LMFDB - Embedded newform 354.6.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.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:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 358x^{4} - 404x^{3} + 26492x^{2} - 11664x - 353376 $ x^6 - 358x^4 - 404x^3 + 26492x^2 - 11664x - 353376
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$5.13506$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +79.8984 q^{5} +36.0000 q^{6} +56.6271 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +79.8984 q^{5} +36.0000 q^{6} +56.6271 q^{7} -64.0000 q^{8} +81.0000 q^{9} -319.594 q^{10} +280.145 q^{11} -144.000 q^{12} +515.405 q^{13} -226.509 q^{14} -719.086 q^{15} +256.000 q^{16} +775.358 q^{17} -324.000 q^{18} +2572.53 q^{19} +1278.38 q^{20} -509.644 q^{21} -1120.58 q^{22} +2133.12 q^{23} +576.000 q^{24} +3258.76 q^{25} -2061.62 q^{26} -729.000 q^{27} +906.034 q^{28} +712.180 q^{29} +2876.34 q^{30} -5223.75 q^{31} -1024.00 q^{32} -2521.31 q^{33} -3101.43 q^{34} +4524.42 q^{35} +1296.00 q^{36} +3015.67 q^{37} -10290.1 q^{38} -4638.65 q^{39} -5113.50 q^{40} -11454.1 q^{41} +2038.58 q^{42} +10490.3 q^{43} +4482.32 q^{44} +6471.77 q^{45} -8532.48 q^{46} -9939.20 q^{47} -2304.00 q^{48} -13600.4 q^{49} -13035.0 q^{50} -6978.22 q^{51} +8246.48 q^{52} -12628.5 q^{53} +2916.00 q^{54} +22383.2 q^{55} -3624.14 q^{56} -23152.7 q^{57} -2848.72 q^{58} +3481.00 q^{59} -11505.4 q^{60} -25220.9 q^{61} +20895.0 q^{62} +4586.80 q^{63} +4096.00 q^{64} +41180.1 q^{65} +10085.2 q^{66} -55905.6 q^{67} +12405.7 q^{68} -19198.1 q^{69} -18097.7 q^{70} -10001.8 q^{71} -5184.00 q^{72} +66911.3 q^{73} -12062.7 q^{74} -29328.9 q^{75} +41160.4 q^{76} +15863.8 q^{77} +18554.6 q^{78} +57856.6 q^{79} +20454.0 q^{80} +6561.00 q^{81} +45816.6 q^{82} +107819. q^{83} -8154.31 q^{84} +61949.9 q^{85} -41961.0 q^{86} -6409.62 q^{87} -17929.3 q^{88} +7355.18 q^{89} -25887.1 q^{90} +29185.9 q^{91} +34129.9 q^{92} +47013.7 q^{93} +39756.8 q^{94} +205541. q^{95} +9216.00 q^{96} -156644. q^{97} +54401.5 q^{98} +22691.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9} - 16 q^{10} + 436 q^{11} - 864 q^{12} - 536 q^{13} + 216 q^{14} - 36 q^{15} + 1536 q^{16} + 910 q^{17} - 1944 q^{18} + 1462 q^{19} + 64 q^{20} + 486 q^{21} - 1744 q^{22} + 1634 q^{23} + 3456 q^{24} - 1186 q^{25} + 2144 q^{26} - 4374 q^{27} - 864 q^{28} - 1598 q^{29} + 144 q^{30} - 5670 q^{31} - 6144 q^{32} - 3924 q^{33} - 3640 q^{34} - 7242 q^{35} + 7776 q^{36} - 20458 q^{37} - 5848 q^{38} + 4824 q^{39} - 256 q^{40} + 262 q^{41} - 1944 q^{42} - 34028 q^{43} + 6976 q^{44} + 324 q^{45} - 6536 q^{46} - 11194 q^{47} - 13824 q^{48} - 32652 q^{49} + 4744 q^{50} - 8190 q^{51} - 8576 q^{52} - 17164 q^{53} + 17496 q^{54} - 37040 q^{55} + 3456 q^{56} - 13158 q^{57} + 6392 q^{58} + 20886 q^{59} - 576 q^{60} - 43546 q^{61} + 22680 q^{62} - 4374 q^{63} + 24576 q^{64} + 65568 q^{65} + 15696 q^{66} - 52772 q^{67} + 14560 q^{68} - 14706 q^{69} + 28968 q^{70} + 84740 q^{71} - 31104 q^{72} - 36578 q^{73} + 81832 q^{74} + 10674 q^{75} + 23392 q^{76} + 90678 q^{77} - 19296 q^{78} + 85196 q^{79} + 1024 q^{80} + 39366 q^{81} - 1048 q^{82} + 217026 q^{83} + 7776 q^{84} + 26570 q^{85} + 136112 q^{86} + 14382 q^{87} - 27904 q^{88} + 333850 q^{89} - 1296 q^{90} + 214914 q^{91} + 26144 q^{92} + 51030 q^{93} + 44776 q^{94} + 458758 q^{95} + 55296 q^{96} + 173148 q^{97} + 130608 q^{98} + 35316 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9 - 16 * q^10 + 436 * q^11 - 864 * q^12 - 536 * q^13 + 216 * q^14 - 36 * q^15 + 1536 * q^16 + 910 * q^17 - 1944 * q^18 + 1462 * q^19 + 64 * q^20 + 486 * q^21 - 1744 * q^22 + 1634 * q^23 + 3456 * q^24 - 1186 * q^25 + 2144 * q^26 - 4374 * q^27 - 864 * q^28 - 1598 * q^29 + 144 * q^30 - 5670 * q^31 - 6144 * q^32 - 3924 * q^33 - 3640 * q^34 - 7242 * q^35 + 7776 * q^36 - 20458 * q^37 - 5848 * q^38 + 4824 * q^39 - 256 * q^40 + 262 * q^41 - 1944 * q^42 - 34028 * q^43 + 6976 * q^44 + 324 * q^45 - 6536 * q^46 - 11194 * q^47 - 13824 * q^48 - 32652 * q^49 + 4744 * q^50 - 8190 * q^51 - 8576 * q^52 - 17164 * q^53 + 17496 * q^54 - 37040 * q^55 + 3456 * q^56 - 13158 * q^57 + 6392 * q^58 + 20886 * q^59 - 576 * q^60 - 43546 * q^61 + 22680 * q^62 - 4374 * q^63 + 24576 * q^64 + 65568 * q^65 + 15696 * q^66 - 52772 * q^67 + 14560 * q^68 - 14706 * q^69 + 28968 * q^70 + 84740 * q^71 - 31104 * q^72 - 36578 * q^73 + 81832 * q^74 + 10674 * q^75 + 23392 * q^76 + 90678 * q^77 - 19296 * q^78 + 85196 * q^79 + 1024 * q^80 + 39366 * q^81 - 1048 * q^82 + 217026 * q^83 + 7776 * q^84 + 26570 * q^85 + 136112 * q^86 + 14382 * q^87 - 27904 * q^88 + 333850 * q^89 - 1296 * q^90 + 214914 * q^91 + 26144 * q^92 + 51030 * q^93 + 44776 * q^94 + 458758 * q^95 + 55296 * q^96 + 173148 * q^97 + 130608 * q^98 + 35316 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	79.8984	1.42927	0.714633	−	0.699499i	$-0.246594\pi$
$5$	79.8984	1.42927	0.714633	+	0.699499i	$0.246594\pi$
$6$	36.0000	0.408248
$7$	56.6271	0.436797	0.218398	−	0.975860i	$-0.429917\pi$
$7$	56.6271	0.436797	0.218398	+	0.975860i	$0.429917\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−319.594	−1.01064
$11$	280.145	0.698074	0.349037	−	0.937109i	$-0.386509\pi$
$11$	280.145	0.698074	0.349037	+	0.937109i	$0.386509\pi$
$12$	−144.000	−0.288675
$13$	515.405	0.845844	0.422922	−	0.906166i	$-0.361004\pi$
$13$	515.405	0.845844	0.422922	+	0.906166i	$0.361004\pi$
$14$	−226.509	−0.308862
$15$	−719.086	−0.825188
$16$	256.000	0.250000
$17$	775.358	0.650699	0.325349	−	0.945594i	$-0.394518\pi$
$17$	775.358	0.650699	0.325349	+	0.945594i	$0.394518\pi$
$18$	−324.000	−0.235702
$19$	2572.53	1.63484	0.817421	−	0.576041i	$-0.195403\pi$
$19$	2572.53	1.63484	0.817421	+	0.576041i	$0.195403\pi$
$20$	1278.38	0.714633
$21$	−509.644	−0.252185
$22$	−1120.58	−0.493613
$23$	2133.12	0.840806	0.420403	−	0.907338i	$-0.361889\pi$
$23$	2133.12	0.840806	0.420403	+	0.907338i	$0.361889\pi$
$24$	576.000	0.204124
$25$	3258.76	1.04280
$26$	−2061.62	−0.598102
$27$	−729.000	−0.192450
$28$	906.034	0.218398
$29$	712.180	0.157252	0.0786258	−	0.996904i	$-0.474947\pi$
$29$	712.180	0.157252	0.0786258	+	0.996904i	$0.474947\pi$
$30$	2876.34	0.583496
$31$	−5223.75	−0.976288	−0.488144	−	0.872763i	$-0.662326\pi$
$31$	−5223.75	−0.976288	−0.488144	+	0.872763i	$0.662326\pi$
$32$	−1024.00	−0.176777
$33$	−2521.31	−0.403033
$34$	−3101.43	−0.460113
$35$	4524.42	0.624299
$36$	1296.00	0.166667
$37$	3015.67	0.362142	0.181071	−	0.983470i	$-0.442044\pi$
$37$	3015.67	0.362142	0.181071	+	0.983470i	$0.442044\pi$
$38$	−10290.1	−1.15601
$39$	−4638.65	−0.488348
$40$	−5113.50	−0.505322
$41$	−11454.1	−1.06415	−0.532075	−	0.846697i	$-0.678588\pi$
$41$	−11454.1	−1.06415	−0.532075	+	0.846697i	$0.678588\pi$
$42$	2038.58	0.178322
$43$	10490.3	0.865197	0.432598	−	0.901587i	$-0.357597\pi$
$43$	10490.3	0.865197	0.432598	+	0.901587i	$0.357597\pi$
$44$	4482.32	0.349037
$45$	6471.77	0.476422
$46$	−8532.48	−0.594540
$47$	−9939.20	−0.656306	−0.328153	−	0.944625i	$-0.606426\pi$
$47$	−9939.20	−0.656306	−0.328153	+	0.944625i	$0.606426\pi$
$48$	−2304.00	−0.144338
$49$	−13600.4	−0.809208
$50$	−13035.0	−0.737374
$51$	−6978.22	−0.375681
$52$	8246.48	0.422922
$53$	−12628.5	−0.617533	−0.308767	−	0.951138i	$-0.599916\pi$
$53$	−12628.5	−0.617533	−0.308767	+	0.951138i	$0.599916\pi$
$54$	2916.00	0.136083
$55$	22383.2	0.997734
$56$	−3624.14	−0.154431
$57$	−23152.7	−0.943876
$58$	−2848.72	−0.111194
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−11505.4	−0.412594
$61$	−25220.9	−0.867831	−0.433916	−	0.900953i	$-0.642868\pi$
$61$	−25220.9	−0.867831	−0.433916	+	0.900953i	$0.642868\pi$
$62$	20895.0	0.690340
$63$	4586.80	0.145599
$64$	4096.00	0.125000
$65$	41180.1	1.20894
$66$	10085.2	0.284987
$67$	−55905.6	−1.52149	−0.760744	−	0.649052i	$-0.775166\pi$
$67$	−55905.6	−1.52149	−0.760744	+	0.649052i	$0.775166\pi$
$68$	12405.7	0.325349
$69$	−19198.1	−0.485440
$70$	−18097.7	−0.441446
$71$	−10001.8	−0.235469	−0.117734	−	0.993045i	$-0.537563\pi$
$71$	−10001.8	−0.235469	−0.117734	+	0.993045i	$0.537563\pi$
$72$	−5184.00	−0.117851
$73$	66911.3	1.46958	0.734789	−	0.678296i	$-0.237281\pi$
$73$	66911.3	1.46958	0.734789	+	0.678296i	$0.237281\pi$
$74$	−12062.7	−0.256073
$75$	−29328.9	−0.602063
$76$	41160.4	0.817421
$77$	15863.8	0.304917
$78$	18554.6	0.345314
$79$	57856.6	1.04300	0.521501	−	0.853250i	$-0.325372\pi$
$79$	57856.6	1.04300	0.521501	+	0.853250i	$0.325372\pi$
$80$	20454.0	0.357317
$81$	6561.00	0.111111
$82$	45816.6	0.752468
$83$	107819.	1.71791	0.858957	−	0.512048i	$-0.171113\pi$
$83$	107819.	1.71791	0.858957	+	0.512048i	$0.171113\pi$
$84$	−8154.31	−0.126092
$85$	61949.9	0.930022
$86$	−41961.0	−0.611786
$87$	−6409.62	−0.0907892
$88$	−17929.3	−0.246806
$89$	7355.18	0.0984279	0.0492140	−	0.998788i	$-0.484328\pi$
$89$	7355.18	0.0984279	0.0492140	+	0.998788i	$0.484328\pi$
$90$	−25887.1	−0.336881
$91$	29185.9	0.369462
$92$	34129.9	0.420403
$93$	47013.7	0.563660
$94$	39756.8	0.464079
$95$	205541.	2.33663
$96$	9216.00	0.102062
$97$	−156644.	−1.69038	−0.845189	−	0.534467i	$-0.820512\pi$
$97$	−156644.	−1.69038	−0.845189	+	0.534467i	$0.820512\pi$
$98$	54401.5	0.572197
$99$	22691.8	0.232691
$100$	52140.2	0.521402
$101$	136529.	1.33175	0.665873	−	0.746065i	$-0.268059\pi$
$101$	136529.	1.33175	0.665873	+	0.746065i	$0.268059\pi$
$102$	27912.9	0.265647
$103$	−60972.5	−0.566293	−0.283146	−	0.959077i	$-0.591378\pi$
$103$	−60972.5	−0.566293	−0.283146	+	0.959077i	$0.591378\pi$
$104$	−32985.9	−0.299051
$105$	−40719.8	−0.360439
$106$	50513.8	0.436662
$107$	63257.5	0.534137	0.267069	−	0.963678i	$-0.413945\pi$
$107$	63257.5	0.534137	0.267069	+	0.963678i	$0.413945\pi$
$108$	−11664.0	−0.0962250
$109$	78430.7	0.632295	0.316148	−	0.948710i	$-0.397611\pi$
$109$	78430.7	0.632295	0.316148	+	0.948710i	$0.397611\pi$
$110$	−89532.6	−0.705504
$111$	−27141.0	−0.209083
$112$	14496.5	0.109199
$113$	−185806.	−1.36888	−0.684438	−	0.729071i	$-0.739952\pi$
$113$	−185806.	−1.36888	−0.684438	+	0.729071i	$0.739952\pi$
$114$	92610.9	0.667421
$115$	170433.	1.20174
$116$	11394.9	0.0786258
$117$	41747.8	0.281948
$118$	−13924.0	−0.0920575
$119$	43906.3	0.284223
$120$	46021.5	0.291748
$121$	−82569.7	−0.512693
$122$	100883.	0.613649
$123$	103087.	0.614387
$124$	−83580.0	−0.488144
$125$	10687.4	0.0611782
$126$	−18347.2	−0.102954
$127$	−103659.	−0.570293	−0.285146	−	0.958484i	$-0.592042\pi$
$127$	−103659.	−0.570293	−0.285146	+	0.958484i	$0.592042\pi$
$128$	−16384.0	−0.0883883
$129$	−94412.3	−0.499522
$130$	−164720.	−0.854848
$131$	257728.	1.31215	0.656074	−	0.754697i	$-0.272216\pi$
$131$	257728.	1.31215	0.656074	+	0.754697i	$0.272216\pi$
$132$	−40340.9	−0.201517
$133$	145675.	0.714094
$134$	223622.	1.07585
$135$	−58246.0	−0.275063
$136$	−49622.9	−0.230057
$137$	81291.4	0.370035	0.185018	−	0.982735i	$-0.440766\pi$
$137$	81291.4	0.370035	0.185018	+	0.982735i	$0.440766\pi$
$138$	76792.3	0.343258
$139$	220558.	0.968245	0.484122	−	0.875000i	$-0.339139\pi$
$139$	220558.	0.968245	0.484122	+	0.875000i	$0.339139\pi$
$140$	72390.7	0.312150
$141$	89452.8	0.378919
$142$	40007.3	0.166501
$143$	144388.	0.590462
$144$	20736.0	0.0833333
$145$	56902.1	0.224754
$146$	−267645.	−1.03915
$147$	122403.	0.467197
$148$	48250.7	0.181071
$149$	333679.	1.23130	0.615649	−	0.788021i	$-0.288894\pi$
$149$	333679.	1.23130	0.615649	+	0.788021i	$0.288894\pi$
$150$	117315.	0.425723
$151$	−144170.	−0.514554	−0.257277	−	0.966338i	$-0.582825\pi$
$151$	−144170.	−0.514554	−0.257277	+	0.966338i	$0.582825\pi$
$152$	−164642.	−0.578004
$153$	62804.0	0.216900
$154$	−63455.3	−0.215609
$155$	−417369.	−1.39538
$156$	−74218.3	−0.244174
$157$	−50504.8	−0.163525	−0.0817625	−	0.996652i	$-0.526055\pi$
$157$	−50504.8	−0.163525	−0.0817625	+	0.996652i	$0.526055\pi$
$158$	−231427.	−0.737514
$159$	113656.	0.356533
$160$	−81816.0	−0.252661
$161$	120793.	0.367261
$162$	−26244.0	−0.0785674
$163$	−413300.	−1.21842	−0.609209	−	0.793010i	$-0.708513\pi$
$163$	−413300.	−1.21842	−0.609209	+	0.793010i	$0.708513\pi$
$164$	−183266.	−0.532075
$165$	−201448.	−0.576042
$166$	−431277.	−1.21475
$167$	330316.	0.916514	0.458257	−	0.888820i	$-0.348474\pi$
$167$	330316.	0.916514	0.458257	+	0.888820i	$0.348474\pi$
$168$	32617.2	0.0891608
$169$	−105651.	−0.284548
$170$	−247800.	−0.657625
$171$	208375.	0.544947
$172$	167844.	0.432598
$173$	438975.	1.11513	0.557564	−	0.830134i	$-0.311736\pi$
$173$	438975.	1.11513	0.557564	+	0.830134i	$0.311736\pi$
$174$	25638.5	0.0641977
$175$	184534.	0.455494
$176$	71717.2	0.174518
$177$	−31329.0	−0.0751646
$178$	−29420.7	−0.0695991
$179$	333458.	0.777873	0.388936	−	0.921265i	$-0.372843\pi$
$179$	333458.	0.777873	0.388936	+	0.921265i	$0.372843\pi$
$180$	103548.	0.238211
$181$	−387148.	−0.878376	−0.439188	−	0.898395i	$-0.644734\pi$
$181$	−387148.	−0.878376	−0.439188	+	0.898395i	$0.644734\pi$
$182$	−116744.	−0.261249
$183$	226988.	0.501043
$184$	−136520.	−0.297270
$185$	240947.	0.517598
$186$	−188055.	−0.398568
$187$	217213.	0.454236
$188$	−159027.	−0.328153
$189$	−41281.2	−0.0840616
$190$	−822163.	−1.65224
$191$	790080.	1.56707	0.783534	−	0.621349i	$-0.213415\pi$
$191$	790080.	1.56707	0.783534	+	0.621349i	$0.213415\pi$
$192$	−36864.0	−0.0721688
$193$	−527258.	−1.01890	−0.509448	−	0.860501i	$-0.670151\pi$
$193$	−527258.	−1.01890	−0.509448	+	0.860501i	$0.670151\pi$
$194$	626575.	1.19528
$195$	−370621.	−0.697980
$196$	−217606.	−0.404604
$197$	307524.	0.564565	0.282282	−	0.959331i	$-0.408909\pi$
$197$	307524.	0.564565	0.282282	+	0.959331i	$0.408909\pi$
$198$	−90767.0	−0.164538
$199$	182454.	0.326603	0.163301	−	0.986576i	$-0.447786\pi$
$199$	182454.	0.326603	0.163301	+	0.986576i	$0.447786\pi$
$200$	−208561.	−0.368687
$201$	503150.	0.878431
$202$	−546116.	−0.941686
$203$	40328.7	0.0686870
$204$	−111652.	−0.187840
$205$	−915168.	−1.52095
$206$	243890.	0.400429
$207$	172783.	0.280269
$208$	131944.	0.211461
$209$	720681.	1.14124
$210$	162879.	0.254869
$211$	484524.	0.749219	0.374609	−	0.927183i	$-0.377777\pi$
$211$	484524.	0.749219	0.374609	+	0.927183i	$0.377777\pi$
$212$	−202055.	−0.308767
$213$	90016.4	0.135948
$214$	−253030.	−0.377692
$215$	838155.	1.23660
$216$	46656.0	0.0680414
$217$	−295806.	−0.426440
$218$	−313723.	−0.447100
$219$	−602202.	−0.848461
$220$	358131.	0.498867
$221$	399623.	0.550390
$222$	108564.	0.147844
$223$	241965.	0.325830	0.162915	−	0.986640i	$-0.447910\pi$
$223$	241965.	0.325830	0.162915	+	0.986640i	$0.447910\pi$
$224$	−57986.2	−0.0772155
$225$	263960.	0.347601
$226$	743225.	0.967941
$227$	−1.14656e6	−1.47683	−0.738417	−	0.674345i	$-0.764426\pi$
$227$	−1.14656e6	−1.47683	−0.738417	+	0.674345i	$0.764426\pi$
$228$	−370444.	−0.471938
$229$	56979.9	0.0718015	0.0359007	−	0.999355i	$-0.488570\pi$
$229$	56979.9	0.0718015	0.0359007	+	0.999355i	$0.488570\pi$
$230$	−681732.	−0.849756
$231$	−142774.	−0.176044
$232$	−45579.5	−0.0555968
$233$	−1.36604e6	−1.64844	−0.824219	−	0.566272i	$-0.808385\pi$
$233$	−1.36604e6	−1.64844	−0.824219	+	0.566272i	$0.808385\pi$
$234$	−166991.	−0.199367
$235$	−794126.	−0.938037
$236$	55696.0	0.0650945
$237$	−520710.	−0.602178
$238$	−175625.	−0.200976
$239$	−918750.	−1.04041	−0.520203	−	0.854043i	$-0.674144\pi$
$239$	−918750.	−1.04041	−0.520203	+	0.854043i	$0.674144\pi$
$240$	−184086.	−0.206297
$241$	−946856.	−1.05013	−0.525063	−	0.851064i	$-0.675958\pi$
$241$	−946856.	−1.05013	−0.525063	+	0.851064i	$0.675958\pi$
$242$	330279.	0.362529
$243$	−59049.0	−0.0641500
$244$	−403534.	−0.433916
$245$	−1.08665e6	−1.15657
$246$	−412349.	−0.434437
$247$	1.32589e6	1.38282
$248$	334320.	0.345170
$249$	−970374.	−0.991838
$250$	−42749.6	−0.0432596
$251$	1.12227e6	1.12438	0.562189	−	0.827009i	$-0.309959\pi$
$251$	1.12227e6	1.12438	0.562189	+	0.827009i	$0.309959\pi$
$252$	73388.8	0.0727995
$253$	597583.	0.586945
$254$	414636.	0.403258
$255$	−557549.	−0.536948
$256$	65536.0	0.0625000
$257$	491522.	0.464206	0.232103	−	0.972691i	$-0.425439\pi$
$257$	491522.	0.464206	0.232103	+	0.972691i	$0.425439\pi$
$258$	377649.	0.353215
$259$	170769.	0.158183
$260$	658881.	0.604469
$261$	57686.6	0.0524172
$262$	−1.03091e6	−0.927828
$263$	553746.	0.493653	0.246826	−	0.969060i	$-0.420612\pi$
$263$	553746.	0.493653	0.246826	+	0.969060i	$0.420612\pi$
$264$	161364.	0.142494
$265$	−1.00899e6	−0.882620
$266$	−582699.	−0.504941
$267$	−66196.6	−0.0568274
$268$	−894490.	−0.760744
$269$	−647101.	−0.545245	−0.272622	−	0.962121i	$-0.587891\pi$
$269$	−647101.	−0.545245	−0.272622	+	0.962121i	$0.587891\pi$
$270$	232984.	0.194499
$271$	280462.	0.231980	0.115990	−	0.993250i	$-0.462996\pi$
$271$	280462.	0.231980	0.115990	+	0.993250i	$0.462996\pi$
$272$	198492.	0.162675
$273$	−262673.	−0.213309
$274$	−325166.	−0.261655
$275$	912926.	0.727954
$276$	−307169.	−0.242720
$277$	82968.2	0.0649699	0.0324850	−	0.999472i	$-0.489658\pi$
$277$	82968.2	0.0649699	0.0324850	+	0.999472i	$0.489658\pi$
$278$	−882230.	−0.684652
$279$	−423124.	−0.325429
$280$	−289563.	−0.220723
$281$	−421160.	−0.318186	−0.159093	−	0.987264i	$-0.550857\pi$
$281$	−421160.	−0.318186	−0.159093	+	0.987264i	$0.550857\pi$
$282$	−357811.	−0.267936
$283$	2.28707e6	1.69752	0.848758	−	0.528782i	$-0.177351\pi$
$283$	2.28707e6	1.69752	0.848758	+	0.528782i	$0.177351\pi$
$284$	−160029.	−0.117734
$285$	−1.84987e6	−1.34905
$286$	−577553.	−0.417519
$287$	−648615.	−0.464817
$288$	−82944.0	−0.0589256
$289$	−818677.	−0.576591
$290$	−227608.	−0.158925
$291$	1.40979e6	0.975941
$292$	1.07058e6	0.734789
$293$	−2.26109e6	−1.53868	−0.769342	−	0.638838i	$-0.779416\pi$
$293$	−2.26109e6	−1.53868	−0.769342	+	0.638838i	$0.779416\pi$
$294$	−489613.	−0.330358
$295$	278127.	0.186075
$296$	−193003.	−0.128037
$297$	−204226.	−0.134344
$298$	−1.33472e6	−0.870659
$299$	1.09942e6	0.711191
$300$	−469262.	−0.301032
$301$	594033.	0.377915
$302$	576678.	0.363845
$303$	−1.22876e6	−0.768884
$304$	658567.	0.408711
$305$	−2.01511e6	−1.24036
$306$	−251216.	−0.153371
$307$	−2.22482e6	−1.34725	−0.673627	−	0.739072i	$-0.735264\pi$
$307$	−2.22482e6	−1.34725	−0.673627	+	0.739072i	$0.735264\pi$
$308$	253821.	0.152458
$309$	548752.	0.326949
$310$	1.66948e6	0.986680
$311$	−165866.	−0.0972427	−0.0486214	−	0.998817i	$-0.515483\pi$
$311$	−165866.	−0.0972427	−0.0486214	+	0.998817i	$0.515483\pi$
$312$	296873.	0.172657
$313$	−756824.	−0.436651	−0.218325	−	0.975876i	$-0.570059\pi$
$313$	−756824.	−0.436651	−0.218325	+	0.975876i	$0.570059\pi$
$314$	202019.	0.115630
$315$	366478.	0.208100
$316$	925706.	0.521501
$317$	1.76189e6	0.984758	0.492379	−	0.870381i	$-0.336127\pi$
$317$	1.76189e6	0.984758	0.492379	+	0.870381i	$0.336127\pi$
$318$	−454624.	−0.252107
$319$	199514.	0.109773
$320$	327264.	0.178658
$321$	−569318.	−0.308384
$322$	−483170.	−0.259693
$323$	1.99463e6	1.06379
$324$	104976.	0.0555556
$325$	1.67958e6	0.882050
$326$	1.65320e6	0.861551
$327$	−705876.	−0.365056
$328$	733065.	0.376234
$329$	−562828.	−0.286673
$330$	805794.	0.407323
$331$	294295.	0.147643	0.0738215	−	0.997271i	$-0.476480\pi$
$331$	294295.	0.147643	0.0738215	+	0.997271i	$0.476480\pi$
$332$	1.72511e6	0.858957
$333$	244269.	0.120714
$334$	−1.32127e6	−0.648073
$335$	−4.46677e6	−2.17461
$336$	−130469.	−0.0630462
$337$	2.70924e6	1.29949	0.649744	−	0.760153i	$-0.274876\pi$
$337$	2.70924e6	1.29949	0.649744	+	0.760153i	$0.274876\pi$
$338$	422602.	0.201206
$339$	1.67226e6	0.790321
$340$	991198.	0.465011
$341$	−1.46341e6	−0.681521
$342$	−833498.	−0.385336
$343$	−1.72188e6	−0.790257
$344$	−671376.	−0.305893
$345$	−1.53390e6	−0.693823
$346$	−1.75590e6	−0.788514
$347$	1.64930e6	0.735318	0.367659	−	0.929961i	$-0.380159\pi$
$347$	1.64930e6	0.735318	0.367659	+	0.929961i	$0.380159\pi$
$348$	−102554.	−0.0453946
$349$	−2.56761e6	−1.12841	−0.564203	−	0.825636i	$-0.690817\pi$
$349$	−2.56761e6	−1.12841	−0.564203	+	0.825636i	$0.690817\pi$
$350$	−738138.	−0.322083
$351$	−375730.	−0.162783
$352$	−286869.	−0.123403
$353$	1.92558e6	0.822480	0.411240	−	0.911527i	$-0.365096\pi$
$353$	1.92558e6	0.822480	0.411240	+	0.911527i	$0.365096\pi$
$354$	125316.	0.0531494
$355$	−799130.	−0.336548
$356$	117683.	0.0492140
$357$	−395157.	−0.164096
$358$	−1.33383e6	−0.550039
$359$	−1.41355e6	−0.578861	−0.289431	−	0.957199i	$-0.593466\pi$
$359$	−1.41355e6	−0.578861	−0.289431	+	0.957199i	$0.593466\pi$
$360$	−414194.	−0.168441
$361$	4.14179e6	1.67271
$362$	1.54859e6	0.621106
$363$	743127.	0.296003
$364$	466975.	0.184731
$365$	5.34611e6	2.10042
$366$	−907951.	−0.354291
$367$	−3.55994e6	−1.37968	−0.689839	−	0.723963i	$-0.742319\pi$
$367$	−3.55994e6	−1.37968	−0.689839	+	0.723963i	$0.742319\pi$
$368$	546079.	0.210201
$369$	−927785.	−0.354717
$370$	−963789.	−0.365997
$371$	−715113.	−0.269737
$372$	752220.	0.281830
$373$	1.87844e6	0.699076	0.349538	−	0.936922i	$-0.386339\pi$
$373$	1.87844e6	0.699076	0.349538	+	0.936922i	$0.386339\pi$
$374$	−868851.	−0.321193
$375$	−96186.6	−0.0353213
$376$	636109.	0.232039
$377$	367061.	0.133010
$378$	165125.	0.0594405
$379$	354913.	0.126918	0.0634590	−	0.997984i	$-0.479787\pi$
$379$	354913.	0.126918	0.0634590	+	0.997984i	$0.479787\pi$
$380$	3.28865e6	1.16831
$381$	932931.	0.329259
$382$	−3.16032e6	−1.10808
$383$	1.05527e6	0.367592	0.183796	−	0.982964i	$-0.441161\pi$
$383$	1.05527e6	0.367592	0.183796	+	0.982964i	$0.441161\pi$
$384$	147456.	0.0510310
$385$	1.26749e6	0.435807
$386$	2.10903e6	0.720469
$387$	849711.	0.288399
$388$	−2.50630e6	−0.845189
$389$	3.70792e6	1.24239	0.621193	−	0.783658i	$-0.286648\pi$
$389$	3.70792e6	1.24239	0.621193	+	0.783658i	$0.286648\pi$
$390$	1.48248e6	0.493546
$391$	1.65393e6	0.547111
$392$	870423.	0.286098
$393$	−2.31955e6	−0.757568
$394$	−1.23010e6	−0.399208
$395$	4.62266e6	1.49073
$396$	363068.	0.116346
$397$	−1.94031e6	−0.617868	−0.308934	−	0.951083i	$-0.599972\pi$
$397$	−1.94031e6	−0.617868	−0.308934	+	0.951083i	$0.599972\pi$
$398$	−729815.	−0.230943
$399$	−1.31107e6	−0.412282
$400$	834243.	0.260701
$401$	4.34357e6	1.34892	0.674459	−	0.738312i	$-0.264377\pi$
$401$	4.34357e6	1.34892	0.674459	+	0.738312i	$0.264377\pi$
$402$	−2.01260e6	−0.621145
$403$	−2.69235e6	−0.825788
$404$	2.18446e6	0.665873
$405$	524214.	0.158807
$406$	−161315.	−0.0485691
$407$	844825.	0.252802
$408$	446606.	0.132823
$409$	−1.07401e6	−0.317469	−0.158734	−	0.987321i	$-0.550741\pi$
$409$	−1.07401e6	−0.317469	−0.158734	+	0.987321i	$0.550741\pi$
$410$	3.66067e6	1.07548
$411$	−731623.	−0.213640
$412$	−975560.	−0.283146
$413$	197119.	0.0568661
$414$	−691131.	−0.198180
$415$	8.61460e6	2.45536
$416$	−527775.	−0.149526
$417$	−1.98502e6	−0.559016
$418$	−2.88272e6	−0.806979
$419$	278263.	0.0774320	0.0387160	−	0.999250i	$-0.487673\pi$
$419$	278263.	0.0774320	0.0387160	+	0.999250i	$0.487673\pi$
$420$	−651517.	−0.180220
$421$	3.40314e6	0.935781	0.467890	−	0.883787i	$-0.345014\pi$
$421$	3.40314e6	0.935781	0.467890	+	0.883787i	$0.345014\pi$
$422$	−1.93809e6	−0.529778
$423$	−805075.	−0.218769
$424$	808221.	0.218331
$425$	2.52671e6	0.678551
$426$	−360066.	−0.0961297
$427$	−1.42819e6	−0.379066
$428$	1.01212e6	0.267069
$429$	−1.29949e6	−0.340903
$430$	−3.35262e6	−0.874406
$431$	−5.95212e6	−1.54340	−0.771700	−	0.635987i	$-0.780593\pi$
$431$	−5.95212e6	−1.54340	−0.771700	+	0.635987i	$0.780593\pi$
$432$	−186624.	−0.0481125
$433$	−4.55458e6	−1.16743	−0.583713	−	0.811960i	$-0.698401\pi$
$433$	−4.55458e6	−1.16743	−0.583713	+	0.811960i	$0.698401\pi$
$434$	1.18322e6	0.301538
$435$	−512119.	−0.129762
$436$	1.25489e6	0.316148
$437$	5.48751e6	1.37458
$438$	2.40881e6	0.599952
$439$	5.01818e6	1.24275	0.621377	−	0.783512i	$-0.286574\pi$
$439$	5.01818e6	1.24275	0.621377	+	0.783512i	$0.286574\pi$
$440$	−1.43252e6	−0.352752
$441$	−1.10163e6	−0.269736
$442$	−1.59849e6	−0.389184
$443$	2.82000e6	0.682715	0.341357	−	0.939934i	$-0.389113\pi$
$443$	2.82000e6	0.682715	0.341357	+	0.939934i	$0.389113\pi$
$444$	−434256.	−0.104541
$445$	587668.	0.140680
$446$	−967861.	−0.230397
$447$	−3.00311e6	−0.710890
$448$	231945.	0.0545996
$449$	1.69329e6	0.396384	0.198192	−	0.980163i	$-0.436493\pi$
$449$	1.69329e6	0.396384	0.198192	+	0.980163i	$0.436493\pi$
$450$	−1.05584e6	−0.245791
$451$	−3.20882e6	−0.742855
$452$	−2.97290e6	−0.684438
$453$	1.29753e6	0.297078
$454$	4.58623e6	1.04428
$455$	2.33191e6	0.528060
$456$	1.48178e6	0.333711
$457$	−4.30344e6	−0.963885	−0.481942	−	0.876203i	$-0.660069\pi$
$457$	−4.30344e6	−0.963885	−0.481942	+	0.876203i	$0.660069\pi$
$458$	−227920.	−0.0507713
$459$	−565236.	−0.125227
$460$	2.72693e6	0.600868
$461$	−7.61287e6	−1.66838	−0.834192	−	0.551473i	$-0.814066\pi$
$461$	−7.61287e6	−1.66838	−0.834192	+	0.551473i	$0.814066\pi$
$462$	571097.	0.124482
$463$	−1.14818e6	−0.248918	−0.124459	−	0.992225i	$-0.539720\pi$
$463$	−1.14818e6	−0.248918	−0.124459	+	0.992225i	$0.539720\pi$
$464$	182318.	0.0393129
$465$	3.75633e6	0.805621
$466$	5.46415e6	1.16562
$467$	−894343.	−0.189763	−0.0948816	−	0.995489i	$-0.530247\pi$
$467$	−894343.	−0.189763	−0.0948816	+	0.995489i	$0.530247\pi$
$468$	667965.	0.140974
$469$	−3.16578e6	−0.664581
$470$	3.17651e6	0.663292
$471$	454544.	0.0944112
$472$	−222784.	−0.0460287
$473$	2.93879e6	0.603971
$474$	2.08284e6	0.425804
$475$	8.38325e6	1.70482
$476$	702501.	0.142112
$477$	−1.02290e6	−0.205844
$478$	3.67500e6	0.735678
$479$	−1.71603e6	−0.341732	−0.170866	−	0.985294i	$-0.554657\pi$
$479$	−1.71603e6	−0.341732	−0.170866	+	0.985294i	$0.554657\pi$
$480$	736344.	0.145874
$481$	1.55429e6	0.306316
$482$	3.78742e6	0.742551
$483$	−1.08713e6	−0.212038
$484$	−1.32112e6	−0.256346
$485$	−1.25156e7	−2.41600
$486$	236196.	0.0453609
$487$	2.42098e6	0.462561	0.231281	−	0.972887i	$-0.425708\pi$
$487$	2.42098e6	0.462561	0.231281	+	0.972887i	$0.425708\pi$
$488$	1.61414e6	0.306825
$489$	3.71970e6	0.703453
$490$	4.34659e6	0.817822
$491$	1.54295e6	0.288834	0.144417	−	0.989517i	$-0.453869\pi$
$491$	1.54295e6	0.288834	0.144417	+	0.989517i	$0.453869\pi$
$492$	1.64940e6	0.307194
$493$	552195.	0.102323
$494$	−5.30357e6	−0.977803
$495$	1.81304e6	0.332578
$496$	−1.33728e6	−0.244072
$497$	−566374.	−0.102852
$498$	3.88150e6	0.701335
$499$	1.32942e6	0.239007	0.119504	−	0.992834i	$-0.461870\pi$
$499$	1.32942e6	0.239007	0.119504	+	0.992834i	$0.461870\pi$
$500$	170998.	0.0305891
$501$	−2.97285e6	−0.529149
$502$	−4.48907e6	−0.795055
$503$	−8.84760e6	−1.55921	−0.779607	−	0.626269i	$-0.784581\pi$
$503$	−8.84760e6	−1.55921	−0.779607	+	0.626269i	$0.784581\pi$
$504$	−293555.	−0.0514770
$505$	1.09085e7	1.90342
$506$	−2.39033e6	−0.415033
$507$	950855.	0.164284
$508$	−1.65854e6	−0.285146
$509$	4.68147e6	0.800917	0.400458	−	0.916315i	$-0.368851\pi$
$509$	4.68147e6	0.800917	0.400458	+	0.916315i	$0.368851\pi$
$510$	2.23020e6	0.379680
$511$	3.78900e6	0.641907
$512$	−262144.	−0.0441942
$513$	−1.87537e6	−0.314625
$514$	−1.96609e6	−0.328243
$515$	−4.87161e6	−0.809383
$516$	−1.51060e6	−0.249761
$517$	−2.78442e6	−0.458150
$518$	−683075.	−0.111852
$519$	−3.95078e6	−0.643819
$520$	−2.63552e6	−0.427424
$521$	−19562.4	−0.00315739	−0.00157869	−	0.999999i	$-0.500503\pi$
$521$	−19562.4	−0.00315739	−0.00157869	+	0.999999i	$0.500503\pi$
$522$	−230746.	−0.0370646
$523$	7.53702e6	1.20489	0.602443	−	0.798162i	$-0.294194\pi$
$523$	7.53702e6	1.20489	0.602443	+	0.798162i	$0.294194\pi$
$524$	4.12364e6	0.656074
$525$	−1.66081e6	−0.262979
$526$	−2.21498e6	−0.349065
$527$	−4.05027e6	−0.635269
$528$	−645454.	−0.100758
$529$	−1.88614e6	−0.293045
$530$	4.03597e6	0.624107
$531$	281961.	0.0433963
$532$	2.33080e6	0.357047
$533$	−5.90352e6	−0.900105
$534$	264787.	0.0401830
$535$	5.05418e6	0.763425
$536$	3.57796e6	0.537927
$537$	−3.00112e6	−0.449105
$538$	2.58841e6	0.385546
$539$	−3.81008e6	−0.564887
$540$	−931936.	−0.137531
$541$	−1.11570e7	−1.63891	−0.819456	−	0.573142i	$-0.805724\pi$
$541$	−1.11570e7	−1.63891	−0.819456	+	0.573142i	$0.805724\pi$
$542$	−1.12185e6	−0.164035
$543$	3.48433e6	0.507131
$544$	−793966.	−0.115028
$545$	6.26649e6	0.903719
$546$	1.05069e6	0.150832
$547$	−1.02738e7	−1.46813	−0.734066	−	0.679079i	$-0.762380\pi$
$547$	−1.02738e7	−1.46813	−0.734066	+	0.679079i	$0.762380\pi$
$548$	1.30066e6	0.185018
$549$	−2.04289e6	−0.289277
$550$	−3.65171e6	−0.514741
$551$	1.83210e6	0.257082
$552$	1.22868e6	0.171629
$553$	3.27626e6	0.455581
$554$	−331873.	−0.0459407
$555$	−2.16852e6	−0.298835
$556$	3.52892e6	0.484122
$557$	4.83509e6	0.660338	0.330169	−	0.943922i	$-0.392894\pi$
$557$	4.83509e6	0.660338	0.330169	+	0.943922i	$0.392894\pi$
$558$	1.69249e6	0.230113
$559$	5.40673e6	0.731822
$560$	1.15825e6	0.156075
$561$	−1.95491e6	−0.262253
$562$	1.68464e6	0.224991
$563$	3.03919e6	0.404098	0.202049	−	0.979375i	$-0.435240\pi$
$563$	3.03919e6	0.404098	0.202049	+	0.979375i	$0.435240\pi$
$564$	1.43124e6	0.189459
$565$	−1.48456e7	−1.95649
$566$	−9.14829e6	−1.20032
$567$	371531.	0.0485330
$568$	640116.	0.0832507
$569$	1.53497e6	0.198756	0.0993778	−	0.995050i	$-0.468315\pi$
$569$	1.53497e6	0.198756	0.0993778	+	0.995050i	$0.468315\pi$
$570$	7.39947e6	0.953923
$571$	1.16376e7	1.49374	0.746870	−	0.664970i	$-0.231556\pi$
$571$	1.16376e7	1.49374	0.746870	+	0.664970i	$0.231556\pi$
$572$	2.31021e6	0.295231
$573$	−7.11072e6	−0.904747
$574$	2.59446e6	0.328676
$575$	6.95133e6	0.876796
$576$	331776.	0.0416667
$577$	−2.12997e6	−0.266338	−0.133169	−	0.991093i	$-0.542515\pi$
$577$	−2.12997e6	−0.266338	−0.133169	+	0.991093i	$0.542515\pi$
$578$	3.27471e6	0.407712
$579$	4.74533e6	0.588260
$580$	910434.	0.112377
$581$	6.10550e6	0.750379
$582$	−5.63918e6	−0.690094
$583$	−3.53780e6	−0.431084
$584$	−4.28232e6	−0.519574
$585$	3.33559e6	0.402979
$586$	9.04437e6	1.08801
$587$	−2.41638e6	−0.289448	−0.144724	−	0.989472i	$-0.546229\pi$
$587$	−2.41638e6	−0.289448	−0.144724	+	0.989472i	$0.546229\pi$
$588$	1.95845e6	0.233598
$589$	−1.34382e7	−1.59608
$590$	−1.11251e6	−0.131575
$591$	−2.76772e6	−0.325952
$592$	772011.	0.0905356
$593$	−8.87480e6	−1.03639	−0.518193	−	0.855263i	$-0.673395\pi$
$593$	−8.87480e6	−1.03639	−0.518193	+	0.855263i	$0.673395\pi$
$594$	816903.	0.0949958
$595$	3.50804e6	0.406231
$596$	5.33886e6	0.615649
$597$	−1.64208e6	−0.188564
$598$	−4.39768e6	−0.502888
$599$	−7.80480e6	−0.888781	−0.444390	−	0.895833i	$-0.646580\pi$
$599$	−7.80480e6	−0.888781	−0.444390	+	0.895833i	$0.646580\pi$
$600$	1.87705e6	0.212861
$601$	−6.06173e6	−0.684558	−0.342279	−	0.939598i	$-0.611199\pi$
$601$	−6.06173e6	−0.684558	−0.342279	+	0.939598i	$0.611199\pi$
$602$	−2.37613e6	−0.267226
$603$	−4.52835e6	−0.507162
$604$	−2.30671e6	−0.257277
$605$	−6.59719e6	−0.732775
$606$	4.91504e6	0.543683
$607$	−1.28775e7	−1.41861	−0.709303	−	0.704904i	$-0.750990\pi$
$607$	−1.28775e7	−1.41861	−0.709303	+	0.704904i	$0.750990\pi$
$608$	−2.63427e6	−0.289002
$609$	−362959.	−0.0396565
$610$	8.06043e6	0.877069
$611$	−5.12271e6	−0.555133
$612$	1.00486e6	0.108450
$613$	1.42515e7	1.53182	0.765911	−	0.642946i	$-0.222288\pi$
$613$	1.42515e7	1.53182	0.765911	+	0.642946i	$0.222288\pi$
$614$	8.89929e6	0.952652
$615$	8.23651e6	0.878123
$616$	−1.01528e6	−0.107804
$617$	−671174.	−0.0709777	−0.0354889	−	0.999370i	$-0.511299\pi$
$617$	−671174.	−0.0709777	−0.0354889	+	0.999370i	$0.511299\pi$
$618$	−2.19501e6	−0.231188
$619$	1.69814e7	1.78134	0.890668	−	0.454654i	$-0.150237\pi$
$619$	1.69814e7	1.78134	0.890668	+	0.454654i	$0.150237\pi$
$620$	−6.67791e6	−0.697688
$621$	−1.55504e6	−0.161813
$622$	663465.	0.0687610
$623$	416503.	0.0429930
$624$	−1.18749e6	−0.122087
$625$	−9.32973e6	−0.955364
$626$	3.02730e6	0.308759
$627$	−6.48613e6	−0.658895
$628$	−808078.	−0.0817625
$629$	2.33822e6	0.235645
$630$	−1.46591e6	−0.147149
$631$	−1.38094e7	−1.38070	−0.690352	−	0.723474i	$-0.742544\pi$
$631$	−1.38094e7	−1.38070	−0.690352	+	0.723474i	$0.742544\pi$
$632$	−3.70283e6	−0.368757
$633$	−4.36071e6	−0.432562
$634$	−7.04754e6	−0.696329
$635$	−8.28219e6	−0.815100
$636$	1.81850e6	0.178267
$637$	−7.00970e6	−0.684464
$638$	−798055.	−0.0776214
$639$	−810147.	−0.0784896
$640$	−1.30906e6	−0.126331
$641$	8.29537e6	0.797427	0.398713	−	0.917076i	$-0.369457\pi$
$641$	8.29537e6	0.797427	0.398713	+	0.917076i	$0.369457\pi$
$642$	2.27727e6	0.218061
$643$	−7.01382e6	−0.669001	−0.334501	−	0.942396i	$-0.608568\pi$
$643$	−7.01382e6	−0.669001	−0.334501	+	0.942396i	$0.608568\pi$
$644$	1.93268e6	0.183631
$645$	−7.54339e6	−0.713950
$646$	−7.97851e6	−0.752213
$647$	−1.70127e7	−1.59777	−0.798883	−	0.601487i	$-0.794575\pi$
$647$	−1.70127e7	−1.59777	−0.798883	+	0.601487i	$0.794575\pi$
$648$	−419904.	−0.0392837
$649$	975185.	0.0908815
$650$	−6.71833e6	−0.623703
$651$	2.66225e6	0.246205
$652$	−6.61279e6	−0.609209
$653$	−1.31575e7	−1.20751	−0.603753	−	0.797171i	$-0.706329\pi$
$653$	−1.31575e7	−1.20751	−0.603753	+	0.797171i	$0.706329\pi$
$654$	2.82351e6	0.258133
$655$	2.05920e7	1.87541
$656$	−2.93226e6	−0.266037
$657$	5.41982e6	0.489859
$658$	2.25131e6	0.202708
$659$	9.58380e6	0.859655	0.429828	−	0.902911i	$-0.358574\pi$
$659$	9.58380e6	0.859655	0.429828	+	0.902911i	$0.358574\pi$
$660$	−3.22318e6	−0.288021
$661$	1.20159e7	1.06967	0.534837	−	0.844956i	$-0.320373\pi$
$661$	1.20159e7	1.06967	0.534837	+	0.844956i	$0.320373\pi$
$662$	−1.17718e6	−0.104399
$663$	−3.59661e6	−0.317768
$664$	−6.90044e6	−0.607374
$665$	1.16392e7	1.02063
$666$	−977076.	−0.0853577
$667$	1.51917e6	0.132218
$668$	5.28506e6	0.458257
$669$	−2.17769e6	−0.188118
$670$	1.78671e7	1.53768
$671$	−7.06550e6	−0.605810
$672$	521876.	0.0445804
$673$	1.16447e7	0.991041	0.495520	−	0.868596i	$-0.334977\pi$
$673$	1.16447e7	0.991041	0.495520	+	0.868596i	$0.334977\pi$
$674$	−1.08370e7	−0.918877
$675$	−2.37564e6	−0.200688
$676$	−1.69041e6	−0.142274
$677$	6.82219e6	0.572074	0.286037	−	0.958219i	$-0.407662\pi$
$677$	6.82219e6	0.572074	0.286037	+	0.958219i	$0.407662\pi$
$678$	−6.68902e6	−0.558841
$679$	−8.87029e6	−0.738352
$680$	−3.96479e6	−0.328812
$681$	1.03190e7	0.852650
$682$	5.85363e6	0.481908
$683$	−1.95186e7	−1.60102	−0.800509	−	0.599321i	$-0.795437\pi$
$683$	−1.95186e7	−1.60102	−0.800509	+	0.599321i	$0.795437\pi$
$684$	3.33399e6	0.272474
$685$	6.49506e6	0.528879
$686$	6.88753e6	0.558796
$687$	−512819.	−0.0414546
$688$	2.68550e6	0.216299
$689$	−6.50877e6	−0.522337
$690$	6.13559e6	0.490607
$691$	9.72447e6	0.774766	0.387383	−	0.921919i	$-0.373379\pi$
$691$	9.72447e6	0.774766	0.387383	+	0.921919i	$0.373379\pi$
$692$	7.02360e6	0.557564
$693$	1.28497e6	0.101639
$694$	−6.59719e6	−0.519949
$695$	1.76222e7	1.38388
$696$	410216.	0.0320988
$697$	−8.88105e6	−0.692441
$698$	1.02704e7	0.797904
$699$	1.22943e7	0.951726
$700$	2.95255e6	0.227747
$701$	5.77050e6	0.443525	0.221763	−	0.975101i	$-0.428819\pi$
$701$	5.77050e6	0.443525	0.221763	+	0.975101i	$0.428819\pi$
$702$	1.50292e6	0.115105
$703$	7.75788e6	0.592045
$704$	1.14747e6	0.0872592
$705$	7.14714e6	0.541576
$706$	−7.70233e6	−0.581581
$707$	7.73124e6	0.581702
$708$	−501264.	−0.0375823
$709$	411540.	0.0307466	0.0153733	−	0.999882i	$-0.495106\pi$
$709$	411540.	0.0307466	0.0153733	+	0.999882i	$0.495106\pi$
$710$	3.19652e6	0.237975
$711$	4.68639e6	0.347668
$712$	−470732.	−0.0347995
$713$	−1.11429e7	−0.820869
$714$	1.58063e6	0.116034
$715$	1.15364e7	0.843927
$716$	5.33533e6	0.388936
$717$	8.26875e6	0.600679
$718$	5.65419e6	0.409317
$719$	1.84224e6	0.132900	0.0664498	−	0.997790i	$-0.478833\pi$
$719$	1.84224e6	0.132900	0.0664498	+	0.997790i	$0.478833\pi$
$720$	1.65677e6	0.119106
$721$	−3.45270e6	−0.247355
$722$	−1.65672e7	−1.18278
$723$	8.52170e6	0.606290
$724$	−6.19437e6	−0.439188
$725$	2.32083e6	0.163983
$726$	−2.97251e6	−0.209306
$727$	3.12677e6	0.219412	0.109706	−	0.993964i	$-0.465009\pi$
$727$	3.12677e6	0.219412	0.109706	+	0.993964i	$0.465009\pi$
$728$	−1.86790e6	−0.130625
$729$	531441.	0.0370370
$730$	−2.13844e7	−1.48522
$731$	8.13370e6	0.562982
$732$	3.63180e6	0.250521
$733$	−2.27547e7	−1.56427	−0.782133	−	0.623112i	$-0.785868\pi$
$733$	−2.27547e7	−1.56427	−0.782133	+	0.623112i	$0.785868\pi$
$734$	1.42398e7	0.975579
$735$	9.77983e6	0.667749
$736$	−2.18432e6	−0.148635
$737$	−1.56617e7	−1.06211
$738$	3.71114e6	0.250823
$739$	−1.44705e7	−0.974706	−0.487353	−	0.873205i	$-0.662037\pi$
$739$	−1.44705e7	−0.974706	−0.487353	+	0.873205i	$0.662037\pi$
$740$	3.85515e6	0.258799
$741$	−1.19330e7	−0.798372
$742$	2.86045e6	0.190733
$743$	9.39929e6	0.624630	0.312315	−	0.949979i	$-0.398896\pi$
$743$	9.39929e6	0.624630	0.312315	+	0.949979i	$0.398896\pi$
$744$	−3.00888e6	−0.199284
$745$	2.66604e7	1.75985
$746$	−7.51374e6	−0.494321
$747$	8.73337e6	0.572638
$748$	3.47540e6	0.227118
$749$	3.58209e6	0.233309
$750$	384746.	0.0249759
$751$	1.00621e7	0.651012	0.325506	−	0.945540i	$-0.394465\pi$
$751$	1.00621e7	0.651012	0.325506	+	0.945540i	$0.394465\pi$
$752$	−2.54443e6	−0.164077
$753$	−1.01004e7	−0.649160
$754$	−1.46825e6	−0.0940525
$755$	−1.15189e7	−0.735436
$756$	−660499.	−0.0420308
$757$	−1.48065e7	−0.939105	−0.469552	−	0.882905i	$-0.655585\pi$
$757$	−1.48065e7	−0.939105	−0.469552	+	0.882905i	$0.655585\pi$
$758$	−1.41965e6	−0.0897446
$759$	−5.37825e6	−0.338873
$760$	−1.31546e7	−0.826122
$761$	−4.09922e6	−0.256590	−0.128295	−	0.991736i	$-0.540950\pi$
$761$	−4.09922e6	−0.256590	−0.128295	+	0.991736i	$0.540950\pi$
$762$	−3.73172e6	−0.232821
$763$	4.44131e6	0.276185
$764$	1.26413e7	0.783534
$765$	5.01794e6	0.310007
$766$	−4.22107e6	−0.259927
$767$	1.79413e6	0.110120
$768$	−589824.	−0.0360844
$769$	−1.67639e7	−1.02226	−0.511128	−	0.859505i	$-0.670772\pi$
$769$	−1.67639e7	−1.02226	−0.511128	+	0.859505i	$0.670772\pi$
$770$	−5.06998e6	−0.308162
$771$	−4.42370e6	−0.268009
$772$	−8.43613e6	−0.509448
$773$	−9.68792e6	−0.583152	−0.291576	−	0.956548i	$-0.594180\pi$
$773$	−9.68792e6	−0.583152	−0.291576	+	0.956548i	$0.594180\pi$
$774$	−3.39884e6	−0.203929
$775$	−1.70230e7	−1.01808
$776$	1.00252e7	0.597639
$777$	−1.53692e6	−0.0913268
$778$	−1.48317e7	−0.878499
$779$	−2.94661e7	−1.73972
$780$	−5.92993e6	−0.348990
$781$	−2.80196e6	−0.164375
$782$	−6.61573e6	−0.386866
$783$	−519180.	−0.0302631
$784$	−3.48169e6	−0.202302
$785$	−4.03526e6	−0.233721
$786$	9.27819e6	0.535682
$787$	−1.32150e7	−0.760555	−0.380278	−	0.924872i	$-0.624172\pi$
$787$	−1.32150e7	−0.760555	−0.380278	+	0.924872i	$0.624172\pi$
$788$	4.92039e6	0.282282
$789$	−4.98372e6	−0.285010
$790$	−1.84906e7	−1.05411
$791$	−1.05217e7	−0.597921
$792$	−1.45227e6	−0.0822688
$793$	−1.29990e7	−0.734050
$794$	7.76125e6	0.436899
$795$	9.08094e6	0.509581
$796$	2.91926e6	0.163301
$797$	−3.25548e7	−1.81539	−0.907695	−	0.419632i	$-0.862159\pi$
$797$	−3.25548e7	−1.81539	−0.907695	+	0.419632i	$0.862159\pi$
$798$	5.24429e6	0.291528
$799$	−7.70643e6	−0.427058
$800$	−3.33697e6	−0.184343
$801$	595770.	0.0328093
$802$	−1.73743e7	−0.953829
$803$	1.87449e7	1.02587
$804$	8.05041e6	0.439216
$805$	9.65113e6	0.524915
$806$	1.07694e7	0.583920
$807$	5.82391e6	0.314797
$808$	−8.73785e6	−0.470843
$809$	−1.88153e7	−1.01074	−0.505370	−	0.862903i	$-0.668644\pi$
$809$	−1.88153e7	−1.01074	−0.505370	+	0.862903i	$0.668644\pi$
$810$	−2.09685e6	−0.112294
$811$	1.61297e7	0.861139	0.430569	−	0.902557i	$-0.358313\pi$
$811$	1.61297e7	0.861139	0.430569	+	0.902557i	$0.358313\pi$
$812$	645260.	0.0343435
$813$	−2.52415e6	−0.133934
$814$	−3.37930e6	−0.178758
$815$	−3.30220e7	−1.74144
$816$	−1.78642e6	−0.0939202
$817$	2.69865e7	1.41446
$818$	4.29605e6	0.224484
$819$	2.36406e6	0.123154
$820$	−1.46427e7	−0.760477
$821$	−1.90738e7	−0.987594	−0.493797	−	0.869577i	$-0.664391\pi$
$821$	−1.90738e7	−0.987594	−0.493797	+	0.869577i	$0.664391\pi$
$822$	2.92649e6	0.151066
$823$	1.19797e7	0.616521	0.308260	−	0.951302i	$-0.400253\pi$
$823$	1.19797e7	0.616521	0.308260	+	0.951302i	$0.400253\pi$
$824$	3.90224e6	0.200215
$825$	−8.21634e6	−0.420285
$826$	−788476.	−0.0402104
$827$	1.82166e7	0.926196	0.463098	−	0.886307i	$-0.346738\pi$
$827$	1.82166e7	0.926196	0.463098	+	0.886307i	$0.346738\pi$
$828$	2.76452e6	0.140134
$829$	8.37541e6	0.423272	0.211636	−	0.977349i	$-0.432121\pi$
$829$	8.37541e6	0.423272	0.211636	+	0.977349i	$0.432121\pi$
$830$	−3.44584e7	−1.73620
$831$	−746714.	−0.0375104
$832$	2.11110e6	0.105731
$833$	−1.05451e7	−0.526551
$834$	7.94007e6	0.395284
$835$	2.63918e7	1.30994
$836$	1.15309e7	0.570620
$837$	3.80811e6	0.187887
$838$	−1.11305e6	−0.0547527
$839$	6.66193e6	0.326735	0.163367	−	0.986565i	$-0.447764\pi$
$839$	6.66193e6	0.326735	0.163367	+	0.986565i	$0.447764\pi$
$840$	2.60607e6	0.127435
$841$	−2.00039e7	−0.975272
$842$	−1.36125e7	−0.661697
$843$	3.79044e6	0.183705
$844$	7.75238e6	0.374609
$845$	−8.44132e6	−0.406695
$846$	3.22030e6	0.154693
$847$	−4.67569e6	−0.223943
$848$	−3.23288e6	−0.154383
$849$	−2.05837e7	−0.980061
$850$	−1.01068e7	−0.479808
$851$	6.43278e6	0.304491
$852$	1.44026e6	0.0679740
$853$	−1.52413e7	−0.717216	−0.358608	−	0.933488i	$-0.616748\pi$
$853$	−1.52413e7	−0.717216	−0.358608	+	0.933488i	$0.616748\pi$
$854$	5.71274e6	0.268040
$855$	1.66488e7	0.778875
$856$	−4.04848e6	−0.188846
$857$	−8.51454e6	−0.396013	−0.198006	−	0.980201i	$-0.563447\pi$
$857$	−8.51454e6	−0.396013	−0.198006	+	0.980201i	$0.563447\pi$
$858$	5.19798e6	0.241055
$859$	2.37074e7	1.09623	0.548113	−	0.836404i	$-0.315346\pi$
$859$	2.37074e7	1.09623	0.548113	+	0.836404i	$0.315346\pi$
$860$	1.34105e7	0.618298
$861$	5.83754e6	0.268362
$862$	2.38085e7	1.09135
$863$	−2.18049e6	−0.0996615	−0.0498308	−	0.998758i	$-0.515868\pi$
$863$	−2.18049e6	−0.0996615	−0.0498308	+	0.998758i	$0.515868\pi$
$864$	746496.	0.0340207
$865$	3.50734e7	1.59381
$866$	1.82183e7	0.825494
$867$	7.36810e6	0.332895
$868$	−4.73290e6	−0.213220
$869$	1.62083e7	0.728093
$870$	2.04848e6	0.0917556
$871$	−2.88140e7	−1.28694
$872$	−5.01957e6	−0.223550
$873$	−1.26882e7	−0.563460
$874$	−2.19500e7	−0.971978
$875$	605197.	0.0267225
$876$	−9.63523e6	−0.424230
$877$	1.78742e7	0.784745	0.392372	−	0.919806i	$-0.371654\pi$
$877$	1.78742e7	0.784745	0.392372	+	0.919806i	$0.371654\pi$
$878$	−2.00727e7	−0.878759
$879$	2.03498e7	0.888359
$880$	5.73009e6	0.249433
$881$	−2.53903e7	−1.10212	−0.551058	−	0.834467i	$-0.685776\pi$
$881$	−2.53903e7	−1.10212	−0.551058	+	0.834467i	$0.685776\pi$
$882$	4.40652e6	0.190732
$883$	−1.52241e7	−0.657096	−0.328548	−	0.944487i	$-0.606559\pi$
$883$	−1.52241e7	−0.657096	−0.328548	+	0.944487i	$0.606559\pi$
$884$	6.39397e6	0.275195
$885$	−2.50314e6	−0.107430
$886$	−1.12800e7	−0.482752
$887$	2.57003e7	1.09680	0.548402	−	0.836215i	$-0.315236\pi$
$887$	2.57003e7	1.09680	0.548402	+	0.836215i	$0.315236\pi$
$888$	1.73702e6	0.0739220
$889$	−5.86991e6	−0.249102
$890$	−2.35067e6	−0.0994756
$891$	1.83803e6	0.0775638
$892$	3.87144e6	0.162915
$893$	−2.55688e7	−1.07296
$894$	1.20124e7	0.502675
$895$	2.66428e7	1.11179
$896$	−927779.	−0.0386078
$897$	−9.89479e6	−0.410606
$898$	−6.77316e6	−0.280285
$899$	−3.72025e6	−0.153523
$900$	4.22336e6	0.173801
$901$	−9.79157e6	−0.401828
$902$	1.28353e7	0.525278
$903$	−5.34630e6	−0.218189
$904$	1.18916e7	0.483971
$905$	−3.09325e7	−1.25543
$906$	−5.19011e6	−0.210066
$907$	6.12972e6	0.247413	0.123707	−	0.992319i	$-0.460522\pi$
$907$	6.12972e6	0.247413	0.123707	+	0.992319i	$0.460522\pi$
$908$	−1.83449e7	−0.738417
$909$	1.10588e7	0.443915
$910$	−9.32764e6	−0.373395
$911$	1.04454e7	0.416994	0.208497	−	0.978023i	$-0.433143\pi$
$911$	1.04454e7	0.416994	0.208497	+	0.978023i	$0.433143\pi$
$912$	−5.92710e6	−0.235969
$913$	3.02051e7	1.19923
$914$	1.72138e7	0.681569
$915$	1.81360e7	0.716124
$916$	911679.	0.0359007
$917$	1.45944e7	0.573142
$918$	2.26094e6	0.0885489
$919$	2.47088e7	0.965078	0.482539	−	0.875875i	$-0.339715\pi$
$919$	2.47088e7	0.965078	0.482539	+	0.875875i	$0.339715\pi$
$920$	−1.09077e7	−0.424878
$921$	2.00234e7	0.777837
$922$	3.04515e7	1.17973
$923$	−5.15499e6	−0.199170
$924$	−2.28439e6	−0.0880218
$925$	9.82734e6	0.377643
$926$	4.59271e6	0.176012
$927$	−4.93877e6	−0.188764
$928$	−729273.	−0.0277984
$929$	3.22285e7	1.22518	0.612591	−	0.790400i	$-0.290127\pi$
$929$	3.22285e7	1.22518	0.612591	+	0.790400i	$0.290127\pi$
$930$	−1.50253e7	−0.569660
$931$	−3.49873e7	−1.32293
$932$	−2.18566e7	−0.824219
$933$	1.49280e6	0.0561431
$934$	3.57737e6	0.134183
$935$	1.73550e7	0.649224
$936$	−2.67186e6	−0.0996837
$937$	3.22051e7	1.19833	0.599165	−	0.800626i	$-0.295499\pi$
$937$	3.22051e7	1.19833	0.599165	+	0.800626i	$0.295499\pi$
$938$	1.26631e7	0.469930
$939$	6.81142e6	0.252100
$940$	−1.27060e7	−0.469018
$941$	1.72270e7	0.634212	0.317106	−	0.948390i	$-0.397289\pi$
$941$	1.72270e7	0.634212	0.317106	+	0.948390i	$0.397289\pi$
$942$	−1.81817e6	−0.0667588
$943$	−2.44331e7	−0.894743
$944$	891136.	0.0325472
$945$	−3.29830e6	−0.120146
$946$	−1.17552e7	−0.427072
$947$	3.96639e7	1.43721	0.718605	−	0.695418i	$-0.244781\pi$
$947$	3.96639e7	1.43721	0.718605	+	0.695418i	$0.244781\pi$
$948$	−8.33136e6	−0.301089
$949$	3.44864e7	1.24303
$950$	−3.35330e7	−1.20549
$951$	−1.58570e7	−0.568550
$952$	−2.81000e6	−0.100488
$953$	−3.87168e7	−1.38091	−0.690457	−	0.723373i	$-0.742591\pi$
$953$	−3.87168e7	−1.38091	−0.690457	+	0.723373i	$0.742591\pi$
$954$	4.09162e6	0.145554
$955$	6.31262e7	2.23976
$956$	−1.47000e7	−0.520203
$957$	−1.79562e6	−0.0633776
$958$	6.86411e6	0.241641
$959$	4.60330e6	0.161630
$960$	−2.94538e6	−0.103148
$961$	−1.34160e6	−0.0468612
$962$	−6.21716e6	−0.216598
$963$	5.12386e6	0.178046
$964$	−1.51497e7	−0.525063
$965$	−4.21271e7	−1.45628
$966$	4.34853e6	0.149934
$967$	2.93714e7	1.01009	0.505043	−	0.863094i	$-0.331477\pi$
$967$	2.93714e7	1.01009	0.505043	+	0.863094i	$0.331477\pi$
$968$	5.28446e6	0.181264
$969$	−1.79517e7	−0.614179
$970$	5.00624e7	1.70837
$971$	4.68057e7	1.59313	0.796564	−	0.604554i	$-0.206649\pi$
$971$	4.68057e7	1.59313	0.796564	+	0.604554i	$0.206649\pi$
$972$	−944784.	−0.0320750
$973$	1.24895e7	0.422926
$974$	−9.68393e6	−0.327080
$975$	−1.51162e7	−0.509252
$976$	−6.45654e6	−0.216958
$977$	3.51999e7	1.17979	0.589895	−	0.807480i	$-0.299169\pi$
$977$	3.51999e7	1.17979	0.589895	+	0.807480i	$0.299169\pi$
$978$	−1.48788e7	−0.497417
$979$	2.06052e6	0.0687100
$980$	−1.73864e7	−0.578287
$981$	6.35289e6	0.210765
$982$	−6.17181e6	−0.204237
$983$	1.50956e7	0.498271	0.249135	−	0.968469i	$-0.419854\pi$
$983$	1.50956e7	0.498271	0.249135	+	0.968469i	$0.419854\pi$
$984$	−6.59758e6	−0.217219
$985$	2.45707e7	0.806914
$986$	−2.20878e6	−0.0723536
$987$	5.06545e6	0.165510
$988$	2.12143e7	0.691411
$989$	2.23770e7	0.727462
$990$	−7.25214e6	−0.235168
$991$	−2.80420e7	−0.907036	−0.453518	−	0.891247i	$-0.649831\pi$
$991$	−2.80420e7	−0.907036	−0.453518	+	0.891247i	$0.649831\pi$
$992$	5.34912e6	0.172585
$993$	−2.64866e6	−0.0852418
$994$	2.26550e6	0.0727273
$995$	1.45778e7	0.466803
$996$	−1.55260e7	−0.495919
$997$	−2.93282e7	−0.934431	−0.467215	−	0.884144i	$-0.654743\pi$
$997$	−2.93282e7	−0.934431	−0.467215	+	0.884144i	$0.654743\pi$
$998$	−5.31768e6	−0.169004
$999$	−2.19842e6	−0.0696943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.g.1.6	✓	6
3.2	odd	2		1062.6.a.h.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.g.1.6	✓	6	1.1	even	1	trivial
1062.6.a.h.1.1		6	3.2	odd	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +79.8984 q^{5} +36.0000 q^{6} +56.6271 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +79.8984 q^{5} +36.0000 q^{6} +56.6271 q^{7} -64.0000 q^{8} +81.0000 q^{9} -319.594 q^{10} +280.145 q^{11} -144.000 q^{12} +515.405 q^{13} -226.509 q^{14} -719.086 q^{15} +256.000 q^{16} +775.358 q^{17} -324.000 q^{18} +2572.53 q^{19} +1278.38 q^{20} -509.644 q^{21} -1120.58 q^{22} +2133.12 q^{23} +576.000 q^{24} +3258.76 q^{25} -2061.62 q^{26} -729.000 q^{27} +906.034 q^{28} +712.180 q^{29} +2876.34 q^{30} -5223.75 q^{31} -1024.00 q^{32} -2521.31 q^{33} -3101.43 q^{34} +4524.42 q^{35} +1296.00 q^{36} +3015.67 q^{37} -10290.1 q^{38} -4638.65 q^{39} -5113.50 q^{40} -11454.1 q^{41} +2038.58 q^{42} +10490.3 q^{43} +4482.32 q^{44} +6471.77 q^{45} -8532.48 q^{46} -9939.20 q^{47} -2304.00 q^{48} -13600.4 q^{49} -13035.0 q^{50} -6978.22 q^{51} +8246.48 q^{52} -12628.5 q^{53} +2916.00 q^{54} +22383.2 q^{55} -3624.14 q^{56} -23152.7 q^{57} -2848.72 q^{58} +3481.00 q^{59} -11505.4 q^{60} -25220.9 q^{61} +20895.0 q^{62} +4586.80 q^{63} +4096.00 q^{64} +41180.1 q^{65} +10085.2 q^{66} -55905.6 q^{67} +12405.7 q^{68} -19198.1 q^{69} -18097.7 q^{70} -10001.8 q^{71} -5184.00 q^{72} +66911.3 q^{73} -12062.7 q^{74} -29328.9 q^{75} +41160.4 q^{76} +15863.8 q^{77} +18554.6 q^{78} +57856.6 q^{79} +20454.0 q^{80} +6561.00 q^{81} +45816.6 q^{82} +107819. q^{83} -8154.31 q^{84} +61949.9 q^{85} -41961.0 q^{86} -6409.62 q^{87} -17929.3 q^{88} +7355.18 q^{89} -25887.1 q^{90} +29185.9 q^{91} +34129.9 q^{92} +47013.7 q^{93} +39756.8 q^{94} +205541. q^{95} +9216.00 q^{96} -156644. q^{97} +54401.5 q^{98} +22691.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9} - 16 q^{10} + 436 q^{11} - 864 q^{12} - 536 q^{13} + 216 q^{14} - 36 q^{15} + 1536 q^{16} + 910 q^{17} - 1944 q^{18} + 1462 q^{19} + 64 q^{20} + 486 q^{21} - 1744 q^{22} + 1634 q^{23} + 3456 q^{24} - 1186 q^{25} + 2144 q^{26} - 4374 q^{27} - 864 q^{28} - 1598 q^{29} + 144 q^{30} - 5670 q^{31} - 6144 q^{32} - 3924 q^{33} - 3640 q^{34} - 7242 q^{35} + 7776 q^{36} - 20458 q^{37} - 5848 q^{38} + 4824 q^{39} - 256 q^{40} + 262 q^{41} - 1944 q^{42} - 34028 q^{43} + 6976 q^{44} + 324 q^{45} - 6536 q^{46} - 11194 q^{47} - 13824 q^{48} - 32652 q^{49} + 4744 q^{50} - 8190 q^{51} - 8576 q^{52} - 17164 q^{53} + 17496 q^{54} - 37040 q^{55} + 3456 q^{56} - 13158 q^{57} + 6392 q^{58} + 20886 q^{59} - 576 q^{60} - 43546 q^{61} + 22680 q^{62} - 4374 q^{63} + 24576 q^{64} + 65568 q^{65} + 15696 q^{66} - 52772 q^{67} + 14560 q^{68} - 14706 q^{69} + 28968 q^{70} + 84740 q^{71} - 31104 q^{72} - 36578 q^{73} + 81832 q^{74} + 10674 q^{75} + 23392 q^{76} + 90678 q^{77} - 19296 q^{78} + 85196 q^{79} + 1024 q^{80} + 39366 q^{81} - 1048 q^{82} + 217026 q^{83} + 7776 q^{84} + 26570 q^{85} + 136112 q^{86} + 14382 q^{87} - 27904 q^{88} + 333850 q^{89} - 1296 q^{90} + 214914 q^{91} + 26144 q^{92} + 51030 q^{93} + 44776 q^{94} + 458758 q^{95} + 55296 q^{96} + 173148 q^{97} + 130608 q^{98} + 35316 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9 - 16 * q^10 + 436 * q^11 - 864 * q^12 - 536 * q^13 + 216 * q^14 - 36 * q^15 + 1536 * q^16 + 910 * q^17 - 1944 * q^18 + 1462 * q^19 + 64 * q^20 + 486 * q^21 - 1744 * q^22 + 1634 * q^23 + 3456 * q^24 - 1186 * q^25 + 2144 * q^26 - 4374 * q^27 - 864 * q^28 - 1598 * q^29 + 144 * q^30 - 5670 * q^31 - 6144 * q^32 - 3924 * q^33 - 3640 * q^34 - 7242 * q^35 + 7776 * q^36 - 20458 * q^37 - 5848 * q^38 + 4824 * q^39 - 256 * q^40 + 262 * q^41 - 1944 * q^42 - 34028 * q^43 + 6976 * q^44 + 324 * q^45 - 6536 * q^46 - 11194 * q^47 - 13824 * q^48 - 32652 * q^49 + 4744 * q^50 - 8190 * q^51 - 8576 * q^52 - 17164 * q^53 + 17496 * q^54 - 37040 * q^55 + 3456 * q^56 - 13158 * q^57 + 6392 * q^58 + 20886 * q^59 - 576 * q^60 - 43546 * q^61 + 22680 * q^62 - 4374 * q^63 + 24576 * q^64 + 65568 * q^65 + 15696 * q^66 - 52772 * q^67 + 14560 * q^68 - 14706 * q^69 + 28968 * q^70 + 84740 * q^71 - 31104 * q^72 - 36578 * q^73 + 81832 * q^74 + 10674 * q^75 + 23392 * q^76 + 90678 * q^77 - 19296 * q^78 + 85196 * q^79 + 1024 * q^80 + 39366 * q^81 - 1048 * q^82 + 217026 * q^83 + 7776 * q^84 + 26570 * q^85 + 136112 * q^86 + 14382 * q^87 - 27904 * q^88 + 333850 * q^89 - 1296 * q^90 + 214914 * q^91 + 26144 * q^92 + 51030 * q^93 + 44776 * q^94 + 458758 * q^95 + 55296 * q^96 + 173148 * q^97 + 130608 * q^98 + 35316 * q^99

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