LMFDB - Embedded newform 80.6.q.a.69.7

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			69.7
Character	$\chi$	$=$	80.69
Dual form			80.6.q.a.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.29707 - 1.98521i) q^{2} +(7.43164 + 7.43164i) q^{3} +(24.1179 + 21.0316i) q^{4} +(-55.3405 - 7.90104i) q^{5} +(-24.6125 - 54.1193i) q^{6} +59.4492 q^{7} +(-86.0017 - 159.285i) q^{8} -132.541i q^{9} +O(q^{10})$	\(q+(-5.29707 - 1.98521i) q^{2} +(7.43164 + 7.43164i) q^{3} +(24.1179 + 21.0316i) q^{4} +(-55.3405 - 7.90104i) q^{5} +(-24.6125 - 54.1193i) q^{6} +59.4492 q^{7} +(-86.0017 - 159.285i) q^{8} -132.541i q^{9} +(277.457 + 151.715i) q^{10} +(-153.290 - 153.290i) q^{11} +(22.9358 + 335.535i) q^{12} +(495.659 + 495.659i) q^{13} +(-314.907 - 118.019i) q^{14} +(-352.553 - 469.989i) q^{15} +(139.342 + 1014.48i) q^{16} +861.157i q^{17} +(-263.123 + 702.081i) q^{18} +(1507.32 - 1507.32i) q^{19} +(-1168.52 - 1354.46i) q^{20} +(441.805 + 441.805i) q^{21} +(507.674 + 1116.30i) q^{22} +998.793 q^{23} +(544.616 - 1822.88i) q^{24} +(3000.15 + 874.495i) q^{25} +(-1641.55 - 3609.53i) q^{26} +(2790.89 - 2790.89i) q^{27} +(1433.79 + 1250.31i) q^{28} +(3889.68 - 3889.68i) q^{29} +(934.471 + 3189.46i) q^{30} +6285.42 q^{31} +(1275.85 - 5650.37i) q^{32} -2278.39i q^{33} +(1709.58 - 4561.61i) q^{34} +(-3289.95 - 469.711i) q^{35} +(2787.56 - 3196.61i) q^{36} +(7913.50 - 7913.50i) q^{37} +(-10976.8 + 4992.04i) q^{38} +7367.12i q^{39} +(3500.86 + 9494.42i) q^{40} +10383.2i q^{41} +(-1463.20 - 3217.35i) q^{42} +(-11904.7 + 11904.7i) q^{43} +(-473.090 - 6920.97i) q^{44} +(-1047.21 + 7334.91i) q^{45} +(-5290.68 - 1982.82i) q^{46} -10518.0i q^{47} +(-6503.68 + 8574.76i) q^{48} -13272.8 q^{49} +(-14155.9 - 10588.2i) q^{50} +(-6399.81 + 6399.81i) q^{51} +(1529.72 + 22378.7i) q^{52} +(5698.77 - 5698.77i) q^{53} +(-20324.0 + 9243.02i) q^{54} +(7272.00 + 9694.30i) q^{55} +(-5112.73 - 9469.37i) q^{56} +22403.8 q^{57} +(-28325.8 + 12882.1i) q^{58} +(22000.0 + 22000.0i) q^{59} +(1381.79 - 18749.9i) q^{60} +(31061.7 - 31061.7i) q^{61} +(-33294.3 - 12477.9i) q^{62} -7879.48i q^{63} +(-17975.4 + 27397.6i) q^{64} +(-23513.8 - 31346.2i) q^{65} +(-4523.10 + 12068.8i) q^{66} +(-703.105 - 703.105i) q^{67} +(-18111.5 + 20769.3i) q^{68} +(7422.67 + 7422.67i) q^{69} +(16494.6 + 9019.34i) q^{70} +27364.3i q^{71} +(-21111.9 + 11398.8i) q^{72} -14815.9 q^{73} +(-57628.4 + 26208.4i) q^{74} +(15797.1 + 28795.0i) q^{75} +(68054.9 - 4651.96i) q^{76} +(-9112.98 - 9112.98i) q^{77} +(14625.3 - 39024.1i) q^{78} -2727.79 q^{79} +(304.146 - 57242.5i) q^{80} +9274.23 q^{81} +(20612.9 - 55000.7i) q^{82} +(-35245.6 - 35245.6i) q^{83} +(1363.52 + 19947.3i) q^{84} +(6804.04 - 47656.9i) q^{85} +(86693.3 - 39426.6i) q^{86} +57813.5 q^{87} +(-11233.6 + 37600.0i) q^{88} -112845. i q^{89} +(20108.5 - 36774.6i) q^{90} +(29466.5 + 29466.5i) q^{91} +(24088.8 + 21006.2i) q^{92} +(46711.0 + 46711.0i) q^{93} +(-20880.5 + 55714.7i) q^{94} +(-95325.6 + 71506.7i) q^{95} +(51473.1 - 32509.9i) q^{96} +49998.0i q^{97} +(70306.9 + 26349.3i) q^{98} +(-20317.3 + 20317.3i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5.29707	−	1.98521i	−0.936398	−	0.350939i
$2$	−5.29707	−	1.98521i	−0.936398	−	0.350939i
$3$	7.43164	+	7.43164i	0.476740	+	0.476740i	0.904087	−	0.427347i	$-0.140552\pi$
$3$	7.43164	+	7.43164i	0.476740	+	0.476740i	−0.427347	+	0.904087i	$0.640552\pi$
$4$	24.1179	+	21.0316i	0.753683	+	0.657238i
$5$	−55.3405	−	7.90104i	−0.989961	−	0.141338i
$5$	−55.3405	−	7.90104i	−0.989961	−	0.141338i
$6$	−24.6125	−	54.1193i	−0.279112	−	0.613725i
$7$	59.4492			0.458565			0.229283	−	0.973360i	$-0.426362\pi$
$7$	59.4492			0.458565			0.229283	+	0.973360i	$0.426362\pi$
$8$	−86.0017	−	159.285i	−0.475097	−	0.879934i
$9$		−	132.541i		−	0.545438i
$10$	277.457	+	151.715i	0.877397	+	0.479765i
$11$	−153.290	−	153.290i	−0.381973	−	0.381973i	0.489840	−	0.871812i	$-0.337055\pi$
$11$	−153.290	−	153.290i	−0.381973	−	0.381973i	−0.871812	+	0.489840i	$0.837055\pi$
$12$	22.9358	+	335.535i	0.0459792	+	0.672643i
$13$	495.659	+	495.659i	0.813438	+	0.813438i	0.985148	−	0.171710i	$-0.0549291\pi$
$13$	495.659	+	495.659i	0.813438	+	0.813438i	−0.171710	+	0.985148i	$0.554929\pi$
$14$	−314.907	−	118.019i	−0.429400	−	0.160929i
$15$	−352.553	−	469.989i	−0.404573	−	0.539336i
$16$	139.342	+	1014.48i	0.136076	+	0.990698i
$17$			861.157i			0.722703i	0.932430	+	0.361352i	$0.117685\pi$
$17$			861.157i			0.722703i	−0.932430	+	0.361352i	$0.882315\pi$
$18$	−263.123	+	702.081i	−0.191416	+	0.510747i
$19$	1507.32	−	1507.32i	0.957906	−	0.957906i	−0.0412433	−	0.999149i	$-0.513132\pi$
$19$	1507.32	−	1507.32i	0.957906	−	0.957906i	0.999149	+	0.0412433i	$0.0131319\pi$
$20$	−1168.52	−	1354.46i	−0.653224	−	0.757164i
$21$	441.805	+	441.805i	0.218616	+	0.218616i
$22$	507.674	+	1116.30i	0.223629	+	0.491728i
$23$	998.793			0.393691			0.196846	−	0.980434i	$-0.436930\pi$
$23$	998.793			0.393691			0.196846	+	0.980434i	$0.436930\pi$
$24$	544.616	−	1822.88i	0.193002	−	0.645997i
$25$	3000.15	+	874.495i	0.960047	+	0.279838i
$26$	−1641.55	−	3609.53i	−0.476234	−	1.04717i
$27$	2790.89	−	2790.89i	0.736772	−	0.736772i
$28$	1433.79	+	1250.31i	0.345613	+	0.301387i
$29$	3889.68	−	3889.68i	0.858854	−	0.858854i	−0.132349	−	0.991203i	$-0.542252\pi$
$29$	3889.68	−	3889.68i	0.858854	−	0.858854i	0.991203	+	0.132349i	$0.0422521\pi$
$30$	934.471	+	3189.46i	0.189567	+	0.647014i
$31$	6285.42			1.17471			0.587354	−	0.809330i	$-0.300170\pi$
$31$	6285.42			1.17471			0.587354	+	0.809330i	$0.300170\pi$
$32$	1275.85	−	5650.37i	0.220254	−	0.975443i
$33$		−	2278.39i		−	0.364203i
$34$	1709.58	−	4561.61i	0.253625	−	0.676738i
$35$	−3289.95	−	469.711i	−0.453962	−	0.0648127i
$36$	2787.56	−	3196.61i	0.358482	−	0.411087i
$37$	7913.50	−	7913.50i	0.950308	−	0.950308i	−0.0485142	−	0.998822i	$-0.515449\pi$
$37$	7913.50	−	7913.50i	0.950308	−	0.950308i	0.998822	+	0.0485142i	$0.0154486\pi$
$38$	−10976.8	+	4992.04i	−1.23315	+	0.560814i
$39$			7367.12i			0.775597i
$40$	3500.86	+	9494.42i	0.345959	+	0.938250i
$41$			10383.2i			0.964657i	0.875991	+	0.482328i	$0.160209\pi$
$41$			10383.2i			0.964657i	−0.875991	+	0.482328i	$0.839791\pi$
$42$	−1463.20	−	3217.35i	−0.127991	−	0.281433i
$43$	−11904.7	+	11904.7i	−0.981854	+	0.981854i	−0.999838	−	0.0179841i	$-0.994275\pi$
$43$	−11904.7	+	11904.7i	−0.981854	+	0.981854i	0.0179841	+	0.999838i	$0.494275\pi$
$44$	−473.090	−	6920.97i	−0.0368393	−	0.538933i
$45$	−1047.21	+	7334.91i	−0.0770911	+	0.539962i
$46$	−5290.68	−	1982.82i	−0.368652	−	0.138162i
$47$		−	10518.0i		−	0.694528i	−0.937767	−	0.347264i	$-0.887111\pi$
$47$		−	10518.0i		−	0.694528i	0.937767	−	0.347264i	$-0.112889\pi$
$48$	−6503.68	+	8574.76i	−0.407433	+	0.537179i
$49$	−13272.8			−0.789718
$50$	−14155.9	−	10588.2i	−0.800780	−	0.598959i
$51$	−6399.81	+	6399.81i	−0.344542	+	0.344542i
$52$	1529.72	+	22378.7i	0.0784520	+	1.14770i
$53$	5698.77	−	5698.77i	0.278671	−	0.278671i	−0.553907	−	0.832578i	$-0.686864\pi$
$53$	5698.77	−	5698.77i	0.278671	−	0.278671i	0.832578	+	0.553907i	$0.186864\pi$
$54$	−20324.0	+	9243.02i	−0.948474	+	0.431350i
$55$	7272.00	+	9694.30i	0.324151	+	0.432126i
$56$	−5112.73	−	9469.37i	−0.217863	−	0.403507i
$57$	22403.8			0.913344
$58$	−28325.8	+	12882.1i	−1.10563	+	0.502823i
$59$	22000.0	+	22000.0i	0.822795	+	0.822795i	0.986508	−	0.163713i	$-0.0523471\pi$
$59$	22000.0	+	22000.0i	0.822795	+	0.822795i	−0.163713	+	0.986508i	$0.552347\pi$
$60$	1381.79	−	18749.9i	0.0495524	−	0.672389i
$61$	31061.7	−	31061.7i	1.06881	−	1.06881i	0.0713582	−	0.997451i	$-0.477267\pi$
$61$	31061.7	−	31061.7i	1.06881	−	1.06881i	0.997451	−	0.0713582i	$-0.0227333\pi$
$62$	−33294.3	−	12477.9i	−1.09999	−	0.412251i
$63$		−	7879.48i		−	0.250119i
$64$	−17975.4	+	27397.6i	−0.548566	+	0.836107i
$65$	−23513.8	−	31346.2i	−0.690303	−	0.920242i
$66$	−4523.10	+	12068.8i	−0.127813	+	0.341039i
$67$	−703.105	−	703.105i	−0.0191352	−	0.0191352i	0.697474	−	0.716610i	$-0.254307\pi$
$67$	−703.105	−	703.105i	−0.0191352	−	0.0191352i	−0.716610	+	0.697474i	$0.754307\pi$
$68$	−18111.5	+	20769.3i	−0.474988	+	0.544689i
$69$	7422.67	+	7422.67i	0.187689	+	0.187689i
$70$	16494.6	+	9019.34i	0.402344	+	0.220004i
$71$			27364.3i			0.644227i	0.946701	+	0.322114i	$0.104393\pi$
$71$			27364.3i			0.644227i	−0.946701	+	0.322114i	$0.895607\pi$
$72$	−21111.9	+	11398.8i	−0.479949	+	0.259136i
$73$	−14815.9			−0.325403			−0.162701	−	0.986675i	$-0.552021\pi$
$73$	−14815.9			−0.325403			−0.162701	+	0.986675i	$0.552021\pi$
$74$	−57628.4	+	26208.4i	−1.22337	+	0.556366i
$75$	15797.1	+	28795.0i	0.324283	+	0.591103i
$76$	68054.9	−	4651.96i	1.35153	−	0.0923852i
$77$	−9112.98	−	9112.98i	−0.175159	−	0.175159i
$78$	14625.3	−	39024.1i	0.272188	−	0.726268i
$79$	−2727.79			−0.0491749			−0.0245874	−	0.999698i	$-0.507827\pi$
$79$	−2727.79			−0.0491749			−0.0245874	+	0.999698i	$0.507827\pi$
$80$	304.146	−	57242.5i	0.00531322	−	0.999986i
$81$	9274.23			0.157060
$82$	20612.9	−	55000.7i	0.338536	−	0.903303i
$83$	−35245.6	−	35245.6i	−0.561577	−	0.561577i	0.368178	−	0.929755i	$-0.379982\pi$
$83$	−35245.6	−	35245.6i	−0.561577	−	0.561577i	−0.929755	+	0.368178i	$0.879982\pi$
$84$	1363.52	+	19947.3i	0.0210844	+	0.308451i
$85$	6804.04	−	47656.9i	0.102146	−	0.715449i
$86$	86693.3	−	39426.6i	1.26398	−	0.574835i
$87$	57813.5			0.818900
$88$	−11233.6	+	37600.0i	−0.154637	+	0.517585i
$89$		−	112845.i		−	1.51011i	−0.655663	−	0.755054i	$-0.727611\pi$
$89$		−	112845.i		−	1.51011i	0.655663	−	0.755054i	$-0.272389\pi$
$90$	20108.5	−	36774.6i	0.261682	−	0.478565i
$91$	29466.5	+	29466.5i	0.373014	+	0.373014i
$92$	24088.8	+	21006.2i	0.296719	+	0.258749i
$93$	46711.0	+	46711.0i	0.560030	+	0.560030i
$94$	−20880.5	+	55714.7i	−0.243737	+	0.650355i
$95$	−95325.6	+	71506.7i	−1.08368	+	0.812901i
$96$	51473.1	−	32509.9i	0.570036	−	0.360029i
$97$			49998.0i			0.539539i	0.962925	+	0.269770i	$0.0869476\pi$
$97$			49998.0i			0.539539i	−0.962925	+	0.269770i	$0.913052\pi$
$98$	70306.9	+	26349.3i	0.739490	+	0.277143i
$99$	−20317.3	+	20317.3i	−0.208342	+	0.208342i
$100$	53965.1	+	84188.9i	0.539651	+	0.841889i
$101$	−61876.4	−	61876.4i	−0.603562	−	0.603562i	0.337694	−	0.941256i	$-0.390353\pi$
$101$	−61876.4	−	61876.4i	−0.603562	−	0.603562i	−0.941256	+	0.337694i	$0.890353\pi$
$102$	46605.2	−	21195.2i	0.443542	−	0.201715i
$103$	−75107.0			−0.697569			−0.348785	−	0.937203i	$-0.613406\pi$
$103$	−75107.0			−0.697569			−0.348785	+	0.937203i	$0.613406\pi$
$104$	36323.5	−	121579.i	0.329310	−	1.10223i
$105$	−20959.0	−	27940.5i	−0.185523	−	0.247321i
$106$	−41500.1	+	18873.5i	−0.358744	+	0.163150i
$107$	−118403.	+	118403.i	−0.999775	+	0.999775i	−1.00000		0.000224863i	$-0.999928\pi$
$107$	−118403.	+	118403.i	−0.999775	+	0.999775i	0.000224863		1.00000i	$0.499928\pi$
$108$	126007.	−	8613.35i	1.03953	−	0.0710579i
$109$	50917.5	−	50917.5i	0.410488	−	0.410488i	−0.471420	−	0.881909i	$-0.656259\pi$
$109$	50917.5	−	50917.5i	0.410488	−	0.410488i	0.881909	+	0.471420i	$0.156259\pi$
$110$	−19275.0	−	65787.9i	−0.151884	−	0.518399i
$111$	117621.			0.906100
$112$	8283.78	+	60309.8i	0.0623998	+	0.454300i
$113$			130018.i			0.957873i	0.877850	+	0.478937i	$0.158978\pi$
$113$			130018.i			0.957873i	−0.877850	+	0.478937i	$0.841022\pi$
$114$	−118674.	−	44476.3i	−0.855254	−	0.320529i
$115$	−55273.7	−	7891.50i	−0.389739	−	0.0556436i
$116$	175617.	−	12004.5i	1.21177	−	0.0828321i
$117$	65695.3	−	65695.3i	0.443680	−	0.443680i
$118$	−72860.6	−	160210.i	−0.481713	−	1.05922i
$119$			51195.1i			0.331407i
$120$	−44542.0	+	96576.3i	−0.282369	+	0.612234i
$121$		−	114055.i		−	0.708194i
$122$	−226200.	+	102872.i	−1.37592	+	0.625744i
$123$	−77164.4	+	77164.4i	−0.459890	+	0.459890i
$124$	151591.	+	132193.i	0.885357	+	0.772063i
$125$	−159120.	−	72099.3i	−0.910858	−	0.412720i
$126$	−15642.5	+	41738.2i	−0.0877766	+	0.234211i
$127$			136398.i			0.750408i	0.926942	+	0.375204i	$0.122427\pi$
$127$			136398.i			0.750408i	−0.926942	+	0.375204i	$0.877573\pi$
$128$	149607.	−	109442.i	0.807099	−	0.590415i
$129$	−176943.			−0.936178
$130$	62325.2	+	212723.i	0.323449	+	1.10397i
$131$	205048.	−	205048.i	1.04394	−	1.04394i	0.0449532	−	0.998989i	$-0.485686\pi$
$131$	205048.	−	205048.i	1.04394	−	1.04394i	0.998989	−	0.0449532i	$-0.0143139\pi$
$132$	47918.3	−	54950.0i	0.239368	−	0.274494i
$133$	89609.3	−	89609.3i	0.439262	−	0.439262i
$134$	2328.58	+	5120.21i	0.0112029	+	0.0246335i
$135$	−176500.	+	132398.i	−0.833510	+	0.625242i
$136$	137169.	−	74061.0i	0.635931	−	0.343354i
$137$	190425.			0.866807			0.433404	−	0.901200i	$-0.357312\pi$
$137$	190425.			0.866807			0.433404	+	0.901200i	$0.357312\pi$
$138$	−24582.8	−	54054.0i	−0.109884	−	0.241618i
$139$	−113923.	−	113923.i	−0.500122	−	0.500122i	0.411354	−	0.911476i	$-0.365056\pi$
$139$	−113923.	−	113923.i	−0.500122	−	0.500122i	−0.911476	+	0.411354i	$0.865056\pi$
$140$	−69467.8	−	80521.4i	−0.299546	−	0.347209i
$141$	78166.3	−	78166.3i	0.331109	−	0.331109i
$142$	54324.1	−	144951.i	0.226085	−	0.603253i
$143$		−	151959.i		−	0.621422i
$144$	134460.	−	18468.6i	0.540364	−	0.0742211i
$145$	−245990.	+	184525.i	−0.971621	+	0.728843i
$146$	78480.9	+	29412.8i	0.304707	+	0.114197i
$147$	−98638.6	−	98638.6i	−0.376490	−	0.376490i
$148$	357291.	−	24423.0i	1.34081	−	0.0916524i
$149$	−15911.7	−	15911.7i	−0.0587152	−	0.0587152i	0.677139	−	0.735855i	$-0.263219\pi$
$149$	−15911.7	−	15911.7i	−0.0587152	−	0.0587152i	−0.735855	+	0.677139i	$0.763219\pi$
$150$	−26514.1	−	183889.i	−0.0962164	−	0.667312i
$151$			384847.i			1.37356i	0.726867	+	0.686778i	$0.240975\pi$
$151$			384847.i			1.37356i	−0.726867	+	0.686778i	$0.759025\pi$
$152$	−369727.	−	110462.i	−1.29799	−	0.387796i
$153$	114139.			0.394190
$154$	30180.9	+	66363.3i	0.102549	+	0.225489i
$155$	−347838.	−	49661.3i	−1.16292	−	0.166031i
$156$	−154942.	+	177679.i	−0.509752	+	0.584554i
$157$	−76600.1	−	76600.1i	−0.248016	−	0.248016i	0.572140	−	0.820156i	$-0.306113\pi$
$157$	−76600.1	−	76600.1i	−0.248016	−	0.248016i	−0.820156	+	0.572140i	$0.806113\pi$
$158$	14449.3	+	5415.25i	0.0460473	+	0.0172574i
$159$	84702.5			0.265707
$160$	−115250.	+	302614.i	−0.355910	+	0.934520i
$161$	59377.5			0.180533
$162$	−49126.2	−	18411.3i	−0.147071	−	0.0551185i
$163$	−266716.	−	266716.i	−0.786286	−	0.786286i	0.194597	−	0.980883i	$-0.437660\pi$
$163$	−266716.	−	266716.i	−0.786286	−	0.786286i	−0.980883	+	0.194597i	$0.937660\pi$
$164$	−218376.	+	250421.i	−0.634009	+	0.727045i
$165$	−18001.7	+	126088.i	−0.0514758	+	0.360547i
$166$	116728.	+	256668.i	0.328780	+	0.722939i
$167$	580995.			1.61206			0.806030	−	0.591874i	$-0.201612\pi$
$167$	580995.			1.61206			0.806030	+	0.591874i	$0.201612\pi$
$168$	32377.0	−	108369.i	0.0885040	−	0.296232i
$169$			120062.i			0.323363i
$170$	−130651.	+	238934.i	−0.346728	+	0.634098i
$171$	−199783.	−	199783.i	−0.522478	−	0.522478i
$172$	−537491.	+	36740.7i	−1.38532	+	0.0946948i
$173$	−288957.	−	288957.i	−0.734036	−	0.734036i	0.237381	−	0.971417i	$-0.423711\pi$
$173$	−288957.	−	288957.i	−0.734036	−	0.734036i	−0.971417	+	0.237381i	$0.923711\pi$
$174$	−306242.	−	114772.i	−0.766816	−	0.287384i
$175$	178356.	+	51988.1i	0.440244	+	0.128324i
$176$	134149.	−	176869.i	0.326442	−	0.430397i
$177$			326992.i			0.784519i
$178$	−224022.	+	597748.i	−0.529956	+	1.41406i
$179$	−300075.	+	300075.i	−0.699999	+	0.699999i	−0.964410	−	0.264411i	$-0.914822\pi$
$179$	−300075.	+	300075.i	−0.699999	+	0.699999i	0.264411	+	0.964410i	$0.414822\pi$
$180$	−179522.	+	154878.i	−0.412986	+	0.356293i
$181$	450607.	+	450607.i	1.02236	+	1.02236i	0.999744	+	0.0226108i	$0.00719784\pi$
$181$	450607.	+	450607.i	1.02236	+	1.02236i	0.0226108	+	0.999744i	$0.492802\pi$
$182$	−97588.9	−	214584.i	−0.218385	−	0.480196i
$183$	461678.			1.01909
$184$	−85897.9	−	159093.i	−0.187041	−	0.346422i
$185$	−500462.	+	375413.i	−1.07508	+	0.806454i
$186$	−154700.	−	340162.i	−0.327875	−	0.720948i
$187$	132007.	−	132007.i	0.276053	−	0.276053i
$188$	221211.	−	253672.i	0.456470	−	0.523454i
$189$	165916.	−	165916.i	0.337858	−	0.337858i
$190$	646902.	−	189534.i	1.30003	−	0.380894i
$191$	−70223.9			−0.139284			−0.0696420	−	0.997572i	$-0.522186\pi$
$191$	−70223.9			−0.139284			−0.0696420	+	0.997572i	$0.522186\pi$
$192$	−337196.	+	70021.9i	−0.660129	+	0.137082i
$193$			593768.i			1.14742i	0.819058	+	0.573711i	$0.194497\pi$
$193$			593768.i			1.14742i	−0.819058	+	0.573711i	$0.805503\pi$
$194$	99256.6	−	264843.i	0.189346	−	0.505224i
$195$	58207.9	−	407700.i	0.109621	−	0.767811i
$196$	−320111.	−	279148.i	−0.595197	−	0.519033i
$197$	685255.	−	685255.i	1.25802	−	1.25802i	0.305978	−	0.952039i	$-0.401017\pi$
$197$	685255.	−	685255.i	1.25802	−	1.25802i	0.952039	−	0.305978i	$-0.0989835\pi$
$198$	147956.	−	67287.9i	0.268207	−	0.121976i
$199$			721164.i			1.29093i	0.763792	+	0.645463i	$0.223336\pi$
$199$			721164.i			1.29093i	−0.763792	+	0.645463i	$0.776664\pi$
$200$	−118724.	−	553086.i	−0.209876	−	0.977728i
$201$		−	10450.4i		−	0.0182450i
$202$	204926.	+	450602.i	0.353361	+	0.776988i
$203$	231239.	−	231239.i	0.393840	−	0.393840i
$204$	−288948.	+	19751.3i	−0.486121	+	0.0332293i
$205$	82038.3	−	574613.i	0.136343	−	0.954973i
$206$	397847.	+	149103.i	0.653203	+	0.244805i
$207$		−	132381.i		−	0.214734i
$208$	−433767.	+	571900.i	−0.695182	+	0.916561i
$209$	−462116.			−0.731788
$210$	55553.6	+	189611.i	0.0869288	+	0.296698i
$211$	654873.	−	654873.i	1.01263	−	1.01263i	0.0127109	−	0.999919i	$-0.495954\pi$
$211$	654873.	−	654873.i	1.01263	−	1.01263i	0.999919	−	0.0127109i	$-0.00404613\pi$
$212$	257297.	−	17587.8i	0.393183	−	0.0268764i
$213$	−203362.	+	203362.i	−0.307129	+	0.307129i
$214$	862242.	−	392133.i	1.28705	−	0.585327i
$215$	752871.	−	564752.i	1.11077	−	0.833224i
$216$	−684568.	−	204526.i	−0.998349	−	0.298273i
$217$	373663.			0.538680
$218$	−370795.	+	168631.i	−0.528437	+	0.240324i
$219$	−110107.	−	110107.i	−0.155133	−	0.155133i
$220$	−28501.8	+	386748.i	−0.0397023	+	0.538730i
$221$	−426840.	+	426840.i	−0.587875	+	0.587875i
$222$	−623045.	−	233502.i	−0.848471	−	0.317986i
$223$		−	57781.0i		−	0.0778077i	−0.999243	−	0.0389039i	$-0.987613\pi$
$223$		−	57781.0i		−	0.0778077i	0.999243	−	0.0389039i	$-0.0123866\pi$
$224$	75848.0	−	335910.i	0.101001	−	0.447304i
$225$	115907.	−	397644.i	0.152634	−	0.523646i
$226$	258114.	−	688715.i	0.336155	−	0.896951i
$227$	871988.	+	871988.i	1.12317	+	1.12317i	0.991262	+	0.131910i	$0.0421109\pi$
$227$	871988.	+	871988.i	1.12317	+	1.12317i	0.131910	+	0.991262i	$0.457889\pi$
$228$	540332.	+	471188.i	0.688372	+	0.600285i
$229$	844221.	+	844221.i	1.06382	+	1.06382i	0.997820	+	0.0659989i	$0.0210234\pi$
$229$	844221.	+	844221.i	1.06382	+	1.06382i	0.0659989	+	0.997820i	$0.478977\pi$
$230$	277122.	+	151532.i	0.345424	+	0.188879i
$231$		−	135449.i		−	0.167011i
$232$	−954087.	−	285049.i	−1.16377	−	0.347696i
$233$	−312305.			−0.376867			−0.188434	−	0.982086i	$-0.560341\pi$
$233$	−312305.			−0.376867			−0.188434	+	0.982086i	$0.560341\pi$
$234$	−478412.	+	217573.i	−0.571166	+	0.259756i
$235$	−83103.4	+	582073.i	−0.0981633	+	0.687556i
$236$	67897.1	+	993286.i	0.0793544	+	1.16090i
$237$	−20272.0	−	20272.0i	−0.0234436	−	0.0234436i
$238$	101633.	−	271184.i	0.116304	−	0.310329i
$239$	−536668.			−0.607731			−0.303865	−	0.952715i	$-0.598277\pi$
$239$	−536668.			−0.607731			−0.303865	+	0.952715i	$0.598277\pi$
$240$	427666.	−	423146.i	0.479266	−	0.474200i
$241$	266483.			0.295547			0.147774	−	0.989021i	$-0.452789\pi$
$241$	266483.			0.295547			0.147774	+	0.989021i	$0.452789\pi$
$242$	−226424.	+	604159.i	−0.248533	+	0.663151i
$243$	−609263.	−	609263.i	−0.661895	−	0.661895i
$244$	1.40242e6	−	95863.7i	1.50801	−	0.103081i
$245$	734523.	+	104869.i	0.781790	+	0.111617i
$246$	561933.	−	255557.i	0.592034	−	0.269247i
$247$	1.49424e6			1.55839
$248$	−540556.	−	1.00117e6i	−0.558100	−	1.03367i
$249$		−	523865.i		−	0.535452i
$250$	699739.	+	697803.i	0.708086	+	0.706127i
$251$	−664803.	−	664803.i	−0.666053	−	0.666053i	0.290747	−	0.956800i	$-0.406096\pi$
$251$	−664803.	−	664803.i	−0.666053	−	0.666053i	−0.956800	+	0.290747i	$0.906096\pi$
$252$	165718.	−	190036.i	0.164388	−	0.188510i
$253$	−153105.	−	153105.i	−0.150379	−	0.150379i
$254$	270778.	−	722507.i	0.263348	−	0.702681i
$255$	404734.	−	303604.i	0.389780	−	0.292386i
$256$	−1.00974e6	+	282718.i	−0.962967	+	0.269621i
$257$			537440.i			0.507572i	0.967260	+	0.253786i	$0.0816758\pi$
$257$			537440.i			0.507572i	−0.967260	+	0.253786i	$0.918324\pi$
$258$	937278.	+	351269.i	0.876636	+	0.328542i
$259$	470452.	−	470452.i	0.435778	−	0.435778i
$260$	92159.7	−	1.25054e6i	0.0845488	−	1.14726i
$261$	−515544.	−	515544.i	−0.468451	−	0.468451i
$262$	−1.49321e6	+	679088.i	−1.34391	+	0.611185i
$263$	−13908.6			−0.0123992			−0.00619961	−	0.999981i	$-0.501973\pi$
$263$	−13908.6			−0.0123992			−0.00619961	+	0.999981i	$0.501973\pi$
$264$	−362914.	+	195946.i	−0.320475	+	0.173032i
$265$	−360399.	+	270347.i	−0.315260	+	0.236487i
$266$	−652560.	+	296773.i	−0.565479	+	0.257170i
$267$	838625.	−	838625.i	0.719929	−	0.719929i
$268$	−2169.95	−	31744.8i	−0.00184549	−	0.0269983i
$269$	705554.	−	705554.i	0.594497	−	0.594497i	−0.344346	−	0.938843i	$-0.611899\pi$
$269$	705554.	−	705554.i	0.594497	−	0.594497i	0.938843	+	0.344346i	$0.111899\pi$
$270$	1.19777e6	−	350933.i	0.999919	−	0.292964i
$271$	−1.23769e6			−1.02374			−0.511868	−	0.859064i	$-0.671046\pi$
$271$	−1.23769e6			−1.02374			−0.511868	+	0.859064i	$0.671046\pi$
$272$	−873623.	+	119995.i	−0.715981	+	0.0983427i
$273$			437970.i			0.355662i
$274$	−1.00869e6	−	378034.i	−0.811677	−	0.304197i
$275$	−325841.	−	593944.i	−0.259821	−	0.473602i
$276$	22908.1	+	335130.i	0.0181016	+	0.264814i
$277$	8261.98	−	8261.98i	0.00646971	−	0.00646971i	−0.703865	−	0.710334i	$-0.748544\pi$
$277$	8261.98	−	8261.98i	0.00646971	−	0.00646971i	0.710334	+	0.703865i	$0.248544\pi$
$278$	377298.	+	829622.i	0.292801	+	0.643826i
$279$		−	833078.i		−	0.640730i
$280$	208123.	+	564436.i	0.158645	+	0.430249i
$281$			2.28352e6i			1.72520i	0.505885	+	0.862601i	$0.331166\pi$
$281$			2.28352e6i			1.72520i	−0.505885	+	0.862601i	$0.668834\pi$
$282$	−569229.	+	258875.i	−0.426250	+	0.193851i
$283$	−1.52649e6	+	1.52649e6i	−1.13300	+	1.13300i	−0.143318	+	0.989677i	$0.545777\pi$
$283$	−1.52649e6	+	1.52649e6i	−1.13300	+	1.13300i	−0.989677	+	0.143318i	$0.954223\pi$
$284$	−575516.	+	659969.i	−0.423411	+	0.485543i
$285$	−1.23984e6	−	177013.i	−0.904176	−	0.129090i
$286$	−301671.	+	804938.i	−0.218082	+	0.581899i
$287$			617275.i			0.442358i
$288$	−748907.	−	169102.i	−0.532043	−	0.120135i
$289$	678265.			0.477700
$290$	1.66934e6	−	489097.i	1.16560	−	0.341507i
$291$	−371567.	+	371567.i	−0.257220	+	0.257220i
$292$	−357328.	−	311603.i	−0.245251	−	0.213867i
$293$	−981488.	+	981488.i	−0.667907	+	0.667907i	−0.957231	−	0.289324i	$-0.906569\pi$
$293$	−981488.	+	981488.i	−0.667907	+	0.667907i	0.289324	+	0.957231i	$0.406569\pi$
$294$	326677.	+	718314.i	0.220419	+	0.484670i
$295$	−1.04367e6	−	1.39131e6i	−0.698243	−	0.930828i
$296$	−1.94108e6	−	579928.i	−1.28770	−	0.384720i
$297$	−855631.			−0.562854
$298$	52697.2	+	115873.i	0.0343754	+	0.0755863i
$299$	495061.	+	495061.i	0.320244	+	0.320244i
$300$	−224613.	+	1.02671e6i	−0.144089	+	0.658635i
$301$	−707725.	+	707725.i	−0.450244	+	0.450244i
$302$	764004.	−	2.03856e6i	0.482035	−	1.28619i
$303$		−	919687.i		−	0.575484i
$304$	1.73918e6	+	1.31911e6i	1.07934	+	0.818648i
$305$	−1.96439e6	+	1.47355e6i	−1.20914	+	0.907016i
$306$	−604602.	−	226590.i	−0.369119	−	0.138337i
$307$	−1.46066e6	−	1.46066e6i	−0.884513	−	0.884513i	0.109477	−	0.993989i	$-0.465083\pi$
$307$	−1.46066e6	−	1.46066e6i	−0.884513	−	0.884513i	−0.993989	+	0.109477i	$0.965083\pi$
$308$	−28124.8	−	411446.i	−0.0168932	−	0.247136i
$309$	−558168.	−	558168.i	−0.332559	−	0.332559i
$310$	1.74393e6	+	953593.i	1.03069	+	0.563584i
$311$			1.04940e6i			0.615232i	0.951511	+	0.307616i	$0.0995312\pi$
$311$			1.04940e6i			0.615232i	−0.951511	+	0.307616i	$0.900469\pi$
$312$	1.17347e6	−	633585.i	0.682474	−	0.368484i
$313$	−1.11537e6			−0.643515			−0.321757	−	0.946822i	$-0.604274\pi$
$313$	−1.11537e6			−0.643515			−0.321757	+	0.946822i	$0.604274\pi$
$314$	253688.	+	557823.i	0.145203	+	0.319281i
$315$	−62256.1	+	436055.i	−0.0353513	+	0.247608i
$316$	−65788.4	−	57369.8i	−0.0370623	−	0.0323196i
$317$	2.11341e6	+	2.11341e6i	1.18123	+	1.18123i	0.979425	+	0.201809i	$0.0646820\pi$
$317$	2.11341e6	+	2.11341e6i	1.18123	+	1.18123i	0.201809	+	0.979425i	$0.435318\pi$
$318$	−448675.	−	168152.i	−0.248808	−	0.0932471i
$319$	−1.19250e6			−0.656117
$320$	1.21124e6	−	1.37417e6i	0.661233	−	0.750180i
$321$	−1.75985e6			−0.953266
$322$	−314527.	−	117877.i	−0.169051	−	0.0633562i
$323$	1.29804e6	+	1.29804e6i	0.692282	+	0.692282i
$324$	223675.	+	195052.i	0.118373	+	0.103226i
$325$	1.05360e6	+	1.92050e6i	0.553308	+	1.00857i
$326$	883325.	+	1.94230e6i	0.460338	+	1.01222i
$327$	756801.			0.391392
$328$	1.65389e6	−	892975.i	0.848834	−	0.458305i
$329$		−	625289.i		−	0.318486i
$330$	345667.	−	632157.i	0.174732	−	0.319551i
$331$	−1.69261e6	−	1.69261e6i	−0.849157	−	0.849157i	0.140871	−	0.990028i	$-0.455010\pi$
$331$	−1.69261e6	−	1.69261e6i	−0.849157	−	0.849157i	−0.990028	+	0.140871i	$0.955010\pi$
$332$	−108776.	−	1.59132e6i	−0.0541612	−	0.792340i
$333$	−1.04887e6	−	1.04887e6i	−0.518334	−	0.518334i
$334$	−3.07757e6	−	1.15340e6i	−1.50953	−	0.565736i
$335$	33354.9	+	44465.4i	0.0162386	+	0.0216476i
$336$	−386639.	+	509763.i	−0.186834	+	0.246331i
$337$		−	86139.5i		−	0.0413169i	−0.999787	−	0.0206585i	$-0.993424\pi$
$337$		−	86139.5i		−	0.0413169i	0.999787	−	0.0206585i	$-0.00657626\pi$
$338$	238349.	−	635979.i	0.113481	−	0.302796i
$339$	−966249.	+	966249.i	−0.456656	+	0.456656i
$340$	1.16640e6	−	1.00628e6i	0.547205	−	0.472087i
$341$	−963492.	−	963492.i	−0.448706	−	0.448706i
$342$	661652.	+	1.45488e6i	0.305889	+	0.672606i
$343$	−1.78822e6			−0.820702
$344$	2.92006e6	+	872415.i	1.33044	+	0.397491i
$345$	−352128.	−	469422.i	−0.159277	−	0.212332i
$346$	956982.	+	2.10426e6i	0.429748	+	0.944952i
$347$	−946713.	+	946713.i	−0.422080	+	0.422080i	−0.885919	−	0.463839i	$-0.846471\pi$
$347$	−946713.	+	946713.i	−0.422080	+	0.422080i	0.463839	+	0.885919i	$0.346471\pi$
$348$	1.39434e6	+	1.21591e6i	0.617191	+	0.538212i
$349$	2.63823e6	−	2.63823e6i	1.15944	−	1.15944i	0.174847	−	0.984596i	$-0.444057\pi$
$349$	2.63823e6	−	2.63823e6i	1.15944	−	1.15944i	0.984596	−	0.174847i	$-0.0559431\pi$
$350$	−841559.	−	629460.i	−0.367210	−	0.274662i
$351$	2.76666e6			1.19864
$352$	−1.06172e6	+	670571.i	−0.456723	+	0.288462i
$353$		−	2.93546e6i		−	1.25383i	−0.779086	−	0.626917i	$-0.784317\pi$
$353$		−	2.93546e6i		−	1.25383i	0.779086	−	0.626917i	$-0.215683\pi$
$354$	649148.	−	1.73210e6i	0.275319	−	0.734622i
$355$	216207.	−	1.51436e6i	0.0910538	−	0.637760i
$356$	2.37332e6	−	2.72158e6i	0.992500	−	1.13814i
$357$	−380464.	+	380464.i	−0.157995	+	0.157995i
$358$	2.18523e6	−	993805.i	0.901135	−	0.409821i
$359$			2.41933e6i			0.990740i	0.868682	+	0.495370i	$0.164968\pi$
$359$			2.41933e6i			0.990740i	−0.868682	+	0.495370i	$0.835032\pi$
$360$	1.25840e6	−	464009.i	0.511757	−	0.188699i
$361$		−	2.06796e6i		−	0.835167i
$362$	−1.49235e6	−	3.28145e6i	−0.598547	−	1.31612i
$363$	847618.	−	847618.i	0.337624	−	0.337624i
$364$	90940.7	+	1.33040e6i	0.0359753	+	0.526294i
$365$	819921.	+	117061.i	0.322136	+	0.0459918i
$366$	−2.44554e6	−	916530.i	−0.954272	−	0.357638i
$367$		−	377226.i		−	0.146196i	−0.997325	−	0.0730982i	$-0.976711\pi$
$367$		−	377226.i		−	0.146196i	0.997325	−	0.0730982i	$-0.0232887\pi$
$368$	139174.	+	1.01325e6i	0.0535720	+	0.390030i
$369$	1.37621e6			0.526160
$370$	3.39626e6	−	995061.i	1.28972	−	0.377873i
$371$	338788.	−	338788.i	0.127789	−	0.127789i
$372$	144161.	+	2.10898e6i	0.0540121	+	0.790159i
$373$	1.71291e6	−	1.71291e6i	0.637473	−	0.637473i	−0.312459	−	0.949931i	$-0.601153\pi$
$373$	1.71291e6	−	1.71291e6i	0.637473	−	0.637473i	0.949931	+	0.312459i	$0.101153\pi$
$374$	−961311.	+	437188.i	−0.355373	+	0.161618i
$375$	−646709.	−	1.71834e6i	−0.237482	−	0.631003i
$376$	−1.67536e6	+	904568.i	−0.611139	+	0.329968i
$377$	3.85591e6			1.39725
$378$	−1.20825e6	+	549490.i	−0.434937	+	0.197802i
$379$	1.59231e6	+	1.59231e6i	0.569416	+	0.569416i	0.931965	−	0.362549i	$-0.118093\pi$
$379$	1.59231e6	+	1.59231e6i	0.569416	+	0.569416i	−0.362549	+	0.931965i	$0.618093\pi$
$380$	−3.80295e6	−	280262.i	−1.35102	−	0.0995648i
$381$	−1.01366e6	+	1.01366e6i	−0.357750	+	0.357750i
$382$	371981.	+	139409.i	0.130425	+	0.0488803i
$383$			2.91005e6i			1.01369i	0.862038	+	0.506844i	$0.169188\pi$
$383$			2.91005e6i			1.01369i	−0.862038	+	0.506844i	$0.830812\pi$
$384$	1.92516e6	+	298495.i	0.666251	+	0.103302i
$385$	432315.	+	576319.i	0.148644	+	0.198158i
$386$	1.17876e6	−	3.14523e6i	0.402676	−	1.07444i
$387$	1.57786e6	+	1.57786e6i	0.535540	+	0.535540i
$388$	−1.05154e6	+	1.20584e6i	−0.354606	+	0.406642i
$389$	−2.78618e6	−	2.78618e6i	−0.933543	−	0.933543i	0.0643819	−	0.997925i	$-0.479492\pi$
$389$	−2.78618e6	−	2.78618e6i	−0.933543	−	0.933543i	−0.997925	+	0.0643819i	$0.979492\pi$
$390$	−1.11770e6	+	2.04406e6i	−0.372104	+	0.680507i
$391$			860118.i			0.284522i
$392$	1.14148e6	+	2.11416e6i	0.375192	+	0.694899i
$393$	3.04768e6			0.995378
$394$	−4.99022e6	+	2.26946e6i	−1.61949	+	0.736517i
$395$	150957.	+	21552.4i	0.0486812	+	0.00695028i
$396$	−917314.	+	62703.9i	−0.293955	+	0.0200936i
$397$	−1.46318e6	−	1.46318e6i	−0.465931	−	0.465931i	0.434663	−	0.900593i	$-0.356868\pi$
$397$	−1.46318e6	−	1.46318e6i	−0.465931	−	0.465931i	−0.900593	+	0.434663i	$0.856868\pi$
$398$	1.43166e6	−	3.82005e6i	0.453037	−	1.20882i
$399$	1.33189e6			0.418828
$400$	−469107.	+	3.16543e6i	−0.146596	+	0.989196i
$401$	2.49761e6			0.775647			0.387824	−	0.921734i	$-0.373227\pi$
$401$	2.49761e6			0.775647			0.387824	+	0.921734i	$0.373227\pi$
$402$	−20746.4	+	55356.7i	−0.00640290	+	0.0170846i
$403$	3.11542e6	+	3.11542e6i	0.955552	+	0.955552i
$404$	−190965.	−	2.79369e6i	−0.0582105	−	0.851578i
$405$	−513241.	−	73276.0i	−0.155483	−	0.0221985i
$406$	−1.68394e6	+	765829.i	−0.507006	+	0.230577i
$407$	−2.42612e6			−0.725984
$408$	1.56979e6	+	469000.i	0.466864	+	0.139483i
$409$		−	5.42197e6i		−	1.60269i	−0.598204	−	0.801344i	$-0.704119\pi$
$409$		−	5.42197e6i		−	1.60269i	0.598204	−	0.801344i	$-0.295881\pi$
$410$	−1.57529e6	+	2.88090e6i	−0.462809	+	0.846387i
$411$	1.41517e6	+	1.41517e6i	0.413242	+	0.413242i
$412$	−1.81142e6	−	1.57962e6i	−0.525746	−	0.458469i
$413$	1.30788e6	+	1.30788e6i	0.377305	+	0.377305i
$414$	−262805.	+	701233.i	−0.0753587	+	0.201077i
$415$	1.67203e6	+	2.22898e6i	0.476567	+	0.635311i
$416$	3.43304e6	−	2.16827e6i	0.972625	−	0.614299i
$417$		−	1.69328e6i		−	0.476856i
$418$	2.44786e6	+	917399.i	0.685245	+	0.256813i
$419$	−4.40081e6	+	4.40081e6i	−1.22461	+	1.22461i	−0.258635	+	0.965975i	$0.583273\pi$
$419$	−4.40081e6	+	4.40081e6i	−1.22461	+	1.22461i	−0.965975	+	0.258635i	$0.916727\pi$
$420$	82146.5	−	1.11467e6i	0.0227230	−	0.308334i
$421$	−2.37338e6	−	2.37338e6i	−0.652623	−	0.652623i	0.301001	−	0.953624i	$-0.402679\pi$
$421$	−2.37338e6	−	2.37338e6i	−0.652623	−	0.652623i	−0.953624	+	0.301001i	$0.902679\pi$
$422$	−4.76897e6	+	2.16884e6i	−1.30360	+	0.592853i
$423$	−1.39407e6			−0.378822
$424$	−1.39783e6	−	417625.i	−0.377608	−	0.112816i
$425$	−753078.	+	2.58360e6i	−0.202240	+	0.693829i
$426$	1.48094e6	−	673505.i	0.395379	−	0.179811i
$427$	1.84659e6	−	1.84659e6i	0.490119	−	0.490119i
$428$	−5.34582e6	+	365419.i	−1.41060	+	0.0964232i
$429$	1.12931e6	−	1.12931e6i	0.296257	−	0.296257i
$430$	−5.10916e6	+	1.49692e6i	−1.33254	+	0.390416i
$431$	−487650.			−0.126449			−0.0632245	−	0.997999i	$-0.520138\pi$
$431$	−487650.			−0.126449			−0.0632245	+	0.997999i	$0.520138\pi$
$432$	3.22018e6	+	2.44240e6i	0.830176	+	0.629662i
$433$		−	3.70876e6i		−	0.950624i	−0.879817	−	0.475312i	$-0.842335\pi$
$433$		−	3.70876e6i		−	0.950624i	0.879817	−	0.475312i	$-0.157665\pi$
$434$	−1.97932e6	−	741801.i	−0.504419	−	0.189044i
$435$	−3.19943e6	−	456786.i	−0.810679	−	0.115742i
$436$	2.29890e6	−	157143.i	0.579167	−	0.0395895i
$437$	1.50551e6	−	1.50551e6i	0.377119	−	0.377119i
$438$	364657.	+	801827.i	0.0908238	+	0.199708i
$439$			5.29801e6i			1.31205i	0.754737	+	0.656027i	$0.227764\pi$
$439$			5.29801e6i			1.31205i	−0.754737	+	0.656027i	$0.772236\pi$
$440$	918753.	−	1.99205e6i	0.226239	−	0.490533i
$441$			1.75919e6i			0.430742i
$442$	3.10837e6	−	1.41363e6i	0.756793	−	0.344176i
$443$	1.51452e6	−	1.51452e6i	0.366661	−	0.366661i	−0.499597	−	0.866258i	$-0.666519\pi$
$443$	1.51452e6	−	1.51452e6i	0.366661	−	0.366661i	0.866258	+	0.499597i	$0.166519\pi$
$444$	2.83676e6	+	2.47375e6i	0.682912	+	0.595524i
$445$	−891594.	+	6.24491e6i	−0.213436	+	1.49495i
$446$	−114708.	+	306070.i	−0.0273058	+	0.0728590i
$447$		−	236500.i		−	0.0559838i
$448$	−1.06863e6	+	1.62876e6i	−0.251553	+	0.383410i
$449$	5.50666e6			1.28906			0.644528	−	0.764580i	$-0.277054\pi$
$449$	5.50666e6			1.28906			0.644528	+	0.764580i	$0.277054\pi$
$450$	−1.40337e6	+	1.87625e6i	−0.326695	+	0.436776i
$451$	1.59165e6	−	1.59165e6i	0.368472	−	0.368472i
$452$	−2.73449e6	+	3.13576e6i	−0.629551	+	0.721933i
$453$	−2.86005e6	+	2.86005e6i	−0.654829	+	0.654829i
$454$	−2.88790e6	−	6.35006e6i	−0.657571	−	1.44590i
$455$	−1.39788e6	−	1.86351e6i	−0.316549	−	0.421991i
$456$	−1.92676e6	−	3.56859e6i	−0.433927	−	0.803682i
$457$	−2.08661e6			−0.467358			−0.233679	−	0.972314i	$-0.575077\pi$
$457$	−2.08661e6			−0.467358			−0.233679	+	0.972314i	$0.575077\pi$
$458$	−2.79594e6	−	6.14786e6i	−0.622822	−	1.36949i
$459$	2.40339e6	+	2.40339e6i	0.532468	+	0.532468i
$460$	−1.16711e6	−	1.35282e6i	−0.257169	−	0.298089i
$461$	−4.65515e6	+	4.65515e6i	−1.02019	+	1.02019i	−0.0203996	+	0.999792i	$0.506494\pi$
$461$	−4.65515e6	+	4.65515e6i	−1.02019	+	1.02019i	−0.999792	+	0.0203996i	$0.993506\pi$
$462$	−268895.	+	717481.i	−0.0586108	+	0.156389i
$463$		−	8.10975e6i		−	1.75815i	−0.476686	−	0.879073i	$-0.658162\pi$
$463$		−	8.10975e6i		−	1.75815i	0.476686	−	0.879073i	$-0.341838\pi$
$464$	4.48798e6	+	3.40399e6i	0.967734	+	0.733995i
$465$	−2.21594e6	−	2.95408e6i	−0.475255	−	0.633562i
$466$	1.65430e6	+	619991.i	0.352898	+	0.132258i
$467$	−586380.	−	586380.i	−0.124419	−	0.124419i	0.642155	−	0.766574i	$-0.278040\pi$
$467$	−586380.	−	586380.i	−0.124419	−	0.124419i	−0.766574	+	0.642155i	$0.778040\pi$
$468$	2.96611e6	−	202751.i	0.625997	−	0.0427907i
$469$	−41799.0	−	41799.0i	−0.00877474	−	0.00877474i
$470$	1.59574e6	−	2.91830e6i	0.333210	−	0.609377i
$471$		−	1.13853e6i		−	0.236479i
$472$	1.61223e6	−	5.39630e6i	0.333098	−	1.11491i
$473$	3.64974e6			0.750083
$474$	67137.8	+	147626.i	0.0137253	+	0.0301799i
$475$	5.84034e6	−	3.20405e6i	1.18769	−	0.651576i
$476$	−1.07672e6	+	1.23472e6i	−0.217813	+	0.249776i
$477$	−755323.	−	755323.i	−0.151998	−	0.151998i
$478$	2.84277e6	+	1.06540e6i	0.569078	+	0.213277i
$479$	−1.20436e6			−0.239837			−0.119919	−	0.992784i	$-0.538263\pi$
$479$	−1.20436e6			−0.239837			−0.119919	+	0.992784i	$0.538263\pi$
$480$	−3.10541e6	+	1.39242e6i	−0.615200	+	0.275847i
$481$	7.84480e6			1.54603
$482$	−1.41158e6	−	529026.i	−0.276750	−	0.103719i
$483$	441272.	+	441272.i	0.0860674	+	0.0860674i
$484$	2.39877e6	−	2.75077e6i	0.465452	−	0.533754i
$485$	395036.	−	2.76691e6i	0.0762574	−	0.534123i
$486$	2.01779e6	+	4.43683e6i	0.387512	+	0.852083i
$487$	−8.29984e6			−1.58580			−0.792898	−	0.609354i	$-0.791429\pi$
$487$	−8.29984e6			−1.58580			−0.792898	+	0.609354i	$0.791429\pi$
$488$	−7.61901e6	−	2.27630e6i	−1.44827	−	0.432693i
$489$		−	3.96428e6i		−	0.749708i
$490$	−3.68263e6	−	2.01368e6i	−0.692896	−	0.378879i
$491$	4.87952e6	+	4.87952e6i	0.913425	+	0.913425i	0.996540	−	0.0831147i	$-0.0264868\pi$
$491$	4.87952e6	+	4.87952e6i	0.913425	+	0.913425i	−0.0831147	+	0.996540i	$0.526487\pi$
$492$	−3.48393e6	+	238148.i	−0.648869	+	0.0443541i
$493$	3.34963e6	+	3.34963e6i	0.620696	+	0.620696i
$494$	−7.91508e6	−	2.96638e6i	−1.45928	−	0.546902i
$495$	1.28490e6	−	963841.i	0.235698	−	0.176804i
$496$	875823.	+	6.37640e6i	0.159850	+	1.16378i
$497$			1.62679e6i			0.295420i
$498$	−1.03998e6	+	2.77495e6i	−0.187911	+	0.501397i
$499$	−5.13074e6	+	5.13074e6i	−0.922419	+	0.922419i	−0.997200	−	0.0747809i	$-0.976174\pi$
$499$	−5.13074e6	+	5.13074e6i	−0.922419	+	0.922419i	0.0747809	+	0.997200i	$0.476174\pi$
$500$	−2.32128e6	−	5.08544e6i	−0.415242	−	0.909711i
$501$	4.31775e6	+	4.31775e6i	0.768534	+	0.768534i
$502$	2.20173e6	+	4.84128e6i	0.389946	+	0.857435i
$503$	−6.77414e6			−1.19381			−0.596904	−	0.802313i	$-0.703603\pi$
$503$	−6.77414e6			−1.19381			−0.596904	+	0.802313i	$0.703603\pi$
$504$	−1.25508e6	+	677649.i	−0.220088	+	0.118831i
$505$	2.93539e6	+	3.91316e6i	0.512197	+	0.682809i
$506$	507062.	+	1.11495e6i	0.0880409	+	0.193589i
$507$	−892261.	+	892261.i	−0.154160	+	0.154160i
$508$	−2.86866e6	+	3.28962e6i	−0.493197	+	0.565570i
$509$	−2.85861e6	+	2.85861e6i	−0.489057	+	0.489057i	−0.908009	−	0.418951i	$-0.862398\pi$
$509$	−2.85861e6	+	2.85861e6i	−0.489057	+	0.489057i	0.418951	+	0.908009i	$0.362398\pi$
$510$	−2.74662e6	+	804726.i	−0.467599	+	0.137001i
$511$	−880795.			−0.149218
$512$	5.90994e6	+	506980.i	0.996341	+	0.0854704i
$513$		−	8.41355e6i		−	1.41152i
$514$	1.06693e6	−	2.84686e6i	0.178127	−	0.475289i
$515$	4.15646e6	+	593423.i	0.690567	+	0.0985931i
$516$	−4.26748e6	−	3.72139e6i	−0.705582	−	0.615292i
$517$	−1.61231e6	+	1.61231e6i	−0.265291	+	0.265291i
$518$	−3.42596e6	+	1.55807e6i	−0.560994	+	0.255130i
$519$		−	4.29484e6i		−	0.699889i
$520$	−2.97076e6	+	6.44123e6i	−0.481792	+	1.04462i
$521$		−	4.77485e6i		−	0.770664i	−0.922778	−	0.385332i	$-0.874087\pi$
$521$		−	4.77485e6i		−	0.770664i	0.922778	−	0.385332i	$-0.125913\pi$
$522$	1.70741e6	+	3.75434e6i	0.274259	+	0.603055i
$523$	875194.	−	875194.i	0.139910	−	0.139910i	−0.633683	−	0.773593i	$-0.718457\pi$
$523$	875194.	−	875194.i	0.139910	−	0.139910i	0.773593	+	0.633683i	$0.218457\pi$
$524$	9.25779e6	−	632826.i	1.47292	−	0.100683i
$525$	939125.	+	1.71184e6i	0.148705	+	0.271059i
$526$	73674.8	+	27611.5i	0.0116106	+	0.00435137i
$527$			5.41273e6i			0.848966i
$528$	2.31137e6	−	317476.i	0.360816	−	0.0495594i
$529$	−5.43875e6			−0.845007
$530$	2.44576e6	−	716576.i	0.378202	−	0.110808i
$531$	2.91590e6	−	2.91590e6i	0.448784	−	0.448784i
$532$	4.04581e6	−	276556.i	0.619765	−	0.0423646i
$533$	−5.14654e6	+	5.14654e6i	−0.784688	+	0.784688i
$534$	−6.10710e6	+	2.77740e6i	−0.926791	+	0.421489i
$535$	7.48797e6	−	5.61697e6i	1.13105	−	0.848432i
$536$	−51525.9	+	172462.i	−0.00774664	+	0.0259288i
$537$	−4.46010e6			−0.667435
$538$	−5.13804e6	+	2.33669e6i	−0.765318	+	0.348053i
$539$	2.03459e6	+	2.03459e6i	0.301651	+	0.301651i
$540$	−7.04136e6	−	518920.i	−1.03914	−	0.0765802i
$541$	3.23621e6	−	3.23621e6i	0.475383	−	0.475383i	−0.428268	−	0.903652i	$-0.640876\pi$
$541$	3.23621e6	−	3.23621e6i	0.475383	−	0.475383i	0.903652	+	0.428268i	$0.140876\pi$
$542$	6.55612e6	+	2.45708e6i	0.958625	+	0.359270i
$543$			6.69750e6i			0.974795i
$544$	4.86585e6	+	1.09870e6i	0.704956	+	0.159178i
$545$	−3.22010e6	+	2.41550e6i	−0.464385	+	0.348350i
$546$	869463.	−	2.31995e6i	0.124816	−	0.333041i
$547$	−3.21839e6	−	3.21839e6i	−0.459908	−	0.459908i	0.438717	−	0.898625i	$-0.355433\pi$
$547$	−3.21839e6	−	3.21839e6i	−0.459908	−	0.459908i	−0.898625	+	0.438717i	$0.855433\pi$
$548$	4.59264e6	+	4.00495e6i	0.653298	+	0.569699i
$549$	−4.11696e6	−	4.11696e6i	−0.582969	−	0.582969i
$550$	546898.	+	3.79303e6i	0.0770903	+	0.534662i
$551$		−	1.17260e7i		−	1.64540i
$552$	543958.	−	1.82068e6i	0.0759833	−	0.254324i
$553$	−162165.			−0.0225499
$554$	−60166.1	+	27362.5i	−0.00832870	+	0.00378775i
$555$	−6.50919e6	−	929325.i	−0.897004	−	0.128066i
$556$	−351595.	−	5.14358e6i	−0.0482342	−	0.705633i
$557$	3.17181e6	+	3.17181e6i	0.433180	+	0.433180i	0.889709	−	0.456529i	$-0.150907\pi$
$557$	3.17181e6	+	3.17181e6i	0.433180	+	0.433180i	−0.456529	+	0.889709i	$0.650907\pi$
$558$	−1.65384e6	+	4.41287e6i	−0.224857	+	0.599978i
$559$	−1.18013e7			−1.59736
$560$	18081.3	−	3.40302e6i	0.00243646	−	0.458559i
$561$	1.96206e6			0.263211
$562$	4.53328e6	−	1.20960e7i	0.605441	−	1.61548i
$563$	1.00218e7	+	1.00218e7i	1.33252	+	1.33252i	0.903110	+	0.429410i	$0.141278\pi$
$563$	1.00218e7	+	1.00218e7i	1.33252	+	1.33252i	0.429410	+	0.903110i	$0.358722\pi$
$564$	3.52917e6	−	241240.i	0.467169	−	0.0319338i
$565$	1.02728e6	−	7.19527e6i	0.135384	−	0.948257i
$566$	1.11163e7	−	5.05551e6i	1.45855	−	0.663322i
$567$	551346.			0.0720222
$568$	4.35873e6	−	2.35338e6i	0.566877	−	0.306070i
$569$			3.52950e6i			0.457017i	0.973542	+	0.228509i	$0.0733849\pi$
$569$			3.52950e6i			0.457017i	−0.973542	+	0.228509i	$0.926615\pi$
$570$	6.21610e6	+	3.39899e6i	0.801365	+	0.438191i
$571$	−5.48683e6	−	5.48683e6i	−0.704258	−	0.704258i	0.261064	−	0.965322i	$-0.415927\pi$
$571$	−5.48683e6	−	5.48683e6i	−0.704258	−	0.704258i	−0.965322	+	0.261064i	$0.915927\pi$
$572$	3.19595e6	−	3.66493e6i	0.408422	−	0.468355i
$573$	−521879.	−	521879.i	−0.0664023	−	0.0664023i
$574$	1.22542e6	−	3.26975e6i	0.155241	−	0.414223i
$575$	2.99653e6	+	873440.i	0.377962	+	0.110170i
$576$	3.63131e6	+	2.38249e6i	0.456044	+	0.299209i
$577$		−	4.75126e6i		−	0.594113i	−0.954860	−	0.297057i	$-0.903995\pi$
$577$		−	4.75126e6i		−	0.594113i	0.954860	−	0.297057i	$-0.0960050\pi$
$578$	−3.59282e6	−	1.34650e6i	−0.447317	−	0.167644i
$579$	−4.41267e6	+	4.41267e6i	−0.547022	+	0.547022i
$580$	−9.81359e6	−	723223.i	−1.21132	−	0.0892693i
$581$	−2.09532e6	−	2.09532e6i	−0.257520	−	0.257520i
$582$	2.70586e6	−	1.23058e6i	0.331129	−	0.150592i
$583$	−1.74713e6			−0.212889
$584$	1.27419e6	+	2.35995e6i	0.154598	+	0.286333i
$585$	−4.15467e6	+	3.11655e6i	−0.501935	+	0.376517i
$586$	7.14747e6	−	3.25055e6i	0.859822	−	0.391032i
$587$	−4.36354e6	+	4.36354e6i	−0.522689	+	0.522689i	−0.918383	−	0.395693i	$-0.870504\pi$
$587$	−4.36354e6	+	4.36354e6i	−0.522689	+	0.522689i	0.395693	+	0.918383i	$0.370504\pi$
$588$	−304422.	−	4.45348e6i	−0.0363106	−	0.531198i
$589$	9.47417e6	−	9.47417e6i	1.12526	−	1.12526i
$590$	2.76632e6	+	9.44177e6i	0.327169	+	1.11667i
$591$	1.01851e7			1.19949
$592$	9.13074e6	+	6.92537e6i	1.07078	+	0.812155i
$593$			913091.i			0.106629i	0.998578	+	0.0533147i	$0.0169787\pi$
$593$			913091.i			0.106629i	−0.998578	+	0.0533147i	$0.983021\pi$
$594$	4.53234e6	+	1.69861e6i	0.527055	+	0.197528i
$595$	404495.	−	2.83317e6i	0.0468404	−	0.328080i
$596$	−49107.3	−	718405.i	−0.00566279	−	0.0828426i
$597$	−5.35943e6	+	5.35943e6i	−0.615436	+	0.615436i
$598$	−1.63957e6	−	3.60517e6i	−0.187489	−	0.412262i
$599$			5.33671e6i			0.607724i	0.952716	+	0.303862i	$0.0982763\pi$
$599$			5.33671e6i			0.607724i	−0.952716	+	0.303862i	$0.901724\pi$
$600$	3.22803e6	−	4.99265e6i	0.366066	−	0.566178i
$601$			1.11751e7i			1.26202i	0.775775	+	0.631009i	$0.217359\pi$
$601$			1.11751e7i			1.26202i	−0.775775	+	0.631009i	$0.782641\pi$
$602$	5.15385e6	−	2.34388e6i	0.579616	−	0.263599i
$603$	−93190.5	+	93190.5i	−0.0104371	+	0.0104371i
$604$	−8.09396e6	+	9.28169e6i	−0.902753	+	1.03523i
$605$	−901155.	+	6.31188e6i	−0.100095	+	0.701084i
$606$	−1.82578e6	+	4.87165e6i	−0.201960	+	0.538883i
$607$		−	1.29062e7i		−	1.42176i	−0.703311	−	0.710882i	$-0.748296\pi$
$607$		−	1.29062e7i		−	1.42176i	0.703311	−	0.710882i	$-0.251704\pi$
$608$	−6.59383e6	−	1.04401e7i	−0.723400	−	1.14536i
$609$	3.43697e6			0.375519
$610$	1.33308e7	−	3.90576e6i	1.45055	−	0.424992i
$611$	5.21336e6	−	5.21336e6i	0.564956	−	0.564956i
$612$	2.75279e6	+	2.40053e6i	0.297094	+	0.259077i
$613$	−1.17131e7	+	1.17131e7i	−1.25898	+	1.25898i	−0.307404	+	0.951579i	$0.599460\pi$
$613$	−1.17131e7	+	1.17131e7i	−1.25898	+	1.25898i	−0.951579	+	0.307404i	$0.900540\pi$
$614$	4.83750e6	+	1.06370e7i	0.517846	+	1.13867i
$615$	4.88000e6	−	3.66064e6i	0.520274	−	0.390274i
$616$	−667829.	+	2.23529e6i	−0.0709110	+	0.237346i
$617$	−1.65473e7			−1.74990			−0.874950	−	0.484213i	$-0.839106\pi$
$617$	−1.65473e7			−1.74990			−0.874950	+	0.484213i	$0.839106\pi$
$618$	1.84857e6	+	4.06474e6i	0.194700	+	0.428116i
$619$	−5.52350e6	−	5.52350e6i	−0.579412	−	0.579412i	0.355329	−	0.934741i	$-0.384369\pi$
$619$	−5.52350e6	−	5.52350e6i	−0.579412	−	0.579412i	−0.934741	+	0.355329i	$0.884369\pi$
$620$	−7.34466e6	−	8.51333e6i	−0.767348	−	0.889447i
$621$	2.78752e6	−	2.78752e6i	0.290061	−	0.290061i
$622$	2.08328e6	−	5.55873e6i	0.215909	−	0.576102i
$623$		−	6.70856e6i		−	0.692483i
$624$	−7.47376e6	+	1.02655e6i	−0.768383	+	0.105540i
$625$	8.23614e6	+	5.24723e6i	0.843381	+	0.537316i
$626$	5.90819e6	+	2.21425e6i	0.602586	+	0.225835i
$627$	−3.43428e6	−	3.43428e6i	−0.348873	−	0.348873i
$628$	−236406.	−	3.45845e6i	−0.0239199	−	0.349931i
$629$	6.81477e6	+	6.81477e6i	0.686791	+	0.686791i
$630$	1.19544e6	−	2.18622e6i	0.119998	−	0.219453i
$631$		−	3.88287e6i		−	0.388221i	−0.980980	−	0.194111i	$-0.937818\pi$
$631$		−	3.88287e6i		−	0.388221i	0.980980	−	0.194111i	$-0.0621821\pi$
$632$	234595.	+	434496.i	0.0233628	+	0.0432706i
$633$	9.73356e6			0.965523
$634$	−6.99931e6	−	1.53905e7i	−0.691564	−	1.52065i
$635$	1.07768e6	−	7.54831e6i	0.106061	−	0.742875i
$636$	2.04284e6	+	1.78143e6i	0.200259	+	0.174633i
$637$	−6.57878e6	−	6.57878e6i	−0.642387	−	0.642387i
$638$	6.31675e6	+	2.36737e6i	0.614387	+	0.230257i
$639$	3.62691e6			0.351386
$640$	−9.14403e6	+	4.87451e6i	−0.882446	+	0.470415i
$641$	−1.51476e7			−1.45612			−0.728062	−	0.685511i	$-0.759579\pi$
$641$	−1.51476e7			−1.45612			−0.728062	+	0.685511i	$0.759579\pi$
$642$	9.32206e6	+	3.49369e6i	0.892636	+	0.334539i
$643$	2.49831e6	+	2.49831e6i	0.238298	+	0.238298i	0.816145	−	0.577847i	$-0.196107\pi$
$643$	2.49831e6	+	2.49831e6i	0.238298	+	0.238298i	−0.577847	+	0.816145i	$0.696107\pi$
$644$	1.43206e6	+	1.24880e6i	0.136065	+	0.118653i
$645$	9.79211e6	+	1.39803e6i	0.926781	+	0.132318i
$646$	−4.29893e6	−	9.45272e6i	−0.405302	−	0.891201i
$647$	1.23878e7			1.16342			0.581708	−	0.813398i	$-0.302385\pi$
$647$	1.23878e7			1.16342			0.581708	+	0.813398i	$0.302385\pi$
$648$	−797599.	−	1.47725e6i	−0.0746186	−	0.138202i
$649$		−	6.74475e6i		−	0.628571i
$650$	−1.76838e6	−	1.22646e7i	−0.164169	−	1.13860i
$651$	2.77693e6	+	2.77693e6i	0.256810	+	0.256810i
$652$	−823150.	−	1.20421e7i	−0.0758333	−	1.10939i
$653$	−5.57836e6	−	5.57836e6i	−0.511945	−	0.511945i	0.403177	−	0.915122i	$-0.367906\pi$
$653$	−5.57836e6	−	5.57836e6i	−0.511945	−	0.511945i	−0.915122	+	0.403177i	$0.867906\pi$
$654$	−4.00883e6	−	1.50241e6i	−0.366499	−	0.137355i
$655$	−1.29675e7	+	9.72735e6i	−1.18101	+	0.885914i
$656$	−1.05335e7	+	1.44682e6i	−0.955684	+	0.131267i
$657$			1.96372e6i			0.177487i
$658$	−1.24133e6	+	3.31220e6i	−0.111769	+	0.298230i
$659$	−2.46778e6	+	2.46778e6i	−0.221357	+	0.221357i	−0.809070	−	0.587713i	$-0.800029\pi$
$659$	−2.46778e6	+	2.46778e6i	−0.221357	+	0.221357i	0.587713	+	0.809070i	$0.300029\pi$
$660$	−3.08599e6	+	2.66236e6i	−0.275762	+	0.237907i
$661$	670915.	+	670915.i	0.0597260	+	0.0597260i	0.736339	−	0.676613i	$-0.236553\pi$
$661$	670915.	+	670915.i	0.0597260	+	0.0597260i	−0.676613	+	0.736339i	$0.736553\pi$
$662$	5.60569e6	+	1.23261e7i	0.497146	+	1.09315i
$663$	−6.34425e6			−0.560527
$664$	−2.58291e6	+	8.64526e6i	−0.227347	+	0.760953i
$665$	−5.66703e6	+	4.25102e6i	−0.496937	+	0.372768i
$666$	3.47369e6	+	7.63814e6i	0.303463	+	0.667271i
$667$	3.88499e6	−	3.88499e6i	0.338123	−	0.338123i
$668$	1.40124e7	+	1.22193e7i	1.21498	+	1.05951i
$669$	429408.	−	429408.i	0.0370941	−	0.0370941i
$670$	−88409.9	−	301753.i	−0.00760876	−	0.0259696i
$671$	−9.52289e6			−0.816512
$672$	3.06004e6	−	1.93269e6i	0.261399	−	0.165097i
$673$			7.51129e6i			0.639259i	0.947543	+	0.319630i	$0.103558\pi$
$673$			7.51129e6i			0.639259i	−0.947543	+	0.319630i	$0.896442\pi$
$674$	−171005.	+	456287.i	−0.0144997	+	0.0386891i
$675$	1.08137e7	−	5.93246e6i	0.913513	−	0.501159i
$676$	−2.52511e6	+	2.89565e6i	−0.212526	+	0.243713i
$677$	−3.76866e6	+	3.76866e6i	−0.316021	+	0.316021i	−0.847237	−	0.531216i	$-0.821735\pi$
$677$	−3.76866e6	+	3.76866e6i	−0.316021	+	0.316021i	0.531216	+	0.847237i	$0.321735\pi$
$678$	7.03649e6	−	3.20007e6i	0.587871	−	0.267354i
$679$			2.97234e6i			0.247414i
$680$	−8.17619e6	+	3.01479e6i	−0.678076	+	0.250026i
$681$			1.29606e7i			1.07092i
$682$	3.19095e6	+	7.01642e6i	0.262699	+	0.577637i
$683$	4.62207e6	−	4.62207e6i	0.379127	−	0.379127i	−0.491660	−	0.870787i	$-0.663610\pi$
$683$	4.62207e6	−	4.62207e6i	0.379127	−	0.379127i	0.870787	+	0.491660i	$0.163610\pi$
$684$	−616577.	−	9.02009e6i	−0.0503904	−	0.737175i
$685$	−1.05382e7	−	1.50455e6i	−0.858106	−	0.122513i
$686$	9.47232e6	+	3.55000e6i	0.768504	+	0.288017i
$687$			1.25479e7i			1.01433i
$688$	−1.37358e7	−	1.04182e7i	−1.10633	−	0.839114i
$689$	5.64929e6			0.453363
$690$	933343.	+	3.18561e6i	0.0746309	+	0.254724i
$691$	−1.19263e7	+	1.19263e7i	−0.950193	+	0.950193i	−0.998817	−	0.0486238i	$-0.984516\pi$
$691$	−1.19263e7	+	1.19263e7i	−0.950193	+	0.950193i	0.0486238	+	0.998817i	$0.484516\pi$
$692$	−891789.	−	1.30462e7i	−0.0707940	−	1.03567i
$693$	−1.20785e6	+	1.20785e6i	−0.0955386	+	0.0955386i
$694$	6.89423e6	−	3.13537e6i	0.543359	−	0.247110i
$695$	5.40447e6	+	7.20469e6i	0.424415	+	0.565788i
$696$	−4.97205e6	−	9.20882e6i	−0.389057	−	0.720578i
$697$	−8.94159e6			−0.697161
$698$	−1.92123e7	+	8.73744e6i	−1.49259	+	0.678806i
$699$	−2.32094e6	−	2.32094e6i	−0.179668	−	0.179668i
$700$	3.20818e6	+	5.00497e6i	0.247465	+	0.386061i
$701$	−5.63268e6	+	5.63268e6i	−0.432932	+	0.432932i	−0.889625	−	0.456693i	$-0.849034\pi$
$701$	−5.63268e6	+	5.63268e6i	−0.432932	+	0.432932i	0.456693	+	0.889625i	$0.349034\pi$
$702$	−1.46552e7	−	5.49241e6i	−1.12240	−	0.420649i
$703$		−	2.38564e7i		−	1.82061i
$704$	6.95523e6	−	1.44432e6i	0.528907	−	0.109833i
$705$	−4.94336e6	+	3.70817e6i	−0.374584	+	0.280987i
$706$	−5.82752e6	+	1.55493e7i	−0.440019	+	1.17409i
$707$	−3.67851e6	−	3.67851e6i	−0.276773	−	0.276773i
$708$	−6.87716e6	+	7.88634e6i	−0.515616	+	0.591279i
$709$	−1.65568e6	−	1.65568e6i	−0.123697	−	0.123697i	0.642548	−	0.766245i	$-0.277877\pi$
$709$	−1.65568e6	−	1.65568e6i	−0.123697	−	0.123697i	−0.766245	+	0.642548i	$0.777877\pi$
$710$	−4.15158e6	+	7.59243e6i	−0.309078	+	0.565243i
$711$			361545.i			0.0268218i
$712$	−1.79745e7	+	9.70487e6i	−1.32879	+	0.717447i
$713$	6.27783e6			0.462473
$714$	2.77065e6	−	1.26004e6i	0.203393	−	0.0924995i
$715$	−1.20064e6	+	8.40950e6i	−0.0878306	+	0.615184i
$716$	−1.35482e7	+	926103.i	−0.987643	+	0.0675114i
$717$	−3.98833e6	−	3.98833e6i	−0.289730	−	0.289730i
$718$	4.80289e6	−	1.28154e7i	0.347690	−	0.927727i
$719$	5.14928e6			0.371470			0.185735	−	0.982600i	$-0.440533\pi$
$719$	5.14928e6			0.371470			0.185735	+	0.982600i	$0.440533\pi$
$720$	−7.58700e6	−	40312.0i	−0.545430	−	0.00289803i
$721$	−4.46505e6			−0.319881
$722$	−4.10534e6	+	1.09541e7i	−0.293093	+	0.782049i
$723$	1.98041e6	+	1.98041e6i	0.140899	+	0.140899i
$724$	1.39068e6	+	2.03447e7i	0.0986010	+	1.44246i
$725$	1.50711e7	−	8.26811e6i	1.06488	−	0.584200i
$726$	−6.17259e6	+	2.80719e6i	−0.434637	+	0.197665i
$727$	−1.36392e7			−0.957092			−0.478546	−	0.878063i	$-0.658836\pi$
$727$	−1.36392e7			−0.957092			−0.478546	+	0.878063i	$0.658836\pi$
$728$	2.15941e6	−	7.22775e6i	0.151010	−	0.505446i
$729$		−	1.13093e7i		−	0.788164i
$730$	−4.11078e6	−	2.24780e6i	−0.285508	−	0.156117i
$731$	−1.02518e7	−	1.02518e7i	−0.709589	−	0.709589i
$732$	1.11347e7	+	9.70984e6i	0.768069	+	0.669784i
$733$	1.51221e7	+	1.51221e7i	1.03956	+	1.03956i	0.999184	+	0.0403802i	$0.0128569\pi$
$733$	1.51221e7	+	1.51221e7i	1.03956	+	1.03956i	0.0403802	+	0.999184i	$0.487143\pi$
$734$	−748875.	+	1.99819e6i	−0.0513061	+	0.136898i
$735$	4.67937e6	+	6.23806e6i	0.319498	+	0.425923i
$736$	1.27431e6	−	5.64355e6i	0.0867120	−	0.384023i
$737$			215558.i			0.0146182i
$738$	−7.28986e6	−	2.73206e6i	−0.492695	−	0.184650i
$739$	9.75126e6	−	9.75126e6i	0.656825	−	0.656825i	−0.297803	−	0.954627i	$-0.596254\pi$
$739$	9.75126e6	−	9.75126e6i	0.656825	−	0.656825i	0.954627	+	0.297803i	$0.0962538\pi$
$740$	−1.99656e7	−	1.47139e6i	−1.34030	−	0.0987751i
$741$	1.11046e7	+	1.11046e7i	0.742949	+	0.742949i
$742$	−2.46715e6	+	1.12202e6i	−0.164507	+	0.0748151i
$743$	1.91198e7			1.27061			0.635304	−	0.772262i	$-0.280875\pi$
$743$	1.91198e7			1.27061			0.635304	+	0.772262i	$0.280875\pi$
$744$	3.42314e6	−	1.14576e7i	0.226721	−	0.758858i
$745$	754843.	+	1.00628e6i	0.0498271	+	0.0664245i
$746$	−1.24739e7	+	5.67290e6i	−0.820643	+	0.373214i
$747$	−4.67149e6	+	4.67149e6i	−0.306305	+	0.306305i
$748$	5.96004e6	−	407405.i	0.389489	−	0.0266239i
$749$	−7.03895e6	+	7.03895e6i	−0.458462	+	0.458462i
$750$	14387.5	+	1.03860e7i	0.000933968	+	0.674212i
$751$	881549.			0.0570357			0.0285178	−	0.999593i	$-0.490921\pi$
$751$	881549.			0.0570357			0.0285178	+	0.999593i	$0.490921\pi$
$752$	1.06703e7	−	1.46560e6i	0.688068	−	0.0945087i
$753$		−	9.88116e6i		−	0.635068i
$754$	−2.04250e7	−	7.65481e6i	−1.30838	−	0.490350i
$755$	3.04069e6	−	2.12977e7i	0.194136	−	1.35977i
$756$	7.49103e6	−	512057.i	0.476691	−	0.0325847i
$757$	1.84441e7	−	1.84441e7i	1.16982	−	1.16982i	0.187567	−	0.982252i	$-0.439940\pi$
$757$	1.84441e7	−	1.84441e7i	1.16982	−	1.16982i	0.982252	−	0.187567i	$-0.0600603\pi$
$758$	−5.27350e6	−	1.15957e7i	−0.333370	−	0.733031i
$759$		−	2.27564e6i		−	0.143384i
$760$	1.95881e7	+	9.03424e6i	1.23015	+	0.567358i
$761$		−	8.41324e6i		−	0.526625i	−0.964711	−	0.263313i	$-0.915185\pi$
$761$		−	8.41324e6i		−	0.526625i	0.964711	−	0.263313i	$-0.0848150\pi$
$762$	7.38174e6	−	3.35709e6i	0.460544	−	0.209448i
$763$	3.02701e6	−	3.02701e6i	0.188236	−	0.188236i
$764$	−1.69365e6	−	1.47692e6i	−0.104976	−	0.0915428i
$765$	−6.31651e6	−	901816.i	−0.390233	−	0.0557140i
$766$	5.77708e6	−	1.54148e7i	0.355743	−	0.949215i
$767$			2.18089e7i			1.33859i
$768$	−9.60511e6	−	5.40299e6i	−0.587624	−	0.330546i
$769$	2.00036e7			1.21981			0.609906	−	0.792474i	$-0.291207\pi$
$769$	2.00036e7			1.21981			0.609906	+	0.792474i	$0.291207\pi$
$770$	−1.14589e6	−	3.91104e6i	−0.0696489	−	0.237720i
$771$	−3.99406e6	+	3.99406e6i	−0.241980	+	0.241980i
$772$	−1.24879e7	+	1.43204e7i	−0.754130	+	0.864793i
$773$	9.81754e6	−	9.81754e6i	0.590954	−	0.590954i	−0.346935	−	0.937889i	$-0.612777\pi$
$773$	9.81754e6	−	9.81754e6i	0.590954	−	0.590954i	0.937889	+	0.346935i	$0.112777\pi$
$774$	−5.22566e6	−	1.14904e7i	−0.313537	−	0.689421i
$775$	1.88572e7	+	5.49657e6i	1.12778	+	0.328728i
$776$	7.96393e6	−	4.29991e6i	0.474759	−	0.256333i
$777$	6.99246e6			0.415506
$778$	9.22741e6	+	2.02897e7i	0.546551	+	1.20179i
$779$	1.56509e7	+	1.56509e7i	0.924050	+	0.924050i
$780$	9.97845e6	−	8.60865e6i	0.587255	−	0.506639i
$781$	4.19468e6	−	4.19468e6i	0.246077	−	0.246077i
$782$	1.70752e6	−	4.55610e6i	0.0998501	−	0.266426i
$783$		−	2.17113e7i		−	1.26556i
$784$	−1.84946e6	−	1.34649e7i	−0.107462	−	0.782372i
$785$	3.63387e6	+	4.84431e6i	0.210472	+	0.280581i
$786$	−1.61438e7	−	6.05030e6i	−0.932070	−	0.349317i
$787$	−1.30921e7	−	1.30921e7i	−0.753481	−	0.753481i	0.221646	−	0.975127i	$-0.428857\pi$
$787$	−1.30921e7	−	1.30921e7i	−0.753481	−	0.753481i	−0.975127	+	0.221646i	$0.928857\pi$
$788$	3.09389e7	−	2.11486e6i	1.77496	−	0.121329i
$789$	−103364.	−	103364.i	−0.00591120	−	0.00591120i
$790$	−756845.	−	413847.i	−0.0431459	−	0.0235924i
$791$			7.72948e6i			0.439247i
$792$	4.98356e6	+	1.48892e6i	0.282310	+	0.0843447i
$793$	3.07920e7			1.73882
$794$	4.84584e6	+	1.06553e7i	0.272783	+	0.599810i
$795$	−4.68748e6	−	669237.i	−0.263040	−	0.0375545i
$796$	−1.51672e7	+	1.73929e7i	−0.848446	+	0.972949i
$797$	−4.13431e6	−	4.13431e6i	−0.230546	−	0.230546i	0.582375	−	0.812920i	$-0.302124\pi$
$797$	−4.13431e6	−	4.13431e6i	−0.230546	−	0.230546i	−0.812920	+	0.582375i	$0.802124\pi$
$798$	−7.05510e6	−	2.64408e6i	−0.392190	−	0.146983i
$799$	9.05768e6			0.501938
$800$	8.76894e6	−	1.58362e7i	0.484420	−	0.874835i
$801$	−1.49566e7			−0.823670
$802$	−1.32300e7	−	4.95829e6i	−0.726315	−	0.272205i
$803$	2.27113e6	+	2.27113e6i	0.124295	+	0.124295i
$804$	219790.	−	252042.i	0.0119913	−	0.0137510i
$805$	−3.28598e6	−	469144.i	−0.178721	−	0.0255162i
$806$	−1.03178e7	−	2.26874e7i	−0.559436	−	1.23012i
$807$	1.04868e7			0.566841
$808$	−4.53451e6	+	1.51775e7i	−0.244344	+	0.817845i
$809$			3.06901e6i			0.164864i	0.996597	+	0.0824321i	$0.0262688\pi$
$809$			3.06901e6i			0.164864i	−0.996597	+	0.0824321i	$0.973731\pi$
$810$	2.57320e6	+	1.40704e6i	0.137804	+	0.0753519i
$811$	1.05654e7	+	1.05654e7i	0.564069	+	0.564069i	0.930461	−	0.366391i	$-0.119407\pi$
$811$	1.05654e7	+	1.05654e7i	0.564069	+	0.564069i	−0.366391	+	0.930461i	$0.619407\pi$
$812$	1.04403e7	−	713657.i	0.555678	−	0.0379839i
$813$	−9.19806e6	−	9.19806e6i	−0.488056	−	0.488056i
$814$	1.28513e7	+	4.81637e6i	0.679810	+	0.254776i
$815$	1.26529e7	+	1.68676e7i	0.667260	+	0.889525i
$816$	−7.38421e6	−	5.60069e6i	−0.388221	−	0.294453i
$817$			3.58885e7i			1.88105i
$818$	−1.07638e7	+	2.87206e7i	−0.562446	+	1.50075i
$819$	3.90554e6	−	3.90554e6i	0.203456	−	0.203456i
$820$	1.40636e7	−	1.21330e7i	0.730404	−	0.630137i
$821$	−1.32137e6	−	1.32137e6i	−0.0684176	−	0.0684176i	0.672070	−	0.740488i	$-0.265405\pi$
$821$	−1.32137e6	−	1.32137e6i	−0.0684176	−	0.0684176i	−0.740488	+	0.672070i	$0.765405\pi$
$822$	−4.68684e6	−	1.03057e7i	−0.241936	−	0.531982i
$823$	−2.27428e7			−1.17043			−0.585214	−	0.810879i	$-0.698989\pi$
$823$	−2.27428e7			−1.17043			−0.585214	+	0.810879i	$0.698989\pi$
$824$	6.45933e6	+	1.19634e7i	0.331413	+	0.613815i
$825$	1.99244e6	−	6.83552e6i	0.101918	−	0.349652i
$826$	−4.33151e6	−	9.52435e6i	−0.220897	−	0.485719i
$827$	9.31913e6	−	9.31913e6i	0.473818	−	0.473818i	−0.429330	−	0.903148i	$-0.641250\pi$
$827$	9.31913e6	−	9.31913e6i	0.473818	−	0.473818i	0.903148	+	0.429330i	$0.141250\pi$
$828$	2.78420e6	−	3.19276e6i	0.141131	−	0.161842i
$829$	2.03074e7	−	2.03074e7i	1.02628	−	1.02628i	0.0266383	−	0.999645i	$-0.491520\pi$
$829$	2.03074e7	−	2.03074e7i	1.02628	−	1.02628i	0.999645	−	0.0266383i	$-0.00848024\pi$
$830$	−4.43185e6	−	1.51264e7i	−0.223301	−	0.762151i
$831$	122800.			0.00616874
$832$	−2.24895e7	+	4.67016e6i	−1.12635	+	0.233896i
$833$		−	1.14300e7i		−	0.570732i
$834$	−3.36151e6	+	8.96940e6i	−0.167348	+	0.446527i
$835$	−3.21526e7	−	4.59046e6i	−1.59588	−	0.227845i
$836$	−1.11452e7	−	9.71904e6i	−0.551536	−	0.480959i
$837$	1.75419e7	−	1.75419e7i	0.865492	−	0.865492i
$838$	3.20480e7	−	1.45749e7i	1.57649	−	0.716959i
$839$			2.73395e7i			1.34087i	0.741970	+	0.670433i	$0.233892\pi$
$839$			2.73395e7i			1.34087i	−0.741970	+	0.670433i	$0.766108\pi$
$840$	−2.64799e6	+	5.74139e6i	−0.129484	+	0.280749i
$841$		−	9.74811e6i		−	0.475259i
$842$	7.86030e6	+	1.72836e7i	0.382084	+	0.840146i
$843$	−1.69703e7	+	1.69703e7i	−0.822473	+	0.822473i
$844$	2.95672e7	−	2.02109e6i	1.42874	−	0.0976630i
$845$	948618.	−	6.64432e6i	0.0457035	−	0.320117i
$846$	7.38451e6	+	2.76753e6i	0.354728	+	0.132944i
$847$		−	6.78050e6i		−	0.324753i
$848$	6.57534e6	+	4.98718e6i	0.313999	+	0.238158i
$849$	−2.26887e7			−1.08029
$850$	9.11810e6	−	1.21905e7i	0.432869	−	0.578726i
$851$	7.90396e6	−	7.90396e6i	0.374128	−	0.374128i
$852$	−9.18169e6	+	627623.i	−0.433335	+	0.0296210i
$853$	−2.59744e7	+	2.59744e7i	−1.22228	+	1.22228i	−0.255467	+	0.966818i	$0.582229\pi$
$853$	−2.59744e7	+	2.59744e7i	−1.22228	+	1.22228i	−0.966818	+	0.255467i	$0.917771\pi$
$854$	−1.34474e7	+	6.11564e6i	−0.630948	+	0.286944i
$855$	9.47760e6	+	1.26346e7i	0.443387	+	0.591079i
$856$	2.90426e7	+	8.67695e6i	1.35473	+	0.404746i
$857$	−497435.			−0.0231358			−0.0115679	−	0.999933i	$-0.503682\pi$
$857$	−497435.			−0.0231358			−0.0115679	+	0.999933i	$0.503682\pi$
$858$	−8.22393e6	+	3.74010e6i	−0.381383	+	0.173446i
$859$	−2.33814e7	−	2.33814e7i	−1.08115	−	1.08115i	−0.996402	−	0.0847528i	$-0.972990\pi$
$859$	−2.33814e7	−	2.33814e7i	−1.08115	−	1.08115i	−0.0847528	−	0.996402i	$-0.527010\pi$
$860$	3.00353e7	+	2.21348e6i	1.38480	+	0.102054i
$861$	−4.58737e6	+	4.58737e6i	−0.210890	+	0.210890i
$862$	2.58312e6	+	968090.i	0.118407	+	0.0443760i
$863$			2.63437e6i			0.120407i	0.998186	+	0.0602033i	$0.0191749\pi$
$863$			2.63437e6i			0.120407i	−0.998186	+	0.0602033i	$0.980825\pi$
$864$	−1.22088e7	−	1.93303e7i	−0.556402	−	0.880956i
$865$	1.37079e7	+	1.82741e7i	0.622920	+	0.830414i
$866$	−7.36267e6	+	1.96455e7i	−0.333611	+	0.890162i
$867$	5.04063e6	+	5.04063e6i	0.227739	+	0.227739i
$868$	9.01196e6	+	7.85874e6i	0.405994	+	0.354041i
$869$	418143.	+	418143.i	0.0187835	+	0.0187835i
$870$	1.60408e7	+	8.77117e6i	0.718500	+	0.392880i
$871$		−	697000.i		−	0.0311306i
$872$	−1.24894e7	−	3.73140e6i	−0.556224	−	0.166181i
$873$	6.62680e6			0.294285
$874$	−1.09635e7	+	4.98602e6i	−0.485480	+	0.220788i
$875$	−9.45958e6	−	4.28625e6i	−0.417688	−	0.189259i
$876$	−339815.	−	4.97126e6i	−0.0149618	−	0.218880i
$877$	4.02854e6	+	4.02854e6i	0.176868	+	0.176868i	0.789989	−	0.613121i	$-0.210086\pi$
$877$	4.02854e6	+	4.02854e6i	0.176868	+	0.176868i	−0.613121	+	0.789989i	$0.710086\pi$
$878$	1.05177e7	−	2.80639e7i	0.460452	−	1.22861i
$879$	−1.45881e7			−0.636836
$880$	−8.82133e6	+	8.72809e6i	−0.383997	+	0.379938i
$881$	−3.10927e7			−1.34964			−0.674820	−	0.737982i	$-0.735779\pi$
$881$	−3.10927e7			−1.34964			−0.674820	+	0.737982i	$0.735779\pi$
$882$	3.49237e6	−	9.31857e6i	0.151164	−	0.403346i
$883$	1.85824e7	+	1.85824e7i	0.802049	+	0.802049i	0.983416	−	0.181367i	$-0.0580521\pi$
$883$	1.85824e7	+	1.85824e7i	0.802049	+	0.802049i	−0.181367	+	0.983416i	$0.558052\pi$
$884$	−1.92716e7	+	1.31733e6i	−0.829445	+	0.0566975i
$885$	2.58357e6	−	1.80959e7i	0.110882	−	0.776643i
$886$	−1.10291e7	+	5.01586e6i	−0.472016	+	0.214665i
$887$	1.56044e7			0.665943			0.332971	−	0.942937i	$-0.391949\pi$
$887$	1.56044e7			0.665943			0.332971	+	0.942937i	$0.391949\pi$
$888$	−1.01156e7	−	1.87352e7i	−0.430485	−	0.797308i
$889$			8.10873e6i			0.344111i
$890$	1.71203e7	−	3.13097e7i	0.724497	−	1.32496i
$891$	−1.42165e6	−	1.42165e6i	−0.0599926	−	0.0599926i
$892$	1.21523e6	−	1.39355e6i	0.0511382	−	0.0586424i
$893$	−1.58541e7	−	1.58541e7i	−0.665293	−	0.665293i
$894$	−469503.	+	1.25276e6i	−0.0196469	+	0.0524232i
$895$	1.89772e7	−	1.42354e7i	0.791909	−	0.594036i
$896$	8.89402e6	−	6.50622e6i	0.370108	−	0.270744i
$897$			7.35823e6i			0.305346i
$898$	−2.91691e7	−	1.09319e7i	−1.20707	−	0.452381i
$899$	2.44483e7	−	2.44483e7i	1.00890	−	1.00890i
$900$	1.11585e7	−	7.15260e6i	0.459198	−	0.294346i
$901$	4.90754e6	+	4.90754e6i	0.201396	+	0.201396i
$902$	−1.15908e7	+	5.27130e6i	−0.474348	+	0.215725i
$903$	−1.05191e7			−0.429299
$904$	2.07099e7	−	1.11818e7i	0.842865	−	0.455082i
$905$	−2.13766e7	−	2.84971e7i	−0.867594	−	1.15659i
$906$	2.08277e7	−	9.47206e6i	0.842986	−	0.383375i
$907$	−2.90764e7	+	2.90764e7i	−1.17361	+	1.17361i	−0.192262	+	0.981344i	$0.561582\pi$
$907$	−2.90764e7	+	2.90764e7i	−1.17361	+	1.17361i	−0.981344	+	0.192262i	$0.938418\pi$
$908$	2.69116e6	+	3.93698e7i	0.108324	+	1.58471i
$909$	−8.20119e6	+	8.20119e6i	−0.329206	+	0.329206i
$910$	3.70519e6	+	1.26462e7i	0.148322	+	0.506241i
$911$	−2.01087e7			−0.802766			−0.401383	−	0.915910i	$-0.631470\pi$
$911$	−2.01087e7			−0.802766			−0.401383	+	0.915910i	$0.631470\pi$
$912$	3.12179e6	+	2.27281e7i	0.124284	+	0.904849i
$913$			1.08056e7i			0.429014i
$914$	1.10529e7	+	4.14236e6i	0.437633	+	0.164014i
$915$	−2.55495e7	−	3.64774e6i	−1.00886	−	0.144036i
$916$	2.60547e6	+	3.81161e7i	0.102600	+	1.50096i
$917$	1.21899e7	−	1.21899e7i	0.478716	−	0.478716i
$918$	−7.95969e6	−	1.75022e7i	−0.311738	−	0.685466i
$919$			3.43234e7i			1.34061i	0.742088	+	0.670303i	$0.233836\pi$
$919$			3.43234e7i			1.34061i	−0.742088	+	0.670303i	$0.766164\pi$
$920$	3.49664e6	+	9.48296e6i	0.136201	+	0.369381i
$921$		−	2.17102e7i		−	0.843365i
$922$	3.39001e7	−	1.54172e7i	1.31333	−	0.597280i
$923$	−1.35634e7	+	1.35634e7i	−0.524039	+	0.524039i
$924$	2.84871e6	−	3.26673e6i	0.109766	−	0.125873i
$925$	3.06620e7	−	1.68214e7i	1.17827	−	0.646408i
$926$	−1.60996e7	+	4.29579e7i	−0.617003	+	1.64633i
$927$			9.95478e6i			0.380481i
$928$	−1.70155e7	−	2.69408e7i	−0.648597	−	1.02693i
$929$	−3.03932e7			−1.15541			−0.577706	−	0.816245i	$-0.696052\pi$
$929$	−3.03932e7			−1.15541			−0.577706	+	0.816245i	$0.696052\pi$
$930$	5.87354e6	+	2.00471e7i	0.222686	+	0.760052i
$931$	−2.00064e7	+	2.00064e7i	−0.756475	+	0.756475i
$932$	−7.53212e6	−	6.56827e6i	−0.284039	−	0.247692i
$933$	−7.79874e6	+	7.79874e6i	−0.293306	+	0.293306i
$934$	1.94200e6	+	4.27018e6i	0.0728422	+	0.160169i
$935$	−8.34832e6	+	6.26234e6i	−0.312299	+	0.234265i
$936$	−1.61142e7	−	4.81437e6i	−0.601200	−	0.179618i
$937$	2.15744e7			0.802766			0.401383	−	0.915910i	$-0.368530\pi$
$937$	2.15744e7			0.802766			0.401383	+	0.915910i	$0.368530\pi$
$938$	138432.	+	304392.i	0.00513725	+	0.0112961i
$939$	−8.28904e6	−	8.28904e6i	−0.306789	−	0.306789i
$940$	−1.42462e7	+	1.22906e7i	−0.525872	+	0.453683i
$941$	3.16174e7	−	3.16174e7i	1.16400	−	1.16400i	0.180405	−	0.983592i	$-0.442259\pi$
$941$	3.16174e7	−	3.16174e7i	1.16400	−	1.16400i	0.983592	−	0.180405i	$-0.0577407\pi$
$942$	−2.26022e6	+	6.03087e6i	−0.0829897	+	0.221438i
$943$			1.03707e7i			0.379777i
$944$	−1.92529e7	+	2.53839e7i	−0.703179	+	0.927105i
$945$	−1.04928e7	+	7.87098e6i	−0.382219	+	0.286714i
$946$	−1.93329e7	−	7.24552e6i	−0.702376	−	0.263234i
$947$	−2.03011e7	−	2.03011e7i	−0.735605	−	0.735605i	0.236119	−	0.971724i	$-0.424124\pi$
$947$	−2.03011e7	−	2.03011e7i	−0.735605	−	0.735605i	−0.971724	+	0.236119i	$0.924124\pi$
$948$	−62564.1	−	915268.i	−0.00226102	−	0.0330771i
$949$	−7.34364e6	−	7.34364e6i	−0.264695	−	0.264695i
$950$	−3.72974e7	+	5.37773e6i	−1.34082	+	0.193326i
$951$			3.14122e7i			1.12628i
$952$	8.15462e6	−	4.40287e6i	0.291616	−	0.157450i
$953$	−3.43843e7			−1.22639			−0.613193	−	0.789933i	$-0.710115\pi$
$953$	−3.43843e7			−1.22639			−0.613193	+	0.789933i	$0.710115\pi$
$954$	2.50152e6	+	5.50048e6i	0.0889883	+	0.195672i
$955$	3.88623e6	+	554842.i	0.137886	+	0.0196861i
$956$	−1.29433e7	−	1.12870e7i	−0.458036	−	0.399424i
$957$	−8.86223e6	−	8.86223e6i	−0.312797	−	0.312797i
$958$	6.37956e6	+	2.39090e6i	0.224583	+	0.0841683i
$959$	1.13206e7			0.397488
$960$	1.92138e7	−	1.21085e6i	0.672877	−	0.0424046i
$961$	1.08773e7			0.379939
$962$	−4.15544e7	−	1.55736e7i	−1.44770	−	0.542564i
$963$	1.56933e7	+	1.56933e7i	0.545315	+	0.545315i
$964$	6.42700e6	+	5.60457e6i	0.222749	+	0.194245i
$965$	4.69138e6	−	3.28594e7i	0.162174	−	1.13590i
$966$	−1.46143e6	−	3.21347e6i	−0.0503889	−	0.110798i
$967$	4.66131e7			1.60303			0.801516	−	0.597974i	$-0.204027\pi$
$967$	4.66131e7			1.60303			0.801516	+	0.597974i	$0.204027\pi$
$968$	−1.81673e7	+	9.80895e6i	−0.623163	+	0.336460i
$969$			1.92932e7i			0.660077i
$970$	−7.58545e6	+	1.38723e7i	−0.258852	+	0.473390i
$971$	1.37472e7	+	1.37472e7i	0.467913	+	0.467913i	0.901238	−	0.433325i	$-0.142660\pi$
$971$	1.37472e7	+	1.37472e7i	0.467913	+	0.467913i	−0.433325	+	0.901238i	$0.642660\pi$
$972$	−1.88033e6	−	2.75079e7i	−0.0638365	−	0.933882i
$973$	−6.77266e6	−	6.77266e6i	−0.229339	−	0.229339i
$974$	4.39648e7	+	1.64770e7i	1.48494	+	0.556518i
$975$	−6.44251e6	+	2.21024e7i	−0.217042	+	0.744610i
$976$	3.58395e7	+	2.71831e7i	1.20431	+	0.913428i
$977$		−	1.61533e7i		−	0.541408i	−0.962663	−	0.270704i	$-0.912744\pi$
$977$		−	1.61533e7i		−	0.541408i	0.962663	−	0.270704i	$-0.0872564\pi$
$978$	−7.86994e6	+	2.09991e7i	−0.263102	+	0.702025i
$979$	−1.72980e7	+	1.72980e7i	−0.576820	+	0.576820i
$980$	1.55096e7	+	1.79774e7i	0.515863	+	0.597946i
$981$	−6.74867e6	−	6.74867e6i	−0.223896	−	0.223896i
$982$	−1.61602e7	−	3.55340e7i	−0.534773	−	1.17589i
$983$	−5.30975e7			−1.75263			−0.876315	−	0.481738i	$-0.840006\pi$
$983$	−5.30975e7			−1.75263			−0.876315	+	0.481738i	$0.840006\pi$
$984$	1.89274e7	+	5.65487e6i	0.623166	+	0.186181i
$985$	−4.33366e7	+	3.25081e7i	−1.42319	+	1.06758i
$986$	−1.10935e7	−	2.43929e7i	−0.363392	−	0.799046i
$987$	4.64692e6	−	4.64692e6i	0.151835	−	0.151835i
$988$	3.60378e7	+	3.14262e7i	1.17454	+	1.02424i
$989$	−1.18903e7	+	1.18903e7i	−0.386548	+	0.386548i
$990$	−8.71961e6	+	2.55474e6i	−0.282754	+	0.0828435i
$991$	8.55611e6			0.276753			0.138376	−	0.990380i	$-0.455812\pi$
$991$	8.55611e6			0.276753			0.138376	+	0.990380i	$0.455812\pi$
$992$	8.01922e6	−	3.55149e7i	0.258734	−	1.14586i
$993$		−	2.51578e7i		−	0.809655i
$994$	3.22952e6	−	8.61721e6i	0.103675	−	0.276631i
$995$	5.69794e6	−	3.99096e7i	0.182457	−	1.27797i
$996$	1.10177e7	−	1.26345e7i	0.351920	−	0.403561i
$997$	7.82815e6	−	7.82815e6i	0.249414	−	0.249414i	−0.571316	−	0.820730i	$-0.693567\pi$
$997$	7.82815e6	−	7.82815e6i	0.249414	−	0.249414i	0.820730	+	0.571316i	$0.193567\pi$
$998$	3.73635e7	−	1.69923e7i	1.18746	−	0.540038i
$999$		−	4.41714e7i		−	1.40032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.69.7	yes	116
5.4	even	2	inner	80.6.q.a.69.52	yes	116
16.13	even	4	inner	80.6.q.a.29.52	yes	116
80.29	even	4	inner	80.6.q.a.29.7	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.7	✓	116	80.29	even	4	inner
80.6.q.a.29.52	yes	116	16.13	even	4	inner
80.6.q.a.69.7	yes	116	1.1	even	1	trivial
80.6.q.a.69.52	yes	116	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-5.29707 - 1.98521i) q^{2} +(7.43164 + 7.43164i) q^{3} +(24.1179 + 21.0316i) q^{4} +(-55.3405 - 7.90104i) q^{5} +(-24.6125 - 54.1193i) q^{6} +59.4492 q^{7} +(-86.0017 - 159.285i) q^{8} -132.541i q^{9} +O(q^{10})\)	\(q+(-5.29707 - 1.98521i) q^{2} +(7.43164 + 7.43164i) q^{3} +(24.1179 + 21.0316i) q^{4} +(-55.3405 - 7.90104i) q^{5} +(-24.6125 - 54.1193i) q^{6} +59.4492 q^{7} +(-86.0017 - 159.285i) q^{8} -132.541i q^{9} +(277.457 + 151.715i) q^{10} +(-153.290 - 153.290i) q^{11} +(22.9358 + 335.535i) q^{12} +(495.659 + 495.659i) q^{13} +(-314.907 - 118.019i) q^{14} +(-352.553 - 469.989i) q^{15} +(139.342 + 1014.48i) q^{16} +861.157i q^{17} +(-263.123 + 702.081i) q^{18} +(1507.32 - 1507.32i) q^{19} +(-1168.52 - 1354.46i) q^{20} +(441.805 + 441.805i) q^{21} +(507.674 + 1116.30i) q^{22} +998.793 q^{23} +(544.616 - 1822.88i) q^{24} +(3000.15 + 874.495i) q^{25} +(-1641.55 - 3609.53i) q^{26} +(2790.89 - 2790.89i) q^{27} +(1433.79 + 1250.31i) q^{28} +(3889.68 - 3889.68i) q^{29} +(934.471 + 3189.46i) q^{30} +6285.42 q^{31} +(1275.85 - 5650.37i) q^{32} -2278.39i q^{33} +(1709.58 - 4561.61i) q^{34} +(-3289.95 - 469.711i) q^{35} +(2787.56 - 3196.61i) q^{36} +(7913.50 - 7913.50i) q^{37} +(-10976.8 + 4992.04i) q^{38} +7367.12i q^{39} +(3500.86 + 9494.42i) q^{40} +10383.2i q^{41} +(-1463.20 - 3217.35i) q^{42} +(-11904.7 + 11904.7i) q^{43} +(-473.090 - 6920.97i) q^{44} +(-1047.21 + 7334.91i) q^{45} +(-5290.68 - 1982.82i) q^{46} -10518.0i q^{47} +(-6503.68 + 8574.76i) q^{48} -13272.8 q^{49} +(-14155.9 - 10588.2i) q^{50} +(-6399.81 + 6399.81i) q^{51} +(1529.72 + 22378.7i) q^{52} +(5698.77 - 5698.77i) q^{53} +(-20324.0 + 9243.02i) q^{54} +(7272.00 + 9694.30i) q^{55} +(-5112.73 - 9469.37i) q^{56} +22403.8 q^{57} +(-28325.8 + 12882.1i) q^{58} +(22000.0 + 22000.0i) q^{59} +(1381.79 - 18749.9i) q^{60} +(31061.7 - 31061.7i) q^{61} +(-33294.3 - 12477.9i) q^{62} -7879.48i q^{63} +(-17975.4 + 27397.6i) q^{64} +(-23513.8 - 31346.2i) q^{65} +(-4523.10 + 12068.8i) q^{66} +(-703.105 - 703.105i) q^{67} +(-18111.5 + 20769.3i) q^{68} +(7422.67 + 7422.67i) q^{69} +(16494.6 + 9019.34i) q^{70} +27364.3i q^{71} +(-21111.9 + 11398.8i) q^{72} -14815.9 q^{73} +(-57628.4 + 26208.4i) q^{74} +(15797.1 + 28795.0i) q^{75} +(68054.9 - 4651.96i) q^{76} +(-9112.98 - 9112.98i) q^{77} +(14625.3 - 39024.1i) q^{78} -2727.79 q^{79} +(304.146 - 57242.5i) q^{80} +9274.23 q^{81} +(20612.9 - 55000.7i) q^{82} +(-35245.6 - 35245.6i) q^{83} +(1363.52 + 19947.3i) q^{84} +(6804.04 - 47656.9i) q^{85} +(86693.3 - 39426.6i) q^{86} +57813.5 q^{87} +(-11233.6 + 37600.0i) q^{88} -112845. i q^{89} +(20108.5 - 36774.6i) q^{90} +(29466.5 + 29466.5i) q^{91} +(24088.8 + 21006.2i) q^{92} +(46711.0 + 46711.0i) q^{93} +(-20880.5 + 55714.7i) q^{94} +(-95325.6 + 71506.7i) q^{95} +(51473.1 - 32509.9i) q^{96} +49998.0i q^{97} +(70306.9 + 26349.3i) q^{98} +(-20317.3 + 20317.3i) 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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