LMFDB - Embedded newform 1045.6.a.e.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:	$1$
Dimension:	$38$
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)

$f(q)$	$=$	$q-1.77527 q^{2} +9.46319 q^{3} -28.8484 q^{4} +25.0000 q^{5} -16.7997 q^{6} +232.548 q^{7} +108.022 q^{8} -153.448 q^{9} +O(q^{10})$	\(q-1.77527 q^{2} +9.46319 q^{3} -28.8484 q^{4} +25.0000 q^{5} -16.7997 q^{6} +232.548 q^{7} +108.022 q^{8} -153.448 q^{9} -44.3817 q^{10} +121.000 q^{11} -272.998 q^{12} -324.970 q^{13} -412.835 q^{14} +236.580 q^{15} +731.382 q^{16} +1087.41 q^{17} +272.411 q^{18} -361.000 q^{19} -721.211 q^{20} +2200.65 q^{21} -214.807 q^{22} -3844.06 q^{23} +1022.23 q^{24} +625.000 q^{25} +576.909 q^{26} -3751.66 q^{27} -6708.64 q^{28} -8211.31 q^{29} -419.992 q^{30} +9381.43 q^{31} -4755.11 q^{32} +1145.05 q^{33} -1930.43 q^{34} +5813.70 q^{35} +4426.74 q^{36} +5813.95 q^{37} +640.871 q^{38} -3075.25 q^{39} +2700.55 q^{40} -2714.65 q^{41} -3906.73 q^{42} -23659.3 q^{43} -3490.66 q^{44} -3836.20 q^{45} +6824.23 q^{46} -9880.76 q^{47} +6921.20 q^{48} +37271.6 q^{49} -1109.54 q^{50} +10290.3 q^{51} +9374.88 q^{52} -40131.1 q^{53} +6660.20 q^{54} +3025.00 q^{55} +25120.3 q^{56} -3416.21 q^{57} +14577.3 q^{58} -39605.2 q^{59} -6824.95 q^{60} +9830.13 q^{61} -16654.5 q^{62} -35684.0 q^{63} -14962.6 q^{64} -8124.25 q^{65} -2032.76 q^{66} +62293.2 q^{67} -31369.9 q^{68} -36377.0 q^{69} -10320.9 q^{70} -24393.0 q^{71} -16575.8 q^{72} +21091.1 q^{73} -10321.3 q^{74} +5914.49 q^{75} +10414.3 q^{76} +28138.3 q^{77} +5459.39 q^{78} -15035.6 q^{79} +18284.5 q^{80} +1785.19 q^{81} +4819.24 q^{82} -73372.2 q^{83} -63485.2 q^{84} +27185.1 q^{85} +42001.6 q^{86} -77705.2 q^{87} +13070.7 q^{88} -23661.5 q^{89} +6810.28 q^{90} -75571.1 q^{91} +110895. q^{92} +88778.3 q^{93} +17541.0 q^{94} -9025.00 q^{95} -44998.5 q^{96} +15362.5 q^{97} -66167.0 q^{98} -18567.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * 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 $

$2$	−1.77527	−0.313826	−0.156913	−	0.987612i	$-0.550154\pi$
$2$	−1.77527	−0.313826	−0.156913	+	0.987612i	$0.550154\pi$
$3$	9.46319	0.607064	0.303532	−	0.952821i	$-0.401834\pi$
$3$	9.46319	0.607064	0.303532	+	0.952821i	$0.401834\pi$
$4$	−28.8484	−0.901513
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−16.7997	−0.190512
$7$	232.548	1.79377	0.896887	−	0.442261i	$-0.145823\pi$
$7$	232.548	1.79377	0.896887	+	0.442261i	$0.145823\pi$
$8$	108.022	0.596744
$9$	−153.448	−0.631474
$10$	−44.3817	−0.140347
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−272.998	−0.547276
$13$	−324.970	−0.533316	−0.266658	−	0.963791i	$-0.585919\pi$
$13$	−324.970	−0.533316	−0.266658	+	0.963791i	$0.585919\pi$
$14$	−412.835	−0.562932
$15$	236.580	0.271487
$16$	731.382	0.714240
$17$	1087.41	0.912576	0.456288	−	0.889832i	$-0.349179\pi$
$17$	1087.41	0.912576	0.456288	+	0.889832i	$0.349179\pi$
$18$	272.411	0.198173
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−721.211	−0.403169
$21$	2200.65	1.08893
$22$	−214.807	−0.0946220
$23$	−3844.06	−1.51520	−0.757601	−	0.652718i	$-0.773629\pi$
$23$	−3844.06	−1.51520	−0.757601	+	0.652718i	$0.773629\pi$
$24$	1022.23	0.362262
$25$	625.000	0.200000
$26$	576.909	0.167368
$27$	−3751.66	−0.990409
$28$	−6708.64	−1.61711
$29$	−8211.31	−1.81308	−0.906541	−	0.422118i	$-0.861287\pi$
$29$	−8211.31	−1.81308	−0.906541	+	0.422118i	$0.861287\pi$
$30$	−419.992	−0.0851997
$31$	9381.43	1.75334	0.876668	−	0.481096i	$-0.159761\pi$
$31$	9381.43	1.75334	0.876668	+	0.481096i	$0.159761\pi$
$32$	−4755.11	−0.820891
$33$	1145.05	0.183037
$34$	−1930.43	−0.286390
$35$	5813.70	0.802200
$36$	4426.74	0.569282
$37$	5813.95	0.698179	0.349089	−	0.937089i	$-0.386491\pi$
$37$	5813.95	0.698179	0.349089	+	0.937089i	$0.386491\pi$
$38$	640.871	0.0719966
$39$	−3075.25	−0.323757
$40$	2700.55	0.266872
$41$	−2714.65	−0.252206	−0.126103	−	0.992017i	$-0.540247\pi$
$41$	−2714.65	−0.252206	−0.126103	+	0.992017i	$0.540247\pi$
$42$	−3906.73	−0.341736
$43$	−23659.3	−1.95133	−0.975667	−	0.219258i	$-0.929636\pi$
$43$	−23659.3	−1.95133	−0.975667	+	0.219258i	$0.929636\pi$
$44$	−3490.66	−0.271817
$45$	−3836.20	−0.282404
$46$	6824.23	0.475509
$47$	−9880.76	−0.652447	−0.326224	−	0.945293i	$-0.605776\pi$
$47$	−9880.76	−0.652447	−0.326224	+	0.945293i	$0.605776\pi$
$48$	6921.20	0.433589
$49$	37271.6	2.21762
$50$	−1109.54	−0.0627651
$51$	10290.3	0.553992
$52$	9374.88	0.480792
$53$	−40131.1	−1.96242	−0.981208	−	0.192955i	$-0.938193\pi$
$53$	−40131.1	−1.96242	−0.981208	+	0.192955i	$0.938193\pi$
$54$	6660.20	0.310816
$55$	3025.00	0.134840
$56$	25120.3	1.07042
$57$	−3416.21	−0.139270
$58$	14577.3	0.568992
$59$	−39605.2	−1.48123	−0.740615	−	0.671930i	$-0.765466\pi$
$59$	−39605.2	−1.48123	−0.740615	+	0.671930i	$0.765466\pi$
$60$	−6824.95	−0.244749
$61$	9830.13	0.338248	0.169124	−	0.985595i	$-0.445906\pi$
$61$	9830.13	0.338248	0.169124	+	0.985595i	$0.445906\pi$
$62$	−16654.5	−0.550242
$63$	−35684.0	−1.13272
$64$	−14962.6	−0.456623
$65$	−8124.25	−0.238506
$66$	−2032.76	−0.0574416
$67$	62293.2	1.69533	0.847663	−	0.530535i	$-0.178009\pi$
$67$	62293.2	1.69533	0.847663	+	0.530535i	$0.178009\pi$
$68$	−31369.9	−0.822700
$69$	−36377.0	−0.919824
$70$	−10320.9	−0.251751
$71$	−24393.0	−0.574274	−0.287137	−	0.957890i	$-0.592703\pi$
$71$	−24393.0	−0.574274	−0.287137	+	0.957890i	$0.592703\pi$
$72$	−16575.8	−0.376828
$73$	21091.1	0.463225	0.231613	−	0.972808i	$-0.425600\pi$
$73$	21091.1	0.463225	0.231613	+	0.972808i	$0.425600\pi$
$74$	−10321.3	−0.219106
$75$	5914.49	0.121413
$76$	10414.3	0.206821
$77$	28138.3	0.540843
$78$	5459.39	0.101603
$79$	−15035.6	−0.271052	−0.135526	−	0.990774i	$-0.543272\pi$
$79$	−15035.6	−0.271052	−0.135526	+	0.990774i	$0.543272\pi$
$80$	18284.5	0.319418
$81$	1785.19	0.0302324
$82$	4819.24	0.0791487
$83$	−73372.2	−1.16906	−0.584529	−	0.811373i	$-0.698721\pi$
$83$	−73372.2	−1.16906	−0.584529	+	0.811373i	$0.698721\pi$
$84$	−63485.2	−0.981689
$85$	27185.1	0.408116
$86$	42001.6	0.612379
$87$	−77705.2	−1.10066
$88$	13070.7	0.179925
$89$	−23661.5	−0.316641	−0.158321	−	0.987388i	$-0.550608\pi$
$89$	−23661.5	−0.316641	−0.158321	+	0.987388i	$0.550608\pi$
$90$	6810.28	0.0886255
$91$	−75571.1	−0.956649
$92$	110895.	1.36597
$93$	88778.3	1.06439
$94$	17541.0	0.204755
$95$	−9025.00	−0.102598
$96$	−44998.5	−0.498333
$97$	15362.5	0.165780	0.0828901	−	0.996559i	$-0.473585\pi$
$97$	15362.5	0.165780	0.0828901	+	0.996559i	$0.473585\pi$
$98$	−66167.0	−0.695947
$99$	−18567.2	−0.190396
$100$	−18030.3	−0.180303
$101$	92075.7	0.898135	0.449068	−	0.893498i	$-0.351756\pi$
$101$	92075.7	0.898135	0.449068	+	0.893498i	$0.351756\pi$
$102$	−18268.1	−0.173857
$103$	−25562.5	−0.237416	−0.118708	−	0.992929i	$-0.537875\pi$
$103$	−25562.5	−0.237416	−0.118708	+	0.992929i	$0.537875\pi$
$104$	−35104.0	−0.318253
$105$	55016.1	0.486986
$106$	71243.3	0.615856
$107$	89197.6	0.753171	0.376586	−	0.926382i	$-0.377098\pi$
$107$	89197.6	0.753171	0.376586	+	0.926382i	$0.377098\pi$
$108$	108230.	0.892867
$109$	85362.0	0.688174	0.344087	−	0.938938i	$-0.388188\pi$
$109$	85362.0	0.688174	0.344087	+	0.938938i	$0.388188\pi$
$110$	−5370.18	−0.0423163
$111$	55018.5	0.423839
$112$	170081.	1.28118
$113$	147303.	1.08521	0.542607	−	0.839987i	$-0.317437\pi$
$113$	147303.	1.08521	0.542607	+	0.839987i	$0.317437\pi$
$114$	6064.68	0.0437065
$115$	−96101.5	−0.677619
$116$	236883.	1.63452
$117$	49866.0	0.336775
$118$	70309.8	0.464848
$119$	252874.	1.63695
$120$	25555.9	0.162008
$121$	14641.0	0.0909091
$122$	−17451.1	−0.106151
$123$	−25689.3	−0.153105
$124$	−270640.	−1.58066
$125$	15625.0	0.0894427
$126$	63348.7	0.355477
$127$	76539.2	0.421090	0.210545	−	0.977584i	$-0.432476\pi$
$127$	76539.2	0.421090	0.210545	+	0.977584i	$0.432476\pi$
$128$	178726.	0.964191
$129$	−223893.	−1.18458
$130$	14422.7	0.0748494
$131$	−206779.	−1.05276	−0.526379	−	0.850250i	$-0.676451\pi$
$131$	−206779.	−1.05276	−0.526379	+	0.850250i	$0.676451\pi$
$132$	−33032.8	−0.165010
$133$	−83949.8	−0.411520
$134$	−110587.	−0.532037
$135$	−93791.6	−0.442924
$136$	117464.	0.544574
$137$	−351524.	−1.60012	−0.800062	−	0.599917i	$-0.795200\pi$
$137$	−351524.	−1.60012	−0.800062	+	0.599917i	$0.795200\pi$
$138$	64579.0	0.288664
$139$	284540.	1.24913	0.624563	−	0.780975i	$-0.285277\pi$
$139$	284540.	1.24913	0.624563	+	0.780975i	$0.285277\pi$
$140$	−167716.	−0.723194
$141$	−93503.4	−0.396077
$142$	43304.0	0.180222
$143$	−39321.4	−0.160801
$144$	−112229.	−0.451024
$145$	−205283.	−0.810835
$146$	−37442.3	−0.145372
$147$	352708.	1.34624
$148$	−167723.	−0.629417
$149$	161068.	0.594352	0.297176	−	0.954823i	$-0.403955\pi$
$149$	161068.	0.594352	0.297176	+	0.954823i	$0.403955\pi$
$150$	−10499.8	−0.0381025
$151$	−418905.	−1.49511	−0.747556	−	0.664199i	$-0.768773\pi$
$151$	−418905.	−1.49511	−0.747556	+	0.664199i	$0.768773\pi$
$152$	−38996.0	−0.136902
$153$	−166860.	−0.576268
$154$	−49953.0	−0.169730
$155$	234536.	0.784115
$156$	88716.2	0.291871
$157$	−528679.	−1.71176	−0.855880	−	0.517174i	$-0.826984\pi$
$157$	−528679.	−1.71176	−0.855880	+	0.517174i	$0.826984\pi$
$158$	26692.1	0.0850630
$159$	−379768.	−1.19131
$160$	−118878.	−0.367113
$161$	−893928.	−2.71793
$162$	−3169.19	−0.00948770
$163$	180282.	0.531476	0.265738	−	0.964045i	$-0.414384\pi$
$163$	180282.	0.531476	0.265738	+	0.964045i	$0.414384\pi$
$164$	78313.5	0.227367
$165$	28626.1	0.0818565
$166$	130255.	0.366881
$167$	14820.6	0.0411222	0.0205611	−	0.999789i	$-0.493455\pi$
$167$	14820.6	0.0411222	0.0205611	+	0.999789i	$0.493455\pi$
$168$	237719.	0.649815
$169$	−265687.	−0.715574
$170$	−48260.9	−0.128077
$171$	55394.8	0.144870
$172$	682535.	1.75915
$173$	100407.	0.255064	0.127532	−	0.991834i	$-0.459294\pi$
$173$	100407.	0.255064	0.127532	+	0.991834i	$0.459294\pi$
$174$	137947.	0.345414
$175$	145343.	0.358755
$176$	88497.2	0.215351
$177$	−374792.	−0.899201
$178$	42005.5	0.0993701
$179$	−29356.7	−0.0684818	−0.0342409	−	0.999414i	$-0.510901\pi$
$179$	−29356.7	−0.0684818	−0.0342409	+	0.999414i	$0.510901\pi$
$180$	110668.	0.254591
$181$	595135.	1.35026	0.675132	−	0.737697i	$-0.264087\pi$
$181$	595135.	1.35026	0.675132	+	0.737697i	$0.264087\pi$
$182$	134159.	0.300221
$183$	93024.4	0.205338
$184$	−415244.	−0.904187
$185$	145349.	0.312235
$186$	−157605.	−0.334032
$187$	131576.	0.275152
$188$	285044.	0.588190
$189$	−872442.	−1.77657
$190$	16021.8	0.0321978
$191$	−828585.	−1.64344	−0.821720	−	0.569892i	$-0.806985\pi$
$191$	−828585.	−1.64344	−0.821720	+	0.569892i	$0.806985\pi$
$192$	−141594.	−0.277199
$193$	441902.	0.853950	0.426975	−	0.904263i	$-0.359579\pi$
$193$	441902.	0.853950	0.426975	+	0.904263i	$0.359579\pi$
$194$	−27272.5	−0.0520261
$195$	−76881.3	−0.144789
$196$	−1.07523e6	−1.99922
$197$	−240631.	−0.441759	−0.220880	−	0.975301i	$-0.570893\pi$
$197$	−240631.	−0.441759	−0.220880	+	0.975301i	$0.570893\pi$
$198$	32961.8	0.0597513
$199$	−424263.	−0.759456	−0.379728	−	0.925098i	$-0.623982\pi$
$199$	−424263.	−0.759456	−0.379728	+	0.925098i	$0.623982\pi$
$200$	67513.9	0.119349
$201$	589492.	1.02917
$202$	−163459.	−0.281858
$203$	−1.90952e6	−3.25226
$204$	−296860.	−0.499431
$205$	−67866.4	−0.112790
$206$	45380.3	0.0745073
$207$	589863.	0.956810
$208$	−237677.	−0.380916
$209$	−43681.0	−0.0691714
$210$	−97668.3	−0.152829
$211$	−727783.	−1.12537	−0.562685	−	0.826671i	$-0.690232\pi$
$211$	−727783.	−1.12537	−0.562685	+	0.826671i	$0.690232\pi$
$212$	1.15772e6	1.76914
$213$	−230835.	−0.348621
$214$	−158349.	−0.236364
$215$	−591484.	−0.872663
$216$	−405263.	−0.591020
$217$	2.18163e6	3.14509
$218$	−151540.	−0.215967
$219$	199589.	0.281207
$220$	−87266.5	−0.121560
$221$	−353374.	−0.486692
$222$	−97672.4	−0.133012
$223$	−1.02549e6	−1.38093	−0.690464	−	0.723367i	$-0.742594\pi$
$223$	−1.02549e6	−1.38093	−0.690464	+	0.723367i	$0.742594\pi$
$224$	−1.10579e6	−1.47249
$225$	−95905.0	−0.126295
$226$	−261502.	−0.340568
$227$	−637447.	−0.821069	−0.410534	−	0.911845i	$-0.634658\pi$
$227$	−637447.	−0.821069	−0.410534	+	0.911845i	$0.634658\pi$
$228$	98552.3	0.125554
$229$	119670.	0.150798	0.0753991	−	0.997153i	$-0.475977\pi$
$229$	119670.	0.150798	0.0753991	+	0.997153i	$0.475977\pi$
$230$	170606.	0.212654
$231$	266278.	0.328326
$232$	−887004.	−1.08195
$233$	1.55099e6	1.87163	0.935814	−	0.352493i	$-0.114666\pi$
$233$	1.55099e6	1.87163	0.935814	+	0.352493i	$0.114666\pi$
$234$	−88525.5	−0.105689
$235$	−247019.	−0.291783
$236$	1.14255e6	1.33535
$237$	−142284.	−0.164546
$238$	−448919.	−0.513719
$239$	−466991.	−0.528827	−0.264414	−	0.964409i	$-0.585178\pi$
$239$	−466991.	−0.528827	−0.264414	+	0.964409i	$0.585178\pi$
$240$	173030.	0.193907
$241$	463416.	0.513959	0.256980	−	0.966417i	$-0.417273\pi$
$241$	463416.	0.513959	0.256980	+	0.966417i	$0.417273\pi$
$242$	−25991.7	−0.0285296
$243$	928548.	1.00876
$244$	−283584.	−0.304935
$245$	931789.	0.991751
$246$	45605.3	0.0480483
$247$	117314.	0.122351
$248$	1.01340e6	1.04629
$249$	−694335.	−0.709693
$250$	−27738.5	−0.0280694
$251$	−1.19384e6	−1.19609	−0.598043	−	0.801464i	$-0.704055\pi$
$251$	−1.19384e6	−1.19609	−0.598043	+	0.801464i	$0.704055\pi$
$252$	1.02943e6	1.02116
$253$	−465131.	−0.456850
$254$	−135877.	−0.132149
$255$	257258.	0.247753
$256$	161518.	0.154035
$257$	−2.10680e6	−1.98971	−0.994856	−	0.101299i	$-0.967700\pi$
$257$	−2.10680e6	−1.98971	−0.994856	+	0.101299i	$0.967700\pi$
$258$	397469.	0.371753
$259$	1.35202e6	1.25237
$260$	234372.	0.215017
$261$	1.26001e6	1.14491
$262$	367088.	0.330383
$263$	1.70074e6	1.51618	0.758088	−	0.652153i	$-0.226134\pi$
$263$	1.70074e6	1.51618	0.758088	+	0.652153i	$0.226134\pi$
$264$	123690.	0.109226
$265$	−1.00328e6	−0.877619
$266$	149033.	0.129146
$267$	−223913.	−0.192221
$268$	−1.79706e6	−1.52836
$269$	−29529.2	−0.0248812	−0.0124406	−	0.999923i	$-0.503960\pi$
$269$	−29529.2	−0.0248812	−0.0124406	+	0.999923i	$0.503960\pi$
$270$	166505.	0.139001
$271$	1.46048e6	1.20802	0.604009	−	0.796977i	$-0.293569\pi$
$271$	1.46048e6	1.20802	0.604009	+	0.796977i	$0.293569\pi$
$272$	795308.	0.651798
$273$	−715144.	−0.580747
$274$	624049.	0.502160
$275$	75625.0	0.0603023
$276$	1.04942e6	0.829234
$277$	795745.	0.623124	0.311562	−	0.950226i	$-0.399148\pi$
$277$	795745.	0.623124	0.311562	+	0.950226i	$0.399148\pi$
$278$	−505134.	−0.392008
$279$	−1.43956e6	−1.10718
$280$	628009.	0.478708
$281$	−2.21644e6	−1.67452	−0.837260	−	0.546806i	$-0.815844\pi$
$281$	−2.21644e6	−1.67452	−0.837260	+	0.546806i	$0.815844\pi$
$282$	165994.	0.124299
$283$	−1.18230e6	−0.877530	−0.438765	−	0.898602i	$-0.644584\pi$
$283$	−1.18230e6	−0.877530	−0.438765	+	0.898602i	$0.644584\pi$
$284$	703699.	0.517715
$285$	−85405.3	−0.0622834
$286$	69805.9	0.0504635
$287$	−631288.	−0.452400
$288$	729662.	0.518371
$289$	−237407.	−0.167205
$290$	364432.	0.254461
$291$	145378.	0.100639
$292$	−608445.	−0.417604
$293$	−374385.	−0.254771	−0.127385	−	0.991853i	$-0.540658\pi$
$293$	−374385.	−0.254771	−0.127385	+	0.991853i	$0.540658\pi$
$294$	−626151.	−0.422484
$295$	−990130.	−0.662426
$296$	628035.	0.416634
$297$	−453951.	−0.298619
$298$	−285939.	−0.186523
$299$	1.24920e6	0.808082
$300$	−170624.	−0.109455
$301$	−5.50193e6	−3.50025
$302$	743669.	0.469205
$303$	871330.	0.545225
$304$	−264029.	−0.163858
$305$	245753.	0.151269
$306$	296221.	0.180848
$307$	−2.10630e6	−1.27548	−0.637741	−	0.770251i	$-0.720131\pi$
$307$	−2.10630e6	−1.27548	−0.637741	+	0.770251i	$0.720131\pi$
$308$	−811746.	−0.487577
$309$	−241903.	−0.144127
$310$	−416364.	−0.246076
$311$	154863.	0.0907917	0.0453958	−	0.998969i	$-0.485545\pi$
$311$	154863.	0.0907917	0.0453958	+	0.998969i	$0.485545\pi$
$312$	−332196.	−0.193200
$313$	1.94901e6	1.12448	0.562241	−	0.826973i	$-0.309939\pi$
$313$	1.94901e6	1.12448	0.562241	+	0.826973i	$0.309939\pi$
$314$	938546.	0.537195
$315$	−892101.	−0.506568
$316$	433752.	0.244357
$317$	−1.03388e6	−0.577856	−0.288928	−	0.957351i	$-0.593299\pi$
$317$	−1.03388e6	−0.577856	−0.288928	+	0.957351i	$0.593299\pi$
$318$	674189.	0.373864
$319$	−993568.	−0.546665
$320$	−374066.	−0.204208
$321$	844093.	0.457223
$322$	1.58696e6	0.852956
$323$	−392553.	−0.209359
$324$	−51500.0	−0.0272549
$325$	−203106.	−0.106663
$326$	−320049.	−0.166791
$327$	807797.	0.417766
$328$	−293243.	−0.150502
$329$	−2.29775e6	−1.17034
$330$	−50819.0	−0.0256887
$331$	871348.	0.437141	0.218571	−	0.975821i	$-0.429861\pi$
$331$	871348.	0.437141	0.218571	+	0.975821i	$0.429861\pi$
$332$	2.11667e6	1.05392
$333$	−892139.	−0.440881
$334$	−26310.6	−0.0129052
$335$	1.55733e6	0.758173
$336$	1.60951e6	0.777761
$337$	−2.79346e6	−1.33988	−0.669942	−	0.742413i	$-0.733681\pi$
$337$	−2.79346e6	−1.33988	−0.669942	+	0.742413i	$0.733681\pi$
$338$	471666.	0.224565
$339$	1.39396e6	0.658794
$340$	−784248.	−0.367922
$341$	1.13515e6	0.528651
$342$	−98340.5	−0.0454639
$343$	4.75900e6	2.18414
$344$	−2.55573e6	−1.16445
$345$	−909426.	−0.411358
$346$	−178250.	−0.0800457
$347$	−1.76467e6	−0.786757	−0.393379	−	0.919377i	$-0.628694\pi$
$347$	−1.76467e6	−0.786757	−0.393379	+	0.919377i	$0.628694\pi$
$348$	2.24167e6	0.992256
$349$	−1.02719e6	−0.451425	−0.225712	−	0.974194i	$-0.572471\pi$
$349$	−1.02719e6	−0.451425	−0.225712	+	0.974194i	$0.572471\pi$
$350$	−258022.	−0.112586
$351$	1.21918e6	0.528201
$352$	−575368.	−0.247508
$353$	1.93327e6	0.825764	0.412882	−	0.910785i	$-0.364522\pi$
$353$	1.93327e6	0.825764	0.412882	+	0.910785i	$0.364522\pi$
$354$	665355.	0.282192
$355$	−609824.	−0.256823
$356$	682597.	0.285456
$357$	2.39299e6	0.993736
$358$	52116.0	0.0214914
$359$	−3.11619e6	−1.27611	−0.638055	−	0.769991i	$-0.720261\pi$
$359$	−3.11619e6	−1.27611	−0.638055	+	0.769991i	$0.720261\pi$
$360$	−414395.	−0.168523
$361$	130321.	0.0526316
$362$	−1.05652e6	−0.423748
$363$	138551.	0.0551876
$364$	2.18011e6	0.862432
$365$	527277.	0.207161
$366$	−165143.	−0.0644403
$367$	584194.	0.226408	0.113204	−	0.993572i	$-0.463889\pi$
$367$	584194.	0.226408	0.113204	+	0.993572i	$0.463889\pi$
$368$	−2.81147e6	−1.08222
$369$	416559.	0.159261
$370$	−258033.	−0.0979874
$371$	−9.33240e6	−3.52013
$372$	−2.56111e6	−0.959559
$373$	−3.70711e6	−1.37963	−0.689817	−	0.723984i	$-0.742309\pi$
$373$	−3.70711e6	−1.37963	−0.689817	+	0.723984i	$0.742309\pi$
$374$	−233583.	−0.0863498
$375$	147862.	0.0542974
$376$	−1.06734e6	−0.389344
$377$	2.66843e6	0.966946
$378$	1.54882e6	0.557533
$379$	−3.69239e6	−1.32041	−0.660207	−	0.751084i	$-0.729531\pi$
$379$	−3.69239e6	−1.32041	−0.660207	+	0.751084i	$0.729531\pi$
$380$	260357.	0.0924933
$381$	724305.	0.255628
$382$	1.47096e6	0.515754
$383$	3.74329e6	1.30394	0.651969	−	0.758245i	$-0.273943\pi$
$383$	3.74329e6	1.30394	0.651969	+	0.758245i	$0.273943\pi$
$384$	1.69132e6	0.585325
$385$	703458.	0.241872
$386$	−784493.	−0.267992
$387$	3.63048e6	1.23222
$388$	−443184.	−0.149453
$389$	−893266.	−0.299300	−0.149650	−	0.988739i	$-0.547815\pi$
$389$	−893266.	−0.299300	−0.149650	+	0.988739i	$0.547815\pi$
$390$	136485.	0.0454384
$391$	−4.18005e6	−1.38274
$392$	4.02616e6	1.32335
$393$	−1.95679e6	−0.639092
$394$	427184.	0.138635
$395$	−375889.	−0.121218
$396$	535635.	0.171645
$397$	−936927.	−0.298352	−0.149176	−	0.988811i	$-0.547662\pi$
$397$	−936927.	−0.298352	−0.149176	+	0.988811i	$0.547662\pi$
$398$	753180.	0.238337
$399$	−794433.	−0.249819
$400$	457113.	0.142848
$401$	583423.	0.181185	0.0905925	−	0.995888i	$-0.471124\pi$
$401$	583423.	0.181185	0.0905925	+	0.995888i	$0.471124\pi$
$402$	−1.04651e6	−0.322980
$403$	−3.04869e6	−0.935083
$404$	−2.65624e6	−0.809681
$405$	44629.8	0.0135203
$406$	3.38991e6	1.02064
$407$	703487.	0.210509
$408$	1.11158e6	0.330591
$409$	463841.	0.137107	0.0685537	−	0.997647i	$-0.478162\pi$
$409$	463841.	0.137107	0.0685537	+	0.997647i	$0.478162\pi$
$410$	120481.	0.0353964
$411$	−3.32654e6	−0.971378
$412$	737438.	0.214034
$413$	−9.21011e6	−2.65699
$414$	−1.04716e6	−0.300271
$415$	−1.83431e6	−0.522819
$416$	1.54527e6	0.437795
$417$	2.69265e6	0.758299
$418$	77545.4	0.0217078
$419$	−2.94681e6	−0.820007	−0.410003	−	0.912084i	$-0.634472\pi$
$419$	−2.94681e6	−0.820007	−0.410003	+	0.912084i	$0.634472\pi$
$420$	−1.58713e6	−0.439025
$421$	−1.75296e6	−0.482022	−0.241011	−	0.970522i	$-0.577479\pi$
$421$	−1.75296e6	−0.482022	−0.241011	+	0.970522i	$0.577479\pi$
$422$	1.29201e6	0.353170
$423$	1.51618e6	0.412003
$424$	−4.33504e6	−1.17106
$425$	679628.	0.182515
$426$	409794.	0.109406
$427$	2.28598e6	0.606740
$428$	−2.57321e6	−0.678994
$429$	−372106.	−0.0976164
$430$	1.05004e6	0.273864
$431$	82550.1	0.0214055	0.0107027	−	0.999943i	$-0.496593\pi$
$431$	82550.1	0.0214055	0.0107027	+	0.999943i	$0.496593\pi$
$432$	−2.74390e6	−0.707389
$433$	−2.82789e6	−0.724840	−0.362420	−	0.932015i	$-0.618049\pi$
$433$	−2.82789e6	−0.724840	−0.362420	+	0.932015i	$0.618049\pi$
$434$	−3.87298e6	−0.987009
$435$	−1.94263e6	−0.492228
$436$	−2.46256e6	−0.620398
$437$	1.38771e6	0.347611
$438$	−354324.	−0.0882501
$439$	7.58354e6	1.87807	0.939033	−	0.343827i	$-0.111723\pi$
$439$	7.58354e6	1.87807	0.939033	+	0.343827i	$0.111723\pi$
$440$	326767.	0.0804649
$441$	−5.71925e6	−1.40037
$442$	627333.	0.152736
$443$	2.42893e6	0.588038	0.294019	−	0.955800i	$-0.405007\pi$
$443$	2.42893e6	0.588038	0.294019	+	0.955800i	$0.405007\pi$
$444$	−1.58720e6	−0.382097
$445$	−591537.	−0.141606
$446$	1.82053e6	0.433371
$447$	1.52422e6	0.360809
$448$	−3.47953e6	−0.819078
$449$	−3.64363e6	−0.852940	−0.426470	−	0.904502i	$-0.640243\pi$
$449$	−3.64363e6	−0.852940	−0.426470	+	0.904502i	$0.640243\pi$
$450$	170257.	0.0396345
$451$	−328473.	−0.0760429
$452$	−4.24946e6	−0.978335
$453$	−3.96418e6	−0.907628
$454$	1.13164e6	0.257672
$455$	−1.88928e6	−0.427826
$456$	−369027.	−0.0831085
$457$	−4.60981e6	−1.03251	−0.516253	−	0.856436i	$-0.672673\pi$
$457$	−4.60981e6	−1.03251	−0.516253	+	0.856436i	$0.672673\pi$
$458$	−212446.	−0.0473244
$459$	−4.07958e6	−0.903823
$460$	2.77238e6	0.610882
$461$	4.79728e6	1.05134	0.525669	−	0.850689i	$-0.323815\pi$
$461$	4.79728e6	1.05134	0.525669	+	0.850689i	$0.323815\pi$
$462$	−472715.	−0.103037
$463$	−3.52337e6	−0.763847	−0.381923	−	0.924194i	$-0.624738\pi$
$463$	−3.52337e6	−0.763847	−0.381923	+	0.924194i	$0.624738\pi$
$464$	−6.00560e6	−1.29498
$465$	2.21946e6	0.476008
$466$	−2.75342e6	−0.587365
$467$	−609920.	−0.129414	−0.0647069	−	0.997904i	$-0.520611\pi$
$467$	−609920.	−0.129414	−0.0647069	+	0.997904i	$0.520611\pi$
$468$	−1.43856e6	−0.303607
$469$	1.44861e7	3.04103
$470$	438524.	0.0915691
$471$	−5.00299e6	−1.03915
$472$	−4.27824e6	−0.883915
$473$	−2.86278e6	−0.588349
$474$	252593.	0.0516387
$475$	−225625.	−0.0458831
$476$	−7.29502e6	−1.47574
$477$	6.15803e6	1.23921
$478$	829033.	0.165960
$479$	6.88518e6	1.37112	0.685562	−	0.728014i	$-0.259556\pi$
$479$	6.88518e6	1.37112	0.685562	+	0.728014i	$0.259556\pi$
$480$	−1.12496e6	−0.222861
$481$	−1.88936e6	−0.372350
$482$	−822687.	−0.161294
$483$	−8.45941e6	−1.64996
$484$	−422370.	−0.0819558
$485$	384063.	0.0741392
$486$	−1.64842e6	−0.316575
$487$	7.87782e6	1.50516	0.752581	−	0.658499i	$-0.228808\pi$
$487$	7.87782e6	1.50516	0.752581	+	0.658499i	$0.228808\pi$
$488$	1.06187e6	0.201847
$489$	1.70604e6	0.322640
$490$	−1.65417e6	−0.311237
$491$	539824.	0.101053	0.0505264	−	0.998723i	$-0.483910\pi$
$491$	539824.	0.101053	0.0505264	+	0.998723i	$0.483910\pi$
$492$	741096.	0.138026
$493$	−8.92902e6	−1.65458
$494$	−208264.	−0.0383970
$495$	−464180.	−0.0851479
$496$	6.86141e6	1.25230
$497$	−5.67254e6	−1.03012
$498$	1.23263e6	0.222720
$499$	8.02214e6	1.44224	0.721122	−	0.692808i	$-0.243627\pi$
$499$	8.02214e6	1.44224	0.721122	+	0.692808i	$0.243627\pi$
$500$	−450757.	−0.0806338
$501$	140251.	0.0249638
$502$	2.11939e6	0.375363
$503$	−1.98662e6	−0.350102	−0.175051	−	0.984559i	$-0.556009\pi$
$503$	−1.98662e6	−0.350102	−0.175051	+	0.984559i	$0.556009\pi$
$504$	−3.85467e6	−0.675944
$505$	2.30189e6	0.401658
$506$	825732.	0.143371
$507$	−2.51425e6	−0.434399
$508$	−2.20804e6	−0.379618
$509$	−7.25610e6	−1.24139	−0.620696	−	0.784051i	$-0.713150\pi$
$509$	−7.25610e6	−1.24139	−0.620696	+	0.784051i	$0.713150\pi$
$510$	−456702.	−0.0777512
$511$	4.90469e6	0.830921
$512$	−6.00597e6	−1.01253
$513$	1.35435e6	0.227215
$514$	3.74013e6	0.624423
$515$	−639063.	−0.106176
$516$	6.45896e6	1.06792
$517$	−1.19557e6	−0.196720
$518$	−2.40020e6	−0.393027
$519$	950172.	0.154840
$520$	−877599.	−0.142327
$521$	−3.66062e6	−0.590827	−0.295413	−	0.955370i	$-0.595457\pi$
$521$	−3.66062e6	−0.590827	−0.295413	+	0.955370i	$0.595457\pi$
$522$	−2.23685e6	−0.359303
$523$	−3.48144e6	−0.556551	−0.278275	−	0.960501i	$-0.589763\pi$
$523$	−3.48144e6	−0.556551	−0.278275	+	0.960501i	$0.589763\pi$
$524$	5.96526e6	0.949076
$525$	1.37540e6	0.217787
$526$	−3.01927e6	−0.475815
$527$	1.02014e7	1.60005
$528$	837465.	0.130732
$529$	8.34044e6	1.29584
$530$	1.78108e6	0.275419
$531$	6.07734e6	0.935357
$532$	2.42182e6	0.370991
$533$	882182.	0.134505
$534$	397506.	0.0603240
$535$	2.22994e6	0.336828
$536$	6.72904e6	1.01168
$537$	−277808.	−0.0415728
$538$	52422.3	0.00780836
$539$	4.50986e6	0.668638
$540$	2.70574e6	0.399302
$541$	−1.16956e6	−0.171802	−0.0859010	−	0.996304i	$-0.527377\pi$
$541$	−1.16956e6	−0.171802	−0.0859010	+	0.996304i	$0.527377\pi$
$542$	−2.59275e6	−0.379107
$543$	5.63187e6	0.819697
$544$	−5.17073e6	−0.749125
$545$	2.13405e6	0.307761
$546$	1.26957e6	0.182253
$547$	−9.19813e6	−1.31441	−0.657205	−	0.753712i	$-0.728262\pi$
$547$	−9.19813e6	−1.31441	−0.657205	+	0.753712i	$0.728262\pi$
$548$	1.01409e7	1.44253
$549$	−1.50841e6	−0.213594
$550$	−134255.	−0.0189244
$551$	2.96428e6	0.415950
$552$	−3.92953e6	−0.548899
$553$	−3.49649e6	−0.486205
$554$	−1.41266e6	−0.195552
$555$	1.37546e6	0.189547
$556$	−8.20853e6	−1.12610
$557$	9.83957e6	1.34381	0.671905	−	0.740637i	$-0.265476\pi$
$557$	9.83957e6	1.34381	0.671905	+	0.740637i	$0.265476\pi$
$558$	2.55561e6	0.347463
$559$	7.68858e6	1.04068
$560$	4.25203e6	0.572963
$561$	1.24513e6	0.167035
$562$	3.93477e6	0.525507
$563$	6.46707e6	0.859878	0.429939	−	0.902858i	$-0.358535\pi$
$563$	6.46707e6	0.859878	0.429939	+	0.902858i	$0.358535\pi$
$564$	2.69743e6	0.357069
$565$	3.68257e6	0.485322
$566$	2.09890e6	0.275392
$567$	415143.	0.0542300
$568$	−2.63498e6	−0.342694
$569$	1.15335e6	0.149341	0.0746707	−	0.997208i	$-0.476209\pi$
$569$	1.15335e6	0.149341	0.0746707	+	0.997208i	$0.476209\pi$
$570$	151617.	0.0195461
$571$	−2.54479e6	−0.326634	−0.163317	−	0.986574i	$-0.552219\pi$
$571$	−2.54479e6	−0.326634	−0.163317	+	0.986574i	$0.552219\pi$
$572$	1.13436e6	0.144964
$573$	−7.84106e6	−0.997672
$574$	1.12070e6	0.141975
$575$	−2.40254e6	−0.303040
$576$	2.29599e6	0.288345
$577$	−3.63684e6	−0.454762	−0.227381	−	0.973806i	$-0.573016\pi$
$577$	−3.63684e6	−0.454762	−0.227381	+	0.973806i	$0.573016\pi$
$578$	421460.	0.0524732
$579$	4.18180e6	0.518402
$580$	5.92208e6	0.730978
$581$	−1.70626e7	−2.09703
$582$	−258085.	−0.0315832
$583$	−4.85586e6	−0.591690
$584$	2.27831e6	0.276427
$585$	1.24665e6	0.150610
$586$	664633.	0.0799536
$587$	−1.35247e7	−1.62006	−0.810032	−	0.586385i	$-0.800550\pi$
$587$	−1.35247e7	−1.62006	−0.810032	+	0.586385i	$0.800550\pi$
$588$	−1.01751e7	−1.21365
$589$	−3.38670e6	−0.402243
$590$	1.75775e6	0.207886
$591$	−2.27713e6	−0.268176
$592$	4.25221e6	0.498667
$593$	584317.	0.0682358	0.0341179	−	0.999418i	$-0.489138\pi$
$593$	584317.	0.0682358	0.0341179	+	0.999418i	$0.489138\pi$
$594$	805884.	0.0937145
$595$	6.32185e6	0.732068
$596$	−4.64656e6	−0.535816
$597$	−4.01488e6	−0.461038
$598$	−2.21767e6	−0.253597
$599$	833327.	0.0948961	0.0474481	−	0.998874i	$-0.484891\pi$
$599$	833327.	0.0948961	0.0474481	+	0.998874i	$0.484891\pi$
$600$	638896.	0.0724523
$601$	−2.32648e6	−0.262733	−0.131366	−	0.991334i	$-0.541936\pi$
$601$	−2.32648e6	−0.262733	−0.131366	+	0.991334i	$0.541936\pi$
$602$	9.76740e6	1.09847
$603$	−9.55876e6	−1.07055
$604$	1.20848e7	1.34786
$605$	366025.	0.0406558
$606$	−1.54684e6	−0.171106
$607$	−1.33601e6	−0.147177	−0.0735883	−	0.997289i	$-0.523445\pi$
$607$	−1.33601e6	−0.147177	−0.0735883	+	0.997289i	$0.523445\pi$
$608$	1.71659e6	0.188325
$609$	−1.80702e7	−1.97433
$610$	−436278.	−0.0474721
$611$	3.21095e6	0.347961
$612$	4.81366e6	0.519513
$613$	−8.89953e6	−0.956568	−0.478284	−	0.878205i	$-0.658741\pi$
$613$	−8.89953e6	−0.956568	−0.478284	+	0.878205i	$0.658741\pi$
$614$	3.73924e6	0.400279
$615$	−642232.	−0.0684706
$616$	3.03956e6	0.322745
$617$	1.01530e7	1.07370	0.536849	−	0.843679i	$-0.319615\pi$
$617$	1.01530e7	1.07370	0.536849	+	0.843679i	$0.319615\pi$
$618$	429442.	0.0452307
$619$	1.18368e6	0.124168	0.0620839	−	0.998071i	$-0.480225\pi$
$619$	1.18368e6	0.124168	0.0620839	+	0.998071i	$0.480225\pi$
$620$	−6.76599e6	−0.706891
$621$	1.44216e7	1.50067
$622$	−274923.	−0.0284928
$623$	−5.50243e6	−0.567982
$624$	−2.24918e6	−0.231240
$625$	390625.	0.0400000
$626$	−3.46001e6	−0.352891
$627$	−413362.	−0.0419915
$628$	1.52516e7	1.54318
$629$	6.32211e6	0.637141
$630$	1.58372e6	0.158974
$631$	−7.63535e6	−0.763406	−0.381703	−	0.924285i	$-0.624662\pi$
$631$	−7.63535e6	−0.763406	−0.381703	+	0.924285i	$0.624662\pi$
$632$	−1.62417e6	−0.161748
$633$	−6.88714e6	−0.683172
$634$	1.83540e6	0.181346
$635$	1.91348e6	0.188317
$636$	1.09557e7	1.07398
$637$	−1.21121e7	−1.18269
$638$	1.76385e6	0.171557
$639$	3.74306e6	0.362639
$640$	4.46815e6	0.431199
$641$	6.35794e6	0.611183	0.305592	−	0.952163i	$-0.401146\pi$
$641$	6.35794e6	0.611183	0.305592	+	0.952163i	$0.401146\pi$
$642$	−1.49849e6	−0.143488
$643$	1.45567e7	1.38846	0.694232	−	0.719751i	$-0.255744\pi$
$643$	1.45567e7	1.38846	0.694232	+	0.719751i	$0.255744\pi$
$644$	2.57884e7	2.45025
$645$	−5.59732e6	−0.529762
$646$	696887.	0.0657023
$647$	1.31034e7	1.23061	0.615307	−	0.788287i	$-0.289032\pi$
$647$	1.31034e7	1.23061	0.615307	+	0.788287i	$0.289032\pi$
$648$	192840.	0.0180410
$649$	−4.79223e6	−0.446607
$650$	360568.	0.0334737
$651$	2.06452e7	1.90927
$652$	−5.20086e6	−0.479133
$653$	−1.05440e7	−0.967658	−0.483829	−	0.875163i	$-0.660754\pi$
$653$	−1.05440e7	−0.967658	−0.483829	+	0.875163i	$0.660754\pi$
$654$	−1.43405e6	−0.131106
$655$	−5.16948e6	−0.470808
$656$	−1.98545e6	−0.180135
$657$	−3.23639e6	−0.292514
$658$	4.07912e6	0.367284
$659$	1.10487e7	0.991058	0.495529	−	0.868592i	$-0.334974\pi$
$659$	1.10487e7	0.991058	0.495529	+	0.868592i	$0.334974\pi$
$660$	−825819.	−0.0737947
$661$	−9.43924e6	−0.840298	−0.420149	−	0.907455i	$-0.638022\pi$
$661$	−9.43924e6	−0.840298	−0.420149	+	0.907455i	$0.638022\pi$
$662$	−1.54687e6	−0.137186
$663$	−3.34405e6	−0.295453
$664$	−7.92583e6	−0.697629
$665$	−2.09875e6	−0.184037
$666$	1.58378e6	0.138360
$667$	3.15648e7	2.74718
$668$	−427552.	−0.0370722
$669$	−9.70444e6	−0.838311
$670$	−2.76467e6	−0.237934
$671$	1.18945e6	0.101985
$672$	−1.04643e7	−0.893896
$673$	−6.94995e6	−0.591485	−0.295743	−	0.955268i	$-0.595567\pi$
$673$	−6.94995e6	−0.591485	−0.295743	+	0.955268i	$0.595567\pi$
$674$	4.95913e6	0.420490
$675$	−2.34479e6	−0.198082
$676$	7.66467e6	0.645099
$677$	4.20605e6	0.352698	0.176349	−	0.984328i	$-0.443571\pi$
$677$	4.20605e6	0.352698	0.176349	+	0.984328i	$0.443571\pi$
$678$	−2.47464e6	−0.206746
$679$	3.57252e6	0.297372
$680$	2.93660e6	0.243541
$681$	−6.03228e6	−0.498441
$682$	−2.01520e6	−0.165904
$683$	9.56313e6	0.784419	0.392210	−	0.919876i	$-0.371711\pi$
$683$	9.56313e6	0.784419	0.392210	+	0.919876i	$0.371711\pi$
$684$	−1.59805e6	−0.130602
$685$	−8.78810e6	−0.715597
$686$	−8.44849e6	−0.685439
$687$	1.13246e6	0.0915442
$688$	−1.73040e7	−1.39372
$689$	1.30414e7	1.04659
$690$	1.61447e6	0.129095
$691$	1.41305e7	1.12580	0.562900	−	0.826525i	$-0.309686\pi$
$691$	1.41305e7	1.12580	0.562900	+	0.826525i	$0.309686\pi$
$692$	−2.89659e6	−0.229944
$693$	−4.31777e6	−0.341528
$694$	3.13277e6	0.246905
$695$	7.11350e6	0.558626
$696$	−8.39388e6	−0.656810
$697$	−2.95193e6	−0.230157
$698$	1.82353e6	0.141669
$699$	1.46773e7	1.13620
$700$	−4.19290e6	−0.323422
$701$	−2.08775e7	−1.60466	−0.802329	−	0.596882i	$-0.796406\pi$
$701$	−2.08775e7	−1.60466	−0.802329	+	0.596882i	$0.796406\pi$
$702$	−2.16437e6	−0.165763
$703$	−2.09883e6	−0.160173
$704$	−1.81048e6	−0.137677
$705$	−2.33759e6	−0.177131
$706$	−3.43207e6	−0.259146
$707$	2.14120e7	1.61105
$708$	1.08121e7	0.810642
$709$	−6.78540e6	−0.506944	−0.253472	−	0.967343i	$-0.581573\pi$
$709$	−6.78540e6	−0.506944	−0.253472	+	0.967343i	$0.581573\pi$
$710$	1.08260e6	0.0805977
$711$	2.30718e6	0.171162
$712$	−2.55597e6	−0.188954
$713$	−3.60628e7	−2.65666
$714$	−4.24820e6	−0.311860
$715$	−983034.	−0.0719124
$716$	846896.	0.0617373
$717$	−4.41922e6	−0.321032
$718$	5.53207e6	0.400476
$719$	−2.82065e6	−0.203482	−0.101741	−	0.994811i	$-0.532441\pi$
$719$	−2.82065e6	−0.203482	−0.101741	+	0.994811i	$0.532441\pi$
$720$	−2.80573e6	−0.201704
$721$	−5.94451e6	−0.425871
$722$	−231355.	−0.0165171
$723$	4.38540e6	0.312006
$724$	−1.71687e7	−1.21728
$725$	−5.13207e6	−0.362616
$726$	−245964.	−0.0173193
$727$	−868209.	−0.0609240	−0.0304620	−	0.999536i	$-0.509698\pi$
$727$	−868209.	−0.0609240	−0.0304620	+	0.999536i	$0.509698\pi$
$728$	−8.16336e6	−0.570874
$729$	8.35322e6	0.582150
$730$	−936058.	−0.0650123
$731$	−2.57273e7	−1.78074
$732$	−2.68361e6	−0.185115
$733$	2.72455e7	1.87298	0.936492	−	0.350689i	$-0.114053\pi$
$733$	2.72455e7	1.87298	0.936492	+	0.350689i	$0.114053\pi$
$734$	−1.03710e6	−0.0710527
$735$	8.81770e6	0.602056
$736$	1.82789e7	1.24381
$737$	7.53747e6	0.511160
$738$	−739502.	−0.0499803
$739$	4.82545e6	0.325032	0.162516	−	0.986706i	$-0.448039\pi$
$739$	4.82545e6	0.325032	0.162516	+	0.986706i	$0.448039\pi$
$740$	−4.19308e6	−0.281484
$741$	1.11017e6	0.0742750
$742$	1.65675e7	1.10471
$743$	1.26073e7	0.837818	0.418909	−	0.908028i	$-0.362413\pi$
$743$	1.26073e7	0.837818	0.418909	+	0.908028i	$0.362413\pi$
$744$	9.59002e6	0.635166
$745$	4.02670e6	0.265802
$746$	6.58111e6	0.432965
$747$	1.12588e7	0.738230
$748$	−3.79576e6	−0.248053
$749$	2.07427e7	1.35102
$750$	−262495.	−0.0170399
$751$	−1.37598e7	−0.890250	−0.445125	−	0.895469i	$-0.646841\pi$
$751$	−1.37598e7	−0.890250	−0.445125	+	0.895469i	$0.646841\pi$
$752$	−7.22660e6	−0.466004
$753$	−1.12976e7	−0.726101
$754$	−4.73717e6	−0.303453
$755$	−1.04726e7	−0.668634
$756$	2.51686e7	1.60160
$757$	6.84154e6	0.433924	0.216962	−	0.976180i	$-0.430385\pi$
$757$	6.84154e6	0.433924	0.216962	+	0.976180i	$0.430385\pi$
$758$	6.55498e6	0.414380
$759$	−4.40162e6	−0.277337
$760$	−974900.	−0.0612246
$761$	1.83711e7	1.14993	0.574967	−	0.818177i	$-0.305015\pi$
$761$	1.83711e7	1.14993	0.574967	+	0.818177i	$0.305015\pi$
$762$	−1.28583e6	−0.0802227
$763$	1.98508e7	1.23443
$764$	2.39034e7	1.48158
$765$	−4.17151e6	−0.257715
$766$	−6.64535e6	−0.409209
$767$	1.28705e7	0.789964
$768$	1.52847e6	0.0935092
$769$	1.83792e7	1.12076	0.560378	−	0.828237i	$-0.310656\pi$
$769$	1.83792e7	1.12076	0.560378	+	0.828237i	$0.310656\pi$
$770$	−1.24882e6	−0.0759058
$771$	−1.99370e7	−1.20788
$772$	−1.27482e7	−0.769847
$773$	−1.21883e7	−0.733662	−0.366831	−	0.930288i	$-0.619557\pi$
$773$	−1.21883e7	−0.733662	−0.366831	+	0.930288i	$0.619557\pi$
$774$	−6.44507e6	−0.386701
$775$	5.86340e6	0.350667
$776$	1.65949e6	0.0989283
$777$	1.27944e7	0.760271
$778$	1.58579e6	0.0939281
$779$	979990.	0.0578600
$780$	2.21791e6	0.130529
$781$	−2.95155e6	−0.173150
$782$	7.42070e6	0.433938
$783$	3.08061e7	1.79569
$784$	2.72597e7	1.58391
$785$	−1.32170e7	−0.765523
$786$	3.47383e6	0.200563
$787$	−915750.	−0.0527036	−0.0263518	−	0.999653i	$-0.508389\pi$
$787$	−915750.	−0.0527036	−0.0263518	+	0.999653i	$0.508389\pi$
$788$	6.94182e6	0.398252
$789$	1.60945e7	0.920415
$790$	667303.	0.0380413
$791$	3.42550e7	1.94663
$792$	−2.00567e6	−0.113618
$793$	−3.19450e6	−0.180393
$794$	1.66330e6	0.0936307
$795$	−9.49419e6	−0.532771
$796$	1.22393e7	0.684660
$797$	2.48262e7	1.38441	0.692206	−	0.721700i	$-0.256639\pi$
$797$	2.48262e7	1.38441	0.692206	+	0.721700i	$0.256639\pi$
$798$	1.41033e6	0.0783996
$799$	−1.07444e7	−0.595408
$800$	−2.97194e6	−0.164178
$801$	3.63081e6	0.199950
$802$	−1.03573e6	−0.0568605
$803$	2.55202e6	0.139668
$804$	−1.70059e7	−0.927812
$805$	−2.23482e7	−1.21549
$806$	5.41223e6	0.293453
$807$	−279441.	−0.0151045
$808$	9.94622e6	0.535957
$809$	−1.98590e6	−0.106681	−0.0533403	−	0.998576i	$-0.516987\pi$
$809$	−1.98590e6	−0.106681	−0.0533403	+	0.998576i	$0.516987\pi$
$810$	−79229.8	−0.00424303
$811$	−1.51830e6	−0.0810599	−0.0405300	−	0.999178i	$-0.512905\pi$
$811$	−1.51830e6	−0.0810599	−0.0405300	+	0.999178i	$0.512905\pi$
$812$	5.50868e7	2.93195
$813$	1.38208e7	0.733344
$814$	−1.24888e6	−0.0660631
$815$	4.50705e6	0.237683
$816$	7.52615e6	0.395683
$817$	8.54102e6	0.447667
$818$	−823441.	−0.0430278
$819$	1.15962e7	0.604098
$820$	1.95784e6	0.101682
$821$	−6.57395e6	−0.340383	−0.170192	−	0.985411i	$-0.554439\pi$
$821$	−6.57395e6	−0.340383	−0.170192	+	0.985411i	$0.554439\pi$
$822$	5.90549e6	0.304843
$823$	2.29055e7	1.17880	0.589401	−	0.807841i	$-0.299364\pi$
$823$	2.29055e7	1.17880	0.589401	+	0.807841i	$0.299364\pi$
$824$	−2.76132e6	−0.141677
$825$	715654.	0.0366073
$826$	1.63504e7	0.833832
$827$	−2.98342e7	−1.51688	−0.758440	−	0.651743i	$-0.774038\pi$
$827$	−2.98342e7	−1.51688	−0.758440	+	0.651743i	$0.774038\pi$
$828$	−1.70166e7	−0.862577
$829$	−3.31472e7	−1.67517	−0.837587	−	0.546304i	$-0.816034\pi$
$829$	−3.31472e7	−1.67517	−0.837587	+	0.546304i	$0.816034\pi$
$830$	3.25638e6	0.164074
$831$	7.53028e6	0.378276
$832$	4.86241e6	0.243525
$833$	4.05293e7	2.02375
$834$	−4.78018e6	−0.237974
$835$	370516.	0.0183904
$836$	1.26013e6	0.0623590
$837$	−3.51960e7	−1.73652
$838$	5.23138e6	0.257339
$839$	1.65815e7	0.813238	0.406619	−	0.913598i	$-0.366708\pi$
$839$	1.65815e7	0.813238	0.406619	+	0.913598i	$0.366708\pi$
$840$	5.94296e6	0.290606
$841$	4.69144e7	2.28727
$842$	3.11197e6	0.151271
$843$	−2.09746e7	−1.01654
$844$	2.09954e7	1.01454
$845$	−6.64219e6	−0.320014
$846$	−2.69163e6	−0.129297
$847$	3.40474e6	0.163070
$848$	−2.93511e7	−1.40164
$849$	−1.11883e7	−0.532717
$850$	−1.20652e6	−0.0572780
$851$	−2.23491e7	−1.05788
$852$	6.65924e6	0.314286
$853$	−3.87653e7	−1.82419	−0.912096	−	0.409977i	$-0.865537\pi$
$853$	−3.87653e7	−1.82419	−0.912096	+	0.409977i	$0.865537\pi$
$854$	−4.05822e6	−0.190410
$855$	1.38487e6	0.0647878
$856$	9.63532e6	0.449450
$857$	2.68627e7	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$857$	2.68627e7	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$858$	660587.	0.0306346
$859$	2.08121e7	0.962351	0.481175	−	0.876624i	$-0.340210\pi$
$859$	2.08121e7	0.962351	0.481175	+	0.876624i	$0.340210\pi$
$860$	1.70634e7	0.786717
$861$	−5.97399e6	−0.274636
$862$	−146548.	−0.00671758
$863$	1.03484e7	0.472982	0.236491	−	0.971634i	$-0.424003\pi$
$863$	1.03484e7	0.472982	0.236491	+	0.971634i	$0.424003\pi$
$864$	1.78396e7	0.813017
$865$	2.51018e6	0.114068
$866$	5.02025e6	0.227474
$867$	−2.24663e6	−0.101504
$868$	−6.29367e7	−2.83534
$869$	−1.81930e6	−0.0817251
$870$	3.44868e6	0.154474
$871$	−2.02434e7	−0.904145
$872$	9.22099e6	0.410664
$873$	−2.35735e6	−0.104686
$874$	−2.46355e6	−0.109089
$875$	3.63356e6	0.160440
$876$	−5.75783e6	−0.253512
$877$	7.34572e6	0.322504	0.161252	−	0.986913i	$-0.448447\pi$
$877$	7.34572e6	0.322504	0.161252	+	0.986913i	$0.448447\pi$
$878$	−1.34628e7	−0.589385
$879$	−3.54288e6	−0.154662
$880$	2.21243e6	0.0963081
$881$	2.43844e6	0.105846	0.0529228	−	0.998599i	$-0.483146\pi$
$881$	2.43844e6	0.105846	0.0529228	+	0.998599i	$0.483146\pi$
$882$	1.01532e7	0.439472
$883$	4.34433e7	1.87508	0.937542	−	0.347871i	$-0.113095\pi$
$883$	4.34433e7	1.87508	0.937542	+	0.347871i	$0.113095\pi$
$884$	1.01943e7	0.438759
$885$	−9.36979e6	−0.402135
$886$	−4.31199e6	−0.184541
$887$	3.96629e7	1.69268	0.846342	−	0.532640i	$-0.178800\pi$
$887$	3.96629e7	1.69268	0.846342	+	0.532640i	$0.178800\pi$
$888$	5.94321e6	0.252923
$889$	1.77990e7	0.755339
$890$	1.05014e6	0.0444397
$891$	216008.	0.00911541
$892$	2.95839e7	1.24493
$893$	3.56695e6	0.149682
$894$	−2.70589e6	−0.113231
$895$	−733919.	−0.0306260
$896$	4.15624e7	1.72954
$897$	1.18215e7	0.490557
$898$	6.46841e6	0.267674
$899$	−7.70339e7	−3.17894
$900$	2.76671e6	0.113856
$901$	−4.36387e7	−1.79085
$902$	583128.	0.0238642
$903$	−5.20658e7	−2.12488
$904$	1.59120e7	0.647595
$905$	1.48784e7	0.603857
$906$	7.03748e6	0.284837
$907$	−9.87746e6	−0.398682	−0.199341	−	0.979930i	$-0.563880\pi$
$907$	−9.87746e6	−0.398682	−0.199341	+	0.979930i	$0.563880\pi$
$908$	1.83893e7	0.740204
$909$	−1.41288e7	−0.567149
$910$	3.35397e6	0.134263
$911$	−3.94391e7	−1.57446	−0.787228	−	0.616662i	$-0.788485\pi$
$911$	−3.94391e7	−1.57446	−0.787228	+	0.616662i	$0.788485\pi$
$912$	−2.49855e6	−0.0994722
$913$	−8.87804e6	−0.352484
$914$	8.18364e6	0.324027
$915$	2.32561e6	0.0918299
$916$	−3.45229e6	−0.135947
$917$	−4.80861e7	−1.88841
$918$	7.24234e6	0.283643
$919$	−2.97893e7	−1.16352	−0.581758	−	0.813362i	$-0.697635\pi$
$919$	−2.97893e7	−1.16352	−0.581758	+	0.813362i	$0.697635\pi$
$920$	−1.03811e7	−0.404365
$921$	−1.99323e7	−0.774299
$922$	−8.51644e6	−0.329937
$923$	7.92699e6	0.306270
$924$	−7.68171e6	−0.295990
$925$	3.63372e6	0.139636
$926$	6.25493e6	0.239715
$927$	3.92252e6	0.149922
$928$	3.90457e7	1.48834
$929$	−2.45250e7	−0.932332	−0.466166	−	0.884697i	$-0.654365\pi$
$929$	−2.45250e7	−0.932332	−0.466166	+	0.884697i	$0.654365\pi$
$930$	−3.94013e6	−0.149384
$931$	−1.34550e7	−0.508757
$932$	−4.47437e7	−1.68730
$933$	1.46550e6	0.0551163
$934$	1.08277e6	0.0406134
$935$	3.28940e6	0.123052
$936$	5.38664e6	0.200969
$937$	−4.26434e7	−1.58673	−0.793366	−	0.608746i	$-0.791673\pi$
$937$	−4.26434e7	−1.58673	−0.793366	+	0.608746i	$0.791673\pi$
$938$	−2.57168e7	−0.954354
$939$	1.84438e7	0.682632
$940$	7.12611e6	0.263047
$941$	5.91358e6	0.217709	0.108855	−	0.994058i	$-0.465282\pi$
$941$	5.91358e6	0.217709	0.108855	+	0.994058i	$0.465282\pi$
$942$	8.88164e6	0.326111
$943$	1.04353e7	0.382143
$944$	−2.89665e7	−1.05795
$945$	−2.18110e7	−0.794505
$946$	5.08220e6	0.184639
$947$	−1.51167e7	−0.547750	−0.273875	−	0.961765i	$-0.588306\pi$
$947$	−1.51167e7	−0.547750	−0.273875	+	0.961765i	$0.588306\pi$
$948$	4.10468e6	0.148340
$949$	−6.85398e6	−0.247046
$950$	400545.	0.0143993
$951$	−9.78376e6	−0.350796
$952$	2.73160e7	0.976843
$953$	3.68083e6	0.131284	0.0656422	−	0.997843i	$-0.479090\pi$
$953$	3.68083e6	0.131284	0.0656422	+	0.997843i	$0.479090\pi$
$954$	−1.09321e7	−0.388897
$955$	−2.07146e7	−0.734968
$956$	1.34720e7	0.476745
$957$	−9.40232e6	−0.331860
$958$	−1.22230e7	−0.430294
$959$	−8.17463e7	−2.87026
$960$	−3.53985e6	−0.123967
$961$	5.93822e7	2.07419
$962$	3.35411e6	0.116853
$963$	−1.36872e7	−0.475608
$964$	−1.33688e7	−0.463341
$965$	1.10475e7	0.381898
$966$	1.50177e7	0.517799
$967$	1.41838e7	0.487784	0.243892	−	0.969802i	$-0.421576\pi$
$967$	1.41838e7	0.487784	0.243892	+	0.969802i	$0.421576\pi$
$968$	1.58155e6	0.0542494
$969$	−3.71481e6	−0.127094
$970$	−681814.	−0.0232668
$971$	1.54665e7	0.526434	0.263217	−	0.964737i	$-0.415216\pi$
$971$	1.54665e7	0.526434	0.263217	+	0.964737i	$0.415216\pi$
$972$	−2.67871e7	−0.909412
$973$	6.61692e7	2.24065
$974$	−1.39852e7	−0.472359
$975$	−1.92203e6	−0.0647514
$976$	7.18958e6	0.241590
$977$	8.79235e6	0.294692	0.147346	−	0.989085i	$-0.452927\pi$
$977$	8.79235e6	0.294692	0.147346	+	0.989085i	$0.452927\pi$
$978$	−3.02868e6	−0.101253
$979$	−2.86304e6	−0.0954709
$980$	−2.68807e7	−0.894077
$981$	−1.30986e7	−0.434564
$982$	−958332.	−0.0317130
$983$	−2.94346e6	−0.0971572	−0.0485786	−	0.998819i	$-0.515469\pi$
$983$	−2.94346e6	−0.0971572	−0.0485786	+	0.998819i	$0.515469\pi$
$984$	−2.77501e6	−0.0913645
$985$	−6.01577e6	−0.197561
$986$	1.58514e7	0.519248
$987$	−2.17440e7	−0.710473
$988$	−3.38433e6	−0.110301
$989$	9.09479e7	2.95666
$990$	824044.	0.0267216
$991$	3.66159e7	1.18436	0.592182	−	0.805804i	$-0.298267\pi$
$991$	3.66159e7	1.18436	0.592182	+	0.805804i	$0.298267\pi$
$992$	−4.46097e7	−1.43930
$993$	8.24573e6	0.265373
$994$	1.00703e7	0.323277
$995$	−1.06066e7	−0.339639
$996$	2.00305e7	0.639798
$997$	616696.	0.0196487	0.00982434	−	0.999952i	$-0.496873\pi$
$997$	616696.	0.0196487	0.00982434	+	0.999952i	$0.496873\pi$
$998$	−1.42414e7	−0.452613
$999$	−2.18120e7	−0.691482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.19	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.19	✓	38	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)

\(f(q)\)	\(=\)	\(q-1.77527 q^{2} +9.46319 q^{3} -28.8484 q^{4} +25.0000 q^{5} -16.7997 q^{6} +232.548 q^{7} +108.022 q^{8} -153.448 q^{9} +O(q^{10})\)	\(q-1.77527 q^{2} +9.46319 q^{3} -28.8484 q^{4} +25.0000 q^{5} -16.7997 q^{6} +232.548 q^{7} +108.022 q^{8} -153.448 q^{9} -44.3817 q^{10} +121.000 q^{11} -272.998 q^{12} -324.970 q^{13} -412.835 q^{14} +236.580 q^{15} +731.382 q^{16} +1087.41 q^{17} +272.411 q^{18} -361.000 q^{19} -721.211 q^{20} +2200.65 q^{21} -214.807 q^{22} -3844.06 q^{23} +1022.23 q^{24} +625.000 q^{25} +576.909 q^{26} -3751.66 q^{27} -6708.64 q^{28} -8211.31 q^{29} -419.992 q^{30} +9381.43 q^{31} -4755.11 q^{32} +1145.05 q^{33} -1930.43 q^{34} +5813.70 q^{35} +4426.74 q^{36} +5813.95 q^{37} +640.871 q^{38} -3075.25 q^{39} +2700.55 q^{40} -2714.65 q^{41} -3906.73 q^{42} -23659.3 q^{43} -3490.66 q^{44} -3836.20 q^{45} +6824.23 q^{46} -9880.76 q^{47} +6921.20 q^{48} +37271.6 q^{49} -1109.54 q^{50} +10290.3 q^{51} +9374.88 q^{52} -40131.1 q^{53} +6660.20 q^{54} +3025.00 q^{55} +25120.3 q^{56} -3416.21 q^{57} +14577.3 q^{58} -39605.2 q^{59} -6824.95 q^{60} +9830.13 q^{61} -16654.5 q^{62} -35684.0 q^{63} -14962.6 q^{64} -8124.25 q^{65} -2032.76 q^{66} +62293.2 q^{67} -31369.9 q^{68} -36377.0 q^{69} -10320.9 q^{70} -24393.0 q^{71} -16575.8 q^{72} +21091.1 q^{73} -10321.3 q^{74} +5914.49 q^{75} +10414.3 q^{76} +28138.3 q^{77} +5459.39 q^{78} -15035.6 q^{79} +18284.5 q^{80} +1785.19 q^{81} +4819.24 q^{82} -73372.2 q^{83} -63485.2 q^{84} +27185.1 q^{85} +42001.6 q^{86} -77705.2 q^{87} +13070.7 q^{88} -23661.5 q^{89} +6810.28 q^{90} -75571.1 q^{91} +110895. q^{92} +88778.3 q^{93} +17541.0 q^{94} -9025.00 q^{95} -44998.5 q^{96} +15362.5 q^{97} -66167.0 q^{98} -18567.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

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