LMFDB - Embedded newform 230.6.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 $ x^5 - x^4 - 774x^3 - 197x^2 + 66287*x + 154128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-25.4526$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -25.4526 q^{3} +16.0000 q^{4} +25.0000 q^{5} +101.810 q^{6} +169.151 q^{7} -64.0000 q^{8} +404.834 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -25.4526 q^{3} +16.0000 q^{4} +25.0000 q^{5} +101.810 q^{6} +169.151 q^{7} -64.0000 q^{8} +404.834 q^{9} -100.000 q^{10} +240.544 q^{11} -407.241 q^{12} +999.685 q^{13} -676.605 q^{14} -636.315 q^{15} +256.000 q^{16} +215.789 q^{17} -1619.34 q^{18} +299.903 q^{19} +400.000 q^{20} -4305.33 q^{21} -962.177 q^{22} -529.000 q^{23} +1628.97 q^{24} +625.000 q^{25} -3998.74 q^{26} -4119.09 q^{27} +2706.42 q^{28} -7682.61 q^{29} +2545.26 q^{30} -588.167 q^{31} -1024.00 q^{32} -6122.47 q^{33} -863.155 q^{34} +4228.78 q^{35} +6477.34 q^{36} +5651.69 q^{37} -1199.61 q^{38} -25444.6 q^{39} -1600.00 q^{40} +6430.35 q^{41} +17221.3 q^{42} +5905.18 q^{43} +3848.71 q^{44} +10120.8 q^{45} +2116.00 q^{46} +460.615 q^{47} -6515.86 q^{48} +11805.1 q^{49} -2500.00 q^{50} -5492.38 q^{51} +15995.0 q^{52} +36032.9 q^{53} +16476.4 q^{54} +6013.61 q^{55} -10825.7 q^{56} -7633.31 q^{57} +30730.4 q^{58} -34687.4 q^{59} -10181.0 q^{60} +21860.1 q^{61} +2352.67 q^{62} +68478.1 q^{63} +4096.00 q^{64} +24992.1 q^{65} +24489.9 q^{66} -14495.5 q^{67} +3452.62 q^{68} +13464.4 q^{69} -16915.1 q^{70} +58307.9 q^{71} -25909.4 q^{72} +42901.9 q^{73} -22606.8 q^{74} -15907.9 q^{75} +4798.45 q^{76} +40688.3 q^{77} +101778. q^{78} -60159.1 q^{79} +6400.00 q^{80} +6466.82 q^{81} -25721.4 q^{82} -76998.4 q^{83} -68885.3 q^{84} +5394.72 q^{85} -23620.7 q^{86} +195542. q^{87} -15394.8 q^{88} -79117.2 q^{89} -40483.4 q^{90} +169098. q^{91} -8464.00 q^{92} +14970.4 q^{93} -1842.46 q^{94} +7497.58 q^{95} +26063.4 q^{96} +39420.5 q^{97} -47220.5 q^{98} +97380.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18} - 845 q^{19} + 2000 q^{20} + 4682 q^{21} - 1004 q^{22} - 2645 q^{23} - 64 q^{24} + 3125 q^{25} - 6972 q^{26} + 2428 q^{27} + 1632 q^{28} - 4021 q^{29} - 100 q^{30} - 15752 q^{31} - 5120 q^{32} + 2931 q^{33} - 7776 q^{34} + 2550 q^{35} + 5344 q^{36} - 3455 q^{37} + 3380 q^{38} - 16708 q^{39} - 8000 q^{40} - 11898 q^{41} - 18728 q^{42} + 6968 q^{43} + 4016 q^{44} + 8350 q^{45} + 10580 q^{46} + 13412 q^{47} + 256 q^{48} + 91041 q^{49} - 12500 q^{50} - 2115 q^{51} + 27888 q^{52} + 53029 q^{53} - 9712 q^{54} + 6275 q^{55} - 6528 q^{56} - 21730 q^{57} + 16084 q^{58} - 31223 q^{59} + 400 q^{60} + 71477 q^{61} + 63008 q^{62} + 262199 q^{63} + 20480 q^{64} + 43575 q^{65} - 11724 q^{66} + 76003 q^{67} + 31104 q^{68} - 529 q^{69} - 10200 q^{70} + 54418 q^{71} - 21376 q^{72} + 69418 q^{73} + 13820 q^{74} + 625 q^{75} - 13520 q^{76} + 283598 q^{77} + 66832 q^{78} + 105024 q^{79} + 32000 q^{80} + 102913 q^{81} + 47592 q^{82} + 89399 q^{83} + 74912 q^{84} + 48600 q^{85} - 27872 q^{86} + 276726 q^{87} - 16064 q^{88} + 96240 q^{89} - 33400 q^{90} + 59261 q^{91} - 42320 q^{92} + 84434 q^{93} - 53648 q^{94} - 21125 q^{95} - 1024 q^{96} + 216087 q^{97} - 364164 q^{98} + 386925 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * 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
$3$	−25.4526	−1.63278	−0.816392	−	0.577498i	$-0.804029\pi$
$3$	−25.4526	−1.63278	−0.816392	+	0.577498i	$0.804029\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	101.810	1.15455
$7$	169.151	1.30476	0.652379	−	0.757893i	$-0.273771\pi$
$7$	169.151	1.30476	0.652379	+	0.757893i	$0.273771\pi$
$8$	−64.0000	−0.353553
$9$	404.834	1.66598
$10$	−100.000	−0.316228
$11$	240.544	0.599395	0.299698	−	0.954034i	$-0.403114\pi$
$11$	240.544	0.599395	0.299698	+	0.954034i	$0.403114\pi$
$12$	−407.241	−0.816392
$13$	999.685	1.64061	0.820304	−	0.571928i	$-0.193804\pi$
$13$	999.685	1.64061	0.820304	+	0.571928i	$0.193804\pi$
$14$	−676.605	−0.922603
$15$	−636.315	−0.730203
$16$	256.000	0.250000
$17$	215.789	0.181095	0.0905475	−	0.995892i	$-0.471138\pi$
$17$	215.789	0.181095	0.0905475	+	0.995892i	$0.471138\pi$
$18$	−1619.34	−1.17803
$19$	299.903	0.190589	0.0952943	−	0.995449i	$-0.469621\pi$
$19$	299.903	0.190589	0.0952943	+	0.995449i	$0.469621\pi$
$20$	400.000	0.223607
$21$	−4305.33	−2.13039
$22$	−962.177	−0.423836
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	1628.97	0.577276
$25$	625.000	0.200000
$26$	−3998.74	−1.16008
$27$	−4119.09	−1.08741
$28$	2706.42	0.652379
$29$	−7682.61	−1.69634	−0.848172	−	0.529721i	$-0.822297\pi$
$29$	−7682.61	−1.69634	−0.848172	+	0.529721i	$0.822297\pi$
$30$	2545.26	0.516332
$31$	−588.167	−0.109925	−0.0549625	−	0.998488i	$-0.517504\pi$
$31$	−588.167	−0.109925	−0.0549625	+	0.998488i	$0.517504\pi$
$32$	−1024.00	−0.176777
$33$	−6122.47	−0.978683
$34$	−863.155	−0.128053
$35$	4228.78	0.583505
$36$	6477.34	0.832991
$37$	5651.69	0.678694	0.339347	−	0.940661i	$-0.389794\pi$
$37$	5651.69	0.678694	0.339347	+	0.940661i	$0.389794\pi$
$38$	−1199.61	−0.134766
$39$	−25444.6	−2.67876
$40$	−1600.00	−0.158114
$41$	6430.35	0.597414	0.298707	−	0.954345i	$-0.403445\pi$
$41$	6430.35	0.597414	0.298707	+	0.954345i	$0.403445\pi$
$42$	17221.3	1.50641
$43$	5905.18	0.487037	0.243519	−	0.969896i	$-0.421698\pi$
$43$	5905.18	0.487037	0.243519	+	0.969896i	$0.421698\pi$
$44$	3848.71	0.299698
$45$	10120.8	0.745050
$46$	2116.00	0.147442
$47$	460.615	0.0304154	0.0152077	−	0.999884i	$-0.495159\pi$
$47$	460.615	0.0304154	0.0152077	+	0.999884i	$0.495159\pi$
$48$	−6515.86	−0.408196
$49$	11805.1	0.702393
$50$	−2500.00	−0.141421
$51$	−5492.38	−0.295689
$52$	15995.0	0.820304
$53$	36032.9	1.76202	0.881008	−	0.473101i	$-0.156865\pi$
$53$	36032.9	1.76202	0.881008	+	0.473101i	$0.156865\pi$
$54$	16476.4	0.768912
$55$	6013.61	0.268058
$56$	−10825.7	−0.461302
$57$	−7633.31	−0.311190
$58$	30730.4	1.19950
$59$	−34687.4	−1.29731	−0.648653	−	0.761084i	$-0.724667\pi$
$59$	−34687.4	−1.29731	−0.648653	+	0.761084i	$0.724667\pi$
$60$	−10181.0	−0.365102
$61$	21860.1	0.752189	0.376094	−	0.926581i	$-0.377267\pi$
$61$	21860.1	0.752189	0.376094	+	0.926581i	$0.377267\pi$
$62$	2352.67	0.0777287
$63$	68478.1	2.17370
$64$	4096.00	0.125000
$65$	24992.1	0.733702
$66$	24489.9	0.692033
$67$	−14495.5	−0.394499	−0.197249	−	0.980353i	$-0.563201\pi$
$67$	−14495.5	−0.394499	−0.197249	+	0.980353i	$0.563201\pi$
$68$	3452.62	0.0905475
$69$	13464.4	0.340459
$70$	−16915.1	−0.412601
$71$	58307.9	1.37272	0.686359	−	0.727263i	$-0.259208\pi$
$71$	58307.9	1.37272	0.686359	+	0.727263i	$0.259208\pi$
$72$	−25909.4	−0.589014
$73$	42901.9	0.942257	0.471129	−	0.882065i	$-0.343847\pi$
$73$	42901.9	0.942257	0.471129	+	0.882065i	$0.343847\pi$
$74$	−22606.8	−0.479909
$75$	−15907.9	−0.326557
$76$	4798.45	0.0952943
$77$	40688.3	0.782066
$78$	101778.	1.89417
$79$	−60159.1	−1.08451	−0.542255	−	0.840214i	$-0.682429\pi$
$79$	−60159.1	−1.08451	−0.542255	+	0.840214i	$0.682429\pi$
$80$	6400.00	0.111803
$81$	6466.82	0.109516
$82$	−25721.4	−0.422435
$83$	−76998.4	−1.22684	−0.613418	−	0.789758i	$-0.710206\pi$
$83$	−76998.4	−1.22684	−0.613418	+	0.789758i	$0.710206\pi$
$84$	−68885.3	−1.06519
$85$	5394.72	0.0809881
$86$	−23620.7	−0.344387
$87$	195542.	2.76976
$88$	−15394.8	−0.211918
$89$	−79117.2	−1.05876	−0.529378	−	0.848386i	$-0.677575\pi$
$89$	−79117.2	−1.05876	−0.529378	+	0.848386i	$0.677575\pi$
$90$	−40483.4	−0.526830
$91$	169098.	2.14060
$92$	−8464.00	−0.104257
$93$	14970.4	0.179484
$94$	−1842.46	−0.0215069
$95$	7497.58	0.0852338
$96$	26063.4	0.288638
$97$	39420.5	0.425395	0.212698	−	0.977118i	$-0.431775\pi$
$97$	39420.5	0.425395	0.212698	+	0.977118i	$0.431775\pi$
$98$	−47220.5	−0.496667
$99$	97380.5	0.998582
$100$	10000.0	0.100000
$101$	8515.21	0.0830600	0.0415300	−	0.999137i	$-0.486777\pi$
$101$	8515.21	0.0830600	0.0415300	+	0.999137i	$0.486777\pi$
$102$	21969.5	0.209084
$103$	−33578.8	−0.311869	−0.155935	−	0.987767i	$-0.549839\pi$
$103$	−33578.8	−0.311869	−0.155935	+	0.987767i	$0.549839\pi$
$104$	−63979.8	−0.580042
$105$	−107633.	−0.952738
$106$	−144132.	−1.24593
$107$	−79790.6	−0.673740	−0.336870	−	0.941551i	$-0.609368\pi$
$107$	−79790.6	−0.673740	−0.336870	+	0.941551i	$0.609368\pi$
$108$	−65905.4	−0.543703
$109$	40944.8	0.330090	0.165045	−	0.986286i	$-0.447223\pi$
$109$	40944.8	0.330090	0.165045	+	0.986286i	$0.447223\pi$
$110$	−24054.4	−0.189545
$111$	−143850.	−1.10816
$112$	43302.7	0.326189
$113$	79669.5	0.586943	0.293471	−	0.955968i	$-0.405189\pi$
$113$	79669.5	0.586943	0.293471	+	0.955968i	$0.405189\pi$
$114$	30533.2	0.220045
$115$	−13225.0	−0.0932505
$116$	−122922.	−0.848172
$117$	404706.	2.73322
$118$	138750.	0.917334
$119$	36500.9	0.236285
$120$	40724.1	0.258166
$121$	−103189.	−0.640725
$122$	−87440.3	−0.531878
$123$	−163669.	−0.975447
$124$	−9410.68	−0.0549625
$125$	15625.0	0.0894427
$126$	−273912.	−1.53704
$127$	34102.4	0.187619	0.0938093	−	0.995590i	$-0.470096\pi$
$127$	34102.4	0.187619	0.0938093	+	0.995590i	$0.470096\pi$
$128$	−16384.0	−0.0883883
$129$	−150302.	−0.795226
$130$	−99968.5	−0.518806
$131$	279481.	1.42290	0.711450	−	0.702737i	$-0.248039\pi$
$131$	279481.	1.42290	0.711450	+	0.702737i	$0.248039\pi$
$132$	−97959.6	−0.489341
$133$	50728.9	0.248672
$134$	57981.9	0.278953
$135$	−102977.	−0.486303
$136$	−13810.5	−0.0640267
$137$	271428.	1.23553	0.617766	−	0.786362i	$-0.288038\pi$
$137$	271428.	1.23553	0.617766	+	0.786362i	$0.288038\pi$
$138$	−53857.7	−0.240741
$139$	212751.	0.933973	0.466986	−	0.884264i	$-0.345340\pi$
$139$	212751.	0.933973	0.466986	+	0.884264i	$0.345340\pi$
$140$	67660.5	0.291753
$141$	−11723.8	−0.0496617
$142$	−233232.	−0.970659
$143$	240468.	0.983372
$144$	103637.	0.416496
$145$	−192065.	−0.758628
$146$	−171608.	−0.666276
$147$	−300471.	−1.14686
$148$	90427.0	0.339347
$149$	−188369.	−0.695093	−0.347547	−	0.937663i	$-0.612985\pi$
$149$	−188369.	−0.695093	−0.347547	+	0.937663i	$0.612985\pi$
$150$	63631.5	0.230910
$151$	−296787.	−1.05926	−0.529631	−	0.848228i	$-0.677669\pi$
$151$	−296787.	−1.05926	−0.529631	+	0.848228i	$0.677669\pi$
$152$	−19193.8	−0.0673832
$153$	87358.6	0.301701
$154$	−162753.	−0.553004
$155$	−14704.2	−0.0491600
$156$	−407113.	−1.33938
$157$	310583.	1.00561	0.502804	−	0.864401i	$-0.332302\pi$
$157$	310583.	1.00561	0.502804	+	0.864401i	$0.332302\pi$
$158$	240636.	0.766865
$159$	−917131.	−2.87699
$160$	−25600.0	−0.0790569
$161$	−89481.0	−0.272061
$162$	−25867.3	−0.0774396
$163$	562164.	1.65727	0.828637	−	0.559787i	$-0.189117\pi$
$163$	562164.	1.65727	0.828637	+	0.559787i	$0.189117\pi$
$164$	102886.	0.298707
$165$	−153062.	−0.437680
$166$	307994.	0.867504
$167$	−371802.	−1.03162	−0.515811	−	0.856703i	$-0.672509\pi$
$167$	−371802.	−1.03162	−0.515811	+	0.856703i	$0.672509\pi$
$168$	275541.	0.753206
$169$	628077.	1.69159
$170$	−21578.9	−0.0572673
$171$	121411.	0.317517
$172$	94482.9	0.243519
$173$	694698.	1.76474	0.882371	−	0.470555i	$-0.155946\pi$
$173$	694698.	1.76474	0.882371	+	0.470555i	$0.155946\pi$
$174$	−782169.	−1.95852
$175$	105719.	0.260952
$176$	61579.3	0.149849
$177$	882885.	2.11822
$178$	316469.	0.748654
$179$	−564212.	−1.31616	−0.658082	−	0.752946i	$-0.728632\pi$
$179$	−564212.	−1.31616	−0.658082	+	0.752946i	$0.728632\pi$
$180$	161934.	0.372525
$181$	−215759.	−0.489523	−0.244762	−	0.969583i	$-0.578710\pi$
$181$	−215759.	−0.489523	−0.244762	+	0.969583i	$0.578710\pi$
$182$	−676392.	−1.51363
$183$	−556395.	−1.22816
$184$	33856.0	0.0737210
$185$	141292.	0.303521
$186$	−59881.5	−0.126914
$187$	51906.7	0.108547
$188$	7369.83	0.0152077
$189$	−696749.	−1.41880
$190$	−29990.3	−0.0602694
$191$	87833.2	0.174211	0.0871054	−	0.996199i	$-0.472238\pi$
$191$	87833.2	0.174211	0.0871054	+	0.996199i	$0.472238\pi$
$192$	−104254.	−0.204098
$193$	−597918.	−1.15544	−0.577721	−	0.816234i	$-0.696058\pi$
$193$	−597918.	−1.15544	−0.577721	+	0.816234i	$0.696058\pi$
$194$	−157682.	−0.300800
$195$	−636114.	−1.19798
$196$	188882.	0.351196
$197$	374115.	0.686814	0.343407	−	0.939187i	$-0.388419\pi$
$197$	374115.	0.686814	0.343407	+	0.939187i	$0.388419\pi$
$198$	−389522.	−0.706104
$199$	477078.	0.853998	0.426999	−	0.904252i	$-0.359571\pi$
$199$	477078.	0.853998	0.426999	+	0.904252i	$0.359571\pi$
$200$	−40000.0	−0.0707107
$201$	368947.	0.644131
$202$	−34060.8	−0.0587323
$203$	−1.29952e6	−2.21332
$204$	−87878.1	−0.147844
$205$	160759.	0.267171
$206$	134315.	0.220525
$207$	−214157.	−0.347381
$208$	255919.	0.410152
$209$	72140.0	0.114238
$210$	430533.	0.673688
$211$	−846061.	−1.30826	−0.654132	−	0.756380i	$-0.726966\pi$
$211$	−846061.	−1.30826	−0.654132	+	0.756380i	$0.726966\pi$
$212$	576527.	0.881008
$213$	−1.48409e6	−2.24135
$214$	319163.	0.476406
$215$	147630.	0.217810
$216$	263622.	0.384456
$217$	−99489.2	−0.143426
$218$	−163779.	−0.233409
$219$	−1.09196e6	−1.53850
$220$	96217.7	0.134029
$221$	215721.	0.297106
$222$	575400.	0.783588
$223$	−303728.	−0.408999	−0.204499	−	0.978867i	$-0.565557\pi$
$223$	−303728.	−0.408999	−0.204499	+	0.978867i	$0.565557\pi$
$224$	−173211.	−0.230651
$225$	253021.	0.333197
$226$	−318678.	−0.415031
$227$	−1.38861e6	−1.78861	−0.894304	−	0.447461i	$-0.852328\pi$
$227$	−1.38861e6	−1.78861	−0.894304	+	0.447461i	$0.852328\pi$
$228$	−122133.	−0.155595
$229$	665265.	0.838313	0.419156	−	0.907914i	$-0.362326\pi$
$229$	665265.	0.838313	0.419156	+	0.907914i	$0.362326\pi$
$230$	52900.0	0.0659380
$231$	−1.03562e6	−1.27694
$232$	491687.	0.599748
$233$	−1.37961e6	−1.66481	−0.832407	−	0.554165i	$-0.813038\pi$
$233$	−1.37961e6	−1.66481	−0.832407	+	0.554165i	$0.813038\pi$
$234$	−1.61883e6	−1.93268
$235$	11515.4	0.0136022
$236$	−554999.	−0.648653
$237$	1.53120e6	1.77077
$238$	−146004.	−0.167079
$239$	1.22532e6	1.38757	0.693783	−	0.720184i	$-0.255943\pi$
$239$	1.22532e6	1.38757	0.693783	+	0.720184i	$0.255943\pi$
$240$	−162897.	−0.182551
$241$	1.47454e6	1.63536	0.817681	−	0.575671i	$-0.195259\pi$
$241$	1.47454e6	1.63536	0.817681	+	0.575671i	$0.195259\pi$
$242$	412758.	0.453061
$243$	836341.	0.908590
$244$	349761.	0.376094
$245$	295128.	0.314120
$246$	654676.	0.689745
$247$	299809.	0.312681
$248$	37642.7	0.0388644
$249$	1.95981e6	2.00316
$250$	−62500.0	−0.0632456
$251$	1.36196e6	1.36452	0.682259	−	0.731111i	$-0.260998\pi$
$251$	1.36196e6	1.36452	0.682259	+	0.731111i	$0.260998\pi$
$252$	1.09565e6	1.08685
$253$	−127248.	−0.124983
$254$	−136410.	−0.132666
$255$	−137309.	−0.132236
$256$	65536.0	0.0625000
$257$	1.46440e6	1.38302	0.691508	−	0.722369i	$-0.256947\pi$
$257$	1.46440e6	1.38302	0.691508	+	0.722369i	$0.256947\pi$
$258$	601208.	0.562310
$259$	955990.	0.885531
$260$	399874.	0.366851
$261$	−3.11018e6	−2.82608
$262$	−1.11792e6	−1.00614
$263$	−190615.	−0.169930	−0.0849648	−	0.996384i	$-0.527078\pi$
$263$	−190615.	−0.169930	−0.0849648	+	0.996384i	$0.527078\pi$
$264$	391838.	0.346017
$265$	900824.	0.787998
$266$	−202916.	−0.175838
$267$	2.01374e6	1.72872
$268$	−231928.	−0.197249
$269$	2.19576e6	1.85014	0.925070	−	0.379798i	$-0.124006\pi$
$269$	2.19576e6	1.85014	0.925070	+	0.379798i	$0.124006\pi$
$270$	411909.	0.343868
$271$	907122.	0.750313	0.375156	−	0.926962i	$-0.377589\pi$
$271$	907122.	0.750313	0.375156	+	0.926962i	$0.377589\pi$
$272$	55241.9	0.0452737
$273$	−4.30398e6	−3.49513
$274$	−1.08571e6	−0.873653
$275$	150340.	0.119879
$276$	215431.	0.170229
$277$	1.78919e6	1.40106	0.700529	−	0.713624i	$-0.252948\pi$
$277$	1.78919e6	1.40106	0.700529	+	0.713624i	$0.252948\pi$
$278$	−851003.	−0.660419
$279$	−238110.	−0.183133
$280$	−270642.	−0.206300
$281$	2.52548e6	1.90800	0.953999	−	0.299810i	$-0.0969231\pi$
$281$	2.52548e6	1.90800	0.953999	+	0.299810i	$0.0969231\pi$
$282$	46895.3	0.0351161
$283$	1.64560e6	1.22140	0.610700	−	0.791862i	$-0.290888\pi$
$283$	1.64560e6	1.22140	0.610700	+	0.791862i	$0.290888\pi$
$284$	932926.	0.686359
$285$	−190833.	−0.139168
$286$	−961874.	−0.695349
$287$	1.08770e6	0.779480
$288$	−414550.	−0.294507
$289$	−1.37329e6	−0.967205
$290$	768261.	0.536431
$291$	−1.00335e6	−0.694578
$292$	686430.	0.471129
$293$	−1.55555e6	−1.05856	−0.529279	−	0.848448i	$-0.677538\pi$
$293$	−1.55555e6	−1.05856	−0.529279	+	0.848448i	$0.677538\pi$
$294$	1.20188e6	0.810950
$295$	−867186.	−0.580173
$296$	−361708.	−0.239955
$297$	−990823.	−0.651786
$298$	753475.	0.491505
$299$	−528833.	−0.342090
$300$	−254526.	−0.163278
$301$	998868.	0.635466
$302$	1.18715e6	0.749011
$303$	−216734.	−0.135619
$304$	76775.2	0.0476471
$305$	546502.	0.336389
$306$	−349434.	−0.213335
$307$	952533.	0.576812	0.288406	−	0.957508i	$-0.406875\pi$
$307$	952533.	0.576812	0.288406	+	0.957508i	$0.406875\pi$
$308$	651013.	0.391033
$309$	854667.	0.509215
$310$	58816.7	0.0347614
$311$	−2.61902e6	−1.53546	−0.767728	−	0.640775i	$-0.778613\pi$
$311$	−2.61902e6	−1.53546	−0.767728	+	0.640775i	$0.778613\pi$
$312$	1.62845e6	0.947084
$313$	−1.07061e6	−0.617691	−0.308846	−	0.951112i	$-0.599943\pi$
$313$	−1.07061e6	−0.617691	−0.308846	+	0.951112i	$0.599943\pi$
$314$	−1.24233e6	−0.711072
$315$	1.71195e6	0.972110
$316$	−962546.	−0.542255
$317$	1.11608e6	0.623802	0.311901	−	0.950115i	$-0.399034\pi$
$317$	1.11608e6	0.623802	0.311901	+	0.950115i	$0.399034\pi$
$318$	3.66853e6	2.03434
$319$	−1.84801e6	−1.01678
$320$	102400.	0.0559017
$321$	2.03088e6	1.10007
$322$	357924.	0.192376
$323$	64715.7	0.0345146
$324$	103469.	0.0547581
$325$	624803.	0.328122
$326$	−2.24866e6	−1.17187
$327$	−1.04215e6	−0.538965
$328$	−411542.	−0.211218
$329$	77913.5	0.0396847
$330$	612247.	0.309487
$331$	1.65065e6	0.828102	0.414051	−	0.910254i	$-0.364114\pi$
$331$	1.65065e6	0.828102	0.414051	+	0.910254i	$0.364114\pi$
$332$	−1.23197e6	−0.613418
$333$	2.28800e6	1.13069
$334$	1.48721e6	0.729467
$335$	−362387.	−0.176425
$336$	−1.10217e6	−0.532597
$337$	3.91464e6	1.87766	0.938830	−	0.344380i	$-0.111911\pi$
$337$	3.91464e6	1.87766	0.938830	+	0.344380i	$0.111911\pi$
$338$	−2.51231e6	−1.19614
$339$	−2.02779e6	−0.958351
$340$	86315.5	0.0404941
$341$	−141480.	−0.0658885
$342$	−485644.	−0.224519
$343$	−846074.	−0.388305
$344$	−377932.	−0.172194
$345$	336610.	0.152258
$346$	−2.77879e6	−1.24786
$347$	−3.61919e6	−1.61357	−0.806785	−	0.590845i	$-0.798794\pi$
$347$	−3.61919e6	−1.61357	−0.806785	+	0.590845i	$0.798794\pi$
$348$	3.12868e6	1.38488
$349$	−2.65790e6	−1.16809	−0.584043	−	0.811723i	$-0.698530\pi$
$349$	−2.65790e6	−1.16809	−0.584043	+	0.811723i	$0.698530\pi$
$350$	−422878.	−0.184521
$351$	−4.11779e6	−1.78401
$352$	−246317.	−0.105959
$353$	−2.77508e6	−1.18533	−0.592664	−	0.805450i	$-0.701924\pi$
$353$	−2.77508e6	−1.18533	−0.592664	+	0.805450i	$0.701924\pi$
$354$	−3.53154e6	−1.49781
$355$	1.45770e6	0.613898
$356$	−1.26588e6	−0.529378
$357$	−929042.	−0.385802
$358$	2.25685e6	0.930668
$359$	−3.79810e6	−1.55536	−0.777678	−	0.628662i	$-0.783603\pi$
$359$	−3.79810e6	−1.55536	−0.777678	+	0.628662i	$0.783603\pi$
$360$	−647734.	−0.263415
$361$	−2.38616e6	−0.963676
$362$	863038.	0.346145
$363$	2.62644e6	1.04617
$364$	2.70557e6	1.07030
$365$	1.07255e6	0.421390
$366$	2.22558e6	0.868441
$367$	−182257.	−0.0706350	−0.0353175	−	0.999376i	$-0.511244\pi$
$367$	−182257.	−0.0706350	−0.0353175	+	0.999376i	$0.511244\pi$
$368$	−135424.	−0.0521286
$369$	2.60322e6	0.995281
$370$	−565169.	−0.214622
$371$	6.09501e6	2.29901
$372$	239526.	0.0897419
$373$	3.35300e6	1.24785	0.623924	−	0.781485i	$-0.285537\pi$
$373$	3.35300e6	1.24785	0.623924	+	0.781485i	$0.285537\pi$
$374$	−207627.	−0.0767546
$375$	−397697.	−0.146041
$376$	−29479.3	−0.0107535
$377$	−7.68019e6	−2.78303
$378$	2.78699e6	1.00324
$379$	3.74552e6	1.33941	0.669706	−	0.742626i	$-0.266420\pi$
$379$	3.74552e6	1.33941	0.669706	+	0.742626i	$0.266420\pi$
$380$	119961.	0.0426169
$381$	−867994.	−0.306341
$382$	−351333.	−0.123186
$383$	−5.35082e6	−1.86390	−0.931951	−	0.362584i	$-0.881894\pi$
$383$	−5.35082e6	−1.86390	−0.931951	+	0.362584i	$0.881894\pi$
$384$	417015.	0.144319
$385$	1.01721e6	0.349750
$386$	2.39167e6	0.817021
$387$	2.39062e6	0.811396
$388$	630728.	0.212698
$389$	−412875.	−0.138339	−0.0691695	−	0.997605i	$-0.522035\pi$
$389$	−412875.	−0.138339	−0.0691695	+	0.997605i	$0.522035\pi$
$390$	2.54446e6	0.847098
$391$	−114152.	−0.0377609
$392$	−755528.	−0.248333
$393$	−7.11352e6	−2.32329
$394$	−1.49646e6	−0.485651
$395$	−1.50398e6	−0.485008
$396$	1.55809e6	0.499291
$397$	368652.	0.117393	0.0586963	−	0.998276i	$-0.481306\pi$
$397$	368652.	0.117393	0.0586963	+	0.998276i	$0.481306\pi$
$398$	−1.90831e6	−0.603868
$399$	−1.29118e6	−0.406027
$400$	160000.	0.0500000
$401$	−3.55558e6	−1.10420	−0.552102	−	0.833776i	$-0.686174\pi$
$401$	−3.55558e6	−1.10420	−0.552102	+	0.833776i	$0.686174\pi$
$402$	−1.47579e6	−0.455469
$403$	−587982.	−0.180344
$404$	136243.	0.0415300
$405$	161670.	0.0489771
$406$	5.19809e6	1.56505
$407$	1.35948e6	0.406806
$408$	351512.	0.104542
$409$	2.15855e6	0.638049	0.319025	−	0.947746i	$-0.396645\pi$
$409$	2.15855e6	0.638049	0.319025	+	0.947746i	$0.396645\pi$
$410$	−643035.	−0.188919
$411$	−6.90855e6	−2.01736
$412$	−537261.	−0.155935
$413$	−5.86742e6	−1.69267
$414$	856628.	0.245636
$415$	−1.92496e6	−0.548658
$416$	−1.02368e6	−0.290021
$417$	−5.41506e6	−1.52498
$418$	−288560.	−0.0807784
$419$	4.89868e6	1.36315	0.681576	−	0.731748i	$-0.261295\pi$
$419$	4.89868e6	1.36315	0.681576	+	0.731748i	$0.261295\pi$
$420$	−1.72213e6	−0.476369
$421$	3.43890e6	0.945615	0.472808	−	0.881166i	$-0.343241\pi$
$421$	3.43890e6	0.945615	0.472808	+	0.881166i	$0.343241\pi$
$422$	3.38424e6	0.925082
$423$	186472.	0.0506715
$424$	−2.30611e6	−0.622967
$425$	134868.	0.0362190
$426$	5.93635e6	1.58488
$427$	3.69766e6	0.981424
$428$	−1.27665e6	−0.336870
$429$	−6.12054e6	−1.60563
$430$	−590518.	−0.154015
$431$	1.71556e6	0.444850	0.222425	−	0.974950i	$-0.428603\pi$
$431$	1.71556e6	0.444850	0.222425	+	0.974950i	$0.428603\pi$
$432$	−1.05449e6	−0.271852
$433$	−313478.	−0.0803502	−0.0401751	−	0.999193i	$-0.512792\pi$
$433$	−313478.	−0.0803502	−0.0401751	+	0.999193i	$0.512792\pi$
$434$	397957.	0.101417
$435$	4.88856e6	1.23868
$436$	655116.	0.165045
$437$	−158649.	−0.0397405
$438$	4.36786e6	1.08789
$439$	−6.71649e6	−1.66334	−0.831670	−	0.555271i	$-0.812615\pi$
$439$	−6.71649e6	−1.66334	−0.831670	+	0.555271i	$0.812615\pi$
$440$	−384871.	−0.0947727
$441$	4.77911e6	1.17017
$442$	−862883.	−0.210086
$443$	1.83925e6	0.445278	0.222639	−	0.974901i	$-0.428533\pi$
$443$	1.83925e6	0.445278	0.222639	+	0.974901i	$0.428533\pi$
$444$	−2.30160e6	−0.554080
$445$	−1.97793e6	−0.473490
$446$	1.21491e6	0.289206
$447$	4.79447e6	1.13494
$448$	692843.	0.163095
$449$	−2.63530e6	−0.616899	−0.308450	−	0.951241i	$-0.599810\pi$
$449$	−2.63530e6	−0.616899	−0.308450	+	0.951241i	$0.599810\pi$
$450$	−1.01208e6	−0.235606
$451$	1.54678e6	0.358087
$452$	1.27471e6	0.293471
$453$	7.55400e6	1.72954
$454$	5.55443e6	1.26474
$455$	4.22745e6	0.957304
$456$	488532.	0.110022
$457$	−401844.	−0.0900051	−0.0450025	−	0.998987i	$-0.514330\pi$
$457$	−401844.	−0.0900051	−0.0450025	+	0.998987i	$0.514330\pi$
$458$	−2.66106e6	−0.592777
$459$	−888853.	−0.196924
$460$	−211600.	−0.0466252
$461$	−4.16723e6	−0.913261	−0.456631	−	0.889656i	$-0.650944\pi$
$461$	−4.16723e6	−0.913261	−0.456631	+	0.889656i	$0.650944\pi$
$462$	4.14249e6	0.902936
$463$	7.48839e6	1.62344	0.811719	−	0.584048i	$-0.198532\pi$
$463$	7.48839e6	1.62344	0.811719	+	0.584048i	$0.198532\pi$
$464$	−1.96675e6	−0.424086
$465$	374259.	0.0802676
$466$	5.51843e6	1.17720
$467$	−3.22859e6	−0.685047	−0.342523	−	0.939509i	$-0.611282\pi$
$467$	−3.22859e6	−0.685047	−0.342523	+	0.939509i	$0.611282\pi$
$468$	6.47530e6	1.36661
$469$	−2.45193e6	−0.514725
$470$	−46061.5	−0.00961818
$471$	−7.90514e6	−1.64194
$472$	2.22000e6	0.458667
$473$	1.42046e6	0.291928
$474$	−6.12482e6	−1.25212
$475$	187439.	0.0381177
$476$	584014.	0.118143
$477$	1.45874e7	2.93549
$478$	−4.90127e6	−0.981157
$479$	154527.	0.0307728	0.0153864	−	0.999882i	$-0.495102\pi$
$479$	154527.	0.0307728	0.0153864	+	0.999882i	$0.495102\pi$
$480$	651586.	0.129083
$481$	5.64991e6	1.11347
$482$	−5.89816e6	−1.15638
$483$	2.27752e6	0.444216
$484$	−1.65103e6	−0.320363
$485$	985512.	0.190243
$486$	−3.34537e6	−0.642470
$487$	−4.84229e6	−0.925185	−0.462592	−	0.886571i	$-0.653081\pi$
$487$	−4.84229e6	−0.925185	−0.462592	+	0.886571i	$0.653081\pi$
$488$	−1.39904e6	−0.265939
$489$	−1.43085e7	−2.70597
$490$	−1.18051e6	−0.222116
$491$	4.55109e6	0.851945	0.425972	−	0.904736i	$-0.359932\pi$
$491$	4.55109e6	0.851945	0.425972	+	0.904736i	$0.359932\pi$
$492$	−2.61870e6	−0.487724
$493$	−1.65782e6	−0.307199
$494$	−1.19923e6	−0.221099
$495$	2.43451e6	0.446580
$496$	−150571.	−0.0274813
$497$	9.86285e6	1.79107
$498$	−7.83923e6	−1.41645
$499$	−2.22752e6	−0.400470	−0.200235	−	0.979748i	$-0.564171\pi$
$499$	−2.22752e6	−0.400470	−0.200235	+	0.979748i	$0.564171\pi$
$500$	250000.	0.0447214
$501$	9.46332e6	1.68441
$502$	−5.44783e6	−0.964860
$503$	−1.03865e7	−1.83041	−0.915206	−	0.402985i	$-0.867973\pi$
$503$	−1.03865e7	−1.83041	−0.915206	+	0.402985i	$0.867973\pi$
$504$	−4.38260e6	−0.768520
$505$	212880.	0.0371456
$506$	508992.	0.0883760
$507$	−1.59862e7	−2.76201
$508$	545639.	0.0938093
$509$	−9.14281e6	−1.56417	−0.782087	−	0.623169i	$-0.785845\pi$
$509$	−9.14281e6	−1.56417	−0.782087	+	0.623169i	$0.785845\pi$
$510$	549238.	0.0935050
$511$	7.25691e6	1.22942
$512$	−262144.	−0.0441942
$513$	−1.23533e6	−0.207247
$514$	−5.85760e6	−0.977939
$515$	−839470.	−0.139472
$516$	−2.40483e6	−0.397613
$517$	110798.	0.0182308
$518$	−3.82396e6	−0.626165
$519$	−1.76819e7	−2.88144
$520$	−1.59950e6	−0.259403
$521$	−2.83343e6	−0.457319	−0.228659	−	0.973507i	$-0.573434\pi$
$521$	−2.83343e6	−0.457319	−0.228659	+	0.973507i	$0.573434\pi$
$522$	1.24407e7	1.99834
$523$	−1.24391e6	−0.198854	−0.0994268	−	0.995045i	$-0.531701\pi$
$523$	−1.24391e6	−0.198854	−0.0994268	+	0.995045i	$0.531701\pi$
$524$	4.47170e6	0.711450
$525$	−2.69083e6	−0.426077
$526$	762462.	0.120158
$527$	−126920.	−0.0199069
$528$	−1.56735e6	−0.244671
$529$	279841.	0.0434783
$530$	−3.60329e6	−0.557199
$531$	−1.40427e7	−2.16129
$532$	811663.	0.124336
$533$	6.42833e6	0.980121
$534$	−8.05495e6	−1.22239
$535$	−1.99477e6	−0.301306
$536$	927710.	0.139476
$537$	1.43607e7	2.14901
$538$	−8.78304e6	−1.30825
$539$	2.83965e6	0.421011
$540$	−1.64764e6	−0.243151
$541$	−5.14966e6	−0.756460	−0.378230	−	0.925712i	$-0.623467\pi$
$541$	−5.14966e6	−0.756460	−0.378230	+	0.925712i	$0.623467\pi$
$542$	−3.62849e6	−0.530551
$543$	5.49164e6	0.799286
$544$	−220968.	−0.0320134
$545$	1.02362e6	0.147621
$546$	1.72159e7	2.47143
$547$	3.02112e6	0.431718	0.215859	−	0.976425i	$-0.430745\pi$
$547$	3.02112e6	0.431718	0.215859	+	0.976425i	$0.430745\pi$
$548$	4.34285e6	0.617766
$549$	8.84969e6	1.25313
$550$	−601361.	−0.0847673
$551$	−2.30404e6	−0.323304
$552$	−861723.	−0.120370
$553$	−1.01760e7	−1.41502
$554$	−7.15674e6	−0.990697
$555$	−3.59625e6	−0.495584
$556$	3.40401e6	0.466986
$557$	2.17046e6	0.296425	0.148212	−	0.988956i	$-0.452648\pi$
$557$	2.17046e6	0.296425	0.148212	+	0.988956i	$0.452648\pi$
$558$	952440.	0.129495
$559$	5.90332e6	0.799037
$560$	1.08257e6	0.145876
$561$	−1.32116e6	−0.177235
$562$	−1.01019e7	−1.34916
$563$	8.97877e6	1.19384	0.596920	−	0.802301i	$-0.296391\pi$
$563$	8.97877e6	1.19384	0.596920	+	0.802301i	$0.296391\pi$
$564$	−187581.	−0.0248309
$565$	1.99174e6	0.262489
$566$	−6.58239e6	−0.863660
$567$	1.09387e6	0.142892
$568$	−3.73171e6	−0.485329
$569$	1.25296e7	1.62240	0.811199	−	0.584771i	$-0.198816\pi$
$569$	1.25296e7	1.62240	0.811199	+	0.584771i	$0.198816\pi$
$570$	763331.	0.0984069
$571$	4.60900e6	0.591583	0.295792	−	0.955252i	$-0.404417\pi$
$571$	4.60900e6	0.591583	0.295792	+	0.955252i	$0.404417\pi$
$572$	3.84750e6	0.491686
$573$	−2.23558e6	−0.284449
$574$	−4.35081e6	−0.551176
$575$	−330625.	−0.0417029
$576$	1.65820e6	0.208248
$577$	−201007.	−0.0251346	−0.0125673	−	0.999921i	$-0.504000\pi$
$577$	−201007.	−0.0251346	−0.0125673	+	0.999921i	$0.504000\pi$
$578$	5.49317e6	0.683917
$579$	1.52186e7	1.88659
$580$	−3.07304e6	−0.379314
$581$	−1.30244e7	−1.60072
$582$	4.01341e6	0.491141
$583$	8.66752e6	1.05614
$584$	−2.74572e6	−0.333138
$585$	1.01177e7	1.22234
$586$	6.22220e6	0.748514
$587$	1.47103e6	0.176208	0.0881040	−	0.996111i	$-0.471919\pi$
$587$	1.47103e6	0.176208	0.0881040	+	0.996111i	$0.471919\pi$
$588$	−4.80753e6	−0.573428
$589$	−176393.	−0.0209505
$590$	3.46874e6	0.410244
$591$	−9.52219e6	−1.12142
$592$	1.44683e6	0.169673
$593$	6.68412e6	0.780562	0.390281	−	0.920696i	$-0.372378\pi$
$593$	6.68412e6	0.780562	0.390281	+	0.920696i	$0.372378\pi$
$594$	3.96329e6	0.460882
$595$	912523.	0.105670
$596$	−3.01390e6	−0.347547
$597$	−1.21429e7	−1.39439
$598$	2.11533e6	0.241894
$599$	−3.51121e6	−0.399843	−0.199922	−	0.979812i	$-0.564069\pi$
$599$	−3.51121e6	−0.399843	−0.199922	+	0.979812i	$0.564069\pi$
$600$	1.01810e6	0.115455
$601$	2.60155e6	0.293797	0.146898	−	0.989152i	$-0.453071\pi$
$601$	2.60155e6	0.293797	0.146898	+	0.989152i	$0.453071\pi$
$602$	−3.99547e6	−0.449342
$603$	−5.86826e6	−0.657228
$604$	−4.74860e6	−0.529631
$605$	−2.57974e6	−0.286541
$606$	866936.	0.0958971
$607$	−9.10876e6	−1.00343	−0.501715	−	0.865033i	$-0.667298\pi$
$607$	−9.10876e6	−1.00343	−0.501715	+	0.865033i	$0.667298\pi$
$608$	−307101.	−0.0336916
$609$	3.30762e7	3.61387
$610$	−2.18601e6	−0.237863
$611$	460469.	0.0498997
$612$	1.39774e6	0.150851
$613$	1.26518e7	1.35988	0.679941	−	0.733267i	$-0.262005\pi$
$613$	1.26518e7	1.35988	0.679941	+	0.733267i	$0.262005\pi$
$614$	−3.81013e6	−0.407867
$615$	−4.09173e6	−0.436233
$616$	−2.60405e6	−0.276502
$617$	−3.93498e6	−0.416130	−0.208065	−	0.978115i	$-0.566717\pi$
$617$	−3.93498e6	−0.416130	−0.208065	+	0.978115i	$0.566717\pi$
$618$	−3.41867e6	−0.360069
$619$	−1.78491e7	−1.87236	−0.936181	−	0.351519i	$-0.885665\pi$
$619$	−1.78491e7	−1.87236	−0.936181	+	0.351519i	$0.885665\pi$
$620$	−235267.	−0.0245800
$621$	2.17900e6	0.226740
$622$	1.04761e7	1.08573
$623$	−1.33828e7	−1.38142
$624$	−6.51381e6	−0.669689
$625$	390625.	0.0400000
$626$	4.28245e6	0.436774
$627$	−1.83615e6	−0.186526
$628$	4.96933e6	0.502804
$629$	1.21957e6	0.122908
$630$	−6.84781e6	−0.687386
$631$	−9.46157e6	−0.945997	−0.472998	−	0.881063i	$-0.656828\pi$
$631$	−9.46157e6	−0.945997	−0.472998	+	0.881063i	$0.656828\pi$
$632$	3.85018e6	0.383432
$633$	2.15344e7	2.13611
$634$	−4.46432e6	−0.441095
$635$	852560.	0.0839056
$636$	−1.46741e7	−1.43850
$637$	1.18014e7	1.15235
$638$	7.39203e6	0.718972
$639$	2.36050e7	2.28693
$640$	−409600.	−0.0395285
$641$	4.84828e6	0.466061	0.233031	−	0.972469i	$-0.425136\pi$
$641$	4.84828e6	0.466061	0.233031	+	0.972469i	$0.425136\pi$
$642$	−8.12351e6	−0.777868
$643$	1.22864e7	1.17192	0.585959	−	0.810341i	$-0.300718\pi$
$643$	1.22864e7	1.17192	0.585959	+	0.810341i	$0.300718\pi$
$644$	−1.43170e6	−0.136030
$645$	−3.75755e6	−0.355636
$646$	−258863.	−0.0244055
$647$	7.30521e6	0.686075	0.343038	−	0.939322i	$-0.388544\pi$
$647$	7.30521e6	0.686075	0.343038	+	0.939322i	$0.388544\pi$
$648$	−413876.	−0.0387198
$649$	−8.34387e6	−0.777599
$650$	−2.49921e6	−0.232017
$651$	2.53226e6	0.234183
$652$	8.99463e6	0.828637
$653$	−7.94070e6	−0.728746	−0.364373	−	0.931253i	$-0.618717\pi$
$653$	−7.94070e6	−0.728746	−0.364373	+	0.931253i	$0.618717\pi$
$654$	4.16860e6	0.381106
$655$	6.98703e6	0.636340
$656$	1.64617e6	0.149353
$657$	1.73681e7	1.56978
$658$	−311654.	−0.0280613
$659$	1.72628e7	1.54845	0.774227	−	0.632908i	$-0.218139\pi$
$659$	1.72628e7	1.54845	0.774227	+	0.632908i	$0.218139\pi$
$660$	−2.44899e6	−0.218840
$661$	−1.09394e7	−0.973848	−0.486924	−	0.873444i	$-0.661881\pi$
$661$	−1.09394e7	−0.973848	−0.486924	+	0.873444i	$0.661881\pi$
$662$	−6.60258e6	−0.585556
$663$	−5.49065e6	−0.485110
$664$	4.92790e6	0.433752
$665$	1.26822e6	0.111209
$666$	−9.15198e6	−0.799520
$667$	4.06410e6	0.353712
$668$	−5.94883e6	−0.515811
$669$	7.73065e6	0.667807
$670$	1.44955e6	0.124751
$671$	5.25831e6	0.450858
$672$	4.40866e6	0.376603
$673$	−1.64061e7	−1.39626	−0.698132	−	0.715969i	$-0.745985\pi$
$673$	−1.64061e7	−1.39626	−0.698132	+	0.715969i	$0.745985\pi$
$674$	−1.56586e7	−1.32771
$675$	−2.57443e6	−0.217481
$676$	1.00492e7	0.845797
$677$	−6.33131e6	−0.530911	−0.265456	−	0.964123i	$-0.585522\pi$
$677$	−6.33131e6	−0.530911	−0.265456	+	0.964123i	$0.585522\pi$
$678$	8.11117e6	0.677656
$679$	6.66802e6	0.555038
$680$	−345262.	−0.0286336
$681$	3.53437e7	2.92041
$682$	565921.	0.0465902
$683$	9.38546e6	0.769846	0.384923	−	0.922949i	$-0.374228\pi$
$683$	9.38546e6	0.769846	0.384923	+	0.922949i	$0.374228\pi$
$684$	1.94257e6	0.158759
$685$	6.78571e6	0.552547
$686$	3.38430e6	0.274573
$687$	−1.69327e7	−1.36878
$688$	1.51173e6	0.121759
$689$	3.60216e7	2.89078
$690$	−1.34644e6	−0.107663
$691$	1.09619e7	0.873351	0.436676	−	0.899619i	$-0.356156\pi$
$691$	1.09619e7	0.873351	0.436676	+	0.899619i	$0.356156\pi$
$692$	1.11152e7	0.882371
$693$	1.64720e7	1.30291
$694$	1.44768e7	1.14097
$695$	5.31877e6	0.417685
$696$	−1.25147e7	−0.979259
$697$	1.38760e6	0.108189
$698$	1.06316e7	0.825962
$699$	3.51146e7	2.71828
$700$	1.69151e6	0.130476
$701$	−689912.	−0.0530272	−0.0265136	−	0.999648i	$-0.508441\pi$
$701$	−689912.	−0.0530272	−0.0265136	+	0.999648i	$0.508441\pi$
$702$	1.64712e7	1.26148
$703$	1.69496e6	0.129351
$704$	985269.	0.0749244
$705$	−293096.	−0.0222094
$706$	1.11003e7	0.838153
$707$	1.44036e6	0.108373
$708$	1.41262e7	1.05911
$709$	1.63410e7	1.22085	0.610427	−	0.792072i	$-0.290998\pi$
$709$	1.63410e7	1.22085	0.610427	+	0.792072i	$0.290998\pi$
$710$	−5.83079e6	−0.434092
$711$	−2.43544e7	−1.80678
$712$	5.06350e6	0.374327
$713$	311141.	0.0229210
$714$	3.71617e6	0.272803
$715$	6.01171e6	0.439778
$716$	−9.02740e6	−0.658082
$717$	−3.11875e7	−2.26560
$718$	1.51924e7	1.09980
$719$	−1.10616e7	−0.797988	−0.398994	−	0.916954i	$-0.630641\pi$
$719$	−1.10616e7	−0.797988	−0.398994	+	0.916954i	$0.630641\pi$
$720$	2.59094e6	0.186263
$721$	−5.67990e6	−0.406914
$722$	9.54463e6	0.681422
$723$	−3.75309e7	−2.67019
$724$	−3.45215e6	−0.244762
$725$	−4.80163e6	−0.339269
$726$	−1.05058e7	−0.739751
$727$	8.18627e6	0.574447	0.287224	−	0.957864i	$-0.407268\pi$
$727$	8.18627e6	0.574447	0.287224	+	0.957864i	$0.407268\pi$
$728$	−1.08223e7	−0.756815
$729$	−2.28585e7	−1.59305
$730$	−4.29019e6	−0.297968
$731$	1.27427e6	0.0882000
$732$	−8.90232e6	−0.614081
$733$	4.88960e6	0.336135	0.168067	−	0.985776i	$-0.446247\pi$
$733$	4.88960e6	0.336135	0.168067	+	0.985776i	$0.446247\pi$
$734$	729029.	0.0499465
$735$	−7.51177e6	−0.512890
$736$	541696.	0.0368605
$737$	−3.48680e6	−0.236461
$738$	−1.04129e7	−0.703770
$739$	8.19880e6	0.552254	0.276127	−	0.961121i	$-0.410949\pi$
$739$	8.19880e6	0.552254	0.276127	+	0.961121i	$0.410949\pi$
$740$	2.26068e6	0.151761
$741$	−7.63090e6	−0.510541
$742$	−2.43801e7	−1.62564
$743$	−1.06637e7	−0.708657	−0.354329	−	0.935121i	$-0.615291\pi$
$743$	−1.06637e7	−0.708657	−0.354329	+	0.935121i	$0.615291\pi$
$744$	−958104.	−0.0634571
$745$	−4.70922e6	−0.310855
$746$	−1.34120e7	−0.882362
$747$	−3.11716e7	−2.04389
$748$	830508.	0.0542737
$749$	−1.34967e7	−0.879068
$750$	1.59079e6	0.103266
$751$	1.59879e7	1.03441	0.517203	−	0.855863i	$-0.326973\pi$
$751$	1.59879e7	1.03441	0.517203	+	0.855863i	$0.326973\pi$
$752$	117917.	0.00760384
$753$	−3.46653e7	−2.22796
$754$	3.07208e7	1.96790
$755$	−7.41968e6	−0.473716
$756$	−1.11480e7	−0.709401
$757$	1.70840e7	1.08355	0.541776	−	0.840523i	$-0.317752\pi$
$757$	1.70840e7	1.08355	0.541776	+	0.840523i	$0.317752\pi$
$758$	−1.49821e7	−0.947107
$759$	3.23879e6	0.204069
$760$	−479845.	−0.0301347
$761$	−7.03448e6	−0.440322	−0.220161	−	0.975464i	$-0.570658\pi$
$761$	−7.03448e6	−0.440322	−0.220161	+	0.975464i	$0.570658\pi$
$762$	3.47198e6	0.216615
$763$	6.92586e6	0.430687
$764$	1.40533e6	0.0871054
$765$	2.18396e6	0.134925
$766$	2.14033e7	1.31798
$767$	−3.46765e7	−2.12837
$768$	−1.66806e6	−0.102049
$769$	4.81600e6	0.293677	0.146839	−	0.989160i	$-0.453090\pi$
$769$	4.81600e6	0.293677	0.146839	+	0.989160i	$0.453090\pi$
$770$	−4.06883e6	−0.247311
$771$	−3.72728e7	−2.25816
$772$	−9.56669e6	−0.577721
$773$	−2.25375e7	−1.35661	−0.678307	−	0.734778i	$-0.737286\pi$
$773$	−2.25375e7	−1.35661	−0.678307	+	0.734778i	$0.737286\pi$
$774$	−9.56247e6	−0.573743
$775$	−367605.	−0.0219850
$776$	−2.52291e6	−0.150400
$777$	−2.43324e7	−1.44588
$778$	1.65150e6	0.0978204
$779$	1.92848e6	0.113860
$780$	−1.01778e7	−0.598988
$781$	1.40256e7	0.822801
$782$	456609.	0.0267010
$783$	3.16454e7	1.84461
$784$	3.02211e6	0.175598
$785$	7.76457e6	0.449721
$786$	2.84541e7	1.64281
$787$	−5.11852e6	−0.294583	−0.147291	−	0.989093i	$-0.547056\pi$
$787$	−5.11852e6	−0.294583	−0.147291	+	0.989093i	$0.547056\pi$
$788$	5.98584e6	0.343407
$789$	4.85166e6	0.277458
$790$	6.01591e6	0.342952
$791$	1.34762e7	0.765818
$792$	−6.23235e6	−0.353052
$793$	2.18532e7	1.23405
$794$	−1.47461e6	−0.0830091
$795$	−2.29283e7	−1.28663
$796$	7.63325e6	0.426999
$797$	9.29099e6	0.518103	0.259052	−	0.965863i	$-0.416590\pi$
$797$	9.29099e6	0.518103	0.259052	+	0.965863i	$0.416590\pi$
$798$	5.16473e6	0.287105
$799$	99395.4	0.00550807
$800$	−640000.	−0.0353553
$801$	−3.20293e7	−1.76387
$802$	1.42223e7	0.780791
$803$	1.03198e7	0.564784
$804$	5.90315e6	0.322065
$805$	−2.23702e6	−0.121669
$806$	2.35193e6	0.127522
$807$	−5.58878e7	−3.02088
$808$	−544973.	−0.0293661
$809$	−2.28564e7	−1.22783	−0.613914	−	0.789373i	$-0.710406\pi$
$809$	−2.28564e7	−1.22783	−0.613914	+	0.789373i	$0.710406\pi$
$810$	−646682.	−0.0346320
$811$	−2.17000e7	−1.15853	−0.579266	−	0.815138i	$-0.696661\pi$
$811$	−2.17000e7	−1.15853	−0.579266	+	0.815138i	$0.696661\pi$
$812$	−2.07924e7	−1.10666
$813$	−2.30886e7	−1.22510
$814$	−5.43793e6	−0.287655
$815$	1.40541e7	0.741155
$816$	−1.40605e6	−0.0739222
$817$	1.77098e6	0.0928237
$818$	−8.63421e6	−0.451169
$819$	6.84565e7	3.56620
$820$	2.57214e6	0.133586
$821$	3.83945e6	0.198798	0.0993989	−	0.995048i	$-0.468308\pi$
$821$	3.83945e6	0.198798	0.0993989	+	0.995048i	$0.468308\pi$
$822$	2.76342e7	1.42649
$823$	−2.86377e7	−1.47380	−0.736899	−	0.676002i	$-0.763711\pi$
$823$	−2.86377e7	−1.47380	−0.736899	+	0.676002i	$0.763711\pi$
$824$	2.14904e6	0.110262
$825$	−3.82654e6	−0.195737
$826$	2.34697e7	1.19690
$827$	2.90771e7	1.47838	0.739192	−	0.673495i	$-0.235208\pi$
$827$	2.90771e7	1.47838	0.739192	+	0.673495i	$0.235208\pi$
$828$	−3.42651e6	−0.173691
$829$	−3.54717e7	−1.79265	−0.896326	−	0.443395i	$-0.853774\pi$
$829$	−3.54717e7	−1.79265	−0.896326	+	0.443395i	$0.853774\pi$
$830$	7.69984e6	0.387960
$831$	−4.55394e7	−2.28762
$832$	4.09471e6	0.205076
$833$	2.54741e6	0.127200
$834$	2.16602e7	1.07832
$835$	−9.29505e6	−0.461355
$836$	1.15424e6	0.0571189
$837$	2.42271e6	0.119533
$838$	−1.95947e7	−0.963894
$839$	1.77405e7	0.870081	0.435041	−	0.900411i	$-0.356734\pi$
$839$	1.77405e7	0.870081	0.435041	+	0.900411i	$0.356734\pi$
$840$	6.88853e6	0.336844
$841$	3.85114e7	1.87758
$842$	−1.37556e7	−0.668651
$843$	−6.42800e7	−3.11535
$844$	−1.35370e7	−0.654132
$845$	1.57019e7	0.756504
$846$	−745889.	−0.0358301
$847$	−1.74546e7	−0.835991
$848$	9.22443e6	0.440504
$849$	−4.18847e7	−1.99428
$850$	−539472.	−0.0256107
$851$	−2.98974e6	−0.141517
$852$	−2.37454e7	−1.12068
$853$	2.78617e7	1.31110	0.655549	−	0.755153i	$-0.272437\pi$
$853$	2.78617e7	1.31110	0.655549	+	0.755153i	$0.272437\pi$
$854$	−1.47906e7	−0.693972
$855$	3.03527e6	0.141998
$856$	5.10660e6	0.238203
$857$	6.75848e6	0.314338	0.157169	−	0.987572i	$-0.449763\pi$
$857$	6.75848e6	0.314338	0.157169	+	0.987572i	$0.449763\pi$
$858$	2.44822e7	1.13536
$859$	4.15982e6	0.192350	0.0961749	−	0.995364i	$-0.469339\pi$
$859$	4.15982e6	0.192350	0.0961749	+	0.995364i	$0.469339\pi$
$860$	2.36207e6	0.108905
$861$	−2.76848e7	−1.27272
$862$	−6.86226e6	−0.314557
$863$	−1.08955e7	−0.497991	−0.248995	−	0.968505i	$-0.580100\pi$
$863$	−1.08955e7	−0.497991	−0.248995	+	0.968505i	$0.580100\pi$
$864$	4.21795e6	0.192228
$865$	1.73675e7	0.789216
$866$	1.25391e6	0.0568161
$867$	3.49538e7	1.57924
$868$	−1.59183e6	−0.0717128
$869$	−1.44709e7	−0.650050
$870$	−1.95542e7	−0.875876
$871$	−1.44909e7	−0.647217
$872$	−2.62047e6	−0.116704
$873$	1.59587e7	0.708701
$874$	634595.	0.0281008
$875$	2.64299e6	0.116701
$876$	−1.74714e7	−0.769251
$877$	−1.39469e7	−0.612322	−0.306161	−	0.951980i	$-0.599045\pi$
$877$	−1.39469e7	−0.612322	−0.306161	+	0.951980i	$0.599045\pi$
$878$	2.68659e7	1.17616
$879$	3.95928e7	1.72840
$880$	1.53948e6	0.0670144
$881$	2.48016e7	1.07656	0.538282	−	0.842765i	$-0.319074\pi$
$881$	2.48016e7	1.07656	0.538282	+	0.842765i	$0.319074\pi$
$882$	−1.91164e7	−0.827438
$883$	−2.41114e7	−1.04069	−0.520344	−	0.853957i	$-0.674196\pi$
$883$	−2.41114e7	−1.04069	−0.520344	+	0.853957i	$0.674196\pi$
$884$	3.45153e6	0.148553
$885$	2.20721e7	0.947297
$886$	−7.35700e6	−0.314859
$887$	−5.49493e6	−0.234506	−0.117253	−	0.993102i	$-0.537409\pi$
$887$	−5.49493e6	−0.234506	−0.117253	+	0.993102i	$0.537409\pi$
$888$	9.20640e6	0.391794
$889$	5.76846e6	0.244797
$890$	7.91172e6	0.334808
$891$	1.55556e6	0.0656434
$892$	−4.85964e6	−0.204499
$893$	138140.	0.00579682
$894$	−1.91779e7	−0.802522
$895$	−1.41053e7	−0.588606
$896$	−2.77137e6	−0.115325
$897$	1.34602e7	0.558560
$898$	1.05412e7	0.436214
$899$	4.51866e6	0.186471
$900$	4.04834e6	0.166598
$901$	7.77550e6	0.319092
$902$	−6.18714e6	−0.253206
$903$	−2.54238e7	−1.03758
$904$	−5.09885e6	−0.207516
$905$	−5.39399e6	−0.218922
$906$	−3.02160e7	−1.22297
$907$	−3.06421e7	−1.23680	−0.618400	−	0.785863i	$-0.712219\pi$
$907$	−3.06421e7	−1.23680	−0.618400	+	0.785863i	$0.712219\pi$
$908$	−2.22177e7	−0.894304
$909$	3.44725e6	0.138377
$910$	−1.69098e7	−0.676916
$911$	3.88470e7	1.55082	0.775411	−	0.631457i	$-0.217543\pi$
$911$	3.88470e7	1.55082	0.775411	+	0.631457i	$0.217543\pi$
$912$	−1.95413e6	−0.0777975
$913$	−1.85215e7	−0.735360
$914$	1.60738e6	0.0636432
$915$	−1.39099e7	−0.549251
$916$	1.06442e7	0.419156
$917$	4.72746e7	1.85654
$918$	3.55541e6	0.139246
$919$	3.44865e7	1.34698	0.673489	−	0.739197i	$-0.264795\pi$
$919$	3.44865e7	1.34698	0.673489	+	0.739197i	$0.264795\pi$
$920$	846400.	0.0329690
$921$	−2.42444e7	−0.941809
$922$	1.66689e7	0.645773
$923$	5.82895e7	2.25209
$924$	−1.65700e7	−0.638472
$925$	3.53231e6	0.135739
$926$	−2.99535e7	−1.14794
$927$	−1.35938e7	−0.519569
$928$	7.86699e6	0.299874
$929$	−7.65498e6	−0.291008	−0.145504	−	0.989358i	$-0.546480\pi$
$929$	−7.65498e6	−0.291008	−0.145504	+	0.989358i	$0.546480\pi$
$930$	−1.49704e6	−0.0567578
$931$	3.54039e6	0.133868
$932$	−2.20737e7	−0.832407
$933$	6.66608e7	2.50707
$934$	1.29143e7	0.484401
$935$	1.29767e6	0.0485439
$936$	−2.59012e7	−0.966341
$937$	2.29765e6	0.0854938	0.0427469	−	0.999086i	$-0.486389\pi$
$937$	2.29765e6	0.0854938	0.0427469	+	0.999086i	$0.486389\pi$
$938$	9.80770e6	0.363966
$939$	2.72498e7	1.00856
$940$	184246.	0.00680108
$941$	−3.43796e7	−1.26569	−0.632844	−	0.774280i	$-0.718112\pi$
$941$	−3.43796e7	−1.26569	−0.632844	+	0.774280i	$0.718112\pi$
$942$	3.16205e7	1.16103
$943$	−3.40166e6	−0.124569
$944$	−8.87999e6	−0.324326
$945$	−1.74187e7	−0.634507
$946$	−5.68183e6	−0.206424
$947$	−2.34166e7	−0.848495	−0.424247	−	0.905546i	$-0.639461\pi$
$947$	−2.34166e7	−0.848495	−0.424247	+	0.905546i	$0.639461\pi$
$948$	2.44993e7	0.885385
$949$	4.28884e7	1.54587
$950$	−749758.	−0.0269533
$951$	−2.84071e7	−1.01853
$952$	−2.33606e6	−0.0835394
$953$	−2.72455e7	−0.971769	−0.485885	−	0.874023i	$-0.661503\pi$
$953$	−2.72455e7	−0.971769	−0.485885	+	0.874023i	$0.661503\pi$
$954$	−5.83494e7	−2.07570
$955$	2.19583e6	0.0779095
$956$	1.96051e7	0.693783
$957$	4.70366e7	1.66018
$958$	−618110.	−0.0217597
$959$	4.59124e7	1.61207
$960$	−2.60634e6	−0.0912754
$961$	−2.82832e7	−0.987916
$962$	−2.25996e7	−0.787343
$963$	−3.23020e7	−1.12244
$964$	2.35926e7	0.817681
$965$	−1.49480e7	−0.516730
$966$	−9.11009e6	−0.314108
$967$	−3.00757e7	−1.03431	−0.517154	−	0.855893i	$-0.673008\pi$
$967$	−3.00757e7	−1.03431	−0.517154	+	0.855893i	$0.673008\pi$
$968$	6.60413e6	0.226531
$969$	−1.64718e6	−0.0563549
$970$	−3.94205e6	−0.134522
$971$	5.24741e6	0.178606	0.0893032	−	0.996004i	$-0.471536\pi$
$971$	5.24741e6	0.178606	0.0893032	+	0.996004i	$0.471536\pi$
$972$	1.33815e7	0.454295
$973$	3.59871e7	1.21861
$974$	1.93692e7	0.654204
$975$	−1.59029e7	−0.535752
$976$	5.59618e6	0.188047
$977$	2.88518e7	0.967024	0.483512	−	0.875338i	$-0.339361\pi$
$977$	2.88518e7	0.967024	0.483512	+	0.875338i	$0.339361\pi$
$978$	5.72341e7	1.91341
$979$	−1.90312e7	−0.634613
$980$	4.72205e6	0.157060
$981$	1.65758e7	0.549924
$982$	−1.82044e7	−0.602416
$983$	−1.84505e7	−0.609008	−0.304504	−	0.952511i	$-0.598491\pi$
$983$	−1.84505e7	−0.609008	−0.304504	+	0.952511i	$0.598491\pi$
$984$	1.04748e7	0.344873
$985$	9.35287e6	0.307153
$986$	6.63128e6	0.217223
$987$	−1.98310e6	−0.0647965
$988$	4.79694e6	0.156341
$989$	−3.12384e6	−0.101554
$990$	−9.73805e6	−0.315779
$991$	1.11449e7	0.360488	0.180244	−	0.983622i	$-0.442311\pi$
$991$	1.11449e7	0.360488	0.180244	+	0.983622i	$0.442311\pi$
$992$	602283.	0.0194322
$993$	−4.20132e7	−1.35211
$994$	−3.94514e7	−1.26647
$995$	1.19270e7	0.381919
$996$	3.13569e7	1.00158
$997$	−1.83396e7	−0.584321	−0.292160	−	0.956369i	$-0.594374\pi$
$997$	−1.83396e7	−0.584321	−0.292160	+	0.956369i	$0.594374\pi$
$998$	8.91007e6	0.283175
$999$	−2.32798e7	−0.738016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.f.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.f.1.1	✓	5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -25.4526 q^{3} +16.0000 q^{4} +25.0000 q^{5} +101.810 q^{6} +169.151 q^{7} -64.0000 q^{8} +404.834 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -25.4526 q^{3} +16.0000 q^{4} +25.0000 q^{5} +101.810 q^{6} +169.151 q^{7} -64.0000 q^{8} +404.834 q^{9} -100.000 q^{10} +240.544 q^{11} -407.241 q^{12} +999.685 q^{13} -676.605 q^{14} -636.315 q^{15} +256.000 q^{16} +215.789 q^{17} -1619.34 q^{18} +299.903 q^{19} +400.000 q^{20} -4305.33 q^{21} -962.177 q^{22} -529.000 q^{23} +1628.97 q^{24} +625.000 q^{25} -3998.74 q^{26} -4119.09 q^{27} +2706.42 q^{28} -7682.61 q^{29} +2545.26 q^{30} -588.167 q^{31} -1024.00 q^{32} -6122.47 q^{33} -863.155 q^{34} +4228.78 q^{35} +6477.34 q^{36} +5651.69 q^{37} -1199.61 q^{38} -25444.6 q^{39} -1600.00 q^{40} +6430.35 q^{41} +17221.3 q^{42} +5905.18 q^{43} +3848.71 q^{44} +10120.8 q^{45} +2116.00 q^{46} +460.615 q^{47} -6515.86 q^{48} +11805.1 q^{49} -2500.00 q^{50} -5492.38 q^{51} +15995.0 q^{52} +36032.9 q^{53} +16476.4 q^{54} +6013.61 q^{55} -10825.7 q^{56} -7633.31 q^{57} +30730.4 q^{58} -34687.4 q^{59} -10181.0 q^{60} +21860.1 q^{61} +2352.67 q^{62} +68478.1 q^{63} +4096.00 q^{64} +24992.1 q^{65} +24489.9 q^{66} -14495.5 q^{67} +3452.62 q^{68} +13464.4 q^{69} -16915.1 q^{70} +58307.9 q^{71} -25909.4 q^{72} +42901.9 q^{73} -22606.8 q^{74} -15907.9 q^{75} +4798.45 q^{76} +40688.3 q^{77} +101778. q^{78} -60159.1 q^{79} +6400.00 q^{80} +6466.82 q^{81} -25721.4 q^{82} -76998.4 q^{83} -68885.3 q^{84} +5394.72 q^{85} -23620.7 q^{86} +195542. q^{87} -15394.8 q^{88} -79117.2 q^{89} -40483.4 q^{90} +169098. q^{91} -8464.00 q^{92} +14970.4 q^{93} -1842.46 q^{94} +7497.58 q^{95} +26063.4 q^{96} +39420.5 q^{97} -47220.5 q^{98} +97380.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18} - 845 q^{19} + 2000 q^{20} + 4682 q^{21} - 1004 q^{22} - 2645 q^{23} - 64 q^{24} + 3125 q^{25} - 6972 q^{26} + 2428 q^{27} + 1632 q^{28} - 4021 q^{29} - 100 q^{30} - 15752 q^{31} - 5120 q^{32} + 2931 q^{33} - 7776 q^{34} + 2550 q^{35} + 5344 q^{36} - 3455 q^{37} + 3380 q^{38} - 16708 q^{39} - 8000 q^{40} - 11898 q^{41} - 18728 q^{42} + 6968 q^{43} + 4016 q^{44} + 8350 q^{45} + 10580 q^{46} + 13412 q^{47} + 256 q^{48} + 91041 q^{49} - 12500 q^{50} - 2115 q^{51} + 27888 q^{52} + 53029 q^{53} - 9712 q^{54} + 6275 q^{55} - 6528 q^{56} - 21730 q^{57} + 16084 q^{58} - 31223 q^{59} + 400 q^{60} + 71477 q^{61} + 63008 q^{62} + 262199 q^{63} + 20480 q^{64} + 43575 q^{65} - 11724 q^{66} + 76003 q^{67} + 31104 q^{68} - 529 q^{69} - 10200 q^{70} + 54418 q^{71} - 21376 q^{72} + 69418 q^{73} + 13820 q^{74} + 625 q^{75} - 13520 q^{76} + 283598 q^{77} + 66832 q^{78} + 105024 q^{79} + 32000 q^{80} + 102913 q^{81} + 47592 q^{82} + 89399 q^{83} + 74912 q^{84} + 48600 q^{85} - 27872 q^{86} + 276726 q^{87} - 16064 q^{88} + 96240 q^{89} - 33400 q^{90} + 59261 q^{91} - 42320 q^{92} + 84434 q^{93} - 53648 q^{94} - 21125 q^{95} - 1024 q^{96} + 216087 q^{97} - 364164 q^{98} + 386925 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * q^99

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