LMFDB - Embedded newform 429.2.b.a.298.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("429.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 54x^{6} + 74x^{4} + 21x^{2} + 1 $ x^10 + 13x^8 + 54x^6 + 74x^4 + 21x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			298.1
Root			$-2.35969i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.a.298.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35969i q^{2} -1.00000 q^{3} -3.56813 q^{4} -1.80373i q^{5} +2.35969i q^{6} -4.78347i q^{7} +3.70030i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.35969i q^{2} -1.00000 q^{3} -3.56813 q^{4} -1.80373i q^{5} +2.35969i q^{6} -4.78347i q^{7} +3.70030i q^{8} +1.00000 q^{9} -4.25625 q^{10} +1.00000i q^{11} +3.56813 q^{12} +(3.14435 - 1.76440i) q^{13} -11.2875 q^{14} +1.80373i q^{15} +1.59529 q^{16} -2.63620 q^{17} -2.35969i q^{18} +6.47687i q^{19} +6.43596i q^{20} +4.78347i q^{21} +2.35969 q^{22} -2.40352 q^{23} -3.70030i q^{24} +1.74654 q^{25} +(-4.16342 - 7.41968i) q^{26} -1.00000 q^{27} +17.0681i q^{28} -1.40868 q^{29} +4.25625 q^{30} +6.06807i q^{31} +3.63620i q^{32} -1.00000i q^{33} +6.22062i q^{34} -8.62812 q^{35} -3.56813 q^{36} -6.63223i q^{37} +15.2834 q^{38} +(-3.14435 + 1.76440i) q^{39} +6.67436 q^{40} -7.21242i q^{41} +11.2875 q^{42} +7.35558 q^{43} -3.56813i q^{44} -1.80373i q^{45} +5.67157i q^{46} -9.35160i q^{47} -1.59529 q^{48} -15.8816 q^{49} -4.12129i q^{50} +2.63620 q^{51} +(-11.2194 + 6.29559i) q^{52} -4.20276 q^{53} +2.35969i q^{54} +1.80373 q^{55} +17.7003 q^{56} -6.47687i q^{57} +3.32405i q^{58} -0.288691i q^{59} -6.43596i q^{60} +12.2851 q^{61} +14.3188 q^{62} -4.78347i q^{63} +11.7709 q^{64} +(-3.18250 - 5.67157i) q^{65} -2.35969 q^{66} -13.1143i q^{67} +9.40632 q^{68} +2.40352 q^{69} +20.3597i q^{70} +8.88039i q^{71} +3.70030i q^{72} -2.61713i q^{73} -15.6500 q^{74} -1.74654 q^{75} -23.1103i q^{76} +4.78347 q^{77} +(4.16342 + 7.41968i) q^{78} +3.32327 q^{79} -2.87749i q^{80} +1.00000 q^{81} -17.0191 q^{82} +9.78588i q^{83} -17.0681i q^{84} +4.75501i q^{85} -17.3569i q^{86} +1.40868 q^{87} -3.70030 q^{88} -14.0514i q^{89} -4.25625 q^{90} +(-8.43994 - 15.0409i) q^{91} +8.57608 q^{92} -6.06807i q^{93} -22.0669 q^{94} +11.6826 q^{95} -3.63620i q^{96} +4.40604i q^{97} +37.4757i q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9	$ 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9} + 6 q^{12} + 12 q^{13} - 32 q^{14} + 6 q^{16} + 20 q^{17} - 2 q^{22} + 8 q^{23} - 14 q^{25} - 2 q^{26} - 10 q^{27} + 8 q^{29} - 6 q^{36} - 12 q^{39} - 20 q^{40} + 32 q^{42} - 24 q^{43} - 6 q^{48} - 26 q^{49} - 20 q^{51} - 48 q^{52} - 4 q^{53} + 4 q^{55} + 16 q^{56} + 36 q^{61} + 24 q^{62} + 50 q^{64} + 28 q^{65} + 2 q^{66} - 12 q^{68} - 8 q^{69} + 24 q^{74} + 14 q^{75} + 12 q^{77} + 2 q^{78} + 36 q^{79} + 10 q^{81} - 20 q^{82} - 8 q^{87} - 6 q^{88} - 24 q^{91} - 8 q^{92} - 32 q^{94} + 44 q^{95}+O(q^{100}) $ 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9 + 6 * q^12 + 12 * q^13 - 32 * q^14 + 6 * q^16 + 20 * q^17 - 2 * q^22 + 8 * q^23 - 14 * q^25 - 2 * q^26 - 10 * q^27 + 8 * q^29 - 6 * q^36 - 12 * q^39 - 20 * q^40 + 32 * q^42 - 24 * q^43 - 6 * q^48 - 26 * q^49 - 20 * q^51 - 48 * q^52 - 4 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^61 + 24 * q^62 + 50 * q^64 + 28 * q^65 + 2 * q^66 - 12 * q^68 - 8 * q^69 + 24 * q^74 + 14 * q^75 + 12 * q^77 + 2 * q^78 + 36 * q^79 + 10 * q^81 - 20 * q^82 - 8 * q^87 - 6 * q^88 - 24 * q^91 - 8 * q^92 - 32 * q^94 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2.35969i		−	1.66855i	−0.551347	−	0.834276i	$-0.685886\pi$
$2$		−	2.35969i		−	1.66855i	0.551347	−	0.834276i	$-0.314114\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−3.56813			−1.78407
$5$		−	1.80373i		−	0.806655i	−0.915056	−	0.403327i	$-0.867854\pi$
$5$		−	1.80373i		−	0.806655i	0.915056	−	0.403327i	$-0.132146\pi$
$6$			2.35969i			0.963339i
$7$		−	4.78347i		−	1.80798i	−0.427550	−	0.903991i	$-0.640623\pi$
$7$		−	4.78347i		−	1.80798i	0.427550	−	0.903991i	$-0.359377\pi$
$8$			3.70030i			1.30825i
$9$	1.00000			0.333333
$10$	−4.25625			−1.34595
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	3.56813			1.03003
$13$	3.14435	−	1.76440i	0.872085	−	0.489355i
$13$	3.14435	−	1.76440i	0.872085	−	0.489355i
$14$	−11.2875			−3.01671
$15$			1.80373i			0.465722i
$16$	1.59529			0.398823
$17$	−2.63620			−0.639373			−0.319687	−	0.947523i	$-0.603578\pi$
$17$	−2.63620			−0.639373			−0.319687	+	0.947523i	$0.603578\pi$
$18$		−	2.35969i		−	0.556184i
$19$			6.47687i			1.48590i	0.669349	+	0.742948i	$0.266573\pi$
$19$			6.47687i			1.48590i	−0.669349	+	0.742948i	$0.733427\pi$
$20$			6.43596i			1.43912i
$21$			4.78347i			1.04384i
$22$	2.35969			0.503087
$23$	−2.40352			−0.501169			−0.250585	−	0.968095i	$-0.580623\pi$
$23$	−2.40352			−0.501169			−0.250585	+	0.968095i	$0.580623\pi$
$24$		−	3.70030i		−	0.755320i
$25$	1.74654			0.349308
$26$	−4.16342	−	7.41968i	−0.816515	−	1.45512i
$27$	−1.00000			−0.192450
$28$			17.0681i			3.22556i
$29$	−1.40868			−0.261586			−0.130793	−	0.991410i	$-0.541752\pi$
$29$	−1.40868			−0.261586			−0.130793	+	0.991410i	$0.541752\pi$
$30$	4.25625			0.777082
$31$			6.06807i			1.08986i	0.838482	+	0.544929i	$0.183443\pi$
$31$			6.06807i			1.08986i	−0.838482	+	0.544929i	$0.816557\pi$
$32$			3.63620i			0.642796i
$33$		−	1.00000i		−	0.174078i
$34$			6.22062i			1.06683i
$35$	−8.62812			−1.45842
$36$	−3.56813			−0.594688
$37$		−	6.63223i		−	1.09033i	−0.838328	−	0.545166i	$-0.816467\pi$
$37$		−	6.63223i		−	1.09033i	0.838328	−	0.545166i	$-0.183533\pi$
$38$	15.2834			2.47929
$39$	−3.14435	+	1.76440i	−0.503498	+	0.282529i
$40$	6.67436			1.05531
$41$		−	7.21242i		−	1.12639i	−0.826324	−	0.563195i	$-0.809572\pi$
$41$		−	7.21242i		−	1.12639i	0.826324	−	0.563195i	$-0.190428\pi$
$42$	11.2875			1.74170
$43$	7.35558			1.12172			0.560858	−	0.827912i	$-0.310471\pi$
$43$	7.35558			1.12172			0.560858	+	0.827912i	$0.310471\pi$
$44$		−	3.56813i		−	0.537916i
$45$		−	1.80373i		−	0.268885i
$46$			5.67157i			0.836227i
$47$		−	9.35160i		−	1.36407i	−0.731319	−	0.682036i	$-0.761095\pi$
$47$		−	9.35160i		−	1.36407i	0.731319	−	0.682036i	$-0.238905\pi$
$48$	−1.59529			−0.230261
$49$	−15.8816			−2.26880
$50$		−	4.12129i		−	0.582839i
$51$	2.63620			0.369142
$52$	−11.2194	+	6.29559i	−1.55586	+	0.873042i
$53$	−4.20276			−0.577294			−0.288647	−	0.957436i	$-0.593205\pi$
$53$	−4.20276			−0.577294			−0.288647	+	0.957436i	$0.593205\pi$
$54$			2.35969i			0.321113i
$55$	1.80373			0.243216
$56$	17.7003			2.36530
$57$		−	6.47687i		−	0.857883i
$58$			3.32405i			0.436470i
$59$		−	0.288691i		−	0.0375844i	−0.999823	−	0.0187922i	$-0.994018\pi$
$59$		−	0.288691i		−	0.0375844i	0.999823	−	0.0187922i	$-0.00598209\pi$
$60$		−	6.43596i		−	0.830879i
$61$	12.2851			1.57295			0.786473	−	0.617625i	$-0.211905\pi$
$61$	12.2851			1.57295			0.786473	+	0.617625i	$0.211905\pi$
$62$	14.3188			1.81848
$63$		−	4.78347i		−	0.602661i
$64$	11.7709			1.47136
$65$	−3.18250	−	5.67157i	−0.394741	−	0.703471i
$66$	−2.35969			−0.290458
$67$		−	13.1143i		−	1.60217i	−0.598553	−	0.801083i	$-0.704257\pi$
$67$		−	13.1143i		−	1.60217i	0.598553	−	0.801083i	$-0.295743\pi$
$68$	9.40632			1.14068
$69$	2.40352			0.289350
$70$			20.3597i			2.43345i
$71$			8.88039i			1.05391i	0.849894	+	0.526954i	$0.176666\pi$
$71$			8.88039i			1.05391i	−0.849894	+	0.526954i	$0.823334\pi$
$72$			3.70030i			0.436084i
$73$		−	2.61713i		−	0.306311i	−0.988202	−	0.153156i	$-0.951056\pi$
$73$		−	2.61713i		−	0.306311i	0.988202	−	0.153156i	$-0.0489436\pi$
$74$	−15.6500			−1.81927
$75$	−1.74654			−0.201673
$76$		−	23.1103i		−	2.65094i
$77$	4.78347			0.545127
$78$	4.16342	+	7.41968i	0.471415	+	0.840113i
$79$	3.32327			0.373897			0.186949	−	0.982370i	$-0.440140\pi$
$79$	3.32327			0.373897			0.186949	+	0.982370i	$0.440140\pi$
$80$		−	2.87749i		−	0.321713i
$81$	1.00000			0.111111
$82$	−17.0191			−1.87944
$83$			9.78588i			1.07414i	0.843538	+	0.537070i	$0.180469\pi$
$83$			9.78588i			1.07414i	−0.843538	+	0.537070i	$0.819531\pi$
$84$		−	17.0681i		−	1.86228i
$85$			4.75501i			0.515753i
$86$		−	17.3569i		−	1.87164i
$87$	1.40868			0.151027
$88$	−3.70030			−0.394453
$89$		−	14.0514i		−	1.48944i	−0.667375	−	0.744722i	$-0.732582\pi$
$89$		−	14.0514i		−	1.48944i	0.667375	−	0.744722i	$-0.267418\pi$
$90$	−4.25625			−0.448648
$91$	−8.43994	−	15.0409i	−0.884746	−	1.57671i
$92$	8.57608			0.894119
$93$		−	6.06807i		−	0.629230i
$94$	−22.0669			−2.27602
$95$	11.6826			1.19861
$96$		−	3.63620i		−	0.371118i
$97$			4.40604i			0.447366i	0.974662	+	0.223683i	$0.0718080\pi$
$97$			4.40604i			0.447366i	−0.974662	+	0.223683i	$0.928192\pi$
$98$			37.4757i			3.78561i
$99$			1.00000i			0.100504i
$100$	−6.23188			−0.623188
$101$	−6.42619			−0.639430			−0.319715	−	0.947514i	$-0.603587\pi$
$101$	−6.42619			−0.639430			−0.319715	+	0.947514i	$0.603587\pi$
$102$		−	6.22062i		−	0.615933i
$103$	−6.42895			−0.633463			−0.316731	−	0.948515i	$-0.602585\pi$
$103$	−6.42895			−0.633463			−0.316731	+	0.948515i	$0.602585\pi$
$104$	6.52879	+	11.6350i	0.640201	+	1.14091i
$105$	8.62812			0.842018
$106$			9.91721i			0.963245i
$107$	−12.7575			−1.23332			−0.616659	−	0.787231i	$-0.711514\pi$
$107$	−12.7575			−1.23332			−0.616659	+	0.787231i	$0.711514\pi$
$108$	3.56813			0.343343
$109$			5.72108i			0.547980i	0.961733	+	0.273990i	$0.0883435\pi$
$109$			5.72108i			0.547980i	−0.961733	+	0.273990i	$0.911656\pi$
$110$		−	4.25625i		−	0.405818i
$111$			6.63223i			0.629503i
$112$		−	7.63104i		−	0.721066i
$113$	2.12408			0.199817			0.0999085	−	0.994997i	$-0.468145\pi$
$113$	2.12408			0.199817			0.0999085	+	0.994997i	$0.468145\pi$
$114$	−15.2834			−1.43142
$115$			4.33532i			0.404271i
$116$	5.02637			0.466686
$117$	3.14435	−	1.76440i	0.290695	−	0.163118i
$118$	−0.681221			−0.0627115
$119$			12.6102i			1.15598i
$120$	−6.67436			−0.609283
$121$	−1.00000			−0.0909091
$122$		−	28.9890i		−	2.62454i
$123$			7.21242i			0.650322i
$124$		−	21.6517i		−	1.94438i
$125$		−	12.1690i		−	1.08843i
$126$	−11.2875			−1.00557
$127$	−3.12818			−0.277581			−0.138790	−	0.990322i	$-0.544321\pi$
$127$	−3.12818			−0.277581			−0.138790	+	0.990322i	$0.544321\pi$
$128$		−	20.5032i		−	1.81225i
$129$	−7.35558			−0.647623
$130$	−13.3831	+	7.50971i	−1.17378	+	0.658645i
$131$	6.62690			0.578995			0.289497	−	0.957179i	$-0.406512\pi$
$131$	6.62690			0.578995			0.289497	+	0.957179i	$0.406512\pi$
$132$			3.56813i			0.310566i
$133$	30.9819			2.68647
$134$	−30.9457			−2.67330
$135$			1.80373i			0.155241i
$136$		−	9.75474i		−	0.836462i
$137$			4.79829i			0.409945i	0.978768	+	0.204973i	$0.0657106\pi$
$137$			4.79829i			0.409945i	−0.978768	+	0.204973i	$0.934289\pi$
$138$		−	5.67157i		−	0.482796i
$139$	−16.9020			−1.43361			−0.716804	−	0.697275i	$-0.754396\pi$
$139$	−16.9020			−1.43361			−0.716804	+	0.697275i	$0.754396\pi$
$140$	30.7862			2.60191
$141$			9.35160i			0.787547i
$142$	20.9550			1.75850
$143$	1.76440	+	3.14435i	0.147546	+	0.262943i
$144$	1.59529			0.132941
$145$			2.54089i			0.211010i
$146$	−6.17560			−0.511096
$147$	15.8816			1.30989
$148$			23.6646i			1.94522i
$149$		−	22.0259i		−	1.80443i	−0.431284	−	0.902216i	$-0.641939\pi$
$149$		−	22.0259i		−	1.80443i	0.431284	−	0.902216i	$-0.358061\pi$
$150$			4.12129i			0.336502i
$151$			6.77937i			0.551697i	0.961201	+	0.275848i	$0.0889588\pi$
$151$			6.77937i			0.551697i	−0.961201	+	0.275848i	$0.911041\pi$
$152$	−23.9664			−1.94393
$153$	−2.63620			−0.213124
$154$		−	11.2875i		−	0.909573i
$155$	10.9452			0.879139
$156$	11.2194	−	6.29559i	0.898274	−	0.504051i
$157$	4.44168			0.354485			0.177242	−	0.984167i	$-0.443282\pi$
$157$	4.44168			0.354485			0.177242	+	0.984167i	$0.443282\pi$
$158$		−	7.84189i		−	0.623867i
$159$	4.20276			0.333301
$160$	6.55875			0.518514
$161$			11.4972i			0.906105i
$162$		−	2.35969i		−	0.185395i
$163$		−	17.9152i		−	1.40323i	−0.712556	−	0.701615i	$-0.752463\pi$
$163$		−	17.9152i		−	1.40323i	0.712556	−	0.701615i	$-0.247537\pi$
$164$			25.7348i			2.00955i
$165$	−1.80373			−0.140421
$166$	23.0916			1.79226
$167$			18.0543i			1.39708i	0.715569	+	0.698542i	$0.246167\pi$
$167$			18.0543i			1.39708i	−0.715569	+	0.698542i	$0.753833\pi$
$168$	−17.7003			−1.36561
$169$	6.77382	−	11.0957i	0.521063	−	0.853518i
$170$	11.2203			0.860561
$171$			6.47687i			0.495299i
$172$	−26.2457			−2.00121
$173$	25.4260			1.93311			0.966553	−	0.256466i	$-0.0825583\pi$
$173$	25.4260			1.93311			0.966553	+	0.256466i	$0.0825583\pi$
$174$		−	3.32405i		−	0.251996i
$175$		−	8.35453i		−	0.631543i
$176$			1.59529i			0.120250i
$177$			0.288691i			0.0216994i
$178$	−33.1569			−2.48521
$179$	13.7969			1.03123			0.515613	−	0.856821i	$-0.327564\pi$
$179$	13.7969			1.03123			0.515613	+	0.856821i	$0.327564\pi$
$180$			6.43596i			0.479708i
$181$	18.0141			1.33898			0.669490	−	0.742821i	$-0.266513\pi$
$181$	18.0141			1.33898			0.669490	+	0.742821i	$0.266513\pi$
$182$	−35.4918	+	19.9156i	−2.63083	+	1.47624i
$183$	−12.2851			−0.908141
$184$		−	8.89375i		−	0.655656i
$185$	−11.9628			−0.879521
$186$	−14.3188			−1.04990
$187$		−	2.63620i		−	0.192778i
$188$			33.3677i			2.43359i
$189$			4.78347i			0.347946i
$190$		−	27.5672i		−	1.99994i
$191$	−8.72663			−0.631436			−0.315718	−	0.948853i	$-0.602245\pi$
$191$	−8.72663			−0.631436			−0.315718	+	0.948853i	$0.602245\pi$
$192$	−11.7709			−0.849491
$193$		−	4.46458i		−	0.321367i	−0.987006	−	0.160684i	$-0.948630\pi$
$193$		−	4.46458i		−	0.321367i	0.987006	−	0.160684i	$-0.0513699\pi$
$194$	10.3969			0.746453
$195$	3.18250	+	5.67157i	0.227904	+	0.406149i
$196$	56.6677			4.04769
$197$			5.53927i			0.394656i	0.980337	+	0.197328i	$0.0632264\pi$
$197$			5.53927i			0.394656i	−0.980337	+	0.197328i	$0.936774\pi$
$198$	2.35969			0.167696
$199$	22.7640			1.61370			0.806848	−	0.590759i	$-0.201172\pi$
$199$	22.7640			1.61370			0.806848	+	0.590759i	$0.201172\pi$
$200$			6.46272i			0.456983i
$201$			13.1143i			0.925011i
$202$			15.1638i			1.06692i
$203$			6.73840i			0.472943i
$204$	−9.40632			−0.658574
$205$	−13.0093			−0.908608
$206$			15.1703i			1.05697i
$207$	−2.40352			−0.167056
$208$	5.01615	−	2.81473i	0.347808	−	0.195166i
$209$	−6.47687			−0.448015
$210$		−	20.3597i		−	1.40495i
$211$	5.58761			0.384667			0.192334	−	0.981330i	$-0.438394\pi$
$211$	5.58761			0.384667			0.192334	+	0.981330i	$0.438394\pi$
$212$	14.9960			1.02993
$213$		−	8.88039i		−	0.608475i
$214$			30.1038i			2.05785i
$215$		−	13.2675i		−	0.904837i
$216$		−	3.70030i		−	0.251773i
$217$	29.0265			1.97044
$218$	13.5000			0.914333
$219$			2.61713i			0.176849i
$220$	−6.43596			−0.433912
$221$	−8.28913	+	4.65130i	−0.557587	+	0.312881i
$222$	15.6500			1.05036
$223$		−	10.1832i		−	0.681920i	−0.940078	−	0.340960i	$-0.889248\pi$
$223$		−	10.1832i		−	0.681920i	0.940078	−	0.340960i	$-0.110752\pi$
$224$	17.3937			1.16216
$225$	1.74654			0.116436
$226$		−	5.01218i		−	0.333405i
$227$		−	0.783473i		−	0.0520010i	−0.999662	−	0.0260005i	$-0.991723\pi$
$227$		−	0.783473i		−	0.0520010i	0.999662	−	0.0260005i	$-0.00827714\pi$
$228$			23.1103i			1.53052i
$229$			20.8340i			1.37675i	0.725355	+	0.688375i	$0.241676\pi$
$229$			20.8340i			1.37675i	−0.725355	+	0.688375i	$0.758324\pi$
$230$	10.2300			0.674546
$231$	−4.78347			−0.314729
$232$		−	5.21255i		−	0.342221i
$233$	−8.50679			−0.557298			−0.278649	−	0.960393i	$-0.589887\pi$
$233$	−8.50679			−0.557298			−0.278649	+	0.960393i	$0.589887\pi$
$234$	−4.16342	−	7.41968i	−0.272172	−	0.485039i
$235$	−16.8678			−1.10033
$236$			1.03009i			0.0670530i
$237$	−3.32327			−0.215870
$238$	29.7562			1.92881
$239$			2.74768i			0.177733i	0.996044	+	0.0888665i	$0.0283244\pi$
$239$			2.74768i			0.177733i	−0.996044	+	0.0888665i	$0.971676\pi$
$240$			2.87749i			0.185741i
$241$		−	10.3746i		−	0.668288i	−0.942522	−	0.334144i	$-0.891553\pi$
$241$		−	10.3746i		−	0.668288i	0.942522	−	0.334144i	$-0.108447\pi$
$242$			2.35969i			0.151687i
$243$	−1.00000			−0.0641500
$244$	−43.8348			−2.80624
$245$			28.6462i			1.83014i
$246$	17.0191			1.08510
$247$	11.4278	+	20.3655i	0.727131	+	1.29583i
$248$	−22.4537			−1.42581
$249$		−	9.78588i		−	0.620155i
$250$	−28.7150			−1.81609
$251$	−24.1897			−1.52684			−0.763421	−	0.645901i	$-0.776482\pi$
$251$	−24.1897			−1.52684			−0.763421	+	0.645901i	$0.776482\pi$
$252$			17.0681i			1.07519i
$253$		−	2.40352i		−	0.151108i
$254$			7.38152i			0.463158i
$255$		−	4.75501i		−	0.297770i
$256$	−24.8395			−1.55247
$257$	−4.06662			−0.253669			−0.126834	−	0.991924i	$-0.540482\pi$
$257$	−4.06662			−0.253669			−0.126834	+	0.991924i	$0.540482\pi$
$258$			17.3569i			1.08059i
$259$	−31.7251			−1.97130
$260$	11.3556	+	20.2369i	0.704243	+	1.25504i
$261$	−1.40868			−0.0871953
$262$		−	15.6374i		−	0.966082i
$263$	−6.36570			−0.392526			−0.196263	−	0.980551i	$-0.562881\pi$
$263$	−6.36570			−0.392526			−0.196263	+	0.980551i	$0.562881\pi$
$264$	3.70030			0.227738
$265$			7.58067i			0.465677i
$266$		−	73.1077i		−	4.48252i
$267$			14.0514i			0.859931i
$268$			46.7935i			2.85837i
$269$	28.4905			1.73710			0.868548	−	0.495605i	$-0.165054\pi$
$269$	28.4905			1.73710			0.868548	+	0.495605i	$0.165054\pi$
$270$	4.25625			0.259027
$271$			13.5110i			0.820737i	0.911920	+	0.410368i	$0.134600\pi$
$271$			13.5110i			0.820737i	−0.911920	+	0.410368i	$0.865400\pi$
$272$	−4.20552			−0.254997
$273$	8.43994	+	15.0409i	0.510808	+	0.910316i
$274$	11.3225			0.684015
$275$			1.74654i			0.105320i
$276$	−8.57608			−0.516220
$277$	−2.04052			−0.122603			−0.0613016	−	0.998119i	$-0.519525\pi$
$277$	−2.04052			−0.122603			−0.0613016	+	0.998119i	$0.519525\pi$
$278$			39.8834i			2.39205i
$279$			6.06807i			0.363286i
$280$		−	31.9266i		−	1.90798i
$281$		−	15.7569i		−	0.939976i	−0.882673	−	0.469988i	$-0.844258\pi$
$281$		−	15.7569i		−	0.939976i	0.882673	−	0.469988i	$-0.155742\pi$
$282$	22.0669			1.31406
$283$	−21.8937			−1.30144			−0.650722	−	0.759316i	$-0.725533\pi$
$283$	−21.8937			−1.30144			−0.650722	+	0.759316i	$0.725533\pi$
$284$		−	31.6864i		−	1.88024i
$285$	−11.6826			−0.692015
$286$	7.41968	−	4.16342i	0.438735	−	0.246188i
$287$	−34.5004			−2.03649
$288$			3.63620i			0.214265i
$289$	−10.0504			−0.591202
$290$	5.99571			0.352080
$291$		−	4.40604i		−	0.258287i
$292$			9.33824i			0.546479i
$293$		−	15.0681i		−	0.880285i	−0.897928	−	0.440143i	$-0.854928\pi$
$293$		−	15.0681i		−	0.880285i	0.897928	−	0.440143i	$-0.145072\pi$
$294$		−	37.4757i		−	2.18563i
$295$	−0.520722			−0.0303176
$296$	24.5412			1.42643
$297$		−	1.00000i		−	0.0580259i
$298$	−51.9743			−3.01079
$299$	−7.55751	+	4.24076i	−0.437062	+	0.245250i
$300$	6.23188			0.359798
$301$		−	35.1852i		−	2.02804i
$302$	15.9972			0.920535
$303$	6.42619			0.369175
$304$			10.3325i			0.592610i
$305$		−	22.1591i		−	1.26882i
$306$			6.22062i			0.355609i
$307$			17.0334i			0.972146i	0.873918	+	0.486073i	$0.161571\pi$
$307$			17.0334i			0.972146i	−0.873918	+	0.486073i	$0.838429\pi$
$308$	−17.0681			−0.972543
$309$	6.42895			0.365730
$310$		−	25.8273i		−	1.46689i
$311$	15.3734			0.871748			0.435874	−	0.900008i	$-0.356439\pi$
$311$	15.3734			0.871748			0.435874	+	0.900008i	$0.356439\pi$
$312$	−6.52879	−	11.6350i	−0.369620	−	0.658703i
$313$	16.7286			0.945558			0.472779	−	0.881181i	$-0.343251\pi$
$313$	16.7286			0.945558			0.472779	+	0.881181i	$0.343251\pi$
$314$		−	10.4810i		−	0.591476i
$315$	−8.62812			−0.486139
$316$	−11.8579			−0.667057
$317$		−	5.33201i		−	0.299475i	−0.988726	−	0.149738i	$-0.952157\pi$
$317$		−	5.33201i		−	0.299475i	0.988726	−	0.149738i	$-0.0478429\pi$
$318$		−	9.91721i		−	0.556130i
$319$		−	1.40868i		−	0.0788711i
$320$		−	21.2316i		−	1.18688i
$321$	12.7575			0.712056
$322$	27.1298			1.51188
$323$		−	17.0743i		−	0.950042i
$324$	−3.56813			−0.198229
$325$	5.49173	−	3.08159i	0.304626	−	0.170936i
$326$	−42.2744			−2.34136
$327$		−	5.72108i		−	0.316376i
$328$	26.6881			1.47360
$329$	−44.7331			−2.46622
$330$			4.25625i			0.234299i
$331$		−	22.1737i		−	1.21878i	−0.792871	−	0.609389i	$-0.791415\pi$
$331$		−	22.1737i		−	1.21878i	0.792871	−	0.609389i	$-0.208585\pi$
$332$		−	34.9173i		−	1.91634i
$333$		−	6.63223i		−	0.363444i
$334$	42.6025			2.33111
$335$	−23.6547			−1.29240
$336$			7.63104i			0.416308i
$337$	12.9050			0.702982			0.351491	−	0.936191i	$-0.385675\pi$
$337$	12.9050			0.702982			0.351491	+	0.936191i	$0.385675\pi$
$338$	−26.1825	−	15.9841i	−1.42414	−	0.869421i
$339$	−2.12408			−0.115364
$340$		−	16.9665i		−	0.920138i
$341$	−6.06807			−0.328605
$342$	15.2834			0.826432
$343$			42.4850i			2.29397i
$344$			27.2178i			1.46749i
$345$		−	4.33532i		−	0.233406i
$346$		−	59.9975i		−	3.22549i
$347$	30.7457			1.65052			0.825259	−	0.564755i	$-0.191029\pi$
$347$	30.7457			1.65052			0.825259	+	0.564755i	$0.191029\pi$
$348$	−5.02637			−0.269441
$349$			15.5239i			0.830974i	0.909599	+	0.415487i	$0.136389\pi$
$349$			15.5239i			0.830974i	−0.909599	+	0.415487i	$0.863611\pi$
$350$	−19.7141			−1.05376
$351$	−3.14435	+	1.76440i	−0.167833	+	0.0941765i
$352$	−3.63620			−0.193810
$353$			21.4800i			1.14326i	0.820510	+	0.571632i	$0.193690\pi$
$353$			21.4800i			1.14326i	−0.820510	+	0.571632i	$0.806310\pi$
$354$	0.681221			0.0362065
$355$	16.0179			0.850141
$356$			50.1372i			2.65726i
$357$		−	12.6102i		−	0.667403i
$358$		−	32.5563i		−	1.72066i
$359$			19.1458i			1.01047i	0.862980	+	0.505237i	$0.168595\pi$
$359$			19.1458i			1.01047i	−0.862980	+	0.505237i	$0.831405\pi$
$360$	6.67436			0.351770
$361$	−22.9499			−1.20789
$362$		−	42.5077i		−	2.23416i
$363$	1.00000			0.0524864
$364$	30.1148	+	53.6679i	1.57844	+	2.81296i
$365$	−4.72060			−0.247087
$366$			28.9890i			1.51528i
$367$	16.7868			0.876262			0.438131	−	0.898911i	$-0.355641\pi$
$367$	16.7868			0.876262			0.438131	+	0.898911i	$0.355641\pi$
$368$	−3.83432			−0.199878
$369$		−	7.21242i		−	0.375464i
$370$			28.2284i			1.46753i
$371$			20.1038i			1.04374i
$372$			21.6517i			1.12259i
$373$	−10.3674			−0.536802			−0.268401	−	0.963307i	$-0.586495\pi$
$373$	−10.3674			−0.536802			−0.268401	+	0.963307i	$0.586495\pi$
$374$	−6.22062			−0.321661
$375$			12.1690i			0.628403i
$376$	34.6037			1.78455
$377$	−4.42939	+	2.48547i	−0.228125	+	0.128008i
$378$	11.2875			0.580567
$379$		−	25.3516i		−	1.30223i	−0.758981	−	0.651113i	$-0.774302\pi$
$379$		−	25.3516i		−	1.30223i	0.758981	−	0.651113i	$-0.225698\pi$
$380$	−41.6849			−2.13839
$381$	3.12818			0.160261
$382$			20.5921i			1.05358i
$383$			27.2749i			1.39368i	0.717227	+	0.696840i	$0.245411\pi$
$383$			27.2749i			1.39368i	−0.717227	+	0.696840i	$0.754589\pi$
$384$			20.5032i			1.04630i
$385$		−	8.62812i		−	0.439730i
$386$	−10.5350			−0.536218
$387$	7.35558			0.373905
$388$		−	15.7213i		−	0.798130i
$389$	5.78177			0.293147			0.146574	−	0.989200i	$-0.453175\pi$
$389$	5.78177			0.293147			0.146574	+	0.989200i	$0.453175\pi$
$390$	13.3831	−	7.50971i	0.677681	−	0.380269i
$391$	6.33618			0.320434
$392$		−	58.7667i		−	2.96817i
$393$	−6.62690			−0.334283
$394$	13.0709			0.658505
$395$		−	5.99430i		−	0.301606i
$396$		−	3.56813i		−	0.179305i
$397$			14.2696i			0.716172i	0.933689	+	0.358086i	$0.116571\pi$
$397$			14.2696i			0.716172i	−0.933689	+	0.358086i	$0.883429\pi$
$398$		−	53.7159i		−	2.69253i
$399$	−30.9819			−1.55104
$400$	2.78624			0.139312
$401$			16.4746i			0.822704i	0.911477	+	0.411352i	$0.134943\pi$
$401$			16.4746i			0.822704i	−0.911477	+	0.411352i	$0.865057\pi$
$402$	30.9457			1.54343
$403$	10.7065	+	19.0801i	0.533328	+	0.950448i
$404$	22.9295			1.14078
$405$		−	1.80373i		−	0.0896283i
$406$	15.9005			0.789130
$407$	6.63223			0.328747
$408$			9.75474i			0.482932i
$409$			4.40230i			0.217680i	0.994059	+	0.108840i	$0.0347136\pi$
$409$			4.40230i			0.217680i	−0.994059	+	0.108840i	$0.965286\pi$
$410$			30.6979i			1.51606i
$411$		−	4.79829i		−	0.236682i
$412$	22.9393			1.13014
$413$	−1.38095			−0.0679519
$414$			5.67157i			0.278742i
$415$	17.6511			0.866460
$416$	6.41570	+	11.4335i	0.314556	+	0.560572i
$417$	16.9020			0.827694
$418$			15.2834i			0.747535i
$419$	37.6890			1.84123			0.920614	−	0.390474i	$-0.127689\pi$
$419$	37.6890			1.84123			0.920614	+	0.390474i	$0.127689\pi$
$420$	−30.7862			−1.50222
$421$		−	13.7632i		−	0.670775i	−0.942080	−	0.335388i	$-0.891133\pi$
$421$		−	13.7632i		−	0.670775i	0.942080	−	0.335388i	$-0.108867\pi$
$422$		−	13.1850i		−	0.641837i
$423$		−	9.35160i		−	0.454691i
$424$		−	15.5515i		−	0.755247i
$425$	−4.60423			−0.223338
$426$	−20.9550			−1.01527
$427$		−	58.7655i		−	2.84386i
$428$	45.5205			2.20032
$429$	−1.76440	−	3.14435i	−0.0851858	−	0.151810i
$430$	−31.3072			−1.50977
$431$			23.4202i			1.12811i	0.825736	+	0.564056i	$0.190760\pi$
$431$			23.4202i			1.12811i	−0.825736	+	0.564056i	$0.809240\pi$
$432$	−1.59529			−0.0767536
$433$	−21.1826			−1.01797			−0.508985	−	0.860775i	$-0.669979\pi$
$433$	−21.1826			−1.01797			−0.508985	+	0.860775i	$0.669979\pi$
$434$		−	68.4934i		−	3.28779i
$435$		−	2.54089i		−	0.121826i
$436$		−	20.4136i		−	0.977632i
$437$		−	15.5673i		−	0.744685i
$438$	6.17560			0.295082
$439$	6.52337			0.311344			0.155672	−	0.987809i	$-0.450246\pi$
$439$	6.52337			0.311344			0.155672	+	0.987809i	$0.450246\pi$
$440$			6.67436i			0.318188i
$441$	−15.8816			−0.756267
$442$	10.9756	+	19.5598i	0.522057	+	0.930364i
$443$	−35.8996			−1.70564			−0.852821	−	0.522203i	$-0.825110\pi$
$443$	−35.8996			−1.70564			−0.852821	+	0.522203i	$0.825110\pi$
$444$		−	23.6646i		−	1.12307i
$445$	−25.3450			−1.20147
$446$	−24.0293			−1.13782
$447$			22.0259i			1.04179i
$448$		−	56.3058i		−	2.66020i
$449$		−	6.86446i		−	0.323954i	−0.986795	−	0.161977i	$-0.948213\pi$
$449$		−	6.86446i		−	0.323954i	0.986795	−	0.161977i	$-0.0517870\pi$
$450$		−	4.12129i		−	0.194280i
$451$	7.21242			0.339620
$452$	−7.57901			−0.356487
$453$		−	6.77937i		−	0.318522i
$454$	−1.84875			−0.0867663
$455$	−27.1298	+	15.2234i	−1.27186	+	0.713685i
$456$	23.9664			1.12233
$457$			34.4445i			1.61124i	0.592430	+	0.805622i	$0.298169\pi$
$457$			34.4445i			1.61124i	−0.592430	+	0.805622i	$0.701831\pi$
$458$	49.1618			2.29718
$459$	2.63620			0.123047
$460$		−	15.4690i		−	0.721245i
$461$			10.0997i			0.470390i	0.971948	+	0.235195i	$0.0755729\pi$
$461$			10.0997i			0.470390i	−0.971948	+	0.235195i	$0.924427\pi$
$462$			11.2875i			0.525142i
$463$			6.44706i			0.299620i	0.988715	+	0.149810i	$0.0478662\pi$
$463$			6.44706i			0.299620i	−0.988715	+	0.149810i	$0.952134\pi$
$464$	−2.24726			−0.104327
$465$	−10.9452			−0.507571
$466$			20.0734i			0.929881i
$467$	17.9485			0.830555			0.415278	−	0.909695i	$-0.363684\pi$
$467$	17.9485			0.830555			0.415278	+	0.909695i	$0.363684\pi$
$468$	−11.2194	+	6.29559i	−0.518619	+	0.291014i
$469$	−62.7319			−2.89669
$470$			39.8028i			1.83597i
$471$	−4.44168			−0.204662
$472$	1.06824			0.0491699
$473$			7.35558i			0.338210i
$474$			7.84189i			0.360190i
$475$			11.3121i			0.519035i
$476$		−	44.9949i		−	2.06234i
$477$	−4.20276			−0.192431
$478$	6.48368			0.296557
$479$			4.09911i			0.187293i	0.995606	+	0.0936466i	$0.0298524\pi$
$479$			4.09911i			0.187293i	−0.995606	+	0.0936466i	$0.970148\pi$
$480$	−6.55875			−0.299364
$481$	−11.7019	−	20.8540i	−0.533559	−	0.950861i
$482$	−24.4809			−1.11507
$483$		−	11.4972i		−	0.523140i
$484$	3.56813			0.162188
$485$	7.94734			0.360870
$486$			2.35969i			0.107038i
$487$		−	6.10989i		−	0.276865i	−0.990372	−	0.138433i	$-0.955794\pi$
$487$		−	6.10989i		−	0.276865i	0.990372	−	0.138433i	$-0.0442065\pi$
$488$			45.4585i			2.05781i
$489$			17.9152i			0.810155i
$490$	67.5962			3.05368
$491$	11.8025			0.532641			0.266320	−	0.963885i	$-0.414192\pi$
$491$	11.8025			0.532641			0.266320	+	0.963885i	$0.414192\pi$
$492$		−	25.7348i		−	1.16022i
$493$	3.71358			0.167251
$494$	48.0563	−	26.9660i	2.16215	−	1.21326i
$495$	1.80373			0.0810719
$496$			9.68036i			0.434661i
$497$	42.4791			1.90545
$498$	−23.0916			−1.03476
$499$			2.07874i			0.0930570i	0.998917	+	0.0465285i	$0.0148158\pi$
$499$			2.07874i			0.0930570i	−0.998917	+	0.0465285i	$0.985184\pi$
$500$			43.4205i			1.94182i
$501$		−	18.0543i		−	0.806606i
$502$			57.0802i			2.54762i
$503$	33.4841			1.49298			0.746490	−	0.665396i	$-0.231737\pi$
$503$	33.4841			1.49298			0.746490	+	0.665396i	$0.231737\pi$
$504$	17.7003			0.788433
$505$			11.5911i			0.515799i
$506$	−5.67157			−0.252132
$507$	−6.77382	+	11.0957i	−0.300836	+	0.492779i
$508$	11.1617			0.495222
$509$		−	25.3434i		−	1.12332i	−0.827366	−	0.561662i	$-0.810162\pi$
$509$		−	25.3434i		−	1.12332i	0.827366	−	0.561662i	$-0.189838\pi$
$510$	−11.2203			−0.496845
$511$	−12.5189			−0.553806
$512$			17.6069i			0.778124i
$513$		−	6.47687i		−	0.285961i
$514$			9.59595i			0.423259i
$515$			11.5961i			0.510986i
$516$	26.2457			1.15540
$517$	9.35160			0.411283
$518$			74.8613i			3.28922i
$519$	−25.4260			−1.11608
$520$	20.9865	−	11.7762i	0.920319	−	0.516421i
$521$	28.6222			1.25396			0.626980	−	0.779036i	$-0.284291\pi$
$521$	28.6222			1.25396			0.626980	+	0.779036i	$0.284291\pi$
$522$			3.32405i			0.145490i
$523$	31.8440			1.39244			0.696221	−	0.717827i	$-0.254863\pi$
$523$	31.8440			1.39244			0.696221	+	0.717827i	$0.254863\pi$
$524$	−23.6456			−1.03296
$525$			8.35453i			0.364622i
$526$			15.0211i			0.654950i
$527$		−	15.9967i		−	0.696826i
$528$		−	1.59529i		−	0.0694262i
$529$	−17.2231			−0.748829
$530$	17.8880			0.777006
$531$		−	0.288691i		−	0.0125281i
$532$	−110.548			−4.79285
$533$	−12.7256	−	22.6783i	−0.551205	−	0.982308i
$534$	33.1569			1.43484
$535$			23.0112i			0.994861i
$536$	48.5268			2.09604
$537$	−13.7969			−0.595379
$538$		−	67.2287i		−	2.89843i
$539$		−	15.8816i		−	0.684070i
$540$		−	6.43596i		−	0.276960i
$541$		−	30.2013i		−	1.29846i	−0.760594	−	0.649228i	$-0.775092\pi$
$541$		−	30.2013i		−	1.29846i	0.760594	−	0.649228i	$-0.224908\pi$
$542$	31.8818			1.36944
$543$	−18.0141			−0.773060
$544$		−	9.58577i		−	0.410986i
$545$	10.3193			0.442031
$546$	35.4918	−	19.9156i	1.51891	−	0.852310i
$547$	−9.53137			−0.407532			−0.203766	−	0.979020i	$-0.565318\pi$
$547$	−9.53137			−0.407532			−0.203766	+	0.979020i	$0.565318\pi$
$548$		−	17.1209i		−	0.731369i
$549$	12.2851			0.524315
$550$	4.12129			0.175732
$551$		−	9.12386i		−	0.388690i
$552$			8.89375i			0.378543i
$553$		−	15.8968i		−	0.676000i
$554$			4.81500i			0.204570i
$555$	11.9628			0.507792
$556$	60.3085			2.55765
$557$		−	15.8630i		−	0.672135i	−0.941838	−	0.336068i	$-0.890903\pi$
$557$		−	15.8630i		−	0.672135i	0.941838	−	0.336068i	$-0.109097\pi$
$558$	14.3188			0.606162
$559$	23.1285	−	12.9782i	0.978231	−	0.548917i
$560$	−13.7644			−0.581651
$561$			2.63620i			0.111301i
$562$	−37.1813			−1.56840
$563$	5.85319			0.246683			0.123341	−	0.992364i	$-0.460639\pi$
$563$	5.85319			0.246683			0.123341	+	0.992364i	$0.460639\pi$
$564$		−	33.3677i		−	1.40504i
$565$		−	3.83128i		−	0.161183i
$566$			51.6622i			2.17153i
$567$		−	4.78347i		−	0.200887i
$568$	−32.8601			−1.37878
$569$	16.3417			0.685078			0.342539	−	0.939504i	$-0.388713\pi$
$569$	16.3417			0.685078			0.342539	+	0.939504i	$0.388713\pi$
$570$			27.5672i			1.15466i
$571$	−27.6986			−1.15915			−0.579574	−	0.814919i	$-0.696781\pi$
$571$	−27.6986			−1.15915			−0.579574	+	0.814919i	$0.696781\pi$
$572$	−6.29559	−	11.2194i	−0.263232	−	0.469108i
$573$	8.72663			0.364560
$574$			81.4102i			3.39800i
$575$	−4.19785			−0.175062
$576$	11.7709			0.490454
$577$		−	5.36008i		−	0.223143i	−0.993756	−	0.111571i	$-0.964412\pi$
$577$		−	5.36008i		−	0.223143i	0.993756	−	0.111571i	$-0.0355884\pi$
$578$			23.7159i			0.986451i
$579$			4.46458i			0.185542i
$580$		−	9.06623i		−	0.376455i
$581$	46.8105			1.94203
$582$	−10.3969			−0.430965
$583$		−	4.20276i		−	0.174061i
$584$	9.68415			0.400733
$585$	−3.18250	−	5.67157i	−0.131580	−	0.234490i
$586$	−35.5559			−1.46880
$587$		−	5.50925i		−	0.227391i	−0.993516	−	0.113696i	$-0.963731\pi$
$587$		−	5.50925i		−	0.227391i	0.993516	−	0.113696i	$-0.0362688\pi$
$588$	−56.6677			−2.33694
$589$	−39.3021			−1.61942
$590$			1.22874i			0.0505865i
$591$		−	5.53927i		−	0.227855i
$592$		−	10.5803i		−	0.434850i
$593$			28.9757i			1.18989i	0.803767	+	0.594944i	$0.202826\pi$
$593$			28.9757i			1.18989i	−0.803767	+	0.594944i	$0.797174\pi$
$594$	−2.35969			−0.0968192
$595$	22.7455			0.932473
$596$			78.5913i			3.21923i
$597$	−22.7640			−0.931667
$598$	10.0069	+	17.8334i	0.409212	+	0.729260i
$599$	−9.17852			−0.375024			−0.187512	−	0.982262i	$-0.560042\pi$
$599$	−9.17852			−0.375024			−0.187512	+	0.982262i	$0.560042\pi$
$600$		−	6.46272i		−	0.263839i
$601$	41.2205			1.68142			0.840710	−	0.541485i	$-0.182138\pi$
$601$	41.2205			1.68142			0.840710	+	0.541485i	$0.182138\pi$
$602$	−83.0262			−3.38389
$603$		−	13.1143i		−	0.534055i
$604$		−	24.1897i		−	0.984263i
$605$			1.80373i			0.0733323i
$606$		−	15.1638i		−	0.615988i
$607$	−36.7876			−1.49316			−0.746581	−	0.665294i	$-0.768306\pi$
$607$	−36.7876			−1.49316			−0.746581	+	0.665294i	$0.768306\pi$
$608$	−23.5512			−0.955128
$609$		−	6.73840i		−	0.273054i
$610$	−52.2885			−2.11710
$611$	−16.4999	−	29.4047i	−0.667516	−	1.18959i
$612$	9.40632			0.380228
$613$			29.7486i			1.20153i	0.799424	+	0.600767i	$0.205138\pi$
$613$			29.7486i			1.20153i	−0.799424	+	0.600767i	$0.794862\pi$
$614$	40.1935			1.62208
$615$	13.0093			0.524585
$616$			17.7003i			0.713165i
$617$			37.5288i			1.51085i	0.655233	+	0.755427i	$0.272570\pi$
$617$			37.5288i			1.51085i	−0.655233	+	0.755427i	$0.727430\pi$
$618$		−	15.1703i		−	0.610239i
$619$		−	14.1147i		−	0.567316i	−0.958925	−	0.283658i	$-0.908452\pi$
$619$		−	14.1147i		−	0.567316i	0.958925	−	0.283658i	$-0.0915481\pi$
$620$	−39.0539			−1.56844
$621$	2.40352			0.0964501
$622$		−	36.2765i		−	1.45456i
$623$	−67.2144			−2.69289
$624$	−5.01615	+	2.81473i	−0.200807	+	0.112679i
$625$	−13.2169			−0.528676
$626$		−	39.4744i		−	1.57771i
$627$	6.47687			0.258661
$628$	−15.8485			−0.632424
$629$			17.4839i			0.697129i
$630$			20.3597i			0.811149i
$631$		−	20.2949i		−	0.807925i	−0.914775	−	0.403963i	$-0.867633\pi$
$631$		−	20.2949i		−	0.807925i	0.914775	−	0.403963i	$-0.132367\pi$
$632$			12.2971i			0.489153i
$633$	−5.58761			−0.222088
$634$	−12.5819			−0.499690
$635$			5.64240i			0.223912i
$636$	−14.9960			−0.594630
$637$	−49.9373	+	28.0215i	−1.97859	+	1.11025i
$638$	−3.32405			−0.131601
$639$			8.88039i			0.351303i
$640$	−36.9824			−1.46186
$641$	−8.88022			−0.350748			−0.175374	−	0.984502i	$-0.556113\pi$
$641$	−8.88022			−0.350748			−0.175374	+	0.984502i	$0.556113\pi$
$642$		−	30.1038i		−	1.18810i
$643$		−	9.48507i		−	0.374055i	−0.982355	−	0.187027i	$-0.940115\pi$
$643$		−	9.48507i		−	0.374055i	0.982355	−	0.187027i	$-0.0598853\pi$
$644$		−	41.0235i		−	1.61655i
$645$			13.2675i			0.522408i
$646$	−40.2901			−1.58519
$647$	5.92069			0.232767			0.116383	−	0.993204i	$-0.462870\pi$
$647$	5.92069			0.232767			0.116383	+	0.993204i	$0.462870\pi$
$648$			3.70030i			0.145361i
$649$	0.288691			0.0113321
$650$	−7.27159	−	12.9588i	−0.285215	−	0.508284i
$651$	−29.0265			−1.13764
$652$			63.9239i			2.50345i
$653$	−12.6446			−0.494821			−0.247410	−	0.968911i	$-0.579580\pi$
$653$	−12.6446			−0.494821			−0.247410	+	0.968911i	$0.579580\pi$
$654$	−13.5000			−0.527890
$655$		−	11.9532i		−	0.467049i
$656$		−	11.5059i		−	0.449231i
$657$		−	2.61713i		−	0.102104i
$658$			105.556i			4.11501i
$659$	28.4668			1.10891			0.554454	−	0.832214i	$-0.312927\pi$
$659$	28.4668			1.10891			0.554454	+	0.832214i	$0.312927\pi$
$660$	6.43596			0.250519
$661$		−	40.5531i		−	1.57733i	−0.614822	−	0.788666i	$-0.710772\pi$
$661$		−	40.5531i		−	1.57733i	0.614822	−	0.788666i	$-0.289228\pi$
$662$	−52.3231			−2.03359
$663$	8.28913	−	4.65130i	0.321923	−	0.180642i
$664$	−36.2107			−1.40525
$665$		−	55.8832i		−	2.16706i
$666$	−15.6500			−0.606425
$667$	3.38580			0.131099
$668$		−	64.4201i		−	2.49249i
$669$			10.1832i			0.393707i
$670$			55.8178i			2.15643i
$671$			12.2851i			0.474261i
$672$	−17.3937			−0.670976
$673$	−10.3646			−0.399525			−0.199763	−	0.979844i	$-0.564017\pi$
$673$	−10.3646			−0.399525			−0.199763	+	0.979844i	$0.564017\pi$
$674$		−	30.4519i		−	1.17296i
$675$	−1.74654			−0.0672244
$676$	−24.1699	+	39.5910i	−0.929610	+	1.52273i
$677$	47.8616			1.83947			0.919734	−	0.392541i	$-0.128404\pi$
$677$	47.8616			1.83947			0.919734	+	0.392541i	$0.128404\pi$
$678$			5.01218i			0.192491i
$679$	21.0762			0.808830
$680$	−17.5950			−0.674736
$681$			0.783473i			0.0300228i
$682$			14.3188i			0.548294i
$683$		−	20.7800i		−	0.795123i	−0.917576	−	0.397562i	$-0.869857\pi$
$683$		−	20.7800i		−	0.795123i	0.917576	−	0.397562i	$-0.130143\pi$
$684$		−	23.1103i		−	0.883645i
$685$	8.65484			0.330684
$686$	100.251			3.82761
$687$		−	20.8340i		−	0.794868i
$688$	11.7343			0.447366
$689$	−13.2149	+	7.41534i	−0.503449	+	0.282502i
$690$	−10.2300			−0.389450
$691$			27.6573i			1.05213i	0.850443	+	0.526067i	$0.176334\pi$
$691$			27.6573i			1.05213i	−0.850443	+	0.526067i	$0.823666\pi$
$692$	−90.7234			−3.44879
$693$	4.78347			0.181709
$694$		−	72.5503i		−	2.75397i
$695$			30.4867i			1.15643i
$696$			5.21255i			0.197581i
$697$			19.0134i			0.720184i
$698$	36.6315			1.38652
$699$	8.50679			0.321756
$700$			29.8100i			1.12671i
$701$	34.9434			1.31979			0.659897	−	0.751356i	$-0.270600\pi$
$701$	34.9434			1.31979			0.659897	+	0.751356i	$0.270600\pi$
$702$	4.16342	+	7.41968i	0.157138	+	0.280038i
$703$	42.9561			1.62012
$704$			11.7709i			0.443632i
$705$	16.8678			0.635279
$706$	50.6861			1.90760
$707$			30.7395i			1.15608i
$708$		−	1.03009i		−	0.0387131i
$709$			2.08738i			0.0783932i	0.999232	+	0.0391966i	$0.0124799\pi$
$709$			2.08738i			0.0783932i	−0.999232	+	0.0391966i	$0.987520\pi$
$710$		−	37.7972i		−	1.41850i
$711$	3.32327			0.124632
$712$	51.9943			1.94857
$713$		−	14.5848i		−	0.546203i
$714$	−29.7562			−1.11360
$715$	5.67157	−	3.18250i	0.212105	−	0.119019i
$716$	−49.2290			−1.83978
$717$		−	2.74768i		−	0.102614i
$718$	45.1780			1.68603
$719$	38.9755			1.45354			0.726770	−	0.686880i	$-0.241020\pi$
$719$	38.9755			1.45354			0.726770	+	0.686880i	$0.241020\pi$
$720$		−	2.87749i		−	0.107238i
$721$			30.7527i			1.14529i
$722$			54.1545i			2.01542i
$723$			10.3746i			0.385836i
$724$	−64.2768			−2.38883
$725$	−2.46032			−0.0913741
$726$		−	2.35969i		−	0.0875763i
$727$	−29.4308			−1.09153			−0.545764	−	0.837939i	$-0.683760\pi$
$727$	−29.4308			−1.09153			−0.545764	+	0.837939i	$0.683760\pi$
$728$	55.6558	−	31.2303i	2.06274	−	1.15747i
$729$	1.00000			0.0370370
$730$			11.1391i			0.412278i
$731$	−19.3908			−0.717195
$732$	43.8348			1.62018
$733$			17.2457i			0.636984i	0.947926	+	0.318492i	$0.103176\pi$
$733$			17.2457i			0.636984i	−0.947926	+	0.318492i	$0.896824\pi$
$734$		−	39.6115i		−	1.46209i
$735$		−	28.6462i		−	1.05663i
$736$		−	8.73970i		−	0.322150i
$737$	13.1143			0.483071
$738$	−17.0191			−0.626480
$739$		−	3.42420i		−	0.125961i	−0.998015	−	0.0629807i	$-0.979939\pi$
$739$		−	3.42420i		−	0.125961i	0.998015	−	0.0629807i	$-0.0200607\pi$
$740$	42.6848			1.56912
$741$	−11.4278	−	20.3655i	−0.419809	−	0.748146i
$742$	47.4387			1.74153
$743$		−	22.5661i		−	0.827870i	−0.910307	−	0.413935i	$-0.864154\pi$
$743$		−	22.5661i		−	0.827870i	0.910307	−	0.413935i	$-0.135846\pi$
$744$	22.4537			0.823192
$745$	−39.7289			−1.45555
$746$			24.4638i			0.895682i
$747$			9.78588i			0.358047i
$748$			9.40632i			0.343929i
$749$			61.0253i			2.22982i
$750$	28.7150			1.04852
$751$	−32.4314			−1.18344			−0.591719	−	0.806145i	$-0.701550\pi$
$751$	−32.4314			−1.18344			−0.591719	+	0.806145i	$0.701550\pi$
$752$		−	14.9186i		−	0.544024i
$753$	24.1897			0.881523
$754$	5.86495	+	10.4520i	0.213589	+	0.380638i
$755$	12.2282			0.445029
$756$		−	17.0681i		−	0.620759i
$757$	−15.2431			−0.554021			−0.277011	−	0.960867i	$-0.589344\pi$
$757$	−15.2431			−0.554021			−0.277011	+	0.960867i	$0.589344\pi$
$758$	−59.8219			−2.17283
$759$			2.40352i			0.0872424i
$760$			43.2290i			1.56808i
$761$			21.2733i			0.771155i	0.922675	+	0.385577i	$0.125998\pi$
$761$			21.2733i			0.771155i	−0.922675	+	0.385577i	$0.874002\pi$
$762$		−	7.38152i		−	0.267404i
$763$	27.3666			0.990738
$764$	31.1377			1.12652
$765$			4.75501i			0.171918i
$766$	64.3602			2.32543
$767$	−0.509365	−	0.907745i	−0.0183921	−	0.0327768i
$768$	24.8395			0.896317
$769$			4.87325i			0.175734i	0.996132	+	0.0878670i	$0.0280051\pi$
$769$			4.87325i			0.175734i	−0.996132	+	0.0878670i	$0.971995\pi$
$770$	−20.3597			−0.733712
$771$	4.06662			0.146456
$772$			15.9302i			0.573340i
$773$			49.7555i			1.78958i	0.446487	+	0.894790i	$0.352675\pi$
$773$			49.7555i			1.78958i	−0.446487	+	0.894790i	$0.647325\pi$
$774$		−	17.3569i		−	0.623880i
$775$			10.5981i			0.380696i
$776$	−16.3037			−0.585268
$777$	31.7251			1.13813
$778$		−	13.6432i		−	0.489132i
$779$	46.7139			1.67370
$780$	−11.3556	−	20.2369i	−0.406595	−	0.724597i
$781$	−8.88039			−0.317765
$782$		−	14.9514i		−	0.534661i
$783$	1.40868			0.0503422
$784$	−25.3358			−0.904851
$785$		−	8.01161i		−	0.285947i
$786$			15.6374i			0.557768i
$787$		−	15.0422i		−	0.536197i	−0.963391	−	0.268099i	$-0.913605\pi$
$787$		−	15.0422i		−	0.536197i	0.963391	−	0.268099i	$-0.0863953\pi$
$788$		−	19.7648i		−	0.704093i
$789$	6.36570			0.226625
$790$	−14.1447			−0.503246
$791$		−	10.1605i		−	0.361266i
$792$	−3.70030			−0.131484
$793$	38.6286	−	21.6758i	1.37174	−	0.769729i
$794$	33.6719			1.19497
$795$		−	7.58067i		−	0.268859i
$796$	−81.2248			−2.87894
$797$	−2.71446			−0.0961512			−0.0480756	−	0.998844i	$-0.515309\pi$
$797$	−2.71446			−0.0961512			−0.0480756	+	0.998844i	$0.515309\pi$
$798$			73.1077i			2.58799i
$799$			24.6527i			0.872151i
$800$			6.35077i			0.224534i
$801$		−	14.0514i		−	0.496481i
$802$	38.8750			1.37272
$803$	2.61713			0.0923563
$804$		−	46.7935i		−	1.65028i
$805$	20.7379			0.730914
$806$	45.0231	−	25.2640i	1.58587	−	0.889885i
$807$	−28.4905			−1.00291
$808$		−	23.7788i		−	0.836536i
$809$	16.8023			0.590737			0.295368	−	0.955383i	$-0.404558\pi$
$809$	16.8023			0.590737			0.295368	+	0.955383i	$0.404558\pi$
$810$	−4.25625			−0.149549
$811$			16.0876i			0.564912i	0.959280	+	0.282456i	$0.0911491\pi$
$811$			16.0876i			0.564912i	−0.959280	+	0.282456i	$0.908851\pi$
$812$		−	24.0435i		−	0.843761i
$813$		−	13.5110i		−	0.473853i
$814$		−	15.6500i		−	0.548532i
$815$	−32.3143			−1.13192
$816$	4.20552			0.147223
$817$			47.6411i			1.66675i
$818$	10.3881			0.363210
$819$	−8.43994	−	15.0409i	−0.294915	−	0.525571i
$820$	46.4188			1.62102
$821$		−	41.9751i		−	1.46494i	−0.680799	−	0.732470i	$-0.738367\pi$
$821$		−	41.9751i		−	1.46494i	0.680799	−	0.732470i	$-0.261633\pi$
$822$	−11.3225			−0.394916
$823$	23.6512			0.824428			0.412214	−	0.911087i	$-0.364756\pi$
$823$	23.6512			0.824428			0.412214	+	0.911087i	$0.364756\pi$
$824$		−	23.7890i		−	0.828730i
$825$		−	1.74654i		−	0.0608067i
$826$			3.25860i			0.113381i
$827$		−	7.51585i		−	0.261352i	−0.991425	−	0.130676i	$-0.958285\pi$
$827$		−	7.51585i		−	0.261352i	0.991425	−	0.130676i	$-0.0417147\pi$
$828$	8.57608			0.298040
$829$	36.7820			1.27749			0.638745	−	0.769418i	$-0.279454\pi$
$829$	36.7820			1.27749			0.638745	+	0.769418i	$0.279454\pi$
$830$		−	41.6512i		−	1.44573i
$831$	2.04052			0.0707850
$832$	37.0118	−	20.7685i	1.28315	−	0.720019i
$833$	41.8672			1.45061
$834$		−	39.8834i		−	1.38105i
$835$	32.5652			1.12696
$836$	23.1103			0.799287
$837$		−	6.06807i		−	0.209743i
$838$		−	88.9343i		−	3.07218i
$839$			13.8418i			0.477873i	0.971035	+	0.238937i	$0.0767988\pi$
$839$			13.8418i			0.477873i	−0.971035	+	0.238937i	$0.923201\pi$
$840$			31.9266i			1.10157i
$841$	−27.0156			−0.931573
$842$	−32.4768			−1.11922
$843$			15.7569i			0.542695i
$844$	−19.9373			−0.686271
$845$	−20.0138	−	12.2182i	−0.688495	−	0.420318i
$846$	−22.0669			−0.758675
$847$			4.78347i			0.164362i
$848$	−6.70464			−0.230238
$849$	21.8937			0.751389
$850$			10.8646i			0.372651i
$851$			15.9407i			0.546440i
$852$			31.6864i			1.08556i
$853$		−	19.6602i		−	0.673152i	−0.941656	−	0.336576i	$-0.890731\pi$
$853$		−	19.6602i		−	0.673152i	0.941656	−	0.336576i	$-0.109269\pi$
$854$	−138.668			−4.74513
$855$	11.6826			0.399535
$856$		−	47.2067i		−	1.61349i
$857$	7.52889			0.257182			0.128591	−	0.991698i	$-0.458955\pi$
$857$	7.52889			0.257182			0.128591	+	0.991698i	$0.458955\pi$
$858$	−7.41968	+	4.16342i	−0.253304	+	0.142137i
$859$	−12.2190			−0.416907			−0.208453	−	0.978032i	$-0.566843\pi$
$859$	−12.2190			−0.416907			−0.208453	+	0.978032i	$0.566843\pi$
$860$			47.3402i			1.61429i
$861$	34.5004			1.17577
$862$	55.2644			1.88231
$863$			2.88331i			0.0981491i	0.998795	+	0.0490746i	$0.0156272\pi$
$863$			2.88331i			0.0981491i	−0.998795	+	0.0490746i	$0.984373\pi$
$864$		−	3.63620i		−	0.123706i
$865$		−	45.8618i		−	1.55935i
$866$			49.9843i			1.69854i
$867$	10.0504			0.341331
$868$	−103.570			−3.51540
$869$			3.32327i			0.112734i
$870$	−5.99571			−0.203274
$871$	−23.1388	−	41.2359i	−0.784028	−	1.39722i
$872$	−21.1697			−0.716897
$873$			4.40604i			0.149122i
$874$	−36.7340			−1.24255
$875$	−58.2099			−1.96786
$876$		−	9.33824i		−	0.315510i
$877$		−	17.6010i		−	0.594343i	−0.954824	−	0.297172i	$-0.903957\pi$
$877$		−	17.6010i		−	0.594343i	0.954824	−	0.297172i	$-0.0960434\pi$
$878$		−	15.3931i		−	0.519493i
$879$			15.0681i			0.508233i
$880$	2.87749			0.0970000
$881$	14.9734			0.504466			0.252233	−	0.967666i	$-0.418835\pi$
$881$	14.9734			0.504466			0.252233	+	0.967666i	$0.418835\pi$
$882$			37.4757i			1.26187i
$883$	−38.1672			−1.28443			−0.642215	−	0.766524i	$-0.721984\pi$
$883$	−38.1672			−1.28443			−0.642215	+	0.766524i	$0.721984\pi$
$884$	29.5767	−	16.5965i	0.994772	−	0.558199i
$885$	0.520722			0.0175039
$886$			84.7119i			2.84595i
$887$	8.74591			0.293659			0.146829	−	0.989162i	$-0.453093\pi$
$887$	8.74591			0.293659			0.146829	+	0.989162i	$0.453093\pi$
$888$	−24.5412			−0.823549
$889$			14.9635i			0.501861i
$890$			59.8062i			2.00471i
$891$			1.00000i			0.0335013i
$892$			36.3351i			1.21659i
$893$	60.5691			2.02687
$894$	51.9743			1.73828
$895$		−	24.8859i		−	0.831844i
$896$	−98.0767			−3.27651
$897$	7.55751	−	4.24076i	0.252338	−	0.141595i
$898$	−16.1980			−0.540534
$899$		−	8.54799i		−	0.285092i
$900$	−6.23188			−0.207729
$901$	11.0793			0.369106
$902$		−	17.0191i		−	0.566673i
$903$			35.1852i			1.17089i
$904$			7.85975i			0.261411i
$905$		−	32.4927i		−	1.08009i
$906$	−15.9972			−0.531471
$907$	35.8443			1.19019			0.595096	−	0.803655i	$-0.297114\pi$
$907$	35.8443			1.19019			0.595096	+	0.803655i	$0.297114\pi$
$908$			2.79553i			0.0927731i
$909$	−6.42619			−0.213143
$910$	35.9225	+	64.0178i	1.19082	+	2.12217i
$911$	−52.9308			−1.75367			−0.876837	−	0.480788i	$-0.840351\pi$
$911$	−52.9308			−1.75367			−0.876837	+	0.480788i	$0.840351\pi$
$912$		−	10.3325i		−	0.342144i
$913$	−9.78588			−0.323865
$914$	81.2782			2.68844
$915$			22.1591i			0.732556i
$916$		−	74.3385i		−	2.45621i
$917$		−	31.6996i		−	1.04681i
$918$		−	6.22062i		−	0.205311i
$919$	23.1774			0.764553			0.382276	−	0.924048i	$-0.375140\pi$
$919$	23.1774			0.764553			0.382276	+	0.924048i	$0.375140\pi$
$920$	−16.0420			−0.528888
$921$		−	17.0334i		−	0.561269i
$922$	23.8322			0.784870
$923$	15.6685	+	27.9230i	0.515736	+	0.919098i
$924$	17.0681			0.561498
$925$		−	11.5834i		−	0.380861i
$926$	15.2130			0.499932
$927$	−6.42895			−0.211154
$928$		−	5.12226i		−	0.168146i
$929$			6.97790i			0.228937i	0.993427	+	0.114469i	$0.0365166\pi$
$929$			6.97790i			0.228937i	−0.993427	+	0.114469i	$0.963483\pi$
$930$			25.8273i			0.846909i
$931$		−	102.863i		−	3.37120i
$932$	30.3533			0.994256
$933$	−15.3734			−0.503304
$934$		−	42.3528i		−	1.38582i
$935$	−4.75501			−0.155506
$936$	6.52879	+	11.6350i	0.213400	+	0.380303i
$937$	33.9630			1.10952			0.554762	−	0.832009i	$-0.312809\pi$
$937$	33.9630			1.10952			0.554762	+	0.832009i	$0.312809\pi$
$938$			148.028i			4.83328i
$939$	−16.7286			−0.545918
$940$	60.1866			1.96307
$941$			25.8486i			0.842641i	0.906912	+	0.421320i	$0.138433\pi$
$941$			25.8486i			0.842641i	−0.906912	+	0.421320i	$0.861567\pi$
$942$			10.4810i			0.341489i
$943$			17.3352i			0.564512i
$944$		−	0.460547i		−	0.0149895i
$945$	8.62812			0.280673
$946$	17.3569			0.564321
$947$		−	38.2502i		−	1.24296i	−0.783428	−	0.621482i	$-0.786531\pi$
$947$		−	38.2502i		−	1.24296i	0.783428	−	0.621482i	$-0.213469\pi$
$948$	11.8579			0.385126
$949$	−4.61764	−	8.22915i	−0.149895	−	0.267129i
$950$	26.6931			0.866038
$951$			5.33201i			0.172902i
$952$	−46.6615			−1.51231
$953$	−50.6456			−1.64057			−0.820286	−	0.571953i	$-0.806186\pi$
$953$	−50.6456			−1.64057			−0.820286	+	0.571953i	$0.806186\pi$
$954$			9.91721i			0.321082i
$955$			15.7405i			0.509351i
$956$		−	9.80410i		−	0.317087i
$957$			1.40868i			0.0455363i
$958$	9.67263			0.312508
$959$	22.9525			0.741174
$960$			21.2316i			0.685246i
$961$	−5.82151			−0.187791
$962$	−49.2090	+	27.6128i	−1.58656	+	0.890271i
$963$	−12.7575			−0.411106
$964$			37.0180i			1.19227i
$965$	−8.05292			−0.259233
$966$	−27.1298			−0.872887
$967$			24.8458i			0.798988i	0.916736	+	0.399494i	$0.130814\pi$
$967$			24.8458i			0.798988i	−0.916736	+	0.399494i	$0.869186\pi$
$968$		−	3.70030i		−	0.118932i
$969$			17.0743i			0.548507i
$970$		−	18.7532i		−	0.602130i
$971$	4.13593			0.132728			0.0663642	−	0.997795i	$-0.478860\pi$
$971$	4.13593			0.132728			0.0663642	+	0.997795i	$0.478860\pi$
$972$	3.56813			0.114448
$973$			80.8502i			2.59194i
$974$	−14.4174			−0.461964
$975$	−5.49173	+	3.08159i	−0.175876	+	0.0986898i
$976$	19.5983			0.627328
$977$		−	45.4528i		−	1.45416i	−0.686551	−	0.727081i	$-0.740876\pi$
$977$		−	45.4528i		−	1.45416i	0.686551	−	0.727081i	$-0.259124\pi$
$978$	42.2744			1.35179
$979$	14.0514			0.449084
$980$		−	102.213i		−	3.26509i
$981$			5.72108i			0.182660i
$982$		−	27.8503i		−	0.888739i
$983$		−	35.2215i		−	1.12339i	−0.827344	−	0.561696i	$-0.810149\pi$
$983$		−	35.2215i		−	1.12339i	0.827344	−	0.561696i	$-0.189851\pi$
$984$	−26.6881			−0.850786
$985$	9.99137			0.318351
$986$		−	8.76288i		−	0.279067i
$987$	44.7331			1.42387
$988$	−40.7757	−	72.6668i	−1.29725	−	2.31184i
$989$	−17.6793			−0.562169
$990$		−	4.25625i		−	0.135273i
$991$	27.4173			0.870939			0.435470	−	0.900203i	$-0.356582\pi$
$991$	27.4173			0.870939			0.435470	+	0.900203i	$0.356582\pi$
$992$	−22.0647			−0.700556
$993$			22.1737i			0.703662i
$994$		−	100.238i		−	3.17934i
$995$		−	41.0602i		−	1.30170i
$996$			34.9173i			1.10640i
$997$	34.0683			1.07895			0.539477	−	0.842000i	$-0.318622\pi$
$997$	34.0683			1.07895			0.539477	+	0.842000i	$0.318622\pi$
$998$	4.90517			0.155270
$999$			6.63223i			0.209834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.a.298.1	✓	10
3.2	odd	2		1287.2.b.a.298.10		10
13.5	odd	4		5577.2.a.t.1.1		5
13.8	odd	4		5577.2.a.q.1.5		5
13.12	even	2	inner	429.2.b.a.298.10	yes	10
39.38	odd	2		1287.2.b.a.298.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.a.298.1	✓	10	1.1	even	1	trivial
429.2.b.a.298.10	yes	10	13.12	even	2	inner
1287.2.b.a.298.1		10	39.38	odd	2
1287.2.b.a.298.10		10	3.2	odd	2
5577.2.a.q.1.5		5	13.8	odd	4
5577.2.a.t.1.1		5	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)

\(f(q)\)	\(=\)	\(q-2.35969i q^{2} -1.00000 q^{3} -3.56813 q^{4} -1.80373i q^{5} +2.35969i q^{6} -4.78347i q^{7} +3.70030i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.35969i q^{2} -1.00000 q^{3} -3.56813 q^{4} -1.80373i q^{5} +2.35969i q^{6} -4.78347i q^{7} +3.70030i q^{8} +1.00000 q^{9} -4.25625 q^{10} +1.00000i q^{11} +3.56813 q^{12} +(3.14435 - 1.76440i) q^{13} -11.2875 q^{14} +1.80373i q^{15} +1.59529 q^{16} -2.63620 q^{17} -2.35969i q^{18} +6.47687i q^{19} +6.43596i q^{20} +4.78347i q^{21} +2.35969 q^{22} -2.40352 q^{23} -3.70030i q^{24} +1.74654 q^{25} +(-4.16342 - 7.41968i) q^{26} -1.00000 q^{27} +17.0681i q^{28} -1.40868 q^{29} +4.25625 q^{30} +6.06807i q^{31} +3.63620i q^{32} -1.00000i q^{33} +6.22062i q^{34} -8.62812 q^{35} -3.56813 q^{36} -6.63223i q^{37} +15.2834 q^{38} +(-3.14435 + 1.76440i) q^{39} +6.67436 q^{40} -7.21242i q^{41} +11.2875 q^{42} +7.35558 q^{43} -3.56813i q^{44} -1.80373i q^{45} +5.67157i q^{46} -9.35160i q^{47} -1.59529 q^{48} -15.8816 q^{49} -4.12129i q^{50} +2.63620 q^{51} +(-11.2194 + 6.29559i) q^{52} -4.20276 q^{53} +2.35969i q^{54} +1.80373 q^{55} +17.7003 q^{56} -6.47687i q^{57} +3.32405i q^{58} -0.288691i q^{59} -6.43596i q^{60} +12.2851 q^{61} +14.3188 q^{62} -4.78347i q^{63} +11.7709 q^{64} +(-3.18250 - 5.67157i) q^{65} -2.35969 q^{66} -13.1143i q^{67} +9.40632 q^{68} +2.40352 q^{69} +20.3597i q^{70} +8.88039i q^{71} +3.70030i q^{72} -2.61713i q^{73} -15.6500 q^{74} -1.74654 q^{75} -23.1103i q^{76} +4.78347 q^{77} +(4.16342 + 7.41968i) q^{78} +3.32327 q^{79} -2.87749i q^{80} +1.00000 q^{81} -17.0191 q^{82} +9.78588i q^{83} -17.0681i q^{84} +4.75501i q^{85} -17.3569i q^{86} +1.40868 q^{87} -3.70030 q^{88} -14.0514i q^{89} -4.25625 q^{90} +(-8.43994 - 15.0409i) q^{91} +8.57608 q^{92} -6.06807i q^{93} -22.0669 q^{94} +11.6826 q^{95} -3.63620i q^{96} +4.40604i q^{97} +37.4757i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9} + 6 q^{12} + 12 q^{13} - 32 q^{14} + 6 q^{16} + 20 q^{17} - 2 q^{22} + 8 q^{23} - 14 q^{25} - 2 q^{26} - 10 q^{27} + 8 q^{29} - 6 q^{36} - 12 q^{39} - 20 q^{40} + 32 q^{42} - 24 q^{43} - 6 q^{48} - 26 q^{49} - 20 q^{51} - 48 q^{52} - 4 q^{53} + 4 q^{55} + 16 q^{56} + 36 q^{61} + 24 q^{62} + 50 q^{64} + 28 q^{65} + 2 q^{66} - 12 q^{68} - 8 q^{69} + 24 q^{74} + 14 q^{75} + 12 q^{77} + 2 q^{78} + 36 q^{79} + 10 q^{81} - 20 q^{82} - 8 q^{87} - 6 q^{88} - 24 q^{91} - 8 q^{92} - 32 q^{94} + 44 q^{95}+O(q^{100}) \) 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9 + 6 * q^12 + 12 * q^13 - 32 * q^14 + 6 * q^16 + 20 * q^17 - 2 * q^22 + 8 * q^23 - 14 * q^25 - 2 * q^26 - 10 * q^27 + 8 * q^29 - 6 * q^36 - 12 * q^39 - 20 * q^40 + 32 * q^42 - 24 * q^43 - 6 * q^48 - 26 * q^49 - 20 * q^51 - 48 * q^52 - 4 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^61 + 24 * q^62 + 50 * q^64 + 28 * q^65 + 2 * q^66 - 12 * q^68 - 8 * q^69 + 24 * q^74 + 14 * q^75 + 12 * q^77 + 2 * q^78 + 36 * q^79 + 10 * q^81 - 20 * q^82 - 8 * q^87 - 6 * q^88 - 24 * q^91 - 8 * q^92 - 32 * q^94 + 44 * q^95

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