LMFDB - Embedded newform 38.6.c.b.11.4

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			11.4
Root			$-6.34386 - 10.9879i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.6.c.b.7.4

$q$-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} +(4.84386 - 8.38982i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-23.1201 + 40.0451i) q^{5} +(19.3755 + 33.5593i) q^{6} +177.800 q^{7} +64.0000 q^{8} +(74.5740 + 129.166i) q^{9} +(-92.4803 - 160.181i) q^{10} +5.50017 q^{11} -155.004 q^{12} +(515.695 + 893.211i) q^{13} +(-355.600 + 615.917i) q^{14} +(223.981 + 387.946i) q^{15} +(-128.000 + 221.703i) q^{16} +(-466.501 + 808.003i) q^{17} -596.592 q^{18} +(1046.56 - 1175.08i) q^{19} +739.842 q^{20} +(861.238 - 1491.71i) q^{21} +(-11.0003 + 19.0531i) q^{22} +(-1770.58 - 3066.73i) q^{23} +(310.007 - 536.948i) q^{24} +(493.425 + 854.637i) q^{25} -4125.56 q^{26} +3799.02 q^{27} +(-1422.40 - 2463.67i) q^{28} +(-2089.31 - 3618.79i) q^{29} -1791.85 q^{30} +3762.40 q^{31} +(-512.000 - 886.810i) q^{32} +(26.6421 - 46.1454i) q^{33} +(-1866.00 - 3232.01i) q^{34} +(-4110.74 + 7120.02i) q^{35} +(1193.18 - 2066.65i) q^{36} -7922.43 q^{37} +(1977.50 + 5975.54i) q^{38} +9991.83 q^{39} +(-1479.68 + 2562.89i) q^{40} +(2497.50 - 4325.80i) q^{41} +(3444.95 + 5966.83i) q^{42} +(-7272.70 + 12596.7i) q^{43} +(-44.0013 - 76.2125i) q^{44} -6896.62 q^{45} +14164.6 q^{46} +(-7679.23 - 13300.8i) q^{47} +(1240.03 + 2147.79i) q^{48} +14805.8 q^{49} -3947.40 q^{50} +(4519.33 + 7827.71i) q^{51} +(8251.13 - 14291.4i) q^{52} +(10286.1 + 17816.1i) q^{53} +(-7598.04 + 13160.2i) q^{54} +(-127.164 + 220.255i) q^{55} +11379.2 q^{56} +(-4789.36 - 14472.4i) q^{57} +16714.5 q^{58} +(-6119.91 + 10600.0i) q^{59} +(3583.69 - 6207.14i) q^{60} +(-9096.89 - 15756.3i) q^{61} +(-7524.80 + 13033.3i) q^{62} +(13259.2 + 22965.7i) q^{63} +4096.00 q^{64} -47691.7 q^{65} +(106.568 + 184.582i) q^{66} +(-11387.1 - 19723.0i) q^{67} +14928.0 q^{68} -34305.8 q^{69} +(-16443.0 - 28480.1i) q^{70} +(-33788.2 + 58522.8i) q^{71} +(4772.73 + 8266.62i) q^{72} +(40463.9 - 70085.6i) q^{73} +(15844.9 - 27444.1i) q^{74} +9560.33 q^{75} +(-24654.9 - 5100.84i) q^{76} +977.929 q^{77} +(-19983.7 + 34612.7i) q^{78} +(43313.1 - 75020.6i) q^{79} +(-5918.74 - 10251.6i) q^{80} +(280.475 - 485.798i) q^{81} +(9990.00 + 17303.2i) q^{82} +29466.9 q^{83} -27559.6 q^{84} +(-21571.1 - 37362.2i) q^{85} +(-29090.8 - 50386.7i) q^{86} -40481.4 q^{87} +352.011 q^{88} +(-23045.4 - 39915.7i) q^{89} +(13793.2 - 23890.6i) q^{90} +(91690.6 + 158813. i) q^{91} +(-28329.3 + 49067.7i) q^{92} +(18224.5 - 31565.8i) q^{93} +61433.8 q^{94} +(22859.9 + 69077.5i) q^{95} -9920.23 q^{96} +(-2229.77 + 3862.07i) q^{97} +(-29611.6 + 51288.7i) q^{98} +(410.169 + 710.434i) 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
$3$	4.84386	−	8.38982i	0.310734	−	0.538207i	−0.667787	−	0.744352i	$-0.732758\pi$
$3$	4.84386	−	8.38982i	0.310734	−	0.538207i	0.978521	+	0.206145i	$0.0660918\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−23.1201	+	40.0451i	−0.413584	+	0.716349i	−0.995279	−	0.0970584i	$-0.969057\pi$
$5$	−23.1201	+	40.0451i	−0.413584	+	0.716349i	0.581694	+	0.813407i	$0.302390\pi$
$6$	19.3755	+	33.5593i	0.219722	+	0.380570i
$7$	177.800			1.37147			0.685735	−	0.727851i	$-0.259481\pi$
$7$	177.800			1.37147			0.685735	+	0.727851i	$0.259481\pi$
$8$	64.0000			0.353553
$9$	74.5740	+	129.166i	0.306889	+	0.531547i
$10$	−92.4803	−	160.181i	−0.292448	−	0.506535i
$11$	5.50017			0.0137055			0.00685274	−	0.999977i	$-0.497819\pi$
$11$	5.50017			0.0137055			0.00685274	+	0.999977i	$0.497819\pi$
$12$	−155.004			−0.310734
$13$	515.695	+	893.211i	0.846321	+	1.46587i	0.884469	+	0.466598i	$0.154521\pi$
$13$	515.695	+	893.211i	0.846321	+	1.46587i	−0.0381488	+	0.999272i	$0.512146\pi$
$14$	−355.600	+	615.917i	−0.484888	+	0.839850i
$15$	223.981	+	387.946i	0.257029	+	0.445188i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−466.501	+	808.003i	−0.391498	+	0.678095i	−0.992647	−	0.121042i	$-0.961377\pi$
$17$	−466.501	+	808.003i	−0.391498	+	0.678095i	0.601149	+	0.799137i	$0.294710\pi$
$18$	−596.592			−0.434006
$19$	1046.56	−	1175.08i	0.665087	−	0.746766i
$19$	1046.56	−	1175.08i	0.665087	−	0.746766i
$20$	739.842			0.413584
$21$	861.238	−	1491.71i	0.426162	−	0.738135i
$22$	−11.0003	+	19.0531i	−0.00484562	+	0.00839286i
$23$	−1770.58	−	3066.73i	−0.697904	−	1.20881i	−0.969192	−	0.246307i	$-0.920783\pi$
$23$	−1770.58	−	3066.73i	−0.697904	−	1.20881i	0.271288	−	0.962498i	$-0.412551\pi$
$24$	310.007	−	536.948i	0.109861	−	0.190285i
$25$	493.425	+	854.637i	0.157896	+	0.273484i
$26$	−4125.56			−1.19688
$27$	3799.02			1.00291
$28$	−1422.40	−	2463.67i	−0.342867	−	0.593864i
$29$	−2089.31	−	3618.79i	−0.461326	−	0.799041i	0.537701	−	0.843136i	$-0.319293\pi$
$29$	−2089.31	−	3618.79i	−0.461326	−	0.799041i	−0.999027	+	0.0440948i	$0.985960\pi$
$30$	−1791.85			−0.363495
$31$	3762.40			0.703170			0.351585	−	0.936156i	$-0.385643\pi$
$31$	3762.40			0.703170			0.351585	+	0.936156i	$0.385643\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	26.6421	−	46.1454i	0.00425876	−	0.00737639i
$34$	−1866.00	−	3232.01i	−0.276831	−	0.479486i
$35$	−4110.74	+	7120.02i	−0.567218	+	0.982451i
$36$	1193.18	−	2066.65i	0.153444	−	0.265773i
$37$	−7922.43			−0.951380			−0.475690	−	0.879613i	$-0.657802\pi$
$37$	−7922.43			−0.951380			−0.475690	+	0.879613i	$0.657802\pi$
$38$	1977.50	+	5975.54i	0.222155	+	0.671303i
$39$	9991.83			1.05192
$40$	−1479.68	+	2562.89i	−0.146224	+	0.253268i
$41$	2497.50	−	4325.80i	0.232031	−	0.401889i	−0.726375	−	0.687299i	$-0.758796\pi$
$41$	2497.50	−	4325.80i	0.232031	−	0.401889i	0.958406	+	0.285409i	$0.0921296\pi$
$42$	3444.95	+	5966.83i	0.301342	+	0.521940i
$43$	−7272.70	+	12596.7i	−0.599825	+	1.03893i	0.393022	+	0.919529i	$0.371430\pi$
$43$	−7272.70	+	12596.7i	−0.599825	+	1.03893i	−0.992847	+	0.119398i	$0.961904\pi$
$44$	−44.0013	−	76.2125i	−0.00342637	−	0.00593465i
$45$	−6896.62			−0.507697
$46$	14164.6			0.986986
$47$	−7679.23	−	13300.8i	−0.507076	−	0.878281i	−0.999966	−	0.00818981i	$-0.997393\pi$
$47$	−7679.23	−	13300.8i	−0.507076	−	0.878281i	0.492891	−	0.870091i	$-0.335940\pi$
$48$	1240.03	+	2147.79i	0.0776835	+	0.134552i
$49$	14805.8			0.880930
$50$	−3947.40			−0.223299
$51$	4519.33	+	7827.71i	0.243304	+	0.421415i
$52$	8251.13	−	14291.4i	0.423160	−	0.732935i
$53$	10286.1	+	17816.1i	0.502994	+	0.871211i	0.999994	+	0.00346060i	$0.00110155\pi$
$53$	10286.1	+	17816.1i	0.502994	+	0.871211i	−0.497000	+	0.867751i	$0.665565\pi$
$54$	−7598.04	+	13160.2i	−0.354583	+	0.614155i
$55$	−127.164	+	220.255i	−0.00566837	+	0.00981791i
$56$	11379.2			0.484888
$57$	−4789.36	−	14472.4i	−0.195250	−	0.590000i
$58$	16714.5			0.652414
$59$	−6119.91	+	10600.0i	−0.228884	+	0.396438i	−0.957478	−	0.288508i	$-0.906841\pi$
$59$	−6119.91	+	10600.0i	−0.228884	+	0.396438i	0.728594	+	0.684946i	$0.240174\pi$
$60$	3583.69	−	6207.14i	0.128515	−	0.222594i
$61$	−9096.89	−	15756.3i	−0.313017	−	0.542162i	0.665997	−	0.745955i	$-0.268006\pi$
$61$	−9096.89	−	15756.3i	−0.313017	−	0.542162i	−0.979014	+	0.203793i	$0.934673\pi$
$62$	−7524.80	+	13033.3i	−0.248608	+	0.430602i
$63$	13259.2	+	22965.7i	0.420889	+	0.729001i
$64$	4096.00			0.125000
$65$	−47691.7			−1.40010
$66$	106.568	+	184.582i	0.00301140	+	0.00521589i
$67$	−11387.1	−	19723.0i	−0.309903	−	0.536768i	0.668438	−	0.743768i	$-0.266963\pi$
$67$	−11387.1	−	19723.0i	−0.309903	−	0.536768i	−0.978341	+	0.207000i	$0.933630\pi$
$68$	14928.0			0.391498
$69$	−34305.8			−0.867450
$70$	−16443.0	−	28480.1i	−0.401084	−	0.694698i
$71$	−33788.2	+	58522.8i	−0.795461	+	1.37778i	0.127086	+	0.991892i	$0.459438\pi$
$71$	−33788.2	+	58522.8i	−0.795461	+	1.37778i	−0.922546	+	0.385886i	$0.873896\pi$
$72$	4772.73	+	8266.62i	0.108502	+	0.187930i
$73$	40463.9	−	70085.6i	0.888711	−	1.53929i	0.0473118	−	0.998880i	$-0.484935\pi$
$73$	40463.9	−	70085.6i	0.888711	−	1.53929i	0.841400	−	0.540413i	$-0.181732\pi$
$74$	15844.9	−	27444.1i	0.336364	−	0.582599i
$75$	9560.33			0.196255
$76$	−24654.9	−	5100.84i	−0.489631	−	0.101300i
$77$	977.929			0.0187966
$78$	−19983.7	+	34612.7i	−0.371911	+	0.644168i
$79$	43313.1	−	75020.6i	0.780822	−	1.35242i	−0.150642	−	0.988588i	$-0.548134\pi$
$79$	43313.1	−	75020.6i	0.780822	−	1.35242i	0.931464	−	0.363835i	$-0.118533\pi$
$80$	−5918.74	−	10251.6i	−0.103396	−	0.179087i
$81$	280.475	−	485.798i	0.00474988	−	0.00822703i
$82$	9990.00	+	17303.2i	0.164071	+	0.284179i
$83$	29466.9			0.469504			0.234752	−	0.972055i	$-0.424572\pi$
$83$	29466.9			0.469504			0.234752	+	0.972055i	$0.424572\pi$
$84$	−27559.6			−0.426162
$85$	−21571.1	−	37362.2i	−0.323835	−	0.560899i
$86$	−29090.8	−	50386.7i	−0.424140	−	0.734632i
$87$	−40481.4			−0.573399
$88$	352.011			0.00484562
$89$	−23045.4	−	39915.7i	−0.308396	−	0.534157i	0.669616	−	0.742708i	$-0.266459\pi$
$89$	−23045.4	−	39915.7i	−0.308396	−	0.534157i	−0.978012	+	0.208550i	$0.933125\pi$
$90$	13793.2	−	23890.6i	0.179498	−	0.310900i
$91$	91690.6	+	158813.i	1.16070	+	2.01040i
$92$	−28329.3	+	49067.7i	−0.348952	+	0.604403i
$93$	18224.5	−	31565.8i	0.218499	−	0.378451i
$94$	61433.8			0.717113
$95$	22859.9	+	69077.5i	0.259876	+	0.785285i
$96$	−9920.23			−0.109861
$97$	−2229.77	+	3862.07i	−0.0240619	+	0.0416765i	−0.877806	−	0.479017i	$-0.840993\pi$
$97$	−2229.77	+	3862.07i	−0.0240619	+	0.0416765i	0.853744	+	0.520693i	$0.174327\pi$
$98$	−29611.6	+	51288.7i	−0.311456	+	0.539457i
$99$	410.169	+	710.434i	0.00420606	+	0.00728510i
$100$	7894.80	−	13674.2i	0.0789480	−	0.136742i
$101$	−44061.3	−	76316.3i	−0.429787	−	0.744413i	0.567067	−	0.823672i	$-0.308078\pi$
$101$	−44061.3	−	76316.3i	−0.429787	−	0.744413i	−0.996854	+	0.0792585i	$0.974745\pi$
$102$	−36154.7			−0.344084
$103$	50601.9			0.469974			0.234987	−	0.971998i	$-0.424495\pi$
$103$	50601.9			0.469974			0.234987	+	0.971998i	$0.424495\pi$
$104$	33004.5	+	57165.5i	0.299220	+	0.518263i
$105$	39823.8	+	68976.8i	0.352508	+	0.610562i
$106$	−82289.1			−0.711341
$107$	63576.1			0.536827			0.268414	−	0.963304i	$-0.413501\pi$
$107$	63576.1			0.536827			0.268414	+	0.963304i	$0.413501\pi$
$108$	−30392.2	−	52640.8i	−0.250728	−	0.434273i
$109$	15795.7	−	27358.9i	0.127342	−	0.220563i	−0.795304	−	0.606211i	$-0.792689\pi$
$109$	15795.7	−	27358.9i	0.127342	−	0.220563i	0.922646	+	0.385648i	$0.126022\pi$
$110$	−508.657	−	881.020i	−0.00400814	−	0.00694231i
$111$	−38375.2	+	66467.8i	−0.295626	+	0.512040i
$112$	−22758.4	+	39418.7i	−0.171434	+	0.296932i
$113$	236103.			1.73942			0.869711	−	0.493561i	$-0.164305\pi$
$113$	236103.			1.73942			0.869711	+	0.493561i	$0.164305\pi$
$114$	59712.4	+	12353.9i	0.430331	+	0.0890310i
$115$	163744.			1.15457
$116$	−33429.0	+	57900.7i	−0.230663	+	0.399520i
$117$	−76914.9	+	133221.i	−0.519453	+	0.899718i
$118$	−24479.6	−	42400.0i	−0.161845	−	0.280324i
$119$	−82943.8	+	143663.i	−0.536928	+	0.929987i
$120$	14334.8	+	24828.6i	0.0908736	+	0.157398i
$121$	−161021.			−0.999812
$122$	72775.1			0.442673
$123$	−24195.1	−	41907.2i	−0.144200	−	0.249761i
$124$	−30099.2	−	52133.3i	−0.175793	−	0.304482i
$125$	−190132.			−1.08838
$126$	−106074.			−0.595226
$127$	−75478.8	−	130733.i	−0.415256	−	0.719244i	0.580200	−	0.814474i	$-0.302975\pi$
$127$	−75478.8	−	130733.i	−0.415256	−	0.719244i	−0.995455	+	0.0952305i	$0.969641\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	70455.9	+	122033.i	0.372772	+	0.645660i
$130$	95383.3	−	165209.i	0.495010	−	0.857383i
$131$	42728.8	−	74008.4i	0.217542	−	0.376793i	−0.736514	−	0.676422i	$-0.763530\pi$
$131$	42728.8	−	74008.4i	0.217542	−	0.376793i	0.954056	+	0.299629i	$0.0968629\pi$
$132$	−852.546			−0.00425876
$133$	186077.	−	208930.i	0.912147	−	1.02417i
$134$	91096.8			0.438270
$135$	−87833.7	+	152132.i	−0.414788	+	0.718434i
$136$	−29856.0	+	51712.2i	−0.138416	+	0.239743i
$137$	−152559.	−	264240.i	−0.694443	−	1.20281i	−0.970368	−	0.241632i	$-0.922317\pi$
$137$	−152559.	−	264240.i	−0.694443	−	1.20281i	0.275924	−	0.961179i	$-0.411016\pi$
$138$	68611.6	−	118839.i	0.306690	−	0.531203i
$139$	−150373.	−	260453.i	−0.660134	−	1.14339i	−0.980580	−	0.196118i	$-0.937166\pi$
$139$	−150373.	−	260453.i	−0.660134	−	1.14339i	0.320447	−	0.947267i	$-0.396167\pi$
$140$	131544.			0.567218
$141$	−148789.			−0.630263
$142$	−135153.	−	234091.i	−0.562476	−	0.974236i
$143$	2836.41	+	4912.81i	0.0115992	+	0.0200905i
$144$	−38181.9			−0.153444
$145$	193220.			0.763190
$146$	161856.	+	280342.i	0.628414	+	1.08844i
$147$	71717.2	−	124218.i	0.273735	−	0.474123i
$148$	63379.5	+	109776.i	0.237845	+	0.411960i
$149$	9608.88	−	16643.1i	0.0354574	−	0.0614140i	−0.847752	−	0.530393i	$-0.822045\pi$
$149$	9608.88	−	16643.1i	0.0354574	−	0.0614140i	0.883210	+	0.468979i	$0.155378\pi$
$150$	−19120.7	+	33118.0i	−0.0693865	+	0.120181i
$151$	−187140.			−0.667920			−0.333960	−	0.942587i	$-0.608385\pi$
$151$	−187140.			−0.667920			−0.333960	+	0.942587i	$0.608385\pi$
$152$	66979.6	−	75205.3i	0.235144	−	0.264022i
$153$	−139155.			−0.480586
$154$	−1955.86	+	3387.64i	−0.00664562	+	0.0115105i
$155$	−86986.9	+	150666.i	−0.290820	+	0.503715i
$156$	−79934.7	−	138451.i	−0.262981	−	0.455496i
$157$	−42664.9	+	73897.8i	−0.138141	+	0.239267i	−0.926793	−	0.375573i	$-0.877446\pi$
$157$	−42664.9	+	73897.8i	−0.138141	+	0.239267i	0.788652	+	0.614840i	$0.210779\pi$
$158$	173253.	+	300082.i	0.552124	+	0.956308i
$159$	199299.			0.625189
$160$	47349.9			0.146224
$161$	−314809.	−	545265.i	−0.957155	−	1.65784i
$162$	1121.90	+	1943.19i	0.00335867	+	0.00581739i
$163$	−47671.9			−0.140538			−0.0702689	−	0.997528i	$-0.522386\pi$
$163$	−47671.9			−0.140538			−0.0702689	+	0.997528i	$0.522386\pi$
$164$	−79920.0			−0.232031
$165$	1231.93	+	2133.77i	0.00352271	+	0.00610151i
$166$	−58933.8	+	102076.i	−0.165995	+	0.287511i
$167$	9863.67	+	17084.4i	0.0273683	+	0.0474032i	0.879385	−	0.476111i	$-0.157954\pi$
$167$	9863.67	+	17084.4i	0.0273683	+	0.0474032i	−0.852017	+	0.523514i	$0.824621\pi$
$168$	55119.2	−	95469.3i	0.150671	−	0.260970i
$169$	−346237.	+	599700.i	−0.932517	+	1.61517i
$170$	172568.			0.457972
$171$	229826.	+	47548.7i	0.601049	+	0.124351i
$172$	232726.			0.599825
$173$	−361533.	+	626194.i	−0.918402	+	1.59072i	−0.116559	+	0.993184i	$0.537187\pi$
$173$	−361533.	+	626194.i	−0.918402	+	1.59072i	−0.801843	+	0.597535i	$0.796147\pi$
$174$	80962.8	−	140232.i	0.202727	−	0.351134i
$175$	87730.9	+	151954.i	0.216550	+	0.375075i
$176$	−704.021	+	1219.40i	−0.00171318	+	0.00296732i
$177$	59288.0	+	102690.i	0.142244	+	0.246374i
$178$	184363.			0.436138
$179$	553218.			1.29052			0.645259	−	0.763964i	$-0.276750\pi$
$179$	553218.			1.29052			0.645259	+	0.763964i	$0.276750\pi$
$180$	55173.0	+	95562.4i	0.126924	+	0.219839i
$181$	332593.	+	576068.i	0.754599	+	1.30700i	0.945573	+	0.325409i	$0.105502\pi$
$181$	332593.	+	576068.i	0.754599	+	1.30700i	−0.190974	+	0.981595i	$0.561165\pi$
$182$	−733525.			−1.64148
$183$	−176256.			−0.389060
$184$	−113317.	−	196271.i	−0.246746	−	0.427377i
$185$	183167.	−	317255.i	0.393476	−	0.681520i
$186$	72898.2	+	126263.i	0.154502	+	0.267605i
$187$	−2565.83	+	4444.15i	−0.00536567	+	0.00929362i
$188$	−122868.	+	212813.i	−0.253538	+	0.439141i
$189$	675466.			1.37546
$190$	−285011.	−	58965.9i	−0.572767	−	0.118500i
$191$	−144263.			−0.286135			−0.143068	−	0.989713i	$-0.545697\pi$
$191$	−144263.			−0.286135			−0.143068	+	0.989713i	$0.545697\pi$
$192$	19840.5	−	34364.7i	0.0388418	−	0.0672759i
$193$	360326.	−	624104.i	0.696310	−	1.20604i	−0.273427	−	0.961893i	$-0.588157\pi$
$193$	360326.	−	624104.i	0.696310	−	1.20604i	0.969737	−	0.244152i	$-0.0785096\pi$
$194$	−8919.08	−	15448.3i	−0.0170144	−	0.0294697i
$195$	−231012.	+	400124.i	−0.435059	+	0.753544i
$196$	−118446.	−	205155.i	−0.220232	−	0.381454i
$197$	1.00249e6			1.84041			0.920207	−	0.391432i	$-0.128020\pi$
$197$	1.00249e6			1.84041			0.920207	+	0.391432i	$0.128020\pi$
$198$	−3281.35			−0.00594826
$199$	−318120.	−	551000.i	−0.569454	−	0.986323i	−0.996620	−	0.0821495i	$-0.973821\pi$
$199$	−318120.	−	551000.i	−0.569454	−	0.986323i	0.427166	−	0.904173i	$-0.359512\pi$
$200$	31579.2	+	54696.8i	0.0558247	+	0.0966912i
$201$	−220630.			−0.385190
$202$	352490.			0.607811
$203$	−371479.	−	643421.i	−0.632695	−	1.09586i
$204$	72309.3	−	125243.i	0.121652	−	0.210707i
$205$	115485.	+	200025.i	0.191929	+	0.332430i
$206$	−101204.	+	175290.i	−0.166161	+	0.287799i
$207$	264078.	−	457397.i	0.428358	−	0.741938i
$208$	−264036.			−0.423160
$209$	5756.23	−	6463.15i	0.00911533	−	0.0102348i
$210$	−318590.			−0.498522
$211$	−528520.	+	915424.i	−0.817251	+	1.41552i	0.0904485	+	0.995901i	$0.471170\pi$
$211$	−528520.	+	915424.i	−0.817251	+	1.41552i	−0.907700	+	0.419620i	$0.862163\pi$
$212$	164578.	−	285058.i	0.251497	−	0.435606i
$213$	327330.	+	566953.i	0.494353	+	0.856245i
$214$	−127152.	+	220234.i	−0.189797	+	0.328738i
$215$	−336291.	−	582472.i	−0.496156	−	0.859368i
$216$	243137.			0.354583
$217$	668954.			0.964377
$218$	63182.7	+	109436.i	0.0900444	+	0.155962i
$219$	−392003.	−	678970.i	−0.552306	−	0.956622i
$220$	4069.26			0.00566837
$221$	−962289.			−1.32533
$222$	−153501.	−	265871.i	−0.209039	−	0.362067i
$223$	81135.2	−	140530.i	0.109256	−	0.189238i	−0.806213	−	0.591626i	$-0.798486\pi$
$223$	81135.2	−	140530.i	0.109256	−	0.189238i	0.915469	+	0.402388i	$0.131820\pi$
$224$	−91033.5	−	157675.i	−0.121222	−	0.209963i
$225$	−73593.3	+	127467.i	−0.0969130	+	0.167858i
$226$	−472206.	+	817884.i	−0.614979	+	1.06517i
$227$	−280544.			−0.361357			−0.180678	−	0.983542i	$-0.557829\pi$
$227$	−280544.			−0.361357			−0.180678	+	0.983542i	$0.557829\pi$
$228$	−162220.	+	182142.i	−0.206665	+	0.232046i
$229$	−555296.			−0.699738			−0.349869	−	0.936799i	$-0.613774\pi$
$229$	−555296.			−0.699738			−0.349869	+	0.936799i	$0.613774\pi$
$230$	−327487.	+	567225.i	−0.408202	+	0.707026i
$231$	4736.95	−	8204.64i	0.00584076	−	0.0101165i
$232$	−133716.	−	231603.i	−0.163104	−	0.282504i
$233$	416075.	−	720664.i	0.502091	−	0.869647i	−0.497906	−	0.867231i	$-0.665898\pi$
$233$	416075.	−	720664.i	0.502091	−	0.869647i	0.999997	−	0.00241578i	$-0.000768967\pi$
$234$	−307660.	−	532882.i	−0.367308	−	0.636197i
$235$	710177.			0.838874
$236$	195837.			0.228884
$237$	−419606.	−	726779.i	−0.485256	−	0.840488i
$238$	−331775.	−	574651.i	−0.379666	−	0.657600i
$239$	61445.3			0.0695815			0.0347907	−	0.999395i	$-0.488924\pi$
$239$	61445.3			0.0695815			0.0347907	+	0.999395i	$0.488924\pi$
$240$	−114678.			−0.128515
$241$	559423.	+	968950.i	0.620437	+	1.07463i	0.989404	+	0.145187i	$0.0463783\pi$
$241$	559423.	+	968950.i	0.620437	+	1.07463i	−0.368967	+	0.929443i	$0.620288\pi$
$242$	322041.	−	557792.i	0.353487	−	0.612257i
$243$	458864.	+	794776.i	0.498504	+	0.863434i
$244$	−145550.	+	252100.i	−0.156509	+	0.271081i
$245$	−342311.	+	592899.i	−0.364339	+	0.631053i
$246$	193561.			0.203929
$247$	1.58930e6	+	328810.i	1.65754	+	0.342928i
$248$	240793.			0.248608
$249$	142734.	−	247222.i	0.145891	−	0.252691i
$250$	380265.	−	658638.i	0.384801	−	0.666495i
$251$	−604896.	−	1.04771e6i	−0.606033	−	1.04968i	−0.991887	−	0.127120i	$-0.959427\pi$
$251$	−604896.	−	1.04771e6i	−0.606033	−	1.04968i	0.385855	−	0.922560i	$-0.373907\pi$
$252$	212148.	−	367451.i	0.210444	−	0.364500i
$253$	−9738.48	−	16867.5i	−0.00956511	−	0.0165673i
$254$	603830.			0.587260
$255$	−417949.			−0.402507
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	27061.0	+	46871.1i	0.0255571	+	0.0442662i	0.878521	−	0.477704i	$-0.158531\pi$
$257$	27061.0	+	46871.1i	0.0255571	+	0.0442662i	−0.852964	+	0.521970i	$0.825197\pi$
$258$	−563647.			−0.527179
$259$	−1.40861e6			−1.30479
$260$	381533.	+	660835.i	0.350025	+	0.606261i
$261$	311617.	−	539736.i	0.283152	−	0.490433i
$262$	170915.	+	296034.i	0.153825	+	0.266433i
$263$	1.07965e6	−	1.87002e6i	0.962489	−	1.66708i	0.246272	−	0.969201i	$-0.420794\pi$
$263$	1.07965e6	−	1.87002e6i	0.962489	−	1.66708i	0.716216	−	0.697878i	$-0.245872\pi$
$264$	1705.09	−	2953.31i	0.00150570	−	0.00260795i
$265$	−951265.			−0.832122
$266$	351598.	+	1.06245e6i	0.304679	+	0.920671i
$267$	−446514.			−0.383316
$268$	−182194.	+	315569.i	−0.154952	+	0.268384i
$269$	−1.02660e6	+	1.77812e6i	−0.865006	+	1.49823i	0.00203447	+	0.999998i	$0.499352\pi$
$269$	−1.02660e6	+	1.77812e6i	−0.865006	+	1.49823i	−0.867041	+	0.498237i	$0.833981\pi$
$270$	−351335.	−	608529.i	−0.293300	−	0.508010i
$271$	−945648.	+	1.63791e6i	−0.782179	+	1.35477i	0.148491	+	0.988914i	$0.452558\pi$
$271$	−945648.	+	1.63791e6i	−0.782179	+	1.35477i	−0.930670	+	0.365860i	$0.880775\pi$
$272$	−119424.	−	206849.i	−0.0978746	−	0.169524i
$273$	1.77655e6			1.44268
$274$	1.22047e6			0.982091
$275$	2713.92	+	4700.65i	0.00216404	+	0.00374823i
$276$	274446.	+	475355.i	0.216863	+	0.375617i
$277$	48008.8			0.0375943			0.0187971	−	0.999823i	$-0.494016\pi$
$277$	48008.8			0.0375943			0.0187971	+	0.999823i	$0.494016\pi$
$278$	1.20298e6			0.933570
$279$	280577.	+	485974.i	0.215795	+	0.373768i
$280$	−263088.	+	455681.i	−0.200542	+	0.347349i
$281$	715331.	+	1.23899e6i	0.540432	+	0.936056i	0.998879	+	0.0473339i	$0.0150725\pi$
$281$	715331.	+	1.23899e6i	0.540432	+	0.936056i	−0.458447	+	0.888722i	$0.651594\pi$
$282$	297577.	−	515419.i	0.222832	−	0.385956i
$283$	−874446.	+	1.51459e6i	−0.649033	+	1.12416i	0.334321	+	0.942459i	$0.391493\pi$
$283$	−874446.	+	1.51459e6i	−0.649033	+	1.12416i	−0.983354	+	0.181699i	$0.941840\pi$
$284$	1.08122e6			0.795461
$285$	690278.	+	142811.i	0.503398	+	0.104148i
$286$	−22691.3			−0.0164038
$287$	444055.	−	769126.i	0.318223	−	0.551179i
$288$	76363.7	−	132266.i	0.0542508	−	0.0939651i
$289$	274683.	+	475764.i	0.193458	+	0.335079i
$290$	−386440.	+	669334.i	−0.269828	+	0.467356i
$291$	21601.4	+	37414.7i	0.0149537	+	0.0259006i
$292$	−1.29485e6			−0.888711
$293$	−2.57086e6			−1.74948			−0.874741	−	0.484591i	$-0.838968\pi$
$293$	−2.57086e6			−1.74948			−0.874741	+	0.484591i	$0.838968\pi$
$294$	286869.	+	496871.i	0.193560	+	0.335255i
$295$	−282985.	−	490145.i	−0.189325	−	0.327921i
$296$	−507036.			−0.336364
$297$	20895.3			0.0137454
$298$	38435.5	+	66572.3i	0.0250722	+	0.0434263i
$299$	1.82616e6	−	3.16300e6i	1.18130	−	2.04607i
$300$	−76482.7	−	132472.i	−0.0490637	−	0.0849807i
$301$	−1.29308e6	+	2.23969e6i	−0.822642	+	1.42486i
$302$	374280.	−	648272.i	0.236145	−	0.409016i
$303$	−853707.			−0.534198
$304$	126560.	+	382435.i	0.0785437	+	0.237341i
$305$	841283.			0.517836
$306$	278310.	−	482048.i	0.169913	−	0.294298i
$307$	453293.	−	785126.i	0.274494	−	0.475438i	−0.695513	−	0.718513i	$-0.744823\pi$
$307$	453293.	−	785126.i	0.274494	−	0.475438i	0.970007	+	0.243076i	$0.0781563\pi$
$308$	−7823.43	−	13550.6i	−0.00469916	−	0.00813919i
$309$	245109.	−	424541.i	0.146037	−	0.252944i
$310$	−347948.	−	602663.i	−0.205641	−	0.356181i
$311$	−1.35970e6			−0.797157			−0.398578	−	0.917134i	$-0.630496\pi$
$311$	−1.35970e6			−0.797157			−0.398578	+	0.917134i	$0.630496\pi$
$312$	639477.			0.371911
$313$	−1.10408e6	−	1.91231e6i	−0.636998	−	1.10331i	−0.986088	−	0.166223i	$-0.946843\pi$
$313$	−1.10408e6	−	1.91231e6i	−0.636998	−	1.10331i	0.349090	−	0.937089i	$-0.386491\pi$
$314$	−170660.	−	295591.i	−0.0976803	−	0.169187i
$315$	−1.22622e6			−0.696292
$316$	−1.38602e6			−0.780822
$317$	514679.	+	891451.i	0.287666	+	0.498252i	0.973252	−	0.229739i	$-0.0737873\pi$
$317$	514679.	+	891451.i	0.287666	+	0.498252i	−0.685586	+	0.727992i	$0.740454\pi$
$318$	−398597.	+	690391.i	−0.221038	+	0.382849i
$319$	−11491.6	−	19904.0i	−0.00632270	−	0.0109512i
$320$	−94699.8	+	164025.i	−0.0516980	+	0.0895436i
$321$	307954.	−	533392.i	0.166810	−	0.288924i
$322$	2.51847e6			1.35362
$323$	461252.	+	1.39380e6i	0.245998	+	0.743350i
$324$	−8975.22			−0.00474988
$325$	−508914.	+	881465.i	−0.267261	+	0.462910i
$326$	95343.8	−	165140.i	0.0496876	−	0.0860615i
$327$	−153024.	−	265046.i	−0.0791390	−	0.137073i
$328$	159840.	−	276851.i	0.0820353	−	0.142089i
$329$	−1.36537e6	−	2.36488e6i	−0.695439	−	1.20454i
$330$	−9855.46			−0.00498187
$331$	1.31278e6			0.658601			0.329300	−	0.944225i	$-0.393187\pi$
$331$	1.31278e6			0.658601			0.329300	+	0.944225i	$0.393187\pi$
$332$	−235735.	−	408306.i	−0.117376	−	0.203301i
$333$	−590807.	−	1.02331e6i	−0.291968	−	0.505703i
$334$	−78909.3			−0.0387046
$335$	1.05308e6			0.512685
$336$	220477.	+	381877.i	0.106541	+	0.184534i
$337$	1.55929e6	−	2.70077e6i	0.747915	−	1.29543i	−0.200906	−	0.979611i	$-0.564389\pi$
$337$	1.55929e6	−	2.70077e6i	0.747915	−	1.29543i	0.948821	−	0.315816i	$-0.102278\pi$
$338$	−1.38495e6	−	2.39880e6i	−0.659389	−	1.14210i
$339$	1.14365e6	−	1.98086e6i	0.540498	−	0.936170i
$340$	−345137.	+	597795.i	−0.161918	+	0.280450i
$341$	20693.8			0.00963728
$342$	−624366.	+	701045.i	−0.288652	+	0.324101i
$343$	−355816.			−0.163302
$344$	−465453.	+	806188.i	−0.212070	+	0.367316i
$345$	793152.	−	1.37378e6i	0.358764	−	0.621397i
$346$	−1.44613e6	−	2.50478e6i	−0.649408	−	1.12481i
$347$	−803660.	+	1.39198e6i	−0.358301	+	0.620596i	−0.987677	−	0.156505i	$-0.949977\pi$
$347$	−803660.	+	1.39198e6i	−0.358301	+	0.620596i	0.629376	+	0.777101i	$0.283311\pi$
$348$	323851.	+	560926.i	0.143350	+	0.248289i
$349$	−724001.			−0.318182			−0.159091	−	0.987264i	$-0.550856\pi$
$349$	−724001.			−0.318182			−0.159091	+	0.987264i	$0.550856\pi$
$350$	−701847.			−0.306247
$351$	1.95914e6	+	3.39333e6i	0.848784	+	1.47014i
$352$	−2816.09	−	4877.60i	−0.00121140	−	0.00209821i
$353$	724652.			0.309523			0.154761	−	0.987952i	$-0.450539\pi$
$353$	724652.			0.309523			0.154761	+	0.987952i	$0.450539\pi$
$354$	−474304.			−0.201163
$355$	−1.56237e6	−	2.70610e6i	−0.657980	−	1.13965i
$356$	−368726.	+	638652.i	−0.154198	+	0.267079i
$357$	803537.	+	1.39177e6i	0.333684	+	0.577957i
$358$	−1.10644e6	+	1.91640e6i	−0.456267	+	0.790278i
$359$	−361869.	+	626775.i	−0.148189	+	0.256670i	−0.930558	−	0.366144i	$-0.880678\pi$
$359$	−361869.	+	626775.i	−0.148189	+	0.256670i	0.782369	+	0.622815i	$0.214011\pi$
$360$	−441384.			−0.179498
$361$	−285541.	−	2.45958e6i	−0.115319	−	0.993329i
$362$	−2.66074e6			−1.06716
$363$	−779963.	+	1.35093e6i	−0.310676	+	0.538106i
$364$	1.46705e6	−	2.54100e6i	0.580352	−	1.00520i
$365$	1.87106e6	+	3.24077e6i	0.735114	+	1.27326i
$366$	352513.	−	610570.i	0.137554	−	0.238250i
$367$	2.43800e6	+	4.22274e6i	0.944863	+	1.63655i	0.756025	+	0.654543i	$0.227139\pi$
$367$	2.43800e6	+	4.22274e6i	0.944863	+	1.63655i	0.188838	+	0.982008i	$0.439528\pi$
$368$	906537.			0.348952
$369$	744994.			0.284831
$370$	732669.	+	1.26902e6i	0.278230	+	0.481908i
$371$	1.82887e6	+	3.16770e6i	0.689841	+	1.19484i
$372$	−583185.			−0.218499
$373$	−1.30910e6			−0.487194			−0.243597	−	0.969877i	$-0.578327\pi$
$373$	−1.30910e6			−0.487194			−0.243597	+	0.969877i	$0.578327\pi$
$374$	−10263.3	−	17776.6i	−0.00379410	−	0.00657158i
$375$	−920976.	+	1.59518e6i	−0.338197	+	0.585775i
$376$	−491471.	−	851252.i	−0.179278	−	0.310519i
$377$	2.15490e6	−	3.73239e6i	0.780860	−	1.35249i
$378$	−1.35093e6	+	2.33988e6i	−0.486299	+	0.842295i
$379$	60313.7			0.0215684			0.0107842	−	0.999942i	$-0.496567\pi$
$379$	60313.7			0.0215684			0.0107842	+	0.999942i	$0.496567\pi$
$380$	774286.	−	869376.i	0.275069	−	0.308851i
$381$	−1.46244e6			−0.516136
$382$	288526.	−	499742.i	0.101164	−	0.175221i
$383$	−510882.	+	884873.i	−0.177960	+	0.308236i	−0.941182	−	0.337901i	$-0.890283\pi$
$383$	−510882.	+	884873.i	−0.177960	+	0.308236i	0.763221	+	0.646137i	$0.223617\pi$
$384$	79361.9	+	137459.i	0.0274653	+	0.0475712i
$385$	−22609.8	+	39161.3i	−0.00777400	+	0.0134650i
$386$	1.44131e6	+	2.49641e6i	0.492366	+	0.852802i
$387$	−2.16942e6			−0.736318
$388$	71352.6			0.0240619
$389$	−1.16397e6	−	2.01606e6i	−0.390004	−	0.675506i	0.602446	−	0.798160i	$-0.294193\pi$
$389$	−1.16397e6	−	2.01606e6i	−0.390004	−	0.675506i	−0.992450	+	0.122654i	$0.960860\pi$
$390$	−924048.	−	1.60050e6i	−0.307633	−	0.532836i
$391$	3.30391e6			1.09291
$392$	947570.			0.311456
$393$	−413945.	−	716973.i	−0.135195	−	0.234165i
$394$	−2.00498e6	+	3.47274e6i	−0.650685	+	1.12702i
$395$	2.00281e6	+	3.46896e6i	0.645871	+	1.11868i
$396$	6562.71	−	11366.9i	0.00210303	−	0.00364255i
$397$	1.75278e6	−	3.03591e6i	0.558152	−	0.966747i	−0.439499	−	0.898243i	$-0.644844\pi$
$397$	1.75278e6	−	3.03591e6i	0.558152	−	0.966747i	0.997651	−	0.0685040i	$-0.0218226\pi$
$398$	2.54496e6			0.805329
$399$	−851547.	−	2.57318e6i	−0.267779	−	0.809167i
$400$	−252634.			−0.0789480
$401$	318265.	−	551251.i	0.0988389	−	0.171194i	−0.812365	−	0.583149i	$-0.801820\pi$
$401$	318265.	−	551251.i	0.0988389	−	0.171194i	0.911204	+	0.411955i	$0.135154\pi$
$402$	441261.	−	764286.i	0.136185	−	0.235880i
$403$	1.94025e6	+	3.36061e6i	0.595108	+	1.03076i
$404$	−704980.	+	1.22106e6i	−0.214894	+	0.372207i
$405$	12969.2	+	22463.4i	0.00392895	+	0.00680514i
$406$	2.97184e6			0.894766
$407$	−43574.7			−0.0130391
$408$	289237.	+	500974.i	0.0860209	+	0.148993i
$409$	844535.	+	1.46278e6i	0.249637	+	0.432384i	0.963425	−	0.267978i	$-0.0863553\pi$
$409$	844535.	+	1.46278e6i	0.249637	+	0.432384i	−0.713788	+	0.700362i	$0.753022\pi$
$410$	−923878.			−0.271428
$411$	−2.95590e6			−0.863149
$412$	−404816.	−	701161.i	−0.117494	−	0.203505i
$413$	−1.08812e6	+	1.88468e6i	−0.313907	+	0.543703i
$414$	1.05631e6	+	1.82959e6i	0.302895	+	0.524629i
$415$	−681277.	+	1.18001e6i	−0.194180	+	0.336329i
$416$	528072.	−	914648.i	0.149610	−	0.259132i
$417$	−2.91354e6			−0.820504
$418$	10876.6	+	32866.5i	0.00304474	+	0.00920052i
$419$	3.97406e6			1.10586			0.552929	−	0.833228i	$-0.313510\pi$
$419$	3.97406e6			1.10586			0.552929	+	0.833228i	$0.313510\pi$
$420$	637180.	−	1.10363e6i	0.176254	−	0.305281i
$421$	−1.71438e6	+	2.96939e6i	−0.471413	+	0.816511i	−0.999465	−	0.0327009i	$-0.989589\pi$
$421$	−1.71438e6	+	2.96939e6i	−0.471413	+	0.816511i	0.528052	+	0.849212i	$0.322922\pi$
$422$	−2.11408e6	−	3.66170e6i	−0.577884	−	1.00092i
$423$	1.14534e6	−	1.98379e6i	0.311232	−	0.539069i
$424$	658313.	+	1.14023e6i	0.177835	+	0.308020i
$425$	−920733.			−0.247264
$426$	−2.61864e6			−0.699121
$427$	−1.61742e6	−	2.80146e6i	−0.429294	−	0.743558i
$428$	−508609.	−	880936.i	−0.134207	−	0.232453i
$429$	54956.8			0.0144171
$430$	2.69032e6			0.701671
$431$	−420749.	−	728758.i	−0.109101	−	0.188969i	0.806305	−	0.591500i	$-0.201464\pi$
$431$	−420749.	−	728758.i	−0.109101	−	0.188969i	−0.915406	+	0.402531i	$0.868131\pi$
$432$	−486275.	+	842253.i	−0.125364	+	0.217137i
$433$	−3.16621e6	−	5.48403e6i	−0.811558	−	1.40566i	−0.911774	−	0.410693i	$-0.865287\pi$
$433$	−3.16621e6	−	5.48403e6i	−0.811558	−	1.40566i	0.100216	−	0.994966i	$-0.468047\pi$
$434$	−1.33791e6	+	2.31732e6i	−0.340959	+	0.590558i
$435$	935932.	−	1.62108e6i	0.237149	−	0.410754i
$436$	−505462.			−0.127342
$437$	−5.45668e6	−	1.12893e6i	−1.36686	−	0.282789i
$438$	3.13603e6			0.781078
$439$	2.56854e6	−	4.44884e6i	0.636099	−	1.10176i	−0.350182	−	0.936682i	$-0.613880\pi$
$439$	2.56854e6	−	4.44884e6i	0.636099	−	1.10176i	0.986281	−	0.165074i	$-0.0527864\pi$
$440$	−8138.51	+	14096.3i	−0.00200407	+	0.00347115i
$441$	1.10413e6	+	1.91240e6i	0.270347	+	0.468255i
$442$	1.92458e6	−	3.33347e6i	0.468576	−	0.811597i
$443$	−1.35968e6	−	2.35504e6i	−0.329175	−	0.570149i	0.653173	−	0.757209i	$-0.273437\pi$
$443$	−1.35968e6	−	2.35504e6i	−0.329175	−	0.570149i	−0.982348	+	0.187060i	$0.940104\pi$
$444$	1.22801e6			0.295626
$445$	2.13124e6			0.510191
$446$	324541.	+	562121.i	0.0772560	+	0.133811i
$447$	−93088.2	−	161234.i	−0.0220356	−	0.0381669i
$448$	728268.			0.171434
$449$	2.65490e6			0.621488			0.310744	−	0.950494i	$-0.399422\pi$
$449$	2.65490e6			0.621488			0.310744	+	0.950494i	$0.399422\pi$
$450$	−294373.	−	509869.i	−0.0685278	−	0.118694i
$451$	13736.7	−	23792.6i	0.00318010	−	0.00550809i
$452$	−1.88882e6	−	3.27154e6i	−0.434856	−	0.753192i
$453$	−906481.	+	1.57007e6i	−0.207545	+	0.359479i
$454$	561088.	−	971833.i	0.127759	−	0.221285i
$455$	−8.47957e6			−1.92019
$456$	−306519.	−	926231.i	−0.0690312	−	0.208597i
$457$	2.65356e6			0.594345			0.297172	−	0.954824i	$-0.403956\pi$
$457$	2.65356e6			0.594345			0.297172	+	0.954824i	$0.403956\pi$
$458$	1.11059e6	−	1.92360e6i	0.247395	−	0.428500i
$459$	−1.77225e6	+	3.06962e6i	−0.392638	+	0.680069i
$460$	−1.30995e6	−	2.26890e6i	−0.288642	−	0.499943i
$461$	−1.76886e6	+	3.06376e6i	−0.387652	+	0.671432i	−0.992133	−	0.125187i	$-0.960047\pi$
$461$	−1.76886e6	+	3.06376e6i	−0.387652	+	0.671432i	0.604481	+	0.796619i	$0.293380\pi$
$462$	18947.8	+	32818.6i	0.00413004	+	0.00715344i
$463$	−5.93347e6			−1.28634			−0.643171	−	0.765723i	$-0.722381\pi$
$463$	−5.93347e6			−1.28634			−0.643171	+	0.765723i	$0.722381\pi$
$464$	1.06973e6			0.230663
$465$	842705.	+	1.45961e6i	0.180735	+	0.313043i
$466$	1.66430e6	+	2.88265e6i	0.355032	+	0.614933i
$467$	5.23855e6			1.11152			0.555762	−	0.831341i	$-0.312427\pi$
$467$	5.23855e6			1.11152			0.555762	+	0.831341i	$0.312427\pi$
$468$	2.46128e6			0.519453
$469$	−2.02463e6	−	3.50675e6i	−0.425023	−	0.736162i
$470$	−1.42035e6	+	2.46013e6i	−0.296587	+	0.513704i
$471$	413326.	+	715902.i	0.0858501	+	0.148697i
$472$	−391674.	+	678400.i	−0.0809226	+	0.140162i
$473$	−40001.0	+	69283.8i	−0.00822088	+	0.0142390i
$474$	3.35685e6			0.686255
$475$	1.52067e6	+	314610.i	0.309243	+	0.0639792i
$476$	2.65420e6			0.536928
$477$	−1.53416e6	+	2.65724e6i	−0.308726	+	0.534730i
$478$	−122891.	+	212853.i	−0.0246008	+	0.0426098i
$479$	857165.	+	1.48465e6i	0.170697	+	0.295656i	0.938664	−	0.344834i	$-0.112065\pi$
$479$	857165.	+	1.48465e6i	0.170697	+	0.295656i	−0.767967	+	0.640490i	$0.778731\pi$
$480$	229356.	−	397257.i	0.0454368	−	0.0786989i
$481$	−4.08556e6	−	7.07640e6i	−0.805173	−	1.39460i
$482$	−4.47539e6			−0.877431
$483$	−6.09956e6			−1.18968
$484$	1.28817e6	+	2.23117e6i	0.249953	+	0.432931i
$485$	−103105.	−	178583.i	−0.0199033	−	0.0344735i
$486$	−3.67091e6			−0.704991
$487$	5.46940e6			1.04500			0.522501	−	0.852639i	$-0.324999\pi$
$487$	5.46940e6			1.04500			0.522501	+	0.852639i	$0.324999\pi$
$488$	−582201.	−	1.00840e6i	−0.110668	−	0.191683i
$489$	−230916.	+	399959.i	−0.0436699	+	0.0756385i
$490$	−1.36924e6	−	2.37160e6i	−0.257626	−	0.446222i
$491$	−570104.	+	987449.i	−0.106721	+	0.184846i	−0.914440	−	0.404721i	$-0.867369\pi$
$491$	−570104.	+	987449.i	−0.106721	+	0.184846i	0.807719	+	0.589568i	$0.200702\pi$
$492$	−387122.	+	670514.i	−0.0720999	+	0.124881i
$493$	3.89866e6			0.722434
$494$	−4.31763e6	+	4.84788e6i	−0.796028	+	0.893788i
$495$	−37932.6			−0.00695824
$496$	−481587.	+	834133.i	−0.0878963	+	0.152241i
$497$	−6.00753e6	+	1.04053e7i	−1.09095	+	1.88958i
$498$	570935.	+	988888.i	0.103160	+	0.178679i
$499$	2.55058e6	−	4.41773e6i	0.458550	−	0.794232i	−0.540334	−	0.841450i	$-0.681702\pi$
$499$	2.55058e6	−	4.41773e6i	0.458550	−	0.794232i	0.998885	+	0.0472181i	$0.0150356\pi$
$500$	1.52106e6	+	2.63455e6i	0.272095	+	0.471283i
$501$	191113.			0.0340170
$502$	4.83916e6			0.857060
$503$	22139.7	+	38347.0i	0.00390168	+	0.00675790i	0.867970	−	0.496617i	$-0.165425\pi$
$503$	22139.7	+	38347.0i	0.00390168	+	0.00675790i	−0.864068	+	0.503375i	$0.832091\pi$
$504$	848591.	+	1.46980e6i	0.148807	+	0.257741i
$505$	4.07480e6			0.711013
$506$	77907.9			0.0135271
$507$	3.35425e6	+	5.80973e6i	0.579530	+	1.00377i
$508$	−1.20766e6	+	2.09173e6i	−0.207628	+	0.359622i
$509$	−1.99430e6	−	3.45423e6i	−0.341190	−	0.590958i	0.643464	−	0.765476i	$-0.277497\pi$
$509$	−1.99430e6	−	3.45423e6i	−0.341190	−	0.590958i	−0.984654	+	0.174518i	$0.944163\pi$
$510$	835898.	−	1.44782e6i	0.142308	−	0.246484i
$511$	7.19448e6	−	1.24612e7i	1.21884	−	2.11109i
$512$	262144.			0.0441942
$513$	3.97589e6	−	4.46417e6i	0.667023	−	0.748940i
$514$	−216488.			−0.0361432
$515$	−1.16992e6	+	2.02636e6i	−0.194374	+	0.336666i
$516$	1.12729e6	−	1.95253e6i	0.186386	−	0.322830i
$517$	−42237.0	−	73156.7i	−0.00694972	−	0.0120373i
$518$	2.81721e6	−	4.87956e6i	0.461313	−	0.799017i
$519$	3.50243e6	+	6.06639e6i	0.570758	+	0.988581i
$520$	−3.05227e6			−0.495010
$521$	−791816.			−0.127800			−0.0638998	−	0.997956i	$-0.520354\pi$
$521$	−791816.			−0.127800			−0.0638998	+	0.997956i	$0.520354\pi$
$522$	1.24647e6	+	2.15894e6i	0.200219	+	0.346789i
$523$	318050.	+	550879.i	0.0508442	+	0.0880648i	0.890327	−	0.455321i	$-0.150475\pi$
$523$	318050.	+	550879.i	0.0508442	+	0.0880648i	−0.839483	+	0.543386i	$0.817142\pi$
$524$	−1.36732e6			−0.217542
$525$	1.69983e6			0.269157
$526$	4.31862e6	+	7.48007e6i	0.680582	+	1.17880i
$527$	−1.75516e6	+	3.04003e6i	−0.275290	+	0.476816i
$528$	6820.37	+	11813.2i	0.00106469	+	0.00184410i
$529$	−3.05173e6	+	5.28575e6i	−0.474140	+	0.821235i
$530$	1.90253e6	−	3.29528e6i	0.294199	−	0.509568i
$531$	−1.82554e6			−0.280967
$532$	−4.38363e6	−	906928.i	−0.671514	−	0.138929i
$533$	5.15180e6			0.785490
$534$	893029.	−	1.54677e6i	0.135523	−	0.234732i
$535$	−1.46988e6	+	2.54591e6i	−0.222023	+	0.384556i
$536$	−728775.	−	1.26227e6i	−0.109567	−	0.189776i
$537$	2.67971e6	−	4.64140e6i	0.401008	−	0.694566i
$538$	−4.10639e6	−	7.11247e6i	−0.611652	−	1.05941i
$539$	81434.3			0.0120736
$540$	2.81068e6			0.414788
$541$	4.33594e6	+	7.51007e6i	0.636928	+	1.10319i	0.986103	+	0.166134i	$0.0531285\pi$
$541$	4.33594e6	+	7.51007e6i	0.636928	+	1.10319i	−0.349175	+	0.937057i	$0.613538\pi$
$542$	−3.78259e6	−	6.55164e6i	−0.553084	−	0.957969i
$543$	6.44414e6			0.937919
$544$	955394.			0.138416
$545$	730394.	+	1.26508e6i	0.105333	+	0.182443i
$546$	−3.55309e6	+	6.15414e6i	−0.510064	+	0.883457i
$547$	4.16293e6	+	7.21041e6i	0.594883	+	1.03037i	0.993563	+	0.113277i	$0.0361348\pi$
$547$	4.16293e6	+	7.21041e6i	0.594883	+	1.03037i	−0.398681	+	0.917090i	$0.630532\pi$
$548$	−2.44095e6	+	4.22784e6i	−0.347222	+	0.601406i
$549$	1.35678e6	−	2.35001e6i	0.192123	−	0.332767i
$550$	−21711.4			−0.00306041
$551$	−6.43897e6	−	1.33216e6i	−0.903519	−	0.186929i
$552$	−2.19557e6			−0.306690
$553$	7.70107e6	−	1.33386e7i	1.07087	−	1.85481i
$554$	−96017.7	+	166307.i	−0.0132916	+	0.0230217i
$555$	−1.77447e6	−	3.07348e6i	−0.244533	−	0.423543i
$556$	−2.40596e6	+	4.16725e6i	−0.330067	+	0.571693i
$557$	7.17085e6	+	1.24203e7i	0.979338	+	1.69626i	0.664804	+	0.747018i	$0.268515\pi$
$557$	7.17085e6	+	1.24203e7i	0.979338	+	1.69626i	0.314534	+	0.949246i	$0.398152\pi$
$558$	−2.24462e6			−0.305180
$559$	−1.50020e7			−2.03058
$560$	−1.05235e6	−	1.82272e6i	−0.141805	−	0.245613i
$561$	24857.1	+	43053.7i	0.00333459	+	0.00577569i
$562$	−5.72264e6			−0.764286
$563$	6.18370e6			0.822201			0.411100	−	0.911590i	$-0.365145\pi$
$563$	6.18370e6			0.822201			0.411100	+	0.911590i	$0.365145\pi$
$564$	1.19031e6	+	2.06167e6i	0.157566	+	0.272912i
$565$	−5.45871e6	+	9.45477e6i	−0.719398	+	1.24603i
$566$	−3.49778e6	−	6.05834e6i	−0.458936	−	0.794900i
$567$	49868.5	−	86374.8i	0.00651431	−	0.0112831i
$568$	−2.16244e6	+	3.74546e6i	−0.281238	+	0.487118i
$569$	−42487.1			−0.00550144			−0.00275072	−	0.999996i	$-0.500876\pi$
$569$	−42487.1			−0.00550144			−0.00275072	+	0.999996i	$0.500876\pi$
$570$	−1.87527e6	+	2.10557e6i	−0.241755	+	0.271445i
$571$	−1.07342e7			−1.37778			−0.688889	−	0.724867i	$-0.741901\pi$
$571$	−1.07342e7			−1.37778			−0.688889	+	0.724867i	$0.741901\pi$
$572$	45382.6	−	78604.9i	0.00579961	−	0.0100452i
$573$	−698790.	+	1.21034e6i	−0.0889120	+	0.154000i
$574$	1.77622e6	+	3.07650e6i	0.225018	+	0.389743i
$575$	1.74730e6	−	3.02641e6i	0.220393	−	0.381731i
$576$	305455.	+	529063.i	0.0383611	+	0.0664434i
$577$	1.19721e6			0.149703			0.0748516	−	0.997195i	$-0.476152\pi$
$577$	1.19721e6			0.149703			0.0748516	+	0.997195i	$0.476152\pi$
$578$	−2.19746e6			−0.273591
$579$	−3.49074e6	−	6.04615e6i	−0.432735	−	0.749518i
$580$	−1.54576e6	−	2.67734e6i	−0.190797	−	0.330471i
$581$	5.23921e6			0.643911
$582$	−172811.			−0.0211478
$583$	56575.5	+	97991.6i	0.00689377	+	0.0119404i
$584$	2.58969e6	−	4.48548e6i	0.314207	−	0.544222i
$585$	−3.55656e6	−	6.16013e6i	−0.429675	−	0.744219i
$586$	5.14172e6	−	8.90572e6i	0.618535	−	1.07133i
$587$	2.84952e6	−	4.93552e6i	0.341332	−	0.591204i	−0.643348	−	0.765574i	$-0.722455\pi$
$587$	2.84952e6	−	4.93552e6i	0.341332	−	0.591204i	0.984680	+	0.174369i	$0.0557886\pi$
$588$	−2.29495e6			−0.273735
$589$	3.93756e6	−	4.42113e6i	0.467669	−	0.525104i
$590$	2.26388e6			0.267747
$591$	4.85594e6	−	8.41073e6i	0.571879	−	0.990524i
$592$	1.01407e6	−	1.75642e6i	0.118923	−	0.205980i
$593$	6.90700e6	+	1.19633e7i	0.806590	+	1.39705i	0.915213	+	0.402971i	$0.132023\pi$
$593$	6.90700e6	+	1.19633e7i	0.806590	+	1.39705i	−0.108623	+	0.994083i	$0.534644\pi$
$594$	−41790.5	+	72383.3i	−0.00485972	+	0.00841729i
$595$	−3.83533e6	−	6.64299e6i	−0.444130	−	0.769256i
$596$	−307484.			−0.0354574
$597$	−6.16372e6			−0.707794
$598$	7.30464e6	+	1.26520e7i	0.835306	+	1.44679i
$599$	−1.30413e6	−	2.25882e6i	−0.148509	−	0.257226i	0.782167	−	0.623068i	$-0.214114\pi$
$599$	−1.30413e6	−	2.25882e6i	−0.148509	−	0.257226i	−0.930677	+	0.365843i	$0.880781\pi$
$600$	611861.			0.0693865
$601$	−1.09276e7			−1.23407			−0.617035	−	0.786935i	$-0.711666\pi$
$601$	−1.09276e7			−1.23407			−0.617035	+	0.786935i	$0.711666\pi$
$602$	−5.17234e6	−	8.95875e6i	−0.581695	−	1.00753i
$603$	1.69836e6	−	2.94165e6i	0.190212	−	0.329456i
$604$	1.49712e6	+	2.59309e6i	0.166980	+	0.289218i
$605$	3.72281e6	−	6.44810e6i	0.413507	−	0.716215i
$606$	1.70741e6	−	2.95733e6i	0.188868	−	0.327128i
$607$	−1.12925e7			−1.24400			−0.621998	−	0.783019i	$-0.713679\pi$
$607$	−1.12925e7			−1.24400			−0.621998	+	0.783019i	$0.713679\pi$
$608$	−1.57791e6	−	326454.i	−0.173111	−	0.0358148i
$609$	−7.19758e6			−0.786400
$610$	−1.68257e6	+	2.91429e6i	−0.183083	+	0.317109i
$611$	7.92029e6	−	1.37183e7i	0.858297	−	1.48661i
$612$	1.11324e6	+	1.92819e6i	0.120146	+	0.208100i
$613$	−6.37503e6	+	1.10419e7i	−0.685221	+	1.18684i	0.288146	+	0.957587i	$0.406961\pi$
$613$	−6.37503e6	+	1.10419e7i	−0.685221	+	1.18684i	−0.973367	+	0.229252i	$0.926372\pi$
$614$	1.81317e6	+	3.14051e6i	0.194097	+	0.336185i
$615$	2.23757e6			0.238555
$616$	62587.4			0.00664562
$617$	4.94864e6	+	8.57129e6i	0.523326	+	0.906428i	0.999631	+	0.0271479i	$0.00864249\pi$
$617$	4.94864e6	+	8.57129e6i	0.523326	+	0.906428i	−0.476305	+	0.879280i	$0.658024\pi$
$618$	980436.	+	1.69816e6i	0.103264	+	0.178858i
$619$	−757549.			−0.0794665			−0.0397332	−	0.999210i	$-0.512651\pi$
$619$	−757549.			−0.0794665			−0.0397332	+	0.999210i	$0.512651\pi$
$620$	2.78358e6			0.290820
$621$	−6.72647e6	−	1.16506e7i	−0.699936	−	1.21232i
$622$	2.71941e6	−	4.71015e6i	0.281837	−	0.488157i
$623$	−4.09746e6	−	7.09701e6i	−0.422956	−	0.732581i
$624$	−1.27895e6	+	2.21521e6i	−0.131490	+	0.227748i
$625$	2.85392e6	−	4.94314e6i	0.292242	−	0.506177i
$626$	8.83260e6			0.900851
$627$	−26342.3	−	79600.4i	−0.00267599	−	0.00808623i
$628$	1.36528e6			0.138141
$629$	3.69582e6	−	6.40135e6i	0.372464	−	0.645127i
$630$	2.45244e6	−	4.24774e6i	0.246176	−	0.426390i
$631$	6.41621e6	+	1.11132e7i	0.641512	+	1.11113i	0.985095	+	0.172010i	$0.0550260\pi$
$631$	6.41621e6	+	1.11132e7i	0.641512	+	1.11113i	−0.343583	+	0.939122i	$0.611641\pi$
$632$	2.77204e6	−	4.80132e6i	0.276062	−	0.478154i
$633$	5.12016e6	+	8.86838e6i	0.507896	+	0.879701i
$634$	−4.11744e6			−0.406821
$635$	6.98030e6			0.686973
$636$	−1.59439e6	−	2.76156e6i	−0.156297	−	0.270715i
$637$	7.63527e6	+	1.32247e7i	0.745549	+	1.29133i
$638$	91932.5			0.00894165
$639$	−1.00789e7			−0.976472
$640$	−378799.	−	656099.i	−0.0365560	−	0.0633169i
$641$	3.63523e6	−	6.29640e6i	0.349451	−	0.605267i	−0.636701	−	0.771111i	$-0.719701\pi$
$641$	3.63523e6	−	6.29640e6i	0.349451	−	0.605267i	0.986152	+	0.165844i	$0.0530347\pi$
$642$	1.23182e6	+	2.13357e6i	0.117953	+	0.204300i
$643$	−1.06040e6	+	1.83666e6i	−0.101144	+	0.175187i	−0.912156	−	0.409842i	$-0.865584\pi$
$643$	−1.06040e6	+	1.83666e6i	−0.101144	+	0.175187i	0.811012	+	0.585029i	$0.198917\pi$
$644$	−5.03694e6	+	8.72424e6i	−0.478577	+	0.828920i
$645$	−6.51578e6			−0.616690
$646$	−5.75076e6	−	1.18977e6i	−0.542180	−	0.112172i
$647$	−1.14421e7			−1.07460			−0.537300	−	0.843391i	$-0.680556\pi$
$647$	−1.14421e7			−1.07460			−0.537300	+	0.843391i	$0.680556\pi$
$648$	17950.4	−	31091.1i	0.00167934	−	0.00290869i
$649$	−33660.5	+	58301.7i	−0.00313696	+	0.00543338i
$650$	−2.03566e6	−	3.52586e6i	−0.188982	−	0.327327i
$651$	3.24032e6	−	5.61240e6i	0.299665	−	0.519034i
$652$	381375.	+	660561.i	0.0351345	+	0.0608547i
$653$	−1.73747e7			−1.59454			−0.797270	−	0.603623i	$-0.793723\pi$
$653$	−1.73747e7			−1.59454			−0.797270	+	0.603623i	$0.793723\pi$
$654$	1.22419e6			0.111919
$655$	1.97578e6	+	3.42216e6i	0.179944	+	0.311671i
$656$	639360.	+	1.10740e6i	0.0580077	+	0.100472i
$657$	1.20702e7			1.09094
$658$	1.09229e7			0.983500
$659$	3.32289e6	+	5.75541e6i	0.298059	+	0.516253i	0.975692	−	0.219147i	$-0.0703275\pi$
$659$	3.32289e6	+	5.75541e6i	0.298059	+	0.516253i	−0.677633	+	0.735400i	$0.736994\pi$
$660$	19710.9	−	34140.3i	0.00176136	−	0.00305076i
$661$	−1.18645e6	−	2.05499e6i	−0.105620	−	0.182939i	0.808371	−	0.588673i	$-0.200349\pi$
$661$	−1.18645e6	−	2.05499e6i	−0.105620	−	0.182939i	−0.913991	+	0.405734i	$0.867016\pi$
$662$	−2.62556e6	+	4.54761e6i	−0.232851	+	0.403309i
$663$	−4.66120e6	+	8.07343e6i	−0.411826	+	0.713304i
$664$	1.88588e6			0.165995
$665$	4.06449e6	+	1.22820e7i	0.356412	+	1.07699i
$666$	4.72646e6			0.412905
$667$	−7.39859e6	+	1.28147e7i	−0.643923	+	1.11531i
$668$	157819.	−	273350.i	0.0136841	−	0.0237016i
$669$	−786015.	−	1.36142e6i	−0.0678994	−	0.117605i
$670$	−2.10617e6	+	3.64798e6i	−0.181261	+	0.313954i
$671$	−50034.4	−	86662.1i	−0.00429005	−	0.00743058i
$672$	−1.76382e6			−0.150671
$673$	−1.92310e6			−0.163668			−0.0818340	−	0.996646i	$-0.526078\pi$
$673$	−1.92310e6			−0.163668			−0.0818340	+	0.996646i	$0.526078\pi$
$674$	6.23716e6	+	1.08031e7i	0.528856	+	0.916005i
$675$	1.87453e6	+	3.24679e6i	0.158356	+	0.274280i
$676$	1.10796e7			0.932517
$677$	−525794.			−0.0440904			−0.0220452	−	0.999757i	$-0.507018\pi$
$677$	−525794.			−0.0440904			−0.0220452	+	0.999757i	$0.507018\pi$
$678$	4.57460e6	+	7.92344e6i	0.382190	+	0.661972i
$679$	−396453.	+	686676.i	−0.0330002	+	0.0571581i
$680$	−1.38055e6	−	2.39118e6i	−0.114493	−	0.198308i
$681$	−1.35892e6	+	2.35371e6i	−0.112286	+	0.194485i
$682$	−41387.6	+	71685.5i	−0.00340729	+	0.00590161i
$683$	3.81145e6			0.312635			0.156318	−	0.987707i	$-0.450038\pi$
$683$	3.81145e6			0.312635			0.156318	+	0.987707i	$0.450038\pi$
$684$	−1.17976e6	−	3.56496e6i	−0.0964167	−	0.291349i
$685$	1.41087e7			1.14884
$686$	711632.	−	1.23258e6i	0.0577358	−	0.100001i
$687$	−2.68978e6	+	4.65883e6i	−0.217433	+	0.376604i
$688$	−1.86181e6	−	3.22475e6i	−0.149956	−	0.259732i
$689$	−1.06090e7	+	1.83754e7i	−0.851388	+	1.47465i
$690$	3.17261e6	+	5.49512e6i	0.253684	+	0.439394i
$691$	−8.54562e6			−0.680845			−0.340423	−	0.940273i	$-0.610570\pi$
$691$	−8.54562e6			−0.680845			−0.340423	+	0.940273i	$0.610570\pi$
$692$	1.15691e7			0.918402
$693$	72928.0	+	126315.i	0.00576848	+	0.00999130i
$694$	−3.21464e6	−	5.56792e6i	−0.253357	−	0.438828i
$695$	1.39065e7			1.09208
$696$	−2.59081e6			−0.202727
$697$	2.33017e6	+	4.03598e6i	0.181680	+	0.314678i
$698$	1.44800e6	−	2.50801e6i	0.112494	−	0.194846i
$699$	−4.03082e6	−	6.98159e6i	−0.312033	−	0.540458i
$700$	1.40369e6	−	2.43127e6i	0.108275	−	0.187537i
$701$	−2.37669e6	+	4.11655e6i	−0.182675	+	0.316402i	−0.942790	−	0.333386i	$-0.891809\pi$
$701$	−2.37669e6	+	4.11655e6i	−0.182675	+	0.316402i	0.760116	+	0.649788i	$0.225142\pi$
$702$	−1.56731e7			−1.20036
$703$	−8.29127e6	+	9.30952e6i	−0.632751	+	0.710459i
$704$	22528.7			0.00171318
$705$	3.44000e6	−	5.95826e6i	0.260667	−	0.451488i
$706$	−1.44930e6	+	2.51027e6i	−0.109433	+	0.189543i
$707$	−7.83408e6	−	1.35690e7i	−0.589440	−	1.02094i
$708$	948608.	−	1.64304e6i	0.0711220	−	0.123187i
$709$	−1.06627e7	−	1.84683e7i	−0.796619	−	1.37978i	−0.921806	−	0.387651i	$-0.873287\pi$
$709$	−1.06627e7	−	1.84683e7i	−0.796619	−	1.37978i	0.125187	−	0.992133i	$-0.460047\pi$
$710$	1.24990e7			0.930524
$711$	1.29201e7			0.958502
$712$	−1.47490e6	−	2.55461e6i	−0.109034	−	0.188853i
$713$	−6.66162e6	−	1.15383e7i	−0.490745	−	0.849996i
$714$	−6.42829e6			−0.471900
$715$	−262312.			−0.0191890
$716$	−4.42575e6	−	7.66562e6i	−0.322629	−	0.558811i
$717$	297633.	−	515515.i	0.0216213	−	0.0374492i
$718$	−1.44747e6	−	2.50710e6i	−0.104785	−	0.181493i
$719$	5.44618e6	−	9.43307e6i	0.392889	−	0.680504i	−0.599940	−	0.800045i	$-0.704809\pi$
$719$	5.44618e6	−	9.43307e6i	0.392889	−	0.680504i	0.992829	+	0.119541i	$0.0381423\pi$
$720$	882767.	−	1.52900e6i	0.0634622	−	0.109920i
$721$	8.99702e6			0.644556
$722$	9.09132e6	+	3.93002e6i	0.649058	+	0.280576i
$723$	1.08391e7			0.771164
$724$	5.32149e6	−	9.21708e6i	0.377300	−	0.653502i
$725$	2.06184e6	−	3.57121e6i	0.145683	−	0.252331i
$726$	−3.11985e6	−	5.40374e6i	−0.219681	−	0.380498i
$727$	5.05507e6	−	8.75563e6i	0.354724	−	0.614400i	−0.632347	−	0.774686i	$-0.717908\pi$
$727$	5.05507e6	−	8.75563e6i	0.354724	−	0.614400i	0.987071	+	0.160285i	$0.0512414\pi$
$728$	5.86820e6	+	1.01640e7i	0.410371	+	0.710783i
$729$	9.02701e6			0.629108
$730$	−1.49685e7			−1.03961
$731$	−6.78544e6	−	1.17527e7i	−0.469661	−	0.813477i
$732$	1.41005e6	+	2.44228e6i	0.0972651	+	0.168468i
$733$	−5.75940e6			−0.395929			−0.197965	−	0.980209i	$-0.563433\pi$
$733$	−5.75940e6			−0.395929			−0.197965	+	0.980209i	$0.563433\pi$
$734$	−1.95040e7			−1.33624
$735$	3.31621e6	+	5.74385e6i	0.226425	+	0.392179i
$736$	−1.81307e6	+	3.14033e6i	−0.123373	+	0.213689i
$737$	−62631.0	−	108480.i	−0.00424737	−	0.00735667i
$738$	−1.48999e6	+	2.58074e6i	−0.100703	+	0.174423i
$739$	−1.21044e7	+	2.09654e7i	−0.815326	+	1.41219i	0.0937672	+	0.995594i	$0.470109\pi$
$739$	−1.21044e7	+	2.09654e7i	−0.815326	+	1.41219i	−0.909093	+	0.416592i	$0.863224\pi$
$740$	−5.86135e6			−0.393476
$741$	1.04570e7	−	1.17412e7i	0.699620	−	0.785540i
$742$	−1.46310e7			−0.975583
$743$	7.10772e6	−	1.23109e7i	0.472344	−	0.818123i	−0.527156	−	0.849769i	$-0.676742\pi$
$743$	7.10772e6	−	1.23109e7i	0.472344	−	0.818123i	0.999499	+	0.0316458i	$0.0100748\pi$
$744$	1.16637e6	−	2.02021e6i	0.0772510	−	0.133803i
$745$	444316.	+	769578.i	0.0293293	+	0.0507998i
$746$	2.61821e6	−	4.53487e6i	0.172249	−	0.298344i
$747$	2.19746e6	+	3.80612e6i	0.144086	+	0.249563i
$748$	82106.6			0.00536567
$749$	1.13038e7			0.736242
$750$	−3.68390e6	−	6.38071e6i	−0.239142	−	0.414205i
$751$	4.15307e6	+	7.19333e6i	0.268701	+	0.465404i	0.968527	−	0.248910i	$-0.0800723\pi$
$751$	4.15307e6	+	7.19333e6i	0.268701	+	0.465404i	−0.699826	+	0.714314i	$0.746739\pi$
$752$	3.93176e6			0.253538
$753$	−1.17201e7			−0.753260
$754$	8.61959e6	+	1.49296e7i	0.552152	+	0.956354i
$755$	4.32669e6	−	7.49405e6i	0.276241	−	0.478464i
$756$	−5.40372e6	−	9.35953e6i	−0.343866	−	0.595593i
$757$	−1.95684e6	+	3.38935e6i	−0.124113	+	0.214969i	−0.921386	−	0.388649i	$-0.872942\pi$
$757$	−1.95684e6	+	3.38935e6i	−0.124113	+	0.214969i	0.797273	+	0.603619i	$0.206275\pi$
$758$	−120627.	+	208933.i	−0.00762559	+	0.0132079i
$759$	−188688.			−0.0118888
$760$	1.46303e6	+	4.42096e6i	0.0918799	+	0.277640i
$761$	−2.93013e7			−1.83411			−0.917056	−	0.398758i	$-0.869441\pi$
$761$	−2.93013e7			−1.83411			−0.917056	+	0.398758i	$0.869441\pi$
$762$	2.92487e6	−	5.06602e6i	0.182482	−	0.316068i
$763$	2.80847e6	−	4.86441e6i	0.174646	−	0.302495i
$764$	1.15410e6	+	1.99897e6i	0.0715338	+	0.123900i
$765$	3.21728e6	−	5.57249e6i	0.198763	−	0.344267i
$766$	−2.04353e6	−	3.53949e6i	−0.125837	−	0.217956i
$767$	−1.26240e7			−0.774836
$768$	−634895.			−0.0388418
$769$	3.04723e6	+	5.27795e6i	0.185818	+	0.321847i	0.943852	−	0.330369i	$-0.107173\pi$
$769$	3.04723e6	+	5.27795e6i	0.185818	+	0.321847i	−0.758034	+	0.652216i	$0.773840\pi$
$770$	−90439.1	−	156645.i	−0.00549705	−	0.00952117i
$771$	524320.			0.0317658
$772$	−1.15304e7			−0.696310
$773$	212714.	+	368431.i	0.0128040	+	0.0221773i	0.872356	−	0.488870i	$-0.162591\pi$
$773$	212714.	+	368431.i	0.0128040	+	0.0221773i	−0.859552	+	0.511048i	$0.829258\pi$
$774$	4.33883e6	−	7.51508e6i	0.260328	−	0.450901i
$775$	1.85646e6	+	3.21549e6i	0.111028	+	0.192306i
$776$	−142705.	+	247173.i	−0.00850718	+	0.0147349i
$777$	−6.82310e6	+	1.18180e7i	−0.405443	+	0.702247i
$778$	9.31178e6			0.551549
$779$	−2.46940e6	−	7.46196e6i	−0.145797	−	0.440564i
$780$	7.39238e6			0.435059
$781$	−185841.	+	321885.i	−0.0109022	+	0.0188831i
$782$	−6.60781e6	+	1.14451e7i	−0.386403	+	0.669270i
$783$	−7.93734e6	−	1.37479e7i	−0.462669	−	0.801367i
$784$	−1.89514e6	+	3.28248e6i	−0.110116	+	0.190727i
$785$	−1.97283e6	−	3.41704e6i	−0.114266	−	0.197914i
$786$	3.31156e6			0.191195
$787$	−1.02091e7			−0.587556			−0.293778	−	0.955874i	$-0.594913\pi$
$787$	−1.02091e7			−0.587556			−0.293778	+	0.955874i	$0.594913\pi$
$788$	−8.01994e6	−	1.38909e7i	−0.460103	−	0.796923i
$789$	−1.04594e7	−	1.81162e7i	−0.598156	−	1.03604i
$790$	−1.60224e7			−0.913400
$791$	4.19790e7			2.38557
$792$	26250.8	+	45467.8i	0.00148707	+	0.00257567i
$793$	9.38245e6	−	1.62509e7i	0.529826	−	0.917685i
$794$	7.01114e6	+	1.21436e7i	0.394673	+	0.683593i
$795$	−4.60780e6	+	7.98094e6i	−0.258569	+	0.447854i
$796$	−5.08992e6	+	8.81600e6i	−0.284727	+	0.493161i
$797$	−6.53033e6			−0.364157			−0.182079	−	0.983284i	$-0.558283\pi$
$797$	−6.53033e6			−0.364157			−0.182079	+	0.983284i	$0.558283\pi$
$798$	1.06169e7	+	2.19652e6i	0.590186	+	0.122103i
$799$	1.43295e7			0.794078
$800$	505267.	−	875148.i	0.0279123	−	0.0483456i
$801$	3.43717e6	−	5.95335e6i	0.189286	−	0.327854i
$802$	1.27306e6	+	2.20500e6i	0.0698896	+	0.121052i
$803$	222558.	−	385482.i	0.0121802	−	0.0210968i
$804$	1.76504e6	+	3.05714e6i	0.0962975	+	0.166792i
$805$	2.91136e7			1.58346
$806$	−1.55220e7			−0.841609
$807$	9.94539e6	+	1.72259e7i	0.537574	+	0.931105i
$808$	−2.81992e6	−	4.88425e6i	−0.151953	−	0.263190i
$809$	−1.81878e7			−0.977032			−0.488516	−	0.872555i	$-0.662462\pi$
$809$	−1.81878e7			−0.977032			−0.488516	+	0.872555i	$0.662462\pi$
$810$	−103754.			−0.00555637
$811$	2.30613e6	+	3.99433e6i	0.123121	+	0.213251i	0.920997	−	0.389570i	$-0.127376\pi$
$811$	2.30613e6	+	3.99433e6i	0.123121	+	0.213251i	−0.797876	+	0.602822i	$0.794043\pi$
$812$	−5.94367e6	+	1.02947e7i	−0.316348	+	0.547930i
$813$	9.16118e6	+	1.58676e7i	0.486099	+	0.841948i
$814$	87149.4	−	150947.i	0.00461003	−	0.00798480i
$815$	1.10218e6	−	1.90903e6i	0.0581243	−	0.100674i
$816$	−2.31390e6			−0.121652
$817$	7.19086e6	+	2.17292e7i	0.376900	+	1.13891i
$818$	−6.75628e6			−0.353040
$819$	−1.36755e7	+	2.36866e7i	−0.712413	+	1.23394i
$820$	1.84776e6	−	3.20041e6i	0.0959644	−	0.166215i
$821$	2.86812e6	+	4.96773e6i	0.148504	+	0.257217i	0.930675	−	0.365847i	$-0.119221\pi$
$821$	2.86812e6	+	4.96773e6i	0.148504	+	0.257217i	−0.782170	+	0.623065i	$0.785887\pi$
$822$	5.91181e6	−	1.02396e7i	0.305169	−	0.528569i
$823$	−1.08809e7	−	1.88463e7i	−0.559972	−	0.969900i	−0.997498	−	0.0706943i	$-0.977479\pi$
$823$	−1.08809e7	−	1.88463e7i	−0.559972	−	0.969900i	0.437526	−	0.899206i	$-0.355855\pi$
$824$	3.23852e6			0.166161
$825$	52583.4			0.00268976
$826$	−4.35248e6	−	7.53871e6i	−0.221966	−	0.384456i
$827$	1.33891e7	+	2.31907e7i	0.680751	+	1.17910i	0.974752	+	0.223291i	$0.0716800\pi$
$827$	1.33891e7	+	2.31907e7i	0.680751	+	1.17910i	−0.294000	+	0.955805i	$0.594987\pi$
$828$	−8.45050e6			−0.428358
$829$	310674.			0.0157007			0.00785035	−	0.999969i	$-0.497501\pi$
$829$	310674.			0.0157007			0.00785035	+	0.999969i	$0.497501\pi$
$830$	−2.72511e6	−	4.72003e6i	−0.137306	−	0.237820i
$831$	232548.	−	402785.i	0.0116818	−	0.0202335i
$832$	2.11229e6	+	3.65859e6i	0.105790	+	0.183234i
$833$	−6.90691e6	+	1.19631e7i	−0.344883	+	0.597354i
$834$	5.82708e6	−	1.00928e7i	0.290092	−	0.502454i
$835$	−912195.			−0.0452763
$836$	−135606.	−	28055.5i	−0.00671062	−	0.00138836i
$837$	1.42934e7			0.705217
$838$	−7.94812e6	+	1.37665e7i	−0.390980	+	0.677197i
$839$	−4.18809e6	+	7.25399e6i	−0.205405	+	0.355772i	−0.950262	−	0.311452i	$-0.899185\pi$
$839$	−4.18809e6	+	7.25399e6i	−0.205405	+	0.355772i	0.744857	+	0.667225i	$0.232518\pi$
$840$	2.54872e6	+	4.41451e6i	0.124630	+	0.215866i
$841$	1.52512e6	−	2.64159e6i	0.0743558	−	0.128788i
$842$	−6.85751e6	−	1.18776e7i	−0.333339	−	0.577360i
$843$	1.38599e7			0.671722
$844$	1.69127e7			0.817251
$845$	−1.60100e7	−	2.77302e7i	−0.771349	−	1.33602i
$846$	4.58136e6	+	7.93515e6i	0.220074	+	0.381179i
$847$	−2.86295e7			−1.37121
$848$	−5.26650e6			−0.251497
$849$	8.47140e6	+	1.46729e7i	0.403353	+	0.698629i
$850$	1.84147e6	−	3.18951e6i	0.0874211	−	0.151418i
$851$	1.40273e7	+	2.42960e7i	0.663972	+	1.15003i
$852$	5.23729e6	−	9.07125e6i	0.247177	−	0.428123i
$853$	1.80296e7	−	3.12283e7i	0.848427	−	1.46952i	−0.0341843	−	0.999416i	$-0.510883\pi$
$853$	1.80296e7	−	3.12283e7i	0.848427	−	1.46952i	0.882611	−	0.470103i	$-0.155783\pi$
$854$	1.29394e7			0.607113
$855$	−7.21770e6	+	8.10410e6i	−0.337663	+	0.379131i
$856$	4.06887e6			0.189797
$857$	−1.53061e7	+	2.65109e7i	−0.711889	+	1.23303i	0.252258	+	0.967660i	$0.418827\pi$
$857$	−1.53061e7	+	2.65109e7i	−0.711889	+	1.23303i	−0.964147	+	0.265368i	$0.914507\pi$
$858$	−109914.	+	190376.i	−0.00509721	+	0.00882863i
$859$	1.53666e7	+	2.66158e7i	0.710551	+	1.23071i	0.964651	+	0.263532i	$0.0848875\pi$
$859$	1.53666e7	+	2.66158e7i	0.710551	+	1.23071i	−0.254100	+	0.967178i	$0.581779\pi$
$860$	−5.38065e6	+	9.31956e6i	−0.248078	+	0.429684i
$861$	−4.30189e6	−	7.45109e6i	−0.197766	−	0.342540i
$862$	3.36599e6			0.154292
$863$	3.77643e7			1.72605			0.863026	−	0.505159i	$-0.168566\pi$
$863$	3.77643e7			1.72605			0.863026	+	0.505159i	$0.168566\pi$
$864$	−1.94510e6	−	3.36901e6i	−0.0886457	−	0.153539i
$865$	−1.67173e7	−	2.89553e7i	−0.759673	−	1.31579i
$866$	2.53296e7			1.14772
$867$	5.32210e6			0.240456
$868$	−5.35163e6	−	9.26930e6i	−0.241094	−	0.417587i
$869$	238229.	−	412626.i	0.0107015	−	0.0185356i
$870$	3.74373e6	+	6.48433e6i	0.167690	+	0.290447i
$871$	1.17446e7	−	2.03422e7i	0.524555	−	0.908556i
$872$	1.01092e6	−	1.75097e6i	0.0450222	−	0.0779808i
$873$	−665131.			−0.0295373
$874$	1.48241e7	−	1.66446e7i	0.656431	−	0.737047i
$875$	−3.38055e7			−1.49268
$876$	−6.27206e6	+	1.08635e7i	−0.276153	+	0.478311i
$877$	4.12280e6	−	7.14090e6i	0.181006	−	0.313512i	−0.761217	−	0.648497i	$-0.775398\pi$
$877$	4.12280e6	−	7.14090e6i	0.181006	−	0.313512i	0.942223	+	0.334985i	$0.108731\pi$
$878$	1.02742e7	+	1.77954e7i	0.449790	+	0.779059i
$879$	−1.24529e7	+	2.15690e7i	−0.543623	+	0.941583i
$880$	−32554.0	−	56385.3i	−0.00141709	−	0.00245448i
$881$	1.71534e7			0.744579			0.372289	−	0.928117i	$-0.378573\pi$
$881$	1.71534e7			0.744579			0.372289	+	0.928117i	$0.378573\pi$
$882$	−8.83301e6			−0.382329
$883$	8.33139e6	+	1.44304e7i	0.359597	+	0.622839i	0.987893	−	0.155134i	$-0.0495810\pi$
$883$	8.33139e6	+	1.44304e7i	0.359597	+	0.622839i	−0.628297	+	0.777974i	$0.716248\pi$
$884$	7.69831e6	+	1.33339e7i	0.331333	+	0.573886i
$885$	−5.48297e6			−0.235319
$886$	1.08774e7			0.465524
$887$	−1.47463e7	−	2.55413e7i	−0.629322	−	1.09002i	−0.987688	−	0.156436i	$-0.949999\pi$
$887$	−1.47463e7	−	2.55413e7i	−0.629322	−	1.09002i	0.358366	−	0.933581i	$-0.383334\pi$
$888$	−2.45601e6	+	4.25394e6i	−0.104520	+	0.181033i
$889$	−1.34201e7	−	2.32443e7i	−0.569510	−	0.986421i
$890$	−4.26248e6	+	7.38284e6i	−0.180380	+	0.312427i
$891$	1542.66	−	2671.97i	6.50993e−5	−	0.000112755i
$892$	−2.59633e6			−0.109256
$893$	−2.36663e7	−	4.89631e6i	−0.993120	−	0.205466i
$894$	744706.			0.0311631
$895$	−1.27904e7	+	2.21537e7i	−0.533738	+	0.924461i
$896$	−1.45654e6	+	2.52279e6i	−0.0606110	+	0.104981i
$897$	−1.76913e7	−	3.06423e7i	−0.734141	−	1.27157i
$898$	−5.30981e6	+	9.19686e6i	−0.219729	+	0.380582i
$899$	−7.86082e6	−	1.36153e7i	−0.324391	−	0.561862i
$900$	2.35499e6			0.0969130
$901$	−1.91940e7			−0.787685
$902$	54946.7	+	95170.4i	0.00224867	+	0.00389481i
$903$	1.25271e7	+	2.16975e7i	0.511245	+	0.885503i
$904$	1.51106e7			0.614979
$905$	−3.07583e7			−1.24836
$906$	−3.62592e6	−	6.28028e6i	−0.146757	−	0.254190i
$907$	3.47306e6	−	6.01551e6i	0.140182	−	0.242803i	−0.787383	−	0.616464i	$-0.788564\pi$
$907$	3.47306e6	−	6.01551e6i	0.140182	−	0.242803i	0.927565	+	0.373661i	$0.121898\pi$
$908$	2.24435e6	+	3.88733e6i	0.0903392	+	0.156472i
$909$	6.57164e6	−	1.13824e7i	0.263794	−	0.456904i
$910$	1.69591e7	−	2.93741e7i	0.678891	−	1.17587i
$911$	1.26026e7			0.503113			0.251556	−	0.967843i	$-0.419058\pi$
$911$	1.26026e7			0.503113			0.251556	+	0.967843i	$0.419058\pi$
$912$	3.82160e6	+	790648.i	0.152145	+	0.0314772i
$913$	162073.			0.00643478
$914$	−5.30712e6	+	9.19220e6i	−0.210133	+	0.363960i
$915$	4.07506e6	−	7.05821e6i	0.160909	−	0.278703i
$916$	4.44237e6	+	7.69440e6i	0.174935	+	0.302996i
$917$	7.59717e6	−	1.31587e7i	0.298352	−	0.516760i
$918$	−7.08899e6	−	1.22785e7i	−0.277637	−	0.480882i
$919$	2.84869e7			1.11264			0.556321	−	0.830967i	$-0.312212\pi$
$919$	2.84869e7			1.11264			0.556321	+	0.830967i	$0.312212\pi$
$920$	1.04796e7			0.408202
$921$	−4.39138e6	−	7.60609e6i	−0.170589	−	0.295469i
$922$	−7.07545e6	−	1.22550e7i	−0.274111	−	0.474774i
$923$	−6.96976e7			−2.69286
$924$	−151583.			−0.00584076
$925$	−3.90913e6	−	6.77080e6i	−0.150219	−	0.260187i
$926$	1.18669e7	−	2.05541e7i	0.454790	−	0.787720i
$927$	3.77359e6	+	6.53604e6i	0.144230	+	0.249813i
$928$	−2.13946e6	+	3.70565e6i	−0.0815518	+	0.141252i
$929$	−1.50033e7	+	2.59864e7i	−0.570357	+	0.987888i	0.426172	+	0.904642i	$0.359862\pi$
$929$	−1.50033e7	+	2.59864e7i	−0.570357	+	0.987888i	−0.996529	+	0.0832453i	$0.973471\pi$
$930$	−6.74164e6			−0.255599
$931$	1.54951e7	−	1.73980e7i	0.585895	−	0.657848i
$932$	−1.33144e7			−0.502091
$933$	−6.58622e6	+	1.14077e7i	−0.247704	+	0.429035i
$934$	−1.04771e7	+	1.81469e7i	−0.392983	+	0.680667i
$935$	−118644.	−	205498.i	−0.00443832	−	0.00768739i
$936$	−4.92255e6	+	8.52611e6i	−0.183654	+	0.318098i
$937$	1.83152e7	+	3.17229e7i	0.681495	+	1.18038i	0.974525	+	0.224281i	$0.0720034\pi$
$937$	1.83152e7	+	3.17229e7i	0.681495	+	1.18038i	−0.293029	+	0.956103i	$0.594663\pi$
$938$	1.61970e7			0.601073
$939$	−2.13920e7			−0.791748
$940$	−5.68142e6	−	9.84050e6i	−0.209719	−	0.363243i
$941$	−1.98334e7	−	3.43524e7i	−0.730167	−	1.26469i	−0.956811	−	0.290709i	$-0.906109\pi$
$941$	−1.98334e7	−	3.43524e7i	−0.730167	−	1.26469i	0.226644	−	0.973978i	$-0.427225\pi$
$942$	−3.30661e6			−0.121410
$943$	−1.76881e7			−0.647742
$944$	−1.56670e6	−	2.71360e6i	−0.0572209	−	0.0991096i
$945$	−1.56168e7	+	2.70491e7i	−0.568870	+	0.985311i
$946$	−160004.	−	277135.i	−0.00581304	−	0.0100685i
$947$	1.96508e7	−	3.40362e7i	0.712041	−	1.23329i	−0.252049	−	0.967714i	$-0.581104\pi$
$947$	1.96508e7	−	3.40362e7i	0.712041	−	1.23329i	0.964090	−	0.265576i	$-0.0855623\pi$
$948$	−6.71369e6	+	1.16285e7i	−0.242628	+	0.420244i
$949$	8.34682e7			3.00854
$950$	−4.13117e6	+	4.63852e6i	−0.148513	+	0.166752i
$951$	9.97215e6			0.357551
$952$	−5.30840e6	+	9.19442e6i	−0.189833	+	0.328800i
$953$	3.63675e6	−	6.29904e6i	0.129712	−	0.224669i	−0.793853	−	0.608110i	$-0.791928\pi$
$953$	3.63675e6	−	6.29904e6i	0.129712	−	0.224669i	0.923565	+	0.383442i	$0.125261\pi$
$954$	−6.13663e6	−	1.06289e7i	−0.218303	−	0.378111i
$955$	3.33537e6	−	5.77703e6i	0.118341	−	0.204973i
$956$	−491562.	−	851411.i	−0.0173954	−	0.0301297i
$957$	−222654.			−0.00785871
$958$	−6.85732e6			−0.241402
$959$	−2.71250e7	−	4.69819e7i	−0.952408	−	1.64962i
$960$	917426.	+	1.58903e6i	0.0321287	+	0.0556485i
$961$	−1.44735e7			−0.505552
$962$	3.26845e7			1.13869
$963$	4.74112e6	+	8.21186e6i	0.164746	+	0.285349i
$964$	8.95077e6	−	1.55032e7i	0.310219	−	0.537315i
$965$	1.66615e7	+	2.88586e7i	0.575966	+	0.997602i
$966$	1.21991e7	−	2.11295e7i	0.420616	−	0.728528i
$967$	−2.26883e7	+	3.92972e7i	−0.780253	+	1.35144i	0.151542	+	0.988451i	$0.451576\pi$
$967$	−2.26883e7	+	3.92972e7i	−0.780253	+	1.35144i	−0.931794	+	0.362986i	$0.881757\pi$
$968$	−1.03053e7			−0.353487
$969$	1.39279e7	+	2.88155e6i	0.476516	+	0.0985862i
$970$	824839.			0.0281475
$971$	4.87437e6	−	8.44266e6i	0.165909	−	0.287363i	−0.771069	−	0.636752i	$-0.780277\pi$
$971$	4.87437e6	−	8.44266e6i	0.165909	−	0.287363i	0.936978	+	0.349389i	$0.113611\pi$
$972$	7.34182e6	−	1.27164e7i	0.249252	−	0.431717i
$973$	−2.67362e7	−	4.63085e7i	−0.905353	−	1.56812i
$974$	−1.09388e7	+	1.89465e7i	−0.369464	+	0.639930i
$975$	4.93022e6	+	8.53939e6i	0.166094	+	0.287684i
$976$	4.65761e6			0.156509
$977$	1.80142e7			0.603779			0.301890	−	0.953343i	$-0.402383\pi$
$977$	1.80142e7			0.603779			0.301890	+	0.953343i	$0.402383\pi$
$978$	−923665.	−	1.59983e6i	−0.0308793	−	0.0534845i
$979$	−126753.	−	219543.i	−0.00422671	−	0.00732088i
$980$	1.09539e7			0.364339
$981$	4.71178e6			0.156319
$982$	−2.28042e6	−	3.94980e6i	−0.0754632	−	0.130706i
$983$	−1.74891e7	+	3.02920e7i	−0.577277	+	0.999872i	0.418514	+	0.908211i	$0.362551\pi$
$983$	−1.74891e7	+	3.02920e7i	−0.577277	+	0.999872i	−0.995790	+	0.0916618i	$0.970782\pi$
$984$	−1.54849e6	−	2.68206e6i	−0.0509823	−	0.0883040i
$985$	−2.31777e7	+	4.01449e7i	−0.761166	+	1.31838i
$986$	−7.79733e6	+	1.35054e7i	−0.255419	+	0.442399i
$987$	−2.64546e7			−0.864386
$988$	−8.15828e6	−	2.46525e7i	−0.265893	−	0.803467i
$989$	5.15076e7			1.67448
$990$	75865.1	−	131402.i	0.00246011	−	0.00426103i
$991$	−1.59799e6	+	2.76780e6i	−0.0516880	+	0.0895262i	−0.890712	−	0.454569i	$-0.849793\pi$
$991$	−1.59799e6	+	2.76780e6i	−0.0516880	+	0.0895262i	0.839024	+	0.544095i	$0.183127\pi$
$992$	−1.92635e6	−	3.33653e6i	−0.0621521	−	0.107651i
$993$	6.35893e6	−	1.10140e7i	0.204650	−	0.354464i
$994$	−2.40301e7	−	4.16214e7i	−0.771418	−	1.33614i
$995$	2.94198e7			0.942068
$996$	−4.56748e6			−0.145891
$997$	−2.30696e7	−	3.99577e7i	−0.735025	−	1.27310i	−0.954712	−	0.297530i	$-0.903837\pi$
$997$	−2.30696e7	−	3.99577e7i	−0.735025	−	1.27310i	0.219687	−	0.975570i	$-0.429496\pi$
$998$	1.02023e7	+	1.76709e7i	0.324244	+	0.561607i
$999$	−3.00975e7			−0.954150

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.c.b.11.4	yes	8
3.2	odd	2		342.6.g.d.163.3		8
4.3	odd	2		304.6.i.b.49.1		8
19.7	even	3	inner	38.6.c.b.7.4	✓	8
19.8	odd	6		722.6.a.g.1.4		4
19.11	even	3		722.6.a.j.1.1		4
57.26	odd	6		342.6.g.d.235.3		8
76.7	odd	6		304.6.i.b.273.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.b.7.4	✓	8	19.7	even	3	inner
38.6.c.b.11.4	yes	8	1.1	even	1	trivial
304.6.i.b.49.1		8	4.3	odd	2
304.6.i.b.273.1		8	76.7	odd	6
342.6.g.d.163.3		8	3.2	odd	2
342.6.g.d.235.3		8	57.26	odd	6
722.6.a.g.1.4		4	19.8	odd	6
722.6.a.j.1.1		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} +(4.84386 - 8.38982i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-23.1201 + 40.0451i) q^{5} +(19.3755 + 33.5593i) q^{6} +177.800 q^{7} +64.0000 q^{8} +(74.5740 + 129.166i) q^{9} +(-92.4803 - 160.181i) q^{10} +5.50017 q^{11} -155.004 q^{12} +(515.695 + 893.211i) q^{13} +(-355.600 + 615.917i) q^{14} +(223.981 + 387.946i) q^{15} +(-128.000 + 221.703i) q^{16} +(-466.501 + 808.003i) q^{17} -596.592 q^{18} +(1046.56 - 1175.08i) q^{19} +739.842 q^{20} +(861.238 - 1491.71i) q^{21} +(-11.0003 + 19.0531i) q^{22} +(-1770.58 - 3066.73i) q^{23} +(310.007 - 536.948i) q^{24} +(493.425 + 854.637i) q^{25} -4125.56 q^{26} +3799.02 q^{27} +(-1422.40 - 2463.67i) q^{28} +(-2089.31 - 3618.79i) q^{29} -1791.85 q^{30} +3762.40 q^{31} +(-512.000 - 886.810i) q^{32} +(26.6421 - 46.1454i) q^{33} +(-1866.00 - 3232.01i) q^{34} +(-4110.74 + 7120.02i) q^{35} +(1193.18 - 2066.65i) q^{36} -7922.43 q^{37} +(1977.50 + 5975.54i) q^{38} +9991.83 q^{39} +(-1479.68 + 2562.89i) q^{40} +(2497.50 - 4325.80i) q^{41} +(3444.95 + 5966.83i) q^{42} +(-7272.70 + 12596.7i) q^{43} +(-44.0013 - 76.2125i) q^{44} -6896.62 q^{45} +14164.6 q^{46} +(-7679.23 - 13300.8i) q^{47} +(1240.03 + 2147.79i) q^{48} +14805.8 q^{49} -3947.40 q^{50} +(4519.33 + 7827.71i) q^{51} +(8251.13 - 14291.4i) q^{52} +(10286.1 + 17816.1i) q^{53} +(-7598.04 + 13160.2i) q^{54} +(-127.164 + 220.255i) q^{55} +11379.2 q^{56} +(-4789.36 - 14472.4i) q^{57} +16714.5 q^{58} +(-6119.91 + 10600.0i) q^{59} +(3583.69 - 6207.14i) q^{60} +(-9096.89 - 15756.3i) q^{61} +(-7524.80 + 13033.3i) q^{62} +(13259.2 + 22965.7i) q^{63} +4096.00 q^{64} -47691.7 q^{65} +(106.568 + 184.582i) q^{66} +(-11387.1 - 19723.0i) q^{67} +14928.0 q^{68} -34305.8 q^{69} +(-16443.0 - 28480.1i) q^{70} +(-33788.2 + 58522.8i) q^{71} +(4772.73 + 8266.62i) q^{72} +(40463.9 - 70085.6i) q^{73} +(15844.9 - 27444.1i) q^{74} +9560.33 q^{75} +(-24654.9 - 5100.84i) q^{76} +977.929 q^{77} +(-19983.7 + 34612.7i) q^{78} +(43313.1 - 75020.6i) q^{79} +(-5918.74 - 10251.6i) q^{80} +(280.475 - 485.798i) q^{81} +(9990.00 + 17303.2i) q^{82} +29466.9 q^{83} -27559.6 q^{84} +(-21571.1 - 37362.2i) q^{85} +(-29090.8 - 50386.7i) q^{86} -40481.4 q^{87} +352.011 q^{88} +(-23045.4 - 39915.7i) q^{89} +(13793.2 - 23890.6i) q^{90} +(91690.6 + 158813. i) q^{91} +(-28329.3 + 49067.7i) q^{92} +(18224.5 - 31565.8i) q^{93} +61433.8 q^{94} +(22859.9 + 69077.5i) q^{95} -9920.23 q^{96} +(-2229.77 + 3862.07i) q^{97} +(-29611.6 + 51288.7i) q^{98} +(410.169 + 710.434i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more