LMFDB - Embedded newform 471.6.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,6,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, 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("471.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	471.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:	$75.5407791319$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.78552 q^{2} -9.00000 q^{3} +63.7563 q^{4} +53.0529 q^{5} +88.0696 q^{6} -2.88714 q^{7} -310.752 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.78552 q^{2} -9.00000 q^{3} +63.7563 q^{4} +53.0529 q^{5} +88.0696 q^{6} -2.88714 q^{7} -310.752 q^{8} +81.0000 q^{9} -519.150 q^{10} +403.570 q^{11} -573.807 q^{12} +810.814 q^{13} +28.2522 q^{14} -477.476 q^{15} +1000.67 q^{16} -485.011 q^{17} -792.627 q^{18} +169.753 q^{19} +3382.46 q^{20} +25.9843 q^{21} -3949.14 q^{22} -779.056 q^{23} +2796.77 q^{24} -310.393 q^{25} -7934.23 q^{26} -729.000 q^{27} -184.074 q^{28} -6483.10 q^{29} +4672.35 q^{30} +3295.64 q^{31} +152.029 q^{32} -3632.13 q^{33} +4746.08 q^{34} -153.171 q^{35} +5164.26 q^{36} -14817.3 q^{37} -1661.12 q^{38} -7297.33 q^{39} -16486.3 q^{40} -19343.1 q^{41} -254.270 q^{42} -17720.0 q^{43} +25730.2 q^{44} +4297.28 q^{45} +7623.47 q^{46} -759.079 q^{47} -9006.00 q^{48} -16798.7 q^{49} +3037.35 q^{50} +4365.10 q^{51} +51694.5 q^{52} +35517.9 q^{53} +7133.64 q^{54} +21410.6 q^{55} +897.185 q^{56} -1527.78 q^{57} +63440.5 q^{58} -24686.1 q^{59} -30442.1 q^{60} +53927.7 q^{61} -32249.6 q^{62} -233.858 q^{63} -33509.0 q^{64} +43016.0 q^{65} +35542.3 q^{66} +44975.2 q^{67} -30922.5 q^{68} +7011.51 q^{69} +1498.86 q^{70} -61782.1 q^{71} -25170.9 q^{72} +70878.8 q^{73} +144995. q^{74} +2793.53 q^{75} +10822.8 q^{76} -1165.16 q^{77} +71408.1 q^{78} -26244.9 q^{79} +53088.2 q^{80} +6561.00 q^{81} +189282. q^{82} -97059.3 q^{83} +1656.66 q^{84} -25731.2 q^{85} +173400. q^{86} +58347.9 q^{87} -125410. q^{88} +269.668 q^{89} -42051.1 q^{90} -2340.93 q^{91} -49669.8 q^{92} -29660.8 q^{93} +7427.98 q^{94} +9005.88 q^{95} -1368.26 q^{96} +106788. q^{97} +164384. q^{98} +32689.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) $ 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * 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 $

$2$	−9.78552	−1.72985	−0.864926	−	0.501900i	$-0.832634\pi$
$2$	−9.78552	−1.72985	−0.864926	+	0.501900i	$0.832634\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	63.7563	1.99239
$5$	53.0529	0.949039	0.474519	−	0.880245i	$-0.342622\pi$
$5$	53.0529	0.949039	0.474519	+	0.880245i	$0.342622\pi$
$6$	88.0696	0.998730
$7$	−2.88714	−0.0222701	−0.0111351	−	0.999938i	$-0.503544\pi$
$7$	−2.88714	−0.0222701	−0.0111351	+	0.999938i	$0.503544\pi$
$8$	−310.752	−1.71668
$9$	81.0000	0.333333
$10$	−519.150	−1.64170
$11$	403.570	1.00563	0.502814	−	0.864395i	$-0.332298\pi$
$11$	403.570	1.00563	0.502814	+	0.864395i	$0.332298\pi$
$12$	−573.807	−1.15030
$13$	810.814	1.33065	0.665323	−	0.746555i	$-0.268294\pi$
$13$	810.814	1.33065	0.665323	+	0.746555i	$0.268294\pi$
$14$	28.2522	0.0385240
$15$	−477.476	−0.547928
$16$	1000.67	0.977213
$17$	−485.011	−0.407032	−0.203516	−	0.979072i	$-0.565237\pi$
$17$	−485.011	−0.407032	−0.203516	+	0.979072i	$0.565237\pi$
$18$	−792.627	−0.576617
$19$	169.753	0.107878	0.0539390	−	0.998544i	$-0.482822\pi$
$19$	169.753	0.107878	0.0539390	+	0.998544i	$0.482822\pi$
$20$	3382.46	1.89085
$21$	25.9843	0.0128577
$22$	−3949.14	−1.73959
$23$	−779.056	−0.307078	−0.153539	−	0.988143i	$-0.549067\pi$
$23$	−779.056	−0.307078	−0.153539	+	0.988143i	$0.549067\pi$
$24$	2796.77	0.991125
$25$	−310.393	−0.0993257
$26$	−7934.23	−2.30182
$27$	−729.000	−0.192450
$28$	−184.074	−0.0443707
$29$	−6483.10	−1.43149	−0.715744	−	0.698363i	$-0.753912\pi$
$29$	−6483.10	−1.43149	−0.715744	+	0.698363i	$0.753912\pi$
$30$	4672.35	0.947833
$31$	3295.64	0.615937	0.307968	−	0.951397i	$-0.400351\pi$
$31$	3295.64	0.615937	0.307968	+	0.951397i	$0.400351\pi$
$32$	152.029	0.0262453
$33$	−3632.13	−0.580600
$34$	4746.08	0.704106
$35$	−153.171	−0.0211352
$36$	5164.26	0.664128
$37$	−14817.3	−1.77937	−0.889685	−	0.456576i	$-0.849076\pi$
$37$	−14817.3	−1.77937	−0.889685	+	0.456576i	$0.849076\pi$
$38$	−1661.12	−0.186613
$39$	−7297.33	−0.768249
$40$	−16486.3	−1.62919
$41$	−19343.1	−1.79708	−0.898538	−	0.438895i	$-0.855370\pi$
$41$	−19343.1	−1.79708	−0.898538	+	0.438895i	$0.855370\pi$
$42$	−254.270	−0.0222419
$43$	−17720.0	−1.46148	−0.730741	−	0.682655i	$-0.760825\pi$
$43$	−17720.0	−1.46148	−0.730741	+	0.682655i	$0.760825\pi$
$44$	25730.2	2.00360
$45$	4297.28	0.316346
$46$	7623.47	0.531200
$47$	−759.079	−0.0501236	−0.0250618	−	0.999686i	$-0.507978\pi$
$47$	−759.079	−0.0501236	−0.0250618	+	0.999686i	$0.507978\pi$
$48$	−9006.00	−0.564194
$49$	−16798.7	−0.999504
$50$	3037.35	0.171819
$51$	4365.10	0.235000
$52$	51694.5	2.65116
$53$	35517.9	1.73683	0.868415	−	0.495839i	$-0.165139\pi$
$53$	35517.9	1.73683	0.868415	+	0.495839i	$0.165139\pi$
$54$	7133.64	0.332910
$55$	21410.6	0.954380
$56$	897.185	0.0382307
$57$	−1527.78	−0.0622834
$58$	63440.5	2.47626
$59$	−24686.1	−0.923258	−0.461629	−	0.887073i	$-0.652735\pi$
$59$	−24686.1	−0.923258	−0.461629	+	0.887073i	$0.652735\pi$
$60$	−30442.1	−1.09168
$61$	53927.7	1.85561	0.927806	−	0.373063i	$-0.121692\pi$
$61$	53927.7	1.85561	0.927806	+	0.373063i	$0.121692\pi$
$62$	−32249.6	−1.06548
$63$	−233.858	−0.00742338
$64$	−33509.0	−1.02261
$65$	43016.0	1.26284
$66$	35542.3	1.00435
$67$	44975.2	1.22401	0.612006	−	0.790853i	$-0.290363\pi$
$67$	44975.2	1.22401	0.612006	+	0.790853i	$0.290363\pi$
$68$	−30922.5	−0.810965
$69$	7011.51	0.177292
$70$	1498.86	0.0365608
$71$	−61782.1	−1.45451	−0.727255	−	0.686368i	$-0.759204\pi$
$71$	−61782.1	−1.45451	−0.727255	+	0.686368i	$0.759204\pi$
$72$	−25170.9	−0.572226
$73$	70878.8	1.55672	0.778358	−	0.627821i	$-0.216053\pi$
$73$	70878.8	1.55672	0.778358	+	0.627821i	$0.216053\pi$
$74$	144995.	3.07804
$75$	2793.53	0.0573457
$76$	10822.8	0.214935
$77$	−1165.16	−0.0223955
$78$	71408.1	1.32896
$79$	−26244.9	−0.473127	−0.236563	−	0.971616i	$-0.576021\pi$
$79$	−26244.9	−0.473127	−0.236563	+	0.971616i	$0.576021\pi$
$80$	53088.2	0.927413
$81$	6561.00	0.111111
$82$	189282.	3.10868
$83$	−97059.3	−1.54647	−0.773236	−	0.634118i	$-0.781363\pi$
$83$	−97059.3	−1.54647	−0.773236	+	0.634118i	$0.781363\pi$
$84$	1656.66	0.0256174
$85$	−25731.2	−0.386290
$86$	173400.	2.52815
$87$	58347.9	0.826470
$88$	−125410.	−1.72634
$89$	269.668	0.00360873	0.00180437	−	0.999998i	$-0.499426\pi$
$89$	269.668	0.00360873	0.00180437	+	0.999998i	$0.499426\pi$
$90$	−42051.1	−0.547232
$91$	−2340.93	−0.0296337
$92$	−49669.8	−0.611818
$93$	−29660.8	−0.355611
$94$	7427.98	0.0867064
$95$	9005.88	0.102380
$96$	−1368.26	−0.0151527
$97$	106788.	1.15237	0.576187	−	0.817318i	$-0.304540\pi$
$97$	106788.	1.15237	0.576187	+	0.817318i	$0.304540\pi$
$98$	164384.	1.72899
$99$	32689.2	0.335209
$100$	−19789.5	−0.197895
$101$	−137350.	−1.33975	−0.669875	−	0.742474i	$-0.733652\pi$
$101$	−137350.	−1.33975	−0.669875	+	0.742474i	$0.733652\pi$
$102$	−42714.7	−0.406516
$103$	−113327.	−1.05254	−0.526271	−	0.850317i	$-0.676410\pi$
$103$	−113327.	−1.05254	−0.526271	+	0.850317i	$0.676410\pi$
$104$	−251962.	−2.28429
$105$	1378.54	0.0122024
$106$	−347561.	−3.00446
$107$	24134.2	0.203785	0.101893	−	0.994795i	$-0.467510\pi$
$107$	24134.2	0.203785	0.101893	+	0.994795i	$0.467510\pi$
$108$	−46478.4	−0.383435
$109$	157439.	1.26925	0.634625	−	0.772820i	$-0.281155\pi$
$109$	157439.	1.26925	0.634625	+	0.772820i	$0.281155\pi$
$110$	−209513.	−1.65094
$111$	133356.	1.02732
$112$	−2889.06	−0.0217627
$113$	−100947.	−0.743698	−0.371849	−	0.928293i	$-0.621276\pi$
$113$	−100947.	−0.743698	−0.371849	+	0.928293i	$0.621276\pi$
$114$	14950.1	0.107741
$115$	−41331.2	−0.291429
$116$	−413339.	−2.85208
$117$	65675.9	0.443549
$118$	241567.	1.59710
$119$	1400.29	0.00906467
$120$	148377.	0.940616
$121$	1817.97	0.0112882
$122$	−527710.	−3.20993
$123$	174088.	1.03754
$124$	210118.	1.22718
$125$	−182257.	−1.04330
$126$	2288.43	0.0128413
$127$	−5250.85	−0.0288882	−0.0144441	−	0.999896i	$-0.504598\pi$
$127$	−5250.85	−0.0288882	−0.0144441	+	0.999896i	$0.504598\pi$
$128$	323038.	1.74272
$129$	159480.	0.843787
$130$	−420934.	−2.18452
$131$	−244384.	−1.24421	−0.622105	−	0.782934i	$-0.713722\pi$
$131$	−244384.	−1.24421	−0.622105	+	0.782934i	$0.713722\pi$
$132$	−231571.	−1.15678
$133$	−490.101	−0.00240246
$134$	−440105.	−2.11736
$135$	−38675.5	−0.182643
$136$	150718.	0.698744
$137$	−274551.	−1.24975	−0.624874	−	0.780726i	$-0.714850\pi$
$137$	−274551.	−1.24975	−0.624874	+	0.780726i	$0.714850\pi$
$138$	−68611.2	−0.306688
$139$	276415.	1.21346	0.606729	−	0.794908i	$-0.292481\pi$
$139$	276415.	1.21346	0.606729	+	0.794908i	$0.292481\pi$
$140$	−9765.63	−0.0421095
$141$	6831.71	0.0289389
$142$	604569.	2.51609
$143$	327220.	1.33814
$144$	81054.0	0.325738
$145$	−343947.	−1.35854
$146$	−693586.	−2.69289
$147$	151188.	0.577064
$148$	−944699.	−3.54519
$149$	−174488.	−0.643873	−0.321937	−	0.946761i	$-0.604334\pi$
$149$	−174488.	−0.643873	−0.321937	+	0.946761i	$0.604334\pi$
$150$	−27336.2	−0.0991995
$151$	−230848.	−0.823919	−0.411959	−	0.911202i	$-0.635155\pi$
$151$	−230848.	−0.823919	−0.411959	+	0.911202i	$0.635155\pi$
$152$	−52751.1	−0.185192
$153$	−39285.9	−0.135677
$154$	11401.7	0.0387409
$155$	174843.	0.584548
$156$	−465251.	−1.53065
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	256820.	0.818439
$159$	−319661.	−1.00276
$160$	8065.58	0.0249078
$161$	2249.25	0.00683868
$162$	−64202.8	−0.192206
$163$	310689.	0.915918	0.457959	−	0.888973i	$-0.348581\pi$
$163$	310689.	0.915918	0.457959	+	0.888973i	$0.348581\pi$
$164$	−1.23325e6	−3.58047
$165$	−192695.	−0.551012
$166$	949775.	2.67517
$167$	488618.	1.35574	0.677872	−	0.735180i	$-0.262902\pi$
$167$	488618.	1.35574	0.677872	+	0.735180i	$0.262902\pi$
$168$	−8074.66	−0.0220725
$169$	286126.	0.770621
$170$	251793.	0.668223
$171$	13750.0	0.0359594
$172$	−1.12976e6	−2.91183
$173$	−1344.38	−0.00341512	−0.00170756	−	0.999999i	$-0.500544\pi$
$173$	−1344.38	−0.00341512	−0.00170756	+	0.999999i	$0.500544\pi$
$174$	−570964.	−1.42967
$175$	896.148	0.00221200
$176$	403839.	0.982713
$177$	222175.	0.533043
$178$	−2638.84	−0.00624257
$179$	351841.	0.820755	0.410378	−	0.911916i	$-0.365397\pi$
$179$	351841.	0.820755	0.410378	+	0.911916i	$0.365397\pi$
$180$	273979.	0.630283
$181$	−818850.	−1.85784	−0.928919	−	0.370283i	$-0.879261\pi$
$181$	−818850.	−1.85784	−0.928919	+	0.370283i	$0.879261\pi$
$182$	22907.3	0.0512619
$183$	−485349.	−1.07134
$184$	242093.	0.527155
$185$	−786103.	−1.68869
$186$	290246.	0.615155
$187$	−195736.	−0.409323
$188$	−48396.1	−0.0998656
$189$	2104.73	0.00428589
$190$	−88127.2	−0.177103
$191$	−260362.	−0.516409	−0.258205	−	0.966090i	$-0.583131\pi$
$191$	−260362.	−0.516409	−0.258205	+	0.966090i	$0.583131\pi$
$192$	301581.	0.590406
$193$	44620.8	0.0862272	0.0431136	−	0.999070i	$-0.486272\pi$
$193$	44620.8	0.0862272	0.0431136	+	0.999070i	$0.486272\pi$
$194$	−1.04498e6	−1.99343
$195$	−387144.	−0.729098
$196$	−1.07102e6	−1.99140
$197$	46297.0	0.0849939	0.0424969	−	0.999097i	$-0.486469\pi$
$197$	46297.0	0.0849939	0.0424969	+	0.999097i	$0.486469\pi$
$198$	−319881.	−0.579862
$199$	642112.	1.14942	0.574710	−	0.818357i	$-0.305115\pi$
$199$	642112.	1.14942	0.574710	+	0.818357i	$0.305115\pi$
$200$	96455.2	0.170510
$201$	−404776.	−0.706684
$202$	1.34404e6	2.31757
$203$	18717.6	0.0318794
$204$	278302.	0.468211
$205$	−1.02621e6	−1.70550
$206$	1.10896e6	1.82074
$207$	−63103.5	−0.102359
$208$	811354.	1.30033
$209$	68507.2	0.108485
$210$	−13489.7	−0.0211084
$211$	−162834.	−0.251790	−0.125895	−	0.992044i	$-0.540180\pi$
$211$	−162834.	−0.251790	−0.125895	+	0.992044i	$0.540180\pi$
$212$	2.26449e6	3.46043
$213$	556039.	0.839762
$214$	−236165.	−0.352518
$215$	−940099.	−1.38700
$216$	226538.	0.330375
$217$	−9514.99	−0.0137170
$218$	−1.54063e6	−2.19561
$219$	−637909.	−0.898770
$220$	1.36506e6	1.90149
$221$	−393253.	−0.541616
$222$	−1.30496e6	−1.77711
$223$	603908.	0.813221	0.406610	−	0.913602i	$-0.366711\pi$
$223$	603908.	0.813221	0.406610	+	0.913602i	$0.366711\pi$
$224$	−438.929	−0.000584486 0
$225$	−25141.8	−0.0331086
$226$	987817.	1.28649
$227$	−1.05882e6	−1.36382	−0.681912	−	0.731434i	$-0.738851\pi$
$227$	−1.05882e6	−1.36382	−0.681912	+	0.731434i	$0.738851\pi$
$228$	−97405.4	−0.124093
$229$	−868484.	−1.09439	−0.547196	−	0.837004i	$-0.684305\pi$
$229$	−868484.	−1.09439	−0.547196	+	0.837004i	$0.684305\pi$
$230$	404447.	0.504129
$231$	10486.5	0.0129300
$232$	2.01464e6	2.45740
$233$	1.14770e6	1.38496	0.692481	−	0.721436i	$-0.256518\pi$
$233$	1.14770e6	1.38496	0.692481	+	0.721436i	$0.256518\pi$
$234$	−642673.	−0.767274
$235$	−40271.3	−0.0475693
$236$	−1.57390e6	−1.83949
$237$	236204.	0.273160
$238$	−13702.6	−0.0156805
$239$	−1.06962e6	−1.21125	−0.605627	−	0.795748i	$-0.707078\pi$
$239$	−1.06962e6	−1.21125	−0.605627	+	0.795748i	$0.707078\pi$
$240$	−477794.	−0.535442
$241$	−456744.	−0.506559	−0.253280	−	0.967393i	$-0.581509\pi$
$241$	−456744.	−0.506559	−0.253280	+	0.967393i	$0.581509\pi$
$242$	−17789.8	−0.0195268
$243$	−59049.0	−0.0641500
$244$	3.43823e6	3.69709
$245$	−891217.	−0.948568
$246$	−1.70354e6	−1.79479
$247$	137638.	0.143548
$248$	−1.02413e6	−1.05737
$249$	873534.	0.892856
$250$	1.78348e6	1.80476
$251$	1.34270e6	1.34522	0.672611	−	0.739996i	$-0.265173\pi$
$251$	1.34270e6	1.34522	0.672611	+	0.739996i	$0.265173\pi$
$252$	−14910.0	−0.0147902
$253$	−314404.	−0.308807
$254$	51382.3	0.0499723
$255$	231581.	0.223024
$256$	−2.08880e6	−1.99204
$257$	−1.50489e6	−1.42126	−0.710628	−	0.703568i	$-0.751589\pi$
$257$	−1.50489e6	−1.42126	−0.710628	+	0.703568i	$0.751589\pi$
$258$	−1.56060e6	−1.45963
$259$	42779.8	0.0396268
$260$	2.74254e6	2.51605
$261$	−525131.	−0.477163
$262$	2.39142e6	2.15230
$263$	−995398.	−0.887375	−0.443687	−	0.896182i	$-0.646330\pi$
$263$	−995398.	−0.887375	−0.443687	+	0.896182i	$0.646330\pi$
$264$	1.12869e6	0.996703
$265$	1.88432e6	1.64832
$266$	4795.89	0.00415590
$267$	−2427.01	−0.00208350
$268$	2.86745e6	2.43870
$269$	2.18602e6	1.84193	0.920965	−	0.389645i	$-0.127402\pi$
$269$	2.18602e6	1.84193	0.920965	+	0.389645i	$0.127402\pi$
$270$	378460.	0.315944
$271$	1.09411e6	0.904975	0.452487	−	0.891771i	$-0.350537\pi$
$271$	1.09411e6	0.904975	0.452487	+	0.891771i	$0.350537\pi$
$272$	−485334.	−0.397757
$273$	21068.4	0.0171090
$274$	2.68663e6	2.16188
$275$	−125265.	−0.0998847
$276$	447028.	0.353233
$277$	−1.80300e6	−1.41188	−0.705938	−	0.708273i	$-0.749474\pi$
$277$	−1.80300e6	−1.41188	−0.705938	+	0.708273i	$0.749474\pi$
$278$	−2.70487e6	−2.09910
$279$	266947.	0.205312
$280$	47598.2	0.0362824
$281$	22579.8	0.0170591	0.00852953	−	0.999964i	$-0.497285\pi$
$281$	22579.8	0.0170591	0.00852953	+	0.999964i	$0.497285\pi$
$282$	−66851.8	−0.0500600
$283$	−1.25264e6	−0.929739	−0.464870	−	0.885379i	$-0.653899\pi$
$283$	−1.25264e6	−0.929739	−0.464870	+	0.885379i	$0.653899\pi$
$284$	−3.93900e6	−2.89794
$285$	−81052.9	−0.0591094
$286$	−3.20202e6	−2.31478
$287$	55846.3	0.0400212
$288$	12314.3	0.00874843
$289$	−1.18462e6	−0.834325
$290$	3.36570e6	2.35007
$291$	−961092.	−0.665323
$292$	4.51897e6	3.10158
$293$	−336550.	−0.229024	−0.114512	−	0.993422i	$-0.536530\pi$
$293$	−336550.	−0.229024	−0.114512	+	0.993422i	$0.536530\pi$
$294$	−1.47945e6	−0.998235
$295$	−1.30967e6	−0.876208
$296$	4.60452e6	3.05460
$297$	−294203.	−0.193533
$298$	1.70746e6	1.11381
$299$	−631670.	−0.408613
$300$	178105.	0.114255
$301$	51160.2	0.0325474
$302$	2.25897e6	1.42526
$303$	1.23615e6	0.773505
$304$	169866.	0.105420
$305$	2.86102e6	1.76105
$306$	384432.	0.234702
$307$	2.63377e6	1.59490	0.797449	−	0.603387i	$-0.206182\pi$
$307$	2.63377e6	1.59490	0.797449	+	0.603387i	$0.206182\pi$
$308$	−74286.6	−0.0446204
$309$	1.01994e6	0.607685
$310$	−1.71093e6	−1.01118
$311$	1.99796e6	1.17135	0.585673	−	0.810547i	$-0.300830\pi$
$311$	1.99796e6	1.17135	0.585673	+	0.810547i	$0.300830\pi$
$312$	2.26766e6	1.31884
$313$	−2.19372e6	−1.26567	−0.632835	−	0.774286i	$-0.718109\pi$
$313$	−2.19372e6	−1.26567	−0.632835	+	0.774286i	$0.718109\pi$
$314$	241203.	0.138057
$315$	−12406.9	−0.00704508
$316$	−1.67328e6	−0.942651
$317$	−829862.	−0.463829	−0.231914	−	0.972736i	$-0.574499\pi$
$317$	−829862.	−0.463829	−0.231914	+	0.972736i	$0.574499\pi$
$318$	3.12805e6	1.73462
$319$	−2.61639e6	−1.43955
$320$	−1.77775e6	−0.970500
$321$	−217207.	−0.117655
$322$	−22010.0	−0.0118299
$323$	−82332.0	−0.0439099
$324$	418305.	0.221376
$325$	−251671.	−0.132167
$326$	−3.04025e6	−1.58440
$327$	−1.41695e6	−0.732802
$328$	6.01091e6	3.08500
$329$	2191.57	0.00111626
$330$	1.88562e6	0.953168
$331$	1.75415e6	0.880031	0.440015	−	0.897990i	$-0.354973\pi$
$331$	1.75415e6	0.880031	0.440015	+	0.897990i	$0.354973\pi$
$332$	−6.18814e6	−3.08117
$333$	−1.20020e6	−0.593123
$334$	−4.78138e6	−2.34524
$335$	2.38606e6	1.16163
$336$	26001.6	0.0125647
$337$	806496.	0.386836	0.193418	−	0.981116i	$-0.438043\pi$
$337$	806496.	0.386836	0.193418	+	0.981116i	$0.438043\pi$
$338$	−2.79989e6	−1.33306
$339$	908521.	0.429374
$340$	−1.64053e6	−0.769637
$341$	1.33002e6	0.619403
$342$	−134551.	−0.0622044
$343$	97024.3	0.0445292
$344$	5.50653e6	2.50889
$345$	371980.	0.168257
$346$	13155.4	0.00590764
$347$	−606421.	−0.270365	−0.135182	−	0.990821i	$-0.543162\pi$
$347$	−606421.	−0.270365	−0.135182	+	0.990821i	$0.543162\pi$
$348$	3.72005e6	1.64665
$349$	−4.45983e6	−1.95999	−0.979997	−	0.199011i	$-0.936227\pi$
$349$	−4.45983e6	−1.95999	−0.979997	+	0.199011i	$0.936227\pi$
$350$	−8769.27	−0.00382643
$351$	−591083.	−0.256083
$352$	61354.4	0.0263930
$353$	769398.	0.328636	0.164318	−	0.986407i	$-0.447458\pi$
$353$	769398.	0.328636	0.164318	+	0.986407i	$0.447458\pi$
$354$	−2.17410e6	−0.922085
$355$	−3.27772e6	−1.38039
$356$	17193.1	0.00718999
$357$	−12602.7	−0.00523349
$358$	−3.44294e6	−1.41978
$359$	−2.77789e6	−1.13757	−0.568786	−	0.822486i	$-0.692587\pi$
$359$	−2.77789e6	−1.13757	−0.568786	+	0.822486i	$0.692587\pi$
$360$	−1.33539e6	−0.543065
$361$	−2.44728e6	−0.988362
$362$	8.01287e6	3.21378
$363$	−16361.7	−0.00651722
$364$	−149249.	−0.0590417
$365$	3.76032e6	1.47738
$366$	4.74939e6	1.85326
$367$	2.29292e6	0.888637	0.444318	−	0.895869i	$-0.353446\pi$
$367$	2.29292e6	0.888637	0.444318	+	0.895869i	$0.353446\pi$
$368$	−779575.	−0.300081
$369$	−1.56679e6	−0.599026
$370$	7.69242e6	2.92118
$371$	−102545.	−0.0386794
$372$	−1.89106e6	−0.708515
$373$	350331.	0.130379	0.0651893	−	0.997873i	$-0.479235\pi$
$373$	350331.	0.130379	0.0651893	+	0.997873i	$0.479235\pi$
$374$	1.91538e6	0.708068
$375$	1.64032e6	0.602351
$376$	235885.	0.0860462
$377$	−5.25659e6	−1.90481
$378$	−20595.8	−0.00741395
$379$	−2.27765e6	−0.814496	−0.407248	−	0.913318i	$-0.633512\pi$
$379$	−2.27765e6	−0.814496	−0.407248	+	0.913318i	$0.633512\pi$
$380$	574182.	0.203981
$381$	47257.6	0.0166786
$382$	2.54777e6	0.893311
$383$	790882.	0.275496	0.137748	−	0.990467i	$-0.456014\pi$
$383$	790882.	0.275496	0.137748	+	0.990467i	$0.456014\pi$
$384$	−2.90734e6	−1.00616
$385$	−61815.3	−0.0212542
$386$	−436638.	−0.149160
$387$	−1.43532e6	−0.487161
$388$	6.80841e6	2.29597
$389$	−893151.	−0.299261	−0.149631	−	0.988742i	$-0.547808\pi$
$389$	−893151.	−0.299261	−0.149631	+	0.988742i	$0.547808\pi$
$390$	3.78840e6	1.26123
$391$	377851.	0.124991
$392$	5.22022e6	1.71583
$393$	2.19945e6	0.718345
$394$	−453040.	−0.147027
$395$	−1.39237e6	−0.449016
$396$	2.08414e6	0.667866
$397$	5.58098e6	1.77719	0.888596	−	0.458690i	$-0.151681\pi$
$397$	5.58098e6	1.77719	0.888596	+	0.458690i	$0.151681\pi$
$398$	−6.28340e6	−1.98832
$399$	4410.91	0.00138706
$400$	−310599.	−0.0970623
$401$	−883304.	−0.274315	−0.137157	−	0.990549i	$-0.543797\pi$
$401$	−883304.	−0.274315	−0.137157	+	0.990549i	$0.543797\pi$
$402$	3.96095e6	1.22246
$403$	2.67215e6	0.819594
$404$	−8.75690e6	−2.66930
$405$	348080.	0.105449
$406$	−183162.	−0.0551467
$407$	−5.97984e6	−1.78938
$408$	−1.35646e6	−0.403420
$409$	−4.53435e6	−1.34032	−0.670158	−	0.742219i	$-0.733774\pi$
$409$	−4.53435e6	−1.34032	−0.670158	+	0.742219i	$0.733774\pi$
$410$	1.00420e7	2.95025
$411$	2.47096e6	0.721542
$412$	−7.22529e6	−2.09707
$413$	71272.4	0.0205611
$414$	617501.	0.177067
$415$	−5.14928e6	−1.46766
$416$	123267.	0.0349232
$417$	−2.48774e6	−0.700591
$418$	−670379.	−0.187663
$419$	1.70249e6	0.473751	0.236876	−	0.971540i	$-0.423877\pi$
$419$	1.70249e6	0.473751	0.236876	+	0.971540i	$0.423877\pi$
$420$	87890.7	0.0243119
$421$	−2.97869e6	−0.819068	−0.409534	−	0.912295i	$-0.634309\pi$
$421$	−2.97869e6	−0.819068	−0.409534	+	0.912295i	$0.634309\pi$
$422$	1.59341e6	0.435560
$423$	−61485.4	−0.0167079
$424$	−1.10372e7	−2.98158
$425$	150544.	0.0404288
$426$	−5.44113e6	−1.45266
$427$	−155697.	−0.0413247
$428$	1.53871e6	0.406019
$429$	−2.94498e6	−0.772573
$430$	9.19935e6	2.39931
$431$	1.64390e6	0.426267	0.213133	−	0.977023i	$-0.431633\pi$
$431$	1.64390e6	0.426267	0.213133	+	0.977023i	$0.431633\pi$
$432$	−729486.	−0.188065
$433$	5.12745e6	1.31426	0.657130	−	0.753777i	$-0.271770\pi$
$433$	5.12745e6	1.31426	0.657130	+	0.753777i	$0.271770\pi$
$434$	93109.1	0.0237284
$435$	3.09552e6	0.784352
$436$	1.00378e7	2.52883
$437$	−132247.	−0.0331270
$438$	6.24227e6	1.55474
$439$	5.93801e6	1.47055	0.735275	−	0.677769i	$-0.237053\pi$
$439$	5.93801e6	1.47055	0.735275	+	0.677769i	$0.237053\pi$
$440$	−6.65337e6	−1.63836
$441$	−1.36069e6	−0.333168
$442$	3.84819e6	0.936916
$443$	−66666.0	−0.0161397	−0.00806984	−	0.999967i	$-0.502569\pi$
$443$	−66666.0	−0.0161397	−0.00806984	+	0.999967i	$0.502569\pi$
$444$	8.50229e6	2.04682
$445$	14306.7	0.00342483
$446$	−5.90955e6	−1.40675
$447$	1.57039e6	0.371741
$448$	96745.2	0.0227737
$449$	187939.	0.0439948	0.0219974	−	0.999758i	$-0.492997\pi$
$449$	187939.	0.0439948	0.0219974	+	0.999758i	$0.492997\pi$
$450$	246026.	0.0572729
$451$	−7.80630e6	−1.80719
$452$	−6.43600e6	−1.48173
$453$	2.07764e6	0.475690
$454$	1.03611e7	2.35921
$455$	−124193.	−0.0281235
$456$	474760.	0.106921
$457$	−814759.	−0.182490	−0.0912449	−	0.995828i	$-0.529085\pi$
$457$	−814759.	−0.182490	−0.0912449	+	0.995828i	$0.529085\pi$
$458$	8.49857e6	1.89314
$459$	353573.	0.0783334
$460$	−2.63512e6	−0.580639
$461$	−6.68045e6	−1.46404	−0.732021	−	0.681282i	$-0.761423\pi$
$461$	−6.68045e6	−1.46404	−0.732021	+	0.681282i	$0.761423\pi$
$462$	−102616.	−0.0223670
$463$	5.25674e6	1.13963	0.569815	−	0.821773i	$-0.307015\pi$
$463$	5.25674e6	1.13963	0.569815	+	0.821773i	$0.307015\pi$
$464$	−6.48742e6	−1.39887
$465$	−1.57359e6	−0.337489
$466$	−1.12308e7	−2.39578
$467$	7.72043e6	1.63813	0.819067	−	0.573698i	$-0.194492\pi$
$467$	7.72043e6	1.63813	0.819067	+	0.573698i	$0.194492\pi$
$468$	4.18726e6	0.883720
$469$	−129850.	−0.0272589
$470$	394076.	0.0822877
$471$	221841.	0.0460776
$472$	7.67127e6	1.58494
$473$	−7.15128e6	−1.46971
$474$	−2.31138e6	−0.472526
$475$	−52690.1	−0.0107151
$476$	89277.6	0.0180603
$477$	2.87695e6	0.578943
$478$	1.04668e7	2.09529
$479$	5.84355e6	1.16369	0.581846	−	0.813299i	$-0.302331\pi$
$479$	5.84355e6	1.16369	0.581846	+	0.813299i	$0.302331\pi$
$480$	−72590.2	−0.0143805
$481$	−1.20141e7	−2.36771
$482$	4.46947e6	0.876272
$483$	−20243.2	−0.00394831
$484$	115907.	0.0224904
$485$	5.66541e6	1.09365
$486$	577825.	0.110970
$487$	−9.41309e6	−1.79850	−0.899249	−	0.437437i	$-0.855886\pi$
$487$	−9.41309e6	−1.79850	−0.899249	+	0.437437i	$0.855886\pi$
$488$	−1.67581e7	−3.18549
$489$	−2.79620e6	−0.528806
$490$	8.72102e6	1.64088
$491$	−1.03189e7	−1.93166	−0.965831	−	0.259172i	$-0.916550\pi$
$491$	−1.03189e7	−1.93166	−0.965831	+	0.259172i	$0.916550\pi$
$492$	1.10992e7	2.06718
$493$	3.14437e6	0.582662
$494$	−1.34686e6	−0.248316
$495$	1.73426e6	0.318127
$496$	3.29784e6	0.601901
$497$	178374.	0.0323921
$498$	−8.54798e6	−1.54451
$499$	−2.85223e6	−0.512782	−0.256391	−	0.966573i	$-0.582533\pi$
$499$	−2.85223e6	−0.512782	−0.256391	+	0.966573i	$0.582533\pi$
$500$	−1.16201e7	−2.07866
$501$	−4.39756e6	−0.782740
$502$	−1.31390e7	−2.32703
$503$	9.04558e6	1.59410	0.797052	−	0.603911i	$-0.206392\pi$
$503$	9.04558e6	1.59410	0.797052	+	0.603911i	$0.206392\pi$
$504$	72672.0	0.0127436
$505$	−7.28679e6	−1.27147
$506$	3.07660e6	0.534190
$507$	−2.57514e6	−0.444918
$508$	−334775.	−0.0575564
$509$	−3.73814e6	−0.639531	−0.319765	−	0.947497i	$-0.603604\pi$
$509$	−3.73814e6	−0.639531	−0.319765	+	0.947497i	$0.603604\pi$
$510$	−2.26614e6	−0.385799
$511$	−204637.	−0.0346683
$512$	1.01028e7	1.70321
$513$	−123750.	−0.0207611
$514$	1.47261e7	2.45856
$515$	−6.01231e6	−0.998902
$516$	1.01679e7	1.68115
$517$	−306342.	−0.0504057
$518$	−418622.	−0.0685485
$519$	12099.4	0.00197172
$520$	−1.33673e7	−2.16788
$521$	5.30907e6	0.856888	0.428444	−	0.903568i	$-0.359062\pi$
$521$	5.30907e6	0.856888	0.428444	+	0.903568i	$0.359062\pi$
$522$	5.13868e6	0.825421
$523$	−2.04414e6	−0.326780	−0.163390	−	0.986562i	$-0.552243\pi$
$523$	−2.04414e6	−0.326780	−0.163390	+	0.986562i	$0.552243\pi$
$524$	−1.55810e7	−2.47895
$525$	−8065.33	−0.00127710
$526$	9.74048e6	1.53503
$527$	−1.59842e6	−0.250706
$528$	−3.63455e6	−0.567370
$529$	−5.82941e6	−0.905703
$530$	−1.84391e7	−2.85135
$531$	−1.99958e6	−0.307753
$532$	−31247.0	−0.00478663
$533$	−1.56837e7	−2.39127
$534$	23749.6	0.00360415
$535$	1.28039e6	0.193400
$536$	−1.39761e7	−2.10123
$537$	−3.16657e6	−0.473863
$538$	−2.13913e7	−3.18627
$539$	−6.77944e6	−1.00513
$540$	−2.46581e6	−0.363894
$541$	1.66094e6	0.243983	0.121992	−	0.992531i	$-0.461072\pi$
$541$	1.66094e6	0.243983	0.121992	+	0.992531i	$0.461072\pi$
$542$	−1.07064e7	−1.56547
$543$	7.36965e6	1.07262
$544$	−73735.7	−0.0106827
$545$	8.35261e6	1.20457
$546$	−206165.	−0.0295961
$547$	−7.98883e6	−1.14160	−0.570801	−	0.821089i	$-0.693367\pi$
$547$	−7.98883e6	−1.14160	−0.570801	+	0.821089i	$0.693367\pi$
$548$	−1.75044e7	−2.48998
$549$	4.36814e6	0.618537
$550$	1.22579e6	0.172786
$551$	−1.10053e6	−0.154426
$552$	−2.17884e6	−0.304353
$553$	75772.8	0.0105366
$554$	1.76433e7	2.44234
$555$	7.07492e6	0.974966
$556$	1.76232e7	2.41768
$557$	−1.14112e7	−1.55845	−0.779226	−	0.626743i	$-0.784387\pi$
$557$	−1.14112e7	−1.55845	−0.779226	+	0.626743i	$0.784387\pi$
$558$	−2.61222e6	−0.355160
$559$	−1.43676e7	−1.94472
$560$	−153273.	−0.0206536
$561$	1.76162e6	0.236323
$562$	−220955.	−0.0295096
$563$	−6.73869e6	−0.895993	−0.447996	−	0.894035i	$-0.647862\pi$
$563$	−6.73869e6	−0.895993	−0.447996	+	0.894035i	$0.647862\pi$
$564$	435565.	0.0576574
$565$	−5.35552e6	−0.705798
$566$	1.22578e7	1.60831
$567$	−18942.5	−0.00247446
$568$	1.91989e7	2.49693
$569$	3.08114e6	0.398961	0.199481	−	0.979902i	$-0.436074\pi$
$569$	3.08114e6	0.398961	0.199481	+	0.979902i	$0.436074\pi$
$570$	793145.	0.102250
$571$	1.42256e7	1.82592	0.912959	−	0.408051i	$-0.133791\pi$
$571$	1.42256e7	1.82592	0.912959	+	0.408051i	$0.133791\pi$
$572$	2.08624e7	2.66608
$573$	2.34326e6	0.298149
$574$	−546485.	−0.0692306
$575$	241813.	0.0305008
$576$	−2.71423e6	−0.340871
$577$	−5.73632e6	−0.717289	−0.358644	−	0.933474i	$-0.616761\pi$
$577$	−5.73632e6	−0.717289	−0.358644	+	0.933474i	$0.616761\pi$
$578$	1.15921e7	1.44326
$579$	−401587.	−0.0497833
$580$	−2.19288e7	−2.70673
$581$	280224.	0.0344401
$582$	9.40479e6	1.15091
$583$	1.43340e7	1.74660
$584$	−2.20257e7	−2.67238
$585$	3.48430e6	0.420945
$586$	3.29332e6	0.396177
$587$	−7.67861e6	−0.919787	−0.459894	−	0.887974i	$-0.652112\pi$
$587$	−7.67861e6	−0.919787	−0.459894	+	0.887974i	$0.652112\pi$
$588$	9.63919e6	1.14973
$589$	559445.	0.0664461
$590$	1.28158e7	1.51571
$591$	−416673.	−0.0490712
$592$	−1.48272e7	−1.73882
$593$	4.61986e6	0.539501	0.269750	−	0.962930i	$-0.413059\pi$
$593$	4.61986e6	0.539501	0.269750	+	0.962930i	$0.413059\pi$
$594$	2.87893e6	0.334784
$595$	74289.7	0.00860272
$596$	−1.11247e7	−1.28284
$597$	−5.77901e6	−0.663617
$598$	6.18121e6	0.706839
$599$	7.31968e6	0.833537	0.416769	−	0.909013i	$-0.363163\pi$
$599$	7.31968e6	0.833537	0.416769	+	0.909013i	$0.363163\pi$
$600$	−868096.	−0.0984441
$601$	−4.76892e6	−0.538560	−0.269280	−	0.963062i	$-0.586786\pi$
$601$	−4.76892e6	−0.538560	−0.269280	+	0.963062i	$0.586786\pi$
$602$	−500629.	−0.0563022
$603$	3.64299e6	0.408004
$604$	−1.47180e7	−1.64156
$605$	96448.5	0.0107129
$606$	−1.20963e7	−1.33805
$607$	1.36637e7	1.50520	0.752601	−	0.658476i	$-0.228799\pi$
$607$	1.36637e7	1.50520	0.752601	+	0.658476i	$0.228799\pi$
$608$	25807.4	0.00283129
$609$	−168459.	−0.0184056
$610$	−2.79965e7	−3.04635
$611$	−615472.	−0.0666969
$612$	−2.50472e6	−0.270322
$613$	5.96020e6	0.640634	0.320317	−	0.947310i	$-0.396211\pi$
$613$	5.96020e6	0.640634	0.320317	+	0.947310i	$0.396211\pi$
$614$	−2.57728e7	−2.75893
$615$	9.23587e6	0.984668
$616$	362077.	0.0384458
$617$	1.16448e7	1.23146	0.615729	−	0.787958i	$-0.288862\pi$
$617$	1.16448e7	1.23146	0.615729	+	0.787958i	$0.288862\pi$
$618$	−9.98064e6	−1.05120
$619$	9.21460e6	0.966607	0.483303	−	0.875453i	$-0.339437\pi$
$619$	9.21460e6	0.966607	0.483303	+	0.875453i	$0.339437\pi$
$620$	1.11474e7	1.16464
$621$	567932.	0.0590973
$622$	−1.95511e7	−2.02626
$623$	−778.571	−8.03670e−5 0
$624$	−7.30219e6	−0.750743
$625$	−8.69930e6	−0.890809
$626$	2.14667e7	2.18942
$627$	−616565.	−0.0626340
$628$	−1.57153e6	−0.159010
$629$	7.18657e6	0.724261
$630$	121408.	0.0121869
$631$	−9.05265e6	−0.905112	−0.452556	−	0.891736i	$-0.649488\pi$
$631$	−9.05265e6	−0.905112	−0.452556	+	0.891736i	$0.649488\pi$
$632$	8.15566e6	0.812207
$633$	1.46551e6	0.145371
$634$	8.12063e6	0.802355
$635$	−278573.	−0.0274160
$636$	−2.03804e7	−1.99788
$637$	−1.36206e7	−1.32999
$638$	2.56027e7	2.49020
$639$	−5.00435e6	−0.484837
$640$	1.71381e7	1.65391
$641$	1.57664e7	1.51561	0.757803	−	0.652483i	$-0.226273\pi$
$641$	1.57664e7	1.51561	0.757803	+	0.652483i	$0.226273\pi$
$642$	2.12549e6	0.203526
$643$	−859971.	−0.0820269	−0.0410134	−	0.999159i	$-0.513059\pi$
$643$	−859971.	−0.0820269	−0.0410134	+	0.999159i	$0.513059\pi$
$644$	143404.	0.0136253
$645$	8.46089e6	0.800786
$646$	805661.	0.0759576
$647$	−8.18847e6	−0.769028	−0.384514	−	0.923119i	$-0.625631\pi$
$647$	−8.18847e6	−0.769028	−0.384514	+	0.923119i	$0.625631\pi$
$648$	−2.03884e6	−0.190742
$649$	−9.96259e6	−0.928454
$650$	2.46273e6	0.228630
$651$	85634.9	0.00791951
$652$	1.98084e7	1.82486
$653$	−1.12399e7	−1.03152	−0.515760	−	0.856733i	$-0.672490\pi$
$653$	−1.12399e7	−1.03152	−0.515760	+	0.856733i	$0.672490\pi$
$654$	1.38656e7	1.26764
$655$	−1.29653e7	−1.18080
$656$	−1.93560e7	−1.75613
$657$	5.74118e6	0.518905
$658$	−21445.6	−0.00193096
$659$	−4.94652e6	−0.443697	−0.221848	−	0.975081i	$-0.571209\pi$
$659$	−4.94652e6	−0.443697	−0.221848	+	0.975081i	$0.571209\pi$
$660$	−1.22855e7	−1.09783
$661$	−1.79092e7	−1.59430	−0.797152	−	0.603778i	$-0.793661\pi$
$661$	−1.79092e7	−1.59430	−0.797152	+	0.603778i	$0.793661\pi$
$662$	−1.71653e7	−1.52232
$663$	3.53928e6	0.312702
$664$	3.01614e7	2.65479
$665$	−26001.3	−0.00228003
$666$	1.17446e7	1.02601
$667$	5.05070e6	0.439579
$668$	3.11525e7	2.70117
$669$	−5.43517e6	−0.469513
$670$	−2.33488e7	−2.00945
$671$	2.17636e7	1.86606
$672$	3950.36	0.000337453 0
$673$	1.74828e7	1.48790	0.743950	−	0.668235i	$-0.232950\pi$
$673$	1.74828e7	1.48790	0.743950	+	0.668235i	$0.232950\pi$
$674$	−7.89198e6	−0.669170
$675$	226276.	0.0191152
$676$	1.82424e7	1.53537
$677$	1.12480e7	0.943198	0.471599	−	0.881813i	$-0.343677\pi$
$677$	1.12480e7	0.943198	0.471599	+	0.881813i	$0.343677\pi$
$678$	−8.89035e6	−0.742753
$679$	−308312.	−0.0256635
$680$	7.99602e6	0.663135
$681$	9.52940e6	0.787404
$682$	−1.30150e7	−1.07148
$683$	1.84401e7	1.51256	0.756279	−	0.654249i	$-0.227015\pi$
$683$	1.84401e7	1.51256	0.756279	+	0.654249i	$0.227015\pi$
$684$	876649.	0.0716449
$685$	−1.45657e7	−1.18606
$686$	−949433.	−0.0770290
$687$	7.81636e6	0.631848
$688$	−1.77318e7	−1.42818
$689$	2.87984e7	2.31111
$690$	−3.64002e6	−0.291059
$691$	−1.07128e7	−0.853508	−0.426754	−	0.904368i	$-0.640343\pi$
$691$	−1.07128e7	−0.853508	−0.426754	+	0.904368i	$0.640343\pi$
$692$	−85712.5	−0.00680423
$693$	−94378.3	−0.00746516
$694$	5.93414e6	0.467691
$695$	1.46646e7	1.15162
$696$	−1.81317e7	−1.41878
$697$	9.38162e6	0.731469
$698$	4.36417e7	3.39050
$699$	−1.03293e7	−0.799608
$700$	57135.1	0.00440715
$701$	−1.51155e7	−1.16179	−0.580896	−	0.813978i	$-0.697298\pi$
$701$	−1.51155e7	−1.16179	−0.580896	+	0.813978i	$0.697298\pi$
$702$	5.78406e6	0.442986
$703$	−2.51529e6	−0.191955
$704$	−1.35232e7	−1.02837
$705$	362442.	0.0274641
$706$	−7.52896e6	−0.568491
$707$	396547.	0.0298364
$708$	1.41651e7	1.06203
$709$	5.61241e6	0.419308	0.209654	−	0.977776i	$-0.432766\pi$
$709$	5.61241e6	0.419308	0.209654	+	0.977776i	$0.432766\pi$
$710$	3.20741e7	2.38786
$711$	−2.12584e6	−0.157709
$712$	−83800.0	−0.00619504
$713$	−2.56749e6	−0.189141
$714$	123323.	0.00905316
$715$	1.73600e7	1.26994
$716$	2.24321e7	1.63526
$717$	9.62660e6	0.699318
$718$	2.71831e7	1.96783
$719$	5.65522e6	0.407969	0.203984	−	0.978974i	$-0.434611\pi$
$719$	5.65522e6	0.407969	0.203984	+	0.978974i	$0.434611\pi$
$720$	4.30015e6	0.309138
$721$	327190.	0.0234402
$722$	2.39479e7	1.70972
$723$	4.11070e6	0.292462
$724$	−5.22068e7	−3.70153
$725$	2.01231e6	0.142184
$726$	160108.	0.0112738
$727$	1.73493e7	1.21744	0.608718	−	0.793386i	$-0.291684\pi$
$727$	1.73493e7	1.21744	0.608718	+	0.793386i	$0.291684\pi$
$728$	727450.	0.0508715
$729$	531441.	0.0370370
$730$	−3.67967e7	−2.55565
$731$	8.59441e6	0.594870
$732$	−3.09441e7	−2.13452
$733$	−4.85597e6	−0.333823	−0.166911	−	0.985972i	$-0.553379\pi$
$733$	−4.85597e6	−0.333823	−0.166911	+	0.985972i	$0.553379\pi$
$734$	−2.24374e7	−1.53721
$735$	8.02096e6	0.547656
$736$	−118439.	−0.00805936
$737$	1.81506e7	1.23090
$738$	1.53319e7	1.03623
$739$	4.64759e6	0.313052	0.156526	−	0.987674i	$-0.449970\pi$
$739$	4.64759e6	0.313052	0.156526	+	0.987674i	$0.449970\pi$
$740$	−5.01190e7	−3.36452
$741$	−1.23874e6	−0.0828773
$742$	1.00346e6	0.0669097
$743$	−5.76103e6	−0.382849	−0.191425	−	0.981507i	$-0.561311\pi$
$743$	−5.76103e6	−0.382849	−0.191425	+	0.981507i	$0.561311\pi$
$744$	9.21715e6	0.610470
$745$	−9.25710e6	−0.611061
$746$	−3.42817e6	−0.225536
$747$	−7.86180e6	−0.515491
$748$	−1.24794e7	−0.815530
$749$	−69678.7	−0.00453833
$750$	−1.60513e7	−1.04198
$751$	2.85506e6	0.184721	0.0923604	−	0.995726i	$-0.470559\pi$
$751$	2.85506e6	0.184721	0.0923604	+	0.995726i	$0.470559\pi$
$752$	−759585.	−0.0489815
$753$	−1.20843e7	−0.776665
$754$	5.14384e7	3.29503
$755$	−1.22472e7	−0.781931
$756$	134190.	0.00853914
$757$	−1.51491e7	−0.960834	−0.480417	−	0.877040i	$-0.659515\pi$
$757$	−1.51491e7	−0.960834	−0.480417	+	0.877040i	$0.659515\pi$
$758$	2.22880e7	1.40896
$759$	2.82964e6	0.178290
$760$	−2.79860e6	−0.175754
$761$	−2.61140e7	−1.63460	−0.817299	−	0.576213i	$-0.804530\pi$
$761$	−2.61140e7	−1.63460	−0.817299	+	0.576213i	$0.804530\pi$
$762$	−462440.	−0.0288515
$763$	−454550.	−0.0282664
$764$	−1.65997e7	−1.02889
$765$	−2.08423e6	−0.128763
$766$	−7.73919e6	−0.476566
$767$	−2.00159e7	−1.22853
$768$	1.87992e7	1.15010
$769$	1.98389e7	1.20977	0.604885	−	0.796313i	$-0.293219\pi$
$769$	1.98389e7	1.20977	0.604885	+	0.796313i	$0.293219\pi$
$770$	604895.	0.0367666
$771$	1.35440e7	0.820562
$772$	2.84486e6	0.171798
$773$	−7.00040e6	−0.421380	−0.210690	−	0.977553i	$-0.567571\pi$
$773$	−7.00040e6	−0.421380	−0.210690	+	0.977553i	$0.567571\pi$
$774$	1.40454e7	0.842715
$775$	−1.02294e6	−0.0611783
$776$	−3.31846e7	−1.97825
$777$	−385018.	−0.0228785
$778$	8.73994e6	0.517678
$779$	−3.28355e6	−0.193865
$780$	−2.46829e7	−1.45264
$781$	−2.49334e7	−1.46270
$782$	−3.69746e6	−0.216216
$783$	4.72618e6	0.275490
$784$	−1.68099e7	−0.976728
$785$	−1.30770e6	−0.0757415
$786$	−2.15228e7	−1.24263
$787$	−395170.	−0.0227430	−0.0113715	−	0.999935i	$-0.503620\pi$
$787$	−395170.	−0.0227430	−0.0113715	+	0.999935i	$0.503620\pi$
$788$	2.95173e6	0.169341
$789$	8.95858e6	0.512326
$790$	1.36250e7	0.776730
$791$	291448.	0.0165623
$792$	−1.01582e7	−0.575447
$793$	4.37253e7	2.46916
$794$	−5.46128e7	−3.07428
$795$	−1.69589e7	−0.951657
$796$	4.09387e7	2.29009
$797$	−2.20837e7	−1.23147	−0.615737	−	0.787952i	$-0.711142\pi$
$797$	−2.20837e7	−1.23147	−0.615737	+	0.787952i	$0.711142\pi$
$798$	−43163.0	−0.00239941
$799$	368162.	0.0204019
$800$	−47188.7	−0.00260683
$801$	21843.1	0.00120291
$802$	8.64359e6	0.474524
$803$	2.86046e7	1.56548
$804$	−2.58071e7	−1.40799
$805$	119329.	0.00649017
$806$	−2.61484e7	−1.41778
$807$	−1.96742e7	−1.06344
$808$	4.26816e7	2.29992
$809$	−2.76269e7	−1.48409	−0.742046	−	0.670349i	$-0.766144\pi$
$809$	−2.76269e7	−1.48409	−0.742046	+	0.670349i	$0.766144\pi$
$810$	−3.40614e6	−0.182411
$811$	−6.83921e6	−0.365135	−0.182568	−	0.983193i	$-0.558441\pi$
$811$	−6.83921e6	−0.365135	−0.182568	+	0.983193i	$0.558441\pi$
$812$	1.19337e6	0.0635161
$813$	−9.84696e6	−0.522487
$814$	5.85158e7	3.09537
$815$	1.64829e7	0.869242
$816$	4.36800e6	0.229645
$817$	−3.00803e6	−0.157662
$818$	4.43710e7	2.31855
$819$	−189616.	−0.00987790
$820$	−6.54272e7	−3.39800
$821$	−2.67856e7	−1.38690	−0.693448	−	0.720507i	$-0.743909\pi$
$821$	−2.67856e7	−1.38690	−0.693448	+	0.720507i	$0.743909\pi$
$822$	−2.41796e7	−1.24816
$823$	5.76142e6	0.296504	0.148252	−	0.988950i	$-0.452635\pi$
$823$	5.76142e6	0.296504	0.148252	+	0.988950i	$0.452635\pi$
$824$	3.52165e7	1.80687
$825$	1.12739e6	0.0576685
$826$	−697437.	−0.0355676
$827$	1.12326e7	0.571106	0.285553	−	0.958363i	$-0.407823\pi$
$827$	1.12326e7	0.571106	0.285553	+	0.958363i	$0.407823\pi$
$828$	−4.02325e6	−0.203939
$829$	−6.64019e6	−0.335578	−0.167789	−	0.985823i	$-0.553663\pi$
$829$	−6.64019e6	−0.335578	−0.167789	+	0.985823i	$0.553663\pi$
$830$	5.03883e7	2.53884
$831$	1.62270e7	0.815147
$832$	−2.71696e7	−1.36074
$833$	8.14753e6	0.406831
$834$	2.43438e7	1.21192
$835$	2.59226e7	1.28665
$836$	4.36777e6	0.216144
$837$	−2.40253e6	−0.118537
$838$	−1.66598e7	−0.819519
$839$	−6.08910e6	−0.298640	−0.149320	−	0.988789i	$-0.547709\pi$
$839$	−6.08910e6	−0.298640	−0.149320	+	0.988789i	$0.547709\pi$
$840$	−428384.	−0.0209476
$841$	2.15194e7	1.04916
$842$	2.91480e7	1.41687
$843$	−203219.	−0.00984905
$844$	−1.03817e7	−0.501663
$845$	1.51798e7	0.731349
$846$	601667.	0.0289021
$847$	−5248.74	−0.000251389 0
$848$	3.55415e7	1.69725
$849$	1.12738e7	0.536785
$850$	−1.47315e6	−0.0699358
$851$	1.15435e7	0.546406
$852$	3.54510e7	1.67313
$853$	1.91564e7	0.901451	0.450726	−	0.892663i	$-0.351165\pi$
$853$	1.91564e7	0.901451	0.450726	+	0.892663i	$0.351165\pi$
$854$	1.52357e6	0.0714857
$855$	729476.	0.0341268
$856$	−7.49974e6	−0.349834
$857$	2.74614e7	1.27723	0.638616	−	0.769525i	$-0.279507\pi$
$857$	2.74614e7	1.27723	0.638616	+	0.769525i	$0.279507\pi$
$858$	2.88182e7	1.33644
$859$	−3.41133e7	−1.57739	−0.788697	−	0.614782i	$-0.789244\pi$
$859$	−3.41133e7	−1.57739	−0.788697	+	0.614782i	$0.789244\pi$
$860$	−5.99372e7	−2.76344
$861$	−502617.	−0.0231062
$862$	−1.60864e7	−0.737378
$863$	−1.08456e7	−0.495709	−0.247855	−	0.968797i	$-0.579726\pi$
$863$	−1.08456e7	−0.495709	−0.247855	+	0.968797i	$0.579726\pi$
$864$	−110829.	−0.00505091
$865$	−71323.0	−0.00324108
$866$	−5.01747e7	−2.27347
$867$	1.06616e7	0.481698
$868$	−606641.	−0.0273295
$869$	−1.05917e7	−0.475790
$870$	−3.02913e7	−1.35681
$871$	3.64665e7	1.62873
$872$	−4.89246e7	−2.17889
$873$	8.64983e6	0.384125
$874$	1.29411e6	0.0573048
$875$	526203.	0.0232345
$876$	−4.06707e7	−1.79070
$877$	−3.06939e7	−1.34757	−0.673787	−	0.738925i	$-0.735334\pi$
$877$	−3.06939e7	−1.34757	−0.673787	+	0.738925i	$0.735334\pi$
$878$	−5.81065e7	−2.54383
$879$	3.02895e6	0.132227
$880$	2.14248e7	0.932633
$881$	1.23504e7	0.536094	0.268047	−	0.963406i	$-0.413622\pi$
$881$	1.23504e7	0.536094	0.268047	+	0.963406i	$0.413622\pi$
$882$	1.33151e7	0.576331
$883$	2.11537e7	0.913031	0.456515	−	0.889715i	$-0.349097\pi$
$883$	2.11537e7	0.913031	0.456515	+	0.889715i	$0.349097\pi$
$884$	−2.50724e7	−1.07911
$885$	1.17870e7	0.505879
$886$	652361.	0.0279193
$887$	3.19410e6	0.136314	0.0681569	−	0.997675i	$-0.478288\pi$
$887$	3.19410e6	0.136314	0.0681569	+	0.997675i	$0.478288\pi$
$888$	−4.14407e7	−1.76358
$889$	15159.9	0.000643344 0
$890$	−139998.	−0.00592444
$891$	2.64782e6	0.111736
$892$	3.85029e7	1.62025
$893$	−128856.	−0.00540724
$894$	−1.53671e7	−0.643056
$895$	1.86662e7	0.778928
$896$	−932656.	−0.0388107
$897$	5.68503e6	0.235913
$898$	−1.83908e6	−0.0761045
$899$	−2.13660e7	−0.881706
$900$	−1.60295e6	−0.0659650
$901$	−1.72265e7	−0.706946
$902$	7.63887e7	3.12617
$903$	−460442.	−0.0187913
$904$	3.13694e7	1.27669
$905$	−4.34423e7	−1.76316
$906$	−2.03307e7	−0.822872
$907$	7.22281e6	0.291533	0.145767	−	0.989319i	$-0.453435\pi$
$907$	7.22281e6	0.291533	0.145767	+	0.989319i	$0.453435\pi$
$908$	−6.75066e7	−2.71726
$909$	−1.11253e7	−0.446583
$910$	1.21530e6	0.0486495
$911$	−1.18060e7	−0.471311	−0.235655	−	0.971837i	$-0.575724\pi$
$911$	−1.18060e7	−0.471311	−0.235655	+	0.971837i	$0.575724\pi$
$912$	−1.52879e6	−0.0608642
$913$	−3.91703e7	−1.55518
$914$	7.97284e6	0.315680
$915$	−2.57492e7	−1.01674
$916$	−5.53714e7	−2.18045
$917$	705570.	0.0277087
$918$	−3.45989e6	−0.135505
$919$	−2.67991e7	−1.04672	−0.523360	−	0.852112i	$-0.675322\pi$
$919$	−2.67991e7	−1.04672	−0.523360	+	0.852112i	$0.675322\pi$
$920$	1.28437e7	0.500290
$921$	−2.37040e7	−0.920814
$922$	6.53716e7	2.53257
$923$	−5.00938e7	−1.93544
$924$	668579.	0.0257616
$925$	4.59920e6	0.176737
$926$	−5.14399e7	−1.97139
$927$	−9.17946e6	−0.350847
$928$	−985619.	−0.0375698
$929$	1.74711e7	0.664172	0.332086	−	0.943249i	$-0.392248\pi$
$929$	1.74711e7	0.664172	0.332086	+	0.943249i	$0.392248\pi$
$930$	1.53984e7	0.583805
$931$	−2.85162e6	−0.107825
$932$	7.31730e7	2.75938
$933$	−1.79816e7	−0.676277
$934$	−7.55484e7	−2.83373
$935$	−1.03844e7	−0.388464
$936$	−2.04089e7	−0.761431
$937$	2.69166e6	0.100155	0.0500773	−	0.998745i	$-0.484053\pi$
$937$	2.69166e6	0.100155	0.0500773	+	0.998745i	$0.484053\pi$
$938$	1.27065e6	0.0471539
$939$	1.97435e7	0.730735
$940$	−2.56755e6	−0.0947763
$941$	−1.23510e7	−0.454702	−0.227351	−	0.973813i	$-0.573006\pi$
$941$	−1.23510e7	−0.454702	−0.227351	+	0.973813i	$0.573006\pi$
$942$	−2.17083e6	−0.0797073
$943$	1.50694e7	0.551843
$944$	−2.47026e7	−0.902220
$945$	111662.	0.00406748
$946$	6.99789e7	2.54237
$947$	3.46472e6	0.125543	0.0627716	−	0.998028i	$-0.480006\pi$
$947$	3.46472e6	0.125543	0.0627716	+	0.998028i	$0.480006\pi$
$948$	1.50595e7	0.544240
$949$	5.74695e7	2.07144
$950$	515600.	0.0185355
$951$	7.46876e6	0.267792
$952$	−435144.	−0.0155611
$953$	−5.03573e6	−0.179610	−0.0898049	−	0.995959i	$-0.528624\pi$
$953$	−5.03573e6	−0.179610	−0.0898049	+	0.995959i	$0.528624\pi$
$954$	−2.81524e7	−1.00149
$955$	−1.38129e7	−0.490092
$956$	−6.81951e7	−2.41329
$957$	2.35475e7	0.831122
$958$	−5.71822e7	−2.01301
$959$	792669.	0.0278321
$960$	1.59997e7	0.560318
$961$	−1.77679e7	−0.620622
$962$	1.17564e8	4.09579
$963$	1.95487e6	0.0679284
$964$	−2.91203e7	−1.00926
$965$	2.36726e6	0.0818330
$966$	198090.	0.00682999
$967$	−4.01218e7	−1.37980	−0.689898	−	0.723907i	$-0.742345\pi$
$967$	−4.01218e7	−1.37980	−0.689898	+	0.723907i	$0.742345\pi$
$968$	−564938.	−0.0193781
$969$	740988.	0.0253514
$970$	−5.54390e7	−1.89185
$971$	1.20741e7	0.410967	0.205484	−	0.978661i	$-0.434123\pi$
$971$	1.20741e7	0.410967	0.205484	+	0.978661i	$0.434123\pi$
$972$	−3.76475e6	−0.127812
$973$	−798050.	−0.0270239
$974$	9.21120e7	3.11113
$975$	2.26504e6	0.0763069
$976$	5.39636e7	1.81333
$977$	−2.47881e7	−0.830819	−0.415409	−	0.909635i	$-0.636362\pi$
$977$	−2.47881e7	−0.830819	−0.415409	+	0.909635i	$0.636362\pi$
$978$	2.73623e7	0.914755
$979$	108830.	0.00362904
$980$	−5.68207e7	−1.88991
$981$	1.27526e7	0.423083
$982$	1.00976e8	3.34149
$983$	−7.13738e6	−0.235589	−0.117794	−	0.993038i	$-0.537582\pi$
$983$	−7.13738e6	−0.235589	−0.117794	+	0.993038i	$0.537582\pi$
$984$	−5.40982e7	−1.78113
$985$	2.45619e6	0.0806625
$986$	−3.07693e7	−1.00792
$987$	−19724.1	−0.000644473 0
$988$	8.77529e6	0.286002
$989$	1.38049e7	0.448789
$990$	−1.69706e7	−0.550312
$991$	4.11298e6	0.133037	0.0665185	−	0.997785i	$-0.478811\pi$
$991$	4.11298e6	0.133037	0.0665185	+	0.997785i	$0.478811\pi$
$992$	501034.	0.0161654
$993$	−1.57874e7	−0.508086
$994$	−1.74548e6	−0.0560336
$995$	3.40659e7	1.09084
$996$	5.56933e7	1.77891
$997$	1.29059e7	0.411196	0.205598	−	0.978637i	$-0.434086\pi$
$997$	1.29059e7	0.411196	0.205598	+	0.978637i	$0.434086\pi$
$998$	2.79105e7	0.887037
$999$	1.08018e7	0.342440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.3	✓	30	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-9.78552 q^{2} -9.00000 q^{3} +63.7563 q^{4} +53.0529 q^{5} +88.0696 q^{6} -2.88714 q^{7} -310.752 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.78552 q^{2} -9.00000 q^{3} +63.7563 q^{4} +53.0529 q^{5} +88.0696 q^{6} -2.88714 q^{7} -310.752 q^{8} +81.0000 q^{9} -519.150 q^{10} +403.570 q^{11} -573.807 q^{12} +810.814 q^{13} +28.2522 q^{14} -477.476 q^{15} +1000.67 q^{16} -485.011 q^{17} -792.627 q^{18} +169.753 q^{19} +3382.46 q^{20} +25.9843 q^{21} -3949.14 q^{22} -779.056 q^{23} +2796.77 q^{24} -310.393 q^{25} -7934.23 q^{26} -729.000 q^{27} -184.074 q^{28} -6483.10 q^{29} +4672.35 q^{30} +3295.64 q^{31} +152.029 q^{32} -3632.13 q^{33} +4746.08 q^{34} -153.171 q^{35} +5164.26 q^{36} -14817.3 q^{37} -1661.12 q^{38} -7297.33 q^{39} -16486.3 q^{40} -19343.1 q^{41} -254.270 q^{42} -17720.0 q^{43} +25730.2 q^{44} +4297.28 q^{45} +7623.47 q^{46} -759.079 q^{47} -9006.00 q^{48} -16798.7 q^{49} +3037.35 q^{50} +4365.10 q^{51} +51694.5 q^{52} +35517.9 q^{53} +7133.64 q^{54} +21410.6 q^{55} +897.185 q^{56} -1527.78 q^{57} +63440.5 q^{58} -24686.1 q^{59} -30442.1 q^{60} +53927.7 q^{61} -32249.6 q^{62} -233.858 q^{63} -33509.0 q^{64} +43016.0 q^{65} +35542.3 q^{66} +44975.2 q^{67} -30922.5 q^{68} +7011.51 q^{69} +1498.86 q^{70} -61782.1 q^{71} -25170.9 q^{72} +70878.8 q^{73} +144995. q^{74} +2793.53 q^{75} +10822.8 q^{76} -1165.16 q^{77} +71408.1 q^{78} -26244.9 q^{79} +53088.2 q^{80} +6561.00 q^{81} +189282. q^{82} -97059.3 q^{83} +1656.66 q^{84} -25731.2 q^{85} +173400. q^{86} +58347.9 q^{87} -125410. q^{88} +269.668 q^{89} -42051.1 q^{90} -2340.93 q^{91} -49669.8 q^{92} -29660.8 q^{93} +7427.98 q^{94} +9005.88 q^{95} -1368.26 q^{96} +106788. q^{97} +164384. q^{98} +32689.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * q^99

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