LMFDB - Embedded newform 471.2.b.a.313.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.b (of order $2$, degree $1$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 15x^{10} + 77x^{8} + 158x^{6} + 111x^{4} + 21x^{2} + 1 $ x^12 + 15x^10 + 77x^8 + 158x^6 + 111x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.11
Root			$2.06731i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.a.313.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.06731i q^{2} -1.00000 q^{3} -2.27376 q^{4} -1.58359i q^{5} -2.06731i q^{6} +2.74875i q^{7} -0.565947i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.06731i q^{2} -1.00000 q^{3} -2.27376 q^{4} -1.58359i q^{5} -2.06731i q^{6} +2.74875i q^{7} -0.565947i q^{8} +1.00000 q^{9} +3.27376 q^{10} -2.88528 q^{11} +2.27376 q^{12} -5.68252 q^{13} -5.68252 q^{14} +1.58359i q^{15} -3.37753 q^{16} +1.55565 q^{17} +2.06731i q^{18} -2.86064 q^{19} +3.60070i q^{20} -2.74875i q^{21} -5.96476i q^{22} +0.736939i q^{23} +0.565947i q^{24} +2.49225 q^{25} -11.7475i q^{26} -1.00000 q^{27} -6.25001i q^{28} -3.04956i q^{29} -3.27376 q^{30} -8.73042 q^{31} -8.11430i q^{32} +2.88528 q^{33} +3.21601i q^{34} +4.35289 q^{35} -2.27376 q^{36} -5.70716 q^{37} -5.91382i q^{38} +5.68252 q^{39} -0.896227 q^{40} +0.515750i q^{41} +5.68252 q^{42} +11.1469i q^{43} +6.56044 q^{44} -1.58359i q^{45} -1.52348 q^{46} +10.8012 q^{47} +3.37753 q^{48} -0.555650 q^{49} +5.15225i q^{50} -1.55565 q^{51} +12.9207 q^{52} -2.51825i q^{53} -2.06731i q^{54} +4.56909i q^{55} +1.55565 q^{56} +2.86064 q^{57} +6.30439 q^{58} +3.36490i q^{59} -3.60070i q^{60} +4.10184i q^{61} -18.0485i q^{62} +2.74875i q^{63} +10.0197 q^{64} +8.99876i q^{65} +5.96476i q^{66} -3.78903 q^{67} -3.53718 q^{68} -0.736939i q^{69} +8.99876i q^{70} -9.38352 q^{71} -0.565947i q^{72} +1.99625i q^{73} -11.7985i q^{74} -2.49225 q^{75} +6.50440 q^{76} -7.93093i q^{77} +11.7475i q^{78} +9.92553i q^{79} +5.34862i q^{80} +1.00000 q^{81} -1.06621 q^{82} -4.11905i q^{83} +6.25001i q^{84} -2.46351i q^{85} -23.0441 q^{86} +3.04956i q^{87} +1.63292i q^{88} +8.34178 q^{89} +3.27376 q^{90} -15.6199i q^{91} -1.67562i q^{92} +8.73042 q^{93} +22.3294i q^{94} +4.53007i q^{95} +8.11430i q^{96} +10.8972i q^{97} -1.14870i q^{98} -2.88528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			2.06731i			1.46181i	0.682481	+	0.730904i	$0.260901\pi$
$2$			2.06731i			1.46181i	−0.682481	+	0.730904i	$0.739099\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−2.27376			−1.13688
$5$		−	1.58359i		−	0.708201i	−0.935207	−	0.354101i	$-0.884787\pi$
$5$		−	1.58359i		−	0.708201i	0.935207	−	0.354101i	$-0.115213\pi$
$6$		−	2.06731i		−	0.843975i
$7$			2.74875i			1.03893i	0.854491	+	0.519466i	$0.173869\pi$
$7$			2.74875i			1.03893i	−0.854491	+	0.519466i	$0.826131\pi$
$8$		−	0.565947i		−	0.200093i
$9$	1.00000			0.333333
$10$	3.27376			1.03525
$11$	−2.88528			−0.869945			−0.434972	−	0.900444i	$-0.643242\pi$
$11$	−2.88528			−0.869945			−0.434972	+	0.900444i	$0.643242\pi$
$12$	2.27376			0.656378
$13$	−5.68252			−1.57605			−0.788024	−	0.615645i	$-0.788896\pi$
$13$	−5.68252			−1.57605			−0.788024	+	0.615645i	$0.788896\pi$
$14$	−5.68252			−1.51872
$15$			1.58359i			0.408880i
$16$	−3.37753			−0.844383
$17$	1.55565			0.377301			0.188650	−	0.982044i	$-0.439589\pi$
$17$	1.55565			0.377301			0.188650	+	0.982044i	$0.439589\pi$
$18$			2.06731i			0.487269i
$19$	−2.86064			−0.656275			−0.328138	−	0.944630i	$-0.606421\pi$
$19$	−2.86064			−0.656275			−0.328138	+	0.944630i	$0.606421\pi$
$20$			3.60070i			0.805140i
$21$		−	2.74875i		−	0.599827i
$22$		−	5.96476i		−	1.27169i
$23$			0.736939i			0.153662i	0.997044	+	0.0768312i	$0.0244803\pi$
$23$			0.736939i			0.153662i	−0.997044	+	0.0768312i	$0.975520\pi$
$24$			0.565947i			0.115524i
$25$	2.49225			0.498451
$26$		−	11.7475i		−	2.30388i
$27$	−1.00000			−0.192450
$28$		−	6.25001i		−	1.18114i
$29$		−	3.04956i		−	0.566290i	−0.959077	−	0.283145i	$-0.908622\pi$
$29$		−	3.04956i		−	0.566290i	0.959077	−	0.283145i	$-0.0913777\pi$
$30$	−3.27376			−0.597704
$31$	−8.73042			−1.56803			−0.784015	−	0.620742i	$-0.786832\pi$
$31$	−8.73042			−1.56803			−0.784015	+	0.620742i	$0.786832\pi$
$32$		−	8.11430i		−	1.43442i
$33$	2.88528			0.502263
$34$			3.21601i			0.551541i
$35$	4.35289			0.735773
$36$	−2.27376			−0.378960
$37$	−5.70716			−0.938252			−0.469126	−	0.883131i	$-0.655431\pi$
$37$	−5.70716			−0.938252			−0.469126	+	0.883131i	$0.655431\pi$
$38$		−	5.91382i		−	0.959348i
$39$	5.68252			0.909932
$40$	−0.896227			−0.141706
$41$			0.515750i			0.0805466i	0.999189	+	0.0402733i	$0.0128229\pi$
$41$			0.515750i			0.0805466i	−0.999189	+	0.0402733i	$0.987177\pi$
$42$	5.68252			0.876832
$43$			11.1469i			1.69989i	0.526870	+	0.849946i	$0.323365\pi$
$43$			11.1469i			1.69989i	−0.526870	+	0.849946i	$0.676635\pi$
$44$	6.56044			0.989023
$45$		−	1.58359i		−	0.236067i
$46$	−1.52348			−0.224625
$47$	10.8012			1.57551			0.787757	−	0.615986i	$-0.211242\pi$
$47$	10.8012			1.57551			0.787757	+	0.615986i	$0.211242\pi$
$48$	3.37753			0.487505
$49$	−0.555650			−0.0793786
$50$			5.15225i			0.728639i
$51$	−1.55565			−0.217835
$52$	12.9207			1.79178
$53$		−	2.51825i		−	0.345908i	−0.984930	−	0.172954i	$-0.944669\pi$
$53$		−	2.51825i		−	0.345908i	0.984930	−	0.172954i	$-0.0553313\pi$
$54$		−	2.06731i		−	0.281325i
$55$			4.56909i			0.616096i
$56$	1.55565			0.207883
$57$	2.86064			0.378901
$58$	6.30439			0.827806
$59$			3.36490i			0.438073i	0.975717	+	0.219036i	$0.0702913\pi$
$59$			3.36490i			0.438073i	−0.975717	+	0.219036i	$0.929709\pi$
$60$		−	3.60070i		−	0.464848i
$61$			4.10184i			0.525187i	0.964907	+	0.262593i	$0.0845777\pi$
$61$			4.10184i			0.525187i	−0.964907	+	0.262593i	$0.915422\pi$
$62$		−	18.0485i		−	2.29216i
$63$			2.74875i			0.346310i
$64$	10.0197			1.25246
$65$			8.99876i			1.11616i
$66$			5.96476i			0.734211i
$67$	−3.78903			−0.462904			−0.231452	−	0.972846i	$-0.574348\pi$
$67$	−3.78903			−0.462904			−0.231452	+	0.972846i	$0.574348\pi$
$68$	−3.53718			−0.428946
$69$		−	0.736939i		−	0.0887170i
$70$			8.99876i			1.07556i
$71$	−9.38352			−1.11362			−0.556809	−	0.830640i	$-0.687975\pi$
$71$	−9.38352			−1.11362			−0.556809	+	0.830640i	$0.687975\pi$
$72$		−	0.565947i		−	0.0666975i
$73$			1.99625i			0.233644i	0.993153	+	0.116822i	$0.0372707\pi$
$73$			1.99625i			0.233644i	−0.993153	+	0.116822i	$0.962729\pi$
$74$		−	11.7985i		−	1.37154i
$75$	−2.49225			−0.287781
$76$	6.50440			0.746106
$77$		−	7.93093i		−	0.903813i
$78$			11.7475i			1.33014i
$79$			9.92553i			1.11671i	0.829602	+	0.558355i	$0.188567\pi$
$79$			9.92553i			1.11671i	−0.829602	+	0.558355i	$0.811433\pi$
$80$			5.34862i			0.597994i
$81$	1.00000			0.111111
$82$	−1.06621			−0.117744
$83$		−	4.11905i		−	0.452125i	−0.974113	−	0.226062i	$-0.927415\pi$
$83$		−	4.11905i		−	0.452125i	0.974113	−	0.226062i	$-0.0725853\pi$
$84$			6.25001i			0.681932i
$85$		−	2.46351i		−	0.267205i
$86$	−23.0441			−2.48491
$87$			3.04956i			0.326947i
$88$			1.63292i			0.174070i
$89$	8.34178			0.884227			0.442113	−	0.896959i	$-0.354229\pi$
$89$	8.34178			0.884227			0.442113	+	0.896959i	$0.354229\pi$
$90$	3.27376			0.345085
$91$		−	15.6199i		−	1.63741i
$92$		−	1.67562i		−	0.174696i
$93$	8.73042			0.905303
$94$			22.3294i			2.30310i
$95$			4.53007i			0.464775i
$96$			8.11430i			0.828162i
$97$			10.8972i			1.10644i	0.833035	+	0.553221i	$0.186602\pi$
$97$			10.8972i			1.10644i	−0.833035	+	0.553221i	$0.813398\pi$
$98$		−	1.14870i		−	0.116036i
$99$	−2.88528			−0.289982
$100$	−5.66679			−0.566679
$101$	−10.0354			−0.998561			−0.499280	−	0.866440i	$-0.666402\pi$
$101$	−10.0354			−0.998561			−0.499280	+	0.866440i	$0.666402\pi$
$102$		−	3.21601i		−	0.318432i
$103$		−	6.53691i		−	0.644101i	−0.946723	−	0.322050i	$-0.895628\pi$
$103$		−	6.53691i		−	0.644101i	0.946723	−	0.322050i	$-0.104372\pi$
$104$			3.21601i			0.315356i
$105$	−4.35289			−0.424799
$106$	5.20600			0.505651
$107$			19.5321i			1.88824i	0.329600	+	0.944121i	$0.393086\pi$
$107$			19.5321i			1.88824i	−0.329600	+	0.944121i	$0.606914\pi$
$108$	2.27376			0.218793
$109$	−0.627253			−0.0600799			−0.0300400	−	0.999549i	$-0.509563\pi$
$109$	−0.627253			−0.0600799			−0.0300400	+	0.999549i	$0.509563\pi$
$110$	−9.44572			−0.900614
$111$	5.70716			0.541700
$112$		−	9.28401i		−	0.877257i
$113$	6.24638			0.587610			0.293805	−	0.955865i	$-0.405078\pi$
$113$	6.24638			0.587610			0.293805	+	0.955865i	$0.405078\pi$
$114$			5.91382i			0.553880i
$115$	1.16701			0.108824
$116$			6.93398i			0.643804i
$117$	−5.68252			−0.525349
$118$	−6.95628			−0.640378
$119$			4.27610i			0.391990i
$120$	0.896227			0.0818139
$121$	−2.67516			−0.243196
$122$	−8.47976			−0.767721
$123$		−	0.515750i		−	0.0465036i
$124$	19.8509			1.78266
$125$		−	11.8646i		−	1.06120i
$126$	−5.68252			−0.506239
$127$	16.6463			1.47712			0.738561	−	0.674186i	$-0.235505\pi$
$127$	16.6463			1.47712			0.738561	+	0.674186i	$0.235505\pi$
$128$			4.48516i			0.396436i
$129$		−	11.1469i		−	0.981433i
$130$	−18.6032			−1.63161
$131$			15.7645i			1.37735i	0.725069	+	0.688676i	$0.241808\pi$
$131$			15.7645i			1.37735i	−0.725069	+	0.688676i	$0.758192\pi$
$132$	−6.56044			−0.571013
$133$		−	7.86319i		−	0.681825i
$134$		−	7.83310i		−	0.676677i
$135$			1.58359i			0.136293i
$136$		−	0.880416i		−	0.0754951i
$137$		−	3.48569i		−	0.297803i	−0.988852	−	0.148901i	$-0.952426\pi$
$137$		−	3.48569i		−	0.297803i	0.988852	−	0.148901i	$-0.0475737\pi$
$138$	1.52348			0.129687
$139$		−	21.9677i		−	1.86328i	−0.363389	−	0.931638i	$-0.618380\pi$
$139$		−	21.9677i		−	1.86328i	0.363389	−	0.931638i	$-0.381620\pi$
$140$	−9.89743			−0.836486
$141$	−10.8012			−0.909624
$142$		−	19.3986i		−	1.62790i
$143$	16.3957			1.37107
$144$	−3.37753			−0.281461
$145$	−4.82925			−0.401047
$146$	−4.12687			−0.341542
$147$	0.555650			0.0458293
$148$	12.9767			1.06668
$149$			13.6164i			1.11550i	0.830011	+	0.557748i	$0.188334\pi$
$149$			13.6164i			1.11550i	−0.830011	+	0.557748i	$0.811666\pi$
$150$		−	5.15225i		−	0.420680i
$151$			18.5429i			1.50900i	0.656302	+	0.754499i	$0.272120\pi$
$151$			18.5429i			1.50900i	−0.656302	+	0.754499i	$0.727880\pi$
$152$			1.61897i			0.131316i
$153$	1.55565			0.125767
$154$	16.3957			1.32120
$155$			13.8254i			1.11048i
$156$	−12.9207			−1.03448
$157$	6.01215	−	10.9934i	0.479822	−	0.877366i
$157$	6.01215	−	10.9934i	0.479822	−	0.877366i
$158$	−20.5191			−1.63241
$159$			2.51825i			0.199710i
$160$	−12.8497			−1.01586
$161$	−2.02566			−0.159645
$162$			2.06731i			0.162423i
$163$			19.5343i			1.53004i	0.644005	+	0.765021i	$0.277271\pi$
$163$			19.5343i			1.53004i	−0.644005	+	0.765021i	$0.722729\pi$
$164$		−	1.17269i		−	0.0915719i
$165$		−	4.56909i		−	0.355703i
$166$	8.51535			0.660919
$167$	22.4140			1.73444			0.867222	−	0.497921i	$-0.165903\pi$
$167$	22.4140			1.73444			0.867222	+	0.497921i	$0.165903\pi$
$168$	−1.55565			−0.120021
$169$	19.2910			1.48393
$170$	5.09283			0.390602
$171$	−2.86064			−0.218758
$172$		−	25.3455i		−	1.93257i
$173$	−5.16280			−0.392521			−0.196260	−	0.980552i	$-0.562880\pi$
$173$	−5.16280			−0.392521			−0.196260	+	0.980552i	$0.562880\pi$
$174$	−6.30439			−0.477934
$175$			6.85059i			0.517856i
$176$	9.74513			0.734567
$177$		−	3.36490i		−	0.252921i
$178$			17.2450i			1.29257i
$179$			7.33341i			0.548125i	0.961712	+	0.274062i	$0.0883675\pi$
$179$			7.33341i			0.548125i	−0.961712	+	0.274062i	$0.911633\pi$
$180$			3.60070i			0.268380i
$181$			5.97957i			0.444458i	0.974994	+	0.222229i	$0.0713333\pi$
$181$			5.97957i			0.444458i	−0.974994	+	0.222229i	$0.928667\pi$
$182$	32.2910			2.39357
$183$		−	4.10184i		−	0.303217i
$184$	0.417069			0.0307467
$185$			9.03779i			0.664471i
$186$			18.0485i			1.32338i
$187$	−4.48849			−0.328231
$188$	−24.5593			−1.79117
$189$		−	2.74875i		−	0.199942i
$190$	−9.36504			−0.679412
$191$		−	22.3856i		−	1.61977i	−0.586591	−	0.809883i	$-0.699531\pi$
$191$		−	22.3856i		−	1.61977i	0.586591	−	0.809883i	$-0.300469\pi$
$192$	−10.0197			−0.723108
$193$	−17.0917			−1.23029			−0.615144	−	0.788415i	$-0.710902\pi$
$193$	−17.0917			−1.23029			−0.615144	+	0.788415i	$0.710902\pi$
$194$	−22.5278			−1.61740
$195$		−	8.99876i		−	0.644415i
$196$	1.26342			0.0902440
$197$	−9.54060			−0.679739			−0.339870	−	0.940473i	$-0.610383\pi$
$197$	−9.54060			−0.679739			−0.339870	+	0.940473i	$0.610383\pi$
$198$		−	5.96476i		−	0.423897i
$199$	9.94737			0.705150			0.352575	−	0.935783i	$-0.385306\pi$
$199$	9.94737			0.705150			0.352575	+	0.935783i	$0.385306\pi$
$200$		−	1.41048i		−	0.0997363i
$201$	3.78903			0.267258
$202$		−	20.7463i		−	1.45970i
$203$	8.38250			0.588336
$204$	3.53718			0.247652
$205$	0.816735			0.0570432
$206$	13.5138			0.941551
$207$			0.736939i			0.0512208i
$208$	19.1929			1.33079
$209$	8.25374			0.570923
$210$		−	8.99876i		−	0.620974i
$211$			14.6931i			1.01151i	0.862676	+	0.505757i	$0.168787\pi$
$211$			14.6931i			1.01151i	−0.862676	+	0.505757i	$0.831213\pi$
$212$			5.72590i			0.393256i
$213$	9.38352			0.642948
$214$	−40.3789			−2.76024
$215$	17.6521			1.20387
$216$			0.565947i			0.0385078i
$217$		−	23.9978i		−	1.62908i
$218$		−	1.29672i		−	0.0878253i
$219$		−	1.99625i		−	0.134894i
$220$		−	10.3890i		−	0.700428i
$221$	−8.84002			−0.594644
$222$			11.7985i			0.791861i
$223$		−	11.9312i		−	0.798971i	−0.916740	−	0.399485i	$-0.869189\pi$
$223$		−	11.9312i		−	0.798971i	0.916740	−	0.399485i	$-0.130811\pi$
$224$	22.3042			1.49026
$225$	2.49225			0.166150
$226$			12.9132i			0.858972i
$227$		−	12.6274i		−	0.838113i	−0.907960	−	0.419056i	$-0.862361\pi$
$227$		−	12.6274i		−	0.838113i	0.907960	−	0.419056i	$-0.137639\pi$
$228$	−6.50440			−0.430765
$229$		−	4.13193i		−	0.273045i	−0.990637	−	0.136523i	$-0.956407\pi$
$229$		−	4.13193i		−	0.273045i	0.990637	−	0.136523i	$-0.0435927\pi$
$230$			2.41256i			0.159080i
$231$			7.93093i			0.521817i
$232$	−1.72589			−0.113310
$233$	14.7428			0.965830			0.482915	−	0.875667i	$-0.339578\pi$
$233$	14.7428			0.965830			0.482915	+	0.875667i	$0.339578\pi$
$234$		−	11.7475i		−	0.767959i
$235$		−	17.1046i		−	1.11578i
$236$		−	7.65097i		−	0.498036i
$237$		−	9.92553i		−	0.644732i
$238$	−8.84002			−0.573013
$239$	−8.16364			−0.528062			−0.264031	−	0.964514i	$-0.585052\pi$
$239$	−8.16364			−0.528062			−0.264031	+	0.964514i	$0.585052\pi$
$240$		−	5.34862i		−	0.345252i
$241$		−	10.9649i		−	0.706313i	−0.935564	−	0.353157i	$-0.885108\pi$
$241$		−	10.9649i		−	0.706313i	0.935564	−	0.353157i	$-0.114892\pi$
$242$		−	5.53037i		−	0.355506i
$243$	−1.00000			−0.0641500
$244$		−	9.32660i		−	0.597074i
$245$			0.879921i			0.0562161i
$246$	1.06621			0.0679793
$247$	16.2556			1.03432
$248$			4.94096i			0.313751i
$249$			4.11905i			0.261034i
$250$	24.5278			1.55128
$251$		−	18.6953i		−	1.18004i	−0.807390	−	0.590018i	$-0.799121\pi$
$251$		−	18.6953i		−	1.18004i	0.807390	−	0.590018i	$-0.200879\pi$
$252$		−	6.25001i		−	0.393714i
$253$		−	2.12628i		−	0.133678i
$254$			34.4131i			2.15927i
$255$			2.46351i			0.154271i
$256$	10.7671			0.672946
$257$	−16.9133			−1.05502			−0.527512	−	0.849547i	$-0.676875\pi$
$257$	−16.9133			−1.05502			−0.527512	+	0.849547i	$0.676875\pi$
$258$	23.0441			1.43467
$259$		−	15.6876i		−	0.974780i
$260$		−	20.4610i		−	1.26894i
$261$		−	3.04956i		−	0.188763i
$262$	−32.5901			−2.01342
$263$	−26.2030			−1.61575			−0.807873	−	0.589356i	$-0.799381\pi$
$263$	−26.2030			−1.61575			−0.807873	+	0.589356i	$0.799381\pi$
$264$		−	1.63292i		−	0.100499i
$265$	−3.98787			−0.244973
$266$	16.2556			0.996697
$267$	−8.34178			−0.510509
$268$	8.61536			0.526267
$269$			2.95174i			0.179971i	0.995943	+	0.0899853i	$0.0286820\pi$
$269$			2.95174i			0.179971i	−0.995943	+	0.0899853i	$0.971318\pi$
$270$	−3.27376			−0.199235
$271$		−	4.85434i		−	0.294880i	−0.989071	−	0.147440i	$-0.952897\pi$
$271$		−	4.85434i		−	0.294880i	0.989071	−	0.147440i	$-0.0471033\pi$
$272$	−5.25426			−0.318586
$273$			15.6199i			0.945357i
$274$	7.20600			0.435330
$275$	−7.19085			−0.433625
$276$			1.67562i			0.100861i
$277$	4.47274			0.268741			0.134370	−	0.990931i	$-0.457099\pi$
$277$	4.47274			0.268741			0.134370	+	0.990931i	$0.457099\pi$
$278$	45.4140			2.72375
$279$	−8.73042			−0.522677
$280$		−	2.46351i		−	0.147223i
$281$	−16.8881			−1.00746			−0.503730	−	0.863861i	$-0.668039\pi$
$281$	−16.8881			−1.00746			−0.503730	+	0.863861i	$0.668039\pi$
$282$		−	22.3294i		−	1.32969i
$283$	0.715293			0.0425198			0.0212599	−	0.999774i	$-0.493232\pi$
$283$	0.715293			0.0425198			0.0212599	+	0.999774i	$0.493232\pi$
$284$	21.3359			1.26605
$285$		−	4.53007i		−	0.268338i
$286$			33.8949i			2.00425i
$287$	−1.41767			−0.0836824
$288$		−	8.11430i		−	0.478139i
$289$	−14.5800			−0.857644
$290$		−	9.98354i		−	0.586254i
$291$		−	10.8972i		−	0.638805i
$292$		−	4.53900i		−	0.265625i
$293$		−	6.07815i		−	0.355089i	−0.984113	−	0.177545i	$-0.943185\pi$
$293$		−	6.07815i		−	0.355089i	0.984113	−	0.177545i	$-0.0568154\pi$
$294$			1.14870i			0.0669936i
$295$	5.32861			0.310244
$296$			3.22995i			0.187737i
$297$	2.88528			0.167421
$298$	−28.1492			−1.63064
$299$		−	4.18767i		−	0.242179i
$300$	5.66679			0.327172
$301$	−30.6402			−1.76607
$302$	−38.3338			−2.20586
$303$	10.0354			0.576519
$304$	9.66190			0.554148
$305$	6.49562			0.371938
$306$			3.21601i			0.183847i
$307$			7.29106i			0.416123i	0.978116	+	0.208062i	$0.0667154\pi$
$307$			7.29106i			0.416123i	−0.978116	+	0.208062i	$0.933285\pi$
$308$			18.0330i			1.02753i
$309$			6.53691i			0.371872i
$310$	−28.5813			−1.62331
$311$	−3.44914			−0.195583			−0.0977913	−	0.995207i	$-0.531178\pi$
$311$	−3.44914			−0.195583			−0.0977913	+	0.995207i	$0.531178\pi$
$312$		−	3.21601i		−	0.182071i
$313$	8.41636			0.475721			0.237861	−	0.971299i	$-0.423554\pi$
$313$	8.41636			0.475721			0.237861	+	0.971299i	$0.423554\pi$
$314$	22.7267	+	12.4290i	1.28254	+	0.701407i
$315$	4.35289			0.245258
$316$		−	22.5683i		−	1.26956i
$317$	9.26725			0.520501			0.260250	−	0.965541i	$-0.416195\pi$
$317$	9.26725			0.520501			0.260250	+	0.965541i	$0.416195\pi$
$318$	−5.20600			−0.291938
$319$			8.79885i			0.492641i
$320$		−	15.8670i		−	0.886994i
$321$		−	19.5321i		−	1.09018i
$322$		−	4.18767i		−	0.233370i
$323$	−4.45015			−0.247613
$324$	−2.27376			−0.126320
$325$	−14.1623			−0.785582
$326$	−40.3833			−2.23663
$327$	0.627253			0.0346872
$328$	0.291887			0.0161168
$329$			29.6898i			1.63685i
$330$	9.44572			0.519970
$331$	−11.4938			−0.631756			−0.315878	−	0.948800i	$-0.602299\pi$
$331$	−11.4938			−0.631756			−0.315878	+	0.948800i	$0.602299\pi$
$332$			9.36574i			0.514012i
$333$	−5.70716			−0.312751
$334$			46.3366i			2.53542i
$335$			6.00026i			0.327829i
$336$			9.28401i			0.506484i
$337$		−	26.4519i		−	1.44093i	−0.693493	−	0.720463i	$-0.743929\pi$
$337$		−	26.4519i		−	1.44093i	0.693493	−	0.720463i	$-0.256071\pi$
$338$			39.8805i			2.16921i
$339$	−6.24638			−0.339257
$340$			5.60143i			0.303780i
$341$	25.1897			1.36410
$342$		−	5.91382i		−	0.319783i
$343$			17.7139i			0.956463i
$344$	6.30858			0.340136
$345$	−1.16701			−0.0628295
$346$		−	10.6731i		−	0.573789i
$347$	24.0428			1.29068			0.645342	−	0.763894i	$-0.276715\pi$
$347$	24.0428			1.29068			0.645342	+	0.763894i	$0.276715\pi$
$348$		−	6.93398i		−	0.371700i
$349$	−30.7542			−1.64623			−0.823117	−	0.567872i	$-0.807767\pi$
$349$	−30.7542			−1.64623			−0.823117	+	0.567872i	$0.807767\pi$
$350$	−14.1623			−0.757006
$351$	5.68252			0.303311
$352$			23.4120i			1.24786i
$353$	−10.4194			−0.554571			−0.277286	−	0.960788i	$-0.589435\pi$
$353$	−10.4194			−0.554571			−0.277286	+	0.960788i	$0.589435\pi$
$354$	6.95628			0.369722
$355$			14.8596i			0.788666i
$356$	−18.9672			−1.00526
$357$		−	4.27610i		−	0.226315i
$358$	−15.1604			−0.801253
$359$		−	1.89536i		−	0.100033i	−0.998748	−	0.0500167i	$-0.984073\pi$
$359$		−	1.89536i		−	0.100033i	0.998748	−	0.0500167i	$-0.0159275\pi$
$360$	−0.896227			−0.0472353
$361$	−10.8168			−0.569303
$362$	−12.3616			−0.649712
$363$	2.67516			0.140409
$364$			35.5158i			1.86153i
$365$	3.16124			0.165467
$366$	8.47976			0.443244
$367$			14.7514i			0.770018i	0.922913	+	0.385009i	$0.125802\pi$
$367$			14.7514i			0.770018i	−0.922913	+	0.385009i	$0.874198\pi$
$368$		−	2.48904i		−	0.129750i
$369$			0.515750i			0.0268489i
$370$	−18.6839			−0.971329
$371$	6.92205			0.359375
$372$	−19.8509			−1.02922
$373$			27.3596i			1.41663i	0.705898	+	0.708314i	$0.250544\pi$
$373$			27.3596i			1.41663i	−0.705898	+	0.708314i	$0.749456\pi$
$374$		−	9.27908i		−	0.479810i
$375$			11.8646i			0.612687i
$376$		−	6.11290i		−	0.315249i
$377$			17.3292i			0.892500i
$378$	5.68252			0.292277
$379$		−	17.2450i		−	0.885818i	−0.896567	−	0.442909i	$-0.853947\pi$
$379$		−	17.2450i		−	0.885818i	0.896567	−	0.442909i	$-0.146053\pi$
$380$		−	10.3003i		−	0.528394i
$381$	−16.6463			−0.852817
$382$	46.2779			2.36779
$383$		−	24.7727i		−	1.26583i	−0.774223	−	0.632913i	$-0.781859\pi$
$383$		−	24.7727i		−	1.26583i	0.774223	−	0.632913i	$-0.218141\pi$
$384$		−	4.48516i		−	0.228883i
$385$	−12.5593			−0.640082
$386$		−	35.3338i		−	1.79844i
$387$			11.1469i			0.566631i
$388$		−	24.7776i		−	1.25789i
$389$	21.6648			1.09845			0.549225	−	0.835675i	$-0.314923\pi$
$389$	21.6648			1.09845			0.549225	+	0.835675i	$0.314923\pi$
$390$	18.6032			0.942010
$391$			1.14642i			0.0579769i
$392$			0.314469i			0.0158831i
$393$		−	15.7645i		−	0.795215i
$394$		−	19.7233i		−	0.993648i
$395$	15.7179			0.790855
$396$	6.56044			0.329674
$397$		−	14.8563i		−	0.745616i	−0.927908	−	0.372808i	$-0.878395\pi$
$397$		−	14.8563i		−	0.745616i	0.927908	−	0.372808i	$-0.121605\pi$
$398$			20.5643i			1.03079i
$399$			7.86319i			0.393652i
$400$	−8.41767			−0.420884
$401$			0.305443i			0.0152531i	0.999971	+	0.00762654i	$0.00242763\pi$
$401$			0.305443i			0.0152531i	−0.999971	+	0.00762654i	$0.997572\pi$
$402$			7.83310i			0.390680i
$403$	49.6108			2.47129
$404$	22.8181			1.13524
$405$		−	1.58359i		−	0.0786891i
$406$			17.3292i			0.860034i
$407$	16.4668			0.816227
$408$			0.880416i			0.0435871i
$409$		−	21.2709i		−	1.05178i	−0.850553	−	0.525890i	$-0.823732\pi$
$409$		−	21.2709i		−	1.05178i	0.850553	−	0.525890i	$-0.176268\pi$
$410$			1.68844i			0.0833862i
$411$			3.48569i			0.171937i
$412$			14.8634i			0.732266i
$413$	−9.24928			−0.455127
$414$	−1.52348			−0.0748749
$415$	−6.52288			−0.320195
$416$			46.1097i			2.26071i
$417$			21.9677i			1.07576i
$418$			17.0630i			0.834580i
$419$	−17.4972			−0.854795			−0.427398	−	0.904064i	$-0.640570\pi$
$419$	−17.4972			−0.854795			−0.427398	+	0.904064i	$0.640570\pi$
$420$	9.89743			0.482945
$421$		−	34.4588i		−	1.67942i	−0.543035	−	0.839710i	$-0.682725\pi$
$421$		−	34.4588i		−	1.67942i	0.543035	−	0.839710i	$-0.317275\pi$
$422$	−30.3751			−1.47864
$423$	10.8012			0.525172
$424$	−1.42520			−0.0692137
$425$	3.87707			0.188066
$426$			19.3986i			0.939866i
$427$	−11.2749			−0.545633
$428$		−	44.4114i		−	2.14670i
$429$	−16.3957			−0.791590
$430$			36.4924i			1.75982i
$431$	−32.6941			−1.57482			−0.787409	−	0.616431i	$-0.788578\pi$
$431$	−32.6941			−1.57482			−0.787409	+	0.616431i	$0.788578\pi$
$432$	3.37753			0.162502
$433$			4.56909i			0.219577i	0.993955	+	0.109788i	$0.0350173\pi$
$433$			4.56909i			0.219577i	−0.993955	+	0.109788i	$0.964983\pi$
$434$	49.6108			2.38140
$435$	4.82925			0.231545
$436$	1.42622			0.0683037
$437$		−	2.10812i		−	0.100845i
$438$	4.12687			0.197189
$439$			7.67246i			0.366187i	0.983096	+	0.183093i	$0.0586110\pi$
$439$			7.67246i			0.366187i	−0.983096	+	0.183093i	$0.941389\pi$
$440$	2.58587			0.123276
$441$	−0.555650			−0.0264595
$442$		−	18.2750i		−	0.869255i
$443$			9.44512i			0.448751i	0.974503	+	0.224376i	$0.0720343\pi$
$443$			9.44512i			0.448751i	−0.974503	+	0.224376i	$0.927966\pi$
$444$	−12.9767			−0.615848
$445$		−	13.2099i		−	0.626211i
$446$	24.6654			1.16794
$447$		−	13.6164i		−	0.644031i
$448$			27.5416i			1.30122i
$449$			24.3503i			1.14916i	0.818448	+	0.574580i	$0.194835\pi$
$449$			24.3503i			1.14916i	−0.818448	+	0.574580i	$0.805165\pi$
$450$			5.15225i			0.242880i
$451$		−	1.48808i		−	0.0700711i
$452$	−14.2028			−0.668042
$453$		−	18.5429i		−	0.871220i
$454$	26.1048			1.22516
$455$	−24.7354			−1.15961
$456$		−	1.61897i		−	0.0758152i
$457$	−3.03832			−0.142126			−0.0710632	−	0.997472i	$-0.522639\pi$
$457$	−3.03832			−0.142126			−0.0710632	+	0.997472i	$0.522639\pi$
$458$	8.54196			0.399140
$459$	−1.55565			−0.0726115
$460$	−2.65349			−0.123720
$461$	16.8881			0.786557			0.393279	−	0.919419i	$-0.371341\pi$
$461$	16.8881			0.786557			0.393279	+	0.919419i	$0.371341\pi$
$462$	−16.3957			−0.762795
$463$		−	0.948155i		−	0.0440645i	−0.999757	−	0.0220322i	$-0.992986\pi$
$463$		−	0.948155i		−	0.0440645i	0.999757	−	0.0220322i	$-0.00701365\pi$
$464$			10.3000i			0.478166i
$465$		−	13.8254i		−	0.641137i
$466$			30.4778i			1.41186i
$467$	0.268796			0.0124384			0.00621919	−	0.999981i	$-0.498020\pi$
$467$	0.268796			0.0124384			0.00621919	+	0.999981i	$0.498020\pi$
$468$	12.9207			0.597259
$469$		−	10.4151i		−	0.480926i
$470$	35.3605			1.63106
$471$	−6.01215	+	10.9934i	−0.277025	+	0.506547i
$472$	1.90436			0.0876551
$473$		−	32.1620i		−	1.47881i
$474$	20.5191			0.942474
$475$	−7.12943			−0.327121
$476$		−	9.72283i		−	0.445645i
$477$		−	2.51825i		−	0.115303i
$478$		−	16.8768i		−	0.771925i
$479$			20.9459i			0.957043i	0.878076	+	0.478522i	$0.158827\pi$
$479$			20.9459i			0.957043i	−0.878076	+	0.478522i	$0.841173\pi$
$480$	12.8497			0.586505
$481$	32.4311			1.47873
$482$	22.6679			1.03249
$483$	2.02566			0.0921709
$484$	6.08267			0.276485
$485$	17.2566			0.783584
$486$		−	2.06731i		−	0.0937750i
$487$	−32.0033			−1.45021			−0.725105	−	0.688638i	$-0.758209\pi$
$487$	−32.0033			−1.45021			−0.725105	+	0.688638i	$0.758209\pi$
$488$	2.32142			0.105086
$489$		−	19.5343i		−	0.883370i
$490$	−1.81907			−0.0821770
$491$		−	18.1911i		−	0.820953i	−0.911871	−	0.410477i	$-0.865362\pi$
$491$		−	18.1911i		−	0.820953i	0.911871	−	0.410477i	$-0.134638\pi$
$492$			1.17269i			0.0528691i
$493$		−	4.74405i		−	0.213661i
$494$			33.6054i			1.51198i
$495$			4.56909i			0.205365i
$496$	29.4873			1.32402
$497$		−	25.7930i		−	1.15697i
$498$	−8.51535			−0.381582
$499$			36.2267i			1.62173i	0.585233	+	0.810865i	$0.301003\pi$
$499$			36.2267i			1.62173i	−0.585233	+	0.810865i	$0.698997\pi$
$500$			26.9773i			1.20646i
$501$	−22.4140			−1.00138
$502$	38.6489			1.72498
$503$		−	36.7734i		−	1.63964i	−0.572619	−	0.819822i	$-0.694072\pi$
$503$		−	36.7734i		−	1.63964i	0.572619	−	0.819822i	$-0.305928\pi$
$504$	1.55565			0.0692942
$505$			15.8919i			0.707182i
$506$	4.39567			0.195411
$507$	−19.2910			−0.856745
$508$	−37.8498			−1.67931
$509$			34.8199i			1.54337i	0.636007	+	0.771683i	$0.280585\pi$
$509$			34.8199i			1.54337i	−0.636007	+	0.771683i	$0.719415\pi$
$510$	−5.09283			−0.225514
$511$	−5.48721			−0.242740
$512$			31.2293i			1.38015i
$513$	2.86064			0.126300
$514$		−	34.9651i		−	1.54224i
$515$	−10.3518			−0.456153
$516$			25.3455i			1.11577i
$517$	−31.1644			−1.37061
$518$	32.4311			1.42494
$519$	5.16280			0.226622
$520$	5.09283			0.223335
$521$			8.54604i			0.374409i	0.982321	+	0.187204i	$0.0599427\pi$
$521$			8.54604i			0.374409i	−0.982321	+	0.187204i	$0.940057\pi$
$522$	6.30439			0.275935
$523$	−14.5635			−0.636818			−0.318409	−	0.947953i	$-0.603149\pi$
$523$	−14.5635			−0.636818			−0.318409	+	0.947953i	$0.603149\pi$
$524$		−	35.8448i		−	1.56589i
$525$		−	6.85059i		−	0.298984i
$526$		−	54.1697i		−	2.36191i
$527$	−13.5815			−0.591619
$528$	−9.74513			−0.424102
$529$	22.4569			0.976388
$530$		−	8.24415i		−	0.358103i
$531$			3.36490i			0.146024i
$532$			17.8790i			0.775153i
$533$		−	2.93076i		−	0.126945i
$534$		−	17.2450i		−	0.746265i
$535$	30.9308			1.33726
$536$			2.14439i			0.0926237i
$537$		−	7.33341i		−	0.316460i
$538$	−6.10215			−0.263082
$539$	1.60321			0.0690550
$540$		−	3.60070i		−	0.154949i
$541$			26.6405i			1.14537i	0.819777	+	0.572683i	$0.194097\pi$
$541$			26.6405i			1.14537i	−0.819777	+	0.572683i	$0.805903\pi$
$542$	10.0354			0.431058
$543$		−	5.97957i		−	0.256608i
$544$		−	12.6230i		−	0.541207i
$545$			0.993309i			0.0425487i
$546$	−32.2910			−1.38193
$547$	6.37633			0.272632			0.136316	−	0.990665i	$-0.456474\pi$
$547$	6.37633			0.272632			0.136316	+	0.990665i	$0.456474\pi$
$548$			7.92563i			0.338566i
$549$			4.10184i			0.175062i
$550$		−	14.8657i		−	0.633876i
$551$			8.72369i			0.371642i
$552$	−0.417069			−0.0177516
$553$	−27.2828			−1.16018
$554$			9.24653i			0.392847i
$555$		−	9.03779i		−	0.383633i
$556$			49.9493i			2.11832i
$557$	−15.4953			−0.656558			−0.328279	−	0.944581i	$-0.606469\pi$
$557$	−15.4953			−0.656558			−0.328279	+	0.944581i	$0.606469\pi$
$558$		−	18.0485i		−	0.764053i
$559$		−	63.3427i		−	2.67911i
$560$	−14.7020			−0.621274
$561$	4.48849			0.189504
$562$		−	34.9129i		−	1.47271i
$563$			41.5307i			1.75031i	0.483842	+	0.875156i	$0.339241\pi$
$563$			41.5307i			1.75031i	−0.483842	+	0.875156i	$0.660759\pi$
$564$	24.5593			1.03413
$565$		−	9.89168i		−	0.416146i
$566$			1.47873i			0.0621557i
$567$			2.74875i			0.115437i
$568$			5.31058i			0.222827i
$569$			31.9987i			1.34146i	0.741703	+	0.670729i	$0.234018\pi$
$569$			31.9987i			1.34146i	−0.741703	+	0.670729i	$0.765982\pi$
$570$	9.36504			0.392258
$571$	45.2019			1.89164			0.945820	−	0.324692i	$-0.105261\pi$
$571$	45.2019			1.89164			0.945820	+	0.324692i	$0.105261\pi$
$572$	−37.2798			−1.55875
$573$			22.3856i			0.935172i
$574$		−	2.93076i		−	0.122328i
$575$			1.83664i			0.0765931i
$576$	10.0197			0.417487
$577$	1.49464			0.0622225			0.0311113	−	0.999516i	$-0.490095\pi$
$577$	1.49464			0.0622225			0.0311113	+	0.999516i	$0.490095\pi$
$578$		−	30.1412i		−	1.25371i
$579$	17.0917			0.710307
$580$	10.9806			0.455943
$581$	11.3223			0.469727
$582$	22.5278			0.933809
$583$			7.26586i			0.300921i
$584$	1.12977			0.0467504
$585$			8.99876i			0.372053i
$586$	12.5654			0.519072
$587$			41.2826i			1.70391i	0.523611	+	0.851957i	$0.324584\pi$
$587$			41.2826i			1.70391i	−0.523611	+	0.851957i	$0.675416\pi$
$588$	−1.26342			−0.0521024
$589$	24.9746			1.02906
$590$			11.0159i			0.453516i
$591$	9.54060			0.392448
$592$	19.2761			0.792244
$593$	19.1456			0.786215			0.393107	−	0.919493i	$-0.371400\pi$
$593$	19.1456			0.786215			0.393107	+	0.919493i	$0.371400\pi$
$594$			5.96476i			0.244737i
$595$	6.77158			0.277608
$596$		−	30.9603i		−	1.26818i
$597$	−9.94737			−0.407119
$598$	8.65720			0.354019
$599$		−	27.3573i		−	1.11779i	−0.829239	−	0.558894i	$-0.811226\pi$
$599$		−	27.3573i		−	1.11779i	0.829239	−	0.558894i	$-0.188774\pi$
$600$			1.41048i			0.0575828i
$601$	20.4015			0.832195			0.416097	−	0.909320i	$-0.363398\pi$
$601$	20.4015			0.832195			0.416097	+	0.909320i	$0.363398\pi$
$602$		−	63.3427i		−	2.58166i
$603$	−3.78903			−0.154301
$604$		−	42.1620i		−	1.71555i
$605$			4.23634i			0.172232i
$606$			20.7463i			0.842760i
$607$			33.2973i			1.35150i	0.737133	+	0.675748i	$0.236179\pi$
$607$			33.2973i			1.35150i	−0.737133	+	0.675748i	$0.763821\pi$
$608$			23.2121i			0.941373i
$609$	−8.38250			−0.339676
$610$			13.4284i			0.543701i
$611$	−61.3780			−2.48309
$612$	−3.53718			−0.142982
$613$		−	25.7514i		−	1.04009i	−0.854139	−	0.520044i	$-0.825915\pi$
$613$		−	25.7514i		−	1.04009i	0.854139	−	0.520044i	$-0.174085\pi$
$614$	−15.0729			−0.608292
$615$	−0.816735			−0.0329339
$616$	−4.48849			−0.180846
$617$	1.15126			0.0463479			0.0231739	−	0.999731i	$-0.492623\pi$
$617$	1.15126			0.0463479			0.0231739	+	0.999731i	$0.492623\pi$
$618$	−13.5138			−0.543605
$619$	−17.2275			−0.692430			−0.346215	−	0.938155i	$-0.612533\pi$
$619$	−17.2275			−0.692430			−0.346215	+	0.938155i	$0.612533\pi$
$620$		−	31.4356i		−	1.26248i
$621$		−	0.736939i		−	0.0295723i
$622$		−	7.13043i		−	0.285904i
$623$			22.9295i			0.918651i
$624$	−19.1929			−0.768331
$625$	−6.32741			−0.253096
$626$			17.3992i			0.695412i
$627$	−8.25374			−0.329623
$628$	−13.6702	+	24.9963i	−0.545500	+	0.997460i
$629$	−8.87835			−0.354003
$630$			8.99876i			0.358519i
$631$	5.08245			0.202329			0.101165	−	0.994870i	$-0.467743\pi$
$631$	5.08245			0.202329			0.101165	+	0.994870i	$0.467743\pi$
$632$	5.61733			0.223445
$633$		−	14.6931i		−	0.583998i
$634$			19.1583i			0.760872i
$635$		−	26.3609i		−	1.04610i
$636$		−	5.72590i		−	0.227047i
$637$	3.15749			0.125104
$638$	−18.1899			−0.720146
$639$	−9.38352			−0.371206
$640$	7.10265			0.280757
$641$	−27.2774			−1.07739			−0.538695	−	0.842501i	$-0.681083\pi$
$641$	−27.2774			−1.07739			−0.538695	+	0.842501i	$0.681083\pi$
$642$	40.3789			1.59363
$643$			33.5284i			1.32223i	0.750283	+	0.661116i	$0.229917\pi$
$643$			33.5284i			1.32223i	−0.750283	+	0.661116i	$0.770083\pi$
$644$	4.60588			0.181497
$645$	−17.6521			−0.695052
$646$		−	9.19983i		−	0.361963i
$647$	6.83163			0.268579			0.134290	−	0.990942i	$-0.457125\pi$
$647$	6.83163			0.268579			0.134290	+	0.990942i	$0.457125\pi$
$648$		−	0.565947i		−	0.0222325i
$649$		−	9.70868i		−	0.381099i
$650$		−	29.2778i		−	1.14837i
$651$			23.9978i			0.940548i
$652$		−	44.4163i		−	1.73947i
$653$	6.97279			0.272867			0.136433	−	0.990649i	$-0.456436\pi$
$653$	6.97279			0.272867			0.136433	+	0.990649i	$0.456436\pi$
$654$			1.29672i			0.0507059i
$655$	24.9645			0.975443
$656$		−	1.74196i		−	0.0680122i
$657$			1.99625i			0.0778813i
$658$	−61.3780			−2.39276
$659$	−36.8186			−1.43425			−0.717125	−	0.696944i	$-0.754543\pi$
$659$	−36.8186			−1.43425			−0.717125	+	0.696944i	$0.754543\pi$
$660$			10.3890i			0.404392i
$661$	18.4970			0.719451			0.359726	−	0.933058i	$-0.382870\pi$
$661$	18.4970			0.719451			0.359726	+	0.933058i	$0.382870\pi$
$662$		−	23.7612i		−	0.923506i
$663$	8.84002			0.343318
$664$	−2.33117			−0.0904668
$665$	−12.4520			−0.482869
$666$		−	11.7985i		−	0.457181i
$667$	2.24734			0.0870174
$668$	−50.9640			−1.97186
$669$			11.9312i			0.461286i
$670$	−12.4044			−0.479223
$671$		−	11.8350i		−	0.456883i
$672$	−22.3042			−0.860403
$673$			3.81969i			0.147238i	0.997286	+	0.0736191i	$0.0234549\pi$
$673$			3.81969i			0.147238i	−0.997286	+	0.0736191i	$0.976545\pi$
$674$	54.6842			2.10636
$675$	−2.49225			−0.0959269
$676$	−43.8632			−1.68705
$677$	17.0272			0.654409			0.327204	−	0.944954i	$-0.393893\pi$
$677$	17.0272			0.654409			0.327204	+	0.944954i	$0.393893\pi$
$678$		−	12.9132i		−	0.495928i
$679$	−29.9537			−1.14952
$680$	−1.39422			−0.0534657
$681$			12.6274i			0.483884i
$682$			52.0749i			1.99405i
$683$		−	22.5696i		−	0.863603i	−0.901969	−	0.431802i	$-0.857878\pi$
$683$		−	22.5696i		−	0.863603i	0.901969	−	0.431802i	$-0.142122\pi$
$684$	6.50440			0.248702
$685$	−5.51990			−0.210904
$686$	−36.6201			−1.39816
$687$			4.13193i			0.157643i
$688$		−	37.6492i		−	1.43536i
$689$			14.3100i			0.545168i
$690$		−	2.41256i		−	0.0918447i
$691$			4.19686i			0.159656i	0.996809	+	0.0798281i	$0.0254371\pi$
$691$			4.19686i			0.159656i	−0.996809	+	0.0798281i	$0.974563\pi$
$692$	11.7390			0.446249
$693$		−	7.93093i		−	0.301271i
$694$			49.7038i			1.88673i
$695$	−34.7877			−1.31957
$696$	1.72589			0.0654198
$697$			0.802327i			0.0303903i
$698$		−	63.5784i		−	2.40648i
$699$	−14.7428			−0.557622
$700$		−	15.5766i		−	0.588740i
$701$		−	30.7837i		−	1.16268i	−0.813660	−	0.581342i	$-0.802528\pi$
$701$		−	30.7837i		−	1.16268i	0.813660	−	0.581342i	$-0.197472\pi$
$702$			11.7475i			0.443381i
$703$	16.3261			0.615751
$704$	−28.9096			−1.08957
$705$			17.1046i			0.644197i
$706$		−	21.5402i		−	0.810676i
$707$		−	27.5849i		−	1.03744i
$708$			7.65097i			0.287541i
$709$	−23.4927			−0.882286			−0.441143	−	0.897437i	$-0.645427\pi$
$709$	−23.4927			−0.882286			−0.441143	+	0.897437i	$0.645427\pi$
$710$	−30.7194			−1.15288
$711$			9.92553i			0.372236i
$712$		−	4.72101i		−	0.176927i
$713$		−	6.43379i		−	0.240947i
$714$	8.84002			0.330829
$715$		−	25.9640i		−	0.970997i
$716$		−	16.6744i		−	0.623152i
$717$	8.16364			0.304877
$718$	3.91830			0.146230
$719$		−	10.2312i		−	0.381559i	−0.981633	−	0.190779i	$-0.938899\pi$
$719$		−	10.2312i		−	0.381559i	0.981633	−	0.190779i	$-0.0611015\pi$
$720$			5.34862i			0.199331i
$721$	17.9684			0.669177
$722$		−	22.3616i		−	0.832211i
$723$			10.9649i			0.407790i
$724$		−	13.5961i		−	0.505296i
$725$		−	7.60028i		−	0.282267i
$726$			5.53037i			0.205251i
$727$	−50.8351			−1.88537			−0.942684	−	0.333687i	$-0.891707\pi$
$727$	−50.8351			−1.88537			−0.942684	+	0.333687i	$0.891707\pi$
$728$	−8.84002			−0.327633
$729$	1.00000			0.0370370
$730$			6.53526i			0.241881i
$731$			17.3407i			0.641370i
$732$			9.32660i			0.344721i
$733$	13.7550			0.508053			0.254026	−	0.967197i	$-0.418245\pi$
$733$	13.7550			0.508053			0.254026	+	0.967197i	$0.418245\pi$
$734$	−30.4957			−1.12562
$735$		−	0.879921i		−	0.0324564i
$736$	5.97974			0.220416
$737$	10.9324			0.402701
$738$	−1.06621			−0.0392479
$739$	52.9235			1.94682			0.973411	−	0.229065i	$-0.0735668\pi$
$739$	52.9235			1.94682			0.973411	+	0.229065i	$0.0735668\pi$
$740$		−	20.5498i		−	0.755424i
$741$	−16.2556			−0.597165
$742$			14.3100i			0.525337i
$743$	−7.30721			−0.268076			−0.134038	−	0.990976i	$-0.542794\pi$
$743$	−7.30721			−0.268076			−0.134038	+	0.990976i	$0.542794\pi$
$744$		−	4.94096i		−	0.181144i
$745$	21.5627			0.789995
$746$	−56.5608			−2.07084
$747$		−	4.11905i		−	0.150708i
$748$	10.2057			0.373159
$749$	−53.6890			−1.96175
$750$	−24.5278			−0.895630
$751$			44.6865i			1.63063i	0.579015	+	0.815317i	$0.303437\pi$
$751$			44.6865i			1.63063i	−0.579015	+	0.815317i	$0.696563\pi$
$752$	−36.4814			−1.33034
$753$			18.6953i			0.681294i
$754$	−35.8248			−1.30466
$755$	29.3642			1.06867
$756$			6.25001i			0.227311i
$757$			7.13800i			0.259435i	0.991551	+	0.129717i	$0.0414070\pi$
$757$			7.13800i			0.259435i	−0.991551	+	0.129717i	$0.958593\pi$
$758$	35.6508			1.29489
$759$			2.12628i			0.0771789i
$760$	2.56378			0.0929981
$761$		−	16.6218i		−	0.602540i	−0.953539	−	0.301270i	$-0.902590\pi$
$761$		−	16.6218i		−	0.602540i	0.953539	−	0.301270i	$-0.0974105\pi$
$762$		−	34.4131i		−	1.24665i
$763$		−	1.72416i		−	0.0624189i
$764$			50.8995i			1.84148i
$765$		−	2.46351i		−	0.0890683i
$766$	51.2128			1.85039
$767$		−	19.1211i		−	0.690423i
$768$	−10.7671			−0.388526
$769$	29.1062			1.04960			0.524798	−	0.851227i	$-0.324141\pi$
$769$	29.1062			1.04960			0.524798	+	0.851227i	$0.324141\pi$
$770$		−	25.9640i		−	0.935676i
$771$	16.9133			0.609119
$772$	38.8624			1.39869
$773$	−28.5485			−1.02682			−0.513410	−	0.858144i	$-0.671618\pi$
$773$	−28.5485			−1.02682			−0.513410	+	0.858144i	$0.671618\pi$
$774$	−23.0441			−0.828305
$775$	−21.7584			−0.781586
$776$	6.16724			0.221391
$777$			15.6876i			0.562789i
$778$			44.7878i			1.60572i
$779$		−	1.47537i		−	0.0528608i
$780$			20.4610i			0.732623i
$781$	27.0741			0.968786
$782$	−2.37000			−0.0847511
$783$			3.04956i			0.108982i
$784$	1.87673			0.0670260
$785$	−17.4089	−	9.52076i	−0.621352	−	0.339811i
$786$	32.5901			1.16245
$787$		−	32.1048i		−	1.14441i	−0.820109	−	0.572207i	$-0.806087\pi$
$787$		−	32.1048i		−	1.14441i	0.820109	−	0.572207i	$-0.193913\pi$
$788$	21.6930			0.772782
$789$	26.2030			0.932852
$790$			32.4938i			1.15608i
$791$			17.1698i			0.610486i
$792$			1.63292i			0.0580232i
$793$		−	23.3088i		−	0.827719i
$794$	30.7125			1.08995
$795$	3.98787			0.141435
$796$	−22.6179			−0.801672
$797$	49.5857			1.75641			0.878207	−	0.478280i	$-0.158740\pi$
$797$	49.5857			1.75641			0.878207	+	0.478280i	$0.158740\pi$
$798$	−16.2556			−0.575443
$799$	16.8029			0.594443
$800$		−	20.2229i		−	0.714987i
$801$	8.34178			0.294742
$802$	−0.631444			−0.0222971
$803$		−	5.75975i		−	0.203257i
$804$	−8.61536			−0.303840
$805$			3.20781i			0.113061i
$806$			102.561i			3.61255i
$807$		−	2.95174i		−	0.103906i
$808$			5.67951i			0.199805i
$809$			34.3950i			1.20927i	0.796505	+	0.604633i	$0.206680\pi$
$809$			34.3950i			1.20927i	−0.796505	+	0.604633i	$0.793320\pi$
$810$	3.27376			0.115028
$811$		−	32.0806i		−	1.12650i	−0.826285	−	0.563252i	$-0.809550\pi$
$811$		−	32.0806i		−	1.12650i	0.826285	−	0.563252i	$-0.190450\pi$
$812$	−19.0598			−0.668868
$813$			4.85434i			0.170249i
$814$			34.0419i			1.19317i
$815$	30.9342			1.08358
$816$	5.25426			0.183936
$817$		−	31.8873i		−	1.11560i
$818$	43.9736			1.53750
$819$		−	15.6199i		−	0.545802i
$820$	−1.85706			−0.0648513
$821$	46.3145			1.61639			0.808194	−	0.588916i	$-0.200445\pi$
$821$	46.3145			1.61639			0.808194	+	0.588916i	$0.200445\pi$
$822$	−7.20600			−0.251338
$823$			40.7911i			1.42189i	0.703249	+	0.710943i	$0.251732\pi$
$823$			40.7911i			1.42189i	−0.703249	+	0.710943i	$0.748268\pi$
$824$	−3.69955			−0.128880
$825$	7.19085			0.250353
$826$		−	19.1211i		−	0.665308i
$827$	−21.4882			−0.747217			−0.373608	−	0.927587i	$-0.621880\pi$
$827$	−21.4882			−0.747217			−0.373608	+	0.927587i	$0.621880\pi$
$828$		−	1.67562i		−	0.0582319i
$829$	−14.6556			−0.509009			−0.254505	−	0.967072i	$-0.581912\pi$
$829$	−14.6556			−0.509009			−0.254505	+	0.967072i	$0.581912\pi$
$830$		−	13.4848i		−	0.468064i
$831$	−4.47274			−0.155158
$832$	−56.9370			−1.97394
$833$	−0.864398			−0.0299496
$834$	−45.4140			−1.57256
$835$		−	35.4945i		−	1.22834i
$836$	−18.7670			−0.649071
$837$	8.73042			0.301768
$838$		−	36.1721i		−	1.24955i
$839$		−	2.67414i		−	0.0923216i	−0.998934	−	0.0461608i	$-0.985301\pi$
$839$		−	2.67414i		−	0.0923216i	0.998934	−	0.0461608i	$-0.0146987\pi$
$840$			2.46351i			0.0849991i
$841$	19.7002			0.679316
$842$	71.2370			2.45499
$843$	16.8881			0.581657
$844$		−	33.4086i		−	1.14997i
$845$		−	30.5490i		−	1.05092i
$846$			22.3294i			0.767700i
$847$		−	7.35335i		−	0.252664i
$848$			8.50548i			0.292079i
$849$	−0.715293			−0.0245488
$850$			8.01511i			0.274916i
$851$		−	4.20583i		−	0.144174i
$852$	−21.3359			−0.730955
$853$	39.9778			1.36881			0.684406	−	0.729101i	$-0.260061\pi$
$853$	39.9778			1.36881			0.684406	+	0.729101i	$0.260061\pi$
$854$		−	23.3088i		−	0.797610i
$855$			4.53007i			0.154925i
$856$	11.0542			0.377823
$857$		−	33.0993i		−	1.13065i	−0.824867	−	0.565326i	$-0.808750\pi$
$857$		−	33.0993i		−	1.13065i	0.824867	−	0.565326i	$-0.191250\pi$
$858$		−	33.8949i		−	1.15715i
$859$		−	15.7964i		−	0.538967i	−0.963005	−	0.269484i	$-0.913147\pi$
$859$		−	15.7964i		−	0.538967i	0.963005	−	0.269484i	$-0.0868530\pi$
$860$	−40.1367			−1.36865
$861$	1.41767			0.0483141
$862$		−	67.5887i		−	2.30208i
$863$		−	50.1962i		−	1.70870i	−0.519698	−	0.854350i	$-0.673956\pi$
$863$		−	50.1962i		−	1.70870i	0.519698	−	0.854350i	$-0.326044\pi$
$864$			8.11430i			0.276054i
$865$			8.17575i			0.277984i
$866$	−9.44572			−0.320979
$867$	14.5800			0.495161
$868$			54.5652i			1.85206i
$869$		−	28.6379i		−	0.971475i
$870$			9.98354i			0.338474i
$871$	21.5313			0.729559
$872$			0.354992i			0.0120215i
$873$			10.8972i			0.368814i
$874$	4.35812			0.147416
$875$	32.6130			1.10252
$876$			4.53900i			0.153359i
$877$			37.9833i			1.28260i	0.767288	+	0.641302i	$0.221605\pi$
$877$			37.9833i			1.28260i	−0.767288	+	0.641302i	$0.778395\pi$
$878$	−15.8613			−0.535294
$879$			6.07815i			0.205011i
$880$		−	15.4323i		−	0.520221i
$881$			52.3940i			1.76520i	0.470125	+	0.882600i	$0.344209\pi$
$881$			52.3940i			1.76520i	−0.470125	+	0.882600i	$0.655791\pi$
$882$		−	1.14870i		−	0.0386787i
$883$		−	13.1902i		−	0.443887i	−0.975060	−	0.221943i	$-0.928760\pi$
$883$		−	13.1902i		−	0.443887i	0.975060	−	0.221943i	$-0.0712400\pi$
$884$	20.1001			0.676039
$885$	−5.32861			−0.179119
$886$	−19.5260			−0.655988
$887$			31.5562i			1.05955i	0.848137	+	0.529777i	$0.177724\pi$
$887$			31.5562i			1.05955i	−0.848137	+	0.529777i	$0.822276\pi$
$888$		−	3.22995i		−	0.108390i
$889$			45.7567i			1.53463i
$890$	27.3090			0.915400
$891$	−2.88528			−0.0966605
$892$			27.1286i			0.908334i
$893$	−30.8983			−1.03397
$894$	28.1492			0.941450
$895$	11.6131			0.388183
$896$	−12.3286			−0.411870
$897$			4.18767i			0.139822i
$898$	−50.3395			−1.67985
$899$			26.6240i			0.887959i
$900$	−5.66679			−0.188893
$901$		−	3.91752i		−	0.130511i
$902$	3.07633			0.102430
$903$	30.6402			1.01964
$904$		−	3.53512i		−	0.117576i
$905$	9.46917			0.314766
$906$	38.3338			1.27356
$907$	−17.7278			−0.588641			−0.294321	−	0.955707i	$-0.595093\pi$
$907$	−17.7278			−0.588641			−0.294321	+	0.955707i	$0.595093\pi$
$908$			28.7118i			0.952834i
$909$	−10.0354			−0.332854
$910$		−	51.1357i		−	1.69513i
$911$	−20.0426			−0.664041			−0.332021	−	0.943272i	$-0.607730\pi$
$911$	−20.0426			−0.664041			−0.332021	+	0.943272i	$0.607730\pi$
$912$	−9.66190			−0.319937
$913$			11.8846i			0.393324i
$914$		−	6.28113i		−	0.207761i
$915$	−6.49562			−0.214738
$916$			9.39501i			0.310420i
$917$	−43.3328			−1.43098
$918$		−	3.21601i		−	0.106144i
$919$			3.63293i			0.119839i	0.998203	+	0.0599197i	$0.0190845\pi$
$919$			3.63293i			0.119839i	−0.998203	+	0.0599197i	$0.980916\pi$
$920$		−	0.660464i		−	0.0217749i
$921$		−	7.29106i		−	0.240249i
$922$			34.9129i			1.14979i
$923$	53.3220			1.75512
$924$		−	18.0330i		−	0.593243i
$925$	−14.2237			−0.467672
$926$	1.96013			0.0644138
$927$		−	6.53691i		−	0.214700i
$928$	−24.7451			−0.812296
$929$	−3.65138			−0.119798			−0.0598990	−	0.998204i	$-0.519078\pi$
$929$	−3.65138			−0.119798			−0.0598990	+	0.998204i	$0.519078\pi$
$930$	28.5813			0.937218
$931$	1.58951			0.0520942
$932$	−33.5215			−1.09803
$933$	3.44914			0.112920
$934$			0.555683i			0.0181825i
$935$			7.10791i			0.232453i
$936$			3.21601i			0.105119i
$937$			28.3423i			0.925904i	0.886383	+	0.462952i	$0.153210\pi$
$937$			28.3423i			0.925904i	−0.886383	+	0.462952i	$0.846790\pi$
$938$	21.5313			0.703021
$939$	−8.41636			−0.274658
$940$			38.8918i			1.26851i
$941$	48.1874			1.57087			0.785433	−	0.618947i	$-0.212440\pi$
$941$	48.1874			1.57087			0.785433	+	0.618947i	$0.212440\pi$
$942$	−22.7267	−	12.4290i	−0.740475	−	0.404958i
$943$	−0.380076			−0.0123770
$944$		−	11.3651i		−	0.369901i
$945$	−4.35289			−0.141600
$946$	66.4888			2.16174
$947$		−	40.8720i		−	1.32816i	−0.747662	−	0.664080i	$-0.768823\pi$
$947$		−	40.8720i		−	1.32816i	0.747662	−	0.664080i	$-0.231177\pi$
$948$			22.5683i			0.732983i
$949$		−	11.3438i		−	0.368234i
$950$		−	14.7387i		−	0.478188i
$951$	−9.26725			−0.300511
$952$	2.42005			0.0784342
$953$	61.4922			1.99193			0.995963	−	0.0897626i	$-0.0286108\pi$
$953$	61.4922			1.99193			0.995963	+	0.0897626i	$0.0286108\pi$
$954$	5.20600			0.168550
$955$	−35.4496			−1.14712
$956$	18.5622			0.600344
$957$		−	8.79885i		−	0.284426i
$958$	−43.3017			−1.39901
$959$	9.58131			0.309397
$960$			15.8670i			0.512106i
$961$	45.2203			1.45872
$962$			67.0450i			2.16162i
$963$			19.5321i			0.629414i
$964$			24.9316i			0.802994i
$965$			27.0662i			0.871291i
$966$			4.18767i			0.134736i
$967$	38.1670			1.22737			0.613683	−	0.789552i	$-0.289687\pi$
$967$	38.1670			1.22737			0.613683	+	0.789552i	$0.289687\pi$
$968$			1.51400i			0.0486617i
$969$	4.45015			0.142959
$970$			35.6748i			1.14545i
$971$		−	28.2965i		−	0.908079i	−0.890982	−	0.454040i	$-0.849982\pi$
$971$		−	28.2965i		−	0.908079i	0.890982	−	0.454040i	$-0.150018\pi$
$972$	2.27376			0.0729309
$973$	60.3838			1.93582
$974$		−	66.1608i		−	2.11993i
$975$	14.1623			0.453556
$976$		−	13.8541i		−	0.443459i
$977$	−7.19951			−0.230333			−0.115166	−	0.993346i	$-0.536740\pi$
$977$	−7.19951			−0.230333			−0.115166	+	0.993346i	$0.536740\pi$
$978$	40.3833			1.29132
$979$	−24.0684			−0.769229
$980$		−	2.00073i		−	0.0639109i
$981$	−0.627253			−0.0200266
$982$	37.6066			1.20008
$983$		−	2.51578i		−	0.0802409i	−0.999195	−	0.0401205i	$-0.987226\pi$
$983$		−	2.51578i		−	0.0802409i	0.999195	−	0.0401205i	$-0.0127742\pi$
$984$	−0.291887			−0.00930503
$985$			15.1084i			0.481392i
$986$	9.80742			0.312332
$987$		−	29.6898i		−	0.945037i
$988$	−36.9614			−1.17590
$989$	−8.21461			−0.261209
$990$	−9.44572			−0.300205
$991$	−5.27647			−0.167613			−0.0838064	−	0.996482i	$-0.526708\pi$
$991$	−5.27647			−0.167613			−0.0838064	+	0.996482i	$0.526708\pi$
$992$			70.8413i			2.24921i
$993$	11.4938			0.364745
$994$	53.3220			1.69127
$995$		−	15.7525i		−	0.499389i
$996$		−	9.36574i		−	0.296765i
$997$		−	12.0777i		−	0.382503i	−0.981541	−	0.191252i	$-0.938745\pi$
$997$		−	12.0777i		−	0.382503i	0.981541	−	0.191252i	$-0.0612547\pi$
$998$	−74.8918			−2.37066
$999$	5.70716			0.180567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.a.313.11	yes	12
3.2	odd	2		1413.2.b.c.784.2		12
157.156	even	2	inner	471.2.b.a.313.2	✓	12
471.470	odd	2		1413.2.b.c.784.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.a.313.2	✓	12	157.156	even	2	inner
471.2.b.a.313.11	yes	12	1.1	even	1	trivial
1413.2.b.c.784.2		12	3.2	odd	2
1413.2.b.c.784.11		12	471.470	odd	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.06731i q^{2} -1.00000 q^{3} -2.27376 q^{4} -1.58359i q^{5} -2.06731i q^{6} +2.74875i q^{7} -0.565947i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.06731i q^{2} -1.00000 q^{3} -2.27376 q^{4} -1.58359i q^{5} -2.06731i q^{6} +2.74875i q^{7} -0.565947i q^{8} +1.00000 q^{9} +3.27376 q^{10} -2.88528 q^{11} +2.27376 q^{12} -5.68252 q^{13} -5.68252 q^{14} +1.58359i q^{15} -3.37753 q^{16} +1.55565 q^{17} +2.06731i q^{18} -2.86064 q^{19} +3.60070i q^{20} -2.74875i q^{21} -5.96476i q^{22} +0.736939i q^{23} +0.565947i q^{24} +2.49225 q^{25} -11.7475i q^{26} -1.00000 q^{27} -6.25001i q^{28} -3.04956i q^{29} -3.27376 q^{30} -8.73042 q^{31} -8.11430i q^{32} +2.88528 q^{33} +3.21601i q^{34} +4.35289 q^{35} -2.27376 q^{36} -5.70716 q^{37} -5.91382i q^{38} +5.68252 q^{39} -0.896227 q^{40} +0.515750i q^{41} +5.68252 q^{42} +11.1469i q^{43} +6.56044 q^{44} -1.58359i q^{45} -1.52348 q^{46} +10.8012 q^{47} +3.37753 q^{48} -0.555650 q^{49} +5.15225i q^{50} -1.55565 q^{51} +12.9207 q^{52} -2.51825i q^{53} -2.06731i q^{54} +4.56909i q^{55} +1.55565 q^{56} +2.86064 q^{57} +6.30439 q^{58} +3.36490i q^{59} -3.60070i q^{60} +4.10184i q^{61} -18.0485i q^{62} +2.74875i q^{63} +10.0197 q^{64} +8.99876i q^{65} +5.96476i q^{66} -3.78903 q^{67} -3.53718 q^{68} -0.736939i q^{69} +8.99876i q^{70} -9.38352 q^{71} -0.565947i q^{72} +1.99625i q^{73} -11.7985i q^{74} -2.49225 q^{75} +6.50440 q^{76} -7.93093i q^{77} +11.7475i q^{78} +9.92553i q^{79} +5.34862i q^{80} +1.00000 q^{81} -1.06621 q^{82} -4.11905i q^{83} +6.25001i q^{84} -2.46351i q^{85} -23.0441 q^{86} +3.04956i q^{87} +1.63292i q^{88} +8.34178 q^{89} +3.27376 q^{90} -15.6199i q^{91} -1.67562i q^{92} +8.73042 q^{93} +22.3294i q^{94} +4.53007i q^{95} +8.11430i q^{96} +10.8972i q^{97} -1.14870i q^{98} -2.88528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Introduction

L-functions

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