LMFDB - Embedded newform 38.6.e.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$38 = 2 \cdot 19$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	38.e (of order $9$ , degree $6$ , 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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	38.5
Dual form			38.6.e.a.23.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.75877 - 1.36808i) q^{2} +(4.62861 - 26.2502i) q^{3} +(12.2567 - 10.2846i) q^{4} +(14.7431 + 12.3709i) q^{5} +(-18.5145 - 105.001i) q^{6} +(4.52908 + 7.84460i) q^{7} +(32.0000 - 55.4256i) q^{8} +(-439.302 - 159.893i) q^{9} +(72.3402 + 26.3297i) q^{10} +(-79.1353 + 137.066i) q^{11} +(-213.241 - 369.344i) q^{12} +(-12.8004 - 72.5945i) q^{13} +(27.7558 + 23.2899i) q^{14} +(392.978 - 329.748i) q^{15} +(44.4539 - 252.111i) q^{16} +(1772.70 - 645.211i) q^{17} -1869.98 q^{18} +(1207.77 + 1008.66i) q^{19} +307.931 q^{20} +(226.885 - 82.5795i) q^{21} +(-109.934 + 623.464i) q^{22} +(-2360.76 + 1980.91i) q^{23} +(-1306.82 - 1096.55i) q^{24} +(-478.332 - 2712.75i) q^{25} +(-147.429 - 255.354i) q^{26} +(-2991.98 + 5182.25i) q^{27} +(136.190 + 49.5692i) q^{28} +(6285.20 + 2287.62i) q^{29} +(1025.99 - 1777.07i) q^{30} +(3473.21 + 6015.78i) q^{31} +(-177.816 - 1008.44i) q^{32} +(3231.73 + 2711.74i) q^{33} +(5780.48 - 4850.40i) q^{34} +(-30.2722 + 171.682i) q^{35} +(-7028.83 + 2558.29i) q^{36} -10596.4 q^{37} +(5919.65 + 2139.01i) q^{38} -1964.86 q^{39} +(1157.44 - 421.275i) q^{40} +(1287.12 - 7299.63i) q^{41} +(739.834 - 620.795i) q^{42} +(7515.14 + 6305.95i) q^{43} +(439.734 + 2493.86i) q^{44} +(-4498.64 - 7791.88i) q^{45} +(-6163.50 + 10675.5i) q^{46} +(-7974.91 - 2902.63i) q^{47} +(-6412.19 - 2333.85i) q^{48} +(8362.47 - 14484.2i) q^{49} +(-5509.20 - 9542.22i) q^{50} +(-8731.74 - 49520.2i) q^{51} +(-903.495 - 758.123i) q^{52} +(-20682.6 + 17354.8i) q^{53} +(-4156.41 + 23572.2i) q^{54} +(-2862.33 + 1041.80i) q^{55} +579.722 q^{56} +(32067.8 - 27035.4i) q^{57} +26754.3 q^{58} +(-14404.4 + 5242.76i) q^{59} +(1425.30 - 8083.25i) q^{60} +(5949.25 - 4992.01i) q^{61} +(21285.1 + 17860.3i) q^{62} +(-735.339 - 4170.31i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(709.343 - 1228.62i) q^{65} +(15857.2 + 5771.55i) q^{66} +(-32752.5 - 11920.9i) q^{67} +(15091.8 - 26139.7i) q^{68} +(41072.2 + 71139.2i) q^{69} +(121.089 + 686.729i) q^{70} +(8827.63 + 7407.26i) q^{71} +(-22919.8 + 19232.0i) q^{72} +(-14590.3 + 82745.9i) q^{73} +(-39829.4 + 14496.7i) q^{74} -73424.3 q^{75} +(25176.9 - 58.5136i) q^{76} -1433.64 q^{77} +(-7385.47 + 2688.09i) q^{78} +(-14109.0 + 80016.3i) q^{79} +(3774.23 - 3166.95i) q^{80} +(35162.6 + 29505.0i) q^{81} +(-5148.49 - 29198.5i) q^{82} +(-32758.7 - 56739.7i) q^{83} +(1931.57 - 3345.58i) q^{84} +(34116.9 + 12417.5i) q^{85} +(36874.7 + 13421.3i) q^{86} +(89142.3 - 154399. i) q^{87} +(5064.66 + 8772.24i) q^{88} +(3382.52 + 19183.2i) q^{89} +(-27569.3 - 23133.4i) q^{90} +(511.500 - 429.200i) q^{91} +(-8562.25 + 48558.9i) q^{92} +(173991. - 63327.7i) q^{93} -33946.9 q^{94} +(5328.12 + 29811.9i) q^{95} -27294.8 q^{96} +(-104024. + 37861.5i) q^{97} +(11617.0 - 65883.4i) q^{98} +(56680.2 - 47560.3i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22}+ \cdots + 656436 q^{99}+O(q^{100})$ 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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

)

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

$2$	3.75877	−	1.36808i	0.664463	−	0.241845i
$2$	3.75877	−	1.36808i	0.664463	−	0.241845i
$3$	4.62861	−	26.2502i	0.296926	−	1.68395i	−0.362346	−	0.932044i	$-0.618024\pi$
$3$	4.62861	−	26.2502i	0.296926	−	1.68395i	0.659271	−	0.751905i	$-0.270865\pi$
$4$	12.2567	−	10.2846i	0.383022	−	0.321394i
$5$	14.7431	+	12.3709i	0.263732	+	0.221298i	0.765059	−	0.643961i	$-0.222710\pi$
$5$	14.7431	+	12.3709i	0.263732	+	0.221298i	−0.501326	+	0.865258i	$0.667154\pi$
$6$	−18.5145	−	105.001i	−0.209958	−	1.19073i
$7$	4.52908	+	7.84460i	0.0349353	+	0.0605098i	0.882964	−	0.469440i	$-0.155544\pi$
$7$	4.52908	+	7.84460i	0.0349353	+	0.0605098i	−0.848029	+	0.529950i	$0.822211\pi$
$8$	32.0000	−	55.4256i	0.176777	−	0.306186i
$9$	−439.302	−	159.893i	−1.80783	−	0.657995i
$10$	72.3402	+	26.3297i	0.228760	+	0.0832618i
$11$	−79.1353	+	137.066i	−0.197192	+	0.341546i	−0.947617	−	0.319410i	$-0.896515\pi$
$11$	−79.1353	+	137.066i	−0.197192	+	0.341546i	0.750425	+	0.660955i	$0.229849\pi$
$12$	−213.241	−	369.344i	−0.427482	−	0.740420i
$13$	−12.8004	−	72.5945i	−0.0210070	−	0.119137i	0.972501	−	0.232899i	$-0.0748210\pi$
$13$	−12.8004	−	72.5945i	−0.0210070	−	0.119137i	−0.993508	+	0.113762i	$0.963710\pi$
$14$	27.7558	+	23.2899i	0.0378472	+	0.0317576i
$15$	392.978	−	329.748i	0.450963	−	0.378403i
$16$	44.4539	−	252.111i	0.0434120	−	0.246202i
$17$	1772.70	−	645.211i	1.48769	−	0.541476i	0.534853	−	0.844945i	$-0.320367\pi$
$17$	1772.70	−	645.211i	1.48769	−	0.541476i	0.952841	+	0.303469i	$0.0981449\pi$
$18$	−1869.98			−1.36037
$19$	1207.77	+	1008.66i	0.767536	+	0.641006i
$19$	1207.77	+	1008.66i	0.767536	+	0.641006i
$20$	307.931			0.172139
$21$	226.885	−	82.5795i	0.112269	−	0.0408624i
$22$	−109.934	+	623.464i	−0.0484254	+	0.274634i
$23$	−2360.76	+	1980.91i	−0.930533	+	0.780810i	−0.975913	−	0.218160i	$-0.929995\pi$
$23$	−2360.76	+	1980.91i	−0.930533	+	0.780810i	0.0453798	+	0.998970i	$0.485550\pi$
$24$	−1306.82	−	1096.55i	−0.463112	−	0.388597i
$25$	−478.332	−	2712.75i	−0.153066	−	0.868081i
$26$	−147.429	−	255.354i	−0.0427709	−	0.0740814i
$27$	−2991.98	+	5182.25i	−0.789857	+	1.36807i
$28$	136.190	+	49.5692i	0.0328285	+	0.0119486i
$29$	6285.20	+	2287.62i	1.38779	+	0.505114i	0.924530	−	0.381108i	$-0.124457\pi$
$29$	6285.20	+	2287.62i	1.38779	+	0.505114i	0.463260	+	0.886223i	$0.346680\pi$
$30$	1025.99	−	1777.07i	0.208133	−	0.360497i
$31$	3473.21	+	6015.78i	0.649123	+	1.12431i	0.983333	+	0.181816i	$0.0581974\pi$
$31$	3473.21	+	6015.78i	0.649123	+	1.12431i	−0.334209	+	0.942499i	$0.608469\pi$
$32$	−177.816	−	1008.44i	−0.0306970	−	0.174091i
$33$	3231.73	+	2711.74i	0.516595	+	0.433474i
$34$	5780.48	−	4850.40i	0.857564	−	0.719582i
$35$	−30.2722	+	171.682i	−0.00417709	+	0.0236895i
$36$	−7028.83	+	2558.29i	−0.903914	+	0.328998i
$37$	−10596.4			−1.27249			−0.636243	−	0.771489i	$-0.719513\pi$
$37$	−10596.4			−1.27249			−0.636243	+	0.771489i	$0.719513\pi$
$38$	5919.65	+	2139.01i	0.665023	+	0.240300i
$39$	−1964.86			−0.206857
$40$	1157.44	−	421.275i	0.114380	−	0.0416309i
$41$	1287.12	−	7299.63i	0.119580	−	0.678174i	−0.864800	−	0.502117i	$-0.832555\pi$
$41$	1287.12	−	7299.63i	0.119580	−	0.678174i	0.984380	−	0.176057i	$-0.0563343\pi$
$42$	739.834	−	620.795i	0.0647159	−	0.0543031i
$43$	7515.14	+	6305.95i	0.619820	+	0.520091i	0.897747	−	0.440511i	$-0.145203\pi$
$43$	7515.14	+	6305.95i	0.619820	+	0.520091i	−0.277927	+	0.960602i	$0.589647\pi$
$44$	439.734	+	2493.86i	0.0342420	+	0.194196i
$45$	−4498.64	−	7791.88i	−0.331169	−	0.573602i
$46$	−6163.50	+	10675.5i	−0.429470	+	0.743864i
$47$	−7974.91	−	2902.63i	−0.526601	−	0.191667i	0.0650192	−	0.997884i	$-0.479289\pi$
$47$	−7974.91	−	2902.63i	−0.526601	−	0.191667i	−0.591620	+	0.806217i	$0.701511\pi$
$48$	−6412.19	−	2333.85i	−0.401701	−	0.146207i
$49$	8362.47	−	14484.2i	0.497559	−	0.861798i
$50$	−5509.20	−	9542.22i	−0.311648	−	0.539790i
$51$	−8731.74	−	49520.2i	−0.470084	−	2.66598i
$52$	−903.495	−	758.123i	−0.0463359	−	0.0388804i
$53$	−20682.6	+	17354.8i	−1.01138	+	0.848653i	−0.988521	−	0.151086i	$-0.951723\pi$
$53$	−20682.6	+	17354.8i	−1.01138	+	0.848653i	−0.0228643	+	0.999739i	$0.507279\pi$
$54$	−4156.41	+	23572.2i	−0.193970	+	1.10006i
$55$	−2862.33	+	1041.80i	−0.127589	+	0.0464386i
$56$	579.722			0.0247030
$57$	32067.8	−	27035.4i	1.30732	−	1.10216i
$58$	26754.3			1.04429
$59$	−14404.4	+	5242.76i	−0.538721	+	0.196078i	−0.597028	−	0.802220i	$-0.703652\pi$
$59$	−14404.4	+	5242.76i	−0.538721	+	0.196078i	0.0583072	+	0.998299i	$0.481430\pi$
$60$	1425.30	−	8083.25i	0.0511125	−	0.289873i
$61$	5949.25	−	4992.01i	0.204709	−	0.171771i	−0.534669	−	0.845061i	$-0.679564\pi$
$61$	5949.25	−	4992.01i	0.204709	−	0.171771i	0.739379	+	0.673290i	$0.235119\pi$
$62$	21285.1	+	17860.3i	0.703228	+	0.590078i
$63$	−735.339	−	4170.31i	−0.0233419	−	0.132378i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	709.343	−	1228.62i	0.0208244	−	0.0360689i
$66$	15857.2	+	5771.55i	0.448091	+	0.163092i
$67$	−32752.5	−	11920.9i	−0.891369	−	0.324432i	−0.144581	−	0.989493i	$-0.546183\pi$
$67$	−32752.5	−	11920.9i	−0.891369	−	0.324432i	−0.746789	+	0.665061i	$0.768405\pi$
$68$	15091.8	−	26139.7i	0.395793	−	0.685533i
$69$	41072.2	+	71139.2i	1.03855	+	1.79881i
$70$	121.089	+	686.729i	0.00295365	+	0.0167510i
$71$	8827.63	+	7407.26i	0.207825	+	0.174386i	0.740759	−	0.671771i	$-0.234466\pi$
$71$	8827.63	+	7407.26i	0.207825	+	0.174386i	−0.532934	+	0.846157i	$0.678910\pi$
$72$	−22919.8	+	19232.0i	−0.521051	+	0.437213i
$73$	−14590.3	+	82745.9i	−0.320449	+	1.81735i	0.219450	+	0.975624i	$0.429574\pi$
$73$	−14590.3	+	82745.9i	−0.320449	+	1.81735i	−0.539899	+	0.841730i	$0.681537\pi$
$74$	−39829.4	+	14496.7i	−0.845520	+	0.307744i
$75$	−73424.3			−1.50725
$76$	25176.9	−	58.5136i	0.499999	−	0.00116204i
$77$	−1433.64			−0.0275558
$78$	−7385.47	+	2688.09i	−0.137449	+	0.0500274i
$79$	−14109.0	+	80016.3i	−0.254349	+	1.44248i	0.543390	+	0.839480i	$0.317141\pi$
$79$	−14109.0	+	80016.3i	−0.254349	+	1.44248i	−0.797739	+	0.603003i	$0.793971\pi$
$80$	3774.23	−	3166.95i	0.0659330	−	0.0553244i
$81$	35162.6	+	29505.0i	0.595482	+	0.499669i
$82$	−5148.49	−	29198.5i	−0.0845561	−	0.479542i
$83$	−32758.7	−	56739.7i	−0.521952	−	0.904048i	−0.999674	−	0.0255367i	$-0.991871\pi$
$83$	−32758.7	−	56739.7i	−0.521952	−	0.904048i	0.477722	−	0.878511i	$-0.341463\pi$
$84$	1931.57	−	3345.58i	0.0298684	−	0.0517336i
$85$	34116.9	+	12417.5i	0.512180	+	0.186418i
$86$	36874.7	+	13421.3i	0.537629	+	0.195681i
$87$	89142.3	−	154399.i	1.26266	−	2.18699i
$88$	5064.66	+	8772.24i	0.0697178	+	0.120755i
$89$	3382.52	+	19183.2i	0.0452652	+	0.256712i	0.999040	−	0.0438109i	$-0.0139499\pi$
$89$	3382.52	+	19183.2i	0.0452652	+	0.256712i	−0.953775	+	0.300523i	$0.902839\pi$
$90$	−27569.3	−	23133.4i	−0.358772	−	0.301046i
$91$	511.500	−	429.200i	0.00647504	−	0.00543320i
$92$	−8562.25	+	48558.9i	−0.105467	+	0.598135i
$93$	173991.	−	63327.7i	2.08603	−	0.759253i
$94$	−33946.9			−0.396260
$95$	5328.12	+	29811.9i	0.0605710	+	0.338908i
$96$	−27294.8			−0.302275
$97$	−104024.	+	37861.5i	−1.12254	+	0.408572i	−0.835580	−	0.549369i	$-0.814868\pi$
$97$	−104024.	+	37861.5i	−1.12254	+	0.408572i	−0.286963	+	0.957942i	$0.592646\pi$
$98$	11617.0	−	65883.4i	0.122188	−	0.692965i
$99$	56680.2	−	47560.3i	0.581224	−	0.487705i
$100$	−33762.4	−	28330.0i	−0.337624	−	0.283300i
$101$	−22509.1	−	127656.i	−0.219561	−	1.24519i	−0.872814	−	0.488052i	$-0.837707\pi$
$101$	−22509.1	−	127656.i	−0.219561	−	1.24519i	0.653253	−	0.757139i	$-0.273404\pi$
$102$	−100568.	−	174189.i	−0.957106	−	1.65776i
$103$	−49142.4	+	85117.1i	−0.456419	+	0.790540i	−0.998769	−	0.0496125i	$-0.984201\pi$
$103$	−49142.4	+	85117.1i	−0.456419	+	0.790540i	0.542350	+	0.840153i	$0.317535\pi$
$104$	−4433.20	−	1613.55i	−0.0401915	−	0.0146285i
$105$	4366.57	+	1589.30i	0.0386516	+	0.0140680i
$106$	−53998.6	+	93528.3i	−0.466786	+	0.808497i
$107$	−79543.1	−	137773.i	−0.671650	−	1.16333i	−0.977436	−	0.211232i	$-0.932253\pi$
$107$	−79543.1	−	137773.i	−0.671650	−	1.16333i	0.305786	−	0.952100i	$-0.401081\pi$
$108$	16625.6	+	94288.7i	0.137157	+	0.777858i
$109$	64477.4	+	54103.0i	0.519806	+	0.436169i	0.864564	−	0.502523i	$-0.167595\pi$
$109$	64477.4	+	54103.0i	0.519806	+	0.436169i	−0.344758	+	0.938692i	$0.612039\pi$
$110$	−9333.58	+	7831.80i	−0.0735472	+	0.0617135i
$111$	−49046.5	+	278157.i	−0.377834	+	2.14280i
$112$	2179.04	−	793.107i	0.0164142	−	0.00597429i
$113$	−75222.9			−0.554184			−0.277092	−	0.960843i	$-0.589371\pi$
$113$	−75222.9			−0.554184			−0.277092	+	0.960843i	$0.589371\pi$
$114$	83549.1	−	145491.i	0.602115	−	1.04851i
$115$	−59310.5			−0.418203
$116$	100563.	−	36602.0i	0.693895	−	0.252557i
$117$	−5984.11	+	33937.6i	−0.0404143	+	0.229201i
$118$	−46970.2	+	39412.6i	−0.310540	+	0.260574i
$119$	13090.1	+	10983.9i	0.0847377	+	0.0711034i
$120$	−5701.18	−	32333.0i	−0.0361420	−	0.204971i
$121$	68000.7	+	117781.i	0.422231	+	0.731325i
$122$	15532.4	−	26902.9i	0.0944797	−	0.163644i
$123$	−185659.	−	67574.3i	−1.10650	−	0.402735i
$124$	104440.	+	38013.1i	0.609976	+	0.222013i
$125$	56578.6	−	97997.0i	0.323875	−	0.560967i
$126$	−8469.30	−	14669.3i	−0.0475249	−	0.0823155i
$127$	1304.20	+	7396.46i	0.00717519	+	0.0406925i	0.988185	−	0.153265i	$-0.0489788\pi$
$127$	1304.20	+	7396.46i	0.00717519	+	0.0406925i	−0.981010	+	0.193957i	$0.937868\pi$
$128$	−12550.9	−	10531.4i	−0.0677094	−	0.0568149i
$129$	200317.	−	168086.i	1.05985	−	0.889317i
$130$	985.408	−	5588.53i	0.00511397	−	0.0290027i
$131$	52347.1	−	19052.8i	0.266511	−	0.0970019i	−0.205309	−	0.978697i	$-0.565820\pi$
$131$	52347.1	−	19052.8i	0.266511	−	0.0970019i	0.471819	+	0.881695i	$0.343598\pi$
$132$	67499.5			0.337183
$133$	−2442.48	+	14042.8i	−0.0119730	+	0.0688372i
$134$	−139418.			−0.670744
$135$	−108220.	+	39388.9i	−0.511062	+	0.186011i
$136$	20965.3	−	118900.i	0.0971970	−	0.551232i
$137$	277466.	−	232821.i	1.26301	−	1.05979i	0.267658	−	0.963514i	$-0.413750\pi$
$137$	277466.	−	232821.i	1.26301	−	1.05979i	0.995354	−	0.0962792i	$-0.0306942\pi$
$138$	251705.	+	211206.i	1.12511	+	0.944078i
$139$	66136.0	+	375076.i	0.290336	+	1.64658i	0.685577	+	0.728000i	$0.259550\pi$
$139$	66136.0	+	375076.i	0.290336	+	1.64658i	−0.395241	+	0.918578i	$0.629339\pi$
$140$	1394.65	+	2415.60i	0.00601373	+	0.0104161i
$141$	−113107.	+	195908.i	−0.479119	+	0.829858i
$142$	43314.8	+	15765.3i	0.180267	+	0.0656117i
$143$	10963.2	+	3990.28i	0.0448330	+	0.0163179i
$144$	−59839.4	+	103645.i	−0.240481	+	0.416526i
$145$	64363.1	+	111480.i	0.254224	+	0.440329i
$146$	58361.4	+	330984.i	0.226591	+	1.28506i
$147$	−341507.	−	286558.i	−1.30349	−	1.09375i
$148$	−129877.	+	108980.i	−0.487391	+	0.408969i
$149$	79709.6	−	452055.i	0.294134	−	1.66811i	−0.376569	−	0.926389i	$-0.622896\pi$
$149$	79709.6	−	452055.i	0.294134	−	1.66811i	0.670703	−	0.741726i	$-0.265993\pi$
$150$	−275985.	+	100450.i	−1.00151	+	0.364521i
$151$	250490.			0.894020			0.447010	−	0.894529i	$-0.352489\pi$
$151$	250490.			0.894020			0.447010	+	0.894529i	$0.352489\pi$
$152$	94554.3	−	34664.0i	0.331950	−	0.121694i
$153$	−881916.			−3.04578
$154$	−5388.72	+	1961.33i	−0.0183098	+	0.00666423i
$155$	−23214.8	+	131658.i	−0.0776134	+	0.440167i
$156$	−24082.8	+	20207.8i	−0.0792310	+	0.0664827i
$157$	−443.254	−	371.935i	−0.00143517	−	0.00120425i	0.642070	−	0.766646i	$-0.278076\pi$
$157$	−443.254	−	371.935i	−0.00143517	−	0.00120425i	−0.643505	+	0.765442i	$0.722520\pi$
$158$	56436.2	+	320065.i	0.179852	+	1.01999i
$159$	359835.	+	623252.i	1.12878	+	1.95511i
$160$	9853.81	−	17067.3i	0.0304301	−	0.0527066i
$161$	−26231.5	−	9547.49i	−0.0797551	−	0.0290285i
$162$	172533.	+	62797.0i	0.516518	+	0.187997i
$163$	134948.	−	233737.i	0.397831	−	0.689064i	−0.595627	−	0.803261i	$-0.703096\pi$
$163$	134948.	−	233737.i	0.397831	−	0.689064i	0.993458	+	0.114198i	$0.0364297\pi$
$164$	−59297.9	−	102707.i	−0.172159	−	0.298188i
$165$	14098.9	+	79958.8i	0.0403158	+	0.228642i
$166$	−200757.	−	168455.i	−0.565457	−	0.474475i
$167$	323202.	−	271199.i	0.896774	−	0.752483i	−0.0727829	−	0.997348i	$-0.523188\pi$
$167$	323202.	−	271199.i	0.896774	−	0.752483i	0.969557	+	0.244865i	$0.0787436\pi$
$168$	2683.31	−	15217.8i	0.00733496	−	0.0415986i
$169$	343795.	−	125131.i	0.925940	−	0.337015i
$170$	145226.			0.385409
$171$	−369296.	−	636221.i	−0.965794	−	1.66386i
$172$	156965.			0.404559
$173$	−105352.	+	38345.1i	−0.267626	+	0.0974081i	−0.472348	−	0.881412i	$-0.656593\pi$
$173$	−105352.	+	38345.1i	−0.267626	+	0.0974081i	0.204721	+	0.978820i	$0.434371\pi$
$174$	123835.	−	702304.i	0.310078	−	1.75854i
$175$	19114.1	−	16038.6i	0.0471800	−	0.0395887i
$176$	31038.0	+	26044.0i	0.0755288	+	0.0633762i
$177$	70951.1	+	402383.i	0.170226	+	0.965399i
$178$	38958.3	+	67477.7i	0.0921615	+	0.159628i
$179$	97892.9	−	169555.i	0.228359	−	0.395530i	−0.728963	−	0.684553i	$-0.759997\pi$
$179$	97892.9	−	169555.i	0.228359	−	0.395530i	0.957322	+	0.289024i	$0.0933306\pi$
$180$	−135275.	−	49236.0i	−0.311197	−	0.113267i
$181$	−350476.	−	127563.i	−0.795174	−	0.289420i	−0.0876887	−	0.996148i	$-0.527948\pi$
$181$	−350476.	−	127563.i	−0.795174	−	0.289420i	−0.707485	+	0.706728i	$0.750170\pi$
$182$	1335.43	−	2313.04i	0.00298843	−	0.00517612i
$183$	−103504.	−	179275.i	−0.228471	−	0.395723i
$184$	34249.0	+	194236.i	0.0745767	+	0.422946i
$185$	−156223.	−	131087.i	−0.335596	−	0.281598i
$186$	567356.	−	476069.i	1.20247	−	1.00899i
$187$	−51846.6	+	294037.i	−0.108422	+	0.614890i
$188$	−127599.	+	46442.1i	−0.263300	+	0.0958335i
$189$	−54203.6			−0.110376
$190$	60812.3	+	104767.i	0.122210	+	0.210543i
$191$	−734089.			−1.45601			−0.728006	−	0.685570i	$-0.759553\pi$
$191$	−734089.			−1.45601			−0.728006	+	0.685570i	$0.759553\pi$
$192$	−102595.	+	37341.5i	−0.200851	+	0.0731037i
$193$	100706.	−	571133.i	0.194609	−	1.10368i	−0.718366	−	0.695666i	$-0.755110\pi$
$193$	100706.	−	571133.i	0.194609	−	1.10368i	0.912975	−	0.408016i	$-0.133779\pi$
$194$	−339204.	+	284626.i	−0.647077	+	0.542962i
$195$	−28968.1	−	24307.2i	−0.0545549	−	0.0457770i
$196$	−46468.1	−	263534.i	−0.0864002	−	0.490000i
$197$	489549.	+	847923.i	0.898732	+	1.55665i	0.829117	+	0.559076i	$0.188844\pi$
$197$	489549.	+	847923.i	0.898732	+	1.55665i	0.0696155	+	0.997574i	$0.477823\pi$
$198$	147981.	−	256311.i	0.268253	−	0.464628i
$199$	−360554.	−	131231.i	−0.645412	−	0.234911i	−0.00148643	−	0.999999i	$-0.500473\pi$
$199$	−360554.	−	131231.i	−0.645412	−	0.234911i	−0.643926	+	0.765088i	$0.722695\pi$
$200$	−165663.	−	60296.3i	−0.292853	−	0.106590i
$201$	−464526.	+	804582.i	−0.810997	+	1.40469i
$202$	−259250.	−	449034.i	−0.447033	−	0.774284i
$203$	10520.7	+	59665.7i	0.0179186	+	0.101621i
$204$	−616318.	−	517152.i	−1.03688	−	0.870047i
$205$	109279.	−	91696.1i	0.181615	−	0.152393i
$206$	−68267.9	+	387167.i	−0.112085	+	0.635667i
$207$	1.35382e6	−	492750.i	2.19601	−	0.799283i
$208$	−18870.9			−0.0302436
$209$	−233831.	+	85723.3i	−0.370284	+	0.135748i
$210$	18587.2			0.0290848
$211$	320989.	−	116830.i	0.496345	−	0.180655i	−0.0817042	−	0.996657i	$-0.526036\pi$
$211$	320989.	−	116830.i	0.496345	−	0.180655i	0.578049	+	0.816002i	$0.303814\pi$
$212$	−75014.0	+	425426.i	−0.114631	+	0.650106i
$213$	235302.	−	197441.i	0.355366	−	0.298187i
$214$	−487468.	−	409035.i	−0.727632	−	0.610556i
$215$	32785.9	+	185938.i	0.0483717	+	0.274329i
$216$	191486.	+	331664.i	0.279257	+	0.483687i
$217$	−31460.9	+	54491.9i	−0.0453547	+	0.0785566i
$218$	316373.	+	115150.i	0.450877	+	0.164106i
$219$	2.10456e6	+	765998.i	2.96518	+	1.07924i
$220$	−24368.2	+	42207.0i	−0.0339443	+	0.0587933i
$221$	−69530.0	−	120429.i	−0.0957616	−	0.165864i
$222$	196186.	+	1.11263e6i	0.267169	+	1.51519i
$223$	132986.	+	111589.i	0.179079	+	0.150265i	0.727921	−	0.685661i	$-0.240487\pi$
$223$	132986.	+	111589.i	0.179079	+	0.150265i	−0.548842	+	0.835926i	$0.684931\pi$
$224$	7105.49	−	5962.21i	0.00946180	−	0.00793939i
$225$	−223618.	+	1.26820e6i	−0.294476	+	1.67006i
$226$	−282745.	+	102911.i	−0.368235	+	0.134026i
$227$	−90943.8			−0.117141			−0.0585704	−	0.998283i	$-0.518654\pi$
$227$	−90943.8			−0.117141			−0.0585704	+	0.998283i	$0.518654\pi$
$228$	114998.	−	661170.i	0.146506	−	0.842317i
$229$	−846676.			−1.06691			−0.533456	−	0.845828i	$-0.679107\pi$
$229$	−846676.			−1.06691			−0.533456	+	0.845828i	$0.679107\pi$
$230$	−222935.	+	81141.6i	−0.277880	+	0.101140i
$231$	−6635.76	+	37633.3i	−0.00818203	+	0.0464026i
$232$	327919.	−	275157.i	0.399988	−	0.335630i
$233$	−1.03867e6	−	871550.i	−1.25340	−	1.05173i	−0.996353	−	0.0853265i	$-0.972807\pi$
$233$	−1.03867e6	−	871550.i	−1.25340	−	1.05173i	−0.257045	−	0.966399i	$-0.582749\pi$
$234$	23936.4	+	135750.i	0.0285772	+	0.162069i
$235$	−81666.6	−	141451.i	−0.0964661	−	0.167084i
$236$	−122630.	+	212402.i	−0.143324	+	0.248244i
$237$	2.03514e6	+	740729.i	2.35355	+	0.856621i
$238$	64229.7	+	23377.7i	0.0735010	+	0.0267522i
$239$	−271684.	+	470570.i	−0.307659	+	0.532880i	−0.977850	−	0.209308i	$-0.932879\pi$
$239$	−271684.	+	470570.i	−0.307659	+	0.532880i	0.670191	+	0.742189i	$0.266212\pi$
$240$	−65663.6	−	113733.i	−0.0735862	−	0.127455i
$241$	47957.9	+	271983.i	0.0531885	+	0.301647i	0.999784	−	0.0207762i	$-0.00661376\pi$
$241$	47957.9	+	271983.i	0.0531885	+	0.301647i	−0.946596	+	0.322423i	$0.895503\pi$
$242$	416733.	+	349680.i	0.457424	+	0.383824i
$243$	−176641.	+	148220.i	−0.191901	+	0.161024i
$244$	21577.4	−	122371.i	0.0232019	−	0.131585i
$245$	302472.	−	110091.i	0.321936	−	0.117175i
$246$	−790297.			−0.832631
$247$	57763.4	−	100588.i	0.0602436	−	0.104907i
$248$	444571.			0.458999
$249$	−1.64105e6	+	597294.i	−1.67735	+	0.610506i
$250$	78598.1	−	445752.i	0.0795357	−	0.451070i
$251$	−306256.	+	256979.i	−0.306831	+	0.257462i	−0.783181	−	0.621794i	$-0.786404\pi$
$251$	−306256.	+	256979.i	−0.306831	+	0.257462i	0.476350	+	0.879256i	$0.341960\pi$
$252$	−51902.9	−	43551.7i	−0.0514861	−	0.0432020i
$253$	−84697.0	−	480340.i	−0.0831891	−	0.471789i
$254$	15021.1	+	26017.3i	0.0146089	+	0.0253034i
$255$	483877.	−	838099.i	0.465998	−	0.807133i
$256$	−61583.7	−	22414.6i	−0.0587308	−	0.0213763i
$257$	−294028.	−	107018.i	−0.277688	−	0.101070i	0.199422	−	0.979914i	$-0.436093\pi$
$257$	−294028.	−	107018.i	−0.277688	−	0.101070i	−0.477110	+	0.878844i	$0.658316\pi$
$258$	522990.	−	905845.i	0.489152	−	0.847237i
$259$	−47991.8	−	83124.3i	−0.0444547	−	0.0769979i
$260$	−3941.63	−	22354.1i	−0.00361612	−	0.0205080i
$261$	−2.39532e6	−	2.00992e6i	−2.17652	−	1.82632i
$262$	170695.	−	143230.i	0.153627	−	0.128908i
$263$	−292760.	+	1.66032e6i	−0.260989	+	1.48014i	0.519231	+	0.854634i	$0.326219\pi$
$263$	−292760.	+	1.66032e6i	−0.260989	+	1.48014i	−0.780219	+	0.625506i	$0.784893\pi$
$264$	253715.	−	92344.8i	0.224046	−	0.0815460i
$265$	−519621.			−0.454539
$266$	10030.9	+	56125.0i	0.00869232	+	0.0486354i
$267$	519219.			0.445730
$268$	−524040.	+	190735.i	−0.445685	+	0.162216i
$269$	336999.	−	1.91121e6i	0.283954	−	1.61038i	−0.425046	−	0.905172i	$-0.639742\pi$
$269$	336999.	−	1.91121e6i	0.283954	−	1.61038i	0.708999	−	0.705209i	$-0.249147\pi$
$270$	−352887.	+	296108.i	−0.294596	+	0.247195i
$271$	405862.	+	340558.i	0.335703	+	0.281688i	0.795019	−	0.606585i	$-0.207461\pi$
$271$	405862.	+	340558.i	0.335703	+	0.281688i	−0.459316	+	0.888273i	$0.651905\pi$
$272$	−83861.0	−	475600.i	−0.0687287	−	0.389780i
$273$	−8899.03	−	15413.6i	−0.00722663	−	0.0125169i
$274$	724411.	−	1.25472e6i	0.582920	−	1.00965i
$275$	409680.	+	149111.i	0.326673	+	0.118899i
$276$	1.23505e6	+	449521.i	0.975913	+	0.355203i
$277$	938112.	−	1.62486e6i	0.734607	−	1.27238i	−0.220288	−	0.975435i	$-0.570700\pi$
$277$	938112.	−	1.62486e6i	0.734607	−	1.27238i	0.954895	−	0.296942i	$-0.0959668\pi$
$278$	761724.	+	1.31935e6i	0.591134	+	1.02387i
$279$	−563909.	−	3.19809e6i	−0.433709	−	2.45969i
$280$	8546.89	+	7171.69i	0.00651498	+	0.00546672i
$281$	−575513.	+	482913.i	−0.434800	+	0.364840i	−0.833759	−	0.552128i	$-0.813816\pi$
$281$	−575513.	+	482913.i	−0.434800	+	0.364840i	0.398959	+	0.916969i	$0.369371\pi$
$282$	−157127.	+	891112.i	−0.117660	+	0.667282i
$283$	−804694.	+	292885.i	−0.597262	+	0.217385i	−0.622920	−	0.782285i	$-0.714054\pi$
$283$	−804694.	+	292885.i	−0.597262	+	0.217385i	0.0256586	+	0.999671i	$0.491832\pi$
$284$	184379.			0.135648
$285$	807230.	−	1876.08i	0.588688	−	0.00136817i
$286$	46667.2			0.0337363
$287$	63092.1	−	22963.7i	0.0452138	−	0.0164565i
$288$	−83128.0	+	471443.i	−0.0590563	+	0.334925i
$289$	1.63850e6	−	1.37487e6i	1.15399	−	0.968314i
$290$	394440.	+	330975.i	0.275414	+	0.231100i
$291$	512386.	+	2.90589e6i	0.354703	+	2.01162i
$292$	672179.	+	1.16425e6i	0.461347	+	0.799077i
$293$	148757.	−	257655.i	0.101230	−	0.175335i	−0.810962	−	0.585099i	$-0.801056\pi$
$293$	148757.	−	257655.i	0.101230	−	0.175335i	0.912192	+	0.409764i	$0.134389\pi$
$294$	−1.67568e6	−	609898.i	−1.13064	−	0.411518i
$295$	−277222.	−	100901.i	−0.185470	−	0.0675054i
$296$	−339084.	+	587311.i	−0.224946	+	0.389618i
$297$	−473542.	−	820198.i	−0.311506	−	0.539545i
$298$	−318838.	−	1.80822e6i	−0.207984	−	1.17954i
$299$	174022.	+	146022.i	0.112571	+	0.0944581i
$300$	−899940.	+	755139.i	−0.577312	+	0.484422i
$301$	−15431.0	+	87513.3i	−0.00981695	+	0.0556747i
$302$	941533.	−	342690.i	0.594043	−	0.216214i
$303$	−3.45517e6			−2.16203
$304$	307985.	−	259652.i	0.191137	−	0.161142i
$305$	149466.			0.0920010
$306$	−3.31492e6	+	1.20653e6i	−2.02381	+	0.736606i
$307$	−50094.5	+	284100.i	−0.0303350	+	0.172039i	−0.996211	−	0.0869652i	$-0.972283\pi$
$307$	−50094.5	+	284100.i	−0.0303350	+	0.172039i	0.965876	+	0.259004i	$0.0833942\pi$
$308$	−17571.7	+	14744.4i	−0.0105545	+	0.00885627i
$309$	2.00688e6	+	1.68397e6i	1.19571	+	1.00332i
$310$	92859.4	+	526632.i	0.0548809	+	0.311245i
$311$	−425699.	−	737332.i	−0.249575	−	0.432277i	0.713833	−	0.700316i	$-0.246958\pi$
$311$	−425699.	−	737332.i	−0.249575	−	0.432277i	−0.963408	+	0.268039i	$0.913624\pi$
$312$	−62875.7	+	108904.i	−0.0365676	+	0.0633369i
$313$	361508.	+	131578.i	0.208572	+	0.0759141i	0.444194	−	0.895931i	$-0.353490\pi$
$313$	361508.	+	131578.i	0.208572	+	0.0759141i	−0.235621	+	0.971845i	$0.575712\pi$
$314$	−2174.93	−	791.609i	−0.00124486	−	0.000453092i
$315$	40749.4	−	70580.1i	0.0231390	−	0.0400780i
$316$	650006.	+	1.12584e6i	0.366184	+	0.634249i
$317$	−51082.4	−	289703.i	−0.0285511	−	0.161922i	0.967199	−	0.254021i	$-0.0817533\pi$
$317$	−51082.4	−	289703.i	−0.0285511	−	0.161922i	−0.995750	+	0.0920996i	$0.970642\pi$
$318$	2.20519e6	+	1.85038e6i	1.22287	+	1.02611i
$319$	−810937.	+	680457.i	−0.446180	+	0.374390i
$320$	13688.8	−	77632.8i	0.00747290	−	0.0423809i
$321$	−3.98473e6	+	1.45032e6i	−2.15842	+	0.785601i
$322$	−111660.			−0.0600147
$323$	2.79181e6	+	1.00879e6i	1.48895	+	0.538017i
$324$	734425.			0.388673
$325$	−190808.	+	69448.5i	−0.100205	+	0.0364715i
$326$	187468.	−	1.06319e6i	0.0976976	−	0.554071i
$327$	1.71865e6	−	1.44212e6i	0.888830	−	0.745817i
$328$	−363399.	−	304928.i	−0.186509	−	0.156499i
$329$	−13349.1	−	75706.2i	−0.00679924	−	0.0385604i
$330$	162385.	+	281258.i	0.0820843	+	0.142174i
$331$	−66717.8	+	115559.i	−0.0334712	+	0.0579739i	−0.882276	−	0.470733i	$-0.843990\pi$
$331$	−66717.8	+	115559.i	−0.0334712	+	0.0579739i	0.848805	+	0.528707i	$0.177323\pi$
$332$	−985058.	−	358532.i	−0.490475	−	0.178518i
$333$	4.65501e6	+	1.69429e6i	2.30044	+	0.837290i
$334$	843821.	−	1.46154e6i	0.413889	−	0.716877i
$335$	−335400.	−	580930.i	−0.163287	−	0.282821i
$336$	−10733.2	−	60871.2i	−0.00518660	−	0.0294147i
$337$	−150344.	−	126154.i	−0.0721126	−	0.0605097i	0.606019	−	0.795450i	$-0.292766\pi$
$337$	−150344.	−	126154.i	−0.0721126	−	0.0605097i	−0.678131	+	0.734941i	$0.737210\pi$
$338$	1.12106e6	−	940679.i	0.533748	−	0.447868i
$339$	−348177.	+	1.97461e6i	−0.164551	+	0.933217i
$340$	545871.	−	198681.i	0.256090	−	0.0932091i
$341$	−1.09941e6			−0.512007
$342$	−2.25850e6	−	1.88618e6i	−1.04413	−	0.872003i
$343$	303738.			0.139400
$344$	589995.	−	214741.i	0.268814	−	0.0978404i
$345$	−274525.	+	1.55691e6i	−0.124175	+	0.704232i
$346$	−343536.	+	288261.i	−0.154270	+	0.129448i
$347$	60397.4	+	50679.4i	0.0269274	+	0.0225948i	0.656152	−	0.754629i	$-0.272183\pi$
$347$	60397.4	+	50679.4i	0.0269274	+	0.0225948i	−0.629225	+	0.777223i	$0.716627\pi$
$348$	−495340.	−	2.80922e6i	−0.219258	−	1.24347i
$349$	187158.	+	324167.i	0.0822517	+	0.142464i	0.904217	−	0.427074i	$-0.140456\pi$
$349$	187158.	+	324167.i	0.0822517	+	0.142464i	−0.821965	+	0.569538i	$0.807122\pi$
$350$	49903.3	−	86435.0i	0.0217750	−	0.0377155i
$351$	414501.	+	150866.i	0.179580	+	0.0653618i
$352$	152295.	+	55430.9i	0.0655133	+	0.0238449i
$353$	396930.	−	687504.i	0.169542	−	0.293656i	−0.768717	−	0.639589i	$-0.779104\pi$
$353$	396930.	−	687504.i	0.169542	−	0.293656i	0.938259	+	0.345934i	$0.112438\pi$
$354$	817182.	+	1.41540e6i	0.346586	+	0.600304i
$355$	38511.9	+	218412.i	0.0162190	+	0.0919824i
$356$	238750.	+	200335.i	0.0998432	+	0.0837784i
$357$	348919.	−	292778.i	0.144895	−	0.121582i
$358$	135991.	−	771246.i	0.0560795	−	0.318042i
$359$	−727448.	+	264769.i	−0.297897	+	0.108426i	−0.486645	−	0.873600i	$-0.661779\pi$
$359$	−727448.	+	264769.i	−0.297897	+	0.108426i	0.188748	+	0.982026i	$0.439557\pi$
$360$	−575826.			−0.234172
$361$	441300.	+	2.43646e6i	0.178224	+	0.983990i
$362$	−1.49188e6			−0.598358
$363$	3.40651e6	−	1.23987e6i	1.35689	−	0.493866i
$364$	1855.16	−	10521.2i	0.000733886	−	0.00416208i
$365$	−1.23875e6	+	1.03943e6i	−0.486688	+	0.408380i
$366$	−634311.	−	532250.i	−0.247514	−	0.207689i
$367$	−408385.	−	2.31607e6i	−0.158272	−	0.897607i	−0.955733	−	0.294236i	$-0.904935\pi$
$367$	−408385.	−	2.31607e6i	−0.158272	−	0.897607i	0.797460	−	0.603371i	$-0.206176\pi$
$368$	394464.	+	683232.i	0.151841	+	0.262996i
$369$	−1.73259e6	+	3.00094e6i	−0.662416	+	1.14734i
$370$	−766545.	−	278999.i	−0.291094	−	0.105950i
$371$	−229815.	−	83645.7i	−0.0866849	−	0.0315507i
$372$	1.48126e6	−	2.56562e6i	0.554977	−	0.961248i
$373$	989355.	+	1.71361e6i	0.368197	+	0.637735i	0.989284	−	0.146006i	$-0.0466420\pi$
$373$	989355.	+	1.71361e6i	0.368197	+	0.637735i	−0.621087	+	0.783742i	$0.713309\pi$
$374$	207386.	+	1.17615e6i	0.0766657	+	0.434793i
$375$	−2.31056e6	−	1.93879e6i	−0.848474	−	0.711954i
$376$	−416077.	+	349130.i	−0.151777	+	0.127356i
$377$	85616.0	−	485553.i	0.0310243	−	0.175947i
$378$	−203739.	+	74154.9i	−0.0733406	+	0.0266938i
$379$	−3.20152e6			−1.14487			−0.572437	−	0.819949i	$-0.694002\pi$
$379$	−3.20152e6			−1.14487			−0.572437	+	0.819949i	$0.694002\pi$
$380$	371909.	+	310599.i	0.132123	+	0.110342i
$381$	200195.			0.0706546
$382$	−2.75927e6	+	1.00429e6i	−0.967467	+	0.352129i
$383$	657287.	−	3.72766e6i	0.228959	−	1.29849i	−0.626011	−	0.779814i	$-0.715313\pi$
$383$	657287.	−	3.72766e6i	0.228959	−	1.29849i	0.854970	−	0.518678i	$-0.173575\pi$
$384$	−334545.	+	280717.i	−0.115778	+	0.0971494i
$385$	−21136.3	−	17735.4i	−0.00726735	−	0.00609803i
$386$	−402825.	−	2.28453e6i	−0.137609	−	0.780421i
$387$	−2.29314e6	−	3.97183e6i	−0.778310	−	1.34807i
$388$	−885598.	+	1.53390e6i	−0.298646	+	0.517271i
$389$	2.36395e6	+	860409.i	0.792073	+	0.288291i	0.706197	−	0.708015i	$-0.250409\pi$
$389$	2.36395e6	+	860409.i	0.792073	+	0.288291i	0.0858753	+	0.996306i	$0.472631\pi$
$390$	−142139.	−	51734.3i	−0.0473207	−	0.0172233i
$391$	−2.90682e6	+	5.03475e6i	−0.961558	+	1.66547i
$392$	−535198.	−	926991.i	−0.175914	−	0.304691i
$393$	−257844.	−	1.46231e6i	−0.0842125	−	0.477593i
$394$	3.00013e6	+	2.51741e6i	0.973642	+	0.816982i
$395$	−1.19789e6	+	1.00515e6i	−0.386298	+	0.324143i
$396$	205574.	−	1.16587e6i	0.0658764	−	0.373603i
$397$	4.36439e6	−	1.58851e6i	1.38978	−	0.505840i	0.464654	−	0.885492i	$-0.346179\pi$
$397$	4.36439e6	−	1.58851e6i	1.38978	−	0.505840i	0.925129	+	0.379653i	$0.123957\pi$
$398$	−1.53477e6			−0.485664
$399$	357319.	+	129114.i	0.112363	+	0.0406014i
$400$	−705178.			−0.220368
$401$	4.43442e6	−	1.61400e6i	1.37713	−	0.501236i	0.455825	−	0.890069i	$-0.349344\pi$
$401$	4.43442e6	−	1.61400e6i	1.37713	−	0.501236i	0.921308	+	0.388834i	$0.127122\pi$
$402$	−645312.	+	3.65975e6i	−0.199161	+	1.12950i
$403$	392254.	−	329140.i	0.120311	−	0.100953i
$404$	−1.58877e6	−	1.33314e6i	−0.484294	−	0.406371i
$405$	153402.	+	869987.i	0.0464723	+	0.263558i
$406$	121172.	+	209876.i	0.0364828	+	0.0631900i
$407$	838547.	−	1.45241e6i	0.250924	−	0.434612i
$408$	−3.02410e6	−	1.10068e6i	−0.899386	−	0.327350i
$409$	−417529.	−	151968.i	−0.123418	−	0.0449205i	0.279573	−	0.960124i	$-0.409807\pi$
$409$	−417529.	−	151968.i	−0.123418	−	0.0449205i	−0.402991	+	0.915204i	$0.632029\pi$
$410$	285308.	−	494168.i	0.0838212	−	0.145183i
$411$	−4.82732e6	−	8.36116e6i	−1.40962	−	2.44153i
$412$	273072.	+	1.54867e6i	0.0792562	+	0.449485i
$413$	−106366.	−	89251.5i	−0.0306850	−	0.0257478i
$414$	4.41457e6	−	3.70427e6i	1.26587	−	1.06219i
$415$	218958.	−	1.24177e6i	0.0624080	−	0.353933i
$416$	−70931.3	+	25816.9i	−0.0200958	+	0.00731426i
$417$	1.01519e7			2.85896
$418$	−761639.	+	642113.i	−0.213210	+	0.179751i
$419$	−1.62507e6			−0.452208			−0.226104	−	0.974103i	$-0.572599\pi$
$419$	−1.62507e6			−0.452208			−0.226104	+	0.974103i	$0.572599\pi$
$420$	69865.1	−	25428.8i	0.0193258	−	0.00703401i
$421$	197213.	−	1.11845e6i	0.0542289	−	0.307547i	−0.945614	−	0.325292i	$-0.894537\pi$
$421$	197213.	−	1.11845e6i	0.0542289	−	0.307547i	0.999843	+	0.0177445i	$0.00564854\pi$
$422$	1.04669e6	−	878277.i	0.286113	−	0.240077i
$423$	3.03929e6	+	2.55026e6i	0.825887	+	0.693001i
$424$	300056.	+	1.70170e6i	0.0810565	+	0.459694i
$425$	−2.59824e6	−	4.50028e6i	−0.697761	−	1.20856i
$426$	614329.	−	1.06405e6i	0.164012	−	0.284078i
$427$	66104.9	+	24060.2i	0.0175454	+	0.00638601i
$428$	−2.39187e6	−	870571.i	−0.631145	−	0.229718i
$429$	155490.	−	269317.i	0.0407905	−	0.0706513i
$430$	377613.	+	654045.i	0.0984863	+	0.170583i
$431$	1.08482e6	+	6.15234e6i	0.281297	+	1.59532i	0.718219	+	0.695817i	$0.244958\pi$
$431$	1.08482e6	+	6.15234e6i	0.281297	+	1.59532i	−0.436922	+	0.899500i	$0.643931\pi$
$432$	1.17350e6	+	984681.i	0.302533	+	0.253855i
$433$	−4.05424e6	+	3.40192e6i	−1.03918	+	0.871974i	−0.991914	−	0.126908i	$-0.959495\pi$
$433$	−4.05424e6	+	3.40192e6i	−1.03918	+	0.871974i	−0.0472642	+	0.998882i	$0.515050\pi$
$434$	−43705.0	+	247864.i	−0.0111380	+	0.0631667i
$435$	3.22429e6	−	1.17354e6i	0.816978	−	0.297356i
$436$	1.34671e6			0.339279
$437$	−4.84931e6	+	11270.3i	−1.21472	+	0.00282313i
$438$	8.95851e6			2.23126
$439$	691388.	−	251645.i	0.171222	−	0.0623199i	−0.254987	−	0.966945i	$-0.582071\pi$
$439$	691388.	−	251645.i	0.171222	−	0.0623199i	0.426209	+	0.904625i	$0.359849\pi$
$440$	−33852.0	+	191984.i	−0.00833590	+	0.0472753i
$441$	−5.98958e6	+	5.02585e6i	−1.46656	+	1.23059i
$442$	−426104.	−	357544.i	−0.103743	−	0.0870510i
$443$	703257.	+	3.98837e6i	0.170257	+	0.965575i	0.943477	+	0.331437i	$0.107534\pi$
$443$	703257.	+	3.98837e6i	0.170257	+	0.965575i	−0.773220	+	0.634137i	$0.781355\pi$
$444$	2.25958e6	+	3.91371e6i	0.543965	+	0.942174i
$445$	−187445.	+	324664.i	−0.0448718	+	0.0777203i
$446$	652528.	+	237501.i	0.155332	+	0.0565363i
$447$	−1.14976e7	−	4.18478e6i	−2.72168	−	0.990612i
$448$	18551.1	−	32131.5i	0.00436692	−	0.00756372i
$449$	1.50956e6	+	2.61463e6i	0.353374	+	0.612061i	0.986838	−	0.161711i	$-0.0517011\pi$
$449$	1.50956e6	+	2.61463e6i	0.353374	+	0.612061i	−0.633465	+	0.773772i	$0.718368\pi$
$450$	894471.	+	5.07280e6i	0.208226	+	1.18091i
$451$	898677.	+	754079.i	0.208047	+	0.174572i
$452$	−921985.	+	773637.i	−0.212265	+	0.178111i
$453$	1.15942e6	−	6.57539e6i	0.265457	−	1.50548i
$454$	−341837.	+	124418.i	−0.0778358	+	0.0283299i
$455$	12850.7			0.00291003
$456$	−472281.	−	2.64251e6i	−0.106362	−	0.595120i
$457$	−7.75813e6			−1.73767			−0.868833	−	0.495105i	$-0.835130\pi$
$457$	−7.75813e6			−1.73767			−0.868833	+	0.495105i	$0.835130\pi$
$458$	−3.18246e6	+	1.15832e6i	−0.708924	+	0.258027i
$459$	−1.96024e6	+	1.11170e7i	−0.434287	+	2.46296i
$460$	−726952.	+	609985.i	−0.160181	+	0.134408i
$461$	671886.	+	563780.i	0.147246	+	0.123554i	0.713435	−	0.700721i	$-0.247138\pi$
$461$	671886.	+	563780.i	0.147246	+	0.123554i	−0.566189	+	0.824275i	$0.691583\pi$
$462$	26543.1	+	150533.i	0.00578557	+	0.0328116i
$463$	2.52329e6	+	4.37046e6i	0.547033	+	0.947490i	0.998476	+	0.0551895i	$0.0175763\pi$
$463$	2.52329e6	+	4.37046e6i	0.547033	+	0.947490i	−0.451442	+	0.892300i	$0.649090\pi$
$464$	856136.	−	1.48287e6i	0.184607	−	0.319749i
$465$	3.34859e6	+	1.21879e6i	0.718174	+	0.261394i
$466$	−5.09648e6	−	1.85497e6i	−1.08719	−	0.395705i
$467$	−3.02566e6	+	5.24059e6i	−0.641989	+	1.11196i	0.342999	+	0.939336i	$0.388557\pi$
$467$	−3.02566e6	+	5.24059e6i	−0.641989	+	1.11196i	−0.984988	+	0.172622i	$0.944776\pi$
$468$	275689.	+	477507.i	0.0581841	+	0.100778i
$469$	−54823.8	−	310921.i	−0.0115090	−	0.0652707i
$470$	−500482.	−	419954.i	−0.104507	−	0.0876914i
$471$	−11815.0	+	9913.96i	−0.00245404	+	0.00205918i
$472$	−170356.	+	966139.i	−0.0351968	+	0.199611i
$473$	−1.45905e6	+	531049.i	−0.299858	+	0.109139i
$474$	8.66299e6			1.77101
$475$	2.15854e6	−	3.75885e6i	0.438961	−	0.764400i
$476$	273407.			0.0553086
$477$	1.18608e7	−	4.31699e6i	2.38682	−	0.868731i
$478$	−377419.	+	2.14045e6i	−0.0755535	+	0.428485i
$479$	5.78623e6	−	4.85522e6i	1.15228	−	0.966875i	0.152507	−	0.988302i	$-0.451265\pi$
$479$	5.78623e6	−	4.85522e6i	1.15228	−	0.966875i	0.999770	+	0.0214273i	$0.00682103\pi$
$480$	−402410.	−	337662.i	−0.0797197	−	0.0668928i
$481$	135637.	+	769238.i	0.0267311	+	0.151600i
$482$	552357.	+	956710.i	0.108293	+	0.187570i
$483$	−372039.	+	644390.i	−0.0725638	+	0.125684i
$484$	2.04479e6	+	744244.i	0.396767	+	0.144411i
$485$	−2.00201e6	−	728672.i	−0.386467	−	0.140662i
$486$	−461177.	+	798782.i	−0.0885681	+	0.153404i
$487$	3.67077e6	+	6.35795e6i	0.701349	+	1.21477i	0.967993	+	0.250977i	$0.0807520\pi$
$487$	3.67077e6	+	6.35795e6i	0.701349	+	1.21477i	−0.266644	+	0.963795i	$0.585915\pi$
$488$	−86309.4	−	489485.i	−0.0164062	−	0.0930443i
$489$	−5.51102e6	−	4.62430e6i	−1.04222	−	0.874528i
$490$	986309.	−	827611.i	0.185576	−	0.155717i
$491$	1.19842e6	−	6.79657e6i	0.224339	−	1.27229i	−0.639605	−	0.768704i	$-0.720902\pi$
$491$	1.19842e6	−	6.79657e6i	0.224339	−	1.27229i	0.863944	−	0.503587i	$-0.167987\pi$
$492$	−2.97054e6	+	1.08119e6i	−0.553252	+	0.201367i
$493$	1.26178e7			2.33811
$494$	79506.5	−	457114.i	0.0146584	−	0.0842766i
$495$	1.42400e6			0.261215
$496$	1.67104e6	−	608209.i	0.304988	−	0.111007i
$497$	−18125.9	+	102797.i	−0.00329162	+	0.0186677i
$498$	−5.35119e6	+	4.49018e6i	−0.966891	+	0.811318i
$499$	−4.44897e6	−	3.73313e6i	−0.799849	−	0.671153i	0.148313	−	0.988940i	$-0.452616\pi$
$499$	−4.44897e6	−	3.73313e6i	−0.799849	−	0.671153i	−0.948162	+	0.317788i	$0.897060\pi$
$500$	−314393.	−	1.78301e6i	−0.0562403	−	0.318954i
$501$	−5.62304e6	−	9.73939e6i	−1.00087	−	1.73355i
$502$	−799576.	+	1.38491e6i	−0.141612	+	0.245280i
$503$	−1.03504e6	−	376724.i	−0.182405	−	0.0663901i	0.249203	−	0.968451i	$-0.419831\pi$
$503$	−1.03504e6	−	376724.i	−0.182405	−	0.0663901i	−0.431608	+	0.902061i	$0.642054\pi$
$504$	−254673.	−	92693.4i	−0.0446588	−	0.0162545i
$505$	1.24736e6	−	2.16049e6i	0.217653	−	0.376985i
$506$	−975501.	−	1.68962e6i	−0.169376	−	0.293367i
$507$	−1.69342e6	−	9.60387e6i	−0.292580	−	1.65930i
$508$	92054.8	+	77243.1i	0.0158266	+	0.0132801i
$509$	4.22636e6	−	3.54634e6i	0.723057	−	0.606717i	−0.205172	−	0.978726i	$-0.565775\pi$
$509$	4.22636e6	−	3.54634e6i	0.723057	−	0.606717i	0.928229	+	0.372009i	$0.121331\pi$
$510$	672195.	−	3.81220e6i	0.114438	−	0.649009i
$511$	−715189.	+	260308.i	−0.121163	+	0.0440996i
$512$	−262144.			−0.0441942
$513$	−8.84075e6	+	3.24106e6i	−1.48319	+	0.543743i
$514$	−1.25159e6			−0.208956
$515$	−1.77749e6	+	646952.i	−0.295317	+	0.107487i
$516$	726530.	−	4.12036e6i	0.120124	−	0.681256i
$517$	1.02895e6	−	863392.i	0.169304	−	0.142063i
$518$	−294111.	−	246789.i	−0.0481601	−	0.0404111i
$519$	518931.	+	2.94300e6i	0.0845651	+	0.479592i
$520$	−45397.9	−	78631.5i	−0.00736254	−	0.0127523i
$521$	−4.50988e6	+	7.81135e6i	−0.727899	+	1.26076i	0.229871	+	0.973221i	$0.426170\pi$
$521$	−4.50988e6	+	7.81135e6i	−0.727899	+	1.26076i	−0.957770	+	0.287537i	$0.907164\pi$
$522$	−1.17532e7	−	4.27781e6i	−1.88790	−	0.687141i
$523$	−1.01710e7	−	3.70196e6i	−1.62597	−	0.591803i	−0.641460	−	0.767156i	$-0.721671\pi$
$523$	−1.01710e7	−	3.70196e6i	−1.62597	−	0.591803i	−0.984506	+	0.175353i	$0.943893\pi$
$524$	445653.	−	771894.i	0.0709037	−	0.122809i
$525$	−332544.	−	575984.i	−0.0526564	−	0.0912036i
$526$	1.17104e6	+	6.64129e6i	0.184547	+	1.04662i
$527$	1.00384e7	+	8.42323e6i	1.57449	+	1.32115i
$528$	827322.	−	694206.i	0.129149	−	0.108369i
$529$	531510.	−	3.01434e6i	0.0825796	−	0.468332i
$530$	−1.95313e6	+	710883.i	−0.302025	+	0.109928i
$531$	7.16614e6			1.10293
$532$	114487.	+	197238.i	0.0175379	+	0.0302142i
$533$	−546388.			−0.0833074
$534$	1.95162e6	−	710333.i	0.296171	−	0.107798i
$535$	531663.	−	3.01521e6i	0.0803068	−	0.455443i
$536$	−1.70881e6	+	1.43386e6i	−0.256910	+	0.215573i
$537$	−3.99775e6	−	3.35451e6i	−0.598246	−	0.501988i
$538$	−1.34799e6	−	7.64486e6i	−0.200786	−	1.13871i
$539$	1.32353e6	+	2.29243e6i	0.196229	+	0.339878i
$540$	−921323.	+	1.59578e6i	−0.135965	+	0.235499i
$541$	3.08233e6	+	1.12187e6i	0.452778	+	0.164798i	0.558335	−	0.829616i	$-0.311440\pi$
$541$	3.08233e6	+	1.12187e6i	0.452778	+	0.164798i	−0.105557	+	0.994413i	$0.533663\pi$
$542$	1.99145e6	+	724829.i	0.291187	+	0.105983i
$543$	−4.97077e6	+	8.60962e6i	−0.723475	+	1.25310i
$544$	−965873.	−	1.67294e6i	−0.139934	−	0.242373i
$545$	281292.	+	1.59529e6i	0.0405664	+	0.230064i
$546$	−54536.4	−	45761.5i	−0.00782898	−	0.00656929i
$547$	3.60466e6	−	3.02466e6i	0.515105	−	0.432224i	−0.347817	−	0.937563i	$-0.613077\pi$
$547$	3.60466e6	−	3.02466e6i	0.515105	−	0.432224i	0.862921	+	0.505339i	$0.168632\pi$
$548$	1.00634e6	−	5.70724e6i	0.143151	−	0.811849i
$549$	−3.41170e6	+	1.24176e6i	−0.483104	+	0.175835i
$550$	1.74389e6			0.245817
$551$	5.28361e6	+	9.10256e6i	0.741398	+	1.27727i
$552$	5.25724e6			0.734362
$553$	−691597.	+	251721.i	−0.0961701	+	0.0350031i
$554$	1.30321e6	−	7.39088e6i	0.180402	−	1.02311i
$555$	−4.16415e6	+	3.49414e6i	−0.573844	+	0.481512i
$556$	4.66812e6	+	3.91702e6i	0.640405	+	0.537364i
$557$	−989245.	−	5.61029e6i	−0.135103	−	0.766209i	−0.974788	−	0.223134i	$-0.928371\pi$
$557$	−989245.	−	5.61029e6i	−0.135103	−	0.766209i	0.839684	−	0.543075i	$-0.182740\pi$
$558$	−6.49484e6	−	1.12494e7i	−0.883046	−	1.52948i
$559$	361580.	−	626276.i	0.0489413	−	0.0847688i
$560$	41937.2	+	15263.9i	0.00565106	+	0.00205682i
$561$	7.47854e6	+	2.72196e6i	1.00325	+	0.365153i
$562$	−1.50256e6	+	2.60251e6i	−0.200674	+	0.347577i
$563$	−2.34633e6	−	4.06397e6i	−0.311974	−	0.540355i	0.666815	−	0.745223i	$-0.267657\pi$
$563$	−2.34633e6	−	4.06397e6i	−0.311974	−	0.540355i	−0.978790	+	0.204868i	$0.934324\pi$
$564$	628508.	+	3.56445e6i	0.0831981	+	0.471840i
$565$	−1.10902e6	−	930575.i	−0.146156	−	0.122639i
$566$	−2.62397e6	+	2.20177e6i	−0.344285	+	0.288889i
$567$	−72200.1	+	409467.i	−0.00943148	+	0.0534886i
$568$	693036.	−	252245.i	0.0901333	−	0.0328058i
$569$	−8.15298e6			−1.05569			−0.527844	−	0.849341i	$-0.677000\pi$
$569$	−8.15298e6			−1.05569			−0.527844	+	0.849341i	$0.677000\pi$
$570$	3.03163e6	−	1.11141e6i	0.390831	−	0.143280i
$571$	9.63131e6			1.23622			0.618109	−	0.786092i	$-0.287899\pi$
$571$	9.63131e6			1.23622			0.618109	+	0.786092i	$0.287899\pi$
$572$	175411.	−	63844.5i	0.0224165	−	0.00815894i
$573$	−3.39781e6	+	1.92700e7i	−0.432328	+	2.45185i
$574$	205733.	−	172630.i	0.0260630	−	0.0218694i
$575$	6.50295e6	+	5.45662e6i	0.820240	+	0.688263i
$576$	332512.	+	1.88577e6i	0.0417591	+	0.236828i
$577$	4.00252e6	+	6.93256e6i	0.500488	+	0.866870i	1.00000		0.000563384i	$0.000179331\pi$
$577$	4.00252e6	+	6.93256e6i	0.500488	+	0.866870i	−0.499512	+	0.866307i	$0.666487\pi$
$578$	4.27783e6	−	7.40942e6i	0.532603	−	0.922496i
$579$	−1.45262e7	−	5.28711e6i	−1.80076	−	0.655423i
$580$	1.93541e6	+	704431.i	0.238893	+	0.0869498i
$581$	296733.	−	513957.i	0.0364692	−	0.0631664i
$582$	5.90143e6	+	1.02216e7i	0.722187	+	1.25086i
$583$	−742032.	−	4.20827e6i	−0.0904172	−	0.512782i
$584$	4.11935e6	+	3.45655e6i	0.499801	+	0.419383i
$585$	−508063.	+	426315.i	−0.0613801	+	0.0515040i
$586$	206651.	−	1.17198e6i	0.0248596	−	0.140986i
$587$	1.37165e7	−	4.99238e6i	1.64303	−	0.598016i	0.655469	−	0.755222i	$-0.272471\pi$
$587$	1.37165e7	−	4.99238e6i	1.64303	−	0.598016i	0.987566	+	0.157206i	$0.0502487\pi$
$588$	−7.13289e6			−0.850789
$589$	−1.87306e6	+	1.07690e7i	−0.222466	+	1.27904i
$590$	−1.18005e6			−0.139564
$591$	2.45241e7	−	8.92603e6i	2.88818	−	1.05121i
$592$	−471051.	+	2.67146e6i	−0.0552412	+	0.313289i
$593$	394969.	−	331419.i	0.0461240	−	0.0387026i	−0.619434	−	0.785049i	$-0.712638\pi$
$593$	394969.	−	331419.i	0.0461240	−	0.0387026i	0.665558	+	0.746346i	$0.268194\pi$
$594$	−2.90203e6	−	2.43509e6i	−0.337471	−	0.283171i
$595$	57107.7	+	323874.i	0.00661305	+	0.0375045i
$596$	−3.67223e6	−	6.36049e6i	−0.423462	−	0.733458i
$597$	−5.11369e6	+	8.85717e6i	−0.587217	+	1.01709i
$598$	853877.	+	310786.i	0.0976433	+	0.0355392i
$599$	−9.15679e6	−	3.33280e6i	−1.04274	−	0.379526i	−0.236822	−	0.971553i	$-0.576106\pi$
$599$	−9.15679e6	−	3.33280e6i	−1.04274	−	0.379526i	−0.805918	+	0.592027i	$0.798328\pi$
$600$	−2.34958e6	+	4.06959e6i	−0.266447	+	0.461500i
$601$	985891.	+	1.70761e6i	0.111338	+	0.192843i	0.916310	−	0.400470i	$-0.131153\pi$
$601$	985891.	+	1.70761e6i	0.111338	+	0.192843i	−0.804972	+	0.593313i	$0.797820\pi$
$602$	61723.9	+	350053.i	0.00694164	+	0.0393680i
$603$	1.24822e7	+	1.04738e7i	1.39797	+	1.17303i
$604$	3.07018e6	−	2.57619e6i	0.342430	−	0.287333i
$605$	−454515.	+	2.57768e6i	−0.0504847	+	0.286313i
$606$	−1.29872e7	+	4.72694e6i	−1.43659	+	0.522876i
$607$	−1.72940e7			−1.90513			−0.952565	−	0.304334i	$-0.901566\pi$
$607$	−1.72940e7			−1.90513			−0.952565	+	0.304334i	$0.901566\pi$
$608$	802419.	−	1.39732e6i	0.0880323	−	0.153298i
$609$	1.61493e6			0.176445
$610$	561808.	−	204481.i	0.0611312	−	0.0222500i
$611$	−108633.	+	616089.i	−0.0117722	+	0.0667637i
$612$	−1.08094e7	+	9.07016e6i	−1.16660	+	0.978895i
$613$	−6.34057e6	−	5.32037e6i	−0.681517	−	0.571861i	0.234932	−	0.972012i	$-0.424513\pi$
$613$	−6.34057e6	−	5.32037e6i	−0.681517	−	0.571861i	−0.916449	+	0.400151i	$0.868958\pi$
$614$	200378.	+	1.13640e6i	0.0214501	+	0.121650i
$615$	−1.90123e6	−	3.29302e6i	−0.202697	−	0.351081i
$616$	−45876.5	+	79460.4i	−0.00487123	+	0.00843721i
$617$	7.25416e6	+	2.64030e6i	0.767139	+	0.279216i	0.695799	−	0.718236i	$-0.255050\pi$
$617$	7.25416e6	+	2.64030e6i	0.767139	+	0.279216i	0.0713396	+	0.997452i	$0.477273\pi$
$618$	9.84720e6	+	3.58409e6i	1.03715	+	0.377492i
$619$	1.10533e6	−	1.91449e6i	0.115949	−	0.200829i	−0.802210	−	0.597042i	$-0.796343\pi$
$619$	1.10533e6	−	1.91449e6i	0.115949	−	0.200829i	0.918159	+	0.396213i	$0.129676\pi$
$620$	1.06951e6	+	1.85245e6i	0.111739	+	0.193538i
$621$	−3.20225e6	−	1.81609e7i	−0.333217	−	1.88977i
$622$	−2.60883e6	−	2.18907e6i	−0.270377	−	0.226874i
$623$	−135165.	+	113417.i	−0.0139522	+	0.0117073i
$624$	−87346.0	+	495364.i	−0.00898010	+	0.0509287i
$625$	−6.04254e6	+	2.19931e6i	−0.618757	+	0.225209i
$626$	1.53883e6			0.156948
$627$	1.16794e6	+	6.53487e6i	0.118646	+	0.663847i
$628$	−9258.04			−0.000936742
$629$	−1.87842e7	+	6.83690e6i	−1.89307	+	0.689021i
$630$	56608.5	−	321043.i	0.00568238	−	0.0322264i
$631$	1.04955e7	−	8.80676e6i	1.04937	−	0.880527i	0.0563440	−	0.998411i	$-0.482056\pi$
$631$	1.04955e7	−	8.80676e6i	1.04937	−	0.880527i	0.993027	+	0.117884i	$0.0376112\pi$
$632$	3.98347e6	+	3.34253e6i	0.396706	+	0.332876i
$633$	−1.58108e6	−	8.96678e6i	−0.156836	−	0.889461i
$634$	−588344.	−	1.01904e6i	−0.0581311	−	0.100686i
$635$	−72273.1	+	125181.i	−0.00711283	+	0.0123198i
$636$	1.08203e7	+	3.93826e6i	1.06071	+	0.386066i
$637$	−1.15852e6	−	421666.i	−0.113124	−	0.0411737i
$638$	−2.11721e6	+	3.66711e6i	−0.205926	+	0.356674i
$639$	−2.69363e6	−	4.66550e6i	−0.260967	−	0.452008i
$640$	−54755.1	−	310531.i	−0.00528414	−	0.0299678i
$641$	−1.26124e6	−	1.05831e6i	−0.121242	−	0.101734i	0.580151	−	0.814509i	$-0.302994\pi$
$641$	−1.26124e6	−	1.05831e6i	−0.121242	−	0.101734i	−0.701393	+	0.712775i	$0.747438\pi$
$642$	−1.29935e7	+	1.09029e7i	−1.24420	+	1.04401i
$643$	2.59707e6	−	1.47287e7i	0.247717	−	1.40488i	−0.566378	−	0.824145i	$-0.691656\pi$
$643$	2.59707e6	−	1.47287e7i	0.247717	−	1.40488i	0.814096	−	0.580730i	$-0.197233\pi$
$644$	−419704.	+	152760.i	−0.0398776	+	0.0145142i
$645$	5.03266e6			0.476319
$646$	1.18739e7	−	27596.0i	1.11947	−	0.00260175i
$647$	5.38213e6			0.505468			0.252734	−	0.967536i	$-0.418670\pi$
$647$	5.38213e6			0.505468			0.252734	+	0.967536i	$0.418670\pi$
$648$	2.76053e6	−	1.00475e6i	0.258259	−	0.0939986i
$649$	421287.	−	2.38924e6i	0.0392615	−	0.222663i
$650$	−622193.	+	522082.i	−0.0577619	+	0.0484680i
$651$	1.28480e6	+	1.07808e6i	0.118818	+	0.0997004i
$652$	−749873.	−	4.25274e6i	−0.0690826	−	0.391787i
$653$	−1.68049e6	−	2.91069e6i	−0.154224	−	0.267124i	0.778552	−	0.627580i	$-0.215954\pi$
$653$	−1.68049e6	−	2.91069e6i	−0.154224	−	0.267124i	−0.932776	+	0.360456i	$0.882621\pi$
$654$	4.48708e6	−	7.77186e6i	0.410223	−	0.710527i
$655$	1.00746e6	+	366685.i	0.0917537	+	0.0333956i
$656$	−1.78310e6	−	648995.i	−0.161777	−	0.0588819i
$657$	1.96400e7	−	3.40176e7i	1.77513	−	3.07461i
$658$	−153748.	−	266300.i	−0.0138435	−	0.0239776i
$659$	−2.48701e6	−	1.41046e7i	−0.223082	−	1.26516i	−0.866318	−	0.499493i	$-0.833520\pi$
$659$	−2.48701e6	−	1.41046e7i	−0.223082	−	1.26516i	0.643236	−	0.765668i	$-0.277592\pi$
$660$	995150.	+	835030.i	0.0889260	+	0.0746178i
$661$	−1.29547e7	+	1.08703e7i	−1.15325	+	0.967693i	−0.999791	−	0.0204621i	$-0.993486\pi$
$661$	−1.29547e7	+	1.08703e7i	−1.15325	+	0.967693i	−0.153461	+	0.988155i	$0.549042\pi$
$662$	−92683.4	+	525634.i	−0.00821972	+	0.0466164i
$663$	−3.48312e6	+	1.26775e6i	−0.307740	+	0.112008i
$664$	−4.19311e6			−0.369076
$665$	−209731.	+	176818.i	−0.0183912	+	0.0155050i
$666$	1.98150e7			1.73105
$667$	−1.93694e7	+	7.04989e6i	−1.68578	+	0.613575i
$668$	1.17222e6	−	6.64801e6i	0.101641	−	0.576435i
$669$	3.54477e6	−	2.97441e6i	0.306212	−	0.256943i
$670$	−2.05545e6	−	1.72473e6i	−0.176897	−	0.148434i
$671$	213441.	+	1.21049e6i	0.0183009	+	0.103789i
$672$	−123621.	−	214117.i	−0.0105601	−	0.0182906i
$673$	−2.39454e6	+	4.14746e6i	−0.203791	+	0.352976i	−0.949747	−	0.313019i	$-0.898660\pi$
$673$	−2.39454e6	+	4.14746e6i	−0.203791	+	0.352976i	0.745956	+	0.665995i	$0.231993\pi$
$674$	−737697.	−	268500.i	−0.0625501	−	0.0227664i
$675$	1.54893e7	+	5.63766e6i	1.30850	+	0.476255i
$676$	2.92687e6	−	5.06949e6i	0.246341	−	0.426676i
$677$	6.26061e6	+	1.08437e7i	0.524982	+	0.909296i	0.999577	+	0.0290915i	$0.00926142\pi$
$677$	6.26061e6	+	1.08437e7i	0.524982	+	0.909296i	−0.474594	+	0.880205i	$0.657405\pi$
$678$	1.39271e6	+	7.89845e6i	0.116355	+	0.659884i
$679$	−768140.	−	644546.i	−0.0639390	−	0.0536512i
$680$	1.77999e6	−	1.49359e6i	0.147620	−	0.123868i
$681$	−420944.	+	2.38729e6i	−0.0347821	+	0.197259i
$682$	−4.13245e6	+	1.50409e6i	−0.340209	+	0.123826i
$683$	−7.82961e6			−0.642227			−0.321113	−	0.947041i	$-0.604057\pi$
$683$	−7.82961e6			−0.642227			−0.321113	+	0.947041i	$0.604057\pi$
$684$	−1.10696e7	−	3.99991e6i	−0.904676	−	0.326896i
$685$	6.97090e6			0.567627
$686$	1.14168e6	−	415538.i	0.0926263	−	0.0337132i
$687$	−3.91894e6	+	2.22254e7i	−0.316794	+	1.79663i
$688$	1.92387e6	−	1.61432e6i	0.154955	−	0.130023i
$689$	1.52461e6	+	1.27930e6i	0.122352	+	0.102665i
$690$	1.09810e6	+	6.22764e6i	0.0878051	+	0.497967i
$691$	−4.14150e6	−	7.17329e6i	−0.329961	−	0.571510i	0.652543	−	0.757752i	$-0.273702\pi$
$691$	−4.14150e6	−	7.17329e6i	−0.329961	−	0.571510i	−0.982504	+	0.186242i	$0.940369\pi$
$692$	−896909.	+	1.55349e6i	−0.0712005	+	0.123323i
$693$	629801.	+	229229.i	0.0498161	+	0.0181316i
$694$	296353.	+	107864.i	0.0233567	+	0.00850114i
$695$	−3.66498e6	+	6.34794e6i	−0.287813	+	0.498506i
$696$	−5.70510e6	−	9.88153e6i	−0.446417	−	0.773217i
$697$	−2.42812e6	−	1.37705e7i	−0.189316	−	1.07367i
$698$	1.14697e6	+	962422.i	0.0891074	+	0.0747700i
$699$	−2.76860e7	+	2.32313e7i	−2.14322	+	1.79837i
$700$	69324.9	−	393161.i	0.00534742	−	0.0303267i
$701$	−1.44089e7	+	5.24440e6i	−1.10748	+	0.403089i	−0.830068	−	0.557663i	$-0.811698\pi$
$701$	−1.44089e7	+	5.24440e6i	−1.10748	+	0.403089i	−0.277410	+	0.960752i	$0.589476\pi$
$702$	1.76441e6			0.135132
$703$	−1.27979e7	−	1.06882e7i	−0.976680	−	0.815671i
$704$	648276.			0.0492979
$705$	−4.09111e6	+	1.48904e6i	−0.310004	+	0.112832i
$706$	551410.	−	3.12720e6i	0.0416354	−	0.236126i
$707$	899461.	−	754737.i	0.0676758	−	0.0567868i
$708$	5.00798e6	+	4.20219e6i	0.375474	+	0.315060i
$709$	−3.16956e6	−	1.79755e7i	−0.236801	−	1.34297i	−0.838787	−	0.544460i	$-0.816735\pi$
$709$	−3.16956e6	−	1.79755e7i	−0.236801	−	1.34297i	0.601986	−	0.798507i	$-0.294376\pi$
$710$	443562.	+	768272.i	0.0330224	+	0.0571965i
$711$	1.89922e7	−	3.28954e7i	1.40897	−	2.44040i
$712$	1.17148e6	+	426384.i	0.0866035	+	0.0315211i
$713$	−2.01161e7	−	7.32168e6i	−1.48191	−	0.539370i
$714$	910963.	−	1.57783e6i	0.0668737	−	0.115829i
$715$	112268.	+	194454.i	0.00821280	+	0.0142250i
$716$	−543966.	−	3.08498e6i	−0.0396542	−	0.224890i
$717$	1.10950e7	+	9.30983e6i	0.805992	+	0.676307i
$718$	−2.37208e6	+	1.99042e6i	−0.171719	+	0.144090i
$719$	−4.53757e6	+	2.57339e7i	−0.327342	+	1.85645i	0.165338	+	0.986237i	$0.447129\pi$
$719$	−4.53757e6	+	2.57339e7i	−0.327342	+	1.85645i	−0.492680	+	0.870211i	$0.663983\pi$
$720$	−2.16440e6	+	787777.i	−0.155599	+	0.0566333i
$721$	−890279.			−0.0637805
$722$	4.99201e6	+	8.55435e6i	0.356396	+	0.610722i
$723$	7.36157e6			0.523751
$724$	−5.60762e6	+	2.04101e6i	−0.397587	+	0.144710i
$725$	3.19935e6	−	1.81444e7i	0.226057	−	1.28203i
$726$	1.11081e7	−	9.32077e6i	0.782162	−	0.656312i
$727$	6.09162e6	+	5.11148e6i	0.427461	+	0.358683i	0.830993	−	0.556283i	$-0.187773\pi$
$727$	6.09162e6	+	5.11148e6i	0.427461	+	0.358683i	−0.403531	+	0.914966i	$0.632217\pi$
$728$	−7420.65	−	42084.6i	−0.000518936	−	0.00294303i
$729$	8.65022e6	+	1.49826e7i	0.602849	+	1.04416i
$730$	−3.23414e6	+	5.60170e6i	−0.224622	+	0.389057i
$731$	1.73908e7	+	6.32972e6i	1.20372	+	0.438118i
$732$	−3.11239e6	−	1.13282e6i	−0.214692	−	0.0781416i
$733$	−5.13849e6	+	8.90013e6i	−0.353245	+	0.611838i	−0.986816	−	0.161847i	$-0.948255\pi$
$733$	−5.13849e6	+	8.90013e6i	−0.353245	+	0.611838i	0.633571	+	0.773684i	$0.281588\pi$
$734$	−4.70360e6	−	8.14687e6i	−0.322248	−	0.558149i
$735$	−1.48987e6	−	8.44950e6i	−0.101726	−	0.576916i
$736$	2.41742e6	+	2.02845e6i	0.164497	+	0.138029i
$737$	4.22584e6	−	3.54590e6i	0.286579	−	0.240468i
$738$	−2.40689e6	+	1.36502e7i	−0.162673	+	0.922566i
$739$	2.65872e7	−	9.67695e6i	1.79086	−	0.651820i	0.791696	−	0.610915i	$-0.209198\pi$
$739$	2.65872e7	−	9.67695e6i	1.79086	−	0.651820i	0.999163	−	0.0409048i	$-0.0130240\pi$
$740$	−3.26296e6			−0.219044
$741$	−2.37310e6	−	1.98188e6i	−0.158771	−	0.132597i
$742$	−978255.			−0.0652293
$743$	8.14086e6	−	2.96303e6i	0.541001	−	0.196908i	−0.0570426	−	0.998372i	$-0.518167\pi$
$743$	8.14086e6	−	2.96303e6i	0.541001	−	0.196908i	0.598044	+	0.801463i	$0.295945\pi$
$744$	2.05775e6	−	1.16701e7i	0.136289	−	0.772932i
$745$	6.76750e6	−	5.67861e6i	0.446722	−	0.374844i
$746$	6.06312e6	+	5.08756e6i	0.398886	+	0.334705i
$747$	5.31868e6	+	3.01637e7i	0.348740	+	1.97780i
$748$	2.38858e6	+	4.13714e6i	0.156094	+	0.270363i
$749$	720514.	−	1.24797e6i	0.0469286	−	0.0812828i
$750$	−1.13373e7	−	4.12643e6i	−0.735962	−	0.267868i
$751$	8.54607e6	+	3.11051e6i	0.552925	+	0.201248i	0.603346	−	0.797480i	$-0.293834\pi$
$751$	8.54607e6	+	3.11051e6i	0.552925	+	0.201248i	−0.0504205	+	0.998728i	$0.516056\pi$
$752$	−1.08630e6	+	1.88153e6i	−0.0700496	+	0.121329i
$753$	5.32820e6	+	9.22872e6i	0.342447	+	0.593135i
$754$	−342464.	−	1.94221e6i	−0.0219375	−	0.124414i
$755$	3.69299e6	+	3.09878e6i	0.235782	+	0.197844i
$756$	−664358.	+	557462.i	−0.0422763	+	0.0354741i
$757$	1.54211e6	−	8.74573e6i	0.0978082	−	0.554698i	−0.896042	−	0.443969i	$-0.853570\pi$
$757$	1.54211e6	−	8.74573e6i	0.0978082	−	0.554698i	0.993851	−	0.110729i	$-0.0353187\pi$
$758$	−1.20338e7	+	4.37993e6i	−0.760727	+	0.276882i
$759$	−1.30010e7			−0.819170
$760$	1.82285e6	+	658668.i	0.114476	+	0.0413650i
$761$	3.96760e6			0.248351			0.124176	−	0.992260i	$-0.460371\pi$
$761$	3.96760e6			0.248351			0.124176	+	0.992260i	$0.460371\pi$
$762$	752487.	−	273883.i	0.0469474	−	0.0170874i
$763$	−132393.	+	750836.i	−0.00823289	+	0.0466910i
$764$	−8.99751e6	+	7.54981e6i	−0.557685	+	0.467953i
$765$	−1.30022e7	−	1.09101e7i	−0.803271	−	0.674024i
$766$	−2.62915e6	−	1.49106e7i	−0.161899	−	0.918172i
$767$	564976.	+	978567.i	0.0346770	+	0.0600623i
$768$	−873435.	+	1.51283e6i	−0.0534352	+	0.0925525i
$769$	2.46990e7	+	8.98971e6i	1.50614	+	0.548189i	0.957641	−	0.287965i	$-0.0929787\pi$
$769$	2.46990e7	+	8.98971e6i	1.50614	+	0.548189i	0.548495	+	0.836154i	$0.315201\pi$
$770$	−103710.	−	37747.3i	−0.00630366	−	0.00229435i
$771$	−4.17017e6	+	7.22295e6i	−0.252649	+	0.437602i
$772$	−4.63955e6	−	8.03594e6i	−0.280177	−	0.485281i
$773$	3.57135e6	+	2.02541e7i	0.214973	+	1.21917i	0.880953	+	0.473203i	$0.156902\pi$
$773$	3.57135e6	+	2.02541e7i	0.214973	+	1.21917i	−0.665980	+	0.745969i	$0.731987\pi$
$774$	−1.40532e7	−	1.17920e7i	−0.843183	−	0.707514i
$775$	1.46580e7	−	1.22995e7i	0.876637	−	0.735586i
$776$	−1.23026e6	+	6.97715e6i	−0.0733402	+	0.415933i
$777$	−2.40416e6	+	875044.i	−0.142860	+	0.0519969i
$778$	1.00627e7			0.596025
$779$	8.91741e6	−	7.51798e6i	0.526496	−	0.443872i
$780$	−605044.			−0.0356082
$781$	−1.71386e6	+	623795.i	−0.100542	+	0.0365944i
$782$	−4.03811e6	+	2.29012e7i	−0.236135	+	1.33919i
$783$	−3.06602e7	+	2.57270e7i	−1.78719	+	1.49963i
$784$	−3.27989e6	−	2.75215e6i	−0.190576	−	0.159912i
$785$	−1933.76	−	10966.9i	−0.000112003	−	0.000635200i
$786$	−2.96973e6	−	5.14373e6i	−0.171459	−	0.296976i
$787$	−4.24313e6	+	7.34932e6i	−0.244202	+	0.422971i	−0.961907	−	0.273377i	$-0.911859\pi$
$787$	−4.24313e6	+	7.34932e6i	−0.244202	+	0.422971i	0.717705	+	0.696347i	$0.245193\pi$
$788$	1.47208e7	+	5.35794e6i	0.844532	+	0.307384i
$789$	4.22287e7	+	1.53700e7i	2.41499	+	0.878983i
$790$	−3.12746e6	+	5.41691e6i	−0.178289	+	0.308805i
$791$	−340690.	−	590093.i	−0.0193606	−	0.0335335i
$792$	−822295.	−	4.66347e6i	−0.0465816	−	0.264178i
$793$	−438545.	−	367983.i	−0.0247646	−	0.0207799i
$794$	1.42315e7	−	1.19417e7i	0.801125	−	0.672223i
$795$	−2.40512e6	+	1.36401e7i	−0.134964	+	0.765421i
$796$	−5.76886e6	+	2.09969e6i	−0.322706	+	0.117455i
$797$	−1.53268e7			−0.854682			−0.427341	−	0.904090i	$-0.640550\pi$
$797$	−1.53268e7			−0.854682			−0.427341	+	0.904090i	$0.640550\pi$
$798$	1.51972e6	−	3531.97i	0.0844804	−	0.000196340i
$799$	−1.60100e7			−0.887204
$800$	−2.65060e6	+	964741.i	−0.146427	+	0.0532949i
$801$	1.58131e6	−	8.96806e6i	0.0870835	−	0.493875i
$802$	1.44599e7	−	1.21333e7i	0.793833	−	0.666105i
$803$	−1.01871e7	−	8.54797e6i	−0.557520	−	0.467815i
$804$	2.58125e6	+	1.46390e7i	0.140828	+	0.798676i
$805$	−268622.	−	465267.i	−0.0146101	−	0.0253054i
$806$	1.02410e6	−	1.77380e6i	0.0555272	−	0.0961759i
$807$	−4.86099e7	−	1.76925e7i	−2.62749	−	0.956327i
$808$	−7.79568e6	−	2.83740e6i	−0.420074	−	0.152894i
$809$	−7.57937e6	+	1.31279e7i	−0.407157	+	0.705217i	−0.994570	−	0.104071i	$-0.966813\pi$
$809$	−7.57937e6	+	1.31279e7i	−0.407157	+	0.705217i	0.587413	+	0.809287i	$0.300146\pi$
$810$	1.76682e6	+	3.06022e6i	0.0946191	+	0.163885i
$811$	4.64283e6	+	2.63308e7i	0.247874	+	1.40576i	0.813723	+	0.581253i	$0.197437\pi$
$811$	4.64283e6	+	2.63308e7i	0.247874	+	1.40576i	−0.565849	+	0.824509i	$0.691452\pi$
$812$	742586.	+	623104.i	0.0395236	+	0.0331643i
$813$	1.08183e7	−	9.07763e6i	0.574027	−	0.481666i
$814$	1.16490e6	−	6.60646e6i	0.0616207	−	0.349468i
$815$	4.88110e6	−	1.77657e6i	0.257409	−	0.0936892i
$816$	−1.28727e7			−0.676776
$817$	2.71596e6	+	1.51963e7i	0.142353	+	0.796497i
$818$	−1.77730e6			−0.0928705
$819$	−293329.	+	106763.i	−0.0152808	+	0.00556175i
$820$	396345.	−	2.24779e6i	0.0205844	−	0.116740i
$821$	4.80990e6	−	4.03598e6i	0.249045	−	0.208974i	−0.509716	−	0.860343i	$-0.670250\pi$
$821$	4.80990e6	−	4.03598e6i	0.249045	−	0.208974i	0.758761	+	0.651369i	$0.225805\pi$
$822$	−2.95835e7	−	2.48235e7i	−1.52711	−	1.28140i
$823$	−3.01319e6	−	1.70886e7i	−0.155069	−	0.879443i	−0.958722	−	0.284344i	$-0.908224\pi$
$823$	−3.01319e6	−	1.70886e7i	−0.155069	−	0.879443i	0.803653	−	0.595098i	$-0.202887\pi$
$824$	3.14511e6	+	5.44750e6i	0.161368	+	0.279498i
$825$	5.81045e6	−	1.00640e7i	0.297218	−	0.514796i
$826$	−521908.	−	189959.i	−0.0266161	−	0.00968745i
$827$	−107887.	−	39267.6i	−0.00548536	−	0.00199651i	0.339276	−	0.940687i	$-0.389818\pi$
$827$	−107887.	−	39267.6i	−0.00548536	−	0.00199651i	−0.344761	+	0.938690i	$0.612040\pi$
$828$	1.15256e7	−	1.99630e7i	0.584237	−	1.01193i
$829$	1.00562e7	+	1.74179e7i	0.508217	+	0.880258i	0.999955	+	0.00951459i	$0.00302863\pi$
$829$	1.00562e7	+	1.74179e7i	0.508217	+	0.880258i	−0.491737	+	0.870743i	$0.663638\pi$
$830$	−875831.	−	4.96709e6i	−0.0441291	−	0.250269i
$831$	−3.83106e7	−	3.21464e7i	−1.92449	−	1.61484i
$832$	−231295.	+	194079.i	−0.0115840	+	0.00972011i
$833$	5.47880e6	−	3.10718e7i	0.273573	−	1.55151i
$834$	3.81588e7	−	1.38887e7i	1.89967	−	0.691425i
$835$	8.11997e6			0.403031
$836$	−1.98436e6	+	3.45554e6i	−0.0981986	+	0.171002i
$837$	−4.15671e7			−2.05086
$838$	−6.10828e6	+	2.22323e6i	−0.300475	+	0.109364i
$839$	2.38339e6	−	1.35169e7i	0.116894	−	0.662936i	−0.868902	−	0.494985i	$-0.835174\pi$
$839$	2.38339e6	−	1.35169e7i	0.116894	−	0.662936i	0.985795	−	0.167952i	$-0.0537152\pi$
$840$	227818.	−	191162.i	0.0111401	−	0.00934768i
$841$	1.85580e7	+	1.55720e7i	0.904777	+	0.759198i
$842$	−788853.	−	4.47381e6i	−0.0383456	−	0.217469i
$843$	1.00127e7	+	1.73425e7i	0.485269	+	0.840511i
$844$	2.73271e6	−	4.73320e6i	0.132050	−	0.228717i
$845$	6.61658e6	+	2.40824e6i	0.318781	+	0.116027i
$846$	1.49129e7	+	5.42787e6i	0.716370	+	0.260737i
$847$	−615961.	+	1.06688e6i	−0.0295016	+	0.0510982i
$848$	3.45591e6	+	5.98581e6i	0.165034	+	0.285847i
$849$	3.96365e6	+	2.24790e7i	0.188724	+	1.07031i
$850$	−1.59229e7	−	1.33609e7i	−0.755920	−	0.634292i
$851$	2.50155e7	−	2.09905e7i	1.18409	−	0.993570i
$852$	853417.	−	4.83997e6i	0.0402775	−	0.228425i
$853$	8.43002e6	−	3.06828e6i	0.396694	−	0.144385i	−0.135967	−	0.990713i	$-0.543414\pi$
$853$	8.43002e6	−	3.06828e6i	0.396694	−	0.144385i	0.532661	+	0.846328i	$0.321192\pi$
$854$	281389.			0.0132027
$855$	2.42606e6	−	1.39484e7i	0.113498	−	0.652542i
$856$	−1.01815e7			−0.474928
$857$	−5.10273e6	+	1.85724e6i	−0.237329	+	0.0863807i	−0.457947	−	0.888980i	$-0.651415\pi$
$857$	−5.10273e6	+	1.85724e6i	−0.237329	+	0.0863807i	0.220618	+	0.975360i	$0.429193\pi$
$858$	216005.	−	1.22502e6i	0.0100172	−	0.0568101i
$859$	−1.94984e6	+	1.63611e6i	−0.0901605	+	0.0756536i	−0.686754	−	0.726890i	$-0.740965\pi$
$859$	−1.94984e6	+	1.63611e6i	−0.0901605	+	0.0756536i	0.596593	+	0.802544i	$0.296521\pi$
$860$	2.31415e6	+	1.94180e6i	0.106695	+	0.0895279i
$861$	−310771.	−	1.76247e6i	−0.0142867	−	0.0810240i
$862$	1.24945e7	+	2.16411e7i	0.572731	+	0.991999i
$863$	7.04130e6	−	1.21959e7i	0.321829	−	0.557425i	−0.659036	−	0.752111i	$-0.729036\pi$
$863$	7.04130e6	−	1.21959e7i	0.321829	−	0.557425i	0.980866	+	0.194686i	$0.0623689\pi$
$864$	5.75803e6	+	2.09575e6i	0.262415	+	0.0955114i
$865$	−2.02758e6	−	737979.i	−0.0921379	−	0.0335354i
$866$	−1.05849e7	+	1.83336e7i	−0.479613	+	0.830715i
$867$	−2.85065e7	−	4.93747e7i	−1.28794	−	2.23078i
$868$	174820.	+	991454.i	0.00787576	+	0.0446656i
$869$	−9.85102e6	−	8.26599e6i	−0.442519	−	0.371317i
$870$	1.05138e7	−	8.82217e6i	0.470938	−	0.395164i
$871$	−446150.	+	2.53024e6i	−0.0199267	+	0.113010i
$872$	5.06197e6	−	1.84241e6i	0.225438	−	0.0820529i
$873$	5.17516e7			2.29820
$874$	−1.82120e7	+	6.67662e6i	−0.806455	+	0.295650i
$875$	1.02500e6			0.0452587
$876$	3.36730e7	−	1.22560e7i	1.48259	−	0.539619i
$877$	7.30656e6	−	4.14376e7i	0.320785	−	1.81926i	−0.216990	−	0.976174i	$-0.569624\pi$
$877$	7.30656e6	−	4.14376e7i	0.320785	−	1.81926i	0.537775	−	0.843088i	$-0.319265\pi$
$878$	2.25450e6	−	1.89175e6i	0.0986993	−	0.0828185i
$879$	−6.07494e6	−	5.09748e6i	−0.265198	−	0.222527i
$880$	135408.	+	767937.i	0.00589437	+	0.0334287i
$881$	−5.83783e6	−	1.01114e7i	−0.253403	−	0.438907i	0.711057	−	0.703134i	$-0.248217\pi$
$881$	−5.83783e6	−	1.01114e7i	−0.253403	−	0.438907i	−0.964461	+	0.264227i	$0.914883\pi$
$882$	−1.56377e7	+	2.70852e7i	−0.676863	+	1.17236i
$883$	−3.50071e7	−	1.27415e7i	−1.51096	−	0.549946i	−0.552092	−	0.833783i	$-0.686170\pi$
$883$	−3.50071e7	−	1.27415e7i	−1.51096	−	0.549946i	−0.958872	+	0.283838i	$0.908392\pi$
$884$	−2.09078e6	−	760981.i	−0.0899865	−	0.0327524i
$885$	−3.93181e6	+	6.81010e6i	−0.168746	+	0.292277i
$886$	8.09979e6	+	1.40292e7i	0.346649	+	0.600413i
$887$	−942199.	−	5.34348e6i	−0.0402100	−	0.228042i	0.958080	−	0.286501i	$-0.0924923\pi$
$887$	−942199.	−	5.34348e6i	−0.0402100	−	0.228042i	−0.998290	+	0.0584594i	$0.981381\pi$
$888$	1.38475e7	+	1.16195e7i	0.589304	+	0.494485i
$889$	−52115.4	+	43730.0i	−0.00221163	+	0.00185578i
$890$	−260396.	+	1.47678e6i	−0.0110194	+	0.0624943i
$891$	−6.82674e6	+	2.48473e6i	−0.288084	+	0.104854i
$892$	2.77762e6			0.116886
$893$	−6.70406e6	−	1.15497e7i	−0.281326	−	0.484665i
$894$	−4.89419e7			−2.04803
$895$	3.54080e6	−	1.28875e6i	0.147755	−	0.0537786i
$896$	25770.9	−	146154.i	0.00107241	−	0.00608193i
$897$	4.63857e6	−	3.89222e6i	0.192488	−	0.161516i
$898$	9.25111e6	+	7.76260e6i	0.382827	+	0.321230i
$899$	8.06798e6	+	4.57558e7i	0.332940	+	1.88819i
$900$	1.03021e7	+	1.78438e7i	0.423955	+	0.734312i
$901$	−2.54667e7	+	4.41096e7i	−1.04511	+	1.81018i
$902$	4.40956e6	+	1.60495e6i	0.180459	+	0.0656818i
$903$	2.22582e6	+	810131.i	0.0908385	+	0.0330625i
$904$	−2.40713e6	+	4.16927e6i	−0.0979668	+	0.169683i
$905$	−3.58903e6	−	6.21638e6i	−0.145665	−	0.252299i
$906$	−4.63768e6	−	2.63016e7i	−0.187707	−	1.06454i
$907$	−2.36772e7	−	1.98675e7i	−0.955680	−	0.801911i	0.0245649	−	0.999698i	$-0.492180\pi$
$907$	−2.36772e7	−	1.98675e7i	−0.955680	−	0.801911i	−0.980245	+	0.197787i	$0.936624\pi$
$908$	−1.11467e6	+	935321.i	−0.0448676	+	0.0376483i
$909$	−1.05229e7	+	5.96784e7i	−0.422402	+	2.39556i
$910$	48302.7	−	17580.8i	0.00193361	−	0.000703776i
$911$	7.30220e6			0.291513			0.145756	−	0.989321i	$-0.453438\pi$
$911$	7.30220e6			0.291513			0.145756	+	0.989321i	$0.453438\pi$
$912$	−5.39036e6	−	9.28648e6i	−0.214601	−	0.369712i
$913$	1.03695e7			0.411698
$914$	−2.91610e7	+	1.06137e7i	−1.15462	+	0.420246i
$915$	691820.	−	3.92350e6i	0.0273174	−	0.154925i
$916$	−1.03775e7	+	8.70773e6i	−0.408651	+	0.342899i
$917$	386546.	+	324350.i	0.0151802	+	0.0127377i
$918$	7.84094e6	+	4.44682e7i	0.307087	+	1.74158i
$919$	1.52820e7	+	2.64692e7i	0.596886	+	1.03384i	0.993278	+	0.115756i	$0.0369289\pi$
$919$	1.52820e7	+	2.64692e7i	0.596886	+	1.03384i	−0.396392	+	0.918082i	$0.629738\pi$
$920$	−1.89794e6	+	3.28732e6i	−0.0739285	+	0.128048i
$921$	7.22581e6	+	2.62998e6i	0.280697	+	0.102165i
$922$	3.29676e6	+	1.19992e6i	0.127720	+	0.0464864i
$923$	424729.	−	735653.i	0.0164100	−	0.0284229i
$924$	305711.	+	529506.i	0.0117796	+	0.0204029i
$925$	5.06858e6	+	2.87454e7i	0.194775	+	1.10462i
$926$	1.54636e7	+	1.29755e7i	0.592629	+	0.497275i
$927$	3.51980e7	−	2.95346e7i	1.34530	−	1.12884i
$928$	1.18933e6	−	6.74504e6i	0.0453350	−	0.257107i
$929$	−1.10919e7	+	4.03714e6i	−0.421666	+	0.153474i	−0.544133	−	0.838999i	$-0.683141\pi$
$929$	−1.10919e7	+	4.03714e6i	−0.421666	+	0.153474i	0.122468	+	0.992472i	$0.460919\pi$
$930$	1.42540e7			0.540417
$931$	2.47096e7	−	9.05865e6i	0.934312	−	0.342523i
$932$	−2.16943e7			−0.818098
$933$	−2.13255e7	+	7.76184e6i	−0.802038	+	0.291918i
$934$	−4.20320e6	+	2.38375e7i	−0.157657	+	0.894116i
$935$	−4.40188e6	+	3.69362e6i	−0.164668	+	0.138173i
$936$	1.68952e6	+	1.41768e6i	0.0630338	+	0.0528917i
$937$	4.28719e6	+	2.43139e7i	0.159523	+	0.904702i	0.954533	+	0.298105i	$0.0963545\pi$
$937$	4.28719e6	+	2.43139e7i	0.159523	+	0.904702i	−0.795010	+	0.606597i	$0.792534\pi$
$938$	−631435.	−	1.09368e6i	−0.0234327	−	0.0405866i
$939$	5.12722e6	−	8.88061e6i	0.189766	−	0.328684i
$940$	−2.45573e6	−	893812.i	−0.0906485	−	0.0329933i
$941$	−2.60065e7	−	9.46559e6i	−0.957431	−	0.348477i	−0.184405	−	0.982850i	$-0.559036\pi$
$941$	−2.60065e7	−	9.46559e6i	−0.957431	−	0.348477i	−0.773026	+	0.634374i	$0.781258\pi$
$942$	−30846.8	+	53428.2i	−0.00113262	+	0.00196175i
$943$	1.14213e7	+	1.97823e7i	0.418252	+	0.724433i
$944$	681425.	+	3.86455e6i	0.0248879	+	0.141146i
$945$	−799127.	−	670548.i	−0.0291096	−	0.0244259i
$946$	−4.75770e6	+	3.99218e6i	−0.172850	+	0.145038i
$947$	5.86481e6	−	3.32610e7i	0.212510	−	1.20520i	−0.672666	−	0.739946i	$-0.734851\pi$
$947$	5.86481e6	−	3.32610e7i	0.212510	−	1.20520i	0.885176	−	0.465256i	$-0.154038\pi$
$948$	3.25622e7	−	1.18517e7i	1.17677	−	0.428310i
$949$	6.19366e6			0.223245
$950$	2.97105e6	−	1.70817e7i	0.106807	−	0.614076i
$951$	−7.84119e6			−0.281145
$952$	1.02767e6	−	374043.i	0.0367505	−	0.0133761i
$953$	5.15305e6	−	2.92244e7i	0.183794	−	1.04235i	−0.743700	−	0.668513i	$-0.766931\pi$
$953$	5.15305e6	−	2.92244e7i	0.183794	−	1.04235i	0.927495	−	0.373836i	$-0.121958\pi$
$954$	3.86762e7	−	3.24532e7i	1.37585	−	1.15448i
$955$	−1.08227e7	−	9.08134e6i	−0.383997	−	0.322212i
$956$	1.50968e6	+	8.56180e6i	0.0534244	+	0.302985i
$957$	1.41086e7	+	2.44368e7i	0.497971	+	0.862511i
$958$	1.51068e7	−	2.61657e7i	0.531812	−	0.921125i
$959$	3.08305e6	+	1.12214e6i	0.108252	+	0.0394004i
$960$	−1.97452e6	−	718665.i	−0.0691484	−	0.0251680i
$961$	−9.81184e6	+	1.69946e7i	−0.342722	+	0.593612i
$962$	1.56221e6	+	2.70583e6i	0.0544254	+	0.0942676i
$963$	1.29146e7	+	7.32422e7i	0.448760	+	2.54505i
$964$	3.38504e6	+	2.84039e6i	0.117320	+	0.0984430i
$965$	8.55015e6	−	7.17443e6i	0.295567	−	0.248010i
$966$	−516831.	+	2.93109e6i	−0.0178199	+	0.101062i
$967$	−4.38278e7	+	1.59520e7i	−1.50724	+	0.548591i	−0.957924	−	0.287022i	$-0.907335\pi$
$967$	−4.38278e7	+	1.59520e7i	−1.50724	+	0.548591i	−0.549318	+	0.835613i	$0.685113\pi$
$968$	8.70409e6			0.298562
$969$	3.94032e7	−	6.86162e7i	1.34810	−	2.34756i
$970$	−8.52198e6			−0.290811
$971$	−1.52651e7	+	5.55606e6i	−0.519580	+	0.189112i	−0.588480	−	0.808512i	$-0.700273\pi$
$971$	−1.52651e7	+	5.55606e6i	−0.519580	+	0.189112i	0.0688996	+	0.997624i	$0.478051\pi$
$972$	−640661.	+	3.63337e6i	−0.0217502	+	0.123351i
$973$	−2.64278e6	+	2.21756e6i	−0.0894911	+	0.0750919i
$974$	2.24958e7	+	1.88762e7i	0.759807	+	0.637554i
$975$	939857.	+	5.33019e6i	0.0316629	+	0.179569i
$976$	−994072.	−	1.72178e6i	−0.0334036	−	0.0578567i
$977$	1.47469e7	−	2.55424e7i	0.494270	−	0.856101i	−0.505708	−	0.862705i	$-0.668769\pi$
$977$	1.47469e7	−	2.55424e7i	0.494270	−	0.856101i	0.999978	+	0.00660354i	$0.00210199\pi$
$978$	−2.70411e7	−	9.84215e6i	−0.904018	−	0.329036i
$979$	−2.89705e6	−	1.05444e6i	−0.0966048	−	0.0351613i
$980$	2.57507e6	−	4.46015e6i	0.0856493	−	0.148349i
$981$	−1.96744e7	−	3.40770e7i	−0.652722	−	1.13055i
$982$	−4.79368e6	−	2.71863e7i	−0.158632	−	0.899645i
$983$	6.78117e6	+	5.69008e6i	0.223831	+	0.187817i	0.747806	−	0.663917i	$-0.231107\pi$
$983$	6.78117e6	+	5.69008e6i	0.223831	+	0.187817i	−0.523975	+	0.851734i	$0.675552\pi$
$984$	−9.68644e6	+	8.12789e6i	−0.318916	+	0.267602i
$985$	−3.27213e6	+	1.85572e7i	−0.107458	+	0.609426i
$986$	4.74273e7	−	1.72621e7i	1.55359	−	0.565461i
$987$	−2.04909e6			−0.0669527
$988$	−326522.	−	1.82696e6i	−0.0106419	−	0.0595437i
$989$	−3.02329e7			−0.982855
$990$	5.35251e6	−	1.94815e6i	0.173568	−	0.0631735i
$991$	−3.38259e6	+	1.91836e7i	−0.109412	+	0.620507i	0.879954	+	0.475059i	$0.157573\pi$
$991$	−3.38259e6	+	1.91836e7i	−0.109412	+	0.620507i	−0.989366	+	0.145448i	$0.953538\pi$
$992$	5.44898e6	−	4.57224e6i	0.175807	−	0.147520i
$993$	2.72462e6	+	2.28623e6i	0.0876866	+	0.0735778i
$994$	72503.8	+	411189.i	0.00232753	+	0.0132001i
$995$	−3.69222e6	−	6.39512e6i	−0.118231	−	0.204782i
$996$	−1.39710e7	+	2.41984e7i	−0.446250	+	0.772928i
$997$	3.78155e7	+	1.37637e7i	1.20485	+	0.438528i	0.864913	−	0.501921i	$-0.167373\pi$
$997$	3.78155e7	+	1.37637e7i	1.20485	+	0.438528i	0.339933	+	0.940450i	$0.389596\pi$
$998$	−2.18299e7	−	7.94542e6i	−0.693785	−	0.252517i
$999$	3.17041e7	−	5.49131e7i	1.00508	−	1.74085i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.a.5.4	✓	24
19.2	odd	18		722.6.a.p.1.1		12
19.4	even	9	inner	38.6.e.a.23.4	yes	24
19.17	even	9		722.6.a.o.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.a.5.4	✓	24	1.1	even	1	trivial
38.6.e.a.23.4	yes	24	19.4	even	9	inner
722.6.a.o.1.12		12	19.17	even	9
722.6.a.p.1.1		12	19.2	odd	18

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	38.6.e.a.5.4

Level	$38$
Weight	$6$
Character	38.5
Analytic conductor	$6.095$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$