LMFDB - Embedded newform 288.2.v.c.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	288.109
Dual form			288.2.v.c.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06920 - 0.925636i) q^{2} +(0.286395 + 1.97939i) q^{4} +(3.41317 - 1.41378i) q^{5} +(-1.42999 + 1.42999i) q^{7} +(1.52598 - 2.38147i) q^{8} +O(q^{10})$	\(q+(-1.06920 - 0.925636i) q^{2} +(0.286395 + 1.97939i) q^{4} +(3.41317 - 1.41378i) q^{5} +(-1.42999 + 1.42999i) q^{7} +(1.52598 - 2.38147i) q^{8} +(-4.95802 - 1.64773i) q^{10} +(0.821853 + 1.98413i) q^{11} +(3.77658 + 1.56431i) q^{13} +(2.85261 - 0.205301i) q^{14} +(-3.83596 + 1.13377i) q^{16} -0.438395i q^{17} +(2.08943 + 0.865472i) q^{19} +(3.77593 + 6.35109i) q^{20} +(0.957853 - 2.88218i) q^{22} +(-4.42643 - 4.42643i) q^{23} +(6.11541 - 6.11541i) q^{25} +(-2.58995 - 5.16831i) q^{26} +(-3.24006 - 2.42097i) q^{28} +(2.48553 - 6.00059i) q^{29} +10.5252 q^{31} +(5.15088 + 2.33847i) q^{32} +(-0.405795 + 0.468734i) q^{34} +(-2.85911 + 6.90251i) q^{35} +(-8.11819 + 3.36267i) q^{37} +(-1.43292 - 2.85942i) q^{38} +(1.84155 - 10.2858i) q^{40} +(-3.71182 - 3.71182i) q^{41} +(-4.47572 - 10.8053i) q^{43} +(-3.69199 + 2.19501i) q^{44} +(0.635492 + 8.83001i) q^{46} +7.94884i q^{47} +2.91023i q^{49} +(-12.1993 + 0.877975i) q^{50} +(-2.01479 + 7.92333i) q^{52} +(1.97877 + 4.77718i) q^{53} +(5.61025 + 5.61025i) q^{55} +(1.22334 + 5.58763i) q^{56} +(-8.21190 + 4.11516i) q^{58} +(-2.54952 + 1.05605i) q^{59} +(-2.65935 + 6.42023i) q^{61} +(-11.2536 - 9.74254i) q^{62} +(-3.34277 - 7.26814i) q^{64} +15.1017 q^{65} +(-0.876739 + 2.11663i) q^{67} +(0.867755 - 0.125554i) q^{68} +(9.44619 - 4.73369i) q^{70} +(-8.63018 + 8.63018i) q^{71} +(-3.27926 - 3.27926i) q^{73} +(11.7926 + 3.91912i) q^{74} +(-1.11470 + 4.38367i) q^{76} +(-4.01254 - 1.66205i) q^{77} +2.97249i q^{79} +(-11.4899 + 9.29296i) q^{80} +(0.532898 + 7.40450i) q^{82} +(-6.25020 - 2.58892i) q^{83} +(-0.619795 - 1.49632i) q^{85} +(-5.21636 + 15.6960i) q^{86} +(5.97927 + 1.07052i) q^{88} +(0.0975126 - 0.0975126i) q^{89} +(-7.63745 + 3.16353i) q^{91} +(7.49391 - 10.0293i) q^{92} +(7.35774 - 8.49894i) q^{94} +8.35518 q^{95} +7.26901 q^{97} +(2.69382 - 3.11163i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.06920	−	0.925636i	−0.756041	−	0.654524i
$2$	−1.06920	−	0.925636i	−0.756041	−	0.654524i
$3$		0			0
$3$		0			0
$4$	0.286395	+	1.97939i	0.143197	+	0.989694i
$5$	3.41317	−	1.41378i	1.52642	−	0.632262i	0.547551	−	0.836772i	$-0.315560\pi$
$5$	3.41317	−	1.41378i	1.52642	−	0.632262i	0.978864	+	0.204510i	$0.0655602\pi$
$6$		0			0
$7$	−1.42999	+	1.42999i	−0.540487	+	0.540487i	−0.923672	−	0.383185i	$-0.874827\pi$
$7$	−1.42999	+	1.42999i	−0.540487	+	0.540487i	0.383185	+	0.923672i	$0.374827\pi$
$8$	1.52598	−	2.38147i	0.539515	−	0.841976i
$9$		0			0
$10$	−4.95802	−	1.64773i	−1.56786	−	0.521059i
$11$	0.821853	+	1.98413i	0.247798	+	0.598237i	0.998017	−	0.0629526i	$-0.0200517\pi$
$11$	0.821853	+	1.98413i	0.247798	+	0.598237i	−0.750218	+	0.661190i	$0.770052\pi$
$12$		0			0
$13$	3.77658	+	1.56431i	1.04744	+	0.433862i	0.838976	−	0.544169i	$-0.183155\pi$
$13$	3.77658	+	1.56431i	1.04744	+	0.433862i	0.208460	+	0.978031i	$0.433155\pi$
$14$	2.85261	−	0.205301i	0.762392	−	0.0548690i
$15$		0			0
$16$	−3.83596	+	1.13377i	−0.958989	+	0.283443i
$17$		−	0.438395i		−	0.106327i	−0.998586	−	0.0531633i	$-0.983070\pi$
$17$		−	0.438395i		−	0.106327i	0.998586	−	0.0531633i	$-0.0169304\pi$
$18$		0			0
$19$	2.08943	+	0.865472i	0.479349	+	0.198553i	0.609257	−	0.792973i	$-0.291468\pi$
$19$	2.08943	+	0.865472i	0.479349	+	0.198553i	−0.129907	+	0.991526i	$0.541468\pi$
$20$	3.77593	+	6.35109i	0.844325	+	1.42015i
$21$		0			0
$22$	0.957853	−	2.88218i	0.204215	−	0.614482i
$23$	−4.42643	−	4.42643i	−0.922974	−	0.922974i	0.0742649	−	0.997239i	$-0.476339\pi$
$23$	−4.42643	−	4.42643i	−0.922974	−	0.922974i	−0.997239	+	0.0742649i	$0.976339\pi$
$24$		0			0
$25$	6.11541	−	6.11541i	1.22308	−	1.22308i
$26$	−2.58995	−	5.16831i	−0.507932	−	1.01359i
$27$		0			0
$28$	−3.24006	−	2.42097i	−0.612313	−	0.457521i
$29$	2.48553	−	6.00059i	0.461550	−	1.11428i	−0.506210	−	0.862410i	$-0.668954\pi$
$29$	2.48553	−	6.00059i	0.461550	−	1.11428i	0.967761	−	0.251871i	$-0.0810460\pi$
$30$		0			0
$31$	10.5252			1.89039			0.945194	−	0.326509i	$-0.105872\pi$
$31$	10.5252			1.89039			0.945194	+	0.326509i	$0.105872\pi$
$32$	5.15088	+	2.33847i	0.910556	+	0.413386i
$33$		0			0
$34$	−0.405795	+	0.468734i	−0.0695932	+	0.0803872i
$35$	−2.85911	+	6.90251i	−0.483278	+	1.16674i
$36$		0			0
$37$	−8.11819	+	3.36267i	−1.33462	+	0.552819i	−0.931971	−	0.362534i	$-0.881912\pi$
$37$	−8.11819	+	3.36267i	−1.33462	+	0.552819i	−0.402652	+	0.915353i	$0.631912\pi$
$38$	−1.43292	−	2.85942i	−0.232450	−	0.463860i
$39$		0			0
$40$	1.84155	−	10.2858i	0.291175	−	1.62632i
$41$	−3.71182	−	3.71182i	−0.579690	−	0.579690i	0.355128	−	0.934818i	$-0.384437\pi$
$41$	−3.71182	−	3.71182i	−0.579690	−	0.579690i	−0.934818	+	0.355128i	$0.884437\pi$
$42$		0			0
$43$	−4.47572	−	10.8053i	−0.682541	−	1.64780i	−0.759293	−	0.650749i	$-0.774455\pi$
$43$	−4.47572	−	10.8053i	−0.682541	−	1.64780i	0.0767520	−	0.997050i	$-0.475545\pi$
$44$	−3.69199	+	2.19501i	−0.556588	+	0.330910i
$45$		0			0
$46$	0.635492	+	8.83001i	0.0936981	+	1.30191i
$47$			7.94884i			1.15946i	0.814809	+	0.579729i	$0.196842\pi$
$47$			7.94884i			1.15946i	−0.814809	+	0.579729i	$0.803158\pi$
$48$		0			0
$49$			2.91023i			0.415748i
$50$	−12.1993	+	0.877975i	−1.72524	+	0.124164i
$51$		0			0
$52$	−2.01479	+	7.92333i	−0.279401	+	1.09877i
$53$	1.97877	+	4.77718i	0.271805	+	0.656196i	0.999561	−	0.0296408i	$-0.00943635\pi$
$53$	1.97877	+	4.77718i	0.271805	+	0.656196i	−0.727755	+	0.685837i	$0.759436\pi$
$54$		0			0
$55$	5.61025	+	5.61025i	0.756486	+	0.756486i
$56$	1.22334	+	5.58763i	0.163476	+	0.746678i
$57$		0			0
$58$	−8.21190	+	4.11516i	−1.07827	+	0.540347i
$59$	−2.54952	+	1.05605i	−0.331919	+	0.137486i	−0.542418	−	0.840109i	$-0.682491\pi$
$59$	−2.54952	+	1.05605i	−0.331919	+	0.137486i	0.210499	+	0.977594i	$0.432491\pi$
$60$		0			0
$61$	−2.65935	+	6.42023i	−0.340494	+	0.822026i	0.657171	+	0.753741i	$0.271753\pi$
$61$	−2.65935	+	6.42023i	−0.340494	+	0.822026i	−0.997666	+	0.0682852i	$0.978247\pi$
$62$	−11.2536	−	9.74254i	−1.42921	−	1.23730i
$63$		0			0
$64$	−3.34277	−	7.26814i	−0.417847	−	0.908518i
$65$	15.1017			1.87314
$66$		0			0
$67$	−0.876739	+	2.11663i	−0.107111	+	0.258588i	−0.968343	−	0.249623i	$-0.919693\pi$
$67$	−0.876739	+	2.11663i	−0.107111	+	0.258588i	0.861232	+	0.508211i	$0.169693\pi$
$68$	0.867755	−	0.125554i	0.105231	−	0.0152257i
$69$		0			0
$70$	9.44619	−	4.73369i	1.12904	−	0.565784i
$71$	−8.63018	+	8.63018i	−1.02421	+	1.02421i	−0.0245142	+	0.999699i	$0.507804\pi$
$71$	−8.63018	+	8.63018i	−1.02421	+	1.02421i	−0.999699	+	0.0245142i	$0.992196\pi$
$72$		0			0
$73$	−3.27926	−	3.27926i	−0.383808	−	0.383808i	0.488664	−	0.872472i	$-0.337484\pi$
$73$	−3.27926	−	3.27926i	−0.383808	−	0.383808i	−0.872472	+	0.488664i	$0.837484\pi$
$74$	11.7926	+	3.91912i	1.37086	+	0.455588i
$75$		0			0
$76$	−1.11470	+	4.38367i	−0.127865	+	0.502841i
$77$	−4.01254	−	1.66205i	−0.457271	−	0.189408i
$78$		0			0
$79$			2.97249i			0.334431i	0.985920	+	0.167216i	$0.0534776\pi$
$79$			2.97249i			0.334431i	−0.985920	+	0.167216i	$0.946522\pi$
$80$	−11.4899	+	9.29296i	−1.28461	+	1.03898i
$81$		0			0
$82$	0.532898	+	7.40450i	0.0588487	+	0.817690i
$83$	−6.25020	−	2.58892i	−0.686049	−	0.284171i	0.0123043	−	0.999924i	$-0.496083\pi$
$83$	−6.25020	−	2.58892i	−0.686049	−	0.284171i	−0.698353	+	0.715754i	$0.746083\pi$
$84$		0			0
$85$	−0.619795	−	1.49632i	−0.0672262	−	0.162298i
$86$	−5.21636	+	15.6960i	−0.562495	+	1.69254i
$87$		0			0
$88$	5.97927	+	1.07052i	0.637392	+	0.114118i
$89$	0.0975126	−	0.0975126i	0.0103363	−	0.0103363i	−0.701920	−	0.712256i	$-0.747673\pi$
$89$	0.0975126	−	0.0975126i	0.0103363	−	0.0103363i	0.712256	+	0.701920i	$0.247673\pi$
$90$		0			0
$91$	−7.63745	+	3.16353i	−0.800622	+	0.331629i
$92$	7.49391	−	10.0293i	0.781294	−	1.04563i
$93$		0			0
$94$	7.35774	−	8.49894i	0.758893	−	0.876598i
$95$	8.35518			0.857224
$96$		0			0
$97$	7.26901			0.738056			0.369028	−	0.929418i	$-0.379691\pi$
$97$	7.26901			0.738056			0.369028	+	0.929418i	$0.379691\pi$
$98$	2.69382	−	3.11163i	0.272117	−	0.314322i
$99$		0			0
$100$	13.8562	+	10.3534i	1.38562	+	1.03534i
$101$	−9.62653	+	3.98744i	−0.957876	+	0.396765i	−0.806185	−	0.591663i	$-0.798472\pi$
$101$	−9.62653	+	3.98744i	−0.957876	+	0.396765i	−0.151690	+	0.988428i	$0.548472\pi$
$102$		0			0
$103$	−2.93955	+	2.93955i	−0.289642	+	0.289642i	−0.836939	−	0.547297i	$-0.815657\pi$
$103$	−2.93955	+	2.93955i	−0.289642	+	0.289642i	0.547297	+	0.836939i	$0.315657\pi$
$104$	9.48835	−	6.60670i	0.930409	−	0.647840i
$105$		0			0
$106$	2.30622	−	6.93940i	0.224000	−	0.674014i
$107$	−7.19771	−	17.3768i	−0.695829	−	1.67988i	−0.732694	−	0.680558i	$-0.761737\pi$
$107$	−7.19771	−	17.3768i	−0.695829	−	1.67988i	0.0368653	−	0.999320i	$-0.488263\pi$
$108$		0			0
$109$	−9.02316	−	3.73751i	−0.864262	−	0.357989i	−0.0938891	−	0.995583i	$-0.529930\pi$
$109$	−9.02316	−	3.73751i	−0.864262	−	0.357989i	−0.770373	+	0.637594i	$0.779930\pi$
$110$	−0.805450	−	11.1915i	−0.0767966	−	1.06707i
$111$		0			0
$112$	3.86411	−	7.10668i	0.365124	−	0.671518i
$113$		−	9.26038i		−	0.871143i	−0.900154	−	0.435572i	$-0.856546\pi$
$113$		−	9.26038i		−	0.871143i	0.900154	−	0.435572i	$-0.143454\pi$
$114$		0			0
$115$	−21.3661	−	8.85014i	−1.99240	−	0.825280i
$116$	12.5893	+	3.20128i	1.16889	+	0.297232i
$117$		0			0
$118$	3.70347	+	1.23080i	0.340932	+	0.113304i
$119$	0.626903	+	0.626903i	0.0574681	+	0.0574681i
$120$		0			0
$121$	4.51685	−	4.51685i	0.410623	−	0.410623i
$122$	8.78618	−	4.40295i	0.795464	−	0.398624i
$123$		0			0
$124$	3.01437	+	20.8335i	0.270698	+	1.87091i
$125$	5.15818	−	12.4529i	0.461361	−	1.11382i
$126$		0			0
$127$	−8.61266			−0.764250			−0.382125	−	0.924111i	$-0.624808\pi$
$127$	−8.61266			−0.764250			−0.382125	+	0.924111i	$0.624808\pi$
$128$	−3.15355	+	10.8653i	−0.278737	+	0.960367i
$129$		0			0
$130$	−16.1468	−	13.9787i	−1.41617	−	1.22601i
$131$	−5.59231	+	13.5010i	−0.488603	+	1.17959i	0.466821	+	0.884352i	$0.345399\pi$
$131$	−5.59231	+	13.5010i	−0.488603	+	1.17959i	−0.955423	+	0.295239i	$0.904601\pi$
$132$		0			0
$133$	−4.22550	+	1.75026i	−0.366397	+	0.151767i
$134$	2.89665	−	1.45157i	0.250232	−	0.125397i
$135$		0			0
$136$	−1.04402	−	0.668982i	−0.0895243	−	0.0573648i
$137$	−1.32063	−	1.32063i	−0.112829	−	0.112829i	0.648438	−	0.761267i	$-0.275422\pi$
$137$	−1.32063	−	1.32063i	−0.112829	−	0.112829i	−0.761267	+	0.648438i	$0.775422\pi$
$138$		0			0
$139$	−1.13226	−	2.73351i	−0.0960367	−	0.231853i	0.868559	−	0.495585i	$-0.165046\pi$
$139$	−1.13226	−	2.73351i	−0.0960367	−	0.231853i	−0.964596	+	0.263732i	$0.915046\pi$
$140$	−14.4816	−	3.68245i	−1.22392	−	0.311224i
$141$		0			0
$142$	17.2158	−	1.23901i	1.44472	−	0.103976i
$143$			8.77886i			0.734125i
$144$		0			0
$145$		−	23.9950i		−	1.99268i
$146$	0.470796	+	6.54160i	0.0389633	+	0.541387i
$147$		0			0
$148$	−8.98103	−	15.1060i	−0.738236	−	1.24171i
$149$	6.59474	+	15.9211i	0.540262	+	1.30431i	0.924538	+	0.381089i	$0.124451\pi$
$149$	6.59474	+	15.9211i	0.540262	+	1.30431i	−0.384276	+	0.923218i	$0.625549\pi$
$150$		0			0
$151$	2.45749	+	2.45749i	0.199987	+	0.199987i	0.799995	−	0.600007i	$-0.204836\pi$
$151$	2.45749	+	2.45749i	0.199987	+	0.199987i	−0.600007	+	0.799995i	$0.704836\pi$
$152$	5.24953	−	3.65523i	0.425793	−	0.296478i
$153$		0			0
$154$	2.75177	+	5.49122i	0.221744	+	0.442495i
$155$	35.9244	−	14.8804i	2.88552	−	1.19522i
$156$		0			0
$157$	−5.23028	+	12.6270i	−0.417422	+	1.00775i	0.565670	+	0.824632i	$0.308618\pi$
$157$	−5.23028	+	12.6270i	−0.417422	+	1.00775i	−0.983092	+	0.183114i	$0.941382\pi$
$158$	2.75145	−	3.17820i	0.218893	−	0.252844i
$159$		0			0
$160$	20.8869	+	0.699367i	1.65125	+	0.0552898i
$161$	12.6595			0.997710
$162$		0			0
$163$	4.41906	−	10.6685i	0.346127	−	0.835625i	−0.650942	−	0.759127i	$-0.725626\pi$
$163$	4.41906	−	10.6685i	0.346127	−	0.835625i	0.997070	−	0.0764981i	$-0.0243739\pi$
$164$	6.28410	−	8.41019i	0.490705	−	0.656725i
$165$		0			0
$166$	4.28634	+	8.55349i	0.332685	+	0.663880i
$167$	15.9377	−	15.9377i	1.23329	−	1.23329i	0.270604	−	0.962691i	$-0.412777\pi$
$167$	15.9377	−	15.9377i	1.23329	−	1.23329i	0.962691	−	0.270604i	$-0.0872233\pi$
$168$		0			0
$169$	2.62312	+	2.62312i	0.201778	+	0.201778i
$170$	−0.722359	+	2.17357i	−0.0554024	+	0.166705i
$171$		0			0
$172$	20.1061	−	11.9538i	1.53308	−	0.911467i
$173$	−7.07909	−	2.93225i	−0.538213	−	0.222935i	0.0969831	−	0.995286i	$-0.469081\pi$
$173$	−7.07909	−	2.93225i	−0.538213	−	0.222935i	−0.635196	+	0.772351i	$0.719081\pi$
$174$		0			0
$175$			17.4900i			1.32212i
$176$	−5.40214	−	6.67924i	−0.407202	−	0.503467i
$177$		0			0
$178$	−0.194522	+	0.0139997i	−0.0145800	+	0.00104932i
$179$	−4.04366	−	1.67494i	−0.302237	−	0.125191i	0.226411	−	0.974032i	$-0.427301\pi$
$179$	−4.04366	−	1.67494i	−0.302237	−	0.125191i	−0.528648	+	0.848841i	$0.677301\pi$
$180$		0			0
$181$	8.33047	+	20.1115i	0.619199	+	1.49488i	0.852636	+	0.522506i	$0.175003\pi$
$181$	8.33047	+	20.1115i	0.619199	+	1.49488i	−0.233437	+	0.972372i	$0.574997\pi$
$182$	11.0943	+	3.68704i	0.822362	+	0.273301i
$183$		0			0
$184$	−17.2960	+	3.78675i	−1.27508	+	0.279163i
$185$	−22.9547	+	22.9547i	−1.68766	+	1.68766i
$186$		0			0
$187$	0.869833	−	0.360297i	0.0636085	−	0.0263475i
$188$	−15.7338	+	2.27651i	−1.14751	+	0.166031i
$189$		0			0
$190$	−8.93339	−	7.73386i	−0.648096	−	0.561073i
$191$	14.8153			1.07200			0.535998	−	0.844219i	$-0.319935\pi$
$191$	14.8153			1.07200			0.535998	+	0.844219i	$0.319935\pi$
$192$		0			0
$193$	−4.09273			−0.294601			−0.147301	−	0.989092i	$-0.547058\pi$
$193$	−4.09273			−0.294601			−0.147301	+	0.989092i	$0.547058\pi$
$194$	−7.77205	−	6.72846i	−0.558001	−	0.483075i
$195$		0			0
$196$	−5.76048	+	0.833475i	−0.411463	+	0.0595339i
$197$	−2.76176	+	1.14396i	−0.196767	+	0.0815036i	−0.478891	−	0.877874i	$-0.658961\pi$
$197$	−2.76176	+	1.14396i	−0.196767	+	0.0815036i	0.282124	+	0.959378i	$0.408961\pi$
$198$		0			0
$199$	18.0242	−	18.0242i	1.27770	−	1.27770i	0.335746	−	0.941953i	$-0.391012\pi$
$199$	18.0242	−	18.0242i	1.27770	−	1.27770i	0.941953	−	0.335746i	$-0.108988\pi$
$200$	−5.23166	−	23.8956i	−0.369934	−	1.68968i
$201$		0			0
$202$	13.9836	+	4.64728i	0.983886	+	0.326982i
$203$	5.02652	+	12.1351i	0.352793	+	0.851717i
$204$		0			0
$205$	−17.9168	−	7.42138i	−1.25136	−	0.518331i
$206$	5.86393	−	0.422024i	0.408559	−	0.0294038i
$207$		0			0
$208$	−16.2604	−	1.71885i	−1.12745	−	0.119181i
$209$			4.85700i			0.335966i
$210$		0			0
$211$	2.87871	+	1.19240i	0.198179	+	0.0820883i	0.479565	−	0.877506i	$-0.340794\pi$
$211$	2.87871	+	1.19240i	0.198179	+	0.0820883i	−0.281387	+	0.959594i	$0.590794\pi$
$212$	−8.88918	+	5.28492i	−0.610512	+	0.362970i
$213$		0			0
$214$	−8.38878	+	25.2418i	−0.573445	+	1.72549i
$215$	−30.5528	−	30.5528i	−2.08368	−	2.08368i
$216$		0			0
$217$	−15.0510	+	15.0510i	−1.02173	+	1.02173i
$218$	6.18802	+	12.3483i	0.419105	+	0.836334i
$219$		0			0
$220$	−9.49811	+	12.7116i	−0.640363	+	0.857016i
$221$	0.685787	−	1.65564i	0.0461310	−	0.111370i
$222$		0			0
$223$	−4.09123			−0.273969			−0.136985	−	0.990573i	$-0.543741\pi$
$223$	−4.09123			−0.273969			−0.136985	+	0.990573i	$0.543741\pi$
$224$	−10.7097	+	4.02173i	−0.715573	+	0.268713i
$225$		0			0
$226$	−8.57174	+	9.90123i	−0.570184	+	0.658620i
$227$	−3.35767	+	8.10614i	−0.222857	+	0.538023i	−0.995276	−	0.0970900i	$-0.969047\pi$
$227$	−3.35767	+	8.10614i	−0.222857	+	0.538023i	0.772419	+	0.635113i	$0.219047\pi$
$228$		0			0
$229$	5.10869	−	2.11609i	0.337592	−	0.139835i	−0.207446	−	0.978246i	$-0.566515\pi$
$229$	5.10869	−	2.11609i	0.337592	−	0.139835i	0.545038	+	0.838411i	$0.316515\pi$
$230$	14.6527	+	29.2399i	0.966173	+	1.92802i
$231$		0			0
$232$	−10.4973	−	15.0760i	−0.689184	−	0.989786i
$233$	−9.10570	−	9.10570i	−0.596534	−	0.596534i	0.342854	−	0.939389i	$-0.388606\pi$
$233$	−9.10570	−	9.10570i	−0.596534	−	0.596534i	−0.939389	+	0.342854i	$0.888606\pi$
$234$		0			0
$235$	11.2379	+	27.1307i	0.733081	+	1.76981i
$236$	−2.82049	−	4.74405i	−0.183599	−	0.308811i
$237$		0			0
$238$	−0.0900030	−	1.25057i	−0.00583403	−	0.0810625i
$239$		−	11.2937i		−	0.730528i	−0.930904	−	0.365264i	$-0.880979\pi$
$239$		−	11.2937i		−	0.730528i	0.930904	−	0.365264i	$-0.119021\pi$
$240$		0			0
$241$		−	4.75635i		−	0.306384i	−0.988196	−	0.153192i	$-0.951045\pi$
$241$		−	4.75635i		−	0.306384i	0.988196	−	0.153192i	$-0.0489552\pi$
$242$	−9.01039	+	0.648473i	−0.579210	+	0.0416854i
$243$		0			0
$244$	−13.4698	−	3.42516i	−0.862313	−	0.219273i
$245$	4.11443	+	9.93312i	0.262861	+	0.634604i
$246$		0			0
$247$	6.53705	+	6.53705i	0.415943	+	0.415943i
$248$	16.0613	−	25.0655i	1.01989	−	1.59166i
$249$		0			0
$250$	−17.0420	+	8.54014i	−1.07783	+	0.540126i
$251$	−6.10196	+	2.52751i	−0.385152	+	0.159535i	−0.566854	−	0.823818i	$-0.691840\pi$
$251$	−6.10196	+	2.52751i	−0.385152	+	0.159535i	0.181702	+	0.983354i	$0.441840\pi$
$252$		0			0
$253$	5.14473	−	12.4205i	0.323446	−	0.780868i
$254$	9.20869	+	7.97219i	0.577804	+	0.500220i
$255$		0			0
$256$	13.4291	−	8.69820i	0.839320	−	0.543637i
$257$	−17.3151			−1.08008			−0.540042	−	0.841638i	$-0.681592\pi$
$257$	−17.3151			−1.08008			−0.540042	+	0.841638i	$0.681592\pi$
$258$		0			0
$259$	6.80038	−	16.4176i	0.422555	−	1.02014i
$260$	4.32505	+	29.8921i	0.268228	+	1.85383i
$261$		0			0
$262$	18.4764	−	9.25892i	1.14147	−	0.572018i
$263$	−9.03440	+	9.03440i	−0.557085	+	0.557085i	−0.928476	−	0.371391i	$-0.878881\pi$
$263$	−9.03440	+	9.03440i	−0.557085	+	0.557085i	0.371391	+	0.928476i	$0.378881\pi$
$264$		0			0
$265$	13.5078	+	13.5078i	0.829776	+	0.829776i
$266$	6.13802	+	2.03989i	0.376346	+	0.125074i
$267$		0			0
$268$	−4.44074	−	1.12921i	−0.271261	−	0.0689777i
$269$	−4.51057	−	1.86834i	−0.275014	−	0.113915i	0.240914	−	0.970546i	$-0.422553\pi$
$269$	−4.51057	−	1.86834i	−0.275014	−	0.113915i	−0.515928	+	0.856632i	$0.672553\pi$
$270$		0			0
$271$		−	12.6543i		−	0.768693i	−0.923189	−	0.384347i	$-0.874427\pi$
$271$		−	12.6543i		−	0.768693i	0.923189	−	0.384347i	$-0.125573\pi$
$272$	0.497040	+	1.68167i	0.0301375	+	0.101966i
$273$		0			0
$274$	0.189600	+	2.63445i	0.0114541	+	0.159153i
$275$	17.1597	+	7.10780i	1.03477	+	0.428616i
$276$		0			0
$277$	−4.36430	−	10.5363i	−0.262225	−	0.633068i	0.736850	−	0.676056i	$-0.236312\pi$
$277$	−4.36430	−	10.5363i	−0.262225	−	0.633068i	−0.999076	+	0.0429883i	$0.986312\pi$
$278$	−1.31962	+	3.97074i	−0.0791457	+	0.238149i
$279$		0			0
$280$	12.0752	+	17.3420i	0.721628	+	1.03638i
$281$	−17.7934	+	17.7934i	−1.06146	+	1.06146i	−0.0634820	+	0.997983i	$0.520221\pi$
$281$	−17.7934	+	17.7934i	−1.06146	+	1.06146i	−0.997983	+	0.0634820i	$0.979779\pi$
$282$		0			0
$283$	13.3215	−	5.51795i	0.791881	−	0.328008i	0.0501815	−	0.998740i	$-0.484020\pi$
$283$	13.3215	−	5.51795i	0.791881	−	0.328008i	0.741700	+	0.670732i	$0.234020\pi$
$284$	−19.5541	−	14.6108i	−1.16032	−	0.866994i
$285$		0			0
$286$	8.12603	−	9.38639i	0.480502	−	0.555029i
$287$	10.6158			0.626629
$288$		0			0
$289$	16.8078			0.988695
$290$	−22.2107	+	25.6556i	−1.30425	+	1.50655i
$291$		0			0
$292$	5.55177	−	7.43009i	0.324893	−	0.434813i
$293$	−2.32953	+	0.964924i	−0.136093	+	0.0563715i	−0.449690	−	0.893184i	$-0.648466\pi$
$293$	−2.32953	+	0.964924i	−0.136093	+	0.0563715i	0.313598	+	0.949556i	$0.398466\pi$
$294$		0			0
$295$	−7.20893	+	7.20893i	−0.419720	+	0.419720i
$296$	−4.38012	+	24.4646i	−0.254589	+	1.42197i
$297$		0			0
$298$	7.68603	−	23.1272i	0.445240	−	1.33972i
$299$	−9.79245	−	23.6411i	−0.566312	−	1.36720i
$300$		0			0
$301$	21.8518	+	9.05132i	1.25952	+	0.521710i
$302$	−0.352816	−	4.90229i	−0.0203023	−	0.282095i
$303$		0			0
$304$	−8.99623	−	0.950971i	−0.515969	−	0.0545419i
$305$			25.6731i			1.47004i
$306$		0			0
$307$	−0.934041	−	0.386892i	−0.0533085	−	0.0220811i	0.355870	−	0.934536i	$-0.384185\pi$
$307$	−0.934041	−	0.386892i	−0.0533085	−	0.0220811i	−0.409178	+	0.912454i	$0.634185\pi$
$308$	2.14067	−	8.41837i	0.121976	−	0.479681i
$309$		0			0
$310$	−52.1843	−	17.3428i	−2.96387	−	0.985004i
$311$	10.5160	+	10.5160i	0.596307	+	0.596307i	0.939328	−	0.343021i	$-0.111450\pi$
$311$	10.5160	+	10.5160i	0.596307	+	0.596307i	−0.343021	+	0.939328i	$0.611450\pi$
$312$		0			0
$313$	3.65381	−	3.65381i	0.206526	−	0.206526i	−0.596263	−	0.802789i	$-0.703349\pi$
$313$	3.65381	−	3.65381i	0.206526	−	0.206526i	0.802789	+	0.596263i	$0.203349\pi$
$314$	17.2803	−	8.65952i	0.975182	−	0.488685i
$315$		0			0
$316$	−5.88371	+	0.851305i	−0.330985	+	0.0478897i
$317$	1.87930	−	4.53704i	0.105552	−	0.254825i	−0.862276	−	0.506439i	$-0.830961\pi$
$317$	1.87930	−	4.53704i	0.105552	−	0.254825i	0.967828	+	0.251614i	$0.0809614\pi$
$318$		0			0
$319$	13.9487			0.780976
$320$	−21.6850	−	20.0814i	−1.21223	−	1.12259i
$321$		0			0
$322$	−13.5356	−	11.7181i	−0.754310	−	0.653025i
$323$	0.379419	−	0.915999i	0.0211114	−	0.0509675i
$324$		0			0
$325$	32.6618	−	13.5289i	1.81175	−	0.750451i
$326$	−14.6001	+	7.31642i	−0.808623	+	0.405219i
$327$		0			0
$328$	−14.5038	+	3.17542i	−0.800836	+	0.175333i
$329$	−11.3668	−	11.3668i	−0.626672	−	0.626672i
$330$		0			0
$331$	−3.52744	−	8.51599i	−0.193886	−	0.468081i	0.796801	−	0.604242i	$-0.206524\pi$
$331$	−3.52744	−	8.51599i	−0.193886	−	0.468081i	−0.990687	+	0.136160i	$0.956524\pi$
$332$	3.33445	−	13.1130i	0.183002	−	0.719671i
$333$		0			0
$334$	−31.7931	+	2.28814i	−1.73964	+	0.125201i
$335$			8.46395i			0.462435i
$336$		0			0
$337$			22.2818i			1.21377i	0.794791	+	0.606883i	$0.207580\pi$
$337$			22.2818i			1.21377i	−0.794791	+	0.606883i	$0.792420\pi$
$338$	−0.376595	−	5.23270i	−0.0204841	−	0.284621i
$339$		0			0
$340$	2.78429	−	1.65535i	0.150999	−	0.0897741i
$341$	8.65020	+	20.8834i	0.468435	+	1.13090i
$342$		0			0
$343$	−14.1716	−	14.1716i	−0.765193	−	0.765193i
$344$	−32.5624	−	5.82995i	−1.75565	−	0.314330i
$345$		0			0
$346$	4.85479	+	9.68784i	0.260995	+	0.520821i
$347$	18.1573	−	7.52100i	0.974735	−	0.403748i	0.162262	−	0.986748i	$-0.448121\pi$
$347$	18.1573	−	7.52100i	0.974735	−	0.403748i	0.812473	+	0.582999i	$0.198121\pi$
$348$		0			0
$349$	5.48079	−	13.2318i	0.293380	−	0.708282i	−0.706620	−	0.707593i	$-0.749781\pi$
$349$	5.48079	−	13.2318i	0.293380	−	0.708282i	1.00000		0.000688266i	$-0.000219082\pi$
$350$	16.1894	−	18.7004i	0.865359	−	0.999578i
$351$		0			0
$352$	−0.406553	+	12.1419i	−0.0216694	+	0.647165i
$353$	25.9736			1.38243			0.691217	−	0.722648i	$-0.257075\pi$
$353$	25.9736			1.38243			0.691217	+	0.722648i	$0.257075\pi$
$354$		0			0
$355$	−17.2551	+	41.6574i	−0.915804	+	2.21095i
$356$	0.220942	+	0.165088i	0.0117099	+	0.00874966i
$357$		0			0
$358$	2.77311	+	5.53381i	0.146563	+	0.292471i
$359$	11.3256	−	11.3256i	0.597741	−	0.597741i	−0.341970	−	0.939711i	$-0.611094\pi$
$359$	11.3256	−	11.3256i	0.597741	−	0.597741i	0.939711	+	0.341970i	$0.111094\pi$
$360$		0			0
$361$	−9.81833	−	9.81833i	−0.516754	−	0.516754i
$362$	9.70899	−	29.2143i	0.510293	−	1.53547i
$363$		0			0
$364$	−8.44919	−	14.2115i	−0.442858	−	0.744883i
$365$	−15.8288	−	6.55651i	−0.828519	−	0.343184i
$366$		0			0
$367$		−	5.73929i		−	0.299588i	−0.988717	−	0.149794i	$-0.952139\pi$
$367$		−	5.73929i		−	0.299588i	0.988717	−	0.149794i	$-0.0478611\pi$
$368$	21.9981	+	11.9610i	1.14673	+	0.623511i
$369$		0			0
$370$	45.7910	−	3.29555i	2.38056	−	0.171328i
$371$	−9.66097	−	4.00171i	−0.501573	−	0.207758i
$372$		0			0
$373$	−4.83415	−	11.6707i	−0.250303	−	0.604284i	0.747926	−	0.663782i	$-0.231050\pi$
$373$	−4.83415	−	11.6707i	−0.250303	−	0.604284i	−0.998228	+	0.0594983i	$0.981050\pi$
$374$	−1.26353	−	0.419919i	−0.0653357	−	0.0217135i
$375$		0			0
$376$	18.9299	+	12.1298i	0.976236	+	0.625545i
$377$	18.7736	−	18.7736i	0.966889	−	0.966889i
$378$		0			0
$379$	−10.2019	+	4.22575i	−0.524034	+	0.217062i	−0.628988	−	0.777415i	$-0.716531\pi$
$379$	−10.2019	+	4.22575i	−0.524034	+	0.217062i	0.104954	+	0.994477i	$0.466531\pi$
$380$	2.39288	+	16.5381i	0.122752	+	0.848389i
$381$		0			0
$382$	−15.8406	−	13.7136i	−0.810474	−	0.701647i
$383$	23.3693			1.19412			0.597058	−	0.802198i	$-0.296336\pi$
$383$	23.3693			1.19412			0.597058	+	0.802198i	$0.296336\pi$
$384$		0			0
$385$	−16.0452			−0.817741
$386$	4.37596	+	3.78838i	0.222731	+	0.192823i
$387$		0			0
$388$	2.08180	+	14.3882i	0.105688	+	0.730450i
$389$	−18.6937	+	7.74317i	−0.947807	+	0.392594i	−0.802406	−	0.596778i	$-0.796447\pi$
$389$	−18.6937	+	7.74317i	−0.947807	+	0.392594i	−0.145401	+	0.989373i	$0.546447\pi$
$390$		0			0
$391$	−1.94052	+	1.94052i	−0.0981366	+	0.0981366i
$392$	6.93063	+	4.44096i	0.350050	+	0.224302i
$393$		0			0
$394$	4.01177	+	1.33326i	0.202110	+	0.0671687i
$395$	4.20245	+	10.1456i	0.211448	+	0.510481i
$396$		0			0
$397$	16.0734	+	6.65781i	0.806700	+	0.334146i	0.747636	−	0.664108i	$-0.231189\pi$
$397$	16.0734	+	6.65781i	0.806700	+	0.334146i	0.0590634	+	0.998254i	$0.481189\pi$
$398$	−35.9553	+	2.58769i	−1.80228	+	0.129709i
$399$		0			0
$400$	−16.5250	+	30.3919i	−0.826248	+	1.51960i
$401$		−	13.1779i		−	0.658073i	−0.944317	−	0.329036i	$-0.893276\pi$
$401$		−	13.1779i		−	0.658073i	0.944317	−	0.329036i	$-0.106724\pi$
$402$		0			0
$403$	39.7494	+	16.4648i	1.98006	+	0.820168i
$404$	−10.6497	−	17.9127i	−0.529841	−	0.891188i
$405$		0			0
$406$	5.85831	−	17.6276i	0.290743	−	0.874844i
$407$	−13.3439	−	13.3439i	−0.661434	−	0.661434i
$408$		0			0
$409$	10.4630	−	10.4630i	0.517361	−	0.517361i	−0.399411	−	0.916772i	$-0.630785\pi$
$409$	10.4630	−	10.4630i	0.517361	−	0.517361i	0.916772	+	0.399411i	$0.130785\pi$
$410$	12.2872	+	24.5194i	0.606822	+	1.21093i
$411$		0			0
$412$	−6.66037	−	4.97663i	−0.328133	−	0.245181i
$413$	2.13566	−	5.15594i	0.105089	−	0.253707i
$414$		0			0
$415$	−24.9931			−1.22687
$416$	15.7946	+	16.8890i	0.774396	+	0.828051i
$417$		0			0
$418$	4.49582	−	5.19312i	0.219898	−	0.254004i
$419$	6.28373	−	15.1703i	0.306980	−	0.741116i	−0.692820	−	0.721111i	$-0.743632\pi$
$419$	6.28373	−	15.1703i	0.306980	−	0.741116i	0.999800	−	0.0200048i	$-0.00636814\pi$
$420$		0			0
$421$	−22.3317	+	9.25011i	−1.08838	+	0.450823i	−0.853442	−	0.521187i	$-0.825489\pi$
$421$	−22.3317	+	9.25011i	−1.08838	+	0.450823i	−0.234940	+	0.972010i	$0.575489\pi$
$422$	−1.97420	−	3.93956i	−0.0961026	−	0.191775i
$423$		0			0
$424$	14.3963	+	2.57750i	0.699144	+	0.125174i
$425$	−2.68097	−	2.68097i	−0.130046	−	0.130046i
$426$		0			0
$427$	−5.37804	−	12.9837i	−0.260262	−	0.628327i
$428$	32.3341	−	19.2237i	1.56293	−	0.929211i
$429$		0			0
$430$	4.38639	+	60.9479i	0.211530	+	2.93917i
$431$			24.2282i			1.16703i	0.812102	+	0.583516i	$0.198323\pi$
$431$			24.2282i			1.16703i	−0.812102	+	0.583516i	$0.801677\pi$
$432$		0			0
$433$			34.2206i			1.64454i	0.569101	+	0.822268i	$0.307291\pi$
$433$			34.2206i			1.64454i	−0.569101	+	0.822268i	$0.692709\pi$
$434$	30.0244	−	2.16084i	1.44122	−	0.103724i
$435$		0			0
$436$	4.81381	−	18.9307i	0.230540	−	0.906618i
$437$	−5.41778	−	13.0797i	−0.259168	−	0.625686i
$438$		0			0
$439$	0.451072	+	0.451072i	0.0215285	+	0.0215285i	0.717789	−	0.696261i	$-0.245154\pi$
$439$	0.451072	+	0.451072i	0.0215285	+	0.0215285i	−0.696261	+	0.717789i	$0.745154\pi$
$440$	21.9217	−	4.79950i	1.04508	−	0.228807i
$441$		0			0
$442$	−2.26576	+	1.13542i	−0.107771	+	0.0540066i
$443$	−14.4425	+	5.98230i	−0.686186	+	0.284228i	−0.698410	−	0.715698i	$-0.746109\pi$
$443$	−14.4425	+	5.98230i	−0.686186	+	0.284228i	0.0122240	+	0.999925i	$0.496109\pi$
$444$		0			0
$445$	0.194966	−	0.470688i	0.00924225	−	0.0223128i
$446$	4.37436	+	3.78700i	0.207132	+	0.179319i
$447$		0			0
$448$	15.1735	+	5.61325i	0.716883	+	0.265201i
$449$	33.7946			1.59487			0.797434	−	0.603407i	$-0.206190\pi$
$449$	33.7946			1.59487			0.797434	+	0.603407i	$0.206190\pi$
$450$		0			0
$451$	4.31416	−	10.4153i	0.203146	−	0.490438i
$452$	18.3299	−	2.65212i	0.862165	−	0.124745i
$453$		0			0
$454$	11.0934	−	5.55913i	0.520638	−	0.260903i
$455$	−21.5954	+	21.5954i	−1.01241	+	1.01241i
$456$		0			0
$457$	−13.4971	−	13.4971i	−0.631368	−	0.631368i	0.317043	−	0.948411i	$-0.397310\pi$
$457$	−13.4971	−	13.4971i	−0.631368	−	0.631368i	−0.948411	+	0.317043i	$0.897310\pi$
$458$	−7.42096	−	2.46626i	−0.346759	−	0.115241i
$459$		0			0
$460$	11.3987	−	44.8265i	0.531468	−	2.09005i
$461$	−1.51739	−	0.628524i	−0.0706720	−	0.0292733i	0.347067	−	0.937840i	$-0.387177\pi$
$461$	−1.51739	−	0.628524i	−0.0706720	−	0.0292733i	−0.417739	+	0.908567i	$0.637177\pi$
$462$		0			0
$463$		−	18.1856i		−	0.845158i	−0.906326	−	0.422579i	$-0.861125\pi$
$463$		−	18.1856i		−	0.845158i	0.906326	−	0.422579i	$-0.138875\pi$
$464$	−2.73107	+	25.8360i	−0.126787	+	1.19941i
$465$		0			0
$466$	1.30728	+	18.1644i	0.0605588	+	0.841451i
$467$	−24.2793	−	10.0568i	−1.12351	−	0.465374i	−0.257942	−	0.966161i	$-0.583044\pi$
$467$	−24.2793	−	10.0568i	−1.12351	−	0.465374i	−0.865571	+	0.500786i	$0.833044\pi$
$468$		0			0
$469$	−1.77304	−	4.28051i	−0.0818716	−	0.197655i
$470$	13.0976	−	39.4105i	0.604146	−	1.81787i
$471$		0			0
$472$	−1.37558	+	7.68311i	−0.0633161	+	0.353644i
$473$	17.7608	−	17.7608i	0.816643	−	0.816643i
$474$		0			0
$475$	18.0705	−	7.48503i	0.829130	−	0.343437i
$476$	−1.06134	+	1.42043i	−0.0486466	+	0.0651051i
$477$		0			0
$478$	−10.4538	+	12.0753i	−0.478148	+	0.552309i
$479$	−10.5346			−0.481336			−0.240668	−	0.970607i	$-0.577367\pi$
$479$	−10.5346			−0.481336			−0.240668	+	0.970607i	$0.577367\pi$
$480$		0			0
$481$	−35.9193			−1.63778
$482$	−4.40265	+	5.08551i	−0.200535	+	0.231639i
$483$		0			0
$484$	10.2342	+	7.64700i	0.465191	+	0.347591i
$485$	24.8104	−	10.2768i	1.12658	−	0.466645i
$486$		0			0
$487$	−22.2836	+	22.2836i	−1.00977	+	1.00977i	−0.00981405	+	0.999952i	$0.503124\pi$
$487$	−22.2836	+	22.2836i	−1.00977	+	1.00977i	−0.999952	+	0.00981405i	$0.996876\pi$
$488$	11.2315	+	16.1303i	0.508424	+	0.730184i
$489$		0			0
$490$	4.79529	−	14.4290i	0.216629	−	0.651836i
$491$	−8.70272	−	21.0102i	−0.392748	−	0.948178i	−0.989339	−	0.145632i	$-0.953478\pi$
$491$	−8.70272	−	21.0102i	−0.392748	−	0.948178i	0.596591	−	0.802546i	$-0.296522\pi$
$492$		0			0
$493$	−2.63063	−	1.08964i	−0.118478	−	0.0490751i
$494$	−0.938510	−	13.0404i	−0.0422255	−	0.586714i
$495$		0			0
$496$	−40.3743	+	11.9332i	−1.81286	+	0.535817i
$497$		−	24.6822i		−	1.10715i
$498$		0			0
$499$	22.0084	+	9.11617i	0.985230	+	0.408096i	0.816360	−	0.577543i	$-0.195988\pi$
$499$	22.0084	+	9.11617i	0.985230	+	0.408096i	0.168870	+	0.985638i	$0.445988\pi$
$500$	26.1265	+	6.64358i	1.16841	+	0.297110i
$501$		0			0
$502$	8.86380	+	2.94577i	0.395611	+	0.131476i
$503$	18.2556	+	18.2556i	0.813978	+	0.813978i	0.985228	−	0.171250i	$-0.0547804\pi$
$503$	18.2556	+	18.2556i	0.813978	+	0.813978i	−0.171250	+	0.985228i	$0.554780\pi$
$504$		0			0
$505$	−27.2196	+	27.2196i	−1.21126	+	1.21126i
$506$	−16.9976	+	8.51787i	−0.755636	+	0.378666i
$507$		0			0
$508$	−2.46662	−	17.0478i	−0.109438	−	0.756373i
$509$	−7.83769	+	18.9218i	−0.347399	+	0.838696i	0.649526	+	0.760339i	$0.274967\pi$
$509$	−7.83769	+	18.9218i	−0.347399	+	0.838696i	−0.996925	+	0.0783568i	$0.975033\pi$
$510$		0			0
$511$	9.37865			0.414887
$512$	−22.4098	−	3.13033i	−0.990384	−	0.138343i
$513$		0			0
$514$	18.5133	+	16.0274i	0.816588	+	0.706940i
$515$	−5.87729	+	14.1890i	−0.258985	+	0.625244i
$516$		0			0
$517$	−15.7715	+	6.53278i	−0.693631	+	0.287311i
$518$	−22.4677	+	11.2590i	−0.987173	+	0.494694i
$519$		0			0
$520$	23.0449	−	35.9642i	1.01059	−	1.57714i
$521$	24.5716	+	24.5716i	1.07650	+	1.07650i	0.996821	+	0.0796799i	$0.0253898\pi$
$521$	24.5716	+	24.5716i	1.07650	+	1.07650i	0.0796799	+	0.996821i	$0.474610\pi$
$522$		0			0
$523$	6.78131	+	16.3715i	0.296526	+	0.715877i	0.999987	+	0.00514324i	$0.00163715\pi$
$523$	6.78131	+	16.3715i	0.296526	+	0.715877i	−0.703461	+	0.710734i	$0.748363\pi$
$524$	−28.3254	−	7.20274i	−1.23740	−	0.314653i
$525$		0			0
$526$	18.0222	−	1.29705i	0.785805	−	0.0565540i
$527$		−	4.61422i		−	0.200998i
$528$		0			0
$529$			16.1865i			0.703761i
$530$	−1.93928	−	26.9458i	−0.0842369	−	1.17045i
$531$		0			0
$532$	−4.67460	−	7.86264i	−0.202670	−	0.340889i
$533$	−8.21156	−	19.8245i	−0.355682	−	0.858693i
$534$		0			0
$535$	−49.1340	−	49.1340i	−2.12425	−	2.12425i
$536$	3.70281	+	5.31787i	0.159937	+	0.229697i
$537$		0			0
$538$	3.09331	+	6.17278i	0.133362	+	0.266127i
$539$	−5.77428	+	2.39178i	−0.248716	+	0.103021i
$540$		0			0
$541$	10.8801	−	26.2669i	0.467773	−	1.12930i	−0.497361	−	0.867544i	$-0.665697\pi$
$541$	10.8801	−	26.2669i	0.467773	−	1.12930i	0.965133	−	0.261759i	$-0.0843026\pi$
$542$	−11.7133	+	13.5300i	−0.503128	+	0.581164i
$543$		0			0
$544$	1.02517	−	2.25812i	0.0439539	−	0.0968162i
$545$	−36.0816			−1.54557
$546$		0			0
$547$	−9.92998	+	23.9731i	−0.424575	+	1.02502i	0.556405	+	0.830911i	$0.312180\pi$
$547$	−9.92998	+	23.9731i	−0.424575	+	1.02502i	−0.980981	+	0.194105i	$0.937820\pi$
$548$	2.23582	−	2.99226i	0.0955094	−	0.127823i
$549$		0			0
$550$	−11.7680	−	23.4834i	−0.501790	−	1.00133i
$551$	10.3867	−	10.3867i	0.442488	−	0.442488i
$552$		0			0
$553$	−4.25065	−	4.25065i	−0.180756	−	0.180756i
$554$	−5.08650	+	15.3053i	−0.216105	+	0.650258i
$555$		0			0
$556$	5.08640	−	3.02404i	0.215712	−	0.128248i
$557$	27.0857	+	11.2193i	1.14766	+	0.475376i	0.873748	−	0.486379i	$-0.161683\pi$
$557$	27.0857	+	11.2193i	1.14766	+	0.475376i	0.273911	+	0.961755i	$0.411683\pi$
$558$		0			0
$559$		−	47.8087i		−	2.02209i
$560$	3.14156	−	29.7193i	0.132755	−	1.25587i
$561$		0			0
$562$	35.4950	−	2.55456i	1.49727	−	0.107757i
$563$	18.9270	+	7.83982i	0.797677	+	0.330409i	0.744026	−	0.668151i	$-0.232914\pi$
$563$	18.9270	+	7.83982i	0.797677	+	0.330409i	0.0536517	+	0.998560i	$0.482914\pi$
$564$		0			0
$565$	−13.0921	−	31.6072i	−0.550791	−	1.32973i
$566$	−19.3510	−	6.43106i	−0.813384	−	0.270317i
$567$		0			0
$568$	7.38301	+	33.7220i	0.309784	+	1.41494i
$569$	−3.99634	+	3.99634i	−0.167535	+	0.167535i	−0.785895	−	0.618360i	$-0.787797\pi$
$569$	−3.99634	+	3.99634i	−0.167535	+	0.167535i	0.618360	+	0.785895i	$0.287797\pi$
$570$		0			0
$571$	4.31458	−	1.78716i	0.180559	−	0.0747902i	−0.290572	−	0.956853i	$-0.593846\pi$
$571$	4.31458	−	1.78716i	0.180559	−	0.0747902i	0.471132	+	0.882063i	$0.343846\pi$
$572$	−17.3768	+	2.51422i	−0.726560	+	0.105125i
$573$		0			0
$574$	−11.3504	−	9.82635i	−0.473758	−	0.410144i
$575$	−54.1388			−2.25775
$576$		0			0
$577$	−22.2416			−0.925929			−0.462965	−	0.886377i	$-0.653214\pi$
$577$	−22.2416			−0.925929			−0.462965	+	0.886377i	$0.653214\pi$
$578$	−17.9710	−	15.5579i	−0.747494	−	0.647124i
$579$		0			0
$580$	47.4954	−	6.87204i	1.97214	−	0.285346i
$581$	12.6399	−	5.23561i	0.524391	−	0.217210i
$582$		0			0
$583$	−7.85228	+	7.85228i	−0.325208	+	0.325208i
$584$	−12.8135	+	2.80537i	−0.530228	+	0.116087i
$585$		0			0
$586$	3.38391	+	1.12460i	0.139788	+	0.0464568i
$587$	14.5909	+	35.2255i	0.602230	+	1.45391i	0.871281	+	0.490785i	$0.163290\pi$
$587$	14.5909	+	35.2255i	0.602230	+	1.45391i	−0.269051	+	0.963126i	$0.586710\pi$
$588$		0			0
$589$	21.9918	+	9.10930i	0.906156	+	0.375342i
$590$	14.3807	−	1.03497i	0.592043	−	0.0426090i
$591$		0			0
$592$	27.3285	−	22.1032i	1.12320	−	0.908437i
$593$		−	22.2300i		−	0.912876i	−0.889755	−	0.456438i	$-0.849125\pi$
$593$		−	22.2300i		−	0.912876i	0.889755	−	0.456438i	$-0.150875\pi$
$594$		0			0
$595$	3.02603	+	1.25342i	0.124055	+	0.0513853i
$596$	−29.6253	+	17.6133i	−1.21350	+	0.721467i
$597$		0			0
$598$	−11.4129	+	34.3414i	−0.466709	+	1.40432i
$599$	12.7672	+	12.7672i	0.521652	+	0.521652i	0.918070	−	0.396418i	$-0.129747\pi$
$599$	12.7672	+	12.7672i	0.521652	+	0.521652i	−0.396418	+	0.918070i	$0.629747\pi$
$600$		0			0
$601$	3.76049	−	3.76049i	0.153393	−	0.153393i	−0.626238	−	0.779632i	$-0.715406\pi$
$601$	3.76049	−	3.76049i	0.153393	−	0.153393i	0.779632	+	0.626238i	$0.215406\pi$
$602$	−14.9858	−	29.9046i	−0.610777	−	1.21882i
$603$		0			0
$604$	−4.16051	+	5.56813i	−0.169289	+	0.226564i
$605$	9.03093	−	21.8026i	0.367160	−	0.886402i
$606$		0			0
$607$	−3.12416			−0.126806			−0.0634029	−	0.997988i	$-0.520195\pi$
$607$	−3.12416			−0.126806			−0.0634029	+	0.997988i	$0.520195\pi$
$608$	8.73855	+	9.34402i	0.354395	+	0.378950i
$609$		0			0
$610$	23.7639	−	27.4497i	0.962173	−	1.11141i
$611$	−12.4345	+	30.0195i	−0.503045	+	1.21446i
$612$		0			0
$613$	24.5587	−	10.1725i	0.991915	−	0.410865i	0.173089	−	0.984906i	$-0.444625\pi$
$613$	24.5587	−	10.1725i	0.991915	−	0.410865i	0.818826	+	0.574042i	$0.194625\pi$
$614$	0.640558	+	1.27825i	0.0258508	+	0.0515859i
$615$		0			0
$616$	−10.0812	+	7.01948i	−0.406182	+	0.282823i
$617$	21.9427	+	21.9427i	0.883381	+	0.883381i	0.993877	−	0.110496i	$-0.0352439\pi$
$617$	21.9427	+	21.9427i	0.883381	+	0.883381i	−0.110496	+	0.993877i	$0.535244\pi$
$618$		0			0
$619$	−4.65627	−	11.2412i	−0.187151	−	0.451823i	0.802258	−	0.596978i	$-0.203632\pi$
$619$	−4.65627	−	11.2412i	−0.187151	−	0.451823i	−0.989409	+	0.145155i	$0.953632\pi$
$620$	39.7426	+	66.8467i	1.59610	+	2.68463i
$621$		0			0
$622$	−1.50975	−	20.9777i	−0.0605357	−	0.841129i
$623$			0.278885i			0.0111733i
$624$		0			0
$625$		−	6.55402i		−	0.262161i
$626$	−7.28877	+	0.524569i	−0.291318	+	0.0209660i
$627$		0			0
$628$	−26.4917	−	6.73645i	−1.05713	−	0.268814i
$629$	1.47418	+	3.55898i	0.0587793	+	0.141906i
$630$		0			0
$631$	14.3503	+	14.3503i	0.571275	+	0.571275i	0.932485	−	0.361210i	$-0.117636\pi$
$631$	14.3503	+	14.3503i	0.571275	+	0.571275i	−0.361210	+	0.932485i	$0.617636\pi$
$632$	7.07889	+	4.53596i	0.281583	+	0.180431i
$633$		0			0
$634$	−6.20901	+	3.11147i	−0.246591	+	0.123572i
$635$	−29.3964	+	12.1764i	−1.16656	+	0.483206i
$636$		0			0
$637$	−4.55251	+	10.9907i	−0.180377	+	0.435469i
$638$	−14.9140	−	12.9114i	−0.590450	−	0.511167i
$639$		0			0
$640$	4.59758	+	41.5436i	0.181735	+	1.64215i
$641$	−28.6116			−1.13009			−0.565045	−	0.825060i	$-0.691141\pi$
$641$	−28.6116			−1.13009			−0.565045	+	0.825060i	$0.691141\pi$
$642$		0			0
$643$	8.41154	−	20.3072i	0.331719	−	0.800840i	−0.666737	−	0.745293i	$-0.732310\pi$
$643$	8.41154	−	20.3072i	0.331719	−	0.800840i	0.998456	−	0.0555470i	$-0.0176903\pi$
$644$	3.62562	+	25.0581i	0.142869	+	0.987428i
$645$		0			0
$646$	−1.25356	+	0.628185i	−0.0493206	+	0.0247156i
$647$	−9.40277	+	9.40277i	−0.369661	+	0.369661i	−0.867354	−	0.497692i	$-0.834181\pi$
$647$	−9.40277	+	9.40277i	−0.369661	+	0.369661i	0.497692	+	0.867354i	$0.334181\pi$
$648$		0			0
$649$	−4.19066	−	4.19066i	−0.164498	−	0.164498i
$650$	−47.4450	−	15.7677i	−1.86095	−	0.618461i
$651$		0			0
$652$	22.3828	+	5.69162i	0.876578	+	0.222901i
$653$	7.49935	+	3.10633i	0.293472	+	0.121560i	0.524562	−	0.851372i	$-0.324229\pi$
$653$	7.49935	+	3.10633i	0.293472	+	0.121560i	−0.231090	+	0.972932i	$0.574229\pi$
$654$		0			0
$655$			53.9876i			2.10947i
$656$	18.4468	+	10.0300i	0.720225	+	0.391607i
$657$		0			0
$658$	1.63190	+	22.6750i	0.0636183	+	0.883962i
$659$	−11.2864	−	4.67496i	−0.439654	−	0.182111i	0.151866	−	0.988401i	$-0.451472\pi$
$659$	−11.2864	−	4.67496i	−0.439654	−	0.182111i	−0.591520	+	0.806290i	$0.701472\pi$
$660$		0			0
$661$	−1.50634	−	3.63662i	−0.0585897	−	0.141448i	0.891874	−	0.452284i	$-0.149391\pi$
$661$	−1.50634	−	3.63662i	−0.0585897	−	0.141448i	−0.950463	+	0.310837i	$0.899391\pi$
$662$	−4.11116	+	12.3705i	−0.159785	+	0.480792i
$663$		0			0
$664$	−15.7031	+	10.9340i	−0.609398	+	0.424322i
$665$	−11.9479	+	11.9479i	−0.463318	+	0.463318i
$666$		0			0
$667$	−37.5632	+	15.5592i	−1.45445	+	0.602453i
$668$	36.1113	+	26.9824i	1.39719	+	1.04398i
$669$		0			0
$670$	7.83454	−	9.04969i	0.302675	−	0.349620i
$671$	−14.9242			−0.576141
$672$		0			0
$673$	27.5194			1.06079			0.530397	−	0.847750i	$-0.322043\pi$
$673$	27.5194			1.06079			0.530397	+	0.847750i	$0.322043\pi$
$674$	20.6248	−	23.8238i	0.794438	−	0.917657i
$675$		0			0
$676$	−4.44092	+	5.94341i	−0.170805	+	0.228593i
$677$	−0.644485	+	0.266954i	−0.0247696	+	0.0102599i	−0.395034	−	0.918667i	$-0.629267\pi$
$677$	−0.644485	+	0.266954i	−0.0247696	+	0.0102599i	0.370264	+	0.928926i	$0.379267\pi$
$678$		0			0
$679$	−10.3946	+	10.3946i	−0.398910	+	0.398910i
$680$	−4.50923	−	0.807329i	−0.172921	−	0.0309596i
$681$		0			0
$682$	10.0816	−	30.3356i	0.386046	−	1.16161i
$683$	9.58949	+	23.1511i	0.366932	+	0.885851i	0.994250	+	0.107088i	$0.0341527\pi$
$683$	9.58949	+	23.1511i	0.366932	+	0.885851i	−0.627318	+	0.778763i	$0.715847\pi$
$684$		0			0
$685$	−6.37461	−	2.64045i	−0.243561	−	0.100886i
$686$	2.03458	+	28.2700i	0.0776806	+	1.07935i
$687$		0			0
$688$	29.4195	+	36.3744i	1.12161	+	1.38676i
$689$			21.1368i			0.805249i
$690$		0			0
$691$	−37.5395	−	15.5494i	−1.42807	−	0.591525i	−0.471195	−	0.882029i	$-0.656177\pi$
$691$	−37.5395	−	15.5494i	−1.42807	−	0.591525i	−0.956874	+	0.290504i	$0.906177\pi$
$692$	3.77666	−	14.8520i	0.143567	−	0.564590i
$693$		0			0
$694$	−26.3756	−	8.76557i	−1.00120	−	0.332737i
$695$	−7.72916	−	7.72916i	−0.293184	−	0.293184i
$696$		0			0
$697$	−1.62725	+	1.62725i	−0.0616364	+	0.0616364i
$698$	−18.1079	+	9.07427i	−0.685394	+	0.343466i
$699$		0			0
$700$	−34.6195	+	5.00904i	−1.30849	+	0.189324i
$701$	8.03431	−	19.3965i	0.303452	−	0.732597i	−0.696436	−	0.717619i	$-0.745232\pi$
$701$	8.03431	−	19.3965i	0.303452	−	0.732597i	0.999888	−	0.0149782i	$-0.00476788\pi$
$702$		0			0
$703$	−19.8727			−0.749514
$704$	11.6737	−	12.6058i	0.439968	−	0.475100i
$705$		0			0
$706$	−27.7710	−	24.0421i	−1.04518	−	0.904835i
$707$	8.06387	−	19.4679i	0.303273	−	0.732166i
$708$		0			0
$709$	−2.92536	+	1.21172i	−0.109864	+	0.0455072i	−0.436938	−	0.899491i	$-0.643937\pi$
$709$	−2.92536	+	1.21172i	−0.109864	+	0.0455072i	0.327074	+	0.944999i	$0.393937\pi$
$710$	57.0088	−	28.5684i	2.13950	−	1.07215i
$711$		0			0
$712$	−0.0834208	−	0.381025i	−0.00312633	−	0.0142795i
$713$	−46.5892	−	46.5892i	−1.74478	−	1.74478i
$714$		0			0
$715$	12.4114	+	29.9637i	0.464160	+	1.12058i
$716$	2.15727	−	8.48366i	0.0806210	−	0.317049i
$717$		0			0
$718$	−22.5927	+	1.62599i	−0.843152	+	0.0606812i
$719$		−	38.4893i		−	1.43541i	−0.696348	−	0.717704i	$-0.745193\pi$
$719$		−	38.4893i		−	1.43541i	0.696348	−	0.717704i	$-0.254807\pi$
$720$		0			0
$721$		−	8.40707i		−	0.313096i
$722$	1.40960	+	19.5860i	0.0524597	+	0.728916i
$723$		0			0
$724$	−37.4227	+	22.2491i	−1.39080	+	0.826880i
$725$	−21.4961	−	51.8961i	−0.798344	−	1.92737i
$726$		0			0
$727$	3.38112	+	3.38112i	0.125399	+	0.125399i	0.767021	−	0.641622i	$-0.221738\pi$
$727$	3.38112	+	3.38112i	0.125399	+	0.125399i	−0.641622	+	0.767021i	$0.721738\pi$
$728$	−4.12074	+	23.0158i	−0.152725	+	0.853023i
$729$		0			0
$730$	10.8553	+	21.6620i	0.401773	+	0.801746i
$731$	−4.73701	+	1.96213i	−0.175205	+	0.0725722i
$732$		0			0
$733$	7.53960	−	18.2022i	0.278481	−	0.672313i	−0.721313	−	0.692610i	$-0.756461\pi$
$733$	7.53960	−	18.2022i	0.278481	−	0.672313i	0.999794	+	0.0202962i	$0.00646092\pi$
$734$	−5.31249	+	6.13647i	−0.196088	+	0.226501i
$735$		0			0
$736$	−12.4489	−	33.1510i	−0.458874	−	1.22196i
$737$	−4.92023			−0.181239
$738$		0			0
$739$	−14.2967	+	34.5153i	−0.525912	+	1.26966i	0.408268	+	0.912862i	$0.366133\pi$
$739$	−14.2967	+	34.5153i	−0.525912	+	1.26966i	−0.934180	+	0.356802i	$0.883867\pi$
$740$	−52.0104	−	38.8622i	−1.91194	−	1.42860i
$741$		0			0
$742$	6.62542	+	13.2212i	0.243227	+	0.485365i
$743$	−21.3212	+	21.3212i	−0.782198	+	0.782198i	−0.980201	−	0.198004i	$-0.936554\pi$
$743$	−21.3212	+	21.3212i	−0.782198	+	0.782198i	0.198004	+	0.980201i	$0.436554\pi$
$744$		0			0
$745$	45.0179	+	45.0179i	1.64933	+	1.64933i
$746$	−5.63410	+	16.9530i	−0.206279	+	0.620693i
$747$		0			0
$748$	0.962282	+	1.61855i	0.0351845	+	0.0591801i
$749$	35.1414	+	14.5560i	1.28404	+	0.531866i
$750$		0			0
$751$		−	13.8811i		−	0.506530i	−0.967397	−	0.253265i	$-0.918495\pi$
$751$		−	13.8811i		−	0.506530i	0.967397	−	0.253265i	$-0.0815045\pi$
$752$	−9.01218	−	30.4914i	−0.328640	−	1.11191i
$753$		0			0
$754$	−37.4503	+	2.69528i	−1.36386	+	0.0981563i
$755$	11.8622	+	4.91347i	0.431708	+	0.178819i
$756$		0			0
$757$	17.5783	+	42.4377i	0.638894	+	1.54243i	0.828155	+	0.560499i	$0.189391\pi$
$757$	17.5783	+	42.4377i	0.638894	+	1.54243i	−0.189261	+	0.981927i	$0.560609\pi$
$758$	14.8194	+	4.92503i	0.538264	+	0.178885i
$759$		0			0
$760$	12.7498	−	19.8976i	0.462485	−	0.721761i
$761$	29.3929	−	29.3929i	1.06549	−	1.06549i	0.0677921	−	0.997699i	$-0.478405\pi$
$761$	29.3929	−	29.3929i	1.06549	−	1.06549i	0.997699	−	0.0677921i	$-0.0215954\pi$
$762$		0			0
$763$	18.2477	−	7.55844i	0.660611	−	0.273634i
$764$	4.24302	+	29.3252i	0.153507	+	1.06095i
$765$		0			0
$766$	−24.9865	−	21.6315i	−0.902801	−	0.781577i
$767$	−11.2805			−0.407314
$768$		0			0
$769$	20.6336			0.744067			0.372034	−	0.928219i	$-0.378661\pi$
$769$	20.6336			0.744067			0.372034	+	0.928219i	$0.378661\pi$
$770$	17.1556	+	14.8521i	0.618246	+	0.535231i
$771$		0			0
$772$	−1.17214	−	8.10110i	−0.0421861	−	0.291565i
$773$	22.0085	−	9.11620i	0.791589	−	0.327887i	0.0500067	−	0.998749i	$-0.484076\pi$
$773$	22.0085	−	9.11620i	0.791589	−	0.327887i	0.741582	+	0.670862i	$0.234076\pi$
$774$		0			0
$775$	64.3662	−	64.3662i	2.31210	−	2.31210i
$776$	11.0924	−	17.3109i	0.398193	−	0.621425i
$777$		0			0
$778$	27.1547	+	9.02451i	0.973543	+	0.323544i
$779$	−4.54313	−	10.9681i	−0.162775	−	0.392973i
$780$		0			0
$781$	−24.2161	−	10.0306i	−0.866521	−	0.358925i
$782$	3.87104	−	0.278597i	0.138428	−	0.00996259i
$783$		0			0
$784$	−3.29954	−	11.1635i	−0.117841	−	0.398698i
$785$			50.4926i			1.80216i
$786$		0			0
$787$	11.9474	+	4.94878i	0.425879	+	0.176405i	0.585320	−	0.810803i	$-0.300969\pi$
$787$	11.9474	+	4.94878i	0.425879	+	0.176405i	−0.159441	+	0.987208i	$0.550969\pi$
$788$	−3.05529	−	5.13897i	−0.108840	−	0.183068i
$789$		0			0
$790$	4.89787	−	14.7377i	0.174258	−	0.524343i
$791$	13.2423	+	13.2423i	0.470841	+	0.470841i
$792$		0			0
$793$	−20.0865	+	20.0865i	−0.713292	+	0.713292i
$794$	−11.0230	−	21.9967i	−0.391192	−	0.780633i
$795$		0			0
$796$	40.8388	+	30.5148i	1.44749	+	1.08157i
$797$	−16.4541	+	39.7238i	−0.582836	+	1.40709i	0.307396	+	0.951582i	$0.400542\pi$
$797$	−16.4541	+	39.7238i	−0.582836	+	1.40709i	−0.890232	+	0.455508i	$0.849458\pi$
$798$		0			0
$799$	3.48474			0.123281
$800$	45.8004	−	17.1991i	1.61929	−	0.608079i
$801$		0			0
$802$	−12.1979	+	14.0899i	−0.430724	+	0.497530i
$803$	3.81141	−	9.20155i	0.134502	−	0.324716i
$804$		0			0
$805$	43.2091	−	17.8978i	1.52292	−	0.630814i
$806$	−27.2599	−	54.3977i	−0.960188	−	1.91608i
$807$		0			0
$808$	−5.19393	+	29.0100i	−0.182722	+	1.02057i
$809$	18.9088	+	18.9088i	0.664798	+	0.664798i	0.956507	−	0.291709i	$-0.0942239\pi$
$809$	18.9088	+	18.9088i	0.664798	+	0.664798i	−0.291709	+	0.956507i	$0.594224\pi$
$810$		0			0
$811$	8.82773	+	21.3120i	0.309984	+	0.748367i	0.999705	+	0.0242916i	$0.00773303\pi$
$811$	8.82773	+	21.3120i	0.309984	+	0.748367i	−0.689721	+	0.724075i	$0.742267\pi$
$812$	−22.5805	+	13.4249i	−0.792420	+	0.471120i
$813$		0			0
$814$	1.91576	+	26.6190i	0.0671472	+	0.932996i
$815$		−	42.6611i		−	1.49435i
$816$		0			0
$817$		−	26.4507i		−	0.925392i
$818$	−20.8720	+	1.50215i	−0.729771	+	0.0525213i
$819$		0			0
$820$	9.55852	−	37.5897i	0.333798	−	1.31269i
$821$	7.98875	+	19.2865i	0.278809	+	0.673105i	0.999803	−	0.0198363i	$-0.00631450\pi$
$821$	7.98875	+	19.2865i	0.278809	+	0.673105i	−0.720994	+	0.692941i	$0.756314\pi$
$822$		0			0
$823$	25.2426	+	25.2426i	0.879900	+	0.879900i	0.993524	−	0.113624i	$-0.0362459\pi$
$823$	25.2426	+	25.2426i	0.879900	+	0.879900i	−0.113624	+	0.993524i	$0.536246\pi$
$824$	2.51475	+	11.4861i	0.0876053	+	0.400138i
$825$		0			0
$826$	−7.05598	+	3.53591i	−0.245509	+	0.123030i
$827$	−13.6656	+	5.66049i	−0.475201	+	0.196835i	−0.607412	−	0.794387i	$-0.707792\pi$
$827$	−13.6656	+	5.66049i	−0.475201	+	0.196835i	0.132211	+	0.991222i	$0.457792\pi$
$828$		0			0
$829$	6.74015	−	16.2722i	0.234095	−	0.565155i	−0.762557	−	0.646922i	$-0.776056\pi$
$829$	6.74015	−	16.2722i	0.234095	−	0.565155i	0.996652	+	0.0817664i	$0.0260561\pi$
$830$	26.7228	+	23.1346i	0.927561	+	0.803013i
$831$		0			0
$832$	−1.25462	−	32.6779i	−0.0434960	−	1.13290i
$833$	1.27583			0.0442050
$834$		0			0
$835$	31.8656	−	76.9304i	1.10275	−	2.66229i
$836$	−9.61389	+	1.39102i	−0.332503	+	0.0481094i
$837$		0			0
$838$	−20.7607	+	10.4037i	−0.717167	+	0.359388i
$839$	36.9593	−	36.9593i	1.27598	−	1.27598i	0.333080	−	0.942899i	$-0.391912\pi$
$839$	36.9593	−	36.9593i	1.27598	−	1.27598i	0.942899	−	0.333080i	$-0.108088\pi$
$840$		0			0
$841$	−9.32314	−	9.32314i	−0.321488	−	0.321488i
$842$	32.4394	+	10.7808i	1.11794	+	0.371531i
$843$		0			0
$844$	−1.53578	+	6.03959i	−0.0528637	+	0.207891i
$845$	12.6617	+	5.24463i	0.435574	+	0.180421i
$846$		0			0
$847$			12.9181i			0.443872i
$848$	−13.0067	−	16.0816i	−0.446652	−	0.552244i
$849$		0			0
$850$	0.384900	+	5.34810i	0.0132020	+	0.183438i
$851$	50.8192	+	21.0500i	1.74206	+	0.721585i
$852$		0			0
$853$	10.1321	+	24.4611i	0.346917	+	0.837532i	0.996981	+	0.0776517i	$0.0247422\pi$
$853$	10.1321	+	24.4611i	0.346917	+	0.837532i	−0.650064	+	0.759880i	$0.725258\pi$
$854$	−6.26800	+	18.8604i	−0.214487	+	0.645389i
$855$		0			0
$856$	−52.3658	−	9.37554i	−1.78983	−	0.320449i
$857$	29.6874	−	29.6874i	1.01410	−	1.01410i	0.0142046	−	0.999899i	$-0.495478\pi$
$857$	29.6874	−	29.6874i	1.01410	−	1.01410i	0.999899	−	0.0142046i	$-0.00452161\pi$
$858$		0			0
$859$	19.6106	−	8.12296i	0.669103	−	0.277152i	−0.0221602	−	0.999754i	$-0.507054\pi$
$859$	19.6106	−	8.12296i	0.669103	−	0.277152i	0.691264	+	0.722603i	$0.257054\pi$
$860$	51.7257	−	69.2259i	1.76383	−	2.36059i
$861$		0			0
$862$	22.4265	−	25.9049i	0.763850	−	0.882325i
$863$	−0.378677			−0.0128903			−0.00644515	−	0.999979i	$-0.502052\pi$
$863$	−0.378677			−0.0128903			−0.00644515	+	0.999979i	$0.502052\pi$
$864$		0			0
$865$	−28.3077			−0.962490
$866$	31.6758	−	36.5888i	1.07639	−	1.24334i
$867$		0			0
$868$	−34.1024	−	25.4813i	−1.15751	−	0.864891i
$869$	−5.89781	+	2.44295i	−0.200069	+	0.0828715i
$870$		0			0
$871$	−6.62215	+	6.62215i	−0.224383	+	0.224383i
$872$	−22.6699	+	15.7850i	−0.767701	+	0.534547i
$873$		0			0
$874$	−6.31431	+	18.9997i	−0.213585	+	0.642676i
$875$	10.4315	+	25.1838i	0.352648	+	0.851367i
$876$		0			0
$877$	−34.8920	−	14.4527i	−1.17822	−	0.488034i	−0.294317	−	0.955708i	$-0.595092\pi$
$877$	−34.8920	−	14.4527i	−1.17822	−	0.488034i	−0.883901	+	0.467674i	$0.845092\pi$
$878$	−0.0647594	−	0.899817i	−0.00218552	−	0.0303674i
$879$		0			0
$880$	−27.8814	−	15.1599i	−0.939882	−	0.511041i
$881$		−	51.9353i		−	1.74974i	−0.484353	−	0.874872i	$-0.660945\pi$
$881$		−	51.9353i		−	1.74974i	0.484353	−	0.874872i	$-0.339055\pi$
$882$		0			0
$883$	−4.46493	−	1.84944i	−0.150257	−	0.0622385i	0.306288	−	0.951939i	$-0.400913\pi$
$883$	−4.46493	−	1.84944i	−0.150257	−	0.0622385i	−0.456545	+	0.889701i	$0.650913\pi$
$884$	3.47355	+	0.883274i	0.116828	+	0.0297077i
$885$		0			0
$886$	20.9795	+	6.97225i	0.704819	+	0.234237i
$887$	37.8951	+	37.8951i	1.27239	+	1.27239i	0.944828	+	0.327566i	$0.106228\pi$
$887$	37.8951	+	37.8951i	1.27239	+	1.27239i	0.327566	+	0.944828i	$0.393772\pi$
$888$		0			0
$889$	12.3160	−	12.3160i	0.413067	−	0.413067i
$890$	−0.644144	+	0.322795i	−0.0215918	+	0.0108201i
$891$		0			0
$892$	−1.17171	−	8.09814i	−0.0392317	−	0.271146i
$893$	−6.87950	+	16.6086i	−0.230214	+	0.555785i
$894$		0			0
$895$	−16.1697			−0.540493
$896$	−11.0278	−	20.0469i	−0.368412	−	0.669720i
$897$		0			0
$898$	−36.1334	−	31.2815i	−1.20579	−	1.04388i
$899$	26.1607	−	63.1576i	0.872510	−	2.10642i
$900$		0			0
$901$	2.09429	−	0.867485i	0.0697710	−	0.0289001i
$902$	−14.2535	+	7.14275i	−0.474590	+	0.237827i
$903$		0			0
$904$	−22.0533	−	14.1311i	−0.733481	−	0.469995i
$905$	56.8666	+	56.8666i	1.89031	+	1.89031i
$906$		0			0
$907$	−3.11690	−	7.52487i	−0.103495	−	0.249859i	0.863646	−	0.504098i	$-0.168175\pi$
$907$	−3.11690	−	7.52487i	−0.103495	−	0.249859i	−0.967141	+	0.254239i	$0.918175\pi$
$908$	−17.0068	−	4.32458i	−0.564391	−	0.143516i
$909$		0			0
$910$	43.0793	−	3.10039i	1.42806	−	0.102777i
$911$			21.5716i			0.714699i	0.933971	+	0.357349i	$0.116319\pi$
$911$			21.5716i			0.714699i	−0.933971	+	0.357349i	$0.883681\pi$
$912$		0			0
$913$		−	14.5289i		−	0.480837i
$914$	1.93775	+	26.9246i	0.0640950	+	0.890586i
$915$		0			0
$916$	5.65166	+	9.50605i	0.186736	+	0.314089i
$917$	−11.3094	−	27.3034i	−0.373470	−	0.901637i
$918$		0			0
$919$	5.85899	+	5.85899i	0.193270	+	0.193270i	0.797108	−	0.603837i	$-0.206362\pi$
$919$	5.85899	+	5.85899i	0.193270	+	0.193270i	−0.603837	+	0.797108i	$0.706362\pi$
$920$	−53.6806	+	37.3776i	−1.76980	+	1.23230i
$921$		0			0
$922$	1.04062	+	2.07657i	0.0342709	+	0.0683883i
$923$	−46.0929	+	19.0923i	−1.51717	+	0.628430i
$924$		0			0
$925$	−29.0820	+	70.2102i	−0.956211	+	2.30850i
$926$	−16.8333	+	19.4442i	−0.553176	+	0.638975i
$927$		0			0
$928$	26.8348	−	25.0960i	0.880896	−	0.823817i
$929$	−40.1642			−1.31775			−0.658873	−	0.752255i	$-0.728966\pi$
$929$	−40.1642			−1.31775			−0.658873	+	0.752255i	$0.728966\pi$
$930$		0			0
$931$	−2.51873	+	6.08074i	−0.0825479	+	0.199288i
$932$	15.4159	−	20.6315i	0.504965	−	0.675809i
$933$		0			0
$934$	16.6506	+	33.2266i	0.544824	+	1.08721i
$935$	2.45951	−	2.45951i	0.0804345	−	0.0804345i
$936$		0			0
$937$	−21.4726	−	21.4726i	−0.701478	−	0.701478i	0.263250	−	0.964728i	$-0.415206\pi$
$937$	−21.4726	−	21.4726i	−0.701478	−	0.701478i	−0.964728	+	0.263250i	$0.915206\pi$
$938$	−2.06645	+	6.21793i	−0.0674719	+	0.203023i
$939$		0			0
$940$	−50.4838	+	30.0143i	−1.64660	+	0.978959i
$941$	−51.5933	−	21.3706i	−1.68189	−	0.696663i	−0.682480	−	0.730905i	$-0.739098\pi$
$941$	−51.5933	−	21.3706i	−1.68189	−	0.696663i	−0.999414	+	0.0342416i	$0.989098\pi$
$942$		0			0
$943$			32.8602i			1.07008i
$944$	8.58254	−	6.94152i	0.279338	−	0.225927i
$945$		0			0
$946$	−35.4300	+	2.54988i	−1.15193	+	0.0829037i
$947$	−20.8380	−	8.63140i	−0.677146	−	0.280483i	0.0174875	−	0.999847i	$-0.494433\pi$
$947$	−20.8380	−	8.63140i	−0.677146	−	0.280483i	−0.694633	+	0.719364i	$0.744433\pi$
$948$		0			0
$949$	−7.25461	−	17.5142i	−0.235495	−	0.568535i
$950$	−26.2494	−	8.72366i	−0.851644	−	0.283033i
$951$		0			0
$952$	2.44959	−	0.536308i	0.0793917	−	0.0173818i
$953$	3.10471	−	3.10471i	0.100571	−	0.100571i	−0.655031	−	0.755602i	$-0.727344\pi$
$953$	3.10471	−	3.10471i	0.100571	−	0.100571i	0.755602	+	0.655031i	$0.227344\pi$
$954$		0			0
$955$	50.5671	−	20.9456i	1.63631	−	0.677783i
$956$	22.3546	−	3.23445i	0.722999	−	0.104610i
$957$		0			0
$958$	11.2636	+	9.75117i	0.363910	+	0.315046i
$959$	3.77699			0.121965
$960$		0			0
$961$	79.7806			2.57357
$962$	38.4051	+	33.2482i	1.23823	+	1.07197i
$963$		0			0
$964$	9.41467	−	1.36219i	0.303226	−	0.0438733i
$965$	−13.9692	+	5.78622i	−0.449684	+	0.186265i
$966$		0			0
$967$	29.4463	−	29.4463i	0.946929	−	0.946929i	−0.0517322	−	0.998661i	$-0.516474\pi$
$967$	29.4463	−	29.4463i	0.946929	−	0.946929i	0.998661	+	0.0517322i	$0.0164742\pi$
$968$	−3.86411	−	17.6493i	−0.124197	−	0.567272i
$969$		0			0
$970$	−36.0399	−	11.9774i	−1.15717	−	0.384571i
$971$	−14.2077	−	34.3004i	−0.455946	−	1.10075i	−0.970024	−	0.243008i	$-0.921866\pi$
$971$	−14.2077	−	34.3004i	−0.455946	−	1.10075i	0.514078	−	0.857743i	$-0.328134\pi$
$972$		0			0
$973$	5.52802	+	2.28978i	0.177220	+	0.0734070i
$974$	44.4522	−	3.19920i	1.42434	−	0.102509i
$975$		0			0
$976$	2.92206	−	27.6428i	0.0935329	−	0.884825i
$977$		−	1.44414i		−	0.0462021i	−0.999733	−	0.0231011i	$-0.992646\pi$
$977$		−	1.44414i		−	0.0462021i	0.999733	−	0.0231011i	$-0.00735395\pi$
$978$		0			0
$979$	0.273619	+	0.113337i	0.00874489	+	0.00362225i
$980$	−18.4832	+	10.9889i	−0.590423	+	0.351026i
$981$		0			0
$982$	−10.1428	+	30.5198i	−0.323671	+	0.973925i
$983$	17.1056	+	17.1056i	0.545583	+	0.545583i	0.925160	−	0.379577i	$-0.123930\pi$
$983$	17.1056	+	17.1056i	0.545583	+	0.545583i	−0.379577	+	0.925160i	$0.623930\pi$
$984$		0			0
$985$	−7.80904	+	7.80904i	−0.248817	+	0.248817i
$986$	1.80407	+	3.60006i	0.0574532	+	0.114649i
$987$		0			0
$988$	−11.0672	+	14.8115i	−0.352094	+	0.471218i
$989$	−28.0176	+	67.6405i	−0.890908	+	2.15084i
$990$		0			0
$991$	23.3829			0.742781			0.371390	−	0.928477i	$-0.378881\pi$
$991$	23.3829			0.742781			0.371390	+	0.928477i	$0.378881\pi$
$992$	54.2142	+	24.6129i	1.72130	+	0.781461i
$993$		0			0
$994$	−22.8467	+	26.3903i	−0.724655	+	0.837050i
$995$	36.0373	−	87.0017i	1.14246	−	2.75814i
$996$		0			0
$997$	−17.3205	+	7.17439i	−0.548546	+	0.227215i	−0.639704	−	0.768621i	$-0.720943\pi$
$997$	−17.3205	+	7.17439i	−0.548546	+	0.227215i	0.0911581	+	0.995836i	$0.470943\pi$
$998$	−15.0932	−	30.1188i	−0.477766	−	0.953394i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.c.109.2	yes	32
3.2	odd	2	inner	288.2.v.c.109.7	yes	32
4.3	odd	2		1152.2.v.d.145.8		32
12.11	even	2		1152.2.v.d.145.1		32
32.5	even	8	inner	288.2.v.c.37.2	✓	32
32.27	odd	8		1152.2.v.d.1009.8		32
96.5	odd	8	inner	288.2.v.c.37.7	yes	32
96.59	even	8		1152.2.v.d.1009.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.v.c.37.2	✓	32	32.5	even	8	inner
288.2.v.c.37.7	yes	32	96.5	odd	8	inner
288.2.v.c.109.2	yes	32	1.1	even	1	trivial
288.2.v.c.109.7	yes	32	3.2	odd	2	inner
1152.2.v.d.145.1		32	12.11	even	2
1152.2.v.d.145.8		32	4.3	odd	2
1152.2.v.d.1009.1		32	96.59	even	8
1152.2.v.d.1009.8		32	32.27	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06920 - 0.925636i) q^{2} +(0.286395 + 1.97939i) q^{4} +(3.41317 - 1.41378i) q^{5} +(-1.42999 + 1.42999i) q^{7} +(1.52598 - 2.38147i) q^{8} +O(q^{10})\)	\(q+(-1.06920 - 0.925636i) q^{2} +(0.286395 + 1.97939i) q^{4} +(3.41317 - 1.41378i) q^{5} +(-1.42999 + 1.42999i) q^{7} +(1.52598 - 2.38147i) q^{8} +(-4.95802 - 1.64773i) q^{10} +(0.821853 + 1.98413i) q^{11} +(3.77658 + 1.56431i) q^{13} +(2.85261 - 0.205301i) q^{14} +(-3.83596 + 1.13377i) q^{16} -0.438395i q^{17} +(2.08943 + 0.865472i) q^{19} +(3.77593 + 6.35109i) q^{20} +(0.957853 - 2.88218i) q^{22} +(-4.42643 - 4.42643i) q^{23} +(6.11541 - 6.11541i) q^{25} +(-2.58995 - 5.16831i) q^{26} +(-3.24006 - 2.42097i) q^{28} +(2.48553 - 6.00059i) q^{29} +10.5252 q^{31} +(5.15088 + 2.33847i) q^{32} +(-0.405795 + 0.468734i) q^{34} +(-2.85911 + 6.90251i) q^{35} +(-8.11819 + 3.36267i) q^{37} +(-1.43292 - 2.85942i) q^{38} +(1.84155 - 10.2858i) q^{40} +(-3.71182 - 3.71182i) q^{41} +(-4.47572 - 10.8053i) q^{43} +(-3.69199 + 2.19501i) q^{44} +(0.635492 + 8.83001i) q^{46} +7.94884i q^{47} +2.91023i q^{49} +(-12.1993 + 0.877975i) q^{50} +(-2.01479 + 7.92333i) q^{52} +(1.97877 + 4.77718i) q^{53} +(5.61025 + 5.61025i) q^{55} +(1.22334 + 5.58763i) q^{56} +(-8.21190 + 4.11516i) q^{58} +(-2.54952 + 1.05605i) q^{59} +(-2.65935 + 6.42023i) q^{61} +(-11.2536 - 9.74254i) q^{62} +(-3.34277 - 7.26814i) q^{64} +15.1017 q^{65} +(-0.876739 + 2.11663i) q^{67} +(0.867755 - 0.125554i) q^{68} +(9.44619 - 4.73369i) q^{70} +(-8.63018 + 8.63018i) q^{71} +(-3.27926 - 3.27926i) q^{73} +(11.7926 + 3.91912i) q^{74} +(-1.11470 + 4.38367i) q^{76} +(-4.01254 - 1.66205i) q^{77} +2.97249i q^{79} +(-11.4899 + 9.29296i) q^{80} +(0.532898 + 7.40450i) q^{82} +(-6.25020 - 2.58892i) q^{83} +(-0.619795 - 1.49632i) q^{85} +(-5.21636 + 15.6960i) q^{86} +(5.97927 + 1.07052i) q^{88} +(0.0975126 - 0.0975126i) q^{89} +(-7.63745 + 3.16353i) q^{91} +(7.49391 - 10.0293i) q^{92} +(7.35774 - 8.49894i) q^{94} +8.35518 q^{95} +7.26901 q^{97} +(2.69382 - 3.11163i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

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