LMFDB - Embedded newform 714.2.b.f.169.7

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			169.7
Root			$-0.274234i$ of defining polynomial
Character	$\chi$	$=$	714.169
Dual form			714.2.b.f.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.13914i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.13914i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} -1.13914i q^{10} -6.43217i q^{11} +1.00000i q^{12} +0.590671 q^{13} +1.00000i q^{14} -1.13914 q^{15} +1.00000 q^{16} +(-2.37228 - 3.37228i) q^{17} +1.00000 q^{18} -2.54847 q^{19} +1.13914i q^{20} +1.00000 q^{21} +6.43217i q^{22} -6.74456i q^{23} -1.00000i q^{24} +3.70236 q^{25} -0.590671 q^{26} -1.00000i q^{27} -1.00000i q^{28} +0.270189i q^{29} +1.13914 q^{30} +2.27828i q^{31} -1.00000 q^{32} +6.43217 q^{33} +(2.37228 + 3.37228i) q^{34} +1.13914 q^{35} -1.00000 q^{36} -2.59067i q^{37} +2.54847 q^{38} +0.590671i q^{39} -1.13914i q^{40} +3.84150i q^{41} -1.00000 q^{42} +7.88370 q^{43} -6.43217i q^{44} -1.13914i q^{45} +6.74456i q^{46} -2.27828 q^{47} +1.00000i q^{48} -1.00000 q^{49} -3.70236 q^{50} +(3.37228 - 2.37228i) q^{51} +0.590671 q^{52} +1.88370 q^{53} +1.00000i q^{54} +7.32714 q^{55} +1.00000i q^{56} -2.54847i q^{57} -0.270189i q^{58} -9.29303 q^{59} -1.13914 q^{60} -7.84150i q^{61} -2.27828i q^{62} +1.00000i q^{63} +1.00000 q^{64} +0.672857i q^{65} -6.43217 q^{66} +7.88370 q^{67} +(-2.37228 - 3.37228i) q^{68} +6.74456 q^{69} -1.13914 q^{70} -9.56322i q^{71} +1.00000 q^{72} -0.0422023i q^{73} +2.59067i q^{74} +3.70236i q^{75} -2.54847 q^{76} -6.43217 q^{77} -0.590671i q^{78} -6.16198i q^{79} +1.13914i q^{80} +1.00000 q^{81} -3.84150i q^{82} +15.4550 q^{83} +1.00000 q^{84} +(3.84150 - 2.70236i) q^{85} -7.88370 q^{86} -0.270189 q^{87} +6.43217i q^{88} +5.41742 q^{89} +1.13914i q^{90} -0.590671i q^{91} -6.74456i q^{92} -2.27828 q^{93} +2.27828 q^{94} -2.90306i q^{95} -1.00000i q^{96} -2.23608i q^{97} +1.00000 q^{98} +6.43217i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$			1.13914i			0.509439i	0.967015	+	0.254719i	$0.0819831\pi$
$5$			1.13914i			0.509439i	−0.967015	+	0.254719i	$0.918017\pi$
$6$		−	1.00000i		−	0.408248i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$		−	1.13914i		−	0.360228i
$11$		−	6.43217i		−	1.93937i	−0.244353	−	0.969686i	$-0.578576\pi$
$11$		−	6.43217i		−	1.93937i	0.244353	−	0.969686i	$-0.421424\pi$
$12$			1.00000i			0.288675i
$13$	0.590671			0.163823			0.0819113	−	0.996640i	$-0.473898\pi$
$13$	0.590671			0.163823			0.0819113	+	0.996640i	$0.473898\pi$
$14$			1.00000i			0.267261i
$15$	−1.13914			−0.294125
$16$	1.00000			0.250000
$17$	−2.37228	−	3.37228i	−0.575363	−	0.817898i
$17$	−2.37228	−	3.37228i	−0.575363	−	0.817898i
$18$	1.00000			0.235702
$19$	−2.54847			−0.584659			−0.292329	−	0.956318i	$-0.594430\pi$
$19$	−2.54847			−0.584659			−0.292329	+	0.956318i	$0.594430\pi$
$20$			1.13914i			0.254719i
$21$	1.00000			0.218218
$22$			6.43217i			1.37134i
$23$		−	6.74456i		−	1.40634i	−0.711022	−	0.703169i	$-0.751768\pi$
$23$		−	6.74456i		−	1.40634i	0.711022	−	0.703169i	$-0.248232\pi$
$24$		−	1.00000i		−	0.204124i
$25$	3.70236			0.740472
$26$	−0.590671			−0.115840
$27$		−	1.00000i		−	0.192450i
$28$		−	1.00000i		−	0.188982i
$29$			0.270189i			0.0501728i	0.999685	+	0.0250864i	$0.00798609\pi$
$29$			0.270189i			0.0501728i	−0.999685	+	0.0250864i	$0.992014\pi$
$30$	1.13914			0.207978
$31$			2.27828i			0.409191i	0.978847	+	0.204596i	$0.0655879\pi$
$31$			2.27828i			0.409191i	−0.978847	+	0.204596i	$0.934412\pi$
$32$	−1.00000			−0.176777
$33$	6.43217			1.11970
$34$	2.37228	+	3.37228i	0.406843	+	0.578341i
$35$	1.13914			0.192550
$36$	−1.00000			−0.166667
$37$		−	2.59067i		−	0.425904i	−0.977063	−	0.212952i	$-0.931692\pi$
$37$		−	2.59067i		−	0.425904i	0.977063	−	0.212952i	$-0.0683077\pi$
$38$	2.54847			0.413416
$39$			0.590671i			0.0945831i
$40$		−	1.13914i		−	0.180114i
$41$			3.84150i			0.599942i	0.953948	+	0.299971i	$0.0969769\pi$
$41$			3.84150i			0.599942i	−0.953948	+	0.299971i	$0.903023\pi$
$42$	−1.00000			−0.154303
$43$	7.88370			1.20225			0.601127	−	0.799154i	$-0.294719\pi$
$43$	7.88370			1.20225			0.601127	+	0.799154i	$0.294719\pi$
$44$		−	6.43217i		−	0.969686i
$45$		−	1.13914i		−	0.169813i
$46$			6.74456i			0.994432i
$47$	−2.27828			−0.332321			−0.166161	−	0.986099i	$-0.553137\pi$
$47$	−2.27828			−0.332321			−0.166161	+	0.986099i	$0.553137\pi$
$48$			1.00000i			0.144338i
$49$	−1.00000			−0.142857
$50$	−3.70236			−0.523593
$51$	3.37228	−	2.37228i	0.472214	−	0.332186i
$52$	0.590671			0.0819113
$53$	1.88370			0.258746			0.129373	−	0.991596i	$-0.458703\pi$
$53$	1.88370			0.258746			0.129373	+	0.991596i	$0.458703\pi$
$54$			1.00000i			0.136083i
$55$	7.32714			0.987992
$56$			1.00000i			0.133631i
$57$		−	2.54847i		−	0.337553i
$58$		−	0.270189i		−	0.0354776i
$59$	−9.29303			−1.20985			−0.604925	−	0.796283i	$-0.706797\pi$
$59$	−9.29303			−1.20985			−0.604925	+	0.796283i	$0.706797\pi$
$60$	−1.13914			−0.147062
$61$		−	7.84150i		−	1.00400i	−0.864867	−	0.502001i	$-0.832598\pi$
$61$		−	7.84150i		−	1.00400i	0.864867	−	0.502001i	$-0.167402\pi$
$62$		−	2.27828i		−	0.289342i
$63$			1.00000i			0.125988i
$64$	1.00000			0.125000
$65$			0.672857i			0.0834576i
$66$	−6.43217			−0.791746
$67$	7.88370			0.963148			0.481574	−	0.876406i	$-0.340065\pi$
$67$	7.88370			0.963148			0.481574	+	0.876406i	$0.340065\pi$
$68$	−2.37228	−	3.37228i	−0.287681	−	0.408949i
$69$	6.74456			0.811950
$70$	−1.13914			−0.136153
$71$		−	9.56322i		−	1.13495i	−0.823392	−	0.567473i	$-0.807921\pi$
$71$		−	9.56322i		−	1.13495i	0.823392	−	0.567473i	$-0.192079\pi$
$72$	1.00000			0.117851
$73$		−	0.0422023i		−	0.00493941i	−0.999997	−	0.00246971i	$-0.999214\pi$
$73$		−	0.0422023i		−	0.00493941i	0.999997	−	0.00246971i	$-0.000786133\pi$
$74$			2.59067i			0.301159i
$75$			3.70236i			0.427512i
$76$	−2.54847			−0.292329
$77$	−6.43217			−0.733014
$78$		−	0.590671i		−	0.0668803i
$79$		−	6.16198i		−	0.693277i	−0.937999	−	0.346639i	$-0.887323\pi$
$79$		−	6.16198i		−	0.693277i	0.937999	−	0.346639i	$-0.112677\pi$
$80$			1.13914i			0.127360i
$81$	1.00000			0.111111
$82$		−	3.84150i		−	0.424223i
$83$	15.4550			1.69641			0.848204	−	0.529670i	$-0.177684\pi$
$83$	15.4550			1.69641			0.848204	+	0.529670i	$0.177684\pi$
$84$	1.00000			0.109109
$85$	3.84150	−	2.70236i	0.416669	−	0.293112i
$86$	−7.88370			−0.850122
$87$	−0.270189			−0.0289673
$88$			6.43217i			0.685672i
$89$	5.41742			0.574245			0.287123	−	0.957894i	$-0.407301\pi$
$89$	5.41742			0.574245			0.287123	+	0.957894i	$0.407301\pi$
$90$			1.13914i			0.120076i
$91$		−	0.590671i		−	0.0619192i
$92$		−	6.74456i		−	0.703169i
$93$	−2.27828			−0.236247
$94$	2.27828			0.234987
$95$		−	2.90306i		−	0.297848i
$96$		−	1.00000i		−	0.102062i
$97$		−	2.23608i		−	0.227039i	−0.993536	−	0.113520i	$-0.963788\pi$
$97$		−	2.23608i		−	0.227039i	0.993536	−	0.113520i	$-0.0362125\pi$
$98$	1.00000			0.101015
$99$			6.43217i			0.646458i
$100$	3.70236			0.370236
$101$	−14.5942			−1.45217			−0.726086	−	0.687604i	$-0.758663\pi$
$101$	−14.5942			−1.45217			−0.726086	+	0.687604i	$0.758663\pi$
$102$	−3.37228	+	2.37228i	−0.333906	+	0.234891i
$103$	2.86086			0.281889			0.140944	−	0.990018i	$-0.454986\pi$
$103$	2.86086			0.281889			0.140944	+	0.990018i	$0.454986\pi$
$104$	−0.590671			−0.0579201
$105$			1.13914i			0.111169i
$106$	−1.88370			−0.182961
$107$		−	8.03759i		−	0.777024i	−0.921444	−	0.388512i	$-0.872989\pi$
$107$		−	8.03759i		−	0.777024i	0.921444	−	0.388512i	$-0.127011\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			6.47437i			0.620133i	0.950715	+	0.310066i	$0.100351\pi$
$109$			6.47437i			0.620133i	−0.950715	+	0.310066i	$0.899649\pi$
$110$	−7.32714			−0.698616
$111$	2.59067			0.245896
$112$		−	1.00000i		−	0.0944911i
$113$			5.13914i			0.483450i	0.970345	+	0.241725i	$0.0777131\pi$
$113$			5.13914i			0.483450i	−0.970345	+	0.241725i	$0.922287\pi$
$114$			2.54847i			0.238686i
$115$	7.68300			0.716443
$116$			0.270189i			0.0250864i
$117$	−0.590671			−0.0546076
$118$	9.29303			0.855493
$119$	−3.37228	+	2.37228i	−0.309137	+	0.217467i
$120$	1.13914			0.103989
$121$	−30.3728			−2.76117
$122$			7.84150i			0.709936i
$123$	−3.84150			−0.346376
$124$			2.27828i			0.204596i
$125$			9.91321i			0.886664i
$126$		−	1.00000i		−	0.0890871i
$127$	−0.540378			−0.0479508			−0.0239754	−	0.999713i	$-0.507632\pi$
$127$	−0.540378			−0.0479508			−0.0239754	+	0.999713i	$0.507632\pi$
$128$	−1.00000			−0.0883883
$129$			7.88370i			0.694121i
$130$		−	0.672857i		−	0.0590135i
$131$			4.54038i			0.396695i	0.980132	+	0.198347i	$0.0635574\pi$
$131$			4.54038i			0.396695i	−0.980132	+	0.198347i	$0.936443\pi$
$132$	6.43217			0.559849
$133$			2.54847i			0.220980i
$134$	−7.88370			−0.681048
$135$	1.13914			0.0980416
$136$	2.37228	+	3.37228i	0.203421	+	0.289171i
$137$	1.44344			0.123321			0.0616607	−	0.998097i	$-0.480360\pi$
$137$	1.44344			0.123321			0.0616607	+	0.998097i	$0.480360\pi$
$138$	−6.74456			−0.574135
$139$		−	2.39458i		−	0.203105i	−0.994830	−	0.101553i	$-0.967619\pi$
$139$		−	2.39458i		−	0.203105i	0.994830	−	0.101553i	$-0.0323810\pi$
$140$	1.13914			0.0962749
$141$		−	2.27828i		−	0.191866i
$142$			9.56322i			0.802528i
$143$		−	3.79930i		−	0.317713i
$144$	−1.00000			−0.0833333
$145$	−0.307783			−0.0255600
$146$			0.0422023i			0.00349269i
$147$		−	1.00000i		−	0.0824786i
$148$		−	2.59067i		−	0.212952i
$149$	−16.4698			−1.34926			−0.674628	−	0.738158i	$-0.735696\pi$
$149$	−16.4698			−1.34926			−0.674628	+	0.738158i	$0.735696\pi$
$150$		−	3.70236i		−	0.302296i
$151$	−10.5861			−0.861482			−0.430741	−	0.902476i	$-0.641748\pi$
$151$	−10.5861			−0.861482			−0.430741	+	0.902476i	$0.641748\pi$
$152$	2.54847			0.206708
$153$	2.37228	+	3.37228i	0.191788	+	0.272633i
$154$	6.43217			0.518319
$155$	−2.59528			−0.208458
$156$			0.590671i			0.0472915i
$157$	0.706969			0.0564222			0.0282111	−	0.999602i	$-0.491019\pi$
$157$	0.706969			0.0564222			0.0282111	+	0.999602i	$0.491019\pi$
$158$			6.16198i			0.490221i
$159$			1.88370i			0.149387i
$160$		−	1.13914i		−	0.0900569i
$161$	−6.74456			−0.531546
$162$	−1.00000			−0.0785674
$163$			5.84959i			0.458175i	0.973406	+	0.229088i	$0.0735742\pi$
$163$			5.84959i			0.458175i	−0.973406	+	0.229088i	$0.926426\pi$
$164$			3.84150i			0.299971i
$165$			7.32714i			0.570417i
$166$	−15.4550			−1.19954
$167$			17.0650i			1.32053i	0.751031	+	0.660266i	$0.229557\pi$
$167$			17.0650i			1.32053i	−0.751031	+	0.660266i	$0.770443\pi$
$168$	−1.00000			−0.0771517
$169$	−12.6511			−0.973162
$170$	−3.84150	+	2.70236i	−0.294630	+	0.207262i
$171$	2.54847			0.194886
$172$	7.88370			0.601127
$173$		−	18.1198i		−	1.37762i	−0.724941	−	0.688811i	$-0.758133\pi$
$173$		−	18.1198i		−	1.37762i	0.724941	−	0.688811i	$-0.241867\pi$
$174$	0.270189			0.0204830
$175$		−	3.70236i		−	0.279872i
$176$		−	6.43217i		−	0.484843i
$177$		−	9.29303i		−	0.698507i
$178$	−5.41742			−0.406053
$179$	22.5861			1.68816			0.844081	−	0.536216i	$-0.180147\pi$
$179$	22.5861			1.68816			0.844081	+	0.536216i	$0.180147\pi$
$180$		−	1.13914i		−	0.0849065i
$181$			25.3468i			1.88401i	0.335594	+	0.942007i	$0.391063\pi$
$181$			25.3468i			1.88401i	−0.335594	+	0.942007i	$0.608937\pi$
$182$			0.590671i			0.0437835i
$183$	7.84150			0.579660
$184$			6.74456i			0.497216i
$185$	2.95114			0.216972
$186$	2.27828			0.167052
$187$	−21.6911	+	15.2589i	−1.58621	+	1.11584i
$188$	−2.27828			−0.166161
$189$	−1.00000			−0.0727393
$190$			2.90306i			0.210610i
$191$	13.5372			0.979517			0.489759	−	0.871858i	$-0.337085\pi$
$191$	13.5372			0.979517			0.489759	+	0.871858i	$0.337085\pi$
$192$			1.00000i			0.0721688i
$193$			10.8187i			0.778744i	0.921081	+	0.389372i	$0.127308\pi$
$193$			10.8187i			0.778744i	−0.921081	+	0.389372i	$0.872692\pi$
$194$			2.23608i			0.160541i
$195$	−0.672857			−0.0481843
$196$	−1.00000			−0.0714286
$197$			10.8563i			0.773476i	0.922190	+	0.386738i	$0.126398\pi$
$197$			10.8563i			0.773476i	−0.922190	+	0.386738i	$0.873602\pi$
$198$		−	6.43217i		−	0.457115i
$199$		−	4.55656i		−	0.323006i	−0.986872	−	0.161503i	$-0.948366\pi$
$199$		−	4.55656i		−	0.323006i	0.986872	−	0.161503i	$-0.0516341\pi$
$200$	−3.70236			−0.261796
$201$			7.88370i			0.556074i
$202$	14.5942			1.02684
$203$	0.270189			0.0189635
$204$	3.37228	−	2.37228i	0.236107	−	0.166093i
$205$	−4.37601			−0.305634
$206$	−2.86086			−0.199326
$207$			6.74456i			0.468780i
$208$	0.590671			0.0409557
$209$			16.3922i			1.13387i
$210$		−	1.13914i		−	0.0786081i
$211$			1.52563i			0.105028i	0.998620	+	0.0525142i	$0.0167235\pi$
$211$			1.52563i			0.105028i	−0.998620	+	0.0525142i	$0.983277\pi$
$212$	1.88370			0.129373
$213$	9.56322			0.655261
$214$			8.03759i			0.549439i
$215$			8.98064i			0.612475i
$216$			1.00000i			0.0680414i
$217$	2.27828			0.154660
$218$		−	6.47437i		−	0.438500i
$219$	0.0422023			0.00285177
$220$	7.32714			0.493996
$221$	−1.40124	−	1.99191i	−0.0942575	−	0.133990i
$222$	−2.59067			−0.173874
$223$	−11.8415			−0.792966			−0.396483	−	0.918042i	$-0.629769\pi$
$223$	−11.8415			−0.792966			−0.396483	+	0.918042i	$0.629769\pi$
$224$			1.00000i			0.0668153i
$225$	−3.70236			−0.246824
$226$		−	5.13914i		−	0.341851i
$227$		−	13.9613i		−	0.926643i	−0.886190	−	0.463321i	$-0.846658\pi$
$227$		−	13.9613i		−	0.926643i	0.886190	−	0.463321i	$-0.153342\pi$
$228$		−	2.54847i		−	0.168776i
$229$	2.78455			0.184008			0.0920040	−	0.995759i	$-0.470673\pi$
$229$	2.78455			0.184008			0.0920040	+	0.995759i	$0.470673\pi$
$230$	−7.68300			−0.506602
$231$		−	6.43217i		−	0.423206i
$232$		−	0.270189i		−	0.0177388i
$233$		−	12.8221i		−	0.840006i	−0.907523	−	0.420003i	$-0.862029\pi$
$233$		−	12.8221i		−	0.840006i	0.907523	−	0.420003i	$-0.137971\pi$
$234$	0.590671			0.0386134
$235$		−	2.59528i		−	0.169297i
$236$	−9.29303			−0.604925
$237$	6.16198			0.400264
$238$	3.37228	−	2.37228i	0.218593	−	0.153772i
$239$	−11.0263			−0.713234			−0.356617	−	0.934251i	$-0.616070\pi$
$239$	−11.0263			−0.713234			−0.356617	+	0.934251i	$0.616070\pi$
$240$	−1.13914			−0.0735312
$241$		−	14.5120i		−	0.934798i	−0.884046	−	0.467399i	$-0.845191\pi$
$241$		−	14.5120i		−	0.934798i	0.884046	−	0.467399i	$-0.154809\pi$
$242$	30.3728			1.95244
$243$			1.00000i			0.0641500i
$244$		−	7.84150i		−	0.502001i
$245$		−	1.13914i		−	0.0727770i
$246$	3.84150			0.244925
$247$	−1.50531			−0.0957804
$248$		−	2.27828i		−	0.144671i
$249$			15.4550i			0.979422i
$250$		−	9.91321i		−	0.626966i
$251$	−7.14723			−0.451129			−0.225565	−	0.974228i	$-0.572423\pi$
$251$	−7.14723			−0.451129			−0.225565	+	0.974228i	$0.572423\pi$
$252$			1.00000i			0.0629941i
$253$	−43.3822			−2.72741
$254$	0.540378			0.0339063
$255$	2.70236	+	3.84150i	0.169228	+	0.240564i
$256$	1.00000			0.0625000
$257$	−23.1391			−1.44338			−0.721690	−	0.692216i	$-0.756634\pi$
$257$	−23.1391			−1.44338			−0.721690	+	0.692216i	$0.756634\pi$
$258$		−	7.88370i		−	0.490818i
$259$	−2.59067			−0.160976
$260$			0.672857i			0.0417288i
$261$		−	0.270189i		−	0.0167243i
$262$		−	4.54038i		−	0.280505i
$263$	−11.4915			−0.708597			−0.354299	−	0.935132i	$-0.615280\pi$
$263$	−11.4915			−0.708597			−0.354299	+	0.935132i	$0.615280\pi$
$264$	−6.43217			−0.395873
$265$			2.14580i			0.131815i
$266$		−	2.54847i		−	0.156257i
$267$			5.41742i			0.331541i
$268$	7.88370			0.481574
$269$			26.5120i			1.61646i	0.588865	+	0.808232i	$0.299575\pi$
$269$			26.5120i			1.61646i	−0.588865	+	0.808232i	$0.700425\pi$
$270$	−1.13914			−0.0693258
$271$	19.7414			1.19920			0.599602	−	0.800298i	$-0.295326\pi$
$271$	19.7414			1.19920			0.599602	+	0.800298i	$0.295326\pi$
$272$	−2.37228	−	3.37228i	−0.143841	−	0.204475i
$273$	0.590671			0.0357490
$274$	−1.44344			−0.0872014
$275$		−	23.8142i		−	1.43605i
$276$	6.74456			0.405975
$277$		−	19.5713i		−	1.17593i	−0.808888	−	0.587963i	$-0.799930\pi$
$277$		−	19.5713i		−	1.17593i	0.808888	−	0.587963i	$-0.200070\pi$
$278$			2.39458i			0.143617i
$279$		−	2.27828i		−	0.136397i
$280$	−1.13914			−0.0680766
$281$	32.5178			1.93985			0.969926	−	0.243401i	$-0.0782630\pi$
$281$	32.5178			1.93985			0.969926	+	0.243401i	$0.0782630\pi$
$282$			2.27828i			0.135670i
$283$		−	32.1915i		−	1.91359i	−0.290771	−	0.956793i	$-0.593912\pi$
$283$		−	32.1915i		−	1.91359i	0.290771	−	0.956793i	$-0.406088\pi$
$284$		−	9.56322i		−	0.567473i
$285$	2.90306			0.171963
$286$			3.79930i			0.224657i
$287$	3.84150			0.226757
$288$	1.00000			0.0589256
$289$	−5.74456	+	16.0000i	−0.337915	+	0.941176i
$290$	0.307783			0.0180736
$291$	2.23608			0.131081
$292$		−	0.0422023i		−	0.00246971i
$293$	26.0376			1.52113			0.760566	−	0.649260i	$-0.224921\pi$
$293$	26.0376			1.52113			0.760566	+	0.649260i	$0.224921\pi$
$294$			1.00000i			0.0583212i
$295$		−	10.5861i		−	0.616344i
$296$			2.59067i			0.150580i
$297$	−6.43217			−0.373232
$298$	16.4698			0.954068
$299$		−	3.98382i		−	0.230390i
$300$			3.70236i			0.213756i
$301$		−	7.88370i		−	0.454409i
$302$	10.5861			0.609159
$303$		−	14.5942i		−	0.838412i
$304$	−2.54847			−0.146165
$305$	8.93257			0.511477
$306$	−2.37228	−	3.37228i	−0.135614	−	0.192780i
$307$	33.9989			1.94042			0.970209	−	0.242269i	$-0.0778916\pi$
$307$	33.9989			1.94042			0.970209	+	0.242269i	$0.0778916\pi$
$308$	−6.43217			−0.366507
$309$			2.86086i			0.162749i
$310$	2.59528			0.147402
$311$			15.2427i			0.864336i	0.901793	+	0.432168i	$0.142251\pi$
$311$			15.2427i			0.864336i	−0.901793	+	0.432168i	$0.857749\pi$
$312$		−	0.590671i		−	0.0334402i
$313$		−	14.5120i		−	0.820265i	−0.912026	−	0.410132i	$-0.865482\pi$
$313$		−	14.5120i		−	0.820265i	0.912026	−	0.410132i	$-0.134518\pi$
$314$	−0.706969			−0.0398965
$315$	−1.13914			−0.0641833
$316$		−	6.16198i		−	0.346639i
$317$			31.4128i			1.76432i	0.470951	+	0.882160i	$0.343911\pi$
$317$			31.4128i			1.76432i	−0.470951	+	0.882160i	$0.656089\pi$
$318$		−	1.88370i		−	0.105633i
$319$	1.73790			0.0973038
$320$			1.13914i			0.0636799i
$321$	8.03759			0.448615
$322$	6.74456			0.375860
$323$	6.04568	+	8.59415i	0.336391	+	0.478192i
$324$	1.00000			0.0555556
$325$	2.18688			0.121306
$326$		−	5.84959i		−	0.323979i
$327$	−6.47437			−0.358034
$328$		−	3.84150i		−	0.212111i
$329$			2.27828i			0.125606i
$330$		−	7.32714i		−	0.403346i
$331$	−8.42408			−0.463029			−0.231515	−	0.972831i	$-0.574368\pi$
$331$	−8.42408			−0.463029			−0.231515	+	0.972831i	$0.574368\pi$
$332$	15.4550			0.848204
$333$			2.59067i			0.141968i
$334$		−	17.0650i		−	0.933758i
$335$			8.98064i			0.490665i
$336$	1.00000			0.0545545
$337$		−	19.2108i		−	1.04648i	−0.852185	−	0.523241i	$-0.824723\pi$
$337$		−	19.2108i		−	1.04648i	0.852185	−	0.523241i	$-0.175277\pi$
$338$	12.6511			0.688130
$339$	−5.13914			−0.279120
$340$	3.84150	−	2.70236i	0.208335	−	0.146556i
$341$	14.6543			0.793574
$342$	−2.54847			−0.137805
$343$			1.00000i			0.0539949i
$344$	−7.88370			−0.425061
$345$			7.68300i			0.413639i
$346$			18.1198i			0.974125i
$347$		−	29.6592i		−	1.59219i	−0.605172	−	0.796095i	$-0.706896\pi$
$347$		−	29.6592i		−	1.59219i	0.605172	−	0.796095i	$-0.293104\pi$
$348$	−0.270189			−0.0144836
$349$	25.6876			1.37503			0.687513	−	0.726172i	$-0.258702\pi$
$349$	25.6876			1.37503			0.687513	+	0.726172i	$0.258702\pi$
$350$			3.70236i			0.197899i
$351$		−	0.590671i		−	0.0315277i
$352$			6.43217i			0.342836i
$353$	7.22354			0.384470			0.192235	−	0.981349i	$-0.438426\pi$
$353$	7.22354			0.384470			0.192235	+	0.981349i	$0.438426\pi$
$354$			9.29303i			0.493919i
$355$	10.8938			0.578185
$356$	5.41742			0.287123
$357$	−2.37228	−	3.37228i	−0.125554	−	0.178480i
$358$	−22.5861			−1.19371
$359$	−36.2396			−1.91265			−0.956325	−	0.292304i	$-0.905578\pi$
$359$	−36.2396			−1.91265			−0.956325	+	0.292304i	$0.905578\pi$
$360$			1.13914i			0.0600379i
$361$	−12.5053			−0.658174
$362$		−	25.3468i		−	1.33220i
$363$		−	30.3728i		−	1.59416i
$364$		−	0.590671i		−	0.0309596i
$365$	0.0480744			0.00251633
$366$	−7.84150			−0.409882
$367$		−	1.16516i		−	0.0608209i	−0.999537	−	0.0304104i	$-0.990319\pi$
$367$		−	1.16516i		−	0.0608209i	0.999537	−	0.0304104i	$-0.00968144\pi$
$368$		−	6.74456i		−	0.351585i
$369$		−	3.84150i		−	0.199981i
$370$	−2.95114			−0.153422
$371$		−	1.88370i		−	0.0977970i
$372$	−2.27828			−0.118123
$373$	2.54038			0.131536			0.0657679	−	0.997835i	$-0.479050\pi$
$373$	2.54038			0.131536			0.0657679	+	0.997835i	$0.479050\pi$
$374$	21.6911	−	15.2589i	1.12162	−	0.789020i
$375$	−9.91321			−0.511916
$376$	2.27828			0.117493
$377$			0.159593i			0.00821945i
$378$	1.00000			0.0514344
$379$		−	16.6682i		−	0.856190i	−0.903734	−	0.428095i	$-0.859185\pi$
$379$		−	16.6682i		−	0.856190i	0.903734	−	0.428095i	$-0.140815\pi$
$380$		−	2.90306i		−	0.148924i
$381$		−	0.540378i		−	0.0276844i
$382$	−13.5372			−0.692623
$383$	18.9031			0.965901			0.482951	−	0.875648i	$-0.339565\pi$
$383$	18.9031			0.965901			0.482951	+	0.875648i	$0.339565\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		−	7.32714i		−	0.373426i
$386$		−	10.8187i		−	0.550655i
$387$	−7.88370			−0.400751
$388$		−	2.23608i		−	0.113520i
$389$	9.14262			0.463549			0.231775	−	0.972769i	$-0.425547\pi$
$389$	9.14262			0.463549			0.231775	+	0.972769i	$0.425547\pi$
$390$	0.672857			0.0340714
$391$	−22.7446	+	16.0000i	−1.15024	+	0.809155i
$392$	1.00000			0.0505076
$393$	−4.54038			−0.229032
$394$		−	10.8563i		−	0.546930i
$395$	7.01936			0.353182
$396$			6.43217i			0.323229i
$397$			21.6476i			1.08646i	0.839583	+	0.543232i	$0.182799\pi$
$397$			21.6476i			1.08646i	−0.839583	+	0.543232i	$0.817201\pi$
$398$			4.55656i			0.228400i
$399$	−2.54847			−0.127583
$400$	3.70236			0.185118
$401$		−	16.7058i		−	0.834250i	−0.908849	−	0.417125i	$-0.863038\pi$
$401$		−	16.7058i		−	0.834250i	0.908849	−	0.417125i	$-0.136962\pi$
$402$		−	7.88370i		−	0.393203i
$403$			1.34571i			0.0670348i
$404$	−14.5942			−0.726086
$405$			1.13914i			0.0566043i
$406$	−0.270189			−0.0134093
$407$	−16.6636			−0.825986
$408$	−3.37228	+	2.37228i	−0.166953	+	0.117445i
$409$	−16.5017			−0.815954			−0.407977	−	0.912992i	$-0.633766\pi$
$409$	−16.5017			−0.815954			−0.407977	+	0.912992i	$0.633766\pi$
$410$	4.37601			0.216116
$411$			1.44344i			0.0711997i
$412$	2.86086			0.140944
$413$			9.29303i			0.457280i
$414$		−	6.74456i		−	0.331477i
$415$			17.6054i			0.864216i
$416$	−0.590671			−0.0289600
$417$	2.39458			0.117263
$418$		−	16.3922i		−	0.801768i
$419$		−	21.7287i		−	1.06152i	−0.847524	−	0.530758i	$-0.821907\pi$
$419$		−	21.7287i		−	1.06152i	0.847524	−	0.530758i	$-0.178093\pi$
$420$			1.13914i			0.0555843i
$421$	14.5566			0.709443			0.354722	−	0.934972i	$-0.384576\pi$
$421$	14.5566			0.709443			0.354722	+	0.934972i	$0.384576\pi$
$422$		−	1.52563i		−	0.0742663i
$423$	2.27828			0.110774
$424$	−1.88370			−0.0914807
$425$	−8.78304	−	12.4854i	−0.426040	−	0.605631i
$426$	−9.56322			−0.463340
$427$	−7.84150			−0.379477
$428$		−	8.03759i		−	0.388512i
$429$	3.79930			0.183432
$430$		−	8.98064i		−	0.433085i
$431$			31.7733i			1.53046i	0.643754	+	0.765232i	$0.277376\pi$
$431$			31.7733i			1.53046i	−0.643754	+	0.765232i	$0.722624\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−9.37522			−0.450544			−0.225272	−	0.974296i	$-0.572327\pi$
$433$	−9.37522			−0.450544			−0.225272	+	0.974296i	$0.572327\pi$
$434$	−2.27828			−0.109361
$435$		−	0.307783i		−	0.0147571i
$436$			6.47437i			0.310066i
$437$			17.1883i			0.822228i
$438$	−0.0422023			−0.00201651
$439$		−	28.2396i		−	1.34780i	−0.738822	−	0.673900i	$-0.764618\pi$
$439$		−	28.2396i		−	1.34780i	0.738822	−	0.673900i	$-0.235382\pi$
$440$	−7.32714			−0.349308
$441$	1.00000			0.0476190
$442$	1.40124	+	1.99191i	0.0666501	+	0.0947455i
$443$	32.9395			1.56500			0.782502	−	0.622648i	$-0.213943\pi$
$443$	32.9395			1.56500			0.782502	+	0.622648i	$0.213943\pi$
$444$	2.59067			0.122948
$445$			6.17120i			0.292543i
$446$	11.8415			0.560711
$447$		−	16.4698i		−	0.778993i
$448$		−	1.00000i		−	0.0472456i
$449$			32.6578i			1.54122i	0.637310	+	0.770608i	$0.280047\pi$
$449$			32.6578i			1.54122i	−0.637310	+	0.770608i	$0.719953\pi$
$450$	3.70236			0.174531
$451$	24.7092			1.16351
$452$			5.13914i			0.241725i
$453$		−	10.5861i		−	0.497377i
$454$			13.9613i			0.655235i
$455$	0.672857			0.0315440
$456$			2.54847i			0.119343i
$457$	−29.7355			−1.39097			−0.695484	−	0.718541i	$-0.744810\pi$
$457$	−29.7355			−1.39097			−0.695484	+	0.718541i	$0.744810\pi$
$458$	−2.78455			−0.130113
$459$	−3.37228	+	2.37228i	−0.157405	+	0.110729i
$460$	7.68300			0.358222
$461$	−10.5097			−0.489488			−0.244744	−	0.969588i	$-0.578704\pi$
$461$	−10.5097			−0.489488			−0.244744	+	0.969588i	$0.578704\pi$
$462$			6.43217i			0.299252i
$463$	23.4504			1.08983			0.544916	−	0.838490i	$-0.316561\pi$
$463$	23.4504			1.08983			0.544916	+	0.838490i	$0.316561\pi$
$464$			0.270189i			0.0125432i
$465$		−	2.59528i		−	0.120353i
$466$			12.8221i			0.593974i
$467$	34.2580			1.58527			0.792635	−	0.609697i	$-0.208709\pi$
$467$	34.2580			1.58527			0.792635	+	0.609697i	$0.208709\pi$
$468$	−0.590671			−0.0273038
$469$		−	7.88370i		−	0.364036i
$470$			2.59528i			0.119711i
$471$			0.706969i			0.0325754i
$472$	9.29303			0.427746
$473$		−	50.7093i		−	2.33162i
$474$	−6.16198			−0.283029
$475$	−9.43535			−0.432924
$476$	−3.37228	+	2.37228i	−0.154568	+	0.108733i
$477$	−1.88370			−0.0862488
$478$	11.0263			0.504332
$479$			37.6124i			1.71855i	0.511511	+	0.859277i	$0.329086\pi$
$479$			37.6124i			1.71855i	−0.511511	+	0.859277i	$0.670914\pi$
$480$	1.13914			0.0519944
$481$		−	1.53023i		−	0.0697727i
$482$			14.5120i			0.661002i
$483$		−	6.74456i		−	0.306888i
$484$	−30.3728			−1.38058
$485$	2.54721			0.115663
$486$		−	1.00000i		−	0.0453609i
$487$		−	0.0480744i		−	0.00217846i	−0.999999	−	0.00108923i	$-0.999653\pi$
$487$		−	0.0480744i		−	0.00217846i	0.999999	−	0.00108923i	$-0.000346712\pi$
$488$			7.84150i			0.354968i
$489$	−5.84959			−0.264528
$490$			1.13914i			0.0514611i
$491$	−34.9100			−1.57547			−0.787734	−	0.616016i	$-0.788746\pi$
$491$	−34.9100			−1.57547			−0.787734	+	0.616016i	$0.788746\pi$
$492$	−3.84150			−0.173188
$493$	0.911153	−	0.640964i	0.0410363	−	0.0288676i
$494$	1.50531			0.0677270
$495$	−7.32714			−0.329331
$496$			2.27828i			0.102298i
$497$	−9.56322			−0.428969
$498$		−	15.4550i		−	0.692556i
$499$			13.9340i			0.623771i	0.950120	+	0.311886i	$0.100961\pi$
$499$			13.9340i			0.623771i	−0.950120	+	0.311886i	$0.899039\pi$
$500$			9.91321i			0.443332i
$501$	−17.0650			−0.762410
$502$	7.14723			0.318997
$503$			7.68300i			0.342568i	0.985222	+	0.171284i	$0.0547916\pi$
$503$			7.68300i			0.342568i	−0.985222	+	0.171284i	$0.945208\pi$
$504$		−	1.00000i		−	0.0445435i
$505$		−	16.6248i		−	0.739793i
$506$	43.3822			1.92857
$507$		−	12.6511i		−	0.561855i
$508$	−0.540378			−0.0239754
$509$	32.0151			1.41904			0.709521	−	0.704684i	$-0.248911\pi$
$509$	32.0151			1.41904			0.709521	+	0.704684i	$0.248911\pi$
$510$	−2.70236	−	3.84150i	−0.119663	−	0.170104i
$511$	−0.0422023			−0.00186692
$512$	−1.00000			−0.0441942
$513$			2.54847i			0.112518i
$514$	23.1391			1.02062
$515$			3.25892i			0.143605i
$516$			7.88370i			0.347061i
$517$			14.6543i			0.644495i
$518$	2.59067			0.113828
$519$	18.1198			0.795370
$520$		−	0.672857i		−	0.0295067i
$521$			40.2407i			1.76298i	0.472207	+	0.881488i	$0.343457\pi$
$521$			40.2407i			1.76298i	−0.472207	+	0.881488i	$0.656543\pi$
$522$			0.270189i			0.0118259i
$523$	20.0214			0.875475			0.437738	−	0.899103i	$-0.355780\pi$
$523$	20.0214			0.875475			0.437738	+	0.899103i	$0.355780\pi$
$524$			4.54038i			0.198347i
$525$	3.70236			0.161584
$526$	11.4915			0.501054
$527$	7.68300	−	5.40472i	0.334677	−	0.235433i
$528$	6.43217			0.279924
$529$	−22.4891			−0.977788
$530$		−	2.14580i		−	0.0932076i
$531$	9.29303			0.403283
$532$			2.54847i			0.110490i
$533$			2.26906i			0.0982840i
$534$		−	5.41742i		−	0.234435i
$535$	9.15594			0.395846
$536$	−7.88370			−0.340524
$537$			22.5861i			0.974661i
$538$		−	26.5120i		−	1.14301i
$539$			6.43217i			0.277053i
$540$	1.13914			0.0490208
$541$		−	6.75504i		−	0.290422i	−0.989401	−	0.145211i	$-0.953614\pi$
$541$		−	6.75504i		−	0.290422i	0.989401	−	0.145211i	$-0.0463861\pi$
$542$	−19.7414			−0.847965
$543$	−25.3468			−1.08774
$544$	2.37228	+	3.37228i	0.101711	+	0.144585i
$545$	−7.37522			−0.315920
$546$	−0.590671			−0.0252784
$547$			43.5621i			1.86258i	0.364278	+	0.931290i	$0.381316\pi$
$547$			43.5621i			1.86258i	−0.364278	+	0.931290i	$0.618684\pi$
$548$	1.44344			0.0616607
$549$			7.84150i			0.334667i
$550$			23.8142i			1.01544i
$551$		−	0.688568i		−	0.0293340i
$552$	−6.74456			−0.287068
$553$	−6.16198			−0.262034
$554$			19.5713i			0.831505i
$555$			2.95114i			0.125269i
$556$		−	2.39458i		−	0.101553i
$557$	46.8551			1.98532			0.992658	−	0.120957i	$-0.0385964\pi$
$557$	46.8551			1.98532			0.992658	+	0.120957i	$0.0385964\pi$
$558$			2.27828i			0.0964473i
$559$	4.65668			0.196956
$560$	1.13914			0.0481374
$561$	−15.2589	−	21.6911i	−0.644232	−	0.915799i
$562$	−32.5178			−1.37168
$563$	−10.0503			−0.423569			−0.211785	−	0.977316i	$-0.567928\pi$
$563$	−10.0503			−0.423569			−0.211785	+	0.977316i	$0.567928\pi$
$564$		−	2.27828i		−	0.0959329i
$565$	−5.85420			−0.246288
$566$			32.1915i			1.35311i
$567$		−	1.00000i		−	0.0419961i
$568$			9.56322i			0.401264i
$569$	−0.362684			−0.0152045			−0.00760226	−	0.999971i	$-0.502420\pi$
$569$	−0.362684			−0.0152045			−0.00760226	+	0.999971i	$0.502420\pi$
$570$	−2.90306			−0.121596
$571$		−	19.8791i		−	0.831914i	−0.909384	−	0.415957i	$-0.863447\pi$
$571$		−	19.8791i		−	0.831914i	0.909384	−	0.415957i	$-0.136553\pi$
$572$		−	3.79930i		−	0.158857i
$573$			13.5372i			0.565525i
$574$	−3.84150			−0.160341
$575$		−	24.9708i		−	1.04135i
$576$	−1.00000			−0.0416667
$577$	−10.8482			−0.451615			−0.225807	−	0.974172i	$-0.572502\pi$
$577$	−10.8482			−0.451615			−0.225807	+	0.974172i	$0.572502\pi$
$578$	5.74456	−	16.0000i	0.238942	−	0.665512i
$579$	−10.8187			−0.449608
$580$	−0.307783			−0.0127800
$581$		−	15.4550i		−	0.641182i
$582$	−2.23608			−0.0926884
$583$		−	12.1163i		−	0.501806i
$584$			0.0422023i			0.00174635i
$585$		−	0.672857i		−	0.0278192i
$586$	−26.0376			−1.07560
$587$	22.5224			0.929601			0.464800	−	0.885415i	$-0.346126\pi$
$587$	22.5224			0.929601			0.464800	+	0.885415i	$0.346126\pi$
$588$		−	1.00000i		−	0.0412393i
$589$		−	5.80612i		−	0.239237i
$590$			10.5861i			0.435821i
$591$	−10.8563			−0.446567
$592$		−	2.59067i		−	0.106476i
$593$	16.8198			0.690704			0.345352	−	0.938473i	$-0.387759\pi$
$593$	16.8198			0.690704			0.345352	+	0.938473i	$0.387759\pi$
$594$	6.43217			0.263915
$595$	−2.70236	−	3.84150i	−0.110786	−	0.157486i
$596$	−16.4698			−0.674628
$597$	4.55656			0.186488
$598$			3.98382i			0.162910i
$599$	−13.4891			−0.551151			−0.275575	−	0.961279i	$-0.588868\pi$
$599$	−13.4891			−0.551151			−0.275575	+	0.961279i	$0.588868\pi$
$600$		−	3.70236i		−	0.151148i
$601$			0.0902767i			0.00368246i	0.999998	+	0.00184123i	$0.000586083\pi$
$601$			0.0902767i			0.00368246i	−0.999998	+	0.00184123i	$0.999414\pi$
$602$			7.88370i			0.321316i
$603$	−7.88370			−0.321049
$604$	−10.5861			−0.430741
$605$		−	34.5989i		−	1.40665i
$606$			14.5942i			0.592847i
$607$			44.7069i			1.81460i	0.420485	+	0.907299i	$0.361860\pi$
$607$			44.7069i			1.81460i	−0.420485	+	0.907299i	$0.638140\pi$
$608$	2.54847			0.103354
$609$			0.270189i			0.0109486i
$610$	−8.93257			−0.361669
$611$	−1.34571			−0.0544418
$612$	2.37228	+	3.37228i	0.0958938	+	0.136316i
$613$	4.83484			0.195277			0.0976387	−	0.995222i	$-0.468871\pi$
$613$	4.83484			0.195277			0.0976387	+	0.995222i	$0.468871\pi$
$614$	−33.9989			−1.37208
$615$		−	4.37601i		−	0.176458i
$616$	6.43217			0.259160
$617$			39.2692i			1.58092i	0.612514	+	0.790460i	$0.290158\pi$
$617$			39.2692i			1.58092i	−0.612514	+	0.790460i	$0.709842\pi$
$618$		−	2.86086i		−	0.115081i
$619$			27.2427i			1.09498i	0.836813	+	0.547489i	$0.184416\pi$
$619$			27.2427i			1.09498i	−0.836813	+	0.547489i	$0.815584\pi$
$620$	−2.59528			−0.104229
$621$	−6.74456			−0.270650
$622$		−	15.2427i		−	0.611178i
$623$		−	5.41742i		−	0.217044i
$624$			0.590671i			0.0236458i
$625$	7.21927			0.288771
$626$			14.5120i			0.580015i
$627$	−16.3922			−0.654641
$628$	0.706969			0.0282111
$629$	−8.73647	+	6.14580i	−0.348346	+	0.245049i
$630$	1.13914			0.0453844
$631$	41.1883			1.63968			0.819840	−	0.572592i	$-0.194062\pi$
$631$	41.1883			1.63968			0.819840	+	0.572592i	$0.194062\pi$
$632$			6.16198i			0.245110i
$633$	−1.52563			−0.0606382
$634$		−	31.4128i		−	1.24756i
$635$		−	0.615566i		−	0.0244280i
$636$			1.88370i			0.0746937i
$637$	−0.590671			−0.0234032
$638$	−1.73790			−0.0688042
$639$			9.56322i			0.378315i
$640$		−	1.13914i		−	0.0450285i
$641$		−	2.08789i		−	0.0824666i	−0.999150	−	0.0412333i	$-0.986871\pi$
$641$		−	2.08789i		−	0.0824666i	0.999150	−	0.0412333i	$-0.0131287\pi$
$642$	−8.03759			−0.317219
$643$		−	20.1233i		−	0.793584i	−0.917909	−	0.396792i	$-0.870123\pi$
$643$		−	20.1233i		−	0.793584i	0.917909	−	0.396792i	$-0.129877\pi$
$644$	−6.74456			−0.265773
$645$	−8.98064			−0.353612
$646$	−6.04568	−	8.59415i	−0.237864	−	0.338132i
$647$	−30.1891			−1.18686			−0.593428	−	0.804887i	$-0.702226\pi$
$647$	−30.1891			−1.18686			−0.593428	+	0.804887i	$0.702226\pi$
$648$	−1.00000			−0.0392837
$649$			59.7744i			2.34635i
$650$	−2.18688			−0.0857764
$651$			2.27828i			0.0892928i
$652$			5.84959i			0.229088i
$653$		−	0.354594i		−	0.0138763i	−0.999976	−	0.00693816i	$-0.997791\pi$
$653$		−	0.354594i		−	0.0138763i	0.999976	−	0.00693816i	$-0.00220850\pi$
$654$	6.47437			0.253168
$655$	−5.17213			−0.202092
$656$			3.84150i			0.149985i
$657$			0.0422023i			0.00164647i
$658$		−	2.27828i		−	0.0888166i
$659$	12.6248			0.491792			0.245896	−	0.969296i	$-0.420918\pi$
$659$	12.6248			0.491792			0.245896	+	0.969296i	$0.420918\pi$
$660$			7.32714i			0.285209i
$661$	34.8278			1.35465			0.677323	−	0.735686i	$-0.263140\pi$
$661$	34.8278			1.35465			0.677323	+	0.735686i	$0.263140\pi$
$662$	8.42408			0.327411
$663$	1.99191	−	1.40124i	0.0773593	−	0.0544196i
$664$	−15.4550			−0.599771
$665$	−2.90306			−0.112576
$666$		−	2.59067i		−	0.100386i
$667$	1.82231			0.0705600
$668$			17.0650i			0.660266i
$669$		−	11.8415i		−	0.457819i
$670$		−	8.98064i		−	0.346952i
$671$	−50.4379			−1.94713
$672$	−1.00000			−0.0385758
$673$		−	11.5186i		−	0.444011i	−0.975045	−	0.222005i	$-0.928740\pi$
$673$		−	11.5186i		−	0.444011i	0.975045	−	0.222005i	$-0.0712602\pi$
$674$			19.2108i			0.739974i
$675$		−	3.70236i		−	0.142504i
$676$	−12.6511			−0.486581
$677$			37.6021i			1.44517i	0.691285	+	0.722583i	$0.257045\pi$
$677$			37.6021i			1.44517i	−0.691285	+	0.722583i	$0.742955\pi$
$678$	5.13914			0.197367
$679$	−2.23608			−0.0858128
$680$	−3.84150	+	2.70236i	−0.147315	+	0.103631i
$681$	13.9613			0.534997
$682$	−14.6543			−0.561142
$683$		−	23.4972i		−	0.899096i	−0.893256	−	0.449548i	$-0.851585\pi$
$683$		−	23.4972i		−	0.899096i	0.893256	−	0.449548i	$-0.148415\pi$
$684$	2.54847			0.0974431
$685$			1.64428i			0.0628247i
$686$		−	1.00000i		−	0.0381802i
$687$			2.78455i			0.106237i
$688$	7.88370			0.300563
$689$	1.11265			0.0423885
$690$		−	7.68300i		−	0.292487i
$691$			3.63493i			0.138279i	0.997607	+	0.0691396i	$0.0220254\pi$
$691$			3.63493i			0.138279i	−0.997607	+	0.0691396i	$0.977975\pi$
$692$		−	18.1198i		−	0.688811i
$693$	6.43217			0.244338
$694$			29.6592i			1.12585i
$695$	2.72776			0.103470
$696$	0.270189			0.0102415
$697$	12.9546	−	9.11312i	0.490691	−	0.345184i
$698$	−25.6876			−0.972290
$699$	12.8221			0.484978
$700$		−	3.70236i		−	0.139936i
$701$	−41.3341			−1.56117			−0.780584	−	0.625051i	$-0.785078\pi$
$701$	−41.3341			−1.56117			−0.780584	+	0.625051i	$0.785078\pi$
$702$			0.590671i			0.0222934i
$703$			6.60224i			0.249008i
$704$		−	6.43217i		−	0.242422i
$705$	2.59528			0.0977439
$706$	−7.22354			−0.271862
$707$			14.5942i			0.548870i
$708$		−	9.29303i		−	0.349254i
$709$			7.06283i			0.265250i	0.991166	+	0.132625i	$0.0423406\pi$
$709$			7.06283i			0.265250i	−0.991166	+	0.132625i	$0.957659\pi$
$710$	−10.8938			−0.408839
$711$			6.16198i			0.231092i
$712$	−5.41742			−0.203026
$713$	15.3660			0.575461
$714$	2.37228	+	3.37228i	0.0887804	+	0.126204i
$715$	4.32793			0.161855
$716$	22.5861			0.844081
$717$		−	11.0263i		−	0.411786i
$718$	36.2396			1.35245
$719$		−	3.69918i		−	0.137956i	−0.997618	−	0.0689781i	$-0.978026\pi$
$719$		−	3.69918i		−	0.137956i	0.997618	−	0.0689781i	$-0.0219739\pi$
$720$		−	1.13914i		−	0.0424532i
$721$		−	2.86086i		−	0.106544i
$722$	12.5053			0.465399
$723$	14.5120			0.539706
$724$			25.3468i			0.942007i
$725$			1.00034i			0.0371516i
$726$			30.3728i			1.12724i
$727$	−41.4539			−1.53744			−0.768720	−	0.639586i	$-0.779106\pi$
$727$	−41.4539			−1.53744			−0.768720	+	0.639586i	$0.779106\pi$
$728$			0.590671i			0.0218917i
$729$	−1.00000			−0.0370370
$730$	−0.0480744			−0.00177931
$731$	−18.7024	−	26.5861i	−0.691732	−	0.983321i
$732$	7.84150			0.289830
$733$	−18.1961			−0.672088			−0.336044	−	0.941846i	$-0.609089\pi$
$733$	−18.1961			−0.672088			−0.336044	+	0.941846i	$0.609089\pi$
$734$			1.16516i			0.0430069i
$735$	1.13914			0.0420178
$736$			6.74456i			0.248608i
$737$		−	50.7093i		−	1.86790i
$738$			3.84150i			0.141408i
$739$	−37.1883			−1.36799			−0.683997	−	0.729485i	$-0.739760\pi$
$739$	−37.1883			−1.36799			−0.683997	+	0.729485i	$0.739760\pi$
$740$	2.95114			0.108486
$741$		−	1.50531i		−	0.0552988i
$742$			1.88370i			0.0691529i
$743$		−	1.47882i		−	0.0542525i	−0.999632	−	0.0271262i	$-0.991364\pi$
$743$		−	1.47882i		−	0.0542525i	0.999632	−	0.0271262i	$-0.00863561\pi$
$744$	2.27828			0.0835258
$745$		−	18.7614i		−	0.687363i
$746$	−2.54038			−0.0930098
$747$	−15.4550			−0.565469
$748$	−21.6911	+	15.2589i	−0.793105	+	0.557921i
$749$	−8.03759			−0.293687
$750$	9.91321			0.361979
$751$			3.29525i			0.120245i	0.998191	+	0.0601227i	$0.0191492\pi$
$751$			3.29525i			0.120245i	−0.998191	+	0.0601227i	$0.980851\pi$
$752$	−2.27828			−0.0830803
$753$		−	7.14723i		−	0.260460i
$754$		−	0.159593i		−	0.00581203i
$755$		−	12.0590i		−	0.438872i
$756$	−1.00000			−0.0363696
$757$	33.2178			1.20732			0.603661	−	0.797241i	$-0.293708\pi$
$757$	33.2178			1.20732			0.603661	+	0.797241i	$0.293708\pi$
$758$			16.6682i			0.605418i
$759$		−	43.3822i		−	1.57467i
$760$			2.90306i			0.105305i
$761$	26.1012			0.946168			0.473084	−	0.881017i	$-0.343141\pi$
$761$	26.1012			0.946168			0.473084	+	0.881017i	$0.343141\pi$
$762$			0.540378i			0.0195758i
$763$	6.47437			0.234388
$764$	13.5372			0.489759
$765$	−3.84150	+	2.70236i	−0.138890	+	0.0977040i
$766$	−18.9031			−0.682995
$767$	−5.48913			−0.198201
$768$			1.00000i			0.0360844i
$769$	7.50531			0.270648			0.135324	−	0.990801i	$-0.456792\pi$
$769$	7.50531			0.270648			0.135324	+	0.990801i	$0.456792\pi$
$770$			7.32714i			0.264052i
$771$		−	23.1391i		−	0.833336i
$772$			10.8187i			0.389372i
$773$	21.4972			0.773201			0.386601	−	0.922247i	$-0.373649\pi$
$773$	21.4972			0.773201			0.386601	+	0.922247i	$0.373649\pi$
$774$	7.88370			0.283374
$775$			8.43501i			0.302995i
$776$			2.23608i			0.0802705i
$777$		−	2.59067i		−	0.0929398i
$778$	−9.14262			−0.327779
$779$		−	9.78994i		−	0.350761i
$780$	−0.672857			−0.0240921
$781$	−61.5123			−2.20108
$782$	22.7446	−	16.0000i	0.813344	−	0.572159i
$783$	0.270189			0.00965577
$784$	−1.00000			−0.0357143
$785$			0.805336i			0.0287437i
$786$	4.54038			0.161950
$787$		−	10.1620i		−	0.362236i	−0.983461	−	0.181118i	$-0.942028\pi$
$787$		−	10.1620i		−	0.362236i	0.983461	−	0.181118i	$-0.0579715\pi$
$788$			10.8563i			0.386738i
$789$		−	11.4915i		−	0.409109i
$790$	−7.01936			−0.249738
$791$	5.13914			0.182727
$792$		−	6.43217i		−	0.228557i
$793$		−	4.63175i		−	0.164478i
$794$		−	21.6476i		−	0.768245i
$795$	−2.14580			−0.0761037
$796$		−	4.55656i		−	0.161503i
$797$	−29.7206			−1.05276			−0.526379	−	0.850250i	$-0.676451\pi$
$797$	−29.7206			−1.05276			−0.526379	+	0.850250i	$0.676451\pi$
$798$	2.54847			0.0902148
$799$	5.40472	+	7.68300i	0.191205	+	0.271805i
$800$	−3.70236			−0.130898
$801$	−5.41742			−0.191415
$802$			16.7058i			0.589904i
$803$	−0.271453			−0.00957936
$804$			7.88370i			0.278037i
$805$		−	7.68300i		−	0.270790i
$806$		−	1.34571i		−	0.0474008i
$807$	−26.5120			−0.933265
$808$	14.5942			0.513421
$809$			3.21672i			0.113094i	0.998400	+	0.0565469i	$0.0180090\pi$
$809$			3.21672i			0.113094i	−0.998400	+	0.0565469i	$0.981991\pi$
$810$		−	1.13914i		−	0.0400253i
$811$		−	36.1233i		−	1.26846i	−0.773145	−	0.634230i	$-0.781317\pi$
$811$		−	36.1233i		−	1.26846i	0.773145	−	0.634230i	$-0.218683\pi$
$812$	0.270189			0.00948177
$813$			19.7414i			0.692361i
$814$	16.6636			0.584060
$815$	−6.66350			−0.233412
$816$	3.37228	−	2.37228i	0.118053	−	0.0830465i
$817$	−20.0914			−0.702908
$818$	16.5017			0.576967
$819$			0.590671i			0.0206397i
$820$	−4.37601			−0.152817
$821$		−	13.4515i		−	0.469462i	−0.972060	−	0.234731i	$-0.924579\pi$
$821$		−	13.4515i		−	0.469462i	0.972060	−	0.234731i	$-0.0754209\pi$
$822$		−	1.44344i		−	0.0503458i
$823$			31.1907i			1.08724i	0.839332	+	0.543620i	$0.182947\pi$
$823$			31.1907i			1.08724i	−0.839332	+	0.543620i	$0.817053\pi$
$824$	−2.86086			−0.0996628
$825$	23.8142			0.829105
$826$		−	9.29303i		−	0.323346i
$827$		−	12.6422i		−	0.439613i	−0.975543	−	0.219807i	$-0.929457\pi$
$827$		−	12.6422i		−	0.439613i	0.975543	−	0.219807i	$-0.0705427\pi$
$828$			6.74456i			0.234390i
$829$	39.4001			1.36842			0.684211	−	0.729284i	$-0.260147\pi$
$829$	39.4001			1.36842			0.684211	+	0.729284i	$0.260147\pi$
$830$		−	17.6054i		−	0.611093i
$831$	19.5713			0.678921
$832$	0.590671			0.0204778
$833$	2.37228	+	3.37228i	0.0821947	+	0.116843i
$834$	−2.39458			−0.0829174
$835$	−19.4395			−0.672731
$836$			16.3922i			0.566936i
$837$	2.27828			0.0787489
$838$			21.7287i			0.750605i
$839$		−	18.2302i		−	0.629377i	−0.949195	−	0.314688i	$-0.898100\pi$
$839$		−	18.2302i		−	0.629377i	0.949195	−	0.314688i	$-0.101900\pi$
$840$		−	1.13914i		−	0.0393041i
$841$	28.9270			0.997483
$842$	−14.5566			−0.501652
$843$			32.5178i			1.11997i
$844$			1.52563i			0.0525142i
$845$		−	14.4114i		−	0.495767i
$846$	−2.27828			−0.0783289
$847$			30.3728i			1.04362i
$848$	1.88370			0.0646866
$849$	32.1915			1.10481
$850$	8.78304	+	12.4854i	0.301256	+	0.428246i
$851$	−17.4729			−0.598965
$852$	9.56322			0.327631
$853$		−	36.8654i		−	1.26225i	−0.775682	−	0.631124i	$-0.782594\pi$
$853$		−	36.8654i		−	1.26225i	0.775682	−	0.631124i	$-0.217406\pi$
$854$	7.84150			0.268331
$855$			2.90306i			0.0992826i
$856$			8.03759i			0.274719i
$857$		−	14.2886i		−	0.488089i	−0.969764	−	0.244044i	$-0.921526\pi$
$857$		−	14.2886i		−	0.488089i	0.969764	−	0.244044i	$-0.0784743\pi$
$858$	−3.79930			−0.129706
$859$	26.8563			0.916323			0.458162	−	0.888869i	$-0.348508\pi$
$859$	26.8563			0.916323			0.458162	+	0.888869i	$0.348508\pi$
$860$			8.98064i			0.306237i
$861$			3.84150i			0.130918i
$862$		−	31.7733i		−	1.08220i
$863$	36.2759			1.23485			0.617423	−	0.786631i	$-0.288177\pi$
$863$	36.2759			1.23485			0.617423	+	0.786631i	$0.288177\pi$
$864$			1.00000i			0.0340207i
$865$	20.6410			0.701814
$866$	9.37522			0.318583
$867$	−16.0000	−	5.74456i	−0.543388	−	0.195096i
$868$	2.27828			0.0773299
$869$	−39.6349			−1.34452
$870$			0.307783i			0.0104348i
$871$	4.65668			0.157785
$872$		−	6.47437i		−	0.219250i
$873$			2.23608i			0.0756798i
$874$		−	17.1883i		−	0.581403i
$875$	9.91321			0.335128
$876$	0.0422023			0.00142589
$877$			24.3876i			0.823510i	0.911295	+	0.411755i	$0.135084\pi$
$877$			24.3876i			0.823510i	−0.911295	+	0.411755i	$0.864916\pi$
$878$			28.2396i			0.953039i
$879$			26.0376i			0.878226i
$880$	7.32714			0.246998
$881$			32.3981i			1.09152i	0.837942	+	0.545759i	$0.183759\pi$
$881$			32.3981i			1.09152i	−0.837942	+	0.545759i	$0.816241\pi$
$882$	−1.00000			−0.0336718
$883$	50.3604			1.69476			0.847382	−	0.530984i	$-0.178178\pi$
$883$	50.3604			1.69476			0.847382	+	0.530984i	$0.178178\pi$
$884$	−1.40124	−	1.99191i	−0.0471287	−	0.0669952i
$885$	10.5861			0.355847
$886$	−32.9395			−1.10663
$887$		−	16.5247i		−	0.554844i	−0.960748	−	0.277422i	$-0.910520\pi$
$887$		−	16.5247i		−	0.554844i	0.960748	−	0.277422i	$-0.0894800\pi$
$888$	−2.59067			−0.0869372
$889$			0.540378i			0.0181237i
$890$		−	6.17120i		−	0.206859i
$891$		−	6.43217i		−	0.215486i
$892$	−11.8415			−0.396483
$893$	5.80612			0.194295
$894$			16.4698i			0.550831i
$895$			25.7287i			0.860015i
$896$			1.00000i			0.0334077i
$897$	3.98382			0.133016
$898$		−	32.6578i		−	1.08980i
$899$	−0.615566			−0.0205303
$900$	−3.70236			−0.123412
$901$	−4.46867	−	6.35237i	−0.148873	−	0.211628i
$902$	−24.7092			−0.822726
$903$	7.88370			0.262353
$904$		−	5.13914i		−	0.170925i
$905$	−28.8736			−0.959790
$906$			10.5861i			0.351698i
$907$			18.6908i			0.620617i	0.950636	+	0.310309i	$0.100432\pi$
$907$			18.6908i			0.620617i	−0.950636	+	0.310309i	$0.899568\pi$
$908$		−	13.9613i		−	0.463321i
$909$	14.5942			0.484058
$910$	−0.672857			−0.0223050
$911$			15.2212i			0.504299i	0.967688	+	0.252150i	$0.0811375\pi$
$911$			15.2212i			0.504299i	−0.967688	+	0.252150i	$0.918862\pi$
$912$		−	2.54847i		−	0.0843882i
$913$		−	99.4093i		−	3.28997i
$914$	29.7355			0.983563
$915$			8.93257i			0.295302i
$916$	2.78455			0.0920040
$917$	4.54038			0.149936
$918$	3.37228	−	2.37228i	0.111302	−	0.0782970i
$919$	52.1666			1.72082			0.860408	−	0.509606i	$-0.170209\pi$
$919$	52.1666			1.72082			0.860408	+	0.509606i	$0.170209\pi$
$920$	−7.68300			−0.253301
$921$			33.9989i			1.12030i
$922$	10.5097			0.346120
$923$		−	5.64872i		−	0.185930i
$924$		−	6.43217i		−	0.211603i
$925$		−	9.59160i		−	0.315370i
$926$	−23.4504			−0.770628
$927$	−2.86086			−0.0939630
$928$		−	0.270189i		−	0.00886939i
$929$		−	6.74456i		−	0.221282i	−0.993860	−	0.110641i	$-0.964710\pi$
$929$		−	6.74456i		−	0.221282i	0.993860	−	0.110641i	$-0.0352904\pi$
$930$			2.59528i			0.0851026i
$931$	2.54847			0.0835227
$932$		−	12.8221i		−	0.420003i
$933$	−15.2427			−0.499025
$934$	−34.2580			−1.12095
$935$	−17.3820	−	24.7092i	−0.568454	−	0.808077i
$936$	0.590671			0.0193067
$937$	31.1721			1.01835			0.509174	−	0.860663i	$-0.329951\pi$
$937$	31.1721			1.01835			0.509174	+	0.860663i	$0.329951\pi$
$938$			7.88370i			0.257412i
$939$	14.5120			0.473580
$940$		−	2.59528i		−	0.0846487i
$941$		−	10.8770i		−	0.354581i	−0.984159	−	0.177291i	$-0.943267\pi$
$941$		−	10.8770i		−	0.354581i	0.984159	−	0.177291i	$-0.0567333\pi$
$942$		−	0.706969i		−	0.0230343i
$943$	25.9092			0.843721
$944$	−9.29303			−0.302462
$945$		−	1.13914i		−	0.0370562i
$946$			50.7093i			1.64870i
$947$			45.3579i			1.47393i	0.675929	+	0.736967i	$0.263743\pi$
$947$			45.3579i			1.47393i	−0.675929	+	0.736967i	$0.736257\pi$
$948$	6.16198			0.200132
$949$		−	0.0249277i		−	0.000809188i
$950$	9.43535			0.306123
$951$	−31.4128			−1.01863
$952$	3.37228	−	2.37228i	0.109296	−	0.0768861i
$953$	45.1334			1.46201			0.731007	−	0.682370i	$-0.239051\pi$
$953$	45.1334			1.46201			0.731007	+	0.682370i	$0.239051\pi$
$954$	1.88370			0.0609871
$955$			15.4208i			0.499004i
$956$	−11.0263			−0.356617
$957$			1.73790i			0.0561784i
$958$		−	37.6124i		−	1.21520i
$959$		−	1.44344i		−	0.0466111i
$960$	−1.13914			−0.0367656
$961$	25.8094			0.832563
$962$			1.53023i			0.0493367i
$963$			8.03759i			0.259008i
$964$		−	14.5120i		−	0.467399i
$965$	−12.3240			−0.396722
$966$			6.74456i			0.217003i
$967$	40.1504			1.29115			0.645575	−	0.763697i	$-0.276618\pi$
$967$	40.1504			1.29115			0.645575	+	0.763697i	$0.276618\pi$
$968$	30.3728			0.976220
$969$	−8.59415	+	6.04568i	−0.276084	+	0.194215i
$970$	−2.54721			−0.0817858
$971$	25.5007			0.818356			0.409178	−	0.912455i	$-0.365815\pi$
$971$	25.5007			0.818356			0.409178	+	0.912455i	$0.365815\pi$
$972$			1.00000i			0.0320750i
$973$	−2.39458			−0.0767666
$974$			0.0480744i			0.00154040i
$975$			2.18688i			0.0700361i
$976$		−	7.84150i		−	0.251000i
$977$	−12.6660			−0.405222			−0.202611	−	0.979259i	$-0.564943\pi$
$977$	−12.6660			−0.405222			−0.202611	+	0.979259i	$0.564943\pi$
$978$	5.84959			0.187049
$979$		−	34.8458i		−	1.11368i
$980$		−	1.13914i		−	0.0363885i
$981$		−	6.47437i		−	0.206711i
$982$	34.9100			1.11402
$983$			48.8389i			1.55772i	0.627198	+	0.778860i	$0.284202\pi$
$983$			48.8389i			1.55772i	−0.627198	+	0.778860i	$0.715798\pi$
$984$	3.84150			0.122463
$985$	−12.3668			−0.394039
$986$	−0.911153	+	0.640964i	−0.0290170	+	0.0204125i
$987$	−2.27828			−0.0725184
$988$	−1.50531			−0.0478902
$989$		−	53.1721i		−	1.69078i
$990$	7.32714			0.232872
$991$		−	15.4753i		−	0.491590i	−0.969322	−	0.245795i	$-0.920951\pi$
$991$		−	15.4753i		−	0.491590i	0.969322	−	0.245795i	$-0.0790490\pi$
$992$		−	2.27828i		−	0.0723355i
$993$		−	8.42408i		−	0.267330i
$994$	9.56322			0.303327
$995$	5.19056			0.164552
$996$			15.4550i			0.489711i
$997$		−	28.7902i		−	0.911796i	−0.890032	−	0.455898i	$-0.849318\pi$
$997$		−	28.7902i		−	0.911796i	0.890032	−	0.455898i	$-0.150682\pi$
$998$		−	13.9340i		−	0.441073i
$999$	−2.59067			−0.0819652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.b.f.169.7	yes	8
3.2	odd	2		2142.2.b.j.883.3		8
17.16	even	2	inner	714.2.b.f.169.2	✓	8
51.50	odd	2		2142.2.b.j.883.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.b.f.169.2	✓	8	17.16	even	2	inner
714.2.b.f.169.7	yes	8	1.1	even	1	trivial
2142.2.b.j.883.3		8	3.2	odd	2
2142.2.b.j.883.6		8	51.50	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.13914i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.13914i q^{5} -1.00000i q^{6} -1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} -1.13914i q^{10} -6.43217i q^{11} +1.00000i q^{12} +0.590671 q^{13} +1.00000i q^{14} -1.13914 q^{15} +1.00000 q^{16} +(-2.37228 - 3.37228i) q^{17} +1.00000 q^{18} -2.54847 q^{19} +1.13914i q^{20} +1.00000 q^{21} +6.43217i q^{22} -6.74456i q^{23} -1.00000i q^{24} +3.70236 q^{25} -0.590671 q^{26} -1.00000i q^{27} -1.00000i q^{28} +0.270189i q^{29} +1.13914 q^{30} +2.27828i q^{31} -1.00000 q^{32} +6.43217 q^{33} +(2.37228 + 3.37228i) q^{34} +1.13914 q^{35} -1.00000 q^{36} -2.59067i q^{37} +2.54847 q^{38} +0.590671i q^{39} -1.13914i q^{40} +3.84150i q^{41} -1.00000 q^{42} +7.88370 q^{43} -6.43217i q^{44} -1.13914i q^{45} +6.74456i q^{46} -2.27828 q^{47} +1.00000i q^{48} -1.00000 q^{49} -3.70236 q^{50} +(3.37228 - 2.37228i) q^{51} +0.590671 q^{52} +1.88370 q^{53} +1.00000i q^{54} +7.32714 q^{55} +1.00000i q^{56} -2.54847i q^{57} -0.270189i q^{58} -9.29303 q^{59} -1.13914 q^{60} -7.84150i q^{61} -2.27828i q^{62} +1.00000i q^{63} +1.00000 q^{64} +0.672857i q^{65} -6.43217 q^{66} +7.88370 q^{67} +(-2.37228 - 3.37228i) q^{68} +6.74456 q^{69} -1.13914 q^{70} -9.56322i q^{71} +1.00000 q^{72} -0.0422023i q^{73} +2.59067i q^{74} +3.70236i q^{75} -2.54847 q^{76} -6.43217 q^{77} -0.590671i q^{78} -6.16198i q^{79} +1.13914i q^{80} +1.00000 q^{81} -3.84150i q^{82} +15.4550 q^{83} +1.00000 q^{84} +(3.84150 - 2.70236i) q^{85} -7.88370 q^{86} -0.270189 q^{87} +6.43217i q^{88} +5.41742 q^{89} +1.13914i q^{90} -0.590671i q^{91} -6.74456i q^{92} -2.27828 q^{93} +2.27828 q^{94} -2.90306i q^{95} -1.00000i q^{96} -2.23608i q^{97} +1.00000 q^{98} +6.43217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 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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