LMFDB - Embedded newform 1045.6.a.g.1.19

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:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-0.429556 q^{2} -22.9509 q^{3} -31.8155 q^{4} -25.0000 q^{5} +9.85872 q^{6} -78.3412 q^{7} +27.4123 q^{8} +283.745 q^{9} +O(q^{10})$	\(q-0.429556 q^{2} -22.9509 q^{3} -31.8155 q^{4} -25.0000 q^{5} +9.85872 q^{6} -78.3412 q^{7} +27.4123 q^{8} +283.745 q^{9} +10.7389 q^{10} -121.000 q^{11} +730.195 q^{12} +215.132 q^{13} +33.6520 q^{14} +573.773 q^{15} +1006.32 q^{16} -352.702 q^{17} -121.885 q^{18} +361.000 q^{19} +795.387 q^{20} +1798.00 q^{21} +51.9763 q^{22} -427.243 q^{23} -629.139 q^{24} +625.000 q^{25} -92.4113 q^{26} -935.147 q^{27} +2492.46 q^{28} +778.489 q^{29} -246.468 q^{30} -1821.76 q^{31} -1309.47 q^{32} +2777.06 q^{33} +151.505 q^{34} +1958.53 q^{35} -9027.50 q^{36} +1939.24 q^{37} -155.070 q^{38} -4937.48 q^{39} -685.309 q^{40} +17145.5 q^{41} -772.344 q^{42} -2171.54 q^{43} +3849.67 q^{44} -7093.64 q^{45} +183.525 q^{46} -14895.0 q^{47} -23096.0 q^{48} -10669.7 q^{49} -268.473 q^{50} +8094.84 q^{51} -6844.52 q^{52} -33380.7 q^{53} +401.698 q^{54} +3025.00 q^{55} -2147.52 q^{56} -8285.29 q^{57} -334.405 q^{58} +11993.8 q^{59} -18254.9 q^{60} -36951.0 q^{61} +782.550 q^{62} -22229.0 q^{63} -31639.8 q^{64} -5378.30 q^{65} -1192.91 q^{66} +28970.0 q^{67} +11221.4 q^{68} +9805.63 q^{69} -841.299 q^{70} -68763.7 q^{71} +7778.13 q^{72} -19223.3 q^{73} -833.012 q^{74} -14344.3 q^{75} -11485.4 q^{76} +9479.28 q^{77} +2120.93 q^{78} +50934.5 q^{79} -25158.0 q^{80} -47487.7 q^{81} -7364.98 q^{82} -15017.2 q^{83} -57204.4 q^{84} +8817.54 q^{85} +932.800 q^{86} -17867.0 q^{87} -3316.89 q^{88} -124957. q^{89} +3047.12 q^{90} -16853.7 q^{91} +13592.9 q^{92} +41811.2 q^{93} +6398.26 q^{94} -9025.00 q^{95} +30053.5 q^{96} -143925. q^{97} +4583.22 q^{98} -34333.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−0.429556	−0.0759356	−0.0379678	−	0.999279i	$-0.512088\pi$
$2$	−0.429556	−0.0759356	−0.0379678	+	0.999279i	$0.512088\pi$
$3$	−22.9509	−1.47230	−0.736152	−	0.676817i	$-0.763359\pi$
$3$	−22.9509	−1.47230	−0.736152	+	0.676817i	$0.763359\pi$
$4$	−31.8155	−0.994234
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	9.85872	0.111800
$7$	−78.3412	−0.604290	−0.302145	−	0.953262i	$-0.597703\pi$
$7$	−78.3412	−0.604290	−0.302145	+	0.953262i	$0.597703\pi$
$8$	27.4123	0.151433
$9$	283.745	1.16768
$10$	10.7389	0.0339594
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	730.195	1.46381
$13$	215.132	0.353058	0.176529	−	0.984295i	$-0.443513\pi$
$13$	215.132	0.353058	0.176529	+	0.984295i	$0.443513\pi$
$14$	33.6520	0.0458871
$15$	573.773	0.658434
$16$	1006.32	0.982735
$17$	−352.702	−0.295996	−0.147998	−	0.988988i	$-0.547283\pi$
$17$	−352.702	−0.295996	−0.147998	+	0.988988i	$0.547283\pi$
$18$	−121.885	−0.0886682
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	795.387	0.444635
$21$	1798.00	0.889697
$22$	51.9763	0.0228954
$23$	−427.243	−0.168405	−0.0842026	−	0.996449i	$-0.526834\pi$
$23$	−427.243	−0.168405	−0.0842026	+	0.996449i	$0.526834\pi$
$24$	−629.139	−0.222956
$25$	625.000	0.200000
$26$	−92.4113	−0.0268097
$27$	−935.147	−0.246871
$28$	2492.46	0.600805
$29$	778.489	0.171893	0.0859463	−	0.996300i	$-0.472609\pi$
$29$	778.489	0.171893	0.0859463	+	0.996300i	$0.472609\pi$
$30$	−246.468	−0.0499986
$31$	−1821.76	−0.340477	−0.170238	−	0.985403i	$-0.554454\pi$
$31$	−1821.76	−0.340477	−0.170238	+	0.985403i	$0.554454\pi$
$32$	−1309.47	−0.226058
$33$	2777.06	0.443916
$34$	151.505	0.0224766
$35$	1958.53	0.270246
$36$	−9027.50	−1.16094
$37$	1939.24	0.232877	0.116439	−	0.993198i	$-0.462852\pi$
$37$	1939.24	0.232877	0.116439	+	0.993198i	$0.462852\pi$
$38$	−155.070	−0.0174208
$39$	−4937.48	−0.519809
$40$	−685.309	−0.0677230
$41$	17145.5	1.59291	0.796456	−	0.604697i	$-0.206706\pi$
$41$	17145.5	1.59291	0.796456	+	0.604697i	$0.206706\pi$
$42$	−772.344	−0.0675597
$43$	−2171.54	−0.179101	−0.0895504	−	0.995982i	$-0.528543\pi$
$43$	−2171.54	−0.179101	−0.0895504	+	0.995982i	$0.528543\pi$
$44$	3849.67	0.299773
$45$	−7093.64	−0.522201
$46$	183.525	0.0127879
$47$	−14895.0	−0.983552	−0.491776	−	0.870722i	$-0.663652\pi$
$47$	−14895.0	−0.983552	−0.491776	+	0.870722i	$0.663652\pi$
$48$	−23096.0	−1.44688
$49$	−10669.7	−0.634834
$50$	−268.473	−0.0151871
$51$	8094.84	0.435795
$52$	−6844.52	−0.351022
$53$	−33380.7	−1.63232	−0.816160	−	0.577826i	$-0.803901\pi$
$53$	−33380.7	−1.63232	−0.816160	+	0.577826i	$0.803901\pi$
$54$	401.698	0.0187463
$55$	3025.00	0.134840
$56$	−2147.52	−0.0915095
$57$	−8285.29	−0.337770
$58$	−334.405	−0.0130528
$59$	11993.8	0.448568	0.224284	−	0.974524i	$-0.427996\pi$
$59$	11993.8	0.448568	0.224284	+	0.974524i	$0.427996\pi$
$60$	−18254.9	−0.654637
$61$	−36951.0	−1.27146	−0.635728	−	0.771913i	$-0.719300\pi$
$61$	−36951.0	−1.27146	−0.635728	+	0.771913i	$0.719300\pi$
$62$	782.550	0.0258543
$63$	−22229.0	−0.705615
$64$	−31639.8	−0.965569
$65$	−5378.30	−0.157892
$66$	−1192.91	−0.0337090
$67$	28970.0	0.788427	0.394214	−	0.919019i	$-0.371017\pi$
$67$	28970.0	0.788427	0.394214	+	0.919019i	$0.371017\pi$
$68$	11221.4	0.294289
$69$	9805.63	0.247943
$70$	−841.299	−0.0205213
$71$	−68763.7	−1.61887	−0.809437	−	0.587207i	$-0.800228\pi$
$71$	−68763.7	−1.61887	−0.809437	+	0.587207i	$0.800228\pi$
$72$	7778.13	0.176825
$73$	−19223.3	−0.422202	−0.211101	−	0.977464i	$-0.567705\pi$
$73$	−19223.3	−0.422202	−0.211101	+	0.977464i	$0.567705\pi$
$74$	−833.012	−0.0176837
$75$	−14344.3	−0.294461
$76$	−11485.4	−0.228093
$77$	9479.28	0.182200
$78$	2120.93	0.0394720
$79$	50934.5	0.918216	0.459108	−	0.888381i	$-0.348169\pi$
$79$	50934.5	0.918216	0.459108	+	0.888381i	$0.348169\pi$
$80$	−25158.0	−0.439492
$81$	−47487.7	−0.804208
$82$	−7364.98	−0.120959
$83$	−15017.2	−0.239273	−0.119637	−	0.992818i	$-0.538173\pi$
$83$	−15017.2	−0.239273	−0.119637	+	0.992818i	$0.538173\pi$
$84$	−57204.4	−0.884567
$85$	8817.54	0.132373
$86$	932.800	0.0136001
$87$	−17867.0	−0.253078
$88$	−3316.89	−0.0456588
$89$	−124957.	−1.67219	−0.836097	−	0.548582i	$-0.815168\pi$
$89$	−124957.	−1.67219	−0.836097	+	0.548582i	$0.815168\pi$
$90$	3047.12	0.0396536
$91$	−16853.7	−0.213349
$92$	13592.9	0.167434
$93$	41811.2	0.501285
$94$	6398.26	0.0746865
$95$	−9025.00	−0.102598
$96$	30053.5	0.332826
$97$	−143925.	−1.55313	−0.776563	−	0.630040i	$-0.783039\pi$
$97$	−143925.	−1.55313	−0.776563	+	0.630040i	$0.783039\pi$
$98$	4583.22	0.0482065
$99$	−34333.2	−0.352068
$100$	−19884.7	−0.198847
$101$	139448.	1.36022	0.680111	−	0.733109i	$-0.261932\pi$
$101$	139448.	1.36022	0.680111	+	0.733109i	$0.261932\pi$
$102$	−3477.19	−0.0330924
$103$	−43446.2	−0.403514	−0.201757	−	0.979436i	$-0.564665\pi$
$103$	−43446.2	−0.403514	−0.201757	+	0.979436i	$0.564665\pi$
$104$	5897.27	0.0534648
$105$	−44950.1	−0.397885
$106$	14338.9	0.123951
$107$	−172231.	−1.45429	−0.727147	−	0.686482i	$-0.759154\pi$
$107$	−172231.	−1.45429	−0.727147	+	0.686482i	$0.759154\pi$
$108$	29752.1	0.245448
$109$	−37269.3	−0.300459	−0.150229	−	0.988651i	$-0.548001\pi$
$109$	−37269.3	−0.300459	−0.150229	+	0.988651i	$0.548001\pi$
$110$	−1299.41	−0.0102391
$111$	−44507.3	−0.342866
$112$	−78836.3	−0.593856
$113$	246410.	1.81536	0.907680	−	0.419662i	$-0.137851\pi$
$113$	246410.	1.81536	0.907680	+	0.419662i	$0.137851\pi$
$114$	3559.00	0.0256487
$115$	10681.1	0.0753131
$116$	−24768.0	−0.170901
$117$	61042.7	0.412258
$118$	−5152.03	−0.0340623
$119$	27631.1	0.178867
$120$	15728.5	0.0997088
$121$	14641.0	0.0909091
$122$	15872.5	0.0965487
$123$	−393506.	−2.34525
$124$	57960.3	0.338514
$125$	−15625.0	−0.0894427
$126$	9548.59	0.0535813
$127$	332052.	1.82683	0.913413	−	0.407035i	$-0.133437\pi$
$127$	332052.	1.82683	0.913413	+	0.407035i	$0.133437\pi$
$128$	55494.0	0.299379
$129$	49839.0	0.263691
$130$	2310.28	0.0119897
$131$	184129.	0.937439	0.468719	−	0.883347i	$-0.344716\pi$
$131$	184129.	0.937439	0.468719	+	0.883347i	$0.344716\pi$
$132$	−88353.6	−0.441356
$133$	−28281.2	−0.138634
$134$	−12444.2	−0.0598696
$135$	23378.7	0.110404
$136$	−9668.38	−0.0448236
$137$	−401570.	−1.82793	−0.913966	−	0.405791i	$-0.866996\pi$
$137$	−401570.	−1.82793	−0.913966	+	0.405791i	$0.866996\pi$
$138$	−4212.07	−0.0188277
$139$	−323298.	−1.41927	−0.709637	−	0.704567i	$-0.751141\pi$
$139$	−323298.	−1.41927	−0.709637	+	0.704567i	$0.751141\pi$
$140$	−62311.6	−0.268688
$141$	341855.	1.44809
$142$	29537.9	0.122930
$143$	−26031.0	−0.106451
$144$	285539.	1.14752
$145$	−19462.2	−0.0768727
$146$	8257.49	0.0320602
$147$	244879.	0.934668
$148$	−61697.8	−0.231534
$149$	21955.6	0.0810177	0.0405088	−	0.999179i	$-0.487102\pi$
$149$	21955.6	0.0810177	0.0405088	+	0.999179i	$0.487102\pi$
$150$	6161.70	0.0223600
$151$	−151250.	−0.539824	−0.269912	−	0.962885i	$-0.586995\pi$
$151$	−151250.	−0.539824	−0.269912	+	0.962885i	$0.586995\pi$
$152$	9895.86	0.0347412
$153$	−100078.	−0.345627
$154$	−4071.89	−0.0138355
$155$	45544.1	0.152266
$156$	157088.	0.516812
$157$	−266769.	−0.863746	−0.431873	−	0.901934i	$-0.642147\pi$
$157$	−266769.	−0.863746	−0.431873	+	0.901934i	$0.642147\pi$
$158$	−21879.3	−0.0697252
$159$	766117.	2.40327
$160$	32736.7	0.101096
$161$	33470.7	0.101765
$162$	20398.6	0.0610680
$163$	−262408.	−0.773585	−0.386793	−	0.922167i	$-0.626417\pi$
$163$	−262408.	−0.773585	−0.386793	+	0.922167i	$0.626417\pi$
$164$	−545494.	−1.58373
$165$	−69426.6	−0.198525
$166$	6450.74	0.0181693
$167$	397910.	1.10406	0.552031	−	0.833824i	$-0.313853\pi$
$167$	397910.	1.10406	0.552031	+	0.833824i	$0.313853\pi$
$168$	49287.5	0.134730
$169$	−325011.	−0.875350
$170$	−3787.63	−0.0100518
$171$	102432.	0.267883
$172$	69088.7	0.178068
$173$	223752.	0.568396	0.284198	−	0.958766i	$-0.408273\pi$
$173$	223752.	0.568396	0.284198	+	0.958766i	$0.408273\pi$
$174$	7674.90	0.0192176
$175$	−48963.2	−0.120858
$176$	−121765.	−0.296306
$177$	−275270.	−0.660429
$178$	53676.2	0.126979
$179$	492573.	1.14905	0.574523	−	0.818488i	$-0.305187\pi$
$179$	492573.	1.14905	0.574523	+	0.818488i	$0.305187\pi$
$180$	225687.	0.519190
$181$	−234419.	−0.531859	−0.265930	−	0.963992i	$-0.585679\pi$
$181$	−234419.	−0.531859	−0.265930	+	0.963992i	$0.585679\pi$
$182$	7239.61	0.0162008
$183$	848060.	1.87197
$184$	−11711.7	−0.0255021
$185$	−48481.0	−0.104146
$186$	−17960.3	−0.0380654
$187$	42676.9	0.0892460
$188$	473893.	0.977880
$189$	73260.5	0.149182
$190$	3876.75	0.00779082
$191$	603536.	1.19707	0.598535	−	0.801097i	$-0.295750\pi$
$191$	603536.	1.19707	0.598535	+	0.801097i	$0.295750\pi$
$192$	726162.	1.42161
$193$	307068.	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$193$	307068.	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$194$	61823.9	0.117937
$195$	123437.	0.232466
$196$	339460.	0.631174
$197$	−657198.	−1.20651	−0.603255	−	0.797548i	$-0.706130\pi$
$197$	−657198.	−1.20651	−0.603255	+	0.797548i	$0.706130\pi$
$198$	14748.0	0.0267345
$199$	−230805.	−0.413155	−0.206578	−	0.978430i	$-0.566233\pi$
$199$	−230805.	−0.413155	−0.206578	+	0.978430i	$0.566233\pi$
$200$	17132.7	0.0302866
$201$	−664889.	−1.16080
$202$	−59900.9	−0.103289
$203$	−60987.7	−0.103873
$204$	−257541.	−0.433282
$205$	−428639.	−0.712372
$206$	18662.6	0.0306411
$207$	−121228.	−0.196643
$208$	216492.	0.346963
$209$	−43681.0	−0.0691714
$210$	19308.6	0.0302136
$211$	−909269.	−1.40600	−0.703001	−	0.711189i	$-0.748157\pi$
$211$	−909269.	−1.40600	−0.703001	+	0.711189i	$0.748157\pi$
$212$	1.06202e6	1.62291
$213$	1.57819e6	2.38347
$214$	73983.0	0.110433
$215$	54288.6	0.0800963
$216$	−25634.6	−0.0373845
$217$	142719.	0.205747
$218$	16009.2	0.0228155
$219$	441193.	0.621610
$220$	−96241.8	−0.134062
$221$	−75877.4	−0.104504
$222$	19118.4	0.0260357
$223$	675081.	0.909063	0.454531	−	0.890731i	$-0.349807\pi$
$223$	675081.	0.909063	0.454531	+	0.890731i	$0.349807\pi$
$224$	102585.	0.136604
$225$	177341.	0.233535
$226$	−105847.	−0.137850
$227$	−548801.	−0.706887	−0.353443	−	0.935456i	$-0.614989\pi$
$227$	−548801.	−0.706887	−0.353443	+	0.935456i	$0.614989\pi$
$228$	263600.	0.335822
$229$	55933.8	0.0704832	0.0352416	−	0.999379i	$-0.488780\pi$
$229$	55933.8	0.0704832	0.0352416	+	0.999379i	$0.488780\pi$
$230$	−4588.12	−0.00571894
$231$	−217558.	−0.268254
$232$	21340.2	0.0260303
$233$	−1.51310e6	−1.82590	−0.912950	−	0.408071i	$-0.866201\pi$
$233$	−1.51310e6	−1.82590	−0.912950	+	0.408071i	$0.866201\pi$
$234$	−26221.3	−0.0313050
$235$	372376.	0.439858
$236$	−381590.	−0.445982
$237$	−1.16900e6	−1.35189
$238$	−11869.1	−0.0135824
$239$	1.47169e6	1.66656	0.833279	−	0.552853i	$-0.186461\pi$
$239$	1.47169e6	1.66656	0.833279	+	0.552853i	$0.186461\pi$
$240$	577400.	0.647066
$241$	1.40077e6	1.55354	0.776771	−	0.629783i	$-0.216856\pi$
$241$	1.40077e6	1.55354	0.776771	+	0.629783i	$0.216856\pi$
$242$	−6289.13	−0.00690323
$243$	1.31713e6	1.43091
$244$	1.17561e6	1.26412
$245$	266741.	0.283906
$246$	169033.	0.178088
$247$	77662.6	0.0809971
$248$	−49938.8	−0.0515595
$249$	344659.	0.352283
$250$	6711.82	0.00679188
$251$	−354016.	−0.354681	−0.177341	−	0.984150i	$-0.556749\pi$
$251$	−354016.	−0.354681	−0.177341	+	0.984150i	$0.556749\pi$
$252$	707225.	0.701546
$253$	51696.4	0.0507761
$254$	−142635.	−0.138721
$255$	−202371.	−0.194894
$256$	988634.	0.942835
$257$	1.12228e6	1.05991	0.529953	−	0.848027i	$-0.322210\pi$
$257$	1.12228e6	1.05991	0.529953	+	0.848027i	$0.322210\pi$
$258$	−21408.6	−0.0200235
$259$	−151922.	−0.140725
$260$	171113.	0.156982
$261$	220893.	0.200715
$262$	−79093.6	−0.0711849
$263$	−1.22715e6	−1.09397	−0.546987	−	0.837141i	$-0.684225\pi$
$263$	−1.22715e6	−1.09397	−0.546987	+	0.837141i	$0.684225\pi$
$264$	76125.8	0.0672237
$265$	834516.	0.729996
$266$	12148.4	0.0105272
$267$	2.86789e6	2.46198
$268$	−921695.	−0.783881
$269$	−849448.	−0.715741	−0.357871	−	0.933771i	$-0.616497\pi$
$269$	−849448.	−0.715741	−0.357871	+	0.933771i	$0.616497\pi$
$270$	−10042.5	−0.00838360
$271$	570246.	0.471671	0.235835	−	0.971793i	$-0.424217\pi$
$271$	570246.	0.471671	0.235835	+	0.971793i	$0.424217\pi$
$272$	−354931.	−0.290885
$273$	386808.	0.314115
$274$	172497.	0.138805
$275$	−75625.0	−0.0603023
$276$	−311971.	−0.246514
$277$	−641708.	−0.502502	−0.251251	−	0.967922i	$-0.580842\pi$
$277$	−641708.	−0.502502	−0.251251	+	0.967922i	$0.580842\pi$
$278$	138875.	0.107773
$279$	−516917.	−0.397567
$280$	53687.9	0.0409243
$281$	1.46990e6	1.11051	0.555254	−	0.831681i	$-0.312621\pi$
$281$	1.46990e6	1.11051	0.555254	+	0.831681i	$0.312621\pi$
$282$	−146846.	−0.109961
$283$	−1.10308e6	−0.818734	−0.409367	−	0.912370i	$-0.634250\pi$
$283$	−1.10308e6	−0.818734	−0.409367	+	0.912370i	$0.634250\pi$
$284$	2.18775e6	1.60954
$285$	207132.	0.151055
$286$	11181.8	0.00808342
$287$	−1.34320e6	−0.962580
$288$	−371555.	−0.263962
$289$	−1.29546e6	−0.912387
$290$	8360.12	0.00583737
$291$	3.30321e6	2.28667
$292$	611599.	0.419768
$293$	−426698.	−0.290370	−0.145185	−	0.989405i	$-0.546378\pi$
$293$	−426698.	−0.290370	−0.145185	+	0.989405i	$0.546378\pi$
$294$	−105189.	−0.0709746
$295$	−299846.	−0.200606
$296$	53159.1	0.0352653
$297$	113153.	0.0744344
$298$	−9431.17	−0.00615212
$299$	−91913.6	−0.0594568
$300$	456372.	0.292763
$301$	170121.	0.108229
$302$	64970.3	0.0409918
$303$	−3.20047e6	−2.00266
$304$	363282.	0.225455
$305$	923775.	0.568613
$306$	42988.9	0.0262454
$307$	−1.33886e6	−0.810755	−0.405377	−	0.914149i	$-0.632860\pi$
$307$	−1.33886e6	−0.810755	−0.405377	+	0.914149i	$0.632860\pi$
$308$	−301588.	−0.181150
$309$	997130.	0.594095
$310$	−19563.7	−0.0115624
$311$	−1.18241e6	−0.693213	−0.346607	−	0.938011i	$-0.612666\pi$
$311$	−1.18241e6	−0.693213	−0.346607	+	0.938011i	$0.612666\pi$
$312$	−135348.	−0.0787163
$313$	1.04351e6	0.602054	0.301027	−	0.953616i	$-0.402671\pi$
$313$	1.04351e6	0.602054	0.301027	+	0.953616i	$0.402671\pi$
$314$	114592.	0.0655890
$315$	555724.	0.315561
$316$	−1.62051e6	−0.912921
$317$	−1.68226e6	−0.940255	−0.470127	−	0.882599i	$-0.655792\pi$
$317$	−1.68226e6	−0.940255	−0.470127	+	0.882599i	$0.655792\pi$
$318$	−329091.	−0.182494
$319$	−94197.1	−0.0518276
$320$	790994.	0.431815
$321$	3.95287e6	2.14116
$322$	−14377.6	−0.00772762
$323$	−127325.	−0.0679061
$324$	1.51084e6	0.799570
$325$	134457.	0.0706117
$326$	112719.	0.0587426
$327$	855364.	0.442366
$328$	470000.	0.241220
$329$	1.16690e6	0.594350
$330$	29822.6	0.0150751
$331$	1.65495e6	0.830259	0.415130	−	0.909762i	$-0.363736\pi$
$331$	1.65495e6	0.830259	0.415130	+	0.909762i	$0.363736\pi$
$332$	477780.	0.237893
$333$	550250.	0.271925
$334$	−170925.	−0.0838375
$335$	−724250.	−0.352595
$336$	1.80937e6	0.874336
$337$	3.73212e6	1.79012	0.895058	−	0.445950i	$-0.147134\pi$
$337$	3.73212e6	1.79012	0.895058	+	0.445950i	$0.147134\pi$
$338$	139611.	0.0664702
$339$	−5.65535e6	−2.67276
$340$	−280534.	−0.131610
$341$	220433.	0.102658
$342$	−44000.4	−0.0203419
$343$	2.15255e6	0.987913
$344$	−59527.1	−0.0271218
$345$	−245141.	−0.110884
$346$	−96113.9	−0.0431614
$347$	842336.	0.375545	0.187772	−	0.982213i	$-0.439873\pi$
$347$	842336.	0.375545	0.187772	+	0.982213i	$0.439873\pi$
$348$	568448.	0.251619
$349$	−1.40154e6	−0.615946	−0.307973	−	0.951395i	$-0.599651\pi$
$349$	−1.40154e6	−0.615946	−0.307973	+	0.951395i	$0.599651\pi$
$350$	21032.5	0.00917741
$351$	−201180.	−0.0871599
$352$	158445.	0.0681590
$353$	−4.02103e6	−1.71751	−0.858757	−	0.512383i	$-0.828763\pi$
$353$	−4.02103e6	−1.71751	−0.858757	+	0.512383i	$0.828763\pi$
$354$	118244.	0.0501500
$355$	1.71909e6	0.723983
$356$	3.97558e6	1.66255
$357$	−634159.	−0.263347
$358$	−211588.	−0.0872535
$359$	3.67480e6	1.50486	0.752432	−	0.658670i	$-0.228881\pi$
$359$	3.67480e6	1.50486	0.752432	+	0.658670i	$0.228881\pi$
$360$	−194453.	−0.0790786
$361$	130321.	0.0526316
$362$	100696.	0.0403870
$363$	−336025.	−0.133846
$364$	536208.	0.212119
$365$	480582.	0.188815
$366$	−364289.	−0.142149
$367$	4.23718e6	1.64215	0.821073	−	0.570823i	$-0.193376\pi$
$367$	4.23718e6	1.64215	0.821073	+	0.570823i	$0.193376\pi$
$368$	−429943.	−0.165498
$369$	4.86497e6	1.86001
$370$	20825.3	0.00790837
$371$	2.61508e6	0.986394
$372$	−1.33024e6	−0.498395
$373$	−4.17050e6	−1.55209	−0.776044	−	0.630679i	$-0.782776\pi$
$373$	−4.17050e6	−1.55209	−0.776044	+	0.630679i	$0.782776\pi$
$374$	−18332.1	−0.00677695
$375$	358608.	0.131687
$376$	−408308.	−0.148942
$377$	167478.	0.0606881
$378$	−31469.5	−0.0113282
$379$	−1.83390e6	−0.655810	−0.327905	−	0.944711i	$-0.606343\pi$
$379$	−1.83390e6	−0.655810	−0.327905	+	0.944711i	$0.606343\pi$
$380$	287135.	0.102006
$381$	−7.62091e6	−2.68964
$382$	−259253.	−0.0909001
$383$	−4.37490e6	−1.52395	−0.761976	−	0.647605i	$-0.775771\pi$
$383$	−4.37490e6	−1.52395	−0.761976	+	0.647605i	$0.775771\pi$
$384$	−1.27364e6	−0.440776
$385$	−236982.	−0.0814824
$386$	−131903.	−0.0450594
$387$	−616166.	−0.209132
$388$	4.57904e6	1.54417
$389$	−1.40651e6	−0.471270	−0.235635	−	0.971842i	$-0.575717\pi$
$389$	−1.40651e6	−0.471270	−0.235635	+	0.971842i	$0.575717\pi$
$390$	−53023.1	−0.0176524
$391$	150689.	0.0498472
$392$	−292480.	−0.0961350
$393$	−4.22592e6	−1.38019
$394$	282304.	0.0916170
$395$	−1.27336e6	−0.410638
$396$	1.09233e6	0.350038
$397$	−2.48056e6	−0.789903	−0.394951	−	0.918702i	$-0.629239\pi$
$397$	−2.48056e6	−0.789903	−0.394951	+	0.918702i	$0.629239\pi$
$398$	99143.9	0.0313732
$399$	649079.	0.204111
$400$	628950.	0.196547
$401$	2.94018e6	0.913088	0.456544	−	0.889701i	$-0.349087\pi$
$401$	2.94018e6	0.913088	0.456544	+	0.889701i	$0.349087\pi$
$402$	285607.	0.0881463
$403$	−391919.	−0.120208
$404$	−4.43662e6	−1.35238
$405$	1.18719e6	0.359653
$406$	26197.7	0.00788765
$407$	−234648.	−0.0702151
$408$	221898.	0.0659939
$409$	−2.78082e6	−0.821987	−0.410993	−	0.911638i	$-0.634818\pi$
$409$	−2.78082e6	−0.821987	−0.410993	+	0.911638i	$0.634818\pi$
$410$	184124.	0.0540943
$411$	9.21641e6	2.69127
$412$	1.38226e6	0.401187
$413$	−939612.	−0.271065
$414$	52074.4	0.0149322
$415$	375430.	0.107006
$416$	−281708.	−0.0798116
$417$	7.42000e6	2.08960
$418$	18763.5	0.00525257
$419$	−6.34476e6	−1.76555	−0.882776	−	0.469795i	$-0.844328\pi$
$419$	−6.34476e6	−1.76555	−0.882776	+	0.469795i	$0.844328\pi$
$420$	1.43011e6	0.395590
$421$	−53076.3	−0.0145947	−0.00729735	−	0.999973i	$-0.502323\pi$
$421$	−53076.3	−0.0145947	−0.00729735	+	0.999973i	$0.502323\pi$
$422$	390582.	0.106766
$423$	−4.22640e6	−1.14847
$424$	−915042.	−0.247187
$425$	−220439.	−0.0591991
$426$	−677922.	−0.180990
$427$	2.89478e6	0.768328
$428$	5.47962e6	1.44591
$429$	597435.	0.156728
$430$	−23320.0	−0.00608216
$431$	−5.82193e6	−1.50964	−0.754821	−	0.655930i	$-0.772276\pi$
$431$	−5.82193e6	−1.50964	−0.754821	+	0.655930i	$0.772276\pi$
$432$	−941057.	−0.242609
$433$	991201.	0.254063	0.127032	−	0.991899i	$-0.459455\pi$
$433$	991201.	0.254063	0.127032	+	0.991899i	$0.459455\pi$
$434$	−61305.9	−0.0156235
$435$	446676.	0.113180
$436$	1.18574e6	0.298726
$437$	−154235.	−0.0386348
$438$	−189517.	−0.0472023
$439$	−2.57560e6	−0.637848	−0.318924	−	0.947780i	$-0.603321\pi$
$439$	−2.57560e6	−0.637848	−0.318924	+	0.947780i	$0.603321\pi$
$440$	82922.3	0.0204193
$441$	−3.02747e6	−0.741281
$442$	32593.6	0.00793555
$443$	−1.81400e6	−0.439164	−0.219582	−	0.975594i	$-0.570469\pi$
$443$	−1.81400e6	−0.439164	−0.219582	+	0.975594i	$0.570469\pi$
$444$	1.41602e6	0.340889
$445$	3.12393e6	0.747828
$446$	−289985.	−0.0690302
$447$	−503902.	−0.119283
$448$	2.47870e6	0.583483
$449$	−7.74663e6	−1.81341	−0.906706	−	0.421762i	$-0.861412\pi$
$449$	−7.74663e6	−1.81341	−0.906706	+	0.421762i	$0.861412\pi$
$450$	−76177.9	−0.0177336
$451$	−2.07461e6	−0.480281
$452$	−7.83967e6	−1.80489
$453$	3.47132e6	0.794785
$454$	235741.	0.0536778
$455$	421342.	0.0954128
$456$	−227119.	−0.0511495
$457$	−1.21179e6	−0.271417	−0.135708	−	0.990749i	$-0.543331\pi$
$457$	−1.21179e6	−0.271417	−0.135708	+	0.990749i	$0.543331\pi$
$458$	−24026.7	−0.00535218
$459$	329828.	0.0730728
$460$	−339824.	−0.0748788
$461$	5.33061e6	1.16822	0.584110	−	0.811675i	$-0.301444\pi$
$461$	5.33061e6	1.16822	0.584110	+	0.811675i	$0.301444\pi$
$462$	93453.6	0.0203700
$463$	1.70750e6	0.370176	0.185088	−	0.982722i	$-0.440743\pi$
$463$	1.70750e6	0.370176	0.185088	+	0.982722i	$0.440743\pi$
$464$	783409.	0.168925
$465$	−1.04528e6	−0.224182
$466$	649960.	0.138651
$467$	−4.07178e6	−0.863957	−0.431978	−	0.901884i	$-0.642184\pi$
$467$	−4.07178e6	−0.863957	−0.431978	+	0.901884i	$0.642184\pi$
$468$	−1.94210e6	−0.409881
$469$	−2.26954e6	−0.476438
$470$	−159957.	−0.0334008
$471$	6.12259e6	1.27170
$472$	328780.	0.0679282
$473$	262757.	0.0540009
$474$	502149.	0.102657
$475$	225625.	0.0458831
$476$	−879096.	−0.177836
$477$	−9.47161e6	−1.90602
$478$	−632172.	−0.126551
$479$	−5.67933e6	−1.13099	−0.565494	−	0.824752i	$-0.691315\pi$
$479$	−5.67933e6	−1.13099	−0.565494	+	0.824752i	$0.691315\pi$
$480$	−751337.	−0.148844
$481$	417192.	0.0822192
$482$	−601708.	−0.117969
$483$	−768185.	−0.149830
$484$	−465810.	−0.0903849
$485$	3.59812e6	0.694579
$486$	−565780.	−0.108657
$487$	−3.70158e6	−0.707237	−0.353618	−	0.935390i	$-0.615049\pi$
$487$	−3.70158e6	−0.707237	−0.353618	+	0.935390i	$0.615049\pi$
$488$	−1.01291e6	−0.192541
$489$	6.02251e6	1.13895
$490$	−114580.	−0.0215586
$491$	8.22348e6	1.53940	0.769701	−	0.638404i	$-0.220405\pi$
$491$	8.22348e6	1.53940	0.769701	+	0.638404i	$0.220405\pi$
$492$	1.25196e7	2.33173
$493$	−274574.	−0.0508795
$494$	−33360.5	−0.00615056
$495$	858330.	0.157450
$496$	−1.83328e6	−0.334598
$497$	5.38703e6	0.978269
$498$	−148050.	−0.0267508
$499$	4.30367e6	0.773728	0.386864	−	0.922137i	$-0.373558\pi$
$499$	4.30367e6	0.773728	0.386864	+	0.922137i	$0.373558\pi$
$500$	497117.	0.0889270
$501$	−9.13240e6	−1.62551
$502$	152070.	0.0269329
$503$	−8.35417e6	−1.47226	−0.736128	−	0.676843i	$-0.763348\pi$
$503$	−8.35417e6	−1.47226	−0.736128	+	0.676843i	$0.763348\pi$
$504$	−609348.	−0.106854
$505$	−3.48621e6	−0.608310
$506$	−22206.5	−0.00385571
$507$	7.45931e6	1.28878
$508$	−1.05644e7	−1.81629
$509$	1.04462e7	1.78717	0.893584	−	0.448895i	$-0.148182\pi$
$509$	1.04462e7	1.78717	0.893584	+	0.448895i	$0.148182\pi$
$510$	86929.7	0.0147994
$511$	1.50598e6	0.255133
$512$	−2.20048e6	−0.370973
$513$	−337588.	−0.0566361
$514$	−482081.	−0.0804846
$515$	1.08615e6	0.180457
$516$	−1.58565e6	−0.262170
$517$	1.80230e6	0.296552
$518$	65259.2	0.0106860
$519$	−5.13531e6	−0.836851
$520$	−147432.	−0.0239102
$521$	6.42722e6	1.03736	0.518679	−	0.854969i	$-0.326424\pi$
$521$	6.42722e6	1.03736	0.518679	+	0.854969i	$0.326424\pi$
$522$	−94885.8	−0.0152414
$523$	9.95806e6	1.59192	0.795958	−	0.605351i	$-0.206967\pi$
$523$	9.95806e6	1.59192	0.795958	+	0.605351i	$0.206967\pi$
$524$	−5.85814e6	−0.932033
$525$	1.12375e6	0.177939
$526$	527129.	0.0830715
$527$	642539.	0.100780
$528$	2.79462e6	0.436252
$529$	−6.25381e6	−0.971640
$530$	−358472.	−0.0554326
$531$	3.40320e6	0.523783
$532$	899779.	0.137834
$533$	3.68855e6	0.562391
$534$	−1.23192e6	−0.186952
$535$	4.30578e6	0.650380
$536$	794136.	0.119394
$537$	−1.13050e7	−1.69175
$538$	364886.	0.0543502
$539$	1.29103e6	0.191410
$540$	−743803.	−0.109768
$541$	9.20275e6	1.35184	0.675919	−	0.736976i	$-0.263747\pi$
$541$	9.20275e6	1.35184	0.675919	+	0.736976i	$0.263747\pi$
$542$	−244953.	−0.0358166
$543$	5.38014e6	0.783058
$544$	461851.	0.0669121
$545$	931732.	0.134369
$546$	−166156.	−0.0238525
$547$	728332.	0.104078	0.0520392	−	0.998645i	$-0.483428\pi$
$547$	728332.	0.104078	0.0520392	+	0.998645i	$0.483428\pi$
$548$	1.27761e7	1.81739
$549$	−1.04847e7	−1.48465
$550$	32485.2	0.00457909
$551$	281034.	0.0394349
$552$	268795.	0.0375469
$553$	−3.99027e6	−0.554868
$554$	275650.	0.0381578
$555$	1.11268e6	0.153334
$556$	1.02859e7	1.41109
$557$	4.89082e6	0.667949	0.333975	−	0.942582i	$-0.391610\pi$
$557$	4.89082e6	0.667949	0.333975	+	0.942582i	$0.391610\pi$
$558$	222045.	0.0301895
$559$	−467168.	−0.0632330
$560$	1.97091e6	0.265581
$561$	−979475.	−0.131397
$562$	−631404.	−0.0843270
$563$	−93105.1	−0.0123795	−0.00618974	−	0.999981i	$-0.501970\pi$
$563$	−93105.1	−0.0123795	−0.00618974	+	0.999981i	$0.501970\pi$
$564$	−1.08763e7	−1.43974
$565$	−6.16026e6	−0.811854
$566$	473837.	0.0621710
$567$	3.72024e6	0.485974
$568$	−1.88497e6	−0.245151
$569$	520646.	0.0674158	0.0337079	−	0.999432i	$-0.489268\pi$
$569$	520646.	0.0674158	0.0337079	+	0.999432i	$0.489268\pi$
$570$	−88975.0	−0.0114705
$571$	1.14848e7	1.47413	0.737064	−	0.675823i	$-0.236212\pi$
$571$	1.14848e7	1.47413	0.737064	+	0.675823i	$0.236212\pi$
$572$	828187.	0.105837
$573$	−1.38517e7	−1.76245
$574$	576981.	0.0730940
$575$	−267027.	−0.0336810
$576$	−8.97764e6	−1.12747
$577$	638941.	0.0798954	0.0399477	−	0.999202i	$-0.487281\pi$
$577$	638941.	0.0798954	0.0399477	+	0.999202i	$0.487281\pi$
$578$	556472.	0.0692826
$579$	−7.04749e6	−0.873651
$580$	619200.	0.0764295
$581$	1.17647e6	0.144590
$582$	−1.41892e6	−0.173640
$583$	4.03906e6	0.492163
$584$	−526956.	−0.0639355
$585$	−1.52607e6	−0.184367
$586$	183291.	0.0220494
$587$	621368.	0.0744310	0.0372155	−	0.999307i	$-0.488151\pi$
$587$	621368.	0.0744310	0.0372155	+	0.999307i	$0.488151\pi$
$588$	−7.79093e6	−0.929279
$589$	−657656.	−0.0781108
$590$	128801.	0.0152331
$591$	1.50833e7	1.77635
$592$	1.95150e6	0.228856
$593$	−2.05875e6	−0.240418	−0.120209	−	0.992749i	$-0.538356\pi$
$593$	−2.05875e6	−0.240418	−0.120209	+	0.992749i	$0.538356\pi$
$594$	−48605.5	−0.00565222
$595$	−690777.	−0.0799918
$596$	−698528.	−0.0805505
$597$	5.29720e6	0.608290
$598$	39482.1	0.00451489
$599$	−1.06513e7	−1.21293	−0.606467	−	0.795108i	$-0.707414\pi$
$599$	−1.06513e7	−1.21293	−0.606467	+	0.795108i	$0.707414\pi$
$600$	−393212.	−0.0445911
$601$	1.64898e6	0.186221	0.0931107	−	0.995656i	$-0.470319\pi$
$601$	1.64898e6	0.186221	0.0931107	+	0.995656i	$0.470319\pi$
$602$	−73076.7	−0.00821841
$603$	8.22011e6	0.920628
$604$	4.81208e6	0.536711
$605$	−366025.	−0.0406558
$606$	1.37478e6	0.152073
$607$	−1.02671e7	−1.13103	−0.565516	−	0.824738i	$-0.691323\pi$
$607$	−1.02671e7	−1.13103	−0.565516	+	0.824738i	$0.691323\pi$
$608$	−472717.	−0.0518612
$609$	1.39973e6	0.152932
$610$	−396813.	−0.0431779
$611$	−3.20440e6	−0.347251
$612$	3.18401e6	0.343634
$613$	1.36706e6	0.146939	0.0734696	−	0.997297i	$-0.476593\pi$
$613$	1.36706e6	0.146939	0.0734696	+	0.997297i	$0.476593\pi$
$614$	575116.	0.0615651
$615$	9.83766e6	1.04883
$616$	259849.	0.0275912
$617$	−1.17534e7	−1.24294	−0.621470	−	0.783438i	$-0.713464\pi$
$617$	−1.17534e7	−1.24294	−0.621470	+	0.783438i	$0.713464\pi$
$618$	−428324.	−0.0451129
$619$	3.32544e6	0.348837	0.174418	−	0.984672i	$-0.444196\pi$
$619$	3.32544e6	0.348837	0.174418	+	0.984672i	$0.444196\pi$
$620$	−1.44901e6	−0.151388
$621$	399535.	0.0415744
$622$	507911.	0.0526395
$623$	9.78930e6	1.01049
$624$	−4.96868e6	−0.510834
$625$	390625.	0.0400000
$626$	−448246.	−0.0457173
$627$	1.00252e6	0.101841
$628$	8.48738e6	0.858765
$629$	−683973.	−0.0689306
$630$	−238715.	−0.0239623
$631$	9.90285e6	0.990117	0.495059	−	0.868860i	$-0.335147\pi$
$631$	9.90285e6	0.990117	0.495059	+	0.868860i	$0.335147\pi$
$632$	1.39624e6	0.139048
$633$	2.08686e7	2.07006
$634$	722626.	0.0713988
$635$	−8.30130e6	−0.816981
$636$	−2.43744e7	−2.38941
$637$	−2.29538e6	−0.224133
$638$	40463.0	0.00393556
$639$	−1.95114e7	−1.89032
$640$	−1.38735e6	−0.133886
$641$	−9.71541e6	−0.933934	−0.466967	−	0.884275i	$-0.654653\pi$
$641$	−9.71541e6	−0.933934	−0.466967	+	0.884275i	$0.654653\pi$
$642$	−1.69798e6	−0.162590
$643$	−8.80539e6	−0.839887	−0.419944	−	0.907550i	$-0.637950\pi$
$643$	−8.80539e6	−0.839887	−0.419944	+	0.907550i	$0.637950\pi$
$644$	−1.06489e6	−0.101179
$645$	−1.24597e6	−0.117926
$646$	54693.4	0.00515648
$647$	−1.17459e7	−1.10313	−0.551564	−	0.834133i	$-0.685969\pi$
$647$	−1.17459e7	−1.10313	−0.551564	+	0.834133i	$0.685969\pi$
$648$	−1.30175e6	−0.121784
$649$	−1.45126e6	−0.135248
$650$	−57757.0	−0.00536194
$651$	−3.27554e6	−0.302921
$652$	8.34864e6	0.769125
$653$	−2.17360e7	−1.99479	−0.997394	−	0.0721445i	$-0.977016\pi$
$653$	−2.17360e7	−1.99479	−0.997394	+	0.0721445i	$0.977016\pi$
$654$	−367427.	−0.0335913
$655$	−4.60321e6	−0.419235
$656$	1.72539e7	1.56541
$657$	−5.45452e6	−0.492996
$658$	−501247.	−0.0451323
$659$	2.02799e7	1.81908	0.909541	−	0.415614i	$-0.136433\pi$
$659$	2.02799e7	1.81908	0.909541	+	0.415614i	$0.136433\pi$
$660$	2.20884e6	0.197381
$661$	−7.20080e6	−0.641028	−0.320514	−	0.947244i	$-0.603856\pi$
$661$	−7.20080e6	−0.641028	−0.320514	+	0.947244i	$0.603856\pi$
$662$	−710892.	−0.0630462
$663$	1.74146e6	0.153861
$664$	−411657.	−0.0362339
$665$	707029.	0.0619988
$666$	−236363.	−0.0206488
$667$	−332604.	−0.0289476
$668$	−1.26597e7	−1.09770
$669$	−1.54937e7	−1.33842
$670$	311106.	0.0267745
$671$	4.47107e6	0.383359
$672$	−2.35443e6	−0.201123
$673$	4.88732e6	0.415943	0.207971	−	0.978135i	$-0.433314\pi$
$673$	4.88732e6	0.415943	0.207971	+	0.978135i	$0.433314\pi$
$674$	−1.60316e6	−0.135933
$675$	−584467.	−0.0493742
$676$	1.03404e7	0.870302
$677$	2.34591e7	1.96716	0.983582	−	0.180464i	$-0.0577599\pi$
$677$	2.34591e7	1.96716	0.983582	+	0.180464i	$0.0577599\pi$
$678$	2.42929e6	0.202958
$679$	1.12752e7	0.938538
$680$	241710.	0.0200457
$681$	1.25955e7	1.04075
$682$	−94688.5	−0.00779536
$683$	1.15715e7	0.949156	0.474578	−	0.880213i	$-0.342601\pi$
$683$	1.15715e7	0.949156	0.474578	+	0.880213i	$0.342601\pi$
$684$	−3.25893e6	−0.266339
$685$	1.00393e7	0.817476
$686$	−924643.	−0.0750177
$687$	−1.28373e6	−0.103773
$688$	−2.18527e6	−0.176009
$689$	−7.18124e6	−0.576304
$690$	105302.	0.00842001
$691$	1.15227e7	0.918038	0.459019	−	0.888427i	$-0.348201\pi$
$691$	1.15227e7	0.918038	0.459019	+	0.888427i	$0.348201\pi$
$692$	−7.11876e6	−0.565118
$693$	2.68970e6	0.212751
$694$	−361831.	−0.0285172
$695$	8.08246e6	0.634719
$696$	−489777.	−0.0383244
$697$	−6.04726e6	−0.471495
$698$	602041.	0.0467722
$699$	3.47270e7	2.68828
$700$	1.55779e6	0.120161
$701$	−2.58046e6	−0.198336	−0.0991680	−	0.995071i	$-0.531618\pi$
$701$	−2.58046e6	−0.198336	−0.0991680	+	0.995071i	$0.531618\pi$
$702$	86418.1	0.00661853
$703$	700065.	0.0534257
$704$	3.82841e6	0.291130
$705$	−8.54638e6	−0.647604
$706$	1.72726e6	0.130420
$707$	−1.09245e7	−0.821968
$708$	8.75785e6	0.656620
$709$	−9.06373e6	−0.677160	−0.338580	−	0.940938i	$-0.609947\pi$
$709$	−9.06373e6	−0.677160	−0.338580	+	0.940938i	$0.609947\pi$
$710$	−738447.	−0.0549760
$711$	1.44524e7	1.07218
$712$	−3.42537e6	−0.253226
$713$	778336.	0.0573381
$714$	272407.	0.0199974
$715$	650774.	0.0476064
$716$	−1.56714e7	−1.14242
$717$	−3.37766e7	−2.45368
$718$	−1.57853e6	−0.114273
$719$	−1.65592e7	−1.19458	−0.597291	−	0.802024i	$-0.703756\pi$
$719$	−1.65592e7	−1.19458	−0.597291	+	0.802024i	$0.703756\pi$
$720$	−7.13847e6	−0.513185
$721$	3.40363e6	0.243839
$722$	−55980.2	−0.00399661
$723$	−3.21489e7	−2.28729
$724$	7.45816e6	0.528793
$725$	486555.	0.0343785
$726$	144342.	0.0101637
$727$	−9.66851e6	−0.678459	−0.339229	−	0.940704i	$-0.610166\pi$
$727$	−9.66851e6	−0.678459	−0.339229	+	0.940704i	$0.610166\pi$
$728$	−461999.	−0.0323082
$729$	−1.86898e7	−1.30252
$730$	−206437.	−0.0143377
$731$	765907.	0.0530130
$732$	−2.69814e7	−1.86118
$733$	−1.96128e7	−1.34828	−0.674140	−	0.738604i	$-0.735486\pi$
$733$	−1.96128e7	−1.34828	−0.674140	+	0.738604i	$0.735486\pi$
$734$	−1.82011e6	−0.124697
$735$	−6.12197e6	−0.417996
$736$	559460.	0.0380693
$737$	−3.50537e6	−0.237720
$738$	−2.08978e6	−0.141241
$739$	1.36688e7	0.920702	0.460351	−	0.887737i	$-0.347724\pi$
$739$	1.36688e7	0.920702	0.460351	+	0.887737i	$0.347724\pi$
$740$	1.54245e6	0.103545
$741$	−1.78243e6	−0.119252
$742$	−1.12332e6	−0.0749023
$743$	1.36498e6	0.0907101	0.0453551	−	0.998971i	$-0.485558\pi$
$743$	1.36498e6	0.0907101	0.0453551	+	0.998971i	$0.485558\pi$
$744$	1.14614e6	0.0759112
$745$	−548890.	−0.0362322
$746$	1.79147e6	0.117859
$747$	−4.26106e6	−0.279394
$748$	−1.35779e6	−0.0887314
$749$	1.34928e7	0.878815
$750$	−154043.	−0.00999971
$751$	2.50688e7	1.62194	0.810969	−	0.585089i	$-0.198941\pi$
$751$	2.50688e7	1.62194	0.810969	+	0.585089i	$0.198941\pi$
$752$	−1.49892e7	−0.966570
$753$	8.12500e6	0.522199
$754$	−71941.1	−0.00460839
$755$	3.78124e6	0.241417
$756$	−2.33082e6	−0.148321
$757$	−1.50931e7	−0.957281	−0.478640	−	0.878011i	$-0.658870\pi$
$757$	−1.50931e7	−0.957281	−0.478640	+	0.878011i	$0.658870\pi$
$758$	787765.	0.0497993
$759$	−1.18648e6	−0.0747578
$760$	−247396.	−0.0155367
$761$	5.27651e6	0.330282	0.165141	−	0.986270i	$-0.447192\pi$
$761$	5.27651e6	0.330282	0.165141	+	0.986270i	$0.447192\pi$
$762$	3.27361e6	0.204239
$763$	2.91972e6	0.181564
$764$	−1.92018e7	−1.19017
$765$	2.50194e6	0.154569
$766$	1.87927e6	0.115722
$767$	2.58026e6	0.158371
$768$	−2.26901e7	−1.38814
$769$	−1.87749e7	−1.14488	−0.572441	−	0.819946i	$-0.694004\pi$
$769$	−1.87749e7	−1.14488	−0.572441	+	0.819946i	$0.694004\pi$
$770$	101797.	0.00618741
$771$	−2.57573e7	−1.56050
$772$	−9.76950e6	−0.589969
$773$	1.06171e7	0.639083	0.319542	−	0.947572i	$-0.396471\pi$
$773$	1.06171e7	0.639083	0.319542	+	0.947572i	$0.396471\pi$
$774$	264678.	0.0158805
$775$	−1.13860e6	−0.0680954
$776$	−3.94532e6	−0.235195
$777$	3.48676e6	0.207190
$778$	604177.	0.0357862
$779$	6.18954e6	0.365439
$780$	−3.92721e6	−0.231125
$781$	8.32040e6	0.488109
$782$	−64729.6	−0.00378517
$783$	−728001.	−0.0424353
$784$	−1.07371e7	−0.623874
$785$	6.66922e6	0.386279
$786$	1.81527e6	0.104806
$787$	−1.25407e7	−0.721747	−0.360873	−	0.932615i	$-0.617521\pi$
$787$	−1.25407e7	−0.721747	−0.360873	+	0.932615i	$0.617521\pi$
$788$	2.09091e7	1.19955
$789$	2.81642e7	1.61066
$790$	546981.	0.0311821
$791$	−1.93041e7	−1.09700
$792$	−941154.	−0.0533148
$793$	−7.94934e6	−0.448898
$794$	1.06554e6	0.0599817
$795$	−1.91529e7	−1.07477
$796$	7.34319e6	0.410773
$797$	1.56038e7	0.870133	0.435067	−	0.900398i	$-0.356725\pi$
$797$	1.56038e7	0.870133	0.435067	+	0.900398i	$0.356725\pi$
$798$	−278816.	−0.0154993
$799$	5.25351e6	0.291127
$800$	−818416.	−0.0452115
$801$	−3.54561e7	−1.95258
$802$	−1.26297e6	−0.0693359
$803$	2.32602e6	0.127299
$804$	2.11538e7	1.15411
$805$	−836768.	−0.0455109
$806$	168351.	0.00912807
$807$	1.94956e7	1.05379
$808$	3.82261e6	0.205983
$809$	−2.22123e7	−1.19323	−0.596613	−	0.802529i	$-0.703487\pi$
$809$	−2.22123e7	−1.19323	−0.596613	+	0.802529i	$0.703487\pi$
$810$	−509966.	−0.0273104
$811$	−1.18454e7	−0.632407	−0.316204	−	0.948691i	$-0.602408\pi$
$811$	−1.18454e7	−0.632407	−0.316204	+	0.948691i	$0.602408\pi$
$812$	1.94035e6	0.103274
$813$	−1.30877e7	−0.694442
$814$	100794.	0.00533182
$815$	6.56020e6	0.345958
$816$	8.14600e6	0.428271
$817$	−783927.	−0.0410885
$818$	1.19452e6	0.0624180
$819$	−4.78216e6	−0.249123
$820$	1.36373e7	0.708264
$821$	1.60094e7	0.828927	0.414463	−	0.910066i	$-0.363969\pi$
$821$	1.60094e7	0.828927	0.414463	+	0.910066i	$0.363969\pi$
$822$	−3.95897e6	−0.204363
$823$	−2.18549e7	−1.12473	−0.562366	−	0.826889i	$-0.690109\pi$
$823$	−2.18549e7	−1.12473	−0.562366	+	0.826889i	$0.690109\pi$
$824$	−1.19096e6	−0.0611054
$825$	1.73566e6	0.0887832
$826$	403617.	0.0205835
$827$	3.53195e7	1.79577	0.897885	−	0.440230i	$-0.145103\pi$
$827$	3.53195e7	1.79577	0.897885	+	0.440230i	$0.145103\pi$
$828$	3.85694e6	0.195509
$829$	2.42889e7	1.22750	0.613750	−	0.789500i	$-0.289660\pi$
$829$	2.42889e7	1.22750	0.613750	+	0.789500i	$0.289660\pi$
$830$	−161268.	−0.00812558
$831$	1.47278e7	0.739836
$832$	−6.80672e6	−0.340902
$833$	3.76321e6	0.187908
$834$	−3.18731e6	−0.158675
$835$	−9.94774e6	−0.493751
$836$	1.38973e6	0.0687726
$837$	1.70362e6	0.0840539
$838$	2.72543e6	0.134068
$839$	2.54847e7	1.24990	0.624948	−	0.780666i	$-0.285120\pi$
$839$	2.54847e7	1.24990	0.624948	+	0.780666i	$0.285120\pi$
$840$	−1.23219e6	−0.0602530
$841$	−1.99051e7	−0.970453
$842$	22799.2	0.00110826
$843$	−3.37356e7	−1.63500
$844$	2.89288e7	1.39790
$845$	8.12528e6	0.391468
$846$	1.81548e6	0.0872097
$847$	−1.14699e6	−0.0549354
$848$	−3.35916e7	−1.60414
$849$	2.53168e7	1.20542
$850$	94690.8	0.00449532
$851$	−828526.	−0.0392177
$852$	−5.02109e7	−2.36973
$853$	3.04034e6	0.143070	0.0715352	−	0.997438i	$-0.477210\pi$
$853$	3.04034e6	0.143070	0.0715352	+	0.997438i	$0.477210\pi$
$854$	−1.24347e6	−0.0583434
$855$	−2.56080e6	−0.119801
$856$	−4.72126e6	−0.220228
$857$	1.34123e7	0.623809	0.311905	−	0.950113i	$-0.399033\pi$
$857$	1.34123e7	0.623809	0.311905	+	0.950113i	$0.399033\pi$
$858$	−256632.	−0.0119012
$859$	2.68892e7	1.24336	0.621678	−	0.783273i	$-0.286451\pi$
$859$	2.68892e7	1.24336	0.621678	+	0.783273i	$0.286451\pi$
$860$	−1.72722e6	−0.0796344
$861$	3.08278e7	1.41721
$862$	2.50085e6	0.114636
$863$	−1.28759e7	−0.588507	−0.294254	−	0.955727i	$-0.595071\pi$
$863$	−1.28759e7	−0.588507	−0.294254	+	0.955727i	$0.595071\pi$
$864$	1.22454e6	0.0558071
$865$	−5.59379e6	−0.254194
$866$	−425777.	−0.0192924
$867$	2.97320e7	1.34331
$868$	−4.54068e6	−0.204560
$869$	−6.16308e6	−0.276852
$870$	−191873.	−0.00859438
$871$	6.23237e6	0.278361
$872$	−1.02164e6	−0.0454994
$873$	−4.08380e7	−1.81355
$874$	66252.5	0.00293375
$875$	1.22408e6	0.0540493
$876$	−1.40368e7	−0.618026
$877$	−3.83455e7	−1.68351	−0.841754	−	0.539862i	$-0.818477\pi$
$877$	−3.83455e7	−1.68351	−0.841754	+	0.539862i	$0.818477\pi$
$878$	1.10637e6	0.0484353
$879$	9.79312e6	0.427513
$880$	3.04412e6	0.132512
$881$	2.70737e7	1.17519	0.587595	−	0.809155i	$-0.300075\pi$
$881$	2.70737e7	1.17519	0.587595	+	0.809155i	$0.300075\pi$
$882$	1.30047e6	0.0562896
$883$	−322579.	−0.0139231	−0.00696153	−	0.999976i	$-0.502216\pi$
$883$	−322579.	−0.0139231	−0.00696153	+	0.999976i	$0.502216\pi$
$884$	2.41408e6	0.103901
$885$	6.88175e6	0.295353
$886$	779213.	0.0333482
$887$	2.27524e7	0.970996	0.485498	−	0.874238i	$-0.338638\pi$
$887$	2.27524e7	0.970996	0.485498	+	0.874238i	$0.338638\pi$
$888$	−1.22005e6	−0.0519213
$889$	−2.60134e7	−1.10393
$890$	−1.34191e6	−0.0567867
$891$	5.74601e6	0.242478
$892$	−2.14780e7	−0.903821
$893$	−5.37711e6	−0.225642
$894$	216454.	0.00905779
$895$	−1.23143e7	−0.513869
$896$	−4.34746e6	−0.180911
$897$	2.10950e6	0.0875385
$898$	3.32761e6	0.137703
$899$	−1.41822e6	−0.0585255
$900$	−5.64219e6	−0.232189
$901$	1.17734e7	0.483160
$902$	891162.	0.0364704
$903$	−3.90444e6	−0.159345
$904$	6.75469e6	0.274906
$905$	5.86048e6	0.237855
$906$	−1.49113e6	−0.0603524
$907$	−1.31074e7	−0.529050	−0.264525	−	0.964379i	$-0.585215\pi$
$907$	−1.31074e7	−0.529050	−0.264525	+	0.964379i	$0.585215\pi$
$908$	1.74604e7	0.702811
$909$	3.95678e7	1.58830
$910$	−180990.	−0.00724522
$911$	−1.76121e7	−0.703099	−0.351549	−	0.936169i	$-0.614345\pi$
$911$	−1.76121e7	−0.703099	−0.351549	+	0.936169i	$0.614345\pi$
$912$	−8.33765e6	−0.331938
$913$	1.81708e6	0.0721436
$914$	520532.	0.0206102
$915$	−2.12015e7	−0.837170
$916$	−1.77956e6	−0.0700768
$917$	−1.44248e7	−0.566484
$918$	−141680.	−0.00554882
$919$	2.06222e7	0.805466	0.402733	−	0.915317i	$-0.368060\pi$
$919$	2.06222e7	0.805466	0.402733	+	0.915317i	$0.368060\pi$
$920$	292793.	0.0114049
$921$	3.07281e7	1.19368
$922$	−2.28980e6	−0.0887094
$923$	−1.47933e7	−0.571557
$924$	6.92173e6	0.266707
$925$	1.21202e6	0.0465754
$926$	−733467.	−0.0281095
$927$	−1.23277e7	−0.471174
$928$	−1.01940e6	−0.0388577
$929$	2.63278e7	1.00087	0.500433	−	0.865775i	$-0.333174\pi$
$929$	2.63278e7	1.00087	0.500433	+	0.865775i	$0.333174\pi$
$930$	449006.	0.0170234
$931$	−3.85175e6	−0.145641
$932$	4.81399e7	1.81537
$933$	2.71374e7	1.02062
$934$	1.74906e6	0.0656050
$935$	−1.06692e6	−0.0399120
$936$	1.67332e6	0.0624296
$937$	1.19126e7	0.443261	0.221630	−	0.975131i	$-0.428862\pi$
$937$	1.19126e7	0.443261	0.221630	+	0.975131i	$0.428862\pi$
$938$	974897.	0.0361786
$939$	−2.39495e7	−0.886407
$940$	−1.18473e7	−0.437321
$941$	8.13633e6	0.299540	0.149770	−	0.988721i	$-0.452147\pi$
$941$	8.13633e6	0.299540	0.149770	+	0.988721i	$0.452147\pi$
$942$	−2.63000e6	−0.0965669
$943$	−7.32532e6	−0.268255
$944$	1.20697e7	0.440824
$945$	−1.83151e6	−0.0667161
$946$	−112869.	−0.00410059
$947$	−1.44161e7	−0.522362	−0.261181	−	0.965290i	$-0.584112\pi$
$947$	−1.44161e7	−0.522362	−0.261181	+	0.965290i	$0.584112\pi$
$948$	3.71921e7	1.34410
$949$	−4.13554e6	−0.149062
$950$	−96918.7	−0.00348416
$951$	3.86095e7	1.38434
$952$	757433.	0.0270864
$953$	−5.56838e7	−1.98608	−0.993039	−	0.117786i	$-0.962420\pi$
$953$	−5.56838e7	−1.98608	−0.993039	+	0.117786i	$0.962420\pi$
$954$	4.06859e6	0.144735
$955$	−1.50884e7	−0.535346
$956$	−4.68224e7	−1.65695
$957$	2.16191e6	0.0763059
$958$	2.43959e6	0.0858822
$959$	3.14595e7	1.10460
$960$	−1.81541e7	−0.635763
$961$	−2.53103e7	−0.884075
$962$	−179208.	−0.00624336
$963$	−4.88698e7	−1.69815
$964$	−4.45660e7	−1.54458
$965$	−7.67669e6	−0.265372
$966$	329979.	0.0113774
$967$	1.66730e7	0.573387	0.286694	−	0.958022i	$-0.407444\pi$
$967$	1.66730e7	0.573387	0.286694	+	0.958022i	$0.407444\pi$
$968$	401344.	0.0137667
$969$	2.92224e6	0.0999783
$970$	−1.54560e6	−0.0527432
$971$	4.10277e7	1.39646	0.698230	−	0.715873i	$-0.253971\pi$
$971$	4.10277e7	1.39646	0.698230	+	0.715873i	$0.253971\pi$
$972$	−4.19050e7	−1.42266
$973$	2.53276e7	0.857653
$974$	1.59004e6	0.0537044
$975$	−3.08592e6	−0.103962
$976$	−3.71845e7	−1.24950
$977$	−5.22819e7	−1.75233	−0.876163	−	0.482016i	$-0.839905\pi$
$977$	−5.22819e7	−1.75233	−0.876163	+	0.482016i	$0.839905\pi$
$978$	−2.58701e6	−0.0864870
$979$	1.51198e7	0.504185
$980$	−8.48651e6	−0.282269
$981$	−1.05750e7	−0.350838
$982$	−3.53245e6	−0.116895
$983$	−1.62721e7	−0.537107	−0.268553	−	0.963265i	$-0.586546\pi$
$983$	−1.62721e7	−0.537107	−0.268553	+	0.963265i	$0.586546\pi$
$984$	−1.07869e7	−0.355149
$985$	1.64300e7	0.539568
$986$	117945.	0.00386356
$987$	−2.67813e7	−0.875063
$988$	−2.47087e6	−0.0805301
$989$	927777.	0.0301615
$990$	−368701.	−0.0119560
$991$	2.18535e7	0.706866	0.353433	−	0.935460i	$-0.385014\pi$
$991$	2.18535e7	0.706866	0.353433	+	0.935460i	$0.385014\pi$
$992$	2.38554e6	0.0769674
$993$	−3.79826e7	−1.22239
$994$	−2.31403e6	−0.0742854
$995$	5.77014e6	0.184769
$996$	−1.09655e7	−0.350251
$997$	2.26097e7	0.720373	0.360186	−	0.932880i	$-0.382713\pi$
$997$	2.26097e7	0.720373	0.360186	+	0.932880i	$0.382713\pi$
$998$	−1.84867e6	−0.0587534
$999$	−1.81347e6	−0.0574907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.19	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.19	✓	39	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)

\(f(q)\)	\(=\)	\(q-0.429556 q^{2} -22.9509 q^{3} -31.8155 q^{4} -25.0000 q^{5} +9.85872 q^{6} -78.3412 q^{7} +27.4123 q^{8} +283.745 q^{9} +O(q^{10})\)	\(q-0.429556 q^{2} -22.9509 q^{3} -31.8155 q^{4} -25.0000 q^{5} +9.85872 q^{6} -78.3412 q^{7} +27.4123 q^{8} +283.745 q^{9} +10.7389 q^{10} -121.000 q^{11} +730.195 q^{12} +215.132 q^{13} +33.6520 q^{14} +573.773 q^{15} +1006.32 q^{16} -352.702 q^{17} -121.885 q^{18} +361.000 q^{19} +795.387 q^{20} +1798.00 q^{21} +51.9763 q^{22} -427.243 q^{23} -629.139 q^{24} +625.000 q^{25} -92.4113 q^{26} -935.147 q^{27} +2492.46 q^{28} +778.489 q^{29} -246.468 q^{30} -1821.76 q^{31} -1309.47 q^{32} +2777.06 q^{33} +151.505 q^{34} +1958.53 q^{35} -9027.50 q^{36} +1939.24 q^{37} -155.070 q^{38} -4937.48 q^{39} -685.309 q^{40} +17145.5 q^{41} -772.344 q^{42} -2171.54 q^{43} +3849.67 q^{44} -7093.64 q^{45} +183.525 q^{46} -14895.0 q^{47} -23096.0 q^{48} -10669.7 q^{49} -268.473 q^{50} +8094.84 q^{51} -6844.52 q^{52} -33380.7 q^{53} +401.698 q^{54} +3025.00 q^{55} -2147.52 q^{56} -8285.29 q^{57} -334.405 q^{58} +11993.8 q^{59} -18254.9 q^{60} -36951.0 q^{61} +782.550 q^{62} -22229.0 q^{63} -31639.8 q^{64} -5378.30 q^{65} -1192.91 q^{66} +28970.0 q^{67} +11221.4 q^{68} +9805.63 q^{69} -841.299 q^{70} -68763.7 q^{71} +7778.13 q^{72} -19223.3 q^{73} -833.012 q^{74} -14344.3 q^{75} -11485.4 q^{76} +9479.28 q^{77} +2120.93 q^{78} +50934.5 q^{79} -25158.0 q^{80} -47487.7 q^{81} -7364.98 q^{82} -15017.2 q^{83} -57204.4 q^{84} +8817.54 q^{85} +932.800 q^{86} -17867.0 q^{87} -3316.89 q^{88} -124957. q^{89} +3047.12 q^{90} -16853.7 q^{91} +13592.9 q^{92} +41811.2 q^{93} +6398.26 q^{94} -9025.00 q^{95} +30053.5 q^{96} -143925. q^{97} +4583.22 q^{98} -34333.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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