LMFDB - Embedded newform 798.2.e.b.265.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(265,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.265"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} + 54x^{8} - 114x^{7} + 120x^{6} + 46x^{5} + 9x^{4} - 4x^{3} + 8x^{2} + 4x + 1 $ x^12 - 2x^11 + 2x^10 + 54x^8 - 114x^7 + 120x^6 + 46x^5 + 9x^4 - 4x^3 + 8x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			265.8
Root			$1.25342 + 1.25342i$ of defining polynomial
Character	$\chi$	$=$	798.265
Dual form			798.2.e.b.265.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -2.50684i q^{5} +1.00000i q^{6} +(-2.53963 - 0.741811i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +2.50684 q^{10} -4.07545 q^{11} -1.00000 q^{12} -0.506836 q^{13} +(0.741811 - 2.53963i) q^{14} -2.50684i q^{15} +1.00000 q^{16} +2.30760i q^{17} +1.00000i q^{18} +(-4.30085 - 0.709018i) q^{19} +2.50684i q^{20} +(-2.53963 - 0.741811i) q^{21} -4.07545i q^{22} -6.34027 q^{23} -1.00000i q^{24} -1.28423 q^{25} -0.506836i q^{26} +1.00000 q^{27} +(2.53963 + 0.741811i) q^{28} -8.66728i q^{29} +2.50684 q^{30} -1.39640 q^{31} +1.00000i q^{32} -4.07545 q^{33} -2.30760 q^{34} +(-1.85960 + 6.36643i) q^{35} -1.00000 q^{36} -1.68285i q^{37} +(0.709018 - 4.30085i) q^{38} -0.506836 q^{39} -2.50684 q^{40} -0.402139 q^{41} +(0.741811 - 2.53963i) q^{42} -6.73509 q^{43} +4.07545 q^{44} -2.50684i q^{45} -6.34027i q^{46} -5.33646i q^{47} +1.00000 q^{48} +(5.89943 + 3.76785i) q^{49} -1.28423i q^{50} +2.30760i q^{51} +0.506836 q^{52} -1.66122i q^{53} +1.00000i q^{54} +10.2165i q^{55} +(-0.741811 + 2.53963i) q^{56} +(-4.30085 - 0.709018i) q^{57} +8.66728 q^{58} +9.42907 q^{59} +2.50684i q^{60} +5.31706i q^{61} -1.39640i q^{62} +(-2.53963 - 0.741811i) q^{63} -1.00000 q^{64} +1.27056i q^{65} -4.07545i q^{66} -3.06939i q^{67} -2.30760i q^{68} -6.34027 q^{69} +(-6.36643 - 1.85960i) q^{70} -8.08532i q^{71} -1.00000i q^{72} +13.5144i q^{73} +1.68285 q^{74} -1.28423 q^{75} +(4.30085 + 0.709018i) q^{76} +(10.3501 + 3.02321i) q^{77} -0.506836i q^{78} -3.37893i q^{79} -2.50684i q^{80} +1.00000 q^{81} -0.402139i q^{82} -10.5106i q^{83} +(2.53963 + 0.741811i) q^{84} +5.78478 q^{85} -6.73509i q^{86} -8.66728i q^{87} +4.07545i q^{88} +11.7389 q^{89} +2.50684 q^{90} +(1.28718 + 0.375977i) q^{91} +6.34027 q^{92} -1.39640 q^{93} +5.33646 q^{94} +(-1.77739 + 10.7815i) q^{95} +1.00000i q^{96} +4.87048 q^{97} +(-3.76785 + 5.89943i) q^{98} -4.07545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} + 12 q^{11} - 12 q^{12} + 20 q^{13} - 4 q^{14} + 12 q^{16} - 8 q^{19} - 12 q^{23} - 12 q^{25} + 12 q^{27} + 4 q^{30} + 24 q^{31} + 12 q^{33} + 4 q^{34} + 4 q^{35}+ \cdots + 12 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 + 12 * q^11 - 12 * q^12 + 20 * q^13 - 4 * q^14 + 12 * q^16 - 8 * q^19 - 12 * q^23 - 12 * q^25 + 12 * q^27 + 4 * q^30 + 24 * q^31 + 12 * q^33 + 4 * q^34 + 4 * q^35 - 12 * q^36 + 20 * q^39 - 4 * q^40 - 16 * q^41 - 4 * q^42 - 12 * q^44 + 12 * q^48 + 4 * q^49 - 20 * q^52 + 4 * q^56 - 8 * q^57 + 8 * q^58 + 40 * q^59 - 12 * q^64 - 12 * q^69 - 24 * q^70 - 12 * q^75 + 8 * q^76 + 8 * q^77 + 12 * q^81 + 8 * q^85 - 16 * q^89 + 4 * q^90 + 24 * q^91 + 12 * q^92 + 24 * q^93 - 44 * q^95 - 60 * q^97 - 16 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	2.50684i		−	1.12109i	−0.828124	−	0.560546i	$-0.810591\pi$
$5$		−	2.50684i		−	1.12109i	0.828124	−	0.560546i	$-0.189409\pi$
$6$			1.00000i			0.408248i
$7$	−2.53963	−	0.741811i	−0.959890	−	0.280378i
$7$	−2.53963	−	0.741811i	−0.959890	−	0.280378i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	2.50684			0.792731
$11$	−4.07545			−1.22880			−0.614398	−	0.788997i	$-0.710601\pi$
$11$	−4.07545			−1.22880			−0.614398	+	0.788997i	$0.710601\pi$
$12$	−1.00000			−0.288675
$13$	−0.506836			−0.140571			−0.0702855	−	0.997527i	$-0.522391\pi$
$13$	−0.506836			−0.140571			−0.0702855	+	0.997527i	$0.522391\pi$
$14$	0.741811	−	2.53963i	0.198257	−	0.678744i
$15$		−	2.50684i		−	0.647262i
$16$	1.00000			0.250000
$17$			2.30760i			0.559676i	0.960047	+	0.279838i	$0.0902807\pi$
$17$			2.30760i			0.559676i	−0.960047	+	0.279838i	$0.909719\pi$
$18$			1.00000i			0.235702i
$19$	−4.30085	−	0.709018i	−0.986682	−	0.162660i
$19$	−4.30085	−	0.709018i	−0.986682	−	0.162660i
$20$			2.50684i			0.560546i
$21$	−2.53963	−	0.741811i	−0.554193	−	0.161876i
$22$		−	4.07545i		−	0.868889i
$23$	−6.34027			−1.32204			−0.661019	−	0.750369i	$-0.729876\pi$
$23$	−6.34027			−1.32204			−0.661019	+	0.750369i	$0.729876\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.28423			−0.256845
$26$		−	0.506836i		−	0.0993987i
$27$	1.00000			0.192450
$28$	2.53963	+	0.741811i	0.479945	+	0.140189i
$29$		−	8.66728i		−	1.60947i	−0.593632	−	0.804737i	$-0.702306\pi$
$29$		−	8.66728i		−	1.60947i	0.593632	−	0.804737i	$-0.297694\pi$
$30$	2.50684			0.457684
$31$	−1.39640			−0.250802			−0.125401	−	0.992106i	$-0.540022\pi$
$31$	−1.39640			−0.250802			−0.125401	+	0.992106i	$0.540022\pi$
$32$			1.00000i			0.176777i
$33$	−4.07545			−0.709445
$34$	−2.30760			−0.395751
$35$	−1.85960	+	6.36643i	−0.314329	+	1.07612i
$36$	−1.00000			−0.166667
$37$		−	1.68285i		−	0.276660i	−0.990386	−	0.138330i	$-0.955827\pi$
$37$		−	1.68285i		−	0.276660i	0.990386	−	0.138330i	$-0.0441734\pi$
$38$	0.709018	−	4.30085i	0.115018	−	0.697690i
$39$	−0.506836			−0.0811587
$40$	−2.50684			−0.396366
$41$	−0.402139			−0.0628036			−0.0314018	−	0.999507i	$-0.509997\pi$
$41$	−0.402139			−0.0628036			−0.0314018	+	0.999507i	$0.509997\pi$
$42$	0.741811	−	2.53963i	0.114464	−	0.391873i
$43$	−6.73509			−1.02709			−0.513546	−	0.858062i	$-0.671668\pi$
$43$	−6.73509			−1.02709			−0.513546	+	0.858062i	$0.671668\pi$
$44$	4.07545			0.614398
$45$		−	2.50684i		−	0.373697i
$46$		−	6.34027i		−	0.934822i
$47$		−	5.33646i		−	0.778403i	−0.921153	−	0.389202i	$-0.872751\pi$
$47$		−	5.33646i		−	0.778403i	0.921153	−	0.389202i	$-0.127249\pi$
$48$	1.00000			0.144338
$49$	5.89943	+	3.76785i	0.842776	+	0.538264i
$50$		−	1.28423i		−	0.181617i
$51$			2.30760i			0.323129i
$52$	0.506836			0.0702855
$53$		−	1.66122i		−	0.228187i	−0.993470	−	0.114093i	$-0.963604\pi$
$53$		−	1.66122i		−	0.228187i	0.993470	−	0.114093i	$-0.0363963\pi$
$54$			1.00000i			0.136083i
$55$			10.2165i			1.37759i
$56$	−0.741811	+	2.53963i	−0.0991286	+	0.339372i
$57$	−4.30085	−	0.709018i	−0.569661	−	0.0939117i
$58$	8.66728			1.13807
$59$	9.42907			1.22756			0.613780	−	0.789477i	$-0.289648\pi$
$59$	9.42907			1.22756			0.613780	+	0.789477i	$0.289648\pi$
$60$			2.50684i			0.323631i
$61$			5.31706i			0.680779i	0.940284	+	0.340390i	$0.110559\pi$
$61$			5.31706i			0.680779i	−0.940284	+	0.340390i	$0.889441\pi$
$62$		−	1.39640i		−	0.177343i
$63$	−2.53963	−	0.741811i	−0.319963	−	0.0934594i
$64$	−1.00000			−0.125000
$65$			1.27056i			0.157593i
$66$		−	4.07545i		−	0.501653i
$67$		−	3.06939i		−	0.374986i	−0.982266	−	0.187493i	$-0.939964\pi$
$67$		−	3.06939i		−	0.374986i	0.982266	−	0.187493i	$-0.0600362\pi$
$68$		−	2.30760i		−	0.279838i
$69$	−6.34027			−0.763279
$70$	−6.36643	−	1.85960i	−0.760934	−	0.222264i
$71$		−	8.08532i		−	0.959551i	−0.877391	−	0.479775i	$-0.840718\pi$
$71$		−	8.08532i		−	0.959551i	0.877391	−	0.479775i	$-0.159282\pi$
$72$		−	1.00000i		−	0.117851i
$73$			13.5144i			1.58174i	0.611984	+	0.790870i	$0.290372\pi$
$73$			13.5144i			1.58174i	−0.611984	+	0.790870i	$0.709628\pi$
$74$	1.68285			0.195628
$75$	−1.28423			−0.148290
$76$	4.30085	+	0.709018i	0.493341	+	0.0813299i
$77$	10.3501	+	3.02321i	1.17951	+	0.344527i
$78$		−	0.506836i		−	0.0573879i
$79$		−	3.37893i		−	0.380159i	−0.981769	−	0.190079i	$-0.939125\pi$
$79$		−	3.37893i		−	0.380159i	0.981769	−	0.190079i	$-0.0608745\pi$
$80$		−	2.50684i		−	0.280273i
$81$	1.00000			0.111111
$82$		−	0.402139i		−	0.0444089i
$83$		−	10.5106i		−	1.15368i	−0.816856	−	0.576842i	$-0.804285\pi$
$83$		−	10.5106i		−	1.15368i	0.816856	−	0.576842i	$-0.195715\pi$
$84$	2.53963	+	0.741811i	0.277096	+	0.0809382i
$85$	5.78478			0.627448
$86$		−	6.73509i		−	0.726264i
$87$		−	8.66728i		−	0.929230i
$88$			4.07545i			0.434445i
$89$	11.7389			1.24432			0.622162	−	0.782889i	$-0.286255\pi$
$89$	11.7389			1.24432			0.622162	+	0.782889i	$0.286255\pi$
$90$	2.50684			0.264244
$91$	1.28718	+	0.375977i	0.134933	+	0.0394130i
$92$	6.34027			0.661019
$93$	−1.39640			−0.144800
$94$	5.33646			0.550414
$95$	−1.77739	+	10.7815i	−0.182356	+	1.10616i
$96$			1.00000i			0.102062i
$97$	4.87048			0.494523			0.247261	−	0.968949i	$-0.420469\pi$
$97$	4.87048			0.494523			0.247261	+	0.968949i	$0.420469\pi$
$98$	−3.76785	+	5.89943i	−0.380610	+	0.595933i
$99$	−4.07545			−0.409598
$100$	1.28423			0.128423
$101$		−	10.8277i		−	1.07740i	−0.842498	−	0.538700i	$-0.818916\pi$
$101$		−	10.8277i		−	1.07740i	0.842498	−	0.538700i	$-0.181084\pi$
$102$	−2.30760			−0.228487
$103$	5.51407			0.543317			0.271659	−	0.962394i	$-0.412428\pi$
$103$	5.51407			0.543317			0.271659	+	0.962394i	$0.412428\pi$
$104$			0.506836i			0.0496994i
$105$	−1.85960	+	6.36643i	−0.181478	+	0.621300i
$106$	1.66122			0.161352
$107$		−	1.64796i		−	0.159315i	−0.996822	−	0.0796573i	$-0.974617\pi$
$107$		−	1.64796i		−	0.159315i	0.996822	−	0.0796573i	$-0.0253826\pi$
$108$	−1.00000			−0.0962250
$109$			18.0910i			1.73281i	0.499345	+	0.866403i	$0.333574\pi$
$109$			18.0910i			1.73281i	−0.499345	+	0.866403i	$0.666426\pi$
$110$	−10.2165			−0.974104
$111$		−	1.68285i		−	0.159730i
$112$	−2.53963	−	0.741811i	−0.239972	−	0.0700945i
$113$		−	2.33655i		−	0.219804i	−0.993942	−	0.109902i	$-0.964946\pi$
$113$		−	2.33655i		−	0.219804i	0.993942	−	0.109902i	$-0.0350538\pi$
$114$	0.709018	−	4.30085i	0.0664056	−	0.402811i
$115$			15.8940i			1.48213i
$116$			8.66728i			0.804737i
$117$	−0.506836			−0.0468570
$118$			9.42907i			0.868016i
$119$	1.71180	−	5.86046i	0.156921	−	0.537227i
$120$	−2.50684			−0.228842
$121$	5.60931			0.509937
$122$	−5.31706			−0.481384
$123$	−0.402139			−0.0362597
$124$	1.39640			0.125401
$125$		−	9.31483i		−	0.833144i
$126$	0.741811	−	2.53963i	0.0660858	−	0.226248i
$127$		−	1.29418i		−	0.114840i	−0.998350	−	0.0574200i	$-0.981713\pi$
$127$		−	1.29418i		−	0.114840i	0.998350	−	0.0574200i	$-0.0182874\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.73509			−0.592992
$130$	−1.27056			−0.111435
$131$		−	4.38528i		−	0.383144i	−0.981479	−	0.191572i	$-0.938642\pi$
$131$		−	4.38528i		−	0.383144i	0.981479	−	0.191572i	$-0.0613585\pi$
$132$	4.07545			0.354723
$133$	10.3966	+	4.99106i	0.901500	+	0.432780i
$134$	3.06939			0.265155
$135$		−	2.50684i		−	0.215754i
$136$	2.30760			0.197875
$137$	−17.3945			−1.48611			−0.743056	−	0.669229i	$-0.766625\pi$
$137$	−17.3945			−1.48611			−0.743056	+	0.669229i	$0.766625\pi$
$138$		−	6.34027i		−	0.539720i
$139$		−	4.29012i		−	0.363884i	−0.983309	−	0.181942i	$-0.941762\pi$
$139$		−	4.29012i		−	0.363884i	0.983309	−	0.181942i	$-0.0582382\pi$
$140$	1.85960	−	6.36643i	0.157165	−	0.538062i
$141$		−	5.33646i		−	0.449411i
$142$	8.08532			0.678505
$143$	2.06559			0.172733
$144$	1.00000			0.0833333
$145$	−21.7275			−1.80437
$146$	−13.5144			−1.11846
$147$	5.89943	+	3.76785i	0.486577	+	0.310767i
$148$			1.68285i			0.138330i
$149$	−9.33082			−0.764410			−0.382205	−	0.924077i	$-0.624835\pi$
$149$	−9.33082			−0.764410			−0.382205	+	0.924077i	$0.624835\pi$
$150$		−	1.28423i		−	0.104857i
$151$			7.62713i			0.620687i	0.950624	+	0.310344i	$0.100444\pi$
$151$			7.62713i			0.620687i	−0.950624	+	0.310344i	$0.899556\pi$
$152$	−0.709018	+	4.30085i	−0.0575089	+	0.348845i
$153$			2.30760i			0.186559i
$154$	−3.02321	+	10.3501i	−0.243618	+	0.834038i
$155$			3.50056i			0.281171i
$156$	0.506836			0.0405794
$157$		−	13.0191i		−	1.03904i	−0.854458	−	0.519520i	$-0.826111\pi$
$157$		−	13.0191i		−	1.03904i	0.854458	−	0.519520i	$-0.173889\pi$
$158$	3.37893			0.268813
$159$		−	1.66122i		−	0.131744i
$160$	2.50684			0.198183
$161$	16.1019	+	4.70328i	1.26901	+	0.370671i
$162$			1.00000i			0.0785674i
$163$	−4.37938			−0.343020			−0.171510	−	0.985182i	$-0.554865\pi$
$163$	−4.37938			−0.343020			−0.171510	+	0.985182i	$0.554865\pi$
$164$	0.402139			0.0314018
$165$			10.2165i			0.795353i
$166$	10.5106			0.815777
$167$	−2.29406			−0.177520			−0.0887600	−	0.996053i	$-0.528290\pi$
$167$	−2.29406			−0.177520			−0.0887600	+	0.996053i	$0.528290\pi$
$168$	−0.741811	+	2.53963i	−0.0572319	+	0.195937i
$169$	−12.7431			−0.980240
$170$			5.78478i			0.443673i
$171$	−4.30085	−	0.709018i	−0.328894	−	0.0542199i
$172$	6.73509			0.513546
$173$	22.4568			1.70736			0.853681	−	0.520797i	$-0.174365\pi$
$173$	22.4568			1.70736			0.853681	+	0.520797i	$0.174365\pi$
$174$	8.66728			0.657065
$175$	3.26146	+	0.952654i	0.246543	+	0.0720139i
$176$	−4.07545			−0.307199
$177$	9.42907			0.708732
$178$			11.7389i			0.879870i
$179$			12.0887i			0.903555i	0.892131	+	0.451777i	$0.149210\pi$
$179$			12.0887i			0.903555i	−0.892131	+	0.451777i	$0.850790\pi$
$180$			2.50684i			0.186849i
$181$	−14.6113			−1.08605			−0.543025	−	0.839716i	$-0.682721\pi$
$181$	−14.6113			−1.08605			−0.543025	+	0.839716i	$0.682721\pi$
$182$	−0.375977	+	1.28718i	−0.0278692	+	0.0954118i
$183$			5.31706i			0.393048i
$184$			6.34027i			0.467411i
$185$	−4.21864			−0.310161
$186$		−	1.39640i		−	0.102389i
$187$		−	9.40453i		−	0.687727i
$188$			5.33646i			0.389202i
$189$	−2.53963	−	0.741811i	−0.184731	−	0.0539588i
$190$	−10.7815	−	1.77739i	−0.782174	−	0.128946i
$191$	0.142938			0.0103427			0.00517133	−	0.999987i	$-0.498354\pi$
$191$	0.142938			0.0103427			0.00517133	+	0.999987i	$0.498354\pi$
$192$	−1.00000			−0.0721688
$193$			5.94006i			0.427575i	0.976880	+	0.213787i	$0.0685800\pi$
$193$			5.94006i			0.427575i	−0.976880	+	0.213787i	$0.931420\pi$
$194$			4.87048i			0.349680i
$195$			1.27056i			0.0909863i
$196$	−5.89943	−	3.76785i	−0.421388	−	0.269132i
$197$	9.50252			0.677027			0.338513	−	0.940962i	$-0.390076\pi$
$197$	9.50252			0.677027			0.338513	+	0.940962i	$0.390076\pi$
$198$		−	4.07545i		−	0.289630i
$199$			23.3287i			1.65373i	0.562404	+	0.826863i	$0.309877\pi$
$199$			23.3287i			1.65373i	−0.562404	+	0.826863i	$0.690123\pi$
$200$			1.28423i			0.0908086i
$201$		−	3.06939i		−	0.216498i
$202$	10.8277			0.761836
$203$	−6.42948	+	22.0117i	−0.451261	+	1.54492i
$204$		−	2.30760i		−	0.161565i
$205$			1.00810i			0.0704086i
$206$			5.51407i			0.384183i
$207$	−6.34027			−0.440679
$208$	−0.506836			−0.0351428
$209$	17.5279	+	2.88957i	1.21243	+	0.199876i
$210$	−6.36643	−	1.85960i	−0.439326	−	0.128324i
$211$		−	23.1860i		−	1.59619i	−0.602532	−	0.798095i	$-0.705841\pi$
$211$		−	23.1860i		−	1.59619i	0.602532	−	0.798095i	$-0.294159\pi$
$212$			1.66122i			0.114093i
$213$		−	8.08532i		−	0.553997i
$214$	1.64796			0.112652
$215$			16.8838i			1.15146i
$216$		−	1.00000i		−	0.0680414i
$217$	3.54635	+	1.03587i	0.240742	+	0.0703193i
$218$	−18.0910			−1.22528
$219$			13.5144i			0.913218i
$220$		−	10.2165i		−	0.688796i
$221$		−	1.16958i		−	0.0786742i
$222$	1.68285			0.112946
$223$	23.0366			1.54264			0.771322	−	0.636446i	$-0.219596\pi$
$223$	23.0366			1.54264			0.771322	+	0.636446i	$0.219596\pi$
$224$	0.741811	−	2.53963i	0.0495643	−	0.169686i
$225$	−1.28423			−0.0856152
$226$	2.33655			0.155425
$227$	−17.6866			−1.17390			−0.586951	−	0.809623i	$-0.699672\pi$
$227$	−17.6866			−1.17390			−0.586951	+	0.809623i	$0.699672\pi$
$228$	4.30085	+	0.709018i	0.284831	+	0.0469558i
$229$		−	3.87815i		−	0.256275i	−0.991756	−	0.128138i	$-0.959100\pi$
$229$		−	3.87815i		−	0.256275i	0.991756	−	0.128138i	$-0.0408999\pi$
$230$	−15.8940			−1.04802
$231$	10.3501	+	3.02321i	0.680989	+	0.198913i
$232$	−8.66728			−0.569035
$233$	−21.9618			−1.43877			−0.719384	−	0.694613i	$-0.755576\pi$
$233$	−21.9618			−1.43877			−0.719384	+	0.694613i	$0.755576\pi$
$234$		−	0.506836i		−	0.0331329i
$235$	−13.3776			−0.872661
$236$	−9.42907			−0.613780
$237$		−	3.37893i		−	0.219485i
$238$	5.86046	+	1.71180i	0.379877	+	0.110960i
$239$	−5.77182			−0.373348			−0.186674	−	0.982422i	$-0.559771\pi$
$239$	−5.77182			−0.373348			−0.186674	+	0.982422i	$0.559771\pi$
$240$		−	2.50684i		−	0.161816i
$241$	−10.8837			−0.701079			−0.350539	−	0.936548i	$-0.614002\pi$
$241$	−10.8837			−0.701079			−0.350539	+	0.936548i	$0.614002\pi$
$242$			5.60931i			0.360580i
$243$	1.00000			0.0641500
$244$		−	5.31706i		−	0.340390i
$245$	9.44538	−	14.7889i	0.603443	−	0.944829i
$246$		−	0.402139i		−	0.0256395i
$247$	2.17983	+	0.359356i	0.138699	+	0.0228653i
$248$			1.39640i			0.0886717i
$249$		−	10.5106i		−	0.666079i
$250$	9.31483			0.589122
$251$			23.2434i			1.46711i	0.679629	+	0.733556i	$0.262141\pi$
$251$			23.2434i			1.46711i	−0.679629	+	0.733556i	$0.737859\pi$
$252$	2.53963	+	0.741811i	0.159982	+	0.0467297i
$253$	25.8395			1.62451
$254$	1.29418			0.0812042
$255$	5.78478			0.362257
$256$	1.00000			0.0625000
$257$	29.4331			1.83599			0.917995	−	0.396593i	$-0.129808\pi$
$257$	29.4331			1.83599			0.917995	+	0.396593i	$0.129808\pi$
$258$		−	6.73509i		−	0.419309i
$259$	−1.24836	+	4.27383i	−0.0775693	+	0.265563i
$260$		−	1.27056i		−	0.0787965i
$261$		−	8.66728i		−	0.536491i
$262$	4.38528			0.270923
$263$	−9.57036			−0.590134			−0.295067	−	0.955477i	$-0.595342\pi$
$263$	−9.57036			−0.590134			−0.295067	+	0.955477i	$0.595342\pi$
$264$			4.07545i			0.250827i
$265$	−4.16441			−0.255818
$266$	−4.99106	+	10.3966i	−0.306021	+	0.637457i
$267$	11.7389			0.718411
$268$			3.06939i			0.187493i
$269$	−20.3251			−1.23924			−0.619621	−	0.784901i	$-0.712714\pi$
$269$	−20.3251			−1.23924			−0.619621	+	0.784901i	$0.712714\pi$
$270$	2.50684			0.152561
$271$		−	27.0034i		−	1.64034i	−0.572120	−	0.820170i	$-0.693879\pi$
$271$		−	27.0034i		−	1.64034i	0.572120	−	0.820170i	$-0.306121\pi$
$272$			2.30760i			0.139919i
$273$	1.28718	+	0.375977i	0.0779034	+	0.0227551i
$274$		−	17.3945i		−	1.05084i
$275$	5.23381			0.315610
$276$	6.34027			0.381639
$277$	1.93416			0.116213			0.0581063	−	0.998310i	$-0.481494\pi$
$277$	1.93416			0.116213			0.0581063	+	0.998310i	$0.481494\pi$
$278$	4.29012			0.257305
$279$	−1.39640			−0.0836005
$280$	6.36643	+	1.85960i	0.380467	+	0.111132i
$281$		−	26.0581i		−	1.55450i	−0.629194	−	0.777248i	$-0.716615\pi$
$281$		−	26.0581i		−	1.55450i	0.629194	−	0.777248i	$-0.283385\pi$
$282$	5.33646			0.317782
$283$			20.4608i			1.21627i	0.793835	+	0.608133i	$0.208081\pi$
$283$			20.4608i			1.21627i	−0.793835	+	0.608133i	$0.791919\pi$
$284$			8.08532i			0.479775i
$285$	−1.77739	+	10.7815i	−0.105284	+	0.638642i
$286$			2.06559i			0.122141i
$287$	1.02129	+	0.298311i	0.0602846	+	0.0176088i
$288$			1.00000i			0.0589256i
$289$	11.6750			0.686763
$290$		−	21.7275i		−	1.27588i
$291$	4.87048			0.285513
$292$		−	13.5144i		−	0.790870i
$293$	−16.4410			−0.960495			−0.480248	−	0.877133i	$-0.659453\pi$
$293$	−16.4410			−0.960495			−0.480248	+	0.877133i	$0.659453\pi$
$294$	−3.76785	+	5.89943i	−0.219745	+	0.344062i
$295$		−	23.6371i		−	1.37621i
$296$	−1.68285			−0.0978139
$297$	−4.07545			−0.236482
$298$		−	9.33082i		−	0.540520i
$299$	3.21348			0.185840
$300$	1.28423			0.0741449
$301$	17.1046	+	4.99616i	0.985895	+	0.287974i
$302$	−7.62713			−0.438892
$303$		−	10.8277i		−	0.622037i
$304$	−4.30085	−	0.709018i	−0.246671	−	0.0406650i
$305$	13.3290			0.763216
$306$	−2.30760			−0.131917
$307$	−8.09858			−0.462210			−0.231105	−	0.972929i	$-0.574234\pi$
$307$	−8.09858			−0.462210			−0.231105	+	0.972929i	$0.574234\pi$
$308$	−10.3501	−	3.02321i	−0.589754	−	0.172264i
$309$	5.51407			0.313684
$310$	−3.50056			−0.198818
$311$		−	8.87438i		−	0.503220i	−0.967829	−	0.251610i	$-0.919040\pi$
$311$		−	8.87438i		−	0.503220i	0.967829	−	0.251610i	$-0.0809600\pi$
$312$			0.506836i			0.0286939i
$313$			22.9535i			1.29741i	0.761039	+	0.648706i	$0.224689\pi$
$313$			22.9535i			1.29741i	−0.761039	+	0.648706i	$0.775311\pi$
$314$	13.0191			0.734712
$315$	−1.85960	+	6.36643i	−0.104776	+	0.358708i
$316$			3.37893i			0.190079i
$317$			19.9885i			1.12267i	0.827589	+	0.561334i	$0.189712\pi$
$317$			19.9885i			1.12267i	−0.827589	+	0.561334i	$0.810288\pi$
$318$	1.66122			0.0931568
$319$			35.3231i			1.97771i
$320$			2.50684i			0.140136i
$321$		−	1.64796i		−	0.0919803i
$322$	−4.70328	+	16.1019i	−0.262104	+	0.897326i
$323$	1.63613	−	9.92465i	0.0910368	−	0.552222i
$324$	−1.00000			−0.0555556
$325$	0.650893			0.0361050
$326$		−	4.37938i		−	0.242552i
$327$			18.0910i			1.00044i
$328$			0.402139i			0.0222044i
$329$	−3.95865	+	13.5526i	−0.218247	+	0.747181i
$330$	−10.2165			−0.562399
$331$		−	19.4117i		−	1.06697i	−0.845811	−	0.533483i	$-0.820883\pi$
$331$		−	19.4117i		−	1.06697i	0.845811	−	0.533483i	$-0.179117\pi$
$332$			10.5106i			0.576842i
$333$		−	1.68285i		−	0.0922199i
$334$		−	2.29406i		−	0.125526i
$335$	−7.69446			−0.420394
$336$	−2.53963	−	0.741811i	−0.138548	−	0.0404691i
$337$			26.3229i			1.43390i	0.697124	+	0.716951i	$0.254463\pi$
$337$			26.3229i			1.43390i	−0.697124	+	0.716951i	$0.745537\pi$
$338$		−	12.7431i		−	0.693134i
$339$		−	2.33655i		−	0.126904i
$340$	−5.78478			−0.313724
$341$	5.69098			0.308184
$342$	0.709018	−	4.30085i	0.0383393	−	0.232563i
$343$	−12.1873	−	13.9452i	−0.658055	−	0.752970i
$344$			6.73509i			0.363132i
$345$			15.8940i			0.855705i
$346$			22.4568i			1.20729i
$347$	−6.55866			−0.352087			−0.176044	−	0.984382i	$-0.556330\pi$
$347$	−6.55866			−0.352087			−0.176044	+	0.984382i	$0.556330\pi$
$348$			8.66728i			0.464615i
$349$		−	28.8644i		−	1.54508i	−0.634968	−	0.772539i	$-0.718987\pi$
$349$		−	28.8644i		−	1.54508i	0.634968	−	0.772539i	$-0.281013\pi$
$350$	−0.952654	+	3.26146i	−0.0509215	+	0.174332i
$351$	−0.506836			−0.0270529
$352$		−	4.07545i		−	0.217222i
$353$		−	34.6309i		−	1.84321i	−0.388124	−	0.921607i	$-0.626877\pi$
$353$		−	34.6309i		−	1.84321i	0.388124	−	0.921607i	$-0.373123\pi$
$354$			9.42907i			0.501150i
$355$	−20.2686			−1.07574
$356$	−11.7389			−0.622162
$357$	1.71180	−	5.86046i	0.0905983	−	0.310168i
$358$	−12.0887			−0.638910
$359$	11.1407			0.587983			0.293992	−	0.955808i	$-0.405016\pi$
$359$	11.1407			0.587983			0.293992	+	0.955808i	$0.405016\pi$
$360$	−2.50684			−0.132122
$361$	17.9946	+	6.09875i	0.947084	+	0.320987i
$362$		−	14.6113i		−	0.767953i
$363$	5.60931			0.294412
$364$	−1.28718	−	0.375977i	−0.0674663	−	0.0197065i
$365$	33.8784			1.77327
$366$	−5.31706			−0.277927
$367$			11.0195i			0.575213i	0.957749	+	0.287607i	$0.0928595\pi$
$367$			11.0195i			0.575213i	−0.957749	+	0.287607i	$0.907140\pi$
$368$	−6.34027			−0.330509
$369$	−0.402139			−0.0209345
$370$		−	4.21864i		−	0.219317i
$371$	−1.23231	+	4.21889i	−0.0639785	+	0.219034i
$372$	1.39640			0.0724002
$373$		−	27.0191i		−	1.39900i	−0.714634	−	0.699499i	$-0.753407\pi$
$373$		−	27.0191i		−	1.39900i	0.714634	−	0.699499i	$-0.246593\pi$
$374$	9.40453			0.486296
$375$		−	9.31483i		−	0.481016i
$376$	−5.33646			−0.275207
$377$			4.39289i			0.226245i
$378$	0.741811	−	2.53963i	0.0381546	−	0.130624i
$379$		−	24.9769i		−	1.28298i	−0.767133	−	0.641488i	$-0.778318\pi$
$379$		−	24.9769i		−	1.28298i	0.767133	−	0.641488i	$-0.221682\pi$
$380$	1.77739	−	10.7815i	0.0911782	−	0.553080i
$381$		−	1.29418i		−	0.0663029i
$382$			0.142938i			0.00731337i
$383$	−12.4870			−0.638057			−0.319029	−	0.947745i	$-0.603357\pi$
$383$	−12.4870			−0.638057			−0.319029	+	0.947745i	$0.603357\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	7.57870	−	25.9461i	0.386246	−	1.32234i
$386$	−5.94006			−0.302341
$387$	−6.73509			−0.342364
$388$	−4.87048			−0.247261
$389$	31.4241			1.59327			0.796634	−	0.604462i	$-0.206612\pi$
$389$	31.4241			1.59327			0.796634	+	0.604462i	$0.206612\pi$
$390$	−1.27056			−0.0643371
$391$		−	14.6308i		−	0.739913i
$392$	3.76785	−	5.89943i	0.190305	−	0.297966i
$393$		−	4.38528i		−	0.221208i
$394$			9.50252i			0.478730i
$395$	−8.47041			−0.426193
$396$	4.07545			0.204799
$397$		−	37.1197i		−	1.86299i	−0.363759	−	0.931493i	$-0.618507\pi$
$397$		−	37.1197i		−	1.86299i	0.363759	−	0.931493i	$-0.381493\pi$
$398$	−23.3287			−1.16936
$399$	10.3966	+	4.99106i	0.520481	+	0.249865i
$400$	−1.28423			−0.0642114
$401$		−	38.8566i		−	1.94041i	−0.242289	−	0.970204i	$-0.577898\pi$
$401$		−	38.8566i		−	1.94041i	0.242289	−	0.970204i	$-0.422102\pi$
$402$	3.06939			0.153087
$403$	0.707748			0.0352554
$404$			10.8277i			0.538700i
$405$		−	2.50684i		−	0.124566i
$406$	−22.0117	−	6.42948i	−1.09242	−	0.319090i
$407$			6.85839i			0.339958i
$408$	2.30760			0.114243
$409$	9.77207			0.483198			0.241599	−	0.970376i	$-0.422328\pi$
$409$	9.77207			0.483198			0.241599	+	0.970376i	$0.422328\pi$
$410$	−1.00810			−0.0497864
$411$	−17.3945			−0.858008
$412$	−5.51407			−0.271659
$413$	−23.9463	−	6.99459i	−1.17832	−	0.344181i
$414$		−	6.34027i		−	0.311607i
$415$	−26.3482			−1.29338
$416$		−	0.506836i		−	0.0248497i
$417$		−	4.29012i		−	0.210088i
$418$	−2.88957	+	17.5279i	−0.141333	+	0.857318i
$419$			30.2647i			1.47853i	0.673416	+	0.739264i	$0.264826\pi$
$419$			30.2647i			1.47853i	−0.673416	+	0.739264i	$0.735174\pi$
$420$	1.85960	−	6.36643i	0.0907391	−	0.310650i
$421$		−	21.7967i		−	1.06231i	−0.847276	−	0.531153i	$-0.821759\pi$
$421$		−	21.7967i		−	1.06231i	0.847276	−	0.531153i	$-0.178241\pi$
$422$	23.1860			1.12868
$423$		−	5.33646i		−	0.259468i
$424$	−1.66122			−0.0806761
$425$		−	2.96349i		−	0.143750i
$426$	8.08532			0.391735
$427$	3.94425	−	13.5034i	0.190876	−	0.653473i
$428$			1.64796i			0.0796573i
$429$	2.06559			0.0997274
$430$	−16.8838			−0.814208
$431$		−	31.4075i		−	1.51285i	−0.654082	−	0.756423i	$-0.726945\pi$
$431$		−	31.4075i		−	1.51285i	0.654082	−	0.756423i	$-0.273055\pi$
$432$	1.00000			0.0481125
$433$	−13.5121			−0.649348			−0.324674	−	0.945826i	$-0.605255\pi$
$433$	−13.5121			−0.649348			−0.324674	+	0.945826i	$0.605255\pi$
$434$	−1.03587	+	3.54635i	−0.0497232	+	0.170230i
$435$	−21.7275			−1.04175
$436$		−	18.0910i		−	0.866403i
$437$	27.2685	+	4.49536i	1.30443	+	0.215042i
$438$	−13.5144			−0.645743
$439$	26.4310			1.26148			0.630742	−	0.775993i	$-0.282751\pi$
$439$	26.4310			1.26148			0.630742	+	0.775993i	$0.282751\pi$
$440$	10.2165			0.487052
$441$	5.89943	+	3.76785i	0.280925	+	0.179421i
$442$	1.16958			0.0556311
$443$	−27.7520			−1.31854			−0.659269	−	0.751907i	$-0.729134\pi$
$443$	−27.7520			−1.31854			−0.659269	+	0.751907i	$0.729134\pi$
$444$			1.68285i			0.0798648i
$445$		−	29.4276i		−	1.39500i
$446$			23.0366i			1.09081i
$447$	−9.33082			−0.441333
$448$	2.53963	+	0.741811i	0.119986	+	0.0350473i
$449$		−	15.1061i		−	0.712900i	−0.934314	−	0.356450i	$-0.883987\pi$
$449$		−	15.1061i		−	0.712900i	0.934314	−	0.356450i	$-0.116013\pi$
$450$		−	1.28423i		−	0.0605391i
$451$	1.63890			0.0771728
$452$			2.33655i			0.109902i
$453$			7.62713i			0.358354i
$454$		−	17.6866i		−	0.830073i
$455$	0.942512	−	3.22674i	0.0441856	−	0.151272i
$456$	−0.709018	+	4.30085i	−0.0332028	+	0.201406i
$457$	−20.9766			−0.981245			−0.490623	−	0.871372i	$-0.663231\pi$
$457$	−20.9766			−0.981245			−0.490623	+	0.871372i	$0.663231\pi$
$458$	3.87815			0.181214
$459$			2.30760i			0.107710i
$460$		−	15.8940i		−	0.741063i
$461$		−	7.85663i		−	0.365920i	−0.983120	−	0.182960i	$-0.941432\pi$
$461$		−	7.85663i		−	0.365920i	0.983120	−	0.182960i	$-0.0585678\pi$
$462$	−3.02321	+	10.3501i	−0.140653	+	0.481532i
$463$	12.6622			0.588463			0.294231	−	0.955734i	$-0.404936\pi$
$463$	12.6622			0.588463			0.294231	+	0.955734i	$0.404936\pi$
$464$		−	8.66728i		−	0.402368i
$465$			3.50056i			0.162334i
$466$		−	21.9618i		−	1.01736i
$467$			8.29420i			0.383810i	0.981414	+	0.191905i	$0.0614665\pi$
$467$			8.29420i			0.383810i	−0.981414	+	0.191905i	$0.938534\pi$
$468$	0.506836			0.0234285
$469$	−2.27691	+	7.79512i	−0.105138	+	0.359945i
$470$		−	13.3776i		−	0.617065i
$471$		−	13.0191i		−	0.599890i
$472$		−	9.42907i		−	0.434008i
$473$	27.4485			1.26209
$474$	3.37893			0.155199
$475$	5.52327	+	0.910540i	0.253425	+	0.0417784i
$476$	−1.71180	+	5.86046i	−0.0784605	+	0.268614i
$477$		−	1.66122i		−	0.0760622i
$478$		−	5.77182i		−	0.263997i
$479$		−	3.93055i		−	0.179591i	−0.995960	−	0.0897957i	$-0.971379\pi$
$479$		−	3.93055i		−	0.179591i	0.995960	−	0.0897957i	$-0.0286214\pi$
$480$	2.50684			0.114421
$481$			0.852932i			0.0388903i
$482$		−	10.8837i		−	0.495738i
$483$	16.1019	+	4.70328i	0.732664	+	0.214007i
$484$	−5.60931			−0.254969
$485$		−	12.2095i		−	0.554405i
$486$			1.00000i			0.0453609i
$487$			19.0464i			0.863077i	0.902095	+	0.431538i	$0.142029\pi$
$487$			19.0464i			0.863077i	−0.902095	+	0.431538i	$0.857971\pi$
$488$	5.31706			0.240692
$489$	−4.37938			−0.198042
$490$	14.7889	+	9.44538i	0.668095	+	0.426699i
$491$	19.5088			0.880419			0.440209	−	0.897895i	$-0.354904\pi$
$491$	19.5088			0.880419			0.440209	+	0.897895i	$0.354904\pi$
$492$	0.402139			0.0181298
$493$	20.0006			0.900784
$494$	−0.359356	+	2.17983i	−0.0161682	+	0.0980750i
$495$			10.2165i			0.459197i
$496$	−1.39640			−0.0627004
$497$	−5.99778	+	20.5337i	−0.269037	+	0.921063i
$498$	10.5106			0.470989
$499$	−14.9906			−0.671074			−0.335537	−	0.942027i	$-0.608918\pi$
$499$	−14.9906			−0.671074			−0.335537	+	0.942027i	$0.608918\pi$
$500$			9.31483i			0.416572i
$501$	−2.29406			−0.102491
$502$	−23.2434			−1.03740
$503$			3.32055i			0.148056i	0.997256	+	0.0740279i	$0.0235854\pi$
$503$			3.32055i			0.148056i	−0.997256	+	0.0740279i	$0.976415\pi$
$504$	−0.741811	+	2.53963i	−0.0330429	+	0.113124i
$505$	−27.1433			−1.20786
$506$			25.8395i			1.14870i
$507$	−12.7431			−0.565942
$508$			1.29418i			0.0574200i
$509$	−7.68285			−0.340537			−0.170268	−	0.985398i	$-0.554463\pi$
$509$	−7.68285			−0.340537			−0.170268	+	0.985398i	$0.554463\pi$
$510$			5.78478i			0.256154i
$511$	10.0251	−	34.3215i	0.443485	−	1.51830i
$512$			1.00000i			0.0441942i
$513$	−4.30085	−	0.709018i	−0.189887	−	0.0313039i
$514$			29.4331i			1.29824i
$515$		−	13.8229i		−	0.609108i
$516$	6.73509			0.296496
$517$			21.7485i			0.956498i
$518$	−4.27383	−	1.24836i	−0.187781	−	0.0548498i
$519$	22.4568			0.985745
$520$	1.27056			0.0557175
$521$	37.1281			1.62661			0.813306	−	0.581836i	$-0.197665\pi$
$521$	37.1281			1.62661			0.813306	+	0.581836i	$0.197665\pi$
$522$	8.66728			0.379357
$523$	−24.7335			−1.08152			−0.540761	−	0.841177i	$-0.681863\pi$
$523$	−24.7335			−1.08152			−0.540761	+	0.841177i	$0.681863\pi$
$524$			4.38528i			0.191572i
$525$	3.26146	+	0.952654i	0.142342	+	0.0415772i
$526$		−	9.57036i		−	0.417288i
$527$		−	3.22235i		−	0.140368i
$528$	−4.07545			−0.177361
$529$	17.1990			0.747784
$530$		−	4.16441i		−	0.180891i
$531$	9.42907			0.409187
$532$	−10.3966	−	4.99106i	−0.450750	−	0.216390i
$533$	0.203819			0.00882837
$534$			11.7389i			0.507993i
$535$	−4.13117			−0.178606
$536$	−3.06939			−0.132578
$537$			12.0887i			0.521668i
$538$		−	20.3251i		−	0.876276i
$539$	−24.0429	−	15.3557i	−1.03560	−	0.661416i
$540$			2.50684i			0.107877i
$541$	−32.9110			−1.41496			−0.707478	−	0.706735i	$-0.750167\pi$
$541$	−32.9110			−1.41496			−0.707478	+	0.706735i	$0.750167\pi$
$542$	27.0034			1.15990
$543$	−14.6113			−0.627031
$544$	−2.30760			−0.0989377
$545$	45.3512			1.94263
$546$	−0.375977	+	1.28718i	−0.0160903	+	0.0550860i
$547$			41.6086i			1.77905i	0.456883	+	0.889527i	$0.348966\pi$
$547$			41.6086i			1.77905i	−0.456883	+	0.889527i	$0.651034\pi$
$548$	17.3945			0.743056
$549$			5.31706i			0.226926i
$550$			5.23381i			0.223170i
$551$	−6.14526	+	37.2767i	−0.261797	+	1.58804i
$552$			6.34027i			0.269860i
$553$	−2.50652	+	8.58122i	−0.106588	+	0.364910i
$554$			1.93416i			0.0821748i
$555$	−4.21864			−0.179071
$556$			4.29012i			0.181942i
$557$	−8.31329			−0.352245			−0.176123	−	0.984368i	$-0.556356\pi$
$557$	−8.31329			−0.352245			−0.176123	+	0.984368i	$0.556356\pi$
$558$		−	1.39640i		−	0.0591145i
$559$	3.41359			0.144379
$560$	−1.85960	+	6.36643i	−0.0785824	+	0.269031i
$561$		−	9.40453i		−	0.397059i
$562$	26.0581			1.09920
$563$	8.97656			0.378317			0.189159	−	0.981947i	$-0.439424\pi$
$563$	8.97656			0.378317			0.189159	+	0.981947i	$0.439424\pi$
$564$			5.33646i			0.224706i
$565$	−5.85736			−0.246421
$566$	−20.4608			−0.860030
$567$	−2.53963	−	0.741811i	−0.106654	−	0.0311531i
$568$	−8.08532			−0.339252
$569$			33.0391i			1.38507i	0.721383	+	0.692536i	$0.243507\pi$
$569$			33.0391i			1.38507i	−0.721383	+	0.692536i	$0.756493\pi$
$570$	−10.7815	−	1.77739i	−0.451588	−	0.0744467i
$571$	−21.4576			−0.897973			−0.448987	−	0.893538i	$-0.648215\pi$
$571$	−21.4576			−0.897973			−0.448987	+	0.893538i	$0.648215\pi$
$572$	−2.06559			−0.0863665
$573$	0.142938			0.00597134
$574$	−0.298311	+	1.02129i	−0.0124513	+	0.0426276i
$575$	8.14235			0.339559
$576$	−1.00000			−0.0416667
$577$		−	22.0341i		−	0.917293i	−0.888619	−	0.458646i	$-0.848334\pi$
$577$		−	22.0341i		−	0.917293i	0.888619	−	0.458646i	$-0.151666\pi$
$578$			11.6750i			0.485615i
$579$			5.94006i			0.246861i
$580$	21.7275			0.902184
$581$	−7.79684	+	26.6929i	−0.323468	+	1.10741i
$582$			4.87048i			0.201888i
$583$			6.77023i			0.280394i
$584$	13.5144			0.559229
$585$			1.27056i			0.0525310i
$586$		−	16.4410i		−	0.679173i
$587$		−	47.5397i		−	1.96217i	−0.193573	−	0.981086i	$-0.562008\pi$
$587$		−	47.5397i		−	1.96217i	0.193573	−	0.981086i	$-0.437992\pi$
$588$	−5.89943	−	3.76785i	−0.243289	−	0.155383i
$589$	6.00572	+	0.990075i	0.247461	+	0.0407953i
$590$	23.6371			0.973126
$591$	9.50252			0.390882
$592$		−	1.68285i		−	0.0691649i
$593$			36.0330i			1.47970i	0.672774	+	0.739848i	$0.265103\pi$
$593$			36.0330i			1.47970i	−0.672774	+	0.739848i	$0.734897\pi$
$594$		−	4.07545i		−	0.167218i
$595$	−14.6912	−	4.29121i	−0.602281	−	0.175923i
$596$	9.33082			0.382205
$597$			23.3287i			0.954779i
$598$			3.21348i			0.131409i
$599$			19.8527i			0.811161i	0.914059	+	0.405580i	$0.132931\pi$
$599$			19.8527i			0.811161i	−0.914059	+	0.405580i	$0.867069\pi$
$600$			1.28423i			0.0524284i
$601$	−32.8582			−1.34032			−0.670158	−	0.742219i	$-0.733774\pi$
$601$	−32.8582			−1.34032			−0.670158	+	0.742219i	$0.733774\pi$
$602$	−4.99616	+	17.1046i	−0.203628	+	0.697133i
$603$		−	3.06939i		−	0.124995i
$604$		−	7.62713i		−	0.310344i
$605$		−	14.0616i		−	0.571686i
$606$	10.8277			0.439846
$607$	16.9412			0.687621			0.343810	−	0.939039i	$-0.388282\pi$
$607$	16.9412			0.687621			0.343810	+	0.939039i	$0.388282\pi$
$608$	0.709018	−	4.30085i	0.0287545	−	0.174422i
$609$	−6.42948	+	22.0117i	−0.260536	+	0.891958i
$610$			13.3290i			0.539675i
$611$			2.70471i			0.109421i
$612$		−	2.30760i		−	0.0932793i
$613$	15.2574			0.616242			0.308121	−	0.951347i	$-0.400300\pi$
$613$	15.2574			0.616242			0.308121	+	0.951347i	$0.400300\pi$
$614$		−	8.09858i		−	0.326832i
$615$			1.00810i			0.0406504i
$616$	3.02321	−	10.3501i	0.121809	−	0.417019i
$617$	−46.9250			−1.88913			−0.944564	−	0.328328i	$-0.893515\pi$
$617$	−46.9250			−1.88913			−0.944564	+	0.328328i	$0.893515\pi$
$618$			5.51407i			0.221808i
$619$		−	8.50433i		−	0.341818i	−0.985287	−	0.170909i	$-0.945330\pi$
$619$		−	8.50433i		−	0.341818i	0.985287	−	0.170909i	$-0.0546704\pi$
$620$		−	3.50056i		−	0.140586i
$621$	−6.34027			−0.254426
$622$	8.87438			0.355830
$623$	−29.8125	−	8.70806i	−1.19441	−	0.348881i
$624$	−0.506836			−0.0202897
$625$	−29.7719			−1.19088
$626$	−22.9535			−0.917408
$627$	17.5279	+	2.88957i	0.699997	+	0.115398i
$628$			13.0191i			0.519520i
$629$	3.88336			0.154840
$630$	−6.36643	−	1.85960i	−0.253645	−	0.0740882i
$631$	43.6369			1.73716			0.868579	−	0.495552i	$-0.165034\pi$
$631$	43.6369			1.73716			0.868579	+	0.495552i	$0.165034\pi$
$632$	−3.37893			−0.134406
$633$		−	23.1860i		−	0.921560i
$634$	−19.9885			−0.793846
$635$	−3.24430			−0.128746
$636$			1.66122i			0.0658718i
$637$	−2.99005	−	1.90968i	−0.118470	−	0.0756644i
$638$	−35.3231			−1.39845
$639$		−	8.08532i		−	0.319850i
$640$	−2.50684			−0.0990914
$641$			16.0386i			0.633488i	0.948511	+	0.316744i	$0.102590\pi$
$641$			16.0386i			0.633488i	−0.948511	+	0.316744i	$0.897410\pi$
$642$	1.64796			0.0650399
$643$			36.3835i			1.43482i	0.696649	+	0.717412i	$0.254673\pi$
$643$			36.3835i			1.43482i	−0.696649	+	0.717412i	$0.745327\pi$
$644$	−16.1019	−	4.70328i	−0.634505	−	0.185335i
$645$			16.8838i			0.664798i
$646$	9.92465	+	1.63613i	0.390480	+	0.0643727i
$647$			31.7012i			1.24630i	0.782101	+	0.623151i	$0.214148\pi$
$647$			31.7012i			1.24630i	−0.782101	+	0.623151i	$0.785852\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−38.4277			−1.50842
$650$			0.650893i			0.0255301i
$651$	3.54635	+	1.03587i	0.138992	+	0.0405988i
$652$	4.37938			0.171510
$653$	4.26096			0.166744			0.0833721	−	0.996518i	$-0.473431\pi$
$653$	4.26096			0.166744			0.0833721	+	0.996518i	$0.473431\pi$
$654$	−18.0910			−0.707415
$655$	−10.9932			−0.429539
$656$	−0.402139			−0.0157009
$657$			13.5144i			0.527247i
$658$	−13.5526	−	3.95865i	−0.528337	−	0.154324i
$659$		−	0.0621626i		−	0.00242151i	−0.999999	−	0.00121076i	$-0.999615\pi$
$659$		−	0.0621626i		−	0.00242151i	0.999999	−	0.00121076i	$-0.000385395\pi$
$660$		−	10.2165i		−	0.397676i
$661$	16.2637			0.632585			0.316293	−	0.948662i	$-0.397562\pi$
$661$	16.2637			0.632585			0.316293	+	0.948662i	$0.397562\pi$
$662$	19.4117			0.754458
$663$		−	1.16958i		−	0.0454226i
$664$	−10.5106			−0.407889
$665$	12.5118	−	26.0626i	0.485185	−	1.01066i
$666$	1.68285			0.0652093
$667$			54.9529i			2.12779i
$668$	2.29406			0.0887600
$669$	23.0366			0.890646
$670$		−	7.69446i		−	0.297263i
$671$		−	21.6694i		−	0.836538i
$672$	0.741811	−	2.53963i	0.0286160	−	0.0979683i
$673$			5.20897i			0.200791i	0.994948	+	0.100395i	$0.0320108\pi$
$673$			5.20897i			0.200791i	−0.994948	+	0.100395i	$0.967989\pi$
$674$	−26.3229			−1.01392
$675$	−1.28423			−0.0494299
$676$	12.7431			0.490120
$677$	40.7978			1.56799			0.783993	−	0.620770i	$-0.213180\pi$
$677$	40.7978			1.56799			0.783993	+	0.620770i	$0.213180\pi$
$678$	2.33655			0.0897348
$679$	−12.3692	−	3.61298i	−0.474687	−	0.138653i
$680$		−	5.78478i		−	0.221836i
$681$	−17.6866			−0.677752
$682$			5.69098i			0.217919i
$683$		−	9.91494i		−	0.379385i	−0.981844	−	0.189692i	$-0.939251\pi$
$683$		−	9.91494i		−	0.379385i	0.981844	−	0.189692i	$-0.0607491\pi$
$684$	4.30085	+	0.709018i	0.164447	+	0.0271100i
$685$			43.6052i			1.66607i
$686$	13.9452	−	12.1873i	0.532430	−	0.465315i
$687$		−	3.87815i		−	0.147961i
$688$	−6.73509			−0.256773
$689$			0.841968i			0.0320764i
$690$	−15.8940			−0.605075
$691$		−	18.4742i		−	0.702790i	−0.936227	−	0.351395i	$-0.885707\pi$
$691$		−	18.4742i		−	0.702790i	0.936227	−	0.351395i	$-0.114293\pi$
$692$	−22.4568			−0.853681
$693$	10.3501	+	3.02321i	0.393169	+	0.114842i
$694$		−	6.55866i		−	0.248963i
$695$	−10.7546			−0.407947
$696$	−8.66728			−0.328532
$697$		−	0.927978i		−	0.0351497i
$698$	28.8644			1.09253
$699$	−21.9618			−0.830673
$700$	−3.26146	−	0.952654i	−0.123272	−	0.0360069i
$701$	−3.23079			−0.122025			−0.0610126	−	0.998137i	$-0.519433\pi$
$701$	−3.23079			−0.122025			−0.0610126	+	0.998137i	$0.519433\pi$
$702$		−	0.506836i		−	0.0191293i
$703$	−1.19317	+	7.23770i	−0.0450014	+	0.272975i
$704$	4.07545			0.153599
$705$	−13.3776			−0.503831
$706$	34.6309			1.30335
$707$	−8.03213	+	27.4984i	−0.302079	+	1.03418i
$708$	−9.42907			−0.354366
$709$	24.7361			0.928984			0.464492	−	0.885577i	$-0.346237\pi$
$709$	24.7361			0.928984			0.464492	+	0.885577i	$0.346237\pi$
$710$		−	20.2686i		−	0.760666i
$711$		−	3.37893i		−	0.126720i
$712$		−	11.7389i		−	0.439935i
$713$	8.85358			0.331569
$714$	5.86046	+	1.71180i	0.219322	+	0.0640627i
$715$		−	5.17809i		−	0.193649i
$716$		−	12.0887i		−	0.451777i
$717$	−5.77182			−0.215552
$718$			11.1407i			0.415767i
$719$		−	13.1215i		−	0.489349i	−0.969605	−	0.244675i	$-0.921319\pi$
$719$		−	13.1215i		−	0.489349i	0.969605	−	0.244675i	$-0.0786811\pi$
$720$		−	2.50684i		−	0.0934243i
$721$	−14.0037	−	4.09039i	−0.521524	−	0.152334i
$722$	−6.09875	+	17.9946i	−0.226972	+	0.669689i
$723$	−10.8837			−0.404768
$724$	14.6113			0.543025
$725$			11.1308i			0.413386i
$726$			5.60931i			0.208181i
$727$		−	5.24285i		−	0.194446i	−0.995263	−	0.0972232i	$-0.969004\pi$
$727$		−	5.24285i		−	0.194446i	0.995263	−	0.0972232i	$-0.0309961\pi$
$728$	0.375977	−	1.28718i	0.0139346	−	0.0477059i
$729$	1.00000			0.0370370
$730$			33.8784i			1.25389i
$731$		−	15.5419i		−	0.574839i
$732$		−	5.31706i		−	0.196524i
$733$		−	28.0831i		−	1.03727i	−0.854995	−	0.518636i	$-0.826440\pi$
$733$		−	28.0831i		−	1.03727i	0.854995	−	0.518636i	$-0.173560\pi$
$734$	−11.0195			−0.406737
$735$	9.44538	−	14.7889i	0.348398	−	0.545497i
$736$		−	6.34027i		−	0.233706i
$737$			12.5092i			0.460781i
$738$		−	0.402139i		−	0.0148030i
$739$	37.2496			1.37025			0.685125	−	0.728425i	$-0.259747\pi$
$739$	37.2496			1.37025			0.685125	+	0.728425i	$0.259747\pi$
$740$	4.21864			0.155080
$741$	2.17983	+	0.359356i	0.0800779	+	0.0132013i
$742$	−4.21889	−	1.23231i	−0.154880	−	0.0452396i
$743$			22.4717i			0.824408i	0.911092	+	0.412204i	$0.135241\pi$
$743$			22.4717i			0.824408i	−0.911092	+	0.412204i	$0.864759\pi$
$744$			1.39640i			0.0511946i
$745$			23.3908i			0.856974i
$746$	27.0191			0.989241
$747$		−	10.5106i		−	0.384561i
$748$			9.40453i			0.343864i
$749$	−1.22248	+	4.18521i	−0.0446683	+	0.152924i
$750$	9.31483			0.340130
$751$			43.1905i			1.57604i	0.615647	+	0.788022i	$0.288895\pi$
$751$			43.1905i			1.57604i	−0.615647	+	0.788022i	$0.711105\pi$
$752$		−	5.33646i		−	0.194601i
$753$			23.2434i			0.847037i
$754$	−4.39289			−0.159980
$755$	19.1200			0.695847
$756$	2.53963	+	0.741811i	0.0923654	+	0.0269794i
$757$	8.50229			0.309021			0.154511	−	0.987991i	$-0.450620\pi$
$757$	8.50229			0.309021			0.154511	+	0.987991i	$0.450620\pi$
$758$	24.9769			0.907200
$759$	25.8395			0.937913
$760$	10.7815	+	1.77739i	0.391087	+	0.0644728i
$761$			4.95250i			0.179528i	0.995963	+	0.0897639i	$0.0286113\pi$
$761$			4.95250i			0.179528i	−0.995963	+	0.0897639i	$0.971389\pi$
$762$	1.29418			0.0468832
$763$	13.4201	−	45.9445i	0.485841	−	1.66330i
$764$	−0.142938			−0.00517133
$765$	5.78478			0.209149
$766$		−	12.4870i		−	0.451174i
$767$	−4.77899			−0.172559
$768$	1.00000			0.0360844
$769$		−	5.92509i		−	0.213664i	−0.994277	−	0.106832i	$-0.965929\pi$
$769$		−	5.92509i		−	0.213664i	0.994277	−	0.106832i	$-0.0340708\pi$
$770$	25.9461	+	7.57870i	0.935032	+	0.273118i
$771$	29.4331			1.06001
$772$		−	5.94006i		−	0.213787i
$773$	−17.3774			−0.625023			−0.312512	−	0.949914i	$-0.601170\pi$
$773$	−17.3774			−0.625023			−0.312512	+	0.949914i	$0.601170\pi$
$774$		−	6.73509i		−	0.242088i
$775$	1.79330			0.0644172
$776$		−	4.87048i		−	0.174840i
$777$	−1.24836	+	4.27383i	−0.0447847	+	0.153323i
$778$			31.4241i			1.12661i
$779$	1.72954	+	0.285124i	0.0619672	+	0.0102156i
$780$		−	1.27056i		−	0.0454932i
$781$			32.9513i			1.17909i
$782$	14.6308			0.523197
$783$		−	8.66728i		−	0.309743i
$784$	5.89943	+	3.76785i	0.210694	+	0.134566i
$785$	−32.6368			−1.16486
$786$	4.38528			0.156418
$787$	11.7715			0.419609			0.209805	−	0.977743i	$-0.432717\pi$
$787$	11.7715			0.419609			0.209805	+	0.977743i	$0.432717\pi$
$788$	−9.50252			−0.338513
$789$	−9.57036			−0.340714
$790$		−	8.47041i		−	0.301364i
$791$	−1.73328	+	5.93398i	−0.0616284	+	0.210988i
$792$			4.07545i			0.144815i
$793$		−	2.69488i		−	0.0956979i
$794$	37.1197			1.31733
$795$	−4.16441			−0.147697
$796$		−	23.3287i		−	0.826863i
$797$	−1.38112			−0.0489218			−0.0244609	−	0.999701i	$-0.507787\pi$
$797$	−1.38112			−0.0489218			−0.0244609	+	0.999701i	$0.507787\pi$
$798$	−4.99106	+	10.3966i	−0.176682	+	0.368036i
$799$	12.3144			0.435654
$800$		−	1.28423i		−	0.0454043i
$801$	11.7389			0.414775
$802$	38.8566			1.37208
$803$		−	55.0772i		−	1.94363i
$804$			3.06939i			0.108249i
$805$	11.7904	−	40.3649i	0.415555	−	1.42268i
$806$			0.707748i			0.0249294i
$807$	−20.3251			−0.715477
$808$	−10.8277			−0.380918
$809$	−0.562056			−0.0197608			−0.00988042	−	0.999951i	$-0.503145\pi$
$809$	−0.562056			−0.0197608			−0.00988042	+	0.999951i	$0.503145\pi$
$810$	2.50684			0.0880812
$811$	27.0061			0.948311			0.474156	−	0.880441i	$-0.342753\pi$
$811$	27.0061			0.948311			0.474156	+	0.880441i	$0.342753\pi$
$812$	6.42948	−	22.0117i	0.225631	−	0.772459i
$813$		−	27.0034i		−	0.947051i
$814$	−6.85839			−0.240387
$815$			10.9784i			0.384556i
$816$			2.30760i			0.0807823i
$817$	28.9666	+	4.77530i	1.01341	+	0.167067i
$818$			9.77207i			0.341672i
$819$	1.28718	+	0.375977i	0.0449776	+	0.0131377i
$820$		−	1.00810i		−	0.0352043i
$821$	5.06969			0.176933			0.0884667	−	0.996079i	$-0.471803\pi$
$821$	5.06969			0.176933			0.0884667	+	0.996079i	$0.471803\pi$
$822$		−	17.3945i		−	0.606703i
$823$	−42.8564			−1.49388			−0.746941	−	0.664890i	$-0.768478\pi$
$823$	−42.8564			−1.49388			−0.746941	+	0.664890i	$0.768478\pi$
$824$		−	5.51407i		−	0.192092i
$825$	5.23381			0.182218
$826$	6.99459	−	23.9463i	0.243373	−	0.833200i
$827$			35.3843i			1.23043i	0.788358	+	0.615217i	$0.210931\pi$
$827$			35.3843i			1.23043i	−0.788358	+	0.615217i	$0.789069\pi$
$828$	6.34027			0.220340
$829$	28.4298			0.987407			0.493703	−	0.869630i	$-0.335643\pi$
$829$	28.4298			0.987407			0.493703	+	0.869630i	$0.335643\pi$
$830$		−	26.3482i		−	0.914561i
$831$	1.93416			0.0670954
$832$	0.506836			0.0175714
$833$	−8.69470	+	13.6136i	−0.301253	+	0.471682i
$834$	4.29012			0.148555
$835$			5.75084i			0.199016i
$836$	−17.5279	−	2.88957i	−0.606215	−	0.0999378i
$837$	−1.39640			−0.0482668
$838$	−30.2647			−1.04548
$839$	−15.7323			−0.543139			−0.271569	−	0.962419i	$-0.587543\pi$
$839$	−15.7323			−0.543139			−0.271569	+	0.962419i	$0.587543\pi$
$840$	6.36643	+	1.85960i	0.219663	+	0.0641622i
$841$	−46.1218			−1.59041
$842$	21.7967			0.751164
$843$		−	26.0581i		−	0.897489i
$844$			23.1860i			0.798095i
$845$			31.9449i			1.09894i
$846$	5.33646			0.183471
$847$	−14.2456	−	4.16105i	−0.489483	−	0.142975i
$848$		−	1.66122i		−	0.0570466i
$849$			20.4608i			0.702211i
$850$	2.96349			0.101647
$851$			10.6698i			0.365755i
$852$			8.08532i			0.276998i
$853$			28.5022i			0.975896i	0.872873	+	0.487948i	$0.162254\pi$
$853$			28.5022i			0.975896i	−0.872873	+	0.487948i	$0.837746\pi$
$854$	13.5034	+	3.94425i	0.462075	+	0.134969i
$855$	−1.77739	+	10.7815i	−0.0607855	+	0.368720i
$856$	−1.64796			−0.0563262
$857$	−51.1600			−1.74759			−0.873796	−	0.486293i	$-0.838349\pi$
$857$	−51.1600			−1.74759			−0.873796	+	0.486293i	$0.838349\pi$
$858$			2.06559i			0.0705180i
$859$		−	44.1527i		−	1.50647i	−0.657752	−	0.753235i	$-0.728492\pi$
$859$		−	44.1527i		−	1.50647i	0.657752	−	0.753235i	$-0.271508\pi$
$860$		−	16.8838i		−	0.575732i
$861$	1.02129	+	0.298311i	0.0348053	+	0.0101664i
$862$	31.4075			1.06974
$863$			17.8212i			0.606640i	0.952889	+	0.303320i	$0.0980952\pi$
$863$			17.8212i			0.606640i	−0.952889	+	0.303320i	$0.901905\pi$
$864$			1.00000i			0.0340207i
$865$		−	56.2956i		−	1.91411i
$866$		−	13.5121i		−	0.459159i
$867$	11.6750			0.396503
$868$	−3.54635	−	1.03587i	−0.120371	−	0.0351596i
$869$			13.7706i			0.467137i
$870$		−	21.7275i		−	0.736630i
$871$			1.55568i			0.0527122i
$872$	18.0910			0.612640
$873$	4.87048			0.164841
$874$	−4.49536	+	27.2685i	−0.152058	+	0.922372i
$875$	−6.90984	+	23.6562i	−0.233595	+	0.799726i
$876$		−	13.5144i		−	0.456609i
$877$			6.47255i			0.218563i	0.994011	+	0.109281i	$0.0348549\pi$
$877$			6.47255i			0.218563i	−0.994011	+	0.109281i	$0.965145\pi$
$878$			26.4310i			0.892004i
$879$	−16.4410			−0.554542
$880$			10.2165i			0.344398i
$881$		−	4.78225i		−	0.161118i	−0.996750	−	0.0805590i	$-0.974329\pi$
$881$		−	4.78225i		−	0.161118i	0.996750	−	0.0805590i	$-0.0256706\pi$
$882$	−3.76785	+	5.89943i	−0.126870	+	0.198644i
$883$	17.8380			0.600297			0.300148	−	0.953892i	$-0.402964\pi$
$883$	17.8380			0.600297			0.300148	+	0.953892i	$0.402964\pi$
$884$			1.16958i			0.0393371i
$885$		−	23.6371i		−	0.794554i
$886$		−	27.7520i		−	0.932348i
$887$	−57.0906			−1.91692			−0.958458	−	0.285234i	$-0.907929\pi$
$887$	−57.0906			−1.91692			−0.958458	+	0.285234i	$0.907929\pi$
$888$	−1.68285			−0.0564729
$889$	−0.960038	+	3.28674i	−0.0321986	+	0.110234i
$890$	29.4276			0.986414
$891$	−4.07545			−0.136533
$892$	−23.0366			−0.771322
$893$	−3.78365	+	22.9513i	−0.126615	+	0.768037i
$894$		−	9.33082i		−	0.312069i
$895$	30.3045			1.01297
$896$	−0.741811	+	2.53963i	−0.0247822	+	0.0848431i
$897$	3.21348			0.107295
$898$	15.1061			0.504097
$899$			12.1030i			0.403659i
$900$	1.28423			0.0428076
$901$	3.83344			0.127711
$902$			1.63890i			0.0545694i
$903$	17.1046	+	4.99616i	0.569207	+	0.166262i
$904$	−2.33655			−0.0777126
$905$			36.6282i			1.21756i
$906$	−7.62713			−0.253395
$907$		−	32.8683i		−	1.09137i	−0.837989	−	0.545687i	$-0.816269\pi$
$907$		−	32.8683i		−	1.09137i	0.837989	−	0.545687i	$-0.183731\pi$
$908$	17.6866			0.586951
$909$		−	10.8277i		−	0.359133i
$910$	3.22674	+	0.942512i	0.106965	+	0.0312440i
$911$		−	35.4594i		−	1.17482i	−0.809289	−	0.587411i	$-0.800147\pi$
$911$		−	35.4594i		−	1.17482i	0.809289	−	0.587411i	$-0.199853\pi$
$912$	−4.30085	−	0.709018i	−0.142415	−	0.0234779i
$913$			42.8353i			1.41764i
$914$		−	20.9766i		−	0.693845i
$915$	13.3290			0.440643
$916$			3.87815i			0.128138i
$917$	−3.25305	+	11.1370i	−0.107425	+	0.367776i
$918$	−2.30760			−0.0761622
$919$	−17.4663			−0.576161			−0.288080	−	0.957606i	$-0.593017\pi$
$919$	−17.4663			−0.576161			−0.288080	+	0.957606i	$0.593017\pi$
$920$	15.8940			0.524010
$921$	−8.09858			−0.266857
$922$	7.85663			0.258744
$923$			4.09793i			0.134885i
$924$	−10.3501	−	3.02321i	−0.340495	−	0.0994565i
$925$			2.16117i			0.0710588i
$926$			12.6622i			0.416106i
$927$	5.51407			0.181106
$928$	8.66728			0.284517
$929$		−	20.8426i		−	0.683825i	−0.939732	−	0.341912i	$-0.888925\pi$
$929$		−	20.8426i		−	0.683825i	0.939732	−	0.341912i	$-0.111075\pi$
$930$	−3.50056			−0.114788
$931$	−22.7011	−	20.3877i	−0.743998	−	0.668181i
$932$	21.9618			0.719384
$933$		−	8.87438i		−	0.290534i
$934$	−8.29420			−0.271394
$935$	−23.5756			−0.771005
$936$			0.506836i			0.0165665i
$937$		−	8.44662i		−	0.275939i	−0.990436	−	0.137969i	$-0.955942\pi$
$937$		−	8.44662i		−	0.275939i	0.990436	−	0.137969i	$-0.0440576\pi$
$938$	−7.79512	−	2.27691i	−0.254520	−	0.0743437i
$939$			22.9535i			0.749061i
$940$	13.3776			0.436331
$941$	−36.0231			−1.17432			−0.587160	−	0.809471i	$-0.699754\pi$
$941$	−36.0231			−1.17432			−0.587160	+	0.809471i	$0.699754\pi$
$942$	13.0191			0.424186
$943$	2.54967			0.0830288
$944$	9.42907			0.306890
$945$	−1.85960	+	6.36643i	−0.0604927	+	0.207100i
$946$			27.4485i			0.892429i
$947$	34.9342			1.13521			0.567605	−	0.823301i	$-0.307870\pi$
$947$	34.9342			1.13521			0.567605	+	0.823301i	$0.307870\pi$
$948$			3.37893i			0.109742i
$949$		−	6.84958i		−	0.222347i
$950$	−0.910540	+	5.52327i	−0.0295418	+	0.179198i
$951$			19.9885i			0.648172i
$952$	−5.86046	−	1.71180i	−0.189938	−	0.0554799i
$953$			44.7390i			1.44924i	0.689149	+	0.724620i	$0.257985\pi$
$953$			44.7390i			1.44924i	−0.689149	+	0.724620i	$0.742015\pi$
$954$	1.66122			0.0537841
$955$		−	0.358323i		−	0.0115951i
$956$	5.77182			0.186674
$957$			35.3231i			1.14183i
$958$	3.93055			0.126990
$959$	44.1756	+	12.9034i	1.42650	+	0.416674i
$960$			2.50684i			0.0809078i
$961$	−29.0501			−0.937099
$962$	−0.852932			−0.0274996
$963$		−	1.64796i		−	0.0531049i
$964$	10.8837			0.350539
$965$	14.8908			0.479351
$966$	−4.70328	+	16.1019i	−0.151326	+	0.518071i
$967$	−29.5592			−0.950559			−0.475280	−	0.879835i	$-0.657653\pi$
$967$	−29.5592			−0.950559			−0.475280	+	0.879835i	$0.657653\pi$
$968$		−	5.60931i		−	0.180290i
$969$	1.63613	−	9.92465i	0.0525601	−	0.318826i
$970$	12.2095			0.392024
$971$	33.7683			1.08368			0.541838	−	0.840483i	$-0.317728\pi$
$971$	33.7683			1.08368			0.541838	+	0.840483i	$0.317728\pi$
$972$	−1.00000			−0.0320750
$973$	−3.18246	+	10.8953i	−0.102025	+	0.349288i
$974$	−19.0464			−0.610287
$975$	0.650893			0.0208453
$976$			5.31706i			0.170195i
$977$		−	51.1745i		−	1.63722i	−0.574351	−	0.818609i	$-0.694745\pi$
$977$		−	51.1745i		−	1.63722i	0.574351	−	0.818609i	$-0.305255\pi$
$978$		−	4.37938i		−	0.140037i
$979$	−47.8414			−1.52902
$980$	−9.44538	+	14.7889i	−0.301722	+	0.472414i
$981$			18.0910i			0.577602i
$982$			19.5088i			0.622550i
$983$	−57.3236			−1.82834			−0.914170	−	0.405331i	$-0.867156\pi$
$983$	−57.3236			−1.82834			−0.914170	+	0.405331i	$0.867156\pi$
$984$			0.402139i			0.0128197i
$985$		−	23.8213i		−	0.759009i
$986$			20.0006i			0.636950i
$987$	−3.95865	+	13.5526i	−0.126005	+	0.431385i
$988$	−2.17983	−	0.359356i	−0.0693495	−	0.0114326i
$989$	42.7023			1.35785
$990$	−10.2165			−0.324701
$991$		−	52.1178i		−	1.65558i	−0.561041	−	0.827788i	$-0.689599\pi$
$991$		−	52.1178i		−	1.65558i	0.561041	−	0.827788i	$-0.310401\pi$
$992$		−	1.39640i		−	0.0443359i
$993$		−	19.4117i		−	0.616013i
$994$	−20.5337	−	5.99778i	−0.651290	−	0.190238i
$995$	58.4811			1.85398
$996$			10.5106i			0.333040i
$997$			15.2597i			0.483281i	0.970366	+	0.241640i	$0.0776854\pi$
$997$			15.2597i			0.483281i	−0.970366	+	0.241640i	$0.922315\pi$
$998$		−	14.9906i		−	0.474521i
$999$		−	1.68285i		−	0.0532432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.e.b.265.8	yes	12
3.2	odd	2		2394.2.e.b.1063.5		12
7.6	odd	2		798.2.e.a.265.11	yes	12
19.18	odd	2		798.2.e.a.265.2	✓	12
21.20	even	2		2394.2.e.a.1063.2		12
57.56	even	2		2394.2.e.a.1063.11		12
133.132	even	2	inner	798.2.e.b.265.5	yes	12
399.398	odd	2		2394.2.e.b.1063.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.e.a.265.2	✓	12	19.18	odd	2
798.2.e.a.265.11	yes	12	7.6	odd	2
798.2.e.b.265.5	yes	12	133.132	even	2	inner
798.2.e.b.265.8	yes	12	1.1	even	1	trivial
2394.2.e.a.1063.2		12	21.20	even	2
2394.2.e.a.1063.11		12	57.56	even	2
2394.2.e.b.1063.5		12	3.2	odd	2
2394.2.e.b.1063.8		12	399.398	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -2.50684i q^{5} +1.00000i q^{6} +(-2.53963 - 0.741811i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +2.50684 q^{10} -4.07545 q^{11} -1.00000 q^{12} -0.506836 q^{13} +(0.741811 - 2.53963i) q^{14} -2.50684i q^{15} +1.00000 q^{16} +2.30760i q^{17} +1.00000i q^{18} +(-4.30085 - 0.709018i) q^{19} +2.50684i q^{20} +(-2.53963 - 0.741811i) q^{21} -4.07545i q^{22} -6.34027 q^{23} -1.00000i q^{24} -1.28423 q^{25} -0.506836i q^{26} +1.00000 q^{27} +(2.53963 + 0.741811i) q^{28} -8.66728i q^{29} +2.50684 q^{30} -1.39640 q^{31} +1.00000i q^{32} -4.07545 q^{33} -2.30760 q^{34} +(-1.85960 + 6.36643i) q^{35} -1.00000 q^{36} -1.68285i q^{37} +(0.709018 - 4.30085i) q^{38} -0.506836 q^{39} -2.50684 q^{40} -0.402139 q^{41} +(0.741811 - 2.53963i) q^{42} -6.73509 q^{43} +4.07545 q^{44} -2.50684i q^{45} -6.34027i q^{46} -5.33646i q^{47} +1.00000 q^{48} +(5.89943 + 3.76785i) q^{49} -1.28423i q^{50} +2.30760i q^{51} +0.506836 q^{52} -1.66122i q^{53} +1.00000i q^{54} +10.2165i q^{55} +(-0.741811 + 2.53963i) q^{56} +(-4.30085 - 0.709018i) q^{57} +8.66728 q^{58} +9.42907 q^{59} +2.50684i q^{60} +5.31706i q^{61} -1.39640i q^{62} +(-2.53963 - 0.741811i) q^{63} -1.00000 q^{64} +1.27056i q^{65} -4.07545i q^{66} -3.06939i q^{67} -2.30760i q^{68} -6.34027 q^{69} +(-6.36643 - 1.85960i) q^{70} -8.08532i q^{71} -1.00000i q^{72} +13.5144i q^{73} +1.68285 q^{74} -1.28423 q^{75} +(4.30085 + 0.709018i) q^{76} +(10.3501 + 3.02321i) q^{77} -0.506836i q^{78} -3.37893i q^{79} -2.50684i q^{80} +1.00000 q^{81} -0.402139i q^{82} -10.5106i q^{83} +(2.53963 + 0.741811i) q^{84} +5.78478 q^{85} -6.73509i q^{86} -8.66728i q^{87} +4.07545i q^{88} +11.7389 q^{89} +2.50684 q^{90} +(1.28718 + 0.375977i) q^{91} +6.34027 q^{92} -1.39640 q^{93} +5.33646 q^{94} +(-1.77739 + 10.7815i) q^{95} +1.00000i q^{96} +4.87048 q^{97} +(-3.76785 + 5.89943i) q^{98} -4.07545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} + 12 q^{11} - 12 q^{12} + 20 q^{13} - 4 q^{14} + 12 q^{16} - 8 q^{19} - 12 q^{23} - 12 q^{25} + 12 q^{27} + 4 q^{30} + 24 q^{31} + 12 q^{33} + 4 q^{34} + 4 q^{35}+ \cdots + 12 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 + 12 * q^11 - 12 * q^12 + 20 * q^13 - 4 * q^14 + 12 * q^16 - 8 * q^19 - 12 * q^23 - 12 * q^25 + 12 * q^27 + 4 * q^30 + 24 * q^31 + 12 * q^33 + 4 * q^34 + 4 * q^35 - 12 * q^36 + 20 * q^39 - 4 * q^40 - 16 * q^41 - 4 * q^42 - 12 * q^44 + 12 * q^48 + 4 * q^49 - 20 * q^52 + 4 * q^56 - 8 * q^57 + 8 * q^58 + 40 * q^59 - 12 * q^64 - 12 * q^69 - 24 * q^70 - 12 * q^75 + 8 * q^76 + 8 * q^77 + 12 * q^81 + 8 * q^85 - 16 * q^89 + 4 * q^90 + 24 * q^91 + 12 * q^92 + 24 * q^93 - 44 * q^95 - 60 * q^97 - 16 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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