LMFDB - Embedded newform 80.6.q.a.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.15884 + 2.32087i) q^{2} +(-9.83803 + 9.83803i) q^{3} +(21.2272 - 23.9459i) q^{4} +(46.4875 - 31.0470i) q^{5} +(27.9200 - 73.5856i) q^{6} -45.7194 q^{7} +(-53.9321 + 172.799i) q^{8} +49.4262i q^{9} +O(q^{10})$	\(q+(-5.15884 + 2.32087i) q^{2} +(-9.83803 + 9.83803i) q^{3} +(21.2272 - 23.9459i) q^{4} +(46.4875 - 31.0470i) q^{5} +(27.9200 - 73.5856i) q^{6} -45.7194 q^{7} +(-53.9321 + 172.799i) q^{8} +49.4262i q^{9} +(-167.765 + 268.057i) q^{10} +(-266.663 + 266.663i) q^{11} +(26.7474 + 444.414i) q^{12} +(-19.5826 + 19.5826i) q^{13} +(235.859 - 106.109i) q^{14} +(-151.904 + 762.787i) q^{15} +(-122.815 - 1016.61i) q^{16} -891.207i q^{17} +(-114.712 - 254.982i) q^{18} +(-334.228 - 334.228i) q^{19} +(243.348 - 1772.23i) q^{20} +(449.789 - 449.789i) q^{21} +(756.782 - 1994.56i) q^{22} -1574.39 q^{23} +(-1169.41 - 2230.58i) q^{24} +(1197.17 - 2886.59i) q^{25} +(55.5749 - 146.472i) q^{26} +(-2876.90 - 2876.90i) q^{27} +(-970.493 + 1094.79i) q^{28} +(-116.945 - 116.945i) q^{29} +(-986.678 - 4287.64i) q^{30} -3236.11 q^{31} +(2993.00 + 4959.48i) q^{32} -5246.88i q^{33} +(2068.37 + 4597.59i) q^{34} +(-2125.38 + 1419.45i) q^{35} +(1183.56 + 1049.18i) q^{36} +(-3959.03 - 3959.03i) q^{37} +(2499.92 + 948.528i) q^{38} -385.309i q^{39} +(2857.70 + 9707.40i) q^{40} -9816.22i q^{41} +(-1276.49 + 3364.29i) q^{42} +(-10555.6 - 10555.6i) q^{43} +(724.996 + 12046.0i) q^{44} +(1534.53 + 2297.70i) q^{45} +(8122.00 - 3653.94i) q^{46} -3833.55i q^{47} +(11209.7 + 8793.17i) q^{48} -14716.7 q^{49} +(523.392 + 17669.9i) q^{50} +(8767.72 + 8767.72i) q^{51} +(53.2407 + 884.608i) q^{52} +(-9373.35 - 9373.35i) q^{53} +(21518.3 + 8164.55i) q^{54} +(-4117.41 + 20675.6i) q^{55} +(2465.74 - 7900.24i) q^{56} +6576.28 q^{57} +(874.715 + 331.887i) q^{58} +(-56.0853 + 56.0853i) q^{59} +(15041.1 + 19829.3i) q^{60} +(20778.0 + 20778.0i) q^{61} +(16694.6 - 7510.59i) q^{62} -2259.73i q^{63} +(-26950.7 - 18638.8i) q^{64} +(-302.365 + 1518.33i) q^{65} +(12177.3 + 27067.8i) q^{66} +(5444.53 - 5444.53i) q^{67} +(-21340.8 - 18917.8i) q^{68} +(15488.9 - 15488.9i) q^{69} +(7670.13 - 12255.4i) q^{70} +80893.1i q^{71} +(-8540.77 - 2665.66i) q^{72} -71776.0 q^{73} +(29612.3 + 11235.6i) q^{74} +(16620.6 + 40176.2i) q^{75} +(-15098.1 + 908.688i) q^{76} +(12191.7 - 12191.7i) q^{77} +(894.251 + 1987.75i) q^{78} -93830.6 q^{79} +(-37272.0 - 43446.5i) q^{80} +44595.5 q^{81} +(22782.1 + 50640.3i) q^{82} +(59342.1 - 59342.1i) q^{83} +(-1222.87 - 20318.4i) q^{84} +(-27669.3 - 41429.9i) q^{85} +(78953.0 + 29956.6i) q^{86} +2301.02 q^{87} +(-31697.3 - 60460.7i) q^{88} -131863. i q^{89} +(-13249.1 - 8292.00i) q^{90} +(895.306 - 895.306i) q^{91} +(-33419.8 + 37700.2i) q^{92} +(31837.0 - 31837.0i) q^{93} +(8897.16 + 19776.7i) q^{94} +(-25914.2 - 5160.64i) q^{95} +(-78236.7 - 19346.3i) q^{96} +74340.6i q^{97} +(75921.2 - 34155.6i) q^{98} +(-13180.2 - 13180.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.15884	+	2.32087i	−0.911962	+	0.410275i
$2$	−5.15884	+	2.32087i	−0.911962	+	0.410275i
$3$	−9.83803	+	9.83803i	−0.631110	+	0.631110i	−0.948347	−	0.317236i	$-0.897245\pi$
$3$	−9.83803	+	9.83803i	−0.631110	+	0.631110i	0.317236	+	0.948347i	$0.397245\pi$
$4$	21.2272	−	23.9459i	0.663349	−	0.748310i
$5$	46.4875	−	31.0470i	0.831593	−	0.555385i
$5$	46.4875	−	31.0470i	0.831593	−	0.555385i
$6$	27.9200	−	73.5856i	0.316620	−	0.834477i
$7$	−45.7194			−0.352659			−0.176330	−	0.984331i	$-0.556422\pi$
$7$	−45.7194			−0.352659			−0.176330	+	0.984331i	$0.556422\pi$
$8$	−53.9321	+	172.799i	−0.297936	+	0.954586i
$9$			49.4262i			0.203400i
$10$	−167.765	+	268.057i	−0.530520	+	0.847672i
$11$	−266.663	+	266.663i	−0.664479	+	0.664479i	−0.956433	−	0.291953i	$-0.905695\pi$
$11$	−266.663	+	266.663i	−0.664479	+	0.664479i	0.291953	+	0.956433i	$0.405695\pi$
$12$	26.7474	+	444.414i	0.0536201	+	0.890912i
$13$	−19.5826	+	19.5826i	−0.0321375	+	0.0321375i	−0.722993	−	0.690855i	$-0.757234\pi$
$13$	−19.5826	+	19.5826i	−0.0321375	+	0.0321375i	0.690855	+	0.722993i	$0.257234\pi$
$14$	235.859	−	106.109i	0.321612	−	0.144687i
$15$	−151.904	+	762.787i	−0.174318	+	0.875336i
$16$	−122.815	−	1016.61i	−0.119937	−	0.992782i
$17$		−	891.207i		−	0.747922i	−0.927444	−	0.373961i	$-0.877999\pi$
$17$		−	891.207i		−	0.747922i	0.927444	−	0.373961i	$-0.122001\pi$
$18$	−114.712	−	254.982i	−0.0834499	−	0.185493i
$19$	−334.228	−	334.228i	−0.212402	−	0.212402i	0.592885	−	0.805287i	$-0.297989\pi$
$19$	−334.228	−	334.228i	−0.212402	−	0.212402i	−0.805287	+	0.592885i	$0.797989\pi$
$20$	243.348	−	1772.23i	0.136036	−	0.990704i
$21$	449.789	−	449.789i	0.222567	−	0.222567i
$22$	756.782	−	1994.56i	0.333361	−	0.878599i
$23$	−1574.39			−0.620572			−0.310286	−	0.950643i	$-0.600425\pi$
$23$	−1574.39			−0.620572			−0.310286	+	0.950643i	$0.600425\pi$
$24$	−1169.41	−	2230.58i	−0.414419	−	0.790479i
$25$	1197.17	−	2886.59i	0.383094	−	0.923709i
$26$	55.5749	−	146.472i	0.0161230	−	0.0424934i
$27$	−2876.90	−	2876.90i	−0.759478	−	0.759478i
$28$	−970.493	+	1094.79i	−0.233936	+	0.263899i
$29$	−116.945	−	116.945i	−0.0258219	−	0.0258219i	0.694078	−	0.719900i	$-0.255812\pi$
$29$	−116.945	−	116.945i	−0.0258219	−	0.0258219i	−0.719900	+	0.694078i	$0.755812\pi$
$30$	−986.678	−	4287.64i	−0.200158	−	0.869791i
$31$	−3236.11			−0.604811			−0.302405	−	0.953179i	$-0.597790\pi$
$31$	−3236.11			−0.604811			−0.302405	+	0.953179i	$0.597790\pi$
$32$	2993.00	+	4959.48i	0.516691	+	0.856172i
$33$		−	5246.88i		−	0.838719i
$34$	2068.37	+	4597.59i	0.306854	+	0.682076i
$35$	−2125.38	+	1419.45i	−0.293269	+	0.195862i
$36$	1183.56	+	1049.18i	0.152206	+	0.134925i
$37$	−3959.03	−	3959.03i	−0.475427	−	0.475427i	0.428238	−	0.903666i	$-0.359134\pi$
$37$	−3959.03	−	3959.03i	−0.475427	−	0.475427i	−0.903666	+	0.428238i	$0.859134\pi$
$38$	2499.92	+	948.528i	0.280846	+	0.106559i
$39$		−	385.309i		−	0.0405647i
$40$	2857.70	+	9707.40i	0.282402	+	0.959296i
$41$		−	9816.22i		−	0.911979i	−0.889985	−	0.455989i	$-0.849285\pi$
$41$		−	9816.22i		−	0.911979i	0.889985	−	0.455989i	$-0.150715\pi$
$42$	−1276.49	+	3364.29i	−0.111659	+	0.294286i
$43$	−10555.6	−	10555.6i	−0.870589	−	0.870589i	0.121948	−	0.992537i	$-0.461086\pi$
$43$	−10555.6	−	10555.6i	−0.870589	−	0.870589i	−0.992537	+	0.121948i	$0.961086\pi$
$44$	724.996	+	12046.0i	0.0564552	+	0.938018i
$45$	1534.53	+	2297.70i	0.112965	+	0.169146i
$46$	8122.00	−	3653.94i	0.565938	−	0.254605i
$47$		−	3833.55i		−	0.253138i	−0.991958	−	0.126569i	$-0.959604\pi$
$47$		−	3833.55i		−	0.253138i	0.991958	−	0.126569i	$-0.0403965\pi$
$48$	11209.7	+	8793.17i	0.702248	+	0.550861i
$49$	−14716.7			−0.875631
$50$	523.392	+	17669.9i	0.0296075	+	0.999562i
$51$	8767.72	+	8767.72i	0.472021	+	0.472021i
$52$	53.2407	+	884.608i	0.00273046	+	0.0453673i
$53$	−9373.35	−	9373.35i	−0.458358	−	0.458358i	0.439758	−	0.898116i	$-0.355064\pi$
$53$	−9373.35	−	9373.35i	−0.458358	−	0.458358i	−0.898116	+	0.439758i	$0.855064\pi$
$54$	21518.3	+	8164.55i	1.00421	+	0.381020i
$55$	−4117.41	+	20675.6i	−0.183534	+	0.921619i
$56$	2465.74	−	7900.24i	0.105070	−	0.336644i
$57$	6576.28			0.268098
$58$	874.715	+	331.887i	0.0341426	+	0.0129545i
$59$	−56.0853	+	56.0853i	−0.00209758	+	0.00209758i	−0.708155	−	0.706057i	$-0.750472\pi$
$59$	−56.0853	+	56.0853i	−0.00209758	+	0.00209758i	0.706057	+	0.708155i	$0.250472\pi$
$60$	15041.1	+	19829.3i	0.539390	+	0.711097i
$61$	20778.0	+	20778.0i	0.714957	+	0.714957i	0.967568	−	0.252611i	$-0.0812892\pi$
$61$	20778.0	+	20778.0i	0.714957	+	0.714957i	−0.252611	+	0.967568i	$0.581289\pi$
$62$	16694.6	−	7510.59i	0.551565	−	0.248139i
$63$		−	2259.73i		−	0.0717309i
$64$	−26950.7	−	18638.8i	−0.822469	−	0.568810i
$65$	−302.365	+	1518.33i	−0.00887664	+	0.0445741i
$66$	12177.3	+	27067.8i	0.344106	+	0.764880i
$67$	5444.53	−	5444.53i	0.148174	−	0.148174i	−0.629128	−	0.777302i	$-0.716588\pi$
$67$	5444.53	−	5444.53i	0.148174	−	0.148174i	0.777302	+	0.629128i	$0.216588\pi$
$68$	−21340.8	−	18917.8i	−0.559678	−	0.496133i
$69$	15488.9	−	15488.9i	0.391649	−	0.391649i
$70$	7670.13	−	12255.4i	0.187093	−	0.298939i
$71$			80893.1i			1.90443i	0.305425	+	0.952216i	$0.401201\pi$
$71$			80893.1i			1.90443i	−0.305425	+	0.952216i	$0.598799\pi$
$72$	−8540.77	−	2665.66i	−0.194163	−	0.0606001i
$73$	−71776.0			−1.57642			−0.788211	−	0.615406i	$-0.788992\pi$
$73$	−71776.0			−1.57642			−0.788211	+	0.615406i	$0.788992\pi$
$74$	29612.3	+	11235.6i	0.628628	+	0.238516i
$75$	16620.6	+	40176.2i	0.341188	+	0.824737i
$76$	−15098.1	+	908.688i	−0.299839	+	0.0180460i
$77$	12191.7	−	12191.7i	0.234335	−	0.234335i
$78$	894.251	+	1987.75i	0.0166427	+	0.0369934i
$79$	−93830.6			−1.69152			−0.845759	−	0.533564i	$-0.820852\pi$
$79$	−93830.6			−1.69152			−0.845759	+	0.533564i	$0.820852\pi$
$80$	−37272.0	−	43446.5i	−0.651115	−	0.758979i
$81$	44595.5			0.755228
$82$	22782.1	+	50640.3i	0.374162	+	0.831690i
$83$	59342.1	−	59342.1i	0.945514	−	0.945514i	−0.0530764	−	0.998590i	$-0.516903\pi$
$83$	59342.1	−	59342.1i	0.945514	−	0.945514i	0.998590	+	0.0530764i	$0.0169027\pi$
$84$	−1222.87	−	20318.4i	−0.0189096	−	0.314188i
$85$	−27669.3	−	41429.9i	−0.415385	−	0.621967i
$86$	78953.0	+	29956.6i	1.15112	+	0.436763i
$87$	2301.02			0.0325929
$88$	−31697.3	−	60460.7i	−0.436331	−	0.832275i
$89$		−	131863.i		−	1.76461i	−0.470675	−	0.882306i	$-0.655990\pi$
$89$		−	131863.i		−	1.76461i	0.470675	−	0.882306i	$-0.344010\pi$
$90$	−13249.1	−	8292.00i	−0.172416	−	0.107908i
$91$	895.306	−	895.306i	0.0113336	−	0.0113336i
$92$	−33419.8	+	37700.2i	−0.411655	+	0.464380i
$93$	31837.0	−	31837.0i	0.381702	−	0.381702i
$94$	8897.16	+	19776.7i	0.103856	+	0.230852i
$95$	−25914.2	−	5160.64i	−0.294597	−	0.0586670i
$96$	−78236.7	−	19346.3i	−0.866428	−	0.214250i
$97$			74340.6i			0.802226i	0.916028	+	0.401113i	$0.131377\pi$
$97$			74340.6i			0.802226i	−0.916028	+	0.401113i	$0.868623\pi$
$98$	75921.2	−	34155.6i	0.798542	−	0.359250i
$99$	−13180.2	−	13180.2i	−0.135155	−	0.135155i
$100$	−43709.6	−	89941.5i	−0.437096	−	0.899415i
$101$	95511.7	−	95511.7i	0.931650	−	0.931650i	−0.0661588	−	0.997809i	$-0.521074\pi$
$101$	95511.7	−	95511.7i	0.931650	−	0.931650i	0.997809	+	0.0661588i	$0.0210744\pi$
$102$	−65579.9	−	24882.5i	−0.624124	−	0.236807i
$103$	−55919.1			−0.519358			−0.259679	−	0.965695i	$-0.583617\pi$
$103$	−55919.1			−0.519358			−0.259679	+	0.965695i	$0.583617\pi$
$104$	−2327.72	−	4439.98i	−0.0211031	−	0.0402530i
$105$	6944.96	−	34874.1i	0.0614747	−	0.308695i
$106$	70109.9	+	26601.3i	0.606058	+	0.229952i
$107$	131751.	+	131751.i	1.11249	+	1.11249i	0.992813	+	0.119675i	$0.0381851\pi$
$107$	131751.	+	131751.i	1.11249	+	1.11249i	0.119675	+	0.992813i	$0.461815\pi$
$108$	−129958.	+	7821.63i	−1.07212	+	0.0645264i
$109$	−89988.4	−	89988.4i	−0.725471	−	0.725471i	0.244243	−	0.969714i	$-0.421461\pi$
$109$	−89988.4	−	89988.4i	−0.725471	−	0.725471i	−0.969714	+	0.244243i	$0.921461\pi$
$110$	−26744.2	−	116218.i	−0.210741	−	0.915781i
$111$	77898.1			0.600094
$112$	5615.04	+	46478.7i	0.0422968	+	0.350114i
$113$			236003.i			1.73869i	0.494209	+	0.869343i	$0.335458\pi$
$113$			236003.i			1.73869i	−0.494209	+	0.869343i	$0.664542\pi$
$114$	−33926.0	+	15262.7i	−0.244495	+	0.109994i
$115$	−73189.3	+	48880.0i	−0.516063	+	0.344656i
$116$	−5282.78	+	317.947i	−0.0364517	+	0.00219387i
$117$	−967.895	−	967.895i	−0.00653678	−	0.00653678i
$118$	159.168	−	419.501i	0.00105233	−	0.00277350i
$119$			40745.4i			0.263761i
$120$	−123616.	−	67387.5i	−0.783648	−	0.427195i
$121$			18832.4i			0.116934i
$122$	−155414.	−	58967.4i	−0.945343	−	0.358685i
$123$	96572.3	+	96572.3i	0.575559	+	0.575559i
$124$	−68693.5	+	77491.8i	−0.401201	+	0.452586i
$125$	−33966.6	−	171359.i	−0.194436	−	0.980915i
$126$	5244.54	+	11657.6i	0.0294294	+	0.0654158i
$127$			99662.0i			0.548303i	0.961687	+	0.274151i	$0.0883969\pi$
$127$			99662.0i			0.548303i	−0.961687	+	0.274151i	$0.911603\pi$
$128$	182292.	+	33605.5i	0.983429	+	0.181295i
$129$	207693.			1.09887
$130$	−1963.98	−	8534.56i	−0.0101925	−	0.0442917i
$131$	91528.2	+	91528.2i	0.465990	+	0.465990i	0.900613	−	0.434623i	$-0.143118\pi$
$131$	91528.2	+	91528.2i	0.465990	+	0.465990i	−0.434623	+	0.900613i	$0.643118\pi$
$132$	−125642.	−	111376.i	−0.627622	−	0.556363i
$133$	15280.7	+	15280.7i	0.0749055	+	0.0749055i
$134$	−15451.4	+	40723.4i	−0.0743371	+	0.195922i
$135$	−223059.	−	44420.7i	−1.05338	−	0.209774i
$136$	153999.	+	48064.7i	0.713956	+	0.222833i
$137$	229311.			1.04381			0.521907	−	0.853003i	$-0.325221\pi$
$137$	229311.			1.04381			0.521907	+	0.853003i	$0.325221\pi$
$138$	−43956.9	+	115852.i	−0.196485	+	0.517853i
$139$	−159785.	+	159785.i	−0.701452	+	0.701452i	−0.964722	−	0.263270i	$-0.915199\pi$
$139$	−159785.	+	159785.i	−0.701452	+	0.701452i	0.263270	+	0.964722i	$0.415199\pi$
$140$	−11125.7	+	81025.0i	−0.0479742	+	0.349381i
$141$	37714.6	+	37714.6i	0.159758	+	0.159758i
$142$	−187742.	−	417314.i	−0.781341	−	1.73677i
$143$		−	10443.9i		−	0.0427095i
$144$	50247.1	−	6070.29i	0.201932	−	0.0243951i
$145$	−9067.29	−	1805.69i	−0.0358144	−	0.00713220i
$146$	370281.	−	166583.i	1.43764	−	0.646766i
$147$	144784.	−	144784.i	0.552620	−	0.552620i
$148$	−178842.	+	10763.7i	−0.671142	+	0.0403931i
$149$	−101218.	+	101218.i	−0.373503	+	0.373503i	−0.868751	−	0.495249i	$-0.835077\pi$
$149$	−101218.	+	101218.i	−0.373503	+	0.373503i	0.495249	+	0.868751i	$0.335077\pi$
$150$	−178986.	−	168688.i	−0.649519	−	0.612148i
$151$			225432.i			0.804587i	0.915511	+	0.402293i	$0.131787\pi$
$151$			225432.i			0.804587i	−0.915511	+	0.402293i	$0.868213\pi$
$152$	75779.6	−	39728.4i	0.266038	−	0.139474i
$153$	44049.0			0.152127
$154$	−34599.6	+	91190.1i	−0.117563	+	0.309846i
$155$	−150439.	+	100472.i	−0.502957	+	0.335903i
$156$	−9226.59	−	8179.02i	−0.0303550	−	0.0269085i
$157$	305972.	−	305972.i	0.990680	−	0.990680i	−0.00927741	−	0.999957i	$-0.502953\pi$
$157$	305972.	−	305972.i	0.990680	−	0.990680i	0.999957	+	0.00927741i	$0.00295313\pi$
$158$	484057.	−	217768.i	1.54260	−	0.693988i
$159$	184431.			0.578549
$160$	293114.	+	137630.i	0.905182	+	0.425024i
$161$	71980.0			0.218850
$162$	−230061.	+	103500.i	−0.688740	+	0.309851i
$163$	245413.	−	245413.i	0.723483	−	0.723483i	−0.245830	−	0.969313i	$-0.579060\pi$
$163$	245413.	−	245413.i	0.723483	−	0.723483i	0.969313	+	0.245830i	$0.0790604\pi$
$164$	−235059.	−	208371.i	−0.682443	−	0.604960i
$165$	−162900.	−	243914.i	−0.465812	−	0.697473i
$166$	−168411.	+	443862.i	−0.474352	+	1.25019i
$167$	−166169.			−0.461060			−0.230530	−	0.973065i	$-0.574046\pi$
$167$	−166169.			−0.461060			−0.230530	+	0.973065i	$0.574046\pi$
$168$	53464.8	+	101981.i	0.146149	+	0.278770i
$169$			370526.i			0.997934i
$170$	238895.	+	149514.i	0.633992	+	0.396788i
$171$	16519.6	−	16519.6i	0.0432025	−	0.0432025i
$172$	−476830.	+	28698.3i	−1.22897	+	0.0739666i
$173$	−228911.	+	228911.i	−0.581503	+	0.581503i	−0.935316	−	0.353813i	$-0.884885\pi$
$173$	−228911.	+	228911.i	−0.581503	+	0.581503i	0.353813	+	0.935316i	$0.384885\pi$
$174$	−11870.6	+	5340.36i	−0.0297235	+	0.0133720i
$175$	−54733.9	+	131973.i	−0.135102	+	0.325755i
$176$	303842.	+	238342.i	0.739378	+	0.579987i
$177$		−	1103.54i		−	0.00264761i
$178$	306037.	+	680262.i	0.723977	+	1.60926i
$179$	−81510.8	−	81510.8i	−0.190144	−	0.190144i	0.605614	−	0.795758i	$-0.292927\pi$
$179$	−81510.8	−	81510.8i	−0.190144	−	0.190144i	−0.795758	+	0.605614i	$0.792927\pi$
$180$	87594.3	+	12027.8i	0.201509	+	0.0276697i
$181$	−18567.7	+	18567.7i	−0.0421272	+	0.0421272i	−0.727857	−	0.685729i	$-0.759483\pi$
$181$	−18567.7	+	18567.7i	−0.0421272	+	0.0421272i	0.685729	+	0.727857i	$0.259483\pi$
$182$	−2540.85	+	6696.62i	−0.00568592	+	0.0149857i
$183$	−408830.			−0.902434
$184$	84910.0	−	272052.i	0.184890	−	0.592389i
$185$	−306961.	−	61129.3i	−0.659408	−	0.131317i
$186$	−90352.4	+	238131.i	−0.191495	+	0.504701i
$187$	237652.	+	237652.i	0.496979	+	0.496979i
$188$	−91798.0	−	81375.5i	−0.189426	−	0.167919i
$189$	131530.	+	131530.i	0.267837	+	0.267837i
$190$	145664.	−	33520.4i	0.292731	−	0.0673636i
$191$	219256.			0.434878			0.217439	−	0.976074i	$-0.430230\pi$
$191$	219256.			0.434878			0.217439	+	0.976074i	$0.430230\pi$
$192$	448510.	−	81772.5i	0.878050	−	0.160086i
$193$			777534.i			1.50254i	0.659995	+	0.751270i	$0.270559\pi$
$193$			777534.i			1.50254i	−0.659995	+	0.751270i	$0.729441\pi$
$194$	−172535.	−	383511.i	−0.329133	−	0.731600i
$195$	−11962.7	−	17912.0i	−0.0225290	−	0.0337333i
$196$	−312395.	+	352406.i	−0.580849	+	0.655244i
$197$	−278563.	−	278563.i	−0.511396	−	0.511396i	0.403558	−	0.914954i	$-0.367773\pi$
$197$	−278563.	−	278563.i	−0.511396	−	0.511396i	−0.914954	+	0.403558i	$0.867773\pi$
$198$	98583.6	+	37404.9i	0.178707	+	0.0678055i
$199$		−	746807.i		−	1.33683i	−0.743789	−	0.668414i	$-0.766973\pi$
$199$		−	746807.i		−	1.33683i	0.743789	−	0.668414i	$-0.233027\pi$
$200$	434233.	+	362549.i	0.767622	+	0.640902i
$201$			107127.i			0.187029i
$202$	−271059.	+	714399.i	−0.467397	+	1.23186i
$203$	5346.66	+	5346.66i	0.00910632	+	0.00910632i
$204$	396065.	−	23837.4i	0.666333	−	0.0401036i
$205$	−304764.	−	456331.i	−0.506500	−	0.758395i
$206$	288477.	−	129781.i	0.473635	−	0.213080i
$207$		−	77815.9i		−	0.126224i
$208$	22312.9	+	17502.8i	0.0357600	+	0.0280511i
$209$	178252.			0.282273
$210$	45110.3	+	196028.i	0.0705874	+	0.306740i
$211$	−549963.	−	549963.i	−0.850408	−	0.850408i	0.139775	−	0.990183i	$-0.455362\pi$
$211$	−549963.	−	549963.i	−0.850408	−	0.850408i	−0.990183	+	0.139775i	$0.955362\pi$
$212$	−423423.	+	25484.0i	−0.647046	+	0.0389429i
$213$	−795829.	−	795829.i	−1.20191	−	1.20191i
$214$	−985460.	−	373906.i	−1.47097	−	0.558120i
$215$	−818425.	−	162984.i	−1.20749	−	0.240463i
$216$	652281.	−	341967.i	0.951263	−	0.498711i
$217$	147953.			0.213292
$218$	673086.	+	255384.i	0.959245	+	0.363959i
$219$	706135.	−	706135.i	0.994895	−	0.994895i
$220$	407695.	+	537479.i	0.567909	+	0.748695i
$221$	17452.2	+	17452.2i	0.0240364	+	0.0240364i
$222$	−401863.	+	180791.i	−0.547263	+	0.246204i
$223$		−	1.19027e6i		−	1.60282i	−0.598118	−	0.801408i	$-0.704085\pi$
$223$		−	1.19027e6i		−	1.60282i	0.598118	−	0.801408i	$-0.295915\pi$
$224$	−136838.	−	226744.i	−0.182216	−	0.301937i
$225$	142673.	+	59171.5i	0.187882	+	0.0779214i
$226$	−547731.	−	1.21750e6i	−0.713339	−	1.58562i
$227$	635906.	−	635906.i	0.819083	−	0.819083i	−0.166892	−	0.985975i	$-0.553373\pi$
$227$	635906.	−	635906.i	0.819083	−	0.819083i	0.985975	+	0.166892i	$0.0533730\pi$
$228$	139596.	−	157475.i	0.177842	−	0.200620i
$229$	−795777.	+	795777.i	−1.00277	+	1.00277i	−0.00277711	+	0.999996i	$0.500884\pi$
$229$	−795777.	+	795777.i	−1.00277	+	1.00277i	−0.999996	+	0.00277711i	$0.999116\pi$
$230$	264127.	−	422026.i	0.329226	−	0.526041i
$231$			239884.i			0.295782i
$232$	26515.1	−	13900.9i	0.0323424	−	0.0169559i
$233$	−531116.			−0.640914			−0.320457	−	0.947263i	$-0.603836\pi$
$233$	−531116.			−0.640914			−0.320457	+	0.947263i	$0.603836\pi$
$234$	7239.57	+	2746.86i	0.00864317	+	0.00327941i
$235$	−119020.	−	178212.i	−0.140589	−	0.210508i
$236$	152.483	+	2533.55i	0.000178214	+	0.00296107i
$237$	923109.	−	923109.i	1.06753	−	1.06753i
$238$	−94564.7	−	210199.i	−0.108215	−	0.240540i
$239$	−349145.			−0.395377			−0.197689	−	0.980265i	$-0.563343\pi$
$239$	−349145.			−0.395377			−0.197689	+	0.980265i	$0.563343\pi$
$240$	794111.	+	60745.0i	0.889925	+	0.0680742i
$241$	−1.36778e6			−1.51696			−0.758480	−	0.651697i	$-0.774057\pi$
$241$	−1.36778e6			−1.51696			−0.758480	+	0.651697i	$0.774057\pi$
$242$	−43707.5	−	97153.2i	−0.0479753	−	0.106640i
$243$	260354.	−	260354.i	0.282846	−	0.282846i
$244$	938609.	−	56490.7i	1.00928	−	0.0607439i
$245$	−684144.	+	456910.i	−0.728169	+	0.486313i
$246$	−722332.	−	274069.i	−0.761025	−	0.288750i
$247$	13090.1			0.0136521
$248$	174531.	−	559196.i	0.180195	−	0.577344i
$249$			1.16762e6i			1.19345i
$250$	572929.	+	805180.i	0.579763	+	0.814785i
$251$	1.17804e6	−	1.17804e6i	1.18025	−	1.18025i	0.200572	−	0.979679i	$-0.435720\pi$
$251$	1.17804e6	−	1.17804e6i	1.18025	−	1.18025i	0.979679	−	0.200572i	$-0.0642800\pi$
$252$	−54111.5	−	47967.8i	−0.0536770	−	0.0475826i
$253$	419831.	−	419831.i	0.412357	−	0.412357i
$254$	−231302.	−	514140.i	−0.224955	−	0.500031i
$255$	679800.	+	135378.i	0.654683	+	0.130376i
$256$	−1.01841e6	+	249710.i	−0.971230	+	0.238142i
$257$			1.84699e6i			1.74434i	0.489204	+	0.872170i	$0.337287\pi$
$257$			1.84699e6i			1.74434i	−0.489204	+	0.872170i	$0.662713\pi$
$258$	−1.07146e6	+	482028.i	−1.00213	+	0.450841i
$259$	181004.	+	181004.i	0.167664	+	0.167664i
$260$	29939.4	+	39470.2i	0.0274669	+	0.0362106i
$261$	5780.16	−	5780.16i	0.00525217	−	0.00525217i
$262$	−684603.	−	259754.i	−0.616149	−	0.233781i
$263$	−1.91938e6			−1.71109			−0.855543	−	0.517732i	$-0.826776\pi$
$263$	−1.91938e6			−1.71109			−0.855543	+	0.517732i	$0.826776\pi$
$264$	906654.	+	282976.i	0.800630	+	0.249884i
$265$	−726758.	−	144729.i	−0.635733	−	0.126602i
$266$	−114295.	−	43366.1i	−0.0990428	−	0.0375791i
$267$	1.29728e6	+	1.29728e6i	1.11367	+	1.11367i
$268$	−14802.4	−	245946.i	−0.0125891	−	0.209172i
$269$	918645.	+	918645.i	0.774046	+	0.774046i	0.978811	−	0.204765i	$-0.0656429\pi$
$269$	918645.	+	918645.i	0.774046	+	0.774046i	−0.204765	+	0.978811i	$0.565643\pi$
$270$	1.25382e6	−	288530.i	1.04671	−	0.240870i
$271$	−879383.			−0.727369			−0.363685	−	0.931522i	$-0.618481\pi$
$271$	−879383.			−0.727369			−0.363685	+	0.931522i	$0.618481\pi$
$272$	−906008.	+	109454.i	−0.742523	+	0.0897033i
$273$			17616.1i			0.0143055i
$274$	−1.18298e6	+	532199.i	−0.951918	+	0.428251i
$275$	450507.	+	1.08899e6i	0.359227	+	0.868344i
$276$	−42110.7	−	699680.i	−0.0332751	−	0.552875i
$277$	1.51409e6	+	1.51409e6i	1.18564	+	1.18564i	0.978261	+	0.207378i	$0.0664931\pi$
$277$	1.51409e6	+	1.51409e6i	1.18564	+	1.18564i	0.207378	+	0.978261i	$0.433507\pi$
$278$	453464.	−	1.19514e6i	0.351909	−	0.927486i
$279$		−	159949.i		−	0.123019i
$280$	−130652.	−	443816.i	−0.0995916	−	0.338305i
$281$		−	458222.i		−	0.346187i	−0.984905	−	0.173093i	$-0.944624\pi$
$281$		−	458222.i		−	0.346187i	0.984905	−	0.173093i	$-0.0553763\pi$
$282$	−282094.	−	107033.i	−0.211238	−	0.0801484i
$283$	56631.6	+	56631.6i	0.0420332	+	0.0420332i	0.727811	−	0.685778i	$-0.240538\pi$
$283$	56631.6	+	56631.6i	0.0420332	+	0.0420332i	−0.685778	+	0.727811i	$0.740538\pi$
$284$	1.93706e6	+	1.71713e6i	1.42511	+	1.26330i
$285$	305715.	−	204174.i	0.222948	−	0.148898i
$286$	24239.0	+	53878.6i	0.0175226	+	0.0389494i
$287$			448792.i			0.321618i
$288$	−245128.	+	147932.i	−0.174145	+	0.105095i
$289$	625608.			0.440613
$290$	50967.4	−	11728.7i	0.0355875	−	0.00818945i
$291$	−731366.	−	731366.i	−0.506293	−	0.506293i
$292$	−1.52360e6	+	1.71874e6i	−1.04572	+	1.17965i
$293$	−513676.	−	513676.i	−0.349559	−	0.349559i	0.510386	−	0.859945i	$-0.329502\pi$
$293$	−513676.	−	513676.i	−0.349559	−	0.349559i	−0.859945	+	0.510386i	$0.829502\pi$
$294$	−410892.	+	1.08294e6i	−0.277242	+	0.730694i
$295$	−865.984	+	4348.54i	−0.000579369	+	0.00290930i
$296$	897633.	−	470595.i	0.595483	−	0.312190i
$297$	1.53433e6			1.00931
$298$	287255.	−	757083.i	0.187381	−	0.493859i
$299$	30830.6	−	30830.6i	0.0199436	−	0.0199436i
$300$	1.31486e6	+	454831.i	0.843486	+	0.291774i
$301$	482597.	+	482597.i	0.307021	+	0.307021i
$302$	−523197.	−	1.16297e6i	−0.330102	−	0.733752i
$303$			1.87929e6i			1.17595i
$304$	−298730.	+	380827.i	−0.185394	+	0.236343i
$305$	1.61101e6	+	320823.i	0.991630	+	0.197477i
$306$	−227241.	+	102232.i	−0.138734	+	0.0624140i
$307$	−56934.5	+	56934.5i	−0.0344770	+	0.0344770i	−0.724135	−	0.689658i	$-0.757761\pi$
$307$	−56934.5	+	56934.5i	−0.0344770	+	0.0344770i	0.689658	+	0.724135i	$0.257761\pi$
$308$	−33146.4	−	550736.i	−0.0199095	−	0.330801i
$309$	550134.	−	550134.i	0.327772	−	0.327772i
$310$	542908.	−	867465.i	0.320865	−	0.512681i
$311$			2.10238e6i			1.23257i	0.787524	+	0.616284i	$0.211362\pi$
$311$			2.10238e6i			1.23257i	−0.787524	+	0.616284i	$0.788638\pi$
$312$	66580.9	+	20780.5i	0.0387225	+	0.0120857i
$313$	1.37805e6			0.795065			0.397533	−	0.917588i	$-0.369867\pi$
$313$	1.37805e6			0.795065			0.397533	+	0.917588i	$0.369867\pi$
$314$	−868340.	+	2.28858e6i	−0.497011	+	1.30991i
$315$	−70158.0	−	105049.i	−0.0398383	−	0.0596509i
$316$	−1.99176e6	+	2.24686e6i	−1.12207	+	1.26578i
$317$	170609.	−	170609.i	0.0953574	−	0.0953574i	−0.657819	−	0.753176i	$-0.728521\pi$
$317$	170609.	−	170609.i	0.0953574	−	0.0953574i	0.753176	+	0.657819i	$0.228521\pi$
$318$	−951447.	+	428039.i	−0.527615	+	0.237364i
$319$	62370.0			0.0343162
$320$	−1.83155e6	−	29733.3i	−0.999868	−	0.0162319i
$321$	−2.59235e6			−1.40420
$322$	−371333.	+	167056.i	−0.199583	+	0.0897888i
$323$	−297866.	+	297866.i	−0.158860	+	0.158860i
$324$	946636.	−	1.06788e6i	0.500980	−	0.565145i
$325$	33083.3	+	79970.8i	0.0173740	+	0.0419975i
$326$	−696474.	+	1.83562e6i	−0.362962	+	0.956616i
$327$	1.77062e6			0.915705
$328$	1.69623e6	+	529410.i	0.870562	+	0.271711i
$329$			175268.i			0.0892714i
$330$	1.40647e6	+	880245.i	0.710959	+	0.444958i
$331$	5862.91	−	5862.91i	0.00294133	−	0.00294133i	−0.705635	−	0.708576i	$-0.749338\pi$
$331$	5862.91	−	5862.91i	0.00294133	−	0.00294133i	0.708576	+	0.705635i	$0.249338\pi$
$332$	−161338.	−	2.68067e6i	−0.0803324	−	1.33474i
$333$	195680.	−	195680.i	0.0967019	−	0.0967019i
$334$	857237.	−	385655.i	0.420470	−	0.189162i
$335$	84066.1	−	422138.i	0.0409269	−	0.205515i
$336$	−512500.	−	402018.i	−0.247654	−	0.194266i
$337$		−	1.59074e6i		−	0.763001i	−0.924369	−	0.381501i	$-0.875407\pi$
$337$		−	1.59074e6i		−	0.763001i	0.924369	−	0.381501i	$-0.124593\pi$
$338$	−859941.	−	1.91148e6i	−0.409428	−	0.910078i
$339$	−2.32180e6	−	2.32180e6i	−1.09730	−	1.09730i
$340$	−1.57942e6	−	216873.i	−0.740969	−	0.101744i
$341$	862953.	−	862953.i	0.401884	−	0.401884i
$342$	−46882.1	+	123562.i	−0.0216741	+	0.0571240i
$343$	1.44125e6			0.661459
$344$	2.39328e6	−	1.25471e6i	1.09043	−	0.571672i
$345$	239156.	−	1.20092e6i	0.108177	−	0.543209i
$346$	649643.	−	1.71219e6i	0.291732	−	0.768884i
$347$	−960548.	−	960548.i	−0.428248	−	0.428248i	0.459783	−	0.888031i	$-0.347927\pi$
$347$	−960548.	−	960548.i	−0.428248	−	0.428248i	−0.888031	+	0.459783i	$0.847927\pi$
$348$	48844.2	−	55100.1i	0.0216204	−	0.0243896i
$349$	−22410.1	−	22410.1i	−0.00984875	−	0.00984875i	0.702165	−	0.712014i	$-0.252217\pi$
$349$	−22410.1	−	22410.1i	−0.00984875	−	0.00984875i	−0.712014	+	0.702165i	$0.752217\pi$
$350$	−23929.1	−	807858.i	−0.0104414	−	0.352505i
$351$	112674.			0.0488155
$352$	−2.12063e6	−	524388.i	−0.912239	−	0.225578i
$353$			606408.i			0.259017i	0.991578	+	0.129508i	$0.0413399\pi$
$353$			606408.i			0.259017i	−0.991578	+	0.129508i	$0.958660\pi$
$354$	2561.16	+	5692.97i	0.00108625	+	0.00241452i
$355$	2.51149e6	+	3.76051e6i	1.05769	+	1.58371i
$356$	−3.15759e6	−	2.79909e6i	−1.32048	−	1.17055i
$357$	−400855.	−	400855.i	−0.166463	−	0.166463i
$358$	609677.	+	231325.i	0.251415	+	0.0953928i
$359$		−	3.78207e6i		−	1.54879i	−0.632701	−	0.774396i	$-0.718054\pi$
$359$		−	3.78207e6i		−	1.54879i	0.632701	−	0.774396i	$-0.281946\pi$
$360$	−479800.	+	141245.i	−0.195121	+	0.0574405i
$361$		−	2.25268e6i		−	0.909771i
$362$	52694.7	−	138881.i	0.0211347	−	0.0557021i
$363$	−185274.	−	185274.i	−0.0737985	−	0.0737985i
$364$	−2434.13	−	40443.7i	−0.000962921	−	0.0159992i
$365$	−3.33669e6	+	2.22843e6i	−1.31094	+	0.875521i
$366$	2.10909e6	−	948840.i	0.822985	−	0.370246i
$367$		−	1.70291e6i		−	0.659972i	−0.943986	−	0.329986i	$-0.892956\pi$
$367$		−	1.70291e6i		−	0.659972i	0.943986	−	0.329986i	$-0.107044\pi$
$368$	193359.	+	1.60053e6i	0.0744294	+	0.616092i
$369$	485179.			0.185496
$370$	1.72543e6	−	397060.i	0.655231	−	0.150783i
$371$	428544.	+	428544.i	0.161644	+	0.161644i
$372$	−86557.5	−	1.43818e6i	−0.0324300	−	0.538834i
$373$	1.09224e6	+	1.09224e6i	0.406486	+	0.406486i	0.880511	−	0.474026i	$-0.157200\pi$
$373$	1.09224e6	+	1.09224e6i	0.406486	+	0.406486i	−0.474026	+	0.880511i	$0.657200\pi$
$374$	−1.77757e6	−	674449.i	−0.657123	−	0.249328i
$375$	2.02000e6	+	1.35167e6i	0.741776	+	0.496355i
$376$	662432.	+	206752.i	0.241642	+	0.0754188i
$377$	4580.19			0.00165970
$378$	−983805.	−	373278.i	−0.354144	−	0.134370i
$379$	−183853.	+	183853.i	−0.0657464	+	0.0657464i	−0.739215	−	0.673469i	$-0.764803\pi$
$379$	−183853.	+	183853.i	−0.0657464	+	0.0657464i	0.673469	+	0.739215i	$0.264803\pi$
$380$	−673660.	+	510993.i	−0.239322	+	0.181533i
$381$	−980478.	−	980478.i	−0.346039	−	0.346039i
$382$	−1.13110e6	+	508864.i	−0.396593	+	0.178420i
$383$			4.47493e6i			1.55880i	0.626528	+	0.779399i	$0.284475\pi$
$383$			4.47493e6i			1.55880i	−0.626528	+	0.779399i	$0.715525\pi$
$384$	−2.12401e6	+	1.46278e6i	−0.735069	+	0.506235i
$385$	188245.	−	945275.i	0.0647251	−	0.325017i
$386$	−1.80455e6	−	4.01117e6i	−0.616455	−	1.37026i
$387$	521725.	−	521725.i	0.177078	−	0.177078i
$388$	1.78016e6	+	1.57804e6i	0.600314	+	0.532156i
$389$	−1.18500e6	+	1.18500e6i	−0.397048	+	0.397048i	−0.877191	−	0.480142i	$-0.840585\pi$
$389$	−1.18500e6	+	1.18500e6i	−0.397048	+	0.397048i	0.480142	+	0.877191i	$0.340585\pi$
$390$	103285.	+	64641.5i	0.0343855	+	0.0215204i
$391$			1.40310e6i			0.464139i
$392$	793705.	−	2.54303e6i	0.260882	−	0.835865i
$393$	−1.80091e6			−0.588182
$394$	2.08357e6	+	790553.i	0.676187	+	0.256561i
$395$	−4.36195e6	+	2.91316e6i	−1.40666	+	0.939445i
$396$	−595388.	+	35833.8i	−0.190793	+	0.0114830i
$397$	−3.27272e6	+	3.27272e6i	−1.04216	+	1.04216i	−0.0430842	+	0.999071i	$0.513718\pi$
$397$	−3.27272e6	+	3.27272e6i	−1.04216	+	1.04216i	−0.999071	+	0.0430842i	$0.986282\pi$
$398$	1.73324e6	+	3.85266e6i	0.548468	+	1.21914i
$399$	−300664.			−0.0945472
$400$	−3.08156e6	−	862535.i	−0.962989	−	0.269542i
$401$	803284.			0.249464			0.124732	−	0.992190i	$-0.460193\pi$
$401$	803284.			0.249464			0.124732	+	0.992190i	$0.460193\pi$
$402$	−248627.	−	552650.i	−0.0767332	−	0.170563i
$403$	63371.6	−	63371.6i	0.0194371	−	0.0194371i
$404$	−259674.	−	4.31456e6i	−0.0791545	−	1.31517i
$405$	2.07313e6	−	1.38456e6i	0.628043	−	0.419443i
$406$	−39991.5	−	15173.7i	−0.0120407	−	0.00456852i
$407$	2.11145e6			0.631823
$408$	−1.98791e6	+	1.04219e6i	−0.591217	+	0.309953i
$409$			2.41122e6i			0.712737i	0.934345	+	0.356369i	$0.115985\pi$
$409$			2.41122e6i			0.712737i	−0.934345	+	0.356369i	$0.884015\pi$
$410$	2.63131e6	+	1.64682e6i	0.773059	+	0.483823i
$411$	−2.25597e6	+	2.25597e6i	−0.658761	+	0.658761i
$412$	−1.18700e6	+	1.33903e6i	−0.344516	+	0.388641i
$413$	2564.19	−	2564.19i	0.000739732	−	0.000739732i
$414$	180600.	+	401440.i	0.0517867	+	0.115112i
$415$	916271.	−	4.60106e6i	0.261158	−	1.31141i
$416$	−155730.	−	38508.9i	−0.0441204	−	0.0109101i
$417$		−	3.14393e6i		−	0.885387i
$418$	−919575.	+	413700.i	−0.257422	+	0.115810i
$419$	−1.82178e6	−	1.82178e6i	−0.506944	−	0.506944i	0.406643	−	0.913587i	$-0.366699\pi$
$419$	−1.82178e6	−	1.82178e6i	−0.506944	−	0.506944i	−0.913587	+	0.406643i	$0.866699\pi$
$420$	−687672.	−	906582.i	−0.190221	−	0.250775i
$421$	3.37333e6	−	3.37333e6i	0.927584	−	0.927584i	−0.0699650	−	0.997549i	$-0.522289\pi$
$421$	3.37333e6	−	3.37333e6i	0.927584	−	0.927584i	0.997549	+	0.0699650i	$0.0222888\pi$
$422$	4.11356e6	+	1.56078e6i	1.12444	+	0.426639i
$423$	189478.			0.0514882
$424$	2.12523e6	−	1.11418e6i	0.574104	−	0.300981i
$425$	−2.57255e6	−	1.06693e6i	−0.690862	−	0.286525i
$426$	5.95256e6	+	2.25854e6i	1.58921	+	0.602981i
$427$	−949959.	−	949959.i	−0.252136	−	0.252136i
$428$	5.95161e6	−	358201.i	1.57045	−	0.0945187i
$429$	102748.	+	102748.i	0.0269544	+	0.0269544i
$430$	4.60038e6	−	1.05865e6i	1.19984	−	0.276109i
$431$	215590.			0.0559031			0.0279515	−	0.999609i	$-0.491102\pi$
$431$	215590.			0.0559031			0.0279515	+	0.999609i	$0.491102\pi$
$432$	−2.57135e6	+	3.27801e6i	−0.662906	+	0.845085i
$433$		−	6.13899e6i		−	1.57354i	−0.617247	−	0.786769i	$-0.711752\pi$
$433$		−	6.13899e6i		−	1.57354i	0.617247	−	0.786769i	$-0.288248\pi$
$434$	−763266.	+	343379.i	−0.194514	+	0.0875085i
$435$	106969.	−	71439.8i	0.0271040	−	0.0181016i
$436$	−4.06505e6	+	244658.i	−1.02412	+	0.0616372i
$437$	526204.	+	526204.i	0.131811	+	0.131811i
$438$	−2.00399e6	+	5.28168e6i	−0.499126	+	1.31549i
$439$		−	1.66663e6i		−	0.412742i	−0.978474	−	0.206371i	$-0.933835\pi$
$439$		−	1.66663e6i		−	0.412742i	0.978474	−	0.206371i	$-0.0661654\pi$
$440$	−3.35065e6	−	1.82656e6i	−0.825083	−	0.449782i
$441$		−	727392.i		−	0.178103i
$442$	−130537.	−	49528.7i	−0.0317818	−	0.0120587i
$443$	−1.11577e6	−	1.11577e6i	−0.270125	−	0.270125i	0.559025	−	0.829150i	$-0.311175\pi$
$443$	−1.11577e6	−	1.11577e6i	−0.270125	−	0.270125i	−0.829150	+	0.559025i	$0.811175\pi$
$444$	1.65356e6	−	1.86534e6i	0.398072	−	0.449057i
$445$	−4.09396e6	−	6.13000e6i	−0.980040	−	1.46744i
$446$	2.76246e6	+	6.14041e6i	0.657595	+	1.46171i
$447$		−	1.99158e6i		−	0.471443i
$448$	1.23217e6	+	852154.i	0.290051	+	0.200596i
$449$	5.03585e6			1.17885			0.589423	−	0.807824i	$-0.299355\pi$
$449$	5.03585e6			1.17885			0.589423	+	0.807824i	$0.299355\pi$
$450$	−873357.	+	25869.3i	−0.203311	+	0.00602217i
$451$	2.61763e6	+	2.61763e6i	0.605991	+	0.605991i
$452$	5.65131e6	+	5.00967e6i	1.30108	+	1.15336i
$453$	−2.21781e6	−	2.21781e6i	−0.507783	−	0.507783i
$454$	−1.80468e6	+	4.75639e6i	−0.410923	+	1.08302i
$455$	13824.0	−	69417.0i	0.00313043	−	0.0157195i
$456$	−354673.	+	1.13637e6i	−0.0798759	+	0.255923i
$457$	−6.06925e6			−1.35939			−0.679696	−	0.733494i	$-0.737888\pi$
$457$	−6.06925e6			−1.35939			−0.679696	+	0.733494i	$0.737888\pi$
$458$	2.25839e6	−	5.95218e6i	0.503078	−	1.32590i
$459$	−2.56391e6	+	2.56391e6i	−0.568030	+	0.568030i
$460$	−383124.	+	2.79017e6i	−0.0844199	+	0.614803i
$461$	594321.	+	594321.i	0.130247	+	0.130247i	0.769225	−	0.638978i	$-0.220642\pi$
$461$	594321.	+	594321.i	0.130247	+	0.130247i	−0.638978	+	0.769225i	$0.720642\pi$
$462$	−556739.	−	1.23752e6i	−0.121352	−	0.269742i
$463$		−	839214.i		−	0.181937i	−0.995854	−	0.0909683i	$-0.971004\pi$
$463$		−	839214.i		−	0.181937i	0.995854	−	0.0909683i	$-0.0289962\pi$
$464$	−104525.	+	133250.i	−0.0225385	+	0.0287325i
$465$	491579.	−	2.46846e6i	0.105429	−	0.529413i
$466$	2.73994e6	−	1.23265e6i	0.584489	−	0.262951i
$467$	−4.86900e6	+	4.86900e6i	−1.03311	+	1.03311i	−0.0336801	+	0.999433i	$0.510723\pi$
$467$	−4.86900e6	+	4.86900e6i	−1.03311	+	1.03311i	−0.999433	+	0.0336801i	$0.989277\pi$
$468$	−43722.8	+	2631.48i	−0.00922770	+	0.000555375i
$469$	−248920.	+	248920.i	−0.0522551	+	0.0522551i
$470$	1.02761e6	+	643137.i	0.214578	+	0.134295i
$471$			6.02033e6i			1.25046i
$472$	−6666.66	−	12716.3i	−0.00137738	−	0.00262727i
$473$	5.62960e6			1.15698
$474$	−2.61975e6	+	6.90458e6i	−0.535568	+	1.41153i
$475$	−1.36491e6	+	564651.i	−0.277567	+	0.114828i
$476$	975687.	+	864910.i	0.197375	+	0.174966i
$477$	463289.	−	463289.i	0.0932301	−	0.0932301i
$478$	1.80118e6	−	810320.i	0.360569	−	0.162213i
$479$	−4.47829e6			−0.891812			−0.445906	−	0.895080i	$-0.647118\pi$
$479$	−4.47829e6			−0.891812			−0.445906	+	0.895080i	$0.647118\pi$
$480$	−4.23767e6	+	1.52965e6i	−0.839506	+	0.303033i
$481$	155056.			0.0305581
$482$	7.05616e6	−	3.17444e6i	1.38341	−	0.622370i
$483$	−708142.	+	708142.i	−0.138119	+	0.138119i
$484$	450959.	+	399758.i	0.0875032	+	0.0775683i
$485$	2.30805e6	+	3.45591e6i	0.445545	+	0.667126i
$486$	−738878.	+	1.94737e6i	−0.141900	+	0.373989i
$487$	2.53902e6			0.485114			0.242557	−	0.970137i	$-0.422014\pi$
$487$	2.53902e6			0.485114			0.242557	+	0.970137i	$0.422014\pi$
$488$	−4.71102e6	+	2.46981e6i	−0.895499	+	0.469477i
$489$			4.82876e6i			0.913195i
$490$	2.46896e6	−	3.94493e6i	0.464540	−	0.742248i
$491$	−737732.	+	737732.i	−0.138100	+	0.138100i	−0.772777	−	0.634677i	$-0.781133\pi$
$491$	−737732.	+	737732.i	−0.138100	+	0.138100i	0.634677	+	0.772777i	$0.281133\pi$
$492$	4.36247e6	−	262558.i	0.812493	−	0.0489004i
$493$	−104222.	+	104222.i	−0.0193127	+	0.0193127i
$494$	−67529.7	+	30380.4i	−0.0124502	+	0.00560114i
$495$	−1.02192e6	−	203508.i	−0.187457	−	0.0373309i
$496$	397444.	+	3.28986e6i	0.0725391	+	0.600445i
$497$		−	3.69838e6i		−	0.671616i
$498$	−2.70989e6	−	6.02356e6i	−0.489642	−	1.08838i
$499$	3.11917e6	+	3.11917e6i	0.560773	+	0.560773i	0.929527	−	0.368754i	$-0.120216\pi$
$499$	3.11917e6	+	3.11917e6i	0.560773	+	0.560773i	−0.368754	+	0.929527i	$0.620216\pi$
$500$	−4.82436e6	−	2.82410e6i	−0.863008	−	0.505190i
$501$	1.63477e6	−	1.63477e6i	0.290980	−	0.290980i
$502$	−3.34323e6	+	8.81136e6i	−0.592116	+	1.56057i
$503$	−2.07775e6			−0.366162			−0.183081	−	0.983098i	$-0.558607\pi$
$503$	−2.07775e6			−0.366162			−0.183081	+	0.983098i	$0.558607\pi$
$504$	390479.	+	121872.i	0.0684733	+	0.0213712i
$505$	1.47475e6	−	7.40544e6i	0.257329	−	1.29218i
$506$	−1.19147e6	+	3.14021e6i	−0.206874	+	0.545234i
$507$	−3.64525e6	−	3.64525e6i	−0.629806	−	0.629806i
$508$	2.38650e6	+	2.11554e6i	0.410301	+	0.363716i
$509$	6.88149e6	+	6.88149e6i	1.17730	+	1.17730i	0.980429	+	0.196874i	$0.0630791\pi$
$509$	6.88149e6	+	6.88149e6i	1.17730	+	1.17730i	0.196874	+	0.980429i	$0.436921\pi$
$510$	−3.82117e6	+	879334.i	−0.650536	+	0.149702i
$511$	3.28156e6			0.555939
$512$	4.67426e6	−	3.65180e6i	0.788021	−	0.615648i
$513$			1.92308e6i			0.322629i
$514$	−4.28661e6	−	9.52830e6i	−0.715659	−	1.59077i
$515$	−2.59954e6	+	1.73612e6i	−0.431895	+	0.288444i
$516$	4.40874e6	−	4.97341e6i	0.728937	−	0.822299i
$517$	1.02227e6	+	1.02227e6i	0.168205	+	0.168205i
$518$	−1.35386e6	−	513685.i	−0.221691	−	0.0841148i
$519$		−	4.50407e6i		−	0.733985i
$520$	−246058.	−	134135.i	−0.0399051	−	0.0217537i
$521$			1.13246e6i			0.182779i	0.995815	+	0.0913896i	$0.0291309\pi$
$521$			1.13246e6i			0.182779i	−0.995815	+	0.0913896i	$0.970869\pi$
$522$	−16403.9	+	43233.9i	−0.00263494	+	0.00694461i
$523$	−514139.	−	514139.i	−0.0821913	−	0.0821913i	0.664816	−	0.747007i	$-0.268510\pi$
$523$	−514139.	−	514139.i	−0.0821913	−	0.0821913i	−0.747007	+	0.664816i	$0.768510\pi$
$524$	4.13461e6	−	248844.i	0.657819	−	0.0395912i
$525$	−759883.	−	1.83683e6i	−0.120323	−	0.290851i
$526$	9.90177e6	−	4.45462e6i	1.56044	−	0.702016i
$527$			2.88405e6i			0.452351i
$528$	−5.33403e6	+	644398.i	−0.832665	+	0.100593i
$529$	−3.95765e6			−0.614891
$530$	4.08512e6	−	940074.i	0.631706	−	0.145369i
$531$	−2772.08	−	2772.08i	−0.000426648	−	0.000426648i
$532$	690276.	−	41544.7i	0.105741	−	0.00636409i
$533$	192227.	+	192227.i	0.0293088	+	0.0293088i
$534$	−9.70325e6	−	3.68163e6i	−1.47253	−	0.558711i
$535$	1.02153e7	+	2.03430e6i	1.54300	+	0.307278i
$536$	647171.	+	1.23444e6i	0.0972988	+	0.185592i
$537$	1.60381e6			0.240004
$538$	−6.87119e6	−	2.60709e6i	−1.02347	−	0.388329i
$539$	3.92441e6	−	3.92441e6i	0.581839	−	0.581839i
$540$	−5.79860e6	+	4.39842e6i	−0.855734	+	0.649102i
$541$	620582.	+	620582.i	0.0911603	+	0.0911603i	0.751216	−	0.660056i	$-0.229467\pi$
$541$	620582.	+	620582.i	0.0911603	+	0.0911603i	−0.660056	+	0.751216i	$0.729467\pi$
$542$	4.53659e6	−	2.04093e6i	0.663333	−	0.298421i
$543$		−	365340.i		−	0.0531738i
$544$	4.41992e6	−	2.66738e6i	0.640349	−	0.386445i
$545$	−6.97720e6	−	1.38946e6i	−1.00621	−	0.200381i
$546$	−40884.6	−	90878.5i	−0.00586919	−	0.0130461i
$547$	−4.19380e6	+	4.19380e6i	−0.599293	+	0.599293i	−0.940125	−	0.340831i	$-0.889292\pi$
$547$	−4.19380e6	+	4.19380e6i	−0.599293	+	0.599293i	0.340831	+	0.940125i	$0.389292\pi$
$548$	4.86762e6	−	5.49106e6i	0.692412	−	0.781097i
$549$	−1.02698e6	+	1.02698e6i	−0.145422	+	0.145422i
$550$	−4.85149e6	−	4.57235e6i	−0.683862	−	0.644514i
$551$			78172.7i			0.0109692i
$552$	1.84111e6	+	3.51180e6i	0.257176	+	0.490549i
$553$	4.28988e6			0.596530
$554$	−1.13249e7	−	4.29694e6i	−1.56770	−	0.594819i
$555$	3.62129e6	−	2.41850e6i	0.499034	−	0.333284i
$556$	434418.	+	7.21797e6i	0.0595965	+	0.990212i
$557$	−6.14757e6	+	6.14757e6i	−0.839587	+	0.839587i	−0.988804	−	0.149218i	$-0.952325\pi$
$557$	−6.14757e6	+	6.14757e6i	−0.839587	+	0.839587i	0.149218	+	0.988804i	$0.452325\pi$
$558$	371220.	+	825150.i	0.0504714	+	0.112188i
$559$	413414.			0.0559572
$560$	1.70405e6	+	1.98635e6i	0.229622	+	0.267661i
$561$	−4.67606e6			−0.627296
$562$	1.06347e6	+	2.36389e6i	0.142032	+	0.315709i
$563$	2.47689e6	−	2.47689e6i	0.329334	−	0.329334i	−0.522999	−	0.852333i	$-0.675187\pi$
$563$	2.47689e6	−	2.47689e6i	0.329334	−	0.329334i	0.852333	+	0.522999i	$0.175187\pi$
$564$	1.70369e6	−	102537.i	0.225524	−	0.0135733i
$565$	7.32718e6	+	1.09712e7i	0.965641	+	1.44588i
$566$	−423587.	−	160719.i	−0.0555778	−	0.0210875i
$567$	−2.03888e6			−0.266338
$568$	−1.39782e7	−	4.36274e6i	−1.81794	−	0.567398i
$569$			5.46045e6i			0.707046i	0.935426	+	0.353523i	$0.115016\pi$
$569$			5.46045e6i			0.707046i	−0.935426	+	0.353523i	$0.884984\pi$
$570$	−1.10327e6	+	1.76282e6i	−0.142231	+	0.227259i
$571$	6.07331e6	−	6.07331e6i	0.779535	−	0.779535i	−0.200217	−	0.979752i	$-0.564165\pi$
$571$	6.07331e6	−	6.07331e6i	0.779535	−	0.779535i	0.979752	+	0.200217i	$0.0641647\pi$
$572$	−250090.	−	221695.i	−0.0319599	−	0.0283313i
$573$	−2.15705e6	+	2.15705e6i	−0.274456	+	0.274456i
$574$	−1.04159e6	−	2.31524e6i	−0.131952	−	0.293303i
$575$	−1.88481e6	+	4.54461e6i	−0.237737	+	0.573228i
$576$	921244.	−	1.33207e6i	0.115696	−	0.167290i
$577$		−	2.28995e6i		−	0.286342i	−0.989698	−	0.143171i	$-0.954270\pi$
$577$		−	2.28995e6i		−	0.286342i	0.989698	−	0.143171i	$-0.0457300\pi$
$578$	−3.22741e6	+	1.45195e6i	−0.401822	+	0.180773i
$579$	−7.64941e6	−	7.64941e6i	−0.948269	−	0.948269i
$580$	−235712.	+	178795.i	−0.0290945	+	0.0220691i
$581$	−2.71309e6	+	2.71309e6i	−0.333444	+	0.333444i
$582$	5.47040e6	+	2.07559e6i	0.669440	+	0.254001i
$583$	4.99906e6			0.609139
$584$	3.87103e6	−	1.24028e7i	0.469672	−	1.50483i
$585$	−75045.2	−	14944.8i	−0.00906637	−	0.00180551i
$586$	3.84214e6	+	1.45780e6i	0.462200	+	0.175369i
$587$	−4.89101e6	−	4.89101e6i	−0.585872	−	0.585872i	0.350639	−	0.936511i	$-0.385965\pi$
$587$	−4.89101e6	−	4.89101e6i	−0.585872	−	0.585872i	−0.936511	+	0.350639i	$0.885965\pi$
$588$	−393634.	−	6.54033e6i	−0.0469515	−	0.780111i
$589$	1.08160e6	+	1.08160e6i	0.128463	+	0.128463i
$590$	−5624.92	−	24443.3i	−0.000665252	−	0.00289087i
$591$	5.48102e6			0.645495
$592$	−3.53855e6	+	4.51101e6i	−0.414974	+	0.529017i
$593$			4.74292e6i			0.553871i	0.960888	+	0.276936i	$0.0893189\pi$
$593$			4.74292e6i			0.553871i	−0.960888	+	0.276936i	$0.910681\pi$
$594$	−7.91534e6	+	3.56097e6i	−0.920457	+	0.414097i
$595$	1.26502e6	+	1.89415e6i	0.146489	+	0.219342i
$596$	275190.	+	4.57235e6i	0.0317334	+	0.527259i
$597$	7.34711e6	+	7.34711e6i	0.843686	+	0.843686i
$598$	−87496.4	+	230604.i	−0.0100055	+	0.0263702i
$599$		−	1.07209e7i		−	1.22085i	−0.792074	−	0.610426i	$-0.790998\pi$
$599$		−	1.07209e7i		−	1.22085i	0.792074	−	0.610426i	$-0.209002\pi$
$600$	−7.83877e6	+	705226.i	−0.888934	+	0.0799743i
$601$		−	7.05198e6i		−	0.796388i	−0.917301	−	0.398194i	$-0.869637\pi$
$601$		−	7.05198e6i		−	0.796388i	0.917301	−	0.398194i	$-0.130363\pi$
$602$	−3.60968e6	−	1.36959e6i	−0.405955	−	0.154028i
$603$	269102.	+	269102.i	0.0301387	+	0.0301387i
$604$	5.39817e6	+	4.78528e6i	0.602080	+	0.533722i
$605$	584689.	+	875471.i	0.0649436	+	0.0972418i
$606$	−4.36159e6	−	9.69497e6i	−0.482462	−	1.07242i
$607$			2.89512e6i			0.318930i	0.987204	+	0.159465i	$0.0509769\pi$
$607$			2.89512e6i			0.318930i	−0.987204	+	0.159465i	$0.949023\pi$
$608$	657252.	−	2.65794e6i	0.0721063	−	0.291599i
$609$	−105201.			−0.0114942
$610$	−9.05554e6	+	2.08388e6i	−0.985349	+	0.226750i
$611$	75071.1	+	75071.1i	0.00813522	+	0.00813522i
$612$	935034.	−	1.05479e6i	0.100913	−	0.113838i
$613$	−7.14700e6	−	7.14700e6i	−0.768197	−	0.768197i	0.209592	−	0.977789i	$-0.432787\pi$
$613$	−7.14700e6	−	7.14700e6i	−0.768197	−	0.768197i	−0.977789	+	0.209592i	$0.932787\pi$
$614$	161578.	−	425853.i	0.0172967	−	0.0455868i
$615$	7.48768e6	+	1.49112e6i	0.798288	+	0.158974i
$616$	1.44918e6	+	2.76423e6i	0.153876	+	0.293509i
$617$	−9.19849e6			−0.972756			−0.486378	−	0.873749i	$-0.661682\pi$
$617$	−9.19849e6			−0.972756			−0.486378	+	0.873749i	$0.661682\pi$
$618$	−1.56126e6	+	4.11484e6i	−0.164439	+	0.433392i
$619$	7.47005e6	−	7.47005e6i	0.783604	−	0.783604i	−0.196833	−	0.980437i	$-0.563066\pi$
$619$	7.47005e6	−	7.47005e6i	0.783604	−	0.783604i	0.980437	+	0.196833i	$0.0630656\pi$
$620$	−787502.	+	5.73512e6i	−0.0822759	+	0.599189i
$621$	4.52935e6	+	4.52935e6i	0.471310	+	0.471310i
$622$	−4.87935e6	−	1.08458e7i	−0.505692	−	1.12405i
$623$			6.02872e6i			0.622307i
$624$	−391709.	+	47321.9i	−0.0402718	+	0.00486520i
$625$	−6.89919e6	−	6.91148e6i	−0.706478	−	0.707735i
$626$	−7.10911e6	+	3.19826e6i	−0.725069	+	0.326195i
$627$	−1.75365e6	+	1.75365e6i	−0.178146	+	0.178146i
$628$	−831869.	−	1.38217e7i	−0.0841697	−	1.39850i
$629$	−3.52831e6	+	3.52831e6i	−0.355583	+	0.355583i
$630$	605739.	+	379105.i	0.0608043	+	0.0380547i
$631$		−	8.70748e6i		−	0.870601i	−0.900285	−	0.435301i	$-0.856642\pi$
$631$		−	8.70748e6i		−	0.870601i	0.900285	−	0.435301i	$-0.143358\pi$
$632$	5.06048e6	−	1.62138e7i	0.503964	−	1.61470i
$633$	1.08211e7			1.07340
$634$	−484184.	+	1.27611e6i	−0.0478395	+	0.126085i
$635$	3.09421e6	+	4.63304e6i	0.304519	+	0.455965i
$636$	3.91494e6	−	4.41636e6i	0.383780	−	0.432934i
$637$	288192.	−	288192.i	0.0281406	−	0.0281406i
$638$	−321757.	+	144752.i	−0.0312951	+	0.0140791i
$639$	−3.99824e6			−0.387361
$640$	9.51765e6	−	4.09738e6i	0.918501	−	0.395418i
$641$	5.66186e6			0.544270			0.272135	−	0.962259i	$-0.412270\pi$
$641$	5.66186e6			0.544270			0.272135	+	0.962259i	$0.412270\pi$
$642$	1.33735e7	−	6.01649e6i	1.28058	−	0.576110i
$643$	1.17379e7	−	1.17379e7i	1.11960	−	1.11960i	0.127795	−	0.991801i	$-0.459210\pi$
$643$	1.17379e7	−	1.17379e7i	1.11960	−	1.11960i	0.991801	−	0.127795i	$-0.0407901\pi$
$644$	1.52793e6	−	1.72363e6i	0.145174	−	0.163768i
$645$	9.65513e6	−	6.44825e6i	0.913817	−	0.610299i
$646$	845334.	−	2.22795e6i	0.0796979	−	0.210050i
$647$	1.20318e6			0.112997			0.0564987	−	0.998403i	$-0.482006\pi$
$647$	1.20318e6			0.112997			0.0564987	+	0.998403i	$0.482006\pi$
$648$	−2.40513e6	+	7.70603e6i	−0.225010	+	0.720930i
$649$		−	29911.8i		−	0.00278760i
$650$	−356273.	−	335774.i	−0.0330750	−	0.0311719i
$651$	−1.45557e6	+	1.45557e6i	−0.134611	+	0.134611i
$652$	−667222.	−	1.10861e7i	−0.0614683	−	1.02131i
$653$	−6.68968e6	+	6.68968e6i	−0.613935	+	0.613935i	−0.943969	−	0.330034i	$-0.892940\pi$
$653$	−6.68968e6	+	6.68968e6i	−0.613935	+	0.613935i	0.330034	+	0.943969i	$0.392940\pi$
$654$	−9.13433e6	+	4.10937e6i	−0.835088	+	0.375691i
$655$	7.09659e6	+	1.41324e6i	0.646318	+	0.128710i
$656$	−9.97925e6	+	1.20558e6i	−0.905396	+	0.109380i
$657$		−	3.54762e6i		−	0.320644i
$658$	−406773.	−	904177.i	−0.0366258	−	0.0814121i
$659$	−5.09399e6	−	5.09399e6i	−0.456924	−	0.456924i	0.440720	−	0.897645i	$-0.354723\pi$
$659$	−5.09399e6	−	5.09399e6i	−0.456924	−	0.456924i	−0.897645	+	0.440720i	$0.854723\pi$
$660$	−9.29866e6	−	1.27682e6i	−0.830923	−	0.114096i
$661$	−6.61294e6	+	6.61294e6i	−0.588696	+	0.588696i	−0.937278	−	0.348582i	$-0.886663\pi$
$661$	−6.61294e6	+	6.61294e6i	−0.588696	+	0.588696i	0.348582	+	0.937278i	$0.386663\pi$
$662$	−16638.8	+	43852.8i	−0.00147563	+	0.00388913i
$663$	−343390.			−0.0303392
$664$	7.05379e6	+	1.34547e7i	0.620872	+	1.18428i
$665$	1.18478e6	+	235941.i	0.103892	+	0.0206895i
$666$	−555333.	+	1.46363e6i	−0.0485141	+	0.127863i
$667$	184117.	+	184117.i	0.0160243	+	0.0160243i
$668$	−3.52729e6	+	3.97906e6i	−0.305844	+	0.345016i
$669$	1.17099e7	+	1.17099e7i	1.01155	+	1.01155i
$670$	546043.	+	2.37285e6i	0.0469938	+	0.204213i
$671$	−1.10815e7			−0.950149
$672$	3.57693e6	+	884501.i	0.305554	+	0.0755571i
$673$			1.72503e7i			1.46811i	0.679089	+	0.734056i	$0.262375\pi$
$673$			1.72503e7i			1.46811i	−0.679089	+	0.734056i	$0.737625\pi$
$674$	3.69190e6	+	8.20638e6i	0.313040	+	0.695828i
$675$	−1.17486e7	+	4.86030e6i	−0.992488	+	0.410585i
$676$	8.87259e6	+	7.86522e6i	0.746765	+	0.661979i
$677$	−9.55582e6	−	9.55582e6i	−0.801302	−	0.801302i	0.181997	−	0.983299i	$-0.441744\pi$
$677$	−9.55582e6	−	9.55582e6i	−0.801302	−	0.801302i	−0.983299	+	0.181997i	$0.941744\pi$
$678$	1.73664e7	+	6.58921e6i	1.45089	+	0.550502i
$679$		−	3.39881e6i		−	0.282913i
$680$	8.65130e6	−	2.54681e6i	0.717478	−	0.211214i
$681$			1.25121e7i			1.03386i
$682$	−2.44903e6	+	6.45463e6i	−0.201620	+	0.531386i
$683$	1.78019e6	+	1.78019e6i	0.146021	+	0.146021i	0.776338	−	0.630317i	$-0.217075\pi$
$683$	1.78019e6	+	1.78019e6i	0.146021	+	0.146021i	−0.630317	+	0.776338i	$0.717075\pi$
$684$	−44913.0	−	746241.i	−0.00367056	−	0.0609872i
$685$	1.06601e7	−	7.11941e6i	0.868028	−	0.579719i
$686$	−7.43515e6	+	3.34494e6i	−0.603225	+	0.271380i
$687$		−	1.56578e7i		−	1.26572i
$688$	−9.43455e6	+	1.20273e7i	−0.759889	+	0.968720i
$689$	367110.			0.0294610
$690$	1.55341e6	+	6.75040e6i	0.124212	+	0.539768i
$691$	1.51265e7	+	1.51265e7i	1.20515	+	1.20515i	0.972579	+	0.232575i	$0.0747150\pi$
$691$	1.51265e7	+	1.51265e7i	1.20515	+	1.20515i	0.232575	+	0.972579i	$0.425285\pi$
$692$	622357.	+	1.03406e7i	0.0494054	+	0.820884i
$693$	602588.	+	602588.i	0.0476637	+	0.0476637i
$694$	7.18461e6	+	2.72601e6i	0.566245	+	0.214846i
$695$	−2.46715e6	+	1.23888e7i	−0.193747	+	0.972899i
$696$	−124099.	+	397613.i	−0.00971058	+	0.0311127i
$697$	−8.74828e6			−0.682089
$698$	167621.	+	63599.3i	0.0130224	+	0.00494099i
$699$	5.22514e6	−	5.22514e6i	0.404487	−	0.404487i
$700$	1.99838e6	+	4.11207e6i	0.154146	+	0.317187i
$701$	−1.06516e7	−	1.06516e7i	−0.818688	−	0.818688i	0.167230	−	0.985918i	$-0.446518\pi$
$701$	−1.06516e7	−	1.06516e7i	−0.818688	−	0.818688i	−0.985918	+	0.167230i	$0.946518\pi$
$702$	−581269.	+	261502.i	−0.0445179	+	0.0200278i
$703$			2.64643e6i			0.201963i
$704$	1.21570e7	−	2.21647e6i	0.924476	−	0.168551i
$705$	2.92418e6	+	582332.i	0.221581	+	0.0441263i
$706$	−1.40739e6	−	3.12836e6i	−0.106268	−	0.236214i
$707$	−4.36673e6	+	4.36673e6i	−0.328555	+	0.328555i
$708$	−26425.3	−	23425.0i	−0.00198124	−	0.00175629i
$709$	−1.67716e7	+	1.67716e7i	−1.25303	+	1.25303i	−0.298668	+	0.954357i	$0.596542\pi$
$709$	−1.67716e7	+	1.67716e7i	−1.25303	+	1.25303i	−0.954357	+	0.298668i	$0.903458\pi$
$710$	−2.16840e7	−	1.35711e7i	−1.61433	−	1.01034i
$711$		−	4.63769e6i		−	0.344055i
$712$	2.27858e7	+	7.11168e6i	1.68447	+	0.525741i
$713$	5.09490e6			0.375328
$714$	2.99827e6	+	1.13761e6i	0.220103	+	0.0835121i
$715$	−324253.	−	485512.i	−0.0237202	−	0.0355169i
$716$	−3.68210e6	+	221609.i	−0.268419	+	0.0161549i
$717$	3.43490e6	−	3.43490e6i	0.249526	−	0.249526i
$718$	8.77767e6	+	1.95111e7i	0.635431	+	1.41244i
$719$	4.89057e6			0.352807			0.176403	−	0.984318i	$-0.443554\pi$
$719$	4.89057e6			0.352807			0.176403	+	0.984318i	$0.443554\pi$
$720$	2.14740e6	−	1.84221e6i	0.154376	−	0.132437i
$721$	2.55659e6			0.183156
$722$	5.22818e6	+	1.16212e7i	0.373256	+	0.829676i
$723$	1.34563e7	−	1.34563e7i	0.957368	−	0.957368i
$724$	50481.4	+	838762.i	0.00357919	+	0.0594693i
$725$	−477576.	+	197570.i	−0.0337441	+	0.0139597i
$726$	1.38579e6	+	525801.i	0.0975791	+	0.0370237i
$727$	−1.99767e7			−1.40181			−0.700904	−	0.713256i	$-0.747220\pi$
$727$	−1.99767e7			−1.40181			−0.700904	+	0.713256i	$0.747220\pi$
$728$	106422.	+	202993.i	0.00744221	+	0.0141956i
$729$			1.59595e7i			1.11224i
$730$	1.20415e7	−	1.92401e7i	0.836324	−	1.33629i
$731$	−9.40725e6	+	9.40725e6i	−0.651132	+	0.651132i
$732$	−8.67830e6	+	9.78982e6i	−0.598628	+	0.675300i
$733$	9.28442e6	−	9.28442e6i	0.638256	−	0.638256i	−0.311869	−	0.950125i	$-0.600955\pi$
$733$	9.28442e6	−	9.28442e6i	0.638256	−	0.638256i	0.950125	+	0.311869i	$0.100955\pi$
$734$	3.95222e6	+	8.78502e6i	0.270770	+	0.601870i
$735$	2.23553e6	−	1.12257e7i	0.152638	−	0.766472i
$736$	−4.71213e6	−	7.80813e6i	−0.320644	−	0.531316i
$737$			2.90371e6i			0.196918i
$738$	−2.50296e6	+	1.12603e6i	−0.169166	+	0.0761046i
$739$	−4.34191e6	−	4.34191e6i	−0.292462	−	0.292462i	0.545590	−	0.838052i	$-0.316306\pi$
$739$	−4.34191e6	−	4.34191e6i	−0.292462	−	0.292462i	−0.838052	+	0.545590i	$0.816306\pi$
$740$	−7.97971e6	+	6.05287e6i	−0.535683	+	0.406333i
$741$	−128781.	+	128781.i	−0.00861601	+	0.00861601i
$742$	−3.20538e6	−	1.21619e6i	−0.213732	−	0.0810948i
$743$	−2.55197e7			−1.69591			−0.847956	−	0.530066i	$-0.822167\pi$
$743$	−2.55197e7			−1.69591			−0.847956	+	0.530066i	$0.822167\pi$
$744$	3.78435e6	+	7.21842e6i	0.250645	+	0.478090i
$745$	−1.56286e6	+	7.84791e6i	−0.103164	+	0.518040i
$746$	−8.16961e6	−	3.09974e6i	−0.537470	−	0.203928i
$747$	2.93306e6	+	2.93306e6i	0.192318	+	0.192318i
$748$	1.07355e7	−	646122.i	0.701564	−	0.0422241i
$749$	−6.02358e6	−	6.02358e6i	−0.392329	−	0.392329i
$750$	−1.35579e7	−	2.28490e6i	−0.880114	−	0.148325i
$751$	1.81595e7			1.17491			0.587454	−	0.809258i	$-0.300130\pi$
$751$	1.81595e7			1.17491			0.587454	+	0.809258i	$0.300130\pi$
$752$	−3.89722e6	+	470819.i	−0.251310	+	0.0303605i
$753$			2.31791e7i			1.48974i
$754$	−23628.5	+	10630.0i	−0.00151359	+	0.000680934i
$755$	6.99898e6	+	1.04798e7i	0.446856	+	0.669089i
$756$	5.94162e6	−	357600.i	0.378094	−	0.0227558i
$757$	−6.72531e6	−	6.72531e6i	−0.426553	−	0.426553i	0.460900	−	0.887452i	$-0.347527\pi$
$757$	−6.72531e6	−	6.72531e6i	−0.426553	−	0.426553i	−0.887452	+	0.460900i	$0.847527\pi$
$758$	521769.	−	1.37516e6i	0.0329841	−	0.0869324i
$759$			8.26063e6i			0.520485i
$760$	2.28936e6	−	4.19960e6i	0.143774	−	0.263739i
$761$		−	403804.i		−	0.0252760i	−0.999920	−	0.0126380i	$-0.995977\pi$
$761$		−	403804.i		−	0.0252760i	0.999920	−	0.0126380i	$-0.00402291\pi$
$762$	7.33368e6	+	2.78257e6i	0.457546	+	0.173603i
$763$	4.11421e6	+	4.11421e6i	0.255844	+	0.255844i
$764$	4.65418e6	−	5.25029e6i	0.288476	−	0.325424i
$765$	2.04772e6	−	1.36759e6i	0.126508	−	0.0844892i
$766$	−1.03857e7	−	2.30855e7i	−0.639536	−	1.42156i
$767$		−	2196.60i		−	0.000134822i
$768$	7.56248e6	−	1.24758e7i	0.462659	−	0.763247i
$769$	1.00104e6			0.0610432			0.0305216	−	0.999534i	$-0.490283\pi$
$769$	1.00104e6			0.0610432			0.0305216	+	0.999534i	$0.490283\pi$
$770$	1.22273e6	+	5.31341e6i	0.0743197	+	0.322958i
$771$	−1.81707e7	−	1.81707e7i	−1.10087	−	1.10087i
$772$	1.86188e7	+	1.65048e7i	1.12437	+	0.996709i
$773$	−1.41432e7	−	1.41432e7i	−0.851333	−	0.851333i	0.138964	−	0.990297i	$-0.455623\pi$
$773$	−1.41432e7	−	1.41432e7i	−0.851333	−	0.851333i	−0.990297	+	0.138964i	$0.955623\pi$
$774$	−1.48064e6	+	3.90234e6i	−0.0888375	+	0.234139i
$775$	−3.87418e6	+	9.34134e6i	−0.231700	+	0.558669i
$776$	−1.28460e7	−	4.00935e6i	−0.765794	−	0.239012i
$777$	−3.56145e6			−0.211629
$778$	3.36299e6	−	8.86343e6i	0.199194	−	0.524992i
$779$	−3.28085e6	+	3.28085e6i	−0.193706	+	0.193706i
$780$	−682855.	−	93764.2i	−0.0401876	−	0.00551824i
$781$	−2.15712e7	−	2.15712e7i	−1.26546	−	1.26546i
$782$	−3.25642e6	−	7.23838e6i	−0.190425	−	0.423277i
$783$			672879.i			0.0392223i
$784$	1.80744e6	+	1.49612e7i	0.105020	+	0.869311i
$785$	4.72436e6	−	2.37234e7i	0.273633	−	1.37405i
$786$	9.29062e6	−	4.17968e6i	0.536400	−	0.241316i
$787$	−2.11152e6	+	2.11152e6i	−0.121523	+	0.121523i	−0.765253	−	0.643730i	$-0.777386\pi$
$787$	−2.11152e6	+	2.11152e6i	−0.121523	+	0.121523i	0.643730	+	0.765253i	$0.277386\pi$
$788$	−1.25835e7	+	757349.i	−0.721918	+	0.0434491i
$789$	1.88829e7	−	1.88829e7i	1.07988	−	1.07988i
$790$	1.57415e7	−	2.51520e7i	0.897385	−	1.43385i
$791$		−	1.07899e7i		−	0.613164i
$792$	2.98834e6	−	1.56668e6i	0.169285	−	0.0887496i
$793$	−813778.			−0.0459539
$794$	9.28788e6	−	2.44790e7i	0.522836	−	1.37798i
$795$	8.57371e6	−	5.72602e6i	0.481118	−	0.321318i
$796$	−1.78830e7	−	1.58526e7i	−1.00036	−	0.886784i
$797$	1.74332e7	−	1.74332e7i	0.972143	−	0.972143i	−0.0274791	−	0.999622i	$-0.508748\pi$
$797$	1.74332e7	−	1.74332e7i	0.972143	−	0.972143i	0.999622	+	0.0274791i	$0.00874797\pi$
$798$	1.55107e6	−	697800.i	0.0862234	−	0.0387904i
$799$	−3.41649e6			−0.189327
$800$	1.78991e7	−	2.70222e6i	0.988795	−	0.149278i
$801$	6.51751e6			0.358922
$802$	−4.14401e6	+	1.86432e6i	−0.227502	+	0.102349i
$803$	1.91400e7	−	1.91400e7i	1.04750	−	1.04750i
$804$	2.56525e6	+	2.27400e6i	0.139956	+	0.124065i
$805$	3.34617e6	−	2.23476e6i	0.181994	−	0.121546i
$806$	−179847.	+	474001.i	−0.00975136	+	0.0257005i
$807$	−1.80753e7			−0.977017
$808$	1.13531e7	+	2.16554e7i	0.611768	+	1.16691i
$809$		−	1.80632e7i		−	0.970338i	−0.874421	−	0.485169i	$-0.838758\pi$
$809$		−	1.80632e7i		−	0.970338i	0.874421	−	0.485169i	$-0.161242\pi$
$810$	−7.48158e6	+	1.19542e7i	−0.400664	+	0.640186i
$811$	−8.45584e6	+	8.45584e6i	−0.451445	+	0.451445i	−0.895834	−	0.444389i	$-0.853421\pi$
$811$	−8.45584e6	+	8.45584e6i	−0.451445	+	0.451445i	0.444389	+	0.895834i	$0.353421\pi$
$812$	241525.	−	14536.4i	0.0128550	−	0.000773687i
$813$	8.65140e6	−	8.65140e6i	0.459050	−	0.459050i
$814$	−1.08926e7	+	4.90040e6i	−0.576199	+	0.259221i
$815$	3.78930e6	−	1.90280e7i	0.199832	−	1.00346i
$816$	7.83653e6	−	9.99015e6i	0.412001	−	0.525226i
$817$			7.05597e6i			0.369829i
$818$	−5.59613e6	−	1.24391e7i	−0.292418	−	0.649989i
$819$	44251.6	+	44251.6i	0.00230525	+	0.00230525i
$820$	−1.73966e7	−	2.38876e6i	−0.903501	−	0.124062i
$821$	−4.07020e6	+	4.07020e6i	−0.210745	+	0.210745i	−0.804584	−	0.593839i	$-0.797612\pi$
$821$	−4.07020e6	+	4.07020e6i	−0.210745	+	0.210745i	0.593839	+	0.804584i	$0.297612\pi$
$822$	6.40236e6	−	1.68740e7i	0.330492	−	0.871039i
$823$	−3.01611e7			−1.55220			−0.776099	−	0.630610i	$-0.782805\pi$
$823$	−3.01611e7			−1.55220			−0.776099	+	0.630610i	$0.782805\pi$
$824$	3.01583e6	−	9.66273e6i	0.154735	−	0.495772i
$825$	−1.51456e7	−	6.28141e6i	−0.774733	−	0.321309i
$826$	−7277.08	+	19179.3i	−0.000371114	+	0.000978101i
$827$	8.34070e6	+	8.34070e6i	0.424071	+	0.424071i	0.886603	−	0.462532i	$-0.153059\pi$
$827$	8.34070e6	+	8.34070e6i	0.424071	+	0.424071i	−0.462532	+	0.886603i	$0.653059\pi$
$828$	−1.86338e6	−	1.65181e6i	−0.0944549	−	0.0837307i
$829$	−1.60405e7	−	1.60405e7i	−0.810649	−	0.810649i	0.174082	−	0.984731i	$-0.444304\pi$
$829$	−1.60405e7	−	1.60405e7i	−0.810649	−	0.810649i	−0.984731	+	0.174082i	$0.944304\pi$
$830$	5.95155e6	+	2.58627e7i	0.299871	+	1.30310i
$831$	−2.97914e7			−1.49654
$832$	892761.	−	162768.i	0.0447123	−	0.00815195i
$833$			1.31157e7i			0.654904i
$834$	7.29665e6	+	1.62190e7i	0.363252	+	0.807439i
$835$	−7.72476e6	+	5.15903e6i	−0.383415	+	0.256066i
$836$	3.78379e6	−	4.26842e6i	0.187246	−	0.211228i
$837$	9.30997e6	+	9.30997e6i	0.459341	+	0.459341i
$838$	1.36263e7	+	5.17015e6i	0.670300	+	0.254327i
$839$			421767.i			0.0206856i	0.999947	+	0.0103428i	$0.00329227\pi$
$839$			421767.i			0.0206856i	−0.999947	+	0.0103428i	$0.996708\pi$
$840$	5.65164e6	+	3.08091e6i	0.276361	+	0.150654i
$841$		−	2.04838e7i		−	0.998666i
$842$	−9.57340e6	+	2.52315e7i	−0.465357	+	1.22649i
$843$	4.50801e6	+	4.50801e6i	0.218482	+	0.218482i
$844$	−2.48435e7	+	1.49522e6i	−1.20049	+	0.0722520i
$845$	1.15037e7	+	1.72248e7i	0.554238	+	0.829875i
$846$	−977486.	+	439753.i	−0.0469553	+	0.0211243i
$847$		−	861006.i		−	0.0412380i
$848$	−8.37783e6	+	1.06802e7i	−0.400076	+	0.510024i
$849$	−1.11429e6			−0.0530552
$850$	1.57476e7	−	466450.i	0.747594	−	0.0221441i
$851$	6.23304e6	+	6.23304e6i	0.295037	+	0.295037i
$852$	−3.59501e7	+	2.16368e6i	−1.69668	+	0.102116i
$853$	−2.29494e7	−	2.29494e7i	−1.07994	−	1.07994i	−0.996514	−	0.0834252i	$-0.973414\pi$
$853$	−2.29494e7	−	2.29494e7i	−1.07994	−	1.07994i	−0.0834252	−	0.996514i	$-0.526586\pi$
$854$	7.10541e6	+	2.69596e6i	0.333384	+	0.126493i
$855$	255071.	−	1.28084e6i	0.0119329	−	0.0599210i
$856$	−2.98720e7	+	1.56608e7i	−1.39342	+	0.730515i
$857$	8.65289e6			0.402448			0.201224	−	0.979545i	$-0.435508\pi$
$857$	8.65289e6			0.402448			0.201224	+	0.979545i	$0.435508\pi$
$858$	−768523.	−	291595.i	−0.0356401	−	0.0135227i
$859$	−1.06006e7	+	1.06006e7i	−0.490173	+	0.490173i	−0.908361	−	0.418188i	$-0.862665\pi$
$859$	−1.06006e7	+	1.06006e7i	−0.490173	+	0.490173i	0.418188	+	0.908361i	$0.362665\pi$
$860$	−2.12756e7	+	1.61383e7i	−0.980927	+	0.744064i
$861$	−4.41523e6	−	4.41523e6i	−0.202976	−	0.202976i
$862$	−1.11219e6	+	500356.i	−0.0509815	+	0.0229356i
$863$			3.47858e7i			1.58992i	0.606661	+	0.794961i	$0.292509\pi$
$863$			3.47858e7i			1.58992i	−0.606661	+	0.794961i	$0.707491\pi$
$864$	5.65737e6	−	2.28785e7i	0.257828	−	1.04266i
$865$	−3.53450e6	+	1.77485e7i	−0.160616	+	0.806532i
$866$	1.42478e7	+	3.16700e7i	0.645584	+	1.43501i
$867$	−6.15475e6	+	6.15475e6i	−0.278075	+	0.278075i
$868$	3.14063e6	−	3.54288e6i	0.141487	−	0.159609i
$869$	2.50212e7	−	2.50212e7i	1.12398	−	1.12398i
$870$	−386032.	+	616806.i	−0.0172912	+	0.0276281i
$871$			213236.i			0.00952392i
$872$	2.04031e7	−	1.06966e7i	0.908669	−	0.476381i
$873$	−3.67437e6			−0.163173
$874$	−3.93585e6	−	1.49335e6i	−0.174285	−	0.0661276i
$875$	1.55293e6	+	7.83442e6i	0.0685697	+	0.345929i
$876$	−1.91982e6	−	3.18983e7i	−0.0845279	−	1.40445i
$877$	−9.38491e6	+	9.38491e6i	−0.412032	+	0.412032i	−0.882446	−	0.470414i	$-0.844105\pi$
$877$	−9.38491e6	+	9.38491e6i	−0.412032	+	0.412032i	0.470414	+	0.882446i	$0.344105\pi$
$878$	3.86803e6	+	8.59788e6i	0.169338	+	0.376405i
$879$	1.01071e7			0.441220
$880$	2.15247e7	+	1.64652e6i	0.936978	+	0.0716736i
$881$	3.49039e7			1.51508			0.757538	−	0.652791i	$-0.226402\pi$
$881$	3.49039e7			1.51508			0.757538	+	0.652791i	$0.226402\pi$
$882$	1.68818e6	+	3.75250e6i	0.0730714	+	0.162424i
$883$	2.94816e7	−	2.94816e7i	1.27248	−	1.27248i	0.327691	−	0.944785i	$-0.393729\pi$
$883$	2.94816e7	−	2.94816e7i	1.27248	−	1.27248i	0.944785	−	0.327691i	$-0.106271\pi$
$884$	788369.	−	47448.5i	0.0339312	−	0.00204217i
$885$	−34261.5	−	51300.7i	−0.00147044	−	0.00220174i
$886$	8.34561e6	+	3.16652e6i	0.357169	+	0.135518i
$887$	4.50930e7			1.92442			0.962210	−	0.272309i	$-0.0877874\pi$
$887$	4.50930e7			1.92442			0.962210	+	0.272309i	$0.0877874\pi$
$888$	−4.20121e6	+	1.34607e7i	−0.178789	+	0.572841i
$889$		−	4.55649e6i		−	0.193364i
$890$	3.53470e7	+	2.21221e7i	1.49581	+	0.936163i
$891$	−1.18920e7	+	1.18920e7i	−0.501834	+	0.501834i
$892$	−2.85021e7	−	2.52661e7i	−1.19940	−	1.06323i
$893$	−1.28128e6	+	1.28128e6i	−0.0537669	+	0.0537669i
$894$	4.62219e6	+	1.02742e7i	0.193421	+	0.429938i
$895$	−6.31990e6	−	1.25857e6i	−0.263726	−	0.0525193i
$896$	−8.33428e6	−	1.53642e6i	−0.346815	−	0.0639354i
$897$			606626.i			0.0251733i
$898$	−2.59791e7	+	1.16875e7i	−1.07506	+	0.483651i
$899$	378448.	+	378448.i	0.0156173	+	0.0156173i
$900$	4.44547e6	−	2.16040e6i	0.182941	−	0.0889053i
$901$	−8.35359e6	+	8.35359e6i	−0.342816	+	0.342816i
$902$	−1.95791e7	−	7.42874e6i	−0.801264	−	0.304018i
$903$	−9.49561e6			−0.387528
$904$	−4.07809e7	−	1.27281e7i	−1.65972	−	0.518017i
$905$	−286695.	+	1.43964e6i	−0.0116359	+	0.0584295i
$906$	1.65885e7	+	6.29406e6i	0.671409	+	0.254748i
$907$	2.49512e7	+	2.49512e7i	1.00710	+	1.00710i	0.999975	+	0.00712657i	$0.00226848\pi$
$907$	2.49512e7	+	2.49512e7i	1.00710	+	1.00710i	0.00712657	+	0.999975i	$0.497732\pi$
$908$	−1.72888e6	−	2.87258e7i	−0.0695906	−	1.15627i
$909$	4.72078e6	+	4.72078e6i	0.189498	+	0.189498i
$910$	89792.2	+	390195.i	0.00359447	+	0.0156199i
$911$	2.42627e6			0.0968597			0.0484299	−	0.998827i	$-0.484578\pi$
$911$	2.42627e6			0.0968597			0.0484299	+	0.998827i	$0.484578\pi$
$912$	−807668.	−	6.68551e6i	−0.0321548	−	0.266163i
$913$			3.16487e7i			1.25655i
$914$	3.13103e7	−	1.40859e7i	1.23971	−	0.557725i
$915$	−1.90055e7	+	1.26929e7i	−0.750458	+	0.501198i
$916$	2.16354e6	+	3.59477e7i	0.0851972	+	1.41557i
$917$	−4.18461e6	−	4.18461e6i	−0.164336	−	0.164336i
$918$	7.27630e6	−	1.91773e7i	0.284973	−	0.751070i
$919$			5.00936e7i			1.95656i	0.207282	+	0.978281i	$0.433538\pi$
$919$			5.00936e7i			1.95656i	−0.207282	+	0.978281i	$0.566462\pi$
$920$	−4.49913e6	−	1.52832e7i	−0.175250	−	0.595312i
$921$		−	1.12025e6i		−	0.0435176i
$922$	−4.44534e6	−	1.68666e6i	−0.172218	−	0.0653434i
$923$	−1.58410e6	−	1.58410e6i	−0.0612038	−	0.0612038i
$924$	5.74425e6	+	5.09206e6i	0.221337	+	0.196207i
$925$	−1.61677e7	+	6.68847e6i	−0.621290	+	0.257023i
$926$	1.94770e6	+	4.32936e6i	0.0746440	+	0.165919i
$927$		−	2.76387e6i		−	0.105637i
$928$	229971.	−	930004.i	0.00876602	−	0.0354499i
$929$	1.54378e7			0.586876			0.293438	−	0.955978i	$-0.405201\pi$
$929$	1.54378e7			0.586876			0.293438	+	0.955978i	$0.405201\pi$
$930$	3.19300e6	+	1.38753e7i	0.121058	+	0.526059i
$931$	4.91874e6	+	4.91874e6i	0.185986	+	0.185986i
$932$	−1.12741e7	+	1.27181e7i	−0.425150	+	0.479603i
$933$	−2.06833e7	−	2.06833e7i	−0.777886	−	0.777886i
$934$	1.38181e7	−	3.64187e7i	0.518299	−	1.36602i
$935$	1.84262e7	+	3.66946e6i	0.689299	+	0.137269i
$936$	219451.	−	115050.i	0.00818745	−	0.00429238i
$937$	6.54446e6			0.243515			0.121757	−	0.992560i	$-0.461147\pi$
$937$	6.54446e6			0.243515			0.121757	+	0.992560i	$0.461147\pi$
$938$	706428.	−	1.86185e6i	0.0262157	−	0.0690936i
$939$	−1.35573e7	+	1.35573e7i	−0.501774	+	0.501774i
$940$	−6.79392e6	−	932888.i	−0.250785	−	0.0344358i
$941$	1.53586e7	+	1.53586e7i	0.565427	+	0.565427i	0.930844	−	0.365417i	$-0.119074\pi$
$941$	1.53586e7	+	1.53586e7i	0.565427	+	0.565427i	−0.365417	+	0.930844i	$0.619074\pi$
$942$	−1.39724e7	−	3.10579e7i	−0.513031	−	1.14037i
$943$			1.54545e7i			0.565948i
$944$	63904.9	+	50128.7i	0.00233402	+	0.00183086i
$945$	1.01981e7	+	2.03089e6i	0.371484	+	0.0739786i
$946$	−2.90422e7	+	1.30655e7i	−1.05512	+	0.474679i
$947$	2.83148e7	−	2.83148e7i	1.02598	−	1.02598i	0.0263270	−	0.999653i	$-0.491619\pi$
$947$	2.83148e7	−	2.83148e7i	1.02598	−	1.02598i	0.999653	−	0.0263270i	$-0.00838111\pi$
$948$	−2.50972e6	−	4.16997e7i	−0.0906994	−	1.50700i
$949$	1.40556e6	−	1.40556e6i	0.0506623	−	0.0506623i
$950$	5.73084e6	−	6.08071e6i	0.206020	−	0.218597i
$951$			3.35692e6i			0.120362i
$952$	−7.04075e6	−	2.19749e6i	−0.251783	−	0.0785840i
$953$	3.84616e7			1.37181			0.685907	−	0.727689i	$-0.259406\pi$
$953$	3.84616e7			1.37181			0.685907	+	0.727689i	$0.259406\pi$
$954$	−1.31480e6	+	3.46526e6i	−0.0467723	+	0.123272i
$955$	1.01927e7	−	6.80723e6i	0.361642	−	0.241525i
$956$	−7.41136e6	+	8.36061e6i	−0.262273	+	0.295865i
$957$	−613598.	+	613598.i	−0.0216573	+	0.0216573i
$958$	2.31027e7	−	1.03935e7i	0.813298	−	0.365888i
$959$	−1.04839e7			−0.368110
$960$	1.83113e7	−	1.77263e7i	0.641271	−	0.620783i
$961$	−1.81567e7			−0.634204
$962$	−799910.	+	359865.i	−0.0278679	+	0.0125372i
$963$	−6.51196e6	+	6.51196e6i	−0.226280	+	0.226280i
$964$	−2.90341e7	+	3.27528e7i	−1.00627	+	1.13516i
$965$	2.41401e7	+	3.61456e7i	0.834489	+	1.24950i
$966$	2.00968e6	−	5.29669e6i	0.0692923	−	0.182626i
$967$	2.33569e7			0.803248			0.401624	−	0.915805i	$-0.368446\pi$
$967$	2.33569e7			0.803248			0.401624	+	0.915805i	$0.368446\pi$
$968$	−3.25421e6	−	1.01567e6i	−0.111624	−	0.0348389i
$969$		−	5.86083e6i		−	0.200516i
$970$	−1.99276e7	−	1.24718e7i	−0.680025	−	0.425598i
$971$	−5.15245e6	+	5.15245e6i	−0.175374	+	0.175374i	−0.789336	−	0.613962i	$-0.789575\pi$
$971$	−5.15245e6	+	5.15245e6i	−0.175374	+	0.175374i	0.613962	+	0.789336i	$0.289575\pi$
$972$	−707844.	−	1.17610e7i	−0.0240310	−	0.399282i
$973$	7.30526e6	−	7.30526e6i	0.247374	−	0.247374i
$974$	−1.30984e7	+	5.89272e6i	−0.442405	+	0.199030i
$975$	−1.11223e6	−	461280.i	−0.0374700	−	0.0155401i
$976$	1.85713e7	−	2.36750e7i	0.624047	−	0.795546i
$977$			4.91321e6i			0.164676i	0.996604	+	0.0823378i	$0.0262386\pi$
$977$			4.91321e6i			0.164676i	−0.996604	+	0.0823378i	$0.973761\pi$
$978$	−1.12069e7	−	2.49108e7i	−0.374661	−	0.832799i
$979$	3.51631e7	+	3.51631e7i	1.17255	+	1.17255i
$980$	−3.58129e6	+	2.60814e7i	−0.119117	+	0.867492i
$981$	4.44778e6	−	4.44778e6i	0.147561	−	0.147561i
$982$	2.09366e6	−	5.51802e6i	0.0692832	−	0.182601i
$983$	−2.41522e7			−0.797209			−0.398605	−	0.917123i	$-0.630505\pi$
$983$	−2.41522e7			−0.797209			−0.398605	+	0.917123i	$0.630505\pi$
$984$	−2.18959e7	+	1.14792e7i	−0.720900	+	0.377941i
$985$	−2.15982e7	−	4.30115e6i	−0.709296	−	0.141252i
$986$	295780.	−	779552.i	0.00968894	−	0.0255360i
$987$	−1.72429e6	−	1.72429e6i	−0.0563401	−	0.0563401i
$988$	277866.	−	313455.i	0.00905614	−	0.0102160i
$989$	1.66186e7	+	1.66186e7i	0.540263	+	0.540263i
$990$	5.74421e6	−	1.32187e6i	0.186270	−	0.0428647i
$991$	5.22786e6			0.169099			0.0845493	−	0.996419i	$-0.473055\pi$
$991$	5.22786e6			0.169099			0.0845493	+	0.996419i	$0.473055\pi$
$992$	−9.68568e6	−	1.60494e7i	−0.312501	−	0.517822i
$993$			115359.i			0.00371260i
$994$	8.58345e6	+	1.90793e7i	0.275547	+	0.612488i
$995$	−2.31861e7	−	3.47172e7i	−0.742455	−	1.11170i
$996$	2.79597e7	+	2.47853e7i	0.893069	+	0.791672i
$997$	3.04939e7	+	3.04939e7i	0.971572	+	0.971572i	0.999607	−	0.0280354i	$-0.00892510\pi$
$997$	3.04939e7	+	3.04939e7i	0.971572	+	0.971572i	−0.0280354	+	0.999607i	$0.508925\pi$
$998$	−2.33304e7	−	8.85210e6i	−0.741475	−	0.281332i
$999$			2.27794e7i			0.722153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.9	✓	116
5.4	even	2	inner	80.6.q.a.29.50	yes	116
16.5	even	4	inner	80.6.q.a.69.50	yes	116
80.69	even	4	inner	80.6.q.a.69.9	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.9	✓	116	1.1	even	1	trivial
80.6.q.a.29.50	yes	116	5.4	even	2	inner
80.6.q.a.69.9	yes	116	80.69	even	4	inner
80.6.q.a.69.50	yes	116	16.5	even	4	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.15884 + 2.32087i) q^{2} +(-9.83803 + 9.83803i) q^{3} +(21.2272 - 23.9459i) q^{4} +(46.4875 - 31.0470i) q^{5} +(27.9200 - 73.5856i) q^{6} -45.7194 q^{7} +(-53.9321 + 172.799i) q^{8} +49.4262i q^{9} +O(q^{10})\)	\(q+(-5.15884 + 2.32087i) q^{2} +(-9.83803 + 9.83803i) q^{3} +(21.2272 - 23.9459i) q^{4} +(46.4875 - 31.0470i) q^{5} +(27.9200 - 73.5856i) q^{6} -45.7194 q^{7} +(-53.9321 + 172.799i) q^{8} +49.4262i q^{9} +(-167.765 + 268.057i) q^{10} +(-266.663 + 266.663i) q^{11} +(26.7474 + 444.414i) q^{12} +(-19.5826 + 19.5826i) q^{13} +(235.859 - 106.109i) q^{14} +(-151.904 + 762.787i) q^{15} +(-122.815 - 1016.61i) q^{16} -891.207i q^{17} +(-114.712 - 254.982i) q^{18} +(-334.228 - 334.228i) q^{19} +(243.348 - 1772.23i) q^{20} +(449.789 - 449.789i) q^{21} +(756.782 - 1994.56i) q^{22} -1574.39 q^{23} +(-1169.41 - 2230.58i) q^{24} +(1197.17 - 2886.59i) q^{25} +(55.5749 - 146.472i) q^{26} +(-2876.90 - 2876.90i) q^{27} +(-970.493 + 1094.79i) q^{28} +(-116.945 - 116.945i) q^{29} +(-986.678 - 4287.64i) q^{30} -3236.11 q^{31} +(2993.00 + 4959.48i) q^{32} -5246.88i q^{33} +(2068.37 + 4597.59i) q^{34} +(-2125.38 + 1419.45i) q^{35} +(1183.56 + 1049.18i) q^{36} +(-3959.03 - 3959.03i) q^{37} +(2499.92 + 948.528i) q^{38} -385.309i q^{39} +(2857.70 + 9707.40i) q^{40} -9816.22i q^{41} +(-1276.49 + 3364.29i) q^{42} +(-10555.6 - 10555.6i) q^{43} +(724.996 + 12046.0i) q^{44} +(1534.53 + 2297.70i) q^{45} +(8122.00 - 3653.94i) q^{46} -3833.55i q^{47} +(11209.7 + 8793.17i) q^{48} -14716.7 q^{49} +(523.392 + 17669.9i) q^{50} +(8767.72 + 8767.72i) q^{51} +(53.2407 + 884.608i) q^{52} +(-9373.35 - 9373.35i) q^{53} +(21518.3 + 8164.55i) q^{54} +(-4117.41 + 20675.6i) q^{55} +(2465.74 - 7900.24i) q^{56} +6576.28 q^{57} +(874.715 + 331.887i) q^{58} +(-56.0853 + 56.0853i) q^{59} +(15041.1 + 19829.3i) q^{60} +(20778.0 + 20778.0i) q^{61} +(16694.6 - 7510.59i) q^{62} -2259.73i q^{63} +(-26950.7 - 18638.8i) q^{64} +(-302.365 + 1518.33i) q^{65} +(12177.3 + 27067.8i) q^{66} +(5444.53 - 5444.53i) q^{67} +(-21340.8 - 18917.8i) q^{68} +(15488.9 - 15488.9i) q^{69} +(7670.13 - 12255.4i) q^{70} +80893.1i q^{71} +(-8540.77 - 2665.66i) q^{72} -71776.0 q^{73} +(29612.3 + 11235.6i) q^{74} +(16620.6 + 40176.2i) q^{75} +(-15098.1 + 908.688i) q^{76} +(12191.7 - 12191.7i) q^{77} +(894.251 + 1987.75i) q^{78} -93830.6 q^{79} +(-37272.0 - 43446.5i) q^{80} +44595.5 q^{81} +(22782.1 + 50640.3i) q^{82} +(59342.1 - 59342.1i) q^{83} +(-1222.87 - 20318.4i) q^{84} +(-27669.3 - 41429.9i) q^{85} +(78953.0 + 29956.6i) q^{86} +2301.02 q^{87} +(-31697.3 - 60460.7i) q^{88} -131863. i q^{89} +(-13249.1 - 8292.00i) q^{90} +(895.306 - 895.306i) q^{91} +(-33419.8 + 37700.2i) q^{92} +(31837.0 - 31837.0i) q^{93} +(8897.16 + 19776.7i) q^{94} +(-25914.2 - 5160.64i) q^{95} +(-78236.7 - 19346.3i) q^{96} +74340.6i q^{97} +(75921.2 - 34155.6i) q^{98} +(-13180.2 - 13180.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more