LMFDB - Embedded newform 354.6.a.f.1.1

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:	$1$
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} - 2x^{5} - 6296x^{4} - 192180x^{3} - 1919598x^{2} - 7344954x - 8433643 $ x^6 - 2x^5 - 6296x^4 - 192180x^3 - 1919598x^2 - 7344954*x - 8433643
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-7.38516$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -94.9298 q^{5} +36.0000 q^{6} -186.983 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -94.9298 q^{5} +36.0000 q^{6} -186.983 q^{7} -64.0000 q^{8} +81.0000 q^{9} +379.719 q^{10} -442.853 q^{11} -144.000 q^{12} +760.277 q^{13} +747.931 q^{14} +854.369 q^{15} +256.000 q^{16} +1612.53 q^{17} -324.000 q^{18} +2067.67 q^{19} -1518.88 q^{20} +1682.84 q^{21} +1771.41 q^{22} -2370.21 q^{23} +576.000 q^{24} +5886.68 q^{25} -3041.11 q^{26} -729.000 q^{27} -2991.72 q^{28} -1274.92 q^{29} -3417.47 q^{30} -2923.39 q^{31} -1024.00 q^{32} +3985.68 q^{33} -6450.12 q^{34} +17750.2 q^{35} +1296.00 q^{36} +6288.50 q^{37} -8270.66 q^{38} -6842.49 q^{39} +6075.51 q^{40} +16455.0 q^{41} -6731.38 q^{42} -15679.0 q^{43} -7085.64 q^{44} -7689.32 q^{45} +9480.86 q^{46} -14982.1 q^{47} -2304.00 q^{48} +18155.5 q^{49} -23546.7 q^{50} -14512.8 q^{51} +12164.4 q^{52} +12595.6 q^{53} +2916.00 q^{54} +42039.9 q^{55} +11966.9 q^{56} -18609.0 q^{57} +5099.67 q^{58} -3481.00 q^{59} +13669.9 q^{60} -20715.6 q^{61} +11693.6 q^{62} -15145.6 q^{63} +4096.00 q^{64} -72172.9 q^{65} -15942.7 q^{66} +46673.0 q^{67} +25800.5 q^{68} +21331.9 q^{69} -71001.0 q^{70} -77332.7 q^{71} -5184.00 q^{72} +70937.2 q^{73} -25154.0 q^{74} -52980.1 q^{75} +33082.7 q^{76} +82805.8 q^{77} +27370.0 q^{78} +27333.8 q^{79} -24302.0 q^{80} +6561.00 q^{81} -65819.9 q^{82} +60679.0 q^{83} +26925.5 q^{84} -153077. q^{85} +62715.9 q^{86} +11474.3 q^{87} +28342.6 q^{88} +137292. q^{89} +30757.3 q^{90} -142159. q^{91} -37923.4 q^{92} +26310.5 q^{93} +59928.5 q^{94} -196283. q^{95} +9216.00 q^{96} +36512.5 q^{97} -72622.1 q^{98} -35871.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9} + 184 q^{10} - 653 q^{11} - 864 q^{12} + 647 q^{13} + 412 q^{14} + 414 q^{15} + 1536 q^{16} + 621 q^{17} - 1944 q^{18} - 454 q^{19} - 736 q^{20} + 927 q^{21} + 2612 q^{22} - 3412 q^{23} + 3456 q^{24} + 3866 q^{25} - 2588 q^{26} - 4374 q^{27} - 1648 q^{28} + 1526 q^{29} - 1656 q^{30} + 5976 q^{31} - 6144 q^{32} + 5877 q^{33} - 2484 q^{34} + 8098 q^{35} + 7776 q^{36} + 37033 q^{37} + 1816 q^{38} - 5823 q^{39} + 2944 q^{40} + 13983 q^{41} - 3708 q^{42} + 11521 q^{43} - 10448 q^{44} - 3726 q^{45} + 13648 q^{46} + 12434 q^{47} - 13824 q^{48} + 54237 q^{49} - 15464 q^{50} - 5589 q^{51} + 10352 q^{52} + 21310 q^{53} + 17496 q^{54} + 57468 q^{55} + 6592 q^{56} + 4086 q^{57} - 6104 q^{58} - 20886 q^{59} + 6624 q^{60} - 23030 q^{61} - 23904 q^{62} - 8343 q^{63} + 24576 q^{64} - 37368 q^{65} - 23508 q^{66} + 24342 q^{67} + 9936 q^{68} + 30708 q^{69} - 32392 q^{70} - 184375 q^{71} - 31104 q^{72} - 24512 q^{73} - 148132 q^{74} - 34794 q^{75} - 7264 q^{76} - 46529 q^{77} + 23292 q^{78} - 17987 q^{79} - 11776 q^{80} + 39366 q^{81} - 55932 q^{82} - 46687 q^{83} + 14832 q^{84} - 29706 q^{85} - 46084 q^{86} - 13734 q^{87} + 41792 q^{88} - 178946 q^{89} + 14904 q^{90} - 340179 q^{91} - 54592 q^{92} - 53784 q^{93} - 49736 q^{94} - 532190 q^{95} + 55296 q^{96} - 214638 q^{97} - 216948 q^{98} - 52893 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9 + 184 * q^10 - 653 * q^11 - 864 * q^12 + 647 * q^13 + 412 * q^14 + 414 * q^15 + 1536 * q^16 + 621 * q^17 - 1944 * q^18 - 454 * q^19 - 736 * q^20 + 927 * q^21 + 2612 * q^22 - 3412 * q^23 + 3456 * q^24 + 3866 * q^25 - 2588 * q^26 - 4374 * q^27 - 1648 * q^28 + 1526 * q^29 - 1656 * q^30 + 5976 * q^31 - 6144 * q^32 + 5877 * q^33 - 2484 * q^34 + 8098 * q^35 + 7776 * q^36 + 37033 * q^37 + 1816 * q^38 - 5823 * q^39 + 2944 * q^40 + 13983 * q^41 - 3708 * q^42 + 11521 * q^43 - 10448 * q^44 - 3726 * q^45 + 13648 * q^46 + 12434 * q^47 - 13824 * q^48 + 54237 * q^49 - 15464 * q^50 - 5589 * q^51 + 10352 * q^52 + 21310 * q^53 + 17496 * q^54 + 57468 * q^55 + 6592 * q^56 + 4086 * q^57 - 6104 * q^58 - 20886 * q^59 + 6624 * q^60 - 23030 * q^61 - 23904 * q^62 - 8343 * q^63 + 24576 * q^64 - 37368 * q^65 - 23508 * q^66 + 24342 * q^67 + 9936 * q^68 + 30708 * q^69 - 32392 * q^70 - 184375 * q^71 - 31104 * q^72 - 24512 * q^73 - 148132 * q^74 - 34794 * q^75 - 7264 * q^76 - 46529 * q^77 + 23292 * q^78 - 17987 * q^79 - 11776 * q^80 + 39366 * q^81 - 55932 * q^82 - 46687 * q^83 + 14832 * q^84 - 29706 * q^85 - 46084 * q^86 - 13734 * q^87 + 41792 * q^88 - 178946 * q^89 + 14904 * q^90 - 340179 * q^91 - 54592 * q^92 - 53784 * q^93 - 49736 * q^94 - 532190 * q^95 + 55296 * q^96 - 214638 * q^97 - 216948 * q^98 - 52893 * 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
$5$	−94.9298	−1.69816	−0.849078	−	0.528267i	$-0.822842\pi$
$5$	−94.9298	−1.69816	−0.849078	+	0.528267i	$0.822842\pi$
$6$	36.0000	0.408248
$7$	−186.983	−1.44230	−0.721151	−	0.692778i	$-0.756387\pi$
$7$	−186.983	−1.44230	−0.721151	+	0.692778i	$0.756387\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	379.719	1.20078
$11$	−442.853	−1.10351	−0.551757	−	0.834005i	$-0.686042\pi$
$11$	−442.853	−1.10351	−0.551757	+	0.834005i	$0.686042\pi$
$12$	−144.000	−0.288675
$13$	760.277	1.24771	0.623854	−	0.781541i	$-0.285566\pi$
$13$	760.277	1.24771	0.623854	+	0.781541i	$0.285566\pi$
$14$	747.931	1.01986
$15$	854.369	0.980431
$16$	256.000	0.250000
$17$	1612.53	1.35327	0.676637	−	0.736317i	$-0.263437\pi$
$17$	1612.53	1.35327	0.676637	+	0.736317i	$0.263437\pi$
$18$	−324.000	−0.235702
$19$	2067.67	1.31400	0.657002	−	0.753889i	$-0.271824\pi$
$19$	2067.67	1.31400	0.657002	+	0.753889i	$0.271824\pi$
$20$	−1518.88	−0.849078
$21$	1682.84	0.832714
$22$	1771.41	0.780302
$23$	−2370.21	−0.934260	−0.467130	−	0.884189i	$-0.654712\pi$
$23$	−2370.21	−0.934260	−0.467130	+	0.884189i	$0.654712\pi$
$24$	576.000	0.204124
$25$	5886.68	1.88374
$26$	−3041.11	−0.882263
$27$	−729.000	−0.192450
$28$	−2991.72	−0.721151
$29$	−1274.92	−0.281506	−0.140753	−	0.990045i	$-0.544952\pi$
$29$	−1274.92	−0.281506	−0.140753	+	0.990045i	$0.544952\pi$
$30$	−3417.47	−0.693270
$31$	−2923.39	−0.546365	−0.273182	−	0.961962i	$-0.588076\pi$
$31$	−2923.39	−0.546365	−0.273182	+	0.961962i	$0.588076\pi$
$32$	−1024.00	−0.176777
$33$	3985.68	0.637114
$34$	−6450.12	−0.956909
$35$	17750.2	2.44926
$36$	1296.00	0.166667
$37$	6288.50	0.755167	0.377583	−	0.925976i	$-0.376755\pi$
$37$	6288.50	0.755167	0.377583	+	0.925976i	$0.376755\pi$
$38$	−8270.66	−0.929141
$39$	−6842.49	−0.720365
$40$	6075.51	0.600389
$41$	16455.0	1.52875	0.764377	−	0.644769i	$-0.223046\pi$
$41$	16455.0	1.52875	0.764377	+	0.644769i	$0.223046\pi$
$42$	−6731.38	−0.588818
$43$	−15679.0	−1.29314	−0.646572	−	0.762853i	$-0.723798\pi$
$43$	−15679.0	−1.29314	−0.646572	+	0.762853i	$0.723798\pi$
$44$	−7085.64	−0.551757
$45$	−7689.32	−0.566052
$46$	9480.86	0.660622
$47$	−14982.1	−0.989302	−0.494651	−	0.869092i	$-0.664704\pi$
$47$	−14982.1	−0.989302	−0.494651	+	0.869092i	$0.664704\pi$
$48$	−2304.00	−0.144338
$49$	18155.5	1.08024
$50$	−23546.7	−1.33200
$51$	−14512.8	−0.781313
$52$	12164.4	0.623854
$53$	12595.6	0.615926	0.307963	−	0.951398i	$-0.400353\pi$
$53$	12595.6	0.615926	0.307963	+	0.951398i	$0.400353\pi$
$54$	2916.00	0.136083
$55$	42039.9	1.87394
$56$	11966.9	0.509931
$57$	−18609.0	−0.758640
$58$	5099.67	0.199055
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	13669.9	0.490216
$61$	−20715.6	−0.712810	−0.356405	−	0.934332i	$-0.615998\pi$
$61$	−20715.6	−0.712810	−0.356405	+	0.934332i	$0.615998\pi$
$62$	11693.6	0.386338
$63$	−15145.6	−0.480767
$64$	4096.00	0.125000
$65$	−72172.9	−2.11881
$66$	−15942.7	−0.450508
$67$	46673.0	1.27022	0.635110	−	0.772422i	$-0.280955\pi$
$67$	46673.0	1.27022	0.635110	+	0.772422i	$0.280955\pi$
$68$	25800.5	0.676637
$69$	21331.9	0.539396
$70$	−71001.0	−1.73189
$71$	−77332.7	−1.82061	−0.910306	−	0.413935i	$-0.864154\pi$
$71$	−77332.7	−1.82061	−0.910306	+	0.413935i	$0.864154\pi$
$72$	−5184.00	−0.117851
$73$	70937.2	1.55800	0.778999	−	0.627025i	$-0.215727\pi$
$73$	70937.2	1.55800	0.778999	+	0.627025i	$0.215727\pi$
$74$	−25154.0	−0.533983
$75$	−52980.1	−1.08758
$76$	33082.7	0.657002
$77$	82805.8	1.59160
$78$	27370.0	0.509375
$79$	27333.8	0.492756	0.246378	−	0.969174i	$-0.420760\pi$
$79$	27333.8	0.492756	0.246378	+	0.969174i	$0.420760\pi$
$80$	−24302.0	−0.424539
$81$	6561.00	0.111111
$82$	−65819.9	−1.08099
$83$	60679.0	0.966815	0.483407	−	0.875395i	$-0.339399\pi$
$83$	60679.0	0.966815	0.483407	+	0.875395i	$0.339399\pi$
$84$	26925.5	0.416357
$85$	−153077.	−2.29807
$86$	62715.9	0.914391
$87$	11474.3	0.162527
$88$	28342.6	0.390151
$89$	137292.	1.83726	0.918628	−	0.395123i	$-0.129298\pi$
$89$	137292.	1.83726	0.918628	+	0.395123i	$0.129298\pi$
$90$	30757.3	0.400259
$91$	−142159.	−1.79957
$92$	−37923.4	−0.467130
$93$	26310.5	0.315444
$94$	59928.5	0.699542
$95$	−196283.	−2.23138
$96$	9216.00	0.102062
$97$	36512.5	0.394014	0.197007	−	0.980402i	$-0.436878\pi$
$97$	36512.5	0.394014	0.197007	+	0.980402i	$0.436878\pi$
$98$	−72622.1	−0.763843
$99$	−35871.1	−0.367838
$100$	94186.8	0.941868
$101$	−176719.	−1.72377	−0.861885	−	0.507103i	$-0.830716\pi$
$101$	−176719.	−1.72377	−0.861885	+	0.507103i	$0.830716\pi$
$102$	58051.1	0.552472
$103$	−65424.2	−0.607639	−0.303819	−	0.952730i	$-0.598262\pi$
$103$	−65424.2	−0.607639	−0.303819	+	0.952730i	$0.598262\pi$
$104$	−48657.7	−0.441132
$105$	−159752.	−1.41408
$106$	−50382.3	−0.435525
$107$	−6757.52	−0.0570595	−0.0285298	−	0.999593i	$-0.509083\pi$
$107$	−6757.52	−0.0570595	−0.0285298	+	0.999593i	$0.509083\pi$
$108$	−11664.0	−0.0962250
$109$	−12271.5	−0.0989308	−0.0494654	−	0.998776i	$-0.515752\pi$
$109$	−12271.5	−0.0989308	−0.0494654	+	0.998776i	$0.515752\pi$
$110$	−168160.	−1.32507
$111$	−56596.5	−0.435996
$112$	−47867.6	−0.360576
$113$	−211263.	−1.55642	−0.778209	−	0.628005i	$-0.783872\pi$
$113$	−211263.	−1.55642	−0.778209	+	0.628005i	$0.783872\pi$
$114$	74436.0	0.536440
$115$	225004.	1.58652
$116$	−20398.7	−0.140753
$117$	61582.4	0.415903
$118$	13924.0	0.0920575
$119$	−301515.	−1.95183
$120$	−54679.6	−0.346635
$121$	35067.6	0.217742
$122$	82862.6	0.504033
$123$	−148095.	−0.882627
$124$	−46774.3	−0.273182
$125$	−262165.	−1.50072
$126$	60582.4	0.339954
$127$	31775.4	0.174816	0.0874082	−	0.996173i	$-0.472142\pi$
$127$	31775.4	0.174816	0.0874082	+	0.996173i	$0.472142\pi$
$128$	−16384.0	−0.0883883
$129$	141111.	0.746597
$130$	288692.	1.49822
$131$	252382.	1.28493	0.642465	−	0.766315i	$-0.277912\pi$
$131$	252382.	1.28493	0.642465	+	0.766315i	$0.277912\pi$
$132$	63770.8	0.318557
$133$	−386618.	−1.89519
$134$	−186692.	−0.898181
$135$	69203.9	0.326810
$136$	−103202.	−0.478455
$137$	−220694.	−1.00459	−0.502295	−	0.864697i	$-0.667511\pi$
$137$	−220694.	−1.00459	−0.502295	+	0.864697i	$0.667511\pi$
$138$	−85327.7	−0.381410
$139$	−258939.	−1.13674	−0.568369	−	0.822774i	$-0.692425\pi$
$139$	−258939.	−1.13674	−0.568369	+	0.822774i	$0.692425\pi$
$140$	284004.	1.22463
$141$	134839.	0.571174
$142$	309331.	1.28737
$143$	−336691.	−1.37686
$144$	20736.0	0.0833333
$145$	121028.	0.478041
$146$	−283749.	−1.10167
$147$	−163400.	−0.623675
$148$	100616.	0.377583
$149$	−341034.	−1.25844	−0.629219	−	0.777228i	$-0.716625\pi$
$149$	−341034.	−1.25844	−0.629219	+	0.777228i	$0.716625\pi$
$150$	211920.	0.769032
$151$	350571.	1.25122	0.625610	−	0.780136i	$-0.284850\pi$
$151$	350571.	1.25122	0.625610	+	0.780136i	$0.284850\pi$
$152$	−132331.	−0.464570
$153$	130615.	0.451091
$154$	−331223.	−1.12543
$155$	277517.	0.927813
$156$	−109480.	−0.360183
$157$	279060.	0.903541	0.451771	−	0.892134i	$-0.350793\pi$
$157$	279060.	0.903541	0.451771	+	0.892134i	$0.350793\pi$
$158$	−109335.	−0.348431
$159$	−113360.	−0.355605
$160$	97208.2	0.300195
$161$	443189.	1.34749
$162$	−26244.0	−0.0785674
$163$	−198442.	−0.585011	−0.292506	−	0.956264i	$-0.594489\pi$
$163$	−198442.	−0.585011	−0.292506	+	0.956264i	$0.594489\pi$
$164$	263280.	0.764377
$165$	−378360.	−1.08192
$166$	−242716.	−0.683641
$167$	26402.0	0.0732563	0.0366282	−	0.999329i	$-0.488338\pi$
$167$	26402.0	0.0732563	0.0366282	+	0.999329i	$0.488338\pi$
$168$	−107702.	−0.294409
$169$	206728.	0.556777
$170$	612309.	1.62498
$171$	167481.	0.438001
$172$	−250864.	−0.646572
$173$	120548.	0.306228	0.153114	−	0.988208i	$-0.451070\pi$
$173$	120548.	0.306228	0.153114	+	0.988208i	$0.451070\pi$
$174$	−45897.0	−0.114924
$175$	−1.10071e6	−2.71692
$176$	−113370.	−0.275878
$177$	31329.0	0.0751646
$178$	−549167.	−1.29914
$179$	151636.	0.353728	0.176864	−	0.984235i	$-0.443405\pi$
$179$	151636.	0.353728	0.176864	+	0.984235i	$0.443405\pi$
$180$	−123029.	−0.283026
$181$	−26480.0	−0.0600788	−0.0300394	−	0.999549i	$-0.509563\pi$
$181$	−26480.0	−0.0600788	−0.0300394	+	0.999549i	$0.509563\pi$
$182$	568634.	1.27249
$183$	186441.	0.411541
$184$	151694.	0.330311
$185$	−596966.	−1.28239
$186$	−105242.	−0.223053
$187$	−714114.	−1.49336
$188$	−239714.	−0.494651
$189$	136310.	0.277571
$190$	785133.	1.57783
$191$	24728.1	0.0490464	0.0245232	−	0.999699i	$-0.492193\pi$
$191$	24728.1	0.0490464	0.0245232	+	0.999699i	$0.492193\pi$
$192$	−36864.0	−0.0721688
$193$	92050.7	0.177883	0.0889414	−	0.996037i	$-0.471652\pi$
$193$	92050.7	0.177883	0.0889414	+	0.996037i	$0.471652\pi$
$194$	−146050.	−0.278610
$195$	649556.	1.22329
$196$	290489.	0.540118
$197$	603326.	1.10761	0.553804	−	0.832647i	$-0.313176\pi$
$197$	603326.	1.10761	0.553804	+	0.832647i	$0.313176\pi$
$198$	143484.	0.260101
$199$	802570.	1.43665	0.718324	−	0.695709i	$-0.244910\pi$
$199$	802570.	1.43665	0.718324	+	0.695709i	$0.244910\pi$
$200$	−376747.	−0.666001
$201$	−420057.	−0.733362
$202$	706876.	1.21889
$203$	238388.	0.406016
$204$	−232204.	−0.390657
$205$	−1.56207e6	−2.59607
$206$	261697.	0.429665
$207$	−191987.	−0.311420
$208$	194631.	0.311927
$209$	−915672.	−1.45002
$210$	639009.	0.999904
$211$	587538.	0.908510	0.454255	−	0.890872i	$-0.349905\pi$
$211$	587538.	0.908510	0.454255	+	0.890872i	$0.349905\pi$
$212$	201529.	0.307963
$213$	695995.	1.05113
$214$	27030.1	0.0403472
$215$	1.48840e6	2.19596
$216$	46656.0	0.0680414
$217$	546624.	0.788024
$218$	49086.0	0.0699546
$219$	−638435.	−0.899511
$220$	672639.	0.936969
$221$	1.22597e6	1.68849
$222$	226386.	0.308295
$223$	406185.	0.546967	0.273484	−	0.961877i	$-0.411824\pi$
$223$	406185.	0.546967	0.273484	+	0.961877i	$0.411824\pi$
$224$	191470.	0.254965
$225$	476821.	0.627912
$226$	845050.	1.10055
$227$	1.07156e6	1.38024	0.690118	−	0.723697i	$-0.257559\pi$
$227$	1.07156e6	1.38024	0.690118	+	0.723697i	$0.257559\pi$
$228$	−297744.	−0.379320
$229$	−286956.	−0.361599	−0.180799	−	0.983520i	$-0.557869\pi$
$229$	−286956.	−0.361599	−0.180799	+	0.983520i	$0.557869\pi$
$230$	−900016.	−1.12184
$231$	−745252.	−0.918911
$232$	81594.7	0.0995273
$233$	−1.12754e6	−1.36064	−0.680318	−	0.732917i	$-0.738158\pi$
$233$	−1.12754e6	−1.36064	−0.680318	+	0.732917i	$0.738158\pi$
$234$	−246330.	−0.294088
$235$	1.42225e6	1.67999
$236$	−55696.0	−0.0650945
$237$	−246004.	−0.284493
$238$	1.20606e6	1.38015
$239$	302835.	0.342934	0.171467	−	0.985190i	$-0.445149\pi$
$239$	302835.	0.342934	0.171467	+	0.985190i	$0.445149\pi$
$240$	218718.	0.245108
$241$	−1.73608e6	−1.92543	−0.962716	−	0.270514i	$-0.912806\pi$
$241$	−1.73608e6	−1.92543	−0.962716	+	0.270514i	$0.912806\pi$
$242$	−140270.	−0.153967
$243$	−59049.0	−0.0641500
$244$	−331450.	−0.356405
$245$	−1.72350e6	−1.83441
$246$	592379.	0.624111
$247$	1.57200e6	1.63949
$248$	187097.	0.193169
$249$	−546111.	−0.558191
$250$	1.04866e6	1.06117
$251$	−689922.	−0.691219	−0.345610	−	0.938378i	$-0.612328\pi$
$251$	−689922.	−0.691219	−0.345610	+	0.938378i	$0.612328\pi$
$252$	−242330.	−0.240384
$253$	1.04966e6	1.03097
$254$	−127102.	−0.123614
$255$	1.37770e6	1.32679
$256$	65536.0	0.0625000
$257$	1.31513e6	1.24205	0.621023	−	0.783793i	$-0.286718\pi$
$257$	1.31513e6	1.24205	0.621023	+	0.783793i	$0.286718\pi$
$258$	−564444.	−0.527924
$259$	−1.17584e6	−1.08918
$260$	−1.15477e6	−1.05940
$261$	−103268.	−0.0938352
$262$	−1.00953e6	−0.908583
$263$	−1.43775e6	−1.28172	−0.640860	−	0.767658i	$-0.721422\pi$
$263$	−1.43775e6	−1.28172	−0.640860	+	0.767658i	$0.721422\pi$
$264$	−255083.	−0.225254
$265$	−1.19570e6	−1.04594
$266$	1.54647e6	1.34010
$267$	−1.23563e6	−1.06074
$268$	746769.	0.635110
$269$	−1.93042e6	−1.62656	−0.813281	−	0.581871i	$-0.802321\pi$
$269$	−1.93042e6	−1.62656	−0.813281	+	0.581871i	$0.802321\pi$
$270$	−276815.	−0.231090
$271$	1.17116e6	0.968705	0.484352	−	0.874873i	$-0.339055\pi$
$271$	1.17116e6	0.968705	0.484352	+	0.874873i	$0.339055\pi$
$272$	412808.	0.338319
$273$	1.27943e6	1.03898
$274$	882775.	0.710352
$275$	−2.60693e6	−2.07873
$276$	341311.	0.269698
$277$	361580.	0.283142	0.141571	−	0.989928i	$-0.454785\pi$
$277$	361580.	0.283142	0.141571	+	0.989928i	$0.454785\pi$
$278$	1.03576e6	0.803795
$279$	−236795.	−0.182122
$280$	−1.13602e6	−0.865943
$281$	−1.85064e6	−1.39816	−0.699080	−	0.715043i	$-0.746407\pi$
$281$	−1.85064e6	−1.39816	−0.699080	+	0.715043i	$0.746407\pi$
$282$	−539357.	−0.403881
$283$	−558848.	−0.414790	−0.207395	−	0.978257i	$-0.566498\pi$
$283$	−558848.	−0.414790	−0.207395	+	0.978257i	$0.566498\pi$
$284$	−1.23732e6	−0.910306
$285$	1.76655e6	1.28829
$286$	1.34676e6	0.973590
$287$	−3.07680e6	−2.20493
$288$	−82944.0	−0.0589256
$289$	1.18040e6	0.831351
$290$	−484111.	−0.338026
$291$	−328612.	−0.227484
$292$	1.13500e6	0.778999
$293$	1.75836e6	1.19657	0.598285	−	0.801283i	$-0.295849\pi$
$293$	1.75836e6	1.19657	0.598285	+	0.801283i	$0.295849\pi$
$294$	653599.	0.441005
$295$	330451.	0.221081
$296$	−402464.	−0.266992
$297$	322840.	0.212371
$298$	1.36414e6	0.889851
$299$	−1.80202e6	−1.16569
$300$	−847681.	−0.543788
$301$	2.93170e6	1.86510
$302$	−1.40228e6	−0.884746
$303$	1.59047e6	0.995220
$304$	529323.	0.328501
$305$	1.96653e6	1.21046
$306$	−522460.	−0.318970
$307$	1.49987e6	0.908257	0.454128	−	0.890936i	$-0.349951\pi$
$307$	1.49987e6	0.908257	0.454128	+	0.890936i	$0.349951\pi$
$308$	1.32489e6	0.795800
$309$	588818.	0.350820
$310$	−1.11007e6	−0.656063
$311$	−1.51118e6	−0.885960	−0.442980	−	0.896531i	$-0.646079\pi$
$311$	−1.51118e6	−0.885960	−0.442980	+	0.896531i	$0.646079\pi$
$312$	437919.	0.254687
$313$	−1.73648e6	−1.00186	−0.500932	−	0.865487i	$-0.667009\pi$
$313$	−1.73648e6	−1.00186	−0.500932	+	0.865487i	$0.667009\pi$
$314$	−1.11624e6	−0.638900
$315$	1.43777e6	0.816419
$316$	437340.	0.246378
$317$	1.67470e6	0.936030	0.468015	−	0.883720i	$-0.344969\pi$
$317$	1.67470e6	0.936030	0.468015	+	0.883720i	$0.344969\pi$
$318$	453441.	0.251451
$319$	564601.	0.310645
$320$	−388833.	−0.212270
$321$	60817.7	0.0329433
$322$	−1.77276e6	−0.952817
$323$	3.33418e6	1.77821
$324$	104976.	0.0555556
$325$	4.47550e6	2.35035
$326$	793768.	0.413666
$327$	110443.	0.0571177
$328$	−1.05312e6	−0.540496
$329$	2.80140e6	1.42687
$330$	1.51344e6	0.765032
$331$	1.44555e6	0.725208	0.362604	−	0.931943i	$-0.381888\pi$
$331$	1.44555e6	0.725208	0.362604	+	0.931943i	$0.381888\pi$
$332$	970864.	0.483407
$333$	509368.	0.251722
$334$	−105608.	−0.0518001
$335$	−4.43066e6	−2.15703
$336$	430808.	0.208178
$337$	−1.13698e6	−0.545352	−0.272676	−	0.962106i	$-0.587909\pi$
$337$	−1.13698e6	−0.545352	−0.272676	+	0.962106i	$0.587909\pi$
$338$	−826910.	−0.393701
$339$	1.90136e6	0.898599
$340$	−2.44924e6	−1.14904
$341$	1.29463e6	0.602921
$342$	−669924.	−0.309714
$343$	−252152.	−0.115725
$344$	1.00346e6	0.457195
$345$	−2.02504e6	−0.915978
$346$	−482193.	−0.216536
$347$	−4.08453e6	−1.82104	−0.910518	−	0.413469i	$-0.864317\pi$
$347$	−4.08453e6	−1.82104	−0.910518	+	0.413469i	$0.864317\pi$
$348$	183588.	0.0812637
$349$	−3.79159e6	−1.66632	−0.833159	−	0.553033i	$-0.813470\pi$
$349$	−3.79159e6	−1.66632	−0.833159	+	0.553033i	$0.813470\pi$
$350$	4.40283e6	1.92115
$351$	−554242.	−0.240122
$352$	453481.	0.195075
$353$	3.58323e6	1.53052	0.765258	−	0.643723i	$-0.222611\pi$
$353$	3.58323e6	1.53052	0.765258	+	0.643723i	$0.222611\pi$
$354$	−125316.	−0.0531494
$355$	7.34118e6	3.09169
$356$	2.19667e6	0.918628
$357$	2.71364e6	1.12689
$358$	−606544.	−0.250124
$359$	−1.83865e6	−0.752945	−0.376472	−	0.926428i	$-0.622863\pi$
$359$	−1.83865e6	−0.752945	−0.376472	+	0.926428i	$0.622863\pi$
$360$	492116.	0.200130
$361$	1.79914e6	0.726604
$362$	105920.	0.0424821
$363$	−315608.	−0.125714
$364$	−2.27454e6	−0.899787
$365$	−6.73406e6	−2.64573
$366$	−745763.	−0.291004
$367$	1.02361e6	0.396706	0.198353	−	0.980131i	$-0.436441\pi$
$367$	1.02361e6	0.396706	0.198353	+	0.980131i	$0.436441\pi$
$368$	−606775.	−0.233565
$369$	1.33285e6	0.509585
$370$	2.38787e6	0.906787
$371$	−2.35516e6	−0.888352
$372$	420968.	0.157722
$373$	−1.78307e6	−0.663586	−0.331793	−	0.943352i	$-0.607653\pi$
$373$	−1.78307e6	−0.663586	−0.331793	+	0.943352i	$0.607653\pi$
$374$	2.85646e6	1.05596
$375$	2.35949e6	0.866443
$376$	958856.	0.349771
$377$	−969290.	−0.351237
$378$	−545242.	−0.196273
$379$	−4.57007e6	−1.63428	−0.817138	−	0.576443i	$-0.804440\pi$
$379$	−4.57007e6	−1.63428	−0.817138	+	0.576443i	$0.804440\pi$
$380$	−3.14053e6	−1.11569
$381$	−285979.	−0.100930
$382$	−98912.3	−0.0346810
$383$	−5.09767e6	−1.77572	−0.887861	−	0.460112i	$-0.847809\pi$
$383$	−5.09767e6	−1.77572	−0.887861	+	0.460112i	$0.847809\pi$
$384$	147456.	0.0510310
$385$	−7.86074e6	−2.70279
$386$	−368203.	−0.125782
$387$	−1.27000e6	−0.431048
$388$	584200.	0.197007
$389$	4.08365e6	1.36828	0.684139	−	0.729352i	$-0.260178\pi$
$389$	4.08365e6	1.36828	0.684139	+	0.729352i	$0.260178\pi$
$390$	−2.59823e6	−0.864999
$391$	−3.82204e6	−1.26431
$392$	−1.16195e6	−0.381921
$393$	−2.27144e6	−0.741855
$394$	−2.41330e6	−0.783198
$395$	−2.59479e6	−0.836777
$396$	−573937.	−0.183919
$397$	2.44852e6	0.779698	0.389849	−	0.920879i	$-0.372527\pi$
$397$	2.44852e6	0.779698	0.389849	+	0.920879i	$0.372527\pi$
$398$	−3.21028e6	−1.01586
$399$	3.47956e6	1.09419
$400$	1.50699e6	0.470934
$401$	5.20803e6	1.61738	0.808691	−	0.588234i	$-0.200177\pi$
$401$	5.20803e6	1.61738	0.808691	+	0.588234i	$0.200177\pi$
$402$	1.68023e6	0.518565
$403$	−2.22259e6	−0.681704
$404$	−2.82750e6	−0.861885
$405$	−622835.	−0.188684
$406$	−953550.	−0.287097
$407$	−2.78488e6	−0.833337
$408$	928818.	0.276236
$409$	−4.35772e6	−1.28810	−0.644052	−	0.764982i	$-0.722748\pi$
$409$	−4.35772e6	−1.28810	−0.644052	+	0.764982i	$0.722748\pi$
$410$	6.24828e6	1.83570
$411$	1.98624e6	0.580000
$412$	−1.04679e6	−0.303819
$413$	650887.	0.187772
$414$	767949.	0.220207
$415$	−5.76025e6	−1.64180
$416$	−778523.	−0.220566
$417$	2.33045e6	0.656296
$418$	3.66269e6	1.02532
$419$	739642.	0.205819	0.102910	−	0.994691i	$-0.467185\pi$
$419$	739642.	0.205819	0.102910	+	0.994691i	$0.467185\pi$
$420$	−2.55603e6	−0.707039
$421$	4.44919e6	1.22342	0.611710	−	0.791082i	$-0.290482\pi$
$421$	4.44919e6	1.22342	0.611710	+	0.791082i	$0.290482\pi$
$422$	−2.35015e6	−0.642414
$423$	−1.21355e6	−0.329767
$424$	−806117.	−0.217763
$425$	9.49245e6	2.54921
$426$	−2.78398e6	−0.743262
$427$	3.87347e6	1.02809
$428$	−108120.	−0.0285298
$429$	3.03022e6	0.794933
$430$	−5.95362e6	−1.55278
$431$	−6.36131e6	−1.64950	−0.824752	−	0.565494i	$-0.808686\pi$
$431$	−6.36131e6	−1.64950	−0.824752	+	0.565494i	$0.808686\pi$
$432$	−186624.	−0.0481125
$433$	3.06352e6	0.785238	0.392619	−	0.919701i	$-0.371569\pi$
$433$	3.06352e6	0.785238	0.392619	+	0.919701i	$0.371569\pi$
$434$	−2.18650e6	−0.557217
$435$	−1.08925e6	−0.275997
$436$	−196344.	−0.0494654
$437$	−4.90081e6	−1.22762
$438$	2.55374e6	0.636050
$439$	−3.59316e6	−0.889846	−0.444923	−	0.895569i	$-0.646769\pi$
$439$	−3.59316e6	−0.889846	−0.444923	+	0.895569i	$0.646769\pi$
$440$	−2.69056e6	−0.662537
$441$	1.47060e6	0.360079
$442$	−4.90388e6	−1.19394
$443$	949396.	0.229847	0.114923	−	0.993374i	$-0.463338\pi$
$443$	949396.	0.229847	0.114923	+	0.993374i	$0.463338\pi$
$444$	−905544.	−0.217998
$445$	−1.30331e7	−3.11995
$446$	−1.62474e6	−0.386764
$447$	3.06931e6	0.726560
$448$	−765881.	−0.180288
$449$	−8.27165e6	−1.93632	−0.968159	−	0.250338i	$-0.919458\pi$
$449$	−8.27165e6	−1.93632	−0.968159	+	0.250338i	$0.919458\pi$
$450$	−1.90728e6	−0.444001
$451$	−7.28714e6	−1.68700
$452$	−3.38020e6	−0.778209
$453$	−3.15514e6	−0.722392
$454$	−4.28626e6	−0.975974
$455$	1.34951e7	3.05596
$456$	1.19098e6	0.268220
$457$	1.46070e6	0.327167	0.163583	−	0.986530i	$-0.447695\pi$
$457$	1.46070e6	0.327167	0.163583	+	0.986530i	$0.447695\pi$
$458$	1.14783e6	0.255689
$459$	−1.17554e6	−0.260438
$460$	3.60006e6	0.793260
$461$	1.15002e6	0.252030	0.126015	−	0.992028i	$-0.459781\pi$
$461$	1.15002e6	0.252030	0.126015	+	0.992028i	$0.459781\pi$
$462$	2.98101e6	0.649768
$463$	−3.20460e6	−0.694737	−0.347369	−	0.937729i	$-0.612925\pi$
$463$	−3.20460e6	−0.694737	−0.347369	+	0.937729i	$0.612925\pi$
$464$	−326379.	−0.0703764
$465$	−2.49765e6	−0.535673
$466$	4.51016e6	0.962115
$467$	−591006.	−0.125401	−0.0627003	−	0.998032i	$-0.519971\pi$
$467$	−591006.	−0.125401	−0.0627003	+	0.998032i	$0.519971\pi$
$468$	985318.	0.207951
$469$	−8.72705e6	−1.83204
$470$	−5.68901e6	−1.18793
$471$	−2.51154e6	−0.521660
$472$	222784.	0.0460287
$473$	6.94348e6	1.42700
$474$	984016.	0.201167
$475$	1.21717e7	2.47524
$476$	−4.82425e6	−0.975915
$477$	1.02024e6	0.205309
$478$	−1.21134e6	−0.242491
$479$	3.85952e6	0.768589	0.384295	−	0.923210i	$-0.374445\pi$
$479$	3.85952e6	0.768589	0.384295	+	0.923210i	$0.374445\pi$
$480$	−874873.	−0.173317
$481$	4.78100e6	0.942228
$482$	6.94434e6	1.36149
$483$	−3.98870e6	−0.777971
$484$	561082.	0.108871
$485$	−3.46612e6	−0.669098
$486$	236196.	0.0453609
$487$	5.56041e6	1.06239	0.531196	−	0.847249i	$-0.321743\pi$
$487$	5.56041e6	1.06239	0.531196	+	0.847249i	$0.321743\pi$
$488$	1.32580e6	0.252016
$489$	1.78598e6	0.337756
$490$	6.89401e6	1.29712
$491$	−1.05287e7	−1.97093	−0.985467	−	0.169866i	$-0.945667\pi$
$491$	−1.05287e7	−1.97093	−0.985467	+	0.169866i	$0.945667\pi$
$492$	−2.36952e6	−0.441313
$493$	−2.05584e6	−0.380954
$494$	−6.28799e6	−1.15930
$495$	3.40524e6	0.624646
$496$	−748388.	−0.136591
$497$	1.44599e7	2.62587
$498$	2.18444e6	0.394701
$499$	−6.42677e6	−1.15542	−0.577712	−	0.816241i	$-0.696054\pi$
$499$	−6.42677e6	−1.15542	−0.577712	+	0.816241i	$0.696054\pi$
$500$	−4.19465e6	−0.750361
$501$	−237618.	−0.0422946
$502$	2.75969e6	0.488766
$503$	2.20954e6	0.389387	0.194693	−	0.980864i	$-0.437629\pi$
$503$	2.20954e6	0.389387	0.194693	+	0.980864i	$0.437629\pi$
$504$	969318.	0.169977
$505$	1.67759e7	2.92723
$506$	−4.19862e6	−0.729005
$507$	−1.86055e6	−0.321456
$508$	508407.	0.0874082
$509$	6.02965e6	1.03157	0.515784	−	0.856719i	$-0.327501\pi$
$509$	6.02965e6	1.03157	0.515784	+	0.856719i	$0.327501\pi$
$510$	−5.51078e6	−0.938184
$511$	−1.32640e7	−2.24711
$512$	−262144.	−0.0441942
$513$	−1.50733e6	−0.252880
$514$	−5.26054e6	−0.878258
$515$	6.21071e6	1.03187
$516$	2.25777e6	0.373298
$517$	6.63488e6	1.09171
$518$	4.70336e6	0.770166
$519$	−1.08493e6	−0.176801
$520$	4.61907e6	0.749111
$521$	−3.99501e6	−0.644797	−0.322399	−	0.946604i	$-0.604489\pi$
$521$	−3.99501e6	−0.644797	−0.322399	+	0.946604i	$0.604489\pi$
$522$	413073.	0.0663515
$523$	3.55566e6	0.568415	0.284208	−	0.958763i	$-0.408269\pi$
$523$	3.55566e6	0.568415	0.284208	+	0.958763i	$0.408269\pi$
$524$	4.03811e6	0.642465
$525$	9.90636e6	1.56861
$526$	5.75099e6	0.906313
$527$	−4.71406e6	−0.739382
$528$	1.02033e6	0.159278
$529$	−818429.	−0.127157
$530$	4.78279e6	0.739591
$531$	−281961.	−0.0433963
$532$	−6.18588e6	−0.947595
$533$	1.25103e7	1.90744
$534$	4.94251e6	0.750057
$535$	641491.	0.0968960
$536$	−2.98707e6	−0.449091
$537$	−1.36472e6	−0.204225
$538$	7.72167e6	1.15015
$539$	−8.04023e6	−1.19206
$540$	1.10726e6	0.163405
$541$	−3.14323e6	−0.461725	−0.230863	−	0.972986i	$-0.574155\pi$
$541$	−3.14323e6	−0.461725	−0.230863	+	0.972986i	$0.574155\pi$
$542$	−4.68462e6	−0.684978
$543$	238320.	0.0346865
$544$	−1.65123e6	−0.239227
$545$	1.16493e6	0.168000
$546$	−5.11771e6	−0.734673
$547$	−2.06456e6	−0.295025	−0.147513	−	0.989060i	$-0.547127\pi$
$547$	−2.06456e6	−0.295025	−0.147513	+	0.989060i	$0.547127\pi$
$548$	−3.53110e6	−0.502295
$549$	−1.67797e6	−0.237603
$550$	1.04277e7	1.46988
$551$	−2.63610e6	−0.369899
$552$	−1.36524e6	−0.190705
$553$	−5.11094e6	−0.710703
$554$	−1.44632e6	−0.200212
$555$	5.37270e6	0.740389
$556$	−4.14302e6	−0.568369
$557$	578878.	0.0790586	0.0395293	−	0.999218i	$-0.487414\pi$
$557$	578878.	0.0790586	0.0395293	+	0.999218i	$0.487414\pi$
$558$	947179.	0.128779
$559$	−1.19204e7	−1.61347
$560$	4.54406e6	0.612314
$561$	6.42702e6	0.862190
$562$	7.40258e6	0.988649
$563$	1.12524e7	1.49615	0.748075	−	0.663615i	$-0.230979\pi$
$563$	1.12524e7	1.49615	0.748075	+	0.663615i	$0.230979\pi$
$564$	2.15743e6	0.285587
$565$	2.00551e7	2.64304
$566$	2.23539e6	0.293301
$567$	−1.22679e6	−0.160256
$568$	4.94930e6	0.643684
$569$	7.39769e6	0.957889	0.478945	−	0.877845i	$-0.341019\pi$
$569$	7.39769e6	0.957889	0.478945	+	0.877845i	$0.341019\pi$
$570$	−7.06620e6	−0.910958
$571$	−2.84574e6	−0.365263	−0.182632	−	0.983181i	$-0.558462\pi$
$571$	−2.84574e6	−0.365263	−0.182632	+	0.983181i	$0.558462\pi$
$572$	−5.38705e6	−0.688432
$573$	−222553.	−0.0283169
$574$	1.23072e7	1.55912
$575$	−1.39527e7	−1.75990
$576$	331776.	0.0416667
$577$	−9.37663e6	−1.17248	−0.586242	−	0.810136i	$-0.699393\pi$
$577$	−9.37663e6	−1.17248	−0.586242	+	0.810136i	$0.699393\pi$
$578$	−4.72160e6	−0.587854
$579$	−828457.	−0.102701
$580$	1.93644e6	0.239020
$581$	−1.13459e7	−1.39444
$582$	1.31445e6	0.160856
$583$	−5.57799e6	−0.679683
$584$	−4.53998e6	−0.550836
$585$	−5.84601e6	−0.706268
$586$	−7.03343e6	−0.846103
$587$	8.31549e6	0.996076	0.498038	−	0.867155i	$-0.334054\pi$
$587$	8.31549e6	0.996076	0.498038	+	0.867155i	$0.334054\pi$
$588$	−2.61440e6	−0.311837
$589$	−6.04460e6	−0.717925
$590$	−1.32180e6	−0.156328
$591$	−5.42993e6	−0.639478
$592$	1.60986e6	0.188792
$593$	322567.	0.0376690	0.0188345	−	0.999823i	$-0.494004\pi$
$593$	322567.	0.0376690	0.0188345	+	0.999823i	$0.494004\pi$
$594$	−1.29136e6	−0.150169
$595$	2.86228e7	3.31451
$596$	−5.45655e6	−0.629219
$597$	−7.22313e6	−0.829449
$598$	7.20807e6	0.824264
$599$	1.19228e7	1.35773	0.678863	−	0.734265i	$-0.262473\pi$
$599$	1.19228e7	1.35773	0.678863	+	0.734265i	$0.262473\pi$
$600$	3.39073e6	0.384516
$601$	−1.74933e7	−1.97554	−0.987770	−	0.155918i	$-0.950167\pi$
$601$	−1.74933e7	−1.97554	−0.987770	+	0.155918i	$0.950167\pi$
$602$	−1.17268e7	−1.31883
$603$	3.78052e6	0.423407
$604$	5.60914e6	0.625610
$605$	−3.32896e6	−0.369760
$606$	−6.36188e6	−0.703727
$607$	−3.48591e6	−0.384012	−0.192006	−	0.981394i	$-0.561499\pi$
$607$	−3.48591e6	−0.384012	−0.192006	+	0.981394i	$0.561499\pi$
$608$	−2.11729e6	−0.232285
$609$	−2.14549e6	−0.234414
$610$	−7.86613e6	−0.855927
$611$	−1.13906e7	−1.23436
$612$	2.08984e6	0.225546
$613$	−7.75073e6	−0.833089	−0.416545	−	0.909115i	$-0.636759\pi$
$613$	−7.75073e6	−0.833089	−0.416545	+	0.909115i	$0.636759\pi$
$614$	−5.99949e6	−0.642235
$615$	1.40586e7	1.49884
$616$	−5.29957e6	−0.562716
$617$	−1.66172e7	−1.75729	−0.878646	−	0.477474i	$-0.841552\pi$
$617$	−1.66172e7	−1.75729	−0.878646	+	0.477474i	$0.841552\pi$
$618$	−2.35527e6	−0.248067
$619$	−362241.	−0.0379989	−0.0189995	−	0.999819i	$-0.506048\pi$
$619$	−362241.	−0.0379989	−0.0189995	+	0.999819i	$0.506048\pi$
$620$	4.44027e6	0.463907
$621$	1.72789e6	0.179799
$622$	6.04470e6	0.626468
$623$	−2.56712e7	−2.64988
$624$	−1.75168e6	−0.180091
$625$	6.49146e6	0.664726
$626$	6.94591e6	0.708425
$627$	8.24105e6	0.837170
$628$	4.46495e6	0.451771
$629$	1.01404e7	1.02195
$630$	−5.75108e6	−0.577295
$631$	2.54450e6	0.254407	0.127204	−	0.991877i	$-0.459400\pi$
$631$	2.54450e6	0.254407	0.127204	+	0.991877i	$0.459400\pi$
$632$	−1.74936e6	−0.174215
$633$	−5.28784e6	−0.524529
$634$	−6.69882e6	−0.661873
$635$	−3.01644e6	−0.296866
$636$	−1.81376e6	−0.177803
$637$	1.38032e7	1.34782
$638$	−2.25840e6	−0.219659
$639$	−6.26395e6	−0.606871
$640$	1.55533e6	0.150097
$641$	1.26959e7	1.22045	0.610224	−	0.792229i	$-0.291079\pi$
$641$	1.26959e7	1.22045	0.610224	+	0.792229i	$0.291079\pi$
$642$	−243271.	−0.0232944
$643$	5.68109e6	0.541881	0.270941	−	0.962596i	$-0.412665\pi$
$643$	5.68109e6	0.541881	0.270941	+	0.962596i	$0.412665\pi$
$644$	7.09102e6	0.673743
$645$	−1.33956e7	−1.26784
$646$	−1.33367e7	−1.25738
$647$	−3.18740e6	−0.299348	−0.149674	−	0.988735i	$-0.547822\pi$
$647$	−3.18740e6	−0.299348	−0.149674	+	0.988735i	$0.547822\pi$
$648$	−419904.	−0.0392837
$649$	1.54157e6	0.143665
$650$	−1.79020e7	−1.66195
$651$	−4.91961e6	−0.454966
$652$	−3.17507e6	−0.292506
$653$	1.06853e7	0.980629	0.490314	−	0.871546i	$-0.336882\pi$
$653$	1.06853e7	0.980629	0.490314	+	0.871546i	$0.336882\pi$
$654$	−441774.	−0.0403883
$655$	−2.39586e7	−2.18201
$656$	4.21248e6	0.382189
$657$	5.74592e6	0.519333
$658$	−1.12056e7	−1.00895
$659$	3.86967e6	0.347104	0.173552	−	0.984825i	$-0.444475\pi$
$659$	3.86967e6	0.347104	0.173552	+	0.984825i	$0.444475\pi$
$660$	−6.05375e6	−0.540960
$661$	−1.06718e7	−0.950027	−0.475014	−	0.879978i	$-0.657557\pi$
$661$	−1.06718e7	−0.950027	−0.475014	+	0.879978i	$0.657557\pi$
$662$	−5.78219e6	−0.512799
$663$	−1.10337e7	−0.974851
$664$	−3.88346e6	−0.341821
$665$	3.67016e7	3.21833
$666$	−2.03747e6	−0.177994
$667$	3.02183e6	0.263000
$668$	422432.	0.0366282
$669$	−3.65566e6	−0.315792
$670$	1.77227e7	1.52525
$671$	9.17398e6	0.786596
$672$	−1.72323e6	−0.147204
$673$	489475.	0.0416575	0.0208287	−	0.999783i	$-0.493370\pi$
$673$	489475.	0.0416575	0.0208287	+	0.999783i	$0.493370\pi$
$674$	4.54791e6	0.385622
$675$	−4.29139e6	−0.362525
$676$	3.30764e6	0.278389
$677$	9.32531e6	0.781973	0.390986	−	0.920396i	$-0.372134\pi$
$677$	9.32531e6	0.781973	0.390986	+	0.920396i	$0.372134\pi$
$678$	−7.60545e6	−0.635405
$679$	−6.82720e6	−0.568288
$680$	9.79695e6	0.812491
$681$	−9.64408e6	−0.796880
$682$	−5.17853e6	−0.426330
$683$	1.55492e7	1.27543	0.637716	−	0.770272i	$-0.279879\pi$
$683$	1.55492e7	1.27543	0.637716	+	0.770272i	$0.279879\pi$
$684$	2.67970e6	0.219001
$685$	2.09504e7	1.70595
$686$	1.00861e6	0.0818301
$687$	2.58261e6	0.208769
$688$	−4.01382e6	−0.323286
$689$	9.57613e6	0.768496
$690$	8.10015e6	0.647694
$691$	9.57576e6	0.762919	0.381459	−	0.924386i	$-0.375422\pi$
$691$	9.57576e6	0.762919	0.381459	+	0.924386i	$0.375422\pi$
$692$	1.92877e6	0.153114
$693$	6.70727e6	0.530533
$694$	1.63381e7	1.28767
$695$	2.45810e7	1.93036
$696$	−734352.	−0.0574621
$697$	2.65342e7	2.06882
$698$	1.51664e7	1.17827
$699$	1.01479e7	0.785564
$700$	−1.76113e7	−1.35846
$701$	8.54438e6	0.656728	0.328364	−	0.944551i	$-0.393503\pi$
$701$	8.54438e6	0.656728	0.328364	+	0.944551i	$0.393503\pi$
$702$	2.21697e6	0.169792
$703$	1.30025e7	0.992291
$704$	−1.81393e6	−0.137939
$705$	−1.28003e7	−0.969943
$706$	−1.43329e7	−1.08224
$707$	3.30434e7	2.48620
$708$	501264.	0.0375823
$709$	−1.64889e7	−1.23191	−0.615953	−	0.787783i	$-0.711229\pi$
$709$	−1.64889e7	−1.23191	−0.615953	+	0.787783i	$0.711229\pi$
$710$	−2.93647e7	−2.18615
$711$	2.21404e6	0.164252
$712$	−8.78668e6	−0.649568
$713$	6.92907e6	0.510447
$714$	−1.08546e7	−0.796831
$715$	3.19620e7	2.33813
$716$	2.42618e6	0.176864
$717$	−2.72551e6	−0.197993
$718$	7.35460e6	0.532412
$719$	−991544.	−0.0715303	−0.0357651	−	0.999360i	$-0.511387\pi$
$719$	−991544.	−0.0715303	−0.0357651	+	0.999360i	$0.511387\pi$
$720$	−1.96847e6	−0.141513
$721$	1.22332e7	0.876399
$722$	−7.19658e6	−0.513787
$723$	1.56248e7	1.11165
$724$	−423680.	−0.0300394
$725$	−7.50503e6	−0.530282
$726$	1.26243e6	0.0888929
$727$	−2.22070e7	−1.55831	−0.779155	−	0.626831i	$-0.784352\pi$
$727$	−2.22070e7	−1.55831	−0.779155	+	0.626831i	$0.784352\pi$
$728$	9.09815e6	0.636245
$729$	531441.	0.0370370
$730$	2.69362e7	1.87081
$731$	−2.52829e7	−1.74998
$732$	2.98305e6	0.205771
$733$	−1.88139e7	−1.29336	−0.646678	−	0.762763i	$-0.723842\pi$
$733$	−1.88139e7	−1.29336	−0.646678	+	0.762763i	$0.723842\pi$
$734$	−4.09443e6	−0.280513
$735$	1.55115e7	1.05910
$736$	2.42710e6	0.165155
$737$	−2.06693e7	−1.40171
$738$	−5.33141e6	−0.360331
$739$	1.87823e6	0.126514	0.0632568	−	0.997997i	$-0.479851\pi$
$739$	1.87823e6	0.126514	0.0632568	+	0.997997i	$0.479851\pi$
$740$	−9.55146e6	−0.641196
$741$	−1.41480e7	−0.946562
$742$	9.42062e6	0.628159
$743$	7.14197e6	0.474620	0.237310	−	0.971434i	$-0.423734\pi$
$743$	7.14197e6	0.474620	0.237310	+	0.971434i	$0.423734\pi$
$744$	−1.68387e6	−0.111526
$745$	3.23743e7	2.13703
$746$	7.13229e6	0.469226
$747$	4.91500e6	0.322272
$748$	−1.14258e7	−0.746678
$749$	1.26354e6	0.0822971
$750$	−9.43796e6	−0.612667
$751$	1.96140e6	0.126902	0.0634508	−	0.997985i	$-0.479789\pi$
$751$	1.96140e6	0.126902	0.0634508	+	0.997985i	$0.479789\pi$
$752$	−3.83543e6	−0.247326
$753$	6.20930e6	0.399076
$754$	3.87716e6	0.248362
$755$	−3.32797e7	−2.12477
$756$	2.18097e6	0.138786
$757$	−2.41062e7	−1.52894	−0.764469	−	0.644661i	$-0.776999\pi$
$757$	−2.41062e7	−1.52894	−0.764469	+	0.644661i	$0.776999\pi$
$758$	1.82803e7	1.15561
$759$	−9.44690e6	−0.595230
$760$	1.25621e7	0.788913
$761$	−578909.	−0.0362367	−0.0181184	−	0.999836i	$-0.505768\pi$
$761$	−578909.	−0.0362367	−0.0181184	+	0.999836i	$0.505768\pi$
$762$	1.14392e6	0.0713685
$763$	2.29456e6	0.142688
$764$	395649.	0.0245232
$765$	−1.23993e7	−0.766024
$766$	2.03907e7	1.25562
$767$	−2.64652e6	−0.162438
$768$	−589824.	−0.0360844
$769$	−2.17505e7	−1.32633	−0.663167	−	0.748471i	$-0.730788\pi$
$769$	−2.17505e7	−1.32633	−0.663167	+	0.748471i	$0.730788\pi$
$770$	3.14430e7	1.91116
$771$	−1.18362e7	−0.717095
$772$	1.47281e6	0.0889414
$773$	−6.44388e6	−0.387881	−0.193941	−	0.981013i	$-0.562127\pi$
$773$	−6.44388e6	−0.387881	−0.193941	+	0.981013i	$0.562127\pi$
$774$	5.07999e6	0.304797
$775$	−1.72091e7	−1.02921
$776$	−2.33680e6	−0.139305
$777$	1.05826e7	0.628838
$778$	−1.63346e7	−0.967518
$779$	3.40234e7	2.00879
$780$	1.03929e7	0.611646
$781$	3.42470e7	2.00907
$782$	1.52882e7	0.894002
$783$	929415.	0.0541758
$784$	4.64782e6	0.270059
$785$	−2.64911e7	−1.53435
$786$	9.08574e6	0.524571
$787$	−738281.	−0.0424898	−0.0212449	−	0.999774i	$-0.506763\pi$
$787$	−738281.	−0.0424898	−0.0212449	+	0.999774i	$0.506763\pi$
$788$	9.65321e6	0.553804
$789$	1.29397e7	0.740001
$790$	1.03792e7	0.591690
$791$	3.95024e7	2.24483
$792$	2.29575e6	0.130050
$793$	−1.57496e7	−0.889380
$794$	−9.79406e6	−0.551330
$795$	1.07613e7	0.603873
$796$	1.28411e7	0.718324
$797$	3.90239e6	0.217613	0.108807	−	0.994063i	$-0.465297\pi$
$797$	3.90239e6	0.217613	0.108807	+	0.994063i	$0.465297\pi$
$798$	−1.39182e7	−0.773708
$799$	−2.41591e7	−1.33880
$800$	−6.02796e6	−0.333001
$801$	1.11206e7	0.612419
$802$	−2.08321e7	−1.14366
$803$	−3.14148e7	−1.71927
$804$	−6.72092e6	−0.366681
$805$	−4.20719e7	−2.28824
$806$	8.89035e6	0.482038
$807$	1.73738e7	0.939096
$808$	1.13100e7	0.609445
$809$	9.37849e6	0.503804	0.251902	−	0.967753i	$-0.418944\pi$
$809$	9.37849e6	0.503804	0.251902	+	0.967753i	$0.418944\pi$
$810$	2.49134e6	0.133420
$811$	−9.68634e6	−0.517139	−0.258570	−	0.965993i	$-0.583251\pi$
$811$	−9.68634e6	−0.517139	−0.258570	+	0.965993i	$0.583251\pi$
$812$	3.81420e6	0.203008
$813$	−1.05404e7	−0.559282
$814$	1.11395e7	0.589258
$815$	1.88381e7	0.993441
$816$	−3.71527e6	−0.195328
$817$	−3.24189e7	−1.69920
$818$	1.74309e7	0.910827
$819$	−1.15148e7	−0.599858
$820$	−2.49931e7	−1.29803
$821$	1.84535e7	0.955479	0.477740	−	0.878501i	$-0.341456\pi$
$821$	1.84535e7	0.955479	0.477740	+	0.878501i	$0.341456\pi$
$822$	−7.94497e6	−0.410122
$823$	−9.81376e6	−0.505052	−0.252526	−	0.967590i	$-0.581261\pi$
$823$	−9.81376e6	−0.505052	−0.252526	+	0.967590i	$0.581261\pi$
$824$	4.18715e6	0.214833
$825$	2.34624e7	1.20015
$826$	−2.60355e6	−0.132775
$827$	−1.83228e7	−0.931595	−0.465797	−	0.884891i	$-0.654232\pi$
$827$	−1.83228e7	−0.931595	−0.465797	+	0.884891i	$0.654232\pi$
$828$	−3.07180e6	−0.155710
$829$	−1.58467e7	−0.800852	−0.400426	−	0.916329i	$-0.631138\pi$
$829$	−1.58467e7	−0.800852	−0.400426	+	0.916329i	$0.631138\pi$
$830$	2.30410e7	1.16093
$831$	−3.25422e6	−0.163472
$832$	3.11409e6	0.155964
$833$	2.92764e7	1.46186
$834$	−9.32180e6	−0.464071
$835$	−2.50634e6	−0.124401
$836$	−1.46507e7	−0.725010
$837$	2.13115e6	0.105148
$838$	−2.95857e6	−0.145536
$839$	−2.45127e7	−1.20223	−0.601114	−	0.799164i	$-0.705276\pi$
$839$	−2.45127e7	−1.20223	−0.601114	+	0.799164i	$0.705276\pi$
$840$	1.02241e7	0.499952
$841$	−1.88857e7	−0.920755
$842$	−1.77968e7	−0.865089
$843$	1.66558e7	0.807229
$844$	9.40061e6	0.454255
$845$	−1.96246e7	−0.945495
$846$	4.85421e6	0.233181
$847$	−6.55703e6	−0.314050
$848$	3.22447e6	0.153982
$849$	5.02964e6	0.239479
$850$	−3.79698e7	−1.80256
$851$	−1.49051e7	−0.705522
$852$	1.11359e7	0.525566
$853$	−2.91074e7	−1.36972	−0.684859	−	0.728675i	$-0.740136\pi$
$853$	−2.91074e7	−1.36972	−0.684859	+	0.728675i	$0.740136\pi$
$854$	−1.54939e7	−0.726968
$855$	−1.58989e7	−0.743794
$856$	432481.	0.0201736
$857$	3.14342e7	1.46201	0.731006	−	0.682371i	$-0.239051\pi$
$857$	3.14342e7	1.46201	0.731006	+	0.682371i	$0.239051\pi$
$858$	−1.21209e7	−0.562102
$859$	1.75625e6	0.0812087	0.0406043	−	0.999175i	$-0.487072\pi$
$859$	1.75625e6	0.0812087	0.0406043	+	0.999175i	$0.487072\pi$
$860$	2.38145e7	1.09798
$861$	2.76912e7	1.27302
$862$	2.54453e7	1.16638
$863$	−3.96703e7	−1.81317	−0.906584	−	0.422026i	$-0.861319\pi$
$863$	−3.96703e7	−1.81317	−0.906584	+	0.422026i	$0.861319\pi$
$864$	746496.	0.0340207
$865$	−1.14436e7	−0.520024
$866$	−1.22541e7	−0.555247
$867$	−1.06236e7	−0.479981
$868$	8.74598e6	0.394012
$869$	−1.21048e7	−0.543763
$870$	4.35700e6	0.195159
$871$	3.54844e7	1.58486
$872$	785376.	0.0349773
$873$	2.95751e6	0.131338
$874$	1.96032e7	0.868059
$875$	4.90204e7	2.16450
$876$	−1.02150e7	−0.449756
$877$	1.58761e7	0.697019	0.348509	−	0.937305i	$-0.386688\pi$
$877$	1.58761e7	0.697019	0.348509	+	0.937305i	$0.386688\pi$
$878$	1.43726e7	0.629216
$879$	−1.58252e7	−0.690840
$880$	1.07622e7	0.468485
$881$	1.09266e7	0.474291	0.237145	−	0.971474i	$-0.423788\pi$
$881$	1.09266e7	0.474291	0.237145	+	0.971474i	$0.423788\pi$
$882$	−5.88239e6	−0.254614
$883$	2.04165e7	0.881211	0.440606	−	0.897701i	$-0.354764\pi$
$883$	2.04165e7	0.881211	0.440606	+	0.897701i	$0.354764\pi$
$884$	1.96155e7	0.844246
$885$	−2.97406e6	−0.127641
$886$	−3.79758e6	−0.162526
$887$	1.07621e7	0.459289	0.229645	−	0.973275i	$-0.426244\pi$
$887$	1.07621e7	0.459289	0.229645	+	0.973275i	$0.426244\pi$
$888$	3.62218e6	0.154148
$889$	−5.94145e6	−0.252138
$890$	5.21324e7	2.20614
$891$	−2.90556e6	−0.122613
$892$	6.49895e6	0.273484
$893$	−3.09780e7	−1.29995
$894$	−1.22772e7	−0.513756
$895$	−1.43948e7	−0.600686
$896$	3.06352e6	0.127483
$897$	1.62182e7	0.673009
$898$	3.30866e7	1.36918
$899$	3.72708e6	0.153805
$900$	7.62913e6	0.313956
$901$	2.03108e7	0.833517
$902$	2.91485e7	1.19289
$903$	−2.63853e7	−1.07682
$904$	1.35208e7	0.550277
$905$	2.51374e6	0.102023
$906$	1.26206e7	0.510808
$907$	7.21289e6	0.291133	0.145566	−	0.989348i	$-0.453500\pi$
$907$	7.21289e6	0.291133	0.145566	+	0.989348i	$0.453500\pi$
$908$	1.71450e7	0.690118
$909$	−1.43142e7	−0.574590
$910$	−5.39804e7	−2.16089
$911$	−3.96897e7	−1.58446	−0.792232	−	0.610220i	$-0.791081\pi$
$911$	−3.96897e7	−1.58446	−0.792232	+	0.610220i	$0.791081\pi$
$912$	−4.76390e6	−0.189660
$913$	−2.68719e7	−1.06689
$914$	−5.84278e6	−0.231342
$915$	−1.76988e7	−0.698861
$916$	−4.59130e6	−0.180799
$917$	−4.71910e7	−1.85326
$918$	4.70214e6	0.184157
$919$	3.51357e6	0.137234	0.0686168	−	0.997643i	$-0.478141\pi$
$919$	3.51357e6	0.137234	0.0686168	+	0.997643i	$0.478141\pi$
$920$	−1.44003e7	−0.560920
$921$	−1.34989e7	−0.524382
$922$	−4.60007e6	−0.178212
$923$	−5.87943e7	−2.27159
$924$	−1.19240e7	−0.459455
$925$	3.70184e7	1.42253
$926$	1.28184e7	0.491254
$927$	−5.29936e6	−0.202546
$928$	1.30552e6	0.0497636
$929$	−1.38719e6	−0.0527348	−0.0263674	−	0.999652i	$-0.508394\pi$
$929$	−1.38719e6	−0.0527348	−0.0263674	+	0.999652i	$0.508394\pi$
$930$	9.99062e6	0.378778
$931$	3.75396e7	1.41943
$932$	−1.80406e7	−0.680318
$933$	1.36006e7	0.511509
$934$	2.36402e6	0.0886716
$935$	6.77907e7	2.53595
$936$	−3.94127e6	−0.147044
$937$	−1.25974e7	−0.468739	−0.234369	−	0.972148i	$-0.575303\pi$
$937$	−1.25974e7	−0.468739	−0.234369	+	0.972148i	$0.575303\pi$
$938$	3.49082e7	1.29545
$939$	1.56283e7	0.578426
$940$	2.27560e7	0.839995
$941$	−3.00048e7	−1.10463	−0.552315	−	0.833635i	$-0.686256\pi$
$941$	−3.00048e7	−1.10463	−0.552315	+	0.833635i	$0.686256\pi$
$942$	1.00461e7	0.368869
$943$	−3.90018e7	−1.42826
$944$	−891136.	−0.0325472
$945$	−1.29399e7	−0.471359
$946$	−2.77739e7	−1.00904
$947$	2.79356e7	1.01224	0.506119	−	0.862464i	$-0.331080\pi$
$947$	2.79356e7	1.01224	0.506119	+	0.862464i	$0.331080\pi$
$948$	−3.93606e6	−0.142246
$949$	5.39319e7	1.94393
$950$	−4.86867e7	−1.75026
$951$	−1.50723e7	−0.540417
$952$	1.92970e7	0.690076
$953$	−1.56803e7	−0.559271	−0.279636	−	0.960106i	$-0.590214\pi$
$953$	−1.56803e7	−0.559271	−0.279636	+	0.960106i	$0.590214\pi$
$954$	−4.08097e6	−0.145175
$955$	−2.34743e6	−0.0832884
$956$	4.84535e6	0.171467
$957$	−5.08141e6	−0.179351
$958$	−1.54381e7	−0.543475
$959$	4.12659e7	1.44892
$960$	3.49949e6	0.122554
$961$	−2.00829e7	−0.701485
$962$	−1.91240e7	−0.666256
$963$	−547359.	−0.0190198
$964$	−2.77773e7	−0.962716
$965$	−8.73836e6	−0.302073
$966$	1.59548e7	0.550109
$967$	−1.78405e7	−0.613535	−0.306768	−	0.951784i	$-0.599247\pi$
$967$	−1.78405e7	−0.613535	−0.306768	+	0.951784i	$0.599247\pi$
$968$	−2.24433e6	−0.0769835
$969$	−3.00076e7	−1.02665
$970$	1.38645e7	0.473124
$971$	−1.50374e7	−0.511830	−0.255915	−	0.966699i	$-0.582377\pi$
$971$	−1.50374e7	−0.511830	−0.255915	+	0.966699i	$0.582377\pi$
$972$	−944784.	−0.0320750
$973$	4.84171e7	1.63952
$974$	−2.22417e7	−0.751224
$975$	−4.02795e7	−1.35698
$976$	−5.30321e6	−0.178203
$977$	−2.93296e7	−0.983037	−0.491519	−	0.870867i	$-0.663558\pi$
$977$	−2.93296e7	−0.983037	−0.491519	+	0.870867i	$0.663558\pi$
$978$	−7.14391e6	−0.238830
$979$	−6.08001e7	−2.02744
$980$	−2.75760e7	−0.917205
$981$	−993991.	−0.0329769
$982$	4.21149e7	1.39366
$983$	−4.58848e7	−1.51456	−0.757278	−	0.653093i	$-0.773471\pi$
$983$	−4.58848e7	−1.51456	−0.757278	+	0.653093i	$0.773471\pi$
$984$	9.47807e6	0.312056
$985$	−5.72736e7	−1.88089
$986$	8.22338e6	0.269375
$987$	−2.52126e7	−0.823805
$988$	2.51520e7	0.819747
$989$	3.71626e7	1.20813
$990$	−1.36209e7	−0.441692
$991$	1.36985e6	0.0443088	0.0221544	−	0.999755i	$-0.492947\pi$
$991$	1.36985e6	0.0443088	0.0221544	+	0.999755i	$0.492947\pi$
$992$	2.99355e6	0.0965846
$993$	−1.30099e7	−0.418699
$994$	−5.78395e7	−1.85677
$995$	−7.61878e7	−2.43965
$996$	−8.73778e6	−0.279095
$997$	3.00510e7	0.957462	0.478731	−	0.877962i	$-0.341097\pi$
$997$	3.00510e7	0.957462	0.478731	+	0.877962i	$0.341097\pi$
$998$	2.57071e7	0.817008
$999$	−4.58432e6	−0.145332

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.f.1.1	✓	6	1.1	even	1	trivial
1062.6.a.i.1.6		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -94.9298 q^{5} +36.0000 q^{6} -186.983 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -94.9298 q^{5} +36.0000 q^{6} -186.983 q^{7} -64.0000 q^{8} +81.0000 q^{9} +379.719 q^{10} -442.853 q^{11} -144.000 q^{12} +760.277 q^{13} +747.931 q^{14} +854.369 q^{15} +256.000 q^{16} +1612.53 q^{17} -324.000 q^{18} +2067.67 q^{19} -1518.88 q^{20} +1682.84 q^{21} +1771.41 q^{22} -2370.21 q^{23} +576.000 q^{24} +5886.68 q^{25} -3041.11 q^{26} -729.000 q^{27} -2991.72 q^{28} -1274.92 q^{29} -3417.47 q^{30} -2923.39 q^{31} -1024.00 q^{32} +3985.68 q^{33} -6450.12 q^{34} +17750.2 q^{35} +1296.00 q^{36} +6288.50 q^{37} -8270.66 q^{38} -6842.49 q^{39} +6075.51 q^{40} +16455.0 q^{41} -6731.38 q^{42} -15679.0 q^{43} -7085.64 q^{44} -7689.32 q^{45} +9480.86 q^{46} -14982.1 q^{47} -2304.00 q^{48} +18155.5 q^{49} -23546.7 q^{50} -14512.8 q^{51} +12164.4 q^{52} +12595.6 q^{53} +2916.00 q^{54} +42039.9 q^{55} +11966.9 q^{56} -18609.0 q^{57} +5099.67 q^{58} -3481.00 q^{59} +13669.9 q^{60} -20715.6 q^{61} +11693.6 q^{62} -15145.6 q^{63} +4096.00 q^{64} -72172.9 q^{65} -15942.7 q^{66} +46673.0 q^{67} +25800.5 q^{68} +21331.9 q^{69} -71001.0 q^{70} -77332.7 q^{71} -5184.00 q^{72} +70937.2 q^{73} -25154.0 q^{74} -52980.1 q^{75} +33082.7 q^{76} +82805.8 q^{77} +27370.0 q^{78} +27333.8 q^{79} -24302.0 q^{80} +6561.00 q^{81} -65819.9 q^{82} +60679.0 q^{83} +26925.5 q^{84} -153077. q^{85} +62715.9 q^{86} +11474.3 q^{87} +28342.6 q^{88} +137292. q^{89} +30757.3 q^{90} -142159. q^{91} -37923.4 q^{92} +26310.5 q^{93} +59928.5 q^{94} -196283. q^{95} +9216.00 q^{96} +36512.5 q^{97} -72622.1 q^{98} -35871.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9} + 184 q^{10} - 653 q^{11} - 864 q^{12} + 647 q^{13} + 412 q^{14} + 414 q^{15} + 1536 q^{16} + 621 q^{17} - 1944 q^{18} - 454 q^{19} - 736 q^{20} + 927 q^{21} + 2612 q^{22} - 3412 q^{23} + 3456 q^{24} + 3866 q^{25} - 2588 q^{26} - 4374 q^{27} - 1648 q^{28} + 1526 q^{29} - 1656 q^{30} + 5976 q^{31} - 6144 q^{32} + 5877 q^{33} - 2484 q^{34} + 8098 q^{35} + 7776 q^{36} + 37033 q^{37} + 1816 q^{38} - 5823 q^{39} + 2944 q^{40} + 13983 q^{41} - 3708 q^{42} + 11521 q^{43} - 10448 q^{44} - 3726 q^{45} + 13648 q^{46} + 12434 q^{47} - 13824 q^{48} + 54237 q^{49} - 15464 q^{50} - 5589 q^{51} + 10352 q^{52} + 21310 q^{53} + 17496 q^{54} + 57468 q^{55} + 6592 q^{56} + 4086 q^{57} - 6104 q^{58} - 20886 q^{59} + 6624 q^{60} - 23030 q^{61} - 23904 q^{62} - 8343 q^{63} + 24576 q^{64} - 37368 q^{65} - 23508 q^{66} + 24342 q^{67} + 9936 q^{68} + 30708 q^{69} - 32392 q^{70} - 184375 q^{71} - 31104 q^{72} - 24512 q^{73} - 148132 q^{74} - 34794 q^{75} - 7264 q^{76} - 46529 q^{77} + 23292 q^{78} - 17987 q^{79} - 11776 q^{80} + 39366 q^{81} - 55932 q^{82} - 46687 q^{83} + 14832 q^{84} - 29706 q^{85} - 46084 q^{86} - 13734 q^{87} + 41792 q^{88} - 178946 q^{89} + 14904 q^{90} - 340179 q^{91} - 54592 q^{92} - 53784 q^{93} - 49736 q^{94} - 532190 q^{95} + 55296 q^{96} - 214638 q^{97} - 216948 q^{98} - 52893 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9 + 184 * q^10 - 653 * q^11 - 864 * q^12 + 647 * q^13 + 412 * q^14 + 414 * q^15 + 1536 * q^16 + 621 * q^17 - 1944 * q^18 - 454 * q^19 - 736 * q^20 + 927 * q^21 + 2612 * q^22 - 3412 * q^23 + 3456 * q^24 + 3866 * q^25 - 2588 * q^26 - 4374 * q^27 - 1648 * q^28 + 1526 * q^29 - 1656 * q^30 + 5976 * q^31 - 6144 * q^32 + 5877 * q^33 - 2484 * q^34 + 8098 * q^35 + 7776 * q^36 + 37033 * q^37 + 1816 * q^38 - 5823 * q^39 + 2944 * q^40 + 13983 * q^41 - 3708 * q^42 + 11521 * q^43 - 10448 * q^44 - 3726 * q^45 + 13648 * q^46 + 12434 * q^47 - 13824 * q^48 + 54237 * q^49 - 15464 * q^50 - 5589 * q^51 + 10352 * q^52 + 21310 * q^53 + 17496 * q^54 + 57468 * q^55 + 6592 * q^56 + 4086 * q^57 - 6104 * q^58 - 20886 * q^59 + 6624 * q^60 - 23030 * q^61 - 23904 * q^62 - 8343 * q^63 + 24576 * q^64 - 37368 * q^65 - 23508 * q^66 + 24342 * q^67 + 9936 * q^68 + 30708 * q^69 - 32392 * q^70 - 184375 * q^71 - 31104 * q^72 - 24512 * q^73 - 148132 * q^74 - 34794 * q^75 - 7264 * q^76 - 46529 * q^77 + 23292 * q^78 - 17987 * q^79 - 11776 * q^80 + 39366 * q^81 - 55932 * q^82 - 46687 * q^83 + 14832 * q^84 - 29706 * q^85 - 46084 * q^86 - 13734 * q^87 + 41792 * q^88 - 178946 * q^89 + 14904 * q^90 - 340179 * q^91 - 54592 * q^92 - 53784 * q^93 - 49736 * q^94 - 532190 * q^95 + 55296 * q^96 - 214638 * q^97 - 216948 * q^98 - 52893 * q^99

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