LMFDB - Embedded newform 128.3.h.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, degree $4$, not 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	128.47
Dual form			128.3.h.a.79.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73217 - 4.18183i) q^{3} +(-1.85856 - 4.48696i) q^{5} +(5.27676 + 5.27676i) q^{7} +(-8.12333 - 8.12333i) q^{9} +O(q^{10})$	\(q+(1.73217 - 4.18183i) q^{3} +(-1.85856 - 4.48696i) q^{5} +(5.27676 + 5.27676i) q^{7} +(-8.12333 - 8.12333i) q^{9} +(-6.20050 - 14.9693i) q^{11} +(-4.22532 + 10.2008i) q^{13} -21.9830 q^{15} -2.84356i q^{17} +(12.4276 + 5.14768i) q^{19} +(31.2068 - 12.9263i) q^{21} +(1.43918 - 1.43918i) q^{23} +(0.999126 - 0.999126i) q^{25} +(-10.4049 + 4.30987i) q^{27} +(36.9596 + 15.3092i) q^{29} +4.73823i q^{31} -73.3396 q^{33} +(13.8694 - 33.4838i) q^{35} +(-6.68390 - 16.1364i) q^{37} +(35.3392 + 35.3392i) q^{39} +(40.4523 + 40.4523i) q^{41} +(24.5000 + 59.1482i) q^{43} +(-21.3514 + 51.5467i) q^{45} +16.5262 q^{47} +6.68842i q^{49} +(-11.8913 - 4.92553i) q^{51} +(-46.9950 + 19.4659i) q^{53} +(-55.6428 + 55.6428i) q^{55} +(43.0535 - 43.0535i) q^{57} +(-50.0578 + 20.7346i) q^{59} +(-54.3116 - 22.4966i) q^{61} -85.7298i q^{63} +53.6237 q^{65} +(25.5017 - 61.5665i) q^{67} +(-3.52550 - 8.51131i) q^{69} +(-7.12641 - 7.12641i) q^{71} +(55.3669 + 55.3669i) q^{73} +(-2.44752 - 5.90883i) q^{75} +(46.2711 - 111.708i) q^{77} -11.0986 q^{79} -52.4160i q^{81} +(29.9476 + 12.4047i) q^{83} +(-12.7589 + 5.28492i) q^{85} +(128.041 - 128.041i) q^{87} +(16.7667 - 16.7667i) q^{89} +(-76.1234 + 31.5313i) q^{91} +(19.8145 + 8.20743i) q^{93} -65.3294i q^{95} -67.8301 q^{97} +(-71.2322 + 171.970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.73217	−	4.18183i	0.577390	−	1.39394i	−0.317756	−	0.948172i	$-0.602929\pi$
$3$	1.73217	−	4.18183i	0.577390	−	1.39394i	0.895147	−	0.445771i	$-0.147071\pi$
$4$		0			0
$5$	−1.85856	−	4.48696i	−0.371712	−	0.897391i	−0.993461	−	0.114175i	$-0.963578\pi$
$5$	−1.85856	−	4.48696i	−0.371712	−	0.897391i	0.621749	−	0.783217i	$-0.286422\pi$
$6$		0			0
$7$	5.27676	+	5.27676i	0.753823	+	0.753823i	0.975190	−	0.221367i	$-0.0710520\pi$
$7$	5.27676	+	5.27676i	0.753823	+	0.753823i	−0.221367	+	0.975190i	$0.571052\pi$
$8$		0			0
$9$	−8.12333	−	8.12333i	−0.902593	−	0.902593i
$10$		0			0
$11$	−6.20050	−	14.9693i	−0.563682	−	1.36085i	−0.906802	−	0.421557i	$-0.861484\pi$
$11$	−6.20050	−	14.9693i	−0.563682	−	1.36085i	0.343120	−	0.939292i	$-0.388516\pi$
$12$		0			0
$13$	−4.22532	+	10.2008i	−0.325025	+	0.784680i	0.673922	+	0.738802i	$0.264608\pi$
$13$	−4.22532	+	10.2008i	−0.325025	+	0.784680i	−0.998947	+	0.0458772i	$0.985392\pi$
$14$		0			0
$15$	−21.9830			−1.46554
$16$		0			0
$17$		−	2.84356i		−	0.167268i	−0.996497	−	0.0836341i	$-0.973347\pi$
$17$		−	2.84356i		−	0.167268i	0.996497	−	0.0836341i	$-0.0266527\pi$
$18$		0			0
$19$	12.4276	+	5.14768i	0.654084	+	0.270931i	0.684947	−	0.728593i	$-0.259825\pi$
$19$	12.4276	+	5.14768i	0.654084	+	0.270931i	−0.0308626	+	0.999524i	$0.509825\pi$
$20$		0			0
$21$	31.2068	−	12.9263i	1.48604	−	0.615537i
$22$		0			0
$23$	1.43918	−	1.43918i	0.0625730	−	0.0625730i	−0.675128	−	0.737701i	$-0.735912\pi$
$23$	1.43918	−	1.43918i	0.0625730	−	0.0625730i	0.737701	+	0.675128i	$0.235912\pi$
$24$		0			0
$25$	0.999126	−	0.999126i	0.0399650	−	0.0399650i
$26$		0			0
$27$	−10.4049	+	4.30987i	−0.385368	+	0.159625i
$28$		0			0
$29$	36.9596	+	15.3092i	1.27447	+	0.527902i	0.914320	−	0.404993i	$-0.132726\pi$
$29$	36.9596	+	15.3092i	1.27447	+	0.527902i	0.360148	+	0.932895i	$0.382726\pi$
$30$		0			0
$31$			4.73823i			0.152846i	0.997075	+	0.0764231i	$0.0243500\pi$
$31$			4.73823i			0.152846i	−0.997075	+	0.0764231i	$0.975650\pi$
$32$		0			0
$33$	−73.3396			−2.22241
$34$		0			0
$35$	13.8694	−	33.4838i	0.396269	−	0.956679i
$36$		0			0
$37$	−6.68390	−	16.1364i	−0.180646	−	0.436118i	0.807454	−	0.589930i	$-0.200845\pi$
$37$	−6.68390	−	16.1364i	−0.180646	−	0.436118i	−0.988100	+	0.153812i	$0.950845\pi$
$38$		0			0
$39$	35.3392	+	35.3392i	0.906133	+	0.906133i
$40$		0			0
$41$	40.4523	+	40.4523i	0.986641	+	0.986641i	0.999912	−	0.0132711i	$-0.00422444\pi$
$41$	40.4523	+	40.4523i	0.986641	+	0.986641i	−0.0132711	+	0.999912i	$0.504224\pi$
$42$		0			0
$43$	24.5000	+	59.1482i	0.569767	+	1.37554i	0.901751	+	0.432255i	$0.142282\pi$
$43$	24.5000	+	59.1482i	0.569767	+	1.37554i	−0.331984	+	0.943285i	$0.607718\pi$
$44$		0			0
$45$	−21.3514	+	51.5467i	−0.474475	+	1.14548i
$46$		0			0
$47$	16.5262			0.351622			0.175811	−	0.984424i	$-0.443745\pi$
$47$	16.5262			0.351622			0.175811	+	0.984424i	$0.443745\pi$
$48$		0			0
$49$			6.68842i			0.136498i
$50$		0			0
$51$	−11.8913	−	4.92553i	−0.233162	−	0.0965790i
$52$		0			0
$53$	−46.9950	+	19.4659i	−0.886697	+	0.367282i	−0.779090	−	0.626912i	$-0.784319\pi$
$53$	−46.9950	+	19.4659i	−0.886697	+	0.367282i	−0.107607	+	0.994194i	$0.534319\pi$
$54$		0			0
$55$	−55.6428	+	55.6428i	−1.01169	+	1.01169i
$56$		0			0
$57$	43.0535	−	43.0535i	0.755324	−	0.755324i
$58$		0			0
$59$	−50.0578	+	20.7346i	−0.848437	+	0.351434i	−0.764174	−	0.645010i	$-0.776853\pi$
$59$	−50.0578	+	20.7346i	−0.848437	+	0.351434i	−0.0842623	+	0.996444i	$0.526853\pi$
$60$		0			0
$61$	−54.3116	−	22.4966i	−0.890353	−	0.368796i	−0.109850	−	0.993948i	$-0.535037\pi$
$61$	−54.3116	−	22.4966i	−0.890353	−	0.368796i	−0.780503	+	0.625152i	$0.785037\pi$
$62$		0			0
$63$		−	85.7298i		−	1.36079i
$64$		0			0
$65$	53.6237			0.824980
$66$		0			0
$67$	25.5017	−	61.5665i	0.380622	−	0.918904i	−0.611223	−	0.791458i	$-0.709322\pi$
$67$	25.5017	−	61.5665i	0.380622	−	0.918904i	0.991846	−	0.127445i	$-0.0406778\pi$
$68$		0			0
$69$	−3.52550	−	8.51131i	−0.0510942	−	0.123352i
$70$		0			0
$71$	−7.12641	−	7.12641i	−0.100372	−	0.100372i	0.655138	−	0.755510i	$-0.272611\pi$
$71$	−7.12641	−	7.12641i	−0.100372	−	0.100372i	−0.755510	+	0.655138i	$0.772611\pi$
$72$		0			0
$73$	55.3669	+	55.3669i	0.758451	+	0.758451i	0.976040	−	0.217590i	$-0.0698194\pi$
$73$	55.3669	+	55.3669i	0.758451	+	0.758451i	−0.217590	+	0.976040i	$0.569819\pi$
$74$		0			0
$75$	−2.44752	−	5.90883i	−0.0326336	−	0.0787844i
$76$		0			0
$77$	46.2711	−	111.708i	0.600923	−	1.45076i
$78$		0			0
$79$	−11.0986			−0.140489			−0.0702446	−	0.997530i	$-0.522378\pi$
$79$	−11.0986			−0.140489			−0.0702446	+	0.997530i	$0.522378\pi$
$80$		0			0
$81$		−	52.4160i		−	0.647112i
$82$		0			0
$83$	29.9476	+	12.4047i	0.360814	+	0.149454i	0.555724	−	0.831367i	$-0.312441\pi$
$83$	29.9476	+	12.4047i	0.360814	+	0.149454i	−0.194909	+	0.980821i	$0.562441\pi$
$84$		0			0
$85$	−12.7589	+	5.28492i	−0.150105	+	0.0621755i
$86$		0			0
$87$	128.041	−	128.041i	1.47173	−	1.47173i
$88$		0			0
$89$	16.7667	−	16.7667i	0.188390	−	0.188390i	−0.606610	−	0.795000i	$-0.707471\pi$
$89$	16.7667	−	16.7667i	0.188390	−	0.188390i	0.795000	+	0.606610i	$0.207471\pi$
$90$		0			0
$91$	−76.1234	+	31.5313i	−0.836521	+	0.346498i
$92$		0			0
$93$	19.8145	+	8.20743i	0.213059	+	0.0882520i
$94$		0			0
$95$		−	65.3294i		−	0.687678i
$96$		0			0
$97$	−67.8301			−0.699280			−0.349640	−	0.936884i	$-0.613696\pi$
$97$	−67.8301			−0.699280			−0.349640	+	0.936884i	$0.613696\pi$
$98$		0			0
$99$	−71.2322	+	171.970i	−0.719517	+	1.73707i
$100$		0			0
$101$	−45.6943	−	110.316i	−0.452419	−	1.09224i	−0.971400	−	0.237450i	$-0.923689\pi$
$101$	−45.6943	−	110.316i	−0.452419	−	1.09224i	0.518981	−	0.854786i	$-0.326311\pi$
$102$		0			0
$103$	−61.7093	−	61.7093i	−0.599120	−	0.599120i	0.340959	−	0.940078i	$-0.389248\pi$
$103$	−61.7093	−	61.7093i	−0.599120	−	0.599120i	−0.940078	+	0.340959i	$0.889248\pi$
$104$		0			0
$105$	−115.999	−	115.999i	−1.10475	−	1.10475i
$106$		0			0
$107$	−7.13652	−	17.2291i	−0.0666965	−	0.161020i	0.887017	−	0.461737i	$-0.152774\pi$
$107$	−7.13652	−	17.2291i	−0.0666965	−	0.161020i	−0.953713	+	0.300718i	$0.902774\pi$
$108$		0			0
$109$	−75.1681	+	181.472i	−0.689616	+	1.66488i	0.0559384	+	0.998434i	$0.482185\pi$
$109$	−75.1681	+	181.472i	−0.689616	+	1.66488i	−0.745554	+	0.666445i	$0.767815\pi$
$110$		0			0
$111$	−79.0572			−0.712227
$112$		0			0
$113$			156.784i			1.38747i	0.720232	+	0.693734i	$0.244035\pi$
$113$			156.784i			1.38747i	−0.720232	+	0.693734i	$0.755965\pi$
$114$		0			0
$115$	−9.13234	−	3.78274i	−0.0794116	−	0.0328934i
$116$		0			0
$117$	117.189	−	48.5411i	1.00161	−	0.414881i
$118$		0			0
$119$	15.0048	−	15.0048i	0.126091	−	0.126091i
$120$		0			0
$121$	−100.075	+	100.075i	−0.827066	+	0.827066i
$122$		0			0
$123$	239.235	−	99.0943i	1.94500	−	0.805645i
$124$		0			0
$125$	−118.514	−	49.0901i	−0.948111	−	0.392720i
$126$		0			0
$127$			192.971i			1.51946i	0.650240	+	0.759729i	$0.274668\pi$
$127$			192.971i			1.51946i	−0.650240	+	0.759729i	$0.725332\pi$
$128$		0			0
$129$	289.786			2.24640
$130$		0			0
$131$	−18.2599	+	44.0834i	−0.139389	+	0.336515i	−0.978123	−	0.208026i	$-0.933296\pi$
$131$	−18.2599	+	44.0834i	−0.139389	+	0.336515i	0.838734	+	0.544541i	$0.183296\pi$
$132$		0			0
$133$	38.4144	+	92.7406i	0.288830	+	0.697297i
$134$		0			0
$135$	38.6764	+	38.6764i	0.286492	+	0.286492i
$136$		0			0
$137$	−27.8671	−	27.8671i	−0.203409	−	0.203409i	0.598050	−	0.801459i	$-0.295943\pi$
$137$	−27.8671	−	27.8671i	−0.203409	−	0.203409i	−0.801459	+	0.598050i	$0.795943\pi$
$138$		0			0
$139$	−33.3447	−	80.5013i	−0.239890	−	0.579146i	0.757381	−	0.652973i	$-0.226479\pi$
$139$	−33.3447	−	80.5013i	−0.239890	−	0.579146i	−0.997271	+	0.0738274i	$0.976479\pi$
$140$		0			0
$141$	28.6263	−	69.1099i	0.203023	−	0.490141i
$142$		0			0
$143$	178.899			1.25104
$144$		0			0
$145$		−	194.289i		−	1.33992i
$146$		0			0
$147$	27.9698	+	11.5855i	0.190271	+	0.0788128i
$148$		0			0
$149$	−125.860	+	52.1327i	−0.844695	+	0.349884i	−0.762703	−	0.646749i	$-0.776128\pi$
$149$	−125.860	+	52.1327i	−0.844695	+	0.349884i	−0.0819919	+	0.996633i	$0.526128\pi$
$150$		0			0
$151$	−106.254	+	106.254i	−0.703672	+	0.703672i	−0.965197	−	0.261525i	$-0.915775\pi$
$151$	−106.254	+	106.254i	−0.703672	+	0.703672i	0.261525	+	0.965197i	$0.415775\pi$
$152$		0			0
$153$	−23.0992	+	23.0992i	−0.150975	+	0.150975i
$154$		0			0
$155$	21.2603	−	8.80629i	0.137163	−	0.0568147i
$156$		0			0
$157$	209.345	+	86.7136i	1.33341	+	0.552316i	0.931626	−	0.363419i	$-0.118391\pi$
$157$	209.345	+	86.7136i	1.33341	+	0.552316i	0.401783	+	0.915735i	$0.368391\pi$
$158$		0			0
$159$			230.243i			1.44807i
$160$		0			0
$161$	15.1884			0.0943380
$162$		0			0
$163$	0.176018	−	0.424946i	0.00107987	−	0.00260703i	−0.923339	−	0.383987i	$-0.874551\pi$
$163$	0.176018	−	0.424946i	0.00107987	−	0.00260703i	0.924419	+	0.381380i	$0.124551\pi$
$164$		0			0
$165$	136.306	+	329.072i	0.826096	+	1.99437i
$166$		0			0
$167$	−96.7499	−	96.7499i	−0.579341	−	0.579341i	0.355381	−	0.934722i	$-0.384351\pi$
$167$	−96.7499	−	96.7499i	−0.579341	−	0.579341i	−0.934722	+	0.355381i	$0.884351\pi$
$168$		0			0
$169$	33.2974	+	33.2974i	0.197026	+	0.197026i
$170$		0			0
$171$	−59.1372	−	142.770i	−0.345832	−	0.834912i
$172$		0			0
$173$	102.242	−	246.834i	0.590994	−	1.42678i	−0.291551	−	0.956555i	$-0.594171\pi$
$173$	102.242	−	246.834i	0.590994	−	1.42678i	0.882544	−	0.470229i	$-0.155829\pi$
$174$		0			0
$175$	10.5443			0.0602531
$176$		0			0
$177$			245.249i			1.38559i
$178$		0			0
$179$	−269.771	−	111.743i	−1.50710	−	0.624262i	−0.532144	−	0.846654i	$-0.678613\pi$
$179$	−269.771	−	111.743i	−1.50710	−	0.624262i	−0.974957	+	0.222393i	$0.928613\pi$
$180$		0			0
$181$	−33.2079	+	13.7552i	−0.183469	+	0.0759954i	−0.472527	−	0.881316i	$-0.656658\pi$
$181$	−33.2079	+	13.7552i	−0.183469	+	0.0759954i	0.289058	+	0.957312i	$0.406658\pi$
$182$		0			0
$183$	−188.154	+	188.154i	−1.02816	+	1.02816i
$184$		0			0
$185$	−59.9808	+	59.9808i	−0.324220	+	0.324220i
$186$		0			0
$187$	−42.5662	+	17.6315i	−0.227627	+	0.0942861i
$188$		0			0
$189$	−77.6465	−	32.1622i	−0.410828	−	0.170171i
$190$		0			0
$191$			47.7299i			0.249895i	0.992163	+	0.124947i	$0.0398762\pi$
$191$			47.7299i			0.249895i	−0.992163	+	0.124947i	$0.960124\pi$
$192$		0			0
$193$	−302.171			−1.56565			−0.782827	−	0.622240i	$-0.786223\pi$
$193$	−302.171			−1.56565			−0.782827	+	0.622240i	$0.786223\pi$
$194$		0			0
$195$	92.8855	−	224.245i	0.476336	−	1.14998i
$196$		0			0
$197$	18.2996	+	44.1791i	0.0928913	+	0.224259i	0.963495	−	0.267725i	$-0.0862718\pi$
$197$	18.2996	+	44.1791i	0.0928913	+	0.224259i	−0.870604	+	0.491984i	$0.836272\pi$
$198$		0			0
$199$	94.2590	+	94.2590i	0.473663	+	0.473663i	0.903098	−	0.429435i	$-0.141287\pi$
$199$	94.2590	+	94.2590i	0.473663	+	0.473663i	−0.429435	+	0.903098i	$0.641287\pi$
$200$		0			0
$201$	−213.288	−	213.288i	−1.06113	−	1.06113i
$202$		0			0
$203$	114.244	+	275.810i	0.562779	+	1.35867i
$204$		0			0
$205$	106.325	−	256.691i	0.518657	−	1.25215i
$206$		0			0
$207$	−23.3819			−0.112956
$208$		0			0
$209$		−	217.951i		−	1.04283i
$210$		0			0
$211$	267.734	+	110.899i	1.26888	+	0.525589i	0.912625	−	0.408799i	$-0.134052\pi$
$211$	267.734	+	110.899i	1.26888	+	0.525589i	0.356259	+	0.934387i	$0.384052\pi$
$212$		0			0
$213$	−42.1456	+	17.4573i	−0.197867	+	0.0819591i
$214$		0			0
$215$	219.861	−	219.861i	1.02261	−	1.02261i
$216$		0			0
$217$	−25.0025	+	25.0025i	−0.115219	+	0.115219i
$218$		0			0
$219$	327.440	−	135.630i	1.49516	−	0.619316i
$220$		0			0
$221$	29.0067	+	12.0150i	0.131252	+	0.0543663i
$222$		0			0
$223$		−	408.363i		−	1.83123i	−0.402061	−	0.915613i	$-0.631706\pi$
$223$		−	408.363i		−	1.83123i	0.402061	−	0.915613i	$-0.368294\pi$
$224$		0			0
$225$	−16.2325			−0.0721443
$226$		0			0
$227$	−82.5132	+	199.204i	−0.363494	+	0.877553i	0.631290	+	0.775547i	$0.282526\pi$
$227$	−82.5132	+	199.204i	−0.363494	+	0.877553i	−0.994784	+	0.102005i	$0.967474\pi$
$228$		0			0
$229$	22.6069	+	54.5778i	0.0987200	+	0.238331i	0.965522	−	0.260321i	$-0.0838284\pi$
$229$	22.6069	+	54.5778i	0.0987200	+	0.238331i	−0.866802	+	0.498652i	$0.833828\pi$
$230$		0			0
$231$	−386.995	−	386.995i	−1.67531	−	1.67531i
$232$		0			0
$233$	58.2826	+	58.2826i	0.250140	+	0.250140i	0.821028	−	0.570888i	$-0.193401\pi$
$233$	58.2826	+	58.2826i	0.250140	+	0.250140i	−0.570888	+	0.821028i	$0.693401\pi$
$234$		0			0
$235$	−30.7150	−	74.1525i	−0.130702	−	0.315543i
$236$		0			0
$237$	−19.2248	+	46.4127i	−0.0811171	+	0.195834i
$238$		0			0
$239$	367.366			1.53710			0.768548	−	0.639792i	$-0.220979\pi$
$239$	367.366			1.53710			0.768548	+	0.639792i	$0.220979\pi$
$240$		0			0
$241$		−	312.345i		−	1.29604i	−0.761624	−	0.648020i	$-0.775597\pi$
$241$		−	312.345i		−	1.29604i	0.761624	−	0.648020i	$-0.224403\pi$
$242$		0			0
$243$	−312.839	−	129.582i	−1.28741	−	0.533261i
$244$		0			0
$245$	30.0106	−	12.4308i	0.122492	−	0.0507380i
$246$		0			0
$247$	−105.021	+	105.021i	−0.425187	+	0.425187i
$248$		0			0
$249$	103.749	−	103.749i	0.416661	−	0.416661i
$250$		0			0
$251$	−223.120	+	92.4192i	−0.888923	+	0.368204i	−0.779951	−	0.625841i	$-0.784756\pi$
$251$	−223.120	+	92.4192i	−0.888923	+	0.368204i	−0.108972	+	0.994045i	$0.534756\pi$
$252$		0			0
$253$	−30.4672	−	12.6199i	−0.120424	−	0.0498811i
$254$		0			0
$255$			62.5101i			0.245138i
$256$		0			0
$257$	178.176			0.693293			0.346646	−	0.937996i	$-0.387320\pi$
$257$	178.176			0.693293			0.346646	+	0.937996i	$0.387320\pi$
$258$		0			0
$259$	49.8784	−	120.417i	0.192581	−	0.464931i
$260$		0			0
$261$	−175.874	−	424.596i	−0.673845	−	1.62681i
$262$		0			0
$263$	147.164	+	147.164i	0.559558	+	0.559558i	0.929182	−	0.369623i	$-0.120513\pi$
$263$	147.164	+	147.164i	0.559558	+	0.559558i	−0.369623	+	0.929182i	$0.620513\pi$
$264$		0			0
$265$	174.686	+	174.686i	0.659191	+	0.659191i
$266$		0			0
$267$	−41.0728	−	99.1585i	−0.153831	−	0.371380i
$268$		0			0
$269$	−138.119	+	333.450i	−0.513455	+	1.23959i	0.428405	+	0.903587i	$0.359076\pi$
$269$	−138.119	+	333.450i	−0.513455	+	1.23959i	−0.941861	+	0.336004i	$0.890924\pi$
$270$		0			0
$271$	−218.643			−0.806801			−0.403400	−	0.915024i	$-0.632172\pi$
$271$	−218.643			−0.806801			−0.403400	+	0.915024i	$0.632172\pi$
$272$		0			0
$273$			372.953i			1.36613i
$274$		0			0
$275$	−21.1513	−	8.76117i	−0.0769139	−	0.0318588i
$276$		0			0
$277$	256.038	−	106.054i	0.924323	−	0.382867i	0.130801	−	0.991409i	$-0.458245\pi$
$277$	256.038	−	106.054i	0.924323	−	0.382867i	0.793522	+	0.608541i	$0.208245\pi$
$278$		0			0
$279$	38.4903	−	38.4903i	0.137958	−	0.137958i
$280$		0			0
$281$	−49.4126	+	49.4126i	−0.175845	+	0.175845i	−0.789542	−	0.613697i	$-0.789682\pi$
$281$	−49.4126	+	49.4126i	−0.175845	+	0.175845i	0.613697	+	0.789542i	$0.289682\pi$
$282$		0			0
$283$	−118.290	+	48.9975i	−0.417987	+	0.173136i	−0.581757	−	0.813363i	$-0.697635\pi$
$283$	−118.290	+	48.9975i	−0.417987	+	0.173136i	0.163770	+	0.986499i	$0.447635\pi$
$284$		0			0
$285$	−273.196	−	113.162i	−0.958584	−	0.397058i
$286$		0			0
$287$			426.914i			1.48751i
$288$		0			0
$289$	280.914			0.972021
$290$		0			0
$291$	−117.493	+	283.654i	−0.403757	+	0.974757i
$292$		0			0
$293$	−100.203	−	241.910i	−0.341988	−	0.825633i	−0.997515	−	0.0704605i	$-0.977553\pi$
$293$	−100.203	−	241.910i	−0.341988	−	0.825633i	0.655526	−	0.755172i	$-0.272447\pi$
$294$		0			0
$295$	186.071	+	186.071i	0.630748	+	0.630748i
$296$		0			0
$297$	129.032	+	129.032i	0.434450	+	0.434450i
$298$		0			0
$299$	8.59983	+	20.7618i	0.0287620	+	0.0694376i
$300$		0			0
$301$	−182.830	+	441.392i	−0.607410	+	1.46642i
$302$		0			0
$303$	−540.472			−1.78374
$304$		0			0
$305$			285.505i			0.936081i
$306$		0			0
$307$	371.163	+	153.741i	1.20900	+	0.500784i	0.893896	−	0.448274i	$-0.147961\pi$
$307$	371.163	+	153.741i	1.20900	+	0.500784i	0.315103	+	0.949058i	$0.397961\pi$
$308$		0			0
$309$	−364.949	+	151.167i	−1.18107	+	0.489213i
$310$		0			0
$311$	312.733	−	312.733i	1.00557	−	1.00557i	0.00558671	−	0.999984i	$-0.498222\pi$
$311$	312.733	−	312.733i	1.00557	−	1.00557i	0.999984	−	0.00558671i	$-0.00177831\pi$
$312$		0			0
$313$	358.245	−	358.245i	1.14455	−	1.14455i	0.156946	−	0.987607i	$-0.449835\pi$
$313$	358.245	−	358.245i	1.14455	−	1.14455i	0.987607	−	0.156946i	$-0.0501649\pi$
$314$		0			0
$315$	−384.666	+	159.334i	−1.22116	+	0.505822i
$316$		0			0
$317$	164.720	+	68.2292i	0.519621	+	0.215234i	0.627051	−	0.778979i	$-0.284262\pi$
$317$	164.720	+	68.2292i	0.519621	+	0.215234i	−0.107429	+	0.994213i	$0.534262\pi$
$318$		0			0
$319$		−	648.185i		−	2.03193i
$320$		0			0
$321$	−84.4108			−0.262962
$322$		0			0
$323$	14.6377	−	35.3386i	0.0453181	−	0.109407i
$324$		0			0
$325$	5.97029	+	14.4135i	0.0183701	+	0.0443494i
$326$		0			0
$327$	628.681	+	628.681i	1.92257	+	1.92257i
$328$		0			0
$329$	87.2050	+	87.2050i	0.265061	+	0.265061i
$330$		0			0
$331$	−21.3130	−	51.4542i	−0.0643898	−	0.155451i	0.888409	−	0.459052i	$-0.151811\pi$
$331$	−21.3130	−	51.4542i	−0.0643898	−	0.155451i	−0.952799	+	0.303601i	$0.901811\pi$
$332$		0			0
$333$	−76.7855	+	185.377i	−0.230587	+	0.556687i
$334$		0			0
$335$	−323.643			−0.966098
$336$		0			0
$337$			173.028i			0.513437i	0.966486	+	0.256718i	$0.0826413\pi$
$337$			173.028i			0.513437i	−0.966486	+	0.256718i	$0.917359\pi$
$338$		0			0
$339$	655.643	+	271.576i	1.93405	+	0.801110i
$340$		0			0
$341$	70.9282	−	29.3794i	0.208001	−	0.0861567i
$342$		0			0
$343$	223.268	−	223.268i	0.650927	−	0.650927i
$344$		0			0
$345$	−31.6375	+	31.6375i	−0.0917030	+	0.0917030i
$346$		0			0
$347$	−48.9563	+	20.2784i	−0.141085	+	0.0584391i	−0.452109	−	0.891963i	$-0.649328\pi$
$347$	−48.9563	+	20.2784i	−0.141085	+	0.0584391i	0.311024	+	0.950402i	$0.399328\pi$
$348$		0			0
$349$	−222.227	−	92.0495i	−0.636754	−	0.263752i	0.0408656	−	0.999165i	$-0.486988\pi$
$349$	−222.227	−	92.0495i	−0.636754	−	0.263752i	−0.677620	+	0.735412i	$0.736988\pi$
$350$		0			0
$351$		−	124.350i		−	0.354273i
$352$		0			0
$353$	−75.1997			−0.213030			−0.106515	−	0.994311i	$-0.533969\pi$
$353$	−75.1997			−0.213030			−0.106515	+	0.994311i	$0.533969\pi$
$354$		0			0
$355$	−18.7310	+	45.2208i	−0.0527635	+	0.127382i
$356$		0			0
$357$	−36.7566	−	88.7383i	−0.102960	−	0.248567i
$358$		0			0
$359$	−369.532	−	369.532i	−1.02934	−	1.02934i	−0.999556	−	0.0297806i	$-0.990519\pi$
$359$	−369.532	−	369.532i	−1.02934	−	1.02934i	−0.0297806	−	0.999556i	$-0.509481\pi$
$360$		0			0
$361$	−127.319	−	127.319i	−0.352684	−	0.352684i
$362$		0			0
$363$	245.150	+	591.844i	0.675343	+	1.63042i
$364$		0			0
$365$	145.526	−	351.332i	0.398702	−	0.962552i
$366$		0			0
$367$	482.888			1.31577			0.657885	−	0.753118i	$-0.271451\pi$
$367$	482.888			1.31577			0.657885	+	0.753118i	$0.271451\pi$
$368$		0			0
$369$		−	657.215i		−	1.78107i
$370$		0			0
$371$	−350.698	−	145.264i	−0.945278	−	0.391547i
$372$		0			0
$373$	459.056	−	190.147i	1.23071	−	0.509778i	0.329913	−	0.944011i	$-0.392980\pi$
$373$	459.056	−	190.147i	1.23071	−	0.509778i	0.900801	+	0.434233i	$0.142980\pi$
$374$		0			0
$375$	−410.573	+	410.573i	−1.09486	+	1.09486i
$376$		0			0
$377$	−312.332	+	312.332i	−0.828468	+	0.828468i
$378$		0			0
$379$	−209.167	+	86.6398i	−0.551891	+	0.228601i	−0.641161	−	0.767407i	$-0.721547\pi$
$379$	−209.167	+	86.6398i	−0.551891	+	0.228601i	0.0892693	+	0.996008i	$0.471547\pi$
$380$		0			0
$381$	806.973	+	334.259i	2.11804	+	0.877320i
$382$		0			0
$383$		−	243.083i		−	0.634682i	−0.948312	−	0.317341i	$-0.897210\pi$
$383$		−	243.083i		−	0.634682i	0.948312	−	0.317341i	$-0.102790\pi$
$384$		0			0
$385$	−587.227			−1.52527
$386$		0			0
$387$	281.459	−	679.503i	0.727285	−	1.75582i
$388$		0			0
$389$	100.024	+	241.479i	0.257131	+	0.620768i	0.998746	−	0.0500566i	$-0.0159402\pi$
$389$	100.024	+	241.479i	0.257131	+	0.620768i	−0.741616	+	0.670825i	$0.765940\pi$
$390$		0			0
$391$	−4.09239	−	4.09239i	−0.0104665	−	0.0104665i
$392$		0			0
$393$	152.720	+	152.720i	0.388601	+	0.388601i
$394$		0			0
$395$	20.6275	+	49.7992i	0.0522215	+	0.126074i
$396$		0			0
$397$	−177.617	+	428.806i	−0.447399	+	1.08012i	0.525894	+	0.850550i	$0.323731\pi$
$397$	−177.617	+	428.806i	−0.447399	+	1.08012i	−0.973293	+	0.229566i	$0.926269\pi$
$398$		0			0
$399$	454.366			1.13876
$400$		0			0
$401$			539.233i			1.34472i	0.740224	+	0.672360i	$0.234719\pi$
$401$			539.233i			1.34472i	−0.740224	+	0.672360i	$0.765281\pi$
$402$		0			0
$403$	−48.3339	−	20.0206i	−0.119935	−	0.0496788i
$404$		0			0
$405$	−235.188	+	97.4183i	−0.580712	+	0.240539i
$406$		0			0
$407$	−200.107	+	200.107i	−0.491664	+	0.491664i
$408$		0			0
$409$	177.821	−	177.821i	0.434769	−	0.434769i	−0.455478	−	0.890247i	$-0.650532\pi$
$409$	177.821	−	177.821i	0.434769	−	0.434769i	0.890247	+	0.455478i	$0.150532\pi$
$410$		0			0
$411$	−164.806	+	68.2648i	−0.400988	+	0.166094i
$412$		0			0
$413$	−373.554	−	154.731i	−0.904490	−	0.374652i
$414$		0			0
$415$		−	157.428i		−	0.379345i
$416$		0			0
$417$	−394.402			−0.945807
$418$		0			0
$419$	−55.0604	+	132.927i	−0.131409	+	0.317249i	−0.975865	−	0.218376i	$-0.929924\pi$
$419$	−55.0604	+	132.927i	−0.131409	+	0.317249i	0.844456	+	0.535625i	$0.179924\pi$
$420$		0			0
$421$	−292.384	−	705.877i	−0.694498	−	1.67667i	−0.735514	−	0.677509i	$-0.763059\pi$
$421$	−292.384	−	705.877i	−0.694498	−	1.67667i	0.0410159	−	0.999158i	$-0.486941\pi$
$422$		0			0
$423$	−134.248	−	134.248i	−0.317371	−	0.317371i
$424$		0			0
$425$	−2.84107	−	2.84107i	−0.00668488	−	0.00668488i
$426$		0			0
$427$	−167.880	−	405.298i	−0.393162	−	0.949176i
$428$		0			0
$429$	309.883	−	748.125i	0.722339	−	1.74388i
$430$		0			0
$431$	−810.711			−1.88100			−0.940500	−	0.339794i	$-0.889643\pi$
$431$	−810.711			−1.88100			−0.940500	+	0.339794i	$0.889643\pi$
$432$		0			0
$433$		−	753.072i		−	1.73920i	−0.493759	−	0.869599i	$-0.664378\pi$
$433$		−	753.072i		−	1.73920i	0.493759	−	0.869599i	$-0.335622\pi$
$434$		0			0
$435$	−812.484	−	336.542i	−1.86778	−	0.773659i
$436$		0			0
$437$	25.2940	−	10.4771i	0.0578810	−	0.0239751i
$438$		0			0
$439$	−504.938	+	504.938i	−1.15020	+	1.15020i	−0.163689	+	0.986512i	$0.552339\pi$
$439$	−504.938	+	504.938i	−1.15020	+	1.15020i	−0.986512	+	0.163689i	$0.947661\pi$
$440$		0			0
$441$	54.3323	−	54.3323i	0.123202	−	0.123202i
$442$		0			0
$443$	697.291	−	288.827i	1.57402	−	0.651981i	0.586569	−	0.809899i	$-0.300478\pi$
$443$	697.291	−	288.827i	1.57402	−	0.651981i	0.987452	+	0.157919i	$0.0504784\pi$
$444$		0			0
$445$	−106.394	−	44.0697i	−0.239087	−	0.0990330i
$446$		0			0
$447$			616.626i			1.37948i
$448$		0			0
$449$	−294.056			−0.654913			−0.327457	−	0.944866i	$-0.606192\pi$
$449$	−294.056			−0.654913			−0.327457	+	0.944866i	$0.606192\pi$
$450$		0			0
$451$	354.719	−	856.368i	0.786517	−	1.89882i
$452$		0			0
$453$	260.287	+	628.389i	0.574585	+	1.38717i
$454$		0			0
$455$	282.960	+	282.960i	0.621889	+	0.621889i
$456$		0			0
$457$	175.139	+	175.139i	0.383237	+	0.383237i	0.872267	−	0.489030i	$-0.162649\pi$
$457$	175.139	+	175.139i	0.383237	+	0.383237i	−0.489030	+	0.872267i	$0.662649\pi$
$458$		0			0
$459$	12.2554	+	29.5871i	0.0267001	+	0.0644598i
$460$		0			0
$461$	−107.290	+	259.020i	−0.232732	+	0.561866i	−0.996497	−	0.0836293i	$-0.973349\pi$
$461$	−107.290	+	259.020i	−0.232732	+	0.561866i	0.763765	+	0.645495i	$0.223349\pi$
$462$		0			0
$463$	−53.7059			−0.115996			−0.0579978	−	0.998317i	$-0.518472\pi$
$463$	−53.7059			−0.115996			−0.0579978	+	0.998317i	$0.518472\pi$
$464$		0			0
$465$		−	104.161i		−	0.224002i
$466$		0			0
$467$	−101.550	−	42.0634i	−0.217452	−	0.0900716i	0.271298	−	0.962495i	$-0.412547\pi$
$467$	−101.550	−	42.0634i	−0.217452	−	0.0900716i	−0.488750	+	0.872424i	$0.662547\pi$
$468$		0			0
$469$	459.438	−	190.306i	0.979613	−	0.405769i
$470$		0			0
$471$	725.243	−	725.243i	1.53979	−	1.53979i
$472$		0			0
$473$	733.498	−	733.498i	1.55074	−	1.55074i
$474$		0			0
$475$	17.5599	−	7.27355i	0.0369682	−	0.0153127i
$476$		0			0
$477$	539.884	+	223.627i	1.13183	+	0.468820i
$478$		0			0
$479$			40.7997i			0.0851769i	0.999093	+	0.0425884i	$0.0135604\pi$
$479$			40.7997i			0.0851769i	−0.999093	+	0.0425884i	$0.986440\pi$
$480$		0			0
$481$	192.846			0.400927
$482$		0			0
$483$	26.3089	−	63.5154i	0.0544698	−	0.131502i
$484$		0			0
$485$	126.066	+	304.351i	0.259931	+	0.627528i
$486$		0			0
$487$	143.660	+	143.660i	0.294989	+	0.294989i	0.839047	−	0.544058i	$-0.183113\pi$
$487$	143.660	+	143.660i	0.294989	+	0.294989i	−0.544058	+	0.839047i	$0.683113\pi$
$488$		0			0
$489$	−1.47216	−	1.47216i	−0.00301055	−	0.00301055i
$490$		0			0
$491$	−182.575	−	440.775i	−0.371843	−	0.897709i	−0.993438	−	0.114370i	$-0.963515\pi$
$491$	−182.575	−	440.775i	−0.371843	−	0.897709i	0.621595	−	0.783339i	$-0.286485\pi$
$492$		0			0
$493$	43.5325	−	105.097i	0.0883012	−	0.213178i
$494$		0			0
$495$	904.010			1.82628
$496$		0			0
$497$		−	75.2087i		−	0.151325i
$498$		0			0
$499$	409.850	+	169.766i	0.821343	+	0.340211i	0.753470	−	0.657482i	$-0.228379\pi$
$499$	409.850	+	169.766i	0.821343	+	0.340211i	0.0678733	+	0.997694i	$0.478379\pi$
$500$		0			0
$501$	−572.179	+	237.004i	−1.14207	+	0.473063i
$502$		0			0
$503$	−453.715	+	453.715i	−0.902019	+	0.902019i	−0.995611	−	0.0935920i	$-0.970165\pi$
$503$	−453.715	+	453.715i	−0.902019	+	0.902019i	0.0935920	+	0.995611i	$0.470165\pi$
$504$		0			0
$505$	−410.057	+	410.057i	−0.811993	+	0.811993i
$506$		0			0
$507$	196.921	−	81.5673i	0.388404	−	0.160882i
$508$		0			0
$509$	−71.5029	−	29.6175i	−0.140477	−	0.0581876i	0.311337	−	0.950299i	$-0.399223\pi$
$509$	−71.5029	−	29.6175i	−0.140477	−	0.0581876i	−0.451815	+	0.892112i	$0.649223\pi$
$510$		0			0
$511$			584.316i			1.14348i
$512$		0			0
$513$	−151.494			−0.295310
$514$		0			0
$515$	−162.197	+	391.578i	−0.314945	+	0.760345i
$516$		0			0
$517$	−102.471	−	247.387i	−0.198203	−	0.478504i
$518$		0			0
$519$	−855.117	−	855.117i	−1.64762	−	1.64762i
$520$		0			0
$521$	−565.729	−	565.729i	−1.08585	−	1.08585i	−0.995951	−	0.0899020i	$-0.971345\pi$
$521$	−565.729	−	565.729i	−1.08585	−	1.08585i	−0.0899020	−	0.995951i	$-0.528655\pi$
$522$		0			0
$523$	1.50925	+	3.64366i	0.00288576	+	0.00696685i	0.925316	−	0.379197i	$-0.123800\pi$
$523$	1.50925	+	3.64366i	0.00288576	+	0.00696685i	−0.922430	+	0.386164i	$0.873800\pi$
$524$		0			0
$525$	18.2645	−	44.0945i	0.0347896	−	0.0839895i
$526$		0			0
$527$	13.4734			0.0255663
$528$		0			0
$529$			524.858i			0.992169i
$530$		0			0
$531$	575.070	+	238.202i	1.08299	+	0.448591i
$532$		0			0
$533$	−583.571	+	241.723i	−1.09488	+	0.453514i
$534$		0			0
$535$	−64.0426	+	64.0426i	−0.119706	+	0.119706i
$536$		0			0
$537$	−934.579	+	934.579i	−1.74037	+	1.74037i
$538$		0			0
$539$	100.121	−	41.4716i	0.185754	−	0.0769417i
$540$		0			0
$541$	−746.681	−	309.286i	−1.38019	−	0.571692i	−0.435656	−	0.900113i	$-0.643483\pi$
$541$	−746.681	−	309.286i	−1.38019	−	0.571692i	−0.944531	+	0.328421i	$0.893483\pi$
$542$		0			0
$543$			162.696i			0.299625i
$544$		0			0
$545$	953.961			1.75039
$546$		0			0
$547$	−298.176	+	719.861i	−0.545112	+	1.31602i	0.375964	+	0.926634i	$0.377312\pi$
$547$	−298.176	+	719.861i	−0.545112	+	1.31602i	−0.921076	+	0.389383i	$0.872688\pi$
$548$		0			0
$549$	258.444	+	623.938i	0.470754	+	1.13650i
$550$		0			0
$551$	380.512	+	380.512i	0.690585	+	0.690585i
$552$		0			0
$553$	−58.5649	−	58.5649i	−0.105904	−	0.105904i
$554$		0			0
$555$	146.932	+	354.726i	0.264743	+	0.639147i
$556$		0			0
$557$	83.4142	−	201.380i	0.149756	−	0.361544i	−0.831143	−	0.556058i	$-0.812313\pi$
$557$	83.4142	−	201.380i	0.149756	−	0.361544i	0.980900	+	0.194515i	$0.0623132\pi$
$558$		0			0
$559$	−706.882			−1.26455
$560$		0			0
$561$			208.545i			0.371739i
$562$		0			0
$563$	19.5811	+	8.11076i	0.0347800	+	0.0144063i	0.400006	−	0.916513i	$-0.369008\pi$
$563$	19.5811	+	8.11076i	0.0347800	+	0.0144063i	−0.365226	+	0.930919i	$0.619008\pi$
$564$		0			0
$565$	703.482	−	291.392i	1.24510	−	0.515738i
$566$		0			0
$567$	276.587	−	276.587i	0.487808	−	0.487808i
$568$		0			0
$569$	−366.760	+	366.760i	−0.644569	+	0.644569i	−0.951675	−	0.307106i	$-0.900639\pi$
$569$	−366.760	+	366.760i	−0.644569	+	0.644569i	0.307106	+	0.951675i	$0.400639\pi$
$570$		0			0
$571$	121.285	−	50.2378i	0.212408	−	0.0879822i	−0.273943	−	0.961746i	$-0.588328\pi$
$571$	121.285	−	50.2378i	0.212408	−	0.0879822i	0.486350	+	0.873764i	$0.338328\pi$
$572$		0			0
$573$	199.599	+	82.6764i	0.348339	+	0.144287i
$574$		0			0
$575$		−	2.87584i		−	0.00500147i
$576$		0			0
$577$	464.948			0.805802			0.402901	−	0.915244i	$-0.368002\pi$
$577$	464.948			0.805802			0.402901	+	0.915244i	$0.368002\pi$
$578$		0			0
$579$	−523.412	+	1263.63i	−0.903993	+	2.18243i
$580$		0			0
$581$	92.5696	+	223.483i	0.159328	+	0.384652i
$582$		0			0
$583$	582.785	+	582.785i	0.999631	+	0.999631i
$584$		0			0
$585$	−435.603	−	435.603i	−0.744621	−	0.744621i
$586$		0			0
$587$	−159.551	−	385.190i	−0.271807	−	0.656201i	0.727753	−	0.685839i	$-0.240565\pi$
$587$	−159.551	−	385.190i	−0.271807	−	0.656201i	−0.999561	+	0.0296380i	$0.990565\pi$
$588$		0			0
$589$	−24.3909	+	58.8849i	−0.0414107	+	0.0999743i
$590$		0			0
$591$	216.448			0.366239
$592$		0			0
$593$			470.422i			0.793292i	0.917972	+	0.396646i	$0.129826\pi$
$593$			470.422i			0.793292i	−0.917972	+	0.396646i	$0.870174\pi$
$594$		0			0
$595$	−95.2131	−	39.4385i	−0.160022	−	0.0662833i
$596$		0			0
$597$	557.448	−	230.903i	0.933749	−	0.386771i
$598$		0			0
$599$	506.817	−	506.817i	0.846105	−	0.846105i	−0.143540	−	0.989645i	$-0.545849\pi$
$599$	506.817	−	506.817i	0.846105	−	0.846105i	0.989645	+	0.143540i	$0.0458485\pi$
$600$		0			0
$601$	−261.398	+	261.398i	−0.434939	+	0.434939i	−0.890305	−	0.455366i	$-0.849509\pi$
$601$	−261.398	+	261.398i	−0.434939	+	0.434939i	0.455366	+	0.890305i	$0.349509\pi$
$602$		0			0
$603$	−707.285	+	292.967i	−1.17294	+	0.485849i
$604$		0			0
$605$	635.027	+	263.037i	1.04963	+	0.434772i
$606$		0			0
$607$		−	812.089i		−	1.33787i	−0.743319	−	0.668937i	$-0.766750\pi$
$607$		−	812.089i		−	1.33787i	0.743319	−	0.668937i	$-0.233250\pi$
$608$		0			0
$609$	1351.28			2.21885
$610$		0			0
$611$	−69.8287	+	168.581i	−0.114286	+	0.275911i
$612$		0			0
$613$	105.168	+	253.898i	0.171563	+	0.414190i	0.986151	−	0.165850i	$-0.0530369\pi$
$613$	105.168	+	253.898i	0.171563	+	0.414190i	−0.814588	+	0.580040i	$0.803037\pi$
$614$		0			0
$615$	−889.264	−	889.264i	−1.44596	−	1.44596i
$616$		0			0
$617$	−508.739	−	508.739i	−0.824536	−	0.824536i	0.162218	−	0.986755i	$-0.448135\pi$
$617$	−508.739	−	508.739i	−0.824536	−	0.824536i	−0.986755	+	0.162218i	$0.948135\pi$
$618$		0			0
$619$	6.64960	+	16.0536i	0.0107425	+	0.0259347i	0.929160	−	0.369678i	$-0.120532\pi$
$619$	6.64960	+	16.0536i	0.0107425	+	0.0259347i	−0.918417	+	0.395613i	$0.870532\pi$
$620$		0			0
$621$	−8.77191	+	21.1773i	−0.0141255	+	0.0341019i
$622$		0			0
$623$	176.948			0.284026
$624$		0			0
$625$			587.679i			0.940287i
$626$		0			0
$627$	−911.435	−	377.529i	−1.45364	−	0.602119i
$628$		0			0
$629$	−45.8847	+	19.0061i	−0.0729487	+	0.0302163i
$630$		0			0
$631$	177.518	−	177.518i	0.281329	−	0.281329i	−0.552310	−	0.833639i	$-0.686254\pi$
$631$	177.518	−	177.518i	0.281329	−	0.281329i	0.833639	+	0.552310i	$0.186254\pi$
$632$		0			0
$633$	927.524	−	927.524i	1.46528	−	1.46528i
$634$		0			0
$635$	865.853	−	358.648i	1.36355	−	0.564800i
$636$		0			0
$637$	−68.2274	−	28.2607i	−0.107107	−	0.0443654i
$638$		0			0
$639$			115.780i			0.181190i
$640$		0			0
$641$	334.058			0.521151			0.260575	−	0.965454i	$-0.416088\pi$
$641$	334.058			0.521151			0.260575	+	0.965454i	$0.416088\pi$
$642$		0			0
$643$	19.9758	−	48.2257i	0.0310665	−	0.0750011i	−0.907585	−	0.419869i	$-0.862076\pi$
$643$	19.9758	−	48.2257i	0.0310665	−	0.0750011i	0.938651	+	0.344867i	$0.112076\pi$
$644$		0			0
$645$	−538.584	−	1300.26i	−0.835015	−	2.01590i
$646$		0			0
$647$	−443.581	−	443.581i	−0.685596	−	0.685596i	0.275659	−	0.961255i	$-0.411104\pi$
$647$	−443.581	−	443.581i	−0.685596	−	0.685596i	−0.961255	+	0.275659i	$0.911104\pi$
$648$		0			0
$649$	620.767	+	620.767i	0.956497	+	0.956497i
$650$		0			0
$651$	61.2477	+	147.865i	0.0940825	+	0.227135i
$652$		0			0
$653$	−14.0746	+	33.9792i	−0.0215538	+	0.0520355i	−0.934290	−	0.356514i	$-0.883965\pi$
$653$	−14.0746	+	33.9792i	−0.0215538	+	0.0520355i	0.912736	+	0.408549i	$0.133965\pi$
$654$		0			0
$655$	231.737			0.353798
$656$		0			0
$657$		−	899.528i		−	1.36914i
$658$		0			0
$659$	845.778	+	350.333i	1.28343	+	0.531613i	0.917020	−	0.398842i	$-0.130588\pi$
$659$	845.778	+	350.333i	1.28343	+	0.531613i	0.366407	+	0.930455i	$0.380588\pi$
$660$		0			0
$661$	−1022.39	+	423.490i	−1.54674	+	0.640680i	−0.982723	−	0.185083i	$-0.940745\pi$
$661$	−1022.39	+	423.490i	−1.54674	+	0.640680i	−0.564017	+	0.825763i	$0.690745\pi$
$662$		0			0
$663$	100.489	−	100.489i	0.151567	−	0.151567i
$664$		0			0
$665$	344.727	−	344.727i	0.518387	−	0.518387i
$666$		0			0
$667$	75.2241	−	31.1588i	0.112780	−	0.0467149i
$668$		0			0
$669$	−1707.71	−	707.355i	−2.55263	−	1.05733i
$670$		0			0
$671$			952.498i			1.41952i
$672$		0			0
$673$	−441.074			−0.655385			−0.327693	−	0.944784i	$-0.606271\pi$
$673$	−441.074			−0.655385			−0.327693	+	0.944784i	$0.606271\pi$
$674$		0			0
$675$	−6.08974	+	14.7019i	−0.00902184	+	0.0217807i
$676$		0			0
$677$	−3.12869	−	7.55333i	−0.00462140	−	0.0111571i	0.921552	−	0.388255i	$-0.126922\pi$
$677$	−3.12869	−	7.55333i	−0.00462140	−	0.0111571i	−0.926173	+	0.377098i	$0.876922\pi$
$678$		0			0
$679$	−357.923	−	357.923i	−0.527133	−	0.527133i
$680$		0			0
$681$	690.112	+	690.112i	1.01338	+	1.01338i
$682$		0			0
$683$	198.853	+	480.073i	0.291146	+	0.702889i	0.999997	−	0.00246964i	$-0.000786112\pi$
$683$	198.853	+	480.073i	0.291146	+	0.702889i	−0.708851	+	0.705358i	$0.750786\pi$
$684$		0			0
$685$	−73.2458	+	176.831i	−0.106928	+	0.258147i
$686$		0			0
$687$	267.394			0.389220
$688$		0			0
$689$		−	561.638i		−	0.815149i
$690$		0			0
$691$	−260.304	−	107.822i	−0.376707	−	0.156037i	0.186293	−	0.982494i	$-0.440353\pi$
$691$	−260.304	−	107.822i	−0.376707	−	0.156037i	−0.563000	+	0.826457i	$0.690353\pi$
$692$		0			0
$693$	−1283.32	+	531.568i	−1.85183	+	0.767053i
$694$		0			0
$695$	−299.233	+	299.233i	−0.430551	+	0.430551i
$696$		0			0
$697$	115.028	−	115.028i	0.165034	−	0.165034i
$698$		0			0
$699$	344.683	−	142.772i	0.493109	−	0.204252i
$700$		0			0
$701$	−487.328	−	201.858i	−0.695189	−	0.287957i	0.00697111	−	0.999976i	$-0.497781\pi$
$701$	−487.328	−	201.858i	−0.695189	−	0.287957i	−0.702160	+	0.712019i	$0.747781\pi$
$702$		0			0
$703$		−	234.943i		−	0.334200i
$704$		0			0
$705$	−363.297			−0.515315
$706$		0			0
$707$	340.992	−	823.228i	0.482309	−	1.16440i
$708$		0			0
$709$	260.932	+	629.945i	0.368028	+	0.888498i	0.994073	+	0.108711i	$0.0346724\pi$
$709$	260.932	+	629.945i	0.368028	+	0.888498i	−0.626046	+	0.779786i	$0.715328\pi$
$710$		0			0
$711$	90.1580	+	90.1580i	0.126805	+	0.126805i
$712$		0			0
$713$	6.81917	+	6.81917i	0.00956405	+	0.00956405i
$714$		0			0
$715$	−332.494	−	802.712i	−0.465027	−	1.12267i
$716$		0			0
$717$	636.341	−	1536.26i	0.887505	−	2.14263i
$718$		0			0
$719$	349.854			0.486585			0.243292	−	0.969953i	$-0.421773\pi$
$719$	349.854			0.486585			0.243292	+	0.969953i	$0.421773\pi$
$720$		0			0
$721$		−	651.251i		−	0.903261i
$722$		0			0
$723$	−1306.18	−	541.036i	−1.80661	−	0.748321i
$724$		0			0
$725$	52.2230	−	21.6315i	0.0720318	−	0.0298365i
$726$		0			0
$727$	58.3736	−	58.3736i	0.0802938	−	0.0802938i	−0.665819	−	0.746113i	$-0.731918\pi$
$727$	58.3736	−	58.3736i	0.0802938	−	0.0802938i	0.746113	+	0.665819i	$0.231918\pi$
$728$		0			0
$729$	−750.210	+	750.210i	−1.02909	+	1.02909i
$730$		0			0
$731$	168.191	−	69.6672i	0.230084	−	0.0953040i
$732$		0			0
$733$	327.632	+	135.710i	0.446975	+	0.185143i	0.594805	−	0.803870i	$-0.297229\pi$
$733$	327.632	+	135.710i	0.446975	+	0.185143i	−0.147831	+	0.989013i	$0.547229\pi$
$734$		0			0
$735$		−	147.032i		−	0.200043i
$736$		0			0
$737$	−1079.73			−1.46504
$738$		0			0
$739$	−328.523	+	793.126i	−0.444551	+	1.07324i	0.529783	+	0.848134i	$0.322274\pi$
$739$	−328.523	+	793.126i	−0.444551	+	1.07324i	−0.974334	+	0.225108i	$0.927726\pi$
$740$		0			0
$741$	257.266	+	621.096i	0.347188	+	0.838186i
$742$		0			0
$743$	−79.8532	−	79.8532i	−0.107474	−	0.107474i	0.651325	−	0.758799i	$-0.274214\pi$
$743$	−79.8532	−	79.8532i	−0.107474	−	0.107474i	−0.758799	+	0.651325i	$0.774214\pi$
$744$		0			0
$745$	467.835	+	467.835i	0.627966	+	0.627966i
$746$		0			0
$747$	−142.507	−	344.042i	−0.190772	−	0.460565i
$748$		0			0
$749$	53.2561	−	128.572i	0.0711029	−	0.171658i
$750$		0			0
$751$	729.615			0.971524			0.485762	−	0.874091i	$-0.338542\pi$
$751$	729.615			0.971524			0.485762	+	0.874091i	$0.338542\pi$
$752$		0			0
$753$			1093.13i			1.45171i
$754$		0			0
$755$	674.239	+	279.279i	0.893032	+	0.369906i
$756$		0			0
$757$	565.974	−	234.434i	0.747654	−	0.309688i	0.0238700	−	0.999715i	$-0.492401\pi$
$757$	565.974	−	234.434i	0.747654	−	0.309688i	0.723784	+	0.690027i	$0.242401\pi$
$758$		0			0
$759$	−105.549	+	105.549i	−0.139063	+	0.139063i
$760$		0			0
$761$	186.563	−	186.563i	0.245155	−	0.245155i	−0.573824	−	0.818979i	$-0.694541\pi$
$761$	186.563	−	186.563i	0.245155	−	0.245155i	0.818979	+	0.573824i	$0.194541\pi$
$762$		0			0
$763$	−1354.23	+	560.940i	−1.77487	+	0.735176i
$764$		0			0
$765$	146.576	+	60.7139i	0.191603	+	0.0793645i
$766$		0			0
$767$		−	598.241i		−	0.779976i
$768$		0			0
$769$	134.178			0.174484			0.0872420	−	0.996187i	$-0.472195\pi$
$769$	134.178			0.174484			0.0872420	+	0.996187i	$0.472195\pi$
$770$		0			0
$771$	308.632	−	745.103i	0.400301	−	0.966411i
$772$		0			0
$773$	−155.016	−	374.241i	−0.200538	−	0.484141i	0.791334	−	0.611384i	$-0.209387\pi$
$773$	−155.016	−	374.241i	−0.200538	−	0.484141i	−0.991872	+	0.127243i	$0.959387\pi$
$774$		0			0
$775$	4.73409	+	4.73409i	0.00610851	+	0.00610851i
$776$		0			0
$777$	−417.166	−	417.166i	−0.536893	−	0.536893i
$778$		0			0
$779$	294.489	+	710.960i	0.378035	+	0.912657i
$780$		0			0
$781$	−62.4903	+	150.865i	−0.0800132	+	0.193169i
$782$		0			0
$783$	−450.543			−0.575406
$784$		0			0
$785$		−	1100.49i		−	1.40189i
$786$		0			0
$787$	−464.245	−	192.297i	−0.589892	−	0.244341i	0.0677120	−	0.997705i	$-0.478430\pi$
$787$	−464.245	−	192.297i	−0.589892	−	0.244341i	−0.657604	+	0.753364i	$0.728430\pi$
$788$		0			0
$789$	870.327	−	360.501i	1.10308	−	0.456909i
$790$		0			0
$791$	−827.311	+	827.311i	−1.04590	+	1.04590i
$792$		0			0
$793$	458.968	−	458.968i	0.578774	−	0.578774i
$794$		0			0
$795$	1033.09	−	427.921i	1.29949	−	0.538265i
$796$		0			0
$797$	1426.93	+	591.055i	1.79038	+	0.741600i	0.989816	+	0.142353i	$0.0454669\pi$
$797$	1426.93	+	591.055i	1.79038	+	0.741600i	0.800564	+	0.599247i	$0.204533\pi$
$798$		0			0
$799$		−	46.9933i		−	0.0588152i
$800$		0			0
$801$	−272.404			−0.340079
$802$		0			0
$803$	485.503	−	1172.11i	0.604612	−	1.45966i
$804$		0			0
$805$	−28.2286	−	68.1498i	−0.0350665	−	0.0846581i
$806$		0			0
$807$	1155.18	+	1155.18i	1.43146	+	1.43146i
$808$		0			0
$809$	−950.297	−	950.297i	−1.17466	−	1.17466i	−0.981086	−	0.193570i	$-0.937993\pi$
$809$	−950.297	−	950.297i	−1.17466	−	1.17466i	−0.193570	−	0.981086i	$-0.562007\pi$
$810$		0			0
$811$	580.036	+	1400.33i	0.715210	+	1.72667i	0.686552	+	0.727081i	$0.259124\pi$
$811$	580.036	+	1400.33i	0.715210	+	1.72667i	0.0286586	+	0.999589i	$0.490876\pi$
$812$		0			0
$813$	−378.727	+	914.328i	−0.465839	+	1.12463i
$814$		0			0
$815$	−2.23385			−0.00274092
$816$		0			0
$817$			861.189i			1.05409i
$818$		0			0
$819$	874.515	+	362.236i	1.06778	+	0.442291i
$820$		0			0
$821$	646.816	−	267.920i	0.787839	−	0.326334i	0.0477645	−	0.998859i	$-0.484790\pi$
$821$	646.816	−	267.920i	0.787839	−	0.326334i	0.740074	+	0.672525i	$0.234790\pi$
$822$		0			0
$823$	262.313	−	262.313i	0.318728	−	0.318728i	−0.529551	−	0.848278i	$-0.677639\pi$
$823$	262.313	−	262.313i	0.318728	−	0.318728i	0.848278	+	0.529551i	$0.177639\pi$
$824$		0			0
$825$	−73.2755	+	73.2755i	−0.0888187	+	0.0888187i
$826$		0			0
$827$	−893.204	+	369.977i	−1.08005	+	0.447373i	−0.850528	−	0.525930i	$-0.823717\pi$
$827$	−893.204	+	369.977i	−1.08005	+	0.447373i	−0.229525	+	0.973303i	$0.573717\pi$
$828$		0			0
$829$	−161.439	−	66.8701i	−0.194739	−	0.0806635i	0.283183	−	0.959066i	$-0.408610\pi$
$829$	−161.439	−	66.8701i	−0.194739	−	0.0806635i	−0.477922	+	0.878402i	$0.658610\pi$
$830$		0			0
$831$		−	1254.41i		−	1.50952i
$832$		0			0
$833$	19.0189			0.0228318
$834$		0			0
$835$	−254.297	+	613.928i	−0.304548	+	0.735243i
$836$		0			0
$837$	−20.4212	−	49.3011i	−0.0243980	−	0.0589021i
$838$		0			0
$839$	−552.802	−	552.802i	−0.658882	−	0.658882i	0.296234	−	0.955116i	$-0.404269\pi$
$839$	−552.802	−	552.802i	−0.658882	−	0.658882i	−0.955116	+	0.296234i	$0.904269\pi$
$840$		0			0
$841$	536.963	+	536.963i	0.638481	+	0.638481i
$842$		0			0
$843$	121.044	+	292.226i	0.143587	+	0.346650i
$844$		0			0
$845$	87.5188	−	211.289i	0.103573	−	0.250046i
$846$		0			0
$847$	−1056.14			−1.24692
$848$		0			0
$849$			579.542i			0.682618i
$850$		0			0
$851$	−32.8425	−	13.6038i	−0.0385928	−	0.0159857i
$852$		0			0
$853$	−653.395	+	270.645i	−0.765997	+	0.317286i	−0.731250	−	0.682110i	$-0.761063\pi$
$853$	−653.395	+	270.645i	−0.765997	+	0.317286i	−0.0347472	+	0.999396i	$0.511063\pi$
$854$		0			0
$855$	−530.692	+	530.692i	−0.620693	+	0.620693i
$856$		0			0
$857$	−26.5894	+	26.5894i	−0.0310261	+	0.0310261i	−0.722450	−	0.691424i	$-0.756984\pi$
$857$	−26.5894	+	26.5894i	−0.0310261	+	0.0310261i	0.691424	+	0.722450i	$0.256984\pi$
$858$		0			0
$859$	−149.594	+	61.9638i	−0.174149	+	0.0721349i	−0.468054	−	0.883700i	$-0.655045\pi$
$859$	−149.594	+	61.9638i	−0.174149	+	0.0721349i	0.293906	+	0.955834i	$0.405045\pi$
$860$		0			0
$861$	1785.28	+	739.488i	2.07350	+	0.858871i
$862$		0			0
$863$			448.190i			0.519339i	0.965698	+	0.259670i	$0.0836137\pi$
$863$			448.190i			0.519339i	−0.965698	+	0.259670i	$0.916386\pi$
$864$		0			0
$865$	−1297.55			−1.50006
$866$		0			0
$867$	486.591	−	1174.74i	0.561236	−	1.35494i
$868$		0			0
$869$	68.8172	+	166.139i	0.0791913	+	0.191185i
$870$		0			0
$871$	520.277	+	520.277i	0.597333	+	0.597333i
$872$		0			0
$873$	551.007	+	551.007i	0.631165	+	0.631165i
$874$		0			0
$875$	−366.333	−	884.406i	−0.418666	−	1.01075i
$876$		0			0
$877$	−285.210	+	688.559i	−0.325211	+	0.785130i	0.673723	+	0.738984i	$0.264694\pi$
$877$	−285.210	+	688.559i	−0.325211	+	0.785130i	−0.998935	+	0.0461461i	$0.985306\pi$
$878$		0			0
$879$	−1185.20			−1.34835
$880$		0			0
$881$		−	140.757i		−	0.159770i	−0.996804	−	0.0798849i	$-0.974545\pi$
$881$		−	140.757i		−	0.159770i	0.996804	−	0.0798849i	$-0.0254553\pi$
$882$		0			0
$883$	644.358	+	266.902i	0.729737	+	0.302267i	0.716444	−	0.697645i	$-0.245769\pi$
$883$	644.358	+	266.902i	0.729737	+	0.302267i	0.0132930	+	0.999912i	$0.495769\pi$
$884$		0			0
$885$	1100.42	−	455.810i	1.24341	−	0.515039i
$886$		0			0
$887$	251.938	−	251.938i	0.284034	−	0.284034i	−0.550682	−	0.834715i	$-0.685632\pi$
$887$	251.938	−	251.938i	0.284034	−	0.284034i	0.834715	+	0.550682i	$0.185632\pi$
$888$		0			0
$889$	−1018.26	+	1018.26i	−1.14540	+	1.14540i
$890$		0			0
$891$	−784.633	+	325.006i	−0.880621	+	0.364765i
$892$		0			0
$893$	205.381	+	85.0718i	0.229990	+	0.0952651i
$894$		0			0
$895$			1418.13i			1.58450i
$896$		0			0
$897$	101.719			0.113399
$898$		0			0
$899$	−72.5384	+	175.123i	−0.0806878	+	0.194798i
$900$		0			0
$901$	55.3526	+	133.633i	0.0614346	+	0.148316i
$902$		0			0
$903$	1529.13	+	1529.13i	1.69339	+	1.69339i
$904$		0			0
$905$	123.438	+	123.438i	0.136395	+	0.136395i
$906$		0			0
$907$	−17.5960	−	42.4804i	−0.0194002	−	0.0468362i	0.913883	−	0.405979i	$-0.133069\pi$
$907$	−17.5960	−	42.4804i	−0.0194002	−	0.0468362i	−0.933283	+	0.359142i	$0.883069\pi$
$908$		0			0
$909$	−524.942	+	1267.32i	−0.577494	+	1.39419i
$910$		0			0
$911$	−425.886			−0.467493			−0.233747	−	0.972298i	$-0.575099\pi$
$911$	−425.886			−0.467493			−0.233747	+	0.972298i	$0.575099\pi$
$912$		0			0
$913$		−	525.211i		−	0.575258i
$914$		0			0
$915$	1193.93	+	494.543i	1.30484	+	0.540484i
$916$		0			0
$917$	−328.971	+	136.264i	−0.358747	+	0.148598i
$918$		0			0
$919$	−339.201	+	339.201i	−0.369098	+	0.369098i	−0.867148	−	0.498050i	$-0.834049\pi$
$919$	−339.201	+	339.201i	−0.369098	+	0.369098i	0.498050	+	0.867148i	$0.334049\pi$
$920$		0			0
$921$	1285.84	−	1285.84i	1.39613	−	1.39613i
$922$		0			0
$923$	102.807	−	42.5839i	0.111383	−	0.0461364i
$924$		0			0
$925$	−22.8003	−	9.44420i	−0.0246490	−	0.0102099i
$926$		0			0
$927$			1002.57i			1.08152i
$928$		0			0
$929$	−674.156			−0.725679			−0.362839	−	0.931852i	$-0.618193\pi$
$929$	−674.156			−0.725679			−0.362839	+	0.931852i	$0.618193\pi$
$930$		0			0
$931$	−34.4298	+	83.1210i	−0.0369816	+	0.0892814i
$932$		0			0
$933$	−766.089	−	1849.50i	−0.821102	−	1.98232i
$934$		0			0
$935$	158.224	+	158.224i	0.169223	+	0.169223i
$936$		0			0
$937$	−810.809	−	810.809i	−0.865325	−	0.865325i	0.126626	−	0.991951i	$-0.459585\pi$
$937$	−810.809	−	810.809i	−0.865325	−	0.865325i	−0.991951	+	0.126626i	$0.959585\pi$
$938$		0			0
$939$	−877.579	−	2118.66i	−0.934589	−	2.25630i
$940$		0			0
$941$	−372.431	+	899.128i	−0.395782	+	0.955503i	0.592873	+	0.805296i	$0.297994\pi$
$941$	−372.431	+	899.128i	−0.395782	+	0.955503i	−0.988655	+	0.150206i	$0.952006\pi$
$942$		0			0
$943$	116.436			0.123474
$944$		0			0
$945$			408.172i			0.431928i
$946$		0			0
$947$	−647.322	−	268.130i	−0.683551	−	0.283136i	0.0137596	−	0.999905i	$-0.495620\pi$
$947$	−647.322	−	268.130i	−0.683551	−	0.283136i	−0.697310	+	0.716769i	$0.745620\pi$
$948$		0			0
$949$	−798.732	+	330.846i	−0.841656	+	0.348625i
$950$		0			0
$951$	570.646	−	570.646i	0.600049	−	0.600049i
$952$		0			0
$953$	−584.883	+	584.883i	−0.613728	+	0.613728i	−0.943916	−	0.330187i	$-0.892888\pi$
$953$	−584.883	+	584.883i	−0.613728	+	0.613728i	0.330187	+	0.943916i	$0.392888\pi$
$954$		0			0
$955$	214.162	−	88.7089i	0.224254	−	0.0928889i
$956$		0			0
$957$	−2710.60	−	1122.77i	−2.83239	−	1.17322i
$958$		0			0
$959$		−	294.096i		−	0.306669i
$960$		0			0
$961$	938.549			0.976638
$962$		0			0
$963$	−81.9853	+	197.930i	−0.0851353	+	0.205535i
$964$		0			0
$965$	561.603	+	1355.83i	0.581972	+	1.40500i
$966$		0			0
$967$	−177.502	−	177.502i	−0.183560	−	0.183560i	0.609345	−	0.792905i	$-0.291432\pi$
$967$	−177.502	−	177.502i	−0.183560	−	0.183560i	−0.792905	+	0.609345i	$0.791432\pi$
$968$		0			0
$969$	−122.425	−	122.425i	−0.126342	−	0.126342i
$970$		0			0
$971$	−130.414	−	314.847i	−0.134309	−	0.324250i	0.842389	−	0.538870i	$-0.181149\pi$
$971$	−130.414	−	314.847i	−0.134309	−	0.324250i	−0.976698	+	0.214620i	$0.931149\pi$
$972$		0			0
$973$	248.834	−	600.738i	0.255739	−	0.617408i
$974$		0			0
$975$	70.6166			0.0724273
$976$		0			0
$977$		−	73.1425i		−	0.0748644i	−0.999299	−	0.0374322i	$-0.988082\pi$
$977$		−	73.1425i		−	0.0748644i	0.999299	−	0.0374322i	$-0.0119178\pi$
$978$		0			0
$979$	−354.949	−	147.025i	−0.362563	−	0.150179i
$980$		0			0
$981$	2084.77	−	863.541i	2.12515	−	0.880266i
$982$		0			0
$983$	614.269	−	614.269i	0.624892	−	0.624892i	−0.321886	−	0.946778i	$-0.604317\pi$
$983$	614.269	−	614.269i	0.624892	−	0.624892i	0.946778	+	0.321886i	$0.104317\pi$
$984$		0			0
$985$	164.219	−	164.219i	0.166720	−	0.166720i
$986$		0			0
$987$	515.731	−	213.623i	0.522523	−	0.216436i
$988$		0			0
$989$	120.385	+	49.8650i	0.121724	+	0.0504197i
$990$		0			0
$991$		−	763.403i		−	0.770336i	−0.922847	−	0.385168i	$-0.874144\pi$
$991$		−	763.403i		−	0.770336i	0.922847	−	0.385168i	$-0.125856\pi$
$992$		0			0
$993$	−252.091			−0.253868
$994$		0			0
$995$	247.750	−	598.122i	0.248995	−	0.601128i
$996$		0			0
$997$	−752.731	−	1817.25i	−0.754996	−	1.82272i	−0.529073	−	0.848576i	$-0.677460\pi$
$997$	−752.731	−	1817.25i	−0.754996	−	1.82272i	−0.225923	−	0.974145i	$-0.572540\pi$
$998$		0			0
$999$	139.091	+	139.091i	0.139230	+	0.139230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.47.7		28
4.3	odd	2		32.3.h.a.3.7	✓	28
8.3	odd	2		256.3.h.b.95.7		28
8.5	even	2		256.3.h.a.95.1		28
12.11	even	2		288.3.u.a.163.1		28
32.5	even	8		256.3.h.b.159.7		28
32.11	odd	8	inner	128.3.h.a.79.7		28
32.21	even	8		32.3.h.a.11.7	yes	28
32.27	odd	8		256.3.h.a.159.1		28
96.53	odd	8		288.3.u.a.235.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.7	✓	28	4.3	odd	2
32.3.h.a.11.7	yes	28	32.21	even	8
128.3.h.a.47.7		28	1.1	even	1	trivial
128.3.h.a.79.7		28	32.11	odd	8	inner
256.3.h.a.95.1		28	8.5	even	2
256.3.h.a.159.1		28	32.27	odd	8
256.3.h.b.95.7		28	8.3	odd	2
256.3.h.b.159.7		28	32.5	even	8
288.3.u.a.163.1		28	12.11	even	2
288.3.u.a.235.1		28	96.53	odd	8

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73217 - 4.18183i) q^{3} +(-1.85856 - 4.48696i) q^{5} +(5.27676 + 5.27676i) q^{7} +(-8.12333 - 8.12333i) q^{9} +O(q^{10})\)	\(q+(1.73217 - 4.18183i) q^{3} +(-1.85856 - 4.48696i) q^{5} +(5.27676 + 5.27676i) q^{7} +(-8.12333 - 8.12333i) q^{9} +(-6.20050 - 14.9693i) q^{11} +(-4.22532 + 10.2008i) q^{13} -21.9830 q^{15} -2.84356i q^{17} +(12.4276 + 5.14768i) q^{19} +(31.2068 - 12.9263i) q^{21} +(1.43918 - 1.43918i) q^{23} +(0.999126 - 0.999126i) q^{25} +(-10.4049 + 4.30987i) q^{27} +(36.9596 + 15.3092i) q^{29} +4.73823i q^{31} -73.3396 q^{33} +(13.8694 - 33.4838i) q^{35} +(-6.68390 - 16.1364i) q^{37} +(35.3392 + 35.3392i) q^{39} +(40.4523 + 40.4523i) q^{41} +(24.5000 + 59.1482i) q^{43} +(-21.3514 + 51.5467i) q^{45} +16.5262 q^{47} +6.68842i q^{49} +(-11.8913 - 4.92553i) q^{51} +(-46.9950 + 19.4659i) q^{53} +(-55.6428 + 55.6428i) q^{55} +(43.0535 - 43.0535i) q^{57} +(-50.0578 + 20.7346i) q^{59} +(-54.3116 - 22.4966i) q^{61} -85.7298i q^{63} +53.6237 q^{65} +(25.5017 - 61.5665i) q^{67} +(-3.52550 - 8.51131i) q^{69} +(-7.12641 - 7.12641i) q^{71} +(55.3669 + 55.3669i) q^{73} +(-2.44752 - 5.90883i) q^{75} +(46.2711 - 111.708i) q^{77} -11.0986 q^{79} -52.4160i q^{81} +(29.9476 + 12.4047i) q^{83} +(-12.7589 + 5.28492i) q^{85} +(128.041 - 128.041i) q^{87} +(16.7667 - 16.7667i) q^{89} +(-76.1234 + 31.5313i) q^{91} +(19.8145 + 8.20743i) q^{93} -65.3294i q^{95} -67.8301 q^{97} +(-71.2322 + 171.970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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