66489	−	15.2512i	0.168542	−	0.964574i
$251$	−12.6453	−	7.30079i	−0.798167	−	0.460822i	0.0446629	−	0.999002i	$-0.485779\pi$
$251$	−12.6453	−	7.30079i	−0.798167	−	0.460822i	−0.842830	+	0.538180i	$0.819112\pi$
$252$		0			0
$253$	−0.891135	+	0.514497i	−0.0560252	+	0.0323461i
$254$	8.47517	+	23.1737i	0.531779	+	1.45405i
$255$		0			0
$256$	12.1285	−	10.4355i	0.758032	−	0.652217i
$257$	−5.43741	−	1.97905i	−0.339176	−	0.123450i	0.166816	−	0.985988i	$-0.446651\pi$
$257$	−5.43741	−	1.97905i	−0.339176	−	0.123450i	−0.505992	+	0.862538i	$0.668874\pi$
$258$		0			0
$259$	0.291963	+	0.0514810i	0.0181417	+	0.00319888i
$260$	−43.6167	+	0.134925i	−2.70499	+	0.00836771i
$261$		0			0
$262$	20.9210	−	0.0323587i	1.29250	−	0.00199913i
$263$	−3.38239	−	2.83816i	−0.208567	−	0.175009i	0.532520	−	0.846417i	$-0.321245\pi$
$263$	−3.38239	−	2.83816i	−0.208567	−	0.175009i	−0.741087	+	0.671409i	$0.765690\pi$
$264$		0			0
$265$	7.80440	+	44.2610i	0.479421	+	2.71893i
$266$	0.695354	+	0.251871i	0.0426349	+	0.0154432i
$267$		0			0
$268$	−6.33832	−	1.09741i	−0.387175	−	0.0670351i
$269$			7.57493i			0.461852i	0.972971	+	0.230926i	$0.0741755\pi$
$269$			7.57493i			0.461852i	−0.972971	+	0.230926i	$0.925825\pi$
$270$		0			0
$271$	6.02446			0.365960			0.182980	−	0.983117i	$-0.441426\pi$
$271$	6.02446			0.365960			0.182980	+	0.983117i	$0.441426\pi$
$272$	−17.0244	−	14.1066i	−1.03226	−	0.855340i
$273$		0			0
$274$	5.82926	−	16.0932i	0.352159	−	0.972224i
$275$	−37.9866	+	6.69806i	−2.29068	+	0.403908i
$276$		0			0
$277$	0.284428	−	0.338968i	0.0170896	−	0.0203666i	−0.757432	−	0.652914i	$-0.773546\pi$
$277$	0.284428	−	0.338968i	0.0170896	−	0.0203666i	0.774522	+	0.632548i	$0.217991\pi$
$278$	−13.9038	+	0.0215051i	−0.833894	+	0.00128979i
$279$		0			0
$280$	−1.32696	−	2.27393i	−0.0793010	−	0.135893i
$281$	−3.92170	+	22.2411i	−0.233949	+	1.32679i	0.610866	+	0.791734i	$0.290821\pi$
$281$	−3.92170	+	22.2411i	−0.233949	+	1.32679i	−0.844816	+	0.535058i	$0.820290\pi$
$282$		0			0
$283$	6.72971	−	18.4897i	0.400040	−	1.09910i	−0.562224	−	0.826985i	$-0.690054\pi$
$283$	6.72971	−	18.4897i	0.400040	−	1.09910i	0.962264	−	0.272116i	$-0.0877235\pi$
$284$	10.4188	−	8.79744i	0.618239	−	0.522032i
$285$		0			0
$286$	14.0911	+	38.5294i	0.833223	+	2.27829i
$287$	−0.648510	−	1.12325i	−0.0382803	−	0.0663034i
$288$		0			0
$289$	−6.77586	+	11.7361i	−0.398580	+	0.690361i
$290$	6.69211	+	1.16933i	0.392974	+	0.0686654i
$291$		0			0
$292$	−5.68571	−	2.04953i	−0.332731	−	0.119940i
$293$	−0.454390	−	0.541521i	−0.0265458	−	0.0316360i	0.752608	−	0.658469i	$-0.228795\pi$
$293$	−0.454390	−	0.541521i	−0.0265458	−	0.0316360i	−0.779154	+	0.626833i	$0.784351\pi$
$294$		0			0
$295$	−35.5331	+	12.9330i	−2.06882	+	0.752987i
$296$	−3.25208	+	0.0150902i	−0.189023	+	0.000877098i
$297$		0			0
$298$	11.7850	+	20.3395i	0.682688	+	1.17824i
$299$	−0.442740	−	1.21642i	−0.0256043	−	0.0703473i
$300$		0			0
$301$	0.841173	+	1.00247i	0.0484844	+	0.0577815i
$302$	−4.17655	−	4.96181i	−0.240333	−	0.285520i
$303$		0			0
$304$	−7.99800	−	1.35930i	−0.458717	−	0.0779610i
$305$	−14.9205	+	25.8431i	−0.854347	+	1.47977i
$306$		0			0
$307$	−16.9763	+	9.80126i	−0.968887	+	0.559387i	−0.898897	−	0.438160i	$-0.855630\pi$
$307$	−16.9763	+	9.80126i	−0.968887	+	0.559387i	−0.0699905	+	0.997548i	$0.522297\pi$
$308$	−1.58589	+	1.90191i	−0.0903646	+	0.108371i
$309$		0			0
$310$	0.00230448	+	0.0129522i	0.000130886	+	0.000735634i
$311$	−23.9780	−	8.72727i	−1.35967	−	0.494878i	−0.443716	−	0.896168i	$-0.646340\pi$
$311$	−23.9780	−	8.72727i	−1.35967	−	0.494878i	−0.915951	+	0.401289i	$0.868562\pi$
$312$		0			0
$313$	3.61764	−	20.5167i	0.204481	−	1.15967i	−0.693773	−	0.720194i	$-0.744053\pi$
$313$	3.61764	−	20.5167i	0.204481	−	1.15967i	0.898254	−	0.439477i	$-0.144836\pi$
$314$	1.20778	−	2.09943i	0.0681590	−	0.118478i
$315$		0			0
$316$	−10.8650	−	18.6851i	−0.611206	−	1.05112i
$317$	5.72173	−	6.81889i	0.321364	−	0.382987i	−0.581042	−	0.813874i	$-0.697355\pi$
$317$	5.72173	−	6.81889i	0.321364	−	0.382987i	0.902406	+	0.430887i	$0.141799\pi$
$318$		0			0
$319$	−1.10958	−	6.29277i	−0.0621248	−	0.352327i
$320$	18.7685	+	21.9505i	1.04919	+	1.22707i
$321$		0			0
$322$	0.0501330	−	0.0599342i	0.00279380	−	0.00334000i
$323$			11.2104i			0.623765i
$324$		0			0
$325$		−	48.5248i		−	2.69167i
$326$	14.0350	+	11.7398i	0.777324	+	0.650206i
$327$		0			0
$328$	9.19587	+	10.8565i	0.507757	+	0.599450i
$329$	0.0691732	+	0.392301i	0.00381364	+	0.0216282i
$330$		0			0
$331$	5.83964	−	6.95942i	0.320976	−	0.382524i	−0.581296	−	0.813692i	$-0.697454\pi$
$331$	5.83964	−	6.95942i	0.320976	−	0.382524i	0.902272	+	0.431168i	$0.141898\pi$
$332$	14.3661	−	8.35362i	0.788441	−	0.458465i
$333$		0			0
$334$	−17.7074	−	10.1869i	−0.968904	−	0.557401i
$335$	2.01624	−	11.4347i	0.110159	−	0.624743i
$336$		0			0
$337$	−8.03414	−	2.92419i	−0.437647	−	0.159291i	0.113794	−	0.993504i	$-0.463700\pi$
$337$	−8.03414	−	2.92419i	−0.437647	−	0.159291i	−0.551441	+	0.834214i	$0.685922\pi$
$338$	−32.7117	+	5.82015i	−1.77928	+	0.316574i
$339$		0			0
$340$	25.5578	−	30.6507i	1.38607	−	1.66227i
$341$	0.0107161	−	0.00618695i	0.000580310	−	0.000335042i
$342$		0			0
$343$	1.79633	−	3.11134i	0.0969930	−	0.167997i
$344$	−11.0393	−	9.17616i	−0.595201	−	0.494745i
$345$		0			0
$346$	−13.1410	+	11.0612i	−0.706462	+	0.594656i
$347$	−18.6424	−	22.2171i	−1.00077	−	1.19268i	−0.981225	−	0.192868i	$-0.938221\pi$
$347$	−18.6424	−	22.2171i	−1.00077	−	1.19268i	−0.0195503	−	0.999809i	$-0.506223\pi$
$348$		0			0
$349$	7.61884	+	20.9326i	0.407827	+	1.12050i	0.958330	+	0.285663i	$0.0922136\pi$
$349$	7.61884	+	20.9326i	0.407827	+	1.12050i	−0.550503	+	0.834833i	$0.685564\pi$
$350$	2.53435	−	1.46844i	0.135467	−	0.0784914i
$351$		0			0
$352$	13.3999	−	23.6294i	0.714217	−	1.25945i
$353$	8.48681	−	3.08895i	0.451707	−	0.164408i	−0.106141	−	0.994351i	$-0.533849\pi$
$353$	8.48681	−	3.08895i	0.451707	−	0.164408i	0.557848	+	0.829943i	$0.311627\pi$
$354$		0			0
$355$	15.8214	+	18.8552i	0.839712	+	1.00073i
$356$	−1.43599	−	0.517632i	−0.0761072	−	0.0274344i
$357$		0			0
$358$	4.61394	−	26.4057i	0.243854	−	1.39559i
$359$	16.7721	−	29.0501i	0.885197	−	1.53321i	0.0397083	−	0.999211i	$-0.487357\pi$
$359$	16.7721	−	29.0501i	0.885197	−	1.53321i	0.845488	−	0.533994i	$-0.179310\pi$
$360$		0			0
$361$	−7.44326	−	12.8921i	−0.391751	−	0.678532i
$362$	4.46633	−	1.63344i	0.234745	−	0.0858517i
$363$		0			0
$364$	−2.00984	−	2.38024i	−0.105344	−	0.124758i
$365$	3.73120	−	10.2514i	0.195300	−	0.536582i
$366$		0			0
$367$	0.629860	−	3.57211i	0.0328784	−	0.186463i	−0.963946	−	0.266100i	$-0.914265\pi$
$367$	0.629860	−	3.57211i	0.0328784	−	0.186463i	0.996824	+	0.0796368i	$0.0253761\pi$
$368$	−0.423964	+	0.744934i	−0.0221007	+	0.0388324i
$369$		0			0
$370$	−0.00907943	−	5.87015i	−0.000472017	−	0.305175i
$371$	−2.06338	+	2.45904i	−0.107125	+	0.127667i
$372$		0			0
$373$	7.64585	−	1.34817i	0.395887	−	0.0698056i	0.0278392	−	0.999612i	$-0.491137\pi$
$373$	7.64585	−	1.34817i	0.395887	−	0.0698056i	0.368048	+	0.929807i	$0.380026\pi$
$374$	−35.2930	−	12.7838i	−1.82496	−	0.661035i
$375$		0			0
$376$	−1.51358	−	4.09924i	−0.0780568	−	0.211402i
$377$	8.03850			0.414004
$378$		0			0
$379$			13.5768i			0.697393i	0.937236	+	0.348696i	$0.113376\pi$
$379$			13.5768i			0.697393i	−0.937236	+	0.348696i	$0.886624\pi$
$380$	2.49822	−	14.4290i	0.128156	−	0.740191i
$381$		0			0
$382$	−2.81643	+	7.77547i	−0.144101	+	0.397828i
$383$	0.0486221	+	0.275749i	0.00248447	+	0.0140901i	0.986025	−	0.166599i	$-0.0532784\pi$
$383$	0.0486221	+	0.275749i	0.00248447	+	0.0140901i	−0.983540	+	0.180689i	$0.942167\pi$
$384$		0			0
$385$	−3.42414	−	2.87319i	−0.174510	−	0.146431i
$386$	−0.0165395	−	10.6934i	−0.000841840	−	0.544277i
$387$		0			0
$388$	10.3920	−	0.0321469i	0.527574	−	0.00163201i
$389$	−31.5106	−	5.55617i	−1.59765	−	0.281709i	−0.697269	−	0.716810i	$-0.745602\pi$
$389$	−31.5106	−	5.55617i	−1.59765	−	0.281709i	−0.900382	+	0.435101i	$0.856713\pi$
$390$		0			0
$391$	1.11299	+	0.405094i	0.0562862	+	0.0204865i
$392$	−6.62176	+	18.4592i	−0.334449	+	0.932330i
$393$		0			0
$394$	−16.1172	+	5.89441i	−0.811971	+	0.296956i
$395$	33.7876	−	19.5073i	1.70004	−	0.981518i
$396$		0			0
$397$	−30.5442	−	17.6347i	−1.53297	−	0.885061i	−0.999223	−	0.0394172i	$-0.987450\pi$
$397$	−30.5442	−	17.6347i	−1.53297	−	0.885061i	−0.533748	−	0.845644i	$-0.679217\pi$
$398$	−17.7107	−	3.09464i	−0.887759	−	0.155120i
$399$		0			0
$400$	−24.4849	+	20.8047i	−1.22424	+	1.04024i
$401$	0.0106231	−	0.00891385i	0.000530493	−	0.000445136i	−0.642522	−	0.766267i	$-0.722112\pi$
$401$	0.0106231	−	0.00891385i	0.000530493	−	0.000445136i	0.643053	+	0.765822i	$0.277668\pi$
$402$		0			0
$403$	0.00532406	+	0.0146277i	0.000265210	+	0.000728659i
$404$	−12.6444	−	7.24820i	−0.629083	−	0.360611i
$405$		0			0
$406$	0.243258	+	0.419834i	0.0120727	+	0.0208360i
$407$	−5.18839	+	1.88842i	−0.257179	+	0.0936054i
$408$		0			0
$409$	−28.7699	+	24.1408i	−1.42258	+	1.19369i	−0.472642	+	0.881254i	$0.656700\pi$
$409$	−28.7699	+	24.1408i	−1.42258	+	1.19369i	−0.949940	+	0.312434i	$0.898856\pi$
$410$	−19.6476	+	16.5381i	−0.970324	+	0.816760i
$411$		0			0
$412$	8.33959	−	3.06461i	0.410862	−	0.150983i
$413$	−2.33894	−	1.35039i	−0.115092	−	0.0664483i
$414$		0			0
$415$	14.9983	+	25.9777i	0.736235	+	1.27520i
$416$	26.3473	+	21.7630i	1.29178	+	1.06702i
$417$		0			0
$418$	−13.5606	+	2.41273i	−0.663269	+	0.118010i
$419$	10.9340	−	30.0410i	0.534162	−	1.46760i	−0.319913	−	0.947447i	$-0.603654\pi$
$419$	10.9340	−	30.0410i	0.534162	−	1.46760i	0.854075	−	0.520150i	$-0.174124\pi$
$420$		0			0
$421$	−10.9684	−	1.93402i	−0.534566	−	0.0942585i	−0.100153	−	0.994972i	$-0.531933\pi$
$421$	−10.9684	−	1.93402i	−0.534566	−	0.0942585i	−0.434413	+	0.900714i	$0.643044\pi$
$422$	−18.4756	+	32.1153i	−0.899379	+	1.56335i
$423$		0			0
$424$	17.4647	−	30.5765i	0.848160	−	1.48493i
$425$	34.0114	+	28.5390i	1.64980	+	1.38434i
$426$		0			0
$427$	−2.09898	+	0.370106i	−0.101577	+	0.0179107i
$428$	−18.7261	+	3.36167i	−0.905159	+	0.162493i
$429$		0			0
$430$	16.6248	−	19.8750i	0.801719	−	0.958458i
$431$	34.2928			1.65182			0.825912	−	0.563799i	$-0.190661\pi$
$431$	34.2928			1.65182			0.825912	+	0.563799i	$0.190661\pi$
$432$		0			0
$433$	−4.97925			−0.239288			−0.119644	−	0.992817i	$-0.538175\pi$
$433$	−4.97925			−0.239288			−0.119644	+	0.992817i	$0.538175\pi$
$434$	−0.000602862	0	0.000720724i	−2.89383e−5	0	3.45958e-5i
$435$		0			0
$436$	15.6280	−	2.80551i	0.748444	−	0.134359i
$437$	0.427999	−	0.0754678i	0.0204740	−	0.00361011i
$438$		0			0
$439$	30.4090	+	25.5162i	1.45134	+	1.21782i	0.931595	+	0.363499i	$0.118418\pi$
$439$	30.4090	+	25.5162i	1.45134	+	1.21782i	0.519746	+	0.854321i	$0.326027\pi$
$440$	42.5768	+	24.3190i	2.02977	+	1.15936i
$441$		0			0
$442$	23.5477	−	40.9318i	1.12005	−	1.94693i
$443$	21.6555	+	3.81846i	1.02889	+	0.181420i	0.662515	−	0.749049i	$-0.269489\pi$
$443$	21.6555	+	3.81846i	1.02889	+	0.181420i	0.366371	+	0.930469i	$0.380600\pi$
$444$		0			0
$445$	0.942354	−	2.58910i	0.0446719	−	0.122735i
$446$	6.14064	−	1.09256i	0.290768	−	0.0517341i
$447$		0			0
$448$	−0.339326	+	2.03465i	−0.0160316	+	0.0961281i
$449$	−5.92233	−	10.2578i	−0.279492	−	0.484094i	0.691767	−	0.722121i	$-0.256833\pi$
$449$	−5.92233	−	10.2578i	−0.279492	−	0.484094i	−0.971259	+	0.238027i	$0.923499\pi$
$450$		0			0
$451$	20.9193	+	12.0777i	0.985050	+	0.568719i
$452$	13.3447	−	4.90388i	0.627682	−	0.230659i
$453$		0			0
$454$	4.74600	−	3.99489i	0.222741	−	0.187490i
$455$	4.30760	−	3.61451i	0.201943	−	0.169451i
$456$		0			0
$457$	−15.6430	+	5.69358i	−0.731748	+	0.266335i	−0.680905	−	0.732372i	$-0.738413\pi$
$457$	−15.6430	+	5.69358i	−0.731748	+	0.266335i	−0.0508437	+	0.998707i	$0.516191\pi$
$458$	−6.27112	−	10.8232i	−0.293030	−	0.505735i
$459$		0			0
$460$	−1.34225	−	0.769424i	−0.0625829	−	0.0358746i
$461$	0.915935	+	2.51651i	0.0426594	+	0.117206i	0.959193	−	0.282752i	$-0.0912472\pi$
$461$	0.915935	+	2.51651i	0.0426594	+	0.117206i	−0.916534	+	0.399957i	$0.869025\pi$
$462$		0			0
$463$	−9.61960	+	8.07180i	−0.447061	+	0.375128i	−0.838344	−	0.545142i	$-0.816476\pi$
$463$	−9.61960	+	8.07180i	−0.447061	+	0.375128i	0.391283	+	0.920270i	$0.372031\pi$
$464$	−3.44647	−	4.05611i	−0.159998	−	0.188300i
$465$		0			0
$466$	−33.7511	−	5.89742i	−1.56349	−	0.273193i
$467$	−20.3871	−	11.7705i	−0.943402	−	0.544673i	−0.0523766	−	0.998627i	$-0.516680\pi$
$467$	−20.3871	−	11.7705i	−0.943402	−	0.544673i	−0.891025	+	0.453954i	$0.850013\pi$
$468$		0			0
$469$	0.718200	−	0.414653i	0.0331634	−	0.0191469i
$470$	7.40767	−	2.70915i	0.341690	−	0.124964i
$471$		0			0
$472$	27.8863	+	10.0035i	1.28357	+	0.460449i
$473$	−22.9020	−	8.33564i	−1.05303	−	0.383273i
$474$		0			0
$475$	16.0439	+	2.82897i	0.736143	+	0.129802i
$476$	2.85038	−	0.00881744i	0.130647	−	0.000404147i
$477$		0			0
$478$	0.0474530	+	30.6799i	0.00217045	+	1.40327i
$479$	7.82522	+	6.56614i	0.357543	+	0.300015i	0.803811	−	0.594885i	$-0.202802\pi$
$479$	7.82522	+	6.56614i	0.357543	+	0.300015i	−0.446267	+	0.894900i	$0.647247\pi$
$480$		0			0
$481$	−1.20615	−	6.84041i	−0.0549957	−	0.311896i
$482$	8.76497	−	24.1979i	0.399233	−	1.10219i
$483$		0			0
$484$	4.11476	−	23.7656i	0.187035	−	1.08026i
$485$			18.7580i			0.851756i
$486$		0			0
$487$	12.9335			0.586075			0.293037	−	0.956101i	$-0.405334\pi$
$487$	12.9335			0.586075			0.293037	+	0.956101i	$0.405334\pi$
$488$	21.9327	−	8.09829i	0.992845	−	0.366592i
$489$		0			0
$490$	−33.2823	−	12.0555i	−1.50354	−	0.544611i
$491$	23.4853	−	4.14108i	1.05987	−	0.186885i	0.383574	−	0.923510i	$-0.374693\pi$
$491$	23.4853	−	4.14108i	1.05987	−	0.186885i	0.676301	+	0.736626i	$0.263582\pi$
$492$		0			0
$493$	−4.72770	+	5.63425i	−0.212925	+	0.253754i
$494$	−0.0268002	−	17.3272i	−0.00120580	−	0.779590i
$495$		0			0
$496$	0.00509827	−	0.00895801i	0.000228919	−	0.000402226i
$497$	−0.305274	+	1.73129i	−0.0136934	+	0.0776591i
$498$		0			0
$499$	11.7879	−	32.3871i	0.527701	−	1.44985i	−0.334071	−	0.942548i	$-0.608422\pi$
$499$	11.7879	−	32.3871i	0.527701	−	1.44985i	0.861771	−	0.507297i	$-0.169355\pi$
$500$	−14.1258	−	16.7292i	−0.631727	−	0.748151i
$501$		0			0
$502$	−19.3935	+	7.09264i	−0.865573	+	0.316560i
$503$	2.19116	+	3.79521i	0.0976991	+	0.169220i	0.910732	−	0.412998i	$-0.135518\pi$
$503$	2.19116	+	3.79521i	0.0976991	+	0.169220i	−0.813033	+	0.582218i	$0.802185\pi$
$504$		0			0
$505$	13.1538	−	22.7830i	0.585334	−	1.01383i
$506$	−0.250479	+	1.43350i	−0.0111351	+	0.0637268i
$507$		0			0
$508$	32.8279	+	11.8335i	1.45650	+	0.525027i
$509$	3.18212	+	3.79231i	0.141045	+	0.168091i	0.831943	−	0.554862i	$-0.187229\pi$
$509$	3.18212	+	3.79231i	0.141045	+	0.168091i	−0.690897	+	0.722953i	$0.742784\pi$
$510$		0			0
$511$	0.732191	−	0.266496i	0.0323902	−	0.0117891i
$512$	−0.314972	−	22.6252i	−0.0139199	−	0.999903i
$513$		0			0
$514$	−7.08049	+	4.10254i	−0.312307	+	0.180955i
$515$	5.48512	+	15.0702i	0.241703	+	0.664075i
$516$		0			0
$517$	−4.76875	−	5.68318i	−0.209729	−	0.249946i
$518$	0.320761	−	0.269997i	0.0140934	−	0.0118630i
$519$		0			0
$520$	−39.4298	+	47.4359i	−1.72911	+	2.08020i
$521$	9.74864	−	16.8851i	0.427096	−	0.739752i	−0.569518	−	0.821979i	$-0.692870\pi$
$521$	9.74864	−	16.8851i	0.427096	−	0.739752i	0.996614	+	0.0822273i	$0.0262034\pi$
$522$		0			0
$523$	−1.05708	+	0.610304i	−0.0462227	+	0.0266867i	−0.522933	−	0.852374i	$-0.675162\pi$
$523$	−1.05708	+	0.610304i	−0.0462227	+	0.0266867i	0.476711	+	0.879060i	$0.341829\pi$
$524$	18.9478	−	22.7235i	0.827738	−	0.992680i
$525$		0			0
$526$	−6.14777	+	1.09382i	−0.268055	+	0.0476930i
$527$	−0.0133839	−	0.00487136i	−0.000583014	−	0.000212200i
$528$		0			0
$529$	−3.98593	+	22.6054i	−0.173302	+	0.982842i
$530$	55.0937	+	31.6949i	2.39312	+	1.37674i
$531$		0			0
$532$	0.904156	−	0.525751i	0.0392001	−	0.0227942i
$533$	−19.5330	+	23.2785i	−0.846066	+	1.00830i
$534$		0			0
$535$	−5.96333	−	33.8197i	−0.257817	−	1.46216i
$536$	−6.94158	+	5.87978i	−0.299830	+	0.253968i
$537$		0			0
$538$	8.21695	+	6.87321i	0.354258	+	0.296325i
$539$			33.2950i			1.43412i
$540$		0			0
$541$			25.7027i			1.10505i	0.833497	+	0.552524i	$0.186335\pi$
$541$			25.7027i			1.10505i	−0.833497	+	0.552524i	$0.813665\pi$
$542$	5.46636	−	6.53506i	0.234800	−	0.280705i
$543$		0			0
$544$	−30.7495	+	5.66751i	−1.31838	+	0.242993i
$545$	4.97674	+	28.2245i	0.213180	+	1.20900i
$546$		0			0
$547$	−1.72787	+	2.05919i	−0.0738783	+	0.0880447i	−0.801718	−	0.597703i	$-0.796080\pi$
$547$	−1.72787	+	2.05919i	−0.0738783	+	0.0880447i	0.727839	+	0.685748i	$0.240525\pi$
$548$	−12.1679	−	20.9257i	−0.519787	−	0.893900i
$549$		0			0
$550$	−27.2018	+	47.2837i	−1.15989	+	2.01618i
$551$	−0.468640	+	2.65779i	−0.0199647	+	0.113226i
$552$		0			0
$553$	2.61851	+	0.953061i	0.111351	+	0.0405283i
$554$	−0.109618	−	0.616101i	−0.00465722	−	0.0261756i
$555$		0			0
$556$	−12.5925	+	15.1017i	−0.534039	+	0.640456i
$557$	−23.1240	+	13.3506i	−0.979795	+	0.565685i	−0.902208	−	0.431301i	$-0.858055\pi$
$557$	−23.1240	+	13.3506i	−0.979795	+	0.565685i	−0.0775865	+	0.996986i	$0.524721\pi$
$558$		0			0
$559$	15.3300	−	26.5523i	0.648389	−	1.12304i
$560$	−3.67069	−	0.623851i	−0.155115	−	0.0263625i
$561$		0			0
$562$	20.5677	+	24.4348i	0.867597	+	1.03072i
$563$	13.8007	+	16.4470i	0.581629	+	0.693159i	0.973974	−	0.226659i	$-0.0727804\pi$
$563$	13.8007	+	16.4470i	0.581629	+	0.693159i	−0.392345	+	0.919818i	$0.628336\pi$
$564$		0			0
$565$	8.77709	+	24.1149i	0.369255	+	1.01452i
$566$	−13.9506	−	24.0770i	−0.586385	−	1.01203i
$567$		0			0
$568$	−0.0894821	−	19.2843i	−0.00375458	−	0.809149i
$569$	−15.7460	+	5.73106i	−0.660105	+	0.240259i	−0.650282	−	0.759693i	$-0.725349\pi$
$569$	−15.7460	+	5.73106i	−0.660105	+	0.240259i	−0.00982343	+	0.999952i	$0.503127\pi$
$570$		0			0
$571$	−7.89328	−	9.40685i	−0.330324	−	0.393664i	0.575163	−	0.818039i	$-0.304939\pi$
$571$	−7.89328	−	9.40685i	−0.330324	−	0.393664i	−0.905487	+	0.424374i	$0.860494\pi$
$572$	54.5807	+	19.6747i	2.28213	+	0.822643i
$573$		0			0
$574$	−1.80689	−	0.315722i	−0.0754180	−	0.0131780i
$575$	0.860616	−	1.49063i	0.0358902	−	0.0621636i
$576$		0			0
$577$	−2.56985	−	4.45111i	−0.106984	−	0.185302i	0.807563	−	0.589781i	$-0.200786\pi$
$577$	−2.56985	−	4.45111i	−0.106984	−	0.185302i	−0.914547	+	0.404479i	$0.867453\pi$
$578$	6.58268	+	17.9991i	0.273803	+	0.748663i
$579$		0			0
$580$	7.34061	−	6.19830i	0.304802	−	0.257370i
$581$	−0.732765	+	2.01325i	−0.0304002	+	0.0835239i
$582$		0			0
$583$	10.3813	−	58.8752i	0.429949	−	2.43836i
$584$	−7.38224	+	4.30793i	−0.305479	+	0.178264i
$585$		0			0
$586$	−0.999714	+	0.00154627i	−0.0412978	+	6.38758e-5i
$587$	−2.99496	+	3.56925i	−0.123615	+	0.147319i	−0.824302	−	0.566150i	$-0.808432\pi$
$587$	−2.99496	+	3.56925i	−0.123615	+	0.147319i	0.700687	+	0.713469i	$0.252877\pi$
$588$		0			0
$589$	−0.00514679		0.000907518i	−0.000212070		3.73936e-5i
$590$	−18.2123	+	50.2796i	−0.749787	+	2.06998i
$591$		0			0
$592$	−2.93444	+	3.54140i	−0.120605	+	0.145551i
$593$	−5.90755			−0.242594			−0.121297	−	0.992616i	$-0.538705\pi$
$593$	−5.90755			−0.242594			−0.121297	+	0.992616i	$0.538705\pi$
$594$		0			0
$595$			5.14504i			0.210926i
$596$	32.7567	+	5.67147i	1.34177	+	0.232312i
$597$		0			0
$598$	−1.72124	−	0.623468i	−0.0703868	−	0.0254955i
$599$	−7.47843	−	42.4123i	−0.305561	−	1.73292i	−0.620854	−	0.783926i	$-0.713214\pi$
$599$	−7.47843	−	42.4123i	−0.305561	−	1.73292i	0.315294	−	0.948994i	$-0.397897\pi$
$600$		0			0
$601$	−30.3485	−	25.4654i	−1.23794	−	1.03876i	−0.997682	−	0.0680483i	$-0.978323\pi$
$601$	−30.3485	−	25.4654i	−1.23794	−	1.03876i	−0.240260	−	0.970709i	$-0.577233\pi$
$602$	1.85068	−	0.00286247i	0.0754283	−	0.000116666i
$603$		0			0
$604$	−9.17200	+	0.0283729i	−0.373203	+	0.00115448i
$605$	42.8745	+	7.55993i	1.74310	+	0.307355i
$606$		0			0
$607$	22.7963	+	8.29716i	0.925272	+	0.336771i	0.760334	−	0.649533i	$-0.225035\pi$
$607$	22.7963	+	8.29716i	0.925272	+	0.336771i	0.164938	+	0.986304i	$0.447258\pi$
$608$	−8.73159	+	7.44250i	−0.354113	+	0.301833i
$609$		0			0
$610$	14.4951	+	39.6342i	0.586890	+	1.60474i
$611$	8.08262	−	4.66650i	0.326988	−	0.188787i
$612$		0			0
$613$	11.1793	+	6.45437i	0.451528	+	0.260690i	0.708475	−	0.705736i	$-0.249383\pi$
$613$	11.1793	+	6.45437i	0.451528	+	0.260690i	−0.256947	+	0.966425i	$0.582717\pi$
$614$	−4.77167	+	27.3084i	−0.192569	+	1.10208i
$615$		0			0
$616$	0.624129	+	3.44603i	0.0251469	+	0.138844i
$617$	−36.0968	+	30.2888i	−1.45320	+	1.21938i	−0.523004	+	0.852330i	$0.675189\pi$
$617$	−36.0968	+	30.2888i	−1.45320	+	1.21938i	−0.930200	+	0.367053i	$0.880367\pi$
$618$		0			0
$619$	12.7178	+	34.9419i	0.511173	+	1.40444i	0.880016	+	0.474944i	$0.157532\pi$
$619$	12.7178	+	34.9419i	0.511173	+	1.40444i	−0.368843	+	0.929492i	$0.620246\pi$
$620$	0.0161409	+	0.00925251i	0.000648235	+	0.000371590i
$621$		0			0
$622$	−31.2237	+	18.0914i	−1.25196	+	0.725401i
$623$	0.184923	−	0.0673064i	0.00740878	−	0.00269657i
$624$		0			0
$625$	−0.491039	+	0.412031i	−0.0196416	+	0.0164812i
$626$	−18.9730	−	22.5403i	−0.758316	−	0.900892i
$627$		0			0
$628$	−1.18147	−	3.21509i	−0.0471459	−	0.128296i
$629$	5.50388	+	3.17767i	0.219454	+	0.126702i
$630$		0			0
$631$	−19.0617	−	33.0158i	−0.758833	−	1.31434i	−0.943446	−	0.331526i	$-0.892436\pi$
$631$	−19.0617	−	33.0158i	−0.758833	−	1.31434i	0.184613	−	0.982811i	$-0.440897\pi$
$632$	−30.1272	−	5.16822i	−1.19840	−	0.205581i
$633$		0			0
$634$	−2.20515	−	12.3939i	−0.0875775	−	0.492224i
$635$	−21.5430	+	59.1890i	−0.854909	+	2.34884i
$636$		0			0
$637$	−41.2492	−	7.27335i	−1.63435	−	0.288180i
$638$	−7.83291	−	4.50619i	−0.310108	−	0.178402i
$639$		0			0
$640$	40.8408	−	0.442199i	1.61437	−	0.0174795i
$641$	−20.1927	−	16.9437i	−0.797565	−	0.669236i	0.150041	−	0.988680i	$-0.452060\pi$
$641$	−20.1927	−	16.9437i	−0.797565	−	0.669236i	−0.947605	+	0.319444i	$0.896504\pi$
$642$		0			0
$643$	−36.5216	+	6.43974i	−1.44027	+	0.253959i	−0.838583	−	0.544773i	$-0.816616\pi$
$643$	−36.5216	+	6.43974i	−1.44027	+	0.253959i	−0.601687	+	0.798732i	$0.705505\pi$
$644$	−0.0195252	−	0.108764i	−0.000769399	−	0.00428591i
$645$		0			0
$646$	12.1606	+	10.1719i	0.478452	+	0.400209i
$647$	−34.9632			−1.37454			−0.687272	−	0.726400i	$-0.741192\pi$
$647$	−34.9632			−1.37454			−0.687272	+	0.726400i	$0.741192\pi$
$648$		0			0
$649$	50.2989			1.97440
$650$	−52.6375	−	44.0295i	−2.06461	−	1.72698i
$651$		0			0
$652$	25.4696	−	4.57226i	0.997466	−	0.179063i
$653$	−7.50466	+	1.32327i	−0.293680	+	0.0517837i	−0.318547	−	0.947907i	$-0.603195\pi$
$653$	−7.50466	+	1.32327i	−0.293680	+	0.0517837i	0.0248671	+	0.999691i	$0.492084\pi$
$654$		0			0
$655$	40.9106	+	34.3280i	1.59851	+	1.34131i
$656$	20.1206	−	0.124485i	0.785579	−	0.00486031i
$657$		0			0
$658$	0.488315	+	0.280923i	0.0190365	+	0.0109515i
$659$	21.1078	+	3.72188i	0.822245	+	0.144984i	0.568915	−	0.822396i	$-0.307363\pi$
$659$	21.1078	+	3.72188i	0.822245	+	0.144984i	0.253329	+	0.967380i	$0.418474\pi$
$660$		0			0
$661$	−5.23825	+	14.3920i	−0.203744	+	0.559783i	−0.998913	−	0.0466051i	$-0.985160\pi$
$661$	−5.23825	+	14.3920i	−0.203744	+	0.559783i	0.795169	+	0.606388i	$0.207382\pi$
$662$	−2.25059	−	12.6493i	−0.0874717	−	0.491629i
$663$		0			0
$664$	3.97361	−	23.1634i	0.154206	−	0.898916i
$665$	0.943943	+	1.63496i	0.0366045	+	0.0634009i
$666$		0			0
$667$	0.246934	+	0.142568i	0.00956134	+	0.00552024i
$668$	−27.1173	+	9.96498i	−1.04920	+	0.385557i
$669$		0			0
$670$	−10.5744	−	12.5625i	−0.408523	−	0.485333i
$671$	30.4074	−	25.5148i	1.17387	−	0.984990i
$672$		0			0
$673$	−6.37794	+	2.32138i	−0.245851	+	0.0894826i	−0.462007	−	0.886876i	$-0.652870\pi$
$673$	−6.37794	+	2.32138i	−0.245851	+	0.0894826i	0.216155	+	0.976359i	$0.430648\pi$
$674$	−10.4619	+	6.06177i	−0.402977	+	0.233491i
$675$		0			0
$676$	−23.3680	+	40.7652i	−0.898768	+	1.56789i
$677$	−5.34948	−	14.6976i	−0.205597	−	0.564874i	0.793444	−	0.608643i	$-0.208286\pi$
$677$	−5.34948	−	14.6976i	−0.205597	−	0.564874i	−0.999042	+	0.0437688i	$0.986063\pi$
$678$		0			0
$679$	−1.02632	+	0.861183i	−0.0393865	+	0.0330492i
$680$	−10.0583	−	55.5352i	−0.385718	−	2.12968i
$681$		0			0
$682$	0.00301207	−	0.0172382i	0.000115338	−	0.000660083i
$683$	−6.24942	−	3.60810i	−0.239127	−	0.138060i	0.375648	−	0.926762i	$-0.377420\pi$
$683$	−6.24942	−	3.60810i	−0.239127	−	0.138060i	−0.614776	+	0.788702i	$0.710753\pi$
$684$		0			0
$685$	37.8392	−	21.8465i	1.44576	−	0.834711i
$686$	−1.74512	−	4.77170i	−0.0666290	−	0.182184i
$687$		0			0
$688$	−19.9706	+	3.64889i	−0.761371	+	0.139112i
$689$	70.6726	+	25.7227i	2.69241	+	0.979958i
$690$		0			0
$691$	42.2279	+	7.44592i	1.60643	+	0.283256i	0.903687	−	0.428193i	$-0.140850\pi$
$691$	42.2279	+	7.44592i	1.60643	+	0.283256i	0.702738	+	0.711449i	$0.251961\pi$
$692$	0.0751433	+	24.2913i	0.00285652	+	0.923416i
$693$		0			0
$694$	−41.0155	+	0.0634391i	−1.55693	+	0.00240812i
$695$	−27.1886	−	22.8140i	−1.03132	−	0.865383i
$696$		0			0
$697$	−4.82812	−	27.3816i	−0.182878	−	1.03715i
$698$	29.6198	+	10.7289i	1.12112	+	0.406093i
$699$		0			0
$700$	0.706677	−	4.08155i	0.0267099	−	0.154268i
$701$			33.1261i			1.25116i	0.780162	+	0.625578i	$0.215137\pi$
$701$			33.1261i			1.25116i	−0.780162	+	0.625578i	$0.784863\pi$
$702$		0			0
$703$	2.33198			0.0879524
$704$	−13.4736	−	35.9761i	−0.507806	−	1.35590i
$705$		0			0
$706$	4.34986	−	12.0089i	0.163709	−	0.451961i
$707$	1.85043	−	0.326281i	0.0695927	−	0.0122711i
$708$		0			0
$709$	28.0590	−	33.4394i	1.05378	−	1.25584i	0.0880950	−	0.996112i	$-0.471922\pi$
$709$	28.0590	−	33.4394i	1.05378	−	1.25584i	0.965681	−	0.259730i	$-0.0836335\pi$
$710$	34.8090	−	0.0538395i	1.30636	−	0.00202056i
$711$		0			0
$712$	−1.86446	+	1.08801i	−0.0698737	+	0.0407751i
$713$	−9.58821e−5	0	0.000543774i	−3.59081e−6	0	2.03645e-5i
$714$		0			0
$715$	−35.8181	+	98.4095i	−1.33952	+	3.68030i
$716$	−24.4572	−	28.9645i	−0.914009	−	1.08246i
$717$		0			0
$718$	−16.2939	−	44.5526i	−0.608083	−	1.66269i
$719$	−7.51355	−	13.0138i	−0.280208	−	0.485335i	0.691228	−	0.722637i	$-0.257070\pi$
$719$	−7.51355	−	13.0138i	−0.280208	−	0.485335i	−0.971436	+	0.237302i	$0.923737\pi$
$720$		0			0
$721$	−0.572726	+	0.991990i	−0.0213294	+	0.0369436i
$722$	−20.7385	−	3.62369i	−0.771807	−	0.134860i
$723$		0			0
$724$	2.28070	−	6.32700i	0.0847615	−	0.235141i
$725$	6.87044	+	8.18787i	0.255162	+	0.304090i
$726$		0			0
$727$	−25.6575	+	9.33858i	−0.951586	+	0.346349i	−0.770731	−	0.637161i	$-0.780109\pi$
$727$	−25.6575	+	9.33858i	−0.951586	+	0.346349i	−0.180855	+	0.983510i	$0.557886\pi$
$728$	−4.40562	+	0.0204428i	−0.163283	+	0.000757661i
$729$		0			0
$730$	−7.73469	−	13.3492i	−0.286274	−	0.494074i
$731$	9.59469	+	26.3612i	0.354872	+	0.975004i
$732$		0			0
$733$	27.3864	+	32.6378i	1.01154	+	1.20551i	0.978541	+	0.206051i	$0.0660612\pi$
$733$	27.3864	+	32.6378i	1.01154	+	1.20551i	0.0329983	+	0.999455i	$0.489494\pi$
$734$	−3.30336	−	3.92445i	−0.121929	−	0.144854i
$735$		0			0
$736$	0.423381	+	1.13582i	0.0156060	+	0.0418670i
$737$	−7.72243	+	13.3756i	−0.284459	+	0.492698i
$738$		0			0
$739$	40.4642	−	23.3620i	1.48850	−	0.859385i	0.488585	−	0.872516i	$-0.337513\pi$
$739$	40.4642	−	23.3620i	1.48850	−	0.859385i	0.999914	+	0.0131310i	$0.00417983\pi$
$740$	−6.37592	−	5.31651i	−0.234383	−	0.195439i
$741$		0			0
$742$	0.795224	+	4.46950i	0.0291936	+	0.164081i
$743$	32.7196	+	11.9089i	1.20036	+	0.436897i	0.863351	−	0.504603i	$-0.168361\pi$
$743$	32.7196	+	11.9089i	1.20036	+	0.436897i	0.337013	+	0.941500i	$0.390583\pi$
$744$		0			0
$745$	−10.4200	+	59.0949i	−0.381760	+	2.16507i
$746$	5.47512	−	9.51715i	0.200458	−	0.348448i
$747$		0			0
$748$	−45.8908	+	26.6847i	−1.67794	+	0.975690i
$749$	1.57662	−	1.87895i	0.0576086	−	0.0686553i
$750$		0			0
$751$	6.08986	+	34.5373i	0.222222	+	1.26028i	0.867925	+	0.496695i	$0.165453\pi$
$751$	6.08986	+	34.5373i	0.222222	+	1.26028i	−0.645703	+	0.763589i	$0.723436\pi$
$752$	−5.82003	−	2.07763i	−0.212235	−	0.0757635i
$753$		0			0
$754$	7.29383	−	8.71980i	0.265626	−	0.317556i
$755$		−	16.5558i		−	0.602528i
$756$		0			0
$757$		−	11.7722i		−	0.427866i	−0.976848	−	0.213933i	$-0.931373\pi$
$757$		−	11.7722i		−	0.427866i	0.976848	−	0.213933i	$-0.0686275\pi$
$758$	14.7275	+	12.3191i	0.534927	+	0.447449i
$759$		0			0
$760$	−13.3851	−	15.8023i	−0.485529	−	0.573208i
$761$	0.482495	+	2.73637i	0.0174904	+	0.0991932i	0.992303	−	0.123831i	$-0.0395181\pi$
$761$	0.482495	+	2.73637i	0.0174904	+	0.0991932i	−0.974813	+	0.223024i	$0.928407\pi$
$762$		0			0
$763$	−1.31578	+	1.56809i	−0.0476345	+	0.0567686i
$764$	5.87896	+	10.1103i	0.212693	+	0.365778i
$765$		0			0
$766$	0.343238	+	0.197462i	0.0124017	+	0.00713458i
$767$	−10.9879	+	62.3153i	−0.396749	+	2.25007i
$768$		0			0
$769$	−21.8665	−	7.95874i	−0.788525	−	0.286999i	−0.0838020	−	0.996482i	$-0.526706\pi$
$769$	−21.8665	−	7.95874i	−0.788525	−	0.286999i	−0.704723	+	0.709483i	$0.748929\pi$
$770$	−6.22364	+	1.10732i	−0.224284	+	0.0399052i
$771$		0			0
$772$	−11.6147	−	9.68480i	−0.418021	−	0.348564i
$773$	15.8287	−	9.13870i	0.569319	−	0.328696i	−0.187558	−	0.982253i	$-0.560057\pi$
$773$	15.8287	−	9.13870i	0.569319	−	0.328696i	0.756877	+	0.653557i	$0.226724\pi$
$774$		0			0
$775$	−0.0103491	+	0.0179252i	−0.000371751	+	0.000643892i
$776$	9.39444	−	11.3020i	0.337241	−	0.405716i
$777$		0			0
$778$	−34.6186	+	29.1398i	−1.24114	+	1.04471i
$779$	−6.55786	−	7.81535i	−0.234960	−	0.280014i
$780$		0			0
$781$	−11.1980	−	30.7662i	−0.400696	−	1.10090i
$782$	1.44931	−	0.839752i	0.0518273	−	0.0300295i
$783$		0			0
$784$	14.0154	+	23.9322i	0.500549	+	0.854720i
$785$	5.80991	−	2.11463i	0.207364	−	0.0754745i
$786$		0			0
$787$	0.462707	+	0.551432i	0.0164937	+	0.0196564i	0.774228	−	0.632906i	$-0.218138\pi$
$787$	0.462707	+	0.551432i	0.0164937	+	0.0196564i	−0.757735	+	0.652563i	$0.773694\pi$
$788$	−8.23010	+	22.8315i	−0.293185	+	0.813340i
$789$		0			0
$790$	9.49697	−	54.3515i	0.337887	−	1.93374i
$791$	−0.916455	+	1.58735i	−0.0325854	+	0.0564395i
$792$		0			0
$793$	24.9678	+	43.2455i	0.886632	+	1.53569i
$794$	−46.8440	+	17.1319i	−1.66243	+	0.607989i
$795$		0			0
$796$	−19.4270	+	16.4038i	−0.688571	+	0.581419i
$797$	10.2956	−	28.2870i	0.364690	−	1.00198i	−0.612660	−	0.790347i	$-0.709901\pi$
$797$	10.2956	−	28.2870i	0.364690	−	1.00198i	0.977350	−	0.211630i	$-0.0678773\pi$
$798$		0			0
$799$	−1.48286	+	8.40970i	−0.0524597	+	0.297514i
$800$	0.351400	+	45.4375i	0.0124239	+	1.60646i
$801$		0			0
$802$	−3.03334e−5	−	0.0196116i	−1.07111e−6	−	0.000692508i
$803$	−9.32772	+	11.1163i	−0.329168	+	0.392287i
$804$		0			0
$805$	0.196431	−	0.0346360i	0.00692327	−	0.00122076i
$806$	0.0206983	+	0.00749735i	0.000729068	+	0.000264083i
$807$		0			0
$808$	−19.3356	+	7.13935i	−0.680223	+	0.251162i
$809$	29.5119			1.03758			0.518792	−	0.854901i	$-0.326382\pi$
$809$	29.5119			1.03758			0.518792	+	0.854901i	$0.326382\pi$
$810$		0			0
$811$			12.2968i			0.431800i	0.976415	+	0.215900i	$0.0692685\pi$
$811$			12.2968i			0.431800i	−0.976415	+	0.215900i	$0.930731\pi$
$812$	0.676141	+	0.117066i	0.0237279	+	0.00410823i
$813$		0			0
$814$	−2.65927	+	7.34161i	−0.0932075	+	0.257323i
$815$	8.11081	+	45.9987i	0.284109	+	1.61126i
$816$		0			0
$817$	7.88533	+	6.61658i	0.275873	+	0.231485i
$818$	0.0821502	+	53.1128i	0.00287231	+	1.85705i
$819$		0			0
$820$	0.112350	+	36.3189i	0.00392343	+	1.26831i
$821$	35.5839	+	6.27441i	1.24189	+	0.218978i	0.755725	−	0.654889i	$-0.227285\pi$
$821$	35.5839	+	6.27441i	1.24189	+	0.218978i	0.486164	+	0.873868i	$0.338396\pi$
$822$		0			0
$823$	−32.2737	−	11.7467i	−1.12499	−	0.409463i	−0.288519	−	0.957474i	$-0.593163\pi$
$823$	−32.2737	−	11.7467i	−1.12499	−	0.409463i	−0.836471	+	0.548011i	$0.815385\pi$
$824$	4.24268	−	11.8271i	0.147801	−	0.412017i
$825$		0			0
$826$	−3.58711	+	1.31189i	−0.124812	+	0.0456464i
$827$	−7.34810	+	4.24243i	−0.255518	+	0.147524i	−0.622289	−	0.782788i	$-0.713797\pi$
$827$	−7.34810	+	4.24243i	−0.255518	+	0.147524i	0.366770	+	0.930312i	$0.380464\pi$
$828$		0			0
$829$	16.3678	+	9.44995i	0.568477	+	0.328210i	0.756541	−	0.653947i	$-0.226888\pi$
$829$	16.3678	+	9.44995i	0.568477	+	0.328210i	−0.188064	+	0.982157i	$0.560221\pi$
$830$	41.7883	+	7.30179i	1.45049	+	0.253449i
$831$		0			0
$832$	47.5140	−	8.83342i	1.64725	−	0.306244i
$833$	29.3579	−	24.6342i	1.01719	−	0.853525i
$834$		0			0
$835$	−17.8356	−	49.0029i	−0.617226	−	1.69581i
$836$	−9.68713	+	16.8991i	−0.335037	+	0.584468i
$837$		0			0
$838$	−22.6660	−	39.1188i	−0.782983	−	1.35133i
$839$	44.5776	−	16.2249i	1.53899	−	0.560147i	0.573188	−	0.819424i	$-0.305707\pi$
$839$	44.5776	−	16.2249i	1.53899	−	0.560147i	0.965803	+	0.259277i	$0.0834844\pi$
$840$		0			0
$841$	20.8589	−	17.5027i	0.719273	−	0.603541i
$842$	−12.0502	+	10.1432i	−0.415279	+	0.349556i
$843$		0			0
$844$	18.0732	+	49.1818i	0.622105	+	1.69291i
$845$	−73.4516	−	42.4073i	−2.52681	−	1.45886i
$846$		0			0
$847$	1.55475	+	2.69290i	0.0534217	+	0.0925292i
$848$	−17.3212	−	46.6889i	−0.594813	−	1.60330i
$849$		0			0
$850$	61.8185	−	10.9989i	2.12036	−	0.377258i
$851$	0.0842673	−	0.231522i	0.00288864	−	0.00793649i
$852$		0			0
$853$	48.7404	+	8.59425i	1.66884	+	0.294262i	0.926649	−	0.375927i	$-0.122676\pi$
$853$	48.7404	+	8.59425i	1.66884	+	0.294262i	0.742191	+	0.670188i	$0.233787\pi$
$854$	−1.50306	+	2.61270i	−0.0514336	+	0.0894046i
$855$		0			0
$856$	−13.3447	+	23.3635i	−0.456114	+	0.798547i
$857$	−21.0814	−	17.6894i	−0.720126	−	0.604257i	0.207294	−	0.978279i	$-0.433534\pi$
$857$	−21.0814	−	17.6894i	−0.720126	−	0.604257i	−0.927420	+	0.374021i	$0.877979\pi$
$858$		0			0
$859$	40.4643	−	7.13496i	1.38063	−	0.243442i	0.566467	−	0.824084i	$-0.308310\pi$
$859$	40.4643	−	7.13496i	1.38063	−	0.243442i	0.814159	+	0.580643i	$0.197199\pi$
$860$	−6.47481	−	36.0677i	−0.220789	−	1.22990i
$861$		0			0
$862$	31.1160	−	37.1993i	1.05981	−	1.26701i
$863$	−28.7460			−0.978524			−0.489262	−	0.872137i	$-0.662734\pi$
$863$	−28.7460			−0.978524			−0.489262	+	0.872137i	$0.662734\pi$
$864$		0			0
$865$	−43.8467			−1.49083
$866$	−4.51799	+	5.40127i	−0.153527	+	0.183543i
$867$		0			0
$868$	0.000234795		0.00130791i	7.96945e−6		4.43935e-5i
$869$	−51.1081	+	9.01174i	−1.73372	+	0.305702i
$870$		0			0
$871$	−14.8841	−	12.4892i	−0.504328	−	0.423182i
$872$	11.1369	−	19.4981i	0.377145	−	0.660290i
$873$		0			0
$874$	0.306486	−	0.532751i	0.0103670	−	0.0180206i
$875$	2.77990	+	0.490171i	0.0939777	+	0.0165708i
$876$		0			0
$877$	8.94594	−	24.5788i	0.302083	−	0.829966i	−0.692055	−	0.721845i	$-0.743294\pi$
$877$	8.94594	−	24.5788i	0.302083	−	0.829966i	0.994138	−	0.108121i	$-0.0344834\pi$
$878$	55.2707	−	9.83389i	1.86530	−	0.331878i
$879$		0			0
$880$	65.0128	−	24.1193i	2.19158	−	0.813060i
$881$	3.99560	+	6.92059i	0.134615	+	0.233160i	0.925450	−	0.378869i	$-0.123687\pi$
$881$	3.99560	+	6.92059i	0.134615	+	0.233160i	−0.790835	+	0.612029i	$0.790353\pi$
$882$		0			0
$883$	−37.6003	−	21.7085i	−1.26535	−	0.730551i	−0.291246	−	0.956648i	$-0.594070\pi$
$883$	−37.6003	−	21.7085i	−1.26535	−	0.730551i	−0.974105	+	0.226097i	$0.927403\pi$
$884$	−23.0348	−	62.6834i	−0.774743	−	2.10827i
$885$		0			0
$886$	23.7915	−	20.0262i	0.799291	−	0.672795i
$887$	41.5415	−	34.8574i	1.39483	−	1.17040i	0.431484	−	0.902121i	$-0.357990\pi$
$887$	41.5415	−	34.8574i	1.39483	−	1.17040i	0.963342	−	0.268277i	$-0.0864543\pi$
$888$		0			0
$889$	−4.22749	+	1.53868i	−0.141786	+	0.0516057i
$890$	−1.95348	−	3.37147i	−0.0654808	−	0.113012i
$891$		0			0
$892$	4.38663	−	7.65244i	0.146875	−	0.256223i
$893$	1.07169	+	2.94443i	0.0358626	+	0.0985317i
$894$		0			0
$895$	52.4182	−	43.9841i	1.75215	−	1.47023i
$896$	1.89920	+	2.21425i	0.0634480	+	0.0739728i
$897$		0			0
$898$	−16.5009	−	2.88324i	−0.550641	−	0.0962150i
$899$	−0.00296945	−	0.00171441i	−9.90366e−5	−	5.71788e-5i
$900$		0			0
$901$	−59.5941	+	34.4067i	−1.98537	+	1.14625i
$902$	32.0827	−	11.7334i	1.06824	−	0.390679i
$903$		0			0
$904$	6.78898	−	18.9253i	0.225798	−	0.629447i
$905$	11.4076	+	4.15204i	0.379203	+	0.138018i
$906$		0			0
$907$	−12.0222	−	2.11983i	−0.399190	−	0.0703879i	−0.0295505	−	0.999563i	$-0.509408\pi$
$907$	−12.0222	−	2.11983i	−0.399190	−	0.0703879i	−0.369639	+	0.929175i	$0.620519\pi$
$908$	−0.0271388	−	8.77306i	−0.000900634	−	0.291144i
$909$		0			0
$910$	−0.0123000	−	7.95236i	−0.000407741	−	0.263618i
$911$	8.79514	+	7.38000i	0.291396	+	0.244510i	0.776752	−	0.629806i	$-0.216866\pi$
$911$	8.79514	+	7.38000i	0.291396	+	0.244510i	−0.485356	+	0.874316i	$0.661310\pi$
$912$		0			0
$913$	−6.92871	−	39.2947i	−0.229307	−	1.30046i
$914$	−8.01772	+	22.1350i	−0.265203	+	0.732160i
$915$		0			0
$916$	−17.4307	−	3.01794i	−0.575926	−	0.0997154i
$917$			3.81438i			0.125962i
$918$		0			0
$919$	−16.5475			−0.545852			−0.272926	−	0.962035i	$-0.587991\pi$
$919$	−16.5475			−0.545852			−0.272926	+	0.962035i	$0.587991\pi$
$920$	−2.05255	+	0.757870i	−0.0676705	+	0.0249863i
$921$		0			0
$922$	3.56088	+	1.28982i	0.117271	+	0.0424780i
$923$	40.5625	−	7.15226i	1.33513	−	0.235420i
$924$		0			0
$925$	5.93664	−	7.07501i	0.195196	−	0.232625i
$926$	0.0274680	+	17.7590i	0.000902653	+	0.583595i
$927$		0			0
$928$	−7.52708	+	0.0582122i	−0.247088	+	0.00191091i
$929$	−2.54299	+	14.4220i	−0.0834326	+	0.473170i	0.914251	+	0.405148i	$0.132780\pi$
$929$	−2.54299	+	14.4220i	−0.0834326	+	0.473170i	−0.997684	+	0.0680222i	$0.978331\pi$
$930$		0			0
$931$	4.80961	−	13.2143i	0.157629	−	0.433081i
$932$	−37.0218	+	31.2606i	−1.21269	+	1.02398i
$933$		0			0
$934$	−31.2666	+	11.4349i	−1.02307	+	0.374161i
$935$	−47.9102	−	82.9830i	−1.56683	−	2.71383i
$936$		0			0
$937$	12.7855	−	22.1452i	0.417685	−	0.723452i	−0.578021	−	0.816022i	$-0.696175\pi$
$937$	12.7855	−	22.1452i	0.417685	−	0.723452i	0.995706	+	0.0925699i	$0.0295082\pi$
$938$	0.201871	−	1.15531i	0.00659131	−	0.0377223i
$939$		0			0
$940$	3.78267	−	10.4937i	0.123377	−	0.342266i
$941$	4.21884	+	5.02781i	0.137530	+	0.163902i	0.830413	−	0.557148i	$-0.188104\pi$
$941$	4.21884	+	5.02781i	0.137530	+	0.163902i	−0.692883	+	0.721050i	$0.743660\pi$
$942$		0			0
$943$	−1.01289	+	0.368662i	−0.0329842	+	0.0120053i
$944$	36.1544	−	21.1730i	1.17672	−	0.689124i
$945$		0			0
$946$	−29.8225	+	17.2796i	−0.969614	+	0.561808i
$947$	−16.2688	−	44.6981i	−0.528664	−	1.45249i	−0.860645	−	0.509206i	$-0.829939\pi$
$947$	−16.2688	−	44.6981i	−0.528664	−	1.45249i	0.331981	−	0.943286i	$-0.392283\pi$
$948$		0			0
$949$	−11.7344	−	13.9845i	−0.380914	−	0.453956i
$950$	17.6263	−	14.8368i	0.571874	−	0.481368i
$951$		0			0
$952$	2.57676	−	3.09996i	0.0835133	−	0.100470i
$953$	−0.186102	+	0.322338i	−0.00602843	+	0.0104416i	−0.869024	−	0.494770i	$-0.835252\pi$
$953$	−0.186102	+	0.322338i	−0.00602843	+	0.0104416i	0.862995	+	0.505212i	$0.168586\pi$
$954$		0			0
$955$	−18.2821	+	10.5552i	−0.591596	+	0.341558i
$956$	33.3233	+	27.7863i	1.07775	+	0.898675i
$957$		0			0
$958$	14.2230	−	2.53058i	0.459523	−	0.0817594i
$959$	2.93251	+	1.06735i	0.0946956	+	0.0344664i
$960$		0			0
$961$	−5.38309	+	30.5290i	−0.173648	+	0.984808i
$962$	−8.51459	−	4.89836i	−0.274521	−	0.157929i
$963$		0			0
$964$	−18.2958	−	31.4641i	−0.589269	−	1.01339i
$965$	17.5461	−	20.9107i	0.564830	−	0.673138i
$966$		0			0
$967$	−1.69350	−	9.60434i	−0.0544594	−	0.308855i	0.945395	−	0.325927i	$-0.105676\pi$
$967$	−1.69350	−	9.60434i	−0.0544594	−	0.308855i	−0.999854	+	0.0170726i	$0.994565\pi$
$968$	−22.0463	−	26.0275i	−0.708595	−	0.836557i
$969$		0			0
$970$	20.3478	+	17.0203i	0.653329	+	0.546488i
$971$			0.0717145i			0.00230143i	0.999999	+	0.00115071i	$0.000366284\pi$
$971$			0.0717145i			0.00230143i	−0.999999	+	0.00115071i	$0.999634\pi$
$972$		0			0
$973$		−	2.53499i		−	0.0812679i
$974$	11.7354	−	14.0297i	0.376027	−	0.449542i
$975$		0			0
$976$	11.1162	−	31.1397i	0.355822	−	0.996756i
$977$	−8.23563	−	46.7066i	−0.263481	−	1.49428i	−0.773325	−	0.634010i	$-0.781408\pi$
$977$	−8.23563	−	46.7066i	−0.263481	−	1.49428i	0.509844	−	0.860267i	$-0.329703\pi$
$978$		0			0
$979$	−2.35582	+	2.80755i	−0.0752922	+	0.0897298i
$980$	−43.2763	+	25.1644i	−1.38241	+	0.803848i
$981$		0			0
$982$	16.8176	−	29.2332i	0.536670	−	0.932869i
$983$	0.121491	−	0.689011i	0.00387497	−	0.0219760i	−0.982809	−	0.184625i	$-0.940893\pi$
$983$	0.121491	−	0.689011i	0.00387497	−	0.0219760i	0.986684	+	0.162649i	$0.0520039\pi$
$984$		0			0
$985$	−41.1655	−	14.9830i	−1.31164	−	0.477398i
$986$	1.82205	+	10.2407i	0.0580258	+	0.326130i
$987$		0			0
$988$	−18.8201	−	15.6930i	−0.598748	−	0.499261i
$989$	0.941843	−	0.543774i	0.0299489	−	0.0172910i
$990$		0			0
$991$	−9.00116	+	15.5905i	−0.285931	+	0.495247i	−0.972835	−	0.231501i	$-0.925636\pi$
$991$	−9.00116	+	15.5905i	−0.285931	+	0.495247i	0.686903	+	0.726749i	$0.258970\pi$
$992$	−0.00509126	−	0.0136585i	−0.000161648	−	0.000433659i
$993$		0			0
$994$	1.60104	+	1.90206i	0.0507818	+	0.0603296i
$995$	−29.5008	−	35.1577i	−0.935239	−	1.11457i
$996$		0			0
$997$	14.7188	+	40.4396i	0.466150	+	1.28074i	0.920789	+	0.390061i	$0.127546\pi$
$997$	14.7188	+	40.4396i	0.466150	+	1.28074i	−0.454639	+	0.890676i	$0.650232\pi$
$998$	−24.4361	−	42.1738i	−0.773512	−	1.33499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.181.24		204
3.2	odd	2		216.2.t.a.61.11	yes	204
8.5	even	2	inner	648.2.t.a.181.33		204
12.11	even	2		864.2.bf.a.817.34		204
24.5	odd	2		216.2.t.a.61.2	✓	204
24.11	even	2		864.2.bf.a.817.1		204
27.4	even	9	inner	648.2.t.a.469.33		204
27.23	odd	18		216.2.t.a.85.2	yes	204
108.23	even	18		864.2.bf.a.625.1		204
216.77	odd	18		216.2.t.a.85.11	yes	204
216.85	even	18	inner	648.2.t.a.469.24		204
216.131	even	18		864.2.bf.a.625.34		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.61.2	✓	204	24.5	odd	2
216.2.t.a.61.11	yes	204	3.2	odd	2
216.2.t.a.85.2	yes	204	27.23	odd	18
216.2.t.a.85.11	yes	204	216.77	odd	18
648.2.t.a.181.24		204	1.1	even	1	trivial
648.2.t.a.181.33		204	8.5	even	2	inner
648.2.t.a.469.24		204	216.85	even	18	inner
648.2.t.a.469.33		204	27.4	even	9	inner
864.2.bf.a.625.1		204	108.23	even	18
864.2.bf.a.625.34		204	216.131	even	18
864.2.bf.a.817.1		204	24.11	even	2
864.2.bf.a.817.34		204	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.907362 - 1.08476i) q^{2} +(-0.353388 - 1.96853i) q^{4} +(3.55522 - 0.626880i) q^{5} +(0.197520 + 0.165739i) q^{7} +(-2.45603 - 1.40283i) q^{8} +O(q^{10})\)	\(q+(0.907362 - 1.08476i) q^{2} +(-0.353388 - 1.96853i) q^{4} +(3.55522 - 0.626880i) q^{5} +(0.197520 + 0.165739i) q^{7} +(-2.45603 - 1.40283i) q^{8} +(2.54586 - 4.42535i) q^{10} +(-4.72909 - 0.833866i) q^{11} +(2.06615 - 5.67671i) q^{13} +(0.359008 - 0.0638755i) q^{14} +(-3.75023 + 1.39131i) q^{16} +(2.76368 + 4.78684i) q^{17} +(1.75645 + 1.01409i) q^{19} +(-2.49040 - 6.77702i) q^{20} +(-5.19554 + 4.37328i) q^{22} +(0.164150 - 0.137738i) q^{23} +(7.54812 - 2.74729i) q^{25} +(-4.28309 - 7.39210i) q^{26} +(0.256461 - 0.447394i) q^{28} +(0.455110 + 1.25040i) q^{29} +(-0.00197394 + 0.00165633i) q^{31} +(-1.89359 + 5.33051i) q^{32} +(7.70020 + 1.34548i) q^{34} +(0.806124 + 0.465416i) q^{35} +(0.995752 - 0.574898i) q^{37} +(2.69377 - 0.985173i) q^{38} +(-9.61111 - 3.44774i) q^{40} +(-4.72689 - 1.72045i) q^{41} +(4.99819 + 0.881316i) q^{43} +(0.0297094 + 9.60404i) q^{44} +(-0.000468717 - 0.303041i) q^{46} +(1.18349 + 0.993067i) q^{47} +(-1.20399 - 6.82818i) q^{49} +(3.86874 - 10.6806i) q^{50} +(-11.9049 - 2.06121i) q^{52} +12.4496i q^{53} -17.3357 q^{55} +(-0.252610 - 0.684146i) q^{56} +(1.76933 + 0.640886i) q^{58} +(-10.3154 + 1.81887i) q^{59} +(-5.31333 + 6.33218i) q^{61} +(5.63643e-6 + 0.00364414i) q^{62} +(4.06412 + 6.89078i) q^{64} +(3.78700 - 21.4771i) q^{65} +(1.10004 - 3.02234i) q^{67} +(8.44639 - 7.13200i) q^{68} +(1.23631 - 0.452146i) q^{70} +(3.40904 + 5.90464i) q^{71} +(1.51096 - 2.61705i) q^{73} +(0.279884 - 1.60179i) q^{74} +(1.37555 - 3.81599i) q^{76} +(-0.795884 - 0.948498i) q^{77} +(10.1554 - 3.69627i) q^{79} +(-12.4607 + 7.29735i) q^{80} +(-6.15527 + 3.56645i) q^{82} +(2.84189 + 7.80804i) q^{83} +(12.8263 + 15.2857i) q^{85} +(5.49118 - 4.62214i) q^{86} +(10.4450 + 8.68211i) q^{88} +(0.381609 - 0.660965i) q^{89} +(1.34896 - 0.778820i) q^{91} +(-0.329150 - 0.274459i) q^{92} +(2.15109 - 0.382727i) q^{94} +(6.88026 + 2.50421i) q^{95} +(-0.902281 + 5.11709i) q^{97} +(-8.49936 - 4.88960i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40} + 24 q^{41} - 21 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} + 99 q^{50} - 33 q^{52} - 24 q^{55} - 99 q^{56} + 21 q^{58} + 36 q^{62} - 3 q^{64} + 12 q^{65} - 75 q^{68} + 9 q^{70} + 90 q^{71} - 6 q^{73} - 9 q^{74} - 18 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} + 30 q^{86} - 30 q^{88} + 6 q^{89} - 111 q^{92} - 33 q^{94} + 42 q^{95} - 12 q^{97} - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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