LMFDB - Embedded newform 380.2.n.a.31.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.19
Character	$\chi$	$=$	380.31
Dual form			380.2.n.a.331.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33731 + 0.460003i) q^{2} +(-0.435984 - 0.755146i) q^{3} +(1.57679 + 1.23033i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.235676 - 1.21042i) q^{6} -4.89965i q^{7} +(1.54270 + 2.37067i) q^{8} +(1.11984 - 1.93961i) q^{9} +O(q^{10})$	\(q+(1.33731 + 0.460003i) q^{2} +(-0.435984 - 0.755146i) q^{3} +(1.57679 + 1.23033i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.235676 - 1.21042i) q^{6} -4.89965i q^{7} +(1.54270 + 2.37067i) q^{8} +(1.11984 - 1.93961i) q^{9} +(0.270280 + 1.38815i) q^{10} -0.00879181i q^{11} +(0.241625 - 1.72712i) q^{12} +(0.420792 + 0.242945i) q^{13} +(2.25385 - 6.55234i) q^{14} +(0.435984 - 0.755146i) q^{15} +(0.972557 + 3.87997i) q^{16} +(3.74761 + 6.49105i) q^{17} +(2.38980 - 2.07873i) q^{18} +(-4.34376 + 0.362980i) q^{19} +(-0.277103 + 1.98071i) q^{20} +(-3.69995 + 2.13617i) q^{21} +(0.00404426 - 0.0117574i) q^{22} +(5.37572 + 3.10367i) q^{23} +(1.11761 - 2.19854i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.450974 + 0.518458i) q^{26} -4.56882 q^{27} +(6.02820 - 7.72573i) q^{28} +(-6.57006 - 3.79323i) q^{29} +(0.930415 - 0.809310i) q^{30} -2.94686 q^{31} +(-0.484187 + 5.63609i) q^{32} +(-0.00663910 + 0.00383309i) q^{33} +(2.02581 + 10.4045i) q^{34} +(4.24322 - 2.44982i) q^{35} +(4.15212 - 1.68060i) q^{36} -2.82994i q^{37} +(-5.97592 - 1.51273i) q^{38} -0.423680i q^{39} +(-1.28171 + 2.52135i) q^{40} +(1.66637 - 0.962078i) q^{41} +(-5.93062 + 1.15473i) q^{42} +(-2.58045 + 1.48982i) q^{43} +(0.0108169 - 0.0138629i) q^{44} +2.23967 q^{45} +(5.76130 + 6.62342i) q^{46} +(1.00323 + 0.579216i) q^{47} +(2.50592 - 2.42603i) q^{48} -17.0065 q^{49} +(-1.06703 + 0.928142i) q^{50} +(3.26779 - 5.65998i) q^{51} +(0.364600 + 0.900789i) q^{52} +(-2.12792 - 1.22856i) q^{53} +(-6.10993 - 2.10167i) q^{54} +(0.00761393 - 0.00439590i) q^{55} +(11.6154 - 7.55870i) q^{56} +(2.16791 + 3.12192i) q^{57} +(-7.04131 - 8.09497i) q^{58} +(-5.18269 - 8.97669i) q^{59} +(1.61654 - 0.654304i) q^{60} +(-0.851042 + 1.47405i) q^{61} +(-3.94086 - 1.35556i) q^{62} +(-9.50342 - 5.48680i) q^{63} +(-3.24013 + 7.31448i) q^{64} +0.485889i q^{65} +(-0.0106418 + 0.00207201i) q^{66} +(-3.12293 + 5.40907i) q^{67} +(-2.07695 + 14.8459i) q^{68} -5.41260i q^{69} +(6.80142 - 1.32428i) q^{70} +(6.62115 + 11.4682i) q^{71} +(6.32575 - 0.337489i) q^{72} +(4.76690 + 8.25652i) q^{73} +(1.30178 - 3.78451i) q^{74} +0.871968 q^{75} +(-7.29580 - 4.77193i) q^{76} -0.0430768 q^{77} +(0.194894 - 0.566591i) q^{78} +(1.52767 + 2.64600i) q^{79} +(-2.87387 + 2.78224i) q^{80} +(-1.36757 - 2.36871i) q^{81} +(2.67101 - 0.520061i) q^{82} +7.01001i q^{83} +(-8.46226 - 1.18388i) q^{84} +(-3.74761 + 6.49105i) q^{85} +(-4.13618 + 0.805338i) q^{86} +6.61514i q^{87} +(0.0208425 - 0.0135632i) q^{88} +(-4.11926 - 2.37826i) q^{89} +(2.99514 + 1.03026i) q^{90} +(1.19034 - 2.06173i) q^{91} +(4.65785 + 11.5078i) q^{92} +(1.28478 + 2.22531i) q^{93} +(1.07519 + 1.23608i) q^{94} +(-2.48623 - 3.58032i) q^{95} +(4.46717 - 2.09161i) q^{96} +(-6.51860 + 3.76352i) q^{97} +(-22.7430 - 7.82306i) q^{98} +(-0.0170527 - 0.00984539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.33731	+	0.460003i	0.945621	+	0.325271i
$2$	1.33731	+	0.460003i	0.945621	+	0.325271i
$3$	−0.435984	−	0.755146i	−0.251715	−	0.435984i	0.712283	−	0.701893i	$-0.247661\pi$
$3$	−0.435984	−	0.755146i	−0.251715	−	0.435984i	−0.963998	+	0.265909i	$0.914328\pi$
$4$	1.57679	+	1.23033i	0.788397	+	0.615167i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.235676	−	1.21042i	−0.0962142	−	0.494151i
$7$		−	4.89965i		−	1.85189i	−0.377656	−	0.925946i	$-0.623270\pi$
$7$		−	4.89965i		−	1.85189i	0.377656	−	0.925946i	$-0.376730\pi$
$8$	1.54270	+	2.37067i	0.545428	+	0.838158i
$9$	1.11984	−	1.93961i	0.373279	−	0.646538i
$10$	0.270280	+	1.38815i	0.0854701	+	0.438970i
$11$		−	0.00879181i		−	0.00265083i	−0.999999	−	0.00132542i	$-0.999578\pi$
$11$		−	0.00879181i		−	0.00265083i	0.999999	−	0.00132542i	$-0.000421893\pi$
$12$	0.241625	−	1.72712i	0.0697512	−	0.498575i
$13$	0.420792	+	0.242945i	0.116707	+	0.0673807i	0.557217	−	0.830367i	$-0.311869\pi$
$13$	0.420792	+	0.242945i	0.116707	+	0.0673807i	−0.440510	+	0.897748i	$0.645202\pi$
$14$	2.25385	−	6.55234i	0.602368	−	1.75119i
$15$	0.435984	−	0.755146i	0.112571	−	0.194978i
$16$	0.972557	+	3.87997i	0.243139	+	0.969991i
$17$	3.74761	+	6.49105i	0.908928	+	1.57431i	0.815555	+	0.578679i	$0.196432\pi$
$17$	3.74761	+	6.49105i	0.908928	+	1.57431i	0.0933732	+	0.995631i	$0.470235\pi$
$18$	2.38980	−	2.07873i	0.563280	−	0.489963i
$19$	−4.34376	+	0.362980i	−0.996527	+	0.0832733i
$19$	−4.34376	+	0.362980i	−0.996527	+	0.0832733i
$20$	−0.277103	+	1.98071i	−0.0619622	+	0.442900i
$21$	−3.69995	+	2.13617i	−0.807395	+	0.466150i
$22$	0.00404426	−	0.0117574i	0.000862240	−	0.00250668i
$23$	5.37572	+	3.10367i	1.12091	+	0.647160i	0.941634	−	0.336638i	$-0.109290\pi$
$23$	5.37572	+	3.10367i	1.12091	+	0.647160i	0.179280	+	0.983798i	$0.442623\pi$
$24$	1.11761	−	2.19854i	0.228130	−	0.448775i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.450974	+	0.518458i	0.0884434	+	0.101678i
$27$	−4.56882			−0.879271
$28$	6.02820	−	7.72573i	1.13922	−	1.46003i
$29$	−6.57006	−	3.79323i	−1.22003	−	0.704385i	−0.255106	−	0.966913i	$-0.582110\pi$
$29$	−6.57006	−	3.79323i	−1.22003	−	0.704385i	−0.964924	+	0.262528i	$0.915444\pi$
$30$	0.930415	−	0.809310i	0.169870	−	0.147759i
$31$	−2.94686			−0.529271			−0.264636	−	0.964349i	$-0.585252\pi$
$31$	−2.94686			−0.529271			−0.264636	+	0.964349i	$0.585252\pi$
$32$	−0.484187	+	5.63609i	−0.0855929	+	0.996330i
$33$	−0.00663910	+	0.00383309i	−0.00115572	+	0.000667255i
$34$	2.02581	+	10.4045i	0.347423	+	1.78435i
$35$	4.24322	−	2.44982i	0.717235	−	0.414096i
$36$	4.15212	−	1.68060i	0.692020	−	0.280100i
$37$		−	2.82994i		−	0.465239i	−0.972568	−	0.232620i	$-0.925270\pi$
$37$		−	2.82994i		−	0.465239i	0.972568	−	0.232620i	$-0.0747297\pi$
$38$	−5.97592	−	1.51273i	−0.969423	−	0.245397i
$39$		−	0.423680i		−	0.0678431i
$40$	−1.28171	+	2.52135i	−0.202656	+	0.398661i
$41$	1.66637	−	0.962078i	0.260243	−	0.150251i	−0.364202	−	0.931320i	$-0.618658\pi$
$41$	1.66637	−	0.962078i	0.260243	−	0.150251i	0.624445	+	0.781068i	$0.285325\pi$
$42$	−5.93062	+	1.15473i	−0.915115	+	0.178178i
$43$	−2.58045	+	1.48982i	−0.393514	+	0.227196i	−0.683682	−	0.729780i	$-0.739622\pi$
$43$	−2.58045	+	1.48982i	−0.393514	+	0.227196i	0.290167	+	0.956976i	$0.406289\pi$
$44$	0.0108169	−	0.0138629i	0.00163070	−	0.00208991i
$45$	2.23967			0.333871
$46$	5.76130	+	6.62342i	0.849457	+	0.976570i
$47$	1.00323	+	0.579216i	0.146336	+	0.0844873i	0.571380	−	0.820685i	$-0.306408\pi$
$47$	1.00323	+	0.579216i	0.146336	+	0.0844873i	−0.425044	+	0.905173i	$0.639741\pi$
$48$	2.50592	−	2.42603i	0.361699	−	0.350167i
$49$	−17.0065			−2.42951
$50$	−1.06703	+	0.928142i	−0.150901	+	0.131259i
$51$	3.26779	−	5.65998i	0.457583	−	0.792556i
$52$	0.364600	+	0.900789i	0.0505609	+	0.124917i
$53$	−2.12792	−	1.22856i	−0.292292	−	0.168755i	0.346683	−	0.937982i	$-0.387308\pi$
$53$	−2.12792	−	1.22856i	−0.292292	−	0.168755i	−0.638975	+	0.769227i	$0.720641\pi$
$54$	−6.10993	−	2.10167i	−0.831457	−	0.286002i
$55$	0.00761393	−	0.00439590i	0.00102666	−	0.000592744i
$56$	11.6154	−	7.55870i	1.55218	−	1.01007i
$57$	2.16791	+	3.12192i	0.287147	+	0.413508i
$58$	−7.04131	−	8.09497i	−0.924570	−	1.06292i
$59$	−5.18269	−	8.97669i	−0.674729	−	1.16866i	−0.976548	−	0.215300i	$-0.930927\pi$
$59$	−5.18269	−	8.97669i	−0.674729	−	1.16866i	0.301819	−	0.953365i	$-0.402406\pi$
$60$	1.61654	−	0.654304i	0.208694	−	0.0844703i
$61$	−0.851042	+	1.47405i	−0.108965	+	0.188733i	−0.915351	−	0.402657i	$-0.868087\pi$
$61$	−0.851042	+	1.47405i	−0.108965	+	0.188733i	0.806386	+	0.591389i	$0.201420\pi$
$62$	−3.94086	−	1.35556i	−0.500490	−	0.172157i
$63$	−9.50342	−	5.48680i	−1.19732	−	0.691272i
$64$	−3.24013	+	7.31448i	−0.405016	+	0.914309i
$65$			0.485889i			0.0602671i
$66$	−0.0106418	+	0.00207201i	−0.00130991	+	0.000255047i
$67$	−3.12293	+	5.40907i	−0.381526	+	0.660823i	−0.991281	−	0.131768i	$-0.957935\pi$
$67$	−3.12293	+	5.40907i	−0.381526	+	0.660823i	0.609754	+	0.792590i	$0.291268\pi$
$68$	−2.07695	+	14.8459i	−0.251867	+	1.80032i
$69$		−	5.41260i		−	0.651601i
$70$	6.80142	−	1.32428i	0.812926	−	0.158281i
$71$	6.62115	+	11.4682i	0.785786	+	1.36102i	0.928529	+	0.371261i	$0.121074\pi$
$71$	6.62115	+	11.4682i	0.785786	+	1.36102i	−0.142743	+	0.989760i	$0.545592\pi$
$72$	6.32575	−	0.337489i	0.745497	−	0.0397735i
$73$	4.76690	+	8.25652i	0.557924	+	0.966352i	0.997670	+	0.0682301i	$0.0217352\pi$
$73$	4.76690	+	8.25652i	0.557924	+	0.966352i	−0.439746	+	0.898122i	$0.644931\pi$
$74$	1.30178	−	3.78451i	0.151329	−	0.439940i
$75$	0.871968			0.100686
$76$	−7.29580	−	4.77193i	−0.836886	−	0.547378i
$77$	−0.0430768			−0.00490905
$78$	0.194894	−	0.566591i	0.0220674	−	0.0641538i
$79$	1.52767	+	2.64600i	0.171876	+	0.297698i	0.939076	−	0.343710i	$-0.111684\pi$
$79$	1.52767	+	2.64600i	0.171876	+	0.297698i	−0.767200	+	0.641408i	$0.778351\pi$
$80$	−2.87387	+	2.78224i	−0.321308	+	0.311064i
$81$	−1.36757	−	2.36871i	−0.151953	−	0.263190i
$82$	2.67101	−	0.520061i	0.294964	−	0.0574312i
$83$			7.01001i			0.769448i	0.923032	+	0.384724i	$0.125703\pi$
$83$			7.01001i			0.769448i	−0.923032	+	0.384724i	$0.874297\pi$
$84$	−8.46226	−	1.18388i	−0.923308	−	0.129172i
$85$	−3.74761	+	6.49105i	−0.406485	+	0.704053i
$86$	−4.13618	+	0.805338i	−0.446015	+	0.0868418i
$87$			6.61514i			0.709218i
$88$	0.0208425	−	0.0135632i	0.00222181	−	0.00144584i
$89$	−4.11926	−	2.37826i	−0.436641	−	0.252095i	0.265531	−	0.964102i	$-0.414453\pi$
$89$	−4.11926	−	2.37826i	−0.436641	−	0.252095i	−0.702172	+	0.712008i	$0.747786\pi$
$90$	2.99514	+	1.03026i	0.315715	+	0.108599i
$91$	1.19034	−	2.06173i	0.124782	−	0.216128i
$92$	4.65785	+	11.5078i	0.485614	+	1.19977i
$93$	1.28478	+	2.22531i	0.133226	+	0.230754i
$94$	1.07519	+	1.23608i	0.110897	+	0.127492i
$95$	−2.48623	−	3.58032i	−0.255082	−	0.367333i
$96$	4.46717	−	2.09161i	0.455929	−	0.213474i
$97$	−6.51860	+	3.76352i	−0.661864	+	0.382127i	−0.792987	−	0.609239i	$-0.791475\pi$
$97$	−6.51860	+	3.76352i	−0.661864	+	0.382127i	0.131123	+	0.991366i	$0.458142\pi$
$98$	−22.7430	−	7.82306i	−2.29739	−	0.790249i
$99$	−0.0170527	−	0.00984539i	−0.00171386	−	0.000989499i
$100$	−1.85390	+	0.750377i	−0.185390	+	0.0750377i
$101$	−6.05192	+	10.4822i	−0.602188	+	1.04302i	0.390301	+	0.920687i	$0.372371\pi$
$101$	−6.05192	+	10.4822i	−0.602188	+	1.04302i	−0.992489	+	0.122333i	$0.960962\pi$
$102$	6.97366	−	6.06595i	0.690495	−	0.600619i
$103$	2.68610			0.264669			0.132334	−	0.991205i	$-0.457753\pi$
$103$	2.68610			0.264669			0.132334	+	0.991205i	$0.457753\pi$
$104$	0.0732171	+	1.37235i	0.00717953	+	0.134570i
$105$	−3.69995	−	2.13617i	−0.361078	−	0.208469i
$106$	−2.28055	−	2.62181i	−0.221506	−	0.254653i
$107$	−2.36876			−0.228997			−0.114498	−	0.993423i	$-0.536526\pi$
$107$	−2.36876			−0.228997			−0.114498	+	0.993423i	$0.536526\pi$
$108$	−7.20409	−	5.62118i	−0.693214	−	0.540898i
$109$	15.6776	−	9.05149i	1.50165	−	0.866976i	0.501648	−	0.865072i	$-0.332727\pi$
$109$	15.6776	−	9.05149i	1.50165	−	0.866976i	0.999998	−	0.00190416i	$-0.000606114\pi$
$110$	0.0122043	−	0.00237625i	0.00116364	−	0.000226567i
$111$	−2.13702	+	1.23381i	−0.202837	+	0.117108i
$112$	19.0105	−	4.76519i	1.79632	−	0.450268i
$113$		−	16.9312i		−	1.59276i	−0.604799	−	0.796378i	$-0.706747\pi$
$113$		−	16.9312i		−	1.59276i	0.604799	−	0.796378i	$-0.293253\pi$
$114$	1.46308	+	5.17222i	0.137030	+	0.484423i
$115$			6.20734i			0.578838i
$116$	−5.69270	−	14.0645i	−0.528554	−	1.30586i
$117$	0.942437	−	0.544116i	0.0871284	−	0.0503036i
$118$	−2.80156	−	14.3887i	−0.257904	−	1.32458i
$119$	31.8038	−	18.3620i	2.91545	−	1.68324i
$120$	2.46279	−	0.131394i	0.224821	−	0.0119946i
$121$	10.9999			0.999993
$122$	−1.81617	+	1.57978i	−0.164429	+	0.143026i
$123$	−1.45302	−	0.838901i	−0.131014	−	0.0756412i
$124$	−4.64659	−	3.62562i	−0.417276	−	0.325590i
$125$	−1.00000			−0.0894427
$126$	−10.1851	−	11.7092i	−0.907358	−	1.04313i
$127$	9.28194	−	16.0768i	0.823639	−	1.42658i	−0.0793162	−	0.996850i	$-0.525274\pi$
$127$	9.28194	−	16.0768i	0.823639	−	1.42658i	0.902955	−	0.429735i	$-0.141393\pi$
$128$	−7.69774	+	8.29125i	−0.680391	+	0.732850i
$129$	2.25007	+	1.29908i	0.198107	+	0.114377i
$130$	−0.223511	+	0.649784i	−0.0196032	+	0.0569899i
$131$	−12.4977	+	7.21555i	−1.09193	+	0.630426i	−0.934090	−	0.357039i	$-0.883786\pi$
$131$	−12.4977	+	7.21555i	−1.09193	+	0.630426i	−0.157840	+	0.987465i	$0.550453\pi$
$132$	−0.0151845	−	0.00212432i	−0.00132164	−	0.000184899i
$133$	1.77847	+	21.2829i	0.154213	+	1.84546i
$134$	−6.66451	+	5.79704i	−0.575726	+	0.500788i
$135$	−2.28441	−	3.95672i	−0.196611	−	0.340540i
$136$	−9.60667	+	18.8981i	−0.823765	+	1.62050i
$137$	3.91079	−	6.77369i	0.334121	−	0.578715i	−0.649194	−	0.760623i	$-0.724894\pi$
$137$	3.91079	−	6.77369i	0.334121	−	0.578715i	0.983316	+	0.181907i	$0.0582271\pi$
$138$	2.48982	−	7.23833i	0.211947	−	0.616167i
$139$	4.09755	+	2.36572i	0.347549	+	0.200658i	0.663605	−	0.748083i	$-0.269025\pi$
$139$	4.09755	+	2.36572i	0.347549	+	0.200658i	−0.316056	+	0.948741i	$0.602359\pi$
$140$	9.70478	+	1.35771i	0.820204	+	0.114747i
$141$		−	1.01011i		−	0.0850670i
$142$	3.57913	+	18.3822i	0.300354	+	1.54260i
$143$	0.00213592	−	0.00369953i	0.000178615	−	0.000309370i
$144$	8.61474	+	2.45854i	0.717895	+	0.204878i
$145$		−	7.58646i		−	0.630021i
$146$	2.57680	+	13.2343i	0.213257	+	1.09528i
$147$	7.41457	+	12.8424i	0.611544	+	1.05922i
$148$	3.48177	−	4.46223i	0.286200	−	0.366793i
$149$	−9.18609	−	15.9108i	−0.752553	−	1.30346i	−0.946581	−	0.322465i	$-0.895489\pi$
$149$	−9.18609	−	15.9108i	−0.752553	−	1.30346i	0.194028	−	0.980996i	$-0.437845\pi$
$150$	1.16609	+	0.401108i	0.0952109	+	0.0327503i
$151$	−7.69808			−0.626461			−0.313231	−	0.949677i	$-0.601411\pi$
$151$	−7.69808			−0.626461			−0.313231	+	0.949677i	$0.601411\pi$
$152$	−7.56164	−	9.73764i	−0.613330	−	0.789827i
$153$	16.7868			1.35713
$154$	−0.0576070	−	0.0198155i	−0.00464210	−	0.00159677i
$155$	−1.47343	−	2.55205i	−0.118349	−	0.204986i
$156$	0.521267	−	0.668056i	0.0417348	−	0.0534873i
$157$	3.63943	+	6.30369i	0.290458	+	0.503089i	0.973918	−	0.226899i	$-0.0728589\pi$
$157$	3.63943	+	6.30369i	0.290458	+	0.503089i	−0.683460	+	0.729988i	$0.739526\pi$
$158$	0.825796	+	4.24125i	0.0656968	+	0.337415i
$159$			2.14252i			0.169913i
$160$	−5.12309	+	2.39873i	−0.405016	+	0.189636i
$161$	15.2069	−	26.3391i	1.19847	−	2.07581i
$162$	−0.739257	−	3.79679i	−0.0580815	−	0.298304i
$163$			1.59022i			0.124556i	0.998059	+	0.0622778i	$0.0198365\pi$
$163$			1.59022i			0.124556i	−0.998059	+	0.0622778i	$0.980164\pi$
$164$	3.81120	+	0.533190i	0.297604	+	0.0416352i
$165$	−0.00663910	−	0.00383309i	−0.000516853	−	0.000298405i
$166$	−3.22463	+	9.37455i	−0.250280	+	0.727606i
$167$	−8.72518	+	15.1125i	−0.675175	+	1.16944i	0.301243	+	0.953547i	$0.402598\pi$
$167$	−8.72518	+	15.1125i	−0.675175	+	1.16944i	−0.976418	+	0.215890i	$0.930735\pi$
$168$	−10.7721	−	5.47588i	−0.831083	−	0.422473i
$169$	−6.38196	−	11.0539i	−0.490920	−	0.850298i
$170$	−7.99762	+	6.95663i	−0.613389	+	0.533549i
$171$	−4.16026	+	8.83169i	−0.318143	+	0.675376i
$172$	−5.90181	−	0.825669i	−0.450009	−	0.0629567i
$173$	15.0864	−	8.71014i	1.14700	−	0.662219i	0.198844	−	0.980031i	$-0.436281\pi$
$173$	15.0864	−	8.71014i	1.14700	−	0.662219i	0.948154	+	0.317812i	$0.102948\pi$
$174$	−3.04299	+	8.84650i	−0.230688	+	0.670651i
$175$	4.24322	+	2.44982i	0.320757	+	0.185189i
$176$	0.0341119	−	0.00855054i	0.00257128	−	0.000644521i
$177$	−4.51914	+	7.82738i	−0.339679	+	0.588342i
$178$	−4.41472	−	5.07534i	−0.330898	−	0.380413i
$179$	1.70840			0.127692			0.0638460	−	0.997960i	$-0.479663\pi$
$179$	1.70840			0.127692			0.0638460	+	0.997960i	$0.479663\pi$
$180$	3.53150	+	2.75554i	0.263223	+	0.205386i
$181$	12.6046	+	7.27728i	0.936894	+	0.540916i	0.888985	−	0.457936i	$-0.151411\pi$
$181$	12.6046	+	7.27728i	0.936894	+	0.540916i	0.0479085	+	0.998852i	$0.484744\pi$
$182$	2.54026	−	2.20962i	0.188297	−	0.163788i
$183$	1.48416			0.109712
$184$	0.935365	+	17.5321i	0.0689560	+	1.29248i
$185$	2.45080	−	1.41497i	0.180186	−	0.104031i
$186$	0.694502	+	3.56693i	0.0509234	+	0.261540i
$187$	0.0570681	−	0.0329483i	0.00417323	−	0.00240942i
$188$	0.869260	+	2.14761i	0.0633973	+	0.156631i
$189$			22.3856i			1.62831i
$190$	−1.67790	−	5.93166i	−0.121728	−	0.430328i
$191$			2.00799i			0.145293i	0.997358	+	0.0726464i	$0.0231445\pi$
$191$			2.00799i			0.145293i	−0.997358	+	0.0726464i	$0.976856\pi$
$192$	6.93614	−	0.742222i	0.500573	−	0.0535652i
$193$	−7.19184	+	4.15221i	−0.517680	+	0.298883i	−0.735985	−	0.676998i	$-0.763281\pi$
$193$	−7.19184	+	4.15221i	−0.517680	+	0.298883i	0.218305	+	0.975881i	$0.429947\pi$
$194$	−10.4486	+	2.03441i	−0.750167	+	0.146062i
$195$	0.366917	−	0.211840i	0.0262755	−	0.0151702i
$196$	−26.8158	−	20.9237i	−1.91541	−	1.49455i
$197$	22.3092			1.58946			0.794732	−	0.606961i	$-0.207612\pi$
$197$	22.3092			1.58946			0.794732	+	0.606961i	$0.207612\pi$
$198$	−0.0182758	−	0.0210106i	−0.00129881	−	0.00149316i
$199$	−6.12600	−	3.53685i	−0.434261	−	0.250721i	0.266899	−	0.963724i	$-0.414001\pi$
$199$	−6.12600	−	3.53685i	−0.434261	−	0.250721i	−0.701160	+	0.713004i	$0.747334\pi$
$200$	−2.82441	+	0.150687i	−0.199716	+	0.0106552i
$201$	5.44618			0.384144
$202$	−12.9151	+	11.2341i	−0.908706	+	0.790427i
$203$	−18.5855	+	32.1910i	−1.30444	+	2.25936i
$204$	12.1163	−	4.90415i	0.848311	−	0.343359i
$205$	1.66637	+	0.962078i	0.116384	+	0.0671945i
$206$	3.59214	+	1.23561i	0.250276	+	0.0860892i
$207$	12.0398	−	6.95121i	0.836827	−	0.483142i
$208$	−0.533372	+	1.86894i	−0.0369827	+	0.129588i
$209$	0.00319125	+	0.0381895i	0.000220743	+	0.00264162i
$210$	−3.96533	−	4.55871i	−0.273634	−	0.314581i
$211$	−4.00908	−	6.94393i	−0.275996	−	0.478040i	0.694390	−	0.719599i	$-0.255674\pi$
$211$	−4.00908	−	6.94393i	−0.275996	−	0.478040i	−0.970386	+	0.241559i	$0.922341\pi$
$212$	−1.84376	−	4.55523i	−0.126630	−	0.312854i
$213$	5.77343	−	9.99987i	0.395589	−	0.685180i
$214$	−3.16777	−	1.08964i	−0.216544	−	0.0744862i
$215$	−2.58045	−	1.48982i	−0.175985	−	0.101605i
$216$	−7.04834	−	10.8312i	−0.479579	−	0.736967i
$217$			14.4386i			0.980153i
$218$	25.1296	−	4.89288i	1.70199	−	0.331388i
$219$	4.15659	−	7.19942i	0.280876	−	0.486492i
$220$	0.0174140	+	0.00243624i	0.00117405	+	0.000164251i
$221$			3.64185i			0.244977i
$222$	−3.42541	+	0.666948i	−0.229899	+	0.0447626i
$223$	2.15027	+	3.72438i	0.143993	+	0.249403i	0.928997	−	0.370088i	$-0.120672\pi$
$223$	2.15027	+	3.72438i	0.143993	+	0.249403i	−0.785004	+	0.619491i	$0.787339\pi$
$224$	27.6149	+	2.37234i	1.84510	+	0.158509i
$225$	1.11984	+	1.93961i	0.0746557	+	0.129308i
$226$	7.78842	−	22.6423i	0.518078	−	1.50614i
$227$	8.93925			0.593319			0.296659	−	0.954983i	$-0.404127\pi$
$227$	8.93925			0.593319			0.296659	+	0.954983i	$0.404127\pi$
$228$	−0.422653	+	7.58988i	−0.0279909	+	0.502652i
$229$	−26.4716			−1.74929			−0.874647	−	0.484761i	$-0.838907\pi$
$229$	−26.4716			−1.74929			−0.874647	+	0.484761i	$0.838907\pi$
$230$	−2.85540	+	8.30114i	−0.188279	+	0.547361i
$231$	0.0187808	+	0.0325292i	0.00123568	+	0.00214027i
$232$	−1.14318	−	21.4273i	−0.0750534	−	1.40677i
$233$	1.90126	+	3.29308i	0.124556	+	0.215737i	0.921559	−	0.388238i	$-0.126916\pi$
$233$	1.90126	+	3.29308i	0.124556	+	0.215737i	−0.797004	+	0.603975i	$0.793583\pi$
$234$	1.51063	−	0.294128i	0.0987527	−	0.0192277i
$235$			1.15843i			0.0755677i
$236$	2.87228	−	20.5308i	0.186970	−	1.33644i
$237$	1.33208	−	2.30722i	0.0865276	−	0.149870i
$238$	50.9781	−	9.92575i	3.30442	−	0.643391i
$239$			1.20706i			0.0780785i	0.999238	+	0.0390393i	$0.0124297\pi$
$239$			1.20706i			0.0780785i	−0.999238	+	0.0390393i	$0.987570\pi$
$240$	3.35396	+	0.957179i	0.216497	+	0.0617856i
$241$	−14.7967	−	8.54290i	−0.953142	−	0.550297i	−0.0590864	−	0.998253i	$-0.518819\pi$
$241$	−14.7967	−	8.54290i	−0.953142	−	0.550297i	−0.894056	+	0.447956i	$0.852152\pi$
$242$	14.7103	+	5.06000i	0.945614	+	0.325269i
$243$	−8.04572	+	13.9356i	−0.516133	+	0.893969i
$244$	−3.15549	+	1.27720i	−0.202010	+	0.0817646i
$245$	−8.50327	−	14.7281i	−0.543254	−	0.940943i
$246$	−1.55724	−	1.79026i	−0.0992860	−	0.114143i
$247$	−1.91601	−	0.902554i	−0.121912	−	0.0574281i
$248$	−4.54613	−	6.98602i	−0.288679	−	0.443613i
$249$	5.29358	−	3.05625i	0.335467	−	0.193682i
$250$	−1.33731	−	0.460003i	−0.0845789	−	0.0290932i
$251$	8.57239	+	4.94927i	0.541085	+	0.312395i	0.745518	−	0.666485i	$-0.232202\pi$
$251$	8.57239	+	4.94927i	0.541085	+	0.312395i	−0.204434	+	0.978880i	$0.565535\pi$
$252$	−8.23434	−	20.3439i	−0.518714	−	1.28155i
$253$	0.0272869	−	0.0472623i	0.00171551	−	0.00297135i
$254$	19.8082	−	17.2299i	1.24288	−	1.08110i
$255$	6.53559			0.409274
$256$	−14.1083	+	7.54698i	−0.881766	+	0.471686i
$257$	−9.88100	−	5.70480i	−0.616360	−	0.355855i	0.159091	−	0.987264i	$-0.449144\pi$
$257$	−9.88100	−	5.70480i	−0.616360	−	0.355855i	−0.775450	+	0.631409i	$0.782477\pi$
$258$	2.41145	+	2.77230i	0.150131	+	0.172596i
$259$	−13.8657			−0.861573
$260$	−0.597806	+	0.766147i	−0.0370744	+	0.0475144i
$261$	−14.7148	+	8.49559i	−0.910823	+	0.525864i
$262$	−20.0325	+	3.90044i	−1.23761	+	0.240970i
$263$	22.4110	−	12.9390i	1.38192	−	0.797852i	0.389534	−	0.921012i	$-0.372636\pi$
$263$	22.4110	−	12.9390i	1.38192	−	0.797852i	0.992387	+	0.123160i	$0.0393029\pi$
$264$	−0.0193291	−	0.00982578i	−0.00118963	−	0.000604735i
$265$		−	2.45711i		−	0.150939i
$266$	−7.41183	+	29.2799i	−0.454448	+	1.79527i
$267$			4.14753i			0.253825i
$268$	−11.5792	+	4.68674i	−0.707310	+	0.286288i
$269$	19.0894	−	11.0212i	1.16390	−	0.671977i	0.211664	−	0.977343i	$-0.432112\pi$
$269$	19.0894	−	11.0212i	1.16390	−	0.671977i	0.952235	+	0.305365i	$0.0987786\pi$
$270$	−1.23486	−	6.34219i	−0.0751514	−	0.385974i
$271$	18.4187	−	10.6340i	1.11886	−	0.645971i	0.177747	−	0.984076i	$-0.443119\pi$
$271$	18.4187	−	10.6340i	1.11886	−	0.645971i	0.941108	+	0.338105i	$0.109786\pi$
$272$	−21.5403	+	20.8535i	−1.30607	+	1.26443i
$273$	−2.07588			−0.125638
$274$	8.34586	−	7.25954i	0.504192	−	0.438565i
$275$	0.00761393	+	0.00439590i	0.000459137	+	0.000265083i
$276$	6.65931	−	8.53456i	0.400843	−	0.513720i
$277$	28.0819			1.68728			0.843638	−	0.536912i	$-0.180409\pi$
$277$	28.0819			1.68728			0.843638	+	0.536912i	$0.180409\pi$
$278$	4.39145	+	5.04858i	0.263382	+	0.302794i
$279$	−3.30000	+	5.71576i	−0.197566	+	0.342194i
$280$	12.3537	+	6.27991i	0.738278	+	0.375296i
$281$	2.90042	+	1.67456i	0.173024	+	0.0998956i	0.584011	−	0.811746i	$-0.301482\pi$
$281$	2.90042	+	1.67456i	0.173024	+	0.0998956i	−0.410987	+	0.911641i	$0.634816\pi$
$282$	0.464656	−	1.35084i	0.0276699	−	0.0804411i
$283$	3.32378	−	1.91898i	0.197578	−	0.114072i	−0.397947	−	0.917408i	$-0.630277\pi$
$283$	3.32378	−	1.91898i	0.197578	−	0.114072i	0.595525	+	0.803337i	$0.296944\pi$
$284$	−3.66948	+	26.2291i	−0.217744	+	1.55641i
$285$	−1.61971	+	3.43843i	−0.0959431	+	0.203675i
$286$	0.00455818	−	0.00396488i	0.000269531	−	0.000234448i
$287$	−4.71384	−	8.16462i	−0.278249	−	0.481942i
$288$	10.3896	+	7.25064i	0.612215	+	0.427248i
$289$	−19.5891	+	33.9294i	−1.15230	+	1.99585i
$290$	3.48980	−	10.1454i	0.204928	−	0.595761i
$291$	5.68401	+	3.28166i	0.333202	+	0.192375i
$292$	−2.64185	+	18.8837i	−0.154603	+	1.10509i
$293$		−	2.77914i		−	0.162359i	−0.996700	−	0.0811794i	$-0.974131\pi$
$293$		−	2.77914i		−	0.162359i	0.996700	−	0.0811794i	$-0.0258687\pi$
$294$	4.00803	+	20.5850i	0.233753	+	1.20054i
$295$	5.18269	−	8.97669i	0.301748	−	0.522643i
$296$	6.70885	−	4.36576i	0.389944	−	0.253755i
$297$			0.0401682i			0.00233080i
$298$	−4.96563	−	25.5033i	−0.287651	−	1.47736i
$299$	1.50804	+	2.61200i	0.0872123	+	0.151056i
$300$	1.37491	+	1.07281i	0.0793807	+	0.0619388i
$301$	7.29960	+	12.6433i	0.420742	+	0.728746i
$302$	−10.2947	−	3.54114i	−0.592395	−	0.203770i
$303$	10.5542			0.606320
$304$	−5.63291	−	16.5006i	−0.323069	−	0.946375i
$305$	−1.70208			−0.0974611
$306$	22.4492	+	7.72200i	1.28333	+	0.441437i
$307$	−11.6272	−	20.1390i	−0.663601	−	1.14939i	−0.979662	−	0.200653i	$-0.935694\pi$
$307$	−11.6272	−	20.1390i	−0.663601	−	1.14939i	0.316061	−	0.948739i	$-0.397640\pi$
$308$	−0.0679232	−	0.0529988i	−0.00387028	−	0.00301989i
$309$	−1.17109	−	2.02839i	−0.0666212	−	0.115391i
$310$	−0.796477	−	4.09067i	−0.0452369	−	0.232334i
$311$		−	29.4624i		−	1.67066i	−0.549748	−	0.835330i	$-0.685276\pi$
$311$		−	29.4624i		−	1.67066i	0.549748	−	0.835330i	$-0.314724\pi$
$312$	1.00440	−	0.653612i	0.0568632	−	0.0370035i
$313$	−4.40620	+	7.63176i	−0.249053	+	0.431373i	−0.963263	−	0.268559i	$-0.913453\pi$
$313$	−4.40620	+	7.63176i	−0.249053	+	0.431373i	0.714210	+	0.699931i	$0.246786\pi$
$314$	1.96733	+	10.1041i	0.111023	+	0.570209i
$315$		−	10.9736i		−	0.618293i
$316$	−0.846643	+	6.05173i	−0.0476274	+	0.340436i
$317$	−14.6334	−	8.44861i	−0.821895	−	0.474521i	0.0291748	−	0.999574i	$-0.490712\pi$
$317$	−14.6334	−	8.44861i	−0.821895	−	0.474521i	−0.851069	+	0.525053i	$0.824045\pi$
$318$	−0.985567	+	2.86521i	−0.0552678	+	0.160673i
$319$	−0.0333493	+	0.0577628i	−0.00186720	+	0.00323409i
$320$	−7.95459	+	0.851203i	−0.444675	+	0.0475837i
$321$	1.03274	+	1.78876i	0.0576420	+	0.0998389i
$322$	32.4524	−	28.2283i	1.80850	−	1.57310i
$323$	−18.6348	−	26.8352i	−1.03687	−	1.49315i
$324$	0.757919	−	5.41754i	0.0421066	−	0.300974i
$325$	−0.420792	+	0.242945i	−0.0233414	+	0.0134761i
$326$	−0.731506	+	2.12661i	−0.0405144	+	0.117782i
$327$	−13.6704	−	7.89261i	−0.755975	−	0.436462i
$328$	4.85148	+	2.46620i	0.267878	+	0.136173i
$329$	2.83795	−	4.91548i	0.156461	−	0.270999i
$330$	−0.00711530	−	0.00818003i	−0.000391684	−	0.000450296i
$331$	−26.9442			−1.48099			−0.740493	−	0.672064i	$-0.765408\pi$
$331$	−26.9442			−1.48099			−0.740493	+	0.672064i	$0.765408\pi$
$332$	−8.62465	+	11.0533i	−0.473339	+	0.606631i
$333$	−5.48899	−	3.16907i	−0.300795	−	0.173664i
$334$	−18.6200	+	16.1964i	−1.01884	+	0.886229i
$335$	−6.24585			−0.341247
$336$	−11.8867	−	12.2781i	−0.648471	−	0.669827i
$337$	−11.6421	+	6.72157i	−0.634186	+	0.366147i	−0.782371	−	0.622812i	$-0.785990\pi$
$337$	−11.6421	+	6.72157i	−0.634186	+	0.366147i	0.148185	+	0.988960i	$0.452657\pi$
$338$	−3.44983	−	17.7182i	−0.187646	−	0.963741i
$339$	−12.7855	+	7.38174i	−0.694416	+	0.400921i
$340$	−13.8954	+	5.62423i	−0.753582	+	0.305017i
$341$			0.0259082i			0.00140301i
$342$	−9.62616	+	9.89697i	−0.520523	+	0.535167i
$343$			49.0285i			2.64729i
$344$	−7.51273	−	3.81903i	−0.405059	−	0.205908i
$345$	4.68745	−	2.70630i	0.252364	−	0.145702i
$346$	24.1819	−	4.70836i	1.30003	−	0.253123i
$347$	25.1608	−	14.5266i	1.35070	−	0.779829i	0.362355	−	0.932040i	$-0.381973\pi$
$347$	25.1608	−	14.5266i	1.35070	−	0.779829i	0.988348	+	0.152212i	$0.0486395\pi$
$348$	−8.13884	+	10.4307i	−0.436287	+	0.559145i
$349$	−7.90174			−0.422971			−0.211485	−	0.977381i	$-0.567830\pi$
$349$	−7.90174			−0.422971			−0.211485	+	0.977381i	$0.567830\pi$
$350$	4.54757	+	5.22807i	0.243078	+	0.279452i
$351$	−1.92253	−	1.10997i	−0.102617	−	0.0592459i
$352$	0.0495515	+	0.00425688i	0.00264110	+	0.000226892i
$353$	−10.9805			−0.584431			−0.292215	−	0.956353i	$-0.594392\pi$
$353$	−10.9805			−0.584431			−0.292215	+	0.956353i	$0.594392\pi$
$354$	−9.64411	+	8.38881i	−0.512579	+	0.445860i
$355$	−6.62115	+	11.4682i	−0.351414	+	0.608667i
$356$	−3.56918	−	8.81809i	−0.189166	−	0.467358i
$357$	−27.7319	−	16.0110i	−1.46773	−	0.847394i
$358$	2.28466	+	0.785871i	0.120748	+	0.0415346i
$359$	14.5084	−	8.37640i	0.765722	−	0.442090i	−0.0656245	−	0.997844i	$-0.520904\pi$
$359$	14.5084	−	8.37640i	0.765722	−	0.442090i	0.831346	+	0.555755i	$0.187571\pi$
$360$	3.45515	+	5.30952i	0.182102	+	0.279836i
$361$	18.7365	−	3.15340i	0.986131	−	0.165968i
$362$	13.5087	+	15.5301i	0.710002	+	0.816246i
$363$	−4.79579	−	8.30655i	−0.251714	−	0.435981i
$364$	4.41355	−	1.78641i	0.231333	−	0.0936334i
$365$	−4.76690	+	8.25652i	−0.249511	+	0.432166i
$366$	1.98478	+	0.682720i	0.103746	+	0.0356863i
$367$	−1.96973	−	1.13722i	−0.102819	−	0.0593625i	0.447709	−	0.894179i	$-0.352240\pi$
$367$	−1.96973	−	1.13722i	−0.102819	−	0.0593625i	−0.550528	+	0.834817i	$0.685573\pi$
$368$	−6.81395	+	23.8761i	−0.355201	+	1.24463i
$369$		−	4.30948i		−	0.224343i
$370$	3.92837	−	0.764877i	0.204226	−	0.0397641i
$371$	−6.01949	+	10.4261i	−0.312516	+	0.541294i
$372$	−0.712035	+	5.08956i	−0.0369173	+	0.263881i
$373$			8.87747i			0.459658i	0.973231	+	0.229829i	$0.0738167\pi$
$373$			8.87747i			0.459658i	−0.973231	+	0.229829i	$0.926183\pi$
$374$	0.0914740	−	0.0178105i	0.00473001	−	0.000920960i
$375$	0.435984	+	0.755146i	0.0225141	+	0.0389956i
$376$	0.174560	+	3.27189i	0.00900227	+	0.168735i
$377$	−1.84309	−	3.19232i	−0.0949239	−	0.164413i
$378$	−10.2975	+	29.9365i	−0.529644	+	1.53977i
$379$	−6.90368			−0.354618			−0.177309	−	0.984155i	$-0.556739\pi$
$379$	−6.90368			−0.354618			−0.177309	+	0.984155i	$0.556739\pi$
$380$	0.484712	−	8.70431i	0.0248652	−	0.446522i
$381$	−16.1871			−0.829290
$382$	−0.923680	+	2.68530i	−0.0472596	+	0.137392i
$383$	−13.1356	−	22.7515i	−0.671197	−	1.16255i	−0.977565	−	0.210634i	$-0.932447\pi$
$383$	−13.1356	−	22.7515i	−0.671197	−	1.16255i	0.306368	−	0.951913i	$-0.400886\pi$
$384$	9.61719	+	2.19807i	0.490775	+	0.112170i
$385$	−0.0215384	−	0.0373056i	−0.00109770	−	0.00190127i
$386$	−11.5278	+	2.24452i	−0.586747	+	0.114243i
$387$			6.67342i			0.339229i
$388$	−14.9089	−	2.08577i	−0.756883	−	0.105889i
$389$	4.21161	−	7.29473i	0.213537	−	0.369858i	−0.739282	−	0.673396i	$-0.764835\pi$
$389$	4.21161	−	7.29473i	0.213537	−	0.369858i	0.952819	+	0.303539i	$0.0981682\pi$
$390$	0.588129	−	0.114512i	0.0297811	−	0.00579855i
$391$			46.5254i			2.35289i
$392$	−26.2360	−	40.3168i	−1.32512	−	2.03631i
$393$	10.8976	+	6.29173i	0.549711	+	0.317376i
$394$	29.8343	+	10.2623i	1.50303	+	0.517007i
$395$	−1.52767	+	2.64600i	−0.0768652	+	0.133134i
$396$	−0.0147755	−	0.0365047i	−0.000742497	−	0.00183443i
$397$	−9.57318	−	16.5812i	−0.480464	−	0.832189i	0.519284	−	0.854601i	$-0.326199\pi$
$397$	−9.57318	−	16.5812i	−0.480464	−	0.832189i	−0.999749	+	0.0224128i	$0.992865\pi$
$398$	−6.56540	−	7.54785i	−0.329094	−	0.378339i
$399$	15.2963	−	10.6220i	0.765773	−	0.531765i
$400$	−3.84643	−	1.09772i	−0.192321	−	0.0548862i
$401$	−9.47533	+	5.47059i	−0.473176	+	0.273188i	−0.717568	−	0.696488i	$-0.754745\pi$
$401$	−9.47533	+	5.47059i	−0.473176	+	0.273188i	0.244393	+	0.969676i	$0.421411\pi$
$402$	7.28323	+	2.50526i	0.363254	+	0.124951i
$403$	−1.24002	−	0.715923i	−0.0617695	−	0.0356627i
$404$	−22.4393	+	9.08243i	−1.11640	+	0.451868i
$405$	1.36757	−	2.36871i	0.0679553	−	0.117702i
$406$	−39.6625	+	34.4999i	−1.96842	+	1.71220i
$407$	−0.0248803			−0.00123327
$408$	18.4592	−	0.984827i	0.913865	−	0.0487562i
$409$	−2.60629	−	1.50474i	−0.128873	−	0.0744047i	0.434178	−	0.900827i	$-0.357039\pi$
$409$	−2.60629	−	1.50474i	−0.128873	−	0.0744047i	−0.563050	+	0.826423i	$0.690372\pi$
$410$	1.78589	+	2.05313i	0.0881989	+	0.101397i
$411$	−6.82016			−0.336414
$412$	4.23542	+	3.30479i	0.208664	+	0.162816i
$413$	−43.9826	+	25.3934i	−2.16424	+	1.24953i
$414$	19.2986	−	3.75755i	0.948473	−	0.184673i
$415$	−6.07084	+	3.50500i	−0.298006	+	0.172054i
$416$	−1.57300	+	2.25400i	−0.0771227	+	0.110511i
$417$		−	4.12566i		−	0.202034i
$418$	−0.0132996	+	0.0525392i	−0.000650505	+	0.00256978i
$419$		−	0.644687i		−	0.0314950i	−0.999876	−	0.0157475i	$-0.994987\pi$
$419$		−	0.644687i		−	0.0314950i	0.999876	−	0.0157475i	$-0.00501279\pi$
$420$	−3.20586	−	7.92047i	−0.156430	−	0.386479i
$421$	−3.52830	+	2.03706i	−0.171959	+	0.0992804i	−0.583509	−	0.812107i	$-0.698321\pi$
$421$	−3.52830	+	2.03706i	−0.171959	+	0.0992804i	0.411550	+	0.911387i	$0.364987\pi$
$422$	−2.16715	−	11.1304i	−0.105495	−	0.541818i
$423$	2.24691	−	1.29725i	0.109248	−	0.0630746i
$424$	−0.370254	−	6.93989i	−0.0179811	−	0.337031i
$425$	−7.49522			−0.363571
$426$	12.3208	−	10.7171i	0.596946	−	0.519246i
$427$	7.22232	+	4.16981i	0.349512	+	0.201791i
$428$	−3.73505	−	2.91437i	−0.180540	−	0.140871i
$429$	−0.00372491			−0.000179840
$430$	−2.76553	−	3.17937i	−0.133366	−	0.153323i
$431$	12.7950	−	22.1616i	0.616314	−	1.06749i	−0.373838	−	0.927494i	$-0.621959\pi$
$431$	12.7950	−	22.1616i	0.616314	−	1.06749i	0.990152	−	0.139993i	$-0.0447082\pi$
$432$	−4.44344	−	17.7269i	−0.213785	−	0.852885i
$433$	20.7128	+	11.9585i	0.995392	+	0.574690i	0.906882	−	0.421386i	$-0.138456\pi$
$433$	20.7128	+	11.9585i	0.995392	+	0.574690i	0.0885101	+	0.996075i	$0.471789\pi$
$434$	−6.64178	+	19.3088i	−0.318816	+	0.926853i
$435$	−5.72888	+	3.30757i	−0.274679	+	0.158586i
$436$	35.8568	+	5.01640i	1.71723	+	0.240242i
$437$	−24.4774	−	11.5303i	−1.17091	−	0.551570i
$438$	8.87040	−	7.71581i	0.423844	−	0.368675i
$439$	3.23165	+	5.59739i	0.154238	+	0.267149i	0.932781	−	0.360442i	$-0.117374\pi$
$439$	3.23165	+	5.59739i	0.154238	+	0.267149i	−0.778543	+	0.627591i	$0.784041\pi$
$440$	0.0221673	+	0.0112685i	0.00105678	+	0.000537206i
$441$	−19.0445	+	32.9861i	−0.906883	+	1.57077i
$442$	−1.67526	+	4.87027i	−0.0796840	+	0.231655i
$443$	4.71055	+	2.71964i	0.223805	+	0.129214i	0.607711	−	0.794158i	$-0.292088\pi$
$443$	4.71055	+	2.71964i	0.223805	+	0.129214i	−0.383906	+	0.923372i	$0.625421\pi$
$444$	−4.88763	−	0.683785i	−0.231957	−	0.0324510i
$445$		−	4.75652i		−	0.225480i
$446$	1.16235	+	5.96978i	0.0550389	+	0.282677i
$447$	−8.00997	+	13.8737i	−0.378859	+	0.656202i
$448$	35.8383	+	15.8755i	1.69320	+	0.750046i
$449$			38.9335i			1.83738i	0.394975	+	0.918692i	$0.370753\pi$
$449$			38.9335i			1.83738i	−0.394975	+	0.918692i	$0.629247\pi$
$450$	0.605339	+	3.10899i	0.0285360	+	0.146559i
$451$	−0.00845841	−	0.0146504i	−0.000398291	−	0.000689860i
$452$	20.8311	−	26.6970i	0.979811	−	1.25572i
$453$	3.35624	+	5.81318i	0.157690	+	0.273127i
$454$	11.9545	+	4.11208i	0.561055	+	0.192990i
$455$	2.38069			0.111608
$456$	−4.05659	+	9.95560i	−0.189967	+	0.466213i
$457$	−26.6761			−1.24786			−0.623928	−	0.781482i	$-0.714464\pi$
$457$	−26.6761			−1.24786			−0.623928	+	0.781482i	$0.714464\pi$
$458$	−35.4007	−	12.1770i	−1.65417	−	0.568995i
$459$	−17.1222	−	29.6565i	−0.799194	−	1.38424i
$460$	−7.63710	+	9.78770i	−0.356082	+	0.456354i
$461$	−4.48117	−	7.76161i	−0.208709	−	0.361494i	0.742599	−	0.669736i	$-0.233593\pi$
$461$	−4.48117	−	7.76161i	−0.208709	−	0.361494i	−0.951308	+	0.308242i	$0.900259\pi$
$462$	0.0101521	+	0.0521409i	0.000472320	+	0.00242581i
$463$		−	29.3966i		−	1.36617i	−0.730337	−	0.683087i	$-0.760637\pi$
$463$		−	29.3966i		−	1.36617i	0.730337	−	0.683087i	$-0.239363\pi$
$464$	8.32783	−	29.1808i	0.386610	−	1.35468i
$465$	−1.28478	+	2.22531i	−0.0595803	+	0.103196i
$466$	1.02775	+	5.27845i	0.0476094	+	0.244519i
$467$			31.3665i			1.45147i	0.687974	+	0.725735i	$0.258500\pi$
$467$			31.3665i			1.45147i	−0.687974	+	0.725735i	$0.741500\pi$
$468$	2.15547	+	0.301553i	0.0996368	+	0.0139393i
$469$	26.5025	+	15.3012i	1.22377	+	0.706545i
$470$	−0.532882	+	1.54918i	−0.0245800	+	0.0714584i
$471$	3.17347	−	5.49661i	0.146226	−	0.253270i
$472$	13.2854	−	26.1348i	0.611509	−	1.20295i
$473$	0.0130982	+	0.0226868i	0.000602257	+	0.00104314i
$474$	2.84273	−	2.47271i	0.130571	−	0.113575i
$475$	1.85753	−	3.94330i	0.0852293	−	0.180931i
$476$	72.7394	+	10.1763i	3.33401	+	0.466431i
$477$	−4.76584	+	2.75156i	−0.218213	+	0.125985i
$478$	−0.555254	+	1.61422i	−0.0253967	+	0.0738327i
$479$	9.30428	+	5.37183i	0.425123	+	0.245445i	0.697267	−	0.716812i	$-0.254399\pi$
$479$	9.30428	+	5.37183i	0.425123	+	0.245445i	−0.272144	+	0.962257i	$0.587733\pi$
$480$	4.04498	+	2.82288i	0.184627	+	0.128846i
$481$	0.687519	−	1.19082i	0.0313482	−	0.0542966i
$482$	−15.8581	−	18.2311i	−0.722315	−	0.830402i
$483$	−26.5198			−1.20669
$484$	17.3446	+	13.5336i	0.788391	+	0.615163i
$485$	−6.51860	−	3.76352i	−0.295994	−	0.170892i
$486$	−17.1700	+	14.9351i	−0.778849	+	0.677472i
$487$	−13.1322			−0.595075			−0.297538	−	0.954710i	$-0.596165\pi$
$487$	−13.1322			−0.595075			−0.297538	+	0.954710i	$0.596165\pi$
$488$	−4.80738	+	0.256482i	−0.217620	+	0.0116104i
$489$	1.20085	−	0.693310i	0.0543042	−	0.0313525i
$490$	−4.59653	−	23.6076i	−0.207650	−	1.06648i
$491$	15.9272	−	9.19556i	0.718783	−	0.414990i	−0.0955215	−	0.995427i	$-0.530452\pi$
$491$	15.9272	−	9.19556i	0.718783	−	0.414990i	0.814305	+	0.580438i	$0.197119\pi$
$492$	−1.25898	−	3.11047i	−0.0567594	−	0.140231i
$493$		−	56.8621i		−	2.56094i
$494$	−2.14711	−	2.08836i	−0.0966032	−	0.0939599i
$495$		−	0.0196908i		−	0.000885034i
$496$	−2.86599	−	11.4337i	−0.128687	−	0.513388i
$497$	56.1899	−	32.4413i	2.52046	−	1.45519i
$498$	8.48504	−	1.65209i	0.380224	−	0.0740318i
$499$	1.69637	−	0.979399i	0.0759399	−	0.0438439i	−0.461549	−	0.887115i	$-0.652706\pi$
$499$	1.69637	−	0.979399i	0.0759399	−	0.0438439i	0.537489	+	0.843271i	$0.319373\pi$
$500$	−1.57679	−	1.23033i	−0.0705164	−	0.0550222i
$501$	15.2162			0.679808
$502$	9.18726	+	10.5620i	0.410048	+	0.471407i
$503$	−0.0504653	−	0.0291362i	−0.00225014	−	0.00129912i	0.498875	−	0.866674i	$-0.333747\pi$
$503$	−0.0504653	−	0.0291362i	−0.00225014	−	0.00129912i	−0.501125	+	0.865375i	$0.667080\pi$
$504$	−1.65358	−	30.9940i	−0.0736562	−	1.38058i
$505$	−12.1038			−0.538614
$506$	0.0582318	−	0.0506522i	0.00258872	−	0.00225177i
$507$	−5.56486	+	9.63862i	−0.247144	+	0.428066i
$508$	34.4155	−	13.9299i	1.52694	−	0.618039i
$509$	14.6532	+	8.46004i	0.649493	+	0.374985i	0.788262	−	0.615340i	$-0.210981\pi$
$509$	14.6532	+	8.46004i	0.649493	+	0.374985i	−0.138769	+	0.990325i	$0.544315\pi$
$510$	8.74010	+	3.00639i	0.387018	+	0.133125i
$511$	40.4540	−	23.3561i	1.78958	−	1.03321i
$512$	−22.3388	+	3.60280i	−0.987243	+	0.159223i
$513$	19.8459	−	1.65839i	0.876217	−	0.0732198i
$514$	−10.5897	−	12.1744i	−0.467093	−	0.536988i
$515$	1.34305	+	2.32623i	0.0591818	+	0.102506i
$516$	1.94959	+	4.81671i	0.0858260	+	0.212044i
$517$	0.00509235	−	0.00882022i	0.000223962	−	0.000387913i
$518$	−18.5427	−	6.37827i	−0.814721	−	0.280245i
$519$	−13.1549	−	7.59496i	−0.577434	−	0.333382i
$520$	−1.15188	+	0.749583i	−0.0505134	+	0.0328714i
$521$			22.5352i			0.987284i	0.869665	+	0.493642i	$0.164335\pi$
$521$			22.5352i			0.987284i	−0.869665	+	0.493642i	$0.835665\pi$
$522$	−23.5862	+	4.59238i	−1.03234	+	0.201003i
$523$	14.7479	−	25.5441i	0.644880	−	1.11696i	−0.339450	−	0.940624i	$-0.610241\pi$
$523$	14.7479	−	25.5441i	0.644880	−	1.11696i	0.984329	−	0.176340i	$-0.0564258\pi$
$524$	−28.5838	−	3.99891i	−1.24869	−	0.174693i
$525$		−	4.27233i		−	0.186460i
$526$	35.9224	−	6.99430i	1.56629	−	0.304966i
$527$	−11.0437	−	19.1282i	−0.481070	−	0.833237i
$528$	−0.0213292	−	0.0220316i	−0.000928232	−	0.000958802i
$529$	7.76556	+	13.4503i	0.337633	+	0.584797i
$530$	1.13028	−	3.28592i	0.0490962	−	0.142731i
$531$	−23.2151			−1.00745
$532$	−23.3808	+	35.7468i	−1.01368	+	1.54982i
$533$	0.934927			0.0404962
$534$	−1.90788	+	5.54653i	−0.0825619	+	0.240022i
$535$	−1.18438	−	2.05141i	−0.0512053	−	0.0886901i
$536$	−17.6408	+	0.941168i	−0.761969	+	0.0406523i
$537$	−0.744836	−	1.29009i	−0.0321420	−	0.0556716i
$538$	30.5982	−	5.95765i	1.31918	−	0.256853i
$539$			0.149518i			0.00644021i
$540$	1.26604	−	9.04952i	0.0544816	−	0.389429i
$541$	8.10577	−	14.0396i	0.348494	−	0.603610i	−0.637488	−	0.770460i	$-0.720026\pi$
$541$	8.10577	−	14.0396i	0.348494	−	0.603610i	0.985982	+	0.166851i	$0.0533598\pi$
$542$	29.5232	−	5.74833i	1.26813	−	0.246912i
$543$		−	12.6911i		−	0.544627i
$544$	−38.3987	+	17.9790i	−1.64633	+	0.770843i
$545$	15.6776	+	9.05149i	0.671557	+	0.387723i
$546$	−2.77610	−	0.954912i	−0.118806	−	0.0408665i
$547$	−11.4165	+	19.7740i	−0.488135	+	0.845475i	−0.999907	−	0.0136462i	$-0.995656\pi$
$547$	−11.4165	+	19.7740i	−0.488135	+	0.845475i	0.511771	+	0.859122i	$0.328989\pi$
$548$	14.5004	−	5.86913i	0.619427	−	0.250717i
$549$	1.90606	+	3.30139i	0.0813485	+	0.140900i
$550$	0.00816005	+	0.00938112i	0.000347946	+	0.000400012i
$551$	29.9156	+	14.0921i	1.27445	+	0.600342i
$552$	12.8315	−	8.35004i	0.546144	−	0.355401i
$553$	12.9644	−	7.48502i	0.551304	−	0.318296i
$554$	37.5542	+	12.9178i	1.59552	+	0.548823i
$555$	−2.13702	−	1.23381i	−0.0907114	−	0.0523722i
$556$	3.55036	+	8.77160i	0.150569	+	0.371999i
$557$	9.05706	−	15.6873i	0.383760	−	0.664692i	−0.607836	−	0.794062i	$-0.707962\pi$
$557$	9.05706	−	15.6873i	0.383760	−	0.664692i	0.991596	+	0.129371i	$0.0412957\pi$
$558$	−7.04239	+	6.12573i	−0.298128	+	0.259323i
$559$	−1.44778			−0.0612344
$560$	13.6320	+	14.0809i	0.576057	+	0.595029i
$561$	−0.0497615	−	0.0287298i	−0.00210093	−	0.00121297i
$562$	3.10845	+	3.57360i	0.131122	+	0.150743i
$563$	32.5999			1.37392			0.686960	−	0.726695i	$-0.258945\pi$
$563$	32.5999			1.37392			0.686960	+	0.726695i	$0.258945\pi$
$564$	1.24278	−	1.59274i	0.0523304	−	0.0670666i
$565$	14.6629	−	8.46561i	0.616872	−	0.356151i
$566$	5.32766	−	1.03733i	0.223938	−	0.0436021i
$567$	−11.6058	+	6.70063i	−0.487399	+	0.281400i
$568$	−16.9727	+	33.3885i	−0.712160	+	1.40095i
$569$		−	1.90902i		−	0.0800303i	−0.999199	−	0.0400151i	$-0.987259\pi$
$569$		−	1.90902i		−	0.0800303i	0.999199	−	0.0400151i	$-0.0127406\pi$
$570$	−3.74774	+	3.85317i	−0.156975	+	0.161392i
$571$			13.8273i			0.578654i	0.957230	+	0.289327i	$0.0934315\pi$
$571$			13.8273i			0.578654i	−0.957230	+	0.289327i	$0.906569\pi$
$572$	0.00791956	−	0.00320549i	0.000331134	−	0.000134028i
$573$	1.51632	−	0.875450i	0.0633453	−	0.0365724i
$574$	−2.54812	−	13.0870i	−0.106356	−	0.546241i
$575$	−5.37572	+	3.10367i	−0.224183	+	0.129432i
$576$	10.5588	+	14.4756i	0.439952	+	0.603151i
$577$	−40.1457			−1.67129			−0.835644	−	0.549272i	$-0.814905\pi$
$577$	−40.1457			−1.67129			−0.835644	+	0.549272i	$0.814905\pi$
$578$	−41.8044	+	36.3630i	−1.73883	+	1.51250i
$579$	6.27105	+	3.62059i	0.260616	+	0.150467i
$580$	9.33387	−	11.9623i	0.387568	−	0.496707i
$581$	34.3466			1.42494
$582$	6.09170	+	7.00326i	0.252509	+	0.290295i
$583$	−0.0108012	+	0.0187083i	−0.000447341	+	0.000774817i
$584$	−12.2195	+	24.0381i	−0.505648	+	0.994704i
$585$	0.942437	+	0.544116i	0.0389650	+	0.0224964i
$586$	1.27841	−	3.71656i	0.0528107	−	0.153530i
$587$	−5.33214	+	3.07851i	−0.220081	+	0.127064i	−0.605988	−	0.795474i	$-0.707222\pi$
$587$	−5.33214	+	3.07851i	−0.220081	+	0.127064i	0.385907	+	0.922538i	$0.373889\pi$
$588$	−4.10921	+	29.3723i	−0.169461	+	1.21129i
$589$	12.8004	−	1.06965i	0.527433	−	0.0440742i
$590$	11.0602	−	9.62055i	0.455340	−	0.396072i
$591$	−9.72644	−	16.8467i	−0.400092	−	0.692980i
$592$	10.9801	−	2.75228i	0.451278	−	0.113118i
$593$	−12.3158	+	21.3316i	−0.505749	+	0.875983i	0.494229	+	0.869332i	$0.335451\pi$
$593$	−12.3158	+	21.3316i	−0.505749	+	0.875983i	−0.999978	+	0.00665125i	$0.997883\pi$
$594$	−0.0184775	+	0.0537174i	−0.000758142	+	0.00220405i
$595$	31.8038	+	18.3620i	1.30383	+	0.752767i
$596$	5.09099	−	36.3900i	0.208535	−	1.49059i
$597$			6.16804i			0.252441i
$598$	0.815187	+	4.18676i	0.0333355	+	0.171209i
$599$	−20.7485	+	35.9374i	−0.847760	+	1.46836i	0.0354432	+	0.999372i	$0.488716\pi$
$599$	−20.7485	+	35.9374i	−0.847760	+	1.46836i	−0.883203	+	0.468991i	$0.844618\pi$
$600$	1.34519	+	2.06715i	0.0549171	+	0.0843909i
$601$		−	27.0981i		−	1.10535i	−0.833395	−	0.552677i	$-0.813606\pi$
$601$		−	27.0981i		−	1.10535i	0.833395	−	0.552677i	$-0.186394\pi$
$602$	3.94587	+	20.2658i	0.160822	+	0.825973i
$603$	6.99433	+	12.1145i	0.284831	+	0.493342i
$604$	−12.1383	−	9.47121i	−0.493900	−	0.385378i
$605$	5.49996	+	9.52621i	0.223605	+	0.387296i
$606$	14.1142	+	4.85494i	0.573349	+	0.197219i
$607$	−35.1986			−1.42867			−0.714333	−	0.699806i	$-0.753270\pi$
$607$	−35.1986			−1.42867			−0.714333	+	0.699806i	$0.753270\pi$
$608$	0.0574008	−	24.6576i	0.00232791	−	0.999997i
$609$	32.4119			1.31340
$610$	−2.27621	−	0.782965i	−0.0921612	−	0.0317013i
$611$	0.281435	+	0.487459i	0.0113856	+	0.0197205i
$612$	26.4694	+	20.6534i	1.06996	+	0.834864i
$613$	20.4595	+	35.4369i	0.826352	+	1.43128i	0.900882	+	0.434064i	$0.142921\pi$
$613$	20.4595	+	35.4369i	0.826352	+	1.43128i	−0.0745301	+	0.997219i	$0.523746\pi$
$614$	−6.28522	−	32.2806i	−0.253651	−	1.30274i
$615$		−	1.67780i		−	0.0676555i
$616$	−0.0664547	−	0.102121i	−0.00267754	−	0.00411456i
$617$	2.74805	−	4.75975i	0.110632	−	0.191620i	−0.805393	−	0.592741i	$-0.798046\pi$
$617$	2.74805	−	4.75975i	0.110632	−	0.191620i	0.916025	+	0.401120i	$0.131379\pi$
$618$	−0.633047	−	3.25130i	−0.0254649	−	0.130786i
$619$		−	5.88877i		−	0.236690i	−0.992973	−	0.118345i	$-0.962241\pi$
$619$		−	5.88877i		−	0.236690i	0.992973	−	0.118345i	$-0.0377588\pi$
$620$	0.816584	−	5.83687i	0.0327948	−	0.234414i
$621$	−24.5607	−	14.1801i	−0.985587	−	0.569029i
$622$	13.5528	−	39.4004i	0.543418	−	1.57981i
$623$	−11.6526	+	20.1829i	−0.466852	+	0.808612i
$624$	1.64386	−	0.412053i	0.0658072	−	0.0164953i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−9.40309	+	8.17916i	−0.375823	+	0.326905i
$627$	0.0274473	−	0.0190599i	0.00109614	−	0.000761178i
$628$	−2.01700	+	14.4173i	−0.0804870	+	0.575314i
$629$	18.3693	−	10.6055i	0.732431	−	0.422869i
$630$	5.04789	−	14.6751i	0.201113	−	0.584670i
$631$	1.07298	+	0.619488i	0.0427148	+	0.0246614i	0.521205	−	0.853431i	$-0.325483\pi$
$631$	1.07298	+	0.619488i	0.0427148	+	0.0246614i	−0.478491	+	0.878093i	$0.658816\pi$
$632$	−3.91604	+	7.70358i	−0.155772	+	0.306432i
$633$	−3.49579	+	6.05488i	−0.138945	+	0.240660i
$634$	−15.6830	−	18.0298i	−0.622852	−	0.716056i
$635$	18.5639			0.736685
$636$	−2.63602	+	3.37831i	−0.104525	+	0.133959i
$637$	−7.15622	−	4.13165i	−0.283540	−	0.163702i
$638$	−0.0711695	+	0.0619059i	−0.00281763	+	0.00245088i
$639$	29.6584			1.17327
$640$	−11.0293	−	2.52081i	−0.435971	−	0.0996440i
$641$	12.2496	−	7.07234i	0.483832	−	0.279341i	−0.238180	−	0.971221i	$-0.576551\pi$
$641$	12.2496	−	7.07234i	0.483832	−	0.279341i	0.722012	+	0.691880i	$0.243217\pi$
$642$	0.558259	+	2.86719i	0.0220327	+	0.113159i
$643$	11.4813	−	6.62873i	0.452778	−	0.261412i	−0.256225	−	0.966617i	$-0.582479\pi$
$643$	11.4813	−	6.62873i	0.452778	−	0.261412i	0.709003	+	0.705206i	$0.249145\pi$
$644$	56.3840	−	22.8218i	2.22184	−	0.899305i
$645$			2.59815i			0.102302i
$646$	−12.5762	−	44.4591i	−0.494805	−	1.74922i
$647$		−	18.8993i		−	0.743010i	−0.928431	−	0.371505i	$-0.878842\pi$
$647$		−	18.8993i		−	0.743010i	0.928431	−	0.371505i	$-0.121158\pi$
$648$	3.50566	−	6.89628i	0.137715	−	0.270912i
$649$	−0.0789213	+	0.0455652i	−0.00309793	+	0.00178859i
$650$	−0.674485	+	0.131326i	−0.0264555	+	0.00515104i
$651$	10.9032	−	6.29498i	0.427331	−	0.246720i
$652$	−1.95650	+	2.50745i	−0.0766224	+	0.0981992i
$653$	−30.1975			−1.18172			−0.590859	−	0.806775i	$-0.701211\pi$
$653$	−30.1975			−1.18172			−0.590859	+	0.806775i	$0.701211\pi$
$654$	−14.6509	−	16.8433i	−0.572897	−	0.658625i
$655$	−12.4977	−	7.21555i	−0.488326	−	0.281935i
$656$	5.35347	+	5.52978i	0.209018	+	0.215901i
$657$	21.3526			0.833044
$658$	6.05636	−	5.26805i	0.236101	−	0.205370i
$659$	−15.3169	+	26.5296i	−0.596661	+	1.03345i	0.396649	+	0.917970i	$0.370173\pi$
$659$	−15.3169	+	26.5296i	−0.596661	+	1.03345i	−0.993310	+	0.115477i	$0.963160\pi$
$660$	−0.00575252	−	0.0142123i	−0.000223916	−	0.000553213i
$661$	−22.5300	−	13.0077i	−0.876315	−	0.505941i	−0.00687314	−	0.999976i	$-0.502188\pi$
$661$	−22.5300	−	13.0077i	−0.876315	−	0.505941i	−0.869442	+	0.494036i	$0.835521\pi$
$662$	−36.0327	−	12.3944i	−1.40045	−	0.481723i
$663$	2.75013	−	1.58779i	0.106806	−	0.0616645i
$664$	−16.6184	+	10.8144i	−0.644919	+	0.419679i
$665$	−17.5423	+	12.1816i	−0.680261	+	0.472384i
$666$	−5.88270	−	6.76298i	−0.227950	−	0.262060i
$667$	−23.5459	−	40.7826i	−0.911700	−	1.57911i
$668$	−32.3512	+	13.0943i	−1.25170	+	0.506635i
$669$	1.87497	−	3.24754i	0.0724904	−	0.125557i
$670$	−8.35264	−	2.87311i	−0.322691	−	0.110998i
$671$	0.0129596	+	0.00748220i	0.000500298	+	0.000288847i
$672$	−10.2482	−	21.8876i	−0.395332	−	0.844331i
$673$		−	28.5848i		−	1.10186i	−0.834550	−	0.550932i	$-0.814272\pi$
$673$		−	28.5848i		−	1.10186i	0.834550	−	0.550932i	$-0.185728\pi$
$674$	−18.6610	+	3.63342i	−0.718797	+	0.139954i
$675$	2.28441	−	3.95672i	0.0879271	−	0.152294i
$676$	3.53692	−	25.2816i	0.136036	−	0.972370i
$677$			19.4486i			0.747470i	0.927536	+	0.373735i	$0.121923\pi$
$677$			19.4486i			0.747470i	−0.927536	+	0.373735i	$0.878077\pi$
$678$	−20.4939	+	3.99028i	−0.787062	+	0.153246i
$679$	18.4399	+	31.9388i	0.707658	+	1.22570i
$680$	−21.1696	+	1.12943i	−0.811816	+	0.0433117i
$681$	−3.89737	−	6.75044i	−0.149347	−	0.258677i
$682$	−0.0119179	+	0.0346473i	−0.000456358	+	0.00132671i
$683$	31.9530			1.22265			0.611324	−	0.791380i	$-0.290637\pi$
$683$	31.9530			1.22265			0.611324	+	0.791380i	$0.290637\pi$
$684$	−17.4258	+	8.80725i	−0.666292	+	0.336754i
$685$	7.82158			0.298847
$686$	−22.5533	+	65.5663i	−0.861088	+	2.50333i
$687$	11.5412	+	19.9899i	0.440324	+	0.762664i
$688$	−8.29009	−	8.56310i	−0.316057	−	0.326465i
$689$	−0.596942	−	1.03393i	−0.0227417	−	0.0393897i
$690$	7.51348	−	1.46292i	0.286033	−	0.0556924i
$691$			5.28237i			0.200951i	0.994940	+	0.100475i	$0.0320364\pi$
$691$			5.28237i			0.200951i	−0.994940	+	0.100475i	$0.967964\pi$
$692$	34.5045	+	4.82722i	1.31166	+	0.183503i
$693$	−0.0482389	+	0.0835522i	−0.00183244	+	0.00317389i
$694$	40.3301	−	7.85250i	1.53091	−	0.298077i
$695$			4.73144i			0.179474i
$696$	−15.6823	+	10.2052i	−0.594436	+	0.386827i
$697$	12.4898	+	7.21098i	0.473085	+	0.273136i
$698$	−10.5671	−	3.63483i	−0.399970	−	0.137580i
$699$	1.65784	−	2.87146i	0.0627051	−	0.108608i
$700$	3.67658	+	9.08344i	0.138962	+	0.343322i
$701$	0.0956396	+	0.165653i	0.00361226	+	0.00625661i	0.867826	−	0.496868i	$-0.165517\pi$
$701$	0.0956396	+	0.165653i	0.00361226	+	0.00625661i	−0.864214	+	0.503125i	$0.832184\pi$
$702$	−2.06042	−	2.36874i	−0.0777657	−	0.0894025i
$703$	1.02721	+	12.2926i	0.0387420	+	0.463624i
$704$	0.0643075	+	0.0284866i	0.00242368	+	0.00107363i
$705$	0.874785	−	0.505057i	0.0329463	−	0.0190216i
$706$	−14.6843	−	5.05105i	−0.552650	−	0.190099i
$707$	51.3592	+	29.6523i	1.93156	+	1.11519i
$708$	−16.7560	+	6.78211i	−0.629731	+	0.254887i
$709$	6.31845	−	10.9439i	0.237294	−	0.411006i	−0.722643	−	0.691222i	$-0.757073\pi$
$709$	6.31845	−	10.9439i	0.237294	−	0.411006i	0.959937	+	0.280216i	$0.0904061\pi$
$710$	−14.1299	+	12.2907i	−0.530286	+	0.461263i
$711$	6.84294			0.256630
$712$	−0.716744	−	13.4344i	−0.0268611	−	0.503474i
$713$	−15.8415	−	9.14608i	−0.593268	−	0.342523i
$714$	−29.7210	−	34.1685i	−1.11228	−	1.27872i
$715$	0.00427185			0.000159758
$716$	2.69380	+	2.10191i	0.100672	+	0.0785519i
$717$	0.911510	−	0.526261i	0.0340410	−	0.0196536i
$718$	23.2553	−	4.52795i	0.867882	−	0.168982i
$719$	−8.88899	+	5.13206i	−0.331503	+	0.191393i	−0.656508	−	0.754319i	$-0.727967\pi$
$719$	−8.88899	+	5.13206i	−0.331503	+	0.191393i	0.325005	+	0.945712i	$0.394634\pi$
$720$	2.17821	+	8.68985i	0.0811771	+	0.323852i
$721$		−	13.1609i		−	0.490138i
$722$	26.5071	+	4.40178i	0.986491	+	0.163817i
$723$			14.8983i			0.554073i
$724$	10.9214	+	26.9827i	0.405891	+	1.00280i
$725$	6.57006	−	3.79323i	0.244006	−	0.140877i
$726$	−2.59241	−	13.3145i	−0.0962135	−	0.494148i
$727$	21.3886	−	12.3487i	0.793259	−	0.457988i	−0.0478496	−	0.998855i	$-0.515237\pi$
$727$	21.3886	−	12.3487i	0.793259	−	0.457988i	0.841109	+	0.540866i	$0.181903\pi$
$728$	6.72403	−	0.358738i	0.249209	−	0.0132957i
$729$	5.82576			0.215769
$730$	−10.1729	+	8.84873i	−0.376514	+	0.327506i
$731$	−19.3410	−	11.1665i	−0.715353	−	0.413009i
$732$	2.34022	+	1.82602i	0.0864970	+	0.0674915i
$733$	−1.08353			−0.0400213			−0.0200106	−	0.999800i	$-0.506370\pi$
$733$	−1.08353			−0.0400213			−0.0200106	+	0.999800i	$0.506370\pi$
$734$	−2.11101	−	2.42690i	−0.0779188	−	0.0895785i
$735$	−7.41457	+	12.8424i	−0.273491	+	0.473700i
$736$	−20.0954	+	28.7953i	−0.740728	+	1.06141i
$737$	0.0475555	+	0.0274562i	0.00175173	+	0.00101136i
$738$	1.98238	−	5.76311i	0.0729722	−	0.212143i
$739$	−32.0728	+	18.5173i	−1.17982	+	0.681168i	−0.955972	−	0.293457i	$-0.905194\pi$
$739$	−32.0728	+	18.5173i	−1.17982	+	0.681168i	−0.223845	+	0.974625i	$0.571861\pi$
$740$	5.60529	+	0.784186i	0.206055	+	0.0288273i
$741$	0.153787	+	1.84036i	0.00564952	+	0.0676074i
$742$	−12.8459	+	11.1739i	−0.471589	+	0.410206i
$743$	6.31181	+	10.9324i	0.231558	+	0.401070i	0.958267	−	0.285876i	$-0.0922844\pi$
$743$	6.31181	+	10.9324i	0.231558	+	0.401070i	−0.726709	+	0.686946i	$0.758951\pi$
$744$	−3.29343	+	6.47878i	−0.120743	+	0.237524i
$745$	9.18609	−	15.9108i	0.336552	−	0.582925i
$746$	−4.08366	+	11.8719i	−0.149514	+	0.434662i
$747$	13.5967	+	7.85006i	0.497477	+	0.287219i
$748$	0.130522	+	0.0182601i	0.00477235	+	0.000667657i
$749$			11.6061i			0.424078i
$750$	0.235676	+	1.21042i	0.00860566	+	0.0441982i
$751$	−23.5345	+	40.7630i	−0.858788	+	1.48746i	0.0142979	+	0.999898i	$0.495449\pi$
$751$	−23.5345	+	40.7630i	−0.858788	+	1.48746i	−0.873086	+	0.487567i	$0.837885\pi$
$752$	−1.27164	+	4.45582i	−0.0463718	+	0.162487i
$753$		−	8.63121i		−	0.314539i
$754$	−0.996301	−	5.11695i	−0.0362831	−	0.186348i
$755$	−3.84904	−	6.66674i	−0.140081	−	0.242627i
$756$	−27.5418	+	35.2975i	−1.00169	+	1.28376i
$757$	8.56450	+	14.8342i	0.311282	+	0.539156i	0.978640	−	0.205581i	$-0.0659082\pi$
$757$	8.56450	+	14.8342i	0.311282	+	0.539156i	−0.667358	+	0.744737i	$0.732575\pi$
$758$	−9.23236	−	3.17572i	−0.335334	−	0.115347i
$759$	−0.0475866			−0.00172728
$760$	4.65222	−	11.4174i	0.168754	−	0.414152i
$761$	−31.6139			−1.14600			−0.573002	−	0.819554i	$-0.694221\pi$
$761$	−31.6139			−1.14600			−0.573002	+	0.819554i	$0.694221\pi$
$762$	−21.6472	−	7.44612i	−0.784194	−	0.269745i
$763$	−44.3491	−	76.8149i	−1.60555	−	2.78089i
$764$	−2.47049	+	3.16618i	−0.0893793	+	0.114548i
$765$	8.39341	+	14.5378i	0.303465	+	0.525616i
$766$	−7.10057	−	36.4682i	−0.256554	−	1.31765i
$767$		−	5.03643i		−	0.181855i
$768$	11.8500	+	7.36344i	0.427602	+	0.265705i
$769$	21.3699	−	37.0138i	0.770619	−	1.33475i	−0.166606	−	0.986024i	$-0.553281\pi$
$769$	21.3699	−	37.0138i	0.770619	−	1.33475i	0.937224	−	0.348727i	$-0.113386\pi$
$770$	−0.0116428	−	0.0597968i	−0.000419577	−	0.00215493i
$771$			9.94879i			0.358297i
$772$	−16.4487	−	2.30118i	−0.592000	−	0.0828214i
$773$	23.5066	+	13.5716i	0.845475	+	0.488135i	0.859121	−	0.511772i	$-0.171011\pi$
$773$	23.5066	+	13.5716i	0.845475	+	0.488135i	−0.0136467	+	0.999907i	$0.504344\pi$
$774$	−3.06980	+	8.92443i	−0.110342	+	0.320782i
$775$	1.47343	−	2.55205i	0.0529271	−	0.0916724i
$776$	−18.9783	−	9.64744i	−0.681282	−	0.346323i
$777$	6.04523	+	10.4706i	0.216871	+	0.375632i
$778$	8.98783	−	7.81796i	0.322229	−	0.280287i
$779$	−6.88909	+	4.78389i	−0.246827	+	0.171401i
$780$	0.839187	+	0.117403i	0.0300477	+	0.00420371i
$781$	0.100826	−	0.0582119i	0.00360783	−	0.00208298i
$782$	−21.4018	+	62.2188i	−0.765328	+	2.22494i
$783$	30.0175	+	17.3306i	1.07274	+	0.619345i
$784$	−16.5398	−	65.9848i	−0.590708	−	2.35660i
$785$	−3.63943	+	6.30369i	−0.129897	+	0.224988i
$786$	11.6792	+	13.4269i	0.416585	+	0.478922i
$787$	40.7464			1.45245			0.726226	−	0.687456i	$-0.241273\pi$
$787$	40.7464			1.45245			0.726226	+	0.687456i	$0.241273\pi$
$788$	35.1770	+	27.4477i	1.25313	+	0.977785i
$789$	−19.5417	−	11.2824i	−0.695701	−	0.401663i
$790$	−3.26013	+	2.83578i	−0.115990	+	0.100893i
$791$	−82.9570			−2.94961
$792$	−0.00296714	−	0.0556148i	−0.000105433	−	0.00197619i
$793$	−0.716224	+	0.413512i	−0.0254339	+	0.0146843i
$794$	−5.17488	−	26.5779i	−0.183650	−	0.943216i
$795$	−1.85548	+	1.07126i	−0.0658070	+	0.0379937i
$796$	−5.30794	−	13.1139i	−0.188135	−	0.464810i
$797$			40.3718i			1.43004i	0.699103	+	0.715021i	$0.253583\pi$
$797$			40.3718i			1.43004i	−0.699103	+	0.715021i	$0.746417\pi$
$798$	25.3420	−	7.16855i	0.897099	−	0.253764i
$799$			8.68270i			0.307172i
$800$	−4.63891	−	3.23737i	−0.164010	−	0.114458i
$801$	−9.22580	+	5.32652i	−0.325978	+	0.188203i
$802$	−15.1879	+	2.95718i	−0.536305	+	0.104422i
$803$	0.0725897	−	0.0419097i	0.00256164	−	0.00147896i
$804$	8.58750	+	6.70062i	0.302858	+	0.236313i
$805$	30.4138			1.07195
$806$	−1.32896	−	1.52782i	−0.0468105	−	0.0538152i
$807$	−16.6453	−	9.61017i	−0.585942	−	0.338294i
$808$	−34.1862	+	1.82389i	−1.20267	+	0.0641642i
$809$	−17.3299			−0.609286			−0.304643	−	0.952467i	$-0.598537\pi$
$809$	−17.3299			−0.609286			−0.304643	+	0.952467i	$0.598537\pi$
$810$	2.91849	−	2.53861i	0.102545	−	0.0891976i
$811$	5.52984	−	9.57796i	0.194179	−	0.336328i	−0.752452	−	0.658647i	$-0.771129\pi$
$811$	5.52984	−	9.57796i	0.194179	−	0.336328i	0.946631	+	0.322319i	$0.104462\pi$
$812$	−68.9111	+	27.8922i	−2.41831	+	0.978825i
$813$	−16.0605	−	9.27253i	−0.563266	−	0.325202i
$814$	−0.0332727	−	0.0114450i	−0.00116621	−	0.000401148i
$815$	−1.37717	+	0.795109i	−0.0482402	+	0.0278515i
$816$	25.1387	+	7.17426i	0.880029	+	0.251149i
$817$	10.6681	−	7.40807i	0.373228	−	0.259176i
$818$	−2.79323	−	3.21121i	−0.0976630	−	0.112277i
$819$	−2.66598	−	4.61761i	−0.0931568	−	0.161352i
$820$	1.44384	+	3.56719i	0.0504212	+	0.124572i
$821$	10.3435	−	17.9155i	0.360992	−	0.625257i	−0.627132	−	0.778913i	$-0.715771\pi$
$821$	10.3435	−	17.9155i	0.360992	−	0.625257i	0.988124	+	0.153656i	$0.0491048\pi$
$822$	−9.12067	−	3.13730i	−0.318120	−	0.109426i
$823$	32.6933	+	18.8755i	1.13962	+	0.657959i	0.946336	−	0.323185i	$-0.104753\pi$
$823$	32.6933	+	18.8755i	1.13962	+	0.657959i	0.193282	+	0.981143i	$0.438087\pi$
$824$	4.14385	+	6.36784i	0.144358	+	0.221834i
$825$		−	0.00766617i		−	0.000266902i
$826$	−70.4994	+	13.7266i	−2.45299	+	0.477611i
$827$	8.17545	−	14.1603i	0.284288	−	0.492402i	−0.688148	−	0.725570i	$-0.741576\pi$
$827$	8.17545	−	14.1603i	0.284288	−	0.492402i	0.972436	+	0.233169i	$0.0749094\pi$
$828$	27.5367	+	3.85241i	0.956965	+	0.133880i
$829$			39.6360i			1.37662i	0.725419	+	0.688308i	$0.241646\pi$
$829$			39.6360i			1.37662i	−0.725419	+	0.688308i	$0.758354\pi$
$830$	−9.73091	+	1.89467i	−0.337765	+	0.0657648i
$831$	−12.2432	−	21.2059i	−0.424714	−	0.735625i
$832$	−3.14043	+	2.29070i	−0.108875	+	0.0794159i
$833$	−63.7338	−	110.390i	−2.20825	−	3.82480i
$834$	1.89782	−	5.51729i	0.0657161	−	0.191048i
$835$	−17.4504			−0.603895
$836$	−0.0419539	+	0.0641433i	−0.00145101	+	0.00221844i
$837$	13.4637			0.465373
$838$	0.296558	−	0.862146i	0.0102444	−	0.0297823i
$839$	27.6024	+	47.8088i	0.952942	+	1.65054i	0.739009	+	0.673696i	$0.235294\pi$
$839$	27.6024	+	47.8088i	0.952942	+	1.65054i	0.213933	+	0.976848i	$0.431372\pi$
$840$	−0.643784	−	12.0668i	−0.0222127	−	0.416345i
$841$	14.2772	+	24.7288i	0.492316	+	0.852716i
$842$	−5.65548	+	1.10116i	−0.194901	+	0.0379483i
$843$		−	2.92032i		−	0.100581i
$844$	2.22186	−	15.8817i	0.0764796	−	0.546669i
$845$	6.38196	−	11.0539i	0.219546	−	0.380265i
$846$	3.60155	−	0.701244i	0.123824	−	0.0241093i
$847$		−	53.8957i		−	1.85188i
$848$	2.69723	−	9.45110i	0.0926232	−	0.324552i
$849$	−2.89823	−	1.67329i	−0.0994669	−	0.0574272i
$850$	−10.0234	−	3.44782i	−0.343801	−	0.118259i
$851$	8.78321	−	15.2130i	0.301084	−	0.521494i
$852$	21.4067	−	8.66449i	0.733381	−	0.296840i
$853$	−5.34286	−	9.25410i	−0.182936	−	0.316854i	0.759943	−	0.649990i	$-0.225227\pi$
$853$	−5.34286	−	9.25410i	−0.182936	−	0.316854i	−0.942879	+	0.333135i	$0.891893\pi$
$854$	7.74035	+	8.89861i	0.264869	+	0.304504i
$855$	−9.72860	+	0.812956i	−0.332711	+	0.0278025i
$856$	−3.65430	−	5.61555i	−0.124901	−	0.191935i
$857$	29.9464	−	17.2896i	1.02295	−	0.590600i	0.107993	−	0.994152i	$-0.465558\pi$
$857$	29.9464	−	17.2896i	1.02295	−	0.590600i	0.914957	+	0.403551i	$0.132224\pi$
$858$	−0.00498136	−	0.00171347i	−0.000170061	−	5.84970e-5i
$859$	−44.5792	−	25.7378i	−1.52102	−	0.878163i	−0.999692	−	0.0248079i	$-0.992103\pi$
$859$	−44.5792	−	25.7378i	−1.52102	−	0.878163i	−0.521330	−	0.853355i	$-0.674564\pi$
$860$	−2.23585	−	5.52395i	−0.0762420	−	0.188365i
$861$	−4.11032	+	7.11928i	−0.140079	+	0.242624i
$862$	27.3053	−	23.7512i	0.930023	−	0.808969i
$863$	9.37688			0.319193			0.159596	−	0.987182i	$-0.448981\pi$
$863$	9.37688			0.319193			0.159596	+	0.987182i	$0.448981\pi$
$864$	2.21216	−	25.7503i	0.0752594	−	0.876044i
$865$	15.0864	+	8.71014i	0.512953	+	0.296154i
$866$	22.1984	+	25.5202i	0.754333	+	0.867211i
$867$	34.1622			1.16021
$868$	−17.7642	+	22.7666i	−0.602958	+	0.772750i
$869$	0.0232631	−	0.0134309i	0.000789146	−	0.000455614i
$870$	−9.18278	+	1.78794i	−0.311326	+	0.0606169i
$871$	−2.62821	+	1.51740i	−0.0890534	+	0.0514150i
$872$	45.6441	+	23.2027i	1.54570	+	0.785743i
$873$			16.8581i			0.570560i
$874$	−27.4299	−	26.6793i	−0.927829	−	0.902441i
$875$			4.89965i			0.165638i
$876$	15.4118	−	6.23801i	0.520715	−	0.210763i
$877$	−22.2550	+	12.8489i	−0.751498	+	0.433878i	−0.826235	−	0.563326i	$-0.809522\pi$
$877$	−22.2550	+	12.8489i	−0.751498	+	0.433878i	0.0747367	+	0.997203i	$0.476188\pi$
$878$	1.74690	+	8.97202i	0.0589552	+	0.302791i
$879$	−2.09865	+	1.21166i	−0.0707858	+	0.0408682i
$880$	0.0244609	+	0.0252665i	0.000824578	+	0.000851734i
$881$	6.37062			0.214632			0.107316	−	0.994225i	$-0.465774\pi$
$881$	6.37062			0.214632			0.107316	+	0.994225i	$0.465774\pi$
$882$	−40.6422	+	35.3521i	−1.36849	+	1.19037i
$883$	−24.3616	−	14.0652i	−0.819833	−	0.473331i	0.0305259	−	0.999534i	$-0.490282\pi$
$883$	−24.3616	−	14.0652i	−0.819833	−	0.473331i	−0.850359	+	0.526203i	$0.823615\pi$
$884$	−4.48069	+	5.74244i	−0.150702	+	0.193139i
$885$	−9.03828			−0.303818
$886$	5.04842	+	5.80387i	0.169605	+	0.194985i
$887$	9.39018	−	16.2643i	0.315291	−	0.546101i	−0.664208	−	0.747548i	$-0.731231\pi$
$887$	9.39018	−	16.2643i	0.315291	−	0.546101i	0.979499	+	0.201447i	$0.0645644\pi$
$888$	−6.22174	−	3.16276i	−0.208788	−	0.106135i
$889$	−78.7706	−	45.4782i	−2.64188	−	1.52529i
$890$	2.18801	−	6.36093i	0.0733424	−	0.213219i
$891$	−0.0208252	+	0.0120235i	−0.000697672	+	0.000402801i
$892$	−1.19169	+	8.51813i	−0.0399009	+	0.285208i
$893$	−4.56804	−	2.15182i	−0.152864	−	0.0720079i
$894$	−17.0937	+	14.8688i	−0.571700	+	0.497287i
$895$	0.854201	+	1.47952i	0.0285528	+	0.0494549i
$896$	40.6242	+	37.7162i	1.35716	+	1.26001i
$897$	1.31496	−	2.27758i	0.0439053	−	0.0760463i
$898$	−17.9095	+	52.0661i	−0.597649	+	1.73747i
$899$	19.3610	+	11.1781i	0.645727	+	0.372810i
$900$	−0.620621	+	4.43614i	−0.0206874	+	0.147871i
$901$		−	18.4166i		−	0.613545i
$902$	−0.00457228	−	0.0234830i	−0.000152240	−	0.000781899i
$903$	6.36501	−	11.0245i	0.211814	−	0.366873i
$904$	40.1383	−	26.1199i	1.33498	−	0.868734i
$905$			14.5546i			0.483810i
$906$	1.81425	+	9.31790i	0.0602744	+	0.309567i
$907$	26.7313	+	46.3000i	0.887598	+	1.53737i	0.842706	+	0.538374i	$0.180961\pi$
$907$	26.7313	+	46.3000i	0.887598	+	1.53737i	0.0448924	+	0.998992i	$0.485706\pi$
$908$	14.0954	+	10.9983i	0.467771	+	0.364990i
$909$	13.5543	+	23.4768i	0.449568	+	0.778675i
$910$	3.18371	+	1.09512i	0.105539	+	0.0363030i
$911$	−25.7979			−0.854722			−0.427361	−	0.904081i	$-0.640557\pi$
$911$	−25.7979			−0.854722			−0.427361	+	0.904081i	$0.640557\pi$
$912$	−10.0045	+	11.4477i	−0.331283	+	0.379070i
$913$	0.0616306			0.00203968
$914$	−35.6742	−	12.2711i	−1.18000	−	0.405892i
$915$	0.742081	+	1.28532i	0.0245325	+	0.0424915i
$916$	−41.7403	−	32.5689i	−1.37914	−	1.07611i
$917$	35.3537	+	61.2343i	1.16748	+	2.02214i
$918$	−9.25556	−	47.5361i	−0.305479	−	1.56893i
$919$			31.6784i			1.04497i	0.852647	+	0.522487i	$0.174996\pi$
$919$			31.6784i			1.04497i	−0.852647	+	0.522487i	$0.825004\pi$
$920$	−14.7155	+	9.57609i	−0.485157	+	0.315714i
$921$	−10.1386	+	17.5605i	−0.334077	+	0.578639i
$922$	−2.42234	−	12.4410i	−0.0797756	−	0.409724i
$923$			6.43429i			0.211787i
$924$	−0.0104084	+	0.0743985i	−0.000342412	+	0.00244753i
$925$	2.45080	+	1.41497i	0.0805818	+	0.0465239i
$926$	13.5225	−	39.3123i	0.444377	−	1.29188i
$927$	3.00799	−	5.20999i	0.0987953	−	0.171118i
$928$	24.5601	−	35.1929i	0.806226	−	1.15526i
$929$	15.5318	+	26.9019i	0.509582	+	0.882621i	0.999938	+	0.0110994i	$0.00353311\pi$
$929$	15.5318	+	26.9019i	0.509582	+	0.882621i	−0.490357	+	0.871522i	$0.663134\pi$
$930$	−2.74180	+	2.38492i	−0.0899072	+	0.0782046i
$931$	73.8723	−	6.17303i	2.42107	−	0.202313i
$932$	−1.05369	+	7.53169i	−0.0345148	+	0.246709i
$933$	−22.2484	+	12.8451i	−0.728381	+	0.420531i
$934$	−14.4287	+	41.9468i	−0.472122	+	1.37254i
$935$	0.0570681	+	0.0329483i	0.00186632	+	0.00107752i
$936$	2.74382	+	1.39480i	0.0896846	+	0.0455903i
$937$	17.9328	−	31.0605i	0.585838	−	1.01470i	−0.408932	−	0.912565i	$-0.634099\pi$
$937$	17.9328	−	31.0605i	0.585838	−	1.01470i	0.994770	−	0.102136i	$-0.0325678\pi$
$938$	28.4034	+	32.6537i	0.927405	+	1.06618i
$939$	7.68413			0.250762
$940$	−1.42526	+	1.82661i	−0.0464868	+	0.0595774i
$941$	−25.0277	−	14.4498i	−0.815881	−	0.471049i	0.0331129	−	0.999452i	$-0.489458\pi$
$941$	−25.0277	−	14.4498i	−0.815881	−	0.471049i	−0.848994	+	0.528402i	$0.822791\pi$
$942$	6.77237	−	5.89086i	0.220656	−	0.191935i
$943$	11.9439			0.388947
$944$	29.7888	−	28.8390i	0.969542	−	0.938630i
$945$	−19.3865	+	11.1928i	−0.630644	+	0.364102i
$946$	0.00708038	+	0.0363645i	0.000230203	+	0.00118231i
$947$	−8.13620	+	4.69744i	−0.264391	+	0.152646i	−0.626336	−	0.779553i	$-0.715446\pi$
$947$	−8.13620	+	4.69744i	−0.264391	+	0.152646i	0.361945	+	0.932199i	$0.382113\pi$
$948$	4.93906	−	1.99912i	0.160413	−	0.0649283i
$949$			4.63237i			0.150373i
$950$	4.29802	−	4.41894i	0.139446	−	0.143369i
$951$			14.7338i			0.477777i
$952$	92.5940	+	47.0693i	3.00099	+	1.52552i
$953$	−21.1356	+	12.2027i	−0.684650	+	0.395283i	−0.801605	−	0.597854i	$-0.796020\pi$
$953$	−21.1356	+	12.2027i	−0.684650	+	0.395283i	0.116954	+	0.993137i	$0.462687\pi$
$954$	−7.63914	+	1.48738i	−0.247326	+	0.0481559i
$955$	−1.73897	+	1.00399i	−0.0562717	+	0.0324885i
$956$	−1.48509	+	1.90329i	−0.0480313	+	0.0615569i
$957$	0.0581591			0.00188002
$958$	9.97164	+	11.4638i	0.322169	+	0.370378i
$959$	−33.1887	−	19.1615i	−1.07172	−	0.618757i
$960$	4.11085	+	5.63576i	0.132677	+	0.181894i
$961$	−22.3160			−0.719872
$962$	1.46721	−	1.27623i	0.0473046	−	0.0411473i
$963$	−2.65263	+	4.59448i	−0.0854797	+	0.148055i
$964$	−12.8208	−	31.6753i	−0.412930	−	1.02019i
$965$	−7.19184	−	4.15221i	−0.231514	−	0.133664i
$966$	−35.4652	−	12.1992i	−1.14108	−	0.392503i
$967$	−12.7646	+	7.36965i	−0.410482	+	0.236992i	−0.690997	−	0.722858i	$-0.742828\pi$
$967$	−12.7646	+	7.36965i	−0.410482	+	0.236992i	0.280515	+	0.959850i	$0.409495\pi$
$968$	16.9696	+	26.0772i	0.545424	+	0.838152i
$969$	−12.1400	+	25.7718i	−0.389994	+	0.827908i
$970$	−6.98616	−	8.03156i	−0.224312	−	0.257878i
$971$	1.44266	+	2.49876i	0.0462971	+	0.0801889i	0.888245	−	0.459369i	$-0.151925\pi$
$971$	1.44266	+	2.49876i	0.0462971	+	0.0801889i	−0.841948	+	0.539558i	$0.818591\pi$
$972$	−29.8319	+	12.0746i	−0.956858	+	0.387294i
$973$	11.5912	−	20.0765i	0.371596	−	0.643624i
$974$	−17.5618	−	6.04084i	−0.562715	−	0.193561i
$975$	0.366917	+	0.211840i	0.0117508	+	0.00678431i
$976$	−6.54694	−	1.86842i	−0.209563	−	0.0598066i
$977$			11.3650i			0.363599i	0.983336	+	0.181800i	$0.0581922\pi$
$977$			11.3650i			0.363599i	−0.983336	+	0.181800i	$0.941808\pi$
$978$	1.92483	−	0.374776i	0.0615493	−	0.0119840i
$979$	−0.0209092	+	0.0362158i	−0.000668261	+	0.00115746i
$980$	4.71257	−	33.6850i	0.150538	−	1.07603i
$981$		−	40.5448i		−	1.29449i
$982$	25.5295	−	4.97075i	0.814681	−	0.158623i
$983$	6.00912	+	10.4081i	0.191661	+	0.331967i	0.945801	−	0.324747i	$-0.105279\pi$
$983$	6.00912	+	10.4081i	0.191661	+	0.331967i	−0.754140	+	0.656714i	$0.771946\pi$
$984$	−0.252823	−	4.73880i	−0.00805969	−	0.151067i
$985$	11.1546	+	19.3203i	0.355415	+	0.615596i
$986$	26.1568	−	76.0423i	0.833001	−	2.42168i
$987$	−4.94921			−0.157535
$988$	−1.91070	−	3.78047i	−0.0607876	−	0.120273i
$989$	−18.4957			−0.588128
$990$	0.00905782	−	0.0263327i	0.000287876	−	0.000836907i
$991$	21.5793	+	37.3765i	0.685490	+	1.18730i	0.973282	+	0.229611i	$0.0737455\pi$
$991$	21.5793	+	37.3765i	0.685490	+	1.18730i	−0.287792	+	0.957693i	$0.592921\pi$
$992$	1.42683	−	16.6088i	0.0453019	−	0.527329i
$993$	11.7472	+	20.3468i	0.372787	+	0.645686i
$994$	90.0664	−	17.5365i	2.85673	−	0.556223i
$995$		−	7.07370i		−	0.224251i
$996$	12.1071	+	1.69379i	0.383628	+	0.0536699i
$997$	−18.2090	+	31.5389i	−0.576685	+	0.998848i	0.419171	+	0.907907i	$0.362321\pi$
$997$	−18.2090	+	31.5389i	−0.576685	+	0.998848i	−0.995856	+	0.0909405i	$0.971013\pi$
$998$	2.71910	−	0.529424i	0.0860715	−	0.0167586i
$999$			12.9295i			0.409071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.a.31.19	yes	40
4.3	odd	2	inner	380.2.n.a.31.12	✓	40
19.8	odd	6	inner	380.2.n.a.331.12	yes	40
76.27	even	6	inner	380.2.n.a.331.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.a.31.12	✓	40	4.3	odd	2	inner
380.2.n.a.31.19	yes	40	1.1	even	1	trivial
380.2.n.a.331.12	yes	40	19.8	odd	6	inner
380.2.n.a.331.19	yes	40	76.27	even	6	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33731 + 0.460003i) q^{2} +(-0.435984 - 0.755146i) q^{3} +(1.57679 + 1.23033i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.235676 - 1.21042i) q^{6} -4.89965i q^{7} +(1.54270 + 2.37067i) q^{8} +(1.11984 - 1.93961i) q^{9} +O(q^{10})\)	\(q+(1.33731 + 0.460003i) q^{2} +(-0.435984 - 0.755146i) q^{3} +(1.57679 + 1.23033i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.235676 - 1.21042i) q^{6} -4.89965i q^{7} +(1.54270 + 2.37067i) q^{8} +(1.11984 - 1.93961i) q^{9} +(0.270280 + 1.38815i) q^{10} -0.00879181i q^{11} +(0.241625 - 1.72712i) q^{12} +(0.420792 + 0.242945i) q^{13} +(2.25385 - 6.55234i) q^{14} +(0.435984 - 0.755146i) q^{15} +(0.972557 + 3.87997i) q^{16} +(3.74761 + 6.49105i) q^{17} +(2.38980 - 2.07873i) q^{18} +(-4.34376 + 0.362980i) q^{19} +(-0.277103 + 1.98071i) q^{20} +(-3.69995 + 2.13617i) q^{21} +(0.00404426 - 0.0117574i) q^{22} +(5.37572 + 3.10367i) q^{23} +(1.11761 - 2.19854i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.450974 + 0.518458i) q^{26} -4.56882 q^{27} +(6.02820 - 7.72573i) q^{28} +(-6.57006 - 3.79323i) q^{29} +(0.930415 - 0.809310i) q^{30} -2.94686 q^{31} +(-0.484187 + 5.63609i) q^{32} +(-0.00663910 + 0.00383309i) q^{33} +(2.02581 + 10.4045i) q^{34} +(4.24322 - 2.44982i) q^{35} +(4.15212 - 1.68060i) q^{36} -2.82994i q^{37} +(-5.97592 - 1.51273i) q^{38} -0.423680i q^{39} +(-1.28171 + 2.52135i) q^{40} +(1.66637 - 0.962078i) q^{41} +(-5.93062 + 1.15473i) q^{42} +(-2.58045 + 1.48982i) q^{43} +(0.0108169 - 0.0138629i) q^{44} +2.23967 q^{45} +(5.76130 + 6.62342i) q^{46} +(1.00323 + 0.579216i) q^{47} +(2.50592 - 2.42603i) q^{48} -17.0065 q^{49} +(-1.06703 + 0.928142i) q^{50} +(3.26779 - 5.65998i) q^{51} +(0.364600 + 0.900789i) q^{52} +(-2.12792 - 1.22856i) q^{53} +(-6.10993 - 2.10167i) q^{54} +(0.00761393 - 0.00439590i) q^{55} +(11.6154 - 7.55870i) q^{56} +(2.16791 + 3.12192i) q^{57} +(-7.04131 - 8.09497i) q^{58} +(-5.18269 - 8.97669i) q^{59} +(1.61654 - 0.654304i) q^{60} +(-0.851042 + 1.47405i) q^{61} +(-3.94086 - 1.35556i) q^{62} +(-9.50342 - 5.48680i) q^{63} +(-3.24013 + 7.31448i) q^{64} +0.485889i q^{65} +(-0.0106418 + 0.00207201i) q^{66} +(-3.12293 + 5.40907i) q^{67} +(-2.07695 + 14.8459i) q^{68} -5.41260i q^{69} +(6.80142 - 1.32428i) q^{70} +(6.62115 + 11.4682i) q^{71} +(6.32575 - 0.337489i) q^{72} +(4.76690 + 8.25652i) q^{73} +(1.30178 - 3.78451i) q^{74} +0.871968 q^{75} +(-7.29580 - 4.77193i) q^{76} -0.0430768 q^{77} +(0.194894 - 0.566591i) q^{78} +(1.52767 + 2.64600i) q^{79} +(-2.87387 + 2.78224i) q^{80} +(-1.36757 - 2.36871i) q^{81} +(2.67101 - 0.520061i) q^{82} +7.01001i q^{83} +(-8.46226 - 1.18388i) q^{84} +(-3.74761 + 6.49105i) q^{85} +(-4.13618 + 0.805338i) q^{86} +6.61514i q^{87} +(0.0208425 - 0.0135632i) q^{88} +(-4.11926 - 2.37826i) q^{89} +(2.99514 + 1.03026i) q^{90} +(1.19034 - 2.06173i) q^{91} +(4.65785 + 11.5078i) q^{92} +(1.28478 + 2.22531i) q^{93} +(1.07519 + 1.23608i) q^{94} +(-2.48623 - 3.58032i) q^{95} +(4.46717 - 2.09161i) q^{96} +(-6.51860 + 3.76352i) q^{97} +(-22.7430 - 7.82306i) q^{98} +(-0.0170527 - 0.00984539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

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