LMFDB - Embedded newform 354.6.a.c.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:	$5$
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} - 290x^{3} - 616x^{2} + 4720x + 11900 $ x^5 - x^4 - 290x^3 - 616x^2 + 4720*x + 11900
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.22515$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -3.84671 q^{5} -36.0000 q^{6} +56.0281 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -3.84671 q^{5} -36.0000 q^{6} +56.0281 q^{7} -64.0000 q^{8} +81.0000 q^{9} +15.3869 q^{10} +11.9353 q^{11} +144.000 q^{12} -332.703 q^{13} -224.112 q^{14} -34.6204 q^{15} +256.000 q^{16} -542.091 q^{17} -324.000 q^{18} -1034.60 q^{19} -61.5474 q^{20} +504.253 q^{21} -47.7414 q^{22} +2801.09 q^{23} -576.000 q^{24} -3110.20 q^{25} +1330.81 q^{26} +729.000 q^{27} +896.449 q^{28} -7312.03 q^{29} +138.482 q^{30} +6976.21 q^{31} -1024.00 q^{32} +107.418 q^{33} +2168.36 q^{34} -215.524 q^{35} +1296.00 q^{36} -14335.3 q^{37} +4138.40 q^{38} -2994.33 q^{39} +246.190 q^{40} +8937.40 q^{41} -2017.01 q^{42} -7695.38 q^{43} +190.965 q^{44} -311.584 q^{45} -11204.4 q^{46} +2137.88 q^{47} +2304.00 q^{48} -13667.9 q^{49} +12440.8 q^{50} -4878.82 q^{51} -5323.24 q^{52} +12834.6 q^{53} -2916.00 q^{54} -45.9118 q^{55} -3585.80 q^{56} -9311.40 q^{57} +29248.1 q^{58} +3481.00 q^{59} -553.927 q^{60} +15716.6 q^{61} -27904.8 q^{62} +4538.27 q^{63} +4096.00 q^{64} +1279.81 q^{65} -429.672 q^{66} +18747.6 q^{67} -8673.45 q^{68} +25209.8 q^{69} +862.096 q^{70} -33560.5 q^{71} -5184.00 q^{72} -3937.01 q^{73} +57341.2 q^{74} -27991.8 q^{75} -16553.6 q^{76} +668.714 q^{77} +11977.3 q^{78} -58173.8 q^{79} -984.759 q^{80} +6561.00 q^{81} -35749.6 q^{82} +62011.5 q^{83} +8068.04 q^{84} +2085.27 q^{85} +30781.5 q^{86} -65808.2 q^{87} -763.862 q^{88} -49765.1 q^{89} +1246.34 q^{90} -18640.7 q^{91} +44817.5 q^{92} +62785.9 q^{93} -8551.53 q^{94} +3979.81 q^{95} -9216.00 q^{96} -137225. q^{97} +54671.4 q^{98} +966.763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9} + 40 q^{10} - 228 q^{11} + 720 q^{12} - 386 q^{13} + 648 q^{14} - 90 q^{15} + 1280 q^{16} + 1304 q^{17} - 1620 q^{18} + 342 q^{19} - 160 q^{20} - 1458 q^{21} + 912 q^{22} - 78 q^{23} - 2880 q^{24} - 3585 q^{25} + 1544 q^{26} + 3645 q^{27} - 2592 q^{28} - 4576 q^{29} + 360 q^{30} - 14456 q^{31} - 5120 q^{32} - 2052 q^{33} - 5216 q^{34} - 5622 q^{35} + 6480 q^{36} - 21684 q^{37} - 1368 q^{38} - 3474 q^{39} + 640 q^{40} - 15484 q^{41} + 5832 q^{42} - 22094 q^{43} - 3648 q^{44} - 810 q^{45} + 312 q^{46} - 4890 q^{47} + 11520 q^{48} + 3955 q^{49} + 14340 q^{50} + 11736 q^{51} - 6176 q^{52} + 12686 q^{53} - 14580 q^{54} - 40468 q^{55} + 10368 q^{56} + 3078 q^{57} + 18304 q^{58} + 17405 q^{59} - 1440 q^{60} - 17792 q^{61} + 57824 q^{62} - 13122 q^{63} + 20480 q^{64} + 67704 q^{65} + 8208 q^{66} - 33042 q^{67} + 20864 q^{68} - 702 q^{69} + 22488 q^{70} + 16172 q^{71} - 25920 q^{72} - 40092 q^{73} + 86736 q^{74} - 32265 q^{75} + 5472 q^{76} + 33330 q^{77} + 13896 q^{78} - 51216 q^{79} - 2560 q^{80} + 32805 q^{81} + 61936 q^{82} + 7526 q^{83} - 23328 q^{84} - 92546 q^{85} + 88376 q^{86} - 41184 q^{87} + 14592 q^{88} + 4210 q^{89} + 3240 q^{90} - 263742 q^{91} - 1248 q^{92} - 130104 q^{93} + 19560 q^{94} - 220798 q^{95} - 46080 q^{96} - 279974 q^{97} - 15820 q^{98} - 18468 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9 + 40 * q^10 - 228 * q^11 + 720 * q^12 - 386 * q^13 + 648 * q^14 - 90 * q^15 + 1280 * q^16 + 1304 * q^17 - 1620 * q^18 + 342 * q^19 - 160 * q^20 - 1458 * q^21 + 912 * q^22 - 78 * q^23 - 2880 * q^24 - 3585 * q^25 + 1544 * q^26 + 3645 * q^27 - 2592 * q^28 - 4576 * q^29 + 360 * q^30 - 14456 * q^31 - 5120 * q^32 - 2052 * q^33 - 5216 * q^34 - 5622 * q^35 + 6480 * q^36 - 21684 * q^37 - 1368 * q^38 - 3474 * q^39 + 640 * q^40 - 15484 * q^41 + 5832 * q^42 - 22094 * q^43 - 3648 * q^44 - 810 * q^45 + 312 * q^46 - 4890 * q^47 + 11520 * q^48 + 3955 * q^49 + 14340 * q^50 + 11736 * q^51 - 6176 * q^52 + 12686 * q^53 - 14580 * q^54 - 40468 * q^55 + 10368 * q^56 + 3078 * q^57 + 18304 * q^58 + 17405 * q^59 - 1440 * q^60 - 17792 * q^61 + 57824 * q^62 - 13122 * q^63 + 20480 * q^64 + 67704 * q^65 + 8208 * q^66 - 33042 * q^67 + 20864 * q^68 - 702 * q^69 + 22488 * q^70 + 16172 * q^71 - 25920 * q^72 - 40092 * q^73 + 86736 * q^74 - 32265 * q^75 + 5472 * q^76 + 33330 * q^77 + 13896 * q^78 - 51216 * q^79 - 2560 * q^80 + 32805 * q^81 + 61936 * q^82 + 7526 * q^83 - 23328 * q^84 - 92546 * q^85 + 88376 * q^86 - 41184 * q^87 + 14592 * q^88 + 4210 * q^89 + 3240 * q^90 - 263742 * q^91 - 1248 * q^92 - 130104 * q^93 + 19560 * q^94 - 220798 * q^95 - 46080 * q^96 - 279974 * q^97 - 15820 * q^98 - 18468 * 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
$5$	−3.84671	−0.0688121	−0.0344061	−	0.999408i	$-0.510954\pi$
$5$	−3.84671	−0.0688121	−0.0344061	+	0.999408i	$0.510954\pi$
$6$	−36.0000	−0.408248
$7$	56.0281	0.432176	0.216088	−	0.976374i	$-0.430670\pi$
$7$	56.0281	0.432176	0.216088	+	0.976374i	$0.430670\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	15.3869	0.0486575
$11$	11.9353	0.0297408	0.0148704	−	0.999889i	$-0.495266\pi$
$11$	11.9353	0.0297408	0.0148704	+	0.999889i	$0.495266\pi$
$12$	144.000	0.288675
$13$	−332.703	−0.546007	−0.273003	−	0.962013i	$-0.588017\pi$
$13$	−332.703	−0.546007	−0.273003	+	0.962013i	$0.588017\pi$
$14$	−224.112	−0.305594
$15$	−34.6204	−0.0397287
$16$	256.000	0.250000
$17$	−542.091	−0.454935	−0.227468	−	0.973786i	$-0.573045\pi$
$17$	−542.091	−0.454935	−0.227468	+	0.973786i	$0.573045\pi$
$18$	−324.000	−0.235702
$19$	−1034.60	−0.657489	−0.328745	−	0.944419i	$-0.606626\pi$
$19$	−1034.60	−0.657489	−0.328745	+	0.944419i	$0.606626\pi$
$20$	−61.5474	−0.0344061
$21$	504.253	0.249517
$22$	−47.7414	−0.0210299
$23$	2801.09	1.10410	0.552049	−	0.833812i	$-0.313846\pi$
$23$	2801.09	1.10410	0.552049	+	0.833812i	$0.313846\pi$
$24$	−576.000	−0.204124
$25$	−3110.20	−0.995265
$26$	1330.81	0.386085
$27$	729.000	0.192450
$28$	896.449	0.216088
$29$	−7312.03	−1.61452	−0.807259	−	0.590197i	$-0.799050\pi$
$29$	−7312.03	−1.61452	−0.807259	+	0.590197i	$0.799050\pi$
$30$	138.482	0.0280924
$31$	6976.21	1.30381	0.651907	−	0.758299i	$-0.273969\pi$
$31$	6976.21	1.30381	0.651907	+	0.758299i	$0.273969\pi$
$32$	−1024.00	−0.176777
$33$	107.418	0.0171709
$34$	2168.36	0.321688
$35$	−215.524	−0.0297389
$36$	1296.00	0.166667
$37$	−14335.3	−1.72148	−0.860742	−	0.509042i	$-0.830000\pi$
$37$	−14335.3	−1.72148	−0.860742	+	0.509042i	$0.830000\pi$
$38$	4138.40	0.464915
$39$	−2994.33	−0.315237
$40$	246.190	0.0243288
$41$	8937.40	0.830332	0.415166	−	0.909746i	$-0.363724\pi$
$41$	8937.40	0.830332	0.415166	+	0.909746i	$0.363724\pi$
$42$	−2017.01	−0.176435
$43$	−7695.38	−0.634686	−0.317343	−	0.948311i	$-0.602791\pi$
$43$	−7695.38	−0.634686	−0.317343	+	0.948311i	$0.602791\pi$
$44$	190.965	0.0148704
$45$	−311.584	−0.0229374
$46$	−11204.4	−0.780715
$47$	2137.88	0.141169	0.0705845	−	0.997506i	$-0.477514\pi$
$47$	2137.88	0.141169	0.0705845	+	0.997506i	$0.477514\pi$
$48$	2304.00	0.144338
$49$	−13667.9	−0.813224
$50$	12440.8	0.703759
$51$	−4878.82	−0.262657
$52$	−5323.24	−0.273003
$53$	12834.6	0.627616	0.313808	−	0.949486i	$-0.398395\pi$
$53$	12834.6	0.627616	0.313808	+	0.949486i	$0.398395\pi$
$54$	−2916.00	−0.136083
$55$	−45.9118	−0.00204653
$56$	−3585.80	−0.152797
$57$	−9311.40	−0.379601
$58$	29248.1	1.14164
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−553.927	−0.0198644
$61$	15716.6	0.540797	0.270398	−	0.962749i	$-0.412845\pi$
$61$	15716.6	0.540797	0.270398	+	0.962749i	$0.412845\pi$
$62$	−27904.8	−0.921935
$63$	4538.27	0.144059
$64$	4096.00	0.125000
$65$	1279.81	0.0375719
$66$	−429.672	−0.0121416
$67$	18747.6	0.510220	0.255110	−	0.966912i	$-0.417888\pi$
$67$	18747.6	0.510220	0.255110	+	0.966912i	$0.417888\pi$
$68$	−8673.45	−0.227468
$69$	25209.8	0.637451
$70$	862.096	0.0210286
$71$	−33560.5	−0.790100	−0.395050	−	0.918660i	$-0.629273\pi$
$71$	−33560.5	−0.790100	−0.395050	+	0.918660i	$0.629273\pi$
$72$	−5184.00	−0.117851
$73$	−3937.01	−0.0864687	−0.0432344	−	0.999065i	$-0.513766\pi$
$73$	−3937.01	−0.0864687	−0.0432344	+	0.999065i	$0.513766\pi$
$74$	57341.2	1.21727
$75$	−27991.8	−0.574616
$76$	−16553.6	−0.328745
$77$	668.714	0.0128533
$78$	11977.3	0.222906
$79$	−58173.8	−1.04872	−0.524360	−	0.851497i	$-0.675695\pi$
$79$	−58173.8	−1.04872	−0.524360	+	0.851497i	$0.675695\pi$
$80$	−984.759	−0.0172030
$81$	6561.00	0.111111
$82$	−35749.6	−0.587133
$83$	62011.5	0.988046	0.494023	−	0.869449i	$-0.335526\pi$
$83$	62011.5	0.988046	0.494023	+	0.869449i	$0.335526\pi$
$84$	8068.04	0.124758
$85$	2085.27	0.0313051
$86$	30781.5	0.448791
$87$	−65808.2	−0.932142
$88$	−763.862	−0.0105150
$89$	−49765.1	−0.665962	−0.332981	−	0.942933i	$-0.608055\pi$
$89$	−49765.1	−0.665962	−0.332981	+	0.942933i	$0.608055\pi$
$90$	1246.34	0.0162192
$91$	−18640.7	−0.235971
$92$	44817.5	0.552049
$93$	62785.9	0.752757
$94$	−8551.53	−0.0998215
$95$	3979.81	0.0452432
$96$	−9216.00	−0.102062
$97$	−137225.	−1.48082	−0.740412	−	0.672153i	$-0.765370\pi$
$97$	−137225.	−1.48082	−0.740412	+	0.672153i	$0.765370\pi$
$98$	54671.4	0.575036
$99$	966.763	0.00991361
$100$	−49763.2	−0.497632
$101$	2248.79	0.0219354	0.0109677	−	0.999940i	$-0.496509\pi$
$101$	2248.79	0.0219354	0.0109677	+	0.999940i	$0.496509\pi$
$102$	19515.3	0.185727
$103$	24776.8	0.230119	0.115059	−	0.993359i	$-0.463294\pi$
$103$	24776.8	0.230119	0.115059	+	0.993359i	$0.463294\pi$
$104$	21293.0	0.193043
$105$	−1939.72	−0.0171698
$106$	−51338.6	−0.443792
$107$	−132705.	−1.12054	−0.560271	−	0.828310i	$-0.689303\pi$
$107$	−132705.	−1.12054	−0.560271	+	0.828310i	$0.689303\pi$
$108$	11664.0	0.0962250
$109$	−118241.	−0.953237	−0.476618	−	0.879110i	$-0.658138\pi$
$109$	−118241.	−0.953237	−0.476618	+	0.879110i	$0.658138\pi$
$110$	183.647	0.00144712
$111$	−129018.	−0.993899
$112$	14343.2	0.108044
$113$	−194270.	−1.43123	−0.715616	−	0.698494i	$-0.753854\pi$
$113$	−194270.	−1.43123	−0.715616	+	0.698494i	$0.753854\pi$
$114$	37245.6	0.268419
$115$	−10775.0	−0.0759754
$116$	−116992.	−0.807259
$117$	−26948.9	−0.182002
$118$	−13924.0	−0.0920575
$119$	−30372.3	−0.196612
$120$	2215.71	0.0140462
$121$	−160909.	−0.999115
$122$	−62866.4	−0.382401
$123$	80436.6	0.479392
$124$	111619.	0.651907
$125$	23985.0	0.137298
$126$	−18153.1	−0.101865
$127$	−165554.	−0.910818	−0.455409	−	0.890282i	$-0.650507\pi$
$127$	−165554.	−0.910818	−0.455409	+	0.890282i	$0.650507\pi$
$128$	−16384.0	−0.0883883
$129$	−69258.4	−0.366436
$130$	−5119.25	−0.0265673
$131$	222967.	1.13518	0.567588	−	0.823313i	$-0.307877\pi$
$131$	222967.	1.13518	0.567588	+	0.823313i	$0.307877\pi$
$132$	1718.69	0.00858544
$133$	−57966.6	−0.284151
$134$	−74990.3	−0.360780
$135$	−2804.26	−0.0132429
$136$	34693.8	0.160844
$137$	−332097.	−1.51169	−0.755846	−	0.654750i	$-0.772774\pi$
$137$	−332097.	−1.51169	−0.755846	+	0.654750i	$0.772774\pi$
$138$	−100839.	−0.450746
$139$	112233.	0.492701	0.246351	−	0.969181i	$-0.420769\pi$
$139$	112233.	0.492701	0.246351	+	0.969181i	$0.420769\pi$
$140$	−3448.38	−0.0148695
$141$	19240.9	0.0815039
$142$	134242.	0.558685
$143$	−3970.92	−0.0162387
$144$	20736.0	0.0833333
$145$	28127.3	0.111098
$146$	15748.0	0.0611426
$147$	−123011.	−0.469515
$148$	−229365.	−0.860742
$149$	−411071.	−1.51688	−0.758440	−	0.651743i	$-0.774038\pi$
$149$	−411071.	−1.51688	−0.758440	+	0.651743i	$0.774038\pi$
$150$	111967.	0.406315
$151$	−415434.	−1.48272	−0.741362	−	0.671106i	$-0.765820\pi$
$151$	−415434.	−1.48272	−0.741362	+	0.671106i	$0.765820\pi$
$152$	66214.4	0.232457
$153$	−43909.3	−0.151645
$154$	−2674.86	−0.00908863
$155$	−26835.5	−0.0897182
$156$	−47909.2	−0.157619
$157$	−235393.	−0.762157	−0.381078	−	0.924543i	$-0.624447\pi$
$157$	−235393.	−0.762157	−0.381078	+	0.924543i	$0.624447\pi$
$158$	232695.	0.741557
$159$	115512.	0.362354
$160$	3939.04	0.0121644
$161$	156940.	0.477165
$162$	−26244.0	−0.0785674
$163$	−665502.	−1.96192	−0.980958	−	0.194218i	$-0.937783\pi$
$163$	−665502.	−1.96192	−0.980958	+	0.194218i	$0.937783\pi$
$164$	142998.	0.415166
$165$	−413.207	−0.00118156
$166$	−248046.	−0.698654
$167$	605932.	1.68125	0.840626	−	0.541616i	$-0.182187\pi$
$167$	605932.	1.68125	0.840626	+	0.541616i	$0.182187\pi$
$168$	−32272.2	−0.0882175
$169$	−260602.	−0.701877
$170$	−8341.07	−0.0221360
$171$	−83802.6	−0.219163
$172$	−123126.	−0.317343
$173$	373287.	0.948261	0.474131	−	0.880454i	$-0.342762\pi$
$173$	373287.	0.948261	0.474131	+	0.880454i	$0.342762\pi$
$174$	263233.	0.659124
$175$	−174259.	−0.430129
$176$	3055.45	0.00743521
$177$	31329.0	0.0751646
$178$	199060.	0.470907
$179$	94160.1	0.219652	0.109826	−	0.993951i	$-0.464971\pi$
$179$	94160.1	0.219652	0.109826	+	0.993951i	$0.464971\pi$
$180$	−4985.34	−0.0114687
$181$	609176.	1.38212	0.691061	−	0.722797i	$-0.257144\pi$
$181$	609176.	1.38212	0.691061	+	0.722797i	$0.257144\pi$
$182$	74562.8	0.166857
$183$	141449.	0.312229
$184$	−179270.	−0.390358
$185$	55143.9	0.118459
$186$	−251144.	−0.532280
$187$	−6470.04	−0.0135302
$188$	34206.1	0.0705845
$189$	40844.5	0.0831723
$190$	−15919.2	−0.0319918
$191$	−513137.	−1.01777	−0.508886	−	0.860834i	$-0.669942\pi$
$191$	−513137.	−1.01777	−0.508886	+	0.860834i	$0.669942\pi$
$192$	36864.0	0.0721688
$193$	−45011.2	−0.0869815	−0.0434908	−	0.999054i	$-0.513848\pi$
$193$	−45011.2	−0.0869815	−0.0434908	+	0.999054i	$0.513848\pi$
$194$	548900.	1.04710
$195$	11518.3	0.0216921
$196$	−218686.	−0.406612
$197$	765004.	1.40442	0.702212	−	0.711968i	$-0.252196\pi$
$197$	765004.	1.40442	0.702212	+	0.711968i	$0.252196\pi$
$198$	−3867.05	−0.00700998
$199$	592525.	1.06066	0.530328	−	0.847793i	$-0.322069\pi$
$199$	592525.	1.06066	0.530328	+	0.847793i	$0.322069\pi$
$200$	199053.	0.351879
$201$	168728.	0.294576
$202$	−8995.17	−0.0155107
$203$	−409679.	−0.697756
$204$	−78061.1	−0.131329
$205$	−34379.6	−0.0571369
$206$	−99107.1	−0.162718
$207$	226888.	0.368033
$208$	−85171.9	−0.136502
$209$	−12348.3	−0.0195543
$210$	7758.86	0.0121409
$211$	942164.	1.45687	0.728435	−	0.685115i	$-0.240248\pi$
$211$	942164.	1.45687	0.728435	+	0.685115i	$0.240248\pi$
$212$	205354.	0.313808
$213$	−302044.	−0.456165
$214$	530820.	0.792342
$215$	29601.9	0.0436741
$216$	−46656.0	−0.0680414
$217$	390864.	0.563477
$218$	472963.	0.674040
$219$	−35433.1	−0.0499227
$220$	−734.590	−0.00102326
$221$	180355.	0.248398
$222$	516071.	0.702793
$223$	−834107.	−1.12321	−0.561603	−	0.827407i	$-0.689815\pi$
$223$	−834107.	−1.12321	−0.561603	+	0.827407i	$0.689815\pi$
$224$	−57372.7	−0.0763986
$225$	−251926.	−0.331755
$226$	777081.	1.01203
$227$	−160293.	−0.206467	−0.103233	−	0.994657i	$-0.532919\pi$
$227$	−160293.	−0.206467	−0.103233	+	0.994657i	$0.532919\pi$
$228$	−148982.	−0.189801
$229$	−1.45056e6	−1.82787	−0.913937	−	0.405857i	$-0.866973\pi$
$229$	−1.45056e6	−1.82787	−0.913937	+	0.405857i	$0.866973\pi$
$230$	43100.0	0.0537227
$231$	6018.43	0.00742084
$232$	467970.	0.570818
$233$	29109.3	0.0351271	0.0175635	−	0.999846i	$-0.494409\pi$
$233$	29109.3	0.0351271	0.0175635	+	0.999846i	$0.494409\pi$
$234$	107796.	0.128695
$235$	−8223.82	−0.00971414
$236$	55696.0	0.0650945
$237$	−523564.	−0.605479
$238$	121489.	0.139026
$239$	652150.	0.738504	0.369252	−	0.929329i	$-0.379614\pi$
$239$	652150.	0.738504	0.369252	+	0.929329i	$0.379614\pi$
$240$	−8862.83	−0.00993218
$241$	−62780.9	−0.0696281	−0.0348141	−	0.999394i	$-0.511084\pi$
$241$	−62780.9	−0.0696281	−0.0348141	+	0.999394i	$0.511084\pi$
$242$	643634.	0.706481
$243$	59049.0	0.0641500
$244$	251466.	0.270398
$245$	52576.3	0.0559597
$246$	−321746.	−0.338982
$247$	344214.	0.358993
$248$	−446478.	−0.460968
$249$	558104.	0.570449
$250$	−95940.2	−0.0970846
$251$	951482.	0.953271	0.476636	−	0.879101i	$-0.341856\pi$
$251$	951482.	0.953271	0.476636	+	0.879101i	$0.341856\pi$
$252$	72612.4	0.0720293
$253$	33432.0	0.0328368
$254$	662218.	0.644046
$255$	18767.4	0.0180740
$256$	65536.0	0.0625000
$257$	1.82587e6	1.72440	0.862199	−	0.506570i	$-0.169087\pi$
$257$	1.82587e6	1.72440	0.862199	+	0.506570i	$0.169087\pi$
$258$	277034.	0.259109
$259$	−803180.	−0.743983
$260$	20477.0	0.0187859
$261$	−592274.	−0.538173
$262$	−891869.	−0.802690
$263$	1.79365e6	1.59900	0.799500	−	0.600666i	$-0.205098\pi$
$263$	1.79365e6	1.59900	0.799500	+	0.600666i	$0.205098\pi$
$264$	−6874.76	−0.00607082
$265$	−49371.2	−0.0431876
$266$	231867.	0.200925
$267$	−447886.	−0.384494
$268$	299961.	0.255110
$269$	1.18796e6	1.00097	0.500485	−	0.865745i	$-0.333155\pi$
$269$	1.18796e6	1.00097	0.500485	+	0.865745i	$0.333155\pi$
$270$	11217.0	0.00936414
$271$	1.40374e6	1.16109	0.580543	−	0.814230i	$-0.302840\pi$
$271$	1.40374e6	1.16109	0.580543	+	0.814230i	$0.302840\pi$
$272$	−138775.	−0.113734
$273$	−167766.	−0.136238
$274$	1.32839e6	1.06893
$275$	−37121.3	−0.0296000
$276$	403357.	0.318726
$277$	−72688.1	−0.0569199	−0.0284599	−	0.999595i	$-0.509060\pi$
$277$	−72688.1	−0.0569199	−0.0284599	+	0.999595i	$0.509060\pi$
$278$	−448932.	−0.348392
$279$	565073.	0.434604
$280$	13793.5	0.0105143
$281$	−2.26275e6	−1.70950	−0.854751	−	0.519038i	$-0.826290\pi$
$281$	−2.26275e6	−1.70950	−0.854751	+	0.519038i	$0.826290\pi$
$282$	−76963.8	−0.0576320
$283$	−244837.	−0.181723	−0.0908616	−	0.995864i	$-0.528962\pi$
$283$	−244837.	−0.181723	−0.0908616	+	0.995864i	$0.528962\pi$
$284$	−536967.	−0.395050
$285$	35818.3	0.0261212
$286$	15883.7	0.0114825
$287$	500745.	0.358849
$288$	−82944.0	−0.0589256
$289$	−1.12599e6	−0.793034
$290$	−112509.	−0.0785584
$291$	−1.23502e6	−0.854954
$292$	−62992.1	−0.0432344
$293$	869270.	0.591542	0.295771	−	0.955259i	$-0.404423\pi$
$293$	869270.	0.591542	0.295771	+	0.955259i	$0.404423\pi$
$294$	492043.	0.331997
$295$	−13390.4	−0.00895858
$296$	917460.	0.608636
$297$	8700.86	0.00572363
$298$	1.64428e6	1.07260
$299$	−931931.	−0.602845
$300$	−447869.	−0.287308
$301$	−431157.	−0.274296
$302$	1.66174e6	1.04844
$303$	20239.1	0.0126644
$304$	−264858.	−0.164372
$305$	−60457.3	−0.0372134
$306$	175637.	0.107229
$307$	1.90712e6	1.15486	0.577432	−	0.816439i	$-0.304055\pi$
$307$	1.90712e6	1.15486	0.577432	+	0.816439i	$0.304055\pi$
$308$	10699.4	0.00642663
$309$	222991.	0.132859
$310$	107342.	0.0634403
$311$	−1.95290e6	−1.14493	−0.572465	−	0.819929i	$-0.694013\pi$
$311$	−1.95290e6	−1.14493	−0.572465	+	0.819929i	$0.694013\pi$
$312$	191637.	0.111453
$313$	−915889.	−0.528423	−0.264212	−	0.964465i	$-0.585112\pi$
$313$	−915889.	−0.528423	−0.264212	+	0.964465i	$0.585112\pi$
$314$	941572.	0.538926
$315$	−17457.4	−0.00991298
$316$	−930781.	−0.524360
$317$	732828.	0.409594	0.204797	−	0.978804i	$-0.434346\pi$
$317$	732828.	0.409594	0.204797	+	0.978804i	$0.434346\pi$
$318$	−462047.	−0.256223
$319$	−87271.5	−0.0480171
$320$	−15756.1	−0.00860152
$321$	−1.19434e6	−0.646945
$322$	−627759.	−0.337406
$323$	560847.	0.299115
$324$	104976.	0.0555556
$325$	1.03477e6	0.543421
$326$	2.66201e6	1.38728
$327$	−1.06417e6	−0.550351
$328$	−571994.	−0.293567
$329$	119781.	0.0610098
$330$	1652.83	0.000835492 0
$331$	1.54652e6	0.775862	0.387931	−	0.921688i	$-0.373190\pi$
$331$	1.54652e6	0.775862	0.387931	+	0.921688i	$0.373190\pi$
$332$	992185.	0.494023
$333$	−1.16116e6	−0.573828
$334$	−2.42373e6	−1.18882
$335$	−72116.5	−0.0351094
$336$	129089.	0.0623792
$337$	1.72789e6	0.828785	0.414393	−	0.910098i	$-0.363994\pi$
$337$	1.72789e6	0.828785	0.414393	+	0.910098i	$0.363994\pi$
$338$	1.04241e6	0.496302
$339$	−1.74843e6	−0.826322
$340$	33364.3	0.0156525
$341$	83263.5	0.0387765
$342$	335210.	0.154972
$343$	−1.70745e6	−0.783632
$344$	492504.	0.224395
$345$	−96975.0	−0.0438644
$346$	−1.49315e6	−0.670522
$347$	1.69181e6	0.754272	0.377136	−	0.926158i	$-0.376909\pi$
$347$	1.69181e6	0.754272	0.377136	+	0.926158i	$0.376909\pi$
$348$	−1.05293e6	−0.466071
$349$	−703883.	−0.309340	−0.154670	−	0.987966i	$-0.549431\pi$
$349$	−703883.	−0.309340	−0.154670	+	0.987966i	$0.549431\pi$
$350$	697035.	0.304147
$351$	−242540.	−0.105079
$352$	−12221.8	−0.00525749
$353$	907096.	0.387451	0.193725	−	0.981056i	$-0.437943\pi$
$353$	907096.	0.387451	0.193725	+	0.981056i	$0.437943\pi$
$354$	−125316.	−0.0531494
$355$	129098.	0.0543685
$356$	−796241.	−0.332981
$357$	−273351.	−0.113514
$358$	−376641.	−0.155317
$359$	−3.02098e6	−1.23712	−0.618560	−	0.785738i	$-0.712283\pi$
$359$	−3.02098e6	−1.23712	−0.618560	+	0.785738i	$0.712283\pi$
$360$	19941.4	0.00810959
$361$	−1.40570e6	−0.567708
$362$	−2.43670e6	−0.977307
$363$	−1.44818e6	−0.576840
$364$	−298251.	−0.117985
$365$	15144.5	0.00595010
$366$	−565798.	−0.220779
$367$	−3.28381e6	−1.27266	−0.636331	−	0.771416i	$-0.719549\pi$
$367$	−3.28381e6	−1.27266	−0.636331	+	0.771416i	$0.719549\pi$
$368$	717079.	0.276025
$369$	723930.	0.276777
$370$	−220575.	−0.0837631
$371$	719100.	0.271241
$372$	1.00457e6	0.376378
$373$	−362447.	−0.134888	−0.0674439	−	0.997723i	$-0.521484\pi$
$373$	−362447.	−0.134888	−0.0674439	+	0.997723i	$0.521484\pi$
$374$	25880.1	0.00956726
$375$	215865.	0.0792693
$376$	−136824.	−0.0499108
$377$	2.43273e6	0.881538
$378$	−163378.	−0.0588117
$379$	5.30531e6	1.89720	0.948600	−	0.316479i	$-0.102501\pi$
$379$	5.30531e6	1.89720	0.948600	+	0.316479i	$0.102501\pi$
$380$	63677.0	0.0226216
$381$	−1.48999e6	−0.525861
$382$	2.05255e6	0.719673
$383$	−1.96109e6	−0.683126	−0.341563	−	0.939859i	$-0.610956\pi$
$383$	−1.96109e6	−0.683126	−0.341563	+	0.939859i	$0.610956\pi$
$384$	−147456.	−0.0510310
$385$	−2572.35	−0.000884461 0
$386$	180045.	0.0615052
$387$	−623325.	−0.211562
$388$	−2.19560e6	−0.740412
$389$	−1.17218e6	−0.392753	−0.196376	−	0.980529i	$-0.562917\pi$
$389$	−1.17218e6	−0.392753	−0.196376	+	0.980529i	$0.562917\pi$
$390$	−46073.3	−0.0153387
$391$	−1.51845e6	−0.502293
$392$	874743.	0.287518
$393$	2.00671e6	0.655394
$394$	−3.06001e6	−0.993077
$395$	223778.	0.0721647
$396$	15468.2	0.00495680
$397$	−4.60634e6	−1.46683	−0.733415	−	0.679781i	$-0.762075\pi$
$397$	−4.60634e6	−1.46683	−0.733415	+	0.679781i	$0.762075\pi$
$398$	−2.37010e6	−0.749996
$399$	−521700.	−0.164055
$400$	−796212.	−0.248816
$401$	405384.	0.125894	0.0629472	−	0.998017i	$-0.479950\pi$
$401$	405384.	0.125894	0.0629472	+	0.998017i	$0.479950\pi$
$402$	−674912.	−0.208297
$403$	−2.32101e6	−0.711891
$404$	35980.7	0.0109677
$405$	−25238.3	−0.00764579
$406$	1.63871e6	0.493388
$407$	−171097.	−0.0511983
$408$	312244.	0.0928633
$409$	2.78581e6	0.823461	0.411730	−	0.911306i	$-0.364925\pi$
$409$	2.78581e6	0.823461	0.411730	+	0.911306i	$0.364925\pi$
$410$	137519.	0.0404019
$411$	−2.98887e6	−0.872775
$412$	396428.	0.115059
$413$	195034.	0.0562645
$414$	−907554.	−0.260238
$415$	−238541.	−0.0679896
$416$	340688.	0.0965213
$417$	1.01010e6	0.284461
$418$	49393.2	0.0138270
$419$	349547.	0.0972682	0.0486341	−	0.998817i	$-0.484513\pi$
$419$	349547.	0.0972682	0.0486341	+	0.998817i	$0.484513\pi$
$420$	−31035.5	−0.00858489
$421$	6.25957e6	1.72123	0.860616	−	0.509254i	$-0.170079\pi$
$421$	6.25957e6	1.72123	0.860616	+	0.509254i	$0.170079\pi$
$422$	−3.76866e6	−1.03016
$423$	173168.	0.0470563
$424$	−821417.	−0.221896
$425$	1.68601e6	0.452781
$426$	1.20818e6	0.322557
$427$	880571.	0.233719
$428$	−2.12328e6	−0.560271
$429$	−35738.3	−0.00937542
$430$	−118408.	−0.0308822
$431$	−2.14092e6	−0.555145	−0.277572	−	0.960705i	$-0.589530\pi$
$431$	−2.14092e6	−0.555145	−0.277572	+	0.960705i	$0.589530\pi$
$432$	186624.	0.0481125
$433$	−2.50951e6	−0.643234	−0.321617	−	0.946870i	$-0.604226\pi$
$433$	−2.50951e6	−0.643234	−0.321617	+	0.946870i	$0.604226\pi$
$434$	−1.56345e6	−0.398438
$435$	253146.	0.0641427
$436$	−1.89185e6	−0.476618
$437$	−2.89801e6	−0.725933
$438$	141732.	0.0353007
$439$	1.07166e6	0.265398	0.132699	−	0.991156i	$-0.457636\pi$
$439$	1.07166e6	0.265398	0.132699	+	0.991156i	$0.457636\pi$
$440$	2938.36	0.000723558 0
$441$	−1.10710e6	−0.271075
$442$	−721420.	−0.175644
$443$	7.83320e6	1.89640	0.948199	−	0.317676i	$-0.102902\pi$
$443$	7.83320e6	1.89640	0.948199	+	0.317676i	$0.102902\pi$
$444$	−2.06428e6	−0.496949
$445$	191432.	0.0458263
$446$	3.33643e6	0.794227
$447$	−3.69964e6	−0.875771
$448$	229491.	0.0540220
$449$	−1.13368e6	−0.265384	−0.132692	−	0.991157i	$-0.542362\pi$
$449$	−1.13368e6	−0.265384	−0.132692	+	0.991157i	$0.542362\pi$
$450$	1.00771e6	0.234586
$451$	106671.	0.0246948
$452$	−3.10832e6	−0.715616
$453$	−3.73891e6	−0.856051
$454$	641172.	0.145994
$455$	71705.4	0.0162377
$456$	595930.	0.134209
$457$	5.90765e6	1.32320	0.661599	−	0.749858i	$-0.269878\pi$
$457$	5.90765e6	1.32320	0.661599	+	0.749858i	$0.269878\pi$
$458$	5.80223e6	1.29250
$459$	−395184.	−0.0875523
$460$	−172400.	−0.0379877
$461$	5.61621e6	1.23081	0.615405	−	0.788211i	$-0.288993\pi$
$461$	5.61621e6	1.23081	0.615405	+	0.788211i	$0.288993\pi$
$462$	−24073.7	−0.00524732
$463$	−647744.	−0.140427	−0.0702136	−	0.997532i	$-0.522368\pi$
$463$	−647744.	−0.140427	−0.0702136	+	0.997532i	$0.522368\pi$
$464$	−1.87188e6	−0.403629
$465$	−241519.	−0.0517988
$466$	−116437.	−0.0248386
$467$	−2.37034e6	−0.502942	−0.251471	−	0.967865i	$-0.580914\pi$
$467$	−2.37034e6	−0.502942	−0.251471	+	0.967865i	$0.580914\pi$
$468$	−431183.	−0.0910011
$469$	1.05039e6	0.220505
$470$	32895.3	0.00686893
$471$	−2.11854e6	−0.440031
$472$	−222784.	−0.0460287
$473$	−91846.9	−0.0188761
$474$	2.09426e6	0.428138
$475$	3.21782e6	0.654376
$476$	−485957.	−0.0983060
$477$	1.03961e6	0.209205
$478$	−2.60860e6	−0.522201
$479$	9.37809e6	1.86756	0.933782	−	0.357843i	$-0.116488\pi$
$479$	9.37809e6	1.86756	0.933782	+	0.357843i	$0.116488\pi$
$480$	35451.3	0.00702311
$481$	4.76940e6	0.939942
$482$	251123.	0.0492345
$483$	1.41246e6	0.275491
$484$	−2.57454e6	−0.499558
$485$	527865.	0.101899
$486$	−236196.	−0.0453609
$487$	−5.99993e6	−1.14637	−0.573183	−	0.819427i	$-0.694292\pi$
$487$	−5.99993e6	−1.14637	−0.573183	+	0.819427i	$0.694292\pi$
$488$	−1.00586e6	−0.191201
$489$	−5.98952e6	−1.13271
$490$	−210305.	−0.0395695
$491$	361791.	0.0677258	0.0338629	−	0.999426i	$-0.489219\pi$
$491$	361791.	0.0677258	0.0338629	+	0.999426i	$0.489219\pi$
$492$	1.28699e6	0.239696
$493$	3.96378e6	0.734501
$494$	−1.37686e6	−0.253847
$495$	−3718.86	−0.000682177 0
$496$	1.78591e6	0.325953
$497$	−1.88033e6	−0.341462
$498$	−2.23242e6	−0.403368
$499$	−1.36591e6	−0.245568	−0.122784	−	0.992433i	$-0.539182\pi$
$499$	−1.36591e6	−0.245568	−0.122784	+	0.992433i	$0.539182\pi$
$500$	383761.	0.0686492
$501$	5.45339e6	0.970672
$502$	−3.80593e6	−0.674064
$503$	−1.04525e7	−1.84204	−0.921020	−	0.389514i	$-0.872643\pi$
$503$	−1.04525e7	−1.84204	−0.921020	+	0.389514i	$0.872643\pi$
$504$	−290449.	−0.0509324
$505$	−8650.46	−0.00150942
$506$	−133728.	−0.0232191
$507$	−2.34542e6	−0.405229
$508$	−2.64887e6	−0.455409
$509$	−2.22371e6	−0.380437	−0.190219	−	0.981742i	$-0.560920\pi$
$509$	−2.22371e6	−0.380437	−0.190219	+	0.981742i	$0.560920\pi$
$510$	−75069.7	−0.0127802
$511$	−220583.	−0.0373697
$512$	−262144.	−0.0441942
$513$	−754223.	−0.126534
$514$	−7.30348e6	−1.21933
$515$	−95309.2	−0.0158349
$516$	−1.10813e6	−0.183218
$517$	25516.4	0.00419848
$518$	3.21272e6	0.526076
$519$	3.35959e6	0.547479
$520$	−81908.0	−0.0132837
$521$	−4.81180e6	−0.776628	−0.388314	−	0.921527i	$-0.626942\pi$
$521$	−4.81180e6	−0.776628	−0.388314	+	0.921527i	$0.626942\pi$
$522$	2.36910e6	0.380545
$523$	−1.48640e6	−0.237620	−0.118810	−	0.992917i	$-0.537908\pi$
$523$	−1.48640e6	−0.237620	−0.118810	+	0.992917i	$0.537908\pi$
$524$	3.56748e6	0.567588
$525$	−1.56833e6	−0.248335
$526$	−7.17460e6	−1.13066
$527$	−3.78174e6	−0.593151
$528$	27499.0	0.00429272
$529$	1.40977e6	0.219033
$530$	197485.	0.0305383
$531$	281961.	0.0433963
$532$	−927466.	−0.142075
$533$	−2.97350e6	−0.453367
$534$	1.79154e6	0.271878
$535$	510478.	0.0771068
$536$	−1.19984e6	−0.180390
$537$	847441.	0.126816
$538$	−4.75184e6	−0.707793
$539$	−163131.	−0.0241860
$540$	−44868.1	−0.00662145
$541$	1.03121e7	1.51480	0.757398	−	0.652954i	$-0.226470\pi$
$541$	1.03121e7	1.51480	0.757398	+	0.652954i	$0.226470\pi$
$542$	−5.61497e6	−0.821011
$543$	5.48258e6	0.797968
$544$	555101.	0.0804220
$545$	454838.	0.0655942
$546$	671065.	0.0963347
$547$	9.49949e6	1.35748	0.678738	−	0.734380i	$-0.262527\pi$
$547$	9.49949e6	1.35748	0.678738	+	0.734380i	$0.262527\pi$
$548$	−5.31355e6	−0.755846
$549$	1.27304e6	0.180266
$550$	148485.	0.0209304
$551$	7.56502e6	1.06153
$552$	−1.61343e6	−0.225373
$553$	−3.25936e6	−0.453232
$554$	290753.	0.0402484
$555$	496295.	0.0683923
$556$	1.79573e6	0.246351
$557$	3.48276e6	0.475648	0.237824	−	0.971308i	$-0.423566\pi$
$557$	3.48276e6	0.475648	0.237824	+	0.971308i	$0.423566\pi$
$558$	−2.26029e6	−0.307312
$559$	2.56027e6	0.346543
$560$	−55174.1	−0.00743474
$561$	−58230.3	−0.00781164
$562$	9.05098e6	1.20880
$563$	−1.93601e6	−0.257417	−0.128709	−	0.991682i	$-0.541083\pi$
$563$	−1.93601e6	−0.257417	−0.128709	+	0.991682i	$0.541083\pi$
$564$	307855.	0.0407520
$565$	747302.	0.0984862
$566$	979346.	0.128498
$567$	367600.	0.0480195
$568$	2.14787e6	0.279343
$569$	−2.29564e6	−0.297251	−0.148625	−	0.988894i	$-0.547485\pi$
$569$	−2.29564e6	−0.297251	−0.148625	+	0.988894i	$0.547485\pi$
$570$	−143273.	−0.0184705
$571$	−9.98740e6	−1.28192	−0.640962	−	0.767573i	$-0.721464\pi$
$571$	−9.98740e6	−1.28192	−0.640962	+	0.767573i	$0.721464\pi$
$572$	−63534.7	−0.00811935
$573$	−4.61823e6	−0.587610
$574$	−2.00298e6	−0.253745
$575$	−8.71196e6	−1.09887
$576$	331776.	0.0416667
$577$	9.12529e6	1.14106	0.570528	−	0.821278i	$-0.306738\pi$
$577$	9.12529e6	1.14106	0.570528	+	0.821278i	$0.306738\pi$
$578$	4.50398e6	0.560760
$579$	−405100.	−0.0502188
$580$	450037.	0.0555492
$581$	3.47439e6	0.427010
$582$	4.94010e6	0.604544
$583$	153186.	0.0186658
$584$	251968.	0.0305713
$585$	103665.	0.0125240
$586$	−3.47708e6	−0.418283
$587$	−1.49765e7	−1.79397	−0.896987	−	0.442056i	$-0.854249\pi$
$587$	−1.49765e7	−1.79397	−0.896987	+	0.442056i	$0.854249\pi$
$588$	−1.96817e6	−0.234758
$589$	−7.21759e6	−0.857243
$590$	53561.7	0.00633467
$591$	6.88503e6	0.810844
$592$	−3.66984e6	−0.430371
$593$	−65101.7	−0.00760248	−0.00380124	−	0.999993i	$-0.501210\pi$
$593$	−65101.7	−0.00760248	−0.00380124	+	0.999993i	$0.501210\pi$
$594$	−34803.5	−0.00404721
$595$	116834.	0.0135293
$596$	−6.57714e6	−0.758440
$597$	5.33273e6	0.612370
$598$	3.72772e6	0.426276
$599$	7.19805e6	0.819687	0.409843	−	0.912156i	$-0.365583\pi$
$599$	7.19805e6	0.819687	0.409843	+	0.912156i	$0.365583\pi$
$600$	1.79148e6	0.203158
$601$	−5.24745e6	−0.592600	−0.296300	−	0.955095i	$-0.595753\pi$
$601$	−5.24745e6	−0.592600	−0.296300	+	0.955095i	$0.595753\pi$
$602$	1.72463e6	0.193956
$603$	1.51855e6	0.170073
$604$	−6.64695e6	−0.741362
$605$	618969.	0.0687513
$606$	−80956.5	−0.00895510
$607$	1.44188e7	1.58839	0.794196	−	0.607661i	$-0.207892\pi$
$607$	1.44188e7	1.58839	0.794196	+	0.607661i	$0.207892\pi$
$608$	1.05943e6	0.116229
$609$	−3.68711e6	−0.402849
$610$	241829.	0.0263138
$611$	−711280.	−0.0770792
$612$	−702550.	−0.0758226
$613$	−7.19815e6	−0.773695	−0.386847	−	0.922144i	$-0.626436\pi$
$613$	−7.19815e6	−0.773695	−0.386847	+	0.922144i	$0.626436\pi$
$614$	−7.62846e6	−0.816613
$615$	−309417.	−0.0329880
$616$	−42797.7	−0.00454432
$617$	578775.	0.0612064	0.0306032	−	0.999532i	$-0.490257\pi$
$617$	578775.	0.0612064	0.0306032	+	0.999532i	$0.490257\pi$
$618$	−891964.	−0.0939455
$619$	−4.16767e6	−0.437187	−0.218593	−	0.975816i	$-0.570147\pi$
$619$	−4.16767e6	−0.437187	−0.218593	+	0.975816i	$0.570147\pi$
$620$	−429368.	−0.0448591
$621$	2.04200e6	0.212484
$622$	7.81159e6	0.809587
$623$	−2.78824e6	−0.287813
$624$	−766547.	−0.0788093
$625$	9.62712e6	0.985817
$626$	3.66356e6	0.373652
$627$	−111135.	−0.0112897
$628$	−3.76629e6	−0.381078
$629$	7.77104e6	0.783163
$630$	69829.8	0.00700954
$631$	−3.67485e6	−0.367423	−0.183711	−	0.982980i	$-0.558811\pi$
$631$	−3.67485e6	−0.367423	−0.183711	+	0.982980i	$0.558811\pi$
$632$	3.72312e6	0.370779
$633$	8.47948e6	0.841124
$634$	−2.93131e6	−0.289627
$635$	636841.	0.0626753
$636$	1.84819e6	0.181177
$637$	4.54733e6	0.444026
$638$	349086.	0.0339532
$639$	−2.71840e6	−0.263367
$640$	63024.6	0.00608219
$641$	1.05758e7	1.01664	0.508321	−	0.861168i	$-0.330267\pi$
$641$	1.05758e7	1.01664	0.508321	+	0.861168i	$0.330267\pi$
$642$	4.77738e6	0.457459
$643$	7.95735e6	0.758999	0.379499	−	0.925192i	$-0.376096\pi$
$643$	7.95735e6	0.758999	0.379499	+	0.925192i	$0.376096\pi$
$644$	2.51104e6	0.238582
$645$	266417.	0.0252152
$646$	−2.24339e6	−0.211506
$647$	9.86680e6	0.926649	0.463325	−	0.886189i	$-0.346656\pi$
$647$	9.86680e6	0.926649	0.463325	+	0.886189i	$0.346656\pi$
$648$	−419904.	−0.0392837
$649$	41546.9	0.00387193
$650$	−4.13909e6	−0.384257
$651$	3.51777e6	0.325323
$652$	−1.06480e7	−0.980958
$653$	−5.93484e6	−0.544661	−0.272331	−	0.962204i	$-0.587794\pi$
$653$	−5.93484e6	−0.544661	−0.272331	+	0.962204i	$0.587794\pi$
$654$	4.25667e6	0.389157
$655$	−857692.	−0.0781138
$656$	2.28798e6	0.207583
$657$	−318897.	−0.0288229
$658$	−479126.	−0.0431405
$659$	−1.88160e7	−1.68777	−0.843887	−	0.536522i	$-0.819738\pi$
$659$	−1.88160e7	−1.68777	−0.843887	+	0.536522i	$0.819738\pi$
$660$	−6611.31	−0.000590782 0
$661$	1.17369e7	1.04484	0.522420	−	0.852689i	$-0.325029\pi$
$661$	1.17369e7	1.04484	0.522420	+	0.852689i	$0.325029\pi$
$662$	−6.18607e6	−0.548617
$663$	1.62320e6	0.143413
$664$	−3.96874e6	−0.349327
$665$	222981.	0.0195530
$666$	4.64464e6	0.405757
$667$	−2.04817e7	−1.78259
$668$	9.69492e6	0.840626
$669$	−7.50696e6	−0.648483
$670$	288466.	0.0248261
$671$	187583.	0.0160837
$672$	−516355.	−0.0441088
$673$	1.29616e7	1.10312	0.551559	−	0.834136i	$-0.314033\pi$
$673$	1.29616e7	1.10312	0.551559	+	0.834136i	$0.314033\pi$
$674$	−6.91157e6	−0.586040
$675$	−2.26734e6	−0.191539
$676$	−4.16963e6	−0.350938
$677$	−4.72777e6	−0.396447	−0.198223	−	0.980157i	$-0.563517\pi$
$677$	−4.72777e6	−0.396447	−0.198223	+	0.980157i	$0.563517\pi$
$678$	6.99373e6	0.584298
$679$	−7.68845e6	−0.639977
$680$	−133457.	−0.0110680
$681$	−1.44264e6	−0.119204
$682$	−333054.	−0.0274191
$683$	8.57737e6	0.703562	0.351781	−	0.936082i	$-0.385576\pi$
$683$	8.57737e6	0.703562	0.351781	+	0.936082i	$0.385576\pi$
$684$	−1.34084e6	−0.109582
$685$	1.27748e6	0.104023
$686$	6.82979e6	0.554111
$687$	−1.30550e7	−1.05532
$688$	−1.97002e6	−0.158671
$689$	−4.27012e6	−0.342683
$690$	387900.	0.0310168
$691$	−1.77711e7	−1.41586	−0.707929	−	0.706284i	$-0.750370\pi$
$691$	−1.77711e7	−1.41586	−0.707929	+	0.706284i	$0.750370\pi$
$692$	5.97260e6	0.474131
$693$	54165.8	0.00428442
$694$	−6.76724e6	−0.533351
$695$	−431729.	−0.0339038
$696$	4.21173e6	0.329562
$697$	−4.84488e6	−0.377747
$698$	2.81553e6	0.218737
$699$	261984.	0.0202806
$700$	−2.78814e6	−0.215065
$701$	−2.48795e6	−0.191226	−0.0956129	−	0.995419i	$-0.530481\pi$
$701$	−2.48795e6	−0.191226	−0.0956129	+	0.995419i	$0.530481\pi$
$702$	970161.	0.0743021
$703$	1.48313e7	1.13186
$704$	48887.2	0.00371760
$705$	−74014.4	−0.00560846
$706$	−3.62838e6	−0.273969
$707$	125995.	0.00947996
$708$	501264.	0.0375823
$709$	8.75924e6	0.654411	0.327206	−	0.944953i	$-0.393893\pi$
$709$	8.75924e6	0.654411	0.327206	+	0.944953i	$0.393893\pi$
$710$	−516390.	−0.0384443
$711$	−4.71208e6	−0.349573
$712$	3.18497e6	0.235453
$713$	1.95410e7	1.43954
$714$	1.09340e6	0.0802665
$715$	15275.0	0.00111742
$716$	1.50656e6	0.109826
$717$	5.86935e6	0.426375
$718$	1.20839e7	0.874775
$719$	−1.83297e7	−1.32231	−0.661156	−	0.750249i	$-0.729934\pi$
$719$	−1.83297e7	−1.32231	−0.661156	+	0.750249i	$0.729934\pi$
$720$	−79765.5	−0.00573434
$721$	1.38819e6	0.0994517
$722$	5.62281e6	0.401430
$723$	−565028.	−0.0401998
$724$	9.74681e6	0.691061
$725$	2.27419e7	1.60687
$726$	5.79271e6	0.407887
$727$	−6.86359e6	−0.481632	−0.240816	−	0.970571i	$-0.577415\pi$
$727$	−6.86359e6	−0.481632	−0.240816	+	0.970571i	$0.577415\pi$
$728$	1.19300e6	0.0834283
$729$	531441.	0.0370370
$730$	−60578.2	−0.00420735
$731$	4.17159e6	0.288741
$732$	2.26319e6	0.156115
$733$	2.58595e7	1.77770	0.888852	−	0.458194i	$-0.151503\pi$
$733$	2.58595e7	1.77770	0.888852	+	0.458194i	$0.151503\pi$
$734$	1.31352e7	0.899907
$735$	473187.	0.0323083
$736$	−2.86832e6	−0.195179
$737$	223759.	0.0151744
$738$	−2.89572e6	−0.195711
$739$	1.09072e7	0.734686	0.367343	−	0.930085i	$-0.380267\pi$
$739$	1.09072e7	0.734686	0.367343	+	0.930085i	$0.380267\pi$
$740$	882302.	0.0592295
$741$	3.09793e6	0.207265
$742$	−2.87640e6	−0.191796
$743$	−5.35885e6	−0.356123	−0.178061	−	0.984019i	$-0.556983\pi$
$743$	−5.35885e6	−0.356123	−0.178061	+	0.984019i	$0.556983\pi$
$744$	−4.01830e6	−0.266140
$745$	1.58127e6	0.104380
$746$	1.44979e6	0.0953801
$747$	5.02293e6	0.329349
$748$	−103521.	−0.00676508
$749$	−7.43520e6	−0.484271
$750$	−863462.	−0.0560518
$751$	2.43107e7	1.57289	0.786443	−	0.617663i	$-0.211920\pi$
$751$	2.43107e7	1.57289	0.786443	+	0.617663i	$0.211920\pi$
$752$	547298.	0.0352922
$753$	8.56334e6	0.550371
$754$	−9.73093e6	−0.623341
$755$	1.59806e6	0.102029
$756$	653511.	0.0415861
$757$	1.49623e7	0.948984	0.474492	−	0.880260i	$-0.342632\pi$
$757$	1.49623e7	0.948984	0.474492	+	0.880260i	$0.342632\pi$
$758$	−2.12213e7	−1.34152
$759$	300888.	0.0189583
$760$	−254708.	−0.0159959
$761$	−6.31860e6	−0.395511	−0.197756	−	0.980251i	$-0.563365\pi$
$761$	−6.31860e6	−0.395511	−0.197756	+	0.980251i	$0.563365\pi$
$762$	5.95996e6	0.371840
$763$	−6.62480e6	−0.411966
$764$	−8.21020e6	−0.508886
$765$	168907.	0.0104350
$766$	7.84436e6	0.483043
$767$	−1.15814e6	−0.0710840
$768$	589824.	0.0360844
$769$	2.14926e6	0.131061	0.0655304	−	0.997851i	$-0.479126\pi$
$769$	2.14926e6	0.131061	0.0655304	+	0.997851i	$0.479126\pi$
$770$	10289.4	0.000625408 0
$771$	1.64328e7	0.995581
$772$	−720179.	−0.0434908
$773$	1.77001e6	0.106543	0.0532717	−	0.998580i	$-0.483035\pi$
$773$	1.77001e6	0.106543	0.0532717	+	0.998580i	$0.483035\pi$
$774$	2.49330e6	0.149597
$775$	−2.16974e7	−1.29764
$776$	8.78239e6	0.523551
$777$	−7.22862e6	−0.429539
$778$	4.68871e6	0.277718
$779$	−9.24664e6	−0.545934
$780$	184293.	0.0108461
$781$	−400556.	−0.0234982
$782$	6.07378e6	0.355175
$783$	−5.33047e6	−0.310714
$784$	−3.49897e6	−0.203306
$785$	905489.	0.0524456
$786$	−8.02682e6	−0.463433
$787$	8.25365e6	0.475017	0.237509	−	0.971385i	$-0.423669\pi$
$787$	8.25365e6	0.475017	0.237509	+	0.971385i	$0.423669\pi$
$788$	1.22401e7	0.702212
$789$	1.61429e7	0.923183
$790$	−895112.	−0.0510281
$791$	−1.08846e7	−0.618544
$792$	−61872.8	−0.00350499
$793$	−5.22896e6	−0.295279
$794$	1.84254e7	1.03721
$795$	−444341.	−0.0249344
$796$	9.48040e6	0.530328
$797$	−3.45082e7	−1.92432	−0.962158	−	0.272492i	$-0.912152\pi$
$797$	−3.45082e7	−1.92432	−0.962158	+	0.272492i	$0.912152\pi$
$798$	2.08680e6	0.116004
$799$	−1.15893e6	−0.0642227
$800$	3.18485e6	0.175940
$801$	−4.03097e6	−0.221987
$802$	−1.62154e6	−0.0890207
$803$	−46989.5	−0.00257165
$804$	2.69965e6	0.147288
$805$	−603702.	−0.0328347
$806$	9.28402e6	0.503383
$807$	1.06916e7	0.577910
$808$	−143923.	−0.00775534
$809$	3.02590e7	1.62549	0.812743	−	0.582622i	$-0.197973\pi$
$809$	3.02590e7	1.62549	0.812743	+	0.582622i	$0.197973\pi$
$810$	100953.	0.00540639
$811$	2.15332e7	1.14963	0.574813	−	0.818285i	$-0.305075\pi$
$811$	2.15332e7	1.14963	0.574813	+	0.818285i	$0.305075\pi$
$812$	−6.55486e6	−0.348878
$813$	1.26337e7	0.670353
$814$	684387.	0.0362027
$815$	2.56000e6	0.135004
$816$	−1.24898e6	−0.0656643
$817$	7.96164e6	0.417299
$818$	−1.11432e7	−0.582275
$819$	−1.50990e6	−0.0786570
$820$	−550074.	−0.0285684
$821$	−1.93543e7	−1.00212	−0.501060	−	0.865412i	$-0.667056\pi$
$821$	−1.93543e7	−1.00212	−0.501060	+	0.865412i	$0.667056\pi$
$822$	1.19555e7	0.617145
$823$	−5.27575e6	−0.271509	−0.135755	−	0.990742i	$-0.543346\pi$
$823$	−5.27575e6	−0.271509	−0.135755	+	0.990742i	$0.543346\pi$
$824$	−1.58571e6	−0.0813592
$825$	−334092.	−0.0170896
$826$	−780135.	−0.0397850
$827$	8.87915e6	0.451448	0.225724	−	0.974191i	$-0.427525\pi$
$827$	8.87915e6	0.451448	0.225724	+	0.974191i	$0.427525\pi$
$828$	3.63021e6	0.184016
$829$	−6.08897e6	−0.307721	−0.153861	−	0.988093i	$-0.549171\pi$
$829$	−6.08897e6	−0.307721	−0.153861	+	0.988093i	$0.549171\pi$
$830$	954163.	0.0480759
$831$	−654193.	−0.0328627
$832$	−1.36275e6	−0.0682509
$833$	7.40922e6	0.369964
$834$	−4.04039e6	−0.201144
$835$	−2.33085e6	−0.115691
$836$	−197573.	−0.00977713
$837$	5.08566e6	0.250919
$838$	−1.39819e6	−0.0687790
$839$	2.92994e6	0.143699	0.0718494	−	0.997415i	$-0.477110\pi$
$839$	2.92994e6	0.143699	0.0718494	+	0.997415i	$0.477110\pi$
$840$	124142.	0.00607044
$841$	3.29546e7	1.60667
$842$	−2.50383e7	−1.21709
$843$	−2.03647e7	−0.986982
$844$	1.50746e7	0.728435
$845$	1.00246e6	0.0482976
$846$	−692674.	−0.0332738
$847$	−9.01539e6	−0.431794
$848$	3.28567e6	0.156904
$849$	−2.20353e6	−0.104918
$850$	−6.74405e6	−0.320165
$851$	−4.01545e7	−1.90069
$852$	−4.83271e6	−0.228082
$853$	1.35688e7	0.638510	0.319255	−	0.947669i	$-0.396567\pi$
$853$	1.35688e7	0.638510	0.319255	+	0.947669i	$0.396567\pi$
$854$	−3.52228e6	−0.165264
$855$	322365.	0.0150811
$856$	8.49312e6	0.396171
$857$	1.57548e7	0.732760	0.366380	−	0.930465i	$-0.380597\pi$
$857$	1.57548e7	0.732760	0.366380	+	0.930465i	$0.380597\pi$
$858$	142953.	0.00662942
$859$	−2.71282e7	−1.25441	−0.627203	−	0.778855i	$-0.715801\pi$
$859$	−2.71282e7	−1.25441	−0.627203	+	0.778855i	$0.715801\pi$
$860$	473631.	0.0218370
$861$	4.50671e6	0.207182
$862$	8.56366e6	0.392547
$863$	−1.37550e6	−0.0628687	−0.0314344	−	0.999506i	$-0.510008\pi$
$863$	−1.37550e6	−0.0628687	−0.0314344	+	0.999506i	$0.510008\pi$
$864$	−746496.	−0.0340207
$865$	−1.43593e6	−0.0652519
$866$	1.00380e7	0.454835
$867$	−1.01340e7	−0.457858
$868$	6.25382e6	0.281738
$869$	−694324.	−0.0311898
$870$	−1.01258e6	−0.0453557
$871$	−6.23737e6	−0.278584
$872$	7.56741e6	0.337020
$873$	−1.11152e7	−0.493608
$874$	1.15920e7	0.513312
$875$	1.34384e6	0.0593371
$876$	−566929.	−0.0249614
$877$	−2.96555e7	−1.30199	−0.650993	−	0.759084i	$-0.725647\pi$
$877$	−2.96555e7	−1.30199	−0.650993	+	0.759084i	$0.725647\pi$
$878$	−4.28665e6	−0.187664
$879$	7.82343e6	0.341527
$880$	−11753.4	−0.000511632 0
$881$	−2.42564e7	−1.05290	−0.526450	−	0.850206i	$-0.676477\pi$
$881$	−2.42564e7	−1.05290	−0.526450	+	0.850206i	$0.676477\pi$
$882$	4.42839e6	0.191679
$883$	−2.11783e6	−0.0914093	−0.0457046	−	0.998955i	$-0.514553\pi$
$883$	−2.11783e6	−0.0914093	−0.0457046	+	0.998955i	$0.514553\pi$
$884$	2.88568e6	0.124199
$885$	−120514.	−0.00517224
$886$	−3.13328e7	−1.34096
$887$	−3.18056e7	−1.35736	−0.678680	−	0.734434i	$-0.737448\pi$
$887$	−3.18056e7	−1.35736	−0.678680	+	0.734434i	$0.737448\pi$
$888$	8.25714e6	0.351396
$889$	−9.27570e6	−0.393634
$890$	−765728.	−0.0324041
$891$	78307.8	0.00330454
$892$	−1.33457e7	−0.561603
$893$	−2.21185e6	−0.0928170
$894$	1.47986e7	0.619264
$895$	−362207.	−0.0151147
$896$	−917964.	−0.0381993
$897$	−8.38738e6	−0.348053
$898$	4.53471e6	0.187655
$899$	−5.10103e7	−2.10503
$900$	−4.03082e6	−0.165877
$901$	−6.95754e6	−0.285525
$902$	−426684.	−0.0174618
$903$	−3.88041e6	−0.158365
$904$	1.24333e7	0.506017
$905$	−2.34333e6	−0.0951067
$906$	1.49556e7	0.605319
$907$	9.64462e6	0.389284	0.194642	−	0.980874i	$-0.437645\pi$
$907$	9.64462e6	0.389284	0.194642	+	0.980874i	$0.437645\pi$
$908$	−2.56469e6	−0.103233
$909$	182152.	0.00731180
$910$	−286822.	−0.0114818
$911$	−1.61560e7	−0.644969	−0.322484	−	0.946575i	$-0.604518\pi$
$911$	−1.61560e7	−0.644969	−0.322484	+	0.946575i	$0.604518\pi$
$912$	−2.38372e6	−0.0949004
$913$	740129.	0.0293853
$914$	−2.36306e7	−0.935642
$915$	−544116.	−0.0214852
$916$	−2.32089e7	−0.913937
$917$	1.24924e7	0.490595
$918$	1.58074e6	0.0619089
$919$	−1.58719e7	−0.619926	−0.309963	−	0.950749i	$-0.600317\pi$
$919$	−1.58719e7	−0.619926	−0.309963	+	0.950749i	$0.600317\pi$
$920$	689600.	0.0268613
$921$	1.71640e7	0.666761
$922$	−2.24648e7	−0.870314
$923$	1.11657e7	0.431400
$924$	96294.8	0.00371042
$925$	4.45857e7	1.71333
$926$	2.59098e6	0.0992970
$927$	2.00692e6	0.0767062
$928$	7.48752e6	0.285409
$929$	4.10831e6	0.156179	0.0780897	−	0.996946i	$-0.475118\pi$
$929$	4.10831e6	0.156179	0.0780897	+	0.996946i	$0.475118\pi$
$930$	966078.	0.0366273
$931$	1.41408e7	0.534686
$932$	465749.	0.0175635
$933$	−1.75761e7	−0.661025
$934$	9.48135e6	0.355634
$935$	24888.4	0.000931039 0
$936$	1.72473e6	0.0643475
$937$	1.81013e7	0.673536	0.336768	−	0.941588i	$-0.390666\pi$
$937$	1.81013e7	0.673536	0.336768	+	0.941588i	$0.390666\pi$
$938$	−4.20156e6	−0.155921
$939$	−8.24300e6	−0.305085
$940$	−131581.	−0.00485707
$941$	−4.88376e7	−1.79796	−0.898980	−	0.437989i	$-0.855691\pi$
$941$	−4.88376e7	−1.79796	−0.898980	+	0.437989i	$0.855691\pi$
$942$	8.47414e6	0.311149
$943$	2.50345e7	0.916768
$944$	891136.	0.0325472
$945$	−157117.	−0.00572326
$946$	367388.	0.0133474
$947$	2.03944e7	0.738985	0.369493	−	0.929234i	$-0.379532\pi$
$947$	2.03944e7	0.738985	0.369493	+	0.929234i	$0.379532\pi$
$948$	−8.37703e6	−0.302739
$949$	1.30985e6	0.0472125
$950$	−1.28713e7	−0.462714
$951$	6.59546e6	0.236479
$952$	1.94383e6	0.0695129
$953$	−3.11786e7	−1.11205	−0.556025	−	0.831166i	$-0.687674\pi$
$953$	−3.11786e7	−1.11205	−0.556025	+	0.831166i	$0.687674\pi$
$954$	−4.15843e6	−0.147931
$955$	1.97389e6	0.0700350
$956$	1.04344e7	0.369252
$957$	−785444.	−0.0277227
$958$	−3.75123e7	−1.32057
$959$	−1.86067e7	−0.653317
$960$	−141805.	−0.00496609
$961$	2.00384e7	0.699929
$962$	−1.90776e7	−0.664639
$963$	−1.07491e7	−0.373514
$964$	−1.00449e6	−0.0348141
$965$	173145.	0.00598538
$966$	−5.64983e6	−0.194802
$967$	−1.97677e7	−0.679813	−0.339906	−	0.940459i	$-0.610395\pi$
$967$	−1.97677e7	−0.679813	−0.339906	+	0.940459i	$0.610395\pi$
$968$	1.02981e7	0.353241
$969$	5.04762e6	0.172694
$970$	−2.11146e6	−0.0720533
$971$	−8.01735e6	−0.272887	−0.136443	−	0.990648i	$-0.543567\pi$
$971$	−8.01735e6	−0.272887	−0.136443	+	0.990648i	$0.543567\pi$
$972$	944784.	0.0320750
$973$	6.28820e6	0.212934
$974$	2.39997e7	0.810604
$975$	9.31296e6	0.313744
$976$	4.02345e6	0.135199
$977$	3.83569e7	1.28560	0.642802	−	0.766033i	$-0.277772\pi$
$977$	3.83569e7	1.28560	0.642802	+	0.766033i	$0.277772\pi$
$978$	2.39581e7	0.800949
$979$	−593963.	−0.0198063
$980$	841222.	0.0279798
$981$	−9.57750e6	−0.317746
$982$	−1.44716e6	−0.0478894
$983$	−4.39437e7	−1.45048	−0.725242	−	0.688494i	$-0.758272\pi$
$983$	−4.39437e7	−1.45048	−0.725242	+	0.688494i	$0.758272\pi$
$984$	−5.14794e6	−0.169491
$985$	−2.94275e6	−0.0966413
$986$	−1.58551e7	−0.519371
$987$	1.07803e6	0.0352240
$988$	5.50743e6	0.179497
$989$	−2.15555e7	−0.700755
$990$	14875.4	0.000482372 0
$991$	−4.70351e7	−1.52138	−0.760690	−	0.649115i	$-0.775139\pi$
$991$	−4.70351e7	−1.52138	−0.760690	+	0.649115i	$0.775139\pi$
$992$	−7.14364e6	−0.230484
$993$	1.39186e7	0.447944
$994$	7.52131e6	0.241450
$995$	−2.27928e6	−0.0729859
$996$	8.92966e6	0.285224
$997$	−1.58777e7	−0.505884	−0.252942	−	0.967481i	$-0.581398\pi$
$997$	−1.58777e7	−0.505884	−0.252942	+	0.967481i	$0.581398\pi$
$998$	5.46365e6	0.173643
$999$	−1.04504e7	−0.331300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.c.1.3	✓	5
3.2	odd	2		1062.6.a.f.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.c.1.3	✓	5	1.1	even	1	trivial
1062.6.a.f.1.3		5	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -3.84671 q^{5} -36.0000 q^{6} +56.0281 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -3.84671 q^{5} -36.0000 q^{6} +56.0281 q^{7} -64.0000 q^{8} +81.0000 q^{9} +15.3869 q^{10} +11.9353 q^{11} +144.000 q^{12} -332.703 q^{13} -224.112 q^{14} -34.6204 q^{15} +256.000 q^{16} -542.091 q^{17} -324.000 q^{18} -1034.60 q^{19} -61.5474 q^{20} +504.253 q^{21} -47.7414 q^{22} +2801.09 q^{23} -576.000 q^{24} -3110.20 q^{25} +1330.81 q^{26} +729.000 q^{27} +896.449 q^{28} -7312.03 q^{29} +138.482 q^{30} +6976.21 q^{31} -1024.00 q^{32} +107.418 q^{33} +2168.36 q^{34} -215.524 q^{35} +1296.00 q^{36} -14335.3 q^{37} +4138.40 q^{38} -2994.33 q^{39} +246.190 q^{40} +8937.40 q^{41} -2017.01 q^{42} -7695.38 q^{43} +190.965 q^{44} -311.584 q^{45} -11204.4 q^{46} +2137.88 q^{47} +2304.00 q^{48} -13667.9 q^{49} +12440.8 q^{50} -4878.82 q^{51} -5323.24 q^{52} +12834.6 q^{53} -2916.00 q^{54} -45.9118 q^{55} -3585.80 q^{56} -9311.40 q^{57} +29248.1 q^{58} +3481.00 q^{59} -553.927 q^{60} +15716.6 q^{61} -27904.8 q^{62} +4538.27 q^{63} +4096.00 q^{64} +1279.81 q^{65} -429.672 q^{66} +18747.6 q^{67} -8673.45 q^{68} +25209.8 q^{69} +862.096 q^{70} -33560.5 q^{71} -5184.00 q^{72} -3937.01 q^{73} +57341.2 q^{74} -27991.8 q^{75} -16553.6 q^{76} +668.714 q^{77} +11977.3 q^{78} -58173.8 q^{79} -984.759 q^{80} +6561.00 q^{81} -35749.6 q^{82} +62011.5 q^{83} +8068.04 q^{84} +2085.27 q^{85} +30781.5 q^{86} -65808.2 q^{87} -763.862 q^{88} -49765.1 q^{89} +1246.34 q^{90} -18640.7 q^{91} +44817.5 q^{92} +62785.9 q^{93} -8551.53 q^{94} +3979.81 q^{95} -9216.00 q^{96} -137225. q^{97} +54671.4 q^{98} +966.763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9} + 40 q^{10} - 228 q^{11} + 720 q^{12} - 386 q^{13} + 648 q^{14} - 90 q^{15} + 1280 q^{16} + 1304 q^{17} - 1620 q^{18} + 342 q^{19} - 160 q^{20} - 1458 q^{21} + 912 q^{22} - 78 q^{23} - 2880 q^{24} - 3585 q^{25} + 1544 q^{26} + 3645 q^{27} - 2592 q^{28} - 4576 q^{29} + 360 q^{30} - 14456 q^{31} - 5120 q^{32} - 2052 q^{33} - 5216 q^{34} - 5622 q^{35} + 6480 q^{36} - 21684 q^{37} - 1368 q^{38} - 3474 q^{39} + 640 q^{40} - 15484 q^{41} + 5832 q^{42} - 22094 q^{43} - 3648 q^{44} - 810 q^{45} + 312 q^{46} - 4890 q^{47} + 11520 q^{48} + 3955 q^{49} + 14340 q^{50} + 11736 q^{51} - 6176 q^{52} + 12686 q^{53} - 14580 q^{54} - 40468 q^{55} + 10368 q^{56} + 3078 q^{57} + 18304 q^{58} + 17405 q^{59} - 1440 q^{60} - 17792 q^{61} + 57824 q^{62} - 13122 q^{63} + 20480 q^{64} + 67704 q^{65} + 8208 q^{66} - 33042 q^{67} + 20864 q^{68} - 702 q^{69} + 22488 q^{70} + 16172 q^{71} - 25920 q^{72} - 40092 q^{73} + 86736 q^{74} - 32265 q^{75} + 5472 q^{76} + 33330 q^{77} + 13896 q^{78} - 51216 q^{79} - 2560 q^{80} + 32805 q^{81} + 61936 q^{82} + 7526 q^{83} - 23328 q^{84} - 92546 q^{85} + 88376 q^{86} - 41184 q^{87} + 14592 q^{88} + 4210 q^{89} + 3240 q^{90} - 263742 q^{91} - 1248 q^{92} - 130104 q^{93} + 19560 q^{94} - 220798 q^{95} - 46080 q^{96} - 279974 q^{97} - 15820 q^{98} - 18468 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9 + 40 * q^10 - 228 * q^11 + 720 * q^12 - 386 * q^13 + 648 * q^14 - 90 * q^15 + 1280 * q^16 + 1304 * q^17 - 1620 * q^18 + 342 * q^19 - 160 * q^20 - 1458 * q^21 + 912 * q^22 - 78 * q^23 - 2880 * q^24 - 3585 * q^25 + 1544 * q^26 + 3645 * q^27 - 2592 * q^28 - 4576 * q^29 + 360 * q^30 - 14456 * q^31 - 5120 * q^32 - 2052 * q^33 - 5216 * q^34 - 5622 * q^35 + 6480 * q^36 - 21684 * q^37 - 1368 * q^38 - 3474 * q^39 + 640 * q^40 - 15484 * q^41 + 5832 * q^42 - 22094 * q^43 - 3648 * q^44 - 810 * q^45 + 312 * q^46 - 4890 * q^47 + 11520 * q^48 + 3955 * q^49 + 14340 * q^50 + 11736 * q^51 - 6176 * q^52 + 12686 * q^53 - 14580 * q^54 - 40468 * q^55 + 10368 * q^56 + 3078 * q^57 + 18304 * q^58 + 17405 * q^59 - 1440 * q^60 - 17792 * q^61 + 57824 * q^62 - 13122 * q^63 + 20480 * q^64 + 67704 * q^65 + 8208 * q^66 - 33042 * q^67 + 20864 * q^68 - 702 * q^69 + 22488 * q^70 + 16172 * q^71 - 25920 * q^72 - 40092 * q^73 + 86736 * q^74 - 32265 * q^75 + 5472 * q^76 + 33330 * q^77 + 13896 * q^78 - 51216 * q^79 - 2560 * q^80 + 32805 * q^81 + 61936 * q^82 + 7526 * q^83 - 23328 * q^84 - 92546 * q^85 + 88376 * q^86 - 41184 * q^87 + 14592 * q^88 + 4210 * q^89 + 3240 * q^90 - 263742 * q^91 - 1248 * q^92 - 130104 * q^93 + 19560 * q^94 - 220798 * q^95 - 46080 * q^96 - 279974 * q^97 - 15820 * q^98 - 18468 * q^99

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