LMFDB - Embedded newform 128.3.h.a.79.7

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			79.7
Character	$\chi$	$=$	128.79
Dual form			128.3.h.a.47.7

$q$-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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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	0.895147	+	0.445771i	$0.147071\pi$
$3$	1.73217	+	4.18183i	0.577390	+	1.39394i	−0.317756	+	0.948172i	$0.602929\pi$
$4$		0			0
$5$	−1.85856	+	4.48696i	−0.371712	+	0.897391i	0.621749	+	0.783217i	$0.286422\pi$
$5$	−1.85856	+	4.48696i	−0.371712	+	0.897391i	−0.993461	+	0.114175i	$0.963578\pi$
$6$		0			0
$7$	5.27676	−	5.27676i	0.753823	−	0.753823i	−0.221367	−	0.975190i	$-0.571052\pi$
$7$	5.27676	−	5.27676i	0.753823	−	0.753823i	0.975190	+	0.221367i	$0.0710520\pi$
$8$		0			0
$9$	−8.12333	+	8.12333i	−0.902593	+	0.902593i
$10$		0			0
$11$	−6.20050	+	14.9693i	−0.563682	+	1.36085i	0.343120	+	0.939292i	$0.388516\pi$
$11$	−6.20050	+	14.9693i	−0.563682	+	1.36085i	−0.906802	+	0.421557i	$0.861484\pi$
$12$		0			0
$13$	−4.22532	−	10.2008i	−0.325025	−	0.784680i	−0.998947	−	0.0458772i	$-0.985392\pi$
$13$	−4.22532	−	10.2008i	−0.325025	−	0.784680i	0.673922	−	0.738802i	$-0.264608\pi$
$14$		0			0
$15$	−21.9830			−1.46554
$16$		0			0
$17$			2.84356i			0.167268i	0.996497	+	0.0836341i	$0.0266527\pi$
$17$			2.84356i			0.167268i	−0.996497	+	0.0836341i	$0.973347\pi$
$18$		0			0
$19$	12.4276	−	5.14768i	0.654084	−	0.270931i	−0.0308626	−	0.999524i	$-0.509825\pi$
$19$	12.4276	−	5.14768i	0.654084	−	0.270931i	0.684947	+	0.728593i	$0.259825\pi$
$20$		0			0
$21$	31.2068	+	12.9263i	1.48604	+	0.615537i
$22$		0			0
$23$	1.43918	+	1.43918i	0.0625730	+	0.0625730i	0.737701	−	0.675128i	$-0.235912\pi$
$23$	1.43918	+	1.43918i	0.0625730	+	0.0625730i	−0.675128	+	0.737701i	$0.735912\pi$
$24$		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	0.360148	−	0.932895i	$-0.382726\pi$
$29$	36.9596	−	15.3092i	1.27447	−	0.527902i	0.914320	+	0.404993i	$0.132726\pi$
$30$		0			0
$31$		−	4.73823i		−	0.152846i	−0.997075	−	0.0764231i	$-0.975650\pi$
$31$		−	4.73823i		−	0.152846i	0.997075	−	0.0764231i	$-0.0243500\pi$
$32$		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	−0.988100	−	0.153812i	$-0.950845\pi$
$37$	−6.68390	+	16.1364i	−0.180646	+	0.436118i	0.807454	+	0.589930i	$0.200845\pi$
$38$		0			0
$39$	35.3392	−	35.3392i	0.906133	−	0.906133i
$40$		0			0
$41$	40.4523	−	40.4523i	0.986641	−	0.986641i	−0.0132711	−	0.999912i	$-0.504224\pi$
$41$	40.4523	−	40.4523i	0.986641	−	0.986641i	0.999912	+	0.0132711i	$0.00422444\pi$
$42$		0			0
$43$	24.5000	−	59.1482i	0.569767	−	1.37554i	−0.331984	−	0.943285i	$-0.607718\pi$
$43$	24.5000	−	59.1482i	0.569767	−	1.37554i	0.901751	−	0.432255i	$-0.142282\pi$
$44$		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	−0.107607	−	0.994194i	$-0.534319\pi$
$53$	−46.9950	−	19.4659i	−0.886697	−	0.367282i	−0.779090	+	0.626912i	$0.784319\pi$
$54$		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	−0.0842623	−	0.996444i	$-0.526853\pi$
$59$	−50.0578	−	20.7346i	−0.848437	−	0.351434i	−0.764174	+	0.645010i	$0.776853\pi$
$60$		0			0
$61$	−54.3116	+	22.4966i	−0.890353	+	0.368796i	−0.780503	−	0.625152i	$-0.785037\pi$
$61$	−54.3116	+	22.4966i	−0.890353	+	0.368796i	−0.109850	+	0.993948i	$0.535037\pi$
$62$		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	0.991846	+	0.127445i	$0.0406778\pi$
$67$	25.5017	+	61.5665i	0.380622	+	0.918904i	−0.611223	+	0.791458i	$0.709322\pi$
$68$		0			0
$69$	−3.52550	+	8.51131i	−0.0510942	+	0.123352i
$70$		0			0
$71$	−7.12641	+	7.12641i	−0.100372	+	0.100372i	−0.755510	−	0.655138i	$-0.772611\pi$
$71$	−7.12641	+	7.12641i	−0.100372	+	0.100372i	0.655138	+	0.755510i	$0.272611\pi$
$72$		0			0
$73$	55.3669	−	55.3669i	0.758451	−	0.758451i	−0.217590	−	0.976040i	$-0.569819\pi$
$73$	55.3669	−	55.3669i	0.758451	−	0.758451i	0.976040	+	0.217590i	$0.0698194\pi$
$74$		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	−0.194909	−	0.980821i	$-0.562441\pi$
$83$	29.9476	−	12.4047i	0.360814	−	0.149454i	0.555724	+	0.831367i	$0.312441\pi$
$84$		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	0.795000	−	0.606610i	$-0.207471\pi$
$89$	16.7667	+	16.7667i	0.188390	+	0.188390i	−0.606610	+	0.795000i	$0.707471\pi$
$90$		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	0.518981	+	0.854786i	$0.326311\pi$
$101$	−45.6943	+	110.316i	−0.452419	+	1.09224i	−0.971400	+	0.237450i	$0.923689\pi$
$102$		0			0
$103$	−61.7093	+	61.7093i	−0.599120	+	0.599120i	−0.940078	−	0.340959i	$-0.889248\pi$
$103$	−61.7093	+	61.7093i	−0.599120	+	0.599120i	0.340959	+	0.940078i	$0.389248\pi$
$104$		0			0
$105$	−115.999	+	115.999i	−1.10475	+	1.10475i
$106$		0			0
$107$	−7.13652	+	17.2291i	−0.0666965	+	0.161020i	−0.953713	−	0.300718i	$-0.902774\pi$
$107$	−7.13652	+	17.2291i	−0.0666965	+	0.161020i	0.887017	+	0.461737i	$0.152774\pi$
$108$		0			0
$109$	−75.1681	−	181.472i	−0.689616	−	1.66488i	−0.745554	−	0.666445i	$-0.767815\pi$
$109$	−75.1681	−	181.472i	−0.689616	−	1.66488i	0.0559384	−	0.998434i	$-0.482185\pi$
$110$		0			0
$111$	−79.0572			−0.712227
$112$		0			0
$113$		−	156.784i		−	1.38747i	−0.720232	−	0.693734i	$-0.755965\pi$
$113$		−	156.784i		−	1.38747i	0.720232	−	0.693734i	$-0.244035\pi$
$114$		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	$-0.725332\pi$
$127$		−	192.971i		−	1.51946i	0.650240	−	0.759729i	$-0.274668\pi$
$128$		0			0
$129$	289.786			2.24640
$130$		0			0
$131$	−18.2599	−	44.0834i	−0.139389	−	0.336515i	0.838734	−	0.544541i	$-0.183296\pi$
$131$	−18.2599	−	44.0834i	−0.139389	−	0.336515i	−0.978123	+	0.208026i	$0.933296\pi$
$132$		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	−0.801459	−	0.598050i	$-0.795943\pi$
$137$	−27.8671	+	27.8671i	−0.203409	+	0.203409i	0.598050	+	0.801459i	$0.295943\pi$
$138$		0			0
$139$	−33.3447	+	80.5013i	−0.239890	+	0.579146i	−0.997271	−	0.0738274i	$-0.976479\pi$
$139$	−33.3447	+	80.5013i	−0.239890	+	0.579146i	0.757381	+	0.652973i	$0.226479\pi$
$140$		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	−0.0819919	−	0.996633i	$-0.526128\pi$
$149$	−125.860	−	52.1327i	−0.844695	−	0.349884i	−0.762703	+	0.646749i	$0.776128\pi$
$150$		0			0
$151$	−106.254	−	106.254i	−0.703672	−	0.703672i	0.261525	−	0.965197i	$-0.415775\pi$
$151$	−106.254	−	106.254i	−0.703672	−	0.703672i	−0.965197	+	0.261525i	$0.915775\pi$
$152$		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	0.401783	−	0.915735i	$-0.368391\pi$
$157$	209.345	−	86.7136i	1.33341	−	0.552316i	0.931626	+	0.363419i	$0.118391\pi$
$158$		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	0.924419	−	0.381380i	$-0.124551\pi$
$163$	0.176018	+	0.424946i	0.00107987	+	0.00260703i	−0.923339	+	0.383987i	$0.874551\pi$
$164$		0			0
$165$	136.306	−	329.072i	0.826096	−	1.99437i
$166$		0			0
$167$	−96.7499	+	96.7499i	−0.579341	+	0.579341i	−0.934722	−	0.355381i	$-0.884351\pi$
$167$	−96.7499	+	96.7499i	−0.579341	+	0.579341i	0.355381	+	0.934722i	$0.384351\pi$
$168$		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	0.882544	+	0.470229i	$0.155829\pi$
$173$	102.242	+	246.834i	0.590994	+	1.42678i	−0.291551	+	0.956555i	$0.594171\pi$
$174$		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	−0.974957	−	0.222393i	$-0.928613\pi$
$179$	−269.771	+	111.743i	−1.50710	+	0.624262i	−0.532144	+	0.846654i	$0.678613\pi$
$180$		0			0
$181$	−33.2079	−	13.7552i	−0.183469	−	0.0759954i	0.289058	−	0.957312i	$-0.406658\pi$
$181$	−33.2079	−	13.7552i	−0.183469	−	0.0759954i	−0.472527	+	0.881316i	$0.656658\pi$
$182$		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	$-0.960124\pi$
$191$		−	47.7299i		−	0.249895i	0.992163	−	0.124947i	$-0.0398762\pi$
$192$		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	−0.870604	−	0.491984i	$-0.836272\pi$
$197$	18.2996	−	44.1791i	0.0928913	−	0.224259i	0.963495	+	0.267725i	$0.0862718\pi$
$198$		0			0
$199$	94.2590	−	94.2590i	0.473663	−	0.473663i	−0.429435	−	0.903098i	$-0.641287\pi$
$199$	94.2590	−	94.2590i	0.473663	−	0.473663i	0.903098	+	0.429435i	$0.141287\pi$
$200$		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	0.356259	−	0.934387i	$-0.384052\pi$
$211$	267.734	−	110.899i	1.26888	−	0.525589i	0.912625	+	0.408799i	$0.134052\pi$
$212$		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	$0.368294\pi$
$223$			408.363i			1.83123i	−0.402061	+	0.915613i	$0.631706\pi$
$224$		0			0
$225$	−16.2325			−0.0721443
$226$		0			0
$227$	−82.5132	−	199.204i	−0.363494	−	0.877553i	−0.994784	−	0.102005i	$-0.967474\pi$
$227$	−82.5132	−	199.204i	−0.363494	−	0.877553i	0.631290	−	0.775547i	$-0.282526\pi$
$228$		0			0
$229$	22.6069	−	54.5778i	0.0987200	−	0.238331i	−0.866802	−	0.498652i	$-0.833828\pi$
$229$	22.6069	−	54.5778i	0.0987200	−	0.238331i	0.965522	+	0.260321i	$0.0838284\pi$
$230$		0			0
$231$	−386.995	+	386.995i	−1.67531	+	1.67531i
$232$		0			0
$233$	58.2826	−	58.2826i	0.250140	−	0.250140i	−0.570888	−	0.821028i	$-0.693401\pi$
$233$	58.2826	−	58.2826i	0.250140	−	0.250140i	0.821028	+	0.570888i	$0.193401\pi$
$234$		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	$0.224403\pi$
$241$			312.345i			1.29604i	−0.761624	+	0.648020i	$0.775597\pi$
$242$		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	−0.108972	−	0.994045i	$-0.534756\pi$
$251$	−223.120	−	92.4192i	−0.888923	−	0.368204i	−0.779951	+	0.625841i	$0.784756\pi$
$252$		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	−0.369623	−	0.929182i	$-0.620513\pi$
$263$	147.164	−	147.164i	0.559558	−	0.559558i	0.929182	+	0.369623i	$0.120513\pi$
$264$		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	−0.941861	−	0.336004i	$-0.890924\pi$
$269$	−138.119	−	333.450i	−0.513455	−	1.23959i	0.428405	−	0.903587i	$-0.359076\pi$
$270$		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	0.793522	−	0.608541i	$-0.208245\pi$
$277$	256.038	+	106.054i	0.924323	+	0.382867i	0.130801	+	0.991409i	$0.458245\pi$
$278$		0			0
$279$	38.4903	+	38.4903i	0.137958	+	0.137958i
$280$		0			0
$281$	−49.4126	−	49.4126i	−0.175845	−	0.175845i	0.613697	−	0.789542i	$-0.289682\pi$
$281$	−49.4126	−	49.4126i	−0.175845	−	0.175845i	−0.789542	+	0.613697i	$0.789682\pi$
$282$		0			0
$283$	−118.290	−	48.9975i	−0.417987	−	0.173136i	0.163770	−	0.986499i	$-0.447635\pi$
$283$	−118.290	−	48.9975i	−0.417987	−	0.173136i	−0.581757	+	0.813363i	$0.697635\pi$
$284$		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	0.655526	+	0.755172i	$0.272447\pi$
$293$	−100.203	+	241.910i	−0.341988	+	0.825633i	−0.997515	+	0.0704605i	$0.977553\pi$
$294$		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	0.315103	−	0.949058i	$-0.397961\pi$
$307$	371.163	−	153.741i	1.20900	−	0.500784i	0.893896	+	0.448274i	$0.147961\pi$
$308$		0			0
$309$	−364.949	−	151.167i	−1.18107	−	0.489213i
$310$		0			0
$311$	312.733	+	312.733i	1.00557	+	1.00557i	0.999984	+	0.00558671i	$0.00177831\pi$
$311$	312.733	+	312.733i	1.00557	+	1.00557i	0.00558671	+	0.999984i	$0.498222\pi$
$312$		0			0
$313$	358.245	+	358.245i	1.14455	+	1.14455i	0.987607	+	0.156946i	$0.0501649\pi$
$313$	358.245	+	358.245i	1.14455	+	1.14455i	0.156946	+	0.987607i	$0.449835\pi$
$314$		0			0
$315$	−384.666	−	159.334i	−1.22116	−	0.505822i
$316$		0			0
$317$	164.720	−	68.2292i	0.519621	−	0.215234i	−0.107429	−	0.994213i	$-0.534262\pi$
$317$	164.720	−	68.2292i	0.519621	−	0.215234i	0.627051	+	0.778979i	$0.284262\pi$
$318$		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	−0.952799	−	0.303601i	$-0.901811\pi$
$331$	−21.3130	+	51.4542i	−0.0643898	+	0.155451i	0.888409	+	0.459052i	$0.151811\pi$
$332$		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	$-0.917359\pi$
$337$		−	173.028i		−	0.513437i	0.966486	−	0.256718i	$-0.0826413\pi$
$338$		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	0.311024	−	0.950402i	$-0.399328\pi$
$347$	−48.9563	−	20.2784i	−0.141085	−	0.0584391i	−0.452109	+	0.891963i	$0.649328\pi$
$348$		0			0
$349$	−222.227	+	92.0495i	−0.636754	+	0.263752i	−0.677620	−	0.735412i	$-0.736988\pi$
$349$	−222.227	+	92.0495i	−0.636754	+	0.263752i	0.0408656	+	0.999165i	$0.486988\pi$
$350$		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	−0.0297806	+	0.999556i	$0.509481\pi$
$359$	−369.532	+	369.532i	−1.02934	+	1.02934i	−0.999556	+	0.0297806i	$0.990519\pi$
$360$		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	0.900801	−	0.434233i	$-0.142980\pi$
$373$	459.056	+	190.147i	1.23071	+	0.509778i	0.329913	+	0.944011i	$0.392980\pi$
$374$		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	0.0892693	−	0.996008i	$-0.471547\pi$
$379$	−209.167	−	86.6398i	−0.551891	−	0.228601i	−0.641161	+	0.767407i	$0.721547\pi$
$380$		0			0
$381$	806.973	−	334.259i	2.11804	−	0.877320i
$382$		0			0
$383$			243.083i			0.634682i	0.948312	+	0.317341i	$0.102790\pi$
$383$			243.083i			0.634682i	−0.948312	+	0.317341i	$0.897210\pi$
$384$		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	−0.741616	−	0.670825i	$-0.765940\pi$
$389$	100.024	−	241.479i	0.257131	−	0.620768i	0.998746	+	0.0500566i	$0.0159402\pi$
$390$		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	−0.973293	−	0.229566i	$-0.926269\pi$
$397$	−177.617	−	428.806i	−0.447399	−	1.08012i	0.525894	−	0.850550i	$-0.323731\pi$
$398$		0			0
$399$	454.366			1.13876
$400$		0			0
$401$		−	539.233i		−	1.34472i	−0.740224	−	0.672360i	$-0.765281\pi$
$401$		−	539.233i		−	1.34472i	0.740224	−	0.672360i	$-0.234719\pi$
$402$		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	0.890247	−	0.455478i	$-0.150532\pi$
$409$	177.821	+	177.821i	0.434769	+	0.434769i	−0.455478	+	0.890247i	$0.650532\pi$
$410$		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	0.844456	−	0.535625i	$-0.179924\pi$
$419$	−55.0604	−	132.927i	−0.131409	−	0.317249i	−0.975865	+	0.218376i	$0.929924\pi$
$420$		0			0
$421$	−292.384	+	705.877i	−0.694498	+	1.67667i	0.0410159	+	0.999158i	$0.486941\pi$
$421$	−292.384	+	705.877i	−0.694498	+	1.67667i	−0.735514	+	0.677509i	$0.763059\pi$
$422$		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	$0.335622\pi$
$433$			753.072i			1.73920i	−0.493759	+	0.869599i	$0.664378\pi$
$434$		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	−0.986512	−	0.163689i	$-0.947661\pi$
$439$	−504.938	−	504.938i	−1.15020	−	1.15020i	−0.163689	−	0.986512i	$-0.552339\pi$
$440$		0			0
$441$	54.3323	+	54.3323i	0.123202	+	0.123202i
$442$		0			0
$443$	697.291	+	288.827i	1.57402	+	0.651981i	0.987452	−	0.157919i	$-0.0504784\pi$
$443$	697.291	+	288.827i	1.57402	+	0.651981i	0.586569	+	0.809899i	$0.300478\pi$
$444$		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	−0.489030	−	0.872267i	$-0.662649\pi$
$457$	175.139	−	175.139i	0.383237	−	0.383237i	0.872267	+	0.489030i	$0.162649\pi$
$458$		0			0
$459$	12.2554	−	29.5871i	0.0267001	−	0.0644598i
$460$		0			0
$461$	−107.290	−	259.020i	−0.232732	−	0.561866i	0.763765	−	0.645495i	$-0.223349\pi$
$461$	−107.290	−	259.020i	−0.232732	−	0.561866i	−0.996497	+	0.0836293i	$0.973349\pi$
$462$		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	−0.488750	−	0.872424i	$-0.662547\pi$
$467$	−101.550	+	42.0634i	−0.217452	+	0.0900716i	0.271298	+	0.962495i	$0.412547\pi$
$468$		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	$-0.986440\pi$
$479$		−	40.7997i		−	0.0851769i	0.999093	−	0.0425884i	$-0.0135604\pi$
$480$		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	−0.544058	−	0.839047i	$-0.683113\pi$
$487$	143.660	−	143.660i	0.294989	−	0.294989i	0.839047	+	0.544058i	$0.183113\pi$
$488$		0			0
$489$	−1.47216	+	1.47216i	−0.00301055	+	0.00301055i
$490$		0			0
$491$	−182.575	+	440.775i	−0.371843	+	0.897709i	0.621595	+	0.783339i	$0.286485\pi$
$491$	−182.575	+	440.775i	−0.371843	+	0.897709i	−0.993438	+	0.114370i	$0.963515\pi$
$492$		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	0.0678733	−	0.997694i	$-0.478379\pi$
$499$	409.850	−	169.766i	0.821343	−	0.340211i	0.753470	+	0.657482i	$0.228379\pi$
$500$		0			0
$501$	−572.179	−	237.004i	−1.14207	−	0.473063i
$502$		0			0
$503$	−453.715	−	453.715i	−0.902019	−	0.902019i	0.0935920	−	0.995611i	$-0.470165\pi$
$503$	−453.715	−	453.715i	−0.902019	−	0.902019i	−0.995611	+	0.0935920i	$0.970165\pi$
$504$		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	−0.451815	−	0.892112i	$-0.649223\pi$
$509$	−71.5029	+	29.6175i	−0.140477	+	0.0581876i	0.311337	+	0.950299i	$0.399223\pi$
$510$		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	−0.0899020	+	0.995951i	$0.528655\pi$
$521$	−565.729	+	565.729i	−1.08585	+	1.08585i	−0.995951	+	0.0899020i	$0.971345\pi$
$522$		0			0
$523$	1.50925	−	3.64366i	0.00288576	−	0.00696685i	−0.922430	−	0.386164i	$-0.873800\pi$
$523$	1.50925	−	3.64366i	0.00288576	−	0.00696685i	0.925316	+	0.379197i	$0.123800\pi$
$524$		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	−0.944531	−	0.328421i	$-0.893483\pi$
$541$	−746.681	+	309.286i	−1.38019	+	0.571692i	−0.435656	+	0.900113i	$0.643483\pi$
$542$		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	−0.921076	−	0.389383i	$-0.872688\pi$
$547$	−298.176	−	719.861i	−0.545112	−	1.31602i	0.375964	−	0.926634i	$-0.377312\pi$
$548$		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	0.980900	−	0.194515i	$-0.0623132\pi$
$557$	83.4142	+	201.380i	0.149756	+	0.361544i	−0.831143	+	0.556058i	$0.812313\pi$
$558$		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	−0.365226	−	0.930919i	$-0.619008\pi$
$563$	19.5811	−	8.11076i	0.0347800	−	0.0144063i	0.400006	+	0.916513i	$0.369008\pi$
$564$		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	0.307106	−	0.951675i	$-0.400639\pi$
$569$	−366.760	−	366.760i	−0.644569	−	0.644569i	−0.951675	+	0.307106i	$0.900639\pi$
$570$		0			0
$571$	121.285	+	50.2378i	0.212408	+	0.0879822i	0.486350	−	0.873764i	$-0.338328\pi$
$571$	121.285	+	50.2378i	0.212408	+	0.0879822i	−0.273943	+	0.961746i	$0.588328\pi$
$572$		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	−0.999561	−	0.0296380i	$-0.990565\pi$
$587$	−159.551	+	385.190i	−0.271807	+	0.656201i	0.727753	+	0.685839i	$0.240565\pi$
$588$		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	$-0.870174\pi$
$593$		−	470.422i		−	0.793292i	0.917972	−	0.396646i	$-0.129826\pi$
$594$		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	0.989645	−	0.143540i	$-0.0458485\pi$
$599$	506.817	+	506.817i	0.846105	+	0.846105i	−0.143540	+	0.989645i	$0.545849\pi$
$600$		0			0
$601$	−261.398	−	261.398i	−0.434939	−	0.434939i	0.455366	−	0.890305i	$-0.349509\pi$
$601$	−261.398	−	261.398i	−0.434939	−	0.434939i	−0.890305	+	0.455366i	$0.849509\pi$
$602$		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	$0.233250\pi$
$607$			812.089i			1.33787i	−0.743319	+	0.668937i	$0.766750\pi$
$608$		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	−0.814588	−	0.580040i	$-0.803037\pi$
$613$	105.168	−	253.898i	0.171563	−	0.414190i	0.986151	+	0.165850i	$0.0530369\pi$
$614$		0			0
$615$	−889.264	+	889.264i	−1.44596	+	1.44596i
$616$		0			0
$617$	−508.739	+	508.739i	−0.824536	+	0.824536i	−0.986755	−	0.162218i	$-0.948135\pi$
$617$	−508.739	+	508.739i	−0.824536	+	0.824536i	0.162218	+	0.986755i	$0.448135\pi$
$618$		0			0
$619$	6.64960	−	16.0536i	0.0107425	−	0.0259347i	−0.918417	−	0.395613i	$-0.870532\pi$
$619$	6.64960	−	16.0536i	0.0107425	−	0.0259347i	0.929160	+	0.369678i	$0.120532\pi$
$620$		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	0.833639	−	0.552310i	$-0.186254\pi$
$631$	177.518	+	177.518i	0.281329	+	0.281329i	−0.552310	+	0.833639i	$0.686254\pi$
$632$		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	0.938651	−	0.344867i	$-0.112076\pi$
$643$	19.9758	+	48.2257i	0.0310665	+	0.0750011i	−0.907585	+	0.419869i	$0.862076\pi$
$644$		0			0
$645$	−538.584	+	1300.26i	−0.835015	+	2.01590i
$646$		0			0
$647$	−443.581	+	443.581i	−0.685596	+	0.685596i	−0.961255	−	0.275659i	$-0.911104\pi$
$647$	−443.581	+	443.581i	−0.685596	+	0.685596i	0.275659	+	0.961255i	$0.411104\pi$
$648$		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	0.912736	−	0.408549i	$-0.133965\pi$
$653$	−14.0746	−	33.9792i	−0.0215538	−	0.0520355i	−0.934290	+	0.356514i	$0.883965\pi$
$654$		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	0.366407	−	0.930455i	$-0.380588\pi$
$659$	845.778	−	350.333i	1.28343	−	0.531613i	0.917020	+	0.398842i	$0.130588\pi$
$660$		0			0
$661$	−1022.39	−	423.490i	−1.54674	−	0.640680i	−0.564017	−	0.825763i	$-0.690745\pi$
$661$	−1022.39	−	423.490i	−1.54674	−	0.640680i	−0.982723	+	0.185083i	$0.940745\pi$
$662$		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	−0.926173	−	0.377098i	$-0.876922\pi$
$677$	−3.12869	+	7.55333i	−0.00462140	+	0.0111571i	0.921552	+	0.388255i	$0.126922\pi$
$678$		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	−0.708851	−	0.705358i	$-0.750786\pi$
$683$	198.853	−	480.073i	0.291146	−	0.702889i	0.999997	+	0.00246964i	$0.000786112\pi$
$684$		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	−0.563000	−	0.826457i	$-0.690353\pi$
$691$	−260.304	+	107.822i	−0.376707	+	0.156037i	0.186293	+	0.982494i	$0.440353\pi$
$692$		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	−0.702160	−	0.712019i	$-0.747781\pi$
$701$	−487.328	+	201.858i	−0.695189	+	0.287957i	0.00697111	+	0.999976i	$0.497781\pi$
$702$		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	−0.626046	−	0.779786i	$-0.715328\pi$
$709$	260.932	−	629.945i	0.368028	−	0.888498i	0.994073	−	0.108711i	$-0.0346724\pi$
$710$		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	0.746113	−	0.665819i	$-0.231918\pi$
$727$	58.3736	+	58.3736i	0.0802938	+	0.0802938i	−0.665819	+	0.746113i	$0.731918\pi$
$728$		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	−0.147831	−	0.989013i	$-0.547229\pi$
$733$	327.632	−	135.710i	0.446975	−	0.185143i	0.594805	+	0.803870i	$0.297229\pi$
$734$		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	−0.974334	−	0.225108i	$-0.927726\pi$
$739$	−328.523	−	793.126i	−0.444551	−	1.07324i	0.529783	−	0.848134i	$-0.322274\pi$
$740$		0			0
$741$	257.266	−	621.096i	0.347188	−	0.838186i
$742$		0			0
$743$	−79.8532	+	79.8532i	−0.107474	+	0.107474i	−0.758799	−	0.651325i	$-0.774214\pi$
$743$	−79.8532	+	79.8532i	−0.107474	+	0.107474i	0.651325	+	0.758799i	$0.274214\pi$
$744$		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	0.723784	−	0.690027i	$-0.242401\pi$
$757$	565.974	+	234.434i	0.747654	+	0.309688i	0.0238700	+	0.999715i	$0.492401\pi$
$758$		0			0
$759$	−105.549	−	105.549i	−0.139063	−	0.139063i
$760$		0			0
$761$	186.563	+	186.563i	0.245155	+	0.245155i	0.818979	−	0.573824i	$-0.194541\pi$
$761$	186.563	+	186.563i	0.245155	+	0.245155i	−0.573824	+	0.818979i	$0.694541\pi$
$762$		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	−0.991872	−	0.127243i	$-0.959387\pi$
$773$	−155.016	+	374.241i	−0.200538	+	0.484141i	0.791334	+	0.611384i	$0.209387\pi$
$774$		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	−0.657604	−	0.753364i	$-0.728430\pi$
$787$	−464.245	+	192.297i	−0.589892	+	0.244341i	0.0677120	+	0.997705i	$0.478430\pi$
$788$		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	0.800564	−	0.599247i	$-0.204533\pi$
$797$	1426.93	−	591.055i	1.79038	−	0.741600i	0.989816	−	0.142353i	$-0.0454669\pi$
$798$		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	−0.193570	+	0.981086i	$0.562007\pi$
$809$	−950.297	+	950.297i	−1.17466	+	1.17466i	−0.981086	+	0.193570i	$0.937993\pi$
$810$		0			0
$811$	580.036	−	1400.33i	0.715210	−	1.72667i	0.0286586	−	0.999589i	$-0.490876\pi$
$811$	580.036	−	1400.33i	0.715210	−	1.72667i	0.686552	−	0.727081i	$-0.259124\pi$
$812$		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	0.740074	−	0.672525i	$-0.234790\pi$
$821$	646.816	+	267.920i	0.787839	+	0.326334i	0.0477645	+	0.998859i	$0.484790\pi$
$822$		0			0
$823$	262.313	+	262.313i	0.318728	+	0.318728i	0.848278	−	0.529551i	$-0.177639\pi$
$823$	262.313	+	262.313i	0.318728	+	0.318728i	−0.529551	+	0.848278i	$0.677639\pi$
$824$		0			0
$825$	−73.2755	−	73.2755i	−0.0888187	−	0.0888187i
$826$		0			0
$827$	−893.204	−	369.977i	−1.08005	−	0.447373i	−0.229525	−	0.973303i	$-0.573717\pi$
$827$	−893.204	−	369.977i	−1.08005	−	0.447373i	−0.850528	+	0.525930i	$0.823717\pi$
$828$		0			0
$829$	−161.439	+	66.8701i	−0.194739	+	0.0806635i	−0.477922	−	0.878402i	$-0.658610\pi$
$829$	−161.439	+	66.8701i	−0.194739	+	0.0806635i	0.283183	+	0.959066i	$0.408610\pi$
$830$		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	−0.955116	−	0.296234i	$-0.904269\pi$
$839$	−552.802	+	552.802i	−0.658882	+	0.658882i	0.296234	+	0.955116i	$0.404269\pi$
$840$		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	−0.0347472	−	0.999396i	$-0.511063\pi$
$853$	−653.395	−	270.645i	−0.765997	−	0.317286i	−0.731250	+	0.682110i	$0.761063\pi$
$854$		0			0
$855$	−530.692	−	530.692i	−0.620693	−	0.620693i
$856$		0			0
$857$	−26.5894	−	26.5894i	−0.0310261	−	0.0310261i	0.691424	−	0.722450i	$-0.256984\pi$
$857$	−26.5894	−	26.5894i	−0.0310261	−	0.0310261i	−0.722450	+	0.691424i	$0.756984\pi$
$858$		0			0
$859$	−149.594	−	61.9638i	−0.174149	−	0.0721349i	0.293906	−	0.955834i	$-0.405045\pi$
$859$	−149.594	−	61.9638i	−0.174149	−	0.0721349i	−0.468054	+	0.883700i	$0.655045\pi$
$860$		0			0
$861$	1785.28	−	739.488i	2.07350	−	0.858871i
$862$		0			0
$863$		−	448.190i		−	0.519339i	−0.965698	−	0.259670i	$-0.916386\pi$
$863$		−	448.190i		−	0.519339i	0.965698	−	0.259670i	$-0.0836137\pi$
$864$		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	−0.998935	−	0.0461461i	$-0.985306\pi$
$877$	−285.210	−	688.559i	−0.325211	−	0.785130i	0.673723	−	0.738984i	$-0.264694\pi$
$878$		0			0
$879$	−1185.20			−1.34835
$880$		0			0
$881$			140.757i			0.159770i	0.996804	+	0.0798849i	$0.0254553\pi$
$881$			140.757i			0.159770i	−0.996804	+	0.0798849i	$0.974545\pi$
$882$		0			0
$883$	644.358	−	266.902i	0.729737	−	0.302267i	0.0132930	−	0.999912i	$-0.495769\pi$
$883$	644.358	−	266.902i	0.729737	−	0.302267i	0.716444	+	0.697645i	$0.245769\pi$
$884$		0			0
$885$	1100.42	+	455.810i	1.24341	+	0.515039i
$886$		0			0
$887$	251.938	+	251.938i	0.284034	+	0.284034i	0.834715	−	0.550682i	$-0.185632\pi$
$887$	251.938	+	251.938i	0.284034	+	0.284034i	−0.550682	+	0.834715i	$0.685632\pi$
$888$		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	−0.933283	−	0.359142i	$-0.883069\pi$
$907$	−17.5960	+	42.4804i	−0.0194002	+	0.0468362i	0.913883	+	0.405979i	$0.133069\pi$
$908$		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	0.498050	−	0.867148i	$-0.334049\pi$
$919$	−339.201	−	339.201i	−0.369098	−	0.369098i	−0.867148	+	0.498050i	$0.834049\pi$
$920$		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	−0.991951	−	0.126626i	$-0.959585\pi$
$937$	−810.809	+	810.809i	−0.865325	+	0.865325i	0.126626	+	0.991951i	$0.459585\pi$
$938$		0			0
$939$	−877.579	+	2118.66i	−0.934589	+	2.25630i
$940$		0			0
$941$	−372.431	−	899.128i	−0.395782	−	0.955503i	−0.988655	−	0.150206i	$-0.952006\pi$
$941$	−372.431	−	899.128i	−0.395782	−	0.955503i	0.592873	−	0.805296i	$-0.297994\pi$
$942$		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	−0.697310	−	0.716769i	$-0.745620\pi$
$947$	−647.322	+	268.130i	−0.683551	+	0.283136i	0.0137596	+	0.999905i	$0.495620\pi$
$948$		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	0.330187	−	0.943916i	$-0.392888\pi$
$953$	−584.883	−	584.883i	−0.613728	−	0.613728i	−0.943916	+	0.330187i	$0.892888\pi$
$954$		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	−0.792905	−	0.609345i	$-0.791432\pi$
$967$	−177.502	+	177.502i	−0.183560	+	0.183560i	0.609345	+	0.792905i	$0.291432\pi$
$968$		0			0
$969$	−122.425	+	122.425i	−0.126342	+	0.126342i
$970$		0			0
$971$	−130.414	+	314.847i	−0.134309	+	0.324250i	−0.976698	−	0.214620i	$-0.931149\pi$
$971$	−130.414	+	314.847i	−0.134309	+	0.324250i	0.842389	+	0.538870i	$0.181149\pi$
$972$		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	$0.0119178\pi$
$977$			73.1425i			0.0748644i	−0.999299	+	0.0374322i	$0.988082\pi$
$978$		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	0.946778	−	0.321886i	$-0.104317\pi$
$983$	614.269	+	614.269i	0.624892	+	0.624892i	−0.321886	+	0.946778i	$0.604317\pi$
$984$		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	$0.125856\pi$
$991$			763.403i			0.770336i	−0.922847	+	0.385168i	$0.874144\pi$
$992$		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	−0.225923	+	0.974145i	$0.572540\pi$
$997$	−752.731	+	1817.25i	−0.754996	+	1.82272i	−0.529073	+	0.848576i	$0.677460\pi$
$998$		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.79.7		28
4.3	odd	2		32.3.h.a.11.7	yes	28
8.3	odd	2		256.3.h.b.159.7		28
8.5	even	2		256.3.h.a.159.1		28
12.11	even	2		288.3.u.a.235.1		28
32.3	odd	8	inner	128.3.h.a.47.7		28
32.13	even	8		256.3.h.b.95.7		28
32.19	odd	8		256.3.h.a.95.1		28
32.29	even	8		32.3.h.a.3.7	✓	28
96.29	odd	8		288.3.u.a.163.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.7	✓	28	32.29	even	8
32.3.h.a.11.7	yes	28	4.3	odd	2
128.3.h.a.47.7		28	32.3	odd	8	inner
128.3.h.a.79.7		28	1.1	even	1	trivial
256.3.h.a.95.1		28	32.19	odd	8
256.3.h.a.159.1		28	8.5	even	2
256.3.h.b.95.7		28	32.13	even	8
256.3.h.b.159.7		28	8.3	odd	2
288.3.u.a.163.1		28	96.29	odd	8
288.3.u.a.235.1		28	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
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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Representations

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Database

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