LMFDB - Embedded newform 920.2.bv.a.217.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.11
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29814 + 0.282393i) q^{3} +(1.73961 - 1.40490i) q^{5} +(3.60560 - 1.96880i) q^{7} +(-1.12348 + 0.513074i) q^{9} +O(q^{10})$	\(q+(-1.29814 + 0.282393i) q^{3} +(1.73961 - 1.40490i) q^{5} +(3.60560 - 1.96880i) q^{7} +(-1.12348 + 0.513074i) q^{9} +(2.33478 + 2.02310i) q^{11} +(2.26521 - 4.14842i) q^{13} +(-1.86152 + 2.31501i) q^{15} +(-1.05088 - 0.786681i) q^{17} +(-0.122216 + 0.850032i) q^{19} +(-4.12459 + 3.57398i) q^{21} +(-3.59026 + 3.17963i) q^{23} +(1.05250 - 4.88797i) q^{25} +(4.50410 - 3.37172i) q^{27} +(-8.53987 + 1.22785i) q^{29} +(3.68522 - 2.36835i) q^{31} +(-3.60218 - 1.96694i) q^{33} +(3.50636 - 8.49046i) q^{35} +(3.20483 + 1.19534i) q^{37} +(-1.76907 + 6.02491i) q^{39} +(4.40558 - 9.64688i) q^{41} +(1.06960 + 4.91689i) q^{43} +(-1.23359 + 2.47092i) q^{45} +(6.51159 + 6.51159i) q^{47} +(5.33965 - 8.30865i) q^{49} +(1.58634 + 0.724459i) q^{51} +(-2.07926 - 3.80788i) q^{53} +(6.90386 + 0.239270i) q^{55} +(-0.0813894 - 1.13797i) q^{57} +(-3.08330 - 10.5007i) q^{59} +(-4.82712 - 7.51115i) q^{61} +(-3.04066 + 4.06184i) q^{63} +(-1.88754 - 10.3990i) q^{65} +(5.82803 + 0.416829i) q^{67} +(3.76275 - 5.14147i) q^{69} +(8.42126 + 9.71865i) q^{71} +(1.50325 + 2.00810i) q^{73} +(0.0140338 + 6.64248i) q^{75} +(12.4014 + 2.69775i) q^{77} +(-7.95411 + 2.33554i) q^{79} +(-2.46836 + 2.84864i) q^{81} +(2.49864 - 6.69913i) q^{83} +(-2.93334 + 0.107867i) q^{85} +(10.7392 - 4.00552i) q^{87} +(12.9522 + 8.32388i) q^{89} -19.4173i q^{91} +(-4.11513 + 4.11513i) q^{93} +(0.981602 + 1.65043i) q^{95} +(0.0800515 + 0.214626i) q^{97} +(-3.66107 - 1.07499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.29814	+	0.282393i	−0.749481	+	0.163040i	−0.571053	−	0.820913i	$-0.693465\pi$
$3$	−1.29814	+	0.282393i	−0.749481	+	0.163040i	−0.178428	+	0.983953i	$0.557101\pi$
$4$		0			0
$5$	1.73961	−	1.40490i	0.777978	−	0.628291i
$5$	1.73961	−	1.40490i	0.777978	−	0.628291i
$6$		0			0
$7$	3.60560	−	1.96880i	1.36279	−	0.744138i	0.379327	−	0.925263i	$-0.376156\pi$
$7$	3.60560	−	1.96880i	1.36279	−	0.744138i	0.983460	+	0.181125i	$0.0579737\pi$
$8$		0			0
$9$	−1.12348	+	0.513074i	−0.374492	+	0.171025i
$10$		0			0
$11$	2.33478	+	2.02310i	0.703962	+	0.609987i	0.931482	−	0.363787i	$-0.118516\pi$
$11$	2.33478	+	2.02310i	0.703962	+	0.609987i	−0.227520	+	0.973773i	$0.573062\pi$
$12$		0			0
$13$	2.26521	−	4.14842i	0.628257	−	1.15057i	−0.348722	−	0.937226i	$-0.613384\pi$
$13$	2.26521	−	4.14842i	0.628257	−	1.15057i	0.976978	−	0.213340i	$-0.0684341\pi$
$14$		0			0
$15$	−1.86152	+	2.31501i	−0.480644	+	0.597734i
$16$		0			0
$17$	−1.05088	−	0.786681i	−0.254876	−	0.190798i	0.464197	−	0.885732i	$-0.346343\pi$
$17$	−1.05088	−	0.786681i	−0.254876	−	0.190798i	−0.719074	+	0.694934i	$0.755434\pi$
$18$		0			0
$19$	−0.122216	+	0.850032i	−0.0280383	+	0.195011i	−0.999026	−	0.0441173i	$-0.985952\pi$
$19$	−0.122216	+	0.850032i	−0.0280383	+	0.195011i	0.970988	+	0.239128i	$0.0768616\pi$
$20$		0			0
$21$	−4.12459	+	3.57398i	−0.900059	+	0.779906i
$22$		0			0
$23$	−3.59026	+	3.17963i	−0.748621	+	0.662999i
$23$	−3.59026	+	3.17963i	−0.748621	+	0.662999i
$24$		0			0
$25$	1.05250	−	4.88797i	0.210500	−	0.977594i
$26$		0			0
$27$	4.50410	−	3.37172i	0.866814	−	0.648889i
$28$		0			0
$29$	−8.53987	+	1.22785i	−1.58581	+	0.228006i	−0.878095	−	0.478487i	$-0.841185\pi$
$29$	−8.53987	+	1.22785i	−1.58581	+	0.228006i	−0.707720	+	0.706493i	$0.750276\pi$
$30$		0			0
$31$	3.68522	−	2.36835i	0.661886	−	0.425368i	−0.166106	−	0.986108i	$-0.553120\pi$
$31$	3.68522	−	2.36835i	0.661886	−	0.425368i	0.827992	+	0.560740i	$0.189483\pi$
$32$		0			0
$33$	−3.60218	−	1.96694i	−0.627059	−	0.342400i
$34$		0			0
$35$	3.50636	−	8.49046i	0.592683	−	1.43515i
$36$		0			0
$37$	3.20483	+	1.19534i	0.526870	+	0.196512i	0.598802	−	0.800897i	$-0.295644\pi$
$37$	3.20483	+	1.19534i	0.526870	+	0.196512i	−0.0719318	+	0.997410i	$0.522916\pi$
$38$		0			0
$39$	−1.76907	+	6.02491i	−0.283279	+	0.964758i
$40$		0			0
$41$	4.40558	−	9.64688i	0.688036	−	1.50659i	−0.165862	−	0.986149i	$-0.553041\pi$
$41$	4.40558	−	9.64688i	0.688036	−	1.50659i	0.853898	−	0.520440i	$-0.174232\pi$
$42$		0			0
$43$	1.06960	+	4.91689i	0.163113	+	0.749818i	0.983920	+	0.178612i	$0.0571606\pi$
$43$	1.06960	+	4.91689i	0.163113	+	0.749818i	−0.820807	+	0.571206i	$0.806476\pi$
$44$		0			0
$45$	−1.23359	+	2.47092i	−0.183893	+	0.368343i
$46$		0			0
$47$	6.51159	+	6.51159i	0.949812	+	0.949812i	0.998799	−	0.0489870i	$-0.0155993\pi$
$47$	6.51159	+	6.51159i	0.949812	+	0.949812i	−0.0489870	+	0.998799i	$0.515599\pi$
$48$		0			0
$49$	5.33965	−	8.30865i	0.762807	−	1.18695i
$50$		0			0
$51$	1.58634	+	0.724459i	0.222133	+	0.101445i
$52$		0			0
$53$	−2.07926	−	3.80788i	−0.285608	−	0.523053i	0.695005	−	0.719005i	$-0.255402\pi$
$53$	−2.07926	−	3.80788i	−0.285608	−	0.523053i	−0.980613	+	0.195952i	$0.937220\pi$
$54$		0			0
$55$	6.90386	+	0.239270i	0.930917	+	0.0322632i
$56$		0			0
$57$	−0.0813894	−	1.13797i	−0.0107803	−	0.150728i
$58$		0			0
$59$	−3.08330	−	10.5007i	−0.401411	−	1.36708i	−0.874055	−	0.485827i	$-0.838519\pi$
$59$	−3.08330	−	10.5007i	−0.401411	−	1.36708i	0.472644	−	0.881253i	$-0.343300\pi$
$60$		0			0
$61$	−4.82712	−	7.51115i	−0.618050	−	0.961704i	−0.999307	−	0.0372351i	$-0.988145\pi$
$61$	−4.82712	−	7.51115i	−0.618050	−	0.961704i	0.381257	−	0.924469i	$-0.375491\pi$
$62$		0			0
$63$	−3.04066	+	4.06184i	−0.383087	+	0.511744i
$64$		0			0
$65$	−1.88754	−	10.3990i	−0.234121	−	1.28984i
$66$		0			0
$67$	5.82803	+	0.416829i	0.712007	+	0.0509238i	0.422644	−	0.906296i	$-0.361102\pi$
$67$	5.82803	+	0.416829i	0.712007	+	0.0509238i	0.289363	+	0.957219i	$0.406557\pi$
$68$		0			0
$69$	3.76275	−	5.14147i	0.452982	−	0.618960i
$70$		0			0
$71$	8.42126	+	9.71865i	0.999419	+	1.15339i	0.988156	+	0.153455i	$0.0490400\pi$
$71$	8.42126	+	9.71865i	0.999419	+	1.15339i	0.0112638	+	0.999937i	$0.496415\pi$
$72$		0			0
$73$	1.50325	+	2.00810i	0.175942	+	0.235030i	0.879840	−	0.475270i	$-0.157650\pi$
$73$	1.50325	+	2.00810i	0.175942	+	0.235030i	−0.703898	+	0.710301i	$0.748559\pi$
$74$		0			0
$75$	0.0140338	+	6.64248i	0.00162048	+	0.767008i
$76$		0			0
$77$	12.4014	+	2.69775i	1.41327	+	0.307437i
$78$		0			0
$79$	−7.95411	+	2.33554i	−0.894907	+	0.262768i	−0.696675	−	0.717387i	$-0.745338\pi$
$79$	−7.95411	+	2.33554i	−0.894907	+	0.262768i	−0.198232	+	0.980155i	$0.563520\pi$
$80$		0			0
$81$	−2.46836	+	2.84864i	−0.274262	+	0.316516i
$82$		0			0
$83$	2.49864	−	6.69913i	0.274262	−	0.735325i	−0.724669	−	0.689097i	$-0.758007\pi$
$83$	2.49864	−	6.69913i	0.274262	−	0.735325i	0.998931	−	0.0462275i	$-0.0147199\pi$
$84$		0			0
$85$	−2.93334	+	0.107867i	−0.318165	+	0.0116998i
$86$		0			0
$87$	10.7392	−	4.00552i	1.15136	−	0.429437i
$88$		0			0
$89$	12.9522	+	8.32388i	1.37293	+	0.882329i	0.998982	−	0.0451197i	$-0.0143669\pi$
$89$	12.9522	+	8.32388i	1.37293	+	0.882329i	0.373950	+	0.927449i	$0.378003\pi$
$90$		0			0
$91$		−	19.4173i		−	2.03549i
$92$		0			0
$93$	−4.11513	+	4.11513i	−0.426719	+	0.426719i
$94$		0			0
$95$	0.981602	+	1.65043i	0.100710	+	0.169330i
$96$		0			0
$97$	0.0800515	+	0.214626i	0.00812800	+	0.0217920i	0.940950	−	0.338545i	$-0.109935\pi$
$97$	0.0800515	+	0.214626i	0.00812800	+	0.0217920i	−0.932822	+	0.360337i	$0.882662\pi$
$98$		0			0
$99$	−3.66107	−	1.07499i	−0.367951	−	0.108040i
$100$		0			0
$101$	4.12147	+	9.02477i	0.410102	+	0.897998i	0.996145	+	0.0877182i	$0.0279575\pi$
$101$	4.12147	+	9.02477i	0.410102	+	0.897998i	−0.586043	+	0.810280i	$0.699315\pi$
$102$		0			0
$103$	7.63586	−	0.546127i	0.752383	−	0.0538115i	0.310121	−	0.950697i	$-0.399631\pi$
$103$	7.63586	−	0.546127i	0.752383	−	0.0538115i	0.442262	+	0.896886i	$0.354176\pi$
$104$		0			0
$105$	−2.15410	+	12.0120i	−0.210219	+	1.17225i
$106$		0			0
$107$	1.62479	−	7.46906i	0.157075	−	0.722061i	−0.829468	−	0.558555i	$-0.811356\pi$
$107$	1.62479	−	7.46906i	0.157075	−	0.722061i	0.986542	−	0.163506i	$-0.0522804\pi$
$108$		0			0
$109$	−2.91524	−	20.2760i	−0.279230	−	1.94208i	−0.331510	−	0.943452i	$-0.607558\pi$
$109$	−2.91524	−	20.2760i	−0.279230	−	1.94208i	0.0522808	−	0.998632i	$-0.483351\pi$
$110$		0			0
$111$	−4.49787	−	0.646695i	−0.426918	−	0.0613816i
$112$		0			0
$113$	−1.01611	+	14.2071i	−0.0955879	+	1.33649i	0.692717	+	0.721209i	$0.256413\pi$
$113$	−1.01611	+	14.2071i	−0.0955879	+	1.33649i	−0.788305	+	0.615284i	$0.789041\pi$
$114$		0			0
$115$	−1.77859	+	10.5753i	−0.165854	+	0.986150i
$116$		0			0
$117$	−0.416460	+	5.82288i	−0.0385018	+	0.538325i
$118$		0			0
$119$	−5.33788	−	0.767471i	−0.489322	−	0.0703539i
$120$		0			0
$121$	−0.207194	−	1.44106i	−0.0188358	−	0.131006i
$122$		0			0
$123$	−2.99485	+	13.7671i	−0.270036	+	1.24134i
$124$		0			0
$125$	−5.03617	−	9.98183i	−0.450449	−	0.892802i
$126$		0			0
$127$	−5.57621	+	0.398818i	−0.494808	+	0.0353894i	−0.316514	−	0.948588i	$-0.602512\pi$
$127$	−5.57621	+	0.398818i	−0.494808	+	0.0353894i	−0.178294	+	0.983977i	$0.557058\pi$
$128$		0			0
$129$	−2.77699	−	6.08075i	−0.244500	−	0.535381i
$130$		0			0
$131$	−18.9824	−	5.57375i	−1.65850	−	0.486981i	−0.687528	−	0.726158i	$-0.741304\pi$
$131$	−18.9824	−	5.57375i	−1.65850	−	0.486981i	−0.970976	+	0.239178i	$0.923122\pi$
$132$		0			0
$133$	1.23288	+	3.30549i	0.106905	+	0.286622i
$134$		0			0
$135$	3.09844	−	12.1933i	0.266671	−	1.04943i
$136$		0			0
$137$	−9.03420	+	9.03420i	−0.771844	+	0.771844i	−0.978429	−	0.206585i	$-0.933765\pi$
$137$	−9.03420	+	9.03420i	−0.771844	+	0.771844i	0.206585	+	0.978429i	$0.433765\pi$
$138$		0			0
$139$			4.77004i			0.404590i	0.979325	+	0.202295i	$0.0648399\pi$
$139$			4.77004i			0.404590i	−0.979325	+	0.202295i	$0.935160\pi$
$140$		0			0
$141$	−10.2918	−	6.61412i	−0.866724	−	0.557009i
$142$		0			0
$143$	13.6814	−	5.10291i	1.14410	−	0.426727i
$144$		0			0
$145$	−13.1311	+	14.1337i	−1.09048	+	1.17374i
$146$		0			0
$147$	−4.58530	+	12.2937i	−0.378189	+	1.01396i
$148$		0			0
$149$	−10.5241	+	12.1455i	−0.862172	+	0.994999i	0.137818	+	0.990458i	$0.455991\pi$
$149$	−10.5241	+	12.1455i	−0.862172	+	0.994999i	−0.999990	+	0.00454183i	$0.998554\pi$
$150$		0			0
$151$	−17.7447	+	5.21032i	−1.44404	+	0.424010i	−0.907568	−	0.419906i	$-0.862063\pi$
$151$	−17.7447	+	5.21032i	−1.44404	+	0.424010i	−0.536476	+	0.843915i	$0.680245\pi$
$152$		0			0
$153$	1.58427	+	0.344636i	0.128080	+	0.0278622i
$154$		0			0
$155$	3.08356	−	9.29739i	0.247678	−	0.746784i
$156$		0			0
$157$	−1.83774	−	2.45493i	−0.146667	−	0.195925i	0.721191	−	0.692736i	$-0.243595\pi$
$157$	−1.83774	−	2.45493i	−0.146667	−	0.195925i	−0.867859	+	0.496811i	$0.834504\pi$
$158$		0			0
$159$	3.77449	+	4.35599i	0.299336	+	0.345453i
$160$		0			0
$161$	−6.68495	+	18.5330i	−0.526848	+	1.46060i
$162$		0			0
$163$	−0.581964	−	0.0416229i	−0.0455829	−	0.00326016i	0.0485291	−	0.998822i	$-0.484547\pi$
$163$	−0.581964	−	0.0416229i	−0.0455829	−	0.00326016i	−0.0941120	+	0.995562i	$0.530001\pi$
$164$		0			0
$165$	−9.02975	+	1.63900i	−0.702965	+	0.127596i
$166$		0			0
$167$	−11.9773	+	15.9998i	−0.926829	+	1.23810i	0.0441721	+	0.999024i	$0.485935\pi$
$167$	−11.9773	+	15.9998i	−0.926829	+	1.23810i	−0.971001	+	0.239075i	$0.923156\pi$
$168$		0			0
$169$	−5.04991	−	7.85782i	−0.388455	−	0.604448i
$170$		0			0
$171$	−0.298823	−	1.01770i	−0.0228515	−	0.0778252i
$172$		0			0
$173$	−0.483649	−	6.76229i	−0.0367711	−	0.514128i	−0.982143	−	0.188135i	$-0.939756\pi$
$173$	−0.483649	−	6.76229i	−0.0367711	−	0.514128i	0.945372	−	0.325993i	$-0.105699\pi$
$174$		0			0
$175$	−5.82856	−	19.6962i	−0.440598	−	1.48889i
$176$		0			0
$177$	6.96788	+	12.7607i	0.523738	+	0.959155i
$178$		0			0
$179$	6.70264	+	3.06100i	0.500979	+	0.228790i	0.649843	−	0.760068i	$-0.274834\pi$
$179$	6.70264	+	3.06100i	0.500979	+	0.228790i	−0.148864	+	0.988858i	$0.547562\pi$
$180$		0			0
$181$	−7.10389	+	11.0539i	−0.528028	+	0.821628i	−0.998139	−	0.0609793i	$-0.980578\pi$
$181$	−7.10389	+	11.0539i	−0.528028	+	0.821628i	0.470111	+	0.882607i	$0.344214\pi$
$182$		0			0
$183$	8.38738	+	8.38738i	0.620013	+	0.620013i
$184$		0			0
$185$	7.25449	−	2.42304i	0.533360	−	0.178145i
$186$		0			0
$187$	−0.862046	−	3.96276i	−0.0630391	−	0.289786i
$188$		0			0
$189$	9.60169	−	21.0248i	0.698420	−	1.52933i
$190$		0			0
$191$	−3.95828	+	13.4807i	−0.286411	+	0.975427i	0.683089	+	0.730335i	$0.260636\pi$
$191$	−3.95828	+	13.4807i	−0.286411	+	0.975427i	−0.969500	+	0.245091i	$0.921182\pi$
$192$		0			0
$193$	22.7233	+	8.47534i	1.63566	+	0.610068i	0.988355	−	0.152166i	$-0.0486249\pi$
$193$	22.7233	+	8.47534i	1.63566	+	0.610068i	0.647301	+	0.762234i	$0.275898\pi$
$194$		0			0
$195$	5.38691	+	12.9664i	0.385765	+	0.928542i
$196$		0			0
$197$	6.41977	+	3.50546i	0.457390	+	0.249754i	0.691388	−	0.722483i	$-0.256999\pi$
$197$	6.41977	+	3.50546i	0.457390	+	0.249754i	−0.233999	+	0.972237i	$0.575181\pi$
$198$		0			0
$199$	−6.90235	+	4.43587i	−0.489295	+	0.314451i	−0.761922	−	0.647669i	$-0.775744\pi$
$199$	−6.90235	+	4.43587i	−0.489295	+	0.314451i	0.272627	+	0.962120i	$0.412108\pi$
$200$		0			0
$201$	−7.68330	+	1.10469i	−0.541938	+	0.0779190i
$202$		0			0
$203$	−28.3739	+	21.2405i	−1.99146	+	1.49079i
$204$		0			0
$205$	−5.88891	−	22.9712i	−0.411299	−	1.60438i
$206$		0			0
$207$	2.40218	−	5.41431i	0.166963	−	0.376320i
$208$		0			0
$209$	−2.00504	+	1.73738i	−0.138692	+	0.120177i
$210$		0			0
$211$	−2.67112	+	18.5781i	−0.183888	+	1.27897i	0.663574	+	0.748110i	$0.269039\pi$
$211$	−2.67112	+	18.5781i	−0.183888	+	1.27897i	−0.847462	+	0.530856i	$0.821870\pi$
$212$		0			0
$213$	−13.6764	−	10.2381i	−0.937095	−	0.701500i
$214$		0			0
$215$	8.76844	+	7.05079i	0.598002	+	0.480860i
$216$		0			0
$217$	8.62461	−	15.7948i	0.585477	−	1.07222i
$218$		0			0
$219$	−2.51850	−	2.18229i	−0.170184	−	0.147465i
$220$		0			0
$221$	−5.64395	+	2.57751i	−0.379653	+	0.173382i
$222$		0			0
$223$	12.0606	−	6.58558i	0.807637	−	0.441003i	−0.0216912	−	0.999765i	$-0.506905\pi$
$223$	12.0606	−	6.58558i	0.807637	−	0.441003i	0.829328	+	0.558761i	$0.188723\pi$
$224$		0			0
$225$	1.32543	+	6.03153i	0.0883620	+	0.402102i
$226$		0			0
$227$	0.643196	−	0.139919i	0.0426904	−	0.00928673i	−0.191169	−	0.981557i	$-0.561228\pi$
$227$	0.643196	−	0.139919i	0.0426904	−	0.00928673i	0.233860	+	0.972270i	$0.424864\pi$
$228$		0			0
$229$	7.26018			0.479766			0.239883	−	0.970802i	$-0.422891\pi$
$229$	7.26018			0.479766			0.239883	+	0.970802i	$0.422891\pi$
$230$		0			0
$231$	−16.8605			−1.10934
$232$		0			0
$233$	−2.17142	+	0.472363i	−0.142254	+	0.0309456i	−0.283129	−	0.959082i	$-0.591372\pi$
$233$	−2.17142	+	0.472363i	−0.142254	+	0.0309456i	0.140874	+	0.990028i	$0.455009\pi$
$234$		0			0
$235$	20.4758	+	2.17950i	1.33569	+	0.142175i
$236$		0			0
$237$	9.66600	−	5.27804i	0.627874	−	0.342845i
$238$		0			0
$239$	6.22504	−	2.84288i	0.402665	−	0.183891i	−0.203780	−	0.979017i	$-0.565323\pi$
$239$	6.22504	−	2.84288i	0.402665	−	0.183891i	0.606444	+	0.795126i	$0.292595\pi$
$240$		0			0
$241$	0.387044	+	0.335376i	0.0249317	+	0.0216034i	0.667237	−	0.744845i	$-0.267477\pi$
$241$	0.387044	+	0.335376i	0.0249317	+	0.0216034i	−0.642306	+	0.766448i	$0.722022\pi$
$242$		0			0
$243$	−5.68937	+	10.4193i	−0.364974	+	0.668399i
$244$		0			0
$245$	−2.38393	−	21.9555i	−0.152303	−	1.40269i
$246$		0			0
$247$	3.24945	+	2.43251i	0.206757	+	0.154777i
$248$		0			0
$249$	−1.35180	+	9.40200i	−0.0856671	+	0.595828i
$250$		0			0
$251$	4.88037	−	4.22887i	0.308046	−	0.266924i	−0.487093	−	0.873350i	$-0.661943\pi$
$251$	4.88037	−	4.22887i	0.308046	−	0.266924i	0.795140	+	0.606426i	$0.207397\pi$
$252$		0			0
$253$	−14.8152	+	0.160292i	−0.931421	+	0.0100775i
$254$		0			0
$255$	3.77742	−	0.968380i	0.236551	−	0.0606423i
$256$		0			0
$257$	4.44688	−	3.32889i	0.277388	−	0.207650i	−0.451521	−	0.892260i	$-0.649118\pi$
$257$	4.44688	−	3.32889i	0.277388	−	0.207650i	0.728909	+	0.684610i	$0.240027\pi$
$258$		0			0
$259$	13.9087	−	1.99977i	0.864244	−	0.124260i
$260$		0			0
$261$	8.96436	−	5.76105i	0.554880	−	0.356600i
$262$		0			0
$263$	1.74318	+	0.951850i	0.107489	+	0.0586936i	0.532094	−	0.846685i	$-0.321405\pi$
$263$	1.74318	+	0.951850i	0.107489	+	0.0586936i	−0.424605	+	0.905379i	$0.639587\pi$
$264$		0			0
$265$	−8.96681	−	3.70308i	−0.550827	−	0.227478i
$266$		0			0
$267$	−19.1644	−	7.14794i	−1.17284	−	0.437447i
$268$		0			0
$269$	−1.29033	+	4.39447i	−0.0786730	+	0.267936i	−0.989431	−	0.145005i	$-0.953680\pi$
$269$	−1.29033	+	4.39447i	−0.0786730	+	0.267936i	0.910758	+	0.412941i	$0.135498\pi$
$270$		0			0
$271$	−6.93662	+	15.1891i	−0.421370	+	0.922671i	0.573280	+	0.819360i	$0.305671\pi$
$271$	−6.93662	+	15.1891i	−0.421370	+	0.922671i	−0.994649	+	0.103311i	$0.967056\pi$
$272$		0			0
$273$	5.48331	+	25.2064i	0.331865	+	1.52556i
$274$		0			0
$275$	12.3462	−	9.28301i	0.744504	−	0.559787i
$276$		0			0
$277$	20.9147	+	20.9147i	1.25664	+	1.25664i	0.952686	+	0.303956i	$0.0983075\pi$
$277$	20.9147	+	20.9147i	1.25664	+	1.25664i	0.303956	+	0.952686i	$0.401692\pi$
$278$		0			0
$279$	−2.92512	+	4.55158i	−0.175122	+	0.272496i
$280$		0			0
$281$	3.91025	+	1.78575i	0.233266	+	0.106529i	0.528619	−	0.848859i	$-0.322710\pi$
$281$	3.91025	+	1.78575i	0.233266	+	0.106529i	−0.295353	+	0.955388i	$0.595437\pi$
$282$		0			0
$283$	−9.17865	−	16.8094i	−0.545614	−	0.999218i	−0.994410	−	0.105584i	$-0.966329\pi$
$283$	−9.17865	−	16.8094i	−0.545614	−	0.999218i	0.448796	−	0.893634i	$-0.351853\pi$
$284$		0			0
$285$	−1.74033	−	1.86529i	−0.103088	−	0.110490i
$286$		0			0
$287$	−3.10807	−	43.4565i	−0.183463	−	2.56515i
$288$		0			0
$289$	−4.30397	−	14.6580i	−0.253174	−	0.862233i
$290$		0			0
$291$	−0.164527	−	0.256009i	−0.00964475	−	0.0150075i
$292$		0			0
$293$	−17.6883	+	23.6288i	−1.03336	+	1.38041i	−0.111117	+	0.993807i	$0.535443\pi$
$293$	−17.6883	+	23.6288i	−1.03336	+	1.38041i	−0.922246	+	0.386604i	$0.873648\pi$
$294$		0			0
$295$	−20.1163	−	13.9355i	−1.17121	−	0.811356i
$296$		0			0
$297$	17.3374	+	1.24000i	1.00602	+	0.0719518i
$298$		0			0
$299$	5.05776	+	22.0964i	0.292498	+	1.27787i
$300$		0			0
$301$	13.5369	+	15.6225i	0.780256	+	0.900464i
$302$		0			0
$303$	−7.89878	−	10.5515i	−0.453773	−	0.606170i
$304$		0			0
$305$	−18.9498	−	6.28486i	−1.08506	−	0.359870i
$306$		0			0
$307$	−2.86463	−	0.623161i	−0.163493	−	0.0355657i	0.130074	−	0.991504i	$-0.458479\pi$
$307$	−2.86463	−	0.623161i	−0.163493	−	0.0355657i	−0.293567	+	0.955939i	$0.594842\pi$
$308$		0			0
$309$	−9.75818	+	2.86526i	−0.555124	+	0.162999i
$310$		0			0
$311$	4.20636	−	4.85439i	0.238521	−	0.275267i	−0.623851	−	0.781543i	$-0.714433\pi$
$311$	4.20636	−	4.85439i	0.238521	−	0.275267i	0.862372	+	0.506276i	$0.168978\pi$
$312$		0			0
$313$	−4.84826	+	12.9987i	−0.274040	+	0.734730i	0.724907	+	0.688847i	$0.241883\pi$
$313$	−4.84826	+	12.9987i	−0.274040	+	0.734730i	−0.998947	+	0.0458829i	$0.985390\pi$
$314$		0			0
$315$	0.416925	+	11.3379i	0.0234911	+	0.638816i
$316$		0			0
$317$	−8.30854	+	3.09893i	−0.466654	+	0.174053i	−0.571782	−	0.820406i	$-0.693748\pi$
$317$	−8.30854	+	3.09893i	−0.466654	+	0.174053i	0.105128	+	0.994459i	$0.466475\pi$
$318$		0			0
$319$	−22.4228	−	14.4102i	−1.25543	−	0.806819i
$320$		0			0
$321$			10.1547i			0.566781i
$322$		0			0
$323$	0.797138	−	0.797138i	0.0443540	−	0.0443540i
$324$		0			0
$325$	−17.8932	−	15.4385i	−0.992538	−	0.856374i
$326$		0			0
$327$	9.51018	+	25.4978i	0.525914	+	1.41003i
$328$		0			0
$329$	36.2982	+	10.6581i	2.00118	+	0.587601i
$330$		0			0
$331$	2.50238	+	5.47946i	0.137543	+	0.301178i	0.965852	−	0.259094i	$-0.0834239\pi$
$331$	2.50238	+	5.47946i	0.137543	+	0.301178i	−0.828309	+	0.560272i	$0.810697\pi$
$332$		0			0
$333$	−4.21384	+	0.301380i	−0.230917	+	0.0165155i
$334$		0			0
$335$	10.7241	−	7.46269i	0.585921	−	0.407730i
$336$		0			0
$337$	−1.01771	+	4.67834i	−0.0554382	+	0.254845i	−0.996522	−	0.0833276i	$-0.973445\pi$
$337$	−1.01771	+	4.67834i	−0.0554382	+	0.254845i	0.941084	+	0.338173i	$0.109809\pi$
$338$		0			0
$339$	−2.69293	−	18.7298i	−0.146260	−	1.01726i
$340$		0			0
$341$	13.3956	+	1.92599i	0.725412	+	0.104298i
$342$		0			0
$343$	0.843016	−	11.7869i	0.0455186	−	0.636433i
$344$		0			0
$345$	−0.677530	−	14.2305i	−0.0364770	−	0.766142i
$346$		0			0
$347$	−0.415485	+	5.80924i	−0.0223044	+	0.311856i	0.974037	+	0.226390i	$0.0726925\pi$
$347$	−0.415485	+	5.80924i	−0.0223044	+	0.311856i	−0.996341	+	0.0854661i	$0.972762\pi$
$348$		0			0
$349$	0.505505	+	0.0726806i	0.0270591	+	0.00389051i	0.155831	−	0.987784i	$-0.450194\pi$
$349$	0.505505	+	0.0726806i	0.0270591	+	0.00389051i	−0.128772	+	0.991674i	$0.541104\pi$
$350$		0			0
$351$	−3.78461	−	26.3226i	−0.202008	−	1.40499i
$352$		0			0
$353$	6.87092	−	31.5851i	0.365702	−	1.68111i	−0.315433	−	0.948948i	$-0.602150\pi$
$353$	6.87092	−	31.5851i	0.365702	−	1.68111i	0.681135	−	0.732158i	$-0.261487\pi$
$354$		0			0
$355$	28.3035	+	5.07564i	1.50219	+	0.269387i
$356$		0			0
$357$	7.14604	−	0.511095i	0.378208	−	0.0270500i
$358$		0			0
$359$	8.15270	+	17.8519i	0.430283	+	0.942189i	0.993281	+	0.115730i	$0.0369208\pi$
$359$	8.15270	+	17.8519i	0.430283	+	0.942189i	−0.562997	+	0.826459i	$0.690352\pi$
$360$		0			0
$361$	17.5227	+	5.14514i	0.922250	+	0.270797i
$362$		0			0
$363$	0.675912	+	1.81219i	0.0354762	+	0.0951154i
$364$		0			0
$365$	5.43625	+	1.38140i	0.284546	+	0.0723060i
$366$		0			0
$367$	9.97583	−	9.97583i	0.520734	−	0.520734i	−0.397059	−	0.917793i	$-0.629969\pi$
$367$	9.97583	−	9.97583i	0.520734	−	0.520734i	0.917793	+	0.397059i	$0.129969\pi$
$368$		0			0
$369$			13.0984i			0.681877i
$370$		0			0
$371$	−14.9939	−	9.63603i	−0.778447	−	0.500278i
$372$		0			0
$373$	11.8742	−	4.42884i	0.614822	−	0.229317i	−0.0227081	−	0.999742i	$-0.507229\pi$
$373$	11.8742	−	4.42884i	0.614822	−	0.229317i	0.637530	+	0.770425i	$0.279956\pi$
$374$		0			0
$375$	9.35645	+	11.5356i	0.483165	+	0.595697i
$376$		0			0
$377$	−14.2510	+	38.2084i	−0.733963	+	1.96783i
$378$		0			0
$379$	14.1689	−	16.3518i	0.727808	−	0.839936i	−0.264414	−	0.964409i	$-0.585179\pi$
$379$	14.1689	−	16.3518i	0.727808	−	0.839936i	0.992223	+	0.124473i	$0.0397241\pi$
$380$		0			0
$381$	7.12607	−	2.09240i	0.365080	−	0.107197i
$382$		0			0
$383$	8.93028	+	1.94266i	0.456316	+	0.0992654i	0.434848	−	0.900504i	$-0.356802\pi$
$383$	8.93028	+	1.94266i	0.456316	+	0.0992654i	0.0214683	+	0.999770i	$0.493166\pi$
$384$		0			0
$385$	25.3636	−	12.7296i	1.29265	−	0.648763i
$386$		0			0
$387$	−3.72440	−	4.97522i	−0.189322	−	0.252904i
$388$		0			0
$389$	−21.7835	−	25.1395i	−1.10447	−	1.27462i	−0.958424	−	0.285346i	$-0.907891\pi$
$389$	−21.7835	−	25.1395i	−1.10447	−	1.27462i	−0.146044	−	0.989278i	$-0.546654\pi$
$390$		0			0
$391$	6.27429	−	0.517031i	0.317305	−	0.0261474i
$392$		0			0
$393$	26.2158	+	1.87499i	1.32241	+	0.0945809i
$394$		0			0
$395$	−10.5559	+	15.2377i	−0.531123	+	0.766691i
$396$		0			0
$397$	8.17626	−	10.9222i	0.410355	−	0.548170i	−0.546982	−	0.837144i	$-0.684223\pi$
$397$	8.17626	−	10.9222i	0.410355	−	0.548170i	0.957337	+	0.288975i	$0.0933143\pi$
$398$		0			0
$399$	−2.53390	−	3.94283i	−0.126854	−	0.197388i
$400$		0			0
$401$	6.17574	+	21.0326i	0.308402	+	1.05032i	0.957216	+	0.289373i	$0.0934468\pi$
$401$	6.17574	+	21.0326i	0.308402	+	1.05032i	−0.648815	+	0.760946i	$0.724735\pi$
$402$		0			0
$403$	−1.47711	−	20.6527i	−0.0735801	−	1.02878i
$404$		0			0
$405$	−0.291931	+	8.42334i	−0.0145062	+	0.418559i
$406$		0			0
$407$	5.06427	+	9.27453i	0.251027	+	0.459721i
$408$		0			0
$409$	5.41650	+	2.47363i	0.267829	+	0.122313i	0.544803	−	0.838564i	$-0.316604\pi$
$409$	5.41650	+	2.47363i	0.267829	+	0.122313i	−0.276974	+	0.960877i	$0.589332\pi$
$410$		0			0
$411$	9.17646	−	14.2789i	0.452641	−	0.704324i
$412$		0			0
$413$	−31.7910	−	31.7910i	−1.56433	−	1.56433i
$414$		0			0
$415$	−5.06494	−	15.1642i	−0.248628	−	0.744383i
$416$		0			0
$417$	−1.34703	−	6.19218i	−0.0659642	−	0.303232i
$418$		0			0
$419$	−5.52164	+	12.0907i	−0.269750	+	0.590669i	−0.995228	−	0.0975756i	$-0.968891\pi$
$419$	−5.52164	+	12.0907i	−0.269750	+	0.590669i	0.725479	+	0.688245i	$0.241619\pi$
$420$		0			0
$421$	0.679953	−	2.31571i	0.0331389	−	0.112861i	−0.941263	−	0.337675i	$-0.890359\pi$
$421$	0.679953	−	2.31571i	0.0331389	−	0.112861i	0.974402	+	0.224815i	$0.0721776\pi$
$422$		0			0
$423$	−10.6565	−	3.97468i	−0.518138	−	0.193256i
$424$		0			0
$425$	−4.95133	+	4.30870i	−0.240175	+	0.209002i
$426$		0			0
$427$	−32.1926	−	17.5785i	−1.55791	−	0.850684i
$428$		0			0
$429$	−16.3194	+	10.4878i	−0.787907	+	0.506357i
$430$		0			0
$431$	−32.0482	+	4.60784i	−1.54371	+	0.221952i	−0.860949	−	0.508692i	$-0.830129\pi$
$431$	−32.0482	+	4.60784i	−1.54371	+	0.221952i	−0.682759	+	0.730644i	$0.739220\pi$
$432$		0			0
$433$	−21.4201	+	16.0348i	−1.02938	+	0.770586i	−0.973693	−	0.227863i	$-0.926826\pi$
$433$	−21.4201	+	16.0348i	−1.02938	+	0.770586i	−0.0556886	+	0.998448i	$0.517735\pi$
$434$		0			0
$435$	13.0547	−	22.0556i	0.625925	−	1.05748i
$436$		0			0
$437$	−2.26400	−	3.44044i	−0.108302	−	0.164578i
$438$		0			0
$439$	−13.7158	+	11.8849i	−0.654622	+	0.567233i	−0.917569	−	0.397577i	$-0.869851\pi$
$439$	−13.7158	+	11.8849i	−0.654622	+	0.567233i	0.262947	+	0.964810i	$0.415306\pi$
$440$		0			0
$441$	−1.73601	+	12.0742i	−0.0826671	+	0.574962i
$442$		0			0
$443$	10.4885	+	7.85157i	0.498322	+	0.373040i	0.818673	−	0.574259i	$-0.194710\pi$
$443$	10.4885	+	7.85157i	0.498322	+	0.373040i	−0.320351	+	0.947299i	$0.603801\pi$
$444$		0			0
$445$	34.2260	−	3.71626i	1.62247	−	0.176168i
$446$		0			0
$447$	10.2320	−	18.7385i	0.483957	−	0.886302i
$448$		0			0
$449$	2.53919	+	2.20022i	0.119832	+	0.103835i	0.712715	−	0.701453i	$-0.247465\pi$
$449$	2.53919	+	2.20022i	0.119832	+	0.103835i	−0.592884	+	0.805288i	$0.702011\pi$
$450$		0			0
$451$	29.8026	−	13.6104i	1.40335	−	0.640889i
$452$		0			0
$453$	21.5638	−	11.7747i	1.01315	−	0.553224i
$454$		0			0
$455$	−27.2794	−	33.7786i	−1.27888	−	1.58356i
$456$		0			0
$457$	−23.0253	+	5.00884i	−1.07708	+	0.234304i	−0.715907	−	0.698196i	$-0.753986\pi$
$457$	−23.0253	+	5.00884i	−1.07708	+	0.234304i	−0.361170	+	0.932500i	$0.617623\pi$
$458$		0			0
$459$	−7.38574			−0.344737
$460$		0			0
$461$	−27.0549			−1.26007			−0.630036	−	0.776566i	$-0.716960\pi$
$461$	−27.0549			−1.26007			−0.630036	+	0.776566i	$0.716960\pi$
$462$		0			0
$463$	−25.9579	+	5.64680i	−1.20637	+	0.262429i	−0.770416	−	0.637541i	$-0.779952\pi$
$463$	−25.9579	+	5.64680i	−1.20637	+	0.262429i	−0.435951	+	0.899970i	$0.643588\pi$
$464$		0			0
$465$	−1.37738	+	12.9401i	−0.0638743	+	0.600082i
$466$		0			0
$467$	−20.8304	+	11.3742i	−0.963915	+	0.526337i	−0.882484	−	0.470342i	$-0.844131\pi$
$467$	−20.8304	+	11.3742i	−0.963915	+	0.526337i	−0.0814305	+	0.996679i	$0.525949\pi$
$468$		0			0
$469$	21.8342	−	9.97133i	1.00821	−	0.460433i
$470$		0			0
$471$	3.07890	+	2.66788i	0.141868	+	0.122929i
$472$		0			0
$473$	−7.45005	+	13.6438i	−0.342554	+	0.627340i
$474$		0			0
$475$	4.02630	+	1.49205i	0.184739	+	0.0684599i
$476$		0			0
$477$	4.28972	+	3.21125i	0.196413	+	0.147033i
$478$		0			0
$479$	−1.79938	+	12.5149i	−0.0822156	+	0.571822i	0.906521	+	0.422160i	$0.138728\pi$
$479$	−1.79938	+	12.5149i	−0.0822156	+	0.571822i	−0.988737	+	0.149663i	$0.952181\pi$
$480$		0			0
$481$	12.2184	−	10.5873i	0.557110	−	0.482739i
$482$		0			0
$483$	3.44441	−	25.9462i	0.156726	−	1.18059i
$484$		0			0
$485$	0.440788	+	0.260902i	0.0200151	+	0.0118470i
$486$		0			0
$487$	23.9072	−	17.8967i	1.08334	−	0.810977i	0.100407	−	0.994946i	$-0.467986\pi$
$487$	23.9072	−	17.8967i	1.08334	−	0.810977i	0.982932	+	0.183969i	$0.0588946\pi$
$488$		0			0
$489$	0.767224	−	0.110310i	0.0346951	−	0.00498840i
$490$		0			0
$491$	−23.4340	+	15.0601i	−1.05756	+	0.679654i	−0.949269	−	0.314465i	$-0.898175\pi$
$491$	−23.4340	+	15.0601i	−1.05756	+	0.679654i	−0.108294	+	0.994119i	$0.534539\pi$
$492$		0			0
$493$	9.94032	+	5.42783i	0.447690	+	0.244457i
$494$		0			0
$495$	−7.87909	+	3.27338i	−0.354139	+	0.147128i
$496$		0			0
$497$	49.4978	+	18.4617i	2.22028	+	0.828121i
$498$		0			0
$499$	−2.00763	+	6.83736i	−0.0898738	+	0.306082i	−0.992146	−	0.125085i	$-0.960080\pi$
$499$	−2.00763	+	6.83736i	−0.0898738	+	0.306082i	0.902272	+	0.431167i	$0.141898\pi$
$500$		0			0
$501$	11.0299	−	24.1522i	0.492782	−	1.07904i
$502$		0			0
$503$	8.99408	+	41.3451i	0.401026	+	1.84349i	0.524865	+	0.851186i	$0.324116\pi$
$503$	8.99408	+	41.3451i	0.401026	+	1.84349i	−0.123838	+	0.992302i	$0.539520\pi$
$504$		0			0
$505$	19.8487	+	9.90933i	0.883254	+	0.440959i
$506$		0			0
$507$	8.77448	+	8.77448i	0.389689	+	0.389689i
$508$		0			0
$509$	−5.86098	+	9.11987i	−0.259783	+	0.404231i	−0.946505	−	0.322690i	$-0.895413\pi$
$509$	−5.86098	+	9.11987i	−0.259783	+	0.404231i	0.686721	+	0.726921i	$0.259049\pi$
$510$		0			0
$511$	9.37365	+	4.28080i	0.414666	+	0.189372i
$512$		0			0
$513$	2.31560	+	4.24070i	0.102236	+	0.187232i
$514$		0			0
$515$	12.5162	−	11.6777i	0.551528	−	0.514580i
$516$		0			0
$517$	2.02954	+	28.3767i	0.0892591	+	1.24801i
$518$		0			0
$519$	2.53747	+	8.64182i	0.111382	+	0.379334i
$520$		0			0
$521$	−13.4890	−	20.9893i	−0.590963	−	0.919557i	−0.999975	−	0.00702798i	$-0.997763\pi$
$521$	−13.4890	−	20.9893i	−0.590963	−	0.919557i	0.409012	−	0.912529i	$-0.365873\pi$
$522$		0			0
$523$	2.21920	−	2.96451i	0.0970390	−	0.129629i	−0.749394	−	0.662125i	$-0.769655\pi$
$523$	2.21920	−	2.96451i	0.0970390	−	0.129629i	0.846433	+	0.532496i	$0.178746\pi$
$524$		0			0
$525$	13.1284	+	23.9225i	0.572968	+	1.04406i
$526$		0			0
$527$	−5.73587	−	0.410238i	−0.249858	−	0.0178702i
$528$		0			0
$529$	2.77990	−	22.8314i	0.120865	−	0.992669i
$530$		0			0
$531$	8.85167	+	10.2154i	0.384130	+	0.443309i
$532$		0			0
$533$	−30.0398	−	40.1284i	−1.30117	−	1.73816i
$534$		0			0
$535$	−7.66678	−	15.2759i	−0.331464	−	0.660436i
$536$		0			0
$537$	−9.56537	−	2.08082i	−0.412776	−	0.0897940i
$538$		0			0
$539$	29.2761	−	8.59624i	1.26101	−	0.370266i
$540$		0			0
$541$	24.4941	−	28.2677i	1.05308	−	1.21532i	0.0772049	−	0.997015i	$-0.475400\pi$
$541$	24.4941	−	28.2677i	1.05308	−	1.21532i	0.975880	−	0.218309i	$-0.0700541\pi$
$542$		0			0
$543$	6.10031	−	16.3556i	0.261789	−	0.701884i
$544$		0			0
$545$	−33.5571	−	31.1767i	−1.43743	−	1.33546i
$546$		0			0
$547$	−10.9120	+	4.06996i	−0.466563	+	0.174019i	−0.571741	−	0.820434i	$-0.693732\pi$
$547$	−10.9120	+	4.06996i	−0.466563	+	0.174019i	0.105177	+	0.994453i	$0.466459\pi$
$548$		0			0
$549$	9.27693	+	5.96192i	0.395930	+	0.254449i
$550$		0			0
$551$		−	7.40923i		−	0.315644i
$552$		0			0
$553$	−24.0811	+	24.0811i	−1.02403	+	1.02403i
$554$		0			0
$555$	−8.73309	+	5.19406i	−0.370699	+	0.220476i
$556$		0			0
$557$	−0.876422	−	2.34978i	−0.0371352	−	0.0995633i	0.917059	−	0.398752i	$-0.130557\pi$
$557$	−0.876422	−	2.34978i	−0.0371352	−	0.0995633i	−0.954194	+	0.299189i	$0.903284\pi$
$558$		0			0
$559$	22.8202	+	6.70062i	0.965192	+	0.283406i
$560$		0			0
$561$	2.23811	+	4.90078i	0.0944932	+	0.206911i
$562$		0			0
$563$	33.8315	−	2.41968i	1.42583	−	0.101977i	0.663020	−	0.748601i	$-0.269274\pi$
$563$	33.8315	−	2.41968i	1.42583	−	0.101977i	0.762809	+	0.646624i	$0.223820\pi$
$564$		0			0
$565$	18.1920	+	26.1424i	0.765342	+	1.09982i
$566$		0			0
$567$	−3.29150	+	15.1308i	−0.138230	+	0.635433i
$568$		0			0
$569$	4.19809	+	29.1983i	0.175993	+	1.22406i	0.865921	+	0.500180i	$0.166733\pi$
$569$	4.19809	+	29.1983i	0.175993	+	1.22406i	−0.689929	+	0.723877i	$0.742358\pi$
$570$		0			0
$571$	−45.2044	−	6.49942i	−1.89175	−	0.271992i	−0.903938	−	0.427664i	$-0.859337\pi$
$571$	−45.2044	−	6.49942i	−1.89175	−	0.271992i	−0.987809	+	0.155672i	$0.950246\pi$
$572$		0			0
$573$	1.33156	−	18.6176i	0.0556265	−	0.777760i
$574$		0			0
$575$	11.7632	+	20.8956i	0.490559	+	0.871408i
$576$		0			0
$577$	1.51015	−	21.1147i	0.0628684	−	0.879015i	−0.863967	−	0.503548i	$-0.832028\pi$
$577$	1.51015	−	21.1147i	0.0628684	−	0.879015i	0.926836	−	0.375467i	$-0.122518\pi$
$578$		0			0
$579$	−31.8913	−	4.58528i	−1.32536	−	0.190558i
$580$		0			0
$581$	−4.18016	−	29.0737i	−0.173422	−	1.20618i
$582$		0			0
$583$	2.84910	−	13.0971i	0.117998	−	0.542427i
$584$		0			0
$585$	7.45609	+	10.7146i	0.308271	+	0.442996i
$586$		0			0
$587$	4.96852	−	0.355356i	0.205073	−	0.0146671i	0.0315752	−	0.999501i	$-0.489948\pi$
$587$	4.96852	−	0.355356i	0.205073	−	0.0146671i	0.173498	+	0.984834i	$0.444493\pi$
$588$		0			0
$589$	1.56278	+	3.42201i	0.0643932	+	0.141001i
$590$		0			0
$591$	−9.32367	−	2.73768i	−0.383525	−	0.112613i
$592$		0			0
$593$	5.75283	+	15.4239i	0.236241	+	0.633385i	0.999926	−	0.0122036i	$-0.00388463\pi$
$593$	5.75283	+	15.4239i	0.236241	+	0.633385i	−0.763685	+	0.645589i	$0.776612\pi$
$594$		0			0
$595$	−10.3641	+	6.16409i	−0.424885	+	0.252703i
$596$		0			0
$597$	7.70756	−	7.70756i	0.315449	−	0.315449i
$598$		0			0
$599$			10.1589i			0.415080i	0.978227	+	0.207540i	$0.0665458\pi$
$599$			10.1589i			0.415080i	−0.978227	+	0.207540i	$0.933454\pi$
$600$		0			0
$601$	12.6133	+	8.10606i	0.514506	+	0.330653i	0.771995	−	0.635628i	$-0.219259\pi$
$601$	12.6133	+	8.10606i	0.514506	+	0.330653i	−0.257489	+	0.966281i	$0.582895\pi$
$602$		0			0
$603$	−6.76151	+	2.52191i	−0.275350	+	0.102700i
$604$		0			0
$605$	−2.38499	−	2.21580i	−0.0969636	−	0.0900853i
$606$		0			0
$607$	14.5861	−	39.1070i	0.592033	−	1.58730i	−0.201971	−	0.979391i	$-0.564735\pi$
$607$	14.5861	−	39.1070i	0.592033	−	1.58730i	0.794005	−	0.607911i	$-0.207992\pi$
$608$		0			0
$609$	30.8352	−	35.5857i	1.24950	−	1.44200i
$610$		0			0
$611$	41.7629	−	12.2627i	1.68955	−	0.496096i
$612$		0			0
$613$	22.7684	+	4.95297i	0.919609	+	0.200049i	0.647365	−	0.762180i	$-0.275871\pi$
$613$	22.7684	+	4.95297i	0.919609	+	0.200049i	0.272243	+	0.962228i	$0.412234\pi$
$614$		0			0
$615$	14.1315	+	28.1569i	0.569839	+	1.13539i
$616$		0			0
$617$	2.35523	+	3.14621i	0.0948179	+	0.126662i	0.845441	−	0.534069i	$-0.179338\pi$
$617$	2.35523	+	3.14621i	0.0948179	+	0.126662i	−0.750623	+	0.660730i	$0.770247\pi$
$618$		0			0
$619$	−11.0476	−	12.7496i	−0.444041	−	0.512450i	0.488969	−	0.872301i	$-0.337373\pi$
$619$	−11.0476	−	12.7496i	−0.444041	−	0.512450i	−0.933010	+	0.359851i	$0.882828\pi$
$620$		0			0
$621$	−5.45003	+	26.4267i	−0.218702	+	1.06047i
$622$		0			0
$623$	63.0885	+	4.51218i	2.52759	+	0.180777i
$624$		0			0
$625$	−22.7845	−	10.2892i	−0.911379	−	0.411568i
$626$		0			0
$627$	2.11220	−	2.82157i	0.0843533	−	0.112683i
$628$		0			0
$629$	−2.42754	−	3.77733i	−0.0967925	−	0.150612i
$630$		0			0
$631$	−5.36879	−	18.2844i	−0.213728	−	0.727891i	−0.994654	−	0.103267i	$-0.967070\pi$
$631$	−5.36879	−	18.2844i	−0.213728	−	0.727891i	0.780925	−	0.624624i	$-0.214748\pi$
$632$		0			0
$633$	−1.77882	−	24.8712i	−0.0707019	−	0.988542i
$634$		0			0
$635$	−9.14014	+	8.52781i	−0.362715	+	0.338416i
$636$		0			0
$637$	−22.3724	−	40.9720i	−0.886426	−	1.62337i
$638$		0			0
$639$	−14.4475	−	6.59794i	−0.571533	−	0.261010i
$640$		0			0
$641$	19.7403	−	30.7165i	0.779696	−	1.21323i	−0.193012	−	0.981196i	$-0.561826\pi$
$641$	19.7403	−	30.7165i	0.779696	−	1.21323i	0.972708	−	0.232034i	$-0.0745381\pi$
$642$		0			0
$643$	9.65361	+	9.65361i	0.380701	+	0.380701i	0.871355	−	0.490654i	$-0.163242\pi$
$643$	9.65361	+	9.65361i	0.380701	+	0.380701i	−0.490654	+	0.871355i	$0.663242\pi$
$644$		0			0
$645$	−13.3737	−	6.67676i	−0.526591	−	0.262897i
$646$		0			0
$647$	2.60600	+	11.9796i	0.102452	+	0.470966i	0.999574	+	0.0291823i	$0.00929033\pi$
$647$	2.60600	+	11.9796i	0.102452	+	0.470966i	−0.897122	+	0.441783i	$0.854346\pi$
$648$		0			0
$649$	14.0452	−	30.7547i	0.551323	−	1.20723i
$650$		0			0
$651$	−6.73561	+	22.9394i	−0.263989	+	0.899065i
$652$		0			0
$653$	9.44321	+	3.52214i	0.369541	+	0.137832i	0.527372	−	0.849634i	$-0.323177\pi$
$653$	9.44321	+	3.52214i	0.369541	+	0.137832i	−0.157831	+	0.987466i	$0.550450\pi$
$654$		0			0
$655$	−40.8527	+	16.9723i	−1.59625	+	0.663163i
$656$		0			0
$657$	−2.71916	−	1.48478i	−0.106085	−	0.0579266i
$658$		0			0
$659$	−17.2333	+	11.0752i	−0.671315	+	0.431428i	−0.831399	−	0.555675i	$-0.812460\pi$
$659$	−17.2333	+	11.0752i	−0.671315	+	0.431428i	0.160084	+	0.987103i	$0.448823\pi$
$660$		0			0
$661$	−9.57686	+	1.37694i	−0.372497	+	0.0535569i	−0.326021	−	0.945363i	$-0.605708\pi$
$661$	−9.57686	+	1.37694i	−0.372497	+	0.0535569i	−0.0464755	+	0.998919i	$0.514799\pi$
$662$		0			0
$663$	6.59877	−	4.93978i	0.256275	−	0.191845i
$664$		0			0
$665$	6.78863	+	4.01819i	0.263252	+	0.155819i
$666$		0			0
$667$	26.7562	−	31.5619i	1.03601	−	1.22208i
$668$		0			0
$669$	−13.7966	+	11.9548i	−0.533408	+	0.462201i
$670$		0			0
$671$	3.92552	−	27.3026i	0.151543	−	1.05401i
$672$		0			0
$673$	20.3001	+	15.1965i	0.782511	+	0.585780i	0.914083	−	0.405526i	$-0.132912\pi$
$673$	20.3001	+	15.1965i	0.782511	+	0.585780i	−0.131573	+	0.991307i	$0.542003\pi$
$674$		0			0
$675$	−11.7403	−	25.5646i	−0.451885	−	0.983983i
$676$		0			0
$677$	−15.9137	+	29.1438i	−0.611614	+	1.12009i	0.369967	+	0.929045i	$0.379369\pi$
$677$	−15.9137	+	29.1438i	−0.611614	+	1.12009i	−0.981582	+	0.191043i	$0.938813\pi$
$678$		0			0
$679$	0.711191	+	0.616250i	0.0272930	+	0.0236495i
$680$		0			0
$681$	−0.795446	+	0.363268i	−0.0304816	+	0.0139205i
$682$		0			0
$683$	25.6349	−	13.9977i	0.980891	−	0.535607i	0.0930022	−	0.995666i	$-0.470354\pi$
$683$	25.6349	−	13.9977i	0.980891	−	0.535607i	0.887888	+	0.460059i	$0.152172\pi$
$684$		0			0
$685$	−3.02384	+	28.4082i	−0.115535	+	1.08542i
$686$		0			0
$687$	−9.42473	+	2.05022i	−0.359576	+	0.0782209i
$688$		0			0
$689$	−20.5067			−0.781242
$690$		0			0
$691$	−21.4238			−0.814999			−0.407500	−	0.913205i	$-0.633599\pi$
$691$	−21.4238			−0.814999			−0.407500	+	0.913205i	$0.633599\pi$
$692$		0			0
$693$	−15.3168	+	3.33196i	−0.581836	+	0.126571i
$694$		0			0
$695$	6.70144	+	8.29802i	0.254200	+	0.314762i
$696$		0			0
$697$	−12.2188	+	6.67195i	−0.462818	+	0.252718i
$698$		0			0
$699$	2.68541	−	1.22639i	0.101572	−	0.0463862i
$700$		0			0
$701$	24.3728	+	21.1192i	0.920549	+	0.797660i	0.979675	−	0.200590i	$-0.0642860\pi$
$701$	24.3728	+	21.1192i	0.920549	+	0.797660i	−0.0591261	+	0.998251i	$0.518831\pi$
$702$		0			0
$703$	−1.40776	+	2.57811i	−0.0530945	+	0.0972354i
$704$		0			0
$705$	−27.1959	+	2.95292i	−1.02426	+	0.111214i
$706$		0			0
$707$	32.6284	+	24.4253i	1.22712	+	0.918607i
$708$		0			0
$709$	−0.602150	+	4.18805i	−0.0226142	+	0.157285i	−0.997999	−	0.0632222i	$-0.979862\pi$
$709$	−0.602150	+	4.18805i	−0.0226142	+	0.157285i	0.975385	+	0.220508i	$0.0707714\pi$
$710$		0			0
$711$	7.73795	−	6.70497i	0.290196	−	0.251456i
$712$		0			0
$713$	−5.70043	+	20.2206i	−0.213483	+	0.757269i
$714$		0			0
$715$	16.6313	−	28.0982i	0.621976	−	1.05081i
$716$		0			0
$717$	−7.27816	+	5.44837i	−0.271808	+	0.203473i
$718$		0			0
$719$	1.63507	−	0.235087i	0.0609777	−	0.00876727i	−0.111758	−	0.993735i	$-0.535648\pi$
$719$	1.63507	−	0.235087i	0.0609777	−	0.00876727i	0.172736	+	0.984968i	$0.444739\pi$
$720$		0			0
$721$	26.4566	−	17.0026i	0.985295	−	0.633211i
$722$		0			0
$723$	−0.597145	−	0.326066i	−0.0222081	−	0.0121265i
$724$		0			0
$725$	−2.98655	+	43.0349i	−0.110918	+	1.59828i
$726$		0			0
$727$	−14.2866	−	5.32863i	−0.529861	−	0.197628i	0.0702726	−	0.997528i	$-0.477613\pi$
$727$	−14.2866	−	5.32863i	−0.529861	−	0.197628i	−0.600133	+	0.799900i	$0.704886\pi$
$728$		0			0
$729$	7.62906	−	25.9822i	0.282558	−	0.962303i
$730$		0			0
$731$	2.74399	−	6.00850i	0.101490	−	0.222232i
$732$		0			0
$733$	7.87075	+	36.1813i	0.290713	+	1.33639i	0.858332	+	0.513094i	$0.171501\pi$
$733$	7.87075	+	36.1813i	0.290713	+	1.33639i	−0.567620	+	0.823291i	$0.692136\pi$
$734$		0			0
$735$	9.29475	+	27.8281i	0.342842	+	1.02646i
$736$		0			0
$737$	12.7639	+	12.7639i	0.470163	+	0.470163i
$738$		0			0
$739$	−26.6730	+	41.5041i	−0.981184	+	1.52675i	−0.137089	+	0.990559i	$0.543775\pi$
$739$	−26.6730	+	41.5041i	−0.981184	+	1.52675i	−0.844095	+	0.536193i	$0.819862\pi$
$740$		0			0
$741$	−4.90516	−	2.24011i	−0.180195	−	0.0822925i
$742$		0			0
$743$	8.25082	+	15.1102i	0.302693	+	0.554341i	0.984111	−	0.177553i	$-0.0568182\pi$
$743$	8.25082	+	15.1102i	0.302693	+	0.554341i	−0.681418	+	0.731894i	$0.738636\pi$
$744$		0			0
$745$	−1.24468	+	35.9139i	−0.0456016	+	1.31578i
$746$		0			0
$747$	0.629982	+	8.80830i	0.0230498	+	0.322279i
$748$		0			0
$749$	−8.84676	−	30.1293i	−0.323254	−	1.10090i
$750$		0			0
$751$	5.68446	+	8.84520i	0.207429	+	0.322766i	0.929343	−	0.369217i	$-0.120374\pi$
$751$	5.68446	+	8.84520i	0.207429	+	0.322766i	−0.721914	+	0.691982i	$0.756738\pi$
$752$		0			0
$753$	−5.14120	+	6.86784i	−0.187356	+	0.250278i
$754$		0			0
$755$	−23.5489	+	33.9935i	−0.857033	+	1.23715i
$756$		0			0
$757$	−39.8528	−	2.85033i	−1.44847	−	0.103597i	−0.675184	−	0.737650i	$-0.735936\pi$
$757$	−39.8528	−	2.85033i	−1.44847	−	0.103597i	−0.773290	+	0.634053i	$0.781390\pi$
$758$		0			0
$759$	19.1869	−	4.39178i	0.696440	−	0.159411i
$760$		0			0
$761$	−25.3389	−	29.2427i	−0.918536	−	1.06005i	−0.998000	−	0.0632094i	$-0.979866\pi$
$761$	−25.3389	−	29.2427i	−0.918536	−	1.06005i	0.0794642	−	0.996838i	$-0.474679\pi$
$762$		0			0
$763$	−50.4306	−	67.3674i	−1.82571	−	2.43886i
$764$		0			0
$765$	3.24019	−	1.62621i	0.117149	−	0.0587956i
$766$		0			0
$767$	−50.5459	−	10.9956i	−1.82511	−	0.397027i
$768$		0			0
$769$	28.7815	−	8.45101i	1.03789	−	0.304751i	0.281973	−	0.959422i	$-0.409011\pi$
$769$	28.7815	−	8.45101i	1.03789	−	0.304751i	0.755914	+	0.654671i	$0.227193\pi$
$770$		0			0
$771$	−4.83261	+	5.57713i	−0.174042	+	0.200855i
$772$		0			0
$773$	6.21104	−	16.6524i	0.223396	−	0.598947i	−0.776103	−	0.630606i	$-0.782806\pi$
$773$	6.21104	−	16.6524i	0.223396	−	0.598947i	0.999499	+	0.0316591i	$0.0100791\pi$
$774$		0			0
$775$	−7.69771	−	20.5060i	−0.276510	−	0.736596i
$776$		0			0
$777$	−17.4907	+	6.52369i	−0.627475	+	0.234036i
$778$		0			0
$779$	7.66172	+	4.92389i	0.274510	+	0.176417i
$780$		0			0
$781$			39.7279i			1.42158i
$782$		0			0
$783$	−34.3244	+	34.3244i	−1.22666	+	1.22666i
$784$		0			0
$785$	−6.64589	−	1.68879i	−0.237202	−	0.0602754i
$786$		0			0
$787$	3.19936	+	8.57781i	0.114045	+	0.305766i	0.981415	−	0.191898i	$-0.0614642\pi$
$787$	3.19936	+	8.57781i	0.114045	+	0.305766i	−0.867370	+	0.497664i	$0.834191\pi$
$788$		0			0
$789$	−2.53169	−	0.743371i	−0.0901306	−	0.0264647i
$790$		0			0
$791$	24.3074	+	53.2257i	0.864270	+	1.89249i
$792$		0			0
$793$	−42.0939	+	3.01061i	−1.49480	+	0.106910i
$794$		0			0
$795$	12.6859	+	2.27495i	0.449922	+	0.0806842i
$796$		0			0
$797$	7.75591	−	35.6533i	0.274728	−	1.26291i	−0.608346	−	0.793672i	$-0.708167\pi$
$797$	7.75591	−	35.6533i	0.274728	−	1.26291i	0.883074	−	0.469234i	$-0.155470\pi$
$798$		0			0
$799$	−1.72037	−	11.9654i	−0.0608624	−	0.423307i
$800$		0			0
$801$	−18.8223	−	2.70623i	−0.665052	−	0.0956200i
$802$		0			0
$803$	−0.552838	+	7.72968i	−0.0195092	+	0.272775i
$804$		0			0
$805$	14.4078	+	41.6319i	0.507808	+	1.46733i
$806$		0			0
$807$	0.434065	−	6.06902i	0.0152798	−	0.213640i
$808$		0			0
$809$	−8.54324	−	1.22833i	−0.300364	−	0.0431859i	−0.00951493	−	0.999955i	$-0.503029\pi$
$809$	−8.54324	−	1.22833i	−0.300364	−	0.0431859i	−0.290849	+	0.956769i	$0.593938\pi$
$810$		0			0
$811$	2.17029	+	15.0947i	0.0762092	+	0.530046i	0.991786	+	0.127904i	$0.0408251\pi$
$811$	2.17029	+	15.0947i	0.0762092	+	0.530046i	−0.915577	+	0.402142i	$0.868266\pi$
$812$		0			0
$813$	4.71541	−	21.6764i	0.165377	−	0.760224i
$814$		0			0
$815$	−1.07087	+	0.745194i	−0.0375109	+	0.0261030i
$816$		0			0
$817$	−4.31023	+	0.308274i	−0.150796	+	0.0107851i
$818$		0			0
$819$	9.96252	+	21.8149i	0.348118	+	0.762273i
$820$		0			0
$821$	−28.0095	−	8.22434i	−0.977539	−	0.287031i	−0.246331	−	0.969186i	$-0.579225\pi$
$821$	−28.0095	−	8.22434i	−0.977539	−	0.287031i	−0.731208	+	0.682154i	$0.761043\pi$
$822$		0			0
$823$	−4.93029	−	13.2186i	−0.171859	−	0.460772i	0.822254	−	0.569121i	$-0.192716\pi$
$823$	−4.93029	−	13.2186i	−0.171859	−	0.460772i	−0.994113	+	0.108349i	$0.965444\pi$
$824$		0			0
$825$	−13.4056	+	15.5371i	−0.466724	+	0.540933i
$826$		0			0
$827$	−4.55736	+	4.55736i	−0.158475	+	0.158475i	−0.781891	−	0.623416i	$-0.785744\pi$
$827$	−4.55736	+	4.55736i	−0.158475	+	0.158475i	0.623416	+	0.781891i	$0.285744\pi$
$828$		0			0
$829$		−	26.7293i		−	0.928346i	−0.885744	−	0.464173i	$-0.846352\pi$
$829$		−	26.7293i		−	0.928346i	0.885744	−	0.464173i	$-0.153648\pi$
$830$		0			0
$831$	−33.0563	−	21.2440i	−1.14671	−	0.736947i
$832$		0			0
$833$	−12.1476	+	4.53082i	−0.420889	+	0.156984i
$834$		0			0
$835$	1.64229	+	44.6603i	0.0568336	+	1.54553i
$836$		0			0
$837$	8.61318	−	23.0928i	0.297715	−	0.798205i
$838$		0			0
$839$	−12.4568	+	14.3759i	−0.430057	+	0.496313i	−0.928874	−	0.370395i	$-0.879222\pi$
$839$	−12.4568	+	14.3759i	−0.430057	+	0.496313i	0.498817	+	0.866707i	$0.333768\pi$
$840$		0			0
$841$	43.5965	−	12.8011i	1.50333	−	0.441417i
$842$		0			0
$843$	−5.58034	−	1.21393i	−0.192197	−	0.0418099i
$844$		0			0
$845$	−19.8244	−	6.57493i	−0.681979	−	0.226184i
$846$		0			0
$847$	−3.58423	−	4.78797i	−0.123156	−	0.164517i
$848$		0			0
$849$	16.6620	+	19.2290i	0.571840	+	0.659938i
$850$		0			0
$851$	−15.3069	+	5.89859i	−0.524713	+	0.202201i
$852$		0			0
$853$	−51.6336	−	3.69291i	−1.76790	−	0.126443i	−0.850901	−	0.525327i	$-0.823943\pi$
$853$	−51.6336	−	3.69291i	−1.76790	−	0.126443i	−0.917001	+	0.398884i	$0.869398\pi$
$854$		0			0
$855$	−1.94960	−	1.35058i	−0.0666749	−	0.0461889i
$856$		0			0
$857$	−12.1948	+	16.2904i	−0.416568	+	0.556469i	−0.958918	−	0.283683i	$-0.908444\pi$
$857$	−12.1948	+	16.2904i	−0.416568	+	0.556469i	0.542350	+	0.840152i	$0.317535\pi$
$858$		0			0
$859$	12.3203	+	19.1707i	0.420362	+	0.654096i	0.985260	−	0.171065i	$-0.0547208\pi$
$859$	12.3203	+	19.1707i	0.420362	+	0.654096i	−0.564898	+	0.825161i	$0.691084\pi$
$860$		0			0
$861$	16.3065	+	55.5349i	0.555724	+	1.89262i
$862$		0			0
$863$	−1.69378	−	23.6821i	−0.0576568	−	0.806148i	−0.941211	−	0.337819i	$-0.890311\pi$
$863$	−1.69378	−	23.6821i	−0.0576568	−	0.806148i	0.883554	−	0.468329i	$-0.155144\pi$
$864$		0			0
$865$	−10.3417	−	11.0843i	−0.351629	−	0.376877i
$866$		0			0
$867$	9.72645	+	17.8127i	0.330328	+	0.604950i
$868$		0			0
$869$	−23.2961	−	10.6390i	−0.790266	−	0.360903i
$870$		0			0
$871$	14.9309	−	23.2329i	0.505914	−	0.787218i
$872$		0			0
$873$	−0.200055	−	0.200055i	−0.00677084	−	0.00677084i
$874$		0			0
$875$	−37.8107	−	26.0752i	−1.27823	−	0.881503i
$876$		0			0
$877$	5.38812	+	24.7688i	0.181944	+	0.836383i	0.974110	+	0.226077i	$0.0725899\pi$
$877$	5.38812	+	24.7688i	0.181944	+	0.836383i	−0.792166	+	0.610306i	$0.791046\pi$
$878$		0			0
$879$	16.2893	−	35.6686i	0.549424	−	1.20307i
$880$		0			0
$881$	3.77416	−	12.8536i	0.127155	−	0.433049i	−0.871165	−	0.490990i	$-0.836635\pi$
$881$	3.77416	−	12.8536i	0.127155	−	0.433049i	0.998320	+	0.0579409i	$0.0184535\pi$
$882$		0			0
$883$	31.1425	+	11.6155i	1.04803	+	0.390894i	0.813713	−	0.581267i	$-0.197443\pi$
$883$	31.1425	+	11.6155i	1.04803	+	0.390894i	0.234314	+	0.972161i	$0.424716\pi$
$884$		0			0
$885$	30.0490	+	12.4095i	1.01009	+	0.417142i
$886$		0			0
$887$	6.00567	+	3.27934i	0.201651	+	0.110110i	0.576902	−	0.816814i	$-0.304262\pi$
$887$	6.00567	+	3.27934i	0.201651	+	0.110110i	−0.375251	+	0.926923i	$0.622443\pi$
$888$		0			0
$889$	−19.3204	+	12.4164i	−0.647984	+	0.416434i
$890$		0			0
$891$	−11.5262	+	1.65721i	−0.386141	+	0.0555187i
$892$		0			0
$893$	−6.33088	+	4.73923i	−0.211855	+	0.158592i
$894$		0			0
$895$	15.9604	−	4.09161i	0.533497	−	0.136768i
$896$		0			0
$897$	−12.8056	−	27.2560i	−0.427565	−	0.910051i
$898$		0			0
$899$	−28.5634	+	24.7503i	−0.952642	+	0.825469i
$900$		0			0
$901$	−0.810528	+	5.63735i	−0.0270026	+	0.187807i
$902$		0			0
$903$	−21.9845	−	16.4574i	−0.731599	−	0.547668i
$904$		0			0
$905$	3.17159	+	29.2097i	0.105427	+	0.970964i
$906$		0			0
$907$	−15.4164	+	28.2331i	−0.511894	+	0.937465i	0.486084	+	0.873912i	$0.338425\pi$
$907$	−15.4164	+	28.2331i	−0.511894	+	0.937465i	−0.997978	+	0.0635526i	$0.979757\pi$
$908$		0			0
$909$	−9.26075	−	8.02448i	−0.307160	−	0.266155i
$910$		0			0
$911$	21.3166	−	9.73498i	0.706252	−	0.322534i	−0.0297090	−	0.999559i	$-0.509458\pi$
$911$	21.3166	−	9.73498i	0.706252	−	0.322534i	0.735961	+	0.677024i	$0.236731\pi$
$912$		0			0
$913$	19.3868	−	10.5860i	0.641608	−	0.350345i
$914$		0			0
$915$	26.3742	+	2.80734i	0.871905	+	0.0928079i
$916$		0			0
$917$	−79.4166	+	17.2760i	−2.62257	+	0.570505i
$918$		0			0
$919$	4.15633			0.137105			0.0685524	−	0.997648i	$-0.478162\pi$
$919$	4.15633			0.137105			0.0685524	+	0.997648i	$0.478162\pi$
$920$		0			0
$921$	3.89466			0.128333
$922$		0			0
$923$	59.3930	−	12.9202i	1.95494	−	0.425272i
$924$		0			0
$925$	9.21586	−	14.4070i	0.303016	−	0.473699i
$926$		0			0
$927$	−8.29849	+	4.53132i	−0.272558	+	0.148828i
$928$		0			0
$929$	−29.7720	+	13.5964i	−0.976788	+	0.446084i	−0.838853	−	0.544357i	$-0.816774\pi$
$929$	−29.7720	+	13.5964i	−0.976788	+	0.446084i	−0.137934	+	0.990441i	$0.544046\pi$
$930$		0			0
$931$	6.41003	+	5.55432i	0.210080	+	0.182035i
$932$		0			0
$933$	−4.08959	+	7.48952i	−0.133887	+	0.245196i
$934$		0			0
$935$	−7.06692	−	5.68258i	−0.231113	−	0.185840i
$936$		0			0
$937$	−39.7355	−	29.7456i	−1.29810	−	0.971747i	−0.999851	−	0.0172600i	$-0.994506\pi$
$937$	−39.7355	−	29.7456i	−1.29810	−	0.971747i	−0.298251	−	0.954487i	$-0.596403\pi$
$938$		0			0
$939$	2.62298	−	18.2432i	0.0855978	−	0.595346i
$940$		0			0
$941$	−12.9399	+	11.2125i	−0.421830	+	0.365518i	−0.839757	−	0.542963i	$-0.817302\pi$
$941$	−12.9399	+	11.2125i	−0.421830	+	0.365518i	0.417927	+	0.908481i	$0.362757\pi$
$942$		0			0
$943$	14.8563	+	48.6429i	0.483789	+	1.58403i
$944$		0			0
$945$	−12.8345	−	50.0644i	−0.417507	−	1.62859i
$946$		0			0
$947$	42.9055	−	32.1187i	1.39424	−	1.04372i	0.402507	−	0.915417i	$-0.368139\pi$
$947$	42.9055	−	32.1187i	1.39424	−	1.04372i	0.991735	−	0.128300i	$-0.0409520\pi$
$948$		0			0
$949$	11.7356	−	1.68733i	0.380954	−	0.0547730i
$950$		0			0
$951$	9.91053	−	6.36911i	0.321371	−	0.206533i
$952$		0			0
$953$	46.9902	+	25.6586i	1.52216	+	0.831164i	0.999768	−	0.0215394i	$-0.00685672\pi$
$953$	46.9902	+	25.6586i	1.52216	+	0.831164i	0.522395	+	0.852703i	$0.325039\pi$
$954$		0			0
$955$	12.0531	+	29.0121i	0.390030	+	0.938810i
$956$		0			0
$957$	33.1772	+	12.3745i	1.07247	+	0.400010i
$958$		0			0
$959$	−14.7871	+	50.3603i	−0.477501	+	1.62622i
$960$		0			0
$961$	−4.90607	+	10.7428i	−0.158260	+	0.346542i
$962$		0			0
$963$	2.00676	+	9.22494i	0.0646671	+	0.297270i
$964$		0			0
$965$	51.4367	−	17.1801i	1.65581	−	0.553048i
$966$		0			0
$967$	−34.7054	−	34.7054i	−1.11605	−	1.11605i	−0.992315	−	0.123734i	$-0.960513\pi$
$967$	−34.7054	−	34.7054i	−1.11605	−	1.11605i	−0.123734	−	0.992315i	$-0.539487\pi$
$968$		0			0
$969$	−0.809690	+	1.25990i	−0.0260110	+	0.0404739i
$970$		0			0
$971$	41.2402	+	18.8338i	1.32346	+	0.604404i	0.946763	−	0.321932i	$-0.104332\pi$
$971$	41.2402	+	18.8338i	1.32346	+	0.604404i	0.376698	+	0.926336i	$0.377059\pi$
$972$		0			0
$973$	9.39128	+	17.1988i	0.301071	+	0.551370i
$974$		0			0
$975$	27.5876	+	14.9884i	0.883511	+	0.480013i
$976$		0			0
$977$	−4.03444	−	56.4089i	−0.129073	−	1.80468i	−0.489618	−	0.871937i	$-0.662864\pi$
$977$	−4.03444	−	56.4089i	−0.129073	−	1.80468i	0.360544	−	0.932742i	$-0.382591\pi$
$978$		0			0
$979$	13.4005	+	45.6380i	0.428283	+	1.45860i
$980$		0			0
$981$	13.6783	+	21.2838i	0.436714	+	0.679540i
$982$		0			0
$983$	16.3646	−	21.8605i	0.521950	−	0.697243i	−0.459670	−	0.888090i	$-0.652032\pi$
$983$	16.3646	−	21.8605i	0.521950	−	0.697243i	0.981620	+	0.190847i	$0.0611233\pi$
$984$		0			0
$985$	16.0927	−	2.92101i	0.512757	−	0.0930710i
$986$		0			0
$987$	−50.1299	−	3.58536i	−1.59565	−	0.114123i
$988$		0			0
$989$	−19.4740	−	14.2519i	−0.619238	−	0.453185i
$990$		0			0
$991$	33.9449	+	39.1744i	1.07829	+	1.24442i	0.968115	+	0.250506i	$0.0805968\pi$
$991$	33.9449	+	39.1744i	1.07829	+	1.24442i	0.110179	+	0.993912i	$0.464858\pi$
$992$		0			0
$993$	−4.79580	−	6.40644i	−0.152190	−	0.203302i
$994$		0			0
$995$	−5.77545	+	17.4138i	−0.183094	+	0.552055i
$996$		0			0
$997$	−0.567817	−	0.123521i	−0.0179829	−	0.00391195i	0.203565	−	0.979061i	$-0.434747\pi$
$997$	−0.567817	−	0.123521i	−0.0179829	−	0.00391195i	−0.221548	+	0.975150i	$0.571111\pi$
$998$		0			0
$999$	18.4652	−	5.42187i	0.584213	−	0.171540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.11	yes	720
5.3	odd	4	inner	920.2.bv.a.33.11	✓	720
23.7	odd	22	inner	920.2.bv.a.697.11	yes	720
115.53	even	44	inner	920.2.bv.a.513.11	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.11	✓	720	5.3	odd	4	inner
920.2.bv.a.217.11	yes	720	1.1	even	1	trivial
920.2.bv.a.513.11	yes	720	115.53	even	44	inner
920.2.bv.a.697.11	yes	720	23.7	odd	22	inner

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29814 + 0.282393i) q^{3} +(1.73961 - 1.40490i) q^{5} +(3.60560 - 1.96880i) q^{7} +(-1.12348 + 0.513074i) q^{9} +O(q^{10})\)	\(q+(-1.29814 + 0.282393i) q^{3} +(1.73961 - 1.40490i) q^{5} +(3.60560 - 1.96880i) q^{7} +(-1.12348 + 0.513074i) q^{9} +(2.33478 + 2.02310i) q^{11} +(2.26521 - 4.14842i) q^{13} +(-1.86152 + 2.31501i) q^{15} +(-1.05088 - 0.786681i) q^{17} +(-0.122216 + 0.850032i) q^{19} +(-4.12459 + 3.57398i) q^{21} +(-3.59026 + 3.17963i) q^{23} +(1.05250 - 4.88797i) q^{25} +(4.50410 - 3.37172i) q^{27} +(-8.53987 + 1.22785i) q^{29} +(3.68522 - 2.36835i) q^{31} +(-3.60218 - 1.96694i) q^{33} +(3.50636 - 8.49046i) q^{35} +(3.20483 + 1.19534i) q^{37} +(-1.76907 + 6.02491i) q^{39} +(4.40558 - 9.64688i) q^{41} +(1.06960 + 4.91689i) q^{43} +(-1.23359 + 2.47092i) q^{45} +(6.51159 + 6.51159i) q^{47} +(5.33965 - 8.30865i) q^{49} +(1.58634 + 0.724459i) q^{51} +(-2.07926 - 3.80788i) q^{53} +(6.90386 + 0.239270i) q^{55} +(-0.0813894 - 1.13797i) q^{57} +(-3.08330 - 10.5007i) q^{59} +(-4.82712 - 7.51115i) q^{61} +(-3.04066 + 4.06184i) q^{63} +(-1.88754 - 10.3990i) q^{65} +(5.82803 + 0.416829i) q^{67} +(3.76275 - 5.14147i) q^{69} +(8.42126 + 9.71865i) q^{71} +(1.50325 + 2.00810i) q^{73} +(0.0140338 + 6.64248i) q^{75} +(12.4014 + 2.69775i) q^{77} +(-7.95411 + 2.33554i) q^{79} +(-2.46836 + 2.84864i) q^{81} +(2.49864 - 6.69913i) q^{83} +(-2.93334 + 0.107867i) q^{85} +(10.7392 - 4.00552i) q^{87} +(12.9522 + 8.32388i) q^{89} -19.4173i q^{91} +(-4.11513 + 4.11513i) q^{93} +(0.981602 + 1.65043i) q^{95} +(0.0800515 + 0.214626i) q^{97} +(-3.66107 - 1.07499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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