LMFDB - Embedded newform 819.2.o.c.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (of order $3$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			568.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	819.568
Dual form			819.2.o.c.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.330792i) q^{2} +(0.927051 + 1.60570i) q^{4} -0.381966 q^{5} +(-0.500000 - 0.866025i) q^{7} +1.47214 q^{8} +O(q^{10})$	\(q+(0.190983 - 0.330792i) q^{2} +(0.927051 + 1.60570i) q^{4} -0.381966 q^{5} +(-0.500000 - 0.866025i) q^{7} +1.47214 q^{8} +(-0.0729490 + 0.126351i) q^{10} +(-2.42705 + 4.20378i) q^{11} +(-2.50000 + 2.59808i) q^{13} -0.381966 q^{14} +(-1.57295 + 2.72443i) q^{16} +(3.73607 + 6.47106i) q^{17} +(-2.42705 - 4.20378i) q^{19} +(-0.354102 - 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +(2.23607 - 3.87298i) q^{23} -4.85410 q^{25} +(0.381966 + 1.32317i) q^{26} +(0.927051 - 1.60570i) q^{28} +(-2.04508 + 3.54219i) q^{29} +8.70820 q^{31} +(2.07295 + 3.59045i) q^{32} +2.85410 q^{34} +(0.190983 + 0.330792i) q^{35} +(-2.00000 + 3.46410i) q^{37} -1.85410 q^{38} -0.562306 q^{40} +(2.61803 - 4.53457i) q^{41} +(3.78115 + 6.54915i) q^{43} -9.00000 q^{44} +(-0.854102 - 1.47935i) q^{46} -2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.927051 + 1.60570i) q^{50} +(-6.48936 - 1.60570i) q^{52} -8.23607 q^{53} +(0.927051 - 1.60570i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(0.781153 + 1.35300i) q^{58} +(1.11803 + 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(1.66312 - 2.88061i) q^{62} -4.70820 q^{64} +(0.954915 - 0.992377i) q^{65} +(-0.354102 + 0.613323i) q^{67} +(-6.92705 + 11.9980i) q^{68} +0.145898 q^{70} +(4.09017 + 7.08438i) q^{71} -2.00000 q^{73} +(0.763932 + 1.32317i) q^{74} +(4.50000 - 7.79423i) q^{76} +4.85410 q^{77} +4.00000 q^{79} +(0.600813 - 1.04064i) q^{80} +(-1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +2.88854 q^{86} +(-3.57295 + 6.18853i) q^{88} +(8.04508 - 13.9345i) q^{89} +(3.50000 + 0.866025i) q^{91} +8.29180 q^{92} +(-0.427051 + 0.739674i) q^{94} +(0.927051 + 1.60570i) q^{95} +(-6.07295 - 10.5187i) q^{97} +(0.190983 + 0.330792i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8	$ 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8} - 7 q^{10} - 3 q^{11} - 10 q^{13} - 6 q^{14} - 13 q^{16} + 6 q^{17} - 3 q^{19} + 12 q^{20} - 3 q^{22} - 6 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 8 q^{31} + 15 q^{32} - 2 q^{34} + 3 q^{35} - 8 q^{37} + 6 q^{38} + 38 q^{40} + 6 q^{41} - 5 q^{43} - 36 q^{44} + 10 q^{46} - 2 q^{49} + 3 q^{50} + 21 q^{52} - 24 q^{53} - 3 q^{55} + 6 q^{56} - 17 q^{58} + 12 q^{61} - 9 q^{62} + 8 q^{64} + 15 q^{65} + 12 q^{67} - 21 q^{68} + 14 q^{70} - 6 q^{71} - 8 q^{73} + 12 q^{74} + 18 q^{76} + 6 q^{77} + 16 q^{79} + 27 q^{80} - 4 q^{82} + q^{85} - 60 q^{86} - 21 q^{88} + 21 q^{89} + 14 q^{91} + 60 q^{92} + 5 q^{94} - 3 q^{95} - 31 q^{97} + 3 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8 - 7 * q^10 - 3 * q^11 - 10 * q^13 - 6 * q^14 - 13 * q^16 + 6 * q^17 - 3 * q^19 + 12 * q^20 - 3 * q^22 - 6 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 8 * q^31 + 15 * q^32 - 2 * q^34 + 3 * q^35 - 8 * q^37 + 6 * q^38 + 38 * q^40 + 6 * q^41 - 5 * q^43 - 36 * q^44 + 10 * q^46 - 2 * q^49 + 3 * q^50 + 21 * q^52 - 24 * q^53 - 3 * q^55 + 6 * q^56 - 17 * q^58 + 12 * q^61 - 9 * q^62 + 8 * q^64 + 15 * q^65 + 12 * q^67 - 21 * q^68 + 14 * q^70 - 6 * q^71 - 8 * q^73 + 12 * q^74 + 18 * q^76 + 6 * q^77 + 16 * q^79 + 27 * q^80 - 4 * q^82 + q^85 - 60 * q^86 - 21 * q^88 + 21 * q^89 + 14 * q^91 + 60 * q^92 + 5 * q^94 - 3 * q^95 - 31 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.190983	−	0.330792i	0.135045	−	0.233905i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	0.190983	−	0.330792i	0.135045	−	0.233905i	0.925615	+	0.378467i	$0.123549\pi$
$3$		0			0
$3$		0			0
$4$	0.927051	+	1.60570i	0.463525	+	0.802850i
$5$	−0.381966			−0.170820			−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966			−0.170820			−0.0854102	+	0.996346i	$0.527220\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.47214			0.520479
$9$		0			0
$10$	−0.0729490	+	0.126351i	−0.0230685	+	0.0399558i
$11$	−2.42705	+	4.20378i	−0.731783	+	1.26749i	0.224337	+	0.974512i	$0.427978\pi$
$11$	−2.42705	+	4.20378i	−0.731783	+	1.26749i	−0.956120	+	0.292974i	$0.905355\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−0.381966			−0.102085
$15$		0			0
$16$	−1.57295	+	2.72443i	−0.393237	+	0.681107i
$17$	3.73607	+	6.47106i	0.906130	+	1.56946i	0.819394	+	0.573231i	$0.194310\pi$
$17$	3.73607	+	6.47106i	0.906130	+	1.56946i	0.0867359	+	0.996231i	$0.472356\pi$
$18$		0			0
$19$	−2.42705	−	4.20378i	−0.556804	−	0.964412i	−0.997761	−	0.0668841i	$-0.978694\pi$
$19$	−2.42705	−	4.20378i	−0.556804	−	0.964412i	0.440957	−	0.897528i	$-0.354639\pi$
$20$	−0.354102	−	0.613323i	−0.0791796	−	0.137143i
$21$		0			0
$22$	0.927051	+	1.60570i	0.197648	+	0.342336i
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	−0.533005	−	0.846112i	$-0.678937\pi$
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	0.999257	+	0.0385394i	$0.0122705\pi$
$24$		0			0
$25$	−4.85410			−0.970820
$26$	0.381966	+	1.32317i	0.0749097	+	0.259495i
$27$		0			0
$28$	0.927051	−	1.60570i	0.175196	−	0.303449i
$29$	−2.04508	+	3.54219i	−0.379763	+	0.657768i	−0.991028	−	0.133658i	$-0.957328\pi$
$29$	−2.04508	+	3.54219i	−0.379763	+	0.657768i	0.611265	+	0.791426i	$0.290661\pi$
$30$		0			0
$31$	8.70820			1.56404			0.782020	−	0.623254i	$-0.214190\pi$
$31$	8.70820			1.56404			0.782020	+	0.623254i	$0.214190\pi$
$32$	2.07295	+	3.59045i	0.366449	+	0.634708i
$33$		0			0
$34$	2.85410			0.489474
$35$	0.190983	+	0.330792i	0.0322820	+	0.0559141i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	−1.85410			−0.300775
$39$		0			0
$40$	−0.562306			−0.0889084
$41$	2.61803	−	4.53457i	0.408868	−	0.708181i	−0.585895	−	0.810387i	$-0.699257\pi$
$41$	2.61803	−	4.53457i	0.408868	−	0.708181i	0.994763	+	0.102206i	$0.0325902\pi$
$42$		0			0
$43$	3.78115	+	6.54915i	0.576620	+	0.998736i	0.995864	+	0.0908618i	$0.0289622\pi$
$43$	3.78115	+	6.54915i	0.576620	+	0.998736i	−0.419243	+	0.907874i	$0.637704\pi$
$44$	−9.00000			−1.35680
$45$		0			0
$46$	−0.854102	−	1.47935i	−0.125930	−	0.218118i
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.927051	+	1.60570i	−0.131105	+	0.227080i
$51$		0			0
$52$	−6.48936	−	1.60570i	−0.899912	−	0.222670i
$53$	−8.23607			−1.13131			−0.565655	−	0.824642i	$-0.691377\pi$
$53$	−8.23607			−1.13131			−0.565655	+	0.824642i	$0.691377\pi$
$54$		0			0
$55$	0.927051	−	1.60570i	0.125004	−	0.216512i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$		0			0
$58$	0.781153	+	1.35300i	0.102570	+	0.177657i
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	0.929580	−	0.368620i	$-0.120170\pi$
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	−0.784024	+	0.620730i	$0.786836\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	1.66312	−	2.88061i	0.211216	−	0.365837i
$63$		0			0
$64$	−4.70820			−0.588525
$65$	0.954915	−	0.992377i	0.118443	−	0.123089i
$66$		0			0
$67$	−0.354102	+	0.613323i	−0.0432604	+	0.0749293i	−0.886845	−	0.462067i	$-0.847108\pi$
$67$	−0.354102	+	0.613323i	−0.0432604	+	0.0749293i	0.843584	+	0.536997i	$0.180441\pi$
$68$	−6.92705	+	11.9980i	−0.840028	+	1.45497i
$69$		0			0
$70$	0.145898			0.0174382
$71$	4.09017	+	7.08438i	0.485414	+	0.840761i	0.999860	−	0.0167615i	$-0.00533560\pi$
$71$	4.09017	+	7.08438i	0.485414	+	0.840761i	−0.514446	+	0.857523i	$0.672002\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	0.763932	+	1.32317i	0.0888053	+	0.153815i
$75$		0			0
$76$	4.50000	−	7.79423i	0.516185	−	0.894059i
$77$	4.85410			0.553176
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	0.600813	−	1.04064i	0.0671729	−	0.116347i
$81$		0			0
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	6.70820			0.736321			0.368161	−	0.929762i	$-0.379988\pi$
$83$	6.70820			0.736321			0.368161	+	0.929762i	$0.379988\pi$
$84$		0			0
$85$	−1.42705	−	2.47172i	−0.154785	−	0.268096i
$86$	2.88854			0.311480
$87$		0			0
$88$	−3.57295	+	6.18853i	−0.380878	+	0.659699i
$89$	8.04508	−	13.9345i	0.852777	−	1.47705i	−0.0259145	−	0.999664i	$-0.508250\pi$
$89$	8.04508	−	13.9345i	0.852777	−	1.47705i	0.878692	−	0.477389i	$-0.158417\pi$
$90$		0			0
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$	8.29180			0.864479
$93$		0			0
$94$	−0.427051	+	0.739674i	−0.0440469	+	0.0762915i
$95$	0.927051	+	1.60570i	0.0951134	+	0.164741i
$96$		0			0
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	−0.990099	−	0.140371i	$-0.955170\pi$
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	0.373484	−	0.927636i	$-0.378163\pi$
$98$	0.190983	+	0.330792i	0.0192922	+	0.0334151i
$99$		0			0
$100$	−4.50000	−	7.79423i	−0.450000	−	0.779423i
$101$	4.28115	−	7.41517i	0.425991	−	0.737837i	−0.570522	−	0.821283i	$-0.693259\pi$
$101$	4.28115	−	7.41517i	0.425991	−	0.737837i	0.996512	+	0.0834451i	$0.0265923\pi$
$102$		0			0
$103$	4.70820			0.463913			0.231957	−	0.972726i	$-0.425487\pi$
$103$	4.70820			0.463913			0.231957	+	0.972726i	$0.425487\pi$
$104$	−3.68034	+	3.82472i	−0.360887	+	0.375045i
$105$		0			0
$106$	−1.57295	+	2.72443i	−0.152778	+	0.264620i
$107$	−2.80902	+	4.86536i	−0.271558	+	0.470352i	−0.969261	−	0.246035i	$-0.920872\pi$
$107$	−2.80902	+	4.86536i	−0.271558	+	0.470352i	0.697703	+	0.716387i	$0.254206\pi$
$108$		0			0
$109$	10.7082			1.02566			0.512830	−	0.858490i	$-0.328597\pi$
$109$	10.7082			1.02566			0.512830	+	0.858490i	$0.328597\pi$
$110$	−0.354102	−	0.613323i	−0.0337623	−	0.0584780i
$111$		0			0
$112$	3.14590			0.297259
$113$	−3.73607	−	6.47106i	−0.351460	−	0.608746i	0.635046	−	0.772475i	$-0.280981\pi$
$113$	−3.73607	−	6.47106i	−0.351460	−	0.608746i	−0.986505	+	0.163728i	$0.947648\pi$
$114$		0			0
$115$	−0.854102	+	1.47935i	−0.0796454	+	0.137950i
$116$	−7.58359			−0.704119
$117$		0			0
$118$	0.854102			0.0786265
$119$	3.73607	−	6.47106i	0.342485	−	0.593201i
$120$		0			0
$121$	−6.28115	−	10.8793i	−0.571014	−	0.989025i
$122$	2.29180			0.207489
$123$		0			0
$124$	8.07295	+	13.9828i	0.724972	+	1.25569i
$125$	3.76393			0.336656
$126$		0			0
$127$	7.07295	−	12.2507i	0.627623	−	1.08707i	−0.360405	−	0.932796i	$-0.617361\pi$
$127$	7.07295	−	12.2507i	0.627623	−	1.08707i	0.988027	−	0.154278i	$-0.0493053\pi$
$128$	−5.04508	+	8.73834i	−0.445927	+	0.772368i
$129$		0			0
$130$	−0.145898	−	0.505406i	−0.0127961	−	0.0443270i
$131$	−0.326238			−0.0285035			−0.0142518	−	0.999898i	$-0.504537\pi$
$131$	−0.326238			−0.0285035			−0.0142518	+	0.999898i	$0.504537\pi$
$132$		0			0
$133$	−2.42705	+	4.20378i	−0.210452	+	0.364514i
$134$	0.135255	+	0.234268i	0.0116842	+	0.0202377i
$135$		0			0
$136$	5.50000	+	9.52628i	0.471621	+	0.816872i
$137$	−0.190983	−	0.330792i	−0.0163168	−	0.0282615i	0.857752	−	0.514064i	$-0.171861\pi$
$137$	−0.190983	−	0.330792i	−0.0163168	−	0.0282615i	−0.874069	+	0.485803i	$0.838527\pi$
$138$		0			0
$139$	7.78115	+	13.4774i	0.659989	+	1.14313i	0.980618	+	0.195929i	$0.0627723\pi$
$139$	7.78115	+	13.4774i	0.659989	+	1.14313i	−0.320629	+	0.947205i	$0.603894\pi$
$140$	−0.354102	+	0.613323i	−0.0299271	+	0.0518352i
$141$		0			0
$142$	3.12461			0.262212
$143$	−4.85410	−	16.8151i	−0.405920	−	1.40615i
$144$		0			0
$145$	0.781153	−	1.35300i	0.0648712	−	0.112360i
$146$	−0.381966	+	0.661585i	−0.0316117	+	0.0547531i
$147$		0			0
$148$	−7.41641			−0.609625
$149$	−2.42705	−	4.20378i	−0.198832	−	0.344387i	0.749318	−	0.662210i	$-0.230381\pi$
$149$	−2.42705	−	4.20378i	−0.198832	−	0.344387i	−0.948150	+	0.317823i	$0.897048\pi$
$150$		0			0
$151$	−14.7082			−1.19694			−0.598468	−	0.801146i	$-0.704224\pi$
$151$	−14.7082			−1.19694			−0.598468	+	0.801146i	$0.704224\pi$
$152$	−3.57295	−	6.18853i	−0.289804	−	0.501956i
$153$		0			0
$154$	0.927051	−	1.60570i	0.0747039	−	0.129391i
$155$	−3.32624			−0.267170
$156$		0			0
$157$	8.14590			0.650113			0.325057	−	0.945695i	$-0.394617\pi$
$157$	8.14590			0.650113			0.325057	+	0.945695i	$0.394617\pi$
$158$	0.763932	−	1.32317i	0.0607752	−	0.105266i
$159$		0			0
$160$	−0.791796	−	1.37143i	−0.0625970	−	0.108421i
$161$	−4.47214			−0.352454
$162$		0			0
$163$	−4.85410	−	8.40755i	−0.380203	−	0.658530i	0.610888	−	0.791717i	$-0.290812\pi$
$163$	−4.85410	−	8.40755i	−0.380203	−	0.658530i	−0.991091	+	0.133186i	$0.957479\pi$
$164$	9.70820			0.758083
$165$		0			0
$166$	1.28115	−	2.21902i	0.0994368	−	0.172230i
$167$	4.88197	−	8.45581i	0.377778	−	0.654330i	−0.612961	−	0.790113i	$-0.710022\pi$
$167$	4.88197	−	8.45581i	0.377778	−	0.654330i	0.990739	+	0.135783i	$0.0433550\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	−1.09017			−0.0836122
$171$		0			0
$172$	−7.01064	+	12.1428i	−0.534557	+	0.925879i
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$	2.42705	+	4.20378i	0.183468	+	0.317776i
$176$	−7.63525	−	13.2246i	−0.575529	−	0.996845i
$177$		0			0
$178$	−3.07295	−	5.32250i	−0.230327	−	0.398939i
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	−3.70820			−0.275629			−0.137814	−	0.990458i	$-0.544008\pi$
$181$	−3.70820			−0.275629			−0.137814	+	0.990458i	$0.544008\pi$
$182$	0.954915	−	0.992377i	0.0707830	−	0.0735599i
$183$		0			0
$184$	3.29180	−	5.70156i	0.242674	−	0.420324i
$185$	0.763932	−	1.32317i	0.0561654	−	0.0972813i
$186$		0			0
$187$	−36.2705			−2.65236
$188$	−2.07295	−	3.59045i	−0.151185	−	0.261861i
$189$		0			0
$190$	0.708204			0.0513785
$191$	11.8090	+	20.4538i	0.854470	+	1.47999i	0.877135	+	0.480243i	$0.159452\pi$
$191$	11.8090	+	20.4538i	0.854470	+	1.47999i	−0.0226649	+	0.999743i	$0.507215\pi$
$192$		0			0
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	−4.63932			−0.333084
$195$		0			0
$196$	−1.85410			−0.132436
$197$	3.89919	−	6.75359i	0.277806	−	0.481173i	−0.693034	−	0.720905i	$-0.743726\pi$
$197$	3.89919	−	6.75359i	0.277806	−	0.481173i	0.970839	+	0.239732i	$0.0770596\pi$
$198$		0			0
$199$	−1.20820	−	2.09267i	−0.0856473	−	0.148345i	0.820020	−	0.572336i	$-0.193962\pi$
$199$	−1.20820	−	2.09267i	−0.0856473	−	0.148345i	−0.905667	+	0.423990i	$0.860629\pi$
$200$	−7.14590			−0.505291
$201$		0			0
$202$	−1.63525	−	2.83234i	−0.115056	−	0.199283i
$203$	4.09017			0.287074
$204$		0			0
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	0.899187	−	1.55744i	0.0626493	−	0.108512i
$207$		0			0
$208$	−3.14590	−	10.8977i	−0.218129	−	0.755620i
$209$	23.5623			1.62984
$210$		0			0
$211$	4.35410	−	7.54153i	0.299749	−	0.519180i	−0.676330	−	0.736599i	$-0.736430\pi$
$211$	4.35410	−	7.54153i	0.299749	−	0.519180i	0.976078	+	0.217419i	$0.0697638\pi$
$212$	−7.63525	−	13.2246i	−0.524391	−	0.908273i
$213$		0			0
$214$	1.07295	+	1.85840i	0.0733453	+	0.127038i
$215$	−1.44427	−	2.50155i	−0.0984985	−	0.170604i
$216$		0			0
$217$	−4.35410	−	7.54153i	−0.295576	−	0.511952i
$218$	2.04508	−	3.54219i	0.138511	−	0.239907i
$219$		0			0
$220$	3.43769			0.231769
$221$	−26.1525	−	6.47106i	−1.75921	−	0.435291i
$222$		0			0
$223$	6.63525	−	11.4926i	0.444330	−	0.769601i	−0.553676	−	0.832732i	$-0.686775\pi$
$223$	6.63525	−	11.4926i	0.444330	−	0.769601i	0.998005	+	0.0631310i	$0.0201086\pi$
$224$	2.07295	−	3.59045i	0.138505	−	0.239897i
$225$		0			0
$226$	−2.85410			−0.189852
$227$	−3.73607	−	6.47106i	−0.247972	−	0.429499i	0.714991	−	0.699133i	$-0.246431\pi$
$227$	−3.73607	−	6.47106i	−0.247972	−	0.429499i	−0.962963	+	0.269634i	$0.913097\pi$
$228$		0			0
$229$	27.1246			1.79244			0.896222	−	0.443605i	$-0.146301\pi$
$229$	27.1246			1.79244			0.896222	+	0.443605i	$0.146301\pi$
$230$	0.326238	+	0.565061i	0.0215115	+	0.0372590i
$231$		0			0
$232$	−3.01064	+	5.21459i	−0.197658	+	0.342354i
$233$	−0.381966			−0.0250234			−0.0125117	−	0.999922i	$-0.503983\pi$
$233$	−0.381966			−0.0250234			−0.0125117	+	0.999922i	$0.503983\pi$
$234$		0			0
$235$	0.854102			0.0557155
$236$	−2.07295	+	3.59045i	−0.134937	+	0.233719i
$237$		0			0
$238$	−1.42705	−	2.47172i	−0.0925020	−	0.160218i
$239$	11.2918			0.730406			0.365203	−	0.930928i	$-0.381000\pi$
$239$	11.2918			0.730406			0.365203	+	0.930928i	$0.381000\pi$
$240$		0			0
$241$	−2.21885	−	3.84316i	−0.142929	−	0.247559i	0.785670	−	0.618646i	$-0.212319\pi$
$241$	−2.21885	−	3.84316i	−0.142929	−	0.247559i	−0.928598	+	0.371087i	$0.878985\pi$
$242$	−4.79837			−0.308451
$243$		0			0
$244$	−5.56231	+	9.63420i	−0.356090	+	0.616766i
$245$	0.190983	−	0.330792i	0.0122015	−	0.0211335i
$246$		0			0
$247$	16.9894	+	4.20378i	1.08101	+	0.267480i
$248$	12.8197			0.814049
$249$		0			0
$250$	0.718847	−	1.24508i	0.0454639	−	0.0787457i
$251$	2.61803	+	4.53457i	0.165249	+	0.286219i	0.936744	−	0.350016i	$-0.113824\pi$
$251$	2.61803	+	4.53457i	0.165249	+	0.286219i	−0.771495	+	0.636236i	$0.780491\pi$
$252$		0			0
$253$	10.8541	+	18.7999i	0.682392	+	1.18194i
$254$	−2.70163	−	4.67935i	−0.169515	−	0.293609i
$255$		0			0
$256$	−2.78115	−	4.81710i	−0.173822	−	0.301069i
$257$	−12.8713	+	22.2938i	−0.802891	+	1.39065i	0.114815	+	0.993387i	$0.463373\pi$
$257$	−12.8713	+	22.2938i	−0.802891	+	1.39065i	−0.917706	+	0.397261i	$0.869961\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$	2.47871	+	0.613323i	0.153723	+	0.0380367i
$261$		0			0
$262$	−0.0623059	+	0.107917i	−0.00384927	+	0.00666713i
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	3.14590			0.193251
$266$	0.927051	+	1.60570i	0.0568411	+	0.0984517i
$267$		0			0
$268$	−1.31308			−0.0802093
$269$	6.87132	+	11.9015i	0.418952	+	0.725646i	0.995834	−	0.0911812i	$-0.0290642\pi$
$269$	6.87132	+	11.9015i	0.418952	+	0.725646i	−0.576882	+	0.816827i	$0.695731\pi$
$270$		0			0
$271$	−9.20820	+	15.9491i	−0.559359	+	0.968837i	0.438192	+	0.898882i	$0.355619\pi$
$271$	−9.20820	+	15.9491i	−0.559359	+	0.968837i	−0.997550	+	0.0699558i	$0.977714\pi$
$272$	−23.5066			−1.42530
$273$		0			0
$274$	−0.145898			−0.00881402
$275$	11.7812	−	20.4056i	0.710430	−	1.23050i
$276$		0			0
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	5.94427			0.356514
$279$		0			0
$280$	0.281153	+	0.486971i	0.0168021	+	0.0291021i
$281$	2.18034			0.130068			0.0650341	−	0.997883i	$-0.479284\pi$
$281$	2.18034			0.130068			0.0650341	+	0.997883i	$0.479284\pi$
$282$		0			0
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	−0.594812	−	0.803865i	$-0.702774\pi$
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	0.993573	+	0.113190i	$0.0361069\pi$
$284$	−7.58359	+	13.1352i	−0.450003	+	0.779429i
$285$		0			0
$286$	−6.48936	−	1.60570i	−0.383724	−	0.0949470i
$287$	−5.23607			−0.309075
$288$		0			0
$289$	−19.4164	+	33.6302i	−1.14214	+	1.97825i
$290$	−0.298374	−	0.516799i	−0.0175211	−	0.0303475i
$291$		0			0
$292$	−1.85410	−	3.21140i	−0.108503	−	0.187933i
$293$	−5.61803	−	9.73072i	−0.328209	−	0.568475i	0.653947	−	0.756540i	$-0.273112\pi$
$293$	−5.61803	−	9.73072i	−0.328209	−	0.568475i	−0.982157	+	0.188065i	$0.939778\pi$
$294$		0			0
$295$	−0.427051	−	0.739674i	−0.0248639	−	0.0430655i
$296$	−2.94427	+	5.09963i	−0.171132	+	0.296410i
$297$		0			0
$298$	−1.85410			−0.107405
$299$	4.47214	+	15.4919i	0.258630	+	0.895922i
$300$		0			0
$301$	3.78115	−	6.54915i	0.217942	−	0.377487i
$302$	−2.80902	+	4.86536i	−0.161641	+	0.279970i
$303$		0			0
$304$	15.2705			0.875824
$305$	−1.14590	−	1.98475i	−0.0656139	−	0.113647i
$306$		0			0
$307$	1.85410			0.105819			0.0529096	−	0.998599i	$-0.483150\pi$
$307$	1.85410			0.105819			0.0529096	+	0.998599i	$0.483150\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$		0			0
$310$	−0.635255	+	1.10029i	−0.0360801	+	0.0624925i
$311$	12.3262			0.698957			0.349478	−	0.936944i	$-0.386359\pi$
$311$	12.3262			0.698957			0.349478	+	0.936944i	$0.386359\pi$
$312$		0			0
$313$	−15.1246			−0.854894			−0.427447	−	0.904041i	$-0.640587\pi$
$313$	−15.1246			−0.854894			−0.427447	+	0.904041i	$0.640587\pi$
$314$	1.55573	−	2.69460i	0.0877948	−	0.152065i
$315$		0			0
$316$	3.70820	+	6.42280i	0.208603	+	0.361311i
$317$	−21.7639			−1.22238			−0.611192	−	0.791482i	$-0.709310\pi$
$317$	−21.7639			−1.22238			−0.611192	+	0.791482i	$0.709310\pi$
$318$		0			0
$319$	−9.92705	−	17.1942i	−0.555808	−	0.962688i
$320$	1.79837			0.100532
$321$		0			0
$322$	−0.854102	+	1.47935i	−0.0475972	+	0.0824408i
$323$	18.1353	−	31.4112i	1.00907	−	1.74776i
$324$		0			0
$325$	12.1353	−	12.6113i	0.673143	−	0.699551i
$326$	−3.70820			−0.205378
$327$		0			0
$328$	3.85410	−	6.67550i	0.212807	−	0.368593i
$329$	1.11803	+	1.93649i	0.0616392	+	0.106762i
$330$		0			0
$331$	8.42705	+	14.5961i	0.463193	+	0.802273i	0.999118	−	0.0419923i	$-0.0133705\pi$
$331$	8.42705	+	14.5961i	0.463193	+	0.802273i	−0.535925	+	0.844265i	$0.680037\pi$
$332$	6.21885	+	10.7714i	0.341304	+	0.591155i
$333$		0			0
$334$	−1.86475	−	3.22983i	−0.102034	−	0.176729i
$335$	0.135255	−	0.234268i	0.00738977	−	0.0127994i
$336$		0			0
$337$	8.56231			0.466419			0.233209	−	0.972427i	$-0.425077\pi$
$337$	8.56231			0.466419			0.233209	+	0.972427i	$0.425077\pi$
$338$	−4.39261	−	2.31555i	−0.238926	−	0.125949i
$339$		0			0
$340$	2.64590	−	4.58283i	0.143494	−	0.248539i
$341$	−21.1353	+	36.6073i	−1.14454	+	1.98240i
$342$		0			0
$343$	1.00000			0.0539949
$344$	5.56637	+	9.64124i	0.300119	+	0.519821i
$345$		0			0
$346$	−3.43769			−0.184812
$347$	17.6180	+	30.5153i	0.945786	+	1.63815i	0.754171	+	0.656679i	$0.228039\pi$
$347$	17.6180	+	30.5153i	0.945786	+	1.63815i	0.191615	+	0.981470i	$0.438627\pi$
$348$		0			0
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	−0.946953	−	0.321372i	$-0.895856\pi$
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	0.751793	+	0.659400i	$0.229189\pi$
$350$	1.85410			0.0991059
$351$		0			0
$352$	−20.1246			−1.07265
$353$	14.4271	−	24.9884i	0.767874	−	1.33000i	−0.170839	−	0.985299i	$-0.554648\pi$
$353$	14.4271	−	24.9884i	0.767874	−	1.33000i	0.938713	−	0.344699i	$-0.112019\pi$
$354$		0			0
$355$	−1.56231	−	2.70599i	−0.0829186	−	0.143619i
$356$	29.8328			1.58114
$357$		0			0
$358$	1.71885	+	2.97713i	0.0908439	+	0.157346i
$359$	10.9098			0.575799			0.287899	−	0.957661i	$-0.407043\pi$
$359$	10.9098			0.575799			0.287899	+	0.957661i	$0.407043\pi$
$360$		0			0
$361$	−2.28115	+	3.95107i	−0.120061	+	0.207951i
$362$	−0.708204	+	1.22665i	−0.0372224	+	0.0644710i
$363$		0			0
$364$	1.85410	+	6.42280i	0.0971813	+	0.336646i
$365$	0.763932			0.0399860
$366$		0			0
$367$	−12.7082	+	22.0113i	−0.663363	+	1.14898i	0.316364	+	0.948638i	$0.397538\pi$
$367$	−12.7082	+	22.0113i	−0.663363	+	1.14898i	−0.979726	+	0.200340i	$0.935795\pi$
$368$	7.03444	+	12.1840i	0.366696	+	0.635135i
$369$		0			0
$370$	−0.291796	−	0.505406i	−0.0151698	−	0.0262748i
$371$	4.11803	+	7.13264i	0.213798	+	0.370308i
$372$		0			0
$373$	0.218847	+	0.379054i	0.0113315	+	0.0196267i	0.871636	−	0.490155i	$-0.163060\pi$
$373$	0.218847	+	0.379054i	0.0113315	+	0.0196267i	−0.860304	+	0.509781i	$0.829726\pi$
$374$	−6.92705	+	11.9980i	−0.358189	+	0.620402i
$375$		0			0
$376$	−3.29180			−0.169761
$377$	−4.09017	−	14.1688i	−0.210654	−	0.729728i
$378$		0			0
$379$	6.42705	−	11.1320i	0.330135	−	0.571811i	−0.652403	−	0.757872i	$-0.726239\pi$
$379$	6.42705	−	11.1320i	0.330135	−	0.571811i	0.982538	+	0.186061i	$0.0595722\pi$
$380$	−1.71885	+	2.97713i	−0.0881750	+	0.152724i
$381$		0			0
$382$	9.02129			0.461569
$383$	12.4894	+	21.6322i	0.638176	+	1.10535i	0.985833	+	0.167732i	$0.0536443\pi$
$383$	12.4894	+	21.6322i	0.638176	+	1.10535i	−0.347656	+	0.937622i	$0.613022\pi$
$384$		0			0
$385$	−1.85410			−0.0944938
$386$	−1.14590	−	1.98475i	−0.0583247	−	0.101021i
$387$		0			0
$388$	11.2599	−	19.5027i	0.571633	−	0.990098i
$389$	−23.8885			−1.21120			−0.605599	−	0.795770i	$-0.707066\pi$
$389$	−23.8885			−1.21120			−0.605599	+	0.795770i	$0.707066\pi$
$390$		0			0
$391$	33.4164			1.68994
$392$	−0.736068	+	1.27491i	−0.0371770	+	0.0643925i
$393$		0			0
$394$	−1.48936	−	2.57964i	−0.0750327	−	0.129960i
$395$	−1.52786			−0.0768752
$396$		0			0
$397$	12.7082	+	22.0113i	0.637806	+	1.10471i	0.985913	+	0.167258i	$0.0534914\pi$
$397$	12.7082	+	22.0113i	0.637806	+	1.10471i	−0.348107	+	0.937455i	$0.613175\pi$
$398$	−0.922986			−0.0462651
$399$		0			0
$400$	7.63525	−	13.2246i	0.381763	−	0.661232i
$401$	−10.2254	+	17.7110i	−0.510633	+	0.884443i	0.489291	+	0.872121i	$0.337256\pi$
$401$	−10.2254	+	17.7110i	−0.510633	+	0.884443i	−0.999924	+	0.0123222i	$0.996078\pi$
$402$		0			0
$403$	−21.7705	+	22.6246i	−1.08447	+	1.12701i
$404$	15.8754			0.789830
$405$		0			0
$406$	0.781153	−	1.35300i	0.0387680	−	0.0671481i
$407$	−9.70820	−	16.8151i	−0.481218	−	0.833494i
$408$		0			0
$409$	−17.2812	−	29.9318i	−0.854498	−	1.48003i	−0.877110	−	0.480290i	$-0.840532\pi$
$409$	−17.2812	−	29.9318i	−0.854498	−	1.48003i	0.0226119	−	0.999744i	$-0.492802\pi$
$410$	0.381966	+	0.661585i	0.0188640	+	0.0326733i
$411$		0			0
$412$	4.36475	+	7.55996i	0.215036	+	0.372453i
$413$	1.11803	−	1.93649i	0.0550149	−	0.0952885i
$414$		0			0
$415$	−2.56231			−0.125779
$416$	−14.5106	−	3.59045i	−0.711443	−	0.176036i
$417$		0			0
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	2.97214	−	5.14789i	0.145198	−	0.251491i	−0.784249	−	0.620447i	$-0.786951\pi$
$419$	2.97214	−	5.14789i	0.145198	−	0.251491i	0.929447	+	0.368956i	$0.120285\pi$
$420$		0			0
$421$	−25.4164			−1.23872			−0.619360	−	0.785107i	$-0.712608\pi$
$421$	−25.4164			−1.23872			−0.619360	+	0.785107i	$0.712608\pi$
$422$	−1.66312	−	2.88061i	−0.0809594	−	0.140226i
$423$		0			0
$424$	−12.1246			−0.588823
$425$	−18.1353	−	31.4112i	−0.879689	−	1.52367i
$426$		0			0
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$	−10.4164			−0.503496
$429$		0			0
$430$	−1.10333			−0.0532071
$431$	−8.39919	+	14.5478i	−0.404575	+	0.700744i	−0.994272	−	0.106881i	$-0.965914\pi$
$431$	−8.39919	+	14.5478i	−0.404575	+	0.700744i	0.589697	+	0.807624i	$0.299247\pi$
$432$		0			0
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$	−3.32624			−0.159665
$435$		0			0
$436$	9.92705	+	17.1942i	0.475420	+	0.823451i
$437$	−21.7082			−1.03844
$438$		0			0
$439$	−4.07295	+	7.05455i	−0.194391	+	0.336696i	−0.946701	−	0.322114i	$-0.895606\pi$
$439$	−4.07295	+	7.05455i	−0.194391	+	0.336696i	0.752310	+	0.658810i	$0.228940\pi$
$440$	1.36475	−	2.36381i	0.0650617	−	0.112690i
$441$		0			0
$442$	−7.13525	+	7.41517i	−0.339389	+	0.352704i
$443$	0.763932			0.0362955			0.0181478	−	0.999835i	$-0.494223\pi$
$443$	0.763932			0.0362955			0.0181478	+	0.999835i	$0.494223\pi$
$444$		0			0
$445$	−3.07295	+	5.32250i	−0.145672	+	0.252311i
$446$	−2.53444	−	4.38978i	−0.120009	−	0.207862i
$447$		0			0
$448$	2.35410	+	4.07742i	0.111221	+	0.192640i
$449$	14.2361	+	24.6576i	0.671842	+	1.16366i	0.977381	+	0.211484i	$0.0678298\pi$
$449$	14.2361	+	24.6576i	0.671842	+	1.16366i	−0.305540	+	0.952179i	$0.598837\pi$
$450$		0			0
$451$	12.7082	+	22.0113i	0.598406	+	1.03647i
$452$	6.92705	−	11.9980i	0.325821	−	0.564339i
$453$		0			0
$454$	−2.85410			−0.133950
$455$	−1.33688	−	0.330792i	−0.0626739	−	0.0155078i
$456$		0			0
$457$	5.70820	−	9.88690i	0.267019	−	0.462490i	−0.701072	−	0.713091i	$-0.747295\pi$
$457$	5.70820	−	9.88690i	0.267019	−	0.462490i	0.968090	+	0.250601i	$0.0806282\pi$
$458$	5.18034	−	8.97261i	0.242061	−	0.419263i
$459$		0			0
$460$	−3.16718			−0.147671
$461$	19.6074	+	33.9610i	0.913207	+	1.58172i	0.809505	+	0.587113i	$0.199736\pi$
$461$	19.6074	+	33.9610i	0.913207	+	1.58172i	0.103702	+	0.994608i	$0.466931\pi$
$462$		0			0
$463$	−6.70820			−0.311757			−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820			−0.311757			−0.155878	+	0.987776i	$0.549821\pi$
$464$	−6.43363	−	11.1434i	−0.298674	−	0.517318i
$465$		0			0
$466$	−0.0729490	+	0.126351i	−0.00337930	+	0.00585312i
$467$	−33.6525			−1.55725			−0.778625	−	0.627489i	$-0.784083\pi$
$467$	−33.6525			−1.55725			−0.778625	+	0.627489i	$0.784083\pi$
$468$		0			0
$469$	0.708204			0.0327018
$470$	0.163119	−	0.282530i	0.00752412	−	0.0130322i
$471$		0			0
$472$	1.64590	+	2.85078i	0.0757586	+	0.131218i
$473$	−36.7082			−1.68785
$474$		0			0
$475$	11.7812	+	20.4056i	0.540556	+	0.936271i
$476$	13.8541			0.635002
$477$		0			0
$478$	2.15654	−	3.73524i	0.0986379	−	0.170846i
$479$	−10.9894	+	19.0341i	−0.502117	+	0.869691i	0.497880	+	0.867246i	$0.334112\pi$
$479$	−10.9894	+	19.0341i	−0.502117	+	0.869691i	−0.999997	+	0.00244569i	$0.999222\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	−1.69505			−0.0772073
$483$		0			0
$484$	11.6459	−	20.1713i	0.529359	−	0.916877i
$485$	2.31966	+	4.01777i	0.105330	+	0.182438i
$486$		0			0
$487$	8.48936	+	14.7040i	0.384689	+	0.666302i	0.991726	−	0.128372i	$-0.0409752\pi$
$487$	8.48936	+	14.7040i	0.384689	+	0.666302i	−0.607037	+	0.794674i	$0.707642\pi$
$488$	4.41641	+	7.64944i	0.199921	+	0.346274i
$489$		0			0
$490$	−0.0729490	−	0.126351i	−0.00329550	−	0.00570797i
$491$	7.30902	−	12.6596i	0.329851	−	0.571319i	−0.652631	−	0.757676i	$-0.726335\pi$
$491$	7.30902	−	12.6596i	0.329851	−	0.571319i	0.982482	+	0.186357i	$0.0596680\pi$
$492$		0			0
$493$	−30.5623			−1.37646
$494$	4.63525	−	4.81710i	0.208550	−	0.216731i
$495$		0			0
$496$	−13.6976	+	23.7249i	−0.615039	+	1.06528i
$497$	4.09017	−	7.08438i	0.183469	−	0.317778i
$498$		0			0
$499$	8.14590			0.364660			0.182330	−	0.983237i	$-0.441636\pi$
$499$	8.14590			0.364660			0.182330	+	0.983237i	$0.441636\pi$
$500$	3.48936	+	6.04374i	0.156049	+	0.270284i
$501$		0			0
$502$	2.00000			0.0892644
$503$	12.1910	+	21.1154i	0.543569	+	0.941489i	0.998695	+	0.0510624i	$0.0162607\pi$
$503$	12.1910	+	21.1154i	0.543569	+	0.941489i	−0.455126	+	0.890427i	$0.650406\pi$
$504$		0			0
$505$	−1.63525	+	2.83234i	−0.0727679	+	0.126038i
$506$	8.29180			0.368615
$507$		0			0
$508$	26.2279			1.16368
$509$	15.2984	−	26.4976i	0.678089	−	1.17448i	−0.297467	−	0.954732i	$-0.596142\pi$
$509$	15.2984	−	26.4976i	0.678089	−	1.17448i	0.975556	−	0.219752i	$-0.0705247\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	−22.3050			−0.985749
$513$		0			0
$514$	4.91641	+	8.51547i	0.216853	+	0.375601i
$515$	−1.79837			−0.0792458
$516$		0			0
$517$	5.42705	−	9.39993i	0.238681	−	0.413408i
$518$	0.763932	−	1.32317i	0.0335652	−	0.0581367i
$519$		0			0
$520$	1.40576	−	1.46091i	0.0616469	−	0.0640653i
$521$	12.6525			0.554315			0.277158	−	0.960824i	$-0.410608\pi$
$521$	12.6525			0.554315			0.277158	+	0.960824i	$0.410608\pi$
$522$		0			0
$523$	19.5623	−	33.8829i	0.855400	−	1.48160i	−0.0208736	−	0.999782i	$-0.506645\pi$
$523$	19.5623	−	33.8829i	0.855400	−	1.48160i	0.876274	−	0.481814i	$-0.160022\pi$
$524$	−0.302439	−	0.523840i	−0.0132121	−	0.0228841i
$525$		0			0
$526$	−1.71885	−	2.97713i	−0.0749453	−	0.129809i
$527$	32.5344	+	56.3513i	1.41722	+	2.45470i
$528$		0			0
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$	0.600813	−	1.04064i	0.0260977	−	0.0452025i
$531$		0			0
$532$	−9.00000			−0.390199
$533$	5.23607	+	18.1383i	0.226799	+	0.785656i
$534$		0			0
$535$	1.07295	−	1.85840i	0.0463876	−	0.0803457i
$536$	−0.521286	+	0.902894i	−0.0225161	+	0.0389991i
$537$		0			0
$538$	5.24922			0.226310
$539$	−2.42705	−	4.20378i	−0.104540	−	0.181069i
$540$		0			0
$541$	1.72949			0.0743566			0.0371783	−	0.999309i	$-0.488163\pi$
$541$	1.72949			0.0743566			0.0371783	+	0.999309i	$0.488163\pi$
$542$	3.51722	+	6.09201i	0.151078	+	0.261674i
$543$		0			0
$544$	−15.4894	+	26.8284i	−0.664101	+	1.15026i
$545$	−4.09017			−0.175204
$546$		0			0
$547$	−3.00000			−0.128271			−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000			−0.128271			−0.0641354	+	0.997941i	$0.520429\pi$
$548$	0.354102	−	0.613323i	0.0151265	−	0.0261998i
$549$		0			0
$550$	−4.50000	−	7.79423i	−0.191881	−	0.332347i
$551$	19.8541			0.845813
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	1.90983			0.0811409
$555$		0			0
$556$	−14.4271	+	24.9884i	−0.611843	+	1.05974i
$557$	9.48936	−	16.4360i	0.402077	−	0.696418i	−0.591899	−	0.806012i	$-0.701622\pi$
$557$	9.48936	−	16.4360i	0.402077	−	0.696418i	0.993976	+	0.109594i	$0.0349551\pi$
$558$		0			0
$559$	−26.4681	−	6.54915i	−1.11948	−	0.276999i
$560$	−1.20163			−0.0507780
$561$		0			0
$562$	0.416408	−	0.721240i	0.0175651	−	0.0304237i
$563$	−19.4721	−	33.7267i	−0.820653	−	1.42141i	−0.905197	−	0.424992i	$-0.860277\pi$
$563$	−19.4721	−	33.7267i	−0.820653	−	1.42141i	0.0845442	−	0.996420i	$-0.473057\pi$
$564$		0			0
$565$	1.42705	+	2.47172i	0.0600365	+	0.103986i
$566$	−2.56231	−	4.43804i	−0.107702	−	0.186545i
$567$		0			0
$568$	6.02129	+	10.4292i	0.252648	+	0.437598i
$569$	−1.47214	+	2.54981i	−0.0617151	+	0.106894i	−0.895232	−	0.445600i	$-0.852990\pi$
$569$	−1.47214	+	2.54981i	−0.0617151	+	0.106894i	0.833517	+	0.552494i	$0.186324\pi$
$570$		0			0
$571$	−35.6869			−1.49345			−0.746726	−	0.665132i	$-0.768375\pi$
$571$	−35.6869			−1.49345			−0.746726	+	0.665132i	$0.768375\pi$
$572$	22.5000	−	23.3827i	0.940772	−	0.977679i
$573$		0			0
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	−10.8541	+	18.7999i	−0.452647	+	0.784008i
$576$		0			0
$577$	9.83282			0.409345			0.204673	−	0.978830i	$-0.434387\pi$
$577$	9.83282			0.409345			0.204673	+	0.978830i	$0.434387\pi$
$578$	7.41641	+	12.8456i	0.308482	+	0.534306i
$579$		0			0
$580$	2.89667			0.120278
$581$	−3.35410	−	5.80948i	−0.139152	−	0.241018i
$582$		0			0
$583$	19.9894	−	34.6226i	0.827875	−	1.43392i
$584$	−2.94427			−0.121835
$585$		0			0
$586$	−4.29180			−0.177292
$587$	−15.5451	+	26.9249i	−0.641614	+	1.11131i	0.343458	+	0.939168i	$0.388402\pi$
$587$	−15.5451	+	26.9249i	−0.641614	+	1.11131i	−0.985072	+	0.172141i	$0.944932\pi$
$588$		0			0
$589$	−21.1353	−	36.6073i	−0.870863	−	1.50838i
$590$	−0.326238			−0.0134310
$591$		0			0
$592$	−6.29180	−	10.8977i	−0.258591	−	0.447893i
$593$	−19.2016			−0.788516			−0.394258	−	0.919000i	$-0.628998\pi$
$593$	−19.2016			−0.788516			−0.394258	+	0.919000i	$0.628998\pi$
$594$		0			0
$595$	−1.42705	+	2.47172i	−0.0585034	+	0.101331i
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$		0			0
$598$	5.97871	+	1.47935i	0.244488	+	0.0604950i
$599$	8.50658			0.347569			0.173785	−	0.984784i	$-0.444400\pi$
$599$	8.50658			0.347569			0.173785	+	0.984784i	$0.444400\pi$
$600$		0			0
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	−0.293535	−	0.955948i	$-0.594832\pi$
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	0.974643	−	0.223765i	$-0.0718348\pi$
$602$	−1.44427	−	2.50155i	−0.0588641	−	0.101956i
$603$		0			0
$604$	−13.6353	−	23.6170i	−0.554811	−	0.960960i
$605$	2.39919	+	4.15551i	0.0975408	+	0.168946i
$606$		0			0
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$	10.0623	−	17.4284i	0.408080	−	0.706816i
$609$		0			0
$610$	−0.875388			−0.0354434
$611$	5.59017	−	5.80948i	0.226154	−	0.235026i
$612$		0			0
$613$	−7.21885	+	12.5034i	−0.291566	+	0.505008i	−0.974180	−	0.225771i	$-0.927510\pi$
$613$	−7.21885	+	12.5034i	−0.291566	+	0.505008i	0.682614	+	0.730779i	$0.260843\pi$
$614$	0.354102	−	0.613323i	0.0142904	−	0.0247517i
$615$		0			0
$616$	7.14590			0.287916
$617$	8.97214	+	15.5402i	0.361205	+	0.625625i	0.988159	−	0.153431i	$-0.0490323\pi$
$617$	8.97214	+	15.5402i	0.361205	+	0.625625i	−0.626955	+	0.779056i	$0.715699\pi$
$618$		0			0
$619$	−17.4164			−0.700025			−0.350012	−	0.936745i	$-0.613823\pi$
$619$	−17.4164			−0.700025			−0.350012	+	0.936745i	$0.613823\pi$
$620$	−3.08359	−	5.34094i	−0.123840	−	0.214497i
$621$		0			0
$622$	2.35410	−	4.07742i	0.0943909	−	0.163490i
$623$	−16.0902			−0.644639
$624$		0			0
$625$	22.8328			0.913313
$626$	−2.88854	+	5.00310i	−0.115449	+	0.199964i
$627$		0			0
$628$	7.55166	+	13.0799i	0.301344	+	0.521943i
$629$	−29.8885			−1.19173
$630$		0			0
$631$	19.6976	+	34.1172i	0.784148	+	1.35818i	0.929507	+	0.368804i	$0.120233\pi$
$631$	19.6976	+	34.1172i	0.784148	+	1.35818i	−0.145360	+	0.989379i	$0.546434\pi$
$632$	5.88854			0.234234
$633$		0			0
$634$	−4.15654	+	7.19934i	−0.165077	+	0.285922i
$635$	−2.70163	+	4.67935i	−0.107211	+	0.185694i
$636$		0			0
$637$	−1.00000	−	3.46410i	−0.0396214	−	0.137253i
$638$	−7.58359			−0.300237
$639$		0			0
$640$	1.92705	−	3.33775i	0.0761734	−	0.131936i
$641$	−4.74671	−	8.22154i	−0.187484	−	0.324731i	0.756927	−	0.653500i	$-0.226700\pi$
$641$	−4.74671	−	8.22154i	−0.187484	−	0.324731i	−0.944411	+	0.328768i	$0.893367\pi$
$642$		0			0
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−4.14590	−	7.18091i	−0.163371	−	0.282967i
$645$		0			0
$646$	−6.92705	−	11.9980i	−0.272541	−	0.472055i
$647$	14.6180	−	25.3192i	0.574694	−	0.995400i	−0.421381	−	0.906884i	$-0.638454\pi$
$647$	14.6180	−	25.3192i	0.574694	−	0.995400i	0.996075	−	0.0885157i	$-0.0282123\pi$
$648$		0			0
$649$	−10.8541			−0.426061
$650$	−1.85410	−	6.42280i	−0.0727239	−	0.251923i
$651$		0			0
$652$	9.00000	−	15.5885i	0.352467	−	0.610491i
$653$	−1.30902	+	2.26728i	−0.0512258	+	0.0887257i	−0.890501	−	0.454981i	$-0.849646\pi$
$653$	−1.30902	+	2.26728i	−0.0512258	+	0.0887257i	0.839275	+	0.543706i	$0.182979\pi$
$654$		0			0
$655$	0.124612			0.00486899
$656$	8.23607	+	14.2653i	0.321564	+	0.556966i
$657$		0			0
$658$	0.854102			0.0332964
$659$	5.94427	+	10.2958i	0.231556	+	0.401067i	0.958266	−	0.285877i	$-0.0922850\pi$
$659$	5.94427	+	10.2958i	0.231556	+	0.401067i	−0.726710	+	0.686944i	$0.758952\pi$
$660$		0			0
$661$	−9.27051	+	16.0570i	−0.360581	+	0.624545i	−0.988057	−	0.154092i	$-0.950755\pi$
$661$	−9.27051	+	16.0570i	−0.360581	+	0.624545i	0.627476	+	0.778636i	$0.284088\pi$
$662$	6.43769			0.250208
$663$		0			0
$664$	9.87539			0.383239
$665$	0.927051	−	1.60570i	0.0359495	−	0.0622664i
$666$		0			0
$667$	9.14590	+	15.8412i	0.354131	+	0.613372i
$668$	18.1033			0.700439
$669$		0			0
$670$	−0.0516628	−	0.0894826i	−0.00199591	−	0.00345701i
$671$	−29.1246			−1.12434
$672$		0			0
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	0.127806	+	0.991799i	$0.459207\pi$
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	−0.922826	+	0.385216i	$0.874127\pi$
$674$	1.63525	−	2.83234i	0.0629877	−	0.109098i
$675$		0			0
$676$	20.3951	−	12.8456i	0.784428	−	0.494061i
$677$	−1.25735			−0.0483240			−0.0241620	−	0.999708i	$-0.507692\pi$
$677$	−1.25735			−0.0483240			−0.0241620	+	0.999708i	$0.507692\pi$
$678$		0			0
$679$	−6.07295	+	10.5187i	−0.233058	+	0.403669i
$680$	−2.10081	−	3.63871i	−0.0805625	−	0.139538i
$681$		0			0
$682$	8.07295	+	13.9828i	0.309129	+	0.535427i
$683$	−3.73607	−	6.47106i	−0.142957	−	0.247608i	0.785652	−	0.618669i	$-0.212328\pi$
$683$	−3.73607	−	6.47106i	−0.142957	−	0.247608i	−0.928609	+	0.371060i	$0.878994\pi$
$684$		0			0
$685$	0.0729490	+	0.126351i	0.00278724	+	0.00482764i
$686$	0.190983	−	0.330792i	0.00729177	−	0.0126297i
$687$		0			0
$688$	−23.7902			−0.906995
$689$	20.5902	−	21.3979i	0.784423	−	0.815196i
$690$		0			0
$691$	−0.427051	+	0.739674i	−0.0162458	+	0.0281385i	−0.874034	−	0.485865i	$-0.838505\pi$
$691$	−0.427051	+	0.739674i	−0.0162458	+	0.0281385i	0.857788	+	0.514003i	$0.171838\pi$
$692$	8.34346	−	14.4513i	0.317171	−	0.549356i
$693$		0			0
$694$	13.4590			0.510896
$695$	−2.97214	−	5.14789i	−0.112740	−	0.195271i
$696$		0			0
$697$	39.1246			1.48195
$698$	1.39261	+	2.41207i	0.0527110	+	0.0912982i
$699$		0			0
$700$	−4.50000	+	7.79423i	−0.170084	+	0.294594i
$701$	−6.76393			−0.255470			−0.127735	−	0.991808i	$-0.540771\pi$
$701$	−6.76393			−0.255470			−0.127735	+	0.991808i	$0.540771\pi$
$702$		0			0
$703$	19.4164			0.732304
$704$	11.4271	−	19.7922i	0.430673	−	0.745948i
$705$		0			0
$706$	−5.51064	−	9.54471i	−0.207396	−	0.359220i
$707$	−8.56231			−0.322019
$708$		0			0
$709$	−1.71885	−	2.97713i	−0.0645527	−	0.111808i	0.831943	−	0.554861i	$-0.187229\pi$
$709$	−1.71885	−	2.97713i	−0.0645527	−	0.111808i	−0.896495	+	0.443053i	$0.853895\pi$
$710$	−1.19350			−0.0447911
$711$		0			0
$712$	11.8435	−	20.5135i	0.443852	−	0.768775i
$713$	19.4721	−	33.7267i	0.729237	−	1.26308i
$714$		0			0
$715$	1.85410	+	6.42280i	0.0693395	+	0.240199i
$716$	−16.6869			−0.623619
$717$		0			0
$718$	2.08359	−	3.60889i	0.0777590	−	0.134682i
$719$	−16.0623	−	27.8207i	−0.599023	−	1.03754i	−0.992966	−	0.118403i	$-0.962222\pi$
$719$	−16.0623	−	27.8207i	−0.599023	−	1.03754i	0.393943	−	0.919135i	$-0.371111\pi$
$720$		0			0
$721$	−2.35410	−	4.07742i	−0.0876713	−	0.151851i
$722$	0.871323	+	1.50918i	0.0324273	+	0.0561657i
$723$		0			0
$724$	−3.43769	−	5.95426i	−0.127761	−	0.221288i
$725$	9.92705	−	17.1942i	0.368681	−	0.638575i
$726$		0			0
$727$	−17.2918			−0.641317			−0.320659	−	0.947195i	$-0.603904\pi$
$727$	−17.2918			−0.641317			−0.320659	+	0.947195i	$0.603904\pi$
$728$	5.15248	+	1.27491i	0.190963	+	0.0472512i
$729$		0			0
$730$	0.145898	−	0.252703i	0.00539993	−	0.00935295i
$731$	−28.2533	+	48.9361i	−1.04499	+	1.80997i
$732$		0			0
$733$	1.27051			0.0469274			0.0234637	−	0.999725i	$-0.492531\pi$
$733$	1.27051			0.0469274			0.0234637	+	0.999725i	$0.492531\pi$
$734$	4.85410	+	8.40755i	0.179168	+	0.310328i
$735$		0			0
$736$	18.5410			0.683431
$737$	−1.71885	−	2.97713i	−0.0633145	−	0.109664i
$738$		0			0
$739$	23.5623	−	40.8111i	0.866753	−	1.50126i	0.00145790	−	0.999999i	$-0.499536\pi$
$739$	23.5623	−	40.8111i	0.866753	−	1.50126i	0.865296	−	0.501262i	$-0.167131\pi$
$740$	2.83282			0.104136
$741$		0			0
$742$	3.14590			0.115490
$743$	11.8369	−	20.5021i	0.434253	−	0.752148i	−0.562981	−	0.826470i	$-0.690346\pi$
$743$	11.8369	−	20.5021i	0.434253	−	0.752148i	0.997234	+	0.0743213i	$0.0236790\pi$
$744$		0			0
$745$	0.927051	+	1.60570i	0.0339645	+	0.0588283i
$746$	0.167184			0.00612105
$747$		0			0
$748$	−33.6246	−	58.2395i	−1.22944	−	2.12945i
$749$	5.61803			0.205278
$750$		0			0
$751$	−4.64590	+	8.04693i	−0.169531	+	0.293637i	−0.938255	−	0.345944i	$-0.887559\pi$
$751$	−4.64590	+	8.04693i	−0.169531	+	0.293637i	0.768724	+	0.639581i	$0.220892\pi$
$752$	3.51722	−	6.09201i	0.128260	−	0.222153i
$753$		0			0
$754$	−5.46807	−	1.35300i	−0.199135	−	0.0492732i
$755$	5.61803			0.204461
$756$		0			0
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$	−2.45492	−	4.25204i	−0.0891665	−	0.154441i
$759$		0			0
$760$	1.36475	+	2.36381i	0.0495045	+	0.0857443i
$761$	−11.0729	−	19.1789i	−0.401394	−	0.695235i	0.592500	−	0.805570i	$-0.298141\pi$
$761$	−11.0729	−	19.1789i	−0.401394	−	0.695235i	−0.993894	+	0.110335i	$0.964808\pi$
$762$		0			0
$763$	−5.35410	−	9.27358i	−0.193832	−	0.335726i
$764$	−21.8951	+	37.9235i	−0.792138	+	1.37202i
$765$		0			0
$766$	9.54102			0.344731
$767$	−7.82624	−	1.93649i	−0.282589	−	0.0699227i
$768$		0			0
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	−0.931872	−	0.362788i	$-0.881825\pi$
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	0.780120	+	0.625630i	$0.215158\pi$
$770$	−0.354102	+	0.613323i	−0.0127609	+	0.0221026i
$771$		0			0
$772$	11.1246			0.400384
$773$	−9.68034	−	16.7668i	−0.348178	−	0.603061i	0.637748	−	0.770245i	$-0.279866\pi$
$773$	−9.68034	−	16.7668i	−0.348178	−	0.603061i	−0.985926	+	0.167184i	$0.946533\pi$
$774$		0			0
$775$	−42.2705			−1.51840
$776$	−8.94021	−	15.4849i	−0.320935	−	0.555875i
$777$		0			0
$778$	−4.56231	+	7.90215i	−0.163567	+	0.283306i
$779$	−25.4164			−0.910637
$780$		0			0
$781$	−39.7082			−1.42087
$782$	6.38197	−	11.0539i	0.228219	−	0.395286i
$783$		0			0
$784$	−1.57295	−	2.72443i	−0.0561768	−	0.0973010i
$785$	−3.11146			−0.111053
$786$		0			0
$787$	−14.7082	−	25.4754i	−0.524291	−	0.908098i	−0.999600	−	0.0282796i	$-0.990997\pi$
$787$	−14.7082	−	25.4754i	−0.524291	−	0.908098i	0.475309	−	0.879819i	$-0.342336\pi$
$788$	14.4590			0.515080
$789$		0			0
$790$	−0.291796	+	0.505406i	−0.0103816	+	0.0179815i
$791$	−3.73607	+	6.47106i	−0.132839	+	0.230084i
$792$		0			0
$793$	−21.0000	−	5.19615i	−0.745732	−	0.184521i
$794$	9.70820			0.344531
$795$		0			0
$796$	2.24013	−	3.88002i	0.0793994	−	0.137524i
$797$	7.09017	+	12.2805i	0.251147	+	0.434999i	0.963842	−	0.266475i	$-0.0858590\pi$
$797$	7.09017	+	12.2805i	0.251147	+	0.434999i	−0.712695	+	0.701474i	$0.752526\pi$
$798$		0			0
$799$	−8.35410	−	14.4697i	−0.295547	−	0.511902i
$800$	−10.0623	−	17.4284i	−0.355756	−	0.616188i
$801$		0			0
$802$	3.90576	+	6.76498i	0.137917	+	0.238880i
$803$	4.85410	−	8.40755i	0.171298	−	0.296696i
$804$		0			0
$805$	1.70820			0.0602063
$806$	3.32624	+	11.5224i	0.117162	+	0.405860i
$807$		0			0
$808$	6.30244	−	10.9161i	0.221719	−	0.384029i
$809$	11.2082	−	19.4132i	0.394059	−	0.682531i	−0.598921	−	0.800808i	$-0.704404\pi$
$809$	11.2082	−	19.4132i	0.394059	−	0.682531i	0.992981	+	0.118277i	$0.0377371\pi$
$810$		0			0
$811$	5.72949			0.201190			0.100595	−	0.994927i	$-0.467925\pi$
$811$	5.72949			0.201190			0.100595	+	0.994927i	$0.467925\pi$
$812$	3.79180	+	6.56758i	0.133066	+	0.230477i
$813$		0			0
$814$	−7.41641			−0.259945
$815$	1.85410	+	3.21140i	0.0649464	+	0.112490i
$816$		0			0
$817$	18.3541	−	31.7902i	0.642129	−	1.11220i
$818$	−13.2016			−0.461584
$819$		0			0
$820$	−3.70820			−0.129496
$821$	18.6803	−	32.3553i	0.651948	−	1.12921i	−0.330701	−	0.943736i	$-0.607285\pi$
$821$	18.6803	−	32.3553i	0.651948	−	1.12921i	0.982650	−	0.185472i	$-0.0593815\pi$
$822$		0			0
$823$	5.79180	+	10.0317i	0.201889	+	0.349683i	0.949137	−	0.314863i	$-0.101959\pi$
$823$	5.79180	+	10.0317i	0.201889	+	0.349683i	−0.747248	+	0.664545i	$0.768625\pi$
$824$	6.93112			0.241457
$825$		0			0
$826$	−0.427051	−	0.739674i	−0.0148590	−	0.0257366i
$827$	30.9787			1.07724			0.538618	−	0.842550i	$-0.318947\pi$
$827$	30.9787			1.07724			0.538618	+	0.842550i	$0.318947\pi$
$828$		0			0
$829$	6.28115	−	10.8793i	0.218153	−	0.377853i	−0.736090	−	0.676884i	$-0.763330\pi$
$829$	6.28115	−	10.8793i	0.218153	−	0.377853i	0.954243	+	0.299031i	$0.0966633\pi$
$830$	−0.489357	+	0.847591i	−0.0169858	+	0.0294203i
$831$		0			0
$832$	11.7705	−	12.2323i	0.408069	−	0.424078i
$833$	−7.47214			−0.258894
$834$		0			0
$835$	−1.86475	+	3.22983i	−0.0645322	+	0.111773i
$836$	21.8435	+	37.8340i	0.755472	+	1.30852i
$837$		0			0
$838$	−1.13525	−	1.96632i	−0.0392167	−	0.0679254i
$839$	−14.3713	−	24.8919i	−0.496153	−	0.859362i	0.503837	−	0.863799i	$-0.331921\pi$
$839$	−14.3713	−	24.8919i	−0.496153	−	0.859362i	−0.999990	+	0.00443626i	$0.998588\pi$
$840$		0			0
$841$	6.13525	+	10.6266i	0.211561	+	0.366434i
$842$	−4.85410	+	8.40755i	−0.167283	+	0.289743i
$843$		0			0
$844$	16.1459			0.555765
$845$	0.190983	+	4.96188i	0.00657002	+	0.170694i
$846$		0			0
$847$	−6.28115	+	10.8793i	−0.215823	+	0.373816i
$848$	12.9549	−	22.4386i	0.444874	−	0.770544i
$849$		0			0
$850$	−13.8541			−0.475192
$851$	8.94427	+	15.4919i	0.306606	+	0.531057i
$852$		0			0
$853$	−26.1246			−0.894490			−0.447245	−	0.894412i	$-0.647595\pi$
$853$	−26.1246			−0.894490			−0.447245	+	0.894412i	$0.647595\pi$
$854$	−1.14590	−	1.98475i	−0.0392118	−	0.0679169i
$855$		0			0
$856$	−4.13525	+	7.16247i	−0.141340	+	0.244808i
$857$	−29.4508			−1.00602			−0.503011	−	0.864280i	$-0.667774\pi$
$857$	−29.4508			−1.00602			−0.503011	+	0.864280i	$0.667774\pi$
$858$		0			0
$859$	36.2492			1.23681			0.618404	−	0.785861i	$-0.287780\pi$
$859$	36.2492			1.23681			0.618404	+	0.785861i	$0.287780\pi$
$860$	2.67783	−	4.63813i	0.0913132	−	0.158159i
$861$		0			0
$862$	3.20820	+	5.55677i	0.109272	+	0.189264i
$863$	23.8885			0.813175			0.406588	−	0.913612i	$-0.366719\pi$
$863$	23.8885			0.813175			0.406588	+	0.913612i	$0.366719\pi$
$864$		0			0
$865$	1.71885	+	2.97713i	0.0584426	+	0.101225i
$866$	−0.381966			−0.0129797
$867$		0			0
$868$	8.07295	−	13.9828i	0.274014	−	0.474606i
$869$	−9.70820	+	16.8151i	−0.329328	+	0.570413i
$870$		0			0
$871$	−0.708204	−	2.45329i	−0.0239966	−	0.0831266i
$872$	15.7639			0.533834
$873$		0			0
$874$	−4.14590	+	7.18091i	−0.140237	+	0.242898i
$875$	−1.88197	−	3.25966i	−0.0636221	−	0.110197i
$876$		0			0
$877$	6.35410	+	11.0056i	0.214563	+	0.371634i	0.953137	−	0.302538i	$-0.0978340\pi$
$877$	6.35410	+	11.0056i	0.214563	+	0.371634i	−0.738574	+	0.674172i	$0.764501\pi$
$878$	1.55573	+	2.69460i	0.0525033	+	0.0909383i
$879$		0			0
$880$	2.91641	+	5.05137i	0.0983121	+	0.170282i
$881$	6.29837	−	10.9091i	0.212198	−	0.367537i	−0.740204	−	0.672382i	$-0.765271\pi$
$881$	6.29837	−	10.9091i	0.212198	−	0.367537i	0.952402	+	0.304845i	$0.0986046\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	−13.8541	−	47.9920i	−0.465964	−	1.61415i
$885$		0			0
$886$	0.145898	−	0.252703i	0.00490154	−	0.00848972i
$887$	11.6738	−	20.2195i	0.391967	−	0.678906i	−0.600742	−	0.799443i	$-0.705128\pi$
$887$	11.6738	−	20.2195i	0.391967	−	0.678906i	0.992709	+	0.120537i	$0.0384616\pi$
$888$		0			0
$889$	−14.1459			−0.474438
$890$	1.17376	+	2.03302i	0.0393446	+	0.0681468i
$891$		0			0
$892$	24.6049			0.823832
$893$	5.42705	+	9.39993i	0.181609	+	0.314557i
$894$		0			0
$895$	1.71885	−	2.97713i	0.0574547	−	0.0995145i
$896$	10.0902			0.337089
$897$		0			0
$898$	10.8754			0.362916
$899$	−17.8090	+	30.8461i	−0.593964	+	1.02878i
$900$		0			0
$901$	−30.7705	−	53.2961i	−1.02511	−	1.77555i
$902$	9.70820			0.323248
$903$		0			0
$904$	−5.50000	−	9.52628i	−0.182927	−	0.316839i
$905$	1.41641			0.0470830
$906$		0			0
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	−0.595082	−	0.803665i	$-0.702880\pi$
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	0.993535	+	0.113523i	$0.0362137\pi$
$908$	6.92705	−	11.9980i	0.229882	−	0.398168i
$909$		0			0
$910$	−0.364745	+	0.379054i	−0.0120912	+	0.0125655i
$911$	−37.6869			−1.24862			−0.624312	−	0.781175i	$-0.714620\pi$
$911$	−37.6869			−1.24862			−0.624312	+	0.781175i	$0.714620\pi$
$912$		0			0
$913$	−16.2812	+	28.1998i	−0.538828	+	0.933277i
$914$	−2.18034	−	3.77646i	−0.0721192	−	0.124914i
$915$		0			0
$916$	25.1459	+	43.5540i	0.830844	+	1.43906i
$917$	0.163119	+	0.282530i	0.00538666	+	0.00932997i
$918$		0			0
$919$	15.0000	+	25.9808i	0.494804	+	0.857026i	0.999982	−	0.00598907i	$-0.00190639\pi$
$919$	15.0000	+	25.9808i	0.494804	+	0.857026i	−0.505178	+	0.863015i	$0.668573\pi$
$920$	−1.25735	+	2.17780i	−0.0414537	+	0.0718000i
$921$		0			0
$922$	14.9787			0.493298
$923$	−28.6312	−	7.08438i	−0.942407	−	0.233185i
$924$		0			0
$925$	9.70820	−	16.8151i	0.319204	−	0.552877i
$926$	−1.28115	+	2.21902i	−0.0421013	+	0.0729216i
$927$		0			0
$928$	−16.9574			−0.556655
$929$	−23.5344	−	40.7628i	−0.772140	−	1.33739i	−0.936388	−	0.350967i	$-0.885853\pi$
$929$	−23.5344	−	40.7628i	−0.772140	−	1.33739i	0.164248	−	0.986419i	$-0.447480\pi$
$930$		0			0
$931$	4.85410			0.159087
$932$	−0.354102	−	0.613323i	−0.0115990	−	0.0200900i
$933$		0			0
$934$	−6.42705	+	11.1320i	−0.210300	+	0.364249i
$935$	13.8541			0.453078
$936$		0			0
$937$	−56.1246			−1.83351			−0.916756	−	0.399449i	$-0.869202\pi$
$937$	−56.1246			−1.83351			−0.916756	+	0.399449i	$0.869202\pi$
$938$	0.135255	−	0.234268i	0.00441623	−	0.00764913i
$939$		0			0
$940$	0.791796	+	1.37143i	0.0258255	+	0.0447311i
$941$	−51.6525			−1.68382			−0.841911	−	0.539616i	$-0.818569\pi$
$941$	−51.6525			−1.68382			−0.841911	+	0.539616i	$0.818569\pi$
$942$		0			0
$943$	−11.7082	−	20.2792i	−0.381272	−	0.660382i
$944$	−7.03444			−0.228952
$945$		0			0
$946$	−7.01064	+	12.1428i	−0.227936	+	0.394796i
$947$	22.9336	−	39.7222i	0.745243	−	1.29080i	−0.204838	−	0.978796i	$-0.565667\pi$
$947$	22.9336	−	39.7222i	0.745243	−	1.29080i	0.950081	−	0.312003i	$-0.101000\pi$
$948$		0			0
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$	9.00000			0.291999
$951$		0			0
$952$	5.50000	−	9.52628i	0.178256	−	0.308748i
$953$	−22.3885	−	38.7781i	−0.725236	−	1.25615i	−0.958877	−	0.283823i	$-0.908397\pi$
$953$	−22.3885	−	38.7781i	−0.725236	−	1.25615i	0.233641	−	0.972323i	$-0.424936\pi$
$954$		0			0
$955$	−4.51064	−	7.81266i	−0.145961	−	0.252812i
$956$	10.4681	+	18.1312i	0.338562	+	0.586406i
$957$		0			0
$958$	4.19756	+	7.27039i	0.135617	+	0.234896i
$959$	−0.190983	+	0.330792i	−0.00616716	+	0.0106818i
$960$		0			0
$961$	44.8328			1.44622
$962$	−5.34752	−	1.32317i	−0.172411	−	0.0426607i
$963$		0			0
$964$	4.11397	−	7.12560i	0.132502	−	0.229500i
$965$	−1.14590	+	1.98475i	−0.0368878	+	0.0638915i
$966$		0			0
$967$	−39.0000			−1.25416			−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000			−1.25416			−0.627078	+	0.778957i	$0.715749\pi$
$968$	−9.24671	−	16.0158i	−0.297201	−	0.514766i
$969$		0			0
$970$	1.77206			0.0568975
$971$	29.2082	+	50.5901i	0.937336	+	1.62351i	0.770415	+	0.637543i	$0.220049\pi$
$971$	29.2082	+	50.5901i	0.937336	+	1.62351i	0.166921	+	0.985970i	$0.446617\pi$
$972$		0			0
$973$	7.78115	−	13.4774i	0.249452	−	0.432064i
$974$	6.48529			0.207802
$975$		0			0
$976$	−18.8754			−0.604186
$977$	−15.7361	+	27.2557i	−0.503441	+	0.871986i	0.496551	+	0.868008i	$0.334600\pi$
$977$	−15.7361	+	27.2557i	−0.503441	+	0.871986i	−0.999992	+	0.00397838i	$0.998734\pi$
$978$		0			0
$979$	39.0517	+	67.6395i	1.24810	+	2.16177i
$980$	0.708204			0.0226227
$981$		0			0
$982$	−2.79180	−	4.83553i	−0.0890898	−	0.154308i
$983$	−20.6180			−0.657613			−0.328807	−	0.944397i	$-0.606646\pi$
$983$	−20.6180			−0.657613			−0.328807	+	0.944397i	$0.606646\pi$
$984$		0			0
$985$	−1.48936	+	2.57964i	−0.0474549	+	0.0821942i
$986$	−5.83688	+	10.1098i	−0.185884	+	0.321961i
$987$		0			0
$988$	9.00000	+	31.1769i	0.286328	+	0.991870i
$989$	33.8197			1.07540
$990$		0			0
$991$	11.4271	−	19.7922i	0.362992	−	0.628721i	−0.625460	−	0.780257i	$-0.715088\pi$
$991$	11.4271	−	19.7922i	0.362992	−	0.628721i	0.988452	+	0.151536i	$0.0484218\pi$
$992$	18.0517	+	31.2664i	0.573141	+	0.992709i
$993$		0			0
$994$	−1.56231	−	2.70599i	−0.0495533	−	0.0858289i
$995$	0.461493	+	0.799329i	0.0146303	+	0.0253404i
$996$		0			0
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	0.158352	−	0.987383i	$-0.449382\pi$
$998$	1.55573	−	2.69460i	0.0492457	−	0.0852961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.c.568.1		4
3.2	odd	2		91.2.f.a.22.2	✓	4
12.11	even	2		1456.2.s.h.113.2		4
13.3	even	3	inner	819.2.o.c.757.1		4
21.2	odd	6		637.2.h.g.165.1		4
21.5	even	6		637.2.h.f.165.1		4
21.11	odd	6		637.2.g.b.373.2		4
21.17	even	6		637.2.g.c.373.2		4
21.20	even	2		637.2.f.c.295.2		4
39.17	odd	6		1183.2.a.c.1.2		2
39.20	even	12		1183.2.c.c.337.3		4
39.29	odd	6		91.2.f.a.29.2	yes	4
39.32	even	12		1183.2.c.c.337.2		4
39.35	odd	6		1183.2.a.g.1.1		2
156.107	even	6		1456.2.s.h.1121.2		4
273.68	even	6		637.2.g.c.263.2		4
273.107	odd	6		637.2.g.b.263.2		4
273.146	even	6		637.2.f.c.393.2		4
273.185	even	6		637.2.h.f.471.1		4
273.230	even	6		8281.2.a.bb.1.1		2
273.251	even	6		8281.2.a.n.1.2		2
273.263	odd	6		637.2.h.g.471.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.2	✓	4	3.2	odd	2
91.2.f.a.29.2	yes	4	39.29	odd	6
637.2.f.c.295.2		4	21.20	even	2
637.2.f.c.393.2		4	273.146	even	6
637.2.g.b.263.2		4	273.107	odd	6
637.2.g.b.373.2		4	21.11	odd	6
637.2.g.c.263.2		4	273.68	even	6
637.2.g.c.373.2		4	21.17	even	6
637.2.h.f.165.1		4	21.5	even	6
637.2.h.f.471.1		4	273.185	even	6
637.2.h.g.165.1		4	21.2	odd	6
637.2.h.g.471.1		4	273.263	odd	6
819.2.o.c.568.1		4	1.1	even	1	trivial
819.2.o.c.757.1		4	13.3	even	3	inner
1183.2.a.c.1.2		2	39.17	odd	6
1183.2.a.g.1.1		2	39.35	odd	6
1183.2.c.c.337.2		4	39.32	even	12
1183.2.c.c.337.3		4	39.20	even	12
1456.2.s.h.113.2		4	12.11	even	2
1456.2.s.h.1121.2		4	156.107	even	6
8281.2.a.n.1.2		2	273.251	even	6
8281.2.a.bb.1.1		2	273.230	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.330792i) q^{2} +(0.927051 + 1.60570i) q^{4} -0.381966 q^{5} +(-0.500000 - 0.866025i) q^{7} +1.47214 q^{8} +O(q^{10})\)	\(q+(0.190983 - 0.330792i) q^{2} +(0.927051 + 1.60570i) q^{4} -0.381966 q^{5} +(-0.500000 - 0.866025i) q^{7} +1.47214 q^{8} +(-0.0729490 + 0.126351i) q^{10} +(-2.42705 + 4.20378i) q^{11} +(-2.50000 + 2.59808i) q^{13} -0.381966 q^{14} +(-1.57295 + 2.72443i) q^{16} +(3.73607 + 6.47106i) q^{17} +(-2.42705 - 4.20378i) q^{19} +(-0.354102 - 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +(2.23607 - 3.87298i) q^{23} -4.85410 q^{25} +(0.381966 + 1.32317i) q^{26} +(0.927051 - 1.60570i) q^{28} +(-2.04508 + 3.54219i) q^{29} +8.70820 q^{31} +(2.07295 + 3.59045i) q^{32} +2.85410 q^{34} +(0.190983 + 0.330792i) q^{35} +(-2.00000 + 3.46410i) q^{37} -1.85410 q^{38} -0.562306 q^{40} +(2.61803 - 4.53457i) q^{41} +(3.78115 + 6.54915i) q^{43} -9.00000 q^{44} +(-0.854102 - 1.47935i) q^{46} -2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.927051 + 1.60570i) q^{50} +(-6.48936 - 1.60570i) q^{52} -8.23607 q^{53} +(0.927051 - 1.60570i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(0.781153 + 1.35300i) q^{58} +(1.11803 + 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(1.66312 - 2.88061i) q^{62} -4.70820 q^{64} +(0.954915 - 0.992377i) q^{65} +(-0.354102 + 0.613323i) q^{67} +(-6.92705 + 11.9980i) q^{68} +0.145898 q^{70} +(4.09017 + 7.08438i) q^{71} -2.00000 q^{73} +(0.763932 + 1.32317i) q^{74} +(4.50000 - 7.79423i) q^{76} +4.85410 q^{77} +4.00000 q^{79} +(0.600813 - 1.04064i) q^{80} +(-1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +2.88854 q^{86} +(-3.57295 + 6.18853i) q^{88} +(8.04508 - 13.9345i) q^{89} +(3.50000 + 0.866025i) q^{91} +8.29180 q^{92} +(-0.427051 + 0.739674i) q^{94} +(0.927051 + 1.60570i) q^{95} +(-6.07295 - 10.5187i) q^{97} +(0.190983 + 0.330792i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8	\( 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8} - 7 q^{10} - 3 q^{11} - 10 q^{13} - 6 q^{14} - 13 q^{16} + 6 q^{17} - 3 q^{19} + 12 q^{20} - 3 q^{22} - 6 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 8 q^{31} + 15 q^{32} - 2 q^{34} + 3 q^{35} - 8 q^{37} + 6 q^{38} + 38 q^{40} + 6 q^{41} - 5 q^{43} - 36 q^{44} + 10 q^{46} - 2 q^{49} + 3 q^{50} + 21 q^{52} - 24 q^{53} - 3 q^{55} + 6 q^{56} - 17 q^{58} + 12 q^{61} - 9 q^{62} + 8 q^{64} + 15 q^{65} + 12 q^{67} - 21 q^{68} + 14 q^{70} - 6 q^{71} - 8 q^{73} + 12 q^{74} + 18 q^{76} + 6 q^{77} + 16 q^{79} + 27 q^{80} - 4 q^{82} + q^{85} - 60 q^{86} - 21 q^{88} + 21 q^{89} + 14 q^{91} + 60 q^{92} + 5 q^{94} - 3 q^{95} - 31 q^{97} + 3 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8 - 7 * q^10 - 3 * q^11 - 10 * q^13 - 6 * q^14 - 13 * q^16 + 6 * q^17 - 3 * q^19 + 12 * q^20 - 3 * q^22 - 6 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 8 * q^31 + 15 * q^32 - 2 * q^34 + 3 * q^35 - 8 * q^37 + 6 * q^38 + 38 * q^40 + 6 * q^41 - 5 * q^43 - 36 * q^44 + 10 * q^46 - 2 * q^49 + 3 * q^50 + 21 * q^52 - 24 * q^53 - 3 * q^55 + 6 * q^56 - 17 * q^58 + 12 * q^61 - 9 * q^62 + 8 * q^64 + 15 * q^65 + 12 * q^67 - 21 * q^68 + 14 * q^70 - 6 * q^71 - 8 * q^73 + 12 * q^74 + 18 * q^76 + 6 * q^77 + 16 * q^79 + 27 * q^80 - 4 * q^82 + q^85 - 60 * q^86 - 21 * q^88 + 21 * q^89 + 14 * q^91 + 60 * q^92 + 5 * q^94 - 3 * q^95 - 31 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more