LMFDB - Embedded newform 475.2.l.f.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.3
Character	$\chi$	$=$	475.226
Dual form			475.2.l.f.351.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212126 + 1.20303i) q^{2} +(-0.616222 - 0.517072i) q^{3} +(0.477108 + 0.173653i) q^{4} +(0.752768 - 0.631647i) q^{6} +(-1.89590 - 3.28379i) q^{7} +(-1.53170 + 2.65299i) q^{8} +(-0.408578 - 2.31716i) q^{9} +O(q^{10})$	\(q+(-0.212126 + 1.20303i) q^{2} +(-0.616222 - 0.517072i) q^{3} +(0.477108 + 0.173653i) q^{4} +(0.752768 - 0.631647i) q^{6} +(-1.89590 - 3.28379i) q^{7} +(-1.53170 + 2.65299i) q^{8} +(-0.408578 - 2.31716i) q^{9} +(0.618663 - 1.07156i) q^{11} +(-0.204213 - 0.353708i) q^{12} +(2.64744 - 2.22146i) q^{13} +(4.35266 - 1.58424i) q^{14} +(-2.08882 - 1.75273i) q^{16} +(0.522152 - 2.96127i) q^{17} +2.87428 q^{18} +(4.28612 + 0.793231i) q^{19} +(-0.529662 + 3.00386i) q^{21} +(1.15788 + 0.971573i) q^{22} +(-5.77705 - 2.10267i) q^{23} +(2.31565 - 0.842829i) q^{24} +(2.11089 + 3.65617i) q^{26} +(-2.15299 + 3.72910i) q^{27} +(-0.334308 - 1.89595i) q^{28} +(-0.744476 - 4.22213i) q^{29} +(-2.55067 - 4.41789i) q^{31} +(-2.14174 + 1.79713i) q^{32} +(-0.935304 + 0.340423i) q^{33} +(3.45173 + 1.25633i) q^{34} +(0.207446 - 1.17649i) q^{36} +9.13084 q^{37} +(-1.86348 + 4.98805i) q^{38} -2.78006 q^{39} +(4.08318 + 3.42620i) q^{41} +(-3.50137 - 1.27440i) q^{42} +(8.57465 - 3.12092i) q^{43} +(0.481248 - 0.403815i) q^{44} +(3.75504 - 6.50391i) q^{46} +(1.26821 + 7.19237i) q^{47} +(0.380890 + 2.16014i) q^{48} +(-3.68887 + 6.38931i) q^{49} +(-1.85295 + 1.55481i) q^{51} +(1.64888 - 0.600142i) q^{52} +(3.13139 + 1.13973i) q^{53} +(-4.02950 - 3.38115i) q^{54} +11.6158 q^{56} +(-2.23104 - 2.70503i) q^{57} +5.23727 q^{58} +(-0.141926 + 0.804901i) q^{59} +(-6.01592 - 2.18962i) q^{61} +(5.85590 - 2.13137i) q^{62} +(-6.83446 + 5.73479i) q^{63} +(-4.43444 - 7.68067i) q^{64} +(-0.211136 - 1.19741i) q^{66} +(-0.175545 - 0.995566i) q^{67} +(0.763357 - 1.32217i) q^{68} +(2.47271 + 4.28286i) q^{69} +(-12.8546 + 4.67867i) q^{71} +(6.77322 + 2.46525i) q^{72} +(-8.47451 - 7.11096i) q^{73} +(-1.93689 + 10.9846i) q^{74} +(1.90719 + 1.12275i) q^{76} -4.69169 q^{77} +(0.589724 - 3.34449i) q^{78} +(-1.06036 - 0.889746i) q^{79} +(-3.37810 + 1.22953i) q^{81} +(-4.98796 + 4.18539i) q^{82} +(1.26026 + 2.18283i) q^{83} +(-0.774336 + 1.34119i) q^{84} +(1.93564 + 10.9776i) q^{86} +(-1.72438 + 2.98672i) q^{87} +(1.89521 + 3.28261i) q^{88} +(2.06711 - 1.73451i) q^{89} +(-12.3141 - 4.48197i) q^{91} +(-2.39114 - 2.00640i) q^{92} +(-0.712586 + 4.04128i) q^{93} -8.92164 q^{94} +2.24903 q^{96} +(0.531802 - 3.01600i) q^{97} +(-6.90401 - 5.79315i) q^{98} +(-2.73574 - 0.995727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.212126	+	1.20303i	−0.149996	+	0.850669i	0.813223	+	0.581952i	$0.197711\pi$
$2$	−0.212126	+	1.20303i	−0.149996	+	0.850669i	−0.963219	+	0.268717i	$0.913400\pi$
$3$	−0.616222	−	0.517072i	−0.355776	−	0.298531i	0.447329	−	0.894370i	$-0.352375\pi$
$3$	−0.616222	−	0.517072i	−0.355776	−	0.298531i	−0.803104	+	0.595838i	$0.796820\pi$
$4$	0.477108	+	0.173653i	0.238554	+	0.0868266i
$5$		0			0
$5$		0			0
$6$	0.752768	−	0.631647i	0.307316	−	0.257869i
$7$	−1.89590	−	3.28379i	−0.716583	−	1.24116i	−0.962346	−	0.271828i	$-0.912372\pi$
$7$	−1.89590	−	3.28379i	−0.716583	−	1.24116i	0.245763	−	0.969330i	$-0.420961\pi$
$8$	−1.53170	+	2.65299i	−0.541539	+	0.937972i
$9$	−0.408578	−	2.31716i	−0.136193	−	0.772387i
$10$		0			0
$11$	0.618663	−	1.07156i	0.186534	−	0.323086i	−0.757558	−	0.652767i	$-0.773608\pi$
$11$	0.618663	−	1.07156i	0.186534	−	0.323086i	0.944092	+	0.329681i	$0.106941\pi$
$12$	−0.204213	−	0.353708i	−0.0589513	−	0.102107i
$13$	2.64744	−	2.22146i	0.734267	−	0.616123i	−0.197024	−	0.980399i	$-0.563128\pi$
$13$	2.64744	−	2.22146i	0.734267	−	0.616123i	0.931291	+	0.364275i	$0.118683\pi$
$14$	4.35266	−	1.58424i	1.16330	−	0.423406i
$15$		0			0
$16$	−2.08882	−	1.75273i	−0.522204	−	0.438181i
$17$	0.522152	−	2.96127i	0.126640	−	0.718214i	−0.853680	−	0.520799i	$-0.825634\pi$
$17$	0.522152	−	2.96127i	0.126640	−	0.718214i	0.980320	−	0.197415i	$-0.0632547\pi$
$18$	2.87428			0.677474
$19$	4.28612	+	0.793231i	0.983302	+	0.181980i
$19$	4.28612	+	0.793231i	0.983302	+	0.181980i
$20$		0			0
$21$	−0.529662	+	3.00386i	−0.115582	+	0.655496i
$22$	1.15788	+	0.971573i	0.246860	+	0.207140i
$23$	−5.77705	−	2.10267i	−1.20460	−	0.438438i	−0.339771	−	0.940508i	$-0.610350\pi$
$23$	−5.77705	−	2.10267i	−1.20460	−	0.438438i	−0.864827	+	0.502071i	$0.832572\pi$
$24$	2.31565	−	0.842829i	0.472681	−	0.172042i
$25$		0			0
$26$	2.11089	+	3.65617i	0.413980	+	0.717034i
$27$	−2.15299	+	3.72910i	−0.414344	+	0.717665i
$28$	−0.334308	−	1.89595i	−0.0631782	−	0.358302i
$29$	−0.744476	−	4.22213i	−0.138246	−	0.784031i	−0.972544	−	0.232718i	$-0.925238\pi$
$29$	−0.744476	−	4.22213i	−0.138246	−	0.784031i	0.834299	−	0.551313i	$-0.185873\pi$
$30$		0			0
$31$	−2.55067	−	4.41789i	−0.458114	−	0.793476i	0.540748	−	0.841185i	$-0.318141\pi$
$31$	−2.55067	−	4.41789i	−0.458114	−	0.793476i	−0.998861	+	0.0477088i	$0.984808\pi$
$32$	−2.14174	+	1.79713i	−0.378610	+	0.317691i
$33$	−0.935304	+	0.340423i	−0.162816	+	0.0592600i
$34$	3.45173	+	1.25633i	0.591966	+	0.215458i
$35$		0			0
$36$	0.207446	−	1.17649i	0.0345744	−	0.196081i
$37$	9.13084			1.50110			0.750550	−	0.660813i	$-0.229789\pi$
$37$	9.13084			1.50110			0.750550	+	0.660813i	$0.229789\pi$
$38$	−1.86348	+	4.98805i	−0.302296	+	0.809168i
$39$	−2.78006			−0.445167
$40$		0			0
$41$	4.08318	+	3.42620i	0.637686	+	0.535082i	0.903307	−	0.428996i	$-0.141132\pi$
$41$	4.08318	+	3.42620i	0.637686	+	0.535082i	−0.265621	+	0.964078i	$0.585577\pi$
$42$	−3.50137	−	1.27440i	−0.540273	−	0.196643i
$43$	8.57465	−	3.12092i	1.30762	−	0.475935i	0.408150	−	0.912915i	$-0.366174\pi$
$43$	8.57465	−	3.12092i	1.30762	−	0.475935i	0.899471	+	0.436979i	$0.143952\pi$
$44$	0.481248	−	0.403815i	0.0725509	−	0.0608774i
$45$		0			0
$46$	3.75504	−	6.50391i	0.553650	−	0.958950i
$47$	1.26821	+	7.19237i	0.184987	+	1.04912i	0.925972	+	0.377593i	$0.123248\pi$
$47$	1.26821	+	7.19237i	0.184987	+	1.04912i	−0.740984	+	0.671522i	$0.765641\pi$
$48$	0.380890	+	2.16014i	0.0549768	+	0.311789i
$49$	−3.68887	+	6.38931i	−0.526981	+	0.912758i
$50$		0			0
$51$	−1.85295	+	1.55481i	−0.259465	+	0.217717i
$52$	1.64888	−	0.600142i	0.228658	−	0.0832248i
$53$	3.13139	+	1.13973i	0.430129	+	0.156554i	0.548007	−	0.836474i	$-0.315387\pi$
$53$	3.13139	+	1.13973i	0.430129	+	0.156554i	−0.117877	+	0.993028i	$0.537609\pi$
$54$	−4.02950	−	3.38115i	−0.548345	−	0.460116i
$55$		0			0
$56$	11.6158			1.55223
$57$	−2.23104	−	2.70503i	−0.295509	−	0.358291i
$58$	5.23727			0.687687
$59$	−0.141926	+	0.804901i	−0.0184772	+	0.104789i	−0.992652	−	0.121008i	$-0.961387\pi$
$59$	−0.141926	+	0.804901i	−0.0184772	+	0.104789i	0.974174	+	0.225797i	$0.0724986\pi$
$60$		0			0
$61$	−6.01592	−	2.18962i	−0.770260	−	0.280352i	−0.0731548	−	0.997321i	$-0.523307\pi$
$61$	−6.01592	−	2.18962i	−0.770260	−	0.280352i	−0.697105	+	0.716969i	$0.745529\pi$
$62$	5.85590	−	2.13137i	0.743700	−	0.270685i
$63$	−6.83446	+	5.73479i	−0.861061	+	0.722516i
$64$	−4.43444	−	7.68067i	−0.554305	−	0.960084i
$65$		0			0
$66$	−0.211136	−	1.19741i	−0.0259890	−	0.147391i
$67$	−0.175545	−	0.995566i	−0.0214463	−	0.121628i	0.972205	−	0.234131i	$-0.0752244\pi$
$67$	−0.175545	−	0.995566i	−0.0214463	−	0.121628i	−0.993651	+	0.112503i	$0.964113\pi$
$68$	0.763357	−	1.32217i	0.0925706	−	0.160337i
$69$	2.47271	+	4.28286i	0.297679	+	0.515596i
$70$		0			0
$71$	−12.8546	+	4.67867i	−1.52555	+	0.555257i	−0.962528	−	0.271182i	$-0.912585\pi$
$71$	−12.8546	+	4.67867i	−1.52555	+	0.555257i	−0.563027	+	0.826439i	$0.690363\pi$
$72$	6.77322	+	2.46525i	0.798231	+	0.290532i
$73$	−8.47451	−	7.11096i	−0.991867	−	0.832275i	−0.00602966	−	0.999982i	$-0.501919\pi$
$73$	−8.47451	−	7.11096i	−0.991867	−	0.832275i	−0.985837	+	0.167707i	$0.946364\pi$
$74$	−1.93689	+	10.9846i	−0.225159	+	1.27694i
$75$		0			0
$76$	1.90719	+	1.12275i	0.218770	+	0.128789i
$77$	−4.69169			−0.534668
$78$	0.589724	−	3.34449i	0.0667731	−	0.378689i
$79$	−1.06036	−	0.889746i	−0.119300	−	0.100104i	0.581186	−	0.813771i	$-0.302589\pi$
$79$	−1.06036	−	0.889746i	−0.119300	−	0.100104i	−0.700486	+	0.713666i	$0.747033\pi$
$80$		0			0
$81$	−3.37810	+	1.22953i	−0.375344	+	0.136614i
$82$	−4.98796	+	4.18539i	−0.550828	+	0.462199i
$83$	1.26026	+	2.18283i	0.138332	+	0.239597i	0.926865	−	0.375394i	$-0.122493\pi$
$83$	1.26026	+	2.18283i	0.138332	+	0.239597i	−0.788534	+	0.614992i	$0.789159\pi$
$84$	−0.774336	+	1.34119i	−0.0844870	+	0.146336i
$85$		0			0
$86$	1.93564	+	10.9776i	0.208726	+	1.18374i
$87$	−1.72438	+	2.98672i	−0.184873	+	0.320210i
$88$	1.89521	+	3.28261i	0.202031	+	0.349927i
$89$	2.06711	−	1.73451i	0.219113	−	0.183858i	−0.526624	−	0.850099i	$-0.676542\pi$
$89$	2.06711	−	1.73451i	0.219113	−	0.183858i	0.745736	+	0.666241i	$0.232098\pi$
$90$		0			0
$91$	−12.3141	−	4.48197i	−1.29087	−	0.469838i
$92$	−2.39114	−	2.00640i	−0.249294	−	0.209182i
$93$	−0.712586	+	4.04128i	−0.0738918	+	0.419061i
$94$	−8.92164			−0.920197
$95$		0			0
$96$	2.24903			0.229541
$97$	0.531802	−	3.01600i	0.0539963	−	0.306228i	−0.945834	−	0.324651i	$-0.894753\pi$
$97$	0.531802	−	3.01600i	0.0539963	−	0.306228i	0.999830	+	0.0184223i	$0.00586434\pi$
$98$	−6.90401	−	5.79315i	−0.697410	−	0.585196i
$99$	−2.73574	−	0.995727i	−0.274952	−	0.100074i
$100$		0			0
$101$	2.85509	−	2.39570i	0.284092	−	0.238381i	−0.489594	−	0.871950i	$-0.662855\pi$
$101$	2.85509	−	2.39570i	0.284092	−	0.238381i	0.773686	+	0.633569i	$0.218411\pi$
$102$	−1.47742	−	2.55897i	−0.146286	−	0.253375i
$103$	−6.60432	+	11.4390i	−0.650743	+	1.12712i	0.332200	+	0.943209i	$0.392209\pi$
$103$	−6.60432	+	11.4390i	−0.650743	+	1.12712i	−0.982943	+	0.183911i	$0.941124\pi$
$104$	1.83843	+	10.4262i	0.180273	+	1.02238i
$105$		0			0
$106$	−2.03538	+	3.52538i	−0.197693	+	0.342415i
$107$	−2.56652	−	4.44535i	−0.248115	−	0.429748i	0.714888	−	0.699239i	$-0.246478\pi$
$107$	−2.56652	−	4.44535i	−0.248115	−	0.429748i	−0.963003	+	0.269491i	$0.913145\pi$
$108$	−1.67478	+	1.40531i	−0.161156	+	0.135226i
$109$	1.49202	−	0.543049i	0.142909	−	0.0520147i	−0.269575	−	0.962979i	$-0.586883\pi$
$109$	1.49202	−	0.543049i	0.142909	−	0.0520147i	0.412485	+	0.910965i	$0.364661\pi$
$110$		0			0
$111$	−5.62662	−	4.72130i	−0.534055	−	0.448126i
$112$	−1.79540	+	10.1822i	−0.169650	+	0.962131i
$113$	20.0832			1.88927			0.944634	−	0.328126i	$-0.106417\pi$
$113$	20.0832			1.88927			0.944634	+	0.328126i	$0.106417\pi$
$114$	3.72749	−	2.11019i	0.349112	−	0.197638i
$115$		0			0
$116$	0.377991	−	2.14369i	0.0350956	−	0.199037i
$117$	−6.22917	−	5.22690i	−0.575887	−	0.483227i
$118$	−0.938212	−	0.341481i	−0.0863694	−	0.0314359i
$119$	−10.7142	+	3.89963i	−0.982165	+	0.357479i
$120$		0			0
$121$	4.73451	+	8.20042i	0.430410	+	0.745492i
$122$	3.91030	−	6.77284i	0.354022	−	0.613184i
$123$	−0.744557	−	4.22259i	−0.0671345	−	0.380738i
$124$	−0.449765	−	2.55074i	−0.0403901	−	0.229063i
$125$		0			0
$126$	−5.44934	−	9.43854i	−0.485466	−	0.840852i
$127$	2.64518	−	2.21957i	0.234722	−	0.196955i	−0.517838	−	0.855479i	$-0.673263\pi$
$127$	2.64518	−	2.21957i	0.234722	−	0.196955i	0.752560	+	0.658523i	$0.228819\pi$
$128$	4.92625	−	1.79301i	0.435423	−	0.158481i
$129$	−6.89762	−	2.51053i	−0.607302	−	0.221040i
$130$		0			0
$131$	−1.31755	+	7.47219i	−0.115115	+	0.652848i	0.871579	+	0.490256i	$0.163097\pi$
$131$	−1.31755	+	7.47219i	−0.115115	+	0.652848i	−0.986693	+	0.162592i	$0.948014\pi$
$132$	−0.505357			−0.0439857
$133$	−5.52124	−	15.5786i	−0.478752	−	1.35084i
$134$	1.23493			0.106682
$135$		0			0
$136$	7.05643	+	5.92105i	0.605084	+	0.507726i
$137$	3.46401	+	1.26080i	0.295951	+	0.107717i	0.485728	−	0.874110i	$-0.338554\pi$
$137$	3.46401	+	1.26080i	0.295951	+	0.107717i	−0.189778	+	0.981827i	$0.560777\pi$
$138$	−5.67692	+	2.06623i	−0.483252	+	0.175889i
$139$	−14.2693	+	11.9734i	−1.21031	+	1.01557i	−0.211033	+	0.977479i	$0.567683\pi$
$139$	−14.2693	+	11.9734i	−1.21031	+	1.01557i	−0.999274	+	0.0380898i	$0.987873\pi$
$140$		0			0
$141$	2.93747	−	5.08785i	0.247380	−	0.428474i
$142$	−2.90179	−	16.4568i	−0.243512	−	1.38103i
$143$	−0.742550	−	4.21121i	−0.0620952	−	0.352159i
$144$	−3.20790	+	5.55625i	−0.267325	+	0.463021i
$145$		0			0
$146$	10.3523	−	8.68665i	0.856766	−	0.718912i
$147$	5.57689	−	2.02982i	0.459974	−	0.167417i
$148$	4.35640	+	1.58560i	0.358094	+	0.130335i
$149$	1.29297	+	1.08493i	0.105924	+	0.0888807i	0.694212	−	0.719771i	$-0.255753\pi$
$149$	1.29297	+	1.08493i	0.105924	+	0.0888807i	−0.588288	+	0.808652i	$0.700198\pi$
$150$		0			0
$151$	1.33890			0.108958			0.0544791	−	0.998515i	$-0.482650\pi$
$151$	1.33890			0.108958			0.0544791	+	0.998515i	$0.482650\pi$
$152$	−8.66948	+	10.1560i	−0.703188	+	0.823761i
$153$	−7.07508			−0.571987
$154$	0.995230	−	5.64423i	0.0801979	−	0.454825i
$155$		0			0
$156$	−1.32639	−	0.482767i	−0.106196	−	0.0386523i
$157$	−5.67825	+	2.06672i	−0.453174	+	0.164942i	−0.558515	−	0.829494i	$-0.688629\pi$
$157$	−5.67825	+	2.06672i	−0.453174	+	0.164942i	0.105341	+	0.994436i	$0.466407\pi$
$158$	1.29532	−	1.08690i	0.103050	−	0.0864692i
$159$	−1.34031	−	2.32148i	−0.106293	−	0.184105i
$160$		0			0
$161$	4.04795	+	22.9571i	0.319023	+	1.80927i
$162$	−0.762572	−	4.32476i	−0.0599133	−	0.339785i
$163$	4.89864	−	8.48469i	0.383691	−	0.664572i	−0.607896	−	0.794017i	$-0.707986\pi$
$163$	4.89864	−	8.48469i	0.383691	−	0.664572i	0.991587	+	0.129445i	$0.0413195\pi$
$164$	1.35315	+	2.34372i	0.105663	+	0.183014i
$165$		0			0
$166$	−2.89334	+	1.05309i	−0.224567	+	0.0817357i
$167$	−3.64255	−	1.32578i	−0.281869	−	0.102592i	0.197217	−	0.980360i	$-0.436810\pi$
$167$	−3.64255	−	1.32578i	−0.281869	−	0.102592i	−0.479086	+	0.877768i	$0.659032\pi$
$168$	−7.15792	−	6.00621i	−0.552245	−	0.463389i
$169$	−0.183403	+	1.04013i	−0.0141079	+	0.0800101i
$170$		0			0
$171$	0.0868309	−	10.2557i	0.00664012	−	0.784274i
$172$	4.63299			0.353262
$173$	−0.821737	+	4.66030i	−0.0624755	+	0.354316i	0.937504	+	0.347973i	$0.113130\pi$
$173$	−0.821737	+	4.66030i	−0.0624755	+	0.354316i	−0.999980	+	0.00634275i	$0.997981\pi$
$174$	−3.22732	−	2.70804i	−0.244662	−	0.205296i
$175$		0			0
$176$	−3.17042	+	1.15394i	−0.238979	+	0.0869813i
$177$	0.503649	−	0.422612i	0.0378566	−	0.0317655i
$178$	1.64817	+	2.85472i	0.123536	+	0.213970i
$179$	4.68907	−	8.12172i	0.350478	−	0.607045i	−0.635855	−	0.771808i	$-0.719353\pi$
$179$	4.68907	−	8.12172i	0.350478	−	0.607045i	0.986333	+	0.164763i	$0.0526859\pi$
$180$		0			0
$181$	−3.38627	−	19.2045i	−0.251700	−	1.42746i	−0.804404	−	0.594083i	$-0.797515\pi$
$181$	−3.38627	−	19.2045i	−0.251700	−	1.42746i	0.552704	−	0.833377i	$-0.313596\pi$
$182$	8.00407	−	13.8635i	0.593301	−	1.02763i
$183$	2.57495	+	4.45995i	0.190346	+	0.329689i
$184$	14.4271	−	12.1058i	1.06358	−	0.892448i
$185$		0			0
$186$	−4.71061	−	1.71452i	−0.345399	−	0.125715i
$187$	−2.85013	−	2.39154i	−0.208422	−	0.174887i
$188$	−0.643905	+	3.65177i	−0.0469616	+	0.266332i
$189$	16.3274			1.18765
$190$		0			0
$191$	15.5024			1.12171			0.560857	−	0.827913i	$-0.310472\pi$
$191$	15.5024			1.12171			0.560857	+	0.827913i	$0.310472\pi$
$192$	−1.23886	+	7.02592i	−0.0894070	+	0.507052i
$193$	15.2008	+	12.7550i	1.09417	+	0.918122i	0.997020	−	0.0771477i	$-0.0245813\pi$
$193$	15.2008	+	12.7550i	1.09417	+	0.918122i	0.0971550	+	0.995269i	$0.469026\pi$
$194$	3.51552	+	1.27955i	0.252400	+	0.0918660i
$195$		0			0
$196$	−2.86951	+	2.40781i	−0.204965	+	0.171986i
$197$	12.9854	+	22.4913i	0.925170	+	1.60244i	0.791288	+	0.611444i	$0.209411\pi$
$197$	12.9854	+	22.4913i	0.925170	+	1.60244i	0.133882	+	0.990997i	$0.457256\pi$
$198$	1.77821	−	3.07995i	0.126372	−	0.218882i
$199$	−0.940467	−	5.33365i	−0.0666680	−	0.378093i	−0.999826	−	0.0186277i	$-0.994070\pi$
$199$	−0.940467	−	5.33365i	−0.0666680	−	0.378093i	0.933159	−	0.359465i	$-0.117041\pi$
$200$		0			0
$201$	−0.406604	+	0.704259i	−0.0286797	+	0.0496746i
$202$	2.27646	+	3.94294i	0.160171	+	0.277424i
$203$	−12.4532	+	10.4494i	−0.874041	+	0.733407i
$204$	−1.15406	+	0.420042i	−0.0808000	+	0.0294088i
$205$		0			0
$206$	−12.3605	−	10.3717i	−0.861197	−	0.722630i
$207$	−2.51186	+	14.2455i	−0.174586	+	0.990128i
$208$	−9.42363			−0.653411
$209$	3.50165	−	4.10207i	0.242214	−	0.283746i
$210$		0			0
$211$	−3.49375	+	19.8141i	−0.240520	+	1.36406i	0.590151	+	0.807293i	$0.299068\pi$
$211$	−3.49375	+	19.8141i	−0.240520	+	1.36406i	−0.830671	+	0.556764i	$0.812043\pi$
$212$	1.29609	+	1.08755i	0.0890160	+	0.0746933i
$213$	10.3405	+	3.76362i	0.708517	+	0.257879i
$214$	5.89230	−	2.14462i	0.402790	−	0.146603i
$215$		0			0
$216$	−6.59549	−	11.4237i	−0.448767	−	0.777286i
$217$	−9.67162	+	16.7517i	−0.656553	+	1.13718i
$218$	0.336808	+	1.91013i	0.0228115	+	0.129370i
$219$	1.54530	+	8.76386i	0.104422	+	0.592207i
$220$		0			0
$221$	−5.19599	−	8.99972i	−0.349520	−	0.605387i
$222$	6.87340	−	5.76747i	0.461313	−	0.387087i
$223$	10.1953	−	3.71080i	0.682730	−	0.248493i	0.0227106	−	0.999742i	$-0.492770\pi$
$223$	10.1953	−	3.71080i	0.682730	−	0.248493i	0.660019	+	0.751249i	$0.270548\pi$
$224$	9.96194	+	3.62585i	0.665610	+	0.242262i
$225$		0			0
$226$	−4.26017	+	24.1606i	−0.283382	+	1.60714i
$227$	8.78226			0.582899			0.291449	−	0.956586i	$-0.405862\pi$
$227$	8.78226			0.582899			0.291449	+	0.956586i	$0.405862\pi$
$228$	−0.594710	−	1.67802i	−0.0393856	−	0.111130i
$229$	18.0824			1.19492			0.597459	−	0.801899i	$-0.296177\pi$
$229$	18.0824			1.19492			0.597459	+	0.801899i	$0.296177\pi$
$230$		0			0
$231$	2.89112	+	2.42594i	0.190222	+	0.159615i
$232$	12.3416	+	4.49197i	0.810264	+	0.294912i
$233$	−24.7757	+	9.01763i	−1.62311	+	0.590765i	−0.983972	−	0.178325i	$-0.942932\pi$
$233$	−24.7757	+	9.01763i	−1.62311	+	0.590765i	−0.639141	+	0.769090i	$0.720710\pi$
$234$	7.60947	−	6.38511i	0.497447	−	0.417407i
$235$		0			0
$236$	−0.207488	+	0.359379i	−0.0135063	+	0.0233936i
$237$	0.193353	+	1.09656i	0.0125597	+	0.0712293i
$238$	−2.41861	−	13.7166i	−0.156775	−	0.889117i
$239$	4.58448	−	7.94056i	0.296546	−	0.513632i	−0.678798	−	0.734325i	$-0.737499\pi$
$239$	4.58448	−	7.94056i	0.296546	−	0.513632i	0.975343	+	0.220693i	$0.0708320\pi$
$240$		0			0
$241$	20.3130	−	17.0446i	1.30847	−	1.09794i	0.319859	−	0.947465i	$-0.396364\pi$
$241$	20.3130	−	17.0446i	1.30847	−	1.09794i	0.988614	−	0.150474i	$-0.0480800\pi$
$242$	−10.8696	+	3.95623i	−0.698727	+	0.254316i
$243$	14.8563	+	5.40726i	0.953034	+	0.346876i
$244$	−2.49001	−	2.08937i	−0.159407	−	0.133758i
$245$		0			0
$246$	5.23784			0.333952
$247$	13.1094	−	7.42142i	0.834128	−	0.472214i
$248$	15.6275			0.992345
$249$	0.352082	−	1.99676i	0.0223123	−	0.126539i
$250$		0			0
$251$	14.0457	+	5.11220i	0.886554	+	0.322679i	0.744852	−	0.667230i	$-0.232520\pi$
$251$	14.0457	+	5.11220i	0.886554	+	0.322679i	0.141703	+	0.989909i	$0.454742\pi$
$252$	−4.25664	+	1.54929i	−0.268143	+	0.0975961i
$253$	−5.82717	+	4.88958i	−0.366351	+	0.307405i
$254$	2.10909	+	3.65306i	0.132336	+	0.229213i
$255$		0			0
$256$	−1.96808	−	11.1615i	−0.123005	−	0.697595i
$257$	−1.87519	−	10.6347i	−0.116971	−	0.663376i	−0.985755	−	0.168185i	$-0.946209\pi$
$257$	−1.87519	−	10.6347i	−0.116971	−	0.663376i	0.868784	−	0.495191i	$-0.164902\pi$
$258$	4.48340	−	7.76548i	0.279124	−	0.483458i
$259$	−17.3111	−	29.9838i	−1.07566	−	1.86310i
$260$		0			0
$261$	−9.47919	+	3.45014i	−0.586747	+	0.213558i
$262$	−8.70976	−	3.17009i	−0.538091	−	0.195849i
$263$	−0.420687	−	0.352998i	−0.0259407	−	0.0217668i	0.629725	−	0.776818i	$-0.283168\pi$
$263$	−0.420687	−	0.352998i	−0.0259407	−	0.0217668i	−0.655666	+	0.755051i	$0.727612\pi$
$264$	0.529470	−	3.00278i	0.0325867	−	0.184808i
$265$		0			0
$266$	19.9127	−	3.33757i	1.22093	−	0.204639i
$267$	−2.17066			−0.132842
$268$	0.0891292	−	0.505477i	0.00544443	−	0.0308769i
$269$	16.7970	+	14.0944i	1.02413	+	0.859350i	0.990141	−	0.140072i	$-0.0447335\pi$
$269$	16.7970	+	14.0944i	1.02413	+	0.859350i	0.0339919	+	0.999422i	$0.489178\pi$
$270$		0			0
$271$	4.96664	−	1.80771i	0.301702	−	0.109810i	−0.186734	−	0.982411i	$-0.559790\pi$
$271$	4.96664	−	1.80771i	0.301702	−	0.109810i	0.488435	+	0.872600i	$0.337568\pi$
$272$	−6.28098	+	5.27036i	−0.380840	+	0.319563i
$273$	5.27072	+	9.12916i	0.318999	+	0.552522i
$274$	−2.25158	+	3.89985i	−0.136023	+	0.235599i
$275$		0			0
$276$	0.436018	+	2.47278i	0.0262452	+	0.148844i
$277$	8.71954	−	15.1027i	0.523906	−	0.907433i	−0.475706	−	0.879604i	$-0.657807\pi$
$277$	8.71954	−	15.1027i	0.523906	−	0.907433i	0.999613	−	0.0278284i	$-0.00885920\pi$
$278$	−11.3774	−	19.7062i	−0.682371	−	1.18190i
$279$	−9.19481	+	7.71536i	−0.550479	+	0.461907i
$280$		0			0
$281$	21.7859	+	7.92943i	1.29964	+	0.473030i	0.896879	−	0.442275i	$-0.145829\pi$
$281$	21.7859	+	7.92943i	1.29964	+	0.473030i	0.402760	+	0.915305i	$0.368051\pi$
$282$	5.49771	+	4.61313i	0.327384	+	0.274708i
$283$	−0.797719	+	4.52409i	−0.0474195	+	0.268929i	−0.999294	−	0.0375573i	$-0.988042\pi$
$283$	−0.797719	+	4.52409i	−0.0474195	+	0.268929i	0.951875	+	0.306487i	$0.0991534\pi$
$284$	−6.94548			−0.412138
$285$		0			0
$286$	5.22372			0.308885
$287$	3.50962	−	19.9040i	0.207166	−	1.17490i
$288$	5.03932	+	4.22849i	0.296944	+	0.249166i
$289$	7.47829	+	2.72188i	0.439899	+	0.160110i
$290$		0			0
$291$	−1.88720	+	1.58355i	−0.110629	+	0.0928291i
$292$	−2.80842	−	4.86432i	−0.164350	−	0.284663i
$293$	−9.06630	+	15.7033i	−0.529659	+	0.917396i	0.469742	+	0.882804i	$0.344347\pi$
$293$	−9.06630	+	15.7033i	−0.529659	+	0.917396i	−0.999401	+	0.0345929i	$0.988987\pi$
$294$	1.25893	+	7.13973i	0.0734221	+	0.416398i
$295$		0			0
$296$	−13.9857	+	24.2240i	−0.812904	+	1.40799i
$297$	2.66395	+	4.61410i	0.154578	+	0.267738i
$298$	−1.57947	+	1.32533i	−0.0914962	+	0.0767744i
$299$	−19.9654	+	7.26680i	−1.15463	+	0.420250i
$300$		0			0
$301$	−26.5051	−	22.2404i	−1.52773	−	1.28192i
$302$	−0.284016	+	1.61073i	−0.0163433	+	0.0926873i
$303$	−2.99812			−0.172237
$304$	−7.56259	−	9.16930i	−0.433745	−	0.525895i
$305$		0			0
$306$	1.50081	−	8.51152i	0.0857956	−	0.486571i
$307$	−3.38137	−	2.83731i	−0.192985	−	0.161934i	0.541175	−	0.840910i	$-0.317980\pi$
$307$	−3.38137	−	2.83731i	−0.192985	−	0.161934i	−0.734160	+	0.678976i	$0.762424\pi$
$308$	−2.23844	−	0.814726i	−0.127547	−	0.0464234i
$309$	9.98452	−	3.63407i	0.567999	−	0.206735i
$310$		0			0
$311$	−7.51688	−	13.0196i	−0.426243	−	0.738275i	0.570292	−	0.821442i	$-0.306830\pi$
$311$	−7.51688	−	13.0196i	−0.426243	−	0.738275i	−0.996536	+	0.0831667i	$0.973497\pi$
$312$	4.25823	−	7.37547i	0.241075	−	0.417554i
$313$	−1.35541	−	7.68691i	−0.0766123	−	0.434490i	−0.998853	−	0.0478746i	$-0.984755\pi$
$313$	−1.35541	−	7.68691i	−0.0766123	−	0.434490i	0.922241	−	0.386615i	$-0.126356\pi$
$314$	−1.28181	−	7.26950i	−0.0723367	−	0.410242i
$315$		0			0
$316$	−0.351398	−	0.608639i	−0.0197677	−	0.0342386i
$317$	−20.8601	+	17.5037i	−1.17162	+	0.983107i	−0.999998	−	0.00205551i	$-0.999346\pi$
$317$	−20.8601	+	17.5037i	−1.17162	+	0.983107i	−0.171624	+	0.985163i	$0.554901\pi$
$318$	3.07712	−	1.11998i	0.172556	−	0.0628053i
$319$	−4.98483	−	1.81433i	−0.279097	−	0.101583i
$320$		0			0
$321$	−0.717016	+	4.06640i	−0.0400199	+	0.226964i
$322$	−28.4767			−1.58694
$323$	4.58697	−	12.2782i	0.255226	−	0.683175i
$324$	−1.82523			−0.101402
$325$		0			0
$326$	9.16818	+	7.69302i	0.507779	+	0.426077i
$327$	−1.20021	−	0.436840i	−0.0663717	−	0.0241573i
$328$	−15.3439	+	5.58471i	−0.847224	+	0.308364i
$329$	21.2139	−	17.8005i	1.16956	−	0.981376i
$330$		0			0
$331$	5.98999	−	10.3750i	0.329240	−	0.570260i	−0.653121	−	0.757253i	$-0.726541\pi$
$331$	5.98999	−	10.3750i	0.329240	−	0.570260i	0.982361	+	0.186993i	$0.0598742\pi$
$332$	0.222224	+	1.26030i	0.0121961	+	0.0691677i
$333$	−3.73066	−	21.1576i	−0.204439	−	1.15943i
$334$	2.36763	−	4.10085i	0.129551	−	0.224389i
$335$		0			0
$336$	6.37131	−	5.34616i	0.347584	−	0.291657i
$337$	3.89355	−	1.41714i	0.212095	−	0.0771963i	−0.233788	−	0.972288i	$-0.575112\pi$
$337$	3.89355	−	1.41714i	0.212095	−	0.0771963i	0.445883	+	0.895091i	$0.352890\pi$
$338$	−1.21240	−	0.441278i	−0.0659460	−	0.0240024i
$339$	−12.3757	−	10.3844i	−0.672156	−	0.564006i
$340$		0			0
$341$	−6.31201			−0.341815
$342$	12.3195	+	2.27997i	0.666162	+	0.123286i
$343$	1.43230			0.0773370
$344$	−4.85406	+	27.5287i	−0.261713	+	1.48425i
$345$		0			0
$346$	−5.43216	−	1.97714i	−0.292035	−	0.106292i
$347$	−8.61637	+	3.13610i	−0.462551	+	0.168355i	−0.562775	−	0.826610i	$-0.690266\pi$
$347$	−8.61637	+	3.13610i	−0.462551	+	0.168355i	0.100224	+	0.994965i	$0.468044\pi$
$348$	−1.34137	+	1.12554i	−0.0719050	+	0.0603355i
$349$	16.3441	+	28.3089i	0.874881	+	1.51534i	0.856889	+	0.515501i	$0.172394\pi$
$349$	16.3441	+	28.3089i	0.874881	+	1.51534i	0.0179923	+	0.999838i	$0.494273\pi$
$350$		0			0
$351$	2.58413	+	14.6553i	0.137931	+	0.782244i
$352$	0.600713	+	3.40681i	0.0320181	+	0.181584i
$353$	13.2351	−	22.9238i	0.704431	−	1.22011i	−0.262466	−	0.964941i	$-0.584536\pi$
$353$	13.2351	−	22.9238i	0.704431	−	1.22011i	0.966897	−	0.255169i	$-0.0821310\pi$
$354$	0.401577	+	0.695551i	0.0213436	+	0.0369681i
$355$		0			0
$356$	1.28744	−	0.468589i	0.0682340	−	0.0248351i
$357$	8.61868	+	3.13694i	0.456149	+	0.166025i
$358$	8.77597	+	7.36391i	0.463824	+	0.389195i
$359$	2.15533	−	12.2235i	0.113754	−	0.645131i	−0.873606	−	0.486635i	$-0.838224\pi$
$359$	2.15533	−	12.2235i	0.113754	−	0.645131i	0.987360	−	0.158496i	$-0.0506646\pi$
$360$		0			0
$361$	17.7416	+	6.79976i	0.933767	+	0.357882i
$362$	23.8219			1.25205
$363$	1.32269	−	7.50136i	0.0694233	−	0.393719i
$364$	−5.09685	−	4.27677i	−0.267148	−	0.224163i
$365$		0			0
$366$	−5.91166	+	2.15167i	−0.309007	+	0.112469i
$367$	4.07628	−	3.42041i	0.212780	−	0.178544i	−0.530168	−	0.847892i	$-0.677871\pi$
$367$	4.07628	−	3.42041i	0.212780	−	0.178544i	0.742948	+	0.669349i	$0.233427\pi$
$368$	8.38178	+	14.5177i	0.436931	+	0.756786i
$369$	6.27075	−	10.8613i	0.326442	−	0.565415i
$370$		0			0
$371$	−2.19415	−	12.4437i	−0.113915	−	0.646042i
$372$	−1.04176	+	1.80438i	−0.0540128	+	0.0935529i
$373$	9.65250	+	16.7186i	0.499788	+	0.865657i	1.00000		0.000245325i	$-7.80894e-5\pi$
$373$	9.65250	+	16.7186i	0.499788	+	0.865657i	−0.500212	+	0.865903i	$0.666745\pi$
$374$	3.48168	−	2.92147i	0.180033	−	0.151066i
$375$		0			0
$376$	−21.0238	−	7.65203i	−1.08422	−	0.394623i
$377$	−11.3503	−	9.52401i	−0.584569	−	0.490511i
$378$	−3.46348	+	19.6424i	−0.178142	+	1.01029i
$379$	20.5109			1.05357			0.526787	−	0.849997i	$-0.323397\pi$
$379$	20.5109			1.05357			0.526787	+	0.849997i	$0.323397\pi$
$380$		0			0
$381$	−2.77770			−0.142306
$382$	−3.28846	+	18.6498i	−0.168252	+	0.954207i
$383$	−17.4086	−	14.6076i	−0.889538	−	0.746411i	0.0785793	−	0.996908i	$-0.474962\pi$
$383$	−17.4086	−	14.6076i	−0.889538	−	0.746411i	−0.968117	+	0.250497i	$0.919406\pi$
$384$	−3.96278	−	1.44233i	−0.202225	−	0.0736038i
$385$		0			0
$386$	−18.5690	+	15.5813i	−0.945139	+	0.793066i
$387$	−10.7351	−	18.5937i	−0.545695	−	0.945171i
$388$	0.777465	−	1.34661i	0.0394698	−	0.0683637i
$389$	0.876043	+	4.96829i	0.0444172	+	0.251902i	0.998929	−	0.0462710i	$-0.0147338\pi$
$389$	0.876043	+	4.96829i	0.0444172	+	0.251902i	−0.954512	+	0.298173i	$0.903623\pi$
$390$		0			0
$391$	−9.24308	+	16.0095i	−0.467443	+	0.809635i
$392$	−11.3005	−	19.5730i	−0.570761	−	0.988588i
$393$	4.67556	−	3.92326i	0.235851	−	0.197902i
$394$	−29.8122	+	10.8508i	−1.50192	+	0.546654i
$395$		0			0
$396$	−1.13233	−	0.950139i	−0.0569018	−	0.0477463i
$397$	3.98399	−	22.5943i	0.199951	−	1.13398i	−0.705239	−	0.708970i	$-0.749160\pi$
$397$	3.98399	−	22.5943i	0.199951	−	1.13398i	0.905190	−	0.425008i	$-0.139729\pi$
$398$	6.61603			0.331632
$399$	−4.65295	+	12.4548i	−0.232939	+	0.623518i
$400$		0			0
$401$	−3.95308	+	22.4191i	−0.197408	+	1.11955i	0.711540	+	0.702645i	$0.247998\pi$
$401$	−3.95308	+	22.4191i	−0.197408	+	1.11955i	−0.908948	+	0.416909i	$0.863113\pi$
$402$	−0.760992	−	0.638548i	−0.0379548	−	0.0318479i
$403$	−16.5669	−	6.02986i	−0.825257	−	0.300369i
$404$	1.77821	−	0.647214i	0.0884691	−	0.0322001i
$405$		0			0
$406$	−9.92933	−	17.1981i	−0.492784	−	0.853527i
$407$	5.64891	−	9.78420i	0.280006	−	0.484985i
$408$	−1.28672	−	7.29736i	−0.0637022	−	0.361273i
$409$	4.13331	+	23.4412i	0.204379	+	1.15909i	0.898414	+	0.439150i	$0.144720\pi$
$409$	4.13331	+	23.4412i	0.204379	+	1.15909i	−0.694035	+	0.719941i	$0.744169\pi$
$410$		0			0
$411$	−1.48268	−	2.56807i	−0.0731351	−	0.126674i
$412$	−5.13740	+	4.31079i	−0.253101	+	0.212377i
$413$	2.91221	−	1.05996i	0.143300	−	0.0521571i
$414$	−16.6048	−	6.04367i	−0.816084	−	0.297030i
$415$		0			0
$416$	−1.67786	+	9.51559i	−0.0822636	+	0.466540i
$417$	14.9842			0.733777
$418$	4.19211	+	5.08274i	0.205043	+	0.248605i
$419$	−15.9374			−0.778593			−0.389296	−	0.921113i	$-0.627282\pi$
$419$	−15.9374			−0.778593			−0.389296	+	0.921113i	$0.627282\pi$
$420$		0			0
$421$	−2.03273	−	1.70566i	−0.0990692	−	0.0831290i	0.591908	−	0.806006i	$-0.298375\pi$
$421$	−2.03273	−	1.70566i	−0.0990692	−	0.0831290i	−0.690977	+	0.722877i	$0.742819\pi$
$422$	−23.0957	−	8.40616i	−1.12428	−	0.409206i
$423$	16.1477	−	5.87729i	0.785129	−	0.285764i
$424$	−7.82005	+	6.56180i	−0.379775	+	0.318669i
$425$		0			0
$426$	−6.72122	+	11.6415i	−0.325644	+	0.564033i
$427$	4.21533	+	23.9063i	0.203994	+	1.15691i
$428$	−0.452560	−	2.56660i	−0.0218753	−	0.124061i
$429$	−1.71992	+	2.97899i	−0.0830386	+	0.143827i
$430$		0			0
$431$	25.5262	−	21.4191i	1.22956	−	1.03172i	0.231288	−	0.972885i	$-0.425706\pi$
$431$	25.5262	−	21.4191i	1.22956	−	1.03172i	0.998268	−	0.0588349i	$-0.0187386\pi$
$432$	11.0333	−	4.01579i	0.530840	−	0.193210i
$433$	−21.0303	−	7.65442i	−1.01065	−	0.367848i	−0.216970	−	0.976178i	$-0.569617\pi$
$433$	−21.0303	−	7.65442i	−1.01065	−	0.367848i	−0.793684	+	0.608330i	$0.791840\pi$
$434$	−18.1012	−	15.1887i	−0.868885	−	0.729081i
$435$		0			0
$436$	0.806155			0.0386078
$437$	−23.0932	−	13.5948i	−1.10470	−	0.650329i
$438$	−10.8710			−0.519435
$439$	−3.03121	+	17.1909i	−0.144672	+	0.820475i	0.822958	+	0.568102i	$0.192322\pi$
$439$	−3.03121	+	17.1909i	−0.144672	+	0.820475i	−0.967630	+	0.252373i	$0.918789\pi$
$440$		0			0
$441$	16.3122	+	5.93717i	0.776774	+	0.282723i
$442$	11.9291	−	4.34184i	0.567410	−	0.206520i
$443$	1.14799	−	0.963275i	0.0545425	−	0.0457666i	−0.615109	−	0.788442i	$-0.710888\pi$
$443$	1.14799	−	0.963275i	0.0545425	−	0.0457666i	0.669651	+	0.742676i	$0.266444\pi$
$444$	−1.86464	−	3.22965i	−0.0884918	−	0.153272i
$445$		0			0
$446$	2.30149	+	13.0524i	0.108979	+	0.618050i
$447$	−0.235769	−	1.33711i	−0.0111515	−	0.0632432i
$448$	−16.8145	+	29.1236i	−0.794410	+	1.37596i
$449$	−5.99556	−	10.3846i	−0.282948	−	0.490081i	0.689161	−	0.724608i	$-0.257979\pi$
$449$	−5.99556	−	10.3846i	−0.282948	−	0.490081i	−0.972110	+	0.234527i	$0.924646\pi$
$450$		0			0
$451$	6.19747	−	2.25569i	0.291827	−	0.106217i
$452$	9.58185	+	3.48751i	0.450693	+	0.164039i
$453$	−0.825059	−	0.692307i	−0.0387647	−	0.0325274i
$454$	−1.86295	+	10.5653i	−0.0874324	+	0.495854i
$455$		0			0
$456$	10.5937	−	1.77561i	0.496096	−	0.0831507i
$457$	−12.9472			−0.605646			−0.302823	−	0.953047i	$-0.597929\pi$
$457$	−12.9472			−0.605646			−0.302823	+	0.953047i	$0.597929\pi$
$458$	−3.83575	+	21.7536i	−0.179233	+	1.01648i
$459$	9.91867	+	8.32276i	0.462964	+	0.388473i
$460$		0			0
$461$	−13.0317	+	4.74315i	−0.606946	+	0.220910i	−0.627166	−	0.778885i	$-0.715785\pi$
$461$	−13.0317	+	4.74315i	−0.606946	+	0.220910i	0.0202204	+	0.999796i	$0.493563\pi$
$462$	−3.53175	+	2.96349i	−0.164312	+	0.137874i
$463$	2.09237	+	3.62408i	0.0972405	+	0.168425i	0.910541	−	0.413418i	$-0.135665\pi$
$463$	2.09237	+	3.62408i	0.0972405	+	0.168425i	−0.813301	+	0.581843i	$0.802332\pi$
$464$	−5.84517	+	10.1241i	−0.271355	+	0.470001i
$465$		0			0
$466$	−5.59287	−	31.7188i	−0.259085	−	1.46934i
$467$	−11.6509	+	20.1800i	−0.539141	+	0.933820i	0.459810	+	0.888018i	$0.347918\pi$
$467$	−11.6509	+	20.1800i	−0.539141	+	0.933820i	−0.998951	+	0.0458021i	$0.985416\pi$
$468$	−2.06432	−	3.57551i	−0.0954233	−	0.165278i
$469$	−2.93642	+	2.46395i	−0.135591	+	0.113775i
$470$		0			0
$471$	4.56770	+	1.66251i	0.210469	+	0.0766043i
$472$	−1.91800	−	1.60940i	−0.0882833	−	0.0740785i
$473$	1.96058	−	11.1190i	0.0901476	−	0.511252i
$474$	−1.36021			−0.0624765
$475$		0			0
$476$	−5.78899			−0.265338
$477$	1.36153	−	7.72160i	0.0623401	−	0.353548i
$478$	8.58022	+	7.19966i	0.392450	+	0.329305i
$479$	−32.9992	−	12.0107i	−1.50777	−	0.548784i	−0.549712	−	0.835354i	$-0.685263\pi$
$479$	−32.9992	−	12.0107i	−1.50777	−	0.548784i	−0.958059	+	0.286570i	$0.907485\pi$
$480$		0			0
$481$	24.1733	−	20.2838i	1.10221	−	0.924863i
$482$	16.1962	+	28.0527i	0.737717	+	1.27776i
$483$	9.37602	−	16.2397i	0.426624	−	0.738934i
$484$	0.834846	+	4.73465i	0.0379476	+	0.215211i
$485$		0			0
$486$	−9.65650	+	16.7255i	−0.438028	+	0.758686i
$487$	16.7105	+	28.9434i	0.757223	+	1.31155i	0.944262	+	0.329196i	$0.106778\pi$
$487$	16.7105	+	28.9434i	0.757223	+	1.31155i	−0.187038	+	0.982353i	$0.559889\pi$
$488$	15.0236	−	12.6063i	0.680088	−	0.570661i
$489$	−7.40584	+	2.69551i	−0.334904	+	0.121895i
$490$		0			0
$491$	−13.4354	−	11.2737i	−0.606332	−	0.508773i	0.287142	−	0.957888i	$-0.407295\pi$
$491$	−13.4354	−	11.2737i	−0.606332	−	0.508773i	−0.893474	+	0.449115i	$0.851739\pi$
$492$	0.378032	−	2.14393i	0.0170430	−	0.0966558i
$493$	−12.8916			−0.580609
$494$	6.14733	+	17.3452i	0.276582	+	0.780397i
$495$		0			0
$496$	−2.41546	+	13.6988i	−0.108458	+	0.615093i
$497$	39.7347	+	33.3414i	1.78235	+	1.49557i
$498$	2.32747	+	0.847128i	0.104296	+	0.0379607i
$499$	−30.7119	+	11.1782i	−1.37486	+	0.500407i	−0.920615	−	0.390472i	$-0.872312\pi$
$499$	−30.7119	+	11.1782i	−1.37486	+	0.500407i	−0.454241	+	0.890879i	$0.650090\pi$
$500$		0			0
$501$	1.55910	+	2.70043i	0.0696552	+	0.120646i
$502$	−9.12957	+	15.8129i	−0.407473	+	0.705764i
$503$	3.04306	+	17.2581i	0.135684	+	0.769499i	0.974381	+	0.224902i	$0.0722063\pi$
$503$	3.04306	+	17.2581i	0.135684	+	0.769499i	−0.838698	+	0.544597i	$0.816683\pi$
$504$	−4.74597	−	26.9157i	−0.211402	−	1.19892i
$505$		0			0
$506$	−4.64620	−	8.04746i	−0.206549	−	0.357753i
$507$	0.650839	−	0.546119i	0.0289048	−	0.0242540i
$508$	1.64748	−	0.599632i	0.0730949	−	0.0266044i
$509$	−28.1903	−	10.2604i	−1.24951	−	0.454786i	−0.369276	−	0.929320i	$-0.620394\pi$
$509$	−28.1903	−	10.2604i	−1.24951	−	0.454786i	−0.880237	+	0.474534i	$0.842617\pi$
$510$		0			0
$511$	−7.28411	+	41.3102i	−0.322230	+	1.82746i
$512$	24.3299			1.07524
$513$	−12.1860	+	14.2755i	−0.538026	+	0.630279i
$514$	13.1916			0.581858
$515$		0			0
$516$	−2.85495	−	2.39559i	−0.125682	−	0.105460i
$517$	8.49162	+	3.09070i	0.373461	+	0.135929i
$518$	39.7435	−	14.4654i	1.74623	−	0.635575i
$519$	2.91608	−	2.44688i	0.128002	−	0.107406i
$520$		0			0
$521$	5.24373	−	9.08241i	0.229732	−	0.397907i	−0.727997	−	0.685581i	$-0.759548\pi$
$521$	5.24373	−	9.08241i	0.229732	−	0.397907i	0.957729	+	0.287673i	$0.0928817\pi$
$522$	−2.13983	−	12.1356i	−0.0936579	−	0.531160i
$523$	5.68848	+	32.2610i	0.248740	+	1.41067i	0.811644	+	0.584152i	$0.198573\pi$
$523$	5.68848	+	32.2610i	0.248740	+	1.41067i	−0.562905	+	0.826522i	$0.690316\pi$
$524$	−1.92618	+	3.33625i	−0.0841457	+	0.145745i
$525$		0			0
$526$	0.513906	−	0.431218i	0.0224073	−	0.0188020i
$527$	−14.4144	+	5.24641i	−0.627901	+	0.228537i
$528$	2.55035	+	0.928250i	0.110990	+	0.0403969i
$529$	11.3340	+	9.51037i	0.492783	+	0.413494i
$530$		0			0
$531$	1.92307			0.0834543
$532$	0.0710470	−	8.39146i	0.00308028	−	0.363816i
$533$	18.4211			0.797908
$534$	0.460454	−	2.61137i	0.0199258	−	0.113005i
$535$		0			0
$536$	2.91011	+	1.05919i	0.125697	+	0.0457501i
$537$	−7.08902	+	2.58019i	−0.305914	+	0.111343i
$538$	−20.5190	+	17.2175i	−0.884638	+	0.742299i
$539$	4.56433	+	7.90565i	0.196600	+	0.340521i
$540$		0			0
$541$	2.56927	+	14.5710i	0.110461	+	0.626458i	0.988898	+	0.148598i	$0.0474761\pi$
$541$	2.56927	+	14.5710i	0.110461	+	0.626458i	−0.878436	+	0.477860i	$0.841413\pi$
$542$	1.12117	+	6.35846i	0.0481583	+	0.273119i
$543$	−7.84341	+	13.5852i	−0.336593	+	0.582996i
$544$	4.20348	+	7.28065i	0.180223	+	0.312155i
$545$		0			0
$546$	−12.1007	+	4.40429i	−0.517862	+	0.188486i
$547$	1.51291	+	0.550656i	0.0646875	+	0.0235443i	0.374161	−	0.927364i	$-0.377931\pi$
$547$	1.51291	+	0.550656i	0.0646875	+	0.0235443i	−0.309474	+	0.950908i	$0.600153\pi$
$548$	1.43377	+	1.20307i	0.0612475	+	0.0513927i
$549$	−2.61572	+	14.8345i	−0.111636	+	0.633121i
$550$		0			0
$551$	0.158216	−	18.6871i	0.00674022	−	0.796097i
$552$	−15.1498			−0.644819
$553$	−0.911410	+	5.16886i	−0.0387571	+	0.219802i
$554$	16.3193	+	13.6935i	0.693341	+	0.581782i
$555$		0			0
$556$	−8.88722	+	3.23468i	−0.376902	+	0.137181i
$557$	17.0954	−	14.3448i	0.724357	−	0.607808i	−0.204230	−	0.978923i	$-0.565469\pi$
$557$	17.0954	−	14.3448i	0.724357	−	0.607808i	0.928587	+	0.371115i	$0.121025\pi$
$558$	−7.33133	−	12.6982i	−0.310360	−	0.537559i
$559$	15.7678	−	27.3107i	0.666909	−	1.15512i
$560$		0			0
$561$	0.519714	+	2.94744i	0.0219423	+	0.124441i
$562$	−14.1607	+	24.5270i	−0.597333	+	1.03461i
$563$	−1.21060	−	2.09682i	−0.0510208	−	0.0883706i	0.839387	−	0.543534i	$-0.182914\pi$
$563$	−1.21060	−	2.09682i	−0.0510208	−	0.0883706i	−0.890408	+	0.455163i	$0.849581\pi$
$564$	2.28501	−	1.91735i	0.0962164	−	0.0807352i
$565$		0			0
$566$	−5.27339	−	1.91936i	−0.221657	−	0.0806766i
$567$	10.4420	+	8.76192i	0.438525	+	0.367966i
$568$	7.27689	−	41.2693i	0.305332	−	1.73162i
$569$	25.3556			1.06296			0.531481	−	0.847070i	$-0.321636\pi$
$569$	25.3556			1.06296			0.531481	+	0.847070i	$0.321636\pi$
$570$		0			0
$571$	3.79252			0.158712			0.0793561	−	0.996846i	$-0.474714\pi$
$571$	3.79252			0.158712			0.0793561	+	0.996846i	$0.474714\pi$
$572$	0.377013	−	2.13815i	0.0157637	−	0.0894005i
$573$	−9.55291	−	8.01585i	−0.399079	−	0.334867i
$574$	23.2006	+	8.44434i	0.968376	+	0.352460i
$575$		0			0
$576$	−15.9855	+	13.4135i	−0.666064	+	0.558894i
$577$	−18.4069	−	31.8817i	−0.766289	−	1.32725i	−0.939562	−	0.342378i	$-0.888768\pi$
$577$	−18.4069	−	31.8817i	−0.766289	−	1.32725i	0.173274	−	0.984874i	$-0.444566\pi$
$578$	−4.86083	+	8.41921i	−0.202184	+	0.350193i
$579$	−2.77182	−	15.7198i	−0.115193	−	0.653291i
$580$		0			0
$581$	4.77865	−	8.27687i	0.198252	−	0.343382i
$582$	−1.50472	−	2.60626i	−0.0623729	−	0.108033i
$583$	3.15856	−	2.65035i	0.130814	−	0.109766i
$584$	31.8457	−	11.5909i	1.31778	−	0.479634i
$585$		0			0
$586$	−16.9683	−	14.2381i	−0.700954	−	0.588170i
$587$	4.78860	−	27.1575i	0.197647	−	1.12091i	−0.710953	−	0.703240i	$-0.751736\pi$
$587$	4.78860	−	27.1575i	0.197647	−	1.12091i	0.908599	−	0.417669i	$-0.137153\pi$
$588$	3.01326			0.124265
$589$	−7.42806	−	20.9588i	−0.306068	−	0.863594i
$590$		0			0
$591$	3.62776	−	20.5740i	0.149226	−	0.846302i
$592$	−19.0726	−	16.0039i	−0.783881	−	0.657754i
$593$	6.98559	+	2.54255i	0.286864	+	0.104410i	0.481444	−	0.876477i	$-0.340112\pi$
$593$	6.98559	+	2.54255i	0.286864	+	0.104410i	−0.194580	+	0.980887i	$0.562335\pi$
$594$	−6.11599	+	2.22604i	−0.250942	+	0.0913354i
$595$		0			0
$596$	0.428484	+	0.742155i	0.0175514	+	0.0303999i
$597$	−2.17834	+	3.77300i	−0.0891537	+	0.154419i
$598$	−4.50698	−	25.5604i	−0.184304	−	1.04524i
$599$	1.30033	+	7.37456i	0.0531302	+	0.301316i	0.999781	−	0.0209459i	$-0.00666778\pi$
$599$	1.30033	+	7.37456i	0.0531302	+	0.301316i	−0.946650	+	0.322262i	$0.895557\pi$
$600$		0			0
$601$	12.4586	+	21.5790i	0.508199	+	0.880226i	0.999955	+	0.00949287i	$0.00302172\pi$
$601$	12.4586	+	21.5790i	0.508199	+	0.880226i	−0.491756	+	0.870733i	$0.663645\pi$
$602$	32.3783	−	27.1686i	1.31964	−	1.10731i
$603$	−2.23516	+	0.813533i	−0.0910229	+	0.0331296i
$604$	0.638800	+	0.232504i	0.0259924	+	0.00946046i
$605$		0			0
$606$	0.635979	−	3.60682i	0.0258349	−	0.146517i
$607$	−13.5201			−0.548764			−0.274382	−	0.961621i	$-0.588473\pi$
$607$	−13.5201			−0.548764			−0.274382	+	0.961621i	$0.588473\pi$
$608$	−10.6053	+	6.00383i	−0.430101	+	0.243487i
$609$	13.0770			0.529908
$610$		0			0
$611$	19.3351	+	16.2241i	0.782214	+	0.656356i
$612$	−3.37558	−	1.22861i	−0.136450	−	0.0496636i
$613$	5.31308	−	1.93380i	0.214593	−	0.0781055i	−0.232487	−	0.972600i	$-0.574686\pi$
$613$	5.31308	−	1.93380i	0.214593	−	0.0781055i	0.447080	+	0.894494i	$0.352464\pi$
$614$	4.13064	−	3.46602i	0.166699	−	0.139877i
$615$		0			0
$616$	7.18627	−	12.4470i	0.289543	−	0.501503i
$617$	−3.20152	−	18.1567i	−0.128888	−	0.730963i	−0.978922	−	0.204234i	$-0.934530\pi$
$617$	−3.20152	−	18.1567i	−0.128888	−	0.730963i	0.850034	−	0.526729i	$-0.176582\pi$
$618$	2.25391	+	12.7825i	0.0906654	+	0.514189i
$619$	3.49951	−	6.06133i	0.140657	−	0.243625i	−0.787087	−	0.616842i	$-0.788412\pi$
$619$	3.49951	−	6.06133i	0.140657	−	0.243625i	0.927744	+	0.373216i	$0.121745\pi$
$620$		0			0
$621$	20.2790	−	17.0161i	0.813769	−	0.682833i
$622$	17.2575	−	6.28121i	0.691962	−	0.251854i
$623$	−9.61480	−	3.49950i	−0.385209	−	0.140205i
$624$	5.80705	+	4.87269i	0.232468	+	0.195064i
$625$		0			0
$626$	9.53508			0.381099
$627$	−4.27886	+	0.717180i	−0.170881	+	0.0286414i
$628$	−3.06803			−0.122428
$629$	4.76768	−	27.0389i	0.190100	−	1.07811i
$630$		0			0
$631$	−26.3690	−	9.59752i	−1.04973	−	0.382071i	−0.241170	−	0.970483i	$-0.577531\pi$
$631$	−26.3690	−	9.59752i	−1.04973	−	0.382071i	−0.808562	+	0.588412i	$0.799753\pi$
$632$	3.98464	−	1.45029i	0.158500	−	0.0576894i
$633$	12.3982	−	10.4033i	0.492785	−	0.413496i
$634$	−16.6325	−	28.8083i	−0.660560	−	1.14412i
$635$		0			0
$636$	−0.236339	−	1.34035i	−0.00937146	−	0.0531482i
$637$	4.42757	+	25.1100i	0.175427	+	0.994893i
$638$	3.24010	−	5.61202i	0.128277	−	0.222182i
$639$	16.0933	+	27.8745i	0.636642	+	1.10270i
$640$		0			0
$641$	−25.2148	+	9.17744i	−0.995925	+	0.362487i	−0.788012	−	0.615660i	$-0.788889\pi$
$641$	−25.2148	+	9.17744i	−0.995925	+	0.362487i	−0.207913	+	0.978147i	$0.566667\pi$
$642$	−4.73989	−	1.72518i	−0.187069	−	0.0680874i
$643$	−20.5900	−	17.2770i	−0.811989	−	0.681339i	0.139093	−	0.990279i	$-0.455581\pi$
$643$	−20.5900	−	17.2770i	−0.811989	−	0.681339i	−0.951082	+	0.308940i	$0.900026\pi$
$644$	−2.05526	+	11.6560i	−0.0809885	+	0.459309i
$645$		0			0
$646$	13.7979	+	8.12278i	0.542873	+	0.319586i
$647$	−8.88424			−0.349275			−0.174638	−	0.984633i	$-0.555875\pi$
$647$	−8.88424			−0.349275			−0.174638	+	0.984633i	$0.555875\pi$
$648$	1.91232	−	10.8453i	0.0751231	−	0.426044i
$649$	0.774692	+	0.650044i	0.0304093	+	0.0255164i
$650$		0			0
$651$	14.6217	−	5.32187i	0.573070	−	0.208580i
$652$	3.81057	−	3.19745i	0.149234	−	0.125222i
$653$	−19.7051	−	34.1303i	−0.771121	−	1.33562i	−0.936949	−	0.349465i	$-0.886363\pi$
$653$	−19.7051	−	34.1303i	−0.771121	−	1.33562i	0.165829	−	0.986155i	$-0.446970\pi$
$654$	0.780126	−	1.35122i	0.0305053	−	0.0528368i
$655$		0			0
$656$	−2.52384	−	14.3134i	−0.0985393	−	0.558844i
$657$	−13.0147	+	22.5422i	−0.507753	+	0.879455i
$658$	16.9145	+	29.2968i	0.659397	+	1.14211i
$659$	13.2617	−	11.1279i	0.516603	−	0.433481i	−0.346843	−	0.937923i	$-0.612746\pi$
$659$	13.2617	−	11.1279i	0.516603	−	0.433481i	0.863446	+	0.504442i	$0.168302\pi$
$660$		0			0
$661$	−13.3832	−	4.87107i	−0.520544	−	0.189463i	0.0683671	−	0.997660i	$-0.478221\pi$
$661$	−13.3832	−	4.87107i	−0.520544	−	0.189463i	−0.588911	+	0.808198i	$0.700443\pi$
$662$	11.2107	+	9.40693i	0.435718	+	0.365611i
$663$	−1.45162	+	8.23252i	−0.0563761	+	0.319725i
$664$	−7.72138			−0.299647
$665$		0			0
$666$	26.2446			1.01696
$667$	−4.57689	+	25.9569i	−0.177218	+	1.00505i
$668$	−1.50766	−	1.26508i	−0.0583332	−	0.0489474i
$669$	−8.20133	−	2.98504i	−0.317082	−	0.115408i
$670$		0			0
$671$	−6.06812	+	5.09176i	−0.234257	+	0.196565i
$672$	−4.26394	−	7.38536i	−0.164485	−	0.284896i
$673$	−1.93350	+	3.34892i	−0.0745310	+	0.129091i	−0.900882	−	0.434064i	$-0.857079\pi$
$673$	−1.93350	+	3.34892i	−0.0745310	+	0.129091i	0.826351	+	0.563155i	$0.190413\pi$
$674$	0.878929	+	4.98466i	0.0338551	+	0.192002i
$675$		0			0
$676$	−0.268125	+	0.464407i	−0.0103125	+	0.0178618i
$677$	−7.85508	−	13.6054i	−0.301895	−	0.522898i	0.674670	−	0.738119i	$-0.264286\pi$
$677$	−7.85508	−	13.6054i	−0.301895	−	0.522898i	−0.976565	+	0.215222i	$0.930953\pi$
$678$	15.1180	−	12.6855i	0.580603	−	0.487184i
$679$	−10.9122	+	3.97170i	−0.418771	+	0.152420i
$680$		0			0
$681$	−5.41182	−	4.54106i	−0.207381	−	0.174014i
$682$	1.33894	−	7.59353i	0.0512708	−	0.290771i
$683$	11.3613			0.434727			0.217364	−	0.976091i	$-0.430254\pi$
$683$	11.3613			0.434727			0.217364	+	0.976091i	$0.430254\pi$
$684$	1.82237	−	4.87801i	0.0696799	−	0.186515i
$685$		0			0
$686$	−0.303829	+	1.72310i	−0.0116002	+	0.0657882i
$687$	−11.1428	−	9.34989i	−0.425123	−	0.356721i
$688$	−23.3810	−	8.50998i	−0.891392	−	0.324440i
$689$	10.8220	−	3.93890i	0.412287	−	0.150060i
$690$		0			0
$691$	1.00544	+	1.74147i	0.0382487	+	0.0662487i	0.884516	−	0.466510i	$-0.154489\pi$
$691$	1.00544	+	1.74147i	0.0382487	+	0.0662487i	−0.846267	+	0.532758i	$0.821155\pi$
$692$	−1.20133	+	2.08077i	−0.0456679	+	0.0790990i
$693$	1.91692	+	10.8714i	0.0728178	+	0.412970i
$694$	−1.94506	−	11.0310i	−0.0738334	−	0.418730i
$695$		0			0
$696$	−5.28248	−	9.14953i	−0.200232	−	0.346812i
$697$	12.2779	−	10.3024i	0.465060	−	0.390232i
$698$	−37.5234	+	13.6574i	−1.42028	+	0.516940i
$699$	19.9301	+	7.25397i	0.753826	+	0.274370i
$700$		0			0
$701$	2.16414	−	12.2735i	0.0817385	−	0.463562i	−0.916274	−	0.400551i	$-0.868819\pi$
$701$	2.16414	−	12.2735i	0.0817385	−	0.463562i	0.998013	−	0.0630107i	$-0.0200702\pi$
$702$	−18.1789			−0.686120
$703$	39.1358	+	7.24286i	1.47604	+	0.273170i
$704$	−10.9737			−0.413586
$705$		0			0
$706$	24.7704	+	20.7849i	0.932248	+	0.782249i
$707$	−13.2800	−	4.83351i	−0.499444	−	0.181783i
$708$	0.313683	−	0.114171i	0.0117889	−	0.00429082i
$709$	−2.69839	+	2.26422i	−0.101340	+	0.0850346i	−0.692050	−	0.721849i	$-0.743292\pi$
$709$	−2.69839	+	2.26422i	−0.101340	+	0.0850346i	0.590710	+	0.806884i	$0.298848\pi$
$710$		0			0
$711$	−1.62845	+	2.82055i	−0.0610715	+	0.105779i
$712$	1.43544	+	8.14076i	0.0537952	+	0.305088i
$713$	5.44596	+	30.8856i	0.203953	+	1.15667i
$714$	−5.60208	+	9.70308i	−0.209653	+	0.363129i
$715$		0			0
$716$	3.64756	−	3.06066i	0.136316	−	0.114382i
$717$	−6.93090	+	2.52264i	−0.258839	+	0.0942097i
$718$	14.2480	+	5.18584i	0.531730	+	0.193534i
$719$	−18.3135	−	15.3668i	−0.682977	−	0.573086i	0.233898	−	0.972261i	$-0.424852\pi$
$719$	−18.3135	−	15.3668i	−0.682977	−	0.573086i	−0.916874	+	0.399176i	$0.869296\pi$
$720$		0			0
$721$	50.0845			1.86524
$722$	−11.9437	+	19.9012i	−0.444500	+	0.740645i
$723$	−21.3306			−0.793293
$724$	1.71931	−	9.75067i	0.0638975	−	0.362381i
$725$		0			0
$726$	8.74376	+	3.18247i	0.324511	+	0.118113i
$727$	5.14882	−	1.87402i	0.190959	−	0.0695034i	−0.244770	−	0.969581i	$-0.578713\pi$
$727$	5.14882	−	1.87402i	0.190959	−	0.0695034i	0.435730	+	0.900078i	$0.356490\pi$
$728$	30.7521	−	25.8041i	1.13975	−	0.956364i
$729$	−0.966510	−	1.67404i	−0.0357967	−	0.0620016i
$730$		0			0
$731$	−4.76461	−	27.0215i	−0.176226	−	0.999424i
$732$	0.454047	+	2.57503i	0.0167821	+	0.0951758i
$733$	−9.44464	+	16.3586i	−0.348846	+	0.604218i	−0.986045	−	0.166481i	$-0.946760\pi$
$733$	−9.44464	+	16.3586i	−0.348846	+	0.604218i	0.637199	+	0.770699i	$0.280093\pi$
$734$	3.25016	+	5.62944i	0.119965	+	0.207786i
$735$		0			0
$736$	16.1517	−	5.87874i	0.595360	−	0.216693i
$737$	−1.17541	−	0.427813i	−0.0432967	−	0.0157587i
$738$	11.7362	+	9.84784i	0.432016	+	0.362504i
$739$	6.07048	−	34.4274i	0.223306	−	1.26643i	−0.642590	−	0.766210i	$-0.722140\pi$
$739$	6.07048	−	34.4274i	0.223306	−	1.26643i	0.865897	−	0.500223i	$-0.166749\pi$
$740$		0			0
$741$	−11.9157	−	2.20523i	−0.437733	−	0.0810112i
$742$	15.4355			0.566655
$743$	4.79935	−	27.2185i	0.176071	−	0.998549i	−0.760829	−	0.648952i	$-0.775208\pi$
$743$	4.79935	−	27.2185i	0.176071	−	0.998549i	0.936900	−	0.349597i	$-0.113681\pi$
$744$	−9.62999	−	8.08052i	−0.353052	−	0.296246i
$745$		0			0
$746$	−22.1605	+	8.06576i	−0.811354	+	0.295309i
$747$	4.54307	−	3.81209i	0.166222	−	0.139477i
$748$	−0.944521	−	1.63596i	−0.0345351	−	0.0598166i
$749$	−9.73174	+	16.8559i	−0.355590	+	0.615900i
$750$		0			0
$751$	9.32641	+	52.8927i	0.340326	+	1.93008i	0.366482	+	0.930425i	$0.380562\pi$
$751$	9.32641	+	52.8927i	0.340326	+	1.93008i	−0.0261566	+	0.999658i	$0.508327\pi$
$752$	9.95720	−	17.2464i	0.363102	−	0.628910i
$753$	−6.01187	−	10.4129i	−0.219085	−	0.379466i
$754$	13.8653	−	11.6344i	0.504946	−	0.423700i
$755$		0			0
$756$	7.78996	+	2.83531i	0.283318	+	0.103119i
$757$	−18.8292	−	15.7996i	−0.684360	−	0.574246i	0.232917	−	0.972497i	$-0.425173\pi$
$757$	−18.8292	−	15.7996i	−0.684360	−	0.574246i	−0.917277	+	0.398251i	$0.869617\pi$
$758$	−4.35090	+	24.6752i	−0.158032	+	0.896242i
$759$	6.11909			0.222109
$760$		0			0
$761$	−0.906887			−0.0328746			−0.0164373	−	0.999865i	$-0.505232\pi$
$761$	−0.906887			−0.0328746			−0.0164373	+	0.999865i	$0.505232\pi$
$762$	0.589223	−	3.34165i	0.0213453	−	0.121055i
$763$	−4.61197	−	3.86991i	−0.166965	−	0.140100i
$764$	7.39632	+	2.69204i	0.267589	+	0.0973945i
$765$		0			0
$766$	21.2661	−	17.8444i	0.768376	−	0.644744i
$767$	1.41232	+	2.44621i	0.0509959	+	0.0883275i
$768$	−4.55853	+	7.89561i	−0.164492	+	0.284908i
$769$	3.70205	+	20.9954i	0.133499	+	0.757113i	0.975893	+	0.218250i	$0.0700348\pi$
$769$	3.70205	+	20.9954i	0.133499	+	0.757113i	−0.842393	+	0.538863i	$0.818854\pi$
$770$		0			0
$771$	−4.34338	+	7.52296i	−0.156423	+	0.270933i
$772$	5.03747	+	8.72515i	0.181302	+	0.314025i
$773$	−12.7191	+	10.6726i	−0.457476	+	0.383868i	−0.842201	−	0.539163i	$-0.818741\pi$
$773$	−12.7191	+	10.6726i	−0.457476	+	0.383868i	0.384725	+	0.923031i	$0.374296\pi$
$774$	24.6459	−	8.97038i	0.885880	−	0.322434i
$775$		0			0
$776$	7.18685	+	6.03048i	0.257993	+	0.216482i
$777$	−4.83626	+	27.4278i	−0.173500	+	0.983966i
$778$	−6.16282			−0.220948
$779$	14.7832	+	17.9240i	0.529664	+	0.642193i
$780$		0			0
$781$	−2.93917	+	16.6689i	−0.105172	+	0.596460i
$782$	−17.2992	−	14.5157i	−0.618616	−	0.519081i
$783$	17.3476	+	6.31401i	0.619952	+	0.225644i
$784$	18.9041	−	6.88052i	0.675145	−	0.245733i
$785$		0			0
$786$	3.72798	+	6.45705i	0.132973	+	0.230315i
$787$	20.6737	−	35.8079i	0.736938	−	1.27641i	−0.216929	−	0.976187i	$-0.569604\pi$
$787$	20.6737	−	35.8079i	0.736938	−	1.27641i	0.953868	−	0.300228i	$-0.0970626\pi$
$788$	2.28974	+	12.9858i	0.0815685	+	0.462598i
$789$	0.0767112	+	0.435051i	0.00273099	+	0.0154882i
$790$		0			0
$791$	−38.0757	−	65.9491i	−1.35382	−	2.34488i
$792$	6.83199	−	5.73272i	0.242764	−	0.203703i
$793$	−20.7909	+	7.56728i	−0.738308	+	0.268722i
$794$	26.3365	+	9.58570i	0.934647	+	0.340184i
$795$		0			0
$796$	0.477501	−	2.70804i	0.0169246	−	0.0959841i
$797$	−22.7002			−0.804083			−0.402042	−	0.915621i	$-0.631699\pi$
$797$	−22.7002			−0.804083			−0.402042	+	0.915621i	$0.631699\pi$
$798$	−13.9964	−	8.23960i	−0.495467	−	0.291679i
$799$	21.9608			0.776916
$800$		0			0
$801$	−4.86371	−	4.08114i	−0.171851	−	0.144200i
$802$	−26.1322	−	9.51134i	−0.922760	−	0.335857i
$803$	−12.8626	+	4.68162i	−0.453913	+	0.165211i
$804$	−0.316291	+	0.265400i	−0.0111547	+	0.00935992i
$805$		0			0
$806$	10.7684	−	18.6514i	0.379299	−	0.656966i
$807$	−3.06289	−	17.3705i	−0.107819	−	0.611472i
$808$	1.98262	+	11.2440i	0.0697484	+	0.395563i
$809$	13.5754	−	23.5133i	0.477285	−	0.826683i	−0.522376	−	0.852715i	$-0.674954\pi$
$809$	13.5754	−	23.5133i	0.477285	−	0.826683i	0.999661	+	0.0260328i	$0.00828745\pi$
$810$		0			0
$811$	−34.6710	+	29.0925i	−1.21746	+	1.02157i	−0.218512	+	0.975834i	$0.570120\pi$
$811$	−34.6710	+	29.0925i	−1.21746	+	1.02157i	−0.998953	+	0.0457400i	$0.985435\pi$
$812$	−7.75609	+	2.82298i	−0.272185	+	0.0990673i
$813$	−3.99526	−	1.45416i	−0.140120	−	0.0509995i
$814$	10.5724	+	8.87127i	0.370561	+	0.310938i
$815$		0			0
$816$	6.59563			0.230893
$817$	39.2275	−	6.57493i	1.37240	−	0.230028i
$818$	−29.0771			−1.01666
$819$	−5.35417	+	30.3650i	−0.187090	+	1.06104i
$820$		0			0
$821$	−13.8883	−	5.05494i	−0.484706	−	0.176419i	0.0880966	−	0.996112i	$-0.471922\pi$
$821$	−13.8883	−	5.05494i	−0.484706	−	0.176419i	−0.572802	+	0.819693i	$0.694144\pi$
$822$	3.40398	−	1.23895i	0.118727	−	0.0432132i
$823$	29.2452	−	24.5396i	1.01942	−	0.855398i	0.0298685	−	0.999554i	$-0.490491\pi$
$823$	29.2452	−	24.5396i	1.01942	−	0.855398i	0.989555	+	0.144156i	$0.0460467\pi$
$824$	−20.2317	−	35.0424i	−0.704805	−	1.22076i
$825$		0			0
$826$	0.657401	+	3.72831i	0.0228739	+	0.129724i
$827$	7.87107	+	44.6391i	0.273704	+	1.55225i	0.743049	+	0.669237i	$0.233379\pi$
$827$	7.87107	+	44.6391i	0.273704	+	1.55225i	−0.469345	+	0.883015i	$0.655510\pi$
$828$	−3.67220	+	6.36043i	−0.127618	+	0.221040i
$829$	−18.9638	−	32.8463i	−0.658640	−	1.14080i	−0.980968	−	0.194170i	$-0.937799\pi$
$829$	−18.9638	−	32.8463i	−0.658640	−	1.14080i	0.322328	−	0.946628i	$-0.395535\pi$
$830$		0			0
$831$	−13.1823	+	4.79798i	−0.457290	+	0.166440i
$832$	−28.8022	−	10.4832i	−0.998537	−	0.363438i
$833$	16.9943	+	14.2599i	0.588818	+	0.494077i
$834$	−3.17853	+	18.0264i	−0.110064	+	0.624202i
$835$		0			0
$836$	2.38300	−	1.34906i	0.0824179	−	0.0466581i
$837$	21.9663			0.759267
$838$	3.38074	−	19.1731i	0.116786	−	0.662324i
$839$	−5.47159	−	4.59121i	−0.188900	−	0.158506i	0.543433	−	0.839453i	$-0.317124\pi$
$839$	−5.47159	−	4.59121i	−0.188900	−	0.158506i	−0.732333	+	0.680946i	$0.761569\pi$
$840$		0			0
$841$	9.97892	−	3.63203i	0.344101	−	0.125242i
$842$	2.48316	−	2.08361i	0.0855752	−	0.0718061i
$843$	−9.32488	−	16.1512i	−0.321166	−	0.556276i
$844$	−5.10767	+	8.84675i	−0.175813	+	0.304518i
$845$		0			0
$846$	3.64519	+	20.6729i	0.125324	+	0.710748i
$847$	17.9523	−	31.0943i	0.616849	−	1.06841i
$848$	−4.54326	−	7.86916i	−0.156016	−	0.270228i
$849$	2.83085	−	2.37537i	0.0971546	−	0.0815223i
$850$		0			0
$851$	−52.7493	−	19.1992i	−1.80822	−	0.658139i
$852$	4.27996	+	3.59131i	0.146629	+	0.123036i
$853$	8.86285	−	50.2637i	0.303458	−	1.72100i	−0.327217	−	0.944949i	$-0.606111\pi$
$853$	8.86285	−	50.2637i	0.303458	−	1.72100i	0.630675	−	0.776047i	$-0.282778\pi$
$854$	−29.6542			−1.01474
$855$		0			0
$856$	15.7246			0.537456
$857$	−2.36234	+	13.3975i	−0.0806961	+	0.457650i	0.917507	+	0.397721i	$0.130199\pi$
$857$	−2.36234	+	13.3975i	−0.0806961	+	0.457650i	−0.998203	+	0.0599294i	$0.980912\pi$
$858$	−3.21897	−	2.70104i	−0.109894	−	0.0922118i
$859$	36.1194	+	13.1464i	1.23238	+	0.448549i	0.874411	−	0.485185i	$-0.161248\pi$
$859$	36.1194	+	13.1464i	1.23238	+	0.448549i	0.357967	+	0.933734i	$0.383470\pi$
$860$		0			0
$861$	−12.4545	+	10.4506i	−0.424449	+	0.356155i
$862$	20.3529	+	35.2523i	0.693224	+	1.20070i
$863$	27.1727	−	47.0645i	0.924970	−	1.60210i	0.133362	−	0.991067i	$-0.457423\pi$
$863$	27.1727	−	47.0645i	0.924970	−	1.60210i	0.791609	−	0.611028i	$-0.209244\pi$
$864$	−2.09053	−	11.8560i	−0.0711212	−	0.403348i
$865$		0			0
$866$	13.6696	−	23.6764i	0.464511	−	0.804556i
$867$	−3.20088	−	5.54409i	−0.108708	−	0.188287i
$868$	−7.52340	+	6.31288i	−0.255361	+	0.214273i
$869$	−1.60942	+	0.585779i	−0.0545957	+	0.0198712i
$870$		0			0
$871$	−2.67636	−	2.24573i	−0.0906850	−	0.0760937i
$872$	−0.844622	+	4.79009i	−0.0286025	+	0.162213i
$873$	−7.20584			−0.243881
$874$	21.2536	−	24.8979i	0.718914	−	0.842184i
$875$		0			0
$876$	−0.784594	+	4.44965i	−0.0265090	+	0.150340i
$877$	10.3665	+	8.69855i	0.350053	+	0.293729i	0.800811	−	0.598917i	$-0.204402\pi$
$877$	10.3665	+	8.69855i	0.350053	+	0.293729i	−0.450759	+	0.892646i	$0.648846\pi$
$878$	−20.0381	−	7.29327i	−0.676253	−	0.246136i
$879$	13.7066	−	4.98879i	0.462312	−	0.168268i
$880$		0			0
$881$	13.9789	+	24.2121i	0.470960	+	0.815726i	0.999448	−	0.0332142i	$-0.0105743\pi$
$881$	13.9789	+	24.2121i	0.470960	+	0.815726i	−0.528488	+	0.848940i	$0.677241\pi$
$882$	−10.6028	+	18.3647i	−0.357016	+	0.618370i
$883$	9.47229	+	53.7200i	0.318768	+	1.80782i	0.550269	+	0.834987i	$0.314525\pi$
$883$	9.47229	+	53.7200i	0.318768	+	1.80782i	−0.231501	+	0.972835i	$0.574364\pi$
$884$	−0.916220	−	5.19614i	−0.0308158	−	0.174765i
$885$		0			0
$886$	0.915328	+	1.58539i	0.0307510	+	0.0532624i
$887$	−27.5606	+	23.1261i	−0.925393	+	0.776497i	−0.974985	−	0.222272i	$-0.928653\pi$
$887$	−27.5606	+	23.1261i	−0.925393	+	0.776497i	0.0495912	+	0.998770i	$0.484208\pi$
$888$	21.1438	−	7.69573i	0.709541	−	0.258252i
$889$	−12.3036	−	4.47815i	−0.412650	−	0.150192i
$890$		0			0
$891$	−0.772397	+	4.38048i	−0.0258763	+	0.146752i
$892$	5.50867			0.184444
$893$	−0.269519	+	31.8333i	−0.00901912	+	1.06526i
$894$	1.65860			0.0554717
$895$		0			0
$896$	−15.2276	−	12.7774i	−0.508717	−	0.426864i
$897$	16.0606	+	5.84557i	0.536247	+	0.195178i
$898$	13.7648	−	5.00998i	0.459337	−	0.167185i
$899$	−16.7540	+	14.0583i	−0.558777	+	0.468870i
$900$		0			0
$901$	5.01012	−	8.67778i	0.166911	−	0.289099i
$902$	1.39902	+	7.93422i	0.0465822	+	0.264181i
$903$	4.83314	+	27.4101i	0.160837	+	0.912151i
$904$	−30.7615	+	53.2804i	−1.02311	+	1.77208i
$905$		0			0
$906$	1.00788	−	0.845712i	0.0334846	−	0.0280969i
$907$	4.13814	−	1.50616i	0.137405	−	0.0500112i	−0.272403	−	0.962183i	$-0.587818\pi$
$907$	4.13814	−	1.50616i	0.137405	−	0.0500112i	0.409807	+	0.912172i	$0.365596\pi$
$908$	4.19009	+	1.52507i	0.139053	+	0.0506111i
$909$	−6.71776	−	5.63687i	−0.222814	−	0.186963i
$910$		0			0
$911$	−14.2563			−0.472333			−0.236166	−	0.971713i	$-0.575891\pi$
$911$	−14.2563			−0.472333			−0.236166	+	0.971713i	$0.575891\pi$
$912$	−0.0809466	+	9.56072i	−0.00268041	+	0.316587i
$913$	3.11870			0.103214
$914$	2.74645	−	15.5759i	0.0908444	−	0.515204i
$915$		0			0
$916$	8.62726	+	3.14006i	0.285053	+	0.103751i
$917$	27.0351	−	9.83996i	0.892777	−	0.324944i
$918$	−12.1165	+	10.1670i	−0.399904	+	0.335560i
$919$	14.3638	+	24.8789i	0.473819	+	0.820678i	0.999551	−	0.0299723i	$-0.00954192\pi$
$919$	14.3638	+	24.8789i	0.473819	+	0.820678i	−0.525732	+	0.850650i	$0.676209\pi$
$920$		0			0
$921$	0.616585	+	3.49682i	0.0203172	+	0.115224i
$922$	−2.94177	−	16.6836i	−0.0968821	−	0.549446i
$923$	−23.6381	+	40.9424i	−0.778058	+	1.34764i
$924$	0.958105	+	1.65949i	0.0315194	+	0.0545931i
$925$		0			0
$926$	−4.80372	+	1.74841i	−0.157860	+	0.0574563i
$927$	29.2044	+	10.6295i	0.959200	+	0.349120i
$928$	9.18221	+	7.70479i	0.301421	+	0.252922i
$929$	−5.32975	+	30.2265i	−0.174864	+	0.991700i	0.763438	+	0.645881i	$0.223510\pi$
$929$	−5.32975	+	30.2265i	−0.174864	+	0.991700i	−0.938301	+	0.345819i	$0.887601\pi$
$930$		0			0
$931$	−20.8791	+	24.4592i	−0.684285	+	0.801617i
$932$	−13.3866			−0.438494
$933$	−2.10001	+	11.9097i	−0.0687512	+	0.389908i
$934$	−21.8056	−	18.2971i	−0.713502	−	0.598699i
$935$		0			0
$936$	23.4081	−	8.51986i	0.765119	−	0.278480i
$937$	−38.6327	+	32.4167i	−1.26208	+	1.05901i	−0.266619	+	0.963802i	$0.585907\pi$
$937$	−38.6327	+	32.4167i	−1.26208	+	1.05901i	−0.995458	+	0.0952059i	$0.969649\pi$
$938$	−2.34131	−	4.05526i	−0.0764463	−	0.132409i
$939$	−3.13945	+	5.43769i	−0.102452	+	0.177452i
$940$		0			0
$941$	1.48399	+	8.41611i	0.0483766	+	0.274357i	0.999395	−	0.0347766i	$-0.0110720\pi$
$941$	1.48399	+	8.41611i	0.0483766	+	0.274357i	−0.951019	+	0.309134i	$0.899961\pi$
$942$	−2.96897	+	5.14241i	−0.0967344	+	0.167549i
$943$	−16.3846	−	28.3789i	−0.533555	−	0.924144i
$944$	1.70723	−	1.43253i	0.0555655	−	0.0466250i
$945$		0			0
$946$	12.9606	+	4.71726i	0.421385	+	0.153371i
$947$	15.7671	+	13.2302i	0.512362	+	0.429923i	0.861959	−	0.506977i	$-0.169237\pi$
$947$	15.7671	+	13.2302i	0.512362	+	0.429923i	−0.349597	+	0.936900i	$0.613682\pi$
$948$	−0.0981709	+	0.556755i	−0.00318844	+	0.0180826i
$949$	−38.2325			−1.24108
$950$		0			0
$951$	21.9051			0.710323
$952$	6.06522	−	34.3976i	0.196575	−	1.11483i
$953$	45.3438	+	38.0480i	1.46883	+	1.23249i	0.917213	+	0.398397i	$0.130433\pi$
$953$	45.3438	+	38.0480i	1.46883	+	1.23249i	0.551617	+	0.834098i	$0.314011\pi$
$954$	9.00049	+	3.27591i	0.291401	+	0.106061i
$955$		0			0
$956$	3.56620	−	2.99239i	0.115339	−	0.0967810i
$957$	2.13362	+	3.69554i	0.0689702	+	0.119460i
$958$	21.4492	−	37.1511i	0.692993	−	1.20030i
$959$	−2.42722	−	13.7654i	−0.0783790	−	0.444510i
$960$		0			0
$961$	2.48818	−	4.30965i	0.0802638	−	0.139021i
$962$	19.2742	+	33.3839i	0.621425	+	1.07634i
$963$	−9.25197	+	7.76332i	−0.298141	+	0.250170i
$964$	12.6513	−	4.60471i	0.407472	−	0.148308i
$965$		0			0
$966$	17.5480	+	14.7245i	0.564596	+	0.473752i
$967$	1.90960	−	10.8299i	0.0614087	−	0.348266i	−0.938586	−	0.345045i	$-0.887864\pi$
$967$	1.90960	−	10.8299i	0.0614087	−	0.348266i	0.999995	−	0.00322103i	$-0.00102529\pi$
$968$	−29.0075			−0.932335
$969$	−9.17528	+	5.19428i	−0.294753	+	0.166864i
$970$		0			0
$971$	5.62086	−	31.8775i	0.180382	−	1.02300i	−0.751365	−	0.659887i	$-0.770604\pi$
$971$	5.62086	−	31.8775i	0.180382	−	1.02300i	0.931746	−	0.363109i	$-0.118285\pi$
$972$	6.14909	+	5.15970i	0.197232	+	0.165497i
$973$	66.3713	+	24.1572i	2.12777	+	0.774444i
$974$	−38.3644	+	13.9635i	−1.22927	+	0.447419i
$975$		0			0
$976$	8.72836	+	15.1180i	0.279388	+	0.483914i
$977$	5.55189	−	9.61615i	0.177621	−	0.307648i	−0.763445	−	0.645873i	$-0.776493\pi$
$977$	5.55189	−	9.61615i	0.177621	−	0.307648i	0.941065	+	0.338226i	$0.109827\pi$
$978$	−1.67179	−	9.48122i	−0.0534581	−	0.303176i
$979$	−0.579780	−	3.28810i	−0.0185298	−	0.105088i
$980$		0			0
$981$	−1.86794	−	3.23536i	−0.0596387	−	0.103297i
$982$	16.4125	−	13.7718i	0.523745	−	0.439474i
$983$	−11.7764	+	4.28627i	−0.375610	+	0.136711i	−0.522925	−	0.852379i	$-0.675159\pi$
$983$	−11.7764	+	4.28627i	−0.375610	+	0.136711i	0.147315	+	0.989090i	$0.452937\pi$
$984$	12.3429	+	4.49246i	0.393478	+	0.143214i
$985$		0			0
$986$	2.73465	−	15.5090i	0.0870889	−	0.493906i
$987$	−22.2766			−0.709072
$988$	7.54333	−	1.26434i	0.239985	−	0.0402240i
$989$	−56.0984			−1.78383
$990$		0			0
$991$	28.1596	+	23.6287i	0.894519	+	0.750591i	0.969111	−	0.246623i	$-0.0793211\pi$
$991$	28.1596	+	23.6287i	0.894519	+	0.750591i	−0.0745922	+	0.997214i	$0.523766\pi$
$992$	13.4024	+	4.87807i	0.425527	+	0.154879i
$993$	−9.05577	+	3.29603i	−0.287376	+	0.104596i
$994$	−48.5394	+	40.7294i	−1.53958	+	1.29186i
$995$		0			0
$996$	0.514724	−	0.891528i	0.0163097	−	0.0282491i
$997$	4.25092	+	24.1082i	0.134628	+	0.763513i	0.975118	+	0.221686i	$0.0711560\pi$
$997$	4.25092	+	24.1082i	0.134628	+	0.763513i	−0.840490	+	0.541827i	$0.817733\pi$
$998$	−6.93291	−	39.3185i	−0.219458	−	1.24461i
$999$	−19.6586	+	34.0498i	−0.621972	+	1.07729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.226.3		48
5.2	odd	4		95.2.p.a.74.3	yes	48
5.3	odd	4		95.2.p.a.74.6	yes	48
5.4	even	2	inner	475.2.l.f.226.6		48
15.2	even	4		855.2.da.b.739.6		48
15.8	even	4		855.2.da.b.739.3		48
19.3	odd	18		9025.2.a.ct.1.17		24
19.9	even	9	inner	475.2.l.f.351.3		48
19.16	even	9		9025.2.a.cu.1.8		24
95.3	even	36		1805.2.b.l.1084.8		24
95.9	even	18	inner	475.2.l.f.351.6		48
95.22	even	36		1805.2.b.l.1084.17		24
95.28	odd	36		95.2.p.a.9.3	✓	48
95.47	odd	36		95.2.p.a.9.6	yes	48
95.54	even	18		9025.2.a.cu.1.17		24
95.73	odd	36		1805.2.b.k.1084.17		24
95.79	odd	18		9025.2.a.ct.1.8		24
95.92	odd	36		1805.2.b.k.1084.8		24
285.47	even	36		855.2.da.b.199.3		48
285.218	even	36		855.2.da.b.199.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.3	✓	48	95.28	odd	36
95.2.p.a.9.6	yes	48	95.47	odd	36
95.2.p.a.74.3	yes	48	5.2	odd	4
95.2.p.a.74.6	yes	48	5.3	odd	4
475.2.l.f.226.3		48	1.1	even	1	trivial
475.2.l.f.226.6		48	5.4	even	2	inner
475.2.l.f.351.3		48	19.9	even	9	inner
475.2.l.f.351.6		48	95.9	even	18	inner
855.2.da.b.199.3		48	285.47	even	36
855.2.da.b.199.6		48	285.218	even	36
855.2.da.b.739.3		48	15.8	even	4
855.2.da.b.739.6		48	15.2	even	4
1805.2.b.k.1084.8		24	95.92	odd	36
1805.2.b.k.1084.17		24	95.73	odd	36
1805.2.b.l.1084.8		24	95.3	even	36
1805.2.b.l.1084.17		24	95.22	even	36
9025.2.a.ct.1.8		24	95.79	odd	18
9025.2.a.ct.1.17		24	19.3	odd	18
9025.2.a.cu.1.8		24	19.16	even	9
9025.2.a.cu.1.17		24	95.54	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212126 + 1.20303i) q^{2} +(-0.616222 - 0.517072i) q^{3} +(0.477108 + 0.173653i) q^{4} +(0.752768 - 0.631647i) q^{6} +(-1.89590 - 3.28379i) q^{7} +(-1.53170 + 2.65299i) q^{8} +(-0.408578 - 2.31716i) q^{9} +O(q^{10})\)	\(q+(-0.212126 + 1.20303i) q^{2} +(-0.616222 - 0.517072i) q^{3} +(0.477108 + 0.173653i) q^{4} +(0.752768 - 0.631647i) q^{6} +(-1.89590 - 3.28379i) q^{7} +(-1.53170 + 2.65299i) q^{8} +(-0.408578 - 2.31716i) q^{9} +(0.618663 - 1.07156i) q^{11} +(-0.204213 - 0.353708i) q^{12} +(2.64744 - 2.22146i) q^{13} +(4.35266 - 1.58424i) q^{14} +(-2.08882 - 1.75273i) q^{16} +(0.522152 - 2.96127i) q^{17} +2.87428 q^{18} +(4.28612 + 0.793231i) q^{19} +(-0.529662 + 3.00386i) q^{21} +(1.15788 + 0.971573i) q^{22} +(-5.77705 - 2.10267i) q^{23} +(2.31565 - 0.842829i) q^{24} +(2.11089 + 3.65617i) q^{26} +(-2.15299 + 3.72910i) q^{27} +(-0.334308 - 1.89595i) q^{28} +(-0.744476 - 4.22213i) q^{29} +(-2.55067 - 4.41789i) q^{31} +(-2.14174 + 1.79713i) q^{32} +(-0.935304 + 0.340423i) q^{33} +(3.45173 + 1.25633i) q^{34} +(0.207446 - 1.17649i) q^{36} +9.13084 q^{37} +(-1.86348 + 4.98805i) q^{38} -2.78006 q^{39} +(4.08318 + 3.42620i) q^{41} +(-3.50137 - 1.27440i) q^{42} +(8.57465 - 3.12092i) q^{43} +(0.481248 - 0.403815i) q^{44} +(3.75504 - 6.50391i) q^{46} +(1.26821 + 7.19237i) q^{47} +(0.380890 + 2.16014i) q^{48} +(-3.68887 + 6.38931i) q^{49} +(-1.85295 + 1.55481i) q^{51} +(1.64888 - 0.600142i) q^{52} +(3.13139 + 1.13973i) q^{53} +(-4.02950 - 3.38115i) q^{54} +11.6158 q^{56} +(-2.23104 - 2.70503i) q^{57} +5.23727 q^{58} +(-0.141926 + 0.804901i) q^{59} +(-6.01592 - 2.18962i) q^{61} +(5.85590 - 2.13137i) q^{62} +(-6.83446 + 5.73479i) q^{63} +(-4.43444 - 7.68067i) q^{64} +(-0.211136 - 1.19741i) q^{66} +(-0.175545 - 0.995566i) q^{67} +(0.763357 - 1.32217i) q^{68} +(2.47271 + 4.28286i) q^{69} +(-12.8546 + 4.67867i) q^{71} +(6.77322 + 2.46525i) q^{72} +(-8.47451 - 7.11096i) q^{73} +(-1.93689 + 10.9846i) q^{74} +(1.90719 + 1.12275i) q^{76} -4.69169 q^{77} +(0.589724 - 3.34449i) q^{78} +(-1.06036 - 0.889746i) q^{79} +(-3.37810 + 1.22953i) q^{81} +(-4.98796 + 4.18539i) q^{82} +(1.26026 + 2.18283i) q^{83} +(-0.774336 + 1.34119i) q^{84} +(1.93564 + 10.9776i) q^{86} +(-1.72438 + 2.98672i) q^{87} +(1.89521 + 3.28261i) q^{88} +(2.06711 - 1.73451i) q^{89} +(-12.3141 - 4.48197i) q^{91} +(-2.39114 - 2.00640i) q^{92} +(-0.712586 + 4.04128i) q^{93} -8.92164 q^{94} +2.24903 q^{96} +(0.531802 - 3.01600i) q^{97} +(-6.90401 - 5.79315i) q^{98} +(-2.73574 - 0.995727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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