LMFDB - Embedded newform 570.6.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.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:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 39154x^{2} - 3172892x - 35506440 $ x^4 - x^3 - 39154x^2 - 3172892x - 35506440
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-89.1990$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +197.010 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +197.010 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +380.119 q^{11} +144.000 q^{12} -672.422 q^{13} -788.042 q^{14} +225.000 q^{15} +256.000 q^{16} -583.456 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1773.09 q^{21} -1520.48 q^{22} +4671.99 q^{23} -576.000 q^{24} +625.000 q^{25} +2689.69 q^{26} +729.000 q^{27} +3152.17 q^{28} +1268.92 q^{29} -900.000 q^{30} +47.9332 q^{31} -1024.00 q^{32} +3421.07 q^{33} +2333.82 q^{34} +4925.26 q^{35} +1296.00 q^{36} +8030.61 q^{37} -1444.00 q^{38} -6051.80 q^{39} -1600.00 q^{40} -3803.90 q^{41} -7092.37 q^{42} +7360.67 q^{43} +6081.91 q^{44} +2025.00 q^{45} -18688.0 q^{46} -12592.8 q^{47} +2304.00 q^{48} +22006.1 q^{49} -2500.00 q^{50} -5251.10 q^{51} -10758.8 q^{52} +7812.71 q^{53} -2916.00 q^{54} +9502.98 q^{55} -12608.7 q^{56} +3249.00 q^{57} -5075.67 q^{58} -17688.7 q^{59} +3600.00 q^{60} +2738.26 q^{61} -191.733 q^{62} +15957.8 q^{63} +4096.00 q^{64} -16810.6 q^{65} -13684.3 q^{66} +14579.3 q^{67} -9335.29 q^{68} +42047.9 q^{69} -19701.0 q^{70} -3576.29 q^{71} -5184.00 q^{72} +29838.9 q^{73} -32122.4 q^{74} +5625.00 q^{75} +5776.00 q^{76} +74887.4 q^{77} +24207.2 q^{78} +28741.8 q^{79} +6400.00 q^{80} +6561.00 q^{81} +15215.6 q^{82} -98445.4 q^{83} +28369.5 q^{84} -14586.4 q^{85} -29442.7 q^{86} +11420.3 q^{87} -24327.6 q^{88} +29985.9 q^{89} -8100.00 q^{90} -132474. q^{91} +74751.9 q^{92} +431.399 q^{93} +50371.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +2993.04 q^{97} -88024.4 q^{98} +30789.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} + 338 q^{11} + 576 q^{12} + 1302 q^{13} - 1072 q^{14} + 900 q^{15} + 1024 q^{16} + 542 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 2412 q^{21} - 1352 q^{22} - 88 q^{23} - 2304 q^{24} + 2500 q^{25} - 5208 q^{26} + 2916 q^{27} + 4288 q^{28} + 5014 q^{29} - 3600 q^{30} + 4962 q^{31} - 4096 q^{32} + 3042 q^{33} - 2168 q^{34} + 6700 q^{35} + 5184 q^{36} + 8022 q^{37} - 5776 q^{38} + 11718 q^{39} - 6400 q^{40} + 2764 q^{41} - 9648 q^{42} + 25346 q^{43} + 5408 q^{44} + 8100 q^{45} + 352 q^{46} + 10008 q^{47} + 9216 q^{48} + 37248 q^{49} - 10000 q^{50} + 4878 q^{51} + 20832 q^{52} - 224 q^{53} - 11664 q^{54} + 8450 q^{55} - 17152 q^{56} + 12996 q^{57} - 20056 q^{58} + 29654 q^{59} + 14400 q^{60} + 27276 q^{61} - 19848 q^{62} + 21708 q^{63} + 16384 q^{64} + 32550 q^{65} - 12168 q^{66} + 26024 q^{67} + 8672 q^{68} - 792 q^{69} - 26800 q^{70} - 26940 q^{71} - 20736 q^{72} - 60916 q^{73} - 32088 q^{74} + 22500 q^{75} + 23104 q^{76} - 21228 q^{77} - 46872 q^{78} + 34902 q^{79} + 25600 q^{80} + 26244 q^{81} - 11056 q^{82} - 48430 q^{83} + 38592 q^{84} + 13550 q^{85} - 101384 q^{86} + 45126 q^{87} - 21632 q^{88} - 38348 q^{89} - 32400 q^{90} + 69280 q^{91} - 1408 q^{92} + 44658 q^{93} - 40032 q^{94} + 36100 q^{95} - 36864 q^{96} + 45942 q^{97} - 148992 q^{98} + 27378 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 + 338 * q^11 + 576 * q^12 + 1302 * q^13 - 1072 * q^14 + 900 * q^15 + 1024 * q^16 + 542 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 2412 * q^21 - 1352 * q^22 - 88 * q^23 - 2304 * q^24 + 2500 * q^25 - 5208 * q^26 + 2916 * q^27 + 4288 * q^28 + 5014 * q^29 - 3600 * q^30 + 4962 * q^31 - 4096 * q^32 + 3042 * q^33 - 2168 * q^34 + 6700 * q^35 + 5184 * q^36 + 8022 * q^37 - 5776 * q^38 + 11718 * q^39 - 6400 * q^40 + 2764 * q^41 - 9648 * q^42 + 25346 * q^43 + 5408 * q^44 + 8100 * q^45 + 352 * q^46 + 10008 * q^47 + 9216 * q^48 + 37248 * q^49 - 10000 * q^50 + 4878 * q^51 + 20832 * q^52 - 224 * q^53 - 11664 * q^54 + 8450 * q^55 - 17152 * q^56 + 12996 * q^57 - 20056 * q^58 + 29654 * q^59 + 14400 * q^60 + 27276 * q^61 - 19848 * q^62 + 21708 * q^63 + 16384 * q^64 + 32550 * q^65 - 12168 * q^66 + 26024 * q^67 + 8672 * q^68 - 792 * q^69 - 26800 * q^70 - 26940 * q^71 - 20736 * q^72 - 60916 * q^73 - 32088 * q^74 + 22500 * q^75 + 23104 * q^76 - 21228 * q^77 - 46872 * q^78 + 34902 * q^79 + 25600 * q^80 + 26244 * q^81 - 11056 * q^82 - 48430 * q^83 + 38592 * q^84 + 13550 * q^85 - 101384 * q^86 + 45126 * q^87 - 21632 * q^88 - 38348 * q^89 - 32400 * q^90 + 69280 * q^91 - 1408 * q^92 + 44658 * q^93 - 40032 * q^94 + 36100 * q^95 - 36864 * q^96 + 45942 * q^97 - 148992 * q^98 + 27378 * 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
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−36.0000	−0.408248
$7$	197.010	1.51965	0.759826	−	0.650127i	$-0.225284\pi$
$7$	197.010	1.51965	0.759826	+	0.650127i	$0.225284\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	380.119	0.947192	0.473596	−	0.880742i	$-0.342956\pi$
$11$	380.119	0.947192	0.473596	+	0.880742i	$0.342956\pi$
$12$	144.000	0.288675
$13$	−672.422	−1.10353	−0.551764	−	0.834000i	$-0.686045\pi$
$13$	−672.422	−1.10353	−0.551764	+	0.834000i	$0.686045\pi$
$14$	−788.042	−1.07456
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−583.456	−0.489650	−0.244825	−	0.969567i	$-0.578730\pi$
$17$	−583.456	−0.489650	−0.244825	+	0.969567i	$0.578730\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	1773.09	0.877371
$22$	−1520.48	−0.669766
$23$	4671.99	1.84155	0.920773	−	0.390099i	$-0.127559\pi$
$23$	4671.99	1.84155	0.920773	+	0.390099i	$0.127559\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	2689.69	0.780313
$27$	729.000	0.192450
$28$	3152.17	0.759826
$29$	1268.92	0.280181	0.140090	−	0.990139i	$-0.455261\pi$
$29$	1268.92	0.280181	0.140090	+	0.990139i	$0.455261\pi$
$30$	−900.000	−0.182574
$31$	47.9332	0.00895844	0.00447922	−	0.999990i	$-0.498574\pi$
$31$	47.9332	0.00895844	0.00447922	+	0.999990i	$0.498574\pi$
$32$	−1024.00	−0.176777
$33$	3421.07	0.546862
$34$	2333.82	0.346235
$35$	4925.26	0.679609
$36$	1296.00	0.166667
$37$	8030.61	0.964371	0.482185	−	0.876069i	$-0.339843\pi$
$37$	8030.61	0.964371	0.482185	+	0.876069i	$0.339843\pi$
$38$	−1444.00	−0.162221
$39$	−6051.80	−0.637123
$40$	−1600.00	−0.158114
$41$	−3803.90	−0.353402	−0.176701	−	0.984265i	$-0.556543\pi$
$41$	−3803.90	−0.353402	−0.176701	+	0.984265i	$0.556543\pi$
$42$	−7092.37	−0.620395
$43$	7360.67	0.607081	0.303540	−	0.952819i	$-0.401831\pi$
$43$	7360.67	0.607081	0.303540	+	0.952819i	$0.401831\pi$
$44$	6081.91	0.473596
$45$	2025.00	0.149071
$46$	−18688.0	−1.30217
$47$	−12592.8	−0.831531	−0.415766	−	0.909472i	$-0.636486\pi$
$47$	−12592.8	−0.831531	−0.415766	+	0.909472i	$0.636486\pi$
$48$	2304.00	0.144338
$49$	22006.1	1.30934
$50$	−2500.00	−0.141421
$51$	−5251.10	−0.282699
$52$	−10758.8	−0.551764
$53$	7812.71	0.382043	0.191021	−	0.981586i	$-0.438820\pi$
$53$	7812.71	0.382043	0.191021	+	0.981586i	$0.438820\pi$
$54$	−2916.00	−0.136083
$55$	9502.98	0.423597
$56$	−12608.7	−0.537278
$57$	3249.00	0.132453
$58$	−5075.67	−0.198118
$59$	−17688.7	−0.661555	−0.330777	−	0.943709i	$-0.607311\pi$
$59$	−17688.7	−0.661555	−0.330777	+	0.943709i	$0.607311\pi$
$60$	3600.00	0.129099
$61$	2738.26	0.0942216	0.0471108	−	0.998890i	$-0.484999\pi$
$61$	2738.26	0.0942216	0.0471108	+	0.998890i	$0.484999\pi$
$62$	−191.733	−0.00633457
$63$	15957.8	0.506551
$64$	4096.00	0.125000
$65$	−16810.6	−0.493513
$66$	−13684.3	−0.386690
$67$	14579.3	0.396779	0.198390	−	0.980123i	$-0.436429\pi$
$67$	14579.3	0.396779	0.198390	+	0.980123i	$0.436429\pi$
$68$	−9335.29	−0.244825
$69$	42047.9	1.06322
$70$	−19701.0	−0.480556
$71$	−3576.29	−0.0841951	−0.0420975	−	0.999114i	$-0.513404\pi$
$71$	−3576.29	−0.0841951	−0.0420975	+	0.999114i	$0.513404\pi$
$72$	−5184.00	−0.117851
$73$	29838.9	0.655354	0.327677	−	0.944790i	$-0.393734\pi$
$73$	29838.9	0.655354	0.327677	+	0.944790i	$0.393734\pi$
$74$	−32122.4	−0.681913
$75$	5625.00	0.115470
$76$	5776.00	0.114708
$77$	74887.4	1.43940
$78$	24207.2	0.450514
$79$	28741.8	0.518139	0.259070	−	0.965859i	$-0.416584\pi$
$79$	28741.8	0.518139	0.259070	+	0.965859i	$0.416584\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	15215.6	0.249893
$83$	−98445.4	−1.56856	−0.784278	−	0.620409i	$-0.786967\pi$
$83$	−98445.4	−1.56856	−0.784278	+	0.620409i	$0.786967\pi$
$84$	28369.5	0.438686
$85$	−14586.4	−0.218978
$86$	−29442.7	−0.429271
$87$	11420.3	0.161763
$88$	−24327.6	−0.334883
$89$	29985.9	0.401276	0.200638	−	0.979665i	$-0.435699\pi$
$89$	29985.9	0.401276	0.200638	+	0.979665i	$0.435699\pi$
$90$	−8100.00	−0.105409
$91$	−132474.	−1.67698
$92$	74751.9	0.920773
$93$	431.399	0.00517216
$94$	50371.3	0.587981
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	2993.04	0.0322986	0.0161493	−	0.999870i	$-0.494859\pi$
$97$	2993.04	0.0322986	0.0161493	+	0.999870i	$0.494859\pi$
$98$	−88024.4	−0.925844
$99$	30789.7	0.315731
$100$	10000.0	0.100000
$101$	−32061.9	−0.312742	−0.156371	−	0.987698i	$-0.549980\pi$
$101$	−32061.9	−0.312742	−0.156371	+	0.987698i	$0.549980\pi$
$102$	21004.4	0.199899
$103$	−123950.	−1.15121	−0.575604	−	0.817729i	$-0.695233\pi$
$103$	−123950.	−1.15121	−0.575604	+	0.817729i	$0.695233\pi$
$104$	43035.0	0.390156
$105$	44327.3	0.392372
$106$	−31250.8	−0.270145
$107$	−150037.	−1.26689	−0.633444	−	0.773789i	$-0.718359\pi$
$107$	−150037.	−1.26689	−0.633444	+	0.773789i	$0.718359\pi$
$108$	11664.0	0.0962250
$109$	158769.	1.27997	0.639983	−	0.768389i	$-0.278941\pi$
$109$	158769.	1.27997	0.639983	+	0.768389i	$0.278941\pi$
$110$	−38011.9	−0.299528
$111$	72275.5	0.556780
$112$	50434.7	0.379913
$113$	−17144.7	−0.126309	−0.0631545	−	0.998004i	$-0.520116\pi$
$113$	−17144.7	−0.126309	−0.0631545	+	0.998004i	$0.520116\pi$
$114$	−12996.0	−0.0936586
$115$	116800.	0.823564
$116$	20302.7	0.140090
$117$	−54466.2	−0.367843
$118$	70754.8	0.467790
$119$	−114947.	−0.744097
$120$	−14400.0	−0.0912871
$121$	−16560.4	−0.102827
$122$	−10953.1	−0.0666248
$123$	−34235.1	−0.204037
$124$	766.931	0.00447922
$125$	15625.0	0.0894427
$126$	−63831.4	−0.358185
$127$	−28136.2	−0.154795	−0.0773973	−	0.997000i	$-0.524661\pi$
$127$	−28136.2	−0.154795	−0.0773973	+	0.997000i	$0.524661\pi$
$128$	−16384.0	−0.0883883
$129$	66246.1	0.350498
$130$	67242.2	0.348966
$131$	130615.	0.664989	0.332495	−	0.943105i	$-0.392110\pi$
$131$	130615.	0.664989	0.332495	+	0.943105i	$0.392110\pi$
$132$	54737.2	0.273431
$133$	71120.8	0.348632
$134$	−58317.1	−0.280565
$135$	18225.0	0.0860663
$136$	37341.2	0.173117
$137$	37242.5	0.169526	0.0847632	−	0.996401i	$-0.472987\pi$
$137$	37242.5	0.169526	0.0847632	+	0.996401i	$0.472987\pi$
$138$	−168192.	−0.751808
$139$	119642.	0.525227	0.262614	−	0.964901i	$-0.415416\pi$
$139$	119642.	0.525227	0.262614	+	0.964901i	$0.415416\pi$
$140$	78804.2	0.339804
$141$	−113335.	−0.480085
$142$	14305.2	0.0595349
$143$	−255601.	−1.04525
$144$	20736.0	0.0833333
$145$	31723.0	0.125301
$146$	−119356.	−0.463405
$147$	198055.	0.755948
$148$	128490.	0.482185
$149$	−30423.0	−0.112263	−0.0561314	−	0.998423i	$-0.517877\pi$
$149$	−30423.0	−0.112263	−0.0561314	+	0.998423i	$0.517877\pi$
$150$	−22500.0	−0.0816497
$151$	460120.	1.64221	0.821105	−	0.570777i	$-0.193358\pi$
$151$	460120.	1.64221	0.821105	+	0.570777i	$0.193358\pi$
$152$	−23104.0	−0.0811107
$153$	−47259.9	−0.163217
$154$	−299550.	−1.01781
$155$	1198.33	0.00400634
$156$	−96828.8	−0.318561
$157$	313042.	1.01357	0.506785	−	0.862072i	$-0.330834\pi$
$157$	313042.	1.01357	0.506785	+	0.862072i	$0.330834\pi$
$158$	−114967.	−0.366380
$159$	70314.4	0.220573
$160$	−25600.0	−0.0790569
$161$	920431.	2.79851
$162$	−26244.0	−0.0785674
$163$	134478.	0.396443	0.198221	−	0.980157i	$-0.436483\pi$
$163$	134478.	0.396443	0.198221	+	0.980157i	$0.436483\pi$
$164$	−60862.4	−0.176701
$165$	85526.8	0.244564
$166$	393782.	1.10914
$167$	−275829.	−0.765329	−0.382664	−	0.923887i	$-0.624993\pi$
$167$	−275829.	−0.765329	−0.382664	+	0.923887i	$0.624993\pi$
$168$	−113478.	−0.310198
$169$	80858.6	0.217776
$170$	58345.6	0.154841
$171$	29241.0	0.0764719
$172$	117771.	0.303540
$173$	405849.	1.03098	0.515489	−	0.856896i	$-0.327610\pi$
$173$	405849.	1.03098	0.515489	+	0.856896i	$0.327610\pi$
$174$	−45681.1	−0.114383
$175$	123131.	0.303930
$176$	97310.5	0.236798
$177$	−159198.	−0.381949
$178$	−119944.	−0.283745
$179$	−240843.	−0.561824	−0.280912	−	0.959733i	$-0.590637\pi$
$179$	−240843.	−0.561824	−0.280912	+	0.959733i	$0.590637\pi$
$180$	32400.0	0.0745356
$181$	−825228.	−1.87231	−0.936154	−	0.351590i	$-0.885641\pi$
$181$	−825228.	−1.87231	−0.936154	+	0.351590i	$0.885641\pi$
$182$	529897.	1.18580
$183$	24644.4	0.0543989
$184$	−299007.	−0.651085
$185$	200765.	0.431280
$186$	−1725.60	−0.00365727
$187$	−221783.	−0.463792
$188$	−201485.	−0.415766
$189$	143621.	0.292457
$190$	−36100.0	−0.0725476
$191$	806960.	1.60055	0.800274	−	0.599634i	$-0.204687\pi$
$191$	806960.	1.60055	0.800274	+	0.599634i	$0.204687\pi$
$192$	36864.0	0.0721688
$193$	777842.	1.50314	0.751568	−	0.659656i	$-0.229298\pi$
$193$	777842.	1.50314	0.751568	+	0.659656i	$0.229298\pi$
$194$	−11972.2	−0.0228385
$195$	−151295.	−0.284930
$196$	352098.	0.654671
$197$	13324.1	0.0244608	0.0122304	−	0.999925i	$-0.496107\pi$
$197$	13324.1	0.0244608	0.0122304	+	0.999925i	$0.496107\pi$
$198$	−123159.	−0.223255
$199$	−73064.3	−0.130789	−0.0653947	−	0.997859i	$-0.520831\pi$
$199$	−73064.3	−0.130789	−0.0653947	+	0.997859i	$0.520831\pi$
$200$	−40000.0	−0.0707107
$201$	131213.	0.229081
$202$	128248.	0.221142
$203$	249990.	0.425777
$204$	−84017.6	−0.141350
$205$	−95097.5	−0.158046
$206$	495800.	0.814027
$207$	378431.	0.613849
$208$	−172140.	−0.275882
$209$	137223.	0.217301
$210$	−177309.	−0.277449
$211$	−272445.	−0.421281	−0.210641	−	0.977564i	$-0.567555\pi$
$211$	−272445.	−0.421281	−0.210641	+	0.977564i	$0.567555\pi$
$212$	125003.	0.191021
$213$	−32186.6	−0.0486100
$214$	600147.	0.895825
$215$	184017.	0.271495
$216$	−46656.0	−0.0680414
$217$	9443.34	0.0136137
$218$	−635075.	−0.905073
$219$	268550.	0.378369
$220$	152048.	0.211799
$221$	392329.	0.540343
$222$	−289102.	−0.393703
$223$	280747.	0.378054	0.189027	−	0.981972i	$-0.439467\pi$
$223$	280747.	0.378054	0.189027	+	0.981972i	$0.439467\pi$
$224$	−201739.	−0.268639
$225$	50625.0	0.0666667
$226$	68578.8	0.0893139
$227$	1.38523e6	1.78425	0.892125	−	0.451788i	$-0.149214\pi$
$227$	1.38523e6	1.78425	0.892125	+	0.451788i	$0.149214\pi$
$228$	51984.0	0.0662266
$229$	1.41899e6	1.78810	0.894048	−	0.447971i	$-0.147853\pi$
$229$	1.41899e6	1.78810	0.894048	+	0.447971i	$0.147853\pi$
$230$	−467199.	−0.582348
$231$	673987.	0.831039
$232$	−81210.8	−0.0990589
$233$	1.31529e6	1.58720	0.793600	−	0.608440i	$-0.208204\pi$
$233$	1.31529e6	1.58720	0.793600	+	0.608440i	$0.208204\pi$
$234$	217865.	0.260104
$235$	−314821.	−0.371872
$236$	−283019.	−0.330777
$237$	258676.	0.299148
$238$	459787.	0.526156
$239$	−774779.	−0.877371	−0.438686	−	0.898641i	$-0.644556\pi$
$239$	−774779.	−0.877371	−0.438686	+	0.898641i	$0.644556\pi$
$240$	57600.0	0.0645497
$241$	17548.8	0.0194628	0.00973140	−	0.999953i	$-0.496902\pi$
$241$	17548.8	0.0194628	0.00973140	+	0.999953i	$0.496902\pi$
$242$	66241.7	0.0727098
$243$	59049.0	0.0641500
$244$	43812.2	0.0471108
$245$	550152.	0.585555
$246$	136940.	0.144276
$247$	−242744.	−0.253167
$248$	−3067.73	−0.00316729
$249$	−886009.	−0.905607
$250$	−62500.0	−0.0632456
$251$	−44645.5	−0.0447295	−0.0223647	−	0.999750i	$-0.507120\pi$
$251$	−44645.5	−0.0447295	−0.0223647	+	0.999750i	$0.507120\pi$
$252$	255325.	0.253275
$253$	1.77591e6	1.74430
$254$	112545.	0.109456
$255$	−131278.	−0.126427
$256$	65536.0	0.0625000
$257$	−1.01057e6	−0.954407	−0.477203	−	0.878793i	$-0.658349\pi$
$257$	−1.01057e6	−0.954407	−0.477203	+	0.878793i	$0.658349\pi$
$258$	−264984.	−0.247840
$259$	1.58211e6	1.46551
$260$	−268969.	−0.246757
$261$	102782.	0.0933936
$262$	−522460.	−0.470218
$263$	750727.	0.669257	0.334628	−	0.942350i	$-0.391389\pi$
$263$	750727.	0.669257	0.334628	+	0.942350i	$0.391389\pi$
$264$	−218949.	−0.193345
$265$	195318.	0.170855
$266$	−284483.	−0.246520
$267$	269873.	0.231677
$268$	233268.	0.198390
$269$	−2.14837e6	−1.81021	−0.905104	−	0.425191i	$-0.860207\pi$
$269$	−2.14837e6	−1.81021	−0.905104	+	0.425191i	$0.860207\pi$
$270$	−72900.0	−0.0608581
$271$	1.19832e6	0.991177	0.495589	−	0.868557i	$-0.334952\pi$
$271$	1.19832e6	0.991177	0.495589	+	0.868557i	$0.334952\pi$
$272$	−149365.	−0.122412
$273$	−1.19227e6	−0.968204
$274$	−148970.	−0.119873
$275$	237574.	0.189438
$276$	672767.	0.531608
$277$	2.21742e6	1.73639	0.868197	−	0.496219i	$-0.165279\pi$
$277$	2.21742e6	1.73639	0.868197	+	0.496219i	$0.165279\pi$
$278$	−478569.	−0.371392
$279$	3882.59	0.00298615
$280$	−315217.	−0.240278
$281$	−1.82310e6	−1.37735	−0.688675	−	0.725070i	$-0.741808\pi$
$281$	−1.82310e6	−1.37735	−0.688675	+	0.725070i	$0.741808\pi$
$282$	453342.	0.339471
$283$	1.10885e6	0.823013	0.411506	−	0.911407i	$-0.365003\pi$
$283$	1.10885e6	0.823013	0.411506	+	0.911407i	$0.365003\pi$
$284$	−57220.6	−0.0420975
$285$	81225.0	0.0592349
$286$	1.02240e6	0.739106
$287$	−749408.	−0.537049
$288$	−82944.0	−0.0589256
$289$	−1.07944e6	−0.760243
$290$	−126892.	−0.0886010
$291$	26937.4	0.0186476
$292$	477422.	0.327677
$293$	668940.	0.455217	0.227608	−	0.973753i	$-0.426909\pi$
$293$	668940.	0.455217	0.227608	+	0.973753i	$0.426909\pi$
$294$	−792219.	−0.534536
$295$	−442217.	−0.295856
$296$	−513959.	−0.340957
$297$	277107.	0.182287
$298$	121692.	0.0793818
$299$	−3.14155e6	−2.03220
$300$	90000.0	0.0577350
$301$	1.45013e6	0.922551
$302$	−1.84048e6	−1.16122
$303$	−288557.	−0.180562
$304$	92416.0	0.0573539
$305$	68456.6	0.0421372
$306$	189040.	0.115412
$307$	−2.30928e6	−1.39840	−0.699198	−	0.714928i	$-0.746460\pi$
$307$	−2.30928e6	−1.39840	−0.699198	+	0.714928i	$0.746460\pi$
$308$	1.19820e6	0.719701
$309$	−1.11555e6	−0.664650
$310$	−4793.32	−0.00283291
$311$	−2.32274e6	−1.36176	−0.680880	−	0.732395i	$-0.738402\pi$
$311$	−2.32274e6	−1.36176	−0.680880	+	0.732395i	$0.738402\pi$
$312$	387315.	0.225257
$313$	303022.	0.174829	0.0874145	−	0.996172i	$-0.472140\pi$
$313$	303022.	0.174829	0.0874145	+	0.996172i	$0.472140\pi$
$314$	−1.25217e6	−0.716702
$315$	398946.	0.226536
$316$	459869.	0.259070
$317$	−1.71217e6	−0.956968	−0.478484	−	0.878096i	$-0.658814\pi$
$317$	−1.71217e6	−0.956968	−0.478484	+	0.878096i	$0.658814\pi$
$318$	−281258.	−0.155968
$319$	482340.	0.265385
$320$	102400.	0.0559017
$321$	−1.35033e6	−0.731438
$322$	−3.68172e6	−1.97884
$323$	−210628.	−0.112333
$324$	104976.	0.0555556
$325$	−420264.	−0.220706
$326$	−537910.	−0.280327
$327$	1.42892e6	0.738989
$328$	243450.	0.124947
$329$	−2.48092e6	−1.26364
$330$	−342107.	−0.172933
$331$	1.19409e6	0.599054	0.299527	−	0.954088i	$-0.403171\pi$
$331$	1.19409e6	0.599054	0.299527	+	0.954088i	$0.403171\pi$
$332$	−1.57513e6	−0.784278
$333$	650479.	0.321457
$334$	1.10331e6	0.541169
$335$	364482.	0.177445
$336$	453912.	0.219343
$337$	202322.	0.0970440	0.0485220	−	0.998822i	$-0.484549\pi$
$337$	202322.	0.0970440	0.0485220	+	0.998822i	$0.484549\pi$
$338$	−323435.	−0.153991
$339$	−154302.	−0.0729245
$340$	−233382.	−0.109489
$341$	18220.3	0.00848536
$342$	−116964.	−0.0540738
$343$	1.02428e6	0.470091
$344$	−471083.	−0.214635
$345$	1.05120e6	0.475485
$346$	−1.62340e6	−0.729011
$347$	−896143.	−0.399534	−0.199767	−	0.979843i	$-0.564019\pi$
$347$	−896143.	−0.399534	−0.199767	+	0.979843i	$0.564019\pi$
$348$	182724.	0.0808813
$349$	735417.	0.323199	0.161600	−	0.986856i	$-0.448335\pi$
$349$	735417.	0.323199	0.161600	+	0.986856i	$0.448335\pi$
$350$	−492526.	−0.214911
$351$	−490196.	−0.212374
$352$	−389242.	−0.167441
$353$	2.19963e6	0.939533	0.469767	−	0.882791i	$-0.344338\pi$
$353$	2.19963e6	0.939533	0.469767	+	0.882791i	$0.344338\pi$
$354$	636793.	0.270079
$355$	−89407.2	−0.0376532
$356$	479775.	0.200638
$357$	−1.03452e6	−0.429605
$358$	963370.	0.397270
$359$	−1.06446e6	−0.435907	−0.217954	−	0.975959i	$-0.569938\pi$
$359$	−1.06446e6	−0.435907	−0.217954	+	0.975959i	$0.569938\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	3.30091e6	1.32392
$363$	−149044.	−0.0593673
$364$	−2.11959e6	−0.838490
$365$	745973.	0.293083
$366$	−98577.5	−0.0384658
$367$	1.26262e6	0.489337	0.244668	−	0.969607i	$-0.421321\pi$
$367$	1.26262e6	0.489337	0.244668	+	0.969607i	$0.421321\pi$
$368$	1.19603e6	0.460386
$369$	−308116.	−0.117801
$370$	−803061.	−0.304961
$371$	1.53919e6	0.580572
$372$	6902.38	0.00258608
$373$	4.98592e6	1.85555	0.927776	−	0.373138i	$-0.121718\pi$
$373$	4.98592e6	1.85555	0.927776	+	0.373138i	$0.121718\pi$
$374$	887131.	0.327951
$375$	140625.	0.0516398
$376$	805941.	0.293991
$377$	−853249.	−0.309188
$378$	−574482.	−0.206798
$379$	−256131.	−0.0915935	−0.0457968	−	0.998951i	$-0.514583\pi$
$379$	−256131.	−0.0915935	−0.0457968	+	0.998951i	$0.514583\pi$
$380$	144400.	0.0512989
$381$	−253226.	−0.0893707
$382$	−3.22784e6	−1.13176
$383$	571433.	0.199053	0.0995263	−	0.995035i	$-0.468267\pi$
$383$	571433.	0.199053	0.0995263	+	0.995035i	$0.468267\pi$
$384$	−147456.	−0.0510310
$385$	1.87219e6	0.643720
$386$	−3.11137e6	−1.06288
$387$	596214.	0.202360
$388$	47888.6	0.0161493
$389$	−4.73099e6	−1.58518	−0.792589	−	0.609756i	$-0.791268\pi$
$389$	−4.73099e6	−1.58518	−0.792589	+	0.609756i	$0.791268\pi$
$390$	605180.	0.201476
$391$	−2.72590e6	−0.901713
$392$	−1.40839e6	−0.462922
$393$	1.17553e6	0.383932
$394$	−53296.2	−0.0172964
$395$	718545.	0.231719
$396$	492634.	0.157865
$397$	−2.84731e6	−0.906690	−0.453345	−	0.891335i	$-0.649769\pi$
$397$	−2.84731e6	−0.906690	−0.453345	+	0.891335i	$0.649769\pi$
$398$	292257.	0.0924820
$399$	640087.	0.201283
$400$	160000.	0.0500000
$401$	−1.20188e6	−0.373251	−0.186626	−	0.982431i	$-0.559755\pi$
$401$	−1.20188e6	−0.373251	−0.186626	+	0.982431i	$0.559755\pi$
$402$	−524854.	−0.161984
$403$	−32231.4	−0.00988589
$404$	−512991.	−0.156371
$405$	164025.	0.0496904
$406$	−999960.	−0.301070
$407$	3.05259e6	0.913445
$408$	336071.	0.0999494
$409$	−5.15592e6	−1.52405	−0.762023	−	0.647550i	$-0.775794\pi$
$409$	−5.15592e6	−1.52405	−0.762023	+	0.647550i	$0.775794\pi$
$410$	380390.	0.111756
$411$	335182.	0.0978761
$412$	−1.98320e6	−0.575604
$413$	−3.48486e6	−1.00533
$414$	−1.51373e6	−0.434056
$415$	−2.46114e6	−0.701480
$416$	688560.	0.195078
$417$	1.07678e6	0.303240
$418$	−548892.	−0.153655
$419$	−2.53122e6	−0.704361	−0.352181	−	0.935932i	$-0.614560\pi$
$419$	−2.53122e6	−0.704361	−0.352181	+	0.935932i	$0.614560\pi$
$420$	709237.	0.196186
$421$	1.19341e6	0.328160	0.164080	−	0.986447i	$-0.447534\pi$
$421$	1.19341e6	0.328160	0.164080	+	0.986447i	$0.447534\pi$
$422$	1.08978e6	0.297891
$423$	−1.02002e6	−0.277177
$424$	−500014.	−0.135073
$425$	−364660.	−0.0979300
$426$	128746.	0.0343725
$427$	539466.	0.143184
$428$	−2.40059e6	−0.633444
$429$	−2.30041e6	−0.603478
$430$	−736067.	−0.191976
$431$	−1.85560e6	−0.481161	−0.240580	−	0.970629i	$-0.577338\pi$
$431$	−1.85560e6	−0.481161	−0.240580	+	0.970629i	$0.577338\pi$
$432$	186624.	0.0481125
$433$	−4.55220e6	−1.16681	−0.583407	−	0.812180i	$-0.698281\pi$
$433$	−4.55220e6	−1.16681	−0.583407	+	0.812180i	$0.698281\pi$
$434$	−37773.4	−0.00962634
$435$	285507.	0.0723424
$436$	2.54030e6	0.639983
$437$	1.68659e6	0.422480
$438$	−1.07420e6	−0.267547
$439$	−683362.	−0.169235	−0.0846174	−	0.996414i	$-0.526967\pi$
$439$	−683362.	−0.169235	−0.0846174	+	0.996414i	$0.526967\pi$
$440$	−608191.	−0.149764
$441$	1.78249e6	0.436447
$442$	−1.56931e6	−0.382080
$443$	4.03950e6	0.977955	0.488977	−	0.872296i	$-0.337370\pi$
$443$	4.03950e6	0.977955	0.488977	+	0.872296i	$0.337370\pi$
$444$	1.15641e6	0.278390
$445$	749649.	0.179456
$446$	−1.12299e6	−0.267324
$447$	−273807.	−0.0648149
$448$	806955.	0.189956
$449$	−7.41760e6	−1.73639	−0.868196	−	0.496222i	$-0.834720\pi$
$449$	−7.41760e6	−1.73639	−0.868196	+	0.496222i	$0.834720\pi$
$450$	−202500.	−0.0471405
$451$	−1.44594e6	−0.334740
$452$	−274315.	−0.0631545
$453$	4.14108e6	0.948130
$454$	−5.54090e6	−1.26166
$455$	−3.31185e6	−0.749968
$456$	−207936.	−0.0468293
$457$	8.28004e6	1.85456	0.927282	−	0.374363i	$-0.122139\pi$
$457$	8.28004e6	1.85456	0.927282	+	0.374363i	$0.122139\pi$
$458$	−5.67596e6	−1.26437
$459$	−425339.	−0.0942332
$460$	1.86880e6	0.411782
$461$	−6.39517e6	−1.40152	−0.700761	−	0.713396i	$-0.747156\pi$
$461$	−6.39517e6	−1.40152	−0.700761	+	0.713396i	$0.747156\pi$
$462$	−2.69595e6	−0.587633
$463$	−6.26670e6	−1.35858	−0.679292	−	0.733868i	$-0.737713\pi$
$463$	−6.26670e6	−1.35858	−0.679292	+	0.733868i	$0.737713\pi$
$464$	324843.	0.0700452
$465$	10785.0	0.00231306
$466$	−5.26116e6	−1.12232
$467$	−7.64352e6	−1.62181	−0.810907	−	0.585174i	$-0.801026\pi$
$467$	−7.64352e6	−1.62181	−0.810907	+	0.585174i	$0.801026\pi$
$468$	−871459.	−0.183921
$469$	2.87227e6	0.602966
$470$	1.25928e6	0.262953
$471$	2.81738e6	0.585185
$472$	1.13208e6	0.233895
$473$	2.79793e6	0.575022
$474$	−1.03471e6	−0.211529
$475$	225625.	0.0458831
$476$	−1.83915e6	−0.372049
$477$	632830.	0.127348
$478$	3.09912e6	0.620395
$479$	525106.	0.104570	0.0522852	−	0.998632i	$-0.483350\pi$
$479$	525106.	0.104570	0.0522852	+	0.998632i	$0.483350\pi$
$480$	−230400.	−0.0456435
$481$	−5.39996e6	−1.06421
$482$	−70195.3	−0.0137623
$483$	8.28388e6	1.61572
$484$	−264967.	−0.0514136
$485$	74826.0	0.0144444
$486$	−236196.	−0.0453609
$487$	−5.32536e6	−1.01748	−0.508741	−	0.860920i	$-0.669889\pi$
$487$	−5.32536e6	−1.01748	−0.508741	+	0.860920i	$0.669889\pi$
$488$	−175249.	−0.0333124
$489$	1.21030e6	0.228886
$490$	−2.20061e6	−0.414050
$491$	6.94802e6	1.30064	0.650320	−	0.759660i	$-0.274635\pi$
$491$	6.94802e6	1.30064	0.650320	+	0.759660i	$0.274635\pi$
$492$	−547762.	−0.102019
$493$	−740358.	−0.137191
$494$	970978.	0.179016
$495$	769741.	0.141199
$496$	12270.9	0.00223961
$497$	−704566.	−0.127947
$498$	3.54403e6	0.640361
$499$	3.40412e6	0.612002	0.306001	−	0.952031i	$-0.401009\pi$
$499$	3.40412e6	0.612002	0.306001	+	0.952031i	$0.401009\pi$
$500$	250000.	0.0447214
$501$	−2.48246e6	−0.441863
$502$	178582.	0.0316285
$503$	1.06481e6	0.187651	0.0938254	−	0.995589i	$-0.470090\pi$
$503$	1.06481e6	0.187651	0.0938254	+	0.995589i	$0.470090\pi$
$504$	−1.02130e6	−0.179093
$505$	−801548.	−0.139862
$506$	−7.10365e6	−1.23340
$507$	727728.	0.125733
$508$	−450179.	−0.0773973
$509$	8.70053e6	1.48851	0.744254	−	0.667897i	$-0.232805\pi$
$509$	8.70053e6	1.48851	0.744254	+	0.667897i	$0.232805\pi$
$510$	525110.	0.0893974
$511$	5.87857e6	0.995909
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	4.04228e6	0.674867
$515$	−3.09875e6	−0.514836
$516$	1.05994e6	0.175249
$517$	−4.78677e6	−0.787620
$518$	−6.32845e6	−1.03627
$519$	3.65264e6	0.595235
$520$	1.07588e6	0.174483
$521$	7.51485e6	1.21290	0.606451	−	0.795121i	$-0.292593\pi$
$521$	7.51485e6	1.21290	0.606451	+	0.795121i	$0.292593\pi$
$522$	−411129.	−0.0660393
$523$	−2.40784e6	−0.384922	−0.192461	−	0.981305i	$-0.561647\pi$
$523$	−2.40784e6	−0.384922	−0.192461	+	0.981305i	$0.561647\pi$
$524$	2.08984e6	0.332495
$525$	1.10818e6	0.175474
$526$	−3.00291e6	−0.473236
$527$	−27966.9	−0.00438650
$528$	875795.	0.136715
$529$	1.53912e7	2.39129
$530$	−781271.	−0.120813
$531$	−1.43278e6	−0.220518
$532$	1.13793e6	0.174316
$533$	2.55783e6	0.389990
$534$	−1.07949e6	−0.163820
$535$	−3.75092e6	−0.566569
$536$	−933073.	−0.140283
$537$	−2.16758e6	−0.324369
$538$	8.59348e6	1.28001
$539$	8.36494e6	1.24020
$540$	291600.	0.0430331
$541$	−687897.	−0.101049	−0.0505243	−	0.998723i	$-0.516089\pi$
$541$	−687897.	−0.101049	−0.0505243	+	0.998723i	$0.516089\pi$
$542$	−4.79330e6	−0.700868
$543$	−7.42705e6	−1.08098
$544$	597459.	0.0865587
$545$	3.96922e6	0.572419
$546$	4.76907e6	0.684624
$547$	−9.97003e6	−1.42472	−0.712358	−	0.701817i	$-0.752373\pi$
$547$	−9.97003e6	−1.42472	−0.712358	+	0.701817i	$0.752373\pi$
$548$	595880.	0.0847632
$549$	221799.	0.0314072
$550$	−950298.	−0.133953
$551$	458079.	0.0642779
$552$	−2.69107e6	−0.375904
$553$	5.66244e6	0.787391
$554$	−8.86968e6	−1.22782
$555$	1.80689e6	0.249000
$556$	1.91427e6	0.262614
$557$	8.72289e6	1.19130	0.595652	−	0.803243i	$-0.296894\pi$
$557$	8.72289e6	1.19130	0.595652	+	0.803243i	$0.296894\pi$
$558$	−15530.4	−0.00211152
$559$	−4.94948e6	−0.669931
$560$	1.26087e6	0.169902
$561$	−1.99604e6	−0.267771
$562$	7.29240e6	0.973934
$563$	933880.	0.124171	0.0620855	−	0.998071i	$-0.480225\pi$
$563$	933880.	0.124171	0.0620855	+	0.998071i	$0.480225\pi$
$564$	−1.81337e6	−0.240042
$565$	−428618.	−0.0564871
$566$	−4.43540e6	−0.581958
$567$	1.29259e6	0.168850
$568$	228882.	0.0297674
$569$	−44406.4	−0.00574997	−0.00287498	−	0.999996i	$-0.500915\pi$
$569$	−44406.4	−0.00574997	−0.00287498	+	0.999996i	$0.500915\pi$
$570$	−324900.	−0.0418854
$571$	4.47973e6	0.574992	0.287496	−	0.957782i	$-0.407177\pi$
$571$	4.47973e6	0.574992	0.287496	+	0.957782i	$0.407177\pi$
$572$	−4.08961e6	−0.522627
$573$	7.26264e6	0.924077
$574$	2.99763e6	0.379751
$575$	2.91999e6	0.368309
$576$	331776.	0.0416667
$577$	−2.00312e6	−0.250477	−0.125238	−	0.992127i	$-0.539970\pi$
$577$	−2.00312e6	−0.250477	−0.125238	+	0.992127i	$0.539970\pi$
$578$	4.31775e6	0.537573
$579$	7.00058e6	0.867835
$580$	507567.	0.0626504
$581$	−1.93948e7	−2.38366
$582$	−107749.	−0.0131858
$583$	2.96976e6	0.361868
$584$	−1.90969e6	−0.231703
$585$	−1.36165e6	−0.164504
$586$	−2.67576e6	−0.321887
$587$	4.22612e6	0.506228	0.253114	−	0.967436i	$-0.418545\pi$
$587$	4.22612e6	0.506228	0.253114	+	0.967436i	$0.418545\pi$
$588$	3.16888e6	0.377974
$589$	17303.9	0.00205521
$590$	1.76887e6	0.209202
$591$	119917.	0.0141225
$592$	2.05584e6	0.241093
$593$	−1.64563e7	−1.92174	−0.960869	−	0.277002i	$-0.910659\pi$
$593$	−1.64563e7	−1.92174	−0.960869	+	0.277002i	$0.910659\pi$
$594$	−1.10843e6	−0.128897
$595$	−2.87367e6	−0.332770
$596$	−486767.	−0.0561314
$597$	−657578.	−0.0755112
$598$	1.25662e7	1.43698
$599$	−2.74490e6	−0.312579	−0.156289	−	0.987711i	$-0.549953\pi$
$599$	−2.74490e6	−0.312579	−0.156289	+	0.987711i	$0.549953\pi$
$600$	−360000.	−0.0408248
$601$	6.48955e6	0.732873	0.366436	−	0.930443i	$-0.380578\pi$
$601$	6.48955e6	0.732873	0.366436	+	0.930443i	$0.380578\pi$
$602$	−5.80052e6	−0.652342
$603$	1.18092e6	0.132260
$604$	7.36192e6	0.821105
$605$	−414011.	−0.0459857
$606$	1.15423e6	0.127676
$607$	7.23071e6	0.796543	0.398271	−	0.917268i	$-0.369610\pi$
$607$	7.23071e6	0.796543	0.398271	+	0.917268i	$0.369610\pi$
$608$	−369664.	−0.0405554
$609$	2.24991e6	0.245823
$610$	−273826.	−0.0297955
$611$	8.46769e6	0.917618
$612$	−756159.	−0.0816083
$613$	−3.87455e6	−0.416457	−0.208228	−	0.978080i	$-0.566770\pi$
$613$	−3.87455e6	−0.416457	−0.208228	+	0.978080i	$0.566770\pi$
$614$	9.23711e6	0.988816
$615$	−855878.	−0.0912481
$616$	−4.79280e6	−0.508905
$617$	8.73449e6	0.923686	0.461843	−	0.886962i	$-0.347188\pi$
$617$	8.73449e6	0.923686	0.461843	+	0.886962i	$0.347188\pi$
$618$	4.46220e6	0.469979
$619$	−2.90336e6	−0.304561	−0.152280	−	0.988337i	$-0.548662\pi$
$619$	−2.90336e6	−0.304561	−0.152280	+	0.988337i	$0.548662\pi$
$620$	19173.3	0.00200317
$621$	3.40588e6	0.354406
$622$	9.29098e6	0.962910
$623$	5.90754e6	0.609799
$624$	−1.54926e6	−0.159281
$625$	390625.	0.0400000
$626$	−1.21209e6	−0.123623
$627$	1.23501e6	0.125459
$628$	5.00868e6	0.506785
$629$	−4.68550e6	−0.472204
$630$	−1.59578e6	−0.160185
$631$	153939.	0.0153913	0.00769566	−	0.999970i	$-0.497550\pi$
$631$	153939.	0.0153913	0.00769566	+	0.999970i	$0.497550\pi$
$632$	−1.83948e6	−0.183190
$633$	−2.45200e6	−0.243227
$634$	6.84866e6	0.676679
$635$	−703405.	−0.0692263
$636$	1.12503e6	0.110286
$637$	−1.47974e7	−1.44490
$638$	−1.92936e6	−0.187656
$639$	−289679.	−0.0280650
$640$	−409600.	−0.0395285
$641$	−1.27540e7	−1.22603	−0.613014	−	0.790072i	$-0.710043\pi$
$641$	−1.27540e7	−1.22603	−0.613014	+	0.790072i	$0.710043\pi$
$642$	5.40132e6	0.517205
$643$	1.25557e7	1.19760	0.598802	−	0.800897i	$-0.295643\pi$
$643$	1.25557e7	1.19760	0.598802	+	0.800897i	$0.295643\pi$
$644$	1.47269e7	1.39925
$645$	1.65615e6	0.156748
$646$	842510.	0.0794317
$647$	−1.36613e7	−1.28301	−0.641506	−	0.767118i	$-0.721690\pi$
$647$	−1.36613e7	−1.28301	−0.641506	+	0.767118i	$0.721690\pi$
$648$	−419904.	−0.0392837
$649$	−6.72381e6	−0.626620
$650$	1.68106e6	0.156063
$651$	84990.1	0.00785988
$652$	2.15164e6	0.198221
$653$	3.83364e6	0.351827	0.175913	−	0.984406i	$-0.443712\pi$
$653$	3.83364e6	0.351827	0.175913	+	0.984406i	$0.443712\pi$
$654$	−5.71567e6	−0.522544
$655$	3.26537e6	0.297392
$656$	−973799.	−0.0883506
$657$	2.41695e6	0.218451
$658$	9.92367e6	0.893527
$659$	−1.15676e7	−1.03760	−0.518798	−	0.854897i	$-0.673620\pi$
$659$	−1.15676e7	−1.03760	−0.518798	+	0.854897i	$0.673620\pi$
$660$	1.36843e6	0.122282
$661$	2.87611e6	0.256036	0.128018	−	0.991772i	$-0.459138\pi$
$661$	2.87611e6	0.256036	0.128018	+	0.991772i	$0.459138\pi$
$662$	−4.77635e6	−0.423595
$663$	3.53096e6	0.311967
$664$	6.30051e6	0.554569
$665$	1.77802e6	0.155913
$666$	−2.60192e6	−0.227304
$667$	5.92838e6	0.515966
$668$	−4.41326e6	−0.382664
$669$	2.52673e6	0.218270
$670$	−1.45793e6	−0.125473
$671$	1.04087e6	0.0892460
$672$	−1.81565e6	−0.155099
$673$	1.14921e7	0.978054	0.489027	−	0.872269i	$-0.337352\pi$
$673$	1.14921e7	0.978054	0.489027	+	0.872269i	$0.337352\pi$
$674$	−809288.	−0.0686205
$675$	455625.	0.0384900
$676$	1.29374e6	0.108888
$677$	−5.02640e6	−0.421488	−0.210744	−	0.977541i	$-0.567589\pi$
$677$	−5.02640e6	−0.421488	−0.210744	+	0.977541i	$0.567589\pi$
$678$	617210.	0.0515654
$679$	589660.	0.0490826
$680$	933529.	0.0774204
$681$	1.24670e7	1.03014
$682$	−72881.3	−0.00600006
$683$	5.62673e6	0.461535	0.230767	−	0.973009i	$-0.425876\pi$
$683$	5.62673e6	0.461535	0.230767	+	0.973009i	$0.425876\pi$
$684$	467856.	0.0382360
$685$	931062.	0.0758145
$686$	−4.09710e6	−0.332404
$687$	1.27709e7	1.03236
$688$	1.88433e6	0.151770
$689$	−5.25344e6	−0.421595
$690$	−4.20479e6	−0.336219
$691$	−1.42173e7	−1.13272	−0.566361	−	0.824157i	$-0.691649\pi$
$691$	−1.42173e7	−1.13272	−0.566361	+	0.824157i	$0.691649\pi$
$692$	6.49359e6	0.515489
$693$	6.06588e6	0.479801
$694$	3.58457e6	0.282513
$695$	2.99105e6	0.234889
$696$	−730897.	−0.0571917
$697$	2.21941e6	0.173043
$698$	−2.94167e6	−0.228536
$699$	1.18376e7	0.916371
$700$	1.97010e6	0.151965
$701$	2.45934e6	0.189027	0.0945133	−	0.995524i	$-0.469871\pi$
$701$	2.45934e6	0.189027	0.0945133	+	0.995524i	$0.469871\pi$
$702$	1.96078e6	0.150171
$703$	2.89905e6	0.221242
$704$	1.55697e6	0.118399
$705$	−2.83339e6	−0.214700
$706$	−8.79850e6	−0.664350
$707$	−6.31653e6	−0.475259
$708$	−2.54717e6	−0.190974
$709$	−7.06855e6	−0.528099	−0.264049	−	0.964509i	$-0.585058\pi$
$709$	−7.06855e6	−0.528099	−0.264049	+	0.964509i	$0.585058\pi$
$710$	357629.	0.0266248
$711$	2.32809e6	0.172713
$712$	−1.91910e6	−0.141872
$713$	223944.	0.0164974
$714$	4.13809e6	0.303776
$715$	−6.39001e6	−0.467452
$716$	−3.85348e6	−0.280912
$717$	−6.97302e6	−0.506550
$718$	4.25785e6	0.308233
$719$	−7.42345e6	−0.535530	−0.267765	−	0.963484i	$-0.586285\pi$
$719$	−7.42345e6	−0.535530	−0.267765	+	0.963484i	$0.586285\pi$
$720$	518400.	0.0372678
$721$	−2.44195e7	−1.74944
$722$	−521284.	−0.0372161
$723$	157939.	0.0112369
$724$	−1.32036e7	−0.936154
$725$	793074.	0.0560362
$726$	596175.	0.0419790
$727$	−1.16530e7	−0.817715	−0.408857	−	0.912598i	$-0.634073\pi$
$727$	−1.16530e7	−0.817715	−0.408857	+	0.912598i	$0.634073\pi$
$728$	8.47835e6	0.592902
$729$	531441.	0.0370370
$730$	−2.98389e6	−0.207241
$731$	−4.29463e6	−0.297257
$732$	394310.	0.0271994
$733$	−1.69274e7	−1.16367	−0.581835	−	0.813307i	$-0.697665\pi$
$733$	−1.69274e7	−1.16367	−0.581835	+	0.813307i	$0.697665\pi$
$734$	−5.05048e6	−0.346013
$735$	4.95137e6	0.338070
$736$	−4.78412e6	−0.325542
$737$	5.54186e6	0.375826
$738$	1.23246e6	0.0832978
$739$	−2.47308e7	−1.66582	−0.832909	−	0.553410i	$-0.813326\pi$
$739$	−2.47308e7	−1.66582	−0.832909	+	0.553410i	$0.813326\pi$
$740$	3.21224e6	0.215640
$741$	−2.18470e6	−0.146166
$742$	−6.15674e6	−0.410527
$743$	−1.97993e6	−0.131576	−0.0657881	−	0.997834i	$-0.520956\pi$
$743$	−1.97993e6	−0.131576	−0.0657881	+	0.997834i	$0.520956\pi$
$744$	−27609.5	−0.00182863
$745$	−760574.	−0.0502054
$746$	−1.99437e7	−1.31207
$747$	−7.97408e6	−0.522852
$748$	−3.54852e6	−0.231896
$749$	−2.95588e7	−1.92523
$750$	−562500.	−0.0365148
$751$	−4.54219e6	−0.293877	−0.146938	−	0.989146i	$-0.546942\pi$
$751$	−4.54219e6	−0.293877	−0.146938	+	0.989146i	$0.546942\pi$
$752$	−3.22376e6	−0.207883
$753$	−401810.	−0.0258246
$754$	3.41299e6	0.218629
$755$	1.15030e7	0.734419
$756$	2.29793e6	0.146229
$757$	2.98125e7	1.89086	0.945428	−	0.325830i	$-0.105644\pi$
$757$	2.98125e7	1.89086	0.945428	+	0.325830i	$0.105644\pi$
$758$	1.02453e6	0.0647664
$759$	1.59832e7	1.00707
$760$	−577600.	−0.0362738
$761$	−5.98609e6	−0.374698	−0.187349	−	0.982293i	$-0.559990\pi$
$761$	−5.98609e6	−0.374698	−0.187349	+	0.982293i	$0.559990\pi$
$762$	1.01290e6	0.0631946
$763$	3.12791e7	1.94510
$764$	1.29114e7	0.800274
$765$	−1.18150e6	−0.0729927
$766$	−2.28573e6	−0.140752
$767$	1.18943e7	0.730045
$768$	589824.	0.0360844
$769$	−1.84407e7	−1.12450	−0.562251	−	0.826966i	$-0.690065\pi$
$769$	−1.84407e7	−1.12450	−0.562251	+	0.826966i	$0.690065\pi$
$770$	−7.48874e6	−0.455179
$771$	−9.09513e6	−0.551027
$772$	1.24455e7	0.751568
$773$	1.39741e7	0.841153	0.420577	−	0.907257i	$-0.361828\pi$
$773$	1.39741e7	0.841153	0.420577	+	0.907257i	$0.361828\pi$
$774$	−2.38486e6	−0.143090
$775$	29958.3	0.00179169
$776$	−191555.	−0.0114193
$777$	1.42390e7	0.846111
$778$	1.89240e7	1.12089
$779$	−1.37321e6	−0.0810761
$780$	−2.42072e6	−0.142465
$781$	−1.35942e6	−0.0797489
$782$	1.09036e7	0.637607
$783$	925041.	0.0539208
$784$	5.63356e6	0.327335
$785$	7.82606e6	0.453282
$786$	−4.70214e6	−0.271481
$787$	2.51310e6	0.144635	0.0723174	−	0.997382i	$-0.476961\pi$
$787$	2.51310e6	0.144635	0.0723174	+	0.997382i	$0.476961\pi$
$788$	213185.	0.0122304
$789$	6.75654e6	0.386396
$790$	−2.87418e6	−0.163850
$791$	−3.37769e6	−0.191946
$792$	−1.97054e6	−0.111628
$793$	−1.84127e6	−0.103976
$794$	1.13892e7	0.641127
$795$	1.75786e6	0.0986431
$796$	−1.16903e6	−0.0653947
$797$	−3.19909e7	−1.78394	−0.891970	−	0.452095i	$-0.850677\pi$
$797$	−3.19909e7	−1.78394	−0.891970	+	0.452095i	$0.850677\pi$
$798$	−2.56035e6	−0.142328
$799$	7.34736e6	0.407159
$800$	−640000.	−0.0353553
$801$	2.42886e6	0.133759
$802$	4.80753e6	0.263928
$803$	1.13423e7	0.620746
$804$	2.09941e6	0.114540
$805$	2.30108e7	1.25153
$806$	128925.	0.00699038
$807$	−1.93353e7	−1.04512
$808$	2.05196e6	0.110571
$809$	6.22287e6	0.334287	0.167144	−	0.985933i	$-0.446546\pi$
$809$	6.22287e6	0.334287	0.167144	+	0.985933i	$0.446546\pi$
$810$	−656100.	−0.0351364
$811$	−2.01280e7	−1.07460	−0.537302	−	0.843390i	$-0.680556\pi$
$811$	−2.01280e7	−1.07460	−0.537302	+	0.843390i	$0.680556\pi$
$812$	3.99984e6	0.212889
$813$	1.07849e7	0.572256
$814$	−1.22104e7	−0.645903
$815$	3.36194e6	0.177295
$816$	−1.34428e6	−0.0706749
$817$	2.65720e6	0.139274
$818$	2.06237e7	1.07766
$819$	−1.07304e7	−0.558993
$820$	−1.52156e6	−0.0790232
$821$	1.59487e7	0.825786	0.412893	−	0.910780i	$-0.364518\pi$
$821$	1.59487e7	0.825786	0.412893	+	0.910780i	$0.364518\pi$
$822$	−1.34073e6	−0.0692089
$823$	−3.13818e6	−0.161502	−0.0807509	−	0.996734i	$-0.525732\pi$
$823$	−3.13818e6	−0.161502	−0.0807509	+	0.996734i	$0.525732\pi$
$824$	7.93281e6	0.407014
$825$	2.13817e6	0.109372
$826$	1.39394e7	0.710878
$827$	1.60959e7	0.818376	0.409188	−	0.912450i	$-0.365812\pi$
$827$	1.60959e7	0.818376	0.409188	+	0.912450i	$0.365812\pi$
$828$	6.05490e6	0.306924
$829$	2.79234e7	1.41118	0.705590	−	0.708620i	$-0.250682\pi$
$829$	2.79234e7	1.41118	0.705590	+	0.708620i	$0.250682\pi$
$830$	9.84454e6	0.496021
$831$	1.99568e7	1.00251
$832$	−2.75424e6	−0.137941
$833$	−1.28396e7	−0.641119
$834$	−4.30712e6	−0.214423
$835$	−6.89572e6	−0.342266
$836$	2.19557e6	0.108650
$837$	34943.3	0.00172405
$838$	1.01249e7	0.498059
$839$	−3.54083e7	−1.73660	−0.868300	−	0.496039i	$-0.834787\pi$
$839$	−3.54083e7	−1.73660	−0.868300	+	0.496039i	$0.834787\pi$
$840$	−2.83695e6	−0.138725
$841$	−1.89010e7	−0.921499
$842$	−4.77365e6	−0.232044
$843$	−1.64079e7	−0.795214
$844$	−4.35911e6	−0.210641
$845$	2.02147e6	0.0973923
$846$	4.08007e6	0.195994
$847$	−3.26258e6	−0.156262
$848$	2.00005e6	0.0955107
$849$	9.97965e6	0.475167
$850$	1.45864e6	0.0692469
$851$	3.75189e7	1.77593
$852$	−514985.	−0.0243050
$853$	−1.34191e7	−0.631469	−0.315735	−	0.948848i	$-0.602251\pi$
$853$	−1.34191e7	−0.631469	−0.315735	+	0.948848i	$0.602251\pi$
$854$	−2.15787e6	−0.101246
$855$	731025.	0.0341993
$856$	9.60235e6	0.447912
$857$	−1.94060e6	−0.0902579	−0.0451289	−	0.998981i	$-0.514370\pi$
$857$	−1.94060e6	−0.0902579	−0.0451289	+	0.998981i	$0.514370\pi$
$858$	9.20162e6	0.426723
$859$	−3.62803e7	−1.67760	−0.838800	−	0.544440i	$-0.816742\pi$
$859$	−3.62803e7	−1.67760	−0.838800	+	0.544440i	$0.816742\pi$
$860$	2.94427e6	0.135747
$861$	−6.74467e6	−0.310065
$862$	7.42238e6	0.340232
$863$	3.68747e7	1.68539	0.842696	−	0.538389i	$-0.180967\pi$
$863$	3.68747e7	1.68539	0.842696	+	0.538389i	$0.180967\pi$
$864$	−746496.	−0.0340207
$865$	1.01462e7	0.461067
$866$	1.82088e7	0.825063
$867$	−9.71493e6	−0.438927
$868$	151093.	0.00680685
$869$	1.09253e7	0.490777
$870$	−1.14203e6	−0.0511538
$871$	−9.80343e6	−0.437857
$872$	−1.01612e7	−0.452537
$873$	242436.	0.0107662
$874$	−6.74636e6	−0.298738
$875$	3.07829e6	0.135922
$876$	4.29680e6	0.189184
$877$	2.48608e7	1.09148	0.545741	−	0.837954i	$-0.316248\pi$
$877$	2.48608e7	1.09148	0.545741	+	0.837954i	$0.316248\pi$
$878$	2.73345e6	0.119667
$879$	6.02046e6	0.262819
$880$	2.43276e6	0.105899
$881$	2.32562e7	1.00948	0.504740	−	0.863271i	$-0.331588\pi$
$881$	2.32562e7	1.00948	0.504740	+	0.863271i	$0.331588\pi$
$882$	−7.12997e6	−0.308615
$883$	3.73212e7	1.61084	0.805422	−	0.592702i	$-0.201939\pi$
$883$	3.73212e7	1.61084	0.805422	+	0.592702i	$0.201939\pi$
$884$	6.27726e6	0.270171
$885$	−3.97996e6	−0.170813
$886$	−1.61580e7	−0.691518
$887$	1.50942e7	0.644173	0.322086	−	0.946710i	$-0.395616\pi$
$887$	1.50942e7	0.644173	0.322086	+	0.946710i	$0.395616\pi$
$888$	−4.62563e6	−0.196851
$889$	−5.54312e6	−0.235234
$890$	−2.99859e6	−0.126894
$891$	2.49396e6	0.105244
$892$	4.49196e6	0.189027
$893$	−4.54601e6	−0.190766
$894$	1.09523e6	0.0458311
$895$	−6.02106e6	−0.251255
$896$	−3.22782e6	−0.134319
$897$	−2.82740e7	−1.17329
$898$	2.96704e7	1.22781
$899$	60823.3	0.00250998
$900$	810000.	0.0333333
$901$	−4.55837e6	−0.187067
$902$	5.78374e6	0.236697
$903$	1.30512e7	0.532635
$904$	1.09726e6	0.0446570
$905$	−2.06307e7	−0.837322
$906$	−1.65643e7	−0.670429
$907$	−1.39715e7	−0.563931	−0.281965	−	0.959425i	$-0.590986\pi$
$907$	−1.39715e7	−0.563931	−0.281965	+	0.959425i	$0.590986\pi$
$908$	2.21636e7	0.892125
$909$	−2.59702e6	−0.104247
$910$	1.32474e7	0.530307
$911$	−3.92485e7	−1.56685	−0.783425	−	0.621486i	$-0.786529\pi$
$911$	−3.92485e7	−1.56685	−0.783425	+	0.621486i	$0.786529\pi$
$912$	831744.	0.0331133
$913$	−3.74210e7	−1.48572
$914$	−3.31202e7	−1.31138
$915$	616109.	0.0243279
$916$	2.27038e7	0.894048
$917$	2.57325e7	1.01055
$918$	1.70136e6	0.0666329
$919$	8.24119e6	0.321885	0.160943	−	0.986964i	$-0.448547\pi$
$919$	8.24119e6	0.321885	0.160943	+	0.986964i	$0.448547\pi$
$920$	−7.47519e6	−0.291174
$921$	−2.07835e7	−0.807365
$922$	2.55807e7	0.991025
$923$	2.40478e6	0.0929117
$924$	1.07838e7	0.415520
$925$	5.01913e6	0.192874
$926$	2.50668e7	0.960664
$927$	−1.00400e7	−0.383736
$928$	−1.29937e6	−0.0495295
$929$	−3.19115e7	−1.21313	−0.606566	−	0.795033i	$-0.707453\pi$
$929$	−3.19115e7	−1.21313	−0.606566	+	0.795033i	$0.707453\pi$
$930$	−43139.9	−0.00163558
$931$	7.94420e6	0.300383
$932$	2.10446e7	0.793600
$933$	−2.09047e7	−0.786212
$934$	3.05741e7	1.14680
$935$	−5.54457e6	−0.207414
$936$	3.48584e6	0.130052
$937$	−4.28942e7	−1.59606	−0.798031	−	0.602616i	$-0.794125\pi$
$937$	−4.28942e7	−1.59606	−0.798031	+	0.602616i	$0.794125\pi$
$938$	−1.14891e7	−0.426361
$939$	2.72720e6	0.100938
$940$	−5.03713e6	−0.185936
$941$	−1.31571e7	−0.484380	−0.242190	−	0.970229i	$-0.577866\pi$
$941$	−1.31571e7	−0.484380	−0.242190	+	0.970229i	$0.577866\pi$
$942$	−1.12695e7	−0.413788
$943$	−1.77718e7	−0.650807
$944$	−4.52831e6	−0.165389
$945$	3.59051e6	0.130791
$946$	−1.11917e7	−0.406602
$947$	−4.81781e7	−1.74572	−0.872861	−	0.487969i	$-0.837738\pi$
$947$	−4.81781e7	−1.74572	−0.872861	+	0.487969i	$0.837738\pi$
$948$	4.13882e6	0.149574
$949$	−2.00643e7	−0.723202
$950$	−902500.	−0.0324443
$951$	−1.54095e7	−0.552506
$952$	7.35660e6	0.263078
$953$	2.65269e7	0.946137	0.473068	−	0.881026i	$-0.343146\pi$
$953$	2.65269e7	0.946137	0.473068	+	0.881026i	$0.343146\pi$
$954$	−2.53132e6	−0.0900484
$955$	2.01740e7	0.715787
$956$	−1.23965e7	−0.438686
$957$	4.34106e6	0.153220
$958$	−2.10043e6	−0.0739424
$959$	7.33716e6	0.257621
$960$	921600.	0.0322749
$961$	−2.86269e7	−0.999920
$962$	2.15998e7	0.752511
$963$	−1.21530e7	−0.422296
$964$	280781.	0.00973140
$965$	1.94460e7	0.672222
$966$	−3.31355e7	−1.14249
$967$	−2.31096e7	−0.794741	−0.397370	−	0.917658i	$-0.630077\pi$
$967$	−2.31096e7	−0.794741	−0.397370	+	0.917658i	$0.630077\pi$
$968$	1.05987e6	0.0363549
$969$	−1.89565e6	−0.0648557
$970$	−299304.	−0.0102137
$971$	1.09900e7	0.374069	0.187034	−	0.982353i	$-0.440112\pi$
$971$	1.09900e7	0.374069	0.187034	+	0.982353i	$0.440112\pi$
$972$	944784.	0.0320750
$973$	2.35707e7	0.798162
$974$	2.13015e7	0.719469
$975$	−3.78237e6	−0.127425
$976$	700995.	0.0235554
$977$	3.16949e6	0.106231	0.0531157	−	0.998588i	$-0.483085\pi$
$977$	3.16949e6	0.106231	0.0531157	+	0.998588i	$0.483085\pi$
$978$	−4.84119e6	−0.161847
$979$	1.13982e7	0.380085
$980$	8.80244e6	0.292778
$981$	1.28603e7	0.426656
$982$	−2.77921e7	−0.919692
$983$	−4.25969e6	−0.140603	−0.0703015	−	0.997526i	$-0.522396\pi$
$983$	−4.25969e6	−0.140603	−0.0703015	+	0.997526i	$0.522396\pi$
$984$	2.19105e6	0.0721380
$985$	333101.	0.0109392
$986$	2.96143e6	0.0970084
$987$	−2.23283e7	−0.729561
$988$	−3.88391e6	−0.126583
$989$	3.43890e7	1.11797
$990$	−3.07897e6	−0.0998428
$991$	−1.78313e6	−0.0576764	−0.0288382	−	0.999584i	$-0.509181\pi$
$991$	−1.78313e6	−0.0576764	−0.0288382	+	0.999584i	$0.509181\pi$
$992$	−49083.6	−0.00158364
$993$	1.07468e7	0.345864
$994$	2.81826e6	0.0904723
$995$	−1.82661e6	−0.0584908
$996$	−1.41761e7	−0.452803
$997$	−2.23417e6	−0.0711833	−0.0355916	−	0.999366i	$-0.511332\pi$
$997$	−2.23417e6	−0.0711833	−0.0355916	+	0.999366i	$0.511332\pi$
$998$	−1.36165e7	−0.432751
$999$	5.85431e6	0.185593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.m.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.m.1.3	✓	4	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +197.010 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +197.010 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +380.119 q^{11} +144.000 q^{12} -672.422 q^{13} -788.042 q^{14} +225.000 q^{15} +256.000 q^{16} -583.456 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1773.09 q^{21} -1520.48 q^{22} +4671.99 q^{23} -576.000 q^{24} +625.000 q^{25} +2689.69 q^{26} +729.000 q^{27} +3152.17 q^{28} +1268.92 q^{29} -900.000 q^{30} +47.9332 q^{31} -1024.00 q^{32} +3421.07 q^{33} +2333.82 q^{34} +4925.26 q^{35} +1296.00 q^{36} +8030.61 q^{37} -1444.00 q^{38} -6051.80 q^{39} -1600.00 q^{40} -3803.90 q^{41} -7092.37 q^{42} +7360.67 q^{43} +6081.91 q^{44} +2025.00 q^{45} -18688.0 q^{46} -12592.8 q^{47} +2304.00 q^{48} +22006.1 q^{49} -2500.00 q^{50} -5251.10 q^{51} -10758.8 q^{52} +7812.71 q^{53} -2916.00 q^{54} +9502.98 q^{55} -12608.7 q^{56} +3249.00 q^{57} -5075.67 q^{58} -17688.7 q^{59} +3600.00 q^{60} +2738.26 q^{61} -191.733 q^{62} +15957.8 q^{63} +4096.00 q^{64} -16810.6 q^{65} -13684.3 q^{66} +14579.3 q^{67} -9335.29 q^{68} +42047.9 q^{69} -19701.0 q^{70} -3576.29 q^{71} -5184.00 q^{72} +29838.9 q^{73} -32122.4 q^{74} +5625.00 q^{75} +5776.00 q^{76} +74887.4 q^{77} +24207.2 q^{78} +28741.8 q^{79} +6400.00 q^{80} +6561.00 q^{81} +15215.6 q^{82} -98445.4 q^{83} +28369.5 q^{84} -14586.4 q^{85} -29442.7 q^{86} +11420.3 q^{87} -24327.6 q^{88} +29985.9 q^{89} -8100.00 q^{90} -132474. q^{91} +74751.9 q^{92} +431.399 q^{93} +50371.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +2993.04 q^{97} -88024.4 q^{98} +30789.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} + 338 q^{11} + 576 q^{12} + 1302 q^{13} - 1072 q^{14} + 900 q^{15} + 1024 q^{16} + 542 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 2412 q^{21} - 1352 q^{22} - 88 q^{23} - 2304 q^{24} + 2500 q^{25} - 5208 q^{26} + 2916 q^{27} + 4288 q^{28} + 5014 q^{29} - 3600 q^{30} + 4962 q^{31} - 4096 q^{32} + 3042 q^{33} - 2168 q^{34} + 6700 q^{35} + 5184 q^{36} + 8022 q^{37} - 5776 q^{38} + 11718 q^{39} - 6400 q^{40} + 2764 q^{41} - 9648 q^{42} + 25346 q^{43} + 5408 q^{44} + 8100 q^{45} + 352 q^{46} + 10008 q^{47} + 9216 q^{48} + 37248 q^{49} - 10000 q^{50} + 4878 q^{51} + 20832 q^{52} - 224 q^{53} - 11664 q^{54} + 8450 q^{55} - 17152 q^{56} + 12996 q^{57} - 20056 q^{58} + 29654 q^{59} + 14400 q^{60} + 27276 q^{61} - 19848 q^{62} + 21708 q^{63} + 16384 q^{64} + 32550 q^{65} - 12168 q^{66} + 26024 q^{67} + 8672 q^{68} - 792 q^{69} - 26800 q^{70} - 26940 q^{71} - 20736 q^{72} - 60916 q^{73} - 32088 q^{74} + 22500 q^{75} + 23104 q^{76} - 21228 q^{77} - 46872 q^{78} + 34902 q^{79} + 25600 q^{80} + 26244 q^{81} - 11056 q^{82} - 48430 q^{83} + 38592 q^{84} + 13550 q^{85} - 101384 q^{86} + 45126 q^{87} - 21632 q^{88} - 38348 q^{89} - 32400 q^{90} + 69280 q^{91} - 1408 q^{92} + 44658 q^{93} - 40032 q^{94} + 36100 q^{95} - 36864 q^{96} + 45942 q^{97} - 148992 q^{98} + 27378 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 + 338 * q^11 + 576 * q^12 + 1302 * q^13 - 1072 * q^14 + 900 * q^15 + 1024 * q^16 + 542 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 2412 * q^21 - 1352 * q^22 - 88 * q^23 - 2304 * q^24 + 2500 * q^25 - 5208 * q^26 + 2916 * q^27 + 4288 * q^28 + 5014 * q^29 - 3600 * q^30 + 4962 * q^31 - 4096 * q^32 + 3042 * q^33 - 2168 * q^34 + 6700 * q^35 + 5184 * q^36 + 8022 * q^37 - 5776 * q^38 + 11718 * q^39 - 6400 * q^40 + 2764 * q^41 - 9648 * q^42 + 25346 * q^43 + 5408 * q^44 + 8100 * q^45 + 352 * q^46 + 10008 * q^47 + 9216 * q^48 + 37248 * q^49 - 10000 * q^50 + 4878 * q^51 + 20832 * q^52 - 224 * q^53 - 11664 * q^54 + 8450 * q^55 - 17152 * q^56 + 12996 * q^57 - 20056 * q^58 + 29654 * q^59 + 14400 * q^60 + 27276 * q^61 - 19848 * q^62 + 21708 * q^63 + 16384 * q^64 + 32550 * q^65 - 12168 * q^66 + 26024 * q^67 + 8672 * q^68 - 792 * q^69 - 26800 * q^70 - 26940 * q^71 - 20736 * q^72 - 60916 * q^73 - 32088 * q^74 + 22500 * q^75 + 23104 * q^76 - 21228 * q^77 - 46872 * q^78 + 34902 * q^79 + 25600 * q^80 + 26244 * q^81 - 11056 * q^82 - 48430 * q^83 + 38592 * q^84 + 13550 * q^85 - 101384 * q^86 + 45126 * q^87 - 21632 * q^88 - 38348 * q^89 - 32400 * q^90 + 69280 * q^91 - 1408 * q^92 + 44658 * q^93 - 40032 * q^94 + 36100 * q^95 - 36864 * q^96 + 45942 * q^97 - 148992 * q^98 + 27378 * q^99

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