LMFDB - Embedded newform 588.2.b.b.391.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(391,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("588.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.3
Root			$0.856419 + 1.12541i$ of defining polynomial
Character	$\chi$	$=$	588.391
Dual form			588.2.b.b.391.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.856419 - 1.12541i) q^{2} +1.00000 q^{3} +(-0.533092 + 1.92764i) q^{4} -3.85529i q^{5} +(-0.856419 - 1.12541i) q^{6} +(2.62594 - 1.05092i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.856419 - 1.12541i) q^{2} +1.00000 q^{3} +(-0.533092 + 1.92764i) q^{4} -3.85529i q^{5} +(-0.856419 - 1.12541i) q^{6} +(2.62594 - 1.05092i) q^{8} +1.00000 q^{9} +(-4.33878 + 3.30174i) q^{10} -1.36225i q^{11} +(-0.533092 + 1.92764i) q^{12} +0.369798i q^{13} -3.85529i q^{15} +(-3.43162 - 2.05523i) q^{16} -4.50164i q^{17} +(-0.856419 - 1.12541i) q^{18} -0.0661849 q^{19} +(7.43162 + 2.05523i) q^{20} +(-1.53309 + 1.16666i) q^{22} +3.20894i q^{23} +(2.62594 - 1.05092i) q^{24} -9.86325 q^{25} +(0.416174 - 0.316702i) q^{26} +1.00000 q^{27} -3.11951 q^{29} +(-4.33878 + 3.30174i) q^{30} +6.03705 q^{31} +(0.625940 + 5.62212i) q^{32} -1.36225i q^{33} +(-5.06618 + 3.85529i) q^{34} +(-0.533092 + 1.92764i) q^{36} -5.49186 q^{37} +(0.0566820 + 0.0744851i) q^{38} +0.369798i q^{39} +(-4.05162 - 10.1238i) q^{40} -8.45017i q^{41} -6.30324i q^{43} +(2.62594 + 0.726207i) q^{44} -3.85529i q^{45} +(3.61137 - 2.74820i) q^{46} +1.42568 q^{47} +(-3.43162 - 2.05523i) q^{48} +(8.44708 + 11.1002i) q^{50} -4.50164i q^{51} +(-0.712838 - 0.197136i) q^{52} -2.54519 q^{53} +(-0.856419 - 1.12541i) q^{54} -5.25188 q^{55} -0.0661849 q^{57} +(2.67161 + 3.51072i) q^{58} -3.43757 q^{59} +(7.43162 + 2.05523i) q^{60} +1.43181i q^{61} +(-5.17024 - 6.79415i) q^{62} +(5.79112 - 5.51933i) q^{64} +1.42568 q^{65} +(-1.53309 + 1.16666i) q^{66} -9.76735i q^{67} +(8.67756 + 2.39979i) q^{68} +3.20894i q^{69} +12.9518i q^{71} +(2.62594 - 1.05092i) q^{72} +1.80161i q^{73} +(4.70334 + 6.18059i) q^{74} -9.86325 q^{75} +(0.0352827 - 0.127581i) q^{76} +(0.416174 - 0.316702i) q^{78} +12.4888i q^{79} +(-7.92349 + 13.2299i) q^{80} +1.00000 q^{81} +(-9.50990 + 7.23689i) q^{82} +12.2889 q^{83} -17.3551 q^{85} +(-7.09373 + 5.39822i) q^{86} -3.11951 q^{87} +(-1.43162 - 3.57719i) q^{88} +1.29270i q^{89} +(-4.33878 + 3.30174i) q^{90} +(-6.18569 - 1.71066i) q^{92} +6.03705 q^{93} +(-1.22098 - 1.60447i) q^{94} +0.255162i q^{95} +(0.625940 + 5.62212i) q^{96} +2.88422i q^{97} -1.36225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} + 2 q^{12} + 10 q^{16} - 2 q^{18} + 12 q^{19} + 22 q^{20} - 6 q^{22} + 4 q^{24} - 4 q^{25} - 6 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 12 q^{31} - 12 q^{32} - 28 q^{34} + 2 q^{36} - 12 q^{37} - 2 q^{38} + 4 q^{40} + 4 q^{44} - 12 q^{46} - 8 q^{47} + 10 q^{48} + 2 q^{50} + 4 q^{52} + 8 q^{53} - 2 q^{54} - 8 q^{55} + 12 q^{57} - 14 q^{58} + 28 q^{59} + 22 q^{60} - 48 q^{62} + 2 q^{64} - 8 q^{65} - 6 q^{66} + 16 q^{68} + 4 q^{72} + 38 q^{74} - 4 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{80} + 8 q^{81} - 4 q^{82} + 4 q^{83} - 32 q^{85} + 6 q^{86} - 16 q^{87} + 26 q^{88} - 8 q^{90} - 28 q^{92} - 12 q^{93} - 32 q^{94} - 12 q^{96}+O(q^{100}) $ 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 + 2 * q^12 + 10 * q^16 - 2 * q^18 + 12 * q^19 + 22 * q^20 - 6 * q^22 + 4 * q^24 - 4 * q^25 - 6 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 12 * q^31 - 12 * q^32 - 28 * q^34 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 4 * q^40 + 4 * q^44 - 12 * q^46 - 8 * q^47 + 10 * q^48 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 2 * q^54 - 8 * q^55 + 12 * q^57 - 14 * q^58 + 28 * q^59 + 22 * q^60 - 48 * q^62 + 2 * q^64 - 8 * q^65 - 6 * q^66 + 16 * q^68 + 4 * q^72 + 38 * q^74 - 4 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^80 + 8 * q^81 - 4 * q^82 + 4 * q^83 - 32 * q^85 + 6 * q^86 - 16 * q^87 + 26 * q^88 - 8 * q^90 - 28 * q^92 - 12 * q^93 - 32 * q^94 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.856419	−	1.12541i	−0.605580	−	0.795785i
$2$	−0.856419	−	1.12541i	−0.605580	−	0.795785i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.533092	+	1.92764i	−0.266546	+	0.963822i
$5$		−	3.85529i		−	1.72414i	−0.506791	−	0.862069i	$-0.669169\pi$
$5$		−	3.85529i		−	1.72414i	0.506791	−	0.862069i	$-0.330831\pi$
$6$	−0.856419	−	1.12541i	−0.349632	−	0.459446i
$7$		0			0
$7$		0			0
$8$	2.62594	−	1.05092i	0.928410	−	0.371558i
$9$	1.00000			0.333333
$10$	−4.33878	+	3.30174i	−1.37204	+	1.04410i
$11$		−	1.36225i		−	0.410735i	−0.978685	−	0.205367i	$-0.934161\pi$
$11$		−	1.36225i		−	0.410735i	0.978685	−	0.205367i	$-0.0658389\pi$
$12$	−0.533092	+	1.92764i	−0.153891	+	0.556463i
$13$			0.369798i			0.102563i	0.998684	+	0.0512817i	$0.0163306\pi$
$13$			0.369798i			0.102563i	−0.998684	+	0.0512817i	$0.983669\pi$
$14$		0			0
$15$		−	3.85529i		−	0.995431i
$16$	−3.43162	−	2.05523i	−0.857906	−	0.513806i
$17$		−	4.50164i		−	1.09181i	−0.837848	−	0.545904i	$-0.816186\pi$
$17$		−	4.50164i		−	1.09181i	0.837848	−	0.545904i	$-0.183814\pi$
$18$	−0.856419	−	1.12541i	−0.201860	−	0.265262i
$19$	−0.0661849			−0.0151839			−0.00759193	−	0.999971i	$-0.502417\pi$
$19$	−0.0661849			−0.0151839			−0.00759193	+	0.999971i	$0.502417\pi$
$20$	7.43162	+	2.05523i	1.66176	+	0.459562i
$21$		0			0
$22$	−1.53309	+	1.16666i	−0.326856	+	0.248733i
$23$			3.20894i			0.669110i	0.942376	+	0.334555i	$0.108586\pi$
$23$			3.20894i			0.669110i	−0.942376	+	0.334555i	$0.891414\pi$
$24$	2.62594	−	1.05092i	0.536018	−	0.214519i
$25$	−9.86325			−1.97265
$26$	0.416174	−	0.316702i	0.0816184	−	0.0621103i
$27$	1.00000			0.192450
$28$		0			0
$29$	−3.11951			−0.579278			−0.289639	−	0.957136i	$-0.593535\pi$
$29$	−3.11951			−0.579278			−0.289639	+	0.957136i	$0.593535\pi$
$30$	−4.33878	+	3.30174i	−0.792149	+	0.602813i
$31$	6.03705			1.08429			0.542143	−	0.840286i	$-0.317613\pi$
$31$	6.03705			1.08429			0.542143	+	0.840286i	$0.317613\pi$
$32$	0.625940	+	5.62212i	0.110652	+	0.993859i
$33$		−	1.36225i		−	0.237138i
$34$	−5.06618	+	3.85529i	−0.868844	+	0.661177i
$35$		0			0
$36$	−0.533092	+	1.92764i	−0.0888487	+	0.321274i
$37$	−5.49186			−0.902856			−0.451428	−	0.892307i	$-0.649085\pi$
$37$	−5.49186			−0.902856			−0.451428	+	0.892307i	$0.649085\pi$
$38$	0.0566820	+	0.0744851i	0.00919504	+	0.0120831i
$39$			0.369798i			0.0592150i
$40$	−4.05162	−	10.1238i	−0.640617	−	1.60071i
$41$		−	8.45017i		−	1.31970i	−0.751399	−	0.659848i	$-0.770621\pi$
$41$		−	8.45017i		−	1.31970i	0.751399	−	0.659848i	$-0.229379\pi$
$42$		0			0
$43$		−	6.30324i		−	0.961236i	−0.876930	−	0.480618i	$-0.840412\pi$
$43$		−	6.30324i		−	0.961236i	0.876930	−	0.480618i	$-0.159588\pi$
$44$	2.62594	+	0.726207i	0.395875	+	0.109480i
$45$		−	3.85529i		−	0.574712i
$46$	3.61137	−	2.74820i	0.532468	−	0.405200i
$47$	1.42568			0.207956			0.103978	−	0.994580i	$-0.466843\pi$
$47$	1.42568			0.207956			0.103978	+	0.994580i	$0.466843\pi$
$48$	−3.43162	−	2.05523i	−0.495312	−	0.296646i
$49$		0			0
$50$	8.44708	+	11.1002i	1.19460	+	1.56980i
$51$		−	4.50164i		−	0.630355i
$52$	−0.712838	−	0.197136i	−0.0988529	−	0.0273379i
$53$	−2.54519			−0.349608			−0.174804	−	0.984603i	$-0.555929\pi$
$53$	−2.54519			−0.349608			−0.174804	+	0.984603i	$0.555929\pi$
$54$	−0.856419	−	1.12541i	−0.116544	−	0.153149i
$55$	−5.25188			−0.708163
$56$		0			0
$57$	−0.0661849			−0.00876641
$58$	2.67161	+	3.51072i	0.350799	+	0.460981i
$59$	−3.43757			−0.447534			−0.223767	−	0.974643i	$-0.571835\pi$
$59$	−3.43757			−0.447534			−0.223767	+	0.974643i	$0.571835\pi$
$60$	7.43162	+	2.05523i	0.959419	+	0.265328i
$61$			1.43181i			0.183324i	0.995790	+	0.0916621i	$0.0292180\pi$
$61$			1.43181i			0.183324i	−0.995790	+	0.0916621i	$0.970782\pi$
$62$	−5.17024	−	6.79415i	−0.656622	−	0.862858i
$63$		0			0
$64$	5.79112	−	5.51933i	0.723890	−	0.689916i
$65$	1.42568			0.176833
$66$	−1.53309	+	1.16666i	−0.188711	+	0.143606i
$67$		−	9.76735i		−	1.19327i	−0.802512	−	0.596636i	$-0.796504\pi$
$67$		−	9.76735i		−	1.19327i	0.802512	−	0.596636i	$-0.203496\pi$
$68$	8.67756	+	2.39979i	1.05231	+	0.291017i
$69$			3.20894i			0.386311i
$70$		0			0
$71$			12.9518i			1.53710i	0.639792	+	0.768549i	$0.279021\pi$
$71$			12.9518i			1.53710i	−0.639792	+	0.768549i	$0.720979\pi$
$72$	2.62594	−	1.05092i	0.309470	−	0.123853i
$73$			1.80161i			0.210862i	0.994427	+	0.105431i	$0.0336222\pi$
$73$			1.80161i			0.210862i	−0.994427	+	0.105431i	$0.966378\pi$
$74$	4.70334	+	6.18059i	0.546752	+	0.718479i
$75$	−9.86325			−1.13891
$76$	0.0352827	−	0.127581i	0.00404720	−	0.0146345i
$77$		0			0
$78$	0.416174	−	0.316702i	0.0471224	−	0.0358594i
$79$			12.4888i			1.40510i	0.711636	+	0.702548i	$0.247954\pi$
$79$			12.4888i			1.40510i	−0.711636	+	0.702548i	$0.752046\pi$
$80$	−7.92349	+	13.2299i	−0.885873	+	1.47915i
$81$	1.00000			0.111111
$82$	−9.50990	+	7.23689i	−1.05019	+	0.799181i
$83$	12.2889			1.34888			0.674442	−	0.738327i	$-0.264384\pi$
$83$	12.2889			1.34888			0.674442	+	0.738327i	$0.264384\pi$
$84$		0			0
$85$	−17.3551			−1.88243
$86$	−7.09373	+	5.39822i	−0.764937	+	0.582105i
$87$	−3.11951			−0.334446
$88$	−1.43162	−	3.57719i	−0.152612	−	0.381330i
$89$			1.29270i			0.137026i	0.997650	+	0.0685128i	$0.0218254\pi$
$89$			1.29270i			0.137026i	−0.997650	+	0.0685128i	$0.978175\pi$
$90$	−4.33878	+	3.30174i	−0.457347	+	0.348034i
$91$		0			0
$92$	−6.18569	−	1.71066i	−0.644903	−	0.178349i
$93$	6.03705			0.626013
$94$	−1.22098	−	1.60447i	−0.125934	−	0.165488i
$95$			0.255162i			0.0261791i
$96$	0.625940	+	5.62212i	0.0638847	+	0.573805i
$97$			2.88422i			0.292848i	0.989222	+	0.146424i	$0.0467764\pi$
$97$			2.88422i			0.292848i	−0.989222	+	0.146424i	$0.953224\pi$
$98$		0			0
$99$		−	1.36225i		−	0.136912i
$100$	5.25802	−	19.0128i	0.525802	−	1.90128i
$101$		−	6.18861i		−	0.615790i	−0.951420	−	0.307895i	$-0.900376\pi$
$101$		−	6.18861i		−	0.615790i	0.951420	−	0.307895i	$-0.0996245\pi$
$102$	−5.06618	+	3.85529i	−0.501627	+	0.381730i
$103$	17.7927			1.75317			0.876583	−	0.481251i	$-0.159818\pi$
$103$	17.7927			1.75317			0.876583	+	0.481251i	$0.159818\pi$
$104$	0.388629	+	0.971066i	0.0381082	+	0.0952209i
$105$		0			0
$106$	2.17975	+	2.86438i	0.211716	+	0.278213i
$107$		−	6.09316i		−	0.589048i	−0.955644	−	0.294524i	$-0.904839\pi$
$107$		−	6.09316i		−	0.589048i	0.955644	−	0.294524i	$-0.0951611\pi$
$108$	−0.533092	+	1.92764i	−0.0512968	+	0.185488i
$109$	7.86325			0.753163			0.376581	−	0.926384i	$-0.377100\pi$
$109$	7.86325			0.753163			0.376581	+	0.926384i	$0.377100\pi$
$110$	4.49781	+	5.91051i	0.428849	+	0.563545i
$111$	−5.49186			−0.521264
$112$		0			0
$113$	4.70669			0.442768			0.221384	−	0.975187i	$-0.428943\pi$
$113$	4.70669			0.442768			0.221384	+	0.975187i	$0.428943\pi$
$114$	0.0566820	+	0.0744851i	0.00530876	+	0.00697617i
$115$	12.3714			1.15364
$116$	1.66299	−	6.01330i	0.154404	−	0.558321i
$117$			0.369798i			0.0341878i
$118$	2.94400	+	3.86868i	0.271017	+	0.356141i
$119$		0			0
$120$	−4.05162	−	10.1238i	−0.369860	−	0.924168i
$121$	9.14427			0.831297
$122$	1.61137	−	1.22623i	0.145887	−	0.111017i
$123$		−	8.45017i		−	0.761926i
$124$	−3.21830	+	11.6373i	−0.289012	+	1.04506i
$125$			18.7492i			1.67698i
$126$		0			0
$127$			2.70312i			0.239863i	0.992782	+	0.119931i	$0.0382675\pi$
$127$			2.70312i			0.239863i	−0.992782	+	0.119931i	$0.961733\pi$
$128$	−11.1711	−	1.79052i	−0.987397	−	0.158261i
$129$		−	6.30324i		−	0.554970i
$130$	−1.22098	−	1.60447i	−0.107087	−	0.140721i
$131$	7.77288			0.679120			0.339560	−	0.940584i	$-0.389722\pi$
$131$	7.77288			0.679120			0.339560	+	0.940584i	$0.389722\pi$
$132$	2.62594	+	0.726207i	0.228559	+	0.0632082i
$133$		0			0
$134$	−10.9923	+	8.36494i	−0.949587	+	0.722621i
$135$		−	3.85529i		−	0.331810i
$136$	−4.73088	−	11.8210i	−0.405670	−	1.01364i
$137$	2.85135			0.243608			0.121804	−	0.992554i	$-0.461132\pi$
$137$	2.85135			0.243608			0.121804	+	0.992554i	$0.461132\pi$
$138$	3.61137	−	2.74820i	0.307420	−	0.233942i
$139$	−7.15656			−0.607011			−0.303506	−	0.952830i	$-0.598157\pi$
$139$	−7.15656			−0.607011			−0.303506	+	0.952830i	$0.598157\pi$
$140$		0			0
$141$	1.42568			0.120064
$142$	14.5761	−	11.0922i	1.22320	−	0.930835i
$143$	0.503758			0.0421264
$144$	−3.43162	−	2.05523i	−0.285969	−	0.171269i
$145$			12.0266i			0.998755i
$146$	2.02754	−	1.54293i	0.167801	−	0.127694i
$147$		0			0
$148$	2.92767	−	10.5864i	0.240653	−	0.870193i
$149$	21.3551			1.74948			0.874739	−	0.484594i	$-0.161032\pi$
$149$	21.3551			1.74948			0.874739	+	0.484594i	$0.161032\pi$
$150$	8.44708	+	11.1002i	0.689701	+	0.906327i
$151$			22.2133i			1.80770i	0.427854	+	0.903848i	$0.359270\pi$
$151$			22.2133i			1.80770i	−0.427854	+	0.903848i	$0.640730\pi$
$152$	−0.173798	+	0.0695553i	−0.0140968	+	0.00564168i
$153$		−	4.50164i		−	0.363936i
$154$		0			0
$155$		−	23.2746i		−	1.86946i
$156$	−0.712838	−	0.197136i	−0.0570727	−	0.0157835i
$157$			5.44901i			0.434879i	0.976074	+	0.217439i	$0.0697704\pi$
$157$			5.44901i			0.434879i	−0.976074	+	0.217439i	$0.930230\pi$
$158$	14.0550	−	10.6956i	1.11815	−	0.850898i
$159$	−2.54519			−0.201846
$160$	21.6749	−	2.41318i	1.71355	−	0.190778i
$161$		0			0
$162$	−0.856419	−	1.12541i	−0.0672866	−	0.0884205i
$163$			4.75680i			0.372581i	0.982495	+	0.186291i	$0.0596466\pi$
$163$			4.75680i			0.372581i	−0.982495	+	0.186291i	$0.940353\pi$
$164$	16.2889	+	4.50472i	1.27195	+	0.351760i
$165$	−5.25188			−0.408858
$166$	−10.5245	−	13.8301i	−0.816857	−	1.07342i
$167$	14.0618			1.08814			0.544068	−	0.839041i	$-0.316884\pi$
$167$	14.0618			1.08814			0.544068	+	0.839041i	$0.316884\pi$
$168$		0			0
$169$	12.8632			0.989481
$170$	14.8632	+	19.5316i	1.13996	+	1.49801i
$171$	−0.0661849			−0.00506129
$172$	12.1504	+	3.36021i	0.926460	+	0.256214i
$173$			1.77713i			0.135113i	0.997715	+	0.0675564i	$0.0215203\pi$
$173$			1.77713i			0.135113i	−0.997715	+	0.0675564i	$0.978480\pi$
$174$	2.67161	+	3.51072i	0.202534	+	0.266147i
$175$		0			0
$176$	−2.79974	+	4.67474i	−0.211038	+	0.352372i
$177$	−3.43757			−0.258384
$178$	1.45481	−	1.10709i	0.109043	−	0.0829800i
$179$			3.25172i			0.243045i	0.992589	+	0.121522i	$0.0387776\pi$
$179$			3.25172i			0.243045i	−0.992589	+	0.121522i	$0.961222\pi$
$180$	7.43162	+	2.05523i	0.553921	+	0.153187i
$181$		−	23.5015i		−	1.74685i	−0.486954	−	0.873427i	$-0.661892\pi$
$181$		−	23.5015i		−	1.74685i	0.486954	−	0.873427i	$-0.338108\pi$
$182$		0			0
$183$			1.43181i			0.105842i
$184$	3.37235	+	8.42648i	0.248613	+	0.621208i
$185$			21.1727i			1.55665i
$186$	−5.17024	−	6.79415i	−0.379101	−	0.498171i
$187$	−6.13237			−0.448443
$188$	−0.760017	+	2.74820i	−0.0554300	+	0.200433i
$189$		0			0
$190$	0.287162	−	0.218526i	0.0208329	−	0.0158535i
$191$		−	23.8972i		−	1.72914i	−0.502511	−	0.864571i	$-0.667590\pi$
$191$		−	23.8972i		−	1.72914i	0.502511	−	0.864571i	$-0.332410\pi$
$192$	5.79112	−	5.51933i	0.417938	−	0.398323i
$193$	19.8751			1.43064			0.715322	−	0.698795i	$-0.246280\pi$
$193$	19.8751			1.43064			0.715322	+	0.698795i	$0.246280\pi$
$194$	3.24593	−	2.47010i	0.233044	−	0.177343i
$195$	1.42568			0.102095
$196$		0			0
$197$	19.0198			1.35511			0.677553	−	0.735474i	$-0.263041\pi$
$197$	19.0198			1.35511			0.677553	+	0.735474i	$0.263041\pi$
$198$	−1.53309	+	1.16666i	−0.108952	+	0.0829109i
$199$	−14.8514			−1.05278			−0.526392	−	0.850242i	$-0.676456\pi$
$199$	−14.8514			−1.05278			−0.526392	+	0.850242i	$0.676456\pi$
$200$	−25.9003	+	10.3655i	−1.83143	+	0.732954i
$201$		−	9.76735i		−	0.688935i
$202$	−6.96472	+	5.30004i	−0.490036	+	0.372910i
$203$		0			0
$204$	8.67756	+	2.39979i	0.607550	+	0.168019i
$205$	−32.5779			−2.27534
$206$	−15.2380	−	20.0241i	−1.06168	−	1.39514i
$207$			3.20894i			0.223037i
$208$	0.760017	−	1.26901i	0.0526977	−	0.0879898i
$209$			0.0901606i			0.00623654i
$210$		0			0
$211$			19.6676i			1.35398i	0.735994	+	0.676988i	$0.236715\pi$
$211$			19.6676i			1.35398i	−0.735994	+	0.676988i	$0.763285\pi$
$212$	1.35682	−	4.90621i	0.0931867	−	0.336960i
$213$			12.9518i			0.887443i
$214$	−6.85730	+	5.21830i	−0.468755	+	0.356716i
$215$	−24.3008			−1.65730
$216$	2.62594	−	1.05092i	0.178673	−	0.0715063i
$217$		0			0
$218$	−6.73424	−	8.84937i	−0.456100	−	0.599355i
$219$			1.80161i			0.121741i
$220$	2.79974	−	10.1238i	0.188758	−	0.682543i
$221$	1.66469			0.111979
$222$	4.70334	+	6.18059i	0.315667	+	0.414814i
$223$	−8.10323			−0.542633			−0.271316	−	0.962490i	$-0.587459\pi$
$223$	−8.10323			−0.542633			−0.271316	+	0.962490i	$0.587459\pi$
$224$		0			0
$225$	−9.86325			−0.657550
$226$	−4.03090	−	5.29696i	−0.268132	−	0.352348i
$227$	−12.0860			−0.802175			−0.401088	−	0.916040i	$-0.631368\pi$
$227$	−12.0860			−0.802175			−0.401088	+	0.916040i	$0.631368\pi$
$228$	0.0352827	−	0.127581i	0.00233665	−	0.00844926i
$229$			23.7826i			1.57160i	0.618482	+	0.785799i	$0.287748\pi$
$229$			23.7826i			1.57160i	−0.618482	+	0.785799i	$0.712252\pi$
$230$	−10.5951	−	13.9229i	−0.698620	−	0.918047i
$231$		0			0
$232$	−8.19164	+	3.27837i	−0.537808	+	0.215235i
$233$	−19.9294			−1.30562			−0.652810	−	0.757521i	$-0.726410\pi$
$233$	−19.9294			−1.30562			−0.652810	+	0.757521i	$0.726410\pi$
$234$	0.416174	−	0.316702i	0.0272061	−	0.0207034i
$235$		−	5.49639i		−	0.358545i
$236$	1.83254	−	6.62642i	0.119288	−	0.431343i
$237$			12.4888i			0.811233i
$238$		0			0
$239$			9.60993i			0.621615i	0.950473	+	0.310807i	$0.100599\pi$
$239$			9.60993i			0.621615i	−0.950473	+	0.310807i	$0.899401\pi$
$240$	−7.92349	+	13.2299i	−0.511459	+	0.853987i
$241$			10.4083i			0.670458i	0.942137	+	0.335229i	$0.108814\pi$
$241$			10.4083i			0.670458i	−0.942137	+	0.335229i	$0.891186\pi$
$242$	−7.83132	−	10.2910i	−0.503417	−	0.661533i
$243$	1.00000			0.0641500
$244$	−2.76002	−	0.763286i	−0.176692	−	0.0488644i
$245$		0			0
$246$	−9.50990	+	7.23689i	−0.606329	+	0.461407i
$247$		−	0.0244750i		−	0.00155731i
$248$	15.8529	−	6.34448i	1.00666	−	0.402875i
$249$	12.2889			0.778779
$250$	21.1006	−	16.0572i	1.33452	−	1.01555i
$251$	−20.6860			−1.30569			−0.652846	−	0.757491i	$-0.726425\pi$
$251$	−20.6860			−1.30569			−0.652846	+	0.757491i	$0.726425\pi$
$252$		0			0
$253$	4.37139			0.274827
$254$	3.04211	−	2.31500i	0.190879	−	0.145256i
$255$	−17.3551			−1.08682
$256$	7.55210	+	14.1055i	0.472006	+	0.881595i
$257$		−	17.7514i		−	1.10730i	−0.832749	−	0.553651i	$-0.813234\pi$
$257$		−	17.7514i		−	1.10730i	0.832749	−	0.553651i	$-0.186766\pi$
$258$	−7.09373	+	5.39822i	−0.441636	+	0.336078i
$259$		0			0
$260$	−0.760017	+	2.74820i	−0.0471343	+	0.170436i
$261$	−3.11951			−0.193093
$262$	−6.65684	−	8.74767i	−0.411261	−	0.540433i
$263$			2.08124i			0.128335i	0.997939	+	0.0641675i	$0.0204392\pi$
$263$			2.08124i			0.128335i	−0.997939	+	0.0641675i	$0.979561\pi$
$264$	−1.43162	−	3.57719i	−0.0881104	−	0.220161i
$265$			9.81243i			0.602773i
$266$		0			0
$267$			1.29270i			0.0791118i
$268$	18.8280	+	5.20690i	1.15010	+	0.318062i
$269$		−	3.55735i		−	0.216895i	−0.994102	−	0.108448i	$-0.965412\pi$
$269$		−	3.55735i		−	0.216895i	0.994102	−	0.108448i	$-0.0345880\pi$
$270$	−4.33878	+	3.30174i	−0.264050	+	0.200938i
$271$	−12.3680			−0.751301			−0.375650	−	0.926761i	$-0.622581\pi$
$271$	−12.3680			−0.751301			−0.375650	+	0.926761i	$0.622581\pi$
$272$	−9.25188	+	15.4479i	−0.560978	+	0.936668i
$273$		0			0
$274$	−2.44195	−	3.20894i	−0.147524	−	0.193859i
$275$			13.4362i			0.810236i
$276$	−6.18569	−	1.71066i	−0.372335	−	0.102970i
$277$	−11.8632			−0.712794			−0.356397	−	0.934335i	$-0.615995\pi$
$277$	−11.8632			−0.712794			−0.356397	+	0.934335i	$0.615995\pi$
$278$	6.12901	+	8.05406i	0.367594	+	0.483050i
$279$	6.03705			0.361429
$280$		0			0
$281$	−19.3428			−1.15390			−0.576948	−	0.816781i	$-0.695756\pi$
$281$	−19.3428			−1.15390			−0.576948	+	0.816781i	$0.695756\pi$
$282$	−1.22098	−	1.60447i	−0.0727081	−	0.0955448i
$283$	24.9413			1.48261			0.741304	−	0.671169i	$-0.234208\pi$
$283$	24.9413			1.48261			0.741304	+	0.671169i	$0.234208\pi$
$284$	−24.9665	−	6.90451i	−1.48149	−	0.409707i
$285$			0.255162i			0.0151145i
$286$	−0.431428	−	0.566934i	−0.0255109	−	0.0335235i
$287$		0			0
$288$	0.625940	+	5.62212i	0.0368838	+	0.331286i
$289$	−3.26474			−0.192044
$290$	13.5349	−	10.2998i	0.794794	−	0.604826i
$291$			2.88422i			0.169076i
$292$	−3.47286	−	0.960423i	−0.203234	−	0.0562045i
$293$		−	6.88234i		−	0.402071i	−0.979584	−	0.201035i	$-0.935569\pi$
$293$		−	6.88234i		−	0.402071i	0.979584	−	0.201035i	$-0.0644306\pi$
$294$		0			0
$295$			13.2528i			0.771610i
$296$	−14.4213	+	5.77153i	−0.838221	+	0.335463i
$297$		−	1.36225i		−	0.0790459i
$298$	−18.2889	−	24.0332i	−1.05945	−	1.39221i
$299$	−1.18666			−0.0686262
$300$	5.25802	−	19.0128i	0.303572	−	1.09771i
$301$		0			0
$302$	24.9991	−	19.0239i	1.43854	−	1.09470i
$303$		−	6.18861i		−	0.355526i
$304$	0.227122	+	0.136025i	0.0130263	+	0.00780156i
$305$	5.52003			0.316076
$306$	−5.06618	+	3.85529i	−0.289615	+	0.220392i
$307$	17.4213			0.994286			0.497143	−	0.867669i	$-0.334382\pi$
$307$	17.4213			0.994286			0.497143	+	0.867669i	$0.334382\pi$
$308$		0			0
$309$	17.7927			1.01219
$310$	−26.1934	+	19.9328i	−1.48769	+	1.13211i
$311$	−25.1161			−1.42420			−0.712101	−	0.702077i	$-0.752256\pi$
$311$	−25.1161			−1.42420			−0.712101	+	0.702077i	$0.752256\pi$
$312$	0.388629	+	0.971066i	0.0220018	+	0.0549758i
$313$		−	22.0965i		−	1.24897i	−0.781038	−	0.624484i	$-0.785309\pi$
$313$		−	22.0965i		−	1.24897i	0.781038	−	0.624484i	$-0.214691\pi$
$314$	6.13237	−	4.66664i	0.346070	−	0.263354i
$315$		0			0
$316$	−24.0739	−	6.65767i	−1.35426	−	0.374523i
$317$	−1.62327			−0.0911718			−0.0455859	−	0.998960i	$-0.514515\pi$
$317$	−1.62327			−0.0911718			−0.0455859	+	0.998960i	$0.514515\pi$
$318$	2.17975	+	2.86438i	0.122234	+	0.160626i
$319$			4.24956i			0.237930i
$320$	−21.2786	−	22.3264i	−1.18951	−	1.24809i
$321$		−	6.09316i		−	0.340087i
$322$		0			0
$323$			0.297941i			0.0165779i
$324$	−0.533092	+	1.92764i	−0.0296162	+	0.107091i
$325$		−	3.64741i		−	0.202322i
$326$	5.35335	−	4.07381i	0.296494	−	0.225628i
$327$	7.86325			0.434839
$328$	−8.88049	−	22.1896i	−0.490343	−	1.22522i
$329$		0			0
$330$	4.49781	+	5.91051i	0.247596	+	0.325363i
$331$			26.6677i			1.46579i	0.680342	+	0.732894i	$0.261831\pi$
$331$			26.6677i			1.46579i	−0.680342	+	0.732894i	$0.738169\pi$
$332$	−6.55113	+	23.6887i	−0.359540	+	1.30009i
$333$	−5.49186			−0.300952
$334$	−12.0428	−	15.8253i	−0.658953	−	0.865921i
$335$	−37.6559			−2.05736
$336$		0			0
$337$	29.8426			1.62563			0.812815	−	0.582522i	$-0.197934\pi$
$337$	29.8426			1.62563			0.812815	+	0.582522i	$0.197934\pi$
$338$	−11.0163	−	14.4764i	−0.599210	−	0.787414i
$339$	4.70669			0.255632
$340$	9.25188	−	33.4545i	0.501754	−	1.81432i
$341$		−	8.22399i		−	0.445354i
$342$	0.0566820	+	0.0744851i	0.00306501	+	0.00402769i
$343$		0			0
$344$	−6.62423	−	16.5519i	−0.357155	−	0.892421i
$345$	12.3714			0.666053
$346$	2.00000	−	1.52197i	0.107521	−	0.0818216i
$347$		−	0.947375i		−	0.0508578i	−0.999677	−	0.0254289i	$-0.991905\pi$
$347$		−	0.947375i		−	0.0508578i	0.999677	−	0.0254289i	$-0.00809514\pi$
$348$	1.66299	−	6.01330i	0.0891455	−	0.322347i
$349$		−	6.41788i		−	0.343541i	−0.985137	−	0.171771i	$-0.945051\pi$
$349$		−	6.41788i		−	0.343541i	0.985137	−	0.171771i	$-0.0549488\pi$
$350$		0			0
$351$			0.369798i			0.0197383i
$352$	7.65875	−	0.852688i	0.408213	−	0.0454484i
$353$		−	13.8733i		−	0.738401i	−0.929350	−	0.369200i	$-0.879632\pi$
$353$		−	13.8733i		−	0.738401i	0.929350	−	0.369200i	$-0.120368\pi$
$354$	2.94400	+	3.86868i	0.156472	+	0.205618i
$355$	49.9330			2.65017
$356$	−2.49186	−	0.689127i	−0.132068	−	0.0365237i
$357$		0			0
$358$	3.65951	−	2.78483i	0.193411	−	0.147183i
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$	−4.05162	−	10.1238i	−0.213539	−	0.533569i
$361$	−18.9956			−0.999769
$362$	−26.4488	+	20.1272i	−1.39012	+	1.05786i
$363$	9.14427			0.479950
$364$		0			0
$365$	6.94571			0.363555
$366$	1.61137	−	1.22623i	0.0842277	−	0.0640960i
$367$	−19.3181			−1.00839			−0.504197	−	0.863588i	$-0.668212\pi$
$367$	−19.3181			−1.00839			−0.504197	+	0.863588i	$0.668212\pi$
$368$	6.59509	−	11.0119i	0.343793	−	0.574034i
$369$		−	8.45017i		−	0.439898i
$370$	23.8280	−	18.1327i	1.23876	−	0.942675i
$371$		0			0
$372$	−3.21830	+	11.6373i	−0.166861	+	0.603365i
$373$	11.2766			0.583882			0.291941	−	0.956436i	$-0.405699\pi$
$373$	11.2766			0.583882			0.291941	+	0.956436i	$0.405699\pi$
$374$	5.25188	+	6.90143i	0.271568	+	0.356864i
$375$			18.7492i			0.968206i
$376$	3.74374	−	1.49828i	0.193069	−	0.0772678i
$377$		−	1.15359i		−	0.0594128i
$378$		0			0
$379$		−	25.1457i		−	1.29165i	−0.763486	−	0.645824i	$-0.776514\pi$
$379$		−	25.1457i		−	1.29165i	0.763486	−	0.645824i	$-0.223486\pi$
$380$	−0.491862	−	0.136025i	−0.0252320	−	0.00697793i
$381$			2.70312i			0.138485i
$382$	−26.8942	+	20.4660i	−1.37602	+	1.04713i
$383$	−17.7645			−0.907724			−0.453862	−	0.891072i	$-0.649954\pi$
$383$	−17.7645			−0.907724			−0.453862	+	0.891072i	$0.649954\pi$
$384$	−11.1711	−	1.79052i	−0.570074	−	0.0913721i
$385$		0			0
$386$	−17.0215	−	22.3677i	−0.866369	−	1.13848i
$387$		−	6.30324i		−	0.320412i
$388$	−5.55975	−	1.53756i	−0.282254	−	0.0780576i
$389$	14.1447			0.717163			0.358581	−	0.933498i	$-0.383261\pi$
$389$	14.1447			0.717163			0.358581	+	0.933498i	$0.383261\pi$
$390$	−1.22098	−	1.60447i	−0.0618266	−	0.0812455i
$391$	14.4455			0.730539
$392$		0			0
$393$	7.77288			0.392090
$394$	−16.2889	−	21.4051i	−0.820624	−	1.07837i
$395$	48.1478			2.42258
$396$	2.62594	+	0.726207i	0.131958	+	0.0364933i
$397$		−	12.6507i		−	0.634919i	−0.948272	−	0.317460i	$-0.897170\pi$
$397$		−	12.6507i		−	0.634919i	0.948272	−	0.317460i	$-0.102830\pi$
$398$	12.7190	+	16.7139i	0.637545	+	0.837790i
$399$		0			0
$400$	33.8470	+	20.2712i	1.69235	+	1.01356i
$401$	−24.7808			−1.23749			−0.618747	−	0.785591i	$-0.712359\pi$
$401$	−24.7808			−1.23749			−0.618747	+	0.785591i	$0.712359\pi$
$402$	−10.9923	+	8.36494i	−0.548244	+	0.417205i
$403$			2.23249i			0.111208i
$404$	11.9294	+	3.29910i	0.593512	+	0.164136i
$405$		−	3.85529i		−	0.191571i
$406$		0			0
$407$			7.48131i			0.370835i
$408$	−4.73088	−	11.8210i	−0.234213	−	0.585228i
$409$			5.79664i			0.286625i	0.989677	+	0.143313i	$0.0457754\pi$
$409$			5.79664i			0.286625i	−0.989677	+	0.143313i	$0.954225\pi$
$410$	27.9003	+	36.6634i	1.37790	+	1.81068i
$411$	2.85135			0.140647
$412$	−9.48515	+	34.2980i	−0.467300	+	1.68974i
$413$		0			0
$414$	3.61137	−	2.74820i	0.177489	−	0.135067i
$415$		−	47.3774i		−	2.32566i
$416$	−2.07905	+	0.231471i	−0.101934	+	0.0113488i
$417$	−7.15656			−0.350458
$418$	0.101468	−	0.0772153i	0.00496294	−	0.00377672i
$419$	2.42966			0.118697			0.0593484	−	0.998237i	$-0.481098\pi$
$419$	2.42966			0.118697			0.0593484	+	0.998237i	$0.481098\pi$
$420$		0			0
$421$	−25.9373			−1.26411			−0.632054	−	0.774924i	$-0.717788\pi$
$421$	−25.9373			−1.26411			−0.632054	+	0.774924i	$0.717788\pi$
$422$	22.1341	−	16.8437i	1.07747	−	0.819940i
$423$	1.42568			0.0693188
$424$	−6.68350	+	2.67480i	−0.324580	+	0.129900i
$425$			44.4008i			2.15375i
$426$	14.5761	−	11.0922i	0.706214	−	0.537418i
$427$		0			0
$428$	11.7454	+	3.24822i	0.567738	+	0.157009i
$429$	0.503758			0.0243217
$430$	20.8117	+	27.3484i	1.00363	+	1.31886i
$431$			14.7548i			0.710715i	0.934730	+	0.355358i	$0.115641\pi$
$431$			14.7548i			0.710715i	−0.934730	+	0.355358i	$0.884359\pi$
$432$	−3.43162	−	2.05523i	−0.165104	−	0.0988821i
$433$			35.7396i			1.71754i	0.512364	+	0.858769i	$0.328770\pi$
$433$			35.7396i			1.71754i	−0.512364	+	0.858769i	$0.671230\pi$
$434$		0			0
$435$			12.0266i			0.576632i
$436$	−4.19184	+	15.1575i	−0.200753	+	0.725915i
$437$		−	0.212383i		−	0.0101597i
$438$	2.02754	−	1.54293i	0.0968798	−	0.0737240i
$439$	−19.8385			−0.946840			−0.473420	−	0.880837i	$-0.656981\pi$
$439$	−19.8385			−0.946840			−0.473420	+	0.880837i	$0.656981\pi$
$440$	−13.7911	+	5.51933i	−0.657466	+	0.263124i
$441$		0			0
$442$	−1.42568	−	1.87346i	−0.0678125	−	0.0891116i
$443$			18.9807i			0.901800i	0.892574	+	0.450900i	$0.148897\pi$
$443$			18.9807i			0.901800i	−0.892574	+	0.450900i	$0.851103\pi$
$444$	2.92767	−	10.5864i	0.138941	−	0.502406i
$445$	4.98372			0.236251
$446$	6.93976	+	9.11945i	0.328607	+	0.431819i
$447$	21.3551			1.01006
$448$		0			0
$449$	−25.2845			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$449$	−25.2845			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$450$	8.44708	+	11.1002i	0.398199	+	0.523268i
$451$	−11.5113			−0.542045
$452$	−2.50910	+	9.07283i	−0.118018	+	0.426750i
$453$			22.2133i			1.04367i
$454$	10.3507	+	13.6017i	0.485781	+	0.638359i
$455$		0			0
$456$	−0.173798	+	0.0695553i	−0.00813882	+	0.00325723i
$457$	22.9674			1.07437			0.537186	−	0.843464i	$-0.319487\pi$
$457$	22.9674			1.07437			0.537186	+	0.843464i	$0.319487\pi$
$458$	26.7651	−	20.3679i	1.25065	−	0.951728i
$459$		−	4.50164i		−	0.210118i
$460$	−6.59509	+	23.8476i	−0.307498	+	1.11190i
$461$			2.95838i			0.137786i	0.997624	+	0.0688928i	$0.0219466\pi$
$461$			2.95838i			0.137786i	−0.997624	+	0.0688928i	$0.978053\pi$
$462$		0			0
$463$			3.30669i			0.153675i	0.997044	+	0.0768374i	$0.0244822\pi$
$463$			3.30669i			0.153675i	−0.997044	+	0.0768374i	$0.975518\pi$
$464$	10.7050	+	6.41129i	0.496966	+	0.297637i
$465$		−	23.2746i		−	1.07933i
$466$	17.0679	+	22.4288i	0.790657	+	1.03899i
$467$	11.9056			0.550927			0.275464	−	0.961311i	$-0.411169\pi$
$467$	11.9056			0.550927			0.275464	+	0.961311i	$0.411169\pi$
$468$	−0.712838	−	0.197136i	−0.0329510	−	0.00911263i
$469$		0			0
$470$	−6.18569	+	4.70722i	−0.285325	+	0.217128i
$471$			5.44901i			0.251077i
$472$	−9.02686	+	3.61263i	−0.415495	+	0.166285i
$473$	−8.58661			−0.394813
$474$	14.0550	−	10.6956i	0.645566	−	0.491266i
$475$	0.652798			0.0299524
$476$		0			0
$477$	−2.54519			−0.116536
$478$	10.8151	−	8.23013i	0.494671	−	0.376437i
$479$	−11.9037			−0.543895			−0.271947	−	0.962312i	$-0.587668\pi$
$479$	−11.9037			−0.543895			−0.271947	+	0.962312i	$0.587668\pi$
$480$	21.6749	−	2.41318i	0.989319	−	0.110146i
$481$		−	2.03088i		−	0.0926000i
$482$	11.7136	−	8.91387i	0.533540	−	0.406016i
$483$		0			0
$484$	−4.87474	+	17.6269i	−0.221579	+	0.801222i
$485$	11.1195			0.504911
$486$	−0.856419	−	1.12541i	−0.0388480	−	0.0510496i
$487$			7.50730i			0.340188i	0.985428	+	0.170094i	$0.0544072\pi$
$487$			7.50730i			0.340188i	−0.985428	+	0.170094i	$0.945593\pi$
$488$	1.50472	+	3.75984i	0.0681156	+	0.170200i
$489$			4.75680i			0.215110i
$490$		0			0
$491$		−	22.0031i		−	0.992988i	−0.868040	−	0.496494i	$-0.834620\pi$
$491$		−	22.0031i		−	0.992988i	0.868040	−	0.496494i	$-0.165380\pi$
$492$	16.2889	+	4.50472i	0.734362	+	0.203089i
$493$			14.0429i			0.632460i
$494$	−0.0275444	+	0.0209609i	−0.00123928	+	0.000943075i
$495$	−5.25188			−0.236054
$496$	−20.7169	−	12.4075i	−0.930215	−	0.557113i
$497$		0			0
$498$	−10.5245	−	13.8301i	−0.471613	−	0.619740i
$499$		−	1.41194i		−	0.0632070i	−0.999500	−	0.0316035i	$-0.989939\pi$
$499$		−	1.41194i		−	0.0632070i	0.999500	−	0.0316035i	$-0.0100614\pi$
$500$	−36.1418	−	9.99507i	−1.61631	−	0.446993i
$501$	14.0618			0.628235
$502$	17.7159	+	23.2803i	0.790700	+	1.03905i
$503$	26.2303			1.16955			0.584775	−	0.811196i	$-0.301183\pi$
$503$	26.2303			1.16955			0.584775	+	0.811196i	$0.301183\pi$
$504$		0			0
$505$	−23.8589			−1.06171
$506$	−3.74374	−	4.91960i	−0.166430	−	0.218703i
$507$	12.8632			0.571277
$508$	−5.21065	−	1.44101i	−0.231185	−	0.0639345i
$509$		−	5.06243i		−	0.224388i	−0.993686	−	0.112194i	$-0.964212\pi$
$509$		−	5.06243i		−	0.224388i	0.993686	−	0.112194i	$-0.0357878\pi$
$510$	14.8632	+	19.5316i	0.658156	+	0.864874i
$511$		0			0
$512$	9.40673	−	20.5794i	0.415723	−	0.909491i
$513$	−0.0661849			−0.00292214
$514$	−19.9776	+	15.2026i	−0.881173	+	0.670559i
$515$		−	68.5959i		−	3.02270i
$516$	12.1504	+	3.36021i	0.534892	+	0.147925i
$517$		−	1.94213i		−	0.0854149i
$518$		0			0
$519$			1.77713i			0.0780074i
$520$	3.74374	−	1.49828i	0.164174	−	0.0657038i
$521$			9.93093i			0.435082i	0.976051	+	0.217541i	$0.0698036\pi$
$521$			9.93093i			0.435082i	−0.976051	+	0.217541i	$0.930196\pi$
$522$	2.67161	+	3.51072i	0.116933	+	0.153660i
$523$	−31.3373			−1.37028			−0.685142	−	0.728409i	$-0.740260\pi$
$523$	−31.3373			−1.37028			−0.685142	+	0.728409i	$0.740260\pi$
$524$	−4.14366	+	14.9833i	−0.181017	+	0.654550i
$525$		0			0
$526$	2.34225	−	1.78242i	0.102127	−	0.0777171i
$527$		−	27.1766i		−	1.18383i
$528$	−2.79974	+	4.67474i	−0.121843	+	0.203442i
$529$	12.7027			0.552292
$530$	11.0430	−	8.40355i	0.479677	−	0.365027i
$531$	−3.43757			−0.149178
$532$		0			0
$533$	3.12485			0.135352
$534$	1.45481	−	1.10709i	0.0629560	−	0.0479085i
$535$	−23.4909			−1.01560
$536$	−10.2647	−	25.6485i	−0.443369	−	1.10784i
$537$			3.25172i			0.140322i
$538$	−4.00347	+	3.04658i	−0.172602	+	0.131347i
$539$		0			0
$540$	7.43162	+	2.05523i	0.319806	+	0.0884428i
$541$	−4.18626			−0.179982			−0.0899908	−	0.995943i	$-0.528684\pi$
$541$	−4.18626			−0.179982			−0.0899908	+	0.995943i	$0.528684\pi$
$542$	10.5922	+	13.9190i	0.454973	+	0.597874i
$543$		−	23.5015i		−	1.00855i
$544$	25.3087	−	2.81775i	1.08510	−	0.120810i
$545$		−	30.3151i		−	1.29856i
$546$		0			0
$547$		−	12.4674i		−	0.533067i	−0.963826	−	0.266533i	$-0.914122\pi$
$547$		−	12.4674i		−	0.533067i	0.963826	−	0.266533i	$-0.0858782\pi$
$548$	−1.52003	+	5.49639i	−0.0649327	+	0.234794i
$549$			1.43181i			0.0611081i
$550$	15.1213	−	11.5071i	0.644773	−	0.490663i
$551$	0.206464			0.00879568
$552$	3.37235	+	8.42648i	0.143537	+	0.358655i
$553$		0			0
$554$	10.1599	+	13.3510i	0.431653	+	0.567230i
$555$			21.1727i			0.898732i
$556$	3.81511	−	13.7953i	0.161797	−	0.585051i
$557$	−36.5487			−1.54862			−0.774309	−	0.632807i	$-0.781903\pi$
$557$	−36.5487			−1.54862			−0.774309	+	0.632807i	$0.781903\pi$
$558$	−5.17024	−	6.79415i	−0.218874	−	0.287619i
$559$	2.33092			0.0985876
$560$		0			0
$561$	−6.13237			−0.258909
$562$	16.5656	+	21.7686i	0.698776	+	0.918253i
$563$	42.7344			1.80104			0.900520	−	0.434814i	$-0.143186\pi$
$563$	42.7344			1.80104			0.900520	+	0.434814i	$0.143186\pi$
$564$	−0.760017	+	2.74820i	−0.0320025	+	0.115720i
$565$		−	18.1457i		−	0.763394i
$566$	−21.3602	−	28.0692i	−0.897838	−	1.17984i
$567$		0			0
$568$	13.6114	+	34.0107i	0.571120	+	1.42706i
$569$	21.4530			0.899356			0.449678	−	0.893191i	$-0.351539\pi$
$569$	21.4530			0.899356			0.449678	+	0.893191i	$0.351539\pi$
$570$	0.287162	−	0.218526i	0.0120279	−	0.00915303i
$571$		−	21.1713i		−	0.885991i	−0.896524	−	0.442996i	$-0.853916\pi$
$571$		−	21.1713i		−	0.885991i	0.896524	−	0.442996i	$-0.146084\pi$
$572$	−0.268550	+	0.971066i	−0.0112286	+	0.0406023i
$573$		−	23.8972i		−	0.998321i
$574$		0			0
$575$		−	31.6506i		−	1.31992i
$576$	5.79112	−	5.51933i	0.241297	−	0.229972i
$577$		−	4.73761i		−	0.197229i	−0.995126	−	0.0986146i	$-0.968559\pi$
$577$		−	4.73761i		−	0.197229i	0.995126	−	0.0986146i	$-0.0314411\pi$
$578$	2.79599	+	3.67417i	0.116298	+	0.152825i
$579$	19.8751			0.825983
$580$	−23.1830	−	6.41129i	−0.962623	−	0.266214i
$581$		0			0
$582$	3.24593	−	2.47010i	0.134548	−	0.102389i
$583$			3.46719i			0.143596i
$584$	1.89335	+	4.73091i	0.0783474	+	0.195766i
$585$	1.42568			0.0589445
$586$	−7.74545	+	5.89417i	−0.319962	+	0.243486i
$587$	−29.8450			−1.23184			−0.615918	−	0.787810i	$-0.711215\pi$
$587$	−29.8450			−1.23184			−0.615918	+	0.787810i	$0.711215\pi$
$588$		0			0
$589$	−0.399562			−0.0164636
$590$	14.9149	−	11.3500i	0.614035	−	0.467271i
$591$	19.0198			0.782370
$592$	18.8460	+	11.2870i	0.774566	+	0.463893i
$593$			26.5103i			1.08865i	0.838876	+	0.544323i	$0.183214\pi$
$593$			26.5103i			1.08865i	−0.838876	+	0.544323i	$0.816786\pi$
$594$	−1.53309	+	1.16666i	−0.0629035	+	0.0478686i
$595$		0			0
$596$	−11.3842	+	41.1651i	−0.466317	+	1.68619i
$597$	−14.8514			−0.607825
$598$	1.01628	+	1.33548i	0.0415587	+	0.0546117i
$599$			20.7846i			0.849236i	0.905373	+	0.424618i	$0.139592\pi$
$599$			20.7846i			0.849236i	−0.905373	+	0.424618i	$0.860408\pi$
$600$	−25.9003	+	10.3655i	−1.05738	+	0.423171i
$601$		−	10.8255i		−	0.441581i	−0.975321	−	0.220790i	$-0.929136\pi$
$601$		−	10.8255i		−	0.441581i	0.975321	−	0.220790i	$-0.0708637\pi$
$602$		0			0
$603$		−	9.76735i		−	0.397757i
$604$	−42.8194	−	11.8418i	−1.74230	−	0.481834i
$605$		−	35.2538i		−	1.43327i
$606$	−6.96472	+	5.30004i	−0.282922	+	0.215300i
$607$	13.9066			0.564452			0.282226	−	0.959348i	$-0.408927\pi$
$607$	13.9066			0.564452			0.282226	+	0.959348i	$0.408927\pi$
$608$	−0.0414278	−	0.372099i	−0.00168012	−	0.0150906i
$609$		0			0
$610$	−4.72746	−	6.21230i	−0.191409	−	0.251529i
$611$			0.527212i			0.0213287i
$612$	8.67756	+	2.39979i	0.350769	+	0.0970057i
$613$	0.644889			0.0260468			0.0130234	−	0.999915i	$-0.495854\pi$
$613$	0.644889			0.0260468			0.0130234	+	0.999915i	$0.495854\pi$
$614$	−14.9199	−	19.6061i	−0.602119	−	0.791237i
$615$	−32.5779			−1.31367
$616$		0			0
$617$	12.3626			0.497701			0.248850	−	0.968542i	$-0.419947\pi$
$617$	12.3626			0.497701			0.248850	+	0.968542i	$0.419947\pi$
$618$	−15.2380	−	20.0241i	−0.612962	−	0.805486i
$619$	11.3975			0.458104			0.229052	−	0.973414i	$-0.426437\pi$
$619$	11.3975			0.458104			0.229052	+	0.973414i	$0.426437\pi$
$620$	44.8651	+	12.4075i	1.80182	+	0.498297i
$621$			3.20894i			0.128770i
$622$	21.5099	+	28.2659i	0.862469	+	1.13336i
$623$		0			0
$624$	0.760017	−	1.26901i	0.0304250	−	0.0508009i
$625$	22.9674			0.918698
$626$	−24.8676	+	18.9239i	−0.993909	+	0.756350i
$627$			0.0901606i			0.00360067i
$628$	−10.5038	−	2.90483i	−0.419146	−	0.115915i
$629$			24.7224i			0.985745i
$630$		0			0
$631$			10.8050i			0.430140i	0.976599	+	0.215070i	$0.0689979\pi$
$631$			10.8050i			0.430140i	−0.976599	+	0.215070i	$0.931002\pi$
$632$	13.1247	+	32.7947i	0.522074	+	1.30450i
$633$			19.6676i			0.781718i
$634$	1.39020	+	1.82684i	0.0552118	+	0.0725531i
$635$	10.4213			0.413557
$636$	1.35682	−	4.90621i	0.0538014	−	0.194544i
$637$		0			0
$638$	4.78250	−	3.63941i	0.189341	−	0.144085i
$639$			12.9518i			0.512366i
$640$	−6.90297	+	43.0679i	−0.272864	+	1.70241i
$641$	2.25324			0.0889975			0.0444988	−	0.999009i	$-0.485831\pi$
$641$	2.25324			0.0889975			0.0444988	+	0.999009i	$0.485831\pi$
$642$	−6.85730	+	5.21830i	−0.270636	+	0.205950i
$643$	−22.0574			−0.869860			−0.434930	−	0.900464i	$-0.643227\pi$
$643$	−22.0574			−0.869860			−0.434930	+	0.900464i	$0.643227\pi$
$644$		0			0
$645$	−24.3008			−0.956844
$646$	0.335305	−	0.255162i	0.0131924	−	0.0100392i
$647$	4.52834			0.178027			0.0890137	−	0.996030i	$-0.471629\pi$
$647$	4.52834			0.178027			0.0890137	+	0.996030i	$0.471629\pi$
$648$	2.62594	−	1.05092i	0.103157	−	0.0412842i
$649$			4.68284i			0.183818i
$650$	−4.10483	+	3.12371i	−0.161004	+	0.122522i
$651$		0			0
$652$	−9.16942	−	2.53581i	−0.359102	−	0.0993101i
$653$	41.3498			1.61814			0.809071	−	0.587711i	$-0.199971\pi$
$653$	41.3498			1.61814			0.809071	+	0.587711i	$0.199971\pi$
$654$	−6.73424	−	8.84937i	−0.263330	−	0.346038i
$655$		−	29.9667i		−	1.17090i
$656$	−17.3670	+	28.9978i	−0.678068	+	1.13217i
$657$			1.80161i			0.0702874i
$658$		0			0
$659$			10.6413i			0.414526i	0.978285	+	0.207263i	$0.0664556\pi$
$659$			10.6413i			0.414526i	−0.978285	+	0.207263i	$0.933544\pi$
$660$	2.79974	−	10.1238i	0.108980	−	0.394067i
$661$		−	48.2516i		−	1.87677i	−0.345594	−	0.938384i	$-0.612323\pi$
$661$		−	48.2516i		−	1.87677i	0.345594	−	0.938384i	$-0.387677\pi$
$662$	30.0121	−	22.8387i	1.16645	−	0.887652i
$663$	1.66469			0.0646514
$664$	32.2700	−	12.9147i	1.25232	−	0.501189i
$665$		0			0
$666$	4.70334	+	6.18059i	0.182251	+	0.239493i
$667$		−	10.0103i		−	0.387601i
$668$	−7.49624	+	27.1062i	−0.290038	+	1.04877i
$669$	−8.10323			−0.313289
$670$	32.2493	+	42.3783i	1.24590	+	1.63722i
$671$	1.95049			0.0752977
$672$		0			0
$673$	−0.148647			−0.00572991			−0.00286496	−	0.999996i	$-0.500912\pi$
$673$	−0.148647			−0.00572991			−0.00286496	+	0.999996i	$0.500912\pi$
$674$	−25.5578	−	33.5851i	−0.984448	−	1.29365i
$675$	−9.86325			−0.379637
$676$	−6.85730	+	24.7958i	−0.263742	+	0.953683i
$677$		−	39.7142i		−	1.52634i	−0.646198	−	0.763170i	$-0.723642\pi$
$677$		−	39.7142i		−	1.52634i	0.646198	−	0.763170i	$-0.276358\pi$
$678$	−4.03090	−	5.29696i	−0.154806	−	0.203428i
$679$		0			0
$680$	−45.5735	+	18.2389i	−1.74766	+	0.699430i
$681$	−12.0860			−0.463136
$682$	−9.25535	+	7.04318i	−0.354406	+	0.269697i
$683$			42.6166i			1.63068i	0.578984	+	0.815339i	$0.303450\pi$
$683$			42.6166i			1.63068i	−0.578984	+	0.815339i	$0.696550\pi$
$684$	0.0352827	−	0.127581i	0.00134907	−	0.00487818i
$685$		−	10.9928i		−	0.420013i
$686$		0			0
$687$			23.7826i			0.907362i
$688$	−12.9546	+	21.6304i	−0.493889	+	0.824650i
$689$		−	0.941204i		−	0.0358570i
$690$	−10.5951	−	13.9229i	−0.403348	−	0.530035i
$691$	4.44633			0.169147			0.0845733	−	0.996417i	$-0.473047\pi$
$691$	4.44633			0.169147			0.0845733	+	0.996417i	$0.473047\pi$
$692$	−3.42568	−	0.947375i	−0.130225	−	0.0360138i
$693$		0			0
$694$	−1.06618	+	0.811350i	−0.0404718	+	0.0307984i
$695$			27.5906i			1.04657i
$696$	−8.19164	+	3.27837i	−0.310503	+	0.124266i
$697$	−38.0396			−1.44085
$698$	−7.22274	+	5.49639i	−0.273385	+	0.208042i
$699$	−19.9294			−0.753800
$700$		0			0
$701$	−24.9907			−0.943885			−0.471942	−	0.881629i	$-0.656447\pi$
$701$	−24.9907			−0.943885			−0.471942	+	0.881629i	$0.656447\pi$
$702$	0.416174	−	0.316702i	0.0157075	−	0.0119531i
$703$	0.363478			0.0137088
$704$	−7.51872	−	7.88897i	−0.283372	−	0.297327i
$705$		−	5.49639i		−	0.207006i
$706$	−15.6131	+	11.8814i	−0.587608	+	0.447161i
$707$		0			0
$708$	1.83254	−	6.62642i	0.0688712	−	0.249036i
$709$	18.1482			0.681570			0.340785	−	0.940141i	$-0.389307\pi$
$709$	18.1482			0.681570			0.340785	+	0.940141i	$0.389307\pi$
$710$	−42.7635	−	56.1950i	−1.60489	−	2.10896i
$711$			12.4888i			0.468365i
$712$	1.35853	+	3.39455i	0.0509130	+	0.127216i
$713$			19.3725i			0.725507i
$714$		0			0
$715$		−	1.94213i		−	0.0726316i
$716$	−6.26816	−	1.73347i	−0.234252	−	0.0647827i
$717$			9.60993i			0.358889i
$718$	7.79706	−	5.93345i	0.290984	−	0.221434i
$719$	41.1637			1.53515			0.767573	−	0.640961i	$-0.221464\pi$
$719$	41.1637			1.53515			0.767573	+	0.640961i	$0.221464\pi$
$720$	−7.92349	+	13.2299i	−0.295291	+	0.493049i
$721$		0			0
$722$	16.2682	+	21.3778i	0.605440	+	0.795601i
$723$			10.4083i			0.387089i
$724$	45.3026	+	12.5285i	1.68366	+	0.465618i
$725$	30.7685			1.14271
$726$	−7.83132	−	10.2910i	−0.290648	−	0.381936i
$727$	−5.77231			−0.214083			−0.107042	−	0.994255i	$-0.534138\pi$
$727$	−5.77231			−0.214083			−0.107042	+	0.994255i	$0.534138\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.94844	−	7.81677i	−0.220162	−	0.289312i
$731$	−28.3749			−1.04948
$732$	−2.76002	−	0.763286i	−0.102013	−	0.0282119i
$733$		−	7.66638i		−	0.283164i	−0.989927	−	0.141582i	$-0.954781\pi$
$733$		−	7.66638i		−	0.283164i	0.989927	−	0.141582i	$-0.0452189\pi$
$734$	16.5444	+	21.7407i	0.610663	+	0.802465i
$735$		0			0
$736$	−18.0410	+	2.00860i	−0.665001	+	0.0740381i
$737$	−13.3056			−0.490118
$738$	−9.50990	+	7.23689i	−0.350064	+	0.266394i
$739$		−	20.0633i		−	0.738041i	−0.929421	−	0.369021i	$-0.879693\pi$
$739$		−	20.0633i		−	0.738041i	0.929421	−	0.369021i	$-0.120307\pi$
$740$	−40.8135	−	11.2870i	−1.50033	−	0.414919i
$741$		−	0.0244750i		−	0.000899113i
$742$		0			0
$743$			8.26368i			0.303165i	0.988445	+	0.151583i	$0.0484369\pi$
$743$			8.26368i			0.303165i	−0.988445	+	0.151583i	$0.951563\pi$
$744$	15.8529	−	6.34448i	0.581196	−	0.232600i
$745$		−	82.3301i		−	3.01634i
$746$	−9.65753	−	12.6908i	−0.353587	−	0.464644i
$747$	12.2889			0.449628
$748$	3.26912	−	11.8210i	0.119531	−	0.432220i
$749$		0			0
$750$	21.1006	−	16.0572i	0.770484	−	0.586326i
$751$			27.0330i			0.986448i	0.869902	+	0.493224i	$0.164182\pi$
$751$			27.0330i			0.986448i	−0.869902	+	0.493224i	$0.835818\pi$
$752$	−4.89239	−	2.93009i	−0.178407	−	0.106849i
$753$	−20.6860			−0.753841
$754$	−1.29826	+	0.987954i	−0.0472798	+	0.0359792i
$755$	85.6388			3.11672
$756$		0			0
$757$	21.9417			0.797486			0.398743	−	0.917063i	$-0.369447\pi$
$757$	21.9417			0.797486			0.398743	+	0.917063i	$0.369447\pi$
$758$	−28.2992	+	21.5353i	−1.02787	+	0.782196i
$759$	4.37139			0.158671
$760$	0.268156	+	0.670040i	0.00972704	+	0.0243049i
$761$			1.18565i			0.0429798i	0.999769	+	0.0214899i	$0.00684097\pi$
$761$			1.18565i			0.0429798i	−0.999769	+	0.0214899i	$0.993159\pi$
$762$	3.04211	−	2.31500i	0.110204	−	0.0838636i
$763$		0			0
$764$	46.0653	+	12.7394i	1.66659	+	0.460896i
$765$	−17.3551			−0.627475
$766$	15.2139	+	19.9923i	0.549699	+	0.722353i
$767$		−	1.27121i		−	0.0459006i
$768$	7.55210	+	14.1055i	0.272513	+	0.508989i
$769$		−	19.0892i		−	0.688373i	−0.938901	−	0.344186i	$-0.888155\pi$
$769$		−	19.0892i		−	0.688373i	0.938901	−	0.344186i	$-0.111845\pi$
$770$		0			0
$771$		−	17.7514i		−	0.639301i
$772$	−10.5953	+	38.3122i	−0.381333	+	1.37889i
$773$			35.5517i			1.27871i	0.768913	+	0.639353i	$0.220798\pi$
$773$			35.5517i			1.27871i	−0.768913	+	0.639353i	$0.779202\pi$
$774$	−7.09373	+	5.39822i	−0.254979	+	0.194035i
$775$	−59.5449			−2.13892
$776$	3.03110	+	7.57379i	0.108810	+	0.271883i
$777$		0			0
$778$	−12.1138	−	15.9185i	−0.434299	−	0.570707i
$779$			0.559274i			0.0200381i
$780$	−0.760017	+	2.74820i	−0.0272130	+	0.0984013i
$781$	17.6436			0.631339
$782$	−12.3714	−	16.2571i	−0.442400	−	0.581352i
$783$	−3.11951			−0.111482
$784$		0			0
$785$	21.0075			0.749790
$786$	−6.65684	−	8.74767i	−0.237442	−	0.312019i
$787$	42.6036			1.51865			0.759327	−	0.650710i	$-0.225528\pi$
$787$	42.6036			1.51865			0.759327	+	0.650710i	$0.225528\pi$
$788$	−10.1393	+	36.6634i	−0.361198	+	1.30608i
$789$			2.08124i			0.0740942i
$790$	−41.2347	−	54.1860i	−1.46706	−	1.92785i
$791$		0			0
$792$	−1.43162	−	3.57719i	−0.0508706	−	0.127110i
$793$	−0.529479			−0.0188024
$794$	−14.2372	+	10.8343i	−0.505259	+	0.384494i
$795$			9.81243i			0.348011i
$796$	7.91714	−	28.6281i	0.280616	−	1.01470i
$797$			23.1179i			0.818879i	0.912337	+	0.409440i	$0.134276\pi$
$797$			23.1179i			0.818879i	−0.912337	+	0.409440i	$0.865724\pi$
$798$		0			0
$799$		−	6.41788i		−	0.227048i
$800$	−6.17380	−	55.4523i	−0.218277	−	1.96054i
$801$			1.29270i			0.0456752i
$802$	21.2227	+	27.8885i	0.749401	+	0.984778i
$803$	2.45424			0.0866084
$804$	18.8280	+	5.20690i	0.664011	+	0.183633i
$805$		0			0
$806$	2.51246	−	1.91194i	0.0884976	−	0.0673453i
$807$		−	3.55735i		−	0.125225i
$808$	−6.50376	−	16.2509i	−0.228801	−	0.571705i
$809$	−32.1704			−1.13105			−0.565525	−	0.824731i	$-0.691326\pi$
$809$	−32.1704			−1.13105			−0.565525	+	0.824731i	$0.691326\pi$
$810$	−4.33878	+	3.30174i	−0.152449	+	0.116011i
$811$	41.0797			1.44250			0.721251	−	0.692673i	$-0.243567\pi$
$811$	41.0797			1.44250			0.721251	+	0.692673i	$0.243567\pi$
$812$		0			0
$813$	−12.3680			−0.433764
$814$	8.41953	−	6.40713i	0.295104	−	0.224570i
$815$	18.3388			0.642381
$816$	−9.25188	+	15.4479i	−0.323881	+	0.540786i
$817$			0.417180i			0.0145953i
$818$	6.52359	−	4.96435i	0.228092	−	0.173574i
$819$		0			0
$820$	17.3670	−	62.7985i	0.606482	−	2.19302i
$821$	−29.2466			−1.02072			−0.510358	−	0.859962i	$-0.670487\pi$
$821$	−29.2466			−1.02072			−0.510358	+	0.859962i	$0.670487\pi$
$822$	−2.44195	−	3.20894i	−0.0851729	−	0.111925i
$823$			19.7212i			0.687437i	0.939073	+	0.343719i	$0.111687\pi$
$823$			19.7212i			0.687437i	−0.939073	+	0.343719i	$0.888313\pi$
$824$	46.7225	−	18.6988i	1.62766	−	0.651402i
$825$			13.4362i			0.467790i
$826$		0			0
$827$			16.1125i			0.560286i	0.959958	+	0.280143i	$0.0903819\pi$
$827$			16.1125i			0.560286i	−0.959958	+	0.280143i	$0.909618\pi$
$828$	−6.18569	−	1.71066i	−0.214968	−	0.0594496i
$829$			47.2337i			1.64050i	0.572008	+	0.820248i	$0.306165\pi$
$829$			47.2337i			1.64050i	−0.572008	+	0.820248i	$0.693835\pi$
$830$	−53.3189	+	40.5749i	−1.85073	+	1.40837i
$831$	−11.8632			−0.411532
$832$	2.04103	+	2.14154i	0.0707601	+	0.0742446i
$833$		0			0
$834$	6.12901	+	8.05406i	0.212230	+	0.278889i
$835$		−	54.2123i		−	1.87609i
$836$	−0.173798	−	0.0480639i	−0.00601092	−	0.00166233i
$837$	6.03705			0.208671
$838$	−2.08081	−	2.73437i	−0.0718804	−	0.0944571i
$839$	−25.3551			−0.875356			−0.437678	−	0.899132i	$-0.644199\pi$
$839$	−25.3551			−0.875356			−0.437678	+	0.899132i	$0.644199\pi$
$840$		0			0
$841$	−19.2687			−0.664437
$842$	22.2132	+	29.1901i	0.765519	+	1.00596i
$843$	−19.3428			−0.666202
$844$	−37.9122	−	10.4847i	−1.30499	−	0.360897i
$845$		−	49.5915i		−	1.70600i
$846$	−1.22098	−	1.60447i	−0.0419780	−	0.0551628i
$847$		0			0
$848$	8.73412	+	5.23093i	0.299931	+	0.179631i
$849$	24.9413			0.855984
$850$	49.9690	−	38.0257i	1.71392	−	1.30427i
$851$		−	17.6231i		−	0.604110i
$852$	−24.9665	−	6.90451i	−0.855338	−	0.236545i
$853$			24.3802i			0.834763i	0.908731	+	0.417382i	$0.137052\pi$
$853$			24.3802i			0.834763i	−0.908731	+	0.417382i	$0.862948\pi$
$854$		0			0
$855$			0.255162i			0.00872636i
$856$	−6.40345	−	16.0003i	−0.218865	−	0.546878i
$857$			25.9510i			0.886469i	0.896406	+	0.443235i	$0.146169\pi$
$857$			25.9510i			0.886469i	−0.896406	+	0.443235i	$0.853831\pi$
$858$	−0.431428	−	0.566934i	−0.0147287	−	0.0193548i
$859$	−56.8426			−1.93944			−0.969722	−	0.244211i	$-0.921471\pi$
$859$	−56.8426			−1.93944			−0.969722	+	0.244211i	$0.921471\pi$
$860$	12.9546	−	46.8433i	0.441748	−	1.59734i
$861$		0			0
$862$	16.6052	−	12.6363i	0.565576	−	0.430395i
$863$			17.6719i			0.601560i	0.953694	+	0.300780i	$0.0972470\pi$
$863$			17.6719i			0.601560i	−0.953694	+	0.300780i	$0.902753\pi$
$864$	0.625940	+	5.62212i	0.0212949	+	0.191268i
$865$	6.85135			0.232953
$866$	40.2217	−	30.6081i	1.36679	−	1.04011i
$867$	−3.26474			−0.110876
$868$		0			0
$869$	17.0129			0.577122
$870$	13.5349	−	10.2998i	0.458875	−	0.349197i
$871$	3.61194			0.122386
$872$	20.6484	−	8.26368i	0.699244	−	0.279844i
$873$			2.88422i			0.0976161i
$874$	−0.239018	+	0.181889i	−0.00808491	+	0.00615250i
$875$		0			0
$876$	−3.47286	−	0.960423i	−0.117337	−	0.0324497i
$877$	−12.3457			−0.416884			−0.208442	−	0.978035i	$-0.566839\pi$
$877$	−12.3457			−0.416884			−0.208442	+	0.978035i	$0.566839\pi$
$878$	16.9901	+	22.3264i	0.573387	+	0.753480i
$879$		−	6.88234i		−	0.232136i
$880$	18.0225	+	10.7938i	0.607538	+	0.363859i
$881$		−	33.0442i		−	1.11329i	−0.830751	−	0.556644i	$-0.812089\pi$
$881$		−	33.0442i		−	1.11329i	0.830751	−	0.556644i	$-0.187911\pi$
$882$		0			0
$883$		−	39.2680i		−	1.32147i	−0.750618	−	0.660737i	$-0.770244\pi$
$883$		−	39.2680i		−	1.32147i	0.750618	−	0.660737i	$-0.229756\pi$
$884$	−0.887436	+	3.20894i	−0.0298477	+	0.107928i
$885$			13.2528i			0.445489i
$886$	21.3611	−	16.2554i	0.717639	−	0.546112i
$887$	39.5033			1.32639			0.663196	−	0.748446i	$-0.269200\pi$
$887$	39.5033			1.32639			0.663196	+	0.748446i	$0.269200\pi$
$888$	−14.4213	+	5.77153i	−0.483947	+	0.193680i
$889$		0			0
$890$	−4.26816	−	5.60873i	−0.143069	−	0.188005i
$891$		−	1.36225i		−	0.0456372i
$892$	4.31977	−	15.6201i	0.144637	−	0.523001i
$893$	−0.0943583			−0.00315758
$894$	−18.2889	−	24.0332i	−0.611673	−	0.803792i
$895$	12.5363			0.419043
$896$		0			0
$897$	−1.18666			−0.0396214
$898$	21.6542	+	28.4555i	0.722609	+	0.949571i
$899$	−18.8326			−0.628103
$900$	5.25802	−	19.0128i	0.175267	−	0.633761i
$901$			11.4575i			0.381705i
$902$	9.85848	+	12.9549i	0.328251	+	0.431351i
$903$		0			0
$904$	12.3595	−	4.94638i	0.411071	−	0.164514i
$905$	−90.6052			−3.01182
$906$	24.9991	−	19.0239i	0.830539	−	0.632028i
$907$			5.15426i			0.171144i	0.996332	+	0.0855722i	$0.0272718\pi$
$907$			5.15426i			0.171144i	−0.996332	+	0.0855722i	$0.972728\pi$
$908$	6.44295	−	23.2975i	0.213817	−	0.773154i
$909$		−	6.18861i		−	0.205263i
$910$		0			0
$911$			25.8365i			0.856002i	0.903778	+	0.428001i	$0.140782\pi$
$911$			25.8365i			0.856002i	−0.903778	+	0.428001i	$0.859218\pi$
$912$	0.227122	+	0.136025i	0.00752076	+	0.00450424i
$913$		−	16.7406i		−	0.554034i
$914$	−19.6698	−	25.8478i	−0.650618	−	0.854969i
$915$	5.52003			0.182487
$916$	−45.8444	−	12.6783i	−1.51474	−	0.418903i
$917$		0			0
$918$	−5.06618	+	3.85529i	−0.167209	+	0.127243i
$919$		−	35.4355i		−	1.16891i	−0.811426	−	0.584455i	$-0.801308\pi$
$919$		−	35.4355i		−	1.16891i	0.811426	−	0.584455i	$-0.198692\pi$
$920$	32.4865	−	13.0014i	1.07105	−	0.428643i
$921$	17.4213			0.574051
$922$	3.32939	−	2.53361i	0.109648	−	0.0834401i
$923$	−4.78955			−0.157650
$924$		0			0
$925$	54.1676			1.78102
$926$	3.72138	−	2.83191i	0.122292	−	0.0930624i
$927$	17.7927			0.584388
$928$	−1.95262	−	17.5382i	−0.0640980	−	0.575721i
$929$			55.0160i			1.80502i	0.430674	+	0.902508i	$0.358276\pi$
$929$			55.0160i			1.80502i	−0.430674	+	0.902508i	$0.641724\pi$
$930$	−26.1934	+	19.9328i	−0.858916	+	0.653622i
$931$		0			0
$932$	10.6242	−	38.4169i	0.348008	−	1.25839i
$933$	−25.1161			−0.822264
$934$	−10.1962	−	13.3987i	−0.333630	−	0.438420i
$935$			23.6421i			0.773178i
$936$	0.388629	+	0.971066i	0.0127027	+	0.0317403i
$937$		−	6.90001i		−	0.225414i	−0.993628	−	0.112707i	$-0.964048\pi$
$937$		−	6.90001i		−	0.225414i	0.993628	−	0.112707i	$-0.0359521\pi$
$938$		0			0
$939$		−	22.0965i		−	0.721092i
$940$	10.5951	+	2.93009i	0.345574	+	0.0955689i
$941$		−	18.7751i		−	0.612051i	−0.952023	−	0.306026i	$-0.901001\pi$
$941$		−	18.7751i		−	0.612051i	0.952023	−	0.306026i	$-0.0989994\pi$
$942$	6.13237	−	4.66664i	0.199803	−	0.152047i
$943$	27.1161			0.883021
$944$	11.7965	+	7.06499i	0.383942	+	0.229946i
$945$		0			0
$946$	7.35374	+	9.66346i	0.239091	+	0.314186i
$947$		−	29.7833i		−	0.967827i	−0.875116	−	0.483913i	$-0.839215\pi$
$947$		−	29.7833i		−	0.967827i	0.875116	−	0.483913i	$-0.160785\pi$
$948$	−24.0739	−	6.65767i	−0.781884	−	0.216231i
$949$	−0.666230			−0.0216267
$950$	−0.559069	−	0.734665i	−0.0181386	−	0.0238357i
$951$	−1.62327			−0.0526380
$952$		0			0
$953$	−23.2676			−0.753711			−0.376856	−	0.926272i	$-0.622995\pi$
$953$	−23.2676			−0.753711			−0.376856	+	0.926272i	$0.622995\pi$
$954$	2.17975	+	2.86438i	0.0705719	+	0.0927376i
$955$	−92.1307			−2.98128
$956$	−18.5245	−	5.12298i	−0.599126	−	0.165689i
$957$			4.24956i			0.137369i
$958$	10.1946	+	13.3966i	0.329372	+	0.432823i
$959$		0			0
$960$	−21.2786	−	22.3264i	−0.686764	−	0.720582i
$961$	5.44594			0.175675
$962$	−2.28557	+	1.73928i	−0.0736897	+	0.0560767i
$963$		−	6.09316i		−	0.196349i
$964$	−20.0635	−	5.54859i	−0.646202	−	0.178708i
$965$		−	76.6244i		−	2.46663i
$966$		0			0
$967$		−	16.9691i		−	0.545690i	−0.962058	−	0.272845i	$-0.912035\pi$
$967$		−	16.9691i		−	0.545690i	0.962058	−	0.272845i	$-0.0879646\pi$
$968$	24.0123	−	9.60993i	0.771784	−	0.308875i
$969$			0.297941i			0.00957123i
$970$	−9.52296	−	12.5140i	−0.305764	−	0.401800i
$971$	−45.6698			−1.46561			−0.732806	−	0.680437i	$-0.761790\pi$
$971$	−45.6698			−1.46561			−0.732806	+	0.680437i	$0.761790\pi$
$972$	−0.533092	+	1.92764i	−0.0170989	+	0.0618292i
$973$		0			0
$974$	8.44878	−	6.42939i	0.270717	−	0.206011i
$975$		−	3.64741i		−	0.116810i
$976$	2.94269	−	4.91343i	0.0941932	−	0.157275i
$977$	−47.4204			−1.51711			−0.758557	−	0.651606i	$-0.774095\pi$
$977$	−47.4204			−1.51711			−0.758557	+	0.651606i	$0.774095\pi$
$978$	5.35335	−	4.07381i	0.171181	−	0.130266i
$979$	1.76098			0.0562812
$980$		0			0
$981$	7.86325			0.251054
$982$	−24.7625	+	18.8439i	−0.790205	+	0.601334i
$983$	−35.3912			−1.12880			−0.564402	−	0.825500i	$-0.690893\pi$
$983$	−35.3912			−1.12880			−0.564402	+	0.825500i	$0.690893\pi$
$984$	−8.88049	−	22.1896i	−0.283100	−	0.707380i
$985$		−	73.3268i		−	2.33639i
$986$	15.8040	−	12.0266i	0.503302	−	0.383005i
$987$		0			0
$988$	0.0471792	+	0.0130475i	0.00150097	+	0.000415095i
$989$	20.2267			0.643173
$990$	4.49781	+	5.91051i	0.142950	+	0.187848i
$991$			11.5627i			0.367301i	0.982992	+	0.183650i	$0.0587914\pi$
$991$			11.5627i			0.367301i	−0.982992	+	0.183650i	$0.941209\pi$
$992$	3.77883	+	33.9410i	0.119978	+	1.07763i
$993$			26.6677i			0.846274i
$994$		0			0
$995$			57.2563i			1.81515i
$996$	−6.55113	+	23.6887i	−0.207581	+	0.750604i
$997$			12.3359i			0.390680i	0.980736	+	0.195340i	$0.0625811\pi$
$997$			12.3359i			0.390680i	−0.980736	+	0.195340i	$0.937419\pi$
$998$	−1.58901	+	1.20921i	−0.0502991	+	0.0382769i
$999$	−5.49186			−0.173755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.b.b.391.3		8
3.2	odd	2		1764.2.b.i.1567.6		8
4.3	odd	2		588.2.b.a.391.4		8
7.2	even	3		84.2.o.a.31.2	yes	8
7.3	odd	6		84.2.o.b.19.4	yes	8
7.4	even	3		588.2.o.b.19.4		8
7.5	odd	6		588.2.o.d.31.2		8
7.6	odd	2		588.2.b.a.391.3		8
12.11	even	2		1764.2.b.j.1567.5		8
21.2	odd	6		252.2.bf.g.199.3		8
21.17	even	6		252.2.bf.f.19.1		8
21.20	even	2		1764.2.b.j.1567.6		8
28.3	even	6		84.2.o.a.19.2	✓	8
28.11	odd	6		588.2.o.d.19.2		8
28.19	even	6		588.2.o.b.31.4		8
28.23	odd	6		84.2.o.b.31.4	yes	8
28.27	even	2	inner	588.2.b.b.391.4		8
56.3	even	6		1344.2.bl.j.1279.4		8
56.37	even	6		1344.2.bl.j.703.4		8
56.45	odd	6		1344.2.bl.i.1279.4		8
56.51	odd	6		1344.2.bl.i.703.4		8
84.23	even	6		252.2.bf.f.199.1		8
84.59	odd	6		252.2.bf.g.19.3		8
84.83	odd	2		1764.2.b.i.1567.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.2	✓	8	28.3	even	6
84.2.o.a.31.2	yes	8	7.2	even	3
84.2.o.b.19.4	yes	8	7.3	odd	6
84.2.o.b.31.4	yes	8	28.23	odd	6
252.2.bf.f.19.1		8	21.17	even	6
252.2.bf.f.199.1		8	84.23	even	6
252.2.bf.g.19.3		8	84.59	odd	6
252.2.bf.g.199.3		8	21.2	odd	6
588.2.b.a.391.3		8	7.6	odd	2
588.2.b.a.391.4		8	4.3	odd	2
588.2.b.b.391.3		8	1.1	even	1	trivial
588.2.b.b.391.4		8	28.27	even	2	inner
588.2.o.b.19.4		8	7.4	even	3
588.2.o.b.31.4		8	28.19	even	6
588.2.o.d.19.2		8	28.11	odd	6
588.2.o.d.31.2		8	7.5	odd	6
1344.2.bl.i.703.4		8	56.51	odd	6
1344.2.bl.i.1279.4		8	56.45	odd	6
1344.2.bl.j.703.4		8	56.37	even	6
1344.2.bl.j.1279.4		8	56.3	even	6
1764.2.b.i.1567.5		8	84.83	odd	2
1764.2.b.i.1567.6		8	3.2	odd	2
1764.2.b.j.1567.5		8	12.11	even	2
1764.2.b.j.1567.6		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.856419 - 1.12541i) q^{2} +1.00000 q^{3} +(-0.533092 + 1.92764i) q^{4} -3.85529i q^{5} +(-0.856419 - 1.12541i) q^{6} +(2.62594 - 1.05092i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.856419 - 1.12541i) q^{2} +1.00000 q^{3} +(-0.533092 + 1.92764i) q^{4} -3.85529i q^{5} +(-0.856419 - 1.12541i) q^{6} +(2.62594 - 1.05092i) q^{8} +1.00000 q^{9} +(-4.33878 + 3.30174i) q^{10} -1.36225i q^{11} +(-0.533092 + 1.92764i) q^{12} +0.369798i q^{13} -3.85529i q^{15} +(-3.43162 - 2.05523i) q^{16} -4.50164i q^{17} +(-0.856419 - 1.12541i) q^{18} -0.0661849 q^{19} +(7.43162 + 2.05523i) q^{20} +(-1.53309 + 1.16666i) q^{22} +3.20894i q^{23} +(2.62594 - 1.05092i) q^{24} -9.86325 q^{25} +(0.416174 - 0.316702i) q^{26} +1.00000 q^{27} -3.11951 q^{29} +(-4.33878 + 3.30174i) q^{30} +6.03705 q^{31} +(0.625940 + 5.62212i) q^{32} -1.36225i q^{33} +(-5.06618 + 3.85529i) q^{34} +(-0.533092 + 1.92764i) q^{36} -5.49186 q^{37} +(0.0566820 + 0.0744851i) q^{38} +0.369798i q^{39} +(-4.05162 - 10.1238i) q^{40} -8.45017i q^{41} -6.30324i q^{43} +(2.62594 + 0.726207i) q^{44} -3.85529i q^{45} +(3.61137 - 2.74820i) q^{46} +1.42568 q^{47} +(-3.43162 - 2.05523i) q^{48} +(8.44708 + 11.1002i) q^{50} -4.50164i q^{51} +(-0.712838 - 0.197136i) q^{52} -2.54519 q^{53} +(-0.856419 - 1.12541i) q^{54} -5.25188 q^{55} -0.0661849 q^{57} +(2.67161 + 3.51072i) q^{58} -3.43757 q^{59} +(7.43162 + 2.05523i) q^{60} +1.43181i q^{61} +(-5.17024 - 6.79415i) q^{62} +(5.79112 - 5.51933i) q^{64} +1.42568 q^{65} +(-1.53309 + 1.16666i) q^{66} -9.76735i q^{67} +(8.67756 + 2.39979i) q^{68} +3.20894i q^{69} +12.9518i q^{71} +(2.62594 - 1.05092i) q^{72} +1.80161i q^{73} +(4.70334 + 6.18059i) q^{74} -9.86325 q^{75} +(0.0352827 - 0.127581i) q^{76} +(0.416174 - 0.316702i) q^{78} +12.4888i q^{79} +(-7.92349 + 13.2299i) q^{80} +1.00000 q^{81} +(-9.50990 + 7.23689i) q^{82} +12.2889 q^{83} -17.3551 q^{85} +(-7.09373 + 5.39822i) q^{86} -3.11951 q^{87} +(-1.43162 - 3.57719i) q^{88} +1.29270i q^{89} +(-4.33878 + 3.30174i) q^{90} +(-6.18569 - 1.71066i) q^{92} +6.03705 q^{93} +(-1.22098 - 1.60447i) q^{94} +0.255162i q^{95} +(0.625940 + 5.62212i) q^{96} +2.88422i q^{97} -1.36225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} + 2 q^{12} + 10 q^{16} - 2 q^{18} + 12 q^{19} + 22 q^{20} - 6 q^{22} + 4 q^{24} - 4 q^{25} - 6 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 12 q^{31} - 12 q^{32} - 28 q^{34} + 2 q^{36} - 12 q^{37} - 2 q^{38} + 4 q^{40} + 4 q^{44} - 12 q^{46} - 8 q^{47} + 10 q^{48} + 2 q^{50} + 4 q^{52} + 8 q^{53} - 2 q^{54} - 8 q^{55} + 12 q^{57} - 14 q^{58} + 28 q^{59} + 22 q^{60} - 48 q^{62} + 2 q^{64} - 8 q^{65} - 6 q^{66} + 16 q^{68} + 4 q^{72} + 38 q^{74} - 4 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{80} + 8 q^{81} - 4 q^{82} + 4 q^{83} - 32 q^{85} + 6 q^{86} - 16 q^{87} + 26 q^{88} - 8 q^{90} - 28 q^{92} - 12 q^{93} - 32 q^{94} - 12 q^{96}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 + 2 * q^12 + 10 * q^16 - 2 * q^18 + 12 * q^19 + 22 * q^20 - 6 * q^22 + 4 * q^24 - 4 * q^25 - 6 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 12 * q^31 - 12 * q^32 - 28 * q^34 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 4 * q^40 + 4 * q^44 - 12 * q^46 - 8 * q^47 + 10 * q^48 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 2 * q^54 - 8 * q^55 + 12 * q^57 - 14 * q^58 + 28 * q^59 + 22 * q^60 - 48 * q^62 + 2 * q^64 - 8 * q^65 - 6 * q^66 + 16 * q^68 + 4 * q^72 + 38 * q^74 - 4 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^80 + 8 * q^81 - 4 * q^82 + 4 * q^83 - 32 * q^85 + 6 * q^86 - 16 * q^87 + 26 * q^88 - 8 * q^90 - 28 * q^92 - 12 * q^93 - 32 * q^94 - 12 * q^96

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