LMFDB - Embedded newform 256.2.i.a.113.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			113.6
Character	$\chi$	$=$	256.113
Dual form			256.2.i.a.145.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00147 + 1.33734i) q^{3} +(0.756852 + 0.150547i) q^{5} +(1.69148 - 4.08359i) q^{7} +(1.06935 + 2.58163i) q^{9} +(-0.290161 - 0.434257i) q^{11} +(-1.79553 + 0.357153i) q^{13} +(1.31348 + 1.31348i) q^{15} +(-3.04259 + 3.04259i) q^{17} +(1.26776 + 6.37347i) q^{19} +(8.84657 - 5.91109i) q^{21} +(-7.32197 + 3.03286i) q^{23} +(-4.06924 - 1.68553i) q^{25} +(0.0965796 - 0.485538i) q^{27} +(-0.690042 + 1.03272i) q^{29} -1.55847i q^{31} -1.25719i q^{33} +(1.89497 - 2.83602i) q^{35} +(0.371584 - 1.86808i) q^{37} +(-4.07133 - 1.68640i) q^{39} +(6.15380 - 2.54899i) q^{41} +(7.03859 - 4.70304i) q^{43} +(0.420680 + 2.11490i) q^{45} +(-1.12515 + 1.12515i) q^{47} +(-8.86483 - 8.86483i) q^{49} +(-10.1586 + 2.02068i) q^{51} +(3.92962 + 5.88109i) q^{53} +(-0.154233 - 0.372351i) q^{55} +(-5.98610 + 14.4517i) q^{57} +(-0.738882 - 0.146973i) q^{59} +(-3.34952 - 2.23808i) q^{61} +12.3511 q^{63} -1.41272 q^{65} +(-3.05271 - 2.03976i) q^{67} +(-18.7106 - 3.72178i) q^{69} +(0.317495 - 0.766500i) q^{71} +(0.292843 + 0.706986i) q^{73} +(-5.89032 - 8.81548i) q^{75} +(-2.26413 + 0.450363i) q^{77} +(-6.17863 - 6.17863i) q^{79} +(6.77032 - 6.77032i) q^{81} +(0.663054 + 3.33340i) q^{83} +(-2.76085 + 1.84474i) q^{85} +(-2.76219 + 1.14414i) q^{87} +(12.3740 + 5.12547i) q^{89} +(-1.57863 + 7.93632i) q^{91} +(2.08420 - 3.11923i) q^{93} +5.01463i q^{95} -3.44120i q^{97} +(0.810809 - 1.21346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$1$

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
$3$	2.00147	+	1.33734i	1.15555	+	0.772112i	0.977297	−	0.211873i	$-0.0679563\pi$
$3$	2.00147	+	1.33734i	1.15555	+	0.772112i	0.178250	+	0.983985i	$0.442956\pi$
$4$		0			0
$5$	0.756852	+	0.150547i	0.338474	+	0.0673268i	0.361401	−	0.932410i	$-0.382298\pi$
$5$	0.756852	+	0.150547i	0.338474	+	0.0673268i	−0.0229268	+	0.999737i	$0.507298\pi$
$6$		0			0
$7$	1.69148	−	4.08359i	0.639318	−	1.54345i	−0.188272	−	0.982117i	$-0.560289\pi$
$7$	1.69148	−	4.08359i	0.639318	−	1.54345i	0.827590	−	0.561333i	$-0.189711\pi$
$8$		0			0
$9$	1.06935	+	2.58163i	0.356449	+	0.860545i
$10$		0			0
$11$	−0.290161	−	0.434257i	−0.0874869	−	0.130933i	0.785145	−	0.619312i	$-0.212588\pi$
$11$	−0.290161	−	0.434257i	−0.0874869	−	0.130933i	−0.872632	+	0.488379i	$0.837588\pi$
$12$		0			0
$13$	−1.79553	+	0.357153i	−0.497991	+	0.0990565i	−0.437694	−	0.899124i	$-0.644205\pi$
$13$	−1.79553	+	0.357153i	−0.497991	+	0.0990565i	−0.0602967	+	0.998180i	$0.519205\pi$
$14$		0			0
$15$	1.31348	+	1.31348i	0.339140	+	0.339140i
$16$		0			0
$17$	−3.04259	+	3.04259i	−0.737937	+	0.737937i	−0.972179	−	0.234241i	$-0.924739\pi$
$17$	−3.04259	+	3.04259i	−0.737937	+	0.737937i	0.234241	+	0.972179i	$0.424739\pi$
$18$		0			0
$19$	1.26776	+	6.37347i	0.290845	+	1.46217i	0.799220	+	0.601039i	$0.205246\pi$
$19$	1.26776	+	6.37347i	0.290845	+	1.46217i	−0.508375	+	0.861136i	$0.669754\pi$
$20$		0			0
$21$	8.84657	−	5.91109i	1.93048	−	1.28990i
$22$		0			0
$23$	−7.32197	+	3.03286i	−1.52674	+	0.632395i	−0.978928	−	0.204208i	$-0.934538\pi$
$23$	−7.32197	+	3.03286i	−1.52674	+	0.632395i	−0.547810	+	0.836603i	$0.684538\pi$
$24$		0			0
$25$	−4.06924	−	1.68553i	−0.813847	−	0.337107i
$26$		0			0
$27$	0.0965796	−	0.485538i	0.0185867	−	0.0934419i
$28$		0			0
$29$	−0.690042	+	1.03272i	−0.128138	+	0.191771i	−0.889991	−	0.455978i	$-0.849290\pi$
$29$	−0.690042	+	1.03272i	−0.128138	+	0.191771i	0.761854	+	0.647749i	$0.224290\pi$
$30$		0			0
$31$		−	1.55847i		−	0.279910i	−0.990158	−	0.139955i	$-0.955304\pi$
$31$		−	1.55847i		−	0.279910i	0.990158	−	0.139955i	$-0.0446957\pi$
$32$		0			0
$33$		−	1.25719i		−	0.218849i
$34$		0			0
$35$	1.89497	−	2.83602i	0.320308	−	0.479375i
$36$		0			0
$37$	0.371584	−	1.86808i	0.0610880	−	0.307110i	−0.938146	−	0.346239i	$-0.887458\pi$
$37$	0.371584	−	1.86808i	0.0610880	−	0.307110i	0.999234	+	0.0391295i	$0.0124585\pi$
$38$		0			0
$39$	−4.07133	−	1.68640i	−0.651935	−	0.270040i
$40$		0			0
$41$	6.15380	−	2.54899i	0.961062	−	0.398085i	0.153685	−	0.988120i	$-0.450886\pi$
$41$	6.15380	−	2.54899i	0.961062	−	0.398085i	0.807378	+	0.590035i	$0.200886\pi$
$42$		0			0
$43$	7.03859	−	4.70304i	1.07338	−	0.717206i	0.112350	−	0.993669i	$-0.464162\pi$
$43$	7.03859	−	4.70304i	1.07338	−	0.717206i	0.961025	+	0.276462i	$0.0891621\pi$
$44$		0			0
$45$	0.420680	+	2.11490i	0.0627113	+	0.315271i
$46$		0			0
$47$	−1.12515	+	1.12515i	−0.164120	+	0.164120i	−0.784389	−	0.620269i	$-0.787023\pi$
$47$	−1.12515	+	1.12515i	−0.164120	+	0.164120i	0.620269	+	0.784389i	$0.287023\pi$
$48$		0			0
$49$	−8.86483	−	8.86483i	−1.26640	−	1.26640i
$50$		0			0
$51$	−10.1586	+	2.02068i	−1.42249	+	0.282951i
$52$		0			0
$53$	3.92962	+	5.88109i	0.539775	+	0.807830i	0.996657	−	0.0816971i	$-0.0260340\pi$
$53$	3.92962	+	5.88109i	0.539775	+	0.807830i	−0.456882	+	0.889527i	$0.651034\pi$
$54$		0			0
$55$	−0.154233	−	0.372351i	−0.0207968	−	0.0502078i
$56$		0			0
$57$	−5.98610	+	14.4517i	−0.792878	+	1.91418i
$58$		0			0
$59$	−0.738882	−	0.146973i	−0.0961942	−	0.0191342i	0.146758	−	0.989172i	$-0.453116\pi$
$59$	−0.738882	−	0.146973i	−0.0961942	−	0.0191342i	−0.242953	+	0.970038i	$0.578116\pi$
$60$		0			0
$61$	−3.34952	−	2.23808i	−0.428862	−	0.286556i	0.322346	−	0.946622i	$-0.395529\pi$
$61$	−3.34952	−	2.23808i	−0.428862	−	0.286556i	−0.751208	+	0.660065i	$0.770529\pi$
$62$		0			0
$63$	12.3511			1.55609
$64$		0			0
$65$	−1.41272			−0.175226
$66$		0			0
$67$	−3.05271	−	2.03976i	−0.372948	−	0.249196i	0.354944	−	0.934888i	$-0.384500\pi$
$67$	−3.05271	−	2.03976i	−0.372948	−	0.249196i	−0.727892	+	0.685692i	$0.759500\pi$
$68$		0			0
$69$	−18.7106	−	3.72178i	−2.25250	−	0.448050i
$70$		0			0
$71$	0.317495	−	0.766500i	0.0376797	−	0.0909668i	−0.903919	−	0.427703i	$-0.859323\pi$
$71$	0.317495	−	0.766500i	0.0376797	−	0.0909668i	0.941599	+	0.336736i	$0.109323\pi$
$72$		0			0
$73$	0.292843	+	0.706986i	0.0342747	+	0.0827464i	0.940090	−	0.340926i	$-0.110741\pi$
$73$	0.292843	+	0.706986i	0.0342747	+	0.0827464i	−0.905815	+	0.423673i	$0.860741\pi$
$74$		0			0
$75$	−5.89032	−	8.81548i	−0.680155	−	1.01792i
$76$		0			0
$77$	−2.26413	+	0.450363i	−0.258021	+	0.0513236i
$78$		0			0
$79$	−6.17863	−	6.17863i	−0.695150	−	0.695150i	0.268210	−	0.963360i	$-0.413568\pi$
$79$	−6.17863	−	6.17863i	−0.695150	−	0.695150i	−0.963360	+	0.268210i	$0.913568\pi$
$80$		0			0
$81$	6.77032	−	6.77032i	0.752258	−	0.752258i
$82$		0			0
$83$	0.663054	+	3.33340i	0.0727796	+	0.365888i	0.999962	−	0.00872251i	$-0.00277650\pi$
$83$	0.663054	+	3.33340i	0.0727796	+	0.365888i	−0.927182	+	0.374610i	$0.877776\pi$
$84$		0			0
$85$	−2.76085	+	1.84474i	−0.299456	+	0.200090i
$86$		0			0
$87$	−2.76219	+	1.14414i	−0.296138	+	0.122664i
$88$		0			0
$89$	12.3740	+	5.12547i	1.31164	+	0.543299i	0.925362	−	0.379084i	$-0.123761\pi$
$89$	12.3740	+	5.12547i	1.31164	+	0.543299i	0.386277	+	0.922383i	$0.373761\pi$
$90$		0			0
$91$	−1.57863	+	7.93632i	−0.165486	+	0.831953i
$92$		0			0
$93$	2.08420	−	3.11923i	0.216122	−	0.323449i
$94$		0			0
$95$			5.01463i			0.514490i
$96$		0			0
$97$		−	3.44120i		−	0.349401i	−0.984622	−	0.174700i	$-0.944104\pi$
$97$		−	3.44120i		−	0.349401i	0.984622	−	0.174700i	$-0.0558956\pi$
$98$		0			0
$99$	0.810809	−	1.21346i	0.0814894	−	0.121958i
$100$		0			0
$101$	−0.978121	+	4.91735i	−0.0973267	+	0.489294i	0.901120	+	0.433571i	$0.142747\pi$
$101$	−0.978121	+	4.91735i	−0.0973267	+	0.489294i	−0.998446	+	0.0557237i	$0.982253\pi$
$102$		0			0
$103$	1.88632	+	0.781338i	0.185864	+	0.0769875i	0.473675	−	0.880700i	$-0.342927\pi$
$103$	1.88632	+	0.781338i	0.185864	+	0.0769875i	−0.287810	+	0.957687i	$0.592927\pi$
$104$		0			0
$105$	7.58544	−	3.14199i	0.740263	−	0.306627i
$106$		0			0
$107$	−3.54710	+	2.37010i	−0.342911	+	0.229126i	−0.715086	−	0.699037i	$-0.753612\pi$
$107$	−3.54710	+	2.37010i	−0.342911	+	0.229126i	0.372174	+	0.928163i	$0.378612\pi$
$108$		0			0
$109$	2.58869	+	13.0142i	0.247952	+	1.24654i	0.881258	+	0.472636i	$0.156697\pi$
$109$	2.58869	+	13.0142i	0.247952	+	1.24654i	−0.633306	+	0.773901i	$0.718303\pi$
$110$		0			0
$111$	3.24196	−	3.24196i	0.307713	−	0.307713i
$112$		0			0
$113$	−0.380557	−	0.380557i	−0.0357998	−	0.0357998i	0.688980	−	0.724780i	$-0.258059\pi$
$113$	−0.380557	−	0.380557i	−0.0357998	−	0.0357998i	−0.724780	+	0.688980i	$0.758059\pi$
$114$		0			0
$115$	−5.99824	+	1.19312i	−0.559339	+	0.111259i
$116$		0			0
$117$	−2.84209	−	4.25348i	−0.262751	−	0.393235i
$118$		0			0
$119$	7.27821	+	17.5712i	0.667193	+	1.61075i
$120$		0			0
$121$	4.10513	−	9.91067i	0.373194	−	0.900970i
$122$		0			0
$123$	15.7255	+	3.12799i	1.41792	+	0.282042i
$124$		0			0
$125$	−6.03420	−	4.03192i	−0.539715	−	0.360626i
$126$		0			0
$127$	10.5330			0.934651			0.467325	−	0.884085i	$-0.345218\pi$
$127$	10.5330			0.934651			0.467325	+	0.884085i	$0.345218\pi$
$128$		0			0
$129$	20.3771			1.79410
$130$		0			0
$131$	13.0608	+	8.72693i	1.14112	+	0.762475i	0.974686	−	0.223577i	$-0.0717733\pi$
$131$	13.0608	+	8.72693i	1.14112	+	0.762475i	0.166438	+	0.986052i	$0.446773\pi$
$132$		0			0
$133$	28.1710	+	5.60356i	2.44274	+	0.485890i
$134$		0			0
$135$	0.146193	−	0.352941i	0.0125823	−	0.0303763i
$136$		0			0
$137$	−5.91955	−	14.2911i	−0.505742	−	1.22097i	−0.946313	−	0.323251i	$-0.895224\pi$
$137$	−5.91955	−	14.2911i	−0.505742	−	1.22097i	0.440572	−	0.897717i	$-0.354776\pi$
$138$		0			0
$139$	−7.35516	−	11.0078i	−0.623856	−	0.933667i	−0.999975	−	0.00709534i	$-0.997741\pi$
$139$	−7.35516	−	11.0078i	−0.623856	−	0.933667i	0.376119	−	0.926572i	$-0.377259\pi$
$140$		0			0
$141$	−3.75665	+	0.747245i	−0.316367	+	0.0629294i
$142$		0			0
$143$	0.676090	+	0.676090i	0.0565375	+	0.0565375i
$144$		0			0
$145$	−0.677733	+	0.677733i	−0.0562826	+	0.0562826i
$146$		0			0
$147$	−5.88739	−	29.5979i	−0.485584	−	2.44120i
$148$		0			0
$149$	−4.87958	+	3.26043i	−0.399751	+	0.267105i	−0.739155	−	0.673536i	$-0.764775\pi$
$149$	−4.87958	+	3.26043i	−0.399751	+	0.267105i	0.339404	+	0.940641i	$0.389775\pi$
$150$		0			0
$151$	10.8095	−	4.47745i	0.879666	−	0.364369i	0.103298	−	0.994650i	$-0.467060\pi$
$151$	10.8095	−	4.47745i	0.879666	−	0.364369i	0.776367	+	0.630281i	$0.217060\pi$
$152$		0			0
$153$	−11.1085	−	4.60127i	−0.898065	−	0.371991i
$154$		0			0
$155$	0.234623	−	1.17953i	0.0188454	−	0.0947423i
$156$		0			0
$157$	8.18769	−	12.2537i	0.653449	−	0.977955i	−0.345766	−	0.938321i	$-0.612381\pi$
$157$	8.18769	−	12.2537i	0.653449	−	0.977955i	0.999214	−	0.0396342i	$-0.0126193\pi$
$158$		0			0
$159$			17.0260i			1.35025i
$160$		0			0
$161$			35.0299i			2.76074i
$162$		0			0
$163$	2.55092	−	3.81772i	0.199803	−	0.299027i	−0.718015	−	0.696028i	$-0.754949\pi$
$163$	2.55092	−	3.81772i	0.199803	−	0.299027i	0.917818	+	0.397001i	$0.129949\pi$
$164$		0			0
$165$	0.189267	−	0.951510i	0.0147344	−	0.0740749i
$166$		0			0
$167$	6.64505	+	2.75247i	0.514209	+	0.212992i	0.624671	−	0.780888i	$-0.285233\pi$
$167$	6.64505	+	2.75247i	0.514209	+	0.212992i	−0.110462	+	0.993880i	$0.535233\pi$
$168$		0			0
$169$	−8.91406	+	3.69232i	−0.685697	+	0.284025i
$170$		0			0
$171$	−15.0983	+	10.0884i	−1.15460	+	0.771476i
$172$		0			0
$173$	3.19519	+	16.0633i	0.242926	+	1.22127i	0.888968	+	0.457970i	$0.151423\pi$
$173$	3.19519	+	16.0633i	0.242926	+	1.22127i	−0.646042	+	0.763302i	$0.723577\pi$
$174$		0			0
$175$	−13.7660	+	13.7660i	−1.04061	+	1.04061i
$176$		0			0
$177$	−1.28230	−	1.28230i	−0.0963832	−	0.0963832i
$178$		0			0
$179$	9.80775	−	1.95088i	0.733066	−	0.145816i	0.185578	−	0.982630i	$-0.440584\pi$
$179$	9.80775	−	1.95088i	0.733066	−	0.145816i	0.547488	+	0.836814i	$0.315584\pi$
$180$		0			0
$181$	2.78837	+	4.17310i	0.207258	+	0.310184i	0.920506	−	0.390728i	$-0.127777\pi$
$181$	2.78837	+	4.17310i	0.207258	+	0.310184i	−0.713248	+	0.700912i	$0.752777\pi$
$182$		0			0
$183$	−3.71089	−	8.95888i	−0.274317	−	0.662259i
$184$		0			0
$185$	0.562468	−	1.35792i	0.0413534	−	0.0998360i
$186$		0			0
$187$	2.20411	+	0.438425i	0.161180	+	0.0320608i
$188$		0			0
$189$	−1.81937	−	1.21567i	−0.132340	−	0.0884268i
$190$		0			0
$191$	−20.5971			−1.49035			−0.745176	−	0.666868i	$-0.767634\pi$
$191$	−20.5971			−1.49035			−0.745176	+	0.666868i	$0.767634\pi$
$192$		0			0
$193$	−15.8384			−1.14008			−0.570038	−	0.821618i	$-0.693072\pi$
$193$	−15.8384			−1.14008			−0.570038	+	0.821618i	$0.693072\pi$
$194$		0			0
$195$	−2.82751	−	1.88928i	−0.202482	−	0.135294i
$196$		0			0
$197$	−25.5976	−	5.09169i	−1.82376	−	0.362768i	−0.840044	−	0.542518i	$-0.817471\pi$
$197$	−25.5976	−	5.09169i	−1.82376	−	0.362768i	−0.983712	+	0.179750i	$0.942471\pi$
$198$		0			0
$199$	5.61103	−	13.5462i	0.397756	−	0.960267i	−0.590442	−	0.807080i	$-0.701046\pi$
$199$	5.61103	−	13.5462i	0.397756	−	0.960267i	0.988197	−	0.153187i	$-0.0489536\pi$
$200$		0			0
$201$	−3.38206	−	8.16501i	−0.238552	−	0.575916i
$202$		0			0
$203$	3.05001	+	4.56467i	0.214069	+	0.320377i
$204$		0			0
$205$	5.04126	−	1.00277i	0.352097	−	0.0700364i
$206$		0			0
$207$	−15.6595	−	15.6595i	−1.08841	−	1.08841i
$208$		0			0
$209$	2.39987	−	2.39987i	0.166002	−	0.166002i
$210$		0			0
$211$	3.71581	+	18.6806i	0.255807	+	1.28603i	0.868493	+	0.495701i	$0.165089\pi$
$211$	3.71581	+	18.6806i	0.255807	+	1.28603i	−0.612686	+	0.790326i	$0.709911\pi$
$212$		0			0
$213$	1.66052	−	1.10953i	0.113777	−	0.0760235i
$214$		0			0
$215$	6.03520	−	2.49986i	0.411597	−	0.170489i
$216$		0			0
$217$	−6.36415	−	2.63612i	−0.432027	−	0.178951i
$218$		0			0
$219$	−0.359363	+	1.80664i	−0.0242835	+	0.122081i
$220$		0			0
$221$	4.37640	−	6.54974i	0.294388	−	0.440583i
$222$		0			0
$223$		−	9.71045i		−	0.650260i	−0.945669	−	0.325130i	$-0.894592\pi$
$223$		−	9.71045i		−	0.650260i	0.945669	−	0.325130i	$-0.105408\pi$
$224$		0			0
$225$		−	12.3077i		−	0.820514i
$226$		0			0
$227$	−2.12248	+	3.17651i	−0.140874	+	0.210833i	−0.895197	−	0.445671i	$-0.852965\pi$
$227$	−2.12248	+	3.17651i	−0.140874	+	0.210833i	0.754323	+	0.656503i	$0.227965\pi$
$228$		0			0
$229$	−1.76419	+	8.86919i	−0.116581	+	0.586093i	0.877692	+	0.479225i	$0.159082\pi$
$229$	−1.76419	+	8.86919i	−0.116581	+	0.586093i	−0.994273	+	0.106868i	$0.965918\pi$
$230$		0			0
$231$	−5.13386	−	2.12651i	−0.337783	−	0.139914i
$232$		0			0
$233$	−2.54691	+	1.05496i	−0.166854	+	0.0691130i	−0.464547	−	0.885549i	$-0.653783\pi$
$233$	−2.54691	+	1.05496i	−0.166854	+	0.0691130i	0.297693	+	0.954662i	$0.403783\pi$
$234$		0			0
$235$	−1.02096	+	0.682183i	−0.0666000	+	0.0445007i
$236$		0			0
$237$	−4.10341	−	20.6292i	−0.266545	−	1.34001i
$238$		0			0
$239$	8.73109	−	8.73109i	0.564767	−	0.564767i	−0.365891	−	0.930658i	$-0.619236\pi$
$239$	8.73109	−	8.73109i	0.564767	−	0.564767i	0.930658	+	0.365891i	$0.119236\pi$
$240$		0			0
$241$	16.1373	+	16.1373i	1.03949	+	1.03949i	0.999187	+	0.0403070i	$0.0128336\pi$
$241$	16.1373	+	16.1373i	1.03949	+	1.03949i	0.0403070	+	0.999187i	$0.487166\pi$
$242$		0			0
$243$	21.1482	−	4.20663i	1.35666	−	0.269856i
$244$		0			0
$245$	−5.37479	−	8.04394i	−0.343383	−	0.513908i
$246$		0			0
$247$	−4.55261	−	10.9910i	−0.289676	−	0.699339i
$248$		0			0
$249$	−3.13080	+	7.55841i	−0.198406	+	0.478995i
$250$		0			0
$251$	−23.2770	−	4.63008i	−1.46923	−	0.292248i	−0.605355	−	0.795956i	$-0.706969\pi$
$251$	−23.2770	−	4.63008i	−1.46923	−	0.292248i	−0.863874	+	0.503708i	$0.831969\pi$
$252$		0			0
$253$	3.44159	+	2.29960i	0.216371	+	0.144575i
$254$		0			0
$255$	−7.99278			−0.500527
$256$		0			0
$257$	0.938259			0.0585270			0.0292635	−	0.999572i	$-0.490684\pi$
$257$	0.938259			0.0585270			0.0292635	+	0.999572i	$0.490684\pi$
$258$		0			0
$259$	−6.99993	−	4.67720i	−0.434954	−	0.290627i
$260$		0			0
$261$	−3.40400	−	0.677098i	−0.210702	−	0.0419113i
$262$		0			0
$263$	−4.19405	+	10.1253i	−0.258616	+	0.624354i	−0.998847	−	0.0479979i	$-0.984716\pi$
$263$	−4.19405	+	10.1253i	−0.258616	+	0.624354i	0.740231	+	0.672352i	$0.234716\pi$
$264$		0			0
$265$	2.08876	+	5.04271i	0.128311	+	0.309771i
$266$		0			0
$267$	17.9116	+	26.8066i	1.09617	+	1.64054i
$268$		0			0
$269$	23.0601	−	4.58694i	1.40600	−	0.279671i	0.566963	−	0.823744i	$-0.308118\pi$
$269$	23.0601	−	4.58694i	1.40600	−	0.279671i	0.839038	+	0.544073i	$0.183118\pi$
$270$		0			0
$271$	2.19673	+	2.19673i	0.133442	+	0.133442i	0.770673	−	0.637231i	$-0.219920\pi$
$271$	2.19673	+	2.19673i	0.133442	+	0.133442i	−0.637231	+	0.770673i	$0.719920\pi$
$272$		0			0
$273$	−13.7731	+	13.7731i	−0.833587	+	0.833587i
$274$		0			0
$275$	0.448780	+	2.25617i	0.0270625	+	0.136052i
$276$		0			0
$277$	−7.16558	+	4.78789i	−0.430538	+	0.287676i	−0.751896	−	0.659281i	$-0.770861\pi$
$277$	−7.16558	+	4.78789i	−0.430538	+	0.287676i	0.321358	+	0.946958i	$0.395861\pi$
$278$		0			0
$279$	4.02340	−	1.66655i	0.240875	−	0.0997736i
$280$		0			0
$281$	2.11464	+	0.875914i	0.126149	+	0.0522527i	0.444865	−	0.895598i	$-0.353252\pi$
$281$	2.11464	+	0.875914i	0.126149	+	0.0522527i	−0.318716	+	0.947850i	$0.603252\pi$
$282$		0			0
$283$	−4.65354	+	23.3949i	−0.276624	+	1.39068i	0.553381	+	0.832928i	$0.313337\pi$
$283$	−4.65354	+	23.3949i	−0.276624	+	1.39068i	−0.830005	+	0.557755i	$0.811663\pi$
$284$		0			0
$285$	−6.70626	+	10.0366i	−0.397244	+	0.594518i
$286$		0			0
$287$		−	29.4411i		−	1.73785i
$288$		0			0
$289$		−	1.51475i		−	0.0891029i
$290$		0			0
$291$	4.60204	−	6.88744i	0.269776	−	0.403749i
$292$		0			0
$293$	5.30837	−	26.6870i	0.310118	−	1.55907i	−0.440142	−	0.897928i	$-0.645072\pi$
$293$	5.30837	−	26.6870i	0.310118	−	1.55907i	0.750260	−	0.661143i	$-0.229928\pi$
$294$		0			0
$295$	−0.537098	−	0.222473i	−0.0312710	−	0.0129529i
$296$		0			0
$297$	−0.238872	+	0.0989440i	−0.0138608	+	0.00574131i
$298$		0			0
$299$	12.0636	−	8.06067i	0.697658	−	0.466160i
$300$		0			0
$301$	−7.29964	−	36.6978i	−0.420744	−	2.11522i
$302$		0			0
$303$	−8.53383	+	8.53383i	−0.490256	+	0.490256i
$304$		0			0
$305$	−2.19815	−	2.19815i	−0.125866	−	0.125866i
$306$		0			0
$307$	−32.1099	+	6.38706i	−1.83261	+	0.364529i	−0.985874	−	0.167486i	$-0.946435\pi$
$307$	−32.1099	+	6.38706i	−1.83261	+	0.364529i	−0.846735	+	0.532015i	$0.821435\pi$
$308$		0			0
$309$	2.73049	+	4.08646i	0.155332	+	0.232471i
$310$		0			0
$311$	4.28733	+	10.3505i	0.243112	+	0.586924i	0.997589	−	0.0694024i	$-0.0221092\pi$
$311$	4.28733	+	10.3505i	0.243112	+	0.586924i	−0.754477	+	0.656327i	$0.772109\pi$
$312$		0			0
$313$	3.78250	−	9.13175i	0.213799	−	0.516157i	−0.780202	−	0.625528i	$-0.784884\pi$
$313$	3.78250	−	9.13175i	0.213799	−	0.516157i	0.994001	+	0.109371i	$0.0348836\pi$
$314$		0			0
$315$	9.34796	+	1.85942i	0.526698	+	0.104767i
$316$		0			0
$317$	14.8080	+	9.89442i	0.831703	+	0.555726i	0.896944	−	0.442143i	$-0.145782\pi$
$317$	14.8080	+	9.89442i	0.831703	+	0.555726i	−0.0652416	+	0.997869i	$0.520782\pi$
$318$		0			0
$319$	0.648689			0.0363196
$320$		0			0
$321$	−10.2690			−0.573161
$322$		0			0
$323$	−23.2492	−	15.5346i	−1.29362	−	0.864368i
$324$		0			0
$325$	7.90844	+	1.57309i	0.438681	+	0.0872591i
$326$		0			0
$327$	−12.2232	+	29.5095i	−0.675946	+	1.63188i
$328$		0			0
$329$	2.69148	+	6.49781i	0.148386	+	0.358236i
$330$		0			0
$331$	9.69258	+	14.5060i	0.532752	+	0.797320i	0.996042	−	0.0888869i	$-0.0283310\pi$
$331$	9.69258	+	14.5060i	0.532752	+	0.797320i	−0.463289	+	0.886207i	$0.653331\pi$
$332$		0			0
$333$	5.22004	−	1.03833i	0.286057	−	0.0569002i
$334$		0			0
$335$	−2.00337	−	2.00337i	−0.109456	−	0.109456i
$336$		0			0
$337$	8.62689	−	8.62689i	0.469937	−	0.469937i	−0.431957	−	0.901894i	$-0.642177\pi$
$337$	8.62689	−	8.62689i	0.469937	−	0.469937i	0.901894	+	0.431957i	$0.142177\pi$
$338$		0			0
$339$	−0.252739	−	1.27061i	−0.0137269	−	0.0690099i
$340$		0			0
$341$	−0.676777	+	0.452208i	−0.0366495	+	0.0244884i
$342$		0			0
$343$	−22.6098	+	9.36530i	−1.22082	+	0.505679i
$344$		0			0
$345$	−13.6009	−	5.63367i	−0.732247	−	0.303307i
$346$		0			0
$347$	2.46321	−	12.3834i	0.132232	−	0.664776i	−0.856629	−	0.515933i	$-0.827445\pi$
$347$	2.46321	−	12.3834i	0.132232	−	0.664776i	0.988861	−	0.148843i	$-0.0475548\pi$
$348$		0			0
$349$	−9.48101	+	14.1893i	−0.507507	+	0.759538i	−0.993427	−	0.114465i	$-0.963485\pi$
$349$	−9.48101	+	14.1893i	−0.507507	+	0.759538i	0.485920	+	0.874003i	$0.338485\pi$
$350$		0			0
$351$			0.906293i			0.0483743i
$352$		0			0
$353$		−	23.9464i		−	1.27454i	−0.770641	−	0.637270i	$-0.780064\pi$
$353$		−	23.9464i		−	1.27454i	0.770641	−	0.637270i	$-0.219936\pi$
$354$		0			0
$355$	0.355691	−	0.532329i	0.0188781	−	0.0282531i
$356$		0			0
$357$	−8.93147	+	44.9015i	−0.472704	+	2.37644i
$358$		0			0
$359$	23.0491	+	9.54726i	1.21649	+	0.503885i	0.896291	−	0.443467i	$-0.146252\pi$
$359$	23.0491	+	9.54726i	1.21649	+	0.503885i	0.320195	+	0.947352i	$0.396252\pi$
$360$		0			0
$361$	−21.4602	+	8.88911i	−1.12948	+	0.467848i
$362$		0			0
$363$	21.4702	−	14.3459i	1.12689	−	0.752966i
$364$		0			0
$365$	0.115204	+	0.579170i	0.00603006	+	0.0303152i
$366$		0			0
$367$	23.6652	−	23.6652i	1.23532	−	1.23532i	0.273421	−	0.961894i	$-0.411845\pi$
$367$	23.6652	−	23.6652i	1.23532	−	1.23532i	0.961894	−	0.273421i	$-0.0881553\pi$
$368$		0			0
$369$	13.1611	+	13.1611i	0.685140	+	0.685140i
$370$		0			0
$371$	30.6628	−	6.09921i	1.59193	−	0.316655i
$372$		0			0
$373$	10.0109	+	14.9823i	0.518343	+	0.775755i	0.994626	−	0.103537i	$-0.0330160\pi$
$373$	10.0109	+	14.9823i	0.518343	+	0.775755i	−0.476283	+	0.879292i	$0.658016\pi$
$374$		0			0
$375$	−6.68521	−	16.1395i	−0.345223	−	0.833441i
$376$		0			0
$377$	0.870152	−	2.10073i	0.0448151	−	0.108193i
$378$		0			0
$379$	0.376618	+	0.0749139i	0.0193455	+	0.00384807i	0.204754	−	0.978814i	$-0.434361\pi$
$379$	0.376618	+	0.0749139i	0.0193455	+	0.00384807i	−0.185408	+	0.982662i	$0.559361\pi$
$380$		0			0
$381$	21.0814	+	14.0861i	1.08003	+	0.721655i
$382$		0			0
$383$	−17.7262			−0.905768			−0.452884	−	0.891569i	$-0.649605\pi$
$383$	−17.7262			−0.905768			−0.452884	+	0.891569i	$0.649605\pi$
$384$		0			0
$385$	−1.78141			−0.0907890
$386$		0			0
$387$	19.6682	+	13.1419i	0.999792	+	0.668040i
$388$		0			0
$389$	7.58645	+	1.50904i	0.384648	+	0.0765113i	0.383627	−	0.923488i	$-0.374675\pi$
$389$	7.58645	+	1.50904i	0.384648	+	0.0765113i	0.00102139	+	0.999999i	$0.499675\pi$
$390$		0			0
$391$	13.0500	−	31.5056i	0.659968	−	1.59330i
$392$		0			0
$393$	14.4699	+	34.9333i	0.729907	+	1.76215i
$394$		0			0
$395$	−3.74613	−	5.60649i	−0.188488	−	0.282093i
$396$		0			0
$397$	−8.20788	+	1.63265i	−0.411942	+	0.0819403i	−0.396711	−	0.917944i	$-0.629848\pi$
$397$	−8.20788	+	1.63265i	−0.411942	+	0.0819403i	−0.0152310	+	0.999884i	$0.504848\pi$
$398$		0			0
$399$	48.8895	+	48.8895i	2.44754	+	2.44754i
$400$		0			0
$401$	−18.5993	+	18.5993i	−0.928802	+	0.928802i	−0.997629	−	0.0688263i	$-0.978075\pi$
$401$	−18.5993	+	18.5993i	−0.928802	+	0.928802i	0.0688263	+	0.997629i	$0.478075\pi$
$402$		0			0
$403$	0.556613	+	2.79828i	0.0277269	+	0.139392i
$404$		0			0
$405$	6.14338	−	4.10488i	0.305267	−	0.203973i
$406$		0			0
$407$	−0.919044	+	0.380681i	−0.0455553	+	0.0188696i
$408$		0			0
$409$	23.4672	+	9.72045i	1.16038	+	0.480645i	0.878001	−	0.478658i	$-0.158877\pi$
$409$	23.4672	+	9.72045i	1.16038	+	0.480645i	0.282378	+	0.959303i	$0.408877\pi$
$410$		0			0
$411$	7.26419	−	36.5195i	0.358316	−	1.80138i
$412$		0			0
$413$	−1.84998	+	2.76869i	−0.0910314	+	0.136238i
$414$		0			0
$415$			2.62271i			0.128744i
$416$		0			0
$417$		−	31.8680i		−	1.56058i
$418$		0			0
$419$	7.06866	−	10.5790i	0.345326	−	0.516818i	−0.617632	−	0.786467i	$-0.711908\pi$
$419$	7.06866	−	10.5790i	0.345326	−	0.516818i	0.962959	+	0.269650i	$0.0869079\pi$
$420$		0			0
$421$	5.87200	−	29.5205i	0.286184	−	1.43874i	−0.523575	−	0.851980i	$-0.675402\pi$
$421$	5.87200	−	29.5205i	0.286184	−	1.43874i	0.809758	−	0.586763i	$-0.199598\pi$
$422$		0			0
$423$	−4.10790	−	1.70155i	−0.199733	−	0.0827321i
$424$		0			0
$425$	17.5094	−	7.25264i	0.849332	−	0.351805i
$426$		0			0
$427$	−14.8050	+	9.89240i	−0.716465	+	0.478727i
$428$		0			0
$429$	0.449011	+	2.25733i	0.0216785	+	0.108985i
$430$		0			0
$431$	−6.82858	+	6.82858i	−0.328921	+	0.328921i	−0.852176	−	0.523255i	$-0.824718\pi$
$431$	−6.82858	+	6.82858i	−0.328921	+	0.328921i	0.523255	+	0.852176i	$0.324718\pi$
$432$		0			0
$433$	−4.84377	−	4.84377i	−0.232777	−	0.232777i	0.581074	−	0.813851i	$-0.302633\pi$
$433$	−4.84377	−	4.84377i	−0.232777	−	0.232777i	−0.813851	+	0.581074i	$0.802633\pi$
$434$		0			0
$435$	−2.26282	+	0.450102i	−0.108494	+	0.0215807i
$436$		0			0
$437$	−28.6124	−	42.8214i	−1.36872	−	2.04843i
$438$		0			0
$439$	11.2574	+	27.1777i	0.537286	+	1.29712i	0.926611	+	0.376022i	$0.122708\pi$
$439$	11.2574	+	27.1777i	0.537286	+	1.29712i	−0.389325	+	0.921101i	$0.627292\pi$
$440$		0			0
$441$	13.4062	−	32.3653i	0.638389	−	1.54121i
$442$		0			0
$443$	−31.0716	−	6.18053i	−1.47626	−	0.293646i	−0.609663	−	0.792661i	$-0.708695\pi$
$443$	−31.0716	−	6.18053i	−1.47626	−	0.293646i	−0.866593	+	0.499015i	$0.833695\pi$
$444$		0			0
$445$	8.59364	+	5.74209i	0.407378	+	0.272201i
$446$		0			0
$447$	−14.1266			−0.668166
$448$		0			0
$449$	15.3871			0.726163			0.363082	−	0.931757i	$-0.381725\pi$
$449$	15.3871			0.726163			0.363082	+	0.931757i	$0.381725\pi$
$450$		0			0
$451$	−2.89251	−	1.93271i	−0.136203	−	0.0910079i
$452$		0			0
$453$	27.6227	+	5.49450i	1.29783	+	0.258154i
$454$		0			0
$455$	−2.38958	+	5.76896i	−0.112025	+	0.270453i
$456$		0			0
$457$	3.24557	+	7.83549i	0.151821	+	0.366529i	0.981431	−	0.191814i	$-0.0614372\pi$
$457$	3.24557	+	7.83549i	0.151821	+	0.366529i	−0.829610	+	0.558343i	$0.811437\pi$
$458$		0			0
$459$	1.18344	+	1.77115i	0.0552384	+	0.0826701i
$460$		0			0
$461$	−24.4880	+	4.87097i	−1.14052	+	0.226864i	−0.728985	−	0.684530i	$-0.760007\pi$
$461$	−24.4880	+	4.87097i	−1.14052	+	0.226864i	−0.411536	+	0.911394i	$0.635007\pi$
$462$		0			0
$463$	19.0846	+	19.0846i	0.886939	+	0.886939i	0.994228	−	0.107289i	$-0.0342170\pi$
$463$	19.0846	+	19.0846i	0.886939	+	0.886939i	−0.107289	+	0.994228i	$0.534217\pi$
$464$		0			0
$465$	2.04702	−	2.04702i	0.0949284	−	0.0949284i
$466$		0			0
$467$	−0.264167	−	1.32806i	−0.0122242	−	0.0614552i	0.974192	−	0.225722i	$-0.0724741\pi$
$467$	−0.264167	−	1.32806i	−0.0122242	−	0.0614552i	−0.986416	+	0.164267i	$0.947474\pi$
$468$		0			0
$469$	−13.4931	+	9.01581i	−0.623054	+	0.416311i
$470$		0			0
$471$	32.7748	−	13.5758i	1.51018	−	0.625538i
$472$		0			0
$473$	−4.08465	−	1.69192i	−0.187813	−	0.0777945i
$474$		0			0
$475$	5.58387	−	28.0720i	0.256206	−	1.28803i
$476$		0			0
$477$	−10.9807	+	16.4338i	−0.502772	+	0.752451i
$478$		0			0
$479$		−	3.51984i		−	0.160826i	−0.996762	−	0.0804128i	$-0.974376\pi$
$479$		−	3.51984i		−	0.160826i	0.996762	−	0.0804128i	$-0.0256239\pi$
$480$		0			0
$481$			3.48690i			0.158989i
$482$		0			0
$483$	−46.8468	+	70.1112i	−2.13160	+	3.19017i
$484$		0			0
$485$	0.518062	−	2.60448i	0.0235240	−	0.118263i
$486$		0			0
$487$	−25.4932	−	10.5596i	−1.15521	−	0.478503i	−0.278932	−	0.960311i	$-0.589980\pi$
$487$	−25.4932	−	10.5596i	−1.15521	−	0.478503i	−0.876277	+	0.481808i	$0.839980\pi$
$488$		0			0
$489$	10.2112	−	4.22960i	0.461764	−	0.191269i
$490$		0			0
$491$	−18.5780	+	12.4134i	−0.838412	+	0.560209i	−0.898997	−	0.437954i	$-0.855703\pi$
$491$	−18.5780	+	12.4134i	−0.838412	+	0.560209i	0.0605855	+	0.998163i	$0.480703\pi$
$492$		0			0
$493$	−1.04263	−	5.24166i	−0.0469578	−	0.236073i
$494$		0			0
$495$	0.796346	−	0.796346i	0.0357931	−	0.0357931i
$496$		0			0
$497$	−2.59303	−	2.59303i	−0.116313	−	0.116313i
$498$		0			0
$499$	7.61559	−	1.51483i	0.340921	−	0.0678133i	−0.0216610	−	0.999765i	$-0.506895\pi$
$499$	7.61559	−	1.51483i	0.340921	−	0.0678133i	0.362582	+	0.931952i	$0.381895\pi$
$500$		0			0
$501$	9.61886	+	14.3956i	0.429739	+	0.643150i
$502$		0			0
$503$	−16.2329	−	39.1897i	−0.723789	−	1.74738i	−0.662259	−	0.749275i	$-0.730402\pi$
$503$	−16.2329	−	39.1897i	−0.723789	−	1.74738i	−0.0615295	−	0.998105i	$-0.519598\pi$
$504$		0			0
$505$	−1.48059	+	3.57445i	−0.0658852	+	0.159061i
$506$		0			0
$507$	−22.7791	−	4.53104i	−1.01165	−	0.201231i
$508$		0			0
$509$	−27.0838	−	18.0968i	−1.20047	−	0.802126i	−0.215777	−	0.976443i	$-0.569229\pi$
$509$	−27.0838	−	18.0968i	−1.20047	−	0.802126i	−0.984690	+	0.174316i	$0.944229\pi$
$510$		0			0
$511$	3.38237			0.149627
$512$		0			0
$513$	3.21700			0.142034
$514$		0			0
$515$	1.31003	+	0.875337i	0.0577270	+	0.0385719i
$516$		0			0
$517$	0.815078	+	0.162129i	0.0358471	+	0.00713043i
$518$		0			0
$519$	−15.0870	+	36.4233i	−0.662246	+	1.59880i
$520$		0			0
$521$	−9.90054	−	23.9020i	−0.433750	−	1.04717i	−0.978068	−	0.208287i	$-0.933211\pi$
$521$	−9.90054	−	23.9020i	−0.433750	−	1.04717i	0.544318	−	0.838879i	$-0.316789\pi$
$522$		0			0
$523$	−11.2609	−	16.8531i	−0.492404	−	0.736935i	0.499166	−	0.866507i	$-0.333640\pi$
$523$	−11.2609	−	16.8531i	−0.492404	−	0.736935i	−0.991570	+	0.129571i	$0.958640\pi$
$524$		0			0
$525$	−45.9621	+	9.14243i	−2.00595	+	0.399008i
$526$		0			0
$527$	4.74179	+	4.74179i	0.206556	+	0.206556i
$528$		0			0
$529$	28.1496	−	28.1496i	1.22390	−	1.22390i
$530$		0			0
$531$	−0.410692	−	2.06469i	−0.0178225	−	0.0895998i
$532$		0			0
$533$	−10.1390	+	6.77464i	−0.439167	+	0.293442i
$534$		0			0
$535$	−3.04144	+	1.25981i	−0.131493	+	0.0544662i
$536$		0			0
$537$	22.2389	+	9.21165i	0.959678	+	0.397512i
$538$		0			0
$539$	−1.27738	+	6.42184i	−0.0550208	+	0.276608i
$540$		0			0
$541$	−22.9671	+	34.3728i	−0.987435	+	1.47780i	−0.112445	+	0.993658i	$0.535868\pi$
$541$	−22.9671	+	34.3728i	−0.987435	+	1.47780i	−0.874989	+	0.484142i	$0.839132\pi$
$542$		0			0
$543$			12.0813i			0.518459i
$544$		0			0
$545$			10.2396i			0.438615i
$546$		0			0
$547$	7.05928	−	10.5650i	0.301833	−	0.451725i	−0.649288	−	0.760542i	$-0.724933\pi$
$547$	7.05928	−	10.5650i	0.301833	−	0.451725i	0.951121	+	0.308817i	$0.0999332\pi$
$548$		0			0
$549$	2.19610	−	11.0405i	0.0937271	−	0.471198i
$550$		0			0
$551$	−7.45682	−	3.08872i	−0.317671	−	0.131584i
$552$		0			0
$553$	−35.6820	+	14.7800i	−1.51735	+	0.628508i
$554$		0			0
$555$	2.94175	−	1.96562i	0.124870	−	0.0834358i
$556$		0			0
$557$	3.09194	+	15.5442i	0.131010	+	0.658630i	0.989351	+	0.145551i	$0.0464954\pi$
$557$	3.09194	+	15.5442i	0.131010	+	0.658630i	−0.858341	+	0.513079i	$0.828505\pi$
$558$		0			0
$559$	−10.9583	+	10.9583i	−0.463487	+	0.463487i
$560$		0			0
$561$	3.82513	+	3.82513i	0.161497	+	0.161497i
$562$		0			0
$563$	4.98076	−	0.990736i	0.209914	−	0.0417545i	−0.0890130	−	0.996030i	$-0.528371\pi$
$563$	4.98076	−	0.990736i	0.209914	−	0.0417545i	0.298927	+	0.954276i	$0.403371\pi$
$564$		0			0
$565$	−0.230734	−	0.345317i	−0.00970704	−	0.0145276i
$566$		0			0
$567$	−16.1953	−	39.0990i	−0.680141	−	1.64200i
$568$		0			0
$569$	10.4799	−	25.3007i	0.439340	−	1.06066i	−0.536837	−	0.843686i	$-0.680381\pi$
$569$	10.4799	−	25.3007i	0.439340	−	1.06066i	0.976177	−	0.216975i	$-0.0696189\pi$
$570$		0			0
$571$	26.9468	+	5.36006i	1.12769	+	0.224311i	0.723474	−	0.690352i	$-0.242544\pi$
$571$	26.9468	+	5.36006i	1.12769	+	0.224311i	0.404216	+	0.914664i	$0.367544\pi$
$572$		0			0
$573$	−41.2243	−	27.5452i	−1.72217	−	1.15072i
$574$		0			0
$575$	34.9068			1.45572
$576$		0			0
$577$	−42.3036			−1.76112			−0.880560	−	0.473935i	$-0.842833\pi$
$577$	−42.3036			−1.76112			−0.880560	+	0.473935i	$0.842833\pi$
$578$		0			0
$579$	−31.7001	−	21.1813i	−1.31741	−	0.880267i
$580$		0			0
$581$	14.7337	+	2.93073i	0.611259	+	0.121587i
$582$		0			0
$583$	1.41368	−	3.41293i	0.0585487	−	0.141349i
$584$		0			0
$585$	−1.51069	−	3.64713i	−0.0624593	−	0.150790i
$586$		0			0
$587$	0.763948	+	1.14333i	0.0315315	+	0.0471902i	0.846901	−	0.531751i	$-0.178466\pi$
$587$	0.763948	+	1.14333i	0.0315315	+	0.0471902i	−0.815369	+	0.578942i	$0.803466\pi$
$588$		0			0
$589$	9.93287	−	1.97577i	0.409277	−	0.0814102i
$590$		0			0
$591$	−44.4235	−	44.4235i	−1.82734	−	1.82734i
$592$		0			0
$593$	5.66121	−	5.66121i	0.232478	−	0.232478i	−0.581248	−	0.813726i	$-0.697436\pi$
$593$	5.66121	−	5.66121i	0.232478	−	0.232478i	0.813726	+	0.581248i	$0.197436\pi$
$594$		0			0
$595$	2.86324	+	14.3945i	0.117381	+	0.590116i
$596$		0			0
$597$	29.3462	−	19.6085i	1.20106	−	0.802522i
$598$		0			0
$599$	−12.4047	+	5.13818i	−0.506841	+	0.209941i	−0.621426	−	0.783473i	$-0.713446\pi$
$599$	−12.4047	+	5.13818i	−0.506841	+	0.209941i	0.114585	+	0.993413i	$0.463446\pi$
$600$		0			0
$601$	−6.28652	−	2.60396i	−0.256433	−	0.106218i	0.250764	−	0.968048i	$-0.419318\pi$
$601$	−6.28652	−	2.60396i	−0.256433	−	0.106218i	−0.507197	+	0.861830i	$0.669318\pi$
$602$		0			0
$603$	2.00150	−	10.0622i	0.0815072	−	0.409764i
$604$		0			0
$605$	4.59900	−	6.88289i	0.186976	−	0.279829i
$606$		0			0
$607$			31.2974i			1.27032i	0.772379	+	0.635161i	$0.219066\pi$
$607$			31.2974i			1.27032i	−0.772379	+	0.635161i	$0.780934\pi$
$608$		0			0
$609$			13.2149i			0.535496i
$610$		0			0
$611$	1.61839	−	2.42209i	0.0654730	−	0.0979873i
$612$		0			0
$613$	4.01591	−	20.1894i	0.162201	−	0.815441i	−0.810922	−	0.585155i	$-0.801034\pi$
$613$	4.01591	−	20.1894i	0.162201	−	0.815441i	0.973123	−	0.230286i	$-0.0739662\pi$
$614$		0			0
$615$	11.4310	+	4.73486i	0.460941	+	0.190928i
$616$		0			0
$617$	0.720564	−	0.298468i	0.0290088	−	0.0120159i	−0.368132	−	0.929774i	$-0.620002\pi$
$617$	0.720564	−	0.298468i	0.0290088	−	0.0120159i	0.397141	+	0.917758i	$0.370002\pi$
$618$		0			0
$619$	12.1862	−	8.14255i	0.489804	−	0.327277i	−0.286022	−	0.958223i	$-0.592333\pi$
$619$	12.1862	−	8.14255i	0.489804	−	0.327277i	0.775826	+	0.630946i	$0.217333\pi$
$620$		0			0
$621$	0.765417	+	3.84801i	0.0307151	+	0.154415i
$622$		0			0
$623$	41.8606	−	41.8606i	1.67711	−	1.67711i
$624$		0			0
$625$	11.6123	+	11.6123i	0.464492	+	0.464492i
$626$		0			0
$627$	8.01269	−	1.59382i	0.319996	−	0.0636512i
$628$		0			0
$629$	4.55322	+	6.81438i	0.181549	+	0.271707i
$630$		0			0
$631$	14.7859	+	35.6964i	0.588619	+	1.42105i	0.884823	+	0.465927i	$0.154279\pi$
$631$	14.7859	+	35.6964i	0.588619	+	1.42105i	−0.296204	+	0.955125i	$0.595721\pi$
$632$		0			0
$633$	−17.5452	+	42.3580i	−0.697361	+	1.68358i
$634$		0			0
$635$	7.97191	+	1.58571i	0.316355	+	0.0629270i
$636$		0			0
$637$	19.0832	+	12.7510i	0.756103	+	0.505212i
$638$		0			0
$639$	2.31834			0.0917119
$640$		0			0
$641$	−39.2736			−1.55121			−0.775607	−	0.631216i	$-0.782556\pi$
$641$	−39.2736			−1.55121			−0.775607	+	0.631216i	$0.782556\pi$
$642$		0			0
$643$	20.6027	+	13.7663i	0.812489	+	0.542888i	0.890988	−	0.454026i	$-0.150013\pi$
$643$	20.6027	+	13.7663i	0.812489	+	0.542888i	−0.0784990	+	0.996914i	$0.525013\pi$
$644$		0			0
$645$	15.4224	+	3.06771i	0.607257	+	0.120791i
$646$		0			0
$647$	−15.7086	+	37.9240i	−0.617570	+	1.49095i	0.236948	+	0.971522i	$0.423853\pi$
$647$	−15.7086	+	37.9240i	−0.617570	+	1.49095i	−0.854517	+	0.519423i	$0.826147\pi$
$648$		0			0
$649$	0.150571	+	0.363510i	0.00591042	+	0.0142690i
$650$		0			0
$651$	−9.21225	−	13.7871i	−0.361057	−	0.540360i
$652$		0			0
$653$	45.4088	−	9.03238i	1.77698	−	0.353464i	0.805873	−	0.592089i	$-0.201696\pi$
$653$	45.4088	−	9.03238i	1.77698	−	0.353464i	0.971112	+	0.238624i	$0.0766965\pi$
$654$		0			0
$655$	8.57125	+	8.57125i	0.334907	+	0.334907i
$656$		0			0
$657$	−1.51203	+	1.51203i	−0.0589898	+	0.0589898i
$658$		0			0
$659$	−7.92659	−	39.8497i	−0.308776	−	1.55232i	−0.753983	−	0.656894i	$-0.771870\pi$
$659$	−7.92659	−	39.8497i	−0.308776	−	1.55232i	0.445206	−	0.895428i	$-0.353130\pi$
$660$		0			0
$661$	−29.3540	+	19.6137i	−1.14174	+	0.762886i	−0.974800	−	0.223081i	$-0.928389\pi$
$661$	−29.3540	+	19.6137i	−1.14174	+	0.762886i	−0.166940	+	0.985967i	$0.553389\pi$
$662$		0			0
$663$	17.5184	−	7.25637i	0.680360	−	0.281814i
$664$		0			0
$665$	20.4777	+	8.48213i	0.794090	+	0.328923i
$666$		0			0
$667$	1.92037	−	9.65435i	0.0743570	−	0.373818i
$668$		0			0
$669$	12.9861	−	19.4351i	0.502073	−	0.751406i
$670$		0			0
$671$			2.10396i			0.0812223i
$672$		0			0
$673$		−	24.2851i		−	0.936122i	−0.883696	−	0.468061i	$-0.844953\pi$
$673$		−	24.2851i		−	0.936122i	0.883696	−	0.468061i	$-0.155047\pi$
$674$		0			0
$675$	−1.21140	+	1.81298i	−0.0466266	+	0.0697817i
$676$		0			0
$677$	−4.33107	+	21.7738i	−0.166456	+	0.836833i	0.803827	+	0.594863i	$0.202794\pi$
$677$	−4.33107	+	21.7738i	−0.166456	+	0.836833i	−0.970284	+	0.241970i	$0.922206\pi$
$678$		0			0
$679$	−14.0524	−	5.82070i	−0.539282	−	0.223378i
$680$		0			0
$681$	−8.49614	+	3.51922i	−0.325573	+	0.134857i
$682$		0			0
$683$	12.0613	−	8.05912i	0.461514	−	0.308374i	−0.302989	−	0.952994i	$-0.597985\pi$
$683$	12.0613	−	8.05912i	0.461514	−	0.308374i	0.764503	+	0.644620i	$0.222985\pi$
$684$		0			0
$685$	−2.32875	−	11.7074i	−0.0889768	−	0.447317i
$686$		0			0
$687$	−15.3921	+	15.3921i	−0.587244	+	0.587244i
$688$		0			0
$689$	−9.15621	−	9.15621i	−0.348824	−	0.348824i
$690$		0			0
$691$	−3.89100	+	0.773968i	−0.148021	+	0.0294431i	−0.268544	−	0.963267i	$-0.586543\pi$
$691$	−3.89100	+	0.773968i	−0.148021	+	0.0294431i	0.120524	+	0.992710i	$0.461543\pi$
$692$		0			0
$693$	−3.58381	−	5.36355i	−0.136138	−	0.203744i
$694$		0			0
$695$	−3.90958	−	9.43855i	−0.148299	−	0.358025i
$696$		0			0
$697$	−10.9680	+	26.4791i	−0.415442	+	1.00297i
$698$		0			0
$699$	−6.50840	−	1.29460i	−0.246170	−	0.0489663i
$700$		0			0
$701$	32.0550	+	21.4185i	1.21070	+	0.808965i	0.986208	−	0.165511i	$-0.0529272\pi$
$701$	32.0550	+	21.4185i	1.21070	+	0.808965i	0.224494	+	0.974476i	$0.427927\pi$
$702$		0			0
$703$	12.3772			0.466815
$704$		0			0
$705$	−2.95573			−0.111319
$706$		0			0
$707$	18.4259	+	12.3118i	0.692979	+	0.463034i
$708$		0			0
$709$	14.3830	+	2.86095i	0.540164	+	0.107445i	0.457630	−	0.889143i	$-0.348699\pi$
$709$	14.3830	+	2.86095i	0.540164	+	0.107445i	0.0825345	+	0.996588i	$0.473699\pi$
$710$		0			0
$711$	9.34386	−	22.5581i	0.350422	−	0.845994i
$712$		0			0
$713$	4.72663	+	11.4111i	0.177014	+	0.427348i
$714$		0			0
$715$	0.409916	+	0.613483i	0.0153300	+	0.0229430i
$716$		0			0
$717$	29.1514	−	5.79857i	1.08868	−	0.216552i
$718$		0			0
$719$	−16.4835	−	16.4835i	−0.614730	−	0.614730i	0.329445	−	0.944175i	$-0.393138\pi$
$719$	−16.4835	−	16.4835i	−0.614730	−	0.614730i	−0.944175	+	0.329445i	$0.893138\pi$
$720$		0			0
$721$	6.38132	−	6.38132i	0.237653	−	0.237653i
$722$		0			0
$723$	10.7173	+	53.8793i	0.398579	+	2.00379i
$724$		0			0
$725$	4.54863	−	3.03930i	0.168932	−	0.112877i
$726$		0			0
$727$	1.94412	−	0.805280i	0.0721034	−	0.0298662i	−0.346340	−	0.938109i	$-0.612576\pi$
$727$	1.94412	−	0.805280i	0.0721034	−	0.0298662i	0.418444	+	0.908243i	$0.362576\pi$
$728$		0			0
$729$	21.4155	+	8.87058i	0.793166	+	0.328540i
$730$		0			0
$731$	−7.10614	+	35.7250i	−0.262830	+	1.32134i
$732$		0			0
$733$	0.341596	−	0.511235i	0.0126171	−	0.0188829i	−0.825107	−	0.564976i	$-0.808885\pi$
$733$	0.341596	−	0.511235i	0.0126171	−	0.0188829i	0.837725	+	0.546093i	$0.183885\pi$
$734$		0			0
$735$		−	23.2876i		−	0.858975i
$736$		0			0
$737$			1.91752i			0.0706327i
$738$		0			0
$739$	−5.04853	+	7.55566i	−0.185713	+	0.277939i	−0.912630	−	0.408786i	$-0.865952\pi$
$739$	−5.04853	+	7.55566i	−0.185713	+	0.277939i	0.726917	+	0.686725i	$0.240952\pi$
$740$		0			0
$741$	5.58675	−	28.0865i	0.205234	−	1.03178i
$742$		0			0
$743$	−38.3032	−	15.8657i	−1.40521	−	0.582056i	−0.454109	−	0.890946i	$-0.650042\pi$
$743$	−38.3032	−	15.8657i	−1.40521	−	0.582056i	−0.951098	+	0.308890i	$0.900042\pi$
$744$		0			0
$745$	−4.18397	+	1.73306i	−0.153289	+	0.0634943i
$746$		0			0
$747$	−7.89658	+	5.27632i	−0.288921	+	0.193051i
$748$		0			0
$749$	3.67865	+	18.4938i	0.134415	+	0.675750i
$750$		0			0
$751$	−24.7263	+	24.7263i	−0.902275	+	0.902275i	−0.995633	−	0.0933574i	$-0.970240\pi$
$751$	−24.7263	+	24.7263i	−0.902275	+	0.902275i	0.0933574	+	0.995633i	$0.470240\pi$
$752$		0			0
$753$	−40.3961	−	40.3961i	−1.47212	−	1.47212i
$754$		0			0
$755$	8.85527	−	1.76142i	0.322276	−	0.0641047i
$756$		0			0
$757$	−15.3171	−	22.9237i	−0.556710	−	0.833175i	0.441226	−	0.897396i	$-0.354544\pi$
$757$	−15.3171	−	22.9237i	−0.556710	−	0.833175i	−0.997936	+	0.0642212i	$0.979544\pi$
$758$		0			0
$759$	3.81290	+	9.20514i	0.138399	+	0.334126i
$760$		0			0
$761$	2.39831	−	5.79004i	0.0869388	−	0.209889i	−0.874430	−	0.485151i	$-0.838765\pi$
$761$	2.39831	−	5.79004i	0.0869388	−	0.209889i	0.961369	+	0.275262i	$0.0887646\pi$
$762$		0			0
$763$	57.5234	+	11.4421i	2.08249	+	0.414232i
$764$		0			0
$765$	−7.71475	−	5.15483i	−0.278927	−	0.186373i
$766$		0			0
$767$	1.37918			0.0497992
$768$		0			0
$769$	13.9845			0.504295			0.252147	−	0.967689i	$-0.418863\pi$
$769$	13.9845			0.504295			0.252147	+	0.967689i	$0.418863\pi$
$770$		0			0
$771$	1.87790	+	1.25477i	0.0676307	+	0.0451894i
$772$		0			0
$773$	−37.5256	−	7.46432i	−1.34970	−	0.268473i	−0.533286	−	0.845935i	$-0.679043\pi$
$773$	−37.5256	−	7.46432i	−1.34970	−	0.268473i	−0.816418	+	0.577462i	$0.804043\pi$
$774$		0			0
$775$	−2.62685	+	6.34179i	−0.0943594	+	0.227804i
$776$		0			0
$777$	−7.75513	−	18.7225i	−0.278214	−	0.671667i
$778$		0			0
$779$	24.0475	+	35.9896i	0.861590	+	1.28946i
$780$		0			0
$781$	−0.424983	+	0.0845343i	−0.0152071	+	0.00302488i
$782$		0			0
$783$	0.434781	+	0.434781i	0.0155378	+	0.0155378i
$784$		0			0
$785$	8.04164	−	8.04164i	0.287018	−	0.287018i
$786$		0			0
$787$	−9.74437	−	48.9883i	−0.347349	−	1.74624i	−0.620439	−	0.784255i	$-0.713046\pi$
$787$	−9.74437	−	48.9883i	−0.347349	−	1.74624i	0.273090	−	0.961989i	$-0.411954\pi$
$788$		0			0
$789$	−21.9352	+	14.6566i	−0.780914	+	0.521790i
$790$		0			0
$791$	−2.19774	+	0.910335i	−0.0781427	+	0.0323678i
$792$		0			0
$793$	6.81351	+	2.82225i	0.241955	+	0.100221i
$794$		0			0
$795$	−2.56322	+	12.8862i	−0.0909081	+	0.457026i
$796$		0			0
$797$	24.7495	−	37.0403i	0.876674	−	1.31203i	−0.0725281	−	0.997366i	$-0.523107\pi$
$797$	24.7495	−	37.0403i	0.876674	−	1.31203i	0.949202	−	0.314668i	$-0.101893\pi$
$798$		0			0
$799$		−	6.84674i		−	0.242220i
$800$		0			0
$801$			37.4260i			1.32238i
$802$		0			0
$803$	0.222042	−	0.332309i	0.00783568	−	0.0117269i
$804$		0			0
$805$	−5.27366	+	26.5125i	−0.185872	+	0.934442i
$806$		0			0
$807$	52.2884	+	21.6586i	1.84064	+	0.762417i
$808$		0			0
$809$	5.38797	−	2.23177i	0.189431	−	0.0784649i	−0.285952	−	0.958244i	$-0.592310\pi$
$809$	5.38797	−	2.23177i	0.189431	−	0.0784649i	0.475383	+	0.879779i	$0.342310\pi$
$810$		0			0
$811$	−8.53124	+	5.70039i	−0.299572	+	0.200168i	−0.696267	−	0.717783i	$-0.745157\pi$
$811$	−8.53124	+	5.70039i	−0.299572	+	0.200168i	0.396695	+	0.917951i	$0.370157\pi$
$812$		0			0
$813$	1.45891	+	7.33444i	0.0511662	+	0.257230i
$814$		0			0
$815$	2.50541	−	2.50541i	0.0877608	−	0.0877608i
$816$		0			0
$817$	38.8979	+	38.8979i	1.36087	+	1.36087i
$818$		0			0
$819$	−22.1768	+	4.41124i	−0.774920	+	0.154141i
$820$		0			0
$821$	19.7190	+	29.5116i	0.688199	+	1.02996i	0.996890	+	0.0788007i	$0.0251091\pi$
$821$	19.7190	+	29.5116i	0.688199	+	1.02996i	−0.308691	+	0.951162i	$0.599891\pi$
$822$		0			0
$823$	−0.550722	−	1.32956i	−0.0191970	−	0.0463456i	0.913990	−	0.405736i	$-0.132985\pi$
$823$	−0.550722	−	1.32956i	−0.0191970	−	0.0463456i	−0.933187	+	0.359390i	$0.882985\pi$
$824$		0			0
$825$	−2.11904	+	5.11582i	−0.0737756	+	0.178110i
$826$		0			0
$827$	13.6122	+	2.70763i	0.473341	+	0.0941534i	0.425996	−	0.904725i	$-0.359924\pi$
$827$	13.6122	+	2.70763i	0.473341	+	0.0941534i	0.0473454	+	0.998879i	$0.484924\pi$
$828$		0			0
$829$	−8.09646	−	5.40988i	−0.281202	−	0.187893i	0.406969	−	0.913442i	$-0.366586\pi$
$829$	−8.09646	−	5.40988i	−0.281202	−	0.187893i	−0.688170	+	0.725549i	$0.741586\pi$
$830$		0			0
$831$	−20.7447			−0.719625
$832$		0			0
$833$	53.9441			1.86905
$834$		0			0
$835$	4.61494	+	3.08361i	0.159707	+	0.106713i
$836$		0			0
$837$	−0.756697	−	0.150516i	−0.0261553	−	0.00520261i
$838$		0			0
$839$	3.39992	−	8.20812i	0.117378	−	0.283376i	−0.854261	−	0.519844i	$-0.825990\pi$
$839$	3.39992	−	8.20812i	0.117378	−	0.283376i	0.971639	+	0.236468i	$0.0759900\pi$
$840$		0			0
$841$	10.5075	+	25.3673i	0.362326	+	0.874733i
$842$		0			0
$843$	3.06100	+	4.58111i	0.105426	+	0.157782i
$844$		0			0
$845$	−7.30249	+	1.45256i	−0.251213	+	0.0499694i
$846$		0			0
$847$	−33.5273	−	33.5273i	−1.15201	−	1.15201i
$848$		0			0
$849$	−40.6008	+	40.6008i	−1.39342	+	1.39342i
$850$		0			0
$851$	2.94489	+	14.8050i	0.100950	+	0.507508i
$852$		0			0
$853$	18.5526	−	12.3964i	0.635228	−	0.424446i	−0.195825	−	0.980639i	$-0.562738\pi$
$853$	18.5526	−	12.3964i	0.635228	−	0.424446i	0.831053	+	0.556193i	$0.187738\pi$
$854$		0			0
$855$	−12.9459	+	5.36239i	−0.442742	+	0.183390i
$856$		0			0
$857$	−34.9162	−	14.4628i	−1.19272	−	0.494039i	−0.304077	−	0.952647i	$-0.598348\pi$
$857$	−34.9162	−	14.4628i	−1.19272	−	0.494039i	−0.888639	+	0.458608i	$0.848348\pi$
$858$		0			0
$859$	−5.27751	+	26.5318i	−0.180066	+	0.905255i	0.780063	+	0.625700i	$0.215187\pi$
$859$	−5.27751	+	26.5318i	−0.180066	+	0.905255i	−0.960130	+	0.279554i	$0.909813\pi$
$860$		0			0
$861$	39.3727	−	58.9254i	1.34182	−	2.00817i
$862$		0			0
$863$		−	21.2314i		−	0.722726i	−0.932425	−	0.361363i	$-0.882311\pi$
$863$		−	21.2314i		−	0.722726i	0.932425	−	0.361363i	$-0.117689\pi$
$864$		0			0
$865$			12.6386i			0.429725i
$866$		0			0
$867$	2.02573	−	3.03172i	0.0687974	−	0.102963i
$868$		0			0
$869$	−0.890314	+	4.47591i	−0.0302019	+	0.151835i
$870$		0			0
$871$	6.20975	+	2.57216i	0.210409	+	0.0871544i
$872$		0			0
$873$	8.88391	−	3.67984i	0.300675	−	0.124544i
$874$		0			0
$875$	−26.6714	+	17.8213i	−0.901658	+	0.602469i
$876$		0			0
$877$	−2.10738	−	10.5945i	−0.0711613	−	0.357752i	0.928755	−	0.370694i	$-0.120880\pi$
$877$	−2.10738	−	10.5945i	−0.0711613	−	0.357752i	−0.999916	+	0.0129422i	$0.995880\pi$
$878$		0			0
$879$	46.3140	−	46.3140i	1.56213	−	1.56213i
$880$		0			0
$881$	−15.1953	−	15.1953i	−0.511944	−	0.511944i	0.403178	−	0.915122i	$-0.367906\pi$
$881$	−15.1953	−	15.1953i	−0.511944	−	0.511944i	−0.915122	+	0.403178i	$0.867906\pi$
$882$		0			0
$883$	−16.8801	+	3.35767i	−0.568062	+	0.112995i	−0.470761	−	0.882261i	$-0.656021\pi$
$883$	−16.8801	+	3.35767i	−0.568062	+	0.112995i	−0.0973004	+	0.995255i	$0.531021\pi$
$884$		0			0
$885$	−0.777462	−	1.16355i	−0.0261341	−	0.0391124i
$886$		0			0
$887$	7.36626	+	17.7837i	0.247335	+	0.597119i	0.997976	−	0.0635908i	$-0.0202552\pi$
$887$	7.36626	+	17.7837i	0.247335	+	0.597119i	−0.750641	+	0.660710i	$0.770255\pi$
$888$		0			0
$889$	17.8163	−	43.0123i	0.597539	−	1.44259i
$890$		0			0
$891$	−4.90454	−	0.975574i	−0.164308	−	0.0326830i
$892$		0			0
$893$	−8.59753	−	5.74468i	−0.287705	−	0.192239i
$894$		0			0
$895$	7.71672			0.257941
$896$		0			0
$897$	34.9248			1.16611
$898$		0			0
$899$	1.60946	+	1.07541i	0.0536786	+	0.0358669i
$900$		0			0
$901$	−29.8500	−	5.93754i	−0.994448	−	0.197808i
$902$		0			0
$903$	34.4673	−	83.2114i	1.14700	−	2.76910i
$904$		0			0
$905$	1.48214	+	3.57820i	0.0492680	+	0.118943i
$906$		0			0
$907$	−2.40873	−	3.60492i	−0.0799806	−	0.119699i	0.789322	−	0.613979i	$-0.210432\pi$
$907$	−2.40873	−	3.60492i	−0.0799806	−	0.119699i	−0.869303	+	0.494279i	$0.835432\pi$
$908$		0			0
$909$	−13.7407	+	2.73320i	−0.455752	+	0.0906547i
$910$		0			0
$911$	32.8907	+	32.8907i	1.08972	+	1.08972i	0.995557	+	0.0941591i	$0.0300162\pi$
$911$	32.8907	+	32.8907i	1.08972	+	1.08972i	0.0941591	+	0.995557i	$0.469984\pi$
$912$		0			0
$913$	1.25516	−	1.25516i	0.0415397	−	0.0415397i
$914$		0			0
$915$	−1.45986	−	7.33921i	−0.0482615	−	0.242627i
$916$		0			0
$917$	57.7291	−	38.5734i	1.90638	−	1.27381i
$918$		0			0
$919$	−31.3195	+	12.9730i	−1.03314	+	0.427939i	−0.833843	−	0.552001i	$-0.813864\pi$
$919$	−31.3195	+	12.9730i	−1.03314	+	0.427939i	−0.199292	+	0.979940i	$0.563864\pi$
$920$		0			0
$921$	−72.8086	−	30.1583i	−2.39912	−	0.993750i
$922$		0			0
$923$	−0.296314	+	1.48967i	−0.00975328	+	0.0490331i
$924$		0			0
$925$	−4.66077	+	6.97533i	−0.153245	+	0.229347i
$926$		0			0
$927$			5.70530i			0.187387i
$928$		0			0
$929$			10.7407i			0.352390i	0.984355	+	0.176195i	$0.0563789\pi$
$929$			10.7407i			0.352390i	−0.984355	+	0.176195i	$0.943621\pi$
$930$		0			0
$931$	45.2612	−	67.7382i	1.48338	−	2.22003i
$932$		0			0
$933$	−5.26120	+	26.4498i	−0.172244	+	0.865929i
$934$		0			0
$935$	1.60218	+	0.663645i	0.0523969	+	0.0217035i
$936$		0			0
$937$	49.2806	−	20.4127i	1.60993	−	0.666853i	0.617151	−	0.786845i	$-0.288287\pi$
$937$	49.2806	−	20.4127i	1.60993	−	0.666853i	0.992775	+	0.119992i	$0.0382869\pi$
$938$		0			0
$939$	19.7828	−	13.2184i	0.645587	−	0.431367i
$940$		0			0
$941$	5.66109	+	28.4602i	0.184546	+	0.927777i	0.956418	+	0.292000i	$0.0943206\pi$
$941$	5.66109	+	28.4602i	0.184546	+	0.927777i	−0.771872	+	0.635778i	$0.780679\pi$
$942$		0			0
$943$	−37.3273	+	37.3273i	−1.21554	+	1.21554i
$944$		0			0
$945$	−1.19398	−	1.19398i	−0.0388402	−	0.0388402i
$946$		0			0
$947$	−23.1134	+	4.59754i	−0.751084	+	0.149400i	−0.555764	−	0.831340i	$-0.687574\pi$
$947$	−23.1134	+	4.59754i	−0.751084	+	0.149400i	−0.195319	+	0.980740i	$0.562574\pi$
$948$		0			0
$949$	−0.778311	−	1.16482i	−0.0252651	−	0.0378118i
$950$		0			0
$951$	16.4056	+	39.6067i	0.531989	+	1.28434i
$952$		0			0
$953$	−17.9673	+	43.3769i	−0.582018	+	1.40512i	0.308963	+	0.951074i	$0.400018\pi$
$953$	−17.9673	+	43.3769i	−0.582018	+	1.40512i	−0.890981	+	0.454041i	$0.849982\pi$
$954$		0			0
$955$	−15.5889	−	3.10083i	−0.504446	−	0.100341i
$956$		0			0
$957$	1.29833	+	0.867516i	0.0419691	+	0.0280428i
$958$		0			0
$959$	−68.3716			−2.20783
$960$		0			0
$961$	28.5712			0.921651
$962$		0			0
$963$	−9.91181	−	6.62286i	−0.319404	−	0.213419i
$964$		0			0
$965$	−11.9874	−	2.38443i	−0.385887	−	0.0767576i
$966$		0			0
$967$	4.97953	−	12.0217i	0.160131	−	0.386590i	−0.823367	−	0.567509i	$-0.807907\pi$
$967$	4.97953	−	12.0217i	0.160131	−	0.386590i	0.983498	+	0.180919i	$0.0579071\pi$
$968$		0			0
$969$	−25.7574	−	62.1840i	−0.827448	−	1.99764i
$970$		0			0
$971$	−20.1628	−	30.1758i	−0.647055	−	0.968386i	−0.999470	−	0.0325425i	$-0.989640\pi$
$971$	−20.1628	−	30.1758i	−0.647055	−	0.968386i	0.352415	−	0.935844i	$-0.385360\pi$
$972$		0			0
$973$	−57.3922	+	11.4160i	−1.83991	+	0.365981i
$974$		0			0
$975$	13.7247	+	13.7247i	0.439543	+	0.439543i
$976$		0			0
$977$	−40.4140	+	40.4140i	−1.29296	+	1.29296i	−0.360009	+	0.932949i	$0.617226\pi$
$977$	−40.4140	+	40.4140i	−1.29296	+	1.29296i	−0.932949	+	0.360009i	$0.882774\pi$
$978$		0			0
$979$	−1.36468	−	6.86070i	−0.0436153	−	0.219269i
$980$		0			0
$981$	−30.8298	+	20.5998i	−0.984319	+	0.657701i
$982$		0			0
$983$	35.5045	−	14.7065i	1.13242	−	0.469063i	0.263816	−	0.964573i	$-0.415019\pi$
$983$	35.5045	−	14.7065i	1.13242	−	0.469063i	0.868602	+	0.495510i	$0.165019\pi$
$984$		0			0
$985$	−18.6071	−	7.70731i	−0.592871	−	0.245575i
$986$		0			0
$987$	−3.30285	+	16.6046i	−0.105131	+	0.528529i
$988$		0			0
$989$	−37.2727	+	55.7826i	−1.18520	+	1.77378i
$990$		0			0
$991$		−	16.3018i		−	0.517845i	−0.965898	−	0.258922i	$-0.916633\pi$
$991$		−	16.3018i		−	0.517845i	0.965898	−	0.258922i	$-0.0833674\pi$
$992$		0			0
$993$			41.9955i			1.33269i
$994$		0			0
$995$	6.28607	−	9.40777i	0.199282	−	0.298246i
$996$		0			0
$997$	3.51164	−	17.6542i	0.111215	−	0.559114i	−0.884493	−	0.466554i	$-0.845495\pi$
$997$	3.51164	−	17.6542i	0.111215	−	0.559114i	0.995707	−	0.0925594i	$-0.0295048\pi$
$998$		0			0
$999$	−0.871135	−	0.360836i	−0.0275615	−	0.0114163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.113.6		56
4.3	odd	2		64.2.i.a.5.7	✓	56
8.3	odd	2		512.2.i.b.481.6		56
8.5	even	2		512.2.i.a.481.2		56
12.11	even	2		576.2.bd.a.325.1		56
64.13	even	16	inner	256.2.i.a.145.6		56
64.19	odd	16		512.2.i.b.33.6		56
64.45	even	16		512.2.i.a.33.2		56
64.51	odd	16		64.2.i.a.13.7	yes	56
192.179	even	16		576.2.bd.a.397.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.7	✓	56	4.3	odd	2
64.2.i.a.13.7	yes	56	64.51	odd	16
256.2.i.a.113.6		56	1.1	even	1	trivial
256.2.i.a.145.6		56	64.13	even	16	inner
512.2.i.a.33.2		56	64.45	even	16
512.2.i.a.481.2		56	8.5	even	2
512.2.i.b.33.6		56	64.19	odd	16
512.2.i.b.481.6		56	8.3	odd	2
576.2.bd.a.325.1		56	12.11	even	2
576.2.bd.a.397.1		56	192.179	even	16

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00147 + 1.33734i) q^{3} +(0.756852 + 0.150547i) q^{5} +(1.69148 - 4.08359i) q^{7} +(1.06935 + 2.58163i) q^{9} +(-0.290161 - 0.434257i) q^{11} +(-1.79553 + 0.357153i) q^{13} +(1.31348 + 1.31348i) q^{15} +(-3.04259 + 3.04259i) q^{17} +(1.26776 + 6.37347i) q^{19} +(8.84657 - 5.91109i) q^{21} +(-7.32197 + 3.03286i) q^{23} +(-4.06924 - 1.68553i) q^{25} +(0.0965796 - 0.485538i) q^{27} +(-0.690042 + 1.03272i) q^{29} -1.55847i q^{31} -1.25719i q^{33} +(1.89497 - 2.83602i) q^{35} +(0.371584 - 1.86808i) q^{37} +(-4.07133 - 1.68640i) q^{39} +(6.15380 - 2.54899i) q^{41} +(7.03859 - 4.70304i) q^{43} +(0.420680 + 2.11490i) q^{45} +(-1.12515 + 1.12515i) q^{47} +(-8.86483 - 8.86483i) q^{49} +(-10.1586 + 2.02068i) q^{51} +(3.92962 + 5.88109i) q^{53} +(-0.154233 - 0.372351i) q^{55} +(-5.98610 + 14.4517i) q^{57} +(-0.738882 - 0.146973i) q^{59} +(-3.34952 - 2.23808i) q^{61} +12.3511 q^{63} -1.41272 q^{65} +(-3.05271 - 2.03976i) q^{67} +(-18.7106 - 3.72178i) q^{69} +(0.317495 - 0.766500i) q^{71} +(0.292843 + 0.706986i) q^{73} +(-5.89032 - 8.81548i) q^{75} +(-2.26413 + 0.450363i) q^{77} +(-6.17863 - 6.17863i) q^{79} +(6.77032 - 6.77032i) q^{81} +(0.663054 + 3.33340i) q^{83} +(-2.76085 + 1.84474i) q^{85} +(-2.76219 + 1.14414i) q^{87} +(12.3740 + 5.12547i) q^{89} +(-1.57863 + 7.93632i) q^{91} +(2.08420 - 3.11923i) q^{93} +5.01463i q^{95} -3.44120i q^{97} +(0.810809 - 1.21346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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