LMFDB - Embedded newform 1045.6.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-3.53022 q^{2} -7.27933 q^{3} -19.5375 q^{4} -25.0000 q^{5} +25.6976 q^{6} -171.265 q^{7} +181.939 q^{8} -190.011 q^{9} +O(q^{10})$	\(q-3.53022 q^{2} -7.27933 q^{3} -19.5375 q^{4} -25.0000 q^{5} +25.6976 q^{6} -171.265 q^{7} +181.939 q^{8} -190.011 q^{9} +88.2555 q^{10} -121.000 q^{11} +142.220 q^{12} -544.583 q^{13} +604.603 q^{14} +181.983 q^{15} -17.0833 q^{16} -539.710 q^{17} +670.782 q^{18} -361.000 q^{19} +488.438 q^{20} +1246.69 q^{21} +427.157 q^{22} -1144.68 q^{23} -1324.39 q^{24} +625.000 q^{25} +1922.50 q^{26} +3152.03 q^{27} +3346.10 q^{28} -6290.66 q^{29} -642.441 q^{30} +1494.17 q^{31} -5761.74 q^{32} +880.799 q^{33} +1905.30 q^{34} +4281.62 q^{35} +3712.35 q^{36} -6221.70 q^{37} +1274.41 q^{38} +3964.20 q^{39} -4548.47 q^{40} +12149.5 q^{41} -4401.10 q^{42} +10982.9 q^{43} +2364.04 q^{44} +4750.28 q^{45} +4040.99 q^{46} +13722.3 q^{47} +124.355 q^{48} +12524.7 q^{49} -2206.39 q^{50} +3928.72 q^{51} +10639.8 q^{52} +4411.40 q^{53} -11127.4 q^{54} +3025.00 q^{55} -31159.8 q^{56} +2627.84 q^{57} +22207.4 q^{58} +9974.23 q^{59} -3555.50 q^{60} -44594.8 q^{61} -5274.74 q^{62} +32542.3 q^{63} +20886.9 q^{64} +13614.6 q^{65} -3109.41 q^{66} -45465.7 q^{67} +10544.6 q^{68} +8332.54 q^{69} -15115.1 q^{70} +16382.9 q^{71} -34570.5 q^{72} +40403.3 q^{73} +21964.0 q^{74} -4549.58 q^{75} +7053.05 q^{76} +20723.1 q^{77} -13994.5 q^{78} +75241.5 q^{79} +427.083 q^{80} +23228.1 q^{81} -42890.3 q^{82} +60170.0 q^{83} -24357.3 q^{84} +13492.7 q^{85} -38772.2 q^{86} +45791.8 q^{87} -22014.6 q^{88} -25248.2 q^{89} -16769.6 q^{90} +93268.0 q^{91} +22364.3 q^{92} -10876.5 q^{93} -48442.6 q^{94} +9025.00 q^{95} +41941.6 q^{96} +173936. q^{97} -44214.9 q^{98} +22991.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.53022	−0.624061	−0.312030	−	0.950072i	$-0.601009\pi$
$2$	−3.53022	−0.624061	−0.312030	+	0.950072i	$0.601009\pi$
$3$	−7.27933	−0.466969	−0.233485	−	0.972361i	$-0.575013\pi$
$3$	−7.27933	−0.466969	−0.233485	+	0.972361i	$0.575013\pi$
$4$	−19.5375	−0.610548
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	25.6976	0.291417
$7$	−171.265	−1.32106	−0.660531	−	0.750799i	$-0.729669\pi$
$7$	−171.265	−1.32106	−0.660531	+	0.750799i	$0.729669\pi$
$8$	181.939	1.00508
$9$	−190.011	−0.781940
$10$	88.2555	0.279088
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	142.220	0.285107
$13$	−544.583	−0.893729	−0.446865	−	0.894602i	$-0.647459\pi$
$13$	−544.583	−0.893729	−0.446865	+	0.894602i	$0.647459\pi$
$14$	604.603	0.824423
$15$	181.983	0.208835
$16$	−17.0833	−0.0166829
$17$	−539.710	−0.452937	−0.226469	−	0.974018i	$-0.572718\pi$
$17$	−539.710	−0.452937	−0.226469	+	0.974018i	$0.572718\pi$
$18$	670.782	0.487978
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	488.438	0.273045
$21$	1246.69	0.616895
$22$	427.157	0.188161
$23$	−1144.68	−0.451197	−0.225599	−	0.974220i	$-0.572434\pi$
$23$	−1144.68	−0.451197	−0.225599	+	0.974220i	$0.572434\pi$
$24$	−1324.39	−0.469341
$25$	625.000	0.200000
$26$	1922.50	0.557741
$27$	3152.03	0.832111
$28$	3346.10	0.806572
$29$	−6290.66	−1.38900	−0.694499	−	0.719494i	$-0.744374\pi$
$29$	−6290.66	−1.38900	−0.694499	+	0.719494i	$0.744374\pi$
$30$	−642.441	−0.130326
$31$	1494.17	0.279251	0.139626	−	0.990204i	$-0.455410\pi$
$31$	1494.17	0.279251	0.139626	+	0.990204i	$0.455410\pi$
$32$	−5761.74	−0.994669
$33$	880.799	0.140796
$34$	1905.30	0.282660
$35$	4281.62	0.590797
$36$	3712.35	0.477412
$37$	−6221.70	−0.747145	−0.373572	−	0.927601i	$-0.621867\pi$
$37$	−6221.70	−0.747145	−0.373572	+	0.927601i	$0.621867\pi$
$38$	1274.41	0.143169
$39$	3964.20	0.417344
$40$	−4548.47	−0.449485
$41$	12149.5	1.12875	0.564375	−	0.825518i	$-0.309117\pi$
$41$	12149.5	1.12875	0.564375	+	0.825518i	$0.309117\pi$
$42$	−4401.10	−0.384980
$43$	10982.9	0.905831	0.452915	−	0.891553i	$-0.350384\pi$
$43$	10982.9	0.905831	0.452915	+	0.891553i	$0.350384\pi$
$44$	2364.04	0.184087
$45$	4750.28	0.349694
$46$	4040.99	0.281574
$47$	13722.3	0.906111	0.453055	−	0.891482i	$-0.350334\pi$
$47$	13722.3	0.906111	0.453055	+	0.891482i	$0.350334\pi$
$48$	124.355	0.00779042
$49$	12524.7	0.745206
$50$	−2206.39	−0.124812
$51$	3928.72	0.211508
$52$	10639.8	0.545665
$53$	4411.40	0.215718	0.107859	−	0.994166i	$-0.465600\pi$
$53$	4411.40	0.215718	0.107859	+	0.994166i	$0.465600\pi$
$54$	−11127.4	−0.519288
$55$	3025.00	0.134840
$56$	−31159.8	−1.32777
$57$	2627.84	0.107130
$58$	22207.4	0.866819
$59$	9974.23	0.373035	0.186517	−	0.982452i	$-0.440280\pi$
$59$	9974.23	0.373035	0.186517	+	0.982452i	$0.440280\pi$
$60$	−3555.50	−0.127504
$61$	−44594.8	−1.53447	−0.767237	−	0.641363i	$-0.778369\pi$
$61$	−44594.8	−1.53447	−0.767237	+	0.641363i	$0.778369\pi$
$62$	−5274.74	−0.174270
$63$	32542.3	1.03299
$64$	20886.9	0.637417
$65$	13614.6	0.399688
$66$	−3109.41	−0.0878656
$67$	−45465.7	−1.23736	−0.618681	−	0.785642i	$-0.712333\pi$
$67$	−45465.7	−1.23736	−0.618681	+	0.785642i	$0.712333\pi$
$68$	10544.6	0.276540
$69$	8332.54	0.210695
$70$	−15115.1	−0.368693
$71$	16382.9	0.385695	0.192847	−	0.981229i	$-0.438228\pi$
$71$	16382.9	0.385695	0.192847	+	0.981229i	$0.438228\pi$
$72$	−34570.5	−0.785912
$73$	40403.3	0.887381	0.443690	−	0.896180i	$-0.353669\pi$
$73$	40403.3	0.887381	0.443690	+	0.896180i	$0.353669\pi$
$74$	21964.0	0.466264
$75$	−4549.58	−0.0933938
$76$	7053.05	0.140069
$77$	20723.1	0.398315
$78$	−13994.5	−0.260448
$79$	75241.5	1.35641	0.678203	−	0.734875i	$-0.262759\pi$
$79$	75241.5	1.35641	0.678203	+	0.734875i	$0.262759\pi$
$80$	427.083	0.00746084
$81$	23228.1	0.393370
$82$	−42890.3	−0.704409
$83$	60170.0	0.958705	0.479353	−	0.877622i	$-0.340871\pi$
$83$	60170.0	0.958705	0.479353	+	0.877622i	$0.340871\pi$
$84$	−24357.3	−0.376644
$85$	13492.7	0.202560
$86$	−38772.2	−0.565294
$87$	45791.8	0.648619
$88$	−22014.6	−0.303043
$89$	−25248.2	−0.337874	−0.168937	−	0.985627i	$-0.554033\pi$
$89$	−25248.2	−0.337874	−0.168937	+	0.985627i	$0.554033\pi$
$90$	−16769.6	−0.218230
$91$	93268.0	1.18067
$92$	22364.3	0.275478
$93$	−10876.5	−0.130402
$94$	−48442.6	−0.565468
$95$	9025.00	0.102598
$96$	41941.6	0.464480
$97$	173936.	1.87699	0.938493	−	0.345300i	$-0.112223\pi$
$97$	173936.	1.87699	0.938493	+	0.345300i	$0.112223\pi$
$98$	−44214.9	−0.465054
$99$	22991.4	0.235764
$100$	−12211.0	−0.122110
$101$	56653.7	0.552618	0.276309	−	0.961069i	$-0.410889\pi$
$101$	56653.7	0.552618	0.276309	+	0.961069i	$0.410889\pi$
$102$	−13869.3	−0.131994
$103$	70057.7	0.650673	0.325337	−	0.945598i	$-0.394522\pi$
$103$	70057.7	0.650673	0.325337	+	0.945598i	$0.394522\pi$
$104$	−99080.9	−0.898269
$105$	−31167.3	−0.275884
$106$	−15573.2	−0.134621
$107$	−80778.1	−0.682078	−0.341039	−	0.940049i	$-0.610779\pi$
$107$	−80778.1	−0.682078	−0.341039	+	0.940049i	$0.610779\pi$
$108$	−61582.9	−0.508044
$109$	−87329.8	−0.704038	−0.352019	−	0.935993i	$-0.614505\pi$
$109$	−87329.8	−0.704038	−0.352019	+	0.935993i	$0.614505\pi$
$110$	−10678.9	−0.0841483
$111$	45289.8	0.348893
$112$	2925.78	0.0220392
$113$	−156479.	−1.15282	−0.576408	−	0.817162i	$-0.695546\pi$
$113$	−156479.	−1.15282	−0.576408	+	0.817162i	$0.695546\pi$
$114$	−9276.85	−0.0668557
$115$	28617.1	0.201781
$116$	122904.	0.848050
$117$	103477.	0.698842
$118$	−35211.2	−0.232796
$119$	92433.4	0.598358
$120$	33109.8	0.209896
$121$	14641.0	0.0909091
$122$	157430.	0.957606
$123$	−88440.0	−0.527092
$124$	−29192.4	−0.170496
$125$	−15625.0	−0.0894427
$126$	−114881.	−0.644649
$127$	−82327.7	−0.452936	−0.226468	−	0.974019i	$-0.572718\pi$
$127$	−82327.7	−0.452936	−0.226468	+	0.974019i	$0.572718\pi$
$128$	110640.	0.596882
$129$	−79948.3	−0.422995
$130$	−48062.5	−0.249430
$131$	162054.	0.825054	0.412527	−	0.910945i	$-0.364646\pi$
$131$	162054.	0.825054	0.412527	+	0.910945i	$0.364646\pi$
$132$	−17208.6	−0.0859630
$133$	61826.6	0.303072
$134$	160504.	0.772190
$135$	−78800.8	−0.372131
$136$	−98194.2	−0.455238
$137$	−47031.1	−0.214084	−0.107042	−	0.994255i	$-0.534138\pi$
$137$	−47031.1	−0.214084	−0.107042	+	0.994255i	$0.534138\pi$
$138$	−29415.7	−0.131487
$139$	380873.	1.67202	0.836012	−	0.548711i	$-0.184881\pi$
$139$	380873.	1.67202	0.836012	+	0.548711i	$0.184881\pi$
$140$	−83652.4	−0.360710
$141$	−99888.9	−0.423126
$142$	−57835.1	−0.240697
$143$	65894.6	0.269469
$144$	3246.03	0.0130451
$145$	157267.	0.621179
$146$	−142633.	−0.553780
$147$	−91171.2	−0.347988
$148$	121557.	0.456168
$149$	−143872.	−0.530898	−0.265449	−	0.964125i	$-0.585520\pi$
$149$	−143872.	−0.530898	−0.265449	+	0.964125i	$0.585520\pi$
$150$	16061.0	0.0582834
$151$	35612.2	0.127103	0.0635515	−	0.997979i	$-0.479757\pi$
$151$	35612.2	0.127103	0.0635515	+	0.997979i	$0.479757\pi$
$152$	−65679.9	−0.230581
$153$	102551.	0.354170
$154$	−73157.0	−0.248573
$155$	−37354.2	−0.124885
$156$	−77450.7	−0.254808
$157$	59316.4	0.192055	0.0960275	−	0.995379i	$-0.469386\pi$
$157$	59316.4	0.192055	0.0960275	+	0.995379i	$0.469386\pi$
$158$	−265619.	−0.846480
$159$	−32112.0	−0.100734
$160$	144043.	0.444829
$161$	196044.	0.596060
$162$	−82000.3	−0.245487
$163$	−272417.	−0.803092	−0.401546	−	0.915839i	$-0.631527\pi$
$163$	−272417.	−0.803092	−0.401546	+	0.915839i	$0.631527\pi$
$164$	−237371.	−0.689156
$165$	−22020.0	−0.0629661
$166$	−212414.	−0.598290
$167$	552431.	1.53281	0.766403	−	0.642361i	$-0.222045\pi$
$167$	552431.	1.53281	0.766403	+	0.642361i	$0.222045\pi$
$168$	226822.	0.620029
$169$	−74722.1	−0.201248
$170$	−47632.4	−0.126410
$171$	68594.1	0.179389
$172$	−214579.	−0.553053
$173$	538401.	1.36770	0.683850	−	0.729623i	$-0.260304\pi$
$173$	538401.	1.36770	0.683850	+	0.729623i	$0.260304\pi$
$174$	−161655.	−0.404778
$175$	−107041.	−0.264212
$176$	2067.08	0.00503010
$177$	−72605.7	−0.174196
$178$	89131.7	0.210854
$179$	−235234.	−0.548740	−0.274370	−	0.961624i	$-0.588469\pi$
$179$	−235234.	−0.548740	−0.274370	+	0.961624i	$0.588469\pi$
$180$	−92808.9	−0.213505
$181$	−88034.5	−0.199736	−0.0998680	−	0.995001i	$-0.531842\pi$
$181$	−88034.5	−0.199736	−0.0998680	+	0.995001i	$0.531842\pi$
$182$	−329257.	−0.736811
$183$	324620.	0.716552
$184$	−208263.	−0.453489
$185$	155542.	0.334133
$186$	38396.6	0.0813786
$187$	65304.9	0.136566
$188$	−268099.	−0.553224
$189$	−539832.	−1.09927
$190$	−31860.2	−0.0640273
$191$	729196.	1.44631	0.723154	−	0.690686i	$-0.242692\pi$
$191$	729196.	1.44631	0.723154	+	0.690686i	$0.242692\pi$
$192$	−152042.	−0.297654
$193$	−98341.9	−0.190040	−0.0950200	−	0.995475i	$-0.530292\pi$
$193$	−98341.9	−0.190040	−0.0950200	+	0.995475i	$0.530292\pi$
$194$	−614033.	−1.17135
$195$	−99105.0	−0.186642
$196$	−244701.	−0.454984
$197$	−231956.	−0.425833	−0.212917	−	0.977070i	$-0.568296\pi$
$197$	−231956.	−0.425833	−0.212917	+	0.977070i	$0.568296\pi$
$198$	−81164.7	−0.147131
$199$	−282333.	−0.505393	−0.252696	−	0.967546i	$-0.581317\pi$
$199$	−282333.	−0.505393	−0.252696	+	0.967546i	$0.581317\pi$
$200$	113712.	0.201016
$201$	330960.	0.577810
$202$	−200000.	−0.344867
$203$	1.07737e6	1.83495
$204$	−76757.6	−0.129136
$205$	−303737.	−0.504793
$206$	−247319.	−0.406060
$207$	217503.	0.352809
$208$	9303.30	0.0149100
$209$	43681.0	0.0691714
$210$	110028.	0.172168
$211$	−604043.	−0.934032	−0.467016	−	0.884249i	$-0.654671\pi$
$211$	−604043.	−0.934032	−0.467016	+	0.884249i	$0.654671\pi$
$212$	−86187.9	−0.131706
$213$	−119256.	−0.180108
$214$	285164.	0.425658
$215$	−274573.	−0.405100
$216$	573477.	0.836338
$217$	−255899.	−0.368908
$218$	308293.	0.439362
$219$	−294109.	−0.414379
$220$	−59101.1	−0.0823263
$221$	293917.	0.404803
$222$	−159883.	−0.217731
$223$	−6340.45	−0.00853804	−0.00426902	−	0.999991i	$-0.501359\pi$
$223$	−6340.45	−0.00853804	−0.00426902	+	0.999991i	$0.501359\pi$
$224$	986783.	1.31402
$225$	−118757.	−0.156388
$226$	552406.	0.719428
$227$	−650604.	−0.838015	−0.419008	−	0.907983i	$-0.637622\pi$
$227$	−650604.	−0.838015	−0.419008	+	0.907983i	$0.637622\pi$
$228$	−51341.5	−0.0654080
$229$	−1.09283e6	−1.37709	−0.688545	−	0.725193i	$-0.741750\pi$
$229$	−1.09283e6	−1.37709	−0.688545	+	0.725193i	$0.741750\pi$
$230$	−101025.	−0.125924
$231$	−150850.	−0.186001
$232$	−1.14452e6	−1.39605
$233$	521341.	0.629118	0.314559	−	0.949238i	$-0.398143\pi$
$233$	521341.	0.629118	0.314559	+	0.949238i	$0.398143\pi$
$234$	−365297.	−0.436120
$235$	−343057.	−0.405225
$236$	−194872.	−0.227756
$237$	−547707.	−0.633399
$238$	−326310.	−0.373412
$239$	196299.	0.222292	0.111146	−	0.993804i	$-0.464548\pi$
$239$	196299.	0.222292	0.111146	+	0.993804i	$0.464548\pi$
$240$	−3108.88	−0.00348398
$241$	19716.4	0.0218668	0.0109334	−	0.999940i	$-0.496520\pi$
$241$	19716.4	0.0218668	0.0109334	+	0.999940i	$0.496520\pi$
$242$	−51686.0	−0.0567328
$243$	−935029.	−1.01580
$244$	871273.	0.936871
$245$	−313117.	−0.333266
$246$	312213.	0.328937
$247$	196595.	0.205036
$248$	271847.	0.280670
$249$	−437997.	−0.447686
$250$	55159.7	0.0558177
$251$	643511.	0.644721	0.322361	−	0.946617i	$-0.395524\pi$
$251$	643511.	0.644721	0.322361	+	0.946617i	$0.395524\pi$
$252$	−635796.	−0.630691
$253$	138507.	0.136041
$254$	290635.	0.282659
$255$	−98218.1	−0.0945891
$256$	−1.05896e6	−1.00991
$257$	−119750.	−0.113095	−0.0565475	−	0.998400i	$-0.518009\pi$
$257$	−119750.	−0.113095	−0.0565475	+	0.998400i	$0.518009\pi$
$258$	282235.	0.263975
$259$	1.06556e6	0.987025
$260$	−265995.	−0.244029
$261$	1.19530e6	1.08611
$262$	−572088.	−0.514884
$263$	−356699.	−0.317990	−0.158995	−	0.987279i	$-0.550825\pi$
$263$	−356699.	−0.317990	−0.158995	+	0.987279i	$0.550825\pi$
$264$	160252.	0.141512
$265$	−110285.	−0.0964721
$266$	−218262.	−0.189136
$267$	183790.	0.157777
$268$	888288.	0.755469
$269$	643644.	0.542332	0.271166	−	0.962533i	$-0.412591\pi$
$269$	643644.	0.542332	0.271166	+	0.962533i	$0.412591\pi$
$270$	278184.	0.232233
$271$	430149.	0.355792	0.177896	−	0.984049i	$-0.443071\pi$
$271$	430149.	0.355792	0.177896	+	0.984049i	$0.443071\pi$
$272$	9220.05	0.00755633
$273$	−678928.	−0.551337
$274$	166030.	0.133601
$275$	−75625.0	−0.0603023
$276$	−162797.	−0.128639
$277$	−1.74029e6	−1.36277	−0.681384	−	0.731926i	$-0.738622\pi$
$277$	−1.74029e6	−1.36277	−0.681384	+	0.731926i	$0.738622\pi$
$278$	−1.34456e6	−1.04345
$279$	−283909.	−0.218358
$280$	778994.	0.593798
$281$	−147401.	−0.111361	−0.0556806	−	0.998449i	$-0.517733\pi$
$281$	−147401.	−0.111361	−0.0556806	+	0.998449i	$0.517733\pi$
$282$	352630.	0.264056
$283$	−1.48493e6	−1.10215	−0.551074	−	0.834456i	$-0.685782\pi$
$283$	−1.48493e6	−1.10215	−0.551074	+	0.834456i	$0.685782\pi$
$284$	−320081.	−0.235485
$285$	−65695.9	−0.0479100
$286$	−232622.	−0.168165
$287$	−2.08078e6	−1.49115
$288$	1.09480e6	0.777771
$289$	−1.12857e6	−0.794848
$290$	−555186.	−0.387653
$291$	−1.26614e6	−0.876494
$292$	−789382.	−0.541789
$293$	908102.	0.617967	0.308984	−	0.951067i	$-0.400011\pi$
$293$	908102.	0.617967	0.308984	+	0.951067i	$0.400011\pi$
$294$	321855.	0.217166
$295$	−249356.	−0.166826
$296$	−1.13197e6	−0.750940
$297$	−381396.	−0.250891
$298$	507900.	0.331312
$299$	623376.	0.403248
$300$	88887.6	0.0570214
$301$	−1.88099e6	−1.19666
$302$	−125719.	−0.0793200
$303$	−412401.	−0.258055
$304$	6167.09	0.00382733
$305$	1.11487e6	0.686238
$306$	−362028.	−0.221023
$307$	−1.96255e6	−1.18843	−0.594216	−	0.804305i	$-0.702538\pi$
$307$	−1.96255e6	−1.18843	−0.594216	+	0.804305i	$0.702538\pi$
$308$	−404878.	−0.243191
$309$	−509973.	−0.303844
$310$	131869.	0.0779358
$311$	1.77468e6	1.04045	0.520224	−	0.854030i	$-0.325849\pi$
$311$	1.77468e6	1.04045	0.520224	+	0.854030i	$0.325849\pi$
$312$	721242.	0.419464
$313$	175879.	0.101474	0.0507369	−	0.998712i	$-0.483843\pi$
$313$	175879.	0.101474	0.0507369	+	0.998712i	$0.483843\pi$
$314$	−209400.	−0.119854
$315$	−813557.	−0.461968
$316$	−1.47003e6	−0.828151
$317$	2.31567e6	1.29428	0.647140	−	0.762371i	$-0.275965\pi$
$317$	2.31567e6	1.29428	0.647140	+	0.762371i	$0.275965\pi$
$318$	113363.	0.0628640
$319$	761170.	0.418799
$320$	−522172.	−0.285061
$321$	588010.	0.318509
$322$	−692080.	−0.371977
$323$	194835.	0.103911
$324$	−453820.	−0.240171
$325$	−340365.	−0.178746
$326$	961692.	0.501178
$327$	635702.	0.328764
$328$	2.21046e6	1.13448
$329$	−2.35014e6	−1.19703
$330$	77735.3	0.0392947
$331$	−2.29703e6	−1.15238	−0.576191	−	0.817315i	$-0.695462\pi$
$331$	−2.29703e6	−1.15238	−0.576191	+	0.817315i	$0.695462\pi$
$332$	−1.17557e6	−0.585336
$333$	1.18219e6	0.584222
$334$	−1.95020e6	−0.956564
$335$	1.13664e6	0.553365
$336$	−21297.7	−0.0102916
$337$	936024.	0.448965	0.224482	−	0.974478i	$-0.427931\pi$
$337$	936024.	0.448965	0.224482	+	0.974478i	$0.427931\pi$
$338$	263785.	0.125591
$339$	1.13906e6	0.538330
$340$	−263615.	−0.123672
$341$	−180794.	−0.0841974
$342$	−242152.	−0.111950
$343$	733412.	0.336599
$344$	1.99822e6	0.910432
$345$	−208313.	−0.0942257
$346$	−1.90067e6	−0.853528
$347$	−1.50437e6	−0.670702	−0.335351	−	0.942093i	$-0.608855\pi$
$347$	−1.50437e6	−0.670702	−0.335351	+	0.942093i	$0.608855\pi$
$348$	−894659.	−0.396013
$349$	−3.65873e6	−1.60793	−0.803964	−	0.594679i	$-0.797279\pi$
$349$	−3.65873e6	−1.60793	−0.803964	+	0.594679i	$0.797279\pi$
$350$	377877.	0.164885
$351$	−1.71654e6	−0.743682
$352$	697170.	0.299904
$353$	1.05443e6	0.450380	0.225190	−	0.974315i	$-0.427700\pi$
$353$	1.05443e6	0.450380	0.225190	+	0.974315i	$0.427700\pi$
$354$	256314.	0.108709
$355$	−409572.	−0.172488
$356$	493287.	0.206289
$357$	−672853.	−0.279415
$358$	830426.	0.342447
$359$	−875247.	−0.358422	−0.179211	−	0.983811i	$-0.557354\pi$
$359$	−875247.	−0.358422	−0.179211	+	0.983811i	$0.557354\pi$
$360$	864262.	0.351471
$361$	130321.	0.0526316
$362$	310781.	0.124647
$363$	−106577.	−0.0424517
$364$	−1.82223e6	−0.720857
$365$	−1.01008e6	−0.396849
$366$	−1.14598e6	−0.447172
$367$	−910146.	−0.352733	−0.176366	−	0.984325i	$-0.556434\pi$
$367$	−910146.	−0.352733	−0.176366	+	0.984325i	$0.556434\pi$
$368$	19555.0	0.00752730
$369$	−2.30854e6	−0.882615
$370$	−549099.	−0.208519
$371$	−755518.	−0.284977
$372$	212501.	0.0796165
$373$	726674.	0.270438	0.135219	−	0.990816i	$-0.456826\pi$
$373$	726674.	0.270438	0.135219	+	0.990816i	$0.456826\pi$
$374$	−230541.	−0.0852253
$375$	113739.	0.0417670
$376$	2.49661e6	0.910714
$377$	3.42579e6	1.24139
$378$	1.90573e6	0.686012
$379$	−1.93968e6	−0.693638	−0.346819	−	0.937932i	$-0.612738\pi$
$379$	−1.93968e6	−0.693638	−0.346819	+	0.937932i	$0.612738\pi$
$380$	−176326.	−0.0626409
$381$	599290.	0.211507
$382$	−2.57422e6	−0.902585
$383$	2.87116e6	1.00014	0.500070	−	0.865985i	$-0.333308\pi$
$383$	2.87116e6	1.00014	0.500070	+	0.865985i	$0.333308\pi$
$384$	−805387.	−0.278725
$385$	−518076.	−0.178132
$386$	347169.	0.118597
$387$	−2.08688e6	−0.708305
$388$	−3.39829e6	−1.14599
$389$	−4.27230e6	−1.43149	−0.715744	−	0.698363i	$-0.753912\pi$
$389$	−4.27230e6	−1.43149	−0.715744	+	0.698363i	$0.753912\pi$
$390$	349863.	0.116476
$391$	617798.	0.204364
$392$	2.27873e6	0.748991
$393$	−1.17965e6	−0.385275
$394$	818855.	0.265746
$395$	−1.88104e6	−0.606603
$396$	−449195.	−0.143945
$397$	−211399.	−0.0673172	−0.0336586	−	0.999433i	$-0.510716\pi$
$397$	−211399.	−0.0673172	−0.0336586	+	0.999433i	$0.510716\pi$
$398$	996698.	0.315396
$399$	−450056.	−0.141525
$400$	−10677.1	−0.00333659
$401$	−605610.	−0.188075	−0.0940377	−	0.995569i	$-0.529977\pi$
$401$	−605610.	−0.188075	−0.0940377	+	0.995569i	$0.529977\pi$
$402$	−1.16836e6	−0.360589
$403$	−813699.	−0.249575
$404$	−1.10687e6	−0.337400
$405$	−580702.	−0.175920
$406$	−3.80335e6	−1.14512
$407$	752826.	0.225273
$408$	714788.	0.212582
$409$	2.52166e6	0.745382	0.372691	−	0.927955i	$-0.378435\pi$
$409$	2.52166e6	0.745382	0.372691	+	0.927955i	$0.378435\pi$
$410$	1.07226e6	0.315021
$411$	342355.	0.0999705
$412$	−1.36876e6	−0.397267
$413$	−1.70823e6	−0.492802
$414$	−767834.	−0.220174
$415$	−1.50425e6	−0.428746
$416$	3.13775e6	0.888964
$417$	−2.77250e6	−0.780784
$418$	−154204.	−0.0431672
$419$	−4.00226e6	−1.11371	−0.556853	−	0.830611i	$-0.687991\pi$
$419$	−4.00226e6	−1.11371	−0.556853	+	0.830611i	$0.687991\pi$
$420$	608933.	0.168440
$421$	1.03324e6	0.284117	0.142058	−	0.989858i	$-0.454628\pi$
$421$	1.03324e6	0.284117	0.142058	+	0.989858i	$0.454628\pi$
$422$	2.13240e6	0.582893
$423$	−2.60739e6	−0.708524
$424$	802605.	0.216814
$425$	−337319.	−0.0905875
$426$	421001.	0.112398
$427$	7.63753e6	2.02714
$428$	1.57820e6	0.416441
$429$	−479668.	−0.125834
$430$	969304.	0.252807
$431$	−3.33069e6	−0.863656	−0.431828	−	0.901956i	$-0.642131\pi$
$431$	−3.33069e6	−0.863656	−0.431828	+	0.901956i	$0.642131\pi$
$432$	−53847.2	−0.0138821
$433$	1.10574e6	0.283422	0.141711	−	0.989908i	$-0.454740\pi$
$433$	1.10574e6	0.283422	0.141711	+	0.989908i	$0.454740\pi$
$434$	903379.	0.230221
$435$	−1.14480e6	−0.290071
$436$	1.70621e6	0.429849
$437$	413231.	0.103512
$438$	1.03827e6	0.258598
$439$	6.42259e6	1.59056	0.795278	−	0.606245i	$-0.207325\pi$
$439$	6.42259e6	1.59056	0.795278	+	0.606245i	$0.207325\pi$
$440$	550365.	0.135525
$441$	−2.37983e6	−0.582706
$442$	−1.03759e6	−0.252622
$443$	−6.69493e6	−1.62083	−0.810414	−	0.585858i	$-0.800758\pi$
$443$	−6.69493e6	−1.62083	−0.810414	+	0.585858i	$0.800758\pi$
$444$	−884851.	−0.213016
$445$	631205.	0.151102
$446$	22383.2	0.00532825
$447$	1.04729e6	0.247913
$448$	−3.57719e6	−0.842067
$449$	1.94219e6	0.454648	0.227324	−	0.973819i	$-0.427002\pi$
$449$	1.94219e6	0.454648	0.227324	+	0.973819i	$0.427002\pi$
$450$	419239.	0.0975956
$451$	−1.47009e6	−0.340331
$452$	3.05722e6	0.703850
$453$	−259233.	−0.0593532
$454$	2.29677e6	0.522972
$455$	−2.33170e6	−0.528013
$456$	478106.	0.107674
$457$	−3.13746e6	−0.702728	−0.351364	−	0.936239i	$-0.614282\pi$
$457$	−3.13746e6	−0.702728	−0.351364	+	0.936239i	$0.614282\pi$
$458$	3.85792e6	0.859389
$459$	−1.70118e6	−0.376894
$460$	−559108.	−0.123197
$461$	−4.34869e6	−0.953030	−0.476515	−	0.879166i	$-0.658100\pi$
$461$	−4.34869e6	−0.953030	−0.476515	+	0.879166i	$0.658100\pi$
$462$	532534.	0.116076
$463$	6.38906e6	1.38511	0.692555	−	0.721365i	$-0.256485\pi$
$463$	6.38906e6	1.38511	0.692555	+	0.721365i	$0.256485\pi$
$464$	107466.	0.0231726
$465$	271913.	0.0583174
$466$	−1.84045e6	−0.392608
$467$	1.31162e6	0.278303	0.139151	−	0.990271i	$-0.455563\pi$
$467$	1.31162e6	0.278303	0.139151	+	0.990271i	$0.455563\pi$
$468$	−2.02169e6	−0.426677
$469$	7.78668e6	1.63463
$470$	1.21107e6	0.252885
$471$	−431784.	−0.0896838
$472$	1.81470e6	0.374930
$473$	−1.32893e6	−0.273118
$474$	1.93353e6	0.395280
$475$	−225625.	−0.0458831
$476$	−1.80592e6	−0.365327
$477$	−838216.	−0.168679
$478$	−692980.	−0.138724
$479$	−6.24610e6	−1.24386	−0.621928	−	0.783074i	$-0.713650\pi$
$479$	−6.24610e6	−1.24386	−0.621928	+	0.783074i	$0.713650\pi$
$480$	−1.04854e6	−0.207722
$481$	3.38823e6	0.667745
$482$	−69603.2	−0.0136462
$483$	−1.42707e6	−0.278341
$484$	−286049.	−0.0555044
$485$	−4.34841e6	−0.839413
$486$	3.30086e6	0.633922
$487$	8.70883e6	1.66394	0.831970	−	0.554821i	$-0.187213\pi$
$487$	8.70883e6	1.66394	0.831970	+	0.554821i	$0.187213\pi$
$488$	−8.11353e6	−1.54227
$489$	1.98301e6	0.375019
$490$	1.10537e6	0.207978
$491$	−3.78860e6	−0.709209	−0.354605	−	0.935016i	$-0.615385\pi$
$491$	−3.78860e6	−0.709209	−0.354605	+	0.935016i	$0.615385\pi$
$492$	1.72790e6	0.321815
$493$	3.39513e6	0.629129
$494$	−694022.	−0.127955
$495$	−574784.	−0.105437
$496$	−25525.4	−0.00465873
$497$	−2.80581e6	−0.509527
$498$	1.54623e6	0.279383
$499$	−7.82596e6	−1.40697	−0.703487	−	0.710708i	$-0.748375\pi$
$499$	−7.82596e6	−1.40697	−0.703487	+	0.710708i	$0.748375\pi$
$500$	305274.	0.0546091
$501$	−4.02133e6	−0.715773
$502$	−2.27174e6	−0.402345
$503$	1.08914e7	1.91938	0.959692	−	0.281053i	$-0.0906838\pi$
$503$	1.08914e7	1.91938	0.959692	+	0.281053i	$0.0906838\pi$
$504$	5.92071e6	1.03824
$505$	−1.41634e6	−0.247138
$506$	−488960.	−0.0848979
$507$	543926.	0.0939767
$508$	1.60848e6	0.276539
$509$	6.34375e6	1.08531	0.542653	−	0.839957i	$-0.317420\pi$
$509$	6.34375e6	1.08531	0.542653	+	0.839957i	$0.317420\pi$
$510$	346732.	0.0590294
$511$	−6.91967e6	−1.17229
$512$	197890.	0.0333617
$513$	−1.13788e6	−0.190899
$514$	422745.	0.0705782
$515$	−1.75144e6	−0.290990
$516$	1.56199e6	0.258259
$517$	−1.66039e6	−0.273203
$518$	−3.76166e6	−0.615963
$519$	−3.91920e6	−0.638673
$520$	2.47702e6	0.401718
$521$	−3.77648e6	−0.609526	−0.304763	−	0.952428i	$-0.598577\pi$
$521$	−3.77648e6	−0.609526	−0.304763	+	0.952428i	$0.598577\pi$
$522$	−4.21967e6	−0.677800
$523$	−4.73171e6	−0.756421	−0.378210	−	0.925720i	$-0.623460\pi$
$523$	−4.73171e6	−0.756421	−0.378210	+	0.925720i	$0.623460\pi$
$524$	−3.16614e6	−0.503735
$525$	779183.	0.123379
$526$	1.25923e6	0.198445
$527$	−806417.	−0.126483
$528$	−15047.0	−0.00234890
$529$	−5.12604e6	−0.796421
$530$	389330.	0.0602044
$531$	−1.89522e6	−0.291691
$532$	−1.20794e6	−0.185040
$533$	−6.61640e6	−1.00880
$534$	−648819.	−0.0984624
$535$	2.01945e6	0.305035
$536$	−8.27198e6	−1.24365
$537$	1.71234e6	0.256245
$538$	−2.27221e6	−0.338448
$539$	−1.51549e6	−0.224688
$540$	1.53957e6	0.227204
$541$	−9.01458e6	−1.32420	−0.662098	−	0.749417i	$-0.730334\pi$
$541$	−9.01458e6	−1.32420	−0.662098	+	0.749417i	$0.730334\pi$
$542$	−1.51852e6	−0.222036
$543$	640832.	0.0932705
$544$	3.10967e6	0.450523
$545$	2.18324e6	0.314855
$546$	2.39677e6	0.344068
$547$	−2.70367e6	−0.386354	−0.193177	−	0.981164i	$-0.561879\pi$
$547$	−2.70367e6	−0.386354	−0.193177	+	0.981164i	$0.561879\pi$
$548$	918872.	0.130708
$549$	8.47352e6	1.19987
$550$	266973.	0.0376323
$551$	2.27093e6	0.318658
$552$	1.51601e6	0.211765
$553$	−1.28862e7	−1.79190
$554$	6.14361e6	0.850451
$555$	−1.13224e6	−0.156030
$556$	−7.44131e6	−1.02085
$557$	6.35699e6	0.868187	0.434094	−	0.900868i	$-0.357069\pi$
$557$	6.35699e6	0.868187	0.434094	+	0.900868i	$0.357069\pi$
$558$	1.00226e6	0.136269
$559$	−5.98112e6	−0.809567
$560$	−73144.4	−0.00985624
$561$	−475376.	−0.0637720
$562$	520357.	0.0694961
$563$	9.06343e6	1.20510	0.602548	−	0.798083i	$-0.294152\pi$
$563$	9.06343e6	1.20510	0.602548	+	0.798083i	$0.294152\pi$
$564$	1.95158e6	0.258339
$565$	3.91198e6	0.515555
$566$	5.24214e6	0.687808
$567$	−3.97816e6	−0.519666
$568$	2.98068e6	0.387654
$569$	7.54997e6	0.977608	0.488804	−	0.872394i	$-0.337433\pi$
$569$	7.54997e6	0.977608	0.488804	+	0.872394i	$0.337433\pi$
$570$	231921.	0.0298988
$571$	725296.	0.0930947	0.0465473	−	0.998916i	$-0.485178\pi$
$571$	725296.	0.0930947	0.0465473	+	0.998916i	$0.485178\pi$
$572$	−1.28742e6	−0.164524
$573$	−5.30806e6	−0.675381
$574$	7.34561e6	0.930568
$575$	−715428.	−0.0902394
$576$	−3.96874e6	−0.498422
$577$	4.17715e6	0.522324	0.261162	−	0.965295i	$-0.415894\pi$
$577$	4.17715e6	0.522324	0.261162	+	0.965295i	$0.415894\pi$
$578$	3.98410e6	0.496033
$579$	715863.	0.0887428
$580$	−3.07260e6	−0.379259
$581$	−1.03050e7	−1.26651
$582$	4.46975e6	0.546986
$583$	−533779.	−0.0650415
$584$	7.35094e6	0.891889
$585$	−2.58693e6	−0.312532
$586$	−3.20580e6	−0.385649
$587$	−4.01299e6	−0.480698	−0.240349	−	0.970687i	$-0.577262\pi$
$587$	−4.01299e6	−0.480698	−0.240349	+	0.970687i	$0.577262\pi$
$588$	1.78126e6	0.212463
$589$	−539395.	−0.0640646
$590$	880281.	0.104110
$591$	1.68848e6	0.198851
$592$	106287.	0.0124646
$593$	−1.24992e6	−0.145964	−0.0729822	−	0.997333i	$-0.523252\pi$
$593$	−1.24992e6	−0.145964	−0.0729822	+	0.997333i	$0.523252\pi$
$594$	1.34641e6	0.156571
$595$	−2.31083e6	−0.267594
$596$	2.81091e6	0.324139
$597$	2.05520e6	0.236003
$598$	−2.20066e6	−0.251651
$599$	7.03447e6	0.801059	0.400530	−	0.916284i	$-0.368826\pi$
$599$	7.03447e6	0.801059	0.400530	+	0.916284i	$0.368826\pi$
$600$	−827746.	−0.0938683
$601$	1.02684e7	1.15963	0.579813	−	0.814749i	$-0.303125\pi$
$601$	1.02684e7	1.15963	0.579813	+	0.814749i	$0.303125\pi$
$602$	6.64031e6	0.746788
$603$	8.63900e6	0.967543
$604$	−695774.	−0.0776025
$605$	−366025.	−0.0406558
$606$	1.45587e6	0.161042
$607$	5.27248e6	0.580823	0.290411	−	0.956902i	$-0.406208\pi$
$607$	5.27248e6	0.580823	0.290411	+	0.956902i	$0.406208\pi$
$608$	2.07999e6	0.228193
$609$	−7.84253e6	−0.856866
$610$	−3.93574e6	−0.428254
$611$	−7.47292e6	−0.809817
$612$	−2.00359e6	−0.216238
$613$	9.48094e6	1.01906	0.509531	−	0.860453i	$-0.329819\pi$
$613$	9.48094e6	1.01906	0.509531	+	0.860453i	$0.329819\pi$
$614$	6.92823e6	0.741654
$615$	2.21100e6	0.235723
$616$	3.77033e6	0.400339
$617$	4.81602e6	0.509302	0.254651	−	0.967033i	$-0.418039\pi$
$617$	4.81602e6	0.509302	0.254651	+	0.967033i	$0.418039\pi$
$618$	1.80032e6	0.189617
$619$	1.69971e7	1.78299	0.891496	−	0.453028i	$-0.149656\pi$
$619$	1.69971e7	1.78299	0.891496	+	0.453028i	$0.149656\pi$
$620$	729809.	0.0762483
$621$	−3.60808e6	−0.375446
$622$	−6.26503e6	−0.649303
$623$	4.32413e6	0.446353
$624$	−67721.8	−0.00696253
$625$	390625.	0.0400000
$626$	−620892.	−0.0633258
$627$	−317968.	−0.0323009
$628$	−1.15890e6	−0.117259
$629$	3.35791e6	0.338410
$630$	2.87204e6	0.288296
$631$	7.54063e6	0.753935	0.376968	−	0.926226i	$-0.376967\pi$
$631$	7.54063e6	0.753935	0.376968	+	0.926226i	$0.376967\pi$
$632$	1.36894e7	1.36330
$633$	4.39703e6	0.436164
$634$	−8.17483e6	−0.807710
$635$	2.05819e6	0.202559
$636$	627390.	0.0615028
$637$	−6.82073e6	−0.666012
$638$	−2.68710e6	−0.261356
$639$	−3.11293e6	−0.301590
$640$	−2.76601e6	−0.266934
$641$	−9.66535e6	−0.929122	−0.464561	−	0.885541i	$-0.653788\pi$
$641$	−9.66535e6	−0.929122	−0.464561	+	0.885541i	$0.653788\pi$
$642$	−2.07581e6	−0.198769
$643$	−2.20861e6	−0.210664	−0.105332	−	0.994437i	$-0.533591\pi$
$643$	−2.20861e6	−0.210664	−0.105332	+	0.994437i	$0.533591\pi$
$644$	−3.83022e6	−0.363923
$645$	1.99871e6	0.189169
$646$	−687812.	−0.0648467
$647$	3.08586e6	0.289812	0.144906	−	0.989445i	$-0.453712\pi$
$647$	3.08586e6	0.289812	0.144906	+	0.989445i	$0.453712\pi$
$648$	4.22609e6	0.395368
$649$	−1.20688e6	−0.112474
$650$	1.20156e6	0.111548
$651$	1.86277e6	0.172269
$652$	5.32236e6	0.490326
$653$	−1.20880e6	−0.110936	−0.0554679	−	0.998460i	$-0.517665\pi$
$653$	−1.20880e6	−0.110936	−0.0554679	+	0.998460i	$0.517665\pi$
$654$	−2.24417e6	−0.205169
$655$	−4.05136e6	−0.368976
$656$	−207554.	−0.0188309
$657$	−7.67709e6	−0.693878
$658$	8.29652e6	0.747019
$659$	3.16858e6	0.284217	0.142109	−	0.989851i	$-0.454612\pi$
$659$	3.16858e6	0.284217	0.142109	+	0.989851i	$0.454612\pi$
$660$	430216.	0.0384438
$661$	1.73420e7	1.54382	0.771909	−	0.635734i	$-0.219302\pi$
$661$	1.73420e7	1.54382	0.771909	+	0.635734i	$0.219302\pi$
$662$	8.10902e6	0.719157
$663$	−2.13952e6	−0.189031
$664$	1.09473e7	0.963576
$665$	−1.54567e6	−0.135538
$666$	−4.17341e6	−0.364590
$667$	7.20083e6	0.626712
$668$	−1.07931e7	−0.935851
$669$	46154.2	0.00398700
$670$	−4.01260e6	−0.345334
$671$	5.39597e6	0.462662
$672$	−7.18312e6	−0.613606
$673$	−1.19365e7	−1.01587	−0.507936	−	0.861395i	$-0.669591\pi$
$673$	−1.19365e7	−1.01587	−0.507936	+	0.861395i	$0.669591\pi$
$674$	−3.30437e6	−0.280181
$675$	1.97002e6	0.166422
$676$	1.45989e6	0.122872
$677$	1.46589e7	1.22922	0.614611	−	0.788831i	$-0.289313\pi$
$677$	1.46589e7	1.22922	0.614611	+	0.788831i	$0.289313\pi$
$678$	−4.02114e6	−0.335950
$679$	−2.97892e7	−2.47961
$680$	2.45486e6	0.203589
$681$	4.73596e6	0.391327
$682$	638244.	0.0525443
$683$	8.35322e6	0.685176	0.342588	−	0.939486i	$-0.388696\pi$
$683$	8.35322e6	0.685176	0.342588	+	0.939486i	$0.388696\pi$
$684$	−1.34016e6	−0.109526
$685$	1.17578e6	0.0957412
$686$	−2.58911e6	−0.210058
$687$	7.95504e6	0.643059
$688$	−187625.	−0.0151119
$689$	−2.40237e6	−0.192794
$690$	735392.	0.0588026
$691$	8.42488e6	0.671226	0.335613	−	0.942000i	$-0.391057\pi$
$691$	8.42488e6	0.671226	0.335613	+	0.942000i	$0.391057\pi$
$692$	−1.05190e7	−0.835046
$693$	−3.93762e6	−0.311459
$694$	5.31074e6	0.418559
$695$	−9.52181e6	−0.747752
$696$	8.33131e6	0.651914
$697$	−6.55719e6	−0.511253
$698$	1.29161e7	1.00344
$699$	−3.79501e6	−0.293779
$700$	2.09131e6	0.161314
$701$	3.60707e6	0.277242	0.138621	−	0.990345i	$-0.455733\pi$
$701$	3.60707e6	0.277242	0.138621	+	0.990345i	$0.455733\pi$
$702$	6.05978e6	0.464103
$703$	2.24603e6	0.171407
$704$	−2.52731e6	−0.192188
$705$	2.49722e6	0.189228
$706$	−3.72235e6	−0.281064
$707$	−9.70279e6	−0.730043
$708$	1.41854e6	0.106355
$709$	4.60024e6	0.343689	0.171844	−	0.985124i	$-0.445027\pi$
$709$	4.60024e6	0.343689	0.171844	+	0.985124i	$0.445027\pi$
$710$	1.44588e6	0.107643
$711$	−1.42967e7	−1.06063
$712$	−4.59363e6	−0.339591
$713$	−1.71035e6	−0.125997
$714$	2.37532e6	0.174372
$715$	−1.64736e6	−0.120510
$716$	4.59588e6	0.335032
$717$	−1.42893e6	−0.103803
$718$	3.08982e6	0.223677
$719$	2.39501e7	1.72777	0.863885	−	0.503690i	$-0.168025\pi$
$719$	2.39501e7	1.72777	0.863885	+	0.503690i	$0.168025\pi$
$720$	−81150.7	−0.00583393
$721$	−1.19984e7	−0.859580
$722$	−460062.	−0.0328453
$723$	−143522.	−0.0102111
$724$	1.71998e6	0.121948
$725$	−3.93167e6	−0.277800
$726$	376239.	0.0264925
$727$	−170934.	−0.0119948	−0.00599739	−	0.999982i	$-0.501909\pi$
$727$	−170934.	−0.0119948	−0.00599739	+	0.999982i	$0.501909\pi$
$728$	1.69691e7	1.18667
$729$	1.16195e6	0.0809784
$730$	3.56582e6	0.247658
$731$	−5.92760e6	−0.410285
$732$	−6.34228e6	−0.437490
$733$	2.26600e7	1.55776	0.778880	−	0.627173i	$-0.215788\pi$
$733$	2.26600e7	1.55776	0.778880	+	0.627173i	$0.215788\pi$
$734$	3.21302e6	0.220127
$735$	2.27928e6	0.155625
$736$	6.59537e6	0.448792
$737$	5.50135e6	0.373079
$738$	8.14965e6	0.550805
$739$	1.59366e7	1.07346	0.536730	−	0.843754i	$-0.319659\pi$
$739$	1.59366e7	1.07346	0.536730	+	0.843754i	$0.319659\pi$
$740$	−3.03892e6	−0.204004
$741$	−1.43108e6	−0.0957452
$742$	2.66715e6	0.177843
$743$	1.56374e7	1.03918	0.519592	−	0.854415i	$-0.326084\pi$
$743$	1.56374e7	1.03918	0.519592	+	0.854415i	$0.326084\pi$
$744$	−1.97887e6	−0.131064
$745$	3.59680e6	0.237425
$746$	−2.56532e6	−0.168770
$747$	−1.14330e7	−0.749650
$748$	−1.27590e6	−0.0833799
$749$	1.38344e7	0.901068
$750$	−401526.	−0.0260651
$751$	−1.14499e7	−0.740799	−0.370399	−	0.928873i	$-0.620779\pi$
$751$	−1.14499e7	−0.740799	−0.370399	+	0.928873i	$0.620779\pi$
$752$	−234422.	−0.0151166
$753$	−4.68433e6	−0.301065
$754$	−1.20938e7	−0.774701
$755$	−890304.	−0.0568422
$756$	1.05470e7	0.671157
$757$	2.42052e7	1.53521	0.767606	−	0.640922i	$-0.221448\pi$
$757$	2.42052e7	1.53521	0.767606	+	0.640922i	$0.221448\pi$
$758$	6.84751e6	0.432872
$759$	−1.00824e6	−0.0635270
$760$	1.64200e6	0.103119
$761$	8.23734e6	0.515615	0.257807	−	0.966196i	$-0.417000\pi$
$761$	8.23734e6	0.515615	0.257807	+	0.966196i	$0.417000\pi$
$762$	−2.11563e6	−0.131993
$763$	1.49565e7	0.930078
$764$	−1.42467e7	−0.883041
$765$	−2.56378e6	−0.158390
$766$	−1.01358e7	−0.624148
$767$	−5.43180e6	−0.333392
$768$	7.70855e6	0.471596
$769$	−4.22850e6	−0.257852	−0.128926	−	0.991654i	$-0.541153\pi$
$769$	−4.22850e6	−0.257852	−0.128926	+	0.991654i	$0.541153\pi$
$770$	1.82892e6	0.111165
$771$	871702.	0.0528119
$772$	1.92136e6	0.116029
$773$	4.81751e6	0.289984	0.144992	−	0.989433i	$-0.453684\pi$
$773$	4.81751e6	0.289984	0.144992	+	0.989433i	$0.453684\pi$
$774$	7.36715e6	0.442026
$775$	933855.	0.0558503
$776$	3.16458e7	1.88652
$777$	−7.75655e6	−0.460910
$778$	1.50822e7	0.893335
$779$	−4.38596e6	−0.258953
$780$	1.93627e6	0.113954
$781$	−1.98233e6	−0.116291
$782$	−2.18096e6	−0.127536
$783$	−1.98284e7	−1.15580
$784$	−213963.	−0.0124322
$785$	−1.48291e6	−0.0858896
$786$	4.16442e6	0.240435
$787$	−6675.36	−0.000384183 0	−0.000192091	−	1.00000i	$-0.500061\pi$
$787$	−6675.36	−0.000384183 0	−0.000192091		1.00000i	$0.500061\pi$
$788$	4.53185e6	0.259992
$789$	2.59653e6	0.148491
$790$	6.64048e6	0.378557
$791$	2.67994e7	1.52294
$792$	4.18303e6	0.236961
$793$	2.42856e7	1.37140
$794$	746284.	0.0420100
$795$	802800.	0.0450495
$796$	5.51609e6	0.308567
$797$	2.24867e7	1.25395	0.626975	−	0.779040i	$-0.284293\pi$
$797$	2.24867e7	1.25395	0.626975	+	0.779040i	$0.284293\pi$
$798$	1.58880e6	0.0883205
$799$	−7.40604e6	−0.410411
$800$	−3.60109e6	−0.198934
$801$	4.79744e6	0.264197
$802$	2.13794e6	0.117370
$803$	−4.88880e6	−0.267555
$804$	−6.46614e6	−0.352781
$805$	−4.90111e6	−0.266566
$806$	2.87254e6	0.155750
$807$	−4.68530e6	−0.253252
$808$	1.03075e7	0.555425
$809$	1.29089e6	0.0693456	0.0346728	−	0.999399i	$-0.488961\pi$
$809$	1.29089e6	0.0693456	0.0346728	+	0.999399i	$0.488961\pi$
$810$	2.05001e6	0.109785
$811$	1.89391e7	1.01113	0.505566	−	0.862788i	$-0.331284\pi$
$811$	1.89391e7	1.01113	0.505566	+	0.862788i	$0.331284\pi$
$812$	−2.10492e7	−1.12033
$813$	−3.13120e6	−0.166144
$814$	−2.65764e6	−0.140584
$815$	6.81042e6	0.359153
$816$	−67115.7	−0.00352857
$817$	−3.96484e6	−0.207812
$818$	−8.90203e6	−0.465164
$819$	−1.77220e7	−0.923214
$820$	5.93427e6	0.308200
$821$	−2.58220e7	−1.33700	−0.668500	−	0.743712i	$-0.733063\pi$
$821$	−2.58220e7	−1.33700	−0.668500	+	0.743712i	$0.733063\pi$
$822$	−1.20859e6	−0.0623877
$823$	1.13362e7	0.583404	0.291702	−	0.956509i	$-0.405778\pi$
$823$	1.13362e7	0.583404	0.291702	+	0.956509i	$0.405778\pi$
$824$	1.27462e7	0.653979
$825$	550499.	0.0281593
$826$	6.03045e6	0.307538
$827$	−1.33802e7	−0.680299	−0.340149	−	0.940371i	$-0.610478\pi$
$827$	−1.33802e7	−0.680299	−0.340149	+	0.940371i	$0.610478\pi$
$828$	−4.24948e6	−0.215407
$829$	−9.29011e6	−0.469499	−0.234749	−	0.972056i	$-0.575427\pi$
$829$	−9.29011e6	−0.469499	−0.234749	+	0.972056i	$0.575427\pi$
$830$	5.31034e6	0.267564
$831$	1.26681e7	0.636371
$832$	−1.13746e7	−0.569678
$833$	−6.75969e6	−0.337531
$834$	9.78752e6	0.487257
$835$	−1.38108e7	−0.685491
$836$	−853419.	−0.0422325
$837$	4.70966e6	0.232368
$838$	1.41289e7	0.695020
$839$	−2.65341e7	−1.30137	−0.650684	−	0.759349i	$-0.725518\pi$
$839$	−2.65341e7	−1.30137	−0.650684	+	0.759349i	$0.725518\pi$
$840$	−5.67055e6	−0.277285
$841$	1.90613e7	0.929314
$842$	−3.64757e6	−0.177306
$843$	1.07298e6	0.0520022
$844$	1.18015e7	0.570271
$845$	1.86805e6	0.0900009
$846$	9.20465e6	0.442162
$847$	−2.50749e6	−0.120097
$848$	−75361.4	−0.00359881
$849$	1.08093e7	0.514669
$850$	1.19081e6	0.0565321
$851$	7.12188e6	0.337110
$852$	2.32997e6	0.109964
$853$	1.84210e7	0.866843	0.433421	−	0.901191i	$-0.357306\pi$
$853$	1.84210e7	0.866843	0.433421	+	0.901191i	$0.357306\pi$
$854$	−2.69622e7	−1.26506
$855$	−1.71485e6	−0.0802253
$856$	−1.46967e7	−0.685543
$857$	−4.17414e7	−1.94140	−0.970700	−	0.240295i	$-0.922756\pi$
$857$	−4.17414e7	−1.94140	−0.970700	+	0.240295i	$0.922756\pi$
$858$	1.69333e6	0.0785280
$859$	−1.41920e7	−0.656237	−0.328118	−	0.944637i	$-0.606414\pi$
$859$	−1.41920e7	−0.656237	−0.328118	+	0.944637i	$0.606414\pi$
$860$	5.36449e6	0.247333
$861$	1.51467e7	0.696321
$862$	1.17581e7	0.538974
$863$	3.73562e7	1.70740	0.853701	−	0.520764i	$-0.174353\pi$
$863$	3.73562e7	1.70740	0.853701	+	0.520764i	$0.174353\pi$
$864$	−1.81612e7	−0.827675
$865$	−1.34600e7	−0.611654
$866$	−3.90351e6	−0.176873
$867$	8.21523e6	0.371169
$868$	4.99963e6	0.225236
$869$	−9.10422e6	−0.408972
$870$	4.04138e6	0.181022
$871$	2.47599e7	1.10587
$872$	−1.58887e7	−0.707614
$873$	−3.30499e7	−1.46769
$874$	−1.45880e6	−0.0645976
$875$	2.67601e6	0.118159
$876$	5.74617e6	0.252999
$877$	1.76940e7	0.776831	0.388415	−	0.921484i	$-0.373023\pi$
$877$	1.76940e7	0.776831	0.388415	+	0.921484i	$0.373023\pi$
$878$	−2.26732e7	−0.992603
$879$	−6.61037e6	−0.288572
$880$	−51677.1	−0.00224953
$881$	−2.42250e6	−0.105154	−0.0525768	−	0.998617i	$-0.516743\pi$
$881$	−2.42250e6	−0.105154	−0.0525768	+	0.998617i	$0.516743\pi$
$882$	8.40133e6	0.363644
$883$	3.44922e7	1.48874	0.744371	−	0.667767i	$-0.232750\pi$
$883$	3.44922e7	1.48874	0.744371	+	0.667767i	$0.232750\pi$
$884$	−5.74241e6	−0.247152
$885$	1.81514e6	0.0779027
$886$	2.36346e7	1.01149
$887$	−1.34790e7	−0.575240	−0.287620	−	0.957745i	$-0.592864\pi$
$887$	−1.34790e7	−0.575240	−0.287620	+	0.957745i	$0.592864\pi$
$888$	8.23997e6	0.350666
$889$	1.40998e7	0.598356
$890$	−2.22829e6	−0.0942968
$891$	−2.81060e6	−0.118605
$892$	123877.	0.00521288
$893$	−4.95374e6	−0.207876
$894$	−3.69717e6	−0.154713
$895$	5.88084e6	0.245404
$896$	−1.89488e7	−0.788518
$897$	−4.53776e6	−0.188304
$898$	−6.85635e6	−0.283728
$899$	−9.39931e6	−0.387879
$900$	2.32022e6	0.0954824
$901$	−2.38088e6	−0.0977068
$902$	5.18973e6	0.212387
$903$	1.36923e7	0.558803
$904$	−2.84696e7	−1.15867
$905$	2.20086e6	0.0893247
$906$	915149.	0.0370400
$907$	−1.96004e7	−0.791128	−0.395564	−	0.918438i	$-0.629451\pi$
$907$	−1.96004e7	−0.791128	−0.395564	+	0.918438i	$0.629451\pi$
$908$	1.27112e7	0.511648
$909$	−1.07649e7	−0.432114
$910$	8.23142e6	0.329512
$911$	−2.63974e7	−1.05382	−0.526909	−	0.849922i	$-0.676649\pi$
$911$	−2.63974e7	−1.05382	−0.526909	+	0.849922i	$0.676649\pi$
$912$	−44892.2	−0.00178725
$913$	−7.28058e6	−0.289061
$914$	1.10759e7	0.438545
$915$	−8.11551e6	−0.320452
$916$	2.13511e7	0.840780
$917$	−2.77542e7	−1.08995
$918$	6.00555e6	0.235205
$919$	−9.04770e6	−0.353386	−0.176693	−	0.984266i	$-0.556540\pi$
$919$	−9.04770e6	−0.353386	−0.176693	+	0.984266i	$0.556540\pi$
$920$	5.20657e6	0.202807
$921$	1.42860e7	0.554961
$922$	1.53518e7	0.594749
$923$	−8.92183e6	−0.344707
$924$	2.94724e6	0.113563
$925$	−3.88856e6	−0.149429
$926$	−2.25548e7	−0.864393
$927$	−1.33118e7	−0.508787
$928$	3.62452e7	1.38159
$929$	−742447.	−0.0282245	−0.0141122	−	0.999900i	$-0.504492\pi$
$929$	−742447.	−0.0282245	−0.0141122	+	0.999900i	$0.504492\pi$
$930$	−959915.	−0.0363936
$931$	−4.52141e6	−0.170962
$932$	−1.01857e7	−0.384107
$933$	−1.29185e7	−0.485857
$934$	−4.63032e6	−0.173678
$935$	−1.63262e6	−0.0610740
$936$	1.88265e7	0.702393
$937$	2.41089e7	0.897076	0.448538	−	0.893764i	$-0.351945\pi$
$937$	2.41089e7	0.897076	0.448538	+	0.893764i	$0.351945\pi$
$938$	−2.74887e7	−1.02011
$939$	−1.28028e6	−0.0473851
$940$	6.70248e6	0.247409
$941$	4.02322e7	1.48115	0.740575	−	0.671973i	$-0.234553\pi$
$941$	4.02322e7	1.48115	0.740575	+	0.671973i	$0.234553\pi$
$942$	1.52429e6	0.0559681
$943$	−1.39073e7	−0.509289
$944$	−170393.	−0.00622332
$945$	1.34958e7	0.491609
$946$	4.69143e6	0.170442
$947$	−1.61467e7	−0.585070	−0.292535	−	0.956255i	$-0.594499\pi$
$947$	−1.61467e7	−0.585070	−0.292535	+	0.956255i	$0.594499\pi$
$948$	1.07009e7	0.386721
$949$	−2.20030e7	−0.793078
$950$	796506.	0.0286339
$951$	−1.68565e7	−0.604389
$952$	1.68172e7	0.601398
$953$	2.46287e7	0.878434	0.439217	−	0.898381i	$-0.355256\pi$
$953$	2.46287e7	0.878434	0.439217	+	0.898381i	$0.355256\pi$
$954$	2.95909e6	0.105266
$955$	−1.82299e7	−0.646809
$956$	−3.83520e6	−0.135720
$957$	−5.54081e6	−0.195566
$958$	2.20501e7	0.776242
$959$	8.05478e6	0.282818
$960$	3.80106e6	0.133115
$961$	−2.63966e7	−0.922019
$962$	−1.19612e7	−0.416713
$963$	1.53488e7	0.533344
$964$	−385209.	−0.0133507
$965$	2.45855e6	0.0849885
$966$	5.03788e6	0.173702
$967$	−3.22241e7	−1.10819	−0.554095	−	0.832454i	$-0.686935\pi$
$967$	−3.22241e7	−1.10819	−0.554095	+	0.832454i	$0.686935\pi$
$968$	2.66377e6	0.0913709
$969$	−1.41827e6	−0.0485232
$970$	1.53508e7	0.523845
$971$	−3.34985e7	−1.14019	−0.570095	−	0.821579i	$-0.693094\pi$
$971$	−3.34985e7	−1.14019	−0.570095	+	0.821579i	$0.693094\pi$
$972$	1.82682e7	0.620196
$973$	−6.52301e7	−2.20885
$974$	−3.07441e7	−1.03840
$975$	2.47762e6	0.0834688
$976$	761828.	0.0255996
$977$	−3.58506e6	−0.120160	−0.0600800	−	0.998194i	$-0.519136\pi$
$977$	−3.58506e6	−0.120160	−0.0600800	+	0.998194i	$0.519136\pi$
$978$	−7.00047e6	−0.234035
$979$	3.05503e6	0.101873
$980$	6.11753e6	0.203475
$981$	1.65936e7	0.550515
$982$	1.33746e7	0.442590
$983$	1.61808e7	0.534093	0.267047	−	0.963684i	$-0.413952\pi$
$983$	1.61808e7	0.534093	0.267047	+	0.963684i	$0.413952\pi$
$984$	−1.60907e7	−0.529769
$985$	5.79890e6	0.190438
$986$	−1.19856e7	−0.392615
$987$	1.71075e7	0.558975
$988$	−3.84097e6	−0.125184
$989$	−1.25720e7	−0.408708
$990$	2.02912e6	0.0657989
$991$	−1.99244e7	−0.644467	−0.322233	−	0.946660i	$-0.604434\pi$
$991$	−1.99244e7	−0.644467	−0.322233	+	0.946660i	$0.604434\pi$
$992$	−8.60900e6	−0.277763
$993$	1.67208e7	0.538127
$994$	9.90513e6	0.317976
$995$	7.05833e6	0.226019
$996$	8.55739e6	0.273334
$997$	5.23056e7	1.66652	0.833260	−	0.552881i	$-0.186472\pi$
$997$	5.23056e7	1.66652	0.833260	+	0.552881i	$0.186472\pi$
$998$	2.76274e7	0.878037
$999$	−1.96110e7	−0.621707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.15	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.15	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-3.53022 q^{2} -7.27933 q^{3} -19.5375 q^{4} -25.0000 q^{5} +25.6976 q^{6} -171.265 q^{7} +181.939 q^{8} -190.011 q^{9} +O(q^{10})\)	\(q-3.53022 q^{2} -7.27933 q^{3} -19.5375 q^{4} -25.0000 q^{5} +25.6976 q^{6} -171.265 q^{7} +181.939 q^{8} -190.011 q^{9} +88.2555 q^{10} -121.000 q^{11} +142.220 q^{12} -544.583 q^{13} +604.603 q^{14} +181.983 q^{15} -17.0833 q^{16} -539.710 q^{17} +670.782 q^{18} -361.000 q^{19} +488.438 q^{20} +1246.69 q^{21} +427.157 q^{22} -1144.68 q^{23} -1324.39 q^{24} +625.000 q^{25} +1922.50 q^{26} +3152.03 q^{27} +3346.10 q^{28} -6290.66 q^{29} -642.441 q^{30} +1494.17 q^{31} -5761.74 q^{32} +880.799 q^{33} +1905.30 q^{34} +4281.62 q^{35} +3712.35 q^{36} -6221.70 q^{37} +1274.41 q^{38} +3964.20 q^{39} -4548.47 q^{40} +12149.5 q^{41} -4401.10 q^{42} +10982.9 q^{43} +2364.04 q^{44} +4750.28 q^{45} +4040.99 q^{46} +13722.3 q^{47} +124.355 q^{48} +12524.7 q^{49} -2206.39 q^{50} +3928.72 q^{51} +10639.8 q^{52} +4411.40 q^{53} -11127.4 q^{54} +3025.00 q^{55} -31159.8 q^{56} +2627.84 q^{57} +22207.4 q^{58} +9974.23 q^{59} -3555.50 q^{60} -44594.8 q^{61} -5274.74 q^{62} +32542.3 q^{63} +20886.9 q^{64} +13614.6 q^{65} -3109.41 q^{66} -45465.7 q^{67} +10544.6 q^{68} +8332.54 q^{69} -15115.1 q^{70} +16382.9 q^{71} -34570.5 q^{72} +40403.3 q^{73} +21964.0 q^{74} -4549.58 q^{75} +7053.05 q^{76} +20723.1 q^{77} -13994.5 q^{78} +75241.5 q^{79} +427.083 q^{80} +23228.1 q^{81} -42890.3 q^{82} +60170.0 q^{83} -24357.3 q^{84} +13492.7 q^{85} -38772.2 q^{86} +45791.8 q^{87} -22014.6 q^{88} -25248.2 q^{89} -16769.6 q^{90} +93268.0 q^{91} +22364.3 q^{92} -10876.5 q^{93} -48442.6 q^{94} +9025.00 q^{95} +41941.6 q^{96} +173936. q^{97} -44214.9 q^{98} +22991.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

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