LMFDB - Embedded newform 165.6.a.c.1.1

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.18257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x + 8 $ x^3 - x^2 - 26*x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.47894$ 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)

$f(q)$	$=$	$q-4.47894 q^{2} -9.00000 q^{3} -11.9391 q^{4} +25.0000 q^{5} +40.3105 q^{6} -168.818 q^{7} +196.801 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.47894 q^{2} -9.00000 q^{3} -11.9391 q^{4} +25.0000 q^{5} +40.3105 q^{6} -168.818 q^{7} +196.801 q^{8} +81.0000 q^{9} -111.974 q^{10} +121.000 q^{11} +107.452 q^{12} +290.259 q^{13} +756.126 q^{14} -225.000 q^{15} -499.408 q^{16} +623.964 q^{17} -362.794 q^{18} -398.456 q^{19} -298.477 q^{20} +1519.36 q^{21} -541.952 q^{22} +3788.06 q^{23} -1771.21 q^{24} +625.000 q^{25} -1300.06 q^{26} -729.000 q^{27} +2015.53 q^{28} +4220.43 q^{29} +1007.76 q^{30} -5594.57 q^{31} -4060.80 q^{32} -1089.00 q^{33} -2794.70 q^{34} -4220.45 q^{35} -967.065 q^{36} +301.266 q^{37} +1784.66 q^{38} -2612.33 q^{39} +4920.01 q^{40} -14636.2 q^{41} -6805.14 q^{42} +151.418 q^{43} -1444.63 q^{44} +2025.00 q^{45} -16966.5 q^{46} -13535.0 q^{47} +4494.67 q^{48} +11692.5 q^{49} -2799.34 q^{50} -5615.68 q^{51} -3465.43 q^{52} -18116.1 q^{53} +3265.15 q^{54} +3025.00 q^{55} -33223.5 q^{56} +3586.10 q^{57} -18903.0 q^{58} -50582.4 q^{59} +2686.29 q^{60} +5984.35 q^{61} +25057.8 q^{62} -13674.3 q^{63} +34169.1 q^{64} +7256.49 q^{65} +4877.57 q^{66} +22450.7 q^{67} -7449.56 q^{68} -34092.6 q^{69} +18903.2 q^{70} +10017.6 q^{71} +15940.8 q^{72} -476.148 q^{73} -1349.35 q^{74} -5625.00 q^{75} +4757.19 q^{76} -20427.0 q^{77} +11700.5 q^{78} -85024.7 q^{79} -12485.2 q^{80} +6561.00 q^{81} +65554.5 q^{82} -25643.4 q^{83} -18139.8 q^{84} +15599.1 q^{85} -678.194 q^{86} -37983.8 q^{87} +23812.9 q^{88} +1807.91 q^{89} -9069.86 q^{90} -49001.0 q^{91} -45226.0 q^{92} +50351.2 q^{93} +60622.4 q^{94} -9961.39 q^{95} +36547.2 q^{96} +11688.5 q^{97} -52370.1 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 378 q^{12} + 290 q^{13} + 916 q^{14} - 675 q^{15} - 590 q^{16} + 434 q^{17} + 162 q^{18} - 2856 q^{19} - 1050 q^{20} + 612 q^{21} + 242 q^{22} - 640 q^{23} + 216 q^{24} + 1875 q^{25} + 2132 q^{26} - 2187 q^{27} - 580 q^{28} - 4538 q^{29} - 450 q^{30} - 14968 q^{31} - 2496 q^{32} - 3267 q^{33} - 13704 q^{34} - 1700 q^{35} - 3402 q^{36} - 6190 q^{37} - 11668 q^{38} - 2610 q^{39} - 600 q^{40} - 8926 q^{41} - 8244 q^{42} - 33592 q^{43} - 5082 q^{44} + 6075 q^{45} - 35680 q^{46} - 24640 q^{47} + 5310 q^{48} - 14693 q^{49} + 1250 q^{50} - 3906 q^{51} + 18780 q^{52} - 22934 q^{53} - 1458 q^{54} + 9075 q^{55} - 40012 q^{56} + 25704 q^{57} - 32304 q^{58} - 13756 q^{59} + 9450 q^{60} + 24602 q^{61} - 7704 q^{62} - 5508 q^{63} + 35474 q^{64} + 7250 q^{65} - 2178 q^{66} + 16868 q^{67} - 71288 q^{68} + 5760 q^{69} + 22900 q^{70} + 4856 q^{71} - 1944 q^{72} + 1910 q^{73} + 29404 q^{74} - 16875 q^{75} + 6116 q^{76} - 8228 q^{77} - 19188 q^{78} - 36844 q^{79} - 14750 q^{80} + 19683 q^{81} + 84000 q^{82} - 48796 q^{83} + 5220 q^{84} + 10850 q^{85} - 83492 q^{86} + 40842 q^{87} - 2904 q^{88} - 188978 q^{89} + 4050 q^{90} - 93208 q^{91} - 6976 q^{92} + 134712 q^{93} + 70472 q^{94} - 71400 q^{95} + 22464 q^{96} + 247526 q^{97} - 154654 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 378 * q^12 + 290 * q^13 + 916 * q^14 - 675 * q^15 - 590 * q^16 + 434 * q^17 + 162 * q^18 - 2856 * q^19 - 1050 * q^20 + 612 * q^21 + 242 * q^22 - 640 * q^23 + 216 * q^24 + 1875 * q^25 + 2132 * q^26 - 2187 * q^27 - 580 * q^28 - 4538 * q^29 - 450 * q^30 - 14968 * q^31 - 2496 * q^32 - 3267 * q^33 - 13704 * q^34 - 1700 * q^35 - 3402 * q^36 - 6190 * q^37 - 11668 * q^38 - 2610 * q^39 - 600 * q^40 - 8926 * q^41 - 8244 * q^42 - 33592 * q^43 - 5082 * q^44 + 6075 * q^45 - 35680 * q^46 - 24640 * q^47 + 5310 * q^48 - 14693 * q^49 + 1250 * q^50 - 3906 * q^51 + 18780 * q^52 - 22934 * q^53 - 1458 * q^54 + 9075 * q^55 - 40012 * q^56 + 25704 * q^57 - 32304 * q^58 - 13756 * q^59 + 9450 * q^60 + 24602 * q^61 - 7704 * q^62 - 5508 * q^63 + 35474 * q^64 + 7250 * q^65 - 2178 * q^66 + 16868 * q^67 - 71288 * q^68 + 5760 * q^69 + 22900 * q^70 + 4856 * q^71 - 1944 * q^72 + 1910 * q^73 + 29404 * q^74 - 16875 * q^75 + 6116 * q^76 - 8228 * q^77 - 19188 * q^78 - 36844 * q^79 - 14750 * q^80 + 19683 * q^81 + 84000 * q^82 - 48796 * q^83 + 5220 * q^84 + 10850 * q^85 - 83492 * q^86 + 40842 * q^87 - 2904 * q^88 - 188978 * q^89 + 4050 * q^90 - 93208 * q^91 - 6976 * q^92 + 134712 * q^93 + 70472 * q^94 - 71400 * q^95 + 22464 * q^96 + 247526 * q^97 - 154654 * 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 $

$2$	−4.47894	−0.791773	−0.395886	−	0.918300i	$-0.629563\pi$
$2$	−4.47894	−0.791773	−0.395886	+	0.918300i	$0.629563\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−11.9391	−0.373096
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	40.3105	0.457130
$7$	−168.818	−1.30219	−0.651094	−	0.758997i	$-0.725690\pi$
$7$	−168.818	−1.30219	−0.651094	+	0.758997i	$0.725690\pi$
$8$	196.801	1.08718
$9$	81.0000	0.333333
$10$	−111.974	−0.354091
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	107.452	0.215407
$13$	290.259	0.476352	0.238176	−	0.971222i	$-0.423451\pi$
$13$	290.259	0.476352	0.238176	+	0.971222i	$0.423451\pi$
$14$	756.126	1.03104
$15$	−225.000	−0.258199
$16$	−499.408	−0.487703
$17$	623.964	0.523645	0.261823	−	0.965116i	$-0.415676\pi$
$17$	623.964	0.523645	0.261823	+	0.965116i	$0.415676\pi$
$18$	−362.794	−0.263924
$19$	−398.456	−0.253219	−0.126609	−	0.991953i	$-0.540409\pi$
$19$	−398.456	−0.253219	−0.126609	+	0.991953i	$0.540409\pi$
$20$	−298.477	−0.166854
$21$	1519.36	0.751819
$22$	−541.952	−0.238728
$23$	3788.06	1.49313	0.746565	−	0.665312i	$-0.231702\pi$
$23$	3788.06	1.49313	0.746565	+	0.665312i	$0.231702\pi$
$24$	−1771.21	−0.627684
$25$	625.000	0.200000
$26$	−1300.06	−0.377162
$27$	−729.000	−0.192450
$28$	2015.53	0.485841
$29$	4220.43	0.931883	0.465941	−	0.884816i	$-0.345716\pi$
$29$	4220.43	0.931883	0.465941	+	0.884816i	$0.345716\pi$
$30$	1007.76	0.204435
$31$	−5594.57	−1.04559	−0.522797	−	0.852457i	$-0.675111\pi$
$31$	−5594.57	−1.04559	−0.522797	+	0.852457i	$0.675111\pi$
$32$	−4060.80	−0.701030
$33$	−1089.00	−0.174078
$34$	−2794.70	−0.414608
$35$	−4220.45	−0.582356
$36$	−967.065	−0.124365
$37$	301.266	0.0361781	0.0180890	−	0.999836i	$-0.494242\pi$
$37$	301.266	0.0361781	0.0180890	+	0.999836i	$0.494242\pi$
$38$	1784.66	0.200492
$39$	−2612.33	−0.275022
$40$	4920.01	0.486202
$41$	−14636.2	−1.35978	−0.679889	−	0.733315i	$-0.737972\pi$
$41$	−14636.2	−1.35978	−0.679889	+	0.733315i	$0.737972\pi$
$42$	−6805.14	−0.595269
$43$	151.418	0.0124884	0.00624421	−	0.999981i	$-0.498012\pi$
$43$	151.418	0.0124884	0.00624421	+	0.999981i	$0.498012\pi$
$44$	−1444.63	−0.112493
$45$	2025.00	0.149071
$46$	−16966.5	−1.18222
$47$	−13535.0	−0.893743	−0.446872	−	0.894598i	$-0.647462\pi$
$47$	−13535.0	−0.893743	−0.446872	+	0.894598i	$0.647462\pi$
$48$	4494.67	0.281575
$49$	11692.5	0.695694
$50$	−2799.34	−0.158355
$51$	−5615.68	−0.302327
$52$	−3465.43	−0.177725
$53$	−18116.1	−0.885880	−0.442940	−	0.896551i	$-0.646065\pi$
$53$	−18116.1	−0.885880	−0.442940	+	0.896551i	$0.646065\pi$
$54$	3265.15	0.152377
$55$	3025.00	0.134840
$56$	−33223.5	−1.41571
$57$	3586.10	0.146196
$58$	−18903.0	−0.737839
$59$	−50582.4	−1.89177	−0.945887	−	0.324495i	$-0.894806\pi$
$59$	−50582.4	−1.89177	−0.945887	+	0.324495i	$0.894806\pi$
$60$	2686.29	0.0963330
$61$	5984.35	0.205917	0.102958	−	0.994686i	$-0.467169\pi$
$61$	5984.35	0.205917	0.102958	+	0.994686i	$0.467169\pi$
$62$	25057.8	0.827872
$63$	−13674.3	−0.434063
$64$	34169.1	1.04276
$65$	7256.49	0.213031
$66$	4877.57	0.137830
$67$	22450.7	0.611002	0.305501	−	0.952192i	$-0.401176\pi$
$67$	22450.7	0.611002	0.305501	+	0.952192i	$0.401176\pi$
$68$	−7449.56	−0.195370
$69$	−34092.6	−0.862059
$70$	18903.2	0.461094
$71$	10017.6	0.235841	0.117921	−	0.993023i	$-0.462377\pi$
$71$	10017.6	0.235841	0.117921	+	0.993023i	$0.462377\pi$
$72$	15940.8	0.362393
$73$	−476.148	−0.0104577	−0.00522883	−	0.999986i	$-0.501664\pi$
$73$	−476.148	−0.0104577	−0.00522883	+	0.999986i	$0.501664\pi$
$74$	−1349.35	−0.0286448
$75$	−5625.00	−0.115470
$76$	4757.19	0.0944750
$77$	−20427.0	−0.392624
$78$	11700.5	0.217755
$79$	−85024.7	−1.53277	−0.766386	−	0.642380i	$-0.777947\pi$
$79$	−85024.7	−1.53277	−0.766386	+	0.642380i	$0.777947\pi$
$80$	−12485.2	−0.218107
$81$	6561.00	0.111111
$82$	65554.5	1.07663
$83$	−25643.4	−0.408583	−0.204292	−	0.978910i	$-0.565489\pi$
$83$	−25643.4	−0.408583	−0.204292	+	0.978910i	$0.565489\pi$
$84$	−18139.8	−0.280501
$85$	15599.1	0.234181
$86$	−678.194	−0.00988799
$87$	−37983.8	−0.538023
$88$	23812.9	0.327797
$89$	1807.91	0.0241937	0.0120968	−	0.999927i	$-0.496149\pi$
$89$	1807.91	0.0241937	0.0120968	+	0.999927i	$0.496149\pi$
$90$	−9069.86	−0.118030
$91$	−49001.0	−0.620300
$92$	−45226.0	−0.557081
$93$	50351.2	0.603674
$94$	60622.4	0.707642
$95$	−9961.39	−0.113243
$96$	36547.2	0.404740
$97$	11688.5	0.126133	0.0630666	−	0.998009i	$-0.479912\pi$
$97$	11688.5	0.126133	0.0630666	+	0.998009i	$0.479912\pi$
$98$	−52370.1	−0.550831
$99$	9801.00	0.100504
$100$	−7461.92	−0.0746192
$101$	−135573.	−1.32242	−0.661210	−	0.750200i	$-0.729957\pi$
$101$	−135573.	−1.32242	−0.661210	+	0.750200i	$0.729957\pi$
$102$	25152.3	0.239374
$103$	−88490.5	−0.821871	−0.410935	−	0.911664i	$-0.634798\pi$
$103$	−88490.5	−0.821871	−0.410935	+	0.911664i	$0.634798\pi$
$104$	57123.2	0.517880
$105$	37984.1	0.336224
$106$	81140.9	0.701416
$107$	218742.	1.84703	0.923514	−	0.383564i	$-0.125304\pi$
$107$	218742.	1.84703	0.923514	+	0.383564i	$0.125304\pi$
$108$	8703.59	0.0718024
$109$	238399.	1.92193	0.960967	−	0.276663i	$-0.0892287\pi$
$109$	238399.	1.92193	0.960967	+	0.276663i	$0.0892287\pi$
$110$	−13548.8	−0.106763
$111$	−2711.39	−0.0208874
$112$	84309.1	0.635081
$113$	187225.	1.37933	0.689664	−	0.724130i	$-0.257758\pi$
$113$	187225.	1.37933	0.689664	+	0.724130i	$0.257758\pi$
$114$	−16061.9	−0.115754
$115$	94701.6	0.667748
$116$	−50388.0	−0.347682
$117$	23511.0	0.158784
$118$	226556.	1.49786
$119$	−105336.	−0.681885
$120$	−44280.1	−0.280709
$121$	14641.0	0.0909091
$122$	−26803.5	−0.163039
$123$	131725.	0.785068
$124$	66794.1	0.390107
$125$	15625.0	0.0894427
$126$	61246.2	0.343679
$127$	27727.6	0.152547	0.0762733	−	0.997087i	$-0.475698\pi$
$127$	27727.6	0.152547	0.0762733	+	0.997087i	$0.475698\pi$
$128$	−23096.0	−0.124598
$129$	−1362.77	−0.00721019
$130$	−32501.4	−0.168672
$131$	−324623.	−1.65273	−0.826363	−	0.563138i	$-0.809594\pi$
$131$	−324623.	−1.65273	−0.826363	+	0.563138i	$0.809594\pi$
$132$	13001.7	0.0649477
$133$	67266.5	0.329739
$134$	−100555.	−0.483775
$135$	−18225.0	−0.0860663
$136$	122797.	0.569297
$137$	−59748.8	−0.271974	−0.135987	−	0.990711i	$-0.543421\pi$
$137$	−59748.8	−0.271974	−0.135987	+	0.990711i	$0.543421\pi$
$138$	152699.	0.682555
$139$	−117646.	−0.516462	−0.258231	−	0.966083i	$-0.583140\pi$
$139$	−117646.	−0.516462	−0.258231	+	0.966083i	$0.583140\pi$
$140$	50388.3	0.217275
$141$	121815.	0.516003
$142$	−44868.5	−0.186733
$143$	35121.4	0.143626
$144$	−40452.0	−0.162568
$145$	105511.	0.416751
$146$	2132.64	0.00828009
$147$	−105233.	−0.401659
$148$	−3596.84	−0.0134979
$149$	52786.3	0.194785	0.0973925	−	0.995246i	$-0.468950\pi$
$149$	52786.3	0.194785	0.0973925	+	0.995246i	$0.468950\pi$
$150$	25194.0	0.0914260
$151$	−430119.	−1.53513	−0.767567	−	0.640969i	$-0.778533\pi$
$151$	−430119.	−1.53513	−0.767567	+	0.640969i	$0.778533\pi$
$152$	−78416.3	−0.275294
$153$	50541.1	0.174548
$154$	91491.3	0.310869
$155$	−139864.	−0.467604
$156$	31188.9	0.102610
$157$	−150989.	−0.488873	−0.244436	−	0.969665i	$-0.578603\pi$
$157$	−150989.	−0.488873	−0.244436	+	0.969665i	$0.578603\pi$
$158$	380821.	1.21361
$159$	163045.	0.511463
$160$	−101520.	−0.313510
$161$	−639493.	−1.94434
$162$	−29386.3	−0.0879747
$163$	142404.	0.419812	0.209906	−	0.977722i	$-0.432684\pi$
$163$	142404.	0.419812	0.209906	+	0.977722i	$0.432684\pi$
$164$	174742.	0.507328
$165$	−27225.0	−0.0778499
$166$	114855.	0.323505
$167$	55468.4	0.153906	0.0769528	−	0.997035i	$-0.475481\pi$
$167$	55468.4	0.153906	0.0769528	+	0.997035i	$0.475481\pi$
$168$	299011.	0.817362
$169$	−287042.	−0.773089
$170$	−69867.5	−0.185418
$171$	−32274.9	−0.0844063
$172$	−1807.80	−0.00465938
$173$	133612.	0.339414	0.169707	−	0.985495i	$-0.445718\pi$
$173$	133612.	0.339414	0.169707	+	0.985495i	$0.445718\pi$
$174$	170127.	0.425992
$175$	−105511.	−0.260438
$176$	−60428.4	−0.147048
$177$	455242.	1.09222
$178$	−8097.52	−0.0191559
$179$	−188254.	−0.439150	−0.219575	−	0.975596i	$-0.570467\pi$
$179$	−188254.	−0.439150	−0.219575	+	0.975596i	$0.570467\pi$
$180$	−24176.6	−0.0556179
$181$	−652252.	−1.47986	−0.739928	−	0.672686i	$-0.765140\pi$
$181$	−652252.	−1.47986	−0.739928	+	0.672686i	$0.765140\pi$
$182$	219473.	0.491136
$183$	−53859.1	−0.118886
$184$	745493.	1.62330
$185$	7531.65	0.0161793
$186$	−225520.	−0.477972
$187$	75499.7	0.157885
$188$	161595.	0.333452
$189$	123068.	0.250606
$190$	44616.5	0.0896626
$191$	−705620.	−1.39955	−0.699774	−	0.714365i	$-0.746716\pi$
$191$	−705620.	−1.39955	−0.699774	+	0.714365i	$0.746716\pi$
$192$	−307522.	−0.602037
$193$	−87143.5	−0.168400	−0.0841999	−	0.996449i	$-0.526833\pi$
$193$	−87143.5	−0.168400	−0.0841999	+	0.996449i	$0.526833\pi$
$194$	−52352.1	−0.0998688
$195$	−65308.4	−0.122994
$196$	−139598.	−0.259561
$197$	−667596.	−1.22560	−0.612800	−	0.790238i	$-0.709957\pi$
$197$	−667596.	−1.22560	−0.612800	+	0.790238i	$0.709957\pi$
$198$	−43898.1	−0.0795761
$199$	−698609.	−1.25055	−0.625276	−	0.780404i	$-0.715013\pi$
$199$	−698609.	−1.25055	−0.625276	+	0.780404i	$0.715013\pi$
$200$	123000.	0.217436
$201$	−202056.	−0.352762
$202$	607224.	1.04706
$203$	−712484.	−1.21349
$204$	67046.0	0.112797
$205$	−365904.	−0.608111
$206$	396344.	0.650735
$207$	306833.	0.497710
$208$	−144958.	−0.232318
$209$	−48213.1	−0.0763484
$210$	−170128.	−0.266213
$211$	−558238.	−0.863203	−0.431602	−	0.902064i	$-0.642051\pi$
$211$	−558238.	−0.863203	−0.431602	+	0.902064i	$0.642051\pi$
$212$	216289.	0.330518
$213$	−90158.8	−0.136163
$214$	−979735.	−1.46243
$215$	3785.46	0.00558499
$216$	−143468.	−0.209228
$217$	944465.	1.36156
$218$	−1.06778e6	−1.52173
$219$	4285.33	0.00603773
$220$	−36115.7	−0.0503083
$221$	181111.	0.249440
$222$	12144.2	0.0165381
$223$	−382897.	−0.515608	−0.257804	−	0.966197i	$-0.582999\pi$
$223$	−382897.	−0.515608	−0.257804	+	0.966197i	$0.582999\pi$
$224$	685536.	0.912873
$225$	50625.0	0.0666667
$226$	−838569.	−1.09211
$227$	−404735.	−0.521322	−0.260661	−	0.965430i	$-0.583941\pi$
$227$	−404735.	−0.521322	−0.260661	+	0.965430i	$0.583941\pi$
$228$	−42814.7	−0.0545452
$229$	664894.	0.837845	0.418922	−	0.908022i	$-0.362408\pi$
$229$	664894.	0.837845	0.418922	+	0.908022i	$0.362408\pi$
$230$	−424163.	−0.528705
$231$	183843.	0.226682
$232$	830582.	1.01312
$233$	61531.4	0.0742518	0.0371259	−	0.999311i	$-0.488180\pi$
$233$	61531.4	0.0742518	0.0371259	+	0.999311i	$0.488180\pi$
$234$	−105304.	−0.125721
$235$	−338374.	−0.399694
$236$	603907.	0.705814
$237$	765223.	0.884946
$238$	471796.	0.539898
$239$	1.71207e6	1.93877	0.969384	−	0.245549i	$-0.0789682\pi$
$239$	1.71207e6	1.93877	0.969384	+	0.245549i	$0.0789682\pi$
$240$	112367.	0.125924
$241$	1.31915e6	1.46302	0.731512	−	0.681828i	$-0.238815\pi$
$241$	1.31915e6	1.46302	0.731512	+	0.681828i	$0.238815\pi$
$242$	−65576.2	−0.0719793
$243$	−59049.0	−0.0641500
$244$	−71447.6	−0.0768268
$245$	292313.	0.311124
$246$	−589991.	−0.621595
$247$	−115656.	−0.120621
$248$	−1.10102e6	−1.13675
$249$	230791.	0.235896
$250$	−69983.5	−0.0708183
$251$	−237992.	−0.238440	−0.119220	−	0.992868i	$-0.538039\pi$
$251$	−237992.	−0.238440	−0.119220	+	0.992868i	$0.538039\pi$
$252$	163258.	0.161947
$253$	458356.	0.450196
$254$	−124190.	−0.120782
$255$	−140392.	−0.135205
$256$	−989967.	−0.944106
$257$	−1.90368e6	−1.79789	−0.898943	−	0.438066i	$-0.855664\pi$
$257$	−1.90368e6	−1.79789	−0.898943	+	0.438066i	$0.855664\pi$
$258$	6103.75	0.00570883
$259$	−50859.1	−0.0471107
$260$	−86635.7	−0.0794811
$261$	341854.	0.310628
$262$	1.45397e6	1.30858
$263$	−907019.	−0.808588	−0.404294	−	0.914629i	$-0.632483\pi$
$263$	−907019.	−0.808588	−0.404294	+	0.914629i	$0.632483\pi$
$264$	−214316.	−0.189254
$265$	−452902.	−0.396178
$266$	−301283.	−0.261078
$267$	−16271.2	−0.0139682
$268$	−268041.	−0.227963
$269$	698485.	0.588541	0.294270	−	0.955722i	$-0.404923\pi$
$269$	698485.	0.588541	0.294270	+	0.955722i	$0.404923\pi$
$270$	81628.7	0.0681449
$271$	1.19097e6	0.985098	0.492549	−	0.870285i	$-0.336065\pi$
$271$	1.19097e6	0.985098	0.492549	+	0.870285i	$0.336065\pi$
$272$	−311613.	−0.255383
$273$	441009.	0.358130
$274$	267611.	0.215342
$275$	75625.0	0.0603023
$276$	407034.	0.321631
$277$	−1.15110e6	−0.901392	−0.450696	−	0.892677i	$-0.648824\pi$
$277$	−1.15110e6	−0.901392	−0.450696	+	0.892677i	$0.648824\pi$
$278$	526928.	0.408921
$279$	−453161.	−0.348531
$280$	−830587.	−0.633126
$281$	−1.54201e6	−1.16498	−0.582492	−	0.812836i	$-0.697922\pi$
$281$	−1.54201e6	−1.16498	−0.582492	+	0.812836i	$0.697922\pi$
$282$	−545601.	−0.408557
$283$	1.28590e6	0.954421	0.477211	−	0.878789i	$-0.341648\pi$
$283$	1.28590e6	0.954421	0.477211	+	0.878789i	$0.341648\pi$
$284$	−119601.	−0.0879915
$285$	89652.5	0.0653808
$286$	−157307.	−0.113719
$287$	2.47085e6	1.77069
$288$	−328925.	−0.233677
$289$	−1.03053e6	−0.725795
$290$	−472576.	−0.329972
$291$	−105196.	−0.0728230
$292$	5684.77	0.00390171
$293$	1.08802e6	0.740404	0.370202	−	0.928951i	$-0.379288\pi$
$293$	1.08802e6	0.740404	0.370202	+	0.928951i	$0.379288\pi$
$294$	471331.	0.318023
$295$	−1.26456e6	−0.846027
$296$	59289.3	0.0393321
$297$	−88209.0	−0.0580259
$298$	−236427.	−0.154225
$299$	1.09952e6	0.711255
$300$	67157.3	0.0430814
$301$	−25562.2	−0.0162623
$302$	1.92648e6	1.21548
$303$	1.22016e6	0.763500
$304$	198992.	0.123496
$305$	149609.	0.0920889
$306$	−226371.	−0.138203
$307$	−580340.	−0.351428	−0.175714	−	0.984441i	$-0.556223\pi$
$307$	−580340.	−0.351428	−0.175714	+	0.984441i	$0.556223\pi$
$308$	243879.	0.146487
$309$	796414.	0.474507
$310$	626444.	0.370236
$311$	−1.68606e6	−0.988492	−0.494246	−	0.869322i	$-0.664556\pi$
$311$	−1.68606e6	−0.988492	−0.494246	+	0.869322i	$0.664556\pi$
$312$	−514109.	−0.298998
$313$	−1.50328e6	−0.867319	−0.433659	−	0.901077i	$-0.642778\pi$
$313$	−1.50328e6	−0.867319	−0.433659	+	0.901077i	$0.642778\pi$
$314$	676270.	0.387076
$315$	−341857.	−0.194119
$316$	1.01512e6	0.571871
$317$	1.31016e6	0.732281	0.366140	−	0.930560i	$-0.380679\pi$
$317$	1.31016e6	0.732281	0.366140	+	0.930560i	$0.380679\pi$
$318$	−730269.	−0.404962
$319$	510671.	0.280973
$320$	854228.	0.466336
$321$	−1.96868e6	−1.06638
$322$	2.86425e6	1.53947
$323$	−248622.	−0.132597
$324$	−78332.3	−0.0414551
$325$	181412.	0.0952704
$326$	−637821.	−0.332395
$327$	−2.14559e6	−1.10963
$328$	−2.88041e6	−1.47832
$329$	2.28495e6	1.16382
$330$	121939.	0.0616394
$331$	2.91035e6	1.46007	0.730037	−	0.683408i	$-0.239503\pi$
$331$	2.91035e6	1.46007	0.730037	+	0.683408i	$0.239503\pi$
$332$	306159.	0.152441
$333$	24402.5	0.0120594
$334$	−248440.	−0.121858
$335$	561267.	0.273248
$336$	−758782.	−0.366664
$337$	2.47133e6	1.18538	0.592688	−	0.805432i	$-0.298067\pi$
$337$	2.47133e6	1.18538	0.592688	+	0.805432i	$0.298067\pi$
$338$	1.28565e6	0.612111
$339$	−1.68502e6	−0.796355
$340$	−186239.	−0.0873722
$341$	−676944.	−0.315258
$342$	144557.	0.0668306
$343$	863415.	0.396264
$344$	29799.2	0.0135772
$345$	−852314.	−0.385525
$346$	−598440.	−0.268739
$347$	1.75988e6	0.784619	0.392309	−	0.919833i	$-0.371676\pi$
$347$	1.75988e6	0.784619	0.392309	+	0.919833i	$0.371676\pi$
$348$	453492.	0.200734
$349$	−386142.	−0.169700	−0.0848502	−	0.996394i	$-0.527041\pi$
$349$	−386142.	−0.169700	−0.0848502	+	0.996394i	$0.527041\pi$
$350$	472579.	0.206207
$351$	−211599.	−0.0916740
$352$	−491357.	−0.211368
$353$	−2.44184e6	−1.04299	−0.521495	−	0.853254i	$-0.674625\pi$
$353$	−2.44184e6	−1.04299	−0.521495	+	0.853254i	$0.674625\pi$
$354$	−2.03900e6	−0.864787
$355$	250441.	0.105471
$356$	−21584.8	−0.00902657
$357$	948028.	0.393686
$358$	843180.	0.347707
$359$	3.77524e6	1.54600	0.772998	−	0.634408i	$-0.218756\pi$
$359$	3.77524e6	1.54600	0.772998	+	0.634408i	$0.218756\pi$
$360$	398521.	0.162067
$361$	−2.31733e6	−0.935880
$362$	2.92140e6	1.17171
$363$	−131769.	−0.0524864
$364$	585027.	0.231431
$365$	−11903.7	−0.00467681
$366$	241232.	0.0941309
$367$	−3.98351e6	−1.54383	−0.771917	−	0.635723i	$-0.780702\pi$
$367$	−3.98351e6	−1.54383	−0.771917	+	0.635723i	$0.780702\pi$
$368$	−1.89179e6	−0.728204
$369$	−1.18553e6	−0.453259
$370$	−33733.8	−0.0128104
$371$	3.05832e6	1.15358
$372$	−601147.	−0.225228
$373$	3.13497e6	1.16670	0.583352	−	0.812219i	$-0.301741\pi$
$373$	3.13497e6	1.16670	0.583352	+	0.812219i	$0.301741\pi$
$374$	−338159.	−0.125009
$375$	−140625.	−0.0516398
$376$	−2.66369e6	−0.971660
$377$	1.22502e6	0.443904
$378$	−551216.	−0.198423
$379$	−2.50995e6	−0.897567	−0.448784	−	0.893640i	$-0.648143\pi$
$379$	−2.50995e6	−0.897567	−0.448784	+	0.893640i	$0.648143\pi$
$380$	118930.	0.0422505
$381$	−249548.	−0.0880728
$382$	3.16043e6	1.10812
$383$	−4.20287e6	−1.46403	−0.732014	−	0.681290i	$-0.761419\pi$
$383$	−4.20287e6	−1.46403	−0.732014	+	0.681290i	$0.761419\pi$
$384$	207864.	0.0719368
$385$	−510675.	−0.175587
$386$	390311.	0.133334
$387$	12264.9	0.00416281
$388$	−139550.	−0.0470598
$389$	−1.91171e6	−0.640543	−0.320271	−	0.947326i	$-0.603774\pi$
$389$	−1.91171e6	−0.640543	−0.320271	+	0.947326i	$0.603774\pi$
$390$	292512.	0.0973829
$391$	2.36362e6	0.781871
$392$	2.30110e6	0.756344
$393$	2.92161e6	0.954202
$394$	2.99013e6	0.970396
$395$	−2.12562e6	−0.685477
$396$	−117015.	−0.0374976
$397$	3.62426e6	1.15410	0.577049	−	0.816709i	$-0.304204\pi$
$397$	3.62426e6	1.15410	0.577049	+	0.816709i	$0.304204\pi$
$398$	3.12903e6	0.990152
$399$	−605399.	−0.190375
$400$	−312130.	−0.0975406
$401$	−2.22052e6	−0.689593	−0.344797	−	0.938677i	$-0.612052\pi$
$401$	−2.22052e6	−0.689593	−0.344797	+	0.938677i	$0.612052\pi$
$402$	904998.	0.279307
$403$	−1.62388e6	−0.498070
$404$	1.61862e6	0.493390
$405$	164025.	0.0496904
$406$	3.19117e6	0.960805
$407$	36453.2	0.0109081
$408$	−1.10517e6	−0.328684
$409$	20564.7	0.00607876	0.00303938	−	0.999995i	$-0.499033\pi$
$409$	20564.7	0.00607876	0.00303938	+	0.999995i	$0.499033\pi$
$410$	1.63886e6	0.481485
$411$	537739.	0.157024
$412$	1.05649e6	0.306637
$413$	8.53922e6	2.46345
$414$	−1.37429e6	−0.394073
$415$	−641086.	−0.182724
$416$	−1.17869e6	−0.333937
$417$	1.05881e6	0.298180
$418$	215944.	0.0604505
$419$	−2.30684e6	−0.641923	−0.320962	−	0.947092i	$-0.604006\pi$
$419$	−2.30684e6	−0.641923	−0.320962	+	0.947092i	$0.604006\pi$
$420$	−453495.	−0.125444
$421$	5.00382e6	1.37593	0.687965	−	0.725744i	$-0.258504\pi$
$421$	5.00382e6	1.37593	0.687965	+	0.725744i	$0.258504\pi$
$422$	2.50032e6	0.683461
$423$	−1.09633e6	−0.297914
$424$	−3.56526e6	−0.963111
$425$	389978.	0.104729
$426$	403816.	0.107810
$427$	−1.01027e6	−0.268143
$428$	−2.61158e6	−0.689119
$429$	−316092.	−0.0829222
$430$	−16954.9	−0.00442204
$431$	−2.70202e6	−0.700641	−0.350320	−	0.936630i	$-0.613927\pi$
$431$	−2.70202e6	−0.700641	−0.350320	+	0.936630i	$0.613927\pi$
$432$	364068.	0.0938585
$433$	−3.92321e6	−1.00559	−0.502796	−	0.864405i	$-0.667695\pi$
$433$	−3.92321e6	−1.00559	−0.502796	+	0.864405i	$0.667695\pi$
$434$	−4.23020e6	−1.07805
$435$	−949596.	−0.240611
$436$	−2.84627e6	−0.717066
$437$	−1.50938e6	−0.378089
$438$	−19193.7	−0.00478051
$439$	−53261.3	−0.0131902	−0.00659508	−	0.999978i	$-0.502099\pi$
$439$	−53261.3	−0.0131902	−0.00659508	+	0.999978i	$0.502099\pi$
$440$	595322.	0.146595
$441$	947095.	0.231898
$442$	−811188.	−0.197499
$443$	3.30457e6	0.800029	0.400015	−	0.916509i	$-0.369005\pi$
$443$	3.30457e6	0.800029	0.400015	+	0.916509i	$0.369005\pi$
$444$	32371.5	0.00779302
$445$	45197.7	0.0108197
$446$	1.71497e6	0.408244
$447$	−475077.	−0.112459
$448$	−5.76837e6	−1.35787
$449$	3.04596e6	0.713031	0.356516	−	0.934289i	$-0.383965\pi$
$449$	3.04596e6	0.713031	0.356516	+	0.934289i	$0.383965\pi$
$450$	−226746.	−0.0527848
$451$	−1.77098e6	−0.409988
$452$	−2.23529e6	−0.514622
$453$	3.87107e6	0.886309
$454$	1.81279e6	0.412769
$455$	−1.22503e6	−0.277407
$456$	705747.	0.158941
$457$	−2.67154e6	−0.598371	−0.299186	−	0.954195i	$-0.596715\pi$
$457$	−2.67154e6	−0.598371	−0.299186	+	0.954195i	$0.596715\pi$
$458$	−2.97802e6	−0.663382
$459$	−454870.	−0.100776
$460$	−1.13065e6	−0.249134
$461$	−3.30382e6	−0.724042	−0.362021	−	0.932170i	$-0.617913\pi$
$461$	−3.30382e6	−0.724042	−0.362021	+	0.932170i	$0.617913\pi$
$462$	−823421.	−0.179480
$463$	−7.66989e6	−1.66279	−0.831394	−	0.555684i	$-0.812457\pi$
$463$	−7.66989e6	−1.66279	−0.831394	+	0.555684i	$0.812457\pi$
$464$	−2.10771e6	−0.454482
$465$	1.25878e6	0.269971
$466$	−275596.	−0.0587905
$467$	−7.91117e6	−1.67860	−0.839302	−	0.543665i	$-0.817036\pi$
$467$	−7.91117e6	−1.67860	−0.839302	+	0.543665i	$0.817036\pi$
$468$	−280700.	−0.0592417
$469$	−3.79008e6	−0.795640
$470$	1.51556e6	0.316467
$471$	1.35890e6	0.282251
$472$	−9.95465e6	−2.05670
$473$	18321.6	0.00376540
$474$	−3.42739e6	−0.700676
$475$	−249035.	−0.0506438
$476$	1.25762e6	0.254409
$477$	−1.46740e6	−0.295293
$478$	−7.66825e6	−1.53506
$479$	5.44099e6	1.08352	0.541762	−	0.840532i	$-0.317757\pi$
$479$	5.44099e6	1.08352	0.541762	+	0.840532i	$0.317757\pi$
$480$	913680.	0.181005
$481$	87445.3	0.0172335
$482$	−5.90840e6	−1.15838
$483$	5.75544e6	1.12256
$484$	−174800.	−0.0339178
$485$	292212.	0.0564085
$486$	264477.	0.0507922
$487$	−8.50740e6	−1.62545	−0.812727	−	0.582645i	$-0.802018\pi$
$487$	−8.50740e6	−1.62545	−0.812727	+	0.582645i	$0.802018\pi$
$488$	1.17772e6	0.223869
$489$	−1.28164e6	−0.242378
$490$	−1.30925e6	−0.246339
$491$	−334168.	−0.0625549	−0.0312775	−	0.999511i	$-0.509958\pi$
$491$	−334168.	−0.0625549	−0.0312775	+	0.999511i	$0.509958\pi$
$492$	−1.57268e6	−0.292906
$493$	2.63339e6	0.487976
$494$	518014.	0.0955046
$495$	245025.	0.0449467
$496$	2.79397e6	0.509939
$497$	−1.69116e6	−0.307110
$498$	−1.03370e6	−0.186776
$499$	−3.50055e6	−0.629339	−0.314669	−	0.949201i	$-0.601894\pi$
$499$	−3.50055e6	−0.629339	−0.314669	+	0.949201i	$0.601894\pi$
$500$	−186548.	−0.0333707
$501$	−499216.	−0.0888574
$502$	1.06595e6	0.188790
$503$	6.56301e6	1.15660	0.578300	−	0.815824i	$-0.303716\pi$
$503$	6.56301e6	1.15660	0.578300	+	0.815824i	$0.303716\pi$
$504$	−2.69110e6	−0.471904
$505$	−3.38932e6	−0.591405
$506$	−2.05295e6	−0.356453
$507$	2.58338e6	0.446343
$508$	−331042.	−0.0569146
$509$	109860.	0.0187952	0.00939760	−	0.999956i	$-0.497009\pi$
$509$	109860.	0.0187952	0.00939760	+	0.999956i	$0.497009\pi$
$510$	628807.	0.107051
$511$	80382.3	0.0136178
$512$	5.17308e6	0.872115
$513$	290474.	0.0487320
$514$	8.52649e6	1.42352
$515$	−2.21226e6	−0.367552
$516$	16270.2	0.00269010
$517$	−1.63773e6	−0.269474
$518$	227795.	0.0373009
$519$	−1.20251e6	−0.195961
$520$	1.42808e6	0.231603
$521$	−914334.	−0.147574	−0.0737872	−	0.997274i	$-0.523509\pi$
$521$	−914334.	−0.147574	−0.0737872	+	0.997274i	$0.523509\pi$
$522$	−1.53115e6	−0.245946
$523$	4.00814e6	0.640750	0.320375	−	0.947291i	$-0.396191\pi$
$523$	4.00814e6	0.640750	0.320375	+	0.947291i	$0.396191\pi$
$524$	3.87570e6	0.616626
$525$	949601.	0.150364
$526$	4.06249e6	0.640218
$527$	−3.49081e6	−0.547520
$528$	543855.	0.0848982
$529$	7.91308e6	1.22944
$530$	2.02852e6	0.313683
$531$	−4.09717e6	−0.630592
$532$	−803100.	−0.123024
$533$	−4.24829e6	−0.647732
$534$	72877.7	0.0110597
$535$	5.46856e6	0.826016
$536$	4.41831e6	0.664269
$537$	1.69429e6	0.253543
$538$	−3.12847e6	−0.465990
$539$	1.41480e6	0.209760
$540$	217590.	0.0321110
$541$	−1.87833e6	−0.275918	−0.137959	−	0.990438i	$-0.544054\pi$
$541$	−1.87833e6	−0.275918	−0.137959	+	0.990438i	$0.544054\pi$
$542$	−5.33431e6	−0.779974
$543$	5.87027e6	0.854395
$544$	−2.53379e6	−0.367091
$545$	5.95998e6	0.859515
$546$	−1.97525e6	−0.283558
$547$	87797.6	0.0125463	0.00627313	−	0.999980i	$-0.498003\pi$
$547$	87797.6	0.0125463	0.00627313	+	0.999980i	$0.498003\pi$
$548$	713346.	0.101473
$549$	484732.	0.0686390
$550$	−338720.	−0.0477457
$551$	−1.68165e6	−0.235970
$552$	−6.70944e6	−0.937213
$553$	1.43537e7	1.99596
$554$	5.15571e6	0.713698
$555$	−67784.8	−0.00934114
$556$	1.40458e6	0.192690
$557$	−3.46548e6	−0.473288	−0.236644	−	0.971596i	$-0.576048\pi$
$557$	−3.46548e6	−0.473288	−0.236644	+	0.971596i	$0.576048\pi$
$558$	2.02968e6	0.275957
$559$	43950.6	0.00594888
$560$	2.10773e6	0.284017
$561$	−679497.	−0.0911550
$562$	6.90655e6	0.922403
$563$	−2.85737e6	−0.379923	−0.189961	−	0.981792i	$-0.560836\pi$
$563$	−2.85737e6	−0.379923	−0.189961	+	0.981792i	$0.560836\pi$
$564$	−1.45436e6	−0.192519
$565$	4.68062e6	0.616854
$566$	−5.75946e6	−0.755685
$567$	−1.10762e6	−0.144688
$568$	1.97148e6	0.256402
$569$	−5.48030e6	−0.709617	−0.354808	−	0.934939i	$-0.615454\pi$
$569$	−5.48030e6	−0.709617	−0.354808	+	0.934939i	$0.615454\pi$
$570$	−401549.	−0.0517667
$571$	8.81180e6	1.13103	0.565515	−	0.824738i	$-0.308677\pi$
$571$	8.81180e6	1.13103	0.565515	+	0.824738i	$0.308677\pi$
$572$	−419317.	−0.0535861
$573$	6.35058e6	0.808029
$574$	−1.10668e7	−1.40198
$575$	2.36754e6	0.298626
$576$	2.76770e6	0.347586
$577$	502598.	0.0628465	0.0314233	−	0.999506i	$-0.489996\pi$
$577$	502598.	0.0628465	0.0314233	+	0.999506i	$0.489996\pi$
$578$	4.61566e6	0.574665
$579$	784291.	0.0972257
$580$	−1.25970e6	−0.155488
$581$	4.32907e6	0.532053
$582$	471169.	0.0576593
$583$	−2.19205e6	−0.267103
$584$	−93706.2	−0.0113694
$585$	587775.	0.0710104
$586$	−4.87319e6	−0.586232
$587$	−7.45878e6	−0.893455	−0.446728	−	0.894670i	$-0.647411\pi$
$587$	−7.45878e6	−0.893455	−0.446728	+	0.894670i	$0.647411\pi$
$588$	1.25638e6	0.149857
$589$	2.22919e6	0.264764
$590$	5.66389e6	0.669861
$591$	6.00837e6	0.707600
$592$	−150455.	−0.0176442
$593$	6.69352e6	0.781660	0.390830	−	0.920463i	$-0.372188\pi$
$593$	6.69352e6	0.781660	0.390830	+	0.920463i	$0.372188\pi$
$594$	395083.	0.0459433
$595$	−2.63341e6	−0.304948
$596$	−630220.	−0.0726736
$597$	6.28748e6	0.722006
$598$	−4.92469e6	−0.563153
$599$	−1.64186e7	−1.86968	−0.934842	−	0.355065i	$-0.884459\pi$
$599$	−1.64186e7	−1.86968	−0.934842	+	0.355065i	$0.884459\pi$
$600$	−1.10700e6	−0.125537
$601$	1.42657e7	1.61105	0.805523	−	0.592564i	$-0.201884\pi$
$601$	1.42657e7	1.61105	0.805523	+	0.592564i	$0.201884\pi$
$602$	114491.	0.0128760
$603$	1.81851e6	0.203667
$604$	5.13522e6	0.572752
$605$	366025.	0.0406558
$606$	−5.46501e6	−0.604518
$607$	2.38734e6	0.262992	0.131496	−	0.991317i	$-0.458022\pi$
$607$	2.38734e6	0.262992	0.131496	+	0.991317i	$0.458022\pi$
$608$	1.61805e6	0.177514
$609$	6.41235e6	0.700607
$610$	−670089.	−0.0729134
$611$	−3.92865e6	−0.425736
$612$	−603414.	−0.0651234
$613$	−1.36125e6	−0.146314	−0.0731570	−	0.997320i	$-0.523307\pi$
$613$	−1.36125e6	−0.146314	−0.0731570	+	0.997320i	$0.523307\pi$
$614$	2.59931e6	0.278251
$615$	3.29314e6	0.351093
$616$	−4.02004e6	−0.426853
$617$	−1.33759e6	−0.141453	−0.0707264	−	0.997496i	$-0.522532\pi$
$617$	−1.33759e6	−0.141453	−0.0707264	+	0.997496i	$0.522532\pi$
$618$	−3.56709e6	−0.375702
$619$	1.70842e7	1.79212	0.896062	−	0.443930i	$-0.146416\pi$
$619$	1.70842e7	1.79212	0.896062	+	0.443930i	$0.146416\pi$
$620$	1.66985e6	0.174461
$621$	−2.76150e6	−0.287353
$622$	7.55179e6	0.782661
$623$	−305208.	−0.0315047
$624$	1.30462e6	0.134129
$625$	390625.	0.0400000
$626$	6.73310e6	0.686719
$627$	433918.	0.0440797
$628$	1.80267e6	0.182397
$629$	187979.	0.0189445
$630$	1.53116e6	0.153698
$631$	1.70136e7	1.70107	0.850534	−	0.525920i	$-0.176279\pi$
$631$	1.70136e7	1.70107	0.850534	+	0.525920i	$0.176279\pi$
$632$	−1.67329e7	−1.66640
$633$	5.02414e6	0.498371
$634$	−5.86815e6	−0.579800
$635$	693189.	0.0682209
$636$	−1.94661e6	−0.190825
$637$	3.39387e6	0.331395
$638$	−2.28727e6	−0.222467
$639$	811429.	0.0786138
$640$	−577400.	−0.0557220
$641$	1.04366e7	1.00326	0.501632	−	0.865081i	$-0.332733\pi$
$641$	1.04366e7	1.00326	0.501632	+	0.865081i	$0.332733\pi$
$642$	8.81761e6	0.844332
$643$	1.32098e7	1.25999	0.629996	−	0.776598i	$-0.283056\pi$
$643$	1.32098e7	1.25999	0.629996	+	0.776598i	$0.283056\pi$
$644$	7.63496e6	0.725424
$645$	−34069.1	−0.00322450
$646$	1.11356e6	0.104987
$647$	3.14204e6	0.295087	0.147544	−	0.989056i	$-0.452863\pi$
$647$	3.14204e6	0.295087	0.147544	+	0.989056i	$0.452863\pi$
$648$	1.29121e6	0.120798
$649$	−6.12047e6	−0.570391
$650$	−812534.	−0.0754325
$651$	−8.50019e6	−0.786097
$652$	−1.70018e6	−0.156630
$653$	9.82598e6	0.901764	0.450882	−	0.892583i	$-0.351109\pi$
$653$	9.82598e6	0.901764	0.450882	+	0.892583i	$0.351109\pi$
$654$	9.60998e6	0.878574
$655$	−8.11557e6	−0.739122
$656$	7.30942e6	0.663167
$657$	−38568.0	−0.00348589
$658$	−1.02341e7	−0.921482
$659$	−1.78524e7	−1.60134	−0.800670	−	0.599105i	$-0.795523\pi$
$659$	−1.78524e7	−1.60134	−0.800670	+	0.599105i	$0.795523\pi$
$660$	325041.	0.0290455
$661$	1.02807e7	0.915207	0.457603	−	0.889156i	$-0.348708\pi$
$661$	1.02807e7	0.915207	0.457603	+	0.889156i	$0.348708\pi$
$662$	−1.30353e7	−1.15605
$663$	−1.63000e6	−0.144014
$664$	−5.04664e6	−0.444204
$665$	1.68166e6	0.147464
$666$	−109298.	−0.00954827
$667$	1.59872e7	1.39142
$668$	−662242.	−0.0574216
$669$	3.44607e6	0.297686
$670$	−2.51388e6	−0.216351
$671$	724106.	0.0620863
$672$	−6.16983e6	−0.527047
$673$	−2.22873e7	−1.89679	−0.948394	−	0.317094i	$-0.897293\pi$
$673$	−2.22873e7	−1.89679	−0.948394	+	0.317094i	$0.897293\pi$
$674$	−1.10690e7	−0.938549
$675$	−455625.	−0.0384900
$676$	3.42702e6	0.288436
$677$	−1.56465e7	−1.31204	−0.656018	−	0.754745i	$-0.727761\pi$
$677$	−1.56465e7	−1.31204	−0.656018	+	0.754745i	$0.727761\pi$
$678$	7.54712e6	0.630532
$679$	−1.97323e6	−0.164249
$680$	3.06991e6	0.254597
$681$	3.64262e6	0.300986
$682$	3.03199e6	0.249613
$683$	−1.82208e7	−1.49457	−0.747283	−	0.664506i	$-0.768642\pi$
$683$	−1.82208e7	−1.49457	−0.747283	+	0.664506i	$0.768642\pi$
$684$	385333.	0.0314917
$685$	−1.49372e6	−0.121631
$686$	−3.86719e6	−0.313751
$687$	−5.98404e6	−0.483730
$688$	−75619.5	−0.00609064
$689$	−5.25837e6	−0.421991
$690$	3.81747e6	0.305248
$691$	1.07957e7	0.860116	0.430058	−	0.902801i	$-0.358493\pi$
$691$	1.07957e7	0.860116	0.430058	+	0.902801i	$0.358493\pi$
$692$	−1.59520e6	−0.126634
$693$	−1.65459e6	−0.130875
$694$	−7.88239e6	−0.621240
$695$	−2.94114e6	−0.230969
$696$	−7.47524e6	−0.584927
$697$	−9.13244e6	−0.712041
$698$	1.72951e6	0.134364
$699$	−553783.	−0.0428693
$700$	1.25971e6	0.0971683
$701$	−7.59781e6	−0.583973	−0.291987	−	0.956422i	$-0.594316\pi$
$701$	−7.59781e6	−0.583973	−0.291987	+	0.956422i	$0.594316\pi$
$702$	947740.	0.0725849
$703$	−120041.	−0.00916098
$704$	4.13447e6	0.314404
$705$	3.04537e6	0.230764
$706$	1.09369e7	0.825811
$707$	2.28872e7	1.72204
$708$	−5.43516e6	−0.407502
$709$	1.26638e7	0.946122	0.473061	−	0.881030i	$-0.343149\pi$
$709$	1.26638e7	0.946122	0.473061	+	0.881030i	$0.343149\pi$
$710$	−1.12171e6	−0.0835094
$711$	−6.88700e6	−0.510924
$712$	355798.	0.0263029
$713$	−2.11926e7	−1.56121
$714$	−4.24616e6	−0.311710
$715$	878035.	0.0642313
$716$	2.24758e6	0.163845
$717$	−1.54086e7	−1.11935
$718$	−1.69091e7	−1.22408
$719$	−8.16704e6	−0.589172	−0.294586	−	0.955625i	$-0.595182\pi$
$719$	−8.16704e6	−0.589172	−0.294586	+	0.955625i	$0.595182\pi$
$720$	−1.01130e6	−0.0727025
$721$	1.49388e7	1.07023
$722$	1.03792e7	0.741004
$723$	−1.18723e7	−0.844677
$724$	7.78729e6	0.552128
$725$	2.63777e6	0.186377
$726$	590186.	0.0415573
$727$	1.99934e6	0.140298	0.0701488	−	0.997537i	$-0.477653\pi$
$727$	1.99934e6	0.140298	0.0701488	+	0.997537i	$0.477653\pi$
$728$	−9.64343e6	−0.674377
$729$	531441.	0.0370370
$730$	53316.0	0.00370297
$731$	94479.6	0.00653950
$732$	643028.	0.0443560
$733$	2.26768e7	1.55892	0.779458	−	0.626455i	$-0.215495\pi$
$733$	2.26768e7	1.55892	0.779458	+	0.626455i	$0.215495\pi$
$734$	1.78419e7	1.22237
$735$	−2.63082e6	−0.179627
$736$	−1.53826e7	−1.04673
$737$	2.71653e6	0.184224
$738$	5.30992e6	0.358878
$739$	−1.49990e7	−1.01030	−0.505151	−	0.863031i	$-0.668563\pi$
$739$	−1.49990e7	−1.01030	−0.505151	+	0.863031i	$0.668563\pi$
$740$	−89920.9	−0.00603645
$741$	1.04090e6	0.0696407
$742$	−1.36981e7	−0.913375
$743$	−8.72196e6	−0.579618	−0.289809	−	0.957084i	$-0.593592\pi$
$743$	−8.72196e6	−0.579618	−0.289809	+	0.957084i	$0.593592\pi$
$744$	9.90914e6	0.656302
$745$	1.31966e6	0.0871105
$746$	−1.40413e7	−0.923765
$747$	−2.07712e6	−0.136194
$748$	−901396.	−0.0589063
$749$	−3.69277e7	−2.40518
$750$	629851.	0.0408870
$751$	3.03235e7	1.96191	0.980957	−	0.194227i	$-0.0622198\pi$
$751$	3.03235e7	1.96191	0.980957	+	0.194227i	$0.0622198\pi$
$752$	6.75947e6	0.435881
$753$	2.14193e6	0.137663
$754$	−5.48679e6	−0.351471
$755$	−1.07530e7	−0.686532
$756$	−1.46932e6	−0.0935002
$757$	999401.	0.0633870	0.0316935	−	0.999498i	$-0.489910\pi$
$757$	999401.	0.0633870	0.0316935	+	0.999498i	$0.489910\pi$
$758$	1.12419e7	0.710669
$759$	−4.12520e6	−0.259921
$760$	−1.96041e6	−0.123115
$761$	1.23318e7	0.771904	0.385952	−	0.922519i	$-0.373873\pi$
$761$	1.23318e7	0.771904	0.385952	+	0.922519i	$0.373873\pi$
$762$	1.11771e6	0.0697336
$763$	−4.02461e7	−2.50272
$764$	8.42445e6	0.522166
$765$	1.26353e6	0.0780605
$766$	1.88244e7	1.15918
$767$	−1.46820e7	−0.901150
$768$	8.90970e6	0.545080
$769$	−3.88179e6	−0.236710	−0.118355	−	0.992971i	$-0.537762\pi$
$769$	−3.88179e6	−0.236710	−0.118355	+	0.992971i	$0.537762\pi$
$770$	2.28728e6	0.139025
$771$	1.71332e7	1.03801
$772$	1.04041e6	0.0628293
$773$	2.35138e7	1.41539	0.707693	−	0.706520i	$-0.249736\pi$
$773$	2.35138e7	1.41539	0.707693	+	0.706520i	$0.249736\pi$
$774$	−54933.7	−0.00329600
$775$	−3.49661e6	−0.209119
$776$	2.30030e6	0.137129
$777$	457732.	0.0271994
$778$	8.56244e6	0.507164
$779$	5.83186e6	0.344321
$780$	779722.	0.0458884
$781$	1.21214e6	0.0711088
$782$	−1.05865e7	−0.619064
$783$	−3.07669e6	−0.179341
$784$	−5.83934e6	−0.339292
$785$	−3.77472e6	−0.218631
$786$	−1.30857e7	−0.755511
$787$	2.16876e6	0.124817	0.0624086	−	0.998051i	$-0.480122\pi$
$787$	2.16876e6	0.124817	0.0624086	+	0.998051i	$0.480122\pi$
$788$	7.97049e6	0.457266
$789$	8.16317e6	0.466838
$790$	9.52052e6	0.542742
$791$	−3.16069e7	−1.79614
$792$	1.92884e6	0.109266
$793$	1.73701e6	0.0980890
$794$	−1.62328e7	−0.913784
$795$	4.07612e6	0.228733
$796$	8.34075e6	0.466576
$797$	−1.85869e7	−1.03648	−0.518241	−	0.855235i	$-0.673413\pi$
$797$	−1.85869e7	−1.03648	−0.518241	+	0.855235i	$0.673413\pi$
$798$	2.71155e6	0.150733
$799$	−8.44534e6	−0.468005
$800$	−2.53800e6	−0.140206
$801$	146441.	0.00806456
$802$	9.94556e6	0.546001
$803$	−57613.9	−0.00315310
$804$	2.41237e6	0.131614
$805$	−1.59873e7	−0.869534
$806$	7.27326e6	0.394359
$807$	−6.28637e6	−0.339794
$808$	−2.66808e7	−1.43771
$809$	2.99966e7	1.61139	0.805694	−	0.592332i	$-0.201793\pi$
$809$	2.99966e7	1.61139	0.805694	+	0.592332i	$0.201793\pi$
$810$	−734658.	−0.0393435
$811$	−1.54479e6	−0.0824740	−0.0412370	−	0.999149i	$-0.513130\pi$
$811$	−1.54479e6	−0.0824740	−0.0412370	+	0.999149i	$0.513130\pi$
$812$	8.50640e6	0.452747
$813$	−1.07188e7	−0.568747
$814$	−163272.	−0.00863674
$815$	3.56011e6	0.187746
$816$	2.80451e6	0.147446
$817$	−60333.5	−0.00316230
$818$	−92108.3	−0.00481299
$819$	−3.96908e6	−0.206767
$820$	4.36856e6	0.226884
$821$	−2.60445e7	−1.34852	−0.674261	−	0.738493i	$-0.735538\pi$
$821$	−2.60445e7	−1.34852	−0.674261	+	0.738493i	$0.735538\pi$
$822$	−2.40850e6	−0.124328
$823$	−9.56891e6	−0.492451	−0.246226	−	0.969213i	$-0.579190\pi$
$823$	−9.56891e6	−0.492451	−0.246226	+	0.969213i	$0.579190\pi$
$824$	−1.74150e7	−0.893521
$825$	−680625.	−0.0348155
$826$	−3.82467e7	−1.95049
$827$	1.07164e7	0.544860	0.272430	−	0.962176i	$-0.412173\pi$
$827$	1.07164e7	0.544860	0.272430	+	0.962176i	$0.412173\pi$
$828$	−3.66330e6	−0.185694
$829$	−1.64337e7	−0.830519	−0.415259	−	0.909703i	$-0.636309\pi$
$829$	−1.64337e7	−0.830519	−0.415259	+	0.909703i	$0.636309\pi$
$830$	2.87139e6	0.144676
$831$	1.03599e7	0.520419
$832$	9.91791e6	0.496720
$833$	7.29572e6	0.364297
$834$	−4.74235e6	−0.236091
$835$	1.38671e6	0.0688287
$836$	575620.	0.0284853
$837$	4.07845e6	0.201225
$838$	1.03322e7	0.508257
$839$	9.64356e6	0.472969	0.236484	−	0.971635i	$-0.424005\pi$
$839$	9.64356e6	0.472969	0.236484	+	0.971635i	$0.424005\pi$
$840$	7.47528e6	0.365535
$841$	−2.69916e6	−0.131595
$842$	−2.24118e7	−1.08942
$843$	1.38781e7	0.672604
$844$	6.66485e6	0.322058
$845$	−7.17606e6	−0.345736
$846$	4.91041e6	0.235881
$847$	−2.47166e6	−0.118381
$848$	9.04732e6	0.432046
$849$	−1.15731e7	−0.551035
$850$	−1.74669e6	−0.0829216
$851$	1.14121e6	0.0540186
$852$	1.07641e6	0.0508019
$853$	−2.52742e7	−1.18934	−0.594669	−	0.803971i	$-0.702717\pi$
$853$	−2.52742e7	−1.18934	−0.594669	+	0.803971i	$0.702717\pi$
$854$	4.52492e6	0.212308
$855$	−806873.	−0.0377476
$856$	4.30486e7	2.00805
$857$	−262739.	−0.0122200	−0.00611002	−	0.999981i	$-0.501945\pi$
$857$	−262739.	−0.0122200	−0.00611002	+	0.999981i	$0.501945\pi$
$858$	1.41576e6	0.0656555
$859$	−9.43849e6	−0.436435	−0.218218	−	0.975900i	$-0.570024\pi$
$859$	−9.43849e6	−0.436435	−0.218218	+	0.975900i	$0.570024\pi$
$860$	−45194.9	−0.00208374
$861$	−2.22376e7	−1.02231
$862$	1.21022e7	0.554748
$863$	3.78002e7	1.72769	0.863847	−	0.503754i	$-0.168048\pi$
$863$	3.78002e7	1.72769	0.863847	+	0.503754i	$0.168048\pi$
$864$	2.96032e6	0.134913
$865$	3.34030e6	0.151791
$866$	1.75718e7	0.796200
$867$	9.27473e6	0.419038
$868$	−1.12760e7	−0.507993
$869$	−1.02880e7	−0.462148
$870$	4.25318e6	0.190509
$871$	6.51653e6	0.291052
$872$	4.69171e7	2.08949
$873$	946768.	0.0420444
$874$	6.76041e6	0.299360
$875$	−2.63778e6	−0.116471
$876$	−51162.9	−0.00225266
$877$	2.42348e7	1.06400	0.531999	−	0.846745i	$-0.321441\pi$
$877$	2.42348e7	1.06400	0.531999	+	0.846745i	$0.321441\pi$
$878$	238554.	0.0104436
$879$	−9.79220e6	−0.427472
$880$	−1.51071e6	−0.0657619
$881$	1.97060e7	0.855377	0.427689	−	0.903926i	$-0.359328\pi$
$881$	1.97060e7	0.855377	0.427689	+	0.903926i	$0.359328\pi$
$882$	−4.24198e6	−0.183610
$883$	−2.09867e7	−0.905822	−0.452911	−	0.891556i	$-0.649614\pi$
$883$	−2.09867e7	−0.905822	−0.452911	+	0.891556i	$0.649614\pi$
$884$	−2.16230e6	−0.0930649
$885$	1.13810e7	0.488454
$886$	−1.48010e7	−0.633441
$887$	−3.47934e7	−1.48487	−0.742434	−	0.669919i	$-0.766329\pi$
$887$	−3.47934e7	−1.48487	−0.742434	+	0.669919i	$0.766329\pi$
$888$	−533604.	−0.0227084
$889$	−4.68091e6	−0.198644
$890$	−202438.	−0.00856677
$891$	793881.	0.0335013
$892$	4.57143e6	0.192371
$893$	5.39309e6	0.226313
$894$	2.12784e6	0.0890421
$895$	−4.70636e6	−0.196394
$896$	3.89902e6	0.162250
$897$	−9.89569e6	−0.410644
$898$	−1.36427e7	−0.564559
$899$	−2.36115e7	−0.974370
$900$	−604416.	−0.0248731
$901$	−1.13038e7	−0.463887
$902$	7.93210e6	0.324617
$903$	230059.	0.00938903
$904$	3.68460e7	1.49958
$905$	−1.63063e7	−0.661811
$906$	−1.73383e7	−0.701756
$907$	−4.14396e7	−1.67262	−0.836310	−	0.548257i	$-0.815291\pi$
$907$	−4.14396e7	−1.67262	−0.836310	+	0.548257i	$0.815291\pi$
$908$	4.83217e6	0.194503
$909$	−1.09814e7	−0.440807
$910$	5.48682e6	0.219643
$911$	−4.55462e7	−1.81826	−0.909131	−	0.416511i	$-0.863253\pi$
$911$	−4.55462e7	−1.81826	−0.909131	+	0.416511i	$0.863253\pi$
$912$	−1.79093e6	−0.0713002
$913$	−3.10285e6	−0.123193
$914$	1.19657e7	0.473774
$915$	−1.34648e6	−0.0531675
$916$	−7.93822e6	−0.312597
$917$	5.48022e7	2.15216
$918$	2.03734e6	0.0797914
$919$	8.41097e6	0.328517	0.164258	−	0.986417i	$-0.447477\pi$
$919$	8.41097e6	0.328517	0.164258	+	0.986417i	$0.447477\pi$
$920$	1.86373e7	0.725962
$921$	5.22306e6	0.202897
$922$	1.47976e7	0.573277
$923$	2.90772e6	0.112343
$924$	−2.19491e6	−0.0845741
$925$	188291.	0.00723562
$926$	3.43530e7	1.31655
$927$	−7.16773e6	−0.273957
$928$	−1.71383e7	−0.653278
$929$	1.89074e6	0.0718773	0.0359386	−	0.999354i	$-0.488558\pi$
$929$	1.89074e6	0.0718773	0.0359386	+	0.999354i	$0.488558\pi$
$930$	−5.63800e6	−0.213756
$931$	−4.65895e6	−0.176163
$932$	−734628.	−0.0277031
$933$	1.51746e7	0.570706
$934$	3.54337e7	1.32907
$935$	1.88749e6	0.0706083
$936$	4.62698e6	0.172627
$937$	3.58861e7	1.33530	0.667648	−	0.744477i	$-0.267301\pi$
$937$	3.58861e7	1.33530	0.667648	+	0.744477i	$0.267301\pi$
$938$	1.69756e7	0.629966
$939$	1.35295e7	0.500747
$940$	4.03988e6	0.149124
$941$	3.25537e7	1.19847	0.599235	−	0.800573i	$-0.295472\pi$
$941$	3.25537e7	1.19847	0.599235	+	0.800573i	$0.295472\pi$
$942$	−6.08643e6	−0.223478
$943$	−5.54427e7	−2.03032
$944$	2.52612e7	0.922624
$945$	3.07671e6	0.112075
$946$	−82061.5	−0.00298134
$947$	6.44146e6	0.233405	0.116702	−	0.993167i	$-0.462768\pi$
$947$	6.44146e6	0.233405	0.116702	+	0.993167i	$0.462768\pi$
$948$	−9.13605e6	−0.330170
$949$	−138206.	−0.00498153
$950$	1.11541e6	0.0400984
$951$	−1.17915e7	−0.422782
$952$	−2.07303e7	−0.741332
$953$	2.40023e7	0.856093	0.428046	−	0.903757i	$-0.359202\pi$
$953$	2.40023e7	0.856093	0.428046	+	0.903757i	$0.359202\pi$
$954$	6.57242e6	0.233805
$955$	−1.76405e7	−0.625897
$956$	−2.04405e7	−0.723347
$957$	−4.59604e6	−0.162220
$958$	−2.43699e7	−0.857905
$959$	1.00867e7	0.354162
$960$	−7.68806e6	−0.269239
$961$	2.67012e6	0.0932656
$962$	−391662.	−0.0136450
$963$	1.77181e7	0.615676
$964$	−1.57494e7	−0.545849
$965$	−2.17859e6	−0.0753107
$966$	−2.57783e7	−0.888815
$967$	4.13239e7	1.42113	0.710567	−	0.703630i	$-0.248439\pi$
$967$	4.13239e7	1.42113	0.710567	+	0.703630i	$0.248439\pi$
$968$	2.88136e6	0.0988345
$969$	2.23760e6	0.0765549
$970$	−1.30880e6	−0.0446627
$971$	8.46004e6	0.287955	0.143977	−	0.989581i	$-0.454011\pi$
$971$	8.46004e6	0.287955	0.143977	+	0.989581i	$0.454011\pi$
$972$	704991.	0.0239341
$973$	1.98607e7	0.672531
$974$	3.81042e7	1.28699
$975$	−1.63271e6	−0.0550044
$976$	−2.98863e6	−0.100426
$977$	1.33050e7	0.445942	0.222971	−	0.974825i	$-0.428425\pi$
$977$	1.33050e7	0.445942	0.222971	+	0.974825i	$0.428425\pi$
$978$	5.74039e6	0.191909
$979$	218757.	0.00729467
$980$	−3.48995e6	−0.116079
$981$	1.93103e7	0.640645
$982$	1.49672e6	0.0495293
$983$	2.90239e7	0.958014	0.479007	−	0.877811i	$-0.340997\pi$
$983$	2.90239e7	0.958014	0.479007	+	0.877811i	$0.340997\pi$
$984$	2.59237e7	0.853510
$985$	−1.66899e7	−0.548105
$986$	−1.17948e7	−0.386366
$987$	−2.05645e7	−0.671933
$988$	1.38082e6	0.0450033
$989$	573582.	0.0186468
$990$	−1.09745e6	−0.0355875
$991$	−4.88551e7	−1.58025	−0.790125	−	0.612946i	$-0.789984\pi$
$991$	−4.88551e7	−1.58025	−0.790125	+	0.612946i	$0.789984\pi$
$992$	2.27184e7	0.732992
$993$	−2.61931e7	−0.842974
$994$	7.57460e6	0.243161
$995$	−1.74652e7	−0.559264
$996$	−2.75543e6	−0.0880118
$997$	−2.19218e7	−0.698453	−0.349227	−	0.937038i	$-0.613556\pi$
$997$	−2.19218e7	−0.698453	−0.349227	+	0.937038i	$0.613556\pi$
$998$	1.56787e7	0.498293
$999$	−219623.	−0.00696248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.c.1.1	✓	3
3.2	odd	2		495.6.a.b.1.3		3
5.4	even	2		825.6.a.g.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.c.1.1	✓	3	1.1	even	1	trivial
495.6.a.b.1.3		3	3.2	odd	2
825.6.a.g.1.3		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)

\(f(q)\)	\(=\)	\(q-4.47894 q^{2} -9.00000 q^{3} -11.9391 q^{4} +25.0000 q^{5} +40.3105 q^{6} -168.818 q^{7} +196.801 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.47894 q^{2} -9.00000 q^{3} -11.9391 q^{4} +25.0000 q^{5} +40.3105 q^{6} -168.818 q^{7} +196.801 q^{8} +81.0000 q^{9} -111.974 q^{10} +121.000 q^{11} +107.452 q^{12} +290.259 q^{13} +756.126 q^{14} -225.000 q^{15} -499.408 q^{16} +623.964 q^{17} -362.794 q^{18} -398.456 q^{19} -298.477 q^{20} +1519.36 q^{21} -541.952 q^{22} +3788.06 q^{23} -1771.21 q^{24} +625.000 q^{25} -1300.06 q^{26} -729.000 q^{27} +2015.53 q^{28} +4220.43 q^{29} +1007.76 q^{30} -5594.57 q^{31} -4060.80 q^{32} -1089.00 q^{33} -2794.70 q^{34} -4220.45 q^{35} -967.065 q^{36} +301.266 q^{37} +1784.66 q^{38} -2612.33 q^{39} +4920.01 q^{40} -14636.2 q^{41} -6805.14 q^{42} +151.418 q^{43} -1444.63 q^{44} +2025.00 q^{45} -16966.5 q^{46} -13535.0 q^{47} +4494.67 q^{48} +11692.5 q^{49} -2799.34 q^{50} -5615.68 q^{51} -3465.43 q^{52} -18116.1 q^{53} +3265.15 q^{54} +3025.00 q^{55} -33223.5 q^{56} +3586.10 q^{57} -18903.0 q^{58} -50582.4 q^{59} +2686.29 q^{60} +5984.35 q^{61} +25057.8 q^{62} -13674.3 q^{63} +34169.1 q^{64} +7256.49 q^{65} +4877.57 q^{66} +22450.7 q^{67} -7449.56 q^{68} -34092.6 q^{69} +18903.2 q^{70} +10017.6 q^{71} +15940.8 q^{72} -476.148 q^{73} -1349.35 q^{74} -5625.00 q^{75} +4757.19 q^{76} -20427.0 q^{77} +11700.5 q^{78} -85024.7 q^{79} -12485.2 q^{80} +6561.00 q^{81} +65554.5 q^{82} -25643.4 q^{83} -18139.8 q^{84} +15599.1 q^{85} -678.194 q^{86} -37983.8 q^{87} +23812.9 q^{88} +1807.91 q^{89} -9069.86 q^{90} -49001.0 q^{91} -45226.0 q^{92} +50351.2 q^{93} +60622.4 q^{94} -9961.39 q^{95} +36547.2 q^{96} +11688.5 q^{97} -52370.1 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 378 q^{12} + 290 q^{13} + 916 q^{14} - 675 q^{15} - 590 q^{16} + 434 q^{17} + 162 q^{18} - 2856 q^{19} - 1050 q^{20} + 612 q^{21} + 242 q^{22} - 640 q^{23} + 216 q^{24} + 1875 q^{25} + 2132 q^{26} - 2187 q^{27} - 580 q^{28} - 4538 q^{29} - 450 q^{30} - 14968 q^{31} - 2496 q^{32} - 3267 q^{33} - 13704 q^{34} - 1700 q^{35} - 3402 q^{36} - 6190 q^{37} - 11668 q^{38} - 2610 q^{39} - 600 q^{40} - 8926 q^{41} - 8244 q^{42} - 33592 q^{43} - 5082 q^{44} + 6075 q^{45} - 35680 q^{46} - 24640 q^{47} + 5310 q^{48} - 14693 q^{49} + 1250 q^{50} - 3906 q^{51} + 18780 q^{52} - 22934 q^{53} - 1458 q^{54} + 9075 q^{55} - 40012 q^{56} + 25704 q^{57} - 32304 q^{58} - 13756 q^{59} + 9450 q^{60} + 24602 q^{61} - 7704 q^{62} - 5508 q^{63} + 35474 q^{64} + 7250 q^{65} - 2178 q^{66} + 16868 q^{67} - 71288 q^{68} + 5760 q^{69} + 22900 q^{70} + 4856 q^{71} - 1944 q^{72} + 1910 q^{73} + 29404 q^{74} - 16875 q^{75} + 6116 q^{76} - 8228 q^{77} - 19188 q^{78} - 36844 q^{79} - 14750 q^{80} + 19683 q^{81} + 84000 q^{82} - 48796 q^{83} + 5220 q^{84} + 10850 q^{85} - 83492 q^{86} + 40842 q^{87} - 2904 q^{88} - 188978 q^{89} + 4050 q^{90} - 93208 q^{91} - 6976 q^{92} + 134712 q^{93} + 70472 q^{94} - 71400 q^{95} + 22464 q^{96} + 247526 q^{97} - 154654 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 378 * q^12 + 290 * q^13 + 916 * q^14 - 675 * q^15 - 590 * q^16 + 434 * q^17 + 162 * q^18 - 2856 * q^19 - 1050 * q^20 + 612 * q^21 + 242 * q^22 - 640 * q^23 + 216 * q^24 + 1875 * q^25 + 2132 * q^26 - 2187 * q^27 - 580 * q^28 - 4538 * q^29 - 450 * q^30 - 14968 * q^31 - 2496 * q^32 - 3267 * q^33 - 13704 * q^34 - 1700 * q^35 - 3402 * q^36 - 6190 * q^37 - 11668 * q^38 - 2610 * q^39 - 600 * q^40 - 8926 * q^41 - 8244 * q^42 - 33592 * q^43 - 5082 * q^44 + 6075 * q^45 - 35680 * q^46 - 24640 * q^47 + 5310 * q^48 - 14693 * q^49 + 1250 * q^50 - 3906 * q^51 + 18780 * q^52 - 22934 * q^53 - 1458 * q^54 + 9075 * q^55 - 40012 * q^56 + 25704 * q^57 - 32304 * q^58 - 13756 * q^59 + 9450 * q^60 + 24602 * q^61 - 7704 * q^62 - 5508 * q^63 + 35474 * q^64 + 7250 * q^65 - 2178 * q^66 + 16868 * q^67 - 71288 * q^68 + 5760 * q^69 + 22900 * q^70 + 4856 * q^71 - 1944 * q^72 + 1910 * q^73 + 29404 * q^74 - 16875 * q^75 + 6116 * q^76 - 8228 * q^77 - 19188 * q^78 - 36844 * q^79 - 14750 * q^80 + 19683 * q^81 + 84000 * q^82 - 48796 * q^83 + 5220 * q^84 + 10850 * q^85 - 83492 * q^86 + 40842 * q^87 - 2904 * q^88 - 188978 * q^89 + 4050 * q^90 - 93208 * q^91 - 6976 * q^92 + 134712 * q^93 + 70472 * q^94 - 71400 * q^95 + 22464 * q^96 + 247526 * q^97 - 154654 * q^98 + 29403 * q^99

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