LMFDB - Embedded newform 462.6.a.f.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{214}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 214 $ x^2 - 214
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			1.1
Root			$-14.6287$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -101.515 q^{5} +36.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -101.515 q^{5} +36.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +406.060 q^{10} -121.000 q^{11} -144.000 q^{12} -23.0000 q^{13} +196.000 q^{14} +913.635 q^{15} +256.000 q^{16} -1917.50 q^{17} -324.000 q^{18} +2286.77 q^{19} -1624.24 q^{20} +441.000 q^{21} +484.000 q^{22} -2034.01 q^{23} +576.000 q^{24} +7180.29 q^{25} +92.0000 q^{26} -729.000 q^{27} -784.000 q^{28} +6018.08 q^{29} -3654.54 q^{30} +4253.42 q^{31} -1024.00 q^{32} +1089.00 q^{33} +7669.99 q^{34} +4974.23 q^{35} +1296.00 q^{36} +3066.84 q^{37} -9147.09 q^{38} +207.000 q^{39} +6496.96 q^{40} +9378.04 q^{41} -1764.00 q^{42} -17900.1 q^{43} -1936.00 q^{44} -8222.71 q^{45} +8136.05 q^{46} +25870.1 q^{47} -2304.00 q^{48} +2401.00 q^{49} -28721.1 q^{50} +17257.5 q^{51} -368.000 q^{52} -24888.7 q^{53} +2916.00 q^{54} +12283.3 q^{55} +3136.00 q^{56} -20581.0 q^{57} -24072.3 q^{58} +22829.0 q^{59} +14618.2 q^{60} +2696.37 q^{61} -17013.7 q^{62} -3969.00 q^{63} +4096.00 q^{64} +2334.84 q^{65} -4356.00 q^{66} +18798.7 q^{67} -30679.9 q^{68} +18306.1 q^{69} -19896.9 q^{70} -12434.8 q^{71} -5184.00 q^{72} +60850.5 q^{73} -12267.4 q^{74} -64622.6 q^{75} +36588.4 q^{76} +5929.00 q^{77} -828.000 q^{78} -30163.8 q^{79} -25987.8 q^{80} +6561.00 q^{81} -37512.1 q^{82} -82172.0 q^{83} +7056.00 q^{84} +194655. q^{85} +71600.3 q^{86} -54162.7 q^{87} +7744.00 q^{88} -2618.35 q^{89} +32890.8 q^{90} +1127.00 q^{91} -32544.2 q^{92} -38280.8 q^{93} -103480. q^{94} -232142. q^{95} +9216.00 q^{96} +18079.4 q^{97} -9604.00 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 86 q^{5} + 72 q^{6} - 98 q^{7} - 128 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 86 * q^5 + 72 * q^6 - 98 * q^7 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 86 q^{5} + 72 q^{6} - 98 q^{7} - 128 q^{8} + 162 q^{9} + 344 q^{10} - 242 q^{11} - 288 q^{12} - 46 q^{13} + 392 q^{14} + 774 q^{15} + 512 q^{16} - 1904 q^{17} - 648 q^{18} + 4398 q^{19} - 1376 q^{20} + 882 q^{21} + 968 q^{22} - 2020 q^{23} + 1152 q^{24} + 4296 q^{25} + 184 q^{26} - 1458 q^{27} - 1568 q^{28} + 3610 q^{29} - 3096 q^{30} - 680 q^{31} - 2048 q^{32} + 2178 q^{33} + 7616 q^{34} + 4214 q^{35} + 2592 q^{36} + 3442 q^{37} - 17592 q^{38} + 414 q^{39} + 5504 q^{40} + 22384 q^{41} - 3528 q^{42} + 5804 q^{43} - 3872 q^{44} - 6966 q^{45} + 8080 q^{46} + 6274 q^{47} - 4608 q^{48} + 4802 q^{49} - 17184 q^{50} + 17136 q^{51} - 736 q^{52} + 4700 q^{53} + 5832 q^{54} + 10406 q^{55} + 6272 q^{56} - 39582 q^{57} - 14440 q^{58} + 28162 q^{59} + 12384 q^{60} - 9236 q^{61} + 2720 q^{62} - 7938 q^{63} + 8192 q^{64} + 1978 q^{65} - 8712 q^{66} - 13018 q^{67} - 30464 q^{68} + 18180 q^{69} - 16856 q^{70} + 24400 q^{71} - 10368 q^{72} + 75006 q^{73} - 13768 q^{74} - 38664 q^{75} + 70368 q^{76} + 11858 q^{77} - 1656 q^{78} + 28264 q^{79} - 22016 q^{80} + 13122 q^{81} - 89536 q^{82} - 185936 q^{83} + 14112 q^{84} + 194864 q^{85} - 23216 q^{86} - 32490 q^{87} + 15488 q^{88} + 36660 q^{89} + 27864 q^{90} + 2254 q^{91} - 32320 q^{92} + 6120 q^{93} - 25096 q^{94} - 199386 q^{95} + 18432 q^{96} + 3332 q^{97} - 19208 q^{98} - 19602 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 86 * q^5 + 72 * q^6 - 98 * q^7 - 128 * q^8 + 162 * q^9 + 344 * q^10 - 242 * q^11 - 288 * q^12 - 46 * q^13 + 392 * q^14 + 774 * q^15 + 512 * q^16 - 1904 * q^17 - 648 * q^18 + 4398 * q^19 - 1376 * q^20 + 882 * q^21 + 968 * q^22 - 2020 * q^23 + 1152 * q^24 + 4296 * q^25 + 184 * q^26 - 1458 * q^27 - 1568 * q^28 + 3610 * q^29 - 3096 * q^30 - 680 * q^31 - 2048 * q^32 + 2178 * q^33 + 7616 * q^34 + 4214 * q^35 + 2592 * q^36 + 3442 * q^37 - 17592 * q^38 + 414 * q^39 + 5504 * q^40 + 22384 * q^41 - 3528 * q^42 + 5804 * q^43 - 3872 * q^44 - 6966 * q^45 + 8080 * q^46 + 6274 * q^47 - 4608 * q^48 + 4802 * q^49 - 17184 * q^50 + 17136 * q^51 - 736 * q^52 + 4700 * q^53 + 5832 * q^54 + 10406 * q^55 + 6272 * q^56 - 39582 * q^57 - 14440 * q^58 + 28162 * q^59 + 12384 * q^60 - 9236 * q^61 + 2720 * q^62 - 7938 * q^63 + 8192 * q^64 + 1978 * q^65 - 8712 * q^66 - 13018 * q^67 - 30464 * q^68 + 18180 * q^69 - 16856 * q^70 + 24400 * q^71 - 10368 * q^72 + 75006 * q^73 - 13768 * q^74 - 38664 * q^75 + 70368 * q^76 + 11858 * q^77 - 1656 * q^78 + 28264 * q^79 - 22016 * q^80 + 13122 * q^81 - 89536 * q^82 - 185936 * q^83 + 14112 * q^84 + 194864 * q^85 - 23216 * q^86 - 32490 * q^87 + 15488 * q^88 + 36660 * q^89 + 27864 * q^90 + 2254 * q^91 - 32320 * q^92 + 6120 * q^93 - 25096 * q^94 - 199386 * q^95 + 18432 * q^96 + 3332 * q^97 - 19208 * q^98 - 19602 * 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
$5$	−101.515	−1.81595	−0.907977	−	0.419019i	$-0.862374\pi$
$5$	−101.515	−1.81595	−0.907977	+	0.419019i	$0.862374\pi$
$6$	36.0000	0.408248
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	406.060	1.28407
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−144.000	−0.288675
$13$	−23.0000	−0.0377459	−0.0188729	−	0.999822i	$-0.506008\pi$
$13$	−23.0000	−0.0377459	−0.0188729	+	0.999822i	$0.506008\pi$
$14$	196.000	0.267261
$15$	913.635	1.04844
$16$	256.000	0.250000
$17$	−1917.50	−1.60921	−0.804604	−	0.593811i	$-0.797623\pi$
$17$	−1917.50	−1.60921	−0.804604	+	0.593811i	$0.797623\pi$
$18$	−324.000	−0.235702
$19$	2286.77	1.45325	0.726623	−	0.687037i	$-0.241089\pi$
$19$	2286.77	1.45325	0.726623	+	0.687037i	$0.241089\pi$
$20$	−1624.24	−0.907977
$21$	441.000	0.218218
$22$	484.000	0.213201
$23$	−2034.01	−0.801741	−0.400870	−	0.916135i	$-0.631292\pi$
$23$	−2034.01	−0.801741	−0.400870	+	0.916135i	$0.631292\pi$
$24$	576.000	0.204124
$25$	7180.29	2.29769
$26$	92.0000	0.0266904
$27$	−729.000	−0.192450
$28$	−784.000	−0.188982
$29$	6018.08	1.32881	0.664405	−	0.747373i	$-0.268685\pi$
$29$	6018.08	1.32881	0.664405	+	0.747373i	$0.268685\pi$
$30$	−3654.54	−0.741360
$31$	4253.42	0.794940	0.397470	−	0.917615i	$-0.369888\pi$
$31$	4253.42	0.794940	0.397470	+	0.917615i	$0.369888\pi$
$32$	−1024.00	−0.176777
$33$	1089.00	0.174078
$34$	7669.99	1.13788
$35$	4974.23	0.686366
$36$	1296.00	0.166667
$37$	3066.84	0.368288	0.184144	−	0.982899i	$-0.441049\pi$
$37$	3066.84	0.368288	0.184144	+	0.982899i	$0.441049\pi$
$38$	−9147.09	−1.02760
$39$	207.000	0.0217926
$40$	6496.96	0.642037
$41$	9378.04	0.871269	0.435635	−	0.900124i	$-0.356524\pi$
$41$	9378.04	0.871269	0.435635	+	0.900124i	$0.356524\pi$
$42$	−1764.00	−0.154303
$43$	−17900.1	−1.47633	−0.738165	−	0.674620i	$-0.764307\pi$
$43$	−17900.1	−1.47633	−0.738165	+	0.674620i	$0.764307\pi$
$44$	−1936.00	−0.150756
$45$	−8222.71	−0.605318
$46$	8136.05	0.566916
$47$	25870.1	1.70826	0.854128	−	0.520063i	$-0.174092\pi$
$47$	25870.1	1.70826	0.854128	+	0.520063i	$0.174092\pi$
$48$	−2304.00	−0.144338
$49$	2401.00	0.142857
$50$	−28721.1	−1.62471
$51$	17257.5	0.929077
$52$	−368.000	−0.0188729
$53$	−24888.7	−1.21706	−0.608531	−	0.793530i	$-0.708241\pi$
$53$	−24888.7	−1.21706	−0.608531	+	0.793530i	$0.708241\pi$
$54$	2916.00	0.136083
$55$	12283.3	0.547531
$56$	3136.00	0.133631
$57$	−20581.0	−0.839032
$58$	−24072.3	−0.939610
$59$	22829.0	0.853801	0.426900	−	0.904299i	$-0.359605\pi$
$59$	22829.0	0.853801	0.426900	+	0.904299i	$0.359605\pi$
$60$	14618.2	0.524221
$61$	2696.37	0.0927801	0.0463900	−	0.998923i	$-0.485228\pi$
$61$	2696.37	0.0927801	0.0463900	+	0.998923i	$0.485228\pi$
$62$	−17013.7	−0.562108
$63$	−3969.00	−0.125988
$64$	4096.00	0.125000
$65$	2334.84	0.0685448
$66$	−4356.00	−0.123091
$67$	18798.7	0.511613	0.255806	−	0.966728i	$-0.417659\pi$
$67$	18798.7	0.511613	0.255806	+	0.966728i	$0.417659\pi$
$68$	−30679.9	−0.804604
$69$	18306.1	0.462885
$70$	−19896.9	−0.485334
$71$	−12434.8	−0.292747	−0.146374	−	0.989229i	$-0.546760\pi$
$71$	−12434.8	−0.292747	−0.146374	+	0.989229i	$0.546760\pi$
$72$	−5184.00	−0.117851
$73$	60850.5	1.33646	0.668231	−	0.743954i	$-0.267052\pi$
$73$	60850.5	1.33646	0.668231	+	0.743954i	$0.267052\pi$
$74$	−12267.4	−0.260419
$75$	−64622.6	−1.32657
$76$	36588.4	0.726623
$77$	5929.00	0.113961
$78$	−828.000	−0.0154097
$79$	−30163.8	−0.543774	−0.271887	−	0.962329i	$-0.587648\pi$
$79$	−30163.8	−0.543774	−0.271887	+	0.962329i	$0.587648\pi$
$80$	−25987.8	−0.453989
$81$	6561.00	0.111111
$82$	−37512.1	−0.616080
$83$	−82172.0	−1.30927	−0.654634	−	0.755946i	$-0.727177\pi$
$83$	−82172.0	−1.30927	−0.654634	+	0.755946i	$0.727177\pi$
$84$	7056.00	0.109109
$85$	194655.	2.92225
$86$	71600.3	1.04392
$87$	−54162.7	−0.767189
$88$	7744.00	0.106600
$89$	−2618.35	−0.0350391	−0.0175196	−	0.999847i	$-0.505577\pi$
$89$	−2618.35	−0.0350391	−0.0175196	+	0.999847i	$0.505577\pi$
$90$	32890.8	0.428025
$91$	1127.00	0.0142666
$92$	−32544.2	−0.400870
$93$	−38280.8	−0.458959
$94$	−103480.	−1.20792
$95$	−232142.	−2.63903
$96$	9216.00	0.102062
$97$	18079.4	0.195099	0.0975497	−	0.995231i	$-0.468900\pi$
$97$	18079.4	0.195099	0.0975497	+	0.995231i	$0.468900\pi$
$98$	−9604.00	−0.101015
$99$	−9801.00	−0.100504
$100$	114885.	1.14885
$101$	178534.	1.74147	0.870737	−	0.491749i	$-0.163642\pi$
$101$	178534.	1.74147	0.870737	+	0.491749i	$0.163642\pi$
$102$	−69029.9	−0.656957
$103$	4844.65	0.0449955	0.0224978	−	0.999747i	$-0.492838\pi$
$103$	4844.65	0.0449955	0.0224978	+	0.999747i	$0.492838\pi$
$104$	1472.00	0.0133452
$105$	−44768.1	−0.396274
$106$	99554.8	0.860593
$107$	64976.6	0.548652	0.274326	−	0.961637i	$-0.411545\pi$
$107$	64976.6	0.548652	0.274326	+	0.961637i	$0.411545\pi$
$108$	−11664.0	−0.0962250
$109$	−29621.3	−0.238802	−0.119401	−	0.992846i	$-0.538097\pi$
$109$	−29621.3	−0.238802	−0.119401	+	0.992846i	$0.538097\pi$
$110$	−49133.2	−0.387163
$111$	−27601.6	−0.212631
$112$	−12544.0	−0.0944911
$113$	−202742.	−1.49365	−0.746824	−	0.665022i	$-0.768422\pi$
$113$	−202742.	−1.49365	−0.746824	+	0.665022i	$0.768422\pi$
$114$	82323.8	0.593285
$115$	206483.	1.45592
$116$	96289.2	0.664405
$117$	−1863.00	−0.0125820
$118$	−91315.9	−0.603728
$119$	93957.3	0.608224
$120$	−58472.6	−0.370680
$121$	14641.0	0.0909091
$122$	−10785.5	−0.0656054
$123$	−84402.3	−0.503027
$124$	68054.8	0.397470
$125$	−411672.	−2.35655
$126$	15876.0	0.0890871
$127$	−284150.	−1.56328	−0.781642	−	0.623728i	$-0.785617\pi$
$127$	−284150.	−1.56328	−0.781642	+	0.623728i	$0.785617\pi$
$128$	−16384.0	−0.0883883
$129$	161101.	0.852360
$130$	−9339.38	−0.0484685
$131$	57000.7	0.290203	0.145101	−	0.989417i	$-0.453649\pi$
$131$	57000.7	0.290203	0.145101	+	0.989417i	$0.453649\pi$
$132$	17424.0	0.0870388
$133$	−112052.	−0.549275
$134$	−75194.9	−0.361765
$135$	74004.4	0.349481
$136$	122720.	0.568941
$137$	−171321.	−0.779845	−0.389922	−	0.920848i	$-0.627498\pi$
$137$	−171321.	−0.779845	−0.389922	+	0.920848i	$0.627498\pi$
$138$	−73224.4	−0.327309
$139$	−348267.	−1.52889	−0.764443	−	0.644692i	$-0.776986\pi$
$139$	−348267.	−1.52889	−0.764443	+	0.644692i	$0.776986\pi$
$140$	79587.7	0.343183
$141$	−232831.	−0.986262
$142$	49739.2	0.207004
$143$	2783.00	0.0113808
$144$	20736.0	0.0833333
$145$	−610925.	−2.41306
$146$	−243402.	−0.945022
$147$	−21609.0	−0.0824786
$148$	49069.5	0.184144
$149$	180235.	0.665080	0.332540	−	0.943089i	$-0.392094\pi$
$149$	180235.	0.665080	0.332540	+	0.943089i	$0.392094\pi$
$150$	258490.	0.938029
$151$	134387.	0.479641	0.239821	−	0.970817i	$-0.422911\pi$
$151$	134387.	0.479641	0.239821	+	0.970817i	$0.422911\pi$
$152$	−146353.	−0.513800
$153$	−155317.	−0.536403
$154$	−23716.0	−0.0805823
$155$	−431786.	−1.44358
$156$	3312.00	0.0108963
$157$	−72481.2	−0.234680	−0.117340	−	0.993092i	$-0.537437\pi$
$157$	−72481.2	−0.234680	−0.117340	+	0.993092i	$0.537437\pi$
$158$	120655.	0.384506
$159$	223998.	0.702671
$160$	103951.	0.321018
$161$	99666.6	0.303029
$162$	−26244.0	−0.0785674
$163$	62740.6	0.184961	0.0924804	−	0.995715i	$-0.470520\pi$
$163$	62740.6	0.184961	0.0924804	+	0.995715i	$0.470520\pi$
$164$	150049.	0.435635
$165$	−110550.	−0.316117
$166$	328688.	0.925792
$167$	−423614.	−1.17538	−0.587691	−	0.809086i	$-0.699963\pi$
$167$	−423614.	−1.17538	−0.587691	+	0.809086i	$0.699963\pi$
$168$	−28224.0	−0.0771517
$169$	−370764.	−0.998575
$170$	−778618.	−2.06634
$171$	185229.	0.484415
$172$	−286401.	−0.738165
$173$	159241.	0.404519	0.202259	−	0.979332i	$-0.435172\pi$
$173$	159241.	0.404519	0.202259	+	0.979332i	$0.435172\pi$
$174$	216651.	0.542484
$175$	−351834.	−0.868446
$176$	−30976.0	−0.0753778
$177$	−205461.	−0.492942
$178$	10473.4	0.0247764
$179$	−328085.	−0.765338	−0.382669	−	0.923886i	$-0.624995\pi$
$179$	−328085.	−0.765338	−0.382669	+	0.923886i	$0.624995\pi$
$180$	−131563.	−0.302659
$181$	−356558.	−0.808972	−0.404486	−	0.914544i	$-0.632550\pi$
$181$	−356558.	−0.808972	−0.404486	+	0.914544i	$0.632550\pi$
$182$	−4508.00	−0.0100880
$183$	−24267.3	−0.0535666
$184$	130177.	0.283458
$185$	−311331.	−0.668794
$186$	153123.	0.324533
$187$	232017.	0.485195
$188$	413921.	0.854128
$189$	35721.0	0.0727393
$190$	928566.	1.86607
$191$	−494839.	−0.981478	−0.490739	−	0.871307i	$-0.663273\pi$
$191$	−494839.	−0.981478	−0.490739	+	0.871307i	$0.663273\pi$
$192$	−36864.0	−0.0721688
$193$	998965.	1.93044	0.965221	−	0.261435i	$-0.0841957\pi$
$193$	998965.	1.93044	0.965221	+	0.261435i	$0.0841957\pi$
$194$	−72317.8	−0.137956
$195$	−21013.6	−0.0395744
$196$	38416.0	0.0714286
$197$	−636446.	−1.16841	−0.584206	−	0.811606i	$-0.698594\pi$
$197$	−636446.	−1.16841	−0.584206	+	0.811606i	$0.698594\pi$
$198$	39204.0	0.0710669
$199$	457203.	0.818420	0.409210	−	0.912440i	$-0.365804\pi$
$199$	457203.	0.818420	0.409210	+	0.912440i	$0.365804\pi$
$200$	−459538.	−0.812357
$201$	−169188.	−0.295380
$202$	−714135.	−1.23141
$203$	−294886.	−0.502243
$204$	276120.	0.464538
$205$	−952011.	−1.58219
$206$	−19378.6	−0.0318166
$207$	−164755.	−0.267247
$208$	−5888.00	−0.00943647
$209$	−276699.	−0.438170
$210$	179072.	0.280208
$211$	−149669.	−0.231434	−0.115717	−	0.993282i	$-0.536917\pi$
$211$	−149669.	−0.231434	−0.115717	+	0.993282i	$0.536917\pi$
$212$	−398219.	−0.608531
$213$	111913.	0.169018
$214$	−259906.	−0.387956
$215$	1.81712e6	2.68095
$216$	46656.0	0.0680414
$217$	−208418.	−0.300459
$218$	118485.	0.168859
$219$	−547654.	−0.771607
$220$	196533.	0.273765
$221$	44102.4	0.0607410
$222$	110406.	0.150353
$223$	98722.0	0.132939	0.0664694	−	0.997788i	$-0.478827\pi$
$223$	98722.0	0.132939	0.0664694	+	0.997788i	$0.478827\pi$
$224$	50176.0	0.0668153
$225$	581603.	0.765897
$226$	810969.	1.05617
$227$	120939.	0.155776	0.0778881	−	0.996962i	$-0.475182\pi$
$227$	120939.	0.155776	0.0778881	+	0.996962i	$0.475182\pi$
$228$	−329295.	−0.419516
$229$	107037.	0.134879	0.0674394	−	0.997723i	$-0.478517\pi$
$229$	107037.	0.134879	0.0674394	+	0.997723i	$0.478517\pi$
$230$	−825930.	−1.02949
$231$	−53361.0	−0.0657952
$232$	−385157.	−0.469805
$233$	95991.4	0.115836	0.0579178	−	0.998321i	$-0.481554\pi$
$233$	95991.4	0.115836	0.0579178	+	0.998321i	$0.481554\pi$
$234$	7452.00	0.00889679
$235$	−2.62620e6	−3.10211
$236$	365264.	0.426900
$237$	271474.	0.313948
$238$	−375829.	−0.430079
$239$	−331888.	−0.375835	−0.187918	−	0.982185i	$-0.560174\pi$
$239$	−331888.	−0.375835	−0.187918	+	0.982185i	$0.560174\pi$
$240$	233890.	0.262110
$241$	−89119.2	−0.0988391	−0.0494195	−	0.998778i	$-0.515737\pi$
$241$	−89119.2	−0.0988391	−0.0494195	+	0.998778i	$0.515737\pi$
$242$	−58564.0	−0.0642824
$243$	−59049.0	−0.0641500
$244$	43141.9	0.0463900
$245$	−243737.	−0.259422
$246$	337609.	0.355694
$247$	−52595.8	−0.0548540
$248$	−272219.	−0.281054
$249$	739548.	0.755906
$250$	1.64669e6	1.66633
$251$	1.69465e6	1.69783	0.848916	−	0.528528i	$-0.177256\pi$
$251$	1.69465e6	1.69783	0.848916	+	0.528528i	$0.177256\pi$
$252$	−63504.0	−0.0629941
$253$	246115.	0.241734
$254$	1.13660e6	1.10541
$255$	−1.75189e6	−1.68716
$256$	65536.0	0.0625000
$257$	871865.	0.823410	0.411705	−	0.911317i	$-0.364933\pi$
$257$	871865.	0.823410	0.411705	+	0.911317i	$0.364933\pi$
$258$	−644402.	−0.602709
$259$	−150275.	−0.139200
$260$	37357.5	0.0342724
$261$	487464.	0.442937
$262$	−228003.	−0.205204
$263$	792596.	0.706582	0.353291	−	0.935513i	$-0.385063\pi$
$263$	792596.	0.706582	0.353291	+	0.935513i	$0.385063\pi$
$264$	−69696.0	−0.0615457
$265$	2.52658e6	2.21013
$266$	448207.	0.388396
$267$	23565.2	0.0202299
$268$	300779.	0.255806
$269$	−1.07871e6	−0.908917	−0.454458	−	0.890768i	$-0.650167\pi$
$269$	−1.07871e6	−0.908917	−0.454458	+	0.890768i	$0.650167\pi$
$270$	−296018.	−0.247120
$271$	1.74734e6	1.44529	0.722644	−	0.691220i	$-0.242927\pi$
$271$	1.74734e6	1.44529	0.722644	+	0.691220i	$0.242927\pi$
$272$	−490879.	−0.402302
$273$	−10143.0	−0.00823682
$274$	685282.	0.551433
$275$	−868815.	−0.692780
$276$	292898.	0.231443
$277$	633380.	0.495981	0.247990	−	0.968763i	$-0.420230\pi$
$277$	633380.	0.495981	0.247990	+	0.968763i	$0.420230\pi$
$278$	1.39307e6	1.08109
$279$	344527.	0.264980
$280$	−318351.	−0.242667
$281$	−70966.1	−0.0536149	−0.0268074	−	0.999641i	$-0.508534\pi$
$281$	−70966.1	−0.0536149	−0.0268074	+	0.999641i	$0.508534\pi$
$282$	931322.	0.697392
$283$	2.60267e6	1.93176	0.965881	−	0.258985i	$-0.0833880\pi$
$283$	2.60267e6	1.93176	0.965881	+	0.258985i	$0.0833880\pi$
$284$	−198957.	−0.146374
$285$	2.08927e6	1.52364
$286$	−11132.0	−0.00804745
$287$	−459524.	−0.329309
$288$	−82944.0	−0.0589256
$289$	2.25694e6	1.58955
$290$	2.44370e6	1.70629
$291$	−162715.	−0.112641
$292$	973607.	0.668231
$293$	1.79236e6	1.21971	0.609854	−	0.792514i	$-0.291228\pi$
$293$	1.79236e6	1.21971	0.609854	+	0.792514i	$0.291228\pi$
$294$	86436.0	0.0583212
$295$	−2.31748e6	−1.55046
$296$	−196278.	−0.130209
$297$	88209.0	0.0580259
$298$	−720940.	−0.470282
$299$	46782.3	0.0302624
$300$	−1.03396e6	−0.663286
$301$	877103.	0.558000
$302$	−537550.	−0.339158
$303$	−1.60680e6	−1.00544
$304$	585414.	0.363311
$305$	−273722.	−0.168484
$306$	621269.	0.379294
$307$	−1.65583e6	−1.00269	−0.501347	−	0.865246i	$-0.667162\pi$
$307$	−1.65583e6	−1.00269	−0.501347	+	0.865246i	$0.667162\pi$
$308$	94864.0	0.0569803
$309$	−43601.8	−0.0259782
$310$	1.72714e6	1.02076
$311$	−1.38874e6	−0.814177	−0.407088	−	0.913389i	$-0.633456\pi$
$311$	−1.38874e6	−0.814177	−0.407088	+	0.913389i	$0.633456\pi$
$312$	−13248.0	−0.00770484
$313$	−3.16108e6	−1.82379	−0.911896	−	0.410421i	$-0.865382\pi$
$313$	−3.16108e6	−1.82379	−0.911896	+	0.410421i	$0.865382\pi$
$314$	289925.	0.165944
$315$	402913.	0.228789
$316$	−482621.	−0.271887
$317$	1.88565e6	1.05393	0.526965	−	0.849887i	$-0.323330\pi$
$317$	1.88565e6	1.05393	0.526965	+	0.849887i	$0.323330\pi$
$318$	−895994.	−0.496864
$319$	−728187.	−0.400651
$320$	−415805.	−0.226994
$321$	−584789.	−0.316765
$322$	−398666.	−0.214274
$323$	−4.38488e6	−2.33857
$324$	104976.	0.0555556
$325$	−165147.	−0.0867284
$326$	−250962.	−0.130787
$327$	266592.	0.137872
$328$	−600194.	−0.308040
$329$	−1.26763e6	−0.645660
$330$	442199.	0.223529
$331$	−3.81187e6	−1.91235	−0.956177	−	0.292791i	$-0.905416\pi$
$331$	−3.81187e6	−1.91235	−0.956177	+	0.292791i	$0.905416\pi$
$332$	−1.31475e6	−0.654634
$333$	248414.	0.122763
$334$	1.69445e6	0.831120
$335$	−1.90835e6	−0.929065
$336$	112896.	0.0545545
$337$	2.13216e6	1.02269	0.511346	−	0.859375i	$-0.329147\pi$
$337$	2.13216e6	1.02269	0.511346	+	0.859375i	$0.329147\pi$
$338$	1.48306e6	0.706099
$339$	1.82468e6	0.862358
$340$	3.11447e6	1.46112
$341$	−514664.	−0.239683
$342$	−740914.	−0.342533
$343$	−117649.	−0.0539949
$344$	1.14560e6	0.521962
$345$	−1.85834e6	−0.840578
$346$	−636963.	−0.286038
$347$	273302.	0.121848	0.0609242	−	0.998142i	$-0.480595\pi$
$347$	273302.	0.121848	0.0609242	+	0.998142i	$0.480595\pi$
$348$	−866603.	−0.383594
$349$	57315.0	0.0251886	0.0125943	−	0.999921i	$-0.495991\pi$
$349$	57315.0	0.0251886	0.0125943	+	0.999921i	$0.495991\pi$
$350$	1.40734e6	0.614084
$351$	16767.0	0.00726420
$352$	123904.	0.0533002
$353$	−2.60670e6	−1.11341	−0.556703	−	0.830712i	$-0.687934\pi$
$353$	−2.60670e6	−1.11341	−0.556703	+	0.830712i	$0.687934\pi$
$354$	821843.	0.348563
$355$	1.26232e6	0.531616
$356$	−41893.7	−0.0175196
$357$	−845616.	−0.351158
$358$	1.31234e6	0.541176
$359$	−3.92444e6	−1.60710	−0.803548	−	0.595240i	$-0.797057\pi$
$359$	−3.92444e6	−1.60710	−0.803548	+	0.595240i	$0.797057\pi$
$360$	526254.	0.214012
$361$	2.75323e6	1.11192
$362$	1.42623e6	0.572029
$363$	−131769.	−0.0524864
$364$	18032.0	0.00713330
$365$	−6.17723e6	−2.42696
$366$	97069.3	0.0378773
$367$	2.68440e6	1.04036	0.520179	−	0.854057i	$-0.325865\pi$
$367$	2.68440e6	1.04036	0.520179	+	0.854057i	$0.325865\pi$
$368$	−520707.	−0.200435
$369$	759621.	0.290423
$370$	1.24532e6	0.472909
$371$	1.21955e6	0.460006
$372$	−612493.	−0.229479
$373$	3.21719e6	1.19731	0.598653	−	0.801009i	$-0.295703\pi$
$373$	3.21719e6	1.19731	0.598653	+	0.801009i	$0.295703\pi$
$374$	−928068.	−0.343084
$375$	3.70505e6	1.36055
$376$	−1.65568e6	−0.603959
$377$	−138416.	−0.0501571
$378$	−142884.	−0.0514344
$379$	4.11353e6	1.47101	0.735506	−	0.677518i	$-0.236944\pi$
$379$	4.11353e6	1.47101	0.735506	+	0.677518i	$0.236944\pi$
$380$	−3.71427e6	−1.31951
$381$	2.55735e6	0.902562
$382$	1.97936e6	0.694009
$383$	4.27453e6	1.48899	0.744494	−	0.667629i	$-0.232691\pi$
$383$	4.27453e6	1.48899	0.744494	+	0.667629i	$0.232691\pi$
$384$	147456.	0.0510310
$385$	−601882.	−0.206947
$386$	−3.99586e6	−1.36503
$387$	−1.44991e6	−0.492110
$388$	289271.	0.0975497
$389$	−2.10165e6	−0.704183	−0.352092	−	0.935966i	$-0.614529\pi$
$389$	−2.10165e6	−0.704183	−0.352092	+	0.935966i	$0.614529\pi$
$390$	84054.4	0.0279833
$391$	3.90021e6	1.29017
$392$	−153664.	−0.0505076
$393$	−513006.	−0.167549
$394$	2.54578e6	0.826191
$395$	3.06208e6	0.987469
$396$	−156816.	−0.0502519
$397$	1.73999e6	0.554076	0.277038	−	0.960859i	$-0.410647\pi$
$397$	1.73999e6	0.554076	0.277038	+	0.960859i	$0.410647\pi$
$398$	−1.82881e6	−0.578711
$399$	1.00847e6	0.317124
$400$	1.83815e6	0.574423
$401$	−2.01242e6	−0.624969	−0.312484	−	0.949923i	$-0.601161\pi$
$401$	−2.01242e6	−0.624969	−0.312484	+	0.949923i	$0.601161\pi$
$402$	676754.	0.208865
$403$	−97828.8	−0.0300057
$404$	2.85654e6	0.870737
$405$	−666040.	−0.201773
$406$	1.17954e6	0.355139
$407$	−371088.	−0.111043
$408$	−1.10448e6	−0.328478
$409$	−5.46960e6	−1.61677	−0.808383	−	0.588657i	$-0.799657\pi$
$409$	−5.46960e6	−1.61677	−0.808383	+	0.588657i	$0.799657\pi$
$410$	3.80804e6	1.11877
$411$	1.54189e6	0.450244
$412$	77514.4	0.0224978
$413$	−1.11862e6	−0.322706
$414$	659020.	0.188972
$415$	8.34169e6	2.37757
$416$	23552.0	0.00667259
$417$	3.13440e6	0.882702
$418$	1.10680e6	0.309833
$419$	1.13767e6	0.316580	0.158290	−	0.987393i	$-0.449402\pi$
$419$	1.13767e6	0.316580	0.158290	+	0.987393i	$0.449402\pi$
$420$	−716290.	−0.198137
$421$	−1.52402e6	−0.419069	−0.209534	−	0.977801i	$-0.567195\pi$
$421$	−1.52402e6	−0.419069	−0.209534	+	0.977801i	$0.567195\pi$
$422$	598678.	0.163649
$423$	2.09547e6	0.569418
$424$	1.59288e6	0.430296
$425$	−1.37682e7	−3.69746
$426$	−447653.	−0.119514
$427$	−132122.	−0.0350676
$428$	1.03963e6	0.274326
$429$	−25047.0	−0.00657071
$430$	−7.26850e6	−1.89572
$431$	3.50010e6	0.907586	0.453793	−	0.891107i	$-0.350071\pi$
$431$	3.50010e6	0.907586	0.453793	+	0.891107i	$0.350071\pi$
$432$	−186624.	−0.0481125
$433$	4.53803e6	1.16318	0.581591	−	0.813482i	$-0.302431\pi$
$433$	4.53803e6	1.16318	0.581591	+	0.813482i	$0.302431\pi$
$434$	833671.	0.212457
$435$	5.49832e6	1.39318
$436$	−473941.	−0.119401
$437$	−4.65132e6	−1.16513
$438$	2.19062e6	0.545609
$439$	−5.74464e6	−1.42266	−0.711331	−	0.702857i	$-0.751907\pi$
$439$	−5.74464e6	−1.42266	−0.711331	+	0.702857i	$0.751907\pi$
$440$	−786132.	−0.193581
$441$	194481.	0.0476190
$442$	−176410.	−0.0429504
$443$	6.80360e6	1.64714	0.823568	−	0.567218i	$-0.191980\pi$
$443$	6.80360e6	1.64714	0.823568	+	0.567218i	$0.191980\pi$
$444$	−441626.	−0.106316
$445$	265802.	0.0636295
$446$	−394888.	−0.0940019
$447$	−1.62212e6	−0.383984
$448$	−200704.	−0.0472456
$449$	4.74747e6	1.11134	0.555669	−	0.831404i	$-0.312462\pi$
$449$	4.74747e6	1.11134	0.555669	+	0.831404i	$0.312462\pi$
$450$	−2.32641e6	−0.541571
$451$	−1.13474e6	−0.262697
$452$	−3.24388e6	−0.746824
$453$	−1.20949e6	−0.276921
$454$	−483755.	−0.110150
$455$	−114407.	−0.0259075
$456$	1.31718e6	0.296642
$457$	1.62543e6	0.364064	0.182032	−	0.983293i	$-0.441733\pi$
$457$	1.62543e6	0.364064	0.182032	+	0.983293i	$0.441733\pi$
$458$	−428147.	−0.0953737
$459$	1.39786e6	0.309692
$460$	3.30372e6	0.727962
$461$	−308764.	−0.0676667	−0.0338334	−	0.999427i	$-0.510772\pi$
$461$	−308764.	−0.0676667	−0.0338334	+	0.999427i	$0.510772\pi$
$462$	213444.	0.0465242
$463$	−1.52781e6	−0.331220	−0.165610	−	0.986191i	$-0.552959\pi$
$463$	−1.52781e6	−0.331220	−0.165610	+	0.986191i	$0.552959\pi$
$464$	1.54063e6	0.332202
$465$	3.88608e6	0.833449
$466$	−383965.	−0.0819082
$467$	1.83955e6	0.390319	0.195160	−	0.980771i	$-0.437478\pi$
$467$	1.83955e6	0.390319	0.195160	+	0.980771i	$0.437478\pi$
$468$	−29808.0	−0.00629098
$469$	−921137.	−0.193371
$470$	1.05048e7	2.19353
$471$	652331.	0.135493
$472$	−1.46106e6	−0.301864
$473$	2.16591e6	0.445130
$474$	−1.08590e6	−0.221995
$475$	1.64197e7	3.33911
$476$	1.50332e6	0.304112
$477$	−2.01599e6	−0.405687
$478$	1.32755e6	0.265756
$479$	−7.92237e6	−1.57767	−0.788836	−	0.614604i	$-0.789316\pi$
$479$	−7.92237e6	−1.57767	−0.788836	+	0.614604i	$0.789316\pi$
$480$	−935562.	−0.185340
$481$	−70537.4	−0.0139013
$482$	356477.	0.0698898
$483$	−896999.	−0.174954
$484$	234256.	0.0454545
$485$	−1.83533e6	−0.354292
$486$	236196.	0.0453609
$487$	1.90995e6	0.364922	0.182461	−	0.983213i	$-0.441594\pi$
$487$	1.90995e6	0.364922	0.182461	+	0.983213i	$0.441594\pi$
$488$	−172568.	−0.0328027
$489$	−564665.	−0.106787
$490$	974950.	0.183439
$491$	8.32212e6	1.55787	0.778934	−	0.627106i	$-0.215761\pi$
$491$	8.32212e6	1.55787	0.778934	+	0.627106i	$0.215761\pi$
$492$	−1.35044e6	−0.251514
$493$	−1.15396e7	−2.13833
$494$	210383.	0.0387876
$495$	994948.	0.182510
$496$	1.08888e6	0.198735
$497$	609305.	0.110648
$498$	−2.95819e6	−0.534506
$499$	−8.58557e6	−1.54354	−0.771769	−	0.635902i	$-0.780628\pi$
$499$	−8.58557e6	−1.54354	−0.771769	+	0.635902i	$0.780628\pi$
$500$	−6.58676e6	−1.17827
$501$	3.81252e6	0.678607
$502$	−6.77858e6	−1.20055
$503$	−1.05086e7	−1.85193	−0.925967	−	0.377604i	$-0.876748\pi$
$503$	−1.05086e7	−1.85193	−0.925967	+	0.377604i	$0.876748\pi$
$504$	254016.	0.0445435
$505$	−1.81238e7	−3.16244
$506$	−984462.	−0.170932
$507$	3.33688e6	0.576528
$508$	−4.54639e6	−0.781642
$509$	8.27628e6	1.41593	0.707963	−	0.706250i	$-0.249614\pi$
$509$	8.27628e6	1.41593	0.707963	+	0.706250i	$0.249614\pi$
$510$	7.00757e6	1.19300
$511$	−2.98167e6	−0.505135
$512$	−262144.	−0.0441942
$513$	−1.66706e6	−0.279677
$514$	−3.48746e6	−0.582239
$515$	−491804.	−0.0817098
$516$	2.57761e6	0.426180
$517$	−3.13028e6	−0.515058
$518$	601101.	0.0984291
$519$	−1.43317e6	−0.233549
$520$	−149430.	−0.0242342
$521$	−1.19608e7	−1.93048	−0.965242	−	0.261356i	$-0.915830\pi$
$521$	−1.19608e7	−1.93048	−0.965242	+	0.261356i	$0.915830\pi$
$522$	−1.94986e6	−0.313203
$523$	−6.62849e6	−1.05965	−0.529823	−	0.848108i	$-0.677742\pi$
$523$	−6.62849e6	−1.05965	−0.529823	+	0.848108i	$0.677742\pi$
$524$	912011.	0.145101
$525$	3.16651e6	0.501397
$526$	−3.17038e6	−0.499629
$527$	−8.15593e6	−1.27922
$528$	278784.	0.0435194
$529$	−2.29914e6	−0.357212
$530$	−1.01063e7	−1.56280
$531$	1.84915e6	0.284600
$532$	−1.79283e6	−0.274638
$533$	−215695.	−0.0328868
$534$	−94260.7	−0.0143047
$535$	−6.59609e6	−0.996328
$536$	−1.20312e6	−0.180882
$537$	2.95276e6	0.441868
$538$	4.31484e6	0.642701
$539$	−290521.	−0.0430730
$540$	1.18407e6	0.174740
$541$	−4.60850e6	−0.676965	−0.338483	−	0.940973i	$-0.609914\pi$
$541$	−4.60850e6	−0.676965	−0.338483	+	0.940973i	$0.609914\pi$
$542$	−6.98936e6	−1.02197
$543$	3.20902e6	0.467060
$544$	1.96352e6	0.284471
$545$	3.00701e6	0.433654
$546$	40572.0	0.00582431
$547$	−4.05863e6	−0.579977	−0.289988	−	0.957030i	$-0.593651\pi$
$547$	−4.05863e6	−0.579977	−0.289988	+	0.957030i	$0.593651\pi$
$548$	−2.74113e6	−0.389922
$549$	218406.	0.0309267
$550$	3.47526e6	0.489869
$551$	1.37620e7	1.93109
$552$	−1.17159e6	−0.163655
$553$	1.47803e6	0.205527
$554$	−2.53352e6	−0.350711
$555$	2.80197e6	0.386128
$556$	−5.57227e6	−0.764443
$557$	7.74251e6	1.05741	0.528705	−	0.848805i	$-0.322678\pi$
$557$	7.74251e6	1.05741	0.528705	+	0.848805i	$0.322678\pi$
$558$	−1.37811e6	−0.187369
$559$	411702.	0.0557254
$560$	1.27340e6	0.171592
$561$	−2.08815e6	−0.280127
$562$	283864.	0.0379114
$563$	8.93995e6	1.18868	0.594339	−	0.804215i	$-0.297414\pi$
$563$	8.93995e6	1.18868	0.594339	+	0.804215i	$0.297414\pi$
$564$	−3.72529e6	−0.493131
$565$	2.05814e7	2.71240
$566$	−1.04107e7	−1.36596
$567$	−321489.	−0.0419961
$568$	795827.	0.103502
$569$	−7.92308e6	−1.02592	−0.512960	−	0.858413i	$-0.671451\pi$
$569$	−7.92308e6	−1.02592	−0.512960	+	0.858413i	$0.671451\pi$
$570$	−8.35710e6	−1.07738
$571$	−9.08618e6	−1.16625	−0.583124	−	0.812383i	$-0.698170\pi$
$571$	−9.08618e6	−1.16625	−0.583124	+	0.812383i	$0.698170\pi$
$572$	44528.0	0.00569040
$573$	4.45355e6	0.566656
$574$	1.83810e6	0.232856
$575$	−1.46048e7	−1.84215
$576$	331776.	0.0416667
$577$	−7.85301e6	−0.981967	−0.490983	−	0.871169i	$-0.663362\pi$
$577$	−7.85301e6	−0.981967	−0.490983	+	0.871169i	$0.663362\pi$
$578$	−9.02775e6	−1.12398
$579$	−8.99068e6	−1.11454
$580$	−9.77480e6	−1.20653
$581$	4.02643e6	0.494857
$582$	650860.	0.0796490
$583$	3.01153e6	0.366958
$584$	−3.89443e6	−0.472511
$585$	189122.	0.0228483
$586$	−7.16943e6	−0.862464
$587$	−2.01360e6	−0.241200	−0.120600	−	0.992701i	$-0.538482\pi$
$587$	−2.01360e6	−0.241200	−0.120600	+	0.992701i	$0.538482\pi$
$588$	−345744.	−0.0412393
$589$	9.72661e6	1.15524
$590$	9.26993e6	1.09634
$591$	5.72801e6	0.674583
$592$	785112.	0.0920720
$593$	−1.26771e7	−1.48041	−0.740206	−	0.672381i	$-0.765272\pi$
$593$	−1.26771e7	−1.48041	−0.740206	+	0.672381i	$0.765272\pi$
$594$	−352836.	−0.0410305
$595$	−9.53808e6	−1.10451
$596$	2.88376e6	0.332540
$597$	−4.11483e6	−0.472515
$598$	−187129.	−0.0213987
$599$	4.74863e6	0.540756	0.270378	−	0.962754i	$-0.412851\pi$
$599$	4.74863e6	0.540756	0.270378	+	0.962754i	$0.412851\pi$
$600$	4.13584e6	0.469014
$601$	−1.17962e7	−1.33216	−0.666082	−	0.745879i	$-0.732030\pi$
$601$	−1.17962e7	−1.33216	−0.666082	+	0.745879i	$0.732030\pi$
$602$	−3.50841e6	−0.394566
$603$	1.52270e6	0.170538
$604$	2.15020e6	0.239821
$605$	−1.48628e6	−0.165087
$606$	6.42722e6	0.710954
$607$	9.14045e6	1.00692	0.503461	−	0.864018i	$-0.332060\pi$
$607$	9.14045e6	1.00692	0.503461	+	0.864018i	$0.332060\pi$
$608$	−2.34165e6	−0.256900
$609$	2.65397e6	0.289970
$610$	1.09489e6	0.119136
$611$	−595011.	−0.0644796
$612$	−2.48508e6	−0.268201
$613$	−6.75425e6	−0.725983	−0.362991	−	0.931793i	$-0.618245\pi$
$613$	−6.75425e6	−0.725983	−0.362991	+	0.931793i	$0.618245\pi$
$614$	6.62330e6	0.709012
$615$	8.56810e6	0.913475
$616$	−379456.	−0.0402911
$617$	−1.42472e7	−1.50667	−0.753334	−	0.657638i	$-0.771556\pi$
$617$	−1.42472e7	−1.50667	−0.753334	+	0.657638i	$0.771556\pi$
$618$	174407.	0.0183693
$619$	−2.59483e6	−0.272196	−0.136098	−	0.990695i	$-0.543456\pi$
$619$	−2.59483e6	−0.272196	−0.136098	+	0.990695i	$0.543456\pi$
$620$	−6.90858e6	−0.721788
$621$	1.48279e6	0.154295
$622$	5.55494e6	0.575710
$623$	128299.	0.0132435
$624$	52992.0	0.00544815
$625$	1.93525e7	1.98169
$626$	1.26443e7	1.28962
$627$	2.49030e6	0.252978
$628$	−1.15970e6	−0.117340
$629$	−5.88066e6	−0.592652
$630$	−1.61165e6	−0.161778
$631$	4.28382e6	0.428310	0.214155	−	0.976800i	$-0.431300\pi$
$631$	4.28382e6	0.428310	0.214155	+	0.976800i	$0.431300\pi$
$632$	1.93048e6	0.192253
$633$	1.34703e6	0.133618
$634$	−7.54258e6	−0.745241
$635$	2.88454e7	2.83885
$636$	3.58397e6	0.351336
$637$	−55223.0	−0.00539227
$638$	2.91275e6	0.283303
$639$	−1.00722e6	−0.0975824
$640$	1.66322e6	0.160509
$641$	−8.05455e6	−0.774277	−0.387138	−	0.922022i	$-0.626536\pi$
$641$	−8.05455e6	−0.774277	−0.387138	+	0.922022i	$0.626536\pi$
$642$	2.33916e6	0.223986
$643$	−9.76710e6	−0.931619	−0.465809	−	0.884885i	$-0.654237\pi$
$643$	−9.76710e6	−0.931619	−0.465809	+	0.884885i	$0.654237\pi$
$644$	1.59467e6	0.151515
$645$	−1.63541e7	−1.54785
$646$	1.75395e7	1.65362
$647$	8.65576e6	0.812914	0.406457	−	0.913670i	$-0.366764\pi$
$647$	8.65576e6	0.812914	0.406457	+	0.913670i	$0.366764\pi$
$648$	−419904.	−0.0392837
$649$	−2.76231e6	−0.257431
$650$	660586.	0.0613262
$651$	1.87576e6	0.173470
$652$	1.00385e6	0.0924804
$653$	−1.82561e7	−1.67542	−0.837712	−	0.546112i	$-0.816107\pi$
$653$	−1.82561e7	−1.67542	−0.837712	+	0.546112i	$0.816107\pi$
$654$	−1.06637e6	−0.0974905
$655$	−5.78642e6	−0.526995
$656$	2.40078e6	0.217817
$657$	4.92889e6	0.445487
$658$	5.07053e6	0.456550
$659$	1.77884e7	1.59560	0.797799	−	0.602923i	$-0.205998\pi$
$659$	1.77884e7	1.59560	0.797799	+	0.602923i	$0.205998\pi$
$660$	−1.76880e6	−0.158059
$661$	−5.21110e6	−0.463902	−0.231951	−	0.972728i	$-0.574511\pi$
$661$	−5.21110e6	−0.463902	−0.231951	+	0.972728i	$0.574511\pi$
$662$	1.52475e7	1.35224
$663$	−396922.	−0.0350688
$664$	5.25901e6	0.462896
$665$	1.13749e7	0.997459
$666$	−993657.	−0.0868063
$667$	−1.22408e7	−1.06536
$668$	−6.77782e6	−0.587691
$669$	−888498.	−0.0767522
$670$	7.63340e6	0.656948
$671$	−326261.	−0.0279743
$672$	−451584.	−0.0385758
$673$	−1.44731e7	−1.23175	−0.615875	−	0.787843i	$-0.711198\pi$
$673$	−1.44731e7	−1.23175	−0.615875	+	0.787843i	$0.711198\pi$
$674$	−8.52863e6	−0.723152
$675$	−5.23443e6	−0.442191
$676$	−5.93222e6	−0.499288
$677$	1.50165e6	0.125921	0.0629603	−	0.998016i	$-0.479946\pi$
$677$	1.50165e6	0.125921	0.0629603	+	0.998016i	$0.479946\pi$
$678$	−7.29872e6	−0.609779
$679$	−885893.	−0.0737406
$680$	−1.24579e7	−1.03317
$681$	−1.08845e6	−0.0899374
$682$	2.05866e6	0.169482
$683$	1.05225e7	0.863110	0.431555	−	0.902087i	$-0.357965\pi$
$683$	1.05225e7	0.863110	0.431555	+	0.902087i	$0.357965\pi$
$684$	2.96366e6	0.242208
$685$	1.73916e7	1.41616
$686$	470596.	0.0381802
$687$	−963330.	−0.0778723
$688$	−4.58242e6	−0.369083
$689$	572440.	0.0459391
$690$	7.43337e6	0.594379
$691$	−1.14184e7	−0.909724	−0.454862	−	0.890562i	$-0.650311\pi$
$691$	−1.14184e7	−0.909724	−0.454862	+	0.890562i	$0.650311\pi$
$692$	2.54785e6	0.202259
$693$	480249.	0.0379869
$694$	−1.09321e6	−0.0861598
$695$	3.53543e7	2.77639
$696$	3.46641e6	0.271242
$697$	−1.79824e7	−1.40205
$698$	−229260.	−0.0178110
$699$	−863922.	−0.0668778
$700$	−5.62934e6	−0.434223
$701$	−2.27137e7	−1.74580	−0.872898	−	0.487903i	$-0.837762\pi$
$701$	−2.27137e7	−1.74580	−0.872898	+	0.487903i	$0.837762\pi$
$702$	−67068.0	−0.00513656
$703$	7.01317e6	0.535213
$704$	−495616.	−0.0376889
$705$	2.36358e7	1.79101
$706$	1.04268e7	0.787297
$707$	−8.74815e6	−0.658215
$708$	−3.28737e6	−0.246471
$709$	2.59854e7	1.94139	0.970697	−	0.240305i	$-0.0772476\pi$
$709$	2.59854e7	1.94139	0.970697	+	0.240305i	$0.0772476\pi$
$710$	−5.04927e6	−0.375909
$711$	−2.44327e6	−0.181258
$712$	167575.	0.0123882
$713$	−8.65151e6	−0.637336
$714$	3.38246e6	0.248306
$715$	−282516.	−0.0206670
$716$	−5.24935e6	−0.382669
$717$	2.98700e6	0.216988
$718$	1.56978e7	1.13639
$719$	−1.34632e7	−0.971238	−0.485619	−	0.874171i	$-0.661406\pi$
$719$	−1.34632e7	−0.971238	−0.485619	+	0.874171i	$0.661406\pi$
$720$	−2.10501e6	−0.151330
$721$	−237388.	−0.0170067
$722$	−1.10129e7	−0.786248
$723$	802073.	0.0570648
$724$	−5.70492e6	−0.404486
$725$	4.32115e7	3.05319
$726$	527076.	0.0371135
$727$	1.47615e7	1.03584	0.517922	−	0.855428i	$-0.326706\pi$
$727$	1.47615e7	1.03584	0.517922	+	0.855428i	$0.326706\pi$
$728$	−72128.0	−0.00504400
$729$	531441.	0.0370370
$730$	2.47089e7	1.71612
$731$	3.43233e7	2.37572
$732$	−388277.	−0.0267833
$733$	−1.40296e7	−0.964465	−0.482233	−	0.876043i	$-0.660174\pi$
$733$	−1.40296e7	−0.964465	−0.482233	+	0.876043i	$0.660174\pi$
$734$	−1.07376e7	−0.735644
$735$	2.19364e6	0.149777
$736$	2.08283e6	0.141729
$737$	−2.27464e6	−0.154257
$738$	−3.03848e6	−0.205360
$739$	1.87536e7	1.26320	0.631601	−	0.775293i	$-0.282398\pi$
$739$	1.87536e7	1.26320	0.631601	+	0.775293i	$0.282398\pi$
$740$	−4.98129e6	−0.334397
$741$	473362.	0.0316700
$742$	−4.87819e6	−0.325274
$743$	−4.98698e6	−0.331410	−0.165705	−	0.986175i	$-0.552990\pi$
$743$	−4.98698e6	−0.331410	−0.165705	+	0.986175i	$0.552990\pi$
$744$	2.44997e6	0.162266
$745$	−1.82966e7	−1.20775
$746$	−1.28688e7	−0.846623
$747$	−6.65593e6	−0.436423
$748$	3.71227e6	0.242597
$749$	−3.18385e6	−0.207371
$750$	−1.48202e7	−0.962057
$751$	2.03304e7	1.31536	0.657681	−	0.753297i	$-0.271538\pi$
$751$	2.03304e7	1.31536	0.657681	+	0.753297i	$0.271538\pi$
$752$	6.62274e6	0.427064
$753$	−1.52518e7	−0.980244
$754$	553663.	0.0354664
$755$	−1.36423e7	−0.871007
$756$	571536.	0.0363696
$757$	2.39813e7	1.52101	0.760506	−	0.649331i	$-0.224951\pi$
$757$	2.39813e7	1.52101	0.760506	+	0.649331i	$0.224951\pi$
$758$	−1.64541e7	−1.04016
$759$	−2.21504e6	−0.139565
$760$	1.48571e7	0.933037
$761$	−9.21172e6	−0.576606	−0.288303	−	0.957539i	$-0.593091\pi$
$761$	−9.21172e6	−0.576606	−0.288303	+	0.957539i	$0.593091\pi$
$762$	−1.02294e7	−0.638208
$763$	1.45144e6	0.0902587
$764$	−7.91742e6	−0.490739
$765$	1.57670e7	0.974083
$766$	−1.70981e7	−1.05287
$767$	−525067.	−0.0322275
$768$	−589824.	−0.0360844
$769$	−8.20524e6	−0.500352	−0.250176	−	0.968200i	$-0.580488\pi$
$769$	−8.20524e6	−0.500352	−0.250176	+	0.968200i	$0.580488\pi$
$770$	2.40753e6	0.146334
$771$	−7.84678e6	−0.475396
$772$	1.59834e7	0.965221
$773$	9.58449e6	0.576926	0.288463	−	0.957491i	$-0.406856\pi$
$773$	9.58449e6	0.576926	0.288463	+	0.957491i	$0.406856\pi$
$774$	5.79962e6	0.347974
$775$	3.05408e7	1.82653
$776$	−1.15708e6	−0.0689780
$777$	1.35248e6	0.0803670
$778$	8.40659e6	0.497933
$779$	2.14454e7	1.26617
$780$	−336218.	−0.0197872
$781$	1.50461e6	0.0882666
$782$	−1.56008e7	−0.912286
$783$	−4.38718e6	−0.255730
$784$	614656.	0.0357143
$785$	7.35793e6	0.426169
$786$	2.05202e6	0.118475
$787$	−1.62430e7	−0.934824	−0.467412	−	0.884040i	$-0.654814\pi$
$787$	−1.62430e7	−0.934824	−0.467412	+	0.884040i	$0.654814\pi$
$788$	−1.01831e7	−0.584206
$789$	−7.13337e6	−0.407945
$790$	−1.22483e7	−0.698246
$791$	9.93438e6	0.564546
$792$	627264.	0.0355335
$793$	−62016.5	−0.00350207
$794$	−6.95995e6	−0.391791
$795$	−2.27392e7	−1.27602
$796$	7.31525e6	0.409210
$797$	4.91866e6	0.274284	0.137142	−	0.990551i	$-0.456208\pi$
$797$	4.91866e6	0.274284	0.137142	+	0.990551i	$0.456208\pi$
$798$	−4.03387e6	−0.224241
$799$	−4.96058e7	−2.74894
$800$	−7.35261e6	−0.406178
$801$	−212087.	−0.0116797
$802$	8.04969e6	0.441920
$803$	−7.36291e6	−0.402959
$804$	−2.70702e6	−0.147690
$805$	−1.01176e7	−0.550288
$806$	391315.	0.0212172
$807$	9.70839e6	0.524763
$808$	−1.14262e7	−0.615704
$809$	−1.83132e7	−0.983771	−0.491886	−	0.870660i	$-0.663692\pi$
$809$	−1.83132e7	−0.983771	−0.491886	+	0.870660i	$0.663692\pi$
$810$	2.66416e6	0.142675
$811$	−1.73038e7	−0.923825	−0.461912	−	0.886926i	$-0.652837\pi$
$811$	−1.73038e7	−0.923825	−0.461912	+	0.886926i	$0.652837\pi$
$812$	−4.71817e6	−0.251121
$813$	−1.57261e7	−0.834438
$814$	1.48435e6	0.0785192
$815$	−6.36911e6	−0.335880
$816$	4.41791e6	0.232269
$817$	−4.09334e7	−2.14547
$818$	2.18784e7	1.14323
$819$	91287.0	0.00475553
$820$	−1.52322e7	−0.791093
$821$	−2.45869e7	−1.27305	−0.636526	−	0.771255i	$-0.719629\pi$
$821$	−2.45869e7	−1.27305	−0.636526	+	0.771255i	$0.719629\pi$
$822$	−6.16754e6	−0.318370
$823$	−1.98197e7	−1.01999	−0.509997	−	0.860176i	$-0.670353\pi$
$823$	−1.98197e7	−1.01999	−0.509997	+	0.860176i	$0.670353\pi$
$824$	−310058.	−0.0159083
$825$	7.81933e6	0.399977
$826$	4.47448e6	0.228188
$827$	−2.28720e7	−1.16289	−0.581447	−	0.813584i	$-0.697513\pi$
$827$	−2.28720e7	−1.16289	−0.581447	+	0.813584i	$0.697513\pi$
$828$	−2.63608e6	−0.133623
$829$	2.00490e7	1.01323	0.506613	−	0.862173i	$-0.330897\pi$
$829$	2.00490e7	1.01323	0.506613	+	0.862173i	$0.330897\pi$
$830$	−3.33667e7	−1.68120
$831$	−5.70042e6	−0.286354
$832$	−94208.0	−0.00471823
$833$	−4.60391e6	−0.229887
$834$	−1.25376e7	−0.624165
$835$	4.30031e7	2.13444
$836$	−4.42719e6	−0.219085
$837$	−3.10075e6	−0.152986
$838$	−4.55070e6	−0.223856
$839$	2.22907e7	1.09325	0.546624	−	0.837378i	$-0.315913\pi$
$839$	2.22907e7	1.09325	0.546624	+	0.837378i	$0.315913\pi$
$840$	2.86516e6	0.140104
$841$	1.57061e7	0.765735
$842$	6.09608e6	0.296326
$843$	638695.	0.0309546
$844$	−2.39471e6	−0.115717
$845$	3.76381e7	1.81337
$846$	−8.38190e6	−0.402640
$847$	−717409.	−0.0343604
$848$	−6.37151e6	−0.304266
$849$	−2.34241e7	−1.11530
$850$	5.50727e7	2.61450
$851$	−6.23800e6	−0.295271
$852$	1.79061e6	0.0845088
$853$	1.05461e7	0.496273	0.248137	−	0.968725i	$-0.420182\pi$
$853$	1.05461e7	0.496273	0.248137	+	0.968725i	$0.420182\pi$
$854$	528488.	0.0247965
$855$	−1.88035e7	−0.879676
$856$	−4.15850e6	−0.193978
$857$	−3.67051e7	−1.70716	−0.853581	−	0.520960i	$-0.825574\pi$
$857$	−3.67051e7	−1.70716	−0.853581	+	0.520960i	$0.825574\pi$
$858$	100188.	0.00464620
$859$	2.86754e6	0.132595	0.0662975	−	0.997800i	$-0.478881\pi$
$859$	2.86754e6	0.132595	0.0662975	+	0.997800i	$0.478881\pi$
$860$	2.90740e7	1.34047
$861$	4.13571e6	0.190126
$862$	−1.40004e7	−0.641760
$863$	1.19550e7	0.546414	0.273207	−	0.961955i	$-0.411916\pi$
$863$	1.19550e7	0.546414	0.273207	+	0.961955i	$0.411916\pi$
$864$	746496.	0.0340207
$865$	−1.61653e7	−0.734588
$866$	−1.81521e7	−0.822493
$867$	−2.03124e7	−0.917728
$868$	−3.33468e6	−0.150230
$869$	3.64982e6	0.163954
$870$	−2.19933e7	−0.985127
$871$	−432371.	−0.0193113
$872$	1.89576e6	0.0844293
$873$	1.46444e6	0.0650331
$874$	1.86053e7	0.823868
$875$	2.01719e7	0.890692
$876$	−8.76247e6	−0.385803
$877$	−4.39140e6	−0.192799	−0.0963993	−	0.995343i	$-0.530733\pi$
$877$	−4.39140e6	−0.192799	−0.0963993	+	0.995343i	$0.530733\pi$
$878$	2.29786e7	1.00597
$879$	−1.61312e7	−0.704199
$880$	3.14453e6	0.136883
$881$	2.47289e7	1.07341	0.536705	−	0.843770i	$-0.319669\pi$
$881$	2.47289e7	1.07341	0.536705	+	0.843770i	$0.319669\pi$
$882$	−777924.	−0.0336718
$883$	−2.15306e7	−0.929297	−0.464648	−	0.885495i	$-0.653819\pi$
$883$	−2.15306e7	−0.929297	−0.464648	+	0.885495i	$0.653819\pi$
$884$	705639.	0.0303705
$885$	2.08574e7	0.895161
$886$	−2.72144e7	−1.16470
$887$	4.13028e7	1.76267	0.881335	−	0.472492i	$-0.156646\pi$
$887$	4.13028e7	1.76267	0.881335	+	0.472492i	$0.156646\pi$
$888$	1.76650e6	0.0751764
$889$	1.39233e7	0.590866
$890$	−1.06321e6	−0.0449928
$891$	−793881.	−0.0335013
$892$	1.57955e6	0.0664694
$893$	5.91589e7	2.48251
$894$	6.48846e6	0.271518
$895$	3.33055e7	1.38982
$896$	802816.	0.0334077
$897$	−421040.	−0.0174720
$898$	−1.89899e7	−0.785835
$899$	2.55974e7	1.05632
$900$	9.30565e6	0.382949
$901$	4.77240e7	1.95851
$902$	4.53897e6	0.185755
$903$	−7.89393e6	−0.322162
$904$	1.29755e7	0.528084
$905$	3.61959e7	1.46906
$906$	4.83795e6	0.195813
$907$	3.91650e6	0.158081	0.0790405	−	0.996871i	$-0.474814\pi$
$907$	3.91650e6	0.158081	0.0790405	+	0.996871i	$0.474814\pi$
$908$	1.93502e6	0.0778881
$909$	1.44612e7	0.580491
$910$	457629.	0.0183194
$911$	3.49628e7	1.39576	0.697879	−	0.716216i	$-0.254127\pi$
$911$	3.49628e7	1.39576	0.697879	+	0.716216i	$0.254127\pi$
$912$	−5.26872e6	−0.209758
$913$	9.94281e6	0.394759
$914$	−6.50171e6	−0.257432
$915$	2.46350e6	0.0972745
$916$	1.71259e6	0.0674394
$917$	−2.79303e6	−0.109686
$918$	−5.59142e6	−0.218986
$919$	1.64415e7	0.642176	0.321088	−	0.947049i	$-0.395952\pi$
$919$	1.64415e7	0.642176	0.321088	+	0.947049i	$0.395952\pi$
$920$	−1.32149e7	−0.514747
$921$	1.49024e7	0.578906
$922$	1.23506e6	0.0478476
$923$	286000.	0.0110500
$924$	−853776.	−0.0328976
$925$	2.20208e7	0.846212
$926$	6.11124e6	0.234208
$927$	392417.	0.0149985
$928$	−6.16251e6	−0.234903
$929$	2.40895e7	0.915773	0.457887	−	0.889011i	$-0.348607\pi$
$929$	2.40895e7	0.915773	0.457887	+	0.889011i	$0.348607\pi$
$930$	−1.55443e7	−0.589337
$931$	5.49054e6	0.207606
$932$	1.53586e6	0.0579178
$933$	1.24986e7	0.470065
$934$	−7.35821e6	−0.275997
$935$	−2.35532e7	−0.881091
$936$	119232.	0.00444839
$937$	−4.42120e7	−1.64510	−0.822548	−	0.568696i	$-0.807448\pi$
$937$	−4.42120e7	−1.64510	−0.822548	+	0.568696i	$0.807448\pi$
$938$	3.68455e6	0.136734
$939$	2.84498e7	1.05297
$940$	−4.20192e7	−1.55106
$941$	7.03131e6	0.258858	0.129429	−	0.991589i	$-0.458686\pi$
$941$	7.03131e6	0.258858	0.129429	+	0.991589i	$0.458686\pi$
$942$	−2.60932e6	−0.0958078
$943$	−1.90750e7	−0.698532
$944$	5.84422e6	0.213450
$945$	−3.62622e6	−0.132091
$946$	−8.66363e6	−0.314755
$947$	1.62075e7	0.587273	0.293636	−	0.955917i	$-0.405135\pi$
$947$	1.62075e7	0.587273	0.293636	+	0.955917i	$0.405135\pi$
$948$	4.34359e6	0.156974
$949$	−1.39956e6	−0.0504459
$950$	−6.56787e7	−2.36111
$951$	−1.69708e7	−0.608487
$952$	−6.01327e6	−0.215040
$953$	−4.33622e7	−1.54660	−0.773302	−	0.634038i	$-0.781396\pi$
$953$	−4.33622e7	−1.54660	−0.773302	+	0.634038i	$0.781396\pi$
$954$	8.06394e6	0.286864
$955$	5.02335e7	1.78232
$956$	−5.31021e6	−0.187918
$957$	6.55369e6	0.231316
$958$	3.16895e7	1.11558
$959$	8.39471e6	0.294754
$960$	3.74225e6	0.131055
$961$	−1.05375e7	−0.368070
$962$	282150.	0.00982974
$963$	5.26310e6	0.182884
$964$	−1.42591e6	−0.0494195
$965$	−1.01410e8	−3.50560
$966$	3.58800e6	0.123711
$967$	−3.92277e7	−1.34905	−0.674523	−	0.738254i	$-0.735651\pi$
$967$	−3.92277e7	−1.34905	−0.674523	+	0.738254i	$0.735651\pi$
$968$	−937024.	−0.0321412
$969$	3.94639e7	1.35018
$970$	7.34134e6	0.250522
$971$	3.83746e7	1.30616	0.653078	−	0.757290i	$-0.273477\pi$
$971$	3.83746e7	1.30616	0.653078	+	0.757290i	$0.273477\pi$
$972$	−944784.	−0.0320750
$973$	1.70651e7	0.577864
$974$	−7.63980e6	−0.258038
$975$	1.48632e6	0.0500726
$976$	690271.	0.0231950
$977$	−3.61787e7	−1.21260	−0.606299	−	0.795237i	$-0.707347\pi$
$977$	−3.61787e7	−1.21260	−0.606299	+	0.795237i	$0.707347\pi$
$978$	2.25866e6	0.0755099
$979$	316821.	0.0105647
$980$	−3.89980e6	−0.129711
$981$	−2.39933e6	−0.0796007
$982$	−3.32885e7	−1.10158
$983$	−1.38010e7	−0.455541	−0.227771	−	0.973715i	$-0.573144\pi$
$983$	−1.38010e7	−0.455541	−0.227771	+	0.973715i	$0.573144\pi$
$984$	5.40175e6	0.177847
$985$	6.46087e7	2.12178
$986$	4.61586e7	1.51203
$987$	1.14087e7	0.372772
$988$	−841532.	−0.0274270
$989$	3.64089e7	1.18363
$990$	−3.97979e6	−0.129054
$991$	2.73144e7	0.883501	0.441751	−	0.897138i	$-0.354358\pi$
$991$	2.73144e7	0.883501	0.441751	+	0.897138i	$0.354358\pi$
$992$	−4.35551e6	−0.140527
$993$	3.43068e7	1.10410
$994$	−2.43722e6	−0.0782400
$995$	−4.64129e7	−1.48621
$996$	1.18328e7	0.377953
$997$	9.81415e6	0.312691	0.156345	−	0.987702i	$-0.450029\pi$
$997$	9.81415e6	0.312691	0.156345	+	0.987702i	$0.450029\pi$
$998$	3.43423e7	1.09145
$999$	−2.23573e6	−0.0708770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.6.a.f.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.6.a.f.1.1	✓	2	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -101.515 q^{5} +36.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -101.515 q^{5} +36.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +406.060 q^{10} -121.000 q^{11} -144.000 q^{12} -23.0000 q^{13} +196.000 q^{14} +913.635 q^{15} +256.000 q^{16} -1917.50 q^{17} -324.000 q^{18} +2286.77 q^{19} -1624.24 q^{20} +441.000 q^{21} +484.000 q^{22} -2034.01 q^{23} +576.000 q^{24} +7180.29 q^{25} +92.0000 q^{26} -729.000 q^{27} -784.000 q^{28} +6018.08 q^{29} -3654.54 q^{30} +4253.42 q^{31} -1024.00 q^{32} +1089.00 q^{33} +7669.99 q^{34} +4974.23 q^{35} +1296.00 q^{36} +3066.84 q^{37} -9147.09 q^{38} +207.000 q^{39} +6496.96 q^{40} +9378.04 q^{41} -1764.00 q^{42} -17900.1 q^{43} -1936.00 q^{44} -8222.71 q^{45} +8136.05 q^{46} +25870.1 q^{47} -2304.00 q^{48} +2401.00 q^{49} -28721.1 q^{50} +17257.5 q^{51} -368.000 q^{52} -24888.7 q^{53} +2916.00 q^{54} +12283.3 q^{55} +3136.00 q^{56} -20581.0 q^{57} -24072.3 q^{58} +22829.0 q^{59} +14618.2 q^{60} +2696.37 q^{61} -17013.7 q^{62} -3969.00 q^{63} +4096.00 q^{64} +2334.84 q^{65} -4356.00 q^{66} +18798.7 q^{67} -30679.9 q^{68} +18306.1 q^{69} -19896.9 q^{70} -12434.8 q^{71} -5184.00 q^{72} +60850.5 q^{73} -12267.4 q^{74} -64622.6 q^{75} +36588.4 q^{76} +5929.00 q^{77} -828.000 q^{78} -30163.8 q^{79} -25987.8 q^{80} +6561.00 q^{81} -37512.1 q^{82} -82172.0 q^{83} +7056.00 q^{84} +194655. q^{85} +71600.3 q^{86} -54162.7 q^{87} +7744.00 q^{88} -2618.35 q^{89} +32890.8 q^{90} +1127.00 q^{91} -32544.2 q^{92} -38280.8 q^{93} -103480. q^{94} -232142. q^{95} +9216.00 q^{96} +18079.4 q^{97} -9604.00 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 86 q^{5} + 72 q^{6} - 98 q^{7} - 128 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 86 * q^5 + 72 * q^6 - 98 * q^7 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 86 q^{5} + 72 q^{6} - 98 q^{7} - 128 q^{8} + 162 q^{9} + 344 q^{10} - 242 q^{11} - 288 q^{12} - 46 q^{13} + 392 q^{14} + 774 q^{15} + 512 q^{16} - 1904 q^{17} - 648 q^{18} + 4398 q^{19} - 1376 q^{20} + 882 q^{21} + 968 q^{22} - 2020 q^{23} + 1152 q^{24} + 4296 q^{25} + 184 q^{26} - 1458 q^{27} - 1568 q^{28} + 3610 q^{29} - 3096 q^{30} - 680 q^{31} - 2048 q^{32} + 2178 q^{33} + 7616 q^{34} + 4214 q^{35} + 2592 q^{36} + 3442 q^{37} - 17592 q^{38} + 414 q^{39} + 5504 q^{40} + 22384 q^{41} - 3528 q^{42} + 5804 q^{43} - 3872 q^{44} - 6966 q^{45} + 8080 q^{46} + 6274 q^{47} - 4608 q^{48} + 4802 q^{49} - 17184 q^{50} + 17136 q^{51} - 736 q^{52} + 4700 q^{53} + 5832 q^{54} + 10406 q^{55} + 6272 q^{56} - 39582 q^{57} - 14440 q^{58} + 28162 q^{59} + 12384 q^{60} - 9236 q^{61} + 2720 q^{62} - 7938 q^{63} + 8192 q^{64} + 1978 q^{65} - 8712 q^{66} - 13018 q^{67} - 30464 q^{68} + 18180 q^{69} - 16856 q^{70} + 24400 q^{71} - 10368 q^{72} + 75006 q^{73} - 13768 q^{74} - 38664 q^{75} + 70368 q^{76} + 11858 q^{77} - 1656 q^{78} + 28264 q^{79} - 22016 q^{80} + 13122 q^{81} - 89536 q^{82} - 185936 q^{83} + 14112 q^{84} + 194864 q^{85} - 23216 q^{86} - 32490 q^{87} + 15488 q^{88} + 36660 q^{89} + 27864 q^{90} + 2254 q^{91} - 32320 q^{92} + 6120 q^{93} - 25096 q^{94} - 199386 q^{95} + 18432 q^{96} + 3332 q^{97} - 19208 q^{98} - 19602 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 86 * q^5 + 72 * q^6 - 98 * q^7 - 128 * q^8 + 162 * q^9 + 344 * q^10 - 242 * q^11 - 288 * q^12 - 46 * q^13 + 392 * q^14 + 774 * q^15 + 512 * q^16 - 1904 * q^17 - 648 * q^18 + 4398 * q^19 - 1376 * q^20 + 882 * q^21 + 968 * q^22 - 2020 * q^23 + 1152 * q^24 + 4296 * q^25 + 184 * q^26 - 1458 * q^27 - 1568 * q^28 + 3610 * q^29 - 3096 * q^30 - 680 * q^31 - 2048 * q^32 + 2178 * q^33 + 7616 * q^34 + 4214 * q^35 + 2592 * q^36 + 3442 * q^37 - 17592 * q^38 + 414 * q^39 + 5504 * q^40 + 22384 * q^41 - 3528 * q^42 + 5804 * q^43 - 3872 * q^44 - 6966 * q^45 + 8080 * q^46 + 6274 * q^47 - 4608 * q^48 + 4802 * q^49 - 17184 * q^50 + 17136 * q^51 - 736 * q^52 + 4700 * q^53 + 5832 * q^54 + 10406 * q^55 + 6272 * q^56 - 39582 * q^57 - 14440 * q^58 + 28162 * q^59 + 12384 * q^60 - 9236 * q^61 + 2720 * q^62 - 7938 * q^63 + 8192 * q^64 + 1978 * q^65 - 8712 * q^66 - 13018 * q^67 - 30464 * q^68 + 18180 * q^69 - 16856 * q^70 + 24400 * q^71 - 10368 * q^72 + 75006 * q^73 - 13768 * q^74 - 38664 * q^75 + 70368 * q^76 + 11858 * q^77 - 1656 * q^78 + 28264 * q^79 - 22016 * q^80 + 13122 * q^81 - 89536 * q^82 - 185936 * q^83 + 14112 * q^84 + 194864 * q^85 - 23216 * q^86 - 32490 * q^87 + 15488 * q^88 + 36660 * q^89 + 27864 * q^90 + 2254 * q^91 - 32320 * q^92 + 6120 * q^93 - 25096 * q^94 - 199386 * q^95 + 18432 * q^96 + 3332 * q^97 - 19208 * q^98 - 19602 * q^99

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