LMFDB - Embedded newform 1045.6.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.84120 q^{2} -9.26217 q^{3} +64.8493 q^{4} -25.0000 q^{5} +91.1509 q^{6} -35.6928 q^{7} -323.277 q^{8} -157.212 q^{9} +O(q^{10})$	\(q-9.84120 q^{2} -9.26217 q^{3} +64.8493 q^{4} -25.0000 q^{5} +91.1509 q^{6} -35.6928 q^{7} -323.277 q^{8} -157.212 q^{9} +246.030 q^{10} -121.000 q^{11} -600.645 q^{12} -750.239 q^{13} +351.260 q^{14} +231.554 q^{15} +1106.25 q^{16} -1233.82 q^{17} +1547.16 q^{18} -361.000 q^{19} -1621.23 q^{20} +330.593 q^{21} +1190.79 q^{22} +1212.71 q^{23} +2994.24 q^{24} +625.000 q^{25} +7383.26 q^{26} +3706.83 q^{27} -2314.65 q^{28} -1386.15 q^{29} -2278.77 q^{30} -7294.50 q^{31} -542.015 q^{32} +1120.72 q^{33} +12142.3 q^{34} +892.320 q^{35} -10195.1 q^{36} +11606.7 q^{37} +3552.67 q^{38} +6948.85 q^{39} +8081.91 q^{40} +7189.63 q^{41} -3253.43 q^{42} +10468.0 q^{43} -7846.76 q^{44} +3930.30 q^{45} -11934.5 q^{46} -11242.8 q^{47} -10246.3 q^{48} -15533.0 q^{49} -6150.75 q^{50} +11427.8 q^{51} -48652.5 q^{52} +17528.7 q^{53} -36479.7 q^{54} +3025.00 q^{55} +11538.7 q^{56} +3343.64 q^{57} +13641.4 q^{58} -3795.54 q^{59} +15016.1 q^{60} +24148.3 q^{61} +71786.7 q^{62} +5611.35 q^{63} -30066.0 q^{64} +18756.0 q^{65} -11029.3 q^{66} +29177.5 q^{67} -80012.2 q^{68} -11232.3 q^{69} -8781.51 q^{70} -68849.6 q^{71} +50823.0 q^{72} -44031.0 q^{73} -114224. q^{74} -5788.86 q^{75} -23410.6 q^{76} +4318.83 q^{77} -68385.0 q^{78} +37517.5 q^{79} -27656.3 q^{80} +3869.23 q^{81} -70754.6 q^{82} +75088.2 q^{83} +21438.7 q^{84} +30845.4 q^{85} -103018. q^{86} +12838.8 q^{87} +39116.5 q^{88} -61616.9 q^{89} -38678.9 q^{90} +26778.2 q^{91} +78643.3 q^{92} +67563.0 q^{93} +110643. q^{94} +9025.00 q^{95} +5020.23 q^{96} -49449.2 q^{97} +152864. q^{98} +19022.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−9.84120	−1.73970	−0.869848	−	0.493320i	$-0.835783\pi$
$2$	−9.84120	−1.73970	−0.869848	+	0.493320i	$0.835783\pi$
$3$	−9.26217	−0.594169	−0.297084	−	0.954851i	$-0.596014\pi$
$3$	−9.26217	−0.594169	−0.297084	+	0.954851i	$0.596014\pi$
$4$	64.8493	2.02654
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	91.1509	1.03367
$7$	−35.6928	−0.275319	−0.137659	−	0.990480i	$-0.543958\pi$
$7$	−35.6928	−0.275319	−0.137659	+	0.990480i	$0.543958\pi$
$8$	−323.277	−1.78587
$9$	−157.212	−0.646964
$10$	246.030	0.778015
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−600.645	−1.20411
$13$	−750.239	−1.23124	−0.615618	−	0.788044i	$-0.711094\pi$
$13$	−750.239	−1.23124	−0.615618	+	0.788044i	$0.711094\pi$
$14$	351.260	0.478971
$15$	231.554	0.265720
$16$	1106.25	1.08033
$17$	−1233.82	−1.03545	−0.517725	−	0.855547i	$-0.673221\pi$
$17$	−1233.82	−1.03545	−0.517725	+	0.855547i	$0.673221\pi$
$18$	1547.16	1.12552
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−1621.23	−0.906296
$21$	330.593	0.163586
$22$	1190.79	0.524538
$23$	1212.71	0.478010	0.239005	−	0.971018i	$-0.423179\pi$
$23$	1212.71	0.478010	0.239005	+	0.971018i	$0.423179\pi$
$24$	2994.24	1.06111
$25$	625.000	0.200000
$26$	7383.26	2.14198
$27$	3706.83	0.978574
$28$	−2314.65	−0.557944
$29$	−1386.15	−0.306067	−0.153033	−	0.988221i	$-0.548904\pi$
$29$	−1386.15	−0.306067	−0.153033	+	0.988221i	$0.548904\pi$
$30$	−2278.77	−0.462272
$31$	−7294.50	−1.36330	−0.681650	−	0.731678i	$-0.738737\pi$
$31$	−7294.50	−1.36330	−0.681650	+	0.731678i	$0.738737\pi$
$32$	−542.015	−0.0935699
$33$	1120.72	0.179149
$34$	12142.3	1.80137
$35$	892.320	0.123126
$36$	−10195.1	−1.31110
$37$	11606.7	1.39382	0.696909	−	0.717160i	$-0.254558\pi$
$37$	11606.7	1.39382	0.696909	+	0.717160i	$0.254558\pi$
$38$	3552.67	0.399114
$39$	6948.85	0.731562
$40$	8081.91	0.798664
$41$	7189.63	0.667954	0.333977	−	0.942581i	$-0.391609\pi$
$41$	7189.63	0.667954	0.333977	+	0.942581i	$0.391609\pi$
$42$	−3253.43	−0.284589
$43$	10468.0	0.863363	0.431682	−	0.902026i	$-0.357920\pi$
$43$	10468.0	0.863363	0.431682	+	0.902026i	$0.357920\pi$
$44$	−7846.76	−0.611025
$45$	3930.30	0.289331
$46$	−11934.5	−0.831592
$47$	−11242.8	−0.742389	−0.371194	−	0.928555i	$-0.621052\pi$
$47$	−11242.8	−0.742389	−0.371194	+	0.928555i	$0.621052\pi$
$48$	−10246.3	−0.641896
$49$	−15533.0	−0.924200
$50$	−6150.75	−0.347939
$51$	11427.8	0.615231
$52$	−48652.5	−2.49515
$53$	17528.7	0.857155	0.428578	−	0.903505i	$-0.359015\pi$
$53$	17528.7	0.857155	0.428578	+	0.903505i	$0.359015\pi$
$54$	−36479.7	−1.70242
$55$	3025.00	0.134840
$56$	11538.7	0.491683
$57$	3343.64	0.136312
$58$	13641.4	0.532463
$59$	−3795.54	−0.141953	−0.0709763	−	0.997478i	$-0.522611\pi$
$59$	−3795.54	−0.141953	−0.0709763	+	0.997478i	$0.522611\pi$
$60$	15016.1	0.538493
$61$	24148.3	0.830925	0.415462	−	0.909610i	$-0.363620\pi$
$61$	24148.3	0.830925	0.415462	+	0.909610i	$0.363620\pi$
$62$	71786.7	2.37173
$63$	5611.35	0.178121
$64$	−30066.0	−0.917542
$65$	18756.0	0.550626
$66$	−11029.3	−0.311664
$67$	29177.5	0.794074	0.397037	−	0.917803i	$-0.370038\pi$
$67$	29177.5	0.794074	0.397037	+	0.917803i	$0.370038\pi$
$68$	−80012.2	−2.09838
$69$	−11232.3	−0.284019
$70$	−8781.51	−0.214202
$71$	−68849.6	−1.62090	−0.810449	−	0.585809i	$-0.800777\pi$
$71$	−68849.6	−1.62090	−0.810449	+	0.585809i	$0.800777\pi$
$72$	50823.0	1.15539
$73$	−44031.0	−0.967055	−0.483527	−	0.875329i	$-0.660645\pi$
$73$	−44031.0	−0.967055	−0.483527	+	0.875329i	$0.660645\pi$
$74$	−114224.	−2.42482
$75$	−5788.86	−0.118834
$76$	−23410.6	−0.464920
$77$	4318.83	0.0830117
$78$	−68385.0	−1.27270
$79$	37517.5	0.676342	0.338171	−	0.941085i	$-0.390192\pi$
$79$	37517.5	0.676342	0.338171	+	0.941085i	$0.390192\pi$
$80$	−27656.3	−0.483136
$81$	3869.23	0.0655257
$82$	−70754.6	−1.16204
$83$	75088.2	1.19640	0.598200	−	0.801347i	$-0.295883\pi$
$83$	75088.2	1.19640	0.598200	+	0.801347i	$0.295883\pi$
$84$	21438.7	0.331513
$85$	30845.4	0.463067
$86$	−103018.	−1.50199
$87$	12838.8	0.181855
$88$	39116.5	0.538459
$89$	−61616.9	−0.824565	−0.412283	−	0.911056i	$-0.635268\pi$
$89$	−61616.9	−0.824565	−0.412283	+	0.911056i	$0.635268\pi$
$90$	−38678.9	−0.503348
$91$	26778.2	0.338982
$92$	78643.3	0.968707
$93$	67563.0	0.810030
$94$	110643.	1.29153
$95$	9025.00	0.102598
$96$	5020.23	0.0555963
$97$	−49449.2	−0.533617	−0.266809	−	0.963750i	$-0.585969\pi$
$97$	−49449.2	−0.533617	−0.266809	+	0.963750i	$0.585969\pi$
$98$	152864.	1.60783
$99$	19022.7	0.195067
$100$	40530.8	0.405308
$101$	−54019.6	−0.526924	−0.263462	−	0.964670i	$-0.584864\pi$
$101$	−54019.6	−0.526924	−0.263462	+	0.964670i	$0.584864\pi$
$102$	−112464.	−1.07032
$103$	2349.40	0.0218205	0.0109102	−	0.999940i	$-0.496527\pi$
$103$	2349.40	0.0218205	0.0109102	+	0.999940i	$0.496527\pi$
$104$	242535.	2.19883
$105$	−8264.82	−0.0731578
$106$	−172503.	−1.49119
$107$	9773.25	0.0825239	0.0412619	−	0.999148i	$-0.486862\pi$
$107$	9773.25	0.0825239	0.0412619	+	0.999148i	$0.486862\pi$
$108$	240386.	1.98312
$109$	148387.	1.19627	0.598137	−	0.801394i	$-0.295908\pi$
$109$	148387.	1.19627	0.598137	+	0.801394i	$0.295908\pi$
$110$	−29769.6	−0.234580
$111$	−107504.	−0.828163
$112$	−39485.3	−0.297434
$113$	64565.6	0.475669	0.237835	−	0.971306i	$-0.423562\pi$
$113$	64565.6	0.475669	0.237835	+	0.971306i	$0.423562\pi$
$114$	−32905.5	−0.237141
$115$	−30317.7	−0.213773
$116$	−89891.0	−0.620256
$117$	117947.	0.796565
$118$	37352.7	0.246954
$119$	44038.4	0.285079
$120$	−74856.1	−0.474541
$121$	14641.0	0.0909091
$122$	−237648.	−1.44556
$123$	−66591.5	−0.396877
$124$	−473043.	−2.76278
$125$	−15625.0	−0.0894427
$126$	−55222.4	−0.309877
$127$	−33237.3	−0.182859	−0.0914294	−	0.995812i	$-0.529144\pi$
$127$	−33237.3	−0.182859	−0.0914294	+	0.995812i	$0.529144\pi$
$128$	313230.	1.68981
$129$	−96956.6	−0.512983
$130$	−184581.	−0.957921
$131$	47289.8	0.240763	0.120381	−	0.992728i	$-0.461588\pi$
$131$	47289.8	0.240763	0.120381	+	0.992728i	$0.461588\pi$
$132$	72678.1	0.363052
$133$	12885.1	0.0631624
$134$	−287142.	−1.38145
$135$	−92670.8	−0.437632
$136$	398864.	1.84918
$137$	20679.6	0.0941327	0.0470664	−	0.998892i	$-0.485013\pi$
$137$	20679.6	0.0941327	0.0470664	+	0.998892i	$0.485013\pi$
$138$	110540.	0.494106
$139$	227067.	0.996819	0.498409	−	0.866942i	$-0.333918\pi$
$139$	227067.	0.996819	0.498409	+	0.866942i	$0.333918\pi$
$140$	57866.3	0.249520
$141$	104133.	0.441104
$142$	677563.	2.81987
$143$	90779.0	0.371232
$144$	−173917.	−0.698931
$145$	34653.8	0.136877
$146$	433318.	1.68238
$147$	143870.	0.549130
$148$	752689.	2.82463
$149$	−97948.8	−0.361438	−0.180719	−	0.983535i	$-0.557842\pi$
$149$	−97948.8	−0.361438	−0.180719	+	0.983535i	$0.557842\pi$
$150$	56969.3	0.206734
$151$	122671.	0.437823	0.218912	−	0.975745i	$-0.429749\pi$
$151$	122671.	0.437823	0.218912	+	0.975745i	$0.429749\pi$
$152$	116703.	0.409706
$153$	193971.	0.669898
$154$	−42502.5	−0.144415
$155$	182363.	0.609686
$156$	450628.	1.48254
$157$	601054.	1.94610	0.973049	−	0.230599i	$-0.0740685\pi$
$157$	601054.	1.94610	0.973049	+	0.230599i	$0.0740685\pi$
$158$	−369217.	−1.17663
$159$	−162354.	−0.509295
$160$	13550.4	0.0418457
$161$	−43285.0	−0.131605
$162$	−38077.9	−0.113995
$163$	436047.	1.28548	0.642739	−	0.766086i	$-0.277798\pi$
$163$	436047.	1.28548	0.642739	+	0.766086i	$0.277798\pi$
$164$	466242.	1.35364
$165$	−28018.1	−0.0801177
$166$	−738958.	−2.08137
$167$	−181318.	−0.503093	−0.251547	−	0.967845i	$-0.580939\pi$
$167$	−181318.	−0.503093	−0.251547	+	0.967845i	$0.580939\pi$
$168$	−106873.	−0.292142
$169$	191566.	0.515944
$170$	−303556.	−0.805595
$171$	56753.6	0.148424
$172$	678844.	1.74964
$173$	−200662.	−0.509742	−0.254871	−	0.966975i	$-0.582033\pi$
$173$	−200662.	−0.509742	−0.254871	+	0.966975i	$0.582033\pi$
$174$	−126349.	−0.316373
$175$	−22308.0	−0.0550637
$176$	−133857.	−0.325730
$177$	35154.9	0.0843437
$178$	606385.	1.43449
$179$	529625.	1.23548	0.617740	−	0.786382i	$-0.288048\pi$
$179$	529625.	1.23548	0.617740	+	0.786382i	$0.288048\pi$
$180$	254877.	0.586341
$181$	164371.	0.372932	0.186466	−	0.982461i	$-0.440297\pi$
$181$	164371.	0.372932	0.186466	+	0.982461i	$0.440297\pi$
$182$	−263529.	−0.589726
$183$	−223666.	−0.493709
$184$	−392040.	−0.853663
$185$	−290169.	−0.623334
$186$	−664901.	−1.40921
$187$	149292.	0.312200
$188$	−729090.	−1.50448
$189$	−132307.	−0.269420
$190$	−88816.9	−0.178489
$191$	387714.	0.769003	0.384502	−	0.923124i	$-0.374373\pi$
$191$	387714.	0.769003	0.384502	+	0.923124i	$0.374373\pi$
$192$	278477.	0.545175
$193$	132491.	0.256031	0.128015	−	0.991772i	$-0.459139\pi$
$193$	132491.	0.256031	0.128015	+	0.991772i	$0.459139\pi$
$194$	486640.	0.928332
$195$	−173721.	−0.327165
$196$	−1.00731e6	−1.87293
$197$	588793.	1.08093	0.540465	−	0.841367i	$-0.318248\pi$
$197$	588793.	1.08093	0.540465	+	0.841367i	$0.318248\pi$
$198$	−187206.	−0.339357
$199$	236334.	0.423051	0.211526	−	0.977372i	$-0.432157\pi$
$199$	236334.	0.423051	0.211526	+	0.977372i	$0.432157\pi$
$200$	−202048.	−0.357174
$201$	−270247.	−0.471814
$202$	531618.	0.916687
$203$	49475.7	0.0842659
$204$	741087.	1.24679
$205$	−179741.	−0.298718
$206$	−23120.9	−0.0379609
$207$	−190653.	−0.309255
$208$	−829955.	−1.33014
$209$	43681.0	0.0691714
$210$	81335.8	0.127272
$211$	177555.	0.274553	0.137277	−	0.990533i	$-0.456165\pi$
$211$	177555.	0.274553	0.137277	+	0.990533i	$0.456165\pi$
$212$	1.13672e6	1.73706
$213$	637697.	0.963087
$214$	−96180.6	−0.143566
$215$	−261701.	−0.386108
$216$	−1.19833e6	−1.74760
$217$	260361.	0.375342
$218$	−1.46031e6	−2.08115
$219$	407822.	0.574594
$220$	196169.	0.273259
$221$	925659.	1.27488
$222$	1.05797e6	1.44075
$223$	594723.	0.800853	0.400426	−	0.916329i	$-0.368862\pi$
$223$	594723.	0.800853	0.400426	+	0.916329i	$0.368862\pi$
$224$	19346.0	0.0257615
$225$	−98257.6	−0.129393
$226$	−635403.	−0.827519
$227$	574179.	0.739576	0.369788	−	0.929116i	$-0.379430\pi$
$227$	574179.	0.739576	0.369788	+	0.929116i	$0.379430\pi$
$228$	216833.	0.276241
$229$	143369.	0.180662	0.0903310	−	0.995912i	$-0.471207\pi$
$229$	143369.	0.180662	0.0903310	+	0.995912i	$0.471207\pi$
$230$	298363.	0.371899
$231$	−40001.8	−0.0493229
$232$	448111.	0.546595
$233$	−971701.	−1.17258	−0.586291	−	0.810101i	$-0.699412\pi$
$233$	−971701.	−1.17258	−0.586291	+	0.810101i	$0.699412\pi$
$234$	−1.16074e6	−1.38578
$235$	281071.	0.332006
$236$	−246138.	−0.287673
$237$	−347494.	−0.401861
$238$	−433391.	−0.495950
$239$	10039.2	0.0113686	0.00568428	−	0.999984i	$-0.498191\pi$
$239$	10039.2	0.0113686	0.00568428	+	0.999984i	$0.498191\pi$
$240$	256158.	0.287064
$241$	−872661.	−0.967838	−0.483919	−	0.875113i	$-0.660787\pi$
$241$	−872661.	−0.967838	−0.483919	+	0.875113i	$0.660787\pi$
$242$	−144085.	−0.158154
$243$	−936598.	−1.01751
$244$	1.56600e6	1.68390
$245$	388326.	0.413315
$246$	655341.	0.690446
$247$	270836.	0.282465
$248$	2.35814e6	2.43467
$249$	−695480.	−0.710863
$250$	153769.	0.155603
$251$	−447144.	−0.447984	−0.223992	−	0.974591i	$-0.571909\pi$
$251$	−447144.	−0.447984	−0.223992	+	0.974591i	$0.571909\pi$
$252$	363892.	0.360970
$253$	−146738.	−0.144125
$254$	327095.	0.318119
$255$	−285696.	−0.275140
$256$	−2.12045e6	−2.02222
$257$	−1.12224e6	−1.05987	−0.529933	−	0.848039i	$-0.677783\pi$
$257$	−1.12224e6	−1.05987	−0.529933	+	0.848039i	$0.677783\pi$
$258$	954170.	0.892435
$259$	−414277.	−0.383744
$260$	1.21631e6	1.11587
$261$	217920.	0.198014
$262$	−465389.	−0.418854
$263$	−91282.4	−0.0813762	−0.0406881	−	0.999172i	$-0.512955\pi$
$263$	−91282.4	−0.0813762	−0.0406881	+	0.999172i	$0.512955\pi$
$264$	−362303.	−0.319936
$265$	−438217.	−0.383332
$266$	−126805.	−0.109883
$267$	570707.	0.489931
$268$	1.89214e6	1.60922
$269$	−1.97324e6	−1.66264	−0.831322	−	0.555791i	$-0.812415\pi$
$269$	−1.97324e6	−1.66264	−0.831322	+	0.555791i	$0.812415\pi$
$270$	911993.	0.761346
$271$	−254469.	−0.210481	−0.105240	−	0.994447i	$-0.533561\pi$
$271$	−254469.	−0.210481	−0.105240	+	0.994447i	$0.533561\pi$
$272$	−1.36492e6	−1.11862
$273$	−248024.	−0.201413
$274$	−203512.	−0.163762
$275$	−75625.0	−0.0603023
$276$	−728408.	−0.575575
$277$	−296024.	−0.231807	−0.115904	−	0.993260i	$-0.536976\pi$
$277$	−296024.	−0.231807	−0.115904	+	0.993260i	$0.536976\pi$
$278$	−2.23461e6	−1.73416
$279$	1.14678e6	0.882006
$280$	−288466.	−0.219887
$281$	254086.	0.191962	0.0959811	−	0.995383i	$-0.469401\pi$
$281$	254086.	0.191962	0.0959811	+	0.995383i	$0.469401\pi$
$282$	−1.02479e6	−0.767387
$283$	2.25462e6	1.67343	0.836716	−	0.547637i	$-0.184473\pi$
$283$	2.25462e6	1.67343	0.836716	+	0.547637i	$0.184473\pi$
$284$	−4.46485e6	−3.28482
$285$	−83591.1	−0.0609604
$286$	−893374.	−0.645830
$287$	−256618.	−0.183900
$288$	85211.3	0.0605363
$289$	102450.	0.0721549
$290$	−341035.	−0.238125
$291$	458007.	0.317059
$292$	−2.85538e6	−1.95978
$293$	−1.31042e6	−0.891748	−0.445874	−	0.895096i	$-0.647107\pi$
$293$	−1.31042e6	−0.891748	−0.445874	+	0.895096i	$0.647107\pi$
$294$	−1.41585e6	−0.955320
$295$	94888.4	0.0634831
$296$	−3.75219e6	−2.48917
$297$	−448527.	−0.295051
$298$	963935.	0.628792
$299$	−909822.	−0.588543
$300$	−375403.	−0.240821
$301$	−373633.	−0.237700
$302$	−1.20723e6	−0.761679
$303$	500339.	0.313082
$304$	−399357.	−0.247844
$305$	−603707.	−0.371601
$306$	−1.90891e6	−1.16542
$307$	93866.2	0.0568412	0.0284206	−	0.999596i	$-0.490952\pi$
$307$	93866.2	0.0568412	0.0284206	+	0.999596i	$0.490952\pi$
$308$	280073.	0.168227
$309$	−21760.5	−0.0129650
$310$	−1.79467e6	−1.06067
$311$	−318424.	−0.186683	−0.0933414	−	0.995634i	$-0.529755\pi$
$311$	−318424.	−0.186683	−0.0933414	+	0.995634i	$0.529755\pi$
$312$	−2.24640e6	−1.30647
$313$	−1.49955e6	−0.865167	−0.432583	−	0.901594i	$-0.642398\pi$
$313$	−1.49955e6	−0.865167	−0.432583	+	0.901594i	$0.642398\pi$
$314$	−5.91510e6	−3.38562
$315$	−140284.	−0.0796582
$316$	2.43298e6	1.37063
$317$	29760.5	0.0166338	0.00831692	−	0.999965i	$-0.497353\pi$
$317$	29760.5	0.0166338	0.00831692	+	0.999965i	$0.497353\pi$
$318$	1.59776e6	0.886018
$319$	167724.	0.0922826
$320$	751651.	0.410337
$321$	−90521.5	−0.0490331
$322$	425976.	0.228953
$323$	445408.	0.237548
$324$	250917.	0.132791
$325$	−468900.	−0.246247
$326$	−4.29123e6	−2.23634
$327$	−1.37439e6	−0.710788
$328$	−2.32424e6	−1.19288
$329$	401289.	0.204393
$330$	275732.	0.139380
$331$	975885.	0.489586	0.244793	−	0.969575i	$-0.421280\pi$
$331$	975885.	0.489586	0.244793	+	0.969575i	$0.421280\pi$
$332$	4.86942e6	2.42455
$333$	−1.82472e6	−0.901749
$334$	1.78438e6	0.875229
$335$	−729437.	−0.355121
$336$	365720.	0.176726
$337$	1.77461e6	0.851195	0.425598	−	0.904913i	$-0.360064\pi$
$337$	1.77461e6	0.851195	0.425598	+	0.904913i	$0.360064\pi$
$338$	−1.88524e6	−0.897585
$339$	−598017.	−0.282628
$340$	2.00031e6	0.938424
$341$	882635.	0.411051
$342$	−558524.	−0.258212
$343$	1.15431e6	0.529768
$344$	−3.38407e6	−1.54185
$345$	280808.	0.127017
$346$	1.97476e6	0.886796
$347$	1.15561e6	0.515214	0.257607	−	0.966250i	$-0.417066\pi$
$347$	1.15561e6	0.515214	0.257607	+	0.966250i	$0.417066\pi$
$348$	832586.	0.368537
$349$	−1.09231e6	−0.480045	−0.240023	−	0.970767i	$-0.577155\pi$
$349$	−1.09231e6	−0.480045	−0.240023	+	0.970767i	$0.577155\pi$
$350$	219538.	0.0957941
$351$	−2.78101e6	−1.20486
$352$	65583.8	0.0282124
$353$	−1.76755e6	−0.754980	−0.377490	−	0.926014i	$-0.623213\pi$
$353$	−1.76755e6	−0.754980	−0.377490	+	0.926014i	$0.623213\pi$
$354$	−345967.	−0.146732
$355$	1.72124e6	0.724888
$356$	−3.99581e6	−1.67102
$357$	−407892.	−0.169385
$358$	−5.21215e6	−2.14936
$359$	−1.42346e6	−0.582919	−0.291460	−	0.956583i	$-0.594141\pi$
$359$	−1.42346e6	−0.582919	−0.291460	+	0.956583i	$0.594141\pi$
$360$	−1.27058e6	−0.516707
$361$	130321.	0.0526316
$362$	−1.61761e6	−0.648787
$363$	−135607.	−0.0540153
$364$	1.73654e6	0.686962
$365$	1.10077e6	0.432480
$366$	2.20114e6	0.858904
$367$	801478.	0.310618	0.155309	−	0.987866i	$-0.450363\pi$
$367$	801478.	0.310618	0.155309	+	0.987866i	$0.450363\pi$
$368$	1.34156e6	0.516406
$369$	−1.13030e6	−0.432142
$370$	2.85561e6	1.08441
$371$	−625648.	−0.235991
$372$	4.38141e6	1.64156
$373$	1.48931e6	0.554260	0.277130	−	0.960832i	$-0.410617\pi$
$373$	1.48931e6	0.554260	0.277130	+	0.960832i	$0.410617\pi$
$374$	−1.46921e6	−0.543132
$375$	144721.	0.0531441
$376$	3.63455e6	1.32581
$377$	1.03995e6	0.376840
$378$	1.30206e6	0.468708
$379$	1.69817e6	0.607271	0.303636	−	0.952788i	$-0.401799\pi$
$379$	1.69817e6	0.607271	0.303636	+	0.952788i	$0.401799\pi$
$380$	585265.	0.207919
$381$	307849.	0.108649
$382$	−3.81557e6	−1.33783
$383$	−1.41574e6	−0.493158	−0.246579	−	0.969123i	$-0.579306\pi$
$383$	−1.41574e6	−0.493158	−0.246579	+	0.969123i	$0.579306\pi$
$384$	−2.90119e6	−1.00403
$385$	−107971.	−0.0371240
$386$	−1.30387e6	−0.445415
$387$	−1.64570e6	−0.558565
$388$	−3.20675e6	−1.08140
$389$	898857.	0.301173	0.150587	−	0.988597i	$-0.451884\pi$
$389$	898857.	0.301173	0.150587	+	0.988597i	$0.451884\pi$
$390$	1.70963e6	0.569167
$391$	−1.49626e6	−0.494955
$392$	5.02146e6	1.65050
$393$	−438006.	−0.143054
$394$	−5.79443e6	−1.88049
$395$	−937937.	−0.302469
$396$	1.23361e6	0.395311
$397$	−118712.	−0.0378024	−0.0189012	−	0.999821i	$-0.506017\pi$
$397$	−118712.	−0.0378024	−0.0189012	+	0.999821i	$0.506017\pi$
$398$	−2.32581e6	−0.735981
$399$	−119344.	−0.0375291
$400$	691408.	0.216065
$401$	437667.	0.135920	0.0679599	−	0.997688i	$-0.478351\pi$
$401$	437667.	0.135920	0.0679599	+	0.997688i	$0.478351\pi$
$402$	2.65955e6	0.820812
$403$	5.47263e6	1.67855
$404$	−3.50313e6	−1.06783
$405$	−96730.7	−0.0293040
$406$	−486900.	−0.146597
$407$	−1.40442e6	−0.420252
$408$	−3.69435e6	−1.09872
$409$	−2.57645e6	−0.761577	−0.380788	−	0.924662i	$-0.624347\pi$
$409$	−2.57645e6	−0.761577	−0.380788	+	0.924662i	$0.624347\pi$
$410$	1.76886e6	0.519679
$411$	−191538.	−0.0559307
$412$	152357.	0.0442200
$413$	135473.	0.0390822
$414$	1.87625e6	0.538010
$415$	−1.87721e6	−0.535046
$416$	406641.	0.115207
$417$	−2.10313e6	−0.592278
$418$	−429874.	−0.120337
$419$	2.83495e6	0.788878	0.394439	−	0.918922i	$-0.370939\pi$
$419$	2.83495e6	0.788878	0.394439	+	0.918922i	$0.370939\pi$
$420$	−535968.	−0.148257
$421$	−2.31960e6	−0.637833	−0.318917	−	0.947783i	$-0.603319\pi$
$421$	−2.31960e6	−0.637833	−0.318917	+	0.947783i	$0.603319\pi$
$422$	−1.74735e6	−0.477639
$423$	1.76751e6	0.480298
$424$	−5.66661e6	−1.53077
$425$	−771136.	−0.207090
$426$	−6.27571e6	−1.67548
$427$	−861920.	−0.228769
$428$	633788.	0.167238
$429$	−840810.	−0.220574
$430$	2.57545e6	0.671710
$431$	758535.	0.196690	0.0983450	−	0.995152i	$-0.468645\pi$
$431$	758535.	0.196690	0.0983450	+	0.995152i	$0.468645\pi$
$432$	4.10070e6	1.05718
$433$	−1.41383e6	−0.362390	−0.181195	−	0.983447i	$-0.557997\pi$
$433$	−1.41383e6	−0.362390	−0.181195	+	0.983447i	$0.557997\pi$
$434$	−2.56227e6	−0.652981
$435$	−320970.	−0.0813281
$436$	9.62281e6	2.42430
$437$	−437788.	−0.109663
$438$	−4.01346e6	−0.999618
$439$	−661068.	−0.163714	−0.0818568	−	0.996644i	$-0.526085\pi$
$439$	−661068.	−0.163714	−0.0818568	+	0.996644i	$0.526085\pi$
$440$	−977912.	−0.240806
$441$	2.44198e6	0.597924
$442$	−9.10960e6	−2.21791
$443$	−1.45163e6	−0.351437	−0.175718	−	0.984440i	$-0.556225\pi$
$443$	−1.45163e6	−0.351437	−0.175718	+	0.984440i	$0.556225\pi$
$444$	−6.97153e6	−1.67831
$445$	1.54042e6	0.368757
$446$	−5.85279e6	−1.39324
$447$	907219.	0.214755
$448$	1.07314e6	0.252617
$449$	−6.63970e6	−1.55429	−0.777146	−	0.629320i	$-0.783334\pi$
$449$	−6.63970e6	−1.55429	−0.777146	+	0.629320i	$0.783334\pi$
$450$	966973.	0.225104
$451$	−869945.	−0.201396
$452$	4.18703e6	0.963963
$453$	−1.13620e6	−0.260141
$454$	−5.65062e6	−1.28664
$455$	−669454.	−0.151598
$456$	−1.08092e6	−0.243435
$457$	2.98559e6	0.668713	0.334357	−	0.942447i	$-0.391481\pi$
$457$	2.98559e6	0.668713	0.334357	+	0.942447i	$0.391481\pi$
$458$	−1.41092e6	−0.314297
$459$	−4.57356e6	−1.01326
$460$	−1.96608e6	−0.433219
$461$	1.98102e6	0.434147	0.217074	−	0.976155i	$-0.430349\pi$
$461$	1.98102e6	0.434147	0.217074	+	0.976155i	$0.430349\pi$
$462$	393665.	0.0858069
$463$	4.60608e6	0.998571	0.499286	−	0.866437i	$-0.333596\pi$
$463$	4.60608e6	0.998571	0.499286	+	0.866437i	$0.333596\pi$
$464$	−1.53344e6	−0.330652
$465$	−1.68907e6	−0.362257
$466$	9.56271e6	2.03993
$467$	5.44748e6	1.15586	0.577928	−	0.816088i	$-0.303862\pi$
$467$	5.44748e6	1.15586	0.577928	+	0.816088i	$0.303862\pi$
$468$	7.64877e6	1.61427
$469$	−1.04143e6	−0.218623
$470$	−2.76608e6	−0.577590
$471$	−5.56707e6	−1.15631
$472$	1.22701e6	0.253508
$473$	−1.26663e6	−0.260314
$474$	3.41975e6	0.699116
$475$	−225625.	−0.0458831
$476$	2.85586e6	0.577723
$477$	−2.75572e6	−0.554548
$478$	−98798.1	−0.0197778
$479$	−8.80284e6	−1.75301	−0.876505	−	0.481393i	$-0.840131\pi$
$479$	−8.80284e6	−1.75301	−0.876505	+	0.481393i	$0.840131\pi$
$480$	−125506.	−0.0248634
$481$	−8.70784e6	−1.71612
$482$	8.58803e6	1.68374
$483$	400913.	0.0781956
$484$	949459.	0.184231
$485$	1.23623e6	0.238641
$486$	9.21725e6	1.77015
$487$	−4.09826e6	−0.783028	−0.391514	−	0.920172i	$-0.628048\pi$
$487$	−4.09826e6	−0.783028	−0.391514	+	0.920172i	$0.628048\pi$
$488$	−7.80657e6	−1.48392
$489$	−4.03874e6	−0.763790
$490$	−3.82159e6	−0.719042
$491$	−788583.	−0.147620	−0.0738098	−	0.997272i	$-0.523516\pi$
$491$	−788583.	−0.147620	−0.0738098	+	0.997272i	$0.523516\pi$
$492$	−4.31841e6	−0.804288
$493$	1.71026e6	0.316916
$494$	−2.66536e6	−0.491403
$495$	−475567.	−0.0872366
$496$	−8.06957e6	−1.47281
$497$	2.45744e6	0.446264
$498$	6.84436e6	1.23669
$499$	−9.33795e6	−1.67881	−0.839403	−	0.543510i	$-0.817095\pi$
$499$	−9.33795e6	−1.67881	−0.839403	+	0.543510i	$0.817095\pi$
$500$	−1.01327e6	−0.181259
$501$	1.67939e6	0.298922
$502$	4.40043e6	0.779356
$503$	8.59267e6	1.51429	0.757144	−	0.653248i	$-0.226594\pi$
$503$	8.59267e6	1.51429	0.757144	+	0.653248i	$0.226594\pi$
$504$	−1.81402e6	−0.318101
$505$	1.35049e6	0.235648
$506$	1.44408e6	0.250734
$507$	−1.77432e6	−0.306558
$508$	−2.15541e6	−0.370571
$509$	−2.81039e6	−0.480809	−0.240404	−	0.970673i	$-0.577280\pi$
$509$	−2.81039e6	−0.480809	−0.240404	+	0.970673i	$0.577280\pi$
$510$	2.81159e6	0.478660
$511$	1.57159e6	0.266248
$512$	1.08444e7	1.82823
$513$	−1.33817e6	−0.224500
$514$	1.10441e7	1.84385
$515$	−58735.0	−0.00975840
$516$	−6.28757e6	−1.03958
$517$	1.36038e6	0.223839
$518$	4.07699e6	0.667598
$519$	1.85857e6	0.302873
$520$	−6.06337e6	−0.983345
$521$	−8.48212e6	−1.36902	−0.684510	−	0.729003i	$-0.739984\pi$
$521$	−8.48212e6	−1.36902	−0.684510	+	0.729003i	$0.739984\pi$
$522$	−2.14460e6	−0.344484
$523$	−761764.	−0.121777	−0.0608886	−	0.998145i	$-0.519393\pi$
$523$	−761764.	−0.121777	−0.0608886	+	0.998145i	$0.519393\pi$
$524$	3.06671e6	0.487916
$525$	206621.	0.0327171
$526$	898328.	0.141570
$527$	9.00009e6	1.41163
$528$	1.23980e6	0.193539
$529$	−4.96568e6	−0.771506
$530$	4.31258e6	0.666880
$531$	596705.	0.0918382
$532$	835590.	0.128001
$533$	−5.39394e6	−0.822410
$534$	−5.61644e6	−0.852330
$535$	−244331.	−0.0369058
$536$	−9.43240e6	−1.41811
$537$	−4.90548e6	−0.734084
$538$	1.94191e7	2.89249
$539$	1.87950e6	0.278657
$540$	−6.00964e6	−0.886878
$541$	9.77999e6	1.43663	0.718316	−	0.695717i	$-0.244913\pi$
$541$	9.77999e6	1.43663	0.718316	+	0.695717i	$0.244913\pi$
$542$	2.50428e6	0.366172
$543$	−1.52243e6	−0.221584
$544$	668748.	0.0968869
$545$	−3.70968e6	−0.534990
$546$	2.44085e6	0.350397
$547$	−635098.	−0.0907554	−0.0453777	−	0.998970i	$-0.514449\pi$
$547$	−635098.	−0.0907554	−0.0453777	+	0.998970i	$0.514449\pi$
$548$	1.34106e6	0.190764
$549$	−3.79640e6	−0.537578
$550$	744241.	0.104908
$551$	500401.	0.0702165
$552$	3.63115e6	0.507219
$553$	−1.33911e6	−0.186210
$554$	2.91323e6	0.403274
$555$	2.68759e6	0.370366
$556$	1.47251e7	2.02009
$557$	8.84580e6	1.20809	0.604045	−	0.796950i	$-0.293555\pi$
$557$	8.84580e6	1.20809	0.604045	+	0.796950i	$0.293555\pi$
$558$	−1.12857e7	−1.53442
$559$	−7.85352e6	−1.06300
$560$	987133.	0.133016
$561$	−1.38277e6	−0.185499
$562$	−2.50052e6	−0.333956
$563$	−5.51165e6	−0.732842	−0.366421	−	0.930449i	$-0.619417\pi$
$563$	−5.51165e6	−0.732842	−0.366421	+	0.930449i	$0.619417\pi$
$564$	6.75296e6	0.893915
$565$	−1.61414e6	−0.212726
$566$	−2.21882e7	−2.91126
$567$	−138104.	−0.0180405
$568$	2.22575e7	2.89471
$569$	−8.42502e6	−1.09091	−0.545457	−	0.838139i	$-0.683644\pi$
$569$	−8.42502e6	−1.09091	−0.545457	+	0.838139i	$0.683644\pi$
$570$	822637.	0.106053
$571$	3.94350e6	0.506164	0.253082	−	0.967445i	$-0.418556\pi$
$571$	3.94350e6	0.506164	0.253082	+	0.967445i	$0.418556\pi$
$572$	5.88695e6	0.752316
$573$	−3.59107e6	−0.456918
$574$	2.52543e6	0.319930
$575$	757943.	0.0956020
$576$	4.72675e6	0.593617
$577$	1.12279e7	1.40397	0.701986	−	0.712191i	$-0.252297\pi$
$577$	1.12279e7	1.40397	0.701986	+	0.712191i	$0.252297\pi$
$578$	−1.00823e6	−0.125528
$579$	−1.22715e6	−0.152125
$580$	2.24728e6	0.277387
$581$	−2.68011e6	−0.329391
$582$	−4.50734e6	−0.551585
$583$	−2.12097e6	−0.258442
$584$	1.42342e7	1.72703
$585$	−2.94867e6	−0.356235
$586$	1.28961e7	1.55137
$587$	−6.03739e6	−0.723193	−0.361596	−	0.932335i	$-0.617768\pi$
$587$	−6.03739e6	−0.723193	−0.361596	+	0.932335i	$0.617768\pi$
$588$	9.32984e6	1.11283
$589$	2.63332e6	0.312763
$590$	−933816.	−0.110441
$591$	−5.45350e6	−0.642254
$592$	1.28400e7	1.50578
$593$	7.28362e6	0.850571	0.425285	−	0.905059i	$-0.360174\pi$
$593$	7.28362e6	0.850571	0.425285	+	0.905059i	$0.360174\pi$
$594$	4.41404e6	0.513299
$595$	−1.10096e6	−0.127491
$596$	−6.35191e6	−0.732468
$597$	−2.18896e6	−0.251364
$598$	8.95374e6	1.02389
$599$	1.64862e7	1.87739	0.938695	−	0.344748i	$-0.112036\pi$
$599$	1.64862e7	1.87739	0.938695	+	0.344748i	$0.112036\pi$
$600$	1.87140e6	0.212221
$601$	1.45994e7	1.64873	0.824363	−	0.566061i	$-0.191533\pi$
$601$	1.45994e7	1.64873	0.824363	+	0.566061i	$0.191533\pi$
$602$	3.67700e6	0.413526
$603$	−4.58706e6	−0.513737
$604$	7.95511e6	0.887267
$605$	−366025.	−0.0406558
$606$	−4.92394e6	−0.544667
$607$	1.00550e7	1.10767	0.553834	−	0.832627i	$-0.313164\pi$
$607$	1.00550e7	1.10767	0.553834	+	0.832627i	$0.313164\pi$
$608$	195667.	0.0214664
$609$	−458252.	−0.0500681
$610$	5.94120e6	0.646472
$611$	8.43482e6	0.914056
$612$	1.25789e7	1.35758
$613$	−2.66404e6	−0.286345	−0.143173	−	0.989698i	$-0.545730\pi$
$613$	−2.66404e6	−0.286345	−0.143173	+	0.989698i	$0.545730\pi$
$614$	−923757.	−0.0988864
$615$	1.66479e6	0.177489
$616$	−1.39618e6	−0.148248
$617$	−6.13268e6	−0.648541	−0.324271	−	0.945964i	$-0.605119\pi$
$617$	−6.13268e6	−0.648541	−0.324271	+	0.945964i	$0.605119\pi$
$618$	214150.	0.0225552
$619$	2.47209e6	0.259321	0.129660	−	0.991558i	$-0.458611\pi$
$619$	2.47209e6	0.259321	0.129660	+	0.991558i	$0.458611\pi$
$620$	1.18261e7	1.23555
$621$	4.49531e6	0.467768
$622$	3.13367e6	0.324771
$623$	2.19928e6	0.227018
$624$	7.68719e6	0.790325
$625$	390625.	0.0400000
$626$	1.47574e7	1.50513
$627$	−404581.	−0.0410995
$628$	3.89780e7	3.94385
$629$	−1.43206e7	−1.44323
$630$	1.38056e6	0.138581
$631$	−4.16965e6	−0.416894	−0.208447	−	0.978034i	$-0.566841\pi$
$631$	−4.16965e6	−0.416894	−0.208447	+	0.978034i	$0.566841\pi$
$632$	−1.21285e7	−1.20786
$633$	−1.64454e6	−0.163131
$634$	−292879.	−0.0289378
$635$	830931.	0.0817769
$636$	−1.05285e7	−1.03211
$637$	1.16535e7	1.13791
$638$	−1.65061e6	−0.160544
$639$	1.08240e7	1.04866
$640$	−7.83076e6	−0.755708
$641$	2.02458e7	1.94621	0.973107	−	0.230353i	$-0.0739882\pi$
$641$	2.02458e7	1.94621	0.973107	+	0.230353i	$0.0739882\pi$
$642$	890841.	0.0853027
$643$	2.28399e6	0.217854	0.108927	−	0.994050i	$-0.465258\pi$
$643$	2.28399e6	0.217854	0.108927	+	0.994050i	$0.465258\pi$
$644$	−2.80700e6	−0.266703
$645$	2.42392e6	0.229413
$646$	−4.38335e6	−0.413262
$647$	−1.08505e7	−1.01903	−0.509517	−	0.860461i	$-0.670176\pi$
$647$	−1.08505e7	−1.01903	−0.509517	+	0.860461i	$0.670176\pi$
$648$	−1.25083e6	−0.117020
$649$	459260.	0.0428003
$650$	4.61454e6	0.428395
$651$	−2.41151e6	−0.223016
$652$	2.82773e7	2.60507
$653$	−1.17843e6	−0.108149	−0.0540745	−	0.998537i	$-0.517221\pi$
$653$	−1.17843e6	−0.108149	−0.0540745	+	0.998537i	$0.517221\pi$
$654$	1.35256e7	1.23655
$655$	−1.18225e6	−0.107672
$656$	7.95355e6	0.721608
$657$	6.92221e6	0.625649
$658$	−3.94916e6	−0.355582
$659$	−1.54643e7	−1.38713	−0.693566	−	0.720393i	$-0.743961\pi$
$659$	−1.54643e7	−1.38713	−0.693566	+	0.720393i	$0.743961\pi$
$660$	−1.81695e6	−0.162362
$661$	1.49578e7	1.33157	0.665786	−	0.746143i	$-0.268096\pi$
$661$	1.49578e7	1.33157	0.665786	+	0.746143i	$0.268096\pi$
$662$	−9.60389e6	−0.851730
$663$	−8.57361e6	−0.757495
$664$	−2.42743e7	−2.13661
$665$	−322128.	−0.0282471
$666$	1.79575e7	1.56877
$667$	−1.68100e6	−0.146303
$668$	−1.17583e7	−1.01954
$669$	−5.50843e6	−0.475841
$670$	7.17854e6	0.617802
$671$	−2.92194e6	−0.250533
$672$	−179186.	−0.0153067
$673$	−4.78732e6	−0.407432	−0.203716	−	0.979030i	$-0.565302\pi$
$673$	−4.78732e6	−0.407432	−0.203716	+	0.979030i	$0.565302\pi$
$674$	−1.74643e7	−1.48082
$675$	2.31677e6	0.195715
$676$	1.24229e7	1.04558
$677$	1.19304e7	1.00042	0.500211	−	0.865904i	$-0.333256\pi$
$677$	1.19304e7	1.00042	0.500211	+	0.865904i	$0.333256\pi$
$678$	5.88521e6	0.491686
$679$	1.76498e6	0.146915
$680$	−9.97161e6	−0.826976
$681$	−5.31815e6	−0.439433
$682$	−8.68619e6	−0.715103
$683$	−1.45524e7	−1.19366	−0.596832	−	0.802367i	$-0.703574\pi$
$683$	−1.45524e7	−1.19366	−0.596832	+	0.802367i	$0.703574\pi$
$684$	3.68043e6	0.300787
$685$	−516990.	−0.0420974
$686$	−1.13598e7	−0.921635
$687$	−1.32791e6	−0.107344
$688$	1.15803e7	0.932713
$689$	−1.31507e7	−1.05536
$690$	−2.76349e6	−0.220971
$691$	1.77507e6	0.141423	0.0707116	−	0.997497i	$-0.477473\pi$
$691$	1.77507e6	0.141423	0.0707116	+	0.997497i	$0.477473\pi$
$692$	−1.30128e7	−1.03301
$693$	−678973.	−0.0537056
$694$	−1.13726e7	−0.896316
$695$	−5.67666e6	−0.445791
$696$	−4.15048e6	−0.324769
$697$	−8.87069e6	−0.691633
$698$	1.07496e7	0.835132
$699$	9.00006e6	0.696711
$700$	−1.44666e6	−0.111589
$701$	−1.69545e7	−1.30314	−0.651569	−	0.758590i	$-0.725889\pi$
$701$	−1.69545e7	−1.30314	−0.651569	+	0.758590i	$0.725889\pi$
$702$	2.73685e7	2.09608
$703$	−4.19003e6	−0.319764
$704$	3.63799e6	0.276649
$705$	−2.60333e6	−0.197268
$706$	1.73948e7	1.31343
$707$	1.92811e6	0.145072
$708$	2.27977e6	0.170926
$709$	−3.01547e6	−0.225288	−0.112644	−	0.993635i	$-0.535932\pi$
$709$	−3.01547e6	−0.225288	−0.112644	+	0.993635i	$0.535932\pi$
$710$	−1.69391e7	−1.26108
$711$	−5.89821e6	−0.437569
$712$	1.99193e7	1.47256
$713$	−8.84611e6	−0.651671
$714$	4.01414e6	0.294678
$715$	−2.26947e6	−0.166020
$716$	3.43458e7	2.50375
$717$	−92985.1	−0.00675484
$718$	1.40085e7	1.01410
$719$	−2.06849e7	−1.49221	−0.746106	−	0.665827i	$-0.768079\pi$
$719$	−2.06849e7	−1.49221	−0.746106	+	0.665827i	$0.768079\pi$
$720$	4.34791e6	0.312572
$721$	−83856.7	−0.00600758
$722$	−1.28252e6	−0.0915629
$723$	8.08273e6	0.575059
$724$	1.06594e7	0.755761
$725$	−866345.	−0.0612133
$726$	1.33454e6	0.0939702
$727$	−1.67945e7	−1.17851	−0.589253	−	0.807949i	$-0.700578\pi$
$727$	−1.67945e7	−1.17851	−0.589253	+	0.807949i	$0.700578\pi$
$728$	−8.65675e6	−0.605378
$729$	7.73471e6	0.539045
$730$	−1.08329e7	−0.752384
$731$	−1.29156e7	−0.893969
$732$	−1.45046e7	−1.00052
$733$	1.55869e7	1.07152	0.535761	−	0.844370i	$-0.320025\pi$
$733$	1.55869e7	1.07152	0.535761	+	0.844370i	$0.320025\pi$
$734$	−7.88751e6	−0.540380
$735$	−3.59674e6	−0.245579
$736$	−657306.	−0.0447274
$737$	−3.53048e6	−0.239422
$738$	1.11235e7	0.751796
$739$	−5.66864e6	−0.381828	−0.190914	−	0.981607i	$-0.561145\pi$
$739$	−5.66864e6	−0.381828	−0.190914	+	0.981607i	$0.561145\pi$
$740$	−1.88172e7	−1.26321
$741$	−2.50853e6	−0.167832
$742$	6.15713e6	0.410552
$743$	−7.58535e6	−0.504085	−0.252043	−	0.967716i	$-0.581102\pi$
$743$	−7.58535e6	−0.504085	−0.252043	+	0.967716i	$0.581102\pi$
$744$	−2.18415e7	−1.44661
$745$	2.44872e6	0.161640
$746$	−1.46566e7	−0.964244
$747$	−1.18048e7	−0.774028
$748$	9.68148e6	0.632685
$749$	−348835.	−0.0227204
$750$	−1.42423e6	−0.0924545
$751$	−4.75161e6	−0.307426	−0.153713	−	0.988116i	$-0.549123\pi$
$751$	−4.75161e6	−0.307426	−0.153713	+	0.988116i	$0.549123\pi$
$752$	−1.24374e7	−0.802021
$753$	4.14152e6	0.266178
$754$	−1.02343e7	−0.655588
$755$	−3.06677e6	−0.195801
$756$	−8.58004e6	−0.545990
$757$	−2.66076e7	−1.68759	−0.843794	−	0.536668i	$-0.819683\pi$
$757$	−2.66076e7	−1.68759	−0.843794	+	0.536668i	$0.819683\pi$
$758$	−1.67120e7	−1.05647
$759$	1.35911e6	0.0856348
$760$	−2.91757e6	−0.183226
$761$	6.60498e6	0.413438	0.206719	−	0.978400i	$-0.433721\pi$
$761$	6.60498e6	0.413438	0.206719	+	0.978400i	$0.433721\pi$
$762$	−3.02961e6	−0.189016
$763$	−5.29636e6	−0.329356
$764$	2.51430e7	1.55842
$765$	−4.84928e6	−0.299587
$766$	1.39326e7	0.857945
$767$	2.84756e6	0.174777
$768$	1.96400e7	1.20154
$769$	2.95053e7	1.79922	0.899610	−	0.436695i	$-0.143851\pi$
$769$	2.95053e7	1.79922	0.899610	+	0.436695i	$0.143851\pi$
$770$	1.06256e6	0.0645844
$771$	1.03943e7	0.629739
$772$	8.59192e6	0.518856
$773$	−1.64106e6	−0.0987815	−0.0493907	−	0.998780i	$-0.515728\pi$
$773$	−1.64106e6	−0.0987815	−0.0493907	+	0.998780i	$0.515728\pi$
$774$	1.61957e7	0.971732
$775$	−4.55907e6	−0.272660
$776$	1.59858e7	0.952970
$777$	3.83711e6	0.228009
$778$	−8.84583e6	−0.523950
$779$	−2.59545e6	−0.153239
$780$	−1.12657e7	−0.663012
$781$	8.33080e6	0.488719
$782$	1.47250e7	0.861071
$783$	−5.13824e6	−0.299509
$784$	−1.71835e7	−0.998437
$785$	−1.50264e7	−0.870321
$786$	4.31051e6	0.248870
$787$	−3.25550e7	−1.87361	−0.936807	−	0.349845i	$-0.886234\pi$
$787$	−3.25550e7	−1.87361	−0.936807	+	0.349845i	$0.886234\pi$
$788$	3.81828e7	2.19055
$789$	845473.	0.0483512
$790$	9.23043e6	0.526204
$791$	−2.30453e6	−0.130961
$792$	−6.14959e6	−0.348364
$793$	−1.81170e7	−1.02306
$794$	1.16827e6	0.0657646
$795$	4.05884e6	0.227764
$796$	1.53261e7	0.857331
$797$	−2.37943e7	−1.32687	−0.663434	−	0.748235i	$-0.730902\pi$
$797$	−2.37943e7	−1.32687	−0.663434	+	0.748235i	$0.730902\pi$
$798$	1.17449e6	0.0652893
$799$	1.38716e7	0.768706
$800$	−338759.	−0.0187140
$801$	9.68693e6	0.533464
$802$	−4.30717e6	−0.236459
$803$	5.32775e6	0.291578
$804$	−1.75253e7	−0.956150
$805$	1.08212e6	0.0588556
$806$	−5.38572e7	−2.92016
$807$	1.82765e7	0.987891
$808$	1.74633e7	0.941016
$809$	1.63403e7	0.877784	0.438892	−	0.898540i	$-0.355371\pi$
$809$	1.63403e7	0.877784	0.438892	+	0.898540i	$0.355371\pi$
$810$	951947.	0.0509800
$811$	−1.93410e7	−1.03259	−0.516295	−	0.856411i	$-0.672689\pi$
$811$	−1.93410e7	−1.03259	−0.516295	+	0.856411i	$0.672689\pi$
$812$	3.20846e6	0.170768
$813$	2.35694e6	0.125061
$814$	1.38211e7	0.731110
$815$	−1.09012e7	−0.574883
$816$	1.26421e7	0.664650
$817$	−3.77896e6	−0.198069
$818$	2.53554e7	1.32491
$819$	−4.20985e6	−0.219309
$820$	−1.16561e7	−0.605364
$821$	2.19532e7	1.13668	0.568341	−	0.822793i	$-0.307585\pi$
$821$	2.19532e7	1.13668	0.568341	+	0.822793i	$0.307585\pi$
$822$	1.88496e6	0.0973024
$823$	−9.35874e6	−0.481635	−0.240817	−	0.970570i	$-0.577415\pi$
$823$	−9.35874e6	−0.481635	−0.240817	+	0.970570i	$0.577415\pi$
$824$	−759506.	−0.0389684
$825$	700452.	0.0358297
$826$	−1.33322e6	−0.0679911
$827$	2.99639e6	0.152347	0.0761737	−	0.997095i	$-0.475730\pi$
$827$	2.99639e6	0.152347	0.0761737	+	0.997095i	$0.475730\pi$
$828$	−1.23637e7	−0.626718
$829$	−2.18583e7	−1.10466	−0.552332	−	0.833625i	$-0.686262\pi$
$829$	−2.18583e7	−1.10466	−0.552332	+	0.833625i	$0.686262\pi$
$830$	1.84740e7	0.930818
$831$	2.74182e6	0.137733
$832$	2.25567e7	1.12971
$833$	1.91649e7	0.956962
$834$	2.06973e7	1.03038
$835$	4.53294e6	0.224990
$836$	2.83268e6	0.140179
$837$	−2.70395e7	−1.33409
$838$	−2.78993e7	−1.37241
$839$	−3.77439e7	−1.85115	−0.925575	−	0.378565i	$-0.876417\pi$
$839$	−3.77439e7	−1.85115	−0.925575	+	0.378565i	$0.876417\pi$
$840$	2.67182e6	0.130650
$841$	−1.85897e7	−0.906323
$842$	2.28276e7	1.10964
$843$	−2.35339e6	−0.114058
$844$	1.15143e7	0.556393
$845$	−4.78916e6	−0.230737
$846$	−1.73944e7	−0.835573
$847$	−522579.	−0.0250290
$848$	1.93912e7	0.926007
$849$	−2.08827e7	−0.994300
$850$	7.58891e6	0.360273
$851$	1.40756e7	0.666259
$852$	4.13542e7	1.95173
$853$	−9.37954e6	−0.441376	−0.220688	−	0.975344i	$-0.570830\pi$
$853$	−9.37954e6	−0.441376	−0.220688	+	0.975344i	$0.570830\pi$
$854$	8.48233e6	0.397989
$855$	−1.41884e6	−0.0663771
$856$	−3.15946e6	−0.147377
$857$	−3.38501e7	−1.57437	−0.787186	−	0.616716i	$-0.788463\pi$
$857$	−3.38501e7	−1.57437	−0.787186	+	0.616716i	$0.788463\pi$
$858$	8.27459e6	0.383732
$859$	−6.77759e6	−0.313395	−0.156698	−	0.987647i	$-0.550085\pi$
$859$	−6.77759e6	−0.313395	−0.156698	+	0.987647i	$0.550085\pi$
$860$	−1.69711e7	−0.782463
$861$	2.37684e6	0.109268
$862$	−7.46490e6	−0.342181
$863$	9.49675e6	0.434058	0.217029	−	0.976165i	$-0.430363\pi$
$863$	9.49675e6	0.434058	0.217029	+	0.976165i	$0.430363\pi$
$864$	−2.00916e6	−0.0915651
$865$	5.01655e6	0.227963
$866$	1.39138e7	0.630449
$867$	−948906.	−0.0428722
$868$	1.68843e7	0.760646
$869$	−4.53962e6	−0.203925
$870$	3.15873e6	0.141486
$871$	−2.18901e7	−0.977693
$872$	−4.79701e7	−2.13639
$873$	7.77402e6	0.345231
$874$	4.30836e6	0.190780
$875$	557700.	0.0246253
$876$	2.64470e7	1.16444
$877$	1.28024e7	0.562074	0.281037	−	0.959697i	$-0.409322\pi$
$877$	1.28024e7	0.562074	0.281037	+	0.959697i	$0.409322\pi$
$878$	6.50570e6	0.284812
$879$	1.21373e7	0.529848
$880$	3.34642e6	0.145671
$881$	−1.20500e7	−0.523053	−0.261527	−	0.965196i	$-0.584226\pi$
$881$	−1.20500e7	−0.523053	−0.261527	+	0.965196i	$0.584226\pi$
$882$	−2.40320e7	−1.04020
$883$	3.96993e7	1.71349	0.856744	−	0.515742i	$-0.172484\pi$
$883$	3.96993e7	1.71349	0.856744	+	0.515742i	$0.172484\pi$
$884$	6.00283e7	2.58360
$885$	−878873.	−0.0377197
$886$	1.42858e7	0.611393
$887$	−1.15121e7	−0.491299	−0.245650	−	0.969359i	$-0.579001\pi$
$887$	−1.15121e7	−0.491299	−0.245650	+	0.969359i	$0.579001\pi$
$888$	3.47534e7	1.47899
$889$	1.18633e6	0.0503444
$890$	−1.51596e7	−0.641525
$891$	−468177.	−0.0197567
$892$	3.85674e7	1.62296
$893$	4.05866e6	0.170316
$894$	−8.92813e6	−0.373608
$895$	−1.32406e7	−0.552524
$896$	−1.11801e7	−0.465238
$897$	8.42693e6	0.349694
$898$	6.53427e7	2.70400
$899$	1.01113e7	0.417261
$900$	−6.37194e6	−0.262220
$901$	−2.16272e7	−0.887541
$902$	8.56130e6	0.350367
$903$	3.46066e6	0.141234
$904$	−2.08725e7	−0.849482
$905$	−4.10928e6	−0.166780
$906$	1.11816e7	0.452566
$907$	−2.81838e7	−1.13758	−0.568790	−	0.822483i	$-0.692588\pi$
$907$	−2.81838e7	−1.13758	−0.568790	+	0.822483i	$0.692588\pi$
$908$	3.72351e7	1.49878
$909$	8.49254e6	0.340901
$910$	6.58823e6	0.263734
$911$	2.74170e7	1.09452	0.547261	−	0.836962i	$-0.315671\pi$
$911$	2.74170e7	1.09452	0.547261	+	0.836962i	$0.315671\pi$
$912$	3.69892e6	0.147261
$913$	−9.08567e6	−0.360728
$914$	−2.93818e7	−1.16336
$915$	5.59164e6	0.220794
$916$	9.29739e6	0.366119
$917$	−1.68791e6	−0.0662865
$918$	4.50093e7	1.76277
$919$	4.95240e7	1.93431	0.967156	−	0.254183i	$-0.0818065\pi$
$919$	4.95240e7	1.93431	0.967156	+	0.254183i	$0.0818065\pi$
$920$	9.80101e6	0.381770
$921$	−869405.	−0.0337733
$922$	−1.94956e7	−0.755284
$923$	5.16537e7	1.99571
$924$	−2.59409e6	−0.0999550
$925$	7.25421e6	0.278764
$926$	−4.53294e7	−1.73721
$927$	−369354.	−0.0141170
$928$	751315.	0.0286386
$929$	1.04029e7	0.395471	0.197736	−	0.980255i	$-0.436641\pi$
$929$	1.04029e7	0.395471	0.197736	+	0.980255i	$0.436641\pi$
$930$	1.66225e7	0.630216
$931$	5.60742e6	0.212026
$932$	−6.30141e7	−2.37628
$933$	2.94929e6	0.110921
$934$	−5.36098e7	−2.01084
$935$	−3.73230e6	−0.139620
$936$	−3.81294e7	−1.42256
$937$	9.23484e6	0.343621	0.171811	−	0.985130i	$-0.445038\pi$
$937$	9.23484e6	0.343621	0.171811	+	0.985130i	$0.445038\pi$
$938$	1.02489e7	0.380338
$939$	1.38891e7	0.514055
$940$	1.82273e7	0.672824
$941$	−4.48867e6	−0.165251	−0.0826254	−	0.996581i	$-0.526331\pi$
$941$	−4.48867e6	−0.165251	−0.0826254	+	0.996581i	$0.526331\pi$
$942$	5.47867e7	2.01163
$943$	8.71892e6	0.319289
$944$	−4.19883e6	−0.153355
$945$	3.30768e6	0.120488
$946$	1.24652e7	0.452867
$947$	−1.38374e7	−0.501395	−0.250698	−	0.968065i	$-0.580660\pi$
$947$	−1.38374e7	−0.501395	−0.250698	+	0.968065i	$0.580660\pi$
$948$	−2.25347e7	−0.814388
$949$	3.30338e7	1.19067
$950$	2.22042e6	0.0798227
$951$	−275647.	−0.00988330
$952$	−1.42366e7	−0.509113
$953$	3.71427e7	1.32477	0.662386	−	0.749162i	$-0.269544\pi$
$953$	3.71427e7	1.32477	0.662386	+	0.749162i	$0.269544\pi$
$954$	2.71196e7	0.964745
$955$	−9.69285e6	−0.343909
$956$	651037.	0.0230389
$957$	−1.55349e6	−0.0548314
$958$	8.66306e7	3.04970
$959$	−738113.	−0.0259165
$960$	−6.96192e6	−0.243810
$961$	2.45806e7	0.858588
$962$	8.56956e7	2.98553
$963$	−1.53647e6	−0.0533900
$964$	−5.65914e7	−1.96136
$965$	−3.31227e6	−0.114500
$966$	−3.94547e6	−0.136037
$967$	−5.02299e7	−1.72741	−0.863707	−	0.503995i	$-0.831863\pi$
$967$	−5.02299e7	−1.72741	−0.863707	+	0.503995i	$0.831863\pi$
$968$	−4.73309e6	−0.162352
$969$	−4.12545e6	−0.141144
$970$	−1.21660e7	−0.415162
$971$	−1.49489e7	−0.508816	−0.254408	−	0.967097i	$-0.581881\pi$
$971$	−1.49489e7	−0.508816	−0.254408	+	0.967097i	$0.581881\pi$
$972$	−6.07377e7	−2.06202
$973$	−8.10465e6	−0.274443
$974$	4.03318e7	1.36223
$975$	4.34303e6	0.146312
$976$	2.67141e7	0.897669
$977$	−2.98889e7	−1.00178	−0.500892	−	0.865510i	$-0.666995\pi$
$977$	−2.98889e7	−1.00178	−0.500892	+	0.865510i	$0.666995\pi$
$978$	3.97461e7	1.32876
$979$	7.45565e6	0.248616
$980$	2.51826e7	0.837599
$981$	−2.33283e7	−0.773945
$982$	7.76061e6	0.256813
$983$	9.91790e6	0.327368	0.163684	−	0.986513i	$-0.447662\pi$
$983$	9.91790e6	0.327368	0.163684	+	0.986513i	$0.447662\pi$
$984$	2.15275e7	0.708770
$985$	−1.47198e7	−0.483406
$986$	−1.68310e7	−0.551338
$987$	−3.71680e6	−0.121444
$988$	1.75636e7	0.572427
$989$	1.26947e7	0.412696
$990$	4.68015e6	0.151765
$991$	−9.07149e6	−0.293423	−0.146712	−	0.989179i	$-0.546869\pi$
$991$	−9.07149e6	−0.293423	−0.146712	+	0.989179i	$0.546869\pi$
$992$	3.95373e6	0.127564
$993$	−9.03882e6	−0.290896
$994$	−2.41841e7	−0.776363
$995$	−5.90835e6	−0.189194
$996$	−4.51014e7	−1.44059
$997$	4.93894e7	1.57361	0.786803	−	0.617204i	$-0.211735\pi$
$997$	4.93894e7	1.57361	0.786803	+	0.617204i	$0.211735\pi$
$998$	9.18967e7	2.92061
$999$	4.30243e7	1.36395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.5	✓	37	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-9.84120 q^{2} -9.26217 q^{3} +64.8493 q^{4} -25.0000 q^{5} +91.1509 q^{6} -35.6928 q^{7} -323.277 q^{8} -157.212 q^{9} +O(q^{10})\)	\(q-9.84120 q^{2} -9.26217 q^{3} +64.8493 q^{4} -25.0000 q^{5} +91.1509 q^{6} -35.6928 q^{7} -323.277 q^{8} -157.212 q^{9} +246.030 q^{10} -121.000 q^{11} -600.645 q^{12} -750.239 q^{13} +351.260 q^{14} +231.554 q^{15} +1106.25 q^{16} -1233.82 q^{17} +1547.16 q^{18} -361.000 q^{19} -1621.23 q^{20} +330.593 q^{21} +1190.79 q^{22} +1212.71 q^{23} +2994.24 q^{24} +625.000 q^{25} +7383.26 q^{26} +3706.83 q^{27} -2314.65 q^{28} -1386.15 q^{29} -2278.77 q^{30} -7294.50 q^{31} -542.015 q^{32} +1120.72 q^{33} +12142.3 q^{34} +892.320 q^{35} -10195.1 q^{36} +11606.7 q^{37} +3552.67 q^{38} +6948.85 q^{39} +8081.91 q^{40} +7189.63 q^{41} -3253.43 q^{42} +10468.0 q^{43} -7846.76 q^{44} +3930.30 q^{45} -11934.5 q^{46} -11242.8 q^{47} -10246.3 q^{48} -15533.0 q^{49} -6150.75 q^{50} +11427.8 q^{51} -48652.5 q^{52} +17528.7 q^{53} -36479.7 q^{54} +3025.00 q^{55} +11538.7 q^{56} +3343.64 q^{57} +13641.4 q^{58} -3795.54 q^{59} +15016.1 q^{60} +24148.3 q^{61} +71786.7 q^{62} +5611.35 q^{63} -30066.0 q^{64} +18756.0 q^{65} -11029.3 q^{66} +29177.5 q^{67} -80012.2 q^{68} -11232.3 q^{69} -8781.51 q^{70} -68849.6 q^{71} +50823.0 q^{72} -44031.0 q^{73} -114224. q^{74} -5788.86 q^{75} -23410.6 q^{76} +4318.83 q^{77} -68385.0 q^{78} +37517.5 q^{79} -27656.3 q^{80} +3869.23 q^{81} -70754.6 q^{82} +75088.2 q^{83} +21438.7 q^{84} +30845.4 q^{85} -103018. q^{86} +12838.8 q^{87} +39116.5 q^{88} -61616.9 q^{89} -38678.9 q^{90} +26778.2 q^{91} +78643.3 q^{92} +67563.0 q^{93} +110643. q^{94} +9025.00 q^{95} +5020.23 q^{96} -49449.2 q^{97} +152864. q^{98} +19022.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

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