LMFDB - Embedded newform 354.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.a (trivial)

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:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.32832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 10x + 1 $ x^4 - 2x^3 - 9x^2 + 10*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.0924698$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -38.5011 q^{5} +36.0000 q^{6} -5.25164 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -38.5011 q^{5} +36.0000 q^{6} -5.25164 q^{7} +64.0000 q^{8} +81.0000 q^{9} -154.005 q^{10} -726.485 q^{11} +144.000 q^{12} +796.554 q^{13} -21.0066 q^{14} -346.510 q^{15} +256.000 q^{16} +367.465 q^{17} +324.000 q^{18} -1805.60 q^{19} -616.018 q^{20} -47.2648 q^{21} -2905.94 q^{22} +685.008 q^{23} +576.000 q^{24} -1642.66 q^{25} +3186.22 q^{26} +729.000 q^{27} -84.0263 q^{28} -2471.50 q^{29} -1386.04 q^{30} -6440.06 q^{31} +1024.00 q^{32} -6538.36 q^{33} +1469.86 q^{34} +202.194 q^{35} +1296.00 q^{36} -13484.7 q^{37} -7222.40 q^{38} +7168.99 q^{39} -2464.07 q^{40} +8364.00 q^{41} -189.059 q^{42} -1453.36 q^{43} -11623.8 q^{44} -3118.59 q^{45} +2740.03 q^{46} +18242.9 q^{47} +2304.00 q^{48} -16779.4 q^{49} -6570.65 q^{50} +3307.19 q^{51} +12744.9 q^{52} -29816.3 q^{53} +2916.00 q^{54} +27970.5 q^{55} -336.105 q^{56} -16250.4 q^{57} -9885.99 q^{58} -3481.00 q^{59} -5544.16 q^{60} -53056.9 q^{61} -25760.2 q^{62} -425.383 q^{63} +4096.00 q^{64} -30668.2 q^{65} -26153.5 q^{66} -36166.1 q^{67} +5879.44 q^{68} +6165.07 q^{69} +808.777 q^{70} -21446.1 q^{71} +5184.00 q^{72} +56179.8 q^{73} -53938.8 q^{74} -14784.0 q^{75} -28889.6 q^{76} +3815.24 q^{77} +28675.9 q^{78} +16623.0 q^{79} -9856.29 q^{80} +6561.00 q^{81} +33456.0 q^{82} +94477.5 q^{83} -756.237 q^{84} -14147.8 q^{85} -5813.44 q^{86} -22243.5 q^{87} -46495.0 q^{88} +74418.2 q^{89} -12474.4 q^{90} -4183.22 q^{91} +10960.1 q^{92} -57960.5 q^{93} +72971.6 q^{94} +69517.7 q^{95} +9216.00 q^{96} -130509. q^{97} -67117.7 q^{98} -58845.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−38.5011	−0.688729	−0.344365	−	0.938836i	$-0.611906\pi$
$5$	−38.5011	−0.688729	−0.344365	+	0.938836i	$0.611906\pi$
$6$	36.0000	0.408248
$7$	−5.25164	−0.0405089	−0.0202544	−	0.999795i	$-0.506448\pi$
$7$	−5.25164	−0.0405089	−0.0202544	+	0.999795i	$0.506448\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−154.005	−0.487005
$11$	−726.485	−1.81028	−0.905138	−	0.425118i	$-0.860233\pi$
$11$	−726.485	−1.81028	−0.905138	+	0.425118i	$0.860233\pi$
$12$	144.000	0.288675
$13$	796.554	1.30724	0.653622	−	0.756821i	$-0.273249\pi$
$13$	796.554	1.30724	0.653622	+	0.756821i	$0.273249\pi$
$14$	−21.0066	−0.0286441
$15$	−346.510	−0.397638
$16$	256.000	0.250000
$17$	367.465	0.308386	0.154193	−	0.988041i	$-0.450722\pi$
$17$	367.465	0.308386	0.154193	+	0.988041i	$0.450722\pi$
$18$	324.000	0.235702
$19$	−1805.60	−1.14746	−0.573730	−	0.819044i	$-0.694504\pi$
$19$	−1805.60	−1.14746	−0.573730	+	0.819044i	$0.694504\pi$
$20$	−616.018	−0.344365
$21$	−47.2648	−0.0233878
$22$	−2905.94	−1.28006
$23$	685.008	0.270007	0.135004	−	0.990845i	$-0.456895\pi$
$23$	685.008	0.270007	0.135004	+	0.990845i	$0.456895\pi$
$24$	576.000	0.204124
$25$	−1642.66	−0.525652
$26$	3186.22	0.924362
$27$	729.000	0.192450
$28$	−84.0263	−0.0202544
$29$	−2471.50	−0.545714	−0.272857	−	0.962055i	$-0.587969\pi$
$29$	−2471.50	−0.545714	−0.272857	+	0.962055i	$0.587969\pi$
$30$	−1386.04	−0.281173
$31$	−6440.06	−1.20361	−0.601804	−	0.798644i	$-0.705551\pi$
$31$	−6440.06	−1.20361	−0.601804	+	0.798644i	$0.705551\pi$
$32$	1024.00	0.176777
$33$	−6538.36	−1.04516
$34$	1469.86	0.218061
$35$	202.194	0.0278996
$36$	1296.00	0.166667
$37$	−13484.7	−1.61934	−0.809668	−	0.586888i	$-0.800353\pi$
$37$	−13484.7	−1.61934	−0.809668	+	0.586888i	$0.800353\pi$
$38$	−7222.40	−0.811377
$39$	7168.99	0.754738
$40$	−2464.07	−0.243503
$41$	8364.00	0.777060	0.388530	−	0.921436i	$-0.372983\pi$
$41$	8364.00	0.777060	0.388530	+	0.921436i	$0.372983\pi$
$42$	−189.059	−0.0165377
$43$	−1453.36	−0.119868	−0.0599338	−	0.998202i	$-0.519089\pi$
$43$	−1453.36	−0.119868	−0.0599338	+	0.998202i	$0.519089\pi$
$44$	−11623.8	−0.905138
$45$	−3118.59	−0.229576
$46$	2740.03	0.190924
$47$	18242.9	1.20462	0.602309	−	0.798263i	$-0.294248\pi$
$47$	18242.9	1.20462	0.602309	+	0.798263i	$0.294248\pi$
$48$	2304.00	0.144338
$49$	−16779.4	−0.998359
$50$	−6570.65	−0.371692
$51$	3307.19	0.178046
$52$	12744.9	0.653622
$53$	−29816.3	−1.45802	−0.729011	−	0.684502i	$-0.760020\pi$
$53$	−29816.3	−1.45802	−0.729011	+	0.684502i	$0.760020\pi$
$54$	2916.00	0.136083
$55$	27970.5	1.24679
$56$	−336.105	−0.0143220
$57$	−16250.4	−0.662487
$58$	−9885.99	−0.385878
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−5544.16	−0.198819
$61$	−53056.9	−1.82565	−0.912824	−	0.408353i	$-0.866103\pi$
$61$	−53056.9	−1.82565	−0.912824	+	0.408353i	$0.866103\pi$
$62$	−25760.2	−0.851080
$63$	−425.383	−0.0135030
$64$	4096.00	0.125000
$65$	−30668.2	−0.900338
$66$	−26153.5	−0.739042
$67$	−36166.1	−0.984270	−0.492135	−	0.870519i	$-0.663783\pi$
$67$	−36166.1	−0.984270	−0.492135	+	0.870519i	$0.663783\pi$
$68$	5879.44	0.154193
$69$	6165.07	0.155889
$70$	808.777	0.0197280
$71$	−21446.1	−0.504896	−0.252448	−	0.967610i	$-0.581236\pi$
$71$	−21446.1	−0.504896	−0.252448	+	0.967610i	$0.581236\pi$
$72$	5184.00	0.117851
$73$	56179.8	1.23388	0.616940	−	0.787010i	$-0.288372\pi$
$73$	56179.8	1.23388	0.616940	+	0.787010i	$0.288372\pi$
$74$	−53938.8	−1.14504
$75$	−14784.0	−0.303485
$76$	−28889.6	−0.573730
$77$	3815.24	0.0733322
$78$	28675.9	0.533680
$79$	16623.0	0.299670	0.149835	−	0.988711i	$-0.452126\pi$
$79$	16623.0	0.299670	0.149835	+	0.988711i	$0.452126\pi$
$80$	−9856.29	−0.172182
$81$	6561.00	0.111111
$82$	33456.0	0.549464
$83$	94477.5	1.50533	0.752667	−	0.658401i	$-0.228767\pi$
$83$	94477.5	1.50533	0.752667	+	0.658401i	$0.228767\pi$
$84$	−756.237	−0.0116939
$85$	−14147.8	−0.212394
$86$	−5813.44	−0.0847592
$87$	−22243.5	−0.315068
$88$	−46495.0	−0.640029
$89$	74418.2	0.995873	0.497937	−	0.867213i	$-0.334091\pi$
$89$	74418.2	0.995873	0.497937	+	0.867213i	$0.334091\pi$
$90$	−12474.4	−0.162335
$91$	−4183.22	−0.0529550
$92$	10960.1	0.135004
$93$	−57960.5	−0.694904
$94$	72971.6	0.851793
$95$	69517.7	0.790290
$96$	9216.00	0.102062
$97$	−130509.	−1.40836	−0.704178	−	0.710024i	$-0.748684\pi$
$97$	−130509.	−1.40836	−0.704178	+	0.710024i	$0.748684\pi$
$98$	−67117.7	−0.705946
$99$	−58845.3	−0.603425
$100$	−26282.6	−0.262826
$101$	96852.8	0.944733	0.472366	−	0.881402i	$-0.343400\pi$
$101$	96852.8	0.944733	0.472366	+	0.881402i	$0.343400\pi$
$102$	13228.7	0.125898
$103$	158420.	1.47135	0.735676	−	0.677334i	$-0.236865\pi$
$103$	158420.	1.47135	0.735676	+	0.677334i	$0.236865\pi$
$104$	50979.5	0.462181
$105$	1819.75	0.0161079
$106$	−119265.	−1.03098
$107$	83897.0	0.708414	0.354207	−	0.935167i	$-0.384751\pi$
$107$	83897.0	0.708414	0.354207	+	0.935167i	$0.384751\pi$
$108$	11664.0	0.0962250
$109$	−230737.	−1.86016	−0.930081	−	0.367353i	$-0.880264\pi$
$109$	−230737.	−1.86016	−0.930081	+	0.367353i	$0.880264\pi$
$110$	111882.	0.881614
$111$	−121362.	−0.934925
$112$	−1344.42	−0.0101272
$113$	−239146.	−1.76184	−0.880920	−	0.473265i	$-0.843075\pi$
$113$	−239146.	−1.76184	−0.880920	+	0.473265i	$0.843075\pi$
$114$	−65001.6	−0.468449
$115$	−26373.6	−0.185962
$116$	−39544.0	−0.272857
$117$	64520.9	0.435748
$118$	−13924.0	−0.0920575
$119$	−1929.80	−0.0124923
$120$	−22176.7	−0.140586
$121$	366729.	2.27710
$122$	−212227.	−1.29093
$123$	75276.0	0.448636
$124$	−103041.	−0.601804
$125$	183560.	1.05076
$126$	−1701.53	−0.00954803
$127$	−253410.	−1.39417	−0.697084	−	0.716989i	$-0.745520\pi$
$127$	−253410.	−1.39417	−0.697084	+	0.716989i	$0.745520\pi$
$128$	16384.0	0.0883883
$129$	−13080.2	−0.0692056
$130$	−122673.	−0.636635
$131$	−272236.	−1.38601	−0.693006	−	0.720932i	$-0.743714\pi$
$131$	−272236.	−1.38601	−0.693006	+	0.720932i	$0.743714\pi$
$132$	−104614.	−0.522582
$133$	9482.37	0.0464823
$134$	−144664.	−0.695984
$135$	−28067.3	−0.132546
$136$	23517.8	0.109031
$137$	124715.	0.567697	0.283848	−	0.958869i	$-0.408389\pi$
$137$	124715.	0.567697	0.283848	+	0.958869i	$0.408389\pi$
$138$	24660.3	0.110230
$139$	−81810.2	−0.359145	−0.179573	−	0.983745i	$-0.557472\pi$
$139$	−81810.2	−0.359145	−0.179573	+	0.983745i	$0.557472\pi$
$140$	3235.11	0.0139498
$141$	164186.	0.695486
$142$	−85784.4	−0.357016
$143$	−578684.	−2.36647
$144$	20736.0	0.0833333
$145$	95155.5	0.375849
$146$	224719.	0.872485
$147$	−151015.	−0.576403
$148$	−215755.	−0.809668
$149$	55603.5	0.205181	0.102590	−	0.994724i	$-0.467287\pi$
$149$	55603.5	0.205181	0.102590	+	0.994724i	$0.467287\pi$
$150$	−59135.8	−0.214596
$151$	460594.	1.64390	0.821950	−	0.569559i	$-0.192886\pi$
$151$	460594.	1.64390	0.821950	+	0.569559i	$0.192886\pi$
$152$	−115558.	−0.405689
$153$	29764.7	0.102795
$154$	15261.0	0.0518537
$155$	247949.	0.828961
$156$	114704.	0.377369
$157$	−34035.7	−0.110201	−0.0551006	−	0.998481i	$-0.517548\pi$
$157$	−34035.7	−0.110201	−0.0551006	+	0.998481i	$0.517548\pi$
$158$	66492.2	0.211898
$159$	−268347.	−0.841789
$160$	−39425.2	−0.121751
$161$	−3597.42	−0.0109377
$162$	26244.0	0.0785674
$163$	390397.	1.15090	0.575450	−	0.817837i	$-0.304827\pi$
$163$	390397.	1.15090	0.575450	+	0.817837i	$0.304827\pi$
$164$	133824.	0.388530
$165$	251734.	0.719835
$166$	377910.	1.06443
$167$	−113534.	−0.315018	−0.157509	−	0.987518i	$-0.550346\pi$
$167$	−113534.	−0.315018	−0.157509	+	0.987518i	$0.550346\pi$
$168$	−3024.95	−0.00826884
$169$	263205.	0.708889
$170$	−56591.3	−0.150185
$171$	−146254.	−0.382487
$172$	−23253.7	−0.0599338
$173$	−489984.	−1.24471	−0.622353	−	0.782737i	$-0.713823\pi$
$173$	−489984.	−1.24471	−0.622353	+	0.782737i	$0.713823\pi$
$174$	−88973.9	−0.222787
$175$	8626.67	0.0212936
$176$	−185980.	−0.452569
$177$	−31329.0	−0.0751646
$178$	297673.	0.704189
$179$	−343771.	−0.801930	−0.400965	−	0.916093i	$-0.631325\pi$
$179$	−343771.	−0.801930	−0.400965	+	0.916093i	$0.631325\pi$
$180$	−49897.5	−0.114788
$181$	632457.	1.43494	0.717472	−	0.696588i	$-0.245299\pi$
$181$	632457.	1.43494	0.717472	+	0.696588i	$0.245299\pi$
$182$	−16732.9	−0.0374448
$183$	−477512.	−1.05404
$184$	43840.5	0.0954621
$185$	519177.	1.11528
$186$	−231842.	−0.491371
$187$	−266958.	−0.558263
$188$	291886.	0.602309
$189$	−3828.45	−0.00779593
$190$	278071.	0.558819
$191$	617949.	1.22566	0.612829	−	0.790215i	$-0.290031\pi$
$191$	617949.	1.22566	0.612829	+	0.790215i	$0.290031\pi$
$192$	36864.0	0.0721688
$193$	−536153.	−1.03609	−0.518043	−	0.855355i	$-0.673339\pi$
$193$	−536153.	−1.03609	−0.518043	+	0.855355i	$0.673339\pi$
$194$	−522038.	−0.995858
$195$	−276014.	−0.519810
$196$	−268471.	−0.499180
$197$	−358188.	−0.657575	−0.328787	−	0.944404i	$-0.606640\pi$
$197$	−358188.	−0.657575	−0.328787	+	0.944404i	$0.606640\pi$
$198$	−235381.	−0.426686
$199$	−767031.	−1.37303	−0.686516	−	0.727115i	$-0.740861\pi$
$199$	−767031.	−1.37303	−0.686516	+	0.727115i	$0.740861\pi$
$200$	−105130.	−0.185846
$201$	−325495.	−0.568268
$202$	387411.	0.668027
$203$	12979.4	0.0221063
$204$	52915.0	0.0890232
$205$	−322024.	−0.535184
$206$	633680.	1.04040
$207$	55485.6	0.0900025
$208$	203918.	0.326811
$209$	1.31174e6	2.07722
$210$	7278.99	0.0113900
$211$	572520.	0.885288	0.442644	−	0.896697i	$-0.354040\pi$
$211$	572520.	0.885288	0.442644	+	0.896697i	$0.354040\pi$
$212$	−477061.	−0.729011
$213$	−193015.	−0.291502
$214$	335588.	0.500924
$215$	55956.0	0.0825563
$216$	46656.0	0.0680414
$217$	33820.9	0.0487568
$218$	−922948.	−1.31533
$219$	505618.	0.712381
$220$	447528.	0.623395
$221$	292706.	0.403135
$222$	−485449.	−0.661092
$223$	553741.	0.745666	0.372833	−	0.927898i	$-0.378386\pi$
$223$	553741.	0.745666	0.372833	+	0.927898i	$0.378386\pi$
$224$	−5377.68	−0.00716102
$225$	−133056.	−0.175217
$226$	−956583.	−1.24581
$227$	464075.	0.597756	0.298878	−	0.954291i	$-0.403388\pi$
$227$	464075.	0.597756	0.298878	+	0.954291i	$0.403388\pi$
$228$	−260007.	−0.331243
$229$	1.55328e6	1.95731	0.978656	−	0.205507i	$-0.0658843\pi$
$229$	1.55328e6	1.95731	0.978656	+	0.205507i	$0.0658843\pi$
$230$	−105494.	−0.131495
$231$	34337.1	0.0423384
$232$	−158176.	−0.192939
$233$	464447.	0.560463	0.280231	−	0.959933i	$-0.409589\pi$
$233$	464447.	0.560463	0.280231	+	0.959933i	$0.409589\pi$
$234$	258084.	0.308121
$235$	−702372.	−0.829655
$236$	−55696.0	−0.0650945
$237$	149607.	0.173014
$238$	−7719.18	−0.00883342
$239$	797536.	0.903141	0.451570	−	0.892236i	$-0.350864\pi$
$239$	797536.	0.903141	0.451570	+	0.892236i	$0.350864\pi$
$240$	−88706.6	−0.0994095
$241$	461111.	0.511403	0.255701	−	0.966756i	$-0.417694\pi$
$241$	461111.	0.511403	0.255701	+	0.966756i	$0.417694\pi$
$242$	1.46692e6	1.61015
$243$	59049.0	0.0641500
$244$	−848910.	−0.912824
$245$	646027.	0.687599
$246$	301104.	0.317233
$247$	−1.43826e6	−1.50001
$248$	−412164.	−0.425540
$249$	850297.	0.869105
$250$	734242.	0.743000
$251$	967389.	0.969207	0.484604	−	0.874734i	$-0.338964\pi$
$251$	967389.	0.969207	0.484604	+	0.874734i	$0.338964\pi$
$252$	−6806.13	−0.00675148
$253$	−497648.	−0.488788
$254$	−1.01364e6	−0.985826
$255$	−127330.	−0.122626
$256$	65536.0	0.0625000
$257$	1.87818e6	1.77380	0.886900	−	0.461961i	$-0.152854\pi$
$257$	1.87818e6	1.77380	0.886900	+	0.461961i	$0.152854\pi$
$258$	−52320.9	−0.0489357
$259$	70816.9	0.0655975
$260$	−490692.	−0.450169
$261$	−200191.	−0.181905
$262$	−1.08894e6	−0.980058
$263$	1.49866e6	1.33602	0.668011	−	0.744151i	$-0.267146\pi$
$263$	1.49866e6	1.33602	0.668011	+	0.744151i	$0.267146\pi$
$264$	−418455.	−0.369521
$265$	1.14796e6	1.00418
$266$	37929.5	0.0328680
$267$	669764.	0.574968
$268$	−578657.	−0.492135
$269$	−1.24048e6	−1.04523	−0.522613	−	0.852570i	$-0.675043\pi$
$269$	−1.24048e6	−1.04523	−0.522613	+	0.852570i	$0.675043\pi$
$270$	−112269.	−0.0937242
$271$	−537188.	−0.444327	−0.222164	−	0.975009i	$-0.571312\pi$
$271$	−537188.	−0.444327	−0.222164	+	0.975009i	$0.571312\pi$
$272$	94071.1	0.0770964
$273$	−37649.0	−0.0305736
$274$	498859.	0.401422
$275$	1.19337e6	0.951575
$276$	98641.1	0.0779444
$277$	−2.36267e6	−1.85014	−0.925069	−	0.379799i	$-0.875993\pi$
$277$	−2.36267e6	−1.85014	−0.925069	+	0.379799i	$0.875993\pi$
$278$	−327241.	−0.253954
$279$	−521644.	−0.401203
$280$	12940.4	0.00986401
$281$	5919.96	0.00447253	0.00223626	−	0.999997i	$-0.499288\pi$
$281$	5919.96	0.00447253	0.00223626	+	0.999997i	$0.499288\pi$
$282$	656744.	0.491783
$283$	−1.16100e6	−0.861723	−0.430861	−	0.902418i	$-0.641790\pi$
$283$	−1.16100e6	−0.861723	−0.430861	+	0.902418i	$0.641790\pi$
$284$	−343137.	−0.252448
$285$	625659.	0.456274
$286$	−2.31474e6	−1.67335
$287$	−43924.8	−0.0314778
$288$	82944.0	0.0589256
$289$	−1.28483e6	−0.904898
$290$	380622.	0.265766
$291$	−1.17458e6	−0.813115
$292$	898877.	0.616940
$293$	−2.67792e6	−1.82234	−0.911170	−	0.412031i	$-0.864820\pi$
$293$	−2.67792e6	−1.82234	−0.911170	+	0.412031i	$0.864820\pi$
$294$	−604059.	−0.407578
$295$	134022.	0.0896649
$296$	−863021.	−0.572522
$297$	−529607.	−0.348388
$298$	222414.	0.145085
$299$	545646.	0.352966
$300$	−236543.	−0.151743
$301$	7632.52	0.00485570
$302$	1.84237e6	1.16241
$303$	871676.	0.545442
$304$	−462234.	−0.286865
$305$	2.04275e6	1.25738
$306$	119059.	0.0726872
$307$	2.68681e6	1.62701	0.813507	−	0.581555i	$-0.197556\pi$
$307$	2.68681e6	1.62701	0.813507	+	0.581555i	$0.197556\pi$
$308$	61043.8	0.0366661
$309$	1.42578e6	0.849486
$310$	991798.	0.586164
$311$	3.12248e6	1.83062	0.915311	−	0.402748i	$-0.131945\pi$
$311$	3.12248e6	1.83062	0.915311	+	0.402748i	$0.131945\pi$
$312$	458815.	0.266840
$313$	1.07057e6	0.617667	0.308834	−	0.951116i	$-0.400061\pi$
$313$	1.07057e6	0.617667	0.308834	+	0.951116i	$0.400061\pi$
$314$	−136143.	−0.0779240
$315$	16377.7	0.00929988
$316$	265969.	0.149835
$317$	235161.	0.131437	0.0657184	−	0.997838i	$-0.479066\pi$
$317$	235161.	0.131437	0.0657184	+	0.997838i	$0.479066\pi$
$318$	−1.07339e6	−0.595235
$319$	1.79551e6	0.987894
$320$	−157701.	−0.0860912
$321$	755073.	0.409003
$322$	−14389.7	−0.00773412
$323$	−663496.	−0.353860
$324$	104976.	0.0555556
$325$	−1.30847e6	−0.687156
$326$	1.56159e6	0.813809
$327$	−2.07663e6	−1.07397
$328$	535296.	0.274732
$329$	−95805.2	−0.0487977
$330$	1.00694e6	0.509000
$331$	2.60227e6	1.30551	0.652757	−	0.757567i	$-0.273612\pi$
$331$	2.60227e6	1.30551	0.652757	+	0.757567i	$0.273612\pi$
$332$	1.51164e6	0.752667
$333$	−1.09226e6	−0.539779
$334$	−454137.	−0.222752
$335$	1.39243e6	0.677896
$336$	−12099.8	−0.00584695
$337$	330303.	0.158430	0.0792152	−	0.996858i	$-0.474759\pi$
$337$	330303.	0.158430	0.0792152	+	0.996858i	$0.474759\pi$
$338$	1.05282e6	0.501260
$339$	−2.15231e6	−1.01720
$340$	−226365.	−0.106197
$341$	4.67860e6	2.17886
$342$	−585015.	−0.270459
$343$	176384.	0.0809513
$344$	−93015.0	−0.0423796
$345$	−237362.	−0.107365
$346$	−1.95994e6	−0.880140
$347$	−232592.	−0.103698	−0.0518490	−	0.998655i	$-0.516511\pi$
$347$	−232592.	−0.103698	−0.0518490	+	0.998655i	$0.516511\pi$
$348$	−355896.	−0.157534
$349$	765285.	0.336325	0.168163	−	0.985759i	$-0.446217\pi$
$349$	765285.	0.336325	0.168163	+	0.985759i	$0.446217\pi$
$350$	34506.7	0.0150568
$351$	580688.	0.251579
$352$	−743920.	−0.320015
$353$	2.47913e6	1.05892	0.529459	−	0.848335i	$-0.322395\pi$
$353$	2.47913e6	1.05892	0.529459	+	0.848335i	$0.322395\pi$
$354$	−125316.	−0.0531494
$355$	825699.	0.347737
$356$	1.19069e6	0.497937
$357$	−17368.2	−0.00721246
$358$	−1.37508e6	−0.567050
$359$	−860018.	−0.352185	−0.176093	−	0.984374i	$-0.556346\pi$
$359$	−860018.	−0.352185	−0.176093	+	0.984374i	$0.556346\pi$
$360$	−199590.	−0.0811675
$361$	784096.	0.316666
$362$	2.52983e6	1.01466
$363$	3.30056e6	1.31468
$364$	−66931.5	−0.0264775
$365$	−2.16299e6	−0.849810
$366$	−1.91005e6	−0.745318
$367$	−2.42086e6	−0.938219	−0.469109	−	0.883140i	$-0.655425\pi$
$367$	−2.42086e6	−0.938219	−0.469109	+	0.883140i	$0.655425\pi$
$368$	175362.	0.0675019
$369$	677484.	0.259020
$370$	2.07671e6	0.788626
$371$	156585.	0.0590628
$372$	−927368.	−0.347452
$373$	−3.47915e6	−1.29480	−0.647398	−	0.762152i	$-0.724143\pi$
$373$	−3.47915e6	−1.29480	−0.647398	+	0.762152i	$0.724143\pi$
$374$	−1.06783e6	−0.394752
$375$	1.65204e6	0.606657
$376$	1.16755e6	0.425897
$377$	−1.96868e6	−0.713382
$378$	−15313.8	−0.00551256
$379$	−3.76114e6	−1.34500	−0.672499	−	0.740098i	$-0.734779\pi$
$379$	−3.76114e6	−1.34500	−0.672499	+	0.740098i	$0.734779\pi$
$380$	1.11228e6	0.395145
$381$	−2.28069e6	−0.804923
$382$	2.47180e6	0.866671
$383$	−2.32163e6	−0.808715	−0.404358	−	0.914601i	$-0.632505\pi$
$383$	−2.32163e6	−0.808715	−0.404358	+	0.914601i	$0.632505\pi$
$384$	147456.	0.0510310
$385$	−146891.	−0.0505061
$386$	−2.14461e6	−0.732624
$387$	−117722.	−0.0399559
$388$	−2.08815e6	−0.704178
$389$	2.71526e6	0.909783	0.454891	−	0.890547i	$-0.349678\pi$
$389$	2.71526e6	0.909783	0.454891	+	0.890547i	$0.349678\pi$
$390$	−1.10406e6	−0.367561
$391$	251716.	0.0832664
$392$	−1.07388e6	−0.352973
$393$	−2.45012e6	−0.800214
$394$	−1.43275e6	−0.464976
$395$	−640006.	−0.206391
$396$	−941524.	−0.301713
$397$	1.97877e6	0.630113	0.315056	−	0.949073i	$-0.397977\pi$
$397$	1.97877e6	0.630113	0.315056	+	0.949073i	$0.397977\pi$
$398$	−3.06813e6	−0.970880
$399$	85341.3	0.0268366
$400$	−420521.	−0.131413
$401$	−1.87774e6	−0.583141	−0.291570	−	0.956549i	$-0.594178\pi$
$401$	−1.87774e6	−0.583141	−0.291570	+	0.956549i	$0.594178\pi$
$402$	−1.30198e6	−0.401826
$403$	−5.12985e6	−1.57341
$404$	1.54965e6	0.472366
$405$	−252606.	−0.0765255
$406$	51917.7	0.0156315
$407$	9.79643e6	2.93145
$408$	211660.	0.0629489
$409$	−5.39987e6	−1.59615	−0.798077	−	0.602556i	$-0.794149\pi$
$409$	−5.39987e6	−1.59615	−0.798077	+	0.602556i	$0.794149\pi$
$410$	−1.28809e6	−0.378432
$411$	1.12243e6	0.327760
$412$	2.53472e6	0.735676
$413$	18281.0	0.00527381
$414$	221942.	0.0636414
$415$	−3.63749e6	−1.03677
$416$	815671.	0.231090
$417$	−736292.	−0.207353
$418$	5.24697e6	1.46882
$419$	624652.	0.173821	0.0869107	−	0.996216i	$-0.472301\pi$
$419$	624652.	0.173821	0.0869107	+	0.996216i	$0.472301\pi$
$420$	29116.0	0.00805393
$421$	1.54281e6	0.424236	0.212118	−	0.977244i	$-0.431964\pi$
$421$	1.54281e6	0.424236	0.212118	+	0.977244i	$0.431964\pi$
$422$	2.29008e6	0.625993
$423$	1.47767e6	0.401539
$424$	−1.90824e6	−0.515489
$425$	−603621.	−0.162103
$426$	−772059.	−0.206123
$427$	278636.	0.0739549
$428$	1.34235e6	0.354207
$429$	−5.20816e6	−1.36628
$430$	223824.	0.0583761
$431$	−1.49730e6	−0.388254	−0.194127	−	0.980976i	$-0.562187\pi$
$431$	−1.49730e6	−0.388254	−0.194127	+	0.980976i	$0.562187\pi$
$432$	186624.	0.0481125
$433$	−1.85362e6	−0.475119	−0.237559	−	0.971373i	$-0.576347\pi$
$433$	−1.85362e6	−0.475119	−0.237559	+	0.971373i	$0.576347\pi$
$434$	135283.	0.0344763
$435$	856400.	0.216997
$436$	−3.69179e6	−0.930081
$437$	−1.23685e6	−0.309823
$438$	2.02247e6	0.503730
$439$	3.94601e6	0.977231	0.488615	−	0.872499i	$-0.337502\pi$
$439$	3.94601e6	0.977231	0.488615	+	0.872499i	$0.337502\pi$
$440$	1.79011e6	0.440807
$441$	−1.35913e6	−0.332786
$442$	1.17082e6	0.285060
$443$	−1.21680e6	−0.294584	−0.147292	−	0.989093i	$-0.547056\pi$
$443$	−1.21680e6	−0.294584	−0.147292	+	0.989093i	$0.547056\pi$
$444$	−1.94180e6	−0.467462
$445$	−2.86518e6	−0.685887
$446$	2.21496e6	0.527265
$447$	500432.	0.118461
$448$	−21510.7	−0.00506361
$449$	−1.15867e6	−0.271235	−0.135617	−	0.990761i	$-0.543302\pi$
$449$	−1.15867e6	−0.271235	−0.135617	+	0.990761i	$0.543302\pi$
$450$	−532222.	−0.123897
$451$	−6.07632e6	−1.40669
$452$	−3.82633e6	−0.880920
$453$	4.14534e6	0.949106
$454$	1.85630e6	0.422677
$455$	161059.	0.0364717
$456$	−1.04003e6	−0.234224
$457$	−7.29014e6	−1.63285	−0.816423	−	0.577454i	$-0.804046\pi$
$457$	−7.29014e6	−1.63285	−0.816423	+	0.577454i	$0.804046\pi$
$458$	6.21310e6	1.38403
$459$	267882.	0.0593488
$460$	−421977.	−0.0929810
$461$	−3.83688e6	−0.840864	−0.420432	−	0.907324i	$-0.638122\pi$
$461$	−3.83688e6	−0.840864	−0.420432	+	0.907324i	$0.638122\pi$
$462$	137349.	0.0299378
$463$	−7.92985e6	−1.71915	−0.859573	−	0.511013i	$-0.829270\pi$
$463$	−7.92985e6	−1.71915	−0.859573	+	0.511013i	$0.829270\pi$
$464$	−632704.	−0.136429
$465$	2.23155e6	0.478601
$466$	1.85779e6	0.396307
$467$	−5.16217e6	−1.09532	−0.547659	−	0.836702i	$-0.684481\pi$
$467$	−5.16217e6	−1.09532	−0.547659	+	0.836702i	$0.684481\pi$
$468$	1.03233e6	0.217874
$469$	189931.	0.0398717
$470$	−2.80949e6	−0.586655
$471$	−306322.	−0.0636247
$472$	−222784.	−0.0460287
$473$	1.05584e6	0.216993
$474$	598429.	0.122340
$475$	2.96599e6	0.603165
$476$	−30876.7	−0.00624617
$477$	−2.41512e6	−0.486007
$478$	3.19014e6	0.638617
$479$	−5.91213e6	−1.17735	−0.588675	−	0.808370i	$-0.700350\pi$
$479$	−5.91213e6	−1.17735	−0.588675	+	0.808370i	$0.700350\pi$
$480$	−354827.	−0.0702931
$481$	−1.07413e7	−2.11687
$482$	1.84445e6	0.361616
$483$	−32376.7	−0.00631488
$484$	5.86767e6	1.13855
$485$	5.02476e6	0.969976
$486$	236196.	0.0453609
$487$	−793064.	−0.151526	−0.0757628	−	0.997126i	$-0.524139\pi$
$487$	−793064.	−0.151526	−0.0757628	+	0.997126i	$0.524139\pi$
$488$	−3.39564e6	−0.645464
$489$	3.51357e6	0.664472
$490$	2.58411e6	0.486206
$491$	−7.05328e6	−1.32034	−0.660172	−	0.751114i	$-0.729517\pi$
$491$	−7.05328e6	−1.32034	−0.660172	+	0.751114i	$0.729517\pi$
$492$	1.20442e6	0.224318
$493$	−908190.	−0.168290
$494$	−5.75304e6	−1.06067
$495$	2.26561e6	0.415597
$496$	−1.64865e6	−0.300902
$497$	112627.	0.0204528
$498$	3.40119e6	0.614550
$499$	3.91905e6	0.704578	0.352289	−	0.935891i	$-0.385403\pi$
$499$	3.91905e6	0.704578	0.352289	+	0.935891i	$0.385403\pi$
$500$	2.93697e6	0.525381
$501$	−1.02181e6	−0.181876
$502$	3.86956e6	0.685333
$503$	2.39884e6	0.422748	0.211374	−	0.977405i	$-0.432206\pi$
$503$	2.39884e6	0.422748	0.211374	+	0.977405i	$0.432206\pi$
$504$	−27224.5	−0.00477402
$505$	−3.72895e6	−0.650665
$506$	−1.99059e6	−0.345625
$507$	2.36885e6	0.409277
$508$	−4.05457e6	−0.697084
$509$	−2.96244e6	−0.506821	−0.253410	−	0.967359i	$-0.581552\pi$
$509$	−2.96244e6	−0.506821	−0.253410	+	0.967359i	$0.581552\pi$
$510$	−509322.	−0.0867096
$511$	−295036.	−0.0499831
$512$	262144.	0.0441942
$513$	−1.31628e6	−0.220829
$514$	7.51273e6	1.25427
$515$	−6.09935e6	−1.01336
$516$	−209284.	−0.0346028
$517$	−1.32532e7	−2.18069
$518$	283267.	0.0463844
$519$	−4.40986e6	−0.718631
$520$	−1.96277e6	−0.318317
$521$	4.78031e6	0.771546	0.385773	−	0.922594i	$-0.373935\pi$
$521$	4.78031e6	0.771546	0.385773	+	0.922594i	$0.373935\pi$
$522$	−800765.	−0.128626
$523$	1.83246e6	0.292941	0.146470	−	0.989215i	$-0.453209\pi$
$523$	1.83246e6	0.292941	0.146470	+	0.989215i	$0.453209\pi$
$524$	−4.35577e6	−0.693006
$525$	77640.1	0.0122938
$526$	5.99464e6	0.944711
$527$	−2.36650e6	−0.371176
$528$	−1.67382e6	−0.261291
$529$	−5.96711e6	−0.927096
$530$	4.59185e6	0.710064
$531$	−281961.	−0.0433963
$532$	151718.	0.0232412
$533$	6.66238e6	1.01581
$534$	2.67905e6	0.406564
$535$	−3.23013e6	−0.487905
$536$	−2.31463e6	−0.347992
$537$	−3.09394e6	−0.462995
$538$	−4.96194e6	−0.739087
$539$	1.21900e7	1.80731
$540$	−449077.	−0.0662730
$541$	9.32404e6	1.36965	0.684827	−	0.728706i	$-0.259878\pi$
$541$	9.32404e6	1.36965	0.684827	+	0.728706i	$0.259878\pi$
$542$	−2.14875e6	−0.314187
$543$	5.69212e6	0.828465
$544$	376284.	0.0545154
$545$	8.88364e6	1.28115
$546$	−150596.	−0.0216188
$547$	−4.95120e6	−0.707526	−0.353763	−	0.935335i	$-0.615098\pi$
$547$	−4.95120e6	−0.707526	−0.353763	+	0.935335i	$0.615098\pi$
$548$	1.99544e6	0.283848
$549$	−4.29761e6	−0.608549
$550$	4.77348e6	0.672865
$551$	4.46254e6	0.626186
$552$	394564.	0.0551150
$553$	−87298.3	−0.0121393
$554$	−9.45069e6	−1.30825
$555$	4.67259e6	0.643910
$556$	−1.30896e6	−0.179573
$557$	−3.39220e6	−0.463280	−0.231640	−	0.972802i	$-0.574409\pi$
$557$	−3.39220e6	−0.463280	−0.231640	+	0.972802i	$0.574409\pi$
$558$	−2.08658e6	−0.283693
$559$	−1.15768e6	−0.156696
$560$	51761.7	0.00697491
$561$	−2.40262e6	−0.322313
$562$	23679.8	0.00316255
$563$	−1.14118e6	−0.151734	−0.0758670	−	0.997118i	$-0.524172\pi$
$563$	−1.14118e6	−0.151734	−0.0758670	+	0.997118i	$0.524172\pi$
$564$	2.62698e6	0.347743
$565$	9.20738e6	1.21343
$566$	−4.64402e6	−0.609330
$567$	−34456.0	−0.00450099
$568$	−1.37255e6	−0.178508
$569$	−191931.	−0.0248522	−0.0124261	−	0.999923i	$-0.503955\pi$
$569$	−191931.	−0.0248522	−0.0124261	+	0.999923i	$0.503955\pi$
$570$	2.50264e6	0.322634
$571$	−7.05321e6	−0.905309	−0.452654	−	0.891686i	$-0.649523\pi$
$571$	−7.05321e6	−0.905309	−0.452654	+	0.891686i	$0.649523\pi$
$572$	−9.25895e6	−1.18324
$573$	5.56154e6	0.707634
$574$	−175699.	−0.0222582
$575$	−1.12524e6	−0.141930
$576$	331776.	0.0416667
$577$	4.17676e6	0.522276	0.261138	−	0.965302i	$-0.415902\pi$
$577$	4.17676e6	0.522276	0.261138	+	0.965302i	$0.415902\pi$
$578$	−5.13931e6	−0.639860
$579$	−4.82538e6	−0.598185
$580$	1.52249e6	0.187925
$581$	−496162.	−0.0609794
$582$	−4.69834e6	−0.574959
$583$	2.16611e7	2.63942
$584$	3.59551e6	0.436243
$585$	−2.48413e6	−0.300113
$586$	−1.07117e7	−1.28859
$587$	−1.24694e7	−1.49365	−0.746826	−	0.665020i	$-0.768423\pi$
$587$	−1.24694e7	−1.49365	−0.746826	+	0.665020i	$0.768423\pi$
$588$	−2.41624e6	−0.288201
$589$	1.16282e7	1.38109
$590$	536090.	0.0634027
$591$	−3.22369e6	−0.379651
$592$	−3.45209e6	−0.404834
$593$	3.43217e6	0.400804	0.200402	−	0.979714i	$-0.435775\pi$
$593$	3.43217e6	0.400804	0.200402	+	0.979714i	$0.435775\pi$
$594$	−2.11843e6	−0.246347
$595$	74299.4	0.00860385
$596$	889656.	0.102590
$597$	−6.90328e6	−0.792720
$598$	2.18258e6	0.249585
$599$	−8.38745e6	−0.955131	−0.477566	−	0.878596i	$-0.658481\pi$
$599$	−8.38745e6	−0.955131	−0.477566	+	0.878596i	$0.658481\pi$
$600$	−946173.	−0.107298
$601$	−9.46344e6	−1.06872	−0.534359	−	0.845258i	$-0.679447\pi$
$601$	−9.46344e6	−1.06872	−0.534359	+	0.845258i	$0.679447\pi$
$602$	30530.1	0.00343350
$603$	−2.92945e6	−0.328090
$604$	7.36950e6	0.821950
$605$	−1.41195e7	−1.56831
$606$	3.48670e6	0.385685
$607$	7.88763e6	0.868910	0.434455	−	0.900694i	$-0.356941\pi$
$607$	7.88763e6	0.868910	0.434455	+	0.900694i	$0.356941\pi$
$608$	−1.84894e6	−0.202844
$609$	116815.	0.0127631
$610$	8.17100e6	0.889100
$611$	1.45315e7	1.57473
$612$	476235.	0.0513976
$613$	−1.86620e6	−0.200589	−0.100294	−	0.994958i	$-0.531978\pi$
$613$	−1.86620e6	−0.200589	−0.100294	+	0.994958i	$0.531978\pi$
$614$	1.07472e7	1.15047
$615$	−2.89821e6	−0.308989
$616$	244175.	0.0259269
$617$	−6.00082e6	−0.634597	−0.317298	−	0.948326i	$-0.602776\pi$
$617$	−6.00082e6	−0.634597	−0.317298	+	0.948326i	$0.602776\pi$
$618$	5.70312e6	0.600677
$619$	−1.69070e7	−1.77353	−0.886766	−	0.462219i	$-0.847053\pi$
$619$	−1.69070e7	−1.77353	−0.886766	+	0.462219i	$0.847053\pi$
$620$	3.96719e6	0.414480
$621$	499371.	0.0519630
$622$	1.24899e7	1.29444
$623$	−390818.	−0.0403417
$624$	1.83526e6	0.188685
$625$	−1.93397e6	−0.198038
$626$	4.28228e6	0.436757
$627$	1.18057e7	1.19928
$628$	−544572.	−0.0551006
$629$	−4.95516e6	−0.499380
$630$	65510.9	0.00657601
$631$	−4.16243e6	−0.416173	−0.208086	−	0.978110i	$-0.566724\pi$
$631$	−4.16243e6	−0.416173	−0.208086	+	0.978110i	$0.566724\pi$
$632$	1.06387e6	0.105949
$633$	5.15268e6	0.511122
$634$	940643.	0.0929398
$635$	9.75659e6	0.960205
$636$	−4.29355e6	−0.420895
$637$	−1.33657e7	−1.30510
$638$	7.18202e6	0.698546
$639$	−1.73713e6	−0.168299
$640$	−630803.	−0.0608757
$641$	−1.22687e7	−1.17938	−0.589689	−	0.807630i	$-0.700750\pi$
$641$	−1.22687e7	−1.17938	−0.589689	+	0.807630i	$0.700750\pi$
$642$	3.02029e6	0.289209
$643$	1.29271e7	1.23303	0.616516	−	0.787342i	$-0.288544\pi$
$643$	1.29271e7	1.23303	0.616516	+	0.787342i	$0.288544\pi$
$644$	−57558.6	−0.00546885
$645$	503604.	0.0476639
$646$	−2.65398e6	−0.250217
$647$	−7.41604e6	−0.696484	−0.348242	−	0.937405i	$-0.613221\pi$
$647$	−7.41604e6	−0.696484	−0.348242	+	0.937405i	$0.613221\pi$
$648$	419904.	0.0392837
$649$	2.52889e6	0.235678
$650$	−5.23388e6	−0.485892
$651$	304388.	0.0281498
$652$	6.24635e6	0.575450
$653$	5.31793e6	0.488045	0.244022	−	0.969770i	$-0.421533\pi$
$653$	5.31793e6	0.488045	0.244022	+	0.969770i	$0.421533\pi$
$654$	−8.30653e6	−0.759408
$655$	1.04814e7	0.954587
$656$	2.14119e6	0.194265
$657$	4.55057e6	0.411294
$658$	−383221.	−0.0345052
$659$	−7.40168e6	−0.663921	−0.331961	−	0.943293i	$-0.607710\pi$
$659$	−7.40168e6	−0.663921	−0.331961	+	0.943293i	$0.607710\pi$
$660$	4.02775e6	0.359917
$661$	−1.70552e7	−1.51829	−0.759143	−	0.650924i	$-0.774382\pi$
$661$	−1.70552e7	−1.51829	−0.759143	+	0.650924i	$0.774382\pi$
$662$	1.04091e7	0.923138
$663$	2.63435e6	0.232750
$664$	6.04656e6	0.532216
$665$	−365082.	−0.0320137
$666$	−4.36905e6	−0.381681
$667$	−1.69300e6	−0.147347
$668$	−1.81655e6	−0.157509
$669$	4.98367e6	0.430510
$670$	5.56974e6	0.479345
$671$	3.85450e7	3.30493
$672$	−48399.1	−0.00413442
$673$	−1.37026e7	−1.16618	−0.583091	−	0.812407i	$-0.698157\pi$
$673$	−1.37026e7	−1.16618	−0.583091	+	0.812407i	$0.698157\pi$
$674$	1.32121e6	0.112027
$675$	−1.19750e6	−0.101162
$676$	4.21129e6	0.354444
$677$	1.29972e7	1.08988	0.544938	−	0.838476i	$-0.316553\pi$
$677$	1.29972e7	1.08988	0.544938	+	0.838476i	$0.316553\pi$
$678$	−8.60925e6	−0.719268
$679$	685389.	0.0570509
$680$	−905461.	−0.0750927
$681$	4.17668e6	0.345115
$682$	1.87144e7	1.54069
$683$	2.60488e6	0.213666	0.106833	−	0.994277i	$-0.465929\pi$
$683$	2.60488e6	0.213666	0.106833	+	0.994277i	$0.465929\pi$
$684$	−2.34006e6	−0.191243
$685$	−4.80166e6	−0.390990
$686$	705536.	0.0572412
$687$	1.39795e7	1.13005
$688$	−372060.	−0.0299669
$689$	−2.37503e7	−1.90599
$690$	−949449.	−0.0759187
$691$	6.35911e6	0.506642	0.253321	−	0.967382i	$-0.418477\pi$
$691$	6.35911e6	0.506642	0.253321	+	0.967382i	$0.418477\pi$
$692$	−7.83975e6	−0.622353
$693$	309034.	0.0244441
$694$	−930367.	−0.0733256
$695$	3.14979e6	0.247354
$696$	−1.42358e6	−0.111393
$697$	3.07348e6	0.239634
$698$	3.06114e6	0.237818
$699$	4.18003e6	0.323583
$700$	138027.	0.0106468
$701$	7.42137e6	0.570412	0.285206	−	0.958466i	$-0.407938\pi$
$701$	7.42137e6	0.570412	0.285206	+	0.958466i	$0.407938\pi$
$702$	2.32275e6	0.177893
$703$	2.43480e7	1.85813
$704$	−2.97568e6	−0.226285
$705$	−6.32135e6	−0.479002
$706$	9.91652e6	0.748769
$707$	−508637.	−0.0382700
$708$	−501264.	−0.0375823
$709$	2.03605e7	1.52115	0.760577	−	0.649248i	$-0.224916\pi$
$709$	2.03605e7	1.52115	0.760577	+	0.649248i	$0.224916\pi$
$710$	3.30280e6	0.245887
$711$	1.34647e6	0.0998899
$712$	4.76276e6	0.352094
$713$	−4.41149e6	−0.324983
$714$	−69472.7	−0.00509998
$715$	2.22800e7	1.62986
$716$	−5.50034e6	−0.400965
$717$	7.17782e6	0.521429
$718$	−3.44007e6	−0.249033
$719$	−8.68253e6	−0.626360	−0.313180	−	0.949694i	$-0.601394\pi$
$719$	−8.68253e6	−0.626360	−0.313180	+	0.949694i	$0.601394\pi$
$720$	−798360.	−0.0573941
$721$	−831965.	−0.0596028
$722$	3.13638e6	0.223917
$723$	4.15000e6	0.295259
$724$	1.01193e7	0.717472
$725$	4.05984e6	0.286856
$726$	1.32023e7	0.929622
$727$	1.82909e7	1.28351	0.641754	−	0.766911i	$-0.278207\pi$
$727$	1.82909e7	1.28351	0.641754	+	0.766911i	$0.278207\pi$
$728$	−267726.	−0.0187224
$729$	531441.	0.0370370
$730$	−8.65195e6	−0.600906
$731$	−534059.	−0.0369654
$732$	−7.64019e6	−0.527019
$733$	5.09976e6	0.350582	0.175291	−	0.984517i	$-0.443913\pi$
$733$	5.09976e6	0.350582	0.175291	+	0.984517i	$0.443913\pi$
$734$	−9.68343e6	−0.663421
$735$	5.81424e6	0.396986
$736$	701448.	0.0477310
$737$	2.62741e7	1.78180
$738$	2.70994e6	0.183155
$739$	7.06722e6	0.476034	0.238017	−	0.971261i	$-0.423503\pi$
$739$	7.06722e6	0.476034	0.238017	+	0.971261i	$0.423503\pi$
$740$	8.30683e6	0.557642
$741$	−1.29443e7	−0.866032
$742$	626338.	0.0417637
$743$	1.99220e7	1.32391	0.661957	−	0.749541i	$-0.269726\pi$
$743$	1.99220e7	1.32391	0.661957	+	0.749541i	$0.269726\pi$
$744$	−3.70947e6	−0.245686
$745$	−2.14080e6	−0.141314
$746$	−1.39166e7	−0.915559
$747$	7.65267e6	0.501778
$748$	−4.27133e6	−0.279131
$749$	−440597.	−0.0286970
$750$	6.60818e6	0.428971
$751$	3.18383e6	0.205992	0.102996	−	0.994682i	$-0.467157\pi$
$751$	3.18383e6	0.205992	0.102996	+	0.994682i	$0.467157\pi$
$752$	4.67018e6	0.301154
$753$	8.70650e6	0.559572
$754$	−7.87473e6	−0.504437
$755$	−1.77334e7	−1.13220
$756$	−61255.2	−0.00389797
$757$	−1.75374e7	−1.11231	−0.556154	−	0.831079i	$-0.687723\pi$
$757$	−1.75374e7	−1.11231	−0.556154	+	0.831079i	$0.687723\pi$
$758$	−1.50446e7	−0.951057
$759$	−4.47883e6	−0.282202
$760$	4.44913e6	0.279410
$761$	−1.44490e7	−0.904434	−0.452217	−	0.891908i	$-0.649367\pi$
$761$	−1.44490e7	−0.904434	−0.452217	+	0.891908i	$0.649367\pi$
$762$	−9.12278e6	−0.569167
$763$	1.21175e6	0.0753531
$764$	9.88719e6	0.612829
$765$	−1.14597e6	−0.0707981
$766$	−9.28651e6	−0.571848
$767$	−2.77280e6	−0.170189
$768$	589824.	0.0360844
$769$	2.39415e7	1.45994	0.729972	−	0.683478i	$-0.239533\pi$
$769$	2.39415e7	1.45994	0.729972	+	0.683478i	$0.239533\pi$
$770$	−587564.	−0.0357132
$771$	1.69036e7	1.02410
$772$	−8.57846e6	−0.518043
$773$	2.47465e6	0.148958	0.0744791	−	0.997223i	$-0.476271\pi$
$773$	2.47465e6	0.148958	0.0744791	+	0.997223i	$0.476271\pi$
$774$	−470888.	−0.0282531
$775$	1.05788e7	0.632679
$776$	−8.35260e6	−0.497929
$777$	637352.	0.0378727
$778$	1.08610e7	0.643314
$779$	−1.51021e7	−0.891646
$780$	−4.41623e6	−0.259905
$781$	1.55803e7	0.914002
$782$	1.00687e6	0.0588782
$783$	−1.80172e6	−0.105023
$784$	−4.29553e6	−0.249590
$785$	1.31041e6	0.0758988
$786$	−9.80048e6	−0.565837
$787$	−2.56242e7	−1.47473	−0.737367	−	0.675493i	$-0.763931\pi$
$787$	−2.56242e7	−1.47473	−0.737367	+	0.675493i	$0.763931\pi$
$788$	−5.73101e6	−0.328787
$789$	1.34879e7	0.771353
$790$	−2.56002e6	−0.145941
$791$	1.25591e6	0.0713702
$792$	−3.76610e6	−0.213343
$793$	−4.22627e7	−2.38657
$794$	7.91507e6	0.445557
$795$	1.03317e7	0.579765
$796$	−1.22725e7	−0.686516
$797$	−2.04856e7	−1.14236	−0.571180	−	0.820825i	$-0.693514\pi$
$797$	−2.04856e7	−1.14236	−0.571180	+	0.820825i	$0.693514\pi$
$798$	341365.	0.0189763
$799$	6.70363e6	0.371487
$800$	−1.68209e6	−0.0929230
$801$	6.02787e6	0.331958
$802$	−7.51094e6	−0.412343
$803$	−4.08138e7	−2.23366
$804$	−5.20791e6	−0.284134
$805$	138505.	0.00753311
$806$	−2.05194e7	−1.11257
$807$	−1.11644e7	−0.603462
$808$	6.19858e6	0.334013
$809$	3.21080e7	1.72482	0.862408	−	0.506215i	$-0.168956\pi$
$809$	3.21080e7	1.72482	0.862408	+	0.506215i	$0.168956\pi$
$810$	−1.01042e6	−0.0541117
$811$	2.25578e7	1.20433	0.602164	−	0.798372i	$-0.294305\pi$
$811$	2.25578e7	1.20433	0.602164	+	0.798372i	$0.294305\pi$
$812$	207671.	0.0110531
$813$	−4.83469e6	−0.256532
$814$	3.91857e7	2.07285
$815$	−1.50307e7	−0.792659
$816$	846640.	0.0445116
$817$	2.62419e6	0.137543
$818$	−2.15995e7	−1.12865
$819$	−338841.	−0.0176517
$820$	−5.15238e6	−0.267592
$821$	192671.	0.00997606	0.00498803	−	0.999988i	$-0.498412\pi$
$821$	192671.	0.00997606	0.00498803	+	0.999988i	$0.498412\pi$
$822$	4.48973e6	0.231761
$823$	2.16425e6	0.111380	0.0556900	−	0.998448i	$-0.482264\pi$
$823$	2.16425e6	0.111380	0.0556900	+	0.998448i	$0.482264\pi$
$824$	1.01389e7	0.520202
$825$	1.07403e7	0.549392
$826$	73123.9	0.00372914
$827$	−3.57821e6	−0.181929	−0.0909645	−	0.995854i	$-0.528995\pi$
$827$	−3.57821e6	−0.181929	−0.0909645	+	0.995854i	$0.528995\pi$
$828$	887770.	0.0450012
$829$	3.03208e7	1.53234	0.766169	−	0.642639i	$-0.222161\pi$
$829$	3.03208e7	1.53234	0.766169	+	0.642639i	$0.222161\pi$
$830$	−1.45500e7	−0.733106
$831$	−2.12641e7	−1.06818
$832$	3.26269e6	0.163406
$833$	−6.16585e6	−0.307879
$834$	−2.94517e6	−0.146621
$835$	4.37120e6	0.216962
$836$	2.09879e7	1.03861
$837$	−4.69480e6	−0.231635
$838$	2.49861e6	0.122910
$839$	1.34207e7	0.658221	0.329110	−	0.944291i	$-0.393251\pi$
$839$	1.34207e7	0.658221	0.329110	+	0.944291i	$0.393251\pi$
$840$	116464.	0.00569499
$841$	−1.44028e7	−0.702196
$842$	6.17124e6	0.299980
$843$	53279.7	0.00258222
$844$	9.16033e6	0.442644
$845$	−1.01337e7	−0.488232
$846$	5.91070e6	0.283931
$847$	−1.92593e6	−0.0922427
$848$	−7.63297e6	−0.364505
$849$	−1.04490e7	−0.497516
$850$	−2.41448e6	−0.114624
$851$	−9.23713e6	−0.437233
$852$	−3.08824e6	−0.145751
$853$	−2.42960e7	−1.14331	−0.571654	−	0.820495i	$-0.693698\pi$
$853$	−2.42960e7	−1.14331	−0.571654	+	0.820495i	$0.693698\pi$
$854$	1.11454e6	0.0522940
$855$	5.63093e6	0.263430
$856$	5.36941e6	0.250462
$857$	−3.25871e7	−1.51563	−0.757816	−	0.652468i	$-0.773734\pi$
$857$	−3.25871e7	−1.51563	−0.757816	+	0.652468i	$0.773734\pi$
$858$	−2.08326e7	−0.966109
$859$	−6.81281e6	−0.315024	−0.157512	−	0.987517i	$-0.550347\pi$
$859$	−6.81281e6	−0.315024	−0.157512	+	0.987517i	$0.550347\pi$
$860$	895296.	0.0412782
$861$	−395323.	−0.0181737
$862$	−5.98920e6	−0.274537
$863$	2.14865e7	0.982063	0.491032	−	0.871142i	$-0.336620\pi$
$863$	2.14865e7	0.982063	0.491032	+	0.871142i	$0.336620\pi$
$864$	746496.	0.0340207
$865$	1.88650e7	0.857266
$866$	−7.41450e6	−0.335960
$867$	−1.15634e7	−0.522443
$868$	541134.	0.0243784
$869$	−1.20764e7	−0.542485
$870$	3.42560e6	0.153440
$871$	−2.88082e7	−1.28668
$872$	−1.47672e7	−0.657667
$873$	−1.05713e7	−0.469452
$874$	−4.94740e6	−0.219078
$875$	−963994.	−0.0425651
$876$	8.08989e6	0.356191
$877$	−2.20718e7	−0.969033	−0.484517	−	0.874782i	$-0.661004\pi$
$877$	−2.20718e7	−0.969033	−0.484517	+	0.874782i	$0.661004\pi$
$878$	1.57840e7	0.691006
$879$	−2.41013e7	−1.05213
$880$	7.16045e6	0.311698
$881$	2.02737e7	0.880019	0.440010	−	0.897993i	$-0.354975\pi$
$881$	2.02737e7	0.880019	0.440010	+	0.897993i	$0.354975\pi$
$882$	−5.43653e6	−0.235315
$883$	−3.69556e6	−0.159507	−0.0797533	−	0.996815i	$-0.525413\pi$
$883$	−3.69556e6	−0.159507	−0.0797533	+	0.996815i	$0.525413\pi$
$884$	4.68329e6	0.201568
$885$	1.20620e6	0.0517681
$886$	−4.86719e6	−0.208302
$887$	1.92648e7	0.822157	0.411079	−	0.911600i	$-0.365152\pi$
$887$	1.92648e7	0.822157	0.411079	+	0.911600i	$0.365152\pi$
$888$	−7.76719e6	−0.330546
$889$	1.33082e6	0.0564762
$890$	−1.14607e7	−0.484995
$891$	−4.76647e6	−0.201142
$892$	8.85985e6	0.372833
$893$	−3.29394e7	−1.38225
$894$	2.00173e6	0.0837647
$895$	1.32356e7	0.552313
$896$	−86042.9	−0.00358051
$897$	4.91081e6	0.203785
$898$	−4.63470e6	−0.191792
$899$	1.59166e7	0.656827
$900$	−2.12889e6	−0.0876086
$901$	−1.09565e7	−0.449633
$902$	−2.43053e7	−0.994682
$903$	68692.7	0.00280344
$904$	−1.53053e7	−0.622905
$905$	−2.43503e7	−0.988288
$906$	1.65814e7	0.671120
$907$	1.09046e7	0.440142	0.220071	−	0.975484i	$-0.429371\pi$
$907$	1.09046e7	0.440142	0.220071	+	0.975484i	$0.429371\pi$
$908$	7.42521e6	0.298878
$909$	7.84508e6	0.314911
$910$	644235.	0.0257894
$911$	6.98688e6	0.278925	0.139463	−	0.990227i	$-0.455463\pi$
$911$	6.98688e6	0.278925	0.139463	+	0.990227i	$0.455463\pi$
$912$	−4.16010e6	−0.165622
$913$	−6.86364e7	−2.72507
$914$	−2.91606e7	−1.15460
$915$	1.83848e7	0.725947
$916$	2.48524e7	0.978656
$917$	1.42968e6	0.0561457
$918$	1.07153e6	0.0419660
$919$	1.19623e7	0.467226	0.233613	−	0.972330i	$-0.424945\pi$
$919$	1.19623e7	0.467226	0.233613	+	0.972330i	$0.424945\pi$
$920$	−1.68791e6	−0.0657475
$921$	2.41813e7	0.939357
$922$	−1.53475e7	−0.594581
$923$	−1.70830e7	−0.660023
$924$	549394.	0.0211692
$925$	2.21508e7	0.851207
$926$	−3.17194e7	−1.21562
$927$	1.28320e7	0.490451
$928$	−2.53081e6	−0.0964696
$929$	−3.66913e7	−1.39484	−0.697419	−	0.716663i	$-0.745668\pi$
$929$	−3.66913e7	−1.39484	−0.697419	+	0.716663i	$0.745668\pi$
$930$	8.92618e6	0.338422
$931$	3.02969e7	1.14558
$932$	7.43116e6	0.280231
$933$	2.81023e7	1.05691
$934$	−2.06487e7	−0.774507
$935$	1.02782e7	0.384492
$936$	4.12934e6	0.154060
$937$	−5.02197e7	−1.86864	−0.934319	−	0.356438i	$-0.883991\pi$
$937$	−5.02197e7	−1.86864	−0.934319	+	0.356438i	$0.883991\pi$
$938$	759725.	0.0281935
$939$	9.63514e6	0.356610
$940$	−1.12380e7	−0.414828
$941$	2.40201e7	0.884303	0.442151	−	0.896940i	$-0.354215\pi$
$941$	2.40201e7	0.884303	0.442151	+	0.896940i	$0.354215\pi$
$942$	−1.22529e6	−0.0449894
$943$	5.72941e6	0.209812
$944$	−891136.	−0.0325472
$945$	147400.	0.00536929
$946$	4.22337e6	0.153438
$947$	−1.52938e7	−0.554168	−0.277084	−	0.960846i	$-0.589368\pi$
$947$	−1.52938e7	−0.554168	−0.277084	+	0.960846i	$0.589368\pi$
$948$	2.39372e6	0.0865072
$949$	4.47503e7	1.61298
$950$	1.18640e7	0.426502
$951$	2.11645e6	0.0758851
$952$	−123507.	−0.00441671
$953$	−1.93059e7	−0.688584	−0.344292	−	0.938863i	$-0.611881\pi$
$953$	−1.93059e7	−0.688584	−0.344292	+	0.938863i	$0.611881\pi$
$954$	−9.66048e6	−0.343659
$955$	−2.37918e7	−0.844147
$956$	1.27606e7	0.451570
$957$	1.61596e7	0.570361
$958$	−2.36485e7	−0.832512
$959$	−654958.	−0.0229968
$960$	−1.41931e6	−0.0497048
$961$	1.28452e7	0.448674
$962$	−4.29652e7	−1.49685
$963$	6.79566e6	0.236138
$964$	7.37778e6	0.255701
$965$	2.06425e7	0.713583
$966$	−129507.	−0.00446530
$967$	1.02695e6	0.0353169	0.0176585	−	0.999844i	$-0.494379\pi$
$967$	1.02695e6	0.0353169	0.0176585	+	0.999844i	$0.494379\pi$
$968$	2.34707e7	0.805076
$969$	−5.97146e6	−0.204301
$970$	2.00990e7	0.685877
$971$	−3.48063e7	−1.18470	−0.592352	−	0.805679i	$-0.701800\pi$
$971$	−3.48063e7	−1.18470	−0.592352	+	0.805679i	$0.701800\pi$
$972$	944784.	0.0320750
$973$	429638.	0.0145486
$974$	−3.17226e6	−0.107145
$975$	−1.17762e7	−0.396729
$976$	−1.35826e7	−0.456412
$977$	2.92300e7	0.979697	0.489848	−	0.871808i	$-0.337052\pi$
$977$	2.92300e7	0.979697	0.489848	+	0.871808i	$0.337052\pi$
$978$	1.40543e7	0.469853
$979$	−5.40637e7	−1.80281
$980$	1.03364e7	0.343800
$981$	−1.86897e7	−0.620054
$982$	−2.82131e7	−0.933625
$983$	2.41834e7	0.798239	0.399120	−	0.916899i	$-0.369316\pi$
$983$	2.41834e7	0.798239	0.399120	+	0.916899i	$0.369316\pi$
$984$	4.81767e6	0.158617
$985$	1.37906e7	0.452891
$986$	−3.63276e6	−0.118999
$987$	−862246.	−0.0281734
$988$	−2.30121e7	−0.750006
$989$	−995562.	−0.0323651
$990$	9.06244e6	0.293871
$991$	2.05617e7	0.665081	0.332541	−	0.943089i	$-0.392094\pi$
$991$	2.05617e7	0.665081	0.332541	+	0.943089i	$0.392094\pi$
$992$	−6.59462e6	−0.212770
$993$	2.34204e7	0.753739
$994$	450509.	0.0144623
$995$	2.95316e7	0.945647
$996$	1.36048e7	0.434553
$997$	5.38029e7	1.71422	0.857112	−	0.515130i	$-0.172256\pi$
$997$	5.38029e7	1.71422	0.857112	+	0.515130i	$0.172256\pi$
$998$	1.56762e7	0.498212
$999$	−9.83035e6	−0.311642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.b.1.2	✓	4
3.2	odd	2		1062.6.a.b.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.b.1.2	✓	4	1.1	even	1	trivial
1062.6.a.b.1.3		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -38.5011 q^{5} +36.0000 q^{6} -5.25164 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -38.5011 q^{5} +36.0000 q^{6} -5.25164 q^{7} +64.0000 q^{8} +81.0000 q^{9} -154.005 q^{10} -726.485 q^{11} +144.000 q^{12} +796.554 q^{13} -21.0066 q^{14} -346.510 q^{15} +256.000 q^{16} +367.465 q^{17} +324.000 q^{18} -1805.60 q^{19} -616.018 q^{20} -47.2648 q^{21} -2905.94 q^{22} +685.008 q^{23} +576.000 q^{24} -1642.66 q^{25} +3186.22 q^{26} +729.000 q^{27} -84.0263 q^{28} -2471.50 q^{29} -1386.04 q^{30} -6440.06 q^{31} +1024.00 q^{32} -6538.36 q^{33} +1469.86 q^{34} +202.194 q^{35} +1296.00 q^{36} -13484.7 q^{37} -7222.40 q^{38} +7168.99 q^{39} -2464.07 q^{40} +8364.00 q^{41} -189.059 q^{42} -1453.36 q^{43} -11623.8 q^{44} -3118.59 q^{45} +2740.03 q^{46} +18242.9 q^{47} +2304.00 q^{48} -16779.4 q^{49} -6570.65 q^{50} +3307.19 q^{51} +12744.9 q^{52} -29816.3 q^{53} +2916.00 q^{54} +27970.5 q^{55} -336.105 q^{56} -16250.4 q^{57} -9885.99 q^{58} -3481.00 q^{59} -5544.16 q^{60} -53056.9 q^{61} -25760.2 q^{62} -425.383 q^{63} +4096.00 q^{64} -30668.2 q^{65} -26153.5 q^{66} -36166.1 q^{67} +5879.44 q^{68} +6165.07 q^{69} +808.777 q^{70} -21446.1 q^{71} +5184.00 q^{72} +56179.8 q^{73} -53938.8 q^{74} -14784.0 q^{75} -28889.6 q^{76} +3815.24 q^{77} +28675.9 q^{78} +16623.0 q^{79} -9856.29 q^{80} +6561.00 q^{81} +33456.0 q^{82} +94477.5 q^{83} -756.237 q^{84} -14147.8 q^{85} -5813.44 q^{86} -22243.5 q^{87} -46495.0 q^{88} +74418.2 q^{89} -12474.4 q^{90} -4183.22 q^{91} +10960.1 q^{92} -57960.5 q^{93} +72971.6 q^{94} +69517.7 q^{95} +9216.00 q^{96} -130509. q^{97} -67117.7 q^{98} -58845.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * q^99

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