LMFDB - Embedded newform 1320.2.bw.c.1081.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.2
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.c.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.953245 - 2.93379i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.953245 - 2.93379i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-2.22899 + 2.45593i) q^{11} +(5.22462 - 3.79591i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(0.809017 + 0.587785i) q^{17} +(0.600175 + 1.84715i) q^{19} +3.08477 q^{21} +0.524524 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.424349 - 1.30601i) q^{29} +(6.15604 - 4.47263i) q^{31} +(-3.02452 - 1.36098i) q^{33} +(2.49563 - 1.81318i) q^{35} +(1.12637 - 3.46661i) q^{37} +(5.22462 + 3.79591i) q^{39} +(1.22503 + 3.77026i) q^{41} +4.39530 q^{43} -1.00000 q^{45} +(-0.428721 - 1.31947i) q^{47} +(-2.03531 - 1.47874i) q^{49} +(-0.309017 + 0.951057i) q^{51} +(7.14460 - 5.19085i) q^{53} +(-3.24685 + 0.676718i) q^{55} +(-1.57128 + 1.14160i) q^{57} +(-2.14938 + 6.61511i) q^{59} +(9.02285 + 6.55549i) q^{61} +(0.953245 + 2.93379i) q^{63} +6.45799 q^{65} -5.29335 q^{67} +(0.162087 + 0.498852i) q^{69} +(-10.6228 - 7.71790i) q^{71} +(0.186611 - 0.574329i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(5.08039 + 8.88049i) q^{77} +(-7.76700 + 5.64306i) q^{79} +(0.309017 - 0.951057i) q^{81} +(6.29320 + 4.57228i) q^{83} +(0.309017 + 0.951057i) q^{85} +1.37322 q^{87} +2.07936 q^{89} +(-6.15604 - 18.9464i) q^{91} +(6.15604 + 4.47263i) q^{93} +(-0.600175 + 1.84715i) q^{95} +(-5.43305 + 3.94735i) q^{97} +(0.359735 - 3.29706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{5} + 5 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 2 * q^5 + 5 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} + 2 q^{5} + 5 q^{7} - 2 q^{9} + 5 q^{11} + 4 q^{13} + 2 q^{15} + 2 q^{17} - 6 q^{19} - 10 q^{23} - 2 q^{25} - 2 q^{27} + 13 q^{31} - 10 q^{33} + 5 q^{35} + 9 q^{37} + 4 q^{39} - 7 q^{41} + 12 q^{43} - 8 q^{45} - 15 q^{47} + q^{49} + 2 q^{51} + q^{53} - 5 q^{55} - q^{57} + 3 q^{59} + 33 q^{61} + 5 q^{63} + 6 q^{65} - 22 q^{67} + 5 q^{69} - 33 q^{71} - 9 q^{73} - 2 q^{75} + q^{77} - 12 q^{79} - 2 q^{81} + 11 q^{83} - 2 q^{85} - 10 q^{87} + 12 q^{89} - 13 q^{91} + 13 q^{93} + 6 q^{95} + 9 q^{97} - 5 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^5 + 5 * q^7 - 2 * q^9 + 5 * q^11 + 4 * q^13 + 2 * q^15 + 2 * q^17 - 6 * q^19 - 10 * q^23 - 2 * q^25 - 2 * q^27 + 13 * q^31 - 10 * q^33 + 5 * q^35 + 9 * q^37 + 4 * q^39 - 7 * q^41 + 12 * q^43 - 8 * q^45 - 15 * q^47 + q^49 + 2 * q^51 + q^53 - 5 * q^55 - q^57 + 3 * q^59 + 33 * q^61 + 5 * q^63 + 6 * q^65 - 22 * q^67 + 5 * q^69 - 33 * q^71 - 9 * q^73 - 2 * q^75 + q^77 - 12 * q^79 - 2 * q^81 + 11 * q^83 - 2 * q^85 - 10 * q^87 + 12 * q^89 - 13 * q^91 + 13 * q^93 + 6 * q^95 + 9 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	0.953245	−	2.93379i	0.360293	−	1.10887i	−0.592584	−	0.805509i	$-0.701892\pi$
$7$	0.953245	−	2.93379i	0.360293	−	1.10887i	0.952877	−	0.303358i	$-0.0981079\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−2.22899	+	2.45593i	−0.672067	+	0.740490i
$11$	−2.22899	+	2.45593i	−0.672067	+	0.740490i
$12$		0			0
$13$	5.22462	−	3.79591i	1.44905	−	1.05280i	0.462997	−	0.886360i	$-0.346774\pi$
$13$	5.22462	−	3.79591i	1.44905	−	1.05280i	0.986052	−	0.166436i	$-0.0532260\pi$
$14$		0			0
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i	0.681555	−	0.731767i	$-0.261304\pi$
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i	−0.485340	+	0.874326i	$0.661304\pi$
$18$		0			0
$19$	0.600175	+	1.84715i	0.137690	+	0.423765i	0.995999	−	0.0893680i	$-0.0284847\pi$
$19$	0.600175	+	1.84715i	0.137690	+	0.423765i	−0.858309	+	0.513133i	$0.828485\pi$
$20$		0			0
$21$	3.08477			0.673151
$22$		0			0
$23$	0.524524			0.109371			0.0546854	−	0.998504i	$-0.482584\pi$
$23$	0.524524			0.109371			0.0546854	+	0.998504i	$0.482584\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	0.424349	−	1.30601i	0.0787996	−	0.242520i	−0.903895	−	0.427755i	$-0.859305\pi$
$29$	0.424349	−	1.30601i	0.0787996	−	0.242520i	0.982694	+	0.185235i	$0.0593046\pi$
$30$		0			0
$31$	6.15604	−	4.47263i	1.10566	−	0.803308i	0.123684	−	0.992322i	$-0.460529\pi$
$31$	6.15604	−	4.47263i	1.10566	−	0.803308i	0.981974	+	0.189014i	$0.0605291\pi$
$32$		0			0
$33$	−3.02452	−	1.36098i	−0.526502	−	0.236915i
$34$		0			0
$35$	2.49563	−	1.81318i	0.421838	−	0.306483i
$36$		0			0
$37$	1.12637	−	3.46661i	0.185174	−	0.569907i	−0.814777	−	0.579774i	$-0.803141\pi$
$37$	1.12637	−	3.46661i	0.185174	−	0.569907i	0.999951	+	0.00986711i	$0.00314085\pi$
$38$		0			0
$39$	5.22462	+	3.79591i	0.836609	+	0.607832i
$40$		0			0
$41$	1.22503	+	3.77026i	0.191318	+	0.588815i	1.00000		0.000569370i	$0.000181236\pi$
$41$	1.22503	+	3.77026i	0.191318	+	0.588815i	−0.808682	+	0.588246i	$0.799819\pi$
$42$		0			0
$43$	4.39530			0.670276			0.335138	−	0.942169i	$-0.391217\pi$
$43$	4.39530			0.670276			0.335138	+	0.942169i	$0.391217\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−0.428721	−	1.31947i	−0.0625354	−	0.192464i	0.914908	−	0.403663i	$-0.132263\pi$
$47$	−0.428721	−	1.31947i	−0.0625354	−	0.192464i	−0.977443	+	0.211199i	$0.932263\pi$
$48$		0			0
$49$	−2.03531	−	1.47874i	−0.290758	−	0.211248i
$50$		0			0
$51$	−0.309017	+	0.951057i	−0.0432710	+	0.133175i
$52$		0			0
$53$	7.14460	−	5.19085i	0.981386	−	0.713019i	0.0233681	−	0.999727i	$-0.492561\pi$
$53$	7.14460	−	5.19085i	0.981386	−	0.713019i	0.958018	+	0.286708i	$0.0925610\pi$
$54$		0			0
$55$	−3.24685	+	0.676718i	−0.437806	+	0.0912487i
$56$		0			0
$57$	−1.57128	+	1.14160i	−0.208121	+	0.151209i
$58$		0			0
$59$	−2.14938	+	6.61511i	−0.279825	+	0.861214i	0.708077	+	0.706135i	$0.249563\pi$
$59$	−2.14938	+	6.61511i	−0.279825	+	0.861214i	−0.987902	+	0.155079i	$0.950437\pi$
$60$		0			0
$61$	9.02285	+	6.55549i	1.15526	+	0.839344i	0.989171	−	0.146767i	$-0.0468867\pi$
$61$	9.02285	+	6.55549i	1.15526	+	0.839344i	0.166087	+	0.986111i	$0.446887\pi$
$62$		0			0
$63$	0.953245	+	2.93379i	0.120098	+	0.369622i
$64$		0			0
$65$	6.45799			0.801015
$66$		0			0
$67$	−5.29335			−0.646686			−0.323343	−	0.946282i	$-0.604807\pi$
$67$	−5.29335			−0.646686			−0.323343	+	0.946282i	$0.604807\pi$
$68$		0			0
$69$	0.162087	+	0.498852i	0.0195130	+	0.0600547i
$70$		0			0
$71$	−10.6228	−	7.71790i	−1.26069	−	0.915946i	−0.261900	−	0.965095i	$-0.584349\pi$
$71$	−10.6228	−	7.71790i	−1.26069	−	0.915946i	−0.998791	+	0.0491489i	$0.984349\pi$
$72$		0			0
$73$	0.186611	−	0.574329i	0.0218412	−	0.0672202i	−0.939542	−	0.342434i	$-0.888749\pi$
$73$	0.186611	−	0.574329i	0.0218412	−	0.0672202i	0.961383	+	0.275214i	$0.0887487\pi$
$74$		0			0
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$		0			0
$77$	5.08039	+	8.88049i	0.578965	+	1.01203i
$78$		0			0
$79$	−7.76700	+	5.64306i	−0.873856	+	0.634894i	−0.931619	−	0.363437i	$-0.881603\pi$
$79$	−7.76700	+	5.64306i	−0.873856	+	0.634894i	0.0577626	+	0.998330i	$0.481603\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	6.29320	+	4.57228i	0.690768	+	0.501873i	0.876913	−	0.480650i	$-0.159599\pi$
$83$	6.29320	+	4.57228i	0.690768	+	0.501873i	−0.186144	+	0.982522i	$0.559599\pi$
$84$		0			0
$85$	0.309017	+	0.951057i	0.0335176	+	0.103157i
$86$		0			0
$87$	1.37322			0.147225
$88$		0			0
$89$	2.07936			0.220412			0.110206	−	0.993909i	$-0.464849\pi$
$89$	2.07936			0.220412			0.110206	+	0.993909i	$0.464849\pi$
$90$		0			0
$91$	−6.15604	−	18.9464i	−0.645329	−	1.98612i
$92$		0			0
$93$	6.15604	+	4.47263i	0.638352	+	0.463790i
$94$		0			0
$95$	−0.600175	+	1.84715i	−0.0615767	+	0.189514i
$96$		0			0
$97$	−5.43305	+	3.94735i	−0.551643	+	0.400792i	−0.828391	−	0.560150i	$-0.810743\pi$
$97$	−5.43305	+	3.94735i	−0.551643	+	0.400792i	0.276748	+	0.960943i	$0.410743\pi$
$98$		0			0
$99$	0.359735	−	3.29706i	0.0361547	−	0.331367i
$100$		0			0
$101$	12.6890	−	9.21911i	1.26260	−	0.917336i	0.263722	−	0.964599i	$-0.415050\pi$
$101$	12.6890	−	9.21911i	1.26260	−	0.917336i	0.998883	+	0.0472625i	$0.0150497\pi$
$102$		0			0
$103$	−4.57476	+	14.0797i	−0.450765	+	1.38731i	0.425272	+	0.905066i	$0.360178\pi$
$103$	−4.57476	+	14.0797i	−0.450765	+	1.38731i	−0.876036	+	0.482245i	$0.839822\pi$
$104$		0			0
$105$	2.49563	+	1.81318i	0.243548	+	0.176948i
$106$		0			0
$107$	1.60018	+	4.92483i	0.154695	+	0.476102i	0.998130	−	0.0611296i	$-0.0194703\pi$
$107$	1.60018	+	4.92483i	0.154695	+	0.476102i	−0.843435	+	0.537231i	$0.819470\pi$
$108$		0			0
$109$	5.29052			0.506740			0.253370	−	0.967369i	$-0.418461\pi$
$109$	5.29052			0.506740			0.253370	+	0.967369i	$0.418461\pi$
$110$		0			0
$111$	3.64501			0.345969
$112$		0			0
$113$	3.78241	+	11.6411i	0.355820	+	1.09510i	0.955533	+	0.294885i	$0.0952814\pi$
$113$	3.78241	+	11.6411i	0.355820	+	1.09510i	−0.599713	+	0.800215i	$0.704719\pi$
$114$		0			0
$115$	0.424349	+	0.308308i	0.0395707	+	0.0287498i
$116$		0			0
$117$	−1.99563	+	6.14191i	−0.184496	+	0.567820i
$118$		0			0
$119$	2.49563	−	1.81318i	0.228774	−	0.166214i
$120$		0			0
$121$	−1.06317	−	10.9485i	−0.0966521	−	0.995318i
$122$		0			0
$123$	−3.20717	+	2.33015i	−0.289181	+	0.210102i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	0.813389	+	0.590962i	0.0721766	+	0.0524394i	0.623288	−	0.781992i	$-0.285796\pi$
$127$	0.813389	+	0.590962i	0.0721766	+	0.0524394i	−0.551112	+	0.834431i	$0.685796\pi$
$128$		0			0
$129$	1.35822	+	4.18018i	0.119585	+	0.368044i
$130$		0			0
$131$	−11.3146			−0.988562			−0.494281	−	0.869302i	$-0.664569\pi$
$131$	−11.3146			−0.988562			−0.494281	+	0.869302i	$0.664569\pi$
$132$		0			0
$133$	5.99126			0.519508
$134$		0			0
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$		0			0
$137$	3.93617	+	2.85979i	0.336289	+	0.244328i	0.743095	−	0.669186i	$-0.233357\pi$
$137$	3.93617	+	2.85979i	0.336289	+	0.244328i	−0.406805	+	0.913515i	$0.633357\pi$
$138$		0			0
$139$	−1.91846	+	5.90442i	−0.162722	+	0.500807i	−0.998861	−	0.0477106i	$-0.984807\pi$
$139$	−1.91846	+	5.90442i	−0.162722	+	0.500807i	0.836139	+	0.548517i	$0.184807\pi$
$140$		0			0
$141$	1.12241	−	0.815476i	0.0945236	−	0.0686754i
$142$		0			0
$143$	−2.32317	+	21.2924i	−0.194273	+	1.78056i
$144$		0			0
$145$	1.11096	−	0.807160i	0.0922602	−	0.0670310i
$146$		0			0
$147$	0.777419	−	2.39265i	0.0641204	−	0.197342i
$148$		0			0
$149$	−5.38630	−	3.91338i	−0.441263	−	0.320596i	0.344874	−	0.938649i	$-0.387922\pi$
$149$	−5.38630	−	3.91338i	−0.441263	−	0.320596i	−0.786137	+	0.618053i	$0.787922\pi$
$150$		0			0
$151$	−3.39133	−	10.4375i	−0.275983	−	0.849388i	−0.988958	−	0.148198i	$-0.952653\pi$
$151$	−3.39133	−	10.4375i	−0.275983	−	0.849388i	0.712975	−	0.701190i	$-0.247347\pi$
$152$		0			0
$153$	−1.00000			−0.0808452
$154$		0			0
$155$	7.60929			0.611193
$156$		0			0
$157$	−6.18494	−	19.0353i	−0.493612	−	1.51918i	−0.819109	−	0.573638i	$-0.805531\pi$
$157$	−6.18494	−	19.0353i	−0.493612	−	1.51918i	0.325497	−	0.945543i	$-0.394469\pi$
$158$		0			0
$159$	7.14460	+	5.19085i	0.566604	+	0.411662i
$160$		0			0
$161$	0.500000	−	1.53884i	0.0394055	−	0.121278i
$162$		0			0
$163$	14.7367	−	10.7068i	1.15427	−	0.838624i	0.165224	−	0.986256i	$-0.447165\pi$
$163$	14.7367	−	10.7068i	1.15427	−	0.838624i	0.989042	+	0.147632i	$0.0471652\pi$
$164$		0			0
$165$	−1.64693	−	2.87882i	−0.128213	−	0.224116i
$166$		0			0
$167$	−2.51578	+	1.82782i	−0.194677	+	0.141441i	−0.680854	−	0.732419i	$-0.738391\pi$
$167$	−2.51578	+	1.82782i	−0.194677	+	0.141441i	0.486177	+	0.873860i	$0.338391\pi$
$168$		0			0
$169$	8.87052	−	27.3007i	0.682348	−	2.10005i
$170$		0			0
$171$	−1.57128	−	1.14160i	−0.120159	−	0.0873004i
$172$		0			0
$173$	4.39030	+	13.5120i	0.333788	+	1.02730i	0.967316	+	0.253575i	$0.0816064\pi$
$173$	4.39030	+	13.5120i	0.333788	+	1.02730i	−0.633527	+	0.773720i	$0.718394\pi$
$174$		0			0
$175$	3.08477			0.233186
$176$		0			0
$177$	−6.95554			−0.522810
$178$		0			0
$179$	−6.83084	−	21.0232i	−0.510561	−	1.57134i	−0.791216	−	0.611536i	$-0.790552\pi$
$179$	−6.83084	−	21.0232i	−0.510561	−	1.57134i	0.280656	−	0.959809i	$-0.409448\pi$
$180$		0			0
$181$	−15.7576	−	11.4486i	−1.17125	−	0.850965i	−0.180095	−	0.983649i	$-0.557640\pi$
$181$	−15.7576	−	11.4486i	−1.17125	−	0.850965i	−0.991158	+	0.132684i	$0.957640\pi$
$182$		0			0
$183$	−3.44642	+	10.6070i	−0.254767	+	0.784092i
$184$		0			0
$185$	2.94887	−	2.14248i	0.216805	−	0.157518i
$186$		0			0
$187$	−3.24685	+	0.676718i	−0.237433	+	0.0494866i
$188$		0			0
$189$	−2.49563	+	1.81318i	−0.181530	+	0.131889i
$190$		0			0
$191$	−5.90441	+	18.1719i	−0.427228	+	1.31487i	0.473616	+	0.880731i	$0.342948\pi$
$191$	−5.90441	+	18.1719i	−0.427228	+	1.31487i	−0.900844	+	0.434142i	$0.857052\pi$
$192$		0			0
$193$	−4.61325	−	3.35172i	−0.332069	−	0.241262i	0.409239	−	0.912427i	$-0.365794\pi$
$193$	−4.61325	−	3.35172i	−0.332069	−	0.241262i	−0.741308	+	0.671165i	$0.765794\pi$
$194$		0			0
$195$	1.99563	+	6.14191i	0.142910	+	0.439831i
$196$		0			0
$197$	−16.1035			−1.14733			−0.573663	−	0.819091i	$-0.694478\pi$
$197$	−16.1035			−1.14733			−0.573663	+	0.819091i	$0.694478\pi$
$198$		0			0
$199$	−11.3321			−0.803311			−0.401656	−	0.915791i	$-0.631565\pi$
$199$	−11.3321			−0.803311			−0.401656	+	0.915791i	$0.631565\pi$
$200$		0			0
$201$	−1.63574	−	5.03428i	−0.115376	−	0.355091i
$202$		0			0
$203$	−3.42705	−	2.48990i	−0.240532	−	0.174757i
$204$		0			0
$205$	−1.22503	+	3.77026i	−0.0855599	+	0.263326i
$206$		0			0
$207$	−0.424349	+	0.308308i	−0.0294943	+	0.0214289i
$208$		0			0
$209$	−5.87425	−	2.64330i	−0.406331	−	0.182841i
$210$		0			0
$211$	4.64693	−	3.37619i	0.319908	−	0.232427i	−0.416228	−	0.909260i	$-0.636648\pi$
$211$	4.64693	−	3.37619i	0.319908	−	0.232427i	0.736136	+	0.676833i	$0.236648\pi$
$212$		0			0
$213$	4.05754	−	12.4878i	0.278018	−	0.855652i
$214$		0			0
$215$	3.55587	+	2.58349i	0.242508	+	0.176193i
$216$		0			0
$217$	−7.25352	−	22.3240i	−0.492401	−	1.51545i
$218$		0			0
$219$	0.603886			0.0408068
$220$		0			0
$221$	6.45799			0.434411
$222$		0			0
$223$	−1.40498	−	4.32407i	−0.0940842	−	0.289561i	0.892930	−	0.450196i	$-0.148646\pi$
$223$	−1.40498	−	4.32407i	−0.0940842	−	0.289561i	−0.987014	+	0.160635i	$0.948646\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	6.49563	−	19.9915i	0.431130	−	1.32688i	−0.465871	−	0.884853i	$-0.654259\pi$
$227$	6.49563	−	19.9915i	0.431130	−	1.32688i	0.897001	−	0.442029i	$-0.145741\pi$
$228$		0			0
$229$	5.06361	−	3.67892i	0.334612	−	0.243110i	−0.407773	−	0.913083i	$-0.633694\pi$
$229$	5.06361	−	3.67892i	0.334612	−	0.243110i	0.742385	+	0.669973i	$0.233694\pi$
$230$		0			0
$231$	−6.87592	+	7.57597i	−0.452403	+	0.498462i
$232$		0			0
$233$	−15.4043	+	11.1919i	−1.00917	+	0.733206i	−0.964035	−	0.265775i	$-0.914372\pi$
$233$	−15.4043	+	11.1919i	−1.00917	+	0.733206i	−0.0451366	+	0.998981i	$0.514372\pi$
$234$		0			0
$235$	0.428721	−	1.31947i	0.0279667	−	0.0860726i
$236$		0			0
$237$	−7.76700	−	5.64306i	−0.504521	−	0.366556i
$238$		0			0
$239$	−3.71050	−	11.4197i	−0.240012	−	0.738681i	−0.996417	−	0.0845775i	$-0.973046\pi$
$239$	−3.71050	−	11.4197i	−0.240012	−	0.738681i	0.756405	−	0.654104i	$-0.226954\pi$
$240$		0			0
$241$	−15.1237			−0.974206			−0.487103	−	0.873344i	$-0.661946\pi$
$241$	−15.1237			−0.974206			−0.487103	+	0.873344i	$0.661946\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−0.777419	−	2.39265i	−0.0496675	−	0.152861i
$246$		0			0
$247$	10.1473	+	7.37245i	0.645657	+	0.469097i
$248$		0			0
$249$	−2.40379	+	7.39810i	−0.152334	+	0.468835i
$250$		0			0
$251$	−13.1419	+	9.54812i	−0.829507	+	0.602672i	−0.919420	−	0.393278i	$-0.871341\pi$
$251$	−13.1419	+	9.54812i	−0.829507	+	0.602672i	0.0899130	+	0.995950i	$0.471341\pi$
$252$		0			0
$253$	−1.16916	+	1.28819i	−0.0735045	+	0.0809881i
$254$		0			0
$255$	−0.809017	+	0.587785i	−0.0506626	+	0.0368085i
$256$		0			0
$257$	−1.84417	+	5.67577i	−0.115036	+	0.354045i	−0.991955	−	0.126594i	$-0.959595\pi$
$257$	−1.84417	+	5.67577i	−0.115036	+	0.354045i	0.876918	+	0.480639i	$0.159595\pi$
$258$		0			0
$259$	−9.09658	−	6.60905i	−0.565234	−	0.410667i
$260$		0			0
$261$	0.424349	+	1.30601i	0.0262665	+	0.0808401i
$262$		0			0
$263$	−18.1210			−1.11739			−0.558694	−	0.829374i	$-0.688697\pi$
$263$	−18.1210			−1.11739			−0.558694	+	0.829374i	$0.688697\pi$
$264$		0			0
$265$	8.83121			0.542497
$266$		0			0
$267$	0.642558	+	1.97759i	0.0393239	+	0.121027i
$268$		0			0
$269$	19.0066	+	13.8091i	1.15885	+	0.841954i	0.989632	−	0.143625i	$-0.0458759\pi$
$269$	19.0066	+	13.8091i	1.15885	+	0.841954i	0.169218	+	0.985579i	$0.445876\pi$
$270$		0			0
$271$	−9.87884	+	30.4039i	−0.600097	+	1.84691i	−0.0725817	+	0.997362i	$0.523124\pi$
$271$	−9.87884	+	30.4039i	−0.600097	+	1.84691i	−0.527515	+	0.849546i	$0.676876\pi$
$272$		0			0
$273$	16.1167	−	11.7095i	0.975429	−	0.708691i
$274$		0			0
$275$	−3.02452	−	1.36098i	−0.182386	−	0.0820699i
$276$		0			0
$277$	−20.2004	+	14.6765i	−1.21373	+	0.881824i	−0.995564	−	0.0940888i	$-0.970006\pi$
$277$	−20.2004	+	14.6765i	−1.21373	+	0.881824i	−0.218162	+	0.975912i	$0.570006\pi$
$278$		0			0
$279$	−2.35140	+	7.23686i	−0.140775	+	0.433260i
$280$		0			0
$281$	4.09747	+	2.97699i	0.244435	+	0.177592i	0.703257	−	0.710936i	$-0.251728\pi$
$281$	4.09747	+	2.97699i	0.244435	+	0.177592i	−0.458822	+	0.888528i	$0.651728\pi$
$282$		0			0
$283$	2.31245	+	7.11700i	0.137461	+	0.423062i	0.995965	−	0.0897458i	$-0.0286055\pi$
$283$	2.31245	+	7.11700i	0.137461	+	0.423062i	−0.858504	+	0.512808i	$0.828605\pi$
$284$		0			0
$285$	−1.94221			−0.115046
$286$		0			0
$287$	12.2289			0.721848
$288$		0			0
$289$	−4.94427	−	15.2169i	−0.290840	−	0.895112i
$290$		0			0
$291$	−5.43305	−	3.94735i	−0.318491	−	0.231397i
$292$		0			0
$293$	−4.42831	+	13.6289i	−0.258705	+	0.796211i	0.734372	+	0.678747i	$0.237477\pi$
$293$	−4.42831	+	13.6289i	−0.258705	+	0.796211i	−0.993077	+	0.117465i	$0.962523\pi$
$294$		0			0
$295$	−5.62715	+	4.08836i	−0.327625	+	0.238034i
$296$		0			0
$297$	3.24685	−	0.676718i	0.188401	−	0.0392672i
$298$		0			0
$299$	2.74044	−	1.99105i	0.158484	−	0.115145i
$300$		0			0
$301$	4.18979	−	12.8949i	0.241496	−	0.743248i
$302$		0			0
$303$	12.6890	+	9.21911i	0.728965	+	0.529624i
$304$		0			0
$305$	3.44642	+	10.6070i	0.197342	+	0.607355i
$306$		0			0
$307$	−5.18776			−0.296081			−0.148041	−	0.988981i	$-0.547297\pi$
$307$	−5.18776			−0.296081			−0.148041	+	0.988981i	$0.547297\pi$
$308$		0			0
$309$	−14.8042			−0.842184
$310$		0			0
$311$	−8.92445	−	27.4666i	−0.506059	−	1.55749i	−0.798983	−	0.601353i	$-0.794628\pi$
$311$	−8.92445	−	27.4666i	−0.506059	−	1.55749i	0.292924	−	0.956136i	$-0.405372\pi$
$312$		0			0
$313$	25.1202	+	18.2509i	1.41988	+	1.03160i	0.991792	+	0.127865i	$0.0408123\pi$
$313$	25.1202	+	18.2509i	1.41988	+	1.03160i	0.428087	+	0.903738i	$0.359188\pi$
$314$		0			0
$315$	−0.953245	+	2.93379i	−0.0537093	+	0.165300i
$316$		0			0
$317$	1.37322	−	0.997704i	0.0771278	−	0.0560366i	−0.548553	−	0.836116i	$-0.684821\pi$
$317$	1.37322	−	0.997704i	0.0771278	−	0.0560366i	0.625681	+	0.780079i	$0.284821\pi$
$318$		0			0
$319$	2.26160	+	3.95326i	0.126625	+	0.221340i
$320$		0			0
$321$	−4.18931	+	3.04371i	−0.233825	+	0.169884i
$322$		0			0
$323$	−0.600175	+	1.84715i	−0.0333946	+	0.102778i
$324$		0			0
$325$	5.22462	+	3.79591i	0.289810	+	0.210559i
$326$		0			0
$327$	1.63486	+	5.03158i	0.0904080	+	0.278247i
$328$		0			0
$329$	−4.27971			−0.235948
$330$		0			0
$331$	−23.3241			−1.28201			−0.641004	−	0.767537i	$-0.721482\pi$
$331$	−23.3241			−1.28201			−0.641004	+	0.767537i	$0.721482\pi$
$332$		0			0
$333$	1.12637	+	3.46661i	0.0617247	+	0.189969i
$334$		0			0
$335$	−4.28241	−	3.11136i	−0.233973	−	0.169992i
$336$		0			0
$337$	5.43220	−	16.7186i	0.295911	−	0.910720i	−0.687003	−	0.726655i	$-0.741074\pi$
$337$	5.43220	−	16.7186i	0.295911	−	0.910720i	0.982914	−	0.184066i	$-0.0589259\pi$
$338$		0			0
$339$	−9.90249	+	7.19458i	−0.537829	+	0.390756i
$340$		0			0
$341$	−2.73733	+	25.0883i	−0.148235	+	1.35861i
$342$		0			0
$343$	11.1909	−	8.13070i	0.604254	−	0.439016i
$344$		0			0
$345$	−0.162087	+	0.498852i	−0.00872646	+	0.0268573i
$346$		0			0
$347$	−26.0472	−	18.9244i	−1.39829	−	1.01592i	−0.994898	−	0.100887i	$-0.967832\pi$
$347$	−26.0472	−	18.9244i	−1.39829	−	1.01592i	−0.403389	−	0.915028i	$-0.632168\pi$
$348$		0			0
$349$	4.43076	+	13.6365i	0.237173	+	0.729944i	0.996826	+	0.0796149i	$0.0253691\pi$
$349$	4.43076	+	13.6365i	0.237173	+	0.729944i	−0.759652	+	0.650329i	$0.774631\pi$
$350$		0			0
$351$	−6.45799			−0.344702
$352$		0			0
$353$	5.33128			0.283756			0.141878	−	0.989884i	$-0.454686\pi$
$353$	5.33128			0.283756			0.141878	+	0.989884i	$0.454686\pi$
$354$		0			0
$355$	−4.05754	−	12.4878i	−0.215352	−	0.662785i
$356$		0			0
$357$	2.49563	+	1.81318i	0.132083	+	0.0959637i
$358$		0			0
$359$	5.92577	−	18.2376i	0.312750	−	0.962545i	−0.663921	−	0.747803i	$-0.731109\pi$
$359$	5.92577	−	18.2376i	0.312750	−	0.962545i	0.976671	−	0.214742i	$-0.0688912\pi$
$360$		0			0
$361$	12.3196	−	8.95069i	0.648399	−	0.471089i
$362$		0			0
$363$	10.0841	−	4.39441i	0.529278	−	0.230647i
$364$		0			0
$365$	0.488554	−	0.354955i	0.0255721	−	0.0185792i
$366$		0			0
$367$	3.53172	−	10.8695i	0.184354	−	0.567384i	−0.815583	−	0.578641i	$-0.803583\pi$
$367$	3.53172	−	10.8695i	0.184354	−	0.567384i	0.999937	+	0.0112572i	$0.00358336\pi$
$368$		0			0
$369$	−3.20717	−	2.33015i	−0.166959	−	0.121303i
$370$		0			0
$371$	−8.41831	−	25.9089i	−0.437057	−	1.34512i
$372$		0			0
$373$	−35.4156			−1.83375			−0.916875	−	0.399175i	$-0.869297\pi$
$373$	−35.4156			−1.83375			−0.916875	+	0.399175i	$0.869297\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−2.74044	−	8.43421i	−0.141140	−	0.434384i
$378$		0			0
$379$	5.66271	+	4.11420i	0.290874	+	0.211332i	0.723646	−	0.690171i	$-0.242465\pi$
$379$	5.66271	+	4.11420i	0.290874	+	0.211332i	−0.432773	+	0.901503i	$0.642465\pi$
$380$		0			0
$381$	−0.310687	+	0.956196i	−0.0159170	+	0.0489874i
$382$		0			0
$383$	−14.3591	+	10.4325i	−0.733716	+	0.533076i	−0.890737	−	0.454520i	$-0.849811\pi$
$383$	−14.3591	+	10.4325i	−0.733716	+	0.533076i	0.157021	+	0.987595i	$0.449811\pi$
$384$		0			0
$385$	−1.10970	+	10.1707i	−0.0565555	+	0.518344i
$386$		0			0
$387$	−3.55587	+	2.58349i	−0.180755	+	0.131326i
$388$		0			0
$389$	8.94789	−	27.5388i	0.453676	−	1.39627i	−0.419007	−	0.907983i	$-0.637622\pi$
$389$	8.94789	−	27.5388i	0.453676	−	1.39627i	0.872683	−	0.488288i	$-0.162378\pi$
$390$		0			0
$391$	0.424349	+	0.308308i	0.0214602	+	0.0155918i
$392$		0			0
$393$	−3.49641	−	10.7608i	−0.176370	−	0.542812i
$394$		0			0
$395$	−9.60055			−0.483056
$396$		0			0
$397$	−38.7875			−1.94669			−0.973344	−	0.229349i	$-0.926340\pi$
$397$	−38.7875			−1.94669			−0.973344	+	0.229349i	$0.926340\pi$
$398$		0			0
$399$	1.85140	+	5.69802i	0.0926859	+	0.285258i
$400$		0			0
$401$	−10.1897	−	7.40327i	−0.508850	−	0.369701i	0.303537	−	0.952820i	$-0.401832\pi$
$401$	−10.1897	−	7.40327i	−0.508850	−	0.369701i	−0.812387	+	0.583118i	$0.801832\pi$
$402$		0			0
$403$	15.1853	−	46.7356i	0.756434	−	2.32807i
$404$		0			0
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$		0			0
$407$	6.00307	+	10.4933i	0.297561	+	0.520135i
$408$		0			0
$409$	−31.2913	+	22.7344i	−1.54725	+	1.12415i	−0.601679	+	0.798738i	$0.705502\pi$
$409$	−31.2913	+	22.7344i	−1.54725	+	1.12415i	−0.945574	+	0.325408i	$0.894498\pi$
$410$		0			0
$411$	−1.50348	+	4.62724i	−0.0741613	+	0.228245i
$412$		0			0
$413$	17.3584	+	12.6116i	0.854153	+	0.620578i
$414$		0			0
$415$	2.40379	+	7.39810i	0.117997	+	0.363158i
$416$		0			0
$417$	−6.20828			−0.304021
$418$		0			0
$419$	5.97005			0.291656			0.145828	−	0.989310i	$-0.453415\pi$
$419$	5.97005			0.291656			0.145828	+	0.989310i	$0.453415\pi$
$420$		0			0
$421$	−4.71566	−	14.5133i	−0.229827	−	0.707336i	−0.997766	−	0.0668120i	$-0.978717\pi$
$421$	−4.71566	−	14.5133i	−0.229827	−	0.707336i	0.767938	−	0.640524i	$-0.221283\pi$
$422$		0			0
$423$	1.12241	+	0.815476i	0.0545732	+	0.0396498i
$424$		0			0
$425$	−0.309017	+	0.951057i	−0.0149895	+	0.0461330i
$426$		0			0
$427$	27.8334	−	20.2221i	1.34695	−	0.978618i
$428$		0			0
$429$	−20.9681	+	4.37024i	−1.01235	+	0.210997i
$430$		0			0
$431$	−17.1281	+	12.4443i	−0.825034	+	0.599422i	−0.918150	−	0.396233i	$-0.870317\pi$
$431$	−17.1281	+	12.4443i	−0.825034	+	0.599422i	0.0931163	+	0.995655i	$0.470317\pi$
$432$		0			0
$433$	−2.98276	+	9.18001i	−0.143343	+	0.441163i	−0.996794	−	0.0800092i	$-0.974505\pi$
$433$	−2.98276	+	9.18001i	−0.143343	+	0.441163i	0.853452	+	0.521172i	$0.174505\pi$
$434$		0			0
$435$	1.11096	+	0.807160i	0.0532664	+	0.0387003i
$436$		0			0
$437$	0.314806	+	0.968874i	0.0150592	+	0.0463475i
$438$		0			0
$439$	30.9383			1.47660			0.738302	−	0.674470i	$-0.235628\pi$
$439$	30.9383			1.47660			0.738302	+	0.674470i	$0.235628\pi$
$440$		0			0
$441$	2.51578			0.119799
$442$		0			0
$443$	5.68827	+	17.5067i	0.270258	+	0.831768i	0.990435	+	0.137978i	$0.0440603\pi$
$443$	5.68827	+	17.5067i	0.270258	+	0.831768i	−0.720178	+	0.693790i	$0.755940\pi$
$444$		0			0
$445$	1.68224	+	1.22222i	0.0797458	+	0.0579387i
$446$		0			0
$447$	2.05738	−	6.33198i	0.0973109	−	0.299492i
$448$		0			0
$449$	−11.8075	+	8.57863i	−0.557229	+	0.404850i	−0.830444	−	0.557103i	$-0.811913\pi$
$449$	−11.8075	+	8.57863i	−0.557229	+	0.404850i	0.273215	+	0.961953i	$0.411913\pi$
$450$		0			0
$451$	−11.9901	−	5.39529i	−0.564590	−	0.254054i
$452$		0			0
$453$	8.87863	−	6.45070i	0.417154	−	0.303080i
$454$		0			0
$455$	6.15604	−	18.9464i	0.288600	−	0.888219i
$456$		0			0
$457$	22.0862	+	16.0465i	1.03315	+	0.750626i	0.968936	−	0.247311i	$-0.0795469\pi$
$457$	22.0862	+	16.0465i	1.03315	+	0.750626i	0.0642112	+	0.997936i	$0.479547\pi$
$458$		0			0
$459$	−0.309017	−	0.951057i	−0.0144237	−	0.0443915i
$460$		0			0
$461$	10.2090			0.475481			0.237741	−	0.971329i	$-0.423593\pi$
$461$	10.2090			0.475481			0.237741	+	0.971329i	$0.423593\pi$
$462$		0			0
$463$	28.7077			1.33416			0.667079	−	0.744987i	$-0.267544\pi$
$463$	28.7077			1.33416			0.667079	+	0.744987i	$0.267544\pi$
$464$		0			0
$465$	2.35140	+	7.23686i	0.109044	+	0.335602i
$466$		0			0
$467$	11.0326	+	8.01568i	0.510529	+	0.370921i	0.813024	−	0.582230i	$-0.197820\pi$
$467$	11.0326	+	8.01568i	0.510529	+	0.370921i	−0.302495	+	0.953151i	$0.597820\pi$
$468$		0			0
$469$	−5.04586	+	15.5296i	−0.232996	+	0.717089i
$470$		0			0
$471$	16.1924	−	11.7645i	0.746106	−	0.542078i
$472$		0			0
$473$	−9.79709	+	10.7945i	−0.450471	+	0.496333i
$474$		0			0
$475$	−1.57128	+	1.14160i	−0.0720952	+	0.0523802i
$476$		0			0
$477$	−2.72899	+	8.39898i	−0.124952	+	0.384563i
$478$		0			0
$479$	15.7961	+	11.4765i	0.721741	+	0.524376i	0.886940	−	0.461885i	$-0.152827\pi$
$479$	15.7961	+	11.4765i	0.721741	+	0.524376i	−0.165199	+	0.986260i	$0.552827\pi$
$480$		0			0
$481$	−7.27408	−	22.3873i	−0.331669	−	1.02077i
$482$		0			0
$483$	1.61803			0.0736231
$484$		0			0
$485$	−6.71563			−0.304941
$486$		0			0
$487$	5.31247	+	16.3501i	0.240731	+	0.740894i	0.996309	+	0.0858359i	$0.0273561\pi$
$487$	5.31247	+	16.3501i	0.240731	+	0.740894i	−0.755578	+	0.655059i	$0.772644\pi$
$488$		0			0
$489$	14.7367	+	10.7068i	0.666416	+	0.484180i
$490$		0			0
$491$	9.54286	−	29.3699i	0.430663	−	1.32545i	−0.466802	−	0.884362i	$-0.654594\pi$
$491$	9.54286	−	29.3699i	0.430663	−	1.32545i	0.897466	−	0.441084i	$-0.145406\pi$
$492$		0			0
$493$	1.11096	−	0.807160i	0.0500351	−	0.0363526i
$494$		0			0
$495$	2.22899	−	2.45593i	0.100186	−	0.110386i
$496$		0			0
$497$	−32.7688	+	23.8079i	−1.46988	+	1.06793i
$498$		0			0
$499$	−13.7555	+	42.3350i	−0.615780	+	1.89518i	−0.226741	+	0.973955i	$0.572807\pi$
$499$	−13.7555	+	42.3350i	−0.615780	+	1.89518i	−0.389039	+	0.921221i	$0.627193\pi$
$500$		0			0
$501$	−2.51578	−	1.82782i	−0.112397	−	0.0816610i
$502$		0			0
$503$	7.74827	+	23.8467i	0.345478	+	1.06327i	0.961327	+	0.275409i	$0.0888131\pi$
$503$	7.74827	+	23.8467i	0.345478	+	1.06327i	−0.615849	+	0.787864i	$0.711187\pi$
$504$		0			0
$505$	15.6845			0.697951
$506$		0			0
$507$	28.7056			1.27486
$508$		0			0
$509$	−8.22295	−	25.3076i	−0.364476	−	1.12174i	−0.950309	−	0.311310i	$-0.899232\pi$
$509$	−8.22295	−	25.3076i	−0.364476	−	1.12174i	0.585833	−	0.810432i	$-0.300768\pi$
$510$		0			0
$511$	−1.50707	−	1.09495i	−0.0666690	−	0.0484379i
$512$		0			0
$513$	0.600175	−	1.84715i	0.0264984	−	0.0815536i
$514$		0			0
$515$	−11.9769	+	8.70171i	−0.527764	+	0.383443i
$516$		0			0
$517$	4.19613	+	1.88818i	0.184546	+	0.0830419i
$518$		0			0
$519$	−11.4940	+	8.35085i	−0.504529	+	0.366562i
$520$		0			0
$521$	−3.50235	+	10.7791i	−0.153441	+	0.472242i	−0.998000	−	0.0632205i	$-0.979863\pi$
$521$	−3.50235	+	10.7791i	−0.153441	+	0.472242i	0.844559	+	0.535463i	$0.179863\pi$
$522$		0			0
$523$	−6.79627	−	4.93778i	−0.297180	−	0.215914i	0.429196	−	0.903211i	$-0.358797\pi$
$523$	−6.79627	−	4.93778i	−0.297180	−	0.215914i	−0.726376	+	0.687297i	$0.758797\pi$
$524$		0			0
$525$	0.953245	+	2.93379i	0.0416030	+	0.128041i
$526$		0			0
$527$	7.60929			0.331466
$528$		0			0
$529$	−22.7249			−0.988038
$530$		0			0
$531$	−2.14938	−	6.61511i	−0.0932751	−	0.287071i
$532$		0			0
$533$	20.7119	+	15.0481i	0.897131	+	0.651804i
$534$		0			0
$535$	−1.60018	+	4.92483i	−0.0691816	+	0.212919i
$536$		0			0
$537$	17.8834	−	12.9930i	0.771724	−	0.560691i
$538$		0			0
$539$	8.16837	−	1.70247i	0.351836	−	0.0733308i
$540$		0			0
$541$	−24.0889	+	17.5016i	−1.03566	+	0.752453i	−0.969434	−	0.245351i	$-0.921097\pi$
$541$	−24.0889	+	17.5016i	−1.03566	+	0.752453i	−0.0662288	+	0.997804i	$0.521097\pi$
$542$		0			0
$543$	6.01887	−	18.5242i	0.258294	−	0.794948i
$544$		0			0
$545$	4.28012	+	3.10969i	0.183340	+	0.133204i
$546$		0			0
$547$	4.19639	+	12.9152i	0.179425	+	0.552212i	0.999808	−	0.0196020i	$-0.00623990\pi$
$547$	4.19639	+	12.9152i	0.179425	+	0.552212i	−0.820383	+	0.571814i	$0.806240\pi$
$548$		0			0
$549$	−11.1529			−0.475993
$550$		0			0
$551$	2.66708			0.113622
$552$		0			0
$553$	9.15167	+	28.1660i	0.389169	+	1.19774i
$554$		0			0
$555$	2.94887	+	2.14248i	0.125173	+	0.0909433i
$556$		0			0
$557$	12.3211	−	37.9203i	0.522060	−	1.60674i	−0.247997	−	0.968761i	$-0.579772\pi$
$557$	12.3211	−	37.9203i	0.522060	−	1.60674i	0.770057	−	0.637975i	$-0.220228\pi$
$558$		0			0
$559$	22.9638	−	16.6842i	0.971264	−	0.705664i
$560$		0			0
$561$	−1.64693	−	2.87882i	−0.0695334	−	0.121544i
$562$		0			0
$563$	20.8831	−	15.1725i	0.880118	−	0.639443i	−0.0531644	−	0.998586i	$-0.516931\pi$
$563$	20.8831	−	15.1725i	0.880118	−	0.639443i	0.933283	+	0.359142i	$0.116931\pi$
$564$		0			0
$565$	−3.78241	+	11.6411i	−0.159127	+	0.489744i
$566$		0			0
$567$	−2.49563	−	1.81318i	−0.104807	−	0.0761464i
$568$		0			0
$569$	7.66100	+	23.5781i	0.321166	+	0.988446i	0.973142	+	0.230207i	$0.0739402\pi$
$569$	7.66100	+	23.5781i	0.321166	+	0.988446i	−0.651976	+	0.758239i	$0.726060\pi$
$570$		0			0
$571$	−7.66626			−0.320823			−0.160412	−	0.987050i	$-0.551282\pi$
$571$	−7.66626			−0.320823			−0.160412	+	0.987050i	$0.551282\pi$
$572$		0			0
$573$	−19.1071			−0.798210
$574$		0			0
$575$	0.162087	+	0.498852i	0.00675949	+	0.0208036i
$576$		0			0
$577$	13.7745	+	10.0078i	0.573440	+	0.416629i	0.836353	−	0.548191i	$-0.184683\pi$
$577$	13.7745	+	10.0078i	0.573440	+	0.416629i	−0.262913	+	0.964820i	$0.584683\pi$
$578$		0			0
$579$	1.76211	−	5.42320i	0.0732306	−	0.225381i
$580$		0			0
$581$	19.4130	−	14.1044i	0.805389	−	0.585149i
$582$		0			0
$583$	−3.17690	+	29.1170i	−0.131574	+	1.20590i
$584$		0			0
$585$	−5.22462	+	3.79591i	−0.216012	+	0.156942i
$586$		0			0
$587$	1.56556	−	4.81831i	0.0646177	−	0.198873i	−0.913535	−	0.406760i	$-0.866659\pi$
$587$	1.56556	−	4.81831i	0.0646177	−	0.198873i	0.978153	+	0.207887i	$0.0666586\pi$
$588$		0			0
$589$	11.9563	+	8.68677i	0.492651	+	0.357932i
$590$		0			0
$591$	−4.97626	−	15.3153i	−0.204696	−	0.629989i
$592$		0			0
$593$	−8.21229			−0.337238			−0.168619	−	0.985681i	$-0.553931\pi$
$593$	−8.21229			−0.337238			−0.168619	+	0.985681i	$0.553931\pi$
$594$		0			0
$595$	3.08477			0.126463
$596$		0			0
$597$	−3.50181	−	10.7775i	−0.143320	−	0.441092i
$598$		0			0
$599$	10.3246	+	7.50127i	0.421852	+	0.306493i	0.778383	−	0.627790i	$-0.216040\pi$
$599$	10.3246	+	7.50127i	0.421852	+	0.306493i	−0.356531	+	0.934284i	$0.616040\pi$
$600$		0			0
$601$	6.27106	−	19.3004i	0.255802	−	0.787278i	−0.737869	−	0.674944i	$-0.764168\pi$
$601$	6.27106	−	19.3004i	0.255802	−	0.787278i	0.993671	−	0.112333i	$-0.0358324\pi$
$602$		0			0
$603$	4.28241	−	3.11136i	0.174393	−	0.126704i
$604$		0			0
$605$	5.57524	−	9.48244i	0.226666	−	0.385516i
$606$		0			0
$607$	23.3548	−	16.9682i	0.947941	−	0.688720i	−0.00237774	−	0.999997i	$-0.500757\pi$
$607$	23.3548	−	16.9682i	0.947941	−	0.688720i	0.950319	+	0.311277i	$0.100757\pi$
$608$		0			0
$609$	1.30902	−	4.02874i	0.0530440	−	0.163253i
$610$		0			0
$611$	−7.24848	−	5.26633i	−0.293242	−	0.213053i
$612$		0			0
$613$	0.358309	+	1.10276i	0.0144720	+	0.0445401i	0.958032	−	0.286662i	$-0.0925457\pi$
$613$	0.358309	+	1.10276i	0.0144720	+	0.0445401i	−0.943560	+	0.331202i	$0.892546\pi$
$614$		0			0
$615$	−3.96428			−0.159855
$616$		0			0
$617$	−26.4380			−1.06435			−0.532176	−	0.846633i	$-0.678626\pi$
$617$	−26.4380			−1.06435			−0.532176	+	0.846633i	$0.678626\pi$
$618$		0			0
$619$	−3.38888	−	10.4299i	−0.136211	−	0.419214i	0.859566	−	0.511025i	$-0.170734\pi$
$619$	−3.38888	−	10.4299i	−0.136211	−	0.419214i	−0.995776	+	0.0918118i	$0.970734\pi$
$620$		0			0
$621$	−0.424349	−	0.308308i	−0.0170285	−	0.0123720i
$622$		0			0
$623$	1.98214	−	6.10040i	0.0794128	−	0.244407i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	0.698680	−	6.40357i	0.0279026	−	0.255734i
$628$		0			0
$629$	2.94887	−	2.14248i	0.117579	−	0.0854263i
$630$		0			0
$631$	−12.7044	+	39.1002i	−0.505755	+	1.55655i	0.293744	+	0.955884i	$0.405099\pi$
$631$	−12.7044	+	39.1002i	−0.505755	+	1.55655i	−0.799498	+	0.600668i	$0.794901\pi$
$632$		0			0
$633$	4.64693	+	3.37619i	0.184699	+	0.134192i
$634$		0			0
$635$	0.310687	+	0.956196i	0.0123292	+	0.0379455i
$636$		0			0
$637$	−16.2469			−0.643725
$638$		0			0
$639$	13.1305			0.519434
$640$		0			0
$641$	−1.26654	−	3.89800i	−0.0500252	−	0.153962i	0.922923	−	0.384984i	$-0.125793\pi$
$641$	−1.26654	−	3.89800i	−0.0500252	−	0.153962i	−0.972948	+	0.231022i	$0.925793\pi$
$642$		0			0
$643$	−4.92635	−	3.57920i	−0.194276	−	0.141150i	0.486395	−	0.873739i	$-0.338312\pi$
$643$	−4.92635	−	3.57920i	−0.194276	−	0.141150i	−0.680671	+	0.732589i	$0.738312\pi$
$644$		0			0
$645$	−1.35822	+	4.18018i	−0.0534799	+	0.164594i
$646$		0			0
$647$	−11.2162	+	8.14902i	−0.440953	+	0.320371i	−0.786014	−	0.618209i	$-0.787858\pi$
$647$	−11.2162	+	8.14902i	−0.440953	+	0.320371i	0.345060	+	0.938580i	$0.387858\pi$
$648$		0			0
$649$	−11.4553	−	20.0238i	−0.449659	−	0.786001i
$650$		0			0
$651$	18.9900	−	13.7970i	0.744275	−	0.540747i
$652$		0			0
$653$	8.70393	−	26.7879i	0.340611	−	1.04829i	−0.623281	−	0.781998i	$-0.714201\pi$
$653$	8.70393	−	26.7879i	0.340611	−	1.04829i	0.963892	−	0.266295i	$-0.0857994\pi$
$654$		0			0
$655$	−9.15371	−	6.65056i	−0.357665	−	0.259859i
$656$		0			0
$657$	0.186611	+	0.574329i	0.00728039	+	0.0224067i
$658$		0			0
$659$	43.0065			1.67530			0.837648	−	0.546210i	$-0.183930\pi$
$659$	43.0065			1.67530			0.837648	+	0.546210i	$0.183930\pi$
$660$		0			0
$661$	20.3342			0.790907			0.395454	−	0.918486i	$-0.370587\pi$
$661$	20.3342			0.790907			0.395454	+	0.918486i	$0.370587\pi$
$662$		0			0
$663$	1.99563	+	6.14191i	0.0775038	+	0.238532i
$664$		0			0
$665$	4.84703	+	3.52157i	0.187960	+	0.136561i
$666$		0			0
$667$	0.222581	−	0.685035i	0.00861838	−	0.0265246i
$668$		0			0
$669$	3.67828	−	2.67242i	0.142210	−	0.103322i
$670$		0			0
$671$	−36.2117	+	7.54735i	−1.39794	+	0.291362i
$672$		0			0
$673$	−21.1155	+	15.3413i	−0.813942	+	0.591363i	−0.914971	−	0.403520i	$-0.867786\pi$
$673$	−21.1155	+	15.3413i	−0.813942	+	0.591363i	0.101029	+	0.994883i	$0.467786\pi$
$674$		0			0
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$		0			0
$677$	30.9993	+	22.5223i	1.19140	+	0.865601i	0.993411	−	0.114603i	$-0.0365597\pi$
$677$	30.9993	+	22.5223i	1.19140	+	0.865601i	0.197987	+	0.980205i	$0.436560\pi$
$678$		0			0
$679$	6.40164	+	19.7022i	0.245672	+	0.756101i
$680$		0			0
$681$	21.0203			0.805499
$682$		0			0
$683$	10.1783			0.389463			0.194731	−	0.980857i	$-0.437616\pi$
$683$	10.1783			0.389463			0.194731	+	0.980857i	$0.437616\pi$
$684$		0			0
$685$	1.50348	+	4.62724i	0.0574451	+	0.176798i
$686$		0			0
$687$	5.06361	+	3.67892i	0.193189	+	0.140360i
$688$		0			0
$689$	17.6238	−	54.2405i	0.671414	−	2.06640i
$690$		0			0
$691$	32.9899	−	23.9686i	1.25500	−	0.911808i	0.256495	−	0.966546i	$-0.417432\pi$
$691$	32.9899	−	23.9686i	1.25500	−	0.911808i	0.998501	+	0.0547379i	$0.0174323\pi$
$692$		0			0
$693$	−9.32995	−	4.19829i	−0.354415	−	0.159480i
$694$		0			0
$695$	−5.02260	+	3.64913i	−0.190518	+	0.138420i
$696$		0			0
$697$	−1.22503	+	3.77026i	−0.0464013	+	0.142809i
$698$		0			0
$699$	−15.4043	−	11.1919i	−0.582646	−	0.423317i
$700$		0			0
$701$	12.8909	+	39.6742i	0.486884	+	1.49847i	0.829234	+	0.558901i	$0.188777\pi$
$701$	12.8909	+	39.6742i	0.486884	+	1.49847i	−0.342351	+	0.939572i	$0.611223\pi$
$702$		0			0
$703$	7.07936			0.267003
$704$		0			0
$705$	1.38737			0.0522514
$706$		0			0
$707$	−14.9512	−	46.0150i	−0.562296	−	1.73057i
$708$		0			0
$709$	7.37629	+	5.35919i	0.277023	+	0.201269i	0.717618	−	0.696437i	$-0.245233\pi$
$709$	7.37629	+	5.35919i	0.277023	+	0.201269i	−0.440595	+	0.897706i	$0.645233\pi$
$710$		0			0
$711$	2.96673	−	9.13066i	0.111261	−	0.342427i
$712$		0			0
$713$	3.22899	−	2.34600i	0.120927	−	0.0878584i
$714$		0			0
$715$	−14.3948	+	15.8604i	−0.538336	+	0.593144i
$716$		0			0
$717$	9.71421	−	7.05779i	0.362784	−	0.263578i
$718$		0			0
$719$	15.1738	−	46.7001i	0.565886	−	1.74162i	−0.0994179	−	0.995046i	$-0.531698\pi$
$719$	15.1738	−	46.7001i	0.565886	−	1.74162i	0.665304	−	0.746573i	$-0.268302\pi$
$720$		0			0
$721$	36.9459	+	26.8427i	1.37594	+	0.999676i
$722$		0			0
$723$	−4.67349	−	14.3835i	−0.173809	−	0.534930i
$724$		0			0
$725$	1.37322			0.0510002
$726$		0			0
$727$	11.3373			0.420477			0.210238	−	0.977650i	$-0.432576\pi$
$727$	11.3373			0.420477			0.210238	+	0.977650i	$0.432576\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	3.55587	+	2.58349i	0.131519	+	0.0955538i
$732$		0			0
$733$	0.315727	−	0.971709i	0.0116617	−	0.0358909i	−0.945056	−	0.326907i	$-0.893993\pi$
$733$	0.315727	−	0.971709i	0.0116617	−	0.0358909i	0.956718	+	0.291017i	$0.0939935\pi$
$734$		0			0
$735$	2.03531	−	1.47874i	0.0750735	−	0.0545441i
$736$		0			0
$737$	11.7989	−	13.0001i	0.434616	−	0.478865i
$738$		0			0
$739$	−7.50500	+	5.45270i	−0.276076	+	0.200581i	−0.717204	−	0.696863i	$-0.754578\pi$
$739$	−7.50500	+	5.45270i	−0.276076	+	0.200581i	0.441128	+	0.897444i	$0.354578\pi$
$740$		0			0
$741$	−3.87592	+	11.9289i	−0.142386	+	0.438218i
$742$		0			0
$743$	22.6163	+	16.4317i	0.829711	+	0.602820i	0.919478	−	0.393142i	$-0.128612\pi$
$743$	22.6163	+	16.4317i	0.829711	+	0.602820i	−0.0897665	+	0.995963i	$0.528612\pi$
$744$		0			0
$745$	−2.05738	−	6.33198i	−0.0753767	−	0.231986i
$746$		0			0
$747$	−7.77882			−0.284612
$748$		0			0
$749$	15.9738			0.583669
$750$		0			0
$751$	12.0920	+	37.2155i	0.441245	+	1.35801i	0.886550	+	0.462633i	$0.153095\pi$
$751$	12.0920	+	37.2155i	0.441245	+	1.35801i	−0.445305	+	0.895379i	$0.646905\pi$
$752$		0			0
$753$	−13.1419	−	9.54812i	−0.478916	−	0.347953i
$754$		0			0
$755$	3.39133	−	10.4375i	0.123423	−	0.379858i
$756$		0			0
$757$	−2.48830	+	1.80786i	−0.0904388	+	0.0657077i	−0.632086	−	0.774898i	$-0.717801\pi$
$757$	−2.48830	+	1.80786i	−0.0904388	+	0.0657077i	0.541647	+	0.840606i	$0.317801\pi$
$758$		0			0
$759$	−1.58644	−	0.713864i	−0.0575840	−	0.0259116i
$760$		0			0
$761$	−35.2919	+	25.6411i	−1.27933	+	0.929489i	−0.999533	−	0.0305702i	$-0.990268\pi$
$761$	−35.2919	+	25.6411i	−1.27933	+	0.929489i	−0.279799	+	0.960059i	$0.590268\pi$
$762$		0			0
$763$	5.04316	−	15.5213i	0.182575	−	0.561907i
$764$		0			0
$765$	−0.809017	−	0.587785i	−0.0292501	−	0.0212514i
$766$		0			0
$767$	13.8807	+	42.7203i	0.501202	+	1.54254i
$768$		0			0
$769$	−28.7066			−1.03519			−0.517593	−	0.855627i	$-0.673172\pi$
$769$	−28.7066			−1.03519			−0.517593	+	0.855627i	$0.673172\pi$
$770$		0			0
$771$	−5.96786			−0.214927
$772$		0			0
$773$	−7.56391	−	23.2793i	−0.272055	−	0.837299i	−0.989984	−	0.141182i	$-0.954910\pi$
$773$	−7.56391	−	23.2793i	−0.272055	−	0.837299i	0.717929	−	0.696117i	$-0.245090\pi$
$774$		0			0
$775$	6.15604	+	4.47263i	0.221132	+	0.160662i
$776$		0			0
$777$	3.47459	−	10.6937i	0.124650	−	0.383633i
$778$		0			0
$779$	−6.22899	+	4.52563i	−0.223177	+	0.162147i
$780$		0			0
$781$	42.6327	−	8.88563i	1.52552	−	0.317953i
$782$		0			0
$783$	−1.11096	+	0.807160i	−0.0397025	+	0.0288455i
$784$		0			0
$785$	6.18494	−	19.0353i	0.220750	−	0.679399i
$786$		0			0
$787$	39.1894	+	28.4727i	1.39695	+	1.01494i	0.995062	+	0.0992543i	$0.0316457\pi$
$787$	39.1894	+	28.4727i	1.39695	+	1.01494i	0.401888	+	0.915689i	$0.368354\pi$
$788$		0			0
$789$	−5.59969	−	17.2341i	−0.199354	−	0.613550i
$790$		0			0
$791$	37.7580			1.34252
$792$		0			0
$793$	72.0250			2.55768
$794$		0			0
$795$	2.72899	+	8.39898i	0.0967874	+	0.297881i
$796$		0			0
$797$	−34.0967	−	24.7727i	−1.20777	−	0.877493i	−0.212740	−	0.977109i	$-0.568239\pi$
$797$	−34.0967	−	24.7727i	−1.20777	−	0.877493i	−0.995026	+	0.0996157i	$0.968239\pi$
$798$		0			0
$799$	0.428721	−	1.31947i	0.0151671	−	0.0466794i
$800$		0			0
$801$	−1.68224	+	1.22222i	−0.0594390	+	0.0431850i
$802$		0			0
$803$	0.994558	+	1.73848i	0.0350972	+	0.0613496i
$804$		0			0
$805$	1.30902	−	0.951057i	0.0461368	−	0.0335203i
$806$		0			0
$807$	−7.25986	+	22.3435i	−0.255559	+	0.786530i
$808$		0			0
$809$	23.3024	+	16.9302i	0.819268	+	0.595233i	0.916503	−	0.400029i	$-0.131000\pi$
$809$	23.3024	+	16.9302i	0.819268	+	0.595233i	−0.0972348	+	0.995261i	$0.531000\pi$
$810$		0			0
$811$	−0.124425	−	0.382941i	−0.00436916	−	0.0134469i	0.948848	−	0.315733i	$-0.102250\pi$
$811$	−0.124425	−	0.382941i	−0.00436916	−	0.0134469i	−0.953217	+	0.302286i	$0.902250\pi$
$812$		0			0
$813$	−31.9686			−1.12119
$814$		0			0
$815$	18.2156			0.638063
$816$		0			0
$817$	2.63795	+	8.11877i	0.0922901	+	0.284040i
$818$		0			0
$819$	16.1167	+	11.7095i	0.563164	+	0.409163i
$820$		0			0
$821$	−13.7853	+	42.4267i	−0.481109	+	1.48070i	0.356430	+	0.934322i	$0.383994\pi$
$821$	−13.7853	+	42.4267i	−0.481109	+	1.48070i	−0.837538	+	0.546378i	$0.816006\pi$
$822$		0			0
$823$	−10.4408	+	7.58565i	−0.363942	+	0.264419i	−0.754694	−	0.656077i	$-0.772215\pi$
$823$	−10.4408	+	7.58565i	−0.363942	+	0.264419i	0.390753	+	0.920496i	$0.372215\pi$
$824$		0			0
$825$	0.359735	−	3.29706i	0.0125244	−	0.114789i
$826$		0			0
$827$	13.3258	−	9.68174i	0.463382	−	0.336667i	−0.331474	−	0.943464i	$-0.607546\pi$
$827$	13.3258	−	9.68174i	0.463382	−	0.336667i	0.794857	+	0.606797i	$0.207546\pi$
$828$		0			0
$829$	−15.3633	+	47.2833i	−0.533588	+	1.64222i	0.213092	+	0.977032i	$0.431647\pi$
$829$	−15.3633	+	47.2833i	−0.533588	+	1.64222i	−0.746680	+	0.665183i	$0.768353\pi$
$830$		0			0
$831$	−20.2004	−	14.6765i	−0.700745	−	0.509121i
$832$		0			0
$833$	−0.777419	−	2.39265i	−0.0269360	−	0.0829004i
$834$		0			0
$835$	−3.10968			−0.107615
$836$		0			0
$837$	−7.60929			−0.263016
$838$		0			0
$839$	−15.9938	−	49.2239i	−0.552168	−	1.69940i	−0.703307	−	0.710886i	$-0.748294\pi$
$839$	−15.9938	−	49.2239i	−0.552168	−	1.69940i	0.151139	−	0.988513i	$-0.451706\pi$
$840$		0			0
$841$	21.9359	+	15.9374i	0.756410	+	0.549564i
$842$		0			0
$843$	−1.56510	+	4.81687i	−0.0539048	+	0.165902i
$844$		0			0
$845$	23.2233	−	16.8727i	0.798907	−	0.580440i
$846$		0			0
$847$	−33.1340	−	7.31748i	−1.13850	−	0.251432i
$848$		0			0
$849$	−6.05408	+	4.39855i	−0.207776	+	0.150958i
$850$		0			0
$851$	0.590808	−	1.81832i	0.0202526	−	0.0623312i
$852$		0			0
$853$	−29.6231	−	21.5224i	−1.01428	−	0.736915i	−0.0491743	−	0.998790i	$-0.515659\pi$
$853$	−29.6231	−	21.5224i	−1.01428	−	0.736915i	−0.965102	+	0.261876i	$0.915659\pi$
$854$		0			0
$855$	−0.600175	−	1.84715i	−0.0205256	−	0.0631712i
$856$		0			0
$857$	−23.9957			−0.819677			−0.409839	−	0.912158i	$-0.634415\pi$
$857$	−23.9957			−0.819677			−0.409839	+	0.912158i	$0.634415\pi$
$858$		0			0
$859$	28.6428			0.977281			0.488641	−	0.872485i	$-0.337493\pi$
$859$	28.6428			0.977281			0.488641	+	0.872485i	$0.337493\pi$
$860$		0			0
$861$	3.77893	+	11.6304i	0.128786	+	0.396362i
$862$		0			0
$863$	17.7215	+	12.8754i	0.603246	+	0.438284i	0.847030	−	0.531546i	$-0.178389\pi$
$863$	17.7215	+	12.8754i	0.603246	+	0.438284i	−0.243784	+	0.969830i	$0.578389\pi$
$864$		0			0
$865$	−4.39030	+	13.5120i	−0.149275	+	0.459420i
$866$		0			0
$867$	12.9443	−	9.40456i	0.439611	−	0.319396i
$868$		0			0
$869$	3.45365	−	31.6536i	0.117157	−	1.07377i
$870$		0			0
$871$	−27.6558	+	20.0931i	−0.937080	+	0.680829i
$872$		0			0
$873$	2.07524	−	6.38694i	0.0702363	−	0.216165i
$874$		0			0
$875$	2.49563	+	1.81318i	0.0843676	+	0.0612967i
$876$		0			0
$877$	−17.1719	−	52.8497i	−0.579854	−	1.78461i	−0.619022	−	0.785373i	$-0.712471\pi$
$877$	−17.1719	−	52.8497i	−0.579854	−	1.78461i	0.0391687	−	0.999233i	$-0.487529\pi$
$878$		0			0
$879$	−14.3303			−0.483350
$880$		0			0
$881$	−30.8926			−1.04080			−0.520399	−	0.853923i	$-0.674217\pi$
$881$	−30.8926			−1.04080			−0.520399	+	0.853923i	$0.674217\pi$
$882$		0			0
$883$	−11.7471	−	36.1539i	−0.395322	−	1.21668i	−0.928711	−	0.370805i	$-0.879082\pi$
$883$	−11.7471	−	36.1539i	−0.395322	−	1.21668i	0.533389	−	0.845870i	$-0.320918\pi$
$884$		0			0
$885$	−5.62715	−	4.08836i	−0.189155	−	0.137429i
$886$		0			0
$887$	−10.3184	+	31.7568i	−0.346458	+	1.06629i	0.614340	+	0.789041i	$0.289422\pi$
$887$	−10.3184	+	31.7568i	−0.346458	+	1.06629i	−0.960799	+	0.277247i	$0.910578\pi$
$888$		0			0
$889$	2.50911	−	1.82298i	0.0841530	−	0.0611407i
$890$		0			0
$891$	1.64693	+	2.87882i	0.0551742	+	0.0964442i
$892$		0			0
$893$	2.17995	−	1.58382i	0.0729491	−	0.0530006i
$894$		0			0
$895$	6.83084	−	21.0232i	0.228330	−	0.702727i
$896$		0			0
$897$	2.74044	+	1.99105i	0.0915006	+	0.0664791i
$898$		0			0
$899$	−3.22899	−	9.93782i	−0.107693	−	0.331445i
$900$		0			0
$901$	8.83121			0.294210
$902$		0			0
$903$	13.5585			0.451197
$904$		0			0
$905$	−6.01887	−	18.5242i	−0.200074	−	0.615764i
$906$		0			0
$907$	46.1629	+	33.5393i	1.53281	+	1.11365i	0.954649	+	0.297734i	$0.0962310\pi$
$907$	46.1629	+	33.5393i	1.53281	+	1.11365i	0.578165	+	0.815920i	$0.303769\pi$
$908$		0			0
$909$	−4.84678	+	14.9168i	−0.160757	+	0.494760i
$910$		0			0
$911$	−30.1088	+	21.8753i	−0.997550	+	0.724763i	−0.961562	−	0.274590i	$-0.911458\pi$
$911$	−30.1088	+	21.8753i	−0.997550	+	0.724763i	−0.0359886	+	0.999352i	$0.511458\pi$
$912$		0			0
$913$	−25.2567	+	5.26407i	−0.835874	+	0.174215i
$914$		0			0
$915$	−9.02285	+	6.55549i	−0.298286	+	0.216718i
$916$		0			0
$917$	−10.7856	+	33.1947i	−0.356172	+	1.09618i
$918$		0			0
$919$	6.83300	+	4.96446i	0.225400	+	0.163763i	0.694754	−	0.719247i	$-0.255513\pi$
$919$	6.83300	+	4.96446i	0.225400	+	0.163763i	−0.469354	+	0.883010i	$0.655513\pi$
$920$		0			0
$921$	−1.60311	−	4.93385i	−0.0528241	−	0.162576i
$922$		0			0
$923$	−84.7964			−2.79111
$924$		0			0
$925$	3.64501			0.119847
$926$		0			0
$927$	−4.57476	−	14.0797i	−0.150255	−	0.462437i
$928$		0			0
$929$	−5.25107	−	3.81512i	−0.172282	−	0.125170i	0.498303	−	0.867003i	$-0.333957\pi$
$929$	−5.25107	−	3.81512i	−0.172282	−	0.125170i	−0.670585	+	0.741833i	$0.733957\pi$
$930$		0			0
$931$	1.50991	−	4.64702i	0.0494853	−	0.152300i
$932$		0			0
$933$	23.3645	−	16.9753i	0.764919	−	0.555747i
$934$		0			0
$935$	−3.02452	−	1.36098i	−0.0989125	−	0.0445087i
$936$		0			0
$937$	35.3448	−	25.6795i	1.15466	−	0.838912i	0.165569	−	0.986198i	$-0.447054\pi$
$937$	35.3448	−	25.6795i	1.15466	−	0.838912i	0.989094	+	0.147286i	$0.0470539\pi$
$938$		0			0
$939$	−9.59507	+	29.5306i	−0.313123	+	0.963694i
$940$		0			0
$941$	45.4312	+	33.0077i	1.48101	+	1.07602i	0.977228	+	0.212191i	$0.0680600\pi$
$941$	45.4312	+	33.0077i	1.48101	+	1.07602i	0.503786	+	0.863829i	$0.331940\pi$
$942$		0			0
$943$	0.642558	+	1.97759i	0.0209246	+	0.0643992i
$944$		0			0
$945$	−3.08477			−0.100347
$946$		0			0
$947$	6.73124			0.218736			0.109368	−	0.994001i	$-0.465117\pi$
$947$	6.73124			0.218736			0.109368	+	0.994001i	$0.465117\pi$
$948$		0			0
$949$	−1.20513	−	3.70901i	−0.0391202	−	0.120400i
$950$		0			0
$951$	1.37322	+	0.997704i	0.0445298	+	0.0323528i
$952$		0			0
$953$	−12.6617	+	38.9687i	−0.410153	+	1.26232i	0.506363	+	0.862321i	$0.330990\pi$
$953$	−12.6617	+	38.9687i	−0.410153	+	1.26232i	−0.916515	+	0.400000i	$0.869010\pi$
$954$		0			0
$955$	−15.4579	+	11.2309i	−0.500207	+	0.363422i
$956$		0			0
$957$	−3.06090	+	3.37254i	−0.0989449	+	0.109019i
$958$		0			0
$959$	12.1421	−	8.82179i	0.392090	−	0.284870i
$960$		0			0
$961$	8.31296	−	25.5846i	0.268160	−	0.825311i
$962$		0			0
$963$	−4.18931	−	3.04371i	−0.134999	−	0.0980823i
$964$		0			0
$965$	−1.76211	−	5.42320i	−0.0567242	−	0.174579i
$966$		0			0
$967$	16.1348			0.518859			0.259430	−	0.965762i	$-0.416465\pi$
$967$	16.1348			0.518859			0.259430	+	0.965762i	$0.416465\pi$
$968$		0			0
$969$	−1.94221			−0.0623927
$970$		0			0
$971$	−1.99001	−	6.12462i	−0.0638624	−	0.196548i	0.914034	−	0.405637i	$-0.132950\pi$
$971$	−1.99001	−	6.12462i	−0.0638624	−	0.196548i	−0.977897	+	0.209089i	$0.932950\pi$
$972$		0			0
$973$	15.4935	+	11.2567i	0.496700	+	0.360874i
$974$		0			0
$975$	−1.99563	+	6.14191i	−0.0639112	+	0.196699i
$976$		0			0
$977$	−30.2230	+	21.9583i	−0.966919	+	0.702508i	−0.954747	−	0.297418i	$-0.903875\pi$
$977$	−30.2230	+	21.9583i	−0.966919	+	0.702508i	−0.0121718	+	0.999926i	$0.503875\pi$
$978$		0			0
$979$	−4.63488	+	5.10676i	−0.148132	+	0.163213i
$980$		0			0
$981$	−4.28012	+	3.10969i	−0.136654	+	0.0992848i
$982$		0			0
$983$	−11.1492	+	34.3138i	−0.355606	+	1.09444i	0.600052	+	0.799961i	$0.295147\pi$
$983$	−11.1492	+	34.3138i	−0.355606	+	1.09444i	−0.955657	+	0.294481i	$0.904853\pi$
$984$		0			0
$985$	−13.0280	−	9.46540i	−0.415107	−	0.301593i
$986$		0			0
$987$	−1.32250	−	4.07025i	−0.0420958	−	0.129557i
$988$		0			0
$989$	2.30544			0.0733087
$990$		0			0
$991$	−26.3647			−0.837501			−0.418751	−	0.908101i	$-0.637532\pi$
$991$	−26.3647			−0.837501			−0.418751	+	0.908101i	$0.637532\pi$
$992$		0			0
$993$	−7.20754	−	22.1825i	−0.228724	−	0.703941i
$994$		0			0
$995$	−9.16786	−	6.66084i	−0.290641	−	0.211163i
$996$		0			0
$997$	−14.5445	+	44.7634i	−0.460629	+	1.41767i	0.403768	+	0.914861i	$0.367700\pi$
$997$	−14.5445	+	44.7634i	−0.460629	+	1.41767i	−0.864397	+	0.502809i	$0.832300\pi$
$998$		0			0
$999$	−2.94887	+	2.14248i	−0.0932982	+	0.0677851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.c.1081.2	yes	8
11.4	even	5	inner	1320.2.bw.c.961.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.c.961.2	✓	8	11.4	even	5	inner
1320.2.bw.c.1081.2	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.953245 - 2.93379i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.953245 - 2.93379i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-2.22899 + 2.45593i) q^{11} +(5.22462 - 3.79591i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(0.809017 + 0.587785i) q^{17} +(0.600175 + 1.84715i) q^{19} +3.08477 q^{21} +0.524524 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.424349 - 1.30601i) q^{29} +(6.15604 - 4.47263i) q^{31} +(-3.02452 - 1.36098i) q^{33} +(2.49563 - 1.81318i) q^{35} +(1.12637 - 3.46661i) q^{37} +(5.22462 + 3.79591i) q^{39} +(1.22503 + 3.77026i) q^{41} +4.39530 q^{43} -1.00000 q^{45} +(-0.428721 - 1.31947i) q^{47} +(-2.03531 - 1.47874i) q^{49} +(-0.309017 + 0.951057i) q^{51} +(7.14460 - 5.19085i) q^{53} +(-3.24685 + 0.676718i) q^{55} +(-1.57128 + 1.14160i) q^{57} +(-2.14938 + 6.61511i) q^{59} +(9.02285 + 6.55549i) q^{61} +(0.953245 + 2.93379i) q^{63} +6.45799 q^{65} -5.29335 q^{67} +(0.162087 + 0.498852i) q^{69} +(-10.6228 - 7.71790i) q^{71} +(0.186611 - 0.574329i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(5.08039 + 8.88049i) q^{77} +(-7.76700 + 5.64306i) q^{79} +(0.309017 - 0.951057i) q^{81} +(6.29320 + 4.57228i) q^{83} +(0.309017 + 0.951057i) q^{85} +1.37322 q^{87} +2.07936 q^{89} +(-6.15604 - 18.9464i) q^{91} +(6.15604 + 4.47263i) q^{93} +(-0.600175 + 1.84715i) q^{95} +(-5.43305 + 3.94735i) q^{97} +(0.359735 - 3.29706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{5} + 5 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 2 * q^5 + 5 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} + 2 q^{5} + 5 q^{7} - 2 q^{9} + 5 q^{11} + 4 q^{13} + 2 q^{15} + 2 q^{17} - 6 q^{19} - 10 q^{23} - 2 q^{25} - 2 q^{27} + 13 q^{31} - 10 q^{33} + 5 q^{35} + 9 q^{37} + 4 q^{39} - 7 q^{41} + 12 q^{43} - 8 q^{45} - 15 q^{47} + q^{49} + 2 q^{51} + q^{53} - 5 q^{55} - q^{57} + 3 q^{59} + 33 q^{61} + 5 q^{63} + 6 q^{65} - 22 q^{67} + 5 q^{69} - 33 q^{71} - 9 q^{73} - 2 q^{75} + q^{77} - 12 q^{79} - 2 q^{81} + 11 q^{83} - 2 q^{85} - 10 q^{87} + 12 q^{89} - 13 q^{91} + 13 q^{93} + 6 q^{95} + 9 q^{97} - 5 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^5 + 5 * q^7 - 2 * q^9 + 5 * q^11 + 4 * q^13 + 2 * q^15 + 2 * q^17 - 6 * q^19 - 10 * q^23 - 2 * q^25 - 2 * q^27 + 13 * q^31 - 10 * q^33 + 5 * q^35 + 9 * q^37 + 4 * q^39 - 7 * q^41 + 12 * q^43 - 8 * q^45 - 15 * q^47 + q^49 + 2 * q^51 + q^53 - 5 * q^55 - q^57 + 3 * q^59 + 33 * q^61 + 5 * q^63 + 6 * q^65 - 22 * q^67 + 5 * q^69 - 33 * q^71 - 9 * q^73 - 2 * q^75 + q^77 - 12 * q^79 - 2 * q^81 + 11 * q^83 - 2 * q^85 - 10 * q^87 + 12 * q^89 - 13 * q^91 + 13 * q^93 + 6 * q^95 + 9 * q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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