LMFDB - Embedded newform 483.6.a.b.1.6

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			1.6
Root			$0.238049$ 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)

$f(q)$	$=$	$q-0.238049 q^{2} +9.00000 q^{3} -31.9433 q^{4} -89.8479 q^{5} -2.14244 q^{6} -49.0000 q^{7} +15.2217 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-0.238049 q^{2} +9.00000 q^{3} -31.9433 q^{4} -89.8479 q^{5} -2.14244 q^{6} -49.0000 q^{7} +15.2217 q^{8} +81.0000 q^{9} +21.3882 q^{10} -31.0883 q^{11} -287.490 q^{12} +479.055 q^{13} +11.6644 q^{14} -808.631 q^{15} +1018.56 q^{16} +2321.27 q^{17} -19.2820 q^{18} -1510.80 q^{19} +2870.04 q^{20} -441.000 q^{21} +7.40054 q^{22} +529.000 q^{23} +136.995 q^{24} +4947.65 q^{25} -114.039 q^{26} +729.000 q^{27} +1565.22 q^{28} -2054.25 q^{29} +192.494 q^{30} -897.553 q^{31} -729.561 q^{32} -279.795 q^{33} -552.575 q^{34} +4402.55 q^{35} -2587.41 q^{36} -2080.86 q^{37} +359.644 q^{38} +4311.50 q^{39} -1367.63 q^{40} +16496.0 q^{41} +104.980 q^{42} +12026.3 q^{43} +993.064 q^{44} -7277.68 q^{45} -125.928 q^{46} -29721.2 q^{47} +9167.07 q^{48} +2401.00 q^{49} -1177.78 q^{50} +20891.4 q^{51} -15302.6 q^{52} -14194.8 q^{53} -173.538 q^{54} +2793.22 q^{55} -745.861 q^{56} -13597.2 q^{57} +489.011 q^{58} -15734.4 q^{59} +25830.4 q^{60} -4022.28 q^{61} +213.662 q^{62} -3969.00 q^{63} -32420.3 q^{64} -43042.1 q^{65} +66.6049 q^{66} +295.002 q^{67} -74149.0 q^{68} +4761.00 q^{69} -1048.02 q^{70} +17774.7 q^{71} +1232.95 q^{72} -31078.1 q^{73} +495.348 q^{74} +44528.8 q^{75} +48260.0 q^{76} +1523.33 q^{77} -1026.35 q^{78} -30606.2 q^{79} -91515.8 q^{80} +6561.00 q^{81} -3926.87 q^{82} -60053.9 q^{83} +14087.0 q^{84} -208561. q^{85} -2862.85 q^{86} -18488.2 q^{87} -473.215 q^{88} -83219.7 q^{89} +1732.44 q^{90} -23473.7 q^{91} -16898.0 q^{92} -8077.97 q^{93} +7075.10 q^{94} +135742. q^{95} -6566.05 q^{96} +110772. q^{97} -571.556 q^{98} -2518.15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.238049	−0.0420815	−0.0210408	−	0.999779i	$-0.506698\pi$
$2$	−0.238049	−0.0420815	−0.0210408	+	0.999779i	$0.506698\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−31.9433	−0.998229
$5$	−89.8479	−1.60725	−0.803624	−	0.595137i	$-0.797098\pi$
$5$	−89.8479	−1.60725	−0.803624	+	0.595137i	$0.797098\pi$
$6$	−2.14244	−0.0242958
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	15.2217	0.0840885
$9$	81.0000	0.333333
$10$	21.3882	0.0676355
$11$	−31.0883	−0.0774668	−0.0387334	−	0.999250i	$-0.512332\pi$
$11$	−31.0883	−0.0774668	−0.0387334	+	0.999250i	$0.512332\pi$
$12$	−287.490	−0.576328
$13$	479.055	0.786189	0.393095	−	0.919498i	$-0.371404\pi$
$13$	479.055	0.786189	0.393095	+	0.919498i	$0.371404\pi$
$14$	11.6644	0.0159053
$15$	−808.631	−0.927945
$16$	1018.56	0.994691
$17$	2321.27	1.94806	0.974030	−	0.226417i	$-0.0727013\pi$
$17$	2321.27	1.94806	0.974030	+	0.226417i	$0.0727013\pi$
$18$	−19.2820	−0.0140272
$19$	−1510.80	−0.960114	−0.480057	−	0.877237i	$-0.659384\pi$
$19$	−1510.80	−0.960114	−0.480057	+	0.877237i	$0.659384\pi$
$20$	2870.04	1.60440
$21$	−441.000	−0.218218
$22$	7.40054	0.00325992
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	136.995	0.0485485
$25$	4947.65	1.58325
$26$	−114.039	−0.0330840
$27$	729.000	0.192450
$28$	1565.22	0.377295
$29$	−2054.25	−0.453584	−0.226792	−	0.973943i	$-0.572824\pi$
$29$	−2054.25	−0.453584	−0.226792	+	0.973943i	$0.572824\pi$
$30$	192.494	0.0390493
$31$	−897.553	−0.167747	−0.0838737	−	0.996476i	$-0.526729\pi$
$31$	−897.553	−0.167747	−0.0838737	+	0.996476i	$0.526729\pi$
$32$	−729.561	−0.125947
$33$	−279.795	−0.0447255
$34$	−552.575	−0.0819774
$35$	4402.55	0.607483
$36$	−2587.41	−0.332743
$37$	−2080.86	−0.249884	−0.124942	−	0.992164i	$-0.539875\pi$
$37$	−2080.86	−0.249884	−0.124942	+	0.992164i	$0.539875\pi$
$38$	359.644	0.0404031
$39$	4311.50	0.453907
$40$	−1367.63	−0.135151
$41$	16496.0	1.53257	0.766285	−	0.642501i	$-0.222103\pi$
$41$	16496.0	1.53257	0.766285	+	0.642501i	$0.222103\pi$
$42$	104.980	0.00918294
$43$	12026.3	0.991884	0.495942	−	0.868356i	$-0.334823\pi$
$43$	12026.3	0.991884	0.495942	+	0.868356i	$0.334823\pi$
$44$	993.064	0.0773296
$45$	−7277.68	−0.535749
$46$	−125.928	−0.00877460
$47$	−29721.2	−1.96255	−0.981276	−	0.192606i	$-0.938306\pi$
$47$	−29721.2	−1.96255	−0.981276	+	0.192606i	$0.938306\pi$
$48$	9167.07	0.574285
$49$	2401.00	0.142857
$50$	−1177.78	−0.0666254
$51$	20891.4	1.12471
$52$	−15302.6	−0.784797
$53$	−14194.8	−0.694126	−0.347063	−	0.937842i	$-0.612821\pi$
$53$	−14194.8	−0.694126	−0.347063	+	0.937842i	$0.612821\pi$
$54$	−173.538	−0.00809859
$55$	2793.22	0.124508
$56$	−745.861	−0.0317825
$57$	−13597.2	−0.554322
$58$	489.011	0.0190875
$59$	−15734.4	−0.588464	−0.294232	−	0.955734i	$-0.595064\pi$
$59$	−15734.4	−0.588464	−0.294232	+	0.955734i	$0.595064\pi$
$60$	25830.4	0.926302
$61$	−4022.28	−0.138404	−0.0692018	−	0.997603i	$-0.522045\pi$
$61$	−4022.28	−0.138404	−0.0692018	+	0.997603i	$0.522045\pi$
$62$	213.662	0.00705906
$63$	−3969.00	−0.125988
$64$	−32420.3	−0.989391
$65$	−43042.1	−1.26360
$66$	66.6049	0.00188212
$67$	295.002	0.00802858	0.00401429	−	0.999992i	$-0.498722\pi$
$67$	295.002	0.00802858	0.00401429	+	0.999992i	$0.498722\pi$
$68$	−74149.0	−1.94461
$69$	4761.00	0.120386
$70$	−1048.02	−0.0255638
$71$	17774.7	0.418462	0.209231	−	0.977866i	$-0.432904\pi$
$71$	17774.7	0.418462	0.209231	+	0.977866i	$0.432904\pi$
$72$	1232.95	0.0280295
$73$	−31078.1	−0.682570	−0.341285	−	0.939960i	$-0.610862\pi$
$73$	−31078.1	−0.682570	−0.341285	+	0.939960i	$0.610862\pi$
$74$	495.348	0.0105155
$75$	44528.8	0.914088
$76$	48260.0	0.958414
$77$	1523.33	0.0292797
$78$	−1026.35	−0.0191011
$79$	−30606.2	−0.551750	−0.275875	−	0.961194i	$-0.588968\pi$
$79$	−30606.2	−0.551750	−0.275875	+	0.961194i	$0.588968\pi$
$80$	−91515.8	−1.59871
$81$	6561.00	0.111111
$82$	−3926.87	−0.0644928
$83$	−60053.9	−0.956855	−0.478428	−	0.878127i	$-0.658793\pi$
$83$	−60053.9	−0.956855	−0.478428	+	0.878127i	$0.658793\pi$
$84$	14087.0	0.217831
$85$	−208561.	−3.13102
$86$	−2862.85	−0.0417400
$87$	−18488.2	−0.261877
$88$	−473.215	−0.00651407
$89$	−83219.7	−1.11366	−0.556828	−	0.830628i	$-0.687982\pi$
$89$	−83219.7	−1.11366	−0.556828	+	0.830628i	$0.687982\pi$
$90$	1732.44	0.0225452
$91$	−23473.7	−0.297152
$92$	−16898.0	−0.208145
$93$	−8077.97	−0.0968490
$94$	7075.10	0.0825872
$95$	135742.	1.54314
$96$	−6566.05	−0.0727153
$97$	110772.	1.19537	0.597685	−	0.801731i	$-0.296087\pi$
$97$	110772.	1.19537	0.597685	+	0.801731i	$0.296087\pi$
$98$	−571.556	−0.00601165
$99$	−2518.15	−0.0258223
$100$	−158044.	−1.58044
$101$	68516.2	0.668328	0.334164	−	0.942515i	$-0.391546\pi$
$101$	68516.2	0.668328	0.334164	+	0.942515i	$0.391546\pi$
$102$	−4973.18	−0.0473297
$103$	37963.7	0.352595	0.176297	−	0.984337i	$-0.443588\pi$
$103$	37963.7	0.352595	0.176297	+	0.984337i	$0.443588\pi$
$104$	7292.01	0.0661095
$105$	39622.9	0.350730
$106$	3379.05	0.0292099
$107$	233512.	1.97174	0.985870	−	0.167514i	$-0.0535740\pi$
$107$	233512.	1.97174	0.985870	+	0.167514i	$0.0535740\pi$
$108$	−23286.7	−0.192109
$109$	−17810.1	−0.143582	−0.0717910	−	0.997420i	$-0.522871\pi$
$109$	−17810.1	−0.143582	−0.0717910	+	0.997420i	$0.522871\pi$
$110$	−664.923	−0.00523950
$111$	−18727.8	−0.144271
$112$	−49909.6	−0.375958
$113$	−46746.8	−0.344394	−0.172197	−	0.985062i	$-0.555087\pi$
$113$	−46746.8	−0.344394	−0.172197	+	0.985062i	$0.555087\pi$
$114$	3236.80	0.0233267
$115$	−47529.5	−0.335134
$116$	65619.5	0.452780
$117$	38803.5	0.262063
$118$	3745.55	0.0247634
$119$	−113742.	−0.736298
$120$	−12308.7	−0.0780295
$121$	−160085.	−0.993999
$122$	957.499	0.00582423
$123$	148464.	0.884829
$124$	28670.8	0.167450
$125$	−163761.	−0.937422
$126$	944.817	0.00530177
$127$	212557.	1.16941	0.584703	−	0.811247i	$-0.301211\pi$
$127$	212557.	1.16941	0.584703	+	0.811247i	$0.301211\pi$
$128$	31063.6	0.167582
$129$	108237.	0.572664
$130$	10246.1	0.0531743
$131$	100281.	0.510554	0.255277	−	0.966868i	$-0.417833\pi$
$131$	100281.	0.510554	0.255277	+	0.966868i	$0.417833\pi$
$132$	8937.58	0.0446462
$133$	74029.2	0.362889
$134$	−70.2251	−0.000337855 0
$135$	−65499.1	−0.309315
$136$	35333.5	0.163810
$137$	−390694.	−1.77842	−0.889211	−	0.457497i	$-0.848746\pi$
$137$	−390694.	−1.77842	−0.889211	+	0.457497i	$0.848746\pi$
$138$	−1133.35	−0.00506602
$139$	−80714.5	−0.354335	−0.177168	−	0.984181i	$-0.556693\pi$
$139$	−80714.5	−0.354335	−0.177168	+	0.984181i	$0.556693\pi$
$140$	−140632.	−0.606407
$141$	−267491.	−1.13308
$142$	−4231.25	−0.0176095
$143$	−14893.0	−0.0609035
$144$	82503.6	0.331564
$145$	184570.	0.729022
$146$	7398.11	0.0287236
$147$	21609.0	0.0824786
$148$	66469.7	0.249442
$149$	−404565.	−1.49287	−0.746436	−	0.665458i	$-0.768236\pi$
$149$	−404565.	−1.49287	−0.746436	+	0.665458i	$0.768236\pi$
$150$	−10600.0	−0.0384662
$151$	30239.6	0.107928	0.0539640	−	0.998543i	$-0.482814\pi$
$151$	30239.6	0.107928	0.0539640	+	0.998543i	$0.482814\pi$
$152$	−22996.9	−0.0807346
$153$	188023.	0.649354
$154$	−362.627	−0.00123213
$155$	80643.2	0.269612
$156$	−137724.	−0.453103
$157$	436000.	1.41168	0.705842	−	0.708369i	$-0.250569\pi$
$157$	436000.	1.41168	0.705842	+	0.708369i	$0.250569\pi$
$158$	7285.79	0.0232185
$159$	−127753.	−0.400754
$160$	65549.5	0.202427
$161$	−25921.0	−0.0788110
$162$	−1561.84	−0.00467573
$163$	248065.	0.731301	0.365651	−	0.930752i	$-0.380847\pi$
$163$	248065.	0.731301	0.365651	+	0.930752i	$0.380847\pi$
$164$	−526938.	−1.52986
$165$	25139.0	0.0718849
$166$	14295.8	0.0402659
$167$	90315.4	0.250594	0.125297	−	0.992119i	$-0.460012\pi$
$167$	90315.4	0.250594	0.125297	+	0.992119i	$0.460012\pi$
$168$	−6712.75	−0.0183496
$169$	−141799.	−0.381906
$170$	49647.7	0.131758
$171$	−122375.	−0.320038
$172$	−384160.	−0.990127
$173$	−313817.	−0.797188	−0.398594	−	0.917128i	$-0.630502\pi$
$173$	−313817.	−0.797188	−0.398594	+	0.917128i	$0.630502\pi$
$174$	4401.10	0.0110202
$175$	−242435.	−0.598411
$176$	−31665.4	−0.0770554
$177$	−141609.	−0.339750
$178$	19810.4	0.0468644
$179$	684016.	1.59563	0.797817	−	0.602899i	$-0.205988\pi$
$179$	684016.	1.59563	0.797817	+	0.602899i	$0.205988\pi$
$180$	232473.	0.534801
$181$	−636680.	−1.44452	−0.722262	−	0.691620i	$-0.756897\pi$
$181$	−636680.	−1.44452	−0.722262	+	0.691620i	$0.756897\pi$
$182$	5587.89	0.0125046
$183$	−36200.5	−0.0799073
$184$	8052.25	0.0175337
$185$	186961.	0.401626
$186$	1922.95	0.00407555
$187$	−72164.2	−0.150910
$188$	949393.	1.95908
$189$	−35721.0	−0.0727393
$190$	−32313.3	−0.0649378
$191$	−596543.	−1.18320	−0.591600	−	0.806231i	$-0.701504\pi$
$191$	−596543.	−1.18320	−0.591600	+	0.806231i	$0.701504\pi$
$192$	−291783.	−0.571225
$193$	−480389.	−0.928325	−0.464163	−	0.885750i	$-0.653645\pi$
$193$	−480389.	−0.928325	−0.464163	+	0.885750i	$0.653645\pi$
$194$	−26369.3	−0.0503030
$195$	−387379.	−0.729541
$196$	−76695.9	−0.142604
$197$	−849784.	−1.56007	−0.780033	−	0.625739i	$-0.784798\pi$
$197$	−849784.	−1.56007	−0.780033	+	0.625739i	$0.784798\pi$
$198$	599.444	0.00108664
$199$	202711.	0.362865	0.181432	−	0.983403i	$-0.441927\pi$
$199$	202711.	0.362865	0.181432	+	0.983403i	$0.441927\pi$
$200$	75311.3	0.133133
$201$	2655.02	0.00463530
$202$	−16310.2	−0.0281243
$203$	100658.	0.171439
$204$	−667341.	−1.12272
$205$	−1.48213e6	−2.46322
$206$	−9037.23	−0.0148377
$207$	42849.0	0.0695048
$208$	487948.	0.782015
$209$	46968.2	0.0743769
$210$	−9432.20	−0.0147593
$211$	−980553.	−1.51623	−0.758115	−	0.652121i	$-0.773880\pi$
$211$	−980553.	−1.51623	−0.758115	+	0.652121i	$0.773880\pi$
$212$	453428.	0.692897
$213$	159972.	0.241599
$214$	−55587.3	−0.0829738
$215$	−1.08054e6	−1.59420
$216$	11096.6	0.0161828
$217$	43980.1	0.0634025
$218$	4239.68	0.00604215
$219$	−279703.	−0.394082
$220$	−89224.7	−0.124288
$221$	1.11201e6	1.53154
$222$	4458.13	0.00607114
$223$	229904.	0.309588	0.154794	−	0.987947i	$-0.450529\pi$
$223$	229904.	0.309588	0.154794	+	0.987947i	$0.450529\pi$
$224$	35748.5	0.0476034
$225$	400759.	0.527749
$226$	11128.0	0.0144926
$227$	−860521.	−1.10840	−0.554201	−	0.832383i	$-0.686976\pi$
$227$	−860521.	−1.10840	−0.554201	+	0.832383i	$0.686976\pi$
$228$	434340.	0.553341
$229$	−1.46624e6	−1.84763	−0.923817	−	0.382833i	$-0.874948\pi$
$229$	−1.46624e6	−1.84763	−0.923817	+	0.382833i	$0.874948\pi$
$230$	11314.4	0.0141030
$231$	13709.9	0.0169046
$232$	−31269.0	−0.0381412
$233$	86591.4	0.104492	0.0522462	−	0.998634i	$-0.483362\pi$
$233$	86591.4	0.104492	0.0522462	+	0.998634i	$0.483362\pi$
$234$	−9237.13	−0.0110280
$235$	2.67038e6	3.15431
$236$	502608.	0.587421
$237$	−275456.	−0.318553
$238$	27076.2	0.0309845
$239$	522163.	0.591305	0.295652	−	0.955296i	$-0.404463\pi$
$239$	522163.	0.591305	0.295652	+	0.955296i	$0.404463\pi$
$240$	−823642.	−0.923018
$241$	299779.	0.332475	0.166237	−	0.986086i	$-0.446838\pi$
$241$	299779.	0.332475	0.166237	+	0.986086i	$0.446838\pi$
$242$	38108.0	0.0418290
$243$	59049.0	0.0641500
$244$	128485.	0.138158
$245$	−215725.	−0.229607
$246$	−35341.8	−0.0372350
$247$	−723756.	−0.754832
$248$	−13662.2	−0.0141056
$249$	−540485.	−0.552441
$250$	38983.1	0.0394482
$251$	−244223.	−0.244682	−0.122341	−	0.992488i	$-0.539040\pi$
$251$	−244223.	−0.244682	−0.122341	+	0.992488i	$0.539040\pi$
$252$	126783.	0.125765
$253$	−16445.7	−0.0161529
$254$	−50598.9	−0.0492104
$255$	−1.87705e6	−1.80769
$256$	1.03006e6	0.982338
$257$	−745370.	−0.703946	−0.351973	−	0.936010i	$-0.614489\pi$
$257$	−745370.	−0.703946	−0.351973	+	0.936010i	$0.614489\pi$
$258$	−25765.6	−0.0240986
$259$	101962.	0.0944474
$260$	1.37491e6	1.26136
$261$	−166394.	−0.151195
$262$	−23871.9	−0.0214849
$263$	−912931.	−0.813858	−0.406929	−	0.913460i	$-0.633400\pi$
$263$	−912931.	−0.813858	−0.406929	+	0.913460i	$0.633400\pi$
$264$	−4258.94	−0.00376090
$265$	1.27537e6	1.11563
$266$	−17622.6	−0.0152709
$267$	−748978.	−0.642970
$268$	−9423.36	−0.00801436
$269$	−1.18823e6	−1.00120	−0.500599	−	0.865679i	$-0.666887\pi$
$269$	−1.18823e6	−1.00120	−0.500599	+	0.865679i	$0.666887\pi$
$270$	15592.0	0.0130164
$271$	−89282.2	−0.0738485	−0.0369242	−	0.999318i	$-0.511756\pi$
$271$	−89282.2	−0.0738485	−0.0369242	+	0.999318i	$0.511756\pi$
$272$	2.36436e6	1.93772
$273$	−211263.	−0.171561
$274$	93004.3	0.0748387
$275$	−153814.	−0.122649
$276$	−152082.	−0.120173
$277$	2.21614e6	1.73539	0.867697	−	0.497094i	$-0.165600\pi$
$277$	2.21614e6	1.73539	0.867697	+	0.497094i	$0.165600\pi$
$278$	19214.0	0.0149110
$279$	−72701.8	−0.0559158
$280$	67014.0	0.0510823
$281$	137419.	0.103820	0.0519099	−	0.998652i	$-0.483469\pi$
$281$	137419.	0.103820	0.0519099	+	0.998652i	$0.483469\pi$
$282$	63675.9	0.0476817
$283$	−233132.	−0.173036	−0.0865180	−	0.996250i	$-0.527574\pi$
$283$	−233132.	−0.173036	−0.0865180	+	0.996250i	$0.527574\pi$
$284$	−567783.	−0.417721
$285$	1.22168e6	0.890933
$286$	3545.27	0.00256291
$287$	−808306.	−0.579257
$288$	−59094.4	−0.0419822
$289$	3.96842e6	2.79494
$290$	−43936.6	−0.0306783
$291$	996952.	0.690147
$292$	992738.	0.681361
$293$	−398590.	−0.271242	−0.135621	−	0.990761i	$-0.543303\pi$
$293$	−398590.	−0.271242	−0.135621	+	0.990761i	$0.543303\pi$
$294$	−5144.00	−0.00347083
$295$	1.41370e6	0.945807
$296$	−31674.2	−0.0210124
$297$	−22663.4	−0.0149085
$298$	96306.2	0.0628223
$299$	253420.	0.163932
$300$	−1.42240e6	−0.912469
$301$	−589289.	−0.374897
$302$	−7198.51	−0.00454177
$303$	616646.	0.385860
$304$	−1.53885e6	−0.955017
$305$	361393.	0.222449
$306$	−44758.6	−0.0273258
$307$	502391.	0.304226	0.152113	−	0.988363i	$-0.451392\pi$
$307$	502391.	0.304226	0.152113	+	0.988363i	$0.451392\pi$
$308$	−48660.1	−0.0292278
$309$	341674.	0.203571
$310$	−19197.0	−0.0113457
$311$	−1.88344e6	−1.10421	−0.552103	−	0.833776i	$-0.686174\pi$
$311$	−1.88344e6	−1.10421	−0.552103	+	0.833776i	$0.686174\pi$
$312$	65628.1	0.0381683
$313$	1.43427e6	0.827507	0.413753	−	0.910389i	$-0.364218\pi$
$313$	1.43427e6	0.827507	0.413753	+	0.910389i	$0.364218\pi$
$314$	−103789.	−0.0594058
$315$	356606.	0.202494
$316$	977665.	0.550773
$317$	−871223.	−0.486947	−0.243473	−	0.969908i	$-0.578287\pi$
$317$	−871223.	−0.486947	−0.243473	+	0.969908i	$0.578287\pi$
$318$	30411.4	0.0168643
$319$	63863.0	0.0351377
$320$	2.91290e6	1.59020
$321$	2.10161e6	1.13838
$322$	6170.47	0.00331649
$323$	−3.50697e6	−1.87036
$324$	−209580.	−0.110914
$325$	2.37020e6	1.24473
$326$	−59051.6	−0.0307743
$327$	−160291.	−0.0828971
$328$	251097.	0.128871
$329$	1.45634e6	0.741775
$330$	−5984.31	−0.00302503
$331$	1.73401e6	0.869923	0.434961	−	0.900449i	$-0.356762\pi$
$331$	1.73401e6	0.869923	0.434961	+	0.900449i	$0.356762\pi$
$332$	1.91832e6	0.955161
$333$	−168550.	−0.0832948
$334$	−21499.5	−0.0105454
$335$	−26505.4	−0.0129039
$336$	−449186.	−0.217059
$337$	418669.	0.200815	0.100407	−	0.994946i	$-0.467985\pi$
$337$	418669.	0.200815	0.100407	+	0.994946i	$0.467985\pi$
$338$	33755.2	0.0160712
$339$	−420722.	−0.198836
$340$	6.66213e6	3.12547
$341$	27903.4	0.0129948
$342$	29131.2	0.0134677
$343$	−117649.	−0.0539949
$344$	183060.	0.0834060
$345$	−427766.	−0.193490
$346$	74703.7	0.0335469
$347$	−221993.	−0.0989728	−0.0494864	−	0.998775i	$-0.515758\pi$
$347$	−221993.	−0.0989728	−0.0494864	+	0.998775i	$0.515758\pi$
$348$	590575.	0.261413
$349$	−1.83891e6	−0.808157	−0.404079	−	0.914724i	$-0.632408\pi$
$349$	−1.83891e6	−0.808157	−0.404079	+	0.914724i	$0.632408\pi$
$350$	57711.3	0.0251820
$351$	349231.	0.151302
$352$	22680.8	0.00975668
$353$	1.30852e6	0.558911	0.279455	−	0.960159i	$-0.409846\pi$
$353$	1.30852e6	0.558911	0.279455	+	0.960159i	$0.409846\pi$
$354$	33710.0	0.0142972
$355$	−1.59702e6	−0.672573
$356$	2.65832e6	1.11168
$357$	−1.02368e6	−0.425102
$358$	−162829.	−0.0671467
$359$	−2.33603e6	−0.956625	−0.478312	−	0.878190i	$-0.658751\pi$
$359$	−2.33603e6	−0.956625	−0.478312	+	0.878190i	$0.658751\pi$
$360$	−110778.	−0.0450504
$361$	−193583.	−0.0781805
$362$	151561.	0.0607877
$363$	−1.44076e6	−0.573886
$364$	749828.	0.296625
$365$	2.79230e6	1.09706
$366$	8617.49	0.00336262
$367$	2.56422e6	0.993780	0.496890	−	0.867813i	$-0.334475\pi$
$367$	2.56422e6	0.993780	0.496890	+	0.867813i	$0.334475\pi$
$368$	538820.	0.207407
$369$	1.33618e6	0.510856
$370$	−44505.9	−0.0169010
$371$	695543.	0.262355
$372$	258037.	0.0966775
$373$	−1.88066e6	−0.699905	−0.349952	−	0.936767i	$-0.613802\pi$
$373$	−1.88066e6	−0.699905	−0.349952	+	0.936767i	$0.613802\pi$
$374$	17178.6	0.00635052
$375$	−1.47385e6	−0.541221
$376$	−452405.	−0.165028
$377$	−984097.	−0.356603
$378$	8503.35	0.00306098
$379$	−1.37726e6	−0.492513	−0.246257	−	0.969205i	$-0.579201\pi$
$379$	−1.37726e6	−0.492513	−0.246257	+	0.969205i	$0.579201\pi$
$380$	−4.33606e6	−1.54041
$381$	1.91301e6	0.675157
$382$	142007.	0.0497909
$383$	−5.16770e6	−1.80012	−0.900058	−	0.435769i	$-0.856476\pi$
$383$	−5.16770e6	−1.80012	−0.900058	+	0.435769i	$0.856476\pi$
$384$	279572.	0.0967533
$385$	−136868.	−0.0470597
$386$	114356.	0.0390653
$387$	974130.	0.330628
$388$	−3.53844e6	−1.19325
$389$	−4.53364e6	−1.51905	−0.759526	−	0.650477i	$-0.774569\pi$
$389$	−4.53364e6	−1.51905	−0.759526	+	0.650477i	$0.774569\pi$
$390$	92215.2	0.0307002
$391$	1.22795e6	0.406199
$392$	36547.2	0.0120126
$393$	902531.	0.294768
$394$	202290.	0.0656499
$395$	2.74991e6	0.886799
$396$	80438.2	0.0257765
$397$	−467846.	−0.148980	−0.0744898	−	0.997222i	$-0.523733\pi$
$397$	−467846.	−0.148980	−0.0744898	+	0.997222i	$0.523733\pi$
$398$	−48255.2	−0.0152699
$399$	666263.	0.209514
$400$	5.03949e6	1.57484
$401$	872131.	0.270845	0.135422	−	0.990788i	$-0.456761\pi$
$401$	872131.	0.270845	0.135422	+	0.990788i	$0.456761\pi$
$402$	−632.026	−0.000195061 0
$403$	−429977.	−0.131881
$404$	−2.18864e6	−0.667145
$405$	−589492.	−0.178583
$406$	−23961.6	−0.00721439
$407$	64690.5	0.0193577
$408$	318001.	0.0945755
$409$	3.51701e6	1.03960	0.519799	−	0.854289i	$-0.326007\pi$
$409$	3.51701e6	1.03960	0.519799	+	0.854289i	$0.326007\pi$
$410$	352821.	0.103656
$411$	−3.51624e6	−1.02677
$412$	−1.21269e6	−0.351970
$413$	770985.	0.222418
$414$	−10200.2	−0.00292487
$415$	5.39572e6	1.53790
$416$	−349500.	−0.0990179
$417$	−726430.	−0.204576
$418$	−11180.7	−0.00312990
$419$	−7.05021e6	−1.96186	−0.980928	−	0.194373i	$-0.937733\pi$
$419$	−7.05021e6	−1.96186	−0.980928	+	0.194373i	$0.937733\pi$
$420$	−1.26569e6	−0.350109
$421$	114347.	0.0314426	0.0157213	−	0.999876i	$-0.494996\pi$
$421$	114347.	0.0314426	0.0157213	+	0.999876i	$0.494996\pi$
$422$	233420.	0.0638053
$423$	−2.40741e6	−0.654184
$424$	−216068.	−0.0583680
$425$	1.14848e7	3.08426
$426$	−38081.3	−0.0101669
$427$	197092.	0.0523116
$428$	−7.45915e6	−1.96825
$429$	−134037.	−0.0351627
$430$	257221.	0.0670865
$431$	−5.17776e6	−1.34261	−0.671304	−	0.741182i	$-0.734265\pi$
$431$	−5.17776e6	−1.34261	−0.671304	+	0.741182i	$0.734265\pi$
$432$	742533.	0.191428
$433$	−1.19728e6	−0.306885	−0.153443	−	0.988158i	$-0.549036\pi$
$433$	−1.19728e6	−0.306885	−0.153443	+	0.988158i	$0.549036\pi$
$434$	−10469.4	−0.00266808
$435$	1.66113e6	0.420901
$436$	568914.	0.143328
$437$	−799213.	−0.200198
$438$	66583.0	0.0165836
$439$	3.98465e6	0.986800	0.493400	−	0.869802i	$-0.335754\pi$
$439$	3.98465e6	0.986800	0.493400	+	0.869802i	$0.335754\pi$
$440$	42517.4	0.0104697
$441$	194481.	0.0476190
$442$	−264714.	−0.0644497
$443$	638054.	0.154471	0.0772357	−	0.997013i	$-0.475391\pi$
$443$	638054.	0.154471	0.0772357	+	0.997013i	$0.475391\pi$
$444$	598227.	0.144015
$445$	7.47712e6	1.78992
$446$	−54728.4	−0.0130279
$447$	−3.64108e6	−0.861909
$448$	1.58860e6	0.373954
$449$	6.48402e6	1.51785	0.758925	−	0.651178i	$-0.225725\pi$
$449$	6.48402e6	1.51785	0.758925	+	0.651178i	$0.225725\pi$
$450$	−95400.4	−0.0222085
$451$	−512834.	−0.118723
$452$	1.49325e6	0.343785
$453$	272156.	0.0623122
$454$	204846.	0.0466432
$455$	2.10906e6	0.477596
$456$	−206972.	−0.0466121
$457$	2.45658e6	0.550225	0.275112	−	0.961412i	$-0.411285\pi$
$457$	2.45658e6	0.550225	0.275112	+	0.961412i	$0.411285\pi$
$458$	349037.	0.0777513
$459$	1.69220e6	0.374904
$460$	1.51825e6	0.334541
$461$	−799322.	−0.175174	−0.0875869	−	0.996157i	$-0.527916\pi$
$461$	−799322.	−0.175174	−0.0875869	+	0.996157i	$0.527916\pi$
$462$	−3263.64	−0.000711373 0
$463$	1.14756e6	0.248784	0.124392	−	0.992233i	$-0.460302\pi$
$463$	1.14756e6	0.248784	0.124392	+	0.992233i	$0.460302\pi$
$464$	−2.09238e6	−0.451175
$465$	725789.	0.155660
$466$	−20613.0	−0.00439720
$467$	495074.	0.105046	0.0525228	−	0.998620i	$-0.483274\pi$
$467$	495074.	0.105046	0.0525228	+	0.998620i	$0.483274\pi$
$468$	−1.23951e6	−0.261599
$469$	−14455.1	−0.00303452
$470$	−635683.	−0.132738
$471$	3.92400e6	0.815036
$472$	−239503.	−0.0494830
$473$	−373877.	−0.0768380
$474$	65572.1	0.0134052
$475$	−7.47490e6	−1.52010
$476$	3.63330e6	0.734994
$477$	−1.14978e6	−0.231375
$478$	−124300.	−0.0248830
$479$	5.12139e6	1.01988	0.509940	−	0.860210i	$-0.329668\pi$
$479$	5.12139e6	1.01988	0.509940	+	0.860210i	$0.329668\pi$
$480$	589946.	0.116872
$481$	−996848.	−0.196456
$482$	−71362.1	−0.0139910
$483$	−233289.	−0.0455016
$484$	5.11363e6	0.992239
$485$	−9.95267e6	−1.92126
$486$	−14056.6	−0.00269953
$487$	8.04420e6	1.53695	0.768477	−	0.639878i	$-0.221015\pi$
$487$	8.04420e6	1.53695	0.768477	+	0.639878i	$0.221015\pi$
$488$	−61225.7	−0.0116382
$489$	2.23258e6	0.422217
$490$	51353.1	0.00966221
$491$	−2.47343e6	−0.463016	−0.231508	−	0.972833i	$-0.574366\pi$
$491$	−2.47343e6	−0.463016	−0.231508	+	0.972833i	$0.574366\pi$
$492$	−4.74245e6	−0.883262
$493$	−4.76845e6	−0.883609
$494$	172290.	0.0317645
$495$	226251.	0.0415028
$496$	−914214.	−0.166857
$497$	−870960.	−0.158164
$498$	128662.	0.0232475
$499$	−7.18069e6	−1.29097	−0.645483	−	0.763775i	$-0.723344\pi$
$499$	−7.18069e6	−1.29097	−0.645483	+	0.763775i	$0.723344\pi$
$500$	5.23107e6	0.935762
$501$	812839.	0.144681
$502$	58137.1	0.0102966
$503$	5.15269e6	0.908059	0.454029	−	0.890987i	$-0.349986\pi$
$503$	5.15269e6	0.908059	0.454029	+	0.890987i	$0.349986\pi$
$504$	−60414.7	−0.0105942
$505$	−6.15604e6	−1.07417
$506$	3914.89	0.000679740 0
$507$	−1.27619e6	−0.220494
$508$	−6.78977e6	−1.16734
$509$	−4.36094e6	−0.746081	−0.373040	−	0.927815i	$-0.621685\pi$
$509$	−4.36094e6	−0.746081	−0.373040	+	0.927815i	$0.621685\pi$
$510$	446829.	0.0760705
$511$	1.52283e6	0.257987
$512$	−1.23924e6	−0.208920
$513$	−1.10137e6	−0.184774
$514$	177435.	0.0296231
$515$	−3.41096e6	−0.566707
$516$	−3.45744e6	−0.571650
$517$	923981.	0.152033
$518$	−24272.0	−0.00397449
$519$	−2.82435e6	−0.460257
$520$	−655172.	−0.106254
$521$	−8.75342e6	−1.41281	−0.706405	−	0.707808i	$-0.749684\pi$
$521$	−8.75342e6	−1.41281	−0.706405	+	0.707808i	$0.749684\pi$
$522$	39609.9	0.00636250
$523$	4.94585e6	0.790654	0.395327	−	0.918541i	$-0.370631\pi$
$523$	4.94585e6	0.790654	0.395327	+	0.918541i	$0.370631\pi$
$524$	−3.20332e6	−0.509650
$525$	−2.18191e6	−0.345493
$526$	217322.	0.0342484
$527$	−2.08346e6	−0.326782
$528$	−284989.	−0.0444880
$529$	279841.	0.0434783
$530$	−303600.	−0.0469475
$531$	−1.27448e6	−0.196155
$532$	−2.36474e6	−0.362246
$533$	7.90251e6	1.20489
$534$	178293.	0.0270572
$535$	−2.09806e7	−3.16907
$536$	4490.42	0.000675111 0
$537$	6.15614e6	0.921240
$538$	282857.	0.0421319
$539$	−74643.0	−0.0110667
$540$	2.09226e6	0.308767
$541$	2.27280e6	0.333863	0.166932	−	0.985968i	$-0.446614\pi$
$541$	2.27280e6	0.333863	0.166932	+	0.985968i	$0.446614\pi$
$542$	21253.5	0.00310766
$543$	−5.73012e6	−0.833996
$544$	−1.69350e6	−0.245352
$545$	1.60020e6	0.230772
$546$	50291.0	0.00721953
$547$	−307286.	−0.0439111	−0.0219555	−	0.999759i	$-0.506989\pi$
$547$	−307286.	−0.0439111	−0.0219555	+	0.999759i	$0.506989\pi$
$548$	1.24801e7	1.77527
$549$	−325804.	−0.0461345
$550$	36615.3	0.00516126
$551$	3.10355e6	0.435492
$552$	72470.3	0.0101231
$553$	1.49971e6	0.208542
$554$	−527550.	−0.0730280
$555$	1.68265e6	0.231879
$556$	2.57829e6	0.353708
$557$	−4.90587e6	−0.670005	−0.335003	−	0.942217i	$-0.608737\pi$
$557$	−4.90587e6	−0.670005	−0.335003	+	0.942217i	$0.608737\pi$
$558$	17306.6	0.00235302
$559$	5.76126e6	0.779808
$560$	4.48427e6	0.604257
$561$	−649478.	−0.0871279
$562$	−32712.4	−0.00436890
$563$	5.93857e6	0.789606	0.394803	−	0.918766i	$-0.370813\pi$
$563$	5.93857e6	0.789606	0.394803	+	0.918766i	$0.370813\pi$
$564$	8.54454e6	1.13107
$565$	4.20011e6	0.553527
$566$	55497.0	0.00728162
$567$	−321489.	−0.0419961
$568$	270560.	0.0351879
$569$	−9.37418e6	−1.21381	−0.606907	−	0.794773i	$-0.707590\pi$
$569$	−9.37418e6	−1.21381	−0.606907	+	0.794773i	$0.707590\pi$
$570$	−290820.	−0.0374918
$571$	355527.	0.0456333	0.0228167	−	0.999740i	$-0.492737\pi$
$571$	355527.	0.0456333	0.0228167	+	0.999740i	$0.492737\pi$
$572$	475732.	0.0607957
$573$	−5.36889e6	−0.683121
$574$	192416.	0.0243760
$575$	2.61730e6	0.330130
$576$	−2.62605e6	−0.329797
$577$	1.31514e7	1.64450	0.822249	−	0.569127i	$-0.192719\pi$
$577$	1.31514e7	1.64450	0.822249	+	0.569127i	$0.192719\pi$
$578$	−944678.	−0.117615
$579$	−4.32350e6	−0.535969
$580$	−5.89577e6	−0.727731
$581$	2.94264e6	0.361657
$582$	−237323.	−0.0290424
$583$	441291.	0.0537717
$584$	−473060.	−0.0573963
$585$	−3.48641e6	−0.421200
$586$	94884.0	0.0114143
$587$	−1.74058e6	−0.208497	−0.104248	−	0.994551i	$-0.533244\pi$
$587$	−1.74058e6	−0.208497	−0.104248	+	0.994551i	$0.533244\pi$
$588$	−690263.	−0.0823326
$589$	1.35602e6	0.161057
$590$	−336530.	−0.0398010
$591$	−7.64805e6	−0.900704
$592$	−2.11949e6	−0.248558
$593$	5.28227e6	0.616856	0.308428	−	0.951248i	$-0.400197\pi$
$593$	5.28227e6	0.616856	0.308428	+	0.951248i	$0.400197\pi$
$594$	5395.00	0.000627372 0
$595$	1.02195e7	1.18341
$596$	1.29231e7	1.49023
$597$	1.82440e6	0.209500
$598$	−60326.4	−0.00689850
$599$	−1.67502e7	−1.90745	−0.953725	−	0.300681i	$-0.902786\pi$
$599$	−1.67502e7	−1.90745	−0.953725	+	0.300681i	$0.902786\pi$
$600$	677802.	0.0768643
$601$	−6.63643e6	−0.749460	−0.374730	−	0.927134i	$-0.622265\pi$
$601$	−6.63643e6	−0.749460	−0.374730	+	0.927134i	$0.622265\pi$
$602$	140280.	0.0157762
$603$	23895.2	0.00267619
$604$	−965954.	−0.107737
$605$	1.43833e7	1.59760
$606$	−146792.	−0.0162376
$607$	7.31027e6	0.805307	0.402654	−	0.915352i	$-0.368088\pi$
$607$	7.31027e6	0.805307	0.402654	+	0.915352i	$0.368088\pi$
$608$	1.10222e6	0.120923
$609$	905922.	0.0989801
$610$	−86029.3	−0.00936099
$611$	−1.42381e7	−1.54294
$612$	−6.00607e6	−0.648204
$613$	−1.01014e7	−1.08576	−0.542878	−	0.839811i	$-0.682665\pi$
$613$	−1.01014e7	−1.08576	−0.542878	+	0.839811i	$0.682665\pi$
$614$	−119594.	−0.0128023
$615$	−1.33392e7	−1.42214
$616$	23187.6	0.00246209
$617$	8.01585e6	0.847689	0.423844	−	0.905735i	$-0.360680\pi$
$617$	8.01585e6	0.847689	0.423844	+	0.905735i	$0.360680\pi$
$618$	−81335.1	−0.00856657
$619$	−2.62359e6	−0.275214	−0.137607	−	0.990487i	$-0.543941\pi$
$619$	−2.62359e6	−0.275214	−0.137607	+	0.990487i	$0.543941\pi$
$620$	−2.57601e6	−0.269134
$621$	385641.	0.0401286
$622$	448350.	0.0464667
$623$	4.07777e6	0.420923
$624$	4.39153e6	0.451497
$625$	−747819.	−0.0765766
$626$	−341428.	−0.0348227
$627$	422714.	0.0429415
$628$	−1.39273e7	−1.40918
$629$	−4.83024e6	−0.486790
$630$	−84889.8	−0.00852127
$631$	3.56192e6	0.356132	0.178066	−	0.984019i	$-0.443016\pi$
$631$	3.56192e6	0.356132	0.178066	+	0.984019i	$0.443016\pi$
$632$	−465877.	−0.0463958
$633$	−8.82498e6	−0.875396
$634$	207394.	0.0204915
$635$	−1.90978e7	−1.87953
$636$	4.08085e6	0.400044
$637$	1.15021e6	0.112313
$638$	−15202.5	−0.00147865
$639$	1.43975e6	0.139487
$640$	−2.79100e6	−0.269345
$641$	−2.04196e7	−1.96292	−0.981458	−	0.191679i	$-0.938607\pi$
$641$	−2.04196e7	−1.96292	−0.981458	+	0.191679i	$0.938607\pi$
$642$	−500285.	−0.0479049
$643$	−8.46832e6	−0.807737	−0.403868	−	0.914817i	$-0.632335\pi$
$643$	−8.46832e6	−0.807737	−0.403868	+	0.914817i	$0.632335\pi$
$644$	828003.	0.0786715
$645$	−9.72484e6	−0.920414
$646$	834830.	0.0787076
$647$	1.59901e7	1.50173	0.750863	−	0.660458i	$-0.229638\pi$
$647$	1.59901e7	1.50173	0.750863	+	0.660458i	$0.229638\pi$
$648$	99869.2	0.00934317
$649$	489155.	0.0455864
$650$	−564223.	−0.0523802
$651$	395821.	0.0366055
$652$	−7.92402e6	−0.730006
$653$	−2.33641e6	−0.214420	−0.107210	−	0.994236i	$-0.534192\pi$
$653$	−2.33641e6	−0.214420	−0.107210	+	0.994236i	$0.534192\pi$
$654$	38157.1	0.00348844
$655$	−9.01006e6	−0.820587
$656$	1.68023e7	1.52443
$657$	−2.51732e6	−0.227523
$658$	−346680.	−0.0312150
$659$	−2.15863e6	−0.193627	−0.0968133	−	0.995303i	$-0.530865\pi$
$659$	−2.15863e6	−0.193627	−0.0968133	+	0.995303i	$0.530865\pi$
$660$	−803023.	−0.0717576
$661$	7.07659e6	0.629971	0.314986	−	0.949096i	$-0.398000\pi$
$661$	7.07659e6	0.629971	0.314986	+	0.949096i	$0.398000\pi$
$662$	−412779.	−0.0366077
$663$	1.00081e7	0.884238
$664$	−914120.	−0.0804605
$665$	−6.65137e6	−0.583253
$666$	40123.1	0.00350517
$667$	−1.08670e6	−0.0945787
$668$	−2.88498e6	−0.250150
$669$	2.06914e6	0.178741
$670$	6309.57	0.000543017 0
$671$	125046.	0.0107217
$672$	321736.	0.0274838
$673$	−2.33222e7	−1.98487	−0.992434	−	0.122780i	$-0.960819\pi$
$673$	−2.33222e7	−1.98487	−0.992434	+	0.122780i	$0.960819\pi$
$674$	−99663.7	−0.00845059
$675$	3.60683e6	0.304696
$676$	4.52954e6	0.381230
$677$	−1.70256e7	−1.42768	−0.713841	−	0.700308i	$-0.753046\pi$
$677$	−1.70256e7	−1.42768	−0.713841	+	0.700308i	$0.753046\pi$
$678$	100152.	0.00836733
$679$	−5.42785e6	−0.451807
$680$	−3.17464e6	−0.263283
$681$	−7.74469e6	−0.639936
$682$	−6642.38	−0.000546843 0
$683$	−1.90023e7	−1.55867	−0.779337	−	0.626605i	$-0.784444\pi$
$683$	−1.90023e7	−1.55867	−0.779337	+	0.626605i	$0.784444\pi$
$684$	3.90906e6	0.319471
$685$	3.51030e7	2.85837
$686$	28006.2	0.00227219
$687$	−1.31962e7	−1.06673
$688$	1.22495e7	0.986617
$689$	−6.80007e6	−0.545714
$690$	101829.	0.00814235
$691$	1.76967e7	1.40993	0.704963	−	0.709244i	$-0.250963\pi$
$691$	1.76967e7	1.40993	0.704963	+	0.709244i	$0.250963\pi$
$692$	1.00243e7	0.795776
$693$	123389.	0.00975989
$694$	52845.3	0.00416493
$695$	7.25203e6	0.569505
$696$	−281421.	−0.0220208
$697$	3.82917e7	2.98554
$698$	437750.	0.0340085
$699$	779322.	0.0603287
$700$	7.74417e6	0.597351
$701$	2.26562e7	1.74137	0.870687	−	0.491837i	$-0.163675\pi$
$701$	2.26562e7	1.74137	0.870687	+	0.491837i	$0.163675\pi$
$702$	−83134.2	−0.00636703
$703$	3.14377e6	0.239918
$704$	1.00789e6	0.0766449
$705$	2.40335e7	1.82114
$706$	−311491.	−0.0235198
$707$	−3.35729e6	−0.252604
$708$	4.52348e6	0.339148
$709$	−9.74275e6	−0.727891	−0.363945	−	0.931420i	$-0.618570\pi$
$709$	−9.74275e6	−0.727891	−0.363945	+	0.931420i	$0.618570\pi$
$710$	380169.	0.0283029
$711$	−2.47911e6	−0.183917
$712$	−1.26674e6	−0.0936457
$713$	−474805.	−0.0349777
$714$	243686.	0.0178889
$715$	1.33811e6	0.0978871
$716$	−2.18497e7	−1.59281
$717$	4.69947e6	0.341390
$718$	556089.	0.0402562
$719$	−1.35251e7	−0.975707	−0.487854	−	0.872925i	$-0.662220\pi$
$719$	−1.35251e7	−0.975707	−0.487854	+	0.872925i	$0.662220\pi$
$720$	−7.41278e6	−0.532905
$721$	−1.86022e6	−0.133268
$722$	46082.2	0.00328996
$723$	2.69801e6	0.191954
$724$	2.03377e7	1.44197
$725$	−1.01637e7	−0.718135
$726$	342972.	0.0241500
$727$	−8.50893e6	−0.597089	−0.298545	−	0.954396i	$-0.596501\pi$
$727$	−8.50893e6	−0.597089	−0.298545	+	0.954396i	$0.596501\pi$
$728$	−357308.	−0.0249870
$729$	531441.	0.0370370
$730$	−664705.	−0.0461659
$731$	2.79162e7	1.93225
$732$	1.15636e6	0.0797658
$733$	−2.38936e7	−1.64256	−0.821281	−	0.570524i	$-0.806740\pi$
$733$	−2.38936e7	−1.64256	−0.821281	+	0.570524i	$0.806740\pi$
$734$	−610411.	−0.0418198
$735$	−1.94152e6	−0.132564
$736$	−385938.	−0.0262617
$737$	−9171.13	−0.000621948 0
$738$	−318076.	−0.0214976
$739$	−1.18780e7	−0.800080	−0.400040	−	0.916498i	$-0.631004\pi$
$739$	−1.18780e7	−0.800080	−0.400040	+	0.916498i	$0.631004\pi$
$740$	−5.97216e6	−0.400915
$741$	−6.51381e6	−0.435802
$742$	−165573.	−0.0110403
$743$	1.27988e7	0.850547	0.425274	−	0.905065i	$-0.360178\pi$
$743$	1.27988e7	0.850547	0.425274	+	0.905065i	$0.360178\pi$
$744$	−122960.	−0.00814389
$745$	3.63493e7	2.39941
$746$	447690.	0.0294531
$747$	−4.86437e6	−0.318952
$748$	2.30517e6	0.150643
$749$	−1.14421e7	−0.745247
$750$	350848.	0.0227754
$751$	−2.18467e7	−1.41347	−0.706733	−	0.707481i	$-0.749832\pi$
$751$	−2.18467e7	−1.41347	−0.706733	+	0.707481i	$0.749832\pi$
$752$	−3.02729e7	−1.95213
$753$	−2.19801e6	−0.141267
$754$	234263.	0.0150064
$755$	−2.71697e6	−0.173467
$756$	1.14105e6	0.0726105
$757$	−2.94494e7	−1.86783	−0.933914	−	0.357498i	$-0.883630\pi$
$757$	−2.94494e7	−1.86783	−0.933914	+	0.357498i	$0.883630\pi$
$758$	327856.	0.0207257
$759$	−148011.	−0.00932590
$760$	2.06622e6	0.129761
$761$	−1.30067e7	−0.814151	−0.407075	−	0.913395i	$-0.633451\pi$
$761$	−1.30067e7	−0.814151	−0.407075	+	0.913395i	$0.633451\pi$
$762$	−455390.	−0.0284116
$763$	872695.	0.0542689
$764$	1.90556e7	1.18111
$765$	−1.68934e7	−1.04367
$766$	1.23017e6	0.0757517
$767$	−7.53763e6	−0.462644
$768$	9.27051e6	0.567153
$769$	−2.94798e7	−1.79766	−0.898832	−	0.438293i	$-0.855583\pi$
$769$	−2.94798e7	−1.79766	−0.898832	+	0.438293i	$0.855583\pi$
$770$	32581.2	0.00198034
$771$	−6.70833e6	−0.406423
$772$	1.53452e7	0.926681
$773$	3.21781e7	1.93692	0.968461	−	0.249165i	$-0.0801563\pi$
$773$	3.21781e7	1.93692	0.968461	+	0.249165i	$0.0801563\pi$
$774$	−231891.	−0.0139133
$775$	−4.44077e6	−0.265585
$776$	1.68614e6	0.100517
$777$	917661.	0.0545293
$778$	1.07923e6	0.0639241
$779$	−2.49222e7	−1.47144
$780$	1.23742e7	0.728249
$781$	−552585.	−0.0324169
$782$	−292312.	−0.0170935
$783$	−1.49755e6	−0.0872922
$784$	2.44557e6	0.142099
$785$	−3.91737e7	−2.26893
$786$	−214847.	−0.0124043
$787$	3.42433e7	1.97078	0.985391	−	0.170305i	$-0.0544753\pi$
$787$	3.42433e7	1.97078	0.985391	+	0.170305i	$0.0544753\pi$
$788$	2.71449e7	1.55730
$789$	−8.21638e6	−0.469881
$790$	−654613.	−0.0373179
$791$	2.29060e6	0.130169
$792$	−38330.4	−0.00217136
$793$	−1.92689e6	−0.108811
$794$	111370.	0.00626929
$795$	1.14783e7	0.644111
$796$	−6.47527e6	−0.362222
$797$	−2.34311e7	−1.30661	−0.653305	−	0.757094i	$-0.726618\pi$
$797$	−2.34311e7	−1.30661	−0.653305	+	0.757094i	$0.726618\pi$
$798$	−158603.	−0.00881667
$799$	−6.89907e7	−3.82317
$800$	−3.60961e6	−0.199405
$801$	−6.74080e6	−0.371219
$802$	−207610.	−0.0113976
$803$	966165.	0.0528765
$804$	−84810.3	−0.00462709
$805$	2.32895e6	0.126669
$806$	102356.	0.00554976
$807$	−1.06941e7	−0.578042
$808$	1.04293e6	0.0561987
$809$	−7.99179e6	−0.429312	−0.214656	−	0.976690i	$-0.568863\pi$
$809$	−7.99179e6	−0.429312	−0.214656	+	0.976690i	$0.568863\pi$
$810$	140328.	0.00751505
$811$	−293587.	−0.0156742	−0.00783708	−	0.999969i	$-0.502495\pi$
$811$	−293587.	−0.0156742	−0.00783708	+	0.999969i	$0.502495\pi$
$812$	−3.21535e6	−0.171135
$813$	−803540.	−0.0426364
$814$	−15399.5	−0.000814603 0
$815$	−2.22881e7	−1.17538
$816$	2.12792e7	1.11874
$817$	−1.81693e7	−0.952322
$818$	−837221.	−0.0437479
$819$	−1.90137e6	−0.0990505
$820$	4.73443e7	2.45886
$821$	−1.04961e7	−0.543465	−0.271733	−	0.962373i	$-0.587597\pi$
$821$	−1.04961e7	−0.543465	−0.271733	+	0.962373i	$0.587597\pi$
$822$	837038.	0.0432082
$823$	1.92114e7	0.988686	0.494343	−	0.869267i	$-0.335409\pi$
$823$	1.92114e7	0.988686	0.494343	+	0.869267i	$0.335409\pi$
$824$	577871.	0.0296492
$825$	−1.38433e6	−0.0708114
$826$	−183532.	−0.00935970
$827$	−2.99306e7	−1.52178	−0.760889	−	0.648882i	$-0.775237\pi$
$827$	−2.99306e7	−1.52178	−0.760889	+	0.648882i	$0.775237\pi$
$828$	−1.36874e6	−0.0693817
$829$	2.87348e7	1.45218	0.726092	−	0.687597i	$-0.241335\pi$
$829$	2.87348e7	1.45218	0.726092	+	0.687597i	$0.241335\pi$
$830$	−1.28445e6	−0.0647173
$831$	1.99453e7	1.00193
$832$	−1.55311e7	−0.777848
$833$	5.57336e6	0.278294
$834$	172926.	0.00860885
$835$	−8.11465e6	−0.402767
$836$	−1.50032e6	−0.0742452
$837$	−654316.	−0.0322830
$838$	1.67830e6	0.0825579
$839$	1.46300e7	0.717529	0.358764	−	0.933428i	$-0.383198\pi$
$839$	1.46300e7	0.717529	0.358764	+	0.933428i	$0.383198\pi$
$840$	603126.	0.0294924
$841$	−1.62912e7	−0.794262
$842$	−27220.1	−0.00132315
$843$	1.23677e6	0.0599404
$844$	3.13221e7	1.51355
$845$	1.27404e7	0.613818
$846$	573083.	0.0275291
$847$	7.84414e6	0.375696
$848$	−1.44583e7	−0.690441
$849$	−2.09819e6	−0.0999024
$850$	−2.73395e6	−0.129790
$851$	−1.10078e6	−0.0521045
$852$	−5.11005e6	−0.241172
$853$	1.05764e7	0.497699	0.248849	−	0.968542i	$-0.419948\pi$
$853$	1.05764e7	0.497699	0.248849	+	0.968542i	$0.419948\pi$
$854$	−46917.5	−0.00220135
$855$	1.09951e7	0.514381
$856$	3.55444e6	0.165801
$857$	1.94568e7	0.904938	0.452469	−	0.891780i	$-0.350543\pi$
$857$	1.94568e7	0.904938	0.452469	+	0.891780i	$0.350543\pi$
$858$	31907.4	0.00147970
$859$	5.93986e6	0.274659	0.137329	−	0.990525i	$-0.456148\pi$
$859$	5.93986e6	0.274659	0.137329	+	0.990525i	$0.456148\pi$
$860$	3.45160e7	1.59138
$861$	−7.27475e6	−0.334434
$862$	1.23256e6	0.0564990
$863$	−2.22885e7	−1.01872	−0.509358	−	0.860555i	$-0.670117\pi$
$863$	−2.22885e7	−1.01872	−0.509358	+	0.860555i	$0.670117\pi$
$864$	−531850.	−0.0242384
$865$	2.81958e7	1.28128
$866$	285011.	0.0129142
$867$	3.57158e7	1.61366
$868$	−1.40487e6	−0.0632903
$869$	951496.	0.0427423
$870$	−395430.	−0.0177121
$871$	141322.	0.00631198
$872$	−271099.	−0.0120736
$873$	8.97257e6	0.398457
$874$	190252.	0.00842462
$875$	8.02428e6	0.354312
$876$	8.93464e6	0.393384
$877$	−1.70597e7	−0.748985	−0.374493	−	0.927230i	$-0.622183\pi$
$877$	−1.70597e7	−0.748985	−0.374493	+	0.927230i	$0.622183\pi$
$878$	−948543.	−0.0415261
$879$	−3.58731e6	−0.156602
$880$	2.84507e6	0.123847
$881$	2.85541e7	1.23945	0.619724	−	0.784820i	$-0.287245\pi$
$881$	2.85541e7	1.23945	0.619724	+	0.784820i	$0.287245\pi$
$882$	−46296.0	−0.00200388
$883$	2.13639e7	0.922100	0.461050	−	0.887374i	$-0.347473\pi$
$883$	2.13639e7	0.922100	0.461050	+	0.887374i	$0.347473\pi$
$884$	−3.55214e7	−1.52883
$885$	1.27233e7	0.546062
$886$	−151888.	−0.00650039
$887$	4.26920e7	1.82195	0.910977	−	0.412457i	$-0.135329\pi$
$887$	4.26920e7	1.82195	0.910977	+	0.412457i	$0.135329\pi$
$888$	−285068.	−0.0121315
$889$	−1.04153e7	−0.441994
$890$	−1.77992e6	−0.0753227
$891$	−203970.	−0.00860742
$892$	−7.34390e6	−0.309040
$893$	4.49027e7	1.88427
$894$	866756.	0.0362705
$895$	−6.14574e7	−2.56458
$896$	−1.52212e6	−0.0633399
$897$	2.28078e6	0.0946461
$898$	−1.54352e6	−0.0638734
$899$	1.84379e6	0.0760875
$900$	−1.28016e7	−0.526814
$901$	−3.29498e7	−1.35220
$902$	122080.	0.00499605
$903$	−5.30360e6	−0.216447
$904$	−711564.	−0.0289596
$905$	5.72043e7	2.32171
$906$	−64786.6	−0.00262219
$907$	8.13724e6	0.328442	0.164221	−	0.986424i	$-0.447489\pi$
$907$	8.13724e6	0.328442	0.164221	+	0.986424i	$0.447489\pi$
$908$	2.74879e7	1.10644
$909$	5.54981e6	0.222776
$910$	−502060.	−0.0200980
$911$	−9.87461e6	−0.394207	−0.197103	−	0.980383i	$-0.563153\pi$
$911$	−9.87461e6	−0.394207	−0.197103	+	0.980383i	$0.563153\pi$
$912$	−1.38496e7	−0.551379
$913$	1.86697e6	0.0741245
$914$	−584786.	−0.0231543
$915$	3.25254e6	0.128431
$916$	4.68366e7	1.84436
$917$	−4.91378e6	−0.192971
$918$	−402827.	−0.0157766
$919$	3.83050e7	1.49612	0.748061	−	0.663630i	$-0.230985\pi$
$919$	3.83050e7	1.49612	0.748061	+	0.663630i	$0.230985\pi$
$920$	−723478.	−0.0281810
$921$	4.52152e6	0.175645
$922$	190278.	0.00737158
$923$	8.51506e6	0.328991
$924$	−437941.	−0.0168747
$925$	−1.02954e7	−0.395629
$926$	−273175.	−0.0104692
$927$	3.07506e6	0.117532
$928$	1.49870e6	0.0571273
$929$	−2.14322e7	−0.814754	−0.407377	−	0.913260i	$-0.633556\pi$
$929$	−2.14322e7	−0.814754	−0.407377	+	0.913260i	$0.633556\pi$
$930$	−172773.	−0.00655042
$931$	−3.62743e6	−0.137159
$932$	−2.76602e6	−0.104307
$933$	−1.69509e7	−0.637514
$934$	−117852.	−0.00442048
$935$	6.48380e6	0.242550
$936$	590653.	0.0220365
$937$	2.45274e7	0.912648	0.456324	−	0.889814i	$-0.349166\pi$
$937$	2.45274e7	0.912648	0.456324	+	0.889814i	$0.349166\pi$
$938$	3441.03	0.000127697 0
$939$	1.29085e7	0.477761
$940$	−8.53010e7	−3.14872
$941$	−1.29934e6	−0.0478353	−0.0239177	−	0.999714i	$-0.507614\pi$
$941$	−1.29934e6	−0.0478353	−0.0239177	+	0.999714i	$0.507614\pi$
$942$	−934105.	−0.0342980
$943$	8.72641e6	0.319563
$944$	−1.60265e7	−0.585339
$945$	3.20946e6	0.116910
$946$	89001.1	0.00323346
$947$	4.22013e6	0.152915	0.0764577	−	0.997073i	$-0.475639\pi$
$947$	4.22013e6	0.152915	0.0764577	+	0.997073i	$0.475639\pi$
$948$	8.79899e6	0.317989
$949$	−1.48881e7	−0.536629
$950$	1.77939e6	0.0639680
$951$	−7.84101e6	−0.281139
$952$	−1.73134e6	−0.0619142
$953$	5.07968e7	1.81177	0.905886	−	0.423521i	$-0.139206\pi$
$953$	5.07968e7	1.81177	0.905886	+	0.423521i	$0.139206\pi$
$954$	273703.	0.00973663
$955$	5.35981e7	1.90170
$956$	−1.66796e7	−0.590258
$957$	574767.	0.0202867
$958$	−1.21914e6	−0.0429181
$959$	1.91440e7	0.672181
$960$	2.62161e7	0.918100
$961$	−2.78236e7	−0.971861
$962$	237299.	0.00826719
$963$	1.89145e7	0.657246
$964$	−9.57594e6	−0.331886
$965$	4.31620e7	1.49205
$966$	55534.2	0.00191478
$967$	−2.38547e7	−0.820365	−0.410183	−	0.912003i	$-0.634535\pi$
$967$	−2.38547e7	−0.820365	−0.410183	+	0.912003i	$0.634535\pi$
$968$	−2.43675e6	−0.0835839
$969$	−3.15627e7	−1.07985
$970$	2.36922e6	0.0808494
$971$	3.71284e7	1.26374	0.631870	−	0.775074i	$-0.282288\pi$
$971$	3.71284e7	1.26374	0.631870	+	0.775074i	$0.282288\pi$
$972$	−1.88622e6	−0.0640364
$973$	3.95501e6	0.133926
$974$	−1.91491e6	−0.0646773
$975$	2.13318e7	0.718646
$976$	−4.09694e6	−0.137669
$977$	8.92560e6	0.299158	0.149579	−	0.988750i	$-0.452208\pi$
$977$	8.92560e6	0.299158	0.149579	+	0.988750i	$0.452208\pi$
$978$	−531464.	−0.0177675
$979$	2.58716e6	0.0862714
$980$	6.89097e6	0.229200
$981$	−1.44262e6	−0.0478607
$982$	588798.	0.0194844
$983$	−8.64982e6	−0.285511	−0.142756	−	0.989758i	$-0.545596\pi$
$983$	−8.64982e6	−0.285511	−0.142756	+	0.989758i	$0.545596\pi$
$984$	2.25987e6	0.0744040
$985$	7.63513e7	2.50741
$986$	1.13513e6	0.0371836
$987$	1.31070e7	0.428264
$988$	2.31192e7	0.753495
$989$	6.36191e6	0.206822
$990$	−53858.8	−0.00174650
$991$	1.88950e7	0.611170	0.305585	−	0.952165i	$-0.401148\pi$
$991$	1.88950e7	0.611170	0.305585	+	0.952165i	$0.401148\pi$
$992$	654819.	0.0211272
$993$	1.56061e7	0.502250
$994$	207331.	0.00665578
$995$	−1.82132e7	−0.583214
$996$	1.72649e7	0.551462
$997$	−2.46020e7	−0.783848	−0.391924	−	0.919998i	$-0.628190\pi$
$997$	−2.46020e7	−0.783848	−0.391924	+	0.919998i	$0.628190\pi$
$998$	1.70936e6	0.0543258
$999$	−1.51695e6	−0.0480903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.6.a.b.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.6.a.b.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-0.238049 q^{2} +9.00000 q^{3} -31.9433 q^{4} -89.8479 q^{5} -2.14244 q^{6} -49.0000 q^{7} +15.2217 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-0.238049 q^{2} +9.00000 q^{3} -31.9433 q^{4} -89.8479 q^{5} -2.14244 q^{6} -49.0000 q^{7} +15.2217 q^{8} +81.0000 q^{9} +21.3882 q^{10} -31.0883 q^{11} -287.490 q^{12} +479.055 q^{13} +11.6644 q^{14} -808.631 q^{15} +1018.56 q^{16} +2321.27 q^{17} -19.2820 q^{18} -1510.80 q^{19} +2870.04 q^{20} -441.000 q^{21} +7.40054 q^{22} +529.000 q^{23} +136.995 q^{24} +4947.65 q^{25} -114.039 q^{26} +729.000 q^{27} +1565.22 q^{28} -2054.25 q^{29} +192.494 q^{30} -897.553 q^{31} -729.561 q^{32} -279.795 q^{33} -552.575 q^{34} +4402.55 q^{35} -2587.41 q^{36} -2080.86 q^{37} +359.644 q^{38} +4311.50 q^{39} -1367.63 q^{40} +16496.0 q^{41} +104.980 q^{42} +12026.3 q^{43} +993.064 q^{44} -7277.68 q^{45} -125.928 q^{46} -29721.2 q^{47} +9167.07 q^{48} +2401.00 q^{49} -1177.78 q^{50} +20891.4 q^{51} -15302.6 q^{52} -14194.8 q^{53} -173.538 q^{54} +2793.22 q^{55} -745.861 q^{56} -13597.2 q^{57} +489.011 q^{58} -15734.4 q^{59} +25830.4 q^{60} -4022.28 q^{61} +213.662 q^{62} -3969.00 q^{63} -32420.3 q^{64} -43042.1 q^{65} +66.6049 q^{66} +295.002 q^{67} -74149.0 q^{68} +4761.00 q^{69} -1048.02 q^{70} +17774.7 q^{71} +1232.95 q^{72} -31078.1 q^{73} +495.348 q^{74} +44528.8 q^{75} +48260.0 q^{76} +1523.33 q^{77} -1026.35 q^{78} -30606.2 q^{79} -91515.8 q^{80} +6561.00 q^{81} -3926.87 q^{82} -60053.9 q^{83} +14087.0 q^{84} -208561. q^{85} -2862.85 q^{86} -18488.2 q^{87} -473.215 q^{88} -83219.7 q^{89} +1732.44 q^{90} -23473.7 q^{91} -16898.0 q^{92} -8077.97 q^{93} +7075.10 q^{94} +135742. q^{95} -6566.05 q^{96} +110772. q^{97} -571.556 q^{98} -2518.15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9}+O(q^{10}) \) 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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