LMFDB - Embedded newform 354.6.a.c.1.4

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			1.4
Root			$-2.79263$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +19.3501 q^{5} -36.0000 q^{6} +148.650 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +19.3501 q^{5} -36.0000 q^{6} +148.650 q^{7} -64.0000 q^{8} +81.0000 q^{9} -77.4004 q^{10} -188.262 q^{11} +144.000 q^{12} -416.447 q^{13} -594.602 q^{14} +174.151 q^{15} +256.000 q^{16} -207.809 q^{17} -324.000 q^{18} -2524.76 q^{19} +309.602 q^{20} +1337.85 q^{21} +753.048 q^{22} -2676.38 q^{23} -576.000 q^{24} -2750.57 q^{25} +1665.79 q^{26} +729.000 q^{27} +2378.41 q^{28} +4038.12 q^{29} -696.604 q^{30} -9438.52 q^{31} -1024.00 q^{32} -1694.36 q^{33} +831.237 q^{34} +2876.40 q^{35} +1296.00 q^{36} +4638.16 q^{37} +10099.0 q^{38} -3748.02 q^{39} -1238.41 q^{40} -6058.62 q^{41} -5351.42 q^{42} -6699.19 q^{43} -3012.19 q^{44} +1567.36 q^{45} +10705.5 q^{46} +4851.45 q^{47} +2304.00 q^{48} +5289.95 q^{49} +11002.3 q^{50} -1870.28 q^{51} -6663.15 q^{52} +1035.55 q^{53} -2916.00 q^{54} -3642.89 q^{55} -9513.63 q^{56} -22722.8 q^{57} -16152.5 q^{58} +3481.00 q^{59} +2786.41 q^{60} +9439.69 q^{61} +37754.1 q^{62} +12040.7 q^{63} +4096.00 q^{64} -8058.29 q^{65} +6777.44 q^{66} -33630.7 q^{67} -3324.95 q^{68} -24087.4 q^{69} -11505.6 q^{70} +44039.0 q^{71} -5184.00 q^{72} -334.414 q^{73} -18552.7 q^{74} -24755.2 q^{75} -40396.1 q^{76} -27985.2 q^{77} +14992.1 q^{78} +83630.8 q^{79} +4953.62 q^{80} +6561.00 q^{81} +24234.5 q^{82} -27971.0 q^{83} +21405.7 q^{84} -4021.13 q^{85} +26796.8 q^{86} +36343.0 q^{87} +12048.8 q^{88} +77470.1 q^{89} -6269.43 q^{90} -61905.0 q^{91} -42822.1 q^{92} -84946.7 q^{93} -19405.8 q^{94} -48854.3 q^{95} -9216.00 q^{96} -64874.5 q^{97} -21159.8 q^{98} -15249.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	19.3501	0.346145	0.173073	−	0.984909i	$-0.444630\pi$
$5$	19.3501	0.346145	0.173073	+	0.984909i	$0.444630\pi$
$6$	−36.0000	−0.408248
$7$	148.650	1.14662	0.573312	−	0.819337i	$-0.305658\pi$
$7$	148.650	1.14662	0.573312	+	0.819337i	$0.305658\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−77.4004	−0.244762
$11$	−188.262	−0.469117	−0.234559	−	0.972102i	$-0.575364\pi$
$11$	−188.262	−0.469117	−0.234559	+	0.972102i	$0.575364\pi$
$12$	144.000	0.288675
$13$	−416.447	−0.683441	−0.341721	−	0.939802i	$-0.611010\pi$
$13$	−416.447	−0.683441	−0.341721	+	0.939802i	$0.611010\pi$
$14$	−594.602	−0.810786
$15$	174.151	0.199847
$16$	256.000	0.250000
$17$	−207.809	−0.174398	−0.0871992	−	0.996191i	$-0.527792\pi$
$17$	−207.809	−0.174398	−0.0871992	+	0.996191i	$0.527792\pi$
$18$	−324.000	−0.235702
$19$	−2524.76	−1.60448	−0.802242	−	0.596999i	$-0.796359\pi$
$19$	−2524.76	−1.60448	−0.802242	+	0.596999i	$0.796359\pi$
$20$	309.602	0.173073
$21$	1337.85	0.662004
$22$	753.048	0.331716
$23$	−2676.38	−1.05494	−0.527471	−	0.849573i	$-0.676860\pi$
$23$	−2676.38	−1.05494	−0.527471	+	0.849573i	$0.676860\pi$
$24$	−576.000	−0.204124
$25$	−2750.57	−0.880184
$26$	1665.79	0.483266
$27$	729.000	0.192450
$28$	2378.41	0.573312
$29$	4038.12	0.891628	0.445814	−	0.895126i	$-0.352914\pi$
$29$	4038.12	0.891628	0.445814	+	0.895126i	$0.352914\pi$
$30$	−696.604	−0.141313
$31$	−9438.52	−1.76400	−0.882002	−	0.471245i	$-0.843805\pi$
$31$	−9438.52	−1.76400	−0.882002	+	0.471245i	$0.843805\pi$
$32$	−1024.00	−0.176777
$33$	−1694.36	−0.270845
$34$	831.237	0.123318
$35$	2876.40	0.396898
$36$	1296.00	0.166667
$37$	4638.16	0.556983	0.278491	−	0.960439i	$-0.410166\pi$
$37$	4638.16	0.556983	0.278491	+	0.960439i	$0.410166\pi$
$38$	10099.0	1.13454
$39$	−3748.02	−0.394585
$40$	−1238.41	−0.122381
$41$	−6058.62	−0.562878	−0.281439	−	0.959579i	$-0.590812\pi$
$41$	−6058.62	−0.562878	−0.281439	+	0.959579i	$0.590812\pi$
$42$	−5351.42	−0.468107
$43$	−6699.19	−0.552524	−0.276262	−	0.961082i	$-0.589096\pi$
$43$	−6699.19	−0.552524	−0.276262	+	0.961082i	$0.589096\pi$
$44$	−3012.19	−0.234559
$45$	1567.36	0.115382
$46$	10705.5	0.745957
$47$	4851.45	0.320351	0.160176	−	0.987089i	$-0.448794\pi$
$47$	4851.45	0.320351	0.160176	+	0.987089i	$0.448794\pi$
$48$	2304.00	0.144338
$49$	5289.95	0.314747
$50$	11002.3	0.622384
$51$	−1870.28	−0.100689
$52$	−6663.15	−0.341721
$53$	1035.55	0.0506388	0.0253194	−	0.999679i	$-0.491940\pi$
$53$	1035.55	0.0506388	0.0253194	+	0.999679i	$0.491940\pi$
$54$	−2916.00	−0.136083
$55$	−3642.89	−0.162383
$56$	−9513.63	−0.405393
$57$	−22722.8	−0.926349
$58$	−16152.5	−0.630476
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	2786.41	0.0999235
$61$	9439.69	0.324813	0.162406	−	0.986724i	$-0.448074\pi$
$61$	9439.69	0.324813	0.162406	+	0.986724i	$0.448074\pi$
$62$	37754.1	1.24734
$63$	12040.7	0.382208
$64$	4096.00	0.125000
$65$	−8058.29	−0.236570
$66$	6777.44	0.191516
$67$	−33630.7	−0.915269	−0.457635	−	0.889140i	$-0.651303\pi$
$67$	−33630.7	−0.915269	−0.457635	+	0.889140i	$0.651303\pi$
$68$	−3324.95	−0.0871992
$69$	−24087.4	−0.609071
$70$	−11505.6	−0.280649
$71$	44039.0	1.03679	0.518396	−	0.855140i	$-0.326529\pi$
$71$	44039.0	1.03679	0.518396	+	0.855140i	$0.326529\pi$
$72$	−5184.00	−0.117851
$73$	−334.414	−0.00734475	−0.00367237	−	0.999993i	$-0.501169\pi$
$73$	−334.414	−0.00734475	−0.00367237	+	0.999993i	$0.501169\pi$
$74$	−18552.7	−0.393846
$75$	−24755.2	−0.508174
$76$	−40396.1	−0.802242
$77$	−27985.2	−0.537901
$78$	14992.1	0.279014
$79$	83630.8	1.50764	0.753821	−	0.657080i	$-0.228209\pi$
$79$	83630.8	1.50764	0.753821	+	0.657080i	$0.228209\pi$
$80$	4953.62	0.0865363
$81$	6561.00	0.111111
$82$	24234.5	0.398015
$83$	−27971.0	−0.445670	−0.222835	−	0.974856i	$-0.571531\pi$
$83$	−27971.0	−0.445670	−0.222835	+	0.974856i	$0.571531\pi$
$84$	21405.7	0.331002
$85$	−4021.13	−0.0603671
$86$	26796.8	0.390694
$87$	36343.0	0.514782
$88$	12048.8	0.165858
$89$	77470.1	1.03671	0.518357	−	0.855164i	$-0.326544\pi$
$89$	77470.1	1.03671	0.518357	+	0.855164i	$0.326544\pi$
$90$	−6269.43	−0.0815872
$91$	−61905.0	−0.783650
$92$	−42822.1	−0.527471
$93$	−84946.7	−1.01845
$94$	−19405.8	−0.226523
$95$	−48854.3	−0.555384
$96$	−9216.00	−0.102062
$97$	−64874.5	−0.700075	−0.350038	−	0.936736i	$-0.613831\pi$
$97$	−64874.5	−0.700075	−0.350038	+	0.936736i	$0.613831\pi$
$98$	−21159.8	−0.222560
$99$	−15249.2	−0.156372
$100$	−44009.2	−0.440092
$101$	−116893.	−1.14022	−0.570108	−	0.821570i	$-0.693099\pi$
$101$	−116893.	−1.14022	−0.570108	+	0.821570i	$0.693099\pi$
$102$	7481.13	0.0711978
$103$	−3580.46	−0.0332542	−0.0166271	−	0.999862i	$-0.505293\pi$
$103$	−3580.46	−0.0332542	−0.0166271	+	0.999862i	$0.505293\pi$
$104$	26652.6	0.241633
$105$	25887.6	0.229149
$106$	−4142.22	−0.0358070
$107$	−14922.3	−0.126001	−0.0630007	−	0.998013i	$-0.520067\pi$
$107$	−14922.3	−0.126001	−0.0630007	+	0.998013i	$0.520067\pi$
$108$	11664.0	0.0962250
$109$	−117779.	−0.949514	−0.474757	−	0.880117i	$-0.657464\pi$
$109$	−117779.	−0.949514	−0.474757	+	0.880117i	$0.657464\pi$
$110$	14571.6	0.114822
$111$	41743.5	0.321574
$112$	38054.5	0.286656
$113$	−37396.2	−0.275506	−0.137753	−	0.990467i	$-0.543988\pi$
$113$	−37396.2	−0.275506	−0.137753	+	0.990467i	$0.543988\pi$
$114$	90891.2	0.655028
$115$	−51788.3	−0.365163
$116$	64609.9	0.445814
$117$	−33732.2	−0.227814
$118$	−13924.0	−0.0920575
$119$	−30890.9	−0.199969
$120$	−11145.7	−0.0706566
$121$	−125608.	−0.779929
$122$	−37758.8	−0.229677
$123$	−54527.6	−0.324978
$124$	−151016.	−0.882002
$125$	−113693.	−0.650816
$126$	−48162.7	−0.270262
$127$	−158113.	−0.869880	−0.434940	−	0.900459i	$-0.643230\pi$
$127$	−158113.	−0.869880	−0.434940	+	0.900459i	$0.643230\pi$
$128$	−16384.0	−0.0883883
$129$	−60292.7	−0.319000
$130$	32233.1	0.167280
$131$	−356147.	−1.81322	−0.906611	−	0.421968i	$-0.861339\pi$
$131$	−356147.	−1.81322	−0.906611	+	0.421968i	$0.861339\pi$
$132$	−27109.7	−0.135422
$133$	−375306.	−1.83974
$134$	134523.	0.647193
$135$	14106.2	0.0666156
$136$	13299.8	0.0616591
$137$	−38685.0	−0.176092	−0.0880462	−	0.996116i	$-0.528062\pi$
$137$	−38685.0	−0.176092	−0.0880462	+	0.996116i	$0.528062\pi$
$138$	96349.8	0.430678
$139$	−3041.83	−0.0133536	−0.00667679	−	0.999978i	$-0.502125\pi$
$139$	−3041.83	−0.0133536	−0.00667679	+	0.999978i	$0.502125\pi$
$140$	46022.4	0.198449
$141$	43663.0	0.184955
$142$	−176156.	−0.733123
$143$	78401.2	0.320614
$144$	20736.0	0.0833333
$145$	78138.0	0.308633
$146$	1337.65	0.00519352
$147$	47609.6	0.181719
$148$	74210.6	0.278491
$149$	268267.	0.989924	0.494962	−	0.868915i	$-0.335182\pi$
$149$	268267.	0.989924	0.494962	+	0.868915i	$0.335182\pi$
$150$	99020.7	0.359333
$151$	−244993.	−0.874402	−0.437201	−	0.899364i	$-0.644030\pi$
$151$	−244993.	−0.874402	−0.437201	+	0.899364i	$0.644030\pi$
$152$	161584.	0.567271
$153$	−16832.5	−0.0581328
$154$	111941.	0.380353
$155$	−182636.	−0.610602
$156$	−59968.3	−0.197292
$157$	−223270.	−0.722905	−0.361453	−	0.932390i	$-0.617719\pi$
$157$	−223270.	−0.722905	−0.361453	+	0.932390i	$0.617719\pi$
$158$	−334523.	−1.06606
$159$	9319.99	0.0292363
$160$	−19814.5	−0.0611904
$161$	−397845.	−1.20962
$162$	−26244.0	−0.0785674
$163$	223207.	0.658020	0.329010	−	0.944326i	$-0.393285\pi$
$163$	223207.	0.658020	0.329010	+	0.944326i	$0.393285\pi$
$164$	−96937.9	−0.281439
$165$	−32786.0	−0.0937516
$166$	111884.	0.315136
$167$	−105797.	−0.293549	−0.146775	−	0.989170i	$-0.546889\pi$
$167$	−105797.	−0.293549	−0.146775	+	0.989170i	$0.546889\pi$
$168$	−85622.7	−0.234054
$169$	−197865.	−0.532908
$170$	16084.5	0.0426860
$171$	−204505.	−0.534828
$172$	−107187.	−0.276262
$173$	686526.	1.74398	0.871991	−	0.489522i	$-0.162829\pi$
$173$	686526.	1.74398	0.871991	+	0.489522i	$0.162829\pi$
$174$	−145372.	−0.364006
$175$	−408874.	−1.00924
$176$	−48195.1	−0.117279
$177$	31329.0	0.0751646
$178$	−309881.	−0.733068
$179$	393485.	0.917901	0.458950	−	0.888462i	$-0.348226\pi$
$179$	393485.	0.917901	0.458950	+	0.888462i	$0.348226\pi$
$180$	25077.7	0.0576908
$181$	−353779.	−0.802667	−0.401334	−	0.915932i	$-0.631453\pi$
$181$	−353779.	−0.802667	−0.401334	+	0.915932i	$0.631453\pi$
$182$	247620.	0.554124
$183$	84957.2	0.187531
$184$	171288.	0.372978
$185$	89748.9	0.192797
$186$	339787.	0.720152
$187$	39122.6	0.0818132
$188$	77623.2	0.160176
$189$	108366.	0.220668
$190$	195417.	0.392716
$191$	675641.	1.34009	0.670043	−	0.742323i	$-0.266276\pi$
$191$	675641.	1.34009	0.670043	+	0.742323i	$0.266276\pi$
$192$	36864.0	0.0721688
$193$	286157.	0.552982	0.276491	−	0.961017i	$-0.410828\pi$
$193$	286157.	0.552982	0.276491	+	0.961017i	$0.410828\pi$
$194$	259498.	0.495028
$195$	−72524.6	−0.136584
$196$	84639.3	0.157374
$197$	509863.	0.936025	0.468013	−	0.883722i	$-0.344970\pi$
$197$	509863.	0.936025	0.468013	+	0.883722i	$0.344970\pi$
$198$	60996.9	0.110572
$199$	389157.	0.696615	0.348307	−	0.937380i	$-0.386757\pi$
$199$	389157.	0.696615	0.348307	+	0.937380i	$0.386757\pi$
$200$	176037.	0.311192
$201$	−302676.	−0.528431
$202$	467574.	0.806254
$203$	600268.	1.02236
$204$	−29924.5	−0.0503445
$205$	−117235.	−0.194837
$206$	14321.9	0.0235143
$207$	−216787.	−0.351647
$208$	−106610.	−0.170860
$209$	475316.	0.752691
$210$	−103550.	−0.162033
$211$	−332348.	−0.513910	−0.256955	−	0.966423i	$-0.582719\pi$
$211$	−332348.	−0.513910	−0.256955	+	0.966423i	$0.582719\pi$
$212$	16568.9	0.0253194
$213$	396351.	0.598593
$214$	59689.1	0.0890965
$215$	−129630.	−0.191253
$216$	−46656.0	−0.0680414
$217$	−1.40304e6	−2.02265
$218$	471116.	0.671408
$219$	−3009.72	−0.00424049
$220$	−58286.2	−0.0811913
$221$	86541.5	0.119191
$222$	−166974.	−0.227387
$223$	−850043.	−1.14467	−0.572333	−	0.820021i	$-0.693962\pi$
$223$	−850043.	−1.14467	−0.572333	+	0.820021i	$0.693962\pi$
$224$	−152218.	−0.202696
$225$	−222796.	−0.293395
$226$	149585.	0.194812
$227$	−539012.	−0.694278	−0.347139	−	0.937814i	$-0.612847\pi$
$227$	−539012.	−0.694278	−0.347139	+	0.937814i	$0.612847\pi$
$228$	−363565.	−0.463174
$229$	1.02070e6	1.28620	0.643101	−	0.765781i	$-0.277647\pi$
$229$	1.02070e6	1.28620	0.643101	+	0.765781i	$0.277647\pi$
$230$	207153.	0.258209
$231$	−251867.	−0.310557
$232$	−258439.	−0.315238
$233$	231835.	0.279762	0.139881	−	0.990168i	$-0.455328\pi$
$233$	231835.	0.279762	0.139881	+	0.990168i	$0.455328\pi$
$234$	134929.	0.161089
$235$	93876.0	0.110888
$236$	55696.0	0.0650945
$237$	752677.	0.870438
$238$	123564.	0.141400
$239$	988446.	1.11933	0.559665	−	0.828719i	$-0.310930\pi$
$239$	988446.	1.11933	0.559665	+	0.828719i	$0.310930\pi$
$240$	44582.6	0.0499617
$241$	−1.04712e6	−1.16132	−0.580660	−	0.814146i	$-0.697206\pi$
$241$	−1.04712e6	−1.16132	−0.580660	+	0.814146i	$0.697206\pi$
$242$	502434.	0.551493
$243$	59049.0	0.0641500
$244$	151035.	0.162406
$245$	102361.	0.108948
$246$	218110.	0.229794
$247$	1.05143e6	1.09657
$248$	604065.	0.623670
$249$	−251739.	−0.257307
$250$	454772.	0.460197
$251$	400742.	0.401495	0.200748	−	0.979643i	$-0.435663\pi$
$251$	400742.	0.401495	0.200748	+	0.979643i	$0.435663\pi$
$252$	192651.	0.191104
$253$	503861.	0.494891
$254$	632454.	0.615098
$255$	−36190.1	−0.0348530
$256$	65536.0	0.0625000
$257$	−620964.	−0.586453	−0.293227	−	0.956043i	$-0.594729\pi$
$257$	−620964.	−0.586453	−0.293227	+	0.956043i	$0.594729\pi$
$258$	241171.	0.225567
$259$	689465.	0.638650
$260$	−128933.	−0.118285
$261$	327087.	0.297209
$262$	1.42459e6	1.28214
$263$	−1.50956e6	−1.34574	−0.672870	−	0.739761i	$-0.734938\pi$
$263$	−1.50956e6	−1.34574	−0.672870	+	0.739761i	$0.734938\pi$
$264$	108439.	0.0957581
$265$	20038.1	0.0175284
$266$	1.50122e6	1.30089
$267$	697231.	0.598548
$268$	−538091.	−0.457635
$269$	−860918.	−0.725406	−0.362703	−	0.931905i	$-0.618146\pi$
$269$	−860918.	−0.725406	−0.362703	+	0.931905i	$0.618146\pi$
$270$	−56424.9	−0.0471044
$271$	1.43287e6	1.18518	0.592588	−	0.805506i	$-0.298106\pi$
$271$	1.43287e6	1.18518	0.592588	+	0.805506i	$0.298106\pi$
$272$	−53199.1	−0.0435996
$273$	−557145.	−0.452441
$274$	154740.	0.124516
$275$	517829.	0.412909
$276$	−385399.	−0.304535
$277$	2.06238e6	1.61499	0.807493	−	0.589877i	$-0.200824\pi$
$277$	2.06238e6	1.61499	0.807493	+	0.589877i	$0.200824\pi$
$278$	12167.3	0.00944240
$279$	−764520.	−0.588002
$280$	−184090.	−0.140325
$281$	2.29544e6	1.73420	0.867101	−	0.498132i	$-0.165980\pi$
$281$	2.29544e6	1.73420	0.867101	+	0.498132i	$0.165980\pi$
$282$	−174652.	−0.130783
$283$	644572.	0.478416	0.239208	−	0.970968i	$-0.423112\pi$
$283$	644572.	0.478416	0.239208	+	0.970968i	$0.423112\pi$
$284$	704625.	0.518396
$285$	−439688.	−0.320651
$286$	−313605.	−0.226708
$287$	−900617.	−0.645409
$288$	−82944.0	−0.0589256
$289$	−1.37667e6	−0.969585
$290$	−312552.	−0.218236
$291$	−583871.	−0.404189
$292$	−5350.62	−0.00367237
$293$	−1.14858e6	−0.781612	−0.390806	−	0.920473i	$-0.627804\pi$
$293$	−1.14858e6	−0.781612	−0.390806	+	0.920473i	$0.627804\pi$
$294$	−190438.	−0.128495
$295$	67357.7	0.0450642
$296$	−296843.	−0.196923
$297$	−137243.	−0.0902816
$298$	−1.07307e6	−0.699982
$299$	1.11457e6	0.720991
$300$	−396083.	−0.254087
$301$	−995838.	−0.633537
$302$	979972.	0.618296
$303$	−1.05204e6	−0.658304
$304$	−646337.	−0.401121
$305$	182659.	0.112432
$306$	67330.2	0.0411061
$307$	1.05115e6	0.636529	0.318264	−	0.948002i	$-0.396900\pi$
$307$	1.05115e6	0.636529	0.318264	+	0.948002i	$0.396900\pi$
$308$	−447764.	−0.268950
$309$	−32224.2	−0.0191993
$310$	730545.	0.431761
$311$	1.39284e6	0.816582	0.408291	−	0.912852i	$-0.366125\pi$
$311$	1.39284e6	0.816582	0.408291	+	0.912852i	$0.366125\pi$
$312$	239873.	0.139507
$313$	−1.03192e6	−0.595367	−0.297684	−	0.954665i	$-0.596214\pi$
$313$	−1.03192e6	−0.595367	−0.297684	+	0.954665i	$0.596214\pi$
$314$	893081.	0.511171
$315$	232988.	0.132299
$316$	1.33809e6	0.753821
$317$	1.76427e6	0.986093	0.493047	−	0.870003i	$-0.335883\pi$
$317$	1.76427e6	0.986093	0.493047	+	0.870003i	$0.335883\pi$
$318$	−37280.0	−0.0206732
$319$	−760224.	−0.418278
$320$	79258.0	0.0432681
$321$	−134300.	−0.0727469
$322$	1.59138e6	0.855332
$323$	524667.	0.279819
$324$	104976.	0.0555556
$325$	1.14547e6	0.601554
$326$	−892828.	−0.465290
$327$	−1.06001e6	−0.548202
$328$	387752.	0.199007
$329$	721170.	0.367323
$330$	131144.	0.0662924
$331$	−2.13713e6	−1.07216	−0.536081	−	0.844167i	$-0.680096\pi$
$331$	−2.13713e6	−1.07216	−0.536081	+	0.844167i	$0.680096\pi$
$332$	−447536.	−0.222835
$333$	375691.	0.185661
$334$	423187.	0.207571
$335$	−650757.	−0.316816
$336$	342491.	0.165501
$337$	−2.29860e6	−1.10252	−0.551262	−	0.834332i	$-0.685853\pi$
$337$	−2.29860e6	−1.10252	−0.551262	+	0.834332i	$0.685853\pi$
$338$	791460.	0.376823
$339$	−336566.	−0.159064
$340$	−64338.0	−0.0301836
$341$	1.77692e6	0.827525
$342$	818021.	0.378180
$343$	−1.71201e6	−0.785728
$344$	428748.	0.195347
$345$	−466094.	−0.210827
$346$	−2.74611e6	−1.23318
$347$	−1.60098e6	−0.713778	−0.356889	−	0.934147i	$-0.616163\pi$
$347$	−1.60098e6	−0.713778	−0.356889	+	0.934147i	$0.616163\pi$
$348$	581489.	0.257391
$349$	−2.39722e6	−1.05352	−0.526761	−	0.850013i	$-0.676594\pi$
$349$	−2.39722e6	−1.05352	−0.526761	+	0.850013i	$0.676594\pi$
$350$	1.63550e6	0.713640
$351$	−303590.	−0.131528
$352$	192780.	0.0829290
$353$	−2.87313e6	−1.22721	−0.613604	−	0.789614i	$-0.710281\pi$
$353$	−2.87313e6	−1.22721	−0.613604	+	0.789614i	$0.710281\pi$
$354$	−125316.	−0.0531494
$355$	852160.	0.358881
$356$	1.23952e6	0.518357
$357$	−278018.	−0.115452
$358$	−1.57394e6	−0.649054
$359$	404571.	0.165676	0.0828378	−	0.996563i	$-0.473602\pi$
$359$	404571.	0.165676	0.0828378	+	0.996563i	$0.473602\pi$
$360$	−100311.	−0.0407936
$361$	3.89829e6	1.57437
$362$	1.41512e6	0.567571
$363$	−1.13048e6	−0.450292
$364$	−990480.	−0.391825
$365$	−6470.94	−0.00254235
$366$	−339829.	−0.132604
$367$	838306.	0.324891	0.162445	−	0.986718i	$-0.448062\pi$
$367$	838306.	0.324891	0.162445	+	0.986718i	$0.448062\pi$
$368$	−685154.	−0.263735
$369$	−490748.	−0.187626
$370$	−358996.	−0.136328
$371$	153936.	0.0580637
$372$	−1.35915e6	−0.509224
$373$	−2.22844e6	−0.829332	−0.414666	−	0.909974i	$-0.636102\pi$
$373$	−2.22844e6	−0.829332	−0.414666	+	0.909974i	$0.636102\pi$
$374$	−156490.	−0.0578507
$375$	−1.02324e6	−0.375749
$376$	−310493.	−0.113261
$377$	−1.68166e6	−0.609376
$378$	−433465.	−0.156036
$379$	−428889.	−0.153372	−0.0766861	−	0.997055i	$-0.524434\pi$
$379$	−428889.	−0.153372	−0.0766861	+	0.997055i	$0.524434\pi$
$380$	−781668.	−0.277692
$381$	−1.42302e6	−0.502226
$382$	−2.70256e6	−0.947583
$383$	−4.00129e6	−1.39381	−0.696904	−	0.717164i	$-0.745440\pi$
$383$	−4.00129e6	−1.39381	−0.696904	+	0.717164i	$0.745440\pi$
$384$	−147456.	−0.0510310
$385$	−541517.	−0.186192
$386$	−1.14463e6	−0.391017
$387$	−542634.	−0.184175
$388$	−1.03799e6	−0.350038
$389$	3.93190e6	1.31743	0.658717	−	0.752391i	$-0.271100\pi$
$389$	3.93190e6	1.31743	0.658717	+	0.752391i	$0.271100\pi$
$390$	290098.	0.0965792
$391$	556177.	0.183980
$392$	−338557.	−0.111280
$393$	−3.20532e6	−1.04686
$394$	−2.03945e6	−0.661870
$395$	1.61826e6	0.521863
$396$	−243988.	−0.0781862
$397$	5.70197e6	1.81572	0.907860	−	0.419274i	$-0.137715\pi$
$397$	5.70197e6	1.81572	0.907860	+	0.419274i	$0.137715\pi$
$398$	−1.55663e6	−0.492581
$399$	−3.37775e6	−1.06217
$400$	−704147.	−0.220046
$401$	4.34415e6	1.34910	0.674549	−	0.738230i	$-0.264338\pi$
$401$	4.34415e6	1.34910	0.674549	+	0.738230i	$0.264338\pi$
$402$	1.21071e6	0.373657
$403$	3.93064e6	1.20559
$404$	−1.87030e6	−0.570108
$405$	126956.	0.0384606
$406$	−2.40107e6	−0.722920
$407$	−873191.	−0.261290
$408$	119698.	0.0355989
$409$	−89096.3	−0.0263361	−0.0131680	−	0.999913i	$-0.504192\pi$
$409$	−89096.3	−0.0263361	−0.0131680	+	0.999913i	$0.504192\pi$
$410$	468940.	0.137771
$411$	−348165.	−0.101667
$412$	−57287.4	−0.0166271
$413$	517452.	0.149278
$414$	867148.	0.248652
$415$	−541242.	−0.154266
$416$	426442.	0.120816
$417$	−27376.4	−0.00770969
$418$	−1.90126e6	−0.532233
$419$	−4.92591e6	−1.37073	−0.685364	−	0.728201i	$-0.740357\pi$
$419$	−4.92591e6	−1.37073	−0.685364	+	0.728201i	$0.740357\pi$
$420$	414202.	0.114575
$421$	−1.68186e6	−0.462472	−0.231236	−	0.972898i	$-0.574277\pi$
$421$	−1.68186e6	−0.462472	−0.231236	+	0.972898i	$0.574277\pi$
$422$	1.32939e6	0.363389
$423$	392967.	0.106784
$424$	−66275.5	−0.0179035
$425$	571594.	0.153503
$426$	−1.58541e6	−0.423269
$427$	1.40321e6	0.372438
$428$	−238756.	−0.0630007
$429$	705610.	0.185107
$430$	518520.	0.135237
$431$	505903.	0.131182	0.0655909	−	0.997847i	$-0.479107\pi$
$431$	505903.	0.131182	0.0655909	+	0.997847i	$0.479107\pi$
$432$	186624.	0.0481125
$433$	3.22798e6	0.827393	0.413696	−	0.910415i	$-0.364238\pi$
$433$	3.22798e6	0.827393	0.413696	+	0.910415i	$0.364238\pi$
$434$	5.61216e6	1.43023
$435$	703242.	0.178189
$436$	−1.88446e6	−0.474757
$437$	6.75721e6	1.69264
$438$	12038.9	0.00299848
$439$	−4.95393e6	−1.22684	−0.613421	−	0.789756i	$-0.710207\pi$
$439$	−4.95393e6	−1.22684	−0.613421	+	0.789756i	$0.710207\pi$
$440$	233145.	0.0574109
$441$	428486.	0.104916
$442$	−346166.	−0.0842808
$443$	−1.89188e6	−0.458020	−0.229010	−	0.973424i	$-0.573549\pi$
$443$	−1.89188e6	−0.458020	−0.229010	+	0.973424i	$0.573549\pi$
$444$	667896.	0.160787
$445$	1.49905e6	0.358854
$446$	3.40017e6	0.809401
$447$	2.41440e6	0.571533
$448$	608872.	0.143328
$449$	1.30232e6	0.304861	0.152430	−	0.988314i	$-0.451290\pi$
$449$	1.30232e6	0.304861	0.152430	+	0.988314i	$0.451290\pi$
$450$	891186.	0.207461
$451$	1.14061e6	0.264056
$452$	−598339.	−0.137753
$453$	−2.20494e6	−0.504836
$454$	2.15605e6	0.490929
$455$	−1.19787e6	−0.271257
$456$	1.45426e6	0.327514
$457$	140716.	0.0315176	0.0157588	−	0.999876i	$-0.494984\pi$
$457$	140716.	0.0315176	0.0157588	+	0.999876i	$0.494984\pi$
$458$	−4.08280e6	−0.909483
$459$	−151493.	−0.0335630
$460$	−828612.	−0.182581
$461$	−1.44191e6	−0.315999	−0.158000	−	0.987439i	$-0.550504\pi$
$461$	−1.44191e6	−0.315999	−0.158000	+	0.987439i	$0.550504\pi$
$462$	1.00747e6	0.219597
$463$	3.63641e6	0.788353	0.394177	−	0.919035i	$-0.371030\pi$
$463$	3.63641e6	0.788353	0.394177	+	0.919035i	$0.371030\pi$
$464$	1.03376e6	0.222907
$465$	−1.64373e6	−0.352531
$466$	−927339.	−0.197822
$467$	−6.08448e6	−1.29101	−0.645507	−	0.763754i	$-0.723354\pi$
$467$	−6.08448e6	−1.29101	−0.645507	+	0.763754i	$0.723354\pi$
$468$	−539715.	−0.113907
$469$	−4.99922e6	−1.04947
$470$	−375504.	−0.0784097
$471$	−2.00943e6	−0.417370
$472$	−222784.	−0.0460287
$473$	1.26120e6	0.259198
$474$	−3.01071e6	−0.615492
$475$	6.94452e6	1.41224
$476$	−494255.	−0.0999847
$477$	83879.9	0.0168796
$478$	−3.95378e6	−0.791486
$479$	7.97376e6	1.58790	0.793952	−	0.607981i	$-0.208020\pi$
$479$	7.97376e6	1.58790	0.793952	+	0.607981i	$0.208020\pi$
$480$	−178330.	−0.0353283
$481$	−1.93155e6	−0.380665
$482$	4.18846e6	0.821178
$483$	−3.58061e6	−0.698375
$484$	−2.00973e6	−0.389965
$485$	−1.25533e6	−0.242328
$486$	−236196.	−0.0453609
$487$	3.40445e6	0.650466	0.325233	−	0.945634i	$-0.394557\pi$
$487$	3.40445e6	0.650466	0.325233	+	0.945634i	$0.394557\pi$
$488$	−604140.	−0.114839
$489$	2.00886e6	0.379908
$490$	−409445.	−0.0770380
$491$	−915857.	−0.171445	−0.0857223	−	0.996319i	$-0.527320\pi$
$491$	−915857.	−0.171445	−0.0857223	+	0.996319i	$0.527320\pi$
$492$	−872441.	−0.162489
$493$	−839158.	−0.155499
$494$	−4.20570e6	−0.775392
$495$	−295074.	−0.0541275
$496$	−2.41626e6	−0.441001
$497$	6.54642e6	1.18881
$498$	1.00696e6	0.181944
$499$	−72336.1	−0.0130048	−0.00650240	−	0.999979i	$-0.502070\pi$
$499$	−72336.1	−0.0130048	−0.00650240	+	0.999979i	$0.502070\pi$
$500$	−1.81909e6	−0.325408
$501$	−952170.	−0.169481
$502$	−1.60297e6	−0.283900
$503$	6.24106e6	1.09986	0.549931	−	0.835210i	$-0.314654\pi$
$503$	6.24106e6	1.09986	0.549931	+	0.835210i	$0.314654\pi$
$504$	−770604.	−0.135131
$505$	−2.26190e6	−0.394680
$506$	−2.01545e6	−0.349941
$507$	−1.78079e6	−0.307675
$508$	−2.52981e6	−0.434940
$509$	−5.80602e6	−0.993309	−0.496655	−	0.867948i	$-0.665438\pi$
$509$	−5.80602e6	−0.993309	−0.496655	+	0.867948i	$0.665438\pi$
$510$	144761.	0.0246448
$511$	−49710.7	−0.00842166
$512$	−262144.	−0.0441942
$513$	−1.84055e6	−0.308783
$514$	2.48385e6	0.414685
$515$	−69282.3	−0.0115108
$516$	−964683.	−0.159500
$517$	−913344.	−0.150282
$518$	−2.75786e6	−0.451594
$519$	6.17874e6	1.00689
$520$	515730.	0.0836401
$521$	−2.69746e6	−0.435372	−0.217686	−	0.976019i	$-0.569851\pi$
$521$	−2.69746e6	−0.435372	−0.217686	+	0.976019i	$0.569851\pi$
$522$	−1.30835e6	−0.210159
$523$	−1.19035e6	−0.190293	−0.0951463	−	0.995463i	$-0.530332\pi$
$523$	−1.19035e6	−0.190293	−0.0951463	+	0.995463i	$0.530332\pi$
$524$	−5.69835e6	−0.906611
$525$	−3.67987e6	−0.582685
$526$	6.03824e6	0.951581
$527$	1.96141e6	0.307640
$528$	−433756.	−0.0677112
$529$	726678.	0.112902
$530$	−80152.3	−0.0123944
$531$	281961.	0.0433963
$532$	−6.00490e6	−0.919870
$533$	2.52309e6	0.384694
$534$	−2.78893e6	−0.423237
$535$	−288747.	−0.0436148
$536$	2.15237e6	0.323597
$537$	3.54137e6	0.529950
$538$	3.44367e6	0.512939
$539$	−995898.	−0.147653
$540$	225700.	0.0333078
$541$	−1.01475e7	−1.49062	−0.745310	−	0.666718i	$-0.767699\pi$
$541$	−1.01475e7	−1.49062	−0.745310	+	0.666718i	$0.767699\pi$
$542$	−5.73147e6	−0.838046
$543$	−3.18401e6	−0.463420
$544$	212797.	0.0308296
$545$	−2.27903e6	−0.328670
$546$	2.22858e6	0.319924
$547$	−2.81574e6	−0.402369	−0.201185	−	0.979553i	$-0.564479\pi$
$547$	−2.81574e6	−0.402369	−0.201185	+	0.979553i	$0.564479\pi$
$548$	−618960.	−0.0880462
$549$	764615.	0.108271
$550$	−2.07132e6	−0.291971
$551$	−1.01953e7	−1.43060
$552$	1.54160e6	0.215339
$553$	1.24317e7	1.72870
$554$	−8.24951e6	−1.14197
$555$	807740.	0.111311
$556$	−48669.2	−0.00667679
$557$	−1.28099e7	−1.74947	−0.874737	−	0.484599i	$-0.838966\pi$
$557$	−1.28099e7	−1.74947	−0.874737	+	0.484599i	$0.838966\pi$
$558$	3.05808e6	0.415780
$559$	2.78986e6	0.377618
$560$	736359.	0.0992246
$561$	352103.	0.0472349
$562$	−9.18175e6	−1.22627
$563$	6.56797e6	0.873294	0.436647	−	0.899633i	$-0.356166\pi$
$563$	6.56797e6	0.873294	0.436647	+	0.899633i	$0.356166\pi$
$564$	698608.	0.0924775
$565$	−723620.	−0.0953651
$566$	−2.57829e6	−0.338291
$567$	975296.	0.127403
$568$	−2.81850e6	−0.366562
$569$	−8.20483e6	−1.06240	−0.531201	−	0.847246i	$-0.678259\pi$
$569$	−8.20483e6	−1.06240	−0.531201	+	0.847246i	$0.678259\pi$
$570$	1.75875e6	0.226735
$571$	1.38553e7	1.77838	0.889190	−	0.457538i	$-0.151269\pi$
$571$	1.38553e7	1.77838	0.889190	+	0.457538i	$0.151269\pi$
$572$	1.25442e6	0.160307
$573$	6.08077e6	0.773699
$574$	3.60247e6	0.456373
$575$	7.36159e6	0.928542
$576$	331776.	0.0416667
$577$	4.15500e6	0.519555	0.259778	−	0.965668i	$-0.416351\pi$
$577$	4.15500e6	0.519555	0.259778	+	0.965668i	$0.416351\pi$
$578$	5.50669e6	0.685600
$579$	2.57541e6	0.319264
$580$	1.25021e6	0.154316
$581$	−4.15790e6	−0.511016
$582$	2.33548e6	0.285805
$583$	−194956.	−0.0237555
$584$	21402.5	0.00259676
$585$	−652721.	−0.0788566
$586$	4.59431e6	0.552683
$587$	−1.13785e7	−1.36299	−0.681493	−	0.731824i	$-0.738669\pi$
$587$	−1.13785e7	−1.36299	−0.681493	+	0.731824i	$0.738669\pi$
$588$	761753.	0.0908597
$589$	2.38300e7	2.83032
$590$	−269431.	−0.0318652
$591$	4.58876e6	0.540414
$592$	1.18737e6	0.139246
$593$	839436.	0.0980282	0.0490141	−	0.998798i	$-0.484392\pi$
$593$	839436.	0.0980282	0.0490141	+	0.998798i	$0.484392\pi$
$594$	548972.	0.0638387
$595$	−597742.	−0.0692184
$596$	4.29227e6	0.494962
$597$	3.50242e6	0.402191
$598$	−4.45828e6	−0.509817
$599$	3.26777e6	0.372121	0.186061	−	0.982538i	$-0.440428\pi$
$599$	3.26777e6	0.372121	0.186061	+	0.982538i	$0.440428\pi$
$600$	1.58433e6	0.179667
$601$	−963427.	−0.108801	−0.0544004	−	0.998519i	$-0.517325\pi$
$601$	−963427.	−0.108801	−0.0544004	+	0.998519i	$0.517325\pi$
$602$	3.98335e6	0.447979
$603$	−2.72409e6	−0.305090
$604$	−3.91989e6	−0.437201
$605$	−2.43053e6	−0.269969
$606$	4.20817e6	0.465491
$607$	−6.69905e6	−0.737975	−0.368987	−	0.929434i	$-0.620295\pi$
$607$	−6.69905e6	−0.737975	−0.368987	+	0.929434i	$0.620295\pi$
$608$	2.58535e6	0.283635
$609$	5.40241e6	0.590261
$610$	−730636.	−0.0795017
$611$	−2.02037e6	−0.218941
$612$	−269321.	−0.0290664
$613$	1.24423e7	1.33736	0.668682	−	0.743548i	$-0.266859\pi$
$613$	1.24423e7	1.33736	0.668682	+	0.743548i	$0.266859\pi$
$614$	−4.20459e6	−0.450094
$615$	−1.05511e6	−0.112489
$616$	1.79106e6	0.190177
$617$	−1.11819e6	−0.118251	−0.0591254	−	0.998251i	$-0.518831\pi$
$617$	−1.11819e6	−0.118251	−0.0591254	+	0.998251i	$0.518831\pi$
$618$	128897.	0.0135760
$619$	1.30841e6	0.137252	0.0686258	−	0.997642i	$-0.478139\pi$
$619$	1.30841e6	0.137252	0.0686258	+	0.997642i	$0.478139\pi$
$620$	−2.92218e6	−0.305301
$621$	−1.95108e6	−0.203024
$622$	−5.57135e6	−0.577410
$623$	1.15160e7	1.18872
$624$	−959493.	−0.0986462
$625$	6.39557e6	0.654907
$626$	4.12768e6	0.420988
$627$	4.27784e6	0.434566
$628$	−3.57232e6	−0.361453
$629$	−963853.	−0.0971369
$630$	−931954.	−0.0935498
$631$	−8.73726e6	−0.873578	−0.436789	−	0.899564i	$-0.643884\pi$
$631$	−8.73726e6	−0.873578	−0.436789	+	0.899564i	$0.643884\pi$
$632$	−5.35237e6	−0.533032
$633$	−2.99113e6	−0.296706
$634$	−7.05710e6	−0.697273
$635$	−3.05951e6	−0.301105
$636$	149120.	0.0146182
$637$	−2.20298e6	−0.215111
$638$	3.04090e6	0.295767
$639$	3.56716e6	0.345598
$640$	−317032.	−0.0305952
$641$	1.12331e7	1.07983	0.539914	−	0.841720i	$-0.318457\pi$
$641$	1.12331e7	1.07983	0.539914	+	0.841720i	$0.318457\pi$
$642$	537202.	0.0514399
$643$	−1.26339e7	−1.20506	−0.602531	−	0.798096i	$-0.705841\pi$
$643$	−1.26339e7	−1.20506	−0.602531	+	0.798096i	$0.705841\pi$
$644$	−6.36553e6	−0.604811
$645$	−1.16667e6	−0.110420
$646$	−2.09867e6	−0.197862
$647$	−8.57589e6	−0.805413	−0.402706	−	0.915329i	$-0.631930\pi$
$647$	−8.57589e6	−0.805413	−0.402706	+	0.915329i	$0.631930\pi$
$648$	−419904.	−0.0392837
$649$	−655340.	−0.0610738
$650$	−4.58187e6	−0.425363
$651$	−1.26274e7	−1.16778
$652$	3.57131e6	0.329010
$653$	1.36045e7	1.24853	0.624265	−	0.781212i	$-0.285398\pi$
$653$	1.36045e7	1.24853	0.624265	+	0.781212i	$0.285398\pi$
$654$	4.24004e6	0.387638
$655$	−6.89148e6	−0.627638
$656$	−1.55101e6	−0.140719
$657$	−27087.5	−0.00244825
$658$	−2.88468e6	−0.259736
$659$	5.22594e6	0.468761	0.234380	−	0.972145i	$-0.424694\pi$
$659$	5.22594e6	0.468761	0.234380	+	0.972145i	$0.424694\pi$
$660$	−524576.	−0.0468758
$661$	1.47330e7	1.31156	0.655779	−	0.754953i	$-0.272340\pi$
$661$	1.47330e7	1.31156	0.655779	+	0.754953i	$0.272340\pi$
$662$	8.54851e6	0.758133
$663$	778873.	0.0688150
$664$	1.79014e6	0.157568
$665$	−7.26221e6	−0.636817
$666$	−1.50277e6	−0.131282
$667$	−1.08075e7	−0.940616
$668$	−1.69275e6	−0.146775
$669$	−7.65039e6	−0.660873
$670$	2.60303e6	0.224023
$671$	−1.77714e6	−0.152375
$672$	−1.36996e6	−0.117027
$673$	401389.	0.0341608	0.0170804	−	0.999854i	$-0.494563\pi$
$673$	401389.	0.0341608	0.0170804	+	0.999854i	$0.494563\pi$
$674$	9.19438e6	0.779602
$675$	−2.00517e6	−0.169391
$676$	−3.16584e6	−0.266454
$677$	4.97322e6	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$677$	4.97322e6	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$678$	1.34626e6	0.112475
$679$	−9.64363e6	−0.802723
$680$	257352.	0.0213430
$681$	−4.85111e6	−0.400842
$682$	−7.10766e6	−0.585148
$683$	−1.20550e6	−0.0988818	−0.0494409	−	0.998777i	$-0.515744\pi$
$683$	−1.20550e6	−0.0988818	−0.0494409	+	0.998777i	$0.515744\pi$
$684$	−3.27208e6	−0.267414
$685$	−748558.	−0.0609535
$686$	6.84806e6	0.555593
$687$	9.18630e6	0.742590
$688$	−1.71499e6	−0.138131
$689$	−431253.	−0.0346086
$690$	1.86438e6	0.149077
$691$	3.67333e6	0.292661	0.146331	−	0.989236i	$-0.453254\pi$
$691$	3.67333e6	0.292661	0.146331	+	0.989236i	$0.453254\pi$
$692$	1.09844e7	0.871991
$693$	−2.26680e6	−0.179300
$694$	6.40393e6	0.504717
$695$	−58859.7	−0.00462227
$696$	−2.32596e6	−0.182003
$697$	1.25904e6	0.0981650
$698$	9.58886e6	0.744952
$699$	2.08651e6	0.161521
$700$	−6.54198e6	−0.504620
$701$	2.06576e7	1.58776	0.793881	−	0.608073i	$-0.208057\pi$
$701$	2.06576e7	1.58776	0.793881	+	0.608073i	$0.208057\pi$
$702$	1.21436e6	0.0930046
$703$	−1.17102e7	−0.893670
$704$	−771122.	−0.0586396
$705$	844884.	0.0640213
$706$	1.14925e7	0.867767
$707$	−1.73763e7	−1.30740
$708$	501264.	0.0375823
$709$	1.00691e7	0.752269	0.376135	−	0.926565i	$-0.377253\pi$
$709$	1.00691e7	0.752269	0.376135	+	0.926565i	$0.377253\pi$
$710$	−3.40864e6	−0.253767
$711$	6.77409e6	0.502547
$712$	−4.95809e6	−0.366534
$713$	2.52611e7	1.86092
$714$	1.11207e6	0.0816372
$715$	1.51707e6	0.110979
$716$	6.29576e6	0.458950
$717$	8.89601e6	0.646245
$718$	−1.61828e6	−0.117150
$719$	−2.35892e7	−1.70173	−0.850867	−	0.525381i	$-0.823923\pi$
$719$	−2.35892e7	−1.70173	−0.850867	+	0.525381i	$0.823923\pi$
$720$	401244.	0.0288454
$721$	−532238.	−0.0381301
$722$	−1.55932e7	−1.11325
$723$	−9.42404e6	−0.670489
$724$	−5.66046e6	−0.401334
$725$	−1.11071e7	−0.784797
$726$	4.52190e6	0.318405
$727$	1.96765e6	0.138074	0.0690371	−	0.997614i	$-0.478007\pi$
$727$	1.96765e6	0.138074	0.0690371	+	0.997614i	$0.478007\pi$
$728$	3.96192e6	0.277062
$729$	531441.	0.0370370
$730$	25883.7	0.00179771
$731$	1.39215e6	0.0963593
$732$	1.35932e6	0.0937654
$733$	2.01666e7	1.38635	0.693176	−	0.720768i	$-0.256211\pi$
$733$	2.01666e7	1.38635	0.693176	+	0.720768i	$0.256211\pi$
$734$	−3.35323e6	−0.229733
$735$	921250.	0.0629012
$736$	2.74062e6	0.186489
$737$	6.33139e6	0.429368
$738$	1.96299e6	0.132672
$739$	−2.10379e7	−1.41707	−0.708536	−	0.705675i	$-0.750644\pi$
$739$	−2.10379e7	−1.41707	−0.708536	+	0.705675i	$0.750644\pi$
$740$	1.43598e6	0.0963984
$741$	9.46284e6	0.633105
$742$	−615743.	−0.0410572
$743$	−2.34963e6	−0.156145	−0.0780725	−	0.996948i	$-0.524877\pi$
$743$	−2.34963e6	−0.156145	−0.0780725	+	0.996948i	$0.524877\pi$
$744$	5.43659e6	0.360076
$745$	5.19100e6	0.342657
$746$	8.91375e6	0.586426
$747$	−2.26565e6	−0.148557
$748$	625961.	0.0409066
$749$	−2.21820e6	−0.144476
$750$	4.09295e6	0.265695
$751$	−1.75373e6	−0.113465	−0.0567325	−	0.998389i	$-0.518068\pi$
$751$	−1.75373e6	−0.113465	−0.0567325	+	0.998389i	$0.518068\pi$
$752$	1.24197e6	0.0800879
$753$	3.60668e6	0.231803
$754$	6.72664e6	0.430894
$755$	−4.74064e6	−0.302670
$756$	1.73386e6	0.110334
$757$	2.92935e7	1.85794	0.928969	−	0.370157i	$-0.120696\pi$
$757$	2.92935e7	1.85794	0.928969	+	0.370157i	$0.120696\pi$
$758$	1.71555e6	0.108450
$759$	4.53475e6	0.285726
$760$	3.12667e6	0.196358
$761$	−1.48356e7	−0.928633	−0.464316	−	0.885669i	$-0.653700\pi$
$761$	−1.48356e7	−0.928633	−0.464316	+	0.885669i	$0.653700\pi$
$762$	5.69208e6	0.355127
$763$	−1.75079e7	−1.08874
$764$	1.08103e7	0.670043
$765$	−325711.	−0.0201224
$766$	1.60052e7	0.985571
$767$	−1.44965e6	−0.0889765
$768$	589824.	0.0360844
$769$	8.96309e6	0.546565	0.273282	−	0.961934i	$-0.411891\pi$
$769$	8.96309e6	0.546565	0.273282	+	0.961934i	$0.411891\pi$
$770$	2.16607e6	0.131657
$771$	−5.58867e6	−0.338589
$772$	4.57851e6	0.276491
$773$	−4.91868e6	−0.296074	−0.148037	−	0.988982i	$-0.547295\pi$
$773$	−4.91868e6	−0.296074	−0.148037	+	0.988982i	$0.547295\pi$
$774$	2.17054e6	0.130231
$775$	2.59614e7	1.55265
$776$	4.15197e6	0.247514
$777$	6.20519e6	0.368725
$778$	−1.57276e7	−0.931566
$779$	1.52965e7	0.903128
$780$	−1.16039e6	−0.0682918
$781$	−8.29088e6	−0.486377
$782$	−2.22471e6	−0.130094
$783$	2.94379e6	0.171594
$784$	1.35423e6	0.0786868
$785$	−4.32030e6	−0.250230
$786$	1.28213e7	0.740245
$787$	2.16968e7	1.24870	0.624352	−	0.781143i	$-0.285363\pi$
$787$	2.16968e7	1.24870	0.624352	+	0.781143i	$0.285363\pi$
$788$	8.15780e6	0.468013
$789$	−1.35860e7	−0.776963
$790$	−6.47305e6	−0.369013
$791$	−5.55896e6	−0.315902
$792$	975951.	0.0552860
$793$	−3.93113e6	−0.221990
$794$	−2.28079e7	−1.28391
$795$	180343.	0.0101200
$796$	6.22652e6	0.348307
$797$	1.72044e7	0.959385	0.479693	−	0.877437i	$-0.340748\pi$
$797$	1.72044e7	0.959385	0.479693	+	0.877437i	$0.340748\pi$
$798$	1.35110e7	0.751071
$799$	−1.00818e6	−0.0558688
$800$	2.81659e6	0.155596
$801$	6.27508e6	0.345572
$802$	−1.73766e7	−0.953956
$803$	62957.4	0.00344555
$804$	−4.84282e6	−0.264216
$805$	−7.69835e6	−0.418705
$806$	−1.57226e7	−0.852483
$807$	−7.74826e6	−0.418813
$808$	7.48118e6	0.403127
$809$	−1.53715e7	−0.825742	−0.412871	−	0.910789i	$-0.635474\pi$
$809$	−1.53715e7	−0.825742	−0.412871	+	0.910789i	$0.635474\pi$
$810$	−507824.	−0.0271957
$811$	3.63122e7	1.93865	0.969327	−	0.245775i	$-0.0790425\pi$
$811$	3.63122e7	1.93865	0.969327	+	0.245775i	$0.0790425\pi$
$812$	9.60429e6	0.511181
$813$	1.28958e7	0.684262
$814$	3.49276e6	0.184760
$815$	4.31908e6	0.227770
$816$	−478792.	−0.0251722
$817$	1.69138e7	0.886516
$818$	356385.	0.0186224
$819$	−5.01431e6	−0.261217
$820$	−1.87576e6	−0.0974187
$821$	2.43145e7	1.25895	0.629473	−	0.777023i	$-0.283271\pi$
$821$	2.43145e7	1.25895	0.629473	+	0.777023i	$0.283271\pi$
$822$	1.39266e6	0.0718895
$823$	−3.54275e7	−1.82323	−0.911614	−	0.411047i	$-0.865163\pi$
$823$	−3.54275e7	−1.82323	−0.911614	+	0.411047i	$0.865163\pi$
$824$	229150.	0.0117571
$825$	4.66046e6	0.238393
$826$	−2.06981e6	−0.105555
$827$	−2.44827e7	−1.24479	−0.622395	−	0.782703i	$-0.713840\pi$
$827$	−2.44827e7	−1.24479	−0.622395	+	0.782703i	$0.713840\pi$
$828$	−3.46859e6	−0.175824
$829$	4.97244e6	0.251295	0.125647	−	0.992075i	$-0.459899\pi$
$829$	4.97244e6	0.251295	0.125647	+	0.992075i	$0.459899\pi$
$830$	2.16497e6	0.109083
$831$	1.85614e7	0.932413
$832$	−1.70577e6	−0.0854301
$833$	−1.09930e6	−0.0548914
$834$	109506.	0.00545157
$835$	−2.04718e6	−0.101611
$836$	7.60505e6	0.376345
$837$	−6.88068e6	−0.339483
$838$	1.97036e7	0.969251
$839$	−1.49211e6	−0.0731807	−0.0365904	−	0.999330i	$-0.511650\pi$
$839$	−1.49211e6	−0.0731807	−0.0365904	+	0.999330i	$0.511650\pi$
$840$	−1.65681e6	−0.0810165
$841$	−4.20476e6	−0.204999
$842$	6.72746e6	0.327017
$843$	2.06589e7	1.00124
$844$	−5.31757e6	−0.256955
$845$	−3.82871e6	−0.184464
$846$	−1.57187e6	−0.0755076
$847$	−1.86717e7	−0.894286
$848$	265102.	0.0126597
$849$	5.80115e6	0.276213
$850$	−2.28638e6	−0.108543
$851$	−1.24135e7	−0.587585
$852$	6.34162e6	0.299296
$853$	2.17016e7	1.02122	0.510610	−	0.859813i	$-0.329420\pi$
$853$	2.17016e7	1.02122	0.510610	+	0.859813i	$0.329420\pi$
$854$	−5.61286e6	−0.263354
$855$	−3.95719e6	−0.185128
$856$	955025.	0.0445482
$857$	2.90427e7	1.35078	0.675391	−	0.737460i	$-0.263975\pi$
$857$	2.90427e7	1.35078	0.675391	+	0.737460i	$0.263975\pi$
$858$	−2.82244e6	−0.130890
$859$	−2.10229e7	−0.972098	−0.486049	−	0.873931i	$-0.661562\pi$
$859$	−2.10229e7	−0.972098	−0.486049	+	0.873931i	$0.661562\pi$
$860$	−2.07408e6	−0.0956267
$861$	−8.10555e6	−0.372627
$862$	−2.02361e6	−0.0927596
$863$	1.18377e7	0.541054	0.270527	−	0.962712i	$-0.412802\pi$
$863$	1.18377e7	0.541054	0.270527	+	0.962712i	$0.412802\pi$
$864$	−746496.	−0.0340207
$865$	1.32844e7	0.603671
$866$	−1.29119e7	−0.585055
$867$	−1.23901e7	−0.559790
$868$	−2.24487e7	−1.01133
$869$	−1.57445e7	−0.707261
$870$	−2.81297e6	−0.125999
$871$	1.40054e7	0.625533
$872$	7.53785e6	0.335704
$873$	−5.25484e6	−0.233358
$874$	−2.70288e7	−1.19687
$875$	−1.69005e7	−0.746242
$876$	−48155.6	−0.00212025
$877$	6.65499e6	0.292179	0.146089	−	0.989271i	$-0.453331\pi$
$877$	6.65499e6	0.292179	0.146089	+	0.989271i	$0.453331\pi$
$878$	1.98157e7	0.867508
$879$	−1.03372e7	−0.451264
$880$	−932580.	−0.0405956
$881$	−2.16815e7	−0.941129	−0.470564	−	0.882366i	$-0.655950\pi$
$881$	−2.16815e7	−0.941129	−0.470564	+	0.882366i	$0.655950\pi$
$882$	−1.71395e6	−0.0741866
$883$	2.13153e7	0.920006	0.460003	−	0.887917i	$-0.347848\pi$
$883$	2.13153e7	0.920006	0.460003	+	0.887917i	$0.347848\pi$
$884$	1.38466e6	0.0595955
$885$	606219.	0.0260179
$886$	7.56752e6	0.323869
$887$	−1.81280e7	−0.773642	−0.386821	−	0.922155i	$-0.626427\pi$
$887$	−1.81280e7	−0.773642	−0.386821	+	0.922155i	$0.626427\pi$
$888$	−2.67158e6	−0.113694
$889$	−2.35036e7	−0.997426
$890$	−5.99622e6	−0.253748
$891$	−1.23519e6	−0.0521241
$892$	−1.36007e7	−0.572333
$893$	−1.22487e7	−0.513999
$894$	−9.65762e6	−0.404135
$895$	7.61397e6	0.317727
$896$	−2.43549e6	−0.101348
$897$	1.00311e7	0.416264
$898$	−5.20928e6	−0.215569
$899$	−3.81139e7	−1.57284
$900$	−3.56474e6	−0.146697
$901$	−215198.	−0.00883132
$902$	−4.56243e6	−0.186715
$903$	−8.96254e6	−0.365773
$904$	2.39336e6	0.0974062
$905$	−6.84566e6	−0.277839
$906$	8.81974e6	0.356973
$907$	1.54556e7	0.623832	0.311916	−	0.950110i	$-0.399029\pi$
$907$	1.54556e7	0.623832	0.311916	+	0.950110i	$0.399029\pi$
$908$	−8.62419e6	−0.347139
$909$	−9.46837e6	−0.380072
$910$	4.79147e6	0.191807
$911$	−3.83293e7	−1.53015	−0.765076	−	0.643940i	$-0.777299\pi$
$911$	−3.83293e7	−1.53015	−0.765076	+	0.643940i	$0.777299\pi$
$912$	−5.81704e6	−0.231587
$913$	5.26588e6	0.209071
$914$	−562865.	−0.0222863
$915$	1.64393e6	0.0649128
$916$	1.63312e7	0.643101
$917$	−5.29414e7	−2.07908
$918$	605971.	0.0237326
$919$	−1.17590e7	−0.459284	−0.229642	−	0.973275i	$-0.573756\pi$
$919$	−1.17590e7	−0.459284	−0.229642	+	0.973275i	$0.573756\pi$
$920$	3.31445e6	0.129105
$921$	9.46034e6	0.367500
$922$	5.76764e6	0.223445
$923$	−1.83399e7	−0.708587
$924$	−4.02988e6	−0.155279
$925$	−1.27576e7	−0.490247
$926$	−1.45457e7	−0.557450
$927$	−290018.	−0.0110847
$928$	−4.13503e6	−0.157619
$929$	1.81651e7	0.690556	0.345278	−	0.938501i	$-0.387785\pi$
$929$	1.81651e7	0.690556	0.345278	+	0.938501i	$0.387785\pi$
$930$	6.57491e6	0.249277
$931$	−1.33558e7	−0.505007
$932$	3.70936e6	0.139881
$933$	1.25355e7	0.471454
$934$	2.43379e7	0.912885
$935$	757026.	0.0283192
$936$	2.15886e6	0.0805443
$937$	1.04719e7	0.389653	0.194827	−	0.980838i	$-0.437586\pi$
$937$	1.04719e7	0.389653	0.194827	+	0.980838i	$0.437586\pi$
$938$	1.99969e7	0.742087
$939$	−9.28728e6	−0.343735
$940$	1.50202e6	0.0554440
$941$	−4.22942e7	−1.55706	−0.778532	−	0.627605i	$-0.784035\pi$
$941$	−4.22942e7	−1.55706	−0.778532	+	0.627605i	$0.784035\pi$
$942$	8.03773e6	0.295125
$943$	1.62152e7	0.593803
$944$	891136.	0.0325472
$945$	2.09690e6	0.0763831
$946$	−5.04481e6	−0.183281
$947$	−5.13864e7	−1.86197	−0.930986	−	0.365054i	$-0.881050\pi$
$947$	−5.13864e7	−1.86197	−0.930986	+	0.365054i	$0.881050\pi$
$948$	1.20428e7	0.435219
$949$	139265.	0.00501970
$950$	−2.77781e7	−0.998605
$951$	1.58785e7	0.569321
$952$	1.97702e6	0.0706998
$953$	1.45012e7	0.517216	0.258608	−	0.965982i	$-0.416736\pi$
$953$	1.45012e7	0.517216	0.258608	+	0.965982i	$0.416736\pi$
$954$	−335520.	−0.0119357
$955$	1.30737e7	0.463864
$956$	1.58151e7	0.559665
$957$	−6.84202e6	−0.241493
$958$	−3.18950e7	−1.12282
$959$	−5.75054e6	−0.201912
$960$	713322.	0.0249809
$961$	6.04566e7	2.11171
$962$	7.72620e6	0.269171
$963$	−1.20870e6	−0.0420005
$964$	−1.67539e7	−0.580660
$965$	5.53716e6	0.191412
$966$	1.43224e7	0.493826
$967$	−2.61708e7	−0.900019	−0.450009	−	0.893024i	$-0.648579\pi$
$967$	−2.61708e7	−0.900019	−0.450009	+	0.893024i	$0.648579\pi$
$968$	8.03894e6	0.275747
$969$	4.72200e6	0.161554
$970$	5.02131e6	0.171352
$971$	−2.18990e7	−0.745376	−0.372688	−	0.927957i	$-0.621564\pi$
$971$	−2.18990e7	−0.745376	−0.372688	+	0.927957i	$0.621564\pi$
$972$	944784.	0.0320750
$973$	−452169.	−0.0153115
$974$	−1.36178e7	−0.459949
$975$	1.03092e7	0.347307
$976$	2.41656e6	0.0812032
$977$	−1.13130e7	−0.379175	−0.189588	−	0.981864i	$-0.560715\pi$
$977$	−1.13130e7	−0.379175	−0.189588	+	0.981864i	$0.560715\pi$
$978$	−8.03545e6	−0.268635
$979$	−1.45847e7	−0.486341
$980$	1.63778e6	0.0544741
$981$	−9.54010e6	−0.316505
$982$	3.66343e6	0.121230
$983$	−2.67119e7	−0.881701	−0.440850	−	0.897581i	$-0.645323\pi$
$983$	−2.67119e7	−0.881701	−0.440850	+	0.897581i	$0.645323\pi$
$984$	3.48977e6	0.114897
$985$	9.86589e6	0.324001
$986$	3.35663e6	0.109954
$987$	6.49053e6	0.212074
$988$	1.68228e7	0.548285
$989$	1.79296e7	0.582881
$990$	1.18030e6	0.0382739
$991$	−1.29521e7	−0.418944	−0.209472	−	0.977815i	$-0.567174\pi$
$991$	−1.29521e7	−0.418944	−0.209472	+	0.977815i	$0.567174\pi$
$992$	9.66505e6	0.311835
$993$	−1.92341e7	−0.619013
$994$	−2.61857e7	−0.840617
$995$	7.53023e6	0.241130
$996$	−4.02783e6	−0.128654
$997$	5.44438e7	1.73465	0.867323	−	0.497746i	$-0.165839\pi$
$997$	5.44438e7	1.73465	0.867323	+	0.497746i	$0.165839\pi$
$998$	289344.	0.00919578
$999$	3.38122e6	0.107191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.c.1.4	✓	5
3.2	odd	2		1062.6.a.f.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.c.1.4	✓	5	1.1	even	1	trivial
1062.6.a.f.1.2		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +19.3501 q^{5} -36.0000 q^{6} +148.650 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +19.3501 q^{5} -36.0000 q^{6} +148.650 q^{7} -64.0000 q^{8} +81.0000 q^{9} -77.4004 q^{10} -188.262 q^{11} +144.000 q^{12} -416.447 q^{13} -594.602 q^{14} +174.151 q^{15} +256.000 q^{16} -207.809 q^{17} -324.000 q^{18} -2524.76 q^{19} +309.602 q^{20} +1337.85 q^{21} +753.048 q^{22} -2676.38 q^{23} -576.000 q^{24} -2750.57 q^{25} +1665.79 q^{26} +729.000 q^{27} +2378.41 q^{28} +4038.12 q^{29} -696.604 q^{30} -9438.52 q^{31} -1024.00 q^{32} -1694.36 q^{33} +831.237 q^{34} +2876.40 q^{35} +1296.00 q^{36} +4638.16 q^{37} +10099.0 q^{38} -3748.02 q^{39} -1238.41 q^{40} -6058.62 q^{41} -5351.42 q^{42} -6699.19 q^{43} -3012.19 q^{44} +1567.36 q^{45} +10705.5 q^{46} +4851.45 q^{47} +2304.00 q^{48} +5289.95 q^{49} +11002.3 q^{50} -1870.28 q^{51} -6663.15 q^{52} +1035.55 q^{53} -2916.00 q^{54} -3642.89 q^{55} -9513.63 q^{56} -22722.8 q^{57} -16152.5 q^{58} +3481.00 q^{59} +2786.41 q^{60} +9439.69 q^{61} +37754.1 q^{62} +12040.7 q^{63} +4096.00 q^{64} -8058.29 q^{65} +6777.44 q^{66} -33630.7 q^{67} -3324.95 q^{68} -24087.4 q^{69} -11505.6 q^{70} +44039.0 q^{71} -5184.00 q^{72} -334.414 q^{73} -18552.7 q^{74} -24755.2 q^{75} -40396.1 q^{76} -27985.2 q^{77} +14992.1 q^{78} +83630.8 q^{79} +4953.62 q^{80} +6561.00 q^{81} +24234.5 q^{82} -27971.0 q^{83} +21405.7 q^{84} -4021.13 q^{85} +26796.8 q^{86} +36343.0 q^{87} +12048.8 q^{88} +77470.1 q^{89} -6269.43 q^{90} -61905.0 q^{91} -42822.1 q^{92} -84946.7 q^{93} -19405.8 q^{94} -48854.3 q^{95} -9216.00 q^{96} -64874.5 q^{97} -21159.8 q^{98} -15249.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9}+O(q^{10}) \) 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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