LMFDB - Embedded newform 714.2.b.f.169.1

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			169.1
Root			$-0.365288i$ of defining polynomial
Character	$\chi$	$=$	714.169
Dual form			714.2.b.f.169.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -4.30207i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -4.30207i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +4.30207i q^{10} -3.17307i q^{11} -1.00000i q^{12} +5.03264 q^{13} -1.00000i q^{14} -4.30207 q^{15} +1.00000 q^{16} +(3.37228 - 2.37228i) q^{17} +1.00000 q^{18} -1.26942 q^{19} -4.30207i q^{20} +1.00000 q^{21} +3.17307i q^{22} -4.74456i q^{23} +1.00000i q^{24} -13.5078 q^{25} -5.03264 q^{26} +1.00000i q^{27} +1.00000i q^{28} +7.33471i q^{29} +4.30207 q^{30} -8.60413i q^{31} -1.00000 q^{32} -3.17307 q^{33} +(-3.37228 + 2.37228i) q^{34} +4.30207 q^{35} -1.00000 q^{36} +7.03264i q^{37} +1.26942 q^{38} -5.03264i q^{39} +4.30207i q^{40} +10.2057i q^{41} -1.00000 q^{42} -0.442496 q^{43} -3.17307i q^{44} +4.30207i q^{45} +4.74456i q^{46} -8.60413 q^{47} -1.00000i q^{48} -1.00000 q^{49} +13.5078 q^{50} +(-2.37228 - 3.37228i) q^{51} +5.03264 q^{52} -6.44250 q^{53} -1.00000i q^{54} -13.6508 q^{55} -1.00000i q^{56} +1.26942i q^{57} -7.33471i q^{58} +3.47514 q^{59} -4.30207 q^{60} -6.20571i q^{61} +8.60413i q^{62} -1.00000i q^{63} +1.00000 q^{64} -21.6508i q^{65} +3.17307 q^{66} -0.442496 q^{67} +(3.37228 - 2.37228i) q^{68} -4.74456 q^{69} -4.30207 q^{70} -10.8098i q^{71} +1.00000 q^{72} +5.76322i q^{73} -7.03264i q^{74} +13.5078i q^{75} -1.26942 q^{76} +3.17307 q^{77} +5.03264i q^{78} +4.16164i q^{79} -4.30207i q^{80} +1.00000 q^{81} -10.2057i q^{82} +0.686500 q^{83} +1.00000 q^{84} +(-10.2057 - 14.5078i) q^{85} +0.442496 q^{86} +7.33471 q^{87} +3.17307i q^{88} +14.9062 q^{89} -4.30207i q^{90} +5.03264i q^{91} -4.74456i q^{92} -8.60413 q^{93} +8.60413 q^{94} +5.46115i q^{95} +1.00000i q^{96} +2.84092i q^{97} +1.00000 q^{98} +3.17307i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$		−	4.30207i		−	1.92394i	−0.273150	−	0.961971i	$-0.588066\pi$
$5$		−	4.30207i		−	1.92394i	0.273150	−	0.961971i	$-0.411934\pi$
$6$			1.00000i			0.408248i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$			4.30207i			1.36043i
$11$		−	3.17307i		−	0.956717i	−0.878165	−	0.478358i	$-0.841232\pi$
$11$		−	3.17307i		−	0.956717i	0.878165	−	0.478358i	$-0.158768\pi$
$12$		−	1.00000i		−	0.288675i
$13$	5.03264			1.39580			0.697902	−	0.716193i	$-0.254117\pi$
$13$	5.03264			1.39580			0.697902	+	0.716193i	$0.254117\pi$
$14$		−	1.00000i		−	0.267261i
$15$	−4.30207			−1.11079
$16$	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
$19$	−1.26942			−0.291226			−0.145613	−	0.989342i	$-0.546515\pi$
$19$	−1.26942			−0.291226			−0.145613	+	0.989342i	$0.546515\pi$
$20$		−	4.30207i		−	0.961971i
$21$	1.00000			0.218218
$22$			3.17307i			0.676501i
$23$		−	4.74456i		−	0.989310i	−0.869090	−	0.494655i	$-0.835294\pi$
$23$		−	4.74456i		−	0.989310i	0.869090	−	0.494655i	$-0.164706\pi$
$24$			1.00000i			0.204124i
$25$	−13.5078			−2.70156
$26$	−5.03264			−0.986982
$27$			1.00000i			0.192450i
$28$			1.00000i			0.188982i
$29$			7.33471i			1.36202i	0.732274	+	0.681011i	$0.238459\pi$
$29$			7.33471i			1.36202i	−0.732274	+	0.681011i	$0.761541\pi$
$30$	4.30207			0.785446
$31$		−	8.60413i		−	1.54535i	−0.634803	−	0.772674i	$-0.718919\pi$
$31$		−	8.60413i		−	1.54535i	0.634803	−	0.772674i	$-0.281081\pi$
$32$	−1.00000			−0.176777
$33$	−3.17307			−0.552361
$34$	−3.37228	+	2.37228i	−0.578341	+	0.406843i
$35$	4.30207			0.727182
$36$	−1.00000			−0.166667
$37$			7.03264i			1.15616i	0.815980	+	0.578080i	$0.196198\pi$
$37$			7.03264i			1.15616i	−0.815980	+	0.578080i	$0.803802\pi$
$38$	1.26942			0.205928
$39$		−	5.03264i		−	0.805868i
$40$			4.30207i			0.680217i
$41$			10.2057i			1.59386i	0.604069	+	0.796932i	$0.293545\pi$
$41$			10.2057i			1.59386i	−0.604069	+	0.796932i	$0.706455\pi$
$42$	−1.00000			−0.154303
$43$	−0.442496			−0.0674800			−0.0337400	−	0.999431i	$-0.510742\pi$
$43$	−0.442496			−0.0674800			−0.0337400	+	0.999431i	$0.510742\pi$
$44$		−	3.17307i		−	0.478358i
$45$			4.30207i			0.641314i
$46$			4.74456i			0.699548i
$47$	−8.60413			−1.25504			−0.627521	−	0.778600i	$-0.715930\pi$
$47$	−8.60413			−1.25504			−0.627521	+	0.778600i	$0.715930\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000			−0.142857
$50$	13.5078			1.91029
$51$	−2.37228	−	3.37228i	−0.332186	−	0.472214i
$52$	5.03264			0.697902
$53$	−6.44250			−0.884945			−0.442472	−	0.896782i	$-0.645899\pi$
$53$	−6.44250			−0.884945			−0.442472	+	0.896782i	$0.645899\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−13.6508			−1.84067
$56$		−	1.00000i		−	0.133631i
$57$			1.26942i			0.168139i
$58$		−	7.33471i		−	0.963094i
$59$	3.47514			0.452424			0.226212	−	0.974078i	$-0.427366\pi$
$59$	3.47514			0.452424			0.226212	+	0.974078i	$0.427366\pi$
$60$	−4.30207			−0.555394
$61$		−	6.20571i		−	0.794560i	−0.917697	−	0.397280i	$-0.869954\pi$
$61$		−	6.20571i		−	0.794560i	0.917697	−	0.397280i	$-0.130046\pi$
$62$			8.60413i			1.09273i
$63$		−	1.00000i		−	0.125988i
$64$	1.00000			0.125000
$65$		−	21.6508i		−	2.68545i
$66$	3.17307			0.390578
$67$	−0.442496			−0.0540595			−0.0270297	−	0.999635i	$-0.508605\pi$
$67$	−0.442496			−0.0540595			−0.0270297	+	0.999635i	$0.508605\pi$
$68$	3.37228	−	2.37228i	0.408949	−	0.287681i
$69$	−4.74456			−0.571178
$70$	−4.30207			−0.514195
$71$		−	10.8098i		−	1.28289i	−0.767168	−	0.641446i	$-0.778335\pi$
$71$		−	10.8098i		−	1.28289i	0.767168	−	0.641446i	$-0.221665\pi$
$72$	1.00000			0.117851
$73$			5.76322i			0.674534i	0.941409	+	0.337267i	$0.109502\pi$
$73$			5.76322i			0.674534i	−0.941409	+	0.337267i	$0.890498\pi$
$74$		−	7.03264i		−	0.817528i
$75$			13.5078i			1.55974i
$76$	−1.26942			−0.145613
$77$	3.17307			0.361605
$78$			5.03264i			0.569835i
$79$			4.16164i			0.468221i	0.972210	+	0.234110i	$0.0752177\pi$
$79$			4.16164i			0.468221i	−0.972210	+	0.234110i	$0.924782\pi$
$80$		−	4.30207i		−	0.480986i
$81$	1.00000			0.111111
$82$		−	10.2057i		−	1.12703i
$83$	0.686500			0.0753532			0.0376766	−	0.999290i	$-0.488004\pi$
$83$	0.686500			0.0753532			0.0376766	+	0.999290i	$0.488004\pi$
$84$	1.00000			0.109109
$85$	−10.2057	−	14.5078i	−1.10697	−	1.57359i
$86$	0.442496			0.0477155
$87$	7.33471			0.786363
$88$			3.17307i			0.338250i
$89$	14.9062			1.58005			0.790027	−	0.613072i	$-0.210066\pi$
$89$	14.9062			1.58005			0.790027	+	0.613072i	$0.210066\pi$
$90$		−	4.30207i		−	0.453478i
$91$			5.03264i			0.527564i
$92$		−	4.74456i		−	0.494655i
$93$	−8.60413			−0.892207
$94$	8.60413			0.887449
$95$			5.46115i			0.560302i
$96$			1.00000i			0.102062i
$97$			2.84092i			0.288451i	0.989545	+	0.144226i	$0.0460691\pi$
$97$			2.84092i			0.288451i	−0.989545	+	0.144226i	$0.953931\pi$
$98$	1.00000			0.101015
$99$			3.17307i			0.318906i
$100$	−13.5078			−1.35078
$101$	−2.98857			−0.297374			−0.148687	−	0.988884i	$-0.547505\pi$
$101$	−2.98857			−0.297374			−0.148687	+	0.988884i	$0.547505\pi$
$102$	2.37228	+	3.37228i	0.234891	+	0.333906i
$103$	−0.302067			−0.0297635			−0.0148818	−	0.999889i	$-0.504737\pi$
$103$	−0.302067			−0.0297635			−0.0148818	+	0.999889i	$0.504737\pi$
$104$	−5.03264			−0.493491
$105$		−	4.30207i		−	0.419839i
$106$	6.44250			0.625750
$107$		−	16.2197i		−	1.56802i	−0.620750	−	0.784009i	$-0.713172\pi$
$107$		−	16.2197i		−	1.56802i	0.620750	−	0.784009i	$-0.286828\pi$
$108$			1.00000i			0.0962250i
$109$		−	2.59015i		−	0.248091i	−0.992277	−	0.124046i	$-0.960413\pi$
$109$		−	2.59015i		−	0.248091i	0.992277	−	0.124046i	$-0.0395869\pi$
$110$	13.6508			1.30155
$111$	7.03264			0.667509
$112$			1.00000i			0.0944911i
$113$		−	8.30207i		−	0.780993i	−0.920604	−	0.390496i	$-0.872303\pi$
$113$		−	8.30207i		−	0.780993i	0.920604	−	0.390496i	$-0.127697\pi$
$114$		−	1.26942i		−	0.118893i
$115$	−20.4114			−1.90338
$116$			7.33471i			0.681011i
$117$	−5.03264			−0.465268
$118$	−3.47514			−0.319912
$119$	2.37228	+	3.37228i	0.217467	+	0.309137i
$120$	4.30207			0.392723
$121$	0.931621			0.0846928
$122$			6.20571i			0.561839i
$123$	10.2057			0.920218
$124$		−	8.60413i		−	0.772674i
$125$			36.6010i			3.27370i
$126$			1.00000i			0.0890871i
$127$	14.6694			1.30170			0.650850	−	0.759206i	$-0.274413\pi$
$127$	14.6694			1.30170			0.650850	+	0.759206i	$0.274413\pi$
$128$	−1.00000			−0.0883883
$129$			0.442496i			0.0389596i
$130$			21.6508i			1.89890i
$131$			10.6694i			0.932191i	0.884734	+	0.466096i	$0.154340\pi$
$131$			10.6694i			0.932191i	−0.884734	+	0.466096i	$0.845660\pi$
$132$	−3.17307			−0.276180
$133$		−	1.26942i		−	0.110073i
$134$	0.442496			0.0382258
$135$	4.30207			0.370263
$136$	−3.37228	+	2.37228i	−0.289171	+	0.203421i
$137$	−11.2083			−0.957587			−0.478793	−	0.877928i	$-0.658926\pi$
$137$	−11.2083			−0.957587			−0.478793	+	0.877928i	$0.658926\pi$
$138$	4.74456			0.403884
$139$			17.0466i			1.44588i	0.690913	+	0.722938i	$0.257209\pi$
$139$			17.0466i			1.44588i	−0.690913	+	0.722938i	$0.742791\pi$
$140$	4.30207			0.363591
$141$			8.60413i			0.724599i
$142$			10.8098i			0.907142i
$143$		−	15.9689i		−	1.33539i
$144$	−1.00000			−0.0833333
$145$	31.5544			2.62045
$146$		−	5.76322i		−	0.476967i
$147$			1.00000i			0.0824786i
$148$			7.03264i			0.578080i
$149$	17.3928			1.42487			0.712436	−	0.701737i	$-0.247592\pi$
$149$	17.3928			1.42487			0.712436	+	0.701737i	$0.247592\pi$
$150$		−	13.5078i		−	1.10291i
$151$	14.9503			1.21664			0.608318	−	0.793693i	$-0.291845\pi$
$151$	14.9503			1.21664			0.608318	+	0.793693i	$0.291845\pi$
$152$	1.26942			0.102964
$153$	−3.37228	+	2.37228i	−0.272633	+	0.191788i
$154$	−3.17307			−0.255693
$155$	−37.0156			−2.97316
$156$		−	5.03264i		−	0.402934i
$157$	13.4751			1.07543			0.537717	−	0.843126i	$-0.319287\pi$
$157$	13.4751			1.07543			0.537717	+	0.843126i	$0.319287\pi$
$158$		−	4.16164i		−	0.331082i
$159$			6.44250i			0.510923i
$160$			4.30207i			0.340108i
$161$	4.74456			0.373924
$162$	−1.00000			−0.0785674
$163$		−	5.73313i		−	0.449053i	−0.974468	−	0.224527i	$-0.927916\pi$
$163$		−	5.73313i		−	0.449053i	0.974468	−	0.224527i	$-0.0720836\pi$
$164$			10.2057i			0.796932i
$165$			13.6508i			1.06271i
$166$	−0.686500			−0.0532828
$167$		−	17.6228i		−	1.36369i	−0.731496	−	0.681846i	$-0.761177\pi$
$167$		−	17.6228i		−	1.36369i	0.731496	−	0.681846i	$-0.238823\pi$
$168$	−1.00000			−0.0771517
$169$	12.3275			0.948268
$170$	10.2057	+	14.5078i	0.782742	+	1.11270i
$171$	1.26942			0.0970753
$172$	−0.442496			−0.0337400
$173$			10.3984i			0.790577i	0.918557	+	0.395289i	$0.129355\pi$
$173$			10.3984i			0.790577i	−0.918557	+	0.395289i	$0.870645\pi$
$174$	−7.33471			−0.556043
$175$		−	13.5078i		−	1.02109i
$176$		−	3.17307i		−	0.239179i
$177$		−	3.47514i		−	0.261207i
$178$	−14.9062			−1.11727
$179$	−2.95028			−0.220514			−0.110257	−	0.993903i	$-0.535167\pi$
$179$	−2.95028			−0.220514			−0.110257	+	0.993903i	$0.535167\pi$
$180$			4.30207i			0.320657i
$181$		−	16.1828i		−	1.20286i	−0.798925	−	0.601431i	$-0.794598\pi$
$181$		−	16.1828i		−	1.20286i	0.798925	−	0.601431i	$-0.205402\pi$
$182$		−	5.03264i		−	0.373044i
$183$	−6.20571			−0.458740
$184$			4.74456i			0.349774i
$185$	30.2549			2.22438
$186$	8.60413			0.630886
$187$	−7.52742	−	10.7005i	−0.550459	−	0.782497i
$188$	−8.60413			−0.627521
$189$	−1.00000			−0.0727393
$190$		−	5.46115i		−	0.396193i
$191$	15.3046			1.10740			0.553702	−	0.832715i	$-0.313215\pi$
$191$	15.3046			1.10740			0.553702	+	0.832715i	$0.313215\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	1.93472i		−	0.139264i	−0.997573	−	0.0696319i	$-0.977818\pi$
$193$		−	1.93472i		−	0.139264i	0.997573	−	0.0696319i	$-0.0221825\pi$
$194$		−	2.84092i		−	0.203966i
$195$	−21.6508			−1.55044
$196$	−1.00000			−0.0714286
$197$			22.2850i			1.58774i	0.608088	+	0.793870i	$0.291937\pi$
$197$			22.2850i			1.58774i	−0.608088	+	0.793870i	$0.708063\pi$
$198$		−	3.17307i		−	0.225500i
$199$			17.2083i			1.21986i	0.792455	+	0.609931i	$0.208803\pi$
$199$			17.2083i			1.21986i	−0.792455	+	0.609931i	$0.791197\pi$
$200$	13.5078			0.955144
$201$			0.442496i			0.0312112i
$202$	2.98857			0.210275
$203$	−7.33471			−0.514796
$204$	−2.37228	−	3.37228i	−0.166093	−	0.236107i
$205$	43.9057			3.06650
$206$	0.302067			0.0210460
$207$			4.74456i			0.329770i
$208$	5.03264			0.348951
$209$			4.02797i			0.278621i
$210$			4.30207i			0.296871i
$211$		−	5.40985i		−	0.372430i	−0.982509	−	0.186215i	$-0.940378\pi$
$211$		−	5.40985i		−	0.372430i	0.982509	−	0.186215i	$-0.0596220\pi$
$212$	−6.44250			−0.442472
$213$	−10.8098			−0.740679
$214$			16.2197i			1.10876i
$215$			1.90365i			0.129828i
$216$		−	1.00000i		−	0.0680414i
$217$	8.60413			0.584087
$218$			2.59015i			0.175427i
$219$	5.76322			0.389442
$220$	−13.6508			−0.920334
$221$	16.9715	−	11.9388i	1.14163	−	0.803093i
$222$	−7.03264			−0.472000
$223$	2.20571			0.147705			0.0738527	−	0.997269i	$-0.476471\pi$
$223$	2.20571			0.147705			0.0738527	+	0.997269i	$0.476471\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	13.5078			0.900519
$226$			8.30207i			0.552245i
$227$		−	7.80729i		−	0.518188i	−0.965852	−	0.259094i	$-0.916576\pi$
$227$		−	7.80729i		−	0.518188i	0.965852	−	0.259094i	$-0.0834240\pi$
$228$			1.26942i			0.0840697i
$229$	2.11034			0.139455			0.0697276	−	0.997566i	$-0.477787\pi$
$229$	2.11034			0.139455			0.0697276	+	0.997566i	$0.477787\pi$
$230$	20.4114			1.34589
$231$		−	3.17307i		−	0.208773i
$232$		−	7.33471i		−	0.481547i
$233$		−	12.1094i		−	0.793310i	−0.917968	−	0.396655i	$-0.870171\pi$
$233$		−	12.1094i		−	0.793310i	0.917968	−	0.396655i	$-0.129829\pi$
$234$	5.03264			0.328994
$235$			37.0156i			2.41463i
$236$	3.47514			0.226212
$237$	4.16164			0.270327
$238$	−2.37228	−	3.37228i	−0.153772	−	0.218593i
$239$	10.1845			0.658781			0.329390	−	0.944194i	$-0.393157\pi$
$239$	10.1845			0.658781			0.329390	+	0.944194i	$0.393157\pi$
$240$	−4.30207			−0.277697
$241$		−	13.6296i		−	0.877957i	−0.898498	−	0.438978i	$-0.855340\pi$
$241$		−	13.6296i		−	0.877957i	0.898498	−	0.438978i	$-0.144660\pi$
$242$	−0.931621			−0.0598869
$243$		−	1.00000i		−	0.0641500i
$244$		−	6.20571i		−	0.397280i
$245$			4.30207i			0.274849i
$246$	−10.2057			−0.650692
$247$	−6.38856			−0.406494
$248$			8.60413i			0.546363i
$249$		−	0.686500i		−	0.0435052i
$250$		−	36.6010i		−	2.31485i
$251$	−24.2409			−1.53007			−0.765036	−	0.643987i	$-0.777279\pi$
$251$	−24.2409			−1.53007			−0.765036	+	0.643987i	$0.777279\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	−15.0548			−0.946489
$254$	−14.6694			−0.920441
$255$	−14.5078	+	10.2057i	−0.908512	+	0.639107i
$256$	1.00000			0.0625000
$257$	−26.3021			−1.64068			−0.820339	−	0.571878i	$-0.806215\pi$
$257$	−26.3021			−1.64068			−0.820339	+	0.571878i	$0.806215\pi$
$258$		−	0.442496i		−	0.0275486i
$259$	−7.03264			−0.436987
$260$		−	21.6508i		−	1.34272i
$261$		−	7.33471i		−	0.454007i
$262$		−	10.6694i		−	0.659159i
$263$	−23.5855			−1.45434			−0.727171	−	0.686456i	$-0.759165\pi$
$263$	−23.5855			−1.45434			−0.727171	+	0.686456i	$0.759165\pi$
$264$	3.17307			0.195289
$265$			27.7160i			1.70258i
$266$			1.26942i			0.0778334i
$267$		−	14.9062i		−	0.912245i
$268$	−0.442496			−0.0270297
$269$			1.62955i			0.0993557i	0.998765	+	0.0496778i	$0.0158195\pi$
$269$			1.62955i			0.0993557i	−0.998765	+	0.0496778i	$0.984181\pi$
$270$	−4.30207			−0.261815
$271$	25.2295			1.53258			0.766291	−	0.642494i	$-0.222100\pi$
$271$	25.2295			1.53258			0.766291	+	0.642494i	$0.222100\pi$
$272$	3.37228	−	2.37228i	0.204475	−	0.143841i
$273$	5.03264			0.304589
$274$	11.2083			0.677116
$275$			42.8611i			2.58462i
$276$	−4.74456			−0.285589
$277$			13.1290i			0.788845i	0.918929	+	0.394422i	$0.129055\pi$
$277$			13.1290i			0.788845i	−0.918929	+	0.394422i	$0.870945\pi$
$278$		−	17.0466i		−	1.02239i
$279$			8.60413i			0.515116i
$280$	−4.30207			−0.257098
$281$	23.4010			1.39599			0.697993	−	0.716105i	$-0.254077\pi$
$281$	23.4010			1.39599			0.697993	+	0.716105i	$0.254077\pi$
$282$		−	8.60413i		−	0.512369i
$283$		−	7.99691i		−	0.475367i	−0.971343	−	0.237683i	$-0.923612\pi$
$283$		−	7.99691i		−	0.475367i	0.971343	−	0.237683i	$-0.0763881\pi$
$284$		−	10.8098i		−	0.641446i
$285$	5.46115			0.323491
$286$			15.9689i			0.944263i
$287$	−10.2057			−0.602424
$288$	1.00000			0.0589256
$289$	5.74456	−	16.0000i	0.337915	−	0.941176i
$290$	−31.5544			−1.85294
$291$	2.84092			0.166537
$292$			5.76322i			0.337267i
$293$	1.78030			0.104006			0.0520031	−	0.998647i	$-0.483439\pi$
$293$	1.78030			0.104006			0.0520031	+	0.998647i	$0.483439\pi$
$294$		−	1.00000i		−	0.0583212i
$295$		−	14.9503i		−	0.870439i
$296$		−	7.03264i		−	0.408764i
$297$	3.17307			0.184120
$298$	−17.3928			−1.00754
$299$		−	23.8777i		−	1.38088i
$300$			13.5078i			0.779872i
$301$		−	0.442496i		−	0.0255050i
$302$	−14.9503			−0.860292
$303$			2.98857i			0.171689i
$304$	−1.26942			−0.0728065
$305$	−26.6974			−1.52869
$306$	3.37228	−	2.37228i	0.192780	−	0.135614i
$307$	−12.0270			−0.686417			−0.343208	−	0.939259i	$-0.611514\pi$
$307$	−12.0270			−0.686417			−0.343208	+	0.939259i	$0.611514\pi$
$308$	3.17307			0.180802
$309$			0.302067i			0.0171840i
$310$	37.0156			2.10234
$311$			17.1772i			0.974030i	0.873394	+	0.487015i	$0.161914\pi$
$311$			17.1772i			0.974030i	−0.873394	+	0.487015i	$0.838086\pi$
$312$			5.03264i			0.284917i
$313$		−	13.6296i		−	0.770388i	−0.922836	−	0.385194i	$-0.874135\pi$
$313$		−	13.6296i		−	0.770388i	0.922836	−	0.385194i	$-0.125865\pi$
$314$	−13.4751			−0.760446
$315$	−4.30207			−0.242394
$316$			4.16164i			0.234110i
$317$		−	10.9233i		−	0.613513i	−0.951788	−	0.306756i	$-0.900756\pi$
$317$		−	10.9233i		−	0.613513i	0.951788	−	0.306756i	$-0.0992437\pi$
$318$		−	6.44250i		−	0.361277i
$319$	23.2736			1.30307
$320$		−	4.30207i		−	0.240493i
$321$	−16.2197			−0.905295
$322$	−4.74456			−0.264404
$323$	−4.28086	+	3.01143i	−0.238193	+	0.167561i
$324$	1.00000			0.0555556
$325$	−67.9798			−3.77084
$326$			5.73313i			0.317529i
$327$	−2.59015			−0.143235
$328$		−	10.2057i		−	0.563516i
$329$		−	8.60413i		−	0.474361i
$330$		−	13.6508i		−	0.751450i
$331$	15.1119			0.830626			0.415313	−	0.909679i	$-0.363672\pi$
$331$	15.1119			0.830626			0.415313	+	0.909679i	$0.363672\pi$
$332$	0.686500			0.0376766
$333$		−	7.03264i		−	0.385386i
$334$			17.6228i			0.964276i
$335$			1.90365i			0.104007i
$336$	1.00000			0.0545545
$337$		−	10.0933i		−	0.549815i	−0.961471	−	0.274907i	$-0.911353\pi$
$337$		−	10.0933i		−	0.549815i	0.961471	−	0.274907i	$-0.0886472\pi$
$338$	−12.3275			−0.670527
$339$	−8.30207			−0.450906
$340$	−10.2057	−	14.5078i	−0.553483	−	0.786795i
$341$	−27.3015			−1.47846
$342$	−1.26942			−0.0686426
$343$		−	1.00000i		−	0.0539949i
$344$	0.442496			0.0238578
$345$			20.4114i			1.09891i
$346$		−	10.3984i		−	0.559023i
$347$			18.6114i			0.999110i	0.866282	+	0.499555i	$0.166503\pi$
$347$			18.6114i			0.999110i	−0.866282	+	0.499555i	$0.833497\pi$
$348$	7.33471			0.393182
$349$	27.5715			1.47587			0.737934	−	0.674873i	$-0.235802\pi$
$349$	27.5715			1.47587			0.737934	+	0.674873i	$0.235802\pi$
$350$			13.5078i			0.722021i
$351$			5.03264i			0.268623i
$352$			3.17307i			0.169125i
$353$	21.8285			1.16181			0.580907	−	0.813970i	$-0.302698\pi$
$353$	21.8285			1.16181			0.580907	+	0.813970i	$0.302698\pi$
$354$			3.47514i			0.184701i
$355$	−46.5047			−2.46821
$356$	14.9062			0.790027
$357$	3.37228	−	2.37228i	0.178480	−	0.125554i
$358$	2.95028			0.155927
$359$	−20.7968			−1.09762			−0.548808	−	0.835949i	$-0.684918\pi$
$359$	−20.7968			−1.09762			−0.548808	+	0.835949i	$0.684918\pi$
$360$		−	4.30207i		−	0.226739i
$361$	−17.3886			−0.915187
$362$			16.1828i			0.850552i
$363$		−	0.931621i		−	0.0488974i
$364$			5.03264i			0.263782i
$365$	24.7937			1.29776
$366$	6.20571			0.324378
$367$		−	17.8124i		−	0.929800i	−0.885363	−	0.464900i	$-0.846090\pi$
$367$		−	17.8124i		−	0.929800i	0.885363	−	0.464900i	$-0.153910\pi$
$368$		−	4.74456i		−	0.247327i
$369$		−	10.2057i		−	0.531288i
$370$	−30.2549			−1.57288
$371$		−	6.44250i		−	0.334478i
$372$	−8.60413			−0.446104
$373$	−12.6694			−0.655998			−0.327999	−	0.944678i	$-0.606374\pi$
$373$	−12.6694			−0.655998			−0.327999	+	0.944678i	$0.606374\pi$
$374$	7.52742	+	10.7005i	0.389233	+	0.553309i
$375$	36.6010			1.89007
$376$	8.60413			0.443724
$377$			36.9130i			1.90111i
$378$	1.00000			0.0514344
$379$			7.66785i			0.393871i	0.980416	+	0.196935i	$0.0630989\pi$
$379$			7.66785i			0.393871i	−0.980416	+	0.196935i	$0.936901\pi$
$380$			5.46115i			0.280151i
$381$		−	14.6694i		−	0.751537i
$382$	−15.3046			−0.783053
$383$	21.4612			1.09661			0.548307	−	0.836277i	$-0.315273\pi$
$383$	21.4612			1.09661			0.548307	+	0.836277i	$0.315273\pi$
$384$			1.00000i			0.0510310i
$385$		−	13.6508i		−	0.695707i
$386$			1.93472i			0.0984744i
$387$	0.442496			0.0224933
$388$			2.84092i			0.144226i
$389$	−3.74201			−0.189727			−0.0948637	−	0.995490i	$-0.530242\pi$
$389$	−3.74201			−0.189727			−0.0948637	+	0.995490i	$0.530242\pi$
$390$	21.6508			1.09633
$391$	−11.2554	−	16.0000i	−0.569212	−	0.809155i
$392$	1.00000			0.0505076
$393$	10.6694			0.538201
$394$		−	22.2850i		−	1.12270i
$395$	17.9036			0.900830
$396$			3.17307i			0.159453i
$397$		−	12.7166i		−	0.638227i	−0.947716	−	0.319114i	$-0.896615\pi$
$397$		−	12.7166i		−	0.638227i	0.947716	−	0.319114i	$-0.103385\pi$
$398$		−	17.2083i		−	0.862573i
$399$	−1.26942			−0.0635507
$400$	−13.5078			−0.675389
$401$		−	16.5519i		−	0.826560i	−0.910604	−	0.413280i	$-0.864383\pi$
$401$		−	16.5519i		−	0.826560i	0.910604	−	0.413280i	$-0.135617\pi$
$402$		−	0.442496i		−	0.0220697i
$403$		−	43.3015i		−	2.15700i
$404$	−2.98857			−0.148687
$405$		−	4.30207i		−	0.213771i
$406$	7.33471			0.364016
$407$	22.3151			1.10612
$408$	2.37228	+	3.37228i	0.117445	+	0.166953i
$409$	20.4767			1.01251			0.506254	−	0.862384i	$-0.331030\pi$
$409$	20.4767			1.01251			0.506254	+	0.862384i	$0.331030\pi$
$410$	−43.9057			−2.16835
$411$			11.2083i			0.552863i
$412$	−0.302067			−0.0148818
$413$			3.47514i			0.171000i
$414$		−	4.74456i		−	0.233183i
$415$		−	2.95337i		−	0.144975i
$416$	−5.03264			−0.246746
$417$	17.0466			0.834777
$418$		−	4.02797i		−	0.197015i
$419$		−	16.6923i		−	0.815471i	−0.913100	−	0.407736i	$-0.866318\pi$
$419$		−	16.6923i		−	0.815471i	0.913100	−	0.407736i	$-0.133682\pi$
$420$		−	4.30207i		−	0.209919i
$421$	27.2083			1.32605			0.663025	−	0.748597i	$-0.269272\pi$
$421$	27.2083			1.32605			0.663025	+	0.748597i	$0.269272\pi$
$422$			5.40985i			0.263348i
$423$	8.60413			0.418347
$424$	6.44250			0.312875
$425$	−45.5520	+	32.0443i	−2.20960	+	1.55437i
$426$	10.8098			0.523739
$427$	6.20571			0.300316
$428$		−	16.2197i		−	0.784009i
$429$	−15.9689			−0.770987
$430$		−	1.90365i		−	0.0918020i
$431$		−	34.1455i		−	1.64473i	−0.568958	−	0.822366i	$-0.692653\pi$
$431$		−	34.1455i		−	1.64473i	0.568958	−	0.822366i	$-0.307347\pi$
$432$			1.00000i			0.0481125i
$433$	−13.1430			−0.631611			−0.315806	−	0.948824i	$-0.602275\pi$
$433$	−13.1430			−0.631611			−0.315806	+	0.948824i	$0.602275\pi$
$434$	−8.60413			−0.413012
$435$		−	31.5544i		−	1.51292i
$436$		−	2.59015i		−	0.124046i
$437$			6.02287i			0.288113i
$438$	−5.76322			−0.275377
$439$			12.7968i			0.610760i	0.952231	+	0.305380i	$0.0987835\pi$
$439$			12.7968i			0.610760i	−0.952231	+	0.305380i	$0.901217\pi$
$440$	13.6508			0.650775
$441$	1.00000			0.0476190
$442$	−16.9715	+	11.9388i	−0.807251	+	0.567873i
$443$	−34.7855			−1.65271			−0.826356	−	0.563149i	$-0.809590\pi$
$443$	−34.7855			−1.65271			−0.826356	+	0.563149i	$0.809590\pi$
$444$	7.03264			0.333754
$445$		−	64.1275i		−	3.03993i
$446$	−2.20571			−0.104444
$447$		−	17.3928i		−	0.822650i
$448$			1.00000i			0.0472456i
$449$			25.3456i			1.19613i	0.801447	+	0.598066i	$0.204064\pi$
$449$			25.3456i			1.19613i	−0.801447	+	0.598066i	$0.795936\pi$
$450$	−13.5078			−0.636763
$451$	32.3835			1.52488
$452$		−	8.30207i		−	0.390496i
$453$		−	14.9503i		−	0.702425i
$454$			7.80729i			0.366414i
$455$	21.6508			1.01500
$456$		−	1.26942i		−	0.0594463i
$457$	−16.1989			−0.757755			−0.378877	−	0.925447i	$-0.623690\pi$
$457$	−16.1989			−0.757755			−0.378877	+	0.925447i	$0.623690\pi$
$458$	−2.11034			−0.0986098
$459$	2.37228	+	3.37228i	0.110729	+	0.157405i
$460$	−20.4114			−0.951688
$461$	12.5379			0.583947			0.291973	−	0.956426i	$-0.405688\pi$
$461$	12.5379			0.583947			0.291973	+	0.956426i	$0.405688\pi$
$462$			3.17307i			0.147625i
$463$	−21.2964			−0.989728			−0.494864	−	0.868970i	$-0.664782\pi$
$463$	−21.2964			−0.989728			−0.494864	+	0.868970i	$0.664782\pi$
$464$			7.33471i			0.340505i
$465$			37.0156i			1.71656i
$466$			12.1094i			0.560955i
$467$	41.5828			1.92422			0.962112	−	0.272654i	$-0.0879014\pi$
$467$	41.5828			1.92422			0.962112	+	0.272654i	$0.0879014\pi$
$468$	−5.03264			−0.232634
$469$		−	0.442496i		−	0.0204326i
$470$		−	37.0156i		−	1.70740i
$471$		−	13.4751i		−	0.620902i
$472$	−3.47514			−0.159956
$473$			1.40407i			0.0645592i
$474$	−4.16164			−0.191150
$475$	17.1471			0.786763
$476$	2.37228	+	3.37228i	0.108733	+	0.154568i
$477$	6.44250			0.294982
$478$	−10.1845			−0.465828
$479$			9.13478i			0.417379i	0.977982	+	0.208689i	$0.0669198\pi$
$479$			9.13478i			0.417379i	−0.977982	+	0.208689i	$0.933080\pi$
$480$	4.30207			0.196362
$481$			35.3928i			1.61377i
$482$			13.6296i			0.620809i
$483$		−	4.74456i		−	0.215885i
$484$	0.931621			0.0423464
$485$	12.2218			0.554964
$486$			1.00000i			0.0453609i
$487$			24.7937i			1.12351i	0.827303	+	0.561756i	$0.189874\pi$
$487$			24.7937i			1.12351i	−0.827303	+	0.561756i	$0.810126\pi$
$488$			6.20571i			0.280919i
$489$	−5.73313			−0.259261
$490$		−	4.30207i		−	0.194348i
$491$	−5.37300			−0.242480			−0.121240	−	0.992623i	$-0.538687\pi$
$491$	−5.37300			−0.242480			−0.121240	+	0.992623i	$0.538687\pi$
$492$	10.2057			0.460109
$493$	17.4000	+	24.7347i	0.783656	+	1.11399i
$494$	6.38856			0.287435
$495$	13.6508			0.613556
$496$		−	8.60413i		−	0.386337i
$497$	10.8098			0.484888
$498$			0.686500i			0.0307628i
$499$		−	25.2596i		−	1.13077i	−0.824826	−	0.565387i	$-0.808727\pi$
$499$		−	25.2596i		−	1.13077i	0.824826	−	0.565387i	$-0.191273\pi$
$500$			36.6010i			1.63685i
$501$	−17.6228			−0.787328
$502$	24.2409			1.08192
$503$			20.4114i			0.910101i	0.890466	+	0.455050i	$0.150379\pi$
$503$			20.4114i			0.910101i	−0.890466	+	0.455050i	$0.849621\pi$
$504$			1.00000i			0.0445435i
$505$			12.8570i			0.572130i
$506$	15.0548			0.669269
$507$		−	12.3275i		−	0.547483i
$508$	14.6694			0.650850
$509$	13.8507			0.613921			0.306961	−	0.951722i	$-0.400688\pi$
$509$	13.8507			0.613921			0.306961	+	0.951722i	$0.400688\pi$
$510$	14.5078	−	10.2057i	0.642415	−	0.451917i
$511$	−5.76322			−0.254950
$512$	−1.00000			−0.0441942
$513$		−	1.26942i		−	0.0560465i
$514$	26.3021			1.16013
$515$			1.29951i			0.0572634i
$516$			0.442496i			0.0194798i
$517$			27.3015i			1.20072i
$518$	7.03264			0.308997
$519$	10.3984			0.456440
$520$			21.6508i			0.949449i
$521$			26.3218i			1.15318i	0.817033	+	0.576590i	$0.195617\pi$
$521$			26.3218i			1.15318i	−0.817033	+	0.576590i	$0.804383\pi$
$522$			7.33471i			0.321031i
$523$	−32.0974			−1.40352			−0.701760	−	0.712413i	$-0.747602\pi$
$523$	−32.0974			−1.40352			−0.701760	+	0.712413i	$0.747602\pi$
$524$			10.6694i			0.466096i
$525$	−13.5078			−0.589528
$526$	23.5855			1.02838
$527$	−20.4114	−	29.0156i	−0.889136	−	1.26394i
$528$	−3.17307			−0.138090
$529$	0.489125			0.0212663
$530$		−	27.7160i		−	1.20391i
$531$	−3.47514			−0.150808
$532$		−	1.26942i		−	0.0550365i
$533$			51.3617i			2.22472i
$534$			14.9062i			0.645054i
$535$	−69.7782			−3.01678
$536$	0.442496			0.0191129
$537$			2.95028i			0.127314i
$538$		−	1.62955i		−	0.0702551i
$539$			3.17307i			0.136674i
$540$	4.30207			0.185131
$541$			44.2689i			1.90327i	0.307234	+	0.951634i	$0.400597\pi$
$541$			44.2689i			1.90327i	−0.307234	+	0.951634i	$0.599403\pi$
$542$	−25.2295			−1.08370
$543$	−16.1828			−0.694472
$544$	−3.37228	+	2.37228i	−0.144585	+	0.101711i
$545$	−11.1430			−0.477313
$546$	−5.03264			−0.215377
$547$			22.8368i			0.976433i	0.872723	+	0.488216i	$0.162352\pi$
$547$			22.8368i			0.976433i	−0.872723	+	0.488216i	$0.837648\pi$
$548$	−11.2083			−0.478793
$549$			6.20571i			0.264853i
$550$		−	42.8611i		−	1.82761i
$551$		−	9.31086i		−	0.396656i
$552$	4.74456			0.201942
$553$	−4.16164			−0.176971
$554$		−	13.1290i		−	0.557798i
$555$		−	30.2549i		−	1.28425i
$556$			17.0466i			0.722938i
$557$	−32.3120			−1.36910			−0.684551	−	0.728965i	$-0.740002\pi$
$557$	−32.3120			−1.36910			−0.684551	+	0.728965i	$0.740002\pi$
$558$		−	8.60413i		−	0.364242i
$559$	−2.22692			−0.0941888
$560$	4.30207			0.181796
$561$	−10.7005	+	7.52742i	−0.451775	+	0.317808i
$562$	−23.4010			−0.987111
$563$	−29.7021			−1.25179			−0.625896	−	0.779906i	$-0.715267\pi$
$563$	−29.7021			−1.25179			−0.625896	+	0.779906i	$0.715267\pi$
$564$			8.60413i			0.362299i
$565$	−35.7160			−1.50259
$566$			7.99691i			0.336135i
$567$			1.00000i			0.0419961i
$568$			10.8098i			0.453571i
$569$	−18.1306			−0.760073			−0.380036	−	0.924971i	$-0.624089\pi$
$569$	−18.1306			−0.760073			−0.380036	+	0.924971i	$0.624089\pi$
$570$	−5.46115			−0.228742
$571$		−	18.4254i		−	0.771080i	−0.922691	−	0.385540i	$-0.874015\pi$
$571$		−	18.4254i		−	0.771080i	0.922691	−	0.385540i	$-0.125985\pi$
$572$		−	15.9689i		−	0.667695i
$573$		−	15.3046i		−	0.639360i
$574$	10.2057			0.425978
$575$			64.0885i			2.67268i
$576$	−1.00000			−0.0416667
$577$	36.2238			1.50802			0.754009	−	0.656864i	$-0.228118\pi$
$577$	36.2238			1.50802			0.754009	+	0.656864i	$0.228118\pi$
$578$	−5.74456	+	16.0000i	−0.238942	+	0.665512i
$579$	−1.93472			−0.0804040
$580$	31.5544			1.31023
$581$			0.686500i			0.0284808i
$582$	−2.84092			−0.117760
$583$			20.4425i			0.846642i
$584$		−	5.76322i		−	0.238484i
$585$			21.6508i			0.895149i
$586$	−1.78030			−0.0735435
$587$	43.3839			1.79064			0.895322	−	0.445419i	$-0.146945\pi$
$587$	43.3839			1.79064			0.895322	+	0.445419i	$0.146945\pi$
$588$			1.00000i			0.0412393i
$589$			10.9223i			0.450046i
$590$			14.9503i			0.615493i
$591$	22.2850			0.916682
$592$			7.03264i			0.289040i
$593$	−43.1840			−1.77335			−0.886676	−	0.462390i	$-0.846992\pi$
$593$	−43.1840			−1.77335			−0.886676	+	0.462390i	$0.846992\pi$
$594$	−3.17307			−0.130193
$595$	14.5078	−	10.2057i	0.594761	−	0.418393i
$596$	17.3928			0.712436
$597$	17.2083			0.704288
$598$			23.8777i			0.976431i
$599$	9.48913			0.387715			0.193858	−	0.981030i	$-0.437900\pi$
$599$	9.48913			0.387715			0.193858	+	0.981030i	$0.437900\pi$
$600$		−	13.5078i		−	0.551453i
$601$		−	30.5570i		−	1.24644i	−0.782045	−	0.623222i	$-0.785823\pi$
$601$		−	30.5570i		−	1.24644i	0.782045	−	0.623222i	$-0.214177\pi$
$602$			0.442496i			0.0180348i
$603$	0.442496			0.0180198
$604$	14.9503			0.608318
$605$		−	4.00790i		−	0.162944i
$606$		−	2.98857i		−	0.121402i
$607$			39.6705i			1.61018i	0.593154	+	0.805089i	$0.297882\pi$
$607$			39.6705i			1.61018i	−0.593154	+	0.805089i	$0.702118\pi$
$608$	1.26942			0.0514820
$609$			7.33471i			0.297217i
$610$	26.6974			1.08095
$611$	−43.3015			−1.75179
$612$	−3.37228	+	2.37228i	−0.136316	+	0.0958938i
$613$	23.8124			0.961774			0.480887	−	0.876783i	$-0.340315\pi$
$613$	23.8124			0.961774			0.480887	+	0.876783i	$0.340315\pi$
$614$	12.0270			0.485370
$615$		−	43.9057i		−	1.77045i
$616$	−3.17307			−0.127847
$617$		−	43.5476i		−	1.75316i	−0.481254	−	0.876581i	$-0.659819\pi$
$617$		−	43.5476i		−	1.75316i	0.481254	−	0.876581i	$-0.340181\pi$
$618$		−	0.302067i		−	0.0121509i
$619$			5.17720i			0.208089i	0.994573	+	0.104045i	$0.0331785\pi$
$619$			5.17720i			0.208089i	−0.994573	+	0.104045i	$0.966822\pi$
$620$	−37.0156			−1.48658
$621$	4.74456			0.190393
$622$		−	17.1772i		−	0.688743i
$623$			14.9062i			0.597204i
$624$		−	5.03264i		−	0.201467i
$625$	89.9212			3.59685
$626$			13.6296i			0.544747i
$627$	4.02797			0.160862
$628$	13.4751			0.537717
$629$	16.6834	+	23.7160i	0.665211	+	0.945621i
$630$	4.30207			0.171398
$631$	17.9771			0.715658			0.357829	−	0.933787i	$-0.383517\pi$
$631$	17.9771			0.715658			0.357829	+	0.933787i	$0.383517\pi$
$632$		−	4.16164i		−	0.165541i
$633$	−5.40985			−0.215022
$634$			10.9233i			0.433819i
$635$		−	63.1088i		−	2.50440i
$636$			6.44250i			0.255462i
$637$	−5.03264			−0.199401
$638$	−23.2736			−0.921409
$639$			10.8098i			0.427631i
$640$			4.30207i			0.170054i
$641$		−	2.51764i		−	0.0994408i	−0.998763	−	0.0497204i	$-0.984167\pi$
$641$		−	2.51764i		−	0.0994408i	0.998763	−	0.0497204i	$-0.0158330\pi$
$642$	16.2197			0.640141
$643$		−	3.64565i		−	0.143771i	−0.997413	−	0.0718853i	$-0.977098\pi$
$643$		−	3.64565i		−	0.143771i	0.997413	−	0.0718853i	$-0.0229015\pi$
$644$	4.74456			0.186962
$645$	1.90365			0.0749560
$646$	4.28086	−	3.01143i	0.168428	−	0.118483i
$647$	45.0715			1.77194			0.885972	−	0.463739i	$-0.153492\pi$
$647$	45.0715			1.77194			0.885972	+	0.463739i	$0.153492\pi$
$648$	−1.00000			−0.0392837
$649$		−	11.0269i		−	0.432842i
$650$	67.9798			2.66639
$651$		−	8.60413i		−	0.337223i
$652$		−	5.73313i		−	0.224527i
$653$			4.19173i			0.164035i	0.996631	+	0.0820174i	$0.0261363\pi$
$653$			4.19173i			0.164035i	−0.996631	+	0.0820174i	$0.973864\pi$
$654$	2.59015			0.101283
$655$	45.9006			1.79348
$656$			10.2057i			0.398466i
$657$		−	5.76322i		−	0.224845i
$658$			8.60413i			0.335424i
$659$	8.85702			0.345020			0.172510	−	0.985008i	$-0.444812\pi$
$659$	8.85702			0.345020			0.172510	+	0.985008i	$0.444812\pi$
$660$			13.6508i			0.531355i
$661$	−11.2451			−0.437385			−0.218692	−	0.975794i	$-0.570179\pi$
$661$	−11.2451			−0.437385			−0.218692	+	0.975794i	$0.570179\pi$
$662$	−15.1119			−0.587341
$663$	−11.9388	−	16.9715i	−0.463666	−	0.659118i
$664$	−0.686500			−0.0266414
$665$	−5.46115			−0.211774
$666$			7.03264i			0.272509i
$667$	34.8000			1.34746
$668$		−	17.6228i		−	0.681846i
$669$		−	2.20571i		−	0.0852778i
$670$		−	1.90365i		−	0.0735443i
$671$	−19.6912			−0.760169
$672$	−1.00000			−0.0385758
$673$		−	49.6477i		−	1.91378i	−0.290456	−	0.956888i	$-0.593807\pi$
$673$		−	49.6477i		−	1.91378i	0.290456	−	0.956888i	$-0.406193\pi$
$674$			10.0933i			0.388778i
$675$		−	13.5078i		−	0.519915i
$676$	12.3275			0.474134
$677$			17.9819i			0.691102i	0.938400	+	0.345551i	$0.112308\pi$
$677$			17.9819i			0.691102i	−0.938400	+	0.345551i	$0.887692\pi$
$678$	8.30207			0.318839
$679$	−2.84092			−0.109024
$680$	10.2057	+	14.5078i	0.391371	+	0.556348i
$681$	−7.80729			−0.299176
$682$	27.3015			1.04543
$683$			14.4497i			0.552903i	0.961028	+	0.276452i	$0.0891585\pi$
$683$			14.4497i			0.552903i	−0.961028	+	0.276452i	$0.910841\pi$
$684$	1.26942			0.0485377
$685$			48.2187i			1.84234i
$686$			1.00000i			0.0381802i
$687$		−	2.11034i		−	0.0805145i
$688$	−0.442496			−0.0168700
$689$	−32.4228			−1.23521
$690$		−	20.4114i		−	0.777050i
$691$			49.2052i			1.87185i	0.352195	+	0.935927i	$0.385435\pi$
$691$			49.2052i			1.87185i	−0.352195	+	0.935927i	$0.614565\pi$
$692$			10.3984i			0.395289i
$693$	−3.17307			−0.120535
$694$		−	18.6114i		−	0.706477i
$695$	73.3357			2.78178
$696$	−7.33471			−0.278021
$697$	24.2108	+	34.4165i	0.917050	+	1.30362i
$698$	−27.5715			−1.04360
$699$	−12.1094			−0.458018
$700$		−	13.5078i		−	0.510546i
$701$	11.7389			0.443373			0.221686	−	0.975118i	$-0.428844\pi$
$701$	11.7389			0.443373			0.221686	+	0.975118i	$0.428844\pi$
$702$		−	5.03264i		−	0.189945i
$703$		−	8.92741i		−	0.336704i
$704$		−	3.17307i		−	0.119590i
$705$	37.0156			1.39409
$706$	−21.8285			−0.821526
$707$		−	2.98857i		−	0.112397i
$708$		−	3.47514i		−	0.130604i
$709$		−	12.7145i		−	0.477502i	−0.971081	−	0.238751i	$-0.923262\pi$
$709$		−	12.7145i		−	0.477502i	0.971081	−	0.238751i	$-0.0767380\pi$
$710$	46.5047			1.74529
$711$		−	4.16164i		−	0.156074i
$712$	−14.9062			−0.558633
$713$	−40.8229			−1.52883
$714$	−3.37228	+	2.37228i	−0.126204	+	0.0887804i
$715$	−68.6994			−2.56921
$716$	−2.95028			−0.110257
$717$		−	10.1845i		−	0.380347i
$718$	20.7968			0.776131
$719$			3.46626i			0.129270i	0.997909	+	0.0646348i	$0.0205883\pi$
$719$			3.46626i			0.129270i	−0.997909	+	0.0646348i	$0.979412\pi$
$720$			4.30207i			0.160329i
$721$		−	0.302067i		−	0.0112496i
$722$	17.3886			0.647135
$723$	−13.6296			−0.506889
$724$		−	16.1828i		−	0.601431i
$725$		−	99.0756i		−	3.67958i
$726$			0.931621i			0.0345757i
$727$	19.3405			0.717299			0.358650	−	0.933472i	$-0.383237\pi$
$727$	19.3405			0.717299			0.358650	+	0.933472i	$0.383237\pi$
$728$		−	5.03264i		−	0.186522i
$729$	−1.00000			−0.0370370
$730$	−24.7937			−0.917658
$731$	−1.49222	+	1.04972i	−0.0551917	+	0.0388255i
$732$	−6.20571			−0.229370
$733$	−7.98601			−0.294970			−0.147485	−	0.989064i	$-0.547118\pi$
$733$	−7.98601			−0.294970			−0.147485	+	0.989064i	$0.547118\pi$
$734$			17.8124i			0.657468i
$735$	4.30207			0.158684
$736$			4.74456i			0.174887i
$737$			1.40407i			0.0517196i
$738$			10.2057i			0.375677i
$739$	−13.9771			−0.514157			−0.257079	−	0.966390i	$-0.582760\pi$
$739$	−13.9771			−0.514157			−0.257079	+	0.966390i	$0.582760\pi$
$740$	30.2549			1.11219
$741$			6.38856i			0.234690i
$742$			6.44250i			0.236511i
$743$		−	30.3363i		−	1.11293i	−0.830871	−	0.556465i	$-0.812157\pi$
$743$		−	30.3363i		−	1.11293i	0.830871	−	0.556465i	$-0.187843\pi$
$744$	8.60413			0.315443
$745$		−	74.8249i		−	2.74137i
$746$	12.6694			0.463860
$747$	−0.686500			−0.0251177
$748$	−7.52742	−	10.7005i	−0.275230	−	0.391249i
$749$	16.2197			0.592655
$750$	−36.6010			−1.33648
$751$			14.5668i			0.531551i	0.964035	+	0.265775i	$0.0856280\pi$
$751$			14.5668i			0.531551i	−0.964035	+	0.265775i	$0.914372\pi$
$752$	−8.60413			−0.313760
$753$			24.2409i			0.883388i
$754$		−	36.9130i		−	1.34429i
$755$		−	64.3171i		−	2.34074i
$756$	−1.00000			−0.0363696
$757$	−28.1814			−1.02427			−0.512135	−	0.858905i	$-0.671145\pi$
$757$	−28.1814			−1.02427			−0.512135	+	0.858905i	$0.671145\pi$
$758$		−	7.66785i		−	0.278509i
$759$			15.0548i			0.546456i
$760$		−	5.46115i		−	0.198097i
$761$	−44.5539			−1.61508			−0.807538	−	0.589815i	$-0.799201\pi$
$761$	−44.5539			−1.61508			−0.807538	+	0.589815i	$0.799201\pi$
$762$			14.6694i			0.531417i
$763$	2.59015			0.0937696
$764$	15.3046			0.553702
$765$	10.2057	+	14.5078i	0.368988	+	0.524530i
$766$	−21.4612			−0.775423
$767$	17.4891			0.631496
$768$		−	1.00000i		−	0.0360844i
$769$	12.3886			0.446743			0.223371	−	0.974733i	$-0.428294\pi$
$769$	12.3886			0.446743			0.223371	+	0.974733i	$0.428294\pi$
$770$			13.6508i			0.491939i
$771$			26.3021i			0.947246i
$772$		−	1.93472i		−	0.0696319i
$773$	12.4497			0.447785			0.223893	−	0.974614i	$-0.428124\pi$
$773$	12.4497			0.447785			0.223893	+	0.974614i	$0.428124\pi$
$774$	−0.442496			−0.0159052
$775$			116.223i			4.17484i
$776$		−	2.84092i		−	0.101983i
$777$			7.03264i			0.252295i
$778$	3.74201			0.134157
$779$		−	12.9554i		−	0.464175i
$780$	−21.6508			−0.775222
$781$	−34.3004			−1.22737
$782$	11.2554	+	16.0000i	0.402494	+	0.572159i
$783$	−7.33471			−0.262121
$784$	−1.00000			−0.0357143
$785$		−	57.9709i		−	2.06907i
$786$	−10.6694			−0.380566
$787$			8.16164i			0.290931i	0.989363	+	0.145465i	$0.0464680\pi$
$787$			8.16164i			0.290931i	−0.989363	+	0.145465i	$0.953532\pi$
$788$			22.2850i			0.793870i
$789$			23.5855i			0.839665i
$790$	−17.9036			−0.636983
$791$	8.30207			0.295188
$792$		−	3.17307i		−	0.112750i
$793$		−	31.2311i		−	1.10905i
$794$			12.7166i			0.451295i
$795$	27.7160			0.982987
$796$			17.2083i			0.609931i
$797$	22.6311			0.801636			0.400818	−	0.916158i	$-0.368726\pi$
$797$	22.6311			0.801636			0.400818	+	0.916158i	$0.368726\pi$
$798$	1.26942			0.0449372
$799$	−29.0156	+	20.4114i	−1.02650	+	0.722104i
$800$	13.5078			0.477572
$801$	−14.9062			−0.526685
$802$			16.5519i			0.584466i
$803$	18.2871			0.645338
$804$			0.442496i			0.0156056i
$805$		−	20.4114i		−	0.719408i
$806$			43.3015i			1.52523i
$807$	1.62955			0.0573630
$808$	2.98857			0.105137
$809$			7.06273i			0.248312i	0.992263	+	0.124156i	$0.0396224\pi$
$809$			7.06273i			0.248312i	−0.992263	+	0.124156i	$0.960378\pi$
$810$			4.30207i			0.151159i
$811$			12.3543i			0.433820i	0.976192	+	0.216910i	$0.0695978\pi$
$811$			12.3543i			0.433820i	−0.976192	+	0.216910i	$0.930402\pi$
$812$	−7.33471			−0.257398
$813$		−	25.2295i		−	0.884836i
$814$	−22.3151			−0.782143
$815$	−24.6643			−0.863953
$816$	−2.37228	−	3.37228i	−0.0830465	−	0.118053i
$817$	0.561715			0.0196519
$818$	−20.4767			−0.715951
$819$		−	5.03264i		−	0.175855i
$820$	43.9057			1.53325
$821$			14.7306i			0.514101i	0.966398	+	0.257050i	$0.0827506\pi$
$821$			14.7306i			0.514101i	−0.966398	+	0.257050i	$0.917249\pi$
$822$		−	11.2083i		−	0.390933i
$823$		−	43.0517i		−	1.50069i	−0.661047	−	0.750345i	$-0.729888\pi$
$823$		−	43.0517i		−	1.50069i	0.661047	−	0.750345i	$-0.270112\pi$
$824$	0.302067			0.0105230
$825$	42.8611			1.49223
$826$		−	3.47514i		−	0.120916i
$827$			25.7823i			0.896539i	0.893898	+	0.448269i	$0.147959\pi$
$827$			25.7823i			0.896539i	−0.893898	+	0.448269i	$0.852041\pi$
$828$			4.74456i			0.164885i
$829$	−24.9985			−0.868233			−0.434117	−	0.900857i	$-0.642939\pi$
$829$	−24.9985			−0.868233			−0.434117	+	0.900857i	$0.642939\pi$
$830$			2.95337i			0.102513i
$831$	13.1290			0.455440
$832$	5.03264			0.174475
$833$	−3.37228	+	2.37228i	−0.116843	+	0.0821947i
$834$	−17.0466			−0.590277
$835$	−75.8144			−2.62367
$836$			4.02797i			0.139310i
$837$	8.60413			0.297402
$838$			16.6923i			0.576625i
$839$		−	0.189613i		−	0.00654617i	−0.999995	−	0.00327308i	$-0.998958\pi$
$839$		−	0.189613i		−	0.00654617i	0.999995	−	0.00327308i	$-0.00104186\pi$
$840$			4.30207i			0.148435i
$841$	−24.7980			−0.855102
$842$	−27.2083			−0.937659
$843$		−	23.4010i		−	0.805972i
$844$		−	5.40985i		−	0.186215i
$845$		−	53.0337i		−	1.82441i
$846$	−8.60413			−0.295816
$847$			0.931621i			0.0320109i
$848$	−6.44250			−0.221236
$849$	−7.99691			−0.274453
$850$	45.5520	−	32.0443i	1.56242	−	1.09911i
$851$	33.3668			1.14380
$852$	−10.8098			−0.370339
$853$		−	33.4648i		−	1.14581i	−0.819621	−	0.572907i	$-0.805816\pi$
$853$		−	33.4648i		−	1.14581i	0.819621	−	0.572907i	$-0.194184\pi$
$854$	−6.20571			−0.212355
$855$		−	5.46115i		−	0.186767i
$856$			16.2197i			0.554378i
$857$			29.4513i			1.00604i	0.864276	+	0.503018i	$0.167777\pi$
$857$			29.4513i			1.00604i	−0.864276	+	0.503018i	$0.832223\pi$
$858$	15.9689			0.545170
$859$	−6.28498			−0.214441			−0.107220	−	0.994235i	$-0.534195\pi$
$859$	−6.28498			−0.214441			−0.107220	+	0.994235i	$0.534195\pi$
$860$			1.90365i			0.0649138i
$861$			10.2057i			0.347810i
$862$			34.1455i			1.16300i
$863$	7.52953			0.256308			0.128154	−	0.991754i	$-0.459095\pi$
$863$	7.52953			0.256308			0.128154	+	0.991754i	$0.459095\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	44.7347			1.52103
$866$	13.1430			0.446617
$867$	−16.0000	−	5.74456i	−0.543388	−	0.195096i
$868$	8.60413			0.292043
$869$	13.2052			0.447955
$870$			31.5544i			1.06979i
$871$	−2.22692			−0.0754564
$872$			2.59015i			0.0877134i
$873$		−	2.84092i		−	0.0961505i
$874$		−	6.02287i		−	0.203726i
$875$	−36.6010			−1.23734
$876$	5.76322			0.194721
$877$			26.0109i			0.878325i	0.898408	+	0.439163i	$0.144725\pi$
$877$			26.0109i			0.878325i	−0.898408	+	0.439163i	$0.855275\pi$
$878$		−	12.7968i		−	0.431872i
$879$		−	1.78030i		−	0.0600480i
$880$	−13.6508			−0.460167
$881$		−	31.0026i		−	1.04450i	−0.852792	−	0.522251i	$-0.825092\pi$
$881$		−	31.0026i		−	1.04450i	0.852792	−	0.522251i	$-0.174908\pi$
$882$	−1.00000			−0.0336718
$883$	−23.9234			−0.805087			−0.402544	−	0.915401i	$-0.631874\pi$
$883$	−23.9234			−0.805087			−0.402544	+	0.915401i	$0.631874\pi$
$884$	16.9715	−	11.9388i	0.570813	−	0.401547i
$885$	−14.9503			−0.502548
$886$	34.7855			1.16864
$887$			32.2922i			1.08427i	0.840293	+	0.542133i	$0.182383\pi$
$887$			32.2922i			1.08427i	−0.840293	+	0.542133i	$0.817617\pi$
$888$	−7.03264			−0.236000
$889$			14.6694i			0.491996i
$890$			64.1275i			2.14956i
$891$		−	3.17307i		−	0.106302i
$892$	2.20571			0.0738527
$893$	10.9223			0.365501
$894$			17.3928i			0.581701i
$895$			12.6923i			0.424256i
$896$		−	1.00000i		−	0.0334077i
$897$	−23.8777			−0.797253
$898$		−	25.3456i		−	0.845794i
$899$	63.1088			2.10480
$900$	13.5078			0.450259
$901$	−21.7259	+	15.2834i	−0.723795	+	0.509164i
$902$	−32.3835			−1.07825
$903$	−0.442496			−0.0147253
$904$			8.30207i			0.276123i
$905$	−69.6197			−2.31424
$906$			14.9503i			0.496690i
$907$		−	3.59745i		−	0.119451i	−0.998215	−	0.0597257i	$-0.980977\pi$
$907$		−	3.59745i		−	0.119451i	0.998215	−	0.0597257i	$-0.0190226\pi$
$908$		−	7.80729i		−	0.259094i
$909$	2.98857			0.0991245
$910$	−21.6508			−0.717716
$911$			5.24610i			0.173811i	0.996217	+	0.0869056i	$0.0276978\pi$
$911$			5.24610i			0.173811i	−0.996217	+	0.0869056i	$0.972302\pi$
$912$			1.26942i			0.0420349i
$913$		−	2.17831i		−	0.0720917i
$914$	16.1989			0.535814
$915$			26.6974i			0.882589i
$916$	2.11034			0.0697276
$917$	−10.6694			−0.352335
$918$	−2.37228	−	3.37228i	−0.0782970	−	0.111302i
$919$	−17.0011			−0.560815			−0.280408	−	0.959881i	$-0.590470\pi$
$919$	−17.0011			−0.560815			−0.280408	+	0.959881i	$0.590470\pi$
$920$	20.4114			0.672945
$921$			12.0270i			0.396303i
$922$	−12.5379			−0.412913
$923$		−	54.4021i		−	1.79067i
$924$		−	3.17307i		−	0.104386i
$925$		−	94.9954i		−	3.12343i
$926$	21.2964			0.699844
$927$	0.302067			0.00992118
$928$		−	7.33471i		−	0.240774i
$929$		−	4.74456i		−	0.155664i	−0.996966	−	0.0778320i	$-0.975200\pi$
$929$		−	4.74456i		−	0.155664i	0.996966	−	0.0778320i	$-0.0247998\pi$
$930$		−	37.0156i		−	1.21379i
$931$	1.26942			0.0416037
$932$		−	12.1094i		−	0.396655i
$933$	17.1772			0.562356
$934$	−41.5828			−1.36063
$935$	−46.0342	+	32.3835i	−1.50548	+	1.05905i
$936$	5.03264			0.164497
$937$	−19.9006			−0.650123			−0.325061	−	0.945693i	$-0.605385\pi$
$937$	−19.9006			−0.650123			−0.325061	+	0.945693i	$0.605385\pi$
$938$			0.442496i			0.0144480i
$939$	−13.6296			−0.444784
$940$			37.0156i			1.20731i
$941$			35.5756i			1.15973i	0.814712	+	0.579866i	$0.196895\pi$
$941$			35.5756i			1.15973i	−0.814712	+	0.579866i	$0.803105\pi$
$942$			13.4751i			0.439044i
$943$	48.4216			1.57683
$944$	3.47514			0.113106
$945$			4.30207i			0.139946i
$946$		−	1.40407i		−	0.0456503i
$947$			24.7617i			0.804647i	0.915498	+	0.402323i	$0.131797\pi$
$947$			24.7617i			0.804647i	−0.915498	+	0.402323i	$0.868203\pi$
$948$	4.16164			0.135164
$949$			29.0042i			0.941517i
$950$	−17.1471			−0.556326
$951$	−10.9233			−0.354212
$952$	−2.37228	−	3.37228i	−0.0768861	−	0.109296i
$953$	−27.7078			−0.897545			−0.448773	−	0.893646i	$-0.648139\pi$
$953$	−27.7078			−0.897545			−0.448773	+	0.893646i	$0.648139\pi$
$954$	−6.44250			−0.208583
$955$		−	65.8415i		−	2.13058i
$956$	10.1845			0.329390
$957$		−	23.2736i		−	0.752327i
$958$		−	9.13478i		−	0.295131i
$959$		−	11.2083i		−	0.361934i
$960$	−4.30207			−0.138849
$961$	−43.0311			−1.38810
$962$		−	35.3928i		−	1.14111i
$963$			16.2197i			0.522673i
$964$		−	13.6296i		−	0.438978i
$965$	−8.32328			−0.267936
$966$			4.74456i			0.152654i
$967$	−56.8788			−1.82910			−0.914549	−	0.404474i	$-0.867455\pi$
$967$	−56.8788			−1.82910			−0.914549	+	0.404474i	$0.867455\pi$
$968$	−0.931621			−0.0299434
$969$	3.01143	+	4.28086i	0.0967412	+	0.137521i
$970$	−12.2218			−0.392419
$971$	0.405643			0.0130177			0.00650885	−	0.999979i	$-0.497928\pi$
$971$	0.405643			0.0130177			0.00650885	+	0.999979i	$0.497928\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−17.0466			−0.546490
$974$		−	24.7937i		−	0.794443i
$975$			67.9798i			2.17710i
$976$		−	6.20571i		−	0.198640i
$977$	−8.75953			−0.280242			−0.140121	−	0.990134i	$-0.544749\pi$
$977$	−8.75953			−0.280242			−0.140121	+	0.990134i	$0.544749\pi$
$978$	5.73313			0.183325
$979$		−	47.2984i		−	1.51166i
$980$			4.30207i			0.137424i
$981$			2.59015i			0.0826970i
$982$	5.37300			0.171459
$983$			58.1897i			1.85596i	0.372627	+	0.927981i	$0.378457\pi$
$983$			58.1897i			1.85596i	−0.372627	+	0.927981i	$0.621543\pi$
$984$	−10.2057			−0.325346
$985$	95.8715			3.05472
$986$	−17.4000	−	24.7347i	−0.554129	−	0.787713i
$987$	−8.60413			−0.273873
$988$	−6.38856			−0.203247
$989$			2.09945i			0.0667586i
$990$	−13.6508			−0.433850
$991$		−	0.292207i		−	0.00928226i	−0.999989	−	0.00464113i	$-0.998523\pi$
$991$		−	0.292207i		−	0.00928226i	0.999989	−	0.00464113i	$-0.00147732\pi$
$992$			8.60413i			0.273182i
$993$		−	15.1119i		−	0.479562i
$994$	−10.8098			−0.342868
$995$	74.0311			2.34694
$996$		−	0.686500i		−	0.0217526i
$997$			6.97458i			0.220887i	0.993882	+	0.110444i	$0.0352271\pi$
$997$			6.97458i			0.220887i	−0.993882	+	0.110444i	$0.964773\pi$
$998$			25.2596i			0.799578i
$999$	−7.03264			−0.222503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.b.f.169.1	✓	8
3.2	odd	2		2142.2.b.j.883.8		8
17.16	even	2	inner	714.2.b.f.169.8	yes	8
51.50	odd	2		2142.2.b.j.883.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.b.f.169.1	✓	8	1.1	even	1	trivial
714.2.b.f.169.8	yes	8	17.16	even	2	inner
2142.2.b.j.883.1		8	51.50	odd	2
2142.2.b.j.883.8		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -4.30207i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -4.30207i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +4.30207i q^{10} -3.17307i q^{11} -1.00000i q^{12} +5.03264 q^{13} -1.00000i q^{14} -4.30207 q^{15} +1.00000 q^{16} +(3.37228 - 2.37228i) q^{17} +1.00000 q^{18} -1.26942 q^{19} -4.30207i q^{20} +1.00000 q^{21} +3.17307i q^{22} -4.74456i q^{23} +1.00000i q^{24} -13.5078 q^{25} -5.03264 q^{26} +1.00000i q^{27} +1.00000i q^{28} +7.33471i q^{29} +4.30207 q^{30} -8.60413i q^{31} -1.00000 q^{32} -3.17307 q^{33} +(-3.37228 + 2.37228i) q^{34} +4.30207 q^{35} -1.00000 q^{36} +7.03264i q^{37} +1.26942 q^{38} -5.03264i q^{39} +4.30207i q^{40} +10.2057i q^{41} -1.00000 q^{42} -0.442496 q^{43} -3.17307i q^{44} +4.30207i q^{45} +4.74456i q^{46} -8.60413 q^{47} -1.00000i q^{48} -1.00000 q^{49} +13.5078 q^{50} +(-2.37228 - 3.37228i) q^{51} +5.03264 q^{52} -6.44250 q^{53} -1.00000i q^{54} -13.6508 q^{55} -1.00000i q^{56} +1.26942i q^{57} -7.33471i q^{58} +3.47514 q^{59} -4.30207 q^{60} -6.20571i q^{61} +8.60413i q^{62} -1.00000i q^{63} +1.00000 q^{64} -21.6508i q^{65} +3.17307 q^{66} -0.442496 q^{67} +(3.37228 - 2.37228i) q^{68} -4.74456 q^{69} -4.30207 q^{70} -10.8098i q^{71} +1.00000 q^{72} +5.76322i q^{73} -7.03264i q^{74} +13.5078i q^{75} -1.26942 q^{76} +3.17307 q^{77} +5.03264i q^{78} +4.16164i q^{79} -4.30207i q^{80} +1.00000 q^{81} -10.2057i q^{82} +0.686500 q^{83} +1.00000 q^{84} +(-10.2057 - 14.5078i) q^{85} +0.442496 q^{86} +7.33471 q^{87} +3.17307i q^{88} +14.9062 q^{89} -4.30207i q^{90} +5.03264i q^{91} -4.74456i q^{92} -8.60413 q^{93} +8.60413 q^{94} +5.46115i q^{95} +1.00000i q^{96} +2.84092i q^{97} +1.00000 q^{98} +3.17307i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 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

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