LMFDB - Embedded newform 361.2.c.j.68.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(68,361)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.88259951297$
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			68.1
Root			$0.587785 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	361.68
Dual form			361.2.c.j.292.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 1.64728i) q^{2} +(0.951057 - 1.64728i) q^{3} +(-0.809017 - 1.40126i) q^{4} +(1.61803 - 2.80252i) q^{5} +(1.80902 + 3.13331i) q^{6} +0.236068 q^{7} -0.726543 q^{8} +(-0.309017 - 0.535233i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q - 2 * q^4 + 4 * q^5 + 10 * q^6 - 16 * q^7 + 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.304695	+	0.952450i	$0.401446\pi$
$2$	−0.951057	+	1.64728i	−0.672499	+	1.16480i	−0.977193	+	0.212352i	$0.931888\pi$
$3$	0.951057	−	1.64728i	0.549093	−	0.951057i	−0.449244	−	0.893409i	$-0.648307\pi$
$3$	0.951057	−	1.64728i	0.549093	−	0.951057i	0.998337	−	0.0576475i	$-0.0183600\pi$
$4$	−0.809017	−	1.40126i	−0.404508	−	0.700629i
$5$	1.61803	−	2.80252i	0.723607	−	1.25332i	−0.235938	−	0.971768i	$-0.575816\pi$
$5$	1.61803	−	2.80252i	0.723607	−	1.25332i	0.959545	−	0.281556i	$-0.0908504\pi$
$6$	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	$-0.198792\pi$
$13$	−0.363271	−	0.629204i	−0.100753	−	0.174510i	−0.911995	+	0.410201i	$0.865459\pi$
$14$	−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	−0.144220	−	0.989546i	$-0.546067\pi$
$17$	3.23607	−	5.60503i	0.784862	−	1.35942i	0.929082	−	0.369875i	$-0.120599\pi$
$18$	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	0.885250	−	0.465116i	$-0.153987\pi$
$23$	0.190983	+	0.330792i	0.0398227	+	0.0689750i	−0.845427	+	0.534091i	$0.820654\pi$
$24$	−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	$-0.295889\pi$
$29$	−2.12663	−	3.68343i	−0.394905	−	0.683995i	−0.993089	+	0.117364i	$0.962556\pi$
$30$	11.7082			2.13762
$31$	−1.90211			−0.341630			−0.170815	−	0.985303i	$-0.554640\pi$
$31$	−1.90211			−0.341630			−0.170815	+	0.985303i	$0.554640\pi$
$32$	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	$-0.317335\pi$
$37$	6.60440			1.08576			0.542878	+	0.839812i	$0.317335\pi$
$38$		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	$-0.887775\pi$
$41$	−1.08981	+	1.88761i	−0.170200	+	0.294796i	0.768289	+	0.640103i	$0.221108\pi$
$42$	0.427051	+	0.739674i	0.0658954	+	0.114134i
$43$	−4.66312	+	8.07676i	−0.711119	+	1.23169i	0.253318	+	0.967383i	$0.418478\pi$
$43$	−4.66312	+	8.07676i	−0.711119	+	1.23169i	−0.964437	+	0.264311i	$0.914855\pi$
$44$	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	0.892646	+	0.450759i	$0.148847\pi$
$47$	5.73607	+	9.93516i	0.836692	+	1.44919i	−0.0559542	+	0.998433i	$0.517820\pi$
$48$	−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	$-0.277776\pi$
$53$	−2.48990	−	4.31263i	−0.342014	−	0.592385i	−0.984807	+	0.173655i	$0.944442\pi$
$54$	−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	−0.424591	−	0.905385i	$-0.639582\pi$
$59$	4.39201	−	7.60719i	0.571791	−	0.990371i	0.996382	−	0.0849861i	$-0.0270846\pi$
$60$	−4.97980	+	8.62526i	−0.642889	+	1.11352i
$61$	4.73607	+	8.20311i	0.606391	+	1.05030i	0.991830	+	0.127567i	$0.0407168\pi$
$61$	4.73607	+	8.20311i	0.606391	+	1.05030i	−0.385439	+	0.922733i	$0.625950\pi$
$62$	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	0.921960	+	0.387285i	$0.126587\pi$
$67$	6.51864	+	11.2906i	0.796378	+	1.37937i	−0.125582	+	0.992083i	$0.540080\pi$
$68$	−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	−0.391474	−	0.920189i	$-0.628035\pi$
$71$	5.06555	−	8.77380i	0.601171	−	1.04126i	0.992644	−	0.121069i	$-0.0386321\pi$
$72$	0.224514	+	0.388870i	0.0264592	+	0.0458287i
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	0.472831	+	0.881153i	$0.343232\pi$
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	−0.999517	+	0.0310925i	$0.990101\pi$
$74$	−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	$-0.918548\pi$
$79$	−2.35114	+	4.07230i	−0.264524	+	0.458169i	0.702915	+	0.711274i	$0.251882\pi$
$80$	−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	$-0.0377033\pi$
$89$	3.71847	+	6.44058i	0.394157	+	0.682700i	−0.598836	+	0.800872i	$0.704370\pi$
$90$	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	$-0.905452\pi$
$97$	−2.21238	+	3.83196i	−0.224634	+	0.389077i	0.731576	+	0.681760i	$0.238785\pi$
$98$	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	0.751070	−	0.660223i	$-0.229538\pi$
$101$	−1.97214	−	3.41584i	−0.196235	−	0.339889i	−0.947305	+	0.320334i	$0.896205\pi$
$102$	23.4164			2.31857
$103$	−11.1352			−1.09718			−0.548590	−	0.836091i	$-0.684835\pi$
$103$	−11.1352			−1.09718			−0.548590	+	0.836091i	$0.684835\pi$
$104$	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	$-0.593403\pi$
$107$	−5.98385			−0.578481			−0.289240	+	0.957256i	$0.593403\pi$
$108$	−3.66547	−	6.34878i	−0.352710	−	0.610911i
$109$	−1.53884	+	2.66535i	−0.147394	+	0.255294i	−0.930264	−	0.366892i	$-0.880422\pi$
$109$	−1.53884	+	2.66535i	−0.147394	+	0.255294i	0.782869	+	0.622186i	$0.213755\pi$
$110$	−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	0.997995	+	0.0632922i	$0.0201600\pi$
$127$	6.24112	+	10.8099i	0.553810	+	0.959227i	−0.444185	+	0.895935i	$0.646507\pi$
$128$	−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	−0.967838	−	0.251573i	$-0.919052\pi$
$131$	−3.04508	+	5.27424i	−0.266050	+	0.460813i	0.701788	+	0.712386i	$0.252385\pi$
$132$	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	0.617876	−	0.786275i	$-0.287993\pi$
$137$	−4.35410	−	7.54153i	−0.371996	−	0.644316i	−0.989873	+	0.141959i	$0.954660\pi$
$138$	−0.690983	+	1.19682i	−0.0588204	+	0.101880i
$139$	6.04508	+	10.4704i	0.512737	+	0.888087i	0.999891	+	0.0147709i	$0.00470189\pi$
$139$	6.04508	+	10.4704i	0.512737	+	0.888087i	−0.487153	+	0.873316i	$0.661965\pi$
$140$	−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	−0.962742	−	0.270420i	$-0.912837\pi$
$149$	−3.01722	+	5.22598i	−0.247180	+	0.428129i	0.715562	+	0.698549i	$0.246171\pi$
$150$	9.89919	−	17.1459i	0.808265	−	1.39996i
$151$	17.2905			1.40708			0.703542	−	0.710654i	$-0.251601\pi$
$151$	17.2905			1.40708			0.703542	+	0.710654i	$0.251601\pi$
$152$		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	−0.760525	−	0.649309i	$-0.775058\pi$
$157$	2.28115	−	3.95107i	0.182056	−	0.315330i	0.942580	+	0.333979i	$0.108392\pi$
$158$	−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	$-0.146645\pi$
$167$	0.812299	+	1.40694i	0.0628576	+	0.108873i	−0.832884	+	0.553448i	$0.813312\pi$
$168$	−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	0.353092	+	0.935589i	$0.385130\pi$
$173$	−8.33499	+	14.4366i	−0.633698	+	1.09760i	−0.986789	+	0.162008i	$0.948203\pi$
$174$	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	$-0.394867\pi$
$179$	8.67802			0.648626			0.324313	+	0.945950i	$0.394867\pi$
$180$	1.61803	+	2.80252i	0.120601	+	0.208887i
$181$	−2.90617	−	5.03363i	−0.216014	−	0.374147i	0.737572	−	0.675269i	$-0.235972\pi$
$181$	−2.90617	−	5.03363i	−0.216014	−	0.374147i	−0.953586	+	0.301122i	$0.902639\pi$
$182$	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	$-0.734290\pi$
$193$	4.25325	−	7.36685i	0.306156	−	0.530278i	0.977518	+	0.210852i	$0.0676238\pi$
$194$	−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	0.884129	−	0.467244i	$-0.154753\pi$
$199$	0.527864	+	0.914287i	0.0374193	+	0.0648121i	−0.846709	+	0.532056i	$0.821420\pi$
$200$	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	$-0.826534\pi$
$211$	0.310271	−	0.537405i	0.0213599	−	0.0369965i	0.876508	+	0.481388i	$0.159867\pi$
$212$	−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	0.453276	+	0.891370i	$0.350255\pi$
$223$	−8.14324	+	14.1045i	−0.545311	+	0.944507i	−0.998587	+	0.0531368i	$0.983078\pi$
$224$	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	$-0.674839\pi$
$227$	−15.7314			−1.04413			−0.522066	+	0.852905i	$0.674839\pi$
$228$		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	−0.930605	−	0.366025i	$-0.880718\pi$
$233$	−2.26393	+	3.92125i	−0.148315	+	0.256889i	0.782290	+	0.622915i	$0.214052\pi$
$234$	−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	−0.857556	−	0.514391i	$-0.828018\pi$
$241$	−13.5721	−	23.5075i	−0.874253	−	1.51425i	−0.0166973	−	0.999861i	$-0.505315\pi$
$242$	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	0.999779	+	0.0210245i	$0.00669280\pi$
$251$	8.20820	+	14.2170i	0.518097	+	0.897371i	−0.481682	+	0.876346i	$0.659974\pi$
$252$	−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	$-0.276634\pi$
$257$	−5.42882	−	9.40300i	−0.338641	−	0.586543i	−0.984177	+	0.177186i	$0.943300\pi$
$258$	−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	−0.217540	−	0.976051i	$-0.569803\pi$
$263$	11.9443	−	20.6881i	0.736515	−	1.27568i	0.954055	−	0.299631i	$-0.0968634\pi$
$264$	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	−0.141700	−	0.989910i	$-0.545257\pi$
$269$	12.8985	−	22.3409i	0.786437	−	1.36215i	0.928137	−	0.372239i	$-0.121410\pi$
$270$	13.9443	+	24.1522i	0.848621	+	1.46986i
$271$	9.63525	−	16.6888i	0.585300	−	1.01377i	−0.409538	−	0.912293i	$-0.634310\pi$
$271$	9.63525	−	16.6888i	0.585300	−	1.01377i	0.994838	−	0.101476i	$-0.0323566\pi$
$272$	−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	$-0.321431\pi$
$281$	−7.83297	−	13.5671i	−0.467276	−	0.809345i	−0.999301	+	0.0373833i	$0.988098\pi$
$282$	−20.7533	+	35.9458i	−1.23584	+	2.14054i
$283$	6.04508	−	10.4704i	0.359343	−	0.622400i	−0.628508	−	0.777803i	$-0.716334\pi$
$283$	6.04508	−	10.4704i	0.359343	−	0.622400i	0.987851	+	0.155403i	$0.0496675\pi$
$284$	−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	$-0.352704\pi$
$293$	15.2824			0.892808			0.446404	+	0.894831i	$0.352704\pi$
$294$	−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	0.138277	+	0.990394i	$0.455844\pi$
$307$	−13.8168	+	23.9314i	−0.788568	+	1.36584i	−0.926844	+	0.375445i	$0.877490\pi$
$308$	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	0.779897	−	0.625908i	$-0.215271\pi$
$313$	−2.69098	−	4.66092i	−0.152103	−	0.263451i	−0.932001	+	0.362457i	$0.881938\pi$
$314$	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	0.851465	+	0.524412i	$0.175715\pi$
$317$	15.6659	+	27.1342i	0.879886	+	1.52401i	0.0284217	+	0.999596i	$0.490952\pi$
$318$	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	$-0.687992\pi$
$331$	−20.2622			−1.11371			−0.556856	+	0.830609i	$0.687992\pi$
$332$	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	$-0.838145\pi$
$337$	−0.277515	+	0.480669i	−0.0151172	+	0.0261837i	0.858368	+	0.513035i	$0.171479\pi$
$338$	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	0.161490	+	0.986874i	$0.448370\pi$
$347$	−14.4164	+	24.9700i	−0.773913	+	1.34046i	−0.935403	+	0.353583i	$0.884963\pi$
$348$	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	0.156749	−	0.987639i	$-0.449899\pi$
$359$	17.6910	−	30.6417i	0.933694	−	1.61721i	0.776946	−	0.629568i	$-0.216768\pi$
$360$	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	0.654935	−	0.755685i	$-0.272696\pi$
$367$	−6.26393	−	10.8494i	−0.326975	−	0.566337i	−0.981910	+	0.189348i	$0.939362\pi$
$368$	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	$-0.0993369\pi$
$373$	36.7607			1.90340			0.951698	+	0.307035i	$0.0993369\pi$
$374$	−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	$-0.315043\pi$
$379$	21.3723			1.09782			0.548910	+	0.835882i	$0.315043\pi$
$380$		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	$-0.926614\pi$
$383$	−5.65334	+	9.79187i	−0.288872	+	0.500341i	0.684669	+	0.728854i	$0.259947\pi$
$384$	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	0.840802	−	0.541343i	$-0.182084\pi$
$389$	−0.954915	−	1.65396i	−0.0484161	−	0.0838592i	−0.889218	+	0.457484i	$0.848751\pi$
$390$	−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	−0.881779	−	0.471664i	$-0.843654\pi$
$397$	−0.645898	+	1.11873i	−0.0324167	+	0.0561474i	0.849362	+	0.527811i	$0.176987\pi$
$398$	−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	$-0.795874\pi$
$401$	2.35114	−	4.07230i	0.117410	−	0.203361i	0.918741	+	0.394861i	$0.129207\pi$
$402$	−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	−0.993546	−	0.113428i	$-0.963817\pi$
$409$	−12.0332	−	20.8421i	−0.595004	−	1.03058i	0.398542	−	0.917150i	$-0.369516\pi$
$410$	−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	−0.136653	−	0.990619i	$-0.543635\pi$
$421$	16.2007	−	28.0605i	0.789575	−	1.36758i	0.926228	−	0.376964i	$-0.123032\pi$
$422$	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	$-0.0694716\pi$
$431$	6.24112	+	10.8099i	0.300624	+	0.520697i	−0.675653	+	0.737220i	$0.736138\pi$
$432$	10.4616	−	18.1201i	0.503335	−	0.871802i
$433$	9.45756	+	16.3810i	0.454502	+	0.787220i	0.998659	−	0.0517631i	$-0.0164841\pi$
$433$	9.45756	+	16.3810i	0.454502	+	0.787220i	−0.544158	+	0.838983i	$0.683151\pi$
$434$	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	$-0.878943\pi$
$439$	−2.99193	+	5.18217i	−0.142797	+	0.247331i	0.785752	+	0.618542i	$0.212276\pi$
$440$	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	0.627443	−	0.778662i	$-0.284101\pi$
$443$	−7.59017	−	13.1466i	−0.360620	−	0.624612i	−0.988063	+	0.154050i	$0.950768\pi$
$444$	−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	$-0.693805\pi$
$449$	−24.2380			−1.14386			−0.571930	+	0.820303i	$0.693805\pi$
$450$	−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	−0.694949	−	0.719059i	$-0.744573\pi$
$461$	5.90983	−	10.2361i	0.275248	−	0.476744i	0.970198	+	0.242315i	$0.0779066\pi$
$462$	−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	0.988529	−	0.151029i	$-0.0482588\pi$
$479$	7.95492	+	13.7783i	0.363469	+	0.629547i	−0.625060	+	0.780577i	$0.714925\pi$
$480$	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	$-0.623283\pi$
$487$	−16.6700			−0.755389			−0.377695	+	0.925930i	$0.623283\pi$
$488$	−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	−0.992410	−	0.122977i	$-0.960756\pi$
$491$	−8.63525	+	14.9567i	−0.389704	+	0.674986i	0.602706	+	0.797963i	$0.294089\pi$
$492$	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	0.292291	+	0.956329i	$0.405582\pi$
$499$	−15.2361	+	26.3896i	−0.682060	+	1.18136i	−0.974351	+	0.225033i	$0.927751\pi$
$500$	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	0.539736	−	0.841834i	$-0.318524\pi$
$503$	−10.2984	−	17.8373i	−0.459182	−	0.795326i	−0.998918	+	0.0465081i	$0.985191\pi$
$504$	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	$-0.298733\pi$
$509$	−9.09429	−	15.7518i	−0.403097	−	0.698185i	−0.994098	+	0.108486i	$0.965400\pi$
$510$	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	$-0.658640\pi$
$521$	−21.8213			−0.956008			−0.478004	+	0.878358i	$0.658640\pi$
$522$	−2.50000	−	4.33013i	−0.109422	−	0.189525i
$523$	17.2048	+	29.7995i	0.752312	+	1.30304i	0.946699	+	0.322118i	$0.104395\pi$
$523$	17.2048	+	29.7995i	0.752312	+	1.30304i	−0.194387	+	0.980925i	$0.562272\pi$
$524$	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	0.784872	−	0.619658i	$-0.212729\pi$
$541$	−3.35410	−	5.80948i	−0.144204	−	0.249769i	−0.929076	+	0.369890i	$0.879396\pi$
$542$	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	$-0.312672\pi$
$547$	−10.3556	−	17.9365i	−0.442774	−	0.766908i	−0.997894	+	0.0648627i	$0.979339\pi$
$548$	−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	0.894937	+	0.446193i	$0.147220\pi$
$557$	19.6803	+	34.0873i	0.833883	+	1.44433i	−0.0610541	+	0.998134i	$0.519446\pi$
$558$	−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	$-0.651289\pi$
$563$	−21.7153			−0.915191			−0.457595	+	0.889161i	$0.651289\pi$
$564$	−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	$-0.679140\pi$
$569$	−25.4540			−1.06709			−0.533544	+	0.845772i	$0.679140\pi$
$570$		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	−0.985735	−	0.168305i	$-0.946171\pi$
$587$	−8.40983	+	14.5663i	−0.347111	+	0.601214i	0.638624	+	0.769519i	$0.279504\pi$
$588$	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	0.632081	−	0.774902i	$-0.282201\pi$
$593$	−8.64590	−	14.9751i	−0.355044	−	0.614955i	−0.987126	+	0.159947i	$0.948868\pi$
$594$	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	$-0.134920\pi$
$599$	2.43690	+	4.22083i	0.0995689	+	0.172458i	−0.811937	+	0.583745i	$0.801587\pi$
$600$	7.56231			0.308730
$601$	9.74759			0.397613			0.198806	−	0.980039i	$-0.436294\pi$
$601$	9.74759			0.397613			0.198806	+	0.980039i	$0.436294\pi$
$602$	−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	$-0.307807\pi$
$607$	27.9767			1.13554			0.567769	+	0.823188i	$0.307807\pi$
$608$		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	−0.300223	−	0.953869i	$-0.597061\pi$
$613$	16.7361	−	28.9877i	0.675963	−	1.17080i	0.976186	−	0.216934i	$-0.0696056\pi$
$614$	−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	0.982018	−	0.188789i	$-0.0604561\pi$
$617$	8.13525	+	14.0907i	0.327513	+	0.567269i	−0.654505	+	0.756058i	$0.727123\pi$
$618$	−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	0.999996	−	0.00274930i	$-0.000875132\pi$
$631$	12.5000	+	21.6506i	0.497617	+	0.861898i	−0.502379	+	0.864647i	$0.667542\pi$
$632$	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	−0.130745	+	0.991416i	$0.541737\pi$
$641$	−23.3929	+	40.5177i	−0.923964	+	1.60035i	−0.793219	+	0.608936i	$0.791596\pi$
$642$	−10.8249	−	18.7493i	−0.427224	−	0.739974i
$643$	2.85410	−	4.94345i	0.112555	−	0.194951i	−0.804245	−	0.594298i	$-0.797430\pi$
$643$	2.85410	−	4.94345i	0.112555	−	0.194951i	0.916800	+	0.399347i	$0.130763\pi$
$644$	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	−0.953916	−	0.300073i	$-0.902989\pi$
$659$	−18.9151	−	32.7620i	−0.736829	−	1.27622i	0.217087	−	0.976152i	$-0.430344\pi$
$660$	6.88191	−	11.9198i	0.267878	−	0.463978i
$661$	16.8415	+	29.1703i	0.655059	+	1.13459i	0.981879	+	0.189508i	$0.0606894\pi$
$661$	16.8415	+	29.1703i	0.655059	+	1.13459i	−0.326821	+	0.945086i	$0.605977\pi$
$662$	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	$-0.559088\pi$
$673$	−9.57608			−0.369131			−0.184565	+	0.982820i	$0.559088\pi$
$674$	−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	$-0.593782\pi$
$677$	−15.1109			−0.580759			−0.290380	+	0.956912i	$0.593782\pi$
$678$		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	$-0.779506\pi$
$683$	−40.2219			−1.53905			−0.769524	+	0.638618i	$0.779506\pi$
$684$		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	−0.936692	−	0.350155i	$-0.886129\pi$
$701$	−4.37132	+	7.57135i	−0.165103	+	0.285966i	0.771589	+	0.636121i	$0.219462\pi$
$702$	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	0.964058	−	0.265693i	$-0.0856008\pi$
$709$	6.70820	+	11.6190i	0.251932	+	0.436359i	−0.712126	+	0.702052i	$0.752267\pi$
$710$	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	−0.969522	−	0.245005i	$-0.921210\pi$
$719$	−7.30902	+	12.6596i	−0.272580	+	0.472123i	0.696941	+	0.717128i	$0.254544\pi$
$720$	−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	−0.288314	−	0.957536i	$-0.593095\pi$
$727$	18.4721	−	31.9947i	0.685094	−	1.18662i	0.973407	−	0.229081i	$-0.0735720\pi$
$728$	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	−0.987651	−	0.156668i	$-0.949925\pi$
$739$	−9.73607	+	16.8634i	−0.358147	+	0.620329i	0.629504	+	0.776997i	$0.283258\pi$
$740$	−34.5811			−1.27123
$741$		0			0
$742$	2.23607			0.0820886
$743$	18.3803	−	31.8357i	0.674309	−	1.16794i	−0.302361	−	0.953194i	$-0.597775\pi$
$743$	18.3803	−	31.8357i	0.674309	−	1.16794i	0.976670	−	0.214745i	$-0.0688919\pi$
$744$	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	$-0.0959670\pi$
$751$	6.03685	+	10.4561i	0.220288	+	0.381550i	−0.734607	+	0.678492i	$0.762634\pi$
$752$	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	−0.298478	−	0.954416i	$-0.596479\pi$
$757$	18.6353	−	32.2772i	0.677310	−	1.17314i	0.975788	−	0.218719i	$-0.0701877\pi$
$758$	−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	−0.993135	−	0.116978i	$-0.962679\pi$
$769$	−16.5795	−	28.7166i	−0.597873	−	1.03555i	0.395261	−	0.918569i	$-0.370654\pi$
$770$	−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	$-0.238112\pi$
$773$	−6.18812	−	10.7181i	−0.222571	−	0.385505i	−0.955588	+	0.294706i	$0.904778\pi$
$774$	−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	$-0.387835\pi$
$787$	19.3642			0.690258			0.345129	+	0.938555i	$0.387835\pi$
$788$	−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	$-0.575162\pi$
$797$	−13.2088			−0.467879			−0.233940	+	0.972251i	$0.575162\pi$
$798$		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	$-0.0391907\pi$
$811$	11.1024	+	19.2299i	0.389858	+	0.675254i	−0.602572	+	0.798065i	$0.705857\pi$
$812$	−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	0.765094	−	0.643918i	$-0.222692\pi$
$821$	−5.01722	−	8.69008i	−0.175102	−	0.303286i	−0.940197	+	0.340632i	$0.889359\pi$
$822$	15.7533	−	27.2855i	0.549459	−	0.951691i
$823$	−25.3607	−	43.9260i	−0.884018	−	1.53116i	−0.846835	−	0.531855i	$-0.821495\pi$
$823$	−25.3607	−	43.9260i	−0.884018	−	1.53116i	−0.0371824	−	0.999308i	$-0.511838\pi$
$824$	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	−0.999816	−	0.0191719i	$-0.993897\pi$
$827$	−14.8536	−	25.7272i	−0.516511	−	0.894624i	0.483305	−	0.875452i	$-0.339436\pi$
$828$	−0.381966			−0.0132742
$829$	−15.1109			−0.524823			−0.262412	−	0.964956i	$-0.584518\pi$
$829$	−15.1109			−0.524823			−0.262412	+	0.964956i	$0.584518\pi$
$830$	−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	$-0.927836\pi$
$839$	−8.47375	+	14.6770i	−0.292546	+	0.506705i	0.681865	+	0.731478i	$0.261169\pi$
$840$	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	0.281827	+	0.959465i	$0.409060\pi$
$853$	−20.1525	+	34.9051i	−0.690008	+	1.19513i	−0.971835	+	0.235663i	$0.924274\pi$
$854$	−4.25325			−0.145543
$855$		0			0
$856$	4.34752			0.148595
$857$	−27.6664	+	47.9196i	−0.945066	+	1.63690i	−0.189447	+	0.981891i	$0.560670\pi$
$857$	−27.6664	+	47.9196i	−0.945066	+	1.63690i	−0.755619	+	0.655012i	$0.772664\pi$
$858$	−1.81636	+	3.14602i	−0.0620094	+	0.107403i
$859$	−19.4721	−	33.7267i	−0.664381	−	1.15074i	−0.979453	−	0.201673i	$-0.935362\pi$
$859$	−19.4721	−	33.7267i	−0.664381	−	1.15074i	0.315072	−	0.949068i	$-0.397971\pi$
$860$	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	$-0.312949\pi$
$863$	32.5729			1.10880			0.554398	+	0.832252i	$0.312949\pi$
$864$	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	$-0.885959\pi$
$877$	−4.87380	+	8.44166i	−0.164576	+	0.285055i	0.771928	+	0.635709i	$0.219292\pi$
$878$	−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	0.724280	−	0.689506i	$-0.242172\pi$
$883$	−6.98278	−	12.0945i	−0.234989	−	0.407013i	−0.959270	+	0.282492i	$0.908839\pi$
$884$	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	$-0.255776\pi$
$887$	−8.22899	−	14.2530i	−0.276303	−	0.478570i	−0.970463	+	0.241250i	$0.922443\pi$
$888$	−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	$-0.673555\pi$
$907$	14.4904	−	25.0980i	0.481145	−	0.833367i	0.999766	+	0.0216372i	$0.00688788\pi$
$908$	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	$-0.638554\pi$
$911$	−25.4540			−0.843329			−0.421665	+	0.906752i	$0.638554\pi$
$912$		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	−0.969062	−	0.246817i	$-0.920615\pi$
$929$	−8.25329	+	14.2951i	−0.270782	+	0.469008i	0.698281	+	0.715824i	$0.253949\pi$
$930$	−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	0.971625	−	0.236525i	$-0.0760084\pi$
$937$	8.60081	+	14.8970i	0.280976	+	0.486665i	−0.690649	+	0.723190i	$0.742675\pi$
$938$	−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	$-0.0169451\pi$
$941$	13.9026	+	24.0800i	0.453211	+	0.784985i	−0.545372	+	0.838194i	$0.683612\pi$
$942$	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	−0.540979	−	0.841036i	$-0.681946\pi$
$947$	14.0902	−	24.4049i	0.457869	−	0.793052i	0.998848	+	0.0479836i	$0.0152795\pi$
$948$	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	$-0.940705\pi$
$953$	−10.2169	+	17.6961i	−0.330957	+	0.573234i	0.651743	+	0.758440i	$0.274038\pi$
$954$	−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	−0.981769	−	0.190080i	$-0.939125\pi$
$967$	−10.1459	+	17.5732i	−0.326270	+	0.565116i	0.655498	+	0.755196i	$0.272459\pi$
$968$	6.60440			0.212273
$969$		0			0
$970$	−27.2361			−0.874497
$971$	−22.3233	+	38.6651i	−0.716390	+	1.24082i	0.246031	+	0.969262i	$0.420873\pi$
$971$	−22.3233	+	38.6651i	−0.716390	+	1.24082i	−0.962421	+	0.271561i	$0.912460\pi$
$972$	−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	$-0.548952\pi$
$977$	−9.57608			−0.306366			−0.153183	+	0.988198i	$0.548952\pi$
$978$	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	0.363031	+	0.931777i	$0.381742\pi$
$983$	−19.6089	+	33.9636i	−0.625427	+	1.08327i	−0.988458	+	0.151495i	$0.951591\pi$
$984$	−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	0.0262501	−	0.999655i	$-0.491643\pi$
$991$	27.6664	−	47.9196i	0.878852	−	1.52222i	0.852602	−	0.522561i	$-0.175023\pi$
$992$	−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	0.999592	+	0.0285644i	$0.00909357\pi$
$997$	16.5623	+	28.6868i	0.524533	+	0.908519i	−0.475058	+	0.879954i	$0.657573\pi$
$998$	−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.68.1		8
19.2	odd	18		361.2.e.m.234.1		24
19.3	odd	18		361.2.e.m.99.4		24
19.4	even	9		361.2.e.m.62.1		24
19.5	even	9		361.2.e.m.28.4		24
19.6	even	9		361.2.e.m.54.4		24
19.7	even	3	inner	361.2.c.j.292.1		8
19.8	odd	6		361.2.a.i.1.1	✓	4
19.9	even	9		361.2.e.m.245.4		24
19.10	odd	18		361.2.e.m.245.1		24
19.11	even	3		361.2.a.i.1.4	yes	4
19.12	odd	6	inner	361.2.c.j.292.4		8
19.13	odd	18		361.2.e.m.54.1		24
19.14	odd	18		361.2.e.m.28.1		24
19.15	odd	18		361.2.e.m.62.4		24
19.16	even	9		361.2.e.m.99.1		24
19.17	even	9		361.2.e.m.234.4		24
19.18	odd	2	inner	361.2.c.j.68.4		8
57.8	even	6		3249.2.a.bc.1.4		4
57.11	odd	6		3249.2.a.bc.1.1		4
76.11	odd	6		5776.2.a.bu.1.4		4
76.27	even	6		5776.2.a.bu.1.1		4
95.49	even	6		9025.2.a.bj.1.1		4
95.84	odd	6		9025.2.a.bj.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.1	✓	4	19.8	odd	6
361.2.a.i.1.4	yes	4	19.11	even	3
361.2.c.j.68.1		8	1.1	even	1	trivial
361.2.c.j.68.4		8	19.18	odd	2	inner
361.2.c.j.292.1		8	19.7	even	3	inner
361.2.c.j.292.4		8	19.12	odd	6	inner
361.2.e.m.28.1		24	19.14	odd	18
361.2.e.m.28.4		24	19.5	even	9
361.2.e.m.54.1		24	19.13	odd	18
361.2.e.m.54.4		24	19.6	even	9
361.2.e.m.62.1		24	19.4	even	9
361.2.e.m.62.4		24	19.15	odd	18
361.2.e.m.99.1		24	19.16	even	9
361.2.e.m.99.4		24	19.3	odd	18
361.2.e.m.234.1		24	19.2	odd	18
361.2.e.m.234.4		24	19.17	even	9
361.2.e.m.245.1		24	19.10	odd	18
361.2.e.m.245.4		24	19.9	even	9
3249.2.a.bc.1.1		4	57.11	odd	6
3249.2.a.bc.1.4		4	57.8	even	6
5776.2.a.bu.1.1		4	76.27	even	6
5776.2.a.bu.1.4		4	76.11	odd	6
9025.2.a.bj.1.1		4	95.49	even	6
9025.2.a.bj.1.4		4	95.84	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.951057 + 1.64728i) q^{2} +(0.951057 - 1.64728i) q^{3} +(-0.809017 - 1.40126i) q^{4} +(1.61803 - 2.80252i) q^{5} +(1.80902 + 3.13331i) q^{6} +0.236068 q^{7} -0.726543 q^{8} +(-0.309017 - 0.535233i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} + 10 q^{6} - 16 q^{7} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 + 4 * q^5 + 10 * q^6 - 16 * q^7 + 2 * q^9	\( 8 q - 2 q^{4} + 4 q^{5} + 10 q^{6} - 16 q^{7} + 2 q^{9} - 20 q^{11} + 14 q^{16} + 8 q^{17} - 24 q^{20} + 6 q^{23} - 10 q^{24} - 4 q^{25} + 20 q^{26} - 6 q^{28} + 40 q^{30} + 12 q^{35} - 4 q^{36} - 20 q^{39} - 10 q^{42} - 6 q^{43} - 16 q^{45} + 28 q^{47} + 16 q^{49} - 30 q^{54} + 20 q^{58} + 20 q^{61} + 10 q^{62} - 14 q^{63} + 16 q^{64} - 20 q^{66} - 48 q^{68} - 36 q^{73} - 10 q^{74} + 60 q^{77} - 24 q^{80} + 24 q^{81} - 30 q^{82} - 8 q^{83} - 48 q^{85} - 20 q^{87} - 2 q^{92} - 10 q^{93} + 40 q^{96} - 10 q^{99}+O(q^{100}) \) 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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