LMFDB - Embedded newform 833.2.j.a.373.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(67,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("833.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.j (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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 15 x^{18} + 158 x^{16} - 789 x^{14} + 2811 x^{12} - 5497 x^{10} + 7763 x^{8} - 6130 x^{6} + \cdots + 1 $ x^20 - 15x^18 + 158x^16 - 789x^14 + 2811x^12 - 5497x^10 + 7763x^8 - 6130x^6 + 3256x^4 - 58*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.5
Root			$0.974258 - 0.562488i$ of defining polynomial
Character	$\chi$	$=$	833.373
Dual form			833.2.j.a.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.274428 + 0.475324i) q^{2} +(-0.974258 + 0.562488i) q^{3} +(0.849378 + 1.47117i) q^{4} +(-0.987893 - 0.570360i) q^{5} -0.617451i q^{6} -2.03009 q^{8} +(-0.867214 + 1.50206i) q^{9} +(0.542212 - 0.313046i) q^{10} +(1.75771 - 1.01481i) q^{11} +(-1.65503 - 0.955531i) q^{12} -3.31337 q^{13} +1.28328 q^{15} +(-1.14164 + 1.97738i) q^{16} +(4.11485 + 0.260800i) q^{17} +(-0.475976 - 0.824415i) q^{18} +(-2.05093 + 3.55231i) q^{19} -1.93781i q^{20} +1.11398i q^{22} +(-7.79225 - 4.49886i) q^{23} +(1.97783 - 1.14190i) q^{24} +(-1.84938 - 3.20322i) q^{25} +(0.909284 - 1.57493i) q^{26} -5.32612i q^{27} +5.23430i q^{29} +(-0.352170 + 0.609976i) q^{30} +(-2.49688 + 1.44157i) q^{31} +(-2.65669 - 4.60152i) q^{32} +(-1.14164 + 1.97738i) q^{33} +(-1.25320 + 1.88432i) q^{34} -2.94637 q^{36} +(-3.72601 - 2.15121i) q^{37} +(-1.12566 - 1.94971i) q^{38} +(3.22808 - 1.86373i) q^{39} +(2.00551 + 1.15788i) q^{40} +1.64114i q^{41} +7.25974 q^{43} +(2.98592 + 1.72392i) q^{44} +(1.71343 - 0.989249i) q^{45} +(4.27683 - 2.46923i) q^{46} +(3.08101 - 5.33647i) q^{47} -2.56864i q^{48} +2.03009 q^{50} +(-4.15562 + 2.06047i) q^{51} +(-2.81431 - 4.87452i) q^{52} +(-1.23164 - 2.13326i) q^{53} +(2.53163 + 1.46164i) q^{54} -2.31524 q^{55} -4.61449i q^{57} +(-2.48799 - 1.43644i) q^{58} +(-2.18771 - 3.78922i) q^{59} +(1.08999 + 1.88792i) q^{60} +(-13.0992 - 7.56283i) q^{61} -1.58244i q^{62} -1.65029 q^{64} +(3.27326 + 1.88982i) q^{65} +(-0.626598 - 1.08530i) q^{66} +(2.99102 + 5.18060i) q^{67} +(3.11138 + 6.27514i) q^{68} +10.1222 q^{69} +2.01341i q^{71} +(1.76052 - 3.04931i) q^{72} +(-3.73554 + 2.15671i) q^{73} +(2.04505 - 1.18071i) q^{74} +(3.60354 + 2.08051i) q^{75} -6.96805 q^{76} +2.04585i q^{78} +(-4.82037 - 2.78304i) q^{79} +(2.25564 - 1.30229i) q^{80} +(0.394240 + 0.682843i) q^{81} +(-0.780075 - 0.450376i) q^{82} -6.77689 q^{83} +(-3.91628 - 2.60459i) q^{85} +(-1.99228 + 3.45073i) q^{86} +(-2.94423 - 5.09956i) q^{87} +(-3.56830 + 2.06016i) q^{88} +(2.58195 - 4.47206i) q^{89} +1.08591i q^{90} -15.2849i q^{92} +(1.62174 - 2.80893i) q^{93} +(1.69104 + 2.92896i) q^{94} +(4.05219 - 2.33953i) q^{95} +(5.17660 + 2.98871i) q^{96} -13.6395i q^{97} +3.52024i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 10 q^{4} + 16 q^{13} - 16 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 10 q^{19} - 10 q^{25} - 12 q^{26} - 10 q^{30} - 12 q^{32} - 2 q^{33} - 24 q^{34} + 56 q^{36} + 2 q^{38} - 52 q^{43}+ \cdots - 50 q^{94}+O(q^{100}) $ 20 * q - 2 * q^2 - 10 * q^4 + 16 * q^13 - 16 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 10 * q^19 - 10 * q^25 - 12 * q^26 - 10 * q^30 - 12 * q^32 - 2 * q^33 - 24 * q^34 + 56 * q^36 + 2 * q^38 - 52 * q^43 - 30 * q^47 + 6 * q^51 + 2 * q^52 + 40 * q^53 - 12 * q^55 + 14 * q^59 - 22 * q^60 - 24 * q^64 - 12 * q^66 + 12 * q^67 + 32 * q^68 + 88 * q^69 - 16 * q^72 - 132 * q^76 - 2 * q^81 - 96 * q^83 - 4 * q^85 - 10 * q^86 + 26 * q^87 - 16 * q^89 + 46 * q^93 - 50 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.274428	+	0.475324i	−0.194050	+	0.336105i	−0.946589	−	0.322443i	$-0.895496\pi$
$2$	−0.274428	+	0.475324i	−0.194050	+	0.336105i	0.752539	+	0.658548i	$0.228829\pi$
$3$	−0.974258	+	0.562488i	−0.562488	+	0.324753i	−0.754144	−	0.656709i	$-0.771948\pi$
$3$	−0.974258	+	0.562488i	−0.562488	+	0.324753i	0.191655	+	0.981462i	$0.438614\pi$
$4$	0.849378	+	1.47117i	0.424689	+	0.735583i
$5$	−0.987893	−	0.570360i	−0.441799	−	0.255073i	0.262561	−	0.964915i	$-0.415433\pi$
$5$	−0.987893	−	0.570360i	−0.441799	−	0.255073i	−0.704361	+	0.709842i	$0.748766\pi$
$6$		−	0.617451i		−	0.252073i
$7$		0			0
$7$		0			0
$8$	−2.03009			−0.717744
$9$	−0.867214	+	1.50206i	−0.289071	+	0.500686i
$10$	0.542212	−	0.313046i	0.171462	−	0.0989939i
$11$	1.75771	−	1.01481i	0.529969	−	0.305978i	−0.211035	−	0.977479i	$-0.567683\pi$
$11$	1.75771	−	1.01481i	0.529969	−	0.305978i	0.741004	+	0.671501i	$0.234350\pi$
$12$	−1.65503	−	0.955531i	−0.477765	−	0.275838i
$13$	−3.31337			−0.918964			−0.459482	−	0.888187i	$-0.651965\pi$
$13$	−3.31337			−0.918964			−0.459482	+	0.888187i	$0.651965\pi$
$14$		0			0
$15$	1.28328			0.331343
$16$	−1.14164	+	1.97738i	−0.285411	+	0.494346i
$17$	4.11485	+	0.260800i	0.997997	+	0.0632534i
$17$	4.11485	+	0.260800i	0.997997	+	0.0632534i
$18$	−0.475976	−	0.824415i	−0.112189	−	0.194316i
$19$	−2.05093	+	3.55231i	−0.470515	+	0.814955i	−0.999431	−	0.0337184i	$-0.989265\pi$
$19$	−2.05093	+	3.55231i	−0.470515	+	0.814955i	0.528917	+	0.848674i	$0.322598\pi$
$20$		−	1.93781i		−	0.433307i
$21$		0			0
$22$			1.11398i			0.237500i
$23$	−7.79225	−	4.49886i	−1.62480	−	0.938076i	−0.985612	−	0.169023i	$-0.945939\pi$
$23$	−7.79225	−	4.49886i	−1.62480	−	0.938076i	−0.639184	−	0.769054i	$-0.720728\pi$
$24$	1.97783	−	1.14190i	0.403723	−	0.233090i
$25$	−1.84938	−	3.20322i	−0.369876	−	0.640643i
$26$	0.909284	−	1.57493i	0.178325	−	0.308868i
$27$		−	5.32612i		−	1.02501i
$28$		0			0
$29$			5.23430i			0.971985i	0.873963	+	0.485992i	$0.161542\pi$
$29$			5.23430i			0.971985i	−0.873963	+	0.485992i	$0.838458\pi$
$30$	−0.352170	+	0.609976i	−0.0642971	+	0.111366i
$31$	−2.49688	+	1.44157i	−0.448453	+	0.258914i	−0.707177	−	0.707037i	$-0.750031\pi$
$31$	−2.49688	+	1.44157i	−0.448453	+	0.258914i	0.258724	+	0.965951i	$0.416698\pi$
$32$	−2.65669	−	4.60152i	−0.469640	−	0.813441i
$33$	−1.14164	+	1.97738i	−0.198734	+	0.344218i
$34$	−1.25320	+	1.88432i	−0.214921	+	0.323157i
$35$		0			0
$36$	−2.94637			−0.491062
$37$	−3.72601	−	2.15121i	−0.612553	−	0.353657i	0.161411	−	0.986887i	$-0.448395\pi$
$37$	−3.72601	−	2.15121i	−0.612553	−	0.353657i	−0.773964	+	0.633230i	$0.781729\pi$
$38$	−1.12566	−	1.94971i	−0.182607	−	0.316285i
$39$	3.22808	−	1.86373i	0.516907	−	0.298436i
$40$	2.00551	+	1.15788i	0.317099	+	0.183077i
$41$			1.64114i			0.256304i	0.991755	+	0.128152i	$0.0409045\pi$
$41$			1.64114i			0.256304i	−0.991755	+	0.128152i	$0.959096\pi$
$42$		0			0
$43$	7.25974			1.10710			0.553550	−	0.832816i	$-0.313273\pi$
$43$	7.25974			1.10710			0.553550	+	0.832816i	$0.313273\pi$
$44$	2.98592	+	1.72392i	0.450144	+	0.259891i
$45$	1.71343	−	0.989249i	0.255423	−	0.147468i
$46$	4.27683	−	2.46923i	0.630584	−	0.364068i
$47$	3.08101	−	5.33647i	0.449412	−	0.778404i	−0.548936	−	0.835865i	$-0.684967\pi$
$47$	3.08101	−	5.33647i	0.449412	−	0.778404i	0.998348	+	0.0574601i	$0.0183002\pi$
$48$		−	2.56864i		−	0.370751i
$49$		0			0
$50$	2.03009			0.287098
$51$	−4.15562	+	2.06047i	−0.581904	+	0.288523i
$52$	−2.81431	−	4.87452i	−0.390274	−	0.675974i
$53$	−1.23164	−	2.13326i	−0.169178	−	0.293025i	0.768953	−	0.639305i	$-0.220778\pi$
$53$	−1.23164	−	2.13326i	−0.169178	−	0.293025i	−0.938131	+	0.346280i	$0.887445\pi$
$54$	2.53163	+	1.46164i	0.344512	+	0.198904i
$55$	−2.31524			−0.312187
$56$		0			0
$57$		−	4.61449i		−	0.611204i
$58$	−2.48799	−	1.43644i	−0.326689	−	0.188614i
$59$	−2.18771	−	3.78922i	−0.284815	−	0.493314i	0.687749	−	0.725948i	$-0.258599\pi$
$59$	−2.18771	−	3.78922i	−0.284815	−	0.493314i	−0.972564	+	0.232634i	$0.925266\pi$
$60$	1.08999	+	1.88792i	0.140718	+	0.243730i
$61$	−13.0992	−	7.56283i	−1.67718	−	0.968321i	−0.963445	−	0.267908i	$-0.913668\pi$
$61$	−13.0992	−	7.56283i	−1.67718	−	0.968321i	−0.713737	−	0.700414i	$-0.752999\pi$
$62$		−	1.58244i		−	0.200970i
$63$		0			0
$64$	−1.65029			−0.206286
$65$	3.27326	+	1.88982i	0.405998	+	0.234403i
$66$	−0.626598	−	1.08530i	−0.0771289	−	0.133591i
$67$	2.99102	+	5.18060i	0.365411	+	0.632911i	0.988842	−	0.148968i	$-0.0475950\pi$
$67$	2.99102	+	5.18060i	0.365411	+	0.632911i	−0.623431	+	0.781879i	$0.714262\pi$
$68$	3.11138	+	6.27514i	0.377310	+	0.760973i
$69$	10.1222			1.21857
$70$		0			0
$71$			2.01341i			0.238948i	0.992837	+	0.119474i	$0.0381208\pi$
$71$			2.01341i			0.238948i	−0.992837	+	0.119474i	$0.961879\pi$
$72$	1.76052	−	3.04931i	0.207479	−	0.359365i
$73$	−3.73554	+	2.15671i	−0.437212	+	0.252424i	−0.702414	−	0.711768i	$-0.747895\pi$
$73$	−3.73554	+	2.15671i	−0.437212	+	0.252424i	0.265202	+	0.964193i	$0.414561\pi$
$74$	2.04505	−	1.18071i	0.237732	−	0.137255i
$75$	3.60354	+	2.08051i	0.416101	+	0.240236i
$76$	−6.96805			−0.799290
$77$		0			0
$78$			2.04585i			0.231646i
$79$	−4.82037	−	2.78304i	−0.542334	−	0.313117i	0.203690	−	0.979035i	$-0.434707\pi$
$79$	−4.82037	−	2.78304i	−0.542334	−	0.313117i	−0.746025	+	0.665918i	$0.768040\pi$
$80$	2.25564	−	1.30229i	0.252188	−	0.145601i
$81$	0.394240	+	0.682843i	0.0438044	+	0.0758715i
$82$	−0.780075	−	0.450376i	−0.0861449	−	0.0497358i
$83$	−6.77689			−0.743860			−0.371930	−	0.928261i	$-0.621304\pi$
$83$	−6.77689			−0.743860			−0.371930	+	0.928261i	$0.621304\pi$
$84$		0			0
$85$	−3.91628	−	2.60459i	−0.424780	−	0.282507i
$86$	−1.99228	+	3.45073i	−0.214833	+	0.372102i
$87$	−2.94423	−	5.09956i	−0.315655	−	0.546730i
$88$	−3.56830	+	2.06016i	−0.380383	+	0.219614i
$89$	2.58195	−	4.47206i	0.273686	−	0.474038i	−0.696117	−	0.717928i	$-0.745090\pi$
$89$	2.58195	−	4.47206i	0.273686	−	0.474038i	0.969803	+	0.243891i	$0.0784238\pi$
$90$			1.08591i			0.114465i
$91$		0			0
$92$		−	15.2849i		−	1.59356i
$93$	1.62174	−	2.80893i	0.168166	−	0.291273i
$94$	1.69104	+	2.92896i	0.174417	+	0.302099i
$95$	4.05219	−	2.33953i	0.415746	−	0.240031i
$96$	5.17660	+	2.98871i	0.528334	+	0.305034i
$97$		−	13.6395i		−	1.38488i	−0.721474	−	0.692441i	$-0.756535\pi$
$97$		−	13.6395i		−	1.38488i	0.721474	−	0.692441i	$-0.243465\pi$
$98$		0			0
$99$			3.52024i			0.353798i
$100$	3.14164	−	5.44148i	0.314164	−	0.544148i
$101$	4.47099	+	7.74398i	0.444880	+	0.770555i	0.998044	−	0.0625174i	$-0.0199129\pi$
$101$	4.47099	+	7.74398i	0.444880	+	0.770555i	−0.553164	+	0.833073i	$0.686580\pi$
$102$	0.161032	−	2.54072i	0.0159445	−	0.251569i
$103$	−7.62708	+	13.2105i	−0.751518	+	1.30167i	0.195568	+	0.980690i	$0.437345\pi$
$103$	−7.62708	+	13.2105i	−0.751518	+	1.30167i	−0.947087	+	0.320978i	$0.895988\pi$
$104$	6.72644			0.659581
$105$		0			0
$106$	1.35198			0.131316
$107$	14.5421	+	8.39588i	1.40584	+	0.811660i	0.994983	−	0.100042i	$-0.0318976\pi$
$107$	14.5421	+	8.39588i	1.40584	+	0.811660i	0.410853	+	0.911702i	$0.365231\pi$
$108$	7.83561	−	4.52389i	0.753982	−	0.435312i
$109$	−14.2407	+	8.22187i	−1.36401	+	0.787513i	−0.990155	−	0.139974i	$-0.955298\pi$
$109$	−14.2407	+	8.22187i	−1.36401	+	0.787513i	−0.373857	+	0.927487i	$0.621965\pi$
$110$	0.635367	−	1.10049i	0.0605799	−	0.104927i
$111$	4.84013			0.459405
$112$		0			0
$113$			3.43944i			0.323556i	0.986827	+	0.161778i	$0.0517228\pi$
$113$			3.43944i			0.323556i	−0.986827	+	0.161778i	$0.948277\pi$
$114$	2.19338	+	1.26635i	0.205429	+	0.118604i
$115$	5.13194	+	8.88878i	0.478556	+	0.828883i
$116$	−7.70052	+	4.44590i	−0.714976	+	0.412791i
$117$	2.87340	−	4.97688i	0.265646	−	0.460113i
$118$	2.40148			0.221074
$119$		0			0
$120$	−2.60518			−0.237819
$121$	−3.44030	+	5.95878i	−0.312755	+	0.541708i
$122$	7.18959	−	4.15091i	0.650915	−	0.375806i
$123$	−0.923124	−	1.59890i	−0.0832353	−	0.144168i
$124$	−4.24159	−	2.44888i	−0.380906	−	0.219916i
$125$			9.92285i			0.887527i
$126$		0			0
$127$	−9.80475			−0.870030			−0.435015	−	0.900423i	$-0.643257\pi$
$127$	−9.80475			−0.870030			−0.435015	+	0.900423i	$0.643257\pi$
$128$	5.76626	−	9.98745i	0.509670	−	0.882774i
$129$	−7.07286	+	4.08352i	−0.622731	+	0.359534i
$130$	−1.79655	+	1.03724i	−0.157568	+	0.0909719i
$131$	−2.59864	−	1.50033i	−0.227044	−	0.131084i	0.382164	−	0.924095i	$-0.375179\pi$
$131$	−2.59864	−	1.50033i	−0.227044	−	0.131084i	−0.609208	+	0.793011i	$0.708512\pi$
$132$	−3.87874			−0.337601
$133$		0			0
$134$	−3.28328			−0.283633
$135$	−3.03781	+	5.26164i	−0.261453	+	0.452850i
$136$	−8.35351	−	0.529448i	−0.716307	−	0.0453998i
$137$	7.25154	+	12.5600i	0.619541	+	1.07308i	0.989570	+	0.144056i	$0.0460145\pi$
$137$	7.25154	+	12.5600i	0.619541	+	1.07308i	−0.370029	+	0.929020i	$0.620652\pi$
$138$	−2.77782	+	4.81133i	−0.236464	+	0.409568i
$139$			15.3995i			1.30617i	0.757286	+	0.653083i	$0.226525\pi$
$139$			15.3995i			1.30617i	−0.757286	+	0.653083i	$0.773475\pi$
$140$		0			0
$141$			6.93214i			0.583791i
$142$	−0.957022	−	0.552537i	−0.0803115	−	0.0463679i
$143$	−5.82395	+	3.36246i	−0.487023	+	0.281183i
$144$	−1.98010	−	3.42963i	−0.165008	−	0.285802i
$145$	2.98544	−	5.17093i	0.247927	−	0.429422i
$146$		−	2.36746i		−	0.195932i
$147$		0			0
$148$		−	7.30878i		−	0.600778i
$149$	4.34247	−	7.52137i	0.355749	−	0.616175i	−0.631497	−	0.775378i	$-0.717559\pi$
$149$	4.34247	−	7.52137i	0.355749	−	0.616175i	0.987246	+	0.159203i	$0.0508925\pi$
$150$	−1.97783	+	1.14190i	−0.161489	+	0.0932358i
$151$	−2.06609	−	3.57858i	−0.168136	−	0.291221i	0.769628	−	0.638492i	$-0.220442\pi$
$151$	−2.06609	−	3.57858i	−0.168136	−	0.291221i	−0.937765	+	0.347272i	$0.887108\pi$
$152$	4.16356	−	7.21150i	0.337709	−	0.584930i
$153$	−3.96019	+	5.95457i	−0.320162	+	0.481399i
$154$		0			0
$155$	3.28887			0.264168
$156$	5.48372	+	3.16603i	0.439049	+	0.253485i
$157$	6.90703	+	11.9633i	0.551241	+	0.954778i	0.998185	+	0.0602162i	$0.0191790\pi$
$157$	6.90703	+	11.9633i	0.551241	+	0.954778i	−0.446944	+	0.894562i	$0.647488\pi$
$158$	2.64570	−	1.52749i	0.210480	−	0.121521i
$159$	2.39986	+	1.38556i	0.190322	+	0.109882i
$160$			6.06107i			0.479170i
$161$		0			0
$162$	−0.432762			−0.0340010
$163$	5.24200	+	3.02647i	0.410585	+	0.237051i	0.691041	−	0.722816i	$-0.257152\pi$
$163$	5.24200	+	3.02647i	0.410585	+	0.237051i	−0.280456	+	0.959867i	$0.590486\pi$
$164$	−2.41439	+	1.39395i	−0.188533	+	0.108849i
$165$	2.25564	−	1.30229i	0.175601	−	0.101384i
$166$	1.85977	−	3.22122i	0.144346	−	0.250015i
$167$			14.9772i			1.15897i	0.814982	+	0.579487i	$0.196747\pi$
$167$			14.9772i			1.15897i	−0.814982	+	0.579487i	$0.803253\pi$
$168$		0			0
$169$	−2.02156			−0.155505
$170$	2.31276	−	1.14673i	0.177381	−	0.0879501i
$171$	−3.55718	−	6.16122i	−0.272025	−	0.471160i
$172$	6.16626	+	10.6803i	0.470173	+	0.814364i
$173$	7.70976	+	4.45123i	0.586162	+	0.338421i	0.763579	−	0.645715i	$-0.223441\pi$
$173$	7.70976	+	4.45123i	0.586162	+	0.338421i	−0.177416	+	0.984136i	$0.556774\pi$
$174$	3.23192			0.245012
$175$		0			0
$176$			4.63422i			0.349317i
$177$	4.26278	+	2.46112i	0.320411	+	0.184989i
$178$	1.41712	+	2.45452i	0.106218	+	0.183974i
$179$	−0.172453	−	0.298697i	−0.0128897	−	0.0223257i	0.859509	−	0.511121i	$-0.170770\pi$
$179$	−0.172453	−	0.298697i	−0.0128897	−	0.0223257i	−0.872398	+	0.488796i	$0.837436\pi$
$180$	2.91070	+	1.68049i	0.216951	+	0.125256i
$181$		−	6.20058i		−	0.460885i	−0.973086	−	0.230443i	$-0.925983\pi$
$181$		−	6.20058i		−	0.460885i	0.973086	−	0.230443i	$-0.0740174\pi$
$182$		0			0
$183$	17.0160			1.25786
$184$	15.8189	+	9.13307i	1.16619	+	0.673299i
$185$	2.45393	+	4.25034i	0.180417	+	0.312491i
$186$	0.890102	+	1.54170i	0.0652654	+	0.113043i
$187$	7.49737	−	3.71740i	0.548262	−	0.271843i
$188$	10.4678			0.763441
$189$		0			0
$190$			2.56814i			0.186312i
$191$	−2.95994	+	5.12677i	−0.214174	+	0.370960i	−0.953017	−	0.302918i	$-0.902039\pi$
$191$	−2.95994	+	5.12677i	−0.214174	+	0.370960i	0.738843	+	0.673878i	$0.235373\pi$
$192$	1.60781	−	0.928267i	0.116033	−	0.0669919i
$193$	−2.97231	+	1.71606i	−0.213952	+	0.123525i	−0.603147	−	0.797630i	$-0.706087\pi$
$193$	−2.97231	+	1.71606i	−0.213952	+	0.123525i	0.389195	+	0.921155i	$0.372753\pi$
$194$	6.48319	+	3.74307i	0.465466	+	0.268737i
$195$	−4.25200			−0.304492
$196$		0			0
$197$			2.84776i			0.202895i	0.994841	+	0.101447i	$0.0323473\pi$
$197$			2.84776i			0.202895i	−0.994841	+	0.101447i	$0.967653\pi$
$198$	−1.67326	−	0.966055i	−0.118913	−	0.0686545i
$199$	−1.89381	+	1.09339i	−0.134249	+	0.0775086i	−0.565620	−	0.824666i	$-0.691363\pi$
$199$	−1.89381	+	1.09339i	−0.134249	+	0.0775086i	0.431371	+	0.902174i	$0.358030\pi$
$200$	3.75440	+	6.50281i	0.265476	+	0.459818i
$201$	−5.82805	−	3.36483i	−0.411079	−	0.237337i
$202$	−4.90787			−0.345316
$203$		0			0
$204$	−6.56099	−	4.36350i	−0.459361	−	0.305506i
$205$	0.936043	−	1.62127i	0.0653761	−	0.113235i
$206$	−4.18618	−	7.25067i	−0.291665	−	0.505178i
$207$	13.5151	−	7.80294i	0.939364	−	0.542342i
$208$	3.78269	−	6.55180i	0.262282	−	0.454286i
$209$			8.32523i			0.575868i
$210$		0			0
$211$			13.6122i			0.937103i	0.883436	+	0.468551i	$0.155224\pi$
$211$			13.6122i			0.937103i	−0.883436	+	0.468551i	$0.844776\pi$
$212$	2.09225	−	3.62388i	0.143696	−	0.248889i
$213$	−1.13252	−	1.96158i	−0.0775990	−	0.134405i
$214$	−7.98152	+	4.60813i	−0.545606	+	0.315006i
$215$	−7.17185	−	4.14067i	−0.489116	−	0.282391i
$216$			10.8125i			0.735697i
$217$		0			0
$218$		−	9.02526i		−	0.611268i
$219$	2.42625	−	4.20240i	0.163951	−	0.283972i
$220$	−1.96651	−	3.40610i	−0.132582	−	0.229639i
$221$	−13.6340	−	0.864129i	−0.917124	−	0.0581276i
$222$	−1.32827	+	2.30063i	−0.0891476	+	0.154408i
$223$	20.1620			1.35015			0.675075	−	0.737749i	$-0.264111\pi$
$223$	20.1620			1.35015			0.675075	+	0.737749i	$0.264111\pi$
$224$		0			0
$225$	6.41522			0.427682
$226$	−1.63485	−	0.943882i	−0.108749	−	0.0627861i
$227$	−5.94960	+	3.43500i	−0.394889	+	0.227989i	−0.684276	−	0.729223i	$-0.739882\pi$
$227$	−5.94960	+	3.43500i	−0.394889	+	0.227989i	0.289387	+	0.957212i	$0.406548\pi$
$228$	6.78868	−	3.91944i	0.449591	−	0.259572i
$229$	−2.11263	+	3.65919i	−0.139607	+	0.241806i	−0.927348	−	0.374200i	$-0.877917\pi$
$229$	−2.11263	+	3.65919i	−0.139607	+	0.241806i	0.787741	+	0.616007i	$0.211251\pi$
$230$	−5.63340			−0.371455
$231$		0			0
$232$		−	10.6261i		−	0.697637i
$233$	−11.5702	−	6.68006i	−0.757990	−	0.437626i	0.0705838	−	0.997506i	$-0.477514\pi$
$233$	−11.5702	−	6.68006i	−0.757990	−	0.437626i	−0.828573	+	0.559880i	$0.810847\pi$
$234$	1.57709	+	2.73159i	0.103097	+	0.178570i
$235$	−6.08742	+	3.51458i	−0.397100	+	0.229266i
$236$	3.71638	−	6.43696i	0.241916	−	0.419010i
$237$	6.26172			0.406742
$238$		0			0
$239$	14.9476			0.966878			0.483439	−	0.875378i	$-0.339388\pi$
$239$	14.9476			0.966878			0.483439	+	0.875378i	$0.339388\pi$
$240$	−1.46505	+	2.53754i	−0.0945687	+	0.163798i
$241$	−12.2719	+	7.08519i	−0.790503	+	0.456397i	−0.840140	−	0.542370i	$-0.817527\pi$
$241$	−12.2719	+	7.08519i	−0.790503	+	0.456397i	0.0496364	+	0.998767i	$0.484194\pi$
$242$	−1.88824	−	3.27052i	−0.121380	−	0.210237i
$243$	13.0695	+	7.54567i	0.838408	+	0.484055i
$244$		−	25.6948i		−	1.64494i
$245$		0			0
$246$	1.01333			0.0646073
$247$	6.79548	−	11.7701i	0.432386	−	0.748915i
$248$	5.06889	−	2.92652i	0.321875	−	0.185834i
$249$	6.60244	−	3.81192i	0.418413	−	0.241571i
$250$	−4.71657	−	2.72311i	−0.298302	−	0.172225i
$251$	26.6386			1.68142			0.840708	−	0.541489i	$-0.182139\pi$
$251$	26.6386			1.68142			0.840708	+	0.541489i	$0.182139\pi$
$252$		0			0
$253$	−18.2620			−1.14812
$254$	2.69070	−	4.66043i	0.168830	−	0.292421i
$255$	5.28052	+	0.334681i	0.330679	+	0.0209585i
$256$	1.51456	+	2.62330i	0.0946602	+	0.163956i
$257$	−12.1663	+	21.0726i	−0.758912	+	1.31447i	0.184493	+	0.982834i	$0.440936\pi$
$257$	−12.1663	+	21.0726i	−0.758912	+	1.31447i	−0.943406	+	0.331641i	$0.892398\pi$
$258$		−	4.48254i		−	0.279071i
$259$		0			0
$260$			6.42067i			0.398193i
$261$	−7.86222	−	4.53926i	−0.486659	−	0.280973i
$262$	1.42628	−	0.823464i	0.0881160	−	0.0508738i
$263$	−15.2145	−	26.3523i	−0.938165	−	1.62495i	−0.768890	−	0.639381i	$-0.779191\pi$
$263$	−15.2145	−	26.3523i	−0.938165	−	1.62495i	−0.169276	−	0.985569i	$-0.554143\pi$
$264$	2.31763	−	4.01426i	0.142641	−	0.247061i
$265$			2.80990i			0.172611i
$266$		0			0
$267$			5.80926i			0.355521i
$268$	−5.08101	+	8.80057i	−0.310372	+	0.537581i
$269$	−13.4020	+	7.73765i	−0.817134	+	0.471773i	−0.849427	−	0.527706i	$-0.823052\pi$
$269$	−13.4020	+	7.73765i	−0.817134	+	0.471773i	0.0322929	+	0.999478i	$0.489719\pi$
$270$	−1.66732	−	2.88789i	−0.101470	−	0.175751i
$271$	−7.95501	+	13.7785i	−0.483233	+	0.836984i	−0.999815	−	0.0192542i	$-0.993871\pi$
$271$	−7.95501	+	13.7785i	−0.483233	+	0.836984i	0.516582	+	0.856238i	$0.327204\pi$
$272$	−5.21339	+	7.83889i	−0.316108	+	0.475302i
$273$		0			0
$274$	−7.96012			−0.480888
$275$	−6.50134	−	3.75355i	−0.392045	−	0.226348i
$276$	8.59759	+	14.8915i	0.517514	+	0.896361i
$277$	−16.2478	+	9.38070i	−0.976238	+	0.563631i	−0.901132	−	0.433544i	$-0.857263\pi$
$277$	−16.2478	+	9.38070i	−0.976238	+	0.563631i	−0.0751060	+	0.997176i	$0.523930\pi$
$278$	−7.31974	−	4.22606i	−0.439009	−	0.253462i
$279$		−	5.00061i		−	0.299379i
$280$		0			0
$281$	2.80633			0.167411			0.0837057	−	0.996491i	$-0.473324\pi$
$281$	2.80633			0.167411			0.0837057	+	0.996491i	$0.473324\pi$
$282$	−3.29501	−	1.90238i	−0.196215	−	0.113285i
$283$	14.2770	−	8.24282i	0.848679	−	0.489985i	−0.0115261	−	0.999934i	$-0.503669\pi$
$283$	14.2770	−	8.24282i	0.848679	−	0.489985i	0.860205	+	0.509949i	$0.170336\pi$
$284$	−2.96206	+	1.71015i	−0.175766	+	0.101479i
$285$	−2.63192	+	4.55862i	−0.155902	+	0.270029i
$286$		−	3.69102i		−	0.218254i
$287$		0			0
$288$	9.21566			0.543038
$289$	16.8640	+	2.14631i	0.991998	+	0.126253i
$290$	1.63858	+	2.83810i	0.0962206	+	0.166659i
$291$	7.67206	+	13.2884i	0.449744	+	0.778980i
$292$	−6.34577	−	3.66373i	−0.371358	−	0.214404i
$293$	−32.6415			−1.90693			−0.953467	−	0.301497i	$-0.902514\pi$
$293$	−32.6415			−1.90693			−0.953467	+	0.301497i	$0.902514\pi$
$294$		0			0
$295$			4.99113i			0.290595i
$296$	7.56413	+	4.36715i	0.439656	+	0.253836i
$297$	−5.40502	−	9.36177i	−0.313631	−	0.543225i
$298$	2.38339	+	4.12816i	0.138066	+	0.239138i
$299$	25.8186	+	14.9064i	1.49313	+	0.862059i
$300$			7.06855i			0.408103i
$301$		0			0
$302$	2.26798			0.130508
$303$	−8.71180	−	5.02976i	−0.500480	−	0.288952i
$304$	−4.68285	−	8.11093i	−0.268580	−	0.465194i
$305$	8.62708	+	14.9425i	0.493985	+	0.855607i
$306$	−1.74356	−	3.51648i	−0.0996728	−	0.201024i
$307$	22.5412			1.28649			0.643246	−	0.765659i	$-0.277587\pi$
$307$	22.5412			1.28649			0.643246	+	0.765659i	$0.277587\pi$
$308$		0			0
$309$		−	17.1606i		−	0.976231i
$310$	−0.902559	+	1.56328i	−0.0512619	+	0.0887882i
$311$	−4.94603	+	2.85559i	−0.280463	+	0.161926i	−0.633633	−	0.773634i	$-0.718437\pi$
$311$	−4.94603	+	2.85559i	−0.280463	+	0.161926i	0.353170	+	0.935559i	$0.385104\pi$
$312$	−6.55329	+	3.78354i	−0.371007	+	0.214201i
$313$	−21.0773	−	12.1690i	−1.19136	−	0.687833i	−0.232746	−	0.972538i	$-0.574771\pi$
$313$	−21.0773	−	12.1690i	−1.19136	−	0.687833i	−0.958615	+	0.284705i	$0.908104\pi$
$314$	−7.58195			−0.427874
$315$		0			0
$316$		−	9.45543i		−	0.531909i
$317$	12.2553	+	7.07561i	0.688327	+	0.397406i	0.802985	−	0.595999i	$-0.203244\pi$
$317$	12.2553	+	7.07561i	0.688327	+	0.397406i	−0.114658	+	0.993405i	$0.536577\pi$
$318$	−1.31718	+	0.760475i	−0.0738639	+	0.0426453i
$319$	5.31184	+	9.20038i	0.297406	+	0.515122i
$320$	1.63031	+	0.941259i	0.0911370	+	0.0526180i
$321$	−18.8903			−1.05436
$322$		0			0
$323$	−9.36569	+	14.0823i	−0.521121	+	0.783562i
$324$	−0.669717	+	1.15998i	−0.0372065	+	0.0644436i
$325$	6.12768	+	10.6134i	0.339902	+	0.588728i
$326$	−2.87711	+	1.66110i	−0.159348	+	0.0919997i
$327$	9.24942	−	16.0205i	0.511494	−	0.885933i
$328$		−	3.33167i		−	0.183960i
$329$		0			0
$330$			1.42955i			0.0786940i
$331$	7.07795	−	12.2594i	0.389039	−	0.673836i	−0.603281	−	0.797529i	$-0.706140\pi$
$331$	7.07795	−	12.2594i	0.389039	−	0.673836i	0.992321	+	0.123693i	$0.0394737\pi$
$332$	−5.75614	−	9.96993i	−0.315909	−	0.547171i
$333$	6.46250	−	3.73112i	0.354143	−	0.204464i
$334$	−7.11904	−	4.11018i	−0.389536	−	0.224899i
$335$		−	6.82384i		−	0.372826i
$336$		0			0
$337$		−	18.1667i		−	0.989603i	−0.869006	−	0.494802i	$-0.835241\pi$
$337$		−	18.1667i		−	0.989603i	0.869006	−	0.494802i	$-0.164759\pi$
$338$	0.554775	−	0.960898i	0.0301758	−	0.0522660i
$339$	−1.93465	−	3.35091i	−0.105076	−	0.181996i
$340$	0.505381	−	7.97378i	0.0274081	−	0.432439i
$341$	−2.92586	+	5.06774i	−0.158444	+	0.274433i
$342$	3.90477			0.211146
$343$		0			0
$344$	−14.7379			−0.794615
$345$	−9.99967	−	5.77331i	−0.538364	−	0.310825i
$346$	−4.23156	+	2.44309i	−0.227490	+	0.131341i
$347$	10.7330	−	6.19670i	0.576177	−	0.332656i	−0.183436	−	0.983032i	$-0.558722\pi$
$347$	10.7330	−	6.19670i	0.576177	−	0.332656i	0.759613	+	0.650376i	$0.225389\pi$
$348$	5.00153	−	8.66291i	0.268110	−	0.464381i
$349$	−7.24161			−0.387634			−0.193817	−	0.981038i	$-0.562087\pi$
$349$	−7.24161			−0.387634			−0.193817	+	0.981038i	$0.562087\pi$
$350$		0			0
$351$			17.6474i			0.941950i
$352$	−9.33936	−	5.39208i	−0.497790	−	0.287399i
$353$	−12.8706	−	22.2925i	−0.685031	−	1.18651i	−0.973427	−	0.228998i	$-0.926455\pi$
$353$	−12.8706	−	22.2925i	−0.685031	−	1.18651i	0.288395	−	0.957511i	$-0.406878\pi$
$354$	−2.33966	+	1.35080i	−0.124351	+	0.0717944i
$355$	1.14837	−	1.98903i	0.0609491	−	0.105567i
$356$	8.77220			0.464925
$357$		0			0
$358$	0.189304			0.0100050
$359$	−15.2923	+	26.4870i	−0.807096	+	1.39793i	0.107771	+	0.994176i	$0.465629\pi$
$359$	−15.2923	+	26.4870i	−0.807096	+	1.39793i	−0.914867	+	0.403756i	$0.867705\pi$
$360$	−3.47841	+	2.00826i	−0.183328	+	0.105845i
$361$	1.08741	+	1.88344i	0.0572319	+	0.0991286i
$362$	2.94728	+	1.70162i	0.154906	+	0.0894349i
$363$		−	7.74053i		−	0.406272i
$364$		0			0
$365$	4.92042			0.257546
$366$	−4.66968	+	8.08812i	−0.244088	+	0.422773i
$367$	10.6706	−	6.16066i	0.557000	−	0.321584i	−0.194941	−	0.980815i	$-0.562451\pi$
$367$	10.6706	−	6.16066i	0.557000	−	0.321584i	0.751940	+	0.659231i	$0.229118\pi$
$368$	17.7919	−	10.2722i	0.927468	−	0.535474i
$369$	−2.46509	−	1.42322i	−0.128328	−	0.0740900i
$370$	−2.69372			−0.140040
$371$		0			0
$372$	5.50987			0.285674
$373$	−9.29149	+	16.0933i	−0.481095	+	0.833281i	−0.999765	−	0.0216939i	$-0.993094\pi$
$373$	−9.29149	+	16.0933i	−0.481095	+	0.833281i	0.518670	+	0.854975i	$0.326427\pi$
$374$	−0.290525	+	4.58384i	−0.0150227	+	0.237025i
$375$	−5.58149	−	9.66742i	−0.288227	−	0.499224i
$376$	−6.25473	+	10.8335i	−0.322563	+	0.558696i
$377$		−	17.3432i		−	0.893219i
$378$		0			0
$379$		−	30.4848i		−	1.56590i	−0.622087	−	0.782948i	$-0.713715\pi$
$379$		−	30.4848i		−	1.56590i	0.622087	−	0.782948i	$-0.286285\pi$
$380$	6.88368	+	3.97430i	0.353126	+	0.203877i
$381$	9.55236	−	5.51506i	0.489382	−	0.282545i
$382$	−1.62459	−	2.81386i	−0.0831210	−	0.143970i
$383$	8.83907	−	15.3097i	0.451655	−	0.782290i	−0.546834	−	0.837241i	$-0.684167\pi$
$383$	8.83907	−	15.3097i	0.451655	−	0.782290i	0.998489	+	0.0549512i	$0.0175003\pi$
$384$			12.9738i			0.662067i
$385$		0			0
$386$		−	1.88375i		−	0.0958802i
$387$	−6.29575	+	10.9046i	−0.320031	+	0.554310i
$388$	20.0660	−	11.5851i	1.01870	−	0.588144i
$389$	−6.14671	−	10.6464i	−0.311651	−	0.539795i	0.667069	−	0.744996i	$-0.267549\pi$
$389$	−6.14671	−	10.6464i	−0.311651	−	0.539795i	−0.978720	+	0.205201i	$0.934215\pi$
$390$	1.16687	−	2.02108i	0.0590867	−	0.102341i
$391$	−30.8906	−	20.5443i	−1.56221	−	1.03897i
$392$		0			0
$393$	3.37566			0.170280
$394$	−1.35361	−	0.781507i	−0.0681939	−	0.0393718i
$395$	3.17468	+	5.49870i	0.159735	+	0.276670i
$396$	−5.17886	+	2.99002i	−0.260248	+	0.150254i
$397$	−11.3137	−	6.53199i	−0.567820	−	0.327831i	0.188458	−	0.982081i	$-0.439651\pi$
$397$	−11.3137	−	6.53199i	−0.567820	−	0.327831i	−0.756278	+	0.654250i	$0.772984\pi$
$398$		−	1.20023i		−	0.0601622i
$399$		0			0
$400$	8.44531			0.422266
$401$	−27.2434	−	15.7290i	−1.36047	−	0.785467i	−0.370783	−	0.928719i	$-0.620911\pi$
$401$	−27.2434	−	15.7290i	−1.36047	−	0.785467i	−0.989686	+	0.143252i	$0.954244\pi$
$402$	3.19877	−	1.84681i	0.159540	−	0.0921105i
$403$	8.27309	−	4.77647i	0.412112	−	0.237933i
$404$	−7.59512	+	13.1551i	−0.377872	+	0.654493i
$405$		−	0.899435i		−	0.0446933i
$406$		0			0
$407$	−8.73233			−0.432846
$408$	8.43628	−	4.18293i	0.417658	−	0.207086i
$409$	−13.3672	−	23.1527i	−0.660968	−	1.14483i	−0.980362	−	0.197208i	$-0.936813\pi$
$409$	−13.3672	−	23.1527i	−0.660968	−	1.14483i	0.319394	−	0.947622i	$-0.396521\pi$
$410$	0.513754	+	0.889848i	0.0253725	+	0.0439464i
$411$	−14.1297	−	8.15781i	−0.696969	−	0.402395i
$412$	−25.9131			−1.27665
$413$		0			0
$414$			8.56540i			0.420966i
$415$	6.69484	+	3.86527i	0.328637	+	0.189739i
$416$	8.80259	+	15.2465i	0.431582	+	0.747523i
$417$	−8.66203	−	15.0031i	−0.424181	−	0.734704i
$418$	−3.95718	−	2.28468i	−0.193552	−	0.111747i
$419$		−	3.15118i		−	0.153945i	−0.997033	−	0.0769726i	$-0.975475\pi$
$419$		−	3.15118i		−	0.153945i	0.997033	−	0.0769726i	$-0.0245254\pi$
$420$		0			0
$421$	−1.13129			−0.0551356			−0.0275678	−	0.999620i	$-0.508776\pi$
$421$	−1.13129			−0.0551356			−0.0275678	+	0.999620i	$0.508776\pi$
$422$	−6.47021	−	3.73558i	−0.314965	−	0.181845i
$423$	5.34379	+	9.25572i	0.259824	+	0.450029i
$424$	2.50033	+	4.33070i	0.121427	+	0.210317i
$425$	−6.77451	−	13.6631i	−0.328612	−	0.662756i
$426$	1.24318			0.0602324
$427$		0			0
$428$			28.5251i			1.37881i
$429$	3.78269	−	6.55180i	0.182630	−	0.316324i
$430$	3.93632	−	2.27263i	0.189826	−	0.109596i
$431$	33.5797	−	19.3873i	1.61748	−	0.933852i	0.629910	−	0.776668i	$-0.283092\pi$
$431$	33.5797	−	19.3873i	1.61748	−	0.933852i	0.987569	−	0.157183i	$-0.0502414\pi$
$432$	10.5318	+	6.08052i	0.506710	+	0.292549i
$433$	−21.2104			−1.01930			−0.509652	−	0.860380i	$-0.670226\pi$
$433$	−21.2104			−1.01930			−0.509652	+	0.860380i	$0.670226\pi$
$434$		0			0
$435$			6.71709i			0.322060i
$436$	−24.1915	−	13.9670i	−1.15856	−	0.668896i
$437$	31.9626	−	18.4536i	1.52898	−	0.882757i
$438$	1.33167	+	2.30651i	0.0636295	+	0.110209i
$439$	18.9723	+	10.9536i	0.905496	+	0.522789i	0.878979	−	0.476860i	$-0.158225\pi$
$439$	18.9723	+	10.9536i	0.905496	+	0.522789i	0.0265169	+	0.999648i	$0.491558\pi$
$440$	4.70014			0.224070
$441$		0			0
$442$	4.15231	−	6.24344i	0.197505	−	0.296970i
$443$	−3.09107	+	5.35389i	−0.146861	+	0.254371i	−0.930066	−	0.367393i	$-0.880250\pi$
$443$	−3.09107	+	5.35389i	−0.146861	+	0.254371i	0.783205	+	0.621764i	$0.213584\pi$
$444$	4.11110	+	7.12064i	0.195104	+	0.337930i
$445$	−5.10138	+	2.94528i	−0.241828	+	0.139620i
$446$	−5.53303	+	9.58350i	−0.261997	+	0.453792i
$447$			9.77035i			0.462122i
$448$		0			0
$449$			16.1641i			0.762832i	0.924403	+	0.381416i	$0.124563\pi$
$449$			16.1641i			0.762832i	−0.924403	+	0.381416i	$0.875437\pi$
$450$	−1.76052	+	3.04931i	−0.0829917	+	0.143746i
$451$	1.66546	+	2.88465i	0.0784232	+	0.135833i
$452$	−5.05999	+	2.92139i	−0.238002	+	0.137411i
$453$	4.02582	+	2.32431i	0.189149	+	0.109205i
$454$		−	3.77065i		−	0.176965i
$455$		0			0
$456$			9.36782i			0.438688i
$457$	1.56351	−	2.70807i	0.0731378	−	0.126678i	−0.827137	−	0.562000i	$-0.810032\pi$
$457$	1.56351	−	2.70807i	0.0731378	−	0.126678i	0.900275	+	0.435322i	$0.143365\pi$
$458$	−1.15953	−	2.00837i	−0.0541815	−	0.0938450i
$459$	1.38905	−	21.9162i	0.0648355	−	1.02296i
$460$	−8.71791	+	15.0999i	−0.406475	+	0.704035i
$461$	29.6147			1.37929			0.689646	−	0.724146i	$-0.257766\pi$
$461$	29.6147			1.37929			0.689646	+	0.724146i	$0.257766\pi$
$462$		0			0
$463$	−18.3178			−0.851300			−0.425650	−	0.904888i	$-0.639955\pi$
$463$	−18.3178			−0.851300			−0.425650	+	0.904888i	$0.639955\pi$
$464$	−10.3502	−	5.97570i	−0.480496	−	0.277415i
$465$	−3.20421	+	1.84995i	−0.148592	+	0.0857894i
$466$	6.35039	−	3.66640i	0.294176	−	0.169843i
$467$	14.0873	−	24.3999i	0.651882	−	1.12909i	−0.330784	−	0.943707i	$-0.607313\pi$
$467$	14.0873	−	24.3999i	0.651882	−	1.12909i	0.982666	−	0.185386i	$-0.0593536\pi$
$468$	9.76242			0.451268
$469$		0			0
$470$		−	3.85800i		−	0.177956i
$471$	−13.4585	−	7.77025i	−0.620134	−	0.358034i
$472$	4.44124	+	7.69245i	0.204425	+	0.354074i
$473$	12.7605	−	7.36729i	0.586729	−	0.338748i
$474$	−1.71839	+	2.97635i	−0.0789285	+	0.136708i
$475$	15.1717			0.696128
$476$		0			0
$477$	4.27237			0.195618
$478$	−4.10204	+	7.10494i	−0.187623	+	0.324972i
$479$	28.5734	−	16.4969i	1.30555	−	0.753761i	0.324202	−	0.945988i	$-0.394904\pi$
$479$	28.5734	−	16.4969i	1.30555	−	0.753761i	0.981351	+	0.192227i	$0.0615709\pi$
$480$	−3.40928	−	5.90505i	−0.155612	−	0.269528i
$481$	12.3457	+	7.12777i	0.562914	+	0.324998i
$482$		−	7.77751i		−	0.354256i
$483$		0			0
$484$	−11.6885			−0.531294
$485$	−7.77944	+	13.4744i	−0.353246	+	0.611840i
$486$	−7.17328	+	4.14149i	−0.325386	+	0.187862i
$487$	−34.3475	+	19.8305i	−1.55643	+	0.898607i	−0.558839	+	0.829276i	$0.688753\pi$
$487$	−34.3475	+	19.8305i	−1.55643	+	0.898607i	−0.997594	+	0.0693311i	$0.977914\pi$
$488$	26.5925	+	15.3532i	1.20379	+	0.695007i
$489$	−6.80941			−0.307932
$490$		0			0
$491$	19.5148			0.880693			0.440346	−	0.897828i	$-0.354856\pi$
$491$	19.5148			0.880693			0.440346	+	0.897828i	$0.354856\pi$
$492$	1.56816	−	2.71614i	0.0706982	−	0.122453i
$493$	−1.36511	+	21.5383i	−0.0614813	+	0.970038i
$494$	3.72975	+	6.46011i	0.167809	+	0.290654i
$495$	2.00781	−	3.47762i	0.0902442	−	0.156308i
$496$		−	6.58305i		−	0.295588i
$497$		0			0
$498$			4.18440i			0.187507i
$499$	20.8436	+	12.0340i	0.933087	+	0.538718i	0.887787	−	0.460255i	$-0.152242\pi$
$499$	20.8436	+	12.0340i	0.933087	+	0.538718i	0.0453003	+	0.998973i	$0.485576\pi$
$500$	−14.5982	+	8.42825i	−0.652850	+	0.376923i
$501$	−8.42452	−	14.5917i	−0.376380	−	0.651909i
$502$	−7.31040	+	12.6620i	−0.326279	+	0.565132i
$503$		−	1.23988i		−	0.0552836i	−0.999618	−	0.0276418i	$-0.991200\pi$
$503$		−	1.23988i		−	0.0552836i	0.999618	−	0.0276418i	$-0.00879978\pi$
$504$		0			0
$505$		−	10.2003i		−	0.453908i
$506$	5.01162	−	8.68037i	0.222794	−	0.385890i
$507$	1.96953	−	1.13711i	0.0874697	−	0.0505007i
$508$	−8.32794	−	14.4244i	−0.369492	−	0.639980i
$509$	−11.0587	+	19.1543i	−0.490170	+	0.848999i	−0.999936	−	0.0113141i	$-0.996399\pi$
$509$	−11.0587	+	19.1543i	−0.490170	+	0.848999i	0.509766	+	0.860313i	$0.329732\pi$
$510$	−1.60821	+	2.41811i	−0.0712126	+	0.107076i
$511$		0			0
$512$	21.4025			0.945865
$513$	18.9200	+	10.9235i	0.835339	+	0.482283i
$514$	−6.67755	−	11.5659i	−0.294534	−	0.510148i
$515$	15.0695	−	8.70037i	0.664041	−	0.383384i
$516$	−12.0151	−	6.93690i	−0.528934	−	0.305380i
$517$		−	12.5066i		−	0.550041i
$518$		0			0
$519$	−10.0151			−0.439613
$520$	−6.64500	−	3.83649i	−0.291403	−	0.168241i
$521$	−28.3971	+	16.3951i	−1.24410	+	0.718281i	−0.969926	−	0.243399i	$-0.921738\pi$
$521$	−28.3971	+	16.3951i	−1.24410	+	0.718281i	−0.274173	+	0.961680i	$0.588404\pi$
$522$	4.31523	−	2.49140i	0.188873	−	0.109046i
$523$	−4.79475	+	8.30476i	−0.209660	+	0.363142i	−0.951607	−	0.307316i	$-0.900569\pi$
$523$	−4.79475	+	8.30476i	−0.209660	+	0.363142i	0.741947	+	0.670458i	$0.233902\pi$
$524$		−	5.09737i		−	0.222680i
$525$		0			0
$526$	16.7012			0.728205
$527$	−10.6502	+	5.28067i	−0.463932	+	0.230030i
$528$	−2.60669	−	4.51493i	−0.113442	−	0.196487i
$529$	28.9794	+	50.1938i	1.25998	+	2.18234i
$530$	−1.33562	−	0.771118i	−0.0580154	−	0.0334952i
$531$	7.58884			0.329328
$532$		0			0
$533$		−	5.43772i		−	0.235534i
$534$	−2.76128	−	1.59423i	−0.119492	−	0.0689889i
$535$	−9.57735	−	16.5885i	−0.414065	−	0.717182i
$536$	−6.07203	−	10.5171i	−0.262272	−	0.454268i
$537$	0.336027	+	0.194005i	0.0145007	+	0.00837195i
$538$		−	8.49372i		−	0.366190i
$539$		0			0
$540$	−10.3210			−0.444145
$541$	−2.60991	−	1.50683i	−0.112209	−	0.0647838i	0.442845	−	0.896598i	$-0.353969\pi$
$541$	−2.60991	−	1.50683i	−0.112209	−	0.0647838i	−0.555054	+	0.831814i	$0.687302\pi$
$542$	−4.36616	−	7.56242i	−0.187543	−	0.324834i
$543$	3.48775	+	6.04097i	0.149674	+	0.259243i
$544$	−9.73179	−	19.6274i	−0.417247	−	0.841518i
$545$	18.7577			0.803493
$546$		0			0
$547$		−	15.7999i		−	0.675555i	−0.941226	−	0.337777i	$-0.890325\pi$
$547$		−	15.7999i		−	0.675555i	0.941226	−	0.337777i	$-0.109675\pi$
$548$	−12.3186	+	21.3364i	−0.526224	+	0.911447i
$549$	22.7196	−	13.1172i	0.969650	−	0.559828i
$550$	3.56830	−	2.06016i	0.152153	−	0.0878456i
$551$	−18.5938	−	10.7352i	−0.792124	−	0.457333i
$552$	−20.5490			−0.874623
$553$		0			0
$554$		−	10.2973i		−	0.437491i
$555$	−4.78153	−	2.76062i	−0.202965	−	0.117182i
$556$	−22.6552	+	13.0800i	−0.960794	+	0.554715i
$557$	−0.833611	−	1.44386i	−0.0353212	−	0.0611782i	0.847824	−	0.530277i	$-0.177912\pi$
$557$	−0.833611	−	1.44386i	−0.0353212	−	0.0611782i	−0.883146	+	0.469099i	$0.844579\pi$
$558$	2.37691	+	1.37231i	0.100623	+	0.0580945i
$559$	−24.0542			−1.01739
$560$		0			0
$561$	−5.21339	+	7.83889i	−0.220109	+	0.330958i
$562$	−0.770136	+	1.33391i	−0.0324862	+	0.0562678i
$563$	−6.43750	−	11.1501i	−0.271308	−	0.469920i	0.697889	−	0.716206i	$-0.254123\pi$
$563$	−6.43750	−	11.1501i	−0.271308	−	0.469920i	−0.969197	+	0.246286i	$0.920790\pi$
$564$	−10.1983	+	5.88801i	−0.429427	+	0.247930i
$565$	1.96172	−	3.39780i	0.0825303	−	0.142947i
$566$			9.04826i			0.380327i
$567$		0			0
$568$		−	4.08740i		−	0.171503i
$569$	21.3989	−	37.0639i	0.897087	−	1.55380i	0.0658867	−	0.997827i	$-0.479012\pi$
$569$	21.3989	−	37.0639i	0.897087	−	1.55380i	0.831200	−	0.555973i	$-0.187654\pi$
$570$	−1.44455	−	2.50203i	−0.0605055	−	0.104799i
$571$	0.771225	−	0.445267i	0.0322748	−	0.0186338i	−0.483776	−	0.875192i	$-0.660735\pi$
$571$	0.771225	−	0.445267i	0.0322748	−	0.0186338i	0.516051	+	0.856558i	$0.327402\pi$
$572$	−9.89346	−	5.71199i	−0.413666	−	0.238830i
$573$		−	6.65973i		−	0.278214i
$574$		0			0
$575$			33.2803i			1.38789i
$576$	1.43115	−	2.47883i	0.0596313	−	0.103284i
$577$	−1.69789	−	2.94083i	−0.0706841	−	0.122428i	0.828517	−	0.559964i	$-0.189185\pi$
$577$	−1.69789	−	2.94083i	−0.0706841	−	0.122428i	−0.899201	+	0.437535i	$0.855852\pi$
$578$	−5.64814	+	7.42684i	−0.234932	+	0.308916i
$579$	1.93053	−	3.34378i	0.0802302	−	0.138963i
$580$	10.1431			0.421168
$581$		0			0
$582$	−8.42173			−0.349092
$583$	−4.32972	−	2.49976i	−0.179318	−	0.103530i
$584$	7.58347	−	4.37832i	0.313806	−	0.181176i
$585$	−5.67723	+	3.27775i	−0.234724	+	0.135518i
$586$	8.95774	−	15.5153i	0.370041	−	0.640930i
$587$	−8.27144			−0.341399			−0.170699	−	0.985323i	$-0.554603\pi$
$587$	−8.27144			−0.341399			−0.170699	+	0.985323i	$0.554603\pi$
$588$		0			0
$589$		−	11.8262i		−	0.487292i
$590$	−2.37240	−	1.36971i	−0.0976703	−	0.0563900i
$591$	−1.60183	−	2.77446i	−0.0658906	−	0.114126i
$592$	8.50755	−	4.91183i	0.349658	−	0.201875i
$593$	17.9564	−	31.1014i	0.737382	−	1.27718i	−0.216288	−	0.976330i	$-0.569395\pi$
$593$	17.9564	−	31.1014i	0.737382	−	1.27718i	0.953670	−	0.300854i	$-0.0972716\pi$
$594$	5.93317			0.243441
$595$		0			0
$596$	14.7536			0.604330
$597$	1.23004	−	2.13049i	0.0503423	−	0.0871953i
$598$	−14.1707	+	8.18147i	−0.579484	+	0.334565i
$599$	−16.2375	−	28.1242i	−0.663447	−	1.14912i	−0.979704	−	0.200450i	$-0.935760\pi$
$599$	−16.2375	−	28.1242i	−0.663447	−	1.14912i	0.316257	−	0.948673i	$-0.397574\pi$
$600$	−7.31551	−	4.22361i	−0.298655	−	0.172428i
$601$			28.7082i			1.17103i	0.810660	+	0.585517i	$0.199108\pi$
$601$			28.7082i			1.17103i	−0.810660	+	0.585517i	$0.800892\pi$
$602$		0			0
$603$	−10.3754			−0.422520
$604$	3.50979	−	6.07913i	0.142811	−	0.247356i
$605$	6.79731	−	3.92443i	0.276350	−	0.159551i
$606$	4.78153	−	2.76062i	0.194237	−	0.112143i
$607$	−6.14544	−	3.54807i	−0.249436	−	0.144012i	0.370070	−	0.929004i	$-0.379334\pi$
$607$	−6.14544	−	3.54807i	−0.249436	−	0.144012i	−0.619506	+	0.784992i	$0.712667\pi$
$608$	21.7947			0.883890
$609$		0			0
$610$	−9.47006			−0.383432
$611$	−10.2085	+	17.6817i	−0.412994	+	0.715326i
$612$	−12.1239	−	0.768414i	−0.490078	−	0.0310613i
$613$	18.2405	+	31.5934i	0.736725	+	1.27605i	0.953962	+	0.299926i	$0.0969621\pi$
$613$	18.2405	+	31.5934i	0.736725	+	1.27605i	−0.217237	+	0.976119i	$0.569705\pi$
$614$	−6.18594	+	10.7144i	−0.249644	+	0.432396i
$615$			2.10605i			0.0849243i
$616$		0			0
$617$		−	38.4014i		−	1.54598i	−0.634417	−	0.772991i	$-0.718760\pi$
$617$		−	38.4014i		−	1.54598i	0.634417	−	0.772991i	$-0.281240\pi$
$618$	8.15683	+	4.70935i	0.328116	+	0.189438i
$619$	−17.1212	+	9.88495i	−0.688161	+	0.397310i	−0.802923	−	0.596083i	$-0.796723\pi$
$619$	−17.1212	+	9.88495i	−0.688161	+	0.397310i	0.114762	+	0.993393i	$0.463389\pi$
$620$	2.79349	+	4.83847i	0.112189	+	0.194318i
$621$	−23.9615	+	41.5025i	−0.961540	+	1.66544i
$622$		−	3.13462i		−	0.125687i
$623$		0			0
$624$			8.51087i			0.340707i
$625$	−3.58729	+	6.21337i	−0.143492	+	0.248535i
$626$	11.5684	−	6.67904i	0.462368	−	0.266948i
$627$	−4.68285	−	8.11093i	−0.187015	−	0.323919i
$628$	−11.7334	+	20.3228i	−0.468212	+	0.810968i
$629$	−14.7709	−	9.82367i	−0.588956	−	0.391695i
$630$		0			0
$631$	35.5979			1.41713			0.708566	−	0.705645i	$-0.249343\pi$
$631$	35.5979			1.41713			0.708566	+	0.705645i	$0.249343\pi$
$632$	9.78578	+	5.64982i	0.389258	+	0.224738i
$633$	−7.65670	−	13.2618i	−0.304327	−	0.527109i
$634$	−6.72641	+	3.88350i	−0.267140	+	0.154233i
$635$	9.68604	+	5.59224i	0.384379	+	0.221921i
$636$			4.70746i			0.186663i
$637$		0			0
$638$	−5.83088			−0.230847
$639$	−3.02426	−	1.74606i	−0.119638	−	0.0690729i
$640$	−11.3929	+	6.57769i	−0.450344	+	0.260006i
$641$	−28.5654	+	16.4923i	−1.12827	+	0.651405i	−0.943498	−	0.331377i	$-0.892487\pi$
$641$	−28.5654	+	16.4923i	−1.12827	+	0.651405i	−0.184768	+	0.982782i	$0.559153\pi$
$642$	5.18404	−	8.97903i	0.204598	−	0.354374i
$643$			23.2670i			0.917562i	0.888549	+	0.458781i	$0.151714\pi$
$643$			23.2670i			0.917562i	−0.888549	+	0.458781i	$0.848286\pi$
$644$		0			0
$645$	9.31631			0.366829
$646$	−4.12346	−	8.31633i	−0.162235	−	0.327202i
$647$	5.59248	+	9.68647i	0.219863	+	0.380814i	0.954766	−	0.297358i	$-0.0961056\pi$
$647$	5.59248	+	9.68647i	0.219863	+	0.380814i	−0.734903	+	0.678172i	$0.762772\pi$
$648$	−0.800341	−	1.38623i	−0.0314404	−	0.0544563i
$649$	−7.69071	−	4.44023i	−0.301887	−	0.174294i
$650$	−6.72644			−0.263833
$651$		0			0
$652$			10.2825i			0.402692i
$653$	−9.30736	−	5.37361i	−0.364225	−	0.210286i	0.306707	−	0.951804i	$-0.400773\pi$
$653$	−9.30736	−	5.37361i	−0.364225	−	0.210286i	−0.670933	+	0.741518i	$0.734106\pi$
$654$	5.07661	+	8.79294i	0.198511	+	0.343831i
$655$	1.71145	+	2.96432i	0.0668720	+	0.115826i
$656$	−3.24517	−	1.87360i	−0.126703	−	0.0731517i
$657$		−	7.48133i		−	0.291875i
$658$		0			0
$659$	−14.7868			−0.576012			−0.288006	−	0.957629i	$-0.592992\pi$
$659$	−14.7868			−0.576012			−0.288006	+	0.957629i	$0.592992\pi$
$660$	3.83178	+	2.21228i	0.149152	+	0.0861129i
$661$	16.9628	+	29.3805i	0.659777	+	1.14277i	0.980673	+	0.195653i	$0.0626827\pi$
$661$	16.9628	+	29.3805i	0.659777	+	1.14277i	−0.320896	+	0.947114i	$0.603984\pi$
$662$	3.88478	+	6.72864i	0.150986	+	0.261516i
$663$	13.7691	−	6.82710i	0.534749	−	0.265142i
$664$	13.7577			0.533902
$665$		0			0
$666$			4.09571i			0.158705i
$667$	23.5484	−	40.7870i	0.911796	−	1.57928i
$668$	−22.0340	+	12.7213i	−0.852521	+	0.492203i
$669$	−19.6430	+	11.3409i	−0.759443	+	0.438465i
$670$	3.24353	+	1.87266i	0.125309	+	0.0723470i
$671$	−30.6995			−1.18514
$672$		0			0
$673$		−	6.64520i		−	0.256154i	−0.991764	−	0.128077i	$-0.959120\pi$
$673$		−	6.64520i		−	0.256154i	0.991764	−	0.128077i	$-0.0408804\pi$
$674$	8.63507	+	4.98546i	0.332611	+	0.192033i
$675$	−17.0607	+	9.85001i	−0.656667	+	0.379127i
$676$	−1.71707	−	2.97406i	−0.0660412	−	0.114387i
$677$	6.81492	+	3.93459i	0.261918	+	0.151219i	0.625209	−	0.780457i	$-0.285014\pi$
$677$	6.81492	+	3.93459i	0.261918	+	0.151219i	−0.363291	+	0.931676i	$0.618347\pi$
$678$	2.12369			0.0815598
$679$		0			0
$680$	7.95040	+	5.28755i	0.304884	+	0.202768i
$681$	3.86430	−	6.69316i	0.148080	−	0.256482i
$682$	−1.60588	−	2.78146i	−0.0614923	−	0.106508i
$683$	−9.25324	+	5.34236i	−0.354065	+	0.204420i	−0.666474	−	0.745528i	$-0.732197\pi$
$683$	−9.25324	+	5.34236i	−0.354065	+	0.204420i	0.312409	+	0.949948i	$0.398864\pi$
$684$	6.04278	−	10.4664i	0.231052	−	0.400193i
$685$		−	16.5440i		−	0.632112i
$686$		0			0
$687$		−	4.75333i		−	0.181351i
$688$	−8.28803	+	14.3553i	−0.315978	+	0.547290i
$689$	4.08087	+	7.06827i	0.155469	+	0.269280i
$690$	5.48839	−	3.16872i	0.208939	−	0.120631i
$691$	23.1718	+	13.3783i	0.881498	+	0.508933i	0.871152	−	0.491013i	$-0.163373\pi$
$691$	23.1718	+	13.3783i	0.881498	+	0.508933i	0.0103461	+	0.999946i	$0.496707\pi$
$692$			15.1231i			0.574895i
$693$		0			0
$694$			6.80220i			0.258208i
$695$	8.78325	−	15.2130i	0.333168	−	0.577064i
$696$	5.97705	+	10.3526i	0.226559	+	0.392413i
$697$	−0.428011	+	6.75306i	−0.0162121	+	0.255790i
$698$	1.98730	−	3.44211i	0.0752205	−	0.130286i
$699$	15.0298			0.568480
$700$		0			0
$701$	−6.69611			−0.252909			−0.126454	−	0.991972i	$-0.540360\pi$
$701$	−6.69611			−0.252909			−0.126454	+	0.991972i	$0.540360\pi$
$702$	−8.38824	−	4.84295i	−0.316594	−	0.182786i
$703$	15.2835	−	8.82396i	0.576430	−	0.332802i
$704$	−2.90073	+	1.67473i	−0.109325	+	0.0631189i
$705$	3.95382	−	6.84821i	0.148909	−	0.257919i
$706$	14.1282			0.531722
$707$		0			0
$708$			8.36168i			0.314251i
$709$	26.4352	+	15.2624i	0.992794	+	0.573190i	0.906108	−	0.423046i	$-0.139039\pi$
$709$	26.4352	+	15.2624i	0.992794	+	0.573190i	0.0866857	+	0.996236i	$0.472372\pi$
$710$	0.630291	+	1.09170i	0.0236544	+	0.0409706i
$711$	8.36059	−	4.82699i	0.313547	−	0.181026i
$712$	−5.24158	+	9.07868i	−0.196436	+	0.340238i
$713$	25.9417			0.971526
$714$		0			0
$715$	7.67125			0.286888
$716$	0.292955	−	0.507414i	0.0109483	−	0.0189629i
$717$	−14.5628	+	8.40783i	−0.543857	+	0.313996i
$718$	−8.39328	−	14.5376i	−0.313234	−	0.542538i
$719$	−23.3926	−	13.5057i	−0.872395	−	0.503678i	−0.00425163	−	0.999991i	$-0.501353\pi$
$719$	−23.3926	−	13.5057i	−0.872395	−	0.503678i	−0.868143	+	0.496313i	$0.834687\pi$
$720$			4.51747i			0.168356i
$721$		0			0
$722$	−1.19366			−0.0444235
$723$	7.97068	−	13.8056i	0.296433	−	0.513436i
$724$	9.12208	−	5.26664i	0.339019	−	0.195733i
$725$	16.7666	−	9.68020i	0.622696	−	0.359514i
$726$	3.67926	+	2.12422i	0.136550	+	0.0788372i
$727$	4.21060			0.156162			0.0780812	−	0.996947i	$-0.475121\pi$
$727$	4.21060			0.156162			0.0780812	+	0.996947i	$0.475121\pi$
$728$		0			0
$729$	−19.3428			−0.716402
$730$	−1.35030	+	2.33879i	−0.0499770	+	0.0865626i
$731$	29.8727	+	1.89334i	1.10488	+	0.0700278i
$732$	14.4530	+	25.0334i	0.534199	+	0.925261i
$733$	11.9575	−	20.7110i	0.441661	−	0.764980i	−0.556152	−	0.831081i	$-0.687723\pi$
$733$	11.9575	−	20.7110i	0.441661	−	0.764980i	0.997813	+	0.0661010i	$0.0210560\pi$
$734$			6.76264i			0.249614i
$735$		0			0
$736$			47.8082i			1.76223i
$737$	10.5147	+	6.07066i	0.387314	+	0.223616i
$738$	1.35298	−	0.781145i	0.0498040	−	0.0287544i
$739$	−7.78094	−	13.4770i	−0.286227	−	0.495759i	0.686679	−	0.726960i	$-0.259068\pi$
$739$	−7.78094	−	13.4770i	−0.286227	−	0.495759i	−0.972906	+	0.231201i	$0.925734\pi$
$740$	−4.16864	+	7.22029i	−0.153242	+	0.265423i
$741$			15.2895i			0.561674i
$742$		0			0
$743$		−	0.761676i		−	0.0279432i	−0.999902	−	0.0139716i	$-0.995553\pi$
$743$		−	0.761676i		−	0.0279432i	0.999902	−	0.0139716i	$-0.00444744\pi$
$744$	−3.29227	+	5.70238i	−0.120700	+	0.209059i
$745$	−8.57979	+	4.95354i	−0.314339	+	0.181484i
$746$	−5.09970	−	8.83293i	−0.186713	−	0.323397i
$747$	5.87701	−	10.1793i	0.215029	−	0.372441i
$748$	11.8370	+	7.87241i	0.432804	+	0.287844i
$749$		0			0
$750$	6.12688			0.223722
$751$	7.00604	+	4.04494i	0.255654	+	0.147602i	0.622350	−	0.782739i	$-0.286178\pi$
$751$	7.00604	+	4.04494i	0.255654	+	0.147602i	−0.366696	+	0.930341i	$0.619511\pi$
$752$	7.03483	+	12.1847i	0.256534	+	0.444330i
$753$	−25.9529	+	14.9839i	−0.945776	+	0.546044i
$754$	8.24363	+	4.75946i	0.300215	+	0.173329i
$755$			4.71367i			0.171548i
$756$		0			0
$757$	−31.6796			−1.15142			−0.575708	−	0.817655i	$-0.695274\pi$
$757$	−31.6796			−1.15142			−0.575708	+	0.817655i	$0.695274\pi$
$758$	14.4901	+	8.36588i	0.526305	+	0.303863i
$759$	17.7919	−	10.2722i	0.645806	−	0.372856i
$760$	−8.22630	+	4.74946i	−0.298399	+	0.172281i
$761$	−16.1975	+	28.0549i	−0.587160	+	1.01699i	0.407442	+	0.913231i	$0.366421\pi$
$761$	−16.1975	+	28.0549i	−0.587160	+	1.01699i	−0.994602	+	0.103760i	$0.966913\pi$
$762$			6.05395i			0.219312i
$763$		0			0
$764$	−10.0564			−0.363829
$765$	7.30850	−	3.62375i	0.264239	−	0.131017i
$766$	4.85139	+	8.40285i	0.175288	+	0.303607i
$767$	7.24869	+	12.5551i	0.261735	+	0.453338i
$768$	−2.95115	−	1.70385i	−0.106491	−	0.0614823i
$769$	19.8665			0.716405			0.358203	−	0.933644i	$-0.383390\pi$
$769$	19.8665			0.716405			0.358203	+	0.933644i	$0.383390\pi$
$770$		0			0
$771$		−	27.3736i		−	0.985836i
$772$	−5.04923	−	2.91517i	−0.181726	−	0.104919i
$773$	7.03023	+	12.1767i	0.252860	+	0.437966i	0.964312	−	0.264768i	$-0.0852955\pi$
$773$	7.03023	+	12.1767i	0.252860	+	0.437966i	−0.711452	+	0.702735i	$0.751962\pi$
$774$	−3.45546	−	5.98504i	−0.124204	−	0.215128i
$775$	9.23535	+	5.33203i	0.331744	+	0.191532i
$776$			27.6894i			0.993992i
$777$		0			0
$778$	6.74733			0.241904
$779$	−5.82985	−	3.36586i	−0.208876	−	0.120595i
$780$	−3.61155	−	6.25540i	−0.129314	−	0.223979i
$781$	2.04324	+	3.53899i	0.0731128	+	0.126635i
$782$	18.2425	−	9.04510i	0.652350	−	0.323452i
$783$	27.8785			0.996297
$784$		0			0
$785$		−	15.7580i		−	0.562427i
$786$	−0.926378	+	1.60453i	−0.0330428	+	0.0572318i
$787$	−4.70256	+	2.71502i	−0.167628	+	0.0967802i	−0.581467	−	0.813570i	$-0.697521\pi$
$787$	−4.70256	+	2.71502i	−0.167628	+	0.0967802i	0.413839	+	0.910350i	$0.364188\pi$
$788$	−4.18953	+	2.41883i	−0.149246	+	0.0861671i
$789$	29.6457	+	17.1159i	1.05541	+	0.609344i
$790$	−3.48489			−0.123987
$791$		0			0
$792$		−	7.14640i		−	0.253936i
$793$	43.4026	+	25.0585i	1.54127	+	0.889853i
$794$	6.20963	−	3.58513i	0.220371	−	0.127231i
$795$	−1.58054	−	2.73757i	−0.0560559	−	0.0970917i
$796$	−3.21713	−	1.85741i	−0.114028	−	0.0658341i
$797$	−39.1614			−1.38717			−0.693583	−	0.720376i	$-0.743969\pi$
$797$	−39.1614			−1.38717			−0.693583	+	0.720376i	$0.743969\pi$
$798$		0			0
$799$	14.0697	−	21.1552i	0.497749	−	0.748419i
$800$	−9.82643	+	17.0199i	−0.347417	+	0.601744i
$801$	4.47820	+	7.75647i	0.158229	+	0.274061i
$802$	14.9527	−	8.63296i	0.527999	−	0.304840i
$803$	−4.37733	+	7.58176i	−0.154473	+	0.267554i
$804$		−	11.4320i		−	0.403177i
$805$		0			0
$806$			5.24320i			0.184684i
$807$	8.70467	−	15.0769i	0.306419	−	0.530733i
$808$	−9.07651	−	15.7210i	−0.319310	−	0.553062i
$809$	−18.9733	+	10.9543i	−0.667067	+	0.385131i	−0.794964	−	0.606656i	$-0.792511\pi$
$809$	−18.9733	+	10.9543i	−0.667067	+	0.385131i	0.127897	+	0.991787i	$0.459177\pi$
$810$	0.427523	+	0.246831i	0.0150216	+	0.00867274i
$811$			52.6748i			1.84966i	0.380377	+	0.924832i	$0.375794\pi$
$811$			52.6748i			1.84966i	−0.380377	+	0.924832i	$0.624206\pi$
$812$		0			0
$813$		−	17.8984i		−	0.627725i
$814$	2.39640	−	4.15069i	0.0839938	−	0.145481i
$815$	−3.45235	−	5.97965i	−0.120931	−	0.209458i
$816$	0.669903	−	10.5696i	0.0234513	−	0.370009i
$817$	−14.8892	+	25.7888i	−0.520907	+	0.902237i
$818$	14.6734			0.513044
$819$		0			0
$820$	3.18022			0.111058
$821$	28.5249	+	16.4689i	0.995526	+	0.574767i	0.906922	−	0.421300i	$-0.138426\pi$
$821$	28.5249	+	16.4689i	0.995526	+	0.574767i	0.0886047	+	0.996067i	$0.471759\pi$
$822$	7.75521	−	4.47747i	0.270494	−	0.156170i
$823$	14.7744	−	8.53002i	0.515004	−	0.297338i	−0.219884	−	0.975526i	$-0.570568\pi$
$823$	14.7744	−	8.53002i	0.515004	−	0.297338i	0.734888	+	0.678188i	$0.237235\pi$
$824$	15.4836	−	26.8185i	0.539398	−	0.934265i
$825$	8.44531			0.294028
$826$		0			0
$827$		−	10.9933i		−	0.382275i	−0.981563	−	0.191138i	$-0.938782\pi$
$827$		−	10.9933i		−	0.382275i	0.981563	−	0.191138i	$-0.0612177\pi$
$828$	22.9588	+	13.2553i	0.797875	+	0.460653i
$829$	−7.00673	−	12.1360i	−0.243354	−	0.421501i	0.718314	−	0.695719i	$-0.244914\pi$
$829$	−7.00673	−	12.1360i	−0.243354	−	0.421501i	−0.961667	+	0.274218i	$0.911581\pi$
$830$	−3.67451	+	2.12148i	−0.127544	+	0.0736377i
$831$	10.5531	−	18.2784i	0.366082	−	0.634072i
$832$	5.46802			0.189569
$833$		0			0
$834$	9.50843			0.329250
$835$	8.54242	−	14.7959i	0.295623	−	0.512033i
$836$	−12.2478	+	7.07127i	−0.423599	+	0.244565i
$837$	7.67800	+	13.2987i	0.265390	+	0.459670i
$838$	1.49783	+	0.864774i	0.0517417	+	0.0298731i
$839$			8.65856i			0.298927i	0.988767	+	0.149463i	$0.0477546\pi$
$839$			8.65856i			0.298927i	−0.988767	+	0.149463i	$0.952245\pi$
$840$		0			0
$841$	1.60212			0.0552454
$842$	0.310457	−	0.537728i	0.0106991	−	0.0185313i
$843$	−2.73409	+	1.57853i	−0.0941670	+	0.0543673i
$844$	−20.0258	+	11.5619i	−0.689317	+	0.397977i
$845$	1.99709	+	1.15302i	0.0687020	+	0.0396651i
$846$	−5.86596			−0.201676
$847$		0			0
$848$	5.62435			0.193141
$849$	−9.27298	+	16.0613i	−0.318248	+	0.551222i
$850$	8.35351	+	0.529448i	0.286523	+	0.0181599i
$851$	19.3560	+	33.5256i	0.663515	+	1.14924i
$852$	1.92387	−	3.33225i	0.0659109	−	0.114161i
$853$		−	12.4062i		−	0.424781i	−0.977185	−	0.212390i	$-0.931875\pi$
$853$		−	12.4062i		−	0.424781i	0.977185	−	0.212390i	$-0.0681248\pi$
$854$		0			0
$855$			8.11550i			0.277544i
$856$	−29.5217	−	17.0444i	−1.00903	−	0.582564i
$857$	27.6243	−	15.9489i	0.943628	−	0.544804i	0.0525324	−	0.998619i	$-0.483271\pi$
$857$	27.6243	−	15.9489i	0.943628	−	0.544804i	0.891096	+	0.453815i	$0.149937\pi$
$858$	2.07615	+	3.59600i	0.0708787	+	0.122766i
$859$	12.0930	−	20.9457i	0.412608	−	0.714657i	−0.582566	−	0.812783i	$-0.697951\pi$
$859$	12.0930	−	20.9457i	0.412608	−	0.714657i	0.995174	+	0.0981257i	$0.0312847\pi$
$860$		−	14.0680i		−	0.479714i
$861$		0			0
$862$			21.2817i			0.724857i
$863$	2.76224	−	4.78434i	0.0940278	−	0.162861i	−0.815175	−	0.579215i	$-0.803359\pi$
$863$	2.76224	−	4.78434i	0.0940278	−	0.162861i	0.909202	+	0.416354i	$0.136692\pi$
$864$	−24.5082	+	14.1498i	−0.833787	+	0.481387i
$865$	−5.07761	−	8.79469i	−0.172644	−	0.299028i
$866$	5.82073	−	10.0818i	0.197796	−	0.342593i
$867$	−17.6371	+	7.39473i	−0.598988	+	0.251138i
$868$		0			0
$869$	−11.2971			−0.383228
$870$	−3.19280	−	1.84336i	−0.108246	−	0.0624958i
$871$	−9.91036	−	17.1653i	−0.335800	−	0.581622i
$872$	28.9099	−	16.6911i	0.979012	−	0.565233i
$873$	20.4873	+	11.8284i	0.693391	+	0.400330i
$874$			20.2568i			0.685197i
$875$		0			0
$876$	8.24323			0.278513
$877$	45.2599	+	26.1308i	1.52832	+	0.882376i	0.999433	+	0.0336833i	$0.0107238\pi$
$877$	45.2599	+	26.1308i	1.52832	+	0.882376i	0.528887	+	0.848692i	$0.322610\pi$
$878$	−10.4131	+	6.01198i	−0.351424	+	0.202894i
$879$	31.8012	−	18.3604i	1.07263	−	0.619282i
$880$	2.64317	−	4.57811i	0.0891014	−	0.154328i
$881$		−	40.1220i		−	1.35174i	−0.737019	−	0.675872i	$-0.763767\pi$
$881$		−	40.1220i		−	1.35174i	0.737019	−	0.675872i	$-0.236233\pi$
$882$		0			0
$883$	−22.4561			−0.755709			−0.377854	−	0.925865i	$-0.623338\pi$
$883$	−22.4561			−0.755709			−0.377854	+	0.925865i	$0.623338\pi$
$884$	−10.3092	−	20.7919i	−0.346735	−	0.699307i
$885$	−2.80745	−	4.86265i	−0.0943714	−	0.163456i
$886$	−1.69655	−	2.93852i	−0.0569969	−	0.0987215i
$887$	41.1975	+	23.7854i	1.38328	+	0.798634i	0.992546	−	0.121871i	$-0.0388896\pi$
$887$	41.1975	+	23.7854i	1.38328	+	0.798634i	0.390729	+	0.920506i	$0.372223\pi$
$888$	−9.82589			−0.329735
$889$		0			0
$890$		−	3.23308i		−	0.108373i
$891$	1.38592	+	0.800160i	0.0464300	+	0.0268064i
$892$	17.1252	+	29.6617i	0.573394	+	0.993147i
$893$	12.6379	+	21.8894i	0.422910	+	0.732501i
$894$	−4.64408	−	2.68126i	−0.155321	−	0.0896748i
$895$			0.393441i			0.0131513i
$896$		0			0
$897$	−33.5387			−1.11982
$898$	−7.68320	−	4.43590i	−0.256392	−	0.148028i
$899$	−7.54563	−	13.0694i	−0.251661	−	0.435889i
$900$	5.44895	+	9.43786i	0.181632	+	0.314595i
$901$	−4.51164	−	9.09924i	−0.150305	−	0.303139i
$902$	−1.82819			−0.0608722
$903$		0			0
$904$		−	6.98238i		−	0.232230i
$905$	−3.53656	+	6.12551i	−0.117559	+	0.203619i
$906$	−2.20960	+	1.27571i	−0.0734090	+	0.0423827i
$907$	−25.7030	+	14.8397i	−0.853455	+	0.492743i	−0.861815	−	0.507222i	$-0.830672\pi$
$907$	−25.7030	+	14.8397i	−0.853455	+	0.492743i	0.00835992	+	0.999965i	$0.497339\pi$
$908$	−10.1069	−	5.83523i	−0.335410	−	0.193649i
$909$	−15.5092			−0.514408
$910$		0			0
$911$			25.0521i			0.830014i	0.909818	+	0.415007i	$0.136221\pi$
$911$			25.0521i			0.830014i	−0.909818	+	0.415007i	$0.863779\pi$
$912$	9.12461	+	5.26809i	0.302146	+	0.174444i
$913$	−11.9118	+	6.87728i	−0.394223	+	0.227605i
$914$	0.858142	+	1.48634i	0.0283848	+	0.0491639i
$915$	−16.8100	−	9.70526i	−0.555722	−	0.320846i
$916$	−7.17770			−0.237158
$917$		0			0
$918$	10.0361	+	6.67468i	0.331240	+	0.220297i
$919$	−12.2949	+	21.2955i	−0.405573	+	0.702473i	−0.994388	−	0.105795i	$-0.966261\pi$
$919$	−12.2949	+	21.2955i	−0.405573	+	0.702473i	0.588815	+	0.808268i	$0.299595\pi$
$920$	−10.4183	−	18.0450i	−0.343481	−	0.594926i
$921$	−21.9609	+	12.6791i	−0.723637	+	0.417792i
$922$	−8.12711	+	14.0766i	−0.267652	+	0.463587i
$923$		−	6.67118i		−	0.219584i
$924$		0			0
$925$			15.9136i			0.523237i
$926$	5.02693	−	8.70689i	0.165195	−	0.286126i
$927$	−13.2286	−	22.9126i	−0.434485	−	0.752550i
$928$	24.0857	−	13.9059i	0.790652	−	0.456483i
$929$	−14.4995	−	8.37129i	−0.475713	−	0.274653i	0.242915	−	0.970048i	$-0.421896\pi$
$929$	−14.4995	−	8.37129i	−0.475713	−	0.274653i	−0.718628	+	0.695394i	$0.755230\pi$
$930$		−	2.03072i		−	0.0665898i
$931$		0			0
$932$		−	22.6956i		−	0.743419i
$933$	3.21247	−	5.56417i	0.105172	−	0.182163i
$934$	7.73191	+	13.3921i	0.252996	+	0.438201i
$935$	−9.52686	−	0.603815i	−0.311562	−	0.0197469i
$936$	−5.83326	+	10.1035i	−0.190666	+	0.330243i
$937$	28.1196			0.918627			0.459313	−	0.888274i	$-0.348095\pi$
$937$	28.1196			0.918627			0.459313	+	0.888274i	$0.348095\pi$
$938$		0			0
$939$	27.3797			0.893503
$940$	−10.3411	−	5.97041i	−0.337288	−	0.194733i
$941$	−45.2683	+	26.1357i	−1.47570	+	0.851998i	−0.999624	−	0.0274041i	$-0.991276\pi$
$941$	−45.2683	+	26.1357i	−1.47570	+	0.851998i	−0.476080	+	0.879402i	$0.657943\pi$
$942$	7.38678	−	4.26476i	0.240674	−	0.138953i
$943$	7.38327	−	12.7882i	0.240432	−	0.416441i
$944$	9.99032			0.325157
$945$		0			0
$946$			8.08717i			0.262937i
$947$	33.7929	+	19.5104i	1.09812	+	0.634002i	0.935727	−	0.352724i	$-0.114745\pi$
$947$	33.7929	+	19.5104i	1.09812	+	0.634002i	0.162396	+	0.986726i	$0.448078\pi$
$948$	5.31857	+	9.21203i	0.172739	+	0.299193i
$949$	12.3772	−	7.14600i	0.401782	−	0.231969i
$950$	−4.16356	+	7.21150i	−0.135084	+	0.233972i
$951$	−15.9198			−0.516234
$952$		0			0
$953$	15.4840			0.501576			0.250788	−	0.968042i	$-0.419310\pi$
$953$	15.4840			0.501576			0.250788	+	0.968042i	$0.419310\pi$
$954$	−1.17246	+	2.03076i	−0.0379598	+	0.0657482i
$955$	5.84822	−	3.37647i	0.189244	−	0.109260i
$956$	12.6961	+	21.9904i	0.410622	+	0.711219i
$957$	−10.3502	−	5.97570i	−0.334575	−	0.193167i
$958$			18.1088i			0.585070i
$959$		0			0
$960$	−2.11779			−0.0683513
$961$	−11.3437	+	19.6479i	−0.365927	+	0.633804i
$962$	−6.77600	+	3.91213i	−0.218467	+	0.126132i
$963$	−25.2222	+	14.5620i	−0.812774	+	0.469255i
$964$	−20.8470	−	12.0360i	−0.671436	−	0.387654i
$965$	3.91510			0.126032
$966$		0			0
$967$	−38.1965			−1.22832			−0.614158	−	0.789183i	$-0.710504\pi$
$967$	−38.1965			−1.22832			−0.614158	+	0.789183i	$0.710504\pi$
$968$	6.98412	−	12.0969i	0.224478	−	0.388808i
$969$	1.20346	−	18.9879i	0.0386607	−	0.609980i
$970$	−4.26980	−	7.39551i	−0.137095	−	0.237455i
$971$	−11.1591	+	19.3281i	−0.358113	+	0.620269i	−0.987646	−	0.156705i	$-0.949913\pi$
$971$	−11.1591	+	19.3281i	−0.358113	+	0.620269i	0.629533	+	0.776974i	$0.283246\pi$
$972$			25.6365i			0.822291i
$973$		0			0
$974$		−	21.7682i		−	0.697500i
$975$	−11.9399	−	6.89349i	−0.382382	−	0.220769i
$976$	29.9092	−	17.2681i	0.957371	−	0.552738i
$977$	−11.0963	−	19.2193i	−0.355001	−	0.614880i	0.632117	−	0.774873i	$-0.282186\pi$
$977$	−11.0963	−	19.2193i	−0.355001	−	0.614880i	−0.987118	+	0.159993i	$0.948853\pi$
$978$	1.86870	−	3.23668i	0.0597543	−	0.103498i
$979$		−	10.4808i		−	0.334967i
$980$		0			0
$981$		−	28.5205i		−	0.910589i
$982$	−5.35543	+	9.27588i	−0.170899	+	0.296005i
$983$	17.9676	−	10.3736i	0.573079	−	0.330867i	−0.185299	−	0.982682i	$-0.559325\pi$
$983$	17.9676	−	10.3736i	0.573079	−	0.330867i	0.758378	+	0.651815i	$0.225992\pi$
$984$	1.87402	+	3.24590i	0.0597417	+	0.103476i
$985$	1.62425	−	2.81328i	0.0517529	−	0.0896387i
$986$	−9.86307	−	6.55960i	−0.314104	−	0.208900i
$987$		0			0
$988$	23.0877			0.734518
$989$	−56.5697	−	32.6605i	−1.79881	−	1.03854i
$990$	1.10200	+	1.90872i	0.0350238	+	0.0606630i
$991$	−2.48705	+	1.43590i	−0.0790038	+	0.0456129i	−0.538981	−	0.842318i	$-0.681191\pi$
$991$	−2.48705	+	1.43590i	−0.0790038	+	0.0456129i	0.459978	+	0.887930i	$0.347857\pi$
$992$	13.2669	+	7.65962i	0.421223	+	0.243193i
$993$			15.9251i			0.505367i
$994$		0			0
$995$	2.49451			0.0790814
$996$	11.2159	+	6.47553i	0.355391	+	0.205185i
$997$	24.3282	−	14.0459i	0.770480	−	0.444837i	−0.0625656	−	0.998041i	$-0.519928\pi$
$997$	24.3282	−	14.0459i	0.770480	−	0.444837i	0.833046	+	0.553204i	$0.186595\pi$
$998$	−11.4401	+	6.60497i	−0.362131	+	0.209077i
$999$	−11.4576	+	19.8452i	−0.362503	+	0.627874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.j.a.373.5		20
7.2	even	3		833.2.b.d.50.5		10
7.3	odd	6		119.2.j.a.67.5	yes	20
7.4	even	3	inner	833.2.j.a.67.6		20
7.5	odd	6		833.2.b.c.50.6		10
7.6	odd	2		119.2.j.a.16.6	yes	20
17.16	even	2	inner	833.2.j.a.373.6		20
119.16	even	6		833.2.b.d.50.6		10
119.33	odd	6		833.2.b.c.50.5		10
119.67	even	6	inner	833.2.j.a.67.5		20
119.101	odd	6		119.2.j.a.67.6	yes	20
119.118	odd	2		119.2.j.a.16.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.j.a.16.5	✓	20	119.118	odd	2
119.2.j.a.16.6	yes	20	7.6	odd	2
119.2.j.a.67.5	yes	20	7.3	odd	6
119.2.j.a.67.6	yes	20	119.101	odd	6
833.2.b.c.50.5		10	119.33	odd	6
833.2.b.c.50.6		10	7.5	odd	6
833.2.b.d.50.5		10	7.2	even	3
833.2.b.d.50.6		10	119.16	even	6
833.2.j.a.67.5		20	119.67	even	6	inner
833.2.j.a.67.6		20	7.4	even	3	inner
833.2.j.a.373.5		20	1.1	even	1	trivial
833.2.j.a.373.6		20	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.274428 + 0.475324i) q^{2} +(-0.974258 + 0.562488i) q^{3} +(0.849378 + 1.47117i) q^{4} +(-0.987893 - 0.570360i) q^{5} -0.617451i q^{6} -2.03009 q^{8} +(-0.867214 + 1.50206i) q^{9} +(0.542212 - 0.313046i) q^{10} +(1.75771 - 1.01481i) q^{11} +(-1.65503 - 0.955531i) q^{12} -3.31337 q^{13} +1.28328 q^{15} +(-1.14164 + 1.97738i) q^{16} +(4.11485 + 0.260800i) q^{17} +(-0.475976 - 0.824415i) q^{18} +(-2.05093 + 3.55231i) q^{19} -1.93781i q^{20} +1.11398i q^{22} +(-7.79225 - 4.49886i) q^{23} +(1.97783 - 1.14190i) q^{24} +(-1.84938 - 3.20322i) q^{25} +(0.909284 - 1.57493i) q^{26} -5.32612i q^{27} +5.23430i q^{29} +(-0.352170 + 0.609976i) q^{30} +(-2.49688 + 1.44157i) q^{31} +(-2.65669 - 4.60152i) q^{32} +(-1.14164 + 1.97738i) q^{33} +(-1.25320 + 1.88432i) q^{34} -2.94637 q^{36} +(-3.72601 - 2.15121i) q^{37} +(-1.12566 - 1.94971i) q^{38} +(3.22808 - 1.86373i) q^{39} +(2.00551 + 1.15788i) q^{40} +1.64114i q^{41} +7.25974 q^{43} +(2.98592 + 1.72392i) q^{44} +(1.71343 - 0.989249i) q^{45} +(4.27683 - 2.46923i) q^{46} +(3.08101 - 5.33647i) q^{47} -2.56864i q^{48} +2.03009 q^{50} +(-4.15562 + 2.06047i) q^{51} +(-2.81431 - 4.87452i) q^{52} +(-1.23164 - 2.13326i) q^{53} +(2.53163 + 1.46164i) q^{54} -2.31524 q^{55} -4.61449i q^{57} +(-2.48799 - 1.43644i) q^{58} +(-2.18771 - 3.78922i) q^{59} +(1.08999 + 1.88792i) q^{60} +(-13.0992 - 7.56283i) q^{61} -1.58244i q^{62} -1.65029 q^{64} +(3.27326 + 1.88982i) q^{65} +(-0.626598 - 1.08530i) q^{66} +(2.99102 + 5.18060i) q^{67} +(3.11138 + 6.27514i) q^{68} +10.1222 q^{69} +2.01341i q^{71} +(1.76052 - 3.04931i) q^{72} +(-3.73554 + 2.15671i) q^{73} +(2.04505 - 1.18071i) q^{74} +(3.60354 + 2.08051i) q^{75} -6.96805 q^{76} +2.04585i q^{78} +(-4.82037 - 2.78304i) q^{79} +(2.25564 - 1.30229i) q^{80} +(0.394240 + 0.682843i) q^{81} +(-0.780075 - 0.450376i) q^{82} -6.77689 q^{83} +(-3.91628 - 2.60459i) q^{85} +(-1.99228 + 3.45073i) q^{86} +(-2.94423 - 5.09956i) q^{87} +(-3.56830 + 2.06016i) q^{88} +(2.58195 - 4.47206i) q^{89} +1.08591i q^{90} -15.2849i q^{92} +(1.62174 - 2.80893i) q^{93} +(1.69104 + 2.92896i) q^{94} +(4.05219 - 2.33953i) q^{95} +(5.17660 + 2.98871i) q^{96} -13.6395i q^{97} +3.52024i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 10 q^{4} + 16 q^{13} - 16 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 10 q^{19} - 10 q^{25} - 12 q^{26} - 10 q^{30} - 12 q^{32} - 2 q^{33} - 24 q^{34} + 56 q^{36} + 2 q^{38} - 52 q^{43}+ \cdots - 50 q^{94}+O(q^{100}) \) 20 * q - 2 * q^2 - 10 * q^4 + 16 * q^13 - 16 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 10 * q^19 - 10 * q^25 - 12 * q^26 - 10 * q^30 - 12 * q^32 - 2 * q^33 - 24 * q^34 + 56 * q^36 + 2 * q^38 - 52 * q^43 - 30 * q^47 + 6 * q^51 + 2 * q^52 + 40 * q^53 - 12 * q^55 + 14 * q^59 - 22 * q^60 - 24 * q^64 - 12 * q^66 + 12 * q^67 + 32 * q^68 + 88 * q^69 - 16 * q^72 - 132 * q^76 - 2 * q^81 - 96 * q^83 - 4 * q^85 - 10 * q^86 + 26 * q^87 - 16 * q^89 + 46 * q^93 - 50 * q^94

Introduction

L-functions

Modular forms

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