LMFDB - Embedded newform 403.2.c.b.311.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.28
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.21678i q^{2} -2.59178 q^{3} -2.91410 q^{4} -1.00571i q^{5} -5.74540i q^{6} -1.82096i q^{7} -2.02635i q^{8} +3.71732 q^{9} +O(q^{10})$	\(q+2.21678i q^{2} -2.59178 q^{3} -2.91410 q^{4} -1.00571i q^{5} -5.74540i q^{6} -1.82096i q^{7} -2.02635i q^{8} +3.71732 q^{9} +2.22943 q^{10} -2.73558i q^{11} +7.55270 q^{12} +(2.90778 + 2.13186i) q^{13} +4.03666 q^{14} +2.60657i q^{15} -1.33623 q^{16} +2.66819 q^{17} +8.24047i q^{18} -2.04700i q^{19} +2.93073i q^{20} +4.71953i q^{21} +6.06418 q^{22} +1.36011 q^{23} +5.25186i q^{24} +3.98855 q^{25} +(-4.72587 + 6.44589i) q^{26} -1.85914 q^{27} +5.30645i q^{28} -3.75197 q^{29} -5.77819 q^{30} +1.00000i q^{31} -7.01482i q^{32} +7.09003i q^{33} +5.91478i q^{34} -1.83135 q^{35} -10.8326 q^{36} -5.04610i q^{37} +4.53774 q^{38} +(-7.53631 - 5.52532i) q^{39} -2.03792 q^{40} +3.02730i q^{41} -10.4621 q^{42} +9.12211 q^{43} +7.97176i q^{44} -3.73854i q^{45} +3.01506i q^{46} -7.62683i q^{47} +3.46321 q^{48} +3.68411 q^{49} +8.84173i q^{50} -6.91536 q^{51} +(-8.47354 - 6.21246i) q^{52} +5.26937 q^{53} -4.12130i q^{54} -2.75120 q^{55} -3.68990 q^{56} +5.30537i q^{57} -8.31728i q^{58} -2.66100i q^{59} -7.59581i q^{60} +7.14518 q^{61} -2.21678 q^{62} -6.76909i q^{63} +12.8778 q^{64} +(2.14403 - 2.92437i) q^{65} -15.7170 q^{66} -9.48459i q^{67} -7.77536 q^{68} -3.52511 q^{69} -4.05970i q^{70} -4.99950i q^{71} -7.53260i q^{72} -4.50699i q^{73} +11.1861 q^{74} -10.3374 q^{75} +5.96516i q^{76} -4.98139 q^{77} +(12.2484 - 16.7063i) q^{78} -0.813843 q^{79} +1.34386i q^{80} -6.33348 q^{81} -6.71086 q^{82} +1.18611i q^{83} -13.7532i q^{84} -2.68342i q^{85} +20.2217i q^{86} +9.72428 q^{87} -5.54325 q^{88} +16.2385i q^{89} +8.28751 q^{90} +(3.88204 - 5.29494i) q^{91} -3.96350 q^{92} -2.59178i q^{93} +16.9070 q^{94} -2.05868 q^{95} +18.1809i q^{96} +3.69072i q^{97} +8.16684i q^{98} -10.1690i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.21678i			1.56750i	0.621078	+	0.783749i	$0.286695\pi$
$2$			2.21678i			1.56750i	−0.621078	+	0.783749i	$0.713305\pi$
$3$	−2.59178			−1.49636			−0.748182	−	0.663493i	$-0.769073\pi$
$3$	−2.59178			−1.49636			−0.748182	+	0.663493i	$0.769073\pi$
$4$	−2.91410			−1.45705
$5$		−	1.00571i		−	0.449766i	−0.974386	−	0.224883i	$-0.927800\pi$
$5$		−	1.00571i		−	0.449766i	0.974386	−	0.224883i	$-0.0722001\pi$
$6$		−	5.74540i		−	2.34555i
$7$		−	1.82096i		−	0.688258i	−0.938922	−	0.344129i	$-0.888174\pi$
$7$		−	1.82096i		−	0.688258i	0.938922	−	0.344129i	$-0.111826\pi$
$8$		−	2.02635i		−	0.716423i
$9$	3.71732			1.23911
$10$	2.22943			0.705008
$11$		−	2.73558i		−	0.824810i	−0.911001	−	0.412405i	$-0.864689\pi$
$11$		−	2.73558i		−	0.824810i	0.911001	−	0.412405i	$-0.135311\pi$
$12$	7.55270			2.18028
$13$	2.90778	+	2.13186i	0.806472	+	0.591273i
$13$	2.90778	+	2.13186i	0.806472	+	0.591273i
$14$	4.03666			1.07884
$15$			2.60657i			0.673015i
$16$	−1.33623			−0.334057
$17$	2.66819			0.647131			0.323565	−	0.946206i	$-0.395118\pi$
$17$	2.66819			0.647131			0.323565	+	0.946206i	$0.395118\pi$
$18$			8.24047i			1.94230i
$19$		−	2.04700i		−	0.469614i	−0.972042	−	0.234807i	$-0.924554\pi$
$19$		−	2.04700i		−	0.469614i	0.972042	−	0.234807i	$-0.0754458\pi$
$20$			2.93073i			0.655332i
$21$			4.71953i			1.02988i
$22$	6.06418			1.29289
$23$	1.36011			0.283603			0.141802	−	0.989895i	$-0.454711\pi$
$23$	1.36011			0.283603			0.141802	+	0.989895i	$0.454711\pi$
$24$			5.25186i			1.07203i
$25$	3.98855			0.797710
$26$	−4.72587	+	6.44589i	−0.926818	+	1.26414i
$27$	−1.85914			−0.357792
$28$			5.30645i			1.00283i
$29$	−3.75197			−0.696724			−0.348362	−	0.937360i	$-0.613262\pi$
$29$	−3.75197			−0.696724			−0.348362	+	0.937360i	$0.613262\pi$
$30$	−5.77819			−1.05495
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$		−	7.01482i		−	1.24006i
$33$			7.09003i			1.23422i
$34$			5.91478i			1.01438i
$35$	−1.83135			−0.309555
$36$	−10.8326			−1.80544
$37$		−	5.04610i		−	0.829573i	−0.909919	−	0.414787i	$-0.863856\pi$
$37$		−	5.04610i		−	0.829573i	0.909919	−	0.414787i	$-0.136144\pi$
$38$	4.53774			0.736118
$39$	−7.53631	−	5.52532i	−1.20678	−	0.884759i
$40$	−2.03792			−0.322223
$41$			3.02730i			0.472785i	0.971658	+	0.236393i	$0.0759652\pi$
$41$			3.02730i			0.472785i	−0.971658	+	0.236393i	$0.924035\pi$
$42$	−10.4621			−1.61434
$43$	9.12211			1.39111			0.695554	−	0.718474i	$-0.255159\pi$
$43$	9.12211			1.39111			0.695554	+	0.718474i	$0.255159\pi$
$44$			7.97176i			1.20179i
$45$		−	3.73854i		−	0.557309i
$46$			3.01506i			0.444547i
$47$		−	7.62683i		−	1.11249i	−0.831019	−	0.556244i	$-0.812242\pi$
$47$		−	7.62683i		−	1.11249i	0.831019	−	0.556244i	$-0.187758\pi$
$48$	3.46321			0.499871
$49$	3.68411			0.526301
$50$			8.84173i			1.25041i
$51$	−6.91536			−0.968343
$52$	−8.47354	−	6.21246i	−1.17507	−	0.861513i
$53$	5.26937			0.723804			0.361902	−	0.932216i	$-0.382127\pi$
$53$	5.26937			0.723804			0.361902	+	0.932216i	$0.382127\pi$
$54$		−	4.12130i		−	0.560838i
$55$	−2.75120			−0.370972
$56$	−3.68990			−0.493084
$57$			5.30537i			0.702713i
$58$		−	8.31728i		−	1.09211i
$59$		−	2.66100i		−	0.346433i	−0.984884	−	0.173216i	$-0.944584\pi$
$59$		−	2.66100i		−	0.346433i	0.984884	−	0.173216i	$-0.0554160\pi$
$60$		−	7.59581i		−	0.980615i
$61$	7.14518			0.914847			0.457424	−	0.889249i	$-0.348772\pi$
$61$	7.14518			0.914847			0.457424	+	0.889249i	$0.348772\pi$
$62$	−2.21678			−0.281531
$63$		−	6.76909i		−	0.852825i
$64$	12.8778			1.60973
$65$	2.14403	−	2.92437i	0.265935	−	0.362724i
$66$	−15.7170			−1.93463
$67$		−	9.48459i		−	1.15873i	−0.815069	−	0.579364i	$-0.803301\pi$
$67$		−	9.48459i		−	1.15873i	0.815069	−	0.579364i	$-0.196699\pi$
$68$	−7.77536			−0.942901
$69$	−3.52511			−0.424374
$70$		−	4.05970i		−	0.485227i
$71$		−	4.99950i		−	0.593331i	−0.954981	−	0.296665i	$-0.904125\pi$
$71$		−	4.99950i		−	0.593331i	0.954981	−	0.296665i	$-0.0958746\pi$
$72$		−	7.53260i		−	0.887725i
$73$		−	4.50699i		−	0.527503i	−0.964591	−	0.263751i	$-0.915040\pi$
$73$		−	4.50699i		−	0.527503i	0.964591	−	0.263751i	$-0.0849598\pi$
$74$	11.1861			1.30035
$75$	−10.3374			−1.19367
$76$			5.96516i			0.684250i
$77$	−4.98139			−0.567682
$78$	12.2484	−	16.7063i	1.38686	−	1.89162i
$79$	−0.813843			−0.0915645			−0.0457822	−	0.998951i	$-0.514578\pi$
$79$	−0.813843			−0.0915645			−0.0457822	+	0.998951i	$0.514578\pi$
$80$			1.34386i			0.150248i
$81$	−6.33348			−0.703720
$82$	−6.71086			−0.741090
$83$			1.18611i			0.130193i	0.997879	+	0.0650963i	$0.0207355\pi$
$83$			1.18611i			0.130193i	−0.997879	+	0.0650963i	$0.979265\pi$
$84$		−	13.7532i		−	1.50059i
$85$		−	2.68342i		−	0.291058i
$86$			20.2217i			2.18056i
$87$	9.72428			1.04255
$88$	−5.54325			−0.590913
$89$			16.2385i			1.72128i	0.509212	+	0.860641i	$0.329937\pi$
$89$			16.2385i			1.72128i	−0.509212	+	0.860641i	$0.670063\pi$
$90$	8.28751			0.873580
$91$	3.88204	−	5.29494i	0.406948	−	0.555061i
$92$	−3.96350			−0.413223
$93$		−	2.59178i		−	0.268755i
$94$	16.9070			1.74382
$95$	−2.05868			−0.211216
$96$			18.1809i			1.85558i
$97$			3.69072i			0.374736i	0.982290	+	0.187368i	$0.0599957\pi$
$97$			3.69072i			0.374736i	−0.982290	+	0.187368i	$0.940004\pi$
$98$			8.16684i			0.824976i
$99$		−	10.1690i		−	1.02203i
$100$	−11.6230			−1.16230
$101$	−9.39142			−0.934481			−0.467241	−	0.884130i	$-0.654752\pi$
$101$	−9.39142			−0.934481			−0.467241	+	0.884130i	$0.654752\pi$
$102$		−	15.3298i		−	1.51788i
$103$	7.79135			0.767705			0.383852	−	0.923394i	$-0.374597\pi$
$103$	7.79135			0.767705			0.383852	+	0.923394i	$0.374597\pi$
$104$	4.31990	−	5.89217i	0.423601	−	0.577775i
$105$	4.74647			0.463208
$106$			11.6810i			1.13456i
$107$	−18.3141			−1.77049			−0.885245	−	0.465125i	$-0.846009\pi$
$107$	−18.3141			−1.77049			−0.885245	+	0.465125i	$0.846009\pi$
$108$	5.41772			0.521320
$109$		−	19.3010i		−	1.84870i	−0.381542	−	0.924352i	$-0.624607\pi$
$109$		−	19.3010i		−	1.84870i	0.381542	−	0.924352i	$-0.375393\pi$
$110$		−	6.09879i		−	0.581497i
$111$			13.0784i			1.24134i
$112$			2.43322i			0.229918i
$113$	1.71217			0.161067			0.0805335	−	0.996752i	$-0.474338\pi$
$113$	1.71217			0.161067			0.0805335	+	0.996752i	$0.474338\pi$
$114$	−11.7608			−1.10150
$115$		−	1.36788i		−	0.127555i
$116$	10.9336			1.01516
$117$	10.8091	+	7.92482i	0.999305	+	0.732650i
$118$	5.89884			0.543032
$119$		−	4.85866i		−	0.445393i
$120$	5.28183			0.482163
$121$	3.51658			0.319689
$122$			15.8393i			1.43402i
$123$		−	7.84610i		−	0.707459i
$124$		−	2.91410i		−	0.261694i
$125$		−	9.03986i		−	0.808550i
$126$	15.0056			1.33680
$127$	16.9909			1.50770			0.753849	−	0.657048i	$-0.228195\pi$
$127$	16.9909			1.50770			0.753849	+	0.657048i	$0.228195\pi$
$128$			14.5176i			1.28319i
$129$	−23.6425			−2.08161
$130$	6.48268	+	4.75284i	0.568569	+	0.416852i
$131$	−12.4908			−1.09133			−0.545663	−	0.838005i	$-0.683722\pi$
$131$	−12.4908			−1.09133			−0.545663	+	0.838005i	$0.683722\pi$
$132$		−	20.6610i		−	1.79831i
$133$	−3.72750			−0.323215
$134$	21.0252			1.81630
$135$			1.86975i			0.160923i
$136$		−	5.40669i		−	0.463619i
$137$		−	3.57641i		−	0.305553i	−0.988261	−	0.152777i	$-0.951179\pi$
$137$		−	3.57641i		−	0.305553i	0.988261	−	0.152777i	$-0.0488215\pi$
$138$		−	7.81438i		−	0.665205i
$139$	−17.1808			−1.45725			−0.728627	−	0.684911i	$-0.759841\pi$
$139$	−17.1808			−1.45725			−0.728627	+	0.684911i	$0.759841\pi$
$140$	5.33675			0.451037
$141$			19.7671i			1.66469i
$142$	11.0828			0.930045
$143$	5.83189	−	7.95446i	0.487687	−	0.665186i
$144$	−4.96719			−0.413933
$145$			3.77339i			0.313363i
$146$	9.99098			0.826859
$147$	−9.54839			−0.787538
$148$			14.7048i			1.20873i
$149$			9.50590i			0.778754i	0.921078	+	0.389377i	$0.127310\pi$
$149$			9.50590i			0.778754i	−0.921078	+	0.389377i	$0.872690\pi$
$150$		−	22.9158i		−	1.87107i
$151$			0.701427i			0.0570814i	0.999593	+	0.0285407i	$0.00908601\pi$
$151$			0.701427i			0.0570814i	−0.999593	+	0.0285407i	$0.990914\pi$
$152$	−4.14794			−0.336442
$153$	9.91851			0.801864
$154$		−	11.0426i		−	0.889840i
$155$	1.00571			0.0807804
$156$	21.9616	+	16.1013i	1.75833	+	1.28914i
$157$	−19.7650			−1.57742			−0.788710	−	0.614765i	$-0.789251\pi$
$157$	−19.7650			−1.57742			−0.788710	+	0.614765i	$0.789251\pi$
$158$		−	1.80411i		−	0.143527i
$159$	−13.6571			−1.08307
$160$	−7.05487			−0.557736
$161$		−	2.47671i		−	0.195192i
$162$		−	14.0399i		−	1.10308i
$163$		−	12.0409i		−	0.943115i	−0.881835	−	0.471557i	$-0.843692\pi$
$163$		−	12.0409i		−	0.943115i	0.881835	−	0.471557i	$-0.156308\pi$
$164$		−	8.82186i		−	0.688872i
$165$	7.13050			0.555109
$166$	−2.62934			−0.204077
$167$			20.4561i			1.58294i	0.611205	+	0.791472i	$0.290685\pi$
$167$			20.4561i			1.58294i	−0.611205	+	0.791472i	$0.709315\pi$
$168$	9.56342			0.737834
$169$	3.91031	+	12.3980i	0.300793	+	0.953689i
$170$	5.94854			0.456232
$171$		−	7.60935i		−	0.581902i
$172$	−26.5827			−2.02691
$173$	6.97691			0.530445			0.265222	−	0.964187i	$-0.414555\pi$
$173$	6.97691			0.530445			0.265222	+	0.964187i	$0.414555\pi$
$174$			21.5566i			1.63420i
$175$		−	7.26299i		−	0.549030i
$176$			3.65537i			0.275534i
$177$			6.89672i			0.518389i
$178$	−35.9972			−2.69811
$179$	8.92044			0.666745			0.333372	−	0.942795i	$-0.391813\pi$
$179$	8.92044			0.666745			0.333372	+	0.942795i	$0.391813\pi$
$180$			10.8945i			0.812026i
$181$	−10.7089			−0.795988			−0.397994	−	0.917388i	$-0.630293\pi$
$181$	−10.7089			−0.795988			−0.397994	+	0.917388i	$0.630293\pi$
$182$	11.7377	+	8.60561i	0.870056	+	0.637890i
$183$	−18.5187			−1.36894
$184$		−	2.75606i		−	0.203180i
$185$	−5.07490			−0.373114
$186$	5.74540			0.421273
$187$		−	7.29905i		−	0.533760i
$188$			22.2253i			1.62095i
$189$			3.38542i			0.246253i
$190$		−	4.56364i		−	0.331081i
$191$	−18.3129			−1.32507			−0.662537	−	0.749029i	$-0.730520\pi$
$191$	−18.3129			−1.32507			−0.662537	+	0.749029i	$0.730520\pi$
$192$	−33.3765			−2.40874
$193$			5.31567i			0.382630i	0.981529	+	0.191315i	$0.0612753\pi$
$193$			5.31567i			0.382630i	−0.981529	+	0.191315i	$0.938725\pi$
$194$	−8.18151			−0.587398
$195$	−5.55686	+	7.57933i	−0.397935	+	0.542767i
$196$	−10.7358			−0.766846
$197$		−	6.99284i		−	0.498219i	−0.968475	−	0.249109i	$-0.919862\pi$
$197$		−	6.99284i		−	0.498219i	0.968475	−	0.249109i	$-0.0801379\pi$
$198$	22.5425			1.60203
$199$	−4.55657			−0.323007			−0.161503	−	0.986872i	$-0.551634\pi$
$199$	−4.55657			−0.323007			−0.161503	+	0.986872i	$0.551634\pi$
$200$		−	8.08220i		−	0.571498i
$201$			24.5820i			1.73388i
$202$		−	20.8187i		−	1.46480i
$203$			6.83219i			0.479526i
$204$	20.1520			1.41092
$205$	3.04458			0.212643
$206$			17.2717i			1.20338i
$207$	5.05597			0.351415
$208$	−3.88545	−	2.84866i	−0.269408	−	0.197519i
$209$	−5.59974			−0.387342
$210$			10.5219i			0.726077i
$211$	17.7764			1.22378			0.611889	−	0.790944i	$-0.290410\pi$
$211$	17.7764			1.22378			0.611889	+	0.790944i	$0.290410\pi$
$212$	−15.3555			−1.05462
$213$			12.9576i			0.887839i
$214$		−	40.5983i		−	2.77524i
$215$		−	9.17418i		−	0.625674i
$216$			3.76727i			0.256330i
$217$	1.82096			0.123615
$218$	42.7861			2.89784
$219$			11.6811i			0.789336i
$220$	8.01726			0.540524
$221$	7.75849	+	5.68821i	0.521893	+	0.382631i
$222$	−28.9918			−1.94580
$223$			28.1562i			1.88548i	0.333532	+	0.942739i	$0.391760\pi$
$223$			28.1562i			1.88548i	−0.333532	+	0.942739i	$0.608240\pi$
$224$	−12.7737			−0.853479
$225$	14.8267			0.988448
$226$			3.79549i			0.252472i
$227$			10.2989i			0.683561i	0.939780	+	0.341781i	$0.111030\pi$
$227$			10.2989i			0.683561i	−0.939780	+	0.341781i	$0.888970\pi$
$228$		−	15.4604i		−	1.02389i
$229$			11.7672i			0.777601i	0.921322	+	0.388800i	$0.127110\pi$
$229$			11.7672i			0.777601i	−0.921322	+	0.388800i	$0.872890\pi$
$230$	3.03228			0.199942
$231$	12.9107			0.849459
$232$			7.60281i			0.499149i
$233$	15.0623			0.986765			0.493382	−	0.869813i	$-0.335760\pi$
$233$	15.0623			0.986765			0.493382	+	0.869813i	$0.335760\pi$
$234$	−17.5676	+	23.9614i	−1.14843	+	1.56641i
$235$	−7.67036			−0.500359
$236$			7.75441i			0.504769i
$237$	2.10930			0.137014
$238$	10.7706			0.698152
$239$		−	4.17457i		−	0.270030i	−0.990844	−	0.135015i	$-0.956892\pi$
$239$		−	4.17457i		−	0.270030i	0.990844	−	0.135015i	$-0.0431083\pi$
$240$		−	3.48298i		−	0.224825i
$241$		−	17.7274i		−	1.14192i	−0.820978	−	0.570960i	$-0.806571\pi$
$241$		−	17.7274i		−	1.14192i	0.820978	−	0.570960i	$-0.193429\pi$
$242$			7.79548i			0.501112i
$243$	21.9924			1.41081
$244$	−20.8218			−1.33298
$245$		−	3.70514i		−	0.236713i
$246$	17.3931			1.10894
$247$	4.36392	−	5.95221i	0.277670	−	0.378730i
$248$	2.02635			0.128673
$249$		−	3.07414i		−	0.194816i
$250$	20.0393			1.26740
$251$	1.71621			0.108326			0.0541632	−	0.998532i	$-0.482751\pi$
$251$	1.71621			0.108326			0.0541632	+	0.998532i	$0.482751\pi$
$252$			19.7258i			1.24261i
$253$		−	3.72070i		−	0.233918i
$254$			37.6650i			2.36331i
$255$			6.95483i			0.435528i
$256$	−6.42669			−0.401668
$257$	17.8955			1.11629			0.558147	−	0.829742i	$-0.311513\pi$
$257$	17.8955			1.11629			0.558147	+	0.829742i	$0.311513\pi$
$258$		−	52.4101i		−	3.26291i
$259$	−9.18874			−0.570961
$260$	−6.24792	+	8.52191i	−0.387480	+	0.528507i
$261$	−13.9473			−0.863315
$262$		−	27.6893i		−	1.71065i
$263$	−0.133456			−0.00822927			−0.00411463	−	0.999992i	$-0.501310\pi$
$263$	−0.133456			−0.00822927			−0.00411463	+	0.999992i	$0.501310\pi$
$264$	14.3669			0.884221
$265$		−	5.29945i		−	0.325543i
$266$		−	8.26304i		−	0.506639i
$267$		−	42.0867i		−	2.57567i
$268$			27.6390i			1.68832i
$269$	24.3960			1.48745			0.743725	−	0.668485i	$-0.233057\pi$
$269$	24.3960			1.48745			0.743725	+	0.668485i	$0.233057\pi$
$270$	−4.14482			−0.252246
$271$		−	3.25829i		−	0.197927i	−0.995091	−	0.0989635i	$-0.968447\pi$
$271$		−	3.25829i		−	0.197927i	0.995091	−	0.0989635i	$-0.0315527\pi$
$272$	−3.56531			−0.216179
$273$	−10.0614	+	13.7233i	−0.608943	+	0.830573i
$274$	7.92809			0.478954
$275$		−	10.9110i		−	0.657959i
$276$	10.2725			0.618333
$277$	10.6944			0.642563			0.321282	−	0.946984i	$-0.395886\pi$
$277$	10.6944			0.642563			0.321282	+	0.946984i	$0.395886\pi$
$278$		−	38.0859i		−	2.28424i
$279$			3.71732i			0.222550i
$280$			3.71097i			0.221773i
$281$		−	0.279634i		−	0.0166816i	−0.999965	−	0.00834078i	$-0.997345\pi$
$281$		−	0.279634i		−	0.0166816i	0.999965	−	0.00834078i	$-0.00265498\pi$
$282$	−43.8191			−2.60939
$283$	8.05685			0.478930			0.239465	−	0.970905i	$-0.423028\pi$
$283$	8.05685			0.478930			0.239465	+	0.970905i	$0.423028\pi$
$284$			14.5690i			0.864512i
$285$	5.33565			0.316057
$286$	17.6333	+	12.9280i	1.04268	+	0.764449i
$287$	5.51260			0.325398
$288$		−	26.0764i		−	1.53656i
$289$	−9.88077			−0.581222
$290$	−8.36476			−0.491196
$291$		−	9.56554i		−	0.560742i
$292$			13.1338i			0.768597i
$293$			23.0395i			1.34598i	0.739650	+	0.672992i	$0.234991\pi$
$293$			23.0395i			1.34598i	−0.739650	+	0.672992i	$0.765009\pi$
$294$		−	21.1667i		−	1.23446i
$295$	−2.67619			−0.155814
$296$	−10.2252			−0.594326
$297$			5.08583i			0.295110i
$298$	−21.0725			−1.22070
$299$	3.95490	+	2.89957i	0.228718	+	0.167687i
$300$	30.1243			1.73923
$301$		−	16.6110i		−	0.957441i
$302$	−1.55491			−0.0894749
$303$	24.3405			1.39832
$304$			2.73526i			0.156878i
$305$		−	7.18597i		−	0.411468i
$306$			21.9871i			1.25692i
$307$		−	31.6411i		−	1.80585i	−0.429796	−	0.902926i	$-0.641415\pi$
$307$		−	31.6411i		−	1.80585i	0.429796	−	0.902926i	$-0.358585\pi$
$308$	14.5162			0.827140
$309$	−20.1935			−1.14877
$310$			2.22943i			0.126623i
$311$	−30.7261			−1.74232			−0.871158	−	0.491003i	$-0.836630\pi$
$311$	−30.7261			−1.74232			−0.871158	+	0.491003i	$0.836630\pi$
$312$	−11.1962	+	15.2712i	−0.633862	+	0.864562i
$313$	33.4766			1.89221			0.946105	−	0.323860i	$-0.104981\pi$
$313$	33.4766			1.89221			0.946105	+	0.323860i	$0.104981\pi$
$314$		−	43.8146i		−	2.47260i
$315$	−6.80773			−0.383572
$316$	2.37162			0.133414
$317$		−	6.42234i		−	0.360714i	−0.983601	−	0.180357i	$-0.942275\pi$
$317$		−	6.42234i		−	0.360714i	0.983601	−	0.180357i	$-0.0577254\pi$
$318$		−	30.2746i		−	1.69772i
$319$			10.2638i			0.574664i
$320$		−	12.9513i		−	0.724002i
$321$	47.4661			2.64930
$322$	5.49031			0.305963
$323$		−	5.46178i		−	0.303901i
$324$	18.4564			1.02536
$325$	11.5978	+	8.50305i	0.643331	+	0.471664i
$326$	26.6920			1.47833
$327$			50.0240i			2.76633i
$328$	6.13438			0.338714
$329$	−13.8881			−0.765678
$330$			15.8067i			0.870132i
$331$			33.3045i			1.83058i	0.402792	+	0.915291i	$0.368040\pi$
$331$			33.3045i			1.83058i	−0.402792	+	0.915291i	$0.631960\pi$
$332$		−	3.45644i		−	0.189697i
$333$		−	18.7580i		−	1.02793i
$334$	−45.3467			−2.48126
$335$	−9.53874			−0.521157
$336$		−	6.30637i		−	0.344040i
$337$	−0.475146			−0.0258829			−0.0129414	−	0.999916i	$-0.504120\pi$
$337$	−0.475146			−0.0258829			−0.0129414	+	0.999916i	$0.504120\pi$
$338$	−27.4835	+	8.66829i	−1.49491	+	0.471493i
$339$	−4.43755			−0.241015
$340$			7.81975i			0.424085i
$341$	2.73558			0.148140
$342$	16.8682			0.912130
$343$		−	19.4553i		−	1.05049i
$344$		−	18.4846i		−	0.996622i
$345$			3.54523i			0.190869i
$346$			15.4663i			0.831471i
$347$	12.3110			0.660887			0.330443	−	0.943826i	$-0.392802\pi$
$347$	12.3110			0.660887			0.330443	+	0.943826i	$0.392802\pi$
$348$	−28.3375			−1.51905
$349$			34.9537i			1.87103i	0.353289	+	0.935514i	$0.385063\pi$
$349$			34.9537i			1.87103i	−0.353289	+	0.935514i	$0.614937\pi$
$350$	16.1004			0.860604
$351$	−5.40596	−	3.96343i	−0.288549	−	0.211552i
$352$	−19.1896			−1.02281
$353$		−	10.5811i		−	0.563177i	−0.959535	−	0.281589i	$-0.909139\pi$
$353$		−	10.5811i		−	0.563177i	0.959535	−	0.281589i	$-0.0908614\pi$
$354$	−15.2885			−0.812574
$355$	−5.02803			−0.266860
$356$		−	47.3207i		−	2.50799i
$357$			12.5926i			0.666470i
$358$			19.7746i			1.04512i
$359$		−	16.8943i		−	0.891646i	−0.895121	−	0.445823i	$-0.852911\pi$
$359$		−	16.8943i		−	0.891646i	0.895121	−	0.445823i	$-0.147089\pi$
$360$	−7.57560			−0.399269
$361$	14.8098			0.779463
$362$		−	23.7393i		−	1.24771i
$363$	−9.11421			−0.478372
$364$	−11.3126	+	15.4300i	−0.592943	+	0.808751i
$365$	−4.53271			−0.237253
$366$		−	41.0519i		−	2.14582i
$367$	−10.0627			−0.525270			−0.262635	−	0.964895i	$-0.584592\pi$
$367$	−10.0627			−0.525270			−0.262635	+	0.964895i	$0.584592\pi$
$368$	−1.81742			−0.0947396
$369$			11.2535i			0.585832i
$370$		−	11.2499i		−	0.584856i
$371$		−	9.59531i		−	0.498164i
$372$			7.55270i			0.391589i
$373$	−21.3532			−1.10563			−0.552814	−	0.833305i	$-0.686446\pi$
$373$	−21.3532			−1.10563			−0.552814	+	0.833305i	$0.686446\pi$
$374$	16.1804			0.836667
$375$			23.4293i			1.20989i
$376$	−15.4546			−0.797012
$377$	−10.9099	−	7.99869i	−0.561888	−	0.411954i
$378$	−7.50472			−0.386001
$379$			14.8171i			0.761101i	0.924760	+	0.380551i	$0.124265\pi$
$379$			14.8171i			0.761101i	−0.924760	+	0.380551i	$0.875735\pi$
$380$	5.99921			0.307753
$381$	−44.0366			−2.25607
$382$		−	40.5956i		−	2.07705i
$383$			36.9845i			1.88982i	0.327333	+	0.944909i	$0.393850\pi$
$383$			36.9845i			1.88982i	−0.327333	+	0.944909i	$0.606150\pi$
$384$		−	37.6265i		−	1.92012i
$385$			5.00982i			0.255324i
$386$	−11.7837			−0.599772
$387$	33.9098			1.72373
$388$		−	10.7551i		−	0.546009i
$389$	−4.01436			−0.203536			−0.101768	−	0.994808i	$-0.532450\pi$
$389$	−4.01436			−0.203536			−0.101768	+	0.994808i	$0.532450\pi$
$390$	−16.8017	−	12.3183i	−0.850786	−	0.623762i
$391$	3.62904			0.183528
$392$		−	7.46529i		−	0.377054i
$393$	32.3734			1.63302
$394$	15.5016			0.780957
$395$			0.818488i			0.0411826i
$396$			29.6336i			1.48914i
$397$		−	19.4208i		−	0.974702i	−0.873206	−	0.487351i	$-0.837963\pi$
$397$		−	19.4208i		−	0.974702i	0.873206	−	0.487351i	$-0.162037\pi$
$398$		−	10.1009i		−	0.506312i
$399$	9.66086			0.483648
$400$	−5.32962			−0.266481
$401$			3.27194i			0.163393i	0.996657	+	0.0816965i	$0.0260338\pi$
$401$			3.27194i			0.163393i	−0.996657	+	0.0816965i	$0.973966\pi$
$402$	−54.4928			−2.71785
$403$	−2.13186	+	2.90778i	−0.106196	+	0.144847i
$404$	27.3675			1.36159
$405$			6.36964i			0.316510i
$406$	−15.1454			−0.751655
$407$	−13.8040			−0.684240
$408$			14.0129i			0.693744i
$409$		−	13.7956i		−	0.682149i	−0.940036	−	0.341075i	$-0.889209\pi$
$409$		−	13.7956i		−	0.682149i	0.940036	−	0.341075i	$-0.110791\pi$
$410$			6.74916i			0.333317i
$411$			9.26926i			0.457219i
$412$	−22.7048			−1.11858
$413$	−4.84557			−0.238435
$414$			11.2080i			0.550841i
$415$	1.19288			0.0585562
$416$	14.9546	−	20.3975i	0.733212	−	1.00007i
$417$	44.5287			2.18058
$418$		−	12.4134i		−	0.607157i
$419$	−28.8551			−1.40967			−0.704833	−	0.709374i	$-0.748978\pi$
$419$	−28.8551			−1.40967			−0.704833	+	0.709374i	$0.748978\pi$
$420$	−13.8317			−0.674916
$421$		−	14.0841i		−	0.686417i	−0.939259	−	0.343209i	$-0.888486\pi$
$421$		−	14.0841i		−	0.686417i	0.939259	−	0.343209i	$-0.111514\pi$
$422$			39.4063i			1.91827i
$423$		−	28.3514i		−	1.37849i
$424$		−	10.6776i		−	0.518550i
$425$	10.6422			0.516223
$426$	−28.7241			−1.39169
$427$		−	13.0111i		−	0.629651i
$428$	53.3691			2.57969
$429$	−15.1150	+	20.6162i	−0.729758	+	0.995360i
$430$	20.3371			0.980742
$431$		−	21.1516i		−	1.01884i	−0.860519	−	0.509419i	$-0.829861\pi$
$431$		−	21.1516i		−	1.01884i	0.860519	−	0.509419i	$-0.170139\pi$
$432$	2.48424			0.119523
$433$	−32.6610			−1.56959			−0.784795	−	0.619756i	$-0.787232\pi$
$433$	−32.6610			−1.56959			−0.784795	+	0.619756i	$0.787232\pi$
$434$			4.03666i			0.193766i
$435$		−	9.77979i		−	0.468905i
$436$			56.2451i			2.69365i
$437$		−	2.78415i		−	0.133184i
$438$	−25.8944			−1.23728
$439$	28.3889			1.35493			0.677463	−	0.735557i	$-0.263079\pi$
$439$	28.3889			1.35493			0.677463	+	0.735557i	$0.263079\pi$
$440$			5.57490i			0.265773i
$441$	13.6950			0.652143
$442$	−12.6095	+	17.1988i	−0.599773	+	0.818065i
$443$	34.5066			1.63946			0.819729	−	0.572751i	$-0.194124\pi$
$443$	34.5066			1.63946			0.819729	+	0.572751i	$0.194124\pi$
$444$		−	38.1117i		−	1.80870i
$445$	16.3312			0.774175
$446$	−62.4160			−2.95548
$447$		−	24.6372i		−	1.16530i
$448$		−	23.4500i		−	1.10791i
$449$			8.05040i			0.379922i	0.981792	+	0.189961i	$0.0608362\pi$
$449$			8.05040i			0.379922i	−0.981792	+	0.189961i	$0.939164\pi$
$450$			32.8675i			1.54939i
$451$	8.28144			0.389958
$452$	−4.98942			−0.234682
$453$		−	1.81795i		−	0.0854145i
$454$	−22.8303			−1.07148
$455$	−5.32517	−	3.90420i	−0.249648	−	0.183032i
$456$	10.7505			0.503440
$457$			1.80609i			0.0844853i	0.999107	+	0.0422427i	$0.0134503\pi$
$457$			1.80609i			0.0844853i	−0.999107	+	0.0422427i	$0.986550\pi$
$458$	−26.0853			−1.21889
$459$	−4.96053			−0.231538
$460$			3.98613i			0.185854i
$461$		−	31.7743i		−	1.47988i	−0.672675	−	0.739938i	$-0.734855\pi$
$461$		−	31.7743i		−	1.47988i	0.672675	−	0.739938i	$-0.265145\pi$
$462$			28.6200i			1.33152i
$463$			38.5673i			1.79237i	0.443677	+	0.896187i	$0.353674\pi$
$463$			38.5673i			1.79237i	−0.443677	+	0.896187i	$0.646326\pi$
$464$	5.01349			0.232745
$465$	−2.60657			−0.120877
$466$			33.3898i			1.54675i
$467$	−32.7853			−1.51712			−0.758561	−	0.651602i	$-0.774097\pi$
$467$	−32.7853			−1.51712			−0.758561	+	0.651602i	$0.774097\pi$
$468$	−31.4989	−	23.0937i	−1.45604	−	1.06751i
$469$	−17.2711			−0.797504
$470$		−	17.0035i		−	0.784312i
$471$	51.2266			2.36040
$472$	−5.39212			−0.248192
$473$		−	24.9543i		−	1.14740i
$474$			4.67585i			0.214769i
$475$		−	8.16456i		−	0.374616i
$476$			14.1586i			0.648959i
$477$	19.5880			0.896871
$478$	9.25409			0.423272
$479$			31.2073i			1.42590i	0.701217	+	0.712948i	$0.252641\pi$
$479$			31.2073i			1.42590i	−0.701217	+	0.712948i	$0.747359\pi$
$480$	18.2847			0.834577
$481$	10.7576	−	14.6729i	0.490504	−	0.669028i
$482$	39.2976			1.78996
$483$			6.41908i			0.292078i
$484$	−10.2477			−0.465803
$485$	3.71179			0.168544
$486$			48.7523i			2.21145i
$487$		−	0.361759i		−	0.0163929i	−0.999966	−	0.00819643i	$-0.997391\pi$
$487$		−	0.361759i		−	0.0163929i	0.999966	−	0.00819643i	$-0.00260903\pi$
$488$		−	14.4787i		−	0.655418i
$489$			31.2073i			1.41124i
$490$	8.21346			0.371046
$491$	−40.0199			−1.80607			−0.903036	−	0.429565i	$-0.858667\pi$
$491$	−40.0199			−1.80607			−0.903036	+	0.429565i	$0.858667\pi$
$492$			22.8643i			1.03080i
$493$	−10.0110			−0.450871
$494$	13.1947	+	9.67384i	0.593659	+	0.435247i
$495$	−10.2271			−0.459674
$496$		−	1.33623i		−	0.0599984i
$497$	−9.10388			−0.408365
$498$	6.81468			0.305373
$499$			25.3343i			1.13412i	0.823677	+	0.567060i	$0.191919\pi$
$499$			25.3343i			1.13412i	−0.823677	+	0.567060i	$0.808081\pi$
$500$			26.3430i			1.17810i
$501$		−	53.0178i		−	2.36866i
$502$			3.80446i			0.169801i
$503$	−26.7858			−1.19432			−0.597159	−	0.802123i	$-0.703704\pi$
$503$	−26.7858			−1.19432			−0.597159	+	0.802123i	$0.703704\pi$
$504$	−13.7166			−0.610984
$505$			9.44503i			0.420298i
$506$	8.24796			0.366667
$507$	−10.1347	−	32.1328i	−0.450097	−	1.42707i
$508$	−49.5131			−2.19679
$509$		−	37.9869i		−	1.68374i	−0.539680	−	0.841870i	$-0.681455\pi$
$509$		−	37.9869i		−	1.68374i	0.539680	−	0.841870i	$-0.318545\pi$
$510$	−15.4173			−0.682690
$511$	−8.20704			−0.363058
$512$			14.7887i			0.653576i
$513$			3.80566i			0.168024i
$514$			39.6704i			1.74979i
$515$		−	7.83583i		−	0.345288i
$516$	68.8965			3.03300
$517$	−20.8638			−0.917590
$518$		−	20.3694i		−	0.894979i
$519$	−18.0826			−0.793739
$520$	−5.92581	−	4.34456i	−0.259864	−	0.190522i
$521$	−8.49756			−0.372285			−0.186143	−	0.982523i	$-0.559599\pi$
$521$	−8.49756			−0.372285			−0.186143	+	0.982523i	$0.559599\pi$
$522$		−	30.9180i		−	1.35324i
$523$	16.0250			0.700722			0.350361	−	0.936615i	$-0.386059\pi$
$523$	16.0250			0.700722			0.350361	+	0.936615i	$0.386059\pi$
$524$	36.3994			1.59012
$525$			18.8241i			0.821550i
$526$		−	0.295843i		−	0.0128994i
$527$			2.66819i			0.116228i
$528$		−	9.47390i		−	0.412299i
$529$	−21.1501			−0.919569
$530$	11.7477			0.510288
$531$		−	9.89179i		−	0.429267i
$532$	10.8623			0.470941
$533$	−6.45380	+	8.80272i	−0.279545	+	0.381288i
$534$	93.2969			4.03735
$535$			18.4186i			0.796307i
$536$	−19.2191			−0.830139
$537$	−23.1198			−0.997694
$538$			54.0805i			2.33158i
$539$		−	10.0782i		−	0.434098i
$540$		−	5.44864i		−	0.234472i
$541$		−	26.8172i		−	1.15296i	−0.817111	−	0.576481i	$-0.804425\pi$
$541$		−	26.8172i		−	1.15296i	0.817111	−	0.576481i	$-0.195575\pi$
$542$	7.22290			0.310250
$543$	27.7552			1.19109
$544$		−	18.7169i		−	0.802479i
$545$	−19.4112			−0.831485
$546$	−30.4215	−	22.3038i	−1.30192	−	0.954516i
$547$	0.552928			0.0236415			0.0118207	−	0.999930i	$-0.496237\pi$
$547$	0.552928			0.0236415			0.0118207	+	0.999930i	$0.496237\pi$
$548$			10.4220i			0.445206i
$549$	26.5609			1.13359
$550$	24.1873			1.03135
$551$			7.68028i			0.327191i
$552$			7.14311i			0.304031i
$553$			1.48197i			0.0630200i
$554$			23.7071i			1.00722i
$555$	13.1530			0.558315
$556$	50.0664			2.12329
$557$		−	15.0526i		−	0.637797i	−0.947789	−	0.318899i	$-0.896687\pi$
$557$		−	15.0526i		−	0.637797i	0.947789	−	0.318899i	$-0.103313\pi$
$558$	−8.24047			−0.348847
$559$	26.5250	+	19.4471i	1.12189	+	0.822524i
$560$	2.44711			0.103409
$561$			18.9175i			0.798699i
$562$	0.619886			0.0261483
$563$	−1.95269			−0.0822963			−0.0411481	−	0.999153i	$-0.513102\pi$
$563$	−1.95269			−0.0822963			−0.0411481	+	0.999153i	$0.513102\pi$
$564$		−	57.6031i		−	2.42553i
$565$		−	1.72194i		−	0.0724425i
$566$			17.8602i			0.750721i
$567$			11.5330i			0.484341i
$568$	−10.1307			−0.425076
$569$	−10.6879			−0.448062			−0.224031	−	0.974582i	$-0.571922\pi$
$569$	−10.6879			−0.448062			−0.224031	+	0.974582i	$0.571922\pi$
$570$			11.8280i			0.495418i
$571$	−11.1927			−0.468401			−0.234201	−	0.972188i	$-0.575247\pi$
$571$	−11.1927			−0.468401			−0.234201	+	0.972188i	$0.575247\pi$
$572$	−16.9947	+	23.1801i	−0.710584	+	0.969208i
$573$	47.4630			1.98279
$574$			12.2202i			0.510061i
$575$	5.42488			0.226233
$576$	47.8711			1.99463
$577$			38.1339i			1.58753i	0.608222	+	0.793767i	$0.291883\pi$
$577$			38.1339i			1.58753i	−0.608222	+	0.793767i	$0.708117\pi$
$578$		−	21.9035i		−	0.911064i
$579$		−	13.7770i		−	0.572554i
$580$		−	10.9960i		−	0.456585i
$581$	2.15986			0.0896061
$582$	21.2047			0.878962
$583$		−	14.4148i		−	0.597000i
$584$	−9.13273			−0.377915
$585$	7.97006	−	10.8708i	0.329521	−	0.449454i
$586$	−51.0735			−2.10983
$587$		−	5.26098i		−	0.217144i	−0.994089	−	0.108572i	$-0.965372\pi$
$587$		−	5.26098i		−	0.217144i	0.994089	−	0.108572i	$-0.0346278\pi$
$588$	27.8250			1.14748
$589$	2.04700			0.0843451
$590$		−	5.93251i		−	0.244238i
$591$			18.1239i			0.745517i
$592$			6.74274i			0.277125i
$593$			25.9148i			1.06419i	0.846684	+	0.532096i	$0.178595\pi$
$593$			25.9148i			1.06419i	−0.846684	+	0.532096i	$0.821405\pi$
$594$	−11.2742			−0.462584
$595$	−4.88640			−0.200323
$596$		−	27.7011i		−	1.13468i
$597$	11.8096			0.483336
$598$	−6.42771	+	8.76713i	−0.262848	+	0.358515i
$599$	41.6832			1.70313			0.851564	−	0.524250i	$-0.175654\pi$
$599$	41.6832			1.70313			0.851564	+	0.524250i	$0.175654\pi$
$600$			20.9473i			0.855170i
$601$	21.5712			0.879908			0.439954	−	0.898020i	$-0.354995\pi$
$601$	21.5712			0.879908			0.439954	+	0.898020i	$0.354995\pi$
$602$	36.8228			1.50079
$603$		−	35.2573i		−	1.43579i
$604$		−	2.04403i		−	0.0831703i
$605$		−	3.53666i		−	0.143786i
$606$			53.9574i			2.19187i
$607$	34.8299			1.41370			0.706851	−	0.707362i	$-0.250115\pi$
$607$	34.8299			1.41370			0.706851	+	0.707362i	$0.250115\pi$
$608$	−14.3593			−0.582348
$609$		−	17.7075i		−	0.717545i
$610$	15.9297			0.644974
$611$	16.2594	−	22.1771i	0.657783	−	0.897190i
$612$	−28.9035			−1.16836
$613$			19.2039i			0.775639i	0.921735	+	0.387819i	$0.126772\pi$
$613$			19.2039i			0.775639i	−0.921735	+	0.387819i	$0.873228\pi$
$614$	70.1412			2.83067
$615$	−7.89089			−0.318191
$616$			10.0940i			0.406700i
$617$		−	13.1172i		−	0.528079i	−0.964512	−	0.264040i	$-0.914945\pi$
$617$		−	13.1172i		−	0.528079i	0.964512	−	0.264040i	$-0.0850550\pi$
$618$		−	44.7644i		−	1.80069i
$619$		−	7.80176i		−	0.313579i	−0.987632	−	0.156790i	$-0.949886\pi$
$619$		−	7.80176i		−	0.313579i	0.987632	−	0.156790i	$-0.0501145\pi$
$620$	−2.93073			−0.117701
$621$	−2.52864			−0.101471
$622$		−	68.1128i		−	2.73108i
$623$	29.5697			1.18469
$624$	10.0702	+	7.38309i	0.403132	+	0.295560i
$625$	10.8513			0.434052
$626$			74.2102i			2.96603i
$627$	14.5133			0.579605
$628$	57.5972			2.29838
$629$		−	13.4639i		−	0.536842i
$630$		−	15.0912i		−	0.601249i
$631$		−	4.02885i		−	0.160386i	−0.996779	−	0.0801930i	$-0.974446\pi$
$631$		−	4.02885i		−	0.160386i	0.996779	−	0.0801930i	$-0.0255537\pi$
$632$			1.64913i			0.0655989i
$633$	−46.0725			−1.83122
$634$	14.2369			0.565419
$635$		−	17.0879i		−	0.678112i
$636$	39.7980			1.57809
$637$	10.7126	+	7.85401i	0.424447	+	0.311187i
$638$	−22.7526			−0.900785
$639$		−	18.5847i		−	0.735201i
$640$	14.6005			0.577136
$641$	−2.73730			−0.108117			−0.0540584	−	0.998538i	$-0.517216\pi$
$641$	−2.73730			−0.108117			−0.0540584	+	0.998538i	$0.517216\pi$
$642$			105.222i			4.15277i
$643$			7.54898i			0.297703i	0.988860	+	0.148851i	$0.0475576\pi$
$643$			7.54898i			0.297703i	−0.988860	+	0.148851i	$0.952442\pi$
$644$			7.21737i			0.284404i
$645$			23.7774i			0.936236i
$646$	12.1075			0.476365
$647$	−9.51543			−0.374090			−0.187045	−	0.982351i	$-0.559891\pi$
$647$	−9.51543			−0.374090			−0.187045	+	0.982351i	$0.559891\pi$
$648$			12.8339i			0.504162i
$649$	−7.27939			−0.285741
$650$	−18.8494	+	25.7098i	−0.739332	+	1.00842i
$651$	−4.71953			−0.184973
$652$			35.0883i			1.37416i
$653$	−15.6207			−0.611286			−0.305643	−	0.952146i	$-0.598871\pi$
$653$	−15.6207			−0.611286			−0.305643	+	0.952146i	$0.598871\pi$
$654$	−110.892			−4.33622
$655$			12.5621i			0.490842i
$656$		−	4.04517i		−	0.157937i
$657$		−	16.7539i		−	0.653632i
$658$		−	30.7869i		−	1.20020i
$659$	5.25385			0.204661			0.102330	−	0.994750i	$-0.467370\pi$
$659$	5.25385			0.204661			0.102330	+	0.994750i	$0.467370\pi$
$660$	−20.7790			−0.808821
$661$			27.8552i			1.08344i	0.840558	+	0.541721i	$0.182227\pi$
$661$			27.8552i			1.08344i	−0.840558	+	0.541721i	$0.817773\pi$
$662$	−73.8287			−2.86943
$663$	−20.1083	−	14.7426i	−0.780942	−	0.572555i
$664$	2.40348			0.0932730
$665$			3.74878i			0.145371i
$666$	41.5822			1.61128
$667$	−5.10310			−0.197593
$668$		−	59.6112i		−	2.30643i
$669$		−	72.9746i		−	2.82136i
$670$		−	21.1452i		−	0.816912i
$671$		−	19.5463i		−	0.754575i
$672$	33.1066			1.27712
$673$	−36.1550			−1.39367			−0.696837	−	0.717229i	$-0.745410\pi$
$673$	−36.1550			−1.39367			−0.696837	+	0.717229i	$0.745410\pi$
$674$		−	1.05329i		−	0.0405713i
$675$	−7.41527			−0.285414
$676$	−11.3950	−	36.1289i	−0.438271	−	1.38957i
$677$	−27.9179			−1.07297			−0.536487	−	0.843909i	$-0.680249\pi$
$677$	−27.9179			−1.07297			−0.536487	+	0.843909i	$0.680249\pi$
$678$		−	9.83707i		−	0.377790i
$679$	6.72066			0.257915
$680$	−5.43755			−0.208520
$681$		−	26.6924i		−	1.02286i
$682$			6.06418i			0.232209i
$683$			37.1396i			1.42111i	0.703642	+	0.710554i	$0.251556\pi$
$683$			37.1396i			1.42111i	−0.703642	+	0.710554i	$0.748444\pi$
$684$			22.1744i			0.847859i
$685$	−3.59682			−0.137428
$686$	43.1281			1.64664
$687$		−	30.4981i		−	1.16357i
$688$	−12.1892			−0.464710
$689$	15.3222	+	11.2336i	0.583728	+	0.427965i
$690$	−7.85899			−0.299187
$691$			40.0257i			1.52265i	0.648371	+	0.761324i	$0.275451\pi$
$691$			40.0257i			1.52265i	−0.648371	+	0.761324i	$0.724549\pi$
$692$	−20.3314			−0.772884
$693$	−18.5174			−0.703419
$694$			27.2906i			1.03594i
$695$			17.2788i			0.655424i
$696$		−	19.7048i		−	0.746909i
$697$			8.07742i			0.305954i
$698$	−77.4845			−2.93283
$699$	−39.0382			−1.47656
$700$			21.1651i			0.799964i
$701$	−30.3361			−1.14578			−0.572890	−	0.819632i	$-0.694178\pi$
$701$	−30.3361			−1.14578			−0.572890	+	0.819632i	$0.694178\pi$
$702$	8.78604	−	11.9838i	0.331608	−	0.452300i
$703$	−10.3294			−0.389579
$704$		−	35.2284i		−	1.32772i
$705$	19.8799			0.748720
$706$	23.4560			0.882779
$707$			17.1014i			0.643164i
$708$		−	20.0977i		−	0.755319i
$709$			4.72511i			0.177455i	0.996056	+	0.0887276i	$0.0282801\pi$
$709$			4.72511i			0.177455i	−0.996056	+	0.0887276i	$0.971720\pi$
$710$		−	11.1460i		−	0.418303i
$711$	−3.02532			−0.113458
$712$	32.9050			1.23317
$713$			1.36011i			0.0509366i
$714$	−27.9149			−1.04469
$715$	−7.99987	−	5.86518i	−0.299178	−	0.219345i
$716$	−25.9950			−0.971480
$717$			10.8196i			0.404064i
$718$	37.4509			1.39765
$719$	−0.620833			−0.0231532			−0.0115766	−	0.999933i	$-0.503685\pi$
$719$	−0.620833			−0.0231532			−0.0115766	+	0.999933i	$0.503685\pi$
$720$			4.99555i			0.186173i
$721$		−	14.1877i		−	0.528379i
$722$			32.8300i			1.22181i
$723$			45.9454i			1.70873i
$724$	31.2068			1.15979
$725$	−14.9649			−0.555783
$726$		−	20.2042i		−	0.749847i
$727$	5.87302			0.217818			0.108909	−	0.994052i	$-0.465264\pi$
$727$	5.87302			0.217818			0.108909	+	0.994052i	$0.465264\pi$
$728$	−10.7294	−	7.86637i	−0.397658	−	0.291547i
$729$	−37.9990			−1.40737
$730$		−	10.0480i		−	0.371894i
$731$	24.3395			0.900229
$732$	53.9654			1.99462
$733$		−	37.4352i		−	1.38270i	−0.722520	−	0.691350i	$-0.757016\pi$
$733$		−	37.4352i		−	1.38270i	0.722520	−	0.691350i	$-0.242984\pi$
$734$		−	22.3068i		−	0.823360i
$735$			9.60290i			0.354208i
$736$		−	9.54095i		−	0.351684i
$737$	−25.9459			−0.955730
$738$	−24.9464			−0.918290
$739$		−	2.78103i		−	0.102302i	−0.998691	−	0.0511509i	$-0.983711\pi$
$739$		−	2.78103i		−	0.102302i	0.998691	−	0.0511509i	$-0.0162890\pi$
$740$	14.7888			0.543646
$741$	−11.3103	+	15.4268i	−0.415495	+	0.566719i
$742$	21.2707			0.780871
$743$			18.4482i			0.676799i	0.941003	+	0.338399i	$0.109885\pi$
$743$			18.4482i			0.676799i	−0.941003	+	0.338399i	$0.890115\pi$
$744$	−5.25186			−0.192542
$745$	9.56017			0.350257
$746$		−	47.3353i		−	1.73307i
$747$			4.40916i			0.161323i
$748$			21.2702i			0.777714i
$749$			33.3492i			1.21855i
$750$	−51.9376			−1.89649
$751$	34.9474			1.27525			0.637624	−	0.770348i	$-0.279917\pi$
$751$	34.9474			1.27525			0.637624	+	0.770348i	$0.279917\pi$
$752$			10.1912i			0.371634i
$753$	−4.44805			−0.162096
$754$	17.7313	−	24.1848i	0.645736	−	0.880758i
$755$	0.705431			0.0256733
$756$		−	9.86544i		−	0.358803i
$757$	40.5867			1.47515			0.737574	−	0.675266i	$-0.235971\pi$
$757$	40.5867			1.47515			0.737574	+	0.675266i	$0.235971\pi$
$758$	−32.8461			−1.19302
$759$			9.64324i			0.350027i
$760$			4.17162i			0.151320i
$761$			35.5111i			1.28728i	0.765330	+	0.643638i	$0.222576\pi$
$761$			35.5111i			1.28728i	−0.765330	+	0.643638i	$0.777424\pi$
$762$		−	97.6194i		−	3.53638i
$763$	−35.1464			−1.27238
$764$	53.3655			1.93070
$765$		−	9.97513i		−	0.360652i
$766$	−81.9863			−2.96229
$767$	5.67289	−	7.73759i	0.204836	−	0.279388i
$768$	16.6566			0.601042
$769$		−	5.42518i		−	0.195637i	−0.995204	−	0.0978186i	$-0.968814\pi$
$769$		−	5.42518i		−	0.195637i	0.995204	−	0.0978186i	$-0.0311865\pi$
$770$	−11.1057			−0.400220
$771$	−46.3813			−1.67038
$772$		−	15.4904i		−	0.557511i
$773$			16.2454i			0.584305i	0.956372	+	0.292152i	$0.0943715\pi$
$773$			16.2454i			0.584305i	−0.956372	+	0.292152i	$0.905629\pi$
$774$			75.1705i			2.70195i
$775$			3.98855i			0.143273i
$776$	7.47870			0.268470
$777$	23.8152			0.854365
$778$		−	8.89893i		−	0.319042i
$779$	6.19689			0.222027
$780$	16.1932	−	22.0869i	0.579811	−	0.790839i
$781$	−13.6765			−0.489385
$782$			8.04476i			0.287680i
$783$	6.97544			0.249282
$784$	−4.92281			−0.175815
$785$			19.8779i			0.709471i
$786$			71.7646i			2.55976i
$787$			6.94525i			0.247572i	0.992309	+	0.123786i	$0.0395036\pi$
$787$			6.94525i			0.247572i	−0.992309	+	0.123786i	$0.960496\pi$
$788$			20.3778i			0.725929i
$789$	0.345889			0.0123140
$790$	−1.81441			−0.0645537
$791$		−	3.11778i		−	0.110856i
$792$	−20.6061			−0.732204
$793$	20.7766	+	15.2326i	0.737798	+	0.540924i
$794$	43.0516			1.52784
$795$			13.7350i			0.487131i
$796$	13.2783			0.470637
$797$	−2.95087			−0.104525			−0.0522626	−	0.998633i	$-0.516643\pi$
$797$	−2.95087			−0.104525			−0.0522626	+	0.998633i	$0.516643\pi$
$798$			21.4160i			0.758117i
$799$		−	20.3498i		−	0.719925i
$800$		−	27.9790i		−	0.989206i
$801$			60.3639i			2.13285i
$802$	−7.25317			−0.256118
$803$	−12.3292			−0.435089
$804$		−	71.6343i		−	2.52635i
$805$	−2.49085			−0.0877908
$806$	−6.44589	−	4.72587i	−0.227047	−	0.166462i
$807$	−63.2291			−2.22577
$808$			19.0303i			0.669484i
$809$	−35.5675			−1.25049			−0.625243	−	0.780430i	$-0.715000\pi$
$809$	−35.5675			−1.25049			−0.625243	+	0.780430i	$0.715000\pi$
$810$	−14.1201			−0.496128
$811$			20.4375i			0.717659i	0.933403	+	0.358830i	$0.116824\pi$
$811$			20.4375i			0.717659i	−0.933403	+	0.358830i	$0.883176\pi$
$812$		−	19.9097i		−	0.698692i
$813$			8.44477i			0.296171i
$814$		−	30.6004i		−	1.07254i
$815$	−12.1096			−0.424181
$816$	9.24050			0.323482
$817$		−	18.6729i		−	0.653284i
$818$	30.5818			1.06927
$819$	14.4308	−	19.6830i	0.504252	−	0.687780i
$820$	−8.87222			−0.309831
$821$		−	35.8194i		−	1.25011i	−0.780582	−	0.625053i	$-0.785077\pi$
$821$		−	35.8194i		−	1.25011i	0.780582	−	0.625053i	$-0.214923\pi$
$822$	−20.5479			−0.716689
$823$	−7.45012			−0.259695			−0.129848	−	0.991534i	$-0.541449\pi$
$823$	−7.45012			−0.259695			−0.129848	+	0.991534i	$0.541449\pi$
$824$		−	15.7880i		−	0.550002i
$825$			28.2789i			0.984546i
$826$		−	10.7415i		−	0.373746i
$827$		−	11.2580i		−	0.391478i	−0.980656	−	0.195739i	$-0.937290\pi$
$827$		−	11.2580i		−	0.391478i	0.980656	−	0.195739i	$-0.0627105\pi$
$828$	−14.7336			−0.512028
$829$	−35.2422			−1.22401			−0.612006	−	0.790853i	$-0.709637\pi$
$829$	−35.2422			−1.22401			−0.612006	+	0.790853i	$0.709637\pi$
$830$			2.64435i			0.0917868i
$831$	−27.7175			−0.961509
$832$	37.4459	+	27.4538i	1.29820	+	0.951789i
$833$	9.82989			0.340586
$834$			98.7103i			3.41806i
$835$	20.5729			0.711955
$836$	16.3182			0.564376
$837$		−	1.85914i		−	0.0642613i
$838$		−	63.9654i		−	2.20965i
$839$			43.3244i			1.49572i	0.663854	+	0.747862i	$0.268920\pi$
$839$			43.3244i			1.49572i	−0.663854	+	0.747862i	$0.731080\pi$
$840$		−	9.61801i		−	0.331853i
$841$	−14.9227			−0.514576
$842$	31.2213			1.07596
$843$			0.724749i			0.0249617i
$844$	−51.8022			−1.78311
$845$	12.4687	−	3.93264i	0.428937	−	0.135287i
$846$	62.8487			2.16078
$847$		−	6.40355i		−	0.220029i
$848$	−7.04109			−0.241792
$849$	−20.8816			−0.716654
$850$			23.5914i			0.809178i
$851$		−	6.86326i		−	0.235270i
$852$		−	37.7597i		−	1.29363i
$853$		−	19.0628i		−	0.652699i	−0.945249	−	0.326350i	$-0.894181\pi$
$853$		−	19.0628i		−	0.652699i	0.945249	−	0.326350i	$-0.105819\pi$
$854$	28.8427			0.986976
$855$	−7.65279			−0.261720
$856$			37.1108i			1.26842i
$857$	28.1693			0.962247			0.481123	−	0.876653i	$-0.340229\pi$
$857$	28.1693			0.962247			0.481123	+	0.876653i	$0.340229\pi$
$858$	−45.7015	−	33.5065i	−1.56022	−	1.14389i
$859$	−19.7322			−0.673254			−0.336627	−	0.941638i	$-0.609286\pi$
$859$	−19.7322			−0.673254			−0.336627	+	0.941638i	$0.609286\pi$
$860$			26.7345i			0.911637i
$861$	−14.2874			−0.486915
$862$	46.8884			1.59702
$863$			6.48496i			0.220751i	0.993890	+	0.110375i	$0.0352053\pi$
$863$			6.48496i			0.220751i	−0.993890	+	0.110375i	$0.964795\pi$
$864$			13.0415i			0.443682i
$865$		−	7.01674i		−	0.238576i
$866$		−	72.4022i		−	2.46033i
$867$	25.6088			0.869720
$868$	−5.30645			−0.180113
$869$			2.22633i			0.0755232i
$870$	21.6796			0.735008
$871$	20.2199	−	27.5791i	0.685124	−	0.934481i
$872$	−39.1107			−1.32445
$873$			13.7196i			0.464338i
$874$	6.17183			0.208765
$875$	−16.4612			−0.556491
$876$		−	34.0399i		−	1.15010i
$877$			19.0913i			0.644666i	0.946626	+	0.322333i	$0.104467\pi$
$877$			19.0913i			0.644666i	−0.946626	+	0.322333i	$0.895533\pi$
$878$			62.9318i			2.12384i
$879$		−	59.7134i		−	2.01408i
$880$	3.67623			0.123926
$881$	2.46976			0.0832082			0.0416041	−	0.999134i	$-0.486753\pi$
$881$	2.46976			0.0832082			0.0416041	+	0.999134i	$0.486753\pi$
$882$			30.3588i			1.02223i
$883$	19.1170			0.643338			0.321669	−	0.946852i	$-0.395756\pi$
$883$	19.1170			0.643338			0.321669	+	0.946852i	$0.395756\pi$
$884$	−22.6090	−	16.5760i	−0.760423	−	0.557512i
$885$	6.93609			0.233154
$886$			76.4934i			2.56985i
$887$	23.3018			0.782399			0.391199	−	0.920306i	$-0.372060\pi$
$887$	23.3018			0.782399			0.391199	+	0.920306i	$0.372060\pi$
$888$	26.5014			0.889328
$889$		−	30.9397i		−	1.03769i
$890$			36.2027i			1.21352i
$891$			17.3258i			0.580435i
$892$		−	82.0499i		−	2.74723i
$893$	−15.6121			−0.522439
$894$	54.6152			1.82660
$895$		−	8.97136i		−	0.299880i
$896$	26.4360			0.883166
$897$	−10.2502	−	7.51506i	−0.342245	−	0.250920i
$898$	−17.8459			−0.595527
$899$		−	3.75197i		−	0.125135i
$900$	−43.2065			−1.44022
$901$	14.0597			0.468396
$902$			18.3581i			0.611258i
$903$			43.0520i			1.43268i
$904$		−	3.46945i		−	0.115392i
$905$			10.7700i			0.358009i
$906$	4.02998			0.133887
$907$	2.87726			0.0955379			0.0477689	−	0.998858i	$-0.484789\pi$
$907$	2.87726			0.0955379			0.0477689	+	0.998858i	$0.484789\pi$
$908$		−	30.0120i		−	0.995982i
$909$	−34.9109			−1.15792
$910$	8.65473	−	11.8047i	0.286902	−	0.391322i
$911$	−48.4102			−1.60390			−0.801951	−	0.597390i	$-0.796204\pi$
$911$	−48.4102			−1.60390			−0.801951	+	0.597390i	$0.796204\pi$
$912$		−	7.08919i		−	0.234746i
$913$	3.24471			0.107384
$914$	−4.00370			−0.132431
$915$			18.6245i			0.615705i
$916$		−	34.2909i		−	1.13300i
$917$			22.7452i			0.751114i
$918$		−	10.9964i		−	0.362935i
$919$	−29.7821			−0.982419			−0.491210	−	0.871041i	$-0.663445\pi$
$919$	−29.7821			−0.982419			−0.491210	+	0.871041i	$0.663445\pi$
$920$	−2.77180			−0.0913835
$921$			82.0067i			2.70221i
$922$	70.4365			2.31970
$923$	10.6582	−	14.5374i	0.350820	−	0.478505i
$924$	−37.6229			−1.23770
$925$		−	20.1266i		−	0.661759i
$926$	−85.4950			−2.80954
$927$	28.9630			0.951268
$928$			26.3194i			0.863977i
$929$		−	54.5572i		−	1.78996i	−0.446103	−	0.894982i	$-0.647188\pi$
$929$		−	54.5572i		−	1.78996i	0.446103	−	0.894982i	$-0.352812\pi$
$930$		−	5.77819i		−	0.189474i
$931$		−	7.54136i		−	0.247158i
$932$	−43.8931			−1.43776
$933$	79.6352			2.60714
$934$		−	72.6777i		−	2.37809i
$935$	−7.34072			−0.240067
$936$	16.0585	−	21.9031i	0.524888	−	0.715925i
$937$	31.8081			1.03912			0.519562	−	0.854433i	$-0.326095\pi$
$937$	31.8081			1.03912			0.519562	+	0.854433i	$0.326095\pi$
$938$		−	38.2861i		−	1.25008i
$939$	−86.7640			−2.83144
$940$	22.3522			0.729048
$941$			30.6060i			0.997726i	0.866681	+	0.498863i	$0.166249\pi$
$941$			30.6060i			0.997726i	−0.866681	+	0.498863i	$0.833751\pi$
$942$			113.558i			3.69992i
$943$			4.11747i			0.134083i
$944$			3.55570i			0.115728i
$945$	3.40474			0.110756
$946$	55.3181			1.79855
$947$		−	24.4062i		−	0.793094i	−0.918014	−	0.396547i	$-0.870208\pi$
$947$		−	24.4062i		−	0.793094i	0.918014	−	0.396547i	$-0.129792\pi$
$948$	−6.14671			−0.199636
$949$	9.60828	−	13.1053i	0.311898	−	0.425416i
$950$	18.0990			0.587209
$951$			16.6453i			0.539760i
$952$	−9.84536			−0.319090
$953$	22.7737			0.737712			0.368856	−	0.929487i	$-0.379750\pi$
$953$	22.7737			0.737712			0.368856	+	0.929487i	$0.379750\pi$
$954$			43.4221i			1.40584i
$955$			18.4174i			0.595974i
$956$			12.1651i			0.393448i
$957$		−	26.6016i		−	0.859907i
$958$	−69.1796			−2.23509
$959$	−6.51249			−0.210299
$960$			33.5670i			1.08337i
$961$	−1.00000			−0.0322581
$962$	32.5266	+	23.8472i	1.04870	+	0.768864i
$963$	−68.0794			−2.19383
$964$			51.6593i			1.66383i
$965$	5.34601			0.172094
$966$	−14.2297			−0.457832
$967$		−	48.8154i		−	1.56980i	−0.619623	−	0.784899i	$-0.712715\pi$
$967$		−	48.8154i		−	1.56980i	0.619623	−	0.784899i	$-0.287285\pi$
$968$		−	7.12583i		−	0.229033i
$969$			14.1557i			0.454747i
$970$			8.22821i			0.264192i
$971$	50.6775			1.62632			0.813160	−	0.582041i	$-0.197746\pi$
$971$	50.6775			1.62632			0.813160	+	0.582041i	$0.197746\pi$
$972$	−64.0881			−2.05563
$973$			31.2855i			1.00297i
$974$	0.801939			0.0256958
$975$	−30.0590	−	22.0380i	−0.962657	−	0.705782i
$976$	−9.54760			−0.305611
$977$		−	51.8306i		−	1.65821i	−0.559094	−	0.829105i	$-0.688851\pi$
$977$		−	51.8306i		−	1.65821i	0.559094	−	0.829105i	$-0.311149\pi$
$978$	−69.1797			−2.21212
$979$	44.4219			1.41973
$980$			10.7971i			0.344902i
$981$		−	71.7481i		−	2.29074i
$982$		−	88.7151i		−	2.83101i
$983$			12.0939i			0.385736i	0.981225	+	0.192868i	$0.0617789\pi$
$983$			12.0939i			0.385736i	−0.981225	+	0.192868i	$0.938221\pi$
$984$	−15.8990			−0.506840
$985$	−7.03275			−0.224082
$986$		−	22.1921i		−	0.706740i
$987$	35.9950			1.14573
$988$	−12.7169	+	17.3453i	−0.404578	+	0.551828i
$989$	12.4071			0.394522
$990$		−	22.6712i		−	0.720537i
$991$	49.4882			1.57204			0.786022	−	0.618199i	$-0.212137\pi$
$991$	49.4882			1.57204			0.786022	+	0.618199i	$0.212137\pi$
$992$	7.01482			0.222721
$993$		−	86.3180i		−	2.73922i
$994$		−	20.1813i		−	0.640111i
$995$			4.58258i			0.145278i
$996$			8.95834i			0.283856i
$997$	−9.06621			−0.287130			−0.143565	−	0.989641i	$-0.545857\pi$
$997$	−9.06621			−0.287130			−0.143565	+	0.989641i	$0.545857\pi$
$998$	−56.1605			−1.77773
$999$			9.38140i			0.296814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.28	yes	32
13.5	odd	4		5239.2.a.k.1.15		16
13.8	odd	4		5239.2.a.l.1.2		16
13.12	even	2	inner	403.2.c.b.311.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.5	✓	32	13.12	even	2	inner
403.2.c.b.311.28	yes	32	1.1	even	1	trivial
5239.2.a.k.1.15		16	13.5	odd	4
5239.2.a.l.1.2		16	13.8	odd	4

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.21678i q^{2} -2.59178 q^{3} -2.91410 q^{4} -1.00571i q^{5} -5.74540i q^{6} -1.82096i q^{7} -2.02635i q^{8} +3.71732 q^{9} +O(q^{10})\)	\(q+2.21678i q^{2} -2.59178 q^{3} -2.91410 q^{4} -1.00571i q^{5} -5.74540i q^{6} -1.82096i q^{7} -2.02635i q^{8} +3.71732 q^{9} +2.22943 q^{10} -2.73558i q^{11} +7.55270 q^{12} +(2.90778 + 2.13186i) q^{13} +4.03666 q^{14} +2.60657i q^{15} -1.33623 q^{16} +2.66819 q^{17} +8.24047i q^{18} -2.04700i q^{19} +2.93073i q^{20} +4.71953i q^{21} +6.06418 q^{22} +1.36011 q^{23} +5.25186i q^{24} +3.98855 q^{25} +(-4.72587 + 6.44589i) q^{26} -1.85914 q^{27} +5.30645i q^{28} -3.75197 q^{29} -5.77819 q^{30} +1.00000i q^{31} -7.01482i q^{32} +7.09003i q^{33} +5.91478i q^{34} -1.83135 q^{35} -10.8326 q^{36} -5.04610i q^{37} +4.53774 q^{38} +(-7.53631 - 5.52532i) q^{39} -2.03792 q^{40} +3.02730i q^{41} -10.4621 q^{42} +9.12211 q^{43} +7.97176i q^{44} -3.73854i q^{45} +3.01506i q^{46} -7.62683i q^{47} +3.46321 q^{48} +3.68411 q^{49} +8.84173i q^{50} -6.91536 q^{51} +(-8.47354 - 6.21246i) q^{52} +5.26937 q^{53} -4.12130i q^{54} -2.75120 q^{55} -3.68990 q^{56} +5.30537i q^{57} -8.31728i q^{58} -2.66100i q^{59} -7.59581i q^{60} +7.14518 q^{61} -2.21678 q^{62} -6.76909i q^{63} +12.8778 q^{64} +(2.14403 - 2.92437i) q^{65} -15.7170 q^{66} -9.48459i q^{67} -7.77536 q^{68} -3.52511 q^{69} -4.05970i q^{70} -4.99950i q^{71} -7.53260i q^{72} -4.50699i q^{73} +11.1861 q^{74} -10.3374 q^{75} +5.96516i q^{76} -4.98139 q^{77} +(12.2484 - 16.7063i) q^{78} -0.813843 q^{79} +1.34386i q^{80} -6.33348 q^{81} -6.71086 q^{82} +1.18611i q^{83} -13.7532i q^{84} -2.68342i q^{85} +20.2217i q^{86} +9.72428 q^{87} -5.54325 q^{88} +16.2385i q^{89} +8.28751 q^{90} +(3.88204 - 5.29494i) q^{91} -3.96350 q^{92} -2.59178i q^{93} +16.9070 q^{94} -2.05868 q^{95} +18.1809i q^{96} +3.69072i q^{97} +8.16684i q^{98} -10.1690i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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