LMFDB - Embedded newform 74.6.e.a.27.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(11,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("74.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.e (of order $6$, 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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.6
Character	$\chi$	$=$	74.27
Dual form			74.6.e.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.46410 - 2.00000i) q^{2} +(7.85694 + 13.6086i) q^{3} +(8.00000 + 13.8564i) q^{4} +(-3.80965 + 2.19950i) q^{5} -62.8556i q^{6} +(79.6803 + 138.010i) q^{7} -64.0000i q^{8} +(-1.96314 + 3.40026i) q^{9} +17.5960 q^{10} +161.078 q^{11} +(-125.711 + 217.738i) q^{12} +(-616.776 + 356.096i) q^{13} -637.443i q^{14} +(-59.8644 - 34.5627i) q^{15} +(-128.000 + 221.703i) q^{16} +(-163.639 - 94.4772i) q^{17} +(13.6011 - 7.85257i) q^{18} +(-684.280 + 395.070i) q^{19} +(-60.9544 - 35.1920i) q^{20} +(-1252.09 + 2168.68i) q^{21} +(-557.992 - 322.157i) q^{22} +1767.20i q^{23} +(870.952 - 502.844i) q^{24} +(-1552.82 + 2689.57i) q^{25} +2848.77 q^{26} +3756.78 q^{27} +(-1274.89 + 2208.17i) q^{28} +6240.56i q^{29} +(138.251 + 239.457i) q^{30} +4586.28i q^{31} +(886.810 - 512.000i) q^{32} +(1265.58 + 2192.06i) q^{33} +(377.909 + 654.557i) q^{34} +(-607.108 - 350.514i) q^{35} -62.8206 q^{36} +(-7327.27 - 3956.65i) q^{37} +3160.56 q^{38} +(-9691.95 - 5595.65i) q^{39} +(140.768 + 243.817i) q^{40} +(-671.689 - 1163.40i) q^{41} +(8674.72 - 5008.35i) q^{42} -18772.5i q^{43} +(1288.63 + 2231.97i) q^{44} -17.2717i q^{45} +(3534.39 - 6121.75i) q^{46} +1966.40 q^{47} -4022.76 q^{48} +(-4294.41 + 7438.13i) q^{49} +(10758.3 - 6211.30i) q^{50} -2969.21i q^{51} +(-9868.41 - 5697.53i) q^{52} +(7906.50 - 13694.5i) q^{53} +(-13013.9 - 7513.56i) q^{54} +(-613.652 + 354.292i) q^{55} +(8832.66 - 5099.54i) q^{56} +(-10752.7 - 6208.08i) q^{57} +(12481.1 - 21617.9i) q^{58} +(2614.50 + 1509.48i) q^{59} -1106.01i q^{60} +(-4951.58 + 2858.80i) q^{61} +(9172.56 - 15887.3i) q^{62} -625.695 q^{63} -4096.00 q^{64} +(1566.47 - 2713.20i) q^{65} -10124.7i q^{66} +(17357.5 + 30064.1i) q^{67} -3023.27i q^{68} +(-24049.1 + 13884.8i) q^{69} +(1402.06 + 2428.43i) q^{70} +(14158.7 + 24523.5i) q^{71} +(217.617 + 125.641i) q^{72} +41977.9 q^{73} +(17469.1 + 28360.8i) q^{74} -48801.8 q^{75} +(-10948.5 - 6321.11i) q^{76} +(12834.8 + 22230.5i) q^{77} +(22382.6 + 38767.8i) q^{78} +(45664.7 - 26364.5i) q^{79} -1126.14i q^{80} +(29993.8 + 51950.8i) q^{81} +5373.51i q^{82} +(43238.6 - 74891.5i) q^{83} -40066.8 q^{84} +831.210 q^{85} +(-37545.0 + 65029.9i) q^{86} +(-84925.4 + 49031.7i) q^{87} -10309.0i q^{88} +(-15380.2 - 8879.79i) q^{89} +(-34.5435 + 59.8311i) q^{90} +(-98289.8 - 56747.6i) q^{91} +(-24487.0 + 14137.6i) q^{92} +(-62412.9 + 36034.1i) q^{93} +(-6811.81 - 3932.80i) q^{94} +(1737.91 - 3010.15i) q^{95} +(13935.2 + 8045.51i) q^{96} -35931.9i q^{97} +(29752.5 - 17177.6i) q^{98} +(-316.220 + 547.709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25}+ \cdots - 401224 q^{99}+O(q^{100}) $ 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9 - 736 * q^10 + 464 * q^11 + 320 * q^12 + 72 * q^13 + 3960 * q^15 - 3584 * q^16 + 1530 * q^17 - 1944 * q^19 - 1440 * q^20 - 192 * q^21 - 3028 * q^25 - 5280 * q^26 + 36400 * q^27 + 2496 * q^28 - 4368 * q^30 - 2996 * q^33 + 1360 * q^34 - 21636 * q^35 - 18752 * q^36 + 45178 * q^37 - 14304 * q^38 + 14592 * q^39 - 5888 * q^40 + 12894 * q^41 - 26832 * q^42 + 3712 * q^44 - 22080 * q^46 - 39512 * q^47 + 10240 * q^48 + 8262 * q^49 - 44640 * q^50 + 1152 * q^52 + 47912 * q^53 - 101520 * q^54 + 70236 * q^55 + 99984 * q^57 + 51968 * q^58 - 74568 * q^59 - 8274 * q^61 - 22768 * q^62 - 137048 * q^63 - 114688 * q^64 + 33104 * q^65 - 7904 * q^67 - 69096 * q^69 + 65056 * q^70 + 9788 * q^71 + 256784 * q^73 - 8480 * q^74 + 518544 * q^75 - 31104 * q^76 - 86340 * q^77 + 89776 * q^78 - 82740 * q^79 - 174814 * q^81 + 19892 * q^83 - 6144 * q^84 - 167972 * q^85 + 119536 * q^86 - 200424 * q^87 - 223482 * q^89 + 59504 * q^90 - 53016 * q^91 + 198912 * q^92 - 227844 * q^93 + 158736 * q^94 - 140012 * q^95 - 168864 * q^98 - 401224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−3.46410	−	2.00000i	−0.612372	−	0.353553i
$2$	−3.46410	−	2.00000i	−0.612372	−	0.353553i
$3$	7.85694	+	13.6086i	0.504023	+	0.872994i	0.999989	+	0.00465184i	$0.00148073\pi$
$3$	7.85694	+	13.6086i	0.504023	+	0.872994i	−0.495966	+	0.868342i	$0.665186\pi$
$4$	8.00000	+	13.8564i	0.250000	+	0.433013i
$5$	−3.80965	+	2.19950i	−0.0681490	+	0.0393459i	−0.533687	−	0.845682i	$-0.679194\pi$
$5$	−3.80965	+	2.19950i	−0.0681490	+	0.0393459i	0.465538	+	0.885028i	$0.345861\pi$
$6$		−	62.8556i		−	0.712796i
$7$	79.6803	+	138.010i	0.614619	+	1.06455i	0.990451	+	0.137864i	$0.0440236\pi$
$7$	79.6803	+	138.010i	0.614619	+	1.06455i	−0.375832	+	0.926688i	$0.622643\pi$
$8$		−	64.0000i		−	0.353553i
$9$	−1.96314	+	3.40026i	−0.00807878	+	0.0139929i
$10$	17.5960			0.0556435
$11$	161.078			0.401380			0.200690	−	0.979655i	$-0.435682\pi$
$11$	161.078			0.401380			0.200690	+	0.979655i	$0.435682\pi$
$12$	−125.711	+	217.738i	−0.252012	+	0.436497i
$13$	−616.776	+	356.096i	−1.01221	+	0.584398i	−0.911837	−	0.410553i	$-0.865336\pi$
$13$	−616.776	+	356.096i	−1.01221	+	0.584398i	−0.100369	+	0.994950i	$0.532002\pi$
$14$		−	637.443i		−	0.869202i
$15$	−59.8644	−	34.5627i	−0.0686974	−	0.0396625i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−163.639	−	94.4772i	−0.137330	−	0.0792875i	0.429761	−	0.902943i	$-0.358598\pi$
$17$	−163.639	−	94.4772i	−0.137330	−	0.0792875i	−0.567091	+	0.823655i	$0.691931\pi$
$18$	13.6011	−	7.85257i	0.00989444	−	0.00571256i
$19$	−684.280	+	395.070i	−0.434861	+	0.251067i	−0.701415	−	0.712753i	$-0.747448\pi$
$19$	−684.280	+	395.070i	−0.434861	+	0.251067i	0.266555	+	0.963820i	$0.414115\pi$
$20$	−60.9544	−	35.1920i	−0.0340745	−	0.0196729i
$21$	−1252.09	+	2168.68i	−0.619564	+	1.07312i
$22$	−557.992	−	322.157i	−0.245794	−	0.141909i
$23$			1767.20i			0.696571i	0.937389	+	0.348285i	$0.113236\pi$
$23$			1767.20i			0.696571i	−0.937389	+	0.348285i	$0.886764\pi$
$24$	870.952	−	502.844i	0.308650	−	0.178199i
$25$	−1552.82	+	2689.57i	−0.496904	+	0.860663i
$26$	2848.77			0.826463
$27$	3756.78			0.991759
$28$	−1274.89	+	2208.17i	−0.307309	+	0.532276i
$29$			6240.56i			1.37793i	0.724793	+	0.688967i	$0.241936\pi$
$29$			6240.56i			1.37793i	−0.724793	+	0.688967i	$0.758064\pi$
$30$	138.251	+	239.457i	0.0280456	+	0.0485764i
$31$			4586.28i			0.857149i	0.903507	+	0.428574i	$0.140984\pi$
$31$			4586.28i			0.857149i	−0.903507	+	0.428574i	$0.859016\pi$
$32$	886.810	−	512.000i	0.153093	−	0.0883883i
$33$	1265.58	+	2192.06i	0.202305	+	0.350402i
$34$	377.909	+	654.557i	0.0560647	+	0.0971069i
$35$	−607.108	−	350.514i	−0.0837714	−	0.0483654i
$36$	−62.8206			−0.00807878
$37$	−7327.27	−	3956.65i	−0.879909	−	0.475142i
$37$	−7327.27	−	3956.65i	−0.879909	−	0.475142i
$38$	3160.56			0.355062
$39$	−9691.95	−	5595.65i	−1.02035	−	0.589100i
$40$	140.768	+	243.817i	0.0139109	+	0.0240943i
$41$	−671.689	−	1163.40i	−0.0624035	−	0.108086i	0.833136	−	0.553068i	$-0.186543\pi$
$41$	−671.689	−	1163.40i	−0.0624035	−	0.108086i	−0.895539	+	0.444983i	$0.853210\pi$
$42$	8674.72	−	5008.35i	0.758808	−	0.438098i
$43$		−	18772.5i		−	1.54829i	−0.633010	−	0.774144i	$-0.718181\pi$
$43$		−	18772.5i		−	1.54829i	0.633010	−	0.774144i	$-0.281819\pi$
$44$	1288.63	+	2231.97i	0.100345	+	0.173803i
$45$		−	17.2717i		−	0.00127147i
$46$	3534.39	−	6121.75i	0.246275	−	0.426561i
$47$	1966.40			0.129846			0.0649228	−	0.997890i	$-0.479320\pi$
$47$	1966.40			0.129846			0.0649228	+	0.997890i	$0.479320\pi$
$48$	−4022.76			−0.252012
$49$	−4294.41	+	7438.13i	−0.255513	+	0.442561i
$50$	10758.3	−	6211.30i	0.608580	−	0.351364i
$51$		−	2969.21i		−	0.159851i
$52$	−9868.41	−	5697.53i	−0.506103	−	0.292199i
$53$	7906.50	−	13694.5i	0.386629	−	0.669661i	−0.605365	−	0.795948i	$-0.706973\pi$
$53$	7906.50	−	13694.5i	0.386629	−	0.669661i	0.991994	+	0.126287i	$0.0403060\pi$
$54$	−13013.9	−	7513.56i	−0.607326	−	0.350640i
$55$	−613.652	+	354.292i	−0.0273537	+	0.0157926i
$56$	8832.66	−	5099.54i	0.376376	−	0.217301i
$57$	−10752.7	−	6208.08i	−0.438360	−	0.253087i
$58$	12481.1	−	21617.9i	0.487173	−	0.843809i
$59$	2614.50	+	1509.48i	0.0977818	+	0.0564544i	0.548094	−	0.836417i	$-0.315354\pi$
$59$	2614.50	+	1509.48i	0.0977818	+	0.0564544i	−0.450312	+	0.892871i	$0.648687\pi$
$60$		−	1106.01i		−	0.0396625i
$61$	−4951.58	+	2858.80i	−0.170380	+	0.0983691i	−0.582765	−	0.812641i	$-0.698029\pi$
$61$	−4951.58	+	2858.80i	−0.170380	+	0.0983691i	0.412385	+	0.911010i	$0.364696\pi$
$62$	9172.56	−	15887.3i	0.303048	−	0.524894i
$63$	−625.695			−0.0198615
$64$	−4096.00			−0.125000
$65$	1566.47	−	2713.20i	0.0459873	−	0.0796523i
$66$		−	10124.7i		−	0.286102i
$67$	17357.5	+	30064.1i	0.472390	+	0.818204i	0.999501	−	0.0315929i	$-0.0100580\pi$
$67$	17357.5	+	30064.1i	0.472390	+	0.818204i	−0.527111	+	0.849797i	$0.676725\pi$
$68$		−	3023.27i		−	0.0792875i
$69$	−24049.1	+	13884.8i	−0.608102	+	0.351088i
$70$	1402.06	+	2428.43i	0.0341995	+	0.0592353i
$71$	14158.7	+	24523.5i	0.333332	+	0.577347i	0.983163	−	0.182731i	$-0.0584938\pi$
$71$	14158.7	+	24523.5i	0.333332	+	0.577347i	−0.649831	+	0.760078i	$0.725160\pi$
$72$	217.617	+	125.641i	0.00494722	+	0.00285628i
$73$	41977.9			0.921962			0.460981	−	0.887410i	$-0.347498\pi$
$73$	41977.9			0.921962			0.460981	+	0.887410i	$0.347498\pi$
$74$	17469.1	+	28360.8i	0.370844	+	0.602059i
$75$	−48801.8			−1.00180
$76$	−10948.5	−	6321.11i	−0.217430	−	0.125533i
$77$	12834.8	+	22230.5i	0.246696	+	0.427290i
$78$	22382.6	+	38767.8i	0.416556	+	0.721497i
$79$	45664.7	−	26364.5i	0.823214	−	0.475283i	−0.0283098	−	0.999599i	$-0.509012\pi$
$79$	45664.7	−	26364.5i	0.823214	−	0.475283i	0.851523	+	0.524317i	$0.175679\pi$
$80$		−	1126.14i		−	0.0196729i
$81$	29993.8	+	51950.8i	0.507948	+	0.879792i
$82$			5373.51i			0.0882518i
$83$	43238.6	−	74891.5i	0.688932	−	1.19327i	−0.283251	−	0.959046i	$-0.591413\pi$
$83$	43238.6	−	74891.5i	0.688932	−	1.19327i	0.972184	−	0.234220i	$-0.0752537\pi$
$84$	−40066.8			−0.619564
$85$	831.210			0.0124785
$86$	−37545.0	+	65029.9i	−0.547402	+	0.948128i
$87$	−84925.4	+	49031.7i	−1.20293	+	0.694511i
$88$		−	10309.0i		−	0.141909i
$89$	−15380.2	−	8879.79i	−0.205820	−	0.118830i	0.393547	−	0.919304i	$-0.371248\pi$
$89$	−15380.2	−	8879.79i	−0.205820	−	0.118830i	−0.599367	+	0.800474i	$0.704581\pi$
$90$	−34.5435	+	59.8311i	−0.000449531	+	0.000778611i
$91$	−98289.8	−	56747.6i	−1.24424	−	0.718364i
$92$	−24487.0	+	14137.6i	−0.301624	+	0.174143i
$93$	−62412.9	+	36034.1i	−0.748285	+	0.432023i
$94$	−6811.81	−	3932.80i	−0.0795139	−	0.0459073i
$95$	1737.91	−	3010.15i	0.0197569	−	0.0342199i
$96$	13935.2	+	8045.51i	0.154325	+	0.0890996i
$97$		−	35931.9i		−	0.387749i	−0.981026	−	0.193874i	$-0.937895\pi$
$97$		−	35931.9i		−	0.387749i	0.981026	−	0.193874i	$-0.0621055\pi$
$98$	29752.5	−	17177.6i	0.312938	−	0.180675i
$99$	−316.220	+	547.709i	−0.00324266	+	0.00561645i
$100$	−49690.4			−0.496904
$101$	99509.6			0.970647			0.485324	−	0.874335i	$-0.338702\pi$
$101$	99509.6			0.970647			0.485324	+	0.874335i	$0.338702\pi$
$102$	−5938.41	+	10285.6i	−0.0565158	+	0.0978883i
$103$		−	43203.6i		−	0.401261i	−0.979667	−	0.200631i	$-0.935701\pi$
$103$		−	43203.6i		−	0.401261i	0.979667	−	0.200631i	$-0.0642991\pi$
$104$	22790.1	+	39473.7i	0.206616	+	0.357869i
$105$		−	11015.9i		−	0.0975092i
$106$	−54777.8	+	31626.0i	−0.473522	+	0.273388i
$107$	66635.6	+	115416.i	0.562661	+	0.974558i	0.997263	+	0.0739351i	$0.0235558\pi$
$107$	66635.6	+	115416.i	0.562661	+	0.974558i	−0.434602	+	0.900623i	$0.643111\pi$
$108$	30054.2	+	52055.4i	0.247940	+	0.429444i
$109$	31144.3	+	17981.2i	0.251080	+	0.144961i	0.620259	−	0.784397i	$-0.287028\pi$
$109$	31144.3	+	17981.2i	0.251080	+	0.144961i	−0.369179	+	0.929358i	$0.620361\pi$
$110$	2834.34			0.0223342
$111$	−3725.32	−	130801.i	−0.0286983	−	1.00764i
$112$	−40796.3			−0.307309
$113$	129821.	+	74952.0i	0.956418	+	0.552188i	0.895069	−	0.445928i	$-0.147126\pi$
$113$	129821.	+	74952.0i	0.956418	+	0.552188i	0.0613495	+	0.998116i	$0.480460\pi$
$114$	24832.3	+	43010.8i	0.178960	+	0.309967i
$115$	−3886.95	−	6732.39i	−0.0274072	−	0.0474706i
$116$	−86471.7	+	49924.5i	−0.596663	+	0.344484i
$117$		−	2796.27i		−	0.0188849i
$118$	−6037.92	−	10458.0i	−0.0399193	−	0.0691422i
$119$		−	30111.9i		−	0.194926i
$120$	−2212.01	+	3831.32i	−0.0140228	+	0.0242882i
$121$	−135105.			−0.838894
$122$	22870.4			0.139115
$123$	10554.8	−	18281.5i	0.0629056	−	0.108956i
$124$	−63549.3	+	36690.2i	−0.371156	+	0.214287i
$125$		−	27408.6i		−	0.156896i
$126$	2167.47	+	1251.39i	0.0121626	+	0.00702209i
$127$	−13861.1	+	24008.1i	−0.0762586	+	0.132084i	−0.901633	−	0.432502i	$-0.857631\pi$
$127$	−13861.1	+	24008.1i	−0.0762586	+	0.132084i	0.825374	+	0.564586i	$0.190964\pi$
$128$	14189.0	+	8192.00i	0.0765466	+	0.0441942i
$129$	255468.	−	147495.i	1.35165	−	0.780373i
$130$	−10852.8	+	6265.86i	−0.0563227	+	0.0325179i
$131$	−18406.7	−	10627.1i	−0.0937127	−	0.0541051i	0.452411	−	0.891809i	$-0.350564\pi$
$131$	−18406.7	−	10627.1i	−0.0937127	−	0.0541051i	−0.546124	+	0.837704i	$0.683897\pi$
$132$	−20249.3	+	35072.9i	−0.101152	+	0.175201i
$133$	−109047.	−	62958.5i	−0.534547	−	0.308621i
$134$		−	138860.i		−	0.668061i
$135$	−14312.0	+	8263.04i	−0.0675874	+	0.0390216i
$136$	−6046.54	+	10472.9i	−0.0280324	+	0.0485535i
$137$	303688.			1.38237			0.691187	−	0.722676i	$-0.257088\pi$
$137$	303688.			1.38237			0.691187	+	0.722676i	$0.257088\pi$
$138$	111078.			0.496513
$139$	−103517.	+	179297.i	−0.454439	+	0.787111i	−0.998656	−	0.0518335i	$-0.983493\pi$
$139$	−103517.	+	179297.i	−0.454439	+	0.787111i	0.544217	+	0.838944i	$0.316827\pi$
$140$		−	11216.4i		−	0.0483654i
$141$	15449.9	+	26760.0i	0.0654452	+	0.113354i
$142$		−	113269.i		−	0.471402i
$143$	−99349.3	+	57359.3i	−0.406279	+	0.234565i
$144$	−502.565	−	870.467i	−0.00201969	−	0.00349821i
$145$	−13726.1	−	23774.3i	−0.0542160	−	0.0939049i
$146$	−145416.	−	83955.7i	−0.564584	−	0.325963i
$147$	−134964.			−0.515138
$148$	−3793.15	−	133183.i	−0.0142346	−	0.499797i
$149$	371975.			1.37261			0.686306	−	0.727312i	$-0.259231\pi$
$149$	371975.			1.37261			0.686306	+	0.727312i	$0.259231\pi$
$150$	169054.	+	97603.6i	0.613477	+	0.354191i
$151$	−112331.	−	194563.i	−0.400920	−	0.694414i	0.592917	−	0.805263i	$-0.297976\pi$
$151$	−112331.	−	194563.i	−0.400920	−	0.694414i	−0.993837	+	0.110850i	$0.964643\pi$
$152$	25284.4	+	43794.0i	0.0887656	+	0.153746i
$153$	642.494	−	370.944i	0.00221892	−	0.00128109i
$154$		−	102678.i		−	0.348880i
$155$	−10087.5	−	17472.1i	−0.0337253	−	0.0584139i
$156$		−	179061.i		−	0.589100i
$157$	276775.	−	479388.i	0.896143	−	1.55216i	0.0637584	−	0.997965i	$-0.479691\pi$
$157$	276775.	−	479388.i	0.896143	−	1.55216i	0.832384	−	0.554199i	$-0.186975\pi$
$158$	−210916.			−0.672151
$159$	248484.			0.779480
$160$	−2252.29	+	3901.08i	−0.00695543	+	0.0120472i
$161$	−243891.	+	140811.i	−0.741535	+	0.428126i
$162$		−	239951.i		−	0.718347i
$163$	−409499.	−	236424.i	−1.20721	−	0.696984i	−0.245063	−	0.969507i	$-0.578809\pi$
$163$	−409499.	−	236424.i	−1.20721	−	0.696984i	−0.962149	+	0.272523i	$0.912142\pi$
$164$	10747.0	−	18614.4i	0.0312017	−	0.0540430i
$165$	−9642.86	−	5567.31i	−0.0275738	−	0.0159197i
$166$	−299566.	+	172954.i	−0.843766	+	0.487149i
$167$	−431878.	+	249345.i	−1.19831	+	0.691846i	−0.960179	−	0.279386i	$-0.909869\pi$
$167$	−431878.	+	249345.i	−1.19831	+	0.691846i	−0.238134	+	0.971232i	$0.576536\pi$
$168$	138795.	+	80133.6i	0.379404	+	0.219049i
$169$	67961.8	−	117713.i	0.183041	−	0.317036i
$170$	−2879.40	−	1662.42i	−0.00764151	−	0.00441183i
$171$		−	3102.31i		−	0.00811326i
$172$	260120.	−	150180.i	0.670428	−	0.387072i
$173$	136319.	−	236111.i	0.346290	−	0.599792i	−0.639297	−	0.768960i	$-0.720775\pi$
$173$	136319.	−	236111.i	0.346290	−	0.599792i	0.985587	+	0.169168i	$0.0541079\pi$
$174$	392254.			0.982186
$175$	−494918.			−1.22163
$176$	−20618.0	+	35711.5i	−0.0501725	+	0.0869013i
$177$			47439.6i			0.113817i
$178$	35519.1	+	61521.0i	0.0840258	+	0.145537i
$179$		−	234132.i		−	0.546171i	−0.961990	−	0.273085i	$-0.911956\pi$
$179$		−	234132.i		−	0.546171i	0.961990	−	0.273085i	$-0.0880442\pi$
$180$	239.324	−	138.174i	0.000550561	−	0.000317867i
$181$	343072.	+	594218.i	0.778375	+	1.34819i	0.932878	+	0.360193i	$0.117289\pi$
$181$	343072.	+	594218.i	0.778375	+	1.34819i	−0.154503	+	0.987992i	$0.549377\pi$
$182$	226991.	+	393159.i	0.507960	+	0.879812i
$183$	−77808.6	−	44922.8i	−0.171751	−	0.0991606i
$184$	113101.			0.246275
$185$	36617.0	−	1042.88i	0.0786598	−	0.00224030i
$186$	288273.			0.610972
$187$	−26358.8	−	15218.2i	−0.0551215	−	0.0318244i
$188$	15731.2	+	27247.2i	0.0324614	+	0.0562248i
$189$	299341.	+	518474.i	0.609554	+	1.05578i
$190$	−12040.6	+	6951.65i	−0.0241972	+	0.0139702i
$191$			831529.i			1.64928i	0.565658	+	0.824640i	$0.308622\pi$
$191$			831529.i			1.64928i	−0.565658	+	0.824640i	$0.691378\pi$
$192$	−32182.0	−	55740.9i	−0.0630029	−	0.109124i
$193$		−	160574.i		−	0.310299i	−0.987891	−	0.155150i	$-0.950414\pi$
$193$		−	160574.i		−	0.310299i	0.987891	−	0.155150i	$-0.0495860\pi$
$194$	−71863.8	+	124472.i	−0.137090	+	0.237447i
$195$	49230.5			0.0927146
$196$	−137421.			−0.255513
$197$	244246.	−	423046.i	0.448396	−	0.776644i	−0.549886	−	0.835240i	$-0.685329\pi$
$197$	244246.	−	423046.i	0.448396	−	0.776644i	0.998282	+	0.0585953i	$0.0186622\pi$
$198$	2190.84	−	1264.88i	0.00397143	−	0.00229291i
$199$		−	381186.i		−	0.682345i	−0.940001	−	0.341173i	$-0.889176\pi$
$199$		−	381186.i		−	0.682345i	0.940001	−	0.341173i	$-0.110824\pi$
$200$	172133.	+	99380.8i	0.304290	+	0.175682i
$201$	−272754.	+	472424.i	−0.476191	+	0.824787i
$202$	−344711.	−	199019.i	−0.594398	−	0.343176i
$203$	−861262.	+	497250.i	−1.46688	+	0.846904i
$204$	41142.5	−	23753.7i	0.0692175	−	0.0399627i
$205$	5117.80	+	2954.76i	0.00850547	+	0.00491064i
$206$	−86407.2	+	149662.i	−0.141867	+	0.245721i
$207$	−6008.93	−	3469.26i	−0.00974701	−	0.00562744i
$208$		−	182321.i		−	0.292199i
$209$	−110223.	+	63637.2i	−0.174544	+	0.100773i
$210$	−22031.7	+	38160.1i	−0.0344747	+	0.0597119i
$211$	−607592.			−0.939519			−0.469760	−	0.882794i	$-0.655659\pi$
$211$	−607592.			−0.939519			−0.469760	+	0.882794i	$0.655659\pi$
$212$	253008.			0.386629
$213$	−222488.	+	385360.i	−0.336014	+	0.581993i
$214$		−	533085.i		−	0.795723i
$215$	41290.2	+	71516.7i	0.0609187	+	0.105514i
$216$		−	240434.i		−	0.350640i
$217$	−632954.	+	365436.i	−0.912479	+	0.526820i
$218$	−71924.7	−	124577.i	−0.102503	−	0.177541i
$219$	329818.	+	571261.i	0.464690	+	0.804867i
$220$	−9818.43	−	5668.67i	−0.0136768	−	0.00789632i
$221$	134572.			0.185342
$222$	−248698.	+	460559.i	−0.338680	+	0.627196i
$223$	−428540.			−0.577071			−0.288536	−	0.957469i	$-0.593168\pi$
$223$	−428540.			−0.577071			−0.288536	+	0.957469i	$0.593168\pi$
$224$	141323.	+	81592.6i	0.188188	+	0.108650i
$225$	−6096.83	−	10560.0i	−0.00802875	−	0.0139062i
$226$	−299808.	−	519283.i	−0.390456	−	0.676290i
$227$	1.10771e6	−	639535.i	1.42679	−	0.823758i	0.429924	−	0.902865i	$-0.358540\pi$
$227$	1.10771e6	−	639535.i	1.42679	−	0.823758i	0.996866	+	0.0791071i	$0.0252069\pi$
$228$		−	198659.i		−	0.253087i
$229$	621091.	+	1.07576e6i	0.782649	+	1.35559i	0.930394	+	0.366562i	$0.119465\pi$
$229$	621091.	+	1.07576e6i	0.782649	+	1.35559i	−0.147745	+	0.989025i	$0.547202\pi$
$230$			31095.6i			0.0387596i
$231$	−201684.	+	349327.i	−0.248681	+	0.430728i
$232$	399396.			0.487173
$233$	−1.39263e6			−1.68052			−0.840262	−	0.542180i	$-0.817599\pi$
$233$	−1.39263e6			−1.68052			−0.840262	+	0.542180i	$0.817599\pi$
$234$	−5592.53	+	9686.55i	−0.00667681	+	0.0115646i
$235$	−7491.29	+	4325.10i	−0.00884885	+	0.00510889i
$236$			48303.4i			0.0564544i
$237$	717569.	+	414289.i	0.829838	+	0.479107i
$238$	−60223.8	+	104311.i	−0.0689169	+	0.119367i
$239$	710835.	+	410401.i	0.804960	+	0.464744i	0.845203	−	0.534446i	$-0.179480\pi$
$239$	710835.	+	410401.i	0.804960	+	0.464744i	−0.0402427	+	0.999190i	$0.512813\pi$
$240$	15325.3	−	8848.05i	0.0171743	−	0.00991562i
$241$	−161269.	+	93108.8i	−0.178858	+	0.103264i	−0.586756	−	0.809764i	$-0.699595\pi$
$241$	−161269.	+	93108.8i	−0.178858	+	0.103264i	0.407898	+	0.913028i	$0.366262\pi$
$242$	468017.	+	270209.i	0.513716	+	0.296594i
$243$	−14871.3	+	25757.9i	−0.0161560	+	0.0279830i
$244$	−79225.3	−	45740.7i	−0.0851901	−	0.0491845i
$245$		−	37782.2i		−	0.0402135i
$246$	−73126.1	+	42219.4i	−0.0770433	+	0.0444810i
$247$	281365.	−	487339.i	0.293446	−	0.508263i
$248$	293522.			0.303048
$249$	1.35889e6			1.38895
$250$	−54817.3	+	94946.3i	−0.0554712	+	0.0960789i
$251$		−	1.46261e6i		−	1.46536i	−0.680574	−	0.732679i	$-0.738270\pi$
$251$		−	1.46261e6i		−	1.46536i	0.680574	−	0.732679i	$-0.261730\pi$
$252$	−5005.56	−	8669.89i	−0.00496537	−	0.00860027i
$253$			284657.i			0.279590i
$254$	96032.6	−	55444.4i	0.0933973	−	0.0539229i
$255$	6530.77	+	11311.6i	0.00628947	+	0.0108937i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−349824.	−	201971.i	−0.330382	−	0.190746i	0.325629	−	0.945498i	$-0.394424\pi$
$257$	−349824.	−	201971.i	−0.330382	−	0.190746i	−0.656011	+	0.754752i	$0.727757\pi$
$258$	−1.17996e6			−1.10361
$259$	−37780.0	−	1.32651e6i	−0.0349955	−	1.22874i
$260$	50126.9			0.0459873
$261$	−21219.5	−	12251.1i	−0.0192812	−	0.0111320i
$262$	42508.5	+	73626.9i	0.0382581	+	0.0662649i
$263$	−592037.	−	1.02544e6i	−0.527788	−	0.914155i	−0.999475	−	0.0323893i	$-0.989688\pi$
$263$	−592037.	−	1.02544e6i	−0.527788	−	0.914155i	0.471688	−	0.881766i	$-0.343645\pi$
$264$	140292.	−	80997.4i	0.123886	−	0.0715256i
$265$			69561.4i			0.0608490i
$266$	251834.	+	436189.i	0.218228	+	0.377982i
$267$		−	279072.i		−	0.239573i
$268$	−277720.	+	481026.i	−0.236195	+	0.409102i
$269$	1.83711e6			1.54794			0.773969	−	0.633224i	$-0.218269\pi$
$269$	1.83711e6			1.54794			0.773969	+	0.633224i	$0.218269\pi$
$270$	66104.3			0.0551849
$271$	553843.	−	959284.i	0.458103	−	0.793458i	−0.540757	−	0.841179i	$-0.681862\pi$
$271$	553843.	−	959284.i	0.458103	−	0.793458i	0.998861	+	0.0477202i	$0.0151956\pi$
$272$	41891.6	−	24186.2i	0.0343325	−	0.0198219i
$273$		−	1.78345e6i		−	1.44829i
$274$	−1.05200e6	−	607375.i	−0.846528	−	0.488743i
$275$	−250127.	+	433232.i	−0.199447	+	0.345453i
$276$	−384786.	−	222156.i	−0.304051	−	0.175544i
$277$	−690025.	+	398386.i	−0.540338	+	0.311964i	−0.745216	−	0.666823i	$-0.767654\pi$
$277$	−690025.	+	398386.i	−0.540338	+	0.311964i	0.204878	+	0.978788i	$0.434320\pi$
$278$	717188.	−	414069.i	0.556571	−	0.321337i
$279$	−15594.6	−	9003.52i	−0.0119940	−	0.00692471i
$280$	−22432.9	+	38854.9i	−0.0170998	+	0.0296177i
$281$	−1.91126e6	−	1.10346e6i	−1.44395	−	0.833667i	−0.445843	−	0.895111i	$-0.647096\pi$
$281$	−1.91126e6	−	1.10346e6i	−1.44395	−	0.833667i	−0.998110	+	0.0614445i	$0.980429\pi$
$282$		−	123599.i		−	0.0925535i
$283$	633863.	−	365961.i	0.470467	−	0.271624i	−0.245968	−	0.969278i	$-0.579106\pi$
$283$	633863.	−	365961.i	0.470467	−	0.271624i	0.716435	+	0.697654i	$0.245772\pi$
$284$	−226539.	+	392377.i	−0.166666	+	0.288674i
$285$	54618.7			0.0398317
$286$	458875.			0.331726
$287$	107041.	−	185400.i	0.0767087	−	0.132863i
$288$			4020.52i			0.00285628i
$289$	−692077.	−	1.19871e6i	−0.487427	−	0.844248i
$290$			109809.i			0.0766730i
$291$	488984.	−	282315.i	0.338502	−	0.195434i
$292$	335823.	+	581662.i	0.230491	+	0.399221i
$293$	147776.	+	255956.i	0.100562	+	0.174179i	0.911916	−	0.410376i	$-0.134602\pi$
$293$	147776.	+	255956.i	0.100562	+	0.174179i	−0.811354	+	0.584555i	$0.801269\pi$
$294$	467528.	+	269927.i	0.315456	+	0.182129i
$295$	−13280.4			−0.00888498
$296$	−253226.	+	468945.i	−0.167988	+	0.311095i
$297$	605136.			0.398072
$298$	−1.28856e6	−	743950.i	−0.840550	−	0.485292i
$299$	−629291.	−	1.08996e6i	−0.407074	−	0.705073i
$300$	−390415.	−	676218.i	−0.250451	−	0.433794i
$301$	2.59080e6	−	1.49580e6i	1.64823	−	0.951607i
$302$			898649.i			0.566987i
$303$	781841.	+	1.35419e6i	0.489229	+	0.847369i
$304$		−	202276.i		−	0.125533i
$305$	12575.8	−	21782.0i	0.00774083	−	0.0134075i
$306$	−2967.55			−0.00181174
$307$	−2.10418e6			−1.27420			−0.637099	−	0.770782i	$-0.719866\pi$
$307$	−2.10418e6			−1.27420			−0.637099	+	0.770782i	$0.719866\pi$
$308$	−205356.	+	355688.i	−0.123348	+	0.213645i
$309$	587942.	−	339448.i	0.350298	−	0.202245i
$310$			80700.2i			0.0476947i
$311$	697577.	+	402747.i	0.408970	+	0.236119i	0.690347	−	0.723478i	$-0.257458\pi$
$311$	697577.	+	402747.i	0.408970	+	0.236119i	−0.281377	+	0.959597i	$0.590791\pi$
$312$	−358122.	+	620285.i	−0.208278	+	0.360749i
$313$	−261736.	−	151114.i	−0.151009	−	0.0871852i	0.422591	−	0.906320i	$-0.361121\pi$
$313$	−261736.	−	151114.i	−0.151009	−	0.0871852i	−0.573601	+	0.819135i	$0.694454\pi$
$314$	−1.91755e6	+	1.10710e6i	−1.09755	+	0.633668i
$315$	2383.68	−	1376.22i	0.00135354	−	0.000781467i
$316$	730635.	+	421832.i	0.411607	+	0.237641i
$317$	−219938.	+	380944.i	−0.122929	+	0.212919i	−0.920921	−	0.389748i	$-0.872562\pi$
$317$	−219938.	+	380944.i	−0.122929	+	0.212919i	0.797993	+	0.602667i	$0.205895\pi$
$318$	−860773.	−	496967.i	−0.477332	−	0.275588i
$319$			1.00522e6i			0.553075i
$320$	15604.3	−	9009.16i	0.00851863	−	0.00491823i
$321$	−1.04710e6	+	1.81364e6i	−0.567189	+	0.982399i
$322$	1.12649e6			0.605461
$323$	149300.			0.0796258
$324$	−479901.	+	831214.i	−0.253974	+	0.439896i
$325$		−	2.21182e6i		−	1.16156i
$326$	945697.	+	1.63800e6i	0.492842	+	0.853628i
$327$			565108.i			0.292255i
$328$	−74457.6	+	42988.1i	−0.0382142	+	0.0220630i
$329$	156683.	+	271384.i	0.0798056	+	0.138227i
$330$	22269.2	+	38571.4i	0.0112569	+	0.0194976i
$331$	1.93653e6	+	1.11806e6i	0.971527	+	0.560911i	0.899701	−	0.436506i	$-0.143784\pi$
$331$	1.93653e6	+	1.11806e6i	0.971527	+	0.560911i	0.0718253	+	0.997417i	$0.477118\pi$
$332$	1.38364e6			0.688932
$333$	27838.1	−	17147.2i	0.0137572	−	0.00847387i
$334$	1.99476e6			0.978418
$335$	−132252.	−	76355.8i	−0.0643859	−	0.0371732i
$336$	−320534.	−	555182.i	−0.154891	−	0.268279i
$337$	1.27064e6	+	2.20081e6i	0.609464	+	1.05562i	0.991329	+	0.131404i	$0.0419487\pi$
$337$	1.27064e6	+	2.20081e6i	0.609464	+	1.05562i	−0.381865	+	0.924218i	$0.624718\pi$
$338$	−470853.	+	271847.i	−0.224179	+	0.129430i
$339$			2.35558e6i			1.11326i
$340$	6649.68	+	11517.6i	0.00311963	+	0.00540336i
$341$			738750.i			0.344042i
$342$	−6204.62	+	10746.7i	−0.00286847	+	0.00496833i
$343$	1.30966e6			0.601066
$344$	−1.20144e6			−0.547402
$345$	61079.1	−	105792.i	0.0276277	−	0.0478526i
$346$	−944444.	+	545275.i	−0.424117	+	0.244864i
$347$			55547.5i			0.0247651i	0.999923	+	0.0123826i	$0.00394159\pi$
$347$			55547.5i			0.0247651i	−0.999923	+	0.0123826i	$0.996058\pi$
$348$	−1.35881e6	−	784507.i	−0.601464	−	0.347255i
$349$	−1.60339e6	+	2.77715e6i	−0.704653	+	1.22049i	0.262164	+	0.965023i	$0.415564\pi$
$349$	−1.60339e6	+	2.77715e6i	−0.704653	+	1.22049i	−0.966817	+	0.255471i	$0.917769\pi$
$350$	1.71445e6	+	989836.i	0.748090	+	0.431910i
$351$	−2.31709e6	+	1.33777e6i	−1.00386	+	0.579581i
$352$	142846.	−	82472.2i	0.0614485	−	0.0354773i
$353$	297879.	+	171980.i	0.127234	+	0.0734585i	0.562266	−	0.826956i	$-0.309930\pi$
$353$	297879.	+	171980.i	0.127234	+	0.0734585i	−0.435032	+	0.900415i	$0.643263\pi$
$354$	94879.2	−	164336.i	0.0402405	−	0.0696985i
$355$	−107879.	−	62284.0i	−0.0454325	−	0.0262304i
$356$		−	284153.i		−	0.118830i
$357$	409781.	−	236587.i	0.170169	−	0.0982474i
$358$	−468264.	+	811058.i	−0.193101	+	0.334460i
$359$	−1.00073e6			−0.409807			−0.204904	−	0.978782i	$-0.565688\pi$
$359$	−1.00073e6			−0.409807			−0.204904	+	0.978782i	$0.565688\pi$
$360$	−1105.39			−0.000449531
$361$	−925890.	+	1.60369e6i	−0.373931	+	0.647667i
$362$		−	2.74458e6i		−	1.10079i
$363$	−1.06151e6	−	1.83859e6i	−0.422822	−	0.732349i
$364$		−	1.81592e6i		−	0.718364i
$365$	−159921.	+	92330.3i	−0.0628308	+	0.0362754i
$366$	179691.	+	311234.i	0.0701171	+	0.121446i
$367$	1.93841e6	+	3.35743e6i	0.751243	+	1.30119i	0.947220	+	0.320583i	$0.103879\pi$
$367$	1.93841e6	+	3.35743e6i	0.751243	+	1.30119i	−0.195977	+	0.980608i	$0.562788\pi$
$368$	−391792.	−	226201.i	−0.150812	−	0.0870713i
$369$	5274.49			0.00201658
$370$	−128931.	−	69621.3i	−0.0489612	−	0.0264386i
$371$	2.51997e6			0.950518
$372$	−998607.	−	576546.i	−0.374143	−	0.216011i
$373$	−1.77495e6	−	3.07430e6i	−0.660562	−	1.14413i	−0.980468	−	0.196677i	$-0.936985\pi$
$373$	−1.77495e6	−	3.07430e6i	−0.660562	−	1.14413i	0.319907	−	0.947449i	$-0.396348\pi$
$374$	60872.9	+	105435.i	0.0225032	+	0.0389768i
$375$	372994.	−	215348.i	0.136969	−	0.0790793i
$376$		−	125850.i		−	0.0459073i
$377$	−2.22224e6	−	3.84903e6i	−0.805261	−	1.39475i
$378$		−	2.39473e6i		−	0.862039i
$379$	−1.45372e6	+	2.51792e6i	−0.519856	+	0.900417i	0.479878	+	0.877335i	$0.340681\pi$
$379$	−1.45372e6	+	2.51792e6i	−0.519856	+	0.900417i	−0.999734	+	0.0230814i	$0.992652\pi$
$380$	55613.2			0.0197569
$381$	−435624.			−0.153744
$382$	1.66306e6	−	2.88050e6i	0.583108	−	1.00997i
$383$	−501677.	+	289643.i	−0.174754	+	0.100894i	−0.584826	−	0.811159i	$-0.698837\pi$
$383$	−501677.	+	289643.i	−0.174754	+	0.100894i	0.410072	+	0.912053i	$0.365504\pi$
$384$			257456.i			0.0890996i
$385$	−97792.0	−	56460.2i	−0.0336242	−	0.0194129i
$386$	−321147.	+	556243.i	−0.109707	+	0.190019i
$387$	63831.5	+	36853.1i	0.0216650	+	0.0125083i
$388$	497887.	−	287455.i	0.167900	−	0.0969372i
$389$	−1.95739e6	+	1.13010e6i	−0.655847	+	0.378653i	−0.790693	−	0.612213i	$-0.790279\pi$
$389$	−1.95739e6	+	1.13010e6i	−0.655847	+	0.378653i	0.134846	+	0.990867i	$0.456946\pi$
$390$	−170540.	−	98461.1i	−0.0567759	−	0.0327796i
$391$	166960.	−	289183.i	0.0552293	−	0.0956600i
$392$	476040.	+	274842.i	0.156469	+	0.0903375i
$393$		−	333987.i		−	0.109081i
$394$	−1.69218e6	+	976983.i	−0.549171	+	0.317064i
$395$	−115978.	+	200879.i	−0.0374008	+	0.0647801i
$396$	−10119.0			−0.00324266
$397$	−1.86682e6			−0.594465			−0.297233	−	0.954805i	$-0.596064\pi$
$397$	−1.86682e6			−0.594465			−0.297233	+	0.954805i	$0.596064\pi$
$398$	−762372.	+	1.32047e6i	−0.241245	+	0.417849i
$399$		−	1.97865e6i		−	0.622209i
$400$	−397523.	−	688530.i	−0.124226	−	0.215166i
$401$		−	889578.i		−	0.276263i	−0.990414	−	0.138132i	$-0.955890\pi$
$401$		−	889578.i		−	0.276263i	0.990414	−	0.138132i	$-0.0441097\pi$
$402$	1.88970e6	−	1.09102e6i	0.583213	−	0.336718i
$403$	−1.63315e6	−	2.82871e6i	−0.500916	−	0.867611i
$404$	796077.	+	1.37885e6i	0.242662	+	0.420303i
$405$	−228532.	−	131943.i	−0.0692324	−	0.0399713i
$406$	3.97800e6			1.19770
$407$	−1.18026e6	−	637331.i	−0.353178	−	0.190713i
$408$	−190029.			−0.0565158
$409$	3.54221e6	+	2.04510e6i	1.04705	+	0.604513i	0.921821	−	0.387615i	$-0.126701\pi$
$409$	3.54221e6	+	2.04510e6i	1.04705	+	0.604513i	0.125226	+	0.992128i	$0.460034\pi$
$410$	−11819.0	−	20471.2i	−0.00347234	−	0.00601428i
$411$	2.38606e6	+	4.13277e6i	0.696749	+	1.20680i
$412$	598647.	−	345629.i	0.173751	−	0.100315i
$413$			481104.i			0.138792i
$414$	13877.0	+	24035.7i	0.00397920	+	0.00689218i
$415$			380414.i			0.108427i
$416$	−364642.	+	631579.i	−0.103308	+	0.178934i
$417$	−3.25331e6			−0.916191
$418$	509097.			0.142515
$419$	1.80168e6	−	3.12060e6i	0.501351	−	0.868366i	−0.498647	−	0.866805i	$-0.666170\pi$
$419$	1.80168e6	−	3.12060e6i	0.501351	−	0.868366i	0.999999	−	0.00156111i	$-0.000496918\pi$
$420$	152640.	−	88127.0i	0.0422227	−	0.0243773i
$421$			380552.i			0.104643i	0.998630	+	0.0523214i	$0.0166620\pi$
$421$			380552.i			0.104643i	−0.998630	+	0.0523214i	$0.983338\pi$
$422$	2.10476e6	+	1.21518e6i	0.575336	+	0.332170i
$423$	−3860.32	+	6686.28i	−0.00104899	+	0.00181691i
$424$	−876445.	−	506016.i	−0.236761	−	0.136694i
$425$	508206.	−	293413.i	0.136480	−	0.0787965i
$426$	1.54144e6	−	889951.i	0.411531	−	0.237598i
$427$	−789087.	−	455579.i	−0.209438	−	0.120919i
$428$	−1.06617e6	+	1.84666e6i	−0.281331	+	0.487279i
$429$	−1.56116e6	−	901338.i	−0.409548	−	0.236453i
$430$		−	330321.i		−	0.0861521i
$431$	3.68768e6	−	2.12908e6i	0.956225	−	0.552077i	0.0612159	−	0.998125i	$-0.480502\pi$
$431$	3.68768e6	−	2.12908e6i	0.956225	−	0.552077i	0.895009	+	0.446048i	$0.147169\pi$
$432$	−480868.	+	832887.i	−0.123970	+	0.214722i
$433$	1.76439e6			0.452247			0.226124	−	0.974099i	$-0.427395\pi$
$433$	1.76439e6			0.452247			0.226124	+	0.974099i	$0.427395\pi$
$434$	2.92349e6			0.745036
$435$	215691.	−	373587.i	0.0546523	−	0.0946605i
$436$			575398.i			0.144961i
$437$	−698165.	−	1.20926e6i	−0.174886	−	0.302911i
$438$		−	2.63854e6i		−	0.657171i
$439$	783580.	−	452400.i	0.194054	−	0.112037i	−0.399825	−	0.916591i	$-0.630929\pi$
$439$	783580.	−	452400.i	0.194054	−	0.112037i	0.593879	+	0.804554i	$0.297596\pi$
$440$	22674.7	+	39273.7i	0.00558354	+	0.00967098i
$441$	−16861.1	−	29204.2i	−0.00412846	−	0.00715071i
$442$	−466170.	−	269143.i	−0.113498	−	0.0655281i
$443$	−931147.			−0.225429			−0.112714	−	0.993627i	$-0.535954\pi$
$443$	−931147.			−0.225429			−0.112714	+	0.993627i	$0.535954\pi$
$444$	1.78263e6	−	1.09803e6i	0.429145	−	0.264336i
$445$	78124.4			0.0187019
$446$	1.48451e6	+	857081.i	0.353383	+	0.204026i
$447$	2.92259e6	+	5.06207e6i	0.691829	+	1.19828i
$448$	−326371.	−	565290.i	−0.0768274	−	0.133069i
$449$	3.43626e6	−	1.98393e6i	0.804396	−	0.464418i	−0.0406098	−	0.999175i	$-0.512930\pi$
$449$	3.43626e6	−	1.98393e6i	0.804396	−	0.464418i	0.845006	+	0.534757i	$0.179597\pi$
$450$			48774.7i			0.0113544i
$451$	−108195.	−	187399.i	−0.0250475	−	0.0433835i
$452$			2.39847e6i			0.552188i
$453$	1.76516e6	−	3.05734e6i	0.404146	−	0.700001i
$454$	−5.11628e6			−1.16497
$455$	499266.			0.113059
$456$	−397317.	+	688173.i	−0.0894798	+	0.154984i
$457$	−6.27608e6	+	3.62350e6i	−1.40572	+	0.811591i	−0.994972	−	0.100158i	$-0.968065\pi$
$457$	−6.27608e6	+	3.62350e6i	−1.40572	+	0.811591i	−0.410746	+	0.911750i	$0.634732\pi$
$458$		−	4.96873e6i		−	1.10683i
$459$	−614756.	−	354930.i	−0.136198	−	0.0786340i
$460$	62191.2	−	107718.i	0.0137036	−	0.0237353i
$461$	−5.88436e6	−	3.39733e6i	−1.28958	−	0.744537i	−0.310997	−	0.950411i	$-0.600663\pi$
$461$	−5.88436e6	−	3.39733e6i	−1.28958	−	0.744537i	−0.978578	+	0.205875i	$0.933996\pi$
$462$	1.39731e6	−	806737.i	0.304570	−	0.175844i
$463$	−5.04735e6	+	2.91409e6i	−1.09424	+	0.631757i	−0.934701	−	0.355435i	$-0.884333\pi$
$463$	−5.04735e6	+	2.91409e6i	−1.09424	+	0.631757i	−0.159535	+	0.987192i	$0.550999\pi$
$464$	−1.38355e6	−	798791.i	−0.298331	−	0.172242i
$465$	158514.	−	274555.i	0.0339966	−	0.0588839i
$466$	4.82420e6	+	2.78525e6i	1.02911	+	0.594155i
$467$		−	2.59564e6i		−	0.550747i	−0.961337	−	0.275374i	$-0.911198\pi$
$467$		−	2.59564e6i		−	0.550747i	0.961337	−	0.275374i	$-0.0888016\pi$
$468$	38746.2	−	22370.1i	0.00817739	−	0.00472122i
$469$	−2.76611e6	+	4.79104e6i	−0.580680	+	1.00577i
$470$	34600.8			0.00722506
$471$	8.69841e6			1.80671
$472$	96606.8	−	167328.i	0.0199596	−	0.0345711i
$473$		−	3.02385e6i		−	0.621451i
$474$	−1.65716e6	−	2.87028e6i	−0.338780	−	0.586784i
$475$		−	2.45389e6i		−	0.499024i
$476$	417242.	−	240895.i	0.0844056	−	0.0487316i
$477$	31043.2	+	53768.4i	0.00624698	+	0.0108201i
$478$	−1.64160e6	−	2.84334e6i	−0.328623	−	0.569193i
$479$	5.52922e6	+	3.19230e6i	1.10110	+	0.635718i	0.936509	−	0.350645i	$-0.114037\pi$
$479$	5.52922e6	+	3.19230e6i	1.10110	+	0.635718i	0.164587	+	0.986363i	$0.447371\pi$
$480$	−70784.4			−0.0140228
$481$	5.92823e6	−	168841.i	1.16832	−	0.0332747i
$482$	744870.			0.146037
$483$	−3.83248e6	−	2.21268e6i	−0.747502	−	0.431570i
$484$	−1.08084e6	−	1.87207e6i	−0.209724	−	0.363252i
$485$	79032.2	+	136888.i	0.0152563	+	0.0264247i
$486$	103031.	−	59485.2i	0.0197870	−	0.0114240i
$487$			6.94773e6i			1.32746i	0.747973	+	0.663729i	$0.231027\pi$
$487$			6.94773e6i			1.32746i	−0.747973	+	0.663729i	$0.768973\pi$
$488$	182963.	+	316901.i	0.0347787	+	0.0602385i
$489$		−	7.43029e6i		−	1.40519i
$490$	−75564.4	+	130881.i	−0.0142176	+	0.0246256i
$491$	−4.09343e6			−0.766273			−0.383136	−	0.923692i	$-0.625156\pi$
$491$	−4.09343e6			−0.766273			−0.383136	+	0.923692i	$0.625156\pi$
$492$	337755.			0.0629056
$493$	589590.	−	1.02120e6i	0.109253	−	0.189232i
$494$	−1.94935e6	+	1.12546e6i	−0.359396	+	0.207498i
$495$		−	2782.10i		−	0.000510341i
$496$	−1.01679e6	−	587044.i	−0.185578	−	0.107144i
$497$	−2.25633e6	+	3.90809e6i	−0.409744	+	0.709697i
$498$	−4.70735e6	−	2.71779e6i	−0.850556	−	0.491069i
$499$	3.16649e6	−	1.82817e6i	0.569281	−	0.328675i	−0.187581	−	0.982249i	$-0.560065\pi$
$499$	3.16649e6	−	1.82817e6i	0.569281	−	0.328675i	0.756862	+	0.653574i	$0.226731\pi$
$500$	379785.	−	219269.i	0.0679380	−	0.0392240i
$501$	−6.78649e6	−	3.91818e6i	−1.20795	−	0.697413i
$502$	−2.92522e6	+	5.06663e6i	−0.518082	+	0.897345i
$503$	−6.60140e6	−	3.81132e6i	−1.16336	−	0.671669i	−0.211256	−	0.977431i	$-0.567756\pi$
$503$	−6.60140e6	−	3.81132e6i	−1.16336	−	0.671669i	−0.952108	+	0.305762i	$0.901089\pi$
$504$			40044.5i			0.00702209i
$505$	−379096.	+	218871.i	−0.0661487	+	0.0381910i
$506$	569314.	−	986081.i	0.0988498	−	0.171213i
$507$	2.13589e6			0.369028
$508$	−443555.			−0.0762586
$509$	−1.08030e6	+	1.87113e6i	−0.184820	+	0.320118i	−0.943516	−	0.331327i	$-0.892504\pi$
$509$	−1.08030e6	+	1.87113e6i	−0.184820	+	0.320118i	0.758696	+	0.651445i	$0.225837\pi$
$510$		−	52246.2i		−	0.00889466i
$511$	3.34481e6	+	5.79338e6i	0.566656	+	0.981476i
$512$			262144.i			0.0441942i
$513$	−2.57069e6	+	1.48419e6i	−0.431277	+	0.248998i
$514$	807883.	+	1.39929e6i	0.134878	+	0.233615i
$515$	95026.4	+	164591.i	0.0157880	+	0.0273456i
$516$	4.08749e6	+	2.35991e6i	0.675823	+	0.390186i
$517$	316745.			0.0521174
$518$	−2.52214e6	+	4.67071e6i	−0.412995	+	0.764819i
$519$	4.28419e6			0.698153
$520$	−173645.	−	100254.i	−0.0281613	−	0.0162590i
$521$	4.60089e6	+	7.96898e6i	0.742588	+	1.28620i	0.951313	+	0.308226i	$0.0997353\pi$
$521$	4.60089e6	+	7.96898e6i	0.742588	+	1.28620i	−0.208725	+	0.977974i	$0.566931\pi$
$522$	49004.4	+	84878.2i	0.00787153	+	0.0136339i
$523$	8.80316e6	−	5.08251e6i	1.40729	−	0.812501i	0.412166	−	0.911109i	$-0.364772\pi$
$523$	8.80316e6	−	5.08251e6i	1.40729	−	0.812501i	0.995126	+	0.0986080i	$0.0314390\pi$
$524$		−	340068.i		−	0.0541051i
$525$	−3.88854e6	−	6.73516e6i	−0.615728	−	1.06647i
$526$			4.73629e6i			0.746404i
$527$	433298.	−	750495.i	0.0679611	−	0.117712i
$528$	−647979.			−0.101152
$529$	3.31336e6			0.514789
$530$	139123.	−	240968.i	0.0215134	−	0.0372623i
$531$	−10265.3	+	5926.65i	−0.00157992	+	0.000912164i
$532$		−	2.01467e6i		−	0.308621i
$533$	828563.	+	478371.i	0.126330	+	0.0729369i
$534$	−558144.	+	966734.i	−0.0847019	+	0.146708i
$535$	−507716.	−	293130.i	−0.0766896	−	0.0442768i
$536$	1.92410e6	−	1.11088e6i	0.289279	−	0.167015i
$537$	3.18622e6	−	1.83956e6i	0.476804	−	0.275283i
$538$	−6.36392e6	−	3.67421e6i	−0.947914	−	0.547279i
$539$	−691736.	+	1.19812e6i	−0.102558	+	0.177635i
$540$	−228992.	−	132209.i	−0.0337937	−	0.0195108i
$541$			9.83173e6i			1.44423i	0.691772	+	0.722116i	$0.256830\pi$
$541$			9.83173e6i			1.44423i	−0.691772	+	0.722116i	$0.743170\pi$
$542$	−3.83714e6	+	2.21537e6i	−0.561060	+	0.323928i
$543$	−5.39100e6	+	9.33748e6i	−0.784638	+	1.35903i
$544$	−193489.			−0.0280324
$545$	−158198.			−0.0228145
$546$	−3.56690e6	+	6.17806e6i	−0.512047	+	0.886891i
$547$			19422.9i			0.00277552i	0.999999	+	0.00138776i	$0.000441738\pi$
$547$			19422.9i			0.00277552i	−0.999999	+	0.00138776i	$0.999558\pi$
$548$	2.42950e6	+	4.20802e6i	0.345594	+	0.598586i
$549$		−	22448.9i		−	0.00317881i
$550$	1.73293e6	−	1.00051e6i	0.244272	−	0.141030i
$551$	−2.46545e6	−	4.27029e6i	−0.345954	−	0.599209i
$552$	888625.	+	1.53914e6i	0.124128	+	0.214996i
$553$	7.27715e6	+	4.20146e6i	1.01193	+	0.584235i
$554$	3.18709e6			0.441184
$555$	301890.	+	490113.i	0.0416021	+	0.0675404i
$556$	−3.31255e6			−0.454439
$557$	−9.61094e6	−	5.54888e6i	−1.31259	−	0.757822i	−0.330063	−	0.943959i	$-0.607070\pi$
$557$	−9.61094e6	−	5.54888e6i	−1.31259	−	0.757822i	−0.982524	+	0.186137i	$0.940403\pi$
$558$	36014.1	+	62378.2i	0.00489651	+	0.00848101i
$559$	6.68482e6	+	1.15784e7i	0.904815	+	1.56719i
$560$	155420.	−	89731.5i	0.0209428	−	0.0120914i
$561$		−	478275.i		−	0.0641609i
$562$	4.41386e6	+	7.64503e6i	0.589491	+	1.02103i
$563$		−	1.36121e7i		−	1.80990i	−0.425516	−	0.904951i	$-0.639907\pi$
$563$		−	1.36121e7i		−	1.80990i	0.425516	−	0.904951i	$-0.360093\pi$
$564$	−247198.	+	428160.i	−0.0327226	+	0.0566772i
$565$	−659428.			−0.0869053
$566$	−2.92769e6			−0.384135
$567$	−4.77984e6	+	8.27892e6i	−0.624389	+	1.08147i
$568$	1.56951e6	−	906155.i	0.204123	−	0.117851i
$569$			1.32630e7i			1.71735i	0.512518	+	0.858677i	$0.328713\pi$
$569$			1.32630e7i			1.71735i	−0.512518	+	0.858677i	$0.671287\pi$
$570$	−189205.	−	109237.i	−0.0243919	−	0.0140826i
$571$	6.89767e6	−	1.19471e7i	0.885345	−	1.53346i	0.0400269	−	0.999199i	$-0.487256\pi$
$571$	6.89767e6	−	1.19471e7i	0.885345	−	1.53346i	0.845318	−	0.534264i	$-0.179411\pi$
$572$	−1.58959e6	−	917749.i	−0.203140	−	0.117283i
$573$	−1.13160e7	+	6.53328e6i	−1.43981	+	0.831275i
$574$	−741601.	+	428163.i	−0.0939486	+	0.0542413i
$575$	−4.75300e6	−	2.74415e6i	−0.599512	−	0.346129i
$576$	8041.03	−	13927.5i	0.00100985	−	0.00174911i
$577$	3.20577e6	+	1.85085e6i	0.400860	+	0.231437i	0.686855	−	0.726795i	$-0.258991\pi$
$577$	3.20577e6	+	1.85085e6i	0.400860	+	0.231437i	−0.285995	+	0.958231i	$0.592324\pi$
$578$			5.53661e6i			0.689326i
$579$	2.18519e6	−	1.26162e6i	0.270889	−	0.156398i
$580$	219618.	−	380389.i	0.0271080	−	0.0469524i
$581$	1.37811e7			1.69372
$582$	−2.25852e6			−0.276386
$583$	1.27357e6	−	2.20588e6i	0.155185	−	0.268789i
$584$		−	2.68658e6i		−	0.325963i
$585$	6150.39	+	10652.8i	0.000743042	+	0.00128699i
$586$		−	1.18221e6i		−	0.142217i
$587$	6.05405e6	−	3.49531e6i	0.725188	−	0.418688i	−0.0914712	−	0.995808i	$-0.529157\pi$
$587$	6.05405e6	−	3.49531e6i	0.725188	−	0.418688i	0.816659	+	0.577120i	$0.195824\pi$
$588$	−1.07971e6	−	1.87011e6i	−0.128784	−	0.223061i
$589$	−1.81190e6	−	3.13830e6i	−0.215202	−	0.372740i
$590$	46004.7	+	26560.8i	0.00544092	+	0.00314132i
$591$	7.67610e6			0.904008
$592$	1.81509e6	−	1.11802e6i	0.212860	−	0.131113i
$593$	−1.16797e7			−1.36394			−0.681970	−	0.731380i	$-0.738877\pi$
$593$	−1.16797e7			−1.36394			−0.681970	+	0.731380i	$0.738877\pi$
$594$	−2.09625e6	−	1.21027e6i	−0.243768	−	0.140740i
$595$	66231.1	+	114716.i	0.00766954	+	0.0132840i
$596$	2.97580e6	+	5.15424e6i	0.343153	+	0.594359i
$597$	5.18742e6	−	2.99496e6i	0.595683	−	0.343918i
$598$			5.03433e6i			0.575690i
$599$	−7.23810e6	−	1.25368e7i	−0.824248	−	1.42764i	−0.902493	−	0.430705i	$-0.858265\pi$
$599$	−7.23810e6	−	1.25368e7i	−0.824248	−	1.42764i	0.0782450	−	0.996934i	$-0.475068\pi$
$600$			3.12332e6i			0.354191i
$601$	6.55239e6	−	1.13491e7i	0.739969	−	1.28166i	−0.212539	−	0.977153i	$-0.568173\pi$
$601$	6.55239e6	−	1.13491e7i	0.739969	−	1.28166i	0.952509	−	0.304512i	$-0.0984934\pi$
$602$	−1.19664e7			−1.34578
$603$	−136301.			−0.0152653
$604$	1.79730e6	−	3.11301e6i	0.200460	−	0.347207i
$605$	514701.	−	297163.i	0.0571698	−	0.0330070i
$606$		−	6.25473e6i		−	0.691874i
$607$	1.13383e7	+	6.54618e6i	1.24904	+	0.721134i	0.970918	−	0.239411i	$-0.0769544\pi$
$607$	1.13383e7	+	6.54618e6i	1.24904	+	0.721134i	0.278123	+	0.960546i	$0.410288\pi$
$608$	−404551.	+	700703.i	−0.0443828	+	0.0768732i
$609$	−1.35338e7	−	7.81373e6i	−1.47868	−	0.853719i
$610$	−87128.0	+	50303.4i	−0.00948054	+	0.00547359i
$611$	−1.21283e6	+	700227.i	−0.131431	+	0.0758814i
$612$	10279.9	+	5935.11i	0.00110946	+	0.000640546i
$613$	−4.62941e6	+	8.01837e6i	−0.497593	+	0.861856i	−0.999996	−	0.00277713i	$-0.999116\pi$
$613$	−4.62941e6	+	8.01837e6i	−0.497593	+	0.861856i	0.502403	+	0.864634i	$0.332449\pi$
$614$	7.28910e6	+	4.20836e6i	0.780284	+	0.450497i
$615$			92861.6i			0.00990030i
$616$	1.42275e6	−	821426.i	0.151070	−	0.0872201i
$617$	2.63282e6	−	4.56018e6i	0.278425	−	0.482246i	−0.692569	−	0.721352i	$-0.743521\pi$
$617$	2.63282e6	−	4.56018e6i	0.278425	−	0.482246i	0.970993	+	0.239106i	$0.0768543\pi$
$618$	−2.71559e6			−0.286017
$619$	−2.45785e6			−0.257827			−0.128913	−	0.991656i	$-0.541149\pi$
$619$	−2.45785e6			−0.257827			−0.128913	+	0.991656i	$0.541149\pi$
$620$	161400.	−	279554.i	0.0168626	−	0.0292069i
$621$			6.63896e6i			0.690830i
$622$	−1.61099e6	−	2.79031e6i	−0.166961	−	0.289185i
$623$		−	2.83018e6i		−	0.292142i
$624$	2.48114e6	−	1.43249e6i	0.255088	−	0.147275i
$625$	−4.79229e6	−	8.30049e6i	−0.490731	−	0.849970i
$626$	604454.	+	1.04695e6i	0.0616492	+	0.106780i
$627$	−1.73203e6	−	999988.i	−0.175949	−	0.101584i
$628$	8.85679e6			0.896143
$629$	825215.	+	1.33972e6i	0.0831650	+	0.135017i
$630$	−11009.7			−0.00110516
$631$	−979980.	−	565792.i	−0.0979814	−	0.0565696i	0.450209	−	0.892923i	$-0.351350\pi$
$631$	−979980.	−	565792.i	−0.0979814	−	0.0565696i	−0.548190	+	0.836354i	$0.684683\pi$
$632$	−1.68733e6	−	2.92254e6i	−0.168038	−	0.291050i
$633$	−4.77381e6	−	8.26849e6i	−0.473539	−	0.820194i
$634$	1.52378e6	−	879754.i	0.150556	−	0.0869236i
$635$		−	121950.i		−	0.0120018i
$636$	1.98787e6	+	3.44309e6i	0.194870	+	0.337525i
$637$		−	6.11688e6i		−	0.597285i
$638$	2.01044e6	−	3.48218e6i	0.195542	−	0.338688i
$639$	−111182.			−0.0107716
$640$	−72073.2			−0.00695543
$641$	−2.14623e6	+	3.71738e6i	−0.206315	+	0.357349i	−0.950551	−	0.310568i	$-0.899481\pi$
$641$	−2.14623e6	+	3.71738e6i	−0.206315	+	0.357349i	0.744236	+	0.667917i	$0.232814\pi$
$642$	7.25455e6	−	4.18842e6i	0.694661	−	0.401063i
$643$		−	379129.i		−	0.0361626i	−0.999837	−	0.0180813i	$-0.994244\pi$
$643$		−	379129.i		−	0.0361626i	0.999837	−	0.0180813i	$-0.00575577\pi$
$644$	−3.90226e6	−	2.25297e6i	−0.370768	−	0.214063i
$645$	−648829.	+	1.12381e6i	−0.0614089	+	0.106363i
$646$	−517191.	−	298600.i	−0.0487607	−	0.0281520i
$647$	7.32809e6	−	4.23087e6i	0.688224	−	0.397346i	−0.114722	−	0.993398i	$-0.536598\pi$
$647$	7.32809e6	−	4.23087e6i	0.688224	−	0.397346i	0.802946	+	0.596051i	$0.203264\pi$
$648$	3.32485e6	−	1.91961e6i	0.311054	−	0.179587i
$649$	421139.	+	243145.i	0.0392477	+	0.0226596i
$650$	−4.42363e6	+	7.66196e6i	−0.410673	+	0.711306i
$651$	−9.94617e6	−	5.74242e6i	−0.919821	−	0.531059i
$652$		−	7.56558e6i		−	0.696984i
$653$	1.36463e7	−	7.87871e6i	1.25237	−	0.723057i	0.280791	−	0.959769i	$-0.409403\pi$
$653$	1.36463e7	−	7.87871e6i	1.25237	−	0.723057i	0.971580	+	0.236712i	$0.0760699\pi$
$654$	1.13022e6	−	1.95759e6i	0.103328	−	0.178969i
$655$	93497.6			0.00851524
$656$	343905.			0.0312017
$657$	−82408.5	+	142736.i	−0.00744833	+	0.0129009i
$658$		−	1.25347e6i		−	0.112862i
$659$	−509386.	−	882282.i	−0.0456913	−	0.0791396i	0.842275	−	0.539048i	$-0.181216\pi$
$659$	−509386.	−	882282.i	−0.0456913	−	0.0791396i	−0.887967	+	0.459908i	$0.847882\pi$
$660$		−	178154.i		−	0.0159197i
$661$	9.32074e6	−	5.38133e6i	0.829749	−	0.479056i	−0.0240178	−	0.999712i	$-0.507646\pi$
$661$	9.32074e6	−	5.38133e6i	0.829749	−	0.479056i	0.853767	+	0.520656i	$0.174312\pi$
$662$	−4.47223e6	−	7.74613e6i	−0.396624	−	0.686973i
$663$	1.05732e6	+	1.83134e6i	0.0934165	+	0.161802i
$664$	−4.79306e6	−	2.76727e6i	−0.421883	−	0.243574i
$665$	553909.			0.0485718
$666$	−130728.	+	3723.25i	−0.0114205	+	0.000325265i
$667$	−1.10283e7			−0.959828
$668$	−6.91005e6	−	3.98952e6i	−0.599156	−	0.345923i
$669$	−3.36702e6	−	5.83185e6i	−0.290857	−	0.503780i
$670$	305423.	+	529008.i	0.0262854	+	0.0455277i
$671$	−797593.	+	460490.i	−0.0683872	+	0.0394834i
$672$			2.56428e6i			0.219049i
$673$	5.05818e6	+	8.76102e6i	0.430483	+	0.745619i	0.996915	−	0.0784897i	$-0.0250098\pi$
$673$	5.05818e6	+	8.76102e6i	0.430483	+	0.745619i	−0.566432	+	0.824109i	$0.691676\pi$
$674$		−	1.01651e7i		−	0.861912i
$675$	−5.83362e6	+	1.01041e7i	−0.492809	+	0.853570i
$676$	2.17478e6			0.183041
$677$	1.21728e7			1.02075			0.510375	−	0.859952i	$-0.329507\pi$
$677$	1.21728e7			1.02075			0.510375	+	0.859952i	$0.329507\pi$
$678$	4.71115e6	−	8.15995e6i	0.393598	−	0.681732i
$679$	4.95897e6	−	2.86306e6i	0.412779	−	0.238318i
$680$		−	53197.5i		−	0.00441183i
$681$	1.74064e7	+	1.00496e7i	1.43827	+	0.830386i
$682$	1.47750e6	−	2.55911e6i	0.121637	−	0.210682i
$683$	−1.48872e7	−	8.59514e6i	−1.22113	−	0.705020i	−0.255971	−	0.966684i	$-0.582395\pi$
$683$	−1.48872e7	−	8.59514e6i	−1.22113	−	0.705020i	−0.965159	+	0.261665i	$0.915729\pi$
$684$	42986.9	−	24818.5i	0.00351314	−	0.00202831i
$685$	−1.15694e6	+	667961.i	−0.0942075	+	0.0543907i
$686$	−4.53678e6	−	2.61931e6i	−0.368076	−	0.212509i
$687$	−9.75976e6	+	1.69044e7i	−0.788946	+	1.36649i
$688$	4.16192e6	+	2.40288e6i	0.335214	+	0.193536i
$689$			1.12619e7i			0.903780i
$690$	−423168.	+	244316.i	−0.0338369	+	0.0195357i
$691$	−7.42220e6	+	1.28556e7i	−0.591341	+	1.02423i	0.402711	+	0.915327i	$0.368068\pi$
$691$	−7.42220e6	+	1.28556e7i	−0.591341	+	1.02423i	−0.994052	+	0.108905i	$0.965266\pi$
$692$	4.36220e6			0.346290
$693$	−100786.			−0.00797200
$694$	111095.	−	192422.i	0.00875580	−	0.0151655i
$695$		−	910744.i		−	0.0715211i
$696$	3.13803e6	+	5.43523e6i	0.245547	+	0.425299i
$697$			253837.i			0.0197913i
$698$	1.11086e7	−	6.41355e6i	0.863020	−	0.498265i
$699$	−1.09418e7	−	1.89517e7i	−0.847023	−	1.46709i
$700$	−3.95935e6	−	6.85779e6i	−0.305407	−	0.528980i
$701$	1.31742e7	+	7.60612e6i	1.01258	+	0.584613i	0.911946	−	0.410311i	$-0.134580\pi$
$701$	1.31742e7	+	7.60612e6i	1.01258	+	0.584613i	0.100633	+	0.994924i	$0.467913\pi$
$702$	1.07022e7			0.819652
$703$	6.57706e6	−	187320.i	0.501930	−	0.0142954i
$704$	−659777.			−0.0501725
$705$	−117717.	−	67964.1i	−0.00892005	−	0.00515000i
$706$	−687921.	−	1.19151e6i	−0.0519430	−	0.0899679i
$707$	7.92896e6	+	1.37334e7i	0.596578	+	1.03330i
$708$	−657343.	+	379517.i	−0.0492843	+	0.0284543i
$709$			2.01871e7i			1.50820i	0.656759	+	0.754101i	$0.271927\pi$
$709$			2.01871e7i			1.50820i	−0.656759	+	0.754101i	$0.728073\pi$
$710$	249136.	+	431516.i	0.0185477	+	0.0321256i
$711$			207029.i			0.0153588i
$712$	−568306.	+	984335.i	−0.0420129	+	0.0727684i
$713$	−8.10485e6			−0.597065
$714$	−1.89270e6			−0.138943
$715$	252324.	−	437038.i	0.0184584	−	0.0319708i
$716$	3.24423e6	−	1.87306e6i	0.236499	−	0.136543i
$717$			1.28980e7i			0.936967i
$718$	3.46662e6	+	2.00146e6i	0.250955	+	0.144889i
$719$	−8.21231e6	+	1.42241e7i	−0.592438	+	1.02613i	0.401465	+	0.915874i	$0.368501\pi$
$719$	−8.21231e6	+	1.42241e7i	−0.592438	+	1.02613i	−0.993903	+	0.110258i	$0.964832\pi$
$720$	3829.19	+	2210.78i	0.000275280	+	0.000158933i
$721$	5.96255e6	−	3.44248e6i	0.427163	−	0.246623i
$722$	6.41475e6	−	3.70356e6i	0.457970	−	0.264409i
$723$	−2.53417e6	−	1.46310e6i	−0.180297	−	0.104095i
$724$	−5.48915e6	+	9.50749e6i	−0.389188	+	0.674093i
$725$	−1.67844e7	−	9.69049e6i	−1.18594	−	0.684701i
$726$			8.49208e6i			0.597961i
$727$	−1.08717e7	+	6.27680e6i	−0.762891	+	0.440455i	−0.830333	−	0.557268i	$-0.811850\pi$
$727$	−1.08717e7	+	6.27680e6i	−0.762891	+	0.440455i	0.0674417	+	0.997723i	$0.478516\pi$
$728$	−3.63185e6	+	6.29055e6i	−0.253980	+	0.439906i
$729$	1.41096e7			0.983325
$730$	738643.			0.0513012
$731$	−1.77357e6	+	3.07192e6i	−0.122760	+	0.212626i
$732$		−	1.43753e6i		−	0.0991606i
$733$	−1.42863e7	−	2.47446e7i	−0.982109	−	1.70106i	−0.654140	−	0.756374i	$-0.726969\pi$
$733$	−1.42863e7	−	2.47446e7i	−0.982109	−	1.70106i	−0.327969	−	0.944688i	$-0.606364\pi$
$734$		−	1.55073e7i		−	1.06242i
$735$	514164.	−	296853.i	0.0351061	−	0.0202685i
$736$	904804.	+	1.56717e6i	0.0615687	+	0.106640i
$737$	2.79592e6	+	4.84268e6i	0.189608	+	0.328411i
$738$	−18271.4	−	10549.0i	−0.00123489	−	0.000712967i
$739$	−2.31350e7			−1.55833			−0.779163	−	0.626822i	$-0.784355\pi$
$739$	−2.31350e7			−1.55833			−0.779163	+	0.626822i	$0.784355\pi$
$740$	307386.	+	499037.i	0.0206350	+	0.0335006i
$741$	8.84268e6			0.591614
$742$	−8.72943e6	−	5.03994e6i	−0.582071	−	0.336059i
$743$	1.37734e6	+	2.38562e6i	0.0915313	+	0.158537i	0.908156	−	0.418633i	$-0.137491\pi$
$743$	1.37734e6	+	2.38562e6i	0.0915313	+	0.158537i	−0.816624	+	0.577169i	$0.804157\pi$
$744$	2.30618e6	+	3.99443e6i	0.152743	+	0.264559i
$745$	−1.41709e6	+	818159.i	−0.0935423	+	0.0540066i
$746$			1.41996e7i			0.934175i
$747$	169767.	+	294045.i	0.0111315	+	0.0192803i
$748$		−	486983.i		−	0.0318244i
$749$	−1.06191e7	+	1.83928e7i	−0.691644	+	1.19796i
$750$	−1.72278e6			−0.111835
$751$	−1.22306e7			−0.791312			−0.395656	−	0.918399i	$-0.629483\pi$
$751$	−1.22306e7			−0.791312			−0.395656	+	0.918399i	$0.629483\pi$
$752$	−251699.	+	435956.i	−0.0162307	+	0.0281124i
$753$	1.99041e7	−	1.14916e7i	1.27925	−	0.738575i
$754$			1.77779e7i			1.13881i
$755$	855884.	+	494145.i	0.0546446	+	0.0315491i
$756$	−4.78946e6	+	8.29559e6i	−0.304777	+	0.527889i
$757$	5.16382e6	+	2.98133e6i	0.327515	+	0.189091i	0.654737	−	0.755856i	$-0.272779\pi$
$757$	5.16382e6	+	2.98133e6i	0.327515	+	0.189091i	−0.327222	+	0.944947i	$0.606113\pi$
$758$	1.00717e7	−	5.81488e6i	0.636691	−	0.367594i
$759$	−3.87379e6	+	2.23654e6i	−0.244080	+	0.140920i
$760$	−192650.	−	111226.i	−0.0120986	−	0.00698512i
$761$	−8.85497e6	+	1.53373e7i	−0.554275	+	0.960033i	0.443684	+	0.896183i	$0.353671\pi$
$761$	−8.85497e6	+	1.53373e7i	−0.554275	+	0.960033i	−0.997960	+	0.0638500i	$0.979662\pi$
$762$	1.50905e6	+	871248.i	0.0941488	+	0.0543568i
$763$			5.73098e6i			0.356384i
$764$	−1.15220e7	+	6.65224e6i	−0.714159	+	0.412320i
$765$	−1631.78	+	2826.33i	−0.000100811	+	0.000174610i
$766$	2.31714e6			0.142686
$767$	−2.15008e6			−0.131967
$768$	514913.	−	891855.i	0.0315015	−	0.0545621i
$769$		−	1.94019e7i		−	1.18312i	−0.806261	−	0.591560i	$-0.798512\pi$
$769$		−	1.94019e7i		−	1.18312i	0.806261	−	0.591560i	$-0.201488\pi$
$770$	225841.	+	391168.i	0.0137270	+	0.0237759i
$771$		−	6.34749e6i		−	0.384562i
$772$	2.22497e6	−	1.28459e6i	0.134364	−	0.0775748i
$773$	−5.81221e6	−	1.00670e7i	−0.349859	−	0.605973i	0.636366	−	0.771388i	$-0.280437\pi$
$773$	−5.81221e6	−	1.00670e7i	−0.349859	−	0.605973i	−0.986224	+	0.165415i	$0.947104\pi$
$774$	−147413.	−	255326.i	−0.00884468	−	0.0153194i
$775$	−1.23351e7	−	7.12168e6i	−0.737716	−	0.425920i
$776$	−2.29964e6			−0.137090
$777$	1.77551e7	−	1.09364e7i	1.05504	−	0.649864i
$778$	9.04078e6			0.535497
$779$	919248.	+	530728.i	0.0542736	+	0.0313349i
$780$	393844.	+	682158.i	0.0231786	+	0.0401466i
$781$	2.28066e6	+	3.95021e6i	0.133793	+	0.231736i
$782$	−1.15673e6	+	667839.i	−0.0676418	+	0.0390530i
$783$			2.34444e7i			1.36658i
$784$	−1.09937e6	−	1.90416e6i	−0.0638782	−	0.110640i
$785$			2.43506e6i			0.141038i
$786$	−667974.	+	1.15697e6i	−0.0385659	+	0.0667981i
$787$	−3.73884e6			−0.215179			−0.107590	−	0.994195i	$-0.534313\pi$
$787$	−3.73884e6			−0.215179			−0.107590	+	0.994195i	$0.534313\pi$
$788$	7.81587e6			0.448396
$789$	9.30320e6	−	1.61136e7i	0.532034	−	0.921511i
$790$	803516.	−	463910.i	0.0458065	−	0.0264464i
$791$			2.38888e7i			1.35754i
$792$	35053.4	+	20238.1i	0.00198572	+	0.00114645i
$793$	2.03601e6	−	3.52647e6i	0.114973	−	0.199140i
$794$	6.46686e6	+	3.73364e6i	0.364034	+	0.210175i
$795$	−946635.	+	546540.i	−0.0531208	+	0.0306693i
$796$	5.28187e6	−	3.04949e6i	0.295464	−	0.170586i
$797$	1.06580e7	+	6.15341e6i	0.594335	+	0.343139i	0.766810	−	0.641875i	$-0.221843\pi$
$797$	1.06580e7	+	6.15341e6i	0.594335	+	0.343139i	−0.172475	+	0.985014i	$0.555176\pi$
$798$	−3.95729e6	+	6.85423e6i	−0.219984	+	0.381023i
$799$	−321780.	−	185780.i	−0.0178317	−	0.0102951i
$800$			3.18018e6i			0.175682i
$801$	60387.2	−	34864.6i	0.00332555	−	0.00192001i
$802$	−1.77916e6	+	3.08159e6i	−0.0976738	+	0.169176i
$803$	6.76173e6			0.370057
$804$	−8.72814e6			−0.476191
$805$	619427.	−	1.07288e6i	0.0336899	−	0.0583527i
$806$			1.30652e7i			0.708402i
$807$	1.44340e7	+	2.50005e7i	0.780196	+	1.35134i
$808$		−	6.36861e6i		−	0.343176i
$809$	−9.40097e6	+	5.42765e6i	−0.505011	+	0.291569i	−0.730781	−	0.682612i	$-0.760844\pi$
$809$	−9.40097e6	+	5.42765e6i	−0.505011	+	0.291569i	0.225769	+	0.974181i	$0.427510\pi$
$810$	527772.	+	914127.i	0.0282640	+	0.0489547i
$811$	−1.80132e7	−	3.11998e7i	−0.961698	−	1.66571i	−0.718237	−	0.695798i	$-0.755051\pi$
$811$	−1.80132e7	−	3.11998e7i	−0.961698	−	1.66571i	−0.243460	−	0.969911i	$-0.578283\pi$
$812$	−1.37802e7	−	7.95599e6i	−0.733441	−	0.423452i
$813$	1.74061e7			0.923579
$814$	2.81389e6	+	4.56831e6i	0.148849	+	0.241654i
$815$	2.08006e6			0.109694
$816$	658281.	+	380058.i	0.0346087	+	0.0199814i
$817$	7.41645e6	+	1.28457e7i	0.388724	+	0.673289i
$818$	−8.18039e6	−	1.41688e7i	−0.427455	−	0.740374i
$819$	385914.	−	222807.i	0.0201039	−	0.0116070i
$820$			94552.4i			0.00491064i
$821$	−6.64936e6	−	1.15170e7i	−0.344288	−	0.596325i	0.640936	−	0.767594i	$-0.278546\pi$
$821$	−6.64936e6	−	1.15170e7i	−0.344288	−	0.596325i	−0.985224	+	0.171270i	$0.945213\pi$
$822$		−	1.90885e7i		−	0.985352i
$823$	−9.49689e6	+	1.64491e7i	−0.488744	+	0.846530i	−0.999916	−	0.0129484i	$-0.995878\pi$
$823$	−9.49689e6	+	1.64491e7i	−0.488744	+	0.846530i	0.511172	+	0.859479i	$0.329212\pi$
$824$	−2.76503e6			−0.141867
$825$	−7.86092e6			−0.402104
$826$	962207.	−	1.66659e6i	0.0490703	−	0.0849922i
$827$	3.34687e7	−	1.93232e7i	1.70167	−	0.982459i	0.757595	−	0.652725i	$-0.226374\pi$
$827$	3.34687e7	−	1.93232e7i	1.70167	−	0.982459i	0.944074	−	0.329734i	$-0.106959\pi$
$828$		−	111016.i		−	0.00562744i
$829$	1.95066e7	+	1.12621e7i	0.985815	+	0.569161i	0.904021	−	0.427489i	$-0.140602\pi$
$829$	1.95066e7	+	1.12621e7i	0.985815	+	0.569161i	0.0817943	+	0.996649i	$0.473935\pi$
$830$	760827.	−	1.31779e6i	0.0383346	−	0.0663974i
$831$	−1.08430e7	−	6.26019e6i	−0.544686	−	0.314474i
$832$	2.52631e6	−	1.45857e6i	0.126526	−	0.0730497i
$833$	1.40547e6	−	811447.i	0.0701791	−	0.0405179i
$834$	1.12698e7	+	6.50663e6i	0.561050	+	0.323922i
$835$	1.09687e6	−	1.89983e6i	0.0544426	−	0.0942973i
$836$	−1.76357e6	−	1.01819e6i	−0.0872722	−	0.0503866i
$837$			1.72296e7i			0.850085i
$838$	−1.24824e7	+	7.20671e6i	−0.614028	+	0.354509i
$839$	8.96238e6	−	1.55233e7i	0.439560	−	0.761341i	−0.558095	−	0.829777i	$-0.688468\pi$
$839$	8.96238e6	−	1.55233e7i	0.439560	−	0.761341i	0.997656	+	0.0684361i	$0.0218009\pi$
$840$	−705016.			−0.0344747
$841$	−1.84334e7			−0.898702
$842$	761105.	−	1.31827e6i	0.0369968	−	0.0640804i
$843$		−	3.46794e7i		−	1.68075i
$844$	−4.86073e6	−	8.41904e6i	−0.234880	−	0.406824i
$845$			597928.i			0.0288076i
$846$	26745.1	−	15441.3i	0.00128475	−	0.000741751i
$847$	−1.07652e7	−	1.86459e7i	−0.515600	−	0.893046i
$848$	2.02406e6	+	3.50578e6i	0.0966573	+	0.167415i
$849$	9.96046e6	+	5.75067e6i	0.474253	+	0.273810i
$850$	−2.34730e6			−0.111435
$851$	6.99218e6	−	1.29487e7i	0.330970	−	0.612919i
$852$	−7.11961e6			−0.336014
$853$	−3.13668e7	−	1.81096e7i	−1.47604	−	0.852190i	−0.476402	−	0.879228i	$-0.658059\pi$
$853$	−3.13668e7	−	1.81096e7i	−1.47604	−	0.852190i	−0.999634	+	0.0270375i	$0.991393\pi$
$854$	1.82232e6	+	3.15635e6i	0.0855026	+	0.148095i
$855$	6823.54	+	11818.7i	0.000319223	+	0.000552911i
$856$	7.38664e6	−	4.26468e6i	0.344558	−	0.198931i
$857$			1.46989e7i			0.683650i	0.939764	+	0.341825i	$0.111045\pi$
$857$			1.46989e7i			0.683650i	−0.939764	+	0.341825i	$0.888955\pi$
$858$	3.60535e6	+	6.24465e6i	0.167197	+	0.289594i
$859$		−	3.17818e7i		−	1.46959i	−0.678291	−	0.734793i	$-0.737279\pi$
$859$		−	3.17818e7i		−	1.46959i	0.678291	−	0.734793i	$-0.262721\pi$
$860$	−660643.	+	1.14427e6i	−0.0304594	+	0.0527571i
$861$	3.36406e6			0.154652
$862$	−1.70327e7			−0.780754
$863$	1.59314e6	−	2.75940e6i	0.0728161	−	0.126121i	−0.827318	−	0.561733i	$-0.810135\pi$
$863$	1.59314e6	−	2.75940e6i	0.0728161	−	0.126121i	0.900134	+	0.435612i	$0.143468\pi$
$864$	3.33155e6	−	1.92347e6i	0.151831	−	0.0876599i
$865$			1.19933e6i			0.0545004i
$866$	−6.11204e6	−	3.52879e6i	−0.276944	−	0.159894i
$867$	1.08752e7	−	1.88364e7i	0.491349	−	0.851041i
$868$	−1.01273e7	−	5.84698e6i	−0.456239	−	0.263410i
$869$	7.35559e6	−	4.24675e6i	0.330421	−	0.190769i
$870$	−1.49435e6	+	862762.i	−0.0669351	+	0.0386450i
$871$	−2.14114e7	−	1.23619e7i	−0.956313	−	0.552127i
$872$	1.15080e6	−	1.99324e6i	0.0512515	−	0.0887703i
$873$	122178.	+	70539.4i	0.00542571	+	0.00313254i
$874$			5.58532e6i			0.247326i
$875$	3.78268e6	−	2.18393e6i	0.167024	−	0.0964314i
$876$	−5.27708e6	+	9.14018e6i	−0.232345	+	0.402434i
$877$	3.30317e7			1.45021			0.725107	−	0.688636i	$-0.241790\pi$
$877$	3.30317e7			1.45021			0.725107	+	0.688636i	$0.241790\pi$
$878$	−3.61920e6			−0.158444
$879$	−2.32214e6	+	4.02206e6i	−0.101372	+	0.175581i
$880$		−	181398.i		−	0.00789632i
$881$	2.07263e6	+	3.58990e6i	0.0899667	+	0.155827i	0.907497	−	0.420059i	$-0.137991\pi$
$881$	2.07263e6	+	3.58990e6i	0.0899667	+	0.155827i	−0.817530	+	0.575886i	$0.804657\pi$
$882$			134889.i			0.00583853i
$883$	1.67741e7	−	9.68455e6i	0.724000	−	0.418001i	−0.0922234	−	0.995738i	$-0.529397\pi$
$883$	1.67741e7	−	9.68455e6i	0.724000	−	0.418001i	0.816223	+	0.577737i	$0.196064\pi$
$884$	1.07657e6	+	1.86468e6i	0.0463354	+	0.0802553i
$885$	−104343.	−	180728.i	−0.00447824	−	0.00775654i
$886$	3.22559e6	+	1.86229e6i	0.138046	+	0.0797010i
$887$	2.06711e7			0.882174			0.441087	−	0.897464i	$-0.354593\pi$
$887$	2.06711e7			0.882174			0.441087	+	0.897464i	$0.354593\pi$
$888$	−8.37128e6	+	238421.i	−0.356254	+	0.0101464i
$889$	−4.41783e6			−0.187480
$890$	−270631.	−	156249.i	−0.0114526	−	0.00661213i
$891$	4.83136e6	+	8.36816e6i	0.203880	+	0.353131i
$892$	−3.42832e6	−	5.93803e6i	−0.144268	−	0.249879i
$893$	−1.34557e6	+	776865.i	−0.0564647	+	0.0325999i
$894$		−	2.33807e7i		−	0.978394i
$895$	514974.	+	891961.i	0.0214896	+	0.0372210i
$896$			2.61096e6i			0.108650i
$897$	9.88861e6	−	1.71276e7i	0.410350	−	0.710746i
$898$	−1.58714e7			−0.656787
$899$	−2.86209e7			−1.18109
$900$	97549.3	−	168960.i	0.00401438	−	0.00695310i
$901$	−2.58763e6	+	1.49397e6i	−0.106191	+	0.0613097i
$902$			865557.i			0.0354225i
$903$	4.07116e7	+	2.35048e7i	1.66149	+	0.959264i
$904$	4.79693e6	−	8.30853e6i	0.195228	−	0.338145i
$905$	−2.61397e6	−	1.50917e6i	−0.106091	−	0.0612517i
$906$	−1.22294e7	+	7.06064e6i	−0.494976	+	0.285774i
$907$	−2.69827e7	+	1.55785e7i	−1.08910	+	0.628792i	−0.933337	−	0.359003i	$-0.883117\pi$
$907$	−2.69827e7	+	1.55785e7i	−1.08910	+	0.628792i	−0.155763	+	0.987794i	$0.549784\pi$
$908$	1.77233e7	+	1.02326e7i	0.713395	+	0.411879i
$909$	−195352.	+	338359.i	−0.00784164	+	0.0135821i
$910$	−1.72951e6	−	998532.i	−0.0692339	−	0.0399722i
$911$			1.68638e7i			0.673223i	0.941644	+	0.336612i	$0.109281\pi$
$911$			1.68638e7i			0.673223i	−0.941644	+	0.336612i	$0.890719\pi$
$912$	2.75269e6	−	1.58927e6i	0.109590	−	0.0632718i
$913$	6.96481e6	−	1.20634e7i	0.276524	−	0.478953i
$914$	2.89880e7			1.14776
$915$	395231.			0.0156062
$916$	−9.93746e6	+	1.72122e7i	−0.391324	+	0.677793i
$917$		−	3.38709e6i		−	0.133016i
$918$	1.41972e6	+	2.45902e6i	0.0556027	+	0.0963066i
$919$		−	8.53124e6i		−	0.333214i	−0.986023	−	0.166607i	$-0.946719\pi$
$919$		−	8.53124e6i		−	0.333214i	0.986023	−	0.166607i	$-0.0532812\pi$
$920$	−430873.	+	248765.i	−0.0167834	+	0.00968990i
$921$	−1.65324e7	−	2.86350e7i	−0.642226	−	1.11237i
$922$	1.35893e7	+	2.35374e7i	0.526467	+	0.911867i
$923$	−1.74655e7	−	1.00837e7i	−0.674801	−	0.389596i
$924$	−6.45390e6			−0.248681
$925$	2.20197e7	−	1.35632e7i	0.846167	−	0.521205i
$926$	2.33127e7			0.893440
$927$	146904.	+	84814.9i	0.00561479	+	0.00324170i
$928$	3.19517e6	+	5.53419e6i	0.121793	+	0.210952i
$929$	7.46674e6	+	1.29328e7i	0.283852	+	0.491646i	0.972330	−	0.233611i	$-0.0750543\pi$
$929$	7.46674e6	+	1.29328e7i	0.283852	+	0.491646i	−0.688478	+	0.725257i	$0.741721\pi$
$930$	−1.09822e6	+	634057.i	−0.0416372	+	0.0240392i
$931$		−	6.78636e6i		−	0.256603i
$932$	−1.11410e7	−	1.92968e7i	−0.420131	−	0.727688i
$933$			1.26574e7i			0.476038i
$934$	−5.19128e6	+	8.99157e6i	−0.194719	+	0.337263i
$935$	133890.			0.00500863
$936$	−178961.			−0.00667681
$937$	3.57694e6	−	6.19544e6i	0.133095	−	0.230528i	−0.791773	−	0.610816i	$-0.790842\pi$
$937$	3.57694e6	−	6.19544e6i	0.133095	−	0.230528i	0.924868	+	0.380288i	$0.124175\pi$
$938$	1.91641e7	−	1.10644e7i	0.711185	−	0.410603i
$939$		−	4.74916e6i		−	0.175773i
$940$	−119861.	−	69201.6i	−0.00442443	−	0.00255444i
$941$	346783.	−	600646.i	0.0127668	−	0.0221128i	−0.859571	−	0.511016i	$-0.829269\pi$
$941$	346783.	−	600646.i	0.0127668	−	0.0221128i	0.872338	+	0.488903i	$0.162603\pi$
$942$	−3.01322e7	−	1.73968e7i	−1.10638	−	0.638767i
$943$	2.05596e6	−	1.18701e6i	0.0752895	−	0.0434684i
$944$	−669311.	+	386427.i	−0.0244455	+	0.0141136i
$945$	−2.28077e6	−	1.31680e6i	−0.0830810	−	0.0479668i
$946$	−6.04770e6	+	1.04749e7i	−0.219716	+	0.380560i
$947$	3.33135e7	+	1.92336e7i	1.20711	+	0.696923i	0.962126	−	0.272605i	$-0.0878853\pi$
$947$	3.33135e7	+	1.92336e7i	1.20711	+	0.696923i	0.244980	+	0.969528i	$0.421219\pi$
$948$			1.32572e7i			0.479107i
$949$	−2.58909e7	+	1.49481e7i	−0.933216	+	0.538793i
$950$	−4.90779e6	+	8.50054e6i	−0.176432	+	0.305589i
$951$	−6.91217e6			−0.247835
$952$	−1.92716e6			−0.0689169
$953$	−2.01378e7	+	3.48797e7i	−0.718257	+	1.24406i	0.243433	+	0.969918i	$0.421726\pi$
$953$	−2.01378e7	+	3.48797e7i	−0.718257	+	1.24406i	−0.961690	+	0.274140i	$0.911607\pi$
$954$		−	248345.i		−	0.00883457i
$955$	−1.82895e6	−	3.16783e6i	−0.0648923	−	0.112397i
$956$			1.31328e7i			0.464744i
$957$	−1.36797e7	+	7.89795e6i	−0.482831	+	0.278763i
$958$	−1.27692e7	−	2.21169e7i	−0.449521	−	0.778592i
$959$	2.41979e7	+	4.19120e7i	0.849634	+	1.47161i
$960$	245204.	+	141569.i	0.00858717	+	0.00495781i
$961$	7.59521e6			0.265296
$962$	−2.08737e7	−	1.12716e7i	−0.727212	−	0.392687i
$963$	−523261.			−0.0181825
$964$	−2.58031e6	−	1.48974e6i	−0.0894291	−	0.0516319i
$965$	353182.	+	611729.i	0.0122090	+	0.0211466i
$966$	8.85074e6	+	1.53299e7i	0.305166	+	0.528564i
$967$	2.09673e7	−	1.21055e7i	0.721069	−	0.416309i	−0.0940770	−	0.995565i	$-0.529990\pi$
$967$	2.09673e7	−	1.21055e7i	0.721069	−	0.416309i	0.815146	+	0.579256i	$0.196657\pi$
$968$			8.64670e6i			0.296594i
$969$	1.17304e6	+	2.03177e6i	0.0401333	+	0.0695129i
$970$		−	632258.i		−	0.0215757i
$971$	1.46238e6	−	2.53292e6i	0.0497752	−	0.0862131i	−0.840064	−	0.542487i	$-0.817483\pi$
$971$	1.46238e6	−	2.53292e6i	0.0497752	−	0.0862131i	0.889840	+	0.456274i	$0.150816\pi$
$972$	−475882.			−0.0161560
$973$	−3.29931e7			−1.11723
$974$	1.38955e7	−	2.40676e7i	0.469327	−	0.812898i
$975$	3.00998e7	−	1.73781e7i	1.01403	−	0.585452i
$976$		−	1.46370e6i		−	0.0491845i
$977$	1.84311e7	+	1.06412e7i	0.617752	+	0.356659i	0.775993	−	0.630741i	$-0.217249\pi$
$977$	1.84311e7	+	1.06412e7i	0.617752	+	0.356659i	−0.158241	+	0.987400i	$0.550582\pi$
$978$	−1.48606e7	+	2.57393e7i	−0.496808	+	0.860497i
$979$	−2.47742e6	−	1.43034e6i	−0.0826121	−	0.0476961i
$980$	523526.	−	302258.i	0.0174130	−	0.0100534i
$981$	−122281.	+	70599.2i	−0.00405684	+	0.00234222i
$982$	1.41801e7	+	8.18686e6i	0.469244	+	0.270918i
$983$	4.95646e6	−	8.58484e6i	0.163602	−	0.283366i	−0.772556	−	0.634946i	$-0.781022\pi$
$983$	4.95646e6	−	8.58484e6i	0.163602	−	0.283366i	0.936158	+	0.351580i	$0.114356\pi$
$984$	−1.17002e6	−	675510.i	−0.0385217	−	0.0222405i
$985$			2.14888e6i			0.0705701i
$986$	−4.08480e6	+	2.35836e6i	−0.133807	+	0.0772535i
$987$	−2.46210e6	+	4.26449e6i	−0.0804477	+	0.139340i
$988$	9.00368e6			0.293446
$989$	3.31747e7			1.07849
$990$	−5564.21	+	9637.49i	−0.000180433	+	0.000312519i
$991$		−	3.69947e7i		−	1.19662i	−0.801266	−	0.598308i	$-0.795840\pi$
$991$		−	3.69947e7i		−	1.19662i	0.801266	−	0.598308i	$-0.204160\pi$
$992$	2.34817e6	+	4.06716e6i	0.0757619	+	0.131224i
$993$			3.51381e7i			1.13085i
$994$	1.56323e7	−	9.02534e6i	0.501832	−	0.289733i
$995$	838419.	+	1.45218e6i	0.0268475	+	0.0465012i
$996$	1.08712e7	+	1.88294e7i	0.347238	+	0.601434i
$997$	−1.11536e7	−	6.43954e6i	−0.355367	−	0.205171i	0.311679	−	0.950187i	$-0.399108\pi$
$997$	−1.11536e7	−	6.43954e6i	−0.355367	−	0.205171i	−0.667047	+	0.745016i	$0.732442\pi$
$998$	−1.46254e7			−0.464816
$999$	−2.75269e7	−	1.48643e7i	−0.872658	−	0.471227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.e.a.27.6	yes	28
37.11	even	6	inner	74.6.e.a.11.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.e.a.11.6	✓	28	37.11	even	6	inner
74.6.e.a.27.6	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.46410 - 2.00000i) q^{2} +(7.85694 + 13.6086i) q^{3} +(8.00000 + 13.8564i) q^{4} +(-3.80965 + 2.19950i) q^{5} -62.8556i q^{6} +(79.6803 + 138.010i) q^{7} -64.0000i q^{8} +(-1.96314 + 3.40026i) q^{9} +17.5960 q^{10} +161.078 q^{11} +(-125.711 + 217.738i) q^{12} +(-616.776 + 356.096i) q^{13} -637.443i q^{14} +(-59.8644 - 34.5627i) q^{15} +(-128.000 + 221.703i) q^{16} +(-163.639 - 94.4772i) q^{17} +(13.6011 - 7.85257i) q^{18} +(-684.280 + 395.070i) q^{19} +(-60.9544 - 35.1920i) q^{20} +(-1252.09 + 2168.68i) q^{21} +(-557.992 - 322.157i) q^{22} +1767.20i q^{23} +(870.952 - 502.844i) q^{24} +(-1552.82 + 2689.57i) q^{25} +2848.77 q^{26} +3756.78 q^{27} +(-1274.89 + 2208.17i) q^{28} +6240.56i q^{29} +(138.251 + 239.457i) q^{30} +4586.28i q^{31} +(886.810 - 512.000i) q^{32} +(1265.58 + 2192.06i) q^{33} +(377.909 + 654.557i) q^{34} +(-607.108 - 350.514i) q^{35} -62.8206 q^{36} +(-7327.27 - 3956.65i) q^{37} +3160.56 q^{38} +(-9691.95 - 5595.65i) q^{39} +(140.768 + 243.817i) q^{40} +(-671.689 - 1163.40i) q^{41} +(8674.72 - 5008.35i) q^{42} -18772.5i q^{43} +(1288.63 + 2231.97i) q^{44} -17.2717i q^{45} +(3534.39 - 6121.75i) q^{46} +1966.40 q^{47} -4022.76 q^{48} +(-4294.41 + 7438.13i) q^{49} +(10758.3 - 6211.30i) q^{50} -2969.21i q^{51} +(-9868.41 - 5697.53i) q^{52} +(7906.50 - 13694.5i) q^{53} +(-13013.9 - 7513.56i) q^{54} +(-613.652 + 354.292i) q^{55} +(8832.66 - 5099.54i) q^{56} +(-10752.7 - 6208.08i) q^{57} +(12481.1 - 21617.9i) q^{58} +(2614.50 + 1509.48i) q^{59} -1106.01i q^{60} +(-4951.58 + 2858.80i) q^{61} +(9172.56 - 15887.3i) q^{62} -625.695 q^{63} -4096.00 q^{64} +(1566.47 - 2713.20i) q^{65} -10124.7i q^{66} +(17357.5 + 30064.1i) q^{67} -3023.27i q^{68} +(-24049.1 + 13884.8i) q^{69} +(1402.06 + 2428.43i) q^{70} +(14158.7 + 24523.5i) q^{71} +(217.617 + 125.641i) q^{72} +41977.9 q^{73} +(17469.1 + 28360.8i) q^{74} -48801.8 q^{75} +(-10948.5 - 6321.11i) q^{76} +(12834.8 + 22230.5i) q^{77} +(22382.6 + 38767.8i) q^{78} +(45664.7 - 26364.5i) q^{79} -1126.14i q^{80} +(29993.8 + 51950.8i) q^{81} +5373.51i q^{82} +(43238.6 - 74891.5i) q^{83} -40066.8 q^{84} +831.210 q^{85} +(-37545.0 + 65029.9i) q^{86} +(-84925.4 + 49031.7i) q^{87} -10309.0i q^{88} +(-15380.2 - 8879.79i) q^{89} +(-34.5435 + 59.8311i) q^{90} +(-98289.8 - 56747.6i) q^{91} +(-24487.0 + 14137.6i) q^{92} +(-62412.9 + 36034.1i) q^{93} +(-6811.81 - 3932.80i) q^{94} +(1737.91 - 3010.15i) q^{95} +(13935.2 + 8045.51i) q^{96} -35931.9i q^{97} +(29752.5 - 17177.6i) q^{98} +(-316.220 + 547.709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25}+ \cdots - 401224 q^{99}+O(q^{100}) \) 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9 - 736 * q^10 + 464 * q^11 + 320 * q^12 + 72 * q^13 + 3960 * q^15 - 3584 * q^16 + 1530 * q^17 - 1944 * q^19 - 1440 * q^20 - 192 * q^21 - 3028 * q^25 - 5280 * q^26 + 36400 * q^27 + 2496 * q^28 - 4368 * q^30 - 2996 * q^33 + 1360 * q^34 - 21636 * q^35 - 18752 * q^36 + 45178 * q^37 - 14304 * q^38 + 14592 * q^39 - 5888 * q^40 + 12894 * q^41 - 26832 * q^42 + 3712 * q^44 - 22080 * q^46 - 39512 * q^47 + 10240 * q^48 + 8262 * q^49 - 44640 * q^50 + 1152 * q^52 + 47912 * q^53 - 101520 * q^54 + 70236 * q^55 + 99984 * q^57 + 51968 * q^58 - 74568 * q^59 - 8274 * q^61 - 22768 * q^62 - 137048 * q^63 - 114688 * q^64 + 33104 * q^65 - 7904 * q^67 - 69096 * q^69 + 65056 * q^70 + 9788 * q^71 + 256784 * q^73 - 8480 * q^74 + 518544 * q^75 - 31104 * q^76 - 86340 * q^77 + 89776 * q^78 - 82740 * q^79 - 174814 * q^81 + 19892 * q^83 - 6144 * q^84 - 167972 * q^85 + 119536 * q^86 - 200424 * q^87 - 223482 * q^89 + 59504 * q^90 - 53016 * q^91 + 198912 * q^92 - 227844 * q^93 + 158736 * q^94 - 140012 * q^95 - 168864 * q^98 - 401224 * q^99

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