LMFDB - Embedded newform 165.6.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.788.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x - 3 $ x^3 - x^2 - 7*x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.35386$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.08127 q^{2} -9.00000 q^{3} -30.8308 q^{4} +25.0000 q^{5} -9.73147 q^{6} -139.508 q^{7} -67.9374 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+1.08127 q^{2} -9.00000 q^{3} -30.8308 q^{4} +25.0000 q^{5} -9.73147 q^{6} -139.508 q^{7} -67.9374 q^{8} +81.0000 q^{9} +27.0319 q^{10} -121.000 q^{11} +277.478 q^{12} -646.331 q^{13} -150.846 q^{14} -225.000 q^{15} +913.128 q^{16} -1378.32 q^{17} +87.5832 q^{18} +1908.90 q^{19} -770.771 q^{20} +1255.57 q^{21} -130.834 q^{22} +343.726 q^{23} +611.436 q^{24} +625.000 q^{25} -698.861 q^{26} -729.000 q^{27} +4301.15 q^{28} +53.5092 q^{29} -243.287 q^{30} +634.133 q^{31} +3161.34 q^{32} +1089.00 q^{33} -1490.34 q^{34} -3487.70 q^{35} -2497.30 q^{36} +11674.2 q^{37} +2064.04 q^{38} +5816.98 q^{39} -1698.43 q^{40} +18866.5 q^{41} +1357.62 q^{42} +13379.3 q^{43} +3730.53 q^{44} +2025.00 q^{45} +371.662 q^{46} -2252.95 q^{47} -8218.15 q^{48} +2655.48 q^{49} +675.796 q^{50} +12404.9 q^{51} +19926.9 q^{52} -8900.71 q^{53} -788.249 q^{54} -3025.00 q^{55} +9477.80 q^{56} -17180.1 q^{57} +57.8581 q^{58} -11276.7 q^{59} +6936.94 q^{60} +11852.4 q^{61} +685.672 q^{62} -11300.1 q^{63} -25801.8 q^{64} -16158.3 q^{65} +1177.51 q^{66} -57333.6 q^{67} +42494.7 q^{68} -3093.53 q^{69} -3771.16 q^{70} +31075.8 q^{71} -5502.93 q^{72} +56010.8 q^{73} +12623.0 q^{74} -5625.00 q^{75} -58853.0 q^{76} +16880.5 q^{77} +6289.75 q^{78} -883.036 q^{79} +22828.2 q^{80} +6561.00 q^{81} +20399.9 q^{82} +93986.3 q^{83} -38710.3 q^{84} -34457.9 q^{85} +14466.7 q^{86} -481.583 q^{87} +8220.42 q^{88} +21739.9 q^{89} +2189.58 q^{90} +90168.4 q^{91} -10597.4 q^{92} -5707.20 q^{93} -2436.06 q^{94} +47722.5 q^{95} -28452.0 q^{96} -158059. q^{97} +2871.30 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} - 363 q^{11} + 180 q^{12} - 546 q^{13} - 8 q^{14} - 675 q^{15} - 1360 q^{16} - 314 q^{17} + 162 q^{18} + 1808 q^{19} - 500 q^{20} - 1368 q^{21} - 242 q^{22} + 4288 q^{23} + 216 q^{24} + 1875 q^{25} + 812 q^{26} - 2187 q^{27} + 5888 q^{28} + 5582 q^{29} - 450 q^{30} + 6328 q^{31} - 736 q^{32} + 3267 q^{33} + 11596 q^{34} + 3800 q^{35} - 1620 q^{36} + 16866 q^{37} + 9584 q^{38} + 4914 q^{39} - 600 q^{40} + 23282 q^{41} + 72 q^{42} + 20572 q^{43} + 2420 q^{44} + 6075 q^{45} + 16592 q^{46} + 3432 q^{47} + 12240 q^{48} + 11531 q^{49} + 1250 q^{50} + 2826 q^{51} + 21816 q^{52} + 16138 q^{53} - 1458 q^{54} - 9075 q^{55} + 15648 q^{56} - 16272 q^{57} + 17460 q^{58} + 21972 q^{59} + 4500 q^{60} + 8322 q^{61} + 5056 q^{62} + 12312 q^{63} + 22208 q^{64} - 13650 q^{65} + 2178 q^{66} - 84332 q^{67} + 59832 q^{68} - 38592 q^{69} - 200 q^{70} + 50528 q^{71} - 1944 q^{72} - 53838 q^{73} + 79212 q^{74} - 16875 q^{75} - 52448 q^{76} - 18392 q^{77} - 7308 q^{78} + 6364 q^{79} - 34000 q^{80} + 19683 q^{81} - 68020 q^{82} + 96272 q^{83} - 52992 q^{84} - 7850 q^{85} + 143152 q^{86} - 50238 q^{87} + 2904 q^{88} - 38938 q^{89} + 4050 q^{90} + 104968 q^{91} + 24000 q^{92} - 56952 q^{93} + 49088 q^{94} + 45200 q^{95} + 6624 q^{96} - 103242 q^{97} + 9554 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 - 363 * q^11 + 180 * q^12 - 546 * q^13 - 8 * q^14 - 675 * q^15 - 1360 * q^16 - 314 * q^17 + 162 * q^18 + 1808 * q^19 - 500 * q^20 - 1368 * q^21 - 242 * q^22 + 4288 * q^23 + 216 * q^24 + 1875 * q^25 + 812 * q^26 - 2187 * q^27 + 5888 * q^28 + 5582 * q^29 - 450 * q^30 + 6328 * q^31 - 736 * q^32 + 3267 * q^33 + 11596 * q^34 + 3800 * q^35 - 1620 * q^36 + 16866 * q^37 + 9584 * q^38 + 4914 * q^39 - 600 * q^40 + 23282 * q^41 + 72 * q^42 + 20572 * q^43 + 2420 * q^44 + 6075 * q^45 + 16592 * q^46 + 3432 * q^47 + 12240 * q^48 + 11531 * q^49 + 1250 * q^50 + 2826 * q^51 + 21816 * q^52 + 16138 * q^53 - 1458 * q^54 - 9075 * q^55 + 15648 * q^56 - 16272 * q^57 + 17460 * q^58 + 21972 * q^59 + 4500 * q^60 + 8322 * q^61 + 5056 * q^62 + 12312 * q^63 + 22208 * q^64 - 13650 * q^65 + 2178 * q^66 - 84332 * q^67 + 59832 * q^68 - 38592 * q^69 - 200 * q^70 + 50528 * q^71 - 1944 * q^72 - 53838 * q^73 + 79212 * q^74 - 16875 * q^75 - 52448 * q^76 - 18392 * q^77 - 7308 * q^78 + 6364 * q^79 - 34000 * q^80 + 19683 * q^81 - 68020 * q^82 + 96272 * q^83 - 52992 * q^84 - 7850 * q^85 + 143152 * q^86 - 50238 * q^87 + 2904 * q^88 - 38938 * q^89 + 4050 * q^90 + 104968 * q^91 + 24000 * q^92 - 56952 * q^93 + 49088 * q^94 + 45200 * q^95 + 6624 * q^96 - 103242 * q^97 + 9554 * q^98 - 29403 * 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 $

$2$	1.08127	0.191144	0.0955720	−	0.995423i	$-0.469532\pi$
$2$	1.08127	0.191144	0.0955720	+	0.995423i	$0.469532\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−30.8308	−0.963464
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−9.73147	−0.110357
$7$	−139.508	−1.07610	−0.538052	−	0.842912i	$-0.680839\pi$
$7$	−139.508	−1.07610	−0.538052	+	0.842912i	$0.680839\pi$
$8$	−67.9374	−0.375304
$9$	81.0000	0.333333
$10$	27.0319	0.0854822
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	277.478	0.556256
$13$	−646.331	−1.06071	−0.530355	−	0.847776i	$-0.677941\pi$
$13$	−646.331	−1.06071	−0.530355	+	0.847776i	$0.677941\pi$
$14$	−150.846	−0.205691
$15$	−225.000	−0.258199
$16$	913.128	0.891727
$17$	−1378.32	−1.15672	−0.578358	−	0.815783i	$-0.696306\pi$
$17$	−1378.32	−1.15672	−0.578358	+	0.815783i	$0.696306\pi$
$18$	87.5832	0.0637147
$19$	1908.90	1.21311	0.606553	−	0.795043i	$-0.292552\pi$
$19$	1908.90	1.21311	0.606553	+	0.795043i	$0.292552\pi$
$20$	−770.771	−0.430874
$21$	1255.57	0.621289
$22$	−130.834	−0.0576321
$23$	343.726	0.135485	0.0677427	−	0.997703i	$-0.478420\pi$
$23$	343.726	0.135485	0.0677427	+	0.997703i	$0.478420\pi$
$24$	611.436	0.216682
$25$	625.000	0.200000
$26$	−698.861	−0.202748
$27$	−729.000	−0.192450
$28$	4301.15	1.03679
$29$	53.5092	0.0118150	0.00590750	−	0.999983i	$-0.498120\pi$
$29$	53.5092	0.0118150	0.00590750	+	0.999983i	$0.498120\pi$
$30$	−243.287	−0.0493532
$31$	634.133	0.118516	0.0592579	−	0.998243i	$-0.481127\pi$
$31$	634.133	0.118516	0.0592579	+	0.998243i	$0.481127\pi$
$32$	3161.34	0.545753
$33$	1089.00	0.174078
$34$	−1490.34	−0.221099
$35$	−3487.70	−0.481248
$36$	−2497.30	−0.321155
$37$	11674.2	1.40192	0.700960	−	0.713201i	$-0.252755\pi$
$37$	11674.2	1.40192	0.700960	+	0.713201i	$0.252755\pi$
$38$	2064.04	0.231878
$39$	5816.98	0.612401
$40$	−1698.43	−0.167841
$41$	18866.5	1.75280	0.876399	−	0.481585i	$-0.159939\pi$
$41$	18866.5	1.75280	0.876399	+	0.481585i	$0.159939\pi$
$42$	1357.62	0.118756
$43$	13379.3	1.10347	0.551736	−	0.834018i	$-0.313965\pi$
$43$	13379.3	1.10347	0.551736	+	0.834018i	$0.313965\pi$
$44$	3730.53	0.290495
$45$	2025.00	0.149071
$46$	371.662	0.0258972
$47$	−2252.95	−0.148767	−0.0743835	−	0.997230i	$-0.523699\pi$
$47$	−2252.95	−0.148767	−0.0743835	+	0.997230i	$0.523699\pi$
$48$	−8218.15	−0.514839
$49$	2655.48	0.157998
$50$	675.796	0.0382288
$51$	12404.9	0.667830
$52$	19926.9	1.02196
$53$	−8900.71	−0.435246	−0.217623	−	0.976033i	$-0.569830\pi$
$53$	−8900.71	−0.435246	−0.217623	+	0.976033i	$0.569830\pi$
$54$	−788.249	−0.0367857
$55$	−3025.00	−0.134840
$56$	9477.80	0.403866
$57$	−17180.1	−0.700387
$58$	57.8581	0.00225837
$59$	−11276.7	−0.421746	−0.210873	−	0.977514i	$-0.567631\pi$
$59$	−11276.7	−0.421746	−0.210873	+	0.977514i	$0.567631\pi$
$60$	6936.94	0.248765
$61$	11852.4	0.407834	0.203917	−	0.978988i	$-0.434633\pi$
$61$	11852.4	0.407834	0.203917	+	0.978988i	$0.434633\pi$
$62$	685.672	0.0226536
$63$	−11300.1	−0.358701
$64$	−25801.8	−0.787409
$65$	−16158.3	−0.474364
$66$	1177.51	0.0332739
$67$	−57333.6	−1.56035	−0.780175	−	0.625561i	$-0.784870\pi$
$67$	−57333.6	−1.56035	−0.780175	+	0.625561i	$0.784870\pi$
$68$	42494.7	1.11445
$69$	−3093.53	−0.0782226
$70$	−3771.16	−0.0919877
$71$	31075.8	0.731605	0.365803	−	0.930692i	$-0.380794\pi$
$71$	31075.8	0.731605	0.365803	+	0.930692i	$0.380794\pi$
$72$	−5502.93	−0.125101
$73$	56010.8	1.23017	0.615084	−	0.788462i	$-0.289122\pi$
$73$	56010.8	1.23017	0.615084	+	0.788462i	$0.289122\pi$
$74$	12623.0	0.267969
$75$	−5625.00	−0.115470
$76$	−58853.0	−1.16878
$77$	16880.5	0.324457
$78$	6289.75	0.117057
$79$	−883.036	−0.0159188	−0.00795941	−	0.999968i	$-0.502534\pi$
$79$	−883.036	−0.0159188	−0.00795941	+	0.999968i	$0.502534\pi$
$80$	22828.2	0.398792
$81$	6561.00	0.111111
$82$	20399.9	0.335037
$83$	93986.3	1.49751	0.748754	−	0.662848i	$-0.230652\pi$
$83$	93986.3	1.49751	0.748754	+	0.662848i	$0.230652\pi$
$84$	−38710.3	−0.598589
$85$	−34457.9	−0.517299
$86$	14466.7	0.210922
$87$	−481.583	−0.00682139
$88$	8220.42	0.113159
$89$	21739.9	0.290926	0.145463	−	0.989364i	$-0.453533\pi$
$89$	21739.9	0.290926	0.145463	+	0.989364i	$0.453533\pi$
$90$	2189.58	0.0284941
$91$	90168.4	1.14143
$92$	−10597.4	−0.130535
$93$	−5707.20	−0.0684251
$94$	−2436.06	−0.0284359
$95$	47722.5	0.542518
$96$	−28452.0	−0.315090
$97$	−158059.	−1.70565	−0.852825	−	0.522197i	$-0.825112\pi$
$97$	−158059.	−1.70565	−0.852825	+	0.522197i	$0.825112\pi$
$98$	2871.30	0.0302004
$99$	−9801.00	−0.100504
$100$	−19269.3	−0.192693
$101$	−156968.	−1.53111	−0.765556	−	0.643369i	$-0.777536\pi$
$101$	−156968.	−1.53111	−0.765556	+	0.643369i	$0.777536\pi$
$102$	13413.0	0.127652
$103$	169126.	1.57078	0.785391	−	0.618999i	$-0.212462\pi$
$103$	169126.	1.57078	0.785391	+	0.618999i	$0.212462\pi$
$104$	43910.0	0.398089
$105$	31389.3	0.277849
$106$	−9624.11	−0.0831948
$107$	−13538.5	−0.114317	−0.0571587	−	0.998365i	$-0.518204\pi$
$107$	−13538.5	−0.114317	−0.0571587	+	0.998365i	$0.518204\pi$
$108$	22475.7	0.185419
$109$	−74736.4	−0.602513	−0.301256	−	0.953543i	$-0.597406\pi$
$109$	−74736.4	−0.602513	−0.301256	+	0.953543i	$0.597406\pi$
$110$	−3270.85	−0.0257739
$111$	−105068.	−0.809399
$112$	−127389.	−0.959590
$113$	−205914.	−1.51701	−0.758507	−	0.651665i	$-0.774071\pi$
$113$	−205914.	−1.51701	−0.758507	+	0.651665i	$0.774071\pi$
$114$	−18576.4	−0.133875
$115$	8593.15	0.0605909
$116$	−1649.73	−0.0113833
$117$	−52352.8	−0.353570
$118$	−12193.2	−0.0806142
$119$	192286.	1.24475
$120$	15285.9	0.0969032
$121$	14641.0	0.0909091
$122$	12815.7	0.0779550
$123$	−169799.	−1.01198
$124$	−19550.9	−0.114186
$125$	15625.0	0.0894427
$126$	−12218.6	−0.0685636
$127$	−214682.	−1.18110	−0.590550	−	0.807001i	$-0.701089\pi$
$127$	−214682.	−1.18110	−0.590550	+	0.807001i	$0.701089\pi$
$128$	−129062.	−0.696261
$129$	−120414.	−0.637090
$130$	−17471.5	−0.0906719
$131$	253067.	1.28842	0.644209	−	0.764849i	$-0.277187\pi$
$131$	253067.	1.28842	0.644209	+	0.764849i	$0.277187\pi$
$132$	−33574.8	−0.167718
$133$	−266307.	−1.30543
$134$	−61993.3	−0.298252
$135$	−18225.0	−0.0860663
$136$	93639.2	0.434121
$137$	239398.	1.08973	0.544865	−	0.838524i	$-0.316581\pi$
$137$	239398.	1.08973	0.544865	+	0.838524i	$0.316581\pi$
$138$	−3344.96	−0.0149518
$139$	−166398.	−0.730484	−0.365242	−	0.930913i	$-0.619014\pi$
$139$	−166398.	−0.730484	−0.365242	+	0.930913i	$0.619014\pi$
$140$	107529.	0.463665
$141$	20276.5	0.0858907
$142$	33601.5	0.139842
$143$	78206.1	0.319816
$144$	73963.4	0.297242
$145$	1337.73	0.00528383
$146$	60563.0	0.235139
$147$	−23899.3	−0.0912203
$148$	−359926.	−1.35070
$149$	295512.	1.09046	0.545229	−	0.838287i	$-0.316443\pi$
$149$	295512.	1.09046	0.545229	+	0.838287i	$0.316443\pi$
$150$	−6082.17	−0.0220714
$151$	428373.	1.52890	0.764452	−	0.644681i	$-0.223010\pi$
$151$	428373.	1.52890	0.764452	+	0.644681i	$0.223010\pi$
$152$	−129686.	−0.455284
$153$	−111644.	−0.385572
$154$	18252.4	0.0620181
$155$	15853.3	0.0530019
$156$	−179342.	−0.590027
$157$	−289003.	−0.935735	−0.467867	−	0.883799i	$-0.654978\pi$
$157$	−289003.	−0.935735	−0.467867	+	0.883799i	$0.654978\pi$
$158$	−954.804	−0.00304279
$159$	80106.4	0.251290
$160$	79033.4	0.244068
$161$	−47952.5	−0.145796
$162$	7094.24	0.0212382
$163$	288223.	0.849688	0.424844	−	0.905267i	$-0.360329\pi$
$163$	288223.	0.849688	0.424844	+	0.905267i	$0.360329\pi$
$164$	−581671.	−1.68876
$165$	27225.0	0.0778499
$166$	101625.	0.286240
$167$	−180912.	−0.501969	−0.250985	−	0.967991i	$-0.580754\pi$
$167$	−180912.	−0.501969	−0.250985	+	0.967991i	$0.580754\pi$
$168$	−85300.2	−0.233172
$169$	46451.1	0.125106
$170$	−37258.5	−0.0988787
$171$	154621.	0.404369
$172$	−412495.	−1.06316
$173$	218579.	0.555255	0.277628	−	0.960689i	$-0.410452\pi$
$173$	218579.	0.555255	0.277628	+	0.960689i	$0.410452\pi$
$174$	−520.723	−0.00130387
$175$	−87192.5	−0.215221
$176$	−110489.	−0.268866
$177$	101490.	0.243495
$178$	23506.8	0.0556089
$179$	310916.	0.725287	0.362643	−	0.931928i	$-0.381874\pi$
$179$	310916.	0.725287	0.362643	+	0.931928i	$0.381874\pi$
$180$	−62432.5	−0.143625
$181$	−423637.	−0.961163	−0.480582	−	0.876950i	$-0.659574\pi$
$181$	−423637.	−0.961163	−0.480582	+	0.876950i	$0.659574\pi$
$182$	97496.7	0.218178
$183$	−106672.	−0.235463
$184$	−23351.8	−0.0508483
$185$	291855.	0.626957
$186$	−6171.04	−0.0130791
$187$	166776.	0.348763
$188$	69460.3	0.143332
$189$	101701.	0.207096
$190$	51601.1	0.103699
$191$	861089.	1.70791	0.853954	−	0.520348i	$-0.174198\pi$
$191$	861089.	1.70791	0.853954	+	0.520348i	$0.174198\pi$
$192$	232216.	0.454611
$193$	430583.	0.832077	0.416038	−	0.909347i	$-0.363418\pi$
$193$	430583.	0.832077	0.416038	+	0.909347i	$0.363418\pi$
$194$	−170905.	−0.326025
$195$	145425.	0.273874
$196$	−81870.6	−0.152226
$197$	−184755.	−0.339181	−0.169590	−	0.985515i	$-0.554244\pi$
$197$	−184755.	−0.339181	−0.169590	+	0.985515i	$0.554244\pi$
$198$	−10597.6	−0.0192107
$199$	322993.	0.578177	0.289089	−	0.957302i	$-0.406648\pi$
$199$	322993.	0.578177	0.289089	+	0.957302i	$0.406648\pi$
$200$	−42460.9	−0.0750609
$201$	516002.	0.900869
$202$	−169725.	−0.292663
$203$	−7464.96	−0.0127142
$204$	−382452.	−0.643431
$205$	471663.	0.783875
$206$	182871.	0.300246
$207$	27841.8	0.0451618
$208$	−590183.	−0.945864
$209$	−230977.	−0.365765
$210$	33940.4	0.0531091
$211$	−394106.	−0.609406	−0.304703	−	0.952447i	$-0.598557\pi$
$211$	−394106.	−0.609406	−0.304703	+	0.952447i	$0.598557\pi$
$212$	274417.	0.419344
$213$	−279682.	−0.422393
$214$	−14638.9	−0.0218511
$215$	334482.	0.493488
$216$	49526.3	0.0722274
$217$	−88466.6	−0.127535
$218$	−80810.6	−0.115167
$219$	−504097.	−0.710238
$220$	93263.3	0.129913
$221$	890849.	1.22694
$222$	−113607.	−0.154712
$223$	445038.	0.599287	0.299643	−	0.954051i	$-0.403132\pi$
$223$	445038.	0.599287	0.299643	+	0.954051i	$0.403132\pi$
$224$	−441032.	−0.587286
$225$	50625.0	0.0666667
$226$	−222649.	−0.289968
$227$	1.15887e6	1.49270	0.746349	−	0.665555i	$-0.231805\pi$
$227$	1.15887e6	1.49270	0.746349	+	0.665555i	$0.231805\pi$
$228$	529677.	0.674798
$229$	885853.	1.11628	0.558140	−	0.829747i	$-0.311515\pi$
$229$	885853.	1.11628	0.558140	+	0.829747i	$0.311515\pi$
$230$	9291.55	0.0115816
$231$	−151924.	−0.187326
$232$	−3635.27	−0.00443422
$233$	750392.	0.905520	0.452760	−	0.891632i	$-0.350439\pi$
$233$	750392.	0.905520	0.452760	+	0.891632i	$0.350439\pi$
$234$	−56607.8	−0.0675828
$235$	−56323.7	−0.0665306
$236$	347669.	0.406337
$237$	7947.32	0.00919073
$238$	207914.	0.237926
$239$	617415.	0.699169	0.349585	−	0.936905i	$-0.386323\pi$
$239$	617415.	0.699169	0.349585	+	0.936905i	$0.386323\pi$
$240$	−205454.	−0.230243
$241$	1.20275e6	1.33393	0.666966	−	0.745088i	$-0.267593\pi$
$241$	1.20275e6	1.33393	0.666966	+	0.745088i	$0.267593\pi$
$242$	15830.9	0.0173767
$243$	−59049.0	−0.0641500
$244$	−365421.	−0.392933
$245$	66386.9	0.0706589
$246$	−183599.	−0.193434
$247$	−1.23378e6	−1.28675
$248$	−43081.3	−0.0444795
$249$	−845877.	−0.864587
$250$	16894.9	0.0170964
$251$	1.55775e6	1.56068	0.780338	−	0.625358i	$-0.215047\pi$
$251$	1.55775e6	1.56068	0.780338	+	0.625358i	$0.215047\pi$
$252$	348393.	0.345596
$253$	−41590.8	−0.0408504
$254$	−232130.	−0.225760
$255$	310121.	0.298663
$256$	686107.	0.654323
$257$	92156.0	0.0870344	0.0435172	−	0.999053i	$-0.486144\pi$
$257$	92156.0	0.0870344	0.0435172	+	0.999053i	$0.486144\pi$
$258$	−130200.	−0.121776
$259$	−1.62865e6	−1.50861
$260$	498173.	0.457033
$261$	4334.24	0.00393833
$262$	273635.	0.246274
$263$	−862122.	−0.768563	−0.384281	−	0.923216i	$-0.625551\pi$
$263$	−862122.	−0.768563	−0.384281	+	0.923216i	$0.625551\pi$
$264$	−73983.8	−0.0653321
$265$	−222518.	−0.194648
$266$	−287950.	−0.249525
$267$	−195659.	−0.167966
$268$	1.76764e6	1.50334
$269$	−1.25052e6	−1.05368	−0.526841	−	0.849964i	$-0.676624\pi$
$269$	−1.25052e6	−1.05368	−0.526841	+	0.849964i	$0.676624\pi$
$270$	−19706.2	−0.0164511
$271$	844654.	0.698644	0.349322	−	0.937003i	$-0.386412\pi$
$271$	844654.	0.698644	0.349322	+	0.937003i	$0.386412\pi$
$272$	−1.25858e6	−1.03147
$273$	−811515.	−0.659007
$274$	258855.	0.208295
$275$	−75625.0	−0.0603023
$276$	95376.2	0.0753646
$277$	−1.52990e6	−1.19802	−0.599008	−	0.800743i	$-0.704438\pi$
$277$	−1.52990e6	−1.19802	−0.599008	+	0.800743i	$0.704438\pi$
$278$	−179922.	−0.139628
$279$	51364.8	0.0395053
$280$	236945.	0.180615
$281$	1.13284e6	0.855858	0.427929	−	0.903812i	$-0.359243\pi$
$281$	1.13284e6	0.855858	0.427929	+	0.903812i	$0.359243\pi$
$282$	21924.5	0.0164175
$283$	−411138.	−0.305156	−0.152578	−	0.988291i	$-0.548758\pi$
$283$	−411138.	−0.305156	−0.152578	+	0.988291i	$0.548758\pi$
$284$	−958094.	−0.704875
$285$	−429502.	−0.313223
$286$	84562.2	0.0611310
$287$	−2.63203e6	−1.88619
$288$	256068.	0.181918
$289$	479901.	0.337993
$290$	1446.45	0.00100997
$291$	1.42253e6	0.984757
$292$	−1.72686e6	−1.18522
$293$	314013.	0.213687	0.106843	−	0.994276i	$-0.465926\pi$
$293$	314013.	0.213687	0.106843	+	0.994276i	$0.465926\pi$
$294$	−25841.7	−0.0174362
$295$	−281917.	−0.188610
$296$	−793115.	−0.526147
$297$	88209.0	0.0580259
$298$	319529.	0.208435
$299$	−222161.	−0.143711
$300$	173424.	0.111251
$301$	−1.86652e6	−1.18745
$302$	463189.	0.292241
$303$	1.41271e6	0.883988
$304$	1.74307e6	1.08176
$305$	296311.	0.182389
$306$	−120717.	−0.0736998
$307$	797600.	0.482991	0.241496	−	0.970402i	$-0.422362\pi$
$307$	797600.	0.482991	0.241496	+	0.970402i	$0.422362\pi$
$308$	−520439.	−0.312603
$309$	−1.52213e6	−0.906892
$310$	17141.8	0.0101310
$311$	−618368.	−0.362532	−0.181266	−	0.983434i	$-0.558020\pi$
$311$	−618368.	−0.362532	−0.181266	+	0.983434i	$0.558020\pi$
$312$	−395190.	−0.229837
$313$	−2.60175e6	−1.50108	−0.750541	−	0.660824i	$-0.770207\pi$
$313$	−2.60175e6	−1.50108	−0.750541	+	0.660824i	$0.770207\pi$
$314$	−312491.	−0.178860
$315$	−282504.	−0.160416
$316$	27224.7	0.0153372
$317$	−729701.	−0.407846	−0.203923	−	0.978987i	$-0.565369\pi$
$317$	−729701.	−0.407846	−0.203923	+	0.978987i	$0.565369\pi$
$318$	86617.0	0.0480325
$319$	−6474.61	−0.00356235
$320$	−645046.	−0.352140
$321$	121847.	0.0660011
$322$	−51849.8	−0.0278681
$323$	−2.63107e6	−1.40322
$324$	−202281.	−0.107052
$325$	−403957.	−0.212142
$326$	311648.	0.162413
$327$	672628.	0.347861
$328$	−1.28174e6	−0.657833
$329$	314304.	0.160089
$330$	29437.7	0.0148805
$331$	2.87129e6	1.44048	0.720239	−	0.693726i	$-0.244032\pi$
$331$	2.87129e6	1.44048	0.720239	+	0.693726i	$0.244032\pi$
$332$	−2.89768e6	−1.44280
$333$	945611.	0.467307
$334$	−195616.	−0.0959484
$335$	−1.43334e6	−0.697810
$336$	1.14650e6	0.554020
$337$	2.16558e6	1.03872	0.519361	−	0.854555i	$-0.326170\pi$
$337$	2.16558e6	1.03872	0.519361	+	0.854555i	$0.326170\pi$
$338$	50226.3	0.0239133
$339$	1.85323e6	0.875849
$340$	1.06237e6	0.498399
$341$	−76730.1	−0.0357338
$342$	167187.	0.0772927
$343$	1.97425e6	0.906081
$344$	−908953.	−0.414138
$345$	−77338.3	−0.0349822
$346$	236343.	0.106134
$347$	392930.	0.175183	0.0875913	−	0.996156i	$-0.472083\pi$
$347$	392930.	0.175183	0.0875913	+	0.996156i	$0.472083\pi$
$348$	14847.6	0.00657216
$349$	247840.	0.108920	0.0544601	−	0.998516i	$-0.482656\pi$
$349$	247840.	0.108920	0.0544601	+	0.998516i	$0.482656\pi$
$350$	−94279.0	−0.0411381
$351$	471175.	0.204134
$352$	−382522.	−0.164551
$353$	−2.90847e6	−1.24230	−0.621151	−	0.783691i	$-0.713335\pi$
$353$	−2.90847e6	−1.24230	−0.621151	+	0.783691i	$0.713335\pi$
$354$	109738.	0.0465426
$355$	776896.	0.327184
$356$	−670261.	−0.280297
$357$	−1.73058e6	−0.718655
$358$	336185.	0.138634
$359$	758403.	0.310573	0.155287	−	0.987869i	$-0.450370\pi$
$359$	758403.	0.310573	0.155287	+	0.987869i	$0.450370\pi$
$360$	−137573.	−0.0559471
$361$	1.16779e6	0.471627
$362$	−458067.	−0.183721
$363$	−131769.	−0.0524864
$364$	−2.77997e6	−1.09973
$365$	1.40027e6	0.550148
$366$	−115342.	−0.0450073
$367$	−2.29924e6	−0.891085	−0.445542	−	0.895261i	$-0.646989\pi$
$367$	−2.29924e6	−0.891085	−0.445542	+	0.895261i	$0.646989\pi$
$368$	313866.	0.120816
$369$	1.52819e6	0.584266
$370$	315575.	0.119839
$371$	1.24172e6	0.468370
$372$	175958.	0.0659251
$373$	−19163.9	−0.00713203	−0.00356601	−	0.999994i	$-0.501135\pi$
$373$	−19163.9	−0.00713203	−0.00356601	+	0.999994i	$0.501135\pi$
$374$	180331.	0.0666640
$375$	−140625.	−0.0516398
$376$	153059.	0.0558329
$377$	−34584.7	−0.0125323
$378$	109967.	0.0395852
$379$	346535.	0.123922	0.0619610	−	0.998079i	$-0.480265\pi$
$379$	346535.	0.123922	0.0619610	+	0.998079i	$0.480265\pi$
$380$	−1.47132e6	−0.522696
$381$	1.93214e6	0.681909
$382$	931073.	0.326457
$383$	−5.25066e6	−1.82901	−0.914507	−	0.404571i	$-0.867421\pi$
$383$	−5.25066e6	−1.82901	−0.914507	+	0.404571i	$0.867421\pi$
$384$	1.16155e6	0.401987
$385$	422012.	0.145102
$386$	465578.	0.159047
$387$	1.08372e6	0.367824
$388$	4.87309e6	1.64333
$389$	−4.34474e6	−1.45576	−0.727880	−	0.685704i	$-0.759494\pi$
$389$	−4.34474e6	−1.45576	−0.727880	+	0.685704i	$0.759494\pi$
$390$	157244.	0.0523494
$391$	−473763.	−0.156718
$392$	−180406.	−0.0592974
$393$	−2.27760e6	−0.743869
$394$	−199771.	−0.0648324
$395$	−22075.9	−0.00711911
$396$	302173.	0.0968318
$397$	3.90748e6	1.24429	0.622144	−	0.782903i	$-0.286262\pi$
$397$	3.90748e6	1.24429	0.622144	+	0.782903i	$0.286262\pi$
$398$	349244.	0.110515
$399$	2.39676e6	0.753689
$400$	570705.	0.178345
$401$	−3.05315e6	−0.948171	−0.474085	−	0.880479i	$-0.657221\pi$
$401$	−3.05315e6	−0.948171	−0.474085	+	0.880479i	$0.657221\pi$
$402$	557940.	0.172196
$403$	−409860.	−0.125711
$404$	4.83945e6	1.47517
$405$	164025.	0.0496904
$406$	−8071.67	−0.00243023
$407$	−1.41258e6	−0.422695
$408$	−842753.	−0.250640
$409$	−5.46050e6	−1.61408	−0.807038	−	0.590499i	$-0.798931\pi$
$409$	−5.46050e6	−1.61408	−0.807038	+	0.590499i	$0.798931\pi$
$410$	509997.	0.149833
$411$	−2.15458e6	−0.629156
$412$	−5.21428e6	−1.51339
$413$	1.57318e6	0.453842
$414$	30104.6	0.00863241
$415$	2.34966e6	0.669706
$416$	−2.04327e6	−0.578886
$417$	1.49758e6	0.421745
$418$	−249749.	−0.0699139
$419$	3.02804e6	0.842609	0.421305	−	0.906919i	$-0.361572\pi$
$419$	3.02804e6	0.842609	0.421305	+	0.906919i	$0.361572\pi$
$420$	−967759.	−0.267697
$421$	−3.31510e6	−0.911572	−0.455786	−	0.890089i	$-0.650642\pi$
$421$	−3.31510e6	−0.911572	−0.455786	+	0.890089i	$0.650642\pi$
$422$	−426136.	−0.116484
$423$	−182489.	−0.0495890
$424$	604691.	0.163350
$425$	−861448.	−0.231343
$426$	−302413.	−0.0807378
$427$	−1.65351e6	−0.438871
$428$	417404.	0.110141
$429$	−703855.	−0.184646
$430$	361667.	0.0943273
$431$	−3.02139e6	−0.783455	−0.391728	−	0.920081i	$-0.628122\pi$
$431$	−3.02139e6	−0.783455	−0.391728	+	0.920081i	$0.628122\pi$
$432$	−665670.	−0.171613
$433$	−739663.	−0.189589	−0.0947947	−	0.995497i	$-0.530219\pi$
$433$	−739663.	−0.189589	−0.0947947	+	0.995497i	$0.530219\pi$
$434$	−95656.7	−0.0243776
$435$	−12039.6	−0.00305062
$436$	2.30419e6	0.580499
$437$	656138.	0.164358
$438$	−545067.	−0.135758
$439$	89371.4	0.0221329	0.0110664	−	0.999939i	$-0.496477\pi$
$439$	89371.4	0.0221329	0.0110664	+	0.999939i	$0.496477\pi$
$440$	205511.	0.0506060
$441$	215094.	0.0526661
$442$	963252.	0.234522
$443$	5.06164e6	1.22541	0.612706	−	0.790311i	$-0.290081\pi$
$443$	5.06164e6	1.22541	0.612706	+	0.790311i	$0.290081\pi$
$444$	3.23933e6	0.779826
$445$	543498.	0.130106
$446$	481208.	0.114550
$447$	−2.65961e6	−0.629577
$448$	3.59956e6	0.847334
$449$	6.64598e6	1.55576	0.777881	−	0.628411i	$-0.216294\pi$
$449$	6.64598e6	1.55576	0.777881	+	0.628411i	$0.216294\pi$
$450$	54739.5	0.0127429
$451$	−2.28285e6	−0.528489
$452$	6.34850e6	1.46159
$453$	−3.85536e6	−0.882713
$454$	1.25306e6	0.285320
$455$	2.25421e6	0.510465
$456$	1.16717e6	0.262858
$457$	−176313.	−0.0394905	−0.0197453	−	0.999805i	$-0.506286\pi$
$457$	−176313.	−0.0394905	−0.0197453	+	0.999805i	$0.506286\pi$
$458$	957850.	0.213370
$459$	1.00479e6	0.222610
$460$	−264934.	−0.0583772
$461$	8.43740e6	1.84908	0.924542	−	0.381081i	$-0.124448\pi$
$461$	8.43740e6	1.84908	0.924542	+	0.381081i	$0.124448\pi$
$462$	−164272.	−0.0358062
$463$	5.65739e6	1.22649	0.613244	−	0.789893i	$-0.289864\pi$
$463$	5.65739e6	1.22649	0.613244	+	0.789893i	$0.289864\pi$
$464$	48860.8	0.0105357
$465$	−142680.	−0.0306006
$466$	811379.	0.173085
$467$	−2.54278e6	−0.539532	−0.269766	−	0.962926i	$-0.586946\pi$
$467$	−2.54278e6	−0.539532	−0.269766	+	0.962926i	$0.586946\pi$
$468$	1.61408e6	0.340652
$469$	7.99850e6	1.67910
$470$	−60901.4	−0.0127169
$471$	2.60102e6	0.540247
$472$	766107.	0.158283
$473$	−1.61889e6	−0.332710
$474$	8593.23	0.00175675
$475$	1.19306e6	0.242621
$476$	−5.92835e6	−1.19927
$477$	−720958.	−0.145082
$478$	667594.	0.133642
$479$	6.89136e6	1.37235	0.686177	−	0.727434i	$-0.259287\pi$
$479$	6.89136e6	1.37235	0.686177	+	0.727434i	$0.259287\pi$
$480$	−711301.	−0.140913
$481$	−7.54540e6	−1.48703
$482$	1.30051e6	0.254973
$483$	431573.	0.0841756
$484$	−451394.	−0.0875876
$485$	−3.95147e6	−0.762790
$486$	−63848.2	−0.0122619
$487$	7.89949e6	1.50930	0.754652	−	0.656125i	$-0.227806\pi$
$487$	7.89949e6	1.50930	0.754652	+	0.656125i	$0.227806\pi$
$488$	−805223.	−0.153062
$489$	−2.59401e6	−0.490568
$490$	71782.4	0.0135060
$491$	−2.29000e6	−0.428679	−0.214340	−	0.976759i	$-0.568760\pi$
$491$	−2.29000e6	−0.428679	−0.214340	+	0.976759i	$0.568760\pi$
$492$	5.23504e6	0.975005
$493$	−73752.6	−0.0136666
$494$	−1.33406e6	−0.245955
$495$	−245025.	−0.0449467
$496$	579045.	0.105684
$497$	−4.33533e6	−0.787283
$498$	−914625.	−0.165261
$499$	−5.96310e6	−1.07206	−0.536032	−	0.844198i	$-0.680077\pi$
$499$	−5.96310e6	−1.07206	−0.536032	+	0.844198i	$0.680077\pi$
$500$	−481732.	−0.0861748
$501$	1.62821e6	0.289812
$502$	1.68435e6	0.298314
$503$	2.17453e6	0.383218	0.191609	−	0.981471i	$-0.438629\pi$
$503$	2.17453e6	0.383218	0.191609	+	0.981471i	$0.438629\pi$
$504$	767702.	0.134622
$505$	−3.92420e6	−0.684734
$506$	−44971.1	−0.00780831
$507$	−418060.	−0.0722301
$508$	6.61883e6	1.13795
$509$	−3.33531e6	−0.570613	−0.285307	−	0.958436i	$-0.592095\pi$
$509$	−3.33531e6	−0.570613	−0.285307	+	0.958436i	$0.592095\pi$
$510$	335326.	0.0570876
$511$	−7.81395e6	−1.32379
$512$	4.87184e6	0.821331
$513$	−1.39159e6	−0.233462
$514$	99645.9	0.0166361
$515$	4.22814e6	0.702475
$516$	3.71245e6	0.613814
$517$	272607.	0.0448549
$518$	−1.76101e6	−0.288362
$519$	−1.96721e6	−0.320577
$520$	1.09775e6	0.178031
$521$	9.81327e6	1.58387	0.791935	−	0.610605i	$-0.209074\pi$
$521$	9.81327e6	1.58387	0.791935	+	0.610605i	$0.209074\pi$
$522$	4686.51	0.000752789 0
$523$	7.96466e6	1.27325	0.636624	−	0.771175i	$-0.280330\pi$
$523$	7.96466e6	1.27325	0.636624	+	0.771175i	$0.280330\pi$
$524$	−7.80227e6	−1.24134
$525$	784732.	0.124258
$526$	−932190.	−0.146906
$527$	−874036.	−0.137089
$528$	994397.	0.155230
$529$	−6.31820e6	−0.981644
$530$	−240603.	−0.0372058
$531$	−913410.	−0.140582
$532$	8.21046e6	1.25773
$533$	−1.21940e7	−1.85921
$534$	−211561.	−0.0321058
$535$	−338463.	−0.0511243
$536$	3.89509e6	0.585607
$537$	−2.79824e6	−0.418745
$538$	−1.35215e6	−0.201405
$539$	−321313.	−0.0476383
$540$	561892.	0.0829218
$541$	−5.50616e6	−0.808827	−0.404413	−	0.914576i	$-0.632524\pi$
$541$	−5.50616e6	−0.808827	−0.404413	+	0.914576i	$0.632524\pi$
$542$	913303.	0.133542
$543$	3.81273e6	0.554928
$544$	−4.35733e6	−0.631281
$545$	−1.86841e6	−0.269452
$546$	−877470.	−0.125965
$547$	2.92918e6	0.418580	0.209290	−	0.977854i	$-0.432885\pi$
$547$	2.92918e6	0.418580	0.209290	+	0.977854i	$0.432885\pi$
$548$	−7.38084e6	−1.04992
$549$	960047.	0.135945
$550$	−81771.4	−0.0115264
$551$	102144.	0.0143328
$552$	210167.	0.0293573
$553$	123191.	0.0171303
$554$	−1.65424e6	−0.228994
$555$	−2.62670e6	−0.361974
$556$	5.13018e6	0.703795
$557$	4.05453e6	0.553736	0.276868	−	0.960908i	$-0.410704\pi$
$557$	4.05453e6	0.553736	0.276868	+	0.960908i	$0.410704\pi$
$558$	55539.4	0.00755120
$559$	−8.64745e6	−1.17047
$560$	−3.18472e6	−0.429142
$561$	−1.50099e6	−0.201358
$562$	1.22491e6	0.163592
$563$	−1.65845e6	−0.220512	−0.110256	−	0.993903i	$-0.535167\pi$
$563$	−1.65845e6	−0.220512	−0.110256	+	0.993903i	$0.535167\pi$
$564$	−625143.	−0.0827526
$565$	−5.14785e6	−0.678430
$566$	−444553.	−0.0583288
$567$	−915312.	−0.119567
$568$	−2.11121e6	−0.274575
$569$	1.05475e7	1.36575	0.682873	−	0.730537i	$-0.260730\pi$
$569$	1.05475e7	1.36575	0.682873	+	0.730537i	$0.260730\pi$
$570$	−464410.	−0.0598707
$571$	−1.46769e7	−1.88384	−0.941918	−	0.335843i	$-0.890979\pi$
$571$	−1.46769e7	−1.88384	−0.941918	+	0.335843i	$0.890979\pi$
$572$	−2.41116e6	−0.308131
$573$	−7.74980e6	−0.986062
$574$	−2.84595e6	−0.360534
$575$	214829.	0.0270971
$576$	−2.08995e6	−0.262470
$577$	−8.25271e6	−1.03195	−0.515973	−	0.856605i	$-0.672570\pi$
$577$	−8.25271e6	−1.03195	−0.515973	+	0.856605i	$0.672570\pi$
$578$	518905.	0.0646053
$579$	−3.87525e6	−0.480400
$580$	−41243.3	−0.00509078
$581$	−1.31118e7	−1.61147
$582$	1.53815e6	0.188230
$583$	1.07699e6	0.131232
$584$	−3.80522e6	−0.461687
$585$	−1.30882e6	−0.158121
$586$	339534.	0.0408450
$587$	1.01063e7	1.21059	0.605296	−	0.796000i	$-0.293055\pi$
$587$	1.01063e7	1.21059	0.605296	+	0.796000i	$0.293055\pi$
$588$	736835.	0.0878875
$589$	1.21050e6	0.143772
$590$	−304829.	−0.0360517
$591$	1.66280e6	0.195826
$592$	1.06600e7	1.25013
$593$	1.48922e7	1.73909	0.869543	−	0.493857i	$-0.164413\pi$
$593$	1.48922e7	1.73909	0.869543	+	0.493857i	$0.164413\pi$
$594$	95378.1	0.0110913
$595$	4.80716e6	0.556667
$596$	−9.11088e6	−1.05062
$597$	−2.90694e6	−0.333811
$598$	−240217.	−0.0274695
$599$	1.59013e7	1.81078	0.905390	−	0.424580i	$-0.139578\pi$
$599$	1.59013e7	1.81078	0.905390	+	0.424580i	$0.139578\pi$
$600$	382148.	0.0433364
$601$	−2.84828e6	−0.321660	−0.160830	−	0.986982i	$-0.551417\pi$
$601$	−2.84828e6	−0.321660	−0.160830	+	0.986982i	$0.551417\pi$
$602$	−2.01822e6	−0.226974
$603$	−4.64402e6	−0.520117
$604$	−1.32071e7	−1.47304
$605$	366025.	0.0406558
$606$	1.52753e6	0.168969
$607$	1.32016e6	0.145430	0.0727149	−	0.997353i	$-0.476834\pi$
$607$	1.32016e6	0.145430	0.0727149	+	0.997353i	$0.476834\pi$
$608$	6.03467e6	0.662056
$609$	67184.6	0.00734052
$610$	320393.	0.0348625
$611$	1.45615e6	0.157799
$612$	3.44207e6	0.371485
$613$	−978527.	−0.105177	−0.0525886	−	0.998616i	$-0.516747\pi$
$613$	−978527.	−0.105177	−0.0525886	+	0.998616i	$0.516747\pi$
$614$	862424.	0.0923209
$615$	−4.24497e6	−0.452571
$616$	−1.14681e6	−0.121770
$617$	1.29643e7	1.37100	0.685500	−	0.728073i	$-0.259584\pi$
$617$	1.29643e7	1.37100	0.685500	+	0.728073i	$0.259584\pi$
$618$	−1.64584e6	−0.173347
$619$	1.27406e7	1.33648	0.668240	−	0.743946i	$-0.267048\pi$
$619$	1.27406e7	1.33648	0.668240	+	0.743946i	$0.267048\pi$
$620$	−488771.	−0.0510654
$621$	−250576.	−0.0260742
$622$	−668626.	−0.0692958
$623$	−3.03289e6	−0.313067
$624$	5.31165e6	0.546095
$625$	390625.	0.0400000
$626$	−2.81320e6	−0.286923
$627$	2.07879e6	0.211175
$628$	8.91020e6	0.901547
$629$	−1.60908e7	−1.62162
$630$	−305464.	−0.0306626
$631$	−1.93988e7	−1.93955	−0.969775	−	0.243999i	$-0.921541\pi$
$631$	−1.93988e7	−1.93955	−0.969775	+	0.243999i	$0.921541\pi$
$632$	59991.1	0.00597440
$633$	3.54695e6	0.351840
$634$	−789006.	−0.0779574
$635$	−5.36706e6	−0.528204
$636$	−2.46975e6	−0.242108
$637$	−1.71632e6	−0.167590
$638$	−7000.83	−0.000680923 0
$639$	2.51714e6	0.243868
$640$	−3.22654e6	−0.311378
$641$	6.77844e6	0.651605	0.325803	−	0.945438i	$-0.394366\pi$
$641$	6.77844e6	0.651605	0.325803	+	0.945438i	$0.394366\pi$
$642$	131750.	0.0126157
$643$	−1.74257e7	−1.66212	−0.831060	−	0.556182i	$-0.812266\pi$
$643$	−1.74257e7	−1.66212	−0.831060	+	0.556182i	$0.812266\pi$
$644$	1.47842e6	0.140470
$645$	−3.01034e6	−0.284915
$646$	−2.84491e6	−0.268217
$647$	792517.	0.0744300	0.0372150	−	0.999307i	$-0.488151\pi$
$647$	792517.	0.0744300	0.0372150	+	0.999307i	$0.488151\pi$
$648$	−445737.	−0.0417005
$649$	1.36448e6	0.127161
$650$	−436788.	−0.0405497
$651$	796200.	0.0736325
$652$	−8.88616e6	−0.818644
$653$	−9.09663e6	−0.834829	−0.417414	−	0.908716i	$-0.637064\pi$
$653$	−9.09663e6	−0.834829	−0.417414	+	0.908716i	$0.637064\pi$
$654$	727295.	0.0664915
$655$	6.32667e6	0.576198
$656$	1.72275e7	1.56302
$657$	4.53687e6	0.410056
$658$	339849.	0.0306000
$659$	−8.15992e6	−0.731935	−0.365968	−	0.930628i	$-0.619262\pi$
$659$	−8.15992e6	−0.731935	−0.365968	+	0.930628i	$0.619262\pi$
$660$	−839370.	−0.0750056
$661$	−1.85172e6	−0.164843	−0.0824216	−	0.996598i	$-0.526265\pi$
$661$	−1.85172e6	−0.164843	−0.0824216	+	0.996598i	$0.526265\pi$
$662$	3.10465e6	0.275339
$663$	−8.01765e6	−0.708375
$664$	−6.38518e6	−0.562022
$665$	−6.65766e6	−0.583805
$666$	1.02246e6	0.0893229
$667$	18392.5	0.00160076
$668$	5.57768e6	0.483629
$669$	−4.00534e6	−0.345998
$670$	−1.54983e6	−0.133382
$671$	−1.43414e6	−0.122966
$672$	3.96929e6	0.339070
$673$	1.42740e6	0.121481	0.0607405	−	0.998154i	$-0.480654\pi$
$673$	1.42740e6	0.121481	0.0607405	+	0.998154i	$0.480654\pi$
$674$	2.34158e6	0.198545
$675$	−455625.	−0.0384900
$676$	−1.43213e6	−0.120535
$677$	941868.	0.0789802	0.0394901	−	0.999220i	$-0.487427\pi$
$677$	941868.	0.0789802	0.0394901	+	0.999220i	$0.487427\pi$
$678$	2.00385e6	0.167413
$679$	2.20505e7	1.83545
$680$	2.34098e6	0.194145
$681$	−1.04299e7	−0.861809
$682$	−82966.3	−0.00683031
$683$	9.56089e6	0.784236	0.392118	−	0.919915i	$-0.371743\pi$
$683$	9.56089e6	0.784236	0.392118	+	0.919915i	$0.371743\pi$
$684$	−4.76709e6	−0.389595
$685$	5.98494e6	0.487342
$686$	2.13471e6	0.173192
$687$	−7.97268e6	−0.644484
$688$	1.22170e7	0.983996
$689$	5.75281e6	0.461670
$690$	−83623.9	−0.00668664
$691$	−1.53765e7	−1.22507	−0.612536	−	0.790443i	$-0.709851\pi$
$691$	−1.53765e7	−1.22507	−0.612536	+	0.790443i	$0.709851\pi$
$692$	−6.73897e6	−0.534968
$693$	1.36732e6	0.108152
$694$	424865.	0.0334851
$695$	−4.15994e6	−0.326682
$696$	32717.5	0.00256010
$697$	−2.60040e7	−2.02749
$698$	267983.	0.0208194
$699$	−6.75352e6	−0.522802
$700$	2.68822e6	0.207357
$701$	1.72261e7	1.32401	0.662006	−	0.749499i	$-0.269705\pi$
$701$	1.72261e7	1.32401	0.662006	+	0.749499i	$0.269705\pi$
$702$	509470.	0.0390190
$703$	2.22849e7	1.70068
$704$	3.12202e6	0.237413
$705$	506914.	0.0384115
$706$	−3.14485e6	−0.237459
$707$	2.18983e7	1.64764
$708$	−3.12902e6	−0.234599
$709$	2.47878e7	1.85192	0.925959	−	0.377625i	$-0.123259\pi$
$709$	2.47878e7	1.85192	0.925959	+	0.377625i	$0.123259\pi$
$710$	840037.	0.0625393
$711$	−71525.9	−0.00530627
$712$	−1.47695e6	−0.109186
$713$	217968.	0.0160572
$714$	−1.87123e6	−0.137367
$715$	1.95515e6	0.143026
$716$	−9.58579e6	−0.698788
$717$	−5.55673e6	−0.403665
$718$	820042.	0.0593642
$719$	7.44502e6	0.537086	0.268543	−	0.963268i	$-0.413458\pi$
$719$	7.44502e6	0.537086	0.268543	+	0.963268i	$0.413458\pi$
$720$	1.84908e6	0.132931
$721$	−2.35944e7	−1.69032
$722$	1.26271e6	0.0901486
$723$	−1.08248e7	−0.770146
$724$	1.30611e7	0.926046
$725$	33443.2	0.00236300
$726$	−142478.	−0.0100325
$727$	3.56658e6	0.250274	0.125137	−	0.992139i	$-0.460063\pi$
$727$	3.56658e6	0.250274	0.125137	+	0.992139i	$0.460063\pi$
$728$	−6.12580e6	−0.428385
$729$	531441.	0.0370370
$730$	1.51407e6	0.105157
$731$	−1.84409e7	−1.27641
$732$	3.28879e6	0.226860
$733$	1.38091e7	0.949305	0.474652	−	0.880173i	$-0.342574\pi$
$733$	1.38091e7	0.949305	0.474652	+	0.880173i	$0.342574\pi$
$734$	−2.48611e6	−0.170326
$735$	−597482.	−0.0407950
$736$	1.08663e6	0.0739416
$737$	6.93737e6	0.470463
$738$	1.65239e6	0.111679
$739$	−7.18607e6	−0.484039	−0.242020	−	0.970271i	$-0.577810\pi$
$739$	−7.18607e6	−0.484039	−0.242020	+	0.970271i	$0.577810\pi$
$740$	−8.99814e6	−0.604051
$741$	1.11040e7	0.742908
$742$	1.34264e6	0.0895261
$743$	2.18843e6	0.145432	0.0727161	−	0.997353i	$-0.476833\pi$
$743$	2.18843e6	0.145432	0.0727161	+	0.997353i	$0.476833\pi$
$744$	387732.	0.0256803
$745$	7.38780e6	0.487668
$746$	−20721.5	−0.00136324
$747$	7.61289e6	0.499170
$748$	−5.14186e6	−0.336021
$749$	1.88873e6	0.123017
$750$	−152054.	−0.00987064
$751$	−1.41771e6	−0.0917250	−0.0458625	−	0.998948i	$-0.514604\pi$
$751$	−1.41771e6	−0.0917250	−0.0458625	+	0.998948i	$0.514604\pi$
$752$	−2.05723e6	−0.132660
$753$	−1.40197e7	−0.901056
$754$	−37395.5	−0.00239547
$755$	1.07093e7	0.683746
$756$	−3.13554e6	−0.199530
$757$	−2.05513e7	−1.30347	−0.651734	−	0.758448i	$-0.725958\pi$
$757$	−2.05513e7	−1.30347	−0.651734	+	0.758448i	$0.725958\pi$
$758$	374699.	0.0236870
$759$	374318.	0.0235850
$760$	−3.24214e6	−0.203609
$761$	−1.30587e7	−0.817409	−0.408705	−	0.912667i	$-0.634019\pi$
$761$	−1.30587e7	−0.817409	−0.408705	+	0.912667i	$0.634019\pi$
$762$	2.08917e6	0.130343
$763$	1.04263e7	0.648366
$764$	−2.65481e7	−1.64551
$765$	−2.79109e6	−0.172433
$766$	−5.67740e6	−0.349605
$767$	7.28846e6	0.447350
$768$	−6.17497e6	−0.377774
$769$	1.82667e7	1.11389	0.556946	−	0.830549i	$-0.311973\pi$
$769$	1.82667e7	1.11389	0.556946	+	0.830549i	$0.311973\pi$
$770$	456310.	0.0277353
$771$	−829404.	−0.0502493
$772$	−1.32752e7	−0.801676
$773$	−1.49182e7	−0.897981	−0.448990	−	0.893537i	$-0.648216\pi$
$773$	−1.49182e7	−0.897981	−0.448990	+	0.893537i	$0.648216\pi$
$774$	1.17180e6	0.0703074
$775$	396333.	0.0237032
$776$	1.07381e7	0.640138
$777$	1.46578e7	0.870996
$778$	−4.69786e6	−0.278260
$779$	3.60143e7	2.12633
$780$	−4.48356e6	−0.263868
$781$	−3.76018e6	−0.220587
$782$	−512268.	−0.0299558
$783$	−39008.2	−0.00227380
$784$	2.42479e6	0.140891
$785$	−7.22507e6	−0.418473
$786$	−2.46271e6	−0.142186
$787$	−1.60565e7	−0.924087	−0.462043	−	0.886857i	$-0.652884\pi$
$787$	−1.60565e7	−0.924087	−0.462043	+	0.886857i	$0.652884\pi$
$788$	5.69616e6	0.326788
$789$	7.75910e6	0.443730
$790$	−23870.1	−0.00136078
$791$	2.87266e7	1.63246
$792$	665854.	0.0377195
$793$	−7.66060e6	−0.432593
$794$	4.22506e6	0.237838
$795$	2.00266e6	0.112380
$796$	−9.95816e6	−0.557053
$797$	2.10741e7	1.17518	0.587588	−	0.809160i	$-0.300078\pi$
$797$	2.10741e7	1.17518	0.587588	+	0.809160i	$0.300078\pi$
$798$	2.59155e6	0.144063
$799$	3.10528e6	0.172081
$800$	1.97584e6	0.109151
$801$	1.76093e6	0.0969755
$802$	−3.30129e6	−0.181237
$803$	−6.77730e6	−0.370909
$804$	−1.59088e7	−0.867955
$805$	−1.19881e6	−0.0652021
$806$	−443171.	−0.0240289
$807$	1.12547e7	0.608344
$808$	1.06640e7	0.574633
$809$	2.38181e7	1.27949	0.639744	−	0.768588i	$-0.279040\pi$
$809$	2.38181e7	1.27949	0.639744	+	0.768588i	$0.279040\pi$
$810$	177356.	0.00949802
$811$	2.93046e7	1.56453	0.782264	−	0.622947i	$-0.214065\pi$
$811$	2.93046e7	1.56453	0.782264	+	0.622947i	$0.214065\pi$
$812$	230151.	0.0122496
$813$	−7.60189e6	−0.403362
$814$	−1.52739e6	−0.0807956
$815$	7.20557e6	0.379992
$816$	1.13272e7	0.595522
$817$	2.55397e7	1.33863
$818$	−5.90430e6	−0.308521
$819$	7.30364e6	0.380478
$820$	−1.45418e7	−0.755236
$821$	−3.14594e6	−0.162889	−0.0814446	−	0.996678i	$-0.525953\pi$
$821$	−3.14594e6	−0.162889	−0.0814446	+	0.996678i	$0.525953\pi$
$822$	−2.32969e6	−0.120259
$823$	2.44990e7	1.26081	0.630404	−	0.776267i	$-0.282889\pi$
$823$	2.44990e7	1.26081	0.630404	+	0.776267i	$0.282889\pi$
$824$	−1.14899e7	−0.589522
$825$	680625.	0.0348155
$826$	1.70104e6	0.0867492
$827$	1.34163e7	0.682135	0.341067	−	0.940039i	$-0.389212\pi$
$827$	1.34163e7	0.682135	0.341067	+	0.940039i	$0.389212\pi$
$828$	−858386.	−0.0435118
$829$	1.42349e7	0.719394	0.359697	−	0.933069i	$-0.382880\pi$
$829$	1.42349e7	0.719394	0.359697	+	0.933069i	$0.382880\pi$
$830$	2.54062e6	0.128010
$831$	1.37691e7	0.691675
$832$	1.66765e7	0.835213
$833$	−3.66009e6	−0.182759
$834$	1.61929e6	0.0806140
$835$	−4.52281e6	−0.224487
$836$	7.12121e6	0.352402
$837$	−462283.	−0.0228084
$838$	3.27414e6	0.161060
$839$	1.15794e7	0.567913	0.283957	−	0.958837i	$-0.408353\pi$
$839$	1.15794e7	0.567913	0.283957	+	0.958837i	$0.408353\pi$
$840$	−2.13251e6	−0.104278
$841$	−2.05083e7	−0.999860
$842$	−3.58453e6	−0.174242
$843$	−1.01955e7	−0.494130
$844$	1.21506e7	0.587140
$845$	1.16128e6	0.0559492
$846$	−197320.	−0.00947865
$847$	−2.04254e6	−0.0978276
$848$	−8.12749e6	−0.388121
$849$	3.70025e6	0.176182
$850$	−931462.	−0.0442199
$851$	4.01273e6	0.189940
$852$	8.62285e6	0.406960
$853$	6.61595e6	0.311329	0.155664	−	0.987810i	$-0.450248\pi$
$853$	6.61595e6	0.311329	0.155664	+	0.987810i	$0.450248\pi$
$854$	−1.78790e6	−0.0838876
$855$	3.86552e6	0.180839
$856$	919772.	0.0429038
$857$	−9.97147e6	−0.463775	−0.231887	−	0.972743i	$-0.574490\pi$
$857$	−9.97147e6	−0.463775	−0.231887	+	0.972743i	$0.574490\pi$
$858$	−761060.	−0.0352940
$859$	−3.79757e7	−1.75599	−0.877996	−	0.478667i	$-0.841120\pi$
$859$	−3.79757e7	−1.75599	−0.877996	+	0.478667i	$0.841120\pi$
$860$	−1.03124e7	−0.475458
$861$	2.36883e7	1.08899
$862$	−3.26695e6	−0.149753
$863$	8.18531e6	0.374118	0.187059	−	0.982349i	$-0.440104\pi$
$863$	8.18531e6	0.374118	0.187059	+	0.982349i	$0.440104\pi$
$864$	−2.30462e6	−0.105030
$865$	5.46447e6	0.248318
$866$	−799779.	−0.0362389
$867$	−4.31911e6	−0.195140
$868$	2.72750e6	0.122876
$869$	106847.	0.00479970
$870$	−13018.1	−0.000583108 0
$871$	3.70565e7	1.65508
$872$	5.07740e6	0.226126
$873$	−1.28028e7	−0.568550
$874$	709465.	0.0314161
$875$	−2.17981e6	−0.0962496
$876$	1.55417e7	0.684288
$877$	−3.02517e7	−1.32816	−0.664081	−	0.747660i	$-0.731177\pi$
$877$	−3.02517e7	−1.32816	−0.664081	+	0.747660i	$0.731177\pi$
$878$	96635.0	0.00423056
$879$	−2.82611e6	−0.123372
$880$	−2.76221e6	−0.120240
$881$	6.11414e6	0.265397	0.132698	−	0.991156i	$-0.457636\pi$
$881$	6.11414e6	0.265397	0.132698	+	0.991156i	$0.457636\pi$
$882$	232575.	0.0100668
$883$	−7.72672e6	−0.333498	−0.166749	−	0.985999i	$-0.553327\pi$
$883$	−7.72672e6	−0.333498	−0.166749	+	0.985999i	$0.553327\pi$
$884$	−2.74656e7	−1.18211
$885$	2.53725e6	0.108894
$886$	5.47302e6	0.234230
$887$	−2.48274e7	−1.05955	−0.529775	−	0.848138i	$-0.677724\pi$
$887$	−2.48274e7	−1.05955	−0.529775	+	0.848138i	$0.677724\pi$
$888$	7.13803e6	0.303771
$889$	2.99499e7	1.27099
$890$	587671.	0.0248690
$891$	−793881.	−0.0335013
$892$	−1.37209e7	−0.577391
$893$	−4.30065e6	−0.180470
$894$	−2.87576e6	−0.120340
$895$	7.77289e6	0.324358
$896$	1.80051e7	0.749249
$897$	1.99945e6	0.0829715
$898$	7.18613e6	0.297375
$899$	33931.9	0.00140026
$900$	−1.56081e6	−0.0642309
$901$	1.22680e7	0.503457
$902$	−2.46838e6	−0.101017
$903$	1.67987e7	0.685575
$904$	1.39893e7	0.569342
$905$	−1.05909e7	−0.429845
$906$	−4.16870e6	−0.168725
$907$	−3.64608e6	−0.147166	−0.0735831	−	0.997289i	$-0.523443\pi$
$907$	−3.64608e6	−0.147166	−0.0735831	+	0.997289i	$0.523443\pi$
$908$	−3.57291e7	−1.43816
$909$	−1.27144e7	−0.510371
$910$	2.43742e6	0.0975723
$911$	−1.15898e7	−0.462678	−0.231339	−	0.972873i	$-0.574311\pi$
$911$	−1.15898e7	−0.462678	−0.231339	+	0.972873i	$0.574311\pi$
$912$	−1.56876e7	−0.624554
$913$	−1.13723e7	−0.451516
$914$	−190642.	−0.00754838
$915$	−2.66680e6	−0.105302
$916$	−2.73116e7	−1.07550
$917$	−3.53048e7	−1.38647
$918$	1.08646e6	0.0425506
$919$	−3.48544e7	−1.36135	−0.680674	−	0.732586i	$-0.738313\pi$
$919$	−3.48544e7	−1.36135	−0.680674	+	0.732586i	$0.738313\pi$
$920$	−583796.	−0.0227401
$921$	−7.17840e6	−0.278855
$922$	9.12314e6	0.353441
$923$	−2.00853e7	−0.776021
$924$	4.68395e6	0.180481
$925$	7.29638e6	0.280384
$926$	6.11719e6	0.234436
$927$	1.36992e7	0.523594
$928$	169161.	0.00644806
$929$	−4.11213e7	−1.56325	−0.781624	−	0.623750i	$-0.785608\pi$
$929$	−4.11213e7	−1.56325	−0.781624	+	0.623750i	$0.785608\pi$
$930$	−154276.	−0.00584913
$931$	5.06903e6	0.191669
$932$	−2.31352e7	−0.872436
$933$	5.56532e6	0.209308
$934$	−2.74945e6	−0.103128
$935$	4.16941e6	0.155972
$936$	3.55671e6	0.132696
$937$	−1.53222e6	−0.0570126	−0.0285063	−	0.999594i	$-0.509075\pi$
$937$	−1.53222e6	−0.0570126	−0.0285063	+	0.999594i	$0.509075\pi$
$938$	8.64857e6	0.320950
$939$	2.34157e7	0.866650
$940$	1.73651e6	0.0640999
$941$	−1.91551e7	−0.705196	−0.352598	−	0.935775i	$-0.614702\pi$
$941$	−1.91551e7	−0.705196	−0.352598	+	0.935775i	$0.614702\pi$
$942$	2.81242e6	0.103265
$943$	6.48491e6	0.237479
$944$	−1.02970e7	−0.376082
$945$	2.54253e6	0.0926162
$946$	−1.75047e6	−0.0635955
$947$	2.83184e7	1.02611	0.513054	−	0.858356i	$-0.328514\pi$
$947$	2.83184e7	1.02611	0.513054	+	0.858356i	$0.328514\pi$
$948$	−245023.	−0.00885494
$949$	−3.62015e7	−1.30485
$950$	1.29003e6	0.0463756
$951$	6.56731e6	0.235470
$952$	−1.30634e7	−0.467159
$953$	−5.47682e7	−1.95342	−0.976711	−	0.214559i	$-0.931169\pi$
$953$	−5.47682e7	−1.95342	−0.976711	+	0.214559i	$0.931169\pi$
$954$	−779553.	−0.0277316
$955$	2.15272e7	0.763800
$956$	−1.90354e7	−0.673624
$957$	58271.5	0.00205673
$958$	7.45145e6	0.262318
$959$	−3.33979e7	−1.17266
$960$	5.80541e6	0.203308
$961$	−2.82270e7	−0.985954
$962$	−8.15865e6	−0.284237
$963$	−1.09662e6	−0.0381058
$964$	−3.70819e7	−1.28520
$965$	1.07646e7	0.372116
$966$	466648.	0.0160897
$967$	2.29671e7	0.789843	0.394922	−	0.918715i	$-0.370772\pi$
$967$	2.29671e7	0.789843	0.394922	+	0.918715i	$0.370772\pi$
$968$	−994671.	−0.0341186
$969$	2.36796e7	0.810149
$970$	−4.27263e6	−0.145803
$971$	1.46281e7	0.497898	0.248949	−	0.968517i	$-0.419915\pi$
$971$	1.46281e7	0.497898	0.248949	+	0.968517i	$0.419915\pi$
$972$	1.82053e6	0.0618062
$973$	2.32138e7	0.786076
$974$	8.54152e6	0.288495
$975$	3.63561e6	0.122480
$976$	1.08228e7	0.363676
$977$	−1.54714e7	−0.518552	−0.259276	−	0.965803i	$-0.583484\pi$
$977$	−1.54714e7	−0.518552	−0.259276	+	0.965803i	$0.583484\pi$
$978$	−2.80483e6	−0.0937691
$979$	−2.63053e6	−0.0877176
$980$	−2.04676e6	−0.0680773
$981$	−6.05365e6	−0.200838
$982$	−2.47612e6	−0.0819395
$983$	2.02694e7	0.669047	0.334524	−	0.942387i	$-0.391425\pi$
$983$	2.02694e7	0.669047	0.334524	+	0.942387i	$0.391425\pi$
$984$	1.15357e7	0.379800
$985$	−4.61888e6	−0.151686
$986$	−79746.8	−0.00261229
$987$	−2.82874e6	−0.0924272
$988$	3.80385e7	1.23974
$989$	4.59881e6	0.149505
$990$	−264939.	−0.00859129
$991$	−4.43452e7	−1.43437	−0.717187	−	0.696881i	$-0.754570\pi$
$991$	−4.43452e7	−1.43437	−0.717187	+	0.696881i	$0.754570\pi$
$992$	2.00471e6	0.0646803
$993$	−2.58416e7	−0.831661
$994$	−4.68768e6	−0.150484
$995$	8.07483e6	0.258569
$996$	2.60791e7	0.832998
$997$	2.32293e7	0.740112	0.370056	−	0.929009i	$-0.379338\pi$
$997$	2.32293e7	0.740112	0.370056	+	0.929009i	$0.379338\pi$
$998$	−6.44775e6	−0.204919
$999$	−8.51050e6	−0.269800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.d.1.2	✓	3
3.2	odd	2		495.6.a.c.1.2		3
5.4	even	2		825.6.a.h.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.d.1.2	✓	3	1.1	even	1	trivial
495.6.a.c.1.2		3	3.2	odd	2
825.6.a.h.1.2		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q+1.08127 q^{2} -9.00000 q^{3} -30.8308 q^{4} +25.0000 q^{5} -9.73147 q^{6} -139.508 q^{7} -67.9374 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+1.08127 q^{2} -9.00000 q^{3} -30.8308 q^{4} +25.0000 q^{5} -9.73147 q^{6} -139.508 q^{7} -67.9374 q^{8} +81.0000 q^{9} +27.0319 q^{10} -121.000 q^{11} +277.478 q^{12} -646.331 q^{13} -150.846 q^{14} -225.000 q^{15} +913.128 q^{16} -1378.32 q^{17} +87.5832 q^{18} +1908.90 q^{19} -770.771 q^{20} +1255.57 q^{21} -130.834 q^{22} +343.726 q^{23} +611.436 q^{24} +625.000 q^{25} -698.861 q^{26} -729.000 q^{27} +4301.15 q^{28} +53.5092 q^{29} -243.287 q^{30} +634.133 q^{31} +3161.34 q^{32} +1089.00 q^{33} -1490.34 q^{34} -3487.70 q^{35} -2497.30 q^{36} +11674.2 q^{37} +2064.04 q^{38} +5816.98 q^{39} -1698.43 q^{40} +18866.5 q^{41} +1357.62 q^{42} +13379.3 q^{43} +3730.53 q^{44} +2025.00 q^{45} +371.662 q^{46} -2252.95 q^{47} -8218.15 q^{48} +2655.48 q^{49} +675.796 q^{50} +12404.9 q^{51} +19926.9 q^{52} -8900.71 q^{53} -788.249 q^{54} -3025.00 q^{55} +9477.80 q^{56} -17180.1 q^{57} +57.8581 q^{58} -11276.7 q^{59} +6936.94 q^{60} +11852.4 q^{61} +685.672 q^{62} -11300.1 q^{63} -25801.8 q^{64} -16158.3 q^{65} +1177.51 q^{66} -57333.6 q^{67} +42494.7 q^{68} -3093.53 q^{69} -3771.16 q^{70} +31075.8 q^{71} -5502.93 q^{72} +56010.8 q^{73} +12623.0 q^{74} -5625.00 q^{75} -58853.0 q^{76} +16880.5 q^{77} +6289.75 q^{78} -883.036 q^{79} +22828.2 q^{80} +6561.00 q^{81} +20399.9 q^{82} +93986.3 q^{83} -38710.3 q^{84} -34457.9 q^{85} +14466.7 q^{86} -481.583 q^{87} +8220.42 q^{88} +21739.9 q^{89} +2189.58 q^{90} +90168.4 q^{91} -10597.4 q^{92} -5707.20 q^{93} -2436.06 q^{94} +47722.5 q^{95} -28452.0 q^{96} -158059. q^{97} +2871.30 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} - 363 q^{11} + 180 q^{12} - 546 q^{13} - 8 q^{14} - 675 q^{15} - 1360 q^{16} - 314 q^{17} + 162 q^{18} + 1808 q^{19} - 500 q^{20} - 1368 q^{21} - 242 q^{22} + 4288 q^{23} + 216 q^{24} + 1875 q^{25} + 812 q^{26} - 2187 q^{27} + 5888 q^{28} + 5582 q^{29} - 450 q^{30} + 6328 q^{31} - 736 q^{32} + 3267 q^{33} + 11596 q^{34} + 3800 q^{35} - 1620 q^{36} + 16866 q^{37} + 9584 q^{38} + 4914 q^{39} - 600 q^{40} + 23282 q^{41} + 72 q^{42} + 20572 q^{43} + 2420 q^{44} + 6075 q^{45} + 16592 q^{46} + 3432 q^{47} + 12240 q^{48} + 11531 q^{49} + 1250 q^{50} + 2826 q^{51} + 21816 q^{52} + 16138 q^{53} - 1458 q^{54} - 9075 q^{55} + 15648 q^{56} - 16272 q^{57} + 17460 q^{58} + 21972 q^{59} + 4500 q^{60} + 8322 q^{61} + 5056 q^{62} + 12312 q^{63} + 22208 q^{64} - 13650 q^{65} + 2178 q^{66} - 84332 q^{67} + 59832 q^{68} - 38592 q^{69} - 200 q^{70} + 50528 q^{71} - 1944 q^{72} - 53838 q^{73} + 79212 q^{74} - 16875 q^{75} - 52448 q^{76} - 18392 q^{77} - 7308 q^{78} + 6364 q^{79} - 34000 q^{80} + 19683 q^{81} - 68020 q^{82} + 96272 q^{83} - 52992 q^{84} - 7850 q^{85} + 143152 q^{86} - 50238 q^{87} + 2904 q^{88} - 38938 q^{89} + 4050 q^{90} + 104968 q^{91} + 24000 q^{92} - 56952 q^{93} + 49088 q^{94} + 45200 q^{95} + 6624 q^{96} - 103242 q^{97} + 9554 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 - 363 * q^11 + 180 * q^12 - 546 * q^13 - 8 * q^14 - 675 * q^15 - 1360 * q^16 - 314 * q^17 + 162 * q^18 + 1808 * q^19 - 500 * q^20 - 1368 * q^21 - 242 * q^22 + 4288 * q^23 + 216 * q^24 + 1875 * q^25 + 812 * q^26 - 2187 * q^27 + 5888 * q^28 + 5582 * q^29 - 450 * q^30 + 6328 * q^31 - 736 * q^32 + 3267 * q^33 + 11596 * q^34 + 3800 * q^35 - 1620 * q^36 + 16866 * q^37 + 9584 * q^38 + 4914 * q^39 - 600 * q^40 + 23282 * q^41 + 72 * q^42 + 20572 * q^43 + 2420 * q^44 + 6075 * q^45 + 16592 * q^46 + 3432 * q^47 + 12240 * q^48 + 11531 * q^49 + 1250 * q^50 + 2826 * q^51 + 21816 * q^52 + 16138 * q^53 - 1458 * q^54 - 9075 * q^55 + 15648 * q^56 - 16272 * q^57 + 17460 * q^58 + 21972 * q^59 + 4500 * q^60 + 8322 * q^61 + 5056 * q^62 + 12312 * q^63 + 22208 * q^64 - 13650 * q^65 + 2178 * q^66 - 84332 * q^67 + 59832 * q^68 - 38592 * q^69 - 200 * q^70 + 50528 * q^71 - 1944 * q^72 - 53838 * q^73 + 79212 * q^74 - 16875 * q^75 - 52448 * q^76 - 18392 * q^77 - 7308 * q^78 + 6364 * q^79 - 34000 * q^80 + 19683 * q^81 - 68020 * q^82 + 96272 * q^83 - 52992 * q^84 - 7850 * q^85 + 143152 * q^86 - 50238 * q^87 + 2904 * q^88 - 38938 * q^89 + 4050 * q^90 + 104968 * q^91 + 24000 * q^92 - 56952 * q^93 + 49088 * q^94 + 45200 * q^95 + 6624 * q^96 - 103242 * q^97 + 9554 * q^98 - 29403 * q^99

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