LMFDB - Embedded newform 714.2.b.f.169.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(169,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("714.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.415622617344.23
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 21x^{6} + 104x^{4} + 21x^{2} + 1 $ x^8 + 21x^6 + 104x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.6
Root			$-2.73757i$ of defining polynomial
Character	$\chi$	$=$	714.169
Dual form			714.2.b.f.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.929786i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.929786i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +0.929786i q^{10} +2.19921i q^{11} +1.00000i q^{12} -6.40492 q^{13} +1.00000i q^{14} +0.929786 q^{15} +1.00000 q^{16} +(3.37228 + 2.37228i) q^{17} +1.00000 q^{18} -7.47514 q^{19} -0.929786i q^{20} +1.00000 q^{21} -2.19921i q^{22} +4.74456i q^{23} -1.00000i q^{24} +4.13550 q^{25} +6.40492 q^{26} -1.00000i q^{27} -1.00000i q^{28} +9.33471i q^{29} -0.929786 q^{30} -1.85957i q^{31} -1.00000 q^{32} -2.19921 q^{33} +(-3.37228 - 2.37228i) q^{34} -0.929786 q^{35} -1.00000 q^{36} +4.40492i q^{37} +7.47514 q^{38} -6.40492i q^{39} +0.929786i q^{40} +2.20571i q^{41} -1.00000 q^{42} -5.67435 q^{43} +2.19921i q^{44} +0.929786i q^{45} -4.74456i q^{46} +1.85957 q^{47} +1.00000i q^{48} -1.00000 q^{49} -4.13550 q^{50} +(-2.37228 + 3.37228i) q^{51} -6.40492 q^{52} -11.6743 q^{53} +1.00000i q^{54} +2.04479 q^{55} +1.00000i q^{56} -7.47514i q^{57} -9.33471i q^{58} -2.73058 q^{59} +0.929786 q^{60} -6.20571i q^{61} +1.85957i q^{62} +1.00000i q^{63} +1.00000 q^{64} +5.95521i q^{65} +2.19921 q^{66} -5.67435 q^{67} +(3.37228 + 2.37228i) q^{68} -4.74456 q^{69} +0.929786 q^{70} -12.0653i q^{71} +1.00000 q^{72} +11.8801i q^{73} -4.40492i q^{74} +4.13550i q^{75} -7.47514 q^{76} +2.19921 q^{77} +6.40492i q^{78} +11.5339i q^{79} -0.929786i q^{80} +1.00000 q^{81} -2.20571i q^{82} -8.80334 q^{83} +1.00000 q^{84} +(2.20571 - 3.13550i) q^{85} +5.67435 q^{86} -9.33471 q^{87} -2.19921i q^{88} -0.789357 q^{89} -0.929786i q^{90} +6.40492i q^{91} +4.74456i q^{92} +1.85957 q^{93} -1.85957 q^{94} +6.95028i q^{95} -1.00000i q^{96} -10.0205i q^{97} +1.00000 q^{98} -2.19921i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9} + 6 q^{13} - 2 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} - 12 q^{19} + 8 q^{21} - 26 q^{25} - 6 q^{26} + 2 q^{30} - 8 q^{32} - 10 q^{33} - 4 q^{34} + 2 q^{35} - 8 q^{36} + 12 q^{38} - 8 q^{42} + 10 q^{43} - 4 q^{47} - 8 q^{49} + 26 q^{50} + 4 q^{51} + 6 q^{52} - 38 q^{53} + 34 q^{55} - 20 q^{59} - 2 q^{60} + 8 q^{64} + 10 q^{66} + 10 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} + 8 q^{72} - 12 q^{76} + 10 q^{77} + 8 q^{81} + 2 q^{83} + 8 q^{84} - 32 q^{85} - 10 q^{86} - 8 q^{87} + 22 q^{89} - 4 q^{93} + 4 q^{94} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9 + 6 * q^13 - 2 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 - 12 * q^19 + 8 * q^21 - 26 * q^25 - 6 * q^26 + 2 * q^30 - 8 * q^32 - 10 * q^33 - 4 * q^34 + 2 * q^35 - 8 * q^36 + 12 * q^38 - 8 * q^42 + 10 * q^43 - 4 * q^47 - 8 * q^49 + 26 * q^50 + 4 * q^51 + 6 * q^52 - 38 * q^53 + 34 * q^55 - 20 * q^59 - 2 * q^60 + 8 * q^64 + 10 * q^66 + 10 * q^67 + 4 * q^68 + 8 * q^69 - 2 * q^70 + 8 * q^72 - 12 * q^76 + 10 * q^77 + 8 * q^81 + 2 * q^83 + 8 * q^84 - 32 * q^85 - 10 * q^86 - 8 * q^87 + 22 * q^89 - 4 * q^93 + 4 * q^94 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$		−	0.929786i		−	0.415813i	−0.978149	−	0.207906i	$-0.933335\pi$
$5$		−	0.929786i		−	0.415813i	0.978149	−	0.207906i	$-0.0666649\pi$
$6$		−	1.00000i		−	0.408248i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$			0.929786i			0.294024i
$11$			2.19921i			0.663087i	0.943440	+	0.331543i	$0.107569\pi$
$11$			2.19921i			0.663087i	−0.943440	+	0.331543i	$0.892431\pi$
$12$			1.00000i			0.288675i
$13$	−6.40492			−1.77641			−0.888203	−	0.459451i	$-0.848046\pi$
$13$	−6.40492			−1.77641			−0.888203	+	0.459451i	$0.848046\pi$
$14$			1.00000i			0.267261i
$15$	0.929786			0.240070
$16$	1.00000			0.250000
$17$	3.37228	+	2.37228i	0.817898	+	0.575363i
$17$	3.37228	+	2.37228i	0.817898	+	0.575363i
$18$	1.00000			0.235702
$19$	−7.47514			−1.71491			−0.857457	−	0.514555i	$-0.827957\pi$
$19$	−7.47514			−1.71491			−0.857457	+	0.514555i	$0.827957\pi$
$20$		−	0.929786i		−	0.207906i
$21$	1.00000			0.218218
$22$		−	2.19921i		−	0.468873i
$23$			4.74456i			0.989310i	0.869090	+	0.494655i	$0.164706\pi$
$23$			4.74456i			0.989310i	−0.869090	+	0.494655i	$0.835294\pi$
$24$		−	1.00000i		−	0.204124i
$25$	4.13550			0.827100
$26$	6.40492			1.25611
$27$		−	1.00000i		−	0.192450i
$28$		−	1.00000i		−	0.188982i
$29$			9.33471i			1.73341i	0.498819	+	0.866706i	$0.333767\pi$
$29$			9.33471i			1.73341i	−0.498819	+	0.866706i	$0.666233\pi$
$30$	−0.929786			−0.169755
$31$		−	1.85957i		−	0.333989i	−0.985958	−	0.166994i	$-0.946594\pi$
$31$		−	1.85957i		−	0.333989i	0.985958	−	0.166994i	$-0.0534062\pi$
$32$	−1.00000			−0.176777
$33$	−2.19921			−0.382833
$34$	−3.37228	−	2.37228i	−0.578341	−	0.406843i
$35$	−0.929786			−0.157162
$36$	−1.00000			−0.166667
$37$			4.40492i			0.724165i	0.932146	+	0.362082i	$0.117934\pi$
$37$			4.40492i			0.724165i	−0.932146	+	0.362082i	$0.882066\pi$
$38$	7.47514			1.21263
$39$		−	6.40492i		−	1.02561i
$40$			0.929786i			0.147012i
$41$			2.20571i			0.344475i	0.985055	+	0.172237i	$0.0550996\pi$
$41$			2.20571i			0.344475i	−0.985055	+	0.172237i	$0.944900\pi$
$42$	−1.00000			−0.154303
$43$	−5.67435			−0.865330			−0.432665	−	0.901555i	$-0.642427\pi$
$43$	−5.67435			−0.865330			−0.432665	+	0.901555i	$0.642427\pi$
$44$			2.19921i			0.331543i
$45$			0.929786i			0.138604i
$46$		−	4.74456i		−	0.699548i
$47$	1.85957			0.271246			0.135623	−	0.990760i	$-0.456696\pi$
$47$	1.85957			0.271246			0.135623	+	0.990760i	$0.456696\pi$
$48$			1.00000i			0.144338i
$49$	−1.00000			−0.142857
$50$	−4.13550			−0.584848
$51$	−2.37228	+	3.37228i	−0.332186	+	0.472214i
$52$	−6.40492			−0.888203
$53$	−11.6743			−1.60360			−0.801798	−	0.597596i	$-0.796123\pi$
$53$	−11.6743			−1.60360			−0.801798	+	0.597596i	$0.796123\pi$
$54$			1.00000i			0.136083i
$55$	2.04479			0.275720
$56$			1.00000i			0.133631i
$57$		−	7.47514i		−	0.990106i
$58$		−	9.33471i		−	1.22571i
$59$	−2.73058			−0.355491			−0.177745	−	0.984077i	$-0.556880\pi$
$59$	−2.73058			−0.355491			−0.177745	+	0.984077i	$0.556880\pi$
$60$	0.929786			0.120035
$61$		−	6.20571i		−	0.794560i	−0.917697	−	0.397280i	$-0.869954\pi$
$61$		−	6.20571i		−	0.794560i	0.917697	−	0.397280i	$-0.130046\pi$
$62$			1.85957i			0.236166i
$63$			1.00000i			0.125988i
$64$	1.00000			0.125000
$65$			5.95521i			0.738652i
$66$	2.19921			0.270704
$67$	−5.67435			−0.693232			−0.346616	−	0.938007i	$-0.612669\pi$
$67$	−5.67435			−0.693232			−0.346616	+	0.938007i	$0.612669\pi$
$68$	3.37228	+	2.37228i	0.408949	+	0.287681i
$69$	−4.74456			−0.571178
$70$	0.929786			0.111131
$71$		−	12.0653i		−	1.43189i	−0.698159	−	0.715943i	$-0.745997\pi$
$71$		−	12.0653i		−	1.43189i	0.698159	−	0.715943i	$-0.254003\pi$
$72$	1.00000			0.117851
$73$			11.8801i			1.39046i	0.718789	+	0.695228i	$0.244697\pi$
$73$			11.8801i			1.39046i	−0.718789	+	0.695228i	$0.755303\pi$
$74$		−	4.40492i		−	0.512062i
$75$			4.13550i			0.477526i
$76$	−7.47514			−0.857457
$77$	2.19921			0.250623
$78$			6.40492i			0.725215i
$79$			11.5339i			1.29767i	0.760930	+	0.648834i	$0.224743\pi$
$79$			11.5339i			1.29767i	−0.760930	+	0.648834i	$0.775257\pi$
$80$		−	0.929786i		−	0.103953i
$81$	1.00000			0.111111
$82$		−	2.20571i		−	0.243580i
$83$	−8.80334			−0.966293			−0.483146	−	0.875540i	$-0.660506\pi$
$83$	−8.80334			−0.966293			−0.483146	+	0.875540i	$0.660506\pi$
$84$	1.00000			0.109109
$85$	2.20571	−	3.13550i	0.239243	−	0.340093i
$86$	5.67435			0.611881
$87$	−9.33471			−1.00079
$88$		−	2.19921i		−	0.234437i
$89$	−0.789357			−0.0836717			−0.0418358	−	0.999124i	$-0.513321\pi$
$89$	−0.789357			−0.0836717			−0.0418358	+	0.999124i	$0.513321\pi$
$90$		−	0.929786i		−	0.0980080i
$91$			6.40492i			0.671418i
$92$			4.74456i			0.494655i
$93$	1.85957			0.192829
$94$	−1.85957			−0.191800
$95$			6.95028i			0.713083i
$96$		−	1.00000i		−	0.102062i
$97$		−	10.0205i		−	1.01743i	−0.860936	−	0.508713i	$-0.830121\pi$
$97$		−	10.0205i		−	1.01743i	0.860936	−	0.508713i	$-0.169879\pi$
$98$	1.00000			0.101015
$99$		−	2.19921i		−	0.221029i
$100$	4.13550			0.413550
$101$	11.7331			1.16749			0.583745	−	0.811937i	$-0.301587\pi$
$101$	11.7331			1.16749			0.583745	+	0.811937i	$0.301587\pi$
$102$	2.37228	−	3.37228i	0.234891	−	0.333906i
$103$	4.92979			0.485746			0.242873	−	0.970058i	$-0.421910\pi$
$103$	4.92979			0.485746			0.242873	+	0.970058i	$0.421910\pi$
$104$	6.40492			0.628054
$105$		−	0.929786i		−	0.0907378i
$106$	11.6743			1.13391
$107$			10.0140i			0.968089i	0.875043	+	0.484044i	$0.160833\pi$
$107$			10.0140i			0.968089i	−0.875043	+	0.484044i	$0.839167\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	14.0793i		−	1.34855i	−0.738481	−	0.674275i	$-0.764456\pi$
$109$		−	14.0793i		−	1.34855i	0.738481	−	0.674275i	$-0.235544\pi$
$110$	−2.04479			−0.194963
$111$	−4.40492			−0.418097
$112$		−	1.00000i		−	0.0944911i
$113$			3.07021i			0.288821i	0.989518	+	0.144411i	$0.0461287\pi$
$113$			3.07021i			0.288821i	−0.989518	+	0.144411i	$0.953871\pi$
$114$			7.47514i			0.700111i
$115$	4.41143			0.411368
$116$			9.33471i			0.866706i
$117$	6.40492			0.592135
$118$	2.73058			0.251370
$119$	2.37228	−	3.37228i	0.217467	−	0.309137i
$120$	−0.929786			−0.0848774
$121$	6.16347			0.560316
$122$			6.20571i			0.561839i
$123$	−2.20571			−0.198882
$124$		−	1.85957i		−	0.166994i
$125$		−	8.49406i		−	0.759731i
$126$		−	1.00000i		−	0.0890871i
$127$	−18.6694			−1.65664			−0.828321	−	0.560253i	$-0.810704\pi$
$127$	−18.6694			−1.65664			−0.828321	+	0.560253i	$0.810704\pi$
$128$	−1.00000			−0.0883883
$129$		−	5.67435i		−	0.499599i
$130$		−	5.95521i		−	0.522306i
$131$			22.6694i			1.98064i	0.138816	+	0.990318i	$0.455670\pi$
$131$			22.6694i			1.98064i	−0.138816	+	0.990318i	$0.544330\pi$
$132$	−2.19921			−0.191417
$133$			7.47514i			0.648177i
$134$	5.67435			0.490189
$135$	−0.929786			−0.0800232
$136$	−3.37228	−	2.37228i	−0.289171	−	0.203421i
$137$	9.71914			0.830362			0.415181	−	0.909739i	$-0.363718\pi$
$137$	9.71914			0.830362			0.415181	+	0.909739i	$0.363718\pi$
$138$	4.74456			0.403884
$139$		−	11.8148i		−	1.00212i	−0.865414	−	0.501058i	$-0.832944\pi$
$139$		−	11.8148i		−	1.00212i	0.865414	−	0.501058i	$-0.167056\pi$
$140$	−0.929786			−0.0785812
$141$			1.85957i			0.156604i
$142$			12.0653i			1.01250i
$143$		−	14.0858i		−	1.17791i
$144$	−1.00000			−0.0833333
$145$	8.67928			0.720775
$146$		−	11.8801i		−	0.983201i
$147$		−	1.00000i		−	0.0824786i
$148$			4.40492i			0.362082i
$149$	10.2132			0.836698			0.418349	−	0.908286i	$-0.362609\pi$
$149$	10.2132			0.836698			0.418349	+	0.908286i	$0.362609\pi$
$150$		−	4.13550i		−	0.337662i
$151$	2.53885			0.206609			0.103304	−	0.994650i	$-0.467058\pi$
$151$	2.53885			0.206609			0.103304	+	0.994650i	$0.467058\pi$
$152$	7.47514			0.606314
$153$	−3.37228	−	2.37228i	−0.272633	−	0.191788i
$154$	−2.19921			−0.177217
$155$	−1.72900			−0.138877
$156$		−	6.40492i		−	0.512804i
$157$	7.26942			0.580163			0.290082	−	0.957002i	$-0.406318\pi$
$157$	7.26942			0.580163			0.290082	+	0.957002i	$0.406318\pi$
$158$		−	11.5339i		−	0.917589i
$159$		−	11.6743i		−	0.925836i
$160$			0.929786i			0.0735060i
$161$	4.74456			0.373924
$162$	−1.00000			−0.0785674
$163$		−	8.98857i		−	0.704039i	−0.935993	−	0.352019i	$-0.885495\pi$
$163$		−	8.98857i		−	0.704039i	0.935993	−	0.352019i	$-0.114505\pi$
$164$			2.20571i			0.172237i
$165$			2.04479i			0.159187i
$166$	8.80334			0.683272
$167$		−	10.4842i		−	0.811291i	−0.914030	−	0.405646i	$-0.867047\pi$
$167$		−	10.4842i		−	0.811291i	0.914030	−	0.405646i	$-0.132953\pi$
$168$	−1.00000			−0.0771517
$169$	28.0230			2.15562
$170$	−2.20571	+	3.13550i	−0.169170	+	0.240482i
$171$	7.47514			0.571638
$172$	−5.67435			−0.432665
$173$		−	12.3461i		−	0.938660i	−0.883023	−	0.469330i	$-0.844496\pi$
$173$		−	12.3461i		−	0.938660i	0.883023	−	0.469330i	$-0.155504\pi$
$174$	9.33471			0.707662
$175$		−	4.13550i		−	0.312614i
$176$			2.19921i			0.165772i
$177$		−	2.73058i		−	0.205243i
$178$	0.789357			0.0591648
$179$	9.46115			0.707160			0.353580	−	0.935404i	$-0.384964\pi$
$179$	9.46115			0.707160			0.353580	+	0.935404i	$0.384964\pi$
$180$			0.929786i			0.0693021i
$181$		−	25.6720i		−	1.90818i	−0.299516	−	0.954091i	$-0.596825\pi$
$181$		−	25.6720i		−	1.90818i	0.299516	−	0.954091i	$-0.403175\pi$
$182$		−	6.40492i		−	0.474765i
$183$	6.20571			0.458740
$184$		−	4.74456i		−	0.349774i
$185$	4.09563			0.301117
$186$	−1.85957			−0.136350
$187$	−5.21715	+	7.41636i	−0.381515	+	0.542338i
$188$	1.85957			0.135623
$189$	−1.00000			−0.0727393
$190$		−	6.95028i		−	0.504226i
$191$	1.55678			0.112645			0.0563225	−	0.998413i	$-0.482062\pi$
$191$	1.55678			0.112645			0.0563225	+	0.998413i	$0.482062\pi$
$192$			1.00000i			0.0721688i
$193$			24.8098i			1.78585i	0.450204	+	0.892926i	$0.351351\pi$
$193$			24.8098i			1.78585i	−0.450204	+	0.892926i	$0.648649\pi$
$194$			10.0205i			0.719429i
$195$	−5.95521			−0.426461
$196$	−1.00000			−0.0714286
$197$			6.79586i			0.484185i	0.970253	+	0.242092i	$0.0778337\pi$
$197$			6.79586i			0.484185i	−0.970253	+	0.242092i	$0.922166\pi$
$198$			2.19921i			0.156291i
$199$			3.71914i			0.263643i	0.991273	+	0.131822i	$0.0420826\pi$
$199$			3.71914i			0.263643i	−0.991273	+	0.131822i	$0.957917\pi$
$200$	−4.13550			−0.292424
$201$		−	5.67435i		−	0.400238i
$202$	−11.7331			−0.825540
$203$	9.33471			0.655168
$204$	−2.37228	+	3.37228i	−0.166093	+	0.236107i
$205$	2.05084			0.143237
$206$	−4.92979			−0.343474
$207$		−	4.74456i		−	0.329770i
$208$	−6.40492			−0.444102
$209$		−	16.4394i		−	1.13714i
$210$			0.929786i			0.0641613i
$211$			22.0793i			1.52000i	0.649923	+	0.760000i	$0.274801\pi$
$211$			22.0793i			1.52000i	−0.649923	+	0.760000i	$0.725199\pi$
$212$	−11.6743			−0.801798
$213$	12.0653			0.826700
$214$		−	10.0140i		−	0.684542i
$215$			5.27593i			0.359815i
$216$			1.00000i			0.0680414i
$217$	−1.85957			−0.126236
$218$			14.0793i			0.953569i
$219$	−11.8801			−0.802780
$220$	2.04479			0.137860
$221$	−21.5992	−	15.1943i	−1.45292	−	1.02208i
$222$	4.40492			0.295639
$223$	−10.2057			−0.683425			−0.341713	−	0.939805i	$-0.611007\pi$
$223$	−10.2057			−0.683425			−0.341713	+	0.939805i	$0.611007\pi$
$224$			1.00000i			0.0668153i
$225$	−4.13550			−0.275700
$226$		−	3.07021i		−	0.204228i
$227$		−	6.55185i		−	0.434862i	−0.976076	−	0.217431i	$-0.930232\pi$
$227$		−	6.55185i		−	0.434862i	0.976076	−	0.217431i	$-0.0697677\pi$
$228$		−	7.47514i		−	0.495053i
$229$	15.4956			1.02398			0.511990	−	0.858991i	$-0.328908\pi$
$229$	15.4956			1.02398			0.511990	+	0.858991i	$0.328908\pi$
$230$	−4.41143			−0.290881
$231$			2.19921i			0.144697i
$232$		−	9.33471i		−	0.612854i
$233$		−	7.48164i		−	0.490139i	−0.969506	−	0.245069i	$-0.921189\pi$
$233$		−	7.48164i		−	0.490139i	0.969506	−	0.245069i	$-0.0788107\pi$
$234$	−6.40492			−0.418703
$235$		−	1.72900i		−	0.112788i
$236$	−2.73058			−0.177745
$237$	−11.5339			−0.749209
$238$	−2.37228	+	3.37228i	−0.153772	+	0.218593i
$239$	23.9323			1.54805			0.774027	−	0.633152i	$-0.218239\pi$
$239$	23.9323			1.54805			0.774027	+	0.633152i	$0.218239\pi$
$240$	0.929786			0.0600174
$241$			24.0933i			1.55198i	0.630743	+	0.775992i	$0.282750\pi$
$241$			24.0933i			1.55198i	−0.630743	+	0.775992i	$0.717250\pi$
$242$	−6.16347			−0.396203
$243$			1.00000i			0.0641500i
$244$		−	6.20571i		−	0.397280i
$245$			0.929786i			0.0594018i
$246$	2.20571			0.140631
$247$	47.8777			3.04638
$248$			1.85957i			0.118083i
$249$		−	8.80334i		−	0.557889i
$250$			8.49406i			0.537211i
$251$	8.12407			0.512786			0.256393	−	0.966573i	$-0.417466\pi$
$251$	8.12407			0.512786			0.256393	+	0.966573i	$0.417466\pi$
$252$			1.00000i			0.0629941i
$253$	−10.4343			−0.655998
$254$	18.6694			1.17142
$255$	3.13550	+	2.20571i	0.196353	+	0.138127i
$256$	1.00000			0.0625000
$257$	−21.0702			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$257$	−21.0702			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$258$			5.67435i			0.353269i
$259$	4.40492			0.273709
$260$			5.95521i			0.369326i
$261$		−	9.33471i		−	0.577804i
$262$		−	22.6694i		−	1.40052i
$263$	−30.7651			−1.89705			−0.948527	−	0.316696i	$-0.897427\pi$
$263$	−30.7651			−1.89705			−0.948527	+	0.316696i	$0.897427\pi$
$264$	2.19921			0.135352
$265$			10.8546i			0.666795i
$266$		−	7.47514i		−	0.458330i
$267$		−	0.789357i		−	0.0483079i
$268$	−5.67435			−0.346616
$269$		−	12.0933i		−	0.737339i	−0.929561	−	0.368670i	$-0.879813\pi$
$269$		−	12.0933i		−	0.737339i	0.929561	−	0.368670i	$-0.120187\pi$
$270$	0.929786			0.0565850
$271$	−21.8572			−1.32773			−0.663865	−	0.747852i	$-0.731085\pi$
$271$	−21.8572			−1.32773			−0.663865	+	0.747852i	$0.731085\pi$
$272$	3.37228	+	2.37228i	0.204475	+	0.143841i
$273$	−6.40492			−0.387644
$274$	−9.71914			−0.587155
$275$			9.09483i			0.548439i
$276$	−4.74456			−0.285589
$277$		−	8.87100i		−	0.533007i	−0.963834	−	0.266503i	$-0.914132\pi$
$277$		−	8.87100i		−	0.533007i	0.963834	−	0.266503i	$-0.0858684\pi$
$278$			11.8148i			0.708603i
$279$			1.85957i			0.111330i
$280$	0.929786			0.0555653
$281$	16.8327			1.00416			0.502078	−	0.864823i	$-0.332569\pi$
$281$	16.8327			1.00416			0.502078	+	0.864823i	$0.332569\pi$
$282$		−	1.85957i		−	0.110736i
$283$		−	9.64637i		−	0.573417i	−0.958018	−	0.286709i	$-0.907439\pi$
$283$		−	9.64637i		−	0.573417i	0.958018	−	0.286709i	$-0.0925612\pi$
$284$		−	12.0653i		−	0.715943i
$285$	−6.95028			−0.411699
$286$			14.0858i			0.832909i
$287$	2.20571			0.130199
$288$	1.00000			0.0589256
$289$	5.74456	+	16.0000i	0.337915	+	0.941176i
$290$	−8.67928			−0.509665
$291$	10.0205			0.587412
$292$			11.8801i			0.695228i
$293$	7.98601			0.466548			0.233274	−	0.972411i	$-0.425056\pi$
$293$	7.98601			0.466548			0.233274	+	0.972411i	$0.425056\pi$
$294$			1.00000i			0.0583212i
$295$			2.53885i			0.147818i
$296$		−	4.40492i		−	0.256031i
$297$	2.19921			0.127611
$298$	−10.2132			−0.591635
$299$		−	30.3886i		−	1.75742i
$300$			4.13550i			0.238763i
$301$			5.67435i			0.327064i
$302$	−2.53885			−0.146094
$303$			11.7331i			0.674051i
$304$	−7.47514			−0.428729
$305$	−5.76998			−0.330388
$306$	3.37228	+	2.37228i	0.192780	+	0.135614i
$307$	8.53787			0.487282			0.243641	−	0.969866i	$-0.421658\pi$
$307$	8.53787			0.487282			0.243641	+	0.969866i	$0.421658\pi$
$308$	2.19921			0.125312
$309$			4.92979i			0.280446i
$310$	1.72900			0.0982007
$311$			33.8049i			1.91690i	0.285259	+	0.958450i	$0.407920\pi$
$311$			33.8049i			1.91690i	−0.285259	+	0.958450i	$0.592080\pi$
$312$			6.40492i			0.362607i
$313$			24.0933i			1.36183i	0.732362	+	0.680916i	$0.238418\pi$
$313$			24.0933i			1.36183i	−0.732362	+	0.680916i	$0.761582\pi$
$314$	−7.26942			−0.410237
$315$	0.929786			0.0523875
$316$			11.5339i			0.648834i
$317$			19.0767i			1.07146i	0.844391	+	0.535728i	$0.179963\pi$
$317$			19.0767i			1.07146i	−0.844391	+	0.535728i	$0.820037\pi$
$318$			11.6743i			0.654665i
$319$	−20.5290			−1.14940
$320$		−	0.929786i		−	0.0519766i
$321$	−10.0140			−0.558926
$322$	−4.74456			−0.264404
$323$	−25.2083	−	17.7331i	−1.40263	−	0.986698i
$324$	1.00000			0.0555556
$325$	−26.4876			−1.46927
$326$			8.98857i			0.497831i
$327$	14.0793			0.778586
$328$		−	2.20571i		−	0.121790i
$329$		−	1.85957i		−	0.102521i
$330$		−	2.04479i		−	0.112562i
$331$	−12.9951			−0.714274			−0.357137	−	0.934052i	$-0.616247\pi$
$331$	−12.9951			−0.714274			−0.357137	+	0.934052i	$0.616247\pi$
$332$	−8.80334			−0.483146
$333$		−	4.40492i		−	0.241388i
$334$			10.4842i			0.573670i
$335$			5.27593i			0.288255i
$336$	1.00000			0.0545545
$337$		−	0.370446i		−	0.0201795i	−0.999949	−	0.0100897i	$-0.996788\pi$
$337$		−	0.370446i		−	0.0201795i	0.999949	−	0.0100897i	$-0.00321172\pi$
$338$	−28.0230			−1.52425
$339$	−3.07021			−0.166751
$340$	2.20571	−	3.13550i	0.119622	−	0.170046i
$341$	4.08959			0.221464
$342$	−7.47514			−0.404209
$343$			1.00000i			0.0539949i
$344$	5.67435			0.305940
$345$			4.41143i			0.237503i
$346$			12.3461i			0.663733i
$347$			24.2173i			1.30005i	0.759911	+	0.650027i	$0.225242\pi$
$347$			24.2173i			1.30005i	−0.759911	+	0.650027i	$0.774758\pi$
$348$	−9.33471			−0.500393
$349$	28.5454			1.52800			0.763999	−	0.645218i	$-0.223233\pi$
$349$	28.5454			1.52800			0.763999	+	0.645218i	$0.223233\pi$
$350$			4.13550i			0.221052i
$351$			6.40492i			0.341870i
$352$		−	2.19921i		−	0.117218i
$353$	−18.6899			−0.994763			−0.497382	−	0.867532i	$-0.665705\pi$
$353$	−18.6899			−0.994763			−0.497382	+	0.867532i	$0.665705\pi$
$354$			2.73058i			0.145128i
$355$	−11.2181			−0.595396
$356$	−0.789357			−0.0418358
$357$	3.37228	+	2.37228i	0.178480	+	0.125554i
$358$	−9.46115			−0.500037
$359$	−24.6923			−1.30321			−0.651604	−	0.758559i	$-0.725904\pi$
$359$	−24.6923			−1.30321			−0.651604	+	0.758559i	$0.725904\pi$
$360$		−	0.929786i		−	0.0490040i
$361$	36.8777			1.94093
$362$			25.6720i			1.34929i
$363$			6.16347i			0.323498i
$364$			6.40492i			0.335709i
$365$	11.0459			0.578169
$366$	−6.20571			−0.324378
$367$		−	13.5787i		−	0.708803i	−0.935093	−	0.354402i	$-0.884685\pi$
$367$		−	13.5787i		−	0.708803i	0.935093	−	0.354402i	$-0.115315\pi$
$368$			4.74456i			0.247327i
$369$		−	2.20571i		−	0.114825i
$370$	−4.09563			−0.212922
$371$			11.6743i			0.606102i
$372$	1.85957			0.0964143
$373$	20.6694			1.07022			0.535111	−	0.844782i	$-0.320270\pi$
$373$	20.6694			1.07022			0.535111	+	0.844782i	$0.320270\pi$
$374$	5.21715	−	7.41636i	0.269772	−	0.383491i
$375$	8.49406			0.438631
$376$	−1.85957			−0.0959001
$377$		−	59.7881i		−	3.07924i
$378$	1.00000			0.0514344
$379$		−	15.8213i		−	0.812685i	−0.913721	−	0.406342i	$-0.866804\pi$
$379$		−	15.8213i		−	0.812685i	0.913721	−	0.406342i	$-0.133196\pi$
$380$			6.95028i			0.356542i
$381$		−	18.6694i		−	0.956463i
$382$	−1.55678			−0.0796520
$383$	9.04972			0.462419			0.231210	−	0.972904i	$-0.425732\pi$
$383$	9.04972			0.462419			0.231210	+	0.972904i	$0.425732\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		−	2.04479i		−	0.104212i
$386$		−	24.8098i		−	1.26279i
$387$	5.67435			0.288443
$388$		−	10.0205i		−	0.508713i
$389$	−12.2580			−0.621505			−0.310752	−	0.950491i	$-0.600581\pi$
$389$	−12.2580			−0.621505			−0.310752	+	0.950491i	$0.600581\pi$
$390$	5.95521			0.301554
$391$	−11.2554	+	16.0000i	−0.569212	+	0.809155i
$392$	1.00000			0.0505076
$393$	−22.6694			−1.14352
$394$		−	6.79586i		−	0.342370i
$395$	10.7241			0.539587
$396$		−	2.19921i		−	0.110514i
$397$			0.305162i			0.0153156i	0.999971	+	0.00765781i	$0.00243758\pi$
$397$			0.305162i			0.0153156i	−0.999971	+	0.00765781i	$0.997562\pi$
$398$		−	3.71914i		−	0.186424i
$399$	−7.47514			−0.374225
$400$	4.13550			0.206775
$401$			2.19271i			0.109499i	0.998500	+	0.0547493i	$0.0174360\pi$
$401$			2.19271i			0.109499i	−0.998500	+	0.0547493i	$0.982564\pi$
$402$			5.67435i			0.283011i
$403$			11.9104i			0.593300i
$404$	11.7331			0.583745
$405$		−	0.929786i		−	0.0462014i
$406$	−9.33471			−0.463274
$407$	−9.68735			−0.480184
$408$	2.37228	−	3.37228i	0.117445	−	0.166953i
$409$	−27.2213			−1.34601			−0.673003	−	0.739640i	$-0.734996\pi$
$409$	−27.2213			−1.34601			−0.673003	+	0.739640i	$0.734996\pi$
$410$	−2.05084			−0.101284
$411$			9.71914i			0.479410i
$412$	4.92979			0.242873
$413$			2.73058i			0.134363i
$414$			4.74456i			0.233183i
$415$			8.18522i			0.401797i
$416$	6.40492			0.314027
$417$	11.8148			0.578572
$418$			16.4394i			0.804077i
$419$			12.7968i			0.625167i	0.949890	+	0.312583i	$0.101194\pi$
$419$			12.7968i			0.625167i	−0.949890	+	0.312583i	$0.898806\pi$
$420$		−	0.929786i		−	0.0453689i
$421$	6.28086			0.306110			0.153055	−	0.988218i	$-0.451089\pi$
$421$	6.28086			0.306110			0.153055	+	0.988218i	$0.451089\pi$
$422$		−	22.0793i		−	1.07480i
$423$	−1.85957			−0.0904154
$424$	11.6743			0.566956
$425$	13.9461	+	9.81057i	0.676484	+	0.475882i
$426$	−12.0653			−0.584565
$427$	−6.20571			−0.300316
$428$			10.0140i			0.484044i
$429$	14.0858			0.680068
$430$		−	5.27593i		−	0.254428i
$431$			27.5773i			1.32835i	0.747577	+	0.664175i	$0.231217\pi$
$431$			27.5773i			1.32835i	−0.747577	+	0.664175i	$0.768783\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−15.0907			−0.725213			−0.362606	−	0.931942i	$-0.618113\pi$
$433$	−15.0907			−0.725213			−0.362606	+	0.931942i	$0.618113\pi$
$434$	1.85957			0.0892623
$435$			8.67928i			0.416140i
$436$		−	14.0793i		−	0.674275i
$437$		−	35.4663i		−	1.69658i
$438$	11.8801			0.567651
$439$		−	16.6923i		−	0.796679i	−0.917238	−	0.398340i	$-0.869587\pi$
$439$		−	16.6923i		−	0.796679i	0.917238	−	0.398340i	$-0.130413\pi$
$440$	−2.04479			−0.0974817
$441$	1.00000			0.0476190
$442$	21.5992	+	15.1943i	1.02737	+	0.722718i
$443$	−20.4264			−0.970487			−0.485244	−	0.874379i	$-0.661269\pi$
$443$	−20.4264			−0.970487			−0.485244	+	0.874379i	$0.661269\pi$
$444$	−4.40492			−0.209048
$445$			0.733933i			0.0347917i
$446$	10.2057			0.483255
$447$			10.2132i			0.483068i
$448$		−	1.00000i		−	0.0472456i
$449$			2.76138i			0.130318i	0.997875	+	0.0651588i	$0.0207554\pi$
$449$			2.76138i			0.130318i	−0.997875	+	0.0651588i	$0.979245\pi$
$450$	4.13550			0.194949
$451$	−4.85083			−0.228417
$452$			3.07021i			0.144411i
$453$			2.53885i			0.119286i
$454$			6.55185i			0.307494i
$455$	5.95521			0.279184
$456$			7.47514i			0.350055i
$457$	34.7832			1.62709			0.813544	−	0.581503i	$-0.197535\pi$
$457$	34.7832			1.62709			0.813544	+	0.581503i	$0.197535\pi$
$458$	−15.4956			−0.724063
$459$	2.37228	−	3.37228i	0.110729	−	0.157405i
$460$	4.41143			0.205684
$461$	−8.02699			−0.373854			−0.186927	−	0.982374i	$-0.559853\pi$
$461$	−8.02699			−0.373854			−0.186927	+	0.982374i	$0.559853\pi$
$462$		−	2.19921i		−	0.102317i
$463$	−6.93727			−0.322402			−0.161201	−	0.986922i	$-0.551537\pi$
$463$	−6.93727			−0.322402			−0.161201	+	0.986922i	$0.551537\pi$
$464$			9.33471i			0.433353i
$465$		−	1.72900i		−	0.0801806i
$466$			7.48164i			0.346580i
$467$	−39.8165			−1.84249			−0.921245	−	0.388984i	$-0.872826\pi$
$467$	−39.8165			−1.84249			−0.921245	+	0.388984i	$0.872826\pi$
$468$	6.40492			0.296068
$469$			5.67435i			0.262017i
$470$			1.72900i			0.0797529i
$471$			7.26942i			0.334957i
$472$	2.73058			0.125685
$473$		−	12.4791i		−	0.573789i
$474$	11.5339			0.529770
$475$	−30.9134			−1.41841
$476$	2.37228	−	3.37228i	0.108733	−	0.154568i
$477$	11.6743			0.534532
$478$	−23.9323			−1.09464
$479$		−	10.4712i		−	0.478441i	−0.970965	−	0.239220i	$-0.923108\pi$
$479$		−	10.4712i		−	0.478441i	0.970965	−	0.239220i	$-0.0768919\pi$
$480$	−0.929786			−0.0424387
$481$		−	28.2132i		−	1.28641i
$482$		−	24.0933i		−	1.09742i
$483$			4.74456i			0.215885i
$484$	6.16347			0.280158
$485$	−9.31691			−0.423059
$486$		−	1.00000i		−	0.0453609i
$487$		−	11.0459i		−	0.500538i	−0.968176	−	0.250269i	$-0.919481\pi$
$487$		−	11.0459i		−	0.500538i	0.968176	−	0.250269i	$-0.0805191\pi$
$488$			6.20571i			0.280919i
$489$	8.98857			0.406477
$490$		−	0.929786i		−	0.0420034i
$491$	13.6067			0.614061			0.307031	−	0.951700i	$-0.400665\pi$
$491$	13.6067			0.614061			0.307031	+	0.951700i	$0.400665\pi$
$492$	−2.20571			−0.0994412
$493$	−22.1446	+	31.4793i	−0.997341	+	1.41775i
$494$	−47.8777			−2.15412
$495$	−2.04479			−0.0919067
$496$		−	1.85957i		−	0.0834972i
$497$	−12.0653			−0.541202
$498$			8.80334i			0.394487i
$499$		−	24.7487i		−	1.10790i	−0.832549	−	0.553952i	$-0.813119\pi$
$499$		−	24.7487i		−	1.10790i	0.832549	−	0.553952i	$-0.186881\pi$
$500$		−	8.49406i		−	0.379866i
$501$	10.4842			0.468399
$502$	−8.12407			−0.362595
$503$			4.41143i			0.196696i	0.995152	+	0.0983479i	$0.0313558\pi$
$503$			4.41143i			0.196696i	−0.995152	+	0.0983479i	$0.968644\pi$
$504$		−	1.00000i		−	0.0445435i
$505$		−	10.9093i		−	0.485457i
$506$	10.4343			0.463861
$507$			28.0230i			1.24455i
$508$	−18.6694			−0.828321
$509$	−19.8507			−0.879867			−0.439933	−	0.898030i	$-0.644998\pi$
$509$	−19.8507			−0.879867			−0.439933	+	0.898030i	$0.644998\pi$
$510$	−3.13550	−	2.20571i	−0.138842	−	0.0976706i
$511$	11.8801			0.525543
$512$	−1.00000			−0.0441942
$513$			7.47514i			0.330035i
$514$	21.0702			0.929367
$515$		−	4.58364i		−	0.201979i
$516$		−	5.67435i		−	0.249799i
$517$			4.08959i			0.179860i
$518$	−4.40492			−0.193541
$519$	12.3461			0.541935
$520$		−	5.95521i		−	0.261153i
$521$		−	32.8901i		−	1.44094i	−0.693485	−	0.720471i	$-0.743926\pi$
$521$		−	32.8901i		−	1.44094i	0.693485	−	0.720471i	$-0.256074\pi$
$522$			9.33471i			0.408569i
$523$	28.3746			1.24073			0.620367	−	0.784312i	$-0.286984\pi$
$523$	28.3746			1.24073			0.620367	+	0.784312i	$0.286984\pi$
$524$			22.6694i			0.990318i
$525$	4.13550			0.180488
$526$	30.7651			1.34142
$527$	4.41143	−	6.27100i	0.192165	−	0.273169i
$528$	−2.19921			−0.0957083
$529$	0.489125			0.0212663
$530$		−	10.8546i		−	0.471495i
$531$	2.73058			0.118497
$532$			7.47514i			0.324088i
$533$		−	14.1274i		−	0.611927i
$534$			0.789357i			0.0341588i
$535$	9.31086			0.402544
$536$	5.67435			0.245095
$537$			9.46115i			0.408279i
$538$			12.0933i			0.521377i
$539$		−	2.19921i		−	0.0947267i
$540$	−0.929786			−0.0400116
$541$		−	24.3153i		−	1.04540i	−0.852517	−	0.522699i	$-0.824925\pi$
$541$		−	24.3153i		−	1.04540i	0.852517	−	0.522699i	$-0.175075\pi$
$542$	21.8572			0.938847
$543$	25.6720			1.10169
$544$	−3.37228	−	2.37228i	−0.144585	−	0.101711i
$545$	−13.0907			−0.560744
$546$	6.40492			0.274105
$547$			20.6032i			0.880927i	0.897770	+	0.440464i	$0.145186\pi$
$547$			20.6032i			0.880927i	−0.897770	+	0.440464i	$0.854814\pi$
$548$	9.71914			0.415181
$549$			6.20571i			0.264853i
$550$		−	9.09483i		−	0.387805i
$551$		−	69.7782i		−	2.97265i
$552$	4.74456			0.201942
$553$	11.5339			0.490472
$554$			8.87100i			0.376893i
$555$			4.09563i			0.173850i
$556$		−	11.8148i		−	0.501058i
$557$	17.3337			0.734454			0.367227	−	0.930131i	$-0.380307\pi$
$557$	17.3337			0.734454			0.367227	+	0.930131i	$0.380307\pi$
$558$		−	1.85957i		−	0.0787219i
$559$	36.3438			1.53718
$560$	−0.929786			−0.0392906
$561$	−7.41636	−	5.21715i	−0.313119	−	0.220268i
$562$	−16.8327			−0.710045
$563$	15.0743			0.635308			0.317654	−	0.948207i	$-0.397105\pi$
$563$	15.0743			0.635308			0.317654	+	0.948207i	$0.397105\pi$
$564$			1.85957i			0.0783021i
$565$	2.85464			0.120096
$566$			9.64637i			0.405467i
$567$		−	1.00000i		−	0.0419961i
$568$			12.0653i			0.506248i
$569$	27.6197			1.15788			0.578939	−	0.815371i	$-0.303467\pi$
$569$	27.6197			1.15788			0.578939	+	0.815371i	$0.303467\pi$
$570$	6.95028			0.291115
$571$		−	0.191726i		−	0.00802347i	−0.999992	−	0.00401173i	$-0.998723\pi$
$571$		−	0.191726i		−	0.00802347i	0.999992	−	0.00401173i	$-0.00127698\pi$
$572$		−	14.0858i		−	0.588956i
$573$			1.55678i			0.0650356i
$574$	−2.20571			−0.0920647
$575$			19.6211i			0.818258i
$576$	−1.00000			−0.0416667
$577$	−19.9901			−0.832200			−0.416100	−	0.909319i	$-0.636603\pi$
$577$	−19.9901			−0.832200			−0.416100	+	0.909319i	$0.636603\pi$
$578$	−5.74456	−	16.0000i	−0.238942	−	0.665512i
$579$	−24.8098			−1.03106
$580$	8.67928			0.360387
$581$			8.80334i			0.365224i
$582$	−10.0205			−0.415363
$583$		−	25.6743i		−	1.06332i
$584$		−	11.8801i		−	0.491600i
$585$		−	5.95521i		−	0.246217i
$586$	−7.98601			−0.329899
$587$	12.9666			0.535190			0.267595	−	0.963531i	$-0.413771\pi$
$587$	12.9666			0.535190			0.267595	+	0.963531i	$0.413771\pi$
$588$		−	1.00000i		−	0.0412393i
$589$			13.9006i			0.572762i
$590$		−	2.53885i		−	0.104523i
$591$	−6.79586			−0.279544
$592$			4.40492i			0.181041i
$593$	−30.7725			−1.26368			−0.631838	−	0.775100i	$-0.717699\pi$
$593$	−30.7725			−1.26368			−0.631838	+	0.775100i	$0.717699\pi$
$594$	−2.19921			−0.0902347
$595$	−3.13550	−	2.20571i	−0.128543	−	0.0904254i
$596$	10.2132			0.418349
$597$	−3.71914			−0.152214
$598$			30.3886i			1.24268i
$599$	9.48913			0.387715			0.193858	−	0.981030i	$-0.437900\pi$
$599$	9.48913			0.387715			0.193858	+	0.981030i	$0.437900\pi$
$600$		−	4.13550i		−	0.168831i
$601$		−	0.834151i		−	0.0340257i	−0.999855	−	0.0170129i	$-0.994584\pi$
$601$		−	0.834151i		−	0.0340257i	0.999855	−	0.0170129i	$-0.00541562\pi$
$602$		−	5.67435i		−	0.231269i
$603$	5.67435			0.231077
$604$	2.53885			0.103304
$605$		−	5.73071i		−	0.232986i
$606$		−	11.7331i		−	0.476626i
$607$		−	35.7751i		−	1.45207i	−0.687660	−	0.726033i	$-0.741362\pi$
$607$		−	35.7751i		−	1.45207i	0.687660	−	0.726033i	$-0.258638\pi$
$608$	7.47514			0.303157
$609$			9.33471i			0.378262i
$610$	5.76998			0.233620
$611$	−11.9104			−0.481844
$612$	−3.37228	−	2.37228i	−0.136316	−	0.0958938i
$613$	−7.57871			−0.306101			−0.153051	−	0.988218i	$-0.548910\pi$
$613$	−7.57871			−0.306101			−0.153051	+	0.988218i	$0.548910\pi$
$614$	−8.53787			−0.344560
$615$			2.05084i			0.0826979i
$616$	−2.19921			−0.0886087
$617$		−	17.8982i		−	0.720553i	−0.932845	−	0.360277i	$-0.882682\pi$
$617$		−	17.8982i		−	0.720553i	0.932845	−	0.360277i	$-0.117318\pi$
$618$		−	4.92979i		−	0.198305i
$619$			45.8049i			1.84106i	0.390678	+	0.920528i	$0.372241\pi$
$619$			45.8049i			1.84106i	−0.390678	+	0.920528i	$0.627759\pi$
$620$	−1.72900			−0.0694384
$621$	4.74456			0.190393
$622$		−	33.8049i		−	1.35545i
$623$			0.789357i			0.0316249i
$624$		−	6.40492i		−	0.256402i
$625$	12.7798			0.511194
$626$		−	24.0933i		−	0.962960i
$627$	16.4394			0.656526
$628$	7.26942			0.290082
$629$	−10.4497	+	14.8546i	−0.416658	+	0.592293i
$630$	−0.929786			−0.0370435
$631$	−11.4663			−0.456465			−0.228232	−	0.973607i	$-0.573295\pi$
$631$	−11.4663			−0.456465			−0.228232	+	0.973607i	$0.573295\pi$
$632$		−	11.5339i		−	0.458795i
$633$	−22.0793			−0.877572
$634$		−	19.0767i		−	0.757633i
$635$			17.3586i			0.688853i
$636$		−	11.6743i		−	0.462918i
$637$	6.40492			0.253772
$638$	20.5290			0.812750
$639$			12.0653i			0.477295i
$640$			0.929786i			0.0367530i
$641$			41.0883i			1.62289i	0.584428	+	0.811446i	$0.301319\pi$
$641$			41.0883i			1.62289i	−0.584428	+	0.811446i	$0.698681\pi$
$642$	10.0140			0.395221
$643$			4.98206i			0.196473i	0.995163	+	0.0982367i	$0.0313202\pi$
$643$			4.98206i			0.196473i	−0.995163	+	0.0982367i	$0.968680\pi$
$644$	4.74456			0.186962
$645$	−5.27593			−0.207739
$646$	25.2083	+	17.7331i	0.991806	+	0.697701i
$647$	34.6078			1.36057			0.680287	−	0.732946i	$-0.261855\pi$
$647$	34.6078			1.36057			0.680287	+	0.732946i	$0.261855\pi$
$648$	−1.00000			−0.0392837
$649$		−	6.00511i		−	0.235721i
$650$	26.4876			1.03893
$651$		−	1.85957i		−	0.0728823i
$652$		−	8.98857i		−	0.352019i
$653$			14.4254i			0.564510i	0.959339	+	0.282255i	$0.0910824\pi$
$653$			14.4254i			0.564510i	−0.959339	+	0.282255i	$0.908918\pi$
$654$	−14.0793			−0.550543
$655$	21.0777			0.823574
$656$			2.20571i			0.0861186i
$657$		−	11.8801i		−	0.463485i
$658$			1.85957i			0.0724936i
$659$	6.90930			0.269148			0.134574	−	0.990904i	$-0.457033\pi$
$659$	6.90930			0.269148			0.134574	+	0.990904i	$0.457033\pi$
$660$			2.04479i			0.0795935i
$661$	−25.9668			−1.00999			−0.504996	−	0.863122i	$-0.668506\pi$
$661$	−25.9668			−1.00999			−0.504996	+	0.863122i	$0.668506\pi$
$662$	12.9951			0.505068
$663$	15.1943	−	21.5992i	0.590097	−	0.838844i
$664$	8.80334			0.341636
$665$	6.95028			0.269520
$666$			4.40492i			0.170687i
$667$	−44.2891			−1.71488
$668$		−	10.4842i		−	0.405646i
$669$		−	10.2057i		−	0.394576i
$670$		−	5.27593i		−	0.203827i
$671$	13.6477			0.526862
$672$	−1.00000			−0.0385758
$673$			16.3088i			0.628659i	0.949314	+	0.314330i	$0.101780\pi$
$673$			16.3088i			0.628659i	−0.949314	+	0.314330i	$0.898220\pi$
$674$			0.370446i			0.0142690i
$675$		−	4.13550i		−	0.159175i
$676$	28.0230			1.07781
$677$			38.8433i			1.49287i	0.665458	+	0.746435i	$0.268236\pi$
$677$			38.8433i			1.49287i	−0.665458	+	0.746435i	$0.731764\pi$
$678$	3.07021			0.117911
$679$	−10.0205			−0.384551
$680$	−2.20571	+	3.13550i	−0.0845852	+	0.120241i
$681$	6.55185			0.251068
$682$	−4.08959			−0.156598
$683$			12.6834i			0.485317i	0.970112	+	0.242659i	$0.0780195\pi$
$683$			12.6834i			0.485317i	−0.970112	+	0.242659i	$0.921981\pi$
$684$	7.47514			0.285819
$685$		−	9.03672i		−	0.345275i
$686$		−	1.00000i		−	0.0381802i
$687$			15.4956i			0.591195i
$688$	−5.67435			−0.216332
$689$	74.7733			2.84864
$690$		−	4.41143i		−	0.167940i
$691$		−	10.6345i		−	0.404555i	−0.979328	−	0.202277i	$-0.935166\pi$
$691$		−	10.6345i		−	0.404555i	0.979328	−	0.202277i	$-0.0648343\pi$
$692$		−	12.3461i		−	0.469330i
$693$	−2.19921			−0.0835411
$694$		−	24.2173i		−	0.919277i
$695$	−10.9852			−0.416693
$696$	9.33471			0.353831
$697$	−5.23257	+	7.43828i	−0.198198	+	0.281745i
$698$	−28.5454			−1.08046
$699$	7.48164			0.282982
$700$		−	4.13550i		−	0.156307i
$701$	2.61162			0.0986395			0.0493197	−	0.998783i	$-0.484295\pi$
$701$	2.61162			0.0986395			0.0493197	+	0.998783i	$0.484295\pi$
$702$		−	6.40492i		−	0.241738i
$703$		−	32.9274i		−	1.24188i
$704$			2.19921i			0.0828859i
$705$	1.72900			0.0651180
$706$	18.6899			0.703404
$707$		−	11.7331i		−	0.441270i
$708$		−	2.73058i		−	0.102621i
$709$			15.6361i			0.587224i	0.955925	+	0.293612i	$0.0948574\pi$
$709$			15.6361i			0.587224i	−0.955925	+	0.293612i	$0.905143\pi$
$710$	11.2181			0.421009
$711$		−	11.5339i		−	0.432556i
$712$	0.789357			0.0295824
$713$	8.82285			0.330418
$714$	−3.37228	−	2.37228i	−0.126204	−	0.0887804i
$715$	−13.0968			−0.489791
$716$	9.46115			0.353580
$717$			23.9323i			0.893770i
$718$	24.6923			0.921508
$719$			25.9771i			0.968784i	0.874851	+	0.484392i	$0.160959\pi$
$719$			25.9771i			0.968784i	−0.874851	+	0.484392i	$0.839041\pi$
$720$			0.929786i			0.0346511i
$721$		−	4.92979i		−	0.183595i
$722$	−36.8777			−1.37245
$723$	−24.0933			−0.896038
$724$		−	25.6720i		−	0.954091i
$725$			38.6037i			1.43370i
$726$		−	6.16347i		−	0.228748i
$727$	8.26548			0.306550			0.153275	−	0.988184i	$-0.451018\pi$
$727$	8.26548			0.306550			0.153275	+	0.988184i	$0.451018\pi$
$728$		−	6.40492i		−	0.237382i
$729$	−1.00000			−0.0370370
$730$	−11.0459			−0.408827
$731$	−19.1355	−	13.4612i	−0.707752	−	0.497879i
$732$	6.20571			0.229370
$733$	−1.78030			−0.0657569			−0.0328784	−	0.999459i	$-0.510467\pi$
$733$	−1.78030			−0.0657569			−0.0328784	+	0.999459i	$0.510467\pi$
$734$			13.5787i			0.501199i
$735$	−0.929786			−0.0342957
$736$		−	4.74456i		−	0.174887i
$737$		−	12.4791i		−	0.459673i
$738$			2.20571i			0.0811934i
$739$	15.4663			0.568936			0.284468	−	0.958686i	$-0.408183\pi$
$739$	15.4663			0.568936			0.284468	+	0.958686i	$0.408183\pi$
$740$	4.09563			0.150559
$741$			47.8777i			1.75883i
$742$		−	11.6743i		−	0.428579i
$743$		−	27.8254i		−	1.02082i	−0.859933	−	0.510408i	$-0.829495\pi$
$743$		−	27.8254i		−	1.02082i	0.859933	−	0.510408i	$-0.170505\pi$
$744$	−1.85957			−0.0681752
$745$		−	9.49608i		−	0.347910i
$746$	−20.6694			−0.756761
$747$	8.80334			0.322098
$748$	−5.21715	+	7.41636i	−0.190758	+	0.271169i
$749$	10.0140			0.365903
$750$	−8.49406			−0.310159
$751$		−	39.3897i		−	1.43735i	−0.695346	−	0.718675i	$-0.744749\pi$
$751$		−	39.3897i		−	1.43735i	0.695346	−	0.718675i	$-0.255251\pi$
$752$	1.85957			0.0678116
$753$			8.12407i			0.296057i
$754$			59.7881i			2.17735i
$755$		−	2.36059i		−	0.0859105i
$756$	−1.00000			−0.0363696
$757$	−24.2860			−0.882688			−0.441344	−	0.897338i	$-0.645498\pi$
$757$	−24.2860			−0.882688			−0.441344	+	0.897338i	$0.645498\pi$
$758$			15.8213i			0.574655i
$759$		−	10.4343i		−	0.378741i
$760$		−	6.95028i		−	0.252113i
$761$	4.48052			0.162419			0.0812094	−	0.996697i	$-0.474122\pi$
$761$	4.48052			0.162419			0.0812094	+	0.996697i	$0.474122\pi$
$762$			18.6694i			0.676322i
$763$	−14.0793			−0.509704
$764$	1.55678			0.0563225
$765$	−2.20571	+	3.13550i	−0.0797477	+	0.113364i
$766$	−9.04972			−0.326980
$767$	17.4891			0.631496
$768$			1.00000i			0.0360844i
$769$	−41.8777			−1.51015			−0.755074	−	0.655640i	$-0.772399\pi$
$769$	−41.8777			−1.51015			−0.755074	+	0.655640i	$0.772399\pi$
$770$			2.04479i			0.0736893i
$771$		−	21.0702i		−	0.758825i
$772$			24.8098i			0.892926i
$773$	−14.6834			−0.528125			−0.264063	−	0.964506i	$-0.585063\pi$
$773$	−14.6834			−0.528125			−0.264063	+	0.964506i	$0.585063\pi$
$774$	−5.67435			−0.203960
$775$		−	7.69025i		−	0.276242i
$776$			10.0205i			0.359715i
$777$			4.40492i			0.158026i
$778$	12.2580			0.439470
$779$		−	16.4880i		−	0.590744i
$780$	−5.95521			−0.213231
$781$	26.5341			0.949465
$782$	11.2554	−	16.0000i	0.402494	−	0.572159i
$783$	9.33471			0.333595
$784$	−1.00000			−0.0357143
$785$		−	6.75901i		−	0.241239i
$786$	22.6694			0.808591
$787$			7.53392i			0.268555i	0.990944	+	0.134278i	$0.0428714\pi$
$787$			7.53392i			0.268555i	−0.990944	+	0.134278i	$0.957129\pi$
$788$			6.79586i			0.242092i
$789$		−	30.7651i		−	1.09526i
$790$	−10.7241			−0.381545
$791$	3.07021			0.109164
$792$			2.19921i			0.0781455i
$793$			39.7471i			1.41146i
$794$		−	0.305162i		−	0.0108298i
$795$	−10.8546			−0.384974
$796$			3.71914i			0.131822i
$797$	−8.39744			−0.297453			−0.148726	−	0.988878i	$-0.547517\pi$
$797$	−8.39744			−0.297453			−0.148726	+	0.988878i	$0.547517\pi$
$798$	7.47514			0.264617
$799$	6.27100	+	4.41143i	0.221852	+	0.156065i
$800$	−4.13550			−0.146212
$801$	0.789357			0.0278906
$802$		−	2.19271i		−	0.0774272i
$803$	−26.1268			−0.921993
$804$		−	5.67435i		−	0.200119i
$805$		−	4.41143i		−	0.155482i
$806$		−	11.9104i		−	0.419526i
$807$	12.0933			0.425703
$808$	−11.7331			−0.412770
$809$			7.29642i			0.256528i	0.991740	+	0.128264i	$0.0409405\pi$
$809$			7.29642i			0.256528i	−0.991740	+	0.128264i	$0.959059\pi$
$810$			0.929786i			0.0326693i
$811$		−	11.0179i		−	0.386892i	−0.981111	−	0.193446i	$-0.938034\pi$
$811$		−	11.0179i		−	0.386892i	0.981111	−	0.193446i	$-0.0619664\pi$
$812$	9.33471			0.327584
$813$		−	21.8572i		−	0.766565i
$814$	9.68735			0.339542
$815$	−8.35744			−0.292748
$816$	−2.37228	+	3.37228i	−0.0830465	+	0.118053i
$817$	42.4165			1.48397
$818$	27.2213			0.951769
$819$		−	6.40492i		−	0.223806i
$820$	2.05084			0.0716184
$821$		−	8.52486i		−	0.297520i	−0.988873	−	0.148760i	$-0.952472\pi$
$821$		−	8.52486i		−	0.297520i	0.988873	−	0.148760i	$-0.0475281\pi$
$822$		−	9.71914i		−	0.338994i
$823$			20.7879i			0.724621i	0.932057	+	0.362311i	$0.118012\pi$
$823$			20.7879i			0.724621i	−0.932057	+	0.362311i	$0.881988\pi$
$824$	−4.92979			−0.171737
$825$	−9.09483			−0.316641
$826$		−	2.73058i		−	0.0950089i
$827$			2.68722i			0.0934438i	0.998908	+	0.0467219i	$0.0148775\pi$
$827$			2.68722i			0.0934438i	−0.998908	+	0.0467219i	$0.985123\pi$
$828$		−	4.74456i		−	0.164885i
$829$	34.1371			1.18563			0.592815	−	0.805339i	$-0.298017\pi$
$829$	34.1371			1.18563			0.592815	+	0.805339i	$0.298017\pi$
$830$		−	8.18522i		−	0.284113i
$831$	8.87100			0.307732
$832$	−6.40492			−0.222051
$833$	−3.37228	−	2.37228i	−0.116843	−	0.0821947i
$834$	−11.8148			−0.409112
$835$	−9.74805			−0.337345
$836$		−	16.4394i		−	0.568569i
$837$	−1.85957			−0.0642762
$838$		−	12.7968i		−	0.442060i
$839$		−	3.09452i		−	0.106835i	−0.998572	−	0.0534173i	$-0.982989\pi$
$839$		−	3.09452i		−	0.106835i	0.998572	−	0.0534173i	$-0.0170114\pi$
$840$			0.929786i			0.0320807i
$841$	−58.1368			−2.00472
$842$	−6.28086			−0.216453
$843$			16.8327i			0.579749i
$844$			22.0793i			0.760000i
$845$		−	26.0554i		−	0.896334i
$846$	1.85957			0.0639334
$847$		−	6.16347i		−	0.211779i
$848$	−11.6743			−0.400899
$849$	9.64637			0.331063
$850$	−13.9461	−	9.81057i	−0.478346	−	0.336500i
$851$	−20.8994			−0.716423
$852$	12.0653			0.413350
$853$			41.9808i			1.43740i	0.695323	+	0.718698i	$0.255261\pi$
$853$			41.9808i			1.43740i	−0.695323	+	0.718698i	$0.744739\pi$
$854$	6.20571			0.212355
$855$		−	6.95028i		−	0.237694i
$856$		−	10.0140i		−	0.342271i
$857$			39.1741i			1.33816i	0.743190	+	0.669081i	$0.233312\pi$
$857$			39.1741i			1.33816i	−0.743190	+	0.669081i	$0.766688\pi$
$858$	−14.0858			−0.480880
$859$	22.7959			0.777785			0.388892	−	0.921283i	$-0.372858\pi$
$859$	22.7959			0.777785			0.388892	+	0.921283i	$0.372858\pi$
$860$			5.27593i			0.179908i
$861$			2.20571i			0.0751705i
$862$		−	27.5773i		−	0.939286i
$863$	−10.1137			−0.344276			−0.172138	−	0.985073i	$-0.555068\pi$
$863$	−10.1137			−0.344276			−0.172138	+	0.985073i	$0.555068\pi$
$864$			1.00000i			0.0340207i
$865$	−11.4793			−0.390307
$866$	15.0907			0.512803
$867$	−16.0000	+	5.74456i	−0.543388	+	0.195096i
$868$	−1.85957			−0.0631180
$869$	−25.3655			−0.860466
$870$		−	8.67928i		−	0.294255i
$871$	36.3438			1.23146
$872$			14.0793i			0.476784i
$873$			10.0205i			0.339142i
$874$			35.4663i			1.19966i
$875$	−8.49406			−0.287151
$876$	−11.8801			−0.401390
$877$		−	14.5733i		−	0.492106i	−0.969256	−	0.246053i	$-0.920866\pi$
$877$		−	14.5733i		−	0.492106i	0.969256	−	0.246053i	$-0.0791338\pi$
$878$			16.6923i			0.563337i
$879$			7.98601i			0.269362i
$880$	2.04479			0.0689300
$881$			22.4866i			0.757592i	0.925480	+	0.378796i	$0.123662\pi$
$881$			22.4866i			0.757592i	−0.925480	+	0.378796i	$0.876338\pi$
$882$	−1.00000			−0.0336718
$883$	−28.5440			−0.960581			−0.480290	−	0.877110i	$-0.659469\pi$
$883$	−28.5440			−0.960581			−0.480290	+	0.877110i	$0.659469\pi$
$884$	−21.5992	−	15.1943i	−0.726460	−	0.511039i
$885$	−2.53885			−0.0853425
$886$	20.4264			0.686238
$887$			29.1536i			0.978883i	0.872036	+	0.489441i	$0.162799\pi$
$887$			29.1536i			0.978883i	−0.872036	+	0.489441i	$0.837201\pi$
$888$	4.40492			0.147820
$889$			18.6694i			0.626152i
$890$		−	0.733933i		−	0.0246015i
$891$			2.19921i			0.0736763i
$892$	−10.2057			−0.341713
$893$	−13.9006			−0.465164
$894$		−	10.2132i		−	0.341580i
$895$		−	8.79684i		−	0.294046i
$896$			1.00000i			0.0334077i
$897$	30.3886			1.01464
$898$		−	2.76138i		−	0.0921485i
$899$	17.3586			0.578940
$900$	−4.13550			−0.137850
$901$	−39.3692	−	27.6948i	−1.31158	−	0.922649i
$902$	4.85083			0.161515
$903$	−5.67435			−0.188830
$904$		−	3.07021i		−	0.102114i
$905$	−23.8694			−0.793447
$906$		−	2.53885i		−	0.0843476i
$907$			51.6580i			1.71528i	0.514255	+	0.857638i	$0.328069\pi$
$907$			51.6580i			1.71528i	−0.514255	+	0.857638i	$0.671931\pi$
$908$		−	6.55185i		−	0.217431i
$909$	−11.7331			−0.389163
$910$	−5.95521			−0.197413
$911$		−	52.9441i		−	1.75412i	−0.480385	−	0.877058i	$-0.659503\pi$
$911$		−	52.9441i		−	1.75412i	0.480385	−	0.877058i	$-0.340497\pi$
$912$		−	7.47514i		−	0.247527i
$913$		−	19.3604i		−	0.640736i
$914$	−34.7832			−1.15052
$915$		−	5.76998i		−	0.190750i
$916$	15.4956			0.511990
$917$	22.6694			0.748610
$918$	−2.37228	+	3.37228i	−0.0782970	+	0.111302i
$919$	−46.4445			−1.53206			−0.766032	−	0.642803i	$-0.777771\pi$
$919$	−46.4445			−1.53206			−0.766032	+	0.642803i	$0.777771\pi$
$920$	−4.41143			−0.145440
$921$			8.53787i			0.281332i
$922$	8.02699			0.264355
$923$			77.2772i			2.54361i
$924$			2.19921i			0.0723487i
$925$			18.2166i			0.598957i
$926$	6.93727			0.227973
$927$	−4.92979			−0.161915
$928$		−	9.33471i		−	0.306427i
$929$			4.74456i			0.155664i	0.996966	+	0.0778320i	$0.0247998\pi$
$929$			4.74456i			0.155664i	−0.996966	+	0.0778320i	$0.975200\pi$
$930$			1.72900i			0.0566962i
$931$	7.47514			0.244988
$932$		−	7.48164i		−	0.245069i
$933$	−33.8049			−1.10672
$934$	39.8165			1.30284
$935$	6.89562	+	4.85083i	0.225511	+	0.158639i
$936$	−6.40492			−0.209351
$937$	4.92230			0.160805			0.0804023	−	0.996762i	$-0.474380\pi$
$937$	4.92230			0.160805			0.0804023	+	0.996762i	$0.474380\pi$
$938$		−	5.67435i		−	0.185274i
$939$	−24.0933			−0.786254
$940$		−	1.72900i		−	0.0563938i
$941$			13.4588i			0.438744i	0.975641	+	0.219372i	$0.0704008\pi$
$941$			13.4588i			0.438744i	−0.975641	+	0.219372i	$0.929599\pi$
$942$		−	7.26942i		−	0.236851i
$943$	−10.4651			−0.340792
$944$	−2.73058			−0.0888727
$945$			0.929786i			0.0302459i
$946$			12.4791i			0.405730i
$947$			52.0171i			1.69033i	0.534506	+	0.845165i	$0.320498\pi$
$947$			52.0171i			1.69033i	−0.534506	+	0.845165i	$0.679502\pi$
$948$	−11.5339			−0.374604
$949$		−	76.0909i		−	2.47001i
$950$	30.9134			1.00296
$951$	−19.0767			−0.618605
$952$	−2.37228	+	3.37228i	−0.0768861	+	0.109296i
$953$	11.4742			0.371684			0.185842	−	0.982580i	$-0.440499\pi$
$953$	11.4742			0.371684			0.185842	+	0.982580i	$0.440499\pi$
$954$	−11.6743			−0.377971
$955$		−	1.44748i		−	0.0468392i
$956$	23.9323			0.774027
$957$		−	20.5290i		−	0.663608i
$958$			10.4712i			0.338309i
$959$		−	9.71914i		−	0.313847i
$960$	0.929786			0.0300087
$961$	27.5420			0.888451
$962$			28.2132i			0.909630i
$963$		−	10.0140i		−	0.322696i
$964$			24.0933i			0.775992i
$965$	23.0678			0.742580
$966$		−	4.74456i		−	0.152654i
$967$	−32.0559			−1.03085			−0.515425	−	0.856935i	$-0.672366\pi$
$967$	−32.0559			−1.03085			−0.515425	+	0.856935i	$0.672366\pi$
$968$	−6.16347			−0.198102
$969$	17.7331	−	25.2083i	0.569670	−	0.809806i
$970$	9.31691			0.299148
$971$	−30.0116			−0.963118			−0.481559	−	0.876414i	$-0.659929\pi$
$971$	−30.0116			−0.963118			−0.481559	+	0.876414i	$0.659929\pi$
$972$			1.00000i			0.0320750i
$973$	−11.8148			−0.378764
$974$			11.0459i			0.353934i
$975$		−	26.4876i		−	0.848281i
$976$		−	6.20571i		−	0.198640i
$977$	−47.9415			−1.53379			−0.766893	−	0.641775i	$-0.778198\pi$
$977$	−47.9415			−1.53379			−0.766893	+	0.641775i	$0.778198\pi$
$978$	−8.98857			−0.287423
$979$		−	1.73596i		−	0.0554816i
$980$			0.929786i			0.0297009i
$981$			14.0793i			0.449517i
$982$	−13.6067			−0.434207
$983$			45.7223i			1.45831i	0.684346	+	0.729157i	$0.260088\pi$
$983$			45.7223i			1.45831i	−0.684346	+	0.729157i	$0.739912\pi$
$984$	2.20571			0.0703156
$985$	6.31869			0.201330
$986$	22.1446	−	31.4793i	0.705226	−	1.00250i
$987$	1.85957			0.0591908
$988$	47.8777			1.52319
$989$		−	26.9223i		−	0.856079i
$990$	2.04479			0.0649878
$991$		−	61.1536i		−	1.94261i	−0.237840	−	0.971304i	$-0.576439\pi$
$991$		−	61.1536i		−	1.94261i	0.237840	−	0.971304i	$-0.423561\pi$
$992$			1.85957i			0.0590414i
$993$		−	12.9951i		−	0.412386i
$994$	12.0653			0.382688
$995$	3.45801			0.109626
$996$		−	8.80334i		−	0.278945i
$997$			13.9528i			0.441891i	0.975286	+	0.220945i	$0.0709142\pi$
$997$			13.9528i			0.441891i	−0.975286	+	0.220945i	$0.929086\pi$
$998$			24.7487i			0.783406i
$999$	4.40492			0.139366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.b.f.169.6	yes	8
3.2	odd	2		2142.2.b.j.883.5		8
17.16	even	2	inner	714.2.b.f.169.3	✓	8
51.50	odd	2		2142.2.b.j.883.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.b.f.169.3	✓	8	17.16	even	2	inner
714.2.b.f.169.6	yes	8	1.1	even	1	trivial
2142.2.b.j.883.4		8	51.50	odd	2
2142.2.b.j.883.5		8	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.929786i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.929786i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +0.929786i q^{10} +2.19921i q^{11} +1.00000i q^{12} -6.40492 q^{13} +1.00000i q^{14} +0.929786 q^{15} +1.00000 q^{16} +(3.37228 + 2.37228i) q^{17} +1.00000 q^{18} -7.47514 q^{19} -0.929786i q^{20} +1.00000 q^{21} -2.19921i q^{22} +4.74456i q^{23} -1.00000i q^{24} +4.13550 q^{25} +6.40492 q^{26} -1.00000i q^{27} -1.00000i q^{28} +9.33471i q^{29} -0.929786 q^{30} -1.85957i q^{31} -1.00000 q^{32} -2.19921 q^{33} +(-3.37228 - 2.37228i) q^{34} -0.929786 q^{35} -1.00000 q^{36} +4.40492i q^{37} +7.47514 q^{38} -6.40492i q^{39} +0.929786i q^{40} +2.20571i q^{41} -1.00000 q^{42} -5.67435 q^{43} +2.19921i q^{44} +0.929786i q^{45} -4.74456i q^{46} +1.85957 q^{47} +1.00000i q^{48} -1.00000 q^{49} -4.13550 q^{50} +(-2.37228 + 3.37228i) q^{51} -6.40492 q^{52} -11.6743 q^{53} +1.00000i q^{54} +2.04479 q^{55} +1.00000i q^{56} -7.47514i q^{57} -9.33471i q^{58} -2.73058 q^{59} +0.929786 q^{60} -6.20571i q^{61} +1.85957i q^{62} +1.00000i q^{63} +1.00000 q^{64} +5.95521i q^{65} +2.19921 q^{66} -5.67435 q^{67} +(3.37228 + 2.37228i) q^{68} -4.74456 q^{69} +0.929786 q^{70} -12.0653i q^{71} +1.00000 q^{72} +11.8801i q^{73} -4.40492i q^{74} +4.13550i q^{75} -7.47514 q^{76} +2.19921 q^{77} +6.40492i q^{78} +11.5339i q^{79} -0.929786i q^{80} +1.00000 q^{81} -2.20571i q^{82} -8.80334 q^{83} +1.00000 q^{84} +(2.20571 - 3.13550i) q^{85} +5.67435 q^{86} -9.33471 q^{87} -2.19921i q^{88} -0.789357 q^{89} -0.929786i q^{90} +6.40492i q^{91} +4.74456i q^{92} +1.85957 q^{93} -1.85957 q^{94} +6.95028i q^{95} -1.00000i q^{96} -10.0205i q^{97} +1.00000 q^{98} -2.19921i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9} + 6 q^{13} - 2 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} - 12 q^{19} + 8 q^{21} - 26 q^{25} - 6 q^{26} + 2 q^{30} - 8 q^{32} - 10 q^{33} - 4 q^{34} + 2 q^{35} - 8 q^{36} + 12 q^{38} - 8 q^{42} + 10 q^{43} - 4 q^{47} - 8 q^{49} + 26 q^{50} + 4 q^{51} + 6 q^{52} - 38 q^{53} + 34 q^{55} - 20 q^{59} - 2 q^{60} + 8 q^{64} + 10 q^{66} + 10 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} + 8 q^{72} - 12 q^{76} + 10 q^{77} + 8 q^{81} + 2 q^{83} + 8 q^{84} - 32 q^{85} - 10 q^{86} - 8 q^{87} + 22 q^{89} - 4 q^{93} + 4 q^{94} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^9 + 6 * q^13 - 2 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 - 12 * q^19 + 8 * q^21 - 26 * q^25 - 6 * q^26 + 2 * q^30 - 8 * q^32 - 10 * q^33 - 4 * q^34 + 2 * q^35 - 8 * q^36 + 12 * q^38 - 8 * q^42 + 10 * q^43 - 4 * q^47 - 8 * q^49 + 26 * q^50 + 4 * q^51 + 6 * q^52 - 38 * q^53 + 34 * q^55 - 20 * q^59 - 2 * q^60 + 8 * q^64 + 10 * q^66 + 10 * q^67 + 4 * q^68 + 8 * q^69 - 2 * q^70 + 8 * q^72 - 12 * q^76 + 10 * q^77 + 8 * q^81 + 2 * q^83 + 8 * q^84 - 32 * q^85 - 10 * q^86 - 8 * q^87 + 22 * q^89 - 4 * q^93 + 4 * q^94 + 8 * q^98

Introduction

L-functions

Modular forms

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