LMFDB - Embedded newform 138.5.h.a.7.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,5,Mod(7,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("138.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	138.h (of order $22$, degree $10$, 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:	$14.2650549056$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.13
Character	$\chi$	$=$	138.7
Dual form			138.5.h.a.79.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85223 - 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-26.7504 + 12.2165i) q^{5} +(2.09159 - 14.5473i) q^{6} +(18.8860 + 64.3200i) q^{7} +(-19.0354 - 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +O(q^{10})$	\(q+(1.85223 - 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-26.7504 + 12.2165i) q^{5} +(2.09159 - 14.5473i) q^{6} +(18.8860 + 64.3200i) q^{7} +(-19.0354 - 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +(-23.4340 + 79.8088i) q^{10} +(-171.194 + 148.340i) q^{11} +(-27.2220 - 31.4159i) q^{12} +(267.146 + 78.4411i) q^{13} +(172.470 + 78.7646i) q^{14} +(-82.6142 + 128.550i) q^{15} +(-61.4076 + 18.0309i) q^{16} +(-82.5631 - 11.8708i) q^{17} +(-31.7242 - 69.4664i) q^{18} +(-18.4786 + 2.65683i) q^{19} +(127.193 + 197.916i) q^{20} +(263.247 + 228.105i) q^{21} +640.701i q^{22} +(121.909 + 514.761i) q^{23} -117.576 q^{24} +(157.052 - 181.248i) q^{25} +(662.488 - 425.755i) q^{26} +(-19.9662 - 138.868i) q^{27} +(487.820 - 222.780i) q^{28} +(112.790 - 784.469i) q^{29} +(121.767 + 414.699i) q^{30} +(-451.355 - 290.068i) q^{31} +(-75.1981 + 164.661i) q^{32} +(-331.611 + 1129.36i) q^{33} +(-178.300 + 154.498i) q^{34} +(-1290.97 - 1489.86i) q^{35} +(-207.250 - 60.8542i) q^{36} +(-767.998 - 350.733i) q^{37} +(-28.5474 + 44.4207i) q^{38} +(1388.13 - 407.592i) q^{39} +(658.652 + 94.6999i) q^{40} +(1122.64 + 2458.24i) q^{41} +(975.187 - 140.211i) q^{42} +(907.131 + 1411.52i) q^{43} +(1369.55 + 1186.72i) q^{44} +794.014i q^{45} +(1326.15 + 692.863i) q^{46} -2286.05 q^{47} +(-217.776 + 251.327i) q^{48} +(-1760.53 + 1131.42i) q^{49} +(-96.5363 - 671.424i) q^{50} +(-394.254 + 180.050i) q^{51} +(316.991 - 2204.72i) q^{52} +(879.759 + 2996.18i) q^{53} +(-333.824 - 214.536i) q^{54} +(2767.30 - 6059.55i) q^{55} +(427.343 - 1455.39i) q^{56} +(-73.3117 + 63.5249i) q^{57} +(-1467.96 - 1694.11i) q^{58} +(-1165.00 - 342.074i) q^{59} +(1111.99 + 507.830i) q^{60} +(604.982 - 941.370i) q^{61} +(-1456.06 + 427.536i) q^{62} +(1791.53 + 257.583i) q^{63} +(212.692 + 465.732i) q^{64} +(-8104.52 + 1165.25i) q^{65} +(1799.89 + 2800.68i) q^{66} +(-136.201 - 118.019i) q^{67} +667.297i q^{68} +(1978.99 + 1907.69i) q^{69} -5575.88 q^{70} +(2774.25 - 3201.66i) q^{71} +(-513.956 + 330.299i) q^{72} +(-31.2117 - 217.082i) q^{73} +(-2172.23 + 992.023i) q^{74} +(177.348 - 1233.49i) q^{75} +(42.0766 + 143.300i) q^{76} +(-12774.4 - 8209.62i) q^{77} +(1699.87 - 3722.19i) q^{78} +(900.902 - 3068.19i) q^{79} +(1422.40 - 1232.52i) q^{80} +(-477.393 - 550.941i) q^{81} +(7334.08 + 2153.48i) q^{82} +(-5399.02 - 2465.65i) q^{83} +(1506.55 - 2344.24i) q^{84} +(2353.61 - 691.083i) q^{85} +(4697.46 + 675.393i) q^{86} +(-1710.74 - 3745.99i) q^{87} +(5073.44 - 729.450i) q^{88} +(-8391.26 - 13057.1i) q^{89} +(1697.27 + 1470.69i) q^{90} +18664.2i q^{91} +(3937.38 - 1551.41i) q^{92} -2787.87 q^{93} +(-4234.27 + 4886.61i) q^{94} +(461.854 - 296.815i) q^{95} +(133.862 + 931.030i) q^{96} +(538.971 - 246.140i) q^{97} +(-842.386 + 5858.92i) q^{98} +(1723.10 + 5868.35i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) $ 160 * q - 128 * q^4 - 432 * q^9	$ 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) $ 160 * q - 128 * q^4 - 432 * q^9 + 208 * q^13 - 1024 * q^16 - 1980 * q^17 - 3828 * q^19 - 3168 * q^20 + 3120 * q^23 + 9768 * q^25 + 4416 * q^26 + 5280 * q^28 - 828 * q^29 - 7748 * q^31 + 16464 * q^35 - 3456 * q^36 - 3520 * q^37 - 9072 * q^39 - 5472 * q^41 - 7216 * q^43 - 1280 * q^46 + 6960 * q^47 + 13888 * q^49 - 7296 * q^50 + 17424 * q^51 + 1664 * q^52 + 14784 * q^53 + 37316 * q^55 - 15840 * q^57 - 9984 * q^58 - 29808 * q^59 - 44968 * q^61 - 8192 * q^64 - 5852 * q^67 - 10584 * q^69 + 4352 * q^70 + 30048 * q^71 + 17084 * q^73 + 4176 * q^75 - 14160 * q^77 - 6912 * q^78 + 28424 * q^79 - 11664 * q^81 - 128 * q^82 - 35904 * q^83 - 91892 * q^85 + 8064 * q^87 - 15312 * q^89 - 6720 * q^92 + 11952 * q^93 + 21248 * q^94 + 224268 * q^95 + 41712 * q^97 + 62976 * q^98 + 17820 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	1.85223	−	2.13758i	0.463056	−	0.534396i
$2$	1.85223	−	2.13758i	0.463056	−	0.534396i
$3$	4.37128	−	2.80925i	0.485698	−	0.312139i
$3$	4.37128	−	2.80925i	0.485698	−	0.312139i
$4$	−1.13852	−	7.91857i	−0.0711574	−	0.494911i
$5$	−26.7504	+	12.2165i	−1.07002	+	0.488660i	−0.870973	−	0.491331i	$-0.836510\pi$
$5$	−26.7504	+	12.2165i	−1.07002	+	0.488660i	−0.199042	+	0.979991i	$0.563783\pi$
$6$	2.09159	−	14.5473i	0.0580998	−	0.404093i
$7$	18.8860	+	64.3200i	0.385430	+	1.31265i	0.892617	+	0.450817i	$0.148867\pi$
$7$	18.8860	+	64.3200i	0.385430	+	1.31265i	−0.507187	+	0.861836i	$0.669315\pi$
$8$	−19.0354	−	12.2333i	−0.297428	−	0.191145i
$9$	11.2162	−	24.5601i	0.138472	−	0.303211i
$10$	−23.4340	+	79.8088i	−0.234340	+	0.798088i
$11$	−171.194	+	148.340i	−1.41483	+	1.22595i	−0.476973	+	0.878918i	$0.658266\pi$
$11$	−171.194	+	148.340i	−1.41483	+	1.22595i	−0.937852	+	0.347035i	$0.887188\pi$
$12$	−27.2220	−	31.4159i	−0.189042	−	0.218166i
$13$	267.146	+	78.4411i	1.58074	+	0.464148i	0.950106	−	0.311929i	$-0.100975\pi$
$13$	267.146	+	78.4411i	1.58074	+	0.464148i	0.630638	+	0.776077i	$0.282793\pi$
$14$	172.470	+	78.7646i	0.879951	+	0.401860i
$15$	−82.6142	+	128.550i	−0.367174	+	0.571335i
$16$	−61.4076	+	18.0309i	−0.239873	+	0.0704331i
$17$	−82.5631	−	11.8708i	−0.285685	−	0.0410754i	−0.00201756	−	0.999998i	$-0.500642\pi$
$17$	−82.5631	−	11.8708i	−0.285685	−	0.0410754i	−0.283668	+	0.958923i	$0.591551\pi$
$18$	−31.7242	−	69.4664i	−0.0979143	−	0.214402i
$19$	−18.4786	+	2.65683i	−0.0511874	+	0.00735963i	−0.167861	−	0.985811i	$-0.553686\pi$
$19$	−18.4786	+	2.65683i	−0.0511874	+	0.00735963i	0.116674	+	0.993170i	$0.462777\pi$
$20$	127.193	+	197.916i	0.317982	+	0.494790i
$21$	263.247	+	228.105i	0.596933	+	0.517245i
$22$			640.701i			1.32376i
$23$	121.909	+	514.761i	0.230452	+	0.973084i
$23$	121.909	+	514.761i	0.230452	+	0.973084i
$24$	−117.576			−0.204124
$25$	157.052	−	181.248i	0.251284	−	0.289997i
$26$	662.488	−	425.755i	0.980012	−	0.629816i
$27$	−19.9662	−	138.868i	−0.0273885	−	0.190491i
$28$	487.820	−	222.780i	0.622220	−	0.284158i
$29$	112.790	−	784.469i	0.134114	−	0.932781i	−0.805999	−	0.591917i	$-0.798371\pi$
$29$	112.790	−	784.469i	0.134114	−	0.932781i	0.940113	−	0.340864i	$-0.110720\pi$
$30$	121.767	+	414.699i	0.135296	+	0.460777i
$31$	−451.355	−	290.068i	−0.469672	−	0.301840i	0.284313	−	0.958731i	$-0.408234\pi$
$31$	−451.355	−	290.068i	−0.469672	−	0.301840i	−0.753985	+	0.656892i	$0.771871\pi$
$32$	−75.1981	+	164.661i	−0.0734357	+	0.160802i
$33$	−331.611	+	1129.36i	−0.304510	+	1.03707i
$34$	−178.300	+	154.498i	−0.154239	+	0.133649i
$35$	−1290.97	−	1489.86i	−1.05386	−	1.21621i
$36$	−207.250	−	60.8542i	−0.159915	−	0.0469554i
$37$	−767.998	−	350.733i	−0.560992	−	0.256197i	0.114675	−	0.993403i	$-0.463417\pi$
$37$	−767.998	−	350.733i	−0.560992	−	0.256197i	−0.675668	+	0.737207i	$0.736144\pi$
$38$	−28.5474	+	44.4207i	−0.0197697	+	0.0307622i
$39$	1388.13	−	407.592i	0.912643	−	0.267976i
$40$	658.652	+	94.6999i	0.411658	+	0.0591874i
$41$	1122.64	+	2458.24i	0.667842	+	1.46237i	0.875030	+	0.484068i	$0.160841\pi$
$41$	1122.64	+	2458.24i	0.667842	+	1.46237i	−0.207189	+	0.978301i	$0.566431\pi$
$42$	975.187	−	140.211i	0.552827	−	0.0794845i
$43$	907.131	+	1411.52i	0.490606	+	0.763398i	0.994979	−	0.100088i	$-0.0319124\pi$
$43$	907.131	+	1411.52i	0.490606	+	0.763398i	−0.504372	+	0.863486i	$0.668276\pi$
$44$	1369.55	+	1186.72i	0.707413	+	0.612977i
$45$			794.014i			0.392106i
$46$	1326.15	+	692.863i	0.626724	+	0.327440i
$47$	−2286.05			−1.03488			−0.517439	−	0.855720i	$-0.673115\pi$
$47$	−2286.05			−1.03488			−0.517439	+	0.855720i	$0.673115\pi$
$48$	−217.776	+	251.327i	−0.0945210	+	0.109083i
$49$	−1760.53	+	1131.42i	−0.733247	+	0.471229i
$50$	−96.5363	−	671.424i	−0.0386145	−	0.268570i
$51$	−394.254	+	180.050i	−0.151578	+	0.0692234i
$52$	316.991	−	2204.72i	0.117230	−	0.815355i
$53$	879.759	+	2996.18i	0.313193	+	1.06664i	0.954217	+	0.299116i	$0.0966918\pi$
$53$	879.759	+	2996.18i	0.313193	+	1.06664i	−0.641024	+	0.767521i	$0.721490\pi$
$54$	−333.824	−	214.536i	−0.114480	−	0.0735719i
$55$	2767.30	−	6059.55i	0.914811	−	2.00316i
$56$	427.343	−	1455.39i	0.136270	−	0.464093i
$57$	−73.3117	+	63.5249i	−0.0225644	+	0.0195521i
$58$	−1467.96	−	1694.11i	−0.436372	−	0.503600i
$59$	−1165.00	−	342.074i	−0.334673	−	0.0982690i	0.110078	−	0.993923i	$-0.464890\pi$
$59$	−1165.00	−	342.074i	−0.334673	−	0.0982690i	−0.444752	+	0.895654i	$0.646708\pi$
$60$	1111.99	+	507.830i	0.308887	+	0.141064i
$61$	604.982	−	941.370i	0.162586	−	0.252989i	−0.750396	−	0.660988i	$-0.770137\pi$
$61$	604.982	−	941.370i	0.162586	−	0.252989i	0.912982	+	0.408000i	$0.133774\pi$
$62$	−1456.06	+	427.536i	−0.378786	+	0.111222i
$63$	1791.53	+	257.583i	0.451381	+	0.0648988i
$64$	212.692	+	465.732i	0.0519269	+	0.113704i
$65$	−8104.52	+	1165.25i	−1.91823	+	0.275800i
$66$	1799.89	+	2800.68i	0.413198	+	0.642948i
$67$	−136.201	−	118.019i	−0.0303410	−	0.0262907i	0.639558	−	0.768743i	$-0.279117\pi$
$67$	−136.201	−	118.019i	−0.0303410	−	0.0262907i	−0.669899	+	0.742452i	$0.733663\pi$
$68$			667.297i			0.144312i
$69$	1978.99	+	1907.69i	0.415668	+	0.400692i
$70$	−5575.88			−1.13793
$71$	2774.25	−	3201.66i	0.550337	−	0.635123i	−0.410624	−	0.911805i	$-0.634689\pi$
$71$	2774.25	−	3201.66i	0.550337	−	0.635123i	0.960962	+	0.276682i	$0.0892347\pi$
$72$	−513.956	+	330.299i	−0.0991427	+	0.0637151i
$73$	−31.2117	−	217.082i	−0.00585695	−	0.0407360i	0.986683	−	0.162653i	$-0.0520050\pi$
$73$	−31.2117	−	217.082i	−0.00585695	−	0.0407360i	−0.992540	+	0.121917i	$0.961096\pi$
$74$	−2172.23	+	992.023i	−0.396681	+	0.181158i
$75$	177.348	−	1233.49i	0.0315286	−	0.219286i
$76$	42.0766	+	143.300i	0.00728472	+	0.0248095i
$77$	−12774.4	−	8209.62i	−2.15457	−	1.38466i
$78$	1699.87	−	3722.19i	0.279400	−	0.611800i
$79$	900.902	−	3068.19i	0.144352	−	0.491619i	−0.855296	−	0.518140i	$-0.826625\pi$
$79$	900.902	−	3068.19i	0.144352	−	0.491619i	0.999648	+	0.0265211i	$0.00844290\pi$
$80$	1422.40	−	1232.52i	0.222250	−	0.192581i
$81$	−477.393	−	550.941i	−0.0727623	−	0.0839722i
$82$	7334.08	+	2153.48i	1.09073	+	0.320268i
$83$	−5399.02	−	2465.65i	−0.783715	−	0.357911i	−0.0169649	−	0.999856i	$-0.505400\pi$
$83$	−5399.02	−	2465.65i	−0.783715	−	0.357911i	−0.766750	+	0.641945i	$0.778128\pi$
$84$	1506.55	−	2344.24i	0.213514	−	0.332234i
$85$	2353.61	−	691.083i	0.325760	−	0.0956516i
$86$	4697.46	+	675.393i	0.635135	+	0.0913187i
$87$	−1710.74	−	3745.99i	−0.226019	−	0.494912i
$88$	5073.44	−	729.450i	0.655144	−	0.0941955i
$89$	−8391.26	−	13057.1i	−1.05937	−	1.64841i	−0.698188	−	0.715915i	$-0.746010\pi$
$89$	−8391.26	−	13057.1i	−1.05937	−	1.64841i	−0.361181	−	0.932496i	$-0.617626\pi$
$90$	1697.27	+	1470.69i	0.209539	+	0.181567i
$91$			18664.2i			2.25386i
$92$	3937.38	−	1551.41i	0.465191	−	0.183295i
$93$	−2787.87			−0.322335
$94$	−4234.27	+	4886.61i	−0.479207	+	0.553035i
$95$	461.854	−	296.815i	0.0511749	−	0.0328881i
$96$	133.862	+	931.030i	0.0145249	+	0.101023i
$97$	538.971	−	246.140i	0.0572825	−	0.0261601i	−0.386568	−	0.922261i	$-0.626339\pi$
$97$	538.971	−	246.140i	0.0572825	−	0.0261601i	0.443850	+	0.896101i	$0.353612\pi$
$98$	−842.386	+	5858.92i	−0.0877120	+	0.610050i
$99$	1723.10	+	5868.35i	0.175809	+	0.598750i
$100$	−1614.03	−	1037.28i	−0.161403	−	0.103728i
$101$	2129.84	−	4663.71i	0.208788	−	0.457182i	−0.776047	−	0.630675i	$-0.782778\pi$
$101$	2129.84	−	4663.71i	0.208788	−	0.457182i	0.984835	+	0.173493i	$0.0555055\pi$
$102$	−345.377	+	1176.24i	−0.0331965	+	0.113057i
$103$	−9929.66	+	8604.10i	−0.935966	+	0.811019i	−0.982186	−	0.187912i	$-0.939828\pi$
$103$	−9929.66	+	8604.10i	−0.935966	+	0.811019i	0.0462199	+	0.998931i	$0.485283\pi$
$104$	−4125.63	−	4761.23i	−0.381438	−	0.440203i
$105$	−9828.61	−	2885.94i	−0.891484	−	0.261763i
$106$	8034.10	+	3669.05i	0.715032	+	0.326544i
$107$	−466.336	+	725.632i	−0.0407316	+	0.0633796i	−0.861022	−	0.508567i	$-0.830175\pi$
$107$	−466.336	+	725.632i	−0.0407316	+	0.0633796i	0.820291	+	0.571947i	$0.193812\pi$
$108$	−1076.91	+	316.208i	−0.0923273	+	0.0271097i
$109$	15274.8	+	2196.19i	1.28565	+	0.184849i	0.751044	−	0.660252i	$-0.229551\pi$
$109$	15274.8	+	2196.19i	1.28565	+	0.184849i	0.534607	+	0.845101i	$0.320460\pi$
$110$	−7827.11	−	17139.0i	−0.646869	−	1.41645i
$111$	−4342.43	+	624.348i	−0.352442	+	0.0506735i
$112$	−2319.49	−	3609.20i	−0.184908	−	0.287723i
$113$	9914.09	+	8590.61i	0.776419	+	0.672771i	0.950070	−	0.312036i	$-0.101011\pi$
$113$	9914.09	+	8590.61i	0.776419	+	0.672771i	−0.173651	+	0.984807i	$0.555557\pi$
$114$			274.372i			0.0211121i
$115$	−9549.69	−	12280.8i	−0.722094	−	0.928602i
$116$	−6340.29			−0.471187
$117$	4922.88	−	5681.30i	0.359623	−	0.415027i
$118$	−2889.05	+	1856.68i	−0.207487	+	0.133344i
$119$	−795.762	−	5534.65i	−0.0561939	−	0.390837i
$120$	3145.19	−	1436.36i	0.218416	−	0.0997472i
$121$	5218.85	−	36297.9i	0.356455	−	2.47920i
$122$	−891.694	−	3036.83i	−0.0599095	−	0.204033i
$123$	11813.2	+	7591.89i	0.780832	+	0.501810i
$124$	−1783.05	+	3904.33i	−0.115963	+	0.253924i
$125$	3191.24	−	10868.3i	0.204239	−	0.695574i
$126$	3868.93	−	3352.45i	0.243697	−	0.211164i
$127$	17330.7	+	20000.7i	1.07451	+	1.24005i	0.969374	+	0.245590i	$0.0789817\pi$
$127$	17330.7	+	20000.7i	1.07451	+	1.24005i	0.105134	+	0.994458i	$0.466473\pi$
$128$	1389.49	+	407.992i	0.0848080	+	0.0249019i
$129$	7930.65	+	3621.81i	0.476573	+	0.217644i
$130$	−12520.6	+	19482.4i	−0.740863	+	1.15280i
$131$	28258.7	−	8297.51i	1.64668	−	0.483510i	0.678677	−	0.734437i	$-0.262554\pi$
$131$	28258.7	−	8297.51i	1.64668	−	0.483510i	0.968006	+	0.250927i	$0.0807355\pi$
$132$	9320.50	+	1340.08i	0.534923	+	0.0769103i
$133$	−519.876	−	1138.37i	−0.0293898	−	0.0643546i
$134$	−504.550	+	72.5433i	−0.0280992	+	0.00404006i
$135$	2230.58	+	3470.86i	0.122391	+	0.190445i
$136$	1426.40	+	1235.98i	0.0771195	+	0.0668244i
$137$			28451.5i			1.51588i	0.652325	+	0.757940i	$0.273794\pi$
$137$			28451.5i			1.51588i	−0.652325	+	0.757940i	$0.726206\pi$
$138$	7743.39	−	696.786i	0.406605	−	0.0365882i
$139$	29755.2			1.54005			0.770023	−	0.638016i	$-0.220244\pi$
$139$	29755.2			1.54005			0.770023	+	0.638016i	$0.220244\pi$
$140$	−10327.8	+	11918.9i	−0.526928	+	0.608107i
$141$	−9992.95	+	6422.08i	−0.502638	+	0.323026i
$142$	−1705.26	−	11860.4i	−0.0845698	−	0.588196i
$143$	−57369.7	+	26199.9i	−2.80550	+	1.28123i
$144$	−245.920	+	1710.41i	−0.0118596	+	0.0824851i
$145$	6566.29	+	22362.7i	0.312309	+	1.06363i
$146$	−521.842	−	335.367i	−0.0244812	−	0.0157331i
$147$	−4517.31	+	9891.53i	−0.209048	+	0.457750i
$148$	−1902.92	+	6480.76i	−0.0868757	+	0.295871i
$149$	10106.7	−	8757.54i	0.455238	−	0.394466i	−0.396834	−	0.917890i	$-0.629891\pi$
$149$	10106.7	−	8757.54i	0.455238	−	0.394466i	0.852072	+	0.523424i	$0.175346\pi$
$150$	−2308.19	−	2663.79i	−0.102586	−	0.118391i
$151$	−10012.3	−	2939.88i	−0.439117	−	0.128936i	0.0546987	−	0.998503i	$-0.482580\pi$
$151$	−10012.3	−	2939.88i	−0.439117	−	0.128936i	−0.493816	+	0.869566i	$0.664398\pi$
$152$	384.250	+	175.481i	0.0166313	+	0.00759527i
$153$	−1217.59	+	1894.61i	−0.0520138	+	0.0809351i
$154$	−41209.9	+	12100.3i	−1.73764	+	0.510217i
$155$	15617.5	+	2245.46i	0.650053	+	0.0934635i
$156$	−4807.96	−	10528.0i	−0.197566	−	0.432608i
$157$	39167.5	−	5631.44i	1.58901	−	0.228465i	0.709626	−	0.704578i	$-0.248864\pi$
$157$	39167.5	−	5631.44i	1.58901	−	0.228465i	0.879384	+	0.476113i	$0.157955\pi$
$158$	−4889.84	−	7608.74i	−0.195876	−	0.304788i
$159$	12262.7	+	10625.7i	0.485056	+	0.420304i
$160$		−	5323.40i		−	0.207945i
$161$	−30807.0	+	17563.0i	−1.18850	+	0.677559i
$162$	−2061.92			−0.0785674
$163$	−21092.9	+	24342.6i	−0.793893	+	0.916201i	−0.998030	−	0.0627411i	$-0.980016\pi$
$163$	−21092.9	+	24342.6i	−0.793893	+	0.916201i	0.204137	+	0.978942i	$0.434561\pi$
$164$	18187.6	−	11688.5i	0.676220	−	0.434580i
$165$	−4926.14	−	34262.0i	−0.180942	−	1.25848i
$166$	−15270.7	+	6973.91i	−0.554171	+	0.253081i
$167$	−1571.79	+	10932.1i	−0.0563589	+	0.391985i	0.942044	+	0.335489i	$0.108902\pi$
$167$	−1571.79	+	10932.1i	−0.0563589	+	0.391985i	−0.998403	+	0.0564953i	$0.982007\pi$
$168$	−2220.54	−	7562.45i	−0.0786755	−	0.267944i
$169$	41186.8	+	26469.1i	1.44206	+	0.926758i
$170$	2882.18	−	6311.08i	0.0997293	−	0.218377i
$171$	−142.008	+	483.636i	−0.00485648	+	0.0165397i
$172$	10144.5	−	8790.23i	0.342904	−	0.297128i
$173$	32654.2	+	37685.0i	1.09106	+	1.25915i	0.963614	+	0.267299i	$0.0861312\pi$
$173$	32654.2	+	37685.0i	1.09106	+	1.25915i	0.127442	+	0.991846i	$0.459323\pi$
$174$	−11176.0	−	3281.58i	−0.369138	−	0.108389i
$175$	14624.0	+	6678.54i	0.477517	+	0.218075i
$176$	7837.89	−	12196.0i	0.253031	−	0.393724i
$177$	−6053.51	+	1777.47i	−0.193224	+	0.0567356i
$178$	−43453.1	−	6247.61i	−1.37145	−	0.197185i
$179$	3925.13	+	8594.84i	0.122503	+	0.268245i	0.960941	−	0.276752i	$-0.0892581\pi$
$179$	3925.13	+	8594.84i	0.122503	+	0.268245i	−0.838438	+	0.544997i	$0.816531\pi$
$180$	6287.45	−	903.999i	0.194057	−	0.0279012i
$181$	−10144.5	−	15785.2i	−0.309653	−	0.481829i	0.651193	−	0.758912i	$-0.274269\pi$
$181$	−10144.5	−	15785.2i	−0.309653	−	0.481829i	−0.960846	+	0.277083i	$0.910632\pi$
$182$	39896.4	+	34570.4i	1.20446	+	1.04367i
$183$		−	5814.54i		−	0.173625i
$184$	3976.64	−	11290.0i	0.117457	−	0.333472i
$185$	24829.0			0.725463
$186$	−5163.77	+	5959.31i	−0.149259	+	0.172254i
$187$	15895.2	−	10215.2i	0.454551	−	0.292122i
$188$	2602.71	+	18102.2i	0.0736393	+	0.512172i
$189$	8554.91	−	3906.90i	0.239492	−	0.109373i
$190$	220.990	−	1537.02i	0.00612161	−	0.0425767i
$191$	−15690.7	−	53437.8i	−0.430107	−	1.46481i	−0.834900	−	0.550402i	$-0.814474\pi$
$191$	−15690.7	−	53437.8i	−0.430107	−	1.46481i	0.404792	−	0.914409i	$-0.367344\pi$
$192$	2238.10	+	1438.34i	0.0607122	+	0.0390174i
$193$	22777.0	−	49874.6i	0.611479	−	1.33895i	−0.310079	−	0.950711i	$-0.600356\pi$
$193$	22777.0	−	49874.6i	0.611479	−	1.33895i	0.921558	−	0.388241i	$-0.126917\pi$
$194$	472.152	−	1608.00i	0.0125452	−	0.0427251i
$195$	−32153.7	+	27861.3i	−0.845593	+	0.732710i
$196$	10963.6	+	12652.7i	0.285393	+	0.329361i
$197$	−52012.1	−	15272.1i	−1.34021	−	0.393520i	−0.468463	−	0.883483i	$-0.655192\pi$
$197$	−52012.1	−	15272.1i	−1.34021	−	0.393520i	−0.871743	+	0.489963i	$0.837010\pi$
$198$	15735.7	+	7186.23i	0.401379	+	0.183304i
$199$	−21889.5	+	34060.7i	−0.552750	+	0.860096i	−0.999401	−	0.0346123i	$-0.988980\pi$
$199$	−21889.5	+	34060.7i	−0.552750	+	0.860096i	0.446651	+	0.894708i	$0.352617\pi$
$200$	−5206.81	+	1528.86i	−0.130170	+	0.0382215i
$201$	−926.917	−	133.271i	−0.0229429	−	0.00329869i
$202$	−6024.11	−	13191.0i	−0.147635	−	0.323276i
$203$	52587.2	−	7560.89i	1.27611	−	0.183477i
$204$	1874.60	+	2916.94i	0.0450453	+	0.0700918i
$205$	−60062.2	−	52044.2i	−1.42920	−	1.23841i
$206$			37162.2i			0.875724i
$207$	14009.9	+	2779.57i	0.326960	+	0.0648689i
$208$	−17819.1			−0.411870
$209$	2769.32	−	3195.96i	0.0633986	−	0.0731659i
$210$	−24373.7	+	15664.0i	−0.552692	+	0.355194i
$211$	5814.37	+	40439.8i	0.130598	+	0.908331i	0.944776	+	0.327716i	$0.106279\pi$
$211$	5814.37	+	40439.8i	0.130598	+	0.908331i	−0.814178	+	0.580615i	$0.802812\pi$
$212$	22723.9	−	10377.6i	0.505604	−	0.230902i
$213$	3132.77	−	21788.9i	0.0690509	−	0.480260i
$214$	687.340	+	2340.87i	0.0150087	+	0.0511151i
$215$	−41510.0	−	26676.8i	−0.897998	−	0.577108i
$216$	−1318.75	+	2887.66i	−0.0282654	+	0.0618926i
$217$	10132.9	−	34509.4i	0.215185	−	0.732854i
$218$	32986.9	−	28583.3i	0.694111	−	0.601451i
$219$	−746.273	−	861.245i	−0.0155600	−	0.0179572i
$220$	−51133.6	−	15014.2i	−1.05648	−	0.310210i
$221$	−21125.2	−	9647.56i	−0.432530	−	0.197530i
$222$	−6708.57	+	10438.7i	−0.136121	+	0.211808i
$223$	−17868.3	+	5246.61i	−0.359314	+	0.105504i	−0.456407	−	0.889771i	$-0.650864\pi$
$223$	−17868.3	+	5246.61i	−0.359314	+	0.105504i	0.0970930	+	0.995275i	$0.469046\pi$
$224$	−12011.2	−	1726.95i	−0.239381	−	0.0344178i
$225$	−2689.93	−	5890.13i	−0.0531345	−	0.116348i
$226$	36726.3	−	5280.44i	0.719052	−	0.103384i
$227$	39255.8	+	61083.3i	0.761821	+	1.18542i	0.977907	+	0.209042i	$0.0670344\pi$
$227$	39255.8	+	61083.3i	0.761821	+	1.18542i	−0.216086	+	0.976374i	$0.569329\pi$
$228$	586.493	+	508.199i	0.0112822	+	0.00977607i
$229$		−	16857.5i		−	0.321456i	−0.986999	−	0.160728i	$-0.948616\pi$
$229$		−	16857.5i		−	0.321456i	0.986999	−	0.160728i	$-0.0513842\pi$
$230$	−43939.3	−	2333.47i	−0.830611	−	0.0441110i
$231$	−78903.5			−1.47867
$232$	−11743.6	+	13552.9i	−0.218186	+	0.251800i
$233$	32341.6	−	20784.7i	0.595730	−	0.382852i	−0.207752	−	0.978182i	$-0.566615\pi$
$233$	32341.6	−	20784.7i	0.595730	−	0.382852i	0.803482	+	0.595329i	$0.202978\pi$
$234$	−3025.97	−	21046.1i	−0.0552629	−	0.384362i
$235$	61152.6	−	27927.5i	1.10734	−	0.505703i
$236$	−1382.37	+	9614.58i	−0.0248199	+	0.172626i
$237$	−4681.23	−	15942.8i	−0.0833418	−	0.283836i
$238$	−13304.7	−	8550.41i	−0.234883	−	0.150950i
$239$	−7499.67	+	16422.0i	−0.131294	+	0.287495i	−0.963849	−	0.266448i	$-0.914150\pi$
$239$	−7499.67	+	16422.0i	−0.131294	+	0.287495i	0.832555	+	0.553943i	$0.186877\pi$
$240$	2755.26	−	9383.57i	0.0478344	−	0.162909i
$241$	29008.8	−	25136.2i	0.499454	−	0.432779i	−0.368349	−	0.929687i	$-0.620077\pi$
$241$	29008.8	−	25136.2i	0.499454	−	0.432779i	0.867803	+	0.496908i	$0.165532\pi$
$242$	−67923.3	−	78387.7i	−1.15981	−	1.33850i
$243$	−3634.55	−	1067.20i	−0.0615515	−	0.0180732i
$244$	−8143.09	−	3718.83i	−0.136776	−	0.0624635i
$245$	33272.8	−	51773.4i	0.554315	−	0.862531i
$246$	38109.0	−	11189.8i	0.629734	−	0.184907i
$247$	−5144.89	−	739.724i	−0.0843301	−	0.0121248i
$248$	5043.22	+	11043.1i	0.0819983	+	0.179551i
$249$	−30527.2	+	4389.16i	−0.492367	+	0.0707917i
$250$	−17321.1	−	26952.2i	−0.277138	−	0.431235i
$251$	36056.2	+	31242.9i	0.572312	+	0.495911i	0.892259	−	0.451524i	$-0.149120\pi$
$251$	36056.2	+	31242.9i	0.572312	+	0.495911i	−0.319947	+	0.947436i	$0.603665\pi$
$252$		−	14479.6i		−	0.228012i
$253$	−97230.0	−	70039.9i	−1.51900	−	1.09422i
$254$	74853.7			1.16023
$255$	8346.88	−	9632.81i	0.128364	−	0.148140i
$256$	3445.77	−	2214.46i	0.0525783	−	0.0337901i
$257$	10385.3	+	72231.7i	0.157237	+	1.09361i	0.903696	+	0.428175i	$0.140843\pi$
$257$	10385.3	+	72231.7i	0.157237	+	1.09361i	−0.746459	+	0.665432i	$0.768247\pi$
$258$	22431.3	−	10244.0i	0.336988	−	0.153897i
$259$	8054.69	−	56021.6i	0.120074	−	0.835133i
$260$	18454.3	+	62849.6i	0.272993	+	0.929728i
$261$	−18001.5	−	11568.9i	−0.264258	−	0.169828i
$262$	34604.9	−	75774.2i	0.504122	−	1.10387i
$263$	17796.2	−	60608.2i	0.257286	−	0.876234i	−0.724985	−	0.688765i	$-0.758153\pi$
$263$	17796.2	−	60608.2i	0.257286	−	0.876234i	0.982270	−	0.187469i	$-0.0600285\pi$
$264$	20128.2	−	17441.2i	0.288800	−	0.250247i
$265$	−60136.7	−	69401.5i	−0.856344	−	0.988273i
$266$	−3396.28	−	997.239i	−0.0480000	−	0.0140941i
$267$	−73361.1	−	33502.9i	−1.02907	−	0.469959i
$268$	−779.473	+	1212.88i	−0.0108525	+	0.0168869i
$269$	66754.0	−	19600.7i	0.922513	−	0.270874i	0.214214	−	0.976787i	$-0.431281\pi$
$269$	66754.0	−	19600.7i	0.922513	−	0.270874i	0.708299	+	0.705913i	$0.249463\pi$
$270$	11550.8	+	1660.75i	0.158447	+	0.0227812i
$271$	32558.1	+	71292.3i	0.443323	+	0.970743i	0.990976	+	0.134037i	$0.0427942\pi$
$271$	32558.1	+	71292.3i	0.443323	+	0.970743i	−0.547653	+	0.836706i	$0.684479\pi$
$272$	5284.04	−	759.730i	0.0714213	−	0.0102688i
$273$	52432.6	+	81586.7i	0.703519	+	1.09470i
$274$	60817.5	+	52698.7i	0.810079	+	0.701938i
$275$			54325.7i			0.718357i
$276$	12853.1	−	17842.7i	0.168729	−	0.234231i
$277$	−142909.			−1.86252			−0.931259	−	0.364358i	$-0.881288\pi$
$277$	−142909.			−1.86252			−0.931259	+	0.364358i	$0.881288\pi$
$278$	55113.4	−	63604.3i	0.713129	−	0.822994i
$279$	−12186.6	+	7831.84i	−0.156557	+	0.100613i
$280$	6348.24	+	44153.0i	0.0809725	+	0.563176i
$281$	31729.6	−	14490.4i	0.401839	−	0.183514i	−0.204235	−	0.978922i	$-0.565471\pi$
$281$	31729.6	−	14490.4i	0.401839	−	0.183514i	0.606074	+	0.795408i	$0.292744\pi$
$282$	−4781.48	+	33255.9i	−0.0601262	+	0.418187i
$283$	−44474.0	−	151464.i	−0.555307	−	1.89120i	−0.440336	−	0.897833i	$-0.645141\pi$
$283$	−44474.0	−	151464.i	−0.555307	−	1.89120i	−0.114971	−	0.993369i	$-0.536678\pi$
$284$	−28511.1	−	18323.0i	−0.353490	−	0.227174i
$285$	1185.06	−	2594.93i	0.0145899	−	0.0319474i
$286$	−50257.2	+	171160.i	−0.614422	+	2.09253i
$287$	−136912.	+	118635.i	−1.66218	+	1.44028i
$288$	3200.65	+	3693.74i	0.0385880	+	0.0445330i
$289$	−73462.1	−	21570.4i	−0.879564	−	0.258263i
$290$	59964.4	+	27384.8i	0.713014	+	0.325622i
$291$	1664.53	−	2590.05i	0.0196564	−	0.0305860i
$292$	−1683.44	+	494.304i	−0.0197439	+	0.00579734i
$293$	28338.6	+	4074.47i	0.330098	+	0.0474609i	0.305371	−	0.952233i	$-0.401219\pi$
$293$	28338.6	+	4074.47i	0.330098	+	0.0474609i	0.0247266	+	0.999694i	$0.492128\pi$
$294$	12776.9	+	27977.5i	0.147819	+	0.323678i
$295$	35343.1	−	5081.57i	0.406126	−	0.0583921i
$296$	10328.5	+	16071.5i	0.117884	+	0.183431i
$297$	24017.8	+	20811.6i	0.272283	+	0.235935i
$298$		−	37824.9i		−	0.425937i
$299$	−7810.87	+	147079.i	−0.0873690	+	1.64516i
$300$	−9969.36			−0.110771
$301$	−73657.0	+	85004.8i	−0.812983	+	0.938232i
$302$	−24829.3	+	15956.8i	−0.272239	+	0.174957i
$303$	−3791.38	−	26369.7i	−0.0412964	−	0.287223i
$304$	1086.82	−	496.336i	0.0117601	−	0.00537067i
$305$	−4683.26	+	32572.8i	−0.0503441	+	0.350151i
$306$	1794.63	+	6111.95i	0.0191660	+	0.0652735i
$307$	57311.9	+	36832.1i	0.608090	+	0.390796i	0.808140	−	0.588990i	$-0.200474\pi$
$307$	57311.9	+	36832.1i	0.608090	+	0.390796i	−0.200051	+	0.979786i	$0.564111\pi$
$308$	−50464.6	+	110502.i	−0.531967	+	1.16485i
$309$	−19234.3	+	65505.9i	−0.201446	+	0.686062i
$310$	33727.0	−	29224.6i	0.350958	−	0.304107i
$311$	−13081.4	−	15096.7i	−0.135248	−	0.156085i	0.684085	−	0.729402i	$-0.260202\pi$
$311$	−13081.4	−	15096.7i	−0.135248	−	0.156085i	−0.819333	+	0.573317i	$0.805656\pi$
$312$	−31409.8	−	9222.75i	−0.322668	−	0.0947439i
$313$	139826.	+	63856.3i	1.42725	+	0.651801i	0.971224	−	0.238168i	$-0.0765468\pi$
$313$	139826.	+	63856.3i	1.42725	+	0.651801i	0.456021	+	0.889969i	$0.349274\pi$
$314$	60509.4	−	94154.5i	0.613711	−	0.954953i
$315$	−51070.9	+	14995.8i	−0.514698	+	0.151129i
$316$	−25321.4	−	3640.67i	−0.253579	−	0.0364592i
$317$	−65.8922	−	144.284i	−0.000655716	−	0.00143582i	0.909304	−	0.416133i	$-0.136615\pi$
$317$	−65.8922	−	144.284i	−0.000655716	−	0.00143582i	−0.909960	+	0.414697i	$0.863888\pi$
$318$	45426.6	−	6531.36i	0.449217	−	0.0645877i
$319$	97059.5	+	151027.i	0.953798	+	1.48414i
$320$	−11379.2	−	9860.14i	−0.111125	−	0.0962904i
$321$			4482.00i			0.0434972i
$322$	−19519.2	+	98383.3i	−0.188257	+	0.948876i
$323$	1557.19			0.0149258
$324$	−3819.15	+	4407.53i	−0.0363812	+	0.0419861i
$325$	56173.1	−	36100.3i	0.531817	−	0.341778i
$326$	12965.3	+	90175.8i	0.121997	+	0.848506i
$327$	72940.2	−	33310.7i	0.682136	−	0.311521i
$328$	8702.50	−	60527.2i	0.0808903	−	0.562604i
$329$	−43174.4	−	147038.i	−0.398873	−	1.35844i
$330$	−82362.3	−	52931.0i	−0.756311	−	0.486052i
$331$	−81366.0	+	178167.i	−0.742655	+	1.62619i	0.0364819	+	0.999334i	$0.488385\pi$
$331$	−81366.0	+	178167.i	−0.742655	+	1.62619i	−0.779137	+	0.626854i	$0.784342\pi$
$332$	−13377.5	+	45559.7i	−0.121367	+	0.413337i
$333$	−17228.1	+	14928.2i	−0.155363	+	0.134623i
$334$	20456.9	+	23608.5i	0.183378	+	0.211629i
$335$	5085.20	+	1493.15i	0.0453126	+	0.0133050i
$336$	−20278.3	−	9260.79i	−0.179619	−	0.0820294i
$337$	33008.1	−	51361.6i	0.290644	−	0.452250i	−0.664971	−	0.746869i	$-0.731556\pi$
$337$	33008.1	−	51361.6i	0.290644	−	0.452250i	0.955615	+	0.294619i	$0.0951926\pi$
$338$	132867.	−	39013.3i	1.16301	−	0.341491i
$339$	67470.5	+	9700.79i	0.587103	+	0.0844127i
$340$	−8152.02	−	17850.4i	−0.0705192	−	0.154416i
$341$	120298.	−	17296.2i	1.03454	−	0.148745i
$342$	770.781	+	1199.36i	0.00658990	+	0.0102541i
$343$	15616.9	+	13532.2i	0.132742	+	0.115021i
$344$		−	37966.1i		−	0.320833i
$345$	−76244.1	−	26855.1i	−0.640573	−	0.225626i
$346$	141038.			1.17810
$347$	138777.	−	160157.i	1.15254	−	1.33011i	0.217297	−	0.976105i	$-0.430276\pi$
$347$	138777.	−	160157.i	1.15254	−	1.33011i	0.935246	−	0.354000i	$-0.115179\pi$
$348$	−27715.2	+	17811.5i	−0.228854	+	0.147076i
$349$	11285.9	+	78495.3i	0.0926587	+	0.644456i	0.982233	+	0.187665i	$0.0600920\pi$
$349$	11285.9	+	78495.3i	0.0926587	+	0.644456i	−0.889574	+	0.456790i	$0.848999\pi$
$350$	41362.8	−	18889.8i	0.337656	−	0.154202i
$351$	5559.07	−	38664.2i	0.0451220	−	0.313830i
$352$	−11552.4	−	39343.9i	−0.0932367	−	0.317535i
$353$	−131712.	−	84646.1i	−1.05700	−	0.679293i	−0.107867	−	0.994165i	$-0.534402\pi$
$353$	−131712.	−	84646.1i	−1.05700	−	0.679293i	−0.949134	+	0.314872i	$0.898038\pi$
$354$	−7412.98	+	16232.2i	−0.0591543	+	0.129530i
$355$	−35099.3	+	119537.i	−0.278510	+	0.948519i
$356$	−93839.6	+	81312.5i	−0.740434	+	0.641590i
$357$	−19026.7	−	21958.0i	−0.149289	−	0.172289i
$358$	25642.4	+	7529.29i	0.200075	+	0.0587473i
$359$	−26402.9	−	12057.8i	−0.204862	−	0.0935575i	0.310342	−	0.950625i	$-0.399557\pi$
$359$	−26402.9	−	12057.8i	−0.204862	−	0.0935575i	−0.515204	+	0.857068i	$0.672284\pi$
$360$	9713.41	−	15114.4i	0.0749492	−	0.116623i
$361$	−124708.	+	36617.5i	−0.956927	+	0.280979i
$362$	−52532.2	−	7552.98i	−0.400874	−	0.0576370i
$363$	−79156.9	−	173330.i	−0.600725	−	1.31540i
$364$	147794.	−	21249.6i	1.11546	−	0.160379i
$365$	3486.91	+	5425.73i	0.0261731	+	0.0407261i
$366$	−12429.1	−	10769.8i	−0.0927847	−	0.0803984i
$367$			23564.0i			0.174951i	0.996167	+	0.0874757i	$0.0278800\pi$
$367$			23564.0i			0.174951i	−0.996167	+	0.0874757i	$0.972120\pi$
$368$	−16767.7	−	29412.1i	−0.123817	−	0.217185i
$369$	72966.4			0.535883
$370$	45988.9	−	53074.0i	0.335930	−	0.387684i
$371$	−176099.	+	113172.i	−1.27941	+	0.822227i
$372$	3174.04	+	22076.0i	0.0229365	+	0.159527i
$373$	−102653.	+	46880.0i	−0.737826	+	0.336954i	−0.748630	−	0.662988i	$-0.769288\pi$
$373$	−102653.	+	46880.0i	−0.737826	+	0.336954i	0.0108045	+	0.999942i	$0.496561\pi$
$374$	7605.62	−	52898.2i	0.0543740	−	0.378179i
$375$	−16582.1	−	56473.6i	−0.117917	−	0.401590i
$376$	43515.8	+	27965.9i	0.307802	+	0.197812i
$377$	91665.8	−	200720.i	0.644948	−	1.41224i
$378$	7494.31	−	25523.3i	0.0524503	−	0.178629i
$379$	73586.0	−	63762.6i	0.512291	−	0.443903i	−0.359955	−	0.932970i	$-0.617208\pi$
$379$	73586.0	−	63762.6i	0.512291	−	0.443903i	0.872246	+	0.489067i	$0.162663\pi$
$380$	−2876.18	−	3319.29i	−0.0199182	−	0.0229868i
$381$	131945.	+	38742.4i	0.908954	+	0.266893i
$382$	−143290.	−	65438.6i	−0.981953	−	0.448443i
$383$	−145360.	+	226184.i	−0.990938	+	1.54193i	−0.158838	+	0.987305i	$0.550775\pi$
$383$	−145360.	+	226184.i	−0.990938	+	1.54193i	−0.832100	+	0.554626i	$0.812861\pi$
$384$	7220.02	−	2119.99i	0.0489639	−	0.0143771i
$385$	442013.	+	63551.9i	2.98204	+	0.428753i
$386$	−64423.0	−	141067.i	−0.432381	−	0.946782i
$387$	44841.7	−	6447.26i	0.299406	−	0.0430480i
$388$	−2562.71	−	3987.65i	−0.0170230	−	0.0264883i
$389$	−165689.	−	143570.i	−1.09495	−	0.948777i	−0.0960338	−	0.995378i	$-0.530616\pi$
$389$	−165689.	−	143570.i	−1.09495	−	0.948777i	−0.998914	+	0.0466007i	$0.985161\pi$
$390$			120337.i			0.791167i
$391$	−3954.59	−	43947.4i	−0.0258671	−	0.287462i
$392$	47353.4			0.308162
$393$	100217.	−	115657.i	0.648868	−	0.748834i
$394$	−128984.	+	82892.7i	−0.830887	+	0.533979i
$395$	13383.1	+	93081.2i	0.0857750	+	0.596579i
$396$	44507.1	−	20325.7i	0.283818	−	0.129615i
$397$	−22001.6	+	153025.i	−0.139596	+	0.970912i	0.792802	+	0.609479i	$0.208621\pi$
$397$	−22001.6	+	153025.i	−0.139596	+	0.970912i	−0.932398	+	0.361433i	$0.882288\pi$
$398$	32263.3	+	109879.i	0.203677	+	0.693660i
$399$	−5470.49	−	3515.67i	−0.0343621	−	0.0220832i
$400$	−6376.13	+	13961.8i	−0.0398508	+	0.0872612i
$401$	−59509.6	+	202671.i	−0.370082	+	1.26038i	0.538481	+	0.842638i	$0.318998\pi$
$401$	−59509.6	+	202671.i	−0.370082	+	1.26038i	−0.908563	+	0.417747i	$0.862820\pi$
$402$	−2001.74	+	1734.51i	−0.0123867	+	0.0107331i
$403$	−97824.2	−	112895.i	−0.602332	−	0.695129i
$404$	−39354.8	−	11555.6i	−0.241121	−	0.0707995i
$405$	19501.0	+	8905.82i	0.118891	+	0.0542955i
$406$	81241.3	−	126414.i	0.492861	−	0.766907i
$407$	183504.	−	53881.8i	1.10779	−	0.325277i
$408$	9707.40	+	1395.71i	0.0583153	+	0.00838447i
$409$	−100879.	−	220895.i	−0.603054	−	1.32050i	−0.927225	−	0.374506i	$-0.877812\pi$
$409$	−100879.	−	220895.i	−0.603054	−	1.32050i	0.324171	−	0.945999i	$-0.394915\pi$
$410$	−222497.	+	31990.3i	−1.32360	+	0.190305i
$411$	79927.5	+	124370.i	0.473165	+	0.736259i
$412$	79437.3	+	68832.8i	0.467983	+	0.405510i
$413$		−	81393.1i		−	0.477186i
$414$	31891.1	−	24799.0i	0.186067	−	0.144688i
$415$	174547.			1.01348
$416$	−33005.0	+	38089.8i	−0.190719	+	0.220101i
$417$	130069.	−	83590.0i	0.747998	−	0.480709i
$418$	−1702.23	−	11839.3i	−0.00974240	−	0.0677599i
$419$	697.832	−	318.689i	0.00397487	−	0.00181526i	−0.413427	−	0.910537i	$-0.635668\pi$
$419$	697.832	−	318.689i	0.00397487	−	0.00181526i	0.417401	+	0.908722i	$0.362941\pi$
$420$	−11662.5	+	81114.2i	−0.0661138	+	0.459831i
$421$	−53198.8	−	181178.i	−0.300150	−	1.02222i	−0.962107	−	0.272674i	$-0.912092\pi$
$421$	−53198.8	−	181178.i	−0.300150	−	1.02222i	0.661957	−	0.749542i	$-0.269726\pi$
$422$	97213.0	+	62475.0i	0.545883	+	0.350818i
$423$	−25640.8	+	56145.4i	−0.143301	+	0.313786i
$424$	19906.7	−	67795.9i	0.110730	−	0.377113i
$425$	−15118.3	+	13100.1i	−0.0836998	+	0.0725263i
$426$	−40773.0	−	47054.5i	−0.224674	−	0.259288i
$427$	71974.6	+	21133.7i	0.394752	+	0.115910i
$428$	6276.90	+	2866.57i	0.0342656	+	0.0156486i
$429$	−177177.	+	275693.i	−0.962704	+	1.49800i
$430$	−133910.	+	39319.5i	−0.724228	+	0.212653i
$431$	−148616.	−	21367.8i	−0.800039	−	0.115028i	−0.269844	−	0.962904i	$-0.586972\pi$
$431$	−148616.	−	21367.8i	−0.800039	−	0.115028i	−0.530195	+	0.847876i	$0.677881\pi$
$432$	3729.99	+	8167.54i	0.0199867	+	0.0437647i
$433$	−201592.	+	28984.5i	−1.07522	+	0.154593i	−0.657103	−	0.753801i	$-0.728218\pi$
$433$	−201592.	+	28984.5i	−1.07522	+	0.154593i	−0.418115	+	0.908394i	$0.637309\pi$
$434$	−54998.3	−	85579.0i	−0.291991	−	0.454347i
$435$	91525.7	+	79307.4i	0.483687	+	0.419117i
$436$		−	123455.i		−	0.649436i
$437$	−3620.35	−	9188.20i	−0.0189578	−	0.0481136i
$438$	−3223.25			−0.0168014
$439$	−92190.6	+	106394.i	−0.478363	+	0.552061i	−0.942719	−	0.333588i	$-0.891740\pi$
$439$	−92190.6	+	106394.i	−0.478363	+	0.552061i	0.464356	+	0.885649i	$0.346286\pi$
$440$	−126805.	+	81492.6i	−0.654985	+	0.420933i
$441$	8041.36	+	55928.9i	0.0413478	+	0.287580i
$442$	−59751.1	+	27287.4i	−0.305845	+	0.139675i
$443$	48362.6	−	336369.i	0.246435	−	1.71399i	−0.372065	−	0.928207i	$-0.621350\pi$
$443$	48362.6	−	336369.i	0.246435	−	1.71399i	0.618500	−	0.785785i	$-0.287741\pi$
$444$	9887.88	+	33675.0i	0.0501577	+	0.170821i
$445$	383981.	+	246770.i	1.93905	+	1.24615i
$446$	−21881.1	+	47912.9i	−0.110002	+	0.240870i
$447$	19577.3	−	66674.1i	0.0979799	−	0.333689i
$448$	−25938.9	+	22476.2i	−0.129240	+	0.111987i
$449$	44749.7	+	51643.9i	0.221971	+	0.256169i	0.855802	−	0.517303i	$-0.173064\pi$
$449$	44749.7	+	51643.9i	0.221971	+	0.256169i	−0.633831	+	0.773472i	$0.718518\pi$
$450$	−17573.0	−	5159.90i	−0.0867802	−	0.0254810i
$451$	−556846.	−	254303.i	−2.73768	−	1.25025i
$452$	56738.0	−	88286.0i	0.277714	−	0.432131i
$453$	−52025.5	+	15276.1i	−0.253524	+	0.0744415i
$454$	203281.	+	29227.4i	0.986247	+	0.141801i
$455$	−228012.	−	499276.i	−1.10137	−	2.41167i
$456$	2172.64	−	312.378i	0.0104486	−	0.00150228i
$457$	−80551.6	−	125341.i	−0.385693	−	0.600150i	0.593068	−	0.805152i	$-0.297916\pi$
$457$	−80551.6	−	125341.i	−0.385693	−	0.600150i	−0.978762	+	0.205002i	$0.934280\pi$
$458$	−36034.2	−	31223.8i	−0.171785	−	0.148852i
$459$			11702.4i			0.0555455i
$460$	−86373.5	+	89601.8i	−0.408193	+	0.423449i
$461$	179746.			0.845779			0.422890	−	0.906181i	$-0.361016\pi$
$461$	179746.			0.845779			0.422890	+	0.906181i	$0.361016\pi$
$462$	−146147.	+	168663.i	−0.684709	+	0.790197i
$463$	−45618.0	+	29316.9i	−0.212801	+	0.136759i	−0.642700	−	0.766118i	$-0.722186\pi$
$463$	−45618.0	+	29316.9i	−0.212801	+	0.136759i	0.429898	+	0.902877i	$0.358549\pi$
$464$	7218.53	+	50206.0i	0.0335284	+	0.233195i
$465$	74576.6	−	34058.0i	0.344903	−	0.157512i
$466$	15475.0	−	107631.i	0.0712620	−	0.495638i
$467$	46936.0	+	159849.i	0.215215	+	0.732955i	0.994355	+	0.106105i	$0.0338379\pi$
$467$	46936.0	+	159849.i	0.215215	+	0.732955i	−0.779140	+	0.626850i	$0.784344\pi$
$468$	−50592.6	−	32513.9i	−0.230991	−	0.148449i
$469$	5018.67	−	10989.3i	0.0228162	−	0.0499604i
$470$	53571.2	−	182447.i	0.242513	−	0.825925i
$471$	155392.	−	134648.i	0.700466	−	0.606957i
$472$	17991.5	+	20763.3i	0.0807576	+	0.0931992i
$473$	−364681.	−	107080.i	−1.63001	−	0.478615i
$474$	−42749.7	−	19523.1i	−0.190273	−	0.0868947i
$475$	−2420.57	+	3766.48i	−0.0107283	+	0.0166935i
$476$	−42920.5	+	12602.6i	−0.189431	+	0.0556219i
$477$	83454.0	+	11998.9i	0.366784	+	0.0527356i
$478$	21212.3	+	46448.4i	0.0928392	+	0.203289i
$479$	102565.	−	14746.6i	0.447022	−	0.0642720i	0.0848719	−	0.996392i	$-0.472952\pi$
$479$	102565.	−	14746.6i	0.447022	−	0.0642720i	0.362150	+	0.932120i	$0.382043\pi$
$480$	−14954.8	−	23270.1i	−0.0649079	−	0.100999i
$481$	−177656.	−	153939.i	−0.767872	−	0.665365i
$482$		−	108567.i		−	0.467307i
$483$	−85327.4	+	163318.i	−0.365758	+	0.700066i
$484$	−293370.			−1.25235
$485$	−11410.7	+	13168.7i	−0.0485098	+	0.0559833i
$486$	−9013.25	+	5792.46i	−0.0381600	+	0.0245240i
$487$	40006.8	+	278253.i	0.168685	+	1.17323i	0.881607	+	0.471985i	$0.156462\pi$
$487$	40006.8	+	278253.i	0.168685	+	1.17323i	−0.712922	+	0.701244i	$0.752629\pi$
$488$	−23032.1	+	10518.4i	−0.0967152	+	0.0441684i
$489$	−23818.8	+	165664.i	−0.0996099	+	0.692802i
$490$	−49041.3	−	167019.i	−0.204254	−	0.695624i
$491$	238851.	+	153500.i	0.990752	+	0.636717i	0.932343	−	0.361575i	$-0.117761\pi$
$491$	238851.	+	153500.i	0.990752	+	0.636717i	0.0584088	+	0.998293i	$0.481397\pi$
$492$	46667.3	−	102187.i	0.192789	−	0.422150i
$493$	−18624.5	+	63429.3i	−0.0766286	+	0.260973i
$494$	−11110.7	+	9627.50i	−0.0455291	+	0.0394511i
$495$	−117784.	−	135930.i	−0.480703	−	0.554761i
$496$	32946.8	+	9674.04i	0.133921	+	0.0393228i
$497$	258325.	+	117973.i	1.04581	+	0.477606i
$498$	−47161.2	+	73384.2i	−0.190163	+	0.295899i
$499$	203610.	−	59785.4i	0.817710	−	0.240101i	0.153980	−	0.988074i	$-0.450791\pi$
$499$	203610.	−	59785.4i	0.817710	−	0.240101i	0.663729	+	0.747973i	$0.268973\pi$
$500$	−89695.1	−	12896.2i	−0.358780	−	0.0515848i
$501$	23840.2	+	52202.7i	0.0949804	+	0.207978i
$502$	133569.	−	19204.3i	0.530026	−	0.0762062i
$503$	−11415.3	−	17762.6i	−0.0451183	−	0.0702054i	0.817962	−	0.575273i	$-0.195104\pi$
$503$	−11415.3	−	17762.6i	−0.0451183	−	0.0702054i	−0.863080	+	0.505067i	$0.831468\pi$
$504$	−30951.4	−	26819.6i	−0.121848	−	0.105582i
$505$			150775.i			0.591217i
$506$	−329808.	+	78107.4i	−1.28813	+	0.305064i
$507$	254397.			0.989685
$508$	138646.	−	160006.i	0.537254	−	0.620024i
$509$	−68988.1	+	44336.0i	−0.266280	+	0.171128i	−0.666967	−	0.745087i	$-0.732408\pi$
$509$	−68988.1	+	44336.0i	−0.266280	+	0.171128i	0.400687	+	0.916215i	$0.368771\pi$
$510$	−5130.63	−	35684.3i	−0.0197256	−	0.137194i
$511$	13373.2	−	6107.36i	0.0512148	−	0.0233890i
$512$	1648.75	−	11467.3i	0.00628949	−	0.0437443i
$513$	737.897	+	2513.05i	0.00280389	+	0.00954918i
$514$	173637.	+	111590.i	0.657229	+	0.422375i
$515$	160510.	−	351469.i	0.605186	−	1.32517i
$516$	19650.3	−	66922.9i	0.0738024	−	0.251348i
$517$	391357.	−	339113.i	1.46417	−	1.26871i
$518$	−104832.	−	120982.i	−0.390691	−	0.450881i
$519$	248607.	+	72997.7i	0.922952	+	0.271003i
$520$	168528.	+	76964.0i	0.623253	+	0.284630i
$521$	−88408.6	+	137566.i	−0.325701	+	0.506800i	−0.965032	−	0.262131i	$-0.915575\pi$
$521$	−88408.6	+	137566.i	−0.325701	+	0.506800i	0.639332	+	0.768931i	$0.279211\pi$
$522$	−58072.3	+	17051.6i	−0.213122	+	0.0625783i
$523$	418143.	+	60119.9i	1.52870	+	0.219793i	0.854771	−	0.519005i	$-0.173697\pi$
$523$	418143.	+	60119.9i	1.52870	+	0.219793i	0.673926	+	0.738799i	$0.264607\pi$
$524$	−97877.5	−	214322.i	−0.356468	−	0.780556i
$525$	82687.2	−	11888.6i	0.299999	−	0.0431333i
$526$	−96592.5	−	150301.i	−0.349118	−	0.543238i
$527$	33821.9	+	29306.8i	0.121780	+	0.105523i
$528$		−	75330.7i		−	0.270212i
$529$	−250117.	+	125508.i	−0.893783	+	0.448499i
$530$	−259738.			−0.924665
$531$	−21468.2	+	24775.7i	−0.0761390	+	0.0878691i
$532$	−8422.37	+	5412.73i	−0.0297585	+	0.0191246i
$533$	107082.	+	744770.i	0.376930	+	2.62161i
$534$	−207497.	+	94760.5i	−0.727660	+	0.332311i
$535$	3609.98	−	25107.9i	0.0126124	−	0.0877210i
$536$	1148.88	+	3912.72i	0.00399894	+	0.0136191i
$537$	41302.9	+	26543.8i	0.143229	+	0.0920480i
$538$	81745.2	−	178997.i	0.282422	−	0.618417i
$539$	133556.	−	454850.i	0.459712	−	1.56563i
$540$	24944.7	−	21614.7i	0.0855441	−	0.0741244i
$541$	−287731.	−	332059.i	−0.983088	−	1.13454i	−0.990904	−	0.134574i	$-0.957033\pi$
$541$	−287731.	−	332059.i	−0.983088	−	1.13454i	0.00781576	−	0.999969i	$-0.497512\pi$
$542$	212698.	+	62453.8i	0.724045	+	0.212599i
$543$	−88689.3	−	40503.0i	−0.300796	−	0.137369i
$544$	8163.24	−	12702.3i	0.0275845	−	0.0429223i
$545$	−435437.	+	127856.i	−1.46599	+	0.430455i
$546$	271515.	+	39038.0i	0.910770	+	0.130949i
$547$	11642.8	+	25494.1i	0.0389118	+	0.0852050i	0.928090	−	0.372357i	$-0.121450\pi$
$547$	11642.8	+	25494.1i	0.0389118	+	0.0852050i	−0.889178	+	0.457562i	$0.848723\pi$
$548$	225296.	−	32392.6i	0.750225	−	0.107866i
$549$	−16334.5	−	25417.0i	−0.0541953	−	0.0843295i
$550$	116126.	+	100624.i	0.383887	+	0.332640i
$551$			14795.6i			0.0487336i
$552$	−14333.5	−	60523.3i	−0.0470409	−	0.198630i
$553$	214361.			0.700962
$554$	−264700.	+	305480.i	−0.862451	+	0.995321i
$555$	108534.	−	69750.8i	0.352356	−	0.226445i
$556$	−33876.9	−	235619.i	−0.109586	−	0.762186i
$557$	−100622.	+	45952.5i	−0.324327	+	0.148115i	−0.570924	−	0.821003i	$-0.693415\pi$
$557$	−100622.	+	45952.5i	−0.324327	+	0.148115i	0.246597	+	0.969118i	$0.420688\pi$
$558$	−5831.09	+	40556.1i	−0.0187276	+	0.130253i
$559$	131615.	+	448239.i	0.421193	+	1.43445i
$560$	106139.	+	68211.4i	0.338454	+	0.217511i
$561$	40785.3	−	89307.3i	0.129592	−	0.283767i
$562$	27795.9	−	94664.1i	0.0880051	−	0.299718i
$563$	−89380.1	+	77448.3i	−0.281984	+	0.244340i	−0.784356	−	0.620311i	$-0.787006\pi$
$563$	−89380.1	+	77448.3i	−0.281984	+	0.244340i	0.502372	+	0.864652i	$0.332461\pi$
$564$	62230.9	+	71818.2i	0.195635	+	0.225775i
$565$	−370153.	−	108687.i	−1.15954	−	0.340470i
$566$	−406144.	−	185480.i	−1.26779	−	0.578980i
$567$	26420.5	−	41111.0i	0.0821815	−	0.127877i
$568$	−91975.8	+	27006.5i	−0.285087	+	0.0837090i
$569$	52674.0	+	7573.37i	0.162694	+	0.0233919i	0.223180	−	0.974777i	$-0.428356\pi$
$569$	52674.0	+	7573.37i	0.162694	+	0.0233919i	−0.0604864	+	0.998169i	$0.519265\pi$
$570$	−3351.87	−	7339.56i	−0.0103166	−	0.0225902i
$571$	154034.	−	22146.7i	0.472437	−	0.0679261i	0.0980155	−	0.995185i	$-0.468751\pi$
$571$	154034.	−	22146.7i	0.472437	−	0.0679261i	0.374421	+	0.927259i	$0.377841\pi$
$572$	272782.	+	424457.i	0.833726	+	1.29730i
$573$	−218709.	−	189512.i	−0.666127	−	0.577202i
$574$			512399.i			1.55519i
$575$	112446.	+	58748.6i	0.340100	+	0.177690i
$576$	13824.0			0.0416667
$577$	−246940.	+	284984.i	−0.741719	+	0.855990i	−0.993738	−	0.111733i	$-0.964360\pi$
$577$	−246940.	+	284984.i	−0.741719	+	0.855990i	0.252019	+	0.967722i	$0.418905\pi$
$578$	−182177.	+	117078.i	−0.545303	+	0.350445i
$579$	−40545.8	−	282002.i	−0.120945	−	0.841193i
$580$	169605.	−	77456.0i	0.504177	−	0.230250i
$581$	56624.3	−	393831.i	0.167745	−	1.16670i
$582$	−2453.37	−	8355.43i	−0.00724299	−	0.0246674i
$583$	−595064.	−	382425.i	−1.75076	−	1.12515i
$584$	−2061.50	+	4514.07i	−0.00604448	+	0.0132356i
$585$	−62283.3	+	212117.i	−0.181995	+	0.619818i
$586$	61199.0	−	53029.2i	0.178217	−	0.154426i
$587$	250402.	+	288980.i	0.726711	+	0.838670i	0.992097	−	0.125473i	$-0.0400447\pi$
$587$	250402.	+	288980.i	0.726711	+	0.838670i	−0.265386	+	0.964142i	$0.585499\pi$
$588$	83469.8	+	24508.9i	0.241421	+	0.0708876i
$589$	9111.08	+	4160.89i	0.0262627	+	0.0119938i
$590$	54601.1	−	84961.0i	0.156855	−	0.244071i
$591$	−270263.	+	79356.3i	−0.773769	+	0.227199i
$592$	53484.9	+	7689.97i	0.152612	+	0.0219423i
$593$	45396.4	+	99404.2i	0.129096	+	0.282680i	0.963132	−	0.269030i	$-0.0867029\pi$
$593$	45396.4	+	99404.2i	0.129096	+	0.282680i	−0.834036	+	0.551710i	$0.813976\pi$
$594$	88972.9	−	12792.4i	0.252165	−	0.0362559i
$595$	88900.9	+	138332.i	0.251115	+	0.390742i
$596$	−80853.9	−	70060.3i	−0.227619	−	0.197233i
$597$			210382.i			0.590282i
$598$	299926.	+	289120.i	0.838710	+	0.808492i
$599$	333574.			0.929690			0.464845	−	0.885392i	$-0.346110\pi$
$599$	333574.			0.929690			0.464845	+	0.885392i	$0.346110\pi$
$600$	−18465.5	+	21310.3i	−0.0512931	+	0.0591953i
$601$	174205.	−	111955.i	0.482293	−	0.309951i	−0.276806	−	0.960926i	$-0.589276\pi$
$601$	174205.	−	111955.i	0.482293	−	0.309951i	0.759099	+	0.650975i	$0.225640\pi$
$602$	45275.2	+	314896.i	0.124930	+	0.868909i
$603$	−4426.21	+	2021.38i	−0.0121730	+	0.00555921i
$604$	−11880.4	+	82630.3i	−0.0325656	+	0.226499i
$605$	303827.	+	1.03474e6i	0.830072	+	2.82696i
$606$	−63389.8	−	40738.2i	−0.172613	−	0.110932i
$607$	90362.1	−	197865.i	0.245250	−	0.537022i	−0.746474	−	0.665415i	$-0.768255\pi$
$607$	90362.1	−	197865.i	0.245250	−	0.537022i	0.991723	+	0.128393i	$0.0409818\pi$
$608$	952.084	−	3242.50i	0.00257554	−	0.00877148i
$609$	208633.	−	180781.i	0.562533	−	0.487438i
$610$	60952.5	+	70343.0i	0.163807	+	0.189043i
$611$	−610707.	−	179320.i	−1.63588	−	0.480337i
$612$	16388.8	+	7484.54i	0.0437568	+	0.0199831i
$613$	174550.	−	271606.i	0.464515	−	0.722800i	−0.527412	−	0.849610i	$-0.676838\pi$
$613$	174550.	−	271606.i	0.464515	−	0.722800i	0.991927	+	0.126810i	$0.0404739\pi$
$614$	184886.	−	54287.5i	0.490419	−	0.144000i
$615$	−408754.	−	58770.0i	−1.08072	−	0.155384i
$616$	142735.	+	312547.i	0.376158	+	0.823671i
$617$	518923.	−	74609.8i	1.36311	−	0.195986i	0.578354	−	0.815786i	$-0.303695\pi$
$617$	518923.	−	74609.8i	1.36311	−	0.195986i	0.784760	+	0.619800i	$0.212786\pi$
$618$	104398.	+	162446.i	0.273348	+	0.425337i
$619$	−31403.6	−	27211.4i	−0.0819593	−	0.0710182i	0.612918	−	0.790147i	$-0.289996\pi$
$619$	−31403.6	−	27211.4i	−0.0819593	−	0.0710182i	−0.694877	+	0.719129i	$0.744541\pi$
$620$		−	126225.i		−	0.328369i
$621$	69049.8	−	27207.1i	0.179052	−	0.0705504i
$622$	−56500.1			−0.146039
$623$	681352.	−	786322.i	1.75548	−	2.02593i
$624$	−77892.4	+	50058.4i	−0.200044	+	0.128561i
$625$	68738.0	+	478083.i	0.175969	+	1.22389i
$626$	395487.	−	180613.i	1.00921	−	0.460893i
$627$	3127.20	−	21750.1i	0.00795464	−	0.0553257i
$628$	−89185.9	−	303739.i	−0.226140	−	0.770161i
$629$	59244.8	+	38074.3i	0.149744	+	0.0962345i
$630$	−62540.2	+	136944.i	−0.157572	+	0.345034i
$631$	−139079.	+	473659.i	−0.349303	+	1.18962i	0.578229	+	0.815875i	$0.303744\pi$
$631$	−139079.	+	473659.i	−0.349303	+	1.18962i	−0.927532	+	0.373743i	$0.878074\pi$
$632$	−54683.2	+	47383.2i	−0.136905	+	0.118629i
$633$	139022.	+	160440.i	0.346957	+	0.400410i
$634$	−430.466	−	126.396i	−0.00107093	−	0.000314453i
$635$	−707943.	−	323307.i	−1.75570	−	0.801802i
$636$	70179.0	−	109201.i	0.173497	−	0.269967i
$637$	−559067.	+	164157.i	−1.37780	+	0.404558i
$638$	502610.	+	72264.4i	1.23478	+	0.177535i
$639$	−47516.3	−	104046.i	−0.116370	−	0.254815i
$640$	−42153.7	+	6060.79i	−0.102914	+	0.0147969i
$641$	99962.5	+	155545.i	0.243288	+	0.378564i	0.941327	−	0.337496i	$-0.109580\pi$
$641$	99962.5	+	155545.i	0.243288	+	0.378564i	−0.698039	+	0.716060i	$0.745944\pi$
$642$	9580.64	+	8301.67i	0.0232447	+	0.0201417i
$643$			619930.i			1.49941i	0.661772	+	0.749705i	$0.269805\pi$
$643$			619930.i			1.49941i	−0.661772	+	0.749705i	$0.730195\pi$
$644$	174148.	+	223952.i	0.419902	+	0.539987i
$645$	−256394.			−0.616294
$646$	2884.27	−	3328.63i	0.00691148	−	0.00797627i
$647$	−399680.	+	256859.i	−0.954781	+	0.613600i	−0.922549	−	0.385880i	$-0.873898\pi$
$647$	−399680.	+	256859.i	−0.954781	+	0.613600i	−0.0322317	+	0.999480i	$0.510261\pi$
$648$	2347.54	+	16327.5i	0.00559065	+	0.0388839i
$649$	250184.	−	114255.i	0.593978	−	0.271261i
$650$	26878.0	−	186941.i	0.0636166	−	0.442463i
$651$	−52651.9	−	179316.i	−0.124237	−	0.423113i
$652$	216773.	+	139312.i	0.509929	+	0.327712i
$653$	80512.4	−	176298.i	0.188815	−	0.413447i	−0.791423	−	0.611269i	$-0.790659\pi$
$653$	80512.4	−	176298.i	0.188815	−	0.413447i	0.980238	+	0.197822i	$0.0633867\pi$
$654$	63897.4	−	217614.i	0.149392	−	0.508783i
$655$	−654565.	+	567184.i	−1.52570	+	1.32203i
$656$	−113263.	−	130712.i	−0.263197	−	0.303745i
$657$	−5681.63	−	1668.28i	−0.0131626	−	0.00386489i
$658$	−394276.	−	180060.i	−0.910643	−	0.415877i
$659$	171361.	−	266643.i	0.394586	−	0.613988i	−0.585945	−	0.810351i	$-0.699277\pi$
$659$	171361.	−	266643.i	0.394586	−	0.613988i	0.980531	+	0.196362i	$0.0629129\pi$
$660$	−265698.	+	78016.0i	−0.609959	+	0.179100i
$661$	−407378.	−	58572.1i	−0.932384	−	0.134057i	−0.340650	−	0.940190i	$-0.610647\pi$
$661$	−407378.	−	58572.1i	−0.932384	−	0.134057i	−0.591734	+	0.806133i	$0.701556\pi$
$662$	230138.	+	503932.i	0.525136	+	1.14989i
$663$	−119447.	+	17173.8i	−0.271736	+	0.0390697i
$664$	72609.4	+	112982.i	0.164686	+	0.256256i
$665$	27813.7	+	24100.7i	0.0628950	+	0.0544988i
$666$			64476.8i			0.145363i
$667$	417564.	−	37574.3i	0.938581	−	0.0844577i
$668$	88355.8			0.198008
$669$	−63368.4	+	73131.0i	−0.141586	+	0.163399i
$670$	12610.7	−	8104.39i	0.0280924	−	0.0180539i
$671$	36074.0	+	250900.i	0.0801215	+	0.557257i
$672$	−57355.7	+	26193.5i	−0.127010	+	0.0580036i
$673$	−57223.3	+	397997.i	−0.126341	+	0.878718i	0.823797	+	0.566885i	$0.191852\pi$
$673$	−57223.3	+	397997.i	−0.126341	+	0.878718i	−0.950137	+	0.311832i	$0.899057\pi$
$674$	−48651.2	−	165691.i	−0.107096	−	0.364736i
$675$	−28305.3	−	18190.7i	−0.0621241	−	0.0399248i
$676$	162706.	−	356276.i	0.356049	−	0.779638i
$677$	92850.9	−	316221.i	0.202586	−	0.689944i	−0.794040	−	0.607865i	$-0.792026\pi$
$677$	92850.9	−	316221.i	0.202586	−	0.689944i	0.996626	−	0.0820784i	$-0.0261558\pi$
$678$	145707.	−	126256.i	0.316972	−	0.274658i
$679$	26010.8	+	30018.0i	0.0564174	+	0.0651092i
$680$	−53256.2	−	15637.4i	−0.115173	−	0.0338180i
$681$	343197.	+	156733.i	0.740029	+	0.337960i
$682$	185847.	−	289183.i	0.399564	−	0.621734i
$683$	−404027.	+	118633.i	−0.866101	+	0.254310i	−0.684456	−	0.729054i	$-0.739960\pi$
$683$	−404027.	+	118633.i	−0.866101	+	0.254310i	−0.181645	+	0.983364i	$0.558142\pi$
$684$	3991.39	+	573.875i	0.00853123	+	0.00122661i
$685$	−347578.	−	761089.i	−0.740749	−	1.62201i
$686$	57852.2	−	8317.89i	0.122934	−	0.0176752i
$687$	−47356.9	−	73688.7i	−0.100339	−	0.156130i
$688$	−81155.7	−	70321.8i	−0.171452	−	0.148564i
$689$			869427.i			1.83145i
$690$	−198626.	+	113236.i	−0.417195	+	0.237842i
$691$	−561753.			−1.17649			−0.588246	−	0.808682i	$-0.700181\pi$
$691$	−561753.			−1.17649			−0.588246	+	0.808682i	$0.700181\pi$
$692$	261234.	−	301480.i	0.545528	−	0.629573i
$693$	−344909.	+	221660.i	−0.718189	+	0.461552i
$694$	−85302.6	−	593293.i	−0.177110	−	1.23183i
$695$	−795964.	+	363505.i	−1.64787	+	0.752559i
$696$	−13261.3	+	92234.3i	−0.0273758	+	0.190403i
$697$	−63507.5	−	216287.i	−0.130725	−	0.445209i
$698$	188694.	+	121267.i	0.387301	+	0.248903i
$699$	82984.8	−	181711.i	0.169842	−	0.371901i
$700$	36234.8	−	123405.i	0.0739487	−	0.251846i
$701$	611379.	−	529763.i	1.24416	−	1.07807i	0.250211	−	0.968191i	$-0.419500\pi$
$701$	611379.	−	529763.i	1.24416	−	1.07807i	0.993945	−	0.109876i	$-0.0350453\pi$
$702$	−72351.2	−	83497.8i	−0.146815	−	0.169434i
$703$	15123.4	+	4440.63i	0.0306012	+	0.00898533i
$704$	−105498.	−	48179.5i	−0.212863	−	0.0972114i
$705$	188860.	−	293872.i	0.379981	−	0.591262i
$706$	−424898.	+	124761.i	−0.852463	+	0.250306i
$707$	340194.	+	48912.5i	0.680594	+	0.0978546i
$708$	20967.1	+	45911.5i	0.0418284	+	0.0915914i
$709$	693194.	−	99666.3i	1.37899	−	0.198269i	0.587390	−	0.809304i	$-0.300155\pi$
$709$	693194.	−	99666.3i	1.37899	−	0.198269i	0.791604	+	0.611034i	$0.209246\pi$
$710$	190509.	+	296437.i	0.377918	+	0.588052i
$711$	−65250.3	−	56539.7i	−0.129075	−	0.111844i
$712$			351199.i			0.692777i
$713$	94291.4	−	267702.i	0.185478	−	0.526590i
$714$	−82178.8			−0.161199
$715$	1.21459e6	−	1.40171e6i	2.37584	−	2.74187i
$716$	63590.0	−	40866.8i	0.124040	−	0.0797159i
$717$	13350.3	+	92853.6i	0.0259689	+	0.180618i
$718$	−74678.6	+	34104.6i	−0.144860	+	0.0661552i
$719$	31675.6	−	220309.i	0.0612727	−	0.426161i	−0.935978	−	0.352059i	$-0.885482\pi$
$719$	31675.6	−	220309.i	0.0612727	−	0.426161i	0.997251	−	0.0741023i	$-0.0236091\pi$
$720$	−14316.8	−	48758.4i	−0.0276172	−	0.0940556i
$721$	−740948.	−	476178.i	−1.42534	−	0.916007i
$722$	−152714.	+	334397.i	−0.292957	+	0.641487i
$723$	56191.5	−	191371.i	0.107496	−	0.366099i
$724$	−113447.	+	98302.0i	−0.216428	+	0.187536i
$725$	−124470.	−	143646.i	−0.236803	−	0.273285i
$726$	−517123.	−	151841.i	−0.981116	−	0.288082i
$727$	−376408.	−	171900.i	−0.712180	−	0.325242i	0.0261720	−	0.999657i	$-0.491668\pi$
$727$	−376408.	−	171900.i	−0.712180	−	0.325242i	−0.738352	+	0.674416i	$0.764396\pi$
$728$	228325.	−	355281.i	0.430816	−	0.670362i
$729$	−18885.7	+	5545.34i	−0.0355368	+	0.0104345i
$730$	18056.5	+	2596.13i	0.0338834	+	0.00487170i
$731$	−58139.6	−	127308.i	−0.108802	−	0.238244i
$732$	−46042.9	+	6619.97i	−0.0859291	+	0.0123547i
$733$	23323.8	+	36292.6i	0.0434102	+	0.0675476i	0.862280	−	0.506431i	$-0.169036\pi$
$733$	23323.8	+	36292.6i	0.0434102	+	0.0675476i	−0.818870	+	0.573979i	$0.805399\pi$
$734$	50370.0	+	43645.9i	0.0934932	+	0.0810124i
$735$		−	319788.i		−	0.591953i
$736$	−93928.4	−	18635.4i	−0.173397	−	0.0344019i
$737$	40823.7			0.0751584
$738$	135150.	−	155972.i	0.248144	−	0.286374i
$739$	18285.3	−	11751.3i	0.0334822	−	0.0215177i	−0.523793	−	0.851846i	$-0.675483\pi$
$739$	18285.3	−	11751.3i	0.0334822	−	0.0215177i	0.557275	+	0.830328i	$0.311847\pi$
$740$	−28268.2	−	196610.i	−0.0516221	−	0.359039i
$741$	−24567.9	+	11219.8i	−0.0447436	+	0.0204337i
$742$	−84260.9	+	586047.i	−0.153045	+	1.06445i
$743$	−231648.	−	788919.i	−0.419614	−	1.42908i	−0.850169	−	0.526510i	$-0.823500\pi$
$743$	−231648.	−	788919.i	−0.419614	−	1.42908i	0.430554	−	0.902565i	$-0.358318\pi$
$744$	53068.2	+	34104.9i	0.0958714	+	0.0616128i
$745$	−163373.	+	357736.i	−0.294352	+	0.644541i
$746$	−89926.5	+	306261.i	−0.161588	+	0.550319i
$747$	−121113.	+	104945.i	−0.217045	+	0.188070i
$748$	−98987.0	−	114237.i	−0.176919	−	0.204176i
$749$	−55479.9	−	16290.4i	−0.0988945	−	0.0290380i
$750$	−151431.	−	69156.2i	−0.269210	−	0.122944i
$751$	−61691.7	+	95994.1i	−0.109382	+	0.170202i	−0.891629	−	0.452766i	$-0.850437\pi$
$751$	−61691.7	+	95994.1i	−0.109382	+	0.170202i	0.782247	+	0.622968i	$0.214074\pi$
$752$	140381.	−	41219.4i	0.248240	−	0.0728897i
$753$	245381.	+	35280.5i	0.432764	+	0.0622221i
$754$	−259270.	−	567722.i	−0.456047	−	0.998604i
$755$	303748.	−	43672.4i	0.532868	−	0.0766149i
$756$	−40677.0	−	63294.6i	−0.0711713	−	0.110745i
$757$	−404226.	−	350264.i	−0.705395	−	0.611228i	0.226476	−	0.974017i	$-0.427279\pi$
$757$	−404226.	−	350264.i	−0.705395	−	0.611228i	−0.931872	+	0.362788i	$0.881825\pi$
$758$		−	275399.i		−	0.479318i
$759$	−621779.	−	33020.6i	−1.07933	−	0.0573194i
$760$	−12422.6			−0.0215073
$761$	−151397.	+	174721.i	−0.261425	+	0.301700i	−0.871254	−	0.490833i	$-0.836693\pi$
$761$	−151397.	+	174721.i	−0.261425	+	0.301700i	0.609829	+	0.792533i	$0.291238\pi$
$762$	327206.	−	210283.i	0.563523	−	0.362154i
$763$	147222.	+	1.02395e6i	0.252886	+	1.75886i
$764$	−405287.	+	185088.i	−0.694345	+	0.317097i
$765$	9425.56	−	65556.2i	0.0161059	−	0.112019i
$766$	214248.	+	729663.i	0.365140	+	1.24355i
$767$	−284392.	−	182767.i	−0.483422	−	0.310676i
$768$	8841.46	−	19360.1i	0.0149900	−	0.0328235i
$769$	49319.3	−	167966.i	0.0833997	−	0.284033i	−0.907225	−	0.420646i	$-0.861803\pi$
$769$	49319.3	−	167966.i	0.0833997	−	0.284033i	0.990625	+	0.136613i	$0.0436216\pi$
$770$	954556.	−	827128.i	1.60998	−	1.39505i
$771$	248314.	+	286570.i	0.417727	+	0.482083i
$772$	−420868.	−	123578.i	−0.706173	−	0.207351i
$773$	696691.	+	318168.i	1.16595	+	0.532473i	0.901862	−	0.432024i	$-0.142201\pi$
$773$	696691.	+	318168.i	1.16595	+	0.532473i	0.264092	+	0.964498i	$0.414928\pi$
$774$	69275.4	−	107795.i	0.115637	−	0.179935i
$775$	−123461.	+	36251.3i	−0.205553	+	0.0603559i
$776$	−13270.6	−	1908.03i	−0.0220378	−	0.00316856i
$777$	−122169.	−	267514.i	−0.202358	−	0.443102i
$778$	−613785.	+	88249.0i	−1.01404	+	0.145798i
$779$	−27276.0	−	42442.3i	−0.0449476	−	0.0699398i
$780$	257229.	+	222890.i	0.422796	+	0.366355i
$781$			959637.i			1.57328i
$782$	−101266.	−	72947.3i	−0.165596	−	0.119288i
$783$	−111190.			−0.181360
$784$	87709.1	−	101222.i	0.142696	−	0.164680i
$785$	−978950.	+	629133.i	−1.58862	+	1.02095i
$786$	−61601.0	−	428444.i	−0.0997109	−	0.693505i
$787$	906381.	−	413930.i	1.46339	−	0.668310i	0.484897	−	0.874571i	$-0.338857\pi$
$787$	906381.	−	413930.i	1.46339	−	0.668310i	0.978497	+	0.206262i	$0.0661298\pi$
$788$	−61716.7	+	429249.i	−0.0993917	+	0.691285i
$789$	−92471.7	−	314930.i	−0.148544	−	0.505894i
$790$	223757.	+	143800.i	0.358528	+	0.230412i
$791$	−365310.	+	799917.i	−0.583860	+	1.27847i
$792$	38989.4	−	132786.i	0.0621578	−	0.211690i
$793$	235460.	−	204028.i	0.374431	−	0.324446i
$794$	286351.	+	330466.i	0.454210	+	0.524187i
$795$	−457841.	−	134434.i	−0.724403	−	0.212704i
$796$	294633.	+	134555.i	0.465003	+	0.212360i
$797$	306449.	−	476844.i	0.482438	−	0.750688i	−0.511659	−	0.859189i	$-0.670969\pi$
$797$	306449.	−	476844.i	0.482438	−	0.750688i	0.994096	+	0.108501i	$0.0346051\pi$
$798$	−17647.6	+	5181.81i	−0.0277128	+	0.00813721i
$799$	188743.	+	27137.1i	0.295650	+	0.0425080i
$800$	18034.4	+	39489.9i	0.0281788	+	0.0617030i
$801$	−414800.	+	59639.3i	−0.646508	+	0.0929538i
$802$	323001.	+	502599.i	0.502175	+	0.781399i
$803$	37545.3	+	32533.2i	0.0582270	+	0.0504540i
$804$			7491.59i			0.0115894i
$805$	609542.	−	846171.i	0.940615	−	1.30577i
$806$	−422515.			−0.650388
$807$	236737.	−	273209.i	0.363512	−	0.419515i
$808$	−97595.0	+	62720.5i	−0.149488	+	0.0960698i
$809$	58225.5	+	404967.i	0.0889644	+	0.618761i	0.984711	+	0.174196i	$0.0557327\pi$
$809$	58225.5	+	404967.i	0.0889644	+	0.618761i	−0.895747	+	0.444565i	$0.853358\pi$
$810$	55157.2	−	25189.5i	0.0840683	−	0.0383927i
$811$	−31550.2	+	219437.i	−0.0479690	+	0.333632i	0.951679	+	0.307095i	$0.0993570\pi$
$811$	−31550.2	+	219437.i	−0.0479690	+	0.333632i	−0.999648	+	0.0265367i	$0.991552\pi$
$812$	−119743.	−	407807.i	−0.181609	−	0.618504i
$813$	342599.	+	220175.i	0.518328	+	0.333109i
$814$	224715.	−	492057.i	0.339143	−	0.742620i
$815$	266864.	−	908854.i	0.401767	−	1.36829i
$816$	20963.7	−	18165.2i	0.0314839	−	0.0272809i
$817$	−20512.7	−	23672.9i	−0.0307312	−	0.0354657i
$818$	−659033.	−	193510.i	−0.984920	−	0.289199i
$819$	458395.	+	209342.i	0.683396	+	0.312096i
$820$	−343734.	+	534860.i	−0.511204	+	0.795449i
$821$	−62252.7	+	18279.0i	−0.0923574	+	0.0271186i	−0.327585	−	0.944822i	$-0.606235\pi$
$821$	−62252.7	+	18279.0i	−0.0923574	+	0.0271186i	0.235227	+	0.971940i	$0.424417\pi$
$822$	413894.	+	59509.0i	0.612556	+	0.0880723i
$823$	−476865.	−	1.04419e6i	−0.704037	−	1.54163i	−0.835006	−	0.550240i	$-0.814536\pi$
$823$	−476865.	−	1.04419e6i	−0.704037	−	1.54163i	0.130969	−	0.991386i	$-0.458191\pi$
$824$	294272.	−	42309.9i	0.433405	−	0.0623142i
$825$	152615.	+	237473.i	0.224227	+	0.348904i
$826$	−173984.	−	150758.i	−0.255006	−	0.220964i
$827$			756578.i			1.10622i	0.833107	+	0.553112i	$0.186560\pi$
$827$			756578.i			1.10622i	−0.833107	+	0.553112i	$0.813440\pi$
$828$	6059.64	−	114103.i	0.00883866	−	0.166432i
$829$	−571326.			−0.831333			−0.415667	−	0.909517i	$-0.636452\pi$
$829$	−571326.			−0.831333			−0.415667	+	0.909517i	$0.636452\pi$
$830$	323301.	−	373109.i	0.469300	−	0.541601i
$831$	−624696.	+	401468.i	−0.904621	+	0.581365i
$832$	20287.4	+	141102.i	0.0293076	+	0.203839i
$833$	158785.	−	72514.8i	0.228834	−	0.104505i
$834$	62235.8	−	432860.i	0.0894764	−	0.622322i
$835$	−91505.3	−	311639.i	−0.131242	−	0.446970i
$836$	−28460.4	−	18290.4i	−0.0407219	−	0.0261704i
$837$	−31269.3	+	68470.3i	−0.0446342	+	0.0977353i
$838$	611.318	−	2081.96i	0.000870521	−	0.00296472i
$839$	317190.	−	274847.i	0.450605	−	0.390452i	−0.399781	−	0.916611i	$-0.630914\pi$
$839$	317190.	−	274847.i	0.450605	−	0.390452i	0.850386	+	0.526159i	$0.176368\pi$
$840$	151787.	+	175171.i	0.215117	+	0.248259i
$841$	75961.3	+	22304.2i	0.107399	+	0.0315352i
$842$	−485820.	−	221867.i	−0.685254	−	0.312945i
$843$	97991.7	−	152478.i	0.137890	−	0.214562i
$844$	313606.	−	92083.0i	0.440250	−	0.129269i
$845$	−1.42512e6	−	204902.i	−1.99590	−	0.286967i
$846$	72523.0	+	158803.i	0.101329	+	0.221880i
$847$	2.43325e6	−	349848.i	3.39171	−	0.487655i
$848$	−108048.	−	168125.i	−0.150253	−	0.233799i
$849$	−619910.	−	537155.i	−0.860030	−	0.745220i
$850$			56580.8i			0.0783126i
$851$	86917.7	−	438093.i	0.120019	−	0.604933i
$852$	−176104.			−0.242599
$853$	101665.	−	117328.i	0.139725	−	0.161252i	−0.681574	−	0.731749i	$-0.738704\pi$
$853$	101665.	−	117328.i	0.139725	−	0.161252i	0.821299	+	0.570498i	$0.193250\pi$
$854$	178488.	−	114707.i	0.244734	−	0.157281i
$855$	−2109.56	−	14672.3i	−0.00288575	−	0.0200709i
$856$	17753.8	−	8107.87i	0.0242294	−	0.0110652i
$857$	−109028.	+	758306.i	−0.148449	+	1.03248i	0.770312	+	0.637667i	$0.220101\pi$
$857$	−109028.	+	758306.i	−0.148449	+	1.03248i	−0.918760	+	0.394816i	$0.870809\pi$
$858$	261144.	+	889376.i	0.354737	+	1.20812i
$859$	346109.	+	222431.i	0.469058	+	0.301445i	0.753735	−	0.657178i	$-0.228250\pi$
$859$	346109.	+	222431.i	0.469058	+	0.301445i	−0.284677	+	0.958623i	$0.591886\pi$
$860$	−163983.	+	359072.i	−0.221718	+	0.485494i
$861$	−265205.	+	903206.i	−0.357747	+	1.21837i
$862$	−320946.	+	278101.i	−0.431934	+	0.374273i
$863$	537876.	+	620742.i	0.722205	+	0.833469i	0.991570	−	0.129569i	$-0.0413593\pi$
$863$	537876.	+	620742.i	0.722205	+	0.833469i	−0.269365	+	0.963038i	$0.586814\pi$
$864$	24367.6	+	7154.97i	0.0326426	+	0.00958474i
$865$	−1.33389e6	−	609167.i	−1.78274	−	0.814150i
$866$	−311436.	+	484604.i	−0.415273	+	0.646177i
$867$	−381720.	+	112083.i	−0.507817	+	0.149108i
$868$	−284801.	−	40948.2i	−0.378009	−	0.0543495i
$869$	300908.	+	658896.i	0.398468	+	0.872524i
$870$	339052.	−	48748.4i	0.447949	−	0.0644053i
$871$	−27128.0	−	42211.9i	−0.0357586	−	0.0556415i
$872$	−263896.	−	228667.i	−0.347056	−	0.300725i
$873$		−	15997.9i		−	0.0209911i
$874$	−26346.2	−	9279.82i	−0.0344902	−	0.0121483i
$875$	759322.			0.991767
$876$	−5970.19	+	6889.96i	−0.00778000	+	0.00897860i
$877$	682212.	−	438431.i	0.886993	−	0.570036i	−0.0159134	−	0.999873i	$-0.505066\pi$
$877$	682212.	−	438431.i	0.886993	−	0.570036i	0.902906	+	0.429838i	$0.141429\pi$
$878$	56667.4	+	394130.i	0.0735096	+	0.511270i
$879$	135322.	−	61799.6i	0.175142	−	0.0799848i
$880$	−60674.3	+	421999.i	−0.0783501	+	0.544937i
$881$	−104495.	−	355878.i	−0.134631	−	0.458511i	0.864387	−	0.502828i	$-0.167707\pi$
$881$	−104495.	−	355878.i	−0.134631	−	0.458511i	−0.999018	+	0.0443168i	$0.985889\pi$
$882$	134447.	+	86403.9i	0.172828	+	0.111070i
$883$	−294634.	+	645158.i	−0.377886	+	0.827456i	0.621155	+	0.783687i	$0.286664\pi$
$883$	−294634.	+	645158.i	−0.377886	+	0.827456i	−0.999042	+	0.0437681i	$0.986064\pi$
$884$	−52343.5	+	178265.i	−0.0669820	+	0.228120i
$885$	140219.	−	121501.i	0.179028	−	0.155129i
$886$	−629438.	−	726411.i	−0.801836	−	0.925368i
$887$	1.20478e6	+	353755.i	1.53130	+	0.449630i	0.935448	−	0.353464i	$-0.114996\pi$
$887$	1.20478e6	+	353755.i	1.53130	+	0.449630i	0.595852	+	0.803095i	$0.296815\pi$
$888$	90297.8	+	41237.6i	0.114512	+	0.0522959i
$889$	−959138.	+	1.49245e6i	−1.21361	+	1.88841i
$890$	1.23871e6	−	363718.i	1.56383	−	0.459182i
$891$	163454.	+	23501.1i	0.205892	+	0.0296028i
$892$	61889.0	+	135518.i	0.0777829	+	0.170321i
$893$	42243.0	−	6073.63i	0.0529727	−	0.00761633i
$894$	−106260.	−	165343.i	−0.132952	−	0.206877i
$895$	−209998.	−	181964.i	−0.262161	−	0.227164i
$896$			97077.6i			0.120921i
$897$	379038.	+	664866.i	0.471084	+	0.826322i
$898$	193280.			0.239681
$899$	−278457.	+	321357.i	−0.344540	+	0.397620i
$900$	−43578.9	+	28006.4i	−0.0538011	+	0.0345759i
$901$	−37068.6	−	257818.i	−0.0456621	−	0.317587i
$902$	−1.57500e6	+	719277.i	−1.93583	+	0.884063i
$903$	−83175.9	+	578501.i	−0.102005	+	0.709461i
$904$	−83627.1	−	284808.i	−0.102332	−	0.348510i
$905$	464210.	+	298330.i	0.566784	+	0.364250i
$906$	−63709.1	+	139504.i	−0.0776149	+	0.169953i
$907$	882.694	−	3006.18i	0.00107299	−	0.00365427i	−0.958955	−	0.283559i	$-0.908485\pi$
$907$	882.694	−	3006.18i	0.00107299	−	0.00365427i	0.960028	+	0.279905i	$0.0903029\pi$
$908$	438999.	−	380395.i	0.532466	−	0.461384i
$909$	−90652.2	−	104618.i	−0.109711	−	0.126613i
$910$	−1.48957e6	−	437378.i	−1.79878	−	0.528170i
$911$	−1.05736e6	−	482879.i	−1.27405	−	0.581837i	−0.340483	−	0.940251i	$-0.610591\pi$
$911$	−1.05736e6	−	482879.i	−1.27405	−	0.581837i	−0.933563	+	0.358413i	$0.883318\pi$
$912$	3356.48	−	5222.78i	0.00403547	−	0.00627932i
$913$	1.29003e6	−	378788.i	1.54760	−	0.454417i
$914$	−417126.	−	59973.7i	−0.499316	−	0.0717907i
$915$	71033.3	+	155541.i	0.0848437	+	0.185782i
$916$	−133487.	+	19192.5i	−0.159092	+	0.0228740i
$917$	1.06739e6	+	1.66089e6i	1.26936	+	1.97516i
$918$	25014.8	+	21675.5i	0.0296833	+	0.0257207i
$919$		−	103824.i		−	0.122933i	−0.998109	−	0.0614664i	$-0.980422\pi$
$919$		−	103824.i		−	0.122933i	0.998109	−	0.0614664i	$-0.0195777\pi$
$920$	31548.0	+	350593.i	0.0372731	+	0.414217i
$921$	353997.			0.417331
$922$	332930.	−	384222.i	0.391644	−	0.451981i
$923$	992270.	−	637693.i	1.16473	−	0.748529i
$924$	89833.1	+	624803.i	0.105219	+	0.731811i
$925$	−184186.	+	84114.7i	−0.215264	+	0.0983079i
$926$	−21827.5	+	151814.i	−0.0254556	+	0.177047i
$927$	99944.1	+	340379.i	0.116305	+	0.396098i
$928$	120690.	+	77562.7i	0.140144	+	0.0900651i
$929$	123799.	−	271081.i	0.143445	−	0.314100i	−0.824250	−	0.566227i	$-0.808403\pi$
$929$	123799.	−	271081.i	0.143445	−	0.314100i	0.967694	+	0.252127i	$0.0811299\pi$
$930$	65331.0	−	222497.i	0.0755359	−	0.257252i
$931$	29526.2	−	25584.6i	0.0340649	−	0.0295174i
$932$	−201406.	−	232435.i	−0.231868	−	0.267590i
$933$	−99592.8	−	29243.1i	−0.114410	−	0.0335939i
$934$	428627.	+	195748.i	0.491344	+	0.224389i
$935$	−300409.	+	467445.i	−0.343628	+	0.534696i
$936$	−163210.	+	47922.8i	−0.186292	+	0.0547004i
$937$	407832.	+	58637.5i	0.464518	+	0.0667876i	0.370601	−	0.928792i	$-0.379152\pi$
$937$	407832.	+	58637.5i	0.464518	+	0.0667876i	0.0939175	+	0.995580i	$0.470061\pi$
$938$	−14194.9	−	31082.6i	−0.0161335	−	0.0353274i
$939$	790606.	−	113672.i	0.896663	−	0.128921i
$940$	−290769.	−	452445.i	−0.329073	−	0.512048i
$941$	93081.1	+	80655.2i	0.105119	+	0.0910863i	0.705835	−	0.708377i	$-0.250572\pi$
$941$	93081.1	+	80655.2i	0.105119	+	0.0910863i	−0.600716	+	0.799463i	$0.705118\pi$
$942$		−	581562.i		−	0.655382i
$943$	−1.12855e6	+	877575.i	−1.26910	+	0.986872i
$944$	77707.6			0.0872006
$945$	−181119.	+	209022.i	−0.202815	+	0.234061i
$946$	−904364.	+	581200.i	−1.01056	+	0.649446i
$947$	−143499.	−	998057.i	−0.160011	−	1.11290i	−0.898608	−	0.438752i	$-0.855421\pi$
$947$	−143499.	−	998057.i	−0.160011	−	1.11290i	0.738598	−	0.674147i	$-0.235488\pi$
$948$	−120914.	+	55219.8i	−0.134543	+	0.0614438i
$949$	8690.08	−	60440.8i	0.00964920	−	0.0671117i
$950$	3567.72	+	12150.5i	0.00395315	+	0.0134632i
$951$	−693.363	−	445.597i	−0.000766654	−	0.000492699i
$952$	−52559.4	+	115089.i	−0.0579931	+	0.126987i
$953$	241760.	−	823359.i	0.266194	−	0.906574i	−0.712573	−	0.701598i	$-0.752470\pi$
$953$	241760.	−	823359.i	0.266194	−	0.906574i	0.978767	−	0.204976i	$-0.0657116\pi$
$954$	180224.	−	156165.i	0.198023	−	0.171588i
$955$	1.07256e6	+	1.23779e6i	1.17602	+	1.35719i
$956$	138577.	+	40689.9i	0.151627	+	0.0445216i
$957$	848549.	+	387519.i	0.926516	+	0.423126i
$958$	158452.	−	246556.i	0.172650	−	0.268648i
$959$	−1.83000e6	+	537337.i	−1.98982	+	0.584265i
$960$	−77441.4	−	11134.4i	−0.0840292	−	0.0120816i
$961$	−264063.	−	578217.i	−0.285931	−	0.626101i
$962$	−658116.	+	94622.9i	−0.711136	+	0.102246i
$963$	12591.1	+	19592.1i	0.0135772	+	0.0211265i
$964$	−232070.	−	201090.i	−0.249727	−	0.216390i
$965$			1.61242e6i			1.73150i
$966$	191059.	+	484895.i	0.204745	+	0.519629i
$967$	−961647.			−1.02840			−0.514201	−	0.857670i	$-0.671911\pi$
$967$	−961647.			−1.02840			−0.514201	+	0.857670i	$0.671911\pi$
$968$	−543387.	+	627102.i	−0.579907	+	0.669248i
$969$	6806.93	−	4374.55i	0.00724942	−	0.00465892i
$970$	7013.90	+	48782.7i	0.00745446	+	0.0518469i
$971$	−203472.	+	92922.6i	−0.215808	+	0.0985560i	−0.520386	−	0.853931i	$-0.674212\pi$
$971$	−203472.	+	92922.6i	−0.215808	+	0.0985560i	0.304578	+	0.952487i	$0.401485\pi$
$972$	−4312.70	+	29995.5i	−0.00456475	+	0.0317485i
$973$	561959.	+	1.91386e6i	0.593580	+	2.02155i
$974$	668891.	+	429870.i	0.705079	+	0.453127i
$975$	144134.	−	315609.i	0.151620	−	0.332002i
$976$	−20176.7	+	68715.6i	−0.0211812	+	0.0721366i
$977$	717664.	−	621859.i	0.751851	−	0.651483i	−0.192172	−	0.981361i	$-0.561553\pi$
$977$	717664.	−	621859.i	0.751851	−	0.651483i	0.944023	+	0.329878i	$0.107008\pi$
$978$	310002.	+	357761.i	0.324105	+	0.374038i
$979$	3.37342e6	+	990526.i	3.51970	+	1.03348i
$980$	−447853.	−	204528.i	−0.466319	−	0.212961i
$981$	225264.	−	350518.i	0.234074	−	0.364227i
$982$	770527.	−	226247.i	0.799033	−	0.234617i
$983$	−522932.	−	75186.3i	−0.541176	−	0.0778093i	−0.133694	−	0.991023i	$-0.542684\pi$
$983$	−522932.	−	75186.3i	−0.541176	−	0.0778093i	−0.407482	+	0.913213i	$0.633593\pi$
$984$	−131995.	−	289029.i	−0.136323	−	0.298505i
$985$	1.57791e6	−	226870.i	1.62634	−	0.233832i
$986$	101088.	+	157297.i	0.103980	+	0.161795i
$987$	−601795.	−	521459.i	−0.617753	−	0.535286i
$988$			41582.4i			0.0425986i
$989$	−616010.	+	639034.i	−0.629789	+	0.653328i
$990$	−508725.			−0.519054
$991$	296451.	−	342123.i	0.301860	−	0.348365i	−0.584473	−	0.811413i	$-0.698699\pi$
$991$	296451.	−	342123.i	0.301860	−	0.348365i	0.886333	+	0.463048i	$0.153244\pi$
$992$	81703.9	−	52507.9i	0.0830270	−	0.0533582i
$993$	144842.	+	1.00739e6i	0.146891	+	1.02165i
$994$	730653.	−	333678.i	0.739501	−	0.337719i
$995$	169450.	−	1.17855e6i	0.171157	−	1.19042i
$996$	69511.7	+	236735.i	0.0700711	+	0.238640i
$997$	1.63491e6	+	1.05070e6i	1.64477	+	1.05703i	0.936249	+	0.351336i	$0.114272\pi$
$997$	1.63491e6	+	1.05070e6i	1.64477	+	1.05703i	0.708518	+	0.705692i	$0.249364\pi$
$998$	249336.	−	545970.i	0.250337	−	0.548161i
$999$	−33371.6	+	113653.i	−0.0334385	+	0.113881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.5.h.a.7.13	✓	160
23.10	odd	22	inner	138.5.h.a.79.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.5.h.a.7.13	✓	160	1.1	even	1	trivial
138.5.h.a.79.13	yes	160	23.10	odd	22	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	138.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85223 - 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-26.7504 + 12.2165i) q^{5} +(2.09159 - 14.5473i) q^{6} +(18.8860 + 64.3200i) q^{7} +(-19.0354 - 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +O(q^{10})\)	\(q+(1.85223 - 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-26.7504 + 12.2165i) q^{5} +(2.09159 - 14.5473i) q^{6} +(18.8860 + 64.3200i) q^{7} +(-19.0354 - 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +(-23.4340 + 79.8088i) q^{10} +(-171.194 + 148.340i) q^{11} +(-27.2220 - 31.4159i) q^{12} +(267.146 + 78.4411i) q^{13} +(172.470 + 78.7646i) q^{14} +(-82.6142 + 128.550i) q^{15} +(-61.4076 + 18.0309i) q^{16} +(-82.5631 - 11.8708i) q^{17} +(-31.7242 - 69.4664i) q^{18} +(-18.4786 + 2.65683i) q^{19} +(127.193 + 197.916i) q^{20} +(263.247 + 228.105i) q^{21} +640.701i q^{22} +(121.909 + 514.761i) q^{23} -117.576 q^{24} +(157.052 - 181.248i) q^{25} +(662.488 - 425.755i) q^{26} +(-19.9662 - 138.868i) q^{27} +(487.820 - 222.780i) q^{28} +(112.790 - 784.469i) q^{29} +(121.767 + 414.699i) q^{30} +(-451.355 - 290.068i) q^{31} +(-75.1981 + 164.661i) q^{32} +(-331.611 + 1129.36i) q^{33} +(-178.300 + 154.498i) q^{34} +(-1290.97 - 1489.86i) q^{35} +(-207.250 - 60.8542i) q^{36} +(-767.998 - 350.733i) q^{37} +(-28.5474 + 44.4207i) q^{38} +(1388.13 - 407.592i) q^{39} +(658.652 + 94.6999i) q^{40} +(1122.64 + 2458.24i) q^{41} +(975.187 - 140.211i) q^{42} +(907.131 + 1411.52i) q^{43} +(1369.55 + 1186.72i) q^{44} +794.014i q^{45} +(1326.15 + 692.863i) q^{46} -2286.05 q^{47} +(-217.776 + 251.327i) q^{48} +(-1760.53 + 1131.42i) q^{49} +(-96.5363 - 671.424i) q^{50} +(-394.254 + 180.050i) q^{51} +(316.991 - 2204.72i) q^{52} +(879.759 + 2996.18i) q^{53} +(-333.824 - 214.536i) q^{54} +(2767.30 - 6059.55i) q^{55} +(427.343 - 1455.39i) q^{56} +(-73.3117 + 63.5249i) q^{57} +(-1467.96 - 1694.11i) q^{58} +(-1165.00 - 342.074i) q^{59} +(1111.99 + 507.830i) q^{60} +(604.982 - 941.370i) q^{61} +(-1456.06 + 427.536i) q^{62} +(1791.53 + 257.583i) q^{63} +(212.692 + 465.732i) q^{64} +(-8104.52 + 1165.25i) q^{65} +(1799.89 + 2800.68i) q^{66} +(-136.201 - 118.019i) q^{67} +667.297i q^{68} +(1978.99 + 1907.69i) q^{69} -5575.88 q^{70} +(2774.25 - 3201.66i) q^{71} +(-513.956 + 330.299i) q^{72} +(-31.2117 - 217.082i) q^{73} +(-2172.23 + 992.023i) q^{74} +(177.348 - 1233.49i) q^{75} +(42.0766 + 143.300i) q^{76} +(-12774.4 - 8209.62i) q^{77} +(1699.87 - 3722.19i) q^{78} +(900.902 - 3068.19i) q^{79} +(1422.40 - 1232.52i) q^{80} +(-477.393 - 550.941i) q^{81} +(7334.08 + 2153.48i) q^{82} +(-5399.02 - 2465.65i) q^{83} +(1506.55 - 2344.24i) q^{84} +(2353.61 - 691.083i) q^{85} +(4697.46 + 675.393i) q^{86} +(-1710.74 - 3745.99i) q^{87} +(5073.44 - 729.450i) q^{88} +(-8391.26 - 13057.1i) q^{89} +(1697.27 + 1470.69i) q^{90} +18664.2i q^{91} +(3937.38 - 1551.41i) q^{92} -2787.87 q^{93} +(-4234.27 + 4886.61i) q^{94} +(461.854 - 296.815i) q^{95} +(133.862 + 931.030i) q^{96} +(538.971 - 246.140i) q^{97} +(-842.386 + 5858.92i) q^{98} +(1723.10 + 5868.35i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) \) 160 * q - 128 * q^4 - 432 * q^9	\( 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) \) 160 * q - 128 * q^4 - 432 * q^9 + 208 * q^13 - 1024 * q^16 - 1980 * q^17 - 3828 * q^19 - 3168 * q^20 + 3120 * q^23 + 9768 * q^25 + 4416 * q^26 + 5280 * q^28 - 828 * q^29 - 7748 * q^31 + 16464 * q^35 - 3456 * q^36 - 3520 * q^37 - 9072 * q^39 - 5472 * q^41 - 7216 * q^43 - 1280 * q^46 + 6960 * q^47 + 13888 * q^49 - 7296 * q^50 + 17424 * q^51 + 1664 * q^52 + 14784 * q^53 + 37316 * q^55 - 15840 * q^57 - 9984 * q^58 - 29808 * q^59 - 44968 * q^61 - 8192 * q^64 - 5852 * q^67 - 10584 * q^69 + 4352 * q^70 + 30048 * q^71 + 17084 * q^73 + 4176 * q^75 - 14160 * q^77 - 6912 * q^78 + 28424 * q^79 - 11664 * q^81 - 128 * q^82 - 35904 * q^83 - 91892 * q^85 + 8064 * q^87 - 15312 * q^89 - 6720 * q^92 + 11952 * q^93 + 21248 * q^94 + 224268 * q^95 + 41712 * q^97 + 62976 * q^98 + 17820 * q^99

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