LMFDB - Embedded newform 429.2.b.a.298.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(298,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("429.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 54x^{6} + 74x^{4} + 21x^{2} + 1 $ x^10 + 13x^8 + 54x^6 + 74x^4 + 21x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			298.3
Root			$-1.40449i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.a.298.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.40449i q^{2} -1.00000 q^{3} +0.0273977 q^{4} -3.56736i q^{5} +1.40449i q^{6} -0.116494i q^{7} -2.84747i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.40449i q^{2} -1.00000 q^{3} +0.0273977 q^{4} -3.56736i q^{5} +1.40449i q^{6} -0.116494i q^{7} -2.84747i q^{8} +1.00000 q^{9} -5.01033 q^{10} -1.00000i q^{11} -0.0273977 q^{12} +(0.684603 + 3.53996i) q^{13} -0.163615 q^{14} +3.56736i q^{15} -3.94445 q^{16} +0.845026 q^{17} -1.40449i q^{18} -2.19717i q^{19} -0.0977375i q^{20} +0.116494i q^{21} -1.40449 q^{22} -1.73886 q^{23} +2.84747i q^{24} -7.72604 q^{25} +(4.97185 - 0.961520i) q^{26} -1.00000 q^{27} -0.00319167i q^{28} -4.43433 q^{29} +5.01033 q^{30} -6.18237i q^{31} -0.154974i q^{32} +1.00000i q^{33} -1.18683i q^{34} -0.415576 q^{35} +0.0273977 q^{36} +5.66510i q^{37} -3.08590 q^{38} +(-0.684603 - 3.53996i) q^{39} -10.1579 q^{40} +4.86697i q^{41} +0.163615 q^{42} -3.65401 q^{43} -0.0273977i q^{44} -3.56736i q^{45} +2.44222i q^{46} +0.856108i q^{47} +3.94445 q^{48} +6.98643 q^{49} +10.8512i q^{50} -0.845026 q^{51} +(0.0187565 + 0.0969868i) q^{52} +12.0792 q^{53} +1.40449i q^{54} -3.56736 q^{55} -0.331713 q^{56} +2.19717i q^{57} +6.22799i q^{58} -4.63079i q^{59} +0.0977375i q^{60} +12.8805 q^{61} -8.68310 q^{62} -0.116494i q^{63} -8.10657 q^{64} +(12.6283 - 2.44222i) q^{65} +1.40449 q^{66} -12.5703i q^{67} +0.0231518 q^{68} +1.73886 q^{69} +0.583674i q^{70} -3.93603i q^{71} -2.84747i q^{72} +5.81143i q^{73} +7.95659 q^{74} +7.72604 q^{75} -0.0601973i q^{76} -0.116494 q^{77} +(-4.97185 + 0.961520i) q^{78} +7.74675 q^{79} +14.0713i q^{80} +1.00000 q^{81} +6.83563 q^{82} +6.83336i q^{83} +0.00319167i q^{84} -3.01451i q^{85} +5.13204i q^{86} +4.43433 q^{87} -2.84747 q^{88} -8.05722i q^{89} -5.01033 q^{90} +(0.412384 - 0.0797521i) q^{91} -0.0476409 q^{92} +6.18237i q^{93} +1.20240 q^{94} -7.83808 q^{95} +0.154974i q^{96} +15.3975i q^{97} -9.81240i q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9	$ 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9} + 6 q^{12} + 12 q^{13} - 32 q^{14} + 6 q^{16} + 20 q^{17} - 2 q^{22} + 8 q^{23} - 14 q^{25} - 2 q^{26} - 10 q^{27} + 8 q^{29} - 6 q^{36} - 12 q^{39} - 20 q^{40} + 32 q^{42} - 24 q^{43} - 6 q^{48} - 26 q^{49} - 20 q^{51} - 48 q^{52} - 4 q^{53} + 4 q^{55} + 16 q^{56} + 36 q^{61} + 24 q^{62} + 50 q^{64} + 28 q^{65} + 2 q^{66} - 12 q^{68} - 8 q^{69} + 24 q^{74} + 14 q^{75} + 12 q^{77} + 2 q^{78} + 36 q^{79} + 10 q^{81} - 20 q^{82} - 8 q^{87} - 6 q^{88} - 24 q^{91} - 8 q^{92} - 32 q^{94} + 44 q^{95}+O(q^{100}) $ 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9 + 6 * q^12 + 12 * q^13 - 32 * q^14 + 6 * q^16 + 20 * q^17 - 2 * q^22 + 8 * q^23 - 14 * q^25 - 2 * q^26 - 10 * q^27 + 8 * q^29 - 6 * q^36 - 12 * q^39 - 20 * q^40 + 32 * q^42 - 24 * q^43 - 6 * q^48 - 26 * q^49 - 20 * q^51 - 48 * q^52 - 4 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^61 + 24 * q^62 + 50 * q^64 + 28 * q^65 + 2 * q^66 - 12 * q^68 - 8 * q^69 + 24 * q^74 + 14 * q^75 + 12 * q^77 + 2 * q^78 + 36 * q^79 + 10 * q^81 - 20 * q^82 - 8 * q^87 - 6 * q^88 - 24 * q^91 - 8 * q^92 - 32 * q^94 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.40449i		−	0.993127i	−0.868000	−	0.496563i	$-0.834595\pi$
$2$		−	1.40449i		−	0.993127i	0.868000	−	0.496563i	$-0.165405\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.0273977			0.0136989
$5$		−	3.56736i		−	1.59537i	−0.603074	−	0.797686i	$-0.706058\pi$
$5$		−	3.56736i		−	1.59537i	0.603074	−	0.797686i	$-0.293942\pi$
$6$			1.40449i			0.573382i
$7$		−	0.116494i		−	0.0440306i	−0.999758	−	0.0220153i	$-0.992992\pi$
$7$		−	0.116494i		−	0.0440306i	0.999758	−	0.0220153i	$-0.00700825\pi$
$8$		−	2.84747i		−	1.00673i
$9$	1.00000			0.333333
$10$	−5.01033			−1.58441
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.0273977			−0.00790904
$13$	0.684603	+	3.53996i	0.189875	+	0.981808i
$13$	0.684603	+	3.53996i	0.189875	+	0.981808i
$14$	−0.163615			−0.0437280
$15$			3.56736i			0.921088i
$16$	−3.94445			−0.986113
$17$	0.845026			0.204949			0.102474	−	0.994736i	$-0.467324\pi$
$17$	0.845026			0.204949			0.102474	+	0.994736i	$0.467324\pi$
$18$		−	1.40449i		−	0.331042i
$19$		−	2.19717i		−	0.504064i	−0.967719	−	0.252032i	$-0.918901\pi$
$19$		−	2.19717i		−	0.504064i	0.967719	−	0.252032i	$-0.0810989\pi$
$20$		−	0.0977375i		−	0.0218548i
$21$			0.116494i			0.0254211i
$22$	−1.40449			−0.299439
$23$	−1.73886			−0.362578			−0.181289	−	0.983430i	$-0.558027\pi$
$23$	−1.73886			−0.362578			−0.181289	+	0.983430i	$0.558027\pi$
$24$			2.84747i			0.581237i
$25$	−7.72604			−1.54521
$26$	4.97185	−	0.961520i	0.975060	−	0.188570i
$27$	−1.00000			−0.192450
$28$		−	0.00319167i		−	0.000603169i
$29$	−4.43433			−0.823435			−0.411717	−	0.911312i	$-0.635071\pi$
$29$	−4.43433			−0.823435			−0.411717	+	0.911312i	$0.635071\pi$
$30$	5.01033			0.914757
$31$		−	6.18237i		−	1.11039i	−0.831721	−	0.555193i	$-0.812644\pi$
$31$		−	6.18237i		−	1.11039i	0.831721	−	0.555193i	$-0.187356\pi$
$32$		−	0.154974i		−	0.0273958i
$33$			1.00000i			0.174078i
$34$		−	1.18683i		−	0.203540i
$35$	−0.415576			−0.0702451
$36$	0.0273977			0.00456629
$37$			5.66510i			0.931336i	0.884960	+	0.465668i	$0.154186\pi$
$37$			5.66510i			0.931336i	−0.884960	+	0.465668i	$0.845814\pi$
$38$	−3.08590			−0.500600
$39$	−0.684603	−	3.53996i	−0.109624	−	0.566847i
$40$	−10.1579			−1.60611
$41$			4.86697i			0.760094i	0.924967	+	0.380047i	$0.124092\pi$
$41$			4.86697i			0.760094i	−0.924967	+	0.380047i	$0.875908\pi$
$42$	0.163615			0.0252464
$43$	−3.65401			−0.557232			−0.278616	−	0.960403i	$-0.589876\pi$
$43$	−3.65401			−0.557232			−0.278616	+	0.960403i	$0.589876\pi$
$44$		−	0.0273977i		−	0.00413036i
$45$		−	3.56736i		−	0.531790i
$46$			2.44222i			0.360086i
$47$			0.856108i			0.124876i	0.998049	+	0.0624381i	$0.0198876\pi$
$47$			0.856108i			0.124876i	−0.998049	+	0.0624381i	$0.980112\pi$
$48$	3.94445			0.569333
$49$	6.98643			0.998061
$50$			10.8512i			1.53459i
$51$	−0.845026			−0.118327
$52$	0.0187565	+	0.0969868i	0.00260107	+	0.0134497i
$53$	12.0792			1.65920			0.829601	−	0.558357i	$-0.188568\pi$
$53$	12.0792			1.65920			0.829601	+	0.558357i	$0.188568\pi$
$54$			1.40449i			0.191127i
$55$	−3.56736			−0.481022
$56$	−0.331713			−0.0443270
$57$			2.19717i			0.291022i
$58$			6.22799i			0.817775i
$59$		−	4.63079i		−	0.602878i	−0.953485	−	0.301439i	$-0.902533\pi$
$59$		−	4.63079i		−	0.602878i	0.953485	−	0.301439i	$-0.0974670\pi$
$60$			0.0977375i			0.0126179i
$61$	12.8805			1.64918			0.824588	−	0.565733i	$-0.191407\pi$
$61$	12.8805			1.64918			0.824588	+	0.565733i	$0.191407\pi$
$62$	−8.68310			−1.10275
$63$		−	0.116494i		−	0.0146769i
$64$	−8.10657			−1.01332
$65$	12.6283	−	2.44222i	1.56635	−	0.302920i
$66$	1.40449			0.172881
$67$		−	12.5703i		−	1.53571i	−0.640624	−	0.767854i	$-0.721324\pi$
$67$		−	12.5703i		−	1.53571i	0.640624	−	0.767854i	$-0.278676\pi$
$68$	0.0231518			0.00280757
$69$	1.73886			0.209335
$70$			0.583674i			0.0697623i
$71$		−	3.93603i		−	0.467121i	−0.972342	−	0.233560i	$-0.924962\pi$
$71$		−	3.93603i		−	0.467121i	0.972342	−	0.233560i	$-0.0750376\pi$
$72$		−	2.84747i		−	0.335577i
$73$			5.81143i			0.680176i	0.940394	+	0.340088i	$0.110457\pi$
$73$			5.81143i			0.680176i	−0.940394	+	0.340088i	$0.889543\pi$
$74$	7.95659			0.924935
$75$	7.72604			0.892127
$76$		−	0.0601973i		−	0.00690510i
$77$	−0.116494			−0.0132757
$78$	−4.97185	+	0.961520i	−0.562951	+	0.108871i
$79$	7.74675			0.871578			0.435789	−	0.900049i	$-0.356469\pi$
$79$	7.74675			0.871578			0.435789	+	0.900049i	$0.356469\pi$
$80$			14.0713i			1.57322i
$81$	1.00000			0.111111
$82$	6.83563			0.754870
$83$			6.83336i			0.750059i	0.927013	+	0.375029i	$0.122367\pi$
$83$			6.83336i			0.750059i	−0.927013	+	0.375029i	$0.877633\pi$
$84$			0.00319167i			0.000348240i
$85$		−	3.01451i		−	0.326970i
$86$			5.13204i			0.553402i
$87$	4.43433			0.475410
$88$	−2.84747			−0.303541
$89$		−	8.05722i		−	0.854064i	−0.904237	−	0.427032i	$-0.859559\pi$
$89$		−	8.05722i		−	0.854064i	0.904237	−	0.427032i	$-0.140441\pi$
$90$	−5.01033			−0.528135
$91$	0.412384	−	0.0797521i	0.0432296	−	0.00836029i
$92$	−0.0476409			−0.00496691
$93$			6.18237i			0.641082i
$94$	1.20240			0.124018
$95$	−7.83808			−0.804170
$96$			0.154974i			0.0158170i
$97$			15.3975i			1.56338i	0.623665	+	0.781692i	$0.285643\pi$
$97$			15.3975i			1.56338i	−0.623665	+	0.781692i	$0.714357\pi$
$98$		−	9.81240i		−	0.991202i
$99$		−	1.00000i		−	0.100504i
$100$	−0.211676			−0.0211676
$101$	6.42887			0.639696			0.319848	−	0.947469i	$-0.396368\pi$
$101$	6.42887			0.639696			0.319848	+	0.947469i	$0.396368\pi$
$102$			1.18683i			0.117514i
$103$	−8.98347			−0.885167			−0.442584	−	0.896727i	$-0.645938\pi$
$103$	−8.98347			−0.885167			−0.442584	+	0.896727i	$0.645938\pi$
$104$	10.0799	−	1.94938i	0.988418	−	0.191153i
$105$	0.415576			0.0405560
$106$		−	16.9651i		−	1.64780i
$107$	8.12190			0.785173			0.392587	−	0.919715i	$-0.371580\pi$
$107$	8.12190			0.785173			0.392587	+	0.919715i	$0.371580\pi$
$108$	−0.0273977			−0.00263635
$109$		−	17.1574i		−	1.64338i	−0.569934	−	0.821690i	$-0.693031\pi$
$109$		−	17.1574i		−	1.64338i	0.569934	−	0.821690i	$-0.306969\pi$
$110$			5.01033i			0.477716i
$111$		−	5.66510i		−	0.537707i
$112$			0.459505i			0.0434192i
$113$	0.135467			0.0127436			0.00637182	−	0.999980i	$-0.497972\pi$
$113$	0.135467			0.0127436			0.00637182	+	0.999980i	$0.497972\pi$
$114$	3.08590			0.289021
$115$			6.20315i			0.578447i
$116$	−0.121491			−0.0112801
$117$	0.684603	+	3.53996i	0.0632915	+	0.327269i
$118$	−6.50392			−0.598735
$119$		−	0.0984405i		−	0.00902402i
$120$	10.1579			0.927288
$121$	−1.00000			−0.0909091
$122$		−	18.0906i		−	1.63784i
$123$		−	4.86697i		−	0.438840i
$124$		−	0.169383i		−	0.0152110i
$125$			9.72477i			0.869810i
$126$	−0.163615			−0.0145760
$127$	8.79419			0.780358			0.390179	−	0.920739i	$-0.372413\pi$
$127$	8.79419			0.780358			0.390179	+	0.920739i	$0.372413\pi$
$128$			11.0757i			0.978961i
$129$	3.65401			0.321718
$130$	−3.43009	−	17.7364i	−0.300838	−	1.55558i
$131$	16.3380			1.42746			0.713730	−	0.700421i	$-0.247004\pi$
$131$	16.3380			1.42746			0.713730	+	0.700421i	$0.247004\pi$
$132$			0.0273977i			0.00238466i
$133$	−0.255957			−0.0221942
$134$	−17.6549			−1.52515
$135$			3.56736i			0.307029i
$136$		−	2.40618i		−	0.206329i
$137$		−	17.5251i		−	1.49727i	−0.662981	−	0.748636i	$-0.730709\pi$
$137$		−	17.5251i		−	1.49727i	0.662981	−	0.748636i	$-0.269291\pi$
$138$		−	2.44222i		−	0.207896i
$139$	13.8568			1.17532			0.587661	−	0.809108i	$-0.300049\pi$
$139$	13.8568			1.17532			0.587661	+	0.809108i	$0.300049\pi$
$140$	−0.0113858			−0.000962278
$141$		−	0.856108i		−	0.0720973i
$142$	−5.52813			−0.463910
$143$	3.53996	−	0.684603i	0.296026	−	0.0572494i
$144$	−3.94445			−0.328704
$145$			15.8189i			1.31368i
$146$	8.16211			0.675501
$147$	−6.98643			−0.576231
$148$			0.155211i			0.0127582i
$149$			3.64704i			0.298777i	0.988779	+	0.149389i	$0.0477306\pi$
$149$			3.64704i			0.298777i	−0.988779	+	0.149389i	$0.952269\pi$
$150$		−	10.8512i		−	0.885995i
$151$			5.36601i			0.436680i	0.975873	+	0.218340i	$0.0700642\pi$
$151$			5.36601i			0.436680i	−0.975873	+	0.218340i	$0.929936\pi$
$152$	−6.25636			−0.507457
$153$	0.845026			0.0683163
$154$			0.163615i			0.0131845i
$155$	−22.0547			−1.77148
$156$	−0.0187565	−	0.0969868i	−0.00150173	−	0.00776516i
$157$	−9.57405			−0.764092			−0.382046	−	0.924143i	$-0.624780\pi$
$157$	−9.57405			−0.764092			−0.382046	+	0.924143i	$0.624780\pi$
$158$		−	10.8803i		−	0.865588i
$159$	−12.0792			−0.957940
$160$	−0.552847			−0.0437064
$161$			0.202567i			0.0159645i
$162$		−	1.40449i		−	0.110347i
$163$		−	4.42197i		−	0.346355i	−0.984891	−	0.173178i	$-0.944597\pi$
$163$		−	4.42197i		−	0.346355i	0.984891	−	0.173178i	$-0.0554034\pi$
$164$			0.133344i			0.0104124i
$165$	3.56736			0.277718
$166$	9.59741			0.744904
$167$			20.1925i			1.56254i	0.624193	+	0.781270i	$0.285428\pi$
$167$			20.1925i			1.56254i	−0.624193	+	0.781270i	$0.714572\pi$
$168$	0.331713			0.0255922
$169$	−12.0626	+	4.84693i	−0.927895	+	0.372841i
$170$	−4.23386			−0.324722
$171$		−	2.19717i		−	0.168021i
$172$	−0.100112			−0.00763344
$173$	−14.3677			−1.09236			−0.546178	−	0.837669i	$-0.683918\pi$
$173$	−14.3677			−1.09236			−0.546178	+	0.837669i	$0.683918\pi$
$174$		−	6.22799i		−	0.472143i
$175$			0.900038i			0.0680365i
$176$			3.94445i			0.297324i
$177$			4.63079i			0.348072i
$178$	−11.3163			−0.848194
$179$	−14.2292			−1.06354			−0.531771	−	0.846888i	$-0.678473\pi$
$179$	−14.2292			−1.06354			−0.531771	+	0.846888i	$0.678473\pi$
$180$		−	0.0977375i		−	0.00728492i
$181$	25.0176			1.85955			0.929773	−	0.368133i	$-0.120003\pi$
$181$	25.0176			1.85955			0.929773	+	0.368133i	$0.120003\pi$
$182$	−0.112011	−	0.579191i	−0.00830283	−	0.0429325i
$183$	−12.8805			−0.952153
$184$			4.95136i			0.365019i
$185$	20.2094			1.48583
$186$	8.68310			0.636676
$187$		−	0.845026i		−	0.0617944i
$188$			0.0234554i			0.00171066i
$189$			0.116494i			0.00847369i
$190$			11.0085i			0.798642i
$191$	−26.8540			−1.94309			−0.971545	−	0.236857i	$-0.923883\pi$
$191$	−26.8540			−1.94309			−0.971545	+	0.236857i	$0.923883\pi$
$192$	8.10657			0.585041
$193$			12.8070i			0.921866i	0.887435	+	0.460933i	$0.152485\pi$
$193$			12.8070i			0.921866i	−0.887435	+	0.460933i	$0.847515\pi$
$194$	21.6258			1.55264
$195$	−12.6283	+	2.44222i	−0.904332	+	0.174891i
$196$	0.191412			0.0136723
$197$			15.0767i			1.07417i	0.843527	+	0.537086i	$0.180475\pi$
$197$			15.0767i			1.07417i	−0.843527	+	0.537086i	$0.819525\pi$
$198$	−1.40449			−0.0998130
$199$	−12.8196			−0.908754			−0.454377	−	0.890809i	$-0.650138\pi$
$199$	−12.8196			−0.908754			−0.454377	+	0.890809i	$0.650138\pi$
$200$			21.9997i			1.55561i
$201$			12.5703i			0.886642i
$202$		−	9.02930i		−	0.635300i
$203$			0.516573i			0.0362563i
$204$	−0.0231518			−0.00162095
$205$	17.3622			1.21263
$206$			12.6172i			0.879084i
$207$	−1.73886			−0.120859
$208$	−2.70038	−	13.9632i	−0.187238	−	0.968174i
$209$	−2.19717			−0.151981
$210$		−	0.583674i		−	0.0402773i
$211$	15.4965			1.06682			0.533411	−	0.845856i	$-0.320910\pi$
$211$	15.4965			1.06682			0.533411	+	0.845856i	$0.320910\pi$
$212$	0.330942			0.0227292
$213$			3.93603i			0.269692i
$214$		−	11.4072i		−	0.779777i
$215$			13.0352i			0.888991i
$216$			2.84747i			0.193746i
$217$	−0.720209			−0.0488910
$218$	−24.0975			−1.63209
$219$		−	5.81143i		−	0.392700i
$220$	−0.0977375			−0.00658946
$221$	0.578507	+	2.99136i	0.0389146	+	0.201221i
$222$	−7.95659			−0.534011
$223$			24.5021i			1.64078i	0.571805	+	0.820389i	$0.306243\pi$
$223$			24.5021i			1.64078i	−0.571805	+	0.820389i	$0.693757\pi$
$224$	−0.0180535			−0.00120625
$225$	−7.72604			−0.515070
$226$		−	0.190262i		−	0.0126561i
$227$		−	4.11649i		−	0.273221i	−0.990625	−	0.136611i	$-0.956379\pi$
$227$		−	4.11649i		−	0.273221i	0.990625	−	0.136611i	$-0.0436209\pi$
$228$			0.0601973i			0.00398666i
$229$		−	14.7499i		−	0.974701i	−0.873207	−	0.487350i	$-0.837963\pi$
$229$		−	14.7499i		−	0.974701i	0.873207	−	0.487350i	$-0.162037\pi$
$230$	8.71228			0.574471
$231$	0.116494			0.00766474
$232$			12.6266i			0.828978i
$233$	−17.6924			−1.15907			−0.579535	−	0.814947i	$-0.696766\pi$
$233$	−17.6924			−1.15907			−0.579535	+	0.814947i	$0.696766\pi$
$234$	4.97185	−	0.961520i	0.325020	−	0.0628565i
$235$	3.05404			0.199224
$236$		−	0.126873i		−	0.00825874i
$237$	−7.74675			−0.503206
$238$	−0.138259			−0.00896200
$239$		−	23.6076i		−	1.52705i	−0.645779	−	0.763524i	$-0.723467\pi$
$239$		−	23.6076i		−	1.52705i	0.645779	−	0.763524i	$-0.276533\pi$
$240$		−	14.0713i		−	0.908297i
$241$			16.8176i			1.08332i	0.840599	+	0.541658i	$0.182203\pi$
$241$			16.8176i			1.08332i	−0.840599	+	0.541658i	$0.817797\pi$
$242$			1.40449i			0.0902843i
$243$	−1.00000			−0.0641500
$244$	0.352896			0.0225918
$245$		−	24.9231i		−	1.59228i
$246$	−6.83563			−0.435824
$247$	7.77788	−	1.50419i	0.494895	−	0.0957090i
$248$	−17.6041			−1.11786
$249$		−	6.83336i		−	0.433047i
$250$	13.6584			0.863832
$251$	−16.8555			−1.06391			−0.531956	−	0.846772i	$-0.678543\pi$
$251$	−16.8555			−1.06391			−0.531956	+	0.846772i	$0.678543\pi$
$252$		−	0.00319167i		−	0.000201056i
$253$			1.73886i			0.109321i
$254$		−	12.3514i		−	0.774995i
$255$			3.01451i			0.188776i
$256$	−0.657421			−0.0410888
$257$	12.4439			0.776230			0.388115	−	0.921611i	$-0.373126\pi$
$257$	12.4439			0.776230			0.388115	+	0.921611i	$0.373126\pi$
$258$		−	5.13204i		−	0.319507i
$259$	0.659950			0.0410073
$260$	0.345987	−	0.0669113i	0.0214572	−	0.00414966i
$261$	−4.43433			−0.274478
$262$		−	22.9467i		−	1.41765i
$263$	−29.0018			−1.78833			−0.894164	−	0.447740i	$-0.852229\pi$
$263$	−29.0018			−1.78833			−0.894164	+	0.447740i	$0.852229\pi$
$264$	2.84747			0.175249
$265$		−	43.0907i		−	2.64704i
$266$			0.359489i			0.0220417i
$267$			8.05722i			0.493094i
$268$		−	0.344398i		−	0.0210375i
$269$	18.4540			1.12516			0.562580	−	0.826743i	$-0.309809\pi$
$269$	18.4540			1.12516			0.562580	+	0.826743i	$0.309809\pi$
$270$	5.01033			0.304919
$271$			18.7848i			1.14110i	0.821264	+	0.570548i	$0.193269\pi$
$271$			18.7848i			1.14110i	−0.821264	+	0.570548i	$0.806731\pi$
$272$	−3.33317			−0.202103
$273$	−0.412384	+	0.0797521i	−0.0249586	+	0.00482682i
$274$	−24.6139			−1.48698
$275$			7.72604i			0.465898i
$276$	0.0476409			0.00286764
$277$	−1.09827			−0.0659888			−0.0329944	−	0.999456i	$-0.510504\pi$
$277$	−1.09827			−0.0659888			−0.0329944	+	0.999456i	$0.510504\pi$
$278$		−	19.4618i		−	1.16724i
$279$		−	6.18237i		−	0.370129i
$280$			1.18334i			0.0707180i
$281$			1.43331i			0.0855042i	0.999086	+	0.0427521i	$0.0136126\pi$
$281$			1.43331i			0.0855042i	−0.999086	+	0.0427521i	$0.986387\pi$
$282$	−1.20240			−0.0716018
$283$	15.9363			0.947317			0.473658	−	0.880709i	$-0.342933\pi$
$283$	15.9363			0.947317			0.473658	+	0.880709i	$0.342933\pi$
$284$		−	0.107838i		−	0.00639902i
$285$	7.83808			0.464288
$286$	−0.961520	−	4.97185i	−0.0568559	−	0.293992i
$287$	0.566973			0.0334674
$288$		−	0.154974i		−	0.00913193i
$289$	−16.2859			−0.957996
$290$	22.2175			1.30466
$291$		−	15.3975i		−	0.902620i
$292$			0.159220i			0.00931764i
$293$		−	1.99681i		−	0.116655i	−0.998298	−	0.0583274i	$-0.981423\pi$
$293$		−	1.99681i		−	0.116655i	0.998298	−	0.0583274i	$-0.0185767\pi$
$294$			9.81240i			0.572271i
$295$	−16.5197			−0.961814
$296$	16.1312			0.937605
$297$			1.00000i			0.0580259i
$298$	5.12225			0.296724
$299$	−1.19043	−	6.15551i	−0.0688444	−	0.355982i
$300$	0.211676			0.0122211
$301$			0.425671i			0.0245352i
$302$	7.53653			0.433679
$303$	−6.42887			−0.369329
$304$			8.66662i			0.497065i
$305$		−	45.9493i		−	2.63105i
$306$		−	1.18683i		−	0.0678468i
$307$		−	2.99278i		−	0.170807i	−0.996346	−	0.0854034i	$-0.972782\pi$
$307$		−	2.99278i		−	0.170807i	0.996346	−	0.0854034i	$-0.0272179\pi$
$308$	−0.00319167			−0.000181862
$309$	8.98347			0.511052
$310$			30.9757i			1.75930i
$311$	15.6120			0.885275			0.442637	−	0.896701i	$-0.354043\pi$
$311$	15.6120			0.885275			0.442637	+	0.896701i	$0.354043\pi$
$312$	−10.0799	+	1.94938i	−0.570663	+	0.110362i
$313$	2.95682			0.167129			0.0835647	−	0.996502i	$-0.473369\pi$
$313$	2.95682			0.167129			0.0835647	+	0.996502i	$0.473369\pi$
$314$			13.4467i			0.758840i
$315$	−0.415576			−0.0234150
$316$	0.212243			0.0119396
$317$		−	9.24823i		−	0.519433i	−0.965685	−	0.259716i	$-0.916371\pi$
$317$		−	9.24823i		−	0.519433i	0.965685	−	0.259716i	$-0.0836291\pi$
$318$			16.9651i			0.951357i
$319$			4.43433i			0.248275i
$320$			28.9190i			1.61662i
$321$	−8.12190			−0.453320
$322$	0.284504			0.0158548
$323$		−	1.85666i		−	0.103307i
$324$	0.0273977			0.00152210
$325$	−5.28927	−	27.3499i	−0.293396	−	1.51710i
$326$	−6.21062			−0.343975
$327$			17.1574i			0.948806i
$328$	13.8585			0.765210
$329$	0.0997315			0.00549837
$330$		−	5.01033i		−	0.275810i
$331$			3.23991i			0.178081i	0.996028	+	0.0890407i	$0.0283801\pi$
$331$			3.23991i			0.178081i	−0.996028	+	0.0890407i	$0.971620\pi$
$332$			0.187218i			0.0102749i
$333$			5.66510i			0.310445i
$334$	28.3602			1.55180
$335$	−44.8428			−2.45003
$336$		−	0.459505i		−	0.0250681i
$337$	25.1554			1.37030			0.685150	−	0.728402i	$-0.259736\pi$
$337$	25.1554			1.37030			0.685150	+	0.728402i	$0.259736\pi$
$338$	6.80749	+	16.9419i	0.370278	+	0.921518i
$339$	−0.135467			−0.00735754
$340$		−	0.0825907i		−	0.00447911i
$341$	−6.18237			−0.334794
$342$	−3.08590			−0.166867
$343$		−	1.62934i		−	0.0879758i
$344$			10.4047i			0.560983i
$345$		−	6.20315i		−	0.333966i
$346$			20.1793i			1.08485i
$347$	0.890342			0.0477961			0.0238980	−	0.999714i	$-0.492392\pi$
$347$	0.890342			0.0477961			0.0238980	+	0.999714i	$0.492392\pi$
$348$	0.121491			0.00651258
$349$			28.5303i			1.52719i	0.645695	+	0.763595i	$0.276568\pi$
$349$			28.5303i			1.52719i	−0.645695	+	0.763595i	$0.723432\pi$
$350$	1.26410			0.0675688
$351$	−0.684603	−	3.53996i	−0.0365414	−	0.188949i
$352$	−0.154974			−0.00826014
$353$		−	18.4315i		−	0.981009i	−0.871439	−	0.490504i	$-0.836813\pi$
$353$		−	18.4315i		−	0.981009i	0.871439	−	0.490504i	$-0.163187\pi$
$354$	6.50392			0.345680
$355$	−14.0412			−0.745231
$356$		−	0.220749i		−	0.0116997i
$357$			0.0984405i			0.00521002i
$358$			19.9848i			1.05623i
$359$			1.04747i			0.0552835i	0.999618	+	0.0276417i	$0.00879976\pi$
$359$			1.04747i			0.0552835i	−0.999618	+	0.0276417i	$0.991200\pi$
$360$	−10.1579			−0.535370
$361$	14.1725			0.745919
$362$		−	35.1371i		−	1.84677i
$363$	1.00000			0.0524864
$364$	0.0112984	−	0.00218503i	0.000592196	−	0.000114526i
$365$	20.7314			1.08513
$366$			18.0906i			0.945609i
$367$	−1.25059			−0.0652802			−0.0326401	−	0.999467i	$-0.510392\pi$
$367$	−1.25059			−0.0652802			−0.0326401	+	0.999467i	$0.510392\pi$
$368$	6.85887			0.357543
$369$			4.86697i			0.253365i
$370$		−	28.3840i		−	1.47561i
$371$		−	1.40715i		−	0.0730556i
$372$			0.169383i			0.00878209i
$373$	8.84543			0.457999			0.229000	−	0.973427i	$-0.426455\pi$
$373$	8.84543			0.457999			0.229000	+	0.973427i	$0.426455\pi$
$374$	−1.18683			−0.0613697
$375$		−	9.72477i		−	0.502185i
$376$	2.43774			0.125717
$377$	−3.03576	−	15.6974i	−0.156349	−	0.808455i
$378$	0.163615			0.00841545
$379$		−	24.4511i		−	1.25597i	−0.778226	−	0.627985i	$-0.783880\pi$
$379$		−	24.4511i		−	1.25597i	0.778226	−	0.627985i	$-0.216120\pi$
$380$	−0.214745			−0.0110162
$381$	−8.79419			−0.450540
$382$			37.7163i			1.92973i
$383$			15.5350i			0.793800i	0.917862	+	0.396900i	$0.129914\pi$
$383$			15.5350i			0.793800i	−0.917862	+	0.396900i	$0.870086\pi$
$384$		−	11.0757i		−	0.565203i
$385$			0.415576i			0.0211797i
$386$	17.9873			0.915530
$387$	−3.65401			−0.185744
$388$			0.421857i			0.0214166i
$389$	−18.0829			−0.916838			−0.458419	−	0.888736i	$-0.651584\pi$
$389$	−18.0829			−0.916838			−0.458419	+	0.888736i	$0.651584\pi$
$390$	3.43009	+	17.7364i	0.173689	+	0.898116i
$391$	−1.46939			−0.0743100
$392$		−	19.8936i		−	1.00478i
$393$	−16.3380			−0.824145
$394$	21.1752			1.06679
$395$		−	27.6354i		−	1.39049i
$396$		−	0.0273977i		−	0.00137679i
$397$			25.2816i			1.26885i	0.772986	+	0.634423i	$0.218762\pi$
$397$			25.2816i			1.26885i	−0.772986	+	0.634423i	$0.781238\pi$
$398$			18.0050i			0.902508i
$399$	0.255957			0.0128139
$400$	30.4750			1.52375
$401$		−	9.54563i		−	0.476686i	−0.971181	−	0.238343i	$-0.923396\pi$
$401$		−	9.54563i		−	0.476686i	0.971181	−	0.238343i	$-0.0766042\pi$
$402$	17.6549			0.880548
$403$	21.8854	−	4.23247i	1.09019	−	0.210834i
$404$	0.176136			0.00876311
$405$		−	3.56736i		−	0.177263i
$406$	0.725524			0.0360071
$407$	5.66510			0.280808
$408$			2.40618i			0.119124i
$409$		−	21.6613i		−	1.07108i	−0.844509	−	0.535542i	$-0.820107\pi$
$409$		−	21.6613i		−	1.07108i	0.844509	−	0.535542i	$-0.179893\pi$
$410$		−	24.3852i		−	1.20430i
$411$			17.5251i			0.864450i
$412$	−0.246126			−0.0121258
$413$	−0.539460			−0.0265451
$414$			2.44222i			0.120029i
$415$	24.3770			1.19662
$416$	0.548601	−	0.106096i	0.0268974	−	0.00520176i
$417$	−13.8568			−0.678572
$418$			3.08590i			0.150937i
$419$	23.4413			1.14518			0.572592	−	0.819841i	$-0.305938\pi$
$419$	23.4413			1.14518			0.572592	+	0.819841i	$0.305938\pi$
$420$	0.0113858			0.000555571
$421$			16.2832i			0.793596i	0.917906	+	0.396798i	$0.129879\pi$
$421$			16.2832i			0.793596i	−0.917906	+	0.396798i	$0.870121\pi$
$422$		−	21.7647i		−	1.05949i
$423$			0.856108i			0.0416254i
$424$		−	34.3950i		−	1.67037i
$425$	−6.52871			−0.316689
$426$	5.52813			0.267839
$427$		−	1.50050i		−	0.0726142i
$428$	0.222521			0.0107560
$429$	−3.53996	+	0.684603i	−0.170911	+	0.0330529i
$430$	18.3078			0.882881
$431$			13.5080i			0.650655i	0.945601	+	0.325328i	$0.105475\pi$
$431$			13.5080i			0.650655i	−0.945601	+	0.325328i	$0.894525\pi$
$432$	3.94445			0.189778
$433$	19.2270			0.923992			0.461996	−	0.886882i	$-0.347133\pi$
$433$	19.2270			0.923992			0.461996	+	0.886882i	$0.347133\pi$
$434$			1.01153i			0.0485550i
$435$		−	15.8189i		−	0.758456i
$436$		−	0.470074i		−	0.0225124i
$437$			3.82057i			0.182763i
$438$	−8.16211			−0.390001
$439$	−33.1119			−1.58034			−0.790172	−	0.612885i	$-0.790009\pi$
$439$	−33.1119			−1.58034			−0.790172	+	0.612885i	$0.790009\pi$
$440$			10.1579i			0.484261i
$441$	6.98643			0.332687
$442$	4.20134	−	0.812510i	0.199838	−	0.0386471i
$443$	24.4472			1.16152			0.580761	−	0.814074i	$-0.302755\pi$
$443$	24.4472			1.16152			0.580761	+	0.814074i	$0.302755\pi$
$444$		−	0.155211i		−	0.00736597i
$445$	−28.7430			−1.36255
$446$	34.4130			1.62950
$447$		−	3.64704i		−	0.172499i
$448$			0.944366i			0.0446171i
$449$			27.0060i			1.27449i	0.770661	+	0.637245i	$0.219926\pi$
$449$			27.0060i			1.27449i	−0.770661	+	0.637245i	$0.780074\pi$
$450$			10.8512i			0.511529i
$451$	4.86697			0.229177
$452$	0.00371148			0.000174573
$453$		−	5.36601i		−	0.252117i
$454$	−5.78159			−0.271343
$455$	−0.284504	−	1.47112i	−0.0133378	−	0.0689673i
$456$	6.25636			0.292981
$457$			5.46894i			0.255826i	0.991785	+	0.127913i	$0.0408278\pi$
$457$			5.46894i			0.255826i	−0.991785	+	0.127913i	$0.959172\pi$
$458$	−20.7161			−0.968002
$459$	−0.845026			−0.0394424
$460$			0.169952i			0.00792406i
$461$			35.8194i			1.66828i	0.551555	+	0.834139i	$0.314035\pi$
$461$			35.8194i			1.66828i	−0.551555	+	0.834139i	$0.685965\pi$
$462$		−	0.163615i		−	0.00761206i
$463$		−	13.4910i		−	0.626979i	−0.949592	−	0.313490i	$-0.898502\pi$
$463$		−	13.4910i		−	0.626979i	0.949592	−	0.313490i	$-0.101498\pi$
$464$	17.4910			0.812000
$465$	22.0547			1.02276
$466$			24.8489i			1.15110i
$467$	−4.06078			−0.187910			−0.0939552	−	0.995576i	$-0.529951\pi$
$467$	−4.06078			−0.187910			−0.0939552	+	0.995576i	$0.529951\pi$
$468$	0.0187565	+	0.0969868i	0.000867022	+	0.00448322i
$469$	−1.46437			−0.0676182
$470$		−	4.28939i		−	0.197855i
$471$	9.57405			0.441149
$472$	−13.1860			−0.606936
$473$			3.65401i			0.168012i
$474$			10.8803i			0.499747i
$475$			16.9754i			0.778885i
$476$		−	0.00269704i		−	0.000123619i
$477$	12.0792			0.553067
$478$	−33.1567			−1.51655
$479$			25.0339i			1.14383i	0.820313	+	0.571914i	$0.193799\pi$
$479$			25.0339i			1.14383i	−0.820313	+	0.571914i	$0.806201\pi$
$480$	0.552847			0.0252339
$481$	−20.0542	+	3.87834i	−0.914393	+	0.176837i
$482$	23.6202			1.07587
$483$		−	0.202567i		−	0.00921713i
$484$	−0.0273977			−0.00124535
$485$	54.9285			2.49418
$486$			1.40449i			0.0637091i
$487$			24.0438i			1.08953i	0.838590	+	0.544763i	$0.183380\pi$
$487$			24.0438i			1.08953i	−0.838590	+	0.544763i	$0.816620\pi$
$488$		−	36.6768i		−	1.66028i
$489$			4.42197i			0.199968i
$490$	−35.0043			−1.58133
$491$	−16.9521			−0.765039			−0.382519	−	0.923947i	$-0.624943\pi$
$491$	−16.9521			−0.765039			−0.382519	+	0.923947i	$0.624943\pi$
$492$		−	0.133344i		−	0.00601161i
$493$	−3.74713			−0.168762
$494$	−2.11262	−	10.9240i	−0.0950512	−	0.491493i
$495$	−3.56736			−0.160341
$496$			24.3861i			1.09497i
$497$	−0.458524			−0.0205676
$498$	−9.59741			−0.430070
$499$			19.1635i			0.857876i	0.903334	+	0.428938i	$0.141112\pi$
$499$			19.1635i			0.857876i	−0.903334	+	0.428938i	$0.858888\pi$
$500$			0.266437i			0.0119154i
$501$		−	20.1925i		−	0.902133i
$502$			23.6735i			1.05660i
$503$	−40.3118			−1.79741			−0.898707	−	0.438549i	$-0.855492\pi$
$503$	−40.3118			−1.79741			−0.898707	+	0.438549i	$0.855492\pi$
$504$	−0.331713			−0.0147757
$505$		−	22.9341i		−	1.02055i
$506$	2.44222			0.108570
$507$	12.0626	−	4.84693i	0.535721	−	0.215260i
$508$	0.240941			0.0106900
$509$			43.6643i			1.93539i	0.252132	+	0.967693i	$0.418868\pi$
$509$			43.6643i			1.93539i	−0.252132	+	0.967693i	$0.581132\pi$
$510$	4.23386			0.187479
$511$	0.676997			0.0299486
$512$			23.0747i			1.01977i
$513$			2.19717i			0.0970072i
$514$		−	17.4774i		−	0.770895i
$515$			32.0472i			1.41217i
$516$	0.100112			0.00440717
$517$	0.856108			0.0376516
$518$		−	0.926895i		−	0.0407254i
$519$	14.3677			0.630672
$520$	−6.95415	−	35.9587i	−0.304960	−	1.57689i
$521$	13.5157			0.592132			0.296066	−	0.955167i	$-0.404325\pi$
$521$	13.5157			0.592132			0.296066	+	0.955167i	$0.404325\pi$
$522$			6.22799i			0.272592i
$523$	−30.3480			−1.32703			−0.663513	−	0.748165i	$-0.730935\pi$
$523$	−30.3480			−1.32703			−0.663513	+	0.748165i	$0.730935\pi$
$524$	0.447625			0.0195546
$525$		−	0.900038i		−	0.0392809i
$526$			40.7328i			1.77604i
$527$		−	5.22427i		−	0.227573i
$528$		−	3.94445i		−	0.171660i
$529$	−19.9764			−0.868537
$530$	−60.5206			−2.62885
$531$		−	4.63079i		−	0.200959i
$532$	−0.00701262			−0.000304036
$533$	−17.2289	+	3.33194i	−0.746266	+	0.144323i
$534$	11.3163			0.489705
$535$		−	28.9737i		−	1.25264i
$536$	−35.7936			−1.54605
$537$	14.2292			0.614036
$538$		−	25.9185i		−	1.11743i
$539$		−	6.98643i		−	0.300927i
$540$			0.0977375i			0.00420595i
$541$		−	44.0127i		−	1.89225i	−0.323797	−	0.946127i	$-0.604960\pi$
$541$		−	44.0127i		−	1.89225i	0.323797	−	0.946127i	$-0.395040\pi$
$542$	26.3831			1.13325
$543$	−25.0176			−1.07361
$544$		−	0.130957i		−	0.00561473i
$545$	−61.2066			−2.62180
$546$	0.112011	+	0.579191i	0.00479364	+	0.0247871i
$547$	13.0054			0.556069			0.278034	−	0.960571i	$-0.410317\pi$
$547$	13.0054			0.556069			0.278034	+	0.960571i	$0.410317\pi$
$548$		−	0.480148i		−	0.0205109i
$549$	12.8805			0.549726
$550$	10.8512			0.462696
$551$			9.74296i			0.415064i
$552$		−	4.95136i		−	0.210744i
$553$		−	0.902450i		−	0.0383761i
$554$			1.54252i			0.0655352i
$555$	−20.2094			−0.857842
$556$	0.379646			0.0161006
$557$			43.5077i			1.84348i	0.387806	+	0.921741i	$0.373233\pi$
$557$			43.5077i			1.84348i	−0.387806	+	0.921741i	$0.626767\pi$
$558$	−8.68310			−0.367585
$559$	−2.50155	−	12.9351i	−0.105804	−	0.547095i
$560$	1.63922			0.0692697
$561$			0.845026i			0.0356770i
$562$	2.01308			0.0849165
$563$	26.9811			1.13712			0.568560	−	0.822642i	$-0.307501\pi$
$563$	26.9811			1.13712			0.568560	+	0.822642i	$0.307501\pi$
$564$		−	0.0234554i		−	0.000987651i
$565$		−	0.483258i		−	0.0203308i
$566$		−	22.3825i		−	0.940806i
$567$		−	0.116494i		−	0.00489229i
$568$	−11.2077			−0.470265
$569$	15.6979			0.658091			0.329045	−	0.944314i	$-0.393273\pi$
$569$	15.6979			0.658091			0.329045	+	0.944314i	$0.393273\pi$
$570$		−	11.0085i		−	0.461096i
$571$	26.4773			1.10804			0.554020	−	0.832503i	$-0.313093\pi$
$571$	26.4773			1.10804			0.554020	+	0.832503i	$0.313093\pi$
$572$	0.0969868	−	0.0187565i	0.00405522	−	0.000784251i
$573$	26.8540			1.12184
$574$		−	0.796310i		−	0.0332374i
$575$	13.4345			0.560259
$576$	−8.10657			−0.337774
$577$			4.59666i			0.191362i	0.995412	+	0.0956808i	$0.0305028\pi$
$577$			4.59666i			0.191362i	−0.995412	+	0.0956808i	$0.969497\pi$
$578$			22.8735i			0.951412i
$579$		−	12.8070i		−	0.532239i
$580$			0.433400i			0.0179960i
$581$	0.796046			0.0330255
$582$	−21.6258			−0.896416
$583$		−	12.0792i		−	0.500268i
$584$	16.5479			0.684755
$585$	12.6283	−	2.44222i	0.522116	−	0.100973i
$586$	−2.80450			−0.115853
$587$		−	3.97329i		−	0.163995i	−0.996633	−	0.0819976i	$-0.973870\pi$
$587$		−	3.97329i		−	0.163995i	0.996633	−	0.0819976i	$-0.0261300\pi$
$588$	−0.191412			−0.00789371
$589$	−13.5837			−0.559706
$590$			23.2018i			0.955204i
$591$		−	15.0767i		−	0.620174i
$592$		−	22.3457i		−	0.918403i
$593$			19.1059i			0.784585i	0.919841	+	0.392292i	$0.128318\pi$
$593$			19.1059i			0.784585i	−0.919841	+	0.392292i	$0.871682\pi$
$594$	1.40449			0.0576271
$595$	−0.351172			−0.0143967
$596$			0.0999206i			0.00409291i
$597$	12.8196			0.524669
$598$	−8.64537	+	1.67195i	−0.353536	+	0.0683712i
$599$	4.11818			0.168264			0.0841322	−	0.996455i	$-0.473188\pi$
$599$	4.11818			0.168264			0.0841322	+	0.996455i	$0.473188\pi$
$600$		−	21.9997i		−	0.898132i
$601$	2.29914			0.0937840			0.0468920	−	0.998900i	$-0.485068\pi$
$601$	2.29914			0.0937840			0.0468920	+	0.998900i	$0.485068\pi$
$602$	0.597852			0.0243666
$603$		−	12.5703i		−	0.511903i
$604$			0.147017i			0.00598202i
$605$			3.56736i			0.145034i
$606$			9.02930i			0.366790i
$607$	2.17420			0.0882482			0.0441241	−	0.999026i	$-0.485950\pi$
$607$	2.17420			0.0882482			0.0441241	+	0.999026i	$0.485950\pi$
$608$	−0.340503			−0.0138092
$609$		−	0.516573i		−	0.0209326i
$610$	−64.5355			−2.61297
$611$	−3.03059	+	0.586094i	−0.122605	+	0.0237108i
$612$	0.0231518			0.000935855
$613$		−	49.1904i		−	1.98678i	−0.114787	−	0.993390i	$-0.536619\pi$
$613$		−	49.1904i		−	1.98678i	0.114787	−	0.993390i	$-0.463381\pi$
$614$	−4.20334			−0.169633
$615$	−17.3622			−0.700113
$616$			0.331713i			0.0133651i
$617$			0.227308i			0.00915106i	0.999990	+	0.00457553i	$0.00145644\pi$
$617$			0.227308i			0.00915106i	−0.999990	+	0.00457553i	$0.998544\pi$
$618$		−	12.6172i		−	0.507539i
$619$		−	25.7483i		−	1.03491i	−0.855709	−	0.517457i	$-0.826879\pi$
$619$		−	25.7483i		−	1.03491i	0.855709	−	0.517457i	$-0.173121\pi$
$620$	−0.604249			−0.0242672
$621$	1.73886			0.0697782
$622$		−	21.9269i		−	0.879190i
$623$	−0.938618			−0.0376049
$624$	2.70038	+	13.9632i	0.108102	+	0.558976i
$625$	−3.93847			−0.157539
$626$		−	4.15284i		−	0.165981i
$627$	2.19717			0.0877463
$628$	−0.262307			−0.0104672
$629$			4.78715i			0.190876i
$630$			0.583674i			0.0232541i
$631$			3.74971i			0.149274i	0.997211	+	0.0746368i	$0.0237797\pi$
$631$			3.74971i			0.149274i	−0.997211	+	0.0746368i	$0.976220\pi$
$632$		−	22.0586i		−	0.877445i
$633$	−15.4965			−0.615930
$634$	−12.9891			−0.515863
$635$		−	31.3720i		−	1.24496i
$636$	−0.330942			−0.0131227
$637$	4.78293	+	24.7317i	0.189507	+	0.979905i
$638$	6.22799			0.246569
$639$		−	3.93603i		−	0.155707i
$640$	39.5109			1.56181
$641$	37.5616			1.48359			0.741797	−	0.670625i	$-0.233974\pi$
$641$	37.5616			1.48359			0.741797	+	0.670625i	$0.233974\pi$
$642$			11.4072i			0.450204i
$643$			2.51702i			0.0992618i	0.998768	+	0.0496309i	$0.0158045\pi$
$643$			2.51702i			0.0992618i	−0.998768	+	0.0496309i	$0.984196\pi$
$644$			0.00554988i			0.000218696i
$645$		−	13.0352i		−	0.513259i
$646$	−2.60767			−0.102597
$647$	2.64180			0.103860			0.0519298	−	0.998651i	$-0.483463\pi$
$647$	2.64180			0.103860			0.0519298	+	0.998651i	$0.483463\pi$
$648$		−	2.84747i		−	0.111859i
$649$	−4.63079			−0.181775
$650$	−38.4127	+	7.42875i	−1.50667	+	0.291379i
$651$	0.720209			0.0282272
$652$		−	0.121152i		−	0.00474467i
$653$	−41.4942			−1.62380			−0.811898	−	0.583800i	$-0.801565\pi$
$653$	−41.4942			−1.62380			−0.811898	+	0.583800i	$0.801565\pi$
$654$	24.0975			0.942285
$655$		−	58.2836i		−	2.27733i
$656$		−	19.1976i		−	0.749539i
$657$			5.81143i			0.226725i
$658$		−	0.140072i		−	0.00546058i
$659$	−44.2877			−1.72520			−0.862601	−	0.505884i	$-0.831166\pi$
$659$	−44.2877			−1.72520			−0.862601	+	0.505884i	$0.831166\pi$
$660$	0.0977375			0.00380443
$661$		−	41.4955i		−	1.61399i	−0.590559	−	0.806994i	$-0.701093\pi$
$661$		−	41.4955i		−	1.61399i	0.590559	−	0.806994i	$-0.298907\pi$
$662$	4.55043			0.176857
$663$	−0.578507	−	2.99136i	−0.0224674	−	0.116175i
$664$	19.4578			0.755108
$665$			0.913089i			0.0354081i
$666$	7.95659			0.308312
$667$	7.71070			0.298559
$668$			0.553228i			0.0214050i
$669$		−	24.5021i		−	0.947304i
$670$			62.9815i			2.43319i
$671$		−	12.8805i		−	0.497246i
$672$	0.0180535			0.000696430
$673$	−37.0265			−1.42727			−0.713634	−	0.700519i	$-0.752952\pi$
$673$	−37.0265			−1.42727			−0.713634	+	0.700519i	$0.752952\pi$
$674$		−	35.3306i		−	1.36088i
$675$	7.72604			0.297376
$676$	−0.330489	+	0.132795i	−0.0127111	+	0.00510749i
$677$	−23.7330			−0.912133			−0.456067	−	0.889946i	$-0.650742\pi$
$677$	−23.7330			−0.912133			−0.456067	+	0.889946i	$0.650742\pi$
$678$			0.190262i			0.00730697i
$679$	1.79372			0.0688367
$680$	−8.58372			−0.329171
$681$			4.11649i			0.157744i
$682$			8.68310i			0.332493i
$683$			38.1033i			1.45798i	0.684523	+	0.728991i	$0.260010\pi$
$683$			38.1033i			1.45798i	−0.684523	+	0.728991i	$0.739990\pi$
$684$		−	0.0601973i		−	0.00230170i
$685$	−62.5184			−2.38870
$686$	−2.28839			−0.0873712
$687$			14.7499i			0.562744i
$688$	14.4131			0.549494
$689$	8.26943	+	42.7598i	0.315040	+	1.62902i
$690$	−8.71228			−0.331671
$691$		−	22.7576i		−	0.865738i	−0.901457	−	0.432869i	$-0.857501\pi$
$691$		−	22.7576i		−	0.865738i	0.901457	−	0.432869i	$-0.142499\pi$
$692$	−0.393642			−0.0149640
$693$	−0.116494			−0.00442524
$694$		−	1.25048i		−	0.0474676i
$695$		−	49.4323i		−	1.87507i
$696$		−	12.6266i		−	0.478611i
$697$			4.11272i			0.155780i
$698$	40.0706			1.51669
$699$	17.6924			0.669190
$700$			0.0246590i			0.000932022i
$701$	14.0558			0.530880			0.265440	−	0.964127i	$-0.414483\pi$
$701$	14.0558			0.530880			0.265440	+	0.964127i	$0.414483\pi$
$702$	−4.97185	+	0.961520i	−0.187650	+	0.0362902i
$703$	12.4472			0.469453
$704$			8.10657i			0.305528i
$705$	−3.05404			−0.115022
$706$	−25.8869			−0.974266
$707$		−	0.748925i		−	0.0281662i
$708$			0.126873i			0.00476819i
$709$			19.3132i			0.725321i	0.931921	+	0.362660i	$0.118132\pi$
$709$			19.3132i			0.725321i	−0.931921	+	0.362660i	$0.881868\pi$
$710$			19.7208i			0.740109i
$711$	7.74675			0.290526
$712$	−22.9427			−0.859813
$713$			10.7503i			0.402602i
$714$	0.138259			0.00517421
$715$	−2.44222	−	12.6283i	−0.0913340	−	0.472272i
$716$	−0.389848			−0.0145693
$717$			23.6076i			0.881642i
$718$	1.47117			0.0549035
$719$	22.4417			0.836934			0.418467	−	0.908232i	$-0.362567\pi$
$719$	22.4417			0.836934			0.418467	+	0.908232i	$0.362567\pi$
$720$			14.0713i			0.524406i
$721$			1.04652i			0.0389744i
$722$		−	19.9051i		−	0.740792i
$723$		−	16.8176i		−	0.625453i
$724$	0.685426			0.0254737
$725$	34.2598			1.27238
$726$		−	1.40449i		−	0.0521256i
$727$	−19.4023			−0.719590			−0.359795	−	0.933031i	$-0.617153\pi$
$727$	−19.4023			−0.719590			−0.359795	+	0.933031i	$0.617153\pi$
$728$	−0.227091	−	1.17425i	−0.00841657	−	0.0435206i
$729$	1.00000			0.0370370
$730$		−	29.1172i		−	1.07768i
$731$	−3.08774			−0.114204
$732$	−0.352896			−0.0130434
$733$			11.6978i			0.432067i	0.976386	+	0.216033i	$0.0693120\pi$
$733$			11.6978i			0.432067i	−0.976386	+	0.216033i	$0.930688\pi$
$734$			1.75644i			0.0648315i
$735$			24.9231i			0.919302i
$736$			0.269479i			0.00993311i
$737$	−12.5703			−0.463034
$738$	6.83563			0.251623
$739$			39.6475i			1.45846i	0.684270	+	0.729229i	$0.260121\pi$
$739$			39.6475i			1.45846i	−0.684270	+	0.729229i	$0.739879\pi$
$740$	0.553692			0.0203541
$741$	−7.77788	+	1.50419i	−0.285727	+	0.0552576i
$742$	−1.97633			−0.0725535
$743$			16.5114i			0.605746i	0.953031	+	0.302873i	$0.0979458\pi$
$743$			16.5114i			0.605746i	−0.953031	+	0.302873i	$0.902054\pi$
$744$	17.6041			0.645398
$745$	13.0103			0.476661
$746$		−	12.4234i		−	0.454851i
$747$			6.83336i			0.250020i
$748$		−	0.0231518i		−	0.000846513i
$749$		−	0.946152i		−	0.0345716i
$750$	−13.6584			−0.498734
$751$	35.2198			1.28519			0.642595	−	0.766206i	$-0.277858\pi$
$751$	35.2198			1.28519			0.642595	+	0.766206i	$0.277858\pi$
$752$		−	3.37688i		−	0.123142i
$753$	16.8555			0.614250
$754$	−22.0468	+	4.26370i	−0.802899	+	0.155275i
$755$	19.1425			0.696667
$756$			0.00319167i			0.000116080i
$757$	−17.3351			−0.630055			−0.315028	−	0.949083i	$-0.602014\pi$
$757$	−17.3351			−0.630055			−0.315028	+	0.949083i	$0.602014\pi$
$758$	−34.3414			−1.24734
$759$		−	1.73886i		−	0.0631168i
$760$			22.3187i			0.809583i
$761$		−	37.0208i		−	1.34200i	−0.741457	−	0.671001i	$-0.765865\pi$
$761$		−	37.0208i		−	1.34200i	0.741457	−	0.671001i	$-0.234135\pi$
$762$			12.3514i			0.447444i
$763$	−1.99873			−0.0723590
$764$	−0.735739			−0.0266181
$765$		−	3.01451i		−	0.108990i
$766$	21.8188			0.788344
$767$	16.3928	−	3.17025i	0.591911	−	0.114471i
$768$	0.657421			0.0237226
$769$			20.9149i			0.754212i	0.926170	+	0.377106i	$0.123081\pi$
$769$			20.9149i			0.754212i	−0.926170	+	0.377106i	$0.876919\pi$
$770$	0.583674			0.0210341
$771$	−12.4439			−0.448157
$772$			0.350882i			0.0126285i
$773$		−	9.23777i		−	0.332259i	−0.986104	−	0.166130i	$-0.946873\pi$
$773$		−	9.23777i		−	0.332259i	0.986104	−	0.166130i	$-0.0531270\pi$
$774$			5.13204i			0.184467i
$775$			47.7653i			1.71578i
$776$	43.8440			1.57391
$777$	−0.659950			−0.0236756
$778$			25.3973i			0.910537i
$779$	10.6935			0.383136
$780$	−0.345987	+	0.0669113i	−0.0123883	+	0.00239581i
$781$	−3.93603			−0.140842
$782$			2.06374i			0.0737993i
$783$	4.43433			0.158470
$784$	−27.5576			−0.984202
$785$			34.1540i			1.21901i
$786$			22.9467i			0.818480i
$787$			33.0647i			1.17863i	0.807904	+	0.589314i	$0.200602\pi$
$787$			33.0647i			1.17863i	−0.807904	+	0.589314i	$0.799398\pi$
$788$			0.413068i			0.0147149i
$789$	29.0018			1.03249
$790$	−38.8138			−1.38093
$791$		−	0.0157811i		−	0.000561110i
$792$	−2.84747			−0.101180
$793$	8.81801	+	45.5964i	0.313137	+	1.61918i
$794$	35.5078			1.26012
$795$			43.0907i			1.52827i
$796$	−0.351227			−0.0124489
$797$	52.4192			1.85678			0.928391	−	0.371604i	$-0.121192\pi$
$797$	52.4192			1.85678			0.928391	+	0.371604i	$0.121192\pi$
$798$		−	0.359489i		−	0.0127258i
$799$			0.723434i			0.0255932i
$800$			1.19734i			0.0423322i
$801$		−	8.05722i		−	0.284688i
$802$	−13.4068			−0.473410
$803$	5.81143			0.205081
$804$			0.344398i			0.0121460i
$805$	0.722630			0.0254693
$806$	−5.94447	−	30.7378i	−0.209385	−	1.08269i
$807$	−18.4540			−0.649612
$808$		−	18.3060i		−	0.644003i
$809$	−14.2922			−0.502488			−0.251244	−	0.967924i	$-0.580840\pi$
$809$	−14.2922			−0.502488			−0.251244	+	0.967924i	$0.580840\pi$
$810$	−5.01033			−0.176045
$811$		−	5.57820i		−	0.195877i	−0.995192	−	0.0979386i	$-0.968775\pi$
$811$		−	5.57820i		−	0.195877i	0.995192	−	0.0979386i	$-0.0312249\pi$
$812$			0.0141529i			0.000496670i
$813$		−	18.7848i		−	0.658812i
$814$		−	7.95659i		−	0.278878i
$815$	−15.7747			−0.552565
$816$	3.33317			0.116684
$817$			8.02847i			0.280881i
$818$	−30.4232			−1.06372
$819$	0.412384	−	0.0797521i	0.0144099	−	0.00278676i
$820$	0.475686			0.0166117
$821$			17.1578i			0.598812i	0.954126	+	0.299406i	$0.0967886\pi$
$821$			17.1578i			0.598812i	−0.954126	+	0.299406i	$0.903211\pi$
$822$	24.6139			0.858509
$823$	−52.2374			−1.82088			−0.910441	−	0.413639i	$-0.864257\pi$
$823$	−52.2374			−1.82088			−0.910441	+	0.413639i	$0.864257\pi$
$824$			25.5801i			0.891126i
$825$		−	7.72604i		−	0.268986i
$826$			0.757668i			0.0263626i
$827$		−	48.2185i		−	1.67672i	−0.545115	−	0.838361i	$-0.683514\pi$
$827$		−	48.2185i		−	1.67672i	0.545115	−	0.838361i	$-0.316486\pi$
$828$	−0.0476409			−0.00165564
$829$	−42.7585			−1.48506			−0.742532	−	0.669810i	$-0.766375\pi$
$829$	−42.7585			−1.48506			−0.742532	+	0.669810i	$0.766375\pi$
$830$		−	34.2374i		−	1.18840i
$831$	1.09827			0.0380986
$832$	−5.54978	−	28.6969i	−0.192404	−	0.994887i
$833$	5.90371			0.204552
$834$			19.4618i			0.673908i
$835$	72.0338			2.49283
$836$	−0.0601973			−0.00208197
$837$			6.18237i			0.213694i
$838$		−	32.9232i		−	1.13731i
$839$		−	2.06860i		−	0.0714161i	−0.999362	−	0.0357080i	$-0.988631\pi$
$839$		−	2.06860i		−	0.0714161i	0.999362	−	0.0357080i	$-0.0113686\pi$
$840$		−	1.18334i		−	0.0408291i
$841$	−9.33670			−0.321955
$842$	22.8697			0.788142
$843$		−	1.43331i		−	0.0493659i
$844$	0.424568			0.0146142
$845$	17.2907	+	43.0317i	0.594820	+	1.48034i
$846$	1.20240			0.0413393
$847$			0.116494i			0.00400278i
$848$	−47.6457			−1.63616
$849$	−15.9363			−0.546934
$850$			9.16953i			0.314512i
$851$		−	9.85083i		−	0.337682i
$852$			0.107838i			0.00369448i
$853$		−	1.37770i		−	0.0471715i	−0.999722	−	0.0235857i	$-0.992492\pi$
$853$		−	1.37770i		−	0.0471715i	0.999722	−	0.0235857i	$-0.00750827\pi$
$854$	−2.10744			−0.0721152
$855$	−7.83808			−0.268057
$856$		−	23.1268i		−	0.790459i
$857$	−13.5188			−0.461793			−0.230897	−	0.972978i	$-0.574166\pi$
$857$	−13.5188			−0.461793			−0.230897	+	0.972978i	$0.574166\pi$
$858$	0.961520	+	4.97185i	0.0328258	+	0.169736i
$859$	−42.0852			−1.43593			−0.717964	−	0.696080i	$-0.754926\pi$
$859$	−42.0852			−1.43593			−0.717964	+	0.696080i	$0.754926\pi$
$860$			0.357134i			0.0121782i
$861$	−0.566973			−0.0193224
$862$	18.9718			0.646183
$863$		−	57.4664i		−	1.95618i	−0.208187	−	0.978089i	$-0.566756\pi$
$863$		−	57.4664i		−	1.95618i	0.208187	−	0.978089i	$-0.433244\pi$
$864$			0.154974i			0.00527232i
$865$			51.2547i			1.74271i
$866$		−	27.0042i		−	0.917641i
$867$	16.2859			0.553099
$868$	−0.0197321			−0.000669751
$869$		−	7.74675i		−	0.262791i
$870$	−22.2175			−0.753243
$871$	44.4984	−	8.60567i	1.50777	−	0.291592i
$872$	−48.8551			−1.65444
$873$			15.3975i			0.521128i
$874$	5.36597			0.181507
$875$	1.13288			0.0382983
$876$		−	0.159220i		−	0.00537954i
$877$		−	12.7954i		−	0.432071i	−0.976386	−	0.216035i	$-0.930687\pi$
$877$		−	12.7954i		−	0.432071i	0.976386	−	0.216035i	$-0.0693126\pi$
$878$			46.5054i			1.56948i
$879$			1.99681i			0.0673507i
$880$	14.0713			0.474343
$881$	5.54981			0.186978			0.0934888	−	0.995620i	$-0.470198\pi$
$881$	5.54981			0.186978			0.0934888	+	0.995620i	$0.470198\pi$
$882$		−	9.81240i		−	0.330401i
$883$	49.8086			1.67619			0.838097	−	0.545522i	$-0.183668\pi$
$883$	49.8086			1.67619			0.838097	+	0.545522i	$0.183668\pi$
$884$	0.0158498	+	0.0819564i	0.000533086	+	0.00275649i
$885$	16.5197			0.555304
$886$		−	34.3359i		−	1.15354i
$887$	46.6657			1.56688			0.783441	−	0.621466i	$-0.213463\pi$
$887$	46.6657			1.56688			0.783441	+	0.621466i	$0.213463\pi$
$888$	−16.1312			−0.541327
$889$		−	1.02447i		−	0.0343596i
$890$			40.3694i			1.35318i
$891$		−	1.00000i		−	0.0335013i
$892$			0.671300i			0.0224768i
$893$	1.88101			0.0629456
$894$	−5.12225			−0.171314
$895$			50.7607i			1.69674i
$896$	1.29025			0.0431042
$897$	1.19043	+	6.15551i	0.0397473	+	0.205526i
$898$	37.9297			1.26573
$899$			27.4147i			0.914331i
$900$	−0.211676			−0.00705586
$901$	10.2072			0.340052
$902$		−	6.83563i		−	0.227602i
$903$		−	0.425671i		−	0.0141654i
$904$		−	0.385737i		−	0.0128294i
$905$		−	89.2469i		−	2.96667i
$906$	−7.53653			−0.250385
$907$	24.9093			0.827098			0.413549	−	0.910482i	$-0.364289\pi$
$907$	24.9093			0.827098			0.413549	+	0.910482i	$0.364289\pi$
$908$		−	0.112783i		−	0.00374282i
$909$	6.42887			0.213232
$910$	−2.06618	+	0.399584i	−0.0684932	+	0.0132461i
$911$	−43.9916			−1.45751			−0.728754	−	0.684775i	$-0.759900\pi$
$911$	−43.9916			−1.45751			−0.728754	+	0.684775i	$0.759900\pi$
$912$		−	8.66662i		−	0.286980i
$913$	6.83336			0.226151
$914$	7.68109			0.254068
$915$			45.9493i			1.51904i
$916$		−	0.404113i		−	0.0133523i
$917$		−	1.90328i		−	0.0628519i
$918$			1.18683i			0.0391714i
$919$	11.2861			0.372296			0.186148	−	0.982522i	$-0.440400\pi$
$919$	11.2861			0.372296			0.186148	+	0.982522i	$0.440400\pi$
$920$	17.6633			0.582341
$921$			2.99278i			0.0986154i
$922$	50.3082			1.65681
$923$	13.9334	−	2.69462i	0.458623	−	0.0886944i
$924$	0.00319167			0.000104998
$925$		−	43.7688i		−	1.43911i
$926$	−18.9480			−0.622670
$927$	−8.98347			−0.295056
$928$			0.687206i			0.0225586i
$929$			12.1766i			0.399501i	0.979847	+	0.199750i	$0.0640131\pi$
$929$			12.1766i			0.399501i	−0.979847	+	0.199750i	$0.935987\pi$
$930$		−	30.9757i		−	1.01573i
$931$		−	15.3503i		−	0.503087i
$932$	−0.484733			−0.0158779
$933$	−15.6120			−0.511114
$934$			5.70334i			0.186619i
$935$	−3.01451			−0.0985850
$936$	10.0799	−	1.94938i	0.329473	−	0.0637176i
$937$	−4.96791			−0.162295			−0.0811473	−	0.996702i	$-0.525858\pi$
$937$	−4.96791			−0.162295			−0.0811473	+	0.996702i	$0.525858\pi$
$938$			2.05669i			0.0671534i
$939$	−2.95682			−0.0964922
$940$	0.0836738			0.00272914
$941$			9.38881i			0.306067i	0.988221	+	0.153033i	$0.0489042\pi$
$941$			9.38881i			0.306067i	−0.988221	+	0.153033i	$0.951096\pi$
$942$		−	13.4467i		−	0.438117i
$943$		−	8.46300i		−	0.275593i
$944$			18.2660i			0.594506i
$945$	0.415576			0.0135187
$946$	5.13204			0.166857
$947$		−	15.2761i		−	0.496407i	−0.968708	−	0.248204i	$-0.920160\pi$
$947$		−	15.2761i		−	0.496407i	0.968708	−	0.248204i	$-0.0798402\pi$
$948$	−0.212243			−0.00689334
$949$	−20.5722	+	3.97852i	−0.667803	+	0.129148i
$950$	23.8418			0.773531
$951$			9.24823i			0.299895i
$952$	−0.280306			−0.00908477
$953$	−9.37320			−0.303628			−0.151814	−	0.988409i	$-0.548511\pi$
$953$	−9.37320			−0.303628			−0.151814	+	0.988409i	$0.548511\pi$
$954$		−	16.9651i		−	0.549266i
$955$			95.7979i			3.09995i
$956$		−	0.646794i		−	0.0209188i
$957$		−	4.43433i		−	0.143342i
$958$	35.1600			1.13597
$959$	−2.04157			−0.0659258
$960$		−	28.9190i		−	0.933358i
$961$	−7.22172			−0.232959
$962$	5.44710	+	28.1660i	0.175622	+	0.908109i
$963$	8.12190			0.261724
$964$			0.460763i			0.0148402i
$965$	45.6870			1.47072
$966$	−0.284504			−0.00915378
$967$		−	47.7147i		−	1.53440i	−0.641407	−	0.767201i	$-0.721649\pi$
$967$		−	47.7147i		−	1.53440i	0.641407	−	0.767201i	$-0.278351\pi$
$968$			2.84747i			0.0915211i
$969$			1.85666i			0.0596446i
$970$		−	77.1468i		−	2.47703i
$971$	−6.52662			−0.209449			−0.104725	−	0.994501i	$-0.533396\pi$
$971$	−6.52662			−0.209449			−0.104725	+	0.994501i	$0.533396\pi$
$972$	−0.0273977			−0.000878782
$973$		−	1.61424i		−	0.0517501i
$974$	33.7693			1.08204
$975$	5.28927	+	27.3499i	0.169392	+	0.875897i
$976$	−50.8065			−1.62628
$977$			27.6400i			0.884283i	0.896945	+	0.442141i	$0.145781\pi$
$977$			27.6400i			0.884283i	−0.896945	+	0.442141i	$0.854219\pi$
$978$	6.21062			0.198594
$979$	−8.05722			−0.257510
$980$		−	0.682836i		−	0.0218124i
$981$		−	17.1574i		−	0.547794i
$982$			23.8092i			0.759781i
$983$		−	12.5376i		−	0.399888i	−0.979807	−	0.199944i	$-0.935924\pi$
$983$		−	12.5376i		−	0.399888i	0.979807	−	0.199944i	$-0.0640760\pi$
$984$	−13.8585			−0.441794
$985$	53.7841			1.71370
$986$			5.26282i			0.167602i
$987$	−0.0997315			−0.00317449
$988$	0.213096	−	0.0412112i	0.00677949	−	0.00131110i
$989$	6.35383			0.202040
$990$			5.01033i			0.159239i
$991$	−42.7605			−1.35833			−0.679166	−	0.733984i	$-0.737659\pi$
$991$	−42.7605			−1.35833			−0.679166	+	0.733984i	$0.737659\pi$
$992$	−0.958106			−0.0304199
$993$		−	3.23991i		−	0.102815i
$994$			0.643994i			0.0204262i
$995$			45.7319i			1.44980i
$996$		−	0.187218i		−	0.00593224i
$997$	−21.9639			−0.695605			−0.347802	−	0.937568i	$-0.613072\pi$
$997$	−21.9639			−0.695605			−0.347802	+	0.937568i	$0.613072\pi$
$998$	26.9150			0.851980
$999$		−	5.66510i		−	0.179236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.a.298.3	✓	10
3.2	odd	2		1287.2.b.a.298.8		10
13.5	odd	4		5577.2.a.q.1.2		5
13.8	odd	4		5577.2.a.t.1.4		5
13.12	even	2	inner	429.2.b.a.298.8	yes	10
39.38	odd	2		1287.2.b.a.298.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.a.298.3	✓	10	1.1	even	1	trivial
429.2.b.a.298.8	yes	10	13.12	even	2	inner
1287.2.b.a.298.3		10	39.38	odd	2
1287.2.b.a.298.8		10	3.2	odd	2
5577.2.a.q.1.2		5	13.5	odd	4
5577.2.a.t.1.4		5	13.8	odd	4

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.40449i q^{2} -1.00000 q^{3} +0.0273977 q^{4} -3.56736i q^{5} +1.40449i q^{6} -0.116494i q^{7} -2.84747i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.40449i q^{2} -1.00000 q^{3} +0.0273977 q^{4} -3.56736i q^{5} +1.40449i q^{6} -0.116494i q^{7} -2.84747i q^{8} +1.00000 q^{9} -5.01033 q^{10} -1.00000i q^{11} -0.0273977 q^{12} +(0.684603 + 3.53996i) q^{13} -0.163615 q^{14} +3.56736i q^{15} -3.94445 q^{16} +0.845026 q^{17} -1.40449i q^{18} -2.19717i q^{19} -0.0977375i q^{20} +0.116494i q^{21} -1.40449 q^{22} -1.73886 q^{23} +2.84747i q^{24} -7.72604 q^{25} +(4.97185 - 0.961520i) q^{26} -1.00000 q^{27} -0.00319167i q^{28} -4.43433 q^{29} +5.01033 q^{30} -6.18237i q^{31} -0.154974i q^{32} +1.00000i q^{33} -1.18683i q^{34} -0.415576 q^{35} +0.0273977 q^{36} +5.66510i q^{37} -3.08590 q^{38} +(-0.684603 - 3.53996i) q^{39} -10.1579 q^{40} +4.86697i q^{41} +0.163615 q^{42} -3.65401 q^{43} -0.0273977i q^{44} -3.56736i q^{45} +2.44222i q^{46} +0.856108i q^{47} +3.94445 q^{48} +6.98643 q^{49} +10.8512i q^{50} -0.845026 q^{51} +(0.0187565 + 0.0969868i) q^{52} +12.0792 q^{53} +1.40449i q^{54} -3.56736 q^{55} -0.331713 q^{56} +2.19717i q^{57} +6.22799i q^{58} -4.63079i q^{59} +0.0977375i q^{60} +12.8805 q^{61} -8.68310 q^{62} -0.116494i q^{63} -8.10657 q^{64} +(12.6283 - 2.44222i) q^{65} +1.40449 q^{66} -12.5703i q^{67} +0.0231518 q^{68} +1.73886 q^{69} +0.583674i q^{70} -3.93603i q^{71} -2.84747i q^{72} +5.81143i q^{73} +7.95659 q^{74} +7.72604 q^{75} -0.0601973i q^{76} -0.116494 q^{77} +(-4.97185 + 0.961520i) q^{78} +7.74675 q^{79} +14.0713i q^{80} +1.00000 q^{81} +6.83563 q^{82} +6.83336i q^{83} +0.00319167i q^{84} -3.01451i q^{85} +5.13204i q^{86} +4.43433 q^{87} -2.84747 q^{88} -8.05722i q^{89} -5.01033 q^{90} +(0.412384 - 0.0797521i) q^{91} -0.0476409 q^{92} +6.18237i q^{93} +1.20240 q^{94} -7.83808 q^{95} +0.154974i q^{96} +15.3975i q^{97} -9.81240i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9} + 6 q^{12} + 12 q^{13} - 32 q^{14} + 6 q^{16} + 20 q^{17} - 2 q^{22} + 8 q^{23} - 14 q^{25} - 2 q^{26} - 10 q^{27} + 8 q^{29} - 6 q^{36} - 12 q^{39} - 20 q^{40} + 32 q^{42} - 24 q^{43} - 6 q^{48} - 26 q^{49} - 20 q^{51} - 48 q^{52} - 4 q^{53} + 4 q^{55} + 16 q^{56} + 36 q^{61} + 24 q^{62} + 50 q^{64} + 28 q^{65} + 2 q^{66} - 12 q^{68} - 8 q^{69} + 24 q^{74} + 14 q^{75} + 12 q^{77} + 2 q^{78} + 36 q^{79} + 10 q^{81} - 20 q^{82} - 8 q^{87} - 6 q^{88} - 24 q^{91} - 8 q^{92} - 32 q^{94} + 44 q^{95}+O(q^{100}) \) 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9 + 6 * q^12 + 12 * q^13 - 32 * q^14 + 6 * q^16 + 20 * q^17 - 2 * q^22 + 8 * q^23 - 14 * q^25 - 2 * q^26 - 10 * q^27 + 8 * q^29 - 6 * q^36 - 12 * q^39 - 20 * q^40 + 32 * q^42 - 24 * q^43 - 6 * q^48 - 26 * q^49 - 20 * q^51 - 48 * q^52 - 4 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^61 + 24 * q^62 + 50 * q^64 + 28 * q^65 + 2 * q^66 - 12 * q^68 - 8 * q^69 + 24 * q^74 + 14 * q^75 + 12 * q^77 + 2 * q^78 + 36 * q^79 + 10 * q^81 - 20 * q^82 - 8 * q^87 - 6 * q^88 - 24 * q^91 - 8 * q^92 - 32 * q^94 + 44 * q^95

Introduction

L-functions

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