LMFDB - Embedded newform 462.6.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,6,Mod(1,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("462.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	462.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:	$74.0973247536$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1511x + 16911 $ x^3 - x^2 - 1511*x + 16911
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-43.1276$ of defining polynomial
Character	$\chi$	$=$	462.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -20.3563 q^{5} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -20.3563 q^{5} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} -81.4254 q^{10} -121.000 q^{11} -144.000 q^{12} -366.292 q^{13} -196.000 q^{14} +183.207 q^{15} +256.000 q^{16} +1208.20 q^{17} +324.000 q^{18} +554.877 q^{19} -325.702 q^{20} +441.000 q^{21} -484.000 q^{22} -4646.98 q^{23} -576.000 q^{24} -2710.62 q^{25} -1465.17 q^{26} -729.000 q^{27} -784.000 q^{28} +5097.85 q^{29} +732.829 q^{30} +3250.38 q^{31} +1024.00 q^{32} +1089.00 q^{33} +4832.80 q^{34} +997.461 q^{35} +1296.00 q^{36} +2479.02 q^{37} +2219.51 q^{38} +3296.63 q^{39} -1302.81 q^{40} -8517.13 q^{41} +1764.00 q^{42} +17026.2 q^{43} -1936.00 q^{44} -1648.86 q^{45} -18587.9 q^{46} +19310.8 q^{47} -2304.00 q^{48} +2401.00 q^{49} -10842.5 q^{50} -10873.8 q^{51} -5860.67 q^{52} -7521.82 q^{53} -2916.00 q^{54} +2463.12 q^{55} -3136.00 q^{56} -4993.90 q^{57} +20391.4 q^{58} -1940.84 q^{59} +2931.31 q^{60} -18493.6 q^{61} +13001.5 q^{62} -3969.00 q^{63} +4096.00 q^{64} +7456.37 q^{65} +4356.00 q^{66} +58040.0 q^{67} +19331.2 q^{68} +41822.8 q^{69} +3989.84 q^{70} +74760.3 q^{71} +5184.00 q^{72} +20954.5 q^{73} +9916.09 q^{74} +24395.6 q^{75} +8878.04 q^{76} +5929.00 q^{77} +13186.5 q^{78} +19866.5 q^{79} -5211.23 q^{80} +6561.00 q^{81} -34068.5 q^{82} -77049.2 q^{83} +7056.00 q^{84} -24594.5 q^{85} +68105.0 q^{86} -45880.7 q^{87} -7744.00 q^{88} +141671. q^{89} -6595.46 q^{90} +17948.3 q^{91} -74351.7 q^{92} -29253.4 q^{93} +77243.1 q^{94} -11295.3 q^{95} -9216.00 q^{96} -104835. q^{97} +9604.00 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 56 q^{5} - 108 q^{6} - 147 q^{7} + 192 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 56 * q^5 - 108 * q^6 - 147 * q^7 + 192 * q^8 + 243 * q^9	\( 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 56 q^{5} - 108 q^{6} - 147 q^{7} + 192 q^{8} + 243 q^{9} - 224 q^{10} - 363 q^{11} - 432 q^{12} - 552 q^{13} - 588 q^{14} + 504 q^{15} + 768 q^{16} - 778 q^{17} + 972 q^{18} - 34 q^{19} - 896 q^{20} + 1323 q^{21} - 1452 q^{22} + 872 q^{23} - 1728 q^{24} - 537 q^{25} - 2208 q^{26} - 2187 q^{27} - 2352 q^{28} + 4752 q^{29} + 2016 q^{30} + 3116 q^{31} + 3072 q^{32} + 3267 q^{33} - 3112 q^{34} + 2744 q^{35} + 3888 q^{36} + 4768 q^{37} - 136 q^{38} + 4968 q^{39} - 3584 q^{40} - 7166 q^{41} + 5292 q^{42} + 10508 q^{43} - 5808 q^{44} - 4536 q^{45} + 3488 q^{46} + 7782 q^{47} - 6912 q^{48} + 7203 q^{49} - 2148 q^{50} + 7002 q^{51} - 8832 q^{52} + 27742 q^{53} - 8748 q^{54} + 6776 q^{55} - 9408 q^{56} + 306 q^{57} + 19008 q^{58} + 3850 q^{59} + 8064 q^{60} + 50106 q^{61} + 12464 q^{62} - 11907 q^{63} + 12288 q^{64} + 54566 q^{65} + 13068 q^{66} + 110686 q^{67} - 12448 q^{68} - 7848 q^{69} + 10976 q^{70} + 105720 q^{71} + 15552 q^{72} + 74544 q^{73} + 19072 q^{74} + 4833 q^{75} - 544 q^{76} + 17787 q^{77} + 19872 q^{78} + 67952 q^{79} - 14336 q^{80} + 19683 q^{81} - 28664 q^{82} + 46216 q^{83} + 21168 q^{84} + 16240 q^{85} + 42032 q^{86} - 42768 q^{87} - 23232 q^{88} + 124750 q^{89} - 18144 q^{90} + 27048 q^{91} + 13952 q^{92} - 28044 q^{93} + 31128 q^{94} + 176906 q^{95} - 27648 q^{96} - 54110 q^{97} + 28812 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 56 * q^5 - 108 * q^6 - 147 * q^7 + 192 * q^8 + 243 * q^9 - 224 * q^10 - 363 * q^11 - 432 * q^12 - 552 * q^13 - 588 * q^14 + 504 * q^15 + 768 * q^16 - 778 * q^17 + 972 * q^18 - 34 * q^19 - 896 * q^20 + 1323 * q^21 - 1452 * q^22 + 872 * q^23 - 1728 * q^24 - 537 * q^25 - 2208 * q^26 - 2187 * q^27 - 2352 * q^28 + 4752 * q^29 + 2016 * q^30 + 3116 * q^31 + 3072 * q^32 + 3267 * q^33 - 3112 * q^34 + 2744 * q^35 + 3888 * q^36 + 4768 * q^37 - 136 * q^38 + 4968 * q^39 - 3584 * q^40 - 7166 * q^41 + 5292 * q^42 + 10508 * q^43 - 5808 * q^44 - 4536 * q^45 + 3488 * q^46 + 7782 * q^47 - 6912 * q^48 + 7203 * q^49 - 2148 * q^50 + 7002 * q^51 - 8832 * q^52 + 27742 * q^53 - 8748 * q^54 + 6776 * q^55 - 9408 * q^56 + 306 * q^57 + 19008 * q^58 + 3850 * q^59 + 8064 * q^60 + 50106 * q^61 + 12464 * q^62 - 11907 * q^63 + 12288 * q^64 + 54566 * q^65 + 13068 * q^66 + 110686 * q^67 - 12448 * q^68 - 7848 * q^69 + 10976 * q^70 + 105720 * q^71 + 15552 * q^72 + 74544 * q^73 + 19072 * q^74 + 4833 * q^75 - 544 * q^76 + 17787 * q^77 + 19872 * q^78 + 67952 * q^79 - 14336 * q^80 + 19683 * q^81 - 28664 * q^82 + 46216 * q^83 + 21168 * q^84 + 16240 * q^85 + 42032 * q^86 - 42768 * q^87 - 23232 * q^88 + 124750 * q^89 - 18144 * q^90 + 27048 * q^91 + 13952 * q^92 - 28044 * q^93 + 31128 * q^94 + 176906 * q^95 - 27648 * q^96 - 54110 * q^97 + 28812 * q^98 - 29403 * 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
$5$	−20.3563	−0.364145	−0.182073	−	0.983285i	$-0.558281\pi$
$5$	−20.3563	−0.364145	−0.182073	+	0.983285i	$0.558281\pi$
$6$	−36.0000	−0.408248
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−81.4254	−0.257490
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−144.000	−0.288675
$13$	−366.292	−0.601131	−0.300566	−	0.953761i	$-0.597175\pi$
$13$	−366.292	−0.601131	−0.300566	+	0.953761i	$0.597175\pi$
$14$	−196.000	−0.267261
$15$	183.207	0.210239
$16$	256.000	0.250000
$17$	1208.20	1.01395	0.506975	−	0.861961i	$-0.330764\pi$
$17$	1208.20	1.01395	0.506975	+	0.861961i	$0.330764\pi$
$18$	324.000	0.235702
$19$	554.877	0.352625	0.176312	−	0.984334i	$-0.443583\pi$
$19$	554.877	0.352625	0.176312	+	0.984334i	$0.443583\pi$
$20$	−325.702	−0.182073
$21$	441.000	0.218218
$22$	−484.000	−0.213201
$23$	−4646.98	−1.83169	−0.915844	−	0.401535i	$-0.868477\pi$
$23$	−4646.98	−1.83169	−0.915844	+	0.401535i	$0.868477\pi$
$24$	−576.000	−0.204124
$25$	−2710.62	−0.867398
$26$	−1465.17	−0.425064
$27$	−729.000	−0.192450
$28$	−784.000	−0.188982
$29$	5097.85	1.12562	0.562811	−	0.826586i	$-0.309720\pi$
$29$	5097.85	1.12562	0.562811	+	0.826586i	$0.309720\pi$
$30$	732.829	0.148662
$31$	3250.38	0.607477	0.303739	−	0.952755i	$-0.401765\pi$
$31$	3250.38	0.607477	0.303739	+	0.952755i	$0.401765\pi$
$32$	1024.00	0.176777
$33$	1089.00	0.174078
$34$	4832.80	0.716971
$35$	997.461	0.137634
$36$	1296.00	0.166667
$37$	2479.02	0.297698	0.148849	−	0.988860i	$-0.452443\pi$
$37$	2479.02	0.297698	0.148849	+	0.988860i	$0.452443\pi$
$38$	2219.51	0.249343
$39$	3296.63	0.347063
$40$	−1302.81	−0.128745
$41$	−8517.13	−0.791286	−0.395643	−	0.918404i	$-0.629478\pi$
$41$	−8517.13	−0.791286	−0.395643	+	0.918404i	$0.629478\pi$
$42$	1764.00	0.154303
$43$	17026.2	1.40426	0.702130	−	0.712049i	$-0.252232\pi$
$43$	17026.2	1.40426	0.702130	+	0.712049i	$0.252232\pi$
$44$	−1936.00	−0.150756
$45$	−1648.86	−0.121382
$46$	−18587.9	−1.29520
$47$	19310.8	1.27513	0.637566	−	0.770396i	$-0.279941\pi$
$47$	19310.8	1.27513	0.637566	+	0.770396i	$0.279941\pi$
$48$	−2304.00	−0.144338
$49$	2401.00	0.142857
$50$	−10842.5	−0.613343
$51$	−10873.8	−0.585404
$52$	−5860.67	−0.300566
$53$	−7521.82	−0.367818	−0.183909	−	0.982943i	$-0.558875\pi$
$53$	−7521.82	−0.367818	−0.183909	+	0.982943i	$0.558875\pi$
$54$	−2916.00	−0.136083
$55$	2463.12	0.109794
$56$	−3136.00	−0.133631
$57$	−4993.90	−0.203588
$58$	20391.4	0.795934
$59$	−1940.84	−0.0725870	−0.0362935	−	0.999341i	$-0.511555\pi$
$59$	−1940.84	−0.0725870	−0.0362935	+	0.999341i	$0.511555\pi$
$60$	2931.31	0.105120
$61$	−18493.6	−0.636353	−0.318176	−	0.948032i	$-0.603070\pi$
$61$	−18493.6	−0.636353	−0.318176	+	0.948032i	$0.603070\pi$
$62$	13001.5	0.429551
$63$	−3969.00	−0.125988
$64$	4096.00	0.125000
$65$	7456.37	0.218899
$66$	4356.00	0.123091
$67$	58040.0	1.57958	0.789788	−	0.613380i	$-0.210190\pi$
$67$	58040.0	1.57958	0.789788	+	0.613380i	$0.210190\pi$
$68$	19331.2	0.506975
$69$	41822.8	1.05752
$70$	3989.84	0.0973220
$71$	74760.3	1.76005	0.880026	−	0.474926i	$-0.157525\pi$
$71$	74760.3	1.76005	0.880026	+	0.474926i	$0.157525\pi$
$72$	5184.00	0.117851
$73$	20954.5	0.460226	0.230113	−	0.973164i	$-0.426090\pi$
$73$	20954.5	0.460226	0.230113	+	0.973164i	$0.426090\pi$
$74$	9916.09	0.210504
$75$	24395.6	0.500793
$76$	8878.04	0.176312
$77$	5929.00	0.113961
$78$	13186.5	0.245411
$79$	19866.5	0.358141	0.179070	−	0.983836i	$-0.442691\pi$
$79$	19866.5	0.358141	0.179070	+	0.983836i	$0.442691\pi$
$80$	−5211.23	−0.0910364
$81$	6561.00	0.111111
$82$	−34068.5	−0.559524
$83$	−77049.2	−1.22765	−0.613823	−	0.789444i	$-0.710369\pi$
$83$	−77049.2	−1.22765	−0.613823	+	0.789444i	$0.710369\pi$
$84$	7056.00	0.109109
$85$	−24594.5	−0.369225
$86$	68105.0	0.992962
$87$	−45880.7	−0.649878
$88$	−7744.00	−0.106600
$89$	141671.	1.89586	0.947928	−	0.318486i	$-0.103174\pi$
$89$	141671.	1.89586	0.947928	+	0.318486i	$0.103174\pi$
$90$	−6595.46	−0.0858299
$91$	17948.3	0.227206
$92$	−74351.7	−0.915844
$93$	−29253.4	−0.350727
$94$	77243.1	0.901654
$95$	−11295.3	−0.128407
$96$	−9216.00	−0.102062
$97$	−104835.	−1.13130	−0.565650	−	0.824645i	$-0.691375\pi$
$97$	−104835.	−1.13130	−0.565650	+	0.824645i	$0.691375\pi$
$98$	9604.00	0.101015
$99$	−9801.00	−0.100504
$100$	−43369.9	−0.433699
$101$	−44004.5	−0.429233	−0.214617	−	0.976698i	$-0.568850\pi$
$101$	−44004.5	−0.429233	−0.214617	+	0.976698i	$0.568850\pi$
$102$	−43495.2	−0.413943
$103$	−27231.3	−0.252915	−0.126458	−	0.991972i	$-0.540361\pi$
$103$	−27231.3	−0.252915	−0.126458	+	0.991972i	$0.540361\pi$
$104$	−23442.7	−0.212532
$105$	−8977.15	−0.0794630
$106$	−30087.3	−0.260087
$107$	178093.	1.50379	0.751896	−	0.659282i	$-0.229139\pi$
$107$	178093.	1.50379	0.751896	+	0.659282i	$0.229139\pi$
$108$	−11664.0	−0.0962250
$109$	224146.	1.80703	0.903513	−	0.428561i	$-0.140979\pi$
$109$	224146.	1.80703	0.903513	+	0.428561i	$0.140979\pi$
$110$	9852.47	0.0776361
$111$	−22311.2	−0.171876
$112$	−12544.0	−0.0944911
$113$	232612.	1.71371	0.856854	−	0.515559i	$-0.172416\pi$
$113$	232612.	1.71371	0.856854	+	0.515559i	$0.172416\pi$
$114$	−19975.6	−0.143959
$115$	94595.6	0.667000
$116$	81565.6	0.562811
$117$	−29669.7	−0.200377
$118$	−7763.34	−0.0513267
$119$	−59201.8	−0.383237
$120$	11725.3	0.0743309
$121$	14641.0	0.0909091
$122$	−73974.6	−0.449969
$123$	76654.1	0.456849
$124$	52006.1	0.303739
$125$	118792.	0.680004
$126$	−15876.0	−0.0890871
$127$	193399.	1.06401	0.532003	−	0.846742i	$-0.321440\pi$
$127$	193399.	1.06401	0.532003	+	0.846742i	$0.321440\pi$
$128$	16384.0	0.0883883
$129$	−153236.	−0.810750
$130$	29825.5	0.154785
$131$	−341181.	−1.73703	−0.868515	−	0.495663i	$-0.834925\pi$
$131$	−341181.	−1.73703	−0.868515	+	0.495663i	$0.834925\pi$
$132$	17424.0	0.0870388
$133$	−27189.0	−0.133280
$134$	232160.	1.11693
$135$	14839.8	0.0700798
$136$	77324.8	0.358485
$137$	298239.	1.35757	0.678786	−	0.734336i	$-0.262506\pi$
$137$	298239.	1.35757	0.678786	+	0.734336i	$0.262506\pi$
$138$	167291.	0.747783
$139$	92650.7	0.406735	0.203367	−	0.979102i	$-0.434811\pi$
$139$	92650.7	0.406735	0.203367	+	0.979102i	$0.434811\pi$
$140$	15959.4	0.0688170
$141$	−173797.	−0.736198
$142$	299041.	1.24454
$143$	44321.3	0.181248
$144$	20736.0	0.0833333
$145$	−103774.	−0.409890
$146$	83818.2	0.325429
$147$	−21609.0	−0.0824786
$148$	39664.3	0.148849
$149$	−178939.	−0.660296	−0.330148	−	0.943929i	$-0.607099\pi$
$149$	−178939.	−0.660296	−0.330148	+	0.943929i	$0.607099\pi$
$150$	97582.3	0.354114
$151$	−32963.0	−0.117648	−0.0588240	−	0.998268i	$-0.518735\pi$
$151$	−32963.0	−0.117648	−0.0588240	+	0.998268i	$0.518735\pi$
$152$	35512.2	0.124672
$153$	97864.2	0.337983
$154$	23716.0	0.0805823
$155$	−66165.9	−0.221210
$156$	52746.1	0.173532
$157$	−128467.	−0.415952	−0.207976	−	0.978134i	$-0.566688\pi$
$157$	−128467.	−0.415952	−0.207976	+	0.978134i	$0.566688\pi$
$158$	79466.0	0.253244
$159$	67696.4	0.212360
$160$	−20844.9	−0.0643724
$161$	227702.	0.692313
$162$	26244.0	0.0785674
$163$	145363.	0.428532	0.214266	−	0.976775i	$-0.431264\pi$
$163$	145363.	0.428532	0.214266	+	0.976775i	$0.431264\pi$
$164$	−136274.	−0.395643
$165$	−22168.1	−0.0633896
$166$	−308197.	−0.868076
$167$	332118.	0.921513	0.460757	−	0.887527i	$-0.347578\pi$
$167$	332118.	0.921513	0.460757	+	0.887527i	$0.347578\pi$
$168$	28224.0	0.0771517
$169$	−237123.	−0.638642
$170$	−98378.1	−0.261082
$171$	44945.1	0.117542
$172$	272420.	0.702130
$173$	516982.	1.31329	0.656645	−	0.754200i	$-0.271975\pi$
$173$	516982.	1.31329	0.656645	+	0.754200i	$0.271975\pi$
$174$	−183523.	−0.459533
$175$	132820.	0.327846
$176$	−30976.0	−0.0753778
$177$	17467.5	0.0419081
$178$	566683.	1.34057
$179$	−520751.	−1.21478	−0.607390	−	0.794404i	$-0.707783\pi$
$179$	−520751.	−1.21478	−0.607390	+	0.794404i	$0.707783\pi$
$180$	−26381.8	−0.0606909
$181$	−713683.	−1.61923	−0.809616	−	0.586960i	$-0.800325\pi$
$181$	−713683.	−1.61923	−0.809616	+	0.586960i	$0.800325\pi$
$182$	71793.2	0.160659
$183$	166443.	0.367398
$184$	−297407.	−0.647599
$185$	−50463.8	−0.108405
$186$	−117014.	−0.248002
$187$	−146192.	−0.305717
$188$	308972.	0.637566
$189$	35721.0	0.0727393
$190$	−45181.1	−0.0907973
$191$	428180.	0.849265	0.424633	−	0.905366i	$-0.360403\pi$
$191$	428180.	0.849265	0.424633	+	0.905366i	$0.360403\pi$
$192$	−36864.0	−0.0721688
$193$	−75036.9	−0.145005	−0.0725023	−	0.997368i	$-0.523098\pi$
$193$	−75036.9	−0.145005	−0.0725023	+	0.997368i	$0.523098\pi$
$194$	−419341.	−0.799950
$195$	−67107.3	−0.126381
$196$	38416.0	0.0714286
$197$	−251192.	−0.461148	−0.230574	−	0.973055i	$-0.574060\pi$
$197$	−251192.	−0.461148	−0.230574	+	0.973055i	$0.574060\pi$
$198$	−39204.0	−0.0710669
$199$	567462.	1.01579	0.507895	−	0.861419i	$-0.330424\pi$
$199$	567462.	1.01579	0.507895	+	0.861419i	$0.330424\pi$
$200$	−173480.	−0.306672
$201$	−522360.	−0.911969
$202$	−176018.	−0.303514
$203$	−249795.	−0.425445
$204$	−173981.	−0.292702
$205$	173378.	0.288143
$206$	−108925.	−0.178838
$207$	−376405.	−0.610562
$208$	−93770.8	−0.150283
$209$	−67140.2	−0.106320
$210$	−35908.6	−0.0561889
$211$	557973.	0.862793	0.431397	−	0.902162i	$-0.358021\pi$
$211$	557973.	0.862793	0.431397	+	0.902162i	$0.358021\pi$
$212$	−120349.	−0.183909
$213$	−672843.	−1.01617
$214$	712373.	1.06334
$215$	−346592.	−0.511355
$216$	−46656.0	−0.0680414
$217$	−159269.	−0.229605
$218$	896583.	1.27776
$219$	−188591.	−0.265712
$220$	39409.9	0.0548970
$221$	−442554.	−0.609517
$222$	−89244.8	−0.121535
$223$	341769.	0.460226	0.230113	−	0.973164i	$-0.426090\pi$
$223$	341769.	0.460226	0.230113	+	0.973164i	$0.426090\pi$
$224$	−50176.0	−0.0668153
$225$	−219560.	−0.289133
$226$	930450.	1.21177
$227$	−407916.	−0.525420	−0.262710	−	0.964875i	$-0.584616\pi$
$227$	−407916.	−0.525420	−0.262710	+	0.964875i	$0.584616\pi$
$228$	−79902.3	−0.101794
$229$	651380.	0.820815	0.410408	−	0.911902i	$-0.365386\pi$
$229$	651380.	0.820815	0.410408	+	0.911902i	$0.365386\pi$
$230$	378382.	0.471641
$231$	−53361.0	−0.0657952
$232$	326263.	0.397967
$233$	7078.71	0.00854209	0.00427105	−	0.999991i	$-0.498640\pi$
$233$	7078.71	0.00854209	0.00427105	+	0.999991i	$0.498640\pi$
$234$	−118679.	−0.141688
$235$	−393097.	−0.464333
$236$	−31053.4	−0.0362935
$237$	−178799.	−0.206773
$238$	−236807.	−0.270989
$239$	−1.70627e6	−1.93221	−0.966104	−	0.258154i	$-0.916886\pi$
$239$	−1.70627e6	−1.93221	−0.966104	+	0.258154i	$0.916886\pi$
$240$	46901.0	0.0525599
$241$	−1.36999e6	−1.51941	−0.759704	−	0.650269i	$-0.774656\pi$
$241$	−1.36999e6	−1.51941	−0.759704	+	0.650269i	$0.774656\pi$
$242$	58564.0	0.0642824
$243$	−59049.0	−0.0641500
$244$	−295898.	−0.318176
$245$	−48875.6	−0.0520208
$246$	306617.	0.323041
$247$	−203247.	−0.211974
$248$	208024.	0.214776
$249$	693443.	0.708781
$250$	475168.	0.480836
$251$	778446.	0.779909	0.389955	−	0.920834i	$-0.372491\pi$
$251$	778446.	0.779909	0.389955	+	0.920834i	$0.372491\pi$
$252$	−63504.0	−0.0629941
$253$	562285.	0.552274
$254$	773594.	0.752366
$255$	221351.	0.213172
$256$	65536.0	0.0625000
$257$	−764852.	−0.722345	−0.361172	−	0.932499i	$-0.617623\pi$
$257$	−764852.	−0.722345	−0.361172	+	0.932499i	$0.617623\pi$
$258$	−612945.	−0.573287
$259$	−121472.	−0.112519
$260$	119302.	0.109450
$261$	412926.	0.375207
$262$	−1.36473e6	−1.22827
$263$	−248273.	−0.221329	−0.110665	−	0.993858i	$-0.535298\pi$
$263$	−248273.	−0.221329	−0.110665	+	0.993858i	$0.535298\pi$
$264$	69696.0	0.0615457
$265$	153117.	0.133939
$266$	−108756.	−0.0942430
$267$	−1.27504e6	−1.09457
$268$	928640.	0.789788
$269$	466607.	0.393161	0.196580	−	0.980488i	$-0.437016\pi$
$269$	466607.	0.393161	0.196580	+	0.980488i	$0.437016\pi$
$270$	59359.1	0.0495539
$271$	−42789.3	−0.0353925	−0.0176963	−	0.999843i	$-0.505633\pi$
$271$	−42789.3	−0.0353925	−0.0176963	+	0.999843i	$0.505633\pi$
$272$	309299.	0.253487
$273$	−161535.	−0.131178
$274$	1.19296e6	0.959948
$275$	327985.	0.261530
$276$	669165.	0.528762
$277$	1.50195e6	1.17613	0.588066	−	0.808813i	$-0.299890\pi$
$277$	1.50195e6	1.17613	0.588066	+	0.808813i	$0.299890\pi$
$278$	370603.	0.287605
$279$	263281.	0.202492
$280$	63837.5	0.0486610
$281$	−744097.	−0.562165	−0.281083	−	0.959684i	$-0.590693\pi$
$281$	−744097.	−0.562165	−0.281083	+	0.959684i	$0.590693\pi$
$282$	−695188.	−0.520570
$283$	−2.26622e6	−1.68204	−0.841020	−	0.541004i	$-0.818045\pi$
$283$	−2.26622e6	−1.68204	−0.841020	+	0.541004i	$0.818045\pi$
$284$	1.19617e6	0.880026
$285$	101657.	0.0741357
$286$	177285.	0.128162
$287$	417339.	0.299078
$288$	82944.0	0.0589256
$289$	39889.3	0.0280939
$290$	−415095.	−0.289836
$291$	943517.	0.653157
$292$	335273.	0.230113
$293$	−1.86517e6	−1.26925	−0.634627	−	0.772819i	$-0.718846\pi$
$293$	−1.86517e6	−1.26925	−0.634627	+	0.772819i	$0.718846\pi$
$294$	−86436.0	−0.0583212
$295$	39508.3	0.0264322
$296$	158657.	0.105252
$297$	88209.0	0.0580259
$298$	−715755.	−0.466900
$299$	1.70215e6	1.10108
$300$	390329.	0.250396
$301$	−834286.	−0.530760
$302$	−131852.	−0.0831897
$303$	396040.	0.247818
$304$	142049.	0.0881562
$305$	376463.	0.231725
$306$	391457.	0.238990
$307$	713360.	0.431979	0.215989	−	0.976396i	$-0.430702\pi$
$307$	713360.	0.431979	0.215989	+	0.976396i	$0.430702\pi$
$308$	94864.0	0.0569803
$309$	245081.	0.146021
$310$	−264664.	−0.156419
$311$	2.17517e6	1.27524	0.637622	−	0.770350i	$-0.279918\pi$
$311$	2.17517e6	1.27524	0.637622	+	0.770350i	$0.279918\pi$
$312$	210984.	0.122705
$313$	−2.95268e6	−1.70355	−0.851777	−	0.523905i	$-0.824475\pi$
$313$	−2.95268e6	−1.70355	−0.851777	+	0.523905i	$0.824475\pi$
$314$	−513869.	−0.294123
$315$	80794.3	0.0458780
$316$	317864.	0.179070
$317$	1.37803e6	0.770212	0.385106	−	0.922872i	$-0.374165\pi$
$317$	1.37803e6	0.770212	0.385106	+	0.922872i	$0.374165\pi$
$318$	270786.	0.150161
$319$	−616840.	−0.339388
$320$	−83379.6	−0.0455182
$321$	−1.60284e6	−0.868215
$322$	910808.	0.489539
$323$	670403.	0.357544
$324$	104976.	0.0555556
$325$	992878.	0.521420
$326$	581450.	0.303018
$327$	−2.01731e6	−1.04329
$328$	−545096.	−0.279762
$329$	−946228.	−0.481954
$330$	−88672.3	−0.0448232
$331$	−2.55983e6	−1.28422	−0.642111	−	0.766611i	$-0.721941\pi$
$331$	−2.55983e6	−1.28422	−0.642111	+	0.766611i	$0.721941\pi$
$332$	−1.23279e6	−0.613823
$333$	200801.	0.0992327
$334$	1.32847e6	0.651608
$335$	−1.18148e6	−0.575195
$336$	112896.	0.0545545
$337$	418720.	0.200839	0.100420	−	0.994945i	$-0.467981\pi$
$337$	418720.	0.200839	0.100420	+	0.994945i	$0.467981\pi$
$338$	−948493.	−0.451588
$339$	−2.09351e6	−0.989410
$340$	−393513.	−0.184613
$341$	−393296.	−0.183161
$342$	179780.	0.0831145
$343$	−117649.	−0.0539949
$344$	1.08968e6	0.496481
$345$	−851360.	−0.385093
$346$	2.06793e6	0.928636
$347$	3.31201e6	1.47662	0.738308	−	0.674464i	$-0.235625\pi$
$347$	3.31201e6	1.47662	0.738308	+	0.674464i	$0.235625\pi$
$348$	−734091.	−0.324939
$349$	−1.81669e6	−0.798395	−0.399198	−	0.916865i	$-0.630711\pi$
$349$	−1.81669e6	−0.798395	−0.399198	+	0.916865i	$0.630711\pi$
$350$	531281.	0.231822
$351$	267027.	0.115688
$352$	−123904.	−0.0533002
$353$	2.10280e6	0.898174	0.449087	−	0.893488i	$-0.351749\pi$
$353$	2.10280e6	0.898174	0.449087	+	0.893488i	$0.351749\pi$
$354$	69870.1	0.0296335
$355$	−1.52185e6	−0.640915
$356$	2.26673e6	0.947928
$357$	532816.	0.221262
$358$	−2.08300e6	−0.858979
$359$	1.56665e6	0.641560	0.320780	−	0.947154i	$-0.396055\pi$
$359$	1.56665e6	0.641560	0.320780	+	0.947154i	$0.396055\pi$
$360$	−105527.	−0.0429150
$361$	−2.16821e6	−0.875656
$362$	−2.85473e6	−1.14497
$363$	−131769.	−0.0524864
$364$	287173.	0.113603
$365$	−426558.	−0.167589
$366$	665771.	0.259790
$367$	1.59555e6	0.618367	0.309183	−	0.951002i	$-0.399944\pi$
$367$	1.59555e6	0.618367	0.309183	+	0.951002i	$0.399944\pi$
$368$	−1.18963e6	−0.457922
$369$	−689887.	−0.263762
$370$	−201855.	−0.0766542
$371$	368569.	0.139022
$372$	−468055.	−0.175364
$373$	179624.	0.0668486	0.0334243	−	0.999441i	$-0.489359\pi$
$373$	179624.	0.0668486	0.0334243	+	0.999441i	$0.489359\pi$
$374$	−584769.	−0.216175
$375$	−1.06913e6	−0.392601
$376$	1.23589e6	0.450827
$377$	−1.86730e6	−0.676646
$378$	142884.	0.0514344
$379$	−2.71758e6	−0.971816	−0.485908	−	0.874010i	$-0.661511\pi$
$379$	−2.71758e6	−0.971816	−0.485908	+	0.874010i	$0.661511\pi$
$380$	−180724.	−0.0642034
$381$	−1.74059e6	−0.614304
$382$	1.71272e6	0.600521
$383$	−3.01477e6	−1.05016	−0.525082	−	0.851052i	$-0.675965\pi$
$383$	−3.01477e6	−1.05016	−0.525082	+	0.851052i	$0.675965\pi$
$384$	−147456.	−0.0510310
$385$	−120693.	−0.0414982
$386$	−300148.	−0.102534
$387$	1.37913e6	0.468087
$388$	−1.67736e6	−0.565650
$389$	5.52408e6	1.85091	0.925457	−	0.378853i	$-0.123682\pi$
$389$	5.52408e6	1.85091	0.925457	+	0.378853i	$0.123682\pi$
$390$	−268429.	−0.0893652
$391$	−5.61448e6	−1.85724
$392$	153664.	0.0505076
$393$	3.07063e6	1.00287
$394$	−1.00477e6	−0.326081
$395$	−404410.	−0.130415
$396$	−156816.	−0.0502519
$397$	4.13189e6	1.31575	0.657873	−	0.753129i	$-0.271456\pi$
$397$	4.13189e6	1.31575	0.657873	+	0.753129i	$0.271456\pi$
$398$	2.26985e6	0.718273
$399$	244701.	0.0769491
$400$	−693918.	−0.216850
$401$	−1.84872e6	−0.574131	−0.287066	−	0.957911i	$-0.592680\pi$
$401$	−1.84872e6	−0.574131	−0.287066	+	0.957911i	$0.592680\pi$
$402$	−2.08944e6	−0.644859
$403$	−1.19059e6	−0.365173
$404$	−704071.	−0.214617
$405$	−133558.	−0.0404606
$406$	−999179.	−0.300835
$407$	−299962.	−0.0897593
$408$	−695923.	−0.206972
$409$	−799836.	−0.236424	−0.118212	−	0.992988i	$-0.537716\pi$
$409$	−799836.	−0.236424	−0.118212	+	0.992988i	$0.537716\pi$
$410$	693510.	0.203748
$411$	−2.68415e6	−0.783794
$412$	−435700.	−0.126458
$413$	95100.9	0.0274353
$414$	−1.50562e6	−0.431733
$415$	1.56844e6	0.447041
$416$	−375083.	−0.106266
$417$	−833856.	−0.234829
$418$	−268561.	−0.0751799
$419$	3.97616e6	1.10644	0.553222	−	0.833034i	$-0.313398\pi$
$419$	3.97616e6	1.10644	0.553222	+	0.833034i	$0.313398\pi$
$420$	−143634.	−0.0397315
$421$	−6.76533e6	−1.86030	−0.930151	−	0.367177i	$-0.880324\pi$
$421$	−6.76533e6	−1.86030	−0.930151	+	0.367177i	$0.880324\pi$
$422$	2.23189e6	0.610087
$423$	1.56417e6	0.425044
$424$	−481396.	−0.130043
$425$	−3.27497e6	−0.879498
$426$	−2.69137e6	−0.718538
$427$	906188.	0.240519
$428$	2.84949e6	0.751896
$429$	−398892.	−0.104643
$430$	−1.38637e6	−0.361583
$431$	3.97815e6	1.03154	0.515772	−	0.856726i	$-0.327505\pi$
$431$	3.97815e6	1.03154	0.515772	+	0.856726i	$0.327505\pi$
$432$	−186624.	−0.0481125
$433$	−3.13218e6	−0.802835	−0.401418	−	0.915895i	$-0.631482\pi$
$433$	−3.13218e6	−0.802835	−0.401418	+	0.915895i	$0.631482\pi$
$434$	−637075.	−0.162355
$435$	933963.	0.236650
$436$	3.58633e6	0.903513
$437$	−2.57850e6	−0.645899
$438$	−754364.	−0.187886
$439$	−7.05780e6	−1.74787	−0.873933	−	0.486046i	$-0.838439\pi$
$439$	−7.05780e6	−1.74787	−0.873933	+	0.486046i	$0.838439\pi$
$440$	157640.	0.0388180
$441$	194481.	0.0476190
$442$	−1.77022e6	−0.430993
$443$	−5.55598e6	−1.34509	−0.672544	−	0.740057i	$-0.734799\pi$
$443$	−5.55598e6	−1.34509	−0.672544	+	0.740057i	$0.734799\pi$
$444$	−356979.	−0.0859380
$445$	−2.88390e6	−0.690367
$446$	1.36708e6	0.325429
$447$	1.61045e6	0.381222
$448$	−200704.	−0.0472456
$449$	−3.71609e6	−0.869903	−0.434951	−	0.900454i	$-0.643234\pi$
$449$	−3.71609e6	−0.869903	−0.434951	+	0.900454i	$0.643234\pi$
$450$	−878241.	−0.204448
$451$	1.03057e6	0.238582
$452$	3.72180e6	0.856854
$453$	296667.	0.0679241
$454$	−1.63167e6	−0.371528
$455$	−365362.	−0.0827361
$456$	−319609.	−0.0719793
$457$	−6.54975e6	−1.46701	−0.733507	−	0.679682i	$-0.762118\pi$
$457$	−6.54975e6	−1.46701	−0.733507	+	0.679682i	$0.762118\pi$
$458$	2.60552e6	0.580404
$459$	−880778.	−0.195135
$460$	1.51353e6	0.333500
$461$	5.09140e6	1.11580	0.557898	−	0.829909i	$-0.311608\pi$
$461$	5.09140e6	1.11580	0.557898	+	0.829909i	$0.311608\pi$
$462$	−213444.	−0.0465242
$463$	−5.37873e6	−1.16608	−0.583038	−	0.812445i	$-0.698136\pi$
$463$	−5.37873e6	−1.16608	−0.583038	+	0.812445i	$0.698136\pi$
$464$	1.30505e6	0.281405
$465$	595493.	0.127716
$466$	28314.8	0.00604017
$467$	4.67486e6	0.991920	0.495960	−	0.868345i	$-0.334816\pi$
$467$	4.67486e6	0.991920	0.495960	+	0.868345i	$0.334816\pi$
$468$	−474715.	−0.100189
$469$	−2.84396e6	−0.597024
$470$	−1.57239e6	−0.328333
$471$	1.15621e6	0.240150
$472$	−124213.	−0.0256634
$473$	−2.06018e6	−0.423400
$474$	−715194.	−0.146210
$475$	−1.50406e6	−0.305866
$476$	−947228.	−0.191618
$477$	−609267.	−0.122606
$478$	−6.82509e6	−1.36628
$479$	7.23536e6	1.44086	0.720429	−	0.693529i	$-0.243945\pi$
$479$	7.23536e6	1.44086	0.720429	+	0.693529i	$0.243945\pi$
$480$	187604.	0.0371654
$481$	−908046.	−0.178956
$482$	−5.47995e6	−1.07438
$483$	−2.04932e6	−0.399707
$484$	234256.	0.0454545
$485$	2.13406e6	0.411958
$486$	−236196.	−0.0453609
$487$	2.12287e6	0.405603	0.202801	−	0.979220i	$-0.434995\pi$
$487$	2.12287e6	0.405603	0.202801	+	0.979220i	$0.434995\pi$
$488$	−1.18359e6	−0.224985
$489$	−1.30826e6	−0.247413
$490$	−195502.	−0.0367842
$491$	6.97260e6	1.30524	0.652621	−	0.757685i	$-0.273670\pi$
$491$	6.97260e6	1.30524	0.652621	+	0.757685i	$0.273670\pi$
$492$	1.22647e6	0.228425
$493$	6.15922e6	1.14132
$494$	−812989.	−0.149888
$495$	199513.	0.0365980
$496$	832098.	0.151869
$497$	−3.66326e6	−0.665237
$498$	2.77377e6	0.501184
$499$	9.67260e6	1.73897	0.869484	−	0.493961i	$-0.164451\pi$
$499$	9.67260e6	1.73897	0.869484	+	0.493961i	$0.164451\pi$
$500$	1.90067e6	0.340002
$501$	−2.98906e6	−0.532036
$502$	3.11378e6	0.551479
$503$	−2.79155e6	−0.491956	−0.245978	−	0.969275i	$-0.579109\pi$
$503$	−2.79155e6	−0.491956	−0.245978	+	0.969275i	$0.579109\pi$
$504$	−254016.	−0.0445435
$505$	895770.	0.156303
$506$	2.24914e6	0.390517
$507$	2.13411e6	0.368720
$508$	3.09438e6	0.532003
$509$	3.89845e6	0.666957	0.333479	−	0.942758i	$-0.391777\pi$
$509$	3.89845e6	0.666957	0.333479	+	0.942758i	$0.391777\pi$
$510$	885403.	0.150736
$511$	−1.02677e6	−0.173949
$512$	262144.	0.0441942
$513$	−404506.	−0.0678627
$514$	−3.05941e6	−0.510775
$515$	554329.	0.0920979
$516$	−2.45178e6	−0.405375
$517$	−2.33660e6	−0.384467
$518$	−485888.	−0.0795631
$519$	−4.65284e6	−0.758228
$520$	477208.	0.0773925
$521$	−7.32763e6	−1.18269	−0.591343	−	0.806420i	$-0.701402\pi$
$521$	−7.32763e6	−1.18269	−0.591343	+	0.806420i	$0.701402\pi$
$522$	1.65170e6	0.265311
$523$	1.08751e6	0.173852	0.0869258	−	0.996215i	$-0.472296\pi$
$523$	1.08751e6	0.173852	0.0869258	+	0.996215i	$0.472296\pi$
$524$	−5.45890e6	−0.868515
$525$	−1.19538e6	−0.189282
$526$	−993090.	−0.156504
$527$	3.92711e6	0.615951
$528$	278784.	0.0435194
$529$	1.51581e7	2.35508
$530$	612467.	0.0947094
$531$	−157208.	−0.0241957
$532$	−435024.	−0.0666399
$533$	3.11976e6	0.475666
$534$	−5.10015e6	−0.773980
$535$	−3.62533e6	−0.547599
$536$	3.71456e6	0.558465
$537$	4.68676e6	0.701354
$538$	1.86643e6	0.278007
$539$	−290521.	−0.0430730
$540$	237436.	0.0350399
$541$	−7.62863e6	−1.12061	−0.560304	−	0.828287i	$-0.689316\pi$
$541$	−7.62863e6	−1.12061	−0.560304	+	0.828287i	$0.689316\pi$
$542$	−171157.	−0.0250263
$543$	6.42315e6	0.934864
$544$	1.23720e6	0.179243
$545$	−4.56279e6	−0.658020
$546$	−646139.	−0.0927565
$547$	1.22015e7	1.74360	0.871799	−	0.489863i	$-0.162953\pi$
$547$	1.22015e7	1.74360	0.871799	+	0.489863i	$0.162953\pi$
$548$	4.77182e6	0.678786
$549$	−1.49798e6	−0.212118
$550$	1.31194e6	0.184930
$551$	2.82868e6	0.396922
$552$	2.67666e6	0.373892
$553$	−973459.	−0.135365
$554$	6.00780e6	0.831650
$555$	454174.	0.0625879
$556$	1.48241e6	0.203367
$557$	1.27353e7	1.73928	0.869640	−	0.493686i	$-0.164351\pi$
$557$	1.27353e7	1.73928	0.869640	+	0.493686i	$0.164351\pi$
$558$	1.05312e6	0.143184
$559$	−6.23658e6	−0.844144
$560$	255350.	0.0344085
$561$	1.31573e6	0.176506
$562$	−2.97639e6	−0.397511
$563$	1.08918e7	1.44820	0.724098	−	0.689697i	$-0.242256\pi$
$563$	1.08918e7	1.44820	0.724098	+	0.689697i	$0.242256\pi$
$564$	−2.78075e6	−0.368099
$565$	−4.73514e6	−0.624039
$566$	−9.06489e6	−1.18938
$567$	−321489.	−0.0419961
$568$	4.78466e6	0.622272
$569$	1.88168e6	0.243649	0.121825	−	0.992552i	$-0.461125\pi$
$569$	1.88168e6	0.243649	0.121825	+	0.992552i	$0.461125\pi$
$570$	406630.	0.0524218
$571$	2.21788e6	0.284674	0.142337	−	0.989818i	$-0.454538\pi$
$571$	2.21788e6	0.284674	0.142337	+	0.989818i	$0.454538\pi$
$572$	709141.	0.0906239
$573$	−3.85362e6	−0.490324
$574$	1.66936e6	0.211480
$575$	1.25962e7	1.58880
$576$	331776.	0.0416667
$577$	−3.68499e6	−0.460783	−0.230392	−	0.973098i	$-0.574001\pi$
$577$	−3.68499e6	−0.460783	−0.230392	+	0.973098i	$0.574001\pi$
$578$	159557.	0.0198654
$579$	675332.	0.0837184
$580$	−1.66038e6	−0.204945
$581$	3.77541e6	0.464006
$582$	3.77407e6	0.461851
$583$	910140.	0.110901
$584$	1.34109e6	0.162714
$585$	603966.	0.0729664
$586$	−7.46066e6	−0.897498
$587$	9.20133e6	1.10219	0.551094	−	0.834443i	$-0.314211\pi$
$587$	9.20133e6	1.10219	0.551094	+	0.834443i	$0.314211\pi$
$588$	−345744.	−0.0412393
$589$	1.80356e6	0.214212
$590$	158033.	0.0186904
$591$	2.26073e6	0.266244
$592$	634629.	0.0744245
$593$	1.46047e7	1.70552	0.852759	−	0.522305i	$-0.174928\pi$
$593$	1.46047e7	1.70552	0.852759	+	0.522305i	$0.174928\pi$
$594$	352836.	0.0410305
$595$	1.20513e6	0.139554
$596$	−2.86302e6	−0.330148
$597$	−5.10716e6	−0.586467
$598$	6.80861e6	0.778584
$599$	2.99274e6	0.340802	0.170401	−	0.985375i	$-0.445494\pi$
$599$	2.99274e6	0.340802	0.170401	+	0.985375i	$0.445494\pi$
$600$	1.56132e6	0.177057
$601$	55138.3	0.00622684	0.00311342	−	0.999995i	$-0.499009\pi$
$601$	55138.3	0.00622684	0.00311342	+	0.999995i	$0.499009\pi$
$602$	−3.33714e6	−0.375304
$603$	4.70124e6	0.526525
$604$	−527408.	−0.0588240
$605$	−298037.	−0.0331041
$606$	1.58416e6	0.175234
$607$	9.41664e6	1.03735	0.518674	−	0.854972i	$-0.326426\pi$
$607$	9.41664e6	1.03735	0.518674	+	0.854972i	$0.326426\pi$
$608$	568194.	0.0623359
$609$	2.24815e6	0.245631
$610$	1.50585e6	0.163854
$611$	−7.07338e6	−0.766521
$612$	1.56583e6	0.168992
$613$	−1.44038e7	−1.54819	−0.774095	−	0.633069i	$-0.781795\pi$
$613$	−1.44038e7	−1.54819	−0.774095	+	0.633069i	$0.781795\pi$
$614$	2.85344e6	0.305455
$615$	−1.56040e6	−0.166360
$616$	379456.	0.0402911
$617$	4.89967e6	0.518148	0.259074	−	0.965858i	$-0.416583\pi$
$617$	4.89967e6	0.518148	0.259074	+	0.965858i	$0.416583\pi$
$618$	980325.	0.103252
$619$	1.25986e7	1.32159	0.660794	−	0.750568i	$-0.270220\pi$
$619$	1.25986e7	1.32159	0.660794	+	0.750568i	$0.270220\pi$
$620$	−1.05865e6	−0.110605
$621$	3.38765e6	0.352508
$622$	8.70070e6	0.901733
$623$	−6.94187e6	−0.716566
$624$	843937.	0.0867658
$625$	6.05252e6	0.619778
$626$	−1.18107e7	−1.20459
$627$	604261.	0.0613841
$628$	−2.05548e6	−0.207976
$629$	2.99515e6	0.301851
$630$	323177.	0.0324407
$631$	−1.55467e6	−0.155441	−0.0777203	−	0.996975i	$-0.524764\pi$
$631$	−1.55467e6	−0.155441	−0.0777203	+	0.996975i	$0.524764\pi$
$632$	1.27146e6	0.126622
$633$	−5.02175e6	−0.498134
$634$	5.51212e6	0.544622
$635$	−3.93689e6	−0.387453
$636$	1.08314e6	0.106180
$637$	−879467.	−0.0858759
$638$	−2.46736e6	−0.239983
$639$	6.05559e6	0.586684
$640$	−333518.	−0.0321862
$641$	6.89301e6	0.662619	0.331309	−	0.943522i	$-0.392510\pi$
$641$	6.89301e6	0.662619	0.331309	+	0.943522i	$0.392510\pi$
$642$	−6.41135e6	−0.613921
$643$	−7.26745e6	−0.693194	−0.346597	−	0.938014i	$-0.612663\pi$
$643$	−7.26745e6	−0.693194	−0.346597	+	0.938014i	$0.612663\pi$
$644$	3.64323e6	0.346156
$645$	3.11933e6	0.295231
$646$	2.68161e6	0.252822
$647$	1.56920e7	1.47373	0.736863	−	0.676043i	$-0.236306\pi$
$647$	1.56920e7	1.47373	0.736863	+	0.676043i	$0.236306\pi$
$648$	419904.	0.0392837
$649$	234841.	0.0218858
$650$	3.97151e6	0.368700
$651$	1.43342e6	0.132562
$652$	2.32580e6	0.214266
$653$	7.71711e6	0.708226	0.354113	−	0.935203i	$-0.384783\pi$
$653$	7.71711e6	0.708226	0.354113	+	0.935203i	$0.384783\pi$
$654$	−8.06925e6	−0.737715
$655$	6.94521e6	0.632531
$656$	−2.18038e6	−0.197821
$657$	1.69732e6	0.153409
$658$	−3.78491e6	−0.340793
$659$	−1.44038e7	−1.29200	−0.646000	−	0.763338i	$-0.723559\pi$
$659$	−1.44038e7	−1.29200	−0.646000	+	0.763338i	$0.723559\pi$
$660$	−354689.	−0.0316948
$661$	4.00346e6	0.356395	0.178198	−	0.983995i	$-0.442973\pi$
$661$	4.00346e6	0.356395	0.178198	+	0.983995i	$0.442973\pi$
$662$	−1.02393e7	−0.908083
$663$	3.98299e6	0.351905
$664$	−4.93115e6	−0.434038
$665$	553469.	0.0485332
$666$	803203.	0.0701681
$667$	−2.36896e7	−2.06179
$668$	5.31389e6	0.460757
$669$	−3.07593e6	−0.265712
$670$	−4.72593e6	−0.406725
$671$	2.23773e6	0.191868
$672$	451584.	0.0385758
$673$	1.09257e7	0.929847	0.464923	−	0.885351i	$-0.346082\pi$
$673$	1.09257e7	0.929847	0.464923	+	0.885351i	$0.346082\pi$
$674$	1.67488e6	0.142015
$675$	1.97604e6	0.166931
$676$	−3.79397e6	−0.319321
$677$	−1.60335e7	−1.34449	−0.672246	−	0.740328i	$-0.734670\pi$
$677$	−1.60335e7	−1.34449	−0.672246	+	0.740328i	$0.734670\pi$
$678$	−8.37405e6	−0.699618
$679$	5.13693e6	0.427591
$680$	−1.57405e6	−0.130541
$681$	3.67125e6	0.303351
$682$	−1.57318e6	−0.129515
$683$	1.37339e7	1.12653	0.563264	−	0.826277i	$-0.309545\pi$
$683$	1.37339e7	1.12653	0.563264	+	0.826277i	$0.309545\pi$
$684$	719121.	0.0587708
$685$	−6.07105e6	−0.494354
$686$	−470596.	−0.0381802
$687$	−5.86242e6	−0.473898
$688$	4.35872e6	0.351065
$689$	2.75518e6	0.221107
$690$	−3.40544e6	−0.272302
$691$	−1.35450e6	−0.107916	−0.0539579	−	0.998543i	$-0.517184\pi$
$691$	−1.35450e6	−0.107916	−0.0539579	+	0.998543i	$0.517184\pi$
$692$	8.27172e6	0.656645
$693$	480249.	0.0379869
$694$	1.32480e7	1.04413
$695$	−1.88603e6	−0.148111
$696$	−2.93636e6	−0.229766
$697$	−1.02904e7	−0.802324
$698$	−7.26677e6	−0.564551
$699$	−63708.4	−0.00493178
$700$	2.12513e6	0.163923
$701$	1.00410e7	0.771756	0.385878	−	0.922550i	$-0.373899\pi$
$701$	1.00410e7	0.771756	0.385878	+	0.922550i	$0.373899\pi$
$702$	1.06811e6	0.0818036
$703$	1.37555e6	0.104976
$704$	−495616.	−0.0376889
$705$	3.53787e6	0.268083
$706$	8.41119e6	0.635105
$707$	2.15622e6	0.162235
$708$	279480.	0.0209541
$709$	−8.15715e6	−0.609428	−0.304714	−	0.952444i	$-0.598561\pi$
$709$	−8.15715e6	−0.609428	−0.304714	+	0.952444i	$0.598561\pi$
$710$	−6.08739e6	−0.453195
$711$	1.60919e6	0.119380
$712$	9.06693e6	0.670286
$713$	−1.51045e7	−1.11271
$714$	2.13126e6	0.156456
$715$	−902221.	−0.0660006
$716$	−8.33202e6	−0.607390
$717$	1.53565e7	1.11556
$718$	6.26662e6	0.453651
$719$	2.23242e7	1.61047	0.805237	−	0.592953i	$-0.202038\pi$
$719$	2.23242e7	1.61047	0.805237	+	0.592953i	$0.202038\pi$
$720$	−422109.	−0.0303455
$721$	1.33433e6	0.0955929
$722$	−8.67284e6	−0.619182
$723$	1.23299e7	0.877230
$724$	−1.14189e7	−0.809616
$725$	−1.38183e7	−0.976362
$726$	−527076.	−0.0371135
$727$	−7.40198e6	−0.519412	−0.259706	−	0.965688i	$-0.583626\pi$
$727$	−7.40198e6	−0.519412	−0.259706	+	0.965688i	$0.583626\pi$
$728$	1.14869e6	0.0803295
$729$	531441.	0.0370370
$730$	−1.70623e6	−0.118503
$731$	2.05711e7	1.42385
$732$	2.66308e6	0.183699
$733$	1.55557e7	1.06938	0.534688	−	0.845049i	$-0.320429\pi$
$733$	1.55557e7	1.06938	0.534688	+	0.845049i	$0.320429\pi$
$734$	6.38221e6	0.437251
$735$	439880.	0.0300342
$736$	−4.75851e6	−0.323800
$737$	−7.02284e6	−0.476260
$738$	−2.75955e6	−0.186508
$739$	7.20409e6	0.485253	0.242626	−	0.970120i	$-0.421991\pi$
$739$	7.20409e6	0.485253	0.242626	+	0.970120i	$0.421991\pi$
$740$	−807421.	−0.0542027
$741$	1.82922e6	0.122383
$742$	1.47428e6	0.0983036
$743$	1.08807e7	0.723075	0.361538	−	0.932357i	$-0.382252\pi$
$743$	1.08807e7	0.723075	0.361538	+	0.932357i	$0.382252\pi$
$744$	−1.87222e6	−0.124001
$745$	3.64254e6	0.240444
$746$	718496.	0.0472691
$747$	−6.24098e6	−0.409215
$748$	−2.33907e6	−0.152859
$749$	−8.72657e6	−0.568380
$750$	−4.27651e6	−0.277611
$751$	−1.54904e7	−1.00222	−0.501111	−	0.865383i	$-0.667075\pi$
$751$	−1.54904e7	−1.00222	−0.501111	+	0.865383i	$0.667075\pi$
$752$	4.94356e6	0.318783
$753$	−7.00601e6	−0.450281
$754$	−7.46921e6	−0.478461
$755$	671006.	0.0428410
$756$	571536.	0.0363696
$757$	2.05935e7	1.30614	0.653070	−	0.757298i	$-0.273481\pi$
$757$	2.05935e7	1.30614	0.653070	+	0.757298i	$0.273481\pi$
$758$	−1.08703e7	−0.687177
$759$	−5.06056e6	−0.318856
$760$	−722898.	−0.0453986
$761$	−1.39480e7	−0.873073	−0.436536	−	0.899687i	$-0.643795\pi$
$761$	−1.39480e7	−0.873073	−0.436536	+	0.899687i	$0.643795\pi$
$762$	−6.96235e6	−0.434379
$763$	−1.09831e7	−0.682991
$764$	6.85089e6	0.424633
$765$	−1.99216e6	−0.123075
$766$	−1.20591e7	−0.742578
$767$	710913.	0.0436343
$768$	−589824.	−0.0360844
$769$	−2.54900e7	−1.55437	−0.777183	−	0.629275i	$-0.783352\pi$
$769$	−2.54900e7	−1.55437	−0.777183	+	0.629275i	$0.783352\pi$
$770$	−482771.	−0.0293437
$771$	6.88366e6	0.417046
$772$	−1.20059e6	−0.0725023
$773$	−2.95752e7	−1.78024	−0.890119	−	0.455727i	$-0.849379\pi$
$773$	−2.95752e7	−1.78024	−0.890119	+	0.455727i	$0.849379\pi$
$774$	5.51650e6	0.330987
$775$	−8.81055e6	−0.526925
$776$	−6.70945e6	−0.399975
$777$	1.09325e6	0.0649630
$778$	2.20963e7	1.30879
$779$	−4.72596e6	−0.279027
$780$	−1.07372e6	−0.0631907
$781$	−9.04600e6	−0.530676
$782$	−2.24579e7	−1.31327
$783$	−3.71633e6	−0.216626
$784$	614656.	0.0357143
$785$	2.61513e6	0.151467
$786$	1.22825e7	0.709139
$787$	−676549.	−0.0389370	−0.0194685	−	0.999810i	$-0.506197\pi$
$787$	−676549.	−0.0389370	−0.0194685	+	0.999810i	$0.506197\pi$
$788$	−4.01907e6	−0.230574
$789$	2.23445e6	0.127785
$790$	−1.61764e6	−0.0922176
$791$	−1.13980e7	−0.647721
$792$	−627264.	−0.0355335
$793$	6.77407e6	0.382531
$794$	1.65275e7	0.930373
$795$	−1.37805e6	−0.0773299
$796$	9.07940e6	0.507895
$797$	−4.11492e6	−0.229464	−0.114732	−	0.993396i	$-0.536601\pi$
$797$	−4.11492e6	−0.229464	−0.114732	+	0.993396i	$0.536601\pi$
$798$	978804.	0.0544112
$799$	2.33313e7	1.29292
$800$	−2.77567e6	−0.153336
$801$	1.14753e7	0.631952
$802$	−7.39489e6	−0.405972
$803$	−2.53550e6	−0.138763
$804$	−8.35776e6	−0.455984
$805$	−4.63518e6	−0.252102
$806$	−4.76236e6	−0.258217
$807$	−4.19946e6	−0.226992
$808$	−2.81628e6	−0.151757
$809$	1.04758e7	0.562749	0.281375	−	0.959598i	$-0.409210\pi$
$809$	1.04758e7	0.562749	0.281375	+	0.959598i	$0.409210\pi$
$810$	−534232.	−0.0286100
$811$	4.13506e6	0.220764	0.110382	−	0.993889i	$-0.464792\pi$
$811$	4.13506e6	0.220764	0.110382	+	0.993889i	$0.464792\pi$
$812$	−3.99672e6	−0.212722
$813$	385103.	0.0204339
$814$	−1.19985e6	−0.0634694
$815$	−2.95905e6	−0.156048
$816$	−2.78369e6	−0.146351
$817$	9.44748e6	0.495177
$818$	−3.19934e6	−0.167177
$819$	1.45381e6	0.0757354
$820$	2.77404e6	0.144072
$821$	1.41179e7	0.730991	0.365496	−	0.930813i	$-0.380900\pi$
$821$	1.41179e7	0.730991	0.365496	+	0.930813i	$0.380900\pi$
$822$	−1.07366e7	−0.554226
$823$	1.90085e7	0.978246	0.489123	−	0.872215i	$-0.337317\pi$
$823$	1.90085e7	0.978246	0.489123	+	0.872215i	$0.337317\pi$
$824$	−1.74280e6	−0.0894190
$825$	−2.95186e6	−0.150995
$826$	380404.	0.0193997
$827$	1.38790e6	0.0705657	0.0352828	−	0.999377i	$-0.488767\pi$
$827$	1.38790e6	0.0705657	0.0352828	+	0.999377i	$0.488767\pi$
$828$	−6.02249e6	−0.305281
$829$	8.19892e6	0.414353	0.207176	−	0.978304i	$-0.433573\pi$
$829$	8.19892e6	0.414353	0.207176	+	0.978304i	$0.433573\pi$
$830$	6.27376e6	0.316106
$831$	−1.35175e7	−0.679040
$832$	−1.50033e6	−0.0751414
$833$	2.90089e6	0.144850
$834$	−3.33542e6	−0.166049
$835$	−6.76071e6	−0.335565
$836$	−1.07424e6	−0.0531602
$837$	−2.36953e6	−0.116909
$838$	1.59047e7	0.782374
$839$	−2.87260e7	−1.40887	−0.704435	−	0.709769i	$-0.748800\pi$
$839$	−2.87260e7	−1.40887	−0.704435	+	0.709769i	$0.748800\pi$
$840$	−574538.	−0.0280944
$841$	5.47695e6	0.267023
$842$	−2.70613e7	−1.31543
$843$	6.69688e6	0.324566
$844$	8.92756e6	0.431397
$845$	4.82696e6	0.232558
$846$	6.25669e6	0.300551
$847$	−717409.	−0.0343604
$848$	−1.92559e6	−0.0919546
$849$	2.03960e7	0.971127
$850$	−1.30999e7	−0.621899
$851$	−1.15200e7	−0.545290
$852$	−1.07655e7	−0.508083
$853$	1.33724e7	0.629270	0.314635	−	0.949213i	$-0.398118\pi$
$853$	1.33724e7	0.629270	0.314635	+	0.949213i	$0.398118\pi$
$854$	3.62475e6	0.170072
$855$	−914917.	−0.0428023
$856$	1.13980e7	0.531671
$857$	−2.33571e7	−1.08634	−0.543171	−	0.839622i	$-0.682777\pi$
$857$	−2.33571e7	−1.08634	−0.543171	+	0.839622i	$0.682777\pi$
$858$	−1.59557e6	−0.0739941
$859$	1.04782e6	0.0484510	0.0242255	−	0.999707i	$-0.492288\pi$
$859$	1.04782e6	0.0484510	0.0242255	+	0.999707i	$0.492288\pi$
$860$	−5.54547e6	−0.255677
$861$	−3.75605e6	−0.172673
$862$	1.59126e7	0.729411
$863$	−2.52084e6	−0.115218	−0.0576088	−	0.998339i	$-0.518348\pi$
$863$	−2.52084e6	−0.115218	−0.0576088	+	0.998339i	$0.518348\pi$
$864$	−746496.	−0.0340207
$865$	−1.05239e7	−0.478228
$866$	−1.25287e7	−0.567690
$867$	−359004.	−0.0162200
$868$	−2.54830e6	−0.114802
$869$	−2.40385e6	−0.107984
$870$	3.73585e6	0.167337
$871$	−2.12596e7	−0.949532
$872$	1.43453e7	0.638880
$873$	−8.49165e6	−0.377100
$874$	−1.03140e7	−0.456719
$875$	−5.82080e6	−0.257018
$876$	−3.01746e6	−0.132856
$877$	−2.39012e7	−1.04935	−0.524676	−	0.851302i	$-0.675813\pi$
$877$	−2.39012e7	−1.04935	−0.524676	+	0.851302i	$0.675813\pi$
$878$	−2.82312e7	−1.23593
$879$	1.67865e7	0.732804
$880$	630558.	0.0274485
$881$	2.92994e7	1.27180	0.635900	−	0.771772i	$-0.280629\pi$
$881$	2.92994e7	1.27180	0.635900	+	0.771772i	$0.280629\pi$
$882$	777924.	0.0336718
$883$	485653.	0.0209616	0.0104808	−	0.999945i	$-0.496664\pi$
$883$	485653.	0.0209616	0.0104808	+	0.999945i	$0.496664\pi$
$884$	−7.08086e6	−0.304758
$885$	−355575.	−0.0152606
$886$	−2.22239e7	−0.951122
$887$	−3.06452e6	−0.130784	−0.0653919	−	0.997860i	$-0.520830\pi$
$887$	−3.06452e6	−0.130784	−0.0653919	+	0.997860i	$0.520830\pi$
$888$	−1.42792e6	−0.0607674
$889$	−9.47653e6	−0.402156
$890$	−1.15356e7	−0.488163
$891$	−793881.	−0.0335013
$892$	5.46831e6	0.230113
$893$	1.07151e7	0.449643
$894$	6.44179e6	0.269565
$895$	1.06006e7	0.442357
$896$	−802816.	−0.0334077
$897$	−1.53194e7	−0.635711
$898$	−1.48644e7	−0.615114
$899$	1.65700e7	0.683789
$900$	−3.51296e6	−0.144566
$901$	−9.08786e6	−0.372949
$902$	4.12229e6	0.168703
$903$	7.50857e6	0.306435
$904$	1.48872e7	0.605887
$905$	1.45280e7	0.589636
$906$	1.18667e6	0.0480296
$907$	−6.88154e6	−0.277758	−0.138879	−	0.990309i	$-0.544350\pi$
$907$	−6.88154e6	−0.277758	−0.138879	+	0.990309i	$0.544350\pi$
$908$	−6.52666e6	−0.262710
$909$	−3.56436e6	−0.143078
$910$	−1.46145e6	−0.0585032
$911$	2.85532e7	1.13988	0.569940	−	0.821686i	$-0.306966\pi$
$911$	2.85532e7	1.13988	0.569940	+	0.821686i	$0.306966\pi$
$912$	−1.27844e6	−0.0508970
$913$	9.32295e6	0.370149
$914$	−2.61990e7	−1.03734
$915$	−3.38817e6	−0.133786
$916$	1.04221e7	0.410408
$917$	1.67179e7	0.656535
$918$	−3.52311e6	−0.137981
$919$	−1.56851e7	−0.612632	−0.306316	−	0.951930i	$-0.599096\pi$
$919$	−1.56851e7	−0.612632	−0.306316	+	0.951930i	$0.599096\pi$
$920$	6.05412e6	0.235820
$921$	−6.42024e6	−0.249403
$922$	2.03656e7	0.788987
$923$	−2.73841e7	−1.05802
$924$	−853776.	−0.0328976
$925$	−6.71968e6	−0.258223
$926$	−2.15149e7	−0.824541
$927$	−2.20573e6	−0.0843050
$928$	5.22020e6	0.198984
$929$	−2.09250e7	−0.795473	−0.397736	−	0.917500i	$-0.630204\pi$
$929$	−2.09250e7	−0.795473	−0.397736	+	0.917500i	$0.630204\pi$
$930$	2.38197e6	0.0903086
$931$	1.33226e6	0.0503750
$932$	113259.	0.00427105
$933$	−1.95766e7	−0.736262
$934$	1.86995e7	0.701393
$935$	2.97594e6	0.111326
$936$	−1.89886e6	−0.0708440
$937$	−2.28782e7	−0.851282	−0.425641	−	0.904892i	$-0.639951\pi$
$937$	−2.28782e7	−0.851282	−0.425641	+	0.904892i	$0.639951\pi$
$938$	−1.13758e7	−0.422159
$939$	2.65741e7	0.983547
$940$	−6.28955e6	−0.232167
$941$	7.04008e6	0.259181	0.129591	−	0.991568i	$-0.458634\pi$
$941$	7.04008e6	0.259181	0.129591	+	0.991568i	$0.458634\pi$
$942$	4.62482e6	0.169812
$943$	3.95789e7	1.44939
$944$	−496854.	−0.0181467
$945$	−727149.	−0.0264877
$946$	−8.24070e6	−0.299389
$947$	−1.39188e7	−0.504345	−0.252172	−	0.967682i	$-0.581145\pi$
$947$	−1.39188e7	−0.504345	−0.252172	+	0.967682i	$0.581145\pi$
$948$	−2.86078e6	−0.103386
$949$	−7.67549e6	−0.276656
$950$	−6.01624e6	−0.216280
$951$	−1.24023e7	−0.444682
$952$	−3.78891e6	−0.135495
$953$	−1.66398e7	−0.593493	−0.296746	−	0.954956i	$-0.595902\pi$
$953$	−1.66398e7	−0.593493	−0.296746	+	0.954956i	$0.595902\pi$
$954$	−2.43707e6	−0.0866956
$955$	−8.71619e6	−0.309256
$956$	−2.73004e7	−0.966104
$957$	5.55156e6	0.195945
$958$	2.89414e7	1.01884
$959$	−1.46137e7	−0.513114
$960$	750416.	0.0262799
$961$	−1.80642e7	−0.630971
$962$	−3.63218e6	−0.126541
$963$	1.44255e7	0.501264
$964$	−2.19198e7	−0.759704
$965$	1.52748e6	0.0528027
$966$	−8.19727e6	−0.282635
$967$	−4.69379e6	−0.161420	−0.0807100	−	0.996738i	$-0.525719\pi$
$967$	−4.69379e6	−0.161420	−0.0807100	+	0.996738i	$0.525719\pi$
$968$	937024.	0.0321412
$969$	−6.03362e6	−0.206428
$970$	8.53625e6	0.291298
$971$	−5.13825e7	−1.74891	−0.874454	−	0.485108i	$-0.838780\pi$
$971$	−5.13825e7	−1.74891	−0.874454	+	0.485108i	$0.838780\pi$
$972$	−944784.	−0.0320750
$973$	−4.53988e6	−0.153731
$974$	8.49148e6	0.286805
$975$	−8.93590e6	−0.301042
$976$	−4.73437e6	−0.159088
$977$	−1.84378e7	−0.617979	−0.308990	−	0.951065i	$-0.599991\pi$
$977$	−1.84378e7	−0.617979	−0.308990	+	0.951065i	$0.599991\pi$
$978$	−5.23305e6	−0.174948
$979$	−1.71422e7	−0.571622
$980$	−782009.	−0.0260104
$981$	1.81558e7	0.602342
$982$	2.78904e7	0.922945
$983$	4.10596e7	1.35529	0.677643	−	0.735391i	$-0.263002\pi$
$983$	4.10596e7	1.35529	0.677643	+	0.735391i	$0.263002\pi$
$984$	4.90586e6	0.161521
$985$	5.11335e6	0.167925
$986$	2.46369e7	0.807037
$987$	8.51605e6	0.278257
$988$	−3.25195e6	−0.105987
$989$	−7.91206e7	−2.57217
$990$	798050.	0.0258787
$991$	−7.60537e6	−0.246001	−0.123000	−	0.992407i	$-0.539252\pi$
$991$	−7.60537e6	−0.246001	−0.123000	+	0.992407i	$0.539252\pi$
$992$	3.32839e6	0.107388
$993$	2.30384e7	0.741446
$994$	−1.46530e7	−0.470394
$995$	−1.15515e7	−0.369896
$996$	1.10951e7	0.354391
$997$	4.03101e7	1.28433	0.642165	−	0.766567i	$-0.278037\pi$
$997$	4.03101e7	1.28433	0.642165	+	0.766567i	$0.278037\pi$
$998$	3.86904e7	1.22964
$999$	−1.80721e6	−0.0572920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.6.a.n.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.6.a.n.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	462.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -20.3563 q^{5} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -20.3563 q^{5} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} -81.4254 q^{10} -121.000 q^{11} -144.000 q^{12} -366.292 q^{13} -196.000 q^{14} +183.207 q^{15} +256.000 q^{16} +1208.20 q^{17} +324.000 q^{18} +554.877 q^{19} -325.702 q^{20} +441.000 q^{21} -484.000 q^{22} -4646.98 q^{23} -576.000 q^{24} -2710.62 q^{25} -1465.17 q^{26} -729.000 q^{27} -784.000 q^{28} +5097.85 q^{29} +732.829 q^{30} +3250.38 q^{31} +1024.00 q^{32} +1089.00 q^{33} +4832.80 q^{34} +997.461 q^{35} +1296.00 q^{36} +2479.02 q^{37} +2219.51 q^{38} +3296.63 q^{39} -1302.81 q^{40} -8517.13 q^{41} +1764.00 q^{42} +17026.2 q^{43} -1936.00 q^{44} -1648.86 q^{45} -18587.9 q^{46} +19310.8 q^{47} -2304.00 q^{48} +2401.00 q^{49} -10842.5 q^{50} -10873.8 q^{51} -5860.67 q^{52} -7521.82 q^{53} -2916.00 q^{54} +2463.12 q^{55} -3136.00 q^{56} -4993.90 q^{57} +20391.4 q^{58} -1940.84 q^{59} +2931.31 q^{60} -18493.6 q^{61} +13001.5 q^{62} -3969.00 q^{63} +4096.00 q^{64} +7456.37 q^{65} +4356.00 q^{66} +58040.0 q^{67} +19331.2 q^{68} +41822.8 q^{69} +3989.84 q^{70} +74760.3 q^{71} +5184.00 q^{72} +20954.5 q^{73} +9916.09 q^{74} +24395.6 q^{75} +8878.04 q^{76} +5929.00 q^{77} +13186.5 q^{78} +19866.5 q^{79} -5211.23 q^{80} +6561.00 q^{81} -34068.5 q^{82} -77049.2 q^{83} +7056.00 q^{84} -24594.5 q^{85} +68105.0 q^{86} -45880.7 q^{87} -7744.00 q^{88} +141671. q^{89} -6595.46 q^{90} +17948.3 q^{91} -74351.7 q^{92} -29253.4 q^{93} +77243.1 q^{94} -11295.3 q^{95} -9216.00 q^{96} -104835. q^{97} +9604.00 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 56 q^{5} - 108 q^{6} - 147 q^{7} + 192 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 56 * q^5 - 108 * q^6 - 147 * q^7 + 192 * q^8 + 243 * q^9	\( 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 56 q^{5} - 108 q^{6} - 147 q^{7} + 192 q^{8} + 243 q^{9} - 224 q^{10} - 363 q^{11} - 432 q^{12} - 552 q^{13} - 588 q^{14} + 504 q^{15} + 768 q^{16} - 778 q^{17} + 972 q^{18} - 34 q^{19} - 896 q^{20} + 1323 q^{21} - 1452 q^{22} + 872 q^{23} - 1728 q^{24} - 537 q^{25} - 2208 q^{26} - 2187 q^{27} - 2352 q^{28} + 4752 q^{29} + 2016 q^{30} + 3116 q^{31} + 3072 q^{32} + 3267 q^{33} - 3112 q^{34} + 2744 q^{35} + 3888 q^{36} + 4768 q^{37} - 136 q^{38} + 4968 q^{39} - 3584 q^{40} - 7166 q^{41} + 5292 q^{42} + 10508 q^{43} - 5808 q^{44} - 4536 q^{45} + 3488 q^{46} + 7782 q^{47} - 6912 q^{48} + 7203 q^{49} - 2148 q^{50} + 7002 q^{51} - 8832 q^{52} + 27742 q^{53} - 8748 q^{54} + 6776 q^{55} - 9408 q^{56} + 306 q^{57} + 19008 q^{58} + 3850 q^{59} + 8064 q^{60} + 50106 q^{61} + 12464 q^{62} - 11907 q^{63} + 12288 q^{64} + 54566 q^{65} + 13068 q^{66} + 110686 q^{67} - 12448 q^{68} - 7848 q^{69} + 10976 q^{70} + 105720 q^{71} + 15552 q^{72} + 74544 q^{73} + 19072 q^{74} + 4833 q^{75} - 544 q^{76} + 17787 q^{77} + 19872 q^{78} + 67952 q^{79} - 14336 q^{80} + 19683 q^{81} - 28664 q^{82} + 46216 q^{83} + 21168 q^{84} + 16240 q^{85} + 42032 q^{86} - 42768 q^{87} - 23232 q^{88} + 124750 q^{89} - 18144 q^{90} + 27048 q^{91} + 13952 q^{92} - 28044 q^{93} + 31128 q^{94} + 176906 q^{95} - 27648 q^{96} - 54110 q^{97} + 28812 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 56 * q^5 - 108 * q^6 - 147 * q^7 + 192 * q^8 + 243 * q^9 - 224 * q^10 - 363 * q^11 - 432 * q^12 - 552 * q^13 - 588 * q^14 + 504 * q^15 + 768 * q^16 - 778 * q^17 + 972 * q^18 - 34 * q^19 - 896 * q^20 + 1323 * q^21 - 1452 * q^22 + 872 * q^23 - 1728 * q^24 - 537 * q^25 - 2208 * q^26 - 2187 * q^27 - 2352 * q^28 + 4752 * q^29 + 2016 * q^30 + 3116 * q^31 + 3072 * q^32 + 3267 * q^33 - 3112 * q^34 + 2744 * q^35 + 3888 * q^36 + 4768 * q^37 - 136 * q^38 + 4968 * q^39 - 3584 * q^40 - 7166 * q^41 + 5292 * q^42 + 10508 * q^43 - 5808 * q^44 - 4536 * q^45 + 3488 * q^46 + 7782 * q^47 - 6912 * q^48 + 7203 * q^49 - 2148 * q^50 + 7002 * q^51 - 8832 * q^52 + 27742 * q^53 - 8748 * q^54 + 6776 * q^55 - 9408 * q^56 + 306 * q^57 + 19008 * q^58 + 3850 * q^59 + 8064 * q^60 + 50106 * q^61 + 12464 * q^62 - 11907 * q^63 + 12288 * q^64 + 54566 * q^65 + 13068 * q^66 + 110686 * q^67 - 12448 * q^68 - 7848 * q^69 + 10976 * q^70 + 105720 * q^71 + 15552 * q^72 + 74544 * q^73 + 19072 * q^74 + 4833 * q^75 - 544 * q^76 + 17787 * q^77 + 19872 * q^78 + 67952 * q^79 - 14336 * q^80 + 19683 * q^81 - 28664 * q^82 + 46216 * q^83 + 21168 * q^84 + 16240 * q^85 + 42032 * q^86 - 42768 * q^87 - 23232 * q^88 + 124750 * q^89 - 18144 * q^90 + 27048 * q^91 + 13952 * q^92 - 28044 * q^93 + 31128 * q^94 + 176906 * q^95 - 27648 * q^96 - 54110 * q^97 + 28812 * q^98 - 29403 * q^99

Introduction

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