LMFDB - Embedded newform 800.2.bq.c.223.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(63,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 19]))

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

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

chi := DirichletCharacter("800.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.6
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.c.287.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.440304 + 0.864144i) q^{3} +(-2.21992 - 0.268223i) q^{5} +(-2.34980 - 2.34980i) q^{7} +(1.21048 - 1.66608i) q^{9} +(1.76565 + 2.43020i) q^{11} +(0.910159 + 5.74652i) q^{13} +(-0.745656 - 2.03643i) q^{15} +(3.39204 + 1.72833i) q^{17} +(0.0821413 + 0.252805i) q^{19} +(0.995939 - 3.06519i) q^{21} +(-1.20596 + 7.61411i) q^{23} +(4.85611 + 1.19087i) q^{25} +(4.84645 + 0.767602i) q^{27} +(3.49891 + 1.13687i) q^{29} +(-2.21186 + 0.718676i) q^{31} +(-1.32263 + 2.59580i) q^{33} +(4.58609 + 5.84663i) q^{35} +(10.1766 - 1.61182i) q^{37} +(-4.56507 + 3.31672i) q^{39} +(-1.02740 - 0.746453i) q^{41} +(-2.20292 + 2.20292i) q^{43} +(-3.13405 + 3.37389i) q^{45} +(-4.22246 + 2.15145i) q^{47} +4.04308i q^{49} +3.69220i q^{51} +(5.44391 - 2.77381i) q^{53} +(-3.26776 - 5.86845i) q^{55} +(-0.182293 + 0.182293i) q^{57} +(-9.55473 - 6.94192i) q^{59} +(-5.05755 + 3.67453i) q^{61} +(-6.75932 + 1.07057i) q^{63} +(-0.479132 - 13.0009i) q^{65} +(-6.95421 + 13.6484i) q^{67} +(-7.11068 + 2.31040i) q^{69} +(8.86316 + 2.87981i) q^{71} +(-5.17821 - 0.820148i) q^{73} +(1.10908 + 4.72073i) q^{75} +(1.56157 - 9.85939i) q^{77} +(3.72879 - 11.4760i) q^{79} +(-0.438568 - 1.34977i) q^{81} +(7.11391 + 3.62472i) q^{83} +(-7.06648 - 4.74658i) q^{85} +(0.558168 + 3.52413i) q^{87} +(4.48956 + 6.17934i) q^{89} +(11.3645 - 15.6418i) q^{91} +(-1.59493 - 1.59493i) q^{93} +(-0.114539 - 0.583240i) q^{95} +(-1.61088 - 3.16152i) q^{97} +6.18619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{5} - 4 q^{7} + 4 q^{13} - 22 q^{15} + 8 q^{17} + 18 q^{19} - 16 q^{21} - 8 q^{23} + 40 q^{25} - 18 q^{27} + 20 q^{31} + 44 q^{33} - 38 q^{35} - 10 q^{37} + 36 q^{39} - 16 q^{41} - 32 q^{43}+ \cdots - 132 q^{99}+O(q^{100}) $ 64 * q + 2 * q^5 - 4 * q^7 + 4 * q^13 - 22 * q^15 + 8 * q^17 + 18 * q^19 - 16 * q^21 - 8 * q^23 + 40 * q^25 - 18 * q^27 + 20 * q^31 + 44 * q^33 - 38 * q^35 - 10 * q^37 + 36 * q^39 - 16 * q^41 - 32 * q^43 + 14 * q^45 - 8 * q^47 - 22 * q^53 + 24 * q^55 - 8 * q^57 + 4 * q^59 - 36 * q^61 - 18 * q^63 - 24 * q^65 + 26 * q^67 + 60 * q^69 - 70 * q^71 - 12 * q^73 - 66 * q^75 + 48 * q^77 - 16 * q^79 - 24 * q^81 + 52 * q^83 - 46 * q^85 + 144 * q^87 - 60 * q^89 + 30 * q^91 + 20 * q^93 + 8 * q^95 - 56 * q^97 - 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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
$3$	0.440304	+	0.864144i	0.254209	+	0.498914i	0.982478	−	0.186378i	$-0.0596748\pi$
$3$	0.440304	+	0.864144i	0.254209	+	0.498914i	−0.728269	+	0.685292i	$0.759675\pi$
$4$		0			0
$5$	−2.21992	−	0.268223i	−0.992780	−	0.119953i
$5$	−2.21992	−	0.268223i	−0.992780	−	0.119953i
$6$		0			0
$7$	−2.34980	−	2.34980i	−0.888139	−	0.888139i	0.106205	−	0.994344i	$-0.466130\pi$
$7$	−2.34980	−	2.34980i	−0.888139	−	0.888139i	−0.994344	+	0.106205i	$0.966130\pi$
$8$		0			0
$9$	1.21048	−	1.66608i	0.403492	−	0.555360i
$10$		0			0
$11$	1.76565	+	2.43020i	0.532362	+	0.732734i	0.987488	−	0.157693i	$-0.0504057\pi$
$11$	1.76565	+	2.43020i	0.532362	+	0.732734i	−0.455126	+	0.890427i	$0.650406\pi$
$12$		0			0
$13$	0.910159	+	5.74652i	0.252433	+	1.59380i	0.709724	+	0.704480i	$0.248820\pi$
$13$	0.910159	+	5.74652i	0.252433	+	1.59380i	−0.457292	+	0.889317i	$0.651180\pi$
$14$		0			0
$15$	−0.745656	−	2.03643i	−0.192528	−	0.525805i
$16$		0			0
$17$	3.39204	+	1.72833i	0.822690	+	0.419181i	0.814059	−	0.580781i	$-0.197253\pi$
$17$	3.39204	+	1.72833i	0.822690	+	0.419181i	0.00863008	+	0.999963i	$0.497253\pi$
$18$		0			0
$19$	0.0821413	+	0.252805i	0.0188445	+	0.0579974i	0.960037	−	0.279875i	$-0.0902929\pi$
$19$	0.0821413	+	0.252805i	0.0188445	+	0.0579974i	−0.941192	+	0.337872i	$0.890293\pi$
$20$		0			0
$21$	0.995939	−	3.06519i	0.217332	−	0.668879i
$22$		0			0
$23$	−1.20596	+	7.61411i	−0.251459	+	1.58765i	0.461950	+	0.886906i	$0.347150\pi$
$23$	−1.20596	+	7.61411i	−0.251459	+	1.58765i	−0.713410	+	0.700747i	$0.752850\pi$
$24$		0			0
$25$	4.85611	+	1.19087i	0.971222	+	0.238174i
$26$		0			0
$27$	4.84645	+	0.767602i	0.932699	+	0.147725i
$28$		0			0
$29$	3.49891	+	1.13687i	0.649732	+	0.211111i	0.615296	−	0.788296i	$-0.289036\pi$
$29$	3.49891	+	1.13687i	0.649732	+	0.211111i	0.0344361	+	0.999407i	$0.489036\pi$
$30$		0			0
$31$	−2.21186	+	0.718676i	−0.397261	+	0.129078i	−0.500833	−	0.865544i	$-0.666973\pi$
$31$	−2.21186	+	0.718676i	−0.397261	+	0.129078i	0.103572	+	0.994622i	$0.466973\pi$
$32$		0			0
$33$	−1.32263	+	2.59580i	−0.230240	+	0.451871i
$34$		0			0
$35$	4.58609	+	5.84663i	0.775191	+	0.988262i
$36$		0			0
$37$	10.1766	−	1.61182i	1.67303	−	0.264981i	0.753339	−	0.657632i	$-0.228442\pi$
$37$	10.1766	−	1.61182i	1.67303	−	0.264981i	0.919688	+	0.392651i	$0.128442\pi$
$38$		0			0
$39$	−4.56507	+	3.31672i	−0.730997	+	0.531100i
$40$		0			0
$41$	−1.02740	−	0.746453i	−0.160454	−	0.116576i	0.504661	−	0.863317i	$-0.331617\pi$
$41$	−1.02740	−	0.746453i	−0.160454	−	0.116576i	−0.665115	+	0.746741i	$0.731617\pi$
$42$		0			0
$43$	−2.20292	+	2.20292i	−0.335942	+	0.335942i	−0.854838	−	0.518895i	$-0.826343\pi$
$43$	−2.20292	+	2.20292i	−0.335942	+	0.335942i	0.518895	+	0.854838i	$0.326343\pi$
$44$		0			0
$45$	−3.13405	+	3.37389i	−0.467196	+	0.502950i
$46$		0			0
$47$	−4.22246	+	2.15145i	−0.615909	+	0.313822i	−0.733967	−	0.679185i	$-0.762333\pi$
$47$	−4.22246	+	2.15145i	−0.615909	+	0.313822i	0.118057	+	0.993007i	$0.462333\pi$
$48$		0			0
$49$			4.04308i			0.577583i
$50$		0			0
$51$			3.69220i			0.517011i
$52$		0			0
$53$	5.44391	−	2.77381i	0.747779	−	0.381012i	−0.0381964	−	0.999270i	$-0.512161\pi$
$53$	5.44391	−	2.77381i	0.747779	−	0.381012i	0.785975	+	0.618258i	$0.212161\pi$
$54$		0			0
$55$	−3.26776	−	5.86845i	−0.440625	−	0.791302i
$56$		0			0
$57$	−0.182293	+	0.182293i	−0.0241453	+	0.0241453i
$58$		0			0
$59$	−9.55473	−	6.94192i	−1.24392	−	0.903761i	−0.246067	−	0.969253i	$-0.579138\pi$
$59$	−9.55473	−	6.94192i	−1.24392	−	0.903761i	−0.997853	+	0.0654918i	$0.979138\pi$
$60$		0			0
$61$	−5.05755	+	3.67453i	−0.647553	+	0.470475i	−0.862437	−	0.506165i	$-0.831063\pi$
$61$	−5.05755	+	3.67453i	−0.647553	+	0.470475i	0.214884	+	0.976640i	$0.431063\pi$
$62$		0			0
$63$	−6.75932	+	1.07057i	−0.851594	+	0.134879i
$64$		0			0
$65$	−0.479132	−	13.0009i	−0.0594290	−	1.61257i
$66$		0			0
$67$	−6.95421	+	13.6484i	−0.849592	+	1.66742i	−0.110437	+	0.993883i	$0.535225\pi$
$67$	−6.95421	+	13.6484i	−0.849592	+	1.66742i	−0.739155	+	0.673536i	$0.764775\pi$
$68$		0			0
$69$	−7.11068	+	2.31040i	−0.856026	+	0.278140i
$70$		0			0
$71$	8.86316	+	2.87981i	1.05186	+	0.341771i	0.783399	−	0.621519i	$-0.213484\pi$
$71$	8.86316	+	2.87981i	1.05186	+	0.341771i	0.268464	+	0.963290i	$0.413484\pi$
$72$		0			0
$73$	−5.17821	−	0.820148i	−0.606064	−	0.0959911i	−0.154142	−	0.988049i	$-0.549261\pi$
$73$	−5.17821	−	0.820148i	−0.606064	−	0.0959911i	−0.451922	+	0.892058i	$0.649261\pi$
$74$		0			0
$75$	1.10908	+	4.72073i	0.128065	+	0.545103i
$76$		0			0
$77$	1.56157	−	9.85939i	0.177958	−	1.12358i
$78$		0			0
$79$	3.72879	−	11.4760i	0.419522	−	1.29116i	−0.488621	−	0.872496i	$-0.662500\pi$
$79$	3.72879	−	11.4760i	0.419522	−	1.29116i	0.908143	−	0.418660i	$-0.137500\pi$
$80$		0			0
$81$	−0.438568	−	1.34977i	−0.0487298	−	0.149975i
$82$		0			0
$83$	7.11391	+	3.62472i	0.780853	+	0.397865i	0.798512	−	0.601980i	$-0.205621\pi$
$83$	7.11391	+	3.62472i	0.780853	+	0.397865i	−0.0176584	+	0.999844i	$0.505621\pi$
$84$		0			0
$85$	−7.06648	−	4.74658i	−0.766467	−	0.514839i
$86$		0			0
$87$	0.558168	+	3.52413i	0.0598419	+	0.377827i
$88$		0			0
$89$	4.48956	+	6.17934i	0.475892	+	0.655009i	0.977709	−	0.209965i	$-0.0673349\pi$
$89$	4.48956	+	6.17934i	0.475892	+	0.655009i	−0.501817	+	0.864974i	$0.667335\pi$
$90$		0			0
$91$	11.3645	−	15.6418i	1.19132	−	1.63971i
$92$		0			0
$93$	−1.59493	−	1.59493i	−0.165386	−	0.165386i
$94$		0			0
$95$	−0.114539	−	0.583240i	−0.0117515	−	0.0598391i
$96$		0			0
$97$	−1.61088	−	3.16152i	−0.163560	−	0.321004i	0.794651	−	0.607066i	$-0.207654\pi$
$97$	−1.61088	−	3.16152i	−0.163560	−	0.321004i	−0.958211	+	0.286062i	$0.907654\pi$
$98$		0			0
$99$	6.18619			0.621735
$100$		0			0
$101$	13.9341			1.38650			0.693249	−	0.720698i	$-0.256179\pi$
$101$	13.9341			1.38650			0.693249	+	0.720698i	$0.256179\pi$
$102$		0			0
$103$	−8.27427	−	16.2392i	−0.815288	−	1.60009i	−0.799841	−	0.600212i	$-0.795083\pi$
$103$	−8.27427	−	16.2392i	−0.815288	−	1.60009i	−0.0154471	−	0.999881i	$-0.504917\pi$
$104$		0			0
$105$	−3.03306	+	6.53734i	−0.295997	+	0.637979i
$106$		0			0
$107$	5.81311	+	5.81311i	0.561974	+	0.561974i	0.929868	−	0.367894i	$-0.119921\pi$
$107$	5.81311	+	5.81311i	0.561974	+	0.561974i	−0.367894	+	0.929868i	$0.619921\pi$
$108$		0			0
$109$	−7.07187	+	9.73360i	−0.677362	+	0.932309i	−0.999898	−	0.0142477i	$-0.995465\pi$
$109$	−7.07187	+	9.73360i	−0.677362	+	0.932309i	0.322536	+	0.946557i	$0.395465\pi$
$110$		0			0
$111$	5.87365	+	8.08438i	0.557502	+	0.767336i
$112$		0			0
$113$	2.22642	+	14.0571i	0.209444	+	1.32238i	0.838450	+	0.544978i	$0.183462\pi$
$113$	2.22642	+	14.0571i	0.209444	+	1.32238i	−0.629006	+	0.777400i	$0.716538\pi$
$114$		0			0
$115$	4.71942	−	16.5793i	0.440088	−	1.54603i
$116$		0			0
$117$	10.6759	+	5.43963i	0.986985	+	0.502894i
$118$		0			0
$119$	−3.90937	−	12.0318i	−0.358372	−	1.10295i
$120$		0			0
$121$	0.610803	−	1.87986i	0.0555275	−	0.170896i
$122$		0			0
$123$	0.192673	−	1.21649i	0.0173728	−	0.109687i
$124$		0			0
$125$	−10.4608	−	3.94616i	−0.935640	−	0.352956i
$126$		0			0
$127$	4.42038	+	0.700119i	0.392245	+	0.0621255i	0.349442	−	0.936958i	$-0.386371\pi$
$127$	4.42038	+	0.700119i	0.392245	+	0.0621255i	0.0428031	+	0.999084i	$0.486371\pi$
$128$		0			0
$129$	−2.87360	−	0.933688i	−0.253006	−	0.0822067i
$130$		0			0
$131$	6.31482	−	2.05181i	0.551728	−	0.179267i	−0.0198678	−	0.999803i	$-0.506325\pi$
$131$	6.31482	−	2.05181i	0.551728	−	0.179267i	0.571596	+	0.820535i	$0.306325\pi$
$132$		0			0
$133$	0.401025	−	0.787055i	0.0347733	−	0.0682464i
$134$		0			0
$135$	−10.5528	−	3.00395i	−0.908244	−	0.258539i
$136$		0			0
$137$	−5.61256	+	0.888943i	−0.479514	+	0.0759475i	−0.391512	−	0.920173i	$-0.628048\pi$
$137$	−5.61256	+	0.888943i	−0.479514	+	0.0759475i	−0.0880013	+	0.996120i	$0.528048\pi$
$138$		0			0
$139$	−4.63268	+	3.36584i	−0.392939	+	0.285487i	−0.766659	−	0.642055i	$-0.778082\pi$
$139$	−4.63268	+	3.36584i	−0.392939	+	0.285487i	0.373720	+	0.927542i	$0.378082\pi$
$140$		0			0
$141$	−3.71833	−	2.70153i	−0.313140	−	0.227509i
$142$		0			0
$143$	−12.3582	+	12.3582i	−1.03344	+	1.03344i
$144$		0			0
$145$	−7.46239	−	3.46225i	−0.619717	−	0.287524i
$146$		0			0
$147$	−3.49381	+	1.78018i	−0.288164	+	0.146827i
$148$		0			0
$149$			2.53170i			0.207405i	0.994608	+	0.103703i	$0.0330690\pi$
$149$			2.53170i			0.207405i	−0.994608	+	0.103703i	$0.966931\pi$
$150$		0			0
$151$			10.2816i			0.836702i	0.908285	+	0.418351i	$0.137392\pi$
$151$			10.2816i			0.836702i	−0.908285	+	0.418351i	$0.862608\pi$
$152$		0			0
$153$	6.98552	−	3.55930i	0.564745	−	0.287752i
$154$		0			0
$155$	5.10292	−	1.00213i	0.409876	−	0.0804933i
$156$		0			0
$157$	−9.52582	+	9.52582i	−0.760243	+	0.760243i	−0.976366	−	0.216123i	$-0.930659\pi$
$157$	−9.52582	+	9.52582i	−0.760243	+	0.760243i	0.216123	+	0.976366i	$0.430659\pi$
$158$		0			0
$159$	4.79395	+	3.48301i	0.380185	+	0.276220i
$160$		0			0
$161$	20.7254	−	15.0579i	1.63339	−	1.18673i
$162$		0			0
$163$	−0.962613	+	0.152463i	−0.0753977	+	0.0119418i	−0.194019	−	0.980998i	$-0.562152\pi$
$163$	−0.962613	+	0.152463i	−0.0753977	+	0.0119418i	0.118622	+	0.992940i	$0.462152\pi$
$164$		0			0
$165$	3.63238	−	5.40772i	0.282781	−	0.420990i
$166$		0			0
$167$	11.1549	−	21.8927i	0.863192	−	1.69411i	0.155208	−	0.987882i	$-0.450395\pi$
$167$	11.1549	−	21.8927i	0.863192	−	1.69411i	0.707984	−	0.706229i	$-0.249605\pi$
$168$		0			0
$169$	−19.8303	+	6.44326i	−1.52541	+	0.495635i
$170$		0			0
$171$	0.520623	+	0.169161i	0.0398131	+	0.0129360i
$172$		0			0
$173$	11.6353	+	1.84285i	0.884616	+	0.140109i	0.582180	−	0.813060i	$-0.302200\pi$
$173$	11.6353	+	1.84285i	0.884616	+	0.140109i	0.302436	+	0.953170i	$0.402200\pi$
$174$		0			0
$175$	−8.61257	−	14.2092i	−0.651049	−	1.07411i
$176$		0			0
$177$	1.79184	−	11.3132i	0.134683	−	0.850354i
$178$		0			0
$179$	−1.26429	+	3.89109i	−0.0944977	+	0.290834i	−0.987122	−	0.159966i	$-0.948861\pi$
$179$	−1.26429	+	3.89109i	−0.0944977	+	0.290834i	0.892625	+	0.450800i	$0.148861\pi$
$180$		0			0
$181$	−8.27653	−	25.4726i	−0.615190	−	1.89336i	−0.398729	−	0.917069i	$-0.630548\pi$
$181$	−8.27653	−	25.4726i	−0.615190	−	1.89336i	−0.216461	−	0.976291i	$-0.569452\pi$
$182$		0			0
$183$	−5.40218	−	2.75255i	−0.399341	−	0.203474i
$184$		0			0
$185$	−23.0236	+	0.848504i	−1.69273	+	0.0623833i
$186$		0			0
$187$	1.78895	+	11.2950i	0.130821	+	0.825969i
$188$		0			0
$189$	−9.58445	−	13.1919i	−0.697166	−	0.959567i
$190$		0			0
$191$	9.12058	−	12.5534i	0.659942	−	0.908332i	−0.339538	−	0.940592i	$-0.610271\pi$
$191$	9.12058	−	12.5534i	0.659942	−	0.908332i	0.999479	+	0.0322605i	$0.0102706\pi$
$192$		0			0
$193$	4.89168	+	4.89168i	0.352111	+	0.352111i	0.860894	−	0.508784i	$-0.169905\pi$
$193$	4.89168	+	4.89168i	0.352111	+	0.352111i	−0.508784	+	0.860894i	$0.669905\pi$
$194$		0			0
$195$	11.0237	−	6.13840i	0.789426	−	0.439580i
$196$		0			0
$197$	−1.49942	−	2.94277i	−0.106829	−	0.209664i	0.831404	−	0.555669i	$-0.187538\pi$
$197$	−1.49942	−	2.94277i	−0.106829	−	0.209664i	−0.938232	+	0.346006i	$0.887538\pi$
$198$		0			0
$199$	6.73535			0.477456			0.238728	−	0.971086i	$-0.423270\pi$
$199$	6.73535			0.477456			0.238728	+	0.971086i	$0.423270\pi$
$200$		0			0
$201$	−14.8562			−1.04787
$202$		0			0
$203$	−5.55033	−	10.8931i	−0.389557	−	0.764548i
$204$		0			0
$205$	2.08054	+	1.93264i	0.145311	+	0.134981i
$206$		0			0
$207$	11.2259	+	11.2259i	0.780256	+	0.780256i
$208$		0			0
$209$	−0.469335	+	0.645985i	−0.0324646	+	0.0446837i
$210$		0			0
$211$	−10.7152	−	14.7482i	−0.737667	−	1.01531i	−0.998749	−	0.0499945i	$-0.984080\pi$
$211$	−10.7152	−	14.7482i	−0.737667	−	1.01531i	0.261083	−	0.965316i	$-0.415920\pi$
$212$		0			0
$213$	1.41390	+	8.92704i	0.0968791	+	0.611671i
$214$		0			0
$215$	5.48119	−	4.29944i	0.373814	−	0.293219i
$216$		0			0
$217$	6.88616	+	3.50867i	0.467463	+	0.238184i
$218$		0			0
$219$	−1.57126	−	4.83584i	−0.106176	−	0.326776i
$220$		0			0
$221$	−6.84458	+	21.0654i	−0.460416	+	1.41701i
$222$		0			0
$223$	−3.45959	+	21.8430i	−0.231671	+	1.46271i	0.547976	+	0.836494i	$0.315398\pi$
$223$	−3.45959	+	21.8430i	−0.231671	+	1.46271i	−0.779647	+	0.626219i	$0.784602\pi$
$224$		0			0
$225$	7.86230	−	6.64915i	0.524153	−	0.443276i
$226$		0			0
$227$	−12.3685	−	1.95898i	−0.820925	−	0.130022i	−0.268177	−	0.963370i	$-0.586421\pi$
$227$	−12.3685	−	1.95898i	−0.820925	−	0.130022i	−0.552749	+	0.833348i	$0.686421\pi$
$228$		0			0
$229$	−6.47424	−	2.10361i	−0.427830	−	0.139010i	0.0871839	−	0.996192i	$-0.472213\pi$
$229$	−6.47424	−	2.10361i	−0.427830	−	0.139010i	−0.515014	+	0.857182i	$0.672213\pi$
$230$		0			0
$231$	9.20751	−	2.99170i	0.605809	−	0.196839i
$232$		0			0
$233$	−8.57788	+	16.8350i	−0.561955	+	1.10290i	0.418876	+	0.908043i	$0.362424\pi$
$233$	−8.57788	+	16.8350i	−0.561955	+	1.10290i	−0.980832	+	0.194856i	$0.937576\pi$
$234$		0			0
$235$	9.95061	−	3.64349i	0.649106	−	0.237675i
$236$		0			0
$237$	11.5588	−	1.83073i	0.750822	−	0.118919i
$238$		0			0
$239$	7.61440	−	5.53218i	0.492534	−	0.357847i	−0.313624	−	0.949547i	$-0.601543\pi$
$239$	7.61440	−	5.53218i	0.492534	−	0.357847i	0.806158	+	0.591700i	$0.201543\pi$
$240$		0			0
$241$	−14.8665	−	10.8012i	−0.957636	−	0.695764i	−0.00503585	−	0.999987i	$-0.501603\pi$
$241$	−14.8665	−	10.8012i	−0.957636	−	0.695764i	−0.952601	+	0.304224i	$0.901603\pi$
$242$		0			0
$243$	11.3823	−	11.3823i	0.730176	−	0.730176i
$244$		0			0
$245$	1.08445	−	8.97532i	0.0692829	−	0.573412i
$246$		0			0
$247$	−1.37799	+	0.702119i	−0.0876792	+	0.0446748i
$248$		0			0
$249$			7.74342i			0.490720i
$250$		0			0
$251$			6.68014i			0.421647i	0.977524	+	0.210823i	$0.0676145\pi$
$251$			6.68014i			0.421647i	−0.977524	+	0.210823i	$0.932386\pi$
$252$		0			0
$253$	−20.6331	+	10.5131i	−1.29719	+	0.660954i
$254$		0			0
$255$	0.990334	−	8.19639i	0.0620171	−	0.513278i
$256$		0			0
$257$	12.2378	−	12.2378i	0.763371	−	0.763371i	−0.213559	−	0.976930i	$-0.568506\pi$
$257$	12.2378	−	12.2378i	0.763371	−	0.763371i	0.976930	+	0.213559i	$0.0685057\pi$
$258$		0			0
$259$	−27.7004	−	20.1255i	−1.72122	−	1.25054i
$260$		0			0
$261$	6.12947	−	4.45332i	0.379404	−	0.275653i
$262$		0			0
$263$	−3.59543	+	0.569460i	−0.221704	+	0.0351144i	−0.266298	−	0.963891i	$-0.585801\pi$
$263$	−3.59543	+	0.569460i	−0.221704	+	0.0351144i	0.0445942	+	0.999005i	$0.485801\pi$
$264$		0			0
$265$	−12.8291	+	4.69746i	−0.788083	+	0.288563i
$266$		0			0
$267$	−3.36308	+	6.60041i	−0.205817	+	0.403939i
$268$		0			0
$269$	−3.79488	+	1.23303i	−0.231378	+	0.0751793i	−0.422411	−	0.906404i	$-0.638816\pi$
$269$	−3.79488	+	1.23303i	−0.231378	+	0.0751793i	0.191033	+	0.981584i	$0.438816\pi$
$270$		0			0
$271$	−15.1903	−	4.93561i	−0.922742	−	0.299817i	−0.191151	−	0.981561i	$-0.561222\pi$
$271$	−15.1903	−	4.93561i	−0.922742	−	0.299817i	−0.731591	+	0.681743i	$0.761222\pi$
$272$		0			0
$273$	18.5206	+	2.93338i	1.12092	+	0.177536i
$274$		0			0
$275$	5.68012	+	13.9040i	0.342524	+	0.838443i
$276$		0			0
$277$	−3.00189	+	18.9532i	−0.180366	+	1.13879i	0.716860	+	0.697217i	$0.245579\pi$
$277$	−3.00189	+	18.9532i	−0.180366	+	1.13879i	−0.897226	+	0.441571i	$0.854421\pi$
$278$		0			0
$279$	−1.48003	+	4.55507i	−0.0886072	+	0.272705i
$280$		0			0
$281$	−7.26446	−	22.3577i	−0.433361	−	1.33375i	−0.894757	−	0.446554i	$-0.852651\pi$
$281$	−7.26446	−	22.3577i	−0.433361	−	1.33375i	0.461395	−	0.887195i	$-0.347349\pi$
$282$		0			0
$283$	−6.88753	−	3.50937i	−0.409421	−	0.208611i	0.237135	−	0.971477i	$-0.423792\pi$
$283$	−6.88753	−	3.50937i	−0.409421	−	0.208611i	−0.646557	+	0.762866i	$0.723792\pi$
$284$		0			0
$285$	0.453571	−	0.355781i	0.0268673	−	0.0210746i
$286$		0			0
$287$	0.660178	+	4.16820i	0.0389691	+	0.246041i
$288$		0			0
$289$	−1.47356	−	2.02818i	−0.0866801	−	0.119305i
$290$		0			0
$291$	2.02274	−	2.78406i	0.118575	−	0.163204i
$292$		0			0
$293$	−13.9853	−	13.9853i	−0.817029	−	0.817029i	0.168647	−	0.985676i	$-0.446060\pi$
$293$	−13.9853	−	13.9853i	−0.817029	−	0.817029i	−0.985676	+	0.168647i	$0.946060\pi$
$294$		0			0
$295$	19.3488	+	17.9733i	1.12653	+	1.04645i
$296$		0			0
$297$	6.69168	+	13.1332i	0.388291	+	0.762063i
$298$		0			0
$299$	−44.8522			−2.59387
$300$		0			0
$301$	10.3528			0.596727
$302$		0			0
$303$	6.13525	+	12.0411i	0.352461	+	0.691744i
$304$		0			0
$305$	12.2130	−	6.80061i	0.699313	−	0.389402i
$306$		0			0
$307$	11.1632	+	11.1632i	0.637116	+	0.637116i	0.949843	−	0.312727i	$-0.101242\pi$
$307$	11.1632	+	11.1632i	0.637116	+	0.637116i	−0.312727	+	0.949843i	$0.601242\pi$
$308$		0			0
$309$	10.3898	−	14.3003i	0.591055	−	0.813517i
$310$		0			0
$311$	18.2910	+	25.1754i	1.03719	+	1.42757i	0.899411	+	0.437103i	$0.143996\pi$
$311$	18.2910	+	25.1754i	1.03719	+	1.42757i	0.137777	+	0.990463i	$0.456004\pi$
$312$		0			0
$313$	−1.20851	−	7.63026i	−0.0683093	−	0.431288i	−0.998015	−	0.0629835i	$-0.979938\pi$
$313$	−1.20851	−	7.63026i	−0.0683093	−	0.431288i	0.929705	−	0.368304i	$-0.120062\pi$
$314$		0			0
$315$	15.2923	−	0.563577i	0.861625	−	0.0317540i
$316$		0			0
$317$	−4.97480	−	2.53479i	−0.279413	−	0.142368i	0.308669	−	0.951170i	$-0.400117\pi$
$317$	−4.97480	−	2.53479i	−0.279413	−	0.142368i	−0.588081	+	0.808802i	$0.700117\pi$
$318$		0			0
$319$	3.41503	+	10.5104i	0.191205	+	0.588468i
$320$		0			0
$321$	−2.46383	+	7.58290i	−0.137518	+	0.423236i
$322$		0			0
$323$	−0.158304	+	0.999491i	−0.00880826	+	0.0556132i
$324$		0			0
$325$	−2.42352	+	28.9896i	−0.134433	+	1.60805i
$326$		0			0
$327$	−11.5250	−	1.82538i	−0.637334	−	0.100944i
$328$		0			0
$329$	14.9774	+	4.86645i	0.825731	+	0.268296i
$330$		0			0
$331$	−4.34883	+	1.41302i	−0.239033	+	0.0776667i	−0.426084	−	0.904684i	$-0.640107\pi$
$331$	−4.34883	+	1.41302i	−0.239033	+	0.0776667i	0.187051	+	0.982350i	$0.440107\pi$
$332$		0			0
$333$	9.63315	−	18.9061i	0.527894	−	1.03605i
$334$		0			0
$335$	19.0986	−	28.4331i	1.04347	−	1.55347i
$336$		0			0
$337$	18.7668	−	2.97237i	1.02229	−	0.161915i	0.377289	−	0.926095i	$-0.376856\pi$
$337$	18.7668	−	2.97237i	1.02229	−	0.161915i	0.645003	+	0.764180i	$0.276856\pi$
$338$		0			0
$339$	−11.1670	+	8.11333i	−0.606511	+	0.440656i
$340$		0			0
$341$	−5.65189	−	4.10634i	−0.306067	−	0.222371i
$342$		0			0
$343$	−6.94816	+	6.94816i	−0.375165	+	0.375165i
$344$		0			0
$345$	16.4049	−	3.22166i	0.883208	−	0.173448i
$346$		0			0
$347$	−16.9260	+	8.62424i	−0.908637	+	0.462974i	−0.844858	−	0.534991i	$-0.820315\pi$
$347$	−16.9260	+	8.62424i	−0.908637	+	0.462974i	−0.0637787	+	0.997964i	$0.520315\pi$
$348$		0			0
$349$			14.3317i			0.767161i	0.923507	+	0.383580i	$0.125309\pi$
$349$			14.3317i			0.767161i	−0.923507	+	0.383580i	$0.874691\pi$
$350$		0			0
$351$			28.5488i			1.52382i
$352$		0			0
$353$	1.48111	−	0.754662i	0.0788314	−	0.0401666i	−0.414130	−	0.910218i	$-0.635914\pi$
$353$	1.48111	−	0.754662i	0.0788314	−	0.0401666i	0.492962	+	0.870051i	$0.335914\pi$
$354$		0			0
$355$	−18.9031	−	8.77027i	−1.00327	−	0.465478i
$356$		0			0
$357$	8.67591	−	8.67591i	0.459178	−	0.459178i
$358$		0			0
$359$	20.4682	+	14.8710i	1.08027	+	0.784864i	0.977730	−	0.209865i	$-0.0673025\pi$
$359$	20.4682	+	14.8710i	1.08027	+	0.784864i	0.102542	+	0.994729i	$0.467302\pi$
$360$		0			0
$361$	15.3142	−	11.1264i	0.806008	−	0.585599i
$362$		0			0
$363$	1.89341	−	0.299886i	0.0993781	−	0.0157400i
$364$		0			0
$365$	11.2752	+	3.20958i	0.590173	+	0.167997i
$366$		0			0
$367$	8.16520	−	16.0251i	0.426220	−	0.836503i	−0.573629	−	0.819115i	$-0.694465\pi$
$367$	8.16520	−	16.0251i	0.426220	−	0.836503i	0.999849	−	0.0173882i	$-0.00553511\pi$
$368$		0			0
$369$	−2.48730	+	0.808172i	−0.129484	+	0.0420718i
$370$		0			0
$371$	−19.3100	−	6.27419i	−1.00252	−	0.325740i
$372$		0			0
$373$	19.3738	+	3.06851i	1.00314	+	0.158881i	0.636331	−	0.771416i	$-0.280451\pi$
$373$	19.3738	+	3.06851i	1.00314	+	0.158881i	0.366806	+	0.930297i	$0.380451\pi$
$374$		0			0
$375$	−1.19586	−	10.7771i	−0.0617540	−	0.556529i
$376$		0			0
$377$	−3.34845	+	21.1413i	−0.172454	+	1.08883i
$378$		0			0
$379$	2.80980	−	8.64766i	0.144330	−	0.444201i	−0.852595	−	0.522573i	$-0.824972\pi$
$379$	2.80980	−	8.64766i	0.144330	−	0.444201i	0.996924	+	0.0783722i	$0.0249723\pi$
$380$		0			0
$381$	1.34130	+	4.12811i	0.0687171	+	0.211489i
$382$		0			0
$383$	−2.26052	−	1.15179i	−0.115507	−	0.0588540i	0.395282	−	0.918560i	$-0.370647\pi$
$383$	−2.26052	−	1.15179i	−0.115507	−	0.0588540i	−0.510790	+	0.859706i	$0.670647\pi$
$384$		0			0
$385$	−6.11109	+	21.4682i	−0.311450	+	1.09412i
$386$		0			0
$387$	1.00366	+	6.33683i	0.0510187	+	0.322119i
$388$		0			0
$389$	5.19740	+	7.15360i	0.263518	+	0.362702i	0.920188	−	0.391476i	$-0.128035\pi$
$389$	5.19740	+	7.15360i	0.263518	+	0.362702i	−0.656670	+	0.754178i	$0.728035\pi$
$390$		0			0
$391$	−17.2503	+	23.7431i	−0.872387	+	1.20074i
$392$		0			0
$393$	4.55350	+	4.55350i	0.229693	+	0.229693i
$394$		0			0
$395$	−11.3558	+	24.4758i	−0.571371	+	1.23151i
$396$		0			0
$397$	−2.32812	−	4.56918i	−0.116845	−	0.229321i	0.825176	−	0.564876i	$-0.191076\pi$
$397$	−2.32812	−	4.56918i	−0.116845	−	0.229321i	−0.942020	+	0.335555i	$0.891076\pi$
$398$		0			0
$399$	0.856702			0.0428888
$400$		0			0
$401$	−2.41447			−0.120573			−0.0602864	−	0.998181i	$-0.519201\pi$
$401$	−2.41447			−0.120573			−0.0602864	+	0.998181i	$0.519201\pi$
$402$		0			0
$403$	−6.14303	−	12.0564i	−0.306006	−	0.600570i
$404$		0			0
$405$	0.611546	+	3.11403i	0.0303880	+	0.154737i
$406$		0			0
$407$	21.8854	+	21.8854i	1.08482	+	1.08482i
$408$		0			0
$409$	−7.39271	+	10.1752i	−0.365546	+	0.503131i	−0.951684	−	0.307081i	$-0.900648\pi$
$409$	−7.39271	+	10.1752i	−0.365546	+	0.503131i	0.586137	+	0.810212i	$0.300648\pi$
$410$		0			0
$411$	−3.23941	−	4.45866i	−0.159788	−	0.219930i
$412$		0			0
$413$	6.13958	+	38.7638i	0.302109	+	1.90744i
$414$		0			0
$415$	−14.8201	−	9.95471i	−0.727490	−	0.488658i
$416$		0			0
$417$	−4.94836	−	2.52132i	−0.242322	−	0.123469i
$418$		0			0
$419$	0.222461	+	0.684664i	0.0108679	+	0.0334480i	0.956343	−	0.292245i	$-0.0944023\pi$
$419$	0.222461	+	0.684664i	0.0108679	+	0.0334480i	−0.945476	+	0.325693i	$0.894402\pi$
$420$		0			0
$421$	−2.82794	+	8.70352i	−0.137826	+	0.424184i	−0.996019	−	0.0891432i	$-0.971587\pi$
$421$	−2.82794	+	8.70352i	−0.137826	+	0.424184i	0.858193	+	0.513327i	$0.171587\pi$
$422$		0			0
$423$	−1.52671	+	9.63924i	−0.0742310	+	0.468676i
$424$		0			0
$425$	14.4139	+	12.4324i	0.699177	+	0.603062i
$426$		0			0
$427$	20.5186	+	3.24983i	0.992965	+	0.157270i
$428$		0			0
$429$	−16.1206	−	5.23790i	−0.778311	−	0.252888i
$430$		0			0
$431$	32.0198	−	10.4038i	1.54234	−	0.501136i	0.590317	−	0.807171i	$-0.299003\pi$
$431$	32.0198	−	10.4038i	1.54234	−	0.501136i	0.952020	+	0.306036i	$0.0990027\pi$
$432$		0			0
$433$	17.6056	−	34.5529i	0.846071	−	1.66051i	0.0996617	−	0.995021i	$-0.468224\pi$
$433$	17.6056	−	34.5529i	0.846071	−	1.66051i	0.746410	−	0.665487i	$-0.231776\pi$
$434$		0			0
$435$	−0.293835	−	7.97302i	−0.0140883	−	0.382277i
$436$		0			0
$437$	−2.02395	+	0.320561i	−0.0968184	+	0.0153345i
$438$		0			0
$439$	16.8861	−	12.2685i	0.805930	−	0.585542i	−0.106718	−	0.994289i	$-0.534034\pi$
$439$	16.8861	−	12.2685i	0.805930	−	0.585542i	0.912648	+	0.408747i	$0.134034\pi$
$440$		0			0
$441$	6.73609	+	4.89406i	0.320766	+	0.233050i
$442$		0			0
$443$	8.09076	−	8.09076i	0.384404	−	0.384404i	−0.488282	−	0.872686i	$-0.662376\pi$
$443$	8.09076	−	8.09076i	0.384404	−	0.384404i	0.872686	+	0.488282i	$0.162376\pi$
$444$		0			0
$445$	−8.30902	−	14.9219i	−0.393885	−	0.707364i
$446$		0			0
$447$	−2.18776	+	1.11472i	−0.103477	+	0.0527243i
$448$		0			0
$449$		−	16.5890i		−	0.782883i	−0.920203	−	0.391442i	$-0.871976\pi$
$449$		−	16.5890i		−	0.782883i	0.920203	−	0.391442i	$-0.128024\pi$
$450$		0			0
$451$		−	3.81477i		−	0.179631i
$452$		0			0
$453$	−8.88476	+	4.52701i	−0.417442	+	0.212697i
$454$		0			0
$455$	−29.4237	+	31.6754i	−1.37940	+	1.48497i
$456$		0			0
$457$	−8.69369	+	8.69369i	−0.406674	+	0.406674i	−0.880577	−	0.473903i	$-0.842845\pi$
$457$	−8.69369	+	8.69369i	−0.406674	+	0.406674i	0.473903	+	0.880577i	$0.342845\pi$
$458$		0			0
$459$	15.1126	+	10.9800i	0.705398	+	0.512502i
$460$		0			0
$461$	26.1698	−	19.0135i	1.21885	−	0.885546i	0.222846	−	0.974854i	$-0.428465\pi$
$461$	26.1698	−	19.0135i	1.21885	−	0.885546i	0.996004	+	0.0893072i	$0.0284653\pi$
$462$		0			0
$463$	−22.3507	+	3.54000i	−1.03872	+	0.164518i	−0.652423	−	0.757855i	$-0.726247\pi$
$463$	−22.3507	+	3.54000i	−1.03872	+	0.164518i	−0.386301	+	0.922373i	$0.626247\pi$
$464$		0			0
$465$	3.11282	+	3.96842i	0.144354	+	0.184031i
$466$		0			0
$467$	−7.00038	+	13.7390i	−0.323939	+	0.635766i	−0.994341	−	0.106231i	$-0.966122\pi$
$467$	−7.00038	+	13.7390i	−0.323939	+	0.635766i	0.670402	+	0.741998i	$0.266122\pi$
$468$		0			0
$469$	48.4120	−	15.7300i	2.23546	−	0.726344i
$470$		0			0
$471$	−12.4259	−	4.03743i	−0.572557	−	0.186035i
$472$		0			0
$473$	−9.24313	−	1.46397i	−0.425000	−	0.0673133i
$474$		0			0
$475$	0.0978295	+	1.32547i	0.00448873	+	0.0608167i
$476$		0			0
$477$	1.96834	−	12.4276i	0.0901242	−	0.569022i
$478$		0			0
$479$	−2.17387	+	6.69048i	−0.0993265	+	0.305696i	−0.988357	−	0.152152i	$-0.951380\pi$
$479$	−2.17387	+	6.69048i	−0.0993265	+	0.305696i	0.889031	+	0.457848i	$0.151380\pi$
$480$		0			0
$481$	18.5247	+	57.0131i	0.844653	+	2.59957i
$482$		0			0
$483$	22.1376	+	11.2797i	1.00730	+	0.513243i
$484$		0			0
$485$	2.72802	+	7.45041i	0.123873	+	0.338306i
$486$		0			0
$487$	−6.08231	−	38.4022i	−0.275616	−	1.74017i	−0.605227	−	0.796053i	$-0.706918\pi$
$487$	−6.08231	−	38.4022i	−0.275616	−	1.74017i	0.329612	−	0.944117i	$-0.393082\pi$
$488$		0			0
$489$	−0.555592	−	0.764707i	−0.0251247	−	0.0345812i
$490$		0			0
$491$	21.8195	−	30.0319i	0.984698	−	1.35532i	0.0504384	−	0.998727i	$-0.483938\pi$
$491$	21.8195	−	30.0319i	0.984698	−	1.35532i	0.934260	−	0.356593i	$-0.116062\pi$
$492$		0			0
$493$	9.90357	+	9.90357i	0.446034	+	0.446034i
$494$		0			0
$495$	−13.7329	−	1.65928i	−0.617246	−	0.0745791i
$496$		0			0
$497$	−14.0596	−	27.5936i	−0.630661	−	1.23774i
$498$		0			0
$499$	22.3039			0.998461			0.499230	−	0.866469i	$-0.333616\pi$
$499$	22.3039			0.998461			0.499230	+	0.866469i	$0.333616\pi$
$500$		0			0
$501$	23.8300			1.06465
$502$		0			0
$503$	−0.820826	−	1.61096i	−0.0365988	−	0.0718292i	0.871983	−	0.489536i	$-0.162834\pi$
$503$	−0.820826	−	1.61096i	−0.0365988	−	0.0718292i	−0.908582	+	0.417707i	$0.862834\pi$
$504$		0			0
$505$	−30.9327	−	3.73746i	−1.37649	−	0.166315i
$506$		0			0
$507$	−14.2993	−	14.2993i	−0.635053	−	0.635053i
$508$		0			0
$509$	−19.5393	+	26.8936i	−0.866066	+	1.19204i	0.114023	+	0.993478i	$0.463626\pi$
$509$	−19.5393	+	26.8936i	−0.866066	+	1.19204i	−0.980089	+	0.198559i	$0.936374\pi$
$510$		0			0
$511$	10.2406	+	14.0949i	0.453016	+	0.623523i
$512$		0			0
$513$	0.204040	+	1.28826i	0.00900858	+	0.0568780i
$514$		0			0
$515$	14.0125	+	38.2690i	0.617465	+	1.68634i
$516$		0			0
$517$	−12.6838	−	6.46274i	−0.557835	−	0.284231i
$518$		0			0
$519$	3.53058	+	10.8660i	0.154975	+	0.476965i
$520$		0			0
$521$	−5.80407	+	17.8631i	−0.254281	+	0.782596i	0.739690	+	0.672948i	$0.234972\pi$
$521$	−5.80407	+	17.8631i	−0.254281	+	0.782596i	−0.993970	+	0.109648i	$0.965028\pi$
$522$		0			0
$523$	0.568623	−	3.59014i	0.0248641	−	0.156986i	−0.972132	−	0.234433i	$-0.924677\pi$
$523$	0.568623	−	3.59014i	0.0248641	−	0.156986i	0.996996	+	0.0774467i	$0.0246768\pi$
$524$		0			0
$525$	8.48663	−	13.6989i	0.370387	−	0.597867i
$526$		0			0
$527$	−8.74481	−	1.38504i	−0.380930	−	0.0603334i
$528$		0			0
$529$	−34.6461	−	11.2572i	−1.50635	−	0.489444i
$530$		0			0
$531$	−23.1316	+	7.51590i	−1.00382	+	0.326162i
$532$		0			0
$533$	3.35440	−	6.58338i	0.145295	−	0.285158i
$534$		0			0
$535$	−11.3454	−	14.4639i	−0.490506	−	0.625327i
$536$		0			0
$537$	−3.91914	+	0.620731i	−0.169123	+	0.0267865i
$538$		0			0
$539$	−9.82551	+	7.13865i	−0.423215	+	0.307483i
$540$		0			0
$541$	−21.4786	−	15.6051i	−0.923438	−	0.670917i	0.0209391	−	0.999781i	$-0.493334\pi$
$541$	−21.4786	−	15.6051i	−0.923438	−	0.670917i	−0.944377	+	0.328864i	$0.893334\pi$
$542$		0			0
$543$	18.3678	−	18.3678i	0.788237	−	0.788237i
$544$		0			0
$545$	18.3098	−	19.7110i	0.784305	−	0.844326i
$546$		0			0
$547$	0.211164	−	0.107594i	0.00902874	−	0.00460037i	−0.449470	−	0.893295i	$-0.648387\pi$
$547$	0.211164	−	0.107594i	0.00902874	−	0.00460037i	0.458499	+	0.888695i	$0.348387\pi$
$548$		0			0
$549$			12.8742i			0.549458i
$550$		0			0
$551$			0.977927i			0.0416611i
$552$		0			0
$553$	−35.7283	+	18.2045i	−1.51932	+	0.774133i
$554$		0			0
$555$	−10.8706	−	19.5222i	−0.461432	−	0.828669i
$556$		0			0
$557$	−3.46747	+	3.46747i	−0.146922	+	0.146922i	−0.776741	−	0.629820i	$-0.783129\pi$
$557$	−3.46747	+	3.46747i	−0.146922	+	0.146922i	0.629820	+	0.776741i	$0.283129\pi$
$558$		0			0
$559$	−14.6641	−	10.6541i	−0.620227	−	0.450621i
$560$		0			0
$561$	−8.97280	+	6.51912i	−0.378832	+	0.275237i
$562$		0			0
$563$	−37.7197	+	5.97421i	−1.58970	+	0.251783i	−0.887708	−	0.460407i	$-0.847704\pi$
$563$	−37.7197	+	5.97421i	−1.58970	+	0.251783i	−0.701987	+	0.712190i	$0.747704\pi$
$564$		0			0
$565$	−1.17205	−	31.8028i	−0.0493084	−	1.33795i
$566$		0			0
$567$	−2.14115	+	4.20224i	−0.0899197	+	0.176477i
$568$		0			0
$569$	24.1916	−	7.86033i	1.01416	−	0.329522i	0.245653	−	0.969358i	$-0.420998\pi$
$569$	24.1916	−	7.86033i	1.01416	−	0.329522i	0.768512	+	0.639836i	$0.220998\pi$
$570$		0			0
$571$	−13.7756	−	4.47597i	−0.576492	−	0.187314i	0.00623640	−	0.999981i	$-0.498015\pi$
$571$	−13.7756	−	4.47597i	−0.576492	−	0.187314i	−0.582728	+	0.812667i	$0.698015\pi$
$572$		0			0
$573$	14.8638	+	2.35419i	0.620943	+	0.0983477i
$574$		0			0
$575$	−14.9237	+	35.5389i	−0.622361	+	1.48207i
$576$		0			0
$577$	−2.43032	+	15.3444i	−0.101175	+	0.638797i	0.884031	+	0.467427i	$0.154819\pi$
$577$	−2.43032	+	15.3444i	−0.101175	+	0.638797i	−0.985207	+	0.171369i	$0.945181\pi$
$578$		0			0
$579$	−2.07329	+	6.38094i	−0.0861632	+	0.265183i
$580$		0			0
$581$	−8.19889	−	25.2336i	−0.340147	−	1.04687i
$582$		0			0
$583$	16.3530	+	8.33225i	0.677270	+	0.345086i
$584$		0			0
$585$	−22.2406	−	14.9391i	−0.919535	−	0.617655i
$586$		0			0
$587$	0.427595	+	2.69973i	0.0176487	+	0.111430i	0.994940	−	0.100471i	$-0.0320348\pi$
$587$	0.427595	+	2.69973i	0.0176487	+	0.111430i	−0.977291	+	0.211900i	$0.932035\pi$
$588$		0			0
$589$	−0.363370	−	0.500136i	−0.0149724	−	0.0206077i
$590$		0			0
$591$	1.88278	−	2.59142i	0.0774472	−	0.106597i
$592$		0			0
$593$	−18.8643	−	18.8643i	−0.774662	−	0.774662i	0.204255	−	0.978918i	$-0.434523\pi$
$593$	−18.8643	−	18.8643i	−0.774662	−	0.774662i	−0.978918	+	0.204255i	$0.934523\pi$
$594$		0			0
$595$	5.45129	+	27.7583i	0.223481	+	1.13798i
$596$		0			0
$597$	2.96560	+	5.82031i	0.121374	+	0.238210i
$598$		0			0
$599$	20.6640			0.844310			0.422155	−	0.906524i	$-0.361274\pi$
$599$	20.6640			0.844310			0.422155	+	0.906524i	$0.361274\pi$
$600$		0			0
$601$	39.7005			1.61942			0.809709	−	0.586832i	$-0.199625\pi$
$601$	39.7005			1.61942			0.809709	+	0.586832i	$0.199625\pi$
$602$		0			0
$603$	14.3214	+	28.1074i	0.583213	+	1.14462i
$604$		0			0
$605$	−1.86016	+	4.00931i	−0.0756261	+	0.163002i
$606$		0			0
$607$	−6.86425	−	6.86425i	−0.278611	−	0.278611i	0.553943	−	0.832554i	$-0.313122\pi$
$607$	−6.86425	−	6.86425i	−0.278611	−	0.278611i	−0.832554	+	0.553943i	$0.813122\pi$
$608$		0			0
$609$	6.96941	−	9.59258i	0.282415	−	0.388711i
$610$		0			0
$611$	−16.2065	−	22.3063i	−0.655643	−	0.902416i
$612$		0			0
$613$	−6.01483	−	37.9762i	−0.242937	−	1.53384i	−0.743851	−	0.668345i	$-0.767003\pi$
$613$	−6.01483	−	37.9762i	−0.242937	−	1.53384i	0.500914	−	0.865497i	$-0.332997\pi$
$614$		0			0
$615$	−0.754011	+	2.64884i	−0.0304047	+	0.106811i
$616$		0			0
$617$	19.3631	+	9.86600i	0.779530	+	0.397190i	0.798014	−	0.602639i	$-0.205884\pi$
$617$	19.3631	+	9.86600i	0.779530	+	0.397190i	−0.0184841	+	0.999829i	$0.505884\pi$
$618$		0			0
$619$	−0.474342	−	1.45988i	−0.0190654	−	0.0586774i	0.941071	−	0.338209i	$-0.109821\pi$
$619$	−0.474342	−	1.45988i	−0.0190654	−	0.0586774i	−0.960137	+	0.279531i	$0.909821\pi$
$620$		0			0
$621$	−11.6892	+	35.9757i	−0.469072	+	1.44365i
$622$		0			0
$623$	3.97066	−	25.0697i	0.159081	−	1.00440i
$624$		0			0
$625$	22.1637	+	11.5660i	0.886546	+	0.462640i
$626$		0			0
$627$	−0.764874	−	0.121144i	−0.0305461	−	0.00483803i
$628$		0			0
$629$	37.3052	+	12.1212i	1.48746	+	0.483304i
$630$		0			0
$631$	−0.101312	+	0.0329182i	−0.00403316	+	0.00131045i	−0.311033	−	0.950399i	$-0.600675\pi$
$631$	−0.101312	+	0.0329182i	−0.00403316	+	0.00131045i	0.307000	+	0.951710i	$0.400675\pi$
$632$		0			0
$633$	8.02666	−	15.7532i	0.319031	−	0.626134i
$634$		0			0
$635$	−9.62511	−	2.73986i	−0.381961	−	0.108728i
$636$		0			0
$637$	−23.2336	+	3.67984i	−0.920550	+	0.145801i
$638$		0			0
$639$	15.5266	−	11.2808i	0.614225	−	0.446260i
$640$		0			0
$641$	−20.2967	−	14.7464i	−0.801671	−	0.582448i	0.109733	−	0.993961i	$-0.465000\pi$
$641$	−20.2967	−	14.7464i	−0.801671	−	0.582448i	−0.911404	+	0.411513i	$0.865000\pi$
$642$		0			0
$643$	30.4402	−	30.4402i	1.20045	−	1.20045i	0.226415	−	0.974031i	$-0.427299\pi$
$643$	30.4402	−	30.4402i	1.20045	−	1.20045i	0.974031	−	0.226415i	$-0.0727007\pi$
$644$		0			0
$645$	6.12873	+	2.84348i	0.241318	+	0.111962i
$646$		0			0
$647$	18.0050	−	9.17400i	0.707849	−	0.360667i	−0.0627133	−	0.998032i	$-0.519975\pi$
$647$	18.0050	−	9.17400i	0.707849	−	0.360667i	0.770563	+	0.637364i	$0.219975\pi$
$648$		0			0
$649$		−	35.4769i		−	1.39259i
$650$		0			0
$651$			7.49552i			0.293772i
$652$		0			0
$653$	−18.8330	+	9.59589i	−0.736992	+	0.375516i	−0.781841	−	0.623478i	$-0.785719\pi$
$653$	−18.8330	+	9.59589i	−0.736992	+	0.375516i	0.0448491	+	0.998994i	$0.485719\pi$
$654$		0			0
$655$	−14.5687	+	2.86107i	−0.569248	+	0.111791i
$656$		0			0
$657$	−7.63454	+	7.63454i	−0.297852	+	0.297852i
$658$		0			0
$659$	29.9609	+	21.7679i	1.16711	+	0.847957i	0.990660	−	0.136352i	$-0.0435378\pi$
$659$	29.9609	+	21.7679i	1.16711	+	0.847957i	0.176452	+	0.984309i	$0.443538\pi$
$660$		0			0
$661$	−25.7181	+	18.6853i	−1.00032	+	0.726774i	−0.962157	−	0.272497i	$-0.912150\pi$
$661$	−25.7181	+	18.6853i	−1.00032	+	0.726774i	−0.0381625	+	0.999272i	$0.512150\pi$
$662$		0			0
$663$	−21.2173	+	3.36049i	−0.824011	+	0.130510i
$664$		0			0
$665$	−1.10135	+	1.63964i	−0.0427085	+	0.0635824i
$666$		0			0
$667$	−12.8758	+	25.2701i	−0.498552	+	0.978463i
$668$		0			0
$669$	−20.3987	+	6.62795i	−0.788661	+	0.256251i
$670$		0			0
$671$	−17.8597	−	5.80297i	−0.689466	−	0.224021i
$672$		0			0
$673$	18.3183	+	2.90134i	0.706120	+	0.111838i	0.499159	−	0.866511i	$-0.333642\pi$
$673$	18.3183	+	2.90134i	0.706120	+	0.111838i	0.206962	+	0.978349i	$0.433642\pi$
$674$		0			0
$675$	22.6208	+	9.49905i	0.870674	+	0.365618i
$676$		0			0
$677$	1.55283	−	9.80421i	0.0596803	−	0.376807i	−0.939713	−	0.341965i	$-0.888907\pi$
$677$	1.55283	−	9.80421i	0.0596803	−	0.376807i	0.999393	−	0.0348412i	$-0.0110925\pi$
$678$		0			0
$679$	−3.64370	+	11.2142i	−0.139832	+	0.430360i
$680$		0			0
$681$	−3.75305	−	11.5507i	−0.143817	−	0.442624i
$682$		0			0
$683$	14.1779	+	7.22400i	0.542503	+	0.276419i	0.703693	−	0.710505i	$-0.251533\pi$
$683$	14.1779	+	7.22400i	0.542503	+	0.276419i	−0.161190	+	0.986923i	$0.551533\pi$
$684$		0			0
$685$	12.6979	−	0.467963i	0.485161	−	0.0178800i
$686$		0			0
$687$	−1.03281	−	6.52091i	−0.0394042	−	0.248788i
$688$		0			0
$689$	20.8946	+	28.7589i	0.796020	+	1.09563i
$690$		0			0
$691$	25.2263	−	34.7210i	0.959654	−	1.32085i	0.0125509	−	0.999921i	$-0.496005\pi$
$691$	25.2263	−	34.7210i	0.959654	−	1.32085i	0.947103	−	0.320929i	$-0.103995\pi$
$692$		0			0
$693$	−14.5363	−	14.5363i	−0.552188	−	0.552188i
$694$		0			0
$695$	11.1870	−	6.22931i	0.424347	−	0.236291i
$696$		0			0
$697$	−2.19488	−	4.30769i	−0.0831368	−	0.163165i
$698$		0			0
$699$	−18.3248			−0.693107
$700$		0			0
$701$	−35.1505			−1.32762			−0.663808	−	0.747903i	$-0.731061\pi$
$701$	−35.1505			−1.32762			−0.663808	+	0.747903i	$0.731061\pi$
$702$		0			0
$703$	1.24340	+	2.44030i	0.0468956	+	0.0920378i
$704$		0			0
$705$	7.52979	+	6.99452i	0.283588	+	0.263429i
$706$		0			0
$707$	−32.7424	−	32.7424i	−1.23140	−	1.23140i
$708$		0			0
$709$	−5.21053	+	7.17168i	−0.195686	+	0.269338i	−0.895573	−	0.444915i	$-0.853234\pi$
$709$	−5.21053	+	7.17168i	−0.195686	+	0.269338i	0.699887	+	0.714254i	$0.253234\pi$
$710$		0			0
$711$	−14.6064	−	20.1040i	−0.547782	−	0.753957i
$712$		0			0
$713$	−2.80468	−	17.7080i	−0.105036	−	0.663171i
$714$		0			0
$715$	30.7490	−	24.1195i	1.14995	−	0.902017i
$716$		0			0
$717$	8.13325	+	4.14410i	0.303742	+	0.154764i
$718$		0			0
$719$	7.06433	+	21.7418i	0.263455	+	0.810831i	0.992045	+	0.125881i	$0.0401759\pi$
$719$	7.06433	+	21.7418i	0.263455	+	0.810831i	−0.728590	+	0.684950i	$0.759824\pi$
$720$		0			0
$721$	−18.7159	+	57.6016i	−0.697016	+	2.14519i
$722$		0			0
$723$	2.78798	−	17.6026i	0.103686	−	0.654648i
$724$		0			0
$725$	15.6373	+	9.68750i	0.580753	+	0.359785i
$726$		0			0
$727$	−31.3330	−	4.96266i	−1.16208	−	0.184055i	−0.454536	−	0.890728i	$-0.650195\pi$
$727$	−31.3330	−	4.96266i	−1.16208	−	0.184055i	−0.707540	+	0.706673i	$0.750195\pi$
$728$		0			0
$729$	10.7983	+	3.50858i	0.399938	+	0.129948i
$730$		0			0
$731$	−11.2798	+	3.66502i	−0.417197	+	0.135556i
$732$		0			0
$733$	2.18971	−	4.29754i	0.0808787	−	0.158733i	−0.847025	−	0.531553i	$-0.821609\pi$
$733$	2.18971	−	4.29754i	0.0808787	−	0.158733i	0.927904	+	0.372819i	$0.121609\pi$
$734$		0			0
$735$	8.23346	−	3.01475i	0.303696	−	0.111201i
$736$		0			0
$737$	−45.4471	+	7.19811i	−1.67407	+	0.265146i
$738$		0			0
$739$	18.5519	−	13.4787i	0.682443	−	0.495824i	−0.191724	−	0.981449i	$-0.561408\pi$
$739$	18.5519	−	13.4787i	0.682443	−	0.495824i	0.874167	+	0.485625i	$0.161408\pi$
$740$		0			0
$741$	−1.21346	−	0.881634i	−0.0445777	−	0.0323876i
$742$		0			0
$743$	22.3520	−	22.3520i	0.820015	−	0.820015i	−0.166095	−	0.986110i	$-0.553116\pi$
$743$	22.3520	−	22.3520i	0.820015	−	0.820015i	0.986110	+	0.166095i	$0.0531159\pi$
$744$		0			0
$745$	0.679062	−	5.62018i	0.0248789	−	0.205908i
$746$		0			0
$747$	14.6503	−	7.46470i	0.536026	−	0.273119i
$748$		0			0
$749$		−	27.3192i		−	0.998223i
$750$		0			0
$751$			13.9720i			0.509844i	0.966962	+	0.254922i	$0.0820498\pi$
$751$			13.9720i			0.509844i	−0.966962	+	0.254922i	$0.917950\pi$
$752$		0			0
$753$	−5.77261	+	2.94129i	−0.210365	+	0.107187i
$754$		0			0
$755$	2.75776	−	22.8243i	0.100365	−	0.830660i
$756$		0			0
$757$	−14.0489	+	14.0489i	−0.510617	+	0.510617i	−0.914715	−	0.404098i	$-0.867585\pi$
$757$	−14.0489	+	14.0489i	−0.510617	+	0.510617i	0.404098	+	0.914715i	$0.367585\pi$
$758$		0			0
$759$	−18.1697	−	13.2011i	−0.659518	−	0.479168i
$760$		0			0
$761$	−15.3727	+	11.1689i	−0.557260	+	0.404873i	−0.830455	−	0.557086i	$-0.811919\pi$
$761$	−15.3727	+	11.1689i	−0.557260	+	0.404873i	0.273195	+	0.961959i	$0.411919\pi$
$762$		0			0
$763$	39.4894	−	6.25451i	1.42961	−	0.226428i
$764$		0			0
$765$	−16.4620	+	6.02769i	−0.595184	+	0.217931i
$766$		0			0
$767$	31.1955	−	61.2247i	1.12641	−	2.21069i
$768$		0			0
$769$	5.80830	−	1.88723i	0.209453	−	0.0680553i	−0.202411	−	0.979301i	$-0.564878\pi$
$769$	5.80830	−	1.88723i	0.209453	−	0.0680553i	0.411864	+	0.911245i	$0.364878\pi$
$770$		0			0
$771$	15.9635	+	5.18686i	0.574912	+	0.186800i
$772$		0			0
$773$	−41.7576	−	6.61375i	−1.50192	−	0.237880i	−0.649346	−	0.760493i	$-0.724957\pi$
$773$	−41.7576	−	6.61375i	−1.50192	−	0.237880i	−0.852570	+	0.522613i	$0.824957\pi$
$774$		0			0
$775$	−11.5969	+	0.855937i	−0.416572	+	0.0307461i
$776$		0			0
$777$	5.19478	−	32.7985i	0.186362	−	1.17664i
$778$		0			0
$779$	0.104315	−	0.321047i	0.00373746	−	0.0115027i
$780$		0			0
$781$	8.65067	+	26.6240i	0.309545	+	0.952682i
$782$		0			0
$783$	16.0846	+	8.19553i	0.574818	+	0.292884i
$784$		0			0
$785$	23.7016	−	18.5915i	0.845947	−	0.663560i
$786$		0			0
$787$	−5.48304	−	34.6186i	−0.195449	−	1.23402i	−0.868975	−	0.494855i	$-0.835221\pi$
$787$	−5.48304	−	34.6186i	−0.195449	−	1.23402i	0.673526	−	0.739163i	$-0.264779\pi$
$788$		0			0
$789$	−2.07518	−	2.85624i	−0.0738783	−	0.101685i
$790$		0			0
$791$	27.7996	−	38.2629i	0.988441	−	1.36047i
$792$		0			0
$793$	−25.7189	−	25.7189i	−0.913305	−	0.913305i
$794$		0			0
$795$	−9.70797	−	9.01786i	−0.344306	−	0.319830i
$796$		0			0
$797$	−1.29027	−	2.53229i	−0.0457036	−	0.0896983i	0.867025	−	0.498264i	$-0.166029\pi$
$797$	−1.29027	−	2.53229i	−0.0457036	−	0.0896983i	−0.912729	+	0.408566i	$0.866029\pi$
$798$		0			0
$799$	−18.0412			−0.638250
$800$		0			0
$801$	15.7298			0.555784
$802$		0			0
$803$	−7.14976	−	14.0322i	−0.252310	−	0.495186i
$804$		0			0
$805$	−50.0476	+	27.8683i	−1.76395	+	0.982227i
$806$		0			0
$807$	−2.73642	−	2.73642i	−0.0963265	−	0.0963265i
$808$		0			0
$809$	33.2152	−	45.7168i	1.16778	−	1.60732i	0.490926	−	0.871202i	$-0.336659\pi$
$809$	33.2152	−	45.7168i	1.16778	−	1.60732i	0.676858	−	0.736114i	$-0.263341\pi$
$810$		0			0
$811$	10.9494	+	15.0706i	0.384486	+	0.529200i	0.956766	−	0.290858i	$-0.0939408\pi$
$811$	10.9494	+	15.0706i	0.384486	+	0.529200i	−0.572280	+	0.820058i	$0.693941\pi$
$812$		0			0
$813$	−2.42324	−	15.2997i	−0.0849868	−	0.536585i
$814$		0			0
$815$	2.17782	−	0.0802606i	0.0762857	−	0.00281140i
$816$		0			0
$817$	−0.737861	−	0.375959i	−0.0258145	−	0.0131531i
$818$		0			0
$819$	−12.3041	−	37.8681i	−0.429940	−	1.32322i
$820$		0			0
$821$	5.19540	−	15.9898i	0.181321	−	0.558048i	−0.818545	−	0.574443i	$-0.805219\pi$
$821$	5.19540	−	15.9898i	0.181321	−	0.558048i	0.999866	+	0.0163947i	$0.00521882\pi$
$822$		0			0
$823$	−3.90298	+	24.6425i	−0.136049	+	0.858982i	0.821394	+	0.570361i	$0.193197\pi$
$823$	−3.90298	+	24.6425i	−0.136049	+	0.858982i	−0.957443	+	0.288621i	$0.906803\pi$
$824$		0			0
$825$	−9.51409	+	11.0304i	−0.331238	+	0.384030i
$826$		0			0
$827$	32.6419	+	5.16997i	1.13507	+	0.179778i	0.695566	−	0.718462i	$-0.255154\pi$
$827$	32.6419	+	5.16997i	1.13507	+	0.179778i	0.439505	+	0.898240i	$0.355154\pi$
$828$		0			0
$829$	−4.83283	−	1.57028i	−0.167851	−	0.0545382i	0.223886	−	0.974615i	$-0.428126\pi$
$829$	−4.83283	−	1.57028i	−0.167851	−	0.0545382i	−0.391737	+	0.920077i	$0.628126\pi$
$830$		0			0
$831$	−17.7001	+	5.75110i	−0.614008	+	0.199503i
$832$		0			0
$833$	−6.98777	+	13.7143i	−0.242112	+	0.475171i
$834$		0			0
$835$	−30.6352	+	45.6082i	−1.06017	+	1.57834i
$836$		0			0
$837$	−11.2713	+	1.78520i	−0.389593	+	0.0617055i
$838$		0			0
$839$	22.9677	−	16.6870i	0.792931	−	0.576098i	−0.115900	−	0.993261i	$-0.536975\pi$
$839$	22.9677	−	16.6870i	0.792931	−	0.576098i	0.908832	+	0.417162i	$0.136975\pi$
$840$		0			0
$841$	−12.5116	−	9.09018i	−0.431433	−	0.313454i
$842$		0			0
$843$	16.1217	−	16.1217i	0.555261	−	0.555261i
$844$		0			0
$845$	45.7500	−	8.98458i	1.57385	−	0.309079i
$846$		0			0
$847$	−5.85255	+	2.98202i	−0.201096	+	0.102463i
$848$		0			0
$849$		−	7.49701i		−	0.257297i
$850$		0			0
$851$			79.4298i			2.72282i
$852$		0			0
$853$	−3.49866	+	1.78265i	−0.119792	+	0.0610369i	−0.512859	−	0.858473i	$-0.671414\pi$
$853$	−3.49866	+	1.78265i	−0.119792	+	0.0610369i	0.393068	+	0.919510i	$0.371414\pi$
$854$		0			0
$855$	−1.11037	−	0.515167i	−0.0379739	−	0.0176183i
$856$		0			0
$857$	−18.6347	+	18.6347i	−0.636549	+	0.636549i	−0.949703	−	0.313154i	$-0.898615\pi$
$857$	−18.6347	+	18.6347i	−0.636549	+	0.636549i	0.313154	+	0.949703i	$0.398615\pi$
$858$		0			0
$859$	33.1025	+	24.0504i	1.12944	+	0.820588i	0.985614	−	0.169014i	$-0.0540584\pi$
$859$	33.1025	+	24.0504i	1.12944	+	0.820588i	0.143829	+	0.989603i	$0.454058\pi$
$860$		0			0
$861$	−3.31125	+	2.40576i	−0.112847	+	0.0819882i
$862$		0			0
$863$	−32.3520	+	5.12405i	−1.10127	+	0.174425i	−0.680505	−	0.732743i	$-0.738240\pi$
$863$	−32.3520	+	5.12405i	−1.10127	+	0.174425i	−0.420769	+	0.907168i	$0.638240\pi$
$864$		0			0
$865$	−25.3352	−	7.21185i	−0.861422	−	0.245210i
$866$		0			0
$867$	1.10383	−	2.16639i	0.0374880	−	0.0735743i
$868$		0			0
$869$	34.4729	−	11.2009i	1.16941	−	0.379965i
$870$		0			0
$871$	−84.7602	−	27.5403i	−2.87199	−	0.933166i
$872$		0			0
$873$	−7.21727	−	1.14310i	−0.244268	−	0.0386882i
$874$		0			0
$875$	15.3080	+	33.8534i	0.517505	+	1.14445i
$876$		0			0
$877$	6.73915	−	42.5493i	0.227565	−	1.43679i	−0.564036	−	0.825750i	$-0.690752\pi$
$877$	6.73915	−	42.5493i	0.227565	−	1.43679i	0.791601	−	0.611038i	$-0.209248\pi$
$878$		0			0
$879$	5.92753	−	18.2431i	0.199931	−	0.615324i
$880$		0			0
$881$	−7.53878	−	23.2020i	−0.253988	−	0.781695i	−0.994027	−	0.109131i	$-0.965193\pi$
$881$	−7.53878	−	23.2020i	−0.253988	−	0.781695i	0.740039	−	0.672564i	$-0.234807\pi$
$882$		0			0
$883$	23.9869	+	12.2219i	0.807223	+	0.411301i	0.808353	−	0.588699i	$-0.200359\pi$
$883$	23.9869	+	12.2219i	0.807223	+	0.411301i	−0.00112935	+	0.999999i	$0.500359\pi$
$884$		0			0
$885$	−7.01221	+	24.6339i	−0.235713	+	0.828058i
$886$		0			0
$887$	−1.89438	−	11.9606i	−0.0636070	−	0.401599i	−0.998865	−	0.0476319i	$-0.984833\pi$
$887$	−1.89438	−	11.9606i	−0.0636070	−	0.401599i	0.935258	−	0.353967i	$-0.115167\pi$
$888$		0			0
$889$	−8.74185	−	12.0321i	−0.293192	−	0.403544i
$890$		0			0
$891$	2.50587	−	3.44903i	0.0839498	−	0.115547i
$892$		0			0
$893$	−0.890737	−	0.890737i	−0.0298074	−	0.0298074i
$894$		0			0
$895$	3.85031	−	8.29881i	0.128702	−	0.277399i
$896$		0			0
$897$	−19.7486	−	38.7588i	−0.659387	−	1.29412i
$898$		0			0
$899$	−8.55614			−0.285363
$900$		0			0
$901$	23.2600			0.774903
$902$		0			0
$903$	4.55839	+	8.94634i	0.151694	+	0.297716i
$904$		0			0
$905$	11.5409	+	58.7671i	0.383634	+	1.95348i
$906$		0			0
$907$	−34.0838	−	34.0838i	−1.13173	−	1.13173i	−0.989889	−	0.141844i	$-0.954697\pi$
$907$	−34.0838	−	34.0838i	−1.13173	−	1.13173i	−0.141844	−	0.989889i	$-0.545303\pi$
$908$		0			0
$909$	16.8670	−	23.2154i	0.559442	−	0.770005i
$910$		0			0
$911$	9.58213	+	13.1887i	0.317470	+	0.436960i	0.937693	−	0.347466i	$-0.112958\pi$
$911$	9.58213	+	13.1887i	0.317470	+	0.436960i	−0.620223	+	0.784426i	$0.712958\pi$
$912$		0			0
$913$	3.75185	+	23.6882i	0.124168	+	0.783966i
$914$		0			0
$915$	11.2541	+	7.55944i	0.372050	+	0.249907i
$916$		0			0
$917$	−19.6599	−	10.0172i	−0.649226	−	0.330797i
$918$		0			0
$919$	−7.75909	−	23.8800i	−0.255949	−	0.787729i	−0.993641	−	0.112592i	$-0.964085\pi$
$919$	−7.75909	−	23.8800i	−0.255949	−	0.787729i	0.737693	−	0.675137i	$-0.235915\pi$
$920$		0			0
$921$	−4.73141	+	14.5618i	−0.155905	+	0.479827i
$922$		0			0
$923$	−8.48202	+	53.5533i	−0.279189	+	1.76273i
$924$		0			0
$925$	51.3383	+	4.29187i	1.68799	+	0.141116i
$926$		0			0
$927$	−37.0716	−	5.87156i	−1.21759	−	0.192847i
$928$		0			0
$929$	−25.9648	−	8.43646i	−0.851876	−	0.276791i	−0.149645	−	0.988740i	$-0.547813\pi$
$929$	−25.9648	−	8.43646i	−0.851876	−	0.276791i	−0.702232	+	0.711949i	$0.747813\pi$
$930$		0			0
$931$	−1.02211	+	0.332104i	−0.0334983	+	0.0108843i
$932$		0			0
$933$	−13.7016	+	26.8909i	−0.448570	+	0.880368i
$934$		0			0
$935$	−0.941749	−	25.5538i	−0.0307985	−	0.835698i
$936$		0			0
$937$	24.3542	−	3.85733i	0.795619	−	0.126014i	0.254625	−	0.967040i	$-0.418048\pi$
$937$	24.3542	−	3.85733i	0.795619	−	0.126014i	0.540994	+	0.841026i	$0.318048\pi$
$938$		0			0
$939$	6.06153	−	4.40396i	0.197811	−	0.143718i
$940$		0			0
$941$	−1.54129	−	1.11981i	−0.0502446	−	0.0365049i	0.562379	−	0.826879i	$-0.309886\pi$
$941$	−1.54129	−	1.11981i	−0.0502446	−	0.0365049i	−0.612624	+	0.790374i	$0.709886\pi$
$942$		0			0
$943$	6.92258	−	6.92258i	0.225430	−	0.225430i
$944$		0			0
$945$	17.7384	+	31.8557i	0.577029	+	1.03627i
$946$		0			0
$947$	44.2985	−	22.5712i	1.43951	−	0.733466i	0.452145	−	0.891945i	$-0.350659\pi$
$947$	44.2985	−	22.5712i	1.43951	−	0.733466i	0.987362	+	0.158479i	$0.0506590\pi$
$948$		0			0
$949$		−	30.5031i		−	0.990174i
$950$		0			0
$951$		−	5.41502i		−	0.175594i
$952$		0			0
$953$	−18.2256	+	9.28640i	−0.590384	+	0.300816i	−0.723544	−	0.690279i	$-0.757488\pi$
$953$	−18.2256	+	9.28640i	−0.590384	+	0.300816i	0.133159	+	0.991095i	$0.457488\pi$
$954$		0			0
$955$	−23.6141	+	25.4212i	−0.764134	+	0.822611i
$956$		0			0
$957$	−7.57884	+	7.57884i	−0.244989	+	0.244989i
$958$		0			0
$959$	15.2772	+	11.0995i	0.493327	+	0.358423i
$960$		0			0
$961$	−20.7037	+	15.0421i	−0.667861	+	0.485230i
$962$		0			0
$963$	16.7217	−	2.64846i	0.538850	−	0.0853455i
$964$		0			0
$965$	−9.54709	−	12.1712i	−0.307332	−	0.391805i
$966$		0			0
$967$	−2.90353	+	5.69850i	−0.0933713	+	0.183252i	−0.932969	−	0.359958i	$-0.882791\pi$
$967$	−2.90353	+	5.69850i	−0.0933713	+	0.183252i	0.839597	+	0.543209i	$0.182791\pi$
$968$		0			0
$969$	−0.933406	+	0.303282i	−0.0299853	+	0.00974282i
$970$		0			0
$971$	−19.6727	−	6.39206i	−0.631329	−	0.205131i	−0.0241650	−	0.999708i	$-0.507693\pi$
$971$	−19.6727	−	6.39206i	−0.631329	−	0.205131i	−0.607164	+	0.794577i	$0.707693\pi$
$972$		0			0
$973$	18.7949	+	2.97682i	0.602537	+	0.0954324i
$974$		0			0
$975$	−26.1183	+	10.6700i	−0.836455	+	0.341712i
$976$		0			0
$977$	−4.11816	+	26.0011i	−0.131752	+	0.831848i	0.829968	+	0.557812i	$0.188359\pi$
$977$	−4.11816	+	26.0011i	−0.131752	+	0.831848i	−0.961719	+	0.274036i	$0.911641\pi$
$978$		0			0
$979$	−7.09010	+	21.8211i	−0.226600	+	0.697404i
$980$		0			0
$981$	7.65660	+	23.5646i	0.244456	+	0.752360i
$982$		0			0
$983$	−22.4815	−	11.4549i	−0.717048	−	0.365354i	0.0570915	−	0.998369i	$-0.481817\pi$
$983$	−22.4815	−	11.4549i	−0.717048	−	0.365354i	−0.774140	+	0.633015i	$0.781817\pi$
$984$		0			0
$985$	2.53927	+	6.93489i	0.0809077	+	0.220964i
$986$		0			0
$987$	2.38928	+	15.0854i	0.0760518	+	0.480172i
$988$		0			0
$989$	−14.1167	−	19.4299i	−0.448884	−	0.617836i
$990$		0			0
$991$	−4.69642	+	6.46407i	−0.149187	+	0.205338i	−0.877069	−	0.480364i	$-0.840505\pi$
$991$	−4.69642	+	6.46407i	−0.149187	+	0.205338i	0.727882	+	0.685702i	$0.240505\pi$
$992$		0			0
$993$	−3.13586	−	3.13586i	−0.0995135	−	0.0995135i
$994$		0			0
$995$	−14.9520	−	1.80658i	−0.474009	−	0.0572724i
$996$		0			0
$997$	23.0303	+	45.1996i	0.729378	+	1.43149i	0.895354	+	0.445356i	$0.146923\pi$
$997$	23.0303	+	45.1996i	0.729378	+	1.43149i	−0.165975	+	0.986130i	$0.553077\pi$
$998$		0			0
$999$	50.5577			1.59957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bq.c.223.6	✓	64
4.3	odd	2		800.2.bq.d.223.3	yes	64
25.12	odd	20		800.2.bq.d.287.3	yes	64
100.87	even	20	inner	800.2.bq.c.287.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.bq.c.223.6	✓	64	1.1	even	1	trivial
800.2.bq.c.287.6	yes	64	100.87	even	20	inner
800.2.bq.d.223.3	yes	64	4.3	odd	2
800.2.bq.d.287.3	yes	64	25.12	odd	20

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.440304 + 0.864144i) q^{3} +(-2.21992 - 0.268223i) q^{5} +(-2.34980 - 2.34980i) q^{7} +(1.21048 - 1.66608i) q^{9} +(1.76565 + 2.43020i) q^{11} +(0.910159 + 5.74652i) q^{13} +(-0.745656 - 2.03643i) q^{15} +(3.39204 + 1.72833i) q^{17} +(0.0821413 + 0.252805i) q^{19} +(0.995939 - 3.06519i) q^{21} +(-1.20596 + 7.61411i) q^{23} +(4.85611 + 1.19087i) q^{25} +(4.84645 + 0.767602i) q^{27} +(3.49891 + 1.13687i) q^{29} +(-2.21186 + 0.718676i) q^{31} +(-1.32263 + 2.59580i) q^{33} +(4.58609 + 5.84663i) q^{35} +(10.1766 - 1.61182i) q^{37} +(-4.56507 + 3.31672i) q^{39} +(-1.02740 - 0.746453i) q^{41} +(-2.20292 + 2.20292i) q^{43} +(-3.13405 + 3.37389i) q^{45} +(-4.22246 + 2.15145i) q^{47} +4.04308i q^{49} +3.69220i q^{51} +(5.44391 - 2.77381i) q^{53} +(-3.26776 - 5.86845i) q^{55} +(-0.182293 + 0.182293i) q^{57} +(-9.55473 - 6.94192i) q^{59} +(-5.05755 + 3.67453i) q^{61} +(-6.75932 + 1.07057i) q^{63} +(-0.479132 - 13.0009i) q^{65} +(-6.95421 + 13.6484i) q^{67} +(-7.11068 + 2.31040i) q^{69} +(8.86316 + 2.87981i) q^{71} +(-5.17821 - 0.820148i) q^{73} +(1.10908 + 4.72073i) q^{75} +(1.56157 - 9.85939i) q^{77} +(3.72879 - 11.4760i) q^{79} +(-0.438568 - 1.34977i) q^{81} +(7.11391 + 3.62472i) q^{83} +(-7.06648 - 4.74658i) q^{85} +(0.558168 + 3.52413i) q^{87} +(4.48956 + 6.17934i) q^{89} +(11.3645 - 15.6418i) q^{91} +(-1.59493 - 1.59493i) q^{93} +(-0.114539 - 0.583240i) q^{95} +(-1.61088 - 3.16152i) q^{97} +6.18619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{5} - 4 q^{7} + 4 q^{13} - 22 q^{15} + 8 q^{17} + 18 q^{19} - 16 q^{21} - 8 q^{23} + 40 q^{25} - 18 q^{27} + 20 q^{31} + 44 q^{33} - 38 q^{35} - 10 q^{37} + 36 q^{39} - 16 q^{41} - 32 q^{43}+ \cdots - 132 q^{99}+O(q^{100}) \) 64 * q + 2 * q^5 - 4 * q^7 + 4 * q^13 - 22 * q^15 + 8 * q^17 + 18 * q^19 - 16 * q^21 - 8 * q^23 + 40 * q^25 - 18 * q^27 + 20 * q^31 + 44 * q^33 - 38 * q^35 - 10 * q^37 + 36 * q^39 - 16 * q^41 - 32 * q^43 + 14 * q^45 - 8 * q^47 - 22 * q^53 + 24 * q^55 - 8 * q^57 + 4 * q^59 - 36 * q^61 - 18 * q^63 - 24 * q^65 + 26 * q^67 + 60 * q^69 - 70 * q^71 - 12 * q^73 - 66 * q^75 + 48 * q^77 - 16 * q^79 - 24 * q^81 + 52 * q^83 - 46 * q^85 + 144 * q^87 - 60 * q^89 + 30 * q^91 + 20 * q^93 + 8 * q^95 - 56 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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