LMFDB - Embedded newform 48.6.k.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.k (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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	48.11
Dual form			48.6.k.a.35.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61933 + 5.42012i) q^{2} +(13.1651 + 8.34740i) q^{3} +(-26.7555 - 17.5540i) q^{4} +(54.1063 - 54.1063i) q^{5} +(-66.5627 + 57.8395i) q^{6} +243.836 q^{7} +(138.471 - 116.592i) q^{8} +(103.642 + 219.789i) q^{9} +O(q^{10})$	\(q+(-1.61933 + 5.42012i) q^{2} +(13.1651 + 8.34740i) q^{3} +(-26.7555 - 17.5540i) q^{4} +(54.1063 - 54.1063i) q^{5} +(-66.5627 + 57.8395i) q^{6} +243.836 q^{7} +(138.471 - 116.592i) q^{8} +(103.642 + 219.789i) q^{9} +(205.647 + 380.879i) q^{10} +(-392.992 - 392.992i) q^{11} +(-205.710 - 454.440i) q^{12} +(-273.665 + 273.665i) q^{13} +(-394.853 + 1321.62i) q^{14} +(1163.96 - 260.670i) q^{15} +(407.714 + 939.332i) q^{16} +391.969i q^{17} +(-1359.12 + 205.840i) q^{18} +(41.8387 + 41.8387i) q^{19} +(-2397.42 + 497.860i) q^{20} +(3210.14 + 2035.40i) q^{21} +(2766.45 - 1493.68i) q^{22} +1173.24i q^{23} +(2796.23 - 379.083i) q^{24} -2729.99i q^{25} +(-1040.14 - 1926.46i) q^{26} +(-470.208 + 3758.70i) q^{27} +(-6523.97 - 4280.30i) q^{28} +(776.308 + 776.308i) q^{29} +(-471.982 + 6730.95i) q^{30} -3174.82i q^{31} +(-5751.52 + 688.770i) q^{32} +(-1893.34 - 8454.26i) q^{33} +(-2124.52 - 634.729i) q^{34} +(13193.1 - 13193.1i) q^{35} +(1085.19 - 7699.91i) q^{36} +(-2781.73 - 2781.73i) q^{37} +(-294.522 + 159.020i) q^{38} +(-5887.24 + 1318.45i) q^{39} +(1183.77 - 13800.5i) q^{40} +6453.74 q^{41} +(-16230.4 + 14103.4i) q^{42} +(-6864.07 + 6864.07i) q^{43} +(3616.12 + 17413.3i) q^{44} +(17499.7 + 6284.31i) q^{45} +(-6359.12 - 1899.87i) q^{46} -25567.1 q^{47} +(-2473.36 + 15769.8i) q^{48} +42649.2 q^{49} +(14796.9 + 4420.77i) q^{50} +(-3271.92 + 5160.33i) q^{51} +(12126.0 - 2518.14i) q^{52} +(-11254.2 + 11254.2i) q^{53} +(-19611.2 - 8635.18i) q^{54} -42526.7 q^{55} +(33764.3 - 28429.5i) q^{56} +(201.568 + 900.057i) q^{57} +(-5464.79 + 2950.58i) q^{58} +(-22133.5 - 22133.5i) q^{59} +(-35718.3 - 13457.9i) q^{60} +(17845.3 - 17845.3i) q^{61} +(17207.9 + 5141.11i) q^{62} +(25271.7 + 53592.7i) q^{63} +(5580.43 - 32289.3i) q^{64} +29614.1i q^{65} +(48889.1 + 3428.16i) q^{66} +(-12511.1 - 12511.1i) q^{67} +(6880.63 - 10487.3i) q^{68} +(-9793.51 + 15445.9i) q^{69} +(50144.2 + 92872.3i) q^{70} +54853.6i q^{71} +(39977.2 + 18350.6i) q^{72} +22499.7i q^{73} +(19581.9 - 10572.8i) q^{74} +(22788.3 - 35940.7i) q^{75} +(-384.979 - 1853.85i) q^{76} +(-95825.8 - 95825.8i) q^{77} +(2387.25 - 34044.6i) q^{78} -77856.3i q^{79} +(72883.7 + 28763.9i) q^{80} +(-37565.7 + 45558.8i) q^{81} +(-10450.8 + 34980.1i) q^{82} +(-18384.0 + 18384.0i) q^{83} +(-50159.6 - 110809. i) q^{84} +(21208.0 + 21208.0i) q^{85} +(-26088.9 - 48319.4i) q^{86} +(3740.06 + 16700.4i) q^{87} +(-100238. - 8598.11i) q^{88} +31761.3 q^{89} +(-62399.6 + 84674.0i) q^{90} +(-66729.6 + 66729.6i) q^{91} +(20595.1 - 31390.7i) q^{92} +(26501.5 - 41797.0i) q^{93} +(41401.7 - 138577. i) q^{94} +4527.48 q^{95} +(-81469.1 - 38942.5i) q^{96} -14118.5 q^{97} +(-69063.4 + 231164. i) q^{98} +(45645.0 - 127106. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7}+O(q^{10}) $ 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7	$ 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99}+O(q^{100}) $ 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7 - 104 * q^10 + 784 * q^12 - 4 * q^13 + 4560 * q^16 - 4076 * q^18 + 2356 * q^19 - 488 * q^21 + 2232 * q^22 + 2568 * q^24 - 3734 * q^27 - 12392 * q^28 + 628 * q^30 - 4 * q^33 + 26248 * q^34 - 30748 * q^36 - 4 * q^37 - 44908 * q^39 + 440 * q^40 + 11256 * q^42 + 652 * q^43 - 6252 * q^45 + 31320 * q^46 - 9168 * q^48 + 124844 * q^49 + 8664 * q^51 - 48448 * q^52 - 19480 * q^54 - 110056 * q^55 + 76088 * q^58 - 85408 * q^60 + 48076 * q^61 - 11080 * q^64 + 91492 * q^66 + 48924 * q^67 + 484 * q^69 + 86200 * q^70 - 16376 * q^72 - 69634 * q^75 + 30920 * q^76 + 13020 * q^78 - 4 * q^81 - 200768 * q^82 + 111760 * q^84 - 119904 * q^85 + 282180 * q^87 - 123616 * q^88 - 17680 * q^90 - 167288 * q^91 + 181660 * q^93 - 13200 * q^94 - 61688 * q^96 - 8 * q^97 - 287860 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.61933	+	5.42012i	−0.286261	+	0.958152i
$2$	−1.61933	+	5.42012i	−0.286261	+	0.958152i
$3$	13.1651	+	8.34740i	0.844544	+	0.535486i
$3$	13.1651	+	8.34740i	0.844544	+	0.535486i
$4$	−26.7555	−	17.5540i	−0.836110	−	0.548562i
$5$	54.1063	−	54.1063i	0.967883	−	0.967883i	−0.0316167	−	0.999500i	$-0.510066\pi$
$5$	54.1063	−	54.1063i	0.967883	−	0.967883i	0.999500	+	0.0316167i	$0.0100656\pi$
$6$	−66.5627	+	57.8395i	−0.754836	+	0.655913i
$7$	243.836			1.88085			0.940424	−	0.340005i	$-0.110429\pi$
$7$	243.836			1.88085			0.940424	+	0.340005i	$0.110429\pi$
$8$	138.471	−	116.592i	0.764951	−	0.644088i
$9$	103.642	+	219.789i	0.426510	+	0.904483i
$10$	205.647	+	380.879i	0.650312	+	1.20445i
$11$	−392.992	−	392.992i	−0.979269	−	0.979269i	0.0205201	−	0.999789i	$-0.493468\pi$
$11$	−392.992	−	392.992i	−0.979269	−	0.979269i	−0.999789	+	0.0205201i	$0.993468\pi$
$12$	−205.710	−	454.440i	−0.412384	−	0.911010i
$13$	−273.665	+	273.665i	−0.449119	+	0.449119i	−0.895062	−	0.445943i	$-0.852869\pi$
$13$	−273.665	+	273.665i	−0.449119	+	0.449119i	0.445943	+	0.895062i	$0.352869\pi$
$14$	−394.853	+	1321.62i	−0.538413	+	1.80214i
$15$	1163.96	−	260.670i	1.33571	−	0.299133i
$16$	407.714	+	939.332i	0.398159	+	0.917317i
$17$			391.969i			0.328950i	0.986381	+	0.164475i	$0.0525930\pi$
$17$			391.969i			0.328950i	−0.986381	+	0.164475i	$0.947407\pi$
$18$	−1359.12	+	205.840i	−0.988725	+	0.149743i
$19$	41.8387	+	41.8387i	0.0265885	+	0.0265885i	0.720276	−	0.693688i	$-0.244015\pi$
$19$	41.8387	+	41.8387i	0.0265885	+	0.0265885i	−0.693688	+	0.720276i	$0.744015\pi$
$20$	−2397.42	+	497.860i	−1.34020	+	0.278312i
$21$	3210.14	+	2035.40i	1.58846	+	1.00717i
$22$	2766.45	−	1493.68i	1.21861	−	0.657962i
$23$			1173.24i			0.462453i	0.972900	+	0.231227i	$0.0742739\pi$
$23$			1173.24i			0.462453i	−0.972900	+	0.231227i	$0.925726\pi$
$24$	2796.23	−	379.083i	0.990935	−	0.134340i
$25$		−	2729.99i		−	0.873596i
$26$	−1040.14	−	1926.46i	−0.301759	−	0.558889i
$27$	−470.208	+	3758.70i	−0.124131	+	0.992266i
$28$	−6523.97	−	4280.30i	−1.57259	−	1.03176i
$29$	776.308	+	776.308i	0.171411	+	0.171411i	0.787599	−	0.616188i	$-0.211324\pi$
$29$	776.308	+	776.308i	0.171411	+	0.171411i	−0.616188	+	0.787599i	$0.711324\pi$
$30$	−471.982	+	6730.95i	−0.0957463	+	1.36544i
$31$		−	3174.82i		−	0.593356i	−0.954978	−	0.296678i	$-0.904121\pi$
$31$		−	3174.82i		−	0.593356i	0.954978	−	0.296678i	$-0.0958789\pi$
$32$	−5751.52	+	688.770i	−0.992906	+	0.118905i
$33$	−1893.34	−	8454.26i	−0.302652	−	1.35142i
$34$	−2124.52	−	634.729i	−0.315184	−	0.0941654i
$35$	13193.1	−	13193.1i	1.82044	−	1.82044i
$36$	1085.19	−	7699.91i	0.139556	−	0.990214i
$37$	−2781.73	−	2781.73i	−0.334050	−	0.334050i	0.520073	−	0.854122i	$-0.325905\pi$
$37$	−2781.73	−	2781.73i	−0.334050	−	0.334050i	−0.854122	+	0.520073i	$0.825905\pi$
$38$	−294.522	+	159.020i	−0.0330871	+	0.0178646i
$39$	−5887.24	+	1318.45i	−0.619798	+	0.138804i
$40$	1183.77	−	13800.5i	0.116982	−	1.36379i
$41$	6453.74			0.599587			0.299793	−	0.954004i	$-0.403082\pi$
$41$	6453.74			0.599587			0.299793	+	0.954004i	$0.403082\pi$
$42$	−16230.4	+	14103.4i	−1.41973	+	1.23367i
$43$	−6864.07	+	6864.07i	−0.566123	+	0.566123i	−0.931040	−	0.364917i	$-0.881097\pi$
$43$	−6864.07	+	6864.07i	−0.566123	+	0.566123i	0.364917	+	0.931040i	$0.381097\pi$
$44$	3616.12	+	17413.3i	0.281586	+	1.35597i
$45$	17499.7	+	6284.31i	1.28825	+	0.462622i
$46$	−6359.12	−	1899.87i	−0.443100	−	0.132382i
$47$	−25567.1			−1.68825			−0.844125	−	0.536146i	$-0.819880\pi$
$47$	−25567.1			−1.68825			−0.844125	+	0.536146i	$0.819880\pi$
$48$	−2473.36	+	15769.8i	−0.154947	+	0.987923i
$49$	42649.2			2.53759
$50$	14796.9	+	4420.77i	0.837038	+	0.250076i
$51$	−3271.92	+	5160.33i	−0.176148	+	0.277813i
$52$	12126.0	−	2518.14i	0.621883	−	0.129143i
$53$	−11254.2	+	11254.2i	−0.550332	+	0.550332i	−0.926536	−	0.376205i	$-0.877229\pi$
$53$	−11254.2	+	11254.2i	−0.550332	+	0.550332i	0.376205	+	0.926536i	$0.377229\pi$
$54$	−19611.2	−	8635.18i	−0.915207	−	0.402983i
$55$	−42526.7			−1.89564
$56$	33764.3	−	28429.5i	1.43876	−	1.21143i
$57$	201.568	+	900.057i	0.00821741	+	0.0366930i
$58$	−5464.79	+	2950.58i	−0.213306	+	0.115170i
$59$	−22133.5	−	22133.5i	−0.827792	−	0.827792i	0.159419	−	0.987211i	$-0.449038\pi$
$59$	−22133.5	−	22133.5i	−0.827792	−	0.827792i	−0.987211	+	0.159419i	$0.949038\pi$
$60$	−35718.3	−	13457.9i	−1.28089	−	0.482612i
$61$	17845.3	−	17845.3i	0.614045	−	0.614045i	−0.329952	−	0.943998i	$-0.607033\pi$
$61$	17845.3	−	17845.3i	0.614045	−	0.614045i	0.943998	+	0.329952i	$0.107033\pi$
$62$	17207.9	+	5141.11i	0.568525	+	0.169855i
$63$	25271.7	+	53592.7i	0.802200	+	1.70119i
$64$	5580.43	−	32289.3i	0.170301	−	0.985392i
$65$			29614.1i			0.869390i
$66$	48889.1	+	3428.16i	1.38150	+	0.0968727i
$67$	−12511.1	−	12511.1i	−0.340494	−	0.340494i	0.516059	−	0.856553i	$-0.327398\pi$
$67$	−12511.1	−	12511.1i	−0.340494	−	0.340494i	−0.856553	+	0.516059i	$0.827398\pi$
$68$	6880.63	−	10487.3i	0.180449	−	0.275038i
$69$	−9793.51	+	15445.9i	−0.247637	+	0.390562i
$70$	50144.2	+	92872.3i	1.22314	+	2.26538i
$71$			54853.6i			1.29140i	0.763593	+	0.645698i	$0.223433\pi$
$71$			54853.6i			1.29140i	−0.763593	+	0.645698i	$0.776567\pi$
$72$	39977.2	+	18350.6i	0.908826	+	0.417175i
$73$			22499.7i			0.494163i	0.968995	+	0.247081i	$0.0794715\pi$
$73$			22499.7i			0.494163i	−0.968995	+	0.247081i	$0.920528\pi$
$74$	19581.9	−	10572.8i	0.415695	−	0.224445i
$75$	22788.3	−	35940.7i	0.467798	−	0.737791i
$76$	−384.979	−	1853.85i	−0.00764546	−	0.0368164i
$77$	−95825.8	−	95825.8i	−1.84186	−	1.84186i
$78$	2387.25	−	34044.6i	0.0444284	−	0.633595i
$79$		−	77856.3i		−	1.40354i	−0.712401	−	0.701772i	$-0.752392\pi$
$79$		−	77856.3i		−	1.40354i	0.712401	−	0.701772i	$-0.247608\pi$
$80$	72883.7	+	28763.9i	1.27323	+	0.502484i
$81$	−37565.7	+	45558.8i	−0.636178	+	0.771542i
$82$	−10450.8	+	34980.1i	−0.171638	+	0.574495i
$83$	−18384.0	+	18384.0i	−0.292917	+	0.292917i	−0.838231	−	0.545315i	$-0.816410\pi$
$83$	−18384.0	+	18384.0i	−0.292917	+	0.292917i	0.545315	+	0.838231i	$0.316410\pi$
$84$	−50159.6	−	110809.i	−0.775632	−	1.71347i
$85$	21208.0	+	21208.0i	0.318385	+	0.318385i
$86$	−26088.9	−	48319.4i	−0.380373	−	0.704490i
$87$	3740.06	+	16700.4i	0.0529761	+	0.236553i
$88$	−100238.	−	8598.11i	−1.37983	−	0.118358i
$89$	31761.3			0.425034			0.212517	−	0.977157i	$-0.431834\pi$
$89$	31761.3			0.425034			0.212517	+	0.977157i	$0.431834\pi$
$90$	−62399.6	+	84674.0i	−0.812036	+	1.10190i
$91$	−66729.6	+	66729.6i	−0.844725	+	0.844725i
$92$	20595.1	−	31390.7i	0.253684	−	0.386662i
$93$	26501.5	−	41797.0i	0.317734	−	0.501116i
$94$	41401.7	−	138577.i	0.483280	−	1.61760i
$95$	4527.48			0.0514692
$96$	−81469.1	−	38942.5i	−0.902225	−	0.431267i
$97$	−14118.5			−0.152356			−0.0761781	−	0.997094i	$-0.524272\pi$
$97$	−14118.5			−0.152356			−0.0761781	+	0.997094i	$0.524272\pi$
$98$	−69063.4	+	231164.i	−0.726412	+	2.43139i
$99$	45645.0	−	127106.i	0.468064	−	1.30340i
$100$	−47922.2	+	73042.2i	−0.479222	+	0.730422i
$101$	−77357.4	+	77357.4i	−0.754568	+	0.754568i	−0.975328	−	0.220760i	$-0.929146\pi$
$101$	−77357.4	+	77357.4i	−0.754568	+	0.754568i	0.220760	+	0.975328i	$0.429146\pi$
$102$	−22671.3	−	26090.5i	−0.215762	−	0.248303i
$103$	41363.9			0.384175			0.192087	−	0.981378i	$-0.438474\pi$
$103$	41363.9			0.384175			0.192087	+	0.981378i	$0.438474\pi$
$104$	−5987.41	+	69802.0i	−0.0542820	+	0.632826i
$105$	283817.	−	63561.0i	2.51226	−	0.562623i
$106$	−42774.8	−	79223.4i	−0.369763	−	0.684839i
$107$	−114432.	−	114432.i	−0.966247	−	0.966247i	0.0332021	−	0.999449i	$-0.489430\pi$
$107$	−114432.	−	114432.i	−0.966247	−	0.966247i	−0.999449	+	0.0332021i	$0.989430\pi$
$108$	78560.8	−	92311.8i	0.648107	−	0.761549i
$109$	−28677.4	+	28677.4i	−0.231193	+	0.231193i	−0.813190	−	0.581998i	$-0.802271\pi$
$109$	−28677.4	+	28677.4i	−0.231193	+	0.231193i	0.581998	+	0.813190i	$0.302271\pi$
$110$	68865.0	−	230500.i	0.542646	−	1.81631i
$111$	−13401.7	−	59842.1i	−0.103241	−	0.460998i
$112$	99415.7	+	229043.i	0.748876	+	1.72533i
$113$		−	120827.i		−	0.890157i	−0.895492	−	0.445078i	$-0.853176\pi$
$113$		−	120827.i		−	0.890157i	0.895492	−	0.445078i	$-0.146824\pi$
$114$	−5204.83	−	364.969i	−0.0375098	−	0.00263023i
$115$	63479.8	+	63479.8i	0.447601	+	0.447601i
$116$	−7143.21	−	34397.8i	−0.0492888	−	0.237348i
$117$	−88511.9	−	31785.5i	−0.597774	−	0.214667i
$118$	155808.	−	84125.0i	1.03011	−	0.556186i
$119$			95576.4i			0.618704i
$120$	130783.	−	171805.i	0.829084	−	1.08914i
$121$			147835.i			0.917937i
$122$	67826.4	+	125622.i	0.412571	+	0.764125i
$123$	84964.4	+	53871.9i	0.506377	+	0.321070i
$124$	−55730.9	+	84944.1i	−0.325493	+	0.496111i
$125$	21372.6	+	21372.6i	0.122344	+	0.122344i
$126$	−331402.	+	50191.2i	−1.85964	+	0.281645i
$127$			217896.i			1.19878i	0.800457	+	0.599391i	$0.204590\pi$
$127$			217896.i			1.19878i	−0.800457	+	0.599391i	$0.795410\pi$
$128$	165976.	+	82533.8i	0.895405	+	0.445253i
$129$	−147664.	+	33069.4i	−0.781267	+	0.174965i
$130$	−160512.	−	47955.1i	−0.833007	−	0.248872i
$131$	122214.	−	122214.i	0.622216	−	0.622216i	−0.323881	−	0.946098i	$-0.604988\pi$
$131$	122214.	−	122214.i	0.622216	−	0.622216i	0.946098	+	0.323881i	$0.104988\pi$
$132$	−97748.9	+	259434.i	−0.488289	+	1.29596i
$133$	10201.8	+	10201.8i	0.0500090	+	0.0500090i
$134$	88071.6	−	47552.2i	0.423715	−	0.228775i
$135$	177928.	+	228811.i	0.840253	+	1.08054i
$136$	45700.6	+	54276.4i	0.211873	+	0.251631i
$137$	172589.			0.785620			0.392810	−	0.919620i	$-0.371503\pi$
$137$	172589.			0.785620			0.392810	+	0.919620i	$0.371503\pi$
$138$	−67859.7	−	78094.1i	−0.303329	−	0.349077i
$139$	278539.	−	278539.i	1.22278	−	1.22278i	0.256144	−	0.966639i	$-0.417548\pi$
$139$	278539.	−	278539.i	1.22278	−	1.22278i	0.966639	−	0.256144i	$-0.0824521\pi$
$140$	−584580.	+	121396.i	−2.52071	+	0.523463i
$141$	−336595.	−	213419.i	−1.42580	−	0.904034i
$142$	−297313.	−	88826.4i	−1.23735	−	0.369676i
$143$	215097.			0.879617
$144$	−164199.	+	186965.i	−0.659878	+	0.751372i
$145$	84006.4			0.331812
$146$	−121951.	−	36434.6i	−0.473483	−	0.141459i
$147$	561483.	+	356010.i	2.14310	+	1.35884i
$148$	25596.1	+	123257.i	0.0960550	+	0.462549i
$149$	145941.	−	145941.i	0.538531	−	0.538531i	−0.384566	−	0.923097i	$-0.625649\pi$
$149$	145941.	−	145941.i	0.538531	−	0.538531i	0.923097	+	0.384566i	$0.125649\pi$
$150$	157901.	+	181715.i	0.573003	+	0.659422i
$151$	−285414.			−1.01867			−0.509334	−	0.860569i	$-0.670108\pi$
$151$	−285414.			−1.01867			−0.509334	+	0.860569i	$0.670108\pi$
$152$	10671.5	+	915.372i	0.0374643	+	0.00321358i
$153$	−86150.6	+	40624.4i	−0.297529	+	0.140300i
$154$	674562.	−	364214.i	2.29203	−	1.23753i
$155$	−171778.	−	171778.i	−0.574300	−	0.574300i
$156$	180660.	+	68068.7i	0.594362	+	0.223942i
$157$	−17693.7	+	17693.7i	−0.0572886	+	0.0572886i	−0.735171	−	0.677882i	$-0.762898\pi$
$157$	−17693.7	+	17693.7i	−0.0572886	+	0.0572886i	0.677882	+	0.735171i	$0.262898\pi$
$158$	421991.	+	126075.i	1.34481	+	0.401780i
$159$	−242106.	+	54219.8i	−0.759474	+	0.170085i
$160$	−273927.	+	348461.i	−0.845931	+	1.07610i
$161$			286079.i			0.869804i
$162$	−186103.	−	277386.i	−0.557141	−	0.830418i
$163$	−379914.	−	379914.i	−1.11999	−	1.11999i	−0.991741	−	0.128253i	$-0.959063\pi$
$163$	−379914.	−	379914.i	−1.11999	−	1.11999i	−0.128253	−	0.991741i	$-0.540937\pi$
$164$	−172673.	−	113289.i	−0.501320	−	0.328911i
$165$	−559870.	−	354987.i	−1.60095	−	1.01509i
$166$	−69873.6	−	129413.i	−0.196808	−	0.364509i
$167$			386483.i			1.07236i	0.844105	+	0.536179i	$0.180133\pi$
$167$			386483.i			1.07236i	−0.844105	+	0.536179i	$0.819867\pi$
$168$	681824.	−	92434.3i	1.86380	−	0.252674i
$169$			221508.i			0.596584i
$170$	−149293.	+	80607.2i	−0.396202	+	0.213920i
$171$	−4859.46	+	13531.9i	−0.0127086	+	0.0353891i
$172$	304144.	−	63159.9i	0.783895	−	0.162787i
$173$	3757.60	+	3757.60i	0.00954543	+	0.00954543i	0.711863	−	0.702318i	$-0.247852\pi$
$173$	3757.60	+	3757.60i	0.00954543	+	0.00954543i	−0.702318	+	0.711863i	$0.747852\pi$
$174$	−96574.5	−	6771.91i	−0.241818	−	0.0169566i
$175$		−	665671.i		−	1.64310i
$176$	208922.	−	529379.i	0.508395	−	1.28820i
$177$	−106634.	−	476149.i	−0.255836	−	1.14238i
$178$	−51432.2	+	172150.i	−0.121670	+	0.407247i
$179$	192720.	−	192720.i	0.449568	−	0.449568i	−0.445643	−	0.895211i	$-0.647025\pi$
$179$	192720.	−	192720.i	0.449568	−	0.449568i	0.895211	+	0.445643i	$0.147025\pi$
$180$	−357898.	−	475329.i	−0.823338	−	1.09349i
$181$	201579.	+	201579.i	0.457351	+	0.457351i	0.897785	−	0.440434i	$-0.145175\pi$
$181$	201579.	+	201579.i	0.457351	+	0.457351i	−0.440434	+	0.897785i	$0.645175\pi$
$182$	−253625.	−	469740.i	−0.567563	−	1.05119i
$183$	383899.	−	85974.3i	0.847401	−	0.189776i
$184$	136791.	+	162460.i	0.297861	+	0.353754i
$185$	−301019.			−0.646642
$186$	183630.	+	211325.i	0.389190	+	0.447887i
$187$	154041.	−	154041.i	0.322130	−	0.322130i
$188$	684061.	+	448805.i	1.41156	+	0.926111i
$189$	−114654.	+	916508.i	−0.233472	+	1.86630i
$190$	−7331.50	+	24539.5i	−0.0147336	+	0.0493153i
$191$	−556407.			−1.10359			−0.551797	−	0.833978i	$-0.686058\pi$
$191$	−556407.			−1.10359			−0.551797	+	0.833978i	$0.686058\pi$
$192$	342999.	−	378512.i	0.671490	−	0.741013i
$193$	−358551.			−0.692879			−0.346440	−	0.938072i	$-0.612609\pi$
$193$	−358551.			−0.692879			−0.346440	+	0.938072i	$0.612609\pi$
$194$	22862.6	−	76524.2i	0.0436136	−	0.145980i
$195$	−247200.	+	389873.i	−0.465546	+	0.734238i
$196$	−1.14110e6	−	748664.i	−2.12170	−	1.39203i
$197$	−375844.	+	375844.i	−0.689989	+	0.689989i	−0.962229	−	0.272241i	$-0.912235\pi$
$197$	−375844.	+	375844.i	−0.689989	+	0.689989i	0.272241	+	0.962229i	$0.412235\pi$
$198$	615016.	+	453229.i	1.11487	+	0.821589i
$199$	−117916.			−0.211076			−0.105538	−	0.994415i	$-0.533657\pi$
$199$	−117916.			−0.211076			−0.105538	+	0.994415i	$0.533657\pi$
$200$	−318296.	−	378024.i	−0.562673	−	0.668259i
$201$	−60275.4	−	269146.i	−0.105233	−	0.469892i
$202$	−294019.	−	544554.i	−0.506987	−	0.938994i
$203$	189292.	+	189292.i	0.322398	+	0.322398i
$204$	178126.	−	80631.9i	0.299677	−	0.135654i
$205$	349188.	−	349188.i	0.580330	−	0.580330i
$206$	−66982.0	+	224198.i	−0.109974	+	0.368098i
$207$	−257866.	+	121597.i	−0.418281	+	0.197241i
$208$	−368640.	−	145485.i	−0.590805	−	0.233164i
$209$		−	32884.6i		−	0.0520747i
$210$	−115086.	+	1.64125e6i	−0.180084	+	2.56819i
$211$	−16071.1	−	16071.1i	−0.0248507	−	0.0248507i	0.694572	−	0.719423i	$-0.255594\pi$
$211$	−16071.1	−	16071.1i	−0.0248507	−	0.0248507i	−0.719423	+	0.694572i	$0.755594\pi$
$212$	498667.	−	103556.i	0.762029	−	0.158246i
$213$	−457885.	+	722156.i	−0.691524	+	1.09064i
$214$	805539.	−	434932.i	1.20241	−	0.649212i
$215$			742780.i			1.09588i
$216$	373125.	+	575293.i	0.544152	+	0.838986i
$217$		−	774138.i		−	1.11601i
$218$	−108997.	−	201874.i	−0.155336	−	0.287699i
$219$	−187814.	+	296212.i	−0.264617	+	0.417342i
$220$	1.13782e6	+	746514.i	1.58496	+	1.03988i
$221$	−107268.	−	107268.i	−0.147738	−	0.147738i
$222$	346053.	+	24265.7i	0.471260	+	0.0330453i
$223$			476629.i			0.641827i	0.947108	+	0.320914i	$0.103990\pi$
$223$			476629.i			0.641827i	−0.947108	+	0.320914i	$0.896010\pi$
$224$	−1.40243e6	+	167947.i	−1.86750	+	0.223642i
$225$	600022.	−	282941.i	0.790153	−	0.372598i
$226$	654895.	+	195659.i	0.852905	+	0.254817i
$227$	44829.4	−	44829.4i	0.0577428	−	0.0577428i	−0.677646	−	0.735389i	$-0.737000\pi$
$227$	44829.4	−	44829.4i	0.0577428	−	0.0577428i	0.735389	+	0.677646i	$0.237000\pi$
$228$	10406.5	−	27619.8i	0.0132577	−	0.0351871i
$229$	959653.	+	959653.i	1.20928	+	1.20928i	0.971261	+	0.238015i	$0.0764967\pi$
$229$	959653.	+	959653.i	1.20928	+	1.20928i	0.238015	+	0.971261i	$0.423503\pi$
$230$	−446863.	+	241273.i	−0.557000	+	0.300739i
$231$	−461664.	−	2.06146e6i	−0.569241	−	2.54182i
$232$	198008.	+	16984.5i	0.241525	+	0.0207173i
$233$	187170.			0.225864			0.112932	−	0.993603i	$-0.463976\pi$
$233$	187170.			0.225864			0.112932	+	0.993603i	$0.463976\pi$
$234$	315612.	−	428274.i	0.376803	−	0.511308i
$235$	−1.38334e6	+	1.38334e6i	−1.63403	+	1.63403i
$236$	203662.	+	980727.i	0.238029	+	1.14622i
$237$	649898.	−	1.02499e6i	0.751578	−	1.18536i
$238$	−518036.	−	154770.i	−0.592813	−	0.177111i
$239$	1.62427e6			1.83935			0.919674	−	0.392684i	$-0.128453\pi$
$239$	1.62427e6			1.83935			0.919674	+	0.392684i	$0.128453\pi$
$240$	719421.	+	987070.i	0.806223	+	1.10616i
$241$	1.16791e6			1.29529			0.647643	−	0.761944i	$-0.275755\pi$
$241$	1.16791e6			1.29529			0.647643	+	0.761944i	$0.275755\pi$
$242$	−801282.	−	239394.i	−0.879523	−	0.262769i
$243$	−874855.	+	286212.i	−0.950431	+	0.310937i
$244$	−790718.	+	164204.i	−0.850251	+	0.176567i
$245$	2.30759e6	−	2.30759e6i	2.45609	−	2.45609i
$246$	−429578.	+	373281.i	−0.452590	+	0.393277i
$247$	−22899.6			−0.0238828
$248$	−370160.	−	439621.i	−0.382174	−	0.453889i
$249$	−395486.	+	88569.3i	−0.404234	+	0.0905284i
$250$	−150452.	+	81232.9i	−0.152246	+	0.0822019i
$251$	−157772.	−	157772.i	−0.158069	−	0.158069i	0.623642	−	0.781710i	$-0.285652\pi$
$251$	−157772.	−	157772.i	−0.158069	−	0.158069i	−0.781710	+	0.623642i	$0.785652\pi$
$252$	264609.	−	1.87752e6i	0.262484	−	1.86244i
$253$	461075.	−	461075.i	0.452866	−	0.452866i
$254$	−1.18102e6	−	352847.i	−1.14861	−	0.343164i
$255$	102175.	+	456238.i	0.0983996	+	0.439381i
$256$	−716114.	+	765959.i	−0.682939	+	0.730475i
$257$			2.11313e6i			1.99569i	0.0655993	+	0.997846i	$0.479104\pi$
$257$			2.11313e6i			1.99569i	−0.0655993	+	0.997846i	$0.520896\pi$
$258$	59876.9	−	853906.i	0.0560028	−	0.798658i
$259$	−678288.	−	678288.i	−0.628296	−	0.628296i
$260$	519845.	−	792339.i	0.476914	−	0.726905i
$261$	−90166.2	+	251082.i	−0.0819299	+	0.228147i
$262$	464508.	+	860318.i	0.418062	+	0.774294i
$263$		−	1.50282e6i		−	1.33973i	−0.742484	−	0.669864i	$-0.766352\pi$
$263$		−	1.50282e6i		−	1.33973i	0.742484	−	0.669864i	$-0.233648\pi$
$264$	−1.24787e6	−	949921.i	−1.10195	−	0.838837i
$265$			1.21785e6i			1.06531i
$266$	−71815.2	+	38774.9i	−0.0622318	+	0.0336006i
$267$	418142.	+	265124.i	0.358960	+	0.227599i
$268$	115121.	+	554362.i	0.0979081	+	0.471472i
$269$	859814.	+	859814.i	0.724476	+	0.724476i	0.969514	−	0.245038i	$-0.0788004\pi$
$269$	859814.	+	859814.i	0.724476	+	0.724476i	−0.245038	+	0.969514i	$0.578800\pi$
$270$	−1.52831e6	+	593872.i	−1.27585	+	0.495773i
$271$			156068.i			0.129089i	0.997915	+	0.0645446i	$0.0205595\pi$
$271$			156068.i			0.129089i	−0.997915	+	0.0645446i	$0.979441\pi$
$272$	−368189.	+	159812.i	−0.301751	+	0.130974i
$273$	−1.43552e6	+	321486.i	−1.16575	+	0.261069i
$274$	−279480.	+	935456.i	−0.224892	+	0.752743i
$275$	−1.07286e6	+	1.07286e6i	−0.855486	+	0.855486i
$276$	533168.	−	241347.i	0.421300	−	0.190708i
$277$	−1.20128e6	−	1.20128e6i	−0.940684	−	0.940684i	0.0576530	−	0.998337i	$-0.481638\pi$
$277$	−1.20128e6	−	1.20128e6i	−0.940684	−	0.940684i	−0.998337	+	0.0576530i	$0.981638\pi$
$278$	1.05867e6	+	1.96077e6i	0.821577	+	1.52165i
$279$	697793.	−	329045.i	0.536681	−	0.253072i
$280$	288646.	−	3.36508e6i	0.220024	−	2.56507i
$281$	−1.33726e6			−1.01030			−0.505149	−	0.863032i	$-0.668563\pi$
$281$	−1.33726e6			−1.01030			−0.505149	+	0.863032i	$0.668563\pi$
$282$	1.70182e6	−	1.47879e6i	1.27435	−	1.10735i
$283$	1.25170e6	−	1.25170e6i	0.929037	−	0.929037i	−0.0686066	−	0.997644i	$-0.521855\pi$
$283$	1.25170e6	−	1.25170e6i	0.929037	−	0.929037i	0.997644	+	0.0686066i	$0.0218553\pi$
$284$	962900.	−	1.46764e6i	0.708411	−	1.07975i
$285$	59604.9	+	37792.7i	0.0434680	+	0.0275610i
$286$	−348314.	+	1.16585e6i	−0.251800	+	0.842807i
$287$	1.57366e6			1.12773
$288$	−747483.	−	1.19274e6i	−0.531031	−	0.847352i
$289$	1.26622e6			0.891792
$290$	−136034.	+	455325.i	−0.0949848	+	0.317926i
$291$	−185873.	−	117853.i	−0.128672	−	0.0815846i
$292$	394960.	−	601992.i	0.271079	−	0.413174i
$293$	426724.	−	426724.i	0.290387	−	0.290387i	−0.546846	−	0.837233i	$-0.684172\pi$
$293$	426724.	−	426724.i	0.290387	−	0.290387i	0.837233	+	0.546846i	$0.184172\pi$
$294$	−2.83885e6	+	2.46681e6i	−1.91546	+	1.66444i
$295$	−2.39513e6			−1.60241
$296$	−709518.	−	60860.3i	−0.470689	−	0.0403743i
$297$	1.66193e6	−	1.29235e6i	1.09325	−	0.850138i
$298$	554690.	+	1.02734e6i	0.361834	+	0.670155i
$299$	−321076.	−	321076.i	−0.207697	−	0.207697i
$300$	−1.24062e6	+	561586.i	−0.795855	+	0.360257i
$301$	−1.67371e6	+	1.67371e6i	−1.06479	+	1.06479i
$302$	462181.	−	1.54698e6i	0.291605	−	0.976039i
$303$	−1.66415e6	+	372688.i	−1.04133	+	0.233206i
$304$	−22242.2	+	56358.7i	−0.0138036	+	0.0349765i
$305$		−	1.93109e6i		−	1.18865i
$306$	−80682.8	−	532732.i	−0.0492581	−	0.325241i
$307$	−25881.4	−	25881.4i	−0.0156726	−	0.0156726i	0.699227	−	0.714900i	$-0.253528\pi$
$307$	−25881.4	−	25881.4i	−0.0156726	−	0.0156726i	−0.714900	+	0.699227i	$0.753528\pi$
$308$	881743.	+	4.24599e6i	0.529621	+	2.55037i
$309$	544562.	+	345281.i	0.324452	+	0.205720i
$310$	1.20923e6	−	652892.i	0.714666	−	0.385867i
$311$		−	1.71603e6i		−	1.00606i	−0.864269	−	0.503030i	$-0.832218\pi$
$311$		−	1.71603e6i		−	1.00606i	0.864269	−	0.503030i	$-0.167782\pi$
$312$	−661490.	+	868974.i	−0.384713	+	0.505383i
$313$			226091.i			0.130443i	0.997871	+	0.0652217i	$0.0207755\pi$
$313$			226091.i			0.130443i	−0.997871	+	0.0652217i	$0.979225\pi$
$314$	−67249.9	−	124554.i	−0.0384917	−	0.0712907i
$315$	4.26706e6	+	1.53234e6i	2.42299	+	0.870121i
$316$	−1.36669e6	+	2.08309e6i	−0.769932	+	1.17352i
$317$	1.55234e6	+	1.55234e6i	0.867638	+	0.867638i	0.992211	−	0.124572i	$-0.0397559\pi$
$317$	1.55234e6	+	1.55234e6i	0.867638	+	0.867638i	−0.124572	+	0.992211i	$0.539756\pi$
$318$	98172.8	−	1.40005e6i	0.0544407	−	0.776380i
$319$		−	610166.i		−	0.335715i
$320$	−1.44512e6	−	2.04899e6i	−0.788913	−	1.11858i
$321$	−551304.	−	2.46172e6i	−0.298627	−	1.33345i
$322$	−1.55058e6	−	463258.i	−0.833404	−	0.248991i
$323$	−16399.5	+	16399.5i	−0.00874629	+	0.00874629i
$324$	1.80483e6	−	559520.i	0.955154	−	0.296110i
$325$	747103.	+	747103.i	0.392349	+	0.392349i
$326$	2.67439e6	−	1.44397e6i	1.39374	−	0.752515i
$327$	−616924.	+	138160.i	−0.319053	+	0.0714520i
$328$	893656.	−	752457.i	0.458655	−	0.386187i
$329$	−6.23419e6			−3.17534
$330$	2.83069e6	−	2.45972e6i	1.43090	−	1.24337i
$331$	−2.06694e6	+	2.06694e6i	−1.03695	+	1.03695i	−0.0376572	+	0.999291i	$0.511989\pi$
$331$	−2.06694e6	+	2.06694e6i	−1.03695	+	1.03695i	−0.999291	+	0.0376572i	$0.988011\pi$
$332$	814585.	−	169160.i	0.405593	−	0.0842274i
$333$	323091.	−	899699.i	0.159667	−	0.444618i
$334$	−2.09479e6	−	625846.i	−1.02748	−	0.306974i
$335$	−1.35386e6			−0.659117
$336$	−603095.	+	3.84525e6i	−0.291432	+	1.85813i
$337$	1.29072e6			0.619094			0.309547	−	0.950884i	$-0.399823\pi$
$337$	1.29072e6			0.619094			0.309547	+	0.950884i	$0.399823\pi$
$338$	−1.20060e6	−	358695.i	−0.571618	−	0.170779i
$339$	1.00859e6	−	1.59070e6i	0.476666	−	0.751777i
$340$	−195146.	−	939717.i	−0.0915507	−	0.440859i
$341$	−1.24768e6	+	1.24768e6i	−0.581056	+	0.581056i
$342$	−65475.8	−	48251.6i	−0.0302702	−	0.0223073i
$343$	6.30128e6			2.89197
$344$	−150176.	+	1.75077e6i	−0.0684235	+	0.797690i
$345$	305829.	+	1.36561e6i	0.138335	+	0.617703i
$346$	−26451.5	+	14281.9i	−0.0118785	+	0.00641349i
$347$	−844248.	−	844248.i	−0.376397	−	0.376397i	0.493403	−	0.869801i	$-0.335753\pi$
$347$	−844248.	−	844248.i	−0.376397	−	0.376397i	−0.869801	+	0.493403i	$0.835753\pi$
$348$	193091.	−	512480.i	0.0854700	−	0.226845i
$349$	−630323.	+	630323.i	−0.277013	+	0.277013i	−0.831915	−	0.554903i	$-0.812756\pi$
$349$	−630323.	+	630323.i	−0.277013	+	0.277013i	0.554903	+	0.831915i	$0.312756\pi$
$350$	3.60802e6	+	1.07794e6i	1.57434	+	0.470355i
$351$	−899946.	−	1.15731e6i	−0.389896	−	0.501395i
$352$	2.53098e6	+	1.98962e6i	1.08876	+	0.855882i
$353$		−	98069.2i		−	0.0418886i	−0.999781	−	0.0209443i	$-0.993333\pi$
$353$		−	98069.2i		−	0.0418886i	0.999781	−	0.0209443i	$-0.00666727\pi$
$354$	2.75346e6	+	193076.i	1.16781	+	0.0818880i
$355$	2.96793e6	+	2.96793e6i	1.24992	+	1.24992i
$356$	−849790.	−	557538.i	−0.355375	−	0.233157i
$357$	−797814.	+	1.25828e6i	−0.331307	+	0.522523i
$358$	732490.	+	1.35665e6i	0.302061	+	0.559448i
$359$			3.22677e6i			1.32139i	0.750654	+	0.660695i	$0.229739\pi$
$359$			3.22677e6i			1.32139i	−0.750654	+	0.660695i	$0.770261\pi$
$360$	3.15590e6	−	1.17013e6i	1.28341	−	0.475860i
$361$		−	2.47260e6i		−	0.998586i
$362$	−1.41901e6	+	766160.i	−0.569133	+	0.307290i
$363$	−1.23403e6	+	1.94626e6i	−0.491542	+	0.775238i
$364$	2.95676e6	−	614013.i	1.16967	−	0.242898i
$365$	1.21738e6	+	1.21738e6i	0.478292	+	0.478292i
$366$	−155669.	+	2.22000e6i	−0.0607434	+	0.866264i
$367$		−	1.77055e6i		−	0.686188i	−0.939301	−	0.343094i	$-0.888525\pi$
$367$		−	1.77055e6i		−	0.686188i	0.939301	−	0.343094i	$-0.111475\pi$
$368$	−1.10206e6	+	478348.i	−0.424216	+	0.184130i
$369$	668878.	+	1.41846e6i	0.255730	+	0.542316i
$370$	487450.	−	1.63156e6i	0.185108	−	0.619581i
$371$	−2.74418e6	+	2.74418e6i	−1.03509	+	1.03509i
$372$	−1.44277e6	+	653093.i	−0.540554	+	0.244691i
$373$	−2.21121e6	−	2.21121e6i	−0.822920	−	0.822920i	0.163606	−	0.986526i	$-0.447687\pi$
$373$	−2.21121e6	−	2.21121e6i	−0.822920	−	0.822920i	−0.986526	+	0.163606i	$0.947687\pi$
$374$	585477.	+	1.08436e6i	0.216437	+	0.400863i
$375$	102968.	+	459779.i	0.0378115	+	0.168838i
$376$	−3.54030e6	+	2.98093e6i	−1.29143	+	1.08738i
$377$	−424897.			−0.153968
$378$	−4.78192e6	−	2.10557e6i	−1.72137	−	0.757950i
$379$	1.47414e6	−	1.47414e6i	0.527159	−	0.527159i	−0.392565	−	0.919724i	$-0.628412\pi$
$379$	1.47414e6	−	1.47414e6i	0.527159	−	0.527159i	0.919724	+	0.392565i	$0.128412\pi$
$380$	−121135.	−	79475.3i	−0.0430339	−	0.0282341i
$381$	−1.81886e6	+	2.86863e6i	−0.641930	+	1.01242i
$382$	901010.	−	3.01580e6i	0.315916	−	1.05741i
$383$	−1.90840e6			−0.664772			−0.332386	−	0.943144i	$-0.607854\pi$
$383$	−1.90840e6			−0.664772			−0.332386	+	0.943144i	$0.607854\pi$
$384$	1.49615e6	+	2.47203e6i	0.517782	+	0.855513i
$385$	−1.03696e7			−3.56540
$386$	580614.	−	1.94339e6i	0.198344	−	0.663883i
$387$	−2.22006e6	−	797244.i	−0.753506	−	0.270591i
$388$	377749.	+	247837.i	0.127387	+	0.0835769i
$389$	4.06091e6	−	4.06091e6i	1.36066	−	1.36066i	0.487580	−	0.873078i	$-0.337880\pi$
$389$	4.06091e6	−	4.06091e6i	1.36066	−	1.36066i	0.873078	−	0.487580i	$-0.162120\pi$
$390$	−1.71286e6	−	1.97119e6i	−0.570244	−	0.656247i
$391$	−459875.			−0.152124
$392$	5.90568e6	−	4.97258e6i	1.94113	−	1.63443i
$393$	2.62913e6	−	588794.i	0.858677	−	0.192301i
$394$	−1.42850e6	−	2.64574e6i	−0.463597	−	0.858630i
$395$	−4.21252e6	−	4.21252e6i	−1.35847	−	1.35847i
$396$	−3.45247e6	+	2.59953e6i	−1.10635	+	0.833023i
$397$	437863.	−	437863.i	0.139432	−	0.139432i	−0.633946	−	0.773378i	$-0.718566\pi$
$397$	437863.	−	437863.i	0.139432	−	0.139432i	0.773378	+	0.633946i	$0.218566\pi$
$398$	190945.	−	639119.i	0.0604229	−	0.202243i
$399$	49149.7	+	219467.i	0.0154557	+	0.0690139i
$400$	2.56437e6	−	1.11306e6i	0.801364	−	0.347830i
$401$			4.35443e6i			1.35229i	0.736768	+	0.676146i	$0.236351\pi$
$401$			4.35443e6i			1.35229i	−0.736768	+	0.676146i	$0.763649\pi$
$402$	1.55641e6	+	109137.i	0.480352	+	0.0336828i
$403$	868840.	+	868840.i	0.266488	+	0.266488i
$404$	3.42767e6	−	711805.i	1.04483	−	0.216974i
$405$	432476.	+	4.49756e6i	0.131016	+	1.36251i
$406$	−1.33252e6	+	719460.i	−0.401197	+	0.216617i
$407$			2.18640e6i			0.654249i
$408$	148589.	+	1.09604e6i	0.0441912	+	0.325968i
$409$		−	4.39918e6i		−	1.30036i	−0.759780	−	0.650180i	$-0.774694\pi$
$409$		−	4.39918e6i		−	1.30036i	0.759780	−	0.650180i	$-0.225306\pi$
$410$	1.32719e6	+	2.45810e6i	0.389918	+	0.722170i
$411$	2.27216e6	+	1.44067e6i	0.663491	+	0.420688i
$412$	−1.10671e6	−	726102.i	−0.321212	−	0.210744i
$413$	−5.39697e6	−	5.39697e6i	−1.55695	−	1.55695i
$414$	−241500.	−	1.59457e6i	−0.0692493	−	0.457239i
$415$			1.98938e6i			0.567018i
$416$	1.38550e6	−	1.76249e6i	0.392530	−	0.499335i
$417$	5.99208e6	−	1.34193e6i	1.68748	−	0.377911i
$418$	178238.	+	53251.1i	0.0498954	+	0.0149069i
$419$	3.78399e6	−	3.78399e6i	1.05297	−	1.05297i	0.0544505	−	0.998516i	$-0.482659\pi$
$419$	3.78399e6	−	3.78399e6i	1.05297	−	1.05297i	0.998516	−	0.0544505i	$-0.0173407\pi$
$420$	−8.70942e6	−	3.28152e6i	−2.40916	−	0.907719i
$421$	−1.12783e6	−	1.12783e6i	−0.310126	−	0.310126i	0.534832	−	0.844958i	$-0.320375\pi$
$421$	−1.12783e6	−	1.12783e6i	−0.310126	−	0.310126i	−0.844958	+	0.534832i	$0.820375\pi$
$422$	113132.	−	61082.7i	0.0309245	−	0.0166970i
$423$	−2.64982e6	−	5.61938e6i	−0.720056	−	1.52699i
$424$	−246226.	+	2.87053e6i	−0.0665149	+	0.775439i
$425$	1.07007e6			0.287369
$426$	−3.17271e6	−	3.65121e6i	−0.847043	−	0.974793i
$427$	4.35135e6	−	4.35135e6i	1.15493	−	1.15493i
$428$	1.05295e6	+	5.07042e6i	0.277842	+	1.33793i
$429$	2.83178e6	+	1.79550e6i	0.742876	+	0.471022i
$430$	−4.02596e6	−	1.20281e6i	−1.05002	−	0.313708i
$431$	6.78289e6			1.75882			0.879410	−	0.476065i	$-0.157937\pi$
$431$	6.78289e6			1.75882			0.879410	+	0.476065i	$0.157937\pi$
$432$	−3.72238e6	+	1.09079e6i	−0.959646	+	0.281212i
$433$	993742.			0.254715			0.127357	−	0.991857i	$-0.459351\pi$
$433$	993742.			0.254715			0.127357	+	0.991857i	$0.459351\pi$
$434$	4.19593e6	+	1.25359e6i	1.06931	+	0.319471i
$435$	1.10596e6	+	701235.i	0.280230	+	0.177681i
$436$	1.27068e6	−	263876.i	0.320126	−	0.0664788i
$437$	−49086.9	+	49086.9i	−0.0122960	+	0.0122960i
$438$	−1.30137e6	−	1.49764e6i	−0.324128	−	0.373012i
$439$	524185.			0.129815			0.0649073	−	0.997891i	$-0.479325\pi$
$439$	524185.			0.129815			0.0649073	+	0.997891i	$0.479325\pi$
$440$	−5.88872e6	+	4.95829e6i	−1.45007	+	1.22096i
$441$	4.42025e6	+	9.37385e6i	1.08231	+	2.29520i
$442$	755112.	−	407705.i	0.183847	−	0.0992636i
$443$	446438.	+	446438.i	0.108082	+	0.108082i	0.759080	−	0.650998i	$-0.225649\pi$
$443$	446438.	+	446438.i	0.108082	+	0.108082i	−0.650998	+	0.759080i	$0.725649\pi$
$444$	−691899.	+	1.83636e6i	−0.166566	+	0.442079i
$445$	1.71849e6	−	1.71849e6i	0.411383	−	0.411383i
$446$	−2.58339e6	−	771822.i	−0.614968	−	0.183730i
$447$	3.13956e6	−	703105.i	0.743189	−	0.166438i
$448$	1.36071e6	−	7.87332e6i	0.320310	−	1.85337i
$449$		−	5.79255e6i		−	1.35598i	−0.735070	−	0.677991i	$-0.762851\pi$
$449$		−	5.79255e6i		−	1.35598i	0.735070	−	0.677991i	$-0.237149\pi$
$450$	561940.	+	3.71037e6i	0.130815	+	0.863746i
$451$	−2.53627e6	−	2.53627e6i	−0.587157	−	0.587157i
$452$	−2.12099e6	+	3.23278e6i	−0.488307	+	0.744269i
$453$	−3.75751e6	−	2.38246e6i	−0.860310	−	0.545482i
$454$	170387.	+	315574.i	0.0387969	+	0.0718559i
$455$			7.22099e6i			1.63519i
$456$	132851.	+	101130.i	0.0299194	+	0.0227756i
$457$			6.10872e6i			1.36823i	0.729373	+	0.684116i	$0.239812\pi$
$457$			6.10872e6i			1.36823i	−0.729373	+	0.684116i	$0.760188\pi$
$458$	−6.75544e6	+	3.64744e6i	−1.50484	+	0.812502i
$459$	−1.47329e6	−	184307.i	−0.326406	−	0.0408329i
$460$	−584110.	−	2.81276e6i	−0.128706	−	0.619780i
$461$	−2.60418e6	−	2.60418e6i	−0.570715	−	0.570715i	0.361613	−	0.932328i	$-0.382226\pi$
$461$	−2.60418e6	−	2.60418e6i	−0.570715	−	0.570715i	−0.932328	+	0.361613i	$0.882226\pi$
$462$	1.19209e7	+	835910.i	2.59840	+	0.182203i
$463$			5.57281e6i			1.20815i	0.796926	+	0.604076i	$0.206458\pi$
$463$			5.57281e6i			1.20815i	−0.796926	+	0.604076i	$0.793542\pi$
$464$	−412699.	+	1.04572e6i	−0.0889895	+	0.225487i
$465$	−827583.	−	3.69538e6i	−0.177492	−	0.792551i
$466$	−303091.	+	1.01448e6i	−0.0646559	+	0.216412i
$467$	4.33253e6	−	4.33253e6i	0.919283	−	0.919283i	−0.0776945	−	0.996977i	$-0.524756\pi$
$467$	4.33253e6	−	4.33253e6i	0.919283	−	0.919283i	0.996977	+	0.0776945i	$0.0247559\pi$
$468$	1.81022e6	+	2.40418e6i	0.382047	+	0.507401i
$469$	−3.05067e6	−	3.05067e6i	−0.640417	−	0.640417i
$470$	−5.25779e6	−	9.73798e6i	−1.09789	−	2.03341i
$471$	−380635.	+	85243.5i	−0.0790600	+	0.0177055i
$472$	−5.64546e6	−	484251.i	−1.16639	−	0.100050i
$473$	5.39505e6			1.10877
$474$	4.50317e6	+	5.18233e6i	0.920603	+	1.05945i
$475$	114219.	−	114219.i	0.0232276	−	0.0232276i
$476$	1.67775e6	−	2.55720e6i	0.339398	−	0.517305i
$477$	−3.63996e6	−	1.30714e6i	−0.732487	−	0.263044i
$478$	−2.63024e6	+	8.80375e6i	−0.526533	+	1.76237i
$479$	−4.25123e6			−0.846596			−0.423298	−	0.905990i	$-0.639128\pi$
$479$	−4.25123e6			−0.846596			−0.423298	+	0.905990i	$0.639128\pi$
$480$	−6.51503e6	+	2.30096e6i	−1.29066	+	0.455832i
$481$	1.52253e6			0.300056
$482$	−1.89123e6	+	6.33020e6i	−0.370789	+	1.24108i
$483$	−2.38802e6	+	3.76627e6i	−0.465768	+	0.734588i
$484$	2.59509e6	−	3.95539e6i	0.503546	−	0.767496i
$485$	−763902.	+	763902.i	−0.147463	+	0.147463i
$486$	−134622.	−	5.20530e6i	−0.0258538	−	0.999666i
$487$	1.42032e6			0.271371			0.135685	−	0.990752i	$-0.456676\pi$
$487$	1.42032e6			0.271371			0.135685	+	0.990752i	$0.456676\pi$
$488$	390431.	−	4.55169e6i	0.0742155	−	0.865214i
$489$	−1.83033e6	−	8.17291e6i	−0.346144	−	1.54563i
$490$	8.77068e6	+	1.62442e7i	1.65022	+	3.05639i
$491$	3.34778e6	+	3.34778e6i	0.626690	+	0.626690i	0.947234	−	0.320543i	$-0.103866\pi$
$491$	3.34778e6	+	3.34778e6i	0.626690	+	0.626690i	−0.320543	+	0.947234i	$0.603866\pi$
$492$	−1.32760e6	−	2.93284e6i	−0.247260	−	0.546229i
$493$	−304289.	+	304289.i	−0.0563857	+	0.0563857i
$494$	37082.1	−	124119.i	0.00683672	−	0.0228834i
$495$	−4.40755e6	−	9.34692e6i	−0.808508	−	1.71457i
$496$	2.98222e6	−	1.29442e6i	0.544296	−	0.236250i
$497$			1.33753e7i			2.42892i
$498$	160368.	−	2.28701e6i	0.0289763	−	0.413232i
$499$	3.44315e6	+	3.44315e6i	0.619019	+	0.619019i	0.945280	−	0.326261i	$-0.105789\pi$
$499$	3.44315e6	+	3.44315e6i	0.619019	+	0.619019i	−0.326261	+	0.945280i	$0.605789\pi$
$500$	−196660.	−	947011.i	−0.0351797	−	0.169406i
$501$	−3.22613e6	+	5.08811e6i	−0.574232	+	0.905653i
$502$	1.11063e6	−	599659.i	0.196703	−	0.106205i
$503$			1.02992e6i			0.181502i	0.995874	+	0.0907511i	$0.0289268\pi$
$503$			1.02992e6i			0.181502i	−0.995874	+	0.0907511i	$0.971073\pi$
$504$	9.74789e6	+	4.47454e6i	1.70936	+	0.784643i
$505$			8.37105e6i			1.46067i
$506$	1.75245e6	+	3.24572e6i	0.304277	+	0.563553i
$507$	−1.84901e6	+	2.91618e6i	−0.319462	+	0.503842i
$508$	3.82494e6	−	5.82992e6i	0.657606	−	1.00231i
$509$	−1.39865e6	−	1.39865e6i	−0.239284	−	0.239284i	0.577270	−	0.816554i	$-0.304118\pi$
$509$	−1.39865e6	−	1.39865e6i	−0.239284	−	0.239284i	−0.816554	+	0.577270i	$0.804118\pi$
$510$	−2.63832e6	−	185002.i	−0.449162	−	0.0314957i
$511$			5.48625e6i			0.929445i
$512$	−2.99196e6	−	5.12177e6i	−0.504407	−	0.863466i
$513$	−176932.	+	137586.i	−0.0296834	+	0.0230824i
$514$	−1.14534e7	−	3.42187e6i	−1.91218	−	0.571288i
$515$	2.23805e6	−	2.23805e6i	0.371836	−	0.371836i
$516$	4.53132e6	+	1.70730e6i	0.749204	+	0.282283i
$517$	1.00477e7	+	1.00477e7i	1.65325	+	1.65325i
$518$	4.77478e6	−	2.57803e6i	0.781860	−	0.422147i
$519$	18103.2	+	80835.6i	0.00295010	+	0.0131730i
$520$	3.45277e6	+	4.10069e6i	0.559964	+	0.665041i
$521$	1.11797e7			1.80441			0.902205	−	0.431306i	$-0.141947\pi$
$521$	1.11797e7			1.80441			0.902205	+	0.431306i	$0.141947\pi$
$522$	−1.21489e6	−	895298.i	−0.195146	−	0.143811i
$523$	−2.17310e6	+	2.17310e6i	−0.347397	+	0.347397i	−0.859139	−	0.511742i	$-0.829000\pi$
$523$	−2.17310e6	+	2.17310e6i	−0.347397	+	0.347397i	0.511742	+	0.859139i	$0.329000\pi$
$524$	−5.41522e6	+	1.12455e6i	−0.861565	+	0.178917i
$525$	5.55662e6	−	8.76365e6i	0.879857	−	1.38767i
$526$	8.14546e6	+	2.43356e6i	1.28366	+	0.383512i
$527$	1.24443e6			0.195184
$528$	7.16942e6	−	5.22539e6i	1.11918	−	0.815707i
$529$	5.05985e6			0.786137
$530$	−6.60087e6	−	1.97210e6i	−1.02073	−	0.304957i
$531$	2.57075e6	−	7.15868e6i	0.395662	−	1.10178i
$532$	−93872.0	−	452037.i	−0.0143799	−	0.0692460i
$533$	−1.76617e6	+	1.76617e6i	−0.269286	+	0.269286i
$534$	−2.11412e6	+	1.83706e6i	−0.320831	+	0.278785i
$535$	−1.23830e7			−1.87043
$536$	−3.19113e6	−	273726.i	−0.479769	−	0.0411532i
$537$	4.14591e6	−	928478.i	0.620417	−	0.138943i
$538$	−6.05263e6	+	3.26797e6i	−0.901547	+	0.486769i
$539$	−1.67608e7	−	1.67608e7i	−2.48498	−	2.48498i
$540$	−744017.	−	9.24529e6i	−0.109799	−	1.36438i
$541$	4.35172e6	−	4.35172e6i	0.639246	−	0.639246i	−0.311123	−	0.950370i	$-0.600705\pi$
$541$	4.35172e6	−	4.35172e6i	0.639246	−	0.639246i	0.950370	+	0.311123i	$0.100705\pi$
$542$	−845907.	−	252726.i	−0.123687	−	0.0369532i
$543$	971157.	+	4.33648e6i	0.141348	+	0.631158i
$544$	−269977.	−	2.25442e6i	−0.0391137	−	0.326616i
$545$			3.10326e6i			0.447535i
$546$	582097.	−	8.30131e6i	0.0835630	−	1.19169i
$547$	−5.46561e6	−	5.46561e6i	−0.781034	−	0.781034i	0.198971	−	0.980005i	$-0.436240\pi$
$547$	−5.46561e6	−	5.46561e6i	−0.781034	−	0.781034i	−0.980005	+	0.198971i	$0.936240\pi$
$548$	−4.61772e6	−	3.02963e6i	−0.656865	−	0.430962i
$549$	5.77174e6	+	2.07269e6i	0.817290	+	0.293497i
$550$	−4.07773e6	−	7.55238e6i	−0.574793	−	1.06458i
$551$			64959.5i			0.00911514i
$552$	444756.	+	3.28066e6i	0.0621261	+	0.458261i
$553$		−	1.89842e7i		−	2.63985i
$554$	8.45634e6	−	4.56580e6i	1.17060	−	0.632037i
$555$	−3.96295e6	−	2.51272e6i	−0.546118	−	0.346268i
$556$	−1.23419e7	+	2.56298e6i	−1.69315	+	0.351608i
$557$	2.71130e6	+	2.71130e6i	0.370288	+	0.370288i	0.867582	−	0.497294i	$-0.165673\pi$
$557$	2.71130e6	+	2.71130e6i	0.370288	+	0.370288i	−0.497294	+	0.867582i	$0.665673\pi$
$558$	653505.	+	4.31496e6i	0.0888512	+	0.586666i
$559$		−	3.75692e6i		−	0.508513i
$560$	1.77717e7	+	7.01368e6i	2.39474	+	0.945096i
$561$	3.31381e6	−	742129.i	0.444550	−	0.0995572i
$562$	2.16547e6	−	7.24811e6i	0.289209	−	0.968020i
$563$	−6.58696e6	+	6.58696e6i	−0.875818	+	0.875818i	−0.993099	−	0.117281i	$-0.962582\pi$
$563$	−6.58696e6	+	6.58696e6i	−0.875818	+	0.875818i	0.117281	+	0.993099i	$0.462582\pi$
$564$	5.25941e6	+	1.16187e7i	0.696208	+	1.53801i
$565$	−6.53748e6	−	6.53748e6i	−0.861568	−	0.861568i
$566$	4.75744e6	+	8.81127e6i	0.624212	+	1.15611i
$567$	−9.15989e6	+	1.11089e7i	−1.19655	+	1.45115i
$568$	6.39552e6	+	7.59563e6i	0.831773	+	0.987855i
$569$	−6.96682e6			−0.902098			−0.451049	−	0.892499i	$-0.648950\pi$
$569$	−6.96682e6			−0.902098			−0.451049	+	0.892499i	$0.648950\pi$
$570$	−301361.	+	261867.i	−0.0388508	+	0.0337593i
$571$	−9.85411e6	+	9.85411e6i	−1.26482	+	1.26482i	−0.316084	+	0.948731i	$0.602368\pi$
$571$	−9.85411e6	+	9.85411e6i	−1.26482	+	1.26482i	−0.948731	+	0.316084i	$0.897632\pi$
$572$	−5.75502e6	−	3.77581e6i	−0.735456	−	0.482525i
$573$	−7.32518e6	−	4.64455e6i	−0.932034	−	0.590959i
$574$	−2.54828e6	+	8.52942e6i	−0.322825	+	1.08054i
$575$	3.20294e6			0.403997
$576$	7.67522e6	−	2.12001e6i	0.963905	−	0.266245i
$577$	−7.40419e6			−0.925845			−0.462922	−	0.886399i	$-0.653199\pi$
$577$	−7.40419e6			−0.925845			−0.462922	+	0.886399i	$0.653199\pi$
$578$	−2.05043e6	+	6.86306e6i	−0.255285	+	0.854472i
$579$	−4.72037e6	−	2.99297e6i	−0.585167	−	0.371027i
$580$	−2.24763e6	−	1.47465e6i	−0.277431	−	0.182020i
$581$	−4.48268e6	+	4.48268e6i	−0.550932	+	0.550932i
$582$	939768.	−	816609.i	0.115004	−	0.0999325i
$583$	8.84561e6			1.07785
$584$	2.62330e6	+	3.11556e6i	0.318284	+	0.378010i
$585$	−6.50885e6	+	3.06926e6i	−0.786348	+	0.370803i
$586$	1.62189e6	+	3.00390e6i	0.195109	+	0.361362i
$587$	7.27299e6	+	7.27299e6i	0.871200	+	0.871200i	0.992603	−	0.121403i	$-0.0387395\pi$
$587$	7.27299e6	+	7.27299e6i	0.871200	+	0.871200i	−0.121403	+	0.992603i	$0.538739\pi$
$588$	−8.77337e6	−	1.93815e7i	−1.04646	−	2.31177i
$589$	132831.	−	132831.i	0.0157765	−	0.0157765i
$590$	3.87852e6	−	1.29819e7i	0.458707	−	1.53535i
$591$	−8.08536e6	+	1.81072e6i	−0.952205	+	0.213247i
$592$	1.47882e6	−	3.74712e6i	0.173424	−	0.439434i
$593$		−	7.75840e6i		−	0.906015i	−0.891507	−	0.453007i	$-0.850351\pi$
$593$		−	7.75840e6i		−	0.906015i	0.891507	−	0.453007i	$-0.149649\pi$
$594$	4.31349e6	+	1.11006e7i	0.501606	+	1.29086i
$595$	5.17129e6	+	5.17129e6i	0.598834	+	0.598834i
$596$	−6.46656e6	+	1.34288e6i	−0.745689	+	0.154853i
$597$	−1.55238e6	−	984291.i	−0.178263	−	0.113028i
$598$	2.26020e6	−	1.22034e6i	0.258460	−	0.139549i
$599$			3.38502e6i			0.385473i	0.981251	+	0.192737i	$0.0617363\pi$
$599$			3.38502e6i			0.385473i	−0.981251	+	0.192737i	$0.938264\pi$
$600$	−1.03489e6	−	7.63368e6i	−0.117359	−	0.865677i
$601$			1.89676e6i			0.214203i	0.994248	+	0.107101i	$0.0341570\pi$
$601$			1.89676e6i			0.214203i	−0.994248	+	0.107101i	$0.965843\pi$
$602$	−6.36143e6	−	1.17820e7i	−0.715424	−	1.32504i
$603$	1.45313e6	−	4.04649e6i	0.162747	−	0.453195i
$604$	7.63639e6	+	5.01015e6i	0.851718	+	0.558803i
$605$	7.99879e6	+	7.99879e6i	0.888456	+	0.888456i
$606$	674806.	−	9.62343e6i	0.0746444	−	1.06451i
$607$		−	8.30954e6i		−	0.915388i	−0.889110	−	0.457694i	$-0.848676\pi$
$607$		−	8.30954e6i		−	0.915388i	0.889110	−	0.457694i	$-0.151324\pi$
$608$	−269454.	−	211819.i	−0.0295614	−	0.0232384i
$609$	911962.	+	4.07216e6i	0.0996400	+	0.444919i
$610$	1.04668e7	+	3.12708e6i	1.13891	+	0.340263i
$611$	6.99683e6	−	6.99683e6i	0.758226	−	0.758226i
$612$	3.01813e6	+	425360.i	0.325731	+	0.0459070i
$613$	−2.64016e6	−	2.64016e6i	−0.283778	−	0.283778i	0.550836	−	0.834614i	$-0.314309\pi$
$613$	−2.64016e6	−	2.64016e6i	−0.283778	−	0.283778i	−0.834614	+	0.550836i	$0.814309\pi$
$614$	182191.	−	98369.6i	0.0195032	−	0.0105303i
$615$	7.51192e6	−	1.68230e6i	0.800873	−	0.179356i
$616$	−2.44417e7	−	2.09653e6i	−2.59525	−	0.222613i
$617$	−5.99313e6			−0.633783			−0.316892	−	0.948462i	$-0.602639\pi$
$617$	−5.99313e6			−0.633783			−0.316892	+	0.948462i	$0.602639\pi$
$618$	−2.75329e6	+	2.39247e6i	−0.289989	+	0.251985i
$619$	6.17847e6	−	6.17847e6i	0.648118	−	0.648118i	−0.304420	−	0.952538i	$-0.598463\pi$
$619$	6.17847e6	−	6.17847e6i	0.648118	−	0.648118i	0.952538	+	0.304420i	$0.0984625\pi$
$620$	1.58062e6	+	7.61140e6i	0.165138	+	0.795217i
$621$	−4.40986e6	−	551668.i	−0.458877	−	0.0574048i
$622$	9.30110e6	+	2.77883e6i	0.963959	+	0.287996i
$623$	7.74456e6			0.799423
$624$	−3.63877e6	−	4.99252e6i	−0.374105	−	0.513285i
$625$	1.08440e7			1.11043
$626$	−1.22544e6	−	366117.i	−0.124985	−	0.0373408i
$627$	274501.	−	432930.i	0.0278852	−	0.0439794i
$628$	783997.	−	162808.i	0.0793260	−	0.0164732i
$629$	1.09035e6	−	1.09035e6i	0.109886	−	0.109886i
$630$	−1.52153e7	+	2.06466e7i	−1.52732	+	2.07251i
$631$	−3.20328e6			−0.320274			−0.160137	−	0.987095i	$-0.551194\pi$
$631$	−3.20328e6			−0.320274			−0.160137	+	0.987095i	$0.551194\pi$
$632$	−9.07746e6	−	1.07808e7i	−0.904006	−	1.07364i
$633$	−77426.3	−	345729.i	−0.00768032	−	0.0342947i
$634$	−1.09276e7	+	5.90012e6i	−1.07970	+	0.582958i
$635$	1.17895e7	+	1.17895e7i	1.16028	+	1.16028i
$636$	7.42945e6	+	2.79925e6i	0.728306	+	0.274409i
$637$	−1.16716e7	+	1.16716e7i	−1.13968	+	1.13968i
$638$	3.30718e6	+	988063.i	0.321666	+	0.0961021i
$639$	−1.20562e7	+	5.68514e6i	−1.16805	+	0.550793i
$640$	1.34459e7	−	4.51473e6i	1.29760	−	0.435694i
$641$		−	1.50940e7i		−	1.45097i	−0.688237	−	0.725486i	$-0.741615\pi$
$641$		−	1.50940e7i		−	1.45097i	0.688237	−	0.725486i	$-0.258385\pi$
$642$	1.42356e7	+	998216.i	1.36313	+	0.0955844i
$643$	1.02258e7	+	1.02258e7i	0.975372	+	0.975372i	0.999704	−	0.0243319i	$-0.00774586\pi$
$643$	1.02258e7	+	1.02258e7i	0.975372	+	0.975372i	−0.0243319	+	0.999704i	$0.507746\pi$
$644$	5.02183e6	−	7.65419e6i	0.477142	−	0.727252i
$645$	−6.20028e6	+	9.77880e6i	−0.586829	+	0.925521i
$646$	−62331.0	−	115444.i	−0.00587656	−	0.0108840i
$647$			2.37317e6i			0.222878i	0.993771	+	0.111439i	$0.0355460\pi$
$647$			2.37317e6i			0.222878i	−0.993771	+	0.111439i	$0.964454\pi$
$648$	110048.	+	1.06884e7i	0.0102954	+	0.999947i
$649$			1.73966e7i			1.62126i
$650$	−5.25920e6	+	2.83958e6i	−0.488244	+	0.263616i
$651$	6.46204e6	−	1.01916e7i	0.597609	−	0.942522i
$652$	3.49578e6	+	1.68338e7i	0.322051	+	1.55083i
$653$	8.29978e6	+	8.29978e6i	0.761700	+	0.761700i	0.976630	−	0.214930i	$-0.0689523\pi$
$653$	8.29978e6	+	8.29978e6i	0.761700	+	0.761700i	−0.214930	+	0.976630i	$0.568952\pi$
$654$	250160.	−	3.56753e6i	0.0228703	−	0.326155i
$655$		−	1.32251e7i		−	1.20447i
$656$	2.63128e6	+	6.06221e6i	0.238731	+	0.550011i
$657$	−4.94520e6	+	2.33191e6i	−0.446962	+	0.210765i
$658$	1.00952e7	−	3.37901e7i	0.908976	−	3.04246i
$659$	4.46270e6	−	4.46270e6i	0.400299	−	0.400299i	−0.478040	−	0.878338i	$-0.658652\pi$
$659$	4.46270e6	−	4.46270e6i	0.400299	−	0.400299i	0.878338	+	0.478040i	$0.158652\pi$
$660$	8.74817e6	+	1.93258e7i	0.781731	+	1.72694i
$661$	−1.42437e6	−	1.42437e6i	−0.126800	−	0.126800i	0.640859	−	0.767659i	$-0.278578\pi$
$661$	−1.42437e6	−	1.42437e6i	−0.126800	−	0.126800i	−0.767659	+	0.640859i	$0.778578\pi$
$662$	−7.85599e6	−	1.45501e7i	−0.696716	−	1.29039i
$663$	−516792.	−	2.30762e6i	−0.0456596	−	0.203882i
$664$	−402215.	+	4.68908e6i	−0.0354029	+	0.412731i
$665$	1.10396e6			0.0968057
$666$	4.35329e6	+	3.20811e6i	0.380305	+	0.280261i
$667$	−910797.	+	910797.i	−0.0792697	+	0.0792697i
$668$	6.78432e6	−	1.03406e7i	0.588255	−	0.896608i
$669$	−3.97861e6	+	6.27489e6i	−0.343689	+	0.542052i
$670$	2.19236e6	−	7.33810e6i	0.188679	−	0.631534i
$671$	−1.40262e7			−1.20263
$672$	−1.98651e7	−	9.49560e6i	−1.69695	−	0.811147i
$673$	3.15109e6			0.268178			0.134089	−	0.990969i	$-0.457189\pi$
$673$	3.15109e6			0.268178			0.134089	+	0.990969i	$0.457189\pi$
$674$	−2.09010e6	+	6.99585e6i	−0.177222	+	0.593186i
$675$	1.02612e7	+	1.28366e6i	0.866840	+	0.108440i
$676$	3.88834e6	−	5.92655e6i	0.327264	−	0.498810i
$677$	8.12126e6	−	8.12126e6i	0.681007	−	0.681007i	−0.279220	−	0.960227i	$-0.590076\pi$
$677$	8.12126e6	−	8.12126e6i	0.681007	−	0.681007i	0.960227	+	0.279220i	$0.0900758\pi$
$678$	6.98855e6	+	8.04255e6i	0.583866	+	0.671923i
$679$	−3.44261e6			−0.286559
$680$	5.40939e6	+	464001.i	0.448617	+	0.0384810i
$681$	964393.	−	215976.i	0.0796868	−	0.0178459i
$682$	−4.74217e6	−	8.78300e6i	−0.390406	−	0.723073i
$683$	9.18310e6	+	9.18310e6i	0.753247	+	0.753247i	0.975084	−	0.221837i	$-0.0712051\pi$
$683$	9.18310e6	+	9.18310e6i	0.753247	+	0.753247i	−0.221837	+	0.975084i	$0.571205\pi$
$684$	367557.	−	276751.i	0.0300389	−	0.0226177i
$685$	9.33818e6	−	9.33818e6i	0.760389	−	0.760389i
$686$	−1.02039e7	+	3.41537e7i	−0.827857	+	2.77094i
$687$	4.62336e6	+	2.06446e7i	0.373737	+	1.66884i
$688$	−9.24623e6	−	3.64906e6i	−0.744721	−	0.293907i
$689$		−	6.15976e6i		−	0.494329i
$690$	−7.89702e6	−	553749.i	−0.631453	−	0.0442782i
$691$	−1.29983e7	−	1.29983e7i	−1.03560	−	1.03560i	−0.999343	−	0.0362547i	$-0.988457\pi$
$691$	−1.29983e7	−	1.29983e7i	−1.03560	−	1.03560i	−0.0362547	−	0.999343i	$-0.511543\pi$
$692$	−34575.6	−	166497.i	−0.00274476	−	0.0132173i
$693$	1.11299e7	−	3.09931e7i	0.880357	−	2.45150i
$694$	5.94305e6	−	3.20881e6i	0.468393	−	0.252898i
$695$		−	3.01415e7i		−	2.36702i
$696$	2.46502e6	+	1.87645e6i	0.192885	+	0.146830i
$697$			2.52967e6i			0.197234i
$698$	−2.39573e6	−	4.43713e6i	−0.186122	−	0.344718i
$699$	2.46412e6	+	1.56238e6i	0.190752	+	0.120947i
$700$	−1.16852e7	+	1.78104e7i	−0.901344	+	1.37381i
$701$	−2.92652e6	−	2.92652e6i	−0.224934	−	0.224934i	0.585638	−	0.810573i	$-0.300844\pi$
$701$	−2.92652e6	−	2.92652e6i	−0.224934	−	0.224934i	−0.810573	+	0.585638i	$0.800844\pi$
$702$	7.73005e6	−	3.00375e6i	0.592025	−	0.230050i
$703$		−	232768.i		−	0.0177638i
$704$	−1.48825e7	+	1.04964e7i	−1.13173	+	0.798194i
$705$	−2.97592e7	+	6.66459e6i	−2.25501	+	0.505011i
$706$	531547.	+	158807.i	0.0401356	+	0.0119911i
$707$	−1.88625e7	+	1.88625e7i	−1.41923	+	1.41923i
$708$	−5.50527e6	+	1.46115e7i	−0.412758	+	1.09549i
$709$	1.08581e7	+	1.08581e7i	0.811219	+	0.811219i	0.984817	−	0.173598i	$-0.0555393\pi$
$709$	1.08581e7	+	1.08581e7i	0.811219	+	0.811219i	−0.173598	+	0.984817i	$0.555539\pi$
$710$	−2.08926e7	+	1.12805e7i	−1.55542	+	0.839811i
$711$	1.71120e7	−	8.06918e6i	1.26948	−	0.598626i
$712$	4.39802e6	−	3.70313e6i	0.325130	−	0.273759i
$713$	3.72484e6			0.274400
$714$	−5.52809e6	−	6.36182e6i	−0.405816	−	0.467021i
$715$	1.16381e7	−	1.16381e7i	0.851367	−	0.851367i
$716$	−8.53935e6	+	1.77332e6i	−0.622504	+	0.129272i
$717$	2.13838e7	+	1.35584e7i	1.55341	+	0.984944i
$718$	−1.74895e7	−	5.22521e6i	−1.26609	−	0.378262i
$719$	2.01107e6			0.145079			0.0725394	−	0.997366i	$-0.476890\pi$
$719$	2.01107e6			0.145079			0.0725394	+	0.997366i	$0.476890\pi$
$720$	1.23182e6	+	1.90002e7i	0.0885554	+	1.36593i
$721$	1.00860e7			0.722574
$722$	1.34018e7	+	4.00396e6i	0.956797	+	0.285856i
$723$	1.53757e7	+	9.74898e6i	1.09393	+	0.693607i
$724$	−1.85483e6	−	8.93188e6i	−0.131510	−	0.633281i
$725$	2.11931e6	−	2.11931e6i	0.149744	−	0.149744i
$726$	−8.55068e6	−	9.84028e6i	−0.602087	−	0.692892i
$727$	1.45351e7			1.01996			0.509980	−	0.860186i	$-0.329653\pi$
$727$	1.45351e7			1.01996			0.509980	+	0.860186i	$0.329653\pi$
$728$	−1.45995e6	+	1.70203e7i	−0.102096	+	1.19025i
$729$	−1.39067e7	−	3.53474e6i	−0.969183	−	0.246342i
$730$	−8.56968e6	+	4.62700e6i	−0.595192	+	0.321360i
$731$	−2.69051e6	−	2.69051e6i	−0.186226	−	0.186226i
$732$	−1.17806e7	−	4.43867e6i	−0.812624	−	0.306179i
$733$	−2.00885e7	+	2.00885e7i	−1.38098	+	1.38098i	−0.538094	+	0.842885i	$0.680855\pi$
$733$	−2.00885e7	+	2.00885e7i	−1.38098	+	1.38098i	−0.842885	+	0.538094i	$0.819145\pi$
$734$	9.59661e6	+	2.86712e6i	0.657472	+	0.196429i
$735$	4.96422e7	−	1.11174e7i	3.38948	−	0.759075i
$736$	−808093.	−	6.74793e6i	−0.0549879	−	0.459172i
$737$			9.83355e6i			0.666870i
$738$	−8.77139e6	+	1.32844e6i	−0.592826	+	0.0897841i
$739$	−9.47802e6	−	9.47802e6i	−0.638420	−	0.638420i	0.311746	−	0.950166i	$-0.399086\pi$
$739$	−9.47802e6	−	9.47802e6i	−0.638420	−	0.638420i	−0.950166	+	0.311746i	$0.899086\pi$
$740$	8.05390e6	+	5.28408e6i	0.540664	+	0.354723i
$741$	−301477.	−	191152.i	−0.0201701	−	0.0127889i
$742$	−1.04301e7	−	1.93176e7i	−0.695468	−	1.28808i
$743$			7.07186e6i			0.469961i	0.972000	+	0.234980i	$0.0755026\pi$
$743$			7.07186e6i			0.469961i	−0.972000	+	0.234980i	$0.924497\pi$
$744$	−1.20352e6	−	8.87755e6i	−0.0797117	−	0.587978i
$745$		−	1.57926e7i		−	1.04247i
$746$	1.55657e7	−	8.40434e6i	1.02405	−	0.552913i
$747$	−5.94595e6	−	2.13525e6i	−0.389870	−	0.140006i
$748$	−6.82547e6	+	1.41741e6i	−0.446045	+	0.0926277i
$749$	−2.79027e7	−	2.79027e7i	−1.81736	−	1.81736i
$750$	−2.65880e6	−	186438.i	−0.172597	−	0.0121027i
$751$			8.71111e6i			0.563603i	0.959473	+	0.281802i	$0.0909320\pi$
$751$			8.71111e6i			0.563603i	−0.959473	+	0.281802i	$0.909068\pi$
$752$	−1.04241e7	−	2.40160e7i	−0.672192	−	1.54866i
$753$	−760106.	−	3.39408e6i	−0.0488525	−	0.218140i
$754$	688051.	−	2.30300e6i	0.0440750	−	0.147525i
$755$	−1.54427e7	+	1.54427e7i	−0.985952	+	0.985952i
$756$	1.91560e7	−	2.25090e7i	1.21899	−	1.43236i
$757$	−1.04388e7	−	1.04388e7i	−0.662080	−	0.662080i	0.293790	−	0.955870i	$-0.405083\pi$
$757$	−1.04388e7	−	1.04388e7i	−0.662080	−	0.662080i	−0.955870	+	0.293790i	$0.905083\pi$
$758$	5.60291e6	+	1.03772e7i	0.354193	+	0.656003i
$759$	9.91889e6	−	2.22134e6i	0.624969	−	0.139962i
$760$	626924.	−	527869.i	0.0393714	−	0.0331507i
$761$	−9.54377e6			−0.597390			−0.298695	−	0.954349i	$-0.596551\pi$
$761$	−9.54377e6			−0.597390			−0.298695	+	0.954349i	$0.596551\pi$
$762$	−1.26030e7	−	1.45037e7i	−0.786296	−	0.904884i
$763$	−6.99260e6	+	6.99260e6i	−0.434838	+	0.434838i
$764$	1.48870e7	+	9.76717e6i	0.922726	+	0.605390i
$765$	−2.46326e6	+	6.85933e6i	−0.152179	+	0.423768i
$766$	3.09034e6	−	1.03438e7i	0.190298	−	0.636952i
$767$	1.21144e7			0.743554
$768$	−1.58215e7	+	4.10627e6i	−0.967932	+	0.251214i
$769$	−1.90284e7			−1.16034			−0.580172	−	0.814494i	$-0.697015\pi$
$769$	−1.90284e7			−1.16034			−0.580172	+	0.814494i	$0.697015\pi$
$770$	1.67918e7	−	5.62043e7i	1.02064	−	3.41620i
$771$	−1.76391e7	+	2.78197e7i	−1.06866	+	1.68545i
$772$	9.59321e6	+	6.29400e6i	0.579323	+	0.380087i
$773$	−5.96628e6	+	5.96628e6i	−0.359133	+	0.359133i	−0.863493	−	0.504361i	$-0.831728\pi$
$773$	−5.96628e6	+	5.96628e6i	−0.359133	+	0.359133i	0.504361	+	0.863493i	$0.331728\pi$
$774$	7.91618e6	−	1.07420e7i	0.474967	−	0.644513i
$775$	−8.66724e6			−0.518354
$776$	−1.95501e6	+	1.64611e6i	−0.116545	+	0.0981309i
$777$	−3.26782e6	−	1.45917e7i	−0.194180	−	0.867068i
$778$	1.54347e7	+	2.85866e7i	0.914214	+	1.69322i
$779$	270016.	+	270016.i	0.0159421	+	0.0159421i
$780$	1.34578e7	−	6.09190e6i	0.792023	−	0.358523i
$781$	2.15570e7	−	2.15570e7i	1.26462	−	1.26462i
$782$	744691.	−	2.49258e6i	0.0435471	−	0.145758i
$783$	−3.28293e6	+	2.55288e6i	−0.191363	+	0.148808i
$784$	1.73887e7	+	4.00618e7i	1.01036	+	2.32777i
$785$			1.91468e6i			0.110897i
$786$	−1.06610e6	+	1.52036e7i	−0.0615517	+	0.877791i
$787$	−1.77983e7	−	1.77983e7i	−1.02433	−	1.02433i	−0.999696	−	0.0246373i	$-0.992157\pi$
$787$	−1.77983e7	−	1.77983e7i	−1.02433	−	1.02433i	−0.0246373	−	0.999696i	$-0.507843\pi$
$788$	1.66535e7	−	3.45833e6i	0.955408	−	0.198404i
$789$	1.25446e7	−	1.97848e7i	0.717405	−	1.13146i
$790$	2.96539e7	−	1.60109e7i	1.69049	−	0.912742i
$791$		−	2.94619e7i		−	1.67425i
$792$	−8.49908e6	−	2.29223e7i	−0.481458	−	1.29851i
$793$			9.76730e6i			0.551559i
$794$	1.66423e6	+	3.08232e6i	0.0936831	+	0.173511i
$795$	−1.01658e7	+	1.60331e7i	−0.570460	+	0.899704i
$796$	3.15490e6	+	2.06989e6i	0.176483	+	0.115789i
$797$	1.09337e7	+	1.09337e7i	0.609710	+	0.609710i	0.942870	−	0.333160i	$-0.108115\pi$
$797$	1.09337e7	+	1.09337e7i	0.609710	+	0.609710i	−0.333160	+	0.942870i	$0.608115\pi$
$798$	−1.26913e6	−	88992.6i	−0.0705501	−	0.00494706i
$799$		−	1.00215e7i		−	0.555350i
$800$	1.88033e6	+	1.57016e7i	0.103875	+	0.867399i
$801$	3.29180e6	+	6.98079e6i	0.181281	+	0.384436i
$802$	−2.36015e7	−	7.05128e6i	−1.29570	−	0.387108i
$803$	8.84222e6	−	8.84222e6i	0.483918	−	0.483918i
$804$	−3.11189e6	+	8.25921e6i	−0.169779	+	0.450608i
$805$	1.54787e7	+	1.54787e7i	0.841869	+	0.841869i
$806$	−6.11616e6	+	3.30228e6i	−0.331621	+	0.179051i
$807$	4.14237e6	+	1.84968e7i	0.223905	+	0.999798i
$808$	−1.69247e6	+	1.97310e7i	−0.0911995	+	1.06322i
$809$	1.02261e7			0.549337			0.274668	−	0.961539i	$-0.411432\pi$
$809$	1.02261e7			0.549337			0.274668	+	0.961539i	$0.411432\pi$
$810$	−2.50777e7	−	4.93898e6i	−1.34300	−	0.264499i
$811$	−1.61040e7	+	1.61040e7i	−0.859771	+	0.859771i	−0.991311	−	0.131540i	$-0.958008\pi$
$811$	−1.61040e7	+	1.61040e7i	−0.859771	+	0.859771i	0.131540	+	0.991311i	$0.458008\pi$
$812$	−1.74178e6	−	8.38745e6i	−0.0927048	−	0.446416i
$813$	−1.30276e6	+	2.05466e6i	−0.0691255	+	0.109022i
$814$	−1.18505e7	−	3.54051e6i	−0.626870	−	0.187286i
$815$	−4.11115e7			−2.16805
$816$	−6.18127e6	−	969481.i	−0.324977	−	0.0509699i
$817$	−574368.			−0.0301048
$818$	2.38441e7	+	7.12375e6i	1.24594	+	0.372242i
$819$	−2.15824e7	−	7.75047e6i	−1.12432	−	0.403755i
$820$	−1.54724e7	+	3.21306e6i	−0.803566	+	0.166872i
$821$	−1.24462e7	+	1.24462e7i	−0.644434	+	0.644434i	−0.951642	−	0.307208i	$-0.900605\pi$
$821$	−1.24462e7	+	1.24462e7i	−0.644434	+	0.644434i	0.307208	+	0.951642i	$0.400605\pi$
$822$	−1.14880e7	+	9.98248e6i	−0.593015	+	0.515299i
$823$	−1.74745e6			−0.0899303			−0.0449651	−	0.998989i	$-0.514318\pi$
$823$	−1.74745e6			−0.0899303			−0.0449651	+	0.998989i	$0.514318\pi$
$824$	5.72770e6	−	4.82272e6i	0.293875	−	0.247442i
$825$	−2.30800e7	+	5.16879e6i	−1.18060	+	0.264395i
$826$	3.79917e7	−	2.05127e7i	1.93749	−	1.04610i
$827$	1.88284e7	+	1.88284e7i	0.957303	+	0.957303i	0.999125	−	0.0418218i	$-0.0133162\pi$
$827$	1.88284e7	+	1.88284e7i	0.957303	+	0.957303i	−0.0418218	+	0.999125i	$0.513316\pi$
$828$	9.03385e6	+	1.27319e6i	0.457928	+	0.0645382i
$829$	163043.	−	163043.i	0.00823978	−	0.00823978i	−0.702975	−	0.711215i	$-0.748145\pi$
$829$	163043.	−	163043.i	0.00823978	−	0.00823978i	0.711215	+	0.702975i	$0.248145\pi$
$830$	−1.07827e7	−	3.22147e6i	−0.543290	−	0.162315i
$831$	−5.78744e6	−	2.58425e7i	−0.290726	−	1.29817i
$832$	7.30930e6	+	1.03636e7i	0.366073	+	0.519044i
$833$			1.67172e7i			0.834739i
$834$	−2.42976e6	+	3.46509e7i	−0.120962	+	1.72504i
$835$	2.09112e7	+	2.09112e7i	1.03792	+	1.03792i
$836$	−577256.	+	879843.i	−0.0285662	+	0.0435401i
$837$	1.19332e7	+	1.49283e6i	0.588767	+	0.0736540i
$838$	1.43821e7	+	2.66372e7i	0.707479	+	1.31033i
$839$		−	2.01713e7i		−	0.989303i	−0.869091	−	0.494652i	$-0.835296\pi$
$839$		−	2.01713e7i		−	0.989303i	0.869091	−	0.494652i	$-0.164704\pi$
$840$	3.18897e7	−	4.18923e7i	1.55938	−	2.04850i
$841$		−	1.93058e7i		−	0.941236i
$842$	7.93932e6	−	4.28665e6i	0.385925	−	0.208371i
$843$	−1.76052e7	−	1.11626e7i	−0.853242	−	0.541001i
$844$	147878.	+	712101.i	0.00714575	+	0.0344101i
$845$	1.19850e7	+	1.19850e7i	0.577424	+	0.577424i
$846$	3.47487e7	−	5.26273e6i	1.66922	−	0.252804i
$847$			3.60475e7i			1.72650i
$848$	−1.51599e7	−	5.98292e6i	−0.723948	−	0.285709i
$849$	2.69272e7	−	6.03036e6i	1.28210	−	0.287127i
$850$	−1.73280e6	+	5.79992e6i	−0.0822625	+	0.275343i
$851$	3.26364e6	−	3.26364e6i	0.154482	−	0.154482i
$852$	2.49277e7	−	1.12839e7i	1.17647	−	0.532551i
$853$	2.42105e7	+	2.42105e7i	1.13928	+	1.13928i	0.988579	+	0.150703i	$0.0481539\pi$
$853$	2.42105e7	+	2.42105e7i	1.13928	+	1.13928i	0.150703	+	0.988579i	$0.451846\pi$
$854$	1.65385e7	+	3.06311e7i	0.775984	+	1.43720i
$855$	469237.	+	995091.i	0.0219521	+	0.0465530i
$856$	−2.91874e7	−	2.50361e6i	−1.36148	−	0.116784i
$857$	−2.50686e7			−1.16595			−0.582973	−	0.812491i	$-0.698111\pi$
$857$	−2.50686e7			−1.16595			−0.582973	+	0.812491i	$0.698111\pi$
$858$	−1.43174e7	+	1.24411e7i	−0.663967	+	0.576952i
$859$	2.38765e7	−	2.38765e7i	1.10405	−	1.10405i	0.110132	−	0.993917i	$-0.464873\pi$
$859$	2.38765e7	−	2.38765e7i	1.10405	−	1.10405i	0.993917	−	0.110132i	$-0.0351273\pi$
$860$	1.30387e7	−	1.98734e7i	0.601160	−	0.916277i
$861$	2.07174e7	+	1.31359e7i	0.952419	+	0.603884i
$862$	−1.09838e7	+	3.67641e7i	−0.503481	+	1.68522i
$863$	−3.68097e7			−1.68242			−0.841211	−	0.540707i	$-0.818157\pi$
$863$	−3.68097e7			−1.68242			−0.841211	+	0.540707i	$0.818157\pi$
$864$	115535.	−	2.19421e7i	0.00526537	−	0.999986i
$865$	406620.			0.0184777
$866$	−1.60920e6	+	5.38621e6i	−0.0729148	+	0.244055i
$867$	1.66699e7	+	1.05696e7i	0.753158	+	0.477542i
$868$	−1.35892e7	+	2.07125e7i	−0.612203	+	0.933109i
$869$	−3.05969e7	+	3.05969e7i	−1.37445	+	1.37445i
$870$	−5.59169e6	+	4.85889e6i	−0.250464	+	0.217640i
$871$	6.84772e6			0.305845
$872$	−627421.	+	7.31456e6i	−0.0279427	+	0.325759i
$873$	−1.46327e6	−	3.10310e6i	−0.0649815	−	0.137804i
$874$	−186569.	−	345545.i	−0.00826154	−	0.0153012i
$875$	5.21143e6	+	5.21143e6i	0.230111	+	0.230111i
$876$	1.02248e7	−	4.62842e6i	0.450187	−	0.203785i
$877$	−7.07729e6	+	7.07729e6i	−0.310719	+	0.310719i	−0.845188	−	0.534469i	$-0.820512\pi$
$877$	−7.07729e6	+	7.07729e6i	−0.310719	+	0.310719i	0.534469	+	0.845188i	$0.320512\pi$
$878$	−848832.	+	2.84115e6i	−0.0371608	+	0.124382i
$879$	9.17991e6	−	2.05585e6i	0.400743	−	0.0897467i
$880$	−1.73388e7	−	3.99467e7i	−0.754764	−	1.73890i
$881$		−	3.59260e7i		−	1.55944i	−0.626126	−	0.779722i	$-0.715361\pi$
$881$		−	3.59260e7i		−	1.55944i	0.626126	−	0.779722i	$-0.284639\pi$
$882$	−5.79653e7	+	8.77890e6i	−2.50898	+	0.379987i
$883$	−1.24498e7	−	1.24498e7i	−0.537356	−	0.537356i	0.385396	−	0.922751i	$-0.374065\pi$
$883$	−1.24498e7	−	1.24498e7i	−0.537356	−	0.537356i	−0.922751	+	0.385396i	$0.874065\pi$
$884$	987032.	+	4.75301e6i	0.0424816	+	0.204568i
$885$	−3.15322e7	−	1.99931e7i	−1.35331	−	0.858068i
$886$	−3.14269e6	+	1.69682e6i	−0.134498	+	0.0726192i
$887$			7.81438e6i			0.333492i	0.986000	+	0.166746i	$0.0533260\pi$
$887$			7.81438e6i			0.333492i	−0.986000	+	0.166746i	$0.946674\pi$
$888$	−8.83288e6	−	6.72386e6i	−0.375898	−	0.286145i
$889$			5.31310e7i			2.25472i
$890$	6.53161e6	+	1.20972e7i	0.276404	+	0.511930i
$891$	3.26673e7	−	3.14122e6i	1.37854	−	0.132557i
$892$	8.36674e6	−	1.27524e7i	0.352082	−	0.536638i
$893$	−1.06969e6	−	1.06969e6i	−0.0448881	−	0.0448881i
$894$	−1.27307e6	+	1.81553e7i	−0.0532733	+	0.759732i
$895$		−	2.08548e7i		−	0.870259i
$896$	4.04709e7	+	2.01248e7i	1.68412	+	0.837454i
$897$	−1.54686e6	−	6.90715e6i	−0.0641904	−	0.286628i
$898$	3.13964e7	+	9.38008e6i	1.29924	+	0.388164i
$899$	2.46464e6	−	2.46464e6i	0.101708	−	0.101708i
$900$	−2.10207e7	−	2.96255e6i	−0.865047	−	0.121916i
$901$	−4.41129e6	−	4.41129e6i	−0.181031	−	0.181031i
$902$	1.78540e7	−	9.63983e6i	0.730665	−	0.394505i
$903$	−3.60058e7	+	8.06352e6i	−1.46944	+	0.329083i
$904$	−1.40875e7	−	1.67310e7i	−0.573339	−	0.680927i
$905$	2.18134e7			0.885324
$906$	1.89979e7	−	1.65082e7i	0.768928	−	0.668158i
$907$	−5.03227e6	+	5.03227e6i	−0.203117	+	0.203117i	−0.801334	−	0.598217i	$-0.795876\pi$
$907$	−5.03227e6	+	5.03227e6i	−0.203117	+	0.203117i	0.598217	+	0.801334i	$0.295876\pi$
$908$	−1.98637e6	+	412498.i	−0.0799549	+	0.0166038i
$909$	−2.50198e7	−	8.98486e6i	−1.00432	−	0.360663i
$910$	−3.91387e7	−	1.16932e7i	−1.56676	−	0.468090i
$911$	1.23967e7			0.494890			0.247445	−	0.968902i	$-0.420409\pi$
$911$	1.23967e7			0.494890			0.247445	+	0.968902i	$0.420409\pi$
$912$	−763270.	+	556306.i	−0.0303872	+	0.0221476i
$913$	1.44495e7			0.573689
$914$	−3.31100e7	−	9.89207e6i	−1.31097	−	0.391671i
$915$	1.61196e7	−	2.54231e7i	0.636504	−	1.00387i
$916$	−8.83026e6	−	4.25218e7i	−0.347724	−	1.67445i
$917$	2.98001e7	−	2.98001e7i	1.17029	−	1.17029i
$918$	3.38472e6	−	7.68698e6i	0.132561	−	0.301057i
$919$	−3.82189e7			−1.49276			−0.746380	−	0.665520i	$-0.768210\pi$
$919$	−3.82189e7			−1.49276			−0.746380	+	0.665520i	$0.768210\pi$
$920$	1.61914e7	+	1.38885e6i	0.630687	+	0.0540985i
$921$	−124690.	−	556774.i	−0.00484375	−	0.0216287i
$922$	1.83320e7	−	9.89795e6i	0.710205	−	0.383458i
$923$	−1.50115e7	−	1.50115e7i	−0.579991	−	0.579991i
$924$	−2.38347e7	+	6.32594e7i	−0.918397	+	2.43750i
$925$	−7.59409e6	+	7.59409e6i	−0.291824	+	0.291824i
$926$	−3.02053e7	−	9.02425e6i	−1.15759	−	0.345847i
$927$	4.28704e6	+	9.09135e6i	0.163854	+	0.347479i
$928$	−4.99965e6	−	3.93026e6i	−0.190577	−	0.149814i
$929$		−	3.50556e7i		−	1.33266i	−0.745659	−	0.666328i	$-0.767865\pi$
$929$		−	3.50556e7i		−	1.33266i	0.745659	−	0.666328i	$-0.232135\pi$
$930$	2.13696e7	+	1.49846e6i	0.810193	+	0.0568117i
$931$	1.78439e6	+	1.78439e6i	0.0674707	+	0.0674707i
$932$	−5.00782e6	−	3.28558e6i	−0.188847	−	0.123900i
$933$	1.43244e7	−	2.25918e7i	0.538731	−	0.849663i
$934$	1.64670e7	+	3.04987e7i	0.617658	+	1.14397i
$935$		−	1.66692e7i		−	0.623569i
$936$	−1.59623e7	+	5.91845e6i	−0.595533	+	0.220810i
$937$		−	4.88614e7i		−	1.81810i	−0.416691	−	0.909048i	$-0.636810\pi$
$937$		−	4.88614e7i		−	1.81810i	0.416691	−	0.909048i	$-0.363190\pi$
$938$	2.14751e7	−	1.15950e7i	0.796943	−	0.430291i
$939$	−1.88727e6	+	2.97652e6i	−0.0698506	+	0.110165i
$940$	6.12952e7	−	1.27288e7i	2.26260	−	0.469861i
$941$	1.42788e7	+	1.42788e7i	0.525676	+	0.525676i	0.919280	−	0.393604i	$-0.128772\pi$
$941$	1.42788e7	+	1.42788e7i	0.525676	+	0.525676i	−0.393604	+	0.919280i	$0.628772\pi$
$942$	154346.	−	2.20113e6i	0.00566719	−	0.0808199i
$943$			7.57180e6i			0.277281i
$944$	1.17666e7	−	2.98149e7i	0.429755	−	1.08894i
$945$	4.33854e7	+	5.57924e7i	1.58039	+	2.03233i
$946$	−8.73640e6	+	2.92419e7i	−0.317398	+	1.06237i
$947$	−863504.	+	863504.i	−0.0312888	+	0.0312888i	−0.722578	−	0.691289i	$-0.757043\pi$
$947$	−863504.	+	863504.i	−0.0312888	+	0.0312888i	0.691289	+	0.722578i	$0.257043\pi$
$948$	−3.53810e7	+	1.60158e7i	−1.27864	+	0.578800i
$949$	−6.15740e6	−	6.15740e6i	−0.221938	−	0.221938i
$950$	434123.	+	804041.i	0.0156064	+	0.0289048i
$951$	7.47878e6	+	3.33948e7i	0.268151	+	1.19737i
$952$	1.11435e7	+	1.32346e7i	0.398500	+	0.473279i
$953$	−1.06696e7			−0.380554			−0.190277	−	0.981730i	$-0.560939\pi$
$953$	−1.06696e7			−0.380554			−0.190277	+	0.981730i	$0.560939\pi$
$954$	1.29792e7	−	1.76123e7i	0.461718	−	0.626535i
$955$	−3.01052e7	+	3.01052e7i	−1.06815	+	1.06815i
$956$	−4.34582e7	−	2.85124e7i	−1.53790	−	1.00900i
$957$	5.09330e6	−	8.03292e6i	0.179771	−	0.283527i
$958$	6.88417e6	−	2.30422e7i	0.242347	−	0.811168i
$959$	4.20836e7			1.47763
$960$	−1.92146e6	−	3.90383e7i	−0.0672903	−	1.36714i
$961$	1.85496e7			0.647928
$962$	−2.46548e6	+	8.25229e6i	−0.0858942	+	0.287499i
$963$	1.32910e7	−	3.70109e7i	0.461840	−	1.28607i
$964$	−3.12479e7	−	2.05014e7i	−1.08300	−	0.710545i
$965$	−1.93999e7	+	1.93999e7i	−0.670626	+	0.670626i
$966$	−1.65467e7	−	1.90422e7i	−0.570516	−	0.656560i
$967$	−3.64417e7			−1.25323			−0.626617	−	0.779328i	$-0.715561\pi$
$967$	−3.64417e7			−1.25323			−0.626617	+	0.779328i	$0.715561\pi$
$968$	1.72364e7	+	2.04708e7i	0.591232	+	0.702177i
$969$	−352795.	+	79008.5i	−0.0120701	+	0.00270312i
$970$	−2.90343e6	−	5.37746e6i	−0.0990791	−	0.183505i
$971$	2.02114e7	+	2.02114e7i	0.687936	+	0.687936i	0.961776	−	0.273839i	$-0.0882936\pi$
$971$	2.02114e7	+	2.02114e7i	0.687936	+	0.687936i	−0.273839	+	0.961776i	$0.588294\pi$
$972$	2.84314e7	+	7.69945e6i	0.965232	+	0.261393i
$973$	6.79180e7	−	6.79180e7i	2.29987	−	2.29987i
$974$	−2.29997e6	+	7.69830e6i	−0.0776828	+	0.260014i
$975$	3.59935e6	+	1.60721e7i	0.121259	+	0.541453i
$976$	2.40385e7	+	9.48690e6i	0.807761	+	0.318786i
$977$			1.91159e7i			0.640705i	0.947298	+	0.320353i	$0.103801\pi$
$977$			1.91159e7i			0.640705i	−0.947298	+	0.320353i	$0.896199\pi$
$978$	4.72621e7	+	3.31407e6i	1.58003	+	0.110794i
$979$	−1.24819e7	−	1.24819e7i	−0.416222	−	0.416222i
$980$	−1.02248e8	+	2.12333e7i	−3.40088	+	0.706242i
$981$	−9.27517e6	−	3.33081e6i	−0.307716	−	0.110504i
$982$	−2.35666e7	+	1.27242e7i	−0.779861	+	0.421068i
$983$			3.63353e7i			1.19935i	0.800245	+	0.599674i	$0.204703\pi$
$983$			3.63353e7i			1.19935i	−0.800245	+	0.599674i	$0.795297\pi$
$984$	1.80462e7	−	2.44650e6i	0.594151	−	0.0805487i
$985$			4.06711e7i			1.33566i
$986$	−1.15654e6	−	2.14203e6i	−0.0378850	−	0.0701671i
$987$	−8.20741e7	−	5.20393e7i	−2.68172	−	1.70035i
$988$	612691.	+	401980.i	0.0199687	+	0.0131012i
$989$	−8.05322e6	−	8.05322e6i	−0.261805	−	0.261805i
$990$	5.77988e7	−	8.75369e6i	1.87426	−	0.283859i
$991$			1.22184e7i			0.395213i	0.980281	+	0.197606i	$0.0633167\pi$
$991$			1.22184e7i			0.395213i	−0.980281	+	0.197606i	$0.936683\pi$
$992$	2.18672e6	+	1.82601e7i	0.0705529	+	0.589147i
$993$	−4.44650e7	+	9.95797e6i	−1.43102	+	0.320478i
$994$	−7.24959e7	−	2.16591e7i	−2.32727	−	0.695304i
$995$	−6.37999e6	+	6.37999e6i	−0.204297	+	0.204297i
$996$	1.21362e7	+	4.57264e6i	0.387644	+	0.146056i
$997$	−7.51432e6	−	7.51432e6i	−0.239415	−	0.239415i	0.577193	−	0.816608i	$-0.304148\pi$
$997$	−7.51432e6	−	7.51432e6i	−0.239415	−	0.239415i	−0.816608	+	0.577193i	$0.804148\pi$
$998$	−2.42379e7	+	1.30867e7i	−0.770315	+	0.415914i
$999$	1.17637e7	−	9.14770e6i	0.372932	−	0.290000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.k.a.11.15	✓	76
3.2	odd	2	inner	48.6.k.a.11.24	yes	76
4.3	odd	2		192.6.k.a.143.8		76
12.11	even	2		192.6.k.a.143.12		76
16.3	odd	4	inner	48.6.k.a.35.24	yes	76
16.13	even	4		192.6.k.a.47.12		76
48.29	odd	4		192.6.k.a.47.8		76
48.35	even	4	inner	48.6.k.a.35.15	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.k.a.11.15	✓	76	1.1	even	1	trivial
48.6.k.a.11.24	yes	76	3.2	odd	2	inner
48.6.k.a.35.15	yes	76	48.35	even	4	inner
48.6.k.a.35.24	yes	76	16.3	odd	4	inner
192.6.k.a.47.8		76	48.29	odd	4
192.6.k.a.47.12		76	16.13	even	4
192.6.k.a.143.8		76	4.3	odd	2
192.6.k.a.143.12		76	12.11	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61933 + 5.42012i) q^{2} +(13.1651 + 8.34740i) q^{3} +(-26.7555 - 17.5540i) q^{4} +(54.1063 - 54.1063i) q^{5} +(-66.5627 + 57.8395i) q^{6} +243.836 q^{7} +(138.471 - 116.592i) q^{8} +(103.642 + 219.789i) q^{9} +O(q^{10})\)	\(q+(-1.61933 + 5.42012i) q^{2} +(13.1651 + 8.34740i) q^{3} +(-26.7555 - 17.5540i) q^{4} +(54.1063 - 54.1063i) q^{5} +(-66.5627 + 57.8395i) q^{6} +243.836 q^{7} +(138.471 - 116.592i) q^{8} +(103.642 + 219.789i) q^{9} +(205.647 + 380.879i) q^{10} +(-392.992 - 392.992i) q^{11} +(-205.710 - 454.440i) q^{12} +(-273.665 + 273.665i) q^{13} +(-394.853 + 1321.62i) q^{14} +(1163.96 - 260.670i) q^{15} +(407.714 + 939.332i) q^{16} +391.969i q^{17} +(-1359.12 + 205.840i) q^{18} +(41.8387 + 41.8387i) q^{19} +(-2397.42 + 497.860i) q^{20} +(3210.14 + 2035.40i) q^{21} +(2766.45 - 1493.68i) q^{22} +1173.24i q^{23} +(2796.23 - 379.083i) q^{24} -2729.99i q^{25} +(-1040.14 - 1926.46i) q^{26} +(-470.208 + 3758.70i) q^{27} +(-6523.97 - 4280.30i) q^{28} +(776.308 + 776.308i) q^{29} +(-471.982 + 6730.95i) q^{30} -3174.82i q^{31} +(-5751.52 + 688.770i) q^{32} +(-1893.34 - 8454.26i) q^{33} +(-2124.52 - 634.729i) q^{34} +(13193.1 - 13193.1i) q^{35} +(1085.19 - 7699.91i) q^{36} +(-2781.73 - 2781.73i) q^{37} +(-294.522 + 159.020i) q^{38} +(-5887.24 + 1318.45i) q^{39} +(1183.77 - 13800.5i) q^{40} +6453.74 q^{41} +(-16230.4 + 14103.4i) q^{42} +(-6864.07 + 6864.07i) q^{43} +(3616.12 + 17413.3i) q^{44} +(17499.7 + 6284.31i) q^{45} +(-6359.12 - 1899.87i) q^{46} -25567.1 q^{47} +(-2473.36 + 15769.8i) q^{48} +42649.2 q^{49} +(14796.9 + 4420.77i) q^{50} +(-3271.92 + 5160.33i) q^{51} +(12126.0 - 2518.14i) q^{52} +(-11254.2 + 11254.2i) q^{53} +(-19611.2 - 8635.18i) q^{54} -42526.7 q^{55} +(33764.3 - 28429.5i) q^{56} +(201.568 + 900.057i) q^{57} +(-5464.79 + 2950.58i) q^{58} +(-22133.5 - 22133.5i) q^{59} +(-35718.3 - 13457.9i) q^{60} +(17845.3 - 17845.3i) q^{61} +(17207.9 + 5141.11i) q^{62} +(25271.7 + 53592.7i) q^{63} +(5580.43 - 32289.3i) q^{64} +29614.1i q^{65} +(48889.1 + 3428.16i) q^{66} +(-12511.1 - 12511.1i) q^{67} +(6880.63 - 10487.3i) q^{68} +(-9793.51 + 15445.9i) q^{69} +(50144.2 + 92872.3i) q^{70} +54853.6i q^{71} +(39977.2 + 18350.6i) q^{72} +22499.7i q^{73} +(19581.9 - 10572.8i) q^{74} +(22788.3 - 35940.7i) q^{75} +(-384.979 - 1853.85i) q^{76} +(-95825.8 - 95825.8i) q^{77} +(2387.25 - 34044.6i) q^{78} -77856.3i q^{79} +(72883.7 + 28763.9i) q^{80} +(-37565.7 + 45558.8i) q^{81} +(-10450.8 + 34980.1i) q^{82} +(-18384.0 + 18384.0i) q^{83} +(-50159.6 - 110809. i) q^{84} +(21208.0 + 21208.0i) q^{85} +(-26088.9 - 48319.4i) q^{86} +(3740.06 + 16700.4i) q^{87} +(-100238. - 8598.11i) q^{88} +31761.3 q^{89} +(-62399.6 + 84674.0i) q^{90} +(-66729.6 + 66729.6i) q^{91} +(20595.1 - 31390.7i) q^{92} +(26501.5 - 41797.0i) q^{93} +(41401.7 - 138577. i) q^{94} +4527.48 q^{95} +(-81469.1 - 38942.5i) q^{96} -14118.5 q^{97} +(-69063.4 + 231164. i) q^{98} +(45645.0 - 127106. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7}+O(q^{10}) \) 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7	\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99}+O(q^{100}) \) 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7 - 104 * q^10 + 784 * q^12 - 4 * q^13 + 4560 * q^16 - 4076 * q^18 + 2356 * q^19 - 488 * q^21 + 2232 * q^22 + 2568 * q^24 - 3734 * q^27 - 12392 * q^28 + 628 * q^30 - 4 * q^33 + 26248 * q^34 - 30748 * q^36 - 4 * q^37 - 44908 * q^39 + 440 * q^40 + 11256 * q^42 + 652 * q^43 - 6252 * q^45 + 31320 * q^46 - 9168 * q^48 + 124844 * q^49 + 8664 * q^51 - 48448 * q^52 - 19480 * q^54 - 110056 * q^55 + 76088 * q^58 - 85408 * q^60 + 48076 * q^61 - 11080 * q^64 + 91492 * q^66 + 48924 * q^67 + 484 * q^69 + 86200 * q^70 - 16376 * q^72 - 69634 * q^75 + 30920 * q^76 + 13020 * q^78 - 4 * q^81 - 200768 * q^82 + 111760 * q^84 - 119904 * q^85 + 282180 * q^87 - 123616 * q^88 - 17680 * q^90 - 167288 * q^91 + 181660 * q^93 - 13200 * q^94 - 61688 * q^96 - 8 * q^97 - 287860 * q^99

Introduction

L-functions

Modular forms

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