LMFDB - Embedded newform 483.6.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,6,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	483.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:	$77.4653849697$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 268 x^{10} + 83 x^{9} + 25315 x^{8} + 5134 x^{7} - 993368 x^{6} - 511968 x^{5} + \cdots + 102912 $ x^12 - x^11 - 268x^10 + 83x^9 + 25315x^8 + 5134x^7 - 993368x^6 - 511968x^5 + 14212480x^4 + 10085312x^3 - 18833856x^2 + 3290240x + 102912
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.0270357$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0270357 q^{2} +9.00000 q^{3} -31.9993 q^{4} -35.6847 q^{5} +0.243322 q^{6} -49.0000 q^{7} -1.73027 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+0.0270357 q^{2} +9.00000 q^{3} -31.9993 q^{4} -35.6847 q^{5} +0.243322 q^{6} -49.0000 q^{7} -1.73027 q^{8} +81.0000 q^{9} -0.964762 q^{10} -51.2783 q^{11} -287.993 q^{12} +48.2978 q^{13} -1.32475 q^{14} -321.162 q^{15} +1023.93 q^{16} +449.713 q^{17} +2.18989 q^{18} +3019.56 q^{19} +1141.88 q^{20} -441.000 q^{21} -1.38635 q^{22} +529.000 q^{23} -15.5724 q^{24} -1851.60 q^{25} +1.30577 q^{26} +729.000 q^{27} +1567.96 q^{28} -176.363 q^{29} -8.68286 q^{30} -3791.57 q^{31} +83.0512 q^{32} -461.504 q^{33} +12.1583 q^{34} +1748.55 q^{35} -2591.94 q^{36} +11322.9 q^{37} +81.6361 q^{38} +434.680 q^{39} +61.7441 q^{40} -18249.5 q^{41} -11.9228 q^{42} -7055.18 q^{43} +1640.87 q^{44} -2890.46 q^{45} +14.3019 q^{46} +16138.3 q^{47} +9215.37 q^{48} +2401.00 q^{49} -50.0594 q^{50} +4047.42 q^{51} -1545.49 q^{52} +12473.1 q^{53} +19.7091 q^{54} +1829.85 q^{55} +84.7831 q^{56} +27176.1 q^{57} -4.76811 q^{58} -33399.0 q^{59} +10277.0 q^{60} -43936.7 q^{61} -102.508 q^{62} -3969.00 q^{63} -32763.5 q^{64} -1723.49 q^{65} -12.4771 q^{66} -27094.7 q^{67} -14390.5 q^{68} +4761.00 q^{69} +47.2734 q^{70} -56930.8 q^{71} -140.152 q^{72} +11286.9 q^{73} +306.122 q^{74} -16664.4 q^{75} -96623.8 q^{76} +2512.63 q^{77} +11.7519 q^{78} -49146.9 q^{79} -36538.6 q^{80} +6561.00 q^{81} -493.389 q^{82} +93818.6 q^{83} +14111.7 q^{84} -16047.9 q^{85} -190.742 q^{86} -1587.27 q^{87} +88.7251 q^{88} +12477.5 q^{89} -78.1457 q^{90} -2366.59 q^{91} -16927.6 q^{92} -34124.2 q^{93} +436.312 q^{94} -107752. q^{95} +747.461 q^{96} -31629.3 q^{97} +64.9128 q^{98} -4153.54 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9} + 528 q^{10} - 1425 q^{11} + 1377 q^{12} - 70 q^{13} + 49 q^{14} - 1458 q^{15} + 3865 q^{16} - 398 q^{17} - 81 q^{18} - 1293 q^{19} - 8593 q^{20} - 5292 q^{21} + 4961 q^{22} + 6348 q^{23} - 4428 q^{24} + 5830 q^{25} - 5187 q^{26} + 8748 q^{27} - 7497 q^{28} - 5127 q^{29} + 4752 q^{30} + 6498 q^{31} - 28485 q^{32} - 12825 q^{33} - 14527 q^{34} + 7938 q^{35} + 12393 q^{36} - 35545 q^{37} - 32617 q^{38} - 630 q^{39} + 35789 q^{40} - 7806 q^{41} + 441 q^{42} - 66142 q^{43} - 83253 q^{44} - 13122 q^{45} - 529 q^{46} - 16432 q^{47} + 34785 q^{48} + 28812 q^{49} - 177328 q^{50} - 3582 q^{51} - 187010 q^{52} - 67456 q^{53} - 729 q^{54} - 10453 q^{55} + 24108 q^{56} - 11637 q^{57} - 92677 q^{58} - 36346 q^{59} - 77337 q^{60} - 8768 q^{61} - 141813 q^{62} - 47628 q^{63} - 24604 q^{64} + 121875 q^{65} + 44649 q^{66} - 123617 q^{67} + 17217 q^{68} + 57132 q^{69} - 25872 q^{70} - 108667 q^{71} - 39852 q^{72} - 107406 q^{73} - 87825 q^{74} + 52470 q^{75} + 120191 q^{76} + 69825 q^{77} - 46683 q^{78} - 39470 q^{79} - 513682 q^{80} + 78732 q^{81} + 150219 q^{82} - 181838 q^{83} - 67473 q^{84} - 52633 q^{85} + 125713 q^{86} - 46143 q^{87} + 120642 q^{88} - 277361 q^{89} + 42768 q^{90} + 3430 q^{91} + 80937 q^{92} + 58482 q^{93} - 40880 q^{94} - 272491 q^{95} - 256365 q^{96} - 169005 q^{97} - 2401 q^{98} - 115425 q^{99}+O(q^{100}) \) 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9 + 528 * q^10 - 1425 * q^11 + 1377 * q^12 - 70 * q^13 + 49 * q^14 - 1458 * q^15 + 3865 * q^16 - 398 * q^17 - 81 * q^18 - 1293 * q^19 - 8593 * q^20 - 5292 * q^21 + 4961 * q^22 + 6348 * q^23 - 4428 * q^24 + 5830 * q^25 - 5187 * q^26 + 8748 * q^27 - 7497 * q^28 - 5127 * q^29 + 4752 * q^30 + 6498 * q^31 - 28485 * q^32 - 12825 * q^33 - 14527 * q^34 + 7938 * q^35 + 12393 * q^36 - 35545 * q^37 - 32617 * q^38 - 630 * q^39 + 35789 * q^40 - 7806 * q^41 + 441 * q^42 - 66142 * q^43 - 83253 * q^44 - 13122 * q^45 - 529 * q^46 - 16432 * q^47 + 34785 * q^48 + 28812 * q^49 - 177328 * q^50 - 3582 * q^51 - 187010 * q^52 - 67456 * q^53 - 729 * q^54 - 10453 * q^55 + 24108 * q^56 - 11637 * q^57 - 92677 * q^58 - 36346 * q^59 - 77337 * q^60 - 8768 * q^61 - 141813 * q^62 - 47628 * q^63 - 24604 * q^64 + 121875 * q^65 + 44649 * q^66 - 123617 * q^67 + 17217 * q^68 + 57132 * q^69 - 25872 * q^70 - 108667 * q^71 - 39852 * q^72 - 107406 * q^73 - 87825 * q^74 + 52470 * q^75 + 120191 * q^76 + 69825 * q^77 - 46683 * q^78 - 39470 * q^79 - 513682 * q^80 + 78732 * q^81 + 150219 * q^82 - 181838 * q^83 - 67473 * q^84 - 52633 * q^85 + 125713 * q^86 - 46143 * q^87 + 120642 * q^88 - 277361 * q^89 + 42768 * q^90 + 3430 * q^91 + 80937 * q^92 + 58482 * q^93 - 40880 * q^94 - 272491 * q^95 - 256365 * q^96 - 169005 * q^97 - 2401 * q^98 - 115425 * 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 $

$2$	0.0270357	0.00477929	0.00238964	−	0.999997i	$-0.499239\pi$
$2$	0.0270357	0.00477929	0.00238964	+	0.999997i	$0.499239\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−31.9993	−0.999977
$5$	−35.6847	−0.638347	−0.319174	−	0.947696i	$-0.603405\pi$
$5$	−35.6847	−0.638347	−0.319174	+	0.947696i	$0.603405\pi$
$6$	0.243322	0.00275932
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	−1.73027	−0.00955847
$9$	81.0000	0.333333
$10$	−0.964762	−0.00305085
$11$	−51.2783	−0.127777	−0.0638883	−	0.997957i	$-0.520350\pi$
$11$	−51.2783	−0.127777	−0.0638883	+	0.997957i	$0.520350\pi$
$12$	−287.993	−0.577337
$13$	48.2978	0.0792627	0.0396314	−	0.999214i	$-0.487382\pi$
$13$	48.2978	0.0792627	0.0396314	+	0.999214i	$0.487382\pi$
$14$	−1.32475	−0.00180640
$15$	−321.162	−0.368550
$16$	1023.93	0.999931
$17$	449.713	0.377410	0.188705	−	0.982034i	$-0.439571\pi$
$17$	449.713	0.377410	0.188705	+	0.982034i	$0.439571\pi$
$18$	2.18989	0.00159310
$19$	3019.56	1.91893	0.959467	−	0.281821i	$-0.0909385\pi$
$19$	3019.56	1.91893	0.959467	+	0.281821i	$0.0909385\pi$
$20$	1141.88	0.638333
$21$	−441.000	−0.218218
$22$	−1.38635	−0.000610681 0
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−15.5724	−0.00551858
$25$	−1851.60	−0.592513
$26$	1.30577	0.000378819 0
$27$	729.000	0.192450
$28$	1567.96	0.377956
$29$	−176.363	−0.0389415	−0.0194708	−	0.999810i	$-0.506198\pi$
$29$	−176.363	−0.0389415	−0.0194708	+	0.999810i	$0.506198\pi$
$30$	−8.68286	−0.00176141
$31$	−3791.57	−0.708623	−0.354312	−	0.935127i	$-0.615285\pi$
$31$	−3791.57	−0.708623	−0.354312	+	0.935127i	$0.615285\pi$
$32$	83.0512	0.0143374
$33$	−461.504	−0.0737719
$34$	12.1583	0.00180375
$35$	1748.55	0.241273
$36$	−2591.94	−0.333326
$37$	11322.9	1.35973	0.679865	−	0.733338i	$-0.262039\pi$
$37$	11322.9	1.35973	0.679865	+	0.733338i	$0.262039\pi$
$38$	81.6361	0.00917114
$39$	434.680	0.0457624
$40$	61.7441	0.00610162
$41$	−18249.5	−1.69548	−0.847738	−	0.530415i	$-0.822036\pi$
$41$	−18249.5	−1.69548	−0.847738	+	0.530415i	$0.822036\pi$
$42$	−11.9228	−0.00104293
$43$	−7055.18	−0.581885	−0.290942	−	0.956741i	$-0.593969\pi$
$43$	−7055.18	−0.581885	−0.290942	+	0.956741i	$0.593969\pi$
$44$	1640.87	0.127774
$45$	−2890.46	−0.212782
$46$	14.3019	0.000996550 0
$47$	16138.3	1.06565	0.532825	−	0.846226i	$-0.321131\pi$
$47$	16138.3	1.06565	0.532825	+	0.846226i	$0.321131\pi$
$48$	9215.37	0.577311
$49$	2401.00	0.142857
$50$	−50.0594	−0.00283179
$51$	4047.42	0.217898
$52$	−1545.49	−0.0792609
$53$	12473.1	0.609937	0.304968	−	0.952362i	$-0.401354\pi$
$53$	12473.1	0.609937	0.304968	+	0.952362i	$0.401354\pi$
$54$	19.7091	0.000919774 0
$55$	1829.85	0.0815659
$56$	84.7831	0.00361276
$57$	27176.1	1.10790
$58$	−4.76811	−0.000186113 0
$59$	−33399.0	−1.24912	−0.624559	−	0.780977i	$-0.714721\pi$
$59$	−33399.0	−1.24912	−0.624559	+	0.780977i	$0.714721\pi$
$60$	10277.0	0.368542
$61$	−43936.7	−1.51183	−0.755914	−	0.654671i	$-0.772807\pi$
$61$	−43936.7	−1.51183	−0.755914	+	0.654671i	$0.772807\pi$
$62$	−102.508	−0.00338671
$63$	−3969.00	−0.125988
$64$	−32763.5	−0.999863
$65$	−1723.49	−0.0505972
$66$	−12.4771	−0.000352577 0
$67$	−27094.7	−0.737390	−0.368695	−	0.929550i	$-0.620195\pi$
$67$	−27094.7	−0.737390	−0.368695	+	0.929550i	$0.620195\pi$
$68$	−14390.5	−0.377401
$69$	4761.00	0.120386
$70$	47.2734	0.00115311
$71$	−56930.8	−1.34030	−0.670149	−	0.742227i	$-0.733770\pi$
$71$	−56930.8	−1.34030	−0.670149	+	0.742227i	$0.733770\pi$
$72$	−140.152	−0.00318616
$73$	11286.9	0.247896	0.123948	−	0.992289i	$-0.460444\pi$
$73$	11286.9	0.247896	0.123948	+	0.992289i	$0.460444\pi$
$74$	306.122	0.00649854
$75$	−16664.4	−0.342087
$76$	−96623.8	−1.91889
$77$	2512.63	0.0482950
$78$	11.7519	0.000218711 0
$79$	−49146.9	−0.885990	−0.442995	−	0.896524i	$-0.646084\pi$
$79$	−49146.9	−0.885990	−0.442995	+	0.896524i	$0.646084\pi$
$80$	−36538.6	−0.638304
$81$	6561.00	0.111111
$82$	−493.389	−0.00810317
$83$	93818.6	1.49484	0.747418	−	0.664354i	$-0.231293\pi$
$83$	93818.6	1.49484	0.747418	+	0.664354i	$0.231293\pi$
$84$	14111.7	0.218213
$85$	−16047.9	−0.240919
$86$	−190.742	−0.00278100
$87$	−1587.27	−0.0224829
$88$	88.7251	0.00122135
$89$	12477.5	0.166975	0.0834874	−	0.996509i	$-0.473394\pi$
$89$	12477.5	0.166975	0.0834874	+	0.996509i	$0.473394\pi$
$90$	−78.1457	−0.00101695
$91$	−2366.59	−0.0299585
$92$	−16927.6	−0.208510
$93$	−34124.2	−0.409124
$94$	436.312	0.00509305
$95$	−107752.	−1.22495
$96$	747.461	0.00827772
$97$	−31629.3	−0.341319	−0.170660	−	0.985330i	$-0.554590\pi$
$97$	−31629.3	−0.341319	−0.170660	+	0.985330i	$0.554590\pi$
$98$	64.9128	0.000682755 0
$99$	−4153.54	−0.0425922
$100$	59249.9	0.592499
$101$	−84505.6	−0.824294	−0.412147	−	0.911117i	$-0.635221\pi$
$101$	−84505.6	−0.824294	−0.412147	+	0.911117i	$0.635221\pi$
$102$	109.425	0.00104140
$103$	54333.5	0.504632	0.252316	−	0.967645i	$-0.418808\pi$
$103$	54333.5	0.504632	0.252316	+	0.967645i	$0.418808\pi$
$104$	−83.5681	−0.000757630 0
$105$	15737.0	0.139299
$106$	337.219	0.00291506
$107$	−41465.0	−0.350125	−0.175062	−	0.984557i	$-0.556013\pi$
$107$	−41465.0	−0.350125	−0.175062	+	0.984557i	$0.556013\pi$
$108$	−23327.5	−0.192446
$109$	178212.	1.43672	0.718359	−	0.695672i	$-0.244893\pi$
$109$	178212.	1.43672	0.718359	+	0.695672i	$0.244893\pi$
$110$	49.4713	0.000389827 0
$111$	101906.	0.785040
$112$	−50172.6	−0.377939
$113$	−3013.80	−0.0222033	−0.0111017	−	0.999938i	$-0.503534\pi$
$113$	−3013.80	−0.0222033	−0.0111017	+	0.999938i	$0.503534\pi$
$114$	734.725	0.00529496
$115$	−18877.2	−0.133105
$116$	5643.49	0.0389406
$117$	3912.12	0.0264209
$118$	−902.967	−0.00596990
$119$	−22035.9	−0.142648
$120$	555.697	0.00352277
$121$	−158422.	−0.983673
$122$	−1187.86	−0.00722546
$123$	−164246.	−0.978884
$124$	121328.	0.708607
$125$	177589.	1.01658
$126$	−107.305	−0.000602134 0
$127$	−240267.	−1.32186	−0.660930	−	0.750448i	$-0.729838\pi$
$127$	−240267.	−1.32186	−0.660930	+	0.750448i	$0.729838\pi$
$128$	−3543.43	−0.0191161
$129$	−63496.6	−0.335951
$130$	−46.5959	−0.000241818 0
$131$	−269111.	−1.37010	−0.685052	−	0.728494i	$-0.740221\pi$
$131$	−269111.	−1.37010	−0.685052	+	0.728494i	$0.740221\pi$
$132$	14767.8	0.0737702
$133$	−147959.	−0.725289
$134$	−732.525	−0.00352420
$135$	−26014.2	−0.122850
$136$	−778.124	−0.00360746
$137$	167758.	0.763627	0.381813	−	0.924239i	$-0.375300\pi$
$137$	167758.	0.763627	0.381813	+	0.924239i	$0.375300\pi$
$138$	128.717	0.000575359 0
$139$	112268.	0.492856	0.246428	−	0.969161i	$-0.420743\pi$
$139$	112268.	0.492856	0.246428	+	0.969161i	$0.420743\pi$
$140$	−55952.3	−0.241267
$141$	145245.	0.615253
$142$	−1539.16	−0.00640567
$143$	−2476.63	−0.0101279
$144$	82938.3	0.333310
$145$	6293.47	0.0248582
$146$	305.150	0.00118476
$147$	21609.0	0.0824786
$148$	−362324.	−1.35970
$149$	−230160.	−0.849307	−0.424654	−	0.905356i	$-0.639604\pi$
$149$	−230160.	−0.849307	−0.424654	+	0.905356i	$0.639604\pi$
$150$	−450.535	−0.00163493
$151$	305695.	1.09105	0.545527	−	0.838093i	$-0.316329\pi$
$151$	305695.	1.09105	0.545527	+	0.838093i	$0.316329\pi$
$152$	−5224.65	−0.0183421
$153$	36426.8	0.125803
$154$	67.9309	0.000230816 0
$155$	135301.	0.452348
$156$	−13909.4	−0.0457613
$157$	−153846.	−0.498124	−0.249062	−	0.968488i	$-0.580122\pi$
$157$	−153846.	−0.498124	−0.249062	+	0.968488i	$0.580122\pi$
$158$	−1328.72	−0.00423440
$159$	112258.	0.352147
$160$	−2963.66	−0.00915226
$161$	−25921.0	−0.0788110
$162$	177.381	0.000531032 0
$163$	−107327.	−0.316402	−0.158201	−	0.987407i	$-0.550569\pi$
$163$	−107327.	−0.316402	−0.158201	+	0.987407i	$0.550569\pi$
$164$	583971.	1.69544
$165$	16468.6	0.0470921
$166$	2536.45	0.00714425
$167$	−213735.	−0.593040	−0.296520	−	0.955027i	$-0.595826\pi$
$167$	−213735.	−0.593040	−0.296520	+	0.955027i	$0.595826\pi$
$168$	763.048	0.00208583
$169$	−368960.	−0.993717
$170$	−433.866	−0.00115142
$171$	244585.	0.639645
$172$	225761.	0.581872
$173$	−519745.	−1.32031	−0.660154	−	0.751131i	$-0.729509\pi$
$173$	−519745.	−1.32031	−0.660154	+	0.751131i	$0.729509\pi$
$174$	−42.9130	−0.000107452 0
$175$	90728.5	0.223949
$176$	−52505.3	−0.127768
$177$	−300591.	−0.721179
$178$	337.337	0.000798021 0
$179$	−156796.	−0.365766	−0.182883	−	0.983135i	$-0.558543\pi$
$179$	−156796.	−0.365766	−0.182883	+	0.983135i	$0.558543\pi$
$180$	92492.7	0.212778
$181$	−600423.	−1.36226	−0.681131	−	0.732161i	$-0.738512\pi$
$181$	−600423.	−1.36226	−0.681131	+	0.732161i	$0.738512\pi$
$182$	−63.9826	−0.000143180 0
$183$	−395430.	−0.872854
$184$	−915.311	−0.00199308
$185$	−404054.	−0.867980
$186$	−922.572	−0.00195532
$187$	−23060.5	−0.0482242
$188$	−516415.	−1.06563
$189$	−35721.0	−0.0727393
$190$	−2913.16	−0.00585437
$191$	−153296.	−0.304052	−0.152026	−	0.988377i	$-0.548580\pi$
$191$	−153296.	−0.304052	−0.152026	+	0.988377i	$0.548580\pi$
$192$	−294872.	−0.577271
$193$	690112.	1.33360	0.666801	−	0.745236i	$-0.267663\pi$
$193$	690112.	1.33360	0.666801	+	0.745236i	$0.267663\pi$
$194$	−855.123	−0.00163126
$195$	−15511.4	−0.0292123
$196$	−76830.2	−0.142854
$197$	987558.	1.81300	0.906498	−	0.422210i	$-0.138746\pi$
$197$	987558.	1.81300	0.906498	+	0.422210i	$0.138746\pi$
$198$	−112.294	−0.000203560 0
$199$	−486474.	−0.870816	−0.435408	−	0.900233i	$-0.643396\pi$
$199$	−486474.	−0.870816	−0.435408	+	0.900233i	$0.643396\pi$
$200$	3203.77	0.00566351
$201$	−243852.	−0.425732
$202$	−2284.67	−0.00393954
$203$	8641.80	0.0147185
$204$	−129514.	−0.217893
$205$	651229.	1.08230
$206$	1468.95	0.00241178
$207$	42849.0	0.0695048
$208$	49453.6	0.0792573
$209$	−154838.	−0.245195
$210$	425.460	0.000665749 0
$211$	528718.	0.817557	0.408779	−	0.912634i	$-0.365955\pi$
$211$	528718.	0.817557	0.408779	+	0.912634i	$0.365955\pi$
$212$	−399130.	−0.609923
$213$	−512377.	−0.773821
$214$	−1121.04	−0.00167335
$215$	251762.	0.371445
$216$	−1261.36	−0.00183953
$217$	185787.	0.267834
$218$	4818.10	0.00686649
$219$	101582.	0.143123
$220$	−58553.8	−0.0815640
$221$	21720.2	0.0299145
$222$	2755.10	0.00375193
$223$	−824938.	−1.11086	−0.555430	−	0.831563i	$-0.687446\pi$
$223$	−824938.	−1.11086	−0.555430	+	0.831563i	$0.687446\pi$
$224$	−4069.51	−0.00541904
$225$	−149980.	−0.197504
$226$	−81.4803	−0.000106116 0
$227$	−1.17887e6	−1.51845	−0.759224	−	0.650830i	$-0.774421\pi$
$227$	−1.17887e6	−1.51845	−0.759224	+	0.650830i	$0.774421\pi$
$228$	−869614.	−1.10787
$229$	−200133.	−0.252191	−0.126095	−	0.992018i	$-0.540245\pi$
$229$	−200133.	−0.252191	−0.126095	+	0.992018i	$0.540245\pi$
$230$	−510.359	−0.000636145 0
$231$	22613.7	0.0278832
$232$	305.156	0.000372221 0
$233$	−217570.	−0.262548	−0.131274	−	0.991346i	$-0.541907\pi$
$233$	−217570.	−0.262548	−0.131274	+	0.991346i	$0.541907\pi$
$234$	105.767	0.000126273 0
$235$	−575892.	−0.680255
$236$	1.06874e6	1.24909
$237$	−442322.	−0.511526
$238$	−595.758	−0.000681754 0
$239$	−1.02225e6	−1.15761	−0.578804	−	0.815467i	$-0.696480\pi$
$239$	−1.02225e6	−1.15761	−0.578804	+	0.815467i	$0.696480\pi$
$240$	−328848.	−0.368525
$241$	−817507.	−0.906669	−0.453335	−	0.891340i	$-0.649766\pi$
$241$	−817507.	−0.906669	−0.453335	+	0.891340i	$0.649766\pi$
$242$	−4283.04	−0.00470126
$243$	59049.0	0.0641500
$244$	1.40594e6	1.51179
$245$	−85679.0	−0.0911925
$246$	−4440.50	−0.00467837
$247$	145838.	0.152100
$248$	6560.44	0.00677335
$249$	844367.	0.863044
$250$	4801.24	0.00485851
$251$	108996.	0.109201	0.0546006	−	0.998508i	$-0.482611\pi$
$251$	108996.	0.109201	0.0546006	+	0.998508i	$0.482611\pi$
$252$	127005.	0.125985
$253$	−27126.2	−0.0266433
$254$	−6495.80	−0.00631755
$255$	−144431.	−0.139094
$256$	1.04834e6	0.999772
$257$	−1.14781e6	−1.08402	−0.542011	−	0.840372i	$-0.682337\pi$
$257$	−1.14781e6	−1.08402	−0.542011	+	0.840372i	$0.682337\pi$
$258$	−1716.68	−0.00160561
$259$	−554821.	−0.513929
$260$	55150.5	0.0505960
$261$	−14285.4	−0.0129805
$262$	−7275.62	−0.00654812
$263$	−261782.	−0.233373	−0.116686	−	0.993169i	$-0.537227\pi$
$263$	−261782.	−0.233373	−0.116686	+	0.993169i	$0.537227\pi$
$264$	798.526	0.000705146 0
$265$	−445099.	−0.389351
$266$	−4000.17	−0.00346636
$267$	112297.	0.0964029
$268$	867011.	0.737373
$269$	−945047.	−0.796292	−0.398146	−	0.917322i	$-0.630346\pi$
$269$	−945047.	−0.796292	−0.398146	+	0.917322i	$0.630346\pi$
$270$	−703.312	−0.000587136 0
$271$	2.24991e6	1.86098	0.930491	−	0.366314i	$-0.119380\pi$
$271$	2.24991e6	1.86098	0.930491	+	0.366314i	$0.119380\pi$
$272$	460475.	0.377384
$273$	−21299.3	−0.0172965
$274$	4535.45	0.00364959
$275$	94946.9	0.0757093
$276$	−152349.	−0.120383
$277$	1.13213e6	0.886535	0.443267	−	0.896389i	$-0.353819\pi$
$277$	1.13213e6	0.886535	0.443267	+	0.896389i	$0.353819\pi$
$278$	3035.25	0.00235550
$279$	−307117.	−0.236208
$280$	−3025.46	−0.00230620
$281$	−1.88325e6	−1.42280	−0.711399	−	0.702788i	$-0.751938\pi$
$281$	−1.88325e6	−1.42280	−0.711399	+	0.702788i	$0.751938\pi$
$282$	3926.81	0.00294047
$283$	883722.	0.655918	0.327959	−	0.944692i	$-0.393639\pi$
$283$	883722.	0.655918	0.327959	+	0.944692i	$0.393639\pi$
$284$	1.82174e6	1.34027
$285$	−969770.	−0.707223
$286$	−66.9574	−4.84043e−5 0
$287$	894227.	0.640830
$288$	6727.15	0.00477914
$289$	−1.21762e6	−0.857562
$290$	170.149	0.000118805 0
$291$	−284664.	−0.197061
$292$	−361174.	−0.247890
$293$	699003.	0.475675	0.237837	−	0.971305i	$-0.423561\pi$
$293$	699003.	0.475675	0.237837	+	0.971305i	$0.423561\pi$
$294$	584.215	0.000394189 0
$295$	1.19183e6	0.797372
$296$	−19591.6	−0.0129969
$297$	−37381.8	−0.0245906
$298$	−6222.55	−0.00405908
$299$	25549.5	0.0165274
$300$	533249.	0.342079
$301$	345704.	0.219932
$302$	8264.70	0.00521447
$303$	−760551.	−0.475906
$304$	3.09182e6	1.91880
$305$	1.56787e6	0.965072
$306$	984.824	0.000601250 0
$307$	424434.	0.257019	0.128509	−	0.991708i	$-0.458981\pi$
$307$	424434.	0.257019	0.128509	+	0.991708i	$0.458981\pi$
$308$	−80402.5	−0.0482939
$309$	489001.	0.291349
$310$	3657.97	0.00216190
$311$	1.94072e6	1.13779	0.568893	−	0.822411i	$-0.307372\pi$
$311$	1.94072e6	1.13779	0.568893	+	0.822411i	$0.307372\pi$
$312$	−752.113	−0.000437418 0
$313$	−595384.	−0.343508	−0.171754	−	0.985140i	$-0.554943\pi$
$313$	−595384.	−0.343508	−0.171754	+	0.985140i	$0.554943\pi$
$314$	−4159.35	−0.00238068
$315$	141633.	0.0804242
$316$	1.57267e6	0.885970
$317$	1.33592e6	0.746675	0.373337	−	0.927696i	$-0.378213\pi$
$317$	1.33592e6	0.746675	0.373337	+	0.927696i	$0.378213\pi$
$318$	3034.97	0.00168301
$319$	9043.60	0.00497582
$320$	1.16916e6	0.638260
$321$	−373185.	−0.202145
$322$	−700.793	−0.000376661 0
$323$	1.35794e6	0.724225
$324$	−209947.	−0.111109
$325$	−89428.3	−0.0469642
$326$	−2901.66	−0.00151218
$327$	1.60391e6	0.829490
$328$	31576.6	0.0162062
$329$	−790779.	−0.402778
$330$	445.242	0.000225067 0
$331$	1.34011e6	0.672312	0.336156	−	0.941806i	$-0.390873\pi$
$331$	1.34011e6	0.672312	0.336156	+	0.941806i	$0.390873\pi$
$332$	−3.00213e6	−1.49480
$333$	917153.	0.453243
$334$	−5778.47	−0.00283431
$335$	966867.	0.470711
$336$	−451553.	−0.218203
$337$	−861846.	−0.413385	−0.206693	−	0.978406i	$-0.566270\pi$
$337$	−861846.	−0.413385	−0.206693	+	0.978406i	$0.566270\pi$
$338$	−9975.11	−0.00474926
$339$	−27124.2	−0.0128191
$340$	513521.	0.240913
$341$	194425.	0.0905455
$342$	6612.52	0.00305705
$343$	−117649.	−0.0539949
$344$	12207.4	0.00556193
$345$	−169895.	−0.0768480
$346$	−14051.7	−0.00631013
$347$	754008.	0.336165	0.168082	−	0.985773i	$-0.446243\pi$
$347$	754008.	0.336165	0.168082	+	0.985773i	$0.446243\pi$
$348$	50791.5	0.0224824
$349$	4.01800e6	1.76582	0.882911	−	0.469541i	$-0.155581\pi$
$349$	4.01800e6	1.76582	0.882911	+	0.469541i	$0.155581\pi$
$350$	2452.91	0.00107032
$351$	35209.1	0.0152541
$352$	−4258.72	−0.00183199
$353$	−1.43303e6	−0.612095	−0.306047	−	0.952016i	$-0.599007\pi$
$353$	−1.43303e6	−0.612095	−0.306047	+	0.952016i	$0.599007\pi$
$354$	−8126.70	−0.00344672
$355$	2.03156e6	0.855575
$356$	−399269.	−0.166971
$357$	−198324.	−0.0823576
$358$	−4239.10	−0.00174810
$359$	−4.62829e6	−1.89533	−0.947664	−	0.319270i	$-0.896562\pi$
$359$	−4.62829e6	−1.89533	−0.947664	+	0.319270i	$0.896562\pi$
$360$	5001.27	0.00203387
$361$	6.64166e6	2.68231
$362$	−16232.9	−0.00651065
$363$	−1.42579e6	−0.567924
$364$	75729.2	0.0299578
$365$	−402771.	−0.158244
$366$	−10690.7	−0.00417162
$367$	−1.07472e6	−0.416515	−0.208257	−	0.978074i	$-0.566779\pi$
$367$	−1.07472e6	−0.416515	−0.208257	+	0.978074i	$0.566779\pi$
$368$	541659.	0.208500
$369$	−1.47821e6	−0.565159
$370$	−10923.9	−0.00414833
$371$	−611182.	−0.230534
$372$	1.09195e6	0.409114
$373$	2.21898e6	0.825811	0.412906	−	0.910774i	$-0.364514\pi$
$373$	2.21898e6	0.825811	0.412906	+	0.910774i	$0.364514\pi$
$374$	−623.458	−0.000230477 0
$375$	1.59830e6	0.586921
$376$	−27923.6	−0.0101860
$377$	−8517.96	−0.00308661
$378$	−965.743	−0.000347642 0
$379$	2.47566e6	0.885306	0.442653	−	0.896693i	$-0.354037\pi$
$379$	2.47566e6	0.885306	0.442653	+	0.896693i	$0.354037\pi$
$380$	3.44799e6	1.22492
$381$	−2.16241e6	−0.763176
$382$	−4144.47	−0.00145315
$383$	−2.13865e6	−0.744977	−0.372488	−	0.928037i	$-0.621495\pi$
$383$	−2.13865e6	−0.744977	−0.372488	+	0.928037i	$0.621495\pi$
$384$	−31890.8	−0.0110367
$385$	−89662.6	−0.0308290
$386$	18657.7	0.00637367
$387$	−571470.	−0.193962
$388$	1.01212e6	0.341312
$389$	−1.54262e6	−0.516874	−0.258437	−	0.966028i	$-0.583207\pi$
$389$	−1.54262e6	−0.516874	−0.258437	+	0.966028i	$0.583207\pi$
$390$	−419.363	−0.000139614 0
$391$	237898.	0.0786954
$392$	−4154.37	−0.00136550
$393$	−2.42200e6	−0.791030
$394$	26699.3	0.00866483
$395$	1.75379e6	0.565569
$396$	132910.	0.0425912
$397$	1.88284e6	0.599566	0.299783	−	0.954007i	$-0.403086\pi$
$397$	1.88284e6	0.599566	0.299783	+	0.954007i	$0.403086\pi$
$398$	−13152.2	−0.00416188
$399$	−1.33163e6	−0.418746
$400$	−1.89591e6	−0.592472
$401$	−4.36276e6	−1.35488	−0.677439	−	0.735579i	$-0.736910\pi$
$401$	−4.36276e6	−1.35488	−0.677439	+	0.735579i	$0.736910\pi$
$402$	−6592.73	−0.00203470
$403$	−183125.	−0.0561674
$404$	2.70412e6	0.824275
$405$	−234127.	−0.0709275
$406$	233.637	7.03440e−5 0
$407$	−580617.	−0.173742
$408$	−7003.12	−0.00208277
$409$	2.80836e6	0.830126	0.415063	−	0.909793i	$-0.363759\pi$
$409$	2.80836e6	0.830126	0.415063	+	0.909793i	$0.363759\pi$
$410$	17606.5	0.00517264
$411$	1.50982e6	0.440880
$412$	−1.73863e6	−0.504620
$413$	1.63655e6	0.472122
$414$	1158.45	0.000332183 0
$415$	−3.34789e6	−0.954225
$416$	4011.19	0.00113642
$417$	1.01041e6	0.284550
$418$	−4186.16	−0.00117186
$419$	327192.	0.0910474	0.0455237	−	0.998963i	$-0.485504\pi$
$419$	327192.	0.0910474	0.0455237	+	0.998963i	$0.485504\pi$
$420$	−503571.	−0.139296
$421$	3.05624e6	0.840392	0.420196	−	0.907433i	$-0.361961\pi$
$421$	3.05624e6	0.840392	0.420196	+	0.907433i	$0.361961\pi$
$422$	14294.3	0.00390734
$423$	1.30721e6	0.355216
$424$	−21581.8	−0.00583006
$425$	−832690.	−0.223620
$426$	−13852.5	−0.00369831
$427$	2.15290e6	0.571417
$428$	1.32685e6	0.350117
$429$	−22289.6	−0.00584736
$430$	6806.57	0.00177524
$431$	−3.24405e6	−0.841192	−0.420596	−	0.907248i	$-0.638179\pi$
$431$	−3.24405e6	−0.841192	−0.420596	+	0.907248i	$0.638179\pi$
$432$	746445.	0.192437
$433$	4.93400e6	1.26468	0.632338	−	0.774692i	$-0.282095\pi$
$433$	4.93400e6	1.26468	0.632338	+	0.774692i	$0.282095\pi$
$434$	5022.89	0.00128006
$435$	56641.2	0.0143519
$436$	−5.70267e6	−1.43669
$437$	1.59735e6	0.400125
$438$	2746.35	0.000684024 0
$439$	−6.27698e6	−1.55450	−0.777248	−	0.629194i	$-0.783385\pi$
$439$	−6.27698e6	−1.55450	−0.777248	+	0.629194i	$0.783385\pi$
$440$	−3166.13	−0.000779645 0
$441$	194481.	0.0476190
$442$	587.220	0.000142970 0
$443$	−1.35004e6	−0.326842	−0.163421	−	0.986556i	$-0.552253\pi$
$443$	−1.35004e6	−0.326842	−0.163421	+	0.986556i	$0.552253\pi$
$444$	−3.26091e6	−0.785022
$445$	−445254.	−0.106588
$446$	−22302.8	−0.00530912
$447$	−2.07144e6	−0.490348
$448$	1.60541e6	0.377913
$449$	−2.57334e6	−0.602396	−0.301198	−	0.953562i	$-0.597386\pi$
$449$	−2.57334e6	−0.602396	−0.301198	+	0.953562i	$0.597386\pi$
$450$	−4054.81	−0.000943929 0
$451$	935804.	0.216642
$452$	96439.4	0.0222028
$453$	2.75126e6	0.629921
$454$	−31871.5	−0.00725710
$455$	84451.1	0.0191239
$456$	−47021.8	−0.0105898
$457$	5.01048e6	1.12225	0.561124	−	0.827732i	$-0.310369\pi$
$457$	5.01048e6	1.12225	0.561124	+	0.827732i	$0.310369\pi$
$458$	−5410.74	−0.00120529
$459$	327841.	0.0726326
$460$	604057.	0.133102
$461$	−6.04782e6	−1.32540	−0.662700	−	0.748885i	$-0.730589\pi$
$461$	−6.04782e6	−1.32540	−0.662700	+	0.748885i	$0.730589\pi$
$462$	611.378	0.000133262 0
$463$	−3.31040e6	−0.717676	−0.358838	−	0.933400i	$-0.616827\pi$
$463$	−3.31040e6	−0.717676	−0.358838	+	0.933400i	$0.616827\pi$
$464$	−180584.	−0.0389389
$465$	1.21771e6	0.261163
$466$	−5882.15	−0.00125479
$467$	7.50529e6	1.59248	0.796242	−	0.604978i	$-0.206818\pi$
$467$	7.50529e6	1.59248	0.796242	+	0.604978i	$0.206818\pi$
$468$	−125185.	−0.0264203
$469$	1.32764e6	0.278707
$470$	−15569.7	−0.00325113
$471$	−1.38462e6	−0.287592
$472$	57789.2	0.0119397
$473$	361777.	0.0743513
$474$	−11958.5	−0.00244473
$475$	−5.59103e6	−1.13699
$476$	705134.	0.142644
$477$	1.01032e6	0.203312
$478$	−27637.2	−0.00553254
$479$	−3.41914e6	−0.680893	−0.340446	−	0.940264i	$-0.610578\pi$
$479$	−3.41914e6	−0.680893	−0.340446	+	0.940264i	$0.610578\pi$
$480$	−26672.9	−0.00528406
$481$	546870.	0.107776
$482$	−22101.9	−0.00433323
$483$	−233289.	−0.0455016
$484$	5.06937e6	0.983651
$485$	1.12868e6	0.217880
$486$	1596.43	0.000306591 0
$487$	−6.36790e6	−1.21667	−0.608337	−	0.793679i	$-0.708163\pi$
$487$	−6.36790e6	−1.21667	−0.608337	+	0.793679i	$0.708163\pi$
$488$	76022.2	0.0144508
$489$	−965943.	−0.182675
$490$	−2316.39	−0.000435835 0
$491$	6.48969e6	1.21484	0.607422	−	0.794379i	$-0.292204\pi$
$491$	6.48969e6	1.21484	0.607422	+	0.794379i	$0.292204\pi$
$492$	5.25574e6	0.978862
$493$	−79312.9	−0.0146969
$494$	3942.84	0.000726929 0
$495$	148218.	0.0271886
$496$	−3.88231e6	−0.708574
$497$	2.78961e6	0.506585
$498$	22828.1	0.00412474
$499$	1.65035e6	0.296706	0.148353	−	0.988934i	$-0.452603\pi$
$499$	1.65035e6	0.296706	0.148353	+	0.988934i	$0.452603\pi$
$500$	−5.68270e6	−1.01655
$501$	−1.92361e6	−0.342392
$502$	2946.79	0.000521904 0
$503$	−7.21883e6	−1.27218	−0.636088	−	0.771617i	$-0.719448\pi$
$503$	−7.21883e6	−1.27218	−0.636088	+	0.771617i	$0.719448\pi$
$504$	6867.43	0.00120425
$505$	3.01556e6	0.526186
$506$	−733.377	−0.000127336 0
$507$	−3.32064e6	−0.573723
$508$	7.68838e6	1.32183
$509$	−5.76238e6	−0.985842	−0.492921	−	0.870074i	$-0.664071\pi$
$509$	−5.76238e6	−0.985842	−0.492921	+	0.870074i	$0.664071\pi$
$510$	−3904.80	−0.000664772 0
$511$	−553060.	−0.0936957
$512$	141732.	0.0238943
$513$	2.20126e6	0.369299
$514$	−31031.9	−0.00518085
$515$	−1.93887e6	−0.322130
$516$	2.03185e6	0.335944
$517$	−827546.	−0.136165
$518$	−15000.0	−0.00245622
$519$	−4.67770e6	−0.762280
$520$	2982.10	0.000483631 0
$521$	1.15733e7	1.86794	0.933968	−	0.357357i	$-0.116322\pi$
$521$	1.15733e7	1.86794	0.933968	+	0.357357i	$0.116322\pi$
$522$	−386.217	−6.20376e−5 0
$523$	−6.81354e6	−1.08923	−0.544614	−	0.838687i	$-0.683324\pi$
$523$	−6.81354e6	−1.08923	−0.544614	+	0.838687i	$0.683324\pi$
$524$	8.61137e6	1.37007
$525$	816556.	0.129297
$526$	−7077.46	−0.00111535
$527$	−1.70512e6	−0.267441
$528$	−472548.	−0.0737668
$529$	279841.	0.0434783
$530$	−12033.6	−0.00186082
$531$	−2.70532e6	−0.416373
$532$	4.73457e6	0.725272
$533$	−881412.	−0.134388
$534$	3036.03	0.000460737 0
$535$	1.47967e6	0.223501
$536$	46881.1	0.00704832
$537$	−1.41117e6	−0.211175
$538$	−25550.0	−0.00380571
$539$	−123119.	−0.0182538
$540$	832434.	0.122847
$541$	4.86637e6	0.714845	0.357422	−	0.933943i	$-0.383656\pi$
$541$	4.86637e6	0.714845	0.357422	+	0.933943i	$0.383656\pi$
$542$	60828.0	0.00889417
$543$	−5.40381e6	−0.786503
$544$	37349.2	0.00541109
$545$	−6.35946e6	−0.917126
$546$	−575.843	−8.26652e−5 0
$547$	1.66890e6	0.238486	0.119243	−	0.992865i	$-0.461953\pi$
$547$	1.66890e6	0.238486	0.119243	+	0.992865i	$0.461953\pi$
$548$	−5.36812e6	−0.763609
$549$	−3.55887e6	−0.503943
$550$	2566.96	0.000361836 0
$551$	−532540.	−0.0747262
$552$	−8237.80	−0.00115070
$553$	2.40820e6	0.334873
$554$	30607.9	0.00423701
$555$	−3.63648e6	−0.501128
$556$	−3.59250e6	−0.492844
$557$	−1.12709e7	−1.53930	−0.769648	−	0.638468i	$-0.779569\pi$
$557$	−1.12709e7	−1.53930	−0.769648	+	0.638468i	$0.779569\pi$
$558$	−8303.15	−0.00112890
$559$	−340750.	−0.0461218
$560$	1.79039e6	0.241256
$561$	−207545.	−0.0278422
$562$	−50915.2	−0.00679996
$563$	1.02986e7	1.36933	0.684665	−	0.728858i	$-0.259949\pi$
$563$	1.02986e7	1.36933	0.684665	+	0.728858i	$0.259949\pi$
$564$	−4.64774e6	−0.615239
$565$	107547.	0.0141734
$566$	23892.1	0.00313482
$567$	−321489.	−0.0419961
$568$	98505.4	0.0128112
$569$	−5.45846e6	−0.706789	−0.353394	−	0.935474i	$-0.614973\pi$
$569$	−5.45846e6	−0.706789	−0.353394	+	0.935474i	$0.614973\pi$
$570$	−26218.4	−0.00338002
$571$	−75323.2	−0.00966804	−0.00483402	−	0.999988i	$-0.501539\pi$
$571$	−75323.2	−0.00966804	−0.00483402	+	0.999988i	$0.501539\pi$
$572$	79250.2	0.0101277
$573$	−1.37967e6	−0.175544
$574$	24176.1	0.00306271
$575$	−979497.	−0.123547
$576$	−2.65384e6	−0.333288
$577$	−961139.	−0.120184	−0.0600920	−	0.998193i	$-0.519139\pi$
$577$	−961139.	−0.120184	−0.0600920	+	0.998193i	$0.519139\pi$
$578$	−32919.1	−0.00409853
$579$	6.21101e6	0.769955
$580$	−201386.	−0.0248577
$581$	−4.59711e6	−0.564995
$582$	−7696.10	−0.000941810 0
$583$	−639599.	−0.0779357
$584$	−19529.4	−0.00236950
$585$	−139603.	−0.0168657
$586$	18898.1	0.00227339
$587$	−936022.	−0.112122	−0.0560610	−	0.998427i	$-0.517854\pi$
$587$	−936022.	−0.112122	−0.0560610	+	0.998427i	$0.517854\pi$
$588$	−691472.	−0.0824767
$589$	−1.14489e7	−1.35980
$590$	32222.1	0.00381087
$591$	8.88802e6	1.04673
$592$	1.15938e7	1.35964
$593$	1.47258e7	1.71965	0.859826	−	0.510586i	$-0.170572\pi$
$593$	1.47258e7	1.71965	0.859826	+	0.510586i	$0.170572\pi$
$594$	−1010.65	−0.000117526 0
$595$	786346.	0.0910587
$596$	7.36496e6	0.849288
$597$	−4.37826e6	−0.502766
$598$	690.750	7.89893e−5 0
$599$	−1.49680e7	−1.70450	−0.852249	−	0.523137i	$-0.824762\pi$
$599$	−1.49680e7	−1.70450	−0.852249	+	0.523137i	$0.824762\pi$
$600$	28833.9	0.00326983
$601$	7.42670e6	0.838706	0.419353	−	0.907823i	$-0.362257\pi$
$601$	7.42670e6	0.838706	0.419353	+	0.907823i	$0.362257\pi$
$602$	9346.36	0.00105112
$603$	−2.19467e6	−0.245797
$604$	−9.78203e6	−1.09103
$605$	5.65323e6	0.627925
$606$	−20562.0	−0.00227449
$607$	2.21817e6	0.244356	0.122178	−	0.992508i	$-0.461012\pi$
$607$	2.21817e6	0.244356	0.122178	+	0.992508i	$0.461012\pi$
$608$	250778.	0.0275126
$609$	77776.2	0.00849774
$610$	42388.4	0.00461236
$611$	779447.	0.0844663
$612$	−1.16563e6	−0.125800
$613$	−1.20782e6	−0.129823	−0.0649116	−	0.997891i	$-0.520677\pi$
$613$	−1.20782e6	−0.129823	−0.0649116	+	0.997891i	$0.520677\pi$
$614$	11474.9	0.00122837
$615$	5.86106e6	0.624868
$616$	−4347.53	−0.000461626 0
$617$	8.50640e6	0.899566	0.449783	−	0.893138i	$-0.351501\pi$
$617$	8.50640e6	0.899566	0.449783	+	0.893138i	$0.351501\pi$
$618$	13220.5	0.00139244
$619$	−9.84260e6	−1.03248	−0.516242	−	0.856443i	$-0.672669\pi$
$619$	−9.84260e6	−1.03248	−0.516242	+	0.856443i	$0.672669\pi$
$620$	−4.32954e6	−0.452337
$621$	385641.	0.0401286
$622$	52468.7	0.00543781
$623$	−611395.	−0.0631105
$624$	445082.	0.0457592
$625$	−550942.	−0.0564164
$626$	−16096.6	−0.00164172
$627$	−1.39354e6	−0.141563
$628$	4.92297e6	0.498113
$629$	5.09205e6	0.513175
$630$	3829.14	0.000384370 0
$631$	−3.59143e6	−0.359082	−0.179541	−	0.983750i	$-0.557461\pi$
$631$	−3.59143e6	−0.359082	−0.179541	+	0.983750i	$0.557461\pi$
$632$	85037.3	0.00846870
$633$	4.75846e6	0.472017
$634$	36117.5	0.00356857
$635$	8.57387e6	0.843806
$636$	−3.59217e6	−0.352139
$637$	115963.	0.0113232
$638$	244.500	2.37809e−5 0
$639$	−4.61139e6	−0.446766
$640$	126446.	0.0122027
$641$	−360962.	−0.0346990	−0.0173495	−	0.999849i	$-0.505523\pi$
$641$	−360962.	−0.0346990	−0.0173495	+	0.999849i	$0.505523\pi$
$642$	−10089.3	−0.000966107 0
$643$	615777.	0.0587348	0.0293674	−	0.999569i	$-0.490651\pi$
$643$	615777.	0.0587348	0.0293674	+	0.999569i	$0.490651\pi$
$644$	829453.	0.0788092
$645$	2.26586e6	0.214454
$646$	36712.8	0.00346128
$647$	−1.49079e7	−1.40009	−0.700043	−	0.714101i	$-0.746836\pi$
$647$	−1.49079e7	−1.40009	−0.700043	+	0.714101i	$0.746836\pi$
$648$	−11352.3	−0.00106205
$649$	1.71264e6	0.159608
$650$	−2417.76	−0.000224455 0
$651$	1.67208e6	0.154634
$652$	3.43438e6	0.316395
$653$	−2.11883e7	−1.94452	−0.972260	−	0.233903i	$-0.924850\pi$
$653$	−2.11883e7	−1.94452	−0.972260	+	0.233903i	$0.924850\pi$
$654$	43362.9	0.00396437
$655$	9.60316e6	0.874603
$656$	−1.86862e7	−1.69536
$657$	914241.	0.0826319
$658$	−21379.3	−0.00192499
$659$	−1.60782e7	−1.44220	−0.721099	−	0.692832i	$-0.756363\pi$
$659$	−1.60782e7	−1.44220	−0.721099	+	0.692832i	$0.756363\pi$
$660$	−526985.	−0.0470910
$661$	−4.30731e6	−0.383444	−0.191722	−	0.981449i	$-0.561407\pi$
$661$	−4.30731e6	−0.383444	−0.191722	+	0.981449i	$0.561407\pi$
$662$	36230.9	0.00321317
$663$	195481.	0.0172712
$664$	−162331.	−0.0142883
$665$	5.27986e6	0.462986
$666$	24795.9	0.00216618
$667$	−93296.2	−0.00811987
$668$	6.83935e6	0.593026
$669$	−7.42444e6	−0.641355
$670$	26139.9	0.00224966
$671$	2.25299e6	0.193176
$672$	−36625.6	−0.00312868
$673$	−2.26007e7	−1.92347	−0.961733	−	0.273989i	$-0.911657\pi$
$673$	−2.26007e7	−1.92347	−0.961733	+	0.273989i	$0.911657\pi$
$674$	−23300.6	−0.00197569
$675$	−1.34982e6	−0.114029
$676$	1.18065e7	0.993695
$677$	−6.08006e6	−0.509843	−0.254921	−	0.966962i	$-0.582050\pi$
$677$	−6.08006e6	−0.509843	−0.254921	+	0.966962i	$0.582050\pi$
$678$	−733.322	−6.12662e−5 0
$679$	1.54984e6	0.129007
$680$	27767.1	0.00230281
$681$	−1.06098e7	−0.876676
$682$	5256.43	0.000432743 0
$683$	−1.28828e7	−1.05671	−0.528357	−	0.849023i	$-0.677192\pi$
$683$	−1.28828e7	−1.05671	−0.528357	+	0.849023i	$0.677192\pi$
$684$	−7.82653e6	−0.639630
$685$	−5.98638e6	−0.487459
$686$	−3180.73	−0.000258057 0
$687$	−1.80119e6	−0.145602
$688$	−7.22401e6	−0.581845
$689$	602423.	0.0483452
$690$	−4593.23	−0.000367279 0
$691$	−512017.	−0.0407933	−0.0203967	−	0.999792i	$-0.506493\pi$
$691$	−512017.	−0.0407933	−0.0203967	+	0.999792i	$0.506493\pi$
$692$	1.66315e7	1.32028
$693$	203523.	0.0160983
$694$	20385.2	0.00160663
$695$	−4.00626e6	−0.314613
$696$	2746.40	0.000214902 0
$697$	−8.20705e6	−0.639890
$698$	108630.	0.00843937
$699$	−1.95813e6	−0.151582
$700$	−2.90324e6	−0.223944
$701$	−7.05184e6	−0.542010	−0.271005	−	0.962578i	$-0.587356\pi$
$701$	−7.05184e6	−0.542010	−0.271005	+	0.962578i	$0.587356\pi$
$702$	951.904	7.29038e−5 0
$703$	3.41901e7	2.60923
$704$	1.68006e6	0.127759
$705$	−5.18303e6	−0.392745
$706$	−38743.0	−0.00292538
$707$	4.14078e6	0.311554
$708$	9.61870e6	0.721163
$709$	2.26777e7	1.69427	0.847137	−	0.531374i	$-0.178324\pi$
$709$	2.26777e7	1.69427	0.847137	+	0.531374i	$0.178324\pi$
$710$	54924.6	0.00408904
$711$	−3.98090e6	−0.295330
$712$	−21589.3	−0.00159602
$713$	−2.00574e6	−0.147758
$714$	−5361.82	−0.000393611 0
$715$	88377.7	0.00646513
$716$	5.01737e6	0.365758
$717$	−9.20023e6	−0.668345
$718$	−125129.	−0.00905832
$719$	−1.49636e7	−1.07948	−0.539740	−	0.841832i	$-0.681477\pi$
$719$	−1.49636e7	−1.07948	−0.539740	+	0.841832i	$0.681477\pi$
$720$	−2.95963e6	−0.212768
$721$	−2.66234e6	−0.190733
$722$	179562.	0.0128195
$723$	−7.35756e6	−0.523466
$724$	1.92131e7	1.36223
$725$	326554.	0.0230733
$726$	−38547.4	−0.00271427
$727$	−1.71234e7	−1.20158	−0.600791	−	0.799406i	$-0.705148\pi$
$727$	−1.71234e7	−1.20158	−0.600791	+	0.799406i	$0.705148\pi$
$728$	4094.84	0.000286357 0
$729$	531441.	0.0370370
$730$	−10889.2	−0.000756291 0
$731$	−3.17281e6	−0.219609
$732$	1.26535e7	0.872834
$733$	−2.31249e7	−1.58972	−0.794859	−	0.606795i	$-0.792455\pi$
$733$	−2.31249e7	−1.58972	−0.794859	+	0.606795i	$0.792455\pi$
$734$	−29055.8	−0.00199064
$735$	−771111.	−0.0526500
$736$	43934.1	0.00298956
$737$	1.38937e6	0.0942213
$738$	−39964.5	−0.00270106
$739$	9.95526e6	0.670566	0.335283	−	0.942117i	$-0.391168\pi$
$739$	9.95526e6	0.670566	0.335283	+	0.942117i	$0.391168\pi$
$740$	1.29294e7	0.867960
$741$	1.31254e6	0.0878149
$742$	−16523.8	−0.00110179
$743$	−9.56247e6	−0.635474	−0.317737	−	0.948179i	$-0.602923\pi$
$743$	−9.56247e6	−0.635474	−0.317737	+	0.948179i	$0.602923\pi$
$744$	59043.9	0.00391060
$745$	8.21320e6	0.542153
$746$	59991.7	0.00394679
$747$	7.59930e6	0.498279
$748$	737919.	0.0482231
$749$	2.03179e6	0.132335
$750$	43211.1	0.00280506
$751$	3.27229e6	0.211715	0.105858	−	0.994381i	$-0.466241\pi$
$751$	3.27229e6	0.211715	0.105858	+	0.994381i	$0.466241\pi$
$752$	1.65245e7	1.06558
$753$	980966.	0.0630473
$754$	−230.289	−1.47518e−5 0
$755$	−1.09087e7	−0.696472
$756$	1.14305e6	0.0727376
$757$	−4.63993e6	−0.294287	−0.147144	−	0.989115i	$-0.547008\pi$
$757$	−4.63993e6	−0.294287	−0.147144	+	0.989115i	$0.547008\pi$
$758$	66931.3	0.00423113
$759$	−244136.	−0.0153825
$760$	186440.	0.0117086
$761$	85671.5	0.00536259	0.00268130	−	0.999996i	$-0.499147\pi$
$761$	85671.5	0.00536259	0.00268130	+	0.999996i	$0.499147\pi$
$762$	−58462.2	−0.00364744
$763$	−8.73241e6	−0.543028
$764$	4.90536e6	0.304045
$765$	−1.29988e6	−0.0803062
$766$	−57819.9	−0.00356046
$767$	−1.61310e6	−0.0990085
$768$	9.43503e6	0.577218
$769$	−1.27984e7	−0.780441	−0.390220	−	0.920721i	$-0.627601\pi$
$769$	−1.27984e7	−0.780441	−0.390220	+	0.920721i	$0.627601\pi$
$770$	−2424.09	−0.000147341 0
$771$	−1.03303e7	−0.625860
$772$	−2.20831e7	−1.33357
$773$	1.27575e7	0.767922	0.383961	−	0.923349i	$-0.374560\pi$
$773$	1.27575e7	0.767922	0.383961	+	0.923349i	$0.374560\pi$
$774$	−15450.1	−0.000926999 0
$775$	7.02048e6	0.419868
$776$	54727.2	0.00326249
$777$	−4.99339e6	−0.296717
$778$	−41705.8	−0.00247029
$779$	−5.51056e7	−3.25351
$780$	496355.	0.0292116
$781$	2.91931e6	0.171259
$782$	6431.75	0.000376108 0
$783$	−128569.	−0.00749430
$784$	2.45846e6	0.142847
$785$	5.48996e6	0.317976
$786$	−65480.6	−0.00378056
$787$	2.58606e7	1.48834	0.744168	−	0.667992i	$-0.232846\pi$
$787$	2.58606e7	1.48834	0.744168	+	0.667992i	$0.232846\pi$
$788$	−3.16011e7	−1.81295
$789$	−2.35603e6	−0.134738
$790$	47415.1	0.00270302
$791$	147676.	0.00839207
$792$	7186.73	0.000407116 0
$793$	−2.12204e6	−0.119832
$794$	50903.9	0.00286550
$795$	−4.00589e6	−0.224792
$796$	1.55668e7	0.870797
$797$	−1.29087e7	−0.719839	−0.359919	−	0.932983i	$-0.617196\pi$
$797$	−1.29087e7	−0.719839	−0.359919	+	0.932983i	$0.617196\pi$
$798$	−36001.5	−0.00200131
$799$	7.25763e6	0.402187
$800$	−153778.	−0.00849510
$801$	1.01067e6	0.0556583
$802$	−117950.	−0.00647535
$803$	−578774.	−0.0316753
$804$	7.80310e6	0.425723
$805$	924983.	0.0503088
$806$	−4950.91	−0.000268440 0
$807$	−8.50542e6	−0.459740
$808$	146217.	0.00787899
$809$	−210750.	−0.0113213	−0.00566064	−	0.999984i	$-0.501802\pi$
$809$	−210750.	−0.0113213	−0.00566064	+	0.999984i	$0.501802\pi$
$810$	−6329.81	−0.000338983 0
$811$	−1.71456e7	−0.915376	−0.457688	−	0.889113i	$-0.651322\pi$
$811$	−1.71456e7	−0.915376	−0.457688	+	0.889113i	$0.651322\pi$
$812$	−276531.	−0.0147182
$813$	2.02492e7	1.07444
$814$	−15697.4	−0.000830361 0
$815$	3.82993e6	0.201975
$816$	4.14427e6	0.217883
$817$	−2.13036e7	−1.11660
$818$	75926.0	0.00396741
$819$	−191694.	−0.00998616
$820$	−2.08388e7	−1.08228
$821$	−3.01957e7	−1.56346	−0.781730	−	0.623617i	$-0.785662\pi$
$821$	−3.01957e7	−1.56346	−0.781730	+	0.623617i	$0.785662\pi$
$822$	40819.1	0.00210709
$823$	9.48273e6	0.488016	0.244008	−	0.969773i	$-0.421538\pi$
$823$	9.48273e6	0.488016	0.244008	+	0.969773i	$0.421538\pi$
$824$	−94011.5	−0.00482351
$825$	854522.	0.0437108
$826$	44245.4	0.00225641
$827$	1.84420e7	0.937658	0.468829	−	0.883289i	$-0.344676\pi$
$827$	1.84420e7	0.937658	0.468829	+	0.883289i	$0.344676\pi$
$828$	−1.37114e6	−0.0695032
$829$	1.76467e7	0.891819	0.445909	−	0.895078i	$-0.352880\pi$
$829$	1.76467e7	0.891819	0.445909	+	0.895078i	$0.352880\pi$
$830$	−90512.6	−0.00456052
$831$	1.01891e7	0.511841
$832$	−1.58241e6	−0.0792519
$833$	1.07976e6	0.0539157
$834$	27317.3	0.00135995
$835$	7.62706e6	0.378565
$836$	4.95470e6	0.245189
$837$	−2.76406e6	−0.136375
$838$	8845.87	0.000435142 0
$839$	8.46366e6	0.415101	0.207550	−	0.978224i	$-0.433451\pi$
$839$	8.46366e6	0.415101	0.207550	+	0.978224i	$0.433451\pi$
$840$	−27229.1	−0.00133148
$841$	−2.04800e7	−0.998484
$842$	82627.6	0.00401647
$843$	−1.69493e7	−0.821453
$844$	−1.69186e7	−0.817538
$845$	1.31662e7	0.634337
$846$	35341.3	0.00169768
$847$	7.76266e6	0.371793
$848$	1.27716e7	0.609895
$849$	7.95350e6	0.378695
$850$	−22512.4	−0.00106874
$851$	5.98980e6	0.283523
$852$	1.63957e7	0.773803
$853$	−9.36957e6	−0.440907	−0.220454	−	0.975397i	$-0.570754\pi$
$853$	−9.36957e6	−0.440907	−0.220454	+	0.975397i	$0.570754\pi$
$854$	58205.1	0.00273097
$855$	−8.72793e6	−0.408316
$856$	71745.6	0.00334665
$857$	2.50380e7	1.16452	0.582261	−	0.813002i	$-0.302168\pi$
$857$	2.50380e7	1.16452	0.582261	+	0.813002i	$0.302168\pi$
$858$	−602.617	−2.79462e−5 0
$859$	2.19821e7	1.01645	0.508226	−	0.861224i	$-0.330301\pi$
$859$	2.19821e7	1.01645	0.508226	+	0.861224i	$0.330301\pi$
$860$	−8.05620e6	−0.371436
$861$	8.04804e6	0.369983
$862$	−87705.4	−0.00402030
$863$	3.82245e7	1.74709	0.873545	−	0.486743i	$-0.161815\pi$
$863$	3.82245e7	1.74709	0.873545	+	0.486743i	$0.161815\pi$
$864$	60544.4	0.00275924
$865$	1.85469e7	0.842815
$866$	133394.	0.00604425
$867$	−1.09585e7	−0.495114
$868$	−5.94505e6	−0.267828
$869$	2.52017e6	0.113209
$870$	1531.34	6.85919e−5 0
$871$	−1.30861e6	−0.0584476
$872$	−308355.	−0.0137328
$873$	−2.56198e6	−0.113773
$874$	43185.5	0.00191231
$875$	−8.70184e6	−0.384230
$876$	−3.25056e6	−0.143119
$877$	−2.69163e7	−1.18173	−0.590863	−	0.806772i	$-0.701213\pi$
$877$	−2.69163e7	−1.18173	−0.590863	+	0.806772i	$0.701213\pi$
$878$	−169703.	−0.00742938
$879$	6.29103e6	0.274631
$880$	1.87364e6	0.0815603
$881$	3.27344e7	1.42091	0.710453	−	0.703745i	$-0.248490\pi$
$881$	3.27344e7	1.42091	0.710453	+	0.703745i	$0.248490\pi$
$882$	5257.94	0.000227585 0
$883$	1.76233e7	0.760652	0.380326	−	0.924852i	$-0.375812\pi$
$883$	1.76233e7	0.760652	0.380326	+	0.924852i	$0.375812\pi$
$884$	−695029.	−0.0299139
$885$	1.07265e7	0.460363
$886$	−36499.4	−0.00156207
$887$	−3.32442e7	−1.41875	−0.709376	−	0.704830i	$-0.751023\pi$
$887$	−3.32442e7	−1.41875	−0.709376	+	0.704830i	$0.751023\pi$
$888$	−176324.	−0.00750378
$889$	1.17731e7	0.499616
$890$	−12037.8	−0.000509414 0
$891$	−336437.	−0.0141974
$892$	2.63974e7	1.11083
$893$	4.87307e7	2.04491
$894$	−56003.0	−0.00234351
$895$	5.59523e6	0.233486
$896$	173628.	0.00722519
$897$	229946.	0.00954211
$898$	−69572.2	−0.00287902
$899$	668694.	0.0275949
$900$	4.79924e6	0.197500
$901$	5.60932e6	0.230196
$902$	25300.1	0.00103540
$903$	3.11134e6	0.126978
$904$	5214.68	0.000212230 0
$905$	2.14259e7	0.869597
$906$	74382.3	0.00301057
$907$	2.35695e7	0.951330	0.475665	−	0.879626i	$-0.342207\pi$
$907$	2.35695e7	0.951330	0.475665	+	0.879626i	$0.342207\pi$
$908$	3.77228e7	1.51841
$909$	−6.84496e6	−0.274765
$910$	2283.20	9.13987e−5 0
$911$	8.26975e6	0.330139	0.165069	−	0.986282i	$-0.447215\pi$
$911$	8.26975e6	0.330139	0.165069	+	0.986282i	$0.447215\pi$
$912$	2.78264e7	1.10782
$913$	−4.81085e6	−0.191005
$914$	135462.	0.00536355
$915$	1.41108e7	0.557184
$916$	6.40410e6	0.252185
$917$	1.31865e7	0.517851
$918$	8863.42	0.000347132 0
$919$	−3.11753e7	−1.21765	−0.608824	−	0.793305i	$-0.708358\pi$
$919$	−3.11753e7	−1.21765	−0.608824	+	0.793305i	$0.708358\pi$
$920$	32662.6	0.00127228
$921$	3.81991e6	0.148390
$922$	−163507.	−0.00633446
$923$	−2.74963e6	−0.106236
$924$	−723622.	−0.0278825
$925$	−2.09655e7	−0.805657
$926$	−89499.2	−0.00342998
$927$	4.40101e6	0.168211
$928$	−14647.2	−0.000558321 0
$929$	4.39341e7	1.67018	0.835089	−	0.550115i	$-0.185416\pi$
$929$	4.39341e7	1.67018	0.835089	+	0.550115i	$0.185416\pi$
$930$	32921.7	0.00124817
$931$	7.24997e6	0.274133
$932$	6.96207e6	0.262542
$933$	1.74664e7	0.656902
$934$	202911.	0.00761094
$935$	822907.	0.0307838
$936$	−6769.02	−0.000252543 0
$937$	1.24662e7	0.463859	0.231930	−	0.972733i	$-0.425496\pi$
$937$	1.24662e7	0.463859	0.231930	+	0.972733i	$0.425496\pi$
$938$	35893.7	0.00133202
$939$	−5.35846e6	−0.198324
$940$	1.84281e7	0.680239
$941$	−2.40360e7	−0.884886	−0.442443	−	0.896797i	$-0.645888\pi$
$941$	−2.40360e7	−0.884886	−0.442443	+	0.896797i	$0.645888\pi$
$942$	−37434.1	−0.00137449
$943$	−9.65400e6	−0.353531
$944$	−3.41983e7	−1.24903
$945$	1.27469e6	0.0464329
$946$	9780.92	0.000355346 0
$947$	−4.44717e7	−1.61142	−0.805711	−	0.592309i	$-0.798216\pi$
$947$	−4.44717e7	−1.61142	−0.805711	+	0.592309i	$0.798216\pi$
$948$	1.41540e7	0.511515
$949$	545134.	0.0196489
$950$	−151158.	−0.00543401
$951$	1.20233e7	0.431093
$952$	38128.1	0.00136349
$953$	−3.03999e7	−1.08428	−0.542139	−	0.840289i	$-0.682385\pi$
$953$	−3.03999e7	−1.08428	−0.542139	+	0.840289i	$0.682385\pi$
$954$	27314.8	0.000971688 0
$955$	5.47033e6	0.194091
$956$	3.27112e7	1.15758
$957$	81392.4	0.00287279
$958$	−92439.1	−0.00325418
$959$	−8.22013e6	−0.288624
$960$	1.05224e7	0.368500
$961$	−1.42531e7	−0.497853
$962$	14785.0	0.000515092 0
$963$	−3.35867e6	−0.116708
$964$	2.61596e7	0.906649
$965$	−2.46264e7	−0.851301
$966$	−6307.14	−0.000217465 0
$967$	−5.35943e7	−1.84312	−0.921558	−	0.388241i	$-0.873083\pi$
$967$	−5.35943e7	−1.84312	−0.921558	+	0.388241i	$0.873083\pi$
$968$	274112.	0.00940241
$969$	1.22214e7	0.418131
$970$	30514.8	0.00104131
$971$	5.07462e7	1.72725	0.863626	−	0.504134i	$-0.168188\pi$
$971$	5.07462e7	1.72725	0.863626	+	0.504134i	$0.168188\pi$
$972$	−1.88952e6	−0.0641486
$973$	−5.50114e6	−0.186282
$974$	−172161.	−0.00581483
$975$	−804855.	−0.0271148
$976$	−4.49881e7	−1.51172
$977$	1.33870e7	0.448692	0.224346	−	0.974510i	$-0.427975\pi$
$977$	1.33870e7	0.448692	0.224346	+	0.974510i	$0.427975\pi$
$978$	−26115.0	−0.000873057 0
$979$	−639822.	−0.0213355
$980$	2.74166e6	0.0911904
$981$	1.44352e7	0.478906
$982$	175454.	0.00580609
$983$	3.47563e7	1.14723	0.573614	−	0.819126i	$-0.305541\pi$
$983$	3.47563e7	1.14723	0.573614	+	0.819126i	$0.305541\pi$
$984$	284189.	0.00935663
$985$	−3.52407e7	−1.15732
$986$	−2144.28	−7.02408e−5 0
$987$	−7.11701e6	−0.232544
$988$	−4.66672e6	−0.152096
$989$	−3.73219e6	−0.121331
$990$	4007.18	0.000129942 0
$991$	1.14038e7	0.368863	0.184431	−	0.982845i	$-0.440956\pi$
$991$	1.14038e7	0.368863	0.184431	+	0.982845i	$0.440956\pi$
$992$	−314895.	−0.0101598
$993$	1.20610e7	0.388159
$994$	75419.1	0.00242111
$995$	1.73597e7	0.555884
$996$	−2.70191e7	−0.863024
$997$	3.75364e7	1.19595	0.597977	−	0.801513i	$-0.295971\pi$
$997$	3.75364e7	1.19595	0.597977	+	0.801513i	$0.295971\pi$
$998$	44618.6	0.00141804
$999$	8.25438e6	0.261680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.6.a.b.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.6.a.b.1.7	✓	12	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0270357 q^{2} +9.00000 q^{3} -31.9993 q^{4} -35.6847 q^{5} +0.243322 q^{6} -49.0000 q^{7} -1.73027 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+0.0270357 q^{2} +9.00000 q^{3} -31.9993 q^{4} -35.6847 q^{5} +0.243322 q^{6} -49.0000 q^{7} -1.73027 q^{8} +81.0000 q^{9} -0.964762 q^{10} -51.2783 q^{11} -287.993 q^{12} +48.2978 q^{13} -1.32475 q^{14} -321.162 q^{15} +1023.93 q^{16} +449.713 q^{17} +2.18989 q^{18} +3019.56 q^{19} +1141.88 q^{20} -441.000 q^{21} -1.38635 q^{22} +529.000 q^{23} -15.5724 q^{24} -1851.60 q^{25} +1.30577 q^{26} +729.000 q^{27} +1567.96 q^{28} -176.363 q^{29} -8.68286 q^{30} -3791.57 q^{31} +83.0512 q^{32} -461.504 q^{33} +12.1583 q^{34} +1748.55 q^{35} -2591.94 q^{36} +11322.9 q^{37} +81.6361 q^{38} +434.680 q^{39} +61.7441 q^{40} -18249.5 q^{41} -11.9228 q^{42} -7055.18 q^{43} +1640.87 q^{44} -2890.46 q^{45} +14.3019 q^{46} +16138.3 q^{47} +9215.37 q^{48} +2401.00 q^{49} -50.0594 q^{50} +4047.42 q^{51} -1545.49 q^{52} +12473.1 q^{53} +19.7091 q^{54} +1829.85 q^{55} +84.7831 q^{56} +27176.1 q^{57} -4.76811 q^{58} -33399.0 q^{59} +10277.0 q^{60} -43936.7 q^{61} -102.508 q^{62} -3969.00 q^{63} -32763.5 q^{64} -1723.49 q^{65} -12.4771 q^{66} -27094.7 q^{67} -14390.5 q^{68} +4761.00 q^{69} +47.2734 q^{70} -56930.8 q^{71} -140.152 q^{72} +11286.9 q^{73} +306.122 q^{74} -16664.4 q^{75} -96623.8 q^{76} +2512.63 q^{77} +11.7519 q^{78} -49146.9 q^{79} -36538.6 q^{80} +6561.00 q^{81} -493.389 q^{82} +93818.6 q^{83} +14111.7 q^{84} -16047.9 q^{85} -190.742 q^{86} -1587.27 q^{87} +88.7251 q^{88} +12477.5 q^{89} -78.1457 q^{90} -2366.59 q^{91} -16927.6 q^{92} -34124.2 q^{93} +436.312 q^{94} -107752. q^{95} +747.461 q^{96} -31629.3 q^{97} +64.9128 q^{98} -4153.54 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9} + 528 q^{10} - 1425 q^{11} + 1377 q^{12} - 70 q^{13} + 49 q^{14} - 1458 q^{15} + 3865 q^{16} - 398 q^{17} - 81 q^{18} - 1293 q^{19} - 8593 q^{20} - 5292 q^{21} + 4961 q^{22} + 6348 q^{23} - 4428 q^{24} + 5830 q^{25} - 5187 q^{26} + 8748 q^{27} - 7497 q^{28} - 5127 q^{29} + 4752 q^{30} + 6498 q^{31} - 28485 q^{32} - 12825 q^{33} - 14527 q^{34} + 7938 q^{35} + 12393 q^{36} - 35545 q^{37} - 32617 q^{38} - 630 q^{39} + 35789 q^{40} - 7806 q^{41} + 441 q^{42} - 66142 q^{43} - 83253 q^{44} - 13122 q^{45} - 529 q^{46} - 16432 q^{47} + 34785 q^{48} + 28812 q^{49} - 177328 q^{50} - 3582 q^{51} - 187010 q^{52} - 67456 q^{53} - 729 q^{54} - 10453 q^{55} + 24108 q^{56} - 11637 q^{57} - 92677 q^{58} - 36346 q^{59} - 77337 q^{60} - 8768 q^{61} - 141813 q^{62} - 47628 q^{63} - 24604 q^{64} + 121875 q^{65} + 44649 q^{66} - 123617 q^{67} + 17217 q^{68} + 57132 q^{69} - 25872 q^{70} - 108667 q^{71} - 39852 q^{72} - 107406 q^{73} - 87825 q^{74} + 52470 q^{75} + 120191 q^{76} + 69825 q^{77} - 46683 q^{78} - 39470 q^{79} - 513682 q^{80} + 78732 q^{81} + 150219 q^{82} - 181838 q^{83} - 67473 q^{84} - 52633 q^{85} + 125713 q^{86} - 46143 q^{87} + 120642 q^{88} - 277361 q^{89} + 42768 q^{90} + 3430 q^{91} + 80937 q^{92} + 58482 q^{93} - 40880 q^{94} - 272491 q^{95} - 256365 q^{96} - 169005 q^{97} - 2401 q^{98} - 115425 q^{99}+O(q^{100}) \) 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9 + 528 * q^10 - 1425 * q^11 + 1377 * q^12 - 70 * q^13 + 49 * q^14 - 1458 * q^15 + 3865 * q^16 - 398 * q^17 - 81 * q^18 - 1293 * q^19 - 8593 * q^20 - 5292 * q^21 + 4961 * q^22 + 6348 * q^23 - 4428 * q^24 + 5830 * q^25 - 5187 * q^26 + 8748 * q^27 - 7497 * q^28 - 5127 * q^29 + 4752 * q^30 + 6498 * q^31 - 28485 * q^32 - 12825 * q^33 - 14527 * q^34 + 7938 * q^35 + 12393 * q^36 - 35545 * q^37 - 32617 * q^38 - 630 * q^39 + 35789 * q^40 - 7806 * q^41 + 441 * q^42 - 66142 * q^43 - 83253 * q^44 - 13122 * q^45 - 529 * q^46 - 16432 * q^47 + 34785 * q^48 + 28812 * q^49 - 177328 * q^50 - 3582 * q^51 - 187010 * q^52 - 67456 * q^53 - 729 * q^54 - 10453 * q^55 + 24108 * q^56 - 11637 * q^57 - 92677 * q^58 - 36346 * q^59 - 77337 * q^60 - 8768 * q^61 - 141813 * q^62 - 47628 * q^63 - 24604 * q^64 + 121875 * q^65 + 44649 * q^66 - 123617 * q^67 + 17217 * q^68 + 57132 * q^69 - 25872 * q^70 - 108667 * q^71 - 39852 * q^72 - 107406 * q^73 - 87825 * q^74 + 52470 * q^75 + 120191 * q^76 + 69825 * q^77 - 46683 * q^78 - 39470 * q^79 - 513682 * q^80 + 78732 * q^81 + 150219 * q^82 - 181838 * q^83 - 67473 * q^84 - 52633 * q^85 + 125713 * q^86 - 46143 * q^87 + 120642 * q^88 - 277361 * q^89 + 42768 * q^90 + 3430 * q^91 + 80937 * q^92 + 58482 * q^93 - 40880 * q^94 - 272491 * q^95 - 256365 * q^96 - 169005 * q^97 - 2401 * q^98 - 115425 * q^99

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