LMFDB - Embedded newform 570.6.a.o.1.5

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 6052x^{3} - 41130x^{2} + 7064712x + 22607640 $ x^5 - 6052x^3 - 41130x^2 + 7064712*x + 22607640
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.16883$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +208.674 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +208.674 q^{7} +64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +593.771 q^{11} -144.000 q^{12} -360.959 q^{13} +834.698 q^{14} -225.000 q^{15} +256.000 q^{16} +1460.02 q^{17} +324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -1878.07 q^{21} +2375.08 q^{22} +2451.71 q^{23} -576.000 q^{24} +625.000 q^{25} -1443.83 q^{26} -729.000 q^{27} +3338.79 q^{28} -6640.01 q^{29} -900.000 q^{30} +9717.92 q^{31} +1024.00 q^{32} -5343.94 q^{33} +5840.08 q^{34} +5216.86 q^{35} +1296.00 q^{36} -7410.60 q^{37} +1444.00 q^{38} +3248.63 q^{39} +1600.00 q^{40} -12130.7 q^{41} -7512.28 q^{42} +37.3245 q^{43} +9500.33 q^{44} +2025.00 q^{45} +9806.83 q^{46} -5536.84 q^{47} -2304.00 q^{48} +26738.0 q^{49} +2500.00 q^{50} -13140.2 q^{51} -5775.34 q^{52} -33641.0 q^{53} -2916.00 q^{54} +14844.3 q^{55} +13355.2 q^{56} -3249.00 q^{57} -26560.0 q^{58} +5299.32 q^{59} -3600.00 q^{60} -27515.0 q^{61} +38871.7 q^{62} +16902.6 q^{63} +4096.00 q^{64} -9023.96 q^{65} -21375.8 q^{66} +23385.8 q^{67} +23360.3 q^{68} -22065.4 q^{69} +20867.4 q^{70} -22999.1 q^{71} +5184.00 q^{72} -50264.6 q^{73} -29642.4 q^{74} -5625.00 q^{75} +5776.00 q^{76} +123905. q^{77} +12994.5 q^{78} +7405.13 q^{79} +6400.00 q^{80} +6561.00 q^{81} -48522.9 q^{82} +108816. q^{83} -30049.1 q^{84} +36500.5 q^{85} +149.298 q^{86} +59760.1 q^{87} +38001.3 q^{88} +49090.8 q^{89} +8100.00 q^{90} -75322.8 q^{91} +39227.3 q^{92} -87461.3 q^{93} -22147.4 q^{94} +9025.00 q^{95} -9216.00 q^{96} +90579.2 q^{97} +106952. q^{98} +48095.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 125 q^{5} - 180 q^{6} + 88 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 125 * q^5 - 180 * q^6 + 88 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 125 q^{5} - 180 q^{6} + 88 q^{7} + 320 q^{8} + 405 q^{9} + 500 q^{10} - 112 q^{11} - 720 q^{12} - 44 q^{13} + 352 q^{14} - 1125 q^{15} + 1280 q^{16} + 2388 q^{17} + 1620 q^{18} + 1805 q^{19} + 2000 q^{20} - 792 q^{21} - 448 q^{22} + 3114 q^{23} - 2880 q^{24} + 3125 q^{25} - 176 q^{26} - 3645 q^{27} + 1408 q^{28} - 2966 q^{29} - 4500 q^{30} + 6930 q^{31} + 5120 q^{32} + 1008 q^{33} + 9552 q^{34} + 2200 q^{35} + 6480 q^{36} + 5608 q^{37} + 7220 q^{38} + 396 q^{39} + 8000 q^{40} + 20948 q^{41} - 3168 q^{42} + 3090 q^{43} - 1792 q^{44} + 10125 q^{45} + 12456 q^{46} + 16490 q^{47} - 11520 q^{48} + 2757 q^{49} + 12500 q^{50} - 21492 q^{51} - 704 q^{52} - 33060 q^{53} - 14580 q^{54} - 2800 q^{55} + 5632 q^{56} - 16245 q^{57} - 11864 q^{58} - 346 q^{59} - 18000 q^{60} + 57698 q^{61} + 27720 q^{62} + 7128 q^{63} + 20480 q^{64} - 1100 q^{65} + 4032 q^{66} + 12364 q^{67} + 38208 q^{68} - 28026 q^{69} + 8800 q^{70} + 9984 q^{71} + 25920 q^{72} + 28050 q^{73} + 22432 q^{74} - 28125 q^{75} + 28880 q^{76} + 235208 q^{77} + 1584 q^{78} + 36498 q^{79} + 32000 q^{80} + 32805 q^{81} + 83792 q^{82} + 89696 q^{83} - 12672 q^{84} + 59700 q^{85} + 12360 q^{86} + 26694 q^{87} - 7168 q^{88} + 114980 q^{89} + 40500 q^{90} + 267260 q^{91} + 49824 q^{92} - 62370 q^{93} + 65960 q^{94} + 45125 q^{95} - 46080 q^{96} + 317596 q^{97} + 11028 q^{98} - 9072 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 125 * q^5 - 180 * q^6 + 88 * q^7 + 320 * q^8 + 405 * q^9 + 500 * q^10 - 112 * q^11 - 720 * q^12 - 44 * q^13 + 352 * q^14 - 1125 * q^15 + 1280 * q^16 + 2388 * q^17 + 1620 * q^18 + 1805 * q^19 + 2000 * q^20 - 792 * q^21 - 448 * q^22 + 3114 * q^23 - 2880 * q^24 + 3125 * q^25 - 176 * q^26 - 3645 * q^27 + 1408 * q^28 - 2966 * q^29 - 4500 * q^30 + 6930 * q^31 + 5120 * q^32 + 1008 * q^33 + 9552 * q^34 + 2200 * q^35 + 6480 * q^36 + 5608 * q^37 + 7220 * q^38 + 396 * q^39 + 8000 * q^40 + 20948 * q^41 - 3168 * q^42 + 3090 * q^43 - 1792 * q^44 + 10125 * q^45 + 12456 * q^46 + 16490 * q^47 - 11520 * q^48 + 2757 * q^49 + 12500 * q^50 - 21492 * q^51 - 704 * q^52 - 33060 * q^53 - 14580 * q^54 - 2800 * q^55 + 5632 * q^56 - 16245 * q^57 - 11864 * q^58 - 346 * q^59 - 18000 * q^60 + 57698 * q^61 + 27720 * q^62 + 7128 * q^63 + 20480 * q^64 - 1100 * q^65 + 4032 * q^66 + 12364 * q^67 + 38208 * q^68 - 28026 * q^69 + 8800 * q^70 + 9984 * q^71 + 25920 * q^72 + 28050 * q^73 + 22432 * q^74 - 28125 * q^75 + 28880 * q^76 + 235208 * q^77 + 1584 * q^78 + 36498 * q^79 + 32000 * q^80 + 32805 * q^81 + 83792 * q^82 + 89696 * q^83 - 12672 * q^84 + 59700 * q^85 + 12360 * q^86 + 26694 * q^87 - 7168 * q^88 + 114980 * q^89 + 40500 * q^90 + 267260 * q^91 + 49824 * q^92 - 62370 * q^93 + 65960 * q^94 + 45125 * q^95 - 46080 * q^96 + 317596 * q^97 + 11028 * q^98 - 9072 * 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
$7$	208.674	1.60962	0.804811	−	0.593531i	$-0.202266\pi$
$7$	208.674	1.60962	0.804811	+	0.593531i	$0.202266\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	593.771	1.47958	0.739788	−	0.672840i	$-0.234926\pi$
$11$	593.771	1.47958	0.739788	+	0.672840i	$0.234926\pi$
$12$	−144.000	−0.288675
$13$	−360.959	−0.592378	−0.296189	−	0.955129i	$-0.595716\pi$
$13$	−360.959	−0.592378	−0.296189	+	0.955129i	$0.595716\pi$
$14$	834.698	1.13818
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	1460.02	1.22528	0.612642	−	0.790361i	$-0.290107\pi$
$17$	1460.02	1.22528	0.612642	+	0.790361i	$0.290107\pi$
$18$	324.000	0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	−1878.07	−0.929316
$22$	2375.08	1.04622
$23$	2451.71	0.966383	0.483191	−	0.875515i	$-0.339478\pi$
$23$	2451.71	0.966383	0.483191	+	0.875515i	$0.339478\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−1443.83	−0.418875
$27$	−729.000	−0.192450
$28$	3338.79	0.804811
$29$	−6640.01	−1.46613	−0.733067	−	0.680156i	$-0.761912\pi$
$29$	−6640.01	−1.46613	−0.733067	+	0.680156i	$0.761912\pi$
$30$	−900.000	−0.182574
$31$	9717.92	1.81622	0.908111	−	0.418729i	$-0.137524\pi$
$31$	9717.92	1.81622	0.908111	+	0.418729i	$0.137524\pi$
$32$	1024.00	0.176777
$33$	−5343.94	−0.854233
$34$	5840.08	0.866407
$35$	5216.86	0.719845
$36$	1296.00	0.166667
$37$	−7410.60	−0.889916	−0.444958	−	0.895551i	$-0.646781\pi$
$37$	−7410.60	−0.889916	−0.444958	+	0.895551i	$0.646781\pi$
$38$	1444.00	0.162221
$39$	3248.63	0.342010
$40$	1600.00	0.158114
$41$	−12130.7	−1.12701	−0.563504	−	0.826113i	$-0.690547\pi$
$41$	−12130.7	−1.12701	−0.563504	+	0.826113i	$0.690547\pi$
$42$	−7512.28	−0.657126
$43$	37.3245	0.00307839	0.00153919	−	0.999999i	$-0.499510\pi$
$43$	37.3245	0.00307839	0.00153919	+	0.999999i	$0.499510\pi$
$44$	9500.33	0.739788
$45$	2025.00	0.149071
$46$	9806.83	0.683336
$47$	−5536.84	−0.365609	−0.182805	−	0.983149i	$-0.558518\pi$
$47$	−5536.84	−0.365609	−0.182805	+	0.983149i	$0.558518\pi$
$48$	−2304.00	−0.144338
$49$	26738.0	1.59089
$50$	2500.00	0.141421
$51$	−13140.2	−0.707418
$52$	−5775.34	−0.296189
$53$	−33641.0	−1.64505	−0.822526	−	0.568727i	$-0.807436\pi$
$53$	−33641.0	−1.64505	−0.822526	+	0.568727i	$0.807436\pi$
$54$	−2916.00	−0.136083
$55$	14844.3	0.661686
$56$	13355.2	0.569088
$57$	−3249.00	−0.132453
$58$	−26560.0	−1.03671
$59$	5299.32	0.198194	0.0990969	−	0.995078i	$-0.468405\pi$
$59$	5299.32	0.198194	0.0990969	+	0.995078i	$0.468405\pi$
$60$	−3600.00	−0.129099
$61$	−27515.0	−0.946772	−0.473386	−	0.880855i	$-0.656968\pi$
$61$	−27515.0	−0.946772	−0.473386	+	0.880855i	$0.656968\pi$
$62$	38871.7	1.28426
$63$	16902.6	0.536541
$64$	4096.00	0.125000
$65$	−9023.96	−0.264920
$66$	−21375.8	−0.604034
$67$	23385.8	0.636451	0.318225	−	0.948015i	$-0.396913\pi$
$67$	23385.8	0.636451	0.318225	+	0.948015i	$0.396913\pi$
$68$	23360.3	0.612642
$69$	−22065.4	−0.557941
$70$	20867.4	0.509007
$71$	−22999.1	−0.541458	−0.270729	−	0.962656i	$-0.587265\pi$
$71$	−22999.1	−0.541458	−0.270729	+	0.962656i	$0.587265\pi$
$72$	5184.00	0.117851
$73$	−50264.6	−1.10396	−0.551982	−	0.833856i	$-0.686128\pi$
$73$	−50264.6	−1.10396	−0.551982	+	0.833856i	$0.686128\pi$
$74$	−29642.4	−0.629266
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	123905.	2.38156
$78$	12994.5	0.241837
$79$	7405.13	0.133495	0.0667475	−	0.997770i	$-0.478738\pi$
$79$	7405.13	0.133495	0.0667475	+	0.997770i	$0.478738\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	−48522.9	−0.796915
$83$	108816.	1.73379	0.866896	−	0.498490i	$-0.166112\pi$
$83$	108816.	1.73379	0.866896	+	0.498490i	$0.166112\pi$
$84$	−30049.1	−0.464658
$85$	36500.5	0.547964
$86$	149.298	0.00217675
$87$	59760.1	0.846473
$88$	38001.3	0.523109
$89$	49090.8	0.656939	0.328469	−	0.944515i	$-0.393467\pi$
$89$	49090.8	0.656939	0.328469	+	0.944515i	$0.393467\pi$
$90$	8100.00	0.105409
$91$	−75322.8	−0.953505
$92$	39227.3	0.483191
$93$	−87461.3	−1.04860
$94$	−22147.4	−0.258525
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	90579.2	0.977461	0.488730	−	0.872435i	$-0.337460\pi$
$97$	90579.2	0.977461	0.488730	+	0.872435i	$0.337460\pi$
$98$	106952.	1.12493
$99$	48095.4	0.493192
$100$	10000.0	0.100000
$101$	138000.	1.34609	0.673047	−	0.739599i	$-0.264985\pi$
$101$	138000.	1.34609	0.673047	+	0.739599i	$0.264985\pi$
$102$	−52560.8	−0.500220
$103$	3660.62	0.0339986	0.0169993	−	0.999856i	$-0.494589\pi$
$103$	3660.62	0.0339986	0.0169993	+	0.999856i	$0.494589\pi$
$104$	−23101.3	−0.209437
$105$	−46951.7	−0.415603
$106$	−134564.	−1.16323
$107$	−132880.	−1.12202	−0.561012	−	0.827808i	$-0.689588\pi$
$107$	−132880.	−1.12202	−0.561012	+	0.827808i	$0.689588\pi$
$108$	−11664.0	−0.0962250
$109$	−8165.42	−0.0658283	−0.0329141	−	0.999458i	$-0.510479\pi$
$109$	−8165.42	−0.0658283	−0.0329141	+	0.999458i	$0.510479\pi$
$110$	59377.1	0.467883
$111$	66695.4	0.513793
$112$	53420.7	0.402406
$113$	41001.4	0.302066	0.151033	−	0.988529i	$-0.451740\pi$
$113$	41001.4	0.302066	0.151033	+	0.988529i	$0.451740\pi$
$114$	−12996.0	−0.0936586
$115$	61292.7	0.432179
$116$	−106240.	−0.733067
$117$	−29237.6	−0.197459
$118$	21197.3	0.140144
$119$	304669.	1.97225
$120$	−14400.0	−0.0912871
$121$	191513.	1.18914
$122$	−110060.	−0.669469
$123$	109176.	0.650678
$124$	155487.	0.908111
$125$	15625.0	0.0894427
$126$	67610.5	0.379392
$127$	177965.	0.979096	0.489548	−	0.871976i	$-0.337162\pi$
$127$	177965.	0.979096	0.489548	+	0.871976i	$0.337162\pi$
$128$	16384.0	0.0883883
$129$	−335.921	−0.00177731
$130$	−36095.9	−0.187326
$131$	−248558.	−1.26546	−0.632730	−	0.774372i	$-0.718066\pi$
$131$	−248558.	−1.26546	−0.632730	+	0.774372i	$0.718066\pi$
$132$	−85503.0	−0.427117
$133$	75331.5	0.369273
$134$	93543.1	0.450039
$135$	−18225.0	−0.0860663
$136$	93441.3	0.433203
$137$	149441.	0.680249	0.340125	−	0.940380i	$-0.389531\pi$
$137$	149441.	0.680249	0.340125	+	0.940380i	$0.389531\pi$
$138$	−88261.5	−0.394524
$139$	52742.8	0.231540	0.115770	−	0.993276i	$-0.463066\pi$
$139$	52742.8	0.231540	0.115770	+	0.993276i	$0.463066\pi$
$140$	83469.8	0.359923
$141$	49831.6	0.211085
$142$	−91996.4	−0.382869
$143$	−214327.	−0.876468
$144$	20736.0	0.0833333
$145$	−166000.	−0.655675
$146$	−201058.	−0.780620
$147$	−240642.	−0.918498
$148$	−118570.	−0.444958
$149$	−13573.3	−0.0500862	−0.0250431	−	0.999686i	$-0.507972\pi$
$149$	−13573.3	−0.0500862	−0.0250431	+	0.999686i	$0.507972\pi$
$150$	−22500.0	−0.0816497
$151$	254117.	0.906968	0.453484	−	0.891264i	$-0.350181\pi$
$151$	254117.	0.906968	0.453484	+	0.891264i	$0.350181\pi$
$152$	23104.0	0.0811107
$153$	118262.	0.408428
$154$	495619.	1.68402
$155$	242948.	0.812240
$156$	51978.0	0.171005
$157$	136390.	0.441604	0.220802	−	0.975319i	$-0.429133\pi$
$157$	136390.	0.441604	0.220802	+	0.975319i	$0.429133\pi$
$158$	29620.5	0.0943952
$159$	302769.	0.949772
$160$	25600.0	0.0790569
$161$	511609.	1.55551
$162$	26244.0	0.0785674
$163$	−428970.	−1.26461	−0.632306	−	0.774718i	$-0.717892\pi$
$163$	−428970.	−1.26461	−0.632306	+	0.774718i	$0.717892\pi$
$164$	−194091.	−0.563504
$165$	−133598.	−0.382025
$166$	435263.	1.22598
$167$	653372.	1.81288	0.906441	−	0.422333i	$-0.138789\pi$
$167$	653372.	1.81288	0.906441	+	0.422333i	$0.138789\pi$
$168$	−120196.	−0.328563
$169$	−241002.	−0.649088
$170$	146002.	0.387469
$171$	29241.0	0.0764719
$172$	597.192	0.00153919
$173$	−620029.	−1.57506	−0.787529	−	0.616277i	$-0.788640\pi$
$173$	−620029.	−1.57506	−0.787529	+	0.616277i	$0.788640\pi$
$174$	239040.	0.598547
$175$	130422.	0.321925
$176$	152005.	0.369894
$177$	−47693.9	−0.114427
$178$	196363.	0.464526
$179$	451469.	1.05316	0.526581	−	0.850125i	$-0.323474\pi$
$179$	451469.	1.05316	0.526581	+	0.850125i	$0.323474\pi$
$180$	32400.0	0.0745356
$181$	−223073.	−0.506117	−0.253058	−	0.967451i	$-0.581436\pi$
$181$	−223073.	−0.506117	−0.253058	+	0.967451i	$0.581436\pi$
$182$	−301291.	−0.674230
$183$	247635.	0.546619
$184$	156909.	0.341668
$185$	−185265.	−0.397983
$186$	−349845.	−0.741470
$187$	866918.	1.81290
$188$	−88589.5	−0.182805
$189$	−152124.	−0.309772
$190$	36100.0	0.0725476
$191$	517106.	1.02564	0.512821	−	0.858495i	$-0.328600\pi$
$191$	517106.	1.02564	0.512821	+	0.858495i	$0.328600\pi$
$192$	−36864.0	−0.0721688
$193$	−583818.	−1.12819	−0.564097	−	0.825708i	$-0.690776\pi$
$193$	−583818.	−1.12819	−0.564097	+	0.825708i	$0.690776\pi$
$194$	362317.	0.691169
$195$	81215.7	0.152951
$196$	427808.	0.795443
$197$	−906851.	−1.66483	−0.832416	−	0.554152i	$-0.813043\pi$
$197$	−906851.	−1.66483	−0.832416	+	0.554152i	$0.813043\pi$
$198$	192382.	0.348739
$199$	−133160.	−0.238364	−0.119182	−	0.992872i	$-0.538027\pi$
$199$	−133160.	−0.238364	−0.119182	+	0.992872i	$0.538027\pi$
$200$	40000.0	0.0707107
$201$	−210472.	−0.367455
$202$	552000.	0.951833
$203$	−1.38560e6	−2.35992
$204$	−210243.	−0.353709
$205$	−303268.	−0.504013
$206$	14642.5	0.0240406
$207$	198588.	0.322128
$208$	−92405.4	−0.148095
$209$	214351.	0.339438
$210$	−187807.	−0.293876
$211$	252888.	0.391040	0.195520	−	0.980700i	$-0.437360\pi$
$211$	252888.	0.391040	0.195520	+	0.980700i	$0.437360\pi$
$212$	−538257.	−0.822526
$213$	206992.	0.312611
$214$	−531522.	−0.793390
$215$	933.113	0.00137670
$216$	−46656.0	−0.0680414
$217$	2.02788e6	2.92343
$218$	−32661.7	−0.0465476
$219$	452381.	0.637374
$220$	237508.	0.330843
$221$	−527007.	−0.725831
$222$	266782.	0.363307
$223$	−206137.	−0.277584	−0.138792	−	0.990322i	$-0.544322\pi$
$223$	−206137.	−0.277584	−0.138792	+	0.990322i	$0.544322\pi$
$224$	213683.	0.284544
$225$	50625.0	0.0666667
$226$	164006.	0.213593
$227$	−95269.5	−0.122713	−0.0613563	−	0.998116i	$-0.519543\pi$
$227$	−95269.5	−0.122713	−0.0613563	+	0.998116i	$0.519543\pi$
$228$	−51984.0	−0.0662266
$229$	210509.	0.265266	0.132633	−	0.991165i	$-0.457657\pi$
$229$	210509.	0.265266	0.132633	+	0.991165i	$0.457657\pi$
$230$	245171.	0.305597
$231$	−1.11514e6	−1.37499
$232$	−424961.	−0.518357
$233$	−476218.	−0.574667	−0.287334	−	0.957831i	$-0.592769\pi$
$233$	−476218.	−0.574667	−0.287334	+	0.957831i	$0.592769\pi$
$234$	−116951.	−0.139625
$235$	−138421.	−0.163506
$236$	84789.1	0.0990969
$237$	−66646.2	−0.0770734
$238$	1.21868e6	1.39459
$239$	1.37976e6	1.56246	0.781229	−	0.624244i	$-0.214593\pi$
$239$	1.37976e6	1.56246	0.781229	+	0.624244i	$0.214593\pi$
$240$	−57600.0	−0.0645497
$241$	−1.73769e6	−1.92721	−0.963604	−	0.267334i	$-0.913857\pi$
$241$	−1.73769e6	−1.92721	−0.963604	+	0.267334i	$0.913857\pi$
$242$	766051.	0.840852
$243$	−59049.0	−0.0641500
$244$	−440240.	−0.473386
$245$	668451.	0.711466
$246$	436706.	0.460099
$247$	−130306.	−0.135901
$248$	621947.	0.642132
$249$	−979342.	−1.00100
$250$	62500.0	0.0632456
$251$	−1.12287e6	−1.12498	−0.562489	−	0.826805i	$-0.690156\pi$
$251$	−1.12287e6	−1.12498	−0.562489	+	0.826805i	$0.690156\pi$
$252$	270442.	0.268270
$253$	1.45575e6	1.42984
$254$	711860.	0.692325
$255$	−328505.	−0.316367
$256$	65536.0	0.0625000
$257$	1.70120e6	1.60666	0.803329	−	0.595536i	$-0.203060\pi$
$257$	1.70120e6	1.60666	0.803329	+	0.595536i	$0.203060\pi$
$258$	−1343.68	−0.00125675
$259$	−1.54640e6	−1.43243
$260$	−144383.	−0.132460
$261$	−537841.	−0.488711
$262$	−994230.	−0.894816
$263$	1.45246e6	1.29483	0.647416	−	0.762137i	$-0.275850\pi$
$263$	1.45246e6	1.29483	0.647416	+	0.762137i	$0.275850\pi$
$264$	−342012.	−0.302017
$265$	−841026.	−0.735690
$266$	301326.	0.261115
$267$	−441817.	−0.379284
$268$	374172.	0.318225
$269$	−1.50042e6	−1.26425	−0.632123	−	0.774868i	$-0.717816\pi$
$269$	−1.50042e6	−1.26425	−0.632123	+	0.774868i	$0.717816\pi$
$270$	−72900.0	−0.0608581
$271$	−1.37984e6	−1.14131	−0.570657	−	0.821188i	$-0.693312\pi$
$271$	−1.37984e6	−1.14131	−0.570657	+	0.821188i	$0.693312\pi$
$272$	373765.	0.306321
$273$	677905.	0.550507
$274$	597764.	0.481009
$275$	371107.	0.295915
$276$	−353046.	−0.278971
$277$	1.35173e6	1.05850	0.529249	−	0.848467i	$-0.322474\pi$
$277$	1.35173e6	1.05850	0.529249	+	0.848467i	$0.322474\pi$
$278$	210971.	0.163724
$279$	787152.	0.605408
$280$	333879.	0.254504
$281$	−605059.	−0.457122	−0.228561	−	0.973530i	$-0.573402\pi$
$281$	−605059.	−0.457122	−0.228561	+	0.973530i	$0.573402\pi$
$282$	199326.	0.149259
$283$	−1.89192e6	−1.40423	−0.702113	−	0.712065i	$-0.747760\pi$
$283$	−1.89192e6	−1.40423	−0.702113	+	0.712065i	$0.747760\pi$
$284$	−367985.	−0.270729
$285$	−81225.0	−0.0592349
$286$	−857307.	−0.619757
$287$	−2.53137e6	−1.81406
$288$	82944.0	0.0589256
$289$	711804.	0.501321
$290$	−664001.	−0.463632
$291$	−815213.	−0.564337
$292$	−804233.	−0.551982
$293$	1.27423e6	0.867122	0.433561	−	0.901124i	$-0.357257\pi$
$293$	1.27423e6	0.867122	0.433561	+	0.901124i	$0.357257\pi$
$294$	−962569.	−0.649477
$295$	132483.	0.0886349
$296$	−474278.	−0.314633
$297$	−432859.	−0.284744
$298$	−54293.0	−0.0354163
$299$	−884965.	−0.572464
$300$	−90000.0	−0.0577350
$301$	7788.67	0.00495504
$302$	1.01647e6	0.641323
$303$	−1.24200e6	−0.777168
$304$	92416.0	0.0573539
$305$	−687876.	−0.423409
$306$	473047.	0.288802
$307$	−1.91252e6	−1.15814	−0.579069	−	0.815279i	$-0.696584\pi$
$307$	−1.91252e6	−1.15814	−0.579069	+	0.815279i	$0.696584\pi$
$308$	1.98248e6	1.19078
$309$	−32945.5	−0.0196291
$310$	971792.	0.574340
$311$	−999366.	−0.585900	−0.292950	−	0.956128i	$-0.594637\pi$
$311$	−999366.	−0.585900	−0.292950	+	0.956128i	$0.594637\pi$
$312$	207912.	0.120919
$313$	−962067.	−0.555066	−0.277533	−	0.960716i	$-0.589517\pi$
$313$	−962067.	−0.555066	−0.277533	+	0.960716i	$0.589517\pi$
$314$	545559.	0.312261
$315$	422566.	0.239948
$316$	118482.	0.0667475
$317$	−1.05904e6	−0.591921	−0.295961	−	0.955200i	$-0.595640\pi$
$317$	−1.05904e6	−0.591921	−0.295961	+	0.955200i	$0.595640\pi$
$318$	1.21108e6	0.671590
$319$	−3.94264e6	−2.16926
$320$	102400.	0.0559017
$321$	1.19592e6	0.647800
$322$	2.04644e6	1.09991
$323$	527068.	0.281099
$324$	104976.	0.0555556
$325$	−225599.	−0.118476
$326$	−1.71588e6	−0.894216
$327$	73488.8	0.0380060
$328$	−776366.	−0.398457
$329$	−1.15540e6	−0.588493
$330$	−534394.	−0.270132
$331$	2.78064e6	1.39500	0.697501	−	0.716583i	$-0.254295\pi$
$331$	2.78064e6	1.39500	0.697501	+	0.716583i	$0.254295\pi$
$332$	1.74105e6	0.866896
$333$	−600259.	−0.296639
$334$	2.61349e6	1.28190
$335$	584644.	0.284629
$336$	−480786.	−0.232329
$337$	923958.	0.443177	0.221589	−	0.975140i	$-0.428876\pi$
$337$	923958.	0.443177	0.221589	+	0.975140i	$0.428876\pi$
$338$	−964008.	−0.458975
$339$	−369013.	−0.174398
$340$	584008.	0.273982
$341$	5.77022e6	2.68724
$342$	116964.	0.0540738
$343$	2.07235e6	0.951104
$344$	2388.77	0.00108837
$345$	−551634.	−0.249519
$346$	−2.48012e6	−1.11373
$347$	652208.	0.290779	0.145389	−	0.989375i	$-0.453557\pi$
$347$	652208.	0.290779	0.145389	+	0.989375i	$0.453557\pi$
$348$	956161.	0.423236
$349$	−1.13492e6	−0.498772	−0.249386	−	0.968404i	$-0.580229\pi$
$349$	−1.13492e6	−0.498772	−0.249386	+	0.968404i	$0.580229\pi$
$350$	521686.	0.227635
$351$	263139.	0.114003
$352$	608021.	0.261554
$353$	499747.	0.213458	0.106729	−	0.994288i	$-0.465962\pi$
$353$	499747.	0.213458	0.106729	+	0.994288i	$0.465962\pi$
$354$	−190775.	−0.0809123
$355$	−574977.	−0.242147
$356$	785452.	0.328469
$357$	−2.74202e6	−1.13868
$358$	1.80588e6	0.744698
$359$	1.86106e6	0.762120	0.381060	−	0.924550i	$-0.375559\pi$
$359$	1.86106e6	0.762120	0.381060	+	0.924550i	$0.375559\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−892292.	−0.357878
$363$	−1.72362e6	−0.686553
$364$	−1.20517e6	−0.476753
$365$	−1.25661e6	−0.493707
$366$	990541.	0.386518
$367$	−719695.	−0.278922	−0.139461	−	0.990228i	$-0.544537\pi$
$367$	−719695.	−0.278922	−0.139461	+	0.990228i	$0.544537\pi$
$368$	627637.	0.241596
$369$	−982588.	−0.375669
$370$	−741060.	−0.281416
$371$	−7.02003e6	−2.64791
$372$	−1.39938e6	−0.524298
$373$	337928.	0.125763	0.0628813	−	0.998021i	$-0.479971\pi$
$373$	337928.	0.125763	0.0628813	+	0.998021i	$0.479971\pi$
$374$	3.46767e6	1.28191
$375$	−140625.	−0.0516398
$376$	−354358.	−0.129262
$377$	2.39677e6	0.868506
$378$	−608495.	−0.219042
$379$	5.06131e6	1.80994	0.904971	−	0.425473i	$-0.139892\pi$
$379$	5.06131e6	1.80994	0.904971	+	0.425473i	$0.139892\pi$
$380$	144400.	0.0512989
$381$	−1.60168e6	−0.565281
$382$	2.06842e6	0.725239
$383$	5.15709e6	1.79642	0.898209	−	0.439568i	$-0.144868\pi$
$383$	5.15709e6	1.79642	0.898209	+	0.439568i	$0.144868\pi$
$384$	−147456.	−0.0510310
$385$	3.09762e6	1.06507
$386$	−2.33527e6	−0.797754
$387$	3023.29	0.00102613
$388$	1.44927e6	0.488730
$389$	4.00743e6	1.34274	0.671370	−	0.741122i	$-0.265706\pi$
$389$	4.00743e6	1.34274	0.671370	+	0.741122i	$0.265706\pi$
$390$	324863.	0.108153
$391$	3.57954e6	1.18409
$392$	1.71123e6	0.562463
$393$	2.23702e6	0.730614
$394$	−3.62740e6	−1.17721
$395$	185128.	0.0597008
$396$	769527.	0.246596
$397$	5.16758e6	1.64555	0.822775	−	0.568367i	$-0.192425\pi$
$397$	5.16758e6	1.64555	0.822775	+	0.568367i	$0.192425\pi$
$398$	−532640.	−0.168549
$399$	−677983.	−0.213200
$400$	160000.	0.0500000
$401$	−3.84132e6	−1.19294	−0.596472	−	0.802634i	$-0.703431\pi$
$401$	−3.84132e6	−1.19294	−0.596472	+	0.802634i	$0.703431\pi$
$402$	−841888.	−0.259830
$403$	−3.50777e6	−1.07589
$404$	2.20800e6	0.673047
$405$	164025.	0.0496904
$406$	−5.54240e6	−1.66872
$407$	−4.40020e6	−1.31670
$408$	−840972.	−0.250110
$409$	−3.59511e6	−1.06268	−0.531342	−	0.847157i	$-0.678312\pi$
$409$	−3.59511e6	−1.06268	−0.531342	+	0.847157i	$0.678312\pi$
$410$	−1.21307e6	−0.356391
$411$	−1.34497e6	−0.392742
$412$	58569.8	0.0169993
$413$	1.10583e6	0.319017
$414$	794353.	0.227779
$415$	2.72040e6	0.775375
$416$	−369622.	−0.104719
$417$	−474685.	−0.133680
$418$	857405.	0.240019
$419$	2.34457e6	0.652422	0.326211	−	0.945297i	$-0.394228\pi$
$419$	2.34457e6	0.652422	0.326211	+	0.945297i	$0.394228\pi$
$420$	−751228.	−0.207801
$421$	527492.	0.145048	0.0725238	−	0.997367i	$-0.476895\pi$
$421$	527492.	0.145048	0.0725238	+	0.997367i	$0.476895\pi$
$422$	1.01155e6	0.276507
$423$	−448484.	−0.121870
$424$	−2.15303e6	−0.581614
$425$	912513.	0.245057
$426$	827967.	0.221049
$427$	−5.74168e6	−1.52395
$428$	−2.12609e6	−0.561012
$429$	1.92894e6	0.506029
$430$	3732.45	0.000973471 0
$431$	654627.	0.169746	0.0848732	−	0.996392i	$-0.472951\pi$
$431$	654627.	0.169746	0.0848732	+	0.996392i	$0.472951\pi$
$432$	−186624.	−0.0481125
$433$	−1.90076e6	−0.487200	−0.243600	−	0.969876i	$-0.578328\pi$
$433$	−1.90076e6	−0.487200	−0.243600	+	0.969876i	$0.578328\pi$
$434$	8.11153e6	2.06718
$435$	1.49400e6	0.378554
$436$	−130647.	−0.0329141
$437$	885067.	0.221703
$438$	1.80952e6	0.450691
$439$	−4.00112e6	−0.990878	−0.495439	−	0.868643i	$-0.664993\pi$
$439$	−4.00112e6	−0.990878	−0.495439	+	0.868643i	$0.664993\pi$
$440$	950033.	0.233941
$441$	2.16578e6	0.530295
$442$	−2.10803e6	−0.513240
$443$	−4.38016e6	−1.06043	−0.530213	−	0.847864i	$-0.677888\pi$
$443$	−4.38016e6	−1.06043	−0.530213	+	0.847864i	$0.677888\pi$
$444$	1.06713e6	0.256897
$445$	1.22727e6	0.293792
$446$	−824548.	−0.196281
$447$	122159.	0.0289173
$448$	854731.	0.201203
$449$	−805858.	−0.188644	−0.0943219	−	0.995542i	$-0.530068\pi$
$449$	−805858.	−0.188644	−0.0943219	+	0.995542i	$0.530068\pi$
$450$	202500.	0.0471405
$451$	−7.20287e6	−1.66749
$452$	656022.	0.151033
$453$	−2.28706e6	−0.523638
$454$	−381078.	−0.0867709
$455$	−1.88307e6	−0.426421
$456$	−207936.	−0.0468293
$457$	−2.96646e6	−0.664428	−0.332214	−	0.943204i	$-0.607796\pi$
$457$	−2.96646e6	−0.664428	−0.332214	+	0.943204i	$0.607796\pi$
$458$	842035.	0.187571
$459$	−1.06436e6	−0.235806
$460$	980683.	0.216090
$461$	−3.47515e6	−0.761590	−0.380795	−	0.924660i	$-0.624350\pi$
$461$	−3.47515e6	−0.761590	−0.380795	+	0.924660i	$0.624350\pi$
$462$	−4.46057e6	−0.972267
$463$	−5.50111e6	−1.19261	−0.596304	−	0.802758i	$-0.703365\pi$
$463$	−5.50111e6	−1.19261	−0.596304	+	0.802758i	$0.703365\pi$
$464$	−1.69984e6	−0.366534
$465$	−2.18653e6	−0.468947
$466$	−1.90487e6	−0.406351
$467$	−9.33309e6	−1.98031	−0.990156	−	0.139971i	$-0.955299\pi$
$467$	−9.33309e6	−1.98031	−0.990156	+	0.139971i	$0.955299\pi$
$468$	−467802.	−0.0987297
$469$	4.88001e6	1.02445
$470$	−553684.	−0.115616
$471$	−1.22751e6	−0.254960
$472$	339156.	0.0700721
$473$	22162.2	0.00455470
$474$	−266585.	−0.0544991
$475$	225625.	0.0458831
$476$	4.87470e6	0.986123
$477$	−2.72492e6	−0.548351
$478$	5.51904e6	1.10483
$479$	−1.88774e6	−0.375927	−0.187963	−	0.982176i	$-0.560189\pi$
$479$	−1.88774e6	−0.375927	−0.187963	+	0.982176i	$0.560189\pi$
$480$	−230400.	−0.0456435
$481$	2.67492e6	0.527167
$482$	−6.95074e6	−1.36274
$483$	−4.60448e6	−0.898075
$484$	3.06420e6	0.594572
$485$	2.26448e6	0.437134
$486$	−236196.	−0.0453609
$487$	−4.15571e6	−0.794005	−0.397002	−	0.917818i	$-0.629950\pi$
$487$	−4.15571e6	−0.794005	−0.397002	+	0.917818i	$0.629950\pi$
$488$	−1.76096e6	−0.334734
$489$	3.86073e6	0.730125
$490$	2.67380e6	0.503082
$491$	−6.33193e6	−1.18531	−0.592656	−	0.805456i	$-0.701921\pi$
$491$	−6.33193e6	−1.18531	−0.592656	+	0.805456i	$0.701921\pi$
$492$	1.74682e6	0.325339
$493$	−9.69455e6	−1.79643
$494$	−521224.	−0.0960964
$495$	1.20239e6	0.220562
$496$	2.48779e6	0.454056
$497$	−4.79932e6	−0.871543
$498$	−3.91737e6	−0.707817
$499$	−4.09281e6	−0.735817	−0.367909	−	0.929862i	$-0.619926\pi$
$499$	−4.09281e6	−0.735817	−0.367909	+	0.929862i	$0.619926\pi$
$500$	250000.	0.0447214
$501$	−5.88035e6	−1.04667
$502$	−4.49147e6	−0.795480
$503$	4.59956e6	0.810581	0.405291	−	0.914188i	$-0.367170\pi$
$503$	4.59956e6	0.810581	0.405291	+	0.914188i	$0.367170\pi$
$504$	1.08177e6	0.189696
$505$	3.45000e6	0.601992
$506$	5.82301e6	1.01105
$507$	2.16902e6	0.374751
$508$	2.84744e6	0.489548
$509$	−8.17567e6	−1.39871	−0.699357	−	0.714773i	$-0.746530\pi$
$509$	−8.17567e6	−1.39871	−0.699357	+	0.714773i	$0.746530\pi$
$510$	−1.31402e6	−0.223705
$511$	−1.04889e7	−1.77696
$512$	262144.	0.0441942
$513$	−263169.	−0.0441511
$514$	6.80481e6	1.13608
$515$	91515.4	0.0152046
$516$	−5374.73	−0.000888653 0
$517$	−3.28762e6	−0.540947
$518$	−6.18561e6	−1.01288
$519$	5.58026e6	0.909360
$520$	−577534.	−0.0936632
$521$	−3.34617e6	−0.540075	−0.270037	−	0.962850i	$-0.587036\pi$
$521$	−3.34617e6	−0.540075	−0.270037	+	0.962850i	$0.587036\pi$
$522$	−2.15136e6	−0.345571
$523$	−1.03086e7	−1.64796	−0.823979	−	0.566620i	$-0.808251\pi$
$523$	−1.03086e7	−1.64796	−0.823979	+	0.566620i	$0.808251\pi$
$524$	−3.97692e6	−0.632730
$525$	−1.17379e6	−0.185863
$526$	5.80982e6	0.915585
$527$	1.41884e7	2.22539
$528$	−1.36805e6	−0.213558
$529$	−425471.	−0.0661045
$530$	−3.36410e6	−0.520211
$531$	429245.	0.0660646
$532$	1.20530e6	0.184636
$533$	4.37869e6	0.667615
$534$	−1.76727e6	−0.268194
$535$	−3.32201e6	−0.501784
$536$	1.49669e6	0.225019
$537$	−4.06322e6	−0.608044
$538$	−6.00167e6	−0.893957
$539$	1.58763e7	2.35384
$540$	−291600.	−0.0430331
$541$	−163471.	−0.0240130	−0.0120065	−	0.999928i	$-0.503822\pi$
$541$	−163471.	−0.0240130	−0.0120065	+	0.999928i	$0.503822\pi$
$542$	−5.51936e6	−0.807032
$543$	2.00766e6	0.292207
$544$	1.49506e6	0.216602
$545$	−204136.	−0.0294393
$546$	2.71162e6	0.389267
$547$	1.00914e7	1.44206	0.721030	−	0.692904i	$-0.243669\pi$
$547$	1.00914e7	1.44206	0.721030	+	0.692904i	$0.243669\pi$
$548$	2.39106e6	0.340125
$549$	−2.22872e6	−0.315591
$550$	1.48443e6	0.209244
$551$	−2.39704e6	−0.336354
$552$	−1.41218e6	−0.197262
$553$	1.54526e6	0.214877
$554$	5.40691e6	0.748471
$555$	1.66739e6	0.229775
$556$	843885.	0.115770
$557$	1.35787e7	1.85447	0.927233	−	0.374485i	$-0.122180\pi$
$557$	1.35787e7	1.85447	0.927233	+	0.374485i	$0.122180\pi$
$558$	3.14861e6	0.428088
$559$	−13472.6	−0.00182357
$560$	1.33552e6	0.179961
$561$	−7.80226e6	−1.04668
$562$	−2.42024e6	−0.323234
$563$	8.61454e6	1.14541	0.572705	−	0.819761i	$-0.305894\pi$
$563$	8.61454e6	1.14541	0.572705	+	0.819761i	$0.305894\pi$
$564$	797305.	0.105542
$565$	1.02503e6	0.135088
$566$	−7.56769e6	−0.992938
$567$	1.36911e6	0.178847
$568$	−1.47194e6	−0.191434
$569$	6.68597e6	0.865732	0.432866	−	0.901458i	$-0.357502\pi$
$569$	6.68597e6	0.865732	0.432866	+	0.901458i	$0.357502\pi$
$570$	−324900.	−0.0418854
$571$	−3.66558e6	−0.470493	−0.235246	−	0.971936i	$-0.575590\pi$
$571$	−3.66558e6	−0.470493	−0.235246	+	0.971936i	$0.575590\pi$
$572$	−3.42923e6	−0.438234
$573$	−4.65395e6	−0.592155
$574$	−1.01255e7	−1.28273
$575$	1.53232e6	0.193277
$576$	331776.	0.0416667
$577$	−5.40355e6	−0.675677	−0.337839	−	0.941204i	$-0.609696\pi$
$577$	−5.40355e6	−0.675677	−0.337839	+	0.941204i	$0.609696\pi$
$578$	2.84722e6	0.354487
$579$	5.25436e6	0.651364
$580$	−2.65600e6	−0.327838
$581$	2.27071e7	2.79075
$582$	−3.26085e6	−0.399047
$583$	−1.99751e7	−2.43398
$584$	−3.21693e6	−0.390310
$585$	−730941.	−0.0883065
$586$	5.09694e6	0.613148
$587$	6.47524e6	0.775640	0.387820	−	0.921735i	$-0.373228\pi$
$587$	6.47524e6	0.775640	0.387820	+	0.921735i	$0.373228\pi$
$588$	−3.85028e6	−0.459249
$589$	3.50817e6	0.416670
$590$	529932.	0.0626744
$591$	8.16166e6	0.961191
$592$	−1.89711e6	−0.222479
$593$	6.61193e6	0.772132	0.386066	−	0.922471i	$-0.373834\pi$
$593$	6.61193e6	0.772132	0.386066	+	0.922471i	$0.373834\pi$
$594$	−1.73144e6	−0.201345
$595$	7.61673e6	0.882015
$596$	−217172.	−0.0250431
$597$	1.19844e6	0.137620
$598$	−3.53986e6	−0.404793
$599$	−9.85703e6	−1.12248	−0.561241	−	0.827653i	$-0.689676\pi$
$599$	−9.85703e6	−1.12248	−0.561241	+	0.827653i	$0.689676\pi$
$600$	−360000.	−0.0408248
$601$	−1.23957e7	−1.39986	−0.699930	−	0.714212i	$-0.746785\pi$
$601$	−1.23957e7	−1.39986	−0.699930	+	0.714212i	$0.746785\pi$
$602$	31154.7	0.00350374
$603$	1.89425e6	0.212150
$604$	4.06588e6	0.453484
$605$	4.78782e6	0.531801
$606$	−4.96800e6	−0.549541
$607$	−389049.	−0.0428580	−0.0214290	−	0.999770i	$-0.506822\pi$
$607$	−389049.	−0.0428580	−0.0214290	+	0.999770i	$0.506822\pi$
$608$	369664.	0.0405554
$609$	1.24704e7	1.36250
$610$	−2.75150e6	−0.299396
$611$	1.99857e6	0.216579
$612$	1.89219e6	0.204214
$613$	6.75258e6	0.725802	0.362901	−	0.931828i	$-0.381786\pi$
$613$	6.75258e6	0.725802	0.362901	+	0.931828i	$0.381786\pi$
$614$	−7.65008e6	−0.818927
$615$	2.72941e6	0.290992
$616$	7.92991e6	0.842008
$617$	−1.45453e6	−0.153819	−0.0769094	−	0.997038i	$-0.524505\pi$
$617$	−1.45453e6	−0.153819	−0.0769094	+	0.997038i	$0.524505\pi$
$618$	−131782.	−0.0138799
$619$	−1.47892e7	−1.55137	−0.775687	−	0.631117i	$-0.782597\pi$
$619$	−1.47892e7	−1.55137	−0.775687	+	0.631117i	$0.782597\pi$
$620$	3.88717e6	0.406120
$621$	−1.78730e6	−0.185980
$622$	−3.99746e6	−0.414294
$623$	1.02440e7	1.05742
$624$	831649.	0.0855024
$625$	390625.	0.0400000
$626$	−3.84827e6	−0.392491
$627$	−1.92916e6	−0.195975
$628$	2.18224e6	0.220802
$629$	−1.08196e7	−1.09040
$630$	1.69026e6	0.169669
$631$	−1.76607e7	−1.76577	−0.882886	−	0.469588i	$-0.844403\pi$
$631$	−1.76607e7	−1.76577	−0.882886	+	0.469588i	$0.844403\pi$
$632$	473928.	0.0471976
$633$	−2.27599e6	−0.225767
$634$	−4.23616e6	−0.418552
$635$	4.44912e6	0.437865
$636$	4.84431e6	0.474886
$637$	−9.65132e6	−0.942406
$638$	−1.57706e7	−1.53390
$639$	−1.86293e6	−0.180486
$640$	409600.	0.0395285
$641$	−2.34713e6	−0.225628	−0.112814	−	0.993616i	$-0.535986\pi$
$641$	−2.34713e6	−0.225628	−0.112814	+	0.993616i	$0.535986\pi$
$642$	4.78370e6	0.458064
$643$	1.80621e7	1.72282	0.861411	−	0.507909i	$-0.169581\pi$
$643$	1.80621e7	1.72282	0.861411	+	0.507909i	$0.169581\pi$
$644$	8.18574e6	0.777756
$645$	−8398.01	−0.000794836 0
$646$	2.10827e6	0.198767
$647$	3.73575e6	0.350847	0.175423	−	0.984493i	$-0.443871\pi$
$647$	3.73575e6	0.350847	0.175423	+	0.984493i	$0.443871\pi$
$648$	419904.	0.0392837
$649$	3.14658e6	0.293243
$650$	−902396.	−0.0837749
$651$	−1.82509e7	−1.68785
$652$	−6.86352e6	−0.632306
$653$	3.70607e6	0.340119	0.170059	−	0.985434i	$-0.445604\pi$
$653$	3.70607e6	0.340119	0.170059	+	0.985434i	$0.445604\pi$
$654$	293955.	0.0268743
$655$	−6.21394e6	−0.565931
$656$	−3.10546e6	−0.281752
$657$	−4.07143e6	−0.367988
$658$	−4.62159e6	−0.416128
$659$	9.64206e6	0.864881	0.432440	−	0.901662i	$-0.357653\pi$
$659$	9.64206e6	0.864881	0.432440	+	0.901662i	$0.357653\pi$
$660$	−2.13758e6	−0.191012
$661$	−1.43205e7	−1.27484	−0.637420	−	0.770517i	$-0.719998\pi$
$661$	−1.43205e7	−1.27484	−0.637420	+	0.770517i	$0.719998\pi$
$662$	1.11226e7	0.986416
$663$	4.74306e6	0.419059
$664$	6.96421e6	0.612988
$665$	1.88329e6	0.165144
$666$	−2.40103e6	−0.209755
$667$	−1.62794e7	−1.41685
$668$	1.04540e7	0.906441
$669$	1.85523e6	0.160263
$670$	2.33858e6	0.201263
$671$	−1.63376e7	−1.40082
$672$	−1.92314e6	−0.164281
$673$	1.69544e7	1.44292	0.721462	−	0.692454i	$-0.243470\pi$
$673$	1.69544e7	1.44292	0.721462	+	0.692454i	$0.243470\pi$
$674$	3.69583e6	0.313374
$675$	−455625.	−0.0384900
$676$	−3.85603e6	−0.324544
$677$	−2.30974e6	−0.193683	−0.0968417	−	0.995300i	$-0.530874\pi$
$677$	−2.30974e6	−0.193683	−0.0968417	+	0.995300i	$0.530874\pi$
$678$	−1.47605e6	−0.123318
$679$	1.89016e7	1.57334
$680$	2.33603e6	0.193734
$681$	857425.	0.0708482
$682$	2.30809e7	1.90016
$683$	1.26418e7	1.03695	0.518474	−	0.855094i	$-0.326500\pi$
$683$	1.26418e7	1.03695	0.518474	+	0.855094i	$0.326500\pi$
$684$	467856.	0.0382360
$685$	3.73602e6	0.304217
$686$	8.28940e6	0.672532
$687$	−1.89458e6	−0.153151
$688$	9555.07	0.000769596 0
$689$	1.21430e7	0.974493
$690$	−2.20654e6	−0.176437
$691$	7.13206e6	0.568225	0.284112	−	0.958791i	$-0.408301\pi$
$691$	7.13206e6	0.568225	0.284112	+	0.958791i	$0.408301\pi$
$692$	−9.92046e6	−0.787529
$693$	1.00363e7	0.793853
$694$	2.60883e6	0.205612
$695$	1.31857e6	0.103548
$696$	3.82465e6	0.299273
$697$	−1.77111e7	−1.38090
$698$	−4.53969e6	−0.352685
$699$	4.28596e6	0.331784
$700$	2.08674e6	0.160962
$701$	2.56532e7	1.97172	0.985862	−	0.167557i	$-0.0535879\pi$
$701$	2.56532e7	1.97172	0.985862	+	0.167557i	$0.0535879\pi$
$702$	1.05256e6	0.0806124
$703$	−2.67523e6	−0.204161
$704$	2.43209e6	0.184947
$705$	1.24579e6	0.0944000
$706$	1.99899e6	0.150938
$707$	2.87971e7	2.16670
$708$	−763102.	−0.0572136
$709$	7.49867e6	0.560233	0.280116	−	0.959966i	$-0.409627\pi$
$709$	7.49867e6	0.560233	0.280116	+	0.959966i	$0.409627\pi$
$710$	−2.29991e6	−0.171224
$711$	599816.	0.0444983
$712$	3.14181e6	0.232263
$713$	2.38255e7	1.75517
$714$	−1.09681e7	−0.805166
$715$	−5.35817e6	−0.391968
$716$	7.22350e6	0.526581
$717$	−1.24178e7	−0.902086
$718$	7.44422e6	0.538900
$719$	−2.55299e7	−1.84173	−0.920866	−	0.389879i	$-0.872517\pi$
$719$	−2.55299e7	−1.84173	−0.920866	+	0.389879i	$0.872517\pi$
$720$	518400.	0.0372678
$721$	763877.	0.0547249
$722$	521284.	0.0372161
$723$	1.56392e7	1.11267
$724$	−3.56917e6	−0.253058
$725$	−4.15001e6	−0.293227
$726$	−6.89446e6	−0.485466
$727$	−2.15914e7	−1.51511	−0.757555	−	0.652771i	$-0.773606\pi$
$727$	−2.15914e7	−1.51511	−0.757555	+	0.652771i	$0.773606\pi$
$728$	−4.82066e6	−0.337115
$729$	531441.	0.0370370
$730$	−5.02646e6	−0.349104
$731$	54494.6	0.00377190
$732$	3.96216e6	0.273309
$733$	1.79952e7	1.23707	0.618537	−	0.785755i	$-0.287726\pi$
$733$	1.79952e7	1.23707	0.618537	+	0.785755i	$0.287726\pi$
$734$	−2.87878e6	−0.197228
$735$	−6.01605e6	−0.410765
$736$	2.51055e6	0.170834
$737$	1.38858e7	0.941677
$738$	−3.93035e6	−0.265638
$739$	1.09391e7	0.736835	0.368417	−	0.929661i	$-0.379900\pi$
$739$	1.09391e7	0.736835	0.368417	+	0.929661i	$0.379900\pi$
$740$	−2.96424e6	−0.198991
$741$	1.17275e6	0.0784624
$742$	−2.80801e7	−1.87236
$743$	1.29768e7	0.862371	0.431186	−	0.902263i	$-0.358095\pi$
$743$	1.29768e7	0.862371	0.431186	+	0.902263i	$0.358095\pi$
$744$	−5.59752e6	−0.370735
$745$	−339331.	−0.0223992
$746$	1.35171e6	0.0889276
$747$	8.81408e6	0.577930
$748$	1.38707e7	0.906450
$749$	−2.77288e7	−1.80603
$750$	−562500.	−0.0365148
$751$	9.06879e6	0.586745	0.293372	−	0.955998i	$-0.405222\pi$
$751$	9.06879e6	0.586745	0.293372	+	0.955998i	$0.405222\pi$
$752$	−1.41743e6	−0.0914024
$753$	1.01058e7	0.649506
$754$	9.58707e6	0.614126
$755$	6.35293e6	0.405608
$756$	−2.43398e6	−0.154886
$757$	−1.03252e7	−0.654875	−0.327437	−	0.944873i	$-0.606185\pi$
$757$	−1.03252e7	−0.654875	−0.327437	+	0.944873i	$0.606185\pi$
$758$	2.02452e7	1.27982
$759$	−1.31018e7	−0.825516
$760$	577600.	0.0362738
$761$	1.67517e7	1.04857	0.524286	−	0.851542i	$-0.324332\pi$
$761$	1.67517e7	1.04857	0.524286	+	0.851542i	$0.324332\pi$
$762$	−6.40674e6	−0.399714
$763$	−1.70391e6	−0.105959
$764$	8.27369e6	0.512821
$765$	2.95654e6	0.182655
$766$	2.06283e7	1.27026
$767$	−1.91283e6	−0.117406
$768$	−589824.	−0.0360844
$769$	5.57580e6	0.340010	0.170005	−	0.985443i	$-0.445622\pi$
$769$	5.57580e6	0.340010	0.170005	+	0.985443i	$0.445622\pi$
$770$	1.23905e7	0.753115
$771$	−1.53108e7	−0.927604
$772$	−9.34109e6	−0.564097
$773$	1.94359e7	1.16992	0.584958	−	0.811063i	$-0.301111\pi$
$773$	1.94359e7	1.16992	0.584958	+	0.811063i	$0.301111\pi$
$774$	12093.1	0.000725582 0
$775$	6.07370e6	0.363245
$776$	5.79707e6	0.345585
$777$	1.39176e7	0.827014
$778$	1.60297e7	0.949461
$779$	−4.37919e6	−0.258553
$780$	1.29945e6	0.0764757
$781$	−1.36562e7	−0.801128
$782$	1.43182e7	0.837280
$783$	4.84057e6	0.282158
$784$	6.84493e6	0.397722
$785$	3.40974e6	0.197491
$786$	8.94807e6	0.516622
$787$	−1.33174e7	−0.766448	−0.383224	−	0.923655i	$-0.625186\pi$
$787$	−1.33174e7	−0.766448	−0.383224	+	0.923655i	$0.625186\pi$
$788$	−1.45096e7	−0.832416
$789$	−1.30721e7	−0.747572
$790$	740513.	0.0422148
$791$	8.55594e6	0.486213
$792$	3.07811e6	0.174370
$793$	9.93178e6	0.560847
$794$	2.06703e7	1.16358
$795$	7.56924e6	0.424751
$796$	−2.13056e6	−0.119182
$797$	1.48233e7	0.826608	0.413304	−	0.910593i	$-0.364375\pi$
$797$	1.48233e7	0.826608	0.413304	+	0.910593i	$0.364375\pi$
$798$	−2.71193e6	−0.150755
$799$	−8.08390e6	−0.447975
$800$	640000.	0.0353553
$801$	3.97635e6	0.218980
$802$	−1.53653e7	−0.843538
$803$	−2.98456e7	−1.63340
$804$	−3.36755e6	−0.183727
$805$	1.27902e7	0.695646
$806$	−1.40311e7	−0.760770
$807$	1.35038e7	0.729912
$808$	8.83200e6	0.475916
$809$	−1.05269e7	−0.565498	−0.282749	−	0.959194i	$-0.591246\pi$
$809$	−1.05269e7	−0.565498	−0.282749	+	0.959194i	$0.591246\pi$
$810$	656100.	0.0351364
$811$	3.42578e6	0.182897	0.0914486	−	0.995810i	$-0.470850\pi$
$811$	3.42578e6	0.182897	0.0914486	+	0.995810i	$0.470850\pi$
$812$	−2.21696e7	−1.17996
$813$	1.24186e7	0.658938
$814$	−1.76008e7	−0.931046
$815$	−1.07242e7	−0.565552
$816$	−3.36389e6	−0.176855
$817$	13474.1	0.000706230 0
$818$	−1.43804e7	−0.751431
$819$	−6.10115e6	−0.317835
$820$	−4.85229e6	−0.252007
$821$	−8.25696e6	−0.427526	−0.213763	−	0.976886i	$-0.568572\pi$
$821$	−8.25696e6	−0.427526	−0.213763	+	0.976886i	$0.568572\pi$
$822$	−5.37987e6	−0.277711
$823$	−9.07314e6	−0.466936	−0.233468	−	0.972364i	$-0.575007\pi$
$823$	−9.07314e6	−0.466936	−0.233468	+	0.972364i	$0.575007\pi$
$824$	234279.	0.0120203
$825$	−3.33996e6	−0.170847
$826$	4.42333e6	0.225579
$827$	3.11181e7	1.58216	0.791079	−	0.611714i	$-0.209520\pi$
$827$	3.11181e7	1.58216	0.791079	+	0.611714i	$0.209520\pi$
$828$	3.17741e6	0.161064
$829$	−6.87544e6	−0.347468	−0.173734	−	0.984793i	$-0.555583\pi$
$829$	−6.87544e6	−0.347468	−0.173734	+	0.984793i	$0.555583\pi$
$830$	1.08816e7	0.548273
$831$	−1.21655e7	−0.611124
$832$	−1.47849e6	−0.0740473
$833$	3.90381e7	1.94929
$834$	−1.89874e6	−0.0945258
$835$	1.63343e7	0.810745
$836$	3.42962e6	0.169719
$837$	−7.08436e6	−0.349532
$838$	9.37829e6	0.461332
$839$	2.83315e6	0.138952	0.0694760	−	0.997584i	$-0.477867\pi$
$839$	2.83315e6	0.138952	0.0694760	+	0.997584i	$0.477867\pi$
$840$	−3.00491e6	−0.146938
$841$	2.35786e7	1.14955
$842$	2.10997e6	0.102564
$843$	5.44553e6	0.263919
$844$	4.04620e6	0.195520
$845$	−6.02505e6	−0.290281
$846$	−1.79394e6	−0.0861750
$847$	3.99638e7	1.91407
$848$	−8.61211e6	−0.411263
$849$	1.70273e7	0.810731
$850$	3.65005e6	0.173281
$851$	−1.81686e7	−0.860000
$852$	3.31187e6	0.156305
$853$	−1.45240e7	−0.683461	−0.341731	−	0.939798i	$-0.611013\pi$
$853$	−1.45240e7	−0.683461	−0.341731	+	0.939798i	$0.611013\pi$
$854$	−2.29667e7	−1.07759
$855$	731025.	0.0341993
$856$	−8.50435e6	−0.396695
$857$	1.31634e7	0.612230	0.306115	−	0.951995i	$-0.400971\pi$
$857$	1.31634e7	0.612230	0.306115	+	0.951995i	$0.400971\pi$
$858$	7.71576e6	0.357817
$859$	9.45972e6	0.437417	0.218708	−	0.975790i	$-0.429816\pi$
$859$	9.45972e6	0.437417	0.218708	+	0.975790i	$0.429816\pi$
$860$	14929.8	0.000688348 0
$861$	2.27823e7	1.04735
$862$	2.61851e6	0.120029
$863$	3.48953e7	1.59492	0.797462	−	0.603369i	$-0.206175\pi$
$863$	3.48953e7	1.59492	0.797462	+	0.603369i	$0.206175\pi$
$864$	−746496.	−0.0340207
$865$	−1.55007e7	−0.704387
$866$	−7.60303e6	−0.344502
$867$	−6.40624e6	−0.289438
$868$	3.24461e7	1.46172
$869$	4.39695e6	0.197516
$870$	5.97601e6	0.267678
$871$	−8.44130e6	−0.377019
$872$	−522587.	−0.0232738
$873$	7.33692e6	0.325820
$874$	3.54027e6	0.156768
$875$	3.26054e6	0.143969
$876$	7.23810e6	0.318687
$877$	−9.92660e6	−0.435814	−0.217907	−	0.975970i	$-0.569923\pi$
$877$	−9.92660e6	−0.435814	−0.217907	+	0.975970i	$0.569923\pi$
$878$	−1.60045e7	−0.700657
$879$	−1.14681e7	−0.500633
$880$	3.80013e6	0.165422
$881$	−3.67767e7	−1.59637	−0.798183	−	0.602415i	$-0.794205\pi$
$881$	−3.67767e7	−1.59637	−0.798183	+	0.602415i	$0.794205\pi$
$882$	8.66312e6	0.374975
$883$	1.03097e6	0.0444984	0.0222492	−	0.999752i	$-0.492917\pi$
$883$	1.03097e6	0.0444984	0.0222492	+	0.999752i	$0.492917\pi$
$884$	−8.43211e6	−0.362916
$885$	−1.19235e6	−0.0511734
$886$	−1.75206e7	−0.749835
$887$	3.28174e7	1.40054	0.700270	−	0.713878i	$-0.253063\pi$
$887$	3.28174e7	1.40054	0.700270	+	0.713878i	$0.253063\pi$
$888$	4.26851e6	0.181653
$889$	3.71367e7	1.57598
$890$	4.90908e6	0.207742
$891$	3.89573e6	0.164397
$892$	−3.29819e6	−0.138792
$893$	−1.99880e6	−0.0838766
$894$	488637.	0.0204476
$895$	1.12867e7	0.470989
$896$	3.41892e6	0.142272
$897$	7.96468e6	0.330512
$898$	−3.22343e6	−0.133391
$899$	−6.45271e7	−2.66283
$900$	810000.	0.0333333
$901$	−4.91166e7	−2.01566
$902$	−2.88115e7	−1.17910
$903$	−70098.0	−0.00286079
$904$	2.62409e6	0.106797
$905$	−5.57682e6	−0.226342
$906$	−9.14822e6	−0.370268
$907$	−2.26089e7	−0.912559	−0.456280	−	0.889836i	$-0.650818\pi$
$907$	−2.26089e7	−0.912559	−0.456280	+	0.889836i	$0.650818\pi$
$908$	−1.52431e6	−0.0613563
$909$	1.11780e7	0.448698
$910$	−7.53228e6	−0.301525
$911$	3.68667e7	1.47176	0.735882	−	0.677110i	$-0.236768\pi$
$911$	3.68667e7	1.47176	0.735882	+	0.677110i	$0.236768\pi$
$912$	−831744.	−0.0331133
$913$	6.46117e7	2.56528
$914$	−1.18658e7	−0.469821
$915$	6.19088e6	0.244455
$916$	3.36814e6	0.132633
$917$	−5.18676e7	−2.03692
$918$	−4.25742e6	−0.166740
$919$	−3.14836e7	−1.22969	−0.614844	−	0.788649i	$-0.710781\pi$
$919$	−3.14836e7	−1.22969	−0.614844	+	0.788649i	$0.710781\pi$
$920$	3.92273e6	0.152799
$921$	1.72127e7	0.668651
$922$	−1.39006e7	−0.538525
$923$	8.30172e6	0.320748
$924$	−1.78423e7	−0.687497
$925$	−4.63163e6	−0.177983
$926$	−2.20044e7	−0.843302
$927$	296510.	0.0113329
$928$	−6.79937e6	−0.259178
$929$	−1.49433e7	−0.568078	−0.284039	−	0.958813i	$-0.591675\pi$
$929$	−1.49433e7	−0.568078	−0.284039	+	0.958813i	$0.591675\pi$
$930$	−8.74613e6	−0.331595
$931$	9.65243e6	0.364974
$932$	−7.61949e6	−0.287334
$933$	8.99429e6	0.338270
$934$	−3.73324e7	−1.40029
$935$	2.16729e7	0.810754
$936$	−1.87121e6	−0.0698124
$937$	4.79288e7	1.78340	0.891698	−	0.452630i	$-0.149514\pi$
$937$	4.79288e7	1.78340	0.891698	+	0.452630i	$0.149514\pi$
$938$	1.95201e7	0.724392
$939$	8.65860e6	0.320467
$940$	−2.21474e6	−0.0817528
$941$	−2.51658e7	−0.926482	−0.463241	−	0.886232i	$-0.653314\pi$
$941$	−2.51658e7	−0.926482	−0.463241	+	0.886232i	$0.653314\pi$
$942$	−4.91003e6	−0.180284
$943$	−2.97410e7	−1.08912
$944$	1.35663e6	0.0495484
$945$	−3.80309e6	−0.138534
$946$	88648.8	0.00322066
$947$	−1.65771e7	−0.600668	−0.300334	−	0.953834i	$-0.597098\pi$
$947$	−1.65771e7	−0.600668	−0.300334	+	0.953834i	$0.597098\pi$
$948$	−1.06634e6	−0.0385367
$949$	1.81434e7	0.653964
$950$	902500.	0.0324443
$951$	9.53135e6	0.341746
$952$	1.94988e7	0.697294
$953$	−2.91621e7	−1.04013	−0.520065	−	0.854127i	$-0.674092\pi$
$953$	−2.91621e7	−1.04013	−0.520065	+	0.854127i	$0.674092\pi$
$954$	−1.08997e7	−0.387743
$955$	1.29276e7	0.458681
$956$	2.20762e7	0.781229
$957$	3.54838e7	1.25242
$958$	−7.55096e6	−0.265820
$959$	3.11845e7	1.09495
$960$	−921600.	−0.0322749
$961$	6.58088e7	2.29867
$962$	1.06997e7	0.372763
$963$	−1.07633e7	−0.374008
$964$	−2.78030e7	−0.963604
$965$	−1.45954e7	−0.504544
$966$	−1.84179e7	−0.635035
$967$	2.32808e7	0.800631	0.400316	−	0.916377i	$-0.368901\pi$
$967$	2.32808e7	0.800631	0.400316	+	0.916377i	$0.368901\pi$
$968$	1.22568e7	0.420426
$969$	−4.74361e6	−0.162293
$970$	9.05792e6	0.309100
$971$	49340.0	0.00167939	0.000839694	−	1.00000i	$-0.499733\pi$
$971$	49340.0	0.00167939	0.000839694		1.00000i	$0.499733\pi$
$972$	−944784.	−0.0320750
$973$	1.10061e7	0.372692
$974$	−1.66229e7	−0.561446
$975$	2.03039e6	0.0684019
$976$	−7.04385e6	−0.236693
$977$	−4.29305e7	−1.43890	−0.719449	−	0.694545i	$-0.755606\pi$
$977$	−4.29305e7	−1.43890	−0.719449	+	0.694545i	$0.755606\pi$
$978$	1.54429e7	0.516276
$979$	2.91487e7	0.971990
$980$	1.06952e7	0.355733
$981$	−661399.	−0.0219428
$982$	−2.53277e7	−0.838142
$983$	−3.42934e7	−1.13195	−0.565975	−	0.824423i	$-0.691500\pi$
$983$	−3.42934e7	−1.13195	−0.565975	+	0.824423i	$0.691500\pi$
$984$	6.98729e6	0.230049
$985$	−2.26713e7	−0.744535
$986$	−3.87782e7	−1.27027
$987$	1.03986e7	0.339767
$988$	−2.08490e6	−0.0679504
$989$	91508.8	0.00297490
$990$	4.80954e6	0.155961
$991$	−1.87220e7	−0.605575	−0.302787	−	0.953058i	$-0.597917\pi$
$991$	−1.87220e7	−0.605575	−0.302787	+	0.953058i	$0.597917\pi$
$992$	9.95115e6	0.321066
$993$	−2.50258e7	−0.805405
$994$	−1.91973e7	−0.616274
$995$	−3.32900e6	−0.106600
$996$	−1.56695e7	−0.500502
$997$	−4.57657e7	−1.45815	−0.729074	−	0.684434i	$-0.760049\pi$
$997$	−4.57657e7	−1.45815	−0.729074	+	0.684434i	$0.760049\pi$
$998$	−1.63712e7	−0.520301
$999$	5.40233e6	0.171264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.o.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.o.1.5	✓	5	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +208.674 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +208.674 q^{7} +64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +593.771 q^{11} -144.000 q^{12} -360.959 q^{13} +834.698 q^{14} -225.000 q^{15} +256.000 q^{16} +1460.02 q^{17} +324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -1878.07 q^{21} +2375.08 q^{22} +2451.71 q^{23} -576.000 q^{24} +625.000 q^{25} -1443.83 q^{26} -729.000 q^{27} +3338.79 q^{28} -6640.01 q^{29} -900.000 q^{30} +9717.92 q^{31} +1024.00 q^{32} -5343.94 q^{33} +5840.08 q^{34} +5216.86 q^{35} +1296.00 q^{36} -7410.60 q^{37} +1444.00 q^{38} +3248.63 q^{39} +1600.00 q^{40} -12130.7 q^{41} -7512.28 q^{42} +37.3245 q^{43} +9500.33 q^{44} +2025.00 q^{45} +9806.83 q^{46} -5536.84 q^{47} -2304.00 q^{48} +26738.0 q^{49} +2500.00 q^{50} -13140.2 q^{51} -5775.34 q^{52} -33641.0 q^{53} -2916.00 q^{54} +14844.3 q^{55} +13355.2 q^{56} -3249.00 q^{57} -26560.0 q^{58} +5299.32 q^{59} -3600.00 q^{60} -27515.0 q^{61} +38871.7 q^{62} +16902.6 q^{63} +4096.00 q^{64} -9023.96 q^{65} -21375.8 q^{66} +23385.8 q^{67} +23360.3 q^{68} -22065.4 q^{69} +20867.4 q^{70} -22999.1 q^{71} +5184.00 q^{72} -50264.6 q^{73} -29642.4 q^{74} -5625.00 q^{75} +5776.00 q^{76} +123905. q^{77} +12994.5 q^{78} +7405.13 q^{79} +6400.00 q^{80} +6561.00 q^{81} -48522.9 q^{82} +108816. q^{83} -30049.1 q^{84} +36500.5 q^{85} +149.298 q^{86} +59760.1 q^{87} +38001.3 q^{88} +49090.8 q^{89} +8100.00 q^{90} -75322.8 q^{91} +39227.3 q^{92} -87461.3 q^{93} -22147.4 q^{94} +9025.00 q^{95} -9216.00 q^{96} +90579.2 q^{97} +106952. q^{98} +48095.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 125 q^{5} - 180 q^{6} + 88 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 125 * q^5 - 180 * q^6 + 88 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 125 q^{5} - 180 q^{6} + 88 q^{7} + 320 q^{8} + 405 q^{9} + 500 q^{10} - 112 q^{11} - 720 q^{12} - 44 q^{13} + 352 q^{14} - 1125 q^{15} + 1280 q^{16} + 2388 q^{17} + 1620 q^{18} + 1805 q^{19} + 2000 q^{20} - 792 q^{21} - 448 q^{22} + 3114 q^{23} - 2880 q^{24} + 3125 q^{25} - 176 q^{26} - 3645 q^{27} + 1408 q^{28} - 2966 q^{29} - 4500 q^{30} + 6930 q^{31} + 5120 q^{32} + 1008 q^{33} + 9552 q^{34} + 2200 q^{35} + 6480 q^{36} + 5608 q^{37} + 7220 q^{38} + 396 q^{39} + 8000 q^{40} + 20948 q^{41} - 3168 q^{42} + 3090 q^{43} - 1792 q^{44} + 10125 q^{45} + 12456 q^{46} + 16490 q^{47} - 11520 q^{48} + 2757 q^{49} + 12500 q^{50} - 21492 q^{51} - 704 q^{52} - 33060 q^{53} - 14580 q^{54} - 2800 q^{55} + 5632 q^{56} - 16245 q^{57} - 11864 q^{58} - 346 q^{59} - 18000 q^{60} + 57698 q^{61} + 27720 q^{62} + 7128 q^{63} + 20480 q^{64} - 1100 q^{65} + 4032 q^{66} + 12364 q^{67} + 38208 q^{68} - 28026 q^{69} + 8800 q^{70} + 9984 q^{71} + 25920 q^{72} + 28050 q^{73} + 22432 q^{74} - 28125 q^{75} + 28880 q^{76} + 235208 q^{77} + 1584 q^{78} + 36498 q^{79} + 32000 q^{80} + 32805 q^{81} + 83792 q^{82} + 89696 q^{83} - 12672 q^{84} + 59700 q^{85} + 12360 q^{86} + 26694 q^{87} - 7168 q^{88} + 114980 q^{89} + 40500 q^{90} + 267260 q^{91} + 49824 q^{92} - 62370 q^{93} + 65960 q^{94} + 45125 q^{95} - 46080 q^{96} + 317596 q^{97} + 11028 q^{98} - 9072 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 125 * q^5 - 180 * q^6 + 88 * q^7 + 320 * q^8 + 405 * q^9 + 500 * q^10 - 112 * q^11 - 720 * q^12 - 44 * q^13 + 352 * q^14 - 1125 * q^15 + 1280 * q^16 + 2388 * q^17 + 1620 * q^18 + 1805 * q^19 + 2000 * q^20 - 792 * q^21 - 448 * q^22 + 3114 * q^23 - 2880 * q^24 + 3125 * q^25 - 176 * q^26 - 3645 * q^27 + 1408 * q^28 - 2966 * q^29 - 4500 * q^30 + 6930 * q^31 + 5120 * q^32 + 1008 * q^33 + 9552 * q^34 + 2200 * q^35 + 6480 * q^36 + 5608 * q^37 + 7220 * q^38 + 396 * q^39 + 8000 * q^40 + 20948 * q^41 - 3168 * q^42 + 3090 * q^43 - 1792 * q^44 + 10125 * q^45 + 12456 * q^46 + 16490 * q^47 - 11520 * q^48 + 2757 * q^49 + 12500 * q^50 - 21492 * q^51 - 704 * q^52 - 33060 * q^53 - 14580 * q^54 - 2800 * q^55 + 5632 * q^56 - 16245 * q^57 - 11864 * q^58 - 346 * q^59 - 18000 * q^60 + 57698 * q^61 + 27720 * q^62 + 7128 * q^63 + 20480 * q^64 - 1100 * q^65 + 4032 * q^66 + 12364 * q^67 + 38208 * q^68 - 28026 * q^69 + 8800 * q^70 + 9984 * q^71 + 25920 * q^72 + 28050 * q^73 + 22432 * q^74 - 28125 * q^75 + 28880 * q^76 + 235208 * q^77 + 1584 * q^78 + 36498 * q^79 + 32000 * q^80 + 32805 * q^81 + 83792 * q^82 + 89696 * q^83 - 12672 * q^84 + 59700 * q^85 + 12360 * q^86 + 26694 * q^87 - 7168 * q^88 + 114980 * q^89 + 40500 * q^90 + 267260 * q^91 + 49824 * q^92 - 62370 * q^93 + 65960 * q^94 + 45125 * q^95 - 46080 * q^96 + 317596 * q^97 + 11028 * q^98 - 9072 * q^99

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