LMFDB - Embedded newform 354.6.a.b.1.3

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:	$4$
Coefficient field:	4.4.32832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 10x + 1 $ x^4 - 2x^3 - 9x^2 + 10*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.09247$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -28.1958 q^{5} +36.0000 q^{6} -61.0514 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -28.1958 q^{5} +36.0000 q^{6} -61.0514 q^{7} +64.0000 q^{8} +81.0000 q^{9} -112.783 q^{10} -67.1203 q^{11} +144.000 q^{12} -428.313 q^{13} -244.206 q^{14} -253.762 q^{15} +256.000 q^{16} +159.167 q^{17} +324.000 q^{18} +374.326 q^{19} -451.133 q^{20} -549.463 q^{21} -268.481 q^{22} -1392.19 q^{23} +576.000 q^{24} -2330.00 q^{25} -1713.25 q^{26} +729.000 q^{27} -976.823 q^{28} -5254.31 q^{29} -1015.05 q^{30} -3683.78 q^{31} +1024.00 q^{32} -604.083 q^{33} +636.669 q^{34} +1721.39 q^{35} +1296.00 q^{36} +11652.6 q^{37} +1497.31 q^{38} -3854.82 q^{39} -1804.53 q^{40} -7208.38 q^{41} -2197.85 q^{42} -13508.9 q^{43} -1073.92 q^{44} -2283.86 q^{45} -5568.76 q^{46} -19495.0 q^{47} +2304.00 q^{48} -13079.7 q^{49} -9319.99 q^{50} +1432.51 q^{51} -6853.01 q^{52} +4849.29 q^{53} +2916.00 q^{54} +1892.51 q^{55} -3907.29 q^{56} +3368.94 q^{57} -21017.2 q^{58} -3481.00 q^{59} -4060.19 q^{60} +6.66838 q^{61} -14735.1 q^{62} -4945.16 q^{63} +4096.00 q^{64} +12076.6 q^{65} -2416.33 q^{66} -5124.15 q^{67} +2546.68 q^{68} -12529.7 q^{69} +6885.57 q^{70} -23438.8 q^{71} +5184.00 q^{72} -87152.9 q^{73} +46610.3 q^{74} -20970.0 q^{75} +5989.22 q^{76} +4097.79 q^{77} -15419.3 q^{78} +84079.1 q^{79} -7218.12 q^{80} +6561.00 q^{81} -28833.5 q^{82} +108036. q^{83} -8791.40 q^{84} -4487.85 q^{85} -54035.4 q^{86} -47288.8 q^{87} -4295.70 q^{88} +31619.8 q^{89} -9135.44 q^{90} +26149.1 q^{91} -22275.0 q^{92} -33154.0 q^{93} -77980.1 q^{94} -10554.4 q^{95} +9216.00 q^{96} +12789.6 q^{97} -52318.9 q^{98} -5436.74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * 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
$5$	−28.1958	−0.504382	−0.252191	−	0.967678i	$-0.581151\pi$
$5$	−28.1958	−0.504382	−0.252191	+	0.967678i	$0.581151\pi$
$6$	36.0000	0.408248
$7$	−61.0514	−0.470924	−0.235462	−	0.971884i	$-0.575660\pi$
$7$	−61.0514	−0.470924	−0.235462	+	0.971884i	$0.575660\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−112.783	−0.356652
$11$	−67.1203	−0.167252	−0.0836261	−	0.996497i	$-0.526650\pi$
$11$	−67.1203	−0.167252	−0.0836261	+	0.996497i	$0.526650\pi$
$12$	144.000	0.288675
$13$	−428.313	−0.702916	−0.351458	−	0.936204i	$-0.614314\pi$
$13$	−428.313	−0.702916	−0.351458	+	0.936204i	$0.614314\pi$
$14$	−244.206	−0.332993
$15$	−253.762	−0.291205
$16$	256.000	0.250000
$17$	159.167	0.133577	0.0667885	−	0.997767i	$-0.478725\pi$
$17$	159.167	0.133577	0.0667885	+	0.997767i	$0.478725\pi$
$18$	324.000	0.235702
$19$	374.326	0.237885	0.118942	−	0.992901i	$-0.462050\pi$
$19$	374.326	0.237885	0.118942	+	0.992901i	$0.462050\pi$
$20$	−451.133	−0.252191
$21$	−549.463	−0.271888
$22$	−268.481	−0.118265
$23$	−1392.19	−0.548755	−0.274378	−	0.961622i	$-0.588472\pi$
$23$	−1392.19	−0.548755	−0.274378	+	0.961622i	$0.588472\pi$
$24$	576.000	0.204124
$25$	−2330.00	−0.745599
$26$	−1713.25	−0.497036
$27$	729.000	0.192450
$28$	−976.823	−0.235462
$29$	−5254.31	−1.16017	−0.580084	−	0.814557i	$-0.696980\pi$
$29$	−5254.31	−1.16017	−0.580084	+	0.814557i	$0.696980\pi$
$30$	−1015.05	−0.205913
$31$	−3683.78	−0.688477	−0.344238	−	0.938882i	$-0.611863\pi$
$31$	−3683.78	−0.688477	−0.344238	+	0.938882i	$0.611863\pi$
$32$	1024.00	0.176777
$33$	−604.083	−0.0965632
$34$	636.669	0.0944532
$35$	1721.39	0.237525
$36$	1296.00	0.166667
$37$	11652.6	1.39932	0.699661	−	0.714475i	$-0.253334\pi$
$37$	11652.6	1.39932	0.699661	+	0.714475i	$0.253334\pi$
$38$	1497.31	0.168210
$39$	−3854.82	−0.405828
$40$	−1804.53	−0.178326
$41$	−7208.38	−0.669697	−0.334848	−	0.942272i	$-0.608685\pi$
$41$	−7208.38	−0.669697	−0.334848	+	0.942272i	$0.608685\pi$
$42$	−2197.85	−0.192254
$43$	−13508.9	−1.11416	−0.557080	−	0.830459i	$-0.688078\pi$
$43$	−13508.9	−1.11416	−0.557080	+	0.830459i	$0.688078\pi$
$44$	−1073.92	−0.0836261
$45$	−2283.86	−0.168127
$46$	−5568.76	−0.388029
$47$	−19495.0	−1.28730	−0.643649	−	0.765321i	$-0.722580\pi$
$47$	−19495.0	−1.28730	−0.643649	+	0.765321i	$0.722580\pi$
$48$	2304.00	0.144338
$49$	−13079.7	−0.778231
$50$	−9319.99	−0.527218
$51$	1432.51	0.0771207
$52$	−6853.01	−0.351458
$53$	4849.29	0.237131	0.118566	−	0.992946i	$-0.462170\pi$
$53$	4849.29	0.237131	0.118566	+	0.992946i	$0.462170\pi$
$54$	2916.00	0.136083
$55$	1892.51	0.0843590
$56$	−3907.29	−0.166497
$57$	3368.94	0.137343
$58$	−21017.2	−0.820362
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−4060.19	−0.145602
$61$	6.66838	0.000229454 0	0.000114727	−	1.00000i	$-0.499963\pi$
$61$	6.66838	0.000229454 0	0.000114727		1.00000i	$0.499963\pi$
$62$	−14735.1	−0.486827
$63$	−4945.16	−0.156975
$64$	4096.00	0.125000
$65$	12076.6	0.354538
$66$	−2416.33	−0.0682805
$67$	−5124.15	−0.139455	−0.0697276	−	0.997566i	$-0.522213\pi$
$67$	−5124.15	−0.139455	−0.0697276	+	0.997566i	$0.522213\pi$
$68$	2546.68	0.0667885
$69$	−12529.7	−0.316824
$70$	6885.57	0.167956
$71$	−23438.8	−0.551811	−0.275906	−	0.961185i	$-0.588978\pi$
$71$	−23438.8	−0.551811	−0.275906	+	0.961185i	$0.588978\pi$
$72$	5184.00	0.117851
$73$	−87152.9	−1.91414	−0.957072	−	0.289851i	$-0.906394\pi$
$73$	−87152.9	−1.91414	−0.957072	+	0.289851i	$0.906394\pi$
$74$	46610.3	0.989470
$75$	−20970.0	−0.430472
$76$	5989.22	0.118942
$77$	4097.79	0.0787631
$78$	−15419.3	−0.286964
$79$	84079.1	1.51572	0.757862	−	0.652415i	$-0.226244\pi$
$79$	84079.1	1.51572	0.757862	+	0.652415i	$0.226244\pi$
$80$	−7218.12	−0.126095
$81$	6561.00	0.111111
$82$	−28833.5	−0.473547
$83$	108036.	1.72136	0.860680	−	0.509146i	$-0.170039\pi$
$83$	108036.	1.72136	0.860680	+	0.509146i	$0.170039\pi$
$84$	−8791.40	−0.135944
$85$	−4487.85	−0.0673738
$86$	−54035.4	−0.787830
$87$	−47288.8	−0.669823
$88$	−4295.70	−0.0591326
$89$	31619.8	0.423140	0.211570	−	0.977363i	$-0.432142\pi$
$89$	31619.8	0.423140	0.211570	+	0.977363i	$0.432142\pi$
$90$	−9135.44	−0.118884
$91$	26149.1	0.331020
$92$	−22275.0	−0.274378
$93$	−33154.0	−0.397492
$94$	−77980.1	−0.910257
$95$	−10554.4	−0.119985
$96$	9216.00	0.102062
$97$	12789.6	0.138015	0.0690077	−	0.997616i	$-0.478017\pi$
$97$	12789.6	0.138015	0.0690077	+	0.997616i	$0.478017\pi$
$98$	−52318.9	−0.550292
$99$	−5436.74	−0.0557508
$100$	−37280.0	−0.372800
$101$	−3161.39	−0.0308372	−0.0154186	−	0.999881i	$-0.504908\pi$
$101$	−3161.39	−0.0308372	−0.0154186	+	0.999881i	$0.504908\pi$
$102$	5730.03	0.0545326
$103$	−161255.	−1.49768	−0.748841	−	0.662750i	$-0.769389\pi$
$103$	−161255.	−1.49768	−0.748841	+	0.662750i	$0.769389\pi$
$104$	−27412.0	−0.248518
$105$	15492.5	0.137135
$106$	19397.2	0.167677
$107$	−49107.6	−0.414657	−0.207329	−	0.978271i	$-0.566477\pi$
$107$	−49107.6	−0.414657	−0.207329	+	0.978271i	$0.566477\pi$
$108$	11664.0	0.0962250
$109$	123780.	0.997893	0.498947	−	0.866633i	$-0.333720\pi$
$109$	123780.	0.997893	0.498947	+	0.866633i	$0.333720\pi$
$110$	7570.04	0.0596508
$111$	104873.	0.807899
$112$	−15629.2	−0.117731
$113$	−11353.0	−0.0836398	−0.0418199	−	0.999125i	$-0.513316\pi$
$113$	−11353.0	−0.0836398	−0.0418199	+	0.999125i	$0.513316\pi$
$114$	13475.8	0.0971160
$115$	39253.9	0.276782
$116$	−84068.9	−0.580084
$117$	−34693.4	−0.234305
$118$	−13924.0	−0.0920575
$119$	−9717.39	−0.0629046
$120$	−16240.8	−0.102956
$121$	−156546.	−0.972027
$122$	26.6735	0.000162248 0
$123$	−64875.5	−0.386650
$124$	−58940.5	−0.344238
$125$	153808.	0.880448
$126$	−19780.7	−0.110998
$127$	149166.	0.820655	0.410328	−	0.911938i	$-0.365414\pi$
$127$	149166.	0.820655	0.410328	+	0.911938i	$0.365414\pi$
$128$	16384.0	0.0883883
$129$	−121580.	−0.643260
$130$	48306.5	0.250696
$131$	−52047.0	−0.264983	−0.132491	−	0.991184i	$-0.542298\pi$
$131$	−52047.0	−0.264983	−0.132491	+	0.991184i	$0.542298\pi$
$132$	−9665.32	−0.0482816
$133$	−22853.2	−0.112026
$134$	−20496.6	−0.0986097
$135$	−20554.7	−0.0970683
$136$	10186.7	0.0472266
$137$	−42136.6	−0.191804	−0.0959020	−	0.995391i	$-0.530574\pi$
$137$	−42136.6	−0.191804	−0.0959020	+	0.995391i	$0.530574\pi$
$138$	−50118.8	−0.224028
$139$	−123528.	−0.542285	−0.271143	−	0.962539i	$-0.587402\pi$
$139$	−123528.	−0.542285	−0.271143	+	0.962539i	$0.587402\pi$
$140$	27542.3	0.118763
$141$	−175455.	−0.743222
$142$	−93755.4	−0.390189
$143$	28748.5	0.117564
$144$	20736.0	0.0833333
$145$	148149.	0.585167
$146$	−348611.	−1.35350
$147$	−117718.	−0.449312
$148$	186441.	0.699661
$149$	−152668.	−0.563354	−0.281677	−	0.959509i	$-0.590891\pi$
$149$	−152668.	−0.563354	−0.281677	+	0.959509i	$0.590891\pi$
$150$	−83879.9	−0.304390
$151$	−136883.	−0.488550	−0.244275	−	0.969706i	$-0.578550\pi$
$151$	−136883.	−0.488550	−0.244275	+	0.969706i	$0.578550\pi$
$152$	23956.9	0.0841049
$153$	12892.6	0.0445257
$154$	16391.2	0.0556939
$155$	103867.	0.347255
$156$	−61677.1	−0.202914
$157$	598821.	1.93887	0.969433	−	0.245355i	$-0.0789047\pi$
$157$	598821.	1.93887	0.969433	+	0.245355i	$0.0789047\pi$
$158$	336316.	1.07178
$159$	43643.7	0.136908
$160$	−28872.5	−0.0891629
$161$	84995.1	0.258422
$162$	26244.0	0.0785674
$163$	−606451.	−1.78783	−0.893917	−	0.448233i	$-0.852053\pi$
$163$	−606451.	−1.78783	−0.893917	+	0.448233i	$0.852053\pi$
$164$	−115334.	−0.334848
$165$	17032.6	0.0487047
$166$	432142.	1.21719
$167$	−207568.	−0.575928	−0.287964	−	0.957641i	$-0.592978\pi$
$167$	−207568.	−0.575928	−0.287964	+	0.957641i	$0.592978\pi$
$168$	−35165.6	−0.0961269
$169$	−187841.	−0.505910
$170$	−17951.4	−0.0476405
$171$	30320.4	0.0792949
$172$	−216142.	−0.557080
$173$	−219392.	−0.557321	−0.278661	−	0.960390i	$-0.589890\pi$
$173$	−219392.	−0.557321	−0.278661	+	0.960390i	$0.589890\pi$
$174$	−189155.	−0.473636
$175$	142250.	0.351120
$176$	−17182.8	−0.0418131
$177$	−31329.0	−0.0751646
$178$	126479.	0.299205
$179$	370791.	0.864960	0.432480	−	0.901643i	$-0.357639\pi$
$179$	370791.	0.864960	0.432480	+	0.901643i	$0.357639\pi$
$180$	−36541.8	−0.0840636
$181$	623853.	1.41542	0.707711	−	0.706502i	$-0.249728\pi$
$181$	623853.	1.41542	0.707711	+	0.706502i	$0.249728\pi$
$182$	104597.	0.234066
$183$	60.0154	0.000132475 0
$184$	−89100.1	−0.194014
$185$	−328554.	−0.705792
$186$	−132616.	−0.281070
$187$	−10683.4	−0.0223411
$188$	−311920.	−0.643649
$189$	−44506.5	−0.0906293
$190$	−42217.7	−0.0848420
$191$	512489.	1.01649	0.508243	−	0.861214i	$-0.330295\pi$
$191$	512489.	1.01649	0.508243	+	0.861214i	$0.330295\pi$
$192$	36864.0	0.0721688
$193$	193040.	0.373040	0.186520	−	0.982451i	$-0.440279\pi$
$193$	193040.	0.373040	0.186520	+	0.982451i	$0.440279\pi$
$194$	51158.4	0.0975916
$195$	108690.	0.204692
$196$	−209276.	−0.389115
$197$	177969.	0.326723	0.163362	−	0.986566i	$-0.447766\pi$
$197$	177969.	0.326723	0.163362	+	0.986566i	$0.447766\pi$
$198$	−21747.0	−0.0394217
$199$	501908.	0.898445	0.449222	−	0.893420i	$-0.351701\pi$
$199$	501908.	0.898445	0.449222	+	0.893420i	$0.351701\pi$
$200$	−149120.	−0.263609
$201$	−46117.3	−0.0805145
$202$	−12645.6	−0.0218052
$203$	320783.	0.546350
$204$	22920.1	0.0385604
$205$	203246.	0.337783
$206$	−645019.	−1.05902
$207$	−112767.	−0.182918
$208$	−109648.	−0.175729
$209$	−25124.9	−0.0397868
$210$	61970.2	0.0969693
$211$	−598038.	−0.924746	−0.462373	−	0.886686i	$-0.653002\pi$
$211$	−598038.	−0.924746	−0.462373	+	0.886686i	$0.653002\pi$
$212$	77588.7	0.118566
$213$	−210950.	−0.318588
$214$	−196431.	−0.293207
$215$	380893.	0.561962
$216$	46656.0	0.0680414
$217$	224900.	0.324220
$218$	495120.	0.705617
$219$	−784376.	−1.10513
$220$	30280.2	0.0421795
$221$	−68173.5	−0.0938934
$222$	419493.	0.571271
$223$	1.04811e6	1.41138	0.705691	−	0.708520i	$-0.250637\pi$
$223$	1.04811e6	1.41138	0.705691	+	0.708520i	$0.250637\pi$
$224$	−62516.7	−0.0832484
$225$	−188730.	−0.248533
$226$	−45411.9	−0.0591423
$227$	−231769.	−0.298532	−0.149266	−	0.988797i	$-0.547691\pi$
$227$	−231769.	−0.298532	−0.149266	+	0.988797i	$0.547691\pi$
$228$	53903.0	0.0686714
$229$	−541822.	−0.682760	−0.341380	−	0.939925i	$-0.610894\pi$
$229$	−541822.	−0.682760	−0.341380	+	0.939925i	$0.610894\pi$
$230$	157016.	0.195715
$231$	36880.1	0.0454739
$232$	−336276.	−0.410181
$233$	1.53765e6	1.85553	0.927767	−	0.373159i	$-0.121726\pi$
$233$	1.53765e6	1.85553	0.927767	+	0.373159i	$0.121726\pi$
$234$	−138773.	−0.165679
$235$	549678.	0.649290
$236$	−55696.0	−0.0650945
$237$	756712.	0.875104
$238$	−38869.6	−0.0444803
$239$	−227474.	−0.257595	−0.128797	−	0.991671i	$-0.541112\pi$
$239$	−227474.	−0.257595	−0.128797	+	0.991671i	$0.541112\pi$
$240$	−64963.1	−0.0728012
$241$	−54648.7	−0.0606091	−0.0303045	−	0.999541i	$-0.509648\pi$
$241$	−54648.7	−0.0606091	−0.0303045	+	0.999541i	$0.509648\pi$
$242$	−626183.	−0.687327
$243$	59049.0	0.0641500
$244$	106.694	0.000114727 0
$245$	368793.	0.392525
$246$	−259502.	−0.273403
$247$	−160329.	−0.167213
$248$	−235762.	−0.243413
$249$	972320.	0.993828
$250$	615232.	0.622571
$251$	284957.	0.285492	0.142746	−	0.989759i	$-0.454407\pi$
$251$	284957.	0.285492	0.142746	+	0.989759i	$0.454407\pi$
$252$	−79122.6	−0.0784873
$253$	93444.1	0.0917806
$254$	596664.	0.580291
$255$	−40390.7	−0.0388983
$256$	65536.0	0.0625000
$257$	506248.	0.478112	0.239056	−	0.971006i	$-0.423162\pi$
$257$	506248.	0.478112	0.239056	+	0.971006i	$0.423162\pi$
$258$	−486319.	−0.454854
$259$	−711406.	−0.658974
$260$	193226.	0.177269
$261$	−425599.	−0.386722
$262$	−208188.	−0.187371
$263$	−13559.9	−0.0120884	−0.00604420	−	0.999982i	$-0.501924\pi$
$263$	−13559.9	−0.0120884	−0.00604420	+	0.999982i	$0.501924\pi$
$264$	−38661.3	−0.0341402
$265$	−136730.	−0.119605
$266$	−91412.7	−0.0792140
$267$	284578.	0.244300
$268$	−81986.4	−0.0697276
$269$	1.46420e6	1.23373	0.616863	−	0.787070i	$-0.288403\pi$
$269$	1.46420e6	1.23373	0.616863	+	0.787070i	$0.288403\pi$
$270$	−82218.9	−0.0686377
$271$	−471723.	−0.390179	−0.195089	−	0.980785i	$-0.562500\pi$
$271$	−471723.	−0.390179	−0.195089	+	0.980785i	$0.562500\pi$
$272$	40746.8	0.0333943
$273$	235342.	0.191114
$274$	−168546.	−0.135626
$275$	156390.	0.124703
$276$	−200475.	−0.158412
$277$	166070.	0.130044	0.0650220	−	0.997884i	$-0.479288\pi$
$277$	166070.	0.130044	0.0650220	+	0.997884i	$0.479288\pi$
$278$	−494111.	−0.383454
$279$	−298386.	−0.229492
$280$	110169.	0.0839779
$281$	2.59764e6	1.96252	0.981258	−	0.192700i	$-0.0617245\pi$
$281$	2.59764e6	1.96252	0.981258	+	0.192700i	$0.0617245\pi$
$282$	−701821.	−0.525537
$283$	155346.	0.115301	0.0576506	−	0.998337i	$-0.481639\pi$
$283$	155346.	0.115301	0.0576506	+	0.998337i	$0.481639\pi$
$284$	−375022.	−0.275906
$285$	−94989.9	−0.0692732
$286$	114994.	0.0831305
$287$	440082.	0.315376
$288$	82944.0	0.0589256
$289$	−1.39452e6	−0.982157
$290$	592598.	0.413776
$291$	115106.	0.0796832
$292$	−1.39445e6	−0.957072
$293$	436509.	0.297046	0.148523	−	0.988909i	$-0.452548\pi$
$293$	436509.	0.297046	0.148523	+	0.988909i	$0.452548\pi$
$294$	−470870.	−0.317711
$295$	98149.6	0.0656649
$296$	745765.	0.494735
$297$	−48930.7	−0.0321877
$298$	−610670.	−0.398351
$299$	596293.	0.385729
$300$	−335520.	−0.215236
$301$	824735.	0.524684
$302$	−547534.	−0.345457
$303$	−28452.5	−0.0178039
$304$	95827.6	0.0594712
$305$	−188.020	−0.000115732 0
$306$	51570.2	0.0314844
$307$	−1.84358e6	−1.11639	−0.558196	−	0.829709i	$-0.688506\pi$
$307$	−1.84358e6	−1.11639	−0.558196	+	0.829709i	$0.688506\pi$
$308$	65564.6	0.0393815
$309$	−1.45129e6	−0.864687
$310$	415468.	0.245546
$311$	1.00742e6	0.590620	0.295310	−	0.955401i	$-0.404577\pi$
$311$	1.00742e6	0.590620	0.295310	+	0.955401i	$0.404577\pi$
$312$	−246708.	−0.143482
$313$	−2.25509e6	−1.30108	−0.650539	−	0.759473i	$-0.725457\pi$
$313$	−2.25509e6	−1.30108	−0.650539	+	0.759473i	$0.725457\pi$
$314$	2.39528e6	1.37099
$315$	139433.	0.0791751
$316$	1.34526e6	0.757862
$317$	2.29215e6	1.28114	0.640568	−	0.767902i	$-0.278699\pi$
$317$	2.29215e6	1.28114	0.640568	+	0.767902i	$0.278699\pi$
$318$	174575.	0.0968085
$319$	352671.	0.194041
$320$	−115490.	−0.0630477
$321$	−441969.	−0.239403
$322$	339981.	0.182732
$323$	59580.6	0.0317759
$324$	104976.	0.0555556
$325$	997969.	0.524093
$326$	−2.42581e6	−1.26419
$327$	1.11402e6	0.576134
$328$	−461337.	−0.236774
$329$	1.19020e6	0.606219
$330$	68130.4	0.0344394
$331$	1.12870e6	0.566250	0.283125	−	0.959083i	$-0.408629\pi$
$331$	1.12870e6	0.566250	0.283125	+	0.959083i	$0.408629\pi$
$332$	1.72857e6	0.860680
$333$	943859.	0.466441
$334$	−830271.	−0.407243
$335$	144479.	0.0703386
$336$	−140662.	−0.0679720
$337$	1.12768e6	0.540895	0.270447	−	0.962735i	$-0.412828\pi$
$337$	1.12768e6	0.540895	0.270447	+	0.962735i	$0.412828\pi$
$338$	−751363.	−0.357732
$339$	−102177.	−0.0482895
$340$	−71805.6	−0.0336869
$341$	247256.	0.115149
$342$	121282.	0.0560700
$343$	1.82463e6	0.837411
$344$	−864567.	−0.393915
$345$	353285.	0.159800
$346$	−877568.	−0.394086
$347$	1.40343e6	0.625700	0.312850	−	0.949802i	$-0.398716\pi$
$347$	1.40343e6	0.625700	0.312850	+	0.949802i	$0.398716\pi$
$348$	−756620.	−0.334911
$349$	338397.	0.148718	0.0743589	−	0.997232i	$-0.476309\pi$
$349$	338397.	0.148718	0.0743589	+	0.997232i	$0.476309\pi$
$350$	568999.	0.248280
$351$	−312240.	−0.135276
$352$	−68731.2	−0.0295663
$353$	1.24787e6	0.533005	0.266502	−	0.963834i	$-0.414132\pi$
$353$	1.24787e6	0.533005	0.266502	+	0.963834i	$0.414132\pi$
$354$	−125316.	−0.0531494
$355$	660877.	0.278323
$356$	505917.	0.211570
$357$	−87456.5	−0.0363180
$358$	1.48316e6	0.611619
$359$	2.14680e6	0.879136	0.439568	−	0.898209i	$-0.355132\pi$
$359$	2.14680e6	0.879136	0.439568	+	0.898209i	$0.355132\pi$
$360$	−146167.	−0.0594420
$361$	−2.33598e6	−0.943411
$362$	2.49541e6	1.00085
$363$	−1.40891e6	−0.561200
$364$	418386.	0.165510
$365$	2.45734e6	0.965459
$366$	240.062	9.36742e−5 0
$367$	−2.63131e6	−1.01978	−0.509890	−	0.860240i	$-0.670314\pi$
$367$	−2.63131e6	−1.01978	−0.509890	+	0.860240i	$0.670314\pi$
$368$	−356400.	−0.137189
$369$	−583879.	−0.223232
$370$	−1.31421e6	−0.499071
$371$	−296056.	−0.111671
$372$	−530464.	−0.198746
$373$	−3.15041e6	−1.17245	−0.586226	−	0.810147i	$-0.699387\pi$
$373$	−3.15041e6	−1.17245	−0.586226	+	0.810147i	$0.699387\pi$
$374$	−42733.4	−0.0157975
$375$	1.38427e6	0.508327
$376$	−1.24768e6	−0.455129
$377$	2.25049e6	0.815500
$378$	−178026.	−0.0640846
$379$	2.32513e6	0.831475	0.415738	−	0.909485i	$-0.363523\pi$
$379$	2.32513e6	0.831475	0.415738	+	0.909485i	$0.363523\pi$
$380$	−168871.	−0.0599924
$381$	1.34249e6	0.473806
$382$	2.04996e6	0.718764
$383$	2.92297e6	1.01819	0.509094	−	0.860711i	$-0.329981\pi$
$383$	2.92297e6	1.01819	0.509094	+	0.860711i	$0.329981\pi$
$384$	147456.	0.0510310
$385$	−115540.	−0.0397267
$386$	772162.	0.263779
$387$	−1.09422e6	−0.371386
$388$	204634.	0.0690077
$389$	−2.84939e6	−0.954724	−0.477362	−	0.878707i	$-0.658407\pi$
$389$	−2.84939e6	−0.954724	−0.477362	+	0.878707i	$0.658407\pi$
$390$	434759.	0.144739
$391$	−221591.	−0.0733011
$392$	−837102.	−0.275146
$393$	−468423.	−0.152988
$394$	711878.	0.231028
$395$	−2.37068e6	−0.764503
$396$	−86987.9	−0.0278754
$397$	−5.45928e6	−1.73844	−0.869218	−	0.494428i	$-0.835377\pi$
$397$	−5.45928e6	−1.73844	−0.869218	+	0.494428i	$0.835377\pi$
$398$	2.00763e6	0.635296
$399$	−205678.	−0.0646780
$400$	−596479.	−0.186400
$401$	−1.48954e6	−0.462584	−0.231292	−	0.972884i	$-0.574295\pi$
$401$	−1.48954e6	−0.462584	−0.231292	+	0.972884i	$0.574295\pi$
$402$	−184469.	−0.0569323
$403$	1.57781e6	0.483941
$404$	−50582.3	−0.0154186
$405$	−184993.	−0.0560424
$406$	1.28313e6	0.386328
$407$	−782124.	−0.234040
$408$	91680.4	0.0272663
$409$	−1.40027e6	−0.413907	−0.206953	−	0.978351i	$-0.566355\pi$
$409$	−1.40027e6	−0.413907	−0.206953	+	0.978351i	$0.566355\pi$
$410$	812985.	0.238849
$411$	−379229.	−0.110738
$412$	−2.58008e6	−0.748841
$413$	212520.	0.0613091
$414$	−451069.	−0.129343
$415$	−3.04615e6	−0.868223
$416$	−438593.	−0.124259
$417$	−1.11175e6	−0.313089
$418$	−100500.	−0.0281335
$419$	−4.32632e6	−1.20388	−0.601941	−	0.798540i	$-0.705606\pi$
$419$	−4.32632e6	−1.20388	−0.601941	+	0.798540i	$0.705606\pi$
$420$	247881.	0.0685677
$421$	−3.07342e6	−0.845118	−0.422559	−	0.906335i	$-0.638868\pi$
$421$	−3.07342e6	−0.845118	−0.422559	+	0.906335i	$0.638868\pi$
$422$	−2.39215e6	−0.653894
$423$	−1.57910e6	−0.429099
$424$	310355.	0.0838386
$425$	−370860.	−0.0995949
$426$	−843799.	−0.225276
$427$	−407.114	−0.000108055 0
$428$	−785722.	−0.207329
$429$	258737.	0.0678757
$430$	1.52357e6	0.397367
$431$	−1.08351e6	−0.280958	−0.140479	−	0.990084i	$-0.544864\pi$
$431$	−1.08351e6	−0.280958	−0.140479	+	0.990084i	$0.544864\pi$
$432$	186624.	0.0481125
$433$	−4.20156e6	−1.07694	−0.538470	−	0.842645i	$-0.680997\pi$
$433$	−4.20156e6	−1.07694	−0.538470	+	0.842645i	$0.680997\pi$
$434$	899600.	0.229258
$435$	1.33334e6	0.337846
$436$	1.98048e6	0.498947
$437$	−521133.	−0.130540
$438$	−3.13750e6	−0.781446
$439$	−2.57925e6	−0.638751	−0.319375	−	0.947628i	$-0.603473\pi$
$439$	−2.57925e6	−0.638751	−0.319375	+	0.947628i	$0.603473\pi$
$440$	121121.	0.0298254
$441$	−1.05946e6	−0.259410
$442$	−272694.	−0.0663926
$443$	1.50694e6	0.364826	0.182413	−	0.983222i	$-0.441609\pi$
$443$	1.50694e6	0.364826	0.182413	+	0.983222i	$0.441609\pi$
$444$	1.67797e6	0.403949
$445$	−891545.	−0.213424
$446$	4.19244e6	0.997997
$447$	−1.37401e6	−0.325252
$448$	−250067.	−0.0588655
$449$	−5.73224e6	−1.34186	−0.670931	−	0.741519i	$-0.734106\pi$
$449$	−5.73224e6	−1.34186	−0.670931	+	0.741519i	$0.734106\pi$
$450$	−754919.	−0.175739
$451$	483829.	0.112008
$452$	−181647.	−0.0418199
$453$	−1.23195e6	−0.282064
$454$	−927075.	−0.211094
$455$	−737296.	−0.166960
$456$	215612.	0.0485580
$457$	20498.2	0.00459119	0.00229559	−	0.999997i	$-0.499269\pi$
$457$	20498.2	0.00459119	0.00229559	+	0.999997i	$0.499269\pi$
$458$	−2.16729e6	−0.482784
$459$	116033.	0.0257069
$460$	628062.	0.138391
$461$	−3.67826e6	−0.806101	−0.403051	−	0.915178i	$-0.632050\pi$
$461$	−3.67826e6	−0.806101	−0.403051	+	0.915178i	$0.632050\pi$
$462$	147520.	0.0321549
$463$	311371.	0.0675034	0.0337517	−	0.999430i	$-0.489254\pi$
$463$	311371.	0.0675034	0.0337517	+	0.999430i	$0.489254\pi$
$464$	−1.34510e6	−0.290042
$465$	934804.	0.200488
$466$	6.15062e6	1.31206
$467$	2.49581e6	0.529565	0.264782	−	0.964308i	$-0.414700\pi$
$467$	2.49581e6	0.529565	0.264782	+	0.964308i	$0.414700\pi$
$468$	−555094.	−0.117153
$469$	312836.	0.0656728
$470$	2.19871e6	0.459117
$471$	5.38939e6	1.11941
$472$	−222784.	−0.0460287
$473$	906718.	0.186346
$474$	3.02685e6	0.618792
$475$	−872180.	−0.177367
$476$	−155478.	−0.0314523
$477$	392793.	0.0790438
$478$	−909895.	−0.182147
$479$	−1.76826e6	−0.352133	−0.176067	−	0.984378i	$-0.556337\pi$
$479$	−1.76826e6	−0.352133	−0.176067	+	0.984378i	$0.556337\pi$
$480$	−259852.	−0.0514782
$481$	−4.99095e6	−0.983605
$482$	−218595.	−0.0428571
$483$	764956.	0.149200
$484$	−2.50473e6	−0.486013
$485$	−360613.	−0.0696125
$486$	236196.	0.0453609
$487$	−8.03050e6	−1.53433	−0.767167	−	0.641447i	$-0.778334\pi$
$487$	−8.03050e6	−1.53433	−0.767167	+	0.641447i	$0.778334\pi$
$488$	426.776	8.11242e−5 0
$489$	−5.45806e6	−1.03221
$490$	1.47517e6	0.277557
$491$	194193.	0.0363522	0.0181761	−	0.999835i	$-0.494214\pi$
$491$	194193.	0.0363522	0.0181761	+	0.999835i	$0.494214\pi$
$492$	−1.03801e6	−0.193325
$493$	−836314.	−0.154972
$494$	−641316.	−0.118237
$495$	153293.	0.0281197
$496$	−943047.	−0.172119
$497$	1.43097e6	0.259861
$498$	3.88928e6	0.702742
$499$	−9.46636e6	−1.70189	−0.850945	−	0.525254i	$-0.823970\pi$
$499$	−9.46636e6	−1.70189	−0.850945	+	0.525254i	$0.823970\pi$
$500$	2.46093e6	0.440224
$501$	−1.86811e6	−0.332512
$502$	1.13983e6	0.201874
$503$	8.24912e6	1.45374	0.726872	−	0.686773i	$-0.240974\pi$
$503$	8.24912e6	1.45374	0.726872	+	0.686773i	$0.240974\pi$
$504$	−316491.	−0.0554989
$505$	89137.9	0.0155537
$506$	373777.	0.0648987
$507$	−1.69057e6	−0.292087
$508$	2.38666e6	0.410328
$509$	−6.97934e6	−1.19404	−0.597021	−	0.802225i	$-0.703649\pi$
$509$	−6.97934e6	−1.19404	−0.597021	+	0.802225i	$0.703649\pi$
$510$	−161563.	−0.0275052
$511$	5.32081e6	0.901416
$512$	262144.	0.0441942
$513$	272884.	0.0457809
$514$	2.02499e6	0.338077
$515$	4.54671e6	0.755403
$516$	−1.94527e6	−0.321630
$517$	1.30851e6	0.215304
$518$	−2.84563e6	−0.465965
$519$	−1.97453e6	−0.321770
$520$	772905.	0.125348
$521$	795928.	0.128463	0.0642317	−	0.997935i	$-0.479540\pi$
$521$	795928.	0.128463	0.0642317	+	0.997935i	$0.479540\pi$
$522$	−1.70240e6	−0.273454
$523$	−7.45576e6	−1.19189	−0.595947	−	0.803023i	$-0.703223\pi$
$523$	−7.45576e6	−1.19189	−0.595947	+	0.803023i	$0.703223\pi$
$524$	−832752.	−0.132491
$525$	1.28025e6	0.202719
$526$	−54239.8	−0.00854778
$527$	−586337.	−0.0919647
$528$	−154645.	−0.0241408
$529$	−4.49815e6	−0.698868
$530$	−546919.	−0.0845733
$531$	−281961.	−0.0433963
$532$	−365651.	−0.0560128
$533$	3.08745e6	0.470740
$534$	1.13831e6	0.172746
$535$	1.38463e6	0.209146
$536$	−327945.	−0.0493048
$537$	3.33712e6	0.499385
$538$	5.85679e6	0.872376
$539$	877915.	0.130161
$540$	−328876.	−0.0485342
$541$	−4.06794e6	−0.597559	−0.298780	−	0.954322i	$-0.596580\pi$
$541$	−4.06794e6	−0.597559	−0.298780	+	0.954322i	$0.596580\pi$
$542$	−1.88689e6	−0.275898
$543$	5.61468e6	0.817195
$544$	162987.	0.0236133
$545$	−3.49007e6	−0.503319
$546$	941369.	0.135138
$547$	−1.73719e6	−0.248244	−0.124122	−	0.992267i	$-0.539611\pi$
$547$	−1.73719e6	−0.248244	−0.124122	+	0.992267i	$0.539611\pi$
$548$	−674185.	−0.0959020
$549$	540.138	7.64846e−5 0
$550$	625560.	0.0881784
$551$	−1.96683e6	−0.275986
$552$	−801901.	−0.112014
$553$	−5.13315e6	−0.713791
$554$	664278.	0.0919550
$555$	−2.95698e6	−0.407489
$556$	−1.97645e6	−0.271143
$557$	2.62442e6	0.358423	0.179211	−	0.983811i	$-0.442645\pi$
$557$	2.62442e6	0.358423	0.179211	+	0.983811i	$0.442645\pi$
$558$	−1.19354e6	−0.162276
$559$	5.78602e6	0.783160
$560$	440677.	0.0593813
$561$	−96150.2	−0.0128986
$562$	1.03906e7	1.38771
$563$	−1.04702e7	−1.39214	−0.696070	−	0.717974i	$-0.745070\pi$
$563$	−1.04702e7	−1.39214	−0.696070	+	0.717974i	$0.745070\pi$
$564$	−2.80728e6	−0.371611
$565$	320106.	0.0421864
$566$	621384.	0.0815303
$567$	−400558.	−0.0523249
$568$	−1.50009e6	−0.195095
$569$	−8.28797e6	−1.07317	−0.536584	−	0.843847i	$-0.680285\pi$
$569$	−8.28797e6	−1.07317	−0.536584	+	0.843847i	$0.680285\pi$
$570$	−379960.	−0.0489836
$571$	9.19356e6	1.18003	0.590016	−	0.807392i	$-0.299122\pi$
$571$	9.19356e6	1.18003	0.590016	+	0.807392i	$0.299122\pi$
$572$	459976.	0.0587821
$573$	4.61240e6	0.586868
$574$	1.76033e6	0.223005
$575$	3.24380e6	0.409151
$576$	331776.	0.0416667
$577$	−1.35629e7	−1.69596	−0.847978	−	0.530032i	$-0.822180\pi$
$577$	−1.35629e7	−1.69596	−0.847978	+	0.530032i	$0.822180\pi$
$578$	−5.57809e6	−0.694490
$579$	1.73736e6	0.215375
$580$	2.37039e6	0.292584
$581$	−6.59573e6	−0.810629
$582$	460426.	0.0563446
$583$	−325486.	−0.0396608
$584$	−5.57778e6	−0.676752
$585$	978207.	0.118179
$586$	1.74604e6	0.210043
$587$	−4.29994e6	−0.515072	−0.257536	−	0.966269i	$-0.582911\pi$
$587$	−4.29994e6	−0.515072	−0.257536	+	0.966269i	$0.582911\pi$
$588$	−1.88348e6	−0.224656
$589$	−1.37894e6	−0.163778
$590$	392598.	0.0464321
$591$	1.60173e6	0.188634
$592$	2.98306e6	0.349830
$593$	−671647.	−0.0784340	−0.0392170	−	0.999231i	$-0.512486\pi$
$593$	−671647.	−0.0784340	−0.0392170	+	0.999231i	$0.512486\pi$
$594$	−195723.	−0.0227602
$595$	273990.	0.0317279
$596$	−2.44268e6	−0.281677
$597$	4.51717e6	0.518717
$598$	2.38517e6	0.272751
$599$	5.65820e6	0.644334	0.322167	−	0.946683i	$-0.395589\pi$
$599$	5.65820e6	0.644334	0.322167	+	0.946683i	$0.395589\pi$
$600$	−1.34208e6	−0.152195
$601$	−9.92573e6	−1.12092	−0.560462	−	0.828180i	$-0.689376\pi$
$601$	−9.92573e6	−1.12092	−0.560462	+	0.828180i	$0.689376\pi$
$602$	3.29894e6	0.371008
$603$	−415056.	−0.0464851
$604$	−2.19014e6	−0.244275
$605$	4.41394e6	0.490272
$606$	−113810.	−0.0125892
$607$	1.04796e7	1.15444	0.577222	−	0.816587i	$-0.304137\pi$
$607$	1.04796e7	1.15444	0.577222	+	0.816587i	$0.304137\pi$
$608$	383310.	0.0420525
$609$	2.88705e6	0.315436
$610$	−752.081	−8.18351e−5 0
$611$	8.34998e6	0.904862
$612$	206281.	0.0222628
$613$	−9.37201e6	−1.00735	−0.503676	−	0.863892i	$-0.668020\pi$
$613$	−9.37201e6	−1.00735	−0.503676	+	0.863892i	$0.668020\pi$
$614$	−7.37433e6	−0.789408
$615$	1.82922e6	0.195019
$616$	262258.	0.0278470
$617$	1.26303e7	1.33567	0.667836	−	0.744309i	$-0.267221\pi$
$617$	1.26303e7	1.33567	0.667836	+	0.744309i	$0.267221\pi$
$618$	−5.80517e6	−0.611426
$619$	−1.42471e6	−0.149451	−0.0747255	−	0.997204i	$-0.523808\pi$
$619$	−1.42471e6	−0.149451	−0.0747255	+	0.997204i	$0.523808\pi$
$620$	1.66187e6	0.173628
$621$	−1.01491e6	−0.105608
$622$	4.02967e6	0.417632
$623$	−1.93043e6	−0.199267
$624$	−986834.	−0.101457
$625$	2.94450e6	0.301517
$626$	−9.02036e6	−0.920000
$627$	−226124.	−0.0229709
$628$	9.58114e6	0.969433
$629$	1.85471e6	0.186917
$630$	557731.	0.0559853
$631$	1.08712e6	0.108694	0.0543469	−	0.998522i	$-0.482692\pi$
$631$	1.08712e6	0.108694	0.0543469	+	0.998522i	$0.482692\pi$
$632$	5.38106e6	0.535889
$633$	−5.38234e6	−0.533902
$634$	9.16860e6	0.905899
$635$	−4.20586e6	−0.413924
$636$	698298.	0.0684539
$637$	5.60222e6	0.547030
$638$	1.41068e6	0.137207
$639$	−1.89855e6	−0.183937
$640$	−461960.	−0.0445815
$641$	−7.45168e6	−0.716324	−0.358162	−	0.933659i	$-0.616596\pi$
$641$	−7.45168e6	−0.716324	−0.358162	+	0.933659i	$0.616596\pi$
$642$	−1.76787e6	−0.169283
$643$	6.96657e6	0.664495	0.332248	−	0.943192i	$-0.392193\pi$
$643$	6.96657e6	0.664495	0.332248	+	0.943192i	$0.392193\pi$
$644$	1.35992e6	0.129211
$645$	3.42804e6	0.324449
$646$	238322.	0.0224690
$647$	−7.92701e6	−0.744473	−0.372236	−	0.928138i	$-0.621409\pi$
$647$	−7.92701e6	−0.744473	−0.372236	+	0.928138i	$0.621409\pi$
$648$	419904.	0.0392837
$649$	233646.	0.0217744
$650$	3.99187e6	0.370590
$651$	2.02410e6	0.187189
$652$	−9.70322e6	−0.893917
$653$	1.12228e7	1.02995	0.514976	−	0.857204i	$-0.327801\pi$
$653$	1.12228e7	1.02995	0.514976	+	0.857204i	$0.327801\pi$
$654$	4.45608e6	0.407388
$655$	1.46751e6	0.133652
$656$	−1.84535e6	−0.167424
$657$	−7.05938e6	−0.638048
$658$	4.76080e6	0.428662
$659$	4.10409e6	0.368132	0.184066	−	0.982914i	$-0.441074\pi$
$659$	4.10409e6	0.368132	0.184066	+	0.982914i	$0.441074\pi$
$660$	272521.	0.0243523
$661$	−1.99160e6	−0.177296	−0.0886478	−	0.996063i	$-0.528255\pi$
$661$	−1.99160e6	−0.177296	−0.0886478	+	0.996063i	$0.528255\pi$
$662$	4.51480e6	0.400399
$663$	−613561.	−0.0542094
$664$	6.91428e6	0.608593
$665$	644363.	0.0565037
$666$	3.77543e6	0.329823
$667$	7.31499e6	0.636648
$668$	−3.32108e6	−0.287964
$669$	9.43298e6	0.814862
$670$	577918.	0.0497369
$671$	−447.583	−3.83767e−5 0
$672$	−562650.	−0.0480635
$673$	2.04608e7	1.74135	0.870674	−	0.491861i	$-0.163683\pi$
$673$	2.04608e7	1.74135	0.870674	+	0.491861i	$0.163683\pi$
$674$	4.51074e6	0.382470
$675$	−1.69857e6	−0.143491
$676$	−3.00545e6	−0.252955
$677$	−1.69111e7	−1.41808	−0.709040	−	0.705168i	$-0.750872\pi$
$677$	−1.69111e7	−1.41808	−0.709040	+	0.705168i	$0.750872\pi$
$678$	−408707.	−0.0341458
$679$	−780823.	−0.0649948
$680$	−287222.	−0.0238202
$681$	−2.08592e6	−0.172357
$682$	989025.	0.0814229
$683$	7.11147e6	0.583321	0.291660	−	0.956522i	$-0.405792\pi$
$683$	7.11147e6	0.583321	0.291660	+	0.956522i	$0.405792\pi$
$684$	485127.	0.0396475
$685$	1.18807e6	0.0967425
$686$	7.29851e6	0.592139
$687$	−4.87640e6	−0.394192
$688$	−3.45827e6	−0.278540
$689$	−2.07702e6	−0.166683
$690$	1.41314e6	0.112996
$691$	1.69283e7	1.34871	0.674353	−	0.738409i	$-0.264423\pi$
$691$	1.69283e7	1.34871	0.674353	+	0.738409i	$0.264423\pi$
$692$	−3.51027e6	−0.278661
$693$	331921.	0.0262544
$694$	5.61371e6	0.442437
$695$	3.48297e6	0.273519
$696$	−3.02648e6	−0.236818
$697$	−1.14734e6	−0.0894561
$698$	1.35359e6	0.105159
$699$	1.38389e7	1.07129
$700$	2.27599e6	0.175560
$701$	1.14085e7	0.876868	0.438434	−	0.898763i	$-0.355533\pi$
$701$	1.14085e7	0.876868	0.438434	+	0.898763i	$0.355533\pi$
$702$	−1.24896e6	−0.0956547
$703$	4.36187e6	0.332877
$704$	−274925.	−0.0209065
$705$	4.94710e6	0.374868
$706$	4.99146e6	0.376891
$707$	193007.	0.0145220
$708$	−501264.	−0.0375823
$709$	−2.65986e6	−0.198721	−0.0993604	−	0.995052i	$-0.531680\pi$
$709$	−2.65986e6	−0.198721	−0.0993604	+	0.995052i	$0.531680\pi$
$710$	2.64351e6	0.196804
$711$	6.81040e6	0.505241
$712$	2.02367e6	0.149603
$713$	5.12852e6	0.377805
$714$	−349826.	−0.0256807
$715$	−810587.	−0.0592973
$716$	5.93265e6	0.432480
$717$	−2.04726e6	−0.148722
$718$	8.58721e6	0.621643
$719$	1.69031e7	1.21939	0.609697	−	0.792635i	$-0.291291\pi$
$719$	1.69031e7	1.21939	0.609697	+	0.792635i	$0.291291\pi$
$720$	−584668.	−0.0420318
$721$	9.84483e6	0.705294
$722$	−9.34391e6	−0.667092
$723$	−491839.	−0.0349927
$724$	9.98166e6	0.707711
$725$	1.22425e7	0.865020
$726$	−5.63565e6	−0.396828
$727$	9.09120e6	0.637948	0.318974	−	0.947763i	$-0.396662\pi$
$727$	9.09120e6	0.637948	0.318974	+	0.947763i	$0.396662\pi$
$728$	1.67354e6	0.117033
$729$	531441.	0.0370370
$730$	9.82938e6	0.682683
$731$	−2.15017e6	−0.148826
$732$	960.246	6.62376e−5 0
$733$	−8.09308e6	−0.556358	−0.278179	−	0.960529i	$-0.589731\pi$
$733$	−8.09308e6	−0.556358	−0.278179	+	0.960529i	$0.589731\pi$
$734$	−1.05252e7	−0.721093
$735$	3.31914e6	0.226625
$736$	−1.42560e6	−0.0970071
$737$	343934.	0.0233242
$738$	−2.33552e6	−0.157849
$739$	1.58743e7	1.06926	0.534630	−	0.845086i	$-0.320451\pi$
$739$	1.58743e7	1.06926	0.534630	+	0.845086i	$0.320451\pi$
$740$	−5.25686e6	−0.352896
$741$	−1.44296e6	−0.0965404
$742$	−1.18423e6	−0.0789632
$743$	−2.63654e7	−1.75211	−0.876055	−	0.482210i	$-0.839834\pi$
$743$	−2.63654e7	−1.75211	−0.876055	+	0.482210i	$0.839834\pi$
$744$	−2.12186e6	−0.140535
$745$	4.30458e6	0.284145
$746$	−1.26016e7	−0.829049
$747$	8.75088e6	0.573787
$748$	−170934.	−0.0111705
$749$	2.99809e6	0.195272
$750$	5.53709e6	0.359442
$751$	−2.44159e6	−0.157970	−0.0789848	−	0.996876i	$-0.525168\pi$
$751$	−2.44159e6	−0.157970	−0.0789848	+	0.996876i	$0.525168\pi$
$752$	−4.99073e6	−0.321825
$753$	2.56461e6	0.164829
$754$	9.00196e6	0.576645
$755$	3.85954e6	0.246415
$756$	−712104.	−0.0453147
$757$	2.49638e6	0.158333	0.0791665	−	0.996861i	$-0.474774\pi$
$757$	2.49638e6	0.158333	0.0791665	+	0.996861i	$0.474774\pi$
$758$	9.30052e6	0.587942
$759$	840997.	0.0529895
$760$	−675484.	−0.0424210
$761$	−2.38904e6	−0.149541	−0.0747706	−	0.997201i	$-0.523822\pi$
$761$	−2.38904e6	−0.149541	−0.0747706	+	0.997201i	$0.523822\pi$
$762$	5.36998e6	0.335031
$763$	−7.55694e6	−0.469932
$764$	8.19983e6	0.508243
$765$	−363516.	−0.0224579
$766$	1.16919e7	0.719968
$767$	1.49096e6	0.0915118
$768$	589824.	0.0360844
$769$	−3.34844e6	−0.204186	−0.102093	−	0.994775i	$-0.532554\pi$
$769$	−3.34844e6	−0.204186	−0.102093	+	0.994775i	$0.532554\pi$
$770$	−462162.	−0.0280910
$771$	4.55623e6	0.276038
$772$	3.08865e6	0.186520
$773$	2.51989e6	0.151682	0.0758408	−	0.997120i	$-0.475836\pi$
$773$	2.51989e6	0.151682	0.0758408	+	0.997120i	$0.475836\pi$
$774$	−4.37687e6	−0.262610
$775$	8.58319e6	0.513328
$776$	818534.	0.0487958
$777$	−6.40266e6	−0.380459
$778$	−1.13976e7	−0.675092
$779$	−2.69829e6	−0.159311
$780$	1.73904e6	0.102346
$781$	1.57322e6	0.0922917
$782$	−886364.	−0.0518317
$783$	−3.83039e6	−0.223274
$784$	−3.34841e6	−0.194558
$785$	−1.68842e7	−0.977929
$786$	−1.87369e6	−0.108179
$787$	1.68042e7	0.967122	0.483561	−	0.875311i	$-0.339343\pi$
$787$	1.68042e7	0.967122	0.483561	+	0.875311i	$0.339343\pi$
$788$	2.84751e6	0.163362
$789$	−122040.	−0.00697924
$790$	−9.48270e6	−0.540586
$791$	693115.	0.0393880
$792$	−347952.	−0.0197109
$793$	−2856.15	−0.000161287 0
$794$	−2.18371e7	−1.22926
$795$	−1.23057e6	−0.0690538
$796$	8.03053e6	0.449222
$797$	−1.79830e7	−1.00281	−0.501403	−	0.865214i	$-0.667182\pi$
$797$	−1.79830e7	−1.00281	−0.501403	+	0.865214i	$0.667182\pi$
$798$	−822714.	−0.0457343
$799$	−3.10297e6	−0.171953
$800$	−2.38592e6	−0.131805
$801$	2.56120e6	0.141047
$802$	−5.95815e6	−0.327096
$803$	5.84972e6	0.320145
$804$	−737877.	−0.0402572
$805$	−2.39651e6	−0.130343
$806$	6.31125e6	0.342198
$807$	1.31778e7	0.712292
$808$	−202329.	−0.0109026
$809$	−2.22200e7	−1.19364	−0.596820	−	0.802375i	$-0.703569\pi$
$809$	−2.22200e7	−1.19364	−0.596820	+	0.802375i	$0.703569\pi$
$810$	−739970.	−0.0396280
$811$	−1.85661e7	−0.991217	−0.495608	−	0.868546i	$-0.665055\pi$
$811$	−1.85661e7	−0.991217	−0.495608	+	0.868546i	$0.665055\pi$
$812$	5.13253e6	0.273175
$813$	−4.24550e6	−0.225270
$814$	−3.12850e6	−0.165491
$815$	1.70994e7	0.901751
$816$	366722.	0.0192802
$817$	−5.05672e6	−0.265042
$818$	−5.60107e6	−0.292676
$819$	2.11808e6	0.110340
$820$	3.25194e6	0.168891
$821$	−1.20615e6	−0.0624516	−0.0312258	−	0.999512i	$-0.509941\pi$
$821$	−1.20615e6	−0.0624516	−0.0312258	+	0.999512i	$0.509941\pi$
$822$	−1.51692e6	−0.0783037
$823$	−1.54322e7	−0.794198	−0.397099	−	0.917776i	$-0.629983\pi$
$823$	−1.54322e7	−0.794198	−0.397099	+	0.917776i	$0.629983\pi$
$824$	−1.03203e7	−0.529510
$825$	1.40751e6	0.0719974
$826$	850080.	0.0433521
$827$	−2.24904e7	−1.14349	−0.571746	−	0.820431i	$-0.693734\pi$
$827$	−2.24904e7	−1.14349	−0.571746	+	0.820431i	$0.693734\pi$
$828$	−1.80428e6	−0.0914592
$829$	6.98091e6	0.352798	0.176399	−	0.984319i	$-0.443555\pi$
$829$	6.98091e6	0.352798	0.176399	+	0.984319i	$0.443555\pi$
$830$	−1.21846e7	−0.613926
$831$	1.49463e6	0.0750810
$832$	−1.75437e6	−0.0878644
$833$	−2.08187e6	−0.103954
$834$	−4.44700e6	−0.221387
$835$	5.85254e6	0.290488
$836$	−401998.	−0.0198934
$837$	−2.68548e6	−0.132497
$838$	−1.73053e7	−0.851273
$839$	4.10027e6	0.201098	0.100549	−	0.994932i	$-0.467940\pi$
$839$	4.10027e6	0.201098	0.100549	+	0.994932i	$0.467940\pi$
$840$	991523.	0.0484847
$841$	7.09661e6	0.345988
$842$	−1.22937e7	−0.597589
$843$	2.33788e7	1.13306
$844$	−9.56860e6	−0.462373
$845$	5.29632e6	0.255172
$846$	−6.31639e6	−0.303419
$847$	9.55735e6	0.457751
$848$	1.24142e6	0.0592828
$849$	1.39811e6	0.0665692
$850$	−1.48344e6	−0.0704242
$851$	−1.62226e7	−0.767885
$852$	−3.37519e6	−0.159294
$853$	−1.22216e7	−0.575115	−0.287557	−	0.957763i	$-0.592843\pi$
$853$	−1.22216e7	−0.575115	−0.287557	+	0.957763i	$0.592843\pi$
$854$	−1628.46	−7.64066e−5 0
$855$	−854909.	−0.0399949
$856$	−3.14289e6	−0.146604
$857$	−4.17465e7	−1.94164	−0.970819	−	0.239815i	$-0.922913\pi$
$857$	−4.17465e7	−1.94164	−0.970819	+	0.239815i	$0.922913\pi$
$858$	1.03495e6	0.0479954
$859$	1.82142e7	0.842224	0.421112	−	0.907009i	$-0.361640\pi$
$859$	1.82142e7	0.842224	0.421112	+	0.907009i	$0.361640\pi$
$860$	6.09429e6	0.280981
$861$	3.96074e6	0.182083
$862$	−4.33405e6	−0.198667
$863$	1.31559e7	0.601305	0.300652	−	0.953734i	$-0.402796\pi$
$863$	1.31559e7	0.601305	0.300652	+	0.953734i	$0.402796\pi$
$864$	746496.	0.0340207
$865$	6.18593e6	0.281103
$866$	−1.68063e7	−0.761511
$867$	−1.25507e7	−0.567049
$868$	3.59840e6	0.162110
$869$	−5.64341e6	−0.253508
$870$	5.33338e6	0.238893
$871$	2.19474e6	0.0980252
$872$	7.92192e6	0.352809
$873$	1.03596e6	0.0460051
$874$	−2.08453e6	−0.0923061
$875$	−9.39020e6	−0.414624
$876$	−1.25500e7	−0.552566
$877$	−1.03845e7	−0.455917	−0.227959	−	0.973671i	$-0.573205\pi$
$877$	−1.03845e7	−0.455917	−0.227959	+	0.973671i	$0.573205\pi$
$878$	−1.03170e7	−0.451665
$879$	3.92858e6	0.171500
$880$	484483.	0.0210898
$881$	−3.63921e7	−1.57967	−0.789837	−	0.613316i	$-0.789835\pi$
$881$	−3.63921e7	−1.57967	−0.789837	+	0.613316i	$0.789835\pi$
$882$	−4.23783e6	−0.183431
$883$	−1.96045e6	−0.0846163	−0.0423082	−	0.999105i	$-0.513471\pi$
$883$	−1.96045e6	−0.0846163	−0.0423082	+	0.999105i	$0.513471\pi$
$884$	−1.09078e6	−0.0469467
$885$	883346.	0.0379117
$886$	6.02774e6	0.257971
$887$	2.48881e7	1.06214	0.531071	−	0.847327i	$-0.321790\pi$
$887$	2.48881e7	1.06214	0.531071	+	0.847327i	$0.321790\pi$
$888$	6.71188e6	0.285635
$889$	−9.10680e6	−0.386466
$890$	−3.56618e6	−0.150914
$891$	−440376.	−0.0185836
$892$	1.67697e7	0.705691
$893$	−7.29750e6	−0.306229
$894$	−5.49603e6	−0.229988
$895$	−1.04547e7	−0.436270
$896$	−1.00027e6	−0.0416242
$897$	5.36664e6	0.222700
$898$	−2.29289e7	−0.948840
$899$	1.93557e7	0.798748
$900$	−3.01968e6	−0.124267
$901$	771849.	0.0316753
$902$	1.93532e6	0.0792019
$903$	7.42261e6	0.302927
$904$	−726590.	−0.0295712
$905$	−1.75900e7	−0.713913
$906$	−4.92780e6	−0.199450
$907$	2.48921e6	0.100472	0.0502359	−	0.998737i	$-0.484003\pi$
$907$	2.48921e6	0.100472	0.0502359	+	0.998737i	$0.484003\pi$
$908$	−3.70830e6	−0.149266
$909$	−256073.	−0.0102791
$910$	−2.94918e6	−0.118059
$911$	−4.60104e6	−0.183679	−0.0918397	−	0.995774i	$-0.529275\pi$
$911$	−4.60104e6	−0.183679	−0.0918397	+	0.995774i	$0.529275\pi$
$912$	862448.	0.0343357
$913$	−7.25138e6	−0.287901
$914$	81992.8	0.00324646
$915$	−1692.18	−6.68181e−5 0
$916$	−8.66916e6	−0.341380
$917$	3.17754e6	0.124787
$918$	464132.	0.0181775
$919$	1.88964e7	0.738058	0.369029	−	0.929418i	$-0.379690\pi$
$919$	1.88964e7	0.738058	0.369029	+	0.929418i	$0.379690\pi$
$920$	2.51225e6	0.0978573
$921$	−1.65922e7	−0.644549
$922$	−1.47130e7	−0.570000
$923$	1.00392e7	0.387877
$924$	590082.	0.0227369
$925$	−2.71505e7	−1.04333
$926$	1.24548e6	0.0477321
$927$	−1.30616e7	−0.499227
$928$	−5.38041e6	−0.205091
$929$	4.35400e7	1.65519	0.827597	−	0.561323i	$-0.189707\pi$
$929$	4.35400e7	1.65519	0.827597	+	0.561323i	$0.189707\pi$
$930$	3.73922e6	0.141766
$931$	−4.89609e6	−0.185129
$932$	2.46025e7	0.927767
$933$	9.06675e6	0.340995
$934$	9.98323e6	0.374459
$935$	301226.	0.0112684
$936$	−2.22038e6	−0.0828394
$937$	1.86768e7	0.694950	0.347475	−	0.937689i	$-0.387039\pi$
$937$	1.86768e7	0.694950	0.347475	+	0.937689i	$0.387039\pi$
$938$	1.25135e6	0.0464377
$939$	−2.02958e7	−0.751177
$940$	8.79484e6	0.324645
$941$	−3.49408e7	−1.28635	−0.643174	−	0.765720i	$-0.722383\pi$
$941$	−3.49408e7	−1.28635	−0.643174	+	0.765720i	$0.722383\pi$
$942$	2.15576e7	0.791539
$943$	1.00354e7	0.367500
$944$	−891136.	−0.0325472
$945$	1.25490e6	0.0457118
$946$	3.62687e6	0.131766
$947$	−8.36562e6	−0.303126	−0.151563	−	0.988448i	$-0.548431\pi$
$947$	−8.36562e6	−0.303126	−0.151563	+	0.988448i	$0.548431\pi$
$948$	1.21074e7	0.437552
$949$	3.73287e7	1.34548
$950$	−3.48872e6	−0.125417
$951$	2.06294e7	0.739664
$952$	−621913.	−0.0222401
$953$	−2.38484e7	−0.850605	−0.425302	−	0.905051i	$-0.639832\pi$
$953$	−2.38484e7	−0.850605	−0.425302	+	0.905051i	$0.639832\pi$
$954$	1.57117e6	0.0558924
$955$	−1.44500e7	−0.512697
$956$	−3.63958e6	−0.128797
$957$	3.17404e6	0.112029
$958$	−7.07303e6	−0.248996
$959$	2.57250e6	0.0903251
$960$	−1.03941e6	−0.0364006
$961$	−1.50589e7	−0.526000
$962$	−1.99638e7	−0.695514
$963$	−3.97772e6	−0.138219
$964$	−874380.	−0.0303045
$965$	−5.44293e6	−0.188154
$966$	3.05982e6	0.105500
$967$	−2.61103e7	−0.897935	−0.448968	−	0.893548i	$-0.648208\pi$
$967$	−2.61103e7	−0.897935	−0.448968	+	0.893548i	$0.648208\pi$
$968$	−1.00189e7	−0.343663
$969$	536225.	0.0183458
$970$	−1.44245e6	−0.0492234
$971$	−624215.	−0.0212465	−0.0106232	−	0.999944i	$-0.503382\pi$
$971$	−624215.	−0.0212465	−0.0106232	+	0.999944i	$0.503382\pi$
$972$	944784.	0.0320750
$973$	7.54155e6	0.255375
$974$	−3.21220e7	−1.08494
$975$	8.98172e6	0.302585
$976$	1707.10	5.73635e−5 0
$977$	1.95190e7	0.654217	0.327109	−	0.944987i	$-0.393926\pi$
$977$	1.95190e7	0.654217	0.327109	+	0.944987i	$0.393926\pi$
$978$	−2.18323e7	−0.729880
$979$	−2.12233e6	−0.0707711
$980$	5.90069e6	0.196263
$981$	1.00262e7	0.332631
$982$	776773.	0.0257049
$983$	−8.47939e6	−0.279886	−0.139943	−	0.990160i	$-0.544692\pi$
$983$	−8.47939e6	−0.279886	−0.139943	+	0.990160i	$0.544692\pi$
$984$	−4.15203e6	−0.136701
$985$	−5.01799e6	−0.164793
$986$	−3.34526e6	−0.109582
$987$	1.07118e7	0.350001
$988$	−2.56526e6	−0.0836064
$989$	1.88069e7	0.611401
$990$	613173.	0.0198836
$991$	−1.59891e7	−0.517179	−0.258590	−	0.965987i	$-0.583258\pi$
$991$	−1.59891e7	−0.517179	−0.258590	+	0.965987i	$0.583258\pi$
$992$	−3.77219e6	−0.121707
$993$	1.01583e7	0.326925
$994$	5.72390e6	0.183749
$995$	−1.41517e7	−0.453159
$996$	1.55571e7	0.496914
$997$	−4.56075e7	−1.45311	−0.726554	−	0.687109i	$-0.758880\pi$
$997$	−4.56075e7	−1.45311	−0.726554	+	0.687109i	$0.758880\pi$
$998$	−3.78654e7	−1.20342
$999$	8.49473e6	0.269300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.b.1.3	✓	4
3.2	odd	2		1062.6.a.b.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.b.1.3	✓	4	1.1	even	1	trivial
1062.6.a.b.1.2		4	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -28.1958 q^{5} +36.0000 q^{6} -61.0514 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -28.1958 q^{5} +36.0000 q^{6} -61.0514 q^{7} +64.0000 q^{8} +81.0000 q^{9} -112.783 q^{10} -67.1203 q^{11} +144.000 q^{12} -428.313 q^{13} -244.206 q^{14} -253.762 q^{15} +256.000 q^{16} +159.167 q^{17} +324.000 q^{18} +374.326 q^{19} -451.133 q^{20} -549.463 q^{21} -268.481 q^{22} -1392.19 q^{23} +576.000 q^{24} -2330.00 q^{25} -1713.25 q^{26} +729.000 q^{27} -976.823 q^{28} -5254.31 q^{29} -1015.05 q^{30} -3683.78 q^{31} +1024.00 q^{32} -604.083 q^{33} +636.669 q^{34} +1721.39 q^{35} +1296.00 q^{36} +11652.6 q^{37} +1497.31 q^{38} -3854.82 q^{39} -1804.53 q^{40} -7208.38 q^{41} -2197.85 q^{42} -13508.9 q^{43} -1073.92 q^{44} -2283.86 q^{45} -5568.76 q^{46} -19495.0 q^{47} +2304.00 q^{48} -13079.7 q^{49} -9319.99 q^{50} +1432.51 q^{51} -6853.01 q^{52} +4849.29 q^{53} +2916.00 q^{54} +1892.51 q^{55} -3907.29 q^{56} +3368.94 q^{57} -21017.2 q^{58} -3481.00 q^{59} -4060.19 q^{60} +6.66838 q^{61} -14735.1 q^{62} -4945.16 q^{63} +4096.00 q^{64} +12076.6 q^{65} -2416.33 q^{66} -5124.15 q^{67} +2546.68 q^{68} -12529.7 q^{69} +6885.57 q^{70} -23438.8 q^{71} +5184.00 q^{72} -87152.9 q^{73} +46610.3 q^{74} -20970.0 q^{75} +5989.22 q^{76} +4097.79 q^{77} -15419.3 q^{78} +84079.1 q^{79} -7218.12 q^{80} +6561.00 q^{81} -28833.5 q^{82} +108036. q^{83} -8791.40 q^{84} -4487.85 q^{85} -54035.4 q^{86} -47288.8 q^{87} -4295.70 q^{88} +31619.8 q^{89} -9135.44 q^{90} +26149.1 q^{91} -22275.0 q^{92} -33154.0 q^{93} -77980.1 q^{94} -10554.4 q^{95} +9216.00 q^{96} +12789.6 q^{97} -52318.9 q^{98} -5436.74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * q^99

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