LMFDB - Embedded newform 256.2.g.c.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(33,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([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("256.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.g (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			33.2
Root			$0.500000 - 0.691860i$ of defining polynomial
Character	$\chi$	$=$	256.33
Dual form			256.2.g.c.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0794708 - 0.191860i) q^{3} +(-0.707107 + 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +O(q^{10})$	\(q+(0.0794708 - 0.191860i) q^{3} +(-0.707107 + 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +(-1.49368 - 3.60607i) q^{11} +(4.50504 + 1.86605i) q^{13} +0.158942i q^{15} -3.05320i q^{17} +(3.87740 + 1.60607i) q^{19} +(-0.255272 - 0.616281i) q^{21} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(1.14288 - 0.473398i) q^{27} +(0.931884 - 2.24977i) q^{29} -6.82843 q^{31} -0.810564 q^{33} +(-0.940816 + 2.27133i) q^{35} +(-3.63349 + 1.50504i) q^{37} +(0.716038 - 0.716038i) q^{39} +(-1.54266 - 1.54266i) q^{41} +(0.748956 + 1.80814i) q^{43} +(-2.09083 - 0.866048i) q^{45} +7.37109i q^{47} -3.31788i q^{49} +(-0.585786 - 0.242641i) q^{51} +(-1.67661 - 4.04770i) q^{53} +(2.11239 + 2.11239i) q^{55} +(0.616281 - 0.616281i) q^{57} +(-10.1200 + 4.19186i) q^{59} +(-1.35873 + 3.28026i) q^{61} +9.49791 q^{63} -3.73210 q^{65} +(-1.99577 + 4.81822i) q^{67} +(-0.0736202 + 0.0304945i) q^{69} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(0.350801 + 0.846909i) q^{75} +(-11.5832 - 4.79793i) q^{77} -9.74996i q^{79} +8.61373i q^{81} +(-9.04642 - 3.74715i) q^{83} +(0.894263 + 2.15894i) q^{85} +(-0.357582 - 0.357582i) q^{87} +(7.58323 - 7.58323i) q^{89} +(14.4708 - 5.99402i) q^{91} +(-0.542661 + 1.31010i) q^{93} -3.21215 q^{95} +3.71423 q^{97} +(4.41664 - 10.6627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 + 8 * q^7	$ 8 q - 4 q^{3} + 8 q^{7} + 4 q^{11} + 8 q^{13} + 4 q^{19} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 32 q^{31} - 16 q^{33} + 16 q^{35} + 8 q^{37} - 16 q^{39} + 8 q^{41} - 12 q^{43} - 16 q^{51} - 8 q^{53} + 16 q^{55} + 16 q^{57} - 20 q^{59} - 24 q^{61} + 40 q^{63} - 36 q^{67} - 32 q^{69} + 24 q^{71} - 32 q^{73} - 12 q^{75} - 16 q^{77} + 20 q^{83} - 8 q^{85} - 56 q^{87} - 16 q^{89} + 40 q^{91} + 16 q^{93} + 8 q^{95} + 32 q^{97} + 28 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 8 * q^7 + 4 * q^11 + 8 * q^13 + 4 * q^19 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 32 * q^31 - 16 * q^33 + 16 * q^35 + 8 * q^37 - 16 * q^39 + 8 * q^41 - 12 * q^43 - 16 * q^51 - 8 * q^53 + 16 * q^55 + 16 * q^57 - 20 * q^59 - 24 * q^61 + 40 * q^63 - 36 * q^67 - 32 * q^69 + 24 * q^71 - 32 * q^73 - 12 * q^75 - 16 * q^77 + 20 * q^83 - 8 * q^85 - 56 * q^87 - 16 * q^89 + 40 * q^91 + 16 * q^93 + 8 * q^95 + 32 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.0794708	−	0.191860i	0.0458825	−	0.110770i	−0.899277	−	0.437380i	$-0.855906\pi$
$3$	0.0794708	−	0.191860i	0.0458825	−	0.110770i	0.945159	+	0.326610i	$0.105906\pi$
$4$		0			0
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	−0.535151	−	0.844756i	$-0.679745\pi$
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	0.218924	+	0.975742i	$0.429745\pi$
$6$		0			0
$7$	2.27133	−	2.27133i	0.858482	−	0.858482i	−0.132677	−	0.991159i	$-0.542357\pi$
$7$	2.27133	−	2.27133i	0.858482	−	0.858482i	0.991159	+	0.132677i	$0.0423573\pi$
$8$		0			0
$9$	2.09083	+	2.09083i	0.696942	+	0.696942i
$10$		0			0
$11$	−1.49368	−	3.60607i	−0.450363	−	1.08727i	−0.972184	−	0.234217i	$-0.924747\pi$
$11$	−1.49368	−	3.60607i	−0.450363	−	1.08727i	0.521821	−	0.853055i	$-0.325253\pi$
$12$		0			0
$13$	4.50504	+	1.86605i	1.24947	+	0.517549i	0.906663	−	0.421856i	$-0.138621\pi$
$13$	4.50504	+	1.86605i	1.24947	+	0.517549i	0.342810	+	0.939405i	$0.388621\pi$
$14$		0			0
$15$			0.158942i			0.0410386i
$16$		0			0
$17$		−	3.05320i		−	0.740511i	−0.928930	−	0.370255i	$-0.879270\pi$
$17$		−	3.05320i		−	0.740511i	0.928930	−	0.370255i	$-0.120730\pi$
$18$		0			0
$19$	3.87740	+	1.60607i	0.889537	+	0.368458i	0.780188	−	0.625545i	$-0.215123\pi$
$19$	3.87740	+	1.60607i	0.889537	+	0.368458i	0.109349	+	0.994003i	$0.465123\pi$
$20$		0			0
$21$	−0.255272	−	0.616281i	−0.0557049	−	0.134484i
$22$		0			0
$23$	−0.271330	−	0.271330i	−0.0565763	−	0.0565763i	0.678253	−	0.734829i	$-0.262738\pi$
$23$	−0.271330	−	0.271330i	−0.0565763	−	0.0565763i	−0.734829	+	0.678253i	$0.762738\pi$
$24$		0			0
$25$	−3.12132	+	3.12132i	−0.624264	+	0.624264i
$26$		0			0
$27$	1.14288	−	0.473398i	0.219948	−	0.0911054i
$28$		0			0
$29$	0.931884	−	2.24977i	0.173047	−	0.417771i	−0.813432	−	0.581660i	$-0.802404\pi$
$29$	0.931884	−	2.24977i	0.173047	−	0.417771i	0.986479	+	0.163888i	$0.0524036\pi$
$30$		0			0
$31$	−6.82843			−1.22642			−0.613211	−	0.789919i	$-0.710122\pi$
$31$	−6.82843			−1.22642			−0.613211	+	0.789919i	$0.710122\pi$
$32$		0			0
$33$	−0.810564			−0.141101
$34$		0			0
$35$	−0.940816	+	2.27133i	−0.159027	+	0.383925i
$36$		0			0
$37$	−3.63349	+	1.50504i	−0.597342	+	0.247427i	−0.660806	−	0.750557i	$-0.729785\pi$
$37$	−3.63349	+	1.50504i	−0.597342	+	0.247427i	0.0634640	+	0.997984i	$0.479785\pi$
$38$		0			0
$39$	0.716038	−	0.716038i	0.114658	−	0.114658i
$40$		0			0
$41$	−1.54266	−	1.54266i	−0.240923	−	0.240923i	0.576309	−	0.817232i	$-0.304493\pi$
$41$	−1.54266	−	1.54266i	−0.240923	−	0.240923i	−0.817232	+	0.576309i	$0.804493\pi$
$42$		0			0
$43$	0.748956	+	1.80814i	0.114215	+	0.275739i	0.970642	−	0.240529i	$-0.0773209\pi$
$43$	0.748956	+	1.80814i	0.114215	+	0.275739i	−0.856427	+	0.516268i	$0.827321\pi$
$44$		0			0
$45$	−2.09083	−	0.866048i	−0.311682	−	0.129103i
$46$		0			0
$47$			7.37109i			1.07518i	0.843205	+	0.537592i	$0.180666\pi$
$47$			7.37109i			1.07518i	−0.843205	+	0.537592i	$0.819334\pi$
$48$		0			0
$49$		−	3.31788i		−	0.473983i
$50$		0			0
$51$	−0.585786	−	0.242641i	−0.0820265	−	0.0339765i
$52$		0			0
$53$	−1.67661	−	4.04770i	−0.230300	−	0.555994i	0.765912	−	0.642945i	$-0.222288\pi$
$53$	−1.67661	−	4.04770i	−0.230300	−	0.555994i	−0.996213	+	0.0869508i	$0.972288\pi$
$54$		0			0
$55$	2.11239	+	2.11239i	0.284834	+	0.284834i
$56$		0			0
$57$	0.616281	−	0.616281i	0.0816284	−	0.0816284i
$58$		0			0
$59$	−10.1200	+	4.19186i	−1.31752	+	0.545734i	−0.927069	−	0.374891i	$-0.877680\pi$
$59$	−10.1200	+	4.19186i	−1.31752	+	0.545734i	−0.390449	+	0.920625i	$0.627680\pi$
$60$		0			0
$61$	−1.35873	+	3.28026i	−0.173967	+	0.419995i	−0.986681	−	0.162669i	$-0.947990\pi$
$61$	−1.35873	+	3.28026i	−0.173967	+	0.419995i	0.812713	+	0.582664i	$0.197990\pi$
$62$		0			0
$63$	9.49791			1.19662
$64$		0			0
$65$	−3.73210			−0.462910
$66$		0			0
$67$	−1.99577	+	4.81822i	−0.243822	+	0.588639i	−0.997656	−	0.0684259i	$-0.978202\pi$
$67$	−1.99577	+	4.81822i	−0.243822	+	0.588639i	0.753834	+	0.657065i	$0.228202\pi$
$68$		0			0
$69$	−0.0736202	+	0.0304945i	−0.00886283	+	0.00367110i
$70$		0			0
$71$	−6.47085	+	6.47085i	−0.767948	+	0.767948i	−0.977745	−	0.209797i	$-0.932720\pi$
$71$	−6.47085	+	6.47085i	−0.767948	+	0.767948i	0.209797	+	0.977745i	$0.432720\pi$
$72$		0			0
$73$	−2.84106	−	2.84106i	−0.332521	−	0.332521i	0.521022	−	0.853543i	$-0.325551\pi$
$73$	−2.84106	−	2.84106i	−0.332521	−	0.332521i	−0.853543	+	0.521022i	$0.825551\pi$
$74$		0			0
$75$	0.350801	+	0.846909i	0.0405070	+	0.0977926i
$76$		0			0
$77$	−11.5832	−	4.79793i	−1.32003	−	0.546775i
$78$		0			0
$79$		−	9.74996i		−	1.09696i	−0.836165	−	0.548478i	$-0.815207\pi$
$79$		−	9.74996i		−	1.09696i	0.836165	−	0.548478i	$-0.184793\pi$
$80$		0			0
$81$			8.61373i			0.957081i
$82$		0			0
$83$	−9.04642	−	3.74715i	−0.992974	−	0.411303i	−0.173758	−	0.984788i	$-0.555591\pi$
$83$	−9.04642	−	3.74715i	−0.992974	−	0.411303i	−0.819216	+	0.573485i	$0.805591\pi$
$84$		0			0
$85$	0.894263	+	2.15894i	0.0969964	+	0.234170i
$86$		0			0
$87$	−0.357582	−	0.357582i	−0.0383368	−	0.0383368i
$88$		0			0
$89$	7.58323	−	7.58323i	0.803821	−	0.803821i	−0.179869	−	0.983691i	$-0.557567\pi$
$89$	7.58323	−	7.58323i	0.803821	−	0.803821i	0.983691	+	0.179869i	$0.0575675\pi$
$90$		0			0
$91$	14.4708	−	5.99402i	1.51696	−	0.628344i
$92$		0			0
$93$	−0.542661	+	1.31010i	−0.0562713	+	0.135851i
$94$		0			0
$95$	−3.21215			−0.329559
$96$		0			0
$97$	3.71423			0.377123			0.188562	−	0.982061i	$-0.439617\pi$
$97$	3.71423			0.377123			0.188562	+	0.982061i	$0.439617\pi$
$98$		0			0
$99$	4.41664	−	10.6627i	0.443889	−	1.07164i
$100$		0			0
$101$	9.04770	−	3.74768i	0.900280	−	0.372908i	0.115952	−	0.993255i	$-0.463008\pi$
$101$	9.04770	−	3.74768i	0.900280	−	0.372908i	0.784328	+	0.620347i	$0.213008\pi$
$102$		0			0
$103$	−0.450688	+	0.450688i	−0.0444076	+	0.0444076i	−0.728962	−	0.684554i	$-0.759997\pi$
$103$	−0.450688	+	0.450688i	−0.0444076	+	0.0444076i	0.684554	+	0.728962i	$0.259997\pi$
$104$		0			0
$105$	0.361009	+	0.361009i	0.0352309	+	0.0352309i
$106$		0			0
$107$	6.82420	+	16.4751i	0.659720	+	1.59271i	0.798236	+	0.602345i	$0.205767\pi$
$107$	6.82420	+	16.4751i	0.659720	+	1.59271i	−0.138515	+	0.990360i	$0.544233\pi$
$108$		0			0
$109$	7.20664	+	2.98509i	0.690271	+	0.285920i	0.700113	−	0.714032i	$-0.253133\pi$
$109$	7.20664	+	2.98509i	0.690271	+	0.285920i	−0.00984205	+	0.999952i	$0.503133\pi$
$110$		0			0
$111$			0.816726i			0.0775202i
$112$		0			0
$113$			8.76744i			0.824771i	0.911009	+	0.412386i	$0.135304\pi$
$113$			8.76744i			0.824771i	−0.911009	+	0.412386i	$0.864696\pi$
$114$		0			0
$115$	0.271330	+	0.112389i	0.0253017	+	0.0104803i
$116$		0			0
$117$	5.51767	+	13.3208i	0.510109	+	1.23151i
$118$		0			0
$119$	−6.93484	−	6.93484i	−0.635715	−	0.635715i
$120$		0			0
$121$	−2.99450	+	2.99450i	−0.272227	+	0.272227i
$122$		0			0
$123$	−0.418571	+	0.173378i	−0.0377412	+	0.0156329i
$124$		0			0
$125$	2.75736	−	6.65685i	0.246626	−	0.595407i
$126$		0			0
$127$	11.4642			1.01728			0.508641	−	0.860979i	$-0.330148\pi$
$127$	11.4642			1.01728			0.508641	+	0.860979i	$0.330148\pi$
$128$		0			0
$129$	0.406429			0.0357841
$130$		0			0
$131$	4.32211	−	10.4345i	0.377625	−	0.911667i	−0.614785	−	0.788694i	$-0.710757\pi$
$131$	4.32211	−	10.4345i	0.377625	−	0.911667i	0.992410	−	0.122972i	$-0.0392426\pi$
$132$		0			0
$133$	12.4548	−	5.15894i	1.07997	−	0.447337i
$134$		0			0
$135$	−0.669485	+	0.669485i	−0.0576201	+	0.0576201i
$136$		0			0
$137$	−3.42429	−	3.42429i	−0.292557	−	0.292557i	0.545533	−	0.838090i	$-0.316327\pi$
$137$	−3.42429	−	3.42429i	−0.292557	−	0.292557i	−0.838090	+	0.545533i	$0.816327\pi$
$138$		0			0
$139$	−7.35745	−	17.7625i	−0.624051	−	1.50659i	−0.846907	−	0.531741i	$-0.821538\pi$
$139$	−7.35745	−	17.7625i	−0.624051	−	1.50659i	0.222856	−	0.974851i	$-0.428462\pi$
$140$		0			0
$141$	1.41421	+	0.585786i	0.119098	+	0.0493321i
$142$		0			0
$143$		−	19.0328i		−	1.59160i
$144$		0			0
$145$			1.86377i			0.154778i
$146$		0			0
$147$	−0.636568	−	0.263675i	−0.0525032	−	0.0217475i
$148$		0			0
$149$	0.931884	+	2.24977i	0.0763429	+	0.184308i	0.957443	−	0.288621i	$-0.0931967\pi$
$149$	0.931884	+	2.24977i	0.0763429	+	0.184308i	−0.881101	+	0.472929i	$0.843197\pi$
$150$		0			0
$151$	4.21395	+	4.21395i	0.342926	+	0.342926i	0.857466	−	0.514540i	$-0.172037\pi$
$151$	4.21395	+	4.21395i	0.342926	+	0.342926i	−0.514540	+	0.857466i	$0.672037\pi$
$152$		0			0
$153$	6.38372	−	6.38372i	0.516093	−	0.516093i
$154$		0			0
$155$	4.82843	−	2.00000i	0.387829	−	0.160644i
$156$		0			0
$157$	−5.84401	+	14.1087i	−0.466403	+	1.12600i	0.499319	+	0.866418i	$0.333583\pi$
$157$	−5.84401	+	14.1087i	−0.466403	+	1.12600i	−0.965722	+	0.259578i	$0.916417\pi$
$158$		0			0
$159$	−0.909832			−0.0721543
$160$		0			0
$161$	−1.23256			−0.0971395
$162$		0			0
$163$	−2.72369	+	6.57558i	−0.213336	+	0.515039i	−0.993932	−	0.109997i	$-0.964916\pi$
$163$	−2.72369	+	6.57558i	−0.213336	+	0.515039i	0.780596	+	0.625036i	$0.214916\pi$
$164$		0			0
$165$	0.573155	−	0.237409i	0.0446201	−	0.0184822i
$166$		0			0
$167$	−3.26355	+	3.26355i	−0.252541	+	0.252541i	−0.822012	−	0.569471i	$-0.807148\pi$
$167$	−3.26355	+	3.26355i	−0.252541	+	0.252541i	0.569471	+	0.822012i	$0.307148\pi$
$168$		0			0
$169$	7.62086	+	7.62086i	0.586220	+	0.586220i
$170$		0			0
$171$	4.74896	+	11.4650i	0.363162	+	0.876750i
$172$		0			0
$173$	−6.86605	−	2.84401i	−0.522016	−	0.216226i	0.106086	−	0.994357i	$-0.466168\pi$
$173$	−6.86605	−	2.84401i	−0.522016	−	0.216226i	−0.628102	+	0.778131i	$0.716168\pi$
$174$		0			0
$175$			14.1791i			1.07184i
$176$		0			0
$177$			2.27476i			0.170981i
$178$		0			0
$179$	−1.79370	−	0.742977i	−0.134068	−	0.0555327i	0.314641	−	0.949211i	$-0.398116\pi$
$179$	−1.79370	−	0.742977i	−0.134068	−	0.0555327i	−0.448709	+	0.893678i	$0.648116\pi$
$180$		0			0
$181$	−6.12132	−	14.7782i	−0.454994	−	1.09845i	−0.970399	−	0.241506i	$-0.922359\pi$
$181$	−6.12132	−	14.7782i	−0.454994	−	1.09845i	0.515405	−	0.856947i	$-0.327641\pi$
$182$		0			0
$183$	0.521370	+	0.521370i	0.0385408	+	0.0385408i
$184$		0			0
$185$	2.12845	−	2.12845i	0.156487	−	0.156487i
$186$		0			0
$187$	−11.0101	+	4.56052i	−0.805137	+	0.333499i
$188$		0			0
$189$	1.52062	−	3.67111i	0.110609	−	0.267034i
$190$		0			0
$191$	6.19266			0.448085			0.224043	−	0.974579i	$-0.428075\pi$
$191$	6.19266			0.448085			0.224043	+	0.974579i	$0.428075\pi$
$192$		0			0
$193$	14.5784			1.04938			0.524688	−	0.851295i	$-0.324182\pi$
$193$	14.5784			1.04938			0.524688	+	0.851295i	$0.324182\pi$
$194$		0			0
$195$	−0.296593	+	0.716038i	−0.0212395	+	0.0512766i
$196$		0			0
$197$	−18.5025	+	7.66398i	−1.31825	+	0.546036i	−0.927280	−	0.374368i	$-0.877860\pi$
$197$	−18.5025	+	7.66398i	−1.31825	+	0.546036i	−0.390968	+	0.920404i	$0.627860\pi$
$198$		0			0
$199$	12.3777	−	12.3777i	0.877435	−	0.877435i	−0.115834	−	0.993269i	$-0.536954\pi$
$199$	12.3777	−	12.3777i	0.877435	−	0.877435i	0.993269	+	0.115834i	$0.0369540\pi$
$200$		0			0
$201$	0.765816	+	0.765816i	0.0540165	+	0.0540165i
$202$		0			0
$203$	−2.99335	−	7.22658i	−0.210092	−	0.507207i
$204$		0			0
$205$	1.54266	+	0.638991i	0.107744	+	0.0446291i
$206$		0			0
$207$		−	1.13461i		−	0.0788608i
$208$		0			0
$209$		−	16.3812i		−	1.13311i
$210$		0			0
$211$	3.54851	+	1.46984i	0.244290	+	0.101188i	0.501469	−	0.865176i	$-0.332793\pi$
$211$	3.54851	+	1.46984i	0.244290	+	0.101188i	−0.257179	+	0.966364i	$0.582793\pi$
$212$		0			0
$213$	0.727250	+	1.75574i	0.0498304	+	0.120301i
$214$		0			0
$215$	−1.05918	−	1.05918i	−0.0722358	−	0.0722358i
$216$		0			0
$217$	−15.5096	+	15.5096i	−1.05286	+	1.05286i
$218$		0			0
$219$	−0.770865	+	0.319303i	−0.0520903	+	0.0215765i
$220$		0			0
$221$	5.69743	−	13.7548i	0.383250	−	0.925248i
$222$		0			0
$223$	−27.5550			−1.84522			−0.922611	−	0.385732i	$-0.873949\pi$
$223$	−27.5550			−1.84522			−0.922611	+	0.385732i	$0.873949\pi$
$224$		0			0
$225$	−13.0523			−0.870152
$226$		0			0
$227$	−6.02694	+	14.5503i	−0.400022	+	0.965738i	0.587638	+	0.809124i	$0.300058\pi$
$227$	−6.02694	+	14.5503i	−0.400022	+	0.965738i	−0.987660	+	0.156614i	$0.949942\pi$
$228$		0			0
$229$	−18.2777	+	7.57088i	−1.20783	+	0.500298i	−0.893520	−	0.449024i	$-0.851772\pi$
$229$	−18.2777	+	7.57088i	−1.20783	+	0.500298i	−0.314306	+	0.949322i	$0.601772\pi$
$230$		0			0
$231$	−1.84106	+	1.84106i	−0.121133	+	0.121133i
$232$		0			0
$233$	−6.70939	−	6.70939i	−0.439547	−	0.439547i	0.452313	−	0.891859i	$-0.350599\pi$
$233$	−6.70939	−	6.70939i	−0.439547	−	0.439547i	−0.891859	+	0.452313i	$0.850599\pi$
$234$		0			0
$235$	−2.15894	−	5.21215i	−0.140834	−	0.340003i
$236$		0			0
$237$	−1.87062	−	0.774837i	−0.121510	−	0.0503311i
$238$		0			0
$239$			26.1995i			1.69471i	0.531030	+	0.847353i	$0.321805\pi$
$239$			26.1995i			1.69471i	−0.531030	+	0.847353i	$0.678195\pi$
$240$		0			0
$241$		−	13.6734i		−	0.880781i	−0.897806	−	0.440391i	$-0.854840\pi$
$241$		−	13.6734i		−	0.880781i	0.897806	−	0.440391i	$-0.145160\pi$
$242$		0			0
$243$	5.08128	+	2.10473i	0.325964	+	0.135019i
$244$		0			0
$245$	0.971786	+	2.34610i	0.0620851	+	0.149887i
$246$		0			0
$247$	14.4708	+	14.4708i	0.920758	+	0.920758i
$248$		0			0
$249$	−1.43785	+	1.43785i	−0.0911203	+	0.0911203i
$250$		0			0
$251$	−13.2054	+	5.46984i	−0.833515	+	0.345253i	−0.758293	−	0.651913i	$-0.773967\pi$
$251$	−13.2054	+	5.46984i	−0.833515	+	0.345253i	−0.0752219	+	0.997167i	$0.523967\pi$
$252$		0			0
$253$	−0.573155	+	1.38372i	−0.0360340	+	0.0869937i
$254$		0			0
$255$	0.485281			0.0303895
$256$		0			0
$257$	−20.0656			−1.25166			−0.625828	−	0.779961i	$-0.715239\pi$
$257$	−20.0656			−1.25166			−0.625828	+	0.779961i	$0.715239\pi$
$258$		0			0
$259$	−4.83441	+	11.6713i	−0.300395	+	0.725219i
$260$		0			0
$261$	6.65228	−	2.75546i	0.411766	−	0.170559i
$262$		0			0
$263$	−4.74976	+	4.74976i	−0.292883	+	0.292883i	−0.838218	−	0.545335i	$-0.816402\pi$
$263$	−4.74976	+	4.74976i	−0.292883	+	0.292883i	0.545335	+	0.838218i	$0.316402\pi$
$264$		0			0
$265$	2.37109	+	2.37109i	0.145655	+	0.145655i
$266$		0			0
$267$	−0.852270	−	2.05756i	−0.0521581	−	0.125921i
$268$		0			0
$269$	22.3818	+	9.27086i	1.36464	+	0.565254i	0.940331	−	0.340262i	$-0.110516\pi$
$269$	22.3818	+	9.27086i	1.36464	+	0.565254i	0.424313	+	0.905516i	$0.360516\pi$
$270$		0			0
$271$			0.693146i			0.0421056i	0.999778	+	0.0210528i	$0.00670181\pi$
$271$			0.693146i			0.0421056i	−0.999778	+	0.0210528i	$0.993298\pi$
$272$		0			0
$273$		−	3.25272i		−	0.196864i
$274$		0			0
$275$	15.9180	+	6.59344i	0.959890	+	0.397600i
$276$		0			0
$277$	−11.1898	−	27.0147i	−0.672332	−	1.62315i	−0.777637	−	0.628713i	$-0.783582\pi$
$277$	−11.1898	−	27.0147i	−0.672332	−	1.62315i	0.105305	−	0.994440i	$-0.466418\pi$
$278$		0			0
$279$	−14.2771	−	14.2771i	−0.854745	−	0.854745i
$280$		0			0
$281$	−6.97958	+	6.97958i	−0.416367	+	0.416367i	−0.883949	−	0.467582i	$-0.845125\pi$
$281$	−6.97958	+	6.97958i	−0.416367	+	0.416367i	0.467582	+	0.883949i	$0.345125\pi$
$282$		0			0
$283$	14.6079	−	6.05078i	0.868348	−	0.359682i	0.0963814	−	0.995344i	$-0.469273\pi$
$283$	14.6079	−	6.05078i	0.868348	−	0.359682i	0.771967	+	0.635663i	$0.219273\pi$
$284$		0			0
$285$	−0.255272	+	0.616281i	−0.0151210	+	0.0365053i
$286$		0			0
$287$	−7.00778			−0.413656
$288$		0			0
$289$	7.67794			0.451644
$290$		0			0
$291$	0.295173	−	0.712611i	0.0173034	−	0.0417740i
$292$		0			0
$293$	9.85571	−	4.08237i	0.575777	−	0.238495i	−0.0757415	−	0.997127i	$-0.524132\pi$
$293$	9.85571	−	4.08237i	0.575777	−	0.238495i	0.651518	+	0.758633i	$0.274132\pi$
$294$		0			0
$295$	5.92818	−	5.92818i	0.345152	−	0.345152i
$296$		0			0
$297$	−3.41421	−	3.41421i	−0.198113	−	0.198113i
$298$		0			0
$299$	−0.716038	−	1.72867i	−0.0414096	−	0.0999715i
$300$		0			0
$301$	5.80801	+	2.40576i	0.334768	+	0.138666i
$302$		0			0
$303$		−	2.03372i		−	0.116834i
$304$		0			0
$305$		−	2.71746i		−	0.155601i
$306$		0			0
$307$	6.96272	+	2.88406i	0.397384	+	0.164602i	0.572421	−	0.819960i	$-0.306004\pi$
$307$	6.96272	+	2.88406i	0.397384	+	0.164602i	−0.175037	+	0.984562i	$0.556004\pi$
$308$		0			0
$309$	0.0506522	+	0.122285i	0.00288150	+	0.00695656i
$310$		0			0
$311$	−4.65020	−	4.65020i	−0.263689	−	0.263689i	0.562862	−	0.826551i	$-0.309700\pi$
$311$	−4.65020	−	4.65020i	−0.263689	−	0.263689i	−0.826551	+	0.562862i	$0.809700\pi$
$312$		0			0
$313$	−0.325668	+	0.325668i	−0.0184078	+	0.0184078i	−0.716251	−	0.697843i	$-0.754143\pi$
$313$	−0.325668	+	0.325668i	−0.0184078	+	0.0184078i	0.697843	+	0.716251i	$0.254143\pi$
$314$		0			0
$315$	−6.71604	+	2.78187i	−0.378406	+	0.156741i
$316$		0			0
$317$	−7.92866	+	19.1415i	−0.445318	+	1.07509i	0.528738	+	0.848785i	$0.322665\pi$
$317$	−7.92866	+	19.1415i	−0.445318	+	1.07509i	−0.974056	+	0.226307i	$0.927335\pi$
$318$		0			0
$319$	−9.50477			−0.532165
$320$		0			0
$321$	3.70322			0.206694
$322$		0			0
$323$	4.90367	−	11.8385i	0.272847	−	0.658712i
$324$		0			0
$325$	−19.8862	+	8.23714i	−1.10309	+	0.456914i
$326$		0			0
$327$	1.14544	−	1.14544i	0.0633427	−	0.0633427i
$328$		0			0
$329$	16.7422	+	16.7422i	0.923026	+	0.923026i
$330$		0			0
$331$	−5.91798	−	14.2873i	−0.325281	−	0.785299i	−0.998930	−	0.0462470i	$-0.985274\pi$
$331$	−5.91798	−	14.2873i	−0.325281	−	0.785299i	0.673649	−	0.739052i	$-0.264726\pi$
$332$		0			0
$333$	−10.7438	−	4.45021i	−0.588755	−	0.243870i
$334$		0			0
$335$		−	3.99154i		−	0.218081i
$336$		0			0
$337$			4.44955i			0.242383i	0.992629	+	0.121191i	$0.0386715\pi$
$337$			4.44955i			0.242383i	−0.992629	+	0.121191i	$0.961329\pi$
$338$		0			0
$339$	1.68212	+	0.696756i	0.0913600	+	0.0378426i
$340$		0			0
$341$	10.1995	+	24.6238i	0.552335	+	1.33345i
$342$		0			0
$343$	8.36330	+	8.36330i	0.451576	+	0.451576i
$344$		0			0
$345$	0.0431257	−	0.0431257i	0.00232181	−	0.00232181i
$346$		0			0
$347$	7.87485	−	3.26187i	0.422744	−	0.175106i	−0.161161	−	0.986928i	$-0.551524\pi$
$347$	7.87485	−	3.26187i	0.422744	−	0.175106i	0.583905	+	0.811822i	$0.301524\pi$
$348$		0			0
$349$	12.9387	−	31.2369i	0.692595	−	1.67207i	−0.0468913	−	0.998900i	$-0.514931\pi$
$349$	12.9387	−	31.2369i	0.692595	−	1.67207i	0.739486	−	0.673172i	$-0.235069\pi$
$350$		0			0
$351$	6.03212			0.321971
$352$		0			0
$353$	20.7013			1.10182			0.550911	−	0.834564i	$-0.314280\pi$
$353$	20.7013			1.10182			0.550911	+	0.834564i	$0.314280\pi$
$354$		0			0
$355$	2.68031	−	6.47085i	0.142256	−	0.343437i
$356$		0			0
$357$	−1.88163	+	0.779397i	−0.0995865	+	0.0412501i
$358$		0			0
$359$	19.9483	−	19.9483i	1.05283	−	1.05283i	0.0543091	−	0.998524i	$-0.482704\pi$
$359$	19.9483	−	19.9483i	1.05283	−	1.05283i	0.998524	−	0.0543091i	$-0.0172956\pi$
$360$		0			0
$361$	−0.980242	−	0.980242i	−0.0515917	−	0.0515917i
$362$		0			0
$363$	0.336548	+	0.812498i	0.0176642	+	0.0426451i
$364$		0			0
$365$	2.84106	+	1.17680i	0.148708	+	0.0615968i
$366$		0			0
$367$		−	9.14270i		−	0.477245i	−0.971112	−	0.238623i	$-0.923304\pi$
$367$		−	9.14270i		−	0.477245i	0.971112	−	0.238623i	$-0.0766959\pi$
$368$		0			0
$369$		−	6.45087i		−	0.335819i
$370$		0			0
$371$	−13.0018	−	5.38552i	−0.675020	−	0.279602i
$372$		0			0
$373$	3.71974	+	8.98024i	0.192601	+	0.464979i	0.990449	−	0.137879i	$-0.0440285\pi$
$373$	3.71974	+	8.98024i	0.192601	+	0.464979i	−0.797848	+	0.602858i	$0.794028\pi$
$374$		0			0
$375$	−1.05805	−	1.05805i	−0.0546375	−	0.0546375i
$376$		0			0
$377$	8.39635	−	8.39635i	0.432434	−	0.432434i
$378$		0			0
$379$	−7.80216	+	3.23176i	−0.400770	+	0.166004i	−0.573959	−	0.818884i	$-0.694593\pi$
$379$	−7.80216	+	3.23176i	−0.400770	+	0.166004i	0.173189	+	0.984889i	$0.444593\pi$
$380$		0			0
$381$	0.911069	−	2.19951i	0.0466755	−	0.112685i
$382$		0			0
$383$	28.4633			1.45440			0.727202	−	0.686423i	$-0.240820\pi$
$383$	28.4633			1.45440			0.727202	+	0.686423i	$0.240820\pi$
$384$		0			0
$385$	9.59587			0.489051
$386$		0			0
$387$	−2.21457	+	5.34644i	−0.112573	+	0.271775i
$388$		0			0
$389$	21.0834	−	8.73304i	1.06897	−	0.442783i	0.222344	−	0.974968i	$-0.428629\pi$
$389$	21.0834	−	8.73304i	1.06897	−	0.442783i	0.846628	+	0.532185i	$0.178629\pi$
$390$		0			0
$391$	−0.828427	+	0.828427i	−0.0418954	+	0.0418954i
$392$		0			0
$393$	−1.65848	−	1.65848i	−0.0836591	−	0.0836591i
$394$		0			0
$395$	2.85570	+	6.89426i	0.143686	+	0.346888i
$396$		0			0
$397$	6.46808	+	2.67916i	0.324623	+	0.134463i	0.539043	−	0.842278i	$-0.318786\pi$
$397$	6.46808	+	2.67916i	0.324623	+	0.134463i	−0.214420	+	0.976742i	$0.568786\pi$
$398$		0			0
$399$		−	2.79956i		−	0.140153i
$400$		0			0
$401$			24.9871i			1.24780i	0.781505	+	0.623898i	$0.214452\pi$
$401$			24.9871i			1.24780i	−0.781505	+	0.623898i	$0.785548\pi$
$402$		0			0
$403$	−30.7623	−	12.7422i	−1.53238	−	0.634733i
$404$		0			0
$405$	−2.52290	−	6.09083i	−0.125364	−	0.302656i
$406$		0			0
$407$	10.8546	+	10.8546i	0.538041	+	0.538041i
$408$		0			0
$409$	9.19951	−	9.19951i	0.454887	−	0.454887i	−0.442086	−	0.896973i	$-0.645761\pi$
$409$	9.19951	−	9.19951i	0.454887	−	0.454887i	0.896973	+	0.442086i	$0.145761\pi$
$410$		0			0
$411$	−0.929115	+	0.384852i	−0.0458298	+	0.0189833i
$412$		0			0
$413$	−13.4649	+	32.5071i	−0.662563	+	1.59957i
$414$		0			0
$415$	7.49430			0.367881
$416$		0			0
$417$	−3.99260			−0.195519
$418$		0			0
$419$	10.4739	−	25.2863i	0.511685	−	1.23532i	−0.431217	−	0.902248i	$-0.641916\pi$
$419$	10.4739	−	25.2863i	0.511685	−	1.23532i	0.942902	−	0.333070i	$-0.108084\pi$
$420$		0			0
$421$	16.6841	−	6.91080i	0.813135	−	0.336812i	0.0629310	−	0.998018i	$-0.479955\pi$
$421$	16.6841	−	6.91080i	0.813135	−	0.336812i	0.750204	+	0.661206i	$0.229955\pi$
$422$		0			0
$423$	−15.4117	+	15.4117i	−0.749341	+	0.749341i
$424$		0			0
$425$	9.53003	+	9.53003i	0.462274	+	0.462274i
$426$		0			0
$427$	4.36444	+	10.5367i	0.211210	+	0.509906i
$428$		0			0
$429$	−3.65162	−	1.51255i	−0.176302	−	0.0730267i
$430$		0			0
$431$		−	26.5985i		−	1.28121i	−0.767872	−	0.640603i	$-0.778684\pi$
$431$		−	26.5985i		−	1.28121i	0.767872	−	0.640603i	$-0.221316\pi$
$432$		0			0
$433$			9.96788i			0.479026i	0.970893	+	0.239513i	$0.0769878\pi$
$433$			9.96788i			0.479026i	−0.970893	+	0.239513i	$0.923012\pi$
$434$		0			0
$435$	0.357582	+	0.148115i	0.0171447	+	0.00710158i
$436$		0			0
$437$	−0.616281	−	1.48783i	−0.0294807	−	0.0711727i
$438$		0			0
$439$	−17.4631	−	17.4631i	−0.833466	−	0.833466i	0.154523	−	0.987989i	$-0.450616\pi$
$439$	−17.4631	−	17.4631i	−0.833466	−	0.833466i	−0.987989	+	0.154523i	$0.950616\pi$
$440$		0			0
$441$	6.93712	−	6.93712i	0.330339	−	0.330339i
$442$		0			0
$443$	34.7377	−	14.3888i	1.65044	−	0.683634i	0.653149	−	0.757229i	$-0.273447\pi$
$443$	34.7377	−	14.3888i	1.65044	−	0.683634i	0.997288	+	0.0735956i	$0.0234474\pi$
$444$		0			0
$445$	−3.14108	+	7.58323i	−0.148901	+	0.359480i
$446$		0			0
$447$	0.505697			0.0239186
$448$		0			0
$449$	−8.35000			−0.394061			−0.197030	−	0.980397i	$-0.563130\pi$
$449$	−8.35000			−0.394061			−0.197030	+	0.980397i	$0.563130\pi$
$450$		0			0
$451$	−3.25870	+	7.86720i	−0.153446	+	0.370452i
$452$		0			0
$453$	1.14337	−	0.473601i	0.0537203	−	0.0222517i
$454$		0			0
$455$	−8.47682	+	8.47682i	−0.397400	+	0.397400i
$456$		0			0
$457$	−18.0734	−	18.0734i	−0.845436	−	0.845436i	0.144123	−	0.989560i	$-0.453964\pi$
$457$	−18.0734	−	18.0734i	−0.845436	−	0.845436i	−0.989560	+	0.144123i	$0.953964\pi$
$458$		0			0
$459$	−1.44538	−	3.48946i	−0.0674646	−	0.162874i
$460$		0			0
$461$	−26.4451	−	10.9539i	−1.23167	−	0.510175i	−0.330569	−	0.943782i	$-0.607241\pi$
$461$	−26.4451	−	10.9539i	−1.23167	−	0.510175i	−0.901102	+	0.433607i	$0.857241\pi$
$462$		0			0
$463$		−	4.94169i		−	0.229660i	−0.993385	−	0.114830i	$-0.963368\pi$
$463$		−	4.94169i		−	0.229660i	0.993385	−	0.114830i	$-0.0366323\pi$
$464$		0			0
$465$		−	1.08532i		−	0.0503306i
$466$		0			0
$467$	20.6806	+	8.56617i	0.956983	+	0.396395i	0.805851	−	0.592118i	$-0.201708\pi$
$467$	20.6806	+	8.56617i	0.956983	+	0.396395i	0.151132	+	0.988514i	$0.451708\pi$
$468$		0			0
$469$	6.41071	+	15.4768i	0.296019	+	0.714653i
$470$		0			0
$471$	2.24246	+	2.24246i	0.103327	+	0.103327i
$472$		0			0
$473$	5.40158	−	5.40158i	0.248365	−	0.248365i
$474$		0			0
$475$	−17.1157	+	7.08955i	−0.785322	+	0.325291i
$476$		0			0
$477$	4.95753	−	11.9685i	0.226990	−	0.548002i
$478$		0			0
$479$	5.50637			0.251592			0.125796	−	0.992056i	$-0.459851\pi$
$479$	5.50637			0.251592			0.125796	+	0.992056i	$0.459851\pi$
$480$		0			0
$481$	−19.1775			−0.874418
$482$		0			0
$483$	−0.0979527	+	0.236479i	−0.00445700	+	0.0107602i
$484$		0			0
$485$	−2.62636	+	1.08787i	−0.119257	+	0.0493978i
$486$		0			0
$487$	−24.9561	+	24.9561i	−1.13087	+	1.13087i	−0.140837	+	0.990033i	$0.544979\pi$
$487$	−24.9561	+	24.9561i	−1.13087	+	1.13087i	−0.990033	+	0.140837i	$0.955021\pi$
$488$		0			0
$489$	1.04513	+	1.04513i	0.0472626	+	0.0472626i
$490$		0			0
$491$	4.79438	+	11.5746i	0.216367	+	0.522357i	0.994377	−	0.105895i	$-0.0337708\pi$
$491$	4.79438	+	11.5746i	0.216367	+	0.522357i	−0.778010	+	0.628252i	$0.783771\pi$
$492$		0			0
$493$	−6.86900	−	2.84523i	−0.309364	−	0.128143i
$494$		0			0
$495$			8.83327i			0.397026i
$496$		0			0
$497$			29.3949i			1.31854i
$498$		0			0
$499$	8.71684	+	3.61063i	0.390219	+	0.161634i	0.569162	−	0.822225i	$-0.307268\pi$
$499$	8.71684	+	3.61063i	0.390219	+	0.161634i	−0.178943	+	0.983859i	$0.557268\pi$
$500$		0			0
$501$	0.366786	+	0.885499i	0.0163868	+	0.0395612i
$502$		0			0
$503$	−5.07960	−	5.07960i	−0.226488	−	0.226488i	0.584736	−	0.811224i	$-0.301198\pi$
$503$	−5.07960	−	5.07960i	−0.226488	−	0.226488i	−0.811224	+	0.584736i	$0.801198\pi$
$504$		0			0
$505$	−5.30002	+	5.30002i	−0.235848	+	0.235848i
$506$		0			0
$507$	2.06777	−	0.856498i	0.0918329	−	0.0380384i
$508$		0			0
$509$	13.5628	−	32.7435i	0.601161	−	1.45133i	−0.271227	−	0.962515i	$-0.587429\pi$
$509$	13.5628	−	32.7435i	0.601161	−	1.45133i	0.872388	−	0.488815i	$-0.162571\pi$
$510$		0			0
$511$	−12.9060			−0.570926
$512$		0			0
$513$	5.19173			0.229221
$514$		0			0
$515$	0.186681	−	0.450688i	0.00822614	−	0.0198597i
$516$		0			0
$517$	26.5807	−	11.0101i	1.16902	−	0.484223i
$518$		0			0
$519$	−1.09130	+	1.09130i	−0.0479028	+	0.0479028i
$520$		0			0
$521$	−17.4496	−	17.4496i	−0.764479	−	0.764479i	0.212650	−	0.977129i	$-0.431791\pi$
$521$	−17.4496	−	17.4496i	−0.764479	−	0.764479i	−0.977129	+	0.212650i	$0.931791\pi$
$522$		0			0
$523$	16.6581	+	40.2163i	0.728410	+	1.75854i	0.647825	+	0.761789i	$0.275679\pi$
$523$	16.6581	+	40.2163i	0.728410	+	1.75854i	0.0805847	+	0.996748i	$0.474321\pi$
$524$		0			0
$525$	2.72040	+	1.12682i	0.118728	+	0.0491787i
$526$		0			0
$527$			20.8486i			0.908179i
$528$		0			0
$529$		−	22.8528i		−	0.993598i
$530$		0			0
$531$	−29.9237	−	12.3948i	−1.29858	−	0.537889i
$532$		0			0
$533$	−4.07107	−	9.82843i	−0.176338	−	0.425716i
$534$		0			0
$535$	−9.65087	−	9.65087i	−0.417244	−	0.417244i
$536$		0			0
$537$	−0.285094	+	0.285094i	−0.0123027	+	0.0123027i
$538$		0			0
$539$	−11.9645	+	4.95587i	−0.515349	+	0.213464i
$540$		0			0
$541$	−15.9692	+	38.5531i	−0.686571	+	1.65753i	0.0650071	+	0.997885i	$0.479293\pi$
$541$	−15.9692	+	38.5531i	−0.686571	+	1.65753i	−0.751578	+	0.659644i	$0.770707\pi$
$542$		0			0
$543$	−3.32180			−0.142552
$544$		0			0
$545$	−5.97018			−0.255734
$546$		0			0
$547$	0.383100	−	0.924886i	0.0163802	−	0.0395453i	−0.915478	−	0.402368i	$-0.868187\pi$
$547$	0.383100	−	0.924886i	0.0163802	−	0.0395453i	0.931858	+	0.362823i	$0.118187\pi$
$548$		0			0
$549$	−9.69932	+	4.01759i	−0.413957	+	0.171467i
$550$		0			0
$551$	7.22658	−	7.22658i	0.307863	−	0.307863i
$552$		0			0
$553$	−22.1454	−	22.1454i	−0.941717	−	0.941717i
$554$		0			0
$555$	−0.239213	−	0.577512i	−0.0101540	−	0.0245140i
$556$		0			0
$557$	−8.29127	−	3.43436i	−0.351312	−	0.145518i	0.200047	−	0.979786i	$-0.435891\pi$
$557$	−8.29127	−	3.43436i	−0.351312	−	0.145518i	−0.551359	+	0.834268i	$0.685891\pi$
$558$		0			0
$559$			9.54333i			0.403640i
$560$		0			0
$561$			2.47482i			0.104487i
$562$		0			0
$563$	−22.7143	−	9.40857i	−0.957293	−	0.396524i	−0.151326	−	0.988484i	$-0.548354\pi$
$563$	−22.7143	−	9.40857i	−0.957293	−	0.396524i	−0.805967	+	0.591960i	$0.798354\pi$
$564$		0			0
$565$	−2.56792	−	6.19951i	−0.108033	−	0.260816i
$566$		0			0
$567$	19.5646	+	19.5646i	0.821637	+	0.821637i
$568$		0			0
$569$	−16.6413	+	16.6413i	−0.697639	+	0.697639i	−0.963901	−	0.266262i	$-0.914211\pi$
$569$	−16.6413	+	16.6413i	−0.697639	+	0.697639i	0.266262	+	0.963901i	$0.414211\pi$
$570$		0			0
$571$	9.37532	−	3.88338i	0.392345	−	0.162515i	−0.177785	−	0.984069i	$-0.556893\pi$
$571$	9.37532	−	3.88338i	0.392345	−	0.162515i	0.570129	+	0.821555i	$0.306893\pi$
$572$		0			0
$573$	0.492136	−	1.18812i	0.0205593	−	0.0496345i
$574$		0			0
$575$	1.69382			0.0706371
$576$		0			0
$577$	−23.0348			−0.958951			−0.479476	−	0.877555i	$-0.659173\pi$
$577$	−23.0348			−0.958951			−0.479476	+	0.877555i	$0.659173\pi$
$578$		0			0
$579$	1.15856	−	2.79700i	0.0481480	−	0.116239i
$580$		0			0
$581$	−29.0584	+	12.0364i	−1.20555	+	0.499354i
$582$		0			0
$583$	−12.0920	+	12.0920i	−0.500798	+	0.500798i
$584$		0			0
$585$	−7.80316	−	7.80316i	−0.322621	−	0.322621i
$586$		0			0
$587$	1.02732	+	2.48018i	0.0424022	+	0.102368i	0.943662	−	0.330912i	$-0.107356\pi$
$587$	1.02732	+	2.48018i	0.0424022	+	0.102368i	−0.901260	+	0.433280i	$0.857356\pi$
$588$		0			0
$589$	−26.4766	−	10.9670i	−1.09095	−	0.451885i
$590$		0			0
$591$			4.15894i			0.171076i
$592$		0			0
$593$			13.9339i			0.572197i	0.958200	+	0.286098i	$0.0923584\pi$
$593$			13.9339i			0.572197i	−0.958200	+	0.286098i	$0.907642\pi$
$594$		0			0
$595$	6.93484	+	2.87250i	0.284301	+	0.117761i
$596$		0			0
$597$	−1.39112	−	3.35846i	−0.0569347	−	0.137452i
$598$		0			0
$599$	7.02222	+	7.02222i	0.286920	+	0.286920i	0.835861	−	0.548941i	$-0.184969\pi$
$599$	7.02222	+	7.02222i	0.286920	+	0.286920i	−0.548941	+	0.835861i	$0.684969\pi$
$600$		0			0
$601$	24.0970	−	24.0970i	0.982938	−	0.982938i	−0.0169188	−	0.999857i	$-0.505386\pi$
$601$	24.0970	−	24.0970i	0.982938	−	0.982938i	0.999857	+	0.0169188i	$0.00538568\pi$
$602$		0			0
$603$	−14.2469	+	5.90125i	−0.580177	+	0.240317i
$604$		0			0
$605$	1.24036	−	2.99450i	0.0504278	−	0.121744i
$606$		0			0
$607$	27.8275			1.12948			0.564742	−	0.825268i	$-0.308976\pi$
$607$	27.8275			1.12948			0.564742	+	0.825268i	$0.308976\pi$
$608$		0			0
$609$	−1.62437			−0.0658229
$610$		0			0
$611$	−13.7548	+	33.2070i	−0.556460	+	1.34341i
$612$		0			0
$613$	9.98279	−	4.13501i	0.403201	−	0.167011i	−0.171861	−	0.985121i	$-0.554978\pi$
$613$	9.98279	−	4.13501i	0.403201	−	0.167011i	0.575062	+	0.818110i	$0.304978\pi$
$614$		0			0
$615$	0.245193	−	0.245193i	0.00988714	−	0.00988714i
$616$		0			0
$617$	23.2080	+	23.2080i	0.934318	+	0.934318i	0.997972	−	0.0636543i	$-0.0202755\pi$
$617$	23.2080	+	23.2080i	0.934318	+	0.934318i	−0.0636543	+	0.997972i	$0.520275\pi$
$618$		0			0
$619$	−11.5644	−	27.9189i	−0.464811	−	1.12215i	−0.966399	−	0.257047i	$-0.917251\pi$
$619$	−11.5644	−	27.9189i	−0.464811	−	1.12215i	0.501588	−	0.865107i	$-0.332749\pi$
$620$		0			0
$621$	−0.438546	−	0.181652i	−0.0175982	−	0.00728943i
$622$		0			0
$623$		−	34.4481i		−	1.38013i
$624$		0			0
$625$		−	16.5563i		−	0.662254i
$626$		0			0
$627$	−3.14288	−	1.30182i	−0.125515	−	0.0519899i
$628$		0			0
$629$	4.59519	+	11.0938i	0.183222	+	0.442338i
$630$		0			0
$631$	1.34980	+	1.34980i	0.0537346	+	0.0537346i	0.733463	−	0.679729i	$-0.237903\pi$
$631$	1.34980	+	1.34980i	0.0537346	+	0.0537346i	−0.679729	+	0.733463i	$0.737903\pi$
$632$		0			0
$633$	0.564006	−	0.564006i	0.0224172	−	0.0224172i
$634$		0			0
$635$	−8.10641	+	3.35778i	−0.321693	+	0.133250i
$636$		0			0
$637$	6.19133	−	14.9472i	0.245309	−	0.592229i
$638$		0			0
$639$	−27.0588			−1.07043
$640$		0			0
$641$	41.5334			1.64047			0.820235	−	0.572027i	$-0.193843\pi$
$641$	41.5334			1.64047			0.820235	+	0.572027i	$0.193843\pi$
$642$		0			0
$643$	−1.57282	+	3.79713i	−0.0620261	+	0.149744i	−0.951854	−	0.306553i	$-0.900824\pi$
$643$	−1.57282	+	3.79713i	−0.0620261	+	0.149744i	0.889828	+	0.456297i	$0.150824\pi$
$644$		0			0
$645$	−0.287389	+	0.119040i	−0.0113159	+	0.00468721i
$646$		0			0
$647$	5.84193	−	5.84193i	0.229670	−	0.229670i	−0.582885	−	0.812555i	$-0.698076\pi$
$647$	5.84193	−	5.84193i	0.229670	−	0.229670i	0.812555	+	0.582885i	$0.198076\pi$
$648$		0			0
$649$	30.2323	+	30.2323i	1.18672	+	1.18672i
$650$		0			0
$651$	1.74311	+	4.20823i	0.0683177	+	0.164934i
$652$		0			0
$653$	26.0231	+	10.7791i	1.01836	+	0.421820i	0.828499	−	0.559991i	$-0.189195\pi$
$653$	26.0231	+	10.7791i	1.01836	+	0.421820i	0.189864	+	0.981810i	$0.439195\pi$
$654$		0			0
$655$			8.64422i			0.337758i
$656$		0			0
$657$		−	11.8803i		−	0.463495i
$658$		0			0
$659$	37.6498	+	15.5951i	1.46663	+	0.607497i	0.966087	−	0.258215i	$-0.0831344\pi$
$659$	37.6498	+	15.5951i	1.46663	+	0.607497i	0.500541	+	0.865713i	$0.333134\pi$
$660$		0			0
$661$	−3.14241	−	7.58644i	−0.122226	−	0.295078i	0.850910	−	0.525311i	$-0.176051\pi$
$661$	−3.14241	−	7.58644i	−0.122226	−	0.295078i	−0.973136	+	0.230233i	$0.926051\pi$
$662$		0			0
$663$	−2.18621	−	2.18621i	−0.0849054	−	0.0849054i
$664$		0			0
$665$	−7.29585	+	7.29585i	−0.282921	+	0.282921i
$666$		0			0
$667$	−0.863279	+	0.357582i	−0.0334263	+	0.0138456i
$668$		0			0
$669$	−2.18982	+	5.28670i	−0.0846634	+	0.204395i
$670$		0			0
$671$	13.8584			0.534997
$672$		0			0
$673$	−5.24262			−0.202088			−0.101044	−	0.994882i	$-0.532218\pi$
$673$	−5.24262			−0.202088			−0.101044	+	0.994882i	$0.532218\pi$
$674$		0			0
$675$	−2.08968	+	5.04493i	−0.0804318	+	0.194179i
$676$		0			0
$677$	−14.5716	+	6.03574i	−0.560031	+	0.231972i	−0.644699	−	0.764437i	$-0.723017\pi$
$677$	−14.5716	+	6.03574i	−0.560031	+	0.231972i	0.0846677	+	0.996409i	$0.473017\pi$
$678$		0			0
$679$	8.43625	−	8.43625i	0.323754	−	0.323754i
$680$		0			0
$681$	2.31265	+	2.31265i	0.0886210	+	0.0886210i
$682$		0			0
$683$	−14.9028	−	35.9785i	−0.570240	−	1.37668i	−0.901351	−	0.433089i	$-0.857424\pi$
$683$	−14.9028	−	35.9785i	−0.570240	−	1.37668i	0.331112	−	0.943592i	$-0.392576\pi$
$684$		0			0
$685$	3.42429	+	1.41839i	0.130835	+	0.0541938i
$686$		0			0
$687$			4.10842i			0.156746i
$688$		0			0
$689$		−	21.3637i		−	0.813892i
$690$		0			0
$691$	14.6714	+	6.07710i	0.558127	+	0.231184i	0.643872	−	0.765133i	$-0.277327\pi$
$691$	14.6714	+	6.07710i	0.558127	+	0.231184i	−0.0857448	+	0.996317i	$0.527327\pi$
$692$		0			0
$693$	−14.1869	−	34.2502i	−0.538915	−	1.30106i
$694$		0			0
$695$	10.4050	+	10.4050i	0.394685	+	0.394685i
$696$		0			0
$697$	−4.71006	+	4.71006i	−0.178406	+	0.178406i
$698$		0			0
$699$	−1.82046	+	0.754059i	−0.0688561	+	0.0285211i
$700$		0			0
$701$	−9.58351	+	23.1366i	−0.361964	+	0.873859i	0.633049	+	0.774112i	$0.281803\pi$
$701$	−9.58351	+	23.1366i	−0.361964	+	0.873859i	−0.995013	+	0.0997466i	$0.968197\pi$
$702$		0			0
$703$	−16.5057			−0.622524
$704$		0			0
$705$	−1.17157			−0.0441240
$706$		0			0
$707$	12.0381	−	29.0625i	0.452739	−	1.09301i
$708$		0			0
$709$	−27.4256	+	11.3601i	−1.02999	+	0.426636i	−0.832709	−	0.553711i	$-0.813211\pi$
$709$	−27.4256	+	11.3601i	−1.02999	+	0.426636i	−0.197282	+	0.980347i	$0.563211\pi$
$710$		0			0
$711$	20.3855	−	20.3855i	0.764515	−	0.764515i
$712$		0			0
$713$	1.85276	+	1.85276i	0.0693864	+	0.0693864i
$714$		0			0
$715$	5.57457	+	13.4582i	0.208477	+	0.503309i
$716$		0			0
$717$	5.02663	+	2.08210i	0.187723	+	0.0777573i
$718$		0			0
$719$			38.9976i			1.45436i	0.686445	+	0.727182i	$0.259170\pi$
$719$			38.9976i			1.45436i	−0.686445	+	0.727182i	$0.740830\pi$
$720$		0			0
$721$			2.04732i			0.0762462i
$722$		0			0
$723$	−2.62337	−	1.08664i	−0.0975643	−	0.0404124i
$724$		0			0
$725$	4.11354	+	9.93095i	0.152773	+	0.368826i
$726$		0			0
$727$	−34.9474	−	34.9474i	−1.29613	−	1.29613i	−0.930930	−	0.365198i	$-0.881001\pi$
$727$	−34.9474	−	34.9474i	−1.29613	−	1.29613i	−0.365198	−	0.930930i	$-0.618999\pi$
$728$		0			0
$729$	−17.4649	+	17.4649i	−0.646846	+	0.646846i
$730$		0			0
$731$	5.52062	−	2.28672i	0.204188	−	0.0845773i
$732$		0			0
$733$	13.8093	−	33.3387i	0.510060	−	1.23139i	−0.433789	−	0.901015i	$-0.642824\pi$
$733$	13.8093	−	33.3387i	0.510060	−	1.23139i	0.943849	−	0.330378i	$-0.107176\pi$
$734$		0			0
$735$	0.527350			0.0194516
$736$		0			0
$737$	20.3559			0.749819
$738$		0			0
$739$	6.75096	−	16.2983i	0.248338	−	0.599542i	−0.749725	−	0.661750i	$-0.769814\pi$
$739$	6.75096	−	16.2983i	0.248338	−	0.599542i	0.998063	+	0.0622080i	$0.0198142\pi$
$740$		0			0
$741$	3.92638	−	1.62636i	0.144239	−	0.0597458i
$742$		0			0
$743$	20.6145	−	20.6145i	0.756272	−	0.756272i	−0.219370	−	0.975642i	$-0.570400\pi$
$743$	20.6145	−	20.6145i	0.756272	−	0.756272i	0.975642	+	0.219370i	$0.0704002\pi$
$744$		0			0
$745$	−1.31788	−	1.31788i	−0.0482835	−	0.0482835i
$746$		0			0
$747$	−11.0799	−	26.7491i	−0.405391	−	0.978700i
$748$		0			0
$749$	52.9203	+	21.9203i	1.93367	+	0.800951i
$750$		0			0
$751$		−	27.0344i		−	0.986499i	−0.869888	−	0.493249i	$-0.835809\pi$
$751$		−	27.0344i		−	0.986499i	0.869888	−	0.493249i	$-0.164191\pi$
$752$		0			0
$753$			2.96827i			0.108170i
$754$		0			0
$755$	−4.21395	−	1.74548i	−0.153361	−	0.0635244i
$756$		0			0
$757$	19.5424	+	47.1795i	0.710280	+	1.71477i	0.699300	+	0.714828i	$0.253495\pi$
$757$	19.5424	+	47.1795i	0.710280	+	1.71477i	0.0109802	+	0.999940i	$0.496505\pi$
$758$		0			0
$759$	0.219931	+	0.219931i	0.00798297	+	0.00798297i
$760$		0			0
$761$	−2.53714	+	2.53714i	−0.0919713	+	0.0919713i	−0.751596	−	0.659624i	$-0.770715\pi$
$761$	−2.53714	+	2.53714i	−0.0919713	+	0.0919713i	0.659624	+	0.751596i	$0.270715\pi$
$762$		0			0
$763$	23.1488	−	9.58854i	0.838042	−	0.347129i
$764$		0			0
$765$	−2.64422	+	6.38372i	−0.0956021	+	0.230804i
$766$		0			0
$767$	−53.4134			−1.92865
$768$		0			0
$769$	−24.0627			−0.867725			−0.433862	−	0.900979i	$-0.642850\pi$
$769$	−24.0627			−0.867725			−0.433862	+	0.900979i	$0.642850\pi$
$770$		0			0
$771$	−1.59463	+	3.84977i	−0.0574291	+	0.138646i
$772$		0			0
$773$	43.4146	−	17.9829i	1.56152	−	0.646801i	0.576163	−	0.817335i	$-0.304549\pi$
$773$	43.4146	−	17.9829i	1.56152	−	0.646801i	0.985352	+	0.170534i	$0.0545492\pi$
$774$		0			0
$775$	21.3137	−	21.3137i	0.765611	−	0.765611i
$776$		0			0
$777$	1.85505	+	1.85505i	0.0665497	+	0.0665497i
$778$		0			0
$779$	−3.50389	−	8.45914i	−0.125540	−	0.303080i
$780$		0			0
$781$	32.9997	+	13.6689i	1.18082	+	0.489113i
$782$		0			0
$783$		−	3.01237i		−	0.107653i
$784$		0			0
$785$		−	11.6880i		−	0.417163i
$786$		0			0
$787$	−4.62213	−	1.91455i	−0.164761	−	0.0682463i	0.298778	−	0.954323i	$-0.403421\pi$
$787$	−4.62213	−	1.91455i	−0.164761	−	0.0682463i	−0.463540	+	0.886076i	$0.653421\pi$
$788$		0			0
$789$	0.533819	+	1.28875i	0.0190045	+	0.0458808i
$790$		0			0
$791$	19.9137	+	19.9137i	0.708051	+	0.708051i
$792$		0			0
$793$	−12.2423	+	12.2423i	−0.434735	+	0.434735i
$794$		0			0
$795$	0.643348	−	0.266484i	0.0228172	−	0.00945120i
$796$		0			0
$797$	7.78397	−	18.7922i	0.275722	−	0.665653i	−0.723986	−	0.689815i	$-0.757692\pi$
$797$	7.78397	−	18.7922i	0.275722	−	0.665653i	0.999708	+	0.0241622i	$0.00769183\pi$
$798$		0			0
$799$	22.5054			0.796185
$800$		0			0
$801$	31.7104			1.12043
$802$		0			0
$803$	−6.00142	+	14.4887i	−0.211785	+	0.511295i
$804$		0			0
$805$	0.871553	−	0.361009i	0.0307182	−	0.0127239i
$806$		0			0
$807$	3.55740	−	3.55740i	0.125227	−	0.125227i
$808$		0			0
$809$	−5.79631	−	5.79631i	−0.203787	−	0.203787i	0.597833	−	0.801621i	$-0.296029\pi$
$809$	−5.79631	−	5.79631i	−0.203787	−	0.203787i	−0.801621	+	0.597833i	$0.796029\pi$
$810$		0			0
$811$	−2.59457	−	6.26386i	−0.0911078	−	0.219954i	0.871757	−	0.489939i	$-0.162981\pi$
$811$	−2.59457	−	6.26386i	−0.0911078	−	0.219954i	−0.962864	+	0.269986i	$0.912981\pi$
$812$		0			0
$813$	0.132987	+	0.0550849i	0.00466405	+	0.00193191i
$814$		0			0
$815$		−	5.44739i		−	0.190814i
$816$		0			0
$817$			8.21377i			0.287363i
$818$		0			0
$819$	42.7885	+	17.7236i	1.49515	+	0.619311i
$820$		0			0
$821$	−14.5014	−	35.0095i	−0.506103	−	1.22184i	−0.946110	−	0.323847i	$-0.895024\pi$
$821$	−14.5014	−	35.0095i	−0.506103	−	1.22184i	0.440006	−	0.897995i	$-0.354976\pi$
$822$		0			0
$823$	6.84972	+	6.84972i	0.238766	+	0.238766i	0.816339	−	0.577573i	$-0.196000\pi$
$823$	6.84972	+	6.84972i	0.238766	+	0.238766i	−0.577573	+	0.816339i	$0.696000\pi$
$824$		0			0
$825$	2.53003	−	2.53003i	0.0880843	−	0.0880843i
$826$		0			0
$827$	27.6932	−	11.4709i	0.962987	−	0.398882i	0.154890	−	0.987932i	$-0.450498\pi$
$827$	27.6932	−	11.4709i	0.962987	−	0.398882i	0.808097	+	0.589049i	$0.200498\pi$
$828$		0			0
$829$	−1.60232	+	3.86834i	−0.0556509	+	0.134353i	−0.949259	−	0.314494i	$-0.898165\pi$
$829$	−1.60232	+	3.86834i	−0.0556509	+	0.134353i	0.893609	+	0.448847i	$0.148165\pi$
$830$		0			0
$831$	−6.07228			−0.210645
$832$		0			0
$833$	−10.1302			−0.350990
$834$		0			0
$835$	1.35181	−	3.26355i	0.0467811	−	0.112940i
$836$		0			0
$837$	−7.80409	+	3.23256i	−0.269749	+	0.111734i
$838$		0			0
$839$	−11.4718	+	11.4718i	−0.396050	+	0.396050i	−0.876837	−	0.480787i	$-0.840351\pi$
$839$	−11.4718	+	11.4718i	−0.396050	+	0.396050i	0.480787	+	0.876837i	$0.340351\pi$
$840$		0			0
$841$	16.3131	+	16.3131i	0.562519	+	0.562519i
$842$		0			0
$843$	0.784427	+	1.89377i	0.0270171	+	0.0652250i
$844$		0			0
$845$	−7.62086	−	3.15666i	−0.262165	−	0.108592i
$846$		0			0
$847$			13.6030i			0.467404i
$848$		0			0
$849$		−	3.28352i		−	0.112690i
$850$		0			0
$851$	1.39424	+	0.577512i	0.0477939	+	0.0197969i
$852$		0			0
$853$	4.85275	+	11.7156i	0.166155	+	0.401133i	0.984924	−	0.172990i	$-0.0553429\pi$
$853$	4.85275	+	11.7156i	0.166155	+	0.401133i	−0.818769	+	0.574124i	$0.805343\pi$
$854$		0			0
$855$	−6.71604	−	6.71604i	−0.229684	−	0.229684i
$856$		0			0
$857$	−13.5307	+	13.5307i	−0.462200	+	0.462200i	−0.899376	−	0.437176i	$-0.855979\pi$
$857$	−13.5307	+	13.5307i	−0.462200	+	0.462200i	0.437176	+	0.899376i	$0.355979\pi$
$858$		0			0
$859$	−50.3433	+	20.8529i	−1.71769	+	0.711491i	−0.717808	+	0.696241i	$0.754855\pi$
$859$	−50.3433	+	20.8529i	−1.71769	+	0.711491i	−0.999884	+	0.0152507i	$0.995145\pi$
$860$		0			0
$861$	−0.556914	+	1.34451i	−0.0189796	+	0.0458208i
$862$		0			0
$863$	9.50637			0.323601			0.161800	−	0.986824i	$-0.448270\pi$
$863$	9.50637			0.323601			0.161800	+	0.986824i	$0.448270\pi$
$864$		0			0
$865$	5.68802			0.193399
$866$		0			0
$867$	0.610172	−	1.47309i	0.0207225	−	0.0500286i
$868$		0			0
$869$	−35.1591	+	14.5634i	−1.19269	+	0.494028i
$870$		0			0
$871$	−17.9821	+	17.9821i	−0.609299	+	0.609299i
$872$		0			0
$873$	7.76582	+	7.76582i	0.262833	+	0.262833i
$874$		0			0
$875$	−8.85704	−	21.3828i	−0.299423	−	0.722870i
$876$		0			0
$877$	−16.7883	−	6.95392i	−0.566899	−	0.234817i	0.0807782	−	0.996732i	$-0.474259\pi$
$877$	−16.7883	−	6.95392i	−0.566899	−	0.234817i	−0.647677	+	0.761915i	$0.724259\pi$
$878$		0			0
$879$		−	2.21534i		−	0.0747216i
$880$		0			0
$881$		−	46.9687i		−	1.58242i	−0.611547	−	0.791208i	$-0.709453\pi$
$881$		−	46.9687i		−	1.58242i	0.611547	−	0.791208i	$-0.290547\pi$
$882$		0			0
$883$	11.0237	+	4.56617i	0.370978	+	0.153664i	0.560380	−	0.828236i	$-0.310655\pi$
$883$	11.0237	+	4.56617i	0.370978	+	0.153664i	−0.189403	+	0.981900i	$0.560655\pi$
$884$		0			0
$885$	−0.666261	−	1.60850i	−0.0223961	−	0.0540690i
$886$		0			0
$887$	−31.9419	−	31.9419i	−1.07250	−	1.07250i	−0.997157	−	0.0753464i	$-0.975994\pi$
$887$	−31.9419	−	31.9419i	−1.07250	−	1.07250i	−0.0753464	−	0.997157i	$-0.524006\pi$
$888$		0			0
$889$	26.0390	−	26.0390i	0.873319	−	0.873319i
$890$		0			0
$891$	31.0617	−	12.8662i	1.04061	−	0.431034i
$892$		0			0
$893$	−11.8385	+	28.5807i	−0.396160	+	0.956416i
$894$		0			0
$895$	1.48595			0.0496699
$896$		0			0
$897$	−0.388566			−0.0129738
$898$		0			0
$899$	−6.36330	+	15.3624i	−0.212228	+	0.512364i
$900$		0			0
$901$	−12.3585	+	5.11904i	−0.411720	+	0.170540i
$902$		0			0
$903$	0.923135	−	0.923135i	0.0307200	−	0.0307200i
$904$		0			0
$905$	8.65685	+	8.65685i	0.287764	+	0.287764i
$906$		0			0
$907$	4.99616	+	12.0618i	0.165895	+	0.400505i	0.984863	−	0.173333i	$-0.0554538\pi$
$907$	4.99616	+	12.0618i	0.165895	+	0.400505i	−0.818969	+	0.573838i	$0.805454\pi$
$908$		0			0
$909$	26.7529	+	11.0814i	0.887338	+	0.367547i
$910$		0			0
$911$			13.1188i			0.434645i	0.976100	+	0.217322i	$0.0697323\pi$
$911$			13.1188i			0.434645i	−0.976100	+	0.217322i	$0.930268\pi$
$912$		0			0
$913$			38.2191i			1.26487i
$914$		0			0
$915$	−0.521370	−	0.215959i	−0.0172360	−	0.00713937i
$916$		0			0
$917$	−13.8833	−	33.5171i	−0.458465	−	1.10683i
$918$		0			0
$919$	17.2415	+	17.2415i	0.568746	+	0.568746i	0.931777	−	0.363031i	$-0.118258\pi$
$919$	17.2415	+	17.2415i	0.568746	+	0.568746i	−0.363031	+	0.931777i	$0.618258\pi$
$920$		0			0
$921$	1.10667	−	1.10667i	0.0364659	−	0.0364659i
$922$		0			0
$923$	−41.2263	+	17.0765i	−1.35698	+	0.562080i
$924$		0			0
$925$	6.64357	−	16.0390i	0.218439	−	0.527359i
$926$		0			0
$927$	−1.88462			−0.0618990
$928$		0			0
$929$	−45.9966			−1.50910			−0.754550	−	0.656242i	$-0.772145\pi$
$929$	−45.9966			−1.50910			−0.754550	+	0.656242i	$0.772145\pi$
$930$		0			0
$931$	5.32876	−	12.8648i	0.174643	−	0.421626i
$932$		0			0
$933$	−1.26174	+	0.522630i	−0.0413076	+	0.0171101i
$934$		0			0
$935$	6.44955	−	6.44955i	0.210923	−	0.210923i
$936$		0			0
$937$	−3.67273	−	3.67273i	−0.119983	−	0.119983i	0.644566	−	0.764549i	$-0.277038\pi$
$937$	−3.67273	−	3.67273i	−0.119983	−	0.119983i	−0.764549	+	0.644566i	$0.777038\pi$
$938$		0			0
$939$	0.0366014	+	0.0883635i	0.00119444	+	0.00288363i
$940$		0			0
$941$	−41.7873	−	17.3089i	−1.36223	−	0.564253i	−0.422558	−	0.906336i	$-0.638868\pi$
$941$	−41.7873	−	17.3089i	−1.36223	−	0.564253i	−0.939670	+	0.342083i	$0.888868\pi$
$942$		0			0
$943$			0.837141i			0.0272611i
$944$		0			0
$945$			3.04125i			0.0989317i
$946$		0			0
$947$	−43.6427	−	18.0774i	−1.41820	−	0.587436i	−0.463790	−	0.885945i	$-0.653511\pi$
$947$	−43.6427	−	18.0774i	−1.41820	−	0.587436i	−0.954407	+	0.298509i	$0.903511\pi$
$948$		0			0
$949$	−7.49753	−	18.1006i	−0.243380	−	0.587571i
$950$		0			0
$951$	3.04238	+	3.04238i	0.0986559	+	0.0986559i
$952$		0			0
$953$	6.12750	−	6.12750i	0.198489	−	0.198489i	−0.600863	−	0.799352i	$-0.705176\pi$
$953$	6.12750	−	6.12750i	0.198489	−	0.198489i	0.799352	+	0.600863i	$0.205176\pi$
$954$		0			0
$955$	−4.37887	+	1.81379i	−0.141697	+	0.0586928i
$956$		0			0
$957$	−0.755352	+	1.82358i	−0.0244171	+	0.0589480i
$958$		0			0
$959$	−15.5554			−0.502310
$960$		0			0
$961$	15.6274			0.504110
$962$		0			0
$963$	−20.1783	+	48.7147i	−0.650237	+	1.56981i
$964$		0			0
$965$	−10.3085	+	4.26991i	−0.331842	+	0.137453i
$966$		0			0
$967$	−1.03516	+	1.03516i	−0.0332885	+	0.0332885i	−0.723555	−	0.690267i	$-0.757493\pi$
$967$	−1.03516	+	1.03516i	−0.0332885	+	0.0332885i	0.690267	+	0.723555i	$0.257493\pi$
$968$		0			0
$969$	−1.88163	−	1.88163i	−0.0604467	−	0.0604467i
$970$		0			0
$971$	15.4218	+	37.2315i	0.494909	+	1.19482i	0.952194	+	0.305495i	$0.0988221\pi$
$971$	15.4218	+	37.2315i	0.494909	+	1.19482i	−0.457285	+	0.889320i	$0.651178\pi$
$972$		0			0
$973$	−57.0556	−	23.6332i	−1.82912	−	0.757646i
$974$		0			0
$975$			4.46997i			0.143154i
$976$		0			0
$977$		−	28.8457i		−	0.922857i	−0.887177	−	0.461429i	$-0.847337\pi$
$977$		−	28.8457i		−	0.922857i	0.887177	−	0.461429i	$-0.152663\pi$
$978$		0			0
$979$	−38.6727	−	16.0187i	−1.23598	−	0.511961i
$980$		0			0
$981$	8.82653	+	21.3091i	0.281809	+	0.680348i
$982$		0			0
$983$	40.9561	+	40.9561i	1.30630	+	1.30630i	0.924067	+	0.382231i	$0.124844\pi$
$983$	40.9561	+	40.9561i	1.30630	+	1.30630i	0.382231	+	0.924067i	$0.375156\pi$
$984$		0			0
$985$	10.8385	−	10.8385i	0.345344	−	0.345344i
$986$		0			0
$987$	4.54266	−	1.88163i	0.144594	−	0.0598930i
$988$		0			0
$989$	0.287389	−	0.693818i	0.00913843	−	0.0220621i
$990$		0			0
$991$	41.9605			1.33292			0.666460	−	0.745541i	$-0.267809\pi$
$991$	41.9605			1.33292			0.666460	+	0.745541i	$0.267809\pi$
$992$		0			0
$993$	−3.21145			−0.101912
$994$		0			0
$995$	−5.12703	+	12.3777i	−0.162538	+	0.392401i
$996$		0			0
$997$	31.4380	−	13.0221i	0.995652	−	0.412413i	0.175451	−	0.984488i	$-0.443862\pi$
$997$	31.4380	−	13.0221i	0.995652	−	0.412413i	0.820201	+	0.572076i	$0.193862\pi$
$998$		0			0
$999$	−3.44017	+	3.44017i	−0.108842	+	0.108842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.g.c.33.2		8
4.3	odd	2		256.2.g.d.33.1		8
8.3	odd	2		32.2.g.b.13.2	yes	8
8.5	even	2		128.2.g.b.17.1		8
16.3	odd	4		512.2.g.h.321.1		8
16.5	even	4		512.2.g.g.321.1		8
16.11	odd	4		512.2.g.e.321.2		8
16.13	even	4		512.2.g.f.321.2		8
24.5	odd	2		1152.2.v.b.145.2		8
24.11	even	2		288.2.v.b.109.1		8
32.3	odd	8		512.2.g.h.193.1		8
32.5	even	8	inner	256.2.g.c.225.2		8
32.11	odd	8		32.2.g.b.5.2	✓	8
32.13	even	8		512.2.g.g.193.1		8
32.19	odd	8		512.2.g.e.193.2		8
32.21	even	8		128.2.g.b.113.1		8
32.27	odd	8		256.2.g.d.225.1		8
32.29	even	8		512.2.g.f.193.2		8
40.3	even	4		800.2.ba.c.749.1		8
40.19	odd	2		800.2.y.b.301.1		8
40.27	even	4		800.2.ba.d.749.2		8
64.5	even	16		4096.2.a.q.1.5		8
64.27	odd	16		4096.2.a.k.1.5		8
64.37	even	16		4096.2.a.q.1.4		8
64.59	odd	16		4096.2.a.k.1.4		8
96.11	even	8		288.2.v.b.37.1		8
96.53	odd	8		1152.2.v.b.1009.2		8
160.43	even	8		800.2.ba.d.549.2		8
160.107	even	8		800.2.ba.c.549.1		8
160.139	odd	8		800.2.y.b.101.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.2	✓	8	32.11	odd	8
32.2.g.b.13.2	yes	8	8.3	odd	2
128.2.g.b.17.1		8	8.5	even	2
128.2.g.b.113.1		8	32.21	even	8
256.2.g.c.33.2		8	1.1	even	1	trivial
256.2.g.c.225.2		8	32.5	even	8	inner
256.2.g.d.33.1		8	4.3	odd	2
256.2.g.d.225.1		8	32.27	odd	8
288.2.v.b.37.1		8	96.11	even	8
288.2.v.b.109.1		8	24.11	even	2
512.2.g.e.193.2		8	32.19	odd	8
512.2.g.e.321.2		8	16.11	odd	4
512.2.g.f.193.2		8	32.29	even	8
512.2.g.f.321.2		8	16.13	even	4
512.2.g.g.193.1		8	32.13	even	8
512.2.g.g.321.1		8	16.5	even	4
512.2.g.h.193.1		8	32.3	odd	8
512.2.g.h.321.1		8	16.3	odd	4
800.2.y.b.101.1		8	160.139	odd	8
800.2.y.b.301.1		8	40.19	odd	2
800.2.ba.c.549.1		8	160.107	even	8
800.2.ba.c.749.1		8	40.3	even	4
800.2.ba.d.549.2		8	160.43	even	8
800.2.ba.d.749.2		8	40.27	even	4
1152.2.v.b.145.2		8	24.5	odd	2
1152.2.v.b.1009.2		8	96.53	odd	8
4096.2.a.k.1.4		8	64.59	odd	16
4096.2.a.k.1.5		8	64.27	odd	16
4096.2.a.q.1.4		8	64.37	even	16
4096.2.a.q.1.5		8	64.5	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.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0794708 - 0.191860i) q^{3} +(-0.707107 + 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +O(q^{10})\)	\(q+(0.0794708 - 0.191860i) q^{3} +(-0.707107 + 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +(-1.49368 - 3.60607i) q^{11} +(4.50504 + 1.86605i) q^{13} +0.158942i q^{15} -3.05320i q^{17} +(3.87740 + 1.60607i) q^{19} +(-0.255272 - 0.616281i) q^{21} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(1.14288 - 0.473398i) q^{27} +(0.931884 - 2.24977i) q^{29} -6.82843 q^{31} -0.810564 q^{33} +(-0.940816 + 2.27133i) q^{35} +(-3.63349 + 1.50504i) q^{37} +(0.716038 - 0.716038i) q^{39} +(-1.54266 - 1.54266i) q^{41} +(0.748956 + 1.80814i) q^{43} +(-2.09083 - 0.866048i) q^{45} +7.37109i q^{47} -3.31788i q^{49} +(-0.585786 - 0.242641i) q^{51} +(-1.67661 - 4.04770i) q^{53} +(2.11239 + 2.11239i) q^{55} +(0.616281 - 0.616281i) q^{57} +(-10.1200 + 4.19186i) q^{59} +(-1.35873 + 3.28026i) q^{61} +9.49791 q^{63} -3.73210 q^{65} +(-1.99577 + 4.81822i) q^{67} +(-0.0736202 + 0.0304945i) q^{69} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(0.350801 + 0.846909i) q^{75} +(-11.5832 - 4.79793i) q^{77} -9.74996i q^{79} +8.61373i q^{81} +(-9.04642 - 3.74715i) q^{83} +(0.894263 + 2.15894i) q^{85} +(-0.357582 - 0.357582i) q^{87} +(7.58323 - 7.58323i) q^{89} +(14.4708 - 5.99402i) q^{91} +(-0.542661 + 1.31010i) q^{93} -3.21215 q^{95} +3.71423 q^{97} +(4.41664 - 10.6627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 + 8 * q^7	\( 8 q - 4 q^{3} + 8 q^{7} + 4 q^{11} + 8 q^{13} + 4 q^{19} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 32 q^{31} - 16 q^{33} + 16 q^{35} + 8 q^{37} - 16 q^{39} + 8 q^{41} - 12 q^{43} - 16 q^{51} - 8 q^{53} + 16 q^{55} + 16 q^{57} - 20 q^{59} - 24 q^{61} + 40 q^{63} - 36 q^{67} - 32 q^{69} + 24 q^{71} - 32 q^{73} - 12 q^{75} - 16 q^{77} + 20 q^{83} - 8 q^{85} - 56 q^{87} - 16 q^{89} + 40 q^{91} + 16 q^{93} + 8 q^{95} + 32 q^{97} + 28 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 8 * q^7 + 4 * q^11 + 8 * q^13 + 4 * q^19 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 32 * q^31 - 16 * q^33 + 16 * q^35 + 8 * q^37 - 16 * q^39 + 8 * q^41 - 12 * q^43 - 16 * q^51 - 8 * q^53 + 16 * q^55 + 16 * q^57 - 20 * q^59 - 24 * q^61 + 40 * q^63 - 36 * q^67 - 32 * q^69 + 24 * q^71 - 32 * q^73 - 12 * q^75 - 16 * q^77 + 20 * q^83 - 8 * q^85 - 56 * q^87 - 16 * q^89 + 40 * q^91 + 16 * q^93 + 8 * q^95 + 32 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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