LMFDB - Embedded newform 256.3.h.b.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, 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("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.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:	$6.97549476762$
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			31.4
Character	$\chi$	$=$	256.31
Dual form			256.3.h.b.223.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.374985 - 0.155324i) q^{3} +(7.60625 + 3.15061i) q^{5} +(6.84161 - 6.84161i) q^{7} +(-6.24747 + 6.24747i) q^{9} +O(q^{10})$	\(q+(0.374985 - 0.155324i) q^{3} +(7.60625 + 3.15061i) q^{5} +(6.84161 - 6.84161i) q^{7} +(-6.24747 + 6.24747i) q^{9} +(2.23818 + 0.927086i) q^{11} +(-1.40964 + 0.583890i) q^{13} +3.34159 q^{15} -2.67812i q^{17} +(-5.38908 - 13.0104i) q^{19} +(1.50283 - 3.62816i) q^{21} +(18.8388 + 18.8388i) q^{23} +(30.2510 + 30.2510i) q^{25} +(-2.77024 + 6.68795i) q^{27} +(10.0298 + 24.2140i) q^{29} -47.5858i q^{31} +0.983283 q^{33} +(73.5942 - 30.4837i) q^{35} +(28.2682 + 11.7091i) q^{37} +(-0.437900 + 0.437900i) q^{39} +(6.93962 - 6.93962i) q^{41} +(-8.48982 - 3.51660i) q^{43} +(-67.2032 + 27.8365i) q^{45} -67.0112 q^{47} -44.6152i q^{49} +(-0.415976 - 1.00426i) q^{51} +(10.5006 - 25.3507i) q^{53} +(14.1033 + 14.1033i) q^{55} +(-4.04165 - 4.04165i) q^{57} +(-27.9364 + 67.4445i) q^{59} +(-31.5752 - 76.2294i) q^{61} +85.4855i q^{63} -12.5616 q^{65} +(-90.1903 + 37.3580i) q^{67} +(9.99035 + 4.13814i) q^{69} +(1.98379 - 1.98379i) q^{71} +(-55.5273 + 55.5273i) q^{73} +(16.0424 + 6.64496i) q^{75} +(21.6555 - 8.97002i) q^{77} +10.9856 q^{79} -76.5792i q^{81} +(-34.1779 - 82.5128i) q^{83} +(8.43772 - 20.3705i) q^{85} +(7.52203 + 7.52203i) q^{87} +(-16.1705 - 16.1705i) q^{89} +(-5.64942 + 13.6389i) q^{91} +(-7.39121 - 17.8440i) q^{93} -115.939i q^{95} -62.6434 q^{97} +(-19.7749 + 8.19105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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
$3$	0.374985	−	0.155324i	0.124995	−	0.0517746i	−0.319309	−	0.947651i	$-0.603451\pi$
$3$	0.374985	−	0.155324i	0.124995	−	0.0517746i	0.444304	+	0.895876i	$0.353451\pi$
$4$		0			0
$5$	7.60625	+	3.15061i	1.52125	+	0.630122i	0.977842	−	0.209346i	$-0.0671336\pi$
$5$	7.60625	+	3.15061i	1.52125	+	0.630122i	0.543408	+	0.839469i	$0.317134\pi$
$6$		0			0
$7$	6.84161	−	6.84161i	0.977372	−	0.977372i	−0.0223772	−	0.999750i	$-0.507123\pi$
$7$	6.84161	−	6.84161i	0.977372	−	0.977372i	0.999750	+	0.0223772i	$0.00712349\pi$
$8$		0			0
$9$	−6.24747	+	6.24747i	−0.694164	+	0.694164i
$10$		0			0
$11$	2.23818	+	0.927086i	0.203471	+	0.0842806i	0.482092	−	0.876121i	$-0.339877\pi$
$11$	2.23818	+	0.927086i	0.203471	+	0.0842806i	−0.278621	+	0.960401i	$0.589877\pi$
$12$		0			0
$13$	−1.40964	+	0.583890i	−0.108433	+	0.0449146i	−0.436241	−	0.899830i	$-0.643690\pi$
$13$	−1.40964	+	0.583890i	−0.108433	+	0.0449146i	0.327807	+	0.944745i	$0.393690\pi$
$14$		0			0
$15$	3.34159			0.222773
$16$		0			0
$17$		−	2.67812i		−	0.157537i	−0.996893	−	0.0787683i	$-0.974901\pi$
$17$		−	2.67812i		−	0.157537i	0.996893	−	0.0787683i	$-0.0250987\pi$
$18$		0			0
$19$	−5.38908	−	13.0104i	−0.283636	−	0.684757i	0.716279	−	0.697814i	$-0.245844\pi$
$19$	−5.38908	−	13.0104i	−0.283636	−	0.684757i	−0.999915	+	0.0130566i	$0.995844\pi$
$20$		0			0
$21$	1.50283	−	3.62816i	0.0715635	−	0.172770i
$22$		0			0
$23$	18.8388	+	18.8388i	0.819076	+	0.819076i	0.985974	−	0.166898i	$-0.0533750\pi$
$23$	18.8388	+	18.8388i	0.819076	+	0.819076i	−0.166898	+	0.985974i	$0.553375\pi$
$24$		0			0
$25$	30.2510	+	30.2510i	1.21004	+	1.21004i
$26$		0			0
$27$	−2.77024	+	6.68795i	−0.102601	+	0.247702i
$28$		0			0
$29$	10.0298	+	24.2140i	0.345855	+	0.834967i	0.997100	+	0.0761000i	$0.0242468\pi$
$29$	10.0298	+	24.2140i	0.345855	+	0.834967i	−0.651245	+	0.758867i	$0.725753\pi$
$30$		0			0
$31$		−	47.5858i		−	1.53503i	−0.641033	−	0.767513i	$-0.721494\pi$
$31$		−	47.5858i		−	1.53503i	0.641033	−	0.767513i	$-0.278506\pi$
$32$		0			0
$33$	0.983283			0.0297965
$34$		0			0
$35$	73.5942	−	30.4837i	2.10269	−	0.870963i
$36$		0			0
$37$	28.2682	+	11.7091i	0.764006	+	0.316462i	0.730442	−	0.682975i	$-0.239314\pi$
$37$	28.2682	+	11.7091i	0.764006	+	0.316462i	0.0335642	+	0.999437i	$0.489314\pi$
$38$		0			0
$39$	−0.437900	+	0.437900i	−0.0112282	+	0.0112282i
$40$		0			0
$41$	6.93962	−	6.93962i	0.169259	−	0.169259i	−0.617395	−	0.786654i	$-0.711812\pi$
$41$	6.93962	−	6.93962i	0.169259	−	0.169259i	0.786654	+	0.617395i	$0.211812\pi$
$42$		0			0
$43$	−8.48982	−	3.51660i	−0.197438	−	0.0817814i	0.281774	−	0.959481i	$-0.409077\pi$
$43$	−8.48982	−	3.51660i	−0.197438	−	0.0817814i	−0.479211	+	0.877700i	$0.659077\pi$
$44$		0			0
$45$	−67.2032	+	27.8365i	−1.49340	+	0.618588i
$46$		0			0
$47$	−67.0112			−1.42577			−0.712885	−	0.701281i	$-0.752612\pi$
$47$	−67.0112			−1.42577			−0.712885	+	0.701281i	$0.752612\pi$
$48$		0			0
$49$		−	44.6152i		−	0.910513i
$50$		0			0
$51$	−0.415976	−	1.00426i	−0.00815639	−	0.0196913i
$52$		0			0
$53$	10.5006	−	25.3507i	0.198124	−	0.478315i	−0.793326	−	0.608797i	$-0.791653\pi$
$53$	10.5006	−	25.3507i	0.198124	−	0.478315i	0.991451	+	0.130482i	$0.0416525\pi$
$54$		0			0
$55$	14.1033	+	14.1033i	0.256424	+	0.256424i
$56$		0			0
$57$	−4.04165	−	4.04165i	−0.0709061	−	0.0709061i
$58$		0			0
$59$	−27.9364	+	67.4445i	−0.473499	+	1.14313i	0.489107	+	0.872224i	$0.337323\pi$
$59$	−27.9364	+	67.4445i	−0.473499	+	1.14313i	−0.962606	+	0.270904i	$0.912677\pi$
$60$		0			0
$61$	−31.5752	−	76.2294i	−0.517627	−	1.24966i	−0.939357	−	0.342941i	$-0.888577\pi$
$61$	−31.5752	−	76.2294i	−0.517627	−	1.24966i	0.421730	−	0.906721i	$-0.361423\pi$
$62$		0			0
$63$			85.4855i			1.35691i
$64$		0			0
$65$	−12.5616			−0.193256
$66$		0			0
$67$	−90.1903	+	37.3580i	−1.34612	+	0.557583i	−0.935211	−	0.354092i	$-0.884790\pi$
$67$	−90.1903	+	37.3580i	−1.34612	+	0.557583i	−0.410913	+	0.911674i	$0.634790\pi$
$68$		0			0
$69$	9.99035	+	4.13814i	0.144788	+	0.0599730i
$70$		0			0
$71$	1.98379	−	1.98379i	0.0279407	−	0.0279407i	−0.692998	−	0.720939i	$-0.743711\pi$
$71$	1.98379	−	1.98379i	0.0279407	−	0.0279407i	0.720939	+	0.692998i	$0.243711\pi$
$72$		0			0
$73$	−55.5273	+	55.5273i	−0.760648	+	0.760648i	−0.976439	−	0.215792i	$-0.930767\pi$
$73$	−55.5273	+	55.5273i	−0.760648	+	0.760648i	0.215792	+	0.976439i	$0.430767\pi$
$74$		0			0
$75$	16.0424	+	6.64496i	0.213898	+	0.0885995i
$76$		0			0
$77$	21.6555	−	8.97002i	0.281241	−	0.116494i
$78$		0			0
$79$	10.9856			0.139058			0.0695292	−	0.997580i	$-0.477850\pi$
$79$	10.9856			0.139058			0.0695292	+	0.997580i	$0.477850\pi$
$80$		0			0
$81$		−	76.5792i		−	0.945422i
$82$		0			0
$83$	−34.1779	−	82.5128i	−0.411782	−	0.994130i	−0.984659	−	0.174489i	$-0.944173\pi$
$83$	−34.1779	−	82.5128i	−0.411782	−	0.994130i	0.572877	−	0.819641i	$-0.305827\pi$
$84$		0			0
$85$	8.43772	−	20.3705i	0.0992674	−	0.239653i
$86$		0			0
$87$	7.52203	+	7.52203i	0.0864602	+	0.0864602i
$88$		0			0
$89$	−16.1705	−	16.1705i	−0.181691	−	0.181691i	0.610401	−	0.792093i	$-0.291008\pi$
$89$	−16.1705	−	16.1705i	−0.181691	−	0.181691i	−0.792093	+	0.610401i	$0.791008\pi$
$90$		0			0
$91$	−5.64942	+	13.6389i	−0.0620816	+	0.149878i
$92$		0			0
$93$	−7.39121	−	17.8440i	−0.0794754	−	0.191870i
$94$		0			0
$95$		−	115.939i		−	1.22041i
$96$		0			0
$97$	−62.6434			−0.645808			−0.322904	−	0.946432i	$-0.604659\pi$
$97$	−62.6434			−0.645808			−0.322904	+	0.946432i	$0.604659\pi$
$98$		0			0
$99$	−19.7749	+	8.19105i	−0.199747	+	0.0827379i
$100$		0			0
$101$	−39.7340	−	16.4584i	−0.393406	−	0.162954i	0.177206	−	0.984174i	$-0.443294\pi$
$101$	−39.7340	−	16.4584i	−0.393406	−	0.162954i	−0.570612	+	0.821220i	$0.693294\pi$
$102$		0			0
$103$	−36.3254	+	36.3254i	−0.352674	+	0.352674i	−0.861104	−	0.508430i	$-0.830226\pi$
$103$	−36.3254	+	36.3254i	−0.352674	+	0.352674i	0.508430	+	0.861104i	$0.330226\pi$
$104$		0			0
$105$	22.8619	−	22.8619i	0.217732	−	0.217732i
$106$		0			0
$107$	−111.798	−	46.3084i	−1.04484	−	0.432789i	−0.206796	−	0.978384i	$-0.566304\pi$
$107$	−111.798	−	46.3084i	−1.04484	−	0.432789i	−0.838049	+	0.545596i	$0.816304\pi$
$108$		0			0
$109$	55.7631	−	23.0978i	0.511588	−	0.211907i	−0.111929	−	0.993716i	$-0.535703\pi$
$109$	55.7631	−	23.0978i	0.511588	−	0.211907i	0.623517	+	0.781809i	$0.285703\pi$
$110$		0			0
$111$	12.4189			0.111882
$112$		0			0
$113$			80.7753i			0.714825i	0.933947	+	0.357413i	$0.116341\pi$
$113$			80.7753i			0.714825i	−0.933947	+	0.357413i	$0.883659\pi$
$114$		0			0
$115$	83.9387	+	202.646i	0.729901	+	1.76214i
$116$		0			0
$117$	5.15882	−	12.4545i	0.0440925	−	0.106449i
$118$		0			0
$119$	−18.3227	−	18.3227i	−0.153972	−	0.153972i
$120$		0			0
$121$	−81.4099	−	81.4099i	−0.672809	−	0.672809i
$122$		0			0
$123$	1.52436	−	3.68014i	0.0123932	−	0.0299198i
$124$		0			0
$125$	56.0222	+	135.250i	0.448178	+	1.08200i
$126$		0			0
$127$			143.036i			1.12627i	0.826365	+	0.563135i	$0.190405\pi$
$127$			143.036i			1.12627i	−0.826365	+	0.563135i	$0.809595\pi$
$128$		0			0
$129$	−3.72976			−0.0289129
$130$		0			0
$131$	56.1430	−	23.2552i	0.428573	−	0.177521i	−0.157961	−	0.987445i	$-0.550492\pi$
$131$	56.1430	−	23.2552i	0.428573	−	0.177521i	0.586534	+	0.809925i	$0.300492\pi$
$132$		0			0
$133$	−125.882	−	52.1420i	−0.946481	−	0.392045i
$134$		0			0
$135$	−42.1423	+	42.1423i	−0.312165	+	0.312165i
$136$		0			0
$137$	168.165	−	168.165i	1.22748	−	1.22748i	0.262563	−	0.964915i	$-0.415432\pi$
$137$	168.165	−	168.165i	1.22748	−	1.22748i	0.964915	−	0.262563i	$-0.0845679\pi$
$138$		0			0
$139$	97.5768	+	40.4176i	0.701991	+	0.290774i	0.704986	−	0.709221i	$-0.250953\pi$
$139$	97.5768	+	40.4176i	0.701991	+	0.290774i	−0.00299484	+	0.999996i	$0.500953\pi$
$140$		0			0
$141$	−25.1282	+	10.4084i	−0.178214	+	0.0738187i
$142$		0			0
$143$	−3.69634			−0.0258485
$144$		0			0
$145$			215.778i			1.48812i
$146$		0			0
$147$	−6.92979	−	16.7300i	−0.0471415	−	0.113810i
$148$		0			0
$149$	−44.3735	+	107.127i	−0.297809	+	0.718974i	0.702167	+	0.712012i	$0.252216\pi$
$149$	−44.3735	+	107.127i	−0.297809	+	0.718974i	−0.999976	+	0.00696156i	$0.997784\pi$
$150$		0			0
$151$	−128.078	−	128.078i	−0.848200	−	0.848200i	0.141708	−	0.989908i	$-0.454741\pi$
$151$	−128.078	−	128.078i	−0.848200	−	0.848200i	−0.989908	+	0.141708i	$0.954741\pi$
$152$		0			0
$153$	16.7315	+	16.7315i	0.109356	+	0.109356i
$154$		0			0
$155$	149.924	−	361.950i	0.967254	−	2.33516i
$156$		0			0
$157$	−20.1590	−	48.6682i	−0.128401	−	0.309988i	0.846585	−	0.532254i	$-0.178655\pi$
$157$	−20.1590	−	48.6682i	−0.128401	−	0.309988i	−0.974986	+	0.222265i	$0.928655\pi$
$158$		0			0
$159$		−	11.1371i		−	0.0700447i
$160$		0			0
$161$	257.775			1.60109
$162$		0			0
$163$	−68.6749	+	28.4461i	−0.421319	+	0.174516i	−0.583262	−	0.812284i	$-0.698224\pi$
$163$	−68.6749	+	28.4461i	−0.421319	+	0.174516i	0.161943	+	0.986800i	$0.448224\pi$
$164$		0			0
$165$	7.47910	+	3.09794i	0.0453279	+	0.0187754i
$166$		0			0
$167$	131.350	−	131.350i	0.786527	−	0.786527i	−0.194396	−	0.980923i	$-0.562275\pi$
$167$	131.350	−	131.350i	0.786527	−	0.786527i	0.980923	+	0.194396i	$0.0622748\pi$
$168$		0			0
$169$	−117.855	+	117.855i	−0.697366	+	0.697366i
$170$		0			0
$171$	114.950	+	47.6139i	0.672223	+	0.278444i
$172$		0			0
$173$	206.045	−	85.3465i	1.19101	−	0.493333i	0.302926	−	0.953014i	$-0.402036\pi$
$173$	206.045	−	85.3465i	1.19101	−	0.493333i	0.888084	+	0.459681i	$0.152036\pi$
$174$		0			0
$175$	413.931			2.36532
$176$		0			0
$177$			29.6299i			0.167400i
$178$		0			0
$179$	−80.2014	−	193.623i	−0.448053	−	1.08169i	−0.973051	−	0.230591i	$-0.925934\pi$
$179$	−80.2014	−	193.623i	−0.448053	−	1.08169i	0.524998	−	0.851104i	$-0.324066\pi$
$180$		0			0
$181$	−93.4345	+	225.571i	−0.516213	+	1.24625i	0.424000	+	0.905662i	$0.360626\pi$
$181$	−93.4345	+	225.571i	−0.516213	+	1.24625i	−0.940213	+	0.340586i	$0.889374\pi$
$182$		0			0
$183$	−23.6805	−	23.6805i	−0.129401	−	0.129401i
$184$		0			0
$185$	178.124	+	178.124i	0.962835	+	0.962835i
$186$		0			0
$187$	2.48285	−	5.99413i	0.0132773	−	0.0320542i
$188$		0			0
$189$	26.8034	+	64.7092i	0.141817	+	0.342377i
$190$		0			0
$191$			20.1639i			0.105570i	0.998606	+	0.0527851i	$0.0168098\pi$
$191$			20.1639i			0.105570i	−0.998606	+	0.0527851i	$0.983190\pi$
$192$		0			0
$193$	115.896			0.600497			0.300248	−	0.953861i	$-0.402930\pi$
$193$	115.896			0.600497			0.300248	+	0.953861i	$0.402930\pi$
$194$		0			0
$195$	−4.71043	+	1.95112i	−0.0241560	+	0.0100058i
$196$		0			0
$197$	177.705	+	73.6077i	0.902055	+	0.373643i	0.785010	−	0.619483i	$-0.212658\pi$
$197$	177.705	+	73.6077i	0.902055	+	0.373643i	0.117045	+	0.993127i	$0.462658\pi$
$198$		0			0
$199$	−22.1763	+	22.1763i	−0.111439	+	0.111439i	−0.760627	−	0.649189i	$-0.775109\pi$
$199$	−22.1763	+	22.1763i	−0.111439	+	0.111439i	0.649189	+	0.760627i	$0.275109\pi$
$200$		0			0
$201$	−28.0174	+	28.0174i	−0.139390	+	0.139390i
$202$		0			0
$203$	234.283	+	97.0431i	1.15410	+	0.478045i
$204$		0			0
$205$	74.6485	−	30.9204i	0.364139	−	0.150831i
$206$		0			0
$207$	−235.389			−1.13715
$208$		0			0
$209$		−	34.1158i		−	0.163233i
$210$		0			0
$211$	116.936	+	282.308i	0.554197	+	1.33795i	0.914300	+	0.405038i	$0.132742\pi$
$211$	116.936	+	282.308i	0.554197	+	1.33795i	−0.360103	+	0.932913i	$0.617258\pi$
$212$		0			0
$213$	0.435761	−	1.05202i	0.00204583	−	0.00493906i
$214$		0			0
$215$	−53.4962	−	53.4962i	−0.248820	−	0.248820i
$216$		0			0
$217$	−325.563	−	325.563i	−1.50029	−	1.50029i
$218$		0			0
$219$	−12.1972	+	29.4466i	−0.0556949	+	0.134459i
$220$		0			0
$221$	1.56373	+	3.77518i	0.00707570	+	0.0170822i
$222$		0			0
$223$		−	12.1409i		−	0.0544434i	−0.999629	−	0.0272217i	$-0.991334\pi$
$223$		−	12.1409i		−	0.0544434i	0.999629	−	0.0272217i	$-0.00866601\pi$
$224$		0			0
$225$	−377.985			−1.67993
$226$		0			0
$227$	−215.118	+	89.1048i	−0.947656	+	0.392532i	−0.802350	−	0.596854i	$-0.796417\pi$
$227$	−215.118	+	89.1048i	−0.947656	+	0.392532i	−0.145307	+	0.989387i	$0.546417\pi$
$228$		0			0
$229$	−85.4872	−	35.4100i	−0.373307	−	0.154629i	0.188139	−	0.982142i	$-0.439755\pi$
$229$	−85.4872	−	35.4100i	−0.373307	−	0.154629i	−0.561445	+	0.827514i	$0.689755\pi$
$230$		0			0
$231$	6.72724	−	6.72724i	0.0291222	−	0.0291222i
$232$		0			0
$233$	33.1162	−	33.1162i	0.142129	−	0.142129i	−0.632462	−	0.774591i	$-0.717956\pi$
$233$	33.1162	−	33.1162i	0.142129	−	0.142129i	0.774591	+	0.632462i	$0.217956\pi$
$234$		0			0
$235$	−509.704	−	211.126i	−2.16895	−	0.898410i
$236$		0			0
$237$	4.11944	−	1.70633i	0.0173816	−	0.00719970i
$238$		0			0
$239$	332.992			1.39327			0.696636	−	0.717425i	$-0.254679\pi$
$239$	332.992			1.39327			0.696636	+	0.717425i	$0.254679\pi$
$240$		0			0
$241$			218.867i			0.908160i	0.890961	+	0.454080i	$0.150032\pi$
$241$			218.867i			0.908160i	−0.890961	+	0.454080i	$0.849968\pi$
$242$		0			0
$243$	−36.8267	−	88.9076i	−0.151550	−	0.365875i
$244$		0			0
$245$	140.565	−	339.354i	0.573735	−	1.38512i
$246$		0			0
$247$	15.1933	+	15.1933i	0.0615112	+	0.0615112i
$248$		0			0
$249$	−25.6324	−	25.6324i	−0.102941	−	0.102941i
$250$		0			0
$251$	−92.6681	+	223.721i	−0.369196	+	0.891318i	0.624687	+	0.780875i	$0.285227\pi$
$251$	−92.6681	+	223.721i	−0.369196	+	0.891318i	−0.993883	+	0.110442i	$0.964773\pi$
$252$		0			0
$253$	24.6995	+	59.6298i	0.0976263	+	0.235691i
$254$		0			0
$255$		−	8.94919i		−	0.0350949i
$256$		0			0
$257$	−138.514			−0.538966			−0.269483	−	0.963005i	$-0.586853\pi$
$257$	−138.514			−0.538966			−0.269483	+	0.963005i	$0.586853\pi$
$258$		0			0
$259$	273.509	−	113.291i	1.05602	−	0.437418i
$260$		0			0
$261$	−213.937	−	88.6158i	−0.819684	−	0.339524i
$262$		0			0
$263$	91.6940	−	91.6940i	0.348647	−	0.348647i	−0.510959	−	0.859605i	$-0.670710\pi$
$263$	91.6940	−	91.6940i	0.348647	−	0.348647i	0.859605	+	0.510959i	$0.170710\pi$
$264$		0			0
$265$	159.740	−	159.740i	0.602793	−	0.602793i
$266$		0			0
$267$	−8.57537	−	3.55204i	−0.0321175	−	0.0133035i
$268$		0			0
$269$	−179.504	+	74.3530i	−0.667301	+	0.276405i	−0.690507	−	0.723325i	$-0.742613\pi$
$269$	−179.504	+	74.3530i	−0.667301	+	0.276405i	0.0232059	+	0.999731i	$0.492613\pi$
$270$		0			0
$271$	−454.375			−1.67666			−0.838331	−	0.545161i	$-0.816468\pi$
$271$	−454.375			−1.67666			−0.838331	+	0.545161i	$0.816468\pi$
$272$		0			0
$273$			5.99188i			0.0219483i
$274$		0			0
$275$	39.6620	+	95.7526i	0.144226	+	0.348191i
$276$		0			0
$277$	12.5345	−	30.2610i	0.0452510	−	0.109246i	−0.899638	−	0.436637i	$-0.856170\pi$
$277$	12.5345	−	30.2610i	0.0452510	−	0.109246i	0.944889	+	0.327391i	$0.106170\pi$
$278$		0			0
$279$	297.291	+	297.291i	1.06556	+	1.06556i
$280$		0			0
$281$	312.777	+	312.777i	1.11308	+	1.11308i	0.992731	+	0.120353i	$0.0384027\pi$
$281$	312.777	+	312.777i	1.11308	+	1.11308i	0.120353	+	0.992731i	$0.461597\pi$
$282$		0			0
$283$	74.2838	−	179.337i	0.262487	−	0.633700i	−0.736604	−	0.676324i	$-0.763572\pi$
$283$	74.2838	−	179.337i	0.262487	−	0.633700i	0.999091	+	0.0426244i	$0.0135719\pi$
$284$		0			0
$285$	−18.0081	−	43.4754i	−0.0631864	−	0.152545i
$286$		0			0
$287$		−	94.9562i		−	0.330858i
$288$		0			0
$289$	281.828			0.975182
$290$		0			0
$291$	−23.4903	+	9.73000i	−0.0807227	+	0.0334364i
$292$		0			0
$293$	156.211	+	64.7046i	0.533143	+	0.220835i	0.632979	−	0.774169i	$-0.281832\pi$
$293$	156.211	+	64.7046i	0.533143	+	0.220835i	−0.0998364	+	0.995004i	$0.531832\pi$
$294$		0			0
$295$	−424.983	+	424.983i	−1.44062	+	1.44062i
$296$		0			0
$297$	−12.4006	+	12.4006i	−0.0417529	+	0.0417529i
$298$		0			0
$299$	−37.5555	−	15.5560i	−0.125604	−	0.0520268i
$300$		0			0
$301$	−82.1432	+	34.0248i	−0.272901	+	0.113039i
$302$		0			0
$303$	−17.4560			−0.0576106
$304$		0			0
$305$		−	679.301i		−	2.22722i
$306$		0			0
$307$	−111.488	−	269.157i	−0.363155	−	0.876733i	−0.994835	−	0.101504i	$-0.967635\pi$
$307$	−111.488	−	269.157i	−0.363155	−	0.876733i	0.631681	−	0.775229i	$-0.282365\pi$
$308$		0			0
$309$	−7.97928	+	19.2637i	−0.0258229	+	0.0623420i
$310$		0			0
$311$	−74.0508	−	74.0508i	−0.238105	−	0.238105i	0.577960	−	0.816065i	$-0.303849\pi$
$311$	−74.0508	−	74.0508i	−0.238105	−	0.238105i	−0.816065	+	0.577960i	$0.803849\pi$
$312$		0			0
$313$	−119.709	−	119.709i	−0.382458	−	0.382458i	0.489529	−	0.871987i	$-0.337169\pi$
$313$	−119.709	−	119.709i	−0.382458	−	0.382458i	−0.871987	+	0.489529i	$0.837169\pi$
$314$		0			0
$315$	−269.332	+	650.224i	−0.855021	+	2.06420i
$316$		0			0
$317$	−154.558	−	373.135i	−0.487563	−	1.17708i	−0.955942	−	0.293554i	$-0.905162\pi$
$317$	−154.558	−	373.135i	−0.487563	−	1.17708i	0.468379	−	0.883528i	$-0.344838\pi$
$318$		0			0
$319$			63.4940i			0.199041i
$320$		0			0
$321$	−49.1155			−0.153008
$322$		0			0
$323$	−34.8434	+	14.4326i	−0.107874	+	0.0446830i
$324$		0			0
$325$	−60.3061	−	24.9796i	−0.185557	−	0.0768604i
$326$		0			0
$327$	17.3227	−	17.3227i	0.0529745	−	0.0529745i
$328$		0			0
$329$	−458.464	+	458.464i	−1.39351	+	1.39351i
$330$		0			0
$331$	376.019	+	155.752i	1.13601	+	0.470551i	0.869820	−	0.493370i	$-0.164235\pi$
$331$	376.019	+	155.752i	1.13601	+	0.470551i	0.266190	+	0.963921i	$0.414235\pi$
$332$		0			0
$333$	−249.757	+	103.453i	−0.750021	+	0.310669i
$334$		0			0
$335$	−803.711			−2.39914
$336$		0			0
$337$		−	584.284i		−	1.73378i	−0.498499	−	0.866890i	$-0.666115\pi$
$337$		−	584.284i		−	1.73378i	0.498499	−	0.866890i	$-0.333885\pi$
$338$		0			0
$339$	12.5463	+	30.2895i	0.0370098	+	0.0893495i
$340$		0			0
$341$	44.1162	−	106.506i	0.129373	−	0.312334i
$342$		0			0
$343$	29.9994	+	29.9994i	0.0874617	+	0.0874617i
$344$		0			0
$345$	62.9514	+	62.9514i	0.182468	+	0.182468i
$346$		0			0
$347$	15.0226	−	36.2679i	0.0432929	−	0.104518i	−0.900754	−	0.434330i	$-0.856985\pi$
$347$	15.0226	−	36.2679i	0.0432929	−	0.104518i	0.944047	+	0.329812i	$0.106985\pi$
$348$		0			0
$349$	−82.9090	−	200.160i	−0.237562	−	0.573525i	0.759468	−	0.650545i	$-0.225459\pi$
$349$	−82.9090	−	200.160i	−0.237562	−	0.573525i	−0.997030	+	0.0770202i	$0.975459\pi$
$350$		0			0
$351$		−	11.0451i		−	0.0314675i
$352$		0			0
$353$	−213.926			−0.606022			−0.303011	−	0.952987i	$-0.597992\pi$
$353$	−213.926			−0.606022			−0.303011	+	0.952987i	$0.597992\pi$
$354$		0			0
$355$	21.3394	−	8.83905i	0.0601109	−	0.0248987i
$356$		0			0
$357$	−9.71666	−	4.02477i	−0.0272175	−	0.0112739i
$358$		0			0
$359$	235.583	−	235.583i	0.656219	−	0.656219i	−0.298264	−	0.954483i	$-0.596408\pi$
$359$	235.583	−	235.583i	0.656219	−	0.656219i	0.954483	+	0.298264i	$0.0964077\pi$
$360$		0			0
$361$	115.037	−	115.037i	0.318663	−	0.318663i
$362$		0			0
$363$	−43.1724	−	17.8826i	−0.118932	−	0.0492633i
$364$		0			0
$365$	−597.299	+	247.410i	−1.63644	+	0.677834i
$366$		0			0
$367$	266.252			0.725482			0.362741	−	0.931890i	$-0.381841\pi$
$367$	266.252			0.725482			0.362741	+	0.931890i	$0.381841\pi$
$368$		0			0
$369$			86.7101i			0.234987i
$370$		0			0
$371$	−101.598	−	245.280i	−0.273850	−	0.661133i
$372$		0			0
$373$	−133.648	+	322.655i	−0.358306	+	0.865028i	0.637232	+	0.770672i	$0.280079\pi$
$373$	−133.648	+	322.655i	−0.358306	+	0.865028i	−0.995539	+	0.0943560i	$0.969921\pi$
$374$		0			0
$375$	42.0150	+	42.0150i	0.112040	+	0.112040i
$376$		0			0
$377$	−28.2767	−	28.2767i	−0.0750045	−	0.0750045i
$378$		0			0
$379$	−1.26349	+	3.05034i	−0.00333376	+	0.00804840i	−0.925538	−	0.378656i	$-0.876386\pi$
$379$	−1.26349	+	3.05034i	−0.00333376	+	0.00804840i	0.922204	+	0.386704i	$0.126386\pi$
$380$		0			0
$381$	22.2169	+	53.6364i	0.0583122	+	0.140778i
$382$		0			0
$383$			310.584i			0.810923i	0.914112	+	0.405462i	$0.132889\pi$
$383$			310.584i			0.810923i	−0.914112	+	0.405462i	$0.867111\pi$
$384$		0			0
$385$	192.978			0.501243
$386$		0			0
$387$	75.0098	−	31.0701i	0.193824	−	0.0802844i
$388$		0			0
$389$	677.246	+	280.524i	1.74099	+	0.721142i	0.998695	+	0.0510705i	$0.0162633\pi$
$389$	677.246	+	280.524i	1.74099	+	0.721142i	0.742296	+	0.670072i	$0.233737\pi$
$390$		0			0
$391$	50.4525	−	50.4525i	0.129035	−	0.129035i
$392$		0			0
$393$	17.4407	−	17.4407i	0.0443783	−	0.0443783i
$394$		0			0
$395$	83.5594	+	34.6114i	0.211543	+	0.0876239i
$396$		0			0
$397$	467.679	−	193.719i	1.17803	−	0.487957i	0.294192	−	0.955746i	$-0.404949\pi$
$397$	467.679	−	193.719i	1.17803	−	0.487957i	0.883840	+	0.467789i	$0.154949\pi$
$398$		0			0
$399$	−55.3027			−0.138603
$400$		0			0
$401$			447.783i			1.11667i	0.829617	+	0.558333i	$0.188559\pi$
$401$			447.783i			1.11667i	−0.829617	+	0.558333i	$0.811441\pi$
$402$		0			0
$403$	27.7849	+	67.0786i	0.0689451	+	0.166448i
$404$		0			0
$405$	241.271	−	582.480i	0.595732	−	1.43822i
$406$		0			0
$407$	52.4142	+	52.4142i	0.128782	+	0.128782i
$408$		0			0
$409$	266.640	+	266.640i	0.651931	+	0.651931i	0.953458	−	0.301527i	$-0.0974962\pi$
$409$	266.640	+	266.640i	0.651931	+	0.651931i	−0.301527	+	0.953458i	$0.597496\pi$
$410$		0			0
$411$	36.9392	−	89.1791i	0.0898763	−	0.216981i
$412$		0			0
$413$	270.299	+	652.559i	0.654477	+	1.58005i
$414$		0			0
$415$		−	735.294i		−	1.77179i
$416$		0			0
$417$	42.8676			0.102800
$418$		0			0
$419$	565.518	−	234.245i	1.34969	−	0.559058i	0.413481	−	0.910513i	$-0.364313\pi$
$419$	565.518	−	234.245i	1.34969	−	0.559058i	0.936205	+	0.351455i	$0.114313\pi$
$420$		0			0
$421$	184.538	+	76.4382i	0.438333	+	0.181564i	0.590926	−	0.806726i	$-0.298762\pi$
$421$	184.538	+	76.4382i	0.438333	+	0.181564i	−0.152593	+	0.988289i	$0.548762\pi$
$422$		0			0
$423$	418.651	−	418.651i	0.989718	−	0.989718i
$424$		0			0
$425$	81.0159	−	81.0159i	0.190626	−	0.190626i
$426$		0			0
$427$	−737.557	−	305.506i	−1.72730	−	0.715471i
$428$		0			0
$429$	−1.38607	+	0.574129i	−0.00323093	+	0.00133830i
$430$		0			0
$431$	329.019			0.763385			0.381692	−	0.924289i	$-0.375341\pi$
$431$	329.019			0.763385			0.381692	+	0.924289i	$0.375341\pi$
$432$		0			0
$433$			403.449i			0.931753i	0.884850	+	0.465877i	$0.154261\pi$
$433$			403.449i			0.931753i	−0.884850	+	0.465877i	$0.845739\pi$
$434$		0			0
$435$	33.5155	+	80.9135i	0.0770470	+	0.186008i
$436$		0			0
$437$	143.576	−	346.623i	0.328549	−	0.793188i
$438$		0			0
$439$	432.214	+	432.214i	0.984542	+	0.984542i	0.999882	−	0.0153402i	$-0.00488314\pi$
$439$	432.214	+	432.214i	0.984542	+	0.984542i	−0.0153402	+	0.999882i	$0.504883\pi$
$440$		0			0
$441$	278.732	+	278.732i	0.632045	+	0.632045i
$442$		0			0
$443$	−138.144	+	333.509i	−0.311838	+	0.752843i	0.687799	+	0.725901i	$0.258577\pi$
$443$	−138.144	+	333.509i	−0.311838	+	0.752843i	−0.999637	+	0.0269419i	$0.991423\pi$
$444$		0			0
$445$	−72.0501	−	173.944i	−0.161910	−	0.390886i
$446$		0			0
$447$			47.0633i			0.105287i
$448$		0			0
$449$	−320.009			−0.712715			−0.356358	−	0.934350i	$-0.615981\pi$
$449$	−320.009			−0.712715			−0.356358	+	0.934350i	$0.615981\pi$
$450$		0			0
$451$	21.9658	−	9.09852i	0.0487046	−	0.0201741i
$452$		0			0
$453$	−67.9210	−	28.1338i	−0.149936	−	0.0621055i
$454$		0			0
$455$	−85.9419	+	85.9419i	−0.188883	+	0.188883i
$456$		0			0
$457$	−148.390	+	148.390i	−0.324705	+	0.324705i	−0.850569	−	0.525864i	$-0.823742\pi$
$457$	−148.390	+	148.390i	−0.324705	+	0.324705i	0.525864	+	0.850569i	$0.323742\pi$
$458$		0			0
$459$	17.9112	+	7.41904i	0.0390221	+	0.0161635i
$460$		0			0
$461$	224.303	−	92.9092i	0.486557	−	0.201538i	−0.125899	−	0.992043i	$-0.540182\pi$
$461$	224.303	−	92.9092i	0.486557	−	0.201538i	0.612456	+	0.790505i	$0.290182\pi$
$462$		0			0
$463$	675.592			1.45916			0.729581	−	0.683894i	$-0.239715\pi$
$463$	675.592			1.45916			0.729581	+	0.683894i	$0.239715\pi$
$464$		0			0
$465$		−	159.012i		−	0.341962i
$466$		0			0
$467$	−190.920	−	460.923i	−0.408823	−	0.986987i	−0.985448	−	0.169977i	$-0.945631\pi$
$467$	−190.920	−	460.923i	−0.408823	−	0.986987i	0.576625	−	0.817009i	$-0.304369\pi$
$468$		0			0
$469$	−361.458	+	872.636i	−0.770698	+	1.86063i
$470$		0			0
$471$	−15.1187	−	15.1187i	−0.0320991	−	0.0320991i
$472$		0			0
$473$	−15.7416	−	15.7416i	−0.0332803	−	0.0332803i
$474$		0			0
$475$	230.552	−	556.603i	0.485373	−	1.17179i
$476$		0			0
$477$	92.7755	+	223.980i	0.194498	+	0.469559i
$478$		0			0
$479$		−	775.709i		−	1.61943i	−0.586821	−	0.809717i	$-0.699621\pi$
$479$		−	775.709i		−	1.61943i	0.586821	−	0.809717i	$-0.300379\pi$
$480$		0			0
$481$	−46.6847			−0.0970576
$482$		0			0
$483$	96.6616	−	40.0385i	0.200127	−	0.0828955i
$484$		0			0
$485$	−476.481	−	197.365i	−0.982435	−	0.406938i
$486$		0			0
$487$	−422.101	+	422.101i	−0.866738	+	0.866738i	−0.992110	−	0.125372i	$-0.959988\pi$
$487$	−422.101	+	422.101i	−0.866738	+	0.866738i	0.125372	+	0.992110i	$0.459988\pi$
$488$		0			0
$489$	−21.3337	+	21.3337i	−0.0436272	+	0.0436272i
$490$		0			0
$491$	277.565	+	114.971i	0.565306	+	0.234157i	0.646987	−	0.762501i	$-0.276029\pi$
$491$	277.565	+	114.971i	0.565306	+	0.234157i	−0.0816809	+	0.996659i	$0.526029\pi$
$492$		0			0
$493$	64.8482	−	26.8610i	0.131538	−	0.0544848i
$494$		0			0
$495$	−176.220			−0.356000
$496$		0			0
$497$		−	27.1446i		−	0.0546170i
$498$		0			0
$499$	328.498	+	793.063i	0.658312	+	1.58930i	0.800410	+	0.599452i	$0.204615\pi$
$499$	328.498	+	793.063i	0.658312	+	1.58930i	−0.142099	+	0.989852i	$0.545385\pi$
$500$		0			0
$501$	28.8525	−	69.6560i	0.0575897	−	0.139034i
$502$		0			0
$503$	−115.459	−	115.459i	−0.229540	−	0.229540i	0.582960	−	0.812501i	$-0.301894\pi$
$503$	−115.459	−	115.459i	−0.229540	−	0.229540i	−0.812501	+	0.582960i	$0.801894\pi$
$504$		0			0
$505$	−250.373	−	250.373i	−0.495788	−	0.495788i
$506$		0			0
$507$	−25.8881	+	62.4995i	−0.0510614	+	0.123273i
$508$		0			0
$509$	97.7110	+	235.895i	0.191967	+	0.463449i	0.990331	−	0.138727i	$-0.0443009\pi$
$509$	97.7110	+	235.895i	0.191967	+	0.463449i	−0.798364	+	0.602175i	$0.794301\pi$
$510$		0			0
$511$			759.792i			1.48687i
$512$		0			0
$513$	101.942			0.198717
$514$		0			0
$515$	−390.747	+	161.853i	−0.758733	+	0.314277i
$516$		0			0
$517$	−149.983	−	62.1252i	−0.290103	−	0.120165i
$518$		0			0
$519$	64.0073	−	64.0073i	0.123328	−	0.123328i
$520$		0			0
$521$	229.899	−	229.899i	0.441264	−	0.441264i	−0.451173	−	0.892437i	$-0.648994\pi$
$521$	229.899	−	229.899i	0.441264	−	0.441264i	0.892437	+	0.451173i	$0.148994\pi$
$522$		0			0
$523$	900.921	+	373.174i	1.72260	+	0.713525i	0.999746	+	0.0225265i	$0.00717100\pi$
$523$	900.921	+	373.174i	1.72260	+	0.713525i	0.722856	+	0.690999i	$0.242829\pi$
$524$		0			0
$525$	155.218	−	64.2933i	0.295653	−	0.122463i
$526$		0			0
$527$	−127.441			−0.241823
$528$		0			0
$529$			180.797i			0.341772i
$530$		0			0
$531$	−246.826	−	595.890i	−0.464832	−	1.12220i
$532$		0			0
$533$	−5.73035	+	13.8343i	−0.0107511	+	0.0259555i
$534$		0			0
$535$	−704.466	−	704.466i	−1.31676	−	1.31676i
$536$		0			0
$537$	−60.1486	−	60.1486i	−0.112009	−	0.112009i
$538$		0			0
$539$	41.3621	−	99.8569i	0.0767386	−	0.185263i
$540$		0			0
$541$	−86.3781	−	208.535i	−0.159664	−	0.385462i	0.823721	−	0.566995i	$-0.191894\pi$
$541$	−86.3781	−	208.535i	−0.159664	−	0.385462i	−0.983385	+	0.181533i	$0.941894\pi$
$542$		0			0
$543$			99.0983i			0.182501i
$544$		0			0
$545$	496.920			0.911780
$546$		0			0
$547$	−497.491	+	206.067i	−0.909489	+	0.376723i	−0.787861	−	0.615853i	$-0.788812\pi$
$547$	−497.491	+	206.067i	−0.909489	+	0.376723i	−0.121628	+	0.992576i	$0.538812\pi$
$548$		0			0
$549$	673.507	+	278.976i	1.22679	+	0.508152i
$550$		0			0
$551$	260.983	−	260.983i	0.473653	−	0.473653i
$552$		0			0
$553$	75.1593	−	75.1593i	0.135912	−	0.135912i
$554$		0			0
$555$	94.4609	+	39.1270i	0.170200	+	0.0704991i
$556$		0			0
$557$	527.914	−	218.669i	0.947782	−	0.392584i	0.145385	−	0.989375i	$-0.453558\pi$
$557$	527.914	−	218.669i	0.947782	−	0.392584i	0.802397	+	0.596791i	$0.203558\pi$
$558$		0			0
$559$	14.0209			0.0250820
$560$		0			0
$561$		−	2.63335i		−	0.00469404i
$562$		0			0
$563$	303.900	+	733.680i	0.539788	+	1.30316i	0.924871	+	0.380281i	$0.124173\pi$
$563$	303.900	+	733.680i	0.539788	+	1.30316i	−0.385084	+	0.922882i	$0.625827\pi$
$564$		0			0
$565$	−254.491	+	614.397i	−0.450427	+	1.08743i
$566$		0			0
$567$	−523.925	−	523.925i	−0.924029	−	0.924029i
$568$		0			0
$569$	−143.631	−	143.631i	−0.252426	−	0.252426i	0.569538	−	0.821965i	$-0.307122\pi$
$569$	−143.631	−	143.631i	−0.252426	−	0.252426i	−0.821965	+	0.569538i	$0.807122\pi$
$570$		0			0
$571$	371.018	−	895.717i	0.649769	−	1.56868i	−0.163339	−	0.986570i	$-0.552227\pi$
$571$	371.018	−	895.717i	0.649769	−	1.56868i	0.813109	−	0.582112i	$-0.197773\pi$
$572$		0			0
$573$	3.13194	+	7.56116i	0.00546586	+	0.0131957i
$574$		0			0
$575$			1139.78i			1.98223i
$576$		0			0
$577$	706.702			1.22479			0.612393	−	0.790553i	$-0.290207\pi$
$577$	706.702			1.22479			0.612393	+	0.790553i	$0.290207\pi$
$578$		0			0
$579$	43.4592	−	18.0014i	0.0750590	−	0.0310905i
$580$		0			0
$581$	−798.352	−	330.688i	−1.37410	−	0.569171i
$582$		0			0
$583$	47.0045	−	47.0045i	0.0806253	−	0.0806253i
$584$		0			0
$585$	78.4786	−	78.4786i	0.134151	−	0.134151i
$586$		0			0
$587$	−293.599	−	121.613i	−0.500169	−	0.207177i	0.118312	−	0.992976i	$-0.462252\pi$
$587$	−293.599	−	121.613i	−0.500169	−	0.207177i	−0.618481	+	0.785800i	$0.712252\pi$
$588$		0			0
$589$	−619.110	+	256.444i	−1.05112	+	0.435389i
$590$		0			0
$591$	78.0696			0.132097
$592$		0			0
$593$			674.627i			1.13765i	0.822458	+	0.568825i	$0.192602\pi$
$593$			674.627i			1.13765i	−0.822458	+	0.568825i	$0.807398\pi$
$594$		0			0
$595$	−81.6391	−	197.094i	−0.137209	−	0.331251i
$596$		0			0
$597$	−4.87127	+	11.7603i	−0.00815958	+	0.0196990i
$598$		0			0
$599$	379.725	+	379.725i	0.633932	+	0.633932i	0.949052	−	0.315120i	$-0.102045\pi$
$599$	379.725	+	379.725i	0.633932	+	0.633932i	−0.315120	+	0.949052i	$0.602045\pi$
$600$		0			0
$601$	−548.542	−	548.542i	−0.912715	−	0.912715i	0.0837700	−	0.996485i	$-0.473304\pi$
$601$	−548.542	−	548.542i	−0.912715	−	0.912715i	−0.996485	+	0.0837700i	$0.973304\pi$
$602$		0			0
$603$	330.068	−	796.855i	0.547377	−	1.32148i
$604$		0			0
$605$	−362.733	−	875.715i	−0.599559	−	1.44746i
$606$		0			0
$607$			1.05067i			0.00173092i	1.00000		0.000865460i	$0.000275484\pi$
$607$			1.05067i			0.00173092i	−1.00000		0.000865460i	$0.999725\pi$
$608$		0			0
$609$	102.926			0.169008
$610$		0			0
$611$	94.4614	−	39.1272i	0.154601	−	0.0640379i
$612$		0			0
$613$	−625.826	−	259.226i	−1.02092	−	0.422881i	−0.191495	−	0.981494i	$-0.561334\pi$
$613$	−625.826	−	259.226i	−1.02092	−	0.422881i	−0.829428	+	0.558613i	$0.811334\pi$
$614$		0			0
$615$	23.1894	−	23.1894i	0.0377063	−	0.0377063i
$616$		0			0
$617$	180.644	−	180.644i	0.292779	−	0.292779i	−0.545398	−	0.838177i	$-0.683622\pi$
$617$	180.644	−	180.644i	0.292779	−	0.292779i	0.838177	+	0.545398i	$0.183622\pi$
$618$		0			0
$619$	−555.651	−	230.158i	−0.897658	−	0.371822i	−0.114339	−	0.993442i	$-0.536475\pi$
$619$	−555.651	−	230.158i	−0.897658	−	0.371822i	−0.783319	+	0.621620i	$0.786475\pi$
$620$		0			0
$621$	−178.181	+	73.8048i	−0.286925	+	0.118848i
$622$		0			0
$623$	−221.265			−0.355160
$624$		0			0
$625$			135.712i			0.217139i
$626$		0			0
$627$	−5.29899	−	12.7929i	−0.00845135	−	0.0204034i
$628$		0			0
$629$	31.3584	−	75.7058i	0.0498543	−	0.120359i
$630$		0			0
$631$	−267.583	−	267.583i	−0.424062	−	0.424062i	0.462537	−	0.886600i	$-0.346939\pi$
$631$	−267.583	−	267.583i	−0.424062	−	0.424062i	−0.886600	+	0.462537i	$0.846939\pi$
$632$		0			0
$633$	87.6981	+	87.6981i	0.138544	+	0.138544i
$634$		0			0
$635$	−450.652	+	1087.97i	−0.709688	+	1.71334i
$636$		0			0
$637$	26.0503	+	62.8911i	0.0408954	+	0.0987301i
$638$		0			0
$639$			24.7874i			0.0387908i
$640$		0			0
$641$	−834.869			−1.30245			−0.651224	−	0.758886i	$-0.725744\pi$
$641$	−834.869			−1.30245			−0.651224	+	0.758886i	$0.725744\pi$
$642$		0			0
$643$	−1006.71	+	416.995i	−1.56565	+	0.648514i	−0.986060	−	0.166393i	$-0.946788\pi$
$643$	−1006.71	+	416.995i	−1.56565	+	0.648514i	−0.579592	+	0.814907i	$0.696788\pi$
$644$		0			0
$645$	−28.3695	−	11.7510i	−0.0439837	−	0.0182187i
$646$		0			0
$647$	−857.194	+	857.194i	−1.32488	+	1.32488i	−0.415099	+	0.909776i	$0.636253\pi$
$647$	−857.194	+	857.194i	−1.32488	+	1.32488i	−0.909776	+	0.415099i	$0.863747\pi$
$648$		0			0
$649$	−125.054	+	125.054i	−0.192687	+	0.192687i
$650$		0			0
$651$	−172.649	−	71.5136i	−0.265206	−	0.109852i
$652$		0			0
$653$	105.248	−	43.5953i	0.161177	−	0.0667616i	−0.300636	−	0.953739i	$-0.597199\pi$
$653$	105.248	−	43.5953i	0.161177	−	0.0667616i	0.461813	+	0.886977i	$0.347199\pi$
$654$		0			0
$655$	500.306			0.763826
$656$		0			0
$657$		−	693.811i		−	1.05603i
$658$		0			0
$659$	222.875	+	538.067i	0.338201	+	0.816490i	0.997889	+	0.0649499i	$0.0206888\pi$
$659$	222.875	+	538.067i	0.338201	+	0.816490i	−0.659687	+	0.751540i	$0.729311\pi$
$660$		0			0
$661$	396.971	−	958.372i	0.600561	−	1.44988i	−0.272445	−	0.962171i	$-0.587832\pi$
$661$	396.971	−	958.372i	0.600561	−	1.44988i	0.873005	−	0.487711i	$-0.162168\pi$
$662$		0			0
$663$	1.17275	+	1.17275i	0.00176885	+	0.00176885i
$664$		0			0
$665$	−793.210	−	793.210i	−1.19280	−	1.19280i
$666$		0			0
$667$	−267.214	+	645.111i	−0.400620	+	0.967183i
$668$		0			0
$669$	−1.88577	−	4.55265i	−0.00281879	−	0.00680515i
$670$		0			0
$671$		−	199.888i		−	0.297896i
$672$		0			0
$673$	−908.805			−1.35038			−0.675190	−	0.737644i	$-0.735938\pi$
$673$	−908.805			−1.35038			−0.675190	+	0.737644i	$0.735938\pi$
$674$		0			0
$675$	−286.120	+	118.515i	−0.423881	+	0.175577i
$676$		0			0
$677$	−963.142	−	398.947i	−1.42266	−	0.589286i	−0.467134	−	0.884186i	$-0.654713\pi$
$677$	−963.142	−	398.947i	−1.42266	−	0.589286i	−0.955528	+	0.294900i	$0.904713\pi$
$678$		0			0
$679$	−428.581	+	428.581i	−0.631195	+	0.631195i
$680$		0			0
$681$	−66.8259	+	66.8259i	−0.0981290	+	0.0981290i
$682$		0			0
$683$	−248.963	−	103.124i	−0.364515	−	0.150987i	0.192906	−	0.981217i	$-0.438209\pi$
$683$	−248.963	−	103.124i	−0.364515	−	0.150987i	−0.557420	+	0.830230i	$0.688209\pi$
$684$		0			0
$685$	1808.92	−	749.280i	2.64076	−	1.09384i
$686$		0			0
$687$	−37.5564			−0.0546673
$688$		0			0
$689$			41.8664i			0.0607640i
$690$		0			0
$691$	222.756	+	537.780i	0.322367	+	0.778263i	0.999116	+	0.0420488i	$0.0133885\pi$
$691$	222.756	+	537.780i	0.322367	+	0.778263i	−0.676748	+	0.736214i	$0.736612\pi$
$692$		0			0
$693$	−79.2524	+	191.332i	−0.114361	+	0.276093i
$694$		0			0
$695$	614.853	+	614.853i	0.884681	+	0.884681i
$696$		0			0
$697$	−18.5851	−	18.5851i	−0.0266645	−	0.0266645i
$698$		0			0
$699$	7.27433	−	17.5618i	0.0104068	−	0.0251242i
$700$		0			0
$701$	236.347	+	570.592i	0.337157	+	0.813969i	0.997986	+	0.0634324i	$0.0202047\pi$
$701$	236.347	+	570.592i	0.337157	+	0.813969i	−0.660829	+	0.750536i	$0.729795\pi$
$702$		0			0
$703$		−	430.882i		−	0.612919i
$704$		0			0
$705$	−223.924			−0.317623
$706$		0			0
$707$	−384.446	+	159.243i	−0.543771	+	0.225237i
$708$		0			0
$709$	599.630	+	248.375i	0.845740	+	0.350317i	0.763114	−	0.646264i	$-0.223669\pi$
$709$	599.630	+	248.375i	0.845740	+	0.350317i	0.0826257	+	0.996581i	$0.473669\pi$
$710$		0			0
$711$	−68.6324	+	68.6324i	−0.0965293	+	0.0965293i
$712$		0			0
$713$	896.458	−	896.458i	1.25730	−	1.25730i
$714$		0			0
$715$	−28.1153	−	11.6457i	−0.0393221	−	0.0162877i
$716$		0			0
$717$	124.867	−	51.7216i	0.174152	−	0.0721361i
$718$		0			0
$719$	96.4410			0.134132			0.0670661	−	0.997749i	$-0.478636\pi$
$719$	96.4410			0.134132			0.0670661	+	0.997749i	$0.478636\pi$
$720$		0			0
$721$			497.048i			0.689388i
$722$		0			0
$723$	33.9952	+	82.0716i	0.0470196	+	0.113515i
$724$		0			0
$725$	−429.088	+	1035.91i	−0.591846	+	1.42884i
$726$		0			0
$727$	−708.402	−	708.402i	−0.974418	−	0.974418i	0.0252626	−	0.999681i	$-0.491958\pi$
$727$	−708.402	−	708.402i	−0.974418	−	0.974418i	−0.999681	+	0.0252626i	$0.991958\pi$
$728$		0			0
$729$	459.728	+	459.728i	0.630628	+	0.630628i
$730$		0			0
$731$	−9.41788	+	22.7368i	−0.0128836	+	0.0311037i
$732$		0			0
$733$	149.531	+	361.000i	0.203999	+	0.492497i	0.992457	−	0.122591i	$-0.0391204\pi$
$733$	149.531	+	361.000i	0.203999	+	0.492497i	−0.788458	+	0.615088i	$0.789120\pi$
$734$		0			0
$735$		−	149.086i		−	0.202838i
$736$		0			0
$737$	−236.497			−0.320891
$738$		0			0
$739$	971.442	−	402.384i	1.31454	−	0.544499i	0.388331	−	0.921520i	$-0.373052\pi$
$739$	971.442	−	402.384i	1.31454	−	0.544499i	0.926205	+	0.377021i	$0.123052\pi$
$740$		0			0
$741$	8.05712	+	3.33737i	0.0108733	+	0.00450387i
$742$		0			0
$743$	117.181	−	117.181i	0.157714	−	0.157714i	−0.623839	−	0.781553i	$-0.714428\pi$
$743$	117.181	−	117.181i	0.157714	−	0.157714i	0.781553	+	0.623839i	$0.214428\pi$
$744$		0			0
$745$	−675.032	+	675.032i	−0.906083	+	0.906083i
$746$		0			0
$747$	729.022	+	301.971i	0.975933	+	0.404245i
$748$		0			0
$749$	−1081.70	+	448.056i	−1.44420	+	0.598206i
$750$		0			0
$751$	604.910			0.805473			0.402736	−	0.915316i	$-0.368059\pi$
$751$	604.910			0.805473			0.402736	+	0.915316i	$0.368059\pi$
$752$		0			0
$753$			98.2854i			0.130525i
$754$		0			0
$755$	−570.670	−	1377.72i	−0.755855	−	1.82479i
$756$		0			0
$757$	459.899	−	1110.29i	0.607528	−	1.46670i	−0.258152	−	0.966104i	$-0.583113\pi$
$757$	459.899	−	1110.29i	0.607528	−	1.46670i	0.865680	−	0.500598i	$-0.166887\pi$
$758$		0			0
$759$	18.5238	+	18.5238i	0.0244056	+	0.0244056i
$760$		0			0
$761$	202.753	+	202.753i	0.266430	+	0.266430i	0.827660	−	0.561230i	$-0.189672\pi$
$761$	202.753	+	202.753i	0.266430	+	0.266430i	−0.561230	+	0.827660i	$0.689672\pi$
$762$		0			0
$763$	223.483	−	539.535i	0.292900	−	0.707124i
$764$		0			0
$765$	74.5495	+	179.978i	0.0974503	+	0.235266i
$766$		0			0
$767$		−	111.384i		−	0.145220i
$768$		0			0
$769$	954.072			1.24067			0.620333	−	0.784338i	$-0.286997\pi$
$769$	954.072			1.24067			0.620333	+	0.784338i	$0.286997\pi$
$770$		0			0
$771$	−51.9407	+	21.5146i	−0.0673680	+	0.0279047i
$772$		0			0
$773$	−244.204	−	101.153i	−0.315918	−	0.130857i	0.219090	−	0.975705i	$-0.429691\pi$
$773$	−244.204	−	101.153i	−0.315918	−	0.130857i	−0.535007	+	0.844847i	$0.679691\pi$
$774$		0			0
$775$	1439.52	−	1439.52i	1.85744	−	1.85744i
$776$		0			0
$777$	84.9649	−	84.9649i	0.109350	−	0.109350i
$778$		0			0
$779$	−127.685	−	52.8890i	−0.163909	−	0.0678934i
$780$		0			0
$781$	6.27923	−	2.60094i	0.00803999	−	0.00333027i
$782$		0			0
$783$	−189.727			−0.242308
$784$		0			0
$785$		−	433.696i		−	0.552479i
$786$		0			0
$787$	19.8368	+	47.8903i	0.0252056	+	0.0608518i	0.935981	−	0.352050i	$-0.114515\pi$
$787$	19.8368	+	47.8903i	0.0252056	+	0.0608518i	−0.910776	+	0.412902i	$0.864515\pi$
$788$		0			0
$789$	20.1416	−	48.6261i	0.0255280	−	0.0616301i
$790$		0			0
$791$	552.633	+	552.633i	0.698650	+	0.698650i
$792$		0			0
$793$	89.0192	+	89.0192i	0.112256	+	0.112256i
$794$		0			0
$795$	35.0887	−	84.7116i	0.0441367	−	0.106556i
$796$		0			0
$797$	−187.462	−	452.574i	−0.235210	−	0.567847i	0.761566	−	0.648088i	$-0.224431\pi$
$797$	−187.462	−	452.574i	−0.235210	−	0.567847i	−0.996775	+	0.0802411i	$0.974431\pi$
$798$		0			0
$799$			179.464i			0.224611i
$800$		0			0
$801$	202.050			0.252247
$802$		0			0
$803$	−175.759	+	72.8017i	−0.218878	+	0.0906622i
$804$		0			0
$805$	1960.70	+	812.148i	2.43565	+	1.00888i
$806$		0			0
$807$	−55.7625	+	55.7625i	−0.0690985	+	0.0690985i
$808$		0			0
$809$	−772.357	+	772.357i	−0.954706	+	0.954706i	−0.999018	−	0.0443114i	$-0.985891\pi$
$809$	−772.357	+	772.357i	−0.954706	+	0.954706i	0.0443114	+	0.999018i	$0.485891\pi$
$810$		0			0
$811$	−518.106	−	214.607i	−0.638849	−	0.264620i	0.0396587	−	0.999213i	$-0.487373\pi$
$811$	−518.106	−	214.607i	−0.638849	−	0.264620i	−0.678508	+	0.734593i	$0.737373\pi$
$812$		0			0
$813$	−170.384	+	70.5753i	−0.209574	+	0.0868085i
$814$		0			0
$815$	−611.981			−0.750897
$816$		0			0
$817$			129.407i			0.158393i
$818$		0			0
$819$	−49.9141	−	120.503i	−0.0609452	−	0.147135i
$820$		0			0
$821$	−328.590	+	793.287i	−0.400232	+	0.966245i	0.587378	+	0.809313i	$0.300160\pi$
$821$	−328.590	+	793.287i	−0.400232	+	0.966245i	−0.987609	+	0.156932i	$0.949840\pi$
$822$		0			0
$823$	−370.318	−	370.318i	−0.449961	−	0.449961i	0.445381	−	0.895341i	$-0.353068\pi$
$823$	−370.318	−	370.318i	−0.449961	−	0.449961i	−0.895341	+	0.445381i	$0.853068\pi$
$824$		0			0
$825$	29.7453	+	29.7453i	0.0360549	+	0.0360549i
$826$		0			0
$827$	55.6405	−	134.328i	0.0672799	−	0.162428i	−0.886663	−	0.462416i	$-0.846983\pi$
$827$	55.6405	−	134.328i	0.0672799	−	0.162428i	0.953943	+	0.299988i	$0.0969827\pi$
$828$		0			0
$829$	−492.586	−	1189.21i	−0.594193	−	1.43451i	−0.879419	−	0.476048i	$-0.842069\pi$
$829$	−492.586	−	1189.21i	−0.594193	−	1.43451i	0.285226	−	0.958460i	$-0.407931\pi$
$830$		0			0
$831$		−	13.2943i		−	0.0159980i
$832$		0			0
$833$	−119.485			−0.143439
$834$		0			0
$835$	1412.91	−	585.248i	1.69211	−	0.700896i
$836$		0			0
$837$	318.252	+	131.824i	0.380229	+	0.157496i
$838$		0			0
$839$	−215.217	+	215.217i	−0.256516	+	0.256516i	−0.823636	−	0.567119i	$-0.808058\pi$
$839$	−215.217	+	215.217i	−0.256516	+	0.256516i	0.567119	+	0.823636i	$0.308058\pi$
$840$		0			0
$841$	108.953	−	108.953i	0.129552	−	0.129552i
$842$		0			0
$843$	165.868	+	68.7048i	0.196759	+	0.0815004i
$844$		0			0
$845$	−1267.75	+	525.119i	−1.50029	+	0.621442i
$846$		0			0
$847$	−1113.95			−1.31517
$848$		0			0
$849$		−	78.7867i		−	0.0927994i
$850$		0			0
$851$	311.954	+	753.123i	0.366573	+	0.884986i
$852$		0			0
$853$	68.6449	−	165.723i	0.0804747	−	0.194283i	−0.878521	−	0.477704i	$-0.841469\pi$
$853$	68.6449	−	165.723i	0.0804747	−	0.194283i	0.958996	+	0.283421i	$0.0914693\pi$
$854$		0			0
$855$	724.327	+	724.327i	0.847166	+	0.847166i
$856$		0			0
$857$	713.771	+	713.771i	0.832871	+	0.832871i	0.987909	−	0.155037i	$-0.0495497\pi$
$857$	713.771	+	713.771i	0.832871	+	0.832871i	−0.155037	+	0.987909i	$0.549550\pi$
$858$		0			0
$859$	−343.845	+	830.116i	−0.400285	+	0.966375i	0.587311	+	0.809361i	$0.300187\pi$
$859$	−343.845	+	830.116i	−0.400285	+	0.966375i	−0.987596	+	0.157013i	$0.949813\pi$
$860$		0			0
$861$	−14.7490	−	35.6071i	−0.0171300	−	0.0413556i
$862$		0			0
$863$			1574.26i			1.82417i	0.410002	+	0.912085i	$0.365528\pi$
$863$			1574.26i			1.82417i	−0.410002	+	0.912085i	$0.634472\pi$
$864$		0			0
$865$	1836.12			2.12268
$866$		0			0
$867$	105.681	−	43.7745i	0.121893	−	0.0504897i
$868$		0			0
$869$	24.5878	+	10.1846i	0.0282944	+	0.0117199i
$870$		0			0
$871$	105.322	−	105.322i	0.120921	−	0.120921i
$872$		0			0
$873$	391.363	−	391.363i	0.448296	−	0.448296i
$874$		0			0
$875$	1308.61	+	542.043i	1.49555	+	0.619477i
$876$		0			0
$877$	−1227.56	+	508.470i	−1.39972	+	0.579784i	−0.949679	−	0.313224i	$-0.898591\pi$
$877$	−1227.56	+	508.470i	−1.39972	+	0.579784i	−0.450042	+	0.893007i	$0.648591\pi$
$878$		0			0
$879$	68.6268			0.0780738
$880$		0			0
$881$		−	1187.59i		−	1.34800i	−0.738732	−	0.674000i	$-0.764575\pi$
$881$		−	1187.59i		−	1.34800i	0.738732	−	0.674000i	$-0.235425\pi$
$882$		0			0
$883$	−544.271	−	1313.99i	−0.616389	−	1.48809i	−0.855869	−	0.517193i	$-0.826977\pi$
$883$	−544.271	−	1313.99i	−0.616389	−	1.48809i	0.239480	−	0.970901i	$-0.423023\pi$
$884$		0			0
$885$	−93.3522	+	225.372i	−0.105483	+	0.254658i
$886$		0			0
$887$	−95.1081	−	95.1081i	−0.107224	−	0.107224i	0.651459	−	0.758684i	$-0.274157\pi$
$887$	−95.1081	−	95.1081i	−0.107224	−	0.107224i	−0.758684	+	0.651459i	$0.774157\pi$
$888$		0			0
$889$	978.598	+	978.598i	1.10079	+	1.10079i
$890$		0			0
$891$	70.9955	−	171.398i	0.0796807	−	0.192366i
$892$		0			0
$893$	361.129	+	871.842i	0.404400	+	0.976307i
$894$		0			0
$895$		−	1725.43i		−	1.92786i
$896$		0			0
$897$	−16.4990			−0.0183935
$898$		0			0
$899$	1152.25	−	477.276i	1.28170	−	0.530896i
$900$		0			0
$901$	−67.8922	−	28.1219i	−0.0753521	−	0.0312119i
$902$		0			0
$903$	−25.5176	+	25.5176i	−0.0282587	+	0.0282587i
$904$		0			0
$905$	−1421.37	+	1421.37i	−1.57058	+	1.57058i
$906$		0			0
$907$	−103.742	−	42.9713i	−0.114379	−	0.0473774i	0.324760	−	0.945796i	$-0.394716\pi$
$907$	−103.742	−	42.9713i	−0.114379	−	0.0473774i	−0.439139	+	0.898419i	$0.644716\pi$
$908$		0			0
$909$	351.060	−	145.414i	0.386205	−	0.159971i
$910$		0			0
$911$	134.755			0.147920			0.0739598	−	0.997261i	$-0.476436\pi$
$911$	134.755			0.147920			0.0739598	+	0.997261i	$0.476436\pi$
$912$		0			0
$913$		−	216.365i		−	0.236982i
$914$		0			0
$915$	−105.512	−	254.728i	−0.115313	−	0.278391i
$916$		0			0
$917$	225.005	−	543.211i	0.245371	−	0.592379i
$918$		0			0
$919$	847.025	+	847.025i	0.921681	+	0.921681i	0.997148	−	0.0754671i	$-0.0240448\pi$
$919$	847.025	+	847.025i	0.921681	+	0.921681i	−0.0754671	+	0.997148i	$0.524045\pi$
$920$		0			0
$921$	−83.6129	−	83.6129i	−0.0907849	−	0.0907849i
$922$		0			0
$923$	−1.63811	+	3.95474i	−0.00177476	+	0.00428465i
$924$		0			0
$925$	500.931	+	1209.35i	0.541547	+	1.30741i
$926$		0			0
$927$		−	453.884i		−	0.489627i
$928$		0			0
$929$	−1150.33			−1.23824			−0.619121	−	0.785295i	$-0.712511\pi$
$929$	−1150.33			−1.23824			−0.619121	+	0.785295i	$0.712511\pi$
$930$		0			0
$931$	−580.461	+	240.435i	−0.623481	+	0.258254i
$932$		0			0
$933$	−39.2698	−	16.2661i	−0.0420898	−	0.0174342i
$934$		0			0
$935$	37.7704	−	37.7704i	0.0403961	−	0.0403961i
$936$		0			0
$937$	1191.07	−	1191.07i	1.27115	−	1.27115i	0.325670	−	0.945484i	$-0.394410\pi$
$937$	1191.07	−	1191.07i	1.27115	−	1.27115i	0.945484	−	0.325670i	$-0.105590\pi$
$938$		0			0
$939$	−63.4828	−	26.2954i	−0.0676068	−	0.0280037i
$940$		0			0
$941$	741.098	−	306.973i	0.787564	−	0.326220i	0.0476005	−	0.998866i	$-0.484843\pi$
$941$	741.098	−	306.973i	0.787564	−	0.326220i	0.739964	+	0.672647i	$0.234843\pi$
$942$		0			0
$943$	261.467			0.277272
$944$		0			0
$945$			576.642i			0.610203i
$946$		0			0
$947$	75.9383	+	183.331i	0.0801883	+	0.193592i	0.958889	−	0.283781i	$-0.0915890\pi$
$947$	75.9383	+	183.331i	0.0801883	+	0.193592i	−0.878701	+	0.477373i	$0.841589\pi$
$948$		0			0
$949$	45.8514	−	110.695i	0.0483155	−	0.116644i
$950$		0			0
$951$	−115.913	−	115.913i	−0.121886	−	0.121886i
$952$		0			0
$953$	−240.916	−	240.916i	−0.252798	−	0.252798i	0.569319	−	0.822117i	$-0.307207\pi$
$953$	−240.916	−	240.916i	−0.252798	−	0.252798i	−0.822117	+	0.569319i	$0.807207\pi$
$954$		0			0
$955$	−63.5287	+	153.372i	−0.0665222	+	0.160599i
$956$		0			0
$957$	9.86212	+	23.8093i	0.0103052	+	0.0248791i
$958$		0			0
$959$		−	2301.03i		−	2.39941i
$960$		0			0
$961$	−1303.41			−1.35631
$962$		0			0
$963$	987.767	−	409.147i	1.02572	−	0.424867i
$964$		0			0
$965$	881.533	+	365.143i	0.913506	+	0.378386i
$966$		0			0
$967$	474.501	−	474.501i	0.490694	−	0.490694i	−0.417831	−	0.908525i	$-0.637209\pi$
$967$	474.501	−	474.501i	0.490694	−	0.490694i	0.908525	+	0.417831i	$0.137209\pi$
$968$		0			0
$969$	−10.8240	+	10.8240i	−0.0111703	+	0.0111703i
$970$		0			0
$971$	−486.579	−	201.548i	−0.501111	−	0.207567i	0.117786	−	0.993039i	$-0.462420\pi$
$971$	−486.579	−	201.548i	−0.501111	−	0.207567i	−0.618897	+	0.785472i	$0.712420\pi$
$972$		0			0
$973$	944.103	−	391.060i	0.970301	−	0.401912i
$974$		0			0
$975$	−26.4938			−0.0271731
$976$		0			0
$977$		−	137.589i		−	0.140828i	−0.997518	−	0.0704140i	$-0.977568\pi$
$977$		−	137.589i		−	0.140828i	0.997518	−	0.0704140i	$-0.0224320\pi$
$978$		0			0
$979$	−21.2012	−	51.1841i	−0.0216559	−	0.0522821i
$980$		0			0
$981$	−204.075	+	492.681i	−0.208028	+	0.502224i
$982$		0			0
$983$	−602.812	−	602.812i	−0.613237	−	0.613237i	0.330551	−	0.943788i	$-0.392765\pi$
$983$	−602.812	−	602.812i	−0.613237	−	0.613237i	−0.943788	+	0.330551i	$0.892765\pi$
$984$		0			0
$985$	1119.76	+	1119.76i	1.13681	+	1.13681i
$986$		0			0
$987$	−100.707	+	243.128i	−0.102033	+	0.246330i
$988$		0			0
$989$	−93.6893	−	226.186i	−0.0947313	−	0.228702i
$990$		0			0
$991$			82.2289i			0.0829757i	0.999139	+	0.0414879i	$0.0132098\pi$
$991$			82.2289i			0.0829757i	−0.999139	+	0.0414879i	$0.986790\pi$
$992$		0			0
$993$	165.193			0.166358
$994$		0			0
$995$	−238.547	+	98.8096i	−0.239746	+	0.0993061i
$996$		0			0
$997$	−1201.68	−	497.750i	−1.20529	−	0.499248i	−0.312586	−	0.949889i	$-0.601195\pi$
$997$	−1201.68	−	497.750i	−1.20529	−	0.499248i	−0.892705	+	0.450641i	$0.851195\pi$
$998$		0			0
$999$	−156.620	+	156.620i	−0.156776	+	0.156776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.3.h.b.31.4		28
4.3	odd	2		256.3.h.a.31.4		28
8.3	odd	2		128.3.h.a.15.4		28
8.5	even	2		32.3.h.a.27.7	yes	28
24.5	odd	2		288.3.u.a.91.1		28
32.3	odd	8		32.3.h.a.19.7	✓	28
32.13	even	8		256.3.h.a.223.4		28
32.19	odd	8	inner	256.3.h.b.223.4		28
32.29	even	8		128.3.h.a.111.4		28
96.35	even	8		288.3.u.a.19.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.7	✓	28	32.3	odd	8
32.3.h.a.27.7	yes	28	8.5	even	2
128.3.h.a.15.4		28	8.3	odd	2
128.3.h.a.111.4		28	32.29	even	8
256.3.h.a.31.4		28	4.3	odd	2
256.3.h.a.223.4		28	32.13	even	8
256.3.h.b.31.4		28	1.1	even	1	trivial
256.3.h.b.223.4		28	32.19	odd	8	inner
288.3.u.a.19.1		28	96.35	even	8
288.3.u.a.91.1		28	24.5	odd	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.374985 - 0.155324i) q^{3} +(7.60625 + 3.15061i) q^{5} +(6.84161 - 6.84161i) q^{7} +(-6.24747 + 6.24747i) q^{9} +O(q^{10})\)	\(q+(0.374985 - 0.155324i) q^{3} +(7.60625 + 3.15061i) q^{5} +(6.84161 - 6.84161i) q^{7} +(-6.24747 + 6.24747i) q^{9} +(2.23818 + 0.927086i) q^{11} +(-1.40964 + 0.583890i) q^{13} +3.34159 q^{15} -2.67812i q^{17} +(-5.38908 - 13.0104i) q^{19} +(1.50283 - 3.62816i) q^{21} +(18.8388 + 18.8388i) q^{23} +(30.2510 + 30.2510i) q^{25} +(-2.77024 + 6.68795i) q^{27} +(10.0298 + 24.2140i) q^{29} -47.5858i q^{31} +0.983283 q^{33} +(73.5942 - 30.4837i) q^{35} +(28.2682 + 11.7091i) q^{37} +(-0.437900 + 0.437900i) q^{39} +(6.93962 - 6.93962i) q^{41} +(-8.48982 - 3.51660i) q^{43} +(-67.2032 + 27.8365i) q^{45} -67.0112 q^{47} -44.6152i q^{49} +(-0.415976 - 1.00426i) q^{51} +(10.5006 - 25.3507i) q^{53} +(14.1033 + 14.1033i) q^{55} +(-4.04165 - 4.04165i) q^{57} +(-27.9364 + 67.4445i) q^{59} +(-31.5752 - 76.2294i) q^{61} +85.4855i q^{63} -12.5616 q^{65} +(-90.1903 + 37.3580i) q^{67} +(9.99035 + 4.13814i) q^{69} +(1.98379 - 1.98379i) q^{71} +(-55.5273 + 55.5273i) q^{73} +(16.0424 + 6.64496i) q^{75} +(21.6555 - 8.97002i) q^{77} +10.9856 q^{79} -76.5792i q^{81} +(-34.1779 - 82.5128i) q^{83} +(8.43772 - 20.3705i) q^{85} +(7.52203 + 7.52203i) q^{87} +(-16.1705 - 16.1705i) q^{89} +(-5.64942 + 13.6389i) q^{91} +(-7.39121 - 17.8440i) q^{93} -115.939i q^{95} -62.6434 q^{97} +(-19.7749 + 8.19105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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Representations

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Database

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