LMFDB - Embedded newform 429.2.b.b.298.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("429.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$14$
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			298.3
Root			$-2.15754i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.b.298.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15754i q^{2} +1.00000 q^{3} -2.65498 q^{4} +0.710210i q^{5} -2.15754i q^{6} -2.30964i q^{7} +1.41315i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15754i q^{2} +1.00000 q^{3} -2.65498 q^{4} +0.710210i q^{5} -2.15754i q^{6} -2.30964i q^{7} +1.41315i q^{8} +1.00000 q^{9} +1.53231 q^{10} -1.00000i q^{11} -2.65498 q^{12} +(-1.40848 - 3.31906i) q^{13} -4.98315 q^{14} +0.710210i q^{15} -2.26104 q^{16} +6.68027 q^{17} -2.15754i q^{18} -0.242517i q^{19} -1.88559i q^{20} -2.30964i q^{21} -2.15754 q^{22} -9.53531 q^{23} +1.41315i q^{24} +4.49560 q^{25} +(-7.16101 + 3.03885i) q^{26} +1.00000 q^{27} +6.13206i q^{28} -2.95273 q^{29} +1.53231 q^{30} -4.02017i q^{31} +7.70458i q^{32} -1.00000i q^{33} -14.4130i q^{34} +1.64033 q^{35} -2.65498 q^{36} -3.42304i q^{37} -0.523240 q^{38} +(-1.40848 - 3.31906i) q^{39} -1.00363 q^{40} +9.46022i q^{41} -4.98315 q^{42} +11.8791 q^{43} +2.65498i q^{44} +0.710210i q^{45} +20.5728i q^{46} +12.9178i q^{47} -2.26104 q^{48} +1.66555 q^{49} -9.69944i q^{50} +6.68027 q^{51} +(3.73948 + 8.81205i) q^{52} +6.78954 q^{53} -2.15754i q^{54} +0.710210 q^{55} +3.26386 q^{56} -0.242517i q^{57} +6.37063i q^{58} -7.81320i q^{59} -1.88559i q^{60} +0.910585 q^{61} -8.67368 q^{62} -2.30964i q^{63} +12.1009 q^{64} +(2.35723 - 1.00032i) q^{65} -2.15754 q^{66} +9.32216i q^{67} -17.7360 q^{68} -9.53531 q^{69} -3.53908i q^{70} +12.9704i q^{71} +1.41315i q^{72} -8.51665i q^{73} -7.38534 q^{74} +4.49560 q^{75} +0.643877i q^{76} -2.30964 q^{77} +(-7.16101 + 3.03885i) q^{78} +1.82360 q^{79} -1.60581i q^{80} +1.00000 q^{81} +20.4108 q^{82} +4.64671i q^{83} +6.13206i q^{84} +4.74440i q^{85} -25.6297i q^{86} -2.95273 q^{87} +1.41315 q^{88} -14.7714i q^{89} +1.53231 q^{90} +(-7.66585 + 3.25308i) q^{91} +25.3161 q^{92} -4.02017i q^{93} +27.8707 q^{94} +0.172238 q^{95} +7.70458i q^{96} +1.86542i q^{97} -3.59349i q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.15754i		−	1.52561i	−0.646628	−	0.762806i	$-0.723821\pi$
$2$		−	2.15754i		−	1.52561i	0.646628	−	0.762806i	$-0.276179\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−2.65498			−1.32749
$5$			0.710210i			0.317616i	0.987310	+	0.158808i	$0.0507650\pi$
$5$			0.710210i			0.317616i	−0.987310	+	0.158808i	$0.949235\pi$
$6$		−	2.15754i		−	0.880812i
$7$		−	2.30964i		−	0.872963i	−0.899713	−	0.436482i	$-0.856224\pi$
$7$		−	2.30964i		−	0.872963i	0.899713	−	0.436482i	$-0.143776\pi$
$8$			1.41315i			0.499622i
$9$	1.00000			0.333333
$10$	1.53231			0.484558
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−2.65498			−0.766427
$13$	−1.40848	−	3.31906i	−0.390642	−	0.920543i
$13$	−1.40848	−	3.31906i	−0.390642	−	0.920543i
$14$	−4.98315			−1.33180
$15$			0.710210i			0.183375i
$16$	−2.26104			−0.565261
$17$	6.68027			1.62020			0.810102	−	0.586289i	$-0.199412\pi$
$17$	6.68027			1.62020			0.810102	+	0.586289i	$0.199412\pi$
$18$		−	2.15754i		−	0.508537i
$19$		−	0.242517i		−	0.0556372i	−0.999613	−	0.0278186i	$-0.991144\pi$
$19$		−	0.242517i		−	0.0556372i	0.999613	−	0.0278186i	$-0.00885607\pi$
$20$		−	1.88559i		−	0.421631i
$21$		−	2.30964i		−	0.504005i
$22$	−2.15754			−0.459989
$23$	−9.53531			−1.98825			−0.994125	−	0.108242i	$-0.965478\pi$
$23$	−9.53531			−1.98825			−0.994125	+	0.108242i	$0.965478\pi$
$24$			1.41315i			0.288457i
$25$	4.49560			0.899120
$26$	−7.16101	+	3.03885i	−1.40439	+	0.595968i
$27$	1.00000			0.192450
$28$			6.13206i			1.15885i
$29$	−2.95273			−0.548308			−0.274154	−	0.961686i	$-0.588398\pi$
$29$	−2.95273			−0.548308			−0.274154	+	0.961686i	$0.588398\pi$
$30$	1.53231			0.279760
$31$		−	4.02017i		−	0.722044i	−0.932557	−	0.361022i	$-0.882428\pi$
$31$		−	4.02017i		−	0.722044i	0.932557	−	0.361022i	$-0.117572\pi$
$32$			7.70458i			1.36199i
$33$		−	1.00000i		−	0.174078i
$34$		−	14.4130i		−	2.47180i
$35$	1.64033			0.277267
$36$	−2.65498			−0.442497
$37$		−	3.42304i		−	0.562744i	−0.959599	−	0.281372i	$-0.909211\pi$
$37$		−	3.42304i		−	0.562744i	0.959599	−	0.281372i	$-0.0907895\pi$
$38$	−0.523240			−0.0848807
$39$	−1.40848	−	3.31906i	−0.225537	−	0.531476i
$40$	−1.00363			−0.158688
$41$			9.46022i			1.47744i	0.674013	+	0.738719i	$0.264569\pi$
$41$			9.46022i			1.47744i	−0.674013	+	0.738719i	$0.735431\pi$
$42$	−4.98315			−0.768916
$43$	11.8791			1.81155			0.905776	−	0.423757i	$-0.139289\pi$
$43$	11.8791			1.81155			0.905776	+	0.423757i	$0.139289\pi$
$44$			2.65498i			0.400253i
$45$			0.710210i			0.105872i
$46$			20.5728i			3.03330i
$47$			12.9178i			1.88426i	0.335249	+	0.942130i	$0.391180\pi$
$47$			12.9178i			1.88426i	−0.335249	+	0.942130i	$0.608820\pi$
$48$	−2.26104			−0.326353
$49$	1.66555			0.237935
$50$		−	9.69944i		−	1.37171i
$51$	6.68027			0.935425
$52$	3.73948	+	8.81205i	0.518573	+	1.22201i
$53$	6.78954			0.932615			0.466307	−	0.884623i	$-0.345584\pi$
$53$	6.78954			0.932615			0.466307	+	0.884623i	$0.345584\pi$
$54$		−	2.15754i		−	0.293604i
$55$	0.710210			0.0957647
$56$	3.26386			0.436152
$57$		−	0.242517i		−	0.0321221i
$58$			6.37063i			0.836504i
$59$		−	7.81320i		−	1.01719i	−0.861005	−	0.508596i	$-0.830165\pi$
$59$		−	7.81320i		−	1.01719i	0.861005	−	0.508596i	$-0.169835\pi$
$60$		−	1.88559i		−	0.243429i
$61$	0.910585			0.116588			0.0582942	−	0.998299i	$-0.481434\pi$
$61$	0.910585			0.116588			0.0582942	+	0.998299i	$0.481434\pi$
$62$	−8.67368			−1.10156
$63$		−	2.30964i		−	0.290988i
$64$	12.1009			1.51261
$65$	2.35723	−	1.00032i	0.292379	−	0.124074i
$66$	−2.15754			−0.265575
$67$			9.32216i			1.13888i	0.822032	+	0.569442i	$0.192841\pi$
$67$			9.32216i			1.13888i	−0.822032	+	0.569442i	$0.807159\pi$
$68$	−17.7360			−2.15080
$69$	−9.53531			−1.14792
$70$		−	3.53908i		−	0.423001i
$71$			12.9704i			1.53930i	0.638466	+	0.769650i	$0.279569\pi$
$71$			12.9704i			1.53930i	−0.638466	+	0.769650i	$0.720431\pi$
$72$			1.41315i			0.166541i
$73$		−	8.51665i		−	0.996798i	−0.866948	−	0.498399i	$-0.833921\pi$
$73$		−	8.51665i		−	0.996798i	0.866948	−	0.498399i	$-0.166079\pi$
$74$	−7.38534			−0.858529
$75$	4.49560			0.519107
$76$			0.643877i			0.0738578i
$77$	−2.30964			−0.263208
$78$	−7.16101	+	3.03885i	−0.810825	+	0.344082i
$79$	1.82360			0.205172			0.102586	−	0.994724i	$-0.467288\pi$
$79$	1.82360			0.205172			0.102586	+	0.994724i	$0.467288\pi$
$80$		−	1.60581i		−	0.179536i
$81$	1.00000			0.111111
$82$	20.4108			2.25400
$83$			4.64671i			0.510042i	0.966935	+	0.255021i	$0.0820824\pi$
$83$			4.64671i			0.510042i	−0.966935	+	0.255021i	$0.917918\pi$
$84$			6.13206i			0.669062i
$85$			4.74440i			0.514602i
$86$		−	25.6297i		−	2.76372i
$87$	−2.95273			−0.316566
$88$	1.41315			0.150642
$89$		−	14.7714i		−	1.56576i	−0.622171	−	0.782881i	$-0.713749\pi$
$89$		−	14.7714i		−	1.56576i	0.622171	−	0.782881i	$-0.286251\pi$
$90$	1.53231			0.161519
$91$	−7.66585	+	3.25308i	−0.803600	+	0.341016i
$92$	25.3161			2.63938
$93$		−	4.02017i		−	0.416872i
$94$	27.8707			2.87465
$95$	0.172238			0.0176712
$96$			7.70458i			0.786345i
$97$			1.86542i			0.189405i	0.995506	+	0.0947025i	$0.0301900\pi$
$97$			1.86542i			0.189405i	−0.995506	+	0.0947025i	$0.969810\pi$
$98$		−	3.59349i		−	0.362997i
$99$		−	1.00000i		−	0.100504i
$100$	−11.9357			−1.19357
$101$	2.45086			0.243870			0.121935	−	0.992538i	$-0.461090\pi$
$101$	2.45086			0.243870			0.121935	+	0.992538i	$0.461090\pi$
$102$		−	14.4130i		−	1.42709i
$103$	−10.2811			−1.01302			−0.506512	−	0.862233i	$-0.669066\pi$
$103$	−10.2811			−1.01302			−0.506512	+	0.862233i	$0.669066\pi$
$104$	4.69032	−	1.99039i	0.459924	−	0.195173i
$105$	1.64033			0.160080
$106$		−	14.6487i		−	1.42281i
$107$	19.6690			1.90148			0.950739	−	0.309993i	$-0.100327\pi$
$107$	19.6690			1.90148			0.950739	+	0.309993i	$0.100327\pi$
$108$	−2.65498			−0.255476
$109$			1.27506i			0.122128i	0.998134	+	0.0610642i	$0.0194494\pi$
$109$			1.27506i			0.122128i	−0.998134	+	0.0610642i	$0.980551\pi$
$110$		−	1.53231i		−	0.146100i
$111$		−	3.42304i		−	0.324900i
$112$			5.22220i			0.493452i
$113$	−0.638739			−0.0600875			−0.0300438	−	0.999549i	$-0.509565\pi$
$113$	−0.638739			−0.0600875			−0.0300438	+	0.999549i	$0.509565\pi$
$114$	−0.523240			−0.0490059
$115$		−	6.77207i		−	0.631499i
$116$	7.83943			0.727873
$117$	−1.40848	−	3.31906i	−0.130214	−	0.306848i
$118$	−16.8573			−1.55184
$119$		−	15.4290i		−	1.41438i
$120$	−1.00363			−0.0916185
$121$	−1.00000			−0.0909091
$122$		−	1.96462i		−	0.177869i
$123$			9.46022i			0.853000i
$124$			10.6735i			0.958506i
$125$			6.74387i			0.603190i
$126$	−4.98315			−0.443934
$127$	−10.3681			−0.920021			−0.460010	−	0.887914i	$-0.652154\pi$
$127$	−10.3681			−0.920021			−0.460010	+	0.887914i	$0.652154\pi$
$128$		−	10.6989i		−	0.945660i
$129$	11.8791			1.04590
$130$	−2.15822	−	5.08582i	−0.189289	−	0.446056i
$131$	−5.68692			−0.496868			−0.248434	−	0.968649i	$-0.579916\pi$
$131$	−5.68692			−0.496868			−0.248434	+	0.968649i	$0.579916\pi$
$132$			2.65498i			0.231086i
$133$	−0.560127			−0.0485692
$134$	20.1129			1.73749
$135$			0.710210i			0.0611251i
$136$			9.44019i			0.809490i
$137$		−	4.86363i		−	0.415528i	−0.978179	−	0.207764i	$-0.933381\pi$
$137$		−	4.86363i		−	0.415528i	0.978179	−	0.207764i	$-0.0666186\pi$
$138$			20.5728i			1.75127i
$139$	−4.41515			−0.374488			−0.187244	−	0.982313i	$-0.559956\pi$
$139$	−4.41515			−0.374488			−0.187244	+	0.982313i	$0.559956\pi$
$140$	−4.35505			−0.368069
$141$			12.9178i			1.08788i
$142$	27.9841			2.34837
$143$	−3.31906	+	1.40848i	−0.277554	+	0.117783i
$144$	−2.26104			−0.188420
$145$		−	2.09706i		−	0.174151i
$146$	−18.3750			−1.52073
$147$	1.66555			0.137372
$148$			9.08810i			0.747037i
$149$			9.50356i			0.778562i	0.921119	+	0.389281i	$0.127276\pi$
$149$			9.50356i			0.778562i	−0.921119	+	0.389281i	$0.872724\pi$
$150$		−	9.69944i		−	0.791956i
$151$		−	15.2126i		−	1.23798i	−0.785398	−	0.618991i	$-0.787542\pi$
$151$		−	15.2126i		−	1.23798i	0.785398	−	0.618991i	$-0.212458\pi$
$152$	0.342711			0.0277976
$153$	6.68027			0.540068
$154$			4.98315i			0.401554i
$155$	2.85516			0.229332
$156$	3.73948	+	8.81205i	0.299398	+	0.705528i
$157$	20.1949			1.61173			0.805866	−	0.592098i	$-0.201700\pi$
$157$	20.1949			1.61173			0.805866	+	0.592098i	$0.201700\pi$
$158$		−	3.93450i		−	0.313012i
$159$	6.78954			0.538445
$160$	−5.47187			−0.432589
$161$			22.0232i			1.73567i
$162$		−	2.15754i		−	0.169512i
$163$			16.4974i			1.29217i	0.763264	+	0.646087i	$0.223596\pi$
$163$			16.4974i			1.29217i	−0.763264	+	0.646087i	$0.776404\pi$
$164$		−	25.1167i		−	1.96129i
$165$	0.710210			0.0552898
$166$	10.0255			0.778126
$167$			5.50507i			0.425995i	0.977053	+	0.212998i	$0.0683226\pi$
$167$			5.50507i			0.425995i	−0.977053	+	0.212998i	$0.931677\pi$
$168$	3.26386			0.251812
$169$	−9.03237	+	9.34967i	−0.694798	+	0.719205i
$170$	10.2362			0.785082
$171$		−	0.242517i		−	0.0185457i
$172$	−31.5389			−2.40482
$173$	12.7126			0.966524			0.483262	−	0.875476i	$-0.339452\pi$
$173$	12.7126			0.966524			0.483262	+	0.875476i	$0.339452\pi$
$174$			6.37063i			0.482956i
$175$		−	10.3832i		−	0.784899i
$176$			2.26104i			0.170432i
$177$		−	7.81320i		−	0.587276i
$178$	−31.8698			−2.38875
$179$	−24.4279			−1.82583			−0.912913	−	0.408154i	$-0.866172\pi$
$179$	−24.4279			−1.82583			−0.912913	+	0.408154i	$0.866172\pi$
$180$		−	1.88559i		−	0.140544i
$181$	−0.931324			−0.0692248			−0.0346124	−	0.999401i	$-0.511020\pi$
$181$	−0.931324			−0.0692248			−0.0346124	+	0.999401i	$0.511020\pi$
$182$	7.01866	+	16.5394i	0.520258	+	1.22598i
$183$	0.910585			0.0673124
$184$		−	13.4748i		−	0.993374i
$185$	2.43108			0.178736
$186$	−8.67368			−0.635985
$187$		−	6.68027i		−	0.488510i
$188$		−	34.2966i		−	2.50134i
$189$		−	2.30964i		−	0.168002i
$190$		−	0.371610i		−	0.0269594i
$191$	4.68209			0.338784			0.169392	−	0.985549i	$-0.445820\pi$
$191$	4.68209			0.338784			0.169392	+	0.985549i	$0.445820\pi$
$192$	12.1009			0.873304
$193$			10.2671i			0.739039i	0.929223	+	0.369520i	$0.120478\pi$
$193$			10.2671i			0.739039i	−0.929223	+	0.369520i	$0.879522\pi$
$194$	4.02473			0.288959
$195$	2.35723	−	1.00032i	0.168805	−	0.0716341i
$196$	−4.42200			−0.315857
$197$			11.5842i			0.825341i	0.910880	+	0.412671i	$0.135404\pi$
$197$			11.5842i			0.825341i	−0.910880	+	0.412671i	$0.864596\pi$
$198$	−2.15754			−0.153330
$199$	−17.2330			−1.22162			−0.610808	−	0.791779i	$-0.709155\pi$
$199$	−17.2330			−1.22162			−0.610808	+	0.791779i	$0.709155\pi$
$200$			6.35294i			0.449221i
$201$			9.32216i			0.657535i
$202$		−	5.28783i		−	0.372050i
$203$			6.81975i			0.478652i
$204$	−17.7360			−1.24177
$205$	−6.71875			−0.469258
$206$			22.1818i			1.54548i
$207$	−9.53531			−0.662750
$208$	3.18463	+	7.50454i	0.220814	+	0.520346i
$209$	−0.242517			−0.0167752
$210$		−	3.53908i		−	0.244220i
$211$	−10.6905			−0.735967			−0.367983	−	0.929832i	$-0.619952\pi$
$211$	−10.6905			−0.735967			−0.367983	+	0.929832i	$0.619952\pi$
$212$	−18.0261			−1.23804
$213$			12.9704i			0.888716i
$214$		−	42.4367i		−	2.90092i
$215$			8.43668i			0.575377i
$216$			1.41315i			0.0961523i
$217$	−9.28516			−0.630318
$218$	2.75099			0.186320
$219$		−	8.51665i		−	0.575502i
$220$	−1.88559			−0.127127
$221$	−9.40902	−	22.1722i	−0.632919	−	1.49147i
$222$	−7.38534			−0.495672
$223$		−	5.33992i		−	0.357587i	−0.983887	−	0.178794i	$-0.942781\pi$
$223$		−	5.33992i		−	0.357587i	0.983887	−	0.178794i	$-0.0572194\pi$
$224$	17.7948			1.18897
$225$	4.49560			0.299707
$226$			1.37811i			0.0916702i
$227$		−	7.82431i		−	0.519318i	−0.965700	−	0.259659i	$-0.916390\pi$
$227$		−	7.82431i		−	0.519318i	0.965700	−	0.259659i	$-0.0836101\pi$
$228$			0.643877i			0.0426418i
$229$			10.6805i			0.705784i	0.935664	+	0.352892i	$0.114802\pi$
$229$			10.6805i			0.705784i	−0.935664	+	0.352892i	$0.885198\pi$
$230$	−14.6110			−0.963422
$231$	−2.30964			−0.151963
$232$		−	4.17263i		−	0.273947i
$233$	−15.4509			−1.01222			−0.506112	−	0.862468i	$-0.668918\pi$
$233$	−15.4509			−1.01222			−0.506112	+	0.862468i	$0.668918\pi$
$234$	−7.16101	+	3.03885i	−0.468130	+	0.198656i
$235$	−9.17437			−0.598470
$236$			20.7439i			1.35031i
$237$	1.82360			0.118456
$238$	−33.2888			−2.15779
$239$		−	16.9365i		−	1.09553i	−0.836632	−	0.547765i	$-0.815479\pi$
$239$		−	16.9365i		−	1.09553i	0.836632	−	0.547765i	$-0.184521\pi$
$240$		−	1.60581i		−	0.103655i
$241$			0.0799646i			0.00515098i	0.999997	+	0.00257549i	$0.000819804\pi$
$241$			0.0799646i			0.00515098i	−0.999997	+	0.00257549i	$0.999180\pi$
$242$			2.15754i			0.138692i
$243$	1.00000			0.0641500
$244$	−2.41758			−0.154770
$245$			1.18289i			0.0755720i
$246$	20.4108			1.30135
$247$	−0.804929	+	0.341580i	−0.0512164	+	0.0217342i
$248$	5.68108			0.360749
$249$			4.64671i			0.294473i
$250$	14.5502			0.920234
$251$	7.57174			0.477924			0.238962	−	0.971029i	$-0.423193\pi$
$251$	7.57174			0.477924			0.238962	+	0.971029i	$0.423193\pi$
$252$			6.13206i			0.386283i
$253$			9.53531i			0.599480i
$254$			22.3696i			1.40359i
$255$			4.74440i			0.297106i
$256$	1.11835			0.0698970
$257$	−23.0242			−1.43621			−0.718105	−	0.695935i	$-0.754990\pi$
$257$	−23.0242			−1.43621			−0.718105	+	0.695935i	$0.754990\pi$
$258$		−	25.6297i		−	1.59564i
$259$	−7.90600			−0.491255
$260$	−6.25840	+	2.65582i	−0.388130	+	0.164707i
$261$	−2.95273			−0.182769
$262$			12.2698i			0.758028i
$263$	−5.95047			−0.366922			−0.183461	−	0.983027i	$-0.558730\pi$
$263$	−5.95047			−0.366922			−0.183461	+	0.983027i	$0.558730\pi$
$264$	1.41315			0.0869731
$265$			4.82200i			0.296213i
$266$			1.20850i			0.0740977i
$267$		−	14.7714i		−	0.903994i
$268$		−	24.7502i		−	1.51186i
$269$	−1.17571			−0.0716841			−0.0358420	−	0.999357i	$-0.511411\pi$
$269$	−1.17571			−0.0716841			−0.0358420	+	0.999357i	$0.511411\pi$
$270$	1.53231			0.0932532
$271$			7.12706i			0.432938i	0.976290	+	0.216469i	$0.0694540\pi$
$271$			7.12706i			0.432938i	−0.976290	+	0.216469i	$0.930546\pi$
$272$	−15.1044			−0.915837
$273$	−7.66585	+	3.25308i	−0.463959	+	0.196886i
$274$	−10.4935			−0.633934
$275$		−	4.49560i		−	0.271095i
$276$	25.3161			1.52385
$277$	11.9736			0.719426			0.359713	−	0.933063i	$-0.382875\pi$
$277$	11.9736			0.719426			0.359713	+	0.933063i	$0.382875\pi$
$278$			9.52586i			0.571323i
$279$		−	4.02017i		−	0.240681i
$280$			2.31803i			0.138529i
$281$		−	18.7901i		−	1.12092i	−0.828181	−	0.560461i	$-0.810624\pi$
$281$		−	18.7901i		−	1.12092i	0.828181	−	0.560461i	$-0.189376\pi$
$282$	27.8707			1.65968
$283$	−10.5237			−0.625568			−0.312784	−	0.949824i	$-0.601262\pi$
$283$	−10.5237			−0.625568			−0.312784	+	0.949824i	$0.601262\pi$
$284$		−	34.4361i		−	2.04341i
$285$	0.172238			0.0102025
$286$	3.03885	+	7.16101i	0.179691	+	0.423440i
$287$	21.8497			1.28975
$288$			7.70458i			0.453997i
$289$	27.6260			1.62506
$290$	−4.52448			−0.265687
$291$			1.86542i			0.109353i
$292$			22.6115i			1.32324i
$293$			14.0111i			0.818540i	0.912413	+	0.409270i	$0.134217\pi$
$293$			14.0111i			0.818540i	−0.912413	+	0.409270i	$0.865783\pi$
$294$		−	3.59349i		−	0.209576i
$295$	5.54901			0.323076
$296$	4.83725			0.281159
$297$		−	1.00000i		−	0.0580259i
$298$	20.5043			1.18778
$299$	13.4303	+	31.6483i	0.776693	+	1.83027i
$300$	−11.9357			−0.689110
$301$		−	27.4366i		−	1.58142i
$302$	−32.8217			−1.88868
$303$	2.45086			0.140798
$304$			0.548341i			0.0314495i
$305$			0.646706i			0.0370303i
$306$		−	14.4130i		−	0.823934i
$307$		−	2.52126i		−	0.143896i	−0.997408	−	0.0719481i	$-0.977078\pi$
$307$		−	2.52126i		−	0.143896i	0.997408	−	0.0719481i	$-0.0229216\pi$
$308$	6.13206			0.349406
$309$	−10.2811			−0.584870
$310$		−	6.16013i		−	0.349872i
$311$	22.9380			1.30069			0.650347	−	0.759638i	$-0.274624\pi$
$311$	22.9380			1.30069			0.650347	+	0.759638i	$0.274624\pi$
$312$	4.69032	−	1.99039i	0.265537	−	0.112683i
$313$	−21.6566			−1.22410			−0.612051	−	0.790818i	$-0.709655\pi$
$313$	−21.6566			−1.22410			−0.612051	+	0.790818i	$0.709655\pi$
$314$		−	43.5714i		−	2.45888i
$315$	1.64033			0.0924222
$316$	−4.84163			−0.272363
$317$			26.6050i			1.49429i	0.664664	+	0.747143i	$0.268575\pi$
$317$			26.6050i			1.49429i	−0.664664	+	0.747143i	$0.731425\pi$
$318$		−	14.6487i		−	0.821458i
$319$			2.95273i			0.165321i
$320$			8.59415i			0.480428i
$321$	19.6690			1.09782
$322$	47.5159			2.64796
$323$		−	1.62008i		−	0.0901435i
$324$	−2.65498			−0.147499
$325$	−6.33196	−	14.9212i	−0.351234	−	0.827679i
$326$	35.5937			1.97135
$327$			1.27506i			0.0705108i
$328$	−13.3687			−0.738161
$329$	29.8356			1.64489
$330$		−	1.53231i		−	0.0843507i
$331$		−	24.7670i		−	1.36132i	−0.732600	−	0.680659i	$-0.761693\pi$
$331$		−	24.7670i		−	1.36132i	0.732600	−	0.680659i	$-0.238307\pi$
$332$		−	12.3369i		−	0.677076i
$333$		−	3.42304i		−	0.187581i
$334$	11.8774			0.649903
$335$	−6.62069			−0.361727
$336$			5.22220i			0.284894i
$337$	28.2890			1.54100			0.770499	−	0.637441i	$-0.220007\pi$
$337$	28.2890			1.54100			0.770499	+	0.637441i	$0.220007\pi$
$338$	20.1723	+	19.4877i	1.09723	+	1.05999i
$339$	−0.638739			−0.0346916
$340$		−	12.5963i		−	0.683129i
$341$	−4.02017			−0.217704
$342$	−0.523240			−0.0282936
$343$		−	20.0143i		−	1.08067i
$344$			16.7869i			0.905091i
$345$		−	6.77207i		−	0.364596i
$346$		−	27.4280i		−	1.47454i
$347$	−18.0814			−0.970661			−0.485331	−	0.874331i	$-0.661301\pi$
$347$	−18.0814			−0.970661			−0.485331	+	0.874331i	$0.661301\pi$
$348$	7.83943			0.420238
$349$		−	21.0326i		−	1.12585i	−0.826508	−	0.562924i	$-0.809676\pi$
$349$		−	21.0326i		−	1.12585i	0.826508	−	0.562924i	$-0.190324\pi$
$350$	−22.4022			−1.19745
$351$	−1.40848	−	3.31906i	−0.0751791	−	0.177159i
$352$	7.70458			0.410655
$353$			2.20127i			0.117162i	0.998283	+	0.0585810i	$0.0186576\pi$
$353$			2.20127i			0.117162i	−0.998283	+	0.0585810i	$0.981342\pi$
$354$	−16.8573			−0.895955
$355$	−9.21169			−0.488906
$356$			39.2177i			2.07853i
$357$		−	15.4290i		−	0.816591i
$358$			52.7041i			2.78550i
$359$			7.76540i			0.409842i	0.978778	+	0.204921i	$0.0656938\pi$
$359$			7.76540i			0.409842i	−0.978778	+	0.204921i	$0.934306\pi$
$360$	−1.00363			−0.0528959
$361$	18.9412			0.996905
$362$			2.00937i			0.105610i
$363$	−1.00000			−0.0524864
$364$	20.3527	−	8.63687i	1.06677	−	0.452695i
$365$	6.04861			0.316599
$366$		−	1.96462i		−	0.102692i
$367$	−11.9604			−0.624326			−0.312163	−	0.950028i	$-0.601054\pi$
$367$	−11.9604			−0.624326			−0.312163	+	0.950028i	$0.601054\pi$
$368$	21.5597			1.12388
$369$			9.46022i			0.492480i
$370$		−	5.24514i		−	0.272682i
$371$		−	15.6814i		−	0.814138i
$372$			10.6735i			0.553394i
$373$	14.1243			0.731330			0.365665	−	0.930747i	$-0.380842\pi$
$373$	14.1243			0.731330			0.365665	+	0.930747i	$0.380842\pi$
$374$	−14.4130			−0.745276
$375$			6.74387i			0.348252i
$376$	−18.2548			−0.941418
$377$	4.15885	+	9.80029i	0.214192	+	0.504741i
$378$	−4.98315			−0.256305
$379$		−	3.34432i		−	0.171786i	−0.996304	−	0.0858931i	$-0.972626\pi$
$379$		−	3.34432i		−	0.171786i	0.996304	−	0.0858931i	$-0.0273744\pi$
$380$	−0.457288			−0.0234584
$381$	−10.3681			−0.531174
$382$		−	10.1018i		−	0.516853i
$383$		−	5.63621i		−	0.287997i	−0.989578	−	0.143998i	$-0.954004\pi$
$383$		−	5.63621i		−	0.287997i	0.989578	−	0.143998i	$-0.0459960\pi$
$384$		−	10.6989i		−	0.545977i
$385$		−	1.64033i		−	0.0835991i
$386$	22.1516			1.12749
$387$	11.8791			0.603850
$388$		−	4.95266i		−	0.251433i
$389$	−14.3490			−0.727523			−0.363761	−	0.931492i	$-0.618508\pi$
$389$	−14.3490			−0.727523			−0.363761	+	0.931492i	$0.618508\pi$
$390$	−2.15822	−	5.08582i	−0.109286	−	0.257531i
$391$	−63.6984			−3.22137
$392$			2.35366i			0.118878i
$393$	−5.68692			−0.286867
$394$	24.9934			1.25915
$395$			1.29514i			0.0651657i
$396$			2.65498i			0.133418i
$397$			14.8769i			0.746648i	0.927701	+	0.373324i	$0.121782\pi$
$397$			14.8769i			0.746648i	−0.927701	+	0.373324i	$0.878218\pi$
$398$			37.1809i			1.86371i
$399$	−0.560127			−0.0280414
$400$	−10.1647			−0.508237
$401$		−	19.6380i		−	0.980675i	−0.871533	−	0.490337i	$-0.836874\pi$
$401$		−	19.6380i		−	0.980675i	0.871533	−	0.490337i	$-0.163126\pi$
$402$	20.1129			1.00314
$403$	−13.3432	+	5.66233i	−0.664672	+	0.282061i
$404$	−6.50698			−0.323734
$405$			0.710210i			0.0352906i
$406$	14.7139			0.730237
$407$	−3.42304			−0.169674
$408$			9.44019i			0.467359i
$409$			23.1731i			1.14584i	0.819613	+	0.572918i	$0.194189\pi$
$409$			23.1731i			1.14584i	−0.819613	+	0.572918i	$0.805811\pi$
$410$			14.4960i			0.715905i
$411$		−	4.86363i		−	0.239905i
$412$	27.2961			1.34478
$413$	−18.0457			−0.887971
$414$			20.5728i			1.01110i
$415$	−3.30014			−0.161997
$416$	25.5720	−	10.8517i	1.25377	−	0.532050i
$417$	−4.41515			−0.216211
$418$			0.523240i			0.0255925i
$419$	−3.70294			−0.180900			−0.0904502	−	0.995901i	$-0.528831\pi$
$419$	−3.70294			−0.180900			−0.0904502	+	0.995901i	$0.528831\pi$
$420$	−4.35505			−0.212505
$421$			23.7239i			1.15623i	0.815955	+	0.578116i	$0.196212\pi$
$421$			23.7239i			1.15623i	−0.815955	+	0.578116i	$0.803788\pi$
$422$			23.0653i			1.12280i
$423$			12.9178i			0.628086i
$424$			9.59460i			0.465955i
$425$	30.0318			1.45676
$426$	27.9841			1.35583
$427$		−	2.10313i		−	0.101777i
$428$	−52.2209			−2.52419
$429$	−3.31906	+	1.40848i	−0.160246	+	0.0680020i
$430$	18.2025			0.877802
$431$		−	31.0695i		−	1.49656i	−0.663381	−	0.748282i	$-0.730879\pi$
$431$		−	31.0695i		−	1.49656i	0.663381	−	0.748282i	$-0.269121\pi$
$432$	−2.26104			−0.108784
$433$	−23.0541			−1.10791			−0.553954	−	0.832547i	$-0.686882\pi$
$433$	−23.0541			−1.10791			−0.553954	+	0.832547i	$0.686882\pi$
$434$			20.0331i			0.961620i
$435$		−	2.09706i		−	0.100546i
$436$		−	3.38525i		−	0.162124i
$437$			2.31247i			0.110621i
$438$	−18.3750			−0.877992
$439$	−2.39273			−0.114199			−0.0570994	−	0.998368i	$-0.518185\pi$
$439$	−2.39273			−0.114199			−0.0570994	+	0.998368i	$0.518185\pi$
$440$			1.00363i			0.0478462i
$441$	1.66555			0.0793118
$442$	−47.8375	+	20.3003i	−2.27540	+	0.965589i
$443$	−17.1624			−0.815411			−0.407705	−	0.913113i	$-0.633671\pi$
$443$	−17.1624			−0.815411			−0.407705	+	0.913113i	$0.633671\pi$
$444$			9.08810i			0.431302i
$445$	10.4908			0.497311
$446$	−11.5211			−0.545539
$447$			9.50356i			0.449503i
$448$		−	27.9487i		−	1.32045i
$449$		−	29.0646i		−	1.37164i	−0.727769	−	0.685822i	$-0.759443\pi$
$449$		−	29.0646i		−	1.37164i	0.727769	−	0.685822i	$-0.240557\pi$
$450$		−	9.69944i		−	0.457236i
$451$	9.46022			0.445465
$452$	1.69584			0.0797656
$453$		−	15.2126i		−	0.714749i
$454$	−16.8813			−0.792277
$455$	−2.31037	−	5.44437i	−0.108312	−	0.255236i
$456$	0.342711			0.0160489
$457$		−	31.9111i		−	1.49274i	−0.665532	−	0.746369i	$-0.731795\pi$
$457$		−	31.9111i		−	1.49274i	0.665532	−	0.746369i	$-0.268205\pi$
$458$	23.0435			1.07675
$459$	6.68027			0.311808
$460$			17.9797i			0.838308i
$461$		−	0.706685i		−	0.0329136i	−0.999865	−	0.0164568i	$-0.994761\pi$
$461$		−	0.706685i		−	0.0329136i	0.999865	−	0.0164568i	$-0.00523860\pi$
$462$			4.98315i			0.231837i
$463$		−	25.7813i		−	1.19816i	−0.800690	−	0.599079i	$-0.795533\pi$
$463$		−	25.7813i		−	1.19816i	0.800690	−	0.599079i	$-0.204467\pi$
$464$	6.67624			0.309937
$465$	2.85516			0.132405
$466$			33.3360i			1.54426i
$467$	−37.3541			−1.72854			−0.864270	−	0.503028i	$-0.832219\pi$
$467$	−37.3541			−1.72854			−0.864270	+	0.503028i	$0.832219\pi$
$468$	3.73948	+	8.81205i	0.172858	+	0.407337i
$469$	21.5309			0.994203
$470$			19.7941i			0.913033i
$471$	20.1949			0.930533
$472$	11.0412			0.508212
$473$		−	11.8791i		−	0.546203i
$474$		−	3.93450i		−	0.180718i
$475$		−	1.09026i		−	0.0500245i
$476$			40.9638i			1.87757i
$477$	6.78954			0.310872
$478$	−36.5411			−1.67135
$479$		−	1.74064i		−	0.0795318i	−0.999209	−	0.0397659i	$-0.987339\pi$
$479$		−	1.74064i		−	0.0795318i	0.999209	−	0.0397659i	$-0.0126612\pi$
$480$	−5.47187			−0.249756
$481$	−11.3613	+	4.82128i	−0.518030	+	0.219831i
$482$	0.172527			0.00785839
$483$			22.0232i			1.00209i
$484$	2.65498			0.120681
$485$	−1.32484			−0.0601580
$486$		−	2.15754i		−	0.0978680i
$487$			5.69783i			0.258193i	0.991632	+	0.129097i	$0.0412078\pi$
$487$			5.69783i			0.258193i	−0.991632	+	0.129097i	$0.958792\pi$
$488$			1.28679i			0.0582502i
$489$			16.4974i			0.746037i
$490$	2.55213			0.115293
$491$	27.7388			1.25183			0.625917	−	0.779890i	$-0.284725\pi$
$491$	27.7388			1.25183			0.625917	+	0.779890i	$0.284725\pi$
$492$		−	25.1167i		−	1.13235i
$493$	−19.7250			−0.888370
$494$	0.736972	+	1.73667i	0.0331580	+	0.0781363i
$495$	0.710210			0.0319216
$496$			9.08977i			0.408143i
$497$	29.9569			1.34375
$498$	10.0255			0.449251
$499$			8.27073i			0.370249i	0.982715	+	0.185124i	$0.0592688\pi$
$499$			8.27073i			0.370249i	−0.982715	+	0.185124i	$0.940731\pi$
$500$		−	17.9048i		−	0.800729i
$501$			5.50507i			0.245948i
$502$		−	16.3363i		−	0.729126i
$503$	−12.7099			−0.566706			−0.283353	−	0.959016i	$-0.591447\pi$
$503$	−12.7099			−0.566706			−0.283353	+	0.959016i	$0.591447\pi$
$504$	3.26386			0.145384
$505$			1.74062i			0.0774568i
$506$	20.5728			0.914573
$507$	−9.03237	+	9.34967i	−0.401142	+	0.415233i
$508$	27.5271			1.22132
$509$			5.55978i			0.246433i	0.992380	+	0.123216i	$0.0393210\pi$
$509$			5.55978i			0.246433i	−0.992380	+	0.123216i	$0.960679\pi$
$510$	10.2362			0.453268
$511$	−19.6704			−0.870168
$512$		−	23.8107i		−	1.05230i
$513$		−	0.242517i		−	0.0107074i
$514$			49.6756i			2.19110i
$515$		−	7.30172i		−	0.321752i
$516$	−31.5389			−1.38842
$517$	12.9178			0.568126
$518$			17.0575i			0.749464i
$519$	12.7126			0.558023
$520$	1.41359	+	3.33111i	0.0619901	+	0.146079i
$521$	−4.41425			−0.193392			−0.0966958	−	0.995314i	$-0.530827\pi$
$521$	−4.41425			−0.193392			−0.0966958	+	0.995314i	$0.530827\pi$
$522$			6.37063i			0.278835i
$523$	15.5162			0.678474			0.339237	−	0.940701i	$-0.389831\pi$
$523$	15.5162			0.678474			0.339237	+	0.940701i	$0.389831\pi$
$524$	15.0986			0.659587
$525$		−	10.3832i		−	0.453162i
$526$			12.8384i			0.559780i
$527$		−	26.8558i		−	1.16986i
$528$			2.26104i			0.0983992i
$529$	67.9221			2.95314
$530$	10.4037			0.451906
$531$		−	7.81320i		−	0.339064i
$532$	1.48713			0.0644751
$533$	31.3991	−	13.3245i	1.36005	−	0.577150i
$534$	−31.8698			−1.37914
$535$			13.9691i			0.603939i
$536$	−13.1736			−0.569011
$537$	−24.4279			−1.05414
$538$			2.53663i			0.109362i
$539$		−	1.66555i		−	0.0717402i
$540$		−	1.88559i		−	0.0811430i
$541$			27.9827i			1.20307i	0.798846	+	0.601536i	$0.205444\pi$
$541$			27.9827i			1.20307i	−0.798846	+	0.601536i	$0.794556\pi$
$542$	15.3769			0.660495
$543$	−0.931324			−0.0399669
$544$			51.4687i			2.20670i
$545$	−0.905559			−0.0387899
$546$	7.01866	+	16.5394i	0.300371	+	0.707820i
$547$	−24.1470			−1.03245			−0.516226	−	0.856453i	$-0.672663\pi$
$547$	−24.1470			−1.03245			−0.516226	+	0.856453i	$0.672663\pi$
$548$			12.9128i			0.551609i
$549$	0.910585			0.0388628
$550$	−9.69944			−0.413586
$551$			0.716086i			0.0305063i
$552$		−	13.4748i		−	0.573524i
$553$		−	4.21188i		−	0.179107i
$554$		−	25.8336i		−	1.09756i
$555$	2.43108			0.103193
$556$	11.7221			0.497129
$557$		−	19.1326i		−	0.810675i	−0.914167	−	0.405337i	$-0.867154\pi$
$557$		−	19.1326i		−	0.810675i	0.914167	−	0.405337i	$-0.132846\pi$
$558$	−8.67368			−0.367186
$559$	−16.7315	−	39.4276i	−0.707668	−	1.66761i
$560$	−3.70886			−0.156728
$561$		−	6.68027i		−	0.282041i
$562$	−40.5404			−1.71009
$563$	3.91199			0.164871			0.0824353	−	0.996596i	$-0.473730\pi$
$563$	3.91199			0.164871			0.0824353	+	0.996596i	$0.473730\pi$
$564$		−	34.2966i		−	1.44415i
$565$		−	0.453639i		−	0.0190847i
$566$			22.7053i			0.954373i
$567$		−	2.30964i		−	0.0969959i
$568$	−18.3290			−0.769069
$569$	15.8002			0.662377			0.331189	−	0.943565i	$-0.392550\pi$
$569$	15.8002			0.662377			0.331189	+	0.943565i	$0.392550\pi$
$570$		−	0.371610i		−	0.0155650i
$571$	−20.2458			−0.847262			−0.423631	−	0.905835i	$-0.639245\pi$
$571$	−20.2458			−0.847262			−0.423631	+	0.905835i	$0.639245\pi$
$572$	8.81205	−	3.73948i	0.368450	−	0.156356i
$573$	4.68209			0.195597
$574$		−	47.1417i		−	1.96766i
$575$	−42.8669			−1.78768
$576$	12.1009			0.504202
$577$		−	7.07073i		−	0.294358i	−0.989110	−	0.147179i	$-0.952981\pi$
$577$		−	7.07073i		−	0.294358i	0.989110	−	0.147179i	$-0.0470194\pi$
$578$		−	59.6042i		−	2.47921i
$579$			10.2671i			0.426685i
$580$			5.56764i			0.231184i
$581$	10.7322			0.445248
$582$	4.02473			0.166830
$583$		−	6.78954i		−	0.281194i
$584$	12.0353			0.498023
$585$	2.35723	−	1.00032i	0.0974596	−	0.0413580i
$586$	30.2296			1.24877
$587$			27.1767i			1.12170i	0.827917	+	0.560851i	$0.189526\pi$
$587$			27.1767i			1.12170i	−0.827917	+	0.560851i	$0.810474\pi$
$588$	−4.42200			−0.182360
$589$	−0.974959			−0.0401725
$590$		−	11.9722i		−	0.492889i
$591$			11.5842i			0.476511i
$592$			7.73963i			0.318097i
$593$		−	20.0431i		−	0.823070i	−0.911394	−	0.411535i	$-0.864993\pi$
$593$		−	20.0431i		−	0.823070i	0.911394	−	0.411535i	$-0.135007\pi$
$594$	−2.15754			−0.0885249
$595$	10.9579			0.449228
$596$		−	25.2318i		−	1.03353i
$597$	−17.2330			−0.705300
$598$	68.2825	−	28.9764i	2.79228	−	1.18493i
$599$	−24.5855			−1.00454			−0.502268	−	0.864712i	$-0.667501\pi$
$599$	−24.5855			−1.00454			−0.502268	+	0.864712i	$0.667501\pi$
$600$			6.35294i			0.259358i
$601$	−34.1098			−1.39137			−0.695683	−	0.718349i	$-0.744898\pi$
$601$	−34.1098			−1.39137			−0.695683	+	0.718349i	$0.744898\pi$
$602$	−59.1955			−2.41263
$603$			9.32216i			0.379628i
$604$			40.3891i			1.64341i
$605$		−	0.710210i		−	0.0288741i
$606$		−	5.28783i		−	0.214803i
$607$	20.9453			0.850143			0.425071	−	0.905160i	$-0.360249\pi$
$607$	20.9453			0.850143			0.425071	+	0.905160i	$0.360249\pi$
$608$	1.86849			0.0757773
$609$			6.81975i			0.276350i
$610$	1.39530			0.0564938
$611$	42.8751	−	18.1945i	1.73454	−	0.736071i
$612$	−17.7360			−0.716935
$613$		−	22.2792i		−	0.899848i	−0.893067	−	0.449924i	$-0.851451\pi$
$613$		−	22.2792i		−	0.899848i	0.893067	−	0.449924i	$-0.148549\pi$
$614$	−5.43973			−0.219530
$615$	−6.71875			−0.270926
$616$		−	3.26386i		−	0.131505i
$617$			27.4366i			1.10456i	0.833660	+	0.552279i	$0.186242\pi$
$617$			27.4366i			1.10456i	−0.833660	+	0.552279i	$0.813758\pi$
$618$			22.1818i			0.892284i
$619$			47.9288i			1.92642i	0.268747	+	0.963211i	$0.413390\pi$
$619$			47.9288i			1.92642i	−0.268747	+	0.963211i	$0.586610\pi$
$620$	−7.58040			−0.304436
$621$	−9.53531			−0.382639
$622$		−	49.4896i		−	1.98435i
$623$	−34.1166			−1.36685
$624$	3.18463	+	7.50454i	0.127487	+	0.300422i
$625$	17.6884			0.707538
$626$			46.7250i			1.86751i
$627$	−0.242517			−0.00968519
$628$	−53.6171			−2.13956
$629$		−	22.8668i		−	0.911760i
$630$		−	3.53908i		−	0.141000i
$631$		−	23.8277i		−	0.948567i	−0.880372	−	0.474284i	$-0.842707\pi$
$631$		−	23.8277i		−	0.948567i	0.880372	−	0.474284i	$-0.157293\pi$
$632$			2.57702i			0.102508i
$633$	−10.6905			−0.424911
$634$	57.4013			2.27970
$635$		−	7.36353i		−	0.292213i
$636$	−18.0261			−0.714781
$637$	−2.34589	−	5.52806i	−0.0929475	−	0.219030i
$638$	6.37063			0.252216
$639$			12.9704i			0.513100i
$640$	7.59848			0.300356
$641$	8.30355			0.327970			0.163985	−	0.986463i	$-0.447565\pi$
$641$	8.30355			0.327970			0.163985	+	0.986463i	$0.447565\pi$
$642$		−	42.4367i		−	1.67484i
$643$			29.9185i			1.17987i	0.807451	+	0.589934i	$0.200846\pi$
$643$			29.9185i			1.17987i	−0.807451	+	0.589934i	$0.799154\pi$
$644$		−	58.4710i		−	2.30408i
$645$			8.43668i			0.332194i
$646$	−3.49538			−0.137524
$647$	−5.87308			−0.230895			−0.115447	−	0.993314i	$-0.536830\pi$
$647$	−5.87308			−0.230895			−0.115447	+	0.993314i	$0.536830\pi$
$648$			1.41315i			0.0555136i
$649$	−7.81320			−0.306695
$650$	−32.1931	+	13.6615i	−1.26272	+	0.535847i
$651$	−9.28516			−0.363914
$652$		−	43.8002i		−	1.71535i
$653$	−5.43262			−0.212595			−0.106297	−	0.994334i	$-0.533900\pi$
$653$	−5.43262			−0.212595			−0.106297	+	0.994334i	$0.533900\pi$
$654$	2.75099			0.107572
$655$		−	4.03891i		−	0.157813i
$656$		−	21.3900i		−	0.835138i
$657$		−	8.51665i		−	0.332266i
$658$		−	64.3715i		−	2.50946i
$659$	26.5954			1.03601			0.518004	−	0.855378i	$-0.326675\pi$
$659$	26.5954			1.03601			0.518004	+	0.855378i	$0.326675\pi$
$660$	−1.88559			−0.0733966
$661$			27.7763i			1.08037i	0.841545	+	0.540187i	$0.181646\pi$
$661$			27.7763i			1.08037i	−0.841545	+	0.540187i	$0.818354\pi$
$662$	−53.4359			−2.07684
$663$	−9.40902	−	22.1722i	−0.365416	−	0.861099i
$664$	−6.56647			−0.254828
$665$		−	0.397808i		−	0.0154263i
$666$	−7.38534			−0.286176
$667$	28.1552			1.09017
$668$		−	14.6158i		−	0.565504i
$669$		−	5.33992i		−	0.206453i
$670$			14.2844i			0.551855i
$671$		−	0.910585i		−	0.0351527i
$672$	17.7948			0.686450
$673$	−3.00054			−0.115663			−0.0578313	−	0.998326i	$-0.518419\pi$
$673$	−3.00054			−0.115663			−0.0578313	+	0.998326i	$0.518419\pi$
$674$		−	61.0346i		−	2.35096i
$675$	4.49560			0.173036
$676$	23.9808	−	24.8232i	0.922337	−	0.954737i
$677$	−25.1724			−0.967452			−0.483726	−	0.875219i	$-0.660717\pi$
$677$	−25.1724			−0.967452			−0.483726	+	0.875219i	$0.660717\pi$
$678$			1.37811i			0.0529258i
$679$	4.30846			0.165344
$680$	−6.70452			−0.257107
$681$		−	7.82431i		−	0.299828i
$682$			8.67368i			0.332132i
$683$		−	39.1652i		−	1.49861i	−0.662223	−	0.749307i	$-0.730387\pi$
$683$		−	39.1652i		−	1.49861i	0.662223	−	0.749307i	$-0.269613\pi$
$684$			0.643877i			0.0246193i
$685$	3.45420			0.131978
$686$	−43.1817			−1.64869
$687$			10.6805i			0.407485i
$688$	−26.8592			−1.02400
$689$	−9.56293	−	22.5349i	−0.364318	−	0.858512i
$690$	−14.6110			−0.556232
$691$			33.3472i			1.26859i	0.773092	+	0.634294i	$0.218709\pi$
$691$			33.3472i			1.26859i	−0.773092	+	0.634294i	$0.781291\pi$
$692$	−33.7518			−1.28305
$693$	−2.30964			−0.0877361
$694$			39.0114i			1.48085i
$695$		−	3.13568i		−	0.118943i
$696$		−	4.17263i		−	0.158163i
$697$			63.1969i			2.39375i
$698$	−45.3787			−1.71761
$699$	−15.4509			−0.584408
$700$			27.5673i			1.04195i
$701$	−8.45704			−0.319418			−0.159709	−	0.987164i	$-0.551056\pi$
$701$	−8.45704			−0.319418			−0.159709	+	0.987164i	$0.551056\pi$
$702$	−7.16101	+	3.03885i	−0.270275	+	0.114694i
$703$	−0.830144			−0.0313095
$704$		−	12.1009i		−	0.456068i
$705$	−9.17437			−0.345527
$706$	4.74934			0.178744
$707$		−	5.66061i		−	0.212889i
$708$			20.7439i			0.779603i
$709$			7.03783i			0.264311i	0.991229	+	0.132156i	$0.0421899\pi$
$709$			7.03783i			0.264311i	−0.991229	+	0.132156i	$0.957810\pi$
$710$			19.8746i			0.745880i
$711$	1.82360			0.0683905
$712$	20.8741			0.782290
$713$			38.3336i			1.43560i
$714$	−33.2888			−1.24580
$715$	−1.00032	−	2.35723i	−0.0374097	−	0.0881555i
$716$	64.8555			2.42377
$717$		−	16.9365i		−	0.632504i
$718$	16.7542			0.625260
$719$	5.52947			0.206215			0.103107	−	0.994670i	$-0.467121\pi$
$719$	5.52947			0.206215			0.103107	+	0.994670i	$0.467121\pi$
$720$		−	1.60581i		−	0.0598452i
$721$			23.7456i			0.884333i
$722$		−	40.8664i		−	1.52089i
$723$			0.0799646i			0.00297392i
$724$	2.47265			0.0918952
$725$	−13.2743			−0.492995
$726$			2.15754i			0.0800738i
$727$	38.7533			1.43728			0.718640	−	0.695383i	$-0.244765\pi$
$727$	38.7533			1.43728			0.718640	+	0.695383i	$0.244765\pi$
$728$	−4.59708	−	10.8330i	−0.170379	−	0.401496i
$729$	1.00000			0.0370370
$730$		−	13.0501i		−	0.483006i
$731$	79.3558			2.93508
$732$	−2.41758			−0.0893565
$733$			9.60595i			0.354804i	0.984138	+	0.177402i	$0.0567693\pi$
$733$			9.60595i			0.354804i	−0.984138	+	0.177402i	$0.943231\pi$
$734$			25.8050i			0.952480i
$735$			1.18289i			0.0436315i
$736$		−	73.4655i		−	2.70798i
$737$	9.32216			0.343386
$738$	20.4108			0.751332
$739$		−	21.6659i		−	0.796995i	−0.917169	−	0.398497i	$-0.869532\pi$
$739$		−	21.6659i		−	0.796995i	0.917169	−	0.398497i	$-0.130468\pi$
$740$	−6.45446			−0.237271
$741$	−0.804929	+	0.341580i	−0.0295698	+	0.0125483i
$742$	−33.8333			−1.24206
$743$			12.3149i			0.451790i	0.974152	+	0.225895i	$0.0725305\pi$
$743$			12.3149i			0.451790i	−0.974152	+	0.225895i	$0.927469\pi$
$744$	5.68108			0.208279
$745$	−6.74952			−0.247283
$746$		−	30.4738i		−	1.11572i
$747$			4.64671i			0.170014i
$748$			17.7360i			0.648492i
$749$		−	45.4285i		−	1.65992i
$750$	14.5502			0.531297
$751$	−2.50813			−0.0915231			−0.0457616	−	0.998952i	$-0.514571\pi$
$751$	−2.50813			−0.0915231			−0.0457616	+	0.998952i	$0.514571\pi$
$752$		−	29.2078i		−	1.06510i
$753$	7.57174			0.275930
$754$	21.1445	−	8.97290i	0.770038	−	0.326774i
$755$	10.8041			0.393202
$756$			6.13206i			0.223021i
$757$	2.89889			0.105362			0.0526809	−	0.998611i	$-0.483223\pi$
$757$	2.89889			0.105362			0.0526809	+	0.998611i	$0.483223\pi$
$758$	−7.21551			−0.262079
$759$			9.53531i			0.346110i
$760$			0.243397i			0.00882894i
$761$			33.6764i			1.22077i	0.792105	+	0.610384i	$0.208985\pi$
$761$			33.6764i			1.22077i	−0.792105	+	0.610384i	$0.791015\pi$
$762$			22.3696i			0.810365i
$763$	2.94493			0.106614
$764$	−12.4309			−0.449733
$765$			4.74440i			0.171534i
$766$	−12.1604			−0.439371
$767$	−25.9325	+	11.0047i	−0.936369	+	0.397358i
$768$	1.11835			0.0403551
$769$			25.1224i			0.905935i	0.891527	+	0.452968i	$0.149635\pi$
$769$			25.1224i			0.905935i	−0.891527	+	0.452968i	$0.850365\pi$
$770$	−3.53908			−0.127540
$771$	−23.0242			−0.829196
$772$		−	27.2588i		−	0.981067i
$773$			31.6336i			1.13778i	0.822413	+	0.568891i	$0.192627\pi$
$773$			31.6336i			1.13778i	−0.822413	+	0.568891i	$0.807373\pi$
$774$		−	25.6297i		−	0.921241i
$775$		−	18.0731i		−	0.649204i
$776$	−2.63611			−0.0946310
$777$	−7.90600			−0.283626
$778$			30.9585i			1.10992i
$779$	2.29426			0.0822005
$780$	−6.25840	+	2.65582i	−0.224087	+	0.0950936i
$781$	12.9704			0.464117
$782$			137.432i			4.91456i
$783$	−2.95273			−0.105522
$784$	−3.76587			−0.134495
$785$			14.3426i			0.511911i
$786$			12.2698i			0.437648i
$787$		−	23.2041i		−	0.827137i	−0.910473	−	0.413569i	$-0.864282\pi$
$787$		−	23.2041i		−	0.827137i	0.910473	−	0.413569i	$-0.135718\pi$
$788$		−	30.7559i		−	1.09563i
$789$	−5.95047			−0.211842
$790$	2.79432			0.0994175
$791$			1.47526i			0.0524542i
$792$	1.41315			0.0502139
$793$	−1.28254	−	3.02229i	−0.0455443	−	0.107325i
$794$	32.0974			1.13909
$795$			4.82200i			0.171019i
$796$	45.7533			1.62168
$797$	−16.5706			−0.586960			−0.293480	−	0.955965i	$-0.594813\pi$
$797$	−16.5706			−0.586960			−0.293480	+	0.955965i	$0.594813\pi$
$798$			1.20850i			0.0427803i
$799$			86.2946i			3.05288i
$800$			34.6367i			1.22459i
$801$		−	14.7714i		−	0.521921i
$802$	−42.3698			−1.49613
$803$	−8.51665			−0.300546
$804$		−	24.7502i		−	0.872871i
$805$	−15.6411			−0.551275
$806$	12.2167	+	28.7885i	0.430315	+	1.01403i
$807$	−1.17571			−0.0413868
$808$			3.46342i			0.121843i
$809$	8.97637			0.315592			0.157796	−	0.987472i	$-0.449561\pi$
$809$	8.97637			0.315592			0.157796	+	0.987472i	$0.449561\pi$
$810$	1.53231			0.0538398
$811$			2.09499i			0.0735651i	0.999323	+	0.0367826i	$0.0117109\pi$
$811$			2.09499i			0.0735651i	−0.999323	+	0.0367826i	$0.988289\pi$
$812$		−	18.1063i		−	0.635406i
$813$			7.12706i			0.249957i
$814$			7.38534i			0.258856i
$815$	−11.7166			−0.410414
$816$	−15.1044			−0.528759
$817$		−	2.88089i		−	0.100790i
$818$	49.9969			1.74810
$819$	−7.66585	+	3.25308i	−0.267867	+	0.113672i
$820$	17.8381			0.622935
$821$		−	32.8066i		−	1.14496i	−0.819919	−	0.572480i	$-0.805982\pi$
$821$		−	32.8066i		−	1.14496i	0.819919	−	0.572480i	$-0.194018\pi$
$822$	−10.4935			−0.366002
$823$	6.37447			0.222200			0.111100	−	0.993809i	$-0.464563\pi$
$823$	6.37447			0.222200			0.111100	+	0.993809i	$0.464563\pi$
$824$		−	14.5287i		−	0.506130i
$825$		−	4.49560i		−	0.156517i
$826$			38.9343i			1.35470i
$827$			14.7476i			0.512825i	0.966567	+	0.256413i	$0.0825406\pi$
$827$			14.7476i			0.512825i	−0.966567	+	0.256413i	$0.917459\pi$
$828$	25.3161			0.879794
$829$	25.4837			0.885085			0.442542	−	0.896748i	$-0.354077\pi$
$829$	25.4837			0.885085			0.442542	+	0.896748i	$0.354077\pi$
$830$			7.12018i			0.247145i
$831$	11.9736			0.415361
$832$	−17.0438	−	40.1635i	−0.590888	−	1.39242i
$833$	11.1263			0.385504
$834$			9.52586i			0.329854i
$835$	−3.90976			−0.135303
$836$	0.643877			0.0222690
$837$		−	4.02017i		−	0.138957i
$838$			7.98924i			0.275984i
$839$			41.7953i			1.44293i	0.692449	+	0.721467i	$0.256532\pi$
$839$			41.7953i			1.44293i	−0.692449	+	0.721467i	$0.743468\pi$
$840$			2.31803i			0.0799795i
$841$	−20.2814			−0.699359
$842$	51.1852			1.76396
$843$		−	18.7901i		−	0.647165i
$844$	28.3831			0.976988
$845$	−6.64023	−	6.41488i	−0.228431	−	0.220679i
$846$	27.8707			0.958216
$847$			2.30964i			0.0793603i
$848$	−15.3514			−0.527170
$849$	−10.5237			−0.361172
$850$		−	64.7949i		−	2.22245i
$851$			32.6397i			1.11888i
$852$		−	34.4361i		−	1.17976i
$853$			25.2825i			0.865655i	0.901477	+	0.432827i	$0.142484\pi$
$853$			25.2825i			0.865655i	−0.901477	+	0.432827i	$0.857516\pi$
$854$	−4.53758			−0.155273
$855$	0.172238			0.00589041
$856$			27.7952i			0.950021i
$857$	26.8626			0.917609			0.458804	−	0.888537i	$-0.348278\pi$
$857$	26.8626			0.917609			0.458804	+	0.888537i	$0.348278\pi$
$858$	3.03885	+	7.16101i	0.103745	+	0.244473i
$859$	6.11713			0.208714			0.104357	−	0.994540i	$-0.466722\pi$
$859$	6.11713			0.208714			0.104357	+	0.994540i	$0.466722\pi$
$860$		−	22.3992i		−	0.763807i
$861$	21.8497			0.744637
$862$	−67.0336			−2.28318
$863$			32.1517i			1.09446i	0.836984	+	0.547228i	$0.184317\pi$
$863$			32.1517i			1.09446i	−0.836984	+	0.547228i	$0.815683\pi$
$864$			7.70458i			0.262115i
$865$			9.02865i			0.306983i
$866$			49.7401i			1.69024i
$867$	27.6260			0.938228
$868$	24.6519			0.836740
$869$		−	1.82360i		−	0.0618616i
$870$	−4.52448			−0.153394
$871$	30.9409	−	13.1301i	1.04839	−	0.444896i
$872$	−1.80184			−0.0610180
$873$			1.86542i			0.0631350i
$874$	4.98925			0.168764
$875$	15.5759			0.526563
$876$			22.6115i			0.763973i
$877$		−	17.9062i		−	0.604648i	−0.953205	−	0.302324i	$-0.902237\pi$
$877$		−	17.9062i		−	0.604648i	0.953205	−	0.302324i	$-0.0977625\pi$
$878$			5.16241i			0.174223i
$879$			14.0111i			0.472584i
$880$	−1.60581			−0.0541320
$881$	−40.5751			−1.36701			−0.683504	−	0.729947i	$-0.739545\pi$
$881$	−40.5751			−1.36701			−0.683504	+	0.729947i	$0.739545\pi$
$882$		−	3.59349i		−	0.120999i
$883$	24.6601			0.829879			0.414940	−	0.909849i	$-0.363803\pi$
$883$	24.6601			0.829879			0.414940	+	0.909849i	$0.363803\pi$
$884$	24.9808	+	58.8669i	0.840194	+	1.97991i
$885$	5.54901			0.186528
$886$			37.0286i			1.24400i
$887$	27.2662			0.915510			0.457755	−	0.889078i	$-0.348654\pi$
$887$	27.2662			0.915510			0.457755	+	0.889078i	$0.348654\pi$
$888$	4.83725			0.162327
$889$			23.9466i			0.803144i
$890$		−	22.6343i		−	0.758703i
$891$		−	1.00000i		−	0.0335013i
$892$			14.1774i			0.474693i
$893$	3.13279			0.104835
$894$	20.5043			0.685767
$895$		−	17.3489i		−	0.579911i
$896$	−24.7107			−0.825526
$897$	13.4303	+	31.6483i	0.448424	+	1.05671i
$898$	−62.7081			−2.09260
$899$			11.8705i			0.395902i
$900$	−11.9357			−0.397858
$901$	45.3560			1.51103
$902$		−	20.4108i		−	0.679606i
$903$		−	27.4366i		−	0.913032i
$904$		−	0.902631i		−	0.0300211i
$905$		−	0.661436i		−	0.0219869i
$906$	−32.8217			−1.09043
$907$	−0.121526			−0.00403521			−0.00201760	−	0.999998i	$-0.500642\pi$
$907$	−0.121526			−0.00403521			−0.00201760	+	0.999998i	$0.500642\pi$
$908$			20.7734i			0.689389i
$909$	2.45086			0.0812898
$910$	−11.7464	+	4.98472i	−0.389391	+	0.165242i
$911$	−40.6736			−1.34758			−0.673788	−	0.738925i	$-0.735334\pi$
$911$	−40.6736			−1.34758			−0.673788	+	0.738925i	$0.735334\pi$
$912$			0.548341i			0.0181574i
$913$	4.64671			0.153784
$914$	−68.8495			−2.27734
$915$			0.646706i			0.0213795i
$916$		−	28.3564i		−	0.936921i
$917$			13.1347i			0.433748i
$918$		−	14.4130i		−	0.475698i
$919$	−26.0713			−0.860012			−0.430006	−	0.902826i	$-0.641489\pi$
$919$	−26.0713			−0.860012			−0.430006	+	0.902826i	$0.641489\pi$
$920$	9.56992			0.315511
$921$		−	2.52126i		−	0.0830785i
$922$	−1.52470			−0.0502134
$923$	43.0495	−	18.2685i	1.41699	−	0.601315i
$924$	6.13206			0.201730
$925$		−	15.3886i		−	0.505975i
$926$	−55.6242			−1.82792
$927$	−10.2811			−0.337675
$928$		−	22.7495i		−	0.746790i
$929$		−	26.9849i		−	0.885346i	−0.896683	−	0.442673i	$-0.854030\pi$
$929$		−	26.9849i		−	0.885346i	0.896683	−	0.442673i	$-0.145970\pi$
$930$		−	6.16013i		−	0.201999i
$931$		−	0.403923i		−	0.0132381i
$932$	41.0219			1.34372
$933$	22.9380			0.750956
$934$			80.5929i			2.63708i
$935$	4.74440			0.155158
$936$	4.69032	−	1.99039i	0.153308	−	0.0650578i
$937$	31.9915			1.04512			0.522559	−	0.852603i	$-0.324977\pi$
$937$	31.9915			1.04512			0.522559	+	0.852603i	$0.324977\pi$
$938$		−	46.4537i		−	1.51677i
$939$	−21.6566			−0.706736
$940$	24.3578			0.794463
$941$		−	31.7257i		−	1.03423i	−0.855916	−	0.517115i	$-0.827006\pi$
$941$		−	31.7257i		−	1.03423i	0.855916	−	0.517115i	$-0.172994\pi$
$942$		−	43.5714i		−	1.41963i
$943$		−	90.2062i		−	2.93752i
$944$			17.6660i			0.574979i
$945$	1.64033			0.0533600
$946$	−25.6297			−0.833294
$947$			46.5444i			1.51249i	0.654289	+	0.756245i	$0.272968\pi$
$947$			46.5444i			1.51249i	−0.654289	+	0.756245i	$0.727032\pi$
$948$	−4.84163			−0.157249
$949$	−28.2673	+	11.9955i	−0.917595	+	0.389391i
$950$	−2.35228			−0.0763180
$951$			26.6050i			0.862726i
$952$	21.8035			0.706655
$953$	−37.1054			−1.20196			−0.600981	−	0.799263i	$-0.705223\pi$
$953$	−37.1054			−1.20196			−0.600981	+	0.799263i	$0.705223\pi$
$954$		−	14.6487i		−	0.474269i
$955$			3.32527i			0.107603i
$956$			44.9660i			1.45430i
$957$			2.95273i			0.0954481i
$958$	−3.75550			−0.121335
$959$	−11.2332			−0.362740
$960$			8.59415i			0.277375i
$961$	14.8382			0.478653
$962$	10.4021	+	24.5124i	0.335377	+	0.790312i
$963$	19.6690			0.633826
$964$		−	0.212305i		−	0.00683787i
$965$	−7.29177			−0.234730
$966$	47.5159			1.52880
$967$			33.1854i			1.06717i	0.845746	+	0.533586i	$0.179156\pi$
$967$			33.1854i			1.06717i	−0.845746	+	0.533586i	$0.820844\pi$
$968$		−	1.41315i		−	0.0454202i
$969$		−	1.62008i		−	0.0520444i
$970$			2.85840i			0.0917777i
$971$	23.0990			0.741283			0.370642	−	0.928776i	$-0.379138\pi$
$971$	23.0990			0.741283			0.370642	+	0.928776i	$0.379138\pi$
$972$	−2.65498			−0.0851585
$973$			10.1974i			0.326914i
$974$	12.2933			0.393903
$975$	−6.33196	−	14.9212i	−0.202785	−	0.477861i
$976$	−2.05887			−0.0659028
$977$			32.4063i			1.03677i	0.855147	+	0.518385i	$0.173467\pi$
$977$			32.4063i			1.03677i	−0.855147	+	0.518385i	$0.826533\pi$
$978$	35.5937			1.13816
$979$	−14.7714			−0.472095
$980$		−	3.14055i		−	0.100321i
$981$			1.27506i			0.0407095i
$982$		−	59.8475i		−	1.90981i
$983$			1.17252i			0.0373976i	0.999825	+	0.0186988i	$0.00595236\pi$
$983$			1.17252i			0.0373976i	−0.999825	+	0.0186988i	$0.994048\pi$
$984$	−13.3687			−0.426178
$985$	−8.22723			−0.262141
$986$			42.5575i			1.35531i
$987$	29.8356			0.949677
$988$	2.13707	−	0.906888i	0.0679892	−	0.0288519i
$989$	−113.271			−3.60182
$990$		−	1.53231i		−	0.0486999i
$991$	−4.78159			−0.151892			−0.0759462	−	0.997112i	$-0.524198\pi$
$991$	−4.78159			−0.151892			−0.0759462	+	0.997112i	$0.524198\pi$
$992$	30.9737			0.983416
$993$		−	24.7670i		−	0.785958i
$994$		−	64.6333i		−	2.05004i
$995$		−	12.2391i		−	0.388004i
$996$		−	12.3369i		−	0.390910i
$997$	55.7577			1.76586			0.882932	−	0.469502i	$-0.155566\pi$
$997$	55.7577			1.76586			0.882932	+	0.469502i	$0.155566\pi$
$998$	17.8444			0.564856
$999$		−	3.42304i		−	0.108300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.b.298.3	✓	14
3.2	odd	2		1287.2.b.c.298.12		14
13.5	odd	4		5577.2.a.y.1.1		7
13.8	odd	4		5577.2.a.x.1.7		7
13.12	even	2	inner	429.2.b.b.298.12	yes	14
39.38	odd	2		1287.2.b.c.298.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.3	✓	14	1.1	even	1	trivial
429.2.b.b.298.12	yes	14	13.12	even	2	inner
1287.2.b.c.298.3		14	39.38	odd	2
1287.2.b.c.298.12		14	3.2	odd	2
5577.2.a.x.1.7		7	13.8	odd	4
5577.2.a.y.1.1		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)

\(f(q)\)	\(=\)	\(q-2.15754i q^{2} +1.00000 q^{3} -2.65498 q^{4} +0.710210i q^{5} -2.15754i q^{6} -2.30964i q^{7} +1.41315i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15754i q^{2} +1.00000 q^{3} -2.65498 q^{4} +0.710210i q^{5} -2.15754i q^{6} -2.30964i q^{7} +1.41315i q^{8} +1.00000 q^{9} +1.53231 q^{10} -1.00000i q^{11} -2.65498 q^{12} +(-1.40848 - 3.31906i) q^{13} -4.98315 q^{14} +0.710210i q^{15} -2.26104 q^{16} +6.68027 q^{17} -2.15754i q^{18} -0.242517i q^{19} -1.88559i q^{20} -2.30964i q^{21} -2.15754 q^{22} -9.53531 q^{23} +1.41315i q^{24} +4.49560 q^{25} +(-7.16101 + 3.03885i) q^{26} +1.00000 q^{27} +6.13206i q^{28} -2.95273 q^{29} +1.53231 q^{30} -4.02017i q^{31} +7.70458i q^{32} -1.00000i q^{33} -14.4130i q^{34} +1.64033 q^{35} -2.65498 q^{36} -3.42304i q^{37} -0.523240 q^{38} +(-1.40848 - 3.31906i) q^{39} -1.00363 q^{40} +9.46022i q^{41} -4.98315 q^{42} +11.8791 q^{43} +2.65498i q^{44} +0.710210i q^{45} +20.5728i q^{46} +12.9178i q^{47} -2.26104 q^{48} +1.66555 q^{49} -9.69944i q^{50} +6.68027 q^{51} +(3.73948 + 8.81205i) q^{52} +6.78954 q^{53} -2.15754i q^{54} +0.710210 q^{55} +3.26386 q^{56} -0.242517i q^{57} +6.37063i q^{58} -7.81320i q^{59} -1.88559i q^{60} +0.910585 q^{61} -8.67368 q^{62} -2.30964i q^{63} +12.1009 q^{64} +(2.35723 - 1.00032i) q^{65} -2.15754 q^{66} +9.32216i q^{67} -17.7360 q^{68} -9.53531 q^{69} -3.53908i q^{70} +12.9704i q^{71} +1.41315i q^{72} -8.51665i q^{73} -7.38534 q^{74} +4.49560 q^{75} +0.643877i q^{76} -2.30964 q^{77} +(-7.16101 + 3.03885i) q^{78} +1.82360 q^{79} -1.60581i q^{80} +1.00000 q^{81} +20.4108 q^{82} +4.64671i q^{83} +6.13206i q^{84} +4.74440i q^{85} -25.6297i q^{86} -2.95273 q^{87} +1.41315 q^{88} -14.7714i q^{89} +1.53231 q^{90} +(-7.66585 + 3.25308i) q^{91} +25.3161 q^{92} -4.02017i q^{93} +27.8707 q^{94} +0.172238 q^{95} +7.70458i q^{96} +1.86542i q^{97} -3.59349i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) \) 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

Introduction

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