LMFDB - Embedded newform 38.6.c.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 386x^{6} + 3436x^{5} + 128708x^{4} + 568528x^{3} + 7340704x^{2} - 19430784x + 211527936 $ x^8 - 2x^7 + 386x^6 + 3436x^5 + 128708x^4 + 568528x^3 + 7340704x^2 - 19430784*x + 211527936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$10.6694 + 18.4800i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.6.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 3.46410i) q^{2} +(-12.1694 + 21.0781i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-28.6588 + 49.6385i) q^{5} +(-48.6777 - 84.3122i) q^{6} +33.7394 q^{7} +64.0000 q^{8} +(-174.689 - 302.571i) q^{9} +(-114.635 - 198.554i) q^{10} +296.625 q^{11} +389.421 q^{12} +(-360.393 - 624.219i) q^{13} +(-67.4789 + 116.877i) q^{14} +(-697.522 - 1208.14i) q^{15} +(-128.000 + 221.703i) q^{16} +(-333.491 + 577.624i) q^{17} +1397.52 q^{18} +(-890.107 + 1297.62i) q^{19} +917.082 q^{20} +(-410.589 + 711.161i) q^{21} +(-593.250 + 1027.54i) q^{22} +(-1332.94 - 2308.72i) q^{23} +(-778.843 + 1349.00i) q^{24} +(-80.1558 - 138.834i) q^{25} +2883.14 q^{26} +2589.14 q^{27} +(-269.915 - 467.507i) q^{28} +(3763.24 + 6518.12i) q^{29} +5580.18 q^{30} -2859.79 q^{31} +(-512.000 - 886.810i) q^{32} +(-3609.75 + 6252.28i) q^{33} +(-1333.97 - 2310.50i) q^{34} +(-966.932 + 1674.78i) q^{35} +(-2795.03 + 4841.14i) q^{36} -15179.2 q^{37} +(-2714.86 - 5678.65i) q^{38} +17543.1 q^{39} +(-1834.16 + 3176.87i) q^{40} +(-924.358 + 1601.03i) q^{41} +(-1642.36 - 2844.65i) q^{42} +(10615.0 - 18385.8i) q^{43} +(-2373.00 - 4110.16i) q^{44} +20025.6 q^{45} +10663.5 q^{46} +(-11622.4 - 20130.6i) q^{47} +(-3115.37 - 5395.98i) q^{48} -15668.7 q^{49} +641.246 q^{50} +(-8116.79 - 14058.7i) q^{51} +(-5766.28 + 9987.50i) q^{52} +(6683.56 + 11576.3i) q^{53} +(-5178.28 + 8969.05i) q^{54} +(-8500.92 + 14724.0i) q^{55} +2159.32 q^{56} +(-16519.1 - 34553.0i) q^{57} -30105.9 q^{58} +(-3996.49 + 6922.13i) q^{59} +(-11160.4 + 19330.3i) q^{60} +(24197.9 + 41912.0i) q^{61} +(5719.57 - 9906.59i) q^{62} +(-5893.92 - 10208.6i) q^{63} +4096.00 q^{64} +41313.7 q^{65} +(-14439.0 - 25009.1i) q^{66} +(10017.1 + 17350.0i) q^{67} +10671.7 q^{68} +64884.3 q^{69} +(-3867.73 - 6699.10i) q^{70} +(-8014.79 + 13882.0i) q^{71} +(-11180.1 - 19364.5i) q^{72} +(-17240.6 + 29861.6i) q^{73} +(30358.5 - 52582.5i) q^{74} +3901.80 q^{75} +(25101.2 + 1952.75i) q^{76} +10008.0 q^{77} +(-35086.2 + 60771.0i) q^{78} +(-31464.2 + 54497.6i) q^{79} +(-7336.66 - 12707.5i) q^{80} +(10941.2 - 18950.7i) q^{81} +(-3697.43 - 6404.14i) q^{82} +81255.2 q^{83} +13138.9 q^{84} +(-19114.9 - 33108.0i) q^{85} +(42460.1 + 73543.0i) q^{86} -183186. q^{87} +18984.0 q^{88} +(25954.4 + 44954.3i) q^{89} +(-40051.2 + 69370.6i) q^{90} +(-12159.4 - 21060.8i) q^{91} +(-21327.0 + 36939.5i) q^{92} +(34801.9 - 60278.7i) q^{93} +92979.2 q^{94} +(-38902.4 - 81371.8i) q^{95} +24923.0 q^{96} +(-85769.2 + 148557. i) q^{97} +(31337.3 - 54277.8i) q^{98} +(-51817.3 - 89750.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9} - 144 q^{10} + 144 q^{11} + 448 q^{12} - 674 q^{13} - 152 q^{14} - 20 q^{15} - 1024 q^{16} + 522 q^{17} - 1248 q^{18}+ \cdots - 138328 q^{99}+O(q^{100}) $ 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9 - 144 * q^10 + 144 * q^11 + 448 * q^12 - 674 * q^13 - 152 * q^14 - 20 * q^15 - 1024 * q^16 + 522 * q^17 - 1248 * q^18 + 320 * q^19 + 1152 * q^20 - 770 * q^21 - 288 * q^22 - 204 * q^23 - 896 * q^24 - 2158 * q^25 + 5392 * q^26 + 13156 * q^27 - 608 * q^28 - 5712 * q^29 + 160 * q^30 - 2324 * q^31 - 4096 * q^32 - 15650 * q^33 + 2088 * q^34 - 4188 * q^35 + 2496 * q^36 - 25508 * q^37 - 2440 * q^38 + 44156 * q^39 - 2304 * q^40 - 3480 * q^41 - 3080 * q^42 + 4066 * q^43 - 1152 * q^44 + 51560 * q^45 + 1632 * q^46 - 45768 * q^47 - 3584 * q^48 + 1416 * q^49 + 17264 * q^50 + 1506 * q^51 - 10784 * q^52 + 45654 * q^53 - 26312 * q^54 + 36570 * q^55 + 4864 * q^56 - 66702 * q^57 + 45696 * q^58 - 84006 * q^59 - 320 * q^60 - 14012 * q^61 + 4648 * q^62 - 15128 * q^63 + 32768 * q^64 - 4020 * q^65 - 62600 * q^66 - 19046 * q^67 - 16704 * q^68 + 111592 * q^69 - 16752 * q^70 - 53274 * q^71 + 9984 * q^72 - 41084 * q^73 + 51016 * q^74 + 153216 * q^75 + 4640 * q^76 + 271524 * q^77 - 88312 * q^78 - 54170 * q^79 - 9216 * q^80 - 9528 * q^81 - 13920 * q^82 + 52392 * q^83 + 24640 * q^84 - 221850 * q^85 + 16264 * q^86 - 457120 * q^87 + 9216 * q^88 - 137862 * q^89 - 103120 * q^90 + 308516 * q^91 - 3264 * q^92 + 112746 * q^93 + 366144 * q^94 + 153078 * q^95 + 28672 * q^96 - 292388 * q^97 - 2832 * q^98 - 138328 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$3$	−12.1694	+	21.0781i	−0.780669	+	1.35216i	0.150884	+	0.988551i	$0.451788\pi$
$3$	−12.1694	+	21.0781i	−0.780669	+	1.35216i	−0.931553	+	0.363606i	$0.881545\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−28.6588	+	49.6385i	−0.512665	+	0.887961i	0.487228	+	0.873275i	$0.338008\pi$
$5$	−28.6588	+	49.6385i	−0.512665	+	0.887961i	−0.999892	+	0.0146860i	$0.995325\pi$
$6$	−48.6777	−	84.3122i	−0.552016	−	0.956120i
$7$	33.7394			0.260251			0.130126	−	0.991498i	$-0.458462\pi$
$7$	33.7394			0.260251			0.130126	+	0.991498i	$0.458462\pi$
$8$	64.0000			0.353553
$9$	−174.689	−	302.571i	−0.718887	−	1.24515i
$10$	−114.635	−	198.554i	−0.362509	−	0.627883i
$11$	296.625			0.739139			0.369569	−	0.929203i	$-0.379505\pi$
$11$	296.625			0.739139			0.369569	+	0.929203i	$0.379505\pi$
$12$	389.421			0.780669
$13$	−360.393	−	624.219i	−0.591450	−	1.02442i	−0.994037	−	0.109039i	$-0.965223\pi$
$13$	−360.393	−	624.219i	−0.591450	−	1.02442i	0.402588	−	0.915381i	$-0.368111\pi$
$14$	−67.4789	+	116.877i	−0.0920127	+	0.159371i
$15$	−697.522	−	1208.14i	−0.800442	−	1.38641i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−333.491	+	577.624i	−0.279874	+	0.484756i	−0.971353	−	0.237640i	$-0.923626\pi$
$17$	−333.491	+	577.624i	−0.279874	+	0.484756i	0.691479	+	0.722396i	$0.256959\pi$
$18$	1397.52			1.01666
$19$	−890.107	+	1297.62i	−0.565664	+	0.824636i
$19$	−890.107	+	1297.62i	−0.565664	+	0.824636i
$20$	917.082			0.512665
$21$	−410.589	+	711.161i	−0.203170	+	0.351901i
$22$	−593.250	+	1027.54i	−0.261325	+	0.452628i
$23$	−1332.94	−	2308.72i	−0.525401	−	0.910020i	−0.999562	−	0.0295827i	$-0.990582\pi$
$23$	−1332.94	−	2308.72i	−0.525401	−	0.910020i	0.474162	−	0.880438i	$-0.342751\pi$
$24$	−778.843	+	1349.00i	−0.276008	+	0.478060i
$25$	−80.1558	−	138.834i	−0.0256499	−	0.0444269i
$26$	2883.14			0.836436
$27$	2589.14			0.683512
$28$	−269.915	−	467.507i	−0.0650628	−	0.112692i
$29$	3763.24	+	6518.12i	0.830934	+	1.43922i	0.897298	+	0.441425i	$0.145527\pi$
$29$	3763.24	+	6518.12i	0.830934	+	1.43922i	−0.0663641	+	0.997795i	$0.521140\pi$
$30$	5580.18			1.13200
$31$	−2859.79			−0.534477			−0.267239	−	0.963630i	$-0.586111\pi$
$31$	−2859.79			−0.534477			−0.267239	+	0.963630i	$0.586111\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	−3609.75	+	6252.28i	−0.577023	+	0.999432i
$34$	−1333.97	−	2310.50i	−0.197901	−	0.342774i
$35$	−966.932	+	1674.78i	−0.133422	+	0.231093i
$36$	−2795.03	+	4841.14i	−0.359443	+	0.622574i
$37$	−15179.2			−1.82283			−0.911415	−	0.411489i	$-0.865009\pi$
$37$	−15179.2			−1.82283			−0.911415	+	0.411489i	$0.865009\pi$
$38$	−2714.86	−	5678.65i	−0.304992	−	0.637950i
$39$	17543.1			1.84690
$40$	−1834.16	+	3176.87i	−0.181254	+	0.313942i
$41$	−924.358	+	1601.03i	−0.0858777	+	0.148745i	−0.905765	−	0.423781i	$-0.860703\pi$
$41$	−924.358	+	1601.03i	−0.0858777	+	0.148745i	0.819887	+	0.572525i	$0.194036\pi$
$42$	−1642.36	−	2844.65i	−0.143663	−	0.248831i
$43$	10615.0	−	18385.8i	0.875487	−	1.51639i	0.0192435	−	0.999815i	$-0.493874\pi$
$43$	10615.0	−	18385.8i	0.875487	−	1.51639i	0.856243	−	0.516573i	$-0.172792\pi$
$44$	−2373.00	−	4110.16i	−0.184785	−	0.320057i
$45$	20025.6			1.47419
$46$	10663.5			0.743029
$47$	−11622.4	−	20130.6i	−0.767452	−	1.32927i	−0.938940	−	0.344080i	$-0.888191\pi$
$47$	−11622.4	−	20130.6i	−0.767452	−	1.32927i	0.171489	−	0.985186i	$-0.445142\pi$
$48$	−3115.37	−	5395.98i	−0.195167	−	0.338039i
$49$	−15668.7			−0.932269
$50$	641.246			0.0362744
$51$	−8116.79	−	14058.7i	−0.436977	−	0.756867i
$52$	−5766.28	+	9987.50i	−0.295725	+	0.512210i
$53$	6683.56	+	11576.3i	0.326827	+	0.566081i	0.981880	−	0.189501i	$-0.0606872\pi$
$53$	6683.56	+	11576.3i	0.326827	+	0.566081i	−0.655053	+	0.755583i	$0.727354\pi$
$54$	−5178.28	+	8969.05i	−0.241658	+	0.418564i
$55$	−8500.92	+	14724.0i	−0.378930	+	0.656327i
$56$	2159.32			0.0920127
$57$	−16519.1	−	34553.0i	−0.673442	−	1.40863i
$58$	−30105.9			−1.17512
$59$	−3996.49	+	6922.13i	−0.149468	+	0.258887i	−0.931031	−	0.364940i	$-0.881089\pi$
$59$	−3996.49	+	6922.13i	−0.149468	+	0.258887i	0.781563	+	0.623827i	$0.214423\pi$
$60$	−11160.4	+	19330.3i	−0.400221	+	0.693203i
$61$	24197.9	+	41912.0i	0.832632	+	1.44216i	0.895944	+	0.444167i	$0.146500\pi$
$61$	24197.9	+	41912.0i	0.832632	+	1.44216i	−0.0633121	+	0.997994i	$0.520166\pi$
$62$	5719.57	−	9906.59i	0.188966	−	0.327299i
$63$	−5893.92	−	10208.6i	−0.187091	−	0.324051i
$64$	4096.00			0.125000
$65$	41313.7			1.21286
$66$	−14439.0	−	25009.1i	−0.408017	−	0.706705i
$67$	10017.1	+	17350.0i	0.272617	+	0.472187i	0.969531	−	0.244968i	$-0.0787775\pi$
$67$	10017.1	+	17350.0i	0.272617	+	0.472187i	−0.696914	+	0.717155i	$0.745444\pi$
$68$	10671.7			0.279874
$69$	64884.3			1.64065
$70$	−3867.73	−	6699.10i	−0.0943433	−	0.163407i
$71$	−8014.79	+	13882.0i	−0.188689	+	0.326819i	−0.944813	−	0.327609i	$-0.893757\pi$
$71$	−8014.79	+	13882.0i	−0.188689	+	0.326819i	0.756124	+	0.654428i	$0.227090\pi$
$72$	−11180.1	−	19364.5i	−0.254165	−	0.440226i
$73$	−17240.6	+	29861.6i	−0.378656	+	0.655851i	−0.990867	−	0.134843i	$-0.956947\pi$
$73$	−17240.6	+	29861.6i	−0.378656	+	0.655851i	0.612211	+	0.790694i	$0.290280\pi$
$74$	30358.5	−	52582.5i	0.644467	−	1.11625i
$75$	3901.80			0.0800962
$76$	25101.2	+	1952.75i	0.498494	+	0.0387805i
$77$	10008.0			0.192362
$78$	−35086.2	+	60771.0i	−0.652979	+	1.13099i
$79$	−31464.2	+	54497.6i	−0.567216	+	0.982447i	0.429623	+	0.903008i	$0.358646\pi$
$79$	−31464.2	+	54497.6i	−0.567216	+	0.982447i	−0.996840	+	0.0794393i	$0.974687\pi$
$80$	−7336.66	−	12707.5i	−0.128166	−	0.221990i
$81$	10941.2	−	18950.7i	0.185290	−	0.320932i
$82$	−3697.43	−	6404.14i	−0.0607247	−	0.105178i
$83$	81255.2			1.29466			0.647330	−	0.762210i	$-0.275885\pi$
$83$	81255.2			1.29466			0.647330	+	0.762210i	$0.275885\pi$
$84$	13138.9			0.203170
$85$	−19114.9	−	33108.0i	−0.286963	−	0.497034i
$86$	42460.1	+	73543.0i	0.619063	+	1.07225i
$87$	−183186.			−2.59474
$88$	18984.0			0.261325
$89$	25954.4	+	44954.3i	0.347324	+	0.601583i	0.985773	−	0.168081i	$-0.0537570\pi$
$89$	25954.4	+	44954.3i	0.347324	+	0.601583i	−0.638449	+	0.769664i	$0.720424\pi$
$90$	−40051.2	+	69370.6i	−0.521205	+	0.902754i
$91$	−12159.4	−	21060.8i	−0.153925	−	0.266607i
$92$	−21327.0	+	36939.5i	−0.262700	+	0.455010i
$93$	34801.9	−	60278.7i	0.417250	−	0.722698i
$94$	92979.2			1.08534
$95$	−38902.4	−	81371.8i	−0.442249	−	0.925049i
$96$	24923.0			0.276008
$97$	−85769.2	+	148557.i	−0.925554	+	1.60311i	−0.134886	+	0.990861i	$0.543067\pi$
$97$	−85769.2	+	148557.i	−0.925554	+	1.60311i	−0.790668	+	0.612246i	$0.790266\pi$
$98$	31337.3	−	54277.8i	0.329607	−	0.570896i
$99$	−51817.3	−	89750.2i	−0.531357	−	0.920338i
$100$	−1282.49	+	2221.34i	−0.0128249	+	0.0222134i
$101$	−20162.5	−	34922.5i	−0.196671	−	0.340645i	0.750776	−	0.660557i	$-0.229680\pi$
$101$	−20162.5	−	34922.5i	−0.196671	−	0.340645i	−0.947447	+	0.319912i	$0.896347\pi$
$102$	64934.3			0.617979
$103$	−145271.			−1.34923			−0.674617	−	0.738168i	$-0.735691\pi$
$103$	−145271.			−1.34923			−0.674617	+	0.738168i	$0.735691\pi$
$104$	−23065.1	−	39950.0i	−0.209109	−	0.362187i
$105$	−23534.0	−	40762.1i	−0.208316	−	0.360814i
$106$	−53468.5			−0.462203
$107$	96115.1			0.811582			0.405791	−	0.913966i	$-0.366996\pi$
$107$	96115.1			0.811582			0.405791	+	0.913966i	$0.366996\pi$
$108$	−20713.1	−	35876.2i	−0.170878	−	0.295969i
$109$	21828.8	−	37808.5i	0.175980	−	0.304806i	−0.764520	−	0.644600i	$-0.777024\pi$
$109$	21828.8	−	37808.5i	0.175980	−	0.304806i	0.940500	+	0.339794i	$0.110357\pi$
$110$	−34003.7	−	58896.1i	−0.267944	−	0.464093i
$111$	184723.	−	319949.i	1.42303	−	2.46475i
$112$	−4318.65	+	7480.12i	−0.0325314	+	0.0563460i
$113$	38244.2			0.281753			0.140877	−	0.990027i	$-0.455008\pi$
$113$	38244.2			0.281753			0.140877	+	0.990027i	$0.455008\pi$
$114$	152733.	+	11881.9i	1.10071	+	0.0856298i
$115$	152802.			1.07742
$116$	60211.8	−	104290.i	0.415467	−	0.719610i
$117$	−125914.	+	218089.i	−0.850371	+	1.47289i
$118$	−15986.0	−	27688.5i	−0.105690	−	0.183060i
$119$	−11251.8	+	19488.7i	−0.0728375	+	0.126158i
$120$	−44641.4	−	77321.2i	−0.282999	−	0.490169i
$121$	−73064.6			−0.453674
$122$	−193583.			−1.17752
$123$	−22497.8	−	38967.3i	−0.134084	−	0.232240i
$124$	22878.3	+	39626.4i	0.133619	+	0.231435i
$125$	−169929.			−0.972730
$126$	47151.4			0.264587
$127$	−53835.3	−	93245.4i	−0.296181	−	0.513001i	0.679078	−	0.734066i	$-0.262380\pi$
$127$	−53835.3	−	93245.4i	−0.296181	−	0.513001i	−0.975259	+	0.221065i	$0.929047\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	258357.	+	447488.i	1.36693	+	2.36759i
$130$	−82627.5	+	143115.i	−0.428811	+	0.742723i
$131$	−74396.7	+	128859.i	−0.378770	+	0.656048i	−0.990884	−	0.134721i	$-0.956986\pi$
$131$	−74396.7	+	128859.i	−0.378770	+	0.656048i	0.612114	+	0.790770i	$0.290319\pi$
$132$	115512.			0.577023
$133$	−30031.7	+	43780.8i	−0.147215	+	0.214612i
$134$	−80136.4			−0.385539
$135$	−74201.7	+	128521.i	−0.350412	+	0.606932i
$136$	−21343.5	+	36967.9i	−0.0989504	+	0.171387i
$137$	5678.22	+	9834.97i	0.0258470	+	0.0447684i	0.878660	−	0.477449i	$-0.158438\pi$
$137$	5678.22	+	9834.97i	0.0258470	+	0.0447684i	−0.852813	+	0.522217i	$0.825105\pi$
$138$	−129769.	+	224766.i	−0.580059	+	1.00469i
$139$	126391.	+	218915.i	0.554853	+	0.961033i	0.997915	+	0.0645420i	$0.0205586\pi$
$139$	126391.	+	218915.i	0.554853	+	0.961033i	−0.443062	+	0.896491i	$0.646108\pi$
$140$	30941.8			0.133422
$141$	565751.			2.39650
$142$	−32059.2	−	55528.1i	−0.133423	−	0.231096i
$143$	−106902.	−	185159.i	−0.437163	−	0.757189i
$144$	89441.0			0.359443
$145$	−431400.			−1.70396
$146$	−68962.3	−	119446.i	−0.267750	−	0.463757i
$147$	190678.	−	330265.i	0.727793	−	1.26058i
$148$	121434.	+	210330.i	0.455707	+	0.789308i
$149$	−32443.4	+	56193.7i	−0.119718	+	0.207358i	−0.919656	−	0.392725i	$-0.871533\pi$
$149$	−32443.4	+	56193.7i	−0.119718	+	0.207358i	0.799938	+	0.600083i	$0.204866\pi$
$150$	−7803.60	+	13516.2i	−0.0283183	+	0.0490487i
$151$	248902.			0.888353			0.444176	−	0.895939i	$-0.353496\pi$
$151$	248902.			0.888353			0.444176	+	0.895939i	$0.353496\pi$
$152$	−56966.8	+	83047.5i	−0.199992	+	0.291553i
$153$	233030.			0.804791
$154$	−20015.9	+	34668.6i	−0.0680102	+	0.117797i
$155$	81958.1	−	141956.i	0.274008	−	0.474595i
$156$	−140345.	−	243084.i	−0.461726	−	0.799733i
$157$	78854.4	−	136580.i	0.255315	−	0.442219i	−0.709666	−	0.704538i	$-0.751154\pi$
$157$	78854.4	−	136580.i	0.255315	−	0.442219i	0.964981	+	0.262319i	$0.0844874\pi$
$158$	−125857.	−	217990.i	−0.401082	−	0.694695i
$159$	−325340.			−1.02057
$160$	58693.3			0.181254
$161$	−44972.6	−	77894.8i	−0.136736	−	0.236834i
$162$	43764.8	+	75802.9i	0.131020	+	0.226933i
$163$	190969.			0.562980			0.281490	−	0.959564i	$-0.409171\pi$
$163$	190969.			0.562980			0.281490	+	0.959564i	$0.409171\pi$
$164$	29579.5			0.0858777
$165$	−206903.	−	358366.i	−0.591638	−	1.02475i
$166$	−162510.	+	281476.i	−0.457732	+	0.792815i
$167$	293052.	+	507581.i	0.813118	+	1.40836i	0.910672	+	0.413131i	$0.135565\pi$
$167$	293052.	+	507581.i	0.813118	+	1.40836i	−0.0975540	+	0.995230i	$0.531102\pi$
$168$	−26277.7	+	45514.3i	−0.0718314	+	0.124416i
$169$	−74119.4	+	128379.i	−0.199625	+	0.345761i
$170$	152920.			0.405827
$171$	548114.	+	42640.7i	1.43344	+	0.111515i
$172$	−339681.			−0.875487
$173$	−215330.	+	372963.i	−0.547003	+	0.947437i	0.451475	+	0.892284i	$0.350898\pi$
$173$	−215330.	+	372963.i	−0.547003	+	0.947437i	−0.998478	+	0.0551529i	$0.982435\pi$
$174$	366371.	−	634574.i	0.917378	−	1.58895i
$175$	−2704.41	−	4684.18i	−0.00667541	−	0.0115621i
$176$	−37968.0	+	65762.5i	−0.0923924	+	0.160028i
$177$	−97269.9	−	168476.i	−0.233370	−	0.404209i
$178$	−207635.			−0.491191
$179$	−434152.			−1.01277			−0.506383	−	0.862308i	$-0.669018\pi$
$179$	−434152.			−1.01277			−0.506383	+	0.862308i	$0.669018\pi$
$180$	−160205.	−	277483.i	−0.368548	−	0.638343i
$181$	−174122.	−	301588.i	−0.395055	−	0.684255i	0.598053	−	0.801456i	$-0.295941\pi$
$181$	−174122.	−	301588.i	−0.395055	−	0.684255i	−0.993108	+	0.117201i	$0.962608\pi$
$182$	97275.6			0.217683
$183$	−1.17790e6			−2.60004
$184$	−85308.1	−	147758.i	−0.185757	−	0.321741i
$185$	435019.	−	753476.i	0.934500	−	1.61860i
$186$	139208.	+	241115.i	0.295040	+	0.511024i
$187$	−98921.9	+	171338.i	−0.206866	+	0.358302i
$188$	−185958.	+	322089.i	−0.383726	+	0.664633i
$189$	87356.1			0.177885
$190$	359685.	+	27981.8i	0.722833	+	0.0562330i
$191$	608995.			1.20790			0.603949	−	0.797023i	$-0.293593\pi$
$191$	608995.			1.20790			0.603949	+	0.797023i	$0.293593\pi$
$192$	−49845.9	+	86335.7i	−0.0975836	+	0.169020i
$193$	468056.	−	810697.i	0.904492	−	1.56663i	0.0828946	−	0.996558i	$-0.473584\pi$
$193$	468056.	−	810697.i	0.904492	−	1.56663i	0.821598	−	0.570068i	$-0.193083\pi$
$194$	−343077.	−	594226.i	−0.654466	−	1.13357i
$195$	−502764.	+	870813.i	−0.946842	+	1.63998i
$196$	125349.	+	217111.i	0.233067	+	0.403684i
$197$	488265.			0.896375			0.448188	−	0.893940i	$-0.352070\pi$
$197$	488265.			0.896375			0.448188	+	0.893940i	$0.352070\pi$
$198$	414538.			0.751453
$199$	−255754.	−	442979.i	−0.457815	−	0.792958i	0.541031	−	0.841003i	$-0.318034\pi$
$199$	−255754.	−	442979.i	−0.457815	−	0.792958i	−0.998845	+	0.0480448i	$0.984701\pi$
$200$	−5129.97	−	8885.37i	−0.00906859	−	0.0157073i
$201$	−487607.			−0.851294
$202$	161300.			0.278135
$203$	126969.	+	219918.i	0.216252	+	0.374559i
$204$	−129869.	+	224939.i	−0.218489	+	0.378434i
$205$	−52982.0	−	91767.5i	−0.0880529	−	0.152512i
$206$	290543.	−	503235.i	0.477026	−	0.826234i
$207$	−465701.	+	806617.i	−0.755407	+	1.30840i
$208$	184521.			0.295725
$209$	−264028.	+	384906.i	−0.418104	+	0.609521i
$210$	188272.			0.294603
$211$	55389.4	−	95937.3i	0.0856487	−	0.148348i	−0.820019	−	0.572337i	$-0.806037\pi$
$211$	55389.4	−	95937.3i	0.0856487	−	0.148348i	0.905667	+	0.423989i	$0.139370\pi$
$212$	106937.	−	185220.i	0.163414	−	0.283041i
$213$	−195071.	−	337872.i	−0.294607	−	0.510274i
$214$	−192230.	+	332953.i	−0.286937	+	0.496990i
$215$	608428.	+	1.05383e6i	0.897662	+	1.55480i
$216$	165705.			0.241658
$217$	−96487.6			−0.139098
$218$	87315.1	+	151234.i	0.124437	+	0.215531i
$219$	−419616.	−	726796.i	−0.591209	−	1.02400i
$220$	272030.			0.378930
$221$	480752.			0.662125
$222$	738891.	+	1.27980e6i	1.00623	+	1.74284i
$223$	326761.	−	565966.i	0.440015	−	0.762129i	−0.557675	−	0.830060i	$-0.688306\pi$
$223$	326761.	−	565966.i	0.440015	−	0.762129i	0.997690	+	0.0679308i	$0.0216397\pi$
$224$	−17274.6	−	29920.5i	−0.0230032	−	0.0398427i
$225$	−28004.8	+	48505.7i	−0.0368787	+	0.0638758i
$226$	−76488.3	+	132482.i	−0.0996148	+	0.172538i
$227$	−407748.			−0.525203			−0.262601	−	0.964904i	$-0.584580\pi$
$227$	−407748.			−0.525203			−0.262601	+	0.964904i	$0.584580\pi$
$228$	−346627.	+	505320.i	−0.441596	+	0.643767i
$229$	−512836.			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$229$	−512836.			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$230$	−305604.	+	529321.i	−0.380924	+	0.659780i
$231$	−121791.	+	210948.i	−0.150171	+	0.260103i
$232$	240847.	+	417160.i	0.293780	+	0.508841i
$233$	−477425.	+	826925.i	−0.576124	+	0.997875i	0.419795	+	0.907619i	$0.362102\pi$
$233$	−477425.	+	826925.i	−0.576124	+	0.997875i	−0.995919	+	0.0902563i	$0.971231\pi$
$234$	−503655.	−	872356.i	−0.601303	−	1.04149i
$235$	1.33234e6			1.57378
$236$	127888.			0.149468
$237$	−765802.	−	1.32641e6i	−0.885616	−	1.53393i
$238$	−45007.2	−	77954.8i	−0.0515039	−	0.0892074i
$239$	−529252.			−0.599332			−0.299666	−	0.954044i	$-0.596875\pi$
$239$	−529252.			−0.599332			−0.299666	+	0.954044i	$0.596875\pi$
$240$	357131.			0.400221
$241$	−54345.9	−	94129.9i	−0.0602732	−	0.104396i	0.834314	−	0.551289i	$-0.185864\pi$
$241$	−54345.9	−	94129.9i	−0.0602732	−	0.104396i	−0.894588	+	0.446893i	$0.852531\pi$
$242$	146129.	−	253103.i	0.160398	−	0.277817i
$243$	580877.	+	1.00611e6i	0.631057	+	1.09302i
$244$	387166.	−	670592.i	0.416316	−	0.721080i
$245$	449045.	−	777769.i	0.477941	−	0.827819i
$246$	179982.			0.189624
$247$	1.13078e6	+	87969.7i	1.17934	+	0.0917468i
$248$	−183026.			−0.188966
$249$	−988829.	+	1.71270e6i	−1.01070	+	1.75059i
$250$	339858.	−	588651.i	0.343912	−	0.595673i
$251$	254764.	+	441264.i	0.255243	+	0.442093i	0.964961	−	0.262392i	$-0.0845113\pi$
$251$	254764.	+	441264.i	0.255243	+	0.442093i	−0.709719	+	0.704485i	$0.751178\pi$
$252$	−94302.8	+	163337.i	−0.0935456	+	0.162026i
$253$	−395383.	−	684823.i	−0.388344	−	0.672631i
$254$	430682.			0.418863
$255$	930471.			0.896091
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	649285.	+	1.12460e6i	0.613201	+	1.06210i	0.990697	+	0.136084i	$0.0434518\pi$
$257$	649285.	+	1.12460e6i	0.613201	+	1.06210i	−0.377496	+	0.926011i	$0.623215\pi$
$258$	−2.06686e6			−1.93313
$259$	−512139.			−0.474393
$260$	−330510.	−	572460.i	−0.303215	−	0.525184i
$261$	1.31480e6	−	2.27729e6i	1.19470	−	2.06927i
$262$	−297587.	−	515435.i	−0.267831	−	0.463896i
$263$	392441.	−	679728.i	0.349853	−	0.605963i	−0.636370	−	0.771384i	$-0.719565\pi$
$263$	392441.	−	679728.i	0.349853	−	0.605963i	0.986223	+	0.165421i	$0.0528983\pi$
$264$	−231024.	+	400146.i	−0.204008	+	0.353353i
$265$	−766172.			−0.670211
$266$	−91597.9	−	191595.i	−0.0793746	−	0.166027i
$267$	−1.26340e6			−1.08458
$268$	160273.	−	277601.i	0.136309	−	0.236093i
$269$	−1.00362e6	+	1.73832e6i	−0.845645	+	1.46470i	0.0394157	+	0.999223i	$0.487450\pi$
$269$	−1.00362e6	+	1.73832e6i	−0.845645	+	1.46470i	−0.885060	+	0.465476i	$0.845883\pi$
$270$	−296807.	−	514085.i	−0.247779	−	0.429166i
$271$	312152.	−	540663.i	0.258192	−	0.447202i	−0.707565	−	0.706648i	$-0.750207\pi$
$271$	312152.	−	540663.i	0.258192	−	0.447202i	0.965758	+	0.259446i	$0.0835399\pi$
$272$	−85373.8	−	147872.i	−0.0699685	−	0.121189i
$273$	591894.			0.480659
$274$	−45425.8			−0.0365532
$275$	−23776.2	−	41181.6i	−0.0189588	−	0.0328376i
$276$	−519075.	−	899064.i	−0.410164	−	0.710424i
$277$	−245409.			−0.192173			−0.0960863	−	0.995373i	$-0.530632\pi$
$277$	−245409.			−0.192173			−0.0960863	+	0.995373i	$0.530632\pi$
$278$	−1.01112e6			−0.784680
$279$	499575.	+	865289.i	0.384229	+	0.665504i
$280$	−61883.7	+	107186.i	−0.0471716	+	0.0817037i
$281$	−605695.	−	1.04909e6i	−0.457602	−	0.792590i	0.541231	−	0.840874i	$-0.317958\pi$
$281$	−605695.	−	1.04909e6i	−0.457602	−	0.792590i	−0.998834	+	0.0482834i	$0.984625\pi$
$282$	−1.13150e6	+	1.95982e6i	−0.847292	+	1.46755i
$283$	−30771.0	+	53297.0i	−0.0228389	+	0.0395582i	−0.877219	−	0.480090i	$-0.840604\pi$
$283$	−30771.0	+	53297.0i	−0.0228389	+	0.0395582i	0.854380	+	0.519649i	$0.173937\pi$
$284$	256473.			0.188689
$285$	2.18858e6	+	170261.i	1.59606	+	0.124166i
$286$	855212.			0.618242
$287$	−31187.3	+	54018.0i	−0.0223498	+	0.0387109i
$288$	−178882.	+	309833.i	−0.127082	+	0.220113i
$289$	487495.	+	844367.i	0.343341	+	0.594684i
$290$	862800.	−	1.49441e6i	0.602442	−	1.04346i
$291$	−2.08752e6	−	3.61569e6i	−1.44510	−	2.50299i
$292$	551698.			0.378656
$293$	−78019.4			−0.0530926			−0.0265463	−	0.999648i	$-0.508451\pi$
$293$	−78019.4			−0.0530926			−0.0265463	+	0.999648i	$0.508451\pi$
$294$	762713.	+	1.32106e6i	0.514628	+	0.891361i
$295$	−229069.	−	396760.i	−0.153254	−	0.265444i
$296$	−971472.			−0.644467
$297$	768004.			0.505211
$298$	−129774.	−	224775.i	−0.0846537	−	0.146625i
$299$	−960763.	+	1.66409e6i	−0.621496	+	1.07646i
$300$	−31214.4	−	54064.9i	−0.0200240	−	0.0346827i
$301$	358145.	−	620325.i	0.227846	−	0.394642i
$302$	−497803.	+	862221.i	−0.314080	+	0.544003i
$303$	981464.			0.614140
$304$	−173751.	−	363434.i	−0.107831	−	0.225549i
$305$	−2.77393e6			−1.70744
$306$	−466060.	+	807239.i	−0.284536	+	0.492832i
$307$	397355.	−	688239.i	0.240620	−	0.416767i	−0.720271	−	0.693693i	$-0.755982\pi$
$307$	397355.	−	688239.i	0.240620	−	0.416767i	0.960891	+	0.276926i	$0.0893158\pi$
$308$	−80063.7	−	138674.i	−0.0480904	−	0.0832951i
$309$	1.76787e6	−	3.06204e6i	1.05330	−	1.82438i
$310$	327832.	+	567822.i	0.193753	+	0.335589i
$311$	3.23144e6			1.89450			0.947251	−	0.320492i	$-0.103848\pi$
$311$	3.23144e6			1.89450			0.947251	+	0.320492i	$0.103848\pi$
$312$	1.12276e6			0.652979
$313$	−524322.	−	908153.i	−0.302509	−	0.523960i	0.674195	−	0.738553i	$-0.264491\pi$
$313$	−524322.	−	908153.i	−0.302509	−	0.523960i	−0.976703	+	0.214593i	$0.931157\pi$
$314$	315418.	+	546319.i	0.180535	+	0.312696i
$315$	675652.			0.383660
$316$	1.00685e6			0.567216
$317$	153654.	+	266137.i	0.0858809	+	0.148750i	0.905766	−	0.423778i	$-0.139296\pi$
$317$	153654.	+	266137.i	0.0858809	+	0.148750i	−0.819885	+	0.572528i	$0.805963\pi$
$318$	650680.	−	1.12701e6i	0.360828	−	0.624972i
$319$	1.11627e6	+	1.93344e6i	0.614176	+	1.06378i
$320$	−117387.	+	203319.i	−0.0640831	+	0.110995i
$321$	−1.16967e6	+	2.02592e6i	−0.633576	+	1.09739i
$322$	359781.			0.193374
$323$	−452691.	−	946891.i	−0.241433	−	0.505003i
$324$	−350119.			−0.185290
$325$	−57775.2	+	100069.i	−0.0303412	+	0.0525525i
$326$	−381937.	+	661535.i	−0.199044	+	0.344754i
$327$	531287.	+	920216.i	0.274764	+	0.475905i
$328$	−59158.9	+	102466.i	−0.0303624	+	0.0525891i
$329$	−392133.	−	679195.i	−0.199730	−	0.345943i
$330$	1.65522e6			0.836702
$331$	−249620.			−0.125230			−0.0626151	−	0.998038i	$-0.519944\pi$
$331$	−249620.			−0.125230			−0.0626151	+	0.998038i	$0.519944\pi$
$332$	−650042.	−	1.12591e6i	−0.323665	−	0.560605i
$333$	2.65166e6	+	4.59280e6i	1.31041	+	2.26969i
$334$	−2.34442e6			−1.14992
$335$	−1.14831e6			−0.559044
$336$	−105111.	−	182057.i	−0.0507925	−	0.0879751i
$337$	−1.86414e6	+	3.22879e6i	−0.894137	+	1.54869i	−0.0592678	+	0.998242i	$0.518877\pi$
$337$	−1.86414e6	+	3.22879e6i	−0.894137	+	1.54869i	−0.834869	+	0.550448i	$0.814457\pi$
$338$	−296478.	−	513515.i	−0.141156	−	0.244490i
$339$	−465409.	+	806112.i	−0.219956	+	0.380975i
$340$	−305839.	+	529729.i	−0.143481	+	0.248517i
$341$	−848284.			−0.395053
$342$	−1.24394e6	+	1.81344e6i	−0.575087	+	0.838374i
$343$	−1.09571e6			−0.502875
$344$	679361.	−	1.17669e6i	0.309531	−	0.536124i
$345$	−1.85951e6	+	3.22076e6i	−0.841105	+	1.45684i
$346$	−861321.	−	1.49185e6i	−0.386789	−	0.669939i
$347$	−1.95191e6	+	3.38080e6i	−0.870233	+	1.50729i	−0.00847784	+	0.999964i	$0.502699\pi$
$347$	−1.95191e6	+	3.38080e6i	−0.870233	+	1.50729i	−0.861755	+	0.507324i	$0.830635\pi$
$348$	1.46549e6	+	2.53829e6i	0.648684	+	1.12355i
$349$	1.31205e6			0.576617			0.288308	−	0.957538i	$-0.406907\pi$
$349$	1.31205e6			0.576617			0.288308	+	0.957538i	$0.406907\pi$
$350$	21635.3			0.00944045
$351$	−933108.	−	1.61619e6i	−0.404263	−	0.700204i
$352$	−151872.	−	263050.i	−0.0653313	−	0.113157i
$353$	1.61557e6			0.690062			0.345031	−	0.938591i	$-0.387868\pi$
$353$	1.61557e6			0.690062			0.345031	+	0.938591i	$0.387868\pi$
$354$	778160.			0.330035
$355$	−459389.	−	795685.i	−0.193468	−	0.335097i
$356$	415270.	−	719268.i	0.173662	−	0.300792i
$357$	−273856.	−	474333.i	−0.113724	−	0.196976i
$358$	868304.	−	1.50395e6i	0.358067	−	0.620190i
$359$	−477177.	+	826495.i	−0.195408	+	0.338457i	−0.947034	−	0.321132i	$-0.895937\pi$
$359$	−477177.	+	826495.i	−0.195408	+	0.338457i	0.751626	+	0.659590i	$0.229270\pi$
$360$	1.28164e6			0.521205
$361$	−891518.	−	2.31004e6i	−0.360049	−	0.932933i
$362$	1.39298e6			0.558692
$363$	889154.	−	1.54006e6i	0.354169	−	0.613438i
$364$	−194551.	+	336973.i	−0.0769627	+	0.133303i
$365$	−988189.	−	1.71159e6i	−0.388247	−	0.672463i
$366$	2.35579e6	−	4.08036e6i	0.919252	−	1.59219i
$367$	−1.67077e6	−	2.89385e6i	−0.647516	−	1.12153i	−0.983714	−	0.179740i	$-0.942474\pi$
$367$	−1.67077e6	−	2.89385e6i	−0.647516	−	1.12153i	0.336198	−	0.941791i	$-0.390859\pi$
$368$	682464.			0.262700
$369$	645902.			0.246945
$370$	1.74008e6	+	3.01390e6i	0.660791	+	1.14452i
$371$	225500.	+	390577.i	0.0850571	+	0.147323i
$372$	−1.11366e6			−0.417250
$373$	1.61445e6			0.600830			0.300415	−	0.953809i	$-0.402875\pi$
$373$	1.61445e6			0.600830			0.300415	+	0.953809i	$0.402875\pi$
$374$	−395688.	−	685351.i	−0.146276	−	0.253358i
$375$	2.06794e6	−	3.58177e6i	0.759380	−	1.31528i
$376$	−743834.	−	1.28836e6i	−0.271335	−	0.469966i
$377$	2.71249e6	−	4.69817e6i	0.982911	−	1.70245i
$378$	−174712.	+	302611.i	−0.0628918	+	0.108932i
$379$	−363580.			−0.130017			−0.0650087	−	0.997885i	$-0.520708\pi$
$379$	−363580.			−0.130017			−0.0650087	+	0.997885i	$0.520708\pi$
$380$	−816301.	+	1.19002e6i	−0.289996	+	0.422762i
$381$	2.62058e6			0.924877
$382$	−1.21799e6	+	2.10962e6i	−0.427056	+	0.739683i
$383$	1.13810e6	−	1.97125e6i	0.396447	−	0.686666i	−0.596838	−	0.802362i	$-0.703576\pi$
$383$	1.13810e6	−	1.97125e6i	0.396447	−	0.686666i	0.993285	+	0.115696i	$0.0369097\pi$
$384$	−199384.	−	345343.i	−0.0690020	−	0.119515i
$385$	−286816.	+	496780.i	−0.0986170	+	0.170810i
$386$	1.87223e6	+	3.24279e6i	0.639573	+	1.10777i
$387$	−7.41733e6			−2.51750
$388$	2.74461e6			0.925554
$389$	−972203.	−	1.68390e6i	−0.325749	−	0.564214i	0.655915	−	0.754835i	$-0.272283\pi$
$389$	−972203.	−	1.68390e6i	−0.325749	−	0.564214i	−0.981664	+	0.190621i	$0.938950\pi$
$390$	−2.01106e6	−	3.48325e6i	−0.669519	−	1.15964i
$391$	1.77809e6			0.588184
$392$	−1.00279e6			−0.329607
$393$	−1.81073e6	−	3.13627e6i	−0.591387	−	1.02431i
$394$	−976529.	+	1.69140e6i	−0.316916	+	0.548915i
$395$	−1.80345e6	−	3.12367e6i	−0.581583	−	1.00733i
$396$	−829076.	+	1.43600e6i	−0.265679	+	0.460169i
$397$	−46924.8	+	81276.2i	−0.0149426	+	0.0258814i	−0.873400	−	0.487003i	$-0.838090\pi$
$397$	−46924.8	+	81276.2i	−0.0149426	+	0.0258814i	0.858457	+	0.512885i	$0.171423\pi$
$398$	2.04603e6			0.647448
$399$	−557346.	−	1.16580e6i	−0.175264	−	0.366599i
$400$	41039.8			0.0128249
$401$	−2.06041e6	+	3.56873e6i	−0.639871	+	1.10829i	0.345590	+	0.938386i	$0.387679\pi$
$401$	−2.06041e6	+	3.56873e6i	−0.639871	+	1.10829i	−0.985461	+	0.169903i	$0.945655\pi$
$402$	975214.	−	1.68912e6i	0.300978	−	0.521309i
$403$	1.03065e6	+	1.78513e6i	0.316116	+	0.547530i
$404$	−322600.	+	558760.i	−0.0983356	+	0.170322i
$405$	627124.	+	1.08621e6i	0.189984	+	0.329061i
$406$	−1.01576e6			−0.305826
$407$	−4.50254e6			−1.34732
$408$	−519475.	−	899757.i	−0.154495	−	0.267593i
$409$	2.27958e6	+	3.94835e6i	0.673825	+	1.16710i	0.976811	+	0.214104i	$0.0686833\pi$
$409$	2.27958e6	+	3.94835e6i	0.673825	+	1.16710i	−0.302986	+	0.952995i	$0.597983\pi$
$410$	423856.			0.124526
$411$	−276403.			−0.0807119
$412$	1.16217e6	+	2.01294e6i	0.337308	+	0.584235i
$413$	−134839.	+	233549.i	−0.0388993	+	0.0673755i
$414$	−1.86280e6	−	3.22647e6i	−0.534153	−	0.925181i
$415$	−2.32868e6	+	4.03339e6i	−0.663727	+	1.14961i
$416$	−369042.	+	639200.i	−0.104555	+	0.181094i
$417$	−6.15240e6			−1.73262
$418$	−805296.	−	1.68443e6i	−0.225432	−	0.471533i
$419$	5.22672e6			1.45444			0.727218	−	0.686407i	$-0.240813\pi$
$419$	5.22672e6			1.45444			0.727218	+	0.686407i	$0.240813\pi$
$420$	−376544.	+	652194.i	−0.104158	+	0.180407i
$421$	1.97324e6	−	3.41775e6i	0.542594	−	0.939800i	−0.456160	−	0.889898i	$-0.650776\pi$
$421$	1.97324e6	−	3.41775e6i	0.542594	−	0.939800i	0.998754	−	0.0499027i	$-0.0158911\pi$
$422$	221558.	+	383749.i	0.0605628	+	0.104898i
$423$	−4.06062e6	+	7.03320e6i	−1.10342	+	1.91118i
$424$	427748.	+	740881.i	0.115551	+	0.200140i
$425$	106925.			0.0287149
$426$	1.56057e6			0.416637
$427$	816423.	+	1.41409e6i	0.216693	+	0.375324i
$428$	−768921.	−	1.33181e6i	−0.202895	−	0.351425i
$429$	5.20372e6			1.36512
$430$	−4.86742e6			−1.26949
$431$	352318.	+	610233.i	0.0913569	+	0.158235i	0.908082	−	0.418792i	$-0.137546\pi$
$431$	352318.	+	610233.i	0.0913569	+	0.158235i	−0.816725	+	0.577027i	$0.804213\pi$
$432$	−331410.	+	574019.i	−0.0854390	+	0.147985i
$433$	3.56192e6	+	6.16942e6i	0.912986	+	1.58134i	0.809823	+	0.586674i	$0.199563\pi$
$433$	3.56192e6	+	6.16942e6i	0.912986	+	1.58134i	0.103163	+	0.994664i	$0.467104\pi$
$434$	192975.	−	334243.i	0.0491787	−	0.0851800i
$435$	5.24988e6	−	9.09307e6i	1.33023	−	2.30403i
$436$	−698521.			−0.175980
$437$	4.18229e6	+	325362.i	1.04764	+	0.0815012i
$438$	3.35692e6			0.836096
$439$	3.83563e6	−	6.64351e6i	0.949896	−	1.64527i	0.204257	−	0.978917i	$-0.434522\pi$
$439$	3.83563e6	−	6.64351e6i	0.949896	−	1.64527i	0.745639	−	0.666350i	$-0.232144\pi$
$440$	−544059.	+	942338.i	−0.133972	+	0.232046i
$441$	2.73715e6	+	4.74088e6i	0.670196	+	1.16081i
$442$	−961503.	+	1.66537e6i	−0.234097	+	0.405467i
$443$	2.04835e6	+	3.54784e6i	0.495900	+	0.858924i	0.999989	−	0.00472801i	$-0.00150498\pi$
$443$	2.04835e6	+	3.54784e6i	0.495900	+	0.858924i	−0.504089	+	0.863652i	$0.668172\pi$
$444$	−5.91112e6			−1.42303
$445$	−2.97528e6			−0.712243
$446$	1.30704e6	+	2.26386e6i	0.311138	+	0.538906i
$447$	−789635.	−	1.36769e6i	−0.186921	−	0.323756i
$448$	138197.			0.0325314
$449$	4.01682e6			0.940301			0.470151	−	0.882586i	$-0.344200\pi$
$449$	4.01682e6			0.940301			0.470151	+	0.882586i	$0.344200\pi$
$450$	−112019.	−	194023.i	−0.0260772	−	0.0451670i
$451$	−274188.	+	474907.i	−0.0634756	+	0.109943i
$452$	−305953.	−	529927.i	−0.0704383	−	0.122003i
$453$	−3.02899e6	+	5.24636e6i	−0.693509	+	1.20119i
$454$	815496.	−	1.41248e6i	0.185687	−	0.321620i
$455$	1.39390e6			0.315648
$456$	−1.05723e6	−	2.21139e6i	−0.238098	−	0.498027i
$457$	−8.59295e6			−1.92465			−0.962325	−	0.271900i	$-0.912348\pi$
$457$	−8.59295e6			−1.92465			−0.962325	+	0.271900i	$0.912348\pi$
$458$	1.02567e6	−	1.77652e6i	0.228478	−	0.395736i
$459$	−863456.	+	1.49555e6i	−0.191297	+	0.331337i
$460$	−1.22241e6	−	2.11728e6i	−0.269354	−	0.466535i
$461$	2.05201e6	−	3.55418e6i	0.449704	−	0.778910i	−0.548663	−	0.836044i	$-0.684863\pi$
$461$	2.05201e6	−	3.55418e6i	0.449704	−	0.778910i	0.998367	+	0.0571337i	$0.0181961\pi$
$462$	−487164.	−	843793.i	−0.106187	−	0.183921i
$463$	−4.50635e6			−0.976950			−0.488475	−	0.872578i	$-0.662447\pi$
$463$	−4.50635e6			−0.976950			−0.488475	+	0.872578i	$0.662447\pi$
$464$	−1.92678e6			−0.415467
$465$	1.99476e6	+	3.45503e6i	0.427818	+	0.741003i
$466$	−1.90970e6	−	3.30770e6i	−0.407381	−	0.705604i
$467$	4.26366e6			0.904669			0.452335	−	0.891848i	$-0.350591\pi$
$467$	4.26366e6			0.904669			0.452335	+	0.891848i	$0.350591\pi$
$468$	4.02924e6			0.850371
$469$	337970.	+	585381.i	0.0709489	+	0.122887i
$470$	−2.66467e6	+	4.61535e6i	−0.556416	+	0.963740i
$471$	1.91922e6	+	3.32419e6i	0.398633	+	0.690453i
$472$	−255775.	+	443016.i	−0.0528450	+	0.0915302i
$473$	3.14868e6	−	5.45367e6i	0.647106	−	1.12082i
$474$	6.12641e6			1.25245
$475$	251500.	+	19565.6i	0.0511452	+	0.00397886i
$476$	360058.			0.0728375
$477$	2.33510e6	−	4.04450e6i	0.469903	−	0.813897i
$478$	1.05850e6	−	1.83338e6i	0.211896	−	0.367014i
$479$	1.05740e6	+	1.83147e6i	0.210572	+	0.364721i	0.951894	−	0.306429i	$-0.0991340\pi$
$479$	1.05740e6	+	1.83147e6i	0.210572	+	0.364721i	−0.741322	+	0.671150i	$0.765801\pi$
$480$	−714263.	+	1.23714e6i	−0.141500	+	0.245084i
$481$	5.47049e6	+	9.47517e6i	1.07811	+	1.86734i
$482$	434767.			0.0852392
$483$	2.18916e6			0.426982
$484$	584517.	+	1.01241e6i	0.113418	+	0.196446i
$485$	−4.91609e6	−	8.51491e6i	−0.948997	−	1.64371i
$486$	−4.64702e6			−0.892449
$487$	−1.97866e6			−0.378050			−0.189025	−	0.981972i	$-0.560533\pi$
$487$	−1.97866e6			−0.378050			−0.189025	+	0.981972i	$0.560533\pi$
$488$	1.54867e6	+	2.68237e6i	0.294380	+	0.509881i
$489$	−2.32398e6	+	4.02525e6i	−0.439501	+	0.761238i
$490$	1.79618e6	+	3.11108e6i	0.337956	+	0.585356i
$491$	3.11318e6	−	5.39218e6i	0.582774	−	1.00939i	−0.412375	−	0.911014i	$-0.635301\pi$
$491$	3.11318e6	−	5.39218e6i	0.582774	−	1.00939i	0.995149	−	0.0983801i	$-0.0313661\pi$
$492$	−359965.	+	623477.i	−0.0670420	+	0.116120i
$493$	−5.02003e6			−0.930227
$494$	−2.56631e6	+	3.74121e6i	−0.473141	+	0.689755i
$495$	5.94009e6			1.08963
$496$	366053.	−	634022.i	0.0668097	−	0.115718i
$497$	−270415.	+	468372.i	−0.0491065	+	0.0850550i
$498$	−3.95531e6	−	6.85081e6i	−0.714674	−	1.23785i
$499$	−2.50306e6	+	4.33543e6i	−0.450008	+	0.779437i	−0.998386	−	0.0567936i	$-0.981912\pi$
$499$	−2.50306e6	+	4.33543e6i	−0.450008	+	0.779437i	0.548378	+	0.836231i	$0.315246\pi$
$500$	1.35943e6	+	2.35460e6i	0.243182	+	0.421204i
$501$	−1.42651e7			−2.53910
$502$	−2.03811e6			−0.360968
$503$	−2.93531e6	−	5.08411e6i	−0.517290	−	0.895972i	−0.999798	−	0.0200811i	$-0.993608\pi$
$503$	−2.93531e6	−	5.08411e6i	−0.517290	−	0.895972i	0.482508	−	0.875891i	$-0.339726\pi$
$504$	−377211.	−	653349.i	−0.0661467	−	0.114569i
$505$	2.31133e6			0.403306
$506$	3.16306e6			0.549201
$507$	−1.80398e6	−	3.12459e6i	−0.311682	−	0.539849i
$508$	−861364.	+	1.49193e6i	−0.148091	+	0.256500i
$509$	2.14690e6	+	3.71853e6i	0.367296	+	0.636176i	0.989142	−	0.146964i	$-0.0469501\pi$
$509$	2.14690e6	+	3.71853e6i	0.367296	+	0.636176i	−0.621845	+	0.783140i	$0.713617\pi$
$510$	−1.86094e6	+	3.22325e6i	−0.316816	+	0.548742i
$511$	−581687.	+	1.00751e6i	−0.0985456	+	0.170686i
$512$	262144.			0.0441942
$513$	−2.30461e6	+	3.35971e6i	−0.386638	+	0.563649i
$514$	−5.19428e6			−0.867197
$515$	4.16331e6	−	7.21106e6i	0.691704	−	1.19807i
$516$	4.13372e6	−	7.15980e6i	0.683465	−	1.18380i
$517$	−3.44749e6	−	5.97124e6i	−0.567254	−	0.982512i
$518$	1.02428e6	−	1.77410e6i	0.167723	−	0.290505i
$519$	−5.24088e6	−	9.07748e6i	−0.854056	−	1.47927i
$520$	2.64408e6			0.428811
$521$	−7.53599e6			−1.21631			−0.608157	−	0.793816i	$-0.708091\pi$
$521$	−7.53599e6			−1.21631			−0.608157	+	0.793816i	$0.708091\pi$
$522$	5.25918e6	+	9.10917e6i	0.844777	+	1.46320i
$523$	96034.9	+	166337.i	0.0153523	+	0.0265910i	0.873600	−	0.486646i	$-0.161780\pi$
$523$	96034.9	+	166337.i	0.0153523	+	0.0265910i	−0.858247	+	0.513237i	$0.828446\pi$
$524$	2.38069e6			0.378770
$525$	131644.			0.0208451
$526$	1.56976e6	+	2.71891e6i	0.247383	+	0.428480i
$527$	953714.	−	1.65188e6i	0.149586	−	0.259091i
$528$	−924097.	−	1.60058e6i	−0.144256	−	0.249858i
$529$	−335278.	+	580719.i	−0.0520914	+	0.0902250i
$530$	1.53234e6	−	2.65410e6i	0.236955	−	0.410419i
$531$	2.79258e6			0.429803
$532$	846899.	+	65884.8i	0.129734	+	0.0100927i
$533$	1.33253e6			0.203169
$534$	2.52679e6	−	4.37654e6i	0.383457	−	0.664167i
$535$	−2.75455e6	+	4.77101e6i	−0.416069	+	0.720653i
$536$	641092.	+	1.11040e6i	0.0963847	+	0.166943i
$537$	5.28338e6	−	9.15108e6i	0.790635	−	1.36942i
$538$	−4.01447e6	−	6.95327e6i	−0.597961	−	1.03570i
$539$	−4.64771e6			−0.689077
$540$	2.37446e6			0.350412
$541$	1.11374e6	+	1.92905e6i	0.163602	+	0.283368i	0.936158	−	0.351579i	$-0.114355\pi$
$541$	1.11374e6	+	1.92905e6i	0.163602	+	0.283368i	−0.772556	+	0.634947i	$0.781022\pi$
$542$	1.24861e6	+	2.16265e6i	0.182569	+	0.316220i
$543$	8.47585e6			1.23363
$544$	682990.			0.0989504
$545$	1.25117e6	+	2.16710e6i	0.180437	+	0.312527i
$546$	−1.18379e6	+	2.05038e6i	−0.169939	+	0.294342i
$547$	−3.25601e6	−	5.63958e6i	−0.465284	−	0.805895i	0.533930	−	0.845528i	$-0.320714\pi$
$547$	−3.25601e6	−	5.63958e6i	−0.465284	−	0.805895i	−0.999214	+	0.0396330i	$0.987381\pi$
$548$	90851.5	−	157359.i	0.0129235	−	0.0223842i
$549$	8.45424e6	−	1.46432e7i	1.19714	−	2.07350i
$550$	190210.			0.0268118
$551$	−1.18077e7	−	918584.i	−1.65686	−	0.128896i
$552$	4.15260e6			0.580059
$553$	−1.06158e6	+	1.83872e6i	−0.147619	+	0.255683i
$554$	490818.	−	850122.i	0.0679433	−	0.117681i
$555$	1.05879e7	+	1.83387e7i	1.45907	+	2.52718i
$556$	2.02225e6	−	3.50264e6i	0.277426	−	0.480516i
$557$	3.67606e6	+	6.36712e6i	0.502047	+	0.869571i	0.999997	+	0.00236531i	$0.000752904\pi$
$557$	3.67606e6	+	6.36712e6i	0.502047	+	0.869571i	−0.497950	+	0.867206i	$0.665914\pi$
$558$	−3.99660e6			−0.543381
$559$	−1.53023e7			−2.07123
$560$	−247535.	−	428743.i	−0.0333554	−	0.0577732i
$561$	−2.40764e6	−	4.17016e6i	−0.322987	−	0.559430i
$562$	4.84556e6			0.647147
$563$	−1.07415e7			−1.42822			−0.714110	−	0.700034i	$-0.753168\pi$
$563$	−1.07415e7			−1.42822			−0.714110	+	0.700034i	$0.753168\pi$
$564$	−4.52601e6	−	7.83928e6i	−0.599126	−	1.03772i
$565$	−1.09603e6	+	1.89838e6i	−0.144445	+	0.250186i
$566$	−123084.	−	213188.i	−0.0161496	−	0.0279719i
$567$	369150.	−	639387.i	0.0482220	−	0.0835230i
$568$	−512947.	+	888450.i	−0.0667116	+	0.115548i
$569$	−5.66678e6			−0.733763			−0.366881	−	0.930268i	$-0.619575\pi$
$569$	−5.66678e6			−0.733763			−0.366881	+	0.930268i	$0.619575\pi$
$570$	−4.96696e6	+	7.24093e6i	−0.640329	+	0.933485i
$571$	1.46351e7			1.87848			0.939238	−	0.343266i	$-0.111533\pi$
$571$	1.46351e7			1.87848			0.939238	+	0.343266i	$0.111533\pi$
$572$	−1.71042e6	+	2.96254e6i	−0.218582	+	0.378595i
$573$	−7.41111e6	+	1.28364e7i	−0.942967	+	1.63327i
$574$	−124749.	−	216072.i	−0.0158037	−	0.0273728i
$575$	−213686.	+	370114.i	−0.0269529	+	0.0466838i
$576$	−715528.	−	1.23933e6i	−0.0898609	−	0.155644i
$577$	1.05971e7			1.32510			0.662550	−	0.749017i	$-0.269474\pi$
$577$	1.05971e7			1.32510			0.662550	+	0.749017i	$0.269474\pi$
$578$	−3.89996e6			−0.485558
$579$	1.13919e7	+	1.97314e7i	1.41222	+	2.44603i
$580$	3.45120e6	+	5.97765e6i	0.425990	+	0.737837i
$581$	2.74150e6			0.336937
$582$	1.67002e7			2.04368
$583$	1.98251e6	+	3.43381e6i	0.241571	+	0.418413i
$584$	−1.10340e6	+	1.91114e6i	−0.133875	+	0.231878i
$585$	−7.21707e6	−	1.25003e7i	−0.871910	−	1.51019i
$586$	156039.	−	270267.i	0.0187711	−	0.0325124i
$587$	−5.63242e6	+	9.75563e6i	−0.674683	+	1.16858i	0.301879	+	0.953346i	$0.402386\pi$
$587$	−5.63242e6	+	9.75563e6i	−0.674683	+	1.16858i	−0.976562	+	0.215238i	$0.930947\pi$
$588$	−6.10171e6			−0.727793
$589$	2.54552e6	−	3.71091e6i	0.302334	−	0.440749i
$590$	1.83256e6			0.216734
$591$	−5.94190e6	+	1.02917e7i	−0.699772	+	1.21204i
$592$	1.94294e6	−	3.36528e6i	0.227854	−	0.394654i
$593$	−4.32058e6	−	7.48347e6i	−0.504552	−	0.873909i	−0.999986	−	0.00526388i	$-0.998324\pi$
$593$	−4.32058e6	−	7.48347e6i	−0.504552	−	0.873909i	0.495434	−	0.868645i	$-0.335009\pi$
$594$	−1.53601e6	+	2.66044e6i	−0.178619	+	0.309377i
$595$	−644927.	−	1.11705e6i	−0.0746824	−	0.129354i
$596$	1.03819e6			0.119718
$597$	1.24495e7			1.42961
$598$	−3.84305e6	−	6.65636e6i	−0.439464	−	0.761174i
$599$	1.50098e6	+	2.59977e6i	0.170925	+	0.296052i	0.938744	−	0.344616i	$-0.111991\pi$
$599$	1.50098e6	+	2.59977e6i	0.170925	+	0.296052i	−0.767818	+	0.640668i	$0.778658\pi$
$600$	249715.			0.0283183
$601$	−1.02562e7			−1.15824			−0.579122	−	0.815241i	$-0.696605\pi$
$601$	−1.02562e7			−1.15824			−0.579122	+	0.815241i	$0.696605\pi$
$602$	1.43258e6	+	2.48130e6i	0.161112	+	0.279054i
$603$	3.49975e6	−	6.06174e6i	0.391962	−	0.678898i
$604$	−1.99121e6	−	3.44888e6i	−0.222088	−	0.384668i
$605$	2.09395e6	−	3.62682e6i	0.232582	−	0.402845i
$606$	−1.96293e6	+	3.39989e6i	−0.217131	+	0.376083i
$607$	1.35691e7			1.49479			0.747395	−	0.664380i	$-0.231304\pi$
$607$	1.35691e7			1.49479			0.747395	+	0.664380i	$0.231304\pi$
$608$	1.60647e6	+	124976.i	0.176244	+	0.0137110i
$609$	−6.18058e6			−0.675283
$610$	5.54787e6	−	9.60918e6i	0.603672	−	1.04559i
$611$	−8.37726e6	+	1.45098e7i	−0.907818	+	1.57239i
$612$	−1.86424e6	−	3.22896e6i	−0.201198	−	0.348485i
$613$	5.59092e6	−	9.68376e6i	0.600941	−	1.04086i	−0.391737	−	0.920077i	$-0.628126\pi$
$613$	5.59092e6	−	9.68376e6i	0.600941	−	1.04086i	0.992679	−	0.120784i	$-0.0385408\pi$
$614$	1.58942e6	+	2.75296e6i	0.170144	+	0.294699i
$615$	2.57904e6			0.274961
$616$	640509.			0.0680102
$617$	−588438.	−	1.01920e6i	−0.0622283	−	0.107783i	0.833233	−	0.552922i	$-0.186487\pi$
$617$	−588438.	−	1.01920e6i	−0.0622283	−	0.107783i	−0.895461	+	0.445140i	$0.853154\pi$
$618$	7.07148e6	+	1.22482e7i	0.744799	+	1.29003i
$619$	302723.			0.0317555			0.0158778	−	0.999874i	$-0.494946\pi$
$619$	302723.			0.0317555			0.0158778	+	0.999874i	$0.494946\pi$
$620$	−2.62266e6			−0.274008
$621$	−3.45117e6	−	5.97759e6i	−0.359118	−	0.622010i
$622$	−6.46288e6	+	1.11940e7i	−0.669808	+	1.16014i
$623$	875685.	+	1.51673e6i	0.0903915	+	0.156563i
$624$	−2.24551e6	+	3.88935e6i	−0.230863	+	0.399867i
$625$	5.12045e6	−	8.86888e6i	0.524334	−	0.908173i
$626$	4.19458e6			0.427812
$627$	−4.89999e6	−	1.02493e7i	−0.497767	−	1.04118i
$628$	−2.52334e6			−0.255315
$629$	5.06215e6	−	8.76790e6i	0.510162	−	0.883627i
$630$	−1.35130e6	+	2.34053e6i	−0.135644	+	0.234943i
$631$	3.40835e6	+	5.90344e6i	0.340778	+	0.590245i	0.984577	−	0.174950i	$-0.0559763\pi$
$631$	3.40835e6	+	5.90344e6i	0.340778	+	0.590245i	−0.643800	+	0.765194i	$0.722643\pi$
$632$	−2.01371e6	+	3.48784e6i	−0.200541	+	0.347348i
$633$	1.34811e6	+	2.33500e6i	0.133727	+	0.231621i
$634$	−1.22923e6			−0.121454
$635$	6.17142e6			0.607366
$636$	2.60272e6	+	4.50805e6i	0.255144	+	0.441922i
$637$	5.64687e6	+	9.78066e6i	0.551390	+	0.955036i
$638$	−8.93016e6			−0.868576
$639$	5.60040e6			0.542584
$640$	−469546.	−	813278.i	−0.0453136	−	0.0784854i
$641$	4.24169e6	−	7.34682e6i	0.407750	−	0.706244i	−0.586887	−	0.809669i	$-0.699647\pi$
$641$	4.24169e6	−	7.34682e6i	0.407750	−	0.706244i	0.994637	+	0.103425i	$0.0329802\pi$
$642$	−4.67866e6	−	8.10368e6i	−0.448006	−	0.775969i
$643$	−2.72674e6	+	4.72286e6i	−0.260086	+	0.450482i	−0.966264	−	0.257552i	$-0.917084\pi$
$643$	−2.72674e6	+	4.72286e6i	−0.260086	+	0.450482i	0.706179	+	0.708034i	$0.250418\pi$
$644$	−719561.	+	1.24632e6i	−0.0683680	+	0.118417i
$645$	−2.96168e7			−2.80311
$646$	4.18551e6	+	325613.i	0.394609	+	0.0306987i
$647$	−1.84581e7			−1.73351			−0.866757	−	0.498731i	$-0.833799\pi$
$647$	−1.84581e7			−1.73351			−0.866757	+	0.498731i	$0.833799\pi$
$648$	700237.	−	1.21285e6i	0.0655100	−	0.113467i
$649$	−1.18546e6	+	2.05328e6i	−0.110478	+	0.191353i
$650$	−231101.	−	400278.i	−0.0214545	−	0.0371602i
$651$	1.17420e6	−	2.03377e6i	0.108590	−	0.188083i
$652$	−1.52775e6	−	2.64614e6i	−0.140745	−	0.243778i
$653$	6.54167e6			0.600352			0.300176	−	0.953884i	$-0.402955\pi$
$653$	6.54167e6			0.600352			0.300176	+	0.953884i	$0.402955\pi$
$654$	−4.25030e6			−0.388575
$655$	−4.26424e6	−	7.38588e6i	−0.388364	−	0.672665i
$656$	−236636.	−	409865.i	−0.0214694	−	0.0371861i
$657$	1.20470e7			1.08884
$658$	3.13707e6			0.282461
$659$	1.77978e6	+	3.08267e6i	0.159644	+	0.276511i	0.934740	−	0.355332i	$-0.115632\pi$
$659$	1.77978e6	+	3.08267e6i	0.159644	+	0.276511i	−0.775096	+	0.631843i	$0.782299\pi$
$660$	−3.31044e6	+	5.73385e6i	−0.295819	+	0.512374i
$661$	−3.54455e6	−	6.13935e6i	−0.315542	−	0.546536i	0.664010	−	0.747723i	$-0.268853\pi$
$661$	−3.54455e6	−	6.13935e6i	−0.315542	−	0.546536i	−0.979553	+	0.201188i	$0.935520\pi$
$662$	499239.	−	864708.i	0.0442755	−	0.0766875i
$663$	−5.85047e6	+	1.01333e7i	−0.516900	+	0.895298i
$664$	5.20033e6			0.457732
$665$	−1.31254e6	−	2.74544e6i	−0.115096	−	0.240745i
$666$	−2.12132e7			−1.85320
$667$	1.00323e7	−	1.73765e7i	0.873147	−	1.51233i
$668$	4.68883e6	−	8.12129e6i	0.406559	−	0.704181i
$669$	7.95298e6	+	1.37750e7i	0.687012	+	1.18994i
$670$	2.29662e6	−	3.97786e6i	0.197652	−	0.342343i
$671$	7.17770e6	+	1.24321e7i	0.615431	+	1.06596i
$672$	840887.			0.0718314
$673$	1.96877e6			0.167555			0.0837777	−	0.996484i	$-0.473301\pi$
$673$	1.96877e6			0.167555			0.0837777	+	0.996484i	$0.473301\pi$
$674$	−7.45656e6	−	1.29151e7i	−0.632250	−	1.09509i
$675$	−207535.	−	359461.i	−0.0175320	−	0.0303663i
$676$	2.37182e6			0.199625
$677$	1.92746e7			1.61627			0.808136	−	0.588996i	$-0.200477\pi$
$677$	1.92746e7			1.61627			0.808136	+	0.588996i	$0.200477\pi$
$678$	−1.86164e6	−	3.22445e6i	−0.155532	−	0.269390i
$679$	−2.89380e6	+	5.01221e6i	−0.240877	+	0.417210i
$680$	−1.22336e6	−	2.11892e6i	−0.101457	−	0.175728i
$681$	4.96205e6	−	8.59453e6i	0.410009	−	0.710157i
$682$	1.69657e6	−	2.93854e6i	0.139672	−	0.241920i
$683$	−1.67630e7			−1.37499			−0.687496	−	0.726189i	$-0.741290\pi$
$683$	−1.67630e7			−1.37499			−0.687496	+	0.726189i	$0.741290\pi$
$684$	−3.79406e6	−	7.93601e6i	−0.310073	−	0.648578i
$685$	−650924.			−0.0530034
$686$	2.19142e6	−	3.79565e6i	0.177793	−	0.307947i
$687$	6.24092e6	−	1.08096e7i	0.504495	−	0.873810i
$688$	2.71744e6	+	4.70675e6i	0.218872	+	0.379097i
$689$	4.81741e6	−	8.34401e6i	0.386604	−	0.669617i
$690$	−7.43803e6	−	1.28831e7i	−0.594751	−	1.03014i
$691$	1.25584e7			1.00055			0.500276	−	0.865866i	$-0.333232\pi$
$691$	1.25584e7			1.00055			0.500276	+	0.865866i	$0.333232\pi$
$692$	6.89056e6			0.547003
$693$	−1.74829e6	−	3.02812e6i	−0.138286	−	0.239519i
$694$	−7.80763e6	−	1.35232e7i	−0.615348	−	1.06581i
$695$	−1.44888e7			−1.13781
$696$	−1.17239e7			−0.917378
$697$	−616531.	−	1.06786e6i	−0.0480699	−	0.0832594i
$698$	−2.62410e6	+	4.54508e6i	−0.203865	+	0.353104i
$699$	−1.16200e7	−	2.01264e7i	−0.899523	−	1.55802i
$700$	−43270.6	+	74946.8i	−0.00333770	+	0.00578107i
$701$	−8.66153e6	+	1.50022e7i	−0.665732	+	1.15308i	0.313354	+	0.949636i	$0.398547\pi$
$701$	−8.66153e6	+	1.50022e7i	−0.665732	+	1.15308i	−0.979086	+	0.203446i	$0.934786\pi$
$702$	7.46486e6			0.571714
$703$	1.35112e7	−	1.96968e7i	1.03111	−	1.50317i
$704$	1.21498e6			0.0923924
$705$	−1.62138e7	+	2.80831e7i	−1.22860	+	2.12800i
$706$	−3.23113e6	+	5.59648e6i	−0.243974	+	0.422575i
$707$	−680271.	−	1.17826e6i	−0.0511839	−	0.0886532i
$708$	−1.55632e6	+	2.69562e6i	−0.116685	+	0.202105i
$709$	4.21055e6	+	7.29288e6i	0.314574	+	0.544858i	0.979347	−	0.202187i	$-0.0648050\pi$
$709$	4.21055e6	+	7.29288e6i	0.314574	+	0.544858i	−0.664773	+	0.747046i	$0.731472\pi$
$710$	3.67511e6			0.273605
$711$	2.19858e7			1.63106
$712$	1.66108e6	+	2.87707e6i	0.122798	+	0.212692i
$713$	3.81192e6	+	6.60244e6i	0.280815	+	0.486385i
$714$	2.19085e6			0.160830
$715$	1.22547e7			0.896473
$716$	3.47322e6	+	6.01579e6i	0.253192	+	0.438541i
$717$	6.44069e6	−	1.11556e7i	0.467880	−	0.810391i
$718$	−1.90871e6	−	3.30598e6i	−0.138175	−	0.239325i
$719$	−3.84763e6	+	6.66429e6i	−0.277569	+	0.480764i	−0.970780	−	0.239971i	$-0.922862\pi$
$719$	−3.84763e6	+	6.66429e6i	−0.277569	+	0.480764i	0.693211	+	0.720735i	$0.256195\pi$
$720$	−2.56327e6	+	4.43972e6i	−0.184274	+	0.319172i
$721$	−4.90138e6			−0.351140
$722$	9.78523e6	+	1.53176e6i	0.698599	+	0.109357i
$723$	2.64543e6			0.188214
$724$	−2.78595e6	+	4.82541e6i	−0.197527	+	0.342127i
$725$	603291.	−	1.04493e6i	0.0426267	−	0.0738316i
$726$	3.55661e6	+	6.16024e6i	0.250435	+	0.433766i
$727$	6.59452e6	−	1.14220e7i	0.462751	−	0.801508i	−0.536346	−	0.843998i	$-0.680196\pi$
$727$	6.59452e6	−	1.14220e7i	0.462751	−	0.801508i	0.999097	+	0.0424900i	$0.0135291\pi$
$728$	−778205.	−	1.34789e6i	−0.0544209	−	0.0942597i
$729$	−2.29583e7			−1.60000
$730$	7.90551e6			0.549064
$731$	7.08004e6	+	1.22630e7i	0.490052	+	0.848795i
$732$	9.42318e6	+	1.63214e7i	0.650010	+	1.12585i
$733$	−2.42817e7			−1.66924			−0.834622	−	0.550823i	$-0.814314\pi$
$733$	−2.42817e7			−1.66924			−0.834622	+	0.550823i	$0.814314\pi$
$734$	1.33661e7			0.915726
$735$	1.09292e7	+	1.89300e7i	0.746228	+	1.29250i
$736$	−1.36493e6	+	2.36413e6i	−0.0928786	+	0.160870i
$737$	2.97131e6	+	5.14646e6i	0.201502	+	0.349012i
$738$	−1.29180e6	+	2.23747e6i	−0.0873084	+	0.151223i
$739$	−3.45695e6	+	5.98761e6i	−0.232853	+	0.403313i	−0.958647	−	0.284599i	$-0.908139\pi$
$739$	−3.45695e6	+	5.98761e6i	−0.232853	+	0.403313i	0.725794	+	0.687912i	$0.241473\pi$
$740$	−1.39206e7			−0.934500
$741$	−1.56152e7	+	2.27642e7i	−1.04473	+	1.52302i
$742$	−1.80400e6			−0.120289
$743$	7.75943e6	−	1.34397e7i	0.515653	−	0.893138i	−0.484182	−	0.874968i	$-0.660883\pi$
$743$	7.75943e6	−	1.34397e7i	0.515653	−	0.893138i	0.999835	−	0.0181702i	$-0.00578408\pi$
$744$	2.22732e6	−	3.85784e6i	0.147520	−	0.255512i
$745$	−1.85958e6	−	3.22089e6i	−0.122751	−	0.212611i
$746$	−3.22889e6	+	5.59261e6i	−0.212425	+	0.367932i
$747$	−1.41944e7	−	2.45855e7i	−0.930715	−	1.61204i
$748$	3.16550e6			0.206866
$749$	3.24287e6			0.211215
$750$	8.27175e6	+	1.43271e7i	0.536963	+	0.930046i
$751$	−3.13252e6	−	5.42569e6i	−0.202672	−	0.351039i	0.746716	−	0.665143i	$-0.231629\pi$
$751$	−3.13252e6	−	5.42569e6i	−0.202672	−	0.351039i	−0.949389	+	0.314104i	$0.898296\pi$
$752$	5.95067e6			0.383726
$753$	−1.24013e7			−0.797040
$754$	1.08499e7	+	1.87927e7i	0.695023	+	1.20382i
$755$	−7.13323e6	+	1.23551e7i	−0.455427	+	0.788823i
$756$	−698849.	−	1.21044e6i	−0.0444712	−	0.0770264i
$757$	−6.24427e6	+	1.08154e7i	−0.396042	+	0.685966i	−0.993234	−	0.116133i	$-0.962950\pi$
$757$	−6.24427e6	+	1.08154e7i	−0.396042	+	0.685966i	0.597191	+	0.802099i	$0.296283\pi$
$758$	727159.	−	1.25948e6i	0.0459681	−	0.0796191i
$759$	1.92463e7			1.21267
$760$	−2.48975e6	−	5.20779e6i	−0.156359	−	0.327054i
$761$	−3.02820e6			−0.189550			−0.0947749	−	0.995499i	$-0.530213\pi$
$761$	−3.02820e6			−0.189550			−0.0947749	+	0.995499i	$0.530213\pi$
$762$	−5.24115e6	+	9.07794e6i	−0.326994	+	0.566369i
$763$	736490.	−	1.27564e6i	0.0457990	−	0.0793262i
$764$	−4.87196e6	−	8.43848e6i	−0.301974	−	0.523035i
$765$	−6.67836e6	+	1.15673e7i	−0.412588	+	0.714623i
$766$	4.55242e6	+	7.88502e6i	0.280330	+	0.485546i
$767$	5.76123e6			0.353612
$768$	1.59507e6			0.0975836
$769$	5.46051e6	+	9.45788e6i	0.332979	+	0.576737i	0.983095	−	0.183099i	$-0.0586128\pi$
$769$	5.46051e6	+	9.45788e6i	0.332979	+	0.576737i	−0.650115	+	0.759836i	$0.725279\pi$
$770$	−1.14727e6	−	1.98712e6i	−0.0697328	−	0.120781i
$771$	−3.16057e7			−1.91483
$772$	−1.49778e7			−0.904492
$773$	−6.98476e6	−	1.20980e7i	−0.420439	−	0.728221i	0.575544	−	0.817771i	$-0.304790\pi$
$773$	−6.98476e6	−	1.20980e7i	−0.420439	−	0.728221i	−0.995982	+	0.0895500i	$0.971457\pi$
$774$	1.48347e7	−	2.56944e7i	0.890072	−	1.54165i
$775$	229228.	+	397035.i	0.0137093	+	0.0237451i
$776$	−5.48923e6	+	9.50762e6i	−0.327233	+	0.566784i
$777$	6.23244e6	−	1.07949e7i	0.370344	−	0.641455i
$778$	7.77762e6			0.460678
$779$	−1.25475e6	−	2.62455e6i	−0.0740822	−	0.154957i
$780$	1.60884e7			0.946842
$781$	−2.37739e6	+	4.11776e6i	−0.139467	+	0.241565i
$782$	−3.55619e6	+	6.15950e6i	−0.207954	+	0.360187i
$783$	9.74355e6	+	1.68763e7i	0.567954	+	0.983725i
$784$	2.00559e6	−	3.47378e6i	0.116534	−	0.201842i
$785$	4.51975e6	+	7.82843e6i	0.261782	+	0.453420i
$786$	1.44858e7			0.836348
$787$	−2.60283e7			−1.49799			−0.748996	−	0.662574i	$-0.769464\pi$
$787$	−2.60283e7			−1.49799			−0.748996	+	0.662574i	$0.769464\pi$
$788$	−3.90612e6	−	6.76559e6i	−0.224094	−	0.388142i
$789$	9.55156e6	+	1.65438e7i	0.546238	+	0.946112i
$790$	1.44276e7			0.822483
$791$	1.29034e6			0.0733266
$792$	−3.31631e6	−	5.74401e6i	−0.187863	−	0.325389i
$793$	1.74415e7	−	3.02096e7i	0.984920	−	1.70593i
$794$	−187699.	−	325105.i	−0.0105660	−	0.0183009i
$795$	9.32386e6	−	1.61494e7i	0.523213	−	0.906231i
$796$	−4.09206e6	+	7.08766e6i	−0.228907	+	0.396479i
$797$	1.55129e7			0.865060			0.432530	−	0.901620i	$-0.357621\pi$
$797$	1.55129e7			0.865060			0.432530	+	0.901620i	$0.357621\pi$
$798$	5.15313e6	+	400890.i	0.286460	+	0.0222853i
$799$	1.55039e7			0.859159
$800$	−82079.5	+	142166.i	−0.00453430	+	0.00785363i
$801$	9.06791e6	−	1.57061e7i	0.499374	−	0.864941i
$802$	−8.24163e6	−	1.42749e7i	−0.452457	−	0.783678i
$803$	−5.11399e6	+	8.85768e6i	−0.279879	+	0.484765i
$804$	3.90086e6	+	6.75648e6i	0.212824	+	0.368621i
$805$	5.15544e6			0.280399
$806$	−8.24517e6			−0.447056
$807$	−2.44269e7	−	4.23086e7i	−1.32034	−	2.28689i
$808$	−1.29040e6	−	2.23504e6i	−0.0695338	−	0.120436i
$809$	3.27273e7			1.75808			0.879039	−	0.476750i	$-0.158185\pi$
$809$	3.27273e7			1.75808			0.879039	+	0.476750i	$0.158185\pi$
$810$	−5.01699e6			−0.268677
$811$	2.24103e6	+	3.88157e6i	0.119645	+	0.207231i	0.919627	−	0.392793i	$-0.128491\pi$
$811$	2.24103e6	+	3.88157e6i	0.119645	+	0.207231i	−0.799982	+	0.600024i	$0.795158\pi$
$812$	2.03151e6	−	3.51868e6i	0.108126	−	0.187279i
$813$	7.59742e6	+	1.31591e7i	0.403125	+	0.698233i
$814$	9.00509e6	−	1.55973e7i	0.476351	−	0.825064i
$815$	−5.47294e6	+	9.47941e6i	−0.288620	+	0.499905i
$816$	4.15580e6			0.218489
$817$	1.44092e7	+	3.01395e7i	0.755237	+	1.57972i
$818$	−1.82367e7			−0.952933
$819$	−4.24826e6	+	7.35819e6i	−0.221310	+	0.383320i
$820$	−847712.	+	1.46828e6i	−0.0440265	+	0.0762561i
$821$	−1.38974e7	−	2.40709e7i	−0.719572	−	1.24634i	−0.961169	−	0.275959i	$-0.911005\pi$
$821$	−1.38974e7	−	2.40709e7i	−0.719572	−	1.24634i	0.241597	−	0.970377i	$-0.422329\pi$
$822$	552805.	−	957486.i	0.0285360	−	0.0494257i
$823$	−1.22564e7	−	2.12287e7i	−0.630758	−	1.09250i	−0.987397	−	0.158262i	$-0.949411\pi$
$823$	−1.22564e7	−	2.12287e7i	−0.630758	−	1.09250i	0.356639	−	0.934242i	$-0.383923\pi$
$824$	−9.29737e6			−0.477026
$825$	1.15737e6			0.0592022
$826$	−539357.	−	934194.i	−0.0275059	−	0.0476417i
$827$	−1.43239e7	−	2.48097e7i	−0.728278	−	1.26142i	−0.957610	−	0.288067i	$-0.906987\pi$
$827$	−1.43239e7	−	2.48097e7i	−0.728278	−	1.26142i	0.229332	−	0.973348i	$-0.426346\pi$
$828$	1.49024e7			0.755407
$829$	−1.77619e7			−0.897640			−0.448820	−	0.893622i	$-0.648156\pi$
$829$	−1.77619e7			−0.897640			−0.448820	+	0.893622i	$0.648156\pi$
$830$	−9.31471e6	−	1.61336e7i	−0.469326	−	0.812896i
$831$	2.98649e6	−	5.17275e6i	0.150023	−	0.259848i
$832$	−1.47617e6	−	2.55680e6i	−0.0739312	−	0.128053i
$833$	5.22536e6	−	9.05059e6i	0.260918	−	0.451923i
$834$	1.23048e7	−	2.13125e7i	0.612575	−	1.06101i
$835$	−3.35941e7			−1.66743
$836$	7.44563e6	+	579235.i	0.368456	+	0.0286642i
$837$	−7.40439e6			−0.365322
$838$	−1.04534e7	+	1.81059e7i	−0.514221	+	0.890656i
$839$	−5.40578e6	+	9.36308e6i	−0.265126	+	0.459213i	−0.967597	−	0.252501i	$-0.918747\pi$
$839$	−5.40578e6	+	9.36308e6i	−0.265126	+	0.459213i	0.702470	+	0.711713i	$0.252080\pi$
$840$	−1.50618e6	−	2.60877e6i	−0.0736508	−	0.127567i
$841$	−1.80683e7	+	3.12953e7i	−0.880903	+	1.52577i
$842$	7.89297e6	+	1.36710e7i	0.383672	+	0.664539i
$843$	2.94838e7			1.42894
$844$	−1.77246e6			−0.0856487
$845$	−4.24835e6	−	7.35836e6i	−0.204682	−	0.354519i
$846$	−1.62425e7	−	2.81328e7i	−0.780237	−	1.35141i
$847$	−2.46516e6			−0.118069
$848$	−3.42198e6			−0.163414
$849$	−748931.	−	1.29719e6i	−0.0356593	−	0.0617637i
$850$	−213850.	+	370399.i	−0.0101523	+	0.0175842i
$851$	2.02330e7	+	3.50446e7i	0.957715	+	1.65881i
$852$	−3.12113e6	+	5.40596e6i	−0.147304	+	0.255137i
$853$	−6.56880e6	+	1.13775e7i	−0.309110	+	0.535395i	−0.978168	−	0.207816i	$-0.933365\pi$
$853$	−6.56880e6	+	1.13775e7i	−0.309110	+	0.535395i	0.669058	+	0.743210i	$0.266698\pi$
$854$	−6.53139e6			−0.306451
$855$	−1.78249e7	+	2.59855e7i	−0.833896	+	1.21567i
$856$	6.15137e6			0.286937
$857$	8.03334e6	−	1.39141e7i	0.373632	−	0.647149i	−0.616489	−	0.787363i	$-0.711446\pi$
$857$	8.03334e6	−	1.39141e7i	0.373632	−	0.647149i	0.990121	+	0.140214i	$0.0447790\pi$
$858$	−1.04074e7	+	1.80262e7i	−0.482642	+	0.835961i
$859$	−7.38118e6	−	1.27846e7i	−0.341305	−	0.591158i	0.643370	−	0.765555i	$-0.277536\pi$
$859$	−7.38118e6	−	1.27846e7i	−0.341305	−	0.591158i	−0.984675	+	0.174397i	$0.944202\pi$
$860$	9.73484e6	−	1.68612e7i	0.448831	−	0.777398i
$861$	−759063.	−	1.31474e6i	−0.0348955	−	0.0604408i
$862$	−2.81854e6			−0.129198
$863$	−1.32374e7			−0.605028			−0.302514	−	0.953145i	$-0.597826\pi$
$863$	−1.32374e7			−0.605028			−0.302514	+	0.953145i	$0.597826\pi$
$864$	−1.32564e6	−	2.29608e6i	−0.0604145	−	0.104641i
$865$	−1.23422e7	−	2.13773e7i	−0.560858	−	0.971434i
$866$	−2.84953e7			−1.29116
$867$	−2.37301e7			−1.07214
$868$	771900.	+	1.33697e6i	0.0347746	+	0.0602314i
$869$	−9.33306e6	+	1.61653e7i	−0.419252	+	0.726165i
$870$	2.09995e7	+	3.63723e7i	0.940614	+	1.62919i
$871$	7.22015e6	−	1.25057e7i	0.322479	−	0.558549i
$872$	1.39704e6	−	2.41975e6i	0.0622183	−	0.107765i
$873$	5.99319e7			2.66147
$874$	−9.49166e6	+	1.38371e7i	−0.420304	+	0.612728i
$875$	−5.73331e6			−0.253154
$876$	−6.71385e6	+	1.16287e7i	−0.295605	+	0.512002i
$877$	8.29768e6	−	1.43720e7i	0.364299	−	0.630984i	−0.624365	−	0.781133i	$-0.714642\pi$
$877$	8.29768e6	−	1.43720e7i	0.364299	−	0.630984i	0.988663	+	0.150149i	$0.0479754\pi$
$878$	1.53425e7	+	2.65741e7i	0.671678	+	1.16338i
$879$	949451.	−	1.64450e6i	0.0414477	−	0.0717895i
$880$	−2.17624e6	−	3.76935e6i	−0.0947326	−	0.164082i
$881$	3.35813e6			0.145766			0.0728832	−	0.997340i	$-0.476780\pi$
$881$	3.35813e6			0.145766			0.0728832	+	0.997340i	$0.476780\pi$
$882$	−2.18972e7			−0.947800
$883$	5.30963e6	+	9.19655e6i	0.229173	+	0.396938i	0.957563	−	0.288224i	$-0.0930647\pi$
$883$	5.30963e6	+	9.19655e6i	0.229173	+	0.396938i	−0.728391	+	0.685162i	$0.759731\pi$
$884$	−3.84601e6	−	6.66149e6i	−0.165531	−	0.286709i
$885$	1.11506e7			0.478563
$886$	−1.63868e7			−0.701308
$887$	3.77927e6	+	6.54589e6i	0.161287	+	0.279357i	0.935330	−	0.353775i	$-0.115102\pi$
$887$	3.77927e6	+	6.54589e6i	0.161287	+	0.279357i	−0.774044	+	0.633132i	$0.781769\pi$
$888$	1.18222e7	−	2.04767e7i	0.503115	−	0.871422i
$889$	−1.81637e6	−	3.14605e6i	−0.0770815	−	0.133509i
$890$	5.95057e6	−	1.03067e7i	0.251816	−	0.436158i
$891$	3.24544e6	−	5.62126e6i	0.136955	−	0.237213i
$892$	−1.04563e7			−0.440015
$893$	3.64670e7	+	2.83696e6i	1.53028	+	0.119049i
$894$	6.31708e6			0.264346
$895$	1.24423e7	−	2.15507e7i	0.519210	−	0.899297i
$896$	−276393.	+	478727.i	−0.0115016	+	0.0199213i
$897$	−2.33839e7	−	4.05020e7i	−0.970365	−	1.68072i
$898$	−8.03365e6	+	1.39147e7i	−0.332447	+	0.575814i
$899$	−1.07621e7	−	1.86404e7i	−0.444115	−	0.769231i
$900$	896152.			0.0368787
$901$	−8.91564e6			−0.365882
$902$	−1.09675e6	−	1.89963e6i	−0.0448840	−	0.0777414i
$903$	8.71682e6	+	1.50980e7i	0.355745	+	0.616169i
$904$	2.44763e6			0.0996148
$905$	1.99605e7			0.810122
$906$	−1.21160e7	−	2.09855e7i	−0.490385	−	0.849372i
$907$	−2.29352e7	+	3.97250e7i	−0.925731	+	1.60341i	−0.135349	+	0.990798i	$0.543215\pi$
$907$	−2.29352e7	+	3.97250e7i	−0.925731	+	1.60341i	−0.790382	+	0.612614i	$0.790118\pi$
$908$	3.26198e6	+	5.64992e6i	0.131301	+	0.227420i
$909$	−7.04435e6	+	1.22012e7i	−0.282769	+	0.489770i
$910$	−2.78780e6	+	4.82862e6i	−0.111599	+	0.193294i
$911$	2.28851e7			0.913601			0.456800	−	0.889569i	$-0.348995\pi$
$911$	2.28851e7			0.913601			0.456800	+	0.889569i	$0.348995\pi$
$912$	9.77493e6	+	760444.i	0.389158	+	0.0302747i
$913$	2.41023e7			0.956934
$914$	1.71859e7	−	2.97669e7i	0.680467	−	1.17860i
$915$	3.37571e7	−	5.84691e7i	1.33295	−	2.30873i
$916$	4.10269e6	+	7.10606e6i	0.161559	+	0.279828i
$917$	−2.51010e6	+	4.34762e6i	−0.0985752	+	0.170737i
$918$	−3.45383e6	−	5.98220e6i	−0.135268	−	0.234290i
$919$	−3.88644e6			−0.151797			−0.0758985	−	0.997116i	$-0.524182\pi$
$919$	−3.88644e6			−0.151797			−0.0758985	+	0.997116i	$0.524182\pi$
$920$	9.77931e6			0.380924
$921$	9.67116e6	+	1.67509e7i	0.375690	+	0.650714i
$922$	8.20803e6	+	1.42167e7i	0.317989	+	0.550773i
$923$	1.15539e7			0.446400
$924$	3.89731e6			0.150171
$925$	1.21670e6	+	2.10739e6i	0.0467553	+	0.0809826i
$926$	9.01270e6	−	1.56104e7i	0.345404	−	0.598257i
$927$	2.53774e7	+	4.39549e7i	0.969946	+	1.68000i
$928$	3.85356e6	−	6.67455e6i	0.146890	−	0.254421i
$929$	1.33876e6	−	2.31881e6i	0.0508937	−	0.0881506i	−0.839456	−	0.543427i	$-0.817126\pi$
$929$	1.33876e6	−	2.31881e6i	0.0508937	−	0.0881506i	0.890350	+	0.455277i	$0.150460\pi$
$930$	−1.59581e7			−0.605026
$931$	1.39468e7	−	2.03319e7i	0.527351	−	0.768783i
$932$	1.52776e7			0.576124
$933$	−3.93247e7	+	6.81125e7i	−1.47898	+	2.56167i
$934$	−8.52731e6	+	1.47697e7i	−0.319849	+	0.553995i
$935$	−5.66997e6	−	9.82068e6i	−0.212105	−	0.367377i
$936$	−8.05848e6	+	1.39577e7i	−0.300651	+	0.520744i
$937$	−5.67826e6	−	9.83503e6i	−0.211284	−	0.365954i	0.740833	−	0.671690i	$-0.234431\pi$
$937$	−5.67826e6	−	9.83503e6i	−0.211284	−	0.365954i	−0.952117	+	0.305735i	$0.901098\pi$
$938$	−2.70376e6			−0.100337
$939$	2.55228e7			0.944636
$940$	−1.06587e7	−	1.84614e7i	−0.393445	−	0.681467i
$941$	−1.27931e7	−	2.21583e7i	−0.470978	−	0.815759i	0.528471	−	0.848952i	$-0.322766\pi$
$941$	−1.27931e7	−	2.21583e7i	−0.470978	−	0.815759i	−0.999449	+	0.0331931i	$0.989432\pi$
$942$	−1.53538e7			−0.563752
$943$	4.92845e6			0.180481
$944$	−1.02310e6	−	1.77206e6i	−0.0373671	−	0.0647216i
$945$	−2.50352e6	+	4.33623e6i	−0.0911953	+	0.157955i
$946$	1.25947e7	+	2.18147e7i	0.457573	+	0.792540i
$947$	−7.70411e6	+	1.33439e7i	−0.279157	+	0.483513i	−0.971175	−	0.238366i	$-0.923388\pi$
$947$	−7.70411e6	+	1.33439e7i	−0.279157	+	0.483513i	0.692019	+	0.721879i	$0.256722\pi$
$948$	−1.22528e7	+	2.12225e7i	−0.442808	+	0.766966i
$949$	2.48535e7			0.895823
$950$	−570778.	+	832092.i	−0.0205191	+	0.0299132i
$951$	−7.47953e6			−0.268178
$952$	−720116.	+	1.24728e6i	−0.0257519	+	0.0446037i
$953$	1.83195e6	−	3.17303e6i	0.0653403	−	0.113173i	−0.831505	−	0.555518i	$-0.812520\pi$
$953$	1.83195e6	−	3.17303e6i	0.0653403	−	0.113173i	0.896845	+	0.442345i	$0.145853\pi$
$954$	9.34038e6	+	1.61780e7i	0.332272	+	0.575512i
$955$	−1.74531e7	+	3.02296e7i	−0.619246	+	1.07257i
$956$	4.23401e6	+	7.33353e6i	0.149833	+	0.259518i
$957$	−5.43374e7			−1.91787
$958$	−8.45920e6			−0.297794
$959$	191580.	+	331826.i	0.00672672	+	0.0116510i
$960$	−2.85705e6	−	4.94856e6i	−0.100055	−	0.173301i
$961$	−2.04508e7			−0.714334
$962$	−4.37639e7			−1.52468
$963$	−1.67903e7	−	2.90817e7i	−0.583435	−	1.01054i
$964$	−869535.	+	1.50608e6i	−0.0301366	+	0.0521981i
$965$	2.68279e7	+	4.64672e7i	0.927402	+	1.60631i
$966$	−4.37832e6	+	7.58348e6i	−0.150961	+	0.261472i
$967$	−1.09546e7	+	1.89740e7i	−0.376732	+	0.652519i	−0.990585	−	0.136902i	$-0.956285\pi$
$967$	−1.09546e7	+	1.89740e7i	−0.376732	+	0.652519i	0.613853	+	0.789420i	$0.289619\pi$
$968$	−4.67613e6			−0.160398
$969$	2.54676e7	+	1.98126e6i	0.871322	+	0.0677848i
$970$	3.93287e7			1.34209
$971$	−1.80456e7	+	3.12559e7i	−0.614220	+	1.06386i	0.376301	+	0.926497i	$0.377196\pi$
$971$	−1.80456e7	+	3.12559e7i	−0.614220	+	1.06386i	−0.990521	+	0.137362i	$0.956138\pi$
$972$	9.29403e6	−	1.60977e7i	0.315528	−	0.546511i
$973$	4.26434e6	+	7.38606e6i	0.144401	+	0.250110i
$974$	3.95733e6	−	6.85429e6i	0.133661	−	0.231507i
$975$	−1.40618e6	−	2.43558e6i	−0.0473728	−	0.0820522i
$976$	−1.23893e7			−0.416316
$977$	4.47841e7			1.50102			0.750512	−	0.660856i	$-0.229807\pi$
$977$	4.47841e7			1.50102			0.750512	+	0.660856i	$0.229807\pi$
$978$	−9.29591e6	−	1.61010e7i	−0.310774	−	0.538277i
$979$	7.69871e6	+	1.33346e7i	0.256721	+	0.444654i
$980$	−1.43694e7			−0.477941
$981$	−1.52530e7			−0.506039
$982$	1.24527e7	+	2.15687e7i	0.412084	+	0.713750i
$983$	1.22783e7	−	2.12666e7i	0.405279	−	0.701964i	−0.589075	−	0.808078i	$-0.700508\pi$
$983$	1.22783e7	−	2.12666e7i	0.405279	−	0.701964i	0.994354	+	0.106115i	$0.0338411\pi$
$984$	−1.43986e6	−	2.49391e6i	−0.0474059	−	0.0821094i
$985$	−1.39931e7	+	2.42367e7i	−0.459540	+	0.795946i
$986$	1.00401e7	−	1.73899e7i	0.328885	−	0.569645i
$987$	1.90881e7			0.623693
$988$	−7.82733e6	−	1.63724e7i	−0.255106	−	0.533604i
$989$	−5.65967e7			−1.83992
$990$	−1.18802e7	+	2.05771e7i	−0.385243	+	0.667261i
$991$	1.12607e7	−	1.95042e7i	0.364236	−	0.630874i	−0.624418	−	0.781091i	$-0.714664\pi$
$991$	1.12607e7	−	1.95042e7i	0.364236	−	0.630874i	0.988653	+	0.150216i	$0.0479970\pi$
$992$	1.46421e6	+	2.53609e6i	0.0472416	+	0.0818248i
$993$	3.03773e6	−	5.26150e6i	0.0977632	−	0.169331i
$994$	−1.08166e6	−	1.87349e6i	−0.0347236	−	0.0601430i
$995$	2.93184e7			0.938821
$996$	3.16425e7			1.01070
$997$	4.55762e6	+	7.89404e6i	0.145211	+	0.251513i	0.929452	−	0.368944i	$-0.120280\pi$
$997$	4.55762e6	+	7.89404e6i	0.145211	+	0.251513i	−0.784240	+	0.620457i	$0.786947\pi$
$998$	−1.00123e7	−	1.73417e7i	−0.318204	−	0.551145i
$999$	−3.93012e7			−1.24593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.c.b.11.1	yes	8
3.2	odd	2		342.6.g.d.163.4		8
4.3	odd	2		304.6.i.b.49.4		8
19.7	even	3	inner	38.6.c.b.7.1	✓	8
19.8	odd	6		722.6.a.g.1.1		4
19.11	even	3		722.6.a.j.1.4		4
57.26	odd	6		342.6.g.d.235.4		8
76.7	odd	6		304.6.i.b.273.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.b.7.1	✓	8	19.7	even	3	inner
38.6.c.b.11.1	yes	8	1.1	even	1	trivial
304.6.i.b.49.4		8	4.3	odd	2
304.6.i.b.273.4		8	76.7	odd	6
342.6.g.d.163.4		8	3.2	odd	2
342.6.g.d.235.4		8	57.26	odd	6
722.6.a.g.1.1		4	19.8	odd	6
722.6.a.j.1.4		4	19.11	even	3

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-12.1694 + 21.0781i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-28.6588 + 49.6385i) q^{5} +(-48.6777 - 84.3122i) q^{6} +33.7394 q^{7} +64.0000 q^{8} +(-174.689 - 302.571i) q^{9} +(-114.635 - 198.554i) q^{10} +296.625 q^{11} +389.421 q^{12} +(-360.393 - 624.219i) q^{13} +(-67.4789 + 116.877i) q^{14} +(-697.522 - 1208.14i) q^{15} +(-128.000 + 221.703i) q^{16} +(-333.491 + 577.624i) q^{17} +1397.52 q^{18} +(-890.107 + 1297.62i) q^{19} +917.082 q^{20} +(-410.589 + 711.161i) q^{21} +(-593.250 + 1027.54i) q^{22} +(-1332.94 - 2308.72i) q^{23} +(-778.843 + 1349.00i) q^{24} +(-80.1558 - 138.834i) q^{25} +2883.14 q^{26} +2589.14 q^{27} +(-269.915 - 467.507i) q^{28} +(3763.24 + 6518.12i) q^{29} +5580.18 q^{30} -2859.79 q^{31} +(-512.000 - 886.810i) q^{32} +(-3609.75 + 6252.28i) q^{33} +(-1333.97 - 2310.50i) q^{34} +(-966.932 + 1674.78i) q^{35} +(-2795.03 + 4841.14i) q^{36} -15179.2 q^{37} +(-2714.86 - 5678.65i) q^{38} +17543.1 q^{39} +(-1834.16 + 3176.87i) q^{40} +(-924.358 + 1601.03i) q^{41} +(-1642.36 - 2844.65i) q^{42} +(10615.0 - 18385.8i) q^{43} +(-2373.00 - 4110.16i) q^{44} +20025.6 q^{45} +10663.5 q^{46} +(-11622.4 - 20130.6i) q^{47} +(-3115.37 - 5395.98i) q^{48} -15668.7 q^{49} +641.246 q^{50} +(-8116.79 - 14058.7i) q^{51} +(-5766.28 + 9987.50i) q^{52} +(6683.56 + 11576.3i) q^{53} +(-5178.28 + 8969.05i) q^{54} +(-8500.92 + 14724.0i) q^{55} +2159.32 q^{56} +(-16519.1 - 34553.0i) q^{57} -30105.9 q^{58} +(-3996.49 + 6922.13i) q^{59} +(-11160.4 + 19330.3i) q^{60} +(24197.9 + 41912.0i) q^{61} +(5719.57 - 9906.59i) q^{62} +(-5893.92 - 10208.6i) q^{63} +4096.00 q^{64} +41313.7 q^{65} +(-14439.0 - 25009.1i) q^{66} +(10017.1 + 17350.0i) q^{67} +10671.7 q^{68} +64884.3 q^{69} +(-3867.73 - 6699.10i) q^{70} +(-8014.79 + 13882.0i) q^{71} +(-11180.1 - 19364.5i) q^{72} +(-17240.6 + 29861.6i) q^{73} +(30358.5 - 52582.5i) q^{74} +3901.80 q^{75} +(25101.2 + 1952.75i) q^{76} +10008.0 q^{77} +(-35086.2 + 60771.0i) q^{78} +(-31464.2 + 54497.6i) q^{79} +(-7336.66 - 12707.5i) q^{80} +(10941.2 - 18950.7i) q^{81} +(-3697.43 - 6404.14i) q^{82} +81255.2 q^{83} +13138.9 q^{84} +(-19114.9 - 33108.0i) q^{85} +(42460.1 + 73543.0i) q^{86} -183186. q^{87} +18984.0 q^{88} +(25954.4 + 44954.3i) q^{89} +(-40051.2 + 69370.6i) q^{90} +(-12159.4 - 21060.8i) q^{91} +(-21327.0 + 36939.5i) q^{92} +(34801.9 - 60278.7i) q^{93} +92979.2 q^{94} +(-38902.4 - 81371.8i) q^{95} +24923.0 q^{96} +(-85769.2 + 148557. i) q^{97} +(31337.3 - 54277.8i) q^{98} +(-51817.3 - 89750.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9} - 144 q^{10} + 144 q^{11} + 448 q^{12} - 674 q^{13} - 152 q^{14} - 20 q^{15} - 1024 q^{16} + 522 q^{17} - 1248 q^{18}+ \cdots - 138328 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9 - 144 * q^10 + 144 * q^11 + 448 * q^12 - 674 * q^13 - 152 * q^14 - 20 * q^15 - 1024 * q^16 + 522 * q^17 - 1248 * q^18 + 320 * q^19 + 1152 * q^20 - 770 * q^21 - 288 * q^22 - 204 * q^23 - 896 * q^24 - 2158 * q^25 + 5392 * q^26 + 13156 * q^27 - 608 * q^28 - 5712 * q^29 + 160 * q^30 - 2324 * q^31 - 4096 * q^32 - 15650 * q^33 + 2088 * q^34 - 4188 * q^35 + 2496 * q^36 - 25508 * q^37 - 2440 * q^38 + 44156 * q^39 - 2304 * q^40 - 3480 * q^41 - 3080 * q^42 + 4066 * q^43 - 1152 * q^44 + 51560 * q^45 + 1632 * q^46 - 45768 * q^47 - 3584 * q^48 + 1416 * q^49 + 17264 * q^50 + 1506 * q^51 - 10784 * q^52 + 45654 * q^53 - 26312 * q^54 + 36570 * q^55 + 4864 * q^56 - 66702 * q^57 + 45696 * q^58 - 84006 * q^59 - 320 * q^60 - 14012 * q^61 + 4648 * q^62 - 15128 * q^63 + 32768 * q^64 - 4020 * q^65 - 62600 * q^66 - 19046 * q^67 - 16704 * q^68 + 111592 * q^69 - 16752 * q^70 - 53274 * q^71 + 9984 * q^72 - 41084 * q^73 + 51016 * q^74 + 153216 * q^75 + 4640 * q^76 + 271524 * q^77 - 88312 * q^78 - 54170 * q^79 - 9216 * q^80 - 9528 * q^81 - 13920 * q^82 + 52392 * q^83 + 24640 * q^84 - 221850 * q^85 + 16264 * q^86 - 457120 * q^87 + 9216 * q^88 - 137862 * q^89 - 103120 * q^90 + 308516 * q^91 - 3264 * q^92 + 112746 * q^93 + 366144 * q^94 + 153078 * q^95 + 28672 * q^96 - 292388 * q^97 - 2832 * q^98 - 138328 * q^99

Introduction

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