LMFDB - Embedded newform 429.2.f.a.131.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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([1, 1, 0]))

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

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

chi := DirichletCharacter("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.f (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95255 q^{2} +(1.45999 - 0.931894i) q^{3} +1.81247 q^{4} +0.144939i q^{5} +(-2.85071 + 1.81957i) q^{6} -1.00140i q^{7} +0.366168 q^{8} +(1.26315 - 2.72111i) q^{9} +O(q^{10})$	\(q-1.95255 q^{2} +(1.45999 - 0.931894i) q^{3} +1.81247 q^{4} +0.144939i q^{5} +(-2.85071 + 1.81957i) q^{6} -1.00140i q^{7} +0.366168 q^{8} +(1.26315 - 2.72111i) q^{9} -0.283002i q^{10} +(-2.78472 - 1.80149i) q^{11} +(2.64619 - 1.68903i) q^{12} +1.00000i q^{13} +1.95528i q^{14} +(0.135068 + 0.211610i) q^{15} -4.33990 q^{16} +4.70174 q^{17} +(-2.46636 + 5.31312i) q^{18} -7.94782i q^{19} +0.262698i q^{20} +(-0.933196 - 1.46203i) q^{21} +(5.43731 + 3.51750i) q^{22} +3.73150i q^{23} +(0.534602 - 0.341230i) q^{24} +4.97899 q^{25} -1.95255i q^{26} +(-0.691606 - 5.14992i) q^{27} -1.81500i q^{28} -3.02233 q^{29} +(-0.263728 - 0.413181i) q^{30} -4.83822 q^{31} +7.74155 q^{32} +(-5.74446 - 0.0350981i) q^{33} -9.18041 q^{34} +0.145142 q^{35} +(2.28941 - 4.93193i) q^{36} -8.14711 q^{37} +15.5185i q^{38} +(0.931894 + 1.45999i) q^{39} +0.0530722i q^{40} +7.45224 q^{41} +(1.82212 + 2.85470i) q^{42} -4.22823i q^{43} +(-5.04720 - 3.26514i) q^{44} +(0.394397 + 0.183080i) q^{45} -7.28595i q^{46} -13.2828i q^{47} +(-6.33621 + 4.04432i) q^{48} +5.99720 q^{49} -9.72175 q^{50} +(6.86450 - 4.38153i) q^{51} +1.81247i q^{52} -8.54217i q^{53} +(1.35040 + 10.0555i) q^{54} +(0.261107 - 0.403615i) q^{55} -0.366680i q^{56} +(-7.40652 - 11.6037i) q^{57} +5.90127 q^{58} +1.35521i q^{59} +(0.244807 + 0.383537i) q^{60} -8.29246i q^{61} +9.44688 q^{62} +(-2.72492 - 1.26491i) q^{63} -6.43599 q^{64} -0.144939 q^{65} +(11.2164 + 0.0685310i) q^{66} -0.886681 q^{67} +8.52175 q^{68} +(3.47736 + 5.44796i) q^{69} -0.283398 q^{70} +13.6473i q^{71} +(0.462524 - 0.996385i) q^{72} +3.02002i q^{73} +15.9077 q^{74} +(7.26928 - 4.63989i) q^{75} -14.4052i q^{76} +(-1.80401 + 2.78861i) q^{77} +(-1.81957 - 2.85071i) q^{78} +13.1964i q^{79} -0.629022i q^{80} +(-5.80892 - 6.87433i) q^{81} -14.5509 q^{82} -6.91723 q^{83} +(-1.69139 - 2.64988i) q^{84} +0.681468i q^{85} +8.25586i q^{86} +(-4.41258 + 2.81649i) q^{87} +(-1.01967 - 0.659648i) q^{88} +12.0906i q^{89} +(-0.770081 - 0.357473i) q^{90} +1.00140 q^{91} +6.76322i q^{92} +(-7.06375 + 4.50870i) q^{93} +25.9353i q^{94} +1.15195 q^{95} +(11.3026 - 7.21430i) q^{96} +17.6399 q^{97} -11.7099 q^{98} +(-8.41956 + 5.30198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.95255			−1.38066			−0.690332	−	0.723493i	$-0.742536\pi$
$2$	−1.95255			−1.38066			−0.690332	+	0.723493i	$0.742536\pi$
$3$	1.45999	−	0.931894i	0.842926	−	0.538029i
$3$	1.45999	−	0.931894i	0.842926	−	0.538029i
$4$	1.81247			0.906234
$5$			0.144939i			0.0648189i	0.999475	+	0.0324095i	$0.0103181\pi$
$5$			0.144939i			0.0648189i	−0.999475	+	0.0324095i	$0.989682\pi$
$6$	−2.85071	+	1.81957i	−1.16380	+	0.742838i
$7$		−	1.00140i		−	0.378493i	−0.981930	−	0.189246i	$-0.939396\pi$
$7$		−	1.00140i		−	0.378493i	0.981930	−	0.189246i	$-0.0606045\pi$
$8$	0.366168			0.129460
$9$	1.26315	−	2.72111i	0.421049	−	0.907038i
$10$		−	0.283002i		−	0.0894931i
$11$	−2.78472	−	1.80149i	−0.839623	−	0.543169i
$11$	−2.78472	−	1.80149i	−0.839623	−	0.543169i
$12$	2.64619	−	1.68903i	0.763888	−	0.487580i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$			1.95528i			0.522571i
$15$	0.135068	+	0.211610i	0.0348745	+	0.0546375i
$16$	−4.33990			−1.08497
$17$	4.70174			1.14034			0.570170	−	0.821527i	$-0.306877\pi$
$17$	4.70174			1.14034			0.570170	+	0.821527i	$0.306877\pi$
$18$	−2.46636	+	5.31312i	−0.581327	+	1.25231i
$19$		−	7.94782i		−	1.82335i	−0.410908	−	0.911677i	$-0.634788\pi$
$19$		−	7.94782i		−	1.82335i	0.410908	−	0.911677i	$-0.365212\pi$
$20$			0.262698i			0.0587411i
$21$	−0.933196	−	1.46203i	−0.203640	−	0.319041i
$22$	5.43731	+	3.51750i	1.15924	+	0.749934i
$23$			3.73150i			0.778071i	0.921223	+	0.389036i	$0.127192\pi$
$23$			3.73150i			0.778071i	−0.921223	+	0.389036i	$0.872808\pi$
$24$	0.534602	−	0.341230i	0.109125	−	0.0696533i
$25$	4.97899			0.995799
$26$		−	1.95255i		−	0.382927i
$27$	−0.691606	−	5.14992i	−0.133100	−	0.991103i
$28$		−	1.81500i		−	0.343003i
$29$	−3.02233			−0.561233			−0.280617	−	0.959820i	$-0.590539\pi$
$29$	−3.02233			−0.561233			−0.280617	+	0.959820i	$0.590539\pi$
$30$	−0.263728	−	0.413181i	−0.0481499	−	0.0754361i
$31$	−4.83822			−0.868969			−0.434485	−	0.900679i	$-0.643069\pi$
$31$	−4.83822			−0.868969			−0.434485	+	0.900679i	$0.643069\pi$
$32$	7.74155			1.36853
$33$	−5.74446	−	0.0350981i	−0.999981	−	0.00610980i
$34$	−9.18041			−1.57443
$35$	0.145142			0.0245335
$36$	2.28941	−	4.93193i	0.381569	−	0.821988i
$37$	−8.14711			−1.33938			−0.669689	−	0.742642i	$-0.733572\pi$
$37$	−8.14711			−1.33938			−0.669689	+	0.742642i	$0.733572\pi$
$38$			15.5185i			2.51744i
$39$	0.931894	+	1.45999i	0.149222	+	0.233786i
$40$			0.0530722i			0.00839145i
$41$	7.45224			1.16384			0.581922	−	0.813245i	$-0.302301\pi$
$41$	7.45224			1.16384			0.581922	+	0.813245i	$0.302301\pi$
$42$	1.82212	+	2.85470i	0.281159	+	0.440489i
$43$		−	4.22823i		−	0.644800i	−0.946604	−	0.322400i	$-0.895510\pi$
$43$		−	4.22823i		−	0.644800i	0.946604	−	0.322400i	$-0.104490\pi$
$44$	−5.04720	−	3.26514i	−0.760895	−	0.492238i
$45$	0.394397	+	0.183080i	0.0587932	+	0.0272919i
$46$		−	7.28595i		−	1.07426i
$47$		−	13.2828i		−	1.93749i	−0.248058	−	0.968745i	$-0.579792\pi$
$47$		−	13.2828i		−	1.93749i	0.248058	−	0.968745i	$-0.420208\pi$
$48$	−6.33621	+	4.04432i	−0.914553	+	0.583748i
$49$	5.99720			0.856743
$50$	−9.72175			−1.37486
$51$	6.86450	−	4.38153i	0.961222	−	0.613536i
$52$			1.81247i			0.251344i
$53$		−	8.54217i		−	1.17336i	−0.809820	−	0.586678i	$-0.800435\pi$
$53$		−	8.54217i		−	1.17336i	0.809820	−	0.586678i	$-0.199565\pi$
$54$	1.35040	+	10.0555i	0.183766	+	1.36838i
$55$	0.261107	−	0.403615i	0.0352076	−	0.0544235i
$56$		−	0.366680i		−	0.0489997i
$57$	−7.40652	−	11.6037i	−0.981018	−	1.53695i
$58$	5.90127			0.774875
$59$			1.35521i			0.176433i	0.996101	+	0.0882164i	$0.0281167\pi$
$59$			1.35521i			0.176433i	−0.996101	+	0.0882164i	$0.971883\pi$
$60$	0.244807	+	0.383537i	0.0316044	+	0.0495144i
$61$		−	8.29246i		−	1.06174i	−0.847453	−	0.530870i	$-0.821865\pi$
$61$		−	8.29246i		−	1.06174i	0.847453	−	0.530870i	$-0.178135\pi$
$62$	9.44688			1.19975
$63$	−2.72492	−	1.26491i	−0.343307	−	0.159364i
$64$	−6.43599			−0.804499
$65$	−0.144939			−0.0179775
$66$	11.2164	+	0.0685310i	1.38064	+	0.00843558i
$67$	−0.886681			−0.108325			−0.0541627	−	0.998532i	$-0.517249\pi$
$67$	−0.886681			−0.108325			−0.0541627	+	0.998532i	$0.517249\pi$
$68$	8.52175			1.03341
$69$	3.47736	+	5.44796i	0.418625	+	0.655857i
$70$	−0.283398			−0.0338725
$71$			13.6473i			1.61963i	0.586682	+	0.809817i	$0.300434\pi$
$71$			13.6473i			1.61963i	−0.586682	+	0.809817i	$0.699566\pi$
$72$	0.462524	−	0.996385i	0.0545090	−	0.117425i
$73$			3.02002i			0.353467i	0.984259	+	0.176733i	$0.0565530\pi$
$73$			3.02002i			0.353467i	−0.984259	+	0.176733i	$0.943447\pi$
$74$	15.9077			1.84923
$75$	7.26928	−	4.63989i	0.839385	−	0.535769i
$76$		−	14.4052i		−	1.65238i
$77$	−1.80401	+	2.78861i	−0.205586	+	0.317791i
$78$	−1.81957	−	2.85071i	−0.206026	−	0.322779i
$79$			13.1964i			1.48472i	0.670003	+	0.742358i	$0.266293\pi$
$79$			13.1964i			1.48472i	−0.670003	+	0.742358i	$0.733707\pi$
$80$		−	0.629022i		−	0.0703268i
$81$	−5.80892	−	6.87433i	−0.645435	−	0.763815i
$82$	−14.5509			−1.60688
$83$	−6.91723			−0.759264			−0.379632	−	0.925137i	$-0.623949\pi$
$83$	−6.91723			−0.759264			−0.379632	+	0.925137i	$0.623949\pi$
$84$	−1.69139	−	2.64988i	−0.184546	−	0.289126i
$85$			0.681468i			0.0739156i
$86$			8.25586i			0.890252i
$87$	−4.41258	+	2.81649i	−0.473078	+	0.301960i
$88$	−1.01967	−	0.659648i	−0.108698	−	0.0703187i
$89$			12.0906i			1.28160i	0.767708	+	0.640800i	$0.221397\pi$
$89$			12.0906i			1.28160i	−0.767708	+	0.640800i	$0.778603\pi$
$90$	−0.770081	−	0.357473i	−0.0811737	−	0.0376810i
$91$	1.00140			0.104975
$92$			6.76322i			0.705114i
$93$	−7.06375	+	4.50870i	−0.732477	+	0.467531i
$94$			25.9353i			2.67502i
$95$	1.15195			0.118188
$96$	11.3026	−	7.21430i	1.15357	−	0.736307i
$97$	17.6399			1.79106			0.895531	−	0.444999i	$-0.146796\pi$
$97$	17.6399			1.79106			0.895531	+	0.444999i	$0.146796\pi$
$98$	−11.7099			−1.18287
$99$	−8.41956	+	5.30198i	−0.846198	+	0.532869i
$100$	9.02426			0.902426
$101$	5.11406			0.508868			0.254434	−	0.967090i	$-0.418111\pi$
$101$	5.11406			0.508868			0.254434	+	0.967090i	$0.418111\pi$
$102$	−13.4033	+	8.55516i	−1.32713	+	0.847087i
$103$	8.23964			0.811876			0.405938	−	0.913901i	$-0.366945\pi$
$103$	8.23964			0.811876			0.405938	+	0.913901i	$0.366945\pi$
$104$			0.366168i			0.0359057i
$105$	0.211906	−	0.135257i	0.0206799	−	0.0131997i
$106$			16.6790i			1.62001i
$107$	−12.5778			−1.21594			−0.607972	−	0.793958i	$-0.708017\pi$
$107$	−12.5778			−1.21594			−0.607972	+	0.793958i	$0.708017\pi$
$108$	−1.25351	−	9.33406i	−0.120619	−	0.898170i
$109$			7.55386i			0.723529i	0.932270	+	0.361764i	$0.117825\pi$
$109$			7.55386i			0.723529i	−0.932270	+	0.361764i	$0.882175\pi$
$110$	−0.509825	+	0.788080i	−0.0486099	+	0.0751405i
$111$	−11.8947	+	7.59225i	−1.12900	+	0.720624i
$112$			4.34596i			0.410655i
$113$			1.45411i			0.136792i	0.997658	+	0.0683958i	$0.0217881\pi$
$113$			1.45411i			0.136792i	−0.997658	+	0.0683958i	$0.978212\pi$
$114$	14.4616	+	22.6569i	1.35446	+	2.12202i
$115$	−0.540842			−0.0504337
$116$	−5.47788			−0.508608
$117$	2.72111	+	1.26315i	0.251567	+	0.116778i
$118$		−	2.64611i		−	0.243595i
$119$		−	4.70831i		−	0.431610i
$120$	0.0494577	+	0.0774849i	0.00451485	+	0.00707338i
$121$	4.50928	+	10.0333i	0.409934	+	0.912115i
$122$			16.1915i			1.46591i
$123$	10.8802	−	6.94469i	0.981034	−	0.626182i
$124$	−8.76911			−0.787489
$125$			1.44635i			0.129365i
$126$	5.32055	+	2.46981i	0.473992	+	0.220028i
$127$			11.0108i			0.977053i	0.872549	+	0.488526i	$0.162465\pi$
$127$			11.0108i			0.977053i	−0.872549	+	0.488526i	$0.837535\pi$
$128$	−2.91647			−0.257782
$129$	−3.94027	−	6.17318i	−0.346921	−	0.543519i
$130$	0.283002			0.0248209
$131$	14.8405			1.29662			0.648312	−	0.761375i	$-0.275475\pi$
$131$	14.8405			1.29662			0.648312	+	0.761375i	$0.275475\pi$
$132$	−10.4116	−	0.0636142i	−0.906217	−	0.00553691i
$133$	−7.95892			−0.690126
$134$	1.73129			0.149561
$135$	0.746427	−	0.100241i	0.0642422	−	0.00862737i
$136$	1.72163			0.147628
$137$			8.44838i			0.721794i	0.932606	+	0.360897i	$0.117529\pi$
$137$			8.44838i			0.721794i	−0.932606	+	0.360897i	$0.882471\pi$
$138$	−6.78974	−	10.6374i	−0.577981	−	0.905518i
$139$			17.1128i			1.45149i	0.687964	+	0.725745i	$0.258505\pi$
$139$			17.1128i			1.45149i	−0.687964	+	0.725745i	$0.741495\pi$
$140$	0.263065			0.0222331
$141$	−12.3781	−	19.3927i	−1.04243	−	1.63316i
$142$		−	26.6471i		−	2.23617i
$143$	1.80149	−	2.78472i	0.150648	−	0.232870i
$144$	−5.48193	+	11.8094i	−0.456827	+	0.984113i
$145$		−	0.438055i		−	0.0363785i
$146$		−	5.89675i		−	0.488019i
$147$	8.75586	−	5.58876i	0.722171	−	0.460953i
$148$	−14.7664			−1.21379
$149$	6.59133			0.539983			0.269992	−	0.962863i	$-0.412979\pi$
$149$	6.59133			0.539983			0.269992	+	0.962863i	$0.412979\pi$
$150$	−14.1937	+	9.05964i	−1.15891	+	0.739717i
$151$			2.91825i			0.237484i	0.992925	+	0.118742i	$0.0378862\pi$
$151$			2.91825i			0.237484i	−0.992925	+	0.118742i	$0.962114\pi$
$152$		−	2.91024i		−	0.236051i
$153$	5.93899	−	12.7940i	0.480139	−	1.03433i
$154$	3.52242	−	5.44491i	0.283845	−	0.438763i
$155$		−	0.701248i		−	0.0563256i
$156$	1.68903	+	2.64619i	0.135230	+	0.211864i
$157$	−2.39679			−0.191284			−0.0956422	−	0.995416i	$-0.530490\pi$
$157$	−2.39679			−0.191284			−0.0956422	+	0.995416i	$0.530490\pi$
$158$		−	25.7668i		−	2.04989i
$159$	−7.96039	−	12.4715i	−0.631300	−	0.989053i
$160$			1.12206i			0.0887063i
$161$	3.73671			0.294494
$162$	11.3422	+	13.4225i	0.891129	+	1.05457i
$163$	22.4858			1.76122			0.880610	−	0.473842i	$-0.157133\pi$
$163$	22.4858			1.76122			0.880610	+	0.473842i	$0.157133\pi$
$164$	13.5069			1.05471
$165$	0.00508710	−	0.832598i	0.000396031	−	0.0648177i
$166$	13.5063			1.04829
$167$	−7.87185			−0.609142			−0.304571	−	0.952490i	$-0.598513\pi$
$167$	−7.87185			−0.609142			−0.304571	+	0.952490i	$0.598513\pi$
$168$	−0.341707	−	0.535349i	−0.0263632	−	0.0413031i
$169$	−1.00000			−0.0769231
$170$		−	1.33060i		−	0.102053i
$171$	−21.6269	−	10.0393i	−1.65385	−	0.767722i
$172$		−	7.66354i		−	0.584339i
$173$	3.73328			0.283836			0.141918	−	0.989878i	$-0.454673\pi$
$173$	3.73328			0.283836			0.141918	+	0.989878i	$0.454673\pi$
$174$	8.61580	−	5.49936i	0.653162	−	0.416905i
$175$		−	4.98595i		−	0.376902i
$176$	12.0854	+	7.81828i	0.910970	+	0.589325i
$177$	1.26291	+	1.97859i	0.0949260	+	0.148720i
$178$		−	23.6075i		−	1.76946i
$179$			3.43338i			0.256623i	0.991734	+	0.128312i	$0.0409558\pi$
$179$			3.43338i			0.256623i	−0.991734	+	0.128312i	$0.959044\pi$
$180$	0.714831	+	0.331826i	0.0532804	+	0.0247329i
$181$	−0.838855			−0.0623516			−0.0311758	−	0.999514i	$-0.509925\pi$
$181$	−0.838855			−0.0623516			−0.0311758	+	0.999514i	$0.509925\pi$
$182$	−1.95528			−0.144935
$183$	−7.72769	−	12.1069i	−0.571247	−	0.894969i
$184$			1.36636i			0.100729i
$185$		−	1.18084i		−	0.0868170i
$186$	13.7924	−	8.80349i	1.01130	−	0.645503i
$187$	−13.0930	−	8.47014i	−0.957456	−	0.619398i
$188$		−	24.0746i		−	1.75582i
$189$	−5.15712	+	0.692572i	−0.375125	+	0.0503772i
$190$	−2.24925			−0.163178
$191$		−	15.8069i		−	1.14374i	−0.820343	−	0.571872i	$-0.806217\pi$
$191$		−	15.8069i		−	1.14374i	0.820343	−	0.571872i	$-0.193783\pi$
$192$	−9.39649	+	5.99766i	−0.678134	+	0.432844i
$193$			15.9862i			1.15071i	0.817904	+	0.575354i	$0.195136\pi$
$193$			15.9862i			1.15071i	−0.817904	+	0.575354i	$0.804864\pi$
$194$	−34.4429			−2.47286
$195$	−0.211610	+	0.135068i	−0.0151537	+	0.00967244i
$196$	10.8697			0.776409
$197$	3.98175			0.283688			0.141844	−	0.989889i	$-0.454697\pi$
$197$	3.98175			0.283688			0.141844	+	0.989889i	$0.454697\pi$
$198$	16.4396	−	10.3524i	1.16831	−	0.735713i
$199$	−9.29103			−0.658624			−0.329312	−	0.944221i	$-0.606817\pi$
$199$	−9.29103			−0.658624			−0.329312	+	0.944221i	$0.606817\pi$
$200$	1.82315			0.128916
$201$	−1.29455	+	0.826293i	−0.0913103	+	0.0582822i
$202$	−9.98547			−0.702575
$203$			3.02656i			0.212423i
$204$	12.4417	−	7.94137i	0.871092	−	0.556007i
$205$			1.08012i			0.0754391i
$206$	−16.0883			−1.12093
$207$	10.1538	+	4.71343i	0.705740	+	0.327606i
$208$		−	4.33990i		−	0.300918i
$209$	−14.3179	+	22.1324i	−0.990390	+	1.53093i
$210$	−0.413758	+	0.264097i	−0.0285520	+	0.0182244i
$211$			1.55315i			0.106923i	0.998570	+	0.0534615i	$0.0170254\pi$
$211$			1.55315i			0.106923i	−0.998570	+	0.0534615i	$0.982975\pi$
$212$		−	15.4824i		−	1.06334i
$213$	12.7178	+	19.9249i	0.871411	+	1.36523i
$214$	24.5589			1.67881
$215$	0.612838			0.0417952
$216$	−0.253244	−	1.88574i	−0.0172311	−	0.128308i
$217$			4.84498i			0.328898i
$218$		−	14.7493i		−	0.998950i
$219$	2.81434	+	4.40920i	0.190175	+	0.297946i
$220$	0.473248	−	0.731539i	0.0319063	−	0.0493204i
$221$			4.70174i			0.316273i
$222$	23.2251	−	14.8243i	1.55876	−	0.994940i
$223$	−10.0088			−0.670240			−0.335120	−	0.942175i	$-0.608777\pi$
$223$	−10.0088			−0.670240			−0.335120	+	0.942175i	$0.608777\pi$
$224$		−	7.75237i		−	0.517977i
$225$	6.28920	−	13.5484i	0.419280	−	0.903227i
$226$		−	2.83924i		−	0.188863i
$227$	3.98537			0.264518			0.132259	−	0.991215i	$-0.457777\pi$
$227$	3.98537			0.264518			0.132259	+	0.991215i	$0.457777\pi$
$228$	−13.4241	−	21.0314i	−0.889031	−	1.39284i
$229$	9.16024			0.605326			0.302663	−	0.953098i	$-0.402124\pi$
$229$	9.16024			0.605326			0.302663	+	0.953098i	$0.402124\pi$
$230$	1.05602			0.0696321
$231$	−0.0351472	+	5.75248i	−0.00231252	+	0.378486i
$232$	−1.10668			−0.0726573
$233$	−5.33274			−0.349359			−0.174680	−	0.984625i	$-0.555889\pi$
$233$	−5.33274			−0.349359			−0.174680	+	0.984625i	$0.555889\pi$
$234$	−5.31312	−	2.46636i	−0.347330	−	0.161231i
$235$	1.92520			0.125586
$236$			2.45627i			0.159889i
$237$	12.2977	+	19.2667i	0.798821	+	1.25151i
$238$			9.19324i			0.595909i
$239$	−4.25381			−0.275156			−0.137578	−	0.990491i	$-0.543932\pi$
$239$	−4.25381			−0.275156			−0.137578	+	0.990491i	$0.543932\pi$
$240$	−0.586182	−	0.918367i	−0.0378379	−	0.0592803i
$241$		−	23.4153i		−	1.50832i	−0.656693	−	0.754158i	$-0.728045\pi$
$241$		−	23.4153i		−	1.50832i	0.656693	−	0.754158i	$-0.271955\pi$
$242$	−8.80461	−	19.5905i	−0.565982	−	1.25932i
$243$	−14.8871	−	4.62317i	−0.955009	−	0.296577i
$244$		−	15.0298i		−	0.962185i
$245$			0.869231i			0.0555332i
$246$	−21.2442	+	13.5599i	−1.35448	+	0.864547i
$247$	7.94782			0.505707
$248$	−1.77160			−0.112497
$249$	−10.0991	+	6.44612i	−0.640004	+	0.408506i
$250$		−	2.82408i		−	0.178610i
$251$		−	2.42444i		−	0.153029i	−0.997068	−	0.0765145i	$-0.975621\pi$
$251$		−	2.42444i		−	0.153029i	0.997068	−	0.0765145i	$-0.0243792\pi$
$252$	−4.93882	−	2.29261i	−0.311117	−	0.144421i
$253$	6.72225	−	10.3912i	0.422625	−	0.653287i
$254$		−	21.4992i		−	1.34898i
$255$	0.635056	+	0.994937i	0.0397687	+	0.0623054i
$256$	18.5665			1.16041
$257$		−	13.8140i		−	0.861692i	−0.902425	−	0.430846i	$-0.858215\pi$
$257$		−	13.8140i		−	0.861692i	0.902425	−	0.430846i	$-0.141785\pi$
$258$	7.69358	+	12.0535i	0.478981	+	0.750417i
$259$			8.15850i			0.506945i
$260$	−0.262698			−0.0162918
$261$	−3.81765	+	8.22411i	−0.236307	+	0.509060i
$262$	−28.9770			−1.79020
$263$	12.0176			0.741034			0.370517	−	0.928826i	$-0.379181\pi$
$263$	12.0176			0.741034			0.370517	+	0.928826i	$0.379181\pi$
$264$	−2.10344	−	0.0128518i	−0.129458	−	0.000790975i
$265$	1.23810			0.0760557
$266$	15.5402			0.952833
$267$	11.2672	+	17.6522i	0.689538	+	1.08029i
$268$	−1.60708			−0.0981681
$269$			15.9151i			0.970360i	0.874414	+	0.485180i	$0.161246\pi$
$269$			15.9151i			0.970360i	−0.874414	+	0.485180i	$0.838754\pi$
$270$	−1.45744	+	0.195726i	−0.0886969	+	0.0119115i
$271$		−	19.7922i		−	1.20229i	−0.799140	−	0.601145i	$-0.794711\pi$
$271$		−	19.7922i		−	1.20229i	0.799140	−	0.601145i	$-0.205289\pi$
$272$	−20.4051			−1.23724
$273$	1.46203	−	0.933196i	0.0884862	−	0.0564796i
$274$		−	16.4959i		−	0.996555i
$275$	−13.8651	−	8.96960i	−0.836096	−	0.540887i
$276$	6.30260	+	9.87424i	0.379372	+	0.594359i
$277$			17.1466i			1.03024i	0.857118	+	0.515121i	$0.172253\pi$
$277$			17.1466i			1.03024i	−0.857118	+	0.515121i	$0.827747\pi$
$278$		−	33.4137i		−	2.00402i
$279$	−6.11138	+	13.1653i	−0.365879	+	0.788188i
$280$	0.0531464			0.00317610
$281$	7.43204			0.443358			0.221679	−	0.975120i	$-0.428846\pi$
$281$	7.43204			0.443358			0.221679	+	0.975120i	$0.428846\pi$
$282$	24.1690	+	37.8653i	1.43924	+	2.25485i
$283$			8.06934i			0.479672i	0.970813	+	0.239836i	$0.0770937\pi$
$283$			8.06934i			0.479672i	−0.970813	+	0.239836i	$0.922906\pi$
$284$			24.7353i			1.46777i
$285$	1.68184	−	1.07350i	0.0996236	−	0.0635885i
$286$	−3.51750	+	5.43731i	−0.207994	+	0.321515i
$287$		−	7.46265i		−	0.440506i
$288$	9.77871	−	21.0656i	0.576216	−	1.24130i
$289$	5.10638			0.300375
$290$			0.855327i			0.0502265i
$291$	25.7541	−	16.4385i	1.50973	−	0.963644i
$292$			5.47369i			0.320323i
$293$	11.4485			0.668826			0.334413	−	0.942427i	$-0.391462\pi$
$293$	11.4485			0.668826			0.334413	+	0.942427i	$0.391462\pi$
$294$	−17.0963	+	10.9124i	−0.997076	+	0.636421i
$295$	−0.196423			−0.0114362
$296$	−2.98321			−0.173396
$297$	−7.35160	+	15.5870i	−0.426583	+	0.904448i
$298$	−12.8699			−0.745535
$299$	−3.73150			−0.215798
$300$	13.1753	−	8.40965i	0.760679	−	0.485532i
$301$	−4.23414			−0.244052
$302$		−	5.69805i		−	0.327886i
$303$	7.46648	−	4.76576i	0.428938	−	0.273786i
$304$			34.4927i			1.97829i
$305$	1.20190			0.0688209
$306$	−11.5962	+	24.9809i	−0.662911	+	1.42806i
$307$		−	18.2319i		−	1.04055i	−0.853999	−	0.520275i	$-0.825829\pi$
$307$		−	18.2319i		−	1.04055i	0.853999	−	0.520275i	$-0.174171\pi$
$308$	−3.26970	+	5.05426i	−0.186309	+	0.287993i
$309$	12.0298	−	7.67847i	0.684352	−	0.436813i
$310$			1.36923i			0.0777668i
$311$			17.0284i			0.965591i	0.875733	+	0.482795i	$0.160378\pi$
$311$			17.0284i			0.965591i	−0.875733	+	0.482795i	$0.839622\pi$
$312$	0.341230	+	0.534602i	0.0193183	+	0.0302659i
$313$	−23.9956			−1.35631			−0.678157	−	0.734917i	$-0.737221\pi$
$313$	−23.9956			−1.35631			−0.678157	+	0.734917i	$0.737221\pi$
$314$	4.67986			0.264100
$315$	0.183336	−	0.394948i	0.0103298	−	0.0222528i
$316$			23.9181i			1.34550i
$317$			12.7507i			0.716150i	0.933693	+	0.358075i	$0.116567\pi$
$317$			12.7507i			0.716150i	−0.933693	+	0.358075i	$0.883433\pi$
$318$	15.5431	+	24.3512i	0.871614	+	1.36555i
$319$	8.41634	+	5.44470i	0.471225	+	0.304845i
$320$		−	0.932830i		−	0.0521468i
$321$	−18.3635	+	11.7212i	−1.02495	+	0.654214i
$322$	−7.29614			−0.406598
$323$		−	37.3686i		−	2.07924i
$324$	−10.5285	−	12.4595i	−0.584915	−	0.692195i
$325$			4.97899i			0.276185i
$326$	−43.9047			−2.43165
$327$	7.03940	+	11.0286i	0.389280	+	0.609881i
$328$	2.72877			0.150671
$329$	−13.3013			−0.733326
$330$	−0.00993285	+	1.62569i	−0.000546785	+	0.0894915i
$331$	8.06742			0.443425			0.221713	−	0.975112i	$-0.428835\pi$
$331$	8.06742			0.443425			0.221713	+	0.975112i	$0.428835\pi$
$332$	−12.5372			−0.688071
$333$	−10.2910	+	22.1692i	−0.563944	+	1.21487i
$334$	15.3702			0.841021
$335$		−	0.128515i		−	0.00702153i
$336$	4.04998	+	6.34507i	0.220944	+	0.346152i
$337$		−	26.7281i		−	1.45597i	−0.685592	−	0.727986i	$-0.740457\pi$
$337$		−	26.7281i		−	1.45597i	0.685592	−	0.727986i	$-0.259543\pi$
$338$	1.95255			0.106205
$339$	1.35508	+	2.12299i	0.0735979	+	0.115305i
$340$			1.23514i			0.0669848i
$341$	13.4731	+	8.71599i	0.729607	+	0.471997i
$342$	42.2277	+	19.6022i	2.28341	+	1.05997i
$343$		−	13.0154i		−	0.702764i
$344$		−	1.54824i		−	0.0834757i
$345$	−0.789624	+	0.504007i	−0.0425119	+	0.0271348i
$346$	−7.28942			−0.391882
$347$	−14.4995			−0.778373			−0.389187	−	0.921159i	$-0.627244\pi$
$347$	−14.4995			−0.778373			−0.389187	+	0.921159i	$0.627244\pi$
$348$	−7.99766	+	5.10480i	−0.428719	+	0.273646i
$349$		−	0.0548226i		−	0.00293459i	−0.999999	−	0.00146729i	$-0.999533\pi$
$349$		−	0.0548226i		−	0.00293459i	0.999999	−	0.00146729i	$-0.000467055\pi$
$350$			9.73534i			0.520376i
$351$	5.14992	−	0.691606i	0.274882	−	0.0369152i
$352$	−21.5580	−	13.9463i	−1.14905	−	0.743341i
$353$			26.6483i			1.41834i	0.705035	+	0.709172i	$0.250931\pi$
$353$			26.6483i			1.41834i	−0.705035	+	0.709172i	$0.749069\pi$
$354$	−2.46590	−	3.86330i	−0.131061	−	0.205332i
$355$	−1.97803			−0.104983
$356$			21.9138i			1.16143i
$357$	−4.38765	−	6.87409i	−0.232219	−	0.363816i
$358$		−	6.70387i		−	0.354310i
$359$	−13.6080			−0.718204			−0.359102	−	0.933298i	$-0.616917\pi$
$359$	−13.6080			−0.718204			−0.359102	+	0.933298i	$0.616917\pi$
$360$	0.144416	+	0.0670380i	0.00761137	+	0.00353321i
$361$	−44.1678			−2.32462
$362$	1.63791			0.0860866
$363$	15.9334	+	10.4463i	0.836289	+	0.548289i
$364$	1.81500			0.0951319
$365$	−0.437720			−0.0229113
$366$	15.0887	+	23.6394i	0.788701	+	1.23565i
$367$	14.3009			0.746503			0.373251	−	0.927730i	$-0.378243\pi$
$367$	14.3009			0.746503			0.373251	+	0.927730i	$0.378243\pi$
$368$		−	16.1943i		−	0.844188i
$369$	9.41327	−	20.2784i	0.490035	−	1.05565i
$370$			2.30565i			0.119865i
$371$	−8.55410			−0.444107
$372$	−12.8028	+	8.17188i	−0.663795	+	0.423692i
$373$		−	10.0057i		−	0.518074i	−0.965867	−	0.259037i	$-0.916595\pi$
$373$		−	10.0057i		−	0.518074i	0.965867	−	0.259037i	$-0.0834052\pi$
$374$	25.5648	+	16.5384i	1.32193	+	0.855180i
$375$	1.34784	+	2.11166i	0.0696024	+	0.109046i
$376$		−	4.86372i		−	0.250827i
$377$		−	3.02233i		−	0.155658i
$378$	10.0696	−	1.35228i	0.517922	−	0.0695540i
$379$	23.6538			1.21501			0.607507	−	0.794315i	$-0.292170\pi$
$379$	23.6538			1.21501			0.607507	+	0.794315i	$0.292170\pi$
$380$	2.08788			0.107106
$381$	10.2609	+	16.0757i	0.525683	+	0.823583i
$382$			30.8637i			1.57913i
$383$		−	16.5189i		−	0.844076i	−0.906578	−	0.422038i	$-0.861315\pi$
$383$		−	16.5189i		−	0.844076i	0.906578	−	0.422038i	$-0.138685\pi$
$384$	−4.25802	+	2.71784i	−0.217291	+	0.138694i
$385$	−0.404179	−	0.261472i	−0.0205989	−	0.0133258i
$386$		−	31.2138i		−	1.58874i
$387$	−11.5055	−	5.34088i	−0.584858	−	0.271492i
$388$	31.9718			1.62312
$389$			23.3714i			1.18498i	0.805578	+	0.592489i	$0.201855\pi$
$389$			23.3714i			1.18498i	−0.805578	+	0.592489i	$0.798145\pi$
$390$	0.413181	−	0.263728i	0.0209222	−	0.0133544i
$391$			17.5445i			0.887266i
$392$	2.19598			0.110914
$393$	21.6671	−	13.8298i	1.09296	−	0.697622i
$394$	−7.77458			−0.391678
$395$	−1.91269			−0.0962377
$396$	−15.2602	+	9.60966i	−0.766853	+	0.482904i
$397$	−24.1585			−1.21248			−0.606239	−	0.795282i	$-0.707323\pi$
$397$	−24.1585			−1.21248			−0.606239	+	0.795282i	$0.707323\pi$
$398$	18.1412			0.909338
$399$	−11.6200	+	7.41687i	−0.581725	+	0.371308i
$400$	−21.6083			−1.08042
$401$			20.0551i			1.00151i	0.865590	+	0.500753i	$0.166943\pi$
$401$			20.0551i			1.00151i	−0.865590	+	0.500753i	$0.833057\pi$
$402$	2.52767	−	1.61338i	0.126069	−	0.0804681i
$403$		−	4.83822i		−	0.241009i
$404$	9.26906			0.461153
$405$	0.996362	−	0.841941i	0.0495096	−	0.0418364i
$406$		−	5.90952i		−	0.293284i
$407$	22.6874	+	14.6769i	1.12457	+	0.727509i
$408$	2.51356	−	1.60437i	0.124440	−	0.0794284i
$409$			35.4639i			1.75357i	0.480878	+	0.876787i	$0.340318\pi$
$409$			35.4639i			1.75357i	−0.480878	+	0.876787i	$0.659682\pi$
$410$		−	2.10900i		−	0.104156i
$411$	7.87300	+	12.3346i	0.388346	+	0.608419i
$412$	14.9341			0.735749
$413$	1.35710			0.0667786
$414$	−19.8259	−	9.20323i	−0.974390	−	0.452314i
$415$		−	1.00258i		−	0.0492147i
$416$			7.74155i			0.379561i
$417$	15.9473	+	24.9845i	0.780944	+	1.22350i
$418$	27.9565	−	43.2147i	1.36740	−	2.11370i
$419$		−	13.9157i		−	0.679828i	−0.940456	−	0.339914i	$-0.889602\pi$
$419$		−	13.9157i		−	0.679828i	0.940456	−	0.339914i	$-0.110398\pi$
$420$	0.384073	−	0.245149i	0.0187408	−	0.0119620i
$421$	−40.4385			−1.97085			−0.985425	−	0.170108i	$-0.945588\pi$
$421$	−40.4385			−1.97085			−0.985425	+	0.170108i	$0.945588\pi$
$422$		−	3.03260i		−	0.147625i
$423$	−36.1439	−	16.7781i	−1.75738	−	0.815779i
$424$		−	3.12787i		−	0.151903i
$425$	23.4099			1.13555
$426$	−24.8322	−	38.9045i	−1.20313	−	1.88493i
$427$	−8.30405			−0.401861
$428$	−22.7969			−1.10193
$429$	0.0350981	−	5.74446i	0.00169455	−	0.277345i
$430$	−1.19660			−0.0577051
$431$	18.1898			0.876170			0.438085	−	0.898934i	$-0.355657\pi$
$431$	18.1898			0.876170			0.438085	+	0.898934i	$0.355657\pi$
$432$	3.00150	+	22.3501i	0.144410	+	1.07532i
$433$	−9.58780			−0.460760			−0.230380	−	0.973101i	$-0.573997\pi$
$433$	−9.58780			−0.460760			−0.230380	+	0.973101i	$0.573997\pi$
$434$		−	9.46008i		−	0.454098i
$435$	−0.408221	−	0.639557i	−0.0195727	−	0.0306644i
$436$			13.6911i			0.655686i
$437$	29.6573			1.41870
$438$	−5.49515	−	8.60920i	−0.262568	−	0.411364i
$439$		−	16.0577i		−	0.766394i	−0.923667	−	0.383197i	$-0.874823\pi$
$439$		−	16.0577i		−	0.766394i	0.923667	−	0.383197i	$-0.125177\pi$
$440$	0.0956090	−	0.147791i	0.00455798	−	0.00704566i
$441$	7.57535	−	16.3191i	0.360731	−	0.777099i
$442$		−	9.18041i		−	0.436667i
$443$		−	15.4504i		−	0.734070i	−0.930207	−	0.367035i	$-0.880373\pi$
$443$		−	15.4504i		−	0.734070i	0.930207	−	0.367035i	$-0.119627\pi$
$444$	−21.5588	+	13.7607i	−1.02313	+	0.653054i
$445$	−1.75240			−0.0830719
$446$	19.5428			0.925376
$447$	9.62329	−	6.14242i	0.455166	−	0.290527i
$448$			6.44499i			0.304497i
$449$			16.2639i			0.767539i	0.923429	+	0.383769i	$0.125374\pi$
$449$			16.2639i			0.767539i	−0.923429	+	0.383769i	$0.874626\pi$
$450$	−12.2800	+	26.4540i	−0.578885	+	1.24705i
$451$	−20.7524	−	13.4251i	−0.977190	−	0.632164i
$452$			2.63553i			0.123965i
$453$	2.71950	+	4.26062i	0.127773	+	0.200182i
$454$	−7.78165			−0.365211
$455$			0.145142i			0.00680436i
$456$	−2.71203	−	4.24892i	−0.127003	−	0.198974i
$457$		−	29.5926i		−	1.38428i	−0.721762	−	0.692142i	$-0.756667\pi$
$457$		−	29.5926i		−	1.38428i	0.721762	−	0.692142i	$-0.243333\pi$
$458$	−17.8859			−0.835751
$459$	−3.25175	−	24.2136i	−0.151779	−	1.13019i
$460$	−0.980258			−0.0457047
$461$	39.0829			1.82027			0.910136	−	0.414310i	$-0.135977\pi$
$461$	39.0829			1.82027			0.910136	+	0.414310i	$0.135977\pi$
$462$	0.0686268	−	11.2320i	0.00319281	−	0.522562i
$463$	29.5726			1.37436			0.687179	−	0.726488i	$-0.258849\pi$
$463$	29.5726			1.37436			0.687179	+	0.726488i	$0.258849\pi$
$464$	13.1166			0.608924
$465$	−0.653489	−	1.02382i	−0.0303048	−	0.0474783i
$466$	10.4125			0.482348
$467$		−	4.51455i		−	0.208909i	−0.994530	−	0.104454i	$-0.966690\pi$
$467$		−	4.51455i		−	0.208909i	0.994530	−	0.104454i	$-0.0333096\pi$
$468$	4.93193	+	2.28941i	0.227978	+	0.105828i
$469$			0.887920i			0.0410004i
$470$	−3.75905			−0.173392
$471$	−3.49929	+	2.23355i	−0.161239	+	0.102917i
$472$			0.496233i			0.0228410i
$473$	−7.61712	+	11.7744i	−0.350235	+	0.541389i
$474$	−24.0119	−	37.6193i	−1.10290	−	1.72791i
$475$		−	39.5721i		−	1.81569i
$476$		−	8.53366i		−	0.391140i
$477$	−23.2442	−	10.7900i	−1.06428	−	0.494041i
$478$	8.30580			0.379898
$479$	27.1562			1.24080			0.620398	−	0.784287i	$-0.286971\pi$
$479$	27.1562			1.24080			0.620398	+	0.784287i	$0.286971\pi$
$480$	1.04564	+	1.63819i	0.0477266	+	0.0747729i
$481$		−	8.14711i		−	0.371476i
$482$			45.7197i			2.08248i
$483$	5.45557	−	3.48222i	0.248237	−	0.158447i
$484$	8.17292	+	18.1850i	0.371496	+	0.826589i
$485$			2.55672i			0.116095i
$486$	29.0679	+	9.02699i	1.31855	+	0.409473i
$487$	−7.81108			−0.353954			−0.176977	−	0.984215i	$-0.556632\pi$
$487$	−7.81108			−0.353954			−0.176977	+	0.984215i	$0.556632\pi$
$488$		−	3.03643i		−	0.137453i
$489$	32.8290	−	20.9543i	1.48458	−	0.947588i
$490$		−	1.69722i		−	0.0766726i
$491$	2.21158			0.0998072			0.0499036	−	0.998754i	$-0.484109\pi$
$491$	2.21158			0.0998072			0.0499036	+	0.998754i	$0.484109\pi$
$492$	19.7200	−	12.5870i	0.889046	−	0.567467i
$493$	−14.2102			−0.639997
$494$	−15.5185			−0.698212
$495$	−0.768466	−	1.22033i	−0.0345400	−	0.0548496i
$496$	20.9974			0.942809
$497$	13.6664			0.613020
$498$	19.7190	−	12.5864i	0.883630	−	0.564010i
$499$	9.33250			0.417780			0.208890	−	0.977939i	$-0.433015\pi$
$499$	9.33250			0.417780			0.208890	+	0.977939i	$0.433015\pi$
$500$			2.62146i			0.117235i
$501$	−11.4928	+	7.33573i	−0.513462	+	0.327736i
$502$			4.73384i			0.211282i
$503$	−25.6422			−1.14333			−0.571664	−	0.820488i	$-0.693702\pi$
$503$	−25.6422			−1.14333			−0.571664	+	0.820488i	$0.693702\pi$
$504$	−0.997778	−	0.463171i	−0.0444445	−	0.0206313i
$505$			0.741229i			0.0329842i
$506$	−13.1256	+	20.2893i	−0.583503	+	0.901970i
$507$	−1.45999	+	0.931894i	−0.0648405	+	0.0413869i
$508$			19.9568i			0.885438i
$509$			11.0615i			0.490294i	0.969486	+	0.245147i	$0.0788363\pi$
$509$			11.0615i			0.490294i	−0.969486	+	0.245147i	$0.921164\pi$
$510$	−1.23998	−	1.94267i	−0.0549073	−	0.0860228i
$511$	3.02424			0.133784
$512$	−30.4193			−1.34435
$513$	−40.9306	+	5.49675i	−1.80713	+	0.242688i
$514$			26.9725i			1.18971i
$515$			1.19425i			0.0526249i
$516$	−7.14160	−	11.1887i	−0.314392	−	0.492555i
$517$	−23.9287	+	36.9887i	−1.05239	+	1.62676i
$518$		−	15.9299i		−	0.699920i
$519$	5.45055	−	3.47902i	0.239253	−	0.152712i
$520$	−0.0530722			−0.00232737
$521$		−	28.1685i		−	1.23408i	−0.786930	−	0.617042i	$-0.788331\pi$
$521$		−	28.1685i		−	1.23408i	0.786930	−	0.617042i	$-0.211669\pi$
$522$	7.45417	−	16.0580i	0.326260	−	0.702841i
$523$		−	9.26004i		−	0.404913i	−0.979291	−	0.202457i	$-0.935108\pi$
$523$		−	9.26004i		−	0.404913i	0.979291	−	0.202457i	$-0.0648925\pi$
$524$	26.8980			1.17504
$525$	−4.64638	−	7.27944i	−0.202785	−	0.317701i
$526$	−23.4649			−1.02312
$527$	−22.7480			−0.990920
$528$	24.9303	+	0.152322i	1.08495	+	0.00662898i
$529$	9.07591			0.394605
$530$	−2.41745			−0.105007
$531$	3.68767	+	1.71183i	0.160031	+	0.0742869i
$532$	−14.4253			−0.625416
$533$			7.45224i			0.322792i
$534$	−21.9997	−	34.4668i	−0.952021	−	1.49152i
$535$		−	1.82302i		−	0.0788162i
$536$	−0.324674			−0.0140238
$537$	3.19955	+	5.01271i	0.138071	+	0.216314i
$538$		−	31.0751i		−	1.33974i
$539$	−16.7005	−	10.8039i	−0.719342	−	0.465357i
$540$	1.35287	−	0.181683i	0.0582184	−	0.00781841i
$541$			10.6734i			0.458885i	0.973322	+	0.229442i	$0.0736902\pi$
$541$			10.6734i			0.458885i	−0.973322	+	0.229442i	$0.926310\pi$
$542$			38.6453i			1.65996i
$543$	−1.22472	+	0.781724i	−0.0525578	+	0.0335470i
$544$	36.3988			1.56058
$545$	−1.09485			−0.0468983
$546$	−2.85470	+	1.82212i	−0.122170	+	0.0779794i
$547$		−	16.9441i		−	0.724478i	−0.932085	−	0.362239i	$-0.882012\pi$
$547$		−	16.9441i		−	0.724478i	0.932085	−	0.362239i	$-0.117988\pi$
$548$			15.3124i			0.654114i
$549$	−22.5647	−	10.4746i	−0.963039	−	0.447045i
$550$	27.0723	+	17.5136i	1.15437	+	0.746784i
$551$			24.0210i			1.02333i
$552$	1.27330	+	1.99487i	0.0541952	+	0.0849072i
$553$	13.2149			0.561954
$554$		−	33.4797i		−	1.42242i
$555$	−1.10042	−	1.72401i	−0.0467101	−	0.0731803i
$556$			31.0164i			1.31539i
$557$	−23.3170			−0.987975			−0.493987	−	0.869469i	$-0.664461\pi$
$557$	−23.3170			−0.987975			−0.493987	+	0.869469i	$0.664461\pi$
$558$	11.9328	−	25.7060i	0.505156	−	1.08822i
$559$	4.22823			0.178835
$560$	−0.629902			−0.0266182
$561$	−27.0089	−	0.165022i	−1.14032	−	0.00696725i
$562$	−14.5115			−0.612129
$563$	−18.0419			−0.760376			−0.380188	−	0.924909i	$-0.624141\pi$
$563$	−18.0419			−0.760376			−0.380188	+	0.924909i	$0.624141\pi$
$564$	−22.4349	−	35.1487i	−0.944682	−	1.48003i
$565$	−0.210759			−0.00886668
$566$		−	15.7558i		−	0.662266i
$567$	−6.88394	+	5.81704i	−0.289098	+	0.244293i
$568$			4.99720i			0.209678i
$569$	24.9383			1.04547			0.522734	−	0.852496i	$-0.324912\pi$
$569$	24.9383			1.04547			0.522734	+	0.852496i	$0.324912\pi$
$570$	−3.28388	+	2.09606i	−0.137547	+	0.0877944i
$571$			38.3440i			1.60465i	0.596889	+	0.802324i	$0.296403\pi$
$571$			38.3440i			1.60465i	−0.596889	+	0.802324i	$0.703597\pi$
$572$	3.26514	−	5.04720i	0.136522	−	0.211034i
$573$	−14.7303	−	23.0779i	−0.615368	−	0.964092i
$574$			14.5712i			0.608191i
$575$			18.5791i			0.774802i
$576$	−8.12961	+	17.5131i	−0.338734	+	0.729711i
$577$	−6.63265			−0.276121			−0.138060	−	0.990424i	$-0.544087\pi$
$577$	−6.63265			−0.276121			−0.138060	+	0.990424i	$0.544087\pi$
$578$	−9.97048			−0.414717
$579$	14.8974	+	23.3396i	0.619115	+	0.969963i
$580$		−	0.793961i		−	0.0329674i
$581$			6.92690i			0.287376i
$582$	−50.2863	+	32.0971i	−2.08443	+	1.33047i
$583$	−15.3886	+	23.7875i	−0.637331	+	0.985177i
$584$			1.10583i			0.0457598i
$585$	−0.183080	+	0.394397i	−0.00756942	+	0.0163063i
$586$	−22.3537			−0.923424
$587$			13.5555i			0.559497i	0.960073	+	0.279749i	$0.0902511\pi$
$587$			13.5555i			0.559497i	−0.960073	+	0.279749i	$0.909749\pi$
$588$	15.8697	−	10.1294i	0.654456	−	0.417731i
$589$			38.4532i			1.58444i
$590$	0.383526			0.0157895
$591$	5.81332	−	3.71057i	0.239128	−	0.152632i
$592$	35.3576			1.45319
$593$	34.9955			1.43709			0.718547	−	0.695478i	$-0.244807\pi$
$593$	34.9955			1.43709			0.718547	+	0.695478i	$0.244807\pi$
$594$	14.3544	−	30.4344i	0.588968	−	1.24874i
$595$	0.682420			0.0279765
$596$	11.9466			0.489351
$597$	−13.5648	+	8.65825i	−0.555171	+	0.354359i
$598$	7.28595			0.297945
$599$		−	12.2424i		−	0.500210i	−0.968219	−	0.250105i	$-0.919535\pi$
$599$		−	12.2424i		−	0.500210i	0.968219	−	0.250105i	$-0.0804652\pi$
$600$	2.66178	−	1.69898i	0.108667	−	0.0693606i
$601$		−	32.2075i		−	1.31377i	−0.753989	−	0.656887i	$-0.771873\pi$
$601$		−	32.2075i		−	1.31377i	0.753989	−	0.656887i	$-0.228127\pi$
$602$	8.26739			0.336954
$603$	−1.12001	+	2.41276i	−0.0456103	+	0.0982552i
$604$			5.28924i			0.215216i
$605$	−1.45422	+	0.653572i	−0.0591223	+	0.0265715i
$606$	−14.5787	+	9.30540i	−0.592219	+	0.378006i
$607$		−	32.3627i		−	1.31356i	−0.754081	−	0.656781i	$-0.771917\pi$
$607$		−	32.3627i		−	1.31356i	0.754081	−	0.656781i	$-0.228083\pi$
$608$		−	61.5284i		−	2.49531i
$609$	2.82043	+	4.41875i	0.114290	+	0.179057i
$610$	−2.34678			−0.0950185
$611$	13.2828			0.537363
$612$	10.7642	−	23.1887i	0.435118	−	0.937346i
$613$			8.19010i			0.330795i	0.986227	+	0.165397i	$0.0528907\pi$
$613$			8.19010i			0.330795i	−0.986227	+	0.165397i	$0.947109\pi$
$614$			35.5988i			1.43665i
$615$	1.00656	+	1.57697i	0.0405884	+	0.0635896i
$616$	−0.660570	+	1.02110i	−0.0266151	+	0.0411412i
$617$		−	10.6068i		−	0.427012i	−0.976942	−	0.213506i	$-0.931512\pi$
$617$		−	10.6068i		−	0.427012i	0.976942	−	0.213506i	$-0.0684883\pi$
$618$	−23.4888	+	14.9926i	−0.944860	+	0.603092i
$619$	7.30062			0.293437			0.146718	−	0.989178i	$-0.453129\pi$
$619$	7.30062			0.293437			0.146718	+	0.989178i	$0.453129\pi$
$620$		−	1.27099i		−	0.0510442i
$621$	19.2169	−	2.58073i	0.771149	−	0.103561i
$622$		−	33.2488i		−	1.33316i
$623$	12.1075			0.485076
$624$	−4.04432	−	6.33621i	−0.161903	−	0.253651i
$625$	24.6853			0.987413
$626$	46.8528			1.87261
$627$	−0.278953	+	45.6559i	−0.0111403	+	1.82332i
$628$	−4.34410			−0.173348
$629$	−38.3056			−1.52735
$630$	−0.357973	+	0.771157i	−0.0142620	+	0.0307236i
$631$	11.0087			0.438249			0.219124	−	0.975697i	$-0.429680\pi$
$631$	11.0087			0.438249			0.219124	+	0.975697i	$0.429680\pi$
$632$			4.83212i			0.192211i
$633$	1.44737	+	2.26758i	0.0575277	+	0.0901281i
$634$		−	24.8964i		−	0.988762i
$635$	−1.59590			−0.0633315
$636$	−14.4279	−	22.6042i	−0.572105	−	0.896313i
$637$			5.99720i			0.237618i
$638$	−16.4334	−	10.6311i	−0.650603	−	0.420888i
$639$	37.1358	+	17.2385i	1.46907	+	0.681946i
$640$		−	0.422711i		−	0.0167091i
$641$		−	1.40587i		−	0.0555284i	−0.999614	−	0.0277642i	$-0.991161\pi$
$641$		−	1.40587i		−	0.0555284i	0.999614	−	0.0277642i	$-0.00883876\pi$
$642$	35.8557	−	22.8863i	1.41511	−	0.903249i
$643$	−2.02656			−0.0799198			−0.0399599	−	0.999201i	$-0.512723\pi$
$643$	−2.02656			−0.0799198			−0.0399599	+	0.999201i	$0.512723\pi$
$644$	6.77267			0.266881
$645$	0.894738	−	0.571100i	0.0352303	−	0.0224870i
$646$			72.9642i			2.87074i
$647$		−	32.3877i		−	1.27329i	−0.771156	−	0.636646i	$-0.780321\pi$
$647$		−	32.3877i		−	1.27329i	0.771156	−	0.636646i	$-0.219679\pi$
$648$	−2.12704	−	2.51716i	−0.0835580	−	0.0988835i
$649$	2.44139	−	3.77386i	0.0958329	−	0.148137i
$650$		−	9.72175i		−	0.381318i
$651$	4.51500	+	7.07362i	0.176957	+	0.277237i
$652$	40.7547			1.59608
$653$		−	0.246701i		−	0.00965417i	−0.999988	−	0.00482708i	$-0.998463\pi$
$653$		−	0.246701i		−	0.00965417i	0.999988	−	0.00482708i	$-0.00153651\pi$
$654$	−13.7448	−	21.5339i	−0.537464	−	0.842041i
$655$			2.15098i			0.0840458i
$656$	−32.3419			−1.26274
$657$	8.21782	+	3.81473i	0.320607	+	0.148827i
$658$	25.9716			1.01248
$659$	−46.8365			−1.82449			−0.912246	−	0.409642i	$-0.865654\pi$
$659$	−46.8365			−1.82449			−0.912246	+	0.409642i	$0.865654\pi$
$660$	0.00922021	−	1.50906i	0.000358896	−	0.0587400i
$661$	12.7201			0.494753			0.247376	−	0.968919i	$-0.420432\pi$
$661$	12.7201			0.494753			0.247376	+	0.968919i	$0.420432\pi$
$662$	−15.7521			−0.612221
$663$	4.38153	+	6.86450i	0.170164	+	0.266595i
$664$	−2.53287			−0.0982944
$665$		−	1.15356i		−	0.0447332i
$666$	20.0937	−	43.2866i	0.778617	−	1.67732i
$667$		−	11.2778i		−	0.436680i
$668$	−14.2675			−0.552025
$669$	−14.6128	+	9.32716i	−0.564963	+	0.360609i
$670$			0.250933i			0.00969437i
$671$	−14.9388	+	23.0921i	−0.576705	+	0.891462i
$672$	−7.22438	−	11.3184i	−0.278687	−	0.436616i
$673$			25.3474i			0.977070i	0.872544	+	0.488535i	$0.162469\pi$
$673$			25.3474i			0.977070i	−0.872544	+	0.488535i	$0.837531\pi$
$674$			52.1880i			2.01021i
$675$	−3.44350	−	25.6414i	−0.132540	−	0.986939i
$676$	−1.81247			−0.0697103
$677$	−12.6936			−0.487856			−0.243928	−	0.969793i	$-0.578436\pi$
$677$	−12.6936			−0.487856			−0.243928	+	0.969793i	$0.578436\pi$
$678$	−2.64587	−	4.14526i	−0.101614	−	0.159198i
$679$		−	17.6646i		−	0.677904i
$680$			0.249532i			0.00956911i
$681$	5.81861	−	3.71394i	0.222969	−	0.142319i
$682$	−26.3069	−	17.0184i	−1.00734	−	0.651670i
$683$		−	28.3674i		−	1.08545i	−0.839911	−	0.542725i	$-0.817393\pi$
$683$		−	28.3674i		−	1.08545i	0.839911	−	0.542725i	$-0.182607\pi$
$684$	−39.1981	−	18.1958i	−1.49878	−	0.695735i
$685$	−1.22450			−0.0467859
$686$			25.4132i			0.970281i
$687$	13.3739	−	8.53637i	0.510245	−	0.325683i
$688$			18.3501i			0.699591i
$689$	8.54217			0.325431
$690$	1.54178	−	0.984101i	0.0586947	−	0.0374641i
$691$	−20.2003			−0.768454			−0.384227	−	0.923239i	$-0.625532\pi$
$691$	−20.2003			−0.768454			−0.384227	+	0.923239i	$0.625532\pi$
$692$	6.76644			0.257222
$693$	5.30939	+	8.43133i	0.201687	+	0.320280i
$694$	28.3110			1.07467
$695$	−2.48032			−0.0940839
$696$	−1.61575	+	1.03131i	−0.0612447	+	0.0390917i
$697$	35.0385			1.32718
$698$			0.107044i			0.00405168i
$699$	−7.78575	+	4.96955i	−0.294484	+	0.187966i
$700$		−	9.03687i		−	0.341562i
$701$	24.6890			0.932490			0.466245	−	0.884656i	$-0.345607\pi$
$701$	24.6890			0.932490			0.466245	+	0.884656i	$0.345607\pi$
$702$	−10.0555	+	1.35040i	−0.379520	+	0.0509675i
$703$			64.7518i			2.44216i
$704$	17.9224	+	11.5944i	0.675476	+	0.436979i
$705$	2.81077	−	1.79408i	0.105860	−	0.0675689i
$706$		−	52.0322i		−	1.95826i
$707$		−	5.12120i		−	0.192603i
$708$	2.28898	+	3.58613i	0.0860252	+	0.134775i
$709$	0.973729			0.0365692			0.0182846	−	0.999833i	$-0.494180\pi$
$709$	0.973729			0.0365692			0.0182846	+	0.999833i	$0.494180\pi$
$710$	3.86221			0.144946
$711$	35.9090	+	16.6691i	1.34669	+	0.625138i
$712$			4.42719i			0.165916i
$713$		−	18.0538i		−	0.676120i
$714$	8.56712	+	13.4220i	0.320616	+	0.502307i
$715$	0.403615	+	0.261107i	0.0150943	+	0.00976484i
$716$			6.22290i			0.232561i
$717$	−6.21053	+	3.96410i	−0.231936	+	0.148042i
$718$	26.5704			0.991599
$719$		−	9.14846i		−	0.341180i	−0.985342	−	0.170590i	$-0.945433\pi$
$719$		−	9.14846i		−	0.341180i	0.985342	−	0.170590i	$-0.0545674\pi$
$720$	−1.71164	−	0.794548i	−0.0637891	−	0.0296111i
$721$		−	8.25116i		−	0.307289i
$722$	86.2400			3.20952
$723$	−21.8206	−	34.1862i	−0.811518	−	1.27140i
$724$	−1.52040			−0.0565051
$725$	−15.0482			−0.558875
$726$	−31.1109	−	20.3970i	−1.15463	−	0.757003i
$727$	29.0139			1.07607			0.538033	−	0.842924i	$-0.319168\pi$
$727$	29.0139			1.07607			0.538033	+	0.842924i	$0.319168\pi$
$728$	0.366680			0.0135901
$729$	−26.0434	+	7.12343i	−0.964569	+	0.263831i
$730$	0.854672			0.0316328
$731$		−	19.8801i		−	0.735291i
$732$	−14.0062	−	21.9434i	−0.517684	−	0.811051i
$733$		−	30.0699i		−	1.11066i	−0.831631	−	0.555328i	$-0.812593\pi$
$733$		−	30.0699i		−	1.11066i	0.831631	−	0.555328i	$-0.187407\pi$
$734$	−27.9233			−1.03067
$735$	0.810031	+	1.26907i	0.0298785	+	0.0468104i
$736$			28.8876i			1.06481i
$737$	2.46915	+	1.59735i	0.0909525	+	0.0588390i
$738$	−18.3799	+	39.5946i	−0.676574	+	1.45750i
$739$			21.2702i			0.782437i	0.920298	+	0.391218i	$0.127946\pi$
$739$			21.2702i			0.782437i	−0.920298	+	0.391218i	$0.872054\pi$
$740$		−	2.14023i		−	0.0786765i
$741$	11.6037	−	7.40652i	0.426274	−	0.272085i
$742$	16.7023			0.613163
$743$	−46.9149			−1.72114			−0.860570	−	0.509332i	$-0.829893\pi$
$743$	−46.9149			−1.72114			−0.860570	+	0.509332i	$0.829893\pi$
$744$	−2.58652	+	1.65094i	−0.0948264	+	0.0605265i
$745$			0.955344i			0.0350011i
$746$			19.5366i			0.715286i
$747$	−8.73748	+	18.8226i	−0.319688	+	0.688682i
$748$	−23.7307	−	15.3518i	−0.867679	−	0.561319i
$749$			12.5954i			0.460226i
$750$	−2.63174	−	4.12313i	−0.0960975	−	0.150555i
$751$	−52.1562			−1.90321			−0.951604	−	0.307327i	$-0.900565\pi$
$751$	−52.1562			−1.90321			−0.951604	+	0.307327i	$0.900565\pi$
$752$			57.6458i			2.10213i
$753$	−2.25932	−	3.53966i	−0.0823341	−	0.128992i
$754$			5.90127i			0.214912i
$755$	−0.422970			−0.0153935
$756$	−9.34711	+	1.25526i	−0.339951	+	0.0456535i
$757$	45.1989			1.64278			0.821390	−	0.570367i	$-0.193199\pi$
$757$	45.1989			1.64278			0.821390	+	0.570367i	$0.193199\pi$
$758$	−46.1853			−1.67753
$759$	0.130969	−	21.4354i	0.00475386	−	0.778057i
$760$	0.421808			0.0153006
$761$	−25.2876			−0.916676			−0.458338	−	0.888778i	$-0.651555\pi$
$761$	−25.2876			−0.916676			−0.458338	+	0.888778i	$0.651555\pi$
$762$	−20.0350	−	31.3887i	−0.725792	−	1.13709i
$763$	7.56442			0.273850
$764$		−	28.6494i		−	1.03650i
$765$	1.85435	+	0.860794i	0.0670442	+	0.0311221i
$766$			32.2540i			1.16539i
$767$	−1.35521			−0.0489337
$768$	27.1070	−	17.3021i	0.978139	−	0.624334i
$769$			3.72216i			0.134224i	0.997745	+	0.0671122i	$0.0213786\pi$
$769$			3.72216i			0.134224i	−0.997745	+	0.0671122i	$0.978621\pi$
$770$	0.789182	+	0.510538i	0.0284401	+	0.0183985i
$771$	−12.8732	−	20.1683i	−0.463616	−	0.726343i
$772$			28.9744i			1.04281i
$773$			31.0597i			1.11714i	0.829457	+	0.558571i	$0.188650\pi$
$773$			31.0597i			1.11714i	−0.829457	+	0.558571i	$0.811350\pi$
$774$	22.4651	+	10.4284i	0.807492	+	0.374840i
$775$	−24.0894			−0.865318
$776$	6.45918			0.231871
$777$	7.60286	+	11.9113i	0.272751	+	0.427317i
$778$		−	45.6340i		−	1.63606i
$779$		−	59.2290i		−	2.12210i
$780$	−0.383537	+	0.244807i	−0.0137328	+	0.00876549i
$781$	24.5854	−	38.0038i	0.879736	−	1.35988i
$782$		−	34.2567i		−	1.22502i
$783$	2.09026	+	15.5648i	0.0746999	+	0.556240i
$784$	−26.0272			−0.929544
$785$		−	0.347389i		−	0.0123988i
$786$	−42.3061	+	27.0035i	−1.50901	+	0.963181i
$787$		−	16.5184i		−	0.588817i	−0.955680	−	0.294408i	$-0.904877\pi$
$787$		−	16.5184i		−	0.588817i	0.955680	−	0.294408i	$-0.0951226\pi$
$788$	7.21679			0.257088
$789$	17.5455	−	11.1991i	0.624637	−	0.398698i
$790$	3.73462			0.132872
$791$	1.45615			0.0517746
$792$	−3.08297	+	1.94142i	−0.109549	+	0.0689852i
$793$	8.29246			0.294474
$794$	47.1707			1.67403
$795$	1.80761	−	1.15378i	0.0641093	−	0.0409202i
$796$	−16.8397			−0.596867
$797$		−	12.3700i		−	0.438167i	−0.975706	−	0.219083i	$-0.929693\pi$
$797$		−	12.3700i		−	0.438167i	0.975706	−	0.219083i	$-0.0703067\pi$
$798$	22.6886	−	14.4818i	0.803167	−	0.512652i
$799$		−	62.4521i		−	2.20940i
$800$	38.5451			1.36278
$801$	32.8999	+	15.2722i	1.16246	+	0.539617i
$802$		−	39.1587i		−	1.38274i
$803$	5.44053	−	8.40989i	0.191992	−	0.296779i
$804$	−2.34632	+	1.49763i	−0.0827484	+	0.0528173i
$805$			0.541597i			0.0190888i
$806$			9.44688i			0.332752i
$807$	14.8312	+	23.2359i	0.522082	+	0.817942i
$808$	1.87260			0.0658780
$809$	−17.1208			−0.601935			−0.300967	−	0.953634i	$-0.597310\pi$
$809$	−17.1208			−0.601935			−0.300967	+	0.953634i	$0.597310\pi$
$810$	−1.94545	+	1.64394i	−0.0683562	+	0.0577620i
$811$			20.0306i			0.703370i	0.936118	+	0.351685i	$0.114391\pi$
$811$			20.0306i			0.703370i	−0.936118	+	0.351685i	$0.885609\pi$
$812$			5.48554i			0.192505i
$813$	−18.4442	−	28.8964i	−0.646868	−	1.01344i
$814$	−44.2984	−	28.6575i	−1.55266	−	1.00445i
$815$			3.25907i			0.114160i
$816$	−29.7912	+	19.0154i	−1.04290	+	0.665671i
$817$	−33.6052			−1.17570
$818$		−	69.2451i		−	2.42110i
$819$	1.26491	−	2.72492i	0.0441996	−	0.0952163i
$820$			1.95769i			0.0683654i
$821$	−10.8233			−0.377737			−0.188869	−	0.982002i	$-0.560482\pi$
$821$	−10.8233			−0.377737			−0.188869	+	0.982002i	$0.560482\pi$
$822$	−15.3725	−	24.0839i	−0.536176	−	0.840022i
$823$	−13.2468			−0.461755			−0.230878	−	0.972983i	$-0.574160\pi$
$823$	−13.2468			−0.461755			−0.230878	+	0.972983i	$0.574160\pi$
$824$	3.01709			0.105105
$825$	−28.6016	−	0.174753i	−0.995780	−	0.00608413i
$826$	−2.64981			−0.0921988
$827$	47.9591			1.66770			0.833851	−	0.551990i	$-0.186131\pi$
$827$	47.9591			1.66770			0.833851	+	0.551990i	$0.186131\pi$
$828$	18.4035	+	8.54294i	0.639566	+	0.296888i
$829$	22.9571			0.797333			0.398667	−	0.917096i	$-0.369473\pi$
$829$	22.9571			0.797333			0.398667	+	0.917096i	$0.369473\pi$
$830$			1.95759i			0.0679490i
$831$	15.9788	+	25.0339i	0.554300	+	0.868418i
$832$		−	6.43599i		−	0.223128i
$833$	28.1973			0.976979
$834$	−31.1380	−	48.7837i	−1.07822	−	1.68924i
$835$		−	1.14094i		−	0.0394839i
$836$	−25.9507	+	40.1143i	−0.897525	+	1.38738i
$837$	3.34614	+	24.9164i	0.115659	+	0.861238i
$838$			27.1712i			0.938615i
$839$			11.6272i			0.401415i	0.979651	+	0.200707i	$0.0643240\pi$
$839$			11.6272i			0.401415i	−0.979651	+	0.200707i	$0.935676\pi$
$840$	0.0775932	−	0.0495268i	0.00267722	−	0.00170884i
$841$	−19.8655			−0.685017
$842$	78.9583			2.72108
$843$	10.8507	−	6.92587i	0.373718	−	0.238540i
$844$			2.81502i			0.0968971i
$845$		−	0.144939i		−	0.00498607i
$846$	70.5729	+	32.7601i	2.42635	+	1.12632i
$847$	10.0473	−	4.51558i	0.345229	−	0.155157i
$848$			37.0721i			1.27306i
$849$	7.51977	+	11.7812i	0.258078	+	0.404328i
$850$	−45.7092			−1.56781
$851$		−	30.4010i		−	1.04213i
$852$	23.0506	+	36.1132i	0.789702	+	1.23722i
$853$		−	1.48595i		−	0.0508779i	−0.999676	−	0.0254390i	$-0.991902\pi$
$853$		−	1.48595i		−	0.0508779i	0.999676	−	0.0254390i	$-0.00809835\pi$
$854$	16.2141			0.554835
$855$	1.45509	−	3.13459i	0.0497629	−	0.107201i
$856$	−4.60560			−0.157416
$857$	−17.7673			−0.606919			−0.303459	−	0.952844i	$-0.598142\pi$
$857$	−17.7673			−0.606919			−0.303459	+	0.952844i	$0.598142\pi$
$858$	−0.0685310	+	11.2164i	−0.00233961	+	0.382920i
$859$	−31.2678			−1.06684			−0.533422	−	0.845850i	$-0.679094\pi$
$859$	−31.2678			−1.06684			−0.533422	+	0.845850i	$0.679094\pi$
$860$	1.11075			0.0378762
$861$	−6.95440	−	10.8954i	−0.237005	−	0.371314i
$862$	−35.5165			−1.20970
$863$			49.4976i			1.68492i	0.538760	+	0.842459i	$0.318893\pi$
$863$			49.4976i			1.68492i	−0.538760	+	0.842459i	$0.681107\pi$
$864$	−5.35410	−	39.8684i	−0.182150	−	1.35635i
$865$			0.541099i			0.0183979i
$866$	18.7207			0.636155
$867$	7.45527	−	4.75860i	0.253194	−	0.161611i
$868$			8.78136i			0.298059i
$869$	23.7732	−	36.7483i	0.806452	−	1.24660i
$870$	0.797074	+	1.24877i	0.0270233	+	0.0423373i
$871$		−	0.886681i		−	0.0300440i
$872$			2.76598i			0.0936680i
$873$	22.2818	−	48.0002i	0.754125	−	1.62456i
$874$	−57.9074			−1.95875
$875$	1.44837			0.0489639
$876$	5.10089	+	7.99153i	0.172343	+	0.270009i
$877$			3.05009i			0.102994i	0.998673	+	0.0514971i	$0.0163993\pi$
$877$			3.05009i			0.102994i	−0.998673	+	0.0514971i	$0.983601\pi$
$878$			31.3536i			1.05813i
$879$	16.7147	−	10.6688i	0.563771	−	0.359848i
$880$	−1.13318	+	1.75165i	−0.0381994	+	0.0590480i
$881$			3.46717i			0.116812i	0.998293	+	0.0584060i	$0.0186018\pi$
$881$			3.46717i			0.116812i	−0.998293	+	0.0584060i	$0.981398\pi$
$882$	−14.7913	+	31.8639i	−0.498048	+	1.07291i
$883$	47.8326			1.60969			0.804847	−	0.593482i	$-0.202247\pi$
$883$	47.8326			1.60969			0.804847	+	0.593482i	$0.202247\pi$
$884$			8.52175i			0.286618i
$885$	−0.286776	+	0.183045i	−0.00963986	+	0.00615300i
$886$			30.1677i			1.01350i
$887$	58.5542			1.96606			0.983029	−	0.183451i	$-0.0587270\pi$
$887$	58.5542			1.96606			0.983029	+	0.183451i	$0.0587270\pi$
$888$	−4.35546	+	2.78004i	−0.146160	+	0.0932920i
$889$	11.0262			0.369807
$890$	3.42166			0.114694
$891$	3.79214	+	29.6078i	0.127042	+	0.991897i
$892$	−18.1407			−0.607394
$893$	−105.569			−3.53273
$894$	−18.7900	+	11.9934i	−0.628431	+	0.401120i
$895$	−0.497633			−0.0166340
$896$			2.92054i			0.0975685i
$897$	−5.44796	+	3.47736i	−0.181902	+	0.116106i
$898$		−	31.7560i		−	1.05971i
$899$	14.6227			0.487694
$900$	11.3990	−	24.5560i	0.379966	−	0.818535i
$901$		−	40.1631i		−	1.33803i
$902$	40.5201	+	26.2133i	1.34917	+	0.872806i
$903$	−6.18181	+	3.94577i	−0.205718	+	0.131307i
$904$			0.532450i			0.0177090i
$905$		−	0.121583i		−	0.00404156i
$906$	−5.30998	−	8.31910i	−0.176412	−	0.276384i
$907$	7.18193			0.238472			0.119236	−	0.992866i	$-0.461955\pi$
$907$	7.18193			0.238472			0.119236	+	0.992866i	$0.461955\pi$
$908$	7.22336			0.239715
$909$	6.45981	−	13.9159i	0.214258	−	0.461562i
$910$		−	0.283398i		−	0.00939454i
$911$			26.1736i			0.867172i	0.901112	+	0.433586i	$0.142752\pi$
$911$			26.1736i			0.867172i	−0.901112	+	0.433586i	$0.857248\pi$
$912$	32.1435	+	50.3590i	1.06438	+	1.66755i
$913$	19.2625	+	12.4613i	0.637496	+	0.412409i
$914$			57.7811i			1.91123i
$915$	1.75477	−	1.12005i	0.0580109	−	0.0370276i
$916$	16.6026			0.548566
$917$		−	14.8613i		−	0.490763i
$918$	6.34922	+	47.2784i	0.209555	+	1.56042i
$919$			32.1620i			1.06093i	0.847708	+	0.530463i	$0.177982\pi$
$919$			32.1620i			1.06093i	−0.847708	+	0.530463i	$0.822018\pi$
$920$	−0.198039			−0.00652915
$921$	−16.9902	−	26.6184i	−0.559846	−	0.877107i
$922$	−76.3114			−2.51318
$923$	−13.6473			−0.449206
$924$	−0.0637031	+	10.4262i	−0.00209568	+	0.342996i
$925$	−40.5644			−1.33375
$926$	−57.7422			−1.89753
$927$	10.4079	−	22.4210i	0.341840	−	0.736402i
$928$	−23.3975			−0.768062
$929$			0.398562i			0.0130764i	0.999979	+	0.00653821i	$0.00208119\pi$
$929$			0.398562i			0.0130764i	−0.999979	+	0.00653821i	$0.997919\pi$
$930$	1.27597	+	1.99906i	0.0418408	+	0.0655516i
$931$		−	47.6647i		−	1.56215i
$932$	−9.66541			−0.316601
$933$	15.8686	+	24.8613i	0.519516	+	0.813922i
$934$			8.81491i			0.288433i
$935$	1.22766	−	1.89769i	0.0401487	−	0.0620612i
$936$	0.996385	+	0.462524i	0.0325679	+	0.0151181i
$937$		−	1.59643i		−	0.0521531i	−0.999660	−	0.0260765i	$-0.991699\pi$
$937$		−	1.59643i		−	0.0521531i	0.999660	−	0.0260765i	$-0.00830136\pi$
$938$		−	1.73371i		−	0.0566077i
$939$	−35.0334	+	22.3614i	−1.14327	+	0.729736i
$940$	3.48936			0.113810
$941$	1.08400			0.0353373			0.0176687	−	0.999844i	$-0.494376\pi$
$941$	1.08400			0.0353373			0.0176687	+	0.999844i	$0.494376\pi$
$942$	6.83255	−	4.36113i	0.222616	−	0.142093i
$943$			27.8080i			0.905554i
$944$		−	5.88146i		−	0.191425i
$945$	−0.100381	−	0.747470i	−0.00326540	−	0.0243152i
$946$	14.8728	−	22.9902i	0.483557	−	0.747476i
$947$		−	23.0488i		−	0.748986i	−0.927230	−	0.374493i	$-0.877817\pi$
$947$		−	23.0488i		−	0.748986i	0.927230	−	0.374493i	$-0.122183\pi$
$948$	22.2892	+	34.9202i	0.723918	+	1.13416i
$949$	−3.02002			−0.0980340
$950$			77.2667i			2.50686i
$951$	11.8823	+	18.6159i	0.385310	+	0.603661i
$952$		−	1.72403i		−	0.0558763i
$953$	3.02294			0.0979228			0.0489614	−	0.998801i	$-0.484409\pi$
$953$	3.02294			0.0979228			0.0489614	+	0.998801i	$0.484409\pi$
$954$	45.3856	+	21.0681i	1.46941	+	0.682104i
$955$	2.29104			0.0741362
$956$	−7.70989			−0.249356
$957$	17.3617	+	0.106078i	0.561223	+	0.00342902i
$958$	−53.0239			−1.71312
$959$	8.46019			0.273194
$960$	−0.869298	−	1.36192i	−0.0280565	−	0.0439559i
$961$	−7.59168			−0.244893
$962$			15.9077i			0.512884i
$963$	−15.8876	+	34.2257i	−0.511972	+	1.10291i
$964$		−	42.4396i		−	1.36689i
$965$	−2.31703			−0.0745877
$966$	−10.6523	+	6.79923i	−0.342732	+	0.218762i
$967$			22.2857i			0.716659i	0.933595	+	0.358329i	$0.116654\pi$
$967$			22.2857i			0.716659i	−0.933595	+	0.358329i	$0.883346\pi$
$968$	1.65115	+	3.67386i	0.0530701	+	0.118082i
$969$	−34.8236	−	54.5578i	−1.11869	−	1.75265i
$970$		−	4.99213i		−	0.160288i
$971$			16.7780i			0.538431i	0.963080	+	0.269215i	$0.0867643\pi$
$971$			16.7780i			0.538431i	−0.963080	+	0.269215i	$0.913236\pi$
$972$	−26.9824	−	8.37935i	−0.865461	−	0.268768i
$973$	17.1367			0.549378
$974$	15.2516			0.488691
$975$	4.63989	+	7.26928i	0.148596	+	0.232803i
$976$			35.9884i			1.15196i
$977$		−	30.9556i		−	0.990358i	−0.868791	−	0.495179i	$-0.835103\pi$
$977$		−	30.9556i		−	0.990358i	0.868791	−	0.495179i	$-0.164897\pi$
$978$	−64.1004	+	40.9145i	−2.04970	+	1.30830i
$979$	21.7811	−	33.6689i	0.696126	−	1.07606i
$980$			1.57545i			0.0503260i
$981$	20.5549	+	9.54164i	0.656268	+	0.304641i
$982$	−4.31823			−0.137800
$983$			30.9250i			0.986353i	0.869929	+	0.493176i	$0.164164\pi$
$983$			30.9250i			0.986353i	−0.869929	+	0.493176i	$0.835836\pi$
$984$	3.98398	−	2.54293i	0.127005	−	0.0810655i
$985$			0.577113i			0.0183883i
$986$	27.7463			0.883621
$987$	−19.4198	+	12.3954i	−0.618140	+	0.394551i
$988$	14.4052			0.458289
$989$	15.7777			0.501700
$990$	1.50047	+	2.38275i	0.0476881	+	0.0757289i
$991$	−6.30442			−0.200266			−0.100133	−	0.994974i	$-0.531927\pi$
$991$	−6.30442			−0.200266			−0.100133	+	0.994974i	$0.531927\pi$
$992$	−37.4553			−1.18921
$993$	11.7784	−	7.51798i	0.373775	−	0.238576i
$994$	−26.6843			−0.846375
$995$		−	1.34664i		−	0.0426913i
$996$	−18.3043	+	11.6834i	−0.579993	+	0.370202i
$997$		−	11.1331i		−	0.352588i	−0.984338	−	0.176294i	$-0.943589\pi$
$997$		−	11.1331i		−	0.352588i	0.984338	−	0.176294i	$-0.0564110\pi$
$998$	−18.2222			−0.576814
$999$	5.63459	+	41.9570i	0.178271	+	1.32746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.9	✓	48
3.2	odd	2	inner	429.2.f.a.131.40	yes	48
11.10	odd	2	inner	429.2.f.a.131.39	yes	48
33.32	even	2	inner	429.2.f.a.131.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.9	✓	48	1.1	even	1	trivial
429.2.f.a.131.10	yes	48	33.32	even	2	inner
429.2.f.a.131.39	yes	48	11.10	odd	2	inner
429.2.f.a.131.40	yes	48	3.2	odd	2	inner

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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.95255 q^{2} +(1.45999 - 0.931894i) q^{3} +1.81247 q^{4} +0.144939i q^{5} +(-2.85071 + 1.81957i) q^{6} -1.00140i q^{7} +0.366168 q^{8} +(1.26315 - 2.72111i) q^{9} +O(q^{10})\)	\(q-1.95255 q^{2} +(1.45999 - 0.931894i) q^{3} +1.81247 q^{4} +0.144939i q^{5} +(-2.85071 + 1.81957i) q^{6} -1.00140i q^{7} +0.366168 q^{8} +(1.26315 - 2.72111i) q^{9} -0.283002i q^{10} +(-2.78472 - 1.80149i) q^{11} +(2.64619 - 1.68903i) q^{12} +1.00000i q^{13} +1.95528i q^{14} +(0.135068 + 0.211610i) q^{15} -4.33990 q^{16} +4.70174 q^{17} +(-2.46636 + 5.31312i) q^{18} -7.94782i q^{19} +0.262698i q^{20} +(-0.933196 - 1.46203i) q^{21} +(5.43731 + 3.51750i) q^{22} +3.73150i q^{23} +(0.534602 - 0.341230i) q^{24} +4.97899 q^{25} -1.95255i q^{26} +(-0.691606 - 5.14992i) q^{27} -1.81500i q^{28} -3.02233 q^{29} +(-0.263728 - 0.413181i) q^{30} -4.83822 q^{31} +7.74155 q^{32} +(-5.74446 - 0.0350981i) q^{33} -9.18041 q^{34} +0.145142 q^{35} +(2.28941 - 4.93193i) q^{36} -8.14711 q^{37} +15.5185i q^{38} +(0.931894 + 1.45999i) q^{39} +0.0530722i q^{40} +7.45224 q^{41} +(1.82212 + 2.85470i) q^{42} -4.22823i q^{43} +(-5.04720 - 3.26514i) q^{44} +(0.394397 + 0.183080i) q^{45} -7.28595i q^{46} -13.2828i q^{47} +(-6.33621 + 4.04432i) q^{48} +5.99720 q^{49} -9.72175 q^{50} +(6.86450 - 4.38153i) q^{51} +1.81247i q^{52} -8.54217i q^{53} +(1.35040 + 10.0555i) q^{54} +(0.261107 - 0.403615i) q^{55} -0.366680i q^{56} +(-7.40652 - 11.6037i) q^{57} +5.90127 q^{58} +1.35521i q^{59} +(0.244807 + 0.383537i) q^{60} -8.29246i q^{61} +9.44688 q^{62} +(-2.72492 - 1.26491i) q^{63} -6.43599 q^{64} -0.144939 q^{65} +(11.2164 + 0.0685310i) q^{66} -0.886681 q^{67} +8.52175 q^{68} +(3.47736 + 5.44796i) q^{69} -0.283398 q^{70} +13.6473i q^{71} +(0.462524 - 0.996385i) q^{72} +3.02002i q^{73} +15.9077 q^{74} +(7.26928 - 4.63989i) q^{75} -14.4052i q^{76} +(-1.80401 + 2.78861i) q^{77} +(-1.81957 - 2.85071i) q^{78} +13.1964i q^{79} -0.629022i q^{80} +(-5.80892 - 6.87433i) q^{81} -14.5509 q^{82} -6.91723 q^{83} +(-1.69139 - 2.64988i) q^{84} +0.681468i q^{85} +8.25586i q^{86} +(-4.41258 + 2.81649i) q^{87} +(-1.01967 - 0.659648i) q^{88} +12.0906i q^{89} +(-0.770081 - 0.357473i) q^{90} +1.00140 q^{91} +6.76322i q^{92} +(-7.06375 + 4.50870i) q^{93} +25.9353i q^{94} +1.15195 q^{95} +(11.3026 - 7.21430i) q^{96} +17.6399 q^{97} -11.7099 q^{98} +(-8.41956 + 5.30198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

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