LMFDB - Embedded newform 429.2.b.b.298.13

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 $ x^14 + 23x^12 + 201x^10 + 835x^8 + 1695x^6 + 1565x^4 + 511x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			298.13
Root			$2.53441i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.b.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.53441i q^{2} +1.00000 q^{3} -4.42325 q^{4} +3.70100i q^{5} +2.53441i q^{6} +0.957295i q^{7} -6.14151i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.53441i q^{2} +1.00000 q^{3} -4.42325 q^{4} +3.70100i q^{5} +2.53441i q^{6} +0.957295i q^{7} -6.14151i q^{8} +1.00000 q^{9} -9.37985 q^{10} -1.00000i q^{11} -4.42325 q^{12} +(-2.10857 - 2.92471i) q^{13} -2.42618 q^{14} +3.70100i q^{15} +6.71863 q^{16} +2.05542 q^{17} +2.53441i q^{18} +7.67886i q^{19} -16.3704i q^{20} +0.957295i q^{21} +2.53441 q^{22} +4.20997 q^{23} -6.14151i q^{24} -8.69737 q^{25} +(7.41243 - 5.34397i) q^{26} +1.00000 q^{27} -4.23435i q^{28} +1.97786 q^{29} -9.37985 q^{30} -10.5475i q^{31} +4.74476i q^{32} -1.00000i q^{33} +5.20928i q^{34} -3.54294 q^{35} -4.42325 q^{36} +8.30741i q^{37} -19.4614 q^{38} +(-2.10857 - 2.92471i) q^{39} +22.7297 q^{40} -5.23142i q^{41} -2.42618 q^{42} -5.26116 q^{43} +4.42325i q^{44} +3.70100i q^{45} +10.6698i q^{46} +1.24656i q^{47} +6.71863 q^{48} +6.08359 q^{49} -22.0427i q^{50} +2.05542 q^{51} +(9.32671 + 12.9367i) q^{52} +2.98297 q^{53} +2.53441i q^{54} +3.70100 q^{55} +5.87924 q^{56} +7.67886i q^{57} +5.01271i q^{58} +12.3548i q^{59} -16.3704i q^{60} -0.183851 q^{61} +26.7317 q^{62} +0.957295i q^{63} +1.41208 q^{64} +(10.8244 - 7.80379i) q^{65} +2.53441 q^{66} +1.40691i q^{67} -9.09163 q^{68} +4.20997 q^{69} -8.97928i q^{70} +12.1582i q^{71} -6.14151i q^{72} +3.32573i q^{73} -21.0544 q^{74} -8.69737 q^{75} -33.9655i q^{76} +0.957295 q^{77} +(7.41243 - 5.34397i) q^{78} -3.64911 q^{79} +24.8656i q^{80} +1.00000 q^{81} +13.2586 q^{82} +3.31957i q^{83} -4.23435i q^{84} +7.60710i q^{85} -13.3340i q^{86} +1.97786 q^{87} -6.14151 q^{88} -5.24302i q^{89} -9.37985 q^{90} +(2.79981 - 2.01852i) q^{91} -18.6217 q^{92} -10.5475i q^{93} -3.15929 q^{94} -28.4194 q^{95} +4.74476i q^{96} +9.82293i q^{97} +15.4183i q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9} - 18 q^{12} + 16 q^{14} + 34 q^{16} + 4 q^{17} + 6 q^{22} - 8 q^{23} - 26 q^{25} - 6 q^{26} + 14 q^{27} - 24 q^{29} - 8 q^{35} - 18 q^{36} - 32 q^{38} - 20 q^{40} + 16 q^{42} + 32 q^{43} + 34 q^{48} - 46 q^{49} + 4 q^{51} + 4 q^{52} + 20 q^{53} + 12 q^{55} - 32 q^{56} - 20 q^{61} + 72 q^{62} - 58 q^{64} + 12 q^{65} + 6 q^{66} - 20 q^{68} - 8 q^{69} - 26 q^{75} - 12 q^{77} - 6 q^{78} + 12 q^{79} + 14 q^{81} + 20 q^{82} - 24 q^{87} - 30 q^{88} + 16 q^{91} - 24 q^{92} + 64 q^{94} - 36 q^{95}+O(q^{100}) $ 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9 - 18 * q^12 + 16 * q^14 + 34 * q^16 + 4 * q^17 + 6 * q^22 - 8 * q^23 - 26 * q^25 - 6 * q^26 + 14 * q^27 - 24 * q^29 - 8 * q^35 - 18 * q^36 - 32 * q^38 - 20 * q^40 + 16 * q^42 + 32 * q^43 + 34 * q^48 - 46 * q^49 + 4 * q^51 + 4 * q^52 + 20 * q^53 + 12 * q^55 - 32 * q^56 - 20 * q^61 + 72 * q^62 - 58 * q^64 + 12 * q^65 + 6 * q^66 - 20 * q^68 - 8 * q^69 - 26 * q^75 - 12 * q^77 - 6 * q^78 + 12 * q^79 + 14 * q^81 + 20 * q^82 - 24 * q^87 - 30 * q^88 + 16 * q^91 - 24 * q^92 + 64 * q^94 - 36 * 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 $

$2$			2.53441i			1.79210i	0.443953	+	0.896050i	$0.353576\pi$
$2$			2.53441i			1.79210i	−0.443953	+	0.896050i	$0.646424\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−4.42325			−2.21162
$5$			3.70100i			1.65514i	0.561366	+	0.827568i	$0.310276\pi$
$5$			3.70100i			1.65514i	−0.561366	+	0.827568i	$0.689724\pi$
$6$			2.53441i			1.03467i
$7$			0.957295i			0.361823i	0.983499	+	0.180912i	$0.0579048\pi$
$7$			0.957295i			0.361823i	−0.983499	+	0.180912i	$0.942095\pi$
$8$		−	6.14151i		−	2.17135i
$9$	1.00000			0.333333
$10$	−9.37985			−2.96617
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−4.42325			−1.27688
$13$	−2.10857	−	2.92471i	−0.584811	−	0.811170i
$13$	−2.10857	−	2.92471i	−0.584811	−	0.811170i
$14$	−2.42618			−0.648424
$15$			3.70100i			0.955593i
$16$	6.71863			1.67966
$17$	2.05542			0.498512			0.249256	−	0.968438i	$-0.419814\pi$
$17$	2.05542			0.498512			0.249256	+	0.968438i	$0.419814\pi$
$18$			2.53441i			0.597367i
$19$			7.67886i			1.76165i	0.473442	+	0.880825i	$0.343012\pi$
$19$			7.67886i			1.76165i	−0.473442	+	0.880825i	$0.656988\pi$
$20$		−	16.3704i		−	3.66054i
$21$			0.957295i			0.208899i
$22$	2.53441			0.540339
$23$	4.20997			0.877840			0.438920	−	0.898526i	$-0.355361\pi$
$23$	4.20997			0.877840			0.438920	+	0.898526i	$0.355361\pi$
$24$		−	6.14151i		−	1.25363i
$25$	−8.69737			−1.73947
$26$	7.41243	−	5.34397i	1.45370	−	1.04804i
$27$	1.00000			0.192450
$28$		−	4.23435i		−	0.800217i
$29$	1.97786			0.367279			0.183640	−	0.982994i	$-0.441212\pi$
$29$	1.97786			0.367279			0.183640	+	0.982994i	$0.441212\pi$
$30$	−9.37985			−1.71252
$31$		−	10.5475i		−	1.89439i	−0.320664	−	0.947193i	$-0.603906\pi$
$31$		−	10.5475i		−	1.89439i	0.320664	−	0.947193i	$-0.396094\pi$
$32$			4.74476i			0.838763i
$33$		−	1.00000i		−	0.174078i
$34$			5.20928i			0.893384i
$35$	−3.54294			−0.598867
$36$	−4.42325			−0.737208
$37$			8.30741i			1.36573i	0.730545	+	0.682865i	$0.239266\pi$
$37$			8.30741i			1.36573i	−0.730545	+	0.682865i	$0.760734\pi$
$38$	−19.4614			−3.15705
$39$	−2.10857	−	2.92471i	−0.337641	−	0.468329i
$40$	22.7297			3.59388
$41$		−	5.23142i		−	0.817011i	−0.912756	−	0.408505i	$-0.866050\pi$
$41$		−	5.23142i		−	0.817011i	0.912756	−	0.408505i	$-0.133950\pi$
$42$	−2.42618			−0.374368
$43$	−5.26116			−0.802320			−0.401160	−	0.916008i	$-0.631393\pi$
$43$	−5.26116			−0.802320			−0.401160	+	0.916008i	$0.631393\pi$
$44$			4.42325i			0.666830i
$45$			3.70100i			0.551712i
$46$			10.6698i			1.57318i
$47$			1.24656i			0.181829i	0.995859	+	0.0909145i	$0.0289790\pi$
$47$			1.24656i			0.181829i	−0.995859	+	0.0909145i	$0.971021\pi$
$48$	6.71863			0.969751
$49$	6.08359			0.869084
$50$		−	22.0427i		−	3.11731i
$51$	2.05542			0.287816
$52$	9.32671	+	12.9367i	1.29338	+	1.79400i
$53$	2.98297			0.409743			0.204871	−	0.978789i	$-0.434322\pi$
$53$	2.98297			0.409743			0.204871	+	0.978789i	$0.434322\pi$
$54$			2.53441i			0.344890i
$55$	3.70100			0.499042
$56$	5.87924			0.785646
$57$			7.67886i			1.01709i
$58$			5.01271i			0.658202i
$59$			12.3548i			1.60846i	0.594321	+	0.804228i	$0.297421\pi$
$59$			12.3548i			1.60846i	−0.594321	+	0.804228i	$0.702579\pi$
$60$		−	16.3704i		−	2.11341i
$61$	−0.183851			−0.0235397			−0.0117698	−	0.999931i	$-0.503747\pi$
$61$	−0.183851			−0.0235397			−0.0117698	+	0.999931i	$0.503747\pi$
$62$	26.7317			3.39493
$63$			0.957295i			0.120608i
$64$	1.41208			0.176510
$65$	10.8244	−	7.80379i	1.34260	−	0.967941i
$66$	2.53441			0.311965
$67$			1.40691i			0.171881i	0.996300	+	0.0859407i	$0.0273896\pi$
$67$			1.40691i			0.171881i	−0.996300	+	0.0859407i	$0.972610\pi$
$68$	−9.09163			−1.10252
$69$	4.20997			0.506821
$70$		−	8.97928i		−	1.07323i
$71$			12.1582i			1.44291i	0.692459	+	0.721457i	$0.256527\pi$
$71$			12.1582i			1.44291i	−0.692459	+	0.721457i	$0.743473\pi$
$72$		−	6.14151i		−	0.723784i
$73$			3.32573i			0.389247i	0.980878	+	0.194624i	$0.0623485\pi$
$73$			3.32573i			0.389247i	−0.980878	+	0.194624i	$0.937651\pi$
$74$	−21.0544			−2.44752
$75$	−8.69737			−1.00429
$76$		−	33.9655i		−	3.89611i
$77$	0.957295			0.109094
$78$	7.41243	−	5.34397i	0.839293	−	0.605086i
$79$	−3.64911			−0.410557			−0.205279	−	0.978704i	$-0.565810\pi$
$79$	−3.64911			−0.410557			−0.205279	+	0.978704i	$0.565810\pi$
$80$			24.8656i			2.78006i
$81$	1.00000			0.111111
$82$	13.2586			1.46417
$83$			3.31957i			0.364370i	0.983264	+	0.182185i	$0.0583170\pi$
$83$			3.31957i			0.364370i	−0.983264	+	0.182185i	$0.941683\pi$
$84$		−	4.23435i		−	0.462006i
$85$			7.60710i			0.825106i
$86$		−	13.3340i		−	1.43784i
$87$	1.97786			0.212049
$88$	−6.14151			−0.654687
$89$		−	5.24302i		−	0.555759i	−0.960616	−	0.277879i	$-0.910368\pi$
$89$		−	5.24302i		−	0.555759i	0.960616	−	0.277879i	$-0.0896316\pi$
$90$	−9.37985			−0.988723
$91$	2.79981	−	2.01852i	0.293500	−	0.211598i
$92$	−18.6217			−1.94145
$93$		−	10.5475i		−	1.09372i
$94$	−3.15929			−0.325856
$95$	−28.4194			−2.91577
$96$			4.74476i			0.484260i
$97$			9.82293i			0.997368i	0.866784	+	0.498684i	$0.166183\pi$
$97$			9.82293i			0.997368i	−0.866784	+	0.498684i	$0.833817\pi$
$98$			15.4183i			1.55749i
$99$		−	1.00000i		−	0.100504i
$100$	38.4706			3.84706
$101$	8.42338			0.838157			0.419079	−	0.907950i	$-0.362353\pi$
$101$	8.42338			0.838157			0.419079	+	0.907950i	$0.362353\pi$
$102$			5.20928i			0.515796i
$103$	13.4029			1.32063			0.660314	−	0.750989i	$-0.270423\pi$
$103$	13.4029			1.32063			0.660314	+	0.750989i	$0.270423\pi$
$104$	−17.9622	+	12.9498i	−1.76134	+	1.26983i
$105$	−3.54294			−0.345756
$106$			7.56008i			0.734300i
$107$	−8.05792			−0.778988			−0.389494	−	0.921029i	$-0.627350\pi$
$107$	−8.05792			−0.778988			−0.389494	+	0.921029i	$0.627350\pi$
$108$	−4.42325			−0.425627
$109$		−	14.3600i		−	1.37544i	−0.725976	−	0.687720i	$-0.758612\pi$
$109$		−	14.3600i		−	1.37544i	0.725976	−	0.687720i	$-0.241388\pi$
$110$			9.37985i			0.894334i
$111$			8.30741i			0.788504i
$112$			6.43171i			0.607739i
$113$	18.6675			1.75609			0.878046	−	0.478577i	$-0.158847\pi$
$113$	18.6675			1.75609			0.878046	+	0.478577i	$0.158847\pi$
$114$	−19.4614			−1.82273
$115$			15.5811i			1.45294i
$116$	−8.74857			−0.812284
$117$	−2.10857	−	2.92471i	−0.194937	−	0.270390i
$118$	−31.3121			−2.88251
$119$			1.96764i			0.180373i
$120$	22.7297			2.07493
$121$	−1.00000			−0.0909091
$122$		−	0.465954i		−	0.0421855i
$123$		−	5.23142i		−	0.471701i
$124$			46.6542i			4.18967i
$125$		−	13.6840i		−	1.22393i
$126$	−2.42618			−0.216141
$127$	−6.60130			−0.585770			−0.292885	−	0.956148i	$-0.594615\pi$
$127$	−6.60130			−0.585770			−0.292885	+	0.956148i	$0.594615\pi$
$128$			13.0683i			1.15509i
$129$	−5.26116			−0.463220
$130$	19.7780	+	27.4334i	1.73465	+	2.40607i
$131$	5.81083			0.507694			0.253847	−	0.967244i	$-0.418304\pi$
$131$	5.81083			0.507694			0.253847	+	0.967244i	$0.418304\pi$
$132$			4.42325i			0.384994i
$133$	−7.35093			−0.637406
$134$	−3.56569			−0.308029
$135$			3.70100i			0.318531i
$136$		−	12.6234i		−	1.08245i
$137$		−	5.64208i		−	0.482035i	−0.970521	−	0.241018i	$-0.922519\pi$
$137$		−	5.64208i		−	0.482035i	0.970521	−	0.241018i	$-0.0774812\pi$
$138$			10.6698i			0.908274i
$139$	−4.46820			−0.378987			−0.189494	−	0.981882i	$-0.560685\pi$
$139$	−4.46820			−0.378987			−0.189494	+	0.981882i	$0.560685\pi$
$140$	15.6713			1.32447
$141$			1.24656i			0.104979i
$142$	−30.8139			−2.58585
$143$	−2.92471	+	2.10857i	−0.244577	+	0.176327i
$144$	6.71863			0.559886
$145$			7.32005i			0.607897i
$146$	−8.42877			−0.697570
$147$	6.08359			0.501766
$148$		−	36.7457i		−	3.02048i
$149$		−	7.39749i		−	0.606026i	−0.952986	−	0.303013i	$-0.902007\pi$
$149$		−	7.39749i		−	0.606026i	0.952986	−	0.303013i	$-0.0979925\pi$
$150$		−	22.0427i		−	1.79978i
$151$		−	23.7454i		−	1.93237i	−0.257841	−	0.966187i	$-0.583011\pi$
$151$		−	23.7454i		−	1.93237i	0.257841	−	0.966187i	$-0.416989\pi$
$152$	47.1598			3.82516
$153$	2.05542			0.166171
$154$			2.42618i			0.195507i
$155$	39.0362			3.13547
$156$	9.32671	+	12.9367i	0.746734	+	1.03577i
$157$	12.9704			1.03515			0.517576	−	0.855637i	$-0.326834\pi$
$157$	12.9704			1.03515			0.517576	+	0.855637i	$0.326834\pi$
$158$		−	9.24836i		−	0.735760i
$159$	2.98297			0.236565
$160$	−17.5603			−1.38827
$161$			4.03018i			0.317623i
$162$			2.53441i			0.199122i
$163$		−	18.6880i		−	1.46376i	−0.681436	−	0.731878i	$-0.738644\pi$
$163$		−	18.6880i		−	1.46376i	0.681436	−	0.731878i	$-0.261356\pi$
$164$			23.1399i			1.80692i
$165$	3.70100			0.288122
$166$	−8.41316			−0.652988
$167$		−	25.0420i		−	1.93781i	−0.247437	−	0.968904i	$-0.579588\pi$
$167$		−	25.0420i		−	1.93781i	0.247437	−	0.968904i	$-0.420412\pi$
$168$	5.87924			0.453593
$169$	−4.10791	+	12.3339i	−0.315993	+	0.948762i
$170$	−19.2795			−1.47867
$171$			7.67886i			0.587217i
$172$	23.2714			1.77443
$173$	3.16333			0.240503			0.120252	−	0.992743i	$-0.461630\pi$
$173$	3.16333			0.240503			0.120252	+	0.992743i	$0.461630\pi$
$174$			5.01271i			0.380013i
$175$		−	8.32595i		−	0.629383i
$176$		−	6.71863i		−	0.506436i
$177$			12.3548i			0.928642i
$178$	13.2880			0.995976
$179$	−1.24977			−0.0934123			−0.0467062	−	0.998909i	$-0.514872\pi$
$179$	−1.24977			−0.0934123			−0.0467062	+	0.998909i	$0.514872\pi$
$180$		−	16.3704i		−	1.22018i
$181$	−16.0712			−1.19456			−0.597281	−	0.802032i	$-0.703752\pi$
$181$	−16.0712			−1.19456			−0.597281	+	0.802032i	$0.703752\pi$
$182$	5.11576	+	7.09588i	0.379205	+	0.525982i
$183$	−0.183851			−0.0135906
$184$		−	25.8556i		−	1.90610i
$185$	−30.7457			−2.26047
$186$	26.7317			1.96006
$187$		−	2.05542i		−	0.150307i
$188$		−	5.51383i		−	0.402137i
$189$			0.957295i			0.0696329i
$190$		−	72.0265i		−	5.22535i
$191$	15.2909			1.10641			0.553207	−	0.833044i	$-0.313404\pi$
$191$	15.2909			1.10641			0.553207	+	0.833044i	$0.313404\pi$
$192$	1.41208			0.101908
$193$		−	6.76152i		−	0.486705i	−0.969938	−	0.243353i	$-0.921753\pi$
$193$		−	6.76152i		−	0.486705i	0.969938	−	0.243353i	$-0.0782472\pi$
$194$	−24.8954			−1.78738
$195$	10.8244	−	7.80379i	0.775148	−	0.558841i
$196$	−26.9092			−1.92209
$197$		−	11.3320i		−	0.807374i	−0.914897	−	0.403687i	$-0.867728\pi$
$197$		−	11.3320i		−	0.807374i	0.914897	−	0.403687i	$-0.132272\pi$
$198$	2.53441			0.180113
$199$	−21.5642			−1.52864			−0.764321	−	0.644836i	$-0.776926\pi$
$199$	−21.5642			−1.52864			−0.764321	+	0.644836i	$0.776926\pi$
$200$			53.4150i			3.77701i
$201$			1.40691i			0.0992358i
$202$			21.3483i			1.50206i
$203$			1.89339i			0.132890i
$204$	−9.09163			−0.636541
$205$	19.3615			1.35226
$206$			33.9685i			2.36670i
$207$	4.20997			0.292613
$208$	−14.1667	−	19.6501i	−0.982282	−	1.36249i
$209$	7.67886			0.531158
$210$		−	8.97928i		−	0.619629i
$211$	−23.5992			−1.62463			−0.812317	−	0.583217i	$-0.801794\pi$
$211$	−23.5992			−1.62463			−0.812317	+	0.583217i	$0.801794\pi$
$212$	−13.1944			−0.906197
$213$			12.1582i			0.833067i
$214$		−	20.4221i		−	1.39603i
$215$		−	19.4715i		−	1.32795i
$216$		−	6.14151i		−	0.417877i
$217$	10.0971			0.685433
$218$	36.3942			2.46493
$219$			3.32573i			0.224732i
$220$	−16.3704			−1.10369
$221$	−4.33399	−	6.01151i	−0.291535	−	0.404378i
$222$	−21.0544			−1.41308
$223$		−	14.7201i		−	0.985730i	−0.870106	−	0.492865i	$-0.835950\pi$
$223$		−	14.7201i		−	0.985730i	0.870106	−	0.492865i	$-0.164050\pi$
$224$	−4.54213			−0.303484
$225$	−8.69737			−0.579825
$226$			47.3112i			3.14709i
$227$			0.0358913i			0.00238219i	0.999999	+	0.00119109i	$0.000379137\pi$
$227$			0.0358913i			0.00238219i	−0.999999	+	0.00119109i	$0.999621\pi$
$228$		−	33.9655i		−	2.24942i
$229$		−	8.37257i		−	0.553275i	−0.960974	−	0.276637i	$-0.910780\pi$
$229$		−	8.37257i		−	0.553275i	0.960974	−	0.276637i	$-0.0892201\pi$
$230$	−39.4889			−2.60382
$231$	0.957295			0.0629854
$232$		−	12.1471i		−	0.797493i
$233$	18.0020			1.17935			0.589674	−	0.807641i	$-0.299256\pi$
$233$	18.0020			1.17935			0.589674	+	0.807641i	$0.299256\pi$
$234$	7.41243	−	5.34397i	0.484566	−	0.349347i
$235$	−4.61350			−0.300952
$236$		−	54.6483i		−	3.55730i
$237$	−3.64911			−0.237035
$238$	−4.98682			−0.323247
$239$		−	5.74497i		−	0.371611i	−0.982587	−	0.185806i	$-0.940511\pi$
$239$		−	5.74497i		−	0.371611i	0.982587	−	0.185806i	$-0.0594895\pi$
$240$			24.8656i			1.60507i
$241$			16.1458i			1.04004i	0.854153	+	0.520022i	$0.174076\pi$
$241$			16.1458i			1.04004i	−0.854153	+	0.520022i	$0.825924\pi$
$242$		−	2.53441i		−	0.162918i
$243$	1.00000			0.0641500
$244$	0.813218			0.0520609
$245$			22.5153i			1.43845i
$246$	13.2586			0.845336
$247$	22.4585	−	16.1914i	1.42900	−	1.03023i
$248$	−64.7776			−4.11338
$249$			3.31957i			0.210369i
$250$	34.6808			2.19341
$251$	6.83631			0.431504			0.215752	−	0.976448i	$-0.430780\pi$
$251$	6.83631			0.431504			0.215752	+	0.976448i	$0.430780\pi$
$252$		−	4.23435i		−	0.266739i
$253$		−	4.20997i		−	0.264679i
$254$		−	16.7304i		−	1.04976i
$255$			7.60710i			0.476375i
$256$	−30.2963			−1.89352
$257$	26.8038			1.67197			0.835987	−	0.548749i	$-0.184896\pi$
$257$	26.8038			1.67197			0.835987	+	0.548749i	$0.184896\pi$
$258$		−	13.3340i		−	0.830136i
$259$	−7.95264			−0.494153
$260$	−47.8788	+	34.5181i	−2.96932	+	2.14072i
$261$	1.97786			0.122426
$262$			14.7270i			0.909839i
$263$	−11.9518			−0.736980			−0.368490	−	0.929632i	$-0.620125\pi$
$263$	−11.9518			−0.736980			−0.368490	+	0.929632i	$0.620125\pi$
$264$	−6.14151			−0.377984
$265$			11.0400i			0.678180i
$266$		−	18.6303i		−	1.14230i
$267$		−	5.24302i		−	0.320868i
$268$		−	6.22311i		−	0.380137i
$269$	4.59663			0.280261			0.140131	−	0.990133i	$-0.455248\pi$
$269$	4.59663			0.280261			0.140131	+	0.990133i	$0.455248\pi$
$270$	−9.37985			−0.570840
$271$		−	19.8969i		−	1.20865i	−0.796738	−	0.604326i	$-0.793443\pi$
$271$		−	19.8969i		−	1.20865i	0.796738	−	0.604326i	$-0.206557\pi$
$272$	13.8096			0.837330
$273$	2.79981	−	2.01852i	0.169452	−	0.122166i
$274$	14.2994			0.863856
$275$			8.69737i			0.524471i
$276$	−18.6217			−1.12090
$277$	11.2319			0.674857			0.337428	−	0.941351i	$-0.390443\pi$
$277$	11.2319			0.674857			0.337428	+	0.941351i	$0.390443\pi$
$278$		−	11.3243i		−	0.679183i
$279$		−	10.5475i		−	0.631462i
$280$			21.7590i			1.30035i
$281$			30.2946i			1.80722i	0.428352	+	0.903612i	$0.359094\pi$
$281$			30.2946i			1.80722i	−0.428352	+	0.903612i	$0.640906\pi$
$282$	−3.15929			−0.188133
$283$	15.3889			0.914777			0.457389	−	0.889267i	$-0.348785\pi$
$283$	15.3889			0.914777			0.457389	+	0.889267i	$0.348785\pi$
$284$		−	53.7788i		−	3.19118i
$285$	−28.4194			−1.68342
$286$	−5.34397	−	7.41243i	−0.315996	−	0.438306i
$287$	5.00801			0.295614
$288$			4.74476i			0.279588i
$289$	−12.7753			−0.751485
$290$	−18.5520			−1.08941
$291$			9.82293i			0.575831i
$292$		−	14.7105i		−	0.860869i
$293$		−	6.95822i		−	0.406503i	−0.979127	−	0.203252i	$-0.934849\pi$
$293$		−	6.95822i		−	0.406503i	0.979127	−	0.203252i	$-0.0651510\pi$
$294$			15.4183i			0.899215i
$295$	−45.7250			−2.66221
$296$	51.0200			2.96548
$297$		−	1.00000i		−	0.0580259i
$298$	18.7483			1.08606
$299$	−8.87700	−	12.3130i	−0.513370	−	0.712077i
$300$	38.4706			2.22110
$301$		−	5.03648i		−	0.290298i
$302$	60.1807			3.46301
$303$	8.42338			0.483910
$304$			51.5914i			2.95897i
$305$		−	0.680431i		−	0.0389614i
$306$			5.20928i			0.297795i
$307$			12.6233i			0.720447i	0.932866	+	0.360224i	$0.117300\pi$
$307$			12.6233i			0.720447i	−0.932866	+	0.360224i	$0.882700\pi$
$308$	−4.23435			−0.241275
$309$	13.4029			0.762465
$310$			98.9339i			5.61907i
$311$	−2.12116			−0.120280			−0.0601399	−	0.998190i	$-0.519155\pi$
$311$	−2.12116			−0.120280			−0.0601399	+	0.998190i	$0.519155\pi$
$312$	−17.9622	+	12.9498i	−1.01691	+	0.733137i
$313$	21.5919			1.22045			0.610224	−	0.792229i	$-0.291079\pi$
$313$	21.5919			1.22045			0.610224	+	0.792229i	$0.291079\pi$
$314$			32.8724i			1.85510i
$315$	−3.54294			−0.199622
$316$	16.1409			0.907999
$317$			15.7684i			0.885640i	0.896611	+	0.442820i	$0.146022\pi$
$317$			15.7684i			0.885640i	−0.896611	+	0.442820i	$0.853978\pi$
$318$			7.56008i			0.423948i
$319$		−	1.97786i		−	0.110739i
$320$			5.22612i			0.292149i
$321$	−8.05792			−0.449749
$322$	−10.2141			−0.569212
$323$			15.7833i			0.878205i
$324$	−4.42325			−0.245736
$325$	18.3390	+	25.4373i	1.01726	+	1.41101i
$326$	47.3631			2.62320
$327$		−	14.3600i		−	0.794111i
$328$	−32.1288			−1.77402
$329$	−1.19332			−0.0657900
$330$			9.37985i			0.516344i
$331$			11.6602i			0.640902i	0.947265	+	0.320451i	$0.103834\pi$
$331$			11.6602i			0.640902i	−0.947265	+	0.320451i	$0.896166\pi$
$332$		−	14.6833i		−	0.805850i
$333$			8.30741i			0.455243i
$334$	63.4668			3.47275
$335$	−5.20697			−0.284487
$336$			6.43171i			0.350879i
$337$	7.63508			0.415909			0.207955	−	0.978138i	$-0.433319\pi$
$337$	7.63508			0.415909			0.207955	+	0.978138i	$0.433319\pi$
$338$	−31.2592	−	10.4111i	−1.70028	−	0.566291i
$339$	18.6675			1.01388
$340$		−	33.6481i		−	1.82482i
$341$	−10.5475			−0.571179
$342$	−19.4614			−1.05235
$343$			12.5248i			0.676278i
$344$			32.3115i			1.74212i
$345$			15.5811i			0.838858i
$346$			8.01717i			0.431006i
$347$	−17.7823			−0.954606			−0.477303	−	0.878739i	$-0.658386\pi$
$347$	−17.7823			−0.954606			−0.477303	+	0.878739i	$0.658386\pi$
$348$	−8.74857			−0.468972
$349$		−	12.1663i		−	0.651245i	−0.945500	−	0.325622i	$-0.894426\pi$
$349$		−	12.1663i		−	0.651245i	0.945500	−	0.325622i	$-0.105574\pi$
$350$	21.1014			1.12792
$351$	−2.10857	−	2.92471i	−0.112547	−	0.156110i
$352$	4.74476			0.252896
$353$		−	32.9025i		−	1.75122i	−0.483014	−	0.875612i	$-0.660458\pi$
$353$		−	32.9025i		−	1.75122i	0.483014	−	0.875612i	$-0.339542\pi$
$354$	−31.3121			−1.66422
$355$	−44.9975			−2.38822
$356$			23.1912i			1.22913i
$357$			1.96764i			0.104139i
$358$		−	3.16744i		−	0.167404i
$359$		−	7.29760i		−	0.385153i	−0.981282	−	0.192576i	$-0.938316\pi$
$359$		−	7.29760i		−	0.385153i	0.981282	−	0.192576i	$-0.0616843\pi$
$360$	22.7297			1.19796
$361$	−39.9648			−2.10341
$362$		−	40.7310i		−	2.14078i
$363$	−1.00000			−0.0524864
$364$	−12.3843	+	8.92841i	−0.649112	+	0.467976i
$365$	−12.3085			−0.644257
$366$		−	0.465954i		−	0.0243558i
$367$	−8.94917			−0.467143			−0.233571	−	0.972340i	$-0.575041\pi$
$367$	−8.94917			−0.467143			−0.233571	+	0.972340i	$0.575041\pi$
$368$	28.2852			1.47447
$369$		−	5.23142i		−	0.272337i
$370$		−	77.9222i		−	4.05098i
$371$			2.85558i			0.148254i
$372$			46.6542i			2.41891i
$373$	−18.1913			−0.941908			−0.470954	−	0.882158i	$-0.656090\pi$
$373$	−18.1913			−0.941908			−0.470954	+	0.882158i	$0.656090\pi$
$374$	5.20928			0.269366
$375$		−	13.6840i		−	0.706637i
$376$	7.65574			0.394815
$377$	−4.17045	−	5.78468i	−0.214789	−	0.297926i
$378$	−2.42618			−0.124789
$379$			20.1063i			1.03279i	0.856350	+	0.516396i	$0.172727\pi$
$379$			20.1063i			1.03279i	−0.856350	+	0.516396i	$0.827273\pi$
$380$	125.706			6.44859
$381$	−6.60130			−0.338195
$382$			38.7536i			1.98281i
$383$		−	7.99092i		−	0.408317i	−0.978938	−	0.204158i	$-0.934554\pi$
$383$		−	7.99092i		−	0.408317i	0.978938	−	0.204158i	$-0.0654458\pi$
$384$			13.0683i			0.666890i
$385$			3.54294i			0.180565i
$386$	17.1365			0.872224
$387$	−5.26116			−0.267440
$388$		−	43.4493i		−	2.20580i
$389$	−4.31617			−0.218839			−0.109419	−	0.993996i	$-0.534899\pi$
$389$	−4.31617			−0.218839			−0.109419	+	0.993996i	$0.534899\pi$
$390$	19.7780	+	27.4334i	1.00150	+	1.38914i
$391$	8.65326			0.437614
$392$		−	37.3624i		−	1.88709i
$393$	5.81083			0.293117
$394$	28.7201			1.44690
$395$		−	13.5054i		−	0.679528i
$396$			4.42325i			0.222277i
$397$		−	23.4560i		−	1.17722i	−0.808416	−	0.588612i	$-0.799675\pi$
$397$		−	23.4560i		−	1.17722i	0.808416	−	0.588612i	$-0.200325\pi$
$398$		−	54.6525i		−	2.73948i
$399$	−7.35093			−0.368007
$400$	−58.4344			−2.92172
$401$			2.38235i			0.118969i	0.998229	+	0.0594844i	$0.0189457\pi$
$401$			2.38235i			0.118969i	−0.998229	+	0.0594844i	$0.981054\pi$
$402$	−3.56569			−0.177841
$403$	−30.8484	+	22.2401i	−1.53667	+	1.10786i
$404$	−37.2587			−1.85369
$405$			3.70100i			0.183904i
$406$	−4.79864			−0.238153
$407$	8.30741			0.411783
$408$		−	12.6234i		−	0.624951i
$409$		−	10.3945i		−	0.513973i	−0.966415	−	0.256987i	$-0.917270\pi$
$409$		−	10.3945i		−	0.513973i	0.966415	−	0.256987i	$-0.0827296\pi$
$410$			49.0700i			2.42339i
$411$		−	5.64208i		−	0.278303i
$412$	−59.2844			−2.92073
$413$	−11.8272			−0.581977
$414$			10.6698i			0.524392i
$415$	−12.2857			−0.603082
$416$	13.8771	−	10.0046i	0.680379	−	0.490517i
$417$	−4.46820			−0.218808
$418$			19.4614i			0.951888i
$419$	13.6447			0.666586			0.333293	−	0.942823i	$-0.391840\pi$
$419$	13.6447			0.666586			0.333293	+	0.942823i	$0.391840\pi$
$420$	15.6713			0.764682
$421$			6.41040i			0.312424i	0.987724	+	0.156212i	$0.0499283\pi$
$421$			6.41040i			0.312424i	−0.987724	+	0.156212i	$0.950072\pi$
$422$		−	59.8100i		−	2.91151i
$423$			1.24656i			0.0606097i
$424$		−	18.3200i		−	0.889696i
$425$	−17.8768			−0.867150
$426$	−30.8139			−1.49294
$427$		−	0.175999i		−	0.00851721i
$428$	35.6422			1.72283
$429$	−2.92471	+	2.10857i	−0.141207	+	0.101802i
$430$	49.3489			2.37982
$431$			15.8350i			0.762747i	0.924421	+	0.381374i	$0.124549\pi$
$431$			15.8350i			0.762747i	−0.924421	+	0.381374i	$0.875451\pi$
$432$	6.71863			0.323250
$433$	10.6273			0.510716			0.255358	−	0.966847i	$-0.417807\pi$
$433$	10.6273			0.510716			0.255358	+	0.966847i	$0.417807\pi$
$434$			25.5901i			1.22836i
$435$			7.32005i			0.350970i
$436$			63.5179i			3.04196i
$437$			32.3278i			1.54645i
$438$	−8.42877			−0.402742
$439$	17.2195			0.821841			0.410920	−	0.911671i	$-0.365207\pi$
$439$	17.2195			0.821841			0.410920	+	0.911671i	$0.365207\pi$
$440$		−	22.7297i		−	1.08360i
$441$	6.08359			0.289695
$442$	15.2357	−	10.9841i	0.724686	−	0.522461i
$443$	−25.1359			−1.19424			−0.597120	−	0.802152i	$-0.703689\pi$
$443$	−25.1359			−1.19424			−0.597120	+	0.802152i	$0.703689\pi$
$444$		−	36.7457i		−	1.74387i
$445$	19.4044			0.919857
$446$	37.3068			1.76653
$447$		−	7.39749i		−	0.349889i
$448$			1.35178i			0.0638656i
$449$			2.01596i			0.0951392i	0.998868	+	0.0475696i	$0.0151476\pi$
$449$			2.01596i			0.0951392i	−0.998868	+	0.0475696i	$0.984852\pi$
$450$		−	22.0427i		−	1.03910i
$451$	−5.23142			−0.246338
$452$	−82.5710			−3.88382
$453$		−	23.7454i		−	1.11566i
$454$	−0.0909634			−0.00426912
$455$	7.47053	+	10.3621i	0.350224	+	0.485783i
$456$	47.1598			2.20846
$457$			33.7659i			1.57950i	0.613426	+	0.789752i	$0.289791\pi$
$457$			33.7659i			1.57950i	−0.613426	+	0.789752i	$0.710209\pi$
$458$	21.2195			0.991524
$459$	2.05542			0.0959388
$460$		−	68.9190i		−	3.21337i
$461$			16.7600i			0.780589i	0.920690	+	0.390294i	$0.127627\pi$
$461$			16.7600i			0.780589i	−0.920690	+	0.390294i	$0.872373\pi$
$462$			2.42618i			0.112876i
$463$		−	27.5446i		−	1.28011i	−0.768330	−	0.640054i	$-0.778912\pi$
$463$		−	27.5446i		−	1.28011i	0.768330	−	0.640054i	$-0.221088\pi$
$464$	13.2885			0.616904
$465$	39.0362			1.81026
$466$			45.6244i			2.11351i
$467$	−22.9318			−1.06116			−0.530578	−	0.847636i	$-0.678025\pi$
$467$	−22.9318			−1.06116			−0.530578	+	0.847636i	$0.678025\pi$
$468$	9.32671	+	12.9367i	0.431127	+	0.598001i
$469$	−1.34683			−0.0621907
$470$		−	11.6925i		−	0.539336i
$471$	12.9704			0.597646
$472$	75.8770			3.49252
$473$			5.26116i			0.241909i
$474$		−	9.24836i		−	0.424791i
$475$		−	66.7859i		−	3.06435i
$476$		−	8.70337i		−	0.398918i
$477$	2.98297			0.136581
$478$	14.5601			0.665965
$479$			5.71495i			0.261123i	0.991440	+	0.130561i	$0.0416780\pi$
$479$			5.71495i			0.261123i	−0.991440	+	0.130561i	$0.958322\pi$
$480$	−17.5603			−0.801516
$481$	24.2968	−	17.5167i	1.10784	−	0.798693i
$482$	−40.9202			−1.86386
$483$			4.03018i			0.183380i
$484$	4.42325			0.201057
$485$	−36.3546			−1.65078
$486$			2.53441i			0.114963i
$487$			10.4987i			0.475742i	0.971297	+	0.237871i	$0.0764496\pi$
$487$			10.4987i			0.475742i	−0.971297	+	0.237871i	$0.923550\pi$
$488$			1.12912i			0.0511129i
$489$		−	18.6880i		−	0.845100i
$490$	−57.0631			−2.57785
$491$	−13.0458			−0.588747			−0.294373	−	0.955691i	$-0.595111\pi$
$491$	−13.0458			−0.588747			−0.294373	+	0.955691i	$0.595111\pi$
$492$			23.1399i			1.04323i
$493$	4.06533			0.183093
$494$	41.0356	+	56.9190i	1.84628	+	2.56091i
$495$	3.70100			0.166347
$496$		−	70.8647i		−	3.18192i
$497$	−11.6390			−0.522080
$498$	−8.41316			−0.377003
$499$		−	38.6395i		−	1.72974i	−0.501995	−	0.864870i	$-0.667400\pi$
$499$		−	38.6395i		−	1.72974i	0.501995	−	0.864870i	$-0.332600\pi$
$500$			60.5276i			2.70688i
$501$		−	25.0420i		−	1.11879i
$502$			17.3260i			0.773298i
$503$	0.330867			0.0147526			0.00737631	−	0.999973i	$-0.497652\pi$
$503$	0.330867			0.0147526			0.00737631	+	0.999973i	$0.497652\pi$
$504$	5.87924			0.261882
$505$			31.1749i			1.38726i
$506$	10.6698			0.474331
$507$	−4.10791	+	12.3339i	−0.182439	+	0.547768i
$508$	29.1992			1.29550
$509$			44.2090i			1.95953i	0.200157	+	0.979764i	$0.435855\pi$
$509$			44.2090i			1.95953i	−0.200157	+	0.979764i	$0.564145\pi$
$510$	−19.2795			−0.853712
$511$	−3.18370			−0.140839
$512$		−	50.6468i		−	2.23829i
$513$			7.67886i			0.339030i
$514$			67.9318i			2.99635i
$515$			49.6041i			2.18582i
$516$	23.2714			1.02447
$517$	1.24656			0.0548235
$518$		−	20.1553i		−	0.885571i
$519$	3.16333			0.138855
$520$	−47.9271	−	66.4779i	−2.10174	−	2.91525i
$521$	9.66049			0.423234			0.211617	−	0.977353i	$-0.432127\pi$
$521$	9.66049			0.423234			0.211617	+	0.977353i	$0.432127\pi$
$522$			5.01271i			0.219401i
$523$	21.7358			0.950440			0.475220	−	0.879867i	$-0.342368\pi$
$523$	21.7358			0.950440			0.475220	+	0.879867i	$0.342368\pi$
$524$	−25.7027			−1.12283
$525$		−	8.32595i		−	0.363374i
$526$		−	30.2908i		−	1.32074i
$527$		−	21.6795i		−	0.944375i
$528$		−	6.71863i		−	0.292391i
$529$	−5.27614			−0.229398
$530$	−27.9798			−1.21537
$531$			12.3548i			0.536152i
$532$	32.5150			1.40970
$533$	−15.3004	+	11.0308i	−0.662734	+	0.477797i
$534$	13.2880			0.575027
$535$		−	29.8223i		−	1.28933i
$536$	8.64056			0.373215
$537$	−1.24977			−0.0539316
$538$			11.6497i			0.502256i
$539$		−	6.08359i		−	0.262039i
$540$		−	16.3704i		−	0.704471i
$541$		−	18.0139i		−	0.774478i	−0.921979	−	0.387239i	$-0.873429\pi$
$541$		−	18.0139i		−	0.774478i	0.921979	−	0.387239i	$-0.126571\pi$
$542$	50.4270			2.16602
$543$	−16.0712			−0.689681
$544$			9.75247i			0.418134i
$545$	53.1464			2.27654
$546$	5.11576	+	7.09588i	0.218934	+	0.303676i
$547$	23.2740			0.995125			0.497563	−	0.867428i	$-0.334228\pi$
$547$	23.2740			0.995125			0.497563	+	0.867428i	$0.334228\pi$
$548$			24.9563i			1.06608i
$549$	−0.183851			−0.00784656
$550$	−22.0427			−0.939906
$551$			15.1877i			0.647018i
$552$		−	25.8556i		−	1.10049i
$553$		−	3.49328i		−	0.148549i
$554$			28.4662i			1.20941i
$555$	−30.7457			−1.30508
$556$	19.7639			0.838178
$557$		−	11.5996i		−	0.491491i	−0.969334	−	0.245745i	$-0.920967\pi$
$557$		−	11.5996i		−	0.491491i	0.969334	−	0.245745i	$-0.0790327\pi$
$558$	26.7317			1.13164
$559$	11.0935	+	15.3874i	0.469205	+	0.650818i
$560$	−23.8037			−1.00589
$561$		−	2.05542i		−	0.0867799i
$562$	−76.7790			−3.23873
$563$	−26.5695			−1.11977			−0.559885	−	0.828570i	$-0.689155\pi$
$563$	−26.5695			−1.11977			−0.559885	+	0.828570i	$0.689155\pi$
$564$		−	5.51383i		−	0.232174i
$565$			69.0884i			2.90657i
$566$			39.0019i			1.63937i
$567$			0.957295i			0.0402026i
$568$	74.6698			3.13308
$569$	22.7470			0.953603			0.476802	−	0.879011i	$-0.341796\pi$
$569$	22.7470			0.953603			0.476802	+	0.879011i	$0.341796\pi$
$570$		−	72.0265i		−	3.01686i
$571$	29.4622			1.23296			0.616478	−	0.787372i	$-0.288559\pi$
$571$	29.4622			1.23296			0.616478	+	0.787372i	$0.288559\pi$
$572$	12.9367	−	9.32671i	0.540912	−	0.389969i
$573$	15.2909			0.638788
$574$			12.6924i			0.529769i
$575$	−36.6157			−1.52698
$576$	1.41208			0.0588368
$577$		−	26.6537i		−	1.10961i	−0.831981	−	0.554803i	$-0.812793\pi$
$577$		−	26.6537i		−	1.10961i	0.831981	−	0.554803i	$-0.187207\pi$
$578$		−	32.3778i		−	1.34674i
$579$		−	6.76152i		−	0.280999i
$580$		−	32.3784i		−	1.34444i
$581$	−3.17781			−0.131838
$582$	−24.8954			−1.03195
$583$		−	2.98297i		−	0.123542i
$584$	20.4250			0.845193
$585$	10.8244	−	7.80379i	0.447532	−	0.322647i
$586$	17.6350			0.728495
$587$			10.9203i			0.450729i	0.974275	+	0.225364i	$0.0723573\pi$
$587$			10.9203i			0.450729i	−0.974275	+	0.225364i	$0.927643\pi$
$588$	−26.9092			−1.10972
$589$	80.9927			3.33725
$590$		−	115.886i		−	4.77095i
$591$		−	11.3320i		−	0.466138i
$592$			55.8144i			2.29396i
$593$		−	19.3064i		−	0.792820i	−0.918074	−	0.396410i	$-0.870256\pi$
$593$		−	19.3064i		−	0.792820i	0.918074	−	0.396410i	$-0.129744\pi$
$594$	2.53441			0.103988
$595$	−7.28224			−0.298543
$596$			32.7209i			1.34030i
$597$	−21.5642			−0.882562
$598$	31.2061	−	22.4980i	1.27611	−	0.920011i
$599$	2.01132			0.0821802			0.0410901	−	0.999155i	$-0.486917\pi$
$599$	2.01132			0.0821802			0.0410901	+	0.999155i	$0.486917\pi$
$600$			53.4150i			2.18066i
$601$	−40.1233			−1.63667			−0.818333	−	0.574745i	$-0.805101\pi$
$601$	−40.1233			−1.63667			−0.818333	+	0.574745i	$0.805101\pi$
$602$	12.7645			0.520243
$603$			1.40691i			0.0572938i
$604$			105.032i			4.27369i
$605$		−	3.70100i		−	0.150467i
$606$			21.3483i			0.867216i
$607$	−35.4310			−1.43810			−0.719049	−	0.694959i	$-0.755422\pi$
$607$	−35.4310			−1.43810			−0.719049	+	0.694959i	$0.755422\pi$
$608$	−36.4343			−1.47761
$609$			1.89339i			0.0767242i
$610$	1.72449			0.0698227
$611$	3.64582	−	2.62845i	0.147494	−	0.106336i
$612$	−9.09163			−0.367507
$613$			0.644081i			0.0260142i	0.999915	+	0.0130071i	$0.00414040\pi$
$613$			0.644081i			0.0260142i	−0.999915	+	0.0130071i	$0.995860\pi$
$614$	−31.9925			−1.29111
$615$	19.3615			0.780730
$616$		−	5.87924i		−	0.236881i
$617$			23.5775i			0.949194i	0.880203	+	0.474597i	$0.157406\pi$
$617$			23.5775i			0.949194i	−0.880203	+	0.474597i	$0.842594\pi$
$618$			33.9685i			1.36641i
$619$			5.86810i			0.235859i	0.993022	+	0.117929i	$0.0376256\pi$
$619$			5.86810i			0.235859i	−0.993022	+	0.117929i	$0.962374\pi$
$620$	−172.667			−6.93447
$621$	4.20997			0.168940
$622$		−	5.37589i		−	0.215553i
$623$	5.01911			0.201087
$624$	−14.1667	−	19.6501i	−0.567121	−	0.786633i
$625$	7.15745			0.286298
$626$			54.7229i			2.18717i
$627$	7.67886			0.306664
$628$	−57.3714			−2.28937
$629$			17.0752i			0.680833i
$630$		−	8.97928i		−	0.357743i
$631$		−	11.0386i		−	0.439441i	−0.975563	−	0.219721i	$-0.929485\pi$
$631$		−	11.0386i		−	0.439441i	0.975563	−	0.219721i	$-0.0705146\pi$
$632$			22.4111i			0.891465i
$633$	−23.5992			−0.937982
$634$	−39.9636			−1.58716
$635$		−	24.4314i		−	0.969529i
$636$	−13.1944			−0.523193
$637$	−12.8276	−	17.7928i	−0.508250	−	0.704975i
$638$	5.01271			0.198455
$639$			12.1582i			0.480972i
$640$	−48.3658			−1.91183
$641$	−11.2924			−0.446022			−0.223011	−	0.974816i	$-0.571589\pi$
$641$	−11.2924			−0.446022			−0.223011	+	0.974816i	$0.571589\pi$
$642$		−	20.4221i		−	0.805996i
$643$			2.73168i			0.107727i	0.998548	+	0.0538634i	$0.0171536\pi$
$643$			2.73168i			0.107727i	−0.998548	+	0.0538634i	$0.982846\pi$
$644$		−	17.8265i		−	0.702463i
$645$		−	19.4715i		−	0.766691i
$646$	−40.0013			−1.57383
$647$	10.3135			0.405465			0.202733	−	0.979234i	$-0.435018\pi$
$647$	10.3135			0.405465			0.202733	+	0.979234i	$0.435018\pi$
$648$		−	6.14151i		−	0.241261i
$649$	12.3548			0.484968
$650$	−64.4687	+	46.4785i	−2.52867	+	1.82304i
$651$	10.0971			0.395735
$652$			82.6616i			3.23728i
$653$	−1.95601			−0.0765446			−0.0382723	−	0.999267i	$-0.512185\pi$
$653$	−1.95601			−0.0765446			−0.0382723	+	0.999267i	$0.512185\pi$
$654$	36.3942			1.42313
$655$			21.5058i			0.840303i
$656$		−	35.1480i		−	1.37230i
$657$			3.32573i			0.129749i
$658$		−	3.02437i		−	0.117902i
$659$	−21.0277			−0.819121			−0.409561	−	0.912283i	$-0.634318\pi$
$659$	−21.0277			−0.819121			−0.409561	+	0.912283i	$0.634318\pi$
$660$	−16.3704			−0.637218
$661$		−	25.7516i		−	1.00162i	−0.865557	−	0.500810i	$-0.833036\pi$
$661$		−	25.7516i		−	1.00162i	0.865557	−	0.500810i	$-0.166964\pi$
$662$	−29.5517			−1.14856
$663$	−4.33399	−	6.01151i	−0.168318	−	0.233468i
$664$	20.3872			0.791176
$665$		−	27.2058i		−	1.05499i
$666$	−21.0544			−0.815841
$667$	8.32673			0.322412
$668$			110.767i			4.28570i
$669$		−	14.7201i		−	0.569111i
$670$		−	13.1966i		−	0.509830i
$671$			0.183851i			0.00709748i
$672$	−4.54213			−0.175217
$673$	18.2077			0.701856			0.350928	−	0.936403i	$-0.385866\pi$
$673$	18.2077			0.701856			0.350928	+	0.936403i	$0.385866\pi$
$674$			19.3504i			0.745351i
$675$	−8.69737			−0.334762
$676$	18.1703	−	54.5559i	0.698857	−	2.09830i
$677$	−10.3281			−0.396941			−0.198470	−	0.980107i	$-0.563597\pi$
$677$	−10.3281			−0.396941			−0.198470	+	0.980107i	$0.563597\pi$
$678$			47.3112i			1.81697i
$679$	−9.40344			−0.360871
$680$	46.7191			1.79160
$681$			0.0358913i			0.00137536i
$682$		−	26.7317i		−	1.02361i
$683$			33.4285i			1.27911i	0.768747	+	0.639553i	$0.220881\pi$
$683$			33.4285i			1.27911i	−0.768747	+	0.639553i	$0.779119\pi$
$684$		−	33.9655i		−	1.29870i
$685$	20.8813			0.797834
$686$	−31.7431			−1.21196
$687$		−	8.37257i		−	0.319433i
$688$	−35.3478			−1.34762
$689$	−6.28979	−	8.72434i	−0.239622	−	0.332371i
$690$	−39.4889			−1.50332
$691$		−	38.8290i		−	1.47712i	−0.674186	−	0.738562i	$-0.735505\pi$
$691$		−	38.8290i		−	1.47712i	0.674186	−	0.738562i	$-0.264495\pi$
$692$	−13.9922			−0.531903
$693$	0.957295			0.0363646
$694$		−	45.0678i		−	1.71075i
$695$		−	16.5368i		−	0.627276i
$696$		−	12.1471i		−	0.460433i
$697$		−	10.7528i		−	0.407290i
$698$	30.8343			1.16710
$699$	18.0020			0.680897
$700$			36.8277i			1.39196i
$701$	−47.5275			−1.79509			−0.897544	−	0.440925i	$-0.854650\pi$
$701$	−47.5275			−1.79509			−0.897544	+	0.440925i	$0.854650\pi$
$702$	7.41243	−	5.34397i	0.279764	−	0.201695i
$703$	−63.7914			−2.40594
$704$		−	1.41208i		−	0.0532199i
$705$	−4.61350			−0.173755
$706$	83.3886			3.13837
$707$			8.06365i			0.303265i
$708$		−	54.6483i		−	2.05381i
$709$			28.9052i			1.08556i	0.839875	+	0.542780i	$0.182628\pi$
$709$			28.9052i			1.08556i	−0.839875	+	0.542780i	$0.817372\pi$
$710$		−	114.042i		−	4.27993i
$711$	−3.64911			−0.136852
$712$	−32.2001			−1.20675
$713$		−	44.4046i		−	1.66297i
$714$	−4.98682			−0.186627
$715$	−7.80379	−	10.8244i	−0.291845	−	0.404808i
$716$	5.52805			0.206593
$717$		−	5.74497i		−	0.214550i
$718$	18.4951			0.690233
$719$	−47.9212			−1.78716			−0.893579	−	0.448906i	$-0.851814\pi$
$719$	−47.9212			−1.78716			−0.893579	+	0.448906i	$0.851814\pi$
$720$			24.8656i			0.926687i
$721$			12.8305i			0.477834i
$722$		−	101.287i		−	3.76953i
$723$			16.1458i			0.600469i
$724$	71.0869			2.64192
$725$	−17.2022			−0.638873
$726$		−	2.53441i		−	0.0940609i
$727$	−23.4347			−0.869146			−0.434573	−	0.900636i	$-0.643101\pi$
$727$	−23.4347			−0.869146			−0.434573	+	0.900636i	$0.643101\pi$
$728$	−12.3968	−	17.1951i	−0.459454	−	0.637292i
$729$	1.00000			0.0370370
$730$		−	31.1949i		−	1.15457i
$731$	−10.8139			−0.399966
$732$	0.813218			0.0300574
$733$			38.8733i			1.43582i	0.696136	+	0.717910i	$0.254901\pi$
$733$			38.8733i			1.43582i	−0.696136	+	0.717910i	$0.745099\pi$
$734$		−	22.6809i		−	0.837167i
$735$			22.5153i			0.830491i
$736$			19.9753i			0.736299i
$737$	1.40691			0.0518242
$738$	13.2586			0.488055
$739$		−	29.3240i		−	1.07870i	−0.842082	−	0.539350i	$-0.818670\pi$
$739$		−	29.3240i		−	1.07870i	0.842082	−	0.539350i	$-0.181330\pi$
$740$	135.996			4.99930
$741$	22.4585	−	16.1914i	0.825032	−	0.594805i
$742$	−7.23723			−0.265687
$743$			40.8183i			1.49748i	0.662864	+	0.748740i	$0.269341\pi$
$743$			40.8183i			1.49748i	−0.662864	+	0.748740i	$0.730659\pi$
$744$	−64.7776			−2.37486
$745$	27.3781			1.00305
$746$		−	46.1042i		−	1.68799i
$747$			3.31957i			0.121457i
$748$			9.09163i			0.332423i
$749$		−	7.71380i		−	0.281856i
$750$	34.6808			1.26636
$751$	−4.36042			−0.159114			−0.0795570	−	0.996830i	$-0.525351\pi$
$751$	−4.36042			−0.159114			−0.0795570	+	0.996830i	$0.525351\pi$
$752$			8.37515i			0.305410i
$753$	6.83631			0.249129
$754$	14.6608	−	10.5696i	0.533913	−	0.384923i
$755$	87.8817			3.19834
$756$		−	4.23435i		−	0.154002i
$757$	40.1387			1.45887			0.729433	−	0.684052i	$-0.239784\pi$
$757$	40.1387			1.45887			0.729433	+	0.684052i	$0.239784\pi$
$758$	−50.9577			−1.85087
$759$		−	4.20997i		−	0.152812i
$760$			174.538i			6.33117i
$761$			38.2425i			1.38629i	0.720799	+	0.693144i	$0.243775\pi$
$761$			38.2425i			1.38629i	−0.720799	+	0.693144i	$0.756225\pi$
$762$		−	16.7304i		−	0.606079i
$763$	13.7468			0.497667
$764$	−67.6357			−2.44697
$765$			7.60710i			0.275035i
$766$	20.2523			0.731745
$767$	36.1342	−	26.0509i	1.30473	−	0.940642i
$768$	−30.2963			−1.09323
$769$		−	35.0140i		−	1.26264i	−0.775523	−	0.631319i	$-0.782514\pi$
$769$		−	35.0140i		−	1.26264i	0.775523	−	0.631319i	$-0.217486\pi$
$770$	−8.97928			−0.323591
$771$	26.8038			0.965315
$772$			29.9079i			1.07641i
$773$		−	5.69564i		−	0.204858i	−0.994740	−	0.102429i	$-0.967339\pi$
$773$		−	5.69564i		−	0.204858i	0.994740	−	0.102429i	$-0.0326614\pi$
$774$		−	13.3340i		−	0.479279i
$775$			91.7355i			3.29524i
$776$	60.3277			2.16564
$777$	−7.95264			−0.285299
$778$		−	10.9390i		−	0.392181i
$779$	40.1713			1.43929
$780$	−47.8788	+	34.5181i	−1.71434	+	1.23595i
$781$	12.1582			0.435055
$782$			21.9309i			0.784248i
$783$	1.97786			0.0706830
$784$	40.8734			1.45976
$785$			48.0035i			1.71332i
$786$			14.7270i			0.525296i
$787$		−	31.2092i		−	1.11249i	−0.831019	−	0.556244i	$-0.812242\pi$
$787$		−	31.2092i		−	1.11249i	0.831019	−	0.556244i	$-0.187758\pi$
$788$			50.1244i			1.78561i
$789$	−11.9518			−0.425496
$790$	34.2282			1.21778
$791$			17.8703i			0.635395i
$792$	−6.14151			−0.218229
$793$	0.387661	+	0.537711i	0.0137663	+	0.0190947i
$794$	59.4472			2.10970
$795$			11.0400i			0.391547i
$796$	95.3836			3.38078
$797$	42.7214			1.51327			0.756634	−	0.653839i	$-0.226843\pi$
$797$	42.7214			1.51327			0.756634	+	0.653839i	$0.226843\pi$
$798$		−	18.6303i		−	0.659505i
$799$			2.56220i			0.0906440i
$800$		−	41.2669i		−	1.45901i
$801$		−	5.24302i		−	0.185253i
$802$	−6.03786			−0.213204
$803$	3.32573			0.117362
$804$		−	6.22311i		−	0.219472i
$805$	−14.9157			−0.525709
$806$	−56.3655	−	78.1826i	−1.98539	−	2.75386i
$807$	4.59663			0.161809
$808$		−	51.7323i		−	1.81993i
$809$	−13.3241			−0.468449			−0.234225	−	0.972182i	$-0.575255\pi$
$809$	−13.3241			−0.468449			−0.234225	+	0.972182i	$0.575255\pi$
$810$	−9.37985			−0.329574
$811$			41.9849i			1.47429i	0.675735	+	0.737144i	$0.263826\pi$
$811$			41.9849i			1.47429i	−0.675735	+	0.737144i	$0.736174\pi$
$812$		−	8.37496i		−	0.293903i
$813$		−	19.8969i		−	0.697815i
$814$			21.0544i			0.737956i
$815$	69.1642			2.42272
$816$	13.8096			0.483433
$817$		−	40.3997i		−	1.41341i
$818$	26.3439			0.921092
$819$	2.79981	−	2.01852i	0.0978334	−	0.0705327i
$820$	−85.6406			−2.99070
$821$			10.0872i			0.352047i	0.984386	+	0.176023i	$0.0563234\pi$
$821$			10.0872i			0.352047i	−0.984386	+	0.176023i	$0.943677\pi$
$822$	14.2994			0.498748
$823$	1.16139			0.0404835			0.0202418	−	0.999795i	$-0.493556\pi$
$823$	1.16139			0.0404835			0.0202418	+	0.999795i	$0.493556\pi$
$824$		−	82.3142i		−	2.86755i
$825$			8.69737i			0.302804i
$826$		−	29.9749i		−	1.04296i
$827$			5.42242i			0.188556i	0.995546	+	0.0942781i	$0.0300543\pi$
$827$			5.42242i			0.188556i	−0.995546	+	0.0942781i	$0.969946\pi$
$828$	−18.6217			−0.647151
$829$	16.1881			0.562237			0.281119	−	0.959673i	$-0.409295\pi$
$829$	16.1881			0.562237			0.281119	+	0.959673i	$0.409295\pi$
$830$		−	31.1371i		−	1.08078i
$831$	11.2319			0.389629
$832$	−2.97747	−	4.12994i	−0.103225	−	0.143180i
$833$	12.5043			0.433249
$834$		−	11.3243i		−	0.392127i
$835$	92.6803			3.20734
$836$	−33.9655			−1.17472
$837$		−	10.5475i		−	0.364575i
$838$			34.5812i			1.19459i
$839$		−	13.1144i		−	0.452759i	−0.974039	−	0.226379i	$-0.927311\pi$
$839$		−	13.1144i		−	0.452759i	0.974039	−	0.226379i	$-0.0726889\pi$
$840$			21.7590i			0.750758i
$841$	−25.0881			−0.865106
$842$	−16.2466			−0.559895
$843$			30.2946i			1.04340i
$844$	104.385			3.59308
$845$	−45.6477	−	15.2033i	−1.57033	−	0.523011i
$846$	−3.15929			−0.108619
$847$		−	0.957295i		−	0.0328930i
$848$	20.0415			0.688227
$849$	15.3889			0.528147
$850$		−	45.3071i		−	1.55402i
$851$			34.9739i			1.19889i
$852$		−	53.7788i		−	1.84243i
$853$			8.66325i			0.296624i	0.988941	+	0.148312i	$0.0473840\pi$
$853$			8.66325i			0.296624i	−0.988941	+	0.148312i	$0.952616\pi$
$854$	0.446055			0.0152637
$855$	−28.4194			−0.971924
$856$			49.4878i			1.69146i
$857$	28.1435			0.961365			0.480683	−	0.876895i	$-0.340389\pi$
$857$	28.1435			0.961365			0.480683	+	0.876895i	$0.340389\pi$
$858$	−5.34397	−	7.41243i	−0.182440	−	0.253056i
$859$	11.7375			0.400479			0.200240	−	0.979747i	$-0.435828\pi$
$859$	11.7375			0.400479			0.200240	+	0.979747i	$0.435828\pi$
$860$			86.1275i			2.93692i
$861$	5.00801			0.170673
$862$	−40.1325			−1.36692
$863$		−	14.6715i		−	0.499424i	−0.968320	−	0.249712i	$-0.919664\pi$
$863$		−	14.6715i		−	0.499424i	0.968320	−	0.249712i	$-0.0803360\pi$
$864$			4.74476i			0.161420i
$865$			11.7075i			0.398066i
$866$			26.9340i			0.915254i
$867$	−12.7753			−0.433870
$868$	−44.6618			−1.51592
$869$			3.64911i			0.123788i
$870$	−18.5520			−0.628973
$871$	4.11481	−	2.96656i	0.139425	−	0.100518i
$872$	−88.1922			−2.98657
$873$			9.82293i			0.332456i
$874$	−81.9319			−2.77139
$875$	13.0996			0.442847
$876$		−	14.7105i		−	0.497023i
$877$		−	18.0884i		−	0.610803i	−0.952224	−	0.305402i	$-0.901209\pi$
$877$		−	18.0884i		−	0.610803i	0.952224	−	0.305402i	$-0.0987907\pi$
$878$			43.6413i			1.47282i
$879$		−	6.95822i		−	0.234695i
$880$	24.8656			0.838220
$881$	31.0695			1.04676			0.523379	−	0.852100i	$-0.324671\pi$
$881$	31.0695			1.04676			0.523379	+	0.852100i	$0.324671\pi$
$882$			15.4183i			0.519162i
$883$	−34.4102			−1.15799			−0.578997	−	0.815330i	$-0.696556\pi$
$883$	−34.4102			−1.15799			−0.578997	+	0.815330i	$0.696556\pi$
$884$	19.1703	+	26.5904i	0.644767	+	0.894333i
$885$	−45.7250			−1.53703
$886$		−	63.7047i		−	2.14020i
$887$	−24.0600			−0.807857			−0.403928	−	0.914791i	$-0.632355\pi$
$887$	−24.0600			−0.807857			−0.403928	+	0.914791i	$0.632355\pi$
$888$	51.0200			1.71212
$889$		−	6.31938i		−	0.211945i
$890$			49.1788i			1.64848i
$891$		−	1.00000i		−	0.0335013i
$892$			65.1106i			2.18006i
$893$	−9.57213			−0.320319
$894$	18.7483			0.627036
$895$		−	4.62540i		−	0.154610i
$896$	−12.5102			−0.417938
$897$	−8.87700	−	12.3130i	−0.296394	−	0.411118i
$898$	−5.10928			−0.170499
$899$		−	20.8615i		−	0.695769i
$900$	38.4706			1.28235
$901$	6.13126			0.204262
$902$		−	13.2586i		−	0.441462i
$903$		−	5.03648i		−	0.167604i
$904$		−	114.647i		−	3.81309i
$905$		−	59.4794i		−	1.97716i
$906$	60.1807			1.99937
$907$	7.79308			0.258765			0.129382	−	0.991595i	$-0.458701\pi$
$907$	7.79308			0.258765			0.129382	+	0.991595i	$0.458701\pi$
$908$		−	0.158756i		−	0.00526851i
$909$	8.42338			0.279386
$910$	−26.2618	+	18.9334i	−0.870571	+	0.627636i
$911$	−4.88300			−0.161781			−0.0808904	−	0.996723i	$-0.525776\pi$
$911$	−4.88300			−0.161781			−0.0808904	+	0.996723i	$0.525776\pi$
$912$			51.5914i			1.70836i
$913$	3.31957			0.109862
$914$	−85.5768			−2.83063
$915$		−	0.680431i		−	0.0224944i
$916$			37.0339i			1.22364i
$917$			5.56267i			0.183696i
$918$			5.20928i			0.171932i
$919$	−53.5402			−1.76613			−0.883065	−	0.469251i	$-0.844524\pi$
$919$	−53.5402			−1.76613			−0.883065	+	0.469251i	$0.844524\pi$
$920$	95.6914			3.15485
$921$			12.6233i			0.415950i
$922$	−42.4766			−1.39889
$923$	35.5593	−	25.6364i	1.17045	−	0.843832i
$924$	−4.23435			−0.139300
$925$		−	72.2526i		−	2.37565i
$926$	69.8095			2.29408
$927$	13.4029			0.440209
$928$			9.38447i			0.308060i
$929$		−	35.1499i		−	1.15323i	−0.817015	−	0.576616i	$-0.804373\pi$
$929$		−	35.1499i		−	1.15323i	0.817015	−	0.576616i	$-0.195627\pi$
$930$			98.9339i			3.24417i
$931$			46.7150i			1.53102i
$932$	−79.6272			−2.60828
$933$	−2.12116			−0.0694435
$934$		−	58.1185i		−	1.90170i
$935$	7.60710			0.248779
$936$	−17.9622	+	12.9498i	−0.587112	+	0.423277i
$937$	12.6307			0.412626			0.206313	−	0.978486i	$-0.433854\pi$
$937$	12.6307			0.412626			0.206313	+	0.978486i	$0.433854\pi$
$938$		−	3.41342i		−	0.111452i
$939$	21.5919			0.704626
$940$	20.4067			0.665592
$941$		−	39.6660i		−	1.29308i	−0.762882	−	0.646538i	$-0.776216\pi$
$941$		−	39.6660i		−	1.29308i	0.762882	−	0.646538i	$-0.223784\pi$
$942$			32.8724i			1.07104i
$943$		−	22.0241i		−	0.717204i
$944$			83.0072i			2.70165i
$945$	−3.54294			−0.115252
$946$	−13.3340			−0.433524
$947$		−	6.08586i		−	0.197764i	−0.995099	−	0.0988819i	$-0.968473\pi$
$947$		−	6.08586i		−	0.197764i	0.995099	−	0.0988819i	$-0.0315266\pi$
$948$	16.1409			0.524233
$949$	9.72681	−	7.01252i	0.315746	−	0.227636i
$950$	169.263			5.49162
$951$			15.7684i			0.511324i
$952$	12.0843			0.391654
$953$	29.8978			0.968484			0.484242	−	0.874934i	$-0.339096\pi$
$953$	29.8978			0.968484			0.484242	+	0.874934i	$0.339096\pi$
$954$			7.56008i			0.244767i
$955$			56.5917i			1.83127i
$956$			25.4114i			0.821865i
$957$		−	1.97786i		−	0.0639351i
$958$	−14.4840			−0.467958
$959$	5.40113			0.174412
$960$			5.22612i			0.168672i
$961$	−80.2496			−2.58870
$962$	44.3946	+	61.5781i	1.43134	+	1.98536i
$963$	−8.05792			−0.259663
$964$		−	71.4170i		−	2.30019i
$965$	25.0244			0.805563
$966$	−10.2141			−0.328635
$967$			23.5725i			0.758039i	0.925389	+	0.379020i	$0.123739\pi$
$967$			23.5725i			0.758039i	−0.925389	+	0.379020i	$0.876261\pi$
$968$			6.14151i			0.197396i
$969$			15.7833i			0.507032i
$970$		−	92.1377i		−	2.95836i
$971$	31.0731			0.997182			0.498591	−	0.866837i	$-0.333851\pi$
$971$	31.0731			0.997182			0.498591	+	0.866837i	$0.333851\pi$
$972$	−4.42325			−0.141876
$973$		−	4.27738i		−	0.137126i
$974$	−26.6081			−0.852578
$975$	18.3390	+	25.4373i	0.587317	+	0.814647i
$976$	−1.23523			−0.0395386
$977$			18.8934i			0.604454i	0.953236	+	0.302227i	$0.0977301\pi$
$977$			18.8934i			0.604454i	−0.953236	+	0.302227i	$0.902270\pi$
$978$	47.3631			1.51450
$979$	−5.24302			−0.167568
$980$		−	99.5909i		−	3.18132i
$981$		−	14.3600i		−	0.458480i
$982$		−	33.0633i		−	1.05509i
$983$		−	32.8458i		−	1.04762i	−0.851836	−	0.523809i	$-0.824511\pi$
$983$		−	32.8458i		−	1.04762i	0.851836	−	0.523809i	$-0.175489\pi$
$984$	−32.1288			−1.02423
$985$	41.9398			1.33631
$986$			10.3032i			0.328122i
$987$	−1.19332			−0.0379839
$988$	−99.3394	+	71.6184i	−3.16041	+	2.27849i
$989$	−22.1493			−0.704308
$990$			9.37985i			0.298111i
$991$	−15.1204			−0.480316			−0.240158	−	0.970734i	$-0.577199\pi$
$991$	−15.1204			−0.480316			−0.240158	+	0.970734i	$0.577199\pi$
$992$	50.0453			1.58894
$993$			11.6602i			0.370025i
$994$		−	29.4980i		−	0.935620i
$995$		−	79.8088i		−	2.53011i
$996$		−	14.6833i		−	0.465257i
$997$	−2.12151			−0.0671889			−0.0335945	−	0.999436i	$-0.510695\pi$
$997$	−2.12151			−0.0671889			−0.0335945	+	0.999436i	$0.510695\pi$
$998$	97.9284			3.09987
$999$			8.30741i			0.262835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.b.298.13	yes	14
3.2	odd	2		1287.2.b.c.298.2		14
13.5	odd	4		5577.2.a.y.1.6		7
13.8	odd	4		5577.2.a.x.1.2		7
13.12	even	2	inner	429.2.b.b.298.2	✓	14
39.38	odd	2		1287.2.b.c.298.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.2	✓	14	13.12	even	2	inner
429.2.b.b.298.13	yes	14	1.1	even	1	trivial
1287.2.b.c.298.2		14	3.2	odd	2
1287.2.b.c.298.13		14	39.38	odd	2
5577.2.a.x.1.2		7	13.8	odd	4
5577.2.a.y.1.6		7	13.5	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)

\(f(q)\)	\(=\)	\(q+2.53441i q^{2} +1.00000 q^{3} -4.42325 q^{4} +3.70100i q^{5} +2.53441i q^{6} +0.957295i q^{7} -6.14151i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.53441i q^{2} +1.00000 q^{3} -4.42325 q^{4} +3.70100i q^{5} +2.53441i q^{6} +0.957295i q^{7} -6.14151i q^{8} +1.00000 q^{9} -9.37985 q^{10} -1.00000i q^{11} -4.42325 q^{12} +(-2.10857 - 2.92471i) q^{13} -2.42618 q^{14} +3.70100i q^{15} +6.71863 q^{16} +2.05542 q^{17} +2.53441i q^{18} +7.67886i q^{19} -16.3704i q^{20} +0.957295i q^{21} +2.53441 q^{22} +4.20997 q^{23} -6.14151i q^{24} -8.69737 q^{25} +(7.41243 - 5.34397i) q^{26} +1.00000 q^{27} -4.23435i q^{28} +1.97786 q^{29} -9.37985 q^{30} -10.5475i q^{31} +4.74476i q^{32} -1.00000i q^{33} +5.20928i q^{34} -3.54294 q^{35} -4.42325 q^{36} +8.30741i q^{37} -19.4614 q^{38} +(-2.10857 - 2.92471i) q^{39} +22.7297 q^{40} -5.23142i q^{41} -2.42618 q^{42} -5.26116 q^{43} +4.42325i q^{44} +3.70100i q^{45} +10.6698i q^{46} +1.24656i q^{47} +6.71863 q^{48} +6.08359 q^{49} -22.0427i q^{50} +2.05542 q^{51} +(9.32671 + 12.9367i) q^{52} +2.98297 q^{53} +2.53441i q^{54} +3.70100 q^{55} +5.87924 q^{56} +7.67886i q^{57} +5.01271i q^{58} +12.3548i q^{59} -16.3704i q^{60} -0.183851 q^{61} +26.7317 q^{62} +0.957295i q^{63} +1.41208 q^{64} +(10.8244 - 7.80379i) q^{65} +2.53441 q^{66} +1.40691i q^{67} -9.09163 q^{68} +4.20997 q^{69} -8.97928i q^{70} +12.1582i q^{71} -6.14151i q^{72} +3.32573i q^{73} -21.0544 q^{74} -8.69737 q^{75} -33.9655i q^{76} +0.957295 q^{77} +(7.41243 - 5.34397i) q^{78} -3.64911 q^{79} +24.8656i q^{80} +1.00000 q^{81} +13.2586 q^{82} +3.31957i q^{83} -4.23435i q^{84} +7.60710i q^{85} -13.3340i q^{86} +1.97786 q^{87} -6.14151 q^{88} -5.24302i q^{89} -9.37985 q^{90} +(2.79981 - 2.01852i) q^{91} -18.6217 q^{92} -10.5475i q^{93} -3.15929 q^{94} -28.4194 q^{95} +4.74476i q^{96} +9.82293i q^{97} +15.4183i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9} - 18 q^{12} + 16 q^{14} + 34 q^{16} + 4 q^{17} + 6 q^{22} - 8 q^{23} - 26 q^{25} - 6 q^{26} + 14 q^{27} - 24 q^{29} - 8 q^{35} - 18 q^{36} - 32 q^{38} - 20 q^{40} + 16 q^{42} + 32 q^{43} + 34 q^{48} - 46 q^{49} + 4 q^{51} + 4 q^{52} + 20 q^{53} + 12 q^{55} - 32 q^{56} - 20 q^{61} + 72 q^{62} - 58 q^{64} + 12 q^{65} + 6 q^{66} - 20 q^{68} - 8 q^{69} - 26 q^{75} - 12 q^{77} - 6 q^{78} + 12 q^{79} + 14 q^{81} + 20 q^{82} - 24 q^{87} - 30 q^{88} + 16 q^{91} - 24 q^{92} + 64 q^{94} - 36 q^{95}+O(q^{100}) \) 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9 - 18 * q^12 + 16 * q^14 + 34 * q^16 + 4 * q^17 + 6 * q^22 - 8 * q^23 - 26 * q^25 - 6 * q^26 + 14 * q^27 - 24 * q^29 - 8 * q^35 - 18 * q^36 - 32 * q^38 - 20 * q^40 + 16 * q^42 + 32 * q^43 + 34 * q^48 - 46 * q^49 + 4 * q^51 + 4 * q^52 + 20 * q^53 + 12 * q^55 - 32 * q^56 - 20 * q^61 + 72 * q^62 - 58 * q^64 + 12 * q^65 + 6 * q^66 - 20 * q^68 - 8 * q^69 - 26 * q^75 - 12 * q^77 - 6 * q^78 + 12 * q^79 + 14 * q^81 + 20 * q^82 - 24 * q^87 - 30 * q^88 + 16 * q^91 - 24 * q^92 + 64 * q^94 - 36 * q^95

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