LMFDB - Embedded newform 128.3.h.a.15.5

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			15.5
Character	$\chi$	$=$	128.15
Dual form			128.3.h.a.111.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37292 - 0.568682i) q^{3} +(2.28872 + 0.948019i) q^{5} +(6.37744 - 6.37744i) q^{7} +(-4.80245 + 4.80245i) q^{9} +O(q^{10})$	\(q+(1.37292 - 0.568682i) q^{3} +(2.28872 + 0.948019i) q^{5} +(6.37744 - 6.37744i) q^{7} +(-4.80245 + 4.80245i) q^{9} +(1.79646 + 0.744117i) q^{11} +(16.7036 - 6.91888i) q^{13} +3.68135 q^{15} -6.19811i q^{17} +(8.50083 + 20.5228i) q^{19} +(5.12898 - 12.3825i) q^{21} +(-23.6476 - 23.6476i) q^{23} +(-13.3382 - 13.3382i) q^{25} +(-8.98045 + 21.6807i) q^{27} +(14.5725 + 35.1811i) q^{29} +14.1609i q^{31} +2.88956 q^{33} +(20.6421 - 8.55025i) q^{35} +(-30.0695 - 12.4552i) q^{37} +(18.9981 - 18.9981i) q^{39} +(-56.9700 + 56.9700i) q^{41} +(-54.5034 - 22.5760i) q^{43} +(-15.5443 + 6.43866i) q^{45} -34.8047 q^{47} -32.3435i q^{49} +(-3.52475 - 8.50951i) q^{51} +(3.92967 - 9.48706i) q^{53} +(3.40615 + 3.40615i) q^{55} +(23.3419 + 23.3419i) q^{57} +(-9.41777 + 22.7365i) q^{59} +(3.00467 + 7.25391i) q^{61} +61.2547i q^{63} +44.7892 q^{65} +(55.9040 - 23.1562i) q^{67} +(-45.9141 - 19.0183i) q^{69} +(-6.27499 + 6.27499i) q^{71} +(66.4597 - 66.4597i) q^{73} +(-25.8974 - 10.7271i) q^{75} +(16.2024 - 6.71124i) q^{77} +75.8508 q^{79} -26.2523i q^{81} +(1.23390 + 2.97891i) q^{83} +(5.87593 - 14.1857i) q^{85} +(40.0138 + 40.0138i) q^{87} +(36.7030 + 36.7030i) q^{89} +(62.4018 - 150.651i) q^{91} +(8.05304 + 19.4417i) q^{93} +55.0300i q^{95} +90.0528 q^{97} +(-12.2010 + 5.05381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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
$3$	1.37292	−	0.568682i	0.457640	−	0.189561i	−0.141940	−	0.989875i	$-0.545334\pi$
$3$	1.37292	−	0.568682i	0.457640	−	0.189561i	0.599580	+	0.800315i	$0.295334\pi$
$4$		0			0
$5$	2.28872	+	0.948019i	0.457744	+	0.189604i	0.599627	−	0.800280i	$-0.295316\pi$
$5$	2.28872	+	0.948019i	0.457744	+	0.189604i	−0.141883	+	0.989883i	$0.545316\pi$
$6$		0			0
$7$	6.37744	−	6.37744i	0.911063	−	0.911063i	−0.0852929	−	0.996356i	$-0.527183\pi$
$7$	6.37744	−	6.37744i	0.911063	−	0.911063i	0.996356	+	0.0852929i	$0.0271826\pi$
$8$		0			0
$9$	−4.80245	+	4.80245i	−0.533606	+	0.533606i
$10$		0			0
$11$	1.79646	+	0.744117i	0.163314	+	0.0676470i	0.462843	−	0.886440i	$-0.346829\pi$
$11$	1.79646	+	0.744117i	0.163314	+	0.0676470i	−0.299529	+	0.954087i	$0.596829\pi$
$12$		0			0
$13$	16.7036	−	6.91888i	1.28490	−	0.532221i	0.367436	−	0.930049i	$-0.380236\pi$
$13$	16.7036	−	6.91888i	1.28490	−	0.532221i	0.917460	+	0.397827i	$0.130236\pi$
$14$		0			0
$15$	3.68135			0.245423
$16$		0			0
$17$		−	6.19811i		−	0.364595i	−0.983243	−	0.182297i	$-0.941647\pi$
$17$		−	6.19811i		−	0.364595i	0.983243	−	0.182297i	$-0.0583533\pi$
$18$		0			0
$19$	8.50083	+	20.5228i	0.447412	+	1.08015i	0.973288	+	0.229587i	$0.0737375\pi$
$19$	8.50083	+	20.5228i	0.447412	+	1.08015i	−0.525876	+	0.850561i	$0.676262\pi$
$20$		0			0
$21$	5.12898	−	12.3825i	0.244237	−	0.589641i
$22$		0			0
$23$	−23.6476	−	23.6476i	−1.02815	−	1.02815i	−0.999592	−	0.0285625i	$-0.990907\pi$
$23$	−23.6476	−	23.6476i	−1.02815	−	1.02815i	−0.0285625	−	0.999592i	$-0.509093\pi$
$24$		0			0
$25$	−13.3382	−	13.3382i	−0.533527	−	0.533527i
$26$		0			0
$27$	−8.98045	+	21.6807i	−0.332609	+	0.802990i
$28$		0			0
$29$	14.5725	+	35.1811i	0.502500	+	1.21314i	0.948118	+	0.317919i	$0.102984\pi$
$29$	14.5725	+	35.1811i	0.502500	+	1.21314i	−0.445618	+	0.895223i	$0.647016\pi$
$30$		0			0
$31$			14.1609i			0.456803i	0.973567	+	0.228401i	$0.0733498\pi$
$31$			14.1609i			0.456803i	−0.973567	+	0.228401i	$0.926650\pi$
$32$		0			0
$33$	2.88956			0.0875623
$34$		0			0
$35$	20.6421	−	8.55025i	0.589775	−	0.244293i
$36$		0			0
$37$	−30.0695	−	12.4552i	−0.812689	−	0.336627i	−0.0626629	−	0.998035i	$-0.519959\pi$
$37$	−30.0695	−	12.4552i	−0.812689	−	0.336627i	−0.750027	+	0.661408i	$0.769959\pi$
$38$		0			0
$39$	18.9981	−	18.9981i	0.487131	−	0.487131i
$40$		0			0
$41$	−56.9700	+	56.9700i	−1.38951	+	1.38951i	−0.563170	+	0.826341i	$0.690418\pi$
$41$	−56.9700	+	56.9700i	−1.38951	+	1.38951i	−0.826341	+	0.563170i	$0.809582\pi$
$42$		0			0
$43$	−54.5034	−	22.5760i	−1.26752	−	0.525024i	−0.355310	−	0.934748i	$-0.615625\pi$
$43$	−54.5034	−	22.5760i	−1.26752	−	0.525024i	−0.912209	+	0.409724i	$0.865625\pi$
$44$		0			0
$45$	−15.5443	+	6.43866i	−0.345429	+	0.143081i
$46$		0			0
$47$	−34.8047			−0.740525			−0.370263	−	0.928927i	$-0.620732\pi$
$47$	−34.8047			−0.740525			−0.370263	+	0.928927i	$0.620732\pi$
$48$		0			0
$49$		−	32.3435i		−	0.660072i
$50$		0			0
$51$	−3.52475	−	8.50951i	−0.0691128	−	0.166853i
$52$		0			0
$53$	3.92967	−	9.48706i	0.0741447	−	0.179001i	−0.882462	−	0.470384i	$-0.844115\pi$
$53$	3.92967	−	9.48706i	0.0741447	−	0.179001i	0.956606	+	0.291383i	$0.0941154\pi$
$54$		0			0
$55$	3.40615	+	3.40615i	0.0619300	+	0.0619300i
$56$		0			0
$57$	23.3419	+	23.3419i	0.409507	+	0.409507i
$58$		0			0
$59$	−9.41777	+	22.7365i	−0.159623	+	0.385365i	−0.983375	−	0.181586i	$-0.941877\pi$
$59$	−9.41777	+	22.7365i	−0.159623	+	0.385365i	0.823752	+	0.566951i	$0.191877\pi$
$60$		0			0
$61$	3.00467	+	7.25391i	0.0492568	+	0.118916i	0.946593	−	0.322432i	$-0.104500\pi$
$61$	3.00467	+	7.25391i	0.0492568	+	0.118916i	−0.897336	+	0.441348i	$0.854500\pi$
$62$		0			0
$63$			61.2547i			0.972297i
$64$		0			0
$65$	44.7892			0.689065
$66$		0			0
$67$	55.9040	−	23.1562i	0.834388	−	0.345615i	0.0757497	−	0.997127i	$-0.475865\pi$
$67$	55.9040	−	23.1562i	0.834388	−	0.345615i	0.758638	+	0.651512i	$0.225865\pi$
$68$		0			0
$69$	−45.9141	−	19.0183i	−0.665422	−	0.275627i
$70$		0			0
$71$	−6.27499	+	6.27499i	−0.0883801	+	0.0883801i	−0.749915	−	0.661535i	$-0.769905\pi$
$71$	−6.27499	+	6.27499i	−0.0883801	+	0.0883801i	0.661535	+	0.749915i	$0.269905\pi$
$72$		0			0
$73$	66.4597	−	66.4597i	0.910406	−	0.910406i	−0.0858977	−	0.996304i	$-0.527376\pi$
$73$	66.4597	−	66.4597i	0.910406	−	0.910406i	0.996304	+	0.0858977i	$0.0273758\pi$
$74$		0			0
$75$	−25.8974	−	10.7271i	−0.345299	−	0.143027i
$76$		0			0
$77$	16.2024	−	6.71124i	0.210420	−	0.0871589i
$78$		0			0
$79$	75.8508			0.960136			0.480068	−	0.877231i	$-0.340612\pi$
$79$	75.8508			0.960136			0.480068	+	0.877231i	$0.340612\pi$
$80$		0			0
$81$		−	26.2523i		−	0.324103i
$82$		0			0
$83$	1.23390	+	2.97891i	0.0148663	+	0.0358905i	0.931138	−	0.364666i	$-0.118817\pi$
$83$	1.23390	+	2.97891i	0.0148663	+	0.0358905i	−0.916272	+	0.400556i	$0.868817\pi$
$84$		0			0
$85$	5.87593	−	14.1857i	0.0691286	−	0.166891i
$86$		0			0
$87$	40.0138	+	40.0138i	0.459928	+	0.459928i
$88$		0			0
$89$	36.7030	+	36.7030i	0.412393	+	0.412393i	0.882572	−	0.470178i	$-0.155810\pi$
$89$	36.7030	+	36.7030i	0.412393	+	0.412393i	−0.470178	+	0.882572i	$0.655810\pi$
$90$		0			0
$91$	62.4018	−	150.651i	0.685734	−	1.65551i
$92$		0			0
$93$	8.05304	+	19.4417i	0.0865918	+	0.209051i
$94$		0			0
$95$			55.0300i			0.579263i
$96$		0			0
$97$	90.0528			0.928379			0.464189	−	0.885736i	$-0.346346\pi$
$97$	90.0528			0.928379			0.464189	+	0.885736i	$0.346346\pi$
$98$		0			0
$99$	−12.2010	+	5.05381i	−0.123242	+	0.0510486i
$100$		0			0
$101$	−20.0870	−	8.32031i	−0.198881	−	0.0823793i	0.281020	−	0.959702i	$-0.409327\pi$
$101$	−20.0870	−	8.32031i	−0.198881	−	0.0823793i	−0.479901	+	0.877323i	$0.659327\pi$
$102$		0			0
$103$	−4.88882	+	4.88882i	−0.0474642	+	0.0474642i	−0.730441	−	0.682976i	$-0.760685\pi$
$103$	−4.88882	+	4.88882i	−0.0474642	+	0.0474642i	0.682976	+	0.730441i	$0.260685\pi$
$104$		0			0
$105$	23.4776	−	23.4776i	0.223596	−	0.223596i
$106$		0			0
$107$	51.9710	+	21.5271i	0.485710	+	0.201188i	0.612080	−	0.790795i	$-0.290333\pi$
$107$	51.9710	+	21.5271i	0.485710	+	0.201188i	−0.126371	+	0.991983i	$0.540333\pi$
$108$		0			0
$109$	−49.8054	+	20.6301i	−0.456931	+	0.189267i	−0.599263	−	0.800552i	$-0.704540\pi$
$109$	−49.8054	+	20.6301i	−0.456931	+	0.189267i	0.142333	+	0.989819i	$0.454540\pi$
$110$		0			0
$111$	−48.3661			−0.435730
$112$		0			0
$113$			62.0870i			0.549442i	0.961524	+	0.274721i	$0.0885855\pi$
$113$			62.0870i			0.549442i	−0.961524	+	0.274721i	$0.911414\pi$
$114$		0			0
$115$	−31.7043	−	76.5410i	−0.275690	−	0.665574i
$116$		0			0
$117$	−46.9909	+	113.446i	−0.401632	+	0.969624i
$118$		0			0
$119$	−39.5281	−	39.5281i	−0.332169	−	0.332169i
$120$		0			0
$121$	−82.8864	−	82.8864i	−0.685011	−	0.685011i
$122$		0			0
$123$	−45.8174	+	110.613i	−0.372499	+	0.899292i
$124$		0			0
$125$	−41.5830	−	100.390i	−0.332664	−	0.803122i
$126$		0			0
$127$		−	177.045i		−	1.39406i	−0.717043	−	0.697029i	$-0.754505\pi$
$127$		−	177.045i		−	1.39406i	0.717043	−	0.697029i	$-0.245495\pi$
$128$		0			0
$129$	−87.6673			−0.679592
$130$		0			0
$131$	−88.7654	+	36.7678i	−0.677598	+	0.280670i	−0.694823	−	0.719181i	$-0.744517\pi$
$131$	−88.7654	+	36.7678i	−0.677598	+	0.280670i	0.0172241	+	0.999852i	$0.494517\pi$
$132$		0			0
$133$	185.097	+	76.6695i	1.39170	+	0.576462i
$134$		0			0
$135$	−41.1075	+	41.1075i	−0.304500	+	0.304500i
$136$		0			0
$137$	−58.5583	+	58.5583i	−0.427433	+	0.427433i	−0.887753	−	0.460320i	$-0.847735\pi$
$137$	−58.5583	+	58.5583i	−0.427433	+	0.427433i	0.460320	+	0.887753i	$0.347735\pi$
$138$		0			0
$139$	166.832	+	69.1039i	1.20023	+	0.497151i	0.891072	−	0.453861i	$-0.149954\pi$
$139$	166.832	+	69.1039i	1.20023	+	0.497151i	0.309155	+	0.951012i	$0.399954\pi$
$140$		0			0
$141$	−47.7840	+	19.7928i	−0.338894	+	0.140374i
$142$		0			0
$143$	35.1558			0.245845
$144$		0			0
$145$			94.3348i			0.650585i
$146$		0			0
$147$	−18.3932	−	44.4050i	−0.125124	−	0.302075i
$148$		0			0
$149$	18.0040	−	43.4655i	0.120832	−	0.291715i	−0.851877	−	0.523742i	$-0.824536\pi$
$149$	18.0040	−	43.4655i	0.120832	−	0.291715i	0.972709	+	0.232027i	$0.0745357\pi$
$150$		0			0
$151$	68.3596	+	68.3596i	0.452713	+	0.452713i	0.896254	−	0.443541i	$-0.146278\pi$
$151$	68.3596	+	68.3596i	0.452713	+	0.452713i	−0.443541	+	0.896254i	$0.646278\pi$
$152$		0			0
$153$	29.7661	+	29.7661i	0.194550	+	0.194550i
$154$		0			0
$155$	−13.4248	+	32.4103i	−0.0866115	+	0.209099i
$156$		0			0
$157$	−74.5650	−	180.016i	−0.474936	−	1.14660i	−0.961956	−	0.273206i	$-0.911916\pi$
$157$	−74.5650	−	180.016i	−0.474936	−	1.14660i	0.487020	−	0.873391i	$-0.338084\pi$
$158$		0			0
$159$		−	15.2597i		−	0.0959730i
$160$		0			0
$161$	−301.622			−1.87343
$162$		0			0
$163$	−267.123	+	110.646i	−1.63879	+	0.678811i	−0.996175	−	0.0873756i	$-0.972152\pi$
$163$	−267.123	+	110.646i	−1.63879	+	0.678811i	−0.642619	+	0.766186i	$0.722152\pi$
$164$		0			0
$165$	6.61339	+	2.73936i	0.0400812	+	0.0166022i
$166$		0			0
$167$	−99.3059	+	99.3059i	−0.594646	+	0.594646i	−0.938883	−	0.344237i	$-0.888138\pi$
$167$	−99.3059	+	99.3059i	−0.594646	+	0.594646i	0.344237	+	0.938883i	$0.388138\pi$
$168$		0			0
$169$	111.640	−	111.640i	0.660592	−	0.660592i
$170$		0			0
$171$	−139.385	−	57.7350i	−0.815115	−	0.337632i
$172$		0			0
$173$	187.259	−	77.5652i	1.08242	−	0.448354i	0.231063	−	0.972939i	$-0.425780\pi$
$173$	187.259	−	77.5652i	1.08242	−	0.448354i	0.851358	+	0.524585i	$0.175780\pi$
$174$		0			0
$175$	−170.127			−0.972153
$176$		0			0
$177$			36.5711i			0.206617i
$178$		0			0
$179$	101.230	+	244.390i	0.565528	+	1.36531i	0.905290	+	0.424795i	$0.139654\pi$
$179$	101.230	+	244.390i	0.565528	+	1.36531i	−0.339761	+	0.940512i	$0.610346\pi$
$180$		0			0
$181$	6.07796	−	14.6735i	0.0335799	−	0.0810690i	−0.906200	−	0.422849i	$-0.861030\pi$
$181$	6.07796	−	14.6735i	0.0335799	−	0.0810690i	0.939780	+	0.341780i	$0.111030\pi$
$182$		0			0
$183$	8.25033	+	8.25033i	0.0450838	+	0.0450838i
$184$		0			0
$185$	−57.0130	−	57.0130i	−0.308178	−	0.308178i
$186$		0			0
$187$	4.61212	−	11.1346i	0.0246637	−	0.0595435i
$188$		0			0
$189$	80.9953	+	195.540i	0.428546	+	1.03460i
$190$		0			0
$191$		−	370.577i		−	1.94019i	−0.242716	−	0.970097i	$-0.578038\pi$
$191$		−	370.577i		−	1.94019i	0.242716	−	0.970097i	$-0.421962\pi$
$192$		0			0
$193$	−132.679			−0.687456			−0.343728	−	0.939069i	$-0.611690\pi$
$193$	−132.679			−0.687456			−0.343728	+	0.939069i	$0.611690\pi$
$194$		0			0
$195$	61.4920	−	25.4708i	0.315344	−	0.130620i
$196$		0			0
$197$	116.390	+	48.2104i	0.590814	+	0.244723i	0.658001	−	0.753017i	$-0.271402\pi$
$197$	116.390	+	48.2104i	0.590814	+	0.244723i	−0.0671870	+	0.997740i	$0.521402\pi$
$198$		0			0
$199$	89.9950	−	89.9950i	0.452236	−	0.452236i	−0.443860	−	0.896096i	$-0.646391\pi$
$199$	89.9950	−	89.9950i	0.452236	−	0.452236i	0.896096	+	0.443860i	$0.146391\pi$
$200$		0			0
$201$	63.5832	−	63.5832i	0.316334	−	0.316334i
$202$		0			0
$203$	317.301	+	131.430i	1.56306	+	0.647440i
$204$		0			0
$205$	−184.397	+	76.3797i	−0.899498	+	0.372584i
$206$		0			0
$207$	227.132			1.09726
$208$		0			0
$209$			43.1940i			0.206670i
$210$		0			0
$211$	−20.9287	−	50.5264i	−0.0991883	−	0.239462i	0.866494	−	0.499187i	$-0.166368\pi$
$211$	−20.9287	−	50.5264i	−0.0991883	−	0.239462i	−0.965683	+	0.259725i	$0.916368\pi$
$212$		0			0
$213$	−5.04658	+	12.1835i	−0.0236929	+	0.0571996i
$214$		0			0
$215$	−103.340	−	103.340i	−0.480653	−	0.480653i
$216$		0			0
$217$	90.3102	+	90.3102i	0.416176	+	0.416176i
$218$		0			0
$219$	53.4494	−	129.038i	0.244061	−	0.589215i
$220$		0			0
$221$	−42.8840	−	103.531i	−0.194045	−	0.468466i
$222$		0			0
$223$			52.7540i			0.236565i	0.992980	+	0.118283i	$0.0377388\pi$
$223$			52.7540i			0.236565i	−0.992980	+	0.118283i	$0.962261\pi$
$224$		0			0
$225$	128.112			0.569386
$226$		0			0
$227$	327.101	−	135.490i	1.44097	−	0.596871i	0.480939	−	0.876754i	$-0.340296\pi$
$227$	327.101	−	135.490i	1.44097	−	0.596871i	0.960034	+	0.279883i	$0.0902957\pi$
$228$		0			0
$229$	245.430	+	101.660i	1.07175	+	0.443932i	0.847606	−	0.530625i	$-0.178043\pi$
$229$	245.430	+	101.660i	1.07175	+	0.443932i	0.224139	+	0.974557i	$0.428043\pi$
$230$		0			0
$231$	18.4280	−	18.4280i	0.0797748	−	0.0797748i
$232$		0			0
$233$	−31.8772	+	31.8772i	−0.136812	+	0.136812i	−0.772196	−	0.635384i	$-0.780842\pi$
$233$	−31.8772	+	31.8772i	−0.136812	+	0.136812i	0.635384	+	0.772196i	$0.280842\pi$
$234$		0			0
$235$	−79.6582	−	32.9955i	−0.338971	−	0.140406i
$236$		0			0
$237$	104.137	−	43.1350i	0.439397	−	0.182004i
$238$		0			0
$239$	−90.0511			−0.376783			−0.188391	−	0.982094i	$-0.560327\pi$
$239$	−90.0511			−0.376783			−0.188391	+	0.982094i	$0.560327\pi$
$240$		0			0
$241$		−	20.9972i		−	0.0871252i	−0.999051	−	0.0435626i	$-0.986129\pi$
$241$		−	20.9972i		−	0.0871252i	0.999051	−	0.0435626i	$-0.0138708\pi$
$242$		0			0
$243$	−95.7533	−	231.169i	−0.394046	−	0.951312i
$244$		0			0
$245$	30.6623	−	74.0253i	0.125152	−	0.302144i
$246$		0			0
$247$	283.990	+	283.990i	1.14976	+	1.14976i
$248$		0			0
$249$	3.38810	+	3.38810i	0.0136068	+	0.0136068i
$250$		0			0
$251$	−105.207	+	253.991i	−0.419150	+	1.01192i	0.563444	+	0.826154i	$0.309476\pi$
$251$	−105.207	+	253.991i	−0.419150	+	1.01192i	−0.982594	+	0.185764i	$0.940524\pi$
$252$		0			0
$253$	−24.8853	−	60.0783i	−0.0983607	−	0.237464i
$254$		0			0
$255$		−	22.8174i		−	0.0894801i
$256$		0			0
$257$	236.584			0.920561			0.460281	−	0.887773i	$-0.347749\pi$
$257$	236.584			0.920561			0.460281	+	0.887773i	$0.347749\pi$
$258$		0			0
$259$	−271.199	+	112.334i	−1.04710	+	0.433723i
$260$		0			0
$261$	−238.939	−	98.9720i	−0.915477	−	0.379203i
$262$		0			0
$263$	−32.0070	+	32.0070i	−0.121700	+	0.121700i	−0.765334	−	0.643634i	$-0.777426\pi$
$263$	−32.0070	+	32.0070i	−0.121700	+	0.121700i	0.643634	+	0.765334i	$0.277426\pi$
$264$		0			0
$265$	17.9878	−	17.9878i	0.0678786	−	0.0678786i
$266$		0			0
$267$	71.2626	+	29.5179i	0.266901	+	0.110554i
$268$		0			0
$269$	115.344	−	47.7769i	0.428787	−	0.177609i	−0.157844	−	0.987464i	$-0.550454\pi$
$269$	115.344	−	47.7769i	0.428787	−	0.177609i	0.586630	+	0.809855i	$0.300454\pi$
$270$		0			0
$271$	55.4325			0.204548			0.102274	−	0.994756i	$-0.467388\pi$
$271$	55.4325			0.204548			0.102274	+	0.994756i	$0.467388\pi$
$272$		0			0
$273$		−	242.319i		−	0.887615i
$274$		0			0
$275$	−14.0363	−	33.8866i	−0.0510410	−	0.123224i
$276$		0			0
$277$	−35.7881	+	86.4001i	−0.129199	+	0.311914i	−0.975221	−	0.221235i	$-0.928991\pi$
$277$	−35.7881	+	86.4001i	−0.129199	+	0.311914i	0.846022	+	0.533148i	$0.178991\pi$
$278$		0			0
$279$	−68.0069	−	68.0069i	−0.243752	−	0.243752i
$280$		0			0
$281$	13.8509	+	13.8509i	0.0492914	+	0.0492914i	0.731323	−	0.682031i	$-0.238903\pi$
$281$	13.8509	+	13.8509i	0.0492914	+	0.0492914i	−0.682031	+	0.731323i	$0.738903\pi$
$282$		0			0
$283$	135.615	−	327.403i	0.479205	−	1.15690i	−0.480778	−	0.876843i	$-0.659646\pi$
$283$	135.615	−	327.403i	0.479205	−	1.15690i	0.959982	−	0.280060i	$-0.0903544\pi$
$284$		0			0
$285$	31.2945	+	75.5517i	0.109805	+	0.265094i
$286$		0			0
$287$			726.645i			2.53186i
$288$		0			0
$289$	250.583			0.867071
$290$		0			0
$291$	123.635	−	51.2114i	0.424863	−	0.175984i
$292$		0			0
$293$	−412.791	−	170.984i	−1.40884	−	0.583562i	−0.456811	−	0.889564i	$-0.651009\pi$
$293$	−412.791	−	170.984i	−1.40884	−	0.583562i	−0.952031	+	0.306002i	$0.901009\pi$
$294$		0			0
$295$	−43.1093	+	43.1093i	−0.146133	+	0.146133i
$296$		0			0
$297$	−32.2660	+	32.2660i	−0.108640	+	0.108640i
$298$		0			0
$299$	−558.615	−	231.386i	−1.86828	−	0.773866i
$300$		0			0
$301$	−491.569	+	203.615i	−1.63312	+	0.676461i
$302$		0			0
$303$	−32.3094			−0.106632
$304$		0			0
$305$			19.4507i			0.0637726i
$306$		0			0
$307$	42.3557	+	102.256i	0.137967	+	0.333081i	0.977728	−	0.209874i	$-0.0673054\pi$
$307$	42.3557	+	102.256i	0.137967	+	0.333081i	−0.839762	+	0.542955i	$0.817305\pi$
$308$		0			0
$309$	−3.93177	+	9.49213i	−0.0127242	+	0.0307189i
$310$		0			0
$311$	−337.326	−	337.326i	−1.08465	−	1.08465i	−0.996069	−	0.0885790i	$-0.971767\pi$
$311$	−337.326	−	337.326i	−1.08465	−	1.08465i	−0.0885790	−	0.996069i	$-0.528233\pi$
$312$		0			0
$313$	−70.0735	−	70.0735i	−0.223877	−	0.223877i	0.586252	−	0.810129i	$-0.300603\pi$
$313$	−70.0735	−	70.0735i	−0.223877	−	0.223877i	−0.810129	+	0.586252i	$0.800603\pi$
$314$		0			0
$315$	−58.0707	+	140.195i	−0.184351	+	0.445063i
$316$		0			0
$317$	32.8632	+	79.3388i	0.103669	+	0.250280i	0.967200	−	0.254017i	$-0.0817518\pi$
$317$	32.8632	+	79.3388i	0.103669	+	0.250280i	−0.863530	+	0.504297i	$0.831752\pi$
$318$		0			0
$319$			74.0450i			0.232116i
$320$		0			0
$321$	83.5940			0.260417
$322$		0			0
$323$	127.203	−	52.6891i	0.393816	−	0.163124i
$324$		0			0
$325$	−315.081	−	130.511i	−0.969480	−	0.401572i
$326$		0			0
$327$	−56.6469	+	56.6469i	−0.173232	+	0.173232i
$328$		0			0
$329$	−221.965	+	221.965i	−0.674665	+	0.674665i
$330$		0			0
$331$	−124.865	−	51.7206i	−0.377234	−	0.156256i	0.186006	−	0.982549i	$-0.440446\pi$
$331$	−124.865	−	51.7206i	−0.377234	−	0.156256i	−0.563240	+	0.826293i	$0.690446\pi$
$332$		0			0
$333$	204.223	−	84.5919i	0.613282	−	0.254030i
$334$		0			0
$335$	149.901			0.447466
$336$		0			0
$337$			323.529i			0.960027i	0.877261	+	0.480014i	$0.159368\pi$
$337$			323.529i			0.960027i	−0.877261	+	0.480014i	$0.840632\pi$
$338$		0			0
$339$	35.3077	+	85.2404i	0.104153	+	0.251447i
$340$		0			0
$341$	−10.5373	+	25.4394i	−0.0309013	+	0.0746024i
$342$		0			0
$343$	106.226	+	106.226i	0.309696	+	0.309696i
$344$		0			0
$345$	−87.0550	−	87.0550i	−0.252333	−	0.252333i
$346$		0			0
$347$	135.065	−	326.076i	0.389236	−	0.939700i	−0.600866	−	0.799350i	$-0.705177\pi$
$347$	135.065	−	326.076i	0.389236	−	0.939700i	0.990102	−	0.140350i	$-0.0448226\pi$
$348$		0			0
$349$	187.869	+	453.555i	0.538305	+	1.29958i	0.925905	+	0.377756i	$0.123304\pi$
$349$	187.869	+	453.555i	0.538305	+	1.29958i	−0.387600	+	0.921828i	$0.626696\pi$
$350$		0			0
$351$			424.282i			1.20878i
$352$		0			0
$353$	−70.5556			−0.199874			−0.0999372	−	0.994994i	$-0.531864\pi$
$353$	−70.5556			−0.199874			−0.0999372	+	0.994994i	$0.531864\pi$
$354$		0			0
$355$	−20.3105	+	8.41289i	−0.0572127	+	0.0236983i
$356$		0			0
$357$	−76.7478	−	31.7900i	−0.214980	−	0.0890475i
$358$		0			0
$359$	409.567	−	409.567i	1.14086	−	1.14086i	0.152561	−	0.988294i	$-0.451248\pi$
$359$	409.567	−	409.567i	1.14086	−	1.14086i	0.988294	−	0.152561i	$-0.0487522\pi$
$360$		0			0
$361$	−93.6563	+	93.6563i	−0.259436	+	0.259436i
$362$		0			0
$363$	−160.932	−	66.6604i	−0.443340	−	0.183637i
$364$		0			0
$365$	215.113	−	89.1026i	0.589350	−	0.244117i
$366$		0			0
$367$	−513.680			−1.39967			−0.699837	−	0.714303i	$-0.746744\pi$
$367$	−513.680			−1.39967			−0.699837	+	0.714303i	$0.746744\pi$
$368$		0			0
$369$		−	547.191i		−	1.48290i
$370$		0			0
$371$	−35.4419	−	85.5644i	−0.0955308	−	0.230632i
$372$		0			0
$373$	−46.5164	+	112.301i	−0.124709	+	0.301074i	−0.973887	−	0.227032i	$-0.927098\pi$
$373$	−46.5164	+	112.301i	−0.124709	+	0.301074i	0.849178	+	0.528106i	$0.177098\pi$
$374$		0			0
$375$	−114.180	−	114.180i	−0.304481	−	0.304481i
$376$		0			0
$377$	486.828	+	486.828i	1.29132	+	1.29132i
$378$		0			0
$379$	−172.090	+	415.462i	−0.454064	+	1.09621i	0.516699	+	0.856167i	$0.327160\pi$
$379$	−172.090	+	415.462i	−0.454064	+	1.09621i	−0.970763	+	0.240040i	$0.922840\pi$
$380$		0			0
$381$	−100.683	−	243.069i	−0.264259	−	0.637977i
$382$		0			0
$383$		−	430.627i		−	1.12435i	−0.827017	−	0.562177i	$-0.809964\pi$
$383$		−	430.627i		−	1.12435i	0.827017	−	0.562177i	$-0.190036\pi$
$384$		0			0
$385$	43.4451			0.112844
$386$		0			0
$387$	370.170	−	153.329i	0.956512	−	0.396200i
$388$		0			0
$389$	55.8615	+	23.1386i	0.143603	+	0.0594823i	0.453327	−	0.891344i	$-0.350237\pi$
$389$	55.8615	+	23.1386i	0.143603	+	0.0594823i	−0.309725	+	0.950826i	$0.600237\pi$
$390$		0			0
$391$	−146.570	+	146.570i	−0.374860	+	0.374860i
$392$		0			0
$393$	−100.959	+	100.959i	−0.256892	+	0.256892i
$394$		0			0
$395$	173.601	+	71.9080i	0.439497	+	0.182046i
$396$		0			0
$397$	−67.6641	+	28.0274i	−0.170439	+	0.0705979i	−0.466271	−	0.884642i	$-0.654403\pi$
$397$	−67.6641	+	28.0274i	−0.170439	+	0.0705979i	0.295833	+	0.955240i	$0.404403\pi$
$398$		0			0
$399$	297.723			0.746174
$400$		0			0
$401$		−	536.024i		−	1.33672i	−0.743839	−	0.668359i	$-0.766997\pi$
$401$		−	536.024i		−	1.33672i	0.743839	−	0.668359i	$-0.233003\pi$
$402$		0			0
$403$	97.9774	+	236.538i	0.243120	+	0.586944i
$404$		0			0
$405$	24.8877	−	60.0842i	0.0614511	−	0.148356i
$406$		0			0
$407$	−44.7505	−	44.7505i	−0.109952	−	0.109952i
$408$		0			0
$409$	−540.379	−	540.379i	−1.32122	−	1.32122i	−0.912790	−	0.408430i	$-0.866077\pi$
$409$	−540.379	−	540.379i	−1.32122	−	1.32122i	−0.408430	−	0.912790i	$-0.633923\pi$
$410$		0			0
$411$	−47.0948	+	113.697i	−0.114586	+	0.276635i
$412$		0			0
$413$	84.9395	+	205.062i	0.205665	+	0.496518i
$414$		0			0
$415$			7.98765i			0.0192474i
$416$		0			0
$417$	268.345			0.643512
$418$		0			0
$419$	341.184	−	141.323i	0.814281	−	0.337286i	0.0636205	−	0.997974i	$-0.479735\pi$
$419$	341.184	−	141.323i	0.814281	−	0.337286i	0.750661	+	0.660688i	$0.229735\pi$
$420$		0			0
$421$	339.196	+	140.500i	0.805692	+	0.333728i	0.747234	−	0.664561i	$-0.231382\pi$
$421$	339.196	+	140.500i	0.805692	+	0.333728i	0.0584581	+	0.998290i	$0.481382\pi$
$422$		0			0
$423$	167.148	−	167.148i	0.395149	−	0.395149i
$424$		0			0
$425$	−82.6714	+	82.6714i	−0.194521	+	0.194521i
$426$		0			0
$427$	65.4234	+	27.0993i	0.153216	+	0.0634643i
$428$		0			0
$429$	48.2661	−	19.9925i	0.112508	−	0.0466025i
$430$		0			0
$431$	−154.504			−0.358478			−0.179239	−	0.983806i	$-0.557363\pi$
$431$	−154.504			−0.358478			−0.179239	+	0.983806i	$0.557363\pi$
$432$		0			0
$433$			506.808i			1.17046i	0.810868	+	0.585228i	$0.198995\pi$
$433$			506.808i			1.17046i	−0.810868	+	0.585228i	$0.801005\pi$
$434$		0			0
$435$	53.6465	+	129.514i	0.123325	+	0.297734i
$436$		0			0
$437$	284.291	−	686.338i	0.650550	−	1.57057i
$438$		0			0
$439$	144.746	+	144.746i	0.329718	+	0.329718i	0.852479	−	0.522761i	$-0.175098\pi$
$439$	144.746	+	144.746i	0.329718	+	0.329718i	−0.522761	+	0.852479i	$0.675098\pi$
$440$		0			0
$441$	155.328	+	155.328i	0.352218	+	0.352218i
$442$		0			0
$443$	−230.959	+	557.584i	−0.521351	+	1.25865i	0.415713	+	0.909496i	$0.363532\pi$
$443$	−230.959	+	557.584i	−0.521351	+	1.25865i	−0.937064	+	0.349158i	$0.886468\pi$
$444$		0			0
$445$	49.2078	+	118.798i	0.110579	+	0.266962i
$446$		0			0
$447$		−	69.9132i		−	0.156405i
$448$		0			0
$449$	−0.201052			−0.000447778			−0.000223889	−	1.00000i	$-0.500071\pi$
$449$	−0.201052			−0.000447778			−0.000223889		1.00000i	$0.500071\pi$
$450$		0			0
$451$	−144.736	+	59.9518i	−0.320923	+	0.132931i
$452$		0			0
$453$	132.727	+	54.9774i	0.292996	+	0.121363i
$454$		0			0
$455$	285.641	−	285.641i	0.627782	−	0.627782i
$456$		0			0
$457$	226.835	−	226.835i	0.496358	−	0.496358i	−0.413944	−	0.910302i	$-0.635849\pi$
$457$	226.835	−	226.835i	0.496358	−	0.496358i	0.910302	+	0.413944i	$0.135849\pi$
$458$		0			0
$459$	134.379	+	55.6618i	0.292766	+	0.121268i
$460$		0			0
$461$	496.600	−	205.699i	1.07722	−	0.446201i	0.227690	−	0.973734i	$-0.426883\pi$
$461$	496.600	−	205.699i	1.07722	−	0.446201i	0.849535	+	0.527533i	$0.176883\pi$
$462$		0			0
$463$	520.019			1.12315			0.561576	−	0.827425i	$-0.310195\pi$
$463$	520.019			1.12315			0.561576	+	0.827425i	$0.310195\pi$
$464$		0			0
$465$			52.1312i			0.112110i
$466$		0			0
$467$	−35.4966	−	85.6964i	−0.0760099	−	0.183504i	0.881307	−	0.472544i	$-0.156664\pi$
$467$	−35.4966	−	85.6964i	−0.0760099	−	0.183504i	−0.957317	+	0.289040i	$0.906664\pi$
$468$		0			0
$469$	208.847	−	504.202i	0.445303	−	1.07506i
$470$		0			0
$471$	−204.743	−	204.743i	−0.434699	−	0.434699i
$472$		0			0
$473$	−81.1137	−	81.1137i	−0.171488	−	0.171488i
$474$		0			0
$475$	160.351	−	387.122i	0.337582	−	0.814994i
$476$		0			0
$477$	26.6891	+	64.4332i	0.0559520	+	0.135080i
$478$		0			0
$479$		−	163.116i		−	0.340535i	−0.985398	−	0.170268i	$-0.945537\pi$
$479$		−	163.116i		−	0.340535i	0.985398	−	0.170268i	$-0.0544632\pi$
$480$		0			0
$481$	−588.447			−1.22338
$482$		0			0
$483$	−414.102	+	171.527i	−0.857355	+	0.355128i
$484$		0			0
$485$	206.106	+	85.3718i	0.424960	+	0.176024i
$486$		0			0
$487$	−371.724	+	371.724i	−0.763294	+	0.763294i	−0.976916	−	0.213622i	$-0.931474\pi$
$487$	−371.724	+	371.724i	−0.763294	+	0.763294i	0.213622	+	0.976916i	$0.431474\pi$
$488$		0			0
$489$	−303.817	+	303.817i	−0.621302	+	0.621302i
$490$		0			0
$491$	−281.201	−	116.477i	−0.572710	−	0.237224i	0.0774824	−	0.996994i	$-0.475312\pi$
$491$	−281.201	−	116.477i	−0.572710	−	0.237224i	−0.650193	+	0.759769i	$0.725312\pi$
$492$		0			0
$493$	218.056	−	90.3220i	0.442305	−	0.183209i
$494$		0			0
$495$	−32.7158			−0.0660924
$496$		0			0
$497$			80.0367i			0.161040i
$498$		0			0
$499$	236.126	+	570.059i	0.473199	+	1.14240i	0.962741	+	0.270424i	$0.0871639\pi$
$499$	236.126	+	570.059i	0.473199	+	1.14240i	−0.489542	+	0.871980i	$0.662836\pi$
$500$		0			0
$501$	−79.8656	+	192.813i	−0.159412	+	0.384855i
$502$		0			0
$503$	−12.8902	−	12.8902i	−0.0256266	−	0.0256266i	0.694177	−	0.719804i	$-0.255768\pi$
$503$	−12.8902	−	12.8902i	−0.0256266	−	0.0256266i	−0.719804	+	0.694177i	$0.755768\pi$
$504$		0			0
$505$	−38.0857	−	38.0857i	−0.0754173	−	0.0754173i
$506$		0			0
$507$	89.7851	−	216.760i	0.177091	−	0.427535i
$508$		0			0
$509$	59.1272	+	142.746i	0.116163	+	0.280443i	0.971258	−	0.238028i	$-0.0765011\pi$
$509$	59.1272	+	142.746i	0.116163	+	0.280443i	−0.855095	+	0.518472i	$0.826501\pi$
$510$		0			0
$511$		−	847.685i		−	1.65888i
$512$		0			0
$513$	−521.291			−1.01616
$514$		0			0
$515$	−15.8238	+	6.55444i	−0.0307259	+	0.0127271i
$516$		0			0
$517$	−62.5251	−	25.8988i	−0.120938	−	0.0500943i
$518$		0			0
$519$	212.982	−	212.982i	0.410369	−	0.410369i
$520$		0			0
$521$	119.838	−	119.838i	0.230015	−	0.230015i	−0.582684	−	0.812699i	$-0.697997\pi$
$521$	119.838	−	119.838i	0.230015	−	0.230015i	0.812699	+	0.582684i	$0.197997\pi$
$522$		0			0
$523$	689.004	+	285.395i	1.31741	+	0.545688i	0.927037	−	0.374970i	$-0.122347\pi$
$523$	689.004	+	285.395i	1.31741	+	0.545688i	0.390370	+	0.920658i	$0.372347\pi$
$524$		0			0
$525$	−233.570	+	96.7480i	−0.444896	+	0.184282i
$526$		0			0
$527$	87.7707			0.166548
$528$		0			0
$529$			589.413i			1.11420i
$530$		0			0
$531$	−63.9626	−	154.419i	−0.120457	−	0.290809i
$532$		0			0
$533$	−557.438	+	1345.77i	−1.04585	+	2.52490i
$534$		0			0
$535$	98.5390	+	98.5390i	0.184185	+	0.184185i
$536$		0			0
$537$	277.960	+	277.960i	0.517617	+	0.517617i
$538$		0			0
$539$	24.0673	−	58.1037i	0.0446519	−	0.107799i
$540$		0			0
$541$	−294.810	−	711.735i	−0.544936	−	1.31559i	−0.921204	−	0.389081i	$-0.872793\pi$
$541$	−294.810	−	711.735i	−0.544936	−	1.31559i	0.376267	−	0.926511i	$-0.377207\pi$
$542$		0			0
$543$		−	23.6020i		−	0.0434658i
$544$		0			0
$545$	−133.549			−0.245043
$546$		0			0
$547$	−518.930	+	214.948i	−0.948683	+	0.392957i	−0.802736	−	0.596335i	$-0.796623\pi$
$547$	−518.930	+	214.948i	−0.948683	+	0.392957i	−0.145948	+	0.989292i	$0.546623\pi$
$548$		0			0
$549$	−49.2663	−	20.4068i	−0.0897382	−	0.0371708i
$550$		0			0
$551$	−598.138	+	598.138i	−1.08555	+	1.08555i
$552$		0			0
$553$	483.734	−	483.734i	0.874745	−	0.874745i
$554$		0			0
$555$	−110.696	−	45.8520i	−0.199453	−	0.0826162i
$556$		0			0
$557$	−883.511	+	365.962i	−1.58620	+	0.657024i	−0.989380	−	0.145355i	$-0.953568\pi$
$557$	−883.511	+	365.962i	−1.58620	+	0.657024i	−0.596816	+	0.802378i	$0.703568\pi$
$558$		0			0
$559$	−1066.61			−1.90806
$560$		0			0
$561$		−	17.9098i		−	0.0319248i
$562$		0			0
$563$	−385.055	−	929.606i	−0.683935	−	1.65117i	−0.756656	−	0.653813i	$-0.773168\pi$
$563$	−385.055	−	929.606i	−0.683935	−	1.65117i	0.0727214	−	0.997352i	$-0.476832\pi$
$564$		0			0
$565$	−58.8596	+	142.100i	−0.104176	+	0.251504i
$566$		0			0
$567$	−167.423	−	167.423i	−0.295278	−	0.295278i
$568$		0			0
$569$	−503.029	−	503.029i	−0.884058	−	0.884058i	0.109886	−	0.993944i	$-0.464951\pi$
$569$	−503.029	−	503.029i	−0.884058	−	0.884058i	−0.993944	+	0.109886i	$0.964951\pi$
$570$		0			0
$571$	48.1525	−	116.250i	0.0843301	−	0.203591i	−0.876089	−	0.482149i	$-0.839856\pi$
$571$	48.1525	−	116.250i	0.0843301	−	0.203591i	0.960419	+	0.278558i	$0.0898564\pi$
$572$		0			0
$573$	−210.741	−	508.773i	−0.367785	−	0.887910i
$574$		0			0
$575$			630.830i			1.09710i
$576$		0			0
$577$	−11.8629			−0.0205595			−0.0102798	−	0.999947i	$-0.503272\pi$
$577$	−11.8629			−0.0205595			−0.0102798	+	0.999947i	$0.503272\pi$
$578$		0			0
$579$	−182.158	+	75.4522i	−0.314607	+	0.130315i
$580$		0			0
$581$	26.8670	+	11.1287i	0.0462426	+	0.0191543i
$582$		0			0
$583$	14.1190	−	14.1190i	0.0242178	−	0.0242178i
$584$		0			0
$585$	−215.098	+	215.098i	−0.367689	+	0.367689i
$586$		0			0
$587$	496.631	+	205.711i	0.846049	+	0.350445i	0.763236	−	0.646120i	$-0.223610\pi$
$587$	496.631	+	205.711i	0.846049	+	0.350445i	0.0828132	+	0.996565i	$0.473610\pi$
$588$		0			0
$589$	−290.621	+	120.379i	−0.493414	+	0.204379i
$590$		0			0
$591$	187.211			0.316770
$592$		0			0
$593$		−	410.471i		−	0.692193i	−0.938199	−	0.346097i	$-0.887507\pi$
$593$		−	410.471i		−	0.692193i	0.938199	−	0.346097i	$-0.112493\pi$
$594$		0			0
$595$	−52.9954	−	127.942i	−0.0890678	−	0.215029i
$596$		0			0
$597$	72.3774	−	174.735i	0.121235	−	0.292688i
$598$		0			0
$599$	565.778	+	565.778i	0.944537	+	0.944537i	0.998541	−	0.0540033i	$-0.0171982\pi$
$599$	565.778	+	565.778i	0.944537	+	0.944537i	−0.0540033	+	0.998541i	$0.517198\pi$
$600$		0			0
$601$	224.391	+	224.391i	0.373362	+	0.373362i	0.868700	−	0.495338i	$-0.164956\pi$
$601$	224.391	+	224.391i	0.373362	+	0.373362i	−0.495338	+	0.868700i	$0.664956\pi$
$602$		0			0
$603$	−157.270	+	379.683i	−0.260812	+	0.629656i
$604$		0			0
$605$	−111.126	−	268.282i	−0.183679	−	0.443441i
$606$		0			0
$607$		−	19.8654i		−	0.0327271i	−0.999866	−	0.0163636i	$-0.994791\pi$
$607$		−	19.8654i		−	0.0327271i	0.999866	−	0.0163636i	$-0.00520892\pi$
$608$		0			0
$609$	510.371			0.838047
$610$		0			0
$611$	−581.365	+	240.809i	−0.951498	+	0.394123i
$612$		0			0
$613$	905.460	+	375.054i	1.47710	+	0.611833i	0.968464	−	0.249152i	$-0.0801518\pi$
$613$	905.460	+	375.054i	1.47710	+	0.611833i	0.508631	+	0.860985i	$0.330152\pi$
$614$		0			0
$615$	−209.726	+	209.726i	−0.341019	+	0.341019i
$616$		0			0
$617$	673.907	−	673.907i	1.09223	−	1.09223i	0.0969409	−	0.995290i	$-0.469094\pi$
$617$	673.907	−	673.907i	1.09223	−	1.09223i	0.995290	−	0.0969409i	$-0.0309058\pi$
$618$		0			0
$619$	−354.963	−	147.030i	−0.573446	−	0.237529i	0.0770649	−	0.997026i	$-0.475445\pi$
$619$	−354.963	−	147.030i	−0.573446	−	0.237529i	−0.650511	+	0.759497i	$0.725445\pi$
$620$		0			0
$621$	725.062	−	300.330i	1.16757	−	0.483624i
$622$		0			0
$623$	468.143			0.751433
$624$		0			0
$625$			202.389i			0.323822i
$626$		0			0
$627$	24.5636	+	59.3018i	0.0391764	+	0.0945803i
$628$		0			0
$629$	−77.1987	+	186.374i	−0.122732	+	0.296302i
$630$		0			0
$631$	494.698	+	494.698i	0.783991	+	0.783991i	0.980502	−	0.196511i	$-0.0629611\pi$
$631$	494.698	+	494.698i	0.783991	+	0.783991i	−0.196511	+	0.980502i	$0.562961\pi$
$632$		0			0
$633$	−57.4669	−	57.4669i	−0.0907850	−	0.0907850i
$634$		0			0
$635$	167.843	−	405.208i	0.264319	−	0.638122i
$636$		0			0
$637$	−223.781	−	540.255i	−0.351304	−	0.848124i
$638$		0			0
$639$		−	60.2706i		−	0.0943202i
$640$		0			0
$641$	440.457			0.687141			0.343571	−	0.939127i	$-0.388364\pi$
$641$	440.457			0.687141			0.343571	+	0.939127i	$0.388364\pi$
$642$		0			0
$643$	211.055	−	87.4220i	0.328235	−	0.135960i	−0.212479	−	0.977166i	$-0.568154\pi$
$643$	211.055	−	87.4220i	0.328235	−	0.135960i	0.540715	+	0.841206i	$0.318154\pi$
$644$		0			0
$645$	−200.646	−	83.1103i	−0.311079	−	0.128853i
$646$		0			0
$647$	−515.935	+	515.935i	−0.797426	+	0.797426i	−0.982689	−	0.185263i	$-0.940686\pi$
$647$	−515.935	+	515.935i	−0.797426	+	0.797426i	0.185263	+	0.982689i	$0.440686\pi$
$648$		0			0
$649$	−33.8372	+	33.8372i	−0.0521375	+	0.0521375i
$650$		0			0
$651$	175.346	+	72.6309i	0.269349	+	0.111568i
$652$		0			0
$653$	−613.161	+	253.980i	−0.938991	+	0.388943i	−0.799082	−	0.601222i	$-0.794681\pi$
$653$	−613.161	+	253.980i	−0.938991	+	0.388943i	−0.139909	+	0.990164i	$0.544681\pi$
$654$		0			0
$655$	−238.016			−0.363383
$656$		0			0
$657$			638.339i			0.971596i
$658$		0			0
$659$	19.4679	+	46.9996i	0.0295416	+	0.0713196i	0.937962	−	0.346738i	$-0.112711\pi$
$659$	19.4679	+	46.9996i	0.0295416	+	0.0713196i	−0.908420	+	0.418058i	$0.862711\pi$
$660$		0			0
$661$	46.1458	−	111.406i	0.0698122	−	0.168541i	−0.885122	−	0.465359i	$-0.845925\pi$
$661$	46.1458	−	111.406i	0.0698122	−	0.168541i	0.954934	+	0.296817i	$0.0959253\pi$
$662$		0			0
$663$	−117.752	−	117.752i	−0.177606	−	0.177606i
$664$		0			0
$665$	350.950	+	350.950i	0.527745	+	0.527745i
$666$		0			0
$667$	487.344	−	1176.55i	0.730650	−	1.76395i
$668$		0			0
$669$	30.0002	+	72.4270i	0.0448434	+	0.108262i
$670$		0			0
$671$			15.2672i			0.0227528i
$672$		0			0
$673$	−352.344			−0.523542			−0.261771	−	0.965130i	$-0.584306\pi$
$673$	−352.344			−0.523542			−0.261771	+	0.965130i	$0.584306\pi$
$674$		0			0
$675$	408.964	−	169.398i	0.605872	−	0.250961i
$676$		0			0
$677$	−1178.26	−	488.051i	−1.74041	−	0.720902i	−0.998742	−	0.0501357i	$-0.984035\pi$
$677$	−1178.26	−	488.051i	−1.74041	−	0.720902i	−0.741669	−	0.670766i	$-0.765965\pi$
$678$		0			0
$679$	574.306	−	574.306i	0.845812	−	0.845812i
$680$		0			0
$681$	372.033	−	372.033i	0.546304	−	0.546304i
$682$		0			0
$683$	414.446	+	171.669i	0.606802	+	0.251346i	0.664861	−	0.746967i	$-0.268491\pi$
$683$	414.446	+	171.669i	0.606802	+	0.251346i	−0.0580582	+	0.998313i	$0.518491\pi$
$684$		0			0
$685$	−189.538	+	78.5093i	−0.276698	+	0.114612i
$686$		0			0
$687$	394.768			0.574626
$688$		0			0
$689$		−	185.657i		−	0.269459i
$690$		0			0
$691$	−268.707	−	648.715i	−0.388866	−	0.938806i	−0.990181	−	0.139794i	$-0.955356\pi$
$691$	−268.707	−	648.715i	−0.388866	−	0.938806i	0.601314	−	0.799012i	$-0.294644\pi$
$692$		0			0
$693$	−45.5807	+	110.041i	−0.0657729	+	0.158790i
$694$		0			0
$695$	316.319	+	316.319i	0.455136	+	0.455136i
$696$		0			0
$697$	353.106	+	353.106i	0.506608	+	0.506608i
$698$		0			0
$699$	−25.6368	+	61.8927i	−0.0366764	+	0.0885447i
$700$		0			0
$701$	464.382	+	1121.12i	0.662457	+	1.59931i	0.793941	+	0.607995i	$0.208026\pi$
$701$	464.382	+	1121.12i	0.662457	+	1.59931i	−0.131484	+	0.991318i	$0.541974\pi$
$702$		0			0
$703$		−	722.990i		−	1.02844i
$704$		0			0
$705$	−128.128			−0.181742
$706$		0			0
$707$	−181.166	+	75.0414i	−0.256246	+	0.106141i
$708$		0			0
$709$	591.984	+	245.208i	0.834957	+	0.345850i	0.758863	−	0.651250i	$-0.225755\pi$
$709$	591.984	+	245.208i	0.834957	+	0.345850i	0.0760937	+	0.997101i	$0.475755\pi$
$710$		0			0
$711$	−364.270	+	364.270i	−0.512334	+	0.512334i
$712$		0			0
$713$	334.870	−	334.870i	0.469664	−	0.469664i
$714$		0			0
$715$	80.4619	+	33.3284i	0.112534	+	0.0466132i
$716$		0			0
$717$	−123.633	+	51.2104i	−0.172431	+	0.0714232i
$718$		0			0
$719$	906.230			1.26040			0.630202	−	0.776432i	$-0.282972\pi$
$719$	906.230			1.26040			0.630202	+	0.776432i	$0.282972\pi$
$720$		0			0
$721$			62.3563i			0.0864858i
$722$		0			0
$723$	−11.9407	−	28.8274i	−0.0165155	−	0.0398720i
$724$		0			0
$725$	274.881	−	663.622i	0.379147	−	0.915341i
$726$		0			0
$727$	−317.957	−	317.957i	−0.437355	−	0.437355i	0.453766	−	0.891121i	$-0.350080\pi$
$727$	−317.957	−	317.957i	−0.437355	−	0.437355i	−0.891121	+	0.453766i	$0.850080\pi$
$728$		0			0
$729$	−95.8544	−	95.8544i	−0.131488	−	0.131488i
$730$		0			0
$731$	−139.929	+	337.818i	−0.191421	+	0.462131i
$732$		0			0
$733$	−159.623	−	385.363i	−0.217766	−	0.525734i	0.776811	−	0.629734i	$-0.216836\pi$
$733$	−159.623	−	385.363i	−0.217766	−	0.525734i	−0.994577	+	0.103999i	$0.966836\pi$
$734$		0			0
$735$		−	119.068i		−	0.161997i
$736$		0			0
$737$	117.660			0.159647
$738$		0			0
$739$	380.514	−	157.614i	0.514904	−	0.213280i	−0.110073	−	0.993924i	$-0.535108\pi$
$739$	380.514	−	157.614i	0.514904	−	0.213280i	0.624977	+	0.780643i	$0.285108\pi$
$740$		0			0
$741$	551.395	+	228.395i	0.744123	+	0.308226i
$742$		0			0
$743$	−5.76228	+	5.76228i	−0.00775542	+	0.00775542i	−0.710974	−	0.703218i	$-0.751746\pi$
$743$	−5.76228	+	5.76228i	−0.00775542	+	0.00775542i	0.703218	+	0.710974i	$0.251746\pi$
$744$		0			0
$745$	82.4123	−	82.4123i	0.110620	−	0.110620i
$746$		0			0
$747$	−20.2318	−	8.38030i	−0.0270841	−	0.0112186i
$748$		0			0
$749$	468.729	−	194.154i	0.625807	−	0.259218i
$750$		0			0
$751$	302.377			0.402632			0.201316	−	0.979526i	$-0.435478\pi$
$751$	302.377			0.402632			0.201316	+	0.979526i	$0.435478\pi$
$752$		0			0
$753$			408.539i			0.542548i
$754$		0			0
$755$	91.6499	+	221.262i	0.121391	+	0.293063i
$756$		0			0
$757$	−9.31627	+	22.4915i	−0.0123068	+	0.0297113i	−0.929914	−	0.367778i	$-0.880119\pi$
$757$	−9.31627	+	22.4915i	−0.0123068	+	0.0297113i	0.917607	+	0.397490i	$0.130119\pi$
$758$		0			0
$759$	−68.3309	−	68.3309i	−0.0900276	−	0.0900276i
$760$		0			0
$761$	−163.034	−	163.034i	−0.214236	−	0.214236i	0.591828	−	0.806064i	$-0.298406\pi$
$761$	−163.034	−	163.034i	−0.214236	−	0.214236i	−0.806064	+	0.591828i	$0.798406\pi$
$762$		0			0
$763$	−186.064	+	449.198i	−0.243859	+	0.588727i
$764$		0			0
$765$	39.9075	+	96.3452i	0.0521667	+	0.125941i
$766$		0			0
$767$			444.943i			0.580109i
$768$		0			0
$769$	180.205			0.234337			0.117168	−	0.993112i	$-0.462618\pi$
$769$	180.205			0.234337			0.117168	+	0.993112i	$0.462618\pi$
$770$		0			0
$771$	324.811	−	134.541i	0.421286	−	0.174502i
$772$		0			0
$773$	196.725	+	81.4860i	0.254495	+	0.105415i	0.506284	−	0.862367i	$-0.331019\pi$
$773$	196.725	+	81.4860i	0.254495	+	0.105415i	−0.251789	+	0.967782i	$0.581019\pi$
$774$		0			0
$775$	188.880	−	188.880i	0.243716	−	0.243716i
$776$		0			0
$777$	−308.452	+	308.452i	−0.396978	+	0.396978i
$778$		0			0
$779$	−1653.48	−	684.892i	−2.12256	−	0.879194i
$780$		0			0
$781$	−15.9421	+	6.60342i	−0.0204124	+	0.00845508i
$782$		0			0
$783$	−893.620			−1.14128
$784$		0			0
$785$		−	482.695i		−	0.614898i
$786$		0			0
$787$	−80.6847	−	194.790i	−0.102522	−	0.247510i	0.864293	−	0.502990i	$-0.167767\pi$
$787$	−80.6847	−	194.790i	−0.102522	−	0.247510i	−0.966814	+	0.255480i	$0.917767\pi$
$788$		0			0
$789$	−25.7412	+	62.1448i	−0.0326251	+	0.0787640i
$790$		0			0
$791$	395.956	+	395.956i	0.500576	+	0.500576i
$792$		0			0
$793$	100.378	+	100.378i	0.126580	+	0.126580i
$794$		0			0
$795$	14.4665	−	34.9252i	0.0181969	−	0.0439311i
$796$		0			0
$797$	−256.509	−	619.268i	−0.321843	−	0.776999i	−0.999147	−	0.0412950i	$-0.986852\pi$
$797$	−256.509	−	619.268i	−0.321843	−	0.776999i	0.677304	−	0.735704i	$-0.263148\pi$
$798$		0			0
$799$			215.723i			0.269992i
$800$		0			0
$801$	−352.529			−0.440111
$802$		0			0
$803$	168.846	−	69.9382i	0.210269	−	0.0870961i
$804$		0			0
$805$	−690.328	−	285.943i	−0.857551	−	0.355209i
$806$		0			0
$807$	131.188	−	131.188i	0.162562	−	0.162562i
$808$		0			0
$809$	−1008.10	+	1008.10i	−1.24611	+	1.24611i	−0.288683	+	0.957425i	$0.593217\pi$
$809$	−1008.10	+	1008.10i	−1.24611	+	1.24611i	−0.957425	+	0.288683i	$0.906783\pi$
$810$		0			0
$811$	1271.85	+	526.816i	1.56825	+	0.649588i	0.986497	−	0.163780i	$-0.0523688\pi$
$811$	1271.85	+	526.816i	1.56825	+	0.649588i	0.581748	+	0.813369i	$0.302369\pi$
$812$		0			0
$813$	76.1044	−	31.5235i	0.0936094	−	0.0387743i
$814$		0			0
$815$	−716.266			−0.878854
$816$		0			0
$817$		−	1310.48i		−	1.60401i
$818$		0			0
$819$	423.814	+	1023.18i	0.517477	+	1.24930i
$820$		0			0
$821$	−119.922	+	289.516i	−0.146068	+	0.352639i	−0.979932	−	0.199330i	$-0.936123\pi$
$821$	−119.922	+	289.516i	−0.146068	+	0.352639i	0.833865	+	0.551969i	$0.186123\pi$
$822$		0			0
$823$	−607.735	−	607.735i	−0.738439	−	0.738439i	0.233837	−	0.972276i	$-0.424872\pi$
$823$	−607.735	−	607.735i	−0.738439	−	0.738439i	−0.972276	+	0.233837i	$0.924872\pi$
$824$		0			0
$825$	−38.5414	−	38.5414i	−0.0467168	−	0.0467168i
$826$		0			0
$827$	−246.520	+	595.152i	−0.298090	+	0.719652i	0.701883	+	0.712292i	$0.252343\pi$
$827$	−246.520	+	595.152i	−0.298090	+	0.719652i	−0.999973	+	0.00736012i	$0.997657\pi$
$828$		0			0
$829$	393.211	+	949.295i	0.474319	+	1.14511i	0.962236	+	0.272218i	$0.0877571\pi$
$829$	393.211	+	949.295i	0.474319	+	1.14511i	−0.487916	+	0.872890i	$0.662243\pi$
$830$		0			0
$831$			138.972i			0.167235i
$832$		0			0
$833$	−200.469			−0.240659
$834$		0			0
$835$	−321.428	+	133.140i	−0.384943	+	0.159449i
$836$		0			0
$837$	−307.018	−	127.171i	−0.366808	−	0.151937i
$838$		0			0
$839$	575.067	−	575.067i	0.685420	−	0.685420i	−0.275796	−	0.961216i	$-0.588941\pi$
$839$	575.067	−	575.067i	0.685420	−	0.685420i	0.961216	+	0.275796i	$0.0889415\pi$
$840$		0			0
$841$	−430.678	+	430.678i	−0.512102	+	0.512102i
$842$		0			0
$843$	26.8929	+	11.1394i	0.0319015	+	0.0132140i
$844$		0			0
$845$	361.350	−	149.676i	0.427633	−	0.177131i
$846$		0			0
$847$	−1057.21			−1.24818
$848$		0			0
$849$		−	526.620i		−	0.620283i
$850$		0			0
$851$	416.535	+	1005.61i	0.489466	+	1.18167i
$852$		0			0
$853$	304.017	−	733.961i	0.356409	−	0.860447i	−0.639390	−	0.768882i	$-0.720813\pi$
$853$	304.017	−	733.961i	0.356409	−	0.860447i	0.995799	−	0.0915645i	$-0.0291868\pi$
$854$		0			0
$855$	−264.279	−	264.279i	−0.309098	−	0.309098i
$856$		0			0
$857$	−241.394	−	241.394i	−0.281673	−	0.281673i	0.552103	−	0.833776i	$-0.313826\pi$
$857$	−241.394	−	241.394i	−0.281673	−	0.281673i	−0.833776	+	0.552103i	$0.813826\pi$
$858$		0			0
$859$	−443.212	+	1070.01i	−0.515963	+	1.24564i	0.424401	+	0.905474i	$0.360485\pi$
$859$	−443.212	+	1070.01i	−0.515963	+	1.24564i	−0.940364	+	0.340170i	$0.889515\pi$
$860$		0			0
$861$	413.230	+	997.625i	0.479942	+	1.15868i
$862$		0			0
$863$		−	167.859i		−	0.194507i	−0.995260	−	0.0972533i	$-0.968994\pi$
$863$		−	167.859i		−	0.194507i	0.995260	−	0.0972533i	$-0.0310057\pi$
$864$		0			0
$865$	502.117			0.580482
$866$		0			0
$867$	344.031	−	142.502i	0.396806	−	0.164363i
$868$		0			0
$869$	136.263	+	56.4418i	0.156804	+	0.0649503i
$870$		0			0
$871$	773.586	−	773.586i	0.888158	−	0.888158i
$872$		0			0
$873$	−432.474	+	432.474i	−0.495388	+	0.495388i
$874$		0			0
$875$	−905.426	−	375.040i	−1.03477	−	0.428617i
$876$		0			0
$877$	659.079	−	272.999i	0.751515	−	0.311288i	0.0261554	−	0.999658i	$-0.491674\pi$
$877$	659.079	−	272.999i	0.751515	−	0.311288i	0.725360	+	0.688370i	$0.241674\pi$
$878$		0			0
$879$	−663.964			−0.755363
$880$		0			0
$881$			806.984i			0.915987i	0.888956	+	0.457993i	$0.151432\pi$
$881$			806.984i			0.915987i	−0.888956	+	0.457993i	$0.848568\pi$
$882$		0			0
$883$	118.704	+	286.577i	0.134433	+	0.324549i	0.976733	−	0.214459i	$-0.0687989\pi$
$883$	118.704	+	286.577i	0.134433	+	0.324549i	−0.842300	+	0.539009i	$0.818799\pi$
$884$		0			0
$885$	−34.6701	+	83.7011i	−0.0391753	+	0.0945776i
$886$		0			0
$887$	−727.865	−	727.865i	−0.820592	−	0.820592i	0.165601	−	0.986193i	$-0.447044\pi$
$887$	−727.865	−	727.865i	−0.820592	−	0.820592i	−0.986193	+	0.165601i	$0.947044\pi$
$888$		0			0
$889$	−1129.10	−	1129.10i	−1.27008	−	1.27008i
$890$		0			0
$891$	19.5348	−	47.1611i	0.0219246	−	0.0529306i
$892$		0			0
$893$	−295.869	−	714.290i	−0.331320	−	0.799877i
$894$		0			0
$895$			655.308i			0.732188i
$896$		0			0
$897$	−898.518			−1.00169
$898$		0			0
$899$	−498.196	+	206.359i	−0.554167	+	0.229543i
$900$		0			0
$901$	−58.8018	−	24.3565i	−0.0652628	−	0.0270328i
$902$		0			0
$903$	−559.093	+	559.093i	−0.619151	+	0.619151i
$904$		0			0
$905$	27.8215	−	27.8215i	0.0307420	−	0.0307420i
$906$		0			0
$907$	−711.116	−	294.554i	−0.784031	−	0.324756i	−0.0454897	−	0.998965i	$-0.514485\pi$
$907$	−711.116	−	294.554i	−0.784031	−	0.324756i	−0.738541	+	0.674209i	$0.764485\pi$
$908$		0			0
$909$	136.425	−	56.5090i	0.150082	−	0.0621661i
$910$		0			0
$911$	758.696			0.832817			0.416409	−	0.909178i	$-0.363289\pi$
$911$	758.696			0.832817			0.416409	+	0.909178i	$0.363289\pi$
$912$		0			0
$913$			6.26965i			0.00686708i
$914$		0			0
$915$	11.0612	+	26.7042i	0.0120888	+	0.0291849i
$916$		0			0
$917$	−331.611	+	800.581i	−0.361626	+	0.873043i
$918$		0			0
$919$	−949.647	−	949.647i	−1.03335	−	1.03335i	−0.999424	−	0.0339243i	$-0.989199\pi$
$919$	−949.647	−	949.647i	−1.03335	−	1.03335i	−0.0339243	−	0.999424i	$-0.510801\pi$
$920$		0			0
$921$	116.302	+	116.302i	0.126278	+	0.126278i
$922$		0			0
$923$	−61.3993	+	148.231i	−0.0665215	+	0.160597i
$924$		0			0
$925$	234.943	+	567.202i	0.253992	+	0.613191i
$926$		0			0
$927$		−	46.9566i		−	0.0506544i
$928$		0			0
$929$	222.645			0.239661			0.119830	−	0.992794i	$-0.461765\pi$
$929$	222.645			0.239661			0.119830	+	0.992794i	$0.461765\pi$
$930$		0			0
$931$	663.780	−	274.947i	0.712975	−	0.295324i
$932$		0			0
$933$	−654.952	−	271.290i	−0.701985	−	0.290772i
$934$		0			0
$935$	21.1117	−	21.1117i	0.0225794	−	0.0225794i
$936$		0			0
$937$	−1027.40	+	1027.40i	−1.09648	+	1.09648i	−0.101659	+	0.994819i	$0.532415\pi$
$937$	−1027.40	+	1027.40i	−1.09648	+	1.09648i	−0.994819	+	0.101659i	$0.967585\pi$
$938$		0			0
$939$	−136.055	−	56.3558i	−0.144893	−	0.0600168i
$940$		0			0
$941$	−892.441	+	369.661i	−0.948397	+	0.392839i	−0.802628	−	0.596480i	$-0.796566\pi$
$941$	−892.441	+	369.661i	−0.948397	+	0.392839i	−0.145769	+	0.989319i	$0.546566\pi$
$942$		0			0
$943$	2694.40			2.85726
$944$		0			0
$945$			524.321i			0.554837i
$946$		0			0
$947$	−385.441	−	930.536i	−0.407012	−	0.982615i	−0.985919	−	0.167221i	$-0.946521\pi$
$947$	−385.441	−	930.536i	−0.407012	−	0.982615i	0.578907	−	0.815394i	$-0.303479\pi$
$948$		0			0
$949$	650.293	−	1569.95i	0.685240	−	1.65432i
$950$		0			0
$951$	90.2371	+	90.2371i	0.0948865	+	0.0948865i
$952$		0			0
$953$	648.910	+	648.910i	0.680913	+	0.680913i	0.960206	−	0.279293i	$-0.0901001\pi$
$953$	648.910	+	648.910i	0.680913	+	0.680913i	−0.279293	+	0.960206i	$0.590100\pi$
$954$		0			0
$955$	351.314	−	848.148i	0.367868	−	0.888113i
$956$		0			0
$957$	42.1081	+	101.658i	0.0440001	+	0.106226i
$958$		0			0
$959$			746.905i			0.778837i
$960$		0			0
$961$	760.470			0.791331
$962$		0			0
$963$	−352.971	+	146.205i	−0.366532	+	0.151823i
$964$		0			0
$965$	−303.665	−	125.782i	−0.314679	−	0.130344i
$966$		0			0
$967$	41.2757	−	41.2757i	0.0426842	−	0.0426842i	−0.685443	−	0.728127i	$-0.740391\pi$
$967$	41.2757	−	41.2757i	0.0426842	−	0.0426842i	0.728127	+	0.685443i	$0.240391\pi$
$968$		0			0
$969$	144.676	−	144.676i	0.149304	−	0.149304i
$970$		0			0
$971$	213.816	+	88.5653i	0.220201	+	0.0912104i	0.490057	−	0.871690i	$-0.336976\pi$
$971$	213.816	+	88.5653i	0.220201	+	0.0912104i	−0.269856	+	0.962901i	$0.586976\pi$
$972$		0			0
$973$	1504.67	−	623.253i	1.54642	−	0.640547i
$974$		0			0
$975$	−506.800			−0.519795
$976$		0			0
$977$			314.091i			0.321485i	0.986996	+	0.160742i	$0.0513888\pi$
$977$			314.091i			0.321485i	−0.986996	+	0.160742i	$0.948611\pi$
$978$		0			0
$979$	38.6240	+	93.2467i	0.0394526	+	0.0952469i
$980$		0			0
$981$	140.113	−	338.263i	0.142827	−	0.344815i
$982$		0			0
$983$	8.50847	+	8.50847i	0.00865562	+	0.00865562i	0.711421	−	0.702766i	$-0.248052\pi$
$983$	8.50847	+	8.50847i	0.00865562	+	0.00865562i	−0.702766	+	0.711421i	$0.748052\pi$
$984$		0			0
$985$	220.680	+	220.680i	0.224041	+	0.224041i
$986$		0			0
$987$	−178.513	+	430.967i	−0.180864	+	0.436644i
$988$		0			0
$989$	755.003	+	1822.74i	0.763400	+	1.84301i
$990$		0			0
$991$			93.7233i			0.0945745i	0.998881	+	0.0472872i	$0.0150576\pi$
$991$			93.7233i			0.0945745i	−0.998881	+	0.0472872i	$0.984942\pi$
$992$		0			0
$993$	−200.842			−0.202257
$994$		0			0
$995$	291.291	−	120.657i	0.292754	−	0.121263i
$996$		0			0
$997$	−287.749	−	119.189i	−0.288614	−	0.119548i	0.233679	−	0.972314i	$-0.424923\pi$
$997$	−287.749	−	119.189i	−0.288614	−	0.119548i	−0.522294	+	0.852766i	$0.674923\pi$
$998$		0			0
$999$	540.075	−	540.075i	0.540616	−	0.540616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.15.5		28
4.3	odd	2		32.3.h.a.27.6	yes	28
8.3	odd	2		256.3.h.b.31.5		28
8.5	even	2		256.3.h.a.31.3		28
12.11	even	2		288.3.u.a.91.2		28
32.3	odd	8		256.3.h.a.223.3		28
32.13	even	8		32.3.h.a.19.6	✓	28
32.19	odd	8	inner	128.3.h.a.111.5		28
32.29	even	8		256.3.h.b.223.5		28
96.77	odd	8		288.3.u.a.19.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.6	✓	28	32.13	even	8
32.3.h.a.27.6	yes	28	4.3	odd	2
128.3.h.a.15.5		28	1.1	even	1	trivial
128.3.h.a.111.5		28	32.19	odd	8	inner
256.3.h.a.31.3		28	8.5	even	2
256.3.h.a.223.3		28	32.3	odd	8
256.3.h.b.31.5		28	8.3	odd	2
256.3.h.b.223.5		28	32.29	even	8
288.3.u.a.19.2		28	96.77	odd	8
288.3.u.a.91.2		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)

\(f(q)\)	\(=\)	\(q+(1.37292 - 0.568682i) q^{3} +(2.28872 + 0.948019i) q^{5} +(6.37744 - 6.37744i) q^{7} +(-4.80245 + 4.80245i) q^{9} +O(q^{10})\)	\(q+(1.37292 - 0.568682i) q^{3} +(2.28872 + 0.948019i) q^{5} +(6.37744 - 6.37744i) q^{7} +(-4.80245 + 4.80245i) q^{9} +(1.79646 + 0.744117i) q^{11} +(16.7036 - 6.91888i) q^{13} +3.68135 q^{15} -6.19811i q^{17} +(8.50083 + 20.5228i) q^{19} +(5.12898 - 12.3825i) q^{21} +(-23.6476 - 23.6476i) q^{23} +(-13.3382 - 13.3382i) q^{25} +(-8.98045 + 21.6807i) q^{27} +(14.5725 + 35.1811i) q^{29} +14.1609i q^{31} +2.88956 q^{33} +(20.6421 - 8.55025i) q^{35} +(-30.0695 - 12.4552i) q^{37} +(18.9981 - 18.9981i) q^{39} +(-56.9700 + 56.9700i) q^{41} +(-54.5034 - 22.5760i) q^{43} +(-15.5443 + 6.43866i) q^{45} -34.8047 q^{47} -32.3435i q^{49} +(-3.52475 - 8.50951i) q^{51} +(3.92967 - 9.48706i) q^{53} +(3.40615 + 3.40615i) q^{55} +(23.3419 + 23.3419i) q^{57} +(-9.41777 + 22.7365i) q^{59} +(3.00467 + 7.25391i) q^{61} +61.2547i q^{63} +44.7892 q^{65} +(55.9040 - 23.1562i) q^{67} +(-45.9141 - 19.0183i) q^{69} +(-6.27499 + 6.27499i) q^{71} +(66.4597 - 66.4597i) q^{73} +(-25.8974 - 10.7271i) q^{75} +(16.2024 - 6.71124i) q^{77} +75.8508 q^{79} -26.2523i q^{81} +(1.23390 + 2.97891i) q^{83} +(5.87593 - 14.1857i) q^{85} +(40.0138 + 40.0138i) q^{87} +(36.7030 + 36.7030i) q^{89} +(62.4018 - 150.651i) q^{91} +(8.05304 + 19.4417i) q^{93} +55.0300i q^{95} +90.0528 q^{97} +(-12.2010 + 5.05381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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