LMFDB - Embedded newform 288.2.v.c.109.7

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			109.7
Character	$\chi$	$=$	288.109
Dual form			288.2.v.c.37.7

$q$-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	−0.978864	−	0.204510i	$-0.934440\pi$
$5$	−3.41317	+	1.41378i	−1.52642	+	0.632262i	−0.547551	+	0.836772i	$0.684440\pi$
$6$		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	0.750218	−	0.661190i	$-0.229948\pi$
$11$	−0.821853	−	1.98413i	−0.247798	−	0.598237i	−0.998017	+	0.0629526i	$0.979948\pi$
$12$		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	$0.0169304\pi$
$17$			0.438395i			0.106327i	−0.998586	+	0.0531633i	$0.983070\pi$
$18$		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	0.997239	−	0.0742649i	$-0.0236610\pi$
$23$	4.42643	+	4.42643i	0.922974	+	0.922974i	−0.0742649	+	0.997239i	$0.523661\pi$
$24$		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	$0.331046\pi$
$29$	−2.48553	+	6.00059i	−0.461550	+	1.11428i	−0.967761	+	0.251871i	$0.918954\pi$
$30$		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	0.934818	−	0.355128i	$-0.115563\pi$
$41$	3.71182	+	3.71182i	0.579690	+	0.579690i	−0.355128	+	0.934818i	$0.615563\pi$
$42$		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	$-0.803158\pi$
$47$		−	7.94884i		−	1.15946i	0.814809	−	0.579729i	$-0.196842\pi$
$48$		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	0.727755	−	0.685837i	$-0.240564\pi$
$53$	−1.97877	−	4.77718i	−0.271805	−	0.656196i	−0.999561	+	0.0296408i	$0.990564\pi$
$54$		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	−0.210499	−	0.977594i	$-0.567509\pi$
$59$	2.54952	−	1.05605i	0.331919	−	0.137486i	0.542418	+	0.840109i	$0.317509\pi$
$60$		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	$-0.492196\pi$
$71$	8.63018	−	8.63018i	1.02421	−	1.02421i	0.999699	−	0.0245142i	$-0.00780389\pi$
$72$		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	0.698353	−	0.715754i	$-0.253917\pi$
$83$	6.25020	+	2.58892i	0.686049	+	0.284171i	−0.0123043	+	0.999924i	$0.503917\pi$
$84$		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	−0.712256	−	0.701920i	$-0.752327\pi$
$89$	−0.0975126	+	0.0975126i	−0.0103363	+	0.0103363i	0.701920	+	0.712256i	$0.252327\pi$
$90$		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	0.151690	−	0.988428i	$-0.451528\pi$
$101$	9.62653	−	3.98744i	0.957876	−	0.396765i	0.806185	+	0.591663i	$0.201528\pi$
$102$		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	$0.238263\pi$
$107$	7.19771	+	17.3768i	0.695829	+	1.67988i	−0.0368653	+	0.999320i	$0.511737\pi$
$108$		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	$0.143454\pi$
$113$			9.26038i			0.871143i	−0.900154	+	0.435572i	$0.856546\pi$
$114$		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	$-0.654601\pi$
$131$	5.59231	−	13.5010i	0.488603	−	1.17959i	0.955423	−	0.295239i	$-0.0953993\pi$
$132$		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	0.761267	−	0.648438i	$-0.224578\pi$
$137$	1.32063	+	1.32063i	0.112829	+	0.112829i	−0.648438	+	0.761267i	$0.724578\pi$
$138$		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	$-0.875549\pi$
$149$	−6.59474	−	15.9211i	−0.540262	−	1.30431i	0.384276	−	0.923218i	$-0.374451\pi$
$150$		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	$0.587223\pi$
$167$	−15.9377	+	15.9377i	−1.23329	+	1.23329i	−0.962691	+	0.270604i	$0.912777\pi$
$168$		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	0.635196	−	0.772351i	$-0.280919\pi$
$173$	7.07909	+	2.93225i	0.538213	+	0.222935i	−0.0969831	+	0.995286i	$0.530919\pi$
$174$		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	0.528648	−	0.848841i	$-0.322699\pi$
$179$	4.04366	+	1.67494i	0.302237	+	0.125191i	−0.226411	+	0.974032i	$0.572699\pi$
$180$		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	$-0.680065\pi$
$191$	−14.8153			−1.07200			−0.535998	+	0.844219i	$0.680065\pi$
$192$		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	−0.282124	−	0.959378i	$-0.591039\pi$
$197$	2.76176	−	1.14396i	0.196767	−	0.0815036i	0.478891	+	0.877874i	$0.341039\pi$
$198$		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	−0.772419	−	0.635113i	$-0.780953\pi$
$227$	3.35767	−	8.10614i	0.222857	−	0.538023i	0.995276	+	0.0970900i	$0.0309535\pi$
$228$		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	0.939389	−	0.342854i	$-0.111394\pi$
$233$	9.10570	+	9.10570i	0.596534	+	0.596534i	−0.342854	+	0.939389i	$0.611394\pi$
$234$		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	$0.119021\pi$
$239$			11.2937i			0.730528i	−0.930904	+	0.365264i	$0.880979\pi$
$240$		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	−0.181702	−	0.983354i	$-0.558160\pi$
$251$	6.10196	−	2.52751i	0.385152	−	0.159535i	0.566854	+	0.823818i	$0.308160\pi$
$252$		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	$-0.318408\pi$
$257$	17.3151			1.08008			0.540042	+	0.841638i	$0.318408\pi$
$258$		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	−0.371391	−	0.928476i	$-0.621119\pi$
$263$	9.03440	−	9.03440i	0.557085	−	0.557085i	0.928476	+	0.371391i	$0.121119\pi$
$264$		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	0.515928	−	0.856632i	$-0.327447\pi$
$269$	4.51057	+	1.86834i	0.275014	+	0.113915i	−0.240914	+	0.970546i	$0.577447\pi$
$270$		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	$-0.479779\pi$
$281$	17.7934	−	17.7934i	1.06146	−	1.06146i	0.997983	−	0.0634820i	$-0.0202205\pi$
$282$		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	−0.313598	−	0.949556i	$-0.601534\pi$
$293$	2.32953	−	0.964924i	0.136093	−	0.0563715i	0.449690	+	0.893184i	$0.351534\pi$
$294$		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	0.343021	−	0.939328i	$-0.388550\pi$
$311$	−10.5160	−	10.5160i	−0.596307	−	0.596307i	−0.939328	+	0.343021i	$0.888550\pi$
$312$		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	−0.967828	−	0.251614i	$-0.919039\pi$
$317$	−1.87930	+	4.53704i	−0.105552	+	0.254825i	0.862276	+	0.506439i	$0.169039\pi$
$318$		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	−0.812473	−	0.582999i	$-0.801879\pi$
$347$	−18.1573	+	7.52100i	−0.974735	+	0.403748i	−0.162262	+	0.986748i	$0.551879\pi$
$348$		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	$-0.742925\pi$
$353$	−25.9736			−1.38243			−0.691217	+	0.722648i	$0.742925\pi$
$354$		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	−0.939711	−	0.341970i	$-0.888906\pi$
$359$	−11.3256	+	11.3256i	−0.597741	+	0.597741i	0.341970	+	0.939711i	$0.388906\pi$
$360$		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	$-0.703664\pi$
$383$	−23.3693			−1.19412			−0.597058	+	0.802198i	$0.703664\pi$
$384$		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	0.145401	−	0.989373i	$-0.453553\pi$
$389$	18.6937	−	7.74317i	0.947807	−	0.392594i	0.802406	+	0.596778i	$0.203553\pi$
$390$		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	$0.106724\pi$
$401$			13.1779i			0.658073i	−0.944317	+	0.329036i	$0.893276\pi$
$402$		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	$0.256368\pi$
$419$	−6.28373	+	15.1703i	−0.306980	+	0.741116i	−0.999800	+	0.0200048i	$0.993632\pi$
$420$		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	$-0.801677\pi$
$431$		−	24.2282i		−	1.16703i	0.812102	−	0.583516i	$-0.198323\pi$
$432$		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	−0.0122240	−	0.999925i	$-0.503891\pi$
$443$	14.4425	−	5.98230i	0.686186	−	0.284228i	0.698410	+	0.715698i	$0.253891\pi$
$444$		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	$-0.793810\pi$
$449$	−33.7946			−1.59487			−0.797434	+	0.603407i	$0.793810\pi$
$450$		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	0.417739	−	0.908567i	$-0.362823\pi$
$461$	1.51739	+	0.628524i	0.0706720	+	0.0292733i	−0.347067	+	0.937840i	$0.612823\pi$
$462$		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	0.865571	−	0.500786i	$-0.166956\pi$
$467$	24.2793	+	10.0568i	1.12351	+	0.465374i	0.257942	+	0.966161i	$0.416956\pi$
$468$		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	$-0.422633\pi$
$479$	10.5346			0.481336			0.240668	+	0.970607i	$0.422633\pi$
$480$		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	$0.0465216\pi$
$491$	8.70272	+	21.0102i	0.392748	+	0.948178i	−0.596591	+	0.802546i	$0.703478\pi$
$492$		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	0.171250	−	0.985228i	$-0.445220\pi$
$503$	−18.2556	−	18.2556i	−0.813978	−	0.813978i	−0.985228	+	0.171250i	$0.945220\pi$
$504$		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	$-0.725033\pi$
$509$	7.83769	−	18.9218i	0.347399	−	0.838696i	0.996925	−	0.0783568i	$-0.0249673\pi$
$510$		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	$-0.974610\pi$
$521$	−24.5716	−	24.5716i	−1.07650	−	1.07650i	−0.0796799	−	0.996821i	$-0.525390\pi$
$522$		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	−0.273911	−	0.961755i	$-0.588317\pi$
$557$	−27.0857	−	11.2193i	−1.14766	−	0.475376i	−0.873748	+	0.486379i	$0.838317\pi$
$558$		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	−0.0536517	−	0.998560i	$-0.517086\pi$
$563$	−18.9270	−	7.83982i	−0.797677	−	0.330409i	−0.744026	+	0.668151i	$0.767086\pi$
$564$		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	−0.618360	−	0.785895i	$-0.712203\pi$
$569$	3.99634	−	3.99634i	0.167535	−	0.167535i	0.785895	+	0.618360i	$0.212203\pi$
$570$		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	$-0.836710\pi$
$587$	−14.5909	−	35.2255i	−0.602230	−	1.45391i	0.269051	−	0.963126i	$-0.413290\pi$
$588$		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	$0.150875\pi$
$593$			22.2300i			0.912876i	−0.889755	+	0.456438i	$0.849125\pi$
$594$		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	0.396418	−	0.918070i	$-0.370253\pi$
$599$	−12.7672	−	12.7672i	−0.521652	−	0.521652i	−0.918070	+	0.396418i	$0.870253\pi$
$600$		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	0.110496	−	0.993877i	$-0.464756\pi$
$617$	−21.9427	−	21.9427i	−0.883381	−	0.883381i	−0.993877	+	0.110496i	$0.964756\pi$
$618$		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	$-0.308859\pi$
$641$	28.6116			1.13009			0.565045	+	0.825060i	$0.308859\pi$
$642$		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	−0.497692	−	0.867354i	$-0.665819\pi$
$647$	9.40277	−	9.40277i	0.369661	−	0.369661i	0.867354	+	0.497692i	$0.165819\pi$
$648$		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	0.231090	−	0.972932i	$-0.425771\pi$
$653$	−7.49935	−	3.10633i	−0.293472	−	0.121560i	−0.524562	+	0.851372i	$0.675771\pi$
$654$		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	0.591520	−	0.806290i	$-0.298528\pi$
$659$	11.2864	+	4.67496i	0.439654	+	0.182111i	−0.151866	+	0.988401i	$0.548528\pi$
$660$		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	−0.370264	−	0.928926i	$-0.620733\pi$
$677$	0.644485	−	0.266954i	0.0247696	−	0.0102599i	0.395034	+	0.918667i	$0.370733\pi$
$678$		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	$-0.965847\pi$
$683$	−9.58949	−	23.1511i	−0.366932	−	0.885851i	0.627318	−	0.778763i	$-0.284153\pi$
$684$		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	$0.254768\pi$
$701$	−8.03431	+	19.3965i	−0.303452	+	0.732597i	−0.999888	+	0.0149782i	$0.995232\pi$
$702$		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	$0.254807\pi$
$719$			38.4893i			1.43541i	−0.696348	+	0.717704i	$0.745193\pi$
$720$		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	−0.198004	−	0.980201i	$-0.563446\pi$
$743$	21.3212	−	21.3212i	0.782198	−	0.782198i	0.980201	+	0.198004i	$0.0634458\pi$
$744$		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	$0.521595\pi$
$761$	−29.3929	+	29.3929i	−1.06549	+	1.06549i	−0.997699	+	0.0677921i	$0.978405\pi$
$762$		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	−0.741582	−	0.670862i	$-0.765924\pi$
$773$	−22.0085	+	9.11620i	−0.791589	+	0.327887i	−0.0500067	+	0.998749i	$0.515924\pi$
$774$		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	$-0.599458\pi$
$797$	16.4541	−	39.7238i	0.582836	−	1.40709i	0.890232	−	0.455508i	$-0.150542\pi$
$798$		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	0.291709	−	0.956507i	$-0.405776\pi$
$809$	−18.9088	−	18.9088i	−0.664798	−	0.664798i	−0.956507	+	0.291709i	$0.905776\pi$
$810$		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	0.720994	−	0.692941i	$-0.243686\pi$
$821$	−7.98875	−	19.2865i	−0.278809	−	0.673105i	−0.999803	+	0.0198363i	$0.993686\pi$
$822$		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	−0.132211	−	0.991222i	$-0.542208\pi$
$827$	13.6656	−	5.66049i	0.475201	−	0.196835i	0.607412	+	0.794387i	$0.292208\pi$
$828$		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	$0.608088\pi$
$839$	−36.9593	+	36.9593i	−1.27598	+	1.27598i	−0.942899	+	0.333080i	$0.891912\pi$
$840$		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	$0.504522\pi$
$857$	−29.6874	+	29.6874i	−1.01410	+	1.01410i	−0.999899	+	0.0142046i	$0.995478\pi$
$858$		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	$-0.497948\pi$
$863$	0.378677			0.0128903			0.00644515	+	0.999979i	$0.497948\pi$
$864$		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	$0.339055\pi$
$881$			51.9353i			1.74974i	−0.484353	+	0.874872i	$0.660945\pi$
$882$		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	$-0.893772\pi$
$887$	−37.8951	−	37.8951i	−1.27239	−	1.27239i	−0.327566	−	0.944828i	$-0.606228\pi$
$888$		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	$-0.883681\pi$
$911$		−	21.5716i		−	0.714699i	0.933971	−	0.357349i	$-0.116319\pi$
$912$		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	$-0.271034\pi$
$929$	40.1642			1.31775			0.658873	+	0.752255i	$0.271034\pi$
$930$		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	0.999414	−	0.0342416i	$-0.0109016\pi$
$941$	51.5933	+	21.3706i	1.68189	+	0.696663i	0.682480	+	0.730905i	$0.260902\pi$
$942$		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	0.694633	−	0.719364i	$-0.255567\pi$
$947$	20.8380	+	8.63140i	0.677146	+	0.280483i	−0.0174875	+	0.999847i	$0.505567\pi$
$948$		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	−0.755602	−	0.655031i	$-0.772656\pi$
$953$	−3.10471	+	3.10471i	−0.100571	+	0.100571i	0.655031	+	0.755602i	$0.272656\pi$
$954$		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	$0.0781340\pi$
$971$	14.2077	+	34.3004i	0.455946	+	1.10075i	−0.514078	+	0.857743i	$0.671866\pi$
$972$		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	$0.00735395\pi$
$977$			1.44414i			0.0462021i	−0.999733	+	0.0231011i	$0.992646\pi$
$978$		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	0.379577	−	0.925160i	$-0.376070\pi$
$983$	−17.1056	−	17.1056i	−0.545583	−	0.545583i	−0.925160	+	0.379577i	$0.876070\pi$
$984$		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.109.7	yes	32
3.2	odd	2	inner	288.2.v.c.109.2	yes	32
4.3	odd	2		1152.2.v.d.145.1		32
12.11	even	2		1152.2.v.d.145.8		32
32.5	even	8	inner	288.2.v.c.37.7	yes	32
32.27	odd	8		1152.2.v.d.1009.1		32
96.5	odd	8	inner	288.2.v.c.37.2	✓	32
96.59	even	8		1152.2.v.d.1009.8		32

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