LMFDB - Embedded newform 38.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 454x + 3760 $ x^3 - x^2 - 454*x + 3760
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-24.1916$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} -20.1916 q^{3} +16.0000 q^{4} +57.7548 q^{5} -80.7665 q^{6} +142.950 q^{7} +64.0000 q^{8} +164.701 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -20.1916 q^{3} +16.0000 q^{4} +57.7548 q^{5} -80.7665 q^{6} +142.950 q^{7} +64.0000 q^{8} +164.701 q^{9} +231.019 q^{10} +643.832 q^{11} -323.066 q^{12} +115.188 q^{13} +571.802 q^{14} -1166.16 q^{15} +256.000 q^{16} -1742.67 q^{17} +658.805 q^{18} -361.000 q^{19} +924.077 q^{20} -2886.40 q^{21} +2575.33 q^{22} +3703.23 q^{23} -1292.26 q^{24} +210.619 q^{25} +460.754 q^{26} +1580.98 q^{27} +2287.21 q^{28} -5364.27 q^{29} -4664.65 q^{30} -4351.75 q^{31} +1024.00 q^{32} -13000.0 q^{33} -6970.68 q^{34} +8256.08 q^{35} +2635.22 q^{36} +5960.55 q^{37} -1444.00 q^{38} -2325.84 q^{39} +3696.31 q^{40} +3578.24 q^{41} -11545.6 q^{42} -9158.79 q^{43} +10301.3 q^{44} +9512.29 q^{45} +14812.9 q^{46} +9304.58 q^{47} -5169.05 q^{48} +3627.83 q^{49} +842.475 q^{50} +35187.3 q^{51} +1843.01 q^{52} -11892.0 q^{53} +6323.91 q^{54} +37184.4 q^{55} +9148.83 q^{56} +7289.17 q^{57} -21457.1 q^{58} -50659.4 q^{59} -18658.6 q^{60} +23482.2 q^{61} -17407.0 q^{62} +23544.1 q^{63} +4096.00 q^{64} +6652.68 q^{65} -52000.0 q^{66} -58209.0 q^{67} -27882.7 q^{68} -74774.2 q^{69} +33024.3 q^{70} +50243.8 q^{71} +10540.9 q^{72} +16524.5 q^{73} +23842.2 q^{74} -4252.73 q^{75} -5776.00 q^{76} +92036.0 q^{77} -9303.36 q^{78} +10201.7 q^{79} +14785.2 q^{80} -71944.9 q^{81} +14312.9 q^{82} -98402.5 q^{83} -46182.4 q^{84} -100648. q^{85} -36635.2 q^{86} +108313. q^{87} +41205.2 q^{88} -144455. q^{89} +38049.2 q^{90} +16466.2 q^{91} +59251.7 q^{92} +87868.9 q^{93} +37218.3 q^{94} -20849.5 q^{95} -20676.2 q^{96} +1182.70 q^{97} +14511.3 q^{98} +106040. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9}+O(q^{10}) $ 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9	\( 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9} + 324 q^{10} + 363 q^{11} + 208 q^{12} + 501 q^{13} + 912 q^{14} - 670 q^{15} + 768 q^{16} - 1206 q^{17} + 944 q^{18} - 1083 q^{19} + 1296 q^{20} - 2085 q^{21} + 1452 q^{22} - 1077 q^{23} + 832 q^{24} - 3882 q^{25} + 2004 q^{26} - 5087 q^{27} + 3648 q^{28} - 8349 q^{29} - 2680 q^{30} - 7332 q^{31} + 3072 q^{32} - 15784 q^{33} - 4824 q^{34} - 1185 q^{35} + 3776 q^{36} - 1650 q^{37} - 4332 q^{38} + 773 q^{39} + 5184 q^{40} + 10140 q^{41} - 8340 q^{42} + 3777 q^{43} + 5808 q^{44} + 14005 q^{45} - 4308 q^{46} + 33231 q^{47} + 3328 q^{48} + 31269 q^{49} - 15528 q^{50} + 46935 q^{51} + 8016 q^{52} + 31029 q^{53} - 20348 q^{54} + 66003 q^{55} + 14592 q^{56} - 4693 q^{57} - 33396 q^{58} + 20409 q^{59} - 10720 q^{60} + 17115 q^{61} - 29328 q^{62} + 6327 q^{63} + 12288 q^{64} - 45348 q^{65} - 63136 q^{66} - 789 q^{67} - 19296 q^{68} - 151147 q^{69} - 4740 q^{70} + 19164 q^{71} + 15104 q^{72} - 76260 q^{73} - 6600 q^{74} - 69607 q^{75} - 17328 q^{76} - 97209 q^{77} + 3092 q^{78} + 68358 q^{79} + 20736 q^{80} - 197713 q^{81} + 40560 q^{82} + 6762 q^{83} - 33360 q^{84} - 45837 q^{85} + 15108 q^{86} + 66805 q^{87} + 23232 q^{88} - 85506 q^{89} + 56020 q^{90} + 345033 q^{91} - 17232 q^{92} + 15688 q^{93} + 132924 q^{94} - 29241 q^{95} + 13312 q^{96} + 105024 q^{97} + 125076 q^{98} + 158317 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9 + 324 * q^10 + 363 * q^11 + 208 * q^12 + 501 * q^13 + 912 * q^14 - 670 * q^15 + 768 * q^16 - 1206 * q^17 + 944 * q^18 - 1083 * q^19 + 1296 * q^20 - 2085 * q^21 + 1452 * q^22 - 1077 * q^23 + 832 * q^24 - 3882 * q^25 + 2004 * q^26 - 5087 * q^27 + 3648 * q^28 - 8349 * q^29 - 2680 * q^30 - 7332 * q^31 + 3072 * q^32 - 15784 * q^33 - 4824 * q^34 - 1185 * q^35 + 3776 * q^36 - 1650 * q^37 - 4332 * q^38 + 773 * q^39 + 5184 * q^40 + 10140 * q^41 - 8340 * q^42 + 3777 * q^43 + 5808 * q^44 + 14005 * q^45 - 4308 * q^46 + 33231 * q^47 + 3328 * q^48 + 31269 * q^49 - 15528 * q^50 + 46935 * q^51 + 8016 * q^52 + 31029 * q^53 - 20348 * q^54 + 66003 * q^55 + 14592 * q^56 - 4693 * q^57 - 33396 * q^58 + 20409 * q^59 - 10720 * q^60 + 17115 * q^61 - 29328 * q^62 + 6327 * q^63 + 12288 * q^64 - 45348 * q^65 - 63136 * q^66 - 789 * q^67 - 19296 * q^68 - 151147 * q^69 - 4740 * q^70 + 19164 * q^71 + 15104 * q^72 - 76260 * q^73 - 6600 * q^74 - 69607 * q^75 - 17328 * q^76 - 97209 * q^77 + 3092 * q^78 + 68358 * q^79 + 20736 * q^80 - 197713 * q^81 + 40560 * q^82 + 6762 * q^83 - 33360 * q^84 - 45837 * q^85 + 15108 * q^86 + 66805 * q^87 + 23232 * q^88 - 85506 * q^89 + 56020 * q^90 + 345033 * q^91 - 17232 * q^92 + 15688 * q^93 + 132924 * q^94 - 29241 * q^95 + 13312 * q^96 + 105024 * q^97 + 125076 * q^98 + 158317 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−20.1916	−1.29529	−0.647646	−	0.761941i	$-0.724247\pi$
$3$	−20.1916	−1.29529	−0.647646	+	0.761941i	$0.724247\pi$
$4$	16.0000	0.500000
$5$	57.7548	1.03315	0.516575	−	0.856242i	$-0.327207\pi$
$5$	57.7548	1.03315	0.516575	+	0.856242i	$0.327207\pi$
$6$	−80.7665	−0.915910
$7$	142.950	1.10266	0.551328	−	0.834288i	$-0.314121\pi$
$7$	142.950	1.10266	0.551328	+	0.834288i	$0.314121\pi$
$8$	64.0000	0.353553
$9$	164.701	0.677783
$10$	231.019	0.730547
$11$	643.832	1.60432	0.802160	−	0.597110i	$-0.203684\pi$
$11$	643.832	1.60432	0.802160	+	0.597110i	$0.203684\pi$
$12$	−323.066	−0.647646
$13$	115.188	0.189039	0.0945193	−	0.995523i	$-0.469869\pi$
$13$	115.188	0.189039	0.0945193	+	0.995523i	$0.469869\pi$
$14$	571.802	0.779696
$15$	−1166.16	−1.33823
$16$	256.000	0.250000
$17$	−1742.67	−1.46249	−0.731245	−	0.682115i	$-0.761060\pi$
$17$	−1742.67	−1.46249	−0.731245	+	0.682115i	$0.761060\pi$
$18$	658.805	0.479265
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	924.077	0.516575
$21$	−2886.40	−1.42826
$22$	2575.33	1.13442
$23$	3703.23	1.45969	0.729846	−	0.683611i	$-0.239592\pi$
$23$	3703.23	1.45969	0.729846	+	0.683611i	$0.239592\pi$
$24$	−1292.26	−0.457955
$25$	210.619	0.0673980
$26$	460.754	0.133670
$27$	1580.98	0.417365
$28$	2287.21	0.551328
$29$	−5364.27	−1.18445	−0.592223	−	0.805774i	$-0.701750\pi$
$29$	−5364.27	−1.18445	−0.592223	+	0.805774i	$0.701750\pi$
$30$	−4664.65	−0.946272
$31$	−4351.75	−0.813317	−0.406659	−	0.913580i	$-0.633306\pi$
$31$	−4351.75	−0.813317	−0.406659	+	0.913580i	$0.633306\pi$
$32$	1024.00	0.176777
$33$	−13000.0	−2.07806
$34$	−6970.68	−1.03414
$35$	8256.08	1.13921
$36$	2635.22	0.338891
$37$	5960.55	0.715784	0.357892	−	0.933763i	$-0.383496\pi$
$37$	5960.55	0.715784	0.357892	+	0.933763i	$0.383496\pi$
$38$	−1444.00	−0.162221
$39$	−2325.84	−0.244860
$40$	3696.31	0.365274
$41$	3578.24	0.332437	0.166219	−	0.986089i	$-0.446844\pi$
$41$	3578.24	0.332437	0.166219	+	0.986089i	$0.446844\pi$
$42$	−11545.6	−1.00993
$43$	−9158.79	−0.755383	−0.377691	−	0.925932i	$-0.623282\pi$
$43$	−9158.79	−0.755383	−0.377691	+	0.925932i	$0.623282\pi$
$44$	10301.3	0.802160
$45$	9512.29	0.700251
$46$	14812.9	1.03216
$47$	9304.58	0.614401	0.307201	−	0.951645i	$-0.400608\pi$
$47$	9304.58	0.614401	0.307201	+	0.951645i	$0.400608\pi$
$48$	−5169.05	−0.323823
$49$	3627.83	0.215852
$50$	842.475	0.0476576
$51$	35187.3	1.89435
$52$	1843.01	0.0945193
$53$	−11892.0	−0.581520	−0.290760	−	0.956796i	$-0.593908\pi$
$53$	−11892.0	−0.581520	−0.290760	+	0.956796i	$0.593908\pi$
$54$	6323.91	0.295122
$55$	37184.4	1.65750
$56$	9148.83	0.389848
$57$	7289.17	0.297161
$58$	−21457.1	−0.837530
$59$	−50659.4	−1.89465	−0.947327	−	0.320267i	$-0.896227\pi$
$59$	−50659.4	−1.89465	−0.947327	+	0.320267i	$0.896227\pi$
$60$	−18658.6	−0.669115
$61$	23482.2	0.808006	0.404003	−	0.914758i	$-0.367619\pi$
$61$	23482.2	0.808006	0.404003	+	0.914758i	$0.367619\pi$
$62$	−17407.0	−0.575102
$63$	23544.1	0.747362
$64$	4096.00	0.125000
$65$	6652.68	0.195305
$66$	−52000.0	−1.46941
$67$	−58209.0	−1.58418	−0.792088	−	0.610407i	$-0.791006\pi$
$67$	−58209.0	−1.58418	−0.792088	+	0.610407i	$0.791006\pi$
$68$	−27882.7	−0.731245
$69$	−74774.2	−1.89073
$70$	33024.3	0.805543
$71$	50243.8	1.18287	0.591434	−	0.806353i	$-0.298562\pi$
$71$	50243.8	1.18287	0.591434	+	0.806353i	$0.298562\pi$
$72$	10540.9	0.239632
$73$	16524.5	0.362928	0.181464	−	0.983398i	$-0.441916\pi$
$73$	16524.5	0.362928	0.181464	+	0.983398i	$0.441916\pi$
$74$	23842.2	0.506136
$75$	−4252.73	−0.0873002
$76$	−5776.00	−0.114708
$77$	92036.0	1.76901
$78$	−9303.36	−0.173142
$79$	10201.7	0.183910	0.0919548	−	0.995763i	$-0.470688\pi$
$79$	10201.7	0.183910	0.0919548	+	0.995763i	$0.470688\pi$
$80$	14785.2	0.258287
$81$	−71944.9	−1.21839
$82$	14312.9	0.235068
$83$	−98402.5	−1.56787	−0.783936	−	0.620841i	$-0.786791\pi$
$83$	−98402.5	−1.56787	−0.783936	+	0.620841i	$0.786791\pi$
$84$	−46182.4	−0.714132
$85$	−100648.	−1.51097
$86$	−36635.2	−0.534136
$87$	108313.	1.53420
$88$	41205.2	0.567212
$89$	−144455.	−1.93311	−0.966555	−	0.256461i	$-0.917444\pi$
$89$	−144455.	−1.93311	−0.966555	+	0.256461i	$0.917444\pi$
$90$	38049.2	0.495152
$91$	16466.2	0.208445
$92$	59251.7	0.729846
$93$	87868.9	1.05348
$94$	37218.3	0.434447
$95$	−20849.5	−0.237021
$96$	−20676.2	−0.228978
$97$	1182.70	0.0127628	0.00638138	−	0.999980i	$-0.497969\pi$
$97$	1182.70	0.0127628	0.00638138	+	0.999980i	$0.497969\pi$
$98$	14511.3	0.152631
$99$	106040.	1.08738
$100$	3369.90	0.0336990
$101$	−23329.3	−0.227561	−0.113780	−	0.993506i	$-0.536296\pi$
$101$	−23329.3	−0.227561	−0.113780	+	0.993506i	$0.536296\pi$
$102$	140749.	1.33951
$103$	143070.	1.32879	0.664393	−	0.747384i	$-0.268690\pi$
$103$	143070.	1.32879	0.664393	+	0.747384i	$0.268690\pi$
$104$	7372.06	0.0668352
$105$	−166703.	−1.47561
$106$	−47568.0	−0.411197
$107$	38417.1	0.324389	0.162194	−	0.986759i	$-0.448143\pi$
$107$	38417.1	0.324389	0.162194	+	0.986759i	$0.448143\pi$
$108$	25295.7	0.208683
$109$	92965.8	0.749475	0.374737	−	0.927131i	$-0.377733\pi$
$109$	92965.8	0.749475	0.374737	+	0.927131i	$0.377733\pi$
$110$	148738.	1.17203
$111$	−120353.	−0.927150
$112$	36595.3	0.275664
$113$	−144056.	−1.06129	−0.530646	−	0.847594i	$-0.678051\pi$
$113$	−144056.	−1.06129	−0.530646	+	0.847594i	$0.678051\pi$
$114$	29156.7	0.210124
$115$	213879.	1.50808
$116$	−85828.3	−0.592223
$117$	18971.7	0.128127
$118$	−202638.	−1.33972
$119$	−249115.	−1.61262
$120$	−74634.4	−0.473136
$121$	253468.	1.57384
$122$	93928.9	0.571346
$123$	−72250.4	−0.430603
$124$	−69628.0	−0.406659
$125$	−168320.	−0.963517
$126$	94176.5	0.528465
$127$	232686.	1.28015	0.640075	−	0.768312i	$-0.278903\pi$
$127$	232686.	1.28015	0.640075	+	0.768312i	$0.278903\pi$
$128$	16384.0	0.0883883
$129$	184931.	0.978441
$130$	26610.7	0.138102
$131$	−304513.	−1.55034	−0.775171	−	0.631752i	$-0.782336\pi$
$131$	−304513.	−1.55034	−0.775171	+	0.631752i	$0.782336\pi$
$132$	−208000.	−1.03903
$133$	−51605.1	−0.252967
$134$	−232836.	−1.12018
$135$	91309.1	0.431201
$136$	−111531.	−0.517068
$137$	264041.	1.20190	0.600952	−	0.799285i	$-0.294788\pi$
$137$	264041.	1.20190	0.600952	+	0.799285i	$0.294788\pi$
$138$	−299097.	−1.33695
$139$	200771.	0.881380	0.440690	−	0.897659i	$-0.354734\pi$
$139$	200771.	0.881380	0.440690	+	0.897659i	$0.354734\pi$
$140$	132097.	0.569605
$141$	−187874.	−0.795829
$142$	200975.	0.836414
$143$	74162.0	0.303278
$144$	42163.5	0.169446
$145$	−309812.	−1.22371
$146$	66097.9	0.256629
$147$	−73251.7	−0.279592
$148$	95368.8	0.357892
$149$	−398140.	−1.46916	−0.734582	−	0.678520i	$-0.762622\pi$
$149$	−398140.	−1.46916	−0.734582	+	0.678520i	$0.762622\pi$
$150$	−17010.9	−0.0617305
$151$	232311.	0.829141	0.414570	−	0.910017i	$-0.363932\pi$
$151$	232311.	0.829141	0.414570	+	0.910017i	$0.363932\pi$
$152$	−23104.0	−0.0811107
$153$	−287020.	−0.991250
$154$	368144.	1.25088
$155$	−251335.	−0.840278
$156$	−37213.4	−0.122430
$157$	79984.5	0.258974	0.129487	−	0.991581i	$-0.458667\pi$
$157$	79984.5	0.258974	0.129487	+	0.991581i	$0.458667\pi$
$158$	40806.7	0.130044
$159$	240118.	0.753239
$160$	59140.9	0.182637
$161$	529379.	1.60954
$162$	−287780.	−0.861534
$163$	567717.	1.67364	0.836821	−	0.547476i	$-0.184411\pi$
$163$	567717.	1.67364	0.836821	+	0.547476i	$0.184411\pi$
$164$	57251.8	0.166219
$165$	−750813.	−2.14695
$166$	−393610.	−1.10865
$167$	193825.	0.537798	0.268899	−	0.963168i	$-0.413340\pi$
$167$	193825.	0.537798	0.268899	+	0.963168i	$0.413340\pi$
$168$	−184730.	−0.504967
$169$	−358025.	−0.964264
$170$	−402590.	−1.06842
$171$	−59457.1	−0.155494
$172$	−146541.	−0.377691
$173$	166827.	0.423791	0.211896	−	0.977292i	$-0.432036\pi$
$173$	166827.	0.423791	0.211896	+	0.977292i	$0.432036\pi$
$174$	433253.	1.08485
$175$	30108.1	0.0743169
$176$	164821.	0.401080
$177$	1.02290e6	2.45413
$178$	−577818.	−1.36691
$179$	554600.	1.29374	0.646871	−	0.762600i	$-0.276077\pi$
$179$	554600.	1.29374	0.646871	+	0.762600i	$0.276077\pi$
$180$	152197.	0.350126
$181$	227012.	0.515054	0.257527	−	0.966271i	$-0.417092\pi$
$181$	227012.	0.515054	0.257527	+	0.966271i	$0.417092\pi$
$182$	65864.9	0.147393
$183$	−474144.	−1.04660
$184$	237007.	0.516079
$185$	344251.	0.739512
$186$	351476.	0.744926
$187$	−1.12199e6	−2.34630
$188$	148873.	0.307201
$189$	226002.	0.460211
$190$	−83398.0	−0.167599
$191$	−273598.	−0.542663	−0.271331	−	0.962486i	$-0.587464\pi$
$191$	−273598.	−0.542663	−0.271331	+	0.962486i	$0.587464\pi$
$192$	−82704.8	−0.161912
$193$	239572.	0.462960	0.231480	−	0.972840i	$-0.425643\pi$
$193$	239572.	0.462960	0.231480	+	0.972840i	$0.425643\pi$
$194$	4730.79	0.00902463
$195$	−134328.	−0.252977
$196$	58045.2	0.107926
$197$	754700.	1.38551	0.692753	−	0.721175i	$-0.256398\pi$
$197$	754700.	1.38551	0.692753	+	0.721175i	$0.256398\pi$
$198$	424160.	0.768894
$199$	−45409.8	−0.0812862	−0.0406431	−	0.999174i	$-0.512941\pi$
$199$	−45409.8	−0.0812862	−0.0406431	+	0.999174i	$0.512941\pi$
$200$	13479.6	0.0238288
$201$	1.17533e6	2.05197
$202$	−93317.0	−0.160910
$203$	−766824.	−1.30604
$204$	562997.	0.947176
$205$	206660.	0.343457
$206$	572279.	0.939593
$207$	609927.	0.989355
$208$	29488.2	0.0472596
$209$	−232423.	−0.368056
$210$	−666814.	−1.04341
$211$	−1.06384e6	−1.64501	−0.822504	−	0.568759i	$-0.807424\pi$
$211$	−1.06384e6	−1.64501	−0.822504	+	0.568759i	$0.807424\pi$
$212$	−190272.	−0.290760
$213$	−1.01450e6	−1.53216
$214$	153669.	0.229377
$215$	−528964.	−0.780423
$216$	101183.	0.147561
$217$	−622085.	−0.896810
$218$	371863.	0.529959
$219$	−333656.	−0.470098
$220$	594950.	0.828751
$221$	−200735.	−0.276467
$222$	−481413.	−0.655594
$223$	−693434.	−0.933777	−0.466888	−	0.884316i	$-0.654625\pi$
$223$	−693434.	−0.933777	−0.466888	+	0.884316i	$0.654625\pi$
$224$	146381.	0.194924
$225$	34689.2	0.0456812
$226$	−576224.	−0.750447
$227$	−856356.	−1.10304	−0.551518	−	0.834163i	$-0.685951\pi$
$227$	−856356.	−1.10304	−0.551518	+	0.834163i	$0.685951\pi$
$228$	116627.	0.148580
$229$	−774759.	−0.976288	−0.488144	−	0.872763i	$-0.662326\pi$
$229$	−774759.	−0.976288	−0.488144	+	0.872763i	$0.662326\pi$
$230$	855518.	1.06637
$231$	−1.85836e6	−2.29139
$232$	−343313.	−0.418765
$233$	402957.	0.486261	0.243130	−	0.969994i	$-0.421826\pi$
$233$	402957.	0.486261	0.243130	+	0.969994i	$0.421826\pi$
$234$	75886.7	0.0905995
$235$	537384.	0.634768
$236$	−810551.	−0.947327
$237$	−205988.	−0.238217
$238$	−996461.	−1.14030
$239$	310461.	0.351570	0.175785	−	0.984429i	$-0.443754\pi$
$239$	310461.	0.351570	0.175785	+	0.984429i	$0.443754\pi$
$240$	−298538.	−0.334558
$241$	201633.	0.223625	0.111812	−	0.993729i	$-0.464334\pi$
$241$	201633.	0.223625	0.111812	+	0.993729i	$0.464334\pi$
$242$	1.01387e6	1.11287
$243$	1.06851e6	1.16081
$244$	375716.	0.404003
$245$	209525.	0.223008
$246$	−289001.	−0.304482
$247$	−41583.0	−0.0433684
$248$	−278512.	−0.287551
$249$	1.98691e6	2.03085
$250$	−673278.	−0.681310
$251$	−1.60994e6	−1.61296	−0.806481	−	0.591260i	$-0.798631\pi$
$251$	−1.60994e6	−1.61296	−0.806481	+	0.591260i	$0.798631\pi$
$252$	376706.	0.373681
$253$	2.38426e6	2.34181
$254$	930744.	0.905203
$255$	2.03224e6	1.95715
$256$	65536.0	0.0625000
$257$	−149432.	−0.141127	−0.0705634	−	0.997507i	$-0.522480\pi$
$257$	−149432.	−0.141127	−0.0705634	+	0.997507i	$0.522480\pi$
$258$	739723.	0.691863
$259$	852064.	0.789265
$260$	106443.	0.0976525
$261$	−883501.	−0.802797
$262$	−1.21805e6	−1.09626
$263$	1.74758e6	1.55793	0.778965	−	0.627068i	$-0.215745\pi$
$263$	1.74758e6	1.55793	0.778965	+	0.627068i	$0.215745\pi$
$264$	−832000.	−0.734706
$265$	−686820.	−0.600797
$266$	−206420.	−0.178875
$267$	2.91677e6	2.50394
$268$	−931345.	−0.792088
$269$	−1.87296e6	−1.57815	−0.789073	−	0.614299i	$-0.789439\pi$
$269$	−1.87296e6	−1.57815	−0.789073	+	0.614299i	$0.789439\pi$
$270$	365236.	0.304905
$271$	−1.02502e6	−0.847833	−0.423916	−	0.905701i	$-0.639345\pi$
$271$	−1.02502e6	−0.847833	−0.423916	+	0.905701i	$0.639345\pi$
$272$	−446123.	−0.365622
$273$	−332480.	−0.269997
$274$	1.05616e6	0.849874
$275$	135603.	0.108128
$276$	−1.19639e6	−0.945364
$277$	317688.	0.248772	0.124386	−	0.992234i	$-0.460304\pi$
$277$	317688.	0.248772	0.124386	+	0.992234i	$0.460304\pi$
$278$	803082.	0.623230
$279$	−716739.	−0.551253
$280$	528389.	0.402771
$281$	−1.13391e6	−0.856667	−0.428333	−	0.903621i	$-0.640899\pi$
$281$	−1.13391e6	−0.856667	−0.428333	+	0.903621i	$0.640899\pi$
$282$	−751498.	−0.562736
$283$	594298.	0.441101	0.220550	−	0.975376i	$-0.429215\pi$
$283$	594298.	0.441101	0.220550	+	0.975376i	$0.429215\pi$
$284$	803900.	0.591434
$285$	420985.	0.307011
$286$	296648.	0.214450
$287$	511510.	0.366564
$288$	168654.	0.119816
$289$	1.61704e6	1.13888
$290$	−1.23925e6	−0.865294
$291$	−23880.6	−0.0165315
$292$	264392.	0.181464
$293$	920802.	0.626610	0.313305	−	0.949653i	$-0.398564\pi$
$293$	920802.	0.626610	0.313305	+	0.949653i	$0.398564\pi$
$294$	−293007.	−0.197701
$295$	−2.92582e6	−1.95746
$296$	381475.	0.253068
$297$	1.01788e6	0.669587
$298$	−1.59256e6	−1.03886
$299$	426569.	0.275938
$300$	−68043.7	−0.0436501
$301$	−1.30925e6	−0.832928
$302$	929246.	0.586291
$303$	471055.	0.294758
$304$	−92416.0	−0.0573539
$305$	1.35621e6	0.834791
$306$	−1.14808e6	−0.700920
$307$	−429602.	−0.260148	−0.130074	−	0.991504i	$-0.541521\pi$
$307$	−429602.	−0.260148	−0.130074	+	0.991504i	$0.541521\pi$
$308$	1.47258e6	0.884507
$309$	−2.88881e6	−1.72117
$310$	−1.00534e6	−0.594167
$311$	2.55559e6	1.49827	0.749136	−	0.662416i	$-0.230469\pi$
$311$	2.55559e6	1.49827	0.749136	+	0.662416i	$0.230469\pi$
$312$	−148854.	−0.0865711
$313$	337207.	0.194552	0.0972761	−	0.995257i	$-0.468987\pi$
$313$	337207.	0.194552	0.0972761	+	0.995257i	$0.468987\pi$
$314$	319938.	0.183122
$315$	1.35979e6	0.772137
$316$	163227.	0.0919548
$317$	−751694.	−0.420139	−0.210069	−	0.977686i	$-0.567369\pi$
$317$	−751694.	−0.420139	−0.210069	+	0.977686i	$0.567369\pi$
$318$	960474.	0.532620
$319$	−3.45369e6	−1.90023
$320$	236564.	0.129144
$321$	−775704.	−0.420178
$322$	2.11751e6	1.13812
$323$	629104.	0.335518
$324$	−1.15112e6	−0.609197
$325$	24260.8	0.0127408
$326$	2.27087e6	1.18344
$327$	−1.87713e6	−0.970789
$328$	229007.	0.117534
$329$	1.33009e6	0.677474
$330$	−3.00325e6	−1.51812
$331$	1.58926e6	0.797307	0.398654	−	0.917102i	$-0.369478\pi$
$331$	1.58926e6	0.797307	0.398654	+	0.917102i	$0.369478\pi$
$332$	−1.57444e6	−0.783936
$333$	981710.	0.485146
$334$	775300.	0.380280
$335$	−3.36185e6	−1.63669
$336$	−738918.	−0.357066
$337$	−759304.	−0.364201	−0.182100	−	0.983280i	$-0.558290\pi$
$337$	−759304.	−0.364201	−0.182100	+	0.983280i	$0.558290\pi$
$338$	−1.43210e6	−0.681838
$339$	2.90872e6	1.37468
$340$	−1.61036e6	−0.755485
$341$	−2.80180e6	−1.30482
$342$	−237829.	−0.109951
$343$	−1.88397e6	−0.864646
$344$	−586163.	−0.267068
$345$	−4.31857e6	−1.95341
$346$	667310.	0.299666
$347$	1.29040e6	0.575307	0.287654	−	0.957734i	$-0.407125\pi$
$347$	1.29040e6	0.575307	0.287654	+	0.957734i	$0.407125\pi$
$348$	1.73301e6	0.767102
$349$	630430.	0.277060	0.138530	−	0.990358i	$-0.455762\pi$
$349$	630430.	0.277060	0.138530	+	0.990358i	$0.455762\pi$
$350$	120432.	0.0525500
$351$	182110.	0.0788981
$352$	659284.	0.283606
$353$	−2.32005e6	−0.990972	−0.495486	−	0.868616i	$-0.665010\pi$
$353$	−2.32005e6	−0.990972	−0.495486	+	0.868616i	$0.665010\pi$
$354$	4.09158e6	1.73533
$355$	2.90182e6	1.22208
$356$	−2.31127e6	−0.966555
$357$	5.03004e6	2.08882
$358$	2.21840e6	0.914814
$359$	−1.89175e6	−0.774691	−0.387345	−	0.921935i	$-0.626608\pi$
$359$	−1.89175e6	−0.774691	−0.387345	+	0.921935i	$0.626608\pi$
$360$	608787.	0.247576
$361$	130321.	0.0526316
$362$	908049.	0.364198
$363$	−5.11794e6	−2.03858
$364$	263460.	0.104222
$365$	954368.	0.374959
$366$	−1.89658e6	−0.740061
$367$	3.32455e6	1.28845	0.644225	−	0.764836i	$-0.277180\pi$
$367$	3.32455e6	1.28845	0.644225	+	0.764836i	$0.277180\pi$
$368$	948027.	0.364923
$369$	589340.	0.225320
$370$	1.37700e6	0.522914
$371$	−1.69996e6	−0.641217
$372$	1.40590e6	0.526742
$373$	−423412.	−0.157576	−0.0787882	−	0.996891i	$-0.525105\pi$
$373$	−423412.	−0.157576	−0.0787882	+	0.996891i	$0.525105\pi$
$374$	−4.48794e6	−1.65908
$375$	3.39864e6	1.24804
$376$	595493.	0.217224
$377$	−617901.	−0.223906
$378$	904006.	0.325418
$379$	1.33440e6	0.477186	0.238593	−	0.971120i	$-0.423314\pi$
$379$	1.33440e6	0.477186	0.238593	+	0.971120i	$0.423314\pi$
$380$	−333592.	−0.118510
$381$	−4.69831e6	−1.65817
$382$	−1.09439e6	−0.383721
$383$	3.20754e6	1.11731	0.558657	−	0.829398i	$-0.311317\pi$
$383$	3.20754e6	1.11731	0.558657	+	0.829398i	$0.311317\pi$
$384$	−330819.	−0.114489
$385$	5.31553e6	1.82766
$386$	958289.	0.327362
$387$	−1.50846e6	−0.511985
$388$	18923.2	0.00638138
$389$	−4.95813e6	−1.66129	−0.830643	−	0.556806i	$-0.812027\pi$
$389$	−4.95813e6	−1.66129	−0.830643	+	0.556806i	$0.812027\pi$
$390$	−537314.	−0.178882
$391$	−6.45351e6	−2.13478
$392$	232181.	0.0763153
$393$	6.14861e6	2.00815
$394$	3.01880e6	0.979701
$395$	589196.	0.190006
$396$	1.69664e6	0.543690
$397$	4.11483e6	1.31031	0.655157	−	0.755493i	$-0.272603\pi$
$397$	4.11483e6	1.31031	0.655157	+	0.755493i	$0.272603\pi$
$398$	−181639.	−0.0574780
$399$	1.04199e6	0.327666
$400$	53918.4	0.0168495
$401$	5.45867e6	1.69522	0.847610	−	0.530620i	$-0.178041\pi$
$401$	5.45867e6	1.69522	0.847610	+	0.530620i	$0.178041\pi$
$402$	4.70134e6	1.45096
$403$	−501271.	−0.153748
$404$	−373268.	−0.113780
$405$	−4.15516e6	−1.25878
$406$	−3.06730e6	−0.923508
$407$	3.83759e6	1.14835
$408$	2.25199e6	0.669754
$409$	1.25432e6	0.370767	0.185383	−	0.982666i	$-0.440647\pi$
$409$	1.25432e6	0.370767	0.185383	+	0.982666i	$0.440647\pi$
$410$	826641.	0.242861
$411$	−5.33141e6	−1.55682
$412$	2.28912e6	0.664393
$413$	−7.24178e6	−2.08915
$414$	2.43971e6	0.699579
$415$	−5.68322e6	−1.61985
$416$	117953.	0.0334176
$417$	−4.05388e6	−1.14164
$418$	−929693.	−0.260255
$419$	4.47653e6	1.24568	0.622840	−	0.782349i	$-0.285979\pi$
$419$	4.47653e6	1.24568	0.622840	+	0.782349i	$0.285979\pi$
$420$	−2.66726e6	−0.737805
$421$	−230678.	−0.0634309	−0.0317154	−	0.999497i	$-0.510097\pi$
$421$	−230678.	−0.0634309	−0.0317154	+	0.999497i	$0.510097\pi$
$422$	−4.25534e6	−1.16320
$423$	1.53248e6	0.416431
$424$	−761087.	−0.205598
$425$	−367039.	−0.0985689
$426$	−4.05801e6	−1.08340
$427$	3.35679e6	0.890953
$428$	614674.	0.162194
$429$	−1.49745e6	−0.392834
$430$	−2.11586e6	−0.551842
$431$	4.04297e6	1.04835	0.524177	−	0.851610i	$-0.324373\pi$
$431$	4.04297e6	1.04835	0.524177	+	0.851610i	$0.324373\pi$
$432$	404730.	0.104341
$433$	545989.	0.139947	0.0699736	−	0.997549i	$-0.477709\pi$
$433$	545989.	0.139947	0.0699736	+	0.997549i	$0.477709\pi$
$434$	−2.48834e6	−0.634140
$435$	6.25561e6	1.58506
$436$	1.48745e6	0.374737
$437$	−1.33687e6	−0.334876
$438$	−1.33462e6	−0.332409
$439$	5.51947e6	1.36690	0.683449	−	0.729998i	$-0.260479\pi$
$439$	5.51947e6	1.36690	0.683449	+	0.729998i	$0.260479\pi$
$440$	2.37980e6	0.586015
$441$	597508.	0.146301
$442$	−802941.	−0.195492
$443$	−3.38518e6	−0.819544	−0.409772	−	0.912188i	$-0.634392\pi$
$443$	−3.38518e6	−0.819544	−0.409772	+	0.912188i	$0.634392\pi$
$444$	−1.92565e6	−0.463575
$445$	−8.34295e6	−1.99719
$446$	−2.77374e6	−0.660280
$447$	8.03909e6	1.90300
$448$	585525.	0.137832
$449$	536837.	0.125669	0.0628343	−	0.998024i	$-0.479986\pi$
$449$	536837.	0.125669	0.0628343	+	0.998024i	$0.479986\pi$
$450$	138757.	0.0323015
$451$	2.30378e6	0.533335
$452$	−2.30489e6	−0.530646
$453$	−4.69074e6	−1.07398
$454$	−3.42542e6	−0.779964
$455$	951004.	0.215354
$456$	466507.	0.105062
$457$	4.58785e6	1.02759	0.513794	−	0.857914i	$-0.328240\pi$
$457$	4.58785e6	1.02759	0.513794	+	0.857914i	$0.328240\pi$
$458$	−3.09904e6	−0.690340
$459$	−2.75512e6	−0.610393
$460$	3.42207e6	0.754040
$461$	8.31564e6	1.82240	0.911199	−	0.411966i	$-0.135158\pi$
$461$	8.31564e6	1.82240	0.911199	+	0.411966i	$0.135158\pi$
$462$	−7.43343e6	−1.62026
$463$	2.50501e6	0.543071	0.271536	−	0.962428i	$-0.412469\pi$
$463$	2.50501e6	0.543071	0.271536	+	0.962428i	$0.412469\pi$
$464$	−1.37325e6	−0.296112
$465$	5.07485e6	1.08841
$466$	1.61183e6	0.343838
$467$	−4.39917e6	−0.933423	−0.466711	−	0.884410i	$-0.654561\pi$
$467$	−4.39917e6	−0.933423	−0.466711	+	0.884410i	$0.654561\pi$
$468$	303547.	0.0640635
$469$	−8.32101e6	−1.74680
$470$	2.14954e6	0.448849
$471$	−1.61502e6	−0.335447
$472$	−3.24220e6	−0.669862
$473$	−5.89672e6	−1.21187
$474$	−823954.	−0.168445
$475$	−76033.4	−0.0154622
$476$	−3.98585e6	−0.806312
$477$	−1.95863e6	−0.394144
$478$	1.24184e6	0.248597
$479$	573246.	0.114157	0.0570784	−	0.998370i	$-0.481821\pi$
$479$	573246.	0.114157	0.0570784	+	0.998370i	$0.481821\pi$
$480$	−1.19415e6	−0.236568
$481$	686586.	0.135311
$482$	806534.	0.158127
$483$	−1.06890e7	−2.08483
$484$	4.05550e6	0.786920
$485$	68306.5	0.0131858
$486$	4.27402e6	0.820817
$487$	358105.	0.0684208	0.0342104	−	0.999415i	$-0.489108\pi$
$487$	358105.	0.0684208	0.0342104	+	0.999415i	$0.489108\pi$
$488$	1.50286e6	0.285673
$489$	−1.14631e7	−2.16786
$490$	838098.	0.157690
$491$	−4.30373e6	−0.805640	−0.402820	−	0.915279i	$-0.631970\pi$
$491$	−4.30373e6	−0.805640	−0.402820	+	0.915279i	$0.631970\pi$
$492$	−1.15601e6	−0.215302
$493$	9.34814e6	1.73224
$494$	−166332.	−0.0306661
$495$	6.12432e6	1.12343
$496$	−1.11405e6	−0.203329
$497$	7.18237e6	1.30430
$498$	7.94762e6	1.43603
$499$	−6.76859e6	−1.21688	−0.608439	−	0.793601i	$-0.708204\pi$
$499$	−6.76859e6	−1.21688	−0.608439	+	0.793601i	$0.708204\pi$
$500$	−2.69311e6	−0.481759
$501$	−3.91364e6	−0.696605
$502$	−6.43974e6	−1.14054
$503$	−3.38948e6	−0.597329	−0.298665	−	0.954358i	$-0.596541\pi$
$503$	−3.38948e6	−0.597329	−0.298665	+	0.954358i	$0.596541\pi$
$504$	1.50682e6	0.264232
$505$	−1.34738e6	−0.235104
$506$	9.53704e6	1.65591
$507$	7.22910e6	1.24900
$508$	3.72298e6	0.640075
$509$	8.54333e6	1.46161	0.730807	−	0.682584i	$-0.239144\pi$
$509$	8.54333e6	1.46161	0.730807	+	0.682584i	$0.239144\pi$
$510$	8.12895e6	1.38391
$511$	2.36218e6	0.400185
$512$	262144.	0.0441942
$513$	−570733.	−0.0957502
$514$	−597727.	−0.0997918
$515$	8.26297e6	1.37283
$516$	2.95889e6	0.489221
$517$	5.99058e6	0.985696
$518$	3.40825e6	0.558094
$519$	−3.36852e6	−0.548934
$520$	425772.	0.0690508
$521$	−1.60001e6	−0.258242	−0.129121	−	0.991629i	$-0.541216\pi$
$521$	−1.60001e6	−0.258242	−0.129121	+	0.991629i	$0.541216\pi$
$522$	−3.53401e6	−0.567664
$523$	9.55689e6	1.52779	0.763893	−	0.645343i	$-0.223285\pi$
$523$	9.55689e6	1.52779	0.763893	+	0.645343i	$0.223285\pi$
$524$	−4.87221e6	−0.775171
$525$	−607930.	−0.0962621
$526$	6.99032e6	1.10162
$527$	7.58367e6	1.18947
$528$	−3.32800e6	−0.519516
$529$	7.27759e6	1.13070
$530$	−2.74728e6	−0.424828
$531$	−8.34367e6	−1.28416
$532$	−825682.	−0.126483
$533$	412171.	0.0628434
$534$	1.16671e7	1.77055
$535$	2.21877e6	0.335142
$536$	−3.72538e6	−0.560091
$537$	−1.11983e7	−1.67577
$538$	−7.49183e6	−1.11592
$539$	2.33571e6	0.346296
$540$	1.46095e6	0.215600
$541$	−7.60745e6	−1.11750	−0.558748	−	0.829337i	$-0.688718\pi$
$541$	−7.60745e6	−1.11750	−0.558748	+	0.829337i	$0.688718\pi$
$542$	−4.10009e6	−0.599508
$543$	−4.58374e6	−0.667146
$544$	−1.78449e6	−0.258534
$545$	5.36922e6	0.774319
$546$	−1.32992e6	−0.190917
$547$	−8.22099e6	−1.17478	−0.587389	−	0.809305i	$-0.699844\pi$
$547$	−8.22099e6	−1.17478	−0.587389	+	0.809305i	$0.699844\pi$
$548$	4.22465e6	0.600952
$549$	3.86755e6	0.547653
$550$	542412.	0.0764580
$551$	1.93650e6	0.271731
$552$	−4.78555e6	−0.668474
$553$	1.45834e6	0.202789
$554$	1.27075e6	0.175908
$555$	−6.95098e6	−0.957885
$556$	3.21233e6	0.440690
$557$	−6.69066e6	−0.913758	−0.456879	−	0.889529i	$-0.651033\pi$
$557$	−6.69066e6	−0.913758	−0.456879	+	0.889529i	$0.651033\pi$
$558$	−2.86696e6	−0.389794
$559$	−1.05499e6	−0.142796
$560$	2.11356e6	0.284802
$561$	2.26547e7	3.03914
$562$	−4.53563e6	−0.605755
$563$	−3.42478e6	−0.455368	−0.227684	−	0.973735i	$-0.573115\pi$
$563$	−3.42478e6	−0.455368	−0.227684	+	0.973735i	$0.573115\pi$
$564$	−3.00599e6	−0.397915
$565$	−8.31992e6	−1.09647
$566$	2.37719e6	0.311905
$567$	−1.02846e7	−1.34347
$568$	3.21560e6	0.418207
$569$	1.17171e6	0.151719	0.0758596	−	0.997119i	$-0.475830\pi$
$569$	1.17171e6	0.151719	0.0758596	+	0.997119i	$0.475830\pi$
$570$	1.68394e6	0.217090
$571$	−1.43837e6	−0.184621	−0.0923104	−	0.995730i	$-0.529425\pi$
$571$	−1.43837e6	−0.184621	−0.0923104	+	0.995730i	$0.529425\pi$
$572$	1.18659e6	0.151639
$573$	5.52439e6	0.702907
$574$	2.04604e6	0.259200
$575$	779970.	0.0983804
$576$	674616.	0.0847229
$577$	−1.18857e6	−0.148623	−0.0743116	−	0.997235i	$-0.523676\pi$
$577$	−1.18857e6	−0.148623	−0.0743116	+	0.997235i	$0.523676\pi$
$578$	6.46816e6	0.805306
$579$	−4.83735e6	−0.599668
$580$	−4.95700e6	−0.611855
$581$	−1.40667e7	−1.72883
$582$	−95522.3	−0.0116895
$583$	−7.65644e6	−0.932944
$584$	1.05757e6	0.128314
$585$	1.09571e6	0.132374
$586$	3.68321e6	0.443080
$587$	853619.	0.102251	0.0511256	−	0.998692i	$-0.483719\pi$
$587$	853619.	0.102251	0.0511256	+	0.998692i	$0.483719\pi$
$588$	−1.17203e6	−0.139796
$589$	1.57098e6	0.186588
$590$	−1.17033e7	−1.38413
$591$	−1.52386e7	−1.79464
$592$	1.52590e6	0.178946
$593$	−2.24799e6	−0.262517	−0.131258	−	0.991348i	$-0.541902\pi$
$593$	−2.24799e6	−0.262517	−0.131258	+	0.991348i	$0.541902\pi$
$594$	4.07154e6	0.473470
$595$	−1.43876e7	−1.66608
$596$	−6.37024e6	−0.734582
$597$	916896.	0.105289
$598$	1.70628e6	0.195118
$599$	2.07233e6	0.235989	0.117995	−	0.993014i	$-0.462353\pi$
$599$	2.07233e6	0.235989	0.117995	+	0.993014i	$0.462353\pi$
$600$	−272175.	−0.0308653
$601$	−1.71300e6	−0.193451	−0.0967255	−	0.995311i	$-0.530837\pi$
$601$	−1.71300e6	−0.193451	−0.0967255	+	0.995311i	$0.530837\pi$
$602$	−5.23701e6	−0.588969
$603$	−9.58710e6	−1.07373
$604$	3.71698e6	0.414570
$605$	1.46390e7	1.62601
$606$	1.88422e6	0.208425
$607$	6.10895e6	0.672969	0.336484	−	0.941689i	$-0.390762\pi$
$607$	6.10895e6	0.672969	0.336484	+	0.941689i	$0.390762\pi$
$608$	−369664.	−0.0405554
$609$	1.54834e7	1.69170
$610$	5.42485e6	0.590286
$611$	1.07178e6	0.116146
$612$	−4.59232e6	−0.495625
$613$	1.25872e7	1.35294	0.676471	−	0.736469i	$-0.263508\pi$
$613$	1.25872e7	1.35294	0.676471	+	0.736469i	$0.263508\pi$
$614$	−1.71841e6	−0.183952
$615$	−4.17281e6	−0.444877
$616$	5.89031e6	0.625441
$617$	−809340.	−0.0855891	−0.0427945	−	0.999084i	$-0.513626\pi$
$617$	−809340.	−0.0855891	−0.0427945	+	0.999084i	$0.513626\pi$
$618$	−1.15552e7	−1.21705
$619$	1.06353e7	1.11563	0.557817	−	0.829964i	$-0.311639\pi$
$619$	1.06353e7	1.11563	0.557817	+	0.829964i	$0.311639\pi$
$620$	−4.02136e6	−0.420139
$621$	5.85473e6	0.609225
$622$	1.02224e7	1.05944
$623$	−2.06498e7	−2.13156
$624$	−595415.	−0.0612150
$625$	−1.03794e7	−1.06286
$626$	1.34883e6	0.137569
$627$	4.69300e6	0.476740
$628$	1.27975e6	0.129487
$629$	−1.03873e7	−1.04683
$630$	5.43914e6	0.545983
$631$	1.18295e7	1.18275	0.591373	−	0.806398i	$-0.298586\pi$
$631$	1.18295e7	1.18275	0.591373	+	0.806398i	$0.298586\pi$
$632$	652908.	0.0650218
$633$	2.14805e7	2.13077
$634$	−3.00678e6	−0.297083
$635$	1.34387e7	1.32259
$636$	3.84189e6	0.376619
$637$	417884.	0.0408044
$638$	−1.38147e7	−1.34367
$639$	8.27521e6	0.801728
$640$	946255.	0.0913184
$641$	9.74470e6	0.936749	0.468375	−	0.883530i	$-0.344840\pi$
$641$	9.74470e6	0.936749	0.468375	+	0.883530i	$0.344840\pi$
$642$	−3.10282e6	−0.297111
$643$	−4.96642e6	−0.473714	−0.236857	−	0.971544i	$-0.576117\pi$
$643$	−4.96642e6	−0.473714	−0.236857	+	0.971544i	$0.576117\pi$
$644$	8.47006e6	0.804770
$645$	1.06806e7	1.01088
$646$	2.51641e6	0.237247
$647$	4.95123e6	0.464999	0.232500	−	0.972597i	$-0.425310\pi$
$647$	4.95123e6	0.464999	0.232500	+	0.972597i	$0.425310\pi$
$648$	−4.60447e6	−0.430767
$649$	−3.26161e7	−3.03963
$650$	97043.4	0.00900912
$651$	1.25609e7	1.16163
$652$	9.08347e6	0.836821
$653$	−1.60070e7	−1.46901	−0.734507	−	0.678601i	$-0.762586\pi$
$653$	−1.60070e7	−1.46901	−0.734507	+	0.678601i	$0.762586\pi$
$654$	−7.50852e6	−0.686451
$655$	−1.75871e7	−1.60173
$656$	916028.	0.0831093
$657$	2.72160e6	0.245986
$658$	5.32037e6	0.479046
$659$	2.65526e6	0.238173	0.119087	−	0.992884i	$-0.462003\pi$
$659$	2.65526e6	0.238173	0.119087	+	0.992884i	$0.462003\pi$
$660$	−1.20130e7	−1.07347
$661$	9.95456e6	0.886173	0.443087	−	0.896479i	$-0.353883\pi$
$661$	9.95456e6	0.886173	0.443087	+	0.896479i	$0.353883\pi$
$662$	6.35705e6	0.563781
$663$	4.05317e6	0.358105
$664$	−6.29776e6	−0.554327
$665$	−2.98044e6	−0.261353
$666$	3.92684e6	0.343050
$667$	−1.98651e7	−1.72893
$668$	3.10120e6	0.268899
$669$	1.40016e7	1.20951
$670$	−1.34474e7	−1.15732
$671$	1.51186e7	1.29630
$672$	−2.95567e6	−0.252484
$673$	−1.59182e7	−1.35474	−0.677371	−	0.735642i	$-0.736881\pi$
$673$	−1.59182e7	−1.35474	−0.677371	+	0.735642i	$0.736881\pi$
$674$	−3.03721e6	−0.257529
$675$	332984.	0.0281296
$676$	−5.72839e6	−0.482132
$677$	−1.08046e7	−0.906015	−0.453007	−	0.891507i	$-0.649649\pi$
$677$	−1.08046e7	−0.906015	−0.453007	+	0.891507i	$0.649649\pi$
$678$	1.16349e7	0.972048
$679$	169067.	0.0140729
$680$	−6.44144e6	−0.534209
$681$	1.72912e7	1.42875
$682$	−1.12072e7	−0.922647
$683$	9.55364e6	0.783641	0.391821	−	0.920042i	$-0.371845\pi$
$683$	9.55364e6	0.783641	0.391821	+	0.920042i	$0.371845\pi$
$684$	−951314.	−0.0777470
$685$	1.52496e7	1.24175
$686$	−7.53587e6	−0.611397
$687$	1.56436e7	1.26458
$688$	−2.34465e6	−0.188846
$689$	−1.36982e6	−0.109930
$690$	−1.72743e7	−1.38127
$691$	4.19119e6	0.333920	0.166960	−	0.985964i	$-0.446605\pi$
$691$	4.19119e6	0.333920	0.166960	+	0.985964i	$0.446605\pi$
$692$	2.66924e6	0.211896
$693$	1.51585e7	1.19901
$694$	5.16159e6	0.406804
$695$	1.15955e7	0.910597
$696$	6.93204e6	0.542423
$697$	−6.23568e6	−0.486186
$698$	2.52172e6	0.195911
$699$	−8.13636e6	−0.629850
$700$	481729.	0.0371584
$701$	1.56295e7	1.20130	0.600648	−	0.799514i	$-0.294909\pi$
$701$	1.56295e7	1.20130	0.600648	+	0.799514i	$0.294909\pi$
$702$	728441.	0.0557894
$703$	−2.15176e6	−0.164212
$704$	2.63714e6	0.200540
$705$	−1.08507e7	−0.822211
$706$	−9.28021e6	−0.700723
$707$	−3.33493e6	−0.250922
$708$	1.63663e7	1.22707
$709$	1.46358e7	1.09346	0.546728	−	0.837310i	$-0.315873\pi$
$709$	1.46358e7	1.09346	0.546728	+	0.837310i	$0.315873\pi$
$710$	1.16073e7	0.864141
$711$	1.68023e6	0.124651
$712$	−9.24510e6	−0.683457
$713$	−1.61156e7	−1.18719
$714$	2.01202e7	1.47702
$715$	4.28321e6	0.313332
$716$	8.87361e6	0.646871
$717$	−6.26870e6	−0.455386
$718$	−7.56701e6	−0.547789
$719$	−1.62504e7	−1.17231	−0.586154	−	0.810199i	$-0.699359\pi$
$719$	−1.62504e7	−1.17231	−0.586154	+	0.810199i	$0.699359\pi$
$720$	2.43515e6	0.175063
$721$	2.04519e7	1.46519
$722$	521284.	0.0372161
$723$	−4.07130e6	−0.289659
$724$	3.63220e6	0.257527
$725$	−1.12982e6	−0.0798293
$726$	−2.04718e7	−1.44150
$727$	1.24766e7	0.875511	0.437755	−	0.899094i	$-0.355774\pi$
$727$	1.24766e7	0.875511	0.437755	+	0.899094i	$0.355774\pi$
$728$	1.05384e6	0.0736963
$729$	−4.09225e6	−0.285196
$730$	3.81747e6	0.265136
$731$	1.59607e7	1.10474
$732$	−7.58630e6	−0.523302
$733$	−2.32918e7	−1.60119	−0.800595	−	0.599206i	$-0.795483\pi$
$733$	−2.32918e7	−1.60119	−0.800595	+	0.599206i	$0.795483\pi$
$734$	1.32982e7	0.911072
$735$	−4.23064e6	−0.288860
$736$	3.79211e6	0.258040
$737$	−3.74768e7	−2.54152
$738$	2.35736e6	0.159325
$739$	−1.63177e7	−1.09913	−0.549564	−	0.835452i	$-0.685206\pi$
$739$	−1.63177e7	−1.09913	−0.549564	+	0.835452i	$0.685206\pi$
$740$	5.50801e6	0.369756
$741$	839628.	0.0561748
$742$	−6.79986e6	−0.453409
$743$	2.10275e7	1.39738	0.698692	−	0.715423i	$-0.253766\pi$
$743$	2.10275e7	1.39738	0.698692	+	0.715423i	$0.253766\pi$
$744$	5.62361e6	0.372463
$745$	−2.29945e7	−1.51787
$746$	−1.69365e6	−0.111423
$747$	−1.62070e7	−1.06268
$748$	−1.79518e7	−1.17315
$749$	5.49175e6	0.357689
$750$	1.35946e7	0.882495
$751$	−1.68245e7	−1.08853	−0.544266	−	0.838913i	$-0.683192\pi$
$751$	−1.68245e7	−1.08853	−0.544266	+	0.838913i	$0.683192\pi$
$752$	2.38197e6	0.153600
$753$	3.25072e7	2.08926
$754$	−2.47160e6	−0.158325
$755$	1.34171e7	0.856627
$756$	3.61602e6	0.230105
$757$	−2.41635e6	−0.153257	−0.0766283	−	0.997060i	$-0.524415\pi$
$757$	−2.41635e6	−0.153257	−0.0766283	+	0.997060i	$0.524415\pi$
$758$	5.33760e6	0.337422
$759$	−4.81420e7	−3.03333
$760$	−1.33437e6	−0.0837995
$761$	−2.26172e6	−0.141572	−0.0707859	−	0.997492i	$-0.522551\pi$
$761$	−2.26172e6	−0.141572	−0.0707859	+	0.997492i	$0.522551\pi$
$762$	−1.87932e7	−1.17250
$763$	1.32895e7	0.826413
$764$	−4.37757e6	−0.271331
$765$	−1.65768e7	−1.02411
$766$	1.28302e7	0.790061
$767$	−5.83538e6	−0.358163
$768$	−1.32328e6	−0.0809558
$769$	−2.09386e7	−1.27683	−0.638413	−	0.769694i	$-0.720409\pi$
$769$	−2.09386e7	−1.27683	−0.638413	+	0.769694i	$0.720409\pi$
$770$	2.12621e7	1.29235
$771$	3.01727e6	0.182801
$772$	3.83315e6	0.231480
$773$	−1.78821e7	−1.07639	−0.538195	−	0.842820i	$-0.680894\pi$
$773$	−1.78821e7	−1.07639	−0.538195	+	0.842820i	$0.680894\pi$
$774$	−6.03386e6	−0.362028
$775$	−916561.	−0.0548160
$776$	75692.7	0.00451232
$777$	−1.72045e7	−1.02233
$778$	−1.98325e7	−1.17471
$779$	−1.29174e6	−0.0762663
$780$	−2.14925e6	−0.126489
$781$	3.23485e7	1.89770
$782$	−2.58140e7	−1.50952
$783$	−8.48079e6	−0.494347
$784$	928724.	0.0539630
$785$	4.61949e6	0.267559
$786$	2.45944e7	1.41997
$787$	2.11999e7	1.22010	0.610052	−	0.792361i	$-0.291148\pi$
$787$	2.11999e7	1.22010	0.610052	+	0.792361i	$0.291148\pi$
$788$	1.20752e7	0.692753
$789$	−3.52865e7	−2.01797
$790$	2.35679e6	0.134355
$791$	−2.05929e7	−1.17024
$792$	6.78655e6	0.384447
$793$	2.70488e6	0.152744
$794$	1.64593e7	0.926532
$795$	1.38680e7	0.778208
$796$	−726556.	−0.0406431
$797$	−4.93791e6	−0.275358	−0.137679	−	0.990477i	$-0.543964\pi$
$797$	−4.93791e6	−0.275358	−0.137679	+	0.990477i	$0.543964\pi$
$798$	4.16796e6	0.231695
$799$	−1.62148e7	−0.898555
$800$	215674.	0.0119144
$801$	−2.37919e7	−1.31023
$802$	2.18347e7	1.19870
$803$	1.06390e7	0.582252
$804$	1.88054e7	1.02599
$805$	3.05742e7	1.66290
$806$	−2.00509e6	−0.108716
$807$	3.78181e7	2.04416
$808$	−1.49307e6	−0.0804549
$809$	−1.40239e6	−0.0753353	−0.0376677	−	0.999290i	$-0.511993\pi$
$809$	−1.40239e6	−0.0753353	−0.0376677	+	0.999290i	$0.511993\pi$
$810$	−1.66207e7	−0.890094
$811$	1.72182e6	0.0919255	0.0459627	−	0.998943i	$-0.485364\pi$
$811$	1.72182e6	0.0919255	0.0459627	+	0.998943i	$0.485364\pi$
$812$	−1.22692e7	−0.653019
$813$	2.06969e7	1.09819
$814$	1.53504e7	0.812004
$815$	3.27884e7	1.72912
$816$	9.00795e6	0.473588
$817$	3.30632e6	0.173297
$818$	5.01729e6	0.262172
$819$	2.71201e6	0.141280
$820$	3.30657e6	0.171729
$821$	8.81433e6	0.456385	0.228193	−	0.973616i	$-0.426718\pi$
$821$	8.81433e6	0.456385	0.228193	+	0.973616i	$0.426718\pi$
$822$	−2.13256e7	−1.10084
$823$	−3.15202e7	−1.62214	−0.811072	−	0.584946i	$-0.801116\pi$
$823$	−3.15202e7	−1.62214	−0.811072	+	0.584946i	$0.801116\pi$
$824$	9.15647e6	0.469797
$825$	−2.73805e6	−0.140057
$826$	−2.89671e7	−1.47726
$827$	2.48469e7	1.26331	0.631653	−	0.775251i	$-0.282377\pi$
$827$	2.48469e7	1.26331	0.631653	+	0.775251i	$0.282377\pi$
$828$	9.75883e6	0.494677
$829$	−6.67208e6	−0.337190	−0.168595	−	0.985685i	$-0.553923\pi$
$829$	−6.67208e6	−0.337190	−0.168595	+	0.985685i	$0.553923\pi$
$830$	−2.27329e7	−1.14540
$831$	−6.41463e6	−0.322232
$832$	471812.	0.0236298
$833$	−6.32210e6	−0.315682
$834$	−1.62155e7	−0.807265
$835$	1.11943e7	0.555625
$836$	−3.71877e6	−0.184028
$837$	−6.88003e6	−0.339451
$838$	1.79061e7	0.880829
$839$	−429286.	−0.0210543	−0.0105272	−	0.999945i	$-0.503351\pi$
$839$	−429286.	−0.0210543	−0.0105272	+	0.999945i	$0.503351\pi$
$840$	−1.06690e7	−0.521707
$841$	8.26421e6	0.402913
$842$	−922711.	−0.0448524
$843$	2.28954e7	1.10963
$844$	−1.70214e7	−0.822504
$845$	−2.06776e7	−0.996229
$846$	6.12990e6	0.294461
$847$	3.62334e7	1.73541
$848$	−3.04435e6	−0.145380
$849$	−1.19998e7	−0.571355
$850$	−1.46816e6	−0.0696987
$851$	2.20733e7	1.04482
$852$	−1.62320e7	−0.766080
$853$	−5.44833e6	−0.256384	−0.128192	−	0.991749i	$-0.540917\pi$
$853$	−5.44833e6	−0.256384	−0.128192	+	0.991749i	$0.540917\pi$
$854$	1.34272e7	0.629999
$855$	−3.43394e6	−0.160649
$856$	2.45870e6	0.114689
$857$	2.40683e7	1.11942	0.559710	−	0.828689i	$-0.310913\pi$
$857$	2.40683e7	1.11942	0.559710	+	0.828689i	$0.310913\pi$
$858$	−5.98980e6	−0.277776
$859$	2.80553e7	1.29728	0.648638	−	0.761097i	$-0.275339\pi$
$859$	2.80553e7	1.29728	0.648638	+	0.761097i	$0.275339\pi$
$860$	−8.46343e6	−0.390212
$861$	−1.03282e7	−0.474808
$862$	1.61719e7	0.741298
$863$	2.37657e6	0.108624	0.0543118	−	0.998524i	$-0.482704\pi$
$863$	2.37657e6	0.108624	0.0543118	+	0.998524i	$0.482704\pi$
$864$	1.61892e6	0.0737805
$865$	9.63509e6	0.437840
$866$	2.18396e6	0.0989576
$867$	−3.26506e7	−1.47518
$868$	−9.95336e6	−0.448405
$869$	6.56817e6	0.295050
$870$	2.50224e7	1.12081
$871$	−6.70501e6	−0.299470
$872$	5.94981e6	0.264979
$873$	194792.	0.00865038
$874$	−5.34747e6	−0.236793
$875$	−2.40614e7	−1.06243
$876$	−5.33849e6	−0.235049
$877$	1.28769e7	0.565342	0.282671	−	0.959217i	$-0.408780\pi$
$877$	1.28769e7	0.565342	0.282671	+	0.959217i	$0.408780\pi$
$878$	2.20779e7	0.966543
$879$	−1.85925e7	−0.811643
$880$	9.51920e6	0.414375
$881$	−3.74732e7	−1.62660	−0.813300	−	0.581845i	$-0.802331\pi$
$881$	−3.74732e7	−1.62660	−0.813300	+	0.581845i	$0.802331\pi$
$882$	2.39003e6	0.103450
$883$	1.53754e6	0.0663626	0.0331813	−	0.999449i	$-0.489436\pi$
$883$	1.53754e6	0.0663626	0.0331813	+	0.999449i	$0.489436\pi$
$884$	−3.21176e6	−0.138233
$885$	5.90771e7	2.53549
$886$	−1.35407e7	−0.579505
$887$	−5.12038e6	−0.218521	−0.109261	−	0.994013i	$-0.534848\pi$
$887$	−5.12038e6	−0.218521	−0.109261	+	0.994013i	$0.534848\pi$
$888$	−7.70260e6	−0.327797
$889$	3.32626e7	1.41157
$890$	−3.33718e7	−1.41223
$891$	−4.63204e7	−1.95469
$892$	−1.10949e7	−0.466888
$893$	−3.35895e6	−0.140953
$894$	3.21563e7	1.34562
$895$	3.20308e7	1.33663
$896$	2.34210e6	0.0974620
$897$	−8.61312e6	−0.357421
$898$	2.14735e6	0.0888611
$899$	2.33440e7	0.963331
$900$	555027.	0.0228406
$901$	2.07238e7	0.850467
$902$	9.21513e6	0.377125
$903$	2.64359e7	1.07889
$904$	−9.21958e6	−0.375223
$905$	1.31111e7	0.532128
$906$	−1.87630e7	−0.759419
$907$	1.86620e7	0.753251	0.376625	−	0.926366i	$-0.377084\pi$
$907$	1.86620e7	0.753251	0.376625	+	0.926366i	$0.377084\pi$
$908$	−1.37017e7	−0.551518
$909$	−3.84236e6	−0.154237
$910$	3.80402e6	0.152279
$911$	−3.00151e7	−1.19824	−0.599121	−	0.800659i	$-0.704483\pi$
$911$	−3.00151e7	−1.19824	−0.599121	+	0.800659i	$0.704483\pi$
$912$	1.86603e6	0.0742901
$913$	−6.33547e7	−2.51537
$914$	1.83514e7	0.726614
$915$	−2.73841e7	−1.08130
$916$	−1.23961e7	−0.488144
$917$	−4.35302e7	−1.70949
$918$	−1.10205e7	−0.431613
$919$	−1.51477e6	−0.0591640	−0.0295820	−	0.999562i	$-0.509418\pi$
$919$	−1.51477e6	−0.0591640	−0.0295820	+	0.999562i	$0.509418\pi$
$920$	1.36883e7	0.533187
$921$	8.67435e6	0.336967
$922$	3.32626e7	1.28863
$923$	5.78750e6	0.223608
$924$	−2.97337e7	−1.14570
$925$	1.25540e6	0.0482424
$926$	1.00200e7	0.384009
$927$	2.35638e7	0.900628
$928$	−5.49301e6	−0.209382
$929$	−8.12932e6	−0.309040	−0.154520	−	0.987990i	$-0.549383\pi$
$929$	−8.12932e6	−0.309040	−0.154520	+	0.987990i	$0.549383\pi$
$930$	2.02994e7	0.769620
$931$	−1.30965e6	−0.0495199
$932$	6.44732e6	0.243130
$933$	−5.16016e7	−1.94070
$934$	−1.75967e7	−0.660029
$935$	−6.48001e7	−2.42408
$936$	1.21419e6	0.0452998
$937$	1.69157e7	0.629422	0.314711	−	0.949188i	$-0.398092\pi$
$937$	1.69157e7	0.629422	0.314711	+	0.949188i	$0.398092\pi$
$938$	−3.32840e7	−1.23518
$939$	−6.80876e6	−0.252002
$940$	8.59815e6	0.317384
$941$	−1.86407e7	−0.686260	−0.343130	−	0.939288i	$-0.611487\pi$
$941$	−1.86407e7	−0.686260	−0.343130	+	0.939288i	$0.611487\pi$
$942$	−6.46006e6	−0.237197
$943$	1.32510e7	0.485256
$944$	−1.29688e7	−0.473664
$945$	1.30527e7	0.475467
$946$	−2.35869e7	−0.856925
$947$	−4.62482e7	−1.67579	−0.837896	−	0.545830i	$-0.816214\pi$
$947$	−4.62482e7	−1.67579	−0.837896	+	0.545830i	$0.816214\pi$
$948$	−3.29582e6	−0.119108
$949$	1.90343e6	0.0686074
$950$	−304134.	−0.0109334
$951$	1.51779e7	0.544203
$952$	−1.59434e7	−0.570149
$953$	1.63386e7	0.582749	0.291374	−	0.956609i	$-0.405887\pi$
$953$	1.63386e7	0.582749	0.291374	+	0.956609i	$0.405887\pi$
$954$	−7.83450e6	−0.278702
$955$	−1.58016e7	−0.560652
$956$	4.96737e6	0.175785
$957$	6.97355e7	2.46135
$958$	2.29298e6	0.0807211
$959$	3.77447e7	1.32529
$960$	−4.77660e6	−0.167279
$961$	−9.69140e6	−0.338515
$962$	2.74635e6	0.0956792
$963$	6.32735e6	0.219865
$964$	3.22613e6	0.111812
$965$	1.38364e7	0.478306
$966$	−4.27560e7	−1.47419
$967$	3.00115e6	0.103210	0.0516049	−	0.998668i	$-0.483566\pi$
$967$	3.00115e6	0.103210	0.0516049	+	0.998668i	$0.483566\pi$
$968$	1.62220e7	0.556436
$969$	−1.27026e7	−0.434594
$970$	273226.	0.00932380
$971$	3.84358e7	1.30824	0.654120	−	0.756391i	$-0.273039\pi$
$971$	3.84358e7	1.30824	0.654120	+	0.756391i	$0.273039\pi$
$972$	1.70961e7	0.580405
$973$	2.87002e7	0.971860
$974$	1.43242e6	0.0483808
$975$	−489865.	−0.0165031
$976$	6.01145e6	0.202001
$977$	−813530.	−0.0272670	−0.0136335	−	0.999907i	$-0.504340\pi$
$977$	−813530.	−0.0272670	−0.0136335	+	0.999907i	$0.504340\pi$
$978$	−4.58525e7	−1.53291
$979$	−9.30045e7	−3.10132
$980$	3.35239e6	0.111504
$981$	1.53116e7	0.507981
$982$	−1.72149e7	−0.569673
$983$	2.70432e7	0.892637	0.446318	−	0.894874i	$-0.352735\pi$
$983$	2.70432e7	0.892637	0.446318	+	0.894874i	$0.352735\pi$
$984$	−4.62402e6	−0.152241
$985$	4.35875e7	1.43144
$986$	3.73926e7	1.22488
$987$	−2.68567e7	−0.877527
$988$	−665328.	−0.0216842
$989$	−3.39171e7	−1.10263
$990$	2.44973e7	0.794382
$991$	5.51117e6	0.178263	0.0891313	−	0.996020i	$-0.471591\pi$
$991$	5.51117e6	0.178263	0.0891313	+	0.996020i	$0.471591\pi$
$992$	−4.45620e6	−0.143776
$993$	−3.20898e7	−1.03275
$994$	2.87295e7	0.922278
$995$	−2.62263e6	−0.0839808
$996$	3.17905e7	1.01543
$997$	6.73290e6	0.214518	0.107259	−	0.994231i	$-0.465793\pi$
$997$	6.73290e6	0.214518	0.107259	+	0.994231i	$0.465793\pi$
$998$	−2.70744e7	−0.860462
$999$	9.42350e6	0.298744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.a.d.1.1	✓	3
3.2	odd	2		342.6.a.l.1.1		3
4.3	odd	2		304.6.a.h.1.3		3
5.4	even	2		950.6.a.f.1.3		3
19.18	odd	2		722.6.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.d.1.1	✓	3	1.1	even	1	trivial
304.6.a.h.1.3		3	4.3	odd	2
342.6.a.l.1.1		3	3.2	odd	2
722.6.a.d.1.3		3	19.18	odd	2
950.6.a.f.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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -20.1916 q^{3} +16.0000 q^{4} +57.7548 q^{5} -80.7665 q^{6} +142.950 q^{7} +64.0000 q^{8} +164.701 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -20.1916 q^{3} +16.0000 q^{4} +57.7548 q^{5} -80.7665 q^{6} +142.950 q^{7} +64.0000 q^{8} +164.701 q^{9} +231.019 q^{10} +643.832 q^{11} -323.066 q^{12} +115.188 q^{13} +571.802 q^{14} -1166.16 q^{15} +256.000 q^{16} -1742.67 q^{17} +658.805 q^{18} -361.000 q^{19} +924.077 q^{20} -2886.40 q^{21} +2575.33 q^{22} +3703.23 q^{23} -1292.26 q^{24} +210.619 q^{25} +460.754 q^{26} +1580.98 q^{27} +2287.21 q^{28} -5364.27 q^{29} -4664.65 q^{30} -4351.75 q^{31} +1024.00 q^{32} -13000.0 q^{33} -6970.68 q^{34} +8256.08 q^{35} +2635.22 q^{36} +5960.55 q^{37} -1444.00 q^{38} -2325.84 q^{39} +3696.31 q^{40} +3578.24 q^{41} -11545.6 q^{42} -9158.79 q^{43} +10301.3 q^{44} +9512.29 q^{45} +14812.9 q^{46} +9304.58 q^{47} -5169.05 q^{48} +3627.83 q^{49} +842.475 q^{50} +35187.3 q^{51} +1843.01 q^{52} -11892.0 q^{53} +6323.91 q^{54} +37184.4 q^{55} +9148.83 q^{56} +7289.17 q^{57} -21457.1 q^{58} -50659.4 q^{59} -18658.6 q^{60} +23482.2 q^{61} -17407.0 q^{62} +23544.1 q^{63} +4096.00 q^{64} +6652.68 q^{65} -52000.0 q^{66} -58209.0 q^{67} -27882.7 q^{68} -74774.2 q^{69} +33024.3 q^{70} +50243.8 q^{71} +10540.9 q^{72} +16524.5 q^{73} +23842.2 q^{74} -4252.73 q^{75} -5776.00 q^{76} +92036.0 q^{77} -9303.36 q^{78} +10201.7 q^{79} +14785.2 q^{80} -71944.9 q^{81} +14312.9 q^{82} -98402.5 q^{83} -46182.4 q^{84} -100648. q^{85} -36635.2 q^{86} +108313. q^{87} +41205.2 q^{88} -144455. q^{89} +38049.2 q^{90} +16466.2 q^{91} +59251.7 q^{92} +87868.9 q^{93} +37218.3 q^{94} -20849.5 q^{95} -20676.2 q^{96} +1182.70 q^{97} +14511.3 q^{98} +106040. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9}+O(q^{10}) \) 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9	\( 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9} + 324 q^{10} + 363 q^{11} + 208 q^{12} + 501 q^{13} + 912 q^{14} - 670 q^{15} + 768 q^{16} - 1206 q^{17} + 944 q^{18} - 1083 q^{19} + 1296 q^{20} - 2085 q^{21} + 1452 q^{22} - 1077 q^{23} + 832 q^{24} - 3882 q^{25} + 2004 q^{26} - 5087 q^{27} + 3648 q^{28} - 8349 q^{29} - 2680 q^{30} - 7332 q^{31} + 3072 q^{32} - 15784 q^{33} - 4824 q^{34} - 1185 q^{35} + 3776 q^{36} - 1650 q^{37} - 4332 q^{38} + 773 q^{39} + 5184 q^{40} + 10140 q^{41} - 8340 q^{42} + 3777 q^{43} + 5808 q^{44} + 14005 q^{45} - 4308 q^{46} + 33231 q^{47} + 3328 q^{48} + 31269 q^{49} - 15528 q^{50} + 46935 q^{51} + 8016 q^{52} + 31029 q^{53} - 20348 q^{54} + 66003 q^{55} + 14592 q^{56} - 4693 q^{57} - 33396 q^{58} + 20409 q^{59} - 10720 q^{60} + 17115 q^{61} - 29328 q^{62} + 6327 q^{63} + 12288 q^{64} - 45348 q^{65} - 63136 q^{66} - 789 q^{67} - 19296 q^{68} - 151147 q^{69} - 4740 q^{70} + 19164 q^{71} + 15104 q^{72} - 76260 q^{73} - 6600 q^{74} - 69607 q^{75} - 17328 q^{76} - 97209 q^{77} + 3092 q^{78} + 68358 q^{79} + 20736 q^{80} - 197713 q^{81} + 40560 q^{82} + 6762 q^{83} - 33360 q^{84} - 45837 q^{85} + 15108 q^{86} + 66805 q^{87} + 23232 q^{88} - 85506 q^{89} + 56020 q^{90} + 345033 q^{91} - 17232 q^{92} + 15688 q^{93} + 132924 q^{94} - 29241 q^{95} + 13312 q^{96} + 105024 q^{97} + 125076 q^{98} + 158317 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9 + 324 * q^10 + 363 * q^11 + 208 * q^12 + 501 * q^13 + 912 * q^14 - 670 * q^15 + 768 * q^16 - 1206 * q^17 + 944 * q^18 - 1083 * q^19 + 1296 * q^20 - 2085 * q^21 + 1452 * q^22 - 1077 * q^23 + 832 * q^24 - 3882 * q^25 + 2004 * q^26 - 5087 * q^27 + 3648 * q^28 - 8349 * q^29 - 2680 * q^30 - 7332 * q^31 + 3072 * q^32 - 15784 * q^33 - 4824 * q^34 - 1185 * q^35 + 3776 * q^36 - 1650 * q^37 - 4332 * q^38 + 773 * q^39 + 5184 * q^40 + 10140 * q^41 - 8340 * q^42 + 3777 * q^43 + 5808 * q^44 + 14005 * q^45 - 4308 * q^46 + 33231 * q^47 + 3328 * q^48 + 31269 * q^49 - 15528 * q^50 + 46935 * q^51 + 8016 * q^52 + 31029 * q^53 - 20348 * q^54 + 66003 * q^55 + 14592 * q^56 - 4693 * q^57 - 33396 * q^58 + 20409 * q^59 - 10720 * q^60 + 17115 * q^61 - 29328 * q^62 + 6327 * q^63 + 12288 * q^64 - 45348 * q^65 - 63136 * q^66 - 789 * q^67 - 19296 * q^68 - 151147 * q^69 - 4740 * q^70 + 19164 * q^71 + 15104 * q^72 - 76260 * q^73 - 6600 * q^74 - 69607 * q^75 - 17328 * q^76 - 97209 * q^77 + 3092 * q^78 + 68358 * q^79 + 20736 * q^80 - 197713 * q^81 + 40560 * q^82 + 6762 * q^83 - 33360 * q^84 - 45837 * q^85 + 15108 * q^86 + 66805 * q^87 + 23232 * q^88 - 85506 * q^89 + 56020 * q^90 + 345033 * q^91 - 17232 * q^92 + 15688 * q^93 + 132924 * q^94 - 29241 * q^95 + 13312 * q^96 + 105024 * q^97 + 125076 * q^98 + 158317 * q^99

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