LMFDB - Embedded newform 80.6.q.a.29.8

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			29.8
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.17693 - 2.28021i) q^{2} +(18.1244 - 18.1244i) q^{3} +(21.6013 + 23.6090i) q^{4} +(-35.0084 + 43.5822i) q^{5} +(-135.156 + 52.5013i) q^{6} +75.8099 q^{7} +(-57.9951 - 171.478i) q^{8} -413.986i q^{9} +O(q^{10})$	\(q+(-5.17693 - 2.28021i) q^{2} +(18.1244 - 18.1244i) q^{3} +(21.6013 + 23.6090i) q^{4} +(-35.0084 + 43.5822i) q^{5} +(-135.156 + 52.5013i) q^{6} +75.8099 q^{7} +(-57.9951 - 171.478i) q^{8} -413.986i q^{9} +(280.613 - 145.796i) q^{10} +(395.586 - 395.586i) q^{11} +(819.408 + 36.3881i) q^{12} +(-121.062 + 121.062i) q^{13} +(-392.463 - 172.862i) q^{14} +(155.396 + 1424.41i) q^{15} +(-90.7681 + 1019.97i) q^{16} -1708.17i q^{17} +(-943.974 + 2143.18i) q^{18} +(-508.967 - 508.967i) q^{19} +(-1785.16 + 114.920i) q^{20} +(1374.01 - 1374.01i) q^{21} +(-2949.94 + 1145.90i) q^{22} +3860.59 q^{23} +(-4159.05 - 2056.80i) q^{24} +(-673.824 - 3051.49i) q^{25} +(902.776 - 350.683i) q^{26} +(-3099.01 - 3099.01i) q^{27} +(1637.59 + 1789.79i) q^{28} +(-2262.59 - 2262.59i) q^{29} +(2443.47 - 7728.39i) q^{30} -4848.76 q^{31} +(2795.64 - 5073.34i) q^{32} -14339.5i q^{33} +(-3894.99 + 8843.11i) q^{34} +(-2653.98 + 3303.97i) q^{35} +(9773.78 - 8942.62i) q^{36} +(-7922.75 - 7922.75i) q^{37} +(1474.34 + 3795.44i) q^{38} +4388.34i q^{39} +(9503.69 + 3475.60i) q^{40} +12485.9i q^{41} +(-10246.2 + 3980.12i) q^{42} +(8754.53 + 8754.53i) q^{43} +(17884.5 + 794.213i) q^{44} +(18042.4 + 14493.0i) q^{45} +(-19986.0 - 8802.94i) q^{46} -13310.3i q^{47} +(16841.2 + 20131.4i) q^{48} -11059.9 q^{49} +(-3469.69 + 17333.8i) q^{50} +(-30959.6 - 30959.6i) q^{51} +(-5473.24 - 243.055i) q^{52} +(10445.2 + 10445.2i) q^{53} +(8976.97 + 23109.7i) q^{54} +(3391.69 + 31089.3i) q^{55} +(-4396.60 - 12999.7i) q^{56} -18449.4 q^{57} +(6554.10 + 16872.5i) q^{58} +(26174.4 - 26174.4i) q^{59} +(-30272.0 + 34437.7i) q^{60} +(37078.8 + 37078.8i) q^{61} +(25101.7 + 11056.2i) q^{62} -31384.2i q^{63} +(-26041.1 + 19889.7i) q^{64} +(-1037.97 - 9514.33i) q^{65} +(-32697.0 + 74234.6i) q^{66} +(17799.5 - 17799.5i) q^{67} +(40328.3 - 36898.8i) q^{68} +(69970.7 - 69970.7i) q^{69} +(21273.2 - 11052.8i) q^{70} +19815.3i q^{71} +(-70989.3 + 24009.1i) q^{72} +6581.86 q^{73} +(22950.0 + 59081.1i) q^{74} +(-67519.0 - 43093.7i) q^{75} +(1021.85 - 23010.5i) q^{76} +(29989.3 - 29989.3i) q^{77} +(10006.3 - 22718.1i) q^{78} -30328.6 q^{79} +(-41274.9 - 39663.4i) q^{80} -11736.6 q^{81} +(28470.5 - 64638.8i) q^{82} +(42.7319 - 42.7319i) q^{83} +(62119.2 + 2758.58i) q^{84} +(74446.1 + 59800.4i) q^{85} +(-25359.5 - 65283.8i) q^{86} -82016.1 q^{87} +(-90776.1 - 44892.1i) q^{88} -2809.87i q^{89} +(-60357.4 - 116170. i) q^{90} +(-9177.69 + 9177.69i) q^{91} +(83393.6 + 91144.5i) q^{92} +(-87880.7 + 87880.7i) q^{93} +(-30350.3 + 68906.6i) q^{94} +(40000.0 - 4363.80i) q^{95} +(-41281.9 - 142620. i) q^{96} +155990. i q^{97} +(57256.2 + 25218.8i) q^{98} +(-163767. - 163767. i) 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 $

$2$	−5.17693	−	2.28021i	−0.915161	−	0.403088i
$2$	−5.17693	−	2.28021i	−0.915161	−	0.403088i
$3$	18.1244	−	18.1244i	1.16268	−	1.16268i	0.178792	−	0.983887i	$-0.442781\pi$
$3$	18.1244	−	18.1244i	1.16268	−	1.16268i	0.983887	−	0.178792i	$-0.0572189\pi$
$4$	21.6013	+	23.6090i	0.675040	+	0.737781i
$5$	−35.0084	+	43.5822i	−0.626249	+	0.779623i
$5$	−35.0084	+	43.5822i	−0.626249	+	0.779623i
$6$	−135.156	+	52.5013i	−1.53270	+	0.595377i
$7$	75.8099			0.584764			0.292382	−	0.956302i	$-0.405552\pi$
$7$	75.8099			0.584764			0.292382	+	0.956302i	$0.405552\pi$
$8$	−57.9951	−	171.478i	−0.320381	−	0.947289i
$9$		−	413.986i		−	1.70364i
$10$	280.613	−	145.796i	0.887376	−	0.461047i
$11$	395.586	−	395.586i	0.985732	−	0.985732i	−0.0141676	−	0.999900i	$-0.504510\pi$
$11$	395.586	−	395.586i	0.985732	−	0.985732i	0.999900	+	0.0141676i	$0.00450983\pi$
$12$	819.408	+	36.3881i	1.64266	+	0.0729468i
$13$	−121.062	+	121.062i	−0.198678	+	0.198678i	−0.799433	−	0.600755i	$-0.794867\pi$
$13$	−121.062	+	121.062i	−0.198678	+	0.198678i	0.600755	+	0.799433i	$0.294867\pi$
$14$	−392.463	−	172.862i	−0.535154	−	0.235711i
$15$	155.396	+	1424.41i	0.178324	+	1.63458i
$16$	−90.7681	+	1019.97i	−0.0886408	+	0.996064i
$17$		−	1708.17i		−	1.43354i	−0.697310	−	0.716770i	$-0.745620\pi$
$17$		−	1708.17i		−	1.43354i	0.697310	−	0.716770i	$-0.254380\pi$
$18$	−943.974	+	2143.18i	−0.686718	+	1.55911i
$19$	−508.967	−	508.967i	−0.323449	−	0.323449i	0.526640	−	0.850089i	$-0.323452\pi$
$19$	−508.967	−	508.967i	−0.323449	−	0.323449i	−0.850089	+	0.526640i	$0.823452\pi$
$20$	−1785.16	+	114.920i	−0.997934	+	0.0642424i
$21$	1374.01	−	1374.01i	0.679893	−	0.679893i
$22$	−2949.94	+	1145.90i	−1.29944	+	0.504767i
$23$	3860.59			1.52172			0.760858	−	0.648919i	$-0.224778\pi$
$23$	3860.59			1.52172			0.760858	+	0.648919i	$0.224778\pi$
$24$	−4159.05	−	2056.80i	−1.47389	−	0.728893i
$25$	−673.824	−	3051.49i	−0.215624	−	0.976477i
$26$	902.776	−	350.683i	0.261907	−	0.101738i
$27$	−3099.01	−	3099.01i	−0.818112	−	0.818112i
$28$	1637.59	+	1789.79i	0.394740	+	0.431428i
$29$	−2262.59	−	2262.59i	−0.499587	−	0.499587i	0.411722	−	0.911309i	$-0.364927\pi$
$29$	−2262.59	−	2262.59i	−0.499587	−	0.499587i	−0.911309	+	0.411722i	$0.864927\pi$
$30$	2443.47	−	7728.39i	0.495683	−	1.56778i
$31$	−4848.76			−0.906205			−0.453103	−	0.891458i	$-0.649683\pi$
$31$	−4848.76			−0.906205			−0.453103	+	0.891458i	$0.649683\pi$
$32$	2795.64	−	5073.34i	0.482622	−	0.875829i
$33$		−	14339.5i		−	2.29218i
$34$	−3894.99	+	8843.11i	−0.577843	+	1.31192i
$35$	−2653.98	+	3303.97i	−0.366208	+	0.455896i
$36$	9773.78	−	8942.62i	1.25692	−	1.15003i
$37$	−7922.75	−	7922.75i	−0.951418	−	0.951418i	0.0474549	−	0.998873i	$-0.484889\pi$
$37$	−7922.75	−	7922.75i	−0.951418	−	0.951418i	−0.998873	+	0.0474549i	$0.984889\pi$
$38$	1474.34	+	3795.44i	0.165630	+	0.426386i
$39$			4388.34i			0.461997i
$40$	9503.69	+	3475.60i	0.939166	+	0.343463i
$41$			12485.9i			1.16001i	0.814613	+	0.580004i	$0.196949\pi$
$41$			12485.9i			1.16001i	−0.814613	+	0.580004i	$0.803051\pi$
$42$	−10246.2	+	3980.12i	−0.896268	+	0.348155i
$43$	8754.53	+	8754.53i	0.722040	+	0.722040i	0.969021	−	0.246980i	$-0.0794382\pi$
$43$	8754.53	+	8754.53i	0.722040	+	0.722040i	−0.246980	+	0.969021i	$0.579438\pi$
$44$	17884.5	+	794.213i	1.39266	+	0.0618451i
$45$	18042.4	+	14493.0i	1.32820	+	1.06691i
$46$	−19986.0	−	8802.94i	−1.39262	−	0.613385i
$47$		−	13310.3i		−	0.878908i	−0.898265	−	0.439454i	$-0.855172\pi$
$47$		−	13310.3i		−	0.878908i	0.898265	−	0.439454i	$-0.144828\pi$
$48$	16841.2	+	20131.4i	1.05504	+	1.26116i
$49$	−11059.9			−0.658051
$50$	−3469.69	+	17333.8i	−0.196275	+	0.980549i
$51$	−30959.6	−	30959.6i	−1.66675	−	1.66675i
$52$	−5473.24	−	243.055i	−0.280696	−	0.0124651i
$53$	10445.2	+	10445.2i	0.510774	+	0.510774i	0.914764	−	0.403990i	$-0.132377\pi$
$53$	10445.2	+	10445.2i	0.510774	+	0.510774i	−0.403990	+	0.914764i	$0.632377\pi$
$54$	8976.97	+	23109.7i	0.418934	+	1.07848i
$55$	3391.69	+	31089.3i	0.151185	+	1.38581i
$56$	−4396.60	−	12999.7i	−0.187347	−	0.553941i
$57$	−18449.4			−0.752134
$58$	6554.10	+	16872.5i	0.255825	+	0.658580i
$59$	26174.4	−	26174.4i	0.978921	−	0.978921i	−0.0208618	−	0.999782i	$-0.506641\pi$
$59$	26174.4	−	26174.4i	0.978921	−	0.978921i	0.999782	+	0.0208618i	$0.00664100\pi$
$60$	−30272.0	+	34437.7i	−1.08558	+	1.23497i
$61$	37078.8	+	37078.8i	1.27585	+	1.27585i	0.942966	+	0.332889i	$0.108023\pi$
$61$	37078.8	+	37078.8i	1.27585	+	1.27585i	0.332889	+	0.942966i	$0.391977\pi$
$62$	25101.7	+	11056.2i	0.829324	+	0.365280i
$63$		−	31384.2i		−	0.996230i
$64$	−26041.1	+	19889.7i	−0.794713	+	0.606986i
$65$	−1037.97	−	9514.33i	−0.0304719	−	0.279315i
$66$	−32697.0	+	74234.6i	−0.923950	+	2.09771i
$67$	17799.5	−	17799.5i	0.484418	−	0.484418i	−0.422122	−	0.906539i	$-0.638714\pi$
$67$	17799.5	−	17799.5i	0.484418	−	0.484418i	0.906539	+	0.422122i	$0.138714\pi$
$68$	40328.3	−	36898.8i	1.05764	−	0.967698i
$69$	69970.7	−	69970.7i	1.76927	−	1.76927i
$70$	21273.2	−	11052.8i	0.518906	−	0.269604i
$71$			19815.3i			0.466503i	0.972416	+	0.233251i	$0.0749365\pi$
$71$			19815.3i			0.466503i	−0.972416	+	0.233251i	$0.925063\pi$
$72$	−70989.3	+	24009.1i	−1.61384	+	0.545814i
$73$	6581.86			0.144558			0.0722789	−	0.997384i	$-0.476973\pi$
$73$	6581.86			0.144558			0.0722789	+	0.997384i	$0.476973\pi$
$74$	22950.0	+	59081.1i	0.487196	+	1.25421i
$75$	−67519.0	−	43093.7i	−1.38603	−	0.884627i
$76$	1021.85	−	23010.5i	0.0202933	−	0.456975i
$77$	29989.3	−	29989.3i	0.576421	−	0.576421i
$78$	10006.3	−	22718.1i	0.186225	−	0.422801i
$79$	−30328.6			−0.546745			−0.273373	−	0.961908i	$-0.588139\pi$
$79$	−30328.6			−0.546745			−0.273373	+	0.961908i	$0.588139\pi$
$80$	−41274.9	−	39663.4i	−0.721043	−	0.692890i
$81$	−11736.6			−0.198760
$82$	28470.5	−	64638.8i	0.467585	−	1.06159i
$83$	42.7319	−	42.7319i	0.000680858	−	0.000680858i	−0.706766	−	0.707447i	$-0.749847\pi$
$83$	42.7319	−	42.7319i	0.000680858	−	0.000680858i	0.707447	+	0.706766i	$0.249847\pi$
$84$	62119.2	+	2758.58i	0.960567	+	0.0426567i
$85$	74446.1	+	59800.4i	1.11762	+	0.897754i
$86$	−25359.5	−	65283.8i	−0.369738	−	0.951829i
$87$	−82016.1			−1.16172
$88$	−90776.1	−	44892.1i	−1.24958	−	0.617964i
$89$		−	2809.87i		−	0.0376020i	−0.999823	−	0.0188010i	$-0.994015\pi$
$89$		−	2809.87i		−	0.0376020i	0.999823	−	0.0188010i	$-0.00598489\pi$
$90$	−60357.4	−	116170.i	−0.785461	−	1.51177i
$91$	−9177.69	+	9177.69i	−0.116180	+	0.116180i
$92$	83393.6	+	91144.5i	1.02722	+	1.12269i
$93$	−87880.7	+	87880.7i	−1.05363	+	1.05363i
$94$	−30350.3	+	68906.6i	−0.354277	+	0.804343i
$95$	40000.0	−	4363.80i	0.454728	−	0.0496085i
$96$	−41281.9	−	142620.i	−0.457174	−	1.57944i
$97$			155990.i			1.68332i	0.540010	+	0.841659i	$0.318421\pi$
$97$			155990.i			1.68332i	−0.540010	+	0.841659i	$0.681579\pi$
$98$	57256.2	+	25218.8i	0.602223	+	0.265252i
$99$	−163767.	−	163767.i	−1.67934	−	1.67934i
$100$	57487.1	−	81824.4i	0.574871	−	0.818244i
$101$	−53602.7	+	53602.7i	−0.522858	+	0.522858i	−0.918433	−	0.395576i	$-0.870545\pi$
$101$	−53602.7	+	53602.7i	−0.522858	+	0.522858i	0.395576	+	0.918433i	$0.370545\pi$
$102$	89681.4	+	230870.i	0.853497	+	2.19719i
$103$	129521.			1.20295			0.601475	−	0.798892i	$-0.294580\pi$
$103$	129521.			1.20295			0.601475	+	0.798892i	$0.294580\pi$
$104$	27780.4	+	13738.4i	0.251858	+	0.124553i
$105$	11780.5	+	107984.i	0.104278	+	0.955843i
$106$	−30257.0	−	77891.6i	−0.261554	−	0.673327i
$107$	28069.1	+	28069.1i	0.237012	+	0.237012i	0.815611	−	0.578600i	$-0.196401\pi$
$107$	28069.1	+	28069.1i	0.237012	+	0.237012i	−0.578600	+	0.815611i	$0.696401\pi$
$108$	6221.84	−	140107.i	0.0513286	−	1.15585i
$109$	70590.2	+	70590.2i	0.569086	+	0.569086i	0.931872	−	0.362786i	$-0.118174\pi$
$109$	70590.2	+	70590.2i	0.569086	+	0.569086i	−0.362786	+	0.931872i	$0.618174\pi$
$110$	53331.6	−	168681.i	0.420245	−	1.32918i
$111$	−287190.			−2.21239
$112$	−6881.12	+	77323.8i	−0.0518340	+	0.582462i
$113$		−	181412.i		−	1.33651i	−0.743934	−	0.668253i	$-0.767042\pi$
$113$		−	181412.i		−	1.33651i	0.743934	−	0.668253i	$-0.232958\pi$
$114$	95511.4	+	42068.5i	0.688324	+	0.303176i
$115$	−135153.	+	168253.i	−0.952973	+	1.18636i
$116$	4542.58	−	102292.i	0.0313442	−	0.705827i
$117$	50117.9	+	50117.9i	0.338476	+	0.338476i
$118$	−195187.	+	75820.2i	−1.29046	+	0.501279i
$119$		−	129497.i		−	0.838283i
$120$	235242.	−	109255.i	1.49129	−	0.692612i
$121$		−	151925.i		−	0.943335i
$122$	−107407.	−	276502.i	−0.653331	−	1.68189i
$123$	226300.	+	226300.i	1.34872	+	1.34872i
$124$	−104740.	−	114474.i	−0.611725	−	0.668581i
$125$	156580.	+	77461.0i	0.896318	+	0.443412i
$126$	−71562.5	+	162474.i	−0.401568	+	0.911712i
$127$		−	86268.0i		−	0.474614i	−0.971435	−	0.237307i	$-0.923735\pi$
$127$		−	86268.0i		−	0.474614i	0.971435	−	0.237307i	$-0.0762647\pi$
$128$	180166.	−	43588.5i	0.971959	−	0.235151i
$129$	317341.			1.67900
$130$	−16321.2	+	51621.8i	−0.0847019	+	0.267901i
$131$	125035.	+	125035.i	0.636578	+	0.636578i	0.949710	−	0.313131i	$-0.101378\pi$
$131$	125035.	+	125035.i	0.636578	+	0.636578i	−0.313131	+	0.949710i	$0.601378\pi$
$132$	338541.	−	309751.i	1.69113	−	1.54731i
$133$	−38584.7	−	38584.7i	−0.189141	−	0.189141i
$134$	−132733.	+	51560.2i	−0.638583	+	0.248057i
$135$	243553.	−	26570.4i	1.15016	−	0.125477i
$136$	−292914.	+	99065.7i	−1.35798	+	0.459278i
$137$	−147926.			−0.673354			−0.336677	−	0.941620i	$-0.609303\pi$
$137$	−147926.			−0.673354			−0.336677	+	0.941620i	$0.609303\pi$
$138$	−521781.	+	202686.i	−2.33233	+	0.905995i
$139$	−285453.	+	285453.i	−1.25313	+	1.25313i	−0.298825	+	0.954308i	$0.596595\pi$
$139$	−285453.	+	285453.i	−1.25313	+	1.25313i	−0.954308	+	0.298825i	$0.903405\pi$
$140$	−135333.	+	8712.09i	−0.583556	+	0.0375666i
$141$	−241241.	−	241241.i	−1.02189	−	1.02189i
$142$	45183.0	−	102582.i	0.188042	−	0.426925i
$143$			95780.7i			0.391686i
$144$	422253.	+	37576.7i	1.69694	+	0.151012i
$145$	177818.	−	19399.1i	0.702355	−	0.0766235i
$146$	−34073.9	−	15008.0i	−0.132294	−	0.0582695i
$147$	−200453.	+	200453.i	−0.765102	+	0.765102i
$148$	15906.4	−	358190.i	0.0596922	−	1.34418i
$149$	−70377.1	+	70377.1i	−0.259696	+	0.259696i	−0.824931	−	0.565234i	$-0.808786\pi$
$149$	−70377.1	+	70377.1i	−0.259696	+	0.259696i	0.565234	+	0.824931i	$0.308786\pi$
$150$	251279.	+	377050.i	0.911858	+	1.36827i
$151$		−	365502.i		−	1.30451i	−0.758000	−	0.652254i	$-0.773824\pi$
$151$		−	365502.i		−	1.30451i	0.758000	−	0.652254i	$-0.226176\pi$
$152$	−57758.9	+	116794.i	−0.202773	+	0.410026i
$153$	−707160.			−2.44224
$154$	−223635.	+	86870.8i	−0.759866	+	0.295170i
$155$	169747.	−	211320.i	0.567510	−	0.706498i
$156$	−103604.	+	94793.8i	−0.340852	+	0.311866i
$157$	195192.	−	195192.i	0.631994	−	0.631994i	−0.316574	−	0.948568i	$-0.602533\pi$
$157$	195192.	−	195192.i	0.631994	−	0.631994i	0.948568	+	0.316574i	$0.102533\pi$
$158$	157009.	+	69155.6i	0.500360	+	0.220386i
$159$	378627.			1.18773
$160$	123237.	+	299450.i	0.380575	+	0.924750i
$161$	292671.			0.889845
$162$	60759.4	+	26761.8i	0.181897	+	0.0801176i
$163$	−297450.	+	297450.i	−0.876890	+	0.876890i	−0.993212	−	0.116322i	$-0.962890\pi$
$163$	−297450.	+	297450.i	−0.876890	+	0.876890i	0.116322	+	0.993212i	$0.462890\pi$
$164$	−294780.	+	269712.i	−0.855832	+	0.783053i
$165$	624947.	+	502002.i	1.78704	+	1.43548i
$166$	−318.658	+	123.783i	−0.000897541	+	0.000348650i
$167$	−209565.			−0.581471			−0.290736	−	0.956803i	$-0.593900\pi$
$167$	−209565.			−0.581471			−0.290736	+	0.956803i	$0.593900\pi$
$168$	−315297.	−	155926.i	−0.861880	−	0.426231i
$169$			341981.i			0.921054i
$170$	−249045.	−	479336.i	−0.660930	−	1.27209i
$171$	−210705.	+	210705.i	−0.551042	+	0.551042i
$172$	−17576.4	+	395795.i	−0.0453010	+	1.02011i
$173$	−226462.	+	226462.i	−0.575281	+	0.575281i	−0.933599	−	0.358319i	$-0.883350\pi$
$173$	−226462.	+	226462.i	−0.575281	+	0.575281i	0.358319	+	0.933599i	$0.383350\pi$
$174$	424592.	+	187014.i	1.06316	+	0.468274i
$175$	−51082.5	−	231333.i	−0.126089	−	0.571009i
$176$	367579.	+	439392.i	0.894476	+	1.06923i
$177$		−	948791.i		−	2.27634i
$178$	−6407.08	+	14546.5i	−0.0151569	+	0.0344119i
$179$	332063.	+	332063.i	0.774619	+	0.774619i	0.978910	−	0.204291i	$-0.0654890\pi$
$179$	332063.	+	332063.i	0.774619	+	0.774619i	−0.204291	+	0.978910i	$0.565489\pi$
$180$	47575.3	+	739030.i	0.109446	+	1.70013i
$181$	−567475.	+	567475.i	−1.28751	+	1.28751i	−0.351214	+	0.936295i	$0.614231\pi$
$181$	−567475.	+	567475.i	−1.28751	+	1.28751i	−0.936295	+	0.351214i	$0.885769\pi$
$182$	68439.3	−	26585.2i	0.153154	−	0.0594925i
$183$	1.34406e6			2.96682
$184$	−223895.	−	662004.i	−0.487528	−	1.44150i
$185$	622654.	−	67928.4i	1.33757	−	0.145923i
$186$	655339.	−	254566.i	1.38894	−	0.539534i
$187$	−675729.	−	675729.i	−1.41309	−	1.41309i
$188$	314243.	−	287520.i	0.648442	−	0.593299i
$189$	−234935.	−	234935.i	−0.478403	−	0.478403i
$190$	−217028.	−	68617.3i	−0.436146	−	0.137895i
$191$	147312.			0.292183			0.146092	−	0.989271i	$-0.453331\pi$
$191$	147312.			0.292183			0.146092	+	0.989271i	$0.453331\pi$
$192$	−111491.	+	832468.i	−0.218266	+	1.62973i
$193$		−	213679.i		−	0.412923i	−0.978455	−	0.206461i	$-0.933805\pi$
$193$		−	213679.i		−	0.412923i	0.978455	−	0.206461i	$-0.0661948\pi$
$194$	355689.	−	807547.i	0.678525	−	1.54051i
$195$	−191254.	−	153629.i	−0.360183	−	0.289325i
$196$	−238907.	−	261112.i	−0.444211	−	0.485497i
$197$	79771.2	+	79771.2i	0.146447	+	0.146447i	0.776529	−	0.630082i	$-0.216979\pi$
$197$	79771.2	+	79771.2i	0.146447	+	0.146447i	−0.630082	+	0.776529i	$0.716979\pi$
$198$	474387.	+	1.22123e6i	0.859944	+	2.21378i
$199$			846754.i			1.51574i	0.652406	+	0.757870i	$0.273760\pi$
$199$			846754.i			1.51574i	−0.652406	+	0.757870i	$0.726240\pi$
$200$	−484184.	+	292517.i	−0.855924	+	0.517102i
$201$		−	645208.i		−	1.12644i
$202$	399723.	−	155272.i	0.689257	−	0.267742i
$203$	−171527.	−	171527.i	−0.292141	−	0.292141i
$204$	62157.2	−	1.39969e6i	0.104572	−	2.35482i
$205$	−544165.	−	437112.i	−0.904369	−	0.726454i
$206$	−670522.	−	295335.i	−1.10089	−	0.484894i
$207$		−	1.59823e6i		−	2.59246i
$208$	−112491.	−	134468.i	−0.180285	−	0.215507i
$209$	−402680.			−0.637668
$210$	185239.	−	585889.i	0.289858	−	0.916783i
$211$	324835.	+	324835.i	0.502293	+	0.502293i	0.912150	−	0.409857i	$-0.134421\pi$
$211$	324835.	+	324835.i	0.502293	+	0.502293i	−0.409857	+	0.912150i	$0.634421\pi$
$212$	−20970.8	+	472232.i	−0.0320461	+	0.721632i
$213$	359139.	+	359139.i	0.542393	+	0.542393i
$214$	−81308.5	−	209315.i	−0.121367	−	0.312440i
$215$	−688024.	+	75060.0i	−1.01510	+	0.110742i
$216$	−351683.	+	711137.i	−0.512882	+	1.03710i
$217$	−367584.			−0.529916
$218$	−204480.	−	526401.i	−0.291414	−	0.750197i
$219$	119292.	−	119292.i	0.168074	−	0.168074i
$220$	−660723.	+	751644.i	−0.920370	+	1.04702i
$221$	206795.	+	206795.i	0.284812	+	0.284812i
$222$	1.48676e6	+	654852.i	2.02469	+	0.891787i
$223$		−	285532.i		−	0.384496i	−0.981346	−	0.192248i	$-0.938422\pi$
$223$		−	285532.i		−	0.384496i	0.981346	−	0.192248i	$-0.0615778\pi$
$224$	211937.	−	384610.i	0.282220	−	0.512153i
$225$	−1.26327e6	+	278953.i	−1.66357	+	0.367346i
$226$	−413658.	+	939160.i	−0.538729	+	1.22312i
$227$	−767705.	+	767705.i	−0.988849	+	0.988849i	−0.999939	−	0.0110897i	$-0.996470\pi$
$227$	−767705.	+	767705.i	−0.988849	+	0.988849i	0.0110897	+	0.999939i	$0.496470\pi$
$228$	−398531.	−	435572.i	−0.507721	−	0.554910i
$229$	425119.	−	425119.i	0.535700	−	0.535700i	−0.386563	−	0.922263i	$-0.626338\pi$
$229$	425119.	−	425119.i	0.535700	−	0.535700i	0.922263	+	0.386563i	$0.126338\pi$
$230$	1.08333e6	−	562858.i	1.35033	−	0.701583i
$231$		−	1.08707e6i		−	1.34038i
$232$	−256765.	+	519203.i	−0.313195	+	0.633311i
$233$	−530468.			−0.640131			−0.320066	−	0.947395i	$-0.603705\pi$
$233$	−530468.			−0.640131			−0.320066	+	0.947395i	$0.603705\pi$
$234$	−145178.	−	373736.i	−0.173325	−	0.446196i
$235$	580093.	+	465973.i	0.685217	+	0.550416i
$236$	1.18335e6	+	52550.1i	1.38304	+	0.0614177i
$237$	−549687.	+	549687.i	−0.635689	+	0.635689i
$238$	−295279.	+	670395.i	−0.337902	+	0.767164i
$239$	−180828.			−0.204772			−0.102386	−	0.994745i	$-0.532648\pi$
$239$	−180828.			−0.204772			−0.102386	+	0.994745i	$0.532648\pi$
$240$	−1.46696e6	+	29208.0i	−1.64395	+	0.0327321i
$241$	170927.			0.189569			0.0947846	−	0.995498i	$-0.469784\pi$
$241$	170927.			0.189569			0.0947846	+	0.995498i	$0.469784\pi$
$242$	−346421.	+	786506.i	−0.380247	+	0.863304i
$243$	540341.	−	540341.i	0.587019	−	0.587019i
$244$	−74442.7	+	1.67634e6i	−0.0800475	+	1.80255i
$245$	387188.	−	482013.i	0.412104	−	0.513031i
$246$	−655528.	−	1.68755e6i	−0.690642	−	1.77795i
$247$	123233.			0.128524
$248$	281204.	+	831454.i	0.290330	+	0.858438i
$249$		−	1548.98i		−	0.00158324i
$250$	−633978.	−	758046.i	−0.641541	−	0.767089i
$251$	1.32474e6	−	1.32474e6i	1.32723	−	1.32723i	0.419460	−	0.907774i	$-0.362219\pi$
$251$	1.32474e6	−	1.32474e6i	1.32723	−	1.32723i	0.907774	−	0.419460i	$-0.137781\pi$
$252$	740949.	−	677939.i	0.735000	−	0.672496i
$253$	1.52719e6	−	1.52719e6i	1.50000	−	1.50000i
$254$	−196709.	+	446604.i	−0.191311	+	0.434348i
$255$	2.43313e6	−	265443.i	2.34323	−	0.255635i
$256$	−1.03210e6	−	185161.i	−0.984286	−	0.176584i
$257$		−	732158.i		−	0.691468i	−0.938333	−	0.345734i	$-0.887630\pi$
$257$		−	732158.i		−	0.691468i	0.938333	−	0.345734i	$-0.112370\pi$
$258$	−1.64285e6	−	723603.i	−1.53656	−	0.676785i
$259$	−600623.	−	600623.i	−0.556356	−	0.556356i
$260$	202202.	−	230027.i	0.185504	−	0.211031i
$261$	−936680.	+	936680.i	−0.851118	+	0.851118i
$262$	−362191.	−	932401.i	−0.325975	−	0.839169i
$263$	−224636.			−0.200258			−0.100129	−	0.994974i	$-0.531926\pi$
$263$	−224636.			−0.200258			−0.100129	+	0.994974i	$0.531926\pi$
$264$	−2.45890e6	+	831619.i	−2.17136	+	0.734370i
$265$	−820898.	+	89555.9i	−0.718083	+	0.0783393i
$266$	111769.	+	287732.i	0.0968542	+	0.249335i
$267$	−50927.0	−	50927.0i	−0.0437190	−	0.0437190i
$268$	804719.	+	35735.8i	0.684395	+	0.0303925i
$269$	372042.	+	372042.i	0.313481	+	0.313481i	0.846257	−	0.532776i	$-0.178851\pi$
$269$	372042.	+	372042.i	0.313481	+	0.313481i	−0.532776	+	0.846257i	$0.678851\pi$
$270$	−1.32144e6	−	417798.i	−1.10316	−	0.348784i
$271$	−611282.			−0.505613			−0.252807	−	0.967517i	$-0.581354\pi$
$271$	−611282.			−0.505613			−0.252807	+	0.967517i	$0.581354\pi$
$272$	1.74229e6	+	155048.i	1.42790	+	0.127070i
$273$			332680.i			0.270159i
$274$	765803.	+	337302.i	0.616227	+	0.271421i
$275$	−1.47368e6	−	940570.i	−1.17509	−	0.749997i
$276$	3.16339e6	+	140479.i	2.49966	+	0.111004i
$277$	779074.	+	779074.i	0.610069	+	0.610069i	0.942964	−	0.332895i	$-0.108025\pi$
$277$	779074.	+	779074.i	0.610069	+	0.610069i	−0.332895	+	0.942964i	$0.608025\pi$
$278$	2.12866e6	−	826878.i	1.65194	−	0.641696i
$279$			2.00732e6i			1.54385i
$280$	720474.	+	263485.i	0.549191	+	0.200845i
$281$		−	815230.i		−	0.615906i	−0.951402	−	0.307953i	$-0.900356\pi$
$281$		−	815230.i		−	0.615906i	0.951402	−	0.307953i	$-0.0996439\pi$
$282$	698809.	+	1.79897e6i	0.523282	+	1.34710i
$283$	1.30250e6	+	1.30250e6i	0.966741	+	0.966741i	0.999464	−	0.0327233i	$-0.0104180\pi$
$283$	1.30250e6	+	1.30250e6i	0.966741	+	0.966741i	−0.0327233	+	0.999464i	$0.510418\pi$
$284$	−467819.	+	428036.i	−0.344177	+	0.314908i
$285$	645884.	−	804067.i	0.471023	−	0.586381i
$286$	218400.	−	495850.i	0.157884	−	0.358456i
$287$			946557.i			0.678332i
$288$	−2.10029e6	−	1.15736e6i	−1.49210	−	0.822216i
$289$	−1.49800e6			−1.05504
$290$	−964788.	−	305035.i	−0.673654	−	0.212988i
$291$	2.82721e6	+	2.82721e6i	1.95716	+	1.95716i
$292$	142177.	+	155391.i	0.0975824	+	0.106652i
$293$	−371718.	−	371718.i	−0.252955	−	0.252955i	0.569226	−	0.822181i	$-0.307243\pi$
$293$	−371718.	−	371718.i	−0.252955	−	0.252955i	−0.822181	+	0.569226i	$0.807243\pi$
$294$	1.49481e6	−	580657.i	1.00859	−	0.391788i
$295$	224416.	+	2.05707e6i	0.150141	+	1.37624i
$296$	−899094.	+	1.81805e6i	−0.596452	+	1.20608i
$297$	−2.45184e6			−1.61288
$298$	524812.	−	203863.i	0.342345	−	0.132984i
$299$	−467370.	+	467370.i	−0.302331	+	0.302331i
$300$	−441099.	−	2.52493e6i	−0.282965	−	1.61975i
$301$	663680.	+	663680.i	0.422223	+	0.422223i
$302$	−833420.	+	1.89218e6i	−0.525831	+	1.19384i
$303$			1.94303e6i			1.21583i
$304$	565328.	−	472932.i	0.350846	−	0.293505i
$305$	−2.91405e6	+	317908.i	−1.79369	+	0.195683i
$306$	3.66092e6	+	1.61247e6i	2.23505	+	0.984438i
$307$	−1.01188e6	+	1.01188e6i	−0.612750	+	0.612750i	−0.943662	−	0.330912i	$-0.892644\pi$
$307$	−1.01188e6	+	1.01188e6i	−0.612750	+	0.612750i	0.330912	+	0.943662i	$0.392644\pi$
$308$	1.35583e6	+	60209.2i	0.814380	+	0.0361648i
$309$	2.34749e6	−	2.34749e6i	1.39864	−	1.39864i
$310$	−1.36062e6	+	706930.i	−0.804144	+	0.417803i
$311$			1.79315e6i			1.05127i	0.850709	+	0.525637i	$0.176173\pi$
$311$			1.79315e6i			1.05127i	−0.850709	+	0.525637i	$0.823827\pi$
$312$	752502.	−	254502.i	0.437644	−	0.148015i
$313$	2.85796e6			1.64890			0.824451	−	0.565934i	$-0.191484\pi$
$313$	2.85796e6			1.64890			0.824451	+	0.565934i	$0.191484\pi$
$314$	−1.45557e6	+	565417.i	−0.833125	+	0.323627i
$315$	1.36779e6	+	1.09871e6i	0.776684	+	0.623889i
$316$	−655138.	−	716028.i	−0.369075	−	0.403378i
$317$	−883408.	+	883408.i	−0.493757	+	0.493757i	−0.909488	−	0.415731i	$-0.863526\pi$
$317$	−883408.	+	883408.i	−0.493757	+	0.493757i	0.415731	+	0.909488i	$0.363526\pi$
$318$	−1.96013e6	−	863348.i	−1.08697	−	0.478760i
$319$	−1.79010e6			−0.984918
$320$	44820.5	−	1.83124e6i	0.0244682	−	0.999701i
$321$	1.01747e6			0.551137
$322$	−1.51514e6	−	667350.i	−0.814352	−	0.358686i
$323$	−869404.	+	869404.i	−0.463677	+	0.463677i
$324$	−253525.	−	277088.i	−0.134171	−	0.146641i
$325$	450993.	+	287845.i	0.236844	+	0.151164i
$326$	2.21813e6	−	861631.i	1.15596	−	0.449032i
$327$	2.55881e6			1.32333
$328$	2.14106e6	−	724122.i	1.09886	−	0.371644i
$329$		−	1.00905e6i		−	0.513954i
$330$	−2.09064e6	−	4.02384e6i	−1.05680	−	2.03402i
$331$	44182.7	−	44182.7i	0.0221657	−	0.0221657i	−0.695937	−	0.718103i	$-0.745011\pi$
$331$	44182.7	−	44182.7i	0.0221657	−	0.0221657i	0.718103	+	0.695937i	$0.245011\pi$
$332$	1931.92	+	85.7923i	0.000961931	+	4.27172e-5i
$333$	−3.27990e6	+	3.27990e6i	−1.62088	+	1.62088i
$334$	1.08491e6	+	477853.i	0.532140	+	0.234384i
$335$	152610.	+	1.39887e6i	0.0742969	+	0.681029i
$336$	1.27673e6	+	1.52616e6i	0.616951	+	0.737483i
$337$		−	3.44388e6i		−	1.65186i	−0.563772	−	0.825931i	$-0.690650\pi$
$337$		−	3.44388e6i		−	1.65186i	0.563772	−	0.825931i	$-0.309350\pi$
$338$	779788.	−	1.77041e6i	0.371266	−	0.842913i
$339$	−3.28798e6	−	3.28798e6i	−1.55393	−	1.55393i
$340$	196304.	+	3.04936e6i	0.0920940	+	1.43058i
$341$	−1.91810e6	+	1.91810e6i	−0.893275	+	0.893275i
$342$	1.57126e6	−	610354.i	0.726410	−	0.282174i
$343$	−2.11258e6			−0.969569
$344$	993486.	−	2.00892e6i	0.452653	−	0.915309i
$345$	599918.	+	5.49904e6i	0.271359	+	2.48736i
$346$	1.68876e6	−	655998.i	0.758363	−	0.294586i
$347$	−1.34939e6	−	1.34939e6i	−0.601609	−	0.601609i	0.339131	−	0.940739i	$-0.389867\pi$
$347$	−1.34939e6	−	1.34939e6i	−0.601609	−	0.601609i	−0.940739	+	0.339131i	$0.889867\pi$
$348$	−1.77165e6	−	1.93632e6i	−0.784207	−	0.857093i
$349$	250676.	+	250676.i	0.110166	+	0.110166i	0.760041	−	0.649875i	$-0.225179\pi$
$349$	250676.	+	250676.i	0.110166	+	0.110166i	−0.649875	+	0.760041i	$0.725179\pi$
$350$	−263037.	+	1.31408e6i	−0.114775	+	0.573390i
$351$	750343.			0.325081
$352$	−901025.	−	3.11286e6i	−0.387597	−	1.33907i
$353$			1.50374e6i			0.642297i	0.947029	+	0.321148i	$0.104069\pi$
$353$			1.50374e6i			0.642297i	−0.947029	+	0.321148i	$0.895931\pi$
$354$	−2.16344e6	+	4.91183e6i	−0.917565	+	2.08322i
$355$	−863594.	−	693701.i	−0.363696	−	0.292147i
$356$	66338.1	−	60696.7i	0.0277420	−	0.0253828i
$357$	−2.34704e6	−	2.34704e6i	−0.974654	−	0.974654i
$358$	−961896.	−	2.47624e6i	−0.396662	−	1.02114i
$359$		−	3.76954e6i		−	1.54366i	−0.635827	−	0.771831i	$-0.719341\pi$
$359$		−	3.76954e6i		−	1.54366i	0.635827	−	0.771831i	$-0.280659\pi$
$360$	1.43885e6	−	3.93439e6i	0.585139	−	1.60001i
$361$		−	1.95800e6i		−	0.790762i
$362$	4.23174e6	−	1.64382e6i	1.69726	−	0.659299i
$363$	−2.75355e6	−	2.75355e6i	−1.09680	−	1.09680i
$364$	−414926.	−	18425.9i	−0.164141	−	0.00728914i
$365$	−230420.	+	286852.i	−0.0905293	+	0.112701i
$366$	−6.95811e6	−	3.06474e6i	−2.71512	−	1.19589i
$367$		−	1.61984e6i		−	0.627780i	−0.949459	−	0.313890i	$-0.898368\pi$
$367$		−	1.61984e6i		−	0.627780i	0.949459	−	0.313890i	$-0.101632\pi$
$368$	−350418.	+	3.93768e6i	−0.134886	+	1.51573i
$369$	5.16899e6			1.97624
$370$	−3.37833e6	−	1.06812e6i	−1.28291	−	0.405617i
$371$	791853.	+	791853.i	0.298682	+	0.298682i
$372$	−3.97311e6	−	176437.i	−1.48858	−	0.0661047i
$373$	3.17324e6	+	3.17324e6i	1.18095	+	1.18095i	0.979499	+	0.201448i	$0.0645647\pi$
$373$	3.17324e6	+	3.17324e6i	1.18095	+	1.18095i	0.201448	+	0.979499i	$0.435435\pi$
$374$	1.95740e6	+	5.03901e6i	0.723604	+	1.86280i
$375$	4.24185e6	−	1.43399e6i	1.55768	−	0.526583i
$376$	−2.28242e6	+	771932.i	−0.832580	+	0.281585i
$377$	547827.			0.198513
$378$	680543.	+	1.75195e6i	0.244977	+	0.630654i
$379$	−1.01539e6	+	1.01539e6i	−0.363108	+	0.363108i	−0.864956	−	0.501848i	$-0.832654\pi$
$379$	−1.01539e6	+	1.01539e6i	−0.363108	+	0.363108i	0.501848	+	0.864956i	$0.332654\pi$
$380$	967077.	+	850096.i	0.343560	+	0.302001i
$381$	−1.56355e6	−	1.56355e6i	−0.551823	−	0.551823i
$382$	−762625.	−	335902.i	−0.267395	−	0.117775i
$383$		−	2.13689e6i		−	0.744362i	−0.928160	−	0.372181i	$-0.878610\pi$
$383$		−	2.13689e6i		−	0.744362i	0.928160	−	0.372181i	$-0.121390\pi$
$384$	2.47538e6	−	4.05541e6i	0.856671	−	1.40348i
$385$	257124.	+	2.35688e6i	0.0884078	+	0.810374i
$386$	−487233.	+	1.10620e6i	−0.166444	+	0.377891i
$387$	3.62425e6	−	3.62425e6i	1.23010	−	1.23010i
$388$	−3.68275e6	+	3.36958e6i	−1.24192	+	1.13631i
$389$	787350.	−	787350.i	0.263812	−	0.263812i	−0.562789	−	0.826601i	$-0.690272\pi$
$389$	787350.	−	787350.i	0.263812	−	0.263812i	0.826601	+	0.562789i	$0.190272\pi$
$390$	639802.	+	1.23142e6i	0.213002	+	0.409964i
$391$		−	6.59455e6i		−	2.18144i
$392$	641417.	+	1.89652e6i	0.210827	+	0.623364i
$393$	4.53235e6			1.48027
$394$	−231075.	−	594865.i	−0.0749916	−	0.193054i
$395$	1.06176e6	−	1.32179e6i	0.342399	−	0.426255i
$396$	328793.	−	7.40394e6i	0.105362	−	2.37260i
$397$	2.18405e6	−	2.18405e6i	0.695482	−	0.695482i	−0.267951	−	0.963433i	$-0.586347\pi$
$397$	2.18405e6	−	2.18405e6i	0.695482	−	0.695482i	0.963433	+	0.267951i	$0.0863465\pi$
$398$	1.93078e6	−	4.38359e6i	0.610976	−	1.38715i
$399$	−1.39865e6			−0.439821
$400$	3.17359e6	−	410302.i	0.991746	−	0.128219i
$401$	5.54165e6			1.72099			0.860495	−	0.509460i	$-0.170155\pi$
$401$	5.54165e6			1.72099			0.860495	+	0.509460i	$0.170155\pi$
$402$	−1.47121e6	+	3.34020e6i	−0.454056	+	1.03088i
$403$	587000.	−	587000.i	0.180043	−	0.180043i
$404$	−2.42339e6	−	107618.i	−0.738704	−	0.0328042i
$405$	410878.	−	511506.i	0.124473	−	0.154958i
$406$	496866.	+	1.27910e6i	0.149597	+	0.385114i
$407$	−6.26825e6			−1.87569
$408$	−3.51337e6	+	7.10438e6i	−1.04490	+	2.11288i
$409$		−	5.62401e6i		−	1.66241i	−0.555966	−	0.831205i	$-0.687652\pi$
$409$		−	5.62401e6i		−	1.66241i	0.555966	−	0.831205i	$-0.312348\pi$
$410$	1.82040e6	+	3.50371e6i	0.534819	+	1.02936i
$411$	−2.68107e6	+	2.68107e6i	−0.782894	+	0.782894i
$412$	2.79782e6	+	3.05786e6i	0.812039	+	0.887513i
$413$	1.98428e6	−	1.98428e6i	0.572438	−	0.572438i
$414$	−3.64429e6	+	8.27391e6i	−1.04499	+	2.37252i
$415$	366.377	+	3358.33i	0.000104426	+	0.000957200i
$416$	275743.	+	952634.i	0.0781215	+	0.269894i
$417$			1.03473e7i			2.91398i
$418$	2.08465e6	+	918195.i	0.583569	+	0.257036i
$419$	606666.	+	606666.i	0.168816	+	0.168816i	0.786459	−	0.617643i	$-0.211912\pi$
$419$	606666.	+	606666.i	0.168816	+	0.168816i	−0.617643	+	0.786459i	$0.711912\pi$
$420$	−2.29492e6	+	2.61072e6i	−0.634811	+	0.722167i
$421$	−2.51245e6	+	2.51245e6i	−0.690863	+	0.690863i	−0.962422	−	0.271559i	$-0.912461\pi$
$421$	−2.51245e6	+	2.51245e6i	−0.690863	+	0.690863i	0.271559	+	0.962422i	$0.412461\pi$
$422$	−940958.	−	2.42234e6i	−0.257211	−	0.662147i
$423$	−5.51028e6			−1.49735
$424$	1.18535e6	−	2.39690e6i	0.320208	−	0.647492i
$425$	−5.21248e6	+	1.15101e6i	−1.39982	+	0.309105i
$426$	−1.04033e6	−	2.67815e6i	−0.277745	−	0.715009i
$427$	2.81094e6	+	2.81094e6i	0.746074	+	0.746074i
$428$	−56354.1	+	1.26901e6i	−0.0148702	+	0.334855i
$429$	1.73596e6	+	1.73596e6i	0.455405	+	0.455405i
$430$	3.73301e6	+	1.18026e6i	0.973616	+	0.307826i
$431$	−7.07026e6			−1.83334			−0.916668	−	0.399649i	$-0.869132\pi$
$431$	−7.07026e6			−1.83334			−0.916668	+	0.399649i	$0.869132\pi$
$432$	3.44218e6	−	2.87960e6i	0.887410	−	0.742374i
$433$		−	1.34061e6i		−	0.343624i	−0.985130	−	0.171812i	$-0.945038\pi$
$433$		−	1.34061e6i		−	0.343624i	0.985130	−	0.171812i	$-0.0549621\pi$
$434$	1.90296e6	+	838168.i	0.484959	+	0.213603i
$435$	2.87125e6	−	3.57444e6i	0.727525	−	0.905702i
$436$	−141723.	+	3.19140e6i	−0.0357046	+	0.804017i
$437$	−1.96491e6	−	1.96491e6i	−0.492197	−	0.492197i
$438$	−889578.	+	345557.i	−0.221564	+	0.0860664i
$439$			3.61051e6i			0.894143i	0.894498	+	0.447072i	$0.147533\pi$
$439$			3.61051e6i			0.894143i	−0.894498	+	0.447072i	$0.852467\pi$
$440$	5.13442e6	−	2.38463e6i	1.26433	−	0.587204i
$441$			4.57862e6i			1.12108i
$442$	−599028.	−	1.54210e6i	−0.145845	−	0.375454i
$443$	−3.85627e6	−	3.85627e6i	−0.933594	−	0.933594i	0.0643341	−	0.997928i	$-0.479508\pi$
$443$	−3.85627e6	−	3.85627e6i	−0.933594	−	0.933594i	−0.997928	+	0.0643341i	$0.979508\pi$
$444$	−6.20367e6	−	6.78026e6i	−1.49345	−	1.63226i
$445$	122460.	+	98368.9i	0.0293154	+	0.0235482i
$446$	−651072.	+	1.47818e6i	−0.154986	+	0.351876i
$447$			2.55108e6i			0.603887i
$448$	−1.97418e6	+	1.50784e6i	−0.464720	+	0.354944i
$449$	2.13218e6			0.499123			0.249561	−	0.968359i	$-0.419714\pi$
$449$	2.13218e6			0.499123			0.249561	+	0.968359i	$0.419714\pi$
$450$	7.17595e6	+	1.43640e6i	1.67051	+	0.334383i
$451$	4.93925e6	+	4.93925e6i	1.14346	+	1.14346i
$452$	4.28296e6	−	3.91874e6i	0.986048	−	0.902195i
$453$	−6.62448e6	−	6.62448e6i	−1.51672	−	1.51672i
$454$	5.72489e6	−	2.22383e6i	1.30355	−	0.506363i
$455$	−78688.1	−	721280.i	−0.0178189	−	0.163334i
$456$	1.06997e6	+	3.16366e6i	0.240969	+	0.712488i
$457$	667772.			0.149568			0.0747838	−	0.997200i	$-0.476173\pi$
$457$	667772.			0.149568			0.0747838	+	0.997200i	$0.476173\pi$
$458$	−3.17017e6	+	1.23145e6i	−0.706186	+	0.274318i
$459$	−5.29364e6	+	5.29364e6i	−1.17280	+	1.17280i
$460$	−6.89176e6	+	443659.i	−1.51857	+	0.0977586i
$461$	651198.	+	651198.i	0.142712	+	0.142712i	0.774853	−	0.632141i	$-0.217824\pi$
$461$	651198.	+	651198.i	0.142712	+	0.142712i	−0.632141	+	0.774853i	$0.717824\pi$
$462$	−2.47876e6	+	5.62772e6i	−0.540293	+	1.22667i
$463$			481339.i			0.104352i	0.998638	+	0.0521758i	$0.0166156\pi$
$463$			481339.i			0.104352i	−0.998638	+	0.0521758i	$0.983384\pi$
$464$	2.51314e6	−	2.10240e6i	0.541904	−	0.453337i
$465$	−753476.	−	6.90660e6i	−0.161598	−	1.48126i
$466$	2.74620e6	+	1.20958e6i	0.585824	+	0.258029i
$467$	2.35241e6	−	2.35241e6i	0.499138	−	0.499138i	−0.412031	−	0.911170i	$-0.635181\pi$
$467$	2.35241e6	−	2.35241e6i	0.499138	−	0.499138i	0.911170	+	0.412031i	$0.135181\pi$
$468$	−100621.	+	2.26584e6i	−0.0212361	+	0.478206i
$469$	1.34938e6	−	1.34938e6i	0.283270	−	0.283270i
$470$	−1.94059e6	−	3.73504e6i	−0.405218	−	0.779922i
$471$		−	7.07546e6i		−	1.46961i
$472$	−6.00632e6	−	2.97034e6i	−1.24095	−	0.613694i
$473$	6.92633e6			1.42348
$474$	4.09910e6	−	1.59229e6i	0.837997	−	0.325520i
$475$	−1.21015e6	+	1.89606e6i	−0.246097	+	0.385583i
$476$	3.05728e6	−	2.79729e6i	0.618469	−	0.565875i
$477$	4.32418e6	−	4.32418e6i	0.870177	−	0.870177i
$478$	936133.	+	412325.i	0.187399	+	0.0825410i
$479$	−6.44927e6			−1.28432			−0.642158	−	0.766573i	$-0.721961\pi$
$479$	−6.44927e6			−1.28432			−0.642158	+	0.766573i	$0.721961\pi$
$480$	7.66093e6	+	3.19376e6i	1.51767	+	0.632701i
$481$	1.91829e6			0.378051
$482$	−884877.	−	389749.i	−0.173486	−	0.0764130i
$483$	5.30447e6	−	5.30447e6i	1.03460	−	1.03460i
$484$	3.58680e6	−	3.28178e6i	0.695975	−	0.636790i
$485$	−6.79837e6	−	5.46094e6i	−1.31235	−	1.05418i
$486$	−4.02940e6	+	1.56522e6i	−0.773837	+	0.300597i
$487$	358765.			0.0685470			0.0342735	−	0.999412i	$-0.489088\pi$
$487$	358765.			0.0685470			0.0342735	+	0.999412i	$0.489088\pi$
$488$	4.20780e6	−	8.50858e6i	0.799844	−	1.61736i
$489$			1.07822e7i			2.03908i
$490$	−3.10354e6	+	1.61248e6i	−0.583938	+	0.303392i
$491$	3.27547e6	−	3.27547e6i	0.613154	−	0.613154i	−0.330613	−	0.943767i	$-0.607255\pi$
$491$	3.27547e6	−	3.27547e6i	0.613154	−	0.613154i	0.943767	+	0.330613i	$0.107255\pi$
$492$	−454339.	+	1.02311e7i	−0.0846189	+	1.90550i
$493$	−3.86490e6	+	3.86490e6i	−0.716178	+	0.716178i
$494$	−637969.	−	280997.i	−0.117620	−	0.0518065i
$495$	1.28705e7	−	1.40411e6i	2.36093	−	0.257566i
$496$	440113.	−	4.94559e6i	0.0803267	−	0.902638i
$497$			1.50219e6i			0.272794i
$498$	−3531.99	+	8018.95i	−0.000638184	+	0.00144892i
$499$	1.88264e6	+	1.88264e6i	0.338467	+	0.338467i	0.855790	−	0.517323i	$-0.173071\pi$
$499$	1.88264e6	+	1.88264e6i	0.338467	+	0.338467i	−0.517323	+	0.855790i	$0.673071\pi$
$500$	1.55356e6	+	5.36996e6i	0.277910	+	0.960607i
$501$	−3.79824e6	+	3.79824e6i	−0.676065	+	0.676065i
$502$	−9.87880e6	+	3.83742e6i	−1.74963	+	0.679641i
$503$	−1.54625e6			−0.272495			−0.136248	−	0.990675i	$-0.543504\pi$
$503$	−1.54625e6			−0.272495			−0.136248	+	0.990675i	$0.543504\pi$
$504$	−5.38169e6	+	1.82013e6i	−0.943718	+	0.319173i
$505$	−459582.	−	4.21267e6i	−0.0801926	−	0.735071i
$506$	−1.13885e7	+	4.42386e6i	−1.97738	+	0.768112i
$507$	6.19819e6	+	6.19819e6i	1.07089	+	1.07089i
$508$	2.03670e6	−	1.86350e6i	0.350161	−	0.320384i
$509$	1.51480e6	+	1.51480e6i	0.259156	+	0.259156i	0.824711	−	0.565554i	$-0.191338\pi$
$509$	1.51480e6	+	1.51480e6i	0.259156	+	0.259156i	−0.565554	+	0.824711i	$0.691338\pi$
$510$	−1.32014e7	−	4.17387e6i	−2.24748	−	0.710581i
$511$	498970.			0.0845323
$512$	4.92090e6	+	3.31197e6i	0.829601	+	0.558356i
$513$			3.15458e6i			0.529235i
$514$	−1.66947e6	+	3.79033e6i	−0.278722	+	0.632805i
$515$	−4.53432e6	+	5.64482e6i	−0.753346	+	0.937847i
$516$	6.85497e6	+	7.49209e6i	1.13339	+	1.23874i
$517$	−5.26537e6	−	5.26537e6i	−0.866368	−	0.866368i
$518$	1.73984e6	+	4.47893e6i	0.284895	+	0.733415i
$519$			8.20896e6i			1.33773i
$520$	−1.57130e6	+	729772.i	−0.254830	+	0.118353i
$521$		−	9.46124e6i		−	1.52705i	−0.645777	−	0.763526i	$-0.723466\pi$
$521$		−	9.46124e6i		−	1.52705i	0.645777	−	0.763526i	$-0.276534\pi$
$522$	6.98496e6	−	2.71330e6i	1.12199	−	0.435835i
$523$	−1.05029e6	−	1.05029e6i	−0.167902	−	0.167902i	0.618154	−	0.786057i	$-0.287881\pi$
$523$	−1.05029e6	−	1.05029e6i	−0.167902	−	0.167902i	−0.786057	+	0.618154i	$0.787881\pi$
$524$	−251030.	+	5.65285e6i	−0.0399391	+	0.899371i
$525$	−5.11861e6	−	3.26693e6i	−0.810501	−	0.517299i
$526$	1.16292e6	+	512217.i	0.183268	+	0.0807215i
$527$			8.28253e6i			1.29908i
$528$	1.46258e7	+	1.30157e6i	2.28316	+	0.203181i
$529$	8.46778e6			1.31562
$530$	4.45394e6	+	1.40819e6i	0.688739	+	0.217757i
$531$	−1.08358e7	−	1.08358e7i	−1.66773	−	1.66773i
$532$	77466.1	−	1.74443e6i	0.0118668	−	0.267223i
$533$	−1.51157e6	−	1.51157e6i	−0.230468	−	0.230468i
$534$	147522.	+	379770.i	0.0223873	+	0.0576325i
$535$	−2.20597e6	+	240660.i	−0.333208	+	0.0363513i
$536$	−4.08449e6	−	2.01993e6i	−0.614081	−	0.303686i
$537$	1.20369e7			1.80127
$538$	−1.07770e6	−	2.77437e6i	−0.160525	−	0.413246i
$539$	−4.37512e6	+	4.37512e6i	−0.648662	+	0.648662i
$540$	5.88836e6	+	5.17608e6i	0.868980	+	0.763865i
$541$	2.67729e6	+	2.67729e6i	0.393281	+	0.393281i	0.875855	−	0.482574i	$-0.160298\pi$
$541$	2.67729e6	+	2.67729e6i	0.393281	+	0.393281i	−0.482574	+	0.875855i	$0.660298\pi$
$542$	3.16457e6	+	1.39385e6i	0.462718	+	0.203806i
$543$			2.05703e7i			2.99392i
$544$	−8.66615e6	−	4.77545e6i	−1.25554	−	0.691858i
$545$	−5.54773e6	+	605229.i	−0.800062	+	0.0872828i
$546$	758579.	−	1.72226e6i	0.108898	−	0.247239i
$547$	1.71378e6	−	1.71378e6i	0.244898	−	0.244898i	−0.573975	−	0.818873i	$-0.694599\pi$
$547$	1.71378e6	−	1.71378e6i	0.244898	−	0.244898i	0.818873	+	0.573975i	$0.194599\pi$
$548$	−3.19539e6	−	3.49238e6i	−0.454541	−	0.496787i
$549$	1.53501e7	−	1.53501e7i	2.17360	−	2.17360i
$550$	5.48445e6	+	8.22957e6i	0.773084	+	1.16003i
$551$			2.30317e6i			0.323181i
$552$	−1.60564e7	−	7.94045e6i	−2.24285	−	1.10917i
$553$	−2.29921e6			−0.319717
$554$	−2.25676e6	−	5.80967e6i	−0.312400	−	0.804224i
$555$	1.00540e7	−	1.25164e7i	1.38551	−	1.72483i
$556$	−1.29054e7	−	573100.i	−1.77045	−	0.0786219i
$557$	−5.72131e6	+	5.72131e6i	−0.781371	+	0.781371i	−0.980062	−	0.198691i	$-0.936331\pi$
$557$	−5.72131e6	+	5.72131e6i	−0.781371	+	0.781371i	0.198691	+	0.980062i	$0.436331\pi$
$558$	4.57710e6	−	1.03917e7i	0.622308	−	1.41287i
$559$	−2.11968e6			−0.286907
$560$	−3.12905e6	−	3.00688e6i	−0.421640	−	0.405178i
$561$	−2.44943e7			−3.28593
$562$	−1.85889e6	+	4.22039e6i	−0.248264	+	0.563653i
$563$	3.57673e6	−	3.57673e6i	0.475571	−	0.475571i	−0.428141	−	0.903712i	$-0.640831\pi$
$563$	3.57673e6	−	3.57673e6i	0.475571	−	0.475571i	0.903712	+	0.428141i	$0.140831\pi$
$564$	484337.	−	1.09066e7i	0.0641135	−	1.44374i
$565$	7.90636e6	+	6.35096e6i	1.04197	+	0.836986i
$566$	−3.77297e6	−	9.71290e6i	−0.495043	−	1.27441i
$567$	−889747.			−0.116228
$568$	3.39788e6	−	1.14919e6i	0.441913	−	0.149458i
$569$			5.56828e6i			0.721009i	0.932758	+	0.360504i	$0.117395\pi$
$569$			5.56828e6i			0.721009i	−0.932758	+	0.360504i	$0.882605\pi$
$570$	−5.17714e6	+	2.68985e6i	−0.667425	+	0.346769i
$571$	6.27398e6	−	6.27398e6i	0.805292	−	0.805292i	−0.178625	−	0.983917i	$-0.557165\pi$
$571$	6.27398e6	−	6.27398e6i	0.805292	−	0.805292i	0.983917	+	0.178625i	$0.0571650\pi$
$572$	−2.26128e6	+	2.06899e6i	−0.288978	+	0.264404i
$573$	2.66994e6	−	2.66994e6i	0.339715	−	0.339715i
$574$	2.15835e6	−	4.90026e6i	0.273427	−	0.620783i
$575$	−2.60136e6	−	1.17805e7i	−0.328118	−	1.48592i
$576$	8.23405e6	+	1.07807e7i	1.03409	+	1.35391i
$577$			3.60595e6i			0.450900i	0.974255	+	0.225450i	$0.0723852\pi$
$577$			3.60595e6i			0.450900i	−0.974255	+	0.225450i	$0.927615\pi$
$578$	7.75506e6	+	3.41576e6i	0.965530	+	0.425273i
$579$	−3.87280e6	−	3.87280e6i	−0.480097	−	0.480097i
$580$	4.29910e6	+	3.77907e6i	0.530650	+	0.466460i
$581$	3239.50	−	3239.50i	0.000398142	−	0.000398142i
$582$	−8.18966e6	−	2.10829e7i	−1.00221	−	2.58002i
$583$	8.26397e6			1.00697
$584$	−381716.	−	1.12864e6i	−0.0463135	−	0.136938i
$585$	−3.93880e6	+	429703.i	−0.475854	+	0.0519133i
$586$	1.07676e6	+	2.77195e6i	0.129532	+	0.333458i
$587$	4.97476e6	+	4.97476e6i	0.595905	+	0.595905i	0.939220	−	0.343315i	$-0.111550\pi$
$587$	4.97476e6	+	4.97476e6i	0.595905	+	0.595905i	−0.343315	+	0.939220i	$0.611550\pi$
$588$	−9.06253e6	−	402447.i	−1.08095	−	0.0480027i
$589$	2.46786e6	+	2.46786e6i	0.293111	+	0.293111i
$590$	3.52876e6	−	1.11610e7i	0.417342	−	1.32000i
$591$	2.89160e6			0.340542
$592$	8.80009e6	−	7.36183e6i	1.03201	−	0.863339i
$593$			2.76669e6i			0.323090i	0.986865	+	0.161545i	$0.0516476\pi$
$593$			2.76669e6i			0.323090i	−0.986865	+	0.161545i	$0.948352\pi$
$594$	1.26930e7	+	5.59072e6i	1.47604	+	0.650132i
$595$	5.64375e6	+	4.53347e6i	0.653545	+	0.524974i
$596$	−3.18177e6	−	141295.i	−0.366905	−	0.0162934i
$597$	1.53469e7	+	1.53469e7i	1.76232	+	1.76232i
$598$	3.48524e6	−	1.35384e6i	0.398547	−	0.154816i
$599$			1.70067e6i			0.193666i	0.995301	+	0.0968328i	$0.0308712\pi$
$599$			1.70067e6i			0.193666i	−0.995301	+	0.0968328i	$0.969129\pi$
$600$	−3.47383e6	+	1.40772e7i	−0.393941	+	1.59639i
$601$		−	2.77118e6i		−	0.312953i	−0.987682	−	0.156476i	$-0.949986\pi$
$601$		−	2.77118e6i		−	0.312953i	0.987682	−	0.156476i	$-0.0500135\pi$
$602$	−1.92250e6	−	4.94916e6i	−0.216209	−	0.556596i
$603$	−7.36872e6	−	7.36872e6i	−0.825275	−	0.825275i
$604$	8.62912e6	−	7.89531e6i	0.962441	−	0.880596i
$605$	6.62124e6	+	5.31865e6i	0.735446	+	0.590763i
$606$	4.43052e6	−	1.00589e7i	0.490087	−	1.11268i
$607$		−	4.78199e6i		−	0.526789i	−0.964688	−	0.263395i	$-0.915158\pi$
$607$		−	4.78199e6i		−	0.526789i	0.964688	−	0.263395i	$-0.0848421\pi$
$608$	−4.00505e6	+	1.15927e6i	−0.439389	+	0.127182i
$609$	−6.21763e6			−0.679331
$610$	1.58107e7	+	4.99885e6i	1.72039	+	0.543933i
$611$	1.61137e6	+	1.61137e6i	0.174619	+	0.174619i
$612$	−1.52756e7	−	1.66953e7i	−1.64861	−	1.80184i
$613$	−8.08618e6	−	8.08618e6i	−0.869145	−	0.869145i	0.123232	−	0.992378i	$-0.460674\pi$
$613$	−8.08618e6	−	8.08618e6i	−0.869145	−	0.869145i	−0.992378	+	0.123232i	$0.960674\pi$
$614$	7.54574e6	−	2.93114e6i	0.807757	−	0.313773i
$615$	−1.77850e7	+	1.94026e6i	−1.89612	+	0.206858i
$616$	−6.88173e6	−	3.40326e6i	−0.730711	−	0.361363i
$617$	−1.63283e7			−1.72675			−0.863373	−	0.504566i	$-0.831653\pi$
$617$	−1.63283e7			−1.72675			−0.863373	+	0.504566i	$0.831653\pi$
$618$	−1.75055e7	+	6.80003e6i	−1.84376	+	0.716208i
$619$	5.63689e6	−	5.63689e6i	0.591307	−	0.591307i	−0.346677	−	0.937984i	$-0.612690\pi$
$619$	5.63689e6	−	5.63689e6i	0.591307	−	0.591307i	0.937984	+	0.346677i	$0.112690\pi$
$620$	8.65581e6	−	557221.i	0.904333	−	0.0582168i
$621$	−1.19640e7	−	1.19640e7i	−1.24493	−	1.24493i
$622$	4.08876e6	−	9.28303e6i	0.423756	−	0.962086i
$623$		−	213016.i		−	0.0219883i
$624$	−4.47597e6	−	398322.i	−0.460178	−	0.0409517i
$625$	−8.85755e6	+	4.11233e6i	−0.907013	+	0.421103i
$626$	−1.47955e7	−	6.51674e6i	−1.50901	−	0.664652i
$627$	−7.29832e6	+	7.29832e6i	−0.741403	+	0.741403i
$628$	8.82468e6	+	391884.i	0.892894	+	0.0396514i
$629$	−1.35334e7	+	1.35334e7i	−1.36390	+	1.36390i
$630$	−4.57569e6	−	8.80681e6i	−0.459309	−	0.884030i
$631$			1.84472e7i			1.84441i	0.386698	+	0.922206i	$0.373616\pi$
$631$			1.84472e7i			1.84441i	−0.386698	+	0.922206i	$0.626384\pi$
$632$	1.75891e6	+	5.20068e6i	0.175167	+	0.517926i
$633$	1.17749e7			1.16801
$634$	6.58770e6	−	2.55899e6i	0.650895	−	0.252840i
$635$	3.75975e6	+	3.02010e6i	0.370020	+	0.297227i
$636$	8.17883e6	+	8.93899e6i	0.801767	+	0.876286i
$637$	1.33893e6	−	1.33893e6i	0.130740	−	0.130740i
$638$	9.26721e6	+	4.08180e6i	0.901358	+	0.397008i
$639$	8.20324e6			0.794755
$640$	−4.40764e6	+	9.37800e6i	−0.425359	+	0.905025i
$641$	−6.66649e6			−0.640843			−0.320422	−	0.947275i	$-0.603825\pi$
$641$	−6.66649e6			−0.640843			−0.320422	+	0.947275i	$0.603825\pi$
$642$	−5.26738e6	−	2.32005e6i	−0.504379	−	0.222156i
$643$	5.50491e6	−	5.50491e6i	0.525077	−	0.525077i	−0.394024	−	0.919100i	$-0.628917\pi$
$643$	5.50491e6	−	5.50491e6i	0.525077	−	0.525077i	0.919100	+	0.394024i	$0.128917\pi$
$644$	6.32206e6	+	6.90966e6i	0.600681	+	0.656511i
$645$	−1.11096e7	+	1.38304e7i	−1.05147	+	1.30899i
$646$	6.48327e6	−	2.51842e6i	0.611242	−	0.237437i
$647$	2.71049e6			0.254559			0.127279	−	0.991867i	$-0.459376\pi$
$647$	2.71049e6			0.254559			0.127279	+	0.991867i	$0.459376\pi$
$648$	680662.	+	2.01256e6i	0.0636787	+	0.188283i
$649$		−	2.07085e7i		−	1.92991i
$650$	−1.67842e6	−	2.51851e6i	−0.155818	−	0.233809i
$651$	−6.66223e6	+	6.66223e6i	−0.616123	+	0.616123i
$652$	−1.34478e7	−	597187.i	−1.23889	−	0.0550163i
$653$	−6.37346e6	+	6.37346e6i	−0.584915	+	0.584915i	−0.936250	−	0.351335i	$-0.885728\pi$
$653$	−6.37346e6	+	6.37346e6i	−0.584915	+	0.584915i	0.351335	+	0.936250i	$0.385728\pi$
$654$	−1.32468e7	−	5.83461e6i	−1.21106	−	0.533418i
$655$	−9.82655e6	+	1.07203e6i	−0.894948	+	0.0976343i
$656$	−1.27353e7	−	1.13332e6i	−1.15544	−	0.102824i
$657$		−	2.72480e6i		−	0.246275i
$658$	−2.30085e6	+	5.22380e6i	−0.207169	+	0.470351i
$659$	3.26786e6	+	3.26786e6i	0.293123	+	0.293123i	0.838313	−	0.545190i	$-0.183542\pi$
$659$	3.26786e6	+	3.26786e6i	0.293123	+	0.293123i	−0.545190	+	0.838313i	$0.683542\pi$
$660$	1.64790e6	+	2.55983e7i	0.147255	+	2.28744i
$661$	1.43758e7	−	1.43758e7i	1.27976	−	1.27976i	0.338956	−	0.940802i	$-0.389926\pi$
$661$	1.43758e7	−	1.43758e7i	1.27976	−	1.27976i	0.940802	−	0.338956i	$-0.110074\pi$
$662$	−329477.	+	127985.i	−0.0292200	+	0.0113505i
$663$	7.49605e6			0.662291
$664$	−9805.80	−	4849.32i	−0.000863103	−	0.000426836i
$665$	3.03240e6	−	330820.i	0.265908	−	0.0290093i
$666$	2.44587e7	−	9.50098e6i	2.13672	−	0.830009i
$667$	−8.73492e6	−	8.73492e6i	−0.760229	−	0.760229i
$668$	−4.52688e6	−	4.94763e6i	−0.392517	−	0.428998i
$669$	−5.17508e6	−	5.17508e6i	−0.447046	−	0.447046i
$670$	2.39967e6	−	7.58985e6i	0.206521	−	0.653200i
$671$	2.93357e7			2.51530
$672$	−3.12957e6	−	1.08120e7i	−0.267339	−	0.923601i
$673$			6.12005e6i			0.520856i	0.965493	+	0.260428i	$0.0838637\pi$
$673$			6.12005e6i			0.520856i	−0.965493	+	0.260428i	$0.916136\pi$
$674$	−7.85277e6	+	1.78288e7i	−0.665845	+	1.51172i
$675$	−7.36840e6	+	1.15448e7i	−0.622463	+	0.975272i
$676$	−8.07382e6	+	7.38723e6i	−0.679536	+	0.621749i
$677$	1.37416e7	+	1.37416e7i	1.15230	+	1.15230i	0.986090	+	0.166211i	$0.0531534\pi$
$677$	1.37416e7	+	1.37416e7i	1.15230	+	1.15230i	0.166211	+	0.986090i	$0.446847\pi$
$678$	9.52439e6	+	2.45190e7i	0.795725	+	2.04846i
$679$			1.18255e7i			0.984344i
$680$	5.93693e6	−	1.62340e7i	0.492368	−	1.34633i
$681$			2.78283e7i			2.29943i
$682$	1.43035e7	−	5.55621e6i	1.17756	−	0.457423i
$683$	5.60418e6	+	5.60418e6i	0.459685	+	0.459685i	0.898552	−	0.438867i	$-0.144620\pi$
$683$	5.60418e6	+	5.60418e6i	0.459685	+	0.459685i	−0.438867	+	0.898552i	$0.644620\pi$
$684$	−9.52603e6	−	423030.i	−0.778523	−	0.0345725i
$685$	5.17865e6	−	6.44695e6i	0.421687	−	0.524962i
$686$	1.09367e7	+	4.81713e6i	0.887312	+	0.390821i
$687$		−	1.54100e7i		−	1.24569i
$688$	−9.72398e6	+	8.13471e6i	−0.783200	+	0.655196i
$689$	−2.52904e6			−0.202959
$690$	9.43323e6	−	2.98361e7i	0.754288	−	2.38572i
$691$	9.26625e6	+	9.26625e6i	0.738259	+	0.738259i	0.972241	−	0.233982i	$-0.0751755\pi$
$691$	9.26625e6	+	9.26625e6i	0.738259	+	0.738259i	−0.233982	+	0.972241i	$0.575176\pi$
$692$	−1.02384e7	−	454665.i	−0.812769	−	0.0360933i
$693$	−1.24151e7	−	1.24151e7i	−0.982016	−	0.982016i
$694$	3.90882e6	+	1.00626e7i	0.308068	+	0.793070i
$695$	−2.44743e6	−	2.24339e7i	−0.192198	−	1.76174i
$696$	4.75653e6	+	1.40639e7i	0.372192	+	1.10048i
$697$	2.13281e7			1.66292
$698$	−726140.	−	1.86933e6i	−0.0564133	−	0.145227i
$699$	−9.61439e6	+	9.61439e6i	−0.744267	+	0.744267i
$700$	4.35809e6	−	6.20310e6i	0.336164	−	0.478480i
$701$	467627.	+	467627.i	0.0359422	+	0.0359422i	0.724849	−	0.688907i	$-0.241909\pi$
$701$	467627.	+	467627.i	0.0359422	+	0.0359422i	−0.688907	+	0.724849i	$0.741909\pi$
$702$	−3.88448e6	−	1.71094e6i	−0.297502	−	0.131036i
$703$			8.06483e6i			0.615470i
$704$	−2.43342e6	+	1.81696e7i	−0.185048	+	1.38170i
$705$	1.89593e7	−	2.06836e6i	1.43664	−	0.156731i
$706$	3.42884e6	−	7.78476e6i	0.258902	−	0.587805i
$707$	−4.06362e6	+	4.06362e6i	−0.305748	+	0.305748i
$708$	2.24000e7	−	2.04951e7i	1.67944	−	1.53662i
$709$	3.66205e6	−	3.66205e6i	0.273595	−	0.273595i	−0.556950	−	0.830546i	$-0.688029\pi$
$709$	3.66205e6	−	3.66205e6i	0.273595	−	0.273595i	0.830546	+	0.556950i	$0.188029\pi$
$710$	2.88899e6	+	5.56042e6i	0.215080	+	0.413963i
$711$			1.25556e7i			0.931460i
$712$	−481829.	+	162958.i	−0.0356199	+	0.0120469i
$713$	−1.87191e7			−1.37899
$714$	6.79874e6	+	1.75022e7i	0.499095	+	1.28484i
$715$	−4.17434e6	−	3.35313e6i	−0.305367	−	0.245293i
$716$	−666679.	+	1.50127e7i	−0.0485998	+	1.09440i
$717$	−3.27739e6	+	3.27739e6i	−0.238084	+	0.238084i
$718$	−8.59534e6	+	1.95147e7i	−0.622232	+	1.41270i
$719$	−4.81979e6			−0.347701			−0.173851	−	0.984772i	$-0.555621\pi$
$719$	−4.81979e6			−0.347701			−0.173851	+	0.984772i	$0.555621\pi$
$720$	−1.64201e7	+	1.70872e7i	−1.18044	+	1.22840i
$721$	9.81898e6			0.703442
$722$	−4.46466e6	+	1.01365e7i	−0.318746	+	0.723675i
$723$	3.09794e6	−	3.09794e6i	0.220408	−	0.220408i
$724$	−2.56557e7	−	1.13931e6i	−1.81902	−	0.0807787i
$725$	−5.37968e6	+	8.42886e6i	−0.380112	+	0.595558i
$726$	7.97627e6	+	2.05336e7i	0.561640	+	1.44585i
$727$	2.24891e7			1.57810			0.789051	−	0.614327i	$-0.210572\pi$
$727$	2.24891e7			1.57810			0.789051	+	0.614327i	$0.210572\pi$
$728$	2.10603e6	+	1.04151e6i	0.147277	+	0.0728340i
$729$		−	2.24387e7i		−	1.56379i
$730$	1.84696e6	−	959609.i	0.128277	−	0.0666480i
$731$	1.49543e7	−	1.49543e7i	1.03507	−	1.03507i
$732$	2.90334e7	+	3.17319e7i	2.00272	+	2.18886i
$733$	−1.44776e7	+	1.44776e7i	−0.995261	+	0.995261i	−0.999989	−	0.00472794i	$-0.998495\pi$
$733$	−1.44776e7	+	1.44776e7i	−0.995261	+	0.995261i	0.00472794	+	0.999989i	$0.498495\pi$
$734$	−3.69358e6	+	8.38582e6i	−0.253051	+	0.574520i
$735$	−1.71865e6	−	1.57537e7i	−0.117346	−	1.07564i
$736$	1.07928e7	−	1.95861e7i	0.734413	−	1.33276i
$737$		−	1.40824e7i		−	0.955012i
$738$	−2.67595e7	−	1.17864e7i	−1.80858	−	0.796599i
$739$	−2.42219e6	−	2.42219e6i	−0.163153	−	0.163153i	0.620809	−	0.783962i	$-0.286804\pi$
$739$	−2.42219e6	−	2.42219e6i	−0.163153	−	0.163153i	−0.783962	+	0.620809i	$0.786804\pi$
$740$	1.50539e7	+	1.32329e7i	1.01057	+	0.888332i
$741$	2.23352e6	−	2.23352e6i	0.149432	−	0.149432i
$742$	−2.29378e6	−	5.90496e6i	−0.152947	−	0.393738i
$743$	−7.10752e6			−0.472331			−0.236165	−	0.971713i	$-0.575891\pi$
$743$	−7.10752e6			−0.472331			−0.236165	+	0.971713i	$0.575891\pi$
$744$	2.01662e7	+	9.97293e6i	1.33565	+	0.660527i
$745$	−603403.	−	5.53098e6i	−0.0398306	−	0.365100i
$746$	−9.19200e6	−	2.36633e7i	−0.604732	−	1.55678i
$747$	−17690.4	−	17690.4i	−0.00115994	−	0.00115994i
$748$	1.35665e6	−	3.05499e7i	0.0886574	−	1.99644i
$749$	2.12792e6	+	2.12792e6i	0.138596	+	0.138596i
$750$	−2.52296e7	−	2.24865e6i	−1.63778	−	0.145972i
$751$	−8.01849e6			−0.518791			−0.259396	−	0.965771i	$-0.583523\pi$
$751$	−8.01849e6			−0.518791			−0.259396	+	0.965771i	$0.583523\pi$
$752$	1.35761e7	+	1.20815e6i	0.875449	+	0.0779071i
$753$		−	4.80203e7i		−	3.08629i
$754$	−2.83606e6	−	1.24916e6i	−0.181672	−	0.0800184i
$755$	1.59294e7	+	1.27956e7i	1.01702	+	0.816947i
$756$	471677.	−	1.06215e7i	0.0300151	−	0.675898i
$757$	−845385.	−	845385.i	−0.0536185	−	0.0536185i	0.679789	−	0.733408i	$-0.262071\pi$
$757$	−845385.	−	845385.i	−0.0536185	−	0.0536185i	−0.733408	+	0.679789i	$0.762071\pi$
$758$	7.57192e6	−	2.94131e6i	0.478666	−	0.185938i
$759$		−	5.53588e7i		−	3.48805i
$760$	−3.06810e6	−	6.60603e6i	−0.192679	−	0.414865i
$761$			1.23445e7i			0.772702i	0.922352	+	0.386351i	$0.126265\pi$
$761$			1.23445e7i			0.772702i	−0.922352	+	0.386351i	$0.873735\pi$
$762$	4.52918e6	+	1.16596e7i	0.282574	+	0.727441i
$763$	5.35144e6	+	5.35144e6i	0.332781	+	0.332781i
$764$	3.18213e6	+	3.47789e6i	0.197235	+	0.215567i
$765$	2.47565e7	−	3.08196e7i	1.52945	−	1.90403i
$766$	−4.87255e6	+	1.10625e7i	−0.300043	+	0.681212i
$767$			6.33745e6i			0.388979i
$768$	−2.20621e7	+	1.53502e7i	−1.34972	+	0.939098i
$769$	1.19058e7			0.726012			0.363006	−	0.931787i	$-0.381751\pi$
$769$	1.19058e7			0.726012			0.363006	+	0.931787i	$0.381751\pi$
$770$	4.04306e6	−	1.27877e7i	0.245745	−	0.777259i
$771$	−1.32699e7	−	1.32699e7i	−0.803955	−	0.803955i
$772$	5.04475e6	−	4.61575e6i	0.304647	−	0.278740i
$773$	−1.19316e7	−	1.19316e7i	−0.718205	−	0.718205i	0.250032	−	0.968237i	$-0.419559\pi$
$773$	−1.19316e7	−	1.19316e7i	−0.718205	−	0.718205i	−0.968237	+	0.250032i	$0.919559\pi$
$774$	−2.70265e7	+	1.04984e7i	−1.62158	+	0.629902i
$775$	3.26721e6	+	1.47959e7i	0.195399	+	0.884888i
$776$	2.67487e7	−	9.04662e6i	1.59459	−	0.539302i
$777$	−2.17718e7			−1.29373
$778$	−5.87138e6	+	2.28074e6i	−0.347769	+	0.135091i
$779$	6.35492e6	−	6.35492e6i	0.375203	−	0.375203i
$780$	−504309.	−	7.83389e6i	−0.0296798	−	0.461042i
$781$	7.83864e6	+	7.83864e6i	0.459847	+	0.459847i
$782$	−1.50370e7	+	3.41396e7i	−0.879312	+	1.99637i
$783$			1.40236e7i			0.817436i
$784$	1.00388e6	−	1.12807e7i	0.0583301	−	0.655460i
$785$	1.67355e6	+	1.53403e7i	0.0969312	+	0.888502i
$786$	−2.34637e7	−	1.03347e7i	−1.35469	−	0.596680i
$787$	−1.32141e7	+	1.32141e7i	−0.760504	+	0.760504i	−0.976413	−	0.215909i	$-0.930728\pi$
$787$	−1.32141e7	+	1.32141e7i	−0.760504	+	0.760504i	0.215909	+	0.976413i	$0.430728\pi$
$788$	−160156.	+	3.60648e6i	−0.00918812	+	0.206903i
$789$	−4.07138e6	+	4.07138e6i	−0.232836	+	0.232836i
$790$	−8.51060e6	+	4.42179e6i	−0.485168	+	0.252075i
$791$		−	1.37529e7i		−	0.781541i
$792$	−1.85847e7	+	3.75800e7i	−1.05279	+	2.12884i
$793$	−8.97766e6			−0.506968
$794$	−1.62867e7	+	6.32658e6i	−0.916818	+	0.356138i
$795$	−1.32551e7	+	1.65014e7i	−0.743816	+	0.925983i
$796$	−1.99910e7	+	1.82910e7i	−1.11828	+	1.02319i
$797$	2.35727e7	−	2.35727e7i	1.31451	−	1.31451i	0.396458	−	0.918053i	$-0.370239\pi$
$797$	2.35727e7	−	2.35727e7i	1.31451	−	1.31451i	0.918053	−	0.396458i	$-0.129761\pi$
$798$	7.24071e6	+	3.18921e6i	0.402507	+	0.177287i
$799$	−2.27363e7			−1.25995
$800$	−1.73650e7	−	5.11233e6i	−0.959291	−	0.282419i
$801$	−1.16324e6			−0.0640604
$802$	−2.86888e7	−	1.26361e7i	−1.57498	−	0.693710i
$803$	2.60369e6	−	2.60369e6i	0.142495	−	0.142495i
$804$	1.52327e7	−	1.39373e7i	0.831069	−	0.760395i
$805$	−1.02459e7	+	1.27552e7i	−0.557265	+	0.693744i
$806$	−4.37734e6	+	1.70038e6i	−0.237341	+	0.0921951i
$807$	1.34861e7			0.728955
$808$	1.23004e7	+	6.08297e6i	0.662811	+	0.327784i
$809$			1.27690e7i			0.685937i	0.939347	+	0.342969i	$0.111432\pi$
$809$			1.27690e7i			0.685937i	−0.939347	+	0.342969i	$0.888568\pi$
$810$	−3.29343e6	+	1.71114e6i	−0.176374	+	0.0916376i
$811$	−2.01777e7	+	2.01777e7i	−1.07726	+	1.07726i	−0.0805055	+	0.996754i	$0.525653\pi$
$811$	−2.01777e7	+	2.01777e7i	−1.07726	+	1.07726i	−0.996754	+	0.0805055i	$0.974347\pi$
$812$	344372.	−	7.75477e6i	0.0183290	−	0.412742i
$813$	−1.10791e7	+	1.10791e7i	−0.587866	+	0.587866i
$814$	3.24503e7	+	1.42929e7i	1.71656	+	0.756067i
$815$	−2.55029e6	−	2.33768e7i	−0.134492	−	1.23279i
$816$	3.43880e7	−	2.87677e7i	1.80793	−	1.51244i
$817$		−	8.91153e6i		−	0.467086i
$818$	−1.28239e7	+	2.91152e7i	−0.670097	+	1.52137i
$819$	3.79943e6	+	3.79943e6i	0.197929	+	0.197929i
$820$	−1.43489e6	−	2.22894e7i	−0.0745217	−	1.15761i
$821$	2.41976e6	−	2.41976e6i	0.125290	−	0.125290i	−0.641682	−	0.766971i	$-0.721763\pi$
$821$	2.41976e6	−	2.41976e6i	0.125290	−	0.125290i	0.766971	+	0.641682i	$0.221763\pi$
$822$	1.99931e7	−	7.76631e6i	1.03205	−	0.400899i
$823$	4.27578e6			0.220047			0.110024	−	0.993929i	$-0.464907\pi$
$823$	4.27578e6			0.220047			0.110024	+	0.993929i	$0.464907\pi$
$824$	−7.51158e6	−	2.22100e7i	−0.385401	−	1.13954i
$825$	−4.37568e7	+	9.66229e6i	−2.23826	+	0.494248i
$826$	−1.47971e7	+	5.74792e6i	−0.754616	+	0.293130i
$827$	1.32487e7	+	1.32487e7i	0.673612	+	0.673612i	0.958547	−	0.284935i	$-0.0919721\pi$
$827$	1.32487e7	+	1.32487e7i	0.673612	+	0.673612i	−0.284935	+	0.958547i	$0.591972\pi$
$828$	3.77325e7	−	3.45238e7i	1.91267	−	1.75002i
$829$	−2.19748e7	−	2.19748e7i	−1.11055	−	1.11055i	−0.993076	−	0.117474i	$-0.962520\pi$
$829$	−2.19748e7	−	2.19748e7i	−1.11055	−	1.11055i	−0.117474	−	0.993076i	$-0.537480\pi$
$830$	5760.98	−	18221.2i	0.000290269	−	0.000918085i
$831$	2.82405e7			1.41863
$832$	744704.	−	5.56048e6i	0.0372971	−	0.278486i
$833$			1.88922e7i			0.943342i
$834$	2.35940e7	−	5.35673e7i	1.17459	−	2.66676i
$835$	7.33655e6	−	9.13333e6i	0.364146	−	0.453328i
$836$	−8.69841e6	−	9.50687e6i	−0.430451	−	0.470459i
$837$	1.50263e7	+	1.50263e7i	0.741378	+	0.741378i
$838$	−1.75734e6	−	4.52400e6i	−0.0864464	−	0.222542i
$839$			1.51106e7i			0.741099i	0.928813	+	0.370550i	$0.120831\pi$
$839$			1.51106e7i			0.741099i	−0.928813	+	0.370550i	$0.879169\pi$
$840$	1.78336e7	−	8.28264e6i	0.872051	−	0.405014i
$841$		−	1.02725e7i		−	0.500826i
$842$	1.87357e7	−	7.27788e6i	0.910730	−	0.353773i
$843$	−1.47755e7	−	1.47755e7i	−0.716100	−	0.716100i
$844$	−652167.	+	1.46859e7i	−0.0315140	+	0.709649i
$845$	−1.49043e7	−	1.19722e7i	−0.718075	−	0.576810i
$846$	2.85263e7	+	1.25646e7i	1.37031	+	0.603562i
$847$		−	1.15174e7i		−	0.551629i
$848$	−1.16019e7	+	9.70573e6i	−0.554039	+	0.463488i
$849$	4.72138e7			2.24802
$850$	2.96092e7	+	5.92683e6i	1.40566	+	0.281369i
$851$	−3.05864e7	−	3.05864e7i	−1.44779	−	1.44779i
$852$	−721040.	+	1.62368e7i	−0.0340299	+	0.766304i
$853$	427495.	+	427495.i	0.0201168	+	0.0201168i	0.717094	−	0.696977i	$-0.245472\pi$
$853$	427495.	+	427495.i	0.0201168	+	0.0201168i	−0.696977	+	0.717094i	$0.745472\pi$
$854$	−8.14253e6	−	2.09616e7i	−0.382045	−	0.983512i
$855$	−1.80655e6	−	1.65594e7i	−0.0845153	−	0.774694i
$856$	3.18536e6	−	6.44110e6i	0.148585	−	0.300452i
$857$	−2.54066e7			−1.18167			−0.590833	−	0.806794i	$-0.701201\pi$
$857$	−2.54066e7			−1.18167			−0.590833	+	0.806794i	$0.701201\pi$
$858$	−5.02861e6	−	1.29453e7i	−0.233201	−	0.600337i
$859$	−2.36145e7	+	2.36145e7i	−1.09193	+	1.09193i	−0.0966108	+	0.995322i	$0.530800\pi$
$859$	−2.36145e7	+	2.36145e7i	−1.09193	+	1.09193i	−0.995322	+	0.0966108i	$0.969200\pi$
$860$	−1.66343e7	−	1.46222e7i	−0.766934	−	0.674163i
$861$	1.71557e7	+	1.71557e7i	0.788682	+	0.788682i
$862$	3.66023e7	+	1.61217e7i	1.67780	+	0.738996i
$863$		−	2.78642e7i		−	1.27356i	−0.771045	−	0.636780i	$-0.780266\pi$
$863$		−	2.78642e7i		−	1.27356i	0.771045	−	0.636780i	$-0.219734\pi$
$864$	−2.43860e7	+	7.05860e6i	−1.11137	+	0.321688i
$865$	−1.94165e6	−	1.77978e7i	−0.0882329	−	0.808771i
$866$	−3.05688e6	+	6.94026e6i	−0.138511	+	0.314471i
$867$	−2.71504e7	+	2.71504e7i	−1.22667	+	1.22667i
$868$	−7.94029e6	−	8.67829e6i	−0.357715	−	0.390962i
$869$	−1.19976e7	+	1.19976e7i	−0.538944	+	0.538944i
$870$	−2.30148e7	+	1.19576e7i	−1.03088	+	0.535607i
$871$			4.30967e6i			0.192486i
$872$	8.01075e6	−	1.61985e7i	0.356765	−	0.721413i
$873$	6.45774e7			2.86777
$874$	5.69180e6	+	1.46526e7i	0.252041	+	0.648838i
$875$	1.18703e7	+	5.87231e6i	0.524135	+	0.259292i
$876$	5.39323e6	+	239501.i	0.237459	+	0.0105450i
$877$	1.46203e6	−	1.46203e6i	0.0641887	−	0.0641887i	−0.674284	−	0.738472i	$-0.735548\pi$
$877$	1.46203e6	−	1.46203e6i	0.0641887	−	0.0641887i	0.738472	+	0.674284i	$0.235548\pi$
$878$	8.23272e6	−	1.86914e7i	0.360418	−	0.818285i
$879$	−1.34743e7			−0.588212
$880$	−3.20180e7	+	637500.i	−1.39376	+	0.0277507i
$881$	9.67429e6			0.419933			0.209966	−	0.977709i	$-0.432665\pi$
$881$	9.67429e6			0.419933			0.209966	+	0.977709i	$0.432665\pi$
$882$	1.04402e7	−	2.37032e7i	0.451895	−	1.02597i
$883$	608967.	−	608967.i	0.0262841	−	0.0262841i	−0.693843	−	0.720127i	$-0.744084\pi$
$883$	608967.	−	608967.i	0.0262841	−	0.0262841i	0.720127	+	0.693843i	$0.244084\pi$
$884$	−415179.	+	9.34925e6i	−0.0178692	+	0.402389i
$885$	4.13504e7	+	3.32156e7i	1.77469	+	1.42556i
$886$	1.11706e7	+	2.87568e7i	0.478069	+	1.23071i
$887$	−1.84590e7			−0.787768			−0.393884	−	0.919160i	$-0.628869\pi$
$887$	−1.84590e7			−0.787768			−0.393884	+	0.919160i	$0.628869\pi$
$888$	1.66556e7	+	4.92466e7i	0.708806	+	2.09577i
$889$		−	6.53997e6i		−	0.277537i
$890$	−409667.	−	788484.i	−0.0173363	−	0.0333671i
$891$	−4.64281e6	+	4.64281e6i	−0.195924	+	0.195924i
$892$	6.74111e6	−	6.16785e6i	0.283674	−	0.259551i
$893$	−6.77451e6	+	6.77451e6i	−0.284282	+	0.284282i
$894$	5.81700e6	−	1.32068e7i	0.243419	−	0.552654i
$895$	−2.60971e7	+	2.84706e6i	−1.08902	+	0.118806i
$896$	1.36584e7	−	3.30444e6i	0.568367	−	0.137508i
$897$			1.69416e7i			0.703028i
$898$	−1.10381e7	−	4.86181e6i	−0.456778	−	0.201190i
$899$	1.09708e7	+	1.09708e7i	0.452728	+	0.452728i
$900$	−3.38741e7	−	2.37988e7i	−1.39400	−	0.979375i
$901$	1.78423e7	−	1.78423e7i	0.732215	−	0.732215i
$902$	−1.43077e7	−	3.68327e7i	−0.585534	−	1.50736i
$903$	2.40576e7			0.981821
$904$	−3.11082e7	+	1.05210e7i	−1.26606	+	0.428190i
$905$	−4.86544e6	−	4.45982e7i	−0.197470	−	1.81007i
$906$	1.91893e7	+	4.93997e7i	0.776674	+	1.99942i
$907$	−1.08111e7	−	1.08111e7i	−0.436366	−	0.436366i	0.454421	−	0.890787i	$-0.349846\pi$
$907$	−1.08111e7	−	1.08111e7i	−0.436366	−	0.436366i	−0.890787	+	0.454421i	$0.849846\pi$
$908$	−3.47082e7	−	1.54131e6i	−1.39707	−	0.0620406i
$909$	2.21908e7	+	2.21908e7i	0.890763	+	0.890763i
$910$	−1.23731e6	+	3.91345e6i	−0.0495306	+	0.156659i
$911$	−9.35392e6			−0.373420			−0.186710	−	0.982415i	$-0.559783\pi$
$911$	−9.35392e6			−0.373420			−0.186710	+	0.982415i	$0.559783\pi$
$912$	1.67462e6	−	1.88178e7i	0.0666697	−	0.749173i
$913$		−	33808.2i		−	0.00134229i
$914$	−3.45701e6	−	1.52266e6i	−0.136878	−	0.0602889i
$915$	−4.70534e7	+	5.85772e7i	−1.85797	+	2.31300i
$916$	1.92197e7	+	853506.i	0.756849	+	0.0336100i
$917$	9.47886e6	+	9.47886e6i	0.372248	+	0.372248i
$918$	3.94754e7	−	1.53342e7i	1.54604	−	0.600558i
$919$		−	7.04729e6i		−	0.275254i	−0.990484	−	0.137627i	$-0.956053\pi$
$919$		−	7.04729e6i		−	0.275254i	0.990484	−	0.137627i	$-0.0439475\pi$
$920$	3.66898e7	+	1.34179e7i	1.42914	+	0.522653i
$921$			3.66794e7i			1.42486i
$922$	−1.88634e6	−	4.85607e6i	−0.0730791	−	0.188130i
$923$	−2.39888e6	−	2.39888e6i	−0.0926837	−	0.0926837i
$924$	2.56647e7	−	2.34822e7i	0.988910	−	0.904814i
$925$	−1.88376e7	+	2.95147e7i	−0.723889	+	1.13419i
$926$	1.09755e6	−	2.49186e6i	0.0420628	−	0.0954985i
$927$		−	5.36198e7i		−	2.04940i
$928$	−1.78043e7	+	5.15350e6i	−0.678664	+	0.196441i
$929$	−2.89619e7			−1.10100			−0.550500	−	0.834835i	$-0.685563\pi$
$929$	−2.89619e7			−1.10100			−0.550500	+	0.834835i	$0.685563\pi$
$930$	−1.18478e7	+	3.74731e7i	−0.449190	+	1.42073i
$931$	5.62910e6	+	5.62910e6i	0.212846	+	0.212846i
$932$	−1.14588e7	−	1.25238e7i	−0.432115	−	0.472277i
$933$	3.24997e7	+	3.24997e7i	1.22229	+	1.22229i
$934$	−1.75423e7	+	6.81429e6i	−0.657989	+	0.255595i
$935$	5.31060e7	−	5.79360e6i	1.98662	−	0.216730i
$936$	5.68750e6	−	1.15007e7i	0.212193	−	0.429076i
$937$	−6.32274e6			−0.235265			−0.117632	−	0.993057i	$-0.537530\pi$
$937$	−6.32274e6			−0.235265			−0.117632	+	0.993057i	$0.537530\pi$
$938$	−1.00625e7	+	3.90877e6i	−0.373421	+	0.145055i
$939$	5.17987e7	−	5.17987e7i	1.91714	−	1.91714i
$940$	1.52962e6	+	2.37610e7i	0.0564632	+	0.877093i
$941$	1.19423e7	+	1.19423e7i	0.439655	+	0.439655i	0.891896	−	0.452241i	$-0.149375\pi$
$941$	1.19423e7	+	1.19423e7i	0.439655	+	0.439655i	−0.452241	+	0.891896i	$0.649375\pi$
$942$	−1.61335e7	+	3.66292e7i	−0.592382	+	1.34493i
$943$			4.82030e7i			1.76520i
$944$	2.43213e7	+	2.90729e7i	0.888295	+	1.06184i
$945$	1.84637e7	−	2.01430e6i	0.672573	−	0.0733744i
$946$	−3.58572e7	−	1.57935e7i	−1.30271	−	0.573786i
$947$	1.83554e7	−	1.83554e7i	0.665104	−	0.665104i	−0.291475	−	0.956579i	$-0.594146\pi$
$947$	1.83554e7	−	1.83554e7i	0.665104	−	0.665104i	0.956579	+	0.291475i	$0.0941459\pi$
$948$	−2.48515e7	−	1.10360e6i	−0.898115	−	0.0398833i
$949$	−796813.	+	796813.i	−0.0287204	+	0.0287204i
$950$	1.05883e7	−	7.05638e6i	0.380642	−	0.253672i
$951$			3.20224e7i			1.14816i
$952$	−2.22058e7	+	7.51016e6i	−0.794096	+	0.268570i
$953$	2.55449e7			0.911113			0.455557	−	0.890207i	$-0.349440\pi$
$953$	2.55449e7			0.911113			0.455557	+	0.890207i	$0.349440\pi$
$954$	−3.22460e7	+	1.25260e7i	−1.14711	+	0.445595i
$955$	−5.15716e6	+	6.42019e6i	−0.182979	+	0.227793i
$956$	−3.90611e6	−	4.26916e6i	−0.138229	−	0.151077i
$957$	−3.24444e7	+	3.24444e7i	−1.14514	+	1.14514i
$958$	3.33874e7	+	1.47057e7i	1.17536	+	0.517692i
$959$	−1.12143e7			−0.393753
$960$	−3.23777e7	−	3.40024e7i	−1.13388	−	1.19078i
$961$	−5.11867e6			−0.178792
$962$	−9.93084e6	−	4.37409e6i	−0.345978	−	0.152388i
$963$	1.16202e7	−	1.16202e7i	0.403783	−	0.403783i
$964$	3.69224e6	+	4.03541e6i	0.127967	+	0.139860i
$965$	9.31262e6	+	7.48057e6i	0.321924	+	0.258593i
$966$	−3.95562e7	+	1.53656e7i	−1.36387	+	0.529793i
$967$	−4.35726e7			−1.49847			−0.749234	−	0.662305i	$-0.769578\pi$
$967$	−4.35726e7			−1.49847			−0.749234	+	0.662305i	$0.769578\pi$
$968$	−2.60518e7	+	8.81091e6i	−0.893611	+	0.302226i
$969$			3.15148e7i			1.07821i
$970$	2.27426e7	+	4.37727e7i	0.776089	+	1.49373i
$971$	2.23582e7	−	2.23582e7i	0.761008	−	0.761008i	−0.215496	−	0.976505i	$-0.569137\pi$
$971$	2.23582e7	−	2.23582e7i	0.761008	−	0.761008i	0.976505	+	0.215496i	$0.0691369\pi$
$972$	2.44290e7	+	1.08484e6i	0.829353	+	0.0368297i
$973$	−2.16401e7	+	2.16401e7i	−0.732787	+	0.732787i
$974$	−1.85731e6	−	818060.i	−0.0627315	−	0.0276304i
$975$	1.33910e7	−	2.95697e6i	0.451129	−	0.0996174i
$976$	−4.11848e7	+	3.44537e7i	−1.38393	+	1.15774i
$977$		−	7.08778e6i		−	0.237560i	−0.992921	−	0.118780i	$-0.962102\pi$
$977$		−	7.08778e6i		−	0.237560i	0.992921	−	0.118780i	$-0.0378984\pi$
$978$	2.45856e7	−	5.58187e7i	0.821929	−	1.86609i
$979$	−1.11154e6	−	1.11154e6i	−0.0370655	−	0.0370655i
$980$	1.97436e7	−	1.27100e6i	0.656691	−	0.0422747i
$981$	2.92233e7	−	2.92233e7i	0.969521	−	0.969521i
$982$	−2.44256e7	+	9.48813e6i	−0.808290	+	0.313980i
$983$	2.29904e7			0.758862			0.379431	−	0.925220i	$-0.376120\pi$
$983$	2.29904e7			0.758862			0.379431	+	0.925220i	$0.376120\pi$
$984$	2.56811e7	−	5.19296e7i	0.845522	−	1.70973i
$985$	−6.26927e6	+	683946.i	−0.205886	+	0.0224611i
$986$	2.88211e7	−	1.11956e7i	0.944101	−	0.366736i
$987$	−1.82885e7	−	1.82885e7i	−0.597564	−	0.597564i
$988$	2.66199e6	+	2.90940e6i	0.0867589	+	0.0948226i
$989$	3.37976e7	+	3.37976e7i	1.09874	+	1.09874i
$990$	−6.98316e7	−	2.20785e7i	−2.26446	−	0.715949i
$991$	1.94825e7			0.630174			0.315087	−	0.949063i	$-0.397966\pi$
$991$	1.94825e7			0.630174			0.315087	+	0.949063i	$0.397966\pi$
$992$	−1.35554e7	+	2.45994e7i	−0.437354	+	0.793681i
$993$		−	1.60157e6i		−	0.0515433i
$994$	3.42532e6	−	7.77676e6i	0.109960	−	0.249651i
$995$	−3.69034e7	−	2.96435e7i	−1.18171	−	0.949231i
$996$	36569.8	−	33459.9i	0.00116808	−	0.00106875i
$997$	−2.24729e7	−	2.24729e7i	−0.716013	−	0.716013i	0.251774	−	0.967786i	$-0.418986\pi$
$997$	−2.24729e7	−	2.24729e7i	−0.716013	−	0.716013i	−0.967786	+	0.251774i	$0.918986\pi$
$998$	−5.45350e6	−	1.40391e7i	−0.173320	−	0.446184i
$999$			4.91053e7i			1.55673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.8	✓	116
5.4	even	2	inner	80.6.q.a.29.51	yes	116
16.5	even	4	inner	80.6.q.a.69.51	yes	116
80.69	even	4	inner	80.6.q.a.69.8	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.8	✓	116	1.1	even	1	trivial
80.6.q.a.29.51	yes	116	5.4	even	2	inner
80.6.q.a.69.8	yes	116	80.69	even	4	inner
80.6.q.a.69.51	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)

\(f(q)\)	\(=\)	\(q+(-5.17693 - 2.28021i) q^{2} +(18.1244 - 18.1244i) q^{3} +(21.6013 + 23.6090i) q^{4} +(-35.0084 + 43.5822i) q^{5} +(-135.156 + 52.5013i) q^{6} +75.8099 q^{7} +(-57.9951 - 171.478i) q^{8} -413.986i q^{9} +O(q^{10})\)	\(q+(-5.17693 - 2.28021i) q^{2} +(18.1244 - 18.1244i) q^{3} +(21.6013 + 23.6090i) q^{4} +(-35.0084 + 43.5822i) q^{5} +(-135.156 + 52.5013i) q^{6} +75.8099 q^{7} +(-57.9951 - 171.478i) q^{8} -413.986i q^{9} +(280.613 - 145.796i) q^{10} +(395.586 - 395.586i) q^{11} +(819.408 + 36.3881i) q^{12} +(-121.062 + 121.062i) q^{13} +(-392.463 - 172.862i) q^{14} +(155.396 + 1424.41i) q^{15} +(-90.7681 + 1019.97i) q^{16} -1708.17i q^{17} +(-943.974 + 2143.18i) q^{18} +(-508.967 - 508.967i) q^{19} +(-1785.16 + 114.920i) q^{20} +(1374.01 - 1374.01i) q^{21} +(-2949.94 + 1145.90i) q^{22} +3860.59 q^{23} +(-4159.05 - 2056.80i) q^{24} +(-673.824 - 3051.49i) q^{25} +(902.776 - 350.683i) q^{26} +(-3099.01 - 3099.01i) q^{27} +(1637.59 + 1789.79i) q^{28} +(-2262.59 - 2262.59i) q^{29} +(2443.47 - 7728.39i) q^{30} -4848.76 q^{31} +(2795.64 - 5073.34i) q^{32} -14339.5i q^{33} +(-3894.99 + 8843.11i) q^{34} +(-2653.98 + 3303.97i) q^{35} +(9773.78 - 8942.62i) q^{36} +(-7922.75 - 7922.75i) q^{37} +(1474.34 + 3795.44i) q^{38} +4388.34i q^{39} +(9503.69 + 3475.60i) q^{40} +12485.9i q^{41} +(-10246.2 + 3980.12i) q^{42} +(8754.53 + 8754.53i) q^{43} +(17884.5 + 794.213i) q^{44} +(18042.4 + 14493.0i) q^{45} +(-19986.0 - 8802.94i) q^{46} -13310.3i q^{47} +(16841.2 + 20131.4i) q^{48} -11059.9 q^{49} +(-3469.69 + 17333.8i) q^{50} +(-30959.6 - 30959.6i) q^{51} +(-5473.24 - 243.055i) q^{52} +(10445.2 + 10445.2i) q^{53} +(8976.97 + 23109.7i) q^{54} +(3391.69 + 31089.3i) q^{55} +(-4396.60 - 12999.7i) q^{56} -18449.4 q^{57} +(6554.10 + 16872.5i) q^{58} +(26174.4 - 26174.4i) q^{59} +(-30272.0 + 34437.7i) q^{60} +(37078.8 + 37078.8i) q^{61} +(25101.7 + 11056.2i) q^{62} -31384.2i q^{63} +(-26041.1 + 19889.7i) q^{64} +(-1037.97 - 9514.33i) q^{65} +(-32697.0 + 74234.6i) q^{66} +(17799.5 - 17799.5i) q^{67} +(40328.3 - 36898.8i) q^{68} +(69970.7 - 69970.7i) q^{69} +(21273.2 - 11052.8i) q^{70} +19815.3i q^{71} +(-70989.3 + 24009.1i) q^{72} +6581.86 q^{73} +(22950.0 + 59081.1i) q^{74} +(-67519.0 - 43093.7i) q^{75} +(1021.85 - 23010.5i) q^{76} +(29989.3 - 29989.3i) q^{77} +(10006.3 - 22718.1i) q^{78} -30328.6 q^{79} +(-41274.9 - 39663.4i) q^{80} -11736.6 q^{81} +(28470.5 - 64638.8i) q^{82} +(42.7319 - 42.7319i) q^{83} +(62119.2 + 2758.58i) q^{84} +(74446.1 + 59800.4i) q^{85} +(-25359.5 - 65283.8i) q^{86} -82016.1 q^{87} +(-90776.1 - 44892.1i) q^{88} -2809.87i q^{89} +(-60357.4 - 116170. i) q^{90} +(-9177.69 + 9177.69i) q^{91} +(83393.6 + 91144.5i) q^{92} +(-87880.7 + 87880.7i) q^{93} +(-30350.3 + 68906.6i) q^{94} +(40000.0 - 4363.80i) q^{95} +(-41281.9 - 142620. i) q^{96} +155990. i q^{97} +(57256.2 + 25218.8i) q^{98} +(-163767. - 163767. i) 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

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