LMFDB - Embedded newform 512.2.i.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.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:	$4.08834058349$
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			33.2
Character	$\chi$	$=$	512.33
Dual form			512.2.i.a.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00147 + 1.33734i) q^{3} +(-0.756852 + 0.150547i) q^{5} +(1.69148 + 4.08359i) q^{7} +(1.06935 - 2.58163i) q^{9} +O(q^{10})$	\(q+(-2.00147 + 1.33734i) q^{3} +(-0.756852 + 0.150547i) q^{5} +(1.69148 + 4.08359i) q^{7} +(1.06935 - 2.58163i) q^{9} +(0.290161 - 0.434257i) q^{11} +(1.79553 + 0.357153i) q^{13} +(1.31348 - 1.31348i) q^{15} +(-3.04259 - 3.04259i) q^{17} +(-1.26776 + 6.37347i) q^{19} +(-8.84657 - 5.91109i) q^{21} +(-7.32197 - 3.03286i) q^{23} +(-4.06924 + 1.68553i) q^{25} +(-0.0965796 - 0.485538i) q^{27} +(0.690042 + 1.03272i) q^{29} +1.55847i q^{31} +1.25719i q^{33} +(-1.89497 - 2.83602i) q^{35} +(-0.371584 - 1.86808i) q^{37} +(-4.07133 + 1.68640i) q^{39} +(6.15380 + 2.54899i) q^{41} +(-7.03859 - 4.70304i) q^{43} +(-0.420680 + 2.11490i) q^{45} +(-1.12515 - 1.12515i) q^{47} +(-8.86483 + 8.86483i) q^{49} +(10.1586 + 2.02068i) q^{51} +(-3.92962 + 5.88109i) q^{53} +(-0.154233 + 0.372351i) q^{55} +(-5.98610 - 14.4517i) q^{57} +(0.738882 - 0.146973i) q^{59} +(3.34952 - 2.23808i) q^{61} +12.3511 q^{63} -1.41272 q^{65} +(3.05271 - 2.03976i) q^{67} +(18.7106 - 3.72178i) q^{69} +(0.317495 + 0.766500i) q^{71} +(0.292843 - 0.706986i) q^{73} +(5.89032 - 8.81548i) q^{75} +(2.26413 + 0.450363i) q^{77} +(-6.17863 + 6.17863i) q^{79} +(6.77032 + 6.77032i) q^{81} +(-0.663054 + 3.33340i) q^{83} +(2.76085 + 1.84474i) q^{85} +(-2.76219 - 1.14414i) q^{87} +(12.3740 - 5.12547i) q^{89} +(1.57863 + 7.93632i) q^{91} +(-2.08420 - 3.11923i) q^{93} -5.01463i q^{95} +3.44120i q^{97} +(-0.810809 - 1.21346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

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	$-0.932044\pi$
$3$	−2.00147	+	1.33734i	−1.15555	+	0.772112i	−0.178250	+	0.983985i	$0.557044\pi$
$4$		0			0
$5$	−0.756852	+	0.150547i	−0.338474	+	0.0673268i	−0.361401	−	0.932410i	$-0.617702\pi$
$5$	−0.756852	+	0.150547i	−0.338474	+	0.0673268i	0.0229268	+	0.999737i	$0.492702\pi$
$6$		0			0
$7$	1.69148	+	4.08359i	0.639318	+	1.54345i	0.827590	+	0.561333i	$0.189711\pi$
$7$	1.69148	+	4.08359i	0.639318	+	1.54345i	−0.188272	+	0.982117i	$0.560289\pi$
$8$		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	$-0.787412\pi$
$11$	0.290161	−	0.434257i	0.0874869	−	0.130933i	0.872632	+	0.488379i	$0.162412\pi$
$12$		0			0
$13$	1.79553	+	0.357153i	0.497991	+	0.0990565i	0.437694	−	0.899124i	$-0.355795\pi$
$13$	1.79553	+	0.357153i	0.497991	+	0.0990565i	0.0602967	+	0.998180i	$0.480795\pi$
$14$		0			0
$15$	1.31348	−	1.31348i	0.339140	−	0.339140i
$16$		0			0
$17$	−3.04259	−	3.04259i	−0.737937	−	0.737937i	0.234241	−	0.972179i	$-0.424739\pi$
$17$	−3.04259	−	3.04259i	−0.737937	−	0.737937i	−0.972179	+	0.234241i	$0.924739\pi$
$18$		0			0
$19$	−1.26776	+	6.37347i	−0.290845	+	1.46217i	0.508375	+	0.861136i	$0.330246\pi$
$19$	−1.26776	+	6.37347i	−0.290845	+	1.46217i	−0.799220	+	0.601039i	$0.794754\pi$
$20$		0			0
$21$	−8.84657	−	5.91109i	−1.93048	−	1.28990i
$22$		0			0
$23$	−7.32197	−	3.03286i	−1.52674	−	0.632395i	−0.547810	−	0.836603i	$-0.684538\pi$
$23$	−7.32197	−	3.03286i	−1.52674	−	0.632395i	−0.978928	+	0.204208i	$0.934538\pi$
$24$		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	$-0.150710\pi$
$29$	0.690042	+	1.03272i	0.128138	+	0.191771i	−0.761854	+	0.647749i	$0.775710\pi$
$30$		0			0
$31$			1.55847i			0.279910i	0.990158	+	0.139955i	$0.0446957\pi$
$31$			1.55847i			0.279910i	−0.990158	+	0.139955i	$0.955304\pi$
$32$		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	$-0.112542\pi$
$37$	−0.371584	−	1.86808i	−0.0610880	−	0.307110i	−0.999234	+	0.0391295i	$0.987542\pi$
$38$		0			0
$39$	−4.07133	+	1.68640i	−0.651935	+	0.270040i
$40$		0			0
$41$	6.15380	+	2.54899i	0.961062	+	0.398085i	0.807378	−	0.590035i	$-0.200886\pi$
$41$	6.15380	+	2.54899i	0.961062	+	0.398085i	0.153685	+	0.988120i	$0.450886\pi$
$42$		0			0
$43$	−7.03859	−	4.70304i	−1.07338	−	0.717206i	−0.112350	−	0.993669i	$-0.535838\pi$
$43$	−7.03859	−	4.70304i	−1.07338	−	0.717206i	−0.961025	+	0.276462i	$0.910838\pi$
$44$		0			0
$45$	−0.420680	+	2.11490i	−0.0627113	+	0.315271i
$46$		0			0
$47$	−1.12515	−	1.12515i	−0.164120	−	0.164120i	0.620269	−	0.784389i	$-0.287023\pi$
$47$	−1.12515	−	1.12515i	−0.164120	−	0.164120i	−0.784389	+	0.620269i	$0.787023\pi$
$48$		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	$-0.973966\pi$
$53$	−3.92962	+	5.88109i	−0.539775	+	0.807830i	0.456882	+	0.889527i	$0.348966\pi$
$54$		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	$-0.546884\pi$
$59$	0.738882	−	0.146973i	0.0961942	−	0.0191342i	0.242953	+	0.970038i	$0.421884\pi$
$60$		0			0
$61$	3.34952	−	2.23808i	0.428862	−	0.286556i	−0.322346	−	0.946622i	$-0.604471\pi$
$61$	3.34952	−	2.23808i	0.428862	−	0.286556i	0.751208	+	0.660065i	$0.229471\pi$
$62$		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	$-0.615500\pi$
$67$	3.05271	−	2.03976i	0.372948	−	0.249196i	0.727892	+	0.685692i	$0.240500\pi$
$68$		0			0
$69$	18.7106	−	3.72178i	2.25250	−	0.448050i
$70$		0			0
$71$	0.317495	+	0.766500i	0.0376797	+	0.0909668i	0.941599	−	0.336736i	$-0.109323\pi$
$71$	0.317495	+	0.766500i	0.0376797	+	0.0909668i	−0.903919	+	0.427703i	$0.859323\pi$
$72$		0			0
$73$	0.292843	−	0.706986i	0.0342747	−	0.0827464i	−0.905815	−	0.423673i	$-0.860741\pi$
$73$	0.292843	−	0.706986i	0.0342747	−	0.0827464i	0.940090	+	0.340926i	$0.110741\pi$
$74$		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	−0.963360	−	0.268210i	$-0.913568\pi$
$79$	−6.17863	+	6.17863i	−0.695150	+	0.695150i	0.268210	+	0.963360i	$0.413568\pi$
$80$		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	$-0.997224\pi$
$83$	−0.663054	+	3.33340i	−0.0727796	+	0.365888i	0.927182	+	0.374610i	$0.122224\pi$
$84$		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	0.386277	−	0.922383i	$-0.373761\pi$
$89$	12.3740	−	5.12547i	1.31164	−	0.543299i	0.925362	+	0.379084i	$0.123761\pi$
$90$		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	$0.0558956\pi$
$97$			3.44120i			0.349401i	−0.984622	+	0.174700i	$0.944104\pi$
$98$		0			0
$99$	−0.810809	−	1.21346i	−0.0814894	−	0.121958i
$100$		0			0
$101$	0.978121	+	4.91735i	0.0973267	+	0.489294i	0.998446	+	0.0557237i	$0.0177466\pi$
$101$	0.978121	+	4.91735i	0.0973267	+	0.489294i	−0.901120	+	0.433571i	$0.857253\pi$
$102$		0			0
$103$	1.88632	−	0.781338i	0.185864	−	0.0769875i	−0.287810	−	0.957687i	$-0.592927\pi$
$103$	1.88632	−	0.781338i	0.185864	−	0.0769875i	0.473675	+	0.880700i	$0.342927\pi$
$104$		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	$-0.246388\pi$
$107$	3.54710	+	2.37010i	0.342911	+	0.229126i	−0.372174	+	0.928163i	$0.621388\pi$
$108$		0			0
$109$	−2.58869	+	13.0142i	−0.247952	+	1.24654i	0.633306	+	0.773901i	$0.281697\pi$
$109$	−2.58869	+	13.0142i	−0.247952	+	1.24654i	−0.881258	+	0.472636i	$0.843303\pi$
$110$		0			0
$111$	3.24196	+	3.24196i	0.307713	+	0.307713i
$112$		0			0
$113$	−0.380557	+	0.380557i	−0.0357998	+	0.0357998i	−0.724780	−	0.688980i	$-0.758059\pi$
$113$	−0.380557	+	0.380557i	−0.0357998	+	0.0357998i	0.688980	+	0.724780i	$0.258059\pi$
$114$		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	$-0.928227\pi$
$131$	−13.0608	+	8.72693i	−1.14112	+	0.762475i	−0.166438	+	0.986052i	$0.553227\pi$
$132$		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	0.440572	+	0.897717i	$0.354776\pi$
$137$	−5.91955	+	14.2911i	−0.505742	+	1.22097i	−0.946313	+	0.323251i	$0.895224\pi$
$138$		0			0
$139$	7.35516	−	11.0078i	0.623856	−	0.933667i	−0.376119	−	0.926572i	$-0.622741\pi$
$139$	7.35516	−	11.0078i	0.623856	−	0.933667i	0.999975	−	0.00709534i	$-0.00225854\pi$
$140$		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	$-0.235225\pi$
$149$	4.87958	+	3.26043i	0.399751	+	0.267105i	−0.339404	+	0.940641i	$0.610225\pi$
$150$		0			0
$151$	10.8095	+	4.47745i	0.879666	+	0.364369i	0.776367	−	0.630281i	$-0.217060\pi$
$151$	10.8095	+	4.47745i	0.879666	+	0.364369i	0.103298	+	0.994650i	$0.467060\pi$
$152$		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	−0.999214	−	0.0396342i	$-0.987381\pi$
$157$	−8.18769	−	12.2537i	−0.653449	−	0.977955i	0.345766	−	0.938321i	$-0.387619\pi$
$158$		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	$-0.245051\pi$
$163$	−2.55092	−	3.81772i	−0.199803	−	0.299027i	−0.917818	+	0.397001i	$0.870051\pi$
$164$		0			0
$165$	−0.189267	−	0.951510i	−0.0147344	−	0.0740749i
$166$		0			0
$167$	6.64505	−	2.75247i	0.514209	−	0.212992i	−0.110462	−	0.993880i	$-0.535233\pi$
$167$	6.64505	−	2.75247i	0.514209	−	0.212992i	0.624671	+	0.780888i	$0.285233\pi$
$168$		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	0.646042	+	0.763302i	$0.276423\pi$
$173$	−3.19519	+	16.0633i	−0.242926	+	1.22127i	−0.888968	+	0.457970i	$0.848577\pi$
$174$		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	$-0.559416\pi$
$179$	−9.80775	−	1.95088i	−0.733066	−	0.145816i	−0.547488	+	0.836814i	$0.684416\pi$
$180$		0			0
$181$	−2.78837	+	4.17310i	−0.207258	+	0.310184i	−0.920506	−	0.390728i	$-0.872223\pi$
$181$	−2.78837	+	4.17310i	−0.207258	+	0.310184i	0.713248	+	0.700912i	$0.247223\pi$
$182$		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	$-0.182529\pi$
$197$	25.5976	−	5.09169i	1.82376	−	0.362768i	0.983712	+	0.179750i	$0.0575290\pi$
$198$		0			0
$199$	5.61103	+	13.5462i	0.397756	+	0.960267i	0.988197	+	0.153187i	$0.0489536\pi$
$199$	5.61103	+	13.5462i	0.397756	+	0.960267i	−0.590442	+	0.807080i	$0.701046\pi$
$200$		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	0.612686	+	0.790326i	$0.290089\pi$
$211$	−3.71581	+	18.6806i	−0.255807	+	1.28603i	−0.868493	+	0.495701i	$0.834911\pi$
$212$		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	$0.105408\pi$
$223$			9.71045i			0.650260i	−0.945669	+	0.325130i	$0.894592\pi$
$224$		0			0
$225$			12.3077i			0.820514i
$226$		0			0
$227$	2.12248	+	3.17651i	0.140874	+	0.210833i	0.895197	−	0.445671i	$-0.147035\pi$
$227$	2.12248	+	3.17651i	0.140874	+	0.210833i	−0.754323	+	0.656503i	$0.772035\pi$
$228$		0			0
$229$	1.76419	+	8.86919i	0.116581	+	0.586093i	0.994273	+	0.106868i	$0.0340822\pi$
$229$	1.76419	+	8.86919i	0.116581	+	0.586093i	−0.877692	+	0.479225i	$0.840918\pi$
$230$		0			0
$231$	−5.13386	+	2.12651i	−0.337783	+	0.139914i
$232$		0			0
$233$	−2.54691	−	1.05496i	−0.166854	−	0.0691130i	0.297693	−	0.954662i	$-0.403783\pi$
$233$	−2.54691	−	1.05496i	−0.166854	−	0.0691130i	−0.464547	+	0.885549i	$0.653783\pi$
$234$		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	0.930658	−	0.365891i	$-0.119236\pi$
$239$	8.73109	+	8.73109i	0.564767	+	0.564767i	−0.365891	+	0.930658i	$0.619236\pi$
$240$		0			0
$241$	16.1373	−	16.1373i	1.03949	−	1.03949i	0.0403070	−	0.999187i	$-0.487166\pi$
$241$	16.1373	−	16.1373i	1.03949	−	1.03949i	0.999187	−	0.0403070i	$-0.0128336\pi$
$242$		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	$-0.293031\pi$
$251$	23.2770	−	4.63008i	1.46923	−	0.292248i	0.863874	+	0.503708i	$0.168031\pi$
$252$		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	0.740231	−	0.672352i	$-0.234716\pi$
$263$	−4.19405	−	10.1253i	−0.258616	−	0.624354i	−0.998847	+	0.0479979i	$0.984716\pi$
$264$		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	$-0.691882\pi$
$269$	−23.0601	−	4.58694i	−1.40600	−	0.279671i	−0.839038	+	0.544073i	$0.816882\pi$
$270$		0			0
$271$	2.19673	−	2.19673i	0.133442	−	0.133442i	−0.637231	−	0.770673i	$-0.719920\pi$
$271$	2.19673	−	2.19673i	0.133442	−	0.133442i	0.770673	+	0.637231i	$0.219920\pi$
$272$		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	$-0.229139\pi$
$277$	7.16558	+	4.78789i	0.430538	+	0.287676i	−0.321358	+	0.946958i	$0.604139\pi$
$278$		0			0
$279$	4.02340	+	1.66655i	0.240875	+	0.0997736i
$280$		0			0
$281$	2.11464	−	0.875914i	0.126149	−	0.0522527i	−0.318716	−	0.947850i	$-0.603252\pi$
$281$	2.11464	−	0.875914i	0.126149	−	0.0522527i	0.444865	+	0.895598i	$0.353252\pi$
$282$		0			0
$283$	4.65354	+	23.3949i	0.276624	+	1.39068i	0.830005	+	0.557755i	$0.188337\pi$
$283$	4.65354	+	23.3949i	0.276624	+	1.39068i	−0.553381	+	0.832928i	$0.686663\pi$
$284$		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	−0.750260	−	0.661143i	$-0.770072\pi$
$293$	−5.30837	−	26.6870i	−0.310118	−	1.55907i	0.440142	−	0.897928i	$-0.354928\pi$
$294$		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	$-0.0535648\pi$
$307$	32.1099	+	6.38706i	1.83261	+	0.364529i	0.846735	+	0.532015i	$0.178565\pi$
$308$		0			0
$309$	−2.73049	+	4.08646i	−0.155332	+	0.232471i
$310$		0			0
$311$	4.28733	−	10.3505i	0.243112	−	0.586924i	−0.754477	−	0.656327i	$-0.772109\pi$
$311$	4.28733	−	10.3505i	0.243112	−	0.586924i	0.997589	+	0.0694024i	$0.0221092\pi$
$312$		0			0
$313$	3.78250	+	9.13175i	0.213799	+	0.516157i	0.994001	−	0.109371i	$-0.0348836\pi$
$313$	3.78250	+	9.13175i	0.213799	+	0.516157i	−0.780202	+	0.625528i	$0.784884\pi$
$314$		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	$-0.854218\pi$
$317$	−14.8080	+	9.89442i	−0.831703	+	0.555726i	0.0652416	+	0.997869i	$0.479218\pi$
$318$		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	$-0.971669\pi$
$331$	−9.69258	+	14.5060i	−0.532752	+	0.797320i	0.463289	+	0.886207i	$0.346669\pi$
$332$		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	0.901894	−	0.431957i	$-0.142177\pi$
$337$	8.62689	+	8.62689i	0.469937	+	0.469937i	−0.431957	+	0.901894i	$0.642177\pi$
$338$		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	−0.988861	−	0.148843i	$-0.952445\pi$
$347$	−2.46321	−	12.3834i	−0.132232	−	0.664776i	0.856629	−	0.515933i	$-0.172555\pi$
$348$		0			0
$349$	9.48101	+	14.1893i	0.507507	+	0.759538i	0.993427	−	0.114465i	$-0.0365155\pi$
$349$	9.48101	+	14.1893i	0.507507	+	0.759538i	−0.485920	+	0.874003i	$0.661515\pi$
$350$		0			0
$351$		−	0.906293i		−	0.0483743i
$352$		0			0
$353$			23.9464i			1.27454i	0.770641	+	0.637270i	$0.219936\pi$
$353$			23.9464i			1.27454i	−0.770641	+	0.637270i	$0.780064\pi$
$354$		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	0.320195	−	0.947352i	$-0.396252\pi$
$359$	23.0491	−	9.54726i	1.21649	−	0.503885i	0.896291	+	0.443467i	$0.146252\pi$
$360$		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	0.961894	+	0.273421i	$0.0881553\pi$
$367$	23.6652	+	23.6652i	1.23532	+	1.23532i	0.273421	+	0.961894i	$0.411845\pi$
$368$		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	$-0.966984\pi$
$373$	−10.0109	+	14.9823i	−0.518343	+	0.775755i	0.476283	+	0.879292i	$0.341984\pi$
$374$		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	$-0.565639\pi$
$379$	−0.376618	+	0.0749139i	−0.0193455	+	0.00384807i	0.185408	+	0.982662i	$0.440639\pi$
$380$		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	$-0.625325\pi$
$389$	−7.58645	+	1.50904i	−0.384648	+	0.0765113i	−0.00102139	+	0.999999i	$0.500325\pi$
$390$		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	$-0.370152\pi$
$397$	8.20788	+	1.63265i	0.411942	+	0.0819403i	0.0152310	+	0.999884i	$0.495152\pi$
$398$		0			0
$399$	48.8895	−	48.8895i	2.44754	−	2.44754i
$400$		0			0
$401$	−18.5993	−	18.5993i	−0.928802	−	0.928802i	0.0688263	−	0.997629i	$-0.478075\pi$
$401$	−18.5993	−	18.5993i	−0.928802	−	0.928802i	−0.997629	+	0.0688263i	$0.978075\pi$
$402$		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	0.282378	−	0.959303i	$-0.408877\pi$
$409$	23.4672	−	9.72045i	1.16038	−	0.480645i	0.878001	+	0.478658i	$0.158877\pi$
$410$		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	$-0.288092\pi$
$419$	−7.06866	−	10.5790i	−0.345326	−	0.516818i	−0.962959	+	0.269650i	$0.913092\pi$
$420$		0			0
$421$	−5.87200	−	29.5205i	−0.286184	−	1.43874i	−0.809758	−	0.586763i	$-0.800402\pi$
$421$	−5.87200	−	29.5205i	−0.286184	−	1.43874i	0.523575	−	0.851980i	$-0.324598\pi$
$422$		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	0.523255	−	0.852176i	$-0.324718\pi$
$431$	−6.82858	−	6.82858i	−0.328921	−	0.328921i	−0.852176	+	0.523255i	$0.824718\pi$
$432$		0			0
$433$	−4.84377	+	4.84377i	−0.232777	+	0.232777i	−0.813851	−	0.581074i	$-0.802633\pi$
$433$	−4.84377	+	4.84377i	−0.232777	+	0.232777i	0.581074	+	0.813851i	$0.302633\pi$
$434$		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	−0.389325	−	0.921101i	$-0.627292\pi$
$439$	11.2574	−	27.1777i	0.537286	−	1.29712i	0.926611	−	0.376022i	$-0.122708\pi$
$440$		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	$-0.291305\pi$
$443$	31.0716	−	6.18053i	1.47626	−	0.293646i	0.866593	+	0.499015i	$0.166305\pi$
$444$		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	−0.829610	−	0.558343i	$-0.811437\pi$
$457$	3.24557	−	7.83549i	0.151821	−	0.366529i	0.981431	+	0.191814i	$0.0614372\pi$
$458$		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	$-0.239993\pi$
$461$	24.4880	+	4.87097i	1.14052	+	0.226864i	0.411536	+	0.911394i	$0.364993\pi$
$462$		0			0
$463$	19.0846	−	19.0846i	0.886939	−	0.886939i	−0.107289	−	0.994228i	$-0.534217\pi$
$463$	19.0846	−	19.0846i	0.886939	−	0.886939i	0.994228	+	0.107289i	$0.0342170\pi$
$464$		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	$-0.927526\pi$
$467$	0.264167	−	1.32806i	0.0122242	−	0.0614552i	0.986416	+	0.164267i	$0.0525259\pi$
$468$		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	$0.0256239\pi$
$479$			3.51984i			0.160826i	−0.996762	+	0.0804128i	$0.974376\pi$
$480$		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	−0.876277	−	0.481808i	$-0.839980\pi$
$487$	−25.4932	+	10.5596i	−1.15521	+	0.478503i	−0.278932	+	0.960311i	$0.589980\pi$
$488$		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	$-0.144297\pi$
$491$	18.5780	+	12.4134i	0.838412	+	0.560209i	−0.0605855	+	0.998163i	$0.519297\pi$
$492$		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	$-0.493105\pi$
$499$	−7.61559	−	1.51483i	−0.340921	−	0.0678133i	−0.362582	+	0.931952i	$0.618105\pi$
$500$		0			0
$501$	−9.61886	+	14.3956i	−0.429739	+	0.643150i
$502$		0			0
$503$	−16.2329	+	39.1897i	−0.723789	+	1.74738i	−0.0615295	+	0.998105i	$0.519598\pi$
$503$	−16.2329	+	39.1897i	−0.723789	+	1.74738i	−0.662259	+	0.749275i	$0.730402\pi$
$504$		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	$-0.430771\pi$
$509$	27.0838	−	18.0968i	1.20047	−	0.802126i	0.984690	+	0.174316i	$0.0557715\pi$
$510$		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	0.544318	+	0.838879i	$0.316789\pi$
$521$	−9.90054	+	23.9020i	−0.433750	+	1.04717i	−0.978068	+	0.208287i	$0.933211\pi$
$522$		0			0
$523$	11.2609	−	16.8531i	0.492404	−	0.736935i	−0.499166	−	0.866507i	$-0.666360\pi$
$523$	11.2609	−	16.8531i	0.492404	−	0.736935i	0.991570	+	0.129571i	$0.0413601\pi$
$524$		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	0.874989	+	0.484142i	$0.160868\pi$
$541$	22.9671	+	34.3728i	0.987435	+	1.47780i	0.112445	+	0.993658i	$0.464132\pi$
$542$		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	$-0.275067\pi$
$547$	−7.05928	−	10.5650i	−0.301833	−	0.451725i	−0.951121	+	0.308817i	$0.900067\pi$
$548$		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	0.858341	+	0.513079i	$0.171495\pi$
$557$	−3.09194	+	15.5442i	−0.131010	+	0.658630i	−0.989351	+	0.145551i	$0.953505\pi$
$558$		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	$-0.471629\pi$
$563$	−4.98076	−	0.990736i	−0.209914	−	0.0417545i	−0.298927	+	0.954276i	$0.596629\pi$
$564$		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	0.976177	+	0.216975i	$0.0696189\pi$
$569$	10.4799	+	25.3007i	0.439340	+	1.06066i	−0.536837	+	0.843686i	$0.680381\pi$
$570$		0			0
$571$	−26.9468	+	5.36006i	−1.12769	+	0.224311i	−0.723474	−	0.690352i	$-0.757456\pi$
$571$	−26.9468	+	5.36006i	−1.12769	+	0.224311i	−0.404216	+	0.914664i	$0.632456\pi$
$572$		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	$-0.821534\pi$
$587$	−0.763948	+	1.14333i	−0.0315315	+	0.0471902i	0.815369	+	0.578942i	$0.196534\pi$
$588$		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	0.813726	−	0.581248i	$-0.197436\pi$
$593$	5.66121	+	5.66121i	0.232478	+	0.232478i	−0.581248	+	0.813726i	$0.697436\pi$
$594$		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	0.114585	−	0.993413i	$-0.463446\pi$
$599$	−12.4047	−	5.13818i	−0.506841	−	0.209941i	−0.621426	+	0.783473i	$0.713446\pi$
$600$		0			0
$601$	−6.28652	+	2.60396i	−0.256433	+	0.106218i	−0.507197	−	0.861830i	$-0.669318\pi$
$601$	−6.28652	+	2.60396i	−0.256433	+	0.106218i	0.250764	+	0.968048i	$0.419318\pi$
$602$		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	$-0.780934\pi$
$607$		−	31.2974i		−	1.27032i	0.772379	−	0.635161i	$-0.219066\pi$
$608$		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	−0.973123	−	0.230286i	$-0.926034\pi$
$613$	−4.01591	−	20.1894i	−0.162201	−	0.815441i	0.810922	−	0.585155i	$-0.198966\pi$
$614$		0			0
$615$	11.4310	−	4.73486i	0.460941	−	0.190928i
$616$		0			0
$617$	0.720564	+	0.298468i	0.0290088	+	0.0120159i	0.397141	−	0.917758i	$-0.370002\pi$
$617$	0.720564	+	0.298468i	0.0290088	+	0.0120159i	−0.368132	+	0.929774i	$0.620002\pi$
$618$		0			0
$619$	−12.1862	−	8.14255i	−0.489804	−	0.327277i	0.286022	−	0.958223i	$-0.407667\pi$
$619$	−12.1862	−	8.14255i	−0.489804	−	0.327277i	−0.775826	+	0.630946i	$0.782667\pi$
$620$		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	−0.296204	−	0.955125i	$-0.595721\pi$
$631$	14.7859	−	35.6964i	0.588619	−	1.42105i	0.884823	−	0.465927i	$-0.154279\pi$
$632$		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	$-0.849987\pi$
$643$	−20.6027	+	13.7663i	−0.812489	+	0.542888i	0.0784990	+	0.996914i	$0.474987\pi$
$644$		0			0
$645$	−15.4224	+	3.06771i	−0.607257	+	0.120791i
$646$		0			0
$647$	−15.7086	−	37.9240i	−0.617570	−	1.49095i	−0.854517	−	0.519423i	$-0.826147\pi$
$647$	−15.7086	−	37.9240i	−0.617570	−	1.49095i	0.236948	−	0.971522i	$-0.423853\pi$
$648$		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	$-0.798304\pi$
$653$	−45.4088	−	9.03238i	−1.77698	−	0.353464i	−0.971112	+	0.238624i	$0.923304\pi$
$654$		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	−0.445206	−	0.895428i	$-0.646870\pi$
$659$	7.92659	−	39.8497i	0.308776	−	1.55232i	0.753983	−	0.656894i	$-0.228130\pi$
$660$		0			0
$661$	29.3540	+	19.6137i	1.14174	+	0.762886i	0.974800	−	0.223081i	$-0.0716114\pi$
$661$	29.3540	+	19.6137i	1.14174	+	0.762886i	0.166940	+	0.985967i	$0.446611\pi$
$662$		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	$0.155047\pi$
$673$			24.2851i			0.936122i	−0.883696	+	0.468061i	$0.844953\pi$
$674$		0			0
$675$	1.21140	+	1.81298i	0.0466266	+	0.0697817i
$676$		0			0
$677$	4.33107	+	21.7738i	0.166456	+	0.836833i	0.970284	+	0.241970i	$0.0777937\pi$
$677$	4.33107	+	21.7738i	0.166456	+	0.836833i	−0.803827	+	0.594863i	$0.797206\pi$
$678$		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	$-0.402015\pi$
$683$	−12.0613	−	8.05912i	−0.461514	−	0.308374i	−0.764503	+	0.644620i	$0.777015\pi$
$684$		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	$-0.413457\pi$
$691$	3.89100	+	0.773968i	0.148021	+	0.0294431i	−0.120524	+	0.992710i	$0.538457\pi$
$692$		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	$-0.947073\pi$
$701$	−32.0550	+	21.4185i	−1.21070	+	0.808965i	−0.224494	+	0.974476i	$0.572073\pi$
$702$		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	$-0.651301\pi$
$709$	−14.3830	+	2.86095i	−0.540164	+	0.107445i	−0.0825345	+	0.996588i	$0.526301\pi$
$710$		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	−0.944175	−	0.329445i	$-0.893138\pi$
$719$	−16.4835	+	16.4835i	−0.614730	+	0.614730i	0.329445	+	0.944175i	$0.393138\pi$
$720$		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	0.418444	−	0.908243i	$-0.362576\pi$
$727$	1.94412	+	0.805280i	0.0721034	+	0.0298662i	−0.346340	+	0.938109i	$0.612576\pi$
$728$		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	$-0.191115\pi$
$733$	−0.341596	−	0.511235i	−0.0126171	−	0.0188829i	−0.837725	+	0.546093i	$0.816115\pi$
$734$		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	$-0.134048\pi$
$739$	5.04853	+	7.55566i	0.185713	+	0.277939i	−0.726917	+	0.686725i	$0.759048\pi$
$740$		0			0
$741$	−5.58675	−	28.0865i	−0.205234	−	1.03178i
$742$		0			0
$743$	−38.3032	+	15.8657i	−1.40521	+	0.582056i	−0.951098	−	0.308890i	$-0.900042\pi$
$743$	−38.3032	+	15.8657i	−1.40521	+	0.582056i	−0.454109	+	0.890946i	$0.650042\pi$
$744$		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	0.0933574	−	0.995633i	$-0.470240\pi$
$751$	−24.7263	−	24.7263i	−0.902275	−	0.902275i	−0.995633	+	0.0933574i	$0.970240\pi$
$752$		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	$-0.645456\pi$
$757$	15.3171	−	22.9237i	0.556710	−	0.833175i	0.997936	+	0.0642212i	$0.0204563\pi$
$758$		0			0
$759$	3.81290	−	9.20514i	0.138399	−	0.334126i
$760$		0			0
$761$	2.39831	+	5.79004i	0.0869388	+	0.209889i	0.961369	−	0.275262i	$-0.0887646\pi$
$761$	2.39831	+	5.79004i	0.0869388	+	0.209889i	−0.874430	+	0.485151i	$0.838765\pi$
$762$		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	$-0.320957\pi$
$773$	37.5256	−	7.46432i	1.34970	−	0.268473i	0.816418	+	0.577462i	$0.195957\pi$
$774$		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	−0.273090	−	0.961989i	$-0.588046\pi$
$787$	9.74437	−	48.9883i	0.347349	−	1.74624i	0.620439	−	0.784255i	$-0.286954\pi$
$788$		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	−0.949202	−	0.314668i	$-0.898107\pi$
$797$	−24.7495	−	37.0403i	−0.876674	−	1.31203i	0.0725281	−	0.997366i	$-0.476893\pi$
$798$		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	0.475383	−	0.879779i	$-0.342310\pi$
$809$	5.38797	+	2.23177i	0.189431	+	0.0784649i	−0.285952	+	0.958244i	$0.592310\pi$
$810$		0			0
$811$	8.53124	+	5.70039i	0.299572	+	0.200168i	0.696267	−	0.717783i	$-0.254843\pi$
$811$	8.53124	+	5.70039i	0.299572	+	0.200168i	−0.396695	+	0.917951i	$0.629843\pi$
$812$		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	0.308691	+	0.951162i	$0.400109\pi$
$821$	−19.7190	+	29.5116i	−0.688199	+	1.02996i	−0.996890	+	0.0788007i	$0.974891\pi$
$822$		0			0
$823$	−0.550722	+	1.32956i	−0.0191970	+	0.0463456i	−0.933187	−	0.359390i	$-0.882985\pi$
$823$	−0.550722	+	1.32956i	−0.0191970	+	0.0463456i	0.913990	+	0.405736i	$0.132985\pi$
$824$		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	$-0.640076\pi$
$827$	−13.6122	+	2.70763i	−0.473341	+	0.0941534i	−0.0473454	+	0.998879i	$0.515076\pi$
$828$		0			0
$829$	8.09646	−	5.40988i	0.281202	−	0.187893i	−0.406969	−	0.913442i	$-0.633414\pi$
$829$	8.09646	−	5.40988i	0.281202	−	0.187893i	0.688170	+	0.725549i	$0.258414\pi$
$830$		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	0.971639	−	0.236468i	$-0.0759900\pi$
$839$	3.39992	+	8.20812i	0.117378	+	0.283376i	−0.854261	+	0.519844i	$0.825990\pi$
$840$		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	$-0.437262\pi$
$853$	−18.5526	−	12.3964i	−0.635228	−	0.424446i	−0.831053	+	0.556193i	$0.812262\pi$
$854$		0			0
$855$	−12.9459	−	5.36239i	−0.442742	−	0.183390i
$856$		0			0
$857$	−34.9162	+	14.4628i	−1.19272	+	0.494039i	−0.888639	−	0.458608i	$-0.848348\pi$
$857$	−34.9162	+	14.4628i	−1.19272	+	0.494039i	−0.304077	+	0.952647i	$0.598348\pi$
$858$		0			0
$859$	5.27751	+	26.5318i	0.180066	+	0.905255i	0.960130	+	0.279554i	$0.0901867\pi$
$859$	5.27751	+	26.5318i	0.180066	+	0.905255i	−0.780063	+	0.625700i	$0.784813\pi$
$860$		0			0
$861$	−39.3727	−	58.9254i	−1.34182	−	2.00817i
$862$		0			0
$863$			21.2314i			0.722726i	0.932425	+	0.361363i	$0.117689\pi$
$863$			21.2314i			0.722726i	−0.932425	+	0.361363i	$0.882311\pi$
$864$		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	$-0.879120\pi$
$877$	2.10738	−	10.5945i	0.0711613	−	0.357752i	0.999916	+	0.0129422i	$0.00411975\pi$
$878$		0			0
$879$	46.3140	+	46.3140i	1.56213	+	1.56213i
$880$		0			0
$881$	−15.1953	+	15.1953i	−0.511944	+	0.511944i	−0.915122	−	0.403178i	$-0.867906\pi$
$881$	−15.1953	+	15.1953i	−0.511944	+	0.511944i	0.403178	+	0.915122i	$0.367906\pi$
$882$		0			0
$883$	16.8801	+	3.35767i	0.568062	+	0.112995i	0.470761	−	0.882261i	$-0.343979\pi$
$883$	16.8801	+	3.35767i	0.568062	+	0.112995i	0.0973004	+	0.995255i	$0.468979\pi$
$884$		0			0
$885$	0.777462	−	1.16355i	0.0261341	−	0.0391124i
$886$		0			0
$887$	7.36626	−	17.7837i	0.247335	−	0.597119i	−0.750641	−	0.660710i	$-0.770255\pi$
$887$	7.36626	−	17.7837i	0.247335	−	0.597119i	0.997976	+	0.0635908i	$0.0202552\pi$
$888$		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	$-0.789568\pi$
$907$	2.40873	−	3.60492i	0.0799806	−	0.119699i	0.869303	+	0.494279i	$0.164568\pi$
$908$		0			0
$909$	13.7407	+	2.73320i	0.455752	+	0.0906547i
$910$		0			0
$911$	32.8907	−	32.8907i	1.08972	−	1.08972i	0.0941591	−	0.995557i	$-0.469984\pi$
$911$	32.8907	−	32.8907i	1.08972	−	1.08972i	0.995557	−	0.0941591i	$-0.0300162\pi$
$912$		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	−0.199292	−	0.979940i	$-0.563864\pi$
$919$	−31.3195	−	12.9730i	−1.03314	−	0.427939i	−0.833843	+	0.552001i	$0.813864\pi$
$920$		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	$-0.943621\pi$
$929$		−	10.7407i		−	0.352390i	0.984355	−	0.176195i	$-0.0563789\pi$
$930$		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	0.992775	−	0.119992i	$-0.0382869\pi$
$937$	49.2806	+	20.4127i	1.60993	+	0.666853i	0.617151	+	0.786845i	$0.288287\pi$
$938$		0			0
$939$	−19.7828	−	13.2184i	−0.645587	−	0.431367i
$940$		0			0
$941$	−5.66109	+	28.4602i	−0.184546	+	0.927777i	0.771872	+	0.635778i	$0.219321\pi$
$941$	−5.66109	+	28.4602i	−0.184546	+	0.927777i	−0.956418	+	0.292000i	$0.905679\pi$
$942$		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	$-0.312426\pi$
$947$	23.1134	+	4.59754i	0.751084	+	0.149400i	0.195319	+	0.980740i	$0.437426\pi$
$948$		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	−0.890981	−	0.454041i	$-0.849982\pi$
$953$	−17.9673	−	43.3769i	−0.582018	−	1.40512i	0.308963	−	0.951074i	$-0.400018\pi$
$954$		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	0.983498	−	0.180919i	$-0.0579071\pi$
$967$	4.97953	+	12.0217i	0.160131	+	0.386590i	−0.823367	+	0.567509i	$0.807907\pi$
$968$		0			0
$969$	−25.7574	+	62.1840i	−0.827448	+	1.99764i
$970$		0			0
$971$	20.1628	−	30.1758i	0.647055	−	0.968386i	−0.352415	−	0.935844i	$-0.614640\pi$
$971$	20.1628	−	30.1758i	0.647055	−	0.968386i	0.999470	−	0.0325425i	$-0.0103604\pi$
$972$		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	−0.932949	−	0.360009i	$-0.882774\pi$
$977$	−40.4140	−	40.4140i	−1.29296	−	1.29296i	−0.360009	−	0.932949i	$-0.617226\pi$
$978$		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	0.868602	−	0.495510i	$-0.165019\pi$
$983$	35.5045	+	14.7065i	1.13242	+	0.469063i	0.263816	+	0.964573i	$0.415019\pi$
$984$		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	$0.0833674\pi$
$991$			16.3018i			0.517845i	−0.965898	+	0.258922i	$0.916633\pi$
$992$		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	−0.995707	−	0.0925594i	$-0.970495\pi$
$997$	−3.51164	−	17.6542i	−0.111215	−	0.559114i	0.884493	−	0.466554i	$-0.154505\pi$
$998$		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	512.2.i.a.33.2		56
4.3	odd	2		512.2.i.b.33.6		56
8.3	odd	2		64.2.i.a.13.7	yes	56
8.5	even	2		256.2.i.a.145.6		56
24.11	even	2		576.2.bd.a.397.1		56
64.5	even	16	inner	512.2.i.a.481.2		56
64.27	odd	16		64.2.i.a.5.7	✓	56
64.37	even	16		256.2.i.a.113.6		56
64.59	odd	16		512.2.i.b.481.6		56
192.155	even	16		576.2.bd.a.325.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.7	✓	56	64.27	odd	16
64.2.i.a.13.7	yes	56	8.3	odd	2
256.2.i.a.113.6		56	64.37	even	16
256.2.i.a.145.6		56	8.5	even	2
512.2.i.a.33.2		56	1.1	even	1	trivial
512.2.i.a.481.2		56	64.5	even	16	inner
512.2.i.b.33.6		56	4.3	odd	2
512.2.i.b.481.6		56	64.59	odd	16
576.2.bd.a.325.1		56	192.155	even	16
576.2.bd.a.397.1		56	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00147 + 1.33734i) q^{3} +(-0.756852 + 0.150547i) q^{5} +(1.69148 + 4.08359i) q^{7} +(1.06935 - 2.58163i) q^{9} +O(q^{10})\)	\(q+(-2.00147 + 1.33734i) q^{3} +(-0.756852 + 0.150547i) q^{5} +(1.69148 + 4.08359i) q^{7} +(1.06935 - 2.58163i) q^{9} +(0.290161 - 0.434257i) q^{11} +(1.79553 + 0.357153i) q^{13} +(1.31348 - 1.31348i) q^{15} +(-3.04259 - 3.04259i) q^{17} +(-1.26776 + 6.37347i) q^{19} +(-8.84657 - 5.91109i) q^{21} +(-7.32197 - 3.03286i) q^{23} +(-4.06924 + 1.68553i) q^{25} +(-0.0965796 - 0.485538i) q^{27} +(0.690042 + 1.03272i) q^{29} +1.55847i q^{31} +1.25719i q^{33} +(-1.89497 - 2.83602i) q^{35} +(-0.371584 - 1.86808i) q^{37} +(-4.07133 + 1.68640i) q^{39} +(6.15380 + 2.54899i) q^{41} +(-7.03859 - 4.70304i) q^{43} +(-0.420680 + 2.11490i) q^{45} +(-1.12515 - 1.12515i) q^{47} +(-8.86483 + 8.86483i) q^{49} +(10.1586 + 2.02068i) q^{51} +(-3.92962 + 5.88109i) q^{53} +(-0.154233 + 0.372351i) q^{55} +(-5.98610 - 14.4517i) q^{57} +(0.738882 - 0.146973i) q^{59} +(3.34952 - 2.23808i) q^{61} +12.3511 q^{63} -1.41272 q^{65} +(3.05271 - 2.03976i) q^{67} +(18.7106 - 3.72178i) q^{69} +(0.317495 + 0.766500i) q^{71} +(0.292843 - 0.706986i) q^{73} +(5.89032 - 8.81548i) q^{75} +(2.26413 + 0.450363i) q^{77} +(-6.17863 + 6.17863i) q^{79} +(6.77032 + 6.77032i) q^{81} +(-0.663054 + 3.33340i) q^{83} +(2.76085 + 1.84474i) q^{85} +(-2.76219 - 1.14414i) q^{87} +(12.3740 - 5.12547i) q^{89} +(1.57863 + 7.93632i) q^{91} +(-2.08420 - 3.11923i) q^{93} -5.01463i q^{95} +3.44120i q^{97} +(-0.810809 - 1.21346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) \) 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

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Representations

Groups

Database

Properties

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