LMFDB - Embedded newform 570.6.a.m.1.4

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			1.4
Root			$-13.3932$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +229.958 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +229.958 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -291.046 q^{11} +144.000 q^{12} +1157.69 q^{13} -919.833 q^{14} +225.000 q^{15} +256.000 q^{16} +1162.12 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +2069.62 q^{21} +1164.18 q^{22} -3807.41 q^{23} -576.000 q^{24} +625.000 q^{25} -4630.76 q^{26} +729.000 q^{27} +3679.33 q^{28} +7366.62 q^{29} -900.000 q^{30} +6149.97 q^{31} -1024.00 q^{32} -2619.41 q^{33} -4648.47 q^{34} +5748.95 q^{35} +1296.00 q^{36} -1728.76 q^{37} -1444.00 q^{38} +10419.2 q^{39} -1600.00 q^{40} -11006.7 q^{41} -8278.49 q^{42} +16853.6 q^{43} -4656.73 q^{44} +2025.00 q^{45} +15229.6 q^{46} -6749.24 q^{47} +2304.00 q^{48} +36073.7 q^{49} -2500.00 q^{50} +10459.1 q^{51} +18523.0 q^{52} -38538.0 q^{53} -2916.00 q^{54} -7276.15 q^{55} -14717.3 q^{56} +3249.00 q^{57} -29466.5 q^{58} +30949.2 q^{59} +3600.00 q^{60} -7283.72 q^{61} -24599.9 q^{62} +18626.6 q^{63} +4096.00 q^{64} +28942.3 q^{65} +10477.6 q^{66} -25655.9 q^{67} +18593.9 q^{68} -34266.7 q^{69} -22995.8 q^{70} -7321.98 q^{71} -5184.00 q^{72} -81106.7 q^{73} +6915.02 q^{74} +5625.00 q^{75} +5776.00 q^{76} -66928.4 q^{77} -41676.9 q^{78} -1786.83 q^{79} +6400.00 q^{80} +6561.00 q^{81} +44026.9 q^{82} +41472.9 q^{83} +33114.0 q^{84} +29052.9 q^{85} -67414.3 q^{86} +66299.6 q^{87} +18626.9 q^{88} +52047.0 q^{89} -8100.00 q^{90} +266220. q^{91} -60918.5 q^{92} +55349.8 q^{93} +26997.0 q^{94} +9025.00 q^{95} -9216.00 q^{96} -91522.8 q^{97} -144295. q^{98} -23574.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	229.958	1.77380	0.886898	−	0.461965i	$-0.152856\pi$
$7$	229.958	1.77380	0.886898	+	0.461965i	$0.152856\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−291.046	−0.725236	−0.362618	−	0.931938i	$-0.618117\pi$
$11$	−291.046	−0.725236	−0.362618	+	0.931938i	$0.618117\pi$
$12$	144.000	0.288675
$13$	1157.69	1.89991	0.949957	−	0.312380i	$-0.101126\pi$
$13$	1157.69	1.89991	0.949957	+	0.312380i	$0.101126\pi$
$14$	−919.833	−1.25426
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	1162.12	0.975277	0.487638	−	0.873046i	$-0.337858\pi$
$17$	1162.12	0.975277	0.487638	+	0.873046i	$0.337858\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	2069.62	1.02410
$22$	1164.18	0.512820
$23$	−3807.41	−1.50075	−0.750377	−	0.661010i	$-0.770128\pi$
$23$	−3807.41	−1.50075	−0.750377	+	0.661010i	$0.770128\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−4630.76	−1.34344
$27$	729.000	0.192450
$28$	3679.33	0.886898
$29$	7366.62	1.62657	0.813286	−	0.581864i	$-0.197677\pi$
$29$	7366.62	1.62657	0.813286	+	0.581864i	$0.197677\pi$
$30$	−900.000	−0.182574
$31$	6149.97	1.14939	0.574697	−	0.818366i	$-0.305120\pi$
$31$	6149.97	1.14939	0.574697	+	0.818366i	$0.305120\pi$
$32$	−1024.00	−0.176777
$33$	−2619.41	−0.418715
$34$	−4648.47	−0.689625
$35$	5748.95	0.793266
$36$	1296.00	0.166667
$37$	−1728.76	−0.207601	−0.103800	−	0.994598i	$-0.533100\pi$
$37$	−1728.76	−0.207601	−0.103800	+	0.994598i	$0.533100\pi$
$38$	−1444.00	−0.162221
$39$	10419.2	1.09692
$40$	−1600.00	−0.158114
$41$	−11006.7	−1.02258	−0.511291	−	0.859408i	$-0.670833\pi$
$41$	−11006.7	−1.02258	−0.511291	+	0.859408i	$0.670833\pi$
$42$	−8278.49	−0.724149
$43$	16853.6	1.39002	0.695010	−	0.719000i	$-0.255400\pi$
$43$	16853.6	1.39002	0.695010	+	0.719000i	$0.255400\pi$
$44$	−4656.73	−0.362618
$45$	2025.00	0.149071
$46$	15229.6	1.06119
$47$	−6749.24	−0.445667	−0.222834	−	0.974857i	$-0.571531\pi$
$47$	−6749.24	−0.445667	−0.222834	+	0.974857i	$0.571531\pi$
$48$	2304.00	0.144338
$49$	36073.7	2.14635
$50$	−2500.00	−0.141421
$51$	10459.1	0.563076
$52$	18523.0	0.949957
$53$	−38538.0	−1.88451	−0.942257	−	0.334889i	$-0.891301\pi$
$53$	−38538.0	−1.88451	−0.942257	+	0.334889i	$0.891301\pi$
$54$	−2916.00	−0.136083
$55$	−7276.15	−0.324336
$56$	−14717.3	−0.627132
$57$	3249.00	0.132453
$58$	−29466.5	−1.15016
$59$	30949.2	1.15750	0.578748	−	0.815507i	$-0.303542\pi$
$59$	30949.2	1.15750	0.578748	+	0.815507i	$0.303542\pi$
$60$	3600.00	0.129099
$61$	−7283.72	−0.250628	−0.125314	−	0.992117i	$-0.539994\pi$
$61$	−7283.72	−0.250628	−0.125314	+	0.992117i	$0.539994\pi$
$62$	−24599.9	−0.812745
$63$	18626.6	0.591265
$64$	4096.00	0.125000
$65$	28942.3	0.849668
$66$	10477.6	0.296077
$67$	−25655.9	−0.698233	−0.349117	−	0.937079i	$-0.613518\pi$
$67$	−25655.9	−0.698233	−0.349117	+	0.937079i	$0.613518\pi$
$68$	18593.9	0.487638
$69$	−34266.7	−0.866461
$70$	−22995.8	−0.560924
$71$	−7321.98	−0.172378	−0.0861892	−	0.996279i	$-0.527469\pi$
$71$	−7321.98	−0.172378	−0.0861892	+	0.996279i	$0.527469\pi$
$72$	−5184.00	−0.117851
$73$	−81106.7	−1.78135	−0.890676	−	0.454638i	$-0.849769\pi$
$73$	−81106.7	−1.78135	−0.890676	+	0.454638i	$0.849769\pi$
$74$	6915.02	0.146796
$75$	5625.00	0.115470
$76$	5776.00	0.114708
$77$	−66928.4	−1.28642
$78$	−41676.9	−0.775637
$79$	−1786.83	−0.0322119	−0.0161059	−	0.999870i	$-0.505127\pi$
$79$	−1786.83	−0.0322119	−0.0161059	+	0.999870i	$0.505127\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	44026.9	0.723074
$83$	41472.9	0.660799	0.330399	−	0.943841i	$-0.392817\pi$
$83$	41472.9	0.660799	0.330399	+	0.943841i	$0.392817\pi$
$84$	33114.0	0.512051
$85$	29052.9	0.436157
$86$	−67414.3	−0.982893
$87$	66299.6	0.939102
$88$	18626.9	0.256410
$89$	52047.0	0.696500	0.348250	−	0.937402i	$-0.386776\pi$
$89$	52047.0	0.696500	0.348250	+	0.937402i	$0.386776\pi$
$90$	−8100.00	−0.105409
$91$	266220.	3.37006
$92$	−60918.5	−0.750377
$93$	55349.8	0.663603
$94$	26997.0	0.315134
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	−91522.8	−0.987643	−0.493822	−	0.869563i	$-0.664400\pi$
$97$	−91522.8	−0.987643	−0.493822	+	0.869563i	$0.664400\pi$
$98$	−144295.	−1.51770
$99$	−23574.7	−0.241745
$100$	10000.0	0.100000
$101$	−93040.6	−0.907546	−0.453773	−	0.891117i	$-0.649922\pi$
$101$	−93040.6	−0.907546	−0.453773	+	0.891117i	$0.649922\pi$
$102$	−41836.2	−0.398155
$103$	−91771.6	−0.852345	−0.426173	−	0.904642i	$-0.640138\pi$
$103$	−91771.6	−0.852345	−0.426173	+	0.904642i	$0.640138\pi$
$104$	−74092.2	−0.671721
$105$	51740.6	0.457992
$106$	154152.	1.33255
$107$	31356.1	0.264766	0.132383	−	0.991199i	$-0.457737\pi$
$107$	31356.1	0.264766	0.132383	+	0.991199i	$0.457737\pi$
$108$	11664.0	0.0962250
$109$	−183541.	−1.47968	−0.739838	−	0.672785i	$-0.765098\pi$
$109$	−183541.	−1.47968	−0.739838	+	0.672785i	$0.765098\pi$
$110$	29104.6	0.229340
$111$	−15558.8	−0.119858
$112$	58869.3	0.443449
$113$	65903.4	0.485525	0.242763	−	0.970086i	$-0.421946\pi$
$113$	65903.4	0.485525	0.242763	+	0.970086i	$0.421946\pi$
$114$	−12996.0	−0.0936586
$115$	−95185.2	−0.671158
$116$	117866.	0.813286
$117$	93772.9	0.633305
$118$	−123797.	−0.818473
$119$	267238.	1.72994
$120$	−14400.0	−0.0912871
$121$	−76343.3	−0.474032
$122$	29134.9	0.177220
$123$	−99060.4	−0.590388
$124$	98399.6	0.574697
$125$	15625.0	0.0894427
$126$	−74506.4	−0.418088
$127$	218617.	1.20275	0.601375	−	0.798967i	$-0.294620\pi$
$127$	218617.	1.20275	0.601375	+	0.798967i	$0.294620\pi$
$128$	−16384.0	−0.0883883
$129$	151682.	0.802528
$130$	−115769.	−0.600806
$131$	−83381.8	−0.424515	−0.212258	−	0.977214i	$-0.568082\pi$
$131$	−83381.8	−0.424515	−0.212258	+	0.977214i	$0.568082\pi$
$132$	−41910.6	−0.209358
$133$	83014.9	0.406937
$134$	102624.	0.493725
$135$	18225.0	0.0860663
$136$	−74375.5	−0.344812
$137$	121233.	0.551849	0.275925	−	0.961179i	$-0.411016\pi$
$137$	121233.	0.551849	0.275925	+	0.961179i	$0.411016\pi$
$138$	137067.	0.612680
$139$	−311739.	−1.36853	−0.684266	−	0.729233i	$-0.739877\pi$
$139$	−311739.	−1.36853	−0.684266	+	0.729233i	$0.739877\pi$
$140$	91983.3	0.396633
$141$	−60743.2	−0.257306
$142$	29287.9	0.121890
$143$	−336941.	−1.37789
$144$	20736.0	0.0833333
$145$	184165.	0.727425
$146$	324427.	1.25961
$147$	324664.	1.23920
$148$	−27660.1	−0.103800
$149$	−1734.58	−0.00640070	−0.00320035	−	0.999995i	$-0.501019\pi$
$149$	−1734.58	−0.00640070	−0.00320035	+	0.999995i	$0.501019\pi$
$150$	−22500.0	−0.0816497
$151$	−324438.	−1.15795	−0.578974	−	0.815346i	$-0.696547\pi$
$151$	−324438.	−1.15795	−0.578974	+	0.815346i	$0.696547\pi$
$152$	−23104.0	−0.0811107
$153$	94131.5	0.325092
$154$	267713.	0.909637
$155$	153749.	0.514025
$156$	166707.	0.548458
$157$	367088.	1.18856	0.594279	−	0.804259i	$-0.297437\pi$
$157$	367088.	1.18856	0.594279	+	0.804259i	$0.297437\pi$
$158$	7147.33	0.0227772
$159$	−346842.	−1.08803
$160$	−25600.0	−0.0790569
$161$	−875544.	−2.66203
$162$	−26244.0	−0.0785674
$163$	−375507.	−1.10700	−0.553502	−	0.832848i	$-0.686709\pi$
$163$	−375507.	−1.10700	−0.553502	+	0.832848i	$0.686709\pi$
$164$	−176107.	−0.511291
$165$	−65485.3	−0.187255
$166$	−165892.	−0.467255
$167$	571913.	1.58686	0.793430	−	0.608661i	$-0.208293\pi$
$167$	571913.	1.58686	0.793430	+	0.608661i	$0.208293\pi$
$168$	−132456.	−0.362075
$169$	968954.	2.60968
$170$	−116212.	−0.308410
$171$	29241.0	0.0764719
$172$	269657.	0.695010
$173$	216729.	0.550557	0.275279	−	0.961364i	$-0.411230\pi$
$173$	216729.	0.550557	0.275279	+	0.961364i	$0.411230\pi$
$174$	−265198.	−0.664045
$175$	143724.	0.354759
$176$	−74507.7	−0.181309
$177$	278543.	0.668280
$178$	−208188.	−0.492500
$179$	−665063.	−1.55142	−0.775711	−	0.631088i	$-0.782609\pi$
$179$	−665063.	−1.55142	−0.775711	+	0.631088i	$0.782609\pi$
$180$	32400.0	0.0745356
$181$	471472.	1.06969	0.534847	−	0.844949i	$-0.320369\pi$
$181$	471472.	1.06969	0.534847	+	0.844949i	$0.320369\pi$
$182$	−1.06488e6	−2.38299
$183$	−65553.5	−0.144700
$184$	243674.	0.530597
$185$	−43218.9	−0.0928420
$186$	−221399.	−0.469238
$187$	−338230.	−0.707306
$188$	−107988.	−0.222834
$189$	167639.	0.341367
$190$	−36100.0	−0.0725476
$191$	569955.	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$191$	569955.	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$192$	36864.0	0.0721688
$193$	980863.	1.89546	0.947731	−	0.319071i	$-0.103371\pi$
$193$	980863.	1.89546	0.947731	+	0.319071i	$0.103371\pi$
$194$	366091.	0.698369
$195$	260480.	0.490556
$196$	577180.	1.07318
$197$	903143.	1.65802	0.829012	−	0.559230i	$-0.188903\pi$
$197$	903143.	1.65802	0.829012	+	0.559230i	$0.188903\pi$
$198$	94298.8	0.170940
$199$	1.01374e6	1.81465	0.907324	−	0.420433i	$-0.138122\pi$
$199$	1.01374e6	1.81465	0.907324	+	0.420433i	$0.138122\pi$
$200$	−40000.0	−0.0707107
$201$	−230903.	−0.403125
$202$	372162.	0.641732
$203$	1.69401e6	2.88521
$204$	167345.	0.281538
$205$	−275168.	−0.457312
$206$	367087.	0.602699
$207$	−308400.	−0.500251
$208$	296369.	0.474979
$209$	−105068.	−0.166381
$210$	−206962.	−0.323849
$211$	115673.	0.178866	0.0894329	−	0.995993i	$-0.471495\pi$
$211$	115673.	0.178866	0.0894329	+	0.995993i	$0.471495\pi$
$212$	−616608.	−0.942257
$213$	−65897.8	−0.0995227
$214$	−125424.	−0.187218
$215$	421339.	0.621636
$216$	−46656.0	−0.0680414
$217$	1.41424e6	2.03879
$218$	734164.	1.04629
$219$	−729961.	−1.02846
$220$	−116418.	−0.162168
$221$	1.34537e6	1.85294
$222$	62235.2	0.0847527
$223$	1.14304e6	1.53921	0.769605	−	0.638520i	$-0.220453\pi$
$223$	1.14304e6	1.53921	0.769605	+	0.638520i	$0.220453\pi$
$224$	−235477.	−0.313566
$225$	50625.0	0.0666667
$226$	−263614.	−0.343318
$227$	−953897.	−1.22867	−0.614337	−	0.789043i	$-0.710577\pi$
$227$	−953897.	−1.22867	−0.614337	+	0.789043i	$0.710577\pi$
$228$	51984.0	0.0662266
$229$	−197852.	−0.249317	−0.124658	−	0.992200i	$-0.539783\pi$
$229$	−197852.	−0.249317	−0.124658	+	0.992200i	$0.539783\pi$
$230$	380741.	0.474580
$231$	−602355.	−0.742716
$232$	−471464.	−0.575080
$233$	−1.27481e6	−1.53835	−0.769174	−	0.639040i	$-0.779332\pi$
$233$	−1.27481e6	−1.53835	−0.769174	+	0.639040i	$0.779332\pi$
$234$	−375092.	−0.447814
$235$	−168731.	−0.199308
$236$	495187.	0.578748
$237$	−16081.5	−0.0185975
$238$	−1.06895e6	−1.22325
$239$	1.28302e6	1.45290	0.726452	−	0.687217i	$-0.241168\pi$
$239$	1.28302e6	1.45290	0.726452	+	0.687217i	$0.241168\pi$
$240$	57600.0	0.0645497
$241$	510281.	0.565936	0.282968	−	0.959129i	$-0.408681\pi$
$241$	510281.	0.565936	0.282968	+	0.959129i	$0.408681\pi$
$242$	305373.	0.335191
$243$	59049.0	0.0641500
$244$	−116540.	−0.125314
$245$	901844.	0.959878
$246$	396242.	0.417467
$247$	417926.	0.435870
$248$	−393598.	−0.406372
$249$	373256.	0.381512
$250$	−62500.0	−0.0632456
$251$	−675369.	−0.676639	−0.338320	−	0.941031i	$-0.609858\pi$
$251$	−675369.	−0.676639	−0.338320	+	0.941031i	$0.609858\pi$
$252$	298026.	0.295633
$253$	1.10813e6	1.08840
$254$	−874470.	−0.850473
$255$	261477.	0.251815
$256$	65536.0	0.0625000
$257$	−1.18632e6	−1.12039	−0.560197	−	0.828360i	$-0.689274\pi$
$257$	−1.18632e6	−1.12039	−0.560197	+	0.828360i	$0.689274\pi$
$258$	−606729.	−0.567473
$259$	−397541.	−0.368242
$260$	463076.	0.424834
$261$	596696.	0.542191
$262$	333527.	0.300178
$263$	1.35875e6	1.21129	0.605646	−	0.795734i	$-0.292915\pi$
$263$	1.35875e6	1.21129	0.605646	+	0.795734i	$0.292915\pi$
$264$	167642.	0.148038
$265$	−963450.	−0.842781
$266$	−332060.	−0.287748
$267$	468423.	0.402124
$268$	−410495.	−0.349117
$269$	−1.47868e6	−1.24593	−0.622966	−	0.782249i	$-0.714073\pi$
$269$	−1.47868e6	−1.24593	−0.622966	+	0.782249i	$0.714073\pi$
$270$	−72900.0	−0.0608581
$271$	726992.	0.601321	0.300661	−	0.953731i	$-0.402793\pi$
$271$	726992.	0.601321	0.300661	+	0.953731i	$0.402793\pi$
$272$	297502.	0.243819
$273$	2.39598e6	1.94571
$274$	−484933.	−0.390216
$275$	−181904.	−0.145047
$276$	−548267.	−0.433230
$277$	−2.45996e6	−1.92632	−0.963159	−	0.268934i	$-0.913329\pi$
$277$	−2.45996e6	−1.92632	−0.963159	+	0.268934i	$0.913329\pi$
$278$	1.24696e6	0.967698
$279$	498148.	0.383131
$280$	−367933.	−0.280462
$281$	1.96509e6	1.48463	0.742313	−	0.670054i	$-0.233729\pi$
$281$	1.96509e6	1.48463	0.742313	+	0.670054i	$0.233729\pi$
$282$	242973.	0.181943
$283$	903195.	0.670371	0.335186	−	0.942152i	$-0.391201\pi$
$283$	903195.	0.670371	0.335186	+	0.942152i	$0.391201\pi$
$284$	−117152.	−0.0861892
$285$	81225.0	0.0592349
$286$	1.34776e6	0.974313
$287$	−2.53108e6	−1.81385
$288$	−82944.0	−0.0589256
$289$	−69339.2	−0.0488353
$290$	−736662.	−0.514367
$291$	−823705.	−0.570216
$292$	−1.29771e6	−0.890676
$293$	−2.30809e6	−1.57066	−0.785331	−	0.619076i	$-0.787507\pi$
$293$	−2.30809e6	−1.57066	−0.785331	+	0.619076i	$0.787507\pi$
$294$	−1.29865e6	−0.876245
$295$	773730.	0.517648
$296$	110640.	0.0733980
$297$	−212172.	−0.139572
$298$	6938.30	0.00452598
$299$	−4.40780e6	−2.85131
$300$	90000.0	0.0577350
$301$	3.87562e6	2.46561
$302$	1.29775e6	0.818793
$303$	−837365.	−0.523972
$304$	92416.0	0.0573539
$305$	−182093.	−0.112084
$306$	−376526.	−0.229875
$307$	−2.00588e6	−1.21467	−0.607335	−	0.794446i	$-0.707761\pi$
$307$	−2.00588e6	−1.21467	−0.607335	+	0.794446i	$0.707761\pi$
$308$	−1.07085e6	−0.643211
$309$	−825945.	−0.492102
$310$	−614997.	−0.363470
$311$	589437.	0.345570	0.172785	−	0.984960i	$-0.444723\pi$
$311$	589437.	0.345570	0.172785	+	0.984960i	$0.444723\pi$
$312$	−666830.	−0.387818
$313$	266249.	0.153612	0.0768062	−	0.997046i	$-0.475528\pi$
$313$	266249.	0.153612	0.0768062	+	0.997046i	$0.475528\pi$
$314$	−1.46835e6	−0.840438
$315$	465665.	0.264422
$316$	−28589.3	−0.0161059
$317$	585368.	0.327175	0.163588	−	0.986529i	$-0.447693\pi$
$317$	585368.	0.327175	0.163588	+	0.986529i	$0.447693\pi$
$318$	1.38737e6	0.769350
$319$	−2.14402e6	−1.17965
$320$	102400.	0.0559017
$321$	282205.	0.152863
$322$	3.50218e6	1.88234
$323$	419525.	0.223744
$324$	104976.	0.0555556
$325$	723557.	0.379983
$326$	1.50203e6	0.782769
$327$	−1.65187e6	−0.854291
$328$	704430.	0.361537
$329$	−1.55204e6	−0.790522
$330$	261941.	0.132409
$331$	3.05508e6	1.53268	0.766341	−	0.642434i	$-0.222075\pi$
$331$	3.05508e6	1.53268	0.766341	+	0.642434i	$0.222075\pi$
$332$	663566.	0.330399
$333$	−140029.	−0.0692003
$334$	−2.28765e6	−1.12208
$335$	−641398.	−0.312259
$336$	529824.	0.256025
$337$	−2.95410e6	−1.41694	−0.708468	−	0.705743i	$-0.750613\pi$
$337$	−2.95410e6	−1.41694	−0.708468	+	0.705743i	$0.750613\pi$
$338$	−3.87582e6	−1.84532
$339$	593131.	0.280318
$340$	464847.	0.218079
$341$	−1.78992e6	−0.833583
$342$	−116964.	−0.0540738
$343$	4.43054e6	2.03340
$344$	−1.07863e6	−0.491446
$345$	−856666.	−0.387493
$346$	−866918.	−0.389303
$347$	−1.13529e6	−0.506156	−0.253078	−	0.967446i	$-0.581443\pi$
$347$	−1.13529e6	−0.506156	−0.253078	+	0.967446i	$0.581443\pi$
$348$	1.06079e6	0.469551
$349$	3.82641e6	1.68162	0.840811	−	0.541328i	$-0.182078\pi$
$349$	3.82641e6	1.68162	0.840811	+	0.541328i	$0.182078\pi$
$350$	−574895.	−0.250853
$351$	843956.	0.365639
$352$	298031.	0.128205
$353$	108668.	0.0464156	0.0232078	−	0.999731i	$-0.492612\pi$
$353$	108668.	0.0464156	0.0232078	+	0.999731i	$0.492612\pi$
$354$	−1.11417e6	−0.472545
$355$	−183050.	−0.0770899
$356$	832752.	0.348250
$357$	2.40515e6	0.998782
$358$	2.66025e6	1.09702
$359$	−1.93771e6	−0.793512	−0.396756	−	0.917924i	$-0.629864\pi$
$359$	−1.93771e6	−0.793512	−0.396756	+	0.917924i	$0.629864\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−1.88589e6	−0.756387
$363$	−687090.	−0.273683
$364$	4.25953e6	1.68503
$365$	−2.02767e6	−0.796645
$366$	262214.	0.102318
$367$	−2.43925e6	−0.945346	−0.472673	−	0.881238i	$-0.656711\pi$
$367$	−2.43925e6	−0.945346	−0.472673	+	0.881238i	$0.656711\pi$
$368$	−974696.	−0.375189
$369$	−891544.	−0.340861
$370$	172876.	0.0656492
$371$	−8.86213e6	−3.34275
$372$	885596.	0.331802
$373$	−1.17165e6	−0.436038	−0.218019	−	0.975945i	$-0.569959\pi$
$373$	−1.17165e6	−0.436038	−0.218019	+	0.975945i	$0.569959\pi$
$374$	1.35292e6	0.500141
$375$	140625.	0.0516398
$376$	431952.	0.157567
$377$	8.52826e6	3.09035
$378$	−670558.	−0.241383
$379$	−61153.7	−0.0218688	−0.0109344	−	0.999940i	$-0.503481\pi$
$379$	−61153.7	−0.0218688	−0.0109344	+	0.999940i	$0.503481\pi$
$380$	144400.	0.0512989
$381$	1.96756e6	0.694408
$382$	−2.27982e6	−0.799360
$383$	1.24915e6	0.435130	0.217565	−	0.976046i	$-0.430189\pi$
$383$	1.24915e6	0.435130	0.217565	+	0.976046i	$0.430189\pi$
$384$	−147456.	−0.0510310
$385$	−1.67321e6	−0.575305
$386$	−3.92345e6	−1.34029
$387$	1.36514e6	0.463340
$388$	−1.46437e6	−0.493822
$389$	−3.81154e6	−1.27710	−0.638552	−	0.769578i	$-0.720466\pi$
$389$	−3.81154e6	−1.27710	−0.638552	+	0.769578i	$0.720466\pi$
$390$	−1.04192e6	−0.346875
$391$	−4.42465e6	−1.46365
$392$	−2.30872e6	−0.758850
$393$	−750437.	−0.245094
$394$	−3.61257e6	−1.17240
$395$	−44670.8	−0.0144056
$396$	−377195.	−0.120873
$397$	3.59979e6	1.14631	0.573153	−	0.819449i	$-0.305720\pi$
$397$	3.59979e6	1.14631	0.573153	+	0.819449i	$0.305720\pi$
$398$	−4.05494e6	−1.28315
$399$	747134.	0.234945
$400$	160000.	0.0500000
$401$	−5.52249e6	−1.71504	−0.857520	−	0.514451i	$-0.827996\pi$
$401$	−5.52249e6	−1.71504	−0.857520	+	0.514451i	$0.827996\pi$
$402$	923613.	0.285052
$403$	7.11977e6	2.18375
$404$	−1.48865e6	−0.453773
$405$	164025.	0.0496904
$406$	−6.77606e6	−2.04015
$407$	503147.	0.150560
$408$	−669380.	−0.199078
$409$	−6.58383e6	−1.94612	−0.973061	−	0.230548i	$-0.925948\pi$
$409$	−6.58383e6	−1.94612	−0.973061	+	0.230548i	$0.925948\pi$
$410$	1.10067e6	0.323369
$411$	1.09110e6	0.318610
$412$	−1.46835e6	−0.426173
$413$	7.11702e6	2.05316
$414$	1.23360e6	0.353731
$415$	1.03682e6	0.295518
$416$	−1.18547e6	−0.335861
$417$	−2.80565e6	−0.790122
$418$	420270.	0.117649
$419$	3.61585e6	1.00618	0.503089	−	0.864235i	$-0.332197\pi$
$419$	3.61585e6	1.00618	0.503089	+	0.864235i	$0.332197\pi$
$420$	827849.	0.228996
$421$	−416769.	−0.114602	−0.0573008	−	0.998357i	$-0.518249\pi$
$421$	−416769.	−0.114602	−0.0573008	+	0.998357i	$0.518249\pi$
$422$	−462694.	−0.126477
$423$	−546689.	−0.148556
$424$	2.46643e6	0.666277
$425$	726324.	0.195055
$426$	263591.	0.0703732
$427$	−1.67495e6	−0.444562
$428$	501698.	0.132383
$429$	−3.03247e6	−0.795524
$430$	−1.68536e6	−0.439563
$431$	−3.47346e6	−0.900677	−0.450338	−	0.892858i	$-0.648697\pi$
$431$	−3.47346e6	−0.900677	−0.450338	+	0.892858i	$0.648697\pi$
$432$	186624.	0.0481125
$433$	1.69137e6	0.433530	0.216765	−	0.976224i	$-0.430450\pi$
$433$	1.69137e6	0.433530	0.216765	+	0.976224i	$0.430450\pi$
$434$	−5.65695e6	−1.44164
$435$	1.65749e6	0.419979
$436$	−2.93665e6	−0.739838
$437$	−1.37447e6	−0.344297
$438$	2.91984e6	0.727234
$439$	275786.	0.0682985	0.0341493	−	0.999417i	$-0.489128\pi$
$439$	275786.	0.0682985	0.0341493	+	0.999417i	$0.489128\pi$
$440$	465673.	0.114670
$441$	2.92197e6	0.715451
$442$	−5.38149e6	−1.31023
$443$	5.60621e6	1.35725	0.678625	−	0.734485i	$-0.262576\pi$
$443$	5.60621e6	1.35725	0.678625	+	0.734485i	$0.262576\pi$
$444$	−248941.	−0.0599292
$445$	1.30118e6	0.311484
$446$	−4.57215e6	−1.08839
$447$	−15611.2	−0.00369545
$448$	941909.	0.221725
$449$	−3.45046e6	−0.807719	−0.403860	−	0.914821i	$-0.632332\pi$
$449$	−3.45046e6	−0.807719	−0.403860	+	0.914821i	$0.632332\pi$
$450$	−202500.	−0.0471405
$451$	3.20346e6	0.741614
$452$	1.05445e6	0.242763
$453$	−2.91994e6	−0.668542
$454$	3.81559e6	0.868804
$455$	6.65551e6	1.50714
$456$	−207936.	−0.0468293
$457$	−5.99883e6	−1.34362	−0.671809	−	0.740724i	$-0.734482\pi$
$457$	−5.99883e6	−1.34362	−0.671809	+	0.740724i	$0.734482\pi$
$458$	791407.	0.176294
$459$	847184.	0.187692
$460$	−1.52296e6	−0.335579
$461$	−282491.	−0.0619088	−0.0309544	−	0.999521i	$-0.509855\pi$
$461$	−282491.	−0.0619088	−0.0309544	+	0.999521i	$0.509855\pi$
$462$	2.40942e6	0.525179
$463$	−4.64797e6	−1.00765	−0.503826	−	0.863805i	$-0.668075\pi$
$463$	−4.64797e6	−1.00765	−0.503826	+	0.863805i	$0.668075\pi$
$464$	1.88585e6	0.406643
$465$	1.38374e6	0.296772
$466$	5.09923e6	1.08778
$467$	6.16529e6	1.30816	0.654080	−	0.756425i	$-0.273056\pi$
$467$	6.16529e6	1.30816	0.654080	+	0.756425i	$0.273056\pi$
$468$	1.50037e6	0.316652
$469$	−5.89979e6	−1.23852
$470$	674924.	0.140932
$471$	3.30379e6	0.686215
$472$	−1.98075e6	−0.409236
$473$	−4.90516e6	−1.00809
$474$	64326.0	0.0131504
$475$	225625.	0.0458831
$476$	4.27582e6	0.864971
$477$	−3.12158e6	−0.628172
$478$	−5.13206e6	−1.02736
$479$	2.53771e6	0.505364	0.252682	−	0.967549i	$-0.418687\pi$
$479$	2.53771e6	0.505364	0.252682	+	0.967549i	$0.418687\pi$
$480$	−230400.	−0.0456435
$481$	−2.00136e6	−0.394424
$482$	−2.04113e6	−0.400177
$483$	−7.87990e6	−1.53693
$484$	−1.22149e6	−0.237016
$485$	−2.28807e6	−0.441687
$486$	−236196.	−0.0453609
$487$	−2.28659e6	−0.436885	−0.218442	−	0.975850i	$-0.570098\pi$
$487$	−2.28659e6	−0.436885	−0.218442	+	0.975850i	$0.570098\pi$
$488$	466158.	0.0886102
$489$	−3.37956e6	−0.639129
$490$	−3.60737e6	−0.678736
$491$	3.43905e6	0.643776	0.321888	−	0.946778i	$-0.395683\pi$
$491$	3.43905e6	0.643776	0.321888	+	0.946778i	$0.395683\pi$
$492$	−1.58497e6	−0.295194
$493$	8.56088e6	1.58636
$494$	−1.67170e6	−0.308207
$495$	−589368.	−0.108112
$496$	1.57439e6	0.287349
$497$	−1.68375e6	−0.305764
$498$	−1.49302e6	−0.269770
$499$	5.40289e6	0.971347	0.485674	−	0.874140i	$-0.338574\pi$
$499$	5.40289e6	0.971347	0.485674	+	0.874140i	$0.338574\pi$
$500$	250000.	0.0447214
$501$	5.14722e6	0.916174
$502$	2.70148e6	0.478456
$503$	399731.	0.0704446	0.0352223	−	0.999380i	$-0.488786\pi$
$503$	399731.	0.0704446	0.0352223	+	0.999380i	$0.488786\pi$
$504$	−1.19210e6	−0.209044
$505$	−2.32601e6	−0.405867
$506$	−4.43252e6	−0.769616
$507$	8.72059e6	1.50670
$508$	3.49788e6	0.601375
$509$	−102806.	−0.0175883	−0.00879413	−	0.999961i	$-0.502799\pi$
$509$	−102806.	−0.0175883	−0.00879413	+	0.999961i	$0.502799\pi$
$510$	−1.04591e6	−0.178060
$511$	−1.86512e7	−3.15976
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	4.74529e6	0.792237
$515$	−2.29429e6	−0.381180
$516$	2.42692e6	0.401264
$517$	1.96434e6	0.323214
$518$	1.59017e6	0.260386
$519$	1.95056e6	0.317864
$520$	−1.85230e6	−0.300403
$521$	2.74729e6	0.443415	0.221708	−	0.975113i	$-0.428837\pi$
$521$	2.74729e6	0.443415	0.221708	+	0.975113i	$0.428837\pi$
$522$	−2.38678e6	−0.383387
$523$	−5.20431e6	−0.831972	−0.415986	−	0.909371i	$-0.636563\pi$
$523$	−5.20431e6	−0.831972	−0.415986	+	0.909371i	$0.636563\pi$
$524$	−1.33411e6	−0.212258
$525$	1.29351e6	0.204820
$526$	−5.43499e6	−0.856513
$527$	7.14699e6	1.12098
$528$	−670570.	−0.104679
$529$	8.06000e6	1.25226
$530$	3.85380e6	0.595936
$531$	2.50688e6	0.385832
$532$	1.32824e6	0.203468
$533$	−1.27424e7	−1.94282
$534$	−1.87369e6	−0.284345
$535$	783903.	0.118407
$536$	1.64198e6	0.246863
$537$	−5.98556e6	−0.895714
$538$	5.91473e6	0.881007
$539$	−1.04991e7	−1.55661
$540$	291600.	0.0430331
$541$	−3.01712e6	−0.443199	−0.221600	−	0.975138i	$-0.571128\pi$
$541$	−3.01712e6	−0.443199	−0.221600	+	0.975138i	$0.571128\pi$
$542$	−2.90797e6	−0.425198
$543$	4.24325e6	0.617588
$544$	−1.19001e6	−0.172406
$545$	−4.58852e6	−0.661731
$546$	−9.58393e6	−1.37582
$547$	−4.91651e6	−0.702568	−0.351284	−	0.936269i	$-0.614255\pi$
$547$	−4.91651e6	−0.702568	−0.351284	+	0.936269i	$0.614255\pi$
$548$	1.93973e6	0.275925
$549$	−589982.	−0.0835425
$550$	727615.	0.102564
$551$	2.65935e6	0.373161
$552$	2.19307e6	0.306340
$553$	−410897.	−0.0571373
$554$	9.83982e6	1.36211
$555$	−388970.	−0.0536023
$556$	−4.98783e6	−0.684266
$557$	−8.90547e6	−1.21624	−0.608119	−	0.793846i	$-0.708076\pi$
$557$	−8.90547e6	−1.21624	−0.608119	+	0.793846i	$0.708076\pi$
$558$	−1.99259e6	−0.270915
$559$	1.95112e7	2.64092
$560$	1.47173e6	0.198316
$561$	−3.04407e6	−0.408363
$562$	−7.86037e6	−1.04979
$563$	−324608.	−0.0431607	−0.0215804	−	0.999767i	$-0.506870\pi$
$563$	−324608.	−0.0431607	−0.0215804	+	0.999767i	$0.506870\pi$
$564$	−971891.	−0.128653
$565$	1.64759e6	0.217133
$566$	−3.61278e6	−0.474024
$567$	1.50876e6	0.197088
$568$	468607.	0.0609449
$569$	−2.63526e6	−0.341227	−0.170613	−	0.985338i	$-0.554575\pi$
$569$	−2.63526e6	−0.341227	−0.170613	+	0.985338i	$0.554575\pi$
$570$	−324900.	−0.0418854
$571$	−1.71414e6	−0.220016	−0.110008	−	0.993931i	$-0.535088\pi$
$571$	−1.71414e6	−0.220016	−0.110008	+	0.993931i	$0.535088\pi$
$572$	−5.39106e6	−0.688944
$573$	5.12960e6	0.652675
$574$	1.01243e7	1.28259
$575$	−2.37963e6	−0.300151
$576$	331776.	0.0416667
$577$	2.34313e6	0.292993	0.146496	−	0.989211i	$-0.453200\pi$
$577$	2.34313e6	0.292993	0.146496	+	0.989211i	$0.453200\pi$
$578$	277357.	0.0345318
$579$	8.82776e6	1.09435
$580$	2.94665e6	0.363713
$581$	9.53703e6	1.17212
$582$	3.29482e6	0.403204
$583$	1.12163e7	1.36672
$584$	5.19083e6	0.629803
$585$	2.34432e6	0.283223
$586$	9.23234e6	1.11063
$587$	−3.07807e6	−0.368709	−0.184354	−	0.982860i	$-0.559019\pi$
$587$	−3.07807e6	−0.368709	−0.184354	+	0.982860i	$0.559019\pi$
$588$	5.19462e6	0.619599
$589$	2.22014e6	0.263689
$590$	−3.09492e6	−0.366032
$591$	8.12829e6	0.957261
$592$	−442561.	−0.0519002
$593$	9.59641e6	1.12066	0.560328	−	0.828271i	$-0.310675\pi$
$593$	9.59641e6	1.12066	0.560328	+	0.828271i	$0.310675\pi$
$594$	848690.	0.0986922
$595$	6.68096e6	0.773654
$596$	−27753.2	−0.00320035
$597$	9.12363e6	1.04769
$598$	1.76312e7	2.01618
$599$	−4.33148e6	−0.493253	−0.246626	−	0.969111i	$-0.579322\pi$
$599$	−4.33148e6	−0.493253	−0.246626	+	0.969111i	$0.579322\pi$
$600$	−360000.	−0.0408248
$601$	9.61995e6	1.08639	0.543196	−	0.839606i	$-0.317214\pi$
$601$	9.61995e6	1.08639	0.543196	+	0.839606i	$0.317214\pi$
$602$	−1.55025e7	−1.74345
$603$	−2.07813e6	−0.232744
$604$	−5.19100e6	−0.578974
$605$	−1.90858e6	−0.211994
$606$	3.34946e6	0.370504
$607$	721982.	0.0795343	0.0397672	−	0.999209i	$-0.487338\pi$
$607$	721982.	0.0795343	0.0397672	+	0.999209i	$0.487338\pi$
$608$	−369664.	−0.0405554
$609$	1.52461e7	1.66577
$610$	728372.	0.0792554
$611$	−7.81354e6	−0.846729
$612$	1.50610e6	0.162546
$613$	182994.	0.0196691	0.00983455	−	0.999952i	$-0.496870\pi$
$613$	182994.	0.0196691	0.00983455	+	0.999952i	$0.496870\pi$
$614$	8.02350e6	0.858901
$615$	−2.47651e6	−0.264029
$616$	4.28341e6	0.454819
$617$	−9.48979e6	−1.00356	−0.501781	−	0.864995i	$-0.667322\pi$
$617$	−9.48979e6	−1.00356	−0.501781	+	0.864995i	$0.667322\pi$
$618$	3.30378e6	0.347968
$619$	−2.44121e6	−0.256082	−0.128041	−	0.991769i	$-0.540869\pi$
$619$	−2.44121e6	−0.256082	−0.128041	+	0.991769i	$0.540869\pi$
$620$	2.45999e6	0.257012
$621$	−2.77560e6	−0.288820
$622$	−2.35775e6	−0.244355
$623$	1.19686e7	1.23545
$624$	2.66732e6	0.274229
$625$	390625.	0.0400000
$626$	−1.06499e6	−0.108620
$627$	−945608.	−0.0960599
$628$	5.87340e6	0.594279
$629$	−2.00902e6	−0.202468
$630$	−1.86266e6	−0.186975
$631$	−9.44666e6	−0.944506	−0.472253	−	0.881463i	$-0.656559\pi$
$631$	−9.44666e6	−0.944506	−0.472253	+	0.881463i	$0.656559\pi$
$632$	114357.	0.0113886
$633$	1.04106e6	0.103268
$634$	−2.34147e6	−0.231348
$635$	5.46544e6	0.537886
$636$	−5.54947e6	−0.544013
$637$	4.17622e7	4.07789
$638$	8.57609e6	0.834138
$639$	−593080.	−0.0574594
$640$	−409600.	−0.0395285
$641$	3.66728e6	0.352532	0.176266	−	0.984343i	$-0.443598\pi$
$641$	3.66728e6	0.352532	0.176266	+	0.984343i	$0.443598\pi$
$642$	−1.12882e6	−0.108090
$643$	3.06676e6	0.292518	0.146259	−	0.989246i	$-0.453277\pi$
$643$	3.06676e6	0.292518	0.146259	+	0.989246i	$0.453277\pi$
$644$	−1.40087e7	−1.33102
$645$	3.79206e6	0.358902
$646$	−1.67810e6	−0.158211
$647$	5.09003e6	0.478035	0.239018	−	0.971015i	$-0.423175\pi$
$647$	5.09003e6	0.478035	0.239018	+	0.971015i	$0.423175\pi$
$648$	−419904.	−0.0392837
$649$	−9.00763e6	−0.839458
$650$	−2.89423e6	−0.268688
$651$	1.27281e7	1.17710
$652$	−6.00811e6	−0.553502
$653$	−5.68522e6	−0.521752	−0.260876	−	0.965372i	$-0.584011\pi$
$653$	−5.68522e6	−0.521752	−0.260876	+	0.965372i	$0.584011\pi$
$654$	6.60747e6	0.604075
$655$	−2.08455e6	−0.189849
$656$	−2.81772e6	−0.255645
$657$	−6.56965e6	−0.593784
$658$	6.20817e6	0.558984
$659$	−1.92464e6	−0.172638	−0.0863188	−	0.996268i	$-0.527510\pi$
$659$	−1.92464e6	−0.172638	−0.0863188	+	0.996268i	$0.527510\pi$
$660$	−1.04776e6	−0.0936276
$661$	−1.97116e7	−1.75476	−0.877380	−	0.479796i	$-0.840711\pi$
$661$	−1.97116e7	−1.75476	−0.877380	+	0.479796i	$0.840711\pi$
$662$	−1.22203e7	−1.08377
$663$	1.21084e7	1.06980
$664$	−2.65427e6	−0.233628
$665$	2.07537e6	0.181988
$666$	560117.	0.0489320
$667$	−2.80477e7	−2.44108
$668$	9.15061e6	0.793430
$669$	1.02873e7	0.888663
$670$	2.56559e6	0.220801
$671$	2.11990e6	0.181764
$672$	−2.11929e6	−0.181037
$673$	−8.94473e6	−0.761254	−0.380627	−	0.924729i	$-0.624292\pi$
$673$	−8.94473e6	−0.761254	−0.380627	+	0.924729i	$0.624292\pi$
$674$	1.18164e7	1.00192
$675$	455625.	0.0384900
$676$	1.55033e7	1.30484
$677$	1.15197e7	0.965982	0.482991	−	0.875625i	$-0.339550\pi$
$677$	1.15197e7	0.965982	0.482991	+	0.875625i	$0.339550\pi$
$678$	−2.37252e6	−0.198215
$679$	−2.10464e7	−1.75188
$680$	−1.85939e6	−0.154205
$681$	−8.58508e6	−0.709376
$682$	7.15970e6	0.589432
$683$	9.96639e6	0.817497	0.408748	−	0.912647i	$-0.365965\pi$
$683$	9.96639e6	0.817497	0.408748	+	0.912647i	$0.365965\pi$
$684$	467856.	0.0382360
$685$	3.03083e6	0.246794
$686$	−1.77222e7	−1.43783
$687$	−1.78067e6	−0.143943
$688$	4.31452e6	0.347505
$689$	−4.46151e7	−3.58042
$690$	3.42667e6	0.273999
$691$	4.75473e6	0.378818	0.189409	−	0.981898i	$-0.439343\pi$
$691$	4.75473e6	0.378818	0.189409	+	0.981898i	$0.439343\pi$
$692$	3.46767e6	0.275279
$693$	−5.42120e6	−0.428807
$694$	4.54117e6	0.357906
$695$	−7.79348e6	−0.612026
$696$	−4.24317e6	−0.332023
$697$	−1.27911e7	−0.997300
$698$	−1.53057e7	−1.18909
$699$	−1.14733e7	−0.888165
$700$	2.29958e6	0.177380
$701$	658865.	0.0506409	0.0253204	−	0.999679i	$-0.491939\pi$
$701$	658865.	0.0506409	0.0253204	+	0.999679i	$0.491939\pi$
$702$	−3.37583e6	−0.258546
$703$	−624081.	−0.0476269
$704$	−1.19212e6	−0.0906546
$705$	−1.51858e6	−0.115071
$706$	−434671.	−0.0328208
$707$	−2.13954e7	−1.60980
$708$	4.45668e6	0.334140
$709$	7.34317e6	0.548615	0.274308	−	0.961642i	$-0.411551\pi$
$709$	7.34317e6	0.548615	0.274308	+	0.961642i	$0.411551\pi$
$710$	732198.	0.0545108
$711$	−144733.	−0.0107373
$712$	−3.33101e6	−0.246250
$713$	−2.34154e7	−1.72496
$714$	−9.62058e6	−0.706246
$715$	−8.42352e6	−0.616210
$716$	−1.06410e7	−0.775711
$717$	1.15471e7	0.838835
$718$	7.75085e6	0.561097
$719$	2.73781e6	0.197507	0.0987533	−	0.995112i	$-0.468515\pi$
$719$	2.73781e6	0.197507	0.0987533	+	0.995112i	$0.468515\pi$
$720$	518400.	0.0372678
$721$	−2.11036e7	−1.51189
$722$	−521284.	−0.0372161
$723$	4.59253e6	0.326743
$724$	7.54355e6	0.534847
$725$	4.60414e6	0.325314
$726$	2.74836e6	0.193523
$727$	−223032.	−0.0156506	−0.00782532	−	0.999969i	$-0.502491\pi$
$727$	−223032.	−0.0156506	−0.00782532	+	0.999969i	$0.502491\pi$
$728$	−1.70381e7	−1.19150
$729$	531441.	0.0370370
$730$	8.11067e6	0.563313
$731$	1.95858e7	1.35565
$732$	−1.04886e6	−0.0723499
$733$	2.39223e7	1.64453	0.822266	−	0.569103i	$-0.192710\pi$
$733$	2.39223e7	1.64453	0.822266	+	0.569103i	$0.192710\pi$
$734$	9.75699e6	0.668460
$735$	8.11659e6	0.554186
$736$	3.89878e6	0.265298
$737$	7.46705e6	0.506384
$738$	3.56618e6	0.241025
$739$	−3.91073e6	−0.263419	−0.131709	−	0.991288i	$-0.542047\pi$
$739$	−3.91073e6	−0.263419	−0.131709	+	0.991288i	$0.542047\pi$
$740$	−691502.	−0.0464210
$741$	3.76134e6	0.251650
$742$	3.54485e7	2.36368
$743$	−1.88216e7	−1.25079	−0.625394	−	0.780309i	$-0.715062\pi$
$743$	−1.88216e7	−1.25079	−0.625394	+	0.780309i	$0.715062\pi$
$744$	−3.54239e6	−0.234619
$745$	−43364.4	−0.00286248
$746$	4.68658e6	0.308325
$747$	3.35930e6	0.220266
$748$	−5.41167e6	−0.353653
$749$	7.21059e6	0.469642
$750$	−562500.	−0.0365148
$751$	−1.84421e6	−0.119320	−0.0596598	−	0.998219i	$-0.519002\pi$
$751$	−1.84421e6	−0.119320	−0.0596598	+	0.998219i	$0.519002\pi$
$752$	−1.72781e6	−0.111417
$753$	−6.07832e6	−0.390658
$754$	−3.41131e7	−2.18521
$755$	−8.11094e6	−0.517850
$756$	2.68223e6	0.170684
$757$	5.64442e6	0.357997	0.178999	−	0.983849i	$-0.442714\pi$
$757$	5.64442e6	0.357997	0.178999	+	0.983849i	$0.442714\pi$
$758$	244615.	0.0154636
$759$	9.97317e6	0.628389
$760$	−577600.	−0.0362738
$761$	−3.50019e6	−0.219094	−0.109547	−	0.993982i	$-0.534940\pi$
$761$	−3.50019e6	−0.219094	−0.109547	+	0.993982i	$0.534940\pi$
$762$	−7.87023e6	−0.491021
$763$	−4.22067e7	−2.62464
$764$	9.11929e6	0.565233
$765$	2.35329e6	0.145386
$766$	−4.99662e6	−0.307683
$767$	3.58296e7	2.19914
$768$	589824.	0.0360844
$769$	9.75513e6	0.594864	0.297432	−	0.954743i	$-0.403870\pi$
$769$	9.75513e6	0.594864	0.297432	+	0.954743i	$0.403870\pi$
$770$	6.69284e6	0.406802
$771$	−1.06769e7	−0.646859
$772$	1.56938e7	0.947731
$773$	2.85516e7	1.71863	0.859315	−	0.511447i	$-0.170890\pi$
$773$	2.85516e7	1.71863	0.859315	+	0.511447i	$0.170890\pi$
$774$	−5.46056e6	−0.327631
$775$	3.84373e6	0.229879
$776$	5.85746e6	0.349185
$777$	−3.57787e6	−0.212604
$778$	1.52462e7	0.903049
$779$	−3.97342e6	−0.234596
$780$	4.16769e6	0.245278
$781$	2.13103e6	0.125015
$782$	1.76986e7	1.03496
$783$	5.37027e6	0.313034
$784$	9.23488e6	0.536588
$785$	9.17719e6	0.531540
$786$	3.00175e6	0.173308
$787$	−5.65502e6	−0.325460	−0.162730	−	0.986671i	$-0.552030\pi$
$787$	−5.65502e6	−0.325460	−0.162730	+	0.986671i	$0.552030\pi$
$788$	1.44503e7	0.829012
$789$	1.22287e7	0.699340
$790$	178683.	0.0101863
$791$	1.51550e7	0.861223
$792$	1.50878e6	0.0854699
$793$	−8.43230e6	−0.476171
$794$	−1.43991e7	−0.810560
$795$	−8.67105e6	−0.486580
$796$	1.62198e7	0.907324
$797$	1.33543e7	0.744688	0.372344	−	0.928095i	$-0.378554\pi$
$797$	1.33543e7	0.744688	0.372344	+	0.928095i	$0.378554\pi$
$798$	−2.98854e6	−0.166131
$799$	−7.84342e6	−0.434649
$800$	−640000.	−0.0353553
$801$	4.21581e6	0.232167
$802$	2.20900e7	1.21272
$803$	2.36058e7	1.29190
$804$	−3.69445e6	−0.201563
$805$	−2.18886e7	−1.19050
$806$	−2.84791e7	−1.54415
$807$	−1.33081e7	−0.719339
$808$	5.95460e6	0.320866
$809$	−2.75572e7	−1.48035	−0.740174	−	0.672416i	$-0.765257\pi$
$809$	−2.75572e7	−1.48035	−0.740174	+	0.672416i	$0.765257\pi$
$810$	−656100.	−0.0351364
$811$	−1.53702e7	−0.820595	−0.410297	−	0.911952i	$-0.634575\pi$
$811$	−1.53702e7	−0.820595	−0.410297	+	0.911952i	$0.634575\pi$
$812$	2.71042e7	1.44260
$813$	6.54293e6	0.347173
$814$	−2.01259e6	−0.106462
$815$	−9.38767e6	−0.495067
$816$	2.67752e6	0.140769
$817$	6.08414e6	0.318892
$818$	2.63353e7	1.37612
$819$	2.15638e7	1.12335
$820$	−4.40269e6	−0.228656
$821$	12638.7	0.000654401 0	0.000327201	−	1.00000i	$-0.499896\pi$
$821$	12638.7	0.000654401 0	0.000327201		1.00000i	$0.499896\pi$
$822$	−4.36440e6	−0.225291
$823$	4.24914e6	0.218676	0.109338	−	0.994005i	$-0.465127\pi$
$823$	4.24914e6	0.218676	0.109338	+	0.994005i	$0.465127\pi$
$824$	5.87339e6	0.301349
$825$	−1.63713e6	−0.0837431
$826$	−2.84681e7	−1.45180
$827$	−3.83907e7	−1.95192	−0.975961	−	0.217945i	$-0.930065\pi$
$827$	−3.83907e7	−1.95192	−0.975961	+	0.217945i	$0.930065\pi$
$828$	−4.93440e6	−0.250126
$829$	−3.82855e7	−1.93485	−0.967427	−	0.253152i	$-0.918533\pi$
$829$	−3.82855e7	−1.93485	−0.967427	+	0.253152i	$0.918533\pi$
$830$	−4.14729e6	−0.208963
$831$	−2.21396e7	−1.11216
$832$	4.74190e6	0.237489
$833$	4.19219e7	2.09329
$834$	1.12226e7	0.558700
$835$	1.42978e7	0.709666
$836$	−1.68108e6	−0.0831903
$837$	4.48333e6	0.221201
$838$	−1.44634e7	−0.711475
$839$	2.01150e7	0.986543	0.493272	−	0.869875i	$-0.335801\pi$
$839$	2.01150e7	0.986543	0.493272	+	0.869875i	$0.335801\pi$
$840$	−3.31140e6	−0.161925
$841$	3.37559e7	1.64574
$842$	1.66708e6	0.0810355
$843$	1.76858e7	0.857149
$844$	1.85077e6	0.0894329
$845$	2.42239e7	1.16708
$846$	2.18676e6	0.105045
$847$	−1.75558e7	−0.840836
$848$	−9.86573e6	−0.471129
$849$	8.12876e6	0.387039
$850$	−2.90529e6	−0.137925
$851$	6.58208e6	0.311558
$852$	−1.05437e6	−0.0497613
$853$	2.66932e7	1.25611	0.628054	−	0.778169i	$-0.283852\pi$
$853$	2.66932e7	1.25611	0.628054	+	0.778169i	$0.283852\pi$
$854$	6.69981e6	0.314353
$855$	731025.	0.0341993
$856$	−2.00679e6	−0.0936090
$857$	−4.71902e6	−0.219482	−0.109741	−	0.993960i	$-0.535002\pi$
$857$	−4.71902e6	−0.219482	−0.109741	+	0.993960i	$0.535002\pi$
$858$	1.21299e7	0.562520
$859$	−7.71598e6	−0.356786	−0.178393	−	0.983959i	$-0.557090\pi$
$859$	−7.71598e6	−0.356786	−0.178393	+	0.983959i	$0.557090\pi$
$860$	6.74143e6	0.310818
$861$	−2.27797e7	−1.04723
$862$	1.38938e7	0.636875
$863$	−1.13038e6	−0.0516651	−0.0258325	−	0.999666i	$-0.508224\pi$
$863$	−1.13038e6	−0.0516651	−0.0258325	+	0.999666i	$0.508224\pi$
$864$	−746496.	−0.0340207
$865$	5.41824e6	0.246217
$866$	−6.76548e6	−0.306552
$867$	−624052.	−0.0281951
$868$	2.26278e7	1.01940
$869$	520050.	0.0233612
$870$	−6.62996e6	−0.296970
$871$	−2.97016e7	−1.32658
$872$	1.17466e7	0.523144
$873$	−7.41335e6	−0.329214
$874$	5.49789e6	0.243455
$875$	3.59310e6	0.158653
$876$	−1.16794e7	−0.514232
$877$	2.04712e7	0.898760	0.449380	−	0.893341i	$-0.351645\pi$
$877$	2.04712e7	0.898760	0.449380	+	0.893341i	$0.351645\pi$
$878$	−1.10314e6	−0.0482943
$879$	−2.07728e7	−0.906823
$880$	−1.86269e6	−0.0810839
$881$	1.62109e6	0.0703668	0.0351834	−	0.999381i	$-0.488798\pi$
$881$	1.62109e6	0.0703668	0.0351834	+	0.999381i	$0.488798\pi$
$882$	−1.16879e7	−0.505900
$883$	1.30184e7	0.561895	0.280947	−	0.959723i	$-0.409351\pi$
$883$	1.30184e7	0.561895	0.280947	+	0.959723i	$0.409351\pi$
$884$	2.15260e7	0.926471
$885$	6.96357e6	0.298864
$886$	−2.24248e7	−0.959721
$887$	−1.11573e7	−0.476158	−0.238079	−	0.971246i	$-0.576518\pi$
$887$	−1.11573e7	−0.476158	−0.238079	+	0.971246i	$0.576518\pi$
$888$	995763.	0.0423764
$889$	5.02729e7	2.13343
$890$	−5.20470e6	−0.220253
$891$	−1.90955e6	−0.0805818
$892$	1.82886e7	0.769605
$893$	−2.43648e6	−0.102243
$894$	62444.7	0.00261307
$895$	−1.66266e7	−0.693817
$896$	−3.76763e6	−0.156783
$897$	−3.96702e7	−1.64620
$898$	1.38018e7	0.571144
$899$	4.53045e7	1.86957
$900$	810000.	0.0333333
$901$	−4.47857e7	−1.83792
$902$	−1.28138e7	−0.524400
$903$	3.48806e7	1.42352
$904$	−4.21782e6	−0.171659
$905$	1.17868e7	0.478381
$906$	1.16798e7	0.472730
$907$	2.58907e7	1.04502	0.522510	−	0.852633i	$-0.324996\pi$
$907$	2.58907e7	1.04502	0.522510	+	0.852633i	$0.324996\pi$
$908$	−1.52624e7	−0.614337
$909$	−7.53628e6	−0.302515
$910$	−2.66220e7	−1.06571
$911$	−3.72906e7	−1.48869	−0.744344	−	0.667796i	$-0.767238\pi$
$911$	−3.72906e7	−1.48869	−0.744344	+	0.667796i	$0.767238\pi$
$912$	831744.	0.0331133
$913$	−1.20705e7	−0.479235
$914$	2.39953e7	0.950081
$915$	−1.63884e6	−0.0647118
$916$	−3.16563e6	−0.124658
$917$	−1.91743e7	−0.753003
$918$	−3.38874e6	−0.132718
$919$	1.12907e7	0.440993	0.220496	−	0.975388i	$-0.429232\pi$
$919$	1.12907e7	0.440993	0.220496	+	0.975388i	$0.429232\pi$
$920$	6.09185e6	0.237290
$921$	−1.80529e7	−0.701290
$922$	1.12996e6	0.0437761
$923$	−8.47659e6	−0.327504
$924$	−9.63768e6	−0.371358
$925$	−1.08047e6	−0.0415202
$926$	1.85919e7	0.712518
$927$	−7.43350e6	−0.284115
$928$	−7.54342e6	−0.287540
$929$	−3.11211e7	−1.18308	−0.591542	−	0.806274i	$-0.701481\pi$
$929$	−3.11211e7	−1.18308	−0.591542	+	0.806274i	$0.701481\pi$
$930$	−5.53498e6	−0.209850
$931$	1.30226e7	0.492407
$932$	−2.03969e7	−0.769174
$933$	5.30493e6	0.199515
$934$	−2.46611e7	−0.925009
$935$	−8.45574e6	−0.316317
$936$	−6.00147e6	−0.223907
$937$	1.89467e7	0.704992	0.352496	−	0.935813i	$-0.385333\pi$
$937$	1.89467e7	0.704992	0.352496	+	0.935813i	$0.385333\pi$
$938$	2.35991e7	0.875768
$939$	2.39624e6	0.0886882
$940$	−2.69970e6	−0.0996542
$941$	−4.92849e7	−1.81443	−0.907214	−	0.420670i	$-0.861795\pi$
$941$	−4.92849e7	−1.81443	−0.907214	+	0.420670i	$0.861795\pi$
$942$	−1.32152e7	−0.485227
$943$	4.19070e7	1.53464
$944$	7.92299e6	0.289374
$945$	4.19099e6	0.152664
$946$	1.96207e7	0.712829
$947$	−5.25001e6	−0.190233	−0.0951164	−	0.995466i	$-0.530322\pi$
$947$	−5.25001e6	−0.190233	−0.0951164	+	0.995466i	$0.530322\pi$
$948$	−257304.	−0.00929877
$949$	−9.38965e7	−3.38442
$950$	−902500.	−0.0324443
$951$	5.26831e6	0.188895
$952$	−1.71033e7	−0.611627
$953$	−2.16938e6	−0.0773755	−0.0386877	−	0.999251i	$-0.512318\pi$
$953$	−2.16938e6	−0.0773755	−0.0386877	+	0.999251i	$0.512318\pi$
$954$	1.24863e7	0.444184
$955$	1.42489e7	0.505560
$956$	2.05282e7	0.726452
$957$	−1.92962e7	−0.681071
$958$	−1.01509e7	−0.357346
$959$	2.78786e7	0.978868
$960$	921600.	0.0322749
$961$	9.19303e6	0.321107
$962$	8.00546e6	0.278900
$963$	2.53985e6	0.0882555
$964$	8.16450e6	0.282968
$965$	2.45216e7	0.847676
$966$	3.15196e7	1.08677
$967$	−3.26345e7	−1.12230	−0.561152	−	0.827713i	$-0.689642\pi$
$967$	−3.26345e7	−1.12230	−0.561152	+	0.827713i	$0.689642\pi$
$968$	4.88597e6	0.167596
$969$	3.77572e6	0.129179
$970$	9.15228e6	0.312320
$971$	−7.38941e6	−0.251514	−0.125757	−	0.992061i	$-0.540136\pi$
$971$	−7.38941e6	−0.251514	−0.125757	+	0.992061i	$0.540136\pi$
$972$	944784.	0.0320750
$973$	−7.16870e7	−2.42749
$974$	9.14638e6	0.308924
$975$	6.51201e6	0.219383
$976$	−1.86463e6	−0.0626569
$977$	−9.47674e6	−0.317631	−0.158815	−	0.987308i	$-0.550767\pi$
$977$	−9.47674e6	−0.317631	−0.158815	+	0.987308i	$0.550767\pi$
$978$	1.35182e7	0.451932
$979$	−1.51481e7	−0.505127
$980$	1.44295e7	0.479939
$981$	−1.48668e7	−0.493225
$982$	−1.37562e7	−0.455218
$983$	2.98870e7	0.986504	0.493252	−	0.869886i	$-0.335808\pi$
$983$	2.98870e7	0.986504	0.493252	+	0.869886i	$0.335808\pi$
$984$	6.33987e6	0.208734
$985$	2.25786e7	0.741491
$986$	−3.42435e7	−1.12172
$987$	−1.39684e7	−0.456408
$988$	6.68682e6	0.217935
$989$	−6.41684e7	−2.08608
$990$	2.35747e6	0.0764466
$991$	−9.13509e6	−0.295481	−0.147740	−	0.989026i	$-0.547200\pi$
$991$	−9.13509e6	−0.295481	−0.147740	+	0.989026i	$0.547200\pi$
$992$	−6.29757e6	−0.203186
$993$	2.74957e7	0.884895
$994$	6.73500e6	0.216208
$995$	2.53434e7	0.811535
$996$	5.97210e6	0.190756
$997$	1.77454e7	0.565389	0.282694	−	0.959210i	$-0.408772\pi$
$997$	1.77454e7	0.565389	0.282694	+	0.959210i	$0.408772\pi$
$998$	−2.16115e7	−0.686846
$999$	−1.26026e6	−0.0399528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.m.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.m.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +229.958 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +229.958 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -291.046 q^{11} +144.000 q^{12} +1157.69 q^{13} -919.833 q^{14} +225.000 q^{15} +256.000 q^{16} +1162.12 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +2069.62 q^{21} +1164.18 q^{22} -3807.41 q^{23} -576.000 q^{24} +625.000 q^{25} -4630.76 q^{26} +729.000 q^{27} +3679.33 q^{28} +7366.62 q^{29} -900.000 q^{30} +6149.97 q^{31} -1024.00 q^{32} -2619.41 q^{33} -4648.47 q^{34} +5748.95 q^{35} +1296.00 q^{36} -1728.76 q^{37} -1444.00 q^{38} +10419.2 q^{39} -1600.00 q^{40} -11006.7 q^{41} -8278.49 q^{42} +16853.6 q^{43} -4656.73 q^{44} +2025.00 q^{45} +15229.6 q^{46} -6749.24 q^{47} +2304.00 q^{48} +36073.7 q^{49} -2500.00 q^{50} +10459.1 q^{51} +18523.0 q^{52} -38538.0 q^{53} -2916.00 q^{54} -7276.15 q^{55} -14717.3 q^{56} +3249.00 q^{57} -29466.5 q^{58} +30949.2 q^{59} +3600.00 q^{60} -7283.72 q^{61} -24599.9 q^{62} +18626.6 q^{63} +4096.00 q^{64} +28942.3 q^{65} +10477.6 q^{66} -25655.9 q^{67} +18593.9 q^{68} -34266.7 q^{69} -22995.8 q^{70} -7321.98 q^{71} -5184.00 q^{72} -81106.7 q^{73} +6915.02 q^{74} +5625.00 q^{75} +5776.00 q^{76} -66928.4 q^{77} -41676.9 q^{78} -1786.83 q^{79} +6400.00 q^{80} +6561.00 q^{81} +44026.9 q^{82} +41472.9 q^{83} +33114.0 q^{84} +29052.9 q^{85} -67414.3 q^{86} +66299.6 q^{87} +18626.9 q^{88} +52047.0 q^{89} -8100.00 q^{90} +266220. q^{91} -60918.5 q^{92} +55349.8 q^{93} +26997.0 q^{94} +9025.00 q^{95} -9216.00 q^{96} -91522.8 q^{97} -144295. q^{98} -23574.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 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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