LMFDB - Embedded newform 361.2.c.j.292.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(68,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.324000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 $ x^8 + 5x^6 + 20x^4 + 25*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			292.4
Root			$-0.587785 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	361.292
Dual form			361.2.c.j.68.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 + 1.64728i) q^{2} +(-0.951057 - 1.64728i) q^{3} +(-0.809017 + 1.40126i) q^{4} +(1.61803 + 2.80252i) q^{5} +(1.80902 - 3.13331i) q^{6} +0.236068 q^{7} +0.726543 q^{8} +(-0.309017 + 0.535233i) q^{9} +(-3.07768 + 5.33070i) q^{10} -1.38197 q^{11} +3.07768 q^{12} +(0.363271 - 0.629204i) q^{13} +(0.224514 + 0.388870i) q^{14} +(3.07768 - 5.33070i) q^{15} +(2.30902 + 3.99933i) q^{16} +(3.23607 + 5.60503i) q^{17} -1.17557 q^{18} -5.23607 q^{20} +(-0.224514 - 0.388870i) q^{21} +(-1.31433 - 2.27648i) q^{22} +(0.190983 - 0.330792i) q^{23} +(-0.690983 - 1.19682i) q^{24} +(-2.73607 + 4.73901i) q^{25} +1.38197 q^{26} -4.53077 q^{27} +(-0.190983 + 0.330792i) q^{28} +(2.12663 - 3.68343i) q^{29} +11.7082 q^{30} +1.90211 q^{31} +(-3.66547 + 6.34878i) q^{32} +(1.31433 + 2.27648i) q^{33} +(-6.15537 + 10.6614i) q^{34} +(0.381966 + 0.661585i) q^{35} +(-0.500000 - 0.866025i) q^{36} -6.60440 q^{37} -1.38197 q^{39} +(1.17557 + 2.03615i) q^{40} +(1.08981 + 1.88761i) q^{41} +(0.427051 - 0.739674i) q^{42} +(-4.66312 - 8.07676i) q^{43} +(1.11803 - 1.93649i) q^{44} -2.00000 q^{45} +0.726543 q^{46} +(5.73607 - 9.93516i) q^{47} +(4.39201 - 7.60719i) q^{48} -6.94427 q^{49} -10.4086 q^{50} +(6.15537 - 10.6614i) q^{51} +(0.587785 + 1.01807i) q^{52} +(2.48990 - 4.31263i) q^{53} +(-4.30902 - 7.46344i) q^{54} +(-2.23607 - 3.87298i) q^{55} +0.171513 q^{56} +8.09017 q^{58} +(-4.39201 - 7.60719i) q^{59} +(4.97980 + 8.62526i) q^{60} +(4.73607 - 8.20311i) q^{61} +(1.80902 + 3.13331i) q^{62} +(-0.0729490 + 0.126351i) q^{63} -4.70820 q^{64} +2.35114 q^{65} +(-2.50000 + 4.33013i) q^{66} +(-6.51864 + 11.2906i) q^{67} -10.4721 q^{68} -0.726543 q^{69} +(-0.726543 + 1.25841i) q^{70} +(-5.06555 - 8.77380i) q^{71} +(-0.224514 + 0.388870i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(-6.28115 - 10.8793i) q^{74} +10.4086 q^{75} -0.326238 q^{77} +(-1.31433 - 2.27648i) q^{78} +(2.35114 + 4.07230i) q^{79} +(-7.47214 + 12.9421i) q^{80} +(5.23607 + 9.06914i) q^{81} +(-2.07295 + 3.59045i) q^{82} -3.23607 q^{83} +0.726543 q^{84} +(-10.4721 + 18.1383i) q^{85} +(8.86978 - 15.3629i) q^{86} -8.09017 q^{87} -1.00406 q^{88} +(-3.71847 + 6.44058i) q^{89} +(-1.90211 - 3.29456i) q^{90} +(0.0857567 - 0.148535i) q^{91} +(0.309017 + 0.535233i) q^{92} +(-1.80902 - 3.13331i) q^{93} +21.8213 q^{94} +13.9443 q^{96} +(2.21238 + 3.83196i) q^{97} +(-6.60440 - 11.4391i) q^{98} +(0.427051 - 0.739674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{5} + 10 q^{6} - 16 q^{7} + 2 q^{9} - 20 q^{11} + 14 q^{16} + 8 q^{17} - 24 q^{20} + 6 q^{23} - 10 q^{24} - 4 q^{25} + 20 q^{26} - 6 q^{28} + 40 q^{30} + 12 q^{35} - 4 q^{36} - 20 q^{39}+ \cdots - 10 q^{99}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^5 + 10 * q^6 - 16 * q^7 + 2 * q^9 - 20 * q^11 + 14 * q^16 + 8 * q^17 - 24 * q^20 + 6 * q^23 - 10 * q^24 - 4 * q^25 + 20 * q^26 - 6 * q^28 + 40 * q^30 + 12 * q^35 - 4 * q^36 - 20 * q^39 - 10 * q^42 - 6 * q^43 - 16 * q^45 + 28 * q^47 + 16 * q^49 - 30 * q^54 + 20 * q^58 + 20 * q^61 + 10 * q^62 - 14 * q^63 + 16 * q^64 - 20 * q^66 - 48 * q^68 - 36 * q^73 - 10 * q^74 + 60 * q^77 - 24 * q^80 + 24 * q^81 - 30 * q^82 - 8 * q^83 - 48 * q^85 - 20 * q^87 - 2 * q^92 - 10 * q^93 + 40 * q^96 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.951057	+	1.64728i	0.672499	+	1.16480i	0.977193	+	0.212352i	$0.0681122\pi$
$2$	0.951057	+	1.64728i	0.672499	+	1.16480i	−0.304695	+	0.952450i	$0.598554\pi$
$3$	−0.951057	−	1.64728i	−0.549093	−	0.951057i	−0.998337	−	0.0576475i	$-0.981640\pi$
$3$	−0.951057	−	1.64728i	−0.549093	−	0.951057i	0.449244	−	0.893409i	$-0.351693\pi$
$4$	−0.809017	+	1.40126i	−0.404508	+	0.700629i
$5$	1.61803	+	2.80252i	0.723607	+	1.25332i	0.959545	+	0.281556i	$0.0908504\pi$
$5$	1.61803	+	2.80252i	0.723607	+	1.25332i	−0.235938	+	0.971768i	$0.575816\pi$
$6$	1.80902	−	3.13331i	0.738528	−	1.27917i
$7$	0.236068			0.0892253			0.0446127	−	0.999004i	$-0.485795\pi$
$7$	0.236068			0.0892253			0.0446127	+	0.999004i	$0.485795\pi$
$8$	0.726543			0.256872
$9$	−0.309017	+	0.535233i	−0.103006	+	0.178411i
$10$	−3.07768	+	5.33070i	−0.973249	+	1.68572i
$11$	−1.38197			−0.416678			−0.208339	−	0.978057i	$-0.566806\pi$
$11$	−1.38197			−0.416678			−0.208339	+	0.978057i	$0.566806\pi$
$12$	3.07768			0.888451
$13$	0.363271	−	0.629204i	0.100753	−	0.174510i	−0.811242	−	0.584711i	$-0.801208\pi$
$13$	0.363271	−	0.629204i	0.100753	−	0.174510i	0.911995	+	0.410201i	$0.134541\pi$
$14$	0.224514	+	0.388870i	0.0600039	+	0.103930i
$15$	3.07768	−	5.33070i	0.794654	−	1.37638i
$16$	2.30902	+	3.99933i	0.577254	+	0.999834i
$17$	3.23607	+	5.60503i	0.784862	+	1.35942i	0.929082	+	0.369875i	$0.120599\pi$
$17$	3.23607	+	5.60503i	0.784862	+	1.35942i	−0.144220	+	0.989546i	$0.546067\pi$
$18$	−1.17557			−0.277085
$19$		0			0
$19$		0			0
$20$	−5.23607			−1.17082
$21$	−0.224514	−	0.388870i	−0.0489930	−	0.0848583i
$22$	−1.31433	−	2.27648i	−0.280216	−	0.485348i
$23$	0.190983	−	0.330792i	0.0398227	−	0.0689750i	−0.845427	−	0.534091i	$-0.820654\pi$
$23$	0.190983	−	0.330792i	0.0398227	−	0.0689750i	0.885250	+	0.465116i	$0.153987\pi$
$24$	−0.690983	−	1.19682i	−0.141046	−	0.244299i
$25$	−2.73607	+	4.73901i	−0.547214	+	0.947802i
$26$	1.38197			0.271026
$27$	−4.53077			−0.871947
$28$	−0.190983	+	0.330792i	−0.0360924	+	0.0625139i
$29$	2.12663	−	3.68343i	0.394905	−	0.683995i	−0.598184	−	0.801359i	$-0.704111\pi$
$29$	2.12663	−	3.68343i	0.394905	−	0.683995i	0.993089	+	0.117364i	$0.0374443\pi$
$30$	11.7082			2.13762
$31$	1.90211			0.341630			0.170815	−	0.985303i	$-0.445360\pi$
$31$	1.90211			0.341630			0.170815	+	0.985303i	$0.445360\pi$
$32$	−3.66547	+	6.34878i	−0.647969	+	1.12232i
$33$	1.31433	+	2.27648i	0.228795	+	0.396285i
$34$	−6.15537	+	10.6614i	−1.05564	+	1.82842i
$35$	0.381966	+	0.661585i	0.0645640	+	0.111828i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−6.60440			−1.08576			−0.542878	−	0.839812i	$-0.682665\pi$
$37$	−6.60440			−1.08576			−0.542878	+	0.839812i	$0.682665\pi$
$38$		0			0
$39$	−1.38197			−0.221292
$40$	1.17557	+	2.03615i	0.185874	+	0.321943i
$41$	1.08981	+	1.88761i	0.170200	+	0.294796i	0.938490	−	0.345307i	$-0.112225\pi$
$41$	1.08981	+	1.88761i	0.170200	+	0.294796i	−0.768289	+	0.640103i	$0.778892\pi$
$42$	0.427051	−	0.739674i	0.0658954	−	0.114134i
$43$	−4.66312	−	8.07676i	−0.711119	−	1.23169i	−0.964437	−	0.264311i	$-0.914855\pi$
$43$	−4.66312	−	8.07676i	−0.711119	−	1.23169i	0.253318	−	0.967383i	$-0.418478\pi$
$44$	1.11803	−	1.93649i	0.168550	−	0.291937i
$45$	−2.00000			−0.298142
$46$	0.726543			0.107123
$47$	5.73607	−	9.93516i	0.836692	−	1.44919i	−0.0559542	−	0.998433i	$-0.517820\pi$
$47$	5.73607	−	9.93516i	0.836692	−	1.44919i	0.892646	−	0.450759i	$-0.148847\pi$
$48$	4.39201	−	7.60719i	0.633932	−	1.09800i
$49$	−6.94427			−0.992039
$50$	−10.4086			−1.47200
$51$	6.15537	−	10.6614i	0.861924	−	1.49290i
$52$	0.587785	+	1.01807i	0.0815111	+	0.141181i
$53$	2.48990	−	4.31263i	0.342014	−	0.592385i	−0.642793	−	0.766040i	$-0.722224\pi$
$53$	2.48990	−	4.31263i	0.342014	−	0.592385i	0.984807	+	0.173655i	$0.0555577\pi$
$54$	−4.30902	−	7.46344i	−0.586383	−	1.01565i
$55$	−2.23607	−	3.87298i	−0.301511	−	0.522233i
$56$	0.171513			0.0229194
$57$		0			0
$58$	8.09017			1.06229
$59$	−4.39201	−	7.60719i	−0.571791	−	0.990371i	−0.996382	−	0.0849861i	$-0.972915\pi$
$59$	−4.39201	−	7.60719i	−0.571791	−	0.990371i	0.424591	−	0.905385i	$-0.360418\pi$
$60$	4.97980	+	8.62526i	0.642889	+	1.11352i
$61$	4.73607	−	8.20311i	0.606391	−	1.05030i	−0.385439	−	0.922733i	$-0.625950\pi$
$61$	4.73607	−	8.20311i	0.606391	−	1.05030i	0.991830	−	0.127567i	$-0.0407168\pi$
$62$	1.80902	+	3.13331i	0.229745	+	0.397931i
$63$	−0.0729490	+	0.126351i	−0.00919071	+	0.0159188i
$64$	−4.70820			−0.588525
$65$	2.35114			0.291623
$66$	−2.50000	+	4.33013i	−0.307729	+	0.533002i
$67$	−6.51864	+	11.2906i	−0.796378	+	1.37937i	0.125582	+	0.992083i	$0.459920\pi$
$67$	−6.51864	+	11.2906i	−0.796378	+	1.37937i	−0.921960	+	0.387285i	$0.873413\pi$
$68$	−10.4721			−1.26993
$69$	−0.726543			−0.0874654
$70$	−0.726543	+	1.25841i	−0.0868384	+	0.150409i
$71$	−5.06555	−	8.77380i	−0.601171	−	1.04126i	−0.992644	−	0.121069i	$-0.961368\pi$
$71$	−5.06555	−	8.77380i	−0.601171	−	1.04126i	0.391474	−	0.920189i	$-0.371965\pi$
$72$	−0.224514	+	0.388870i	−0.0264592	+	0.0458287i
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	−0.999517	−	0.0310925i	$-0.990101\pi$
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	0.472831	−	0.881153i	$-0.343232\pi$
$74$	−6.28115	−	10.8793i	−0.730169	−	1.26469i
$75$	10.4086			1.20188
$76$		0			0
$77$	−0.326238			−0.0371783
$78$	−1.31433	−	2.27648i	−0.148818	−	0.257761i
$79$	2.35114	+	4.07230i	0.264524	+	0.458169i	0.967439	−	0.253105i	$-0.0814518\pi$
$79$	2.35114	+	4.07230i	0.264524	+	0.458169i	−0.702915	+	0.711274i	$0.748118\pi$
$80$	−7.47214	+	12.9421i	−0.835410	+	1.44697i
$81$	5.23607	+	9.06914i	0.581785	+	1.00768i
$82$	−2.07295	+	3.59045i	−0.228919	+	0.396499i
$83$	−3.23607			−0.355205			−0.177602	−	0.984102i	$-0.556834\pi$
$83$	−3.23607			−0.355205			−0.177602	+	0.984102i	$0.556834\pi$
$84$	0.726543			0.0792723
$85$	−10.4721	+	18.1383i	−1.13586	+	1.96737i
$86$	8.86978	−	15.3629i	0.956453	−	1.65663i
$87$	−8.09017			−0.867357
$88$	−1.00406			−0.107033
$89$	−3.71847	+	6.44058i	−0.394157	+	0.682700i	−0.992993	−	0.118172i	$-0.962297\pi$
$89$	−3.71847	+	6.44058i	−0.394157	+	0.682700i	0.598836	+	0.800872i	$0.295630\pi$
$90$	−1.90211	−	3.29456i	−0.200500	−	0.347277i
$91$	0.0857567	−	0.148535i	0.00898975	−	0.0155707i
$92$	0.309017	+	0.535233i	0.0322172	+	0.0558019i
$93$	−1.80902	−	3.13331i	−0.187586	−	0.324909i
$94$	21.8213			2.25070
$95$		0			0
$96$	13.9443			1.42318
$97$	2.21238	+	3.83196i	0.224634	+	0.389077i	0.956209	−	0.292683i	$-0.0945482\pi$
$97$	2.21238	+	3.83196i	0.224634	+	0.389077i	−0.731576	+	0.681760i	$0.761215\pi$
$98$	−6.60440	−	11.4391i	−0.667145	−	1.15553i
$99$	0.427051	−	0.739674i	0.0429202	−	0.0743400i
$100$	−4.42705	−	7.66788i	−0.442705	−	0.766788i
$101$	−1.97214	+	3.41584i	−0.196235	+	0.339889i	−0.947305	−	0.320334i	$-0.896205\pi$
$101$	−1.97214	+	3.41584i	−0.196235	+	0.339889i	0.751070	+	0.660223i	$0.229538\pi$
$102$	23.4164			2.31857
$103$	11.1352			1.09718			0.548590	−	0.836091i	$-0.315165\pi$
$103$	11.1352			1.09718			0.548590	+	0.836091i	$0.315165\pi$
$104$	0.263932	−	0.457144i	0.0258807	−	0.0448266i
$105$	0.726543	−	1.25841i	0.0709033	−	0.122808i
$106$	9.47214			0.920015
$107$	5.98385			0.578481			0.289240	−	0.957256i	$-0.406597\pi$
$107$	5.98385			0.578481			0.289240	+	0.957256i	$0.406597\pi$
$108$	3.66547	−	6.34878i	0.352710	−	0.610911i
$109$	1.53884	+	2.66535i	0.147394	+	0.255294i	0.930264	−	0.366892i	$-0.119578\pi$
$109$	1.53884	+	2.66535i	0.147394	+	0.255294i	−0.782869	+	0.622186i	$0.786245\pi$
$110$	4.25325	−	7.36685i	0.405532	−	0.702402i
$111$	6.28115	+	10.8793i	0.596181	+	1.03262i
$112$	0.545085	+	0.944115i	0.0515057	+	0.0892105i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	1.23607			0.115264
$116$	3.44095	+	5.95991i	0.319485	+	0.553364i
$117$	0.224514	+	0.388870i	0.0207563	+	0.0359510i
$118$	8.35410	−	14.4697i	0.769057	−	1.33205i
$119$	0.763932	+	1.32317i	0.0700295	+	0.121295i
$120$	2.23607	−	3.87298i	0.204124	−	0.353553i
$121$	−9.09017			−0.826379
$122$	18.0171			1.63119
$123$	2.07295	−	3.59045i	0.186912	−	0.323740i
$124$	−1.53884	+	2.66535i	−0.138192	+	0.239356i
$125$	−1.52786			−0.136656
$126$	−0.277515			−0.0247230
$127$	−6.24112	+	10.8099i	−0.553810	+	0.959227i	0.444185	+	0.895935i	$0.353493\pi$
$127$	−6.24112	+	10.8099i	−0.553810	+	0.959227i	−0.997995	+	0.0632922i	$0.979840\pi$
$128$	2.85317	+	4.94183i	0.252187	+	0.436801i
$129$	−8.86978	+	15.3629i	−0.780941	+	1.35263i
$130$	2.23607	+	3.87298i	0.196116	+	0.339683i
$131$	−3.04508	−	5.27424i	−0.266050	−	0.460813i	0.701788	−	0.712386i	$-0.252385\pi$
$131$	−3.04508	−	5.27424i	−0.266050	−	0.460813i	−0.967838	+	0.251573i	$0.919052\pi$
$132$	−4.25325			−0.370198
$133$		0			0
$134$	−24.7984			−2.14225
$135$	−7.33094	−	12.6976i	−0.630947	−	1.09283i
$136$	2.35114	+	4.07230i	0.201609	+	0.349196i
$137$	−4.35410	+	7.54153i	−0.371996	+	0.644316i	−0.989873	−	0.141959i	$-0.954660\pi$
$137$	−4.35410	+	7.54153i	−0.371996	+	0.644316i	0.617876	+	0.786275i	$0.287993\pi$
$138$	−0.690983	−	1.19682i	−0.0588204	−	0.101880i
$139$	6.04508	−	10.4704i	0.512737	−	0.888087i	−0.487153	−	0.873316i	$-0.661965\pi$
$139$	6.04508	−	10.4704i	0.512737	−	0.888087i	0.999891	−	0.0147709i	$-0.00470189\pi$
$140$	−1.23607			−0.104467
$141$	−21.8213			−1.83768
$142$	9.63525	−	16.6888i	0.808573	−	1.40049i
$143$	−0.502029	+	0.869539i	−0.0419817	+	0.0727145i
$144$	−2.85410			−0.237842
$145$	13.7638			1.14302
$146$	8.55951	−	14.8255i	0.708390	−	1.22697i
$147$	6.60440	+	11.4391i	0.544721	+	0.943485i
$148$	5.34307	−	9.25446i	0.439197	−	0.760712i
$149$	−3.01722	−	5.22598i	−0.247180	−	0.428129i	0.715562	−	0.698549i	$-0.246171\pi$
$149$	−3.01722	−	5.22598i	−0.247180	−	0.428129i	−0.962742	+	0.270420i	$0.912837\pi$
$150$	9.89919	+	17.1459i	0.808265	+	1.39996i
$151$	−17.2905			−1.40708			−0.703542	−	0.710654i	$-0.748399\pi$
$151$	−17.2905			−1.40708			−0.703542	+	0.710654i	$0.748399\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	−0.310271	−	0.537405i	−0.0250023	−	0.0433053i
$155$	3.07768	+	5.33070i	0.247205	+	0.428172i
$156$	1.11803	−	1.93649i	0.0895144	−	0.155043i
$157$	2.28115	+	3.95107i	0.182056	+	0.315330i	0.942580	−	0.333979i	$-0.108392\pi$
$157$	2.28115	+	3.95107i	0.182056	+	0.315330i	−0.760525	+	0.649309i	$0.775058\pi$
$158$	−4.47214	+	7.74597i	−0.355784	+	0.616236i
$159$	−9.47214			−0.751189
$160$	−23.7234			−1.87550
$161$	0.0450850	−	0.0780895i	0.00355319	−	0.00615431i
$162$	−9.95959	+	17.2505i	−0.782500	+	1.35533i
$163$	15.4721			1.21187			0.605936	−	0.795514i	$-0.292799\pi$
$163$	15.4721			1.21187			0.605936	+	0.795514i	$0.292799\pi$
$164$	−3.52671			−0.275390
$165$	−4.25325	+	7.36685i	−0.331115	+	0.573509i
$166$	−3.07768	−	5.33070i	−0.238875	−	0.413743i
$167$	−0.812299	+	1.40694i	−0.0628576	+	0.108873i	−0.895742	−	0.444575i	$-0.853355\pi$
$167$	−0.812299	+	1.40694i	−0.0628576	+	0.108873i	0.832884	+	0.553448i	$0.186688\pi$
$168$	−0.163119	−	0.282530i	−0.0125849	−	0.0217977i
$169$	6.23607	+	10.8012i	0.479698	+	0.830861i
$170$	−39.8384			−3.05546
$171$		0			0
$172$	15.0902			1.15061
$173$	8.33499	+	14.4366i	0.633698	+	1.09760i	0.986789	+	0.162008i	$0.0517971\pi$
$173$	8.33499	+	14.4366i	0.633698	+	1.09760i	−0.353092	+	0.935589i	$0.614870\pi$
$174$	−7.69421	−	13.3268i	−0.583296	−	1.01030i
$175$	−0.645898	+	1.11873i	−0.0488253	+	0.0845679i
$176$	−3.19098	−	5.52694i	−0.240529	−	0.416609i
$177$	−8.35410	+	14.4697i	−0.627933	+	1.08761i
$178$	−14.1459			−1.06028
$179$	−8.67802			−0.648626			−0.324313	−	0.945950i	$-0.605133\pi$
$179$	−8.67802			−0.648626			−0.324313	+	0.945950i	$0.605133\pi$
$180$	1.61803	−	2.80252i	0.120601	−	0.208887i
$181$	2.90617	−	5.03363i	0.216014	−	0.374147i	−0.737572	−	0.675269i	$-0.764028\pi$
$181$	2.90617	−	5.03363i	0.216014	−	0.374147i	0.953586	+	0.301122i	$0.0973610\pi$
$182$	0.326238			0.0241824
$183$	−18.0171			−1.33186
$184$	0.138757	−	0.240335i	0.0102293	−	0.0177177i
$185$	−10.6861	−	18.5089i	−0.785660	−	1.36080i
$186$	3.44095	−	5.95991i	0.252303	−	0.437002i
$187$	−4.47214	−	7.74597i	−0.327035	−	0.566441i
$188$	9.28115	+	16.0754i	0.676898	+	1.17242i
$189$	−1.06957			−0.0777997
$190$		0			0
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	4.47777	+	7.75572i	0.323155	+	0.559721i
$193$	−4.25325	−	7.36685i	−0.306156	−	0.530278i	0.671362	−	0.741129i	$-0.265710\pi$
$193$	−4.25325	−	7.36685i	−0.306156	−	0.530278i	−0.977518	+	0.210852i	$0.932376\pi$
$194$	−4.20820	+	7.28882i	−0.302131	+	0.523307i
$195$	−2.23607	−	3.87298i	−0.160128	−	0.277350i
$196$	5.61803	−	9.73072i	0.401288	−	0.695051i
$197$	11.4721			0.817356			0.408678	−	0.912679i	$-0.365990\pi$
$197$	11.4721			0.817356			0.408678	+	0.912679i	$0.365990\pi$
$198$	1.62460			0.115455
$199$	0.527864	−	0.914287i	0.0374193	−	0.0648121i	−0.846709	−	0.532056i	$-0.821420\pi$
$199$	0.527864	−	0.914287i	0.0374193	−	0.0648121i	0.884129	+	0.467244i	$0.154753\pi$
$200$	−1.98787	+	3.44309i	−0.140564	+	0.243463i
$201$	24.7984			1.74914
$202$	−7.50245			−0.527871
$203$	0.502029	−	0.869539i	0.0352355	−	0.0610297i
$204$	9.95959	+	17.2505i	0.697311	+	1.20778i
$205$	−3.52671	+	6.10844i	−0.246316	+	0.426632i
$206$	10.5902	+	18.3427i	0.737852	+	1.27800i
$207$	0.118034	+	0.204441i	0.00820393	+	0.0142096i
$208$	3.35520			0.232641
$209$		0			0
$210$	2.76393			0.190729
$211$	−0.310271	−	0.537405i	−0.0213599	−	0.0369965i	0.855148	−	0.518384i	$-0.173466\pi$
$211$	−0.310271	−	0.537405i	−0.0213599	−	0.0369965i	−0.876508	+	0.481388i	$0.840133\pi$
$212$	4.02874	+	6.97798i	0.276695	+	0.479250i
$213$	−9.63525	+	16.6888i	−0.660197	+	1.14349i
$214$	5.69098	+	9.85707i	0.389028	+	0.673816i
$215$	15.0902	−	26.1369i	1.02914	−	1.78252i
$216$	−3.29180			−0.223978
$217$	0.449028			0.0304820
$218$	−2.92705	+	5.06980i	−0.198245	+	0.343370i
$219$	−8.55951	+	14.8255i	−0.578398	+	1.00181i
$220$	7.23607			0.487856
$221$	4.70228			0.316310
$222$	−11.9475	+	20.6936i	−0.801861	+	1.38886i
$223$	8.14324	+	14.1045i	0.545311	+	0.944507i	0.998587	+	0.0531368i	$0.0169220\pi$
$223$	8.14324	+	14.1045i	0.545311	+	0.944507i	−0.453276	+	0.891370i	$0.649745\pi$
$224$	−0.865300	+	1.49874i	−0.0578153	+	0.100139i
$225$	−1.69098	−	2.92887i	−0.112732	−	0.195258i
$226$		0			0
$227$	15.7314			1.04413			0.522066	−	0.852905i	$-0.325161\pi$
$227$	15.7314			1.04413			0.522066	+	0.852905i	$0.325161\pi$
$228$		0			0
$229$	−7.09017			−0.468532			−0.234266	−	0.972173i	$-0.575269\pi$
$229$	−7.09017			−0.468532			−0.234266	+	0.972173i	$0.575269\pi$
$230$	1.17557	+	2.03615i	0.0775148	+	0.134260i
$231$	0.310271	+	0.537405i	0.0204143	+	0.0353586i
$232$	1.54508	−	2.67617i	0.101440	−	0.175699i
$233$	−2.26393	−	3.92125i	−0.148315	−	0.256889i	0.782290	−	0.622915i	$-0.214052\pi$
$233$	−2.26393	−	3.92125i	−0.148315	−	0.256889i	−0.930605	+	0.366025i	$0.880718\pi$
$234$	−0.427051	+	0.739674i	−0.0279172	+	0.0483540i
$235$	37.1246			2.42174
$236$	14.2128			0.925178
$237$	4.47214	−	7.74597i	0.290496	−	0.503155i
$238$	−1.45309	+	2.51682i	−0.0941895	+	0.163141i
$239$	−9.14590			−0.591599			−0.295799	−	0.955250i	$-0.595586\pi$
$239$	−9.14590			−0.591599			−0.295799	+	0.955250i	$0.595586\pi$
$240$	28.4257			1.83487
$241$	13.5721	−	23.5075i	0.874253	−	1.51425i	0.0166973	−	0.999861i	$-0.494685\pi$
$241$	13.5721	−	23.5075i	0.874253	−	1.51425i	0.857556	−	0.514391i	$-0.171982\pi$
$242$	−8.64527	−	14.9740i	−0.555739	−	0.962568i
$243$	3.16344	−	5.47924i	0.202935	−	0.351493i
$244$	7.66312	+	13.2729i	0.490581	+	0.849711i
$245$	−11.2361	−	19.4614i	−0.717846	−	1.24335i
$246$	7.88597			0.502791
$247$		0			0
$248$	1.38197			0.0877549
$249$	3.07768	+	5.33070i	0.195040	+	0.337820i
$250$	−1.45309	−	2.51682i	−0.0919012	−	0.159177i
$251$	8.20820	−	14.2170i	0.518097	−	0.897371i	−0.481682	−	0.876346i	$-0.659974\pi$
$251$	8.20820	−	14.2170i	0.518097	−	0.897371i	0.999779	−	0.0210245i	$-0.00669280\pi$
$252$	−0.118034	−	0.204441i	−0.00743544	−	0.0128786i
$253$	−0.263932	+	0.457144i	−0.0165933	+	0.0287404i
$254$	−23.7426			−1.48975
$255$	39.8384			2.49478
$256$	−10.1353	+	17.5548i	−0.633453	+	1.09717i
$257$	5.42882	−	9.40300i	0.338641	−	0.586543i	−0.645537	−	0.763729i	$-0.723366\pi$
$257$	5.42882	−	9.40300i	0.338641	−	0.586543i	0.984177	+	0.177186i	$0.0566995\pi$
$258$	−33.7426			−2.10073
$259$	−1.55909			−0.0968769
$260$	−1.90211	+	3.29456i	−0.117964	+	0.204320i
$261$	1.31433	+	2.27648i	0.0813548	+	0.140911i
$262$	5.79210	−	10.0322i	0.357837	−	0.619792i
$263$	11.9443	+	20.6881i	0.736515	+	1.27568i	0.954055	+	0.299631i	$0.0968634\pi$
$263$	11.9443	+	20.6881i	0.736515	+	1.27568i	−0.217540	+	0.976051i	$0.569803\pi$
$264$	0.954915	+	1.65396i	0.0587710	+	0.101794i
$265$	16.1150			0.989934
$266$		0			0
$267$	14.1459			0.865715
$268$	−10.5474	−	18.2686i	−0.644284	−	1.11593i
$269$	−12.8985	−	22.3409i	−0.786437	−	1.36215i	−0.928137	−	0.372239i	$-0.878590\pi$
$269$	−12.8985	−	22.3409i	−0.786437	−	1.36215i	0.141700	−	0.989910i	$-0.454743\pi$
$270$	13.9443	−	24.1522i	0.848621	−	1.46986i
$271$	9.63525	+	16.6888i	0.585300	+	1.01377i	0.994838	+	0.101476i	$0.0323566\pi$
$271$	9.63525	+	16.6888i	0.585300	+	1.01377i	−0.409538	+	0.912293i	$0.634310\pi$
$272$	−14.9443	+	25.8842i	−0.906130	+	1.56946i
$273$	−0.326238			−0.0197448
$274$	−16.5640			−1.00067
$275$	3.78115	−	6.54915i	0.228012	−	0.394929i
$276$	0.587785	−	1.01807i	0.0353805	−	0.0612808i
$277$	−14.7639			−0.887079			−0.443539	−	0.896255i	$-0.646277\pi$
$277$	−14.7639			−0.887079			−0.443539	+	0.896255i	$0.646277\pi$
$278$	22.9969			1.37926
$279$	−0.587785	+	1.01807i	−0.0351898	+	0.0609505i
$280$	0.277515	+	0.480669i	0.0165847	+	0.0287255i
$281$	7.83297	−	13.5671i	0.467276	−	0.809345i	−0.532025	−	0.846728i	$-0.678569\pi$
$281$	7.83297	−	13.5671i	0.467276	−	0.809345i	0.999301	+	0.0373833i	$0.0119023\pi$
$282$	−20.7533	−	35.9458i	−1.23584	−	2.14054i
$283$	6.04508	+	10.4704i	0.359343	+	0.622400i	0.987851	−	0.155403i	$-0.0496675\pi$
$283$	6.04508	+	10.4704i	0.359343	+	0.622400i	−0.628508	+	0.777803i	$0.716334\pi$
$284$	16.3925			0.972714
$285$		0			0
$286$	−1.90983			−0.112931
$287$	0.257270	+	0.445605i	0.0151862	+	0.0263032i
$288$	−2.26538	−	3.92376i	−0.133489	−	0.231210i
$289$	−12.4443	+	21.5541i	−0.732016	+	1.26789i
$290$	13.0902	+	22.6728i	0.768681	+	1.33139i
$291$	4.20820	−	7.28882i	0.246689	−	0.427278i
$292$	14.5623			0.852194
$293$	−15.2824			−0.892808			−0.446404	−	0.894831i	$-0.647296\pi$
$293$	−15.2824			−0.892808			−0.446404	+	0.894831i	$0.647296\pi$
$294$	−12.5623	+	21.7586i	−0.732649	+	1.26898i
$295$	14.2128	−	24.6174i	0.827504	−	1.43328i
$296$	−4.79837			−0.278900
$297$	6.26137			0.363321
$298$	5.73910	−	9.94040i	0.332457	−	0.575832i
$299$	−0.138757	−	0.240335i	−0.00802454	−	0.0138989i
$300$	−8.42075	+	14.5852i	−0.486172	+	0.842075i
$301$	−1.10081	−	1.90666i	−0.0634498	−	0.109898i
$302$	−16.4443	−	28.4823i	−0.946262	−	1.63897i
$303$	7.50245			0.431005
$304$		0			0
$305$	30.6525			1.75516
$306$	−3.80423	−	6.58911i	−0.217473	−	0.376675i
$307$	13.8168	+	23.9314i	0.788568	+	1.36584i	0.926844	+	0.375445i	$0.122510\pi$
$307$	13.8168	+	23.9314i	0.788568	+	1.36584i	−0.138277	+	0.990394i	$0.544156\pi$
$308$	0.263932	−	0.457144i	0.0150389	−	0.0260482i
$309$	−10.5902	−	18.3427i	−0.602454	−	1.04348i
$310$	−5.85410	+	10.1396i	−0.332491	+	0.575891i
$311$	−14.4721			−0.820640			−0.410320	−	0.911942i	$-0.634583\pi$
$311$	−14.4721			−0.820640			−0.410320	+	0.911942i	$0.634583\pi$
$312$	−1.00406			−0.0568435
$313$	−2.69098	+	4.66092i	−0.152103	+	0.263451i	−0.932001	−	0.362457i	$-0.881938\pi$
$313$	−2.69098	+	4.66092i	−0.152103	+	0.263451i	0.779897	+	0.625908i	$0.215271\pi$
$314$	−4.33901	+	7.51539i	−0.244865	+	0.424118i
$315$	−0.472136			−0.0266018
$316$	−7.60845			−0.428009
$317$	−15.6659	+	27.1342i	−0.879886	+	1.52401i	−0.0284217	+	0.999596i	$0.509048\pi$
$317$	−15.6659	+	27.1342i	−0.879886	+	1.52401i	−0.851465	+	0.524412i	$0.824285\pi$
$318$	−9.00854	−	15.6032i	−0.505174	−	0.874986i
$319$	−2.93893	+	5.09037i	−0.164548	+	0.285006i
$320$	−7.61803	−	13.1948i	−0.425861	−	0.737613i
$321$	−5.69098	−	9.85707i	−0.317640	−	0.550168i
$322$	0.171513			0.00955807
$323$		0			0
$324$	−16.9443			−0.941348
$325$	1.98787	+	3.44309i	0.110267	+	0.190988i
$326$	14.7149	+	25.4869i	0.814982	+	1.41159i
$327$	2.92705	−	5.06980i	0.161866	−	0.280361i
$328$	0.791796	+	1.37143i	0.0437196	+	0.0757246i
$329$	1.35410	−	2.34537i	0.0746541	−	0.129305i
$330$	−16.1803			−0.890698
$331$	20.2622			1.11371			0.556856	−	0.830609i	$-0.312008\pi$
$331$	20.2622			1.11371			0.556856	+	0.830609i	$0.312008\pi$
$332$	2.61803	−	4.53457i	0.143683	−	0.248867i
$333$	2.04087	−	3.53489i	0.111839	−	0.193711i
$334$	−3.09017			−0.169087
$335$	−42.1895			−2.30506
$336$	1.03681	−	1.79581i	0.0565628	−	0.0979696i
$337$	0.277515	+	0.480669i	0.0151172	+	0.0261837i	0.873485	−	0.486851i	$-0.161855\pi$
$337$	0.277515	+	0.480669i	0.0151172	+	0.0261837i	−0.858368	+	0.513035i	$0.828521\pi$
$338$	−11.8617	+	20.5451i	−0.645192	+	1.11750i
$339$		0			0
$340$	−16.9443	−	29.3483i	−0.918932	−	1.59164i
$341$	−2.62866			−0.142350
$342$		0			0
$343$	−3.29180			−0.177740
$344$	−3.38795	−	5.86811i	−0.182666	−	0.316387i
$345$	−1.17557	−	2.03615i	−0.0632906	−	0.109623i
$346$	−15.8541	+	27.4601i	−0.852322	+	1.47626i
$347$	−14.4164	−	24.9700i	−0.773913	−	1.34046i	−0.935403	−	0.353583i	$-0.884963\pi$
$347$	−14.4164	−	24.9700i	−0.773913	−	1.34046i	0.161490	−	0.986874i	$-0.448370\pi$
$348$	6.54508	−	11.3364i	0.350853	−	0.607696i
$349$	13.6180			0.728957			0.364478	−	0.931212i	$-0.381247\pi$
$349$	13.6180			0.728957			0.364478	+	0.931212i	$0.381247\pi$
$350$	−2.45714			−0.131340
$351$	−1.64590	+	2.85078i	−0.0878515	+	0.152163i
$352$	5.06555	−	8.77380i	0.269995	−	0.467645i
$353$	25.3820			1.35095			0.675473	−	0.737385i	$-0.263940\pi$
$353$	25.3820			1.35095			0.675473	+	0.737385i	$0.263940\pi$
$354$	−31.7809			−1.68914
$355$	16.3925	−	28.3926i	0.870022	−	1.50692i
$356$	−6.01661	−	10.4211i	−0.318880	−	0.552316i
$357$	1.45309	−	2.51682i	0.0769054	−	0.133204i
$358$	−8.25329	−	14.2951i	−0.436200	−	0.755520i
$359$	17.6910	+	30.6417i	0.933694	+	1.61721i	0.776946	+	0.629568i	$0.216768\pi$
$359$	17.6910	+	30.6417i	0.933694	+	1.61721i	0.156749	+	0.987639i	$0.449899\pi$
$360$	−1.45309			−0.0765843
$361$		0			0
$362$	11.0557			0.581076
$363$	8.64527	+	14.9740i	0.453759	+	0.785933i
$364$	0.138757	+	0.240335i	0.00727286	+	0.0125970i
$365$	14.5623	−	25.2227i	0.762226	−	1.32021i
$366$	−17.1353	−	29.6791i	−0.895674	−	1.55135i
$367$	−6.26393	+	10.8494i	−0.326975	+	0.566337i	−0.981910	−	0.189348i	$-0.939362\pi$
$367$	−6.26393	+	10.8494i	−0.326975	+	0.566337i	0.654935	+	0.755685i	$0.272696\pi$
$368$	1.76393			0.0919513
$369$	−1.34708			−0.0701264
$370$	20.3262	−	35.2061i	1.05671	−	1.83028i
$371$	0.587785	−	1.01807i	0.0305163	−	0.0528558i
$372$	5.85410			0.303521
$373$	−36.7607			−1.90340			−0.951698	−	0.307035i	$-0.900663\pi$
$373$	−36.7607			−1.90340			−0.951698	+	0.307035i	$0.900663\pi$
$374$	8.50651	−	14.7337i	0.439861	−	0.761862i
$375$	1.45309	+	2.51682i	0.0750370	+	0.129968i
$376$	4.16750	−	7.21832i	0.214922	−	0.372256i
$377$	−1.54508	−	2.67617i	−0.0795759	−	0.137830i
$378$	−1.01722	−	1.76188i	−0.0523202	−	0.0906212i
$379$	−21.3723			−1.09782			−0.548910	−	0.835882i	$-0.684957\pi$
$379$	−21.3723			−1.09782			−0.548910	+	0.835882i	$0.684957\pi$
$380$		0			0
$381$	23.7426			1.21637
$382$	−16.1680	−	28.0037i	−0.827225	−	1.43280i
$383$	5.65334	+	9.79187i	0.288872	+	0.500341i	0.973541	−	0.228513i	$-0.0733864\pi$
$383$	5.65334	+	9.79187i	0.288872	+	0.500341i	−0.684669	+	0.728854i	$0.740053\pi$
$384$	5.42705	−	9.39993i	0.276948	−	0.479688i
$385$	−0.527864	−	0.914287i	−0.0269024	−	0.0465964i
$386$	8.09017	−	14.0126i	0.411779	−	0.713222i
$387$	5.76393			0.292997
$388$	−7.15942			−0.363465
$389$	−0.954915	+	1.65396i	−0.0484161	+	0.0838592i	−0.889218	−	0.457484i	$-0.848751\pi$
$389$	−0.954915	+	1.65396i	−0.0484161	+	0.0838592i	0.840802	+	0.541343i	$0.182084\pi$
$390$	4.25325	−	7.36685i	0.215372	−	0.373035i
$391$	2.47214			0.125021
$392$	−5.04531			−0.254827
$393$	−5.79210	+	10.0322i	−0.292173	+	0.506058i
$394$	10.9106	+	18.8978i	0.549671	+	0.952057i
$395$	−7.60845	+	13.1782i	−0.382823	+	0.663068i
$396$	0.690983	+	1.19682i	0.0347232	+	0.0601424i
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	0.849362	−	0.527811i	$-0.176987\pi$
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	−0.881779	+	0.471664i	$0.843654\pi$
$398$	2.00811			0.100658
$399$		0			0
$400$	−25.2705			−1.26353
$401$	−2.35114	−	4.07230i	−0.117410	−	0.203361i	0.801330	−	0.598222i	$-0.204126\pi$
$401$	−2.35114	−	4.07230i	−0.117410	−	0.203361i	−0.918741	+	0.394861i	$0.870793\pi$
$402$	23.5847	+	40.8498i	1.17630	+	2.03740i
$403$	0.690983	−	1.19682i	0.0344203	−	0.0596177i
$404$	−3.19098	−	5.52694i	−0.158757	−	0.274976i
$405$	−16.9443	+	29.3483i	−0.841968	+	1.45833i
$406$	1.90983			0.0947833
$407$	9.12705			0.452411
$408$	4.47214	−	7.74597i	0.221404	−	0.383482i
$409$	12.0332	−	20.8421i	0.595004	−	1.03058i	−0.398542	−	0.917150i	$-0.630484\pi$
$409$	12.0332	−	20.8421i	0.595004	−	1.03058i	0.993546	−	0.113428i	$-0.0361830\pi$
$410$	−13.4164			−0.662589
$411$	16.5640			0.817041
$412$	−9.00854	+	15.6032i	−0.443819	+	0.768717i
$413$	−1.03681	−	1.79581i	−0.0510182	−	0.0883662i
$414$	−0.224514	+	0.388870i	−0.0110343	+	0.0191119i
$415$	−5.23607	−	9.06914i	−0.257028	−	0.445186i
$416$	2.66312	+	4.61266i	0.130570	+	0.226154i
$417$	−22.9969			−1.12616
$418$		0			0
$419$	−6.58359			−0.321630			−0.160815	−	0.986985i	$-0.551412\pi$
$419$	−6.58359			−0.321630			−0.160815	+	0.986985i	$0.551412\pi$
$420$	1.17557	+	2.03615i	0.0573620	+	0.0993538i
$421$	−16.2007	−	28.0605i	−0.789575	−	1.36758i	−0.926228	−	0.376964i	$-0.876968\pi$
$421$	−16.2007	−	28.0605i	−0.789575	−	1.36758i	0.136653	−	0.990619i	$-0.456365\pi$
$422$	0.590170	−	1.02220i	0.0287290	−	0.0497601i
$423$	3.54508	+	6.14027i	0.172368	+	0.298550i
$424$	1.80902	−	3.13331i	0.0878536	−	0.152167i
$425$	−35.4164			−1.71795
$426$	−36.6547			−1.77593
$427$	1.11803	−	1.93649i	0.0541055	−	0.0937134i
$428$	−4.84104	+	8.38493i	−0.234000	+	0.405301i
$429$	1.90983			0.0922075
$430$	57.4064			2.76838
$431$	−6.24112	+	10.8099i	−0.300624	+	0.520697i	−0.976278	−	0.216523i	$-0.930528\pi$
$431$	−6.24112	+	10.8099i	−0.300624	+	0.520697i	0.675653	+	0.737220i	$0.263862\pi$
$432$	−10.4616	−	18.1201i	−0.503335	−	0.871802i
$433$	−9.45756	+	16.3810i	−0.454502	+	0.787220i	−0.998659	−	0.0517631i	$-0.983516\pi$
$433$	−9.45756	+	16.3810i	−0.454502	+	0.787220i	0.544158	+	0.838983i	$0.316849\pi$
$434$	0.427051	+	0.739674i	0.0204991	+	0.0355055i
$435$	−13.0902	−	22.6728i	−0.627626	−	1.08708i
$436$	−4.97980			−0.238489
$437$		0			0
$438$	−32.5623			−1.55589
$439$	2.99193	+	5.18217i	0.142797	+	0.247331i	0.928549	−	0.371210i	$-0.121057\pi$
$439$	2.99193	+	5.18217i	0.142797	+	0.247331i	−0.785752	+	0.618542i	$0.787724\pi$
$440$	−1.62460	−	2.81389i	−0.0774497	−	0.134147i
$441$	2.14590	−	3.71680i	0.102186	−	0.176991i
$442$	4.47214	+	7.74597i	0.212718	+	0.368438i
$443$	−7.59017	+	13.1466i	−0.360620	+	0.624612i	−0.988063	−	0.154050i	$-0.950768\pi$
$443$	−7.59017	+	13.1466i	−0.360620	+	0.624612i	0.627443	+	0.778662i	$0.284101\pi$
$444$	−20.3262			−0.964641
$445$	−24.0664			−1.14086
$446$	−15.4894	+	26.8284i	−0.733442	+	1.27036i
$447$	−5.73910	+	9.94040i	−0.271450	+	0.470165i
$448$	−1.11146			−0.0525114
$449$	24.2380			1.14386			0.571930	−	0.820303i	$-0.306195\pi$
$449$	24.2380			1.14386			0.571930	+	0.820303i	$0.306195\pi$
$450$	3.21644	−	5.57104i	0.151624	−	0.262621i
$451$	−1.50609	−	2.60862i	−0.0709188	−	0.122835i
$452$		0			0
$453$	16.4443	+	28.4823i	0.772619	+	1.33822i
$454$	14.9615	+	25.9141i	0.702178	+	1.21621i
$455$	0.555029			0.0260202
$456$		0			0
$457$	6.29180			0.294318			0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180			0.294318			0.147159	+	0.989113i	$0.452987\pi$
$458$	−6.74315	−	11.6795i	−0.315087	−	0.545746i
$459$	−14.6619	−	25.3951i	−0.684358	−	1.18534i
$460$	−1.00000	+	1.73205i	−0.0466252	+	0.0807573i
$461$	5.90983	+	10.2361i	0.275248	+	0.476744i	0.970198	−	0.242315i	$-0.0779066\pi$
$461$	5.90983	+	10.2361i	0.275248	+	0.476744i	−0.694949	+	0.719059i	$0.744573\pi$
$462$	−0.590170	+	1.02220i	−0.0274572	+	0.0475572i
$463$	10.1459			0.471520			0.235760	−	0.971811i	$-0.424242\pi$
$463$	10.1459			0.471520			0.235760	+	0.971811i	$0.424242\pi$
$464$	19.6417			0.911842
$465$	5.85410	−	10.1396i	0.271477	−	0.470213i
$466$	4.30625	−	7.45865i	0.199483	−	0.345515i
$467$	4.23607			0.196022			0.0980109	−	0.995185i	$-0.468752\pi$
$467$	4.23607			0.196022			0.0980109	+	0.995185i	$0.468752\pi$
$468$	−0.726543			−0.0335844
$469$	−1.53884	+	2.66535i	−0.0710571	+	0.123075i
$470$	35.3076	+	61.1546i	1.62862	+	2.82085i
$471$	4.33901	−	7.51539i	0.199931	−	0.346291i
$472$	−3.19098	−	5.52694i	−0.146877	−	0.254398i
$473$	6.44427	+	11.1618i	0.296308	+	0.513220i
$474$	17.0130			0.781434
$475$		0			0
$476$	−2.47214			−0.113310
$477$	1.53884	+	2.66535i	0.0704587	+	0.122038i
$478$	−8.69827	−	15.0658i	−0.397849	−	0.689095i
$479$	7.95492	−	13.7783i	0.363469	−	0.629547i	−0.625060	−	0.780577i	$-0.714925\pi$
$479$	7.95492	−	13.7783i	0.363469	−	0.629547i	0.988529	+	0.151029i	$0.0482588\pi$
$480$	22.5623	+	39.0791i	1.02982	+	1.78371i
$481$	−2.39919	+	4.15551i	−0.109394	+	0.189475i
$482$	51.6312			2.35174
$483$	−0.171513			−0.00780413
$484$	7.35410	−	12.7377i	0.334277	−	0.578985i
$485$	−7.15942	+	12.4005i	−0.325093	+	0.563077i
$486$	12.0344			0.545893
$487$	16.6700			0.755389			0.377695	−	0.925930i	$-0.376717\pi$
$487$	16.6700			0.755389			0.377695	+	0.925930i	$0.376717\pi$
$488$	3.44095	−	5.95991i	0.155765	−	0.269792i
$489$	−14.7149	−	25.4869i	−0.665430	−	1.15256i
$490$	21.3723	−	37.0179i	0.965501	−	1.67230i
$491$	−8.63525	−	14.9567i	−0.389704	−	0.674986i	0.602706	−	0.797963i	$-0.294089\pi$
$491$	−8.63525	−	14.9567i	−0.389704	−	0.674986i	−0.992410	+	0.122977i	$0.960756\pi$
$492$	3.35410	+	5.80948i	0.151215	+	0.261911i
$493$	27.5276			1.23978
$494$		0			0
$495$	2.76393			0.124230
$496$	4.39201	+	7.60719i	0.197207	+	0.341573i
$497$	−1.19581	−	2.07121i	−0.0536396	−	0.0929066i
$498$	−5.85410	+	10.1396i	−0.262329	+	0.454366i
$499$	−15.2361	−	26.3896i	−0.682060	−	1.18136i	−0.974351	−	0.225033i	$-0.927751\pi$
$499$	−15.2361	−	26.3896i	−0.682060	−	1.18136i	0.292291	−	0.956329i	$-0.405582\pi$
$500$	1.23607	−	2.14093i	0.0552786	−	0.0957454i
$501$	3.09017			0.138059
$502$	31.2259			1.39368
$503$	−10.2984	+	17.8373i	−0.459182	+	0.795326i	−0.998918	−	0.0465081i	$-0.985191\pi$
$503$	−10.2984	+	17.8373i	−0.459182	+	0.795326i	0.539736	+	0.841834i	$0.318524\pi$
$504$	−0.0530006	+	0.0917997i	−0.00236083	+	0.00408908i
$505$	−12.7639			−0.567988
$506$	−1.00406			−0.0446358
$507$	11.8617	−	20.5451i	0.526797	−	0.912439i
$508$	−10.0984	−	17.4909i	−0.448042	−	0.776031i
$509$	9.09429	−	15.7518i	0.403097	−	0.698185i	−0.591001	−	0.806671i	$-0.701267\pi$
$509$	9.09429	−	15.7518i	0.403097	−	0.698185i	0.994098	+	0.108486i	$0.0346002\pi$
$510$	37.8885	+	65.6249i	1.67773	+	2.90592i
$511$	−1.06231	−	1.83997i	−0.0469936	−	0.0813954i
$512$	−27.1441			−1.19961
$513$		0			0
$514$	20.6525			0.910942
$515$	18.0171	+	31.2065i	0.793927	+	1.37512i
$516$	−14.3516	−	24.8577i	−0.631794	−	1.09430i
$517$	−7.92705	+	13.7301i	−0.348631	+	0.603847i
$518$	−1.48278	−	2.56825i	−0.0651496	−	0.112842i
$519$	15.8541	−	27.4601i	0.695918	−	1.20537i
$520$	1.70820			0.0749097
$521$	21.8213			0.956008			0.478004	−	0.878358i	$-0.341360\pi$
$521$	21.8213			0.956008			0.478004	+	0.878358i	$0.341360\pi$
$522$	−2.50000	+	4.33013i	−0.109422	+	0.189525i
$523$	−17.2048	+	29.7995i	−0.752312	+	1.30304i	0.194387	+	0.980925i	$0.437728\pi$
$523$	−17.2048	+	29.7995i	−0.752312	+	1.30304i	−0.946699	+	0.322118i	$0.895605\pi$
$524$	9.85410			0.430478
$525$	2.45714			0.107238
$526$	−22.7194	+	39.3511i	−0.990611	+	1.71579i
$527$	6.15537	+	10.6614i	0.268132	+	0.464418i
$528$	−6.06961	+	10.5129i	−0.264146	+	0.457514i
$529$	11.4271	+	19.7922i	0.496828	+	0.860532i
$530$	15.3262	+	26.5458i	0.665729	+	1.15308i
$531$	5.42882			0.235591
$532$		0			0
$533$	1.58359			0.0685930
$534$	13.4535	+	23.3022i	0.582192	+	1.00839i
$535$	9.68208	+	16.7699i	0.418593	+	0.725024i
$536$	−4.73607	+	8.20311i	−0.204567	+	0.354320i
$537$	8.25329	+	14.2951i	0.356156	+	0.616880i
$538$	24.5344	−	42.4949i	1.05775	−	1.83209i
$539$	9.59675			0.413361
$540$	23.7234			1.02089
$541$	−3.35410	+	5.80948i	−0.144204	+	0.249769i	−0.929076	−	0.369890i	$-0.879396\pi$
$541$	−3.35410	+	5.80948i	−0.144204	+	0.249769i	0.784872	+	0.619658i	$0.212729\pi$
$542$	−18.3273	+	31.7439i	−0.787227	+	1.36352i
$543$	−11.0557			−0.474447
$544$	−47.4468			−2.03427
$545$	−4.97980	+	8.62526i	−0.213311	+	0.369466i
$546$	−0.310271	−	0.537405i	−0.0132784	−	0.0229988i
$547$	10.3556	−	17.9365i	0.442774	−	0.766908i	−0.555120	−	0.831770i	$-0.687328\pi$
$547$	10.3556	−	17.9365i	0.442774	−	0.766908i	0.997894	+	0.0648627i	$0.0206609\pi$
$548$	−7.04508	−	12.2024i	−0.300951	−	0.521263i
$549$	2.92705	+	5.06980i	0.124923	+	0.216374i
$550$	14.3844			0.613351
$551$		0			0
$552$	−0.527864			−0.0224674
$553$	0.555029	+	0.961339i	0.0236022	+	0.0408803i
$554$	−14.0413	−	24.3203i	−0.596559	−	1.03327i
$555$	−20.3262	+	35.2061i	−0.862801	+	1.49441i
$556$	9.78115	+	16.9415i	0.414813	+	0.718478i
$557$	19.6803	−	34.0873i	0.833883	−	1.44433i	−0.0610541	−	0.998134i	$-0.519446\pi$
$557$	19.6803	−	34.0873i	0.833883	−	1.44433i	0.894937	−	0.446193i	$-0.147220\pi$
$558$	−2.23607			−0.0946603
$559$	−6.77591			−0.286590
$560$	−1.76393	+	3.05522i	−0.0745397	+	0.129107i
$561$	−8.50651	+	14.7337i	−0.359145	+	0.622057i
$562$	29.7984			1.25697
$563$	21.7153			0.915191			0.457595	−	0.889161i	$-0.348711\pi$
$563$	21.7153			0.915191			0.457595	+	0.889161i	$0.348711\pi$
$564$	17.6538	−	30.5773i	0.743359	−	1.28754i
$565$		0			0
$566$	−11.4984	+	19.9159i	−0.483315	+	0.837127i
$567$	1.23607	+	2.14093i	0.0519100	+	0.0899107i
$568$	−3.68034	−	6.37454i	−0.154424	−	0.267470i
$569$	25.4540			1.06709			0.533544	−	0.845772i	$-0.320860\pi$
$569$	25.4540			1.06709			0.533544	+	0.845772i	$0.320860\pi$
$570$		0			0
$571$	−46.1033			−1.92936			−0.964682	−	0.263417i	$-0.915150\pi$
$571$	−46.1033			−1.92936			−0.964682	+	0.263417i	$0.915150\pi$
$572$	−0.812299	−	1.40694i	−0.0339639	−	0.0588273i
$573$	16.1680	+	28.0037i	0.675426	+	1.16987i
$574$	−0.489357	+	0.847591i	−0.0204254	+	0.0353778i
$575$	1.04508	+	1.81014i	0.0435831	+	0.0754881i
$576$	1.45492	−	2.51999i	0.0606215	−	0.104999i
$577$	−15.2918			−0.636606			−0.318303	−	0.947989i	$-0.603113\pi$
$577$	−15.2918			−0.636606			−0.318303	+	0.947989i	$0.603113\pi$
$578$	−47.3408			−1.96912
$579$	−8.09017	+	14.0126i	−0.336216	+	0.582343i
$580$	−11.1352	+	19.2867i	−0.462363	+	0.800835i
$581$	−0.763932			−0.0316932
$582$	16.0090			0.663593
$583$	−3.44095	+	5.95991i	−0.142510	+	0.246834i
$584$	−3.26944	−	5.66284i	−0.135290	−	0.234330i
$585$	−0.726543	+	1.25841i	−0.0300388	+	0.0520288i
$586$	−14.5344	−	25.1744i	−0.600412	−	1.03994i
$587$	−8.40983	−	14.5663i	−0.347111	−	0.601214i	0.638624	−	0.769519i	$-0.279504\pi$
$587$	−8.40983	−	14.5663i	−0.347111	−	0.601214i	−0.985735	+	0.168305i	$0.946171\pi$
$588$	−21.3723			−0.881378
$589$		0			0
$590$	54.0689			2.22598
$591$	−10.9106	−	18.8978i	−0.448804	−	0.777352i
$592$	−15.2497	−	26.4132i	−0.626757	−	1.08558i
$593$	−8.64590	+	14.9751i	−0.355044	+	0.614955i	−0.987126	−	0.159947i	$-0.948868\pi$
$593$	−8.64590	+	14.9751i	−0.355044	+	0.614955i	0.632081	+	0.774902i	$0.282201\pi$
$594$	5.95492	+	10.3142i	0.244333	+	0.423197i
$595$	−2.47214	+	4.28187i	−0.101348	+	0.175539i
$596$	9.76393			0.399946
$597$	−2.00811			−0.0821866
$598$	0.263932	−	0.457144i	0.0107930	−	0.0186940i
$599$	−2.43690	+	4.22083i	−0.0995689	+	0.172458i	−0.911506	−	0.411286i	$-0.865080\pi$
$599$	−2.43690	+	4.22083i	−0.0995689	+	0.172458i	0.811937	+	0.583745i	$0.198413\pi$
$600$	7.56231			0.308730
$601$	−9.74759			−0.397613			−0.198806	−	0.980039i	$-0.563706\pi$
$601$	−9.74759			−0.397613			−0.198806	+	0.980039i	$0.563706\pi$
$602$	2.09387	−	3.62669i	0.0853398	−	0.147813i
$603$	−4.02874	−	6.97798i	−0.164063	−	0.284165i
$604$	13.9883	−	24.2285i	0.569177	−	0.985844i
$605$	−14.7082	−	25.4754i	−0.597974	−	1.03572i
$606$	7.13525	+	12.3586i	0.289850	+	0.502035i
$607$	−27.9767			−1.13554			−0.567769	−	0.823188i	$-0.692193\pi$
$607$	−27.9767			−1.13554			−0.567769	+	0.823188i	$0.692193\pi$
$608$		0			0
$609$	−1.90983			−0.0773902
$610$	29.1522	+	50.4932i	1.18034	+	2.04441i
$611$	−4.16750	−	7.21832i	−0.168599	−	0.292022i
$612$	3.23607	−	5.60503i	0.130810	−	0.226570i
$613$	16.7361	+	28.9877i	0.675963	+	1.17080i	0.976186	+	0.216934i	$0.0696056\pi$
$613$	16.7361	+	28.9877i	0.675963	+	1.17080i	−0.300223	+	0.953869i	$0.597061\pi$
$614$	−26.2812	+	45.5203i	−1.06062	+	1.83705i
$615$	13.4164			0.541002
$616$	−0.237026			−0.00955004
$617$	8.13525	−	14.0907i	0.327513	−	0.567269i	−0.654505	−	0.756058i	$-0.727123\pi$
$617$	8.13525	−	14.0907i	0.327513	−	0.567269i	0.982018	+	0.188789i	$0.0604561\pi$
$618$	20.1437	−	34.8899i	0.810298	−	1.40348i
$619$	−34.7771			−1.39781			−0.698905	−	0.715215i	$-0.746329\pi$
$619$	−34.7771			−1.39781			−0.698905	+	0.715215i	$0.746329\pi$
$620$	−9.95959			−0.399987
$621$	−0.865300	+	1.49874i	−0.0347233	+	0.0601425i
$622$	−13.7638	−	23.8396i	−0.551879	−	0.955882i
$623$	−0.877812	+	1.52041i	−0.0351688	+	0.0609141i
$624$	−3.19098	−	5.52694i	−0.127742	−	0.221255i
$625$	11.2082	+	19.4132i	0.448328	+	0.776527i
$626$	−10.2371			−0.409157
$627$		0			0
$628$	−7.38197			−0.294573
$629$	−21.3723	−	37.0179i	−0.852168	−	1.47600i
$630$	−0.449028	−	0.777739i	−0.0178897	−	0.0309859i
$631$	12.5000	−	21.6506i	0.497617	−	0.861898i	−0.502379	−	0.864647i	$-0.667542\pi$
$631$	12.5000	−	21.6506i	0.497617	−	0.861898i	0.999996	+	0.00274930i	$0.000875132\pi$
$632$	1.70820	+	2.95870i	0.0679487	+	0.117691i
$633$	−0.590170	+	1.02220i	−0.0234571	+	0.0406290i
$634$	−59.5967			−2.36689
$635$	−40.3934			−1.60296
$636$	7.66312	−	13.2729i	0.303862	−	0.526305i
$637$	−2.52265	+	4.36937i	−0.0999512	+	0.173121i
$638$	−11.1803			−0.442634
$639$	6.26137			0.247696
$640$	−9.23305	+	15.9921i	−0.364968	+	0.632144i
$641$	23.3929	+	40.5177i	0.923964	+	1.60035i	0.793219	+	0.608936i	$0.208404\pi$
$641$	23.3929	+	40.5177i	0.923964	+	1.60035i	0.130745	+	0.991416i	$0.458263\pi$
$642$	10.8249	−	18.7493i	0.427224	−	0.739974i
$643$	2.85410	+	4.94345i	0.112555	+	0.194951i	0.916800	−	0.399347i	$-0.130763\pi$
$643$	2.85410	+	4.94345i	0.112555	+	0.194951i	−0.804245	+	0.594298i	$0.797430\pi$
$644$	0.0729490	+	0.126351i	0.00287459	+	0.00497894i
$645$	−57.4064			−2.26038
$646$		0			0
$647$	8.12461			0.319411			0.159706	−	0.987165i	$-0.448945\pi$
$647$	8.12461			0.319411			0.159706	+	0.987165i	$0.448945\pi$
$648$	3.80423	+	6.58911i	0.149444	+	0.258845i
$649$	6.06961	+	10.5129i	0.238253	+	0.412666i
$650$	−3.78115	+	6.54915i	−0.148309	+	0.256879i
$651$	−0.427051	−	0.739674i	−0.0167374	−	0.0289901i
$652$	−12.5172	+	21.6805i	−0.490212	+	0.849072i
$653$	−22.7426			−0.889989			−0.444994	−	0.895533i	$-0.646794\pi$
$653$	−22.7426			−0.889989			−0.444994	+	0.895533i	$0.646794\pi$
$654$	11.1352			0.435419
$655$	9.85410	−	17.0678i	0.385032	−	0.666894i
$656$	−5.03280	+	8.71706i	−0.196498	+	0.340344i
$657$	5.56231			0.217006
$658$	5.15131			0.200819
$659$	18.9151	−	32.7620i	0.736829	−	1.27622i	−0.217087	−	0.976152i	$-0.569656\pi$
$659$	18.9151	−	32.7620i	0.736829	−	1.27622i	0.953916	−	0.300073i	$-0.0970110\pi$
$660$	−6.88191	−	11.9198i	−0.267878	−	0.463978i
$661$	−16.8415	+	29.1703i	−0.655059	+	1.13459i	0.326821	+	0.945086i	$0.394023\pi$
$661$	−16.8415	+	29.1703i	−0.655059	+	1.13459i	−0.981879	+	0.189508i	$0.939311\pi$
$662$	19.2705	+	33.3775i	0.748970	+	1.29725i
$663$	−4.47214	−	7.74597i	−0.173683	−	0.300828i
$664$	−2.35114			−0.0912420
$665$		0			0
$666$	7.76393			0.300846
$667$	−0.812299	−	1.40694i	−0.0314524	−	0.0544771i
$668$	−1.31433	−	2.27648i	−0.0508529	−	0.0880798i
$669$	15.4894	−	26.8284i	0.598853	−	1.03724i
$670$	−40.1246	−	69.4979i	−1.55015	−	2.68494i
$671$	−6.54508	+	11.3364i	−0.252670	+	0.437638i
$672$	3.29180			0.126984
$673$	9.57608			0.369131			0.184565	−	0.982820i	$-0.440912\pi$
$673$	9.57608			0.369131			0.184565	+	0.982820i	$0.440912\pi$
$674$	−0.527864	+	0.914287i	−0.0203326	+	0.0352170i
$675$	12.3965	−	21.4714i	0.477141	−	0.826433i
$676$	−20.1803			−0.776167
$677$	15.1109			0.580759			0.290380	−	0.956912i	$-0.406218\pi$
$677$	15.1109			0.580759			0.290380	+	0.956912i	$0.406218\pi$
$678$		0			0
$679$	0.522273	+	0.904603i	0.0200430	+	0.0347155i
$680$	−7.60845	+	13.1782i	−0.291771	+	0.505362i
$681$	−14.9615	−	25.9141i	−0.573326	−	0.993029i
$682$	−2.50000	−	4.33013i	−0.0957299	−	0.165809i
$683$	40.2219			1.53905			0.769524	−	0.638618i	$-0.220494\pi$
$683$	40.2219			1.53905			0.769524	+	0.638618i	$0.220494\pi$
$684$		0			0
$685$	−28.1803			−1.07672
$686$	−3.13068	−	5.42250i	−0.119530	−	0.207032i
$687$	6.74315	+	11.6795i	0.257267	+	0.445600i
$688$	21.5344	−	37.2987i	0.820993	−	1.42200i
$689$	−1.80902	−	3.13331i	−0.0689181	−	0.119370i
$690$	2.23607	−	3.87298i	0.0851257	−	0.147442i
$691$	−16.3050			−0.620270			−0.310135	−	0.950693i	$-0.600374\pi$
$691$	−16.3050			−0.620270			−0.310135	+	0.950693i	$0.600374\pi$
$692$	−26.9726			−1.02534
$693$	0.100813	−	0.174613i	0.00382957	−	0.00663301i
$694$	27.4216	−	47.4957i	1.04091	−	1.80291i
$695$	39.1246			1.48408
$696$	−5.87785			−0.222799
$697$	−7.05342	+	12.2169i	−0.267167	+	0.462748i
$698$	12.9515	+	22.4327i	0.490222	+	0.849090i
$699$	−4.30625	+	7.45865i	−0.162878	+	0.282112i
$700$	−1.04508	−	1.81014i	−0.0395005	−	0.0684169i
$701$	−4.37132	−	7.57135i	−0.165103	−	0.285966i	0.771589	−	0.636121i	$-0.219462\pi$
$701$	−4.37132	−	7.57135i	−0.165103	−	0.285966i	−0.936692	+	0.350155i	$0.886129\pi$
$702$	−6.26137			−0.236320
$703$		0			0
$704$	6.50658			0.245226
$705$	−35.3076	−	61.1546i	−1.32976	−	2.30321i
$706$	24.1397	+	41.8112i	0.908509	+	1.57358i
$707$	−0.465558	+	0.806370i	−0.0175091	+	0.0303267i
$708$	−13.5172	−	23.4125i	−0.508008	−	0.879896i
$709$	6.70820	−	11.6190i	0.251932	−	0.436359i	−0.712126	−	0.702052i	$-0.752267\pi$
$709$	6.70820	−	11.6190i	0.251932	−	0.436359i	0.964058	+	0.265693i	$0.0856008\pi$
$710$	62.3607			2.34035
$711$	−2.90617			−0.108990
$712$	−2.70163	+	4.67935i	−0.101248	+	0.175366i
$713$	0.363271	−	0.629204i	0.0136046	−	0.0235639i
$714$	5.52786			0.206875
$715$	−3.24920			−0.121513
$716$	7.02067	−	12.1602i	0.262375	−	0.454446i
$717$	8.69827	+	15.0658i	0.324843	+	0.562644i
$718$	−33.6502	+	58.2839i	−1.25582	+	2.17514i
$719$	−7.30902	−	12.6596i	−0.272580	−	0.472123i	0.696941	−	0.717128i	$-0.254544\pi$
$719$	−7.30902	−	12.6596i	−0.272580	−	0.472123i	−0.969522	+	0.245005i	$0.921210\pi$
$720$	−4.61803	−	7.99867i	−0.172104	−	0.298093i
$721$	2.62866			0.0978962
$722$		0			0
$723$	−51.6312			−1.92018
$724$	4.70228	+	8.14459i	0.174759	+	0.302691i
$725$	11.6372	+	20.1562i	0.432194	+	0.748583i
$726$	−16.4443	+	28.4823i	−0.610304	+	1.05708i
$727$	18.4721	+	31.9947i	0.685094	+	1.18662i	0.973407	+	0.229081i	$0.0735720\pi$
$727$	18.4721	+	31.9947i	0.685094	+	1.18662i	−0.288314	+	0.957536i	$0.593095\pi$
$728$	0.0623059	−	0.107917i	0.00230921	−	0.00399967i
$729$	19.3820			0.717851
$730$	55.3983			2.05038
$731$	30.1803	−	52.2739i	1.11626	−	1.93342i
$732$	14.5761	−	25.2466i	0.538749	−	0.933140i
$733$	12.8197			0.473505			0.236752	−	0.971570i	$-0.423917\pi$
$733$	12.8197			0.473505			0.236752	+	0.971570i	$0.423917\pi$
$734$	−23.8294			−0.879560
$735$	−21.3723	+	37.0179i	−0.788328	+	1.36542i
$736$	1.40008	+	2.42502i	0.0516078	+	0.0893873i
$737$	9.00854	−	15.6032i	0.331834	−	0.574753i
$738$	−1.28115	−	2.21902i	−0.0471599	−	0.0816833i
$739$	−9.73607	−	16.8634i	−0.358147	−	0.620329i	0.629504	−	0.776997i	$-0.283258\pi$
$739$	−9.73607	−	16.8634i	−0.358147	−	0.620329i	−0.987651	+	0.156668i	$0.949925\pi$
$740$	34.5811			1.27123
$741$		0			0
$742$	2.23607			0.0820886
$743$	−18.3803	−	31.8357i	−0.674309	−	1.16794i	−0.976670	−	0.214745i	$-0.931108\pi$
$743$	−18.3803	−	31.8357i	−0.674309	−	1.16794i	0.302361	−	0.953194i	$-0.402225\pi$
$744$	−1.31433	−	2.27648i	−0.0481856	−	0.0834599i
$745$	9.76393	−	16.9116i	0.357723	−	0.619594i
$746$	−34.9615	−	60.5551i	−1.28003	−	2.21708i
$747$	1.00000	−	1.73205i	0.0365881	−	0.0633724i
$748$	14.4721			0.529154
$749$	1.41260			0.0516151
$750$	−2.76393	+	4.78727i	−0.100925	+	0.174806i
$751$	−6.03685	+	10.4561i	−0.220288	+	0.381550i	−0.954895	−	0.296942i	$-0.904033\pi$
$751$	−6.03685	+	10.4561i	−0.220288	+	0.381550i	0.734607	+	0.678492i	$0.237366\pi$
$752$	52.9787			1.93193
$753$	−31.2259			−1.13793
$754$	2.93893	−	5.09037i	0.107029	−	0.185380i
$755$	−27.9767	−	48.4570i	−1.01818	−	1.76353i
$756$	0.865300	−	1.49874i	0.0314706	−	0.0545088i
$757$	18.6353	+	32.2772i	0.677310	+	1.17314i	0.975788	+	0.218719i	$0.0701877\pi$
$757$	18.6353	+	32.2772i	0.677310	+	1.17314i	−0.298478	+	0.954416i	$0.596479\pi$
$758$	−20.3262	−	35.2061i	−0.738282	−	1.27874i
$759$	1.00406			0.0364450
$760$		0			0
$761$	−23.9443			−0.867979			−0.433990	−	0.900918i	$-0.642895\pi$
$761$	−23.9443			−0.867979			−0.433990	+	0.900918i	$0.642895\pi$
$762$	22.5806	+	39.1107i	0.818009	+	1.41683i
$763$	0.363271	+	0.629204i	0.0131513	+	0.0227787i
$764$	13.7533	−	23.8214i	0.497577	−	0.861828i
$765$	−6.47214	−	11.2101i	−0.234001	−	0.405301i
$766$	−10.7533	+	18.6252i	−0.388532	+	0.672957i
$767$	−6.38197			−0.230439
$768$	38.5568			1.39130
$769$	−16.5795	+	28.7166i	−0.597873	+	1.03555i	0.395261	+	0.918569i	$0.370654\pi$
$769$	−16.5795	+	28.7166i	−0.597873	+	1.03555i	−0.993135	+	0.116978i	$0.962679\pi$
$770$	1.00406	−	1.73908i	0.0361837	−	0.0626720i
$771$	−20.6525			−0.743781
$772$	13.7638			0.495371
$773$	6.18812	−	10.7181i	0.222571	−	0.385505i	−0.733017	−	0.680211i	$-0.761888\pi$
$773$	6.18812	−	10.7181i	0.222571	−	0.385505i	0.955588	+	0.294706i	$0.0952216\pi$
$774$	5.48183	+	9.49480i	0.197040	+	0.341284i
$775$	−5.20431	+	9.01413i	−0.186944	+	0.323797i
$776$	1.60739	+	2.78408i	0.0577020	+	0.0999427i
$777$	1.48278	+	2.56825i	0.0531944	+	0.0921354i
$778$	−3.63271			−0.130239
$779$		0			0
$780$	7.23607			0.259093
$781$	7.00042	+	12.1251i	0.250495	+	0.433870i
$782$	2.35114	+	4.07230i	0.0840766	+	0.145625i
$783$	−9.63525	+	16.6888i	−0.344336	+	0.596407i
$784$	−16.0344	−	27.7725i	−0.572659	−	0.991874i
$785$	−7.38197	+	12.7859i	−0.263474	+	0.456350i
$786$	−22.0344			−0.785943
$787$	−19.3642			−0.690258			−0.345129	−	0.938555i	$-0.612165\pi$
$787$	−19.3642			−0.690258			−0.345129	+	0.938555i	$0.612165\pi$
$788$	−9.28115	+	16.0754i	−0.330627	+	0.572663i
$789$	22.7194	−	39.3511i	0.808830	−	1.40094i
$790$	−28.9443			−1.02979
$791$		0			0
$792$	0.310271	−	0.537405i	0.0110250	−	0.0190958i
$793$	−3.44095	−	5.95991i	−0.122192	−	0.211643i
$794$	1.22857	−	2.12795i	0.0436004	−	0.0755180i
$795$	−15.3262	−	26.5458i	−0.543566	−	0.941483i
$796$	0.854102	+	1.47935i	0.0302728	+	0.0524341i
$797$	13.2088			0.467879			0.233940	−	0.972251i	$-0.424838\pi$
$797$	13.2088			0.467879			0.233940	+	0.972251i	$0.424838\pi$
$798$		0			0
$799$	74.2492			2.62675
$800$	−20.0579	−	34.7414i	−0.709155	−	1.22829i
$801$	−2.29814	−	3.98050i	−0.0812008	−	0.140644i
$802$	4.47214	−	7.74597i	0.157917	−	0.273520i
$803$	6.21885	+	10.7714i	0.219458	+	0.380113i
$804$	−20.0623	+	34.7489i	−0.707543	+	1.22550i
$805$	0.291796			0.0102845
$806$	2.62866			0.0925904
$807$	−24.5344	+	42.4949i	−0.863653	+	1.49589i
$808$	−1.43284	+	2.48175i	−0.0504072	+	0.0873078i
$809$	−34.2705			−1.20489			−0.602443	−	0.798162i	$-0.705806\pi$
$809$	−34.2705			−1.20489			−0.602443	+	0.798162i	$0.705806\pi$
$810$	−64.4598			−2.26489
$811$	−11.1024	+	19.2299i	−0.389858	+	0.675254i	−0.992430	−	0.122810i	$-0.960809\pi$
$811$	−11.1024	+	19.2299i	−0.389858	+	0.675254i	0.602572	+	0.798065i	$0.294143\pi$
$812$	0.812299	+	1.40694i	0.0285061	+	0.0493740i
$813$	18.3273	−	31.7439i	0.642768	−	1.11331i
$814$	8.68034	+	15.0348i	0.304246	+	0.526969i
$815$	25.0344	+	43.3609i	0.876918	+	1.51887i
$816$	56.8514			1.99020
$817$		0			0
$818$	45.7771			1.60056
$819$	0.0530006	+	0.0917997i	0.00185199	+	0.00320774i
$820$	−5.70634	−	9.88367i	−0.199274	−	0.345153i
$821$	−5.01722	+	8.69008i	−0.175102	+	0.303286i	−0.940197	−	0.340632i	$-0.889359\pi$
$821$	−5.01722	+	8.69008i	−0.175102	+	0.303286i	0.765094	+	0.643918i	$0.222692\pi$
$822$	15.7533	+	27.2855i	0.549459	+	0.951691i
$823$	−25.3607	+	43.9260i	−0.884018	+	1.53116i	−0.0371824	+	0.999308i	$0.511838\pi$
$823$	−25.3607	+	43.9260i	−0.884018	+	1.53116i	−0.846835	+	0.531855i	$0.821495\pi$
$824$	8.09017			0.281834
$825$	−14.3844			−0.500799
$826$	1.97214	−	3.41584i	0.0686194	−	0.118852i
$827$	14.8536	−	25.7272i	0.516511	−	0.894624i	−0.483305	−	0.875452i	$-0.660564\pi$
$827$	14.8536	−	25.7272i	0.516511	−	0.894624i	0.999816	−	0.0191719i	$-0.00610297\pi$
$828$	−0.381966			−0.0132742
$829$	15.1109			0.524823			0.262412	−	0.964956i	$-0.415482\pi$
$829$	15.1109			0.524823			0.262412	+	0.964956i	$0.415482\pi$
$830$	9.95959	−	17.2505i	0.345703	−	0.598774i
$831$	14.0413	+	24.3203i	0.487088	+	0.843662i
$832$	−1.71036	+	2.96242i	−0.0592959	+	0.102704i
$833$	−22.4721	−	38.9229i	−0.778613	−	1.34860i
$834$	−21.8713	−	37.8822i	−0.757342	−	1.31175i
$835$	−5.25731			−0.181937
$836$		0			0
$837$	−8.61803			−0.297883
$838$	−6.26137	−	10.8450i	−0.216295	−	0.374635i
$839$	8.47375	+	14.6770i	0.292546	+	0.506705i	0.974411	−	0.224773i	$-0.0721641\pi$
$839$	8.47375	+	14.6770i	0.292546	+	0.506705i	−0.681865	+	0.731478i	$0.738831\pi$
$840$	0.527864	−	0.914287i	0.0182130	−	0.0315459i
$841$	5.45492	+	9.44819i	0.188101	+	0.325800i
$842$	30.8156	−	53.3742i	1.06198	−	1.83940i
$843$	−29.7984			−1.02631
$844$	1.00406			0.0345611
$845$	−20.1803	+	34.9534i	−0.694225	+	1.20243i
$846$	−6.74315	+	11.6795i	−0.231834	+	0.401549i
$847$	−2.14590			−0.0737339
$848$	22.9969			0.789716
$849$	11.4984	−	19.9159i	0.394625	−	0.683511i
$850$	−33.6830	−	58.3407i	−1.15532	−	2.00107i
$851$	−1.26133	+	2.18468i	−0.0432377	+	0.0748900i
$852$	−15.5902	−	27.0030i	−0.534110	−	0.925106i
$853$	−20.1525	−	34.9051i	−0.690008	−	1.19513i	−0.971835	−	0.235663i	$-0.924274\pi$
$853$	−20.1525	−	34.9051i	−0.690008	−	1.19513i	0.281827	−	0.959465i	$-0.409060\pi$
$854$	4.25325			0.145543
$855$		0			0
$856$	4.34752			0.148595
$857$	27.6664	+	47.9196i	0.945066	+	1.63690i	0.755619	+	0.655012i	$0.227336\pi$
$857$	27.6664	+	47.9196i	0.945066	+	1.63690i	0.189447	+	0.981891i	$0.439330\pi$
$858$	1.81636	+	3.14602i	0.0620094	+	0.107403i
$859$	−19.4721	+	33.7267i	−0.664381	+	1.15074i	0.315072	+	0.949068i	$0.397971\pi$
$859$	−19.4721	+	33.7267i	−0.664381	+	1.15074i	−0.979453	+	0.201673i	$0.935362\pi$
$860$	24.4164	+	42.2905i	0.832593	+	1.44209i
$861$	0.489357	−	0.847591i	0.0166772	−	0.0288858i
$862$	−23.7426			−0.808678
$863$	−32.5729			−1.10880			−0.554398	−	0.832252i	$-0.687051\pi$
$863$	−32.5729			−1.10880			−0.554398	+	0.832252i	$0.687051\pi$
$864$	16.6074	−	28.7648i	0.564995	−	0.978600i
$865$	−26.9726	+	46.7179i	−0.917096	+	1.58846i
$866$	−35.9787			−1.22261
$867$	47.3408			1.60778
$868$	−0.363271	+	0.629204i	−0.0123302	+	0.0213566i
$869$	−3.24920	−	5.62777i	−0.110221	−	0.190909i
$870$	24.8990	−	43.1263i	0.844155	−	1.46212i
$871$	4.73607	+	8.20311i	0.160476	+	0.277952i
$872$	1.11803	+	1.93649i	0.0378614	+	0.0655779i
$873$	−2.73466			−0.0925541
$874$		0			0
$875$	−0.360680			−0.0121932
$876$	−13.8496	−	23.9882i	−0.467934	−	0.810485i
$877$	4.87380	+	8.44166i	0.164576	+	0.285055i	0.936505	−	0.350655i	$-0.114041\pi$
$877$	4.87380	+	8.44166i	0.164576	+	0.285055i	−0.771928	+	0.635709i	$0.780708\pi$
$878$	−5.69098	+	9.85707i	−0.192061	+	0.332660i
$879$	14.5344	+	25.1744i	0.490235	+	0.849111i
$880$	10.3262	−	17.8856i	0.348097	−	0.602922i
$881$	40.5755			1.36702			0.683511	−	0.729940i	$-0.260452\pi$
$881$	40.5755			1.36702			0.683511	+	0.729940i	$0.260452\pi$
$882$	8.16348			0.274879
$883$	−6.98278	+	12.0945i	−0.234989	+	0.407013i	−0.959270	−	0.282492i	$-0.908839\pi$
$883$	−6.98278	+	12.0945i	−0.234989	+	0.407013i	0.724280	+	0.689506i	$0.242172\pi$
$884$	−3.80423	+	6.58911i	−0.127950	+	0.221616i
$885$	−54.0689			−1.81751
$886$	−28.8747			−0.970065
$887$	8.22899	−	14.2530i	0.276303	−	0.478570i	−0.694160	−	0.719820i	$-0.744224\pi$
$887$	8.22899	−	14.2530i	0.276303	−	0.478570i	0.970463	+	0.241250i	$0.0775575\pi$
$888$	4.56352	+	7.90426i	0.153142	+	0.265249i
$889$	−1.47333	+	2.55188i	−0.0494139	+	0.0855874i
$890$	−22.8885	−	39.6441i	−0.767226	−	1.32887i
$891$	−7.23607	−	12.5332i	−0.242417	−	0.419879i
$892$	−26.3521			−0.882332
$893$		0			0
$894$	−21.8328			−0.730199
$895$	−14.0413	−	24.3203i	−0.469350	−	0.812938i
$896$	0.673542	+	1.16661i	0.0225015	+	0.0389737i
$897$	−0.263932	+	0.457144i	−0.00881243	+	0.0152636i
$898$	23.0517	+	39.9267i	0.769244	+	1.33237i
$899$	4.04508	−	7.00629i	0.134911	−	0.233673i
$900$	5.47214			0.182405
$901$	32.2299			1.07373
$902$	2.86475	−	4.96188i	0.0953856	−	0.165213i
$903$	−2.09387	+	3.62669i	−0.0696797	+	0.120689i
$904$		0			0
$905$	18.8091			0.625237
$906$	−31.2789	+	54.1766i	−1.03917	+	1.79990i
$907$	−14.4904	−	25.0980i	−0.481145	−	0.833367i	0.518621	−	0.855004i	$-0.326445\pi$
$907$	−14.4904	−	25.0980i	−0.481145	−	0.833367i	−0.999766	+	0.0216372i	$0.993112\pi$
$908$	−12.7270	+	22.0438i	−0.422361	+	0.731550i
$909$	−1.21885	−	2.11111i	−0.0404266	−	0.0700209i
$910$	0.527864	+	0.914287i	0.0174985	+	0.0303083i
$911$	25.4540			0.843329			0.421665	−	0.906752i	$-0.361446\pi$
$911$	25.4540			0.843329			0.421665	+	0.906752i	$0.361446\pi$
$912$		0			0
$913$	4.47214			0.148006
$914$	5.98385	+	10.3643i	0.197928	+	0.342822i
$915$	−29.1522	−	50.4932i	−0.963743	−	1.66925i
$916$	5.73607	−	9.93516i	0.189525	−	0.328267i
$917$	−0.718847	−	1.24508i	−0.0237384	−	0.0411162i
$918$	27.8885	−	48.3044i	0.920459	−	1.59428i
$919$	−47.3607			−1.56228			−0.781142	−	0.624353i	$-0.785363\pi$
$919$	−47.3607			−1.56228			−0.781142	+	0.624353i	$0.785363\pi$
$920$	0.898056			0.0296080
$921$	26.2812	−	45.5203i	0.865993	−	1.49994i
$922$	−11.2412	+	19.4703i	−0.370208	+	0.641219i
$923$	−7.36068			−0.242280
$924$	−1.00406			−0.0330311
$925$	18.0701	−	31.2983i	0.594140	−	1.02908i
$926$	9.64932	+	16.7131i	0.317096	+	0.549227i
$927$	−3.44095	+	5.95991i	−0.113016	+	0.195749i
$928$	15.5902	+	27.0030i	0.511772	+	0.886416i
$929$	−8.25329	−	14.2951i	−0.270782	−	0.469008i	0.698281	−	0.715824i	$-0.253949\pi$
$929$	−8.25329	−	14.2951i	−0.270782	−	0.469008i	−0.969062	+	0.246817i	$0.920615\pi$
$930$	22.2703			0.730273
$931$		0			0
$932$	7.32624			0.239979
$933$	13.7638	+	23.8396i	0.450607	+	0.780475i
$934$	4.02874	+	6.97798i	0.131824	+	0.228327i
$935$	14.4721	−	25.0665i	0.473289	−	0.819761i
$936$	0.163119	+	0.282530i	0.00533171	+	0.00923479i
$937$	8.60081	−	14.8970i	0.280976	−	0.486665i	−0.690649	−	0.723190i	$-0.742675\pi$
$937$	8.60081	−	14.8970i	0.280976	−	0.486665i	0.971625	+	0.236525i	$0.0760084\pi$
$938$	−5.85410			−0.191143
$939$	10.2371			0.334075
$940$	−30.0344	+	52.0212i	−0.979615	+	1.69674i
$941$	−13.9026	+	24.0800i	−0.453211	+	0.784985i	−0.998583	−	0.0532094i	$-0.983055\pi$
$941$	−13.9026	+	24.0800i	−0.453211	+	0.784985i	0.545372	+	0.838194i	$0.316388\pi$
$942$	16.5066			0.537813
$943$	0.832544			0.0271114
$944$	20.2825	−	35.1302i	0.660138	−	1.14339i
$945$	−1.73060	−	2.99749i	−0.0562964	−	0.0975082i
$946$	−12.2577	+	21.2310i	−0.398533	+	0.690280i
$947$	14.0902	+	24.4049i	0.457869	+	0.793052i	0.998848	−	0.0479836i	$-0.0152795\pi$
$947$	14.0902	+	24.4049i	0.457869	+	0.793052i	−0.540979	+	0.841036i	$0.681946\pi$
$948$	7.23607	+	12.5332i	0.235017	+	0.407061i
$949$	−6.53888			−0.212261
$950$		0			0
$951$	59.5967			1.93256
$952$	0.555029	+	0.961339i	0.0179886	+	0.0311572i
$953$	10.2169	+	17.6961i	0.330957	+	0.573234i	0.982700	−	0.185206i	$-0.0592953\pi$
$953$	10.2169	+	17.6961i	0.330957	+	0.573234i	−0.651743	+	0.758440i	$0.725962\pi$
$954$	−2.92705	+	5.06980i	−0.0947668	+	0.164141i
$955$	−27.5066	−	47.6428i	−0.890092	−	1.54168i
$956$	7.39919	−	12.8158i	0.239307	−	0.414492i
$957$	11.1803			0.361409
$958$	30.2623			0.977730
$959$	−1.02786	+	1.78031i	−0.0331915	+	0.0574893i
$960$	−14.4904	+	25.0980i	−0.467674	+	0.810036i
$961$	−27.3820			−0.883289
$962$	−9.12705			−0.294268
$963$	−1.84911	+	3.20276i	−0.0595868	+	0.103207i
$964$	21.9601	+	38.0359i	0.707286	+	1.22505i
$965$	13.7638	−	23.8396i	0.443073	−	0.767425i
$966$	−0.163119	−	0.282530i	−0.00524827	−	0.00909026i
$967$	−10.1459	−	17.5732i	−0.326270	−	0.565116i	0.655498	−	0.755196i	$-0.272459\pi$
$967$	−10.1459	−	17.5732i	−0.326270	−	0.565116i	−0.981769	+	0.190080i	$0.939125\pi$
$968$	−6.60440			−0.212273
$969$		0			0
$970$	−27.2361			−0.874497
$971$	22.3233	+	38.6651i	0.716390	+	1.24082i	0.962421	+	0.271561i	$0.0875400\pi$
$971$	22.3233	+	38.6651i	0.716390	+	1.24082i	−0.246031	+	0.969262i	$0.579127\pi$
$972$	5.11855	+	8.86560i	0.164178	+	0.284364i
$973$	1.42705	−	2.47172i	0.0457492	−	0.0792399i
$974$	15.8541	+	27.4601i	0.507998	+	0.879879i
$975$	3.78115	−	6.54915i	0.121094	−	0.209741i
$976$	43.7426			1.40017
$977$	9.57608			0.306366			0.153183	−	0.988198i	$-0.451048\pi$
$977$	9.57608			0.306366			0.153183	+	0.988198i	$0.451048\pi$
$978$	27.9894	−	48.4790i	0.895001	−	1.55019i
$979$	5.13880	−	8.90066i	0.164237	−	0.284466i
$980$	36.3607			1.16150
$981$	−1.90211			−0.0607298
$982$	16.4252	−	28.4493i	0.524150	−	0.907855i
$983$	19.6089	+	33.9636i	0.625427	+	1.08327i	0.988458	+	0.151495i	$0.0484086\pi$
$983$	19.6089	+	33.9636i	0.625427	+	1.08327i	−0.363031	+	0.931777i	$0.618258\pi$
$984$	1.50609	−	2.60862i	0.0480123	−	0.0831597i
$985$	18.5623	+	32.1509i	0.591444	+	1.02441i
$986$	26.1803	+	45.3457i	0.833752	+	1.44410i
$987$	−5.15131			−0.163968
$988$		0			0
$989$	−3.56231			−0.113275
$990$	2.62866	+	4.55296i	0.0835442	+	0.144703i
$991$	−27.6664	−	47.9196i	−0.878852	−	1.52222i	−0.852602	−	0.522561i	$-0.824977\pi$
$991$	−27.6664	−	47.9196i	−0.878852	−	1.52222i	−0.0262501	−	0.999655i	$-0.508357\pi$
$992$	−6.97214	+	12.0761i	−0.221366	+	0.383416i
$993$	−19.2705	−	33.3775i	−0.611531	−	1.05920i
$994$	2.27458	−	3.93968i	0.0721451	−	0.124959i
$995$	3.41641			0.108307
$996$	−9.95959			−0.315582
$997$	16.5623	−	28.6868i	0.524533	−	0.908519i	−0.475058	−	0.879954i	$-0.657573\pi$
$997$	16.5623	−	28.6868i	0.524533	−	0.908519i	0.999592	−	0.0285644i	$-0.00909357\pi$
$998$	28.9807	−	50.1961i	0.917369	−	1.58893i
$999$	29.9230			0.946721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.j.292.4		8
19.2	odd	18		361.2.e.m.28.4		24
19.3	odd	18		361.2.e.m.234.4		24
19.4	even	9		361.2.e.m.245.1		24
19.5	even	9		361.2.e.m.99.4		24
19.6	even	9		361.2.e.m.62.4		24
19.7	even	3		361.2.a.i.1.1	✓	4
19.8	odd	6	inner	361.2.c.j.68.1		8
19.9	even	9		361.2.e.m.54.1		24
19.10	odd	18		361.2.e.m.54.4		24
19.11	even	3	inner	361.2.c.j.68.4		8
19.12	odd	6		361.2.a.i.1.4	yes	4
19.13	odd	18		361.2.e.m.62.1		24
19.14	odd	18		361.2.e.m.99.1		24
19.15	odd	18		361.2.e.m.245.4		24
19.16	even	9		361.2.e.m.234.1		24
19.17	even	9		361.2.e.m.28.1		24
19.18	odd	2	inner	361.2.c.j.292.1		8
57.26	odd	6		3249.2.a.bc.1.4		4
57.50	even	6		3249.2.a.bc.1.1		4
76.7	odd	6		5776.2.a.bu.1.1		4
76.31	even	6		5776.2.a.bu.1.4		4
95.64	even	6		9025.2.a.bj.1.4		4
95.69	odd	6		9025.2.a.bj.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.1	✓	4	19.7	even	3
361.2.a.i.1.4	yes	4	19.12	odd	6
361.2.c.j.68.1		8	19.8	odd	6	inner
361.2.c.j.68.4		8	19.11	even	3	inner
361.2.c.j.292.1		8	19.18	odd	2	inner
361.2.c.j.292.4		8	1.1	even	1	trivial
361.2.e.m.28.1		24	19.17	even	9
361.2.e.m.28.4		24	19.2	odd	18
361.2.e.m.54.1		24	19.9	even	9
361.2.e.m.54.4		24	19.10	odd	18
361.2.e.m.62.1		24	19.13	odd	18
361.2.e.m.62.4		24	19.6	even	9
361.2.e.m.99.1		24	19.14	odd	18
361.2.e.m.99.4		24	19.5	even	9
361.2.e.m.234.1		24	19.16	even	9
361.2.e.m.234.4		24	19.3	odd	18
361.2.e.m.245.1		24	19.4	even	9
361.2.e.m.245.4		24	19.15	odd	18
3249.2.a.bc.1.1		4	57.50	even	6
3249.2.a.bc.1.4		4	57.26	odd	6
5776.2.a.bu.1.1		4	76.7	odd	6
5776.2.a.bu.1.4		4	76.31	even	6
9025.2.a.bj.1.1		4	95.69	odd	6
9025.2.a.bj.1.4		4	95.64	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 1.64728i) q^{2} +(-0.951057 - 1.64728i) q^{3} +(-0.809017 + 1.40126i) q^{4} +(1.61803 + 2.80252i) q^{5} +(1.80902 - 3.13331i) q^{6} +0.236068 q^{7} +0.726543 q^{8} +(-0.309017 + 0.535233i) q^{9} +(-3.07768 + 5.33070i) q^{10} -1.38197 q^{11} +3.07768 q^{12} +(0.363271 - 0.629204i) q^{13} +(0.224514 + 0.388870i) q^{14} +(3.07768 - 5.33070i) q^{15} +(2.30902 + 3.99933i) q^{16} +(3.23607 + 5.60503i) q^{17} -1.17557 q^{18} -5.23607 q^{20} +(-0.224514 - 0.388870i) q^{21} +(-1.31433 - 2.27648i) q^{22} +(0.190983 - 0.330792i) q^{23} +(-0.690983 - 1.19682i) q^{24} +(-2.73607 + 4.73901i) q^{25} +1.38197 q^{26} -4.53077 q^{27} +(-0.190983 + 0.330792i) q^{28} +(2.12663 - 3.68343i) q^{29} +11.7082 q^{30} +1.90211 q^{31} +(-3.66547 + 6.34878i) q^{32} +(1.31433 + 2.27648i) q^{33} +(-6.15537 + 10.6614i) q^{34} +(0.381966 + 0.661585i) q^{35} +(-0.500000 - 0.866025i) q^{36} -6.60440 q^{37} -1.38197 q^{39} +(1.17557 + 2.03615i) q^{40} +(1.08981 + 1.88761i) q^{41} +(0.427051 - 0.739674i) q^{42} +(-4.66312 - 8.07676i) q^{43} +(1.11803 - 1.93649i) q^{44} -2.00000 q^{45} +0.726543 q^{46} +(5.73607 - 9.93516i) q^{47} +(4.39201 - 7.60719i) q^{48} -6.94427 q^{49} -10.4086 q^{50} +(6.15537 - 10.6614i) q^{51} +(0.587785 + 1.01807i) q^{52} +(2.48990 - 4.31263i) q^{53} +(-4.30902 - 7.46344i) q^{54} +(-2.23607 - 3.87298i) q^{55} +0.171513 q^{56} +8.09017 q^{58} +(-4.39201 - 7.60719i) q^{59} +(4.97980 + 8.62526i) q^{60} +(4.73607 - 8.20311i) q^{61} +(1.80902 + 3.13331i) q^{62} +(-0.0729490 + 0.126351i) q^{63} -4.70820 q^{64} +2.35114 q^{65} +(-2.50000 + 4.33013i) q^{66} +(-6.51864 + 11.2906i) q^{67} -10.4721 q^{68} -0.726543 q^{69} +(-0.726543 + 1.25841i) q^{70} +(-5.06555 - 8.77380i) q^{71} +(-0.224514 + 0.388870i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(-6.28115 - 10.8793i) q^{74} +10.4086 q^{75} -0.326238 q^{77} +(-1.31433 - 2.27648i) q^{78} +(2.35114 + 4.07230i) q^{79} +(-7.47214 + 12.9421i) q^{80} +(5.23607 + 9.06914i) q^{81} +(-2.07295 + 3.59045i) q^{82} -3.23607 q^{83} +0.726543 q^{84} +(-10.4721 + 18.1383i) q^{85} +(8.86978 - 15.3629i) q^{86} -8.09017 q^{87} -1.00406 q^{88} +(-3.71847 + 6.44058i) q^{89} +(-1.90211 - 3.29456i) q^{90} +(0.0857567 - 0.148535i) q^{91} +(0.309017 + 0.535233i) q^{92} +(-1.80902 - 3.13331i) q^{93} +21.8213 q^{94} +13.9443 q^{96} +(2.21238 + 3.83196i) q^{97} +(-6.60440 - 11.4391i) q^{98} +(0.427051 - 0.739674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} + 10 q^{6} - 16 q^{7} + 2 q^{9} - 20 q^{11} + 14 q^{16} + 8 q^{17} - 24 q^{20} + 6 q^{23} - 10 q^{24} - 4 q^{25} + 20 q^{26} - 6 q^{28} + 40 q^{30} + 12 q^{35} - 4 q^{36} - 20 q^{39}+ \cdots - 10 q^{99}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^5 + 10 * q^6 - 16 * q^7 + 2 * q^9 - 20 * q^11 + 14 * q^16 + 8 * q^17 - 24 * q^20 + 6 * q^23 - 10 * q^24 - 4 * q^25 + 20 * q^26 - 6 * q^28 + 40 * q^30 + 12 * q^35 - 4 * q^36 - 20 * q^39 - 10 * q^42 - 6 * q^43 - 16 * q^45 + 28 * q^47 + 16 * q^49 - 30 * q^54 + 20 * q^58 + 20 * q^61 + 10 * q^62 - 14 * q^63 + 16 * q^64 - 20 * q^66 - 48 * q^68 - 36 * q^73 - 10 * q^74 + 60 * q^77 - 24 * q^80 + 24 * q^81 - 30 * q^82 - 8 * q^83 - 48 * q^85 - 20 * q^87 - 2 * q^92 - 10 * q^93 + 40 * q^96 - 10 * q^99

Introduction

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