LMFDB - Embedded newform 1045.6.a.c.1.7

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			1.7
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)

$f(q)$	$=$	$q-8.15394 q^{2} +5.08384 q^{3} +34.4868 q^{4} -25.0000 q^{5} -41.4534 q^{6} +169.957 q^{7} -20.2770 q^{8} -217.155 q^{9} +O(q^{10})$	\(q-8.15394 q^{2} +5.08384 q^{3} +34.4868 q^{4} -25.0000 q^{5} -41.4534 q^{6} +169.957 q^{7} -20.2770 q^{8} -217.155 q^{9} +203.849 q^{10} -121.000 q^{11} +175.325 q^{12} -1135.59 q^{13} -1385.82 q^{14} -127.096 q^{15} -938.239 q^{16} +773.670 q^{17} +1770.67 q^{18} -361.000 q^{19} -862.169 q^{20} +864.034 q^{21} +986.627 q^{22} +1481.33 q^{23} -103.085 q^{24} +625.000 q^{25} +9259.51 q^{26} -2339.35 q^{27} +5861.26 q^{28} +6641.41 q^{29} +1036.33 q^{30} +8504.18 q^{31} +8299.21 q^{32} -615.145 q^{33} -6308.46 q^{34} -4248.92 q^{35} -7488.96 q^{36} -6207.74 q^{37} +2943.57 q^{38} -5773.15 q^{39} +506.925 q^{40} -8655.95 q^{41} -7045.29 q^{42} +7957.45 q^{43} -4172.90 q^{44} +5428.86 q^{45} -12078.6 q^{46} -17978.1 q^{47} -4769.86 q^{48} +12078.3 q^{49} -5096.21 q^{50} +3933.22 q^{51} -39162.7 q^{52} +24511.4 q^{53} +19075.0 q^{54} +3025.00 q^{55} -3446.22 q^{56} -1835.27 q^{57} -54153.7 q^{58} -32778.4 q^{59} -4383.13 q^{60} -31522.5 q^{61} -69342.6 q^{62} -36906.9 q^{63} -37647.6 q^{64} +28389.7 q^{65} +5015.86 q^{66} +24312.9 q^{67} +26681.4 q^{68} +7530.83 q^{69} +34645.5 q^{70} +41391.3 q^{71} +4403.24 q^{72} +21361.9 q^{73} +50617.6 q^{74} +3177.40 q^{75} -12449.7 q^{76} -20564.8 q^{77} +47073.9 q^{78} +52855.9 q^{79} +23456.0 q^{80} +40875.6 q^{81} +70580.1 q^{82} -90051.5 q^{83} +29797.8 q^{84} -19341.7 q^{85} -64884.6 q^{86} +33763.9 q^{87} +2453.52 q^{88} +117685. q^{89} -44266.6 q^{90} -193001. q^{91} +51086.1 q^{92} +43233.9 q^{93} +146592. q^{94} +9025.00 q^{95} +42191.9 q^{96} -126261. q^{97} -98486.1 q^{98} +26275.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−8.15394	−1.44143	−0.720713	−	0.693233i	$-0.756186\pi$
$2$	−8.15394	−1.44143	−0.720713	+	0.693233i	$0.756186\pi$
$3$	5.08384	0.326129	0.163064	−	0.986615i	$-0.447862\pi$
$3$	5.08384	0.326129	0.163064	+	0.986615i	$0.447862\pi$
$4$	34.4868	1.07771
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−41.4534	−0.470091
$7$	169.957	1.31097	0.655486	−	0.755207i	$-0.272464\pi$
$7$	169.957	1.31097	0.655486	+	0.755207i	$0.272464\pi$
$8$	−20.2770	−0.112016
$9$	−217.155	−0.893640
$10$	203.849	0.644626
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	175.325	0.351473
$13$	−1135.59	−1.86364	−0.931820	−	0.362920i	$-0.881780\pi$
$13$	−1135.59	−1.86364	−0.931820	+	0.362920i	$0.881780\pi$
$14$	−1385.82	−1.88967
$15$	−127.096	−0.145849
$16$	−938.239	−0.916249
$17$	773.670	0.649282	0.324641	−	0.945837i	$-0.394757\pi$
$17$	773.670	0.649282	0.324641	+	0.945837i	$0.394757\pi$
$18$	1770.67	1.28812
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−862.169	−0.481967
$21$	864.034	0.427546
$22$	986.627	0.434607
$23$	1481.33	0.583890	0.291945	−	0.956435i	$-0.405698\pi$
$23$	1481.33	0.583890	0.291945	+	0.956435i	$0.405698\pi$
$24$	−103.085	−0.0365315
$25$	625.000	0.200000
$26$	9259.51	2.68630
$27$	−2339.35	−0.617570
$28$	5861.26	1.41285
$29$	6641.41	1.46644	0.733222	−	0.679990i	$-0.238016\pi$
$29$	6641.41	1.46644	0.733222	+	0.679990i	$0.238016\pi$
$30$	1036.33	0.210231
$31$	8504.18	1.58938	0.794691	−	0.607014i	$-0.207633\pi$
$31$	8504.18	1.58938	0.794691	+	0.607014i	$0.207633\pi$
$32$	8299.21	1.43272
$33$	−615.145	−0.0983315
$34$	−6308.46	−0.935892
$35$	−4248.92	−0.586285
$36$	−7488.96	−0.963086
$37$	−6207.74	−0.745468	−0.372734	−	0.927938i	$-0.621580\pi$
$37$	−6207.74	−0.745468	−0.372734	+	0.927938i	$0.621580\pi$
$38$	2943.57	0.330686
$39$	−5773.15	−0.607787
$40$	506.925	0.0500949
$41$	−8655.95	−0.804184	−0.402092	−	0.915599i	$-0.631717\pi$
$41$	−8655.95	−0.804184	−0.402092	+	0.915599i	$0.631717\pi$
$42$	−7045.29	−0.616276
$43$	7957.45	0.656301	0.328150	−	0.944626i	$-0.393575\pi$
$43$	7957.45	0.656301	0.328150	+	0.944626i	$0.393575\pi$
$44$	−4172.90	−0.324942
$45$	5428.86	0.399648
$46$	−12078.6	−0.841634
$47$	−17978.1	−1.18713	−0.593565	−	0.804786i	$-0.702280\pi$
$47$	−17978.1	−1.18713	−0.593565	+	0.804786i	$0.702280\pi$
$48$	−4769.86	−0.298815
$49$	12078.3	0.718650
$50$	−5096.21	−0.288285
$51$	3933.22	0.211749
$52$	−39162.7	−2.00847
$53$	24511.4	1.19861	0.599306	−	0.800520i	$-0.295443\pi$
$53$	24511.4	1.19861	0.599306	+	0.800520i	$0.295443\pi$
$54$	19075.0	0.890183
$55$	3025.00	0.134840
$56$	−3446.22	−0.146850
$57$	−1835.27	−0.0748191
$58$	−54153.7	−2.11377
$59$	−32778.4	−1.22591	−0.612954	−	0.790119i	$-0.710019\pi$
$59$	−32778.4	−1.22591	−0.612954	+	0.790119i	$0.710019\pi$
$60$	−4383.13	−0.157183
$61$	−31522.5	−1.08467	−0.542334	−	0.840163i	$-0.682459\pi$
$61$	−31522.5	−1.08467	−0.542334	+	0.840163i	$0.682459\pi$
$62$	−69342.6	−2.29098
$63$	−36906.9	−1.17154
$64$	−37647.6	−1.14891
$65$	28389.7	0.833445
$66$	5015.86	0.141738
$67$	24312.9	0.661682	0.330841	−	0.943686i	$-0.392668\pi$
$67$	24312.9	0.661682	0.330841	+	0.943686i	$0.392668\pi$
$68$	26681.4	0.699739
$69$	7530.83	0.190423
$70$	34645.5	0.845087
$71$	41391.3	0.974459	0.487229	−	0.873274i	$-0.338008\pi$
$71$	41391.3	0.974459	0.487229	+	0.873274i	$0.338008\pi$
$72$	4403.24	0.100102
$73$	21361.9	0.469173	0.234587	−	0.972095i	$-0.424626\pi$
$73$	21361.9	0.469173	0.234587	+	0.972095i	$0.424626\pi$
$74$	50617.6	1.07454
$75$	3177.40	0.0652257
$76$	−12449.7	−0.247244
$77$	−20564.8	−0.395273
$78$	47073.9	0.876080
$79$	52855.9	0.952853	0.476427	−	0.879214i	$-0.341932\pi$
$79$	52855.9	0.952853	0.476427	+	0.879214i	$0.341932\pi$
$80$	23456.0	0.409759
$81$	40875.6	0.692233
$82$	70580.1	1.15917
$83$	−90051.5	−1.43481	−0.717407	−	0.696654i	$-0.754671\pi$
$83$	−90051.5	−1.43481	−0.717407	+	0.696654i	$0.754671\pi$
$84$	29797.8	0.460771
$85$	−19341.7	−0.290368
$86$	−64884.6	−0.946009
$87$	33763.9	0.478249
$88$	2453.52	0.0337740
$89$	117685.	1.57487	0.787436	−	0.616397i	$-0.211408\pi$
$89$	117685.	1.57487	0.787436	+	0.616397i	$0.211408\pi$
$90$	−44266.6	−0.576063
$91$	−193001.	−2.44318
$92$	51086.1	0.629265
$93$	43233.9	0.518343
$94$	146592.	1.71116
$95$	9025.00	0.102598
$96$	42191.9	0.467252
$97$	−126261.	−1.36251	−0.681257	−	0.732045i	$-0.738566\pi$
$97$	−126261.	−1.36251	−0.681257	+	0.732045i	$0.738566\pi$
$98$	−98486.1	−1.03588
$99$	26275.7	0.269443
$100$	21554.2	0.215542
$101$	144189.	1.40647	0.703233	−	0.710959i	$-0.251739\pi$
$101$	144189.	1.40647	0.703233	+	0.710959i	$0.251739\pi$
$102$	−32071.2	−0.305221
$103$	154904.	1.43869	0.719347	−	0.694651i	$-0.244441\pi$
$103$	154904.	1.43869	0.719347	+	0.694651i	$0.244441\pi$
$104$	23026.3	0.208757
$105$	−21600.9	−0.191204
$106$	−199865.	−1.72771
$107$	−180586.	−1.52484	−0.762419	−	0.647083i	$-0.775989\pi$
$107$	−180586.	−1.52484	−0.762419	+	0.647083i	$0.775989\pi$
$108$	−80676.8	−0.665563
$109$	−143676.	−1.15829	−0.579146	−	0.815224i	$-0.696614\pi$
$109$	−143676.	−1.15829	−0.579146	+	0.815224i	$0.696614\pi$
$110$	−24665.7	−0.194362
$111$	−31559.2	−0.243119
$112$	−159460.	−1.20118
$113$	−151825.	−1.11853	−0.559265	−	0.828989i	$-0.688916\pi$
$113$	−151825.	−1.11853	−0.559265	+	0.828989i	$0.688916\pi$
$114$	14964.7	0.107846
$115$	−37033.1	−0.261123
$116$	229041.	1.58040
$117$	246598.	1.66542
$118$	267273.	1.76706
$119$	131491.	0.851191
$120$	2577.13	0.0163374
$121$	14641.0	0.0909091
$122$	257033.	1.56347
$123$	−44005.5	−0.262267
$124$	293282.	1.71290
$125$	−15625.0	−0.0894427
$126$	300937.	1.68869
$127$	−26737.2	−0.147098	−0.0735490	−	0.997292i	$-0.523433\pi$
$127$	−26737.2	−0.147098	−0.0735490	+	0.997292i	$0.523433\pi$
$128$	41401.9	0.223355
$129$	40454.4	0.214038
$130$	−231488.	−1.20135
$131$	−8389.97	−0.0427152	−0.0213576	−	0.999772i	$-0.506799\pi$
$131$	−8389.97	−0.0427152	−0.0213576	+	0.999772i	$0.506799\pi$
$132$	−21214.4	−0.105973
$133$	−61354.4	−0.300758
$134$	−198246.	−0.953767
$135$	58483.8	0.276186
$136$	−15687.7	−0.0727298
$137$	368226.	1.67615	0.838075	−	0.545555i	$-0.183681\pi$
$137$	368226.	1.67615	0.838075	+	0.545555i	$0.183681\pi$
$138$	−61405.9	−0.274481
$139$	447124.	1.96287	0.981434	−	0.191803i	$-0.0614333\pi$
$139$	447124.	1.96287	0.981434	+	0.191803i	$0.0614333\pi$
$140$	−146532.	−0.631846
$141$	−91397.7	−0.387157
$142$	−337503.	−1.40461
$143$	137406.	0.561909
$144$	203743.	0.818797
$145$	−166035.	−0.655813
$146$	−174184.	−0.676279
$147$	61404.4	0.234372
$148$	−214085.	−0.803400
$149$	−519422.	−1.91670	−0.958351	−	0.285594i	$-0.907809\pi$
$149$	−519422.	−1.91670	−0.958351	+	0.285594i	$0.907809\pi$
$150$	−25908.4	−0.0940181
$151$	−161954.	−0.578027	−0.289014	−	0.957325i	$-0.593327\pi$
$151$	−161954.	−0.578027	−0.289014	+	0.957325i	$0.593327\pi$
$152$	7320.00	0.0256982
$153$	−168006.	−0.580224
$154$	167684.	0.569757
$155$	−212605.	−0.710793
$156$	−199097.	−0.655019
$157$	−24768.9	−0.0801970	−0.0400985	−	0.999196i	$-0.512767\pi$
$157$	−24768.9	−0.0801970	−0.0400985	+	0.999196i	$0.512767\pi$
$158$	−430984.	−1.37347
$159$	124612.	0.390902
$160$	−207480.	−0.640733
$161$	251761.	0.765464
$162$	−333298.	−0.997803
$163$	−139205.	−0.410381	−0.205190	−	0.978722i	$-0.565781\pi$
$163$	−139205.	−0.410381	−0.205190	+	0.978722i	$0.565781\pi$
$164$	−298516.	−0.866678
$165$	15378.6	0.0439752
$166$	734275.	2.06818
$167$	278070.	0.771547	0.385774	−	0.922593i	$-0.373935\pi$
$167$	278070.	0.771547	0.385774	+	0.922593i	$0.373935\pi$
$168$	−17520.0	−0.0478919
$169$	918266.	2.47316
$170$	157711.	0.418544
$171$	78392.8	0.205015
$172$	274427.	0.707303
$173$	−70551.8	−0.179223	−0.0896113	−	0.995977i	$-0.528562\pi$
$173$	−70551.8	−0.179223	−0.0896113	+	0.995977i	$0.528562\pi$
$174$	−275309.	−0.689361
$175$	106223.	0.262195
$176$	113527.	0.276260
$177$	−166640.	−0.399804
$178$	−959594.	−2.27006
$179$	−95805.1	−0.223489	−0.111744	−	0.993737i	$-0.535644\pi$
$179$	−95805.1	−0.223489	−0.111744	+	0.993737i	$0.535644\pi$
$180$	187224.	0.430705
$181$	−139487.	−0.316474	−0.158237	−	0.987401i	$-0.550581\pi$
$181$	−139487.	−0.316474	−0.158237	+	0.987401i	$0.550581\pi$
$182$	1.57372e6	3.52167
$183$	−160256.	−0.353741
$184$	−30036.8	−0.0654048
$185$	155193.	0.333384
$186$	−352527.	−0.747154
$187$	−93614.0	−0.195766
$188$	−620006.	−1.27938
$189$	−397589.	−0.809618
$190$	−73589.3	−0.147887
$191$	−164935.	−0.327137	−0.163568	−	0.986532i	$-0.552300\pi$
$191$	−164935.	−0.327137	−0.163568	+	0.986532i	$0.552300\pi$
$192$	−191395.	−0.374694
$193$	105550.	0.203970	0.101985	−	0.994786i	$-0.467481\pi$
$193$	105550.	0.203970	0.101985	+	0.994786i	$0.467481\pi$
$194$	1.02953e6	1.96396
$195$	144329.	0.271810
$196$	416543.	0.774497
$197$	−868801.	−1.59498	−0.797489	−	0.603334i	$-0.793839\pi$
$197$	−868801.	−1.59498	−0.797489	+	0.603334i	$0.793839\pi$
$198$	−214251.	−0.388382
$199$	550242.	0.984965	0.492482	−	0.870322i	$-0.336090\pi$
$199$	550242.	0.984965	0.492482	+	0.870322i	$0.336090\pi$
$200$	−12673.1	−0.0224031
$201$	123603.	0.215794
$202$	−1.17571e6	−2.02732
$203$	1.12875e6	1.92247
$204$	135644.	0.228205
$205$	216399.	0.359642
$206$	−1.26307e6	−2.07377
$207$	−321676.	−0.521787
$208$	1.06545e6	1.70756
$209$	43681.0	0.0691714
$210$	176132.	0.275607
$211$	15256.8	0.0235916	0.0117958	−	0.999930i	$-0.496245\pi$
$211$	15256.8	0.0235916	0.0117958	+	0.999930i	$0.496245\pi$
$212$	845320.	1.29176
$213$	210427.	0.317799
$214$	1.47249e6	2.19794
$215$	−198936.	−0.293507
$216$	47435.1	0.0691776
$217$	1.44534e6	2.08364
$218$	1.17153e6	1.66959
$219$	108601.	0.153011
$220$	104322.	0.145319
$221$	−878570.	−1.21003
$222$	257332.	0.350438
$223$	−368362.	−0.496036	−0.248018	−	0.968755i	$-0.579779\pi$
$223$	−368362.	−0.496036	−0.248018	+	0.968755i	$0.579779\pi$
$224$	1.41051e6	1.87826
$225$	−135722.	−0.178728
$226$	1.23797e6	1.61228
$227$	−369617.	−0.476088	−0.238044	−	0.971254i	$-0.576506\pi$
$227$	−369617.	−0.476088	−0.238044	+	0.971254i	$0.576506\pi$
$228$	−63292.5	−0.0806334
$229$	−154175.	−0.194279	−0.0971394	−	0.995271i	$-0.530969\pi$
$229$	−154175.	−0.194279	−0.0971394	+	0.995271i	$0.530969\pi$
$230$	301966.	0.376390
$231$	−104548.	−0.128910
$232$	−134668.	−0.164265
$233$	1.31967e6	1.59248	0.796242	−	0.604979i	$-0.206818\pi$
$233$	1.31967e6	1.59248	0.796242	+	0.604979i	$0.206818\pi$
$234$	−2.01075e6	−2.40059
$235$	449452.	0.530901
$236$	−1.13042e6	−1.32118
$237$	268711.	0.310753
$238$	−1.07217e6	−1.22693
$239$	−537385.	−0.608542	−0.304271	−	0.952585i	$-0.598413\pi$
$239$	−537385.	−0.608542	−0.304271	+	0.952585i	$0.598413\pi$
$240$	119247.	0.133634
$241$	341526.	0.378775	0.189387	−	0.981902i	$-0.439350\pi$
$241$	341526.	0.378775	0.189387	+	0.981902i	$0.439350\pi$
$242$	−119382.	−0.131039
$243$	776268.	0.843327
$244$	−1.08711e6	−1.16896
$245$	−301959.	−0.321390
$246$	358818.	0.378039
$247$	409947.	0.427548
$248$	−172439.	−0.178036
$249$	−457808.	−0.467934
$250$	127405.	0.128925
$251$	−532507.	−0.533508	−0.266754	−	0.963765i	$-0.585951\pi$
$251$	−532507.	−0.533508	−0.266754	+	0.963765i	$0.585951\pi$
$252$	−1.27280e6	−1.26258
$253$	−179240.	−0.176049
$254$	218014.	0.212031
$255$	−98330.4	−0.0946972
$256$	867136.	0.826965
$257$	147324.	0.139137	0.0695684	−	0.997577i	$-0.477838\pi$
$257$	147324.	0.139137	0.0695684	+	0.997577i	$0.477838\pi$
$258$	−329863.	−0.308521
$259$	−1.05505e6	−0.977289
$260$	979069.	0.898214
$261$	−1.44221e6	−1.31047
$262$	68411.3	0.0615708
$263$	419716.	0.374167	0.187084	−	0.982344i	$-0.440096\pi$
$263$	419716.	0.374167	0.187084	+	0.982344i	$0.440096\pi$
$264$	12473.3	0.0110147
$265$	−612785.	−0.536036
$266$	500281.	0.433520
$267$	598291.	0.513611
$268$	838473.	0.713103
$269$	−1.56651e6	−1.31993	−0.659965	−	0.751296i	$-0.729429\pi$
$269$	−1.56651e6	−1.31993	−0.659965	+	0.751296i	$0.729429\pi$
$270$	−476874.	−0.398102
$271$	246803.	0.204139	0.102070	−	0.994777i	$-0.467454\pi$
$271$	246803.	0.204139	0.102070	+	0.994777i	$0.467454\pi$
$272$	−725887.	−0.594904
$273$	−981186.	−0.796792
$274$	−3.00249e6	−2.41605
$275$	−75625.0	−0.0603023
$276$	259714.	0.205221
$277$	1.33747e6	1.04733	0.523667	−	0.851923i	$-0.324564\pi$
$277$	1.33747e6	1.04733	0.523667	+	0.851923i	$0.324564\pi$
$278$	−3.64582e6	−2.82933
$279$	−1.84672e6	−1.42034
$280$	86155.4	0.0656731
$281$	−1.51115e6	−1.14167	−0.570836	−	0.821064i	$-0.693381\pi$
$281$	−1.51115e6	−1.14167	−0.570836	+	0.821064i	$0.693381\pi$
$282$	745252.	0.558059
$283$	149572.	0.111016	0.0555078	−	0.998458i	$-0.482322\pi$
$283$	149572.	0.111016	0.0555078	+	0.998458i	$0.482322\pi$
$284$	1.42745e6	1.05019
$285$	45881.7	0.0334601
$286$	−1.12040e6	−0.809950
$287$	−1.47114e6	−1.05426
$288$	−1.80221e6	−1.28034
$289$	−821292.	−0.578433
$290$	1.35384e6	0.945307
$291$	−641893.	−0.444355
$292$	736704.	0.505633
$293$	−1.61646e6	−1.10001	−0.550003	−	0.835163i	$-0.685373\pi$
$293$	−1.61646e6	−1.10001	−0.550003	+	0.835163i	$0.685373\pi$
$294$	−500688.	−0.337831
$295$	819460.	0.548243
$296$	125874.	0.0835042
$297$	283062.	0.186204
$298$	4.23533e6	2.76278
$299$	−1.68217e6	−1.08816
$300$	109578.	0.0702945
$301$	1.35242e6	0.860392
$302$	1.32056e6	0.833184
$303$	733035.	0.458689
$304$	338704.	0.210202
$305$	788063.	0.485078
$306$	1.36991e6	0.836351
$307$	2.51780e6	1.52467	0.762334	−	0.647183i	$-0.224053\pi$
$307$	2.51780e6	1.52467	0.762334	+	0.647183i	$0.224053\pi$
$308$	−709213.	−0.425991
$309$	787506.	0.469199
$310$	1.73356e6	1.02456
$311$	−1.80229e6	−1.05663	−0.528316	−	0.849048i	$-0.677176\pi$
$311$	−1.80229e6	−1.05663	−0.528316	+	0.849048i	$0.677176\pi$
$312$	117062.	0.0680817
$313$	−373606.	−0.215552	−0.107776	−	0.994175i	$-0.534373\pi$
$313$	−373606.	−0.215552	−0.107776	+	0.994175i	$0.534373\pi$
$314$	201965.	0.115598
$315$	922673.	0.523928
$316$	1.82283e6	1.02690
$317$	−3.52436e6	−1.96985	−0.984923	−	0.172994i	$-0.944656\pi$
$317$	−3.52436e6	−1.96985	−0.984923	+	0.172994i	$0.944656\pi$
$318$	−1.01608e6	−0.563457
$319$	−803611.	−0.442149
$320$	941191.	0.513810
$321$	−918070.	−0.497294
$322$	−2.05285e6	−1.10336
$323$	−279295.	−0.148955
$324$	1.40967e6	0.746027
$325$	−709742.	−0.372728
$326$	1.13507e6	0.591534
$327$	−730427.	−0.377752
$328$	175517.	0.0900812
$329$	−3.05550e6	−1.55630
$330$	−125396.	−0.0633870
$331$	−653519.	−0.327860	−0.163930	−	0.986472i	$-0.552417\pi$
$331$	−653519.	−0.327860	−0.163930	+	0.986472i	$0.552417\pi$
$332$	−3.10559e6	−1.54632
$333$	1.34804e6	0.666180
$334$	−2.26736e6	−1.11213
$335$	−607822.	−0.295913
$336$	−810671.	−0.391739
$337$	59812.0	0.0286889	0.0143444	−	0.999897i	$-0.495434\pi$
$337$	59812.0	0.0286889	0.0143444	+	0.999897i	$0.495434\pi$
$338$	−7.48748e6	−3.56487
$339$	−771855.	−0.364784
$340$	−667034.	−0.312933
$341$	−1.02901e6	−0.479217
$342$	−639210.	−0.295514
$343$	−803667.	−0.368843
$344$	−161353.	−0.0735160
$345$	−188271.	−0.0851598
$346$	575275.	0.258336
$347$	1.23723e6	0.551604	0.275802	−	0.961214i	$-0.411057\pi$
$347$	1.23723e6	0.551604	0.275802	+	0.961214i	$0.411057\pi$
$348$	1.16441e6	0.515415
$349$	−2.58448e6	−1.13582	−0.567910	−	0.823090i	$-0.692248\pi$
$349$	−2.58448e6	−1.13582	−0.567910	+	0.823090i	$0.692248\pi$
$350$	−866137.	−0.377934
$351$	2.65654e6	1.15093
$352$	−1.00420e6	−0.431982
$353$	309191.	0.132066	0.0660329	−	0.997817i	$-0.478966\pi$
$353$	309191.	0.132066	0.0660329	+	0.997817i	$0.478966\pi$
$354$	1.35878e6	0.576288
$355$	−1.03478e6	−0.435791
$356$	4.05857e6	1.69726
$357$	668477.	0.277598
$358$	781189.	0.322143
$359$	−3.87367e6	−1.58630	−0.793152	−	0.609024i	$-0.791562\pi$
$359$	−3.87367e6	−1.58630	−0.793152	+	0.609024i	$0.791562\pi$
$360$	−110081.	−0.0447668
$361$	130321.	0.0526316
$362$	1.13737e6	0.456175
$363$	74432.6	0.0296481
$364$	−6.65598e6	−2.63305
$365$	−534048.	−0.209821
$366$	1.30671e6	0.509892
$367$	1.11040e6	0.430344	0.215172	−	0.976576i	$-0.430969\pi$
$367$	1.11040e6	0.430344	0.215172	+	0.976576i	$0.430969\pi$
$368$	−1.38984e6	−0.534988
$369$	1.87968e6	0.718651
$370$	−1.26544e6	−0.480548
$371$	4.16588e6	1.57135
$372$	1.49100e6	0.558624
$373$	1.60008e6	0.595482	0.297741	−	0.954647i	$-0.403767\pi$
$373$	1.60008e6	0.595482	0.297741	+	0.954647i	$0.403767\pi$
$374$	763323.	0.282182
$375$	−79435.1	−0.0291698
$376$	364541.	0.132977
$377$	−7.54190e6	−2.73292
$378$	3.24192e6	1.16701
$379$	140912.	0.0503907	0.0251954	−	0.999683i	$-0.491979\pi$
$379$	140912.	0.0503907	0.0251954	+	0.999683i	$0.491979\pi$
$380$	311243.	0.110571
$381$	−135928.	−0.0479729
$382$	1.34487e6	0.471544
$383$	1.11975e6	0.390054	0.195027	−	0.980798i	$-0.437520\pi$
$383$	1.11975e6	0.390054	0.195027	+	0.980798i	$0.437520\pi$
$384$	210481.	0.0728425
$385$	514120.	0.176772
$386$	−860650.	−0.294008
$387$	−1.72800e6	−0.586496
$388$	−4.35434e6	−1.46840
$389$	−405505.	−0.135869	−0.0679347	−	0.997690i	$-0.521641\pi$
$389$	−405505.	−0.135869	−0.0679347	+	0.997690i	$0.521641\pi$
$390$	−1.17685e6	−0.391795
$391$	1.14606e6	0.379109
$392$	−244913.	−0.0805001
$393$	−42653.3	−0.0139306
$394$	7.08415e6	2.29904
$395$	−1.32140e6	−0.426129
$396$	906164.	0.290381
$397$	−2.44123e6	−0.777378	−0.388689	−	0.921369i	$-0.627072\pi$
$397$	−2.44123e6	−0.777378	−0.388689	+	0.921369i	$0.627072\pi$
$398$	−4.48664e6	−1.41975
$399$	−311916.	−0.0980857
$400$	−586400.	−0.183250
$401$	−2.36826e6	−0.735477	−0.367738	−	0.929929i	$-0.619868\pi$
$401$	−2.36826e6	−0.735477	−0.367738	+	0.929929i	$0.619868\pi$
$402$	−1.00785e6	−0.311051
$403$	−9.65724e6	−2.96204
$404$	4.97262e6	1.51577
$405$	−1.02189e6	−0.309576
$406$	−9.20379e6	−2.77110
$407$	751137.	0.224767
$408$	−79753.8	−0.0237193
$409$	−3.86073e6	−1.14120	−0.570599	−	0.821229i	$-0.693289\pi$
$409$	−3.86073e6	−1.14120	−0.570599	+	0.821229i	$0.693289\pi$
$410$	−1.76450e6	−0.518398
$411$	1.87200e6	0.546640
$412$	5.34212e6	1.55050
$413$	−5.57092e6	−1.60713
$414$	2.62293e6	0.752118
$415$	2.25129e6	0.641668
$416$	−9.42448e6	−2.67008
$417$	2.27311e6	0.640147
$418$	−356172.	−0.0997056
$419$	−5.70973e6	−1.58884	−0.794421	−	0.607368i	$-0.792225\pi$
$419$	−5.70973e6	−1.58884	−0.794421	+	0.607368i	$0.792225\pi$
$420$	−744944.	−0.206063
$421$	1.16341e6	0.319911	0.159955	−	0.987124i	$-0.448865\pi$
$421$	1.16341e6	0.319911	0.159955	+	0.987124i	$0.448865\pi$
$422$	−124403.	−0.0340056
$423$	3.90402e6	1.06087
$424$	−497018.	−0.134263
$425$	483544.	0.129856
$426$	−1.71581e6	−0.458084
$427$	−5.35747e6	−1.42197
$428$	−6.22782e6	−1.64334
$429$	698551.	0.183255
$430$	1.62211e6	0.423068
$431$	4.56458e6	1.18361	0.591804	−	0.806082i	$-0.298416\pi$
$431$	4.56458e6	1.18361	0.591804	+	0.806082i	$0.298416\pi$
$432$	2.19487e6	0.565848
$433$	4.50871e6	1.15567	0.577833	−	0.816155i	$-0.303898\pi$
$433$	4.50871e6	1.15567	0.577833	+	0.816155i	$0.303898\pi$
$434$	−1.17853e7	−3.00341
$435$	−844097.	−0.213880
$436$	−4.95492e6	−1.24831
$437$	−534758.	−0.133953
$438$	−885523.	−0.220554
$439$	−6.13819e6	−1.52012	−0.760062	−	0.649851i	$-0.774831\pi$
$439$	−6.13819e6	−1.52012	−0.760062	+	0.649851i	$0.774831\pi$
$440$	−61337.9	−0.0151042
$441$	−2.62287e6	−0.642214
$442$	7.16381e6	1.74417
$443$	−1.27917e6	−0.309683	−0.154842	−	0.987939i	$-0.549487\pi$
$443$	−1.27917e6	−0.309683	−0.154842	+	0.987939i	$0.549487\pi$
$444$	−1.08837e6	−0.262012
$445$	−2.94212e6	−0.704304
$446$	3.00361e6	0.714999
$447$	−2.64066e6	−0.625091
$448$	−6.39848e6	−1.50620
$449$	−4.18854e6	−0.980497	−0.490249	−	0.871583i	$-0.663094\pi$
$449$	−4.18854e6	−0.980497	−0.490249	+	0.871583i	$0.663094\pi$
$450$	1.10667e6	0.257623
$451$	1.04737e6	0.242471
$452$	−5.23596e6	−1.20545
$453$	−823347.	−0.188511
$454$	3.01384e6	0.686246
$455$	4.82502e6	1.09262
$456$	37213.7	0.00838091
$457$	−6.97780e6	−1.56289	−0.781444	−	0.623975i	$-0.785517\pi$
$457$	−6.97780e6	−1.56289	−0.781444	+	0.623975i	$0.785517\pi$
$458$	1.25714e6	0.280039
$459$	−1.80989e6	−0.400977
$460$	−1.27715e6	−0.281416
$461$	−399499.	−0.0875515	−0.0437757	−	0.999041i	$-0.513939\pi$
$461$	−399499.	−0.0875515	−0.0437757	+	0.999041i	$0.513939\pi$
$462$	852480.	0.185814
$463$	397509.	0.0861775	0.0430888	−	0.999071i	$-0.486280\pi$
$463$	397509.	0.0861775	0.0430888	+	0.999071i	$0.486280\pi$
$464$	−6.23123e6	−1.34363
$465$	−1.08085e6	−0.231810
$466$	−1.07605e7	−2.29545
$467$	8.04368e6	1.70672	0.853361	−	0.521321i	$-0.174561\pi$
$467$	8.04368e6	1.70672	0.853361	+	0.521321i	$0.174561\pi$
$468$	8.50437e6	1.79485
$469$	4.13214e6	0.867447
$470$	−3.66480e6	−0.765255
$471$	−125921.	−0.0261546
$472$	664648.	0.137321
$473$	−962851.	−0.197882
$474$	−2.19106e6	−0.447927
$475$	−225625.	−0.0458831
$476$	4.53468e6	0.917338
$477$	−5.32277e6	−1.07113
$478$	4.38180e6	0.877169
$479$	−1.66493e6	−0.331557	−0.165778	−	0.986163i	$-0.553014\pi$
$479$	−1.66493e6	−0.331557	−0.165778	+	0.986163i	$0.553014\pi$
$480$	−1.05480e6	−0.208961
$481$	7.04943e6	1.38929
$482$	−2.78478e6	−0.545976
$483$	1.27992e6	0.249640
$484$	504921.	0.0979738
$485$	3.15653e6	0.609335
$486$	−6.32965e6	−1.21559
$487$	4.74916e6	0.907392	0.453696	−	0.891157i	$-0.350105\pi$
$487$	4.74916e6	0.907392	0.453696	+	0.891157i	$0.350105\pi$
$488$	639183.	0.121500
$489$	−707698.	−0.133837
$490$	2.46215e6	0.463260
$491$	6.10334e6	1.14252	0.571260	−	0.820769i	$-0.306455\pi$
$491$	6.10334e6	1.14252	0.571260	+	0.820769i	$0.306455\pi$
$492$	−1.51761e6	−0.282649
$493$	5.13826e6	0.952135
$494$	−3.34268e6	−0.616280
$495$	−656892.	−0.120498
$496$	−7.97896e6	−1.45627
$497$	7.03474e6	1.27749
$498$	3.73294e6	0.674493
$499$	438319.	0.0788023	0.0394012	−	0.999223i	$-0.487455\pi$
$499$	438319.	0.0788023	0.0394012	+	0.999223i	$0.487455\pi$
$500$	−538856.	−0.0963935
$501$	1.41366e6	0.251624
$502$	4.34203e6	0.769013
$503$	461678.	0.0813615	0.0406807	−	0.999172i	$-0.487047\pi$
$503$	461678.	0.0813615	0.0406807	+	0.999172i	$0.487047\pi$
$504$	748362.	0.131231
$505$	−3.60473e6	−0.628991
$506$	1.46152e6	0.253762
$507$	4.66832e6	0.806567
$508$	−922080.	−0.158529
$509$	−5.63031e6	−0.963247	−0.481624	−	0.876378i	$-0.659953\pi$
$509$	−5.63031e6	−0.963247	−0.481624	+	0.876378i	$0.659953\pi$
$510$	801780.	0.136499
$511$	3.63060e6	0.615073
$512$	−8.39544e6	−1.41536
$513$	844507.	0.141680
$514$	−1.20127e6	−0.200555
$515$	−3.87259e6	−0.643403
$516$	1.39514e6	0.230672
$517$	2.17535e6	0.357933
$518$	8.60280e6	1.40869
$519$	−358674.	−0.0584496
$520$	−575658.	−0.0933590
$521$	−8.37689e6	−1.35204	−0.676019	−	0.736885i	$-0.736296\pi$
$521$	−8.37689e6	−1.35204	−0.676019	+	0.736885i	$0.736296\pi$
$522$	1.17597e7	1.88895
$523$	−623012.	−0.0995961	−0.0497981	−	0.998759i	$-0.515858\pi$
$523$	−623012.	−0.0995961	−0.0497981	+	0.998759i	$0.515858\pi$
$524$	−289343.	−0.0460346
$525$	540021.	0.0855092
$526$	−3.42234e6	−0.539335
$527$	6.57943e6	1.03196
$528$	577153.	0.0900962
$529$	−4.24202e6	−0.659073
$530$	4.99662e6	0.772656
$531$	7.11798e6	1.09552
$532$	−2.11592e6	−0.324130
$533$	9.82959e6	1.49871
$534$	−4.87843e6	−0.740332
$535$	4.51464e6	0.681929
$536$	−492993.	−0.0741188
$537$	−487058.	−0.0728861
$538$	1.27732e7	1.90258
$539$	−1.46148e6	−0.216681
$540$	2.01692e6	0.297649
$541$	1.90594e6	0.279973	0.139986	−	0.990153i	$-0.455294\pi$
$541$	1.90594e6	0.279973	0.139986	+	0.990153i	$0.455294\pi$
$542$	−2.01241e6	−0.294252
$543$	−709132.	−0.103211
$544$	6.42085e6	0.930240
$545$	3.59190e6	0.518004
$546$	8.00054e6	1.14852
$547$	−323474.	−0.0462244	−0.0231122	−	0.999733i	$-0.507357\pi$
$547$	−323474.	−0.0462244	−0.0231122	+	0.999733i	$0.507357\pi$
$548$	1.26989e7	1.80641
$549$	6.84526e6	0.969302
$550$	616642.	0.0869213
$551$	−2.39755e6	−0.336425
$552$	−152703.	−0.0213304
$553$	8.98323e6	1.24916
$554$	−1.09057e7	−1.50966
$555$	788979.	0.108726
$556$	1.54199e7	2.11540
$557$	−8.43516e6	−1.15201	−0.576004	−	0.817447i	$-0.695389\pi$
$557$	−8.43516e6	−1.15201	−0.576004	+	0.817447i	$0.695389\pi$
$558$	1.50581e7	2.04731
$559$	−9.03638e6	−1.22311
$560$	3.98651e6	0.537183
$561$	−475919.	−0.0638449
$562$	1.23218e7	1.64564
$563$	910051.	0.121003	0.0605013	−	0.998168i	$-0.480730\pi$
$563$	910051.	0.121003	0.0605013	+	0.998168i	$0.480730\pi$
$564$	−3.15201e6	−0.417244
$565$	3.79563e6	0.500221
$566$	−1.21960e6	−0.160021
$567$	6.94710e6	0.907498
$568$	−839292.	−0.109155
$569$	−8.69899e6	−1.12639	−0.563194	−	0.826325i	$-0.690428\pi$
$569$	−8.69899e6	−1.12639	−0.563194	+	0.826325i	$0.690428\pi$
$570$	−374117.	−0.0482303
$571$	6.72039e6	0.862589	0.431295	−	0.902211i	$-0.358057\pi$
$571$	6.72039e6	0.862589	0.431295	+	0.902211i	$0.358057\pi$
$572$	4.73869e6	0.605576
$573$	−838504.	−0.106689
$574$	1.19956e7	1.51964
$575$	925828.	0.116778
$576$	8.17536e6	1.02672
$577$	−1.00980e7	−1.26268	−0.631341	−	0.775506i	$-0.717495\pi$
$577$	−1.00980e7	−1.26268	−0.631341	+	0.775506i	$0.717495\pi$
$578$	6.69677e6	0.833769
$579$	536601.	0.0665204
$580$	−5.72602e6	−0.706778
$581$	−1.53049e7	−1.88100
$582$	5.23395e6	0.640505
$583$	−2.96588e6	−0.361395
$584$	−433156.	−0.0525547
$585$	−6.16495e6	−0.744800
$586$	1.31805e7	1.58558
$587$	8.32289e6	0.996963	0.498482	−	0.866900i	$-0.333891\pi$
$587$	8.32289e6	0.996963	0.498482	+	0.866900i	$0.333891\pi$
$588$	2.11764e6	0.252586
$589$	−3.07001e6	−0.364629
$590$	−6.68183e6	−0.790252
$591$	−4.41685e6	−0.520168
$592$	5.82434e6	0.683035
$593$	−6.96377e6	−0.813220	−0.406610	−	0.913602i	$-0.633289\pi$
$593$	−6.96377e6	−0.813220	−0.406610	+	0.913602i	$0.633289\pi$
$594$	−2.30807e6	−0.268400
$595$	−3.28726e6	−0.380664
$596$	−1.79132e7	−2.06565
$597$	2.79734e6	0.321225
$598$	1.37164e7	1.56850
$599$	8.74354e6	0.995681	0.497841	−	0.867269i	$-0.334126\pi$
$599$	8.74354e6	0.995681	0.497841	+	0.867269i	$0.334126\pi$
$600$	−64428.2	−0.00730631
$601$	−1.08593e7	−1.22636	−0.613178	−	0.789945i	$-0.710109\pi$
$601$	−1.08593e7	−1.22636	−0.613178	+	0.789945i	$0.710109\pi$
$602$	−1.10276e7	−1.24019
$603$	−5.27965e6	−0.591306
$604$	−5.58526e6	−0.622947
$605$	−366025.	−0.0406558
$606$	−5.97713e6	−0.661167
$607$	1.12260e7	1.23667	0.618336	−	0.785914i	$-0.287807\pi$
$607$	1.12260e7	1.23667	0.618336	+	0.785914i	$0.287807\pi$
$608$	−2.99602e6	−0.328689
$609$	5.73841e6	0.626972
$610$	−6.42582e6	−0.699204
$611$	2.04157e7	2.21238
$612$	−5.79398e6	−0.625315
$613$	1.49002e7	1.60155	0.800773	−	0.598968i	$-0.204422\pi$
$613$	1.49002e7	1.60155	0.800773	+	0.598968i	$0.204422\pi$
$614$	−2.05300e7	−2.19770
$615$	1.10014e6	0.117290
$616$	416992.	0.0442768
$617$	−3.12919e6	−0.330917	−0.165459	−	0.986217i	$-0.552910\pi$
$617$	−3.12919e6	−0.330917	−0.165459	+	0.986217i	$0.552910\pi$
$618$	−6.42127e6	−0.676317
$619$	9.45134e6	0.991441	0.495720	−	0.868482i	$-0.334904\pi$
$619$	9.45134e6	0.991441	0.495720	+	0.868482i	$0.334904\pi$
$620$	−7.33204e6	−0.766030
$621$	−3.46534e6	−0.360593
$622$	1.46958e7	1.52306
$623$	2.00013e7	2.06461
$624$	5.41659e6	0.556884
$625$	390625.	0.0400000
$626$	3.04636e6	0.310703
$627$	222067.	0.0225588
$628$	−854201.	−0.0864293
$629$	−4.80274e6	−0.484019
$630$	−7.52342e6	−0.755203
$631$	1.07514e6	0.107496	0.0537479	−	0.998555i	$-0.482883\pi$
$631$	1.07514e6	0.107496	0.0537479	+	0.998555i	$0.482883\pi$
$632$	−1.07176e6	−0.106735
$633$	77563.3	0.00769391
$634$	2.87374e7	2.83939
$635$	668430.	0.0657842
$636$	4.29747e6	0.421280
$637$	−1.37160e7	−1.33930
$638$	6.55259e6	0.637326
$639$	−8.98832e6	−0.870815
$640$	−1.03505e6	−0.0998874
$641$	−3.91245e6	−0.376100	−0.188050	−	0.982159i	$-0.560217\pi$
$641$	−3.91245e6	−0.376100	−0.188050	+	0.982159i	$0.560217\pi$
$642$	7.48589e6	0.716813
$643$	−1.39497e7	−1.33057	−0.665286	−	0.746589i	$-0.731690\pi$
$643$	−1.39497e7	−1.33057	−0.665286	+	0.746589i	$0.731690\pi$
$644$	8.68244e6	0.824949
$645$	−1.01136e6	−0.0957209
$646$	2.27735e6	0.214708
$647$	−1.24225e7	−1.16667	−0.583336	−	0.812231i	$-0.698253\pi$
$647$	−1.24225e7	−1.16667	−0.583336	+	0.812231i	$0.698253\pi$
$648$	−828836.	−0.0775409
$649$	3.96619e6	0.369625
$650$	5.78720e6	0.537260
$651$	7.34790e6	0.679534
$652$	−4.80074e6	−0.442272
$653$	−1.62989e7	−1.49581	−0.747904	−	0.663806i	$-0.768940\pi$
$653$	−1.62989e7	−1.49581	−0.747904	+	0.663806i	$0.768940\pi$
$654$	5.95586e6	0.544503
$655$	209749.	0.0191028
$656$	8.12136e6	0.736833
$657$	−4.63884e6	−0.419272
$658$	2.49143e7	2.24329
$659$	−1.10092e7	−0.987516	−0.493758	−	0.869599i	$-0.664377\pi$
$659$	−1.10092e7	−0.987516	−0.493758	+	0.869599i	$0.664377\pi$
$660$	530359.	0.0473926
$661$	−1.34045e7	−1.19329	−0.596645	−	0.802505i	$-0.703500\pi$
$661$	−1.34045e7	−1.19329	−0.596645	+	0.802505i	$0.703500\pi$
$662$	5.32876e6	0.472586
$663$	−4.46651e6	−0.394625
$664$	1.82597e6	0.160722
$665$	1.53386e6	0.134503
$666$	−1.09918e7	−0.960250
$667$	9.83809e6	0.856241
$668$	9.58973e6	0.831505
$669$	−1.87270e6	−0.161772
$670$	4.95615e6	0.426537
$671$	3.81423e6	0.327039
$672$	7.17080e6	0.612554
$673$	−1.00237e7	−0.853084	−0.426542	−	0.904468i	$-0.640268\pi$
$673$	−1.00237e7	−0.853084	−0.426542	+	0.904468i	$0.640268\pi$
$674$	−487704.	−0.0413529
$675$	−1.46210e6	−0.123514
$676$	3.16680e7	2.66535
$677$	−5.11103e6	−0.428585	−0.214292	−	0.976770i	$-0.568745\pi$
$677$	−5.11103e6	−0.428585	−0.214292	+	0.976770i	$0.568745\pi$
$678$	6.29366e6	0.525810
$679$	−2.14590e7	−1.78622
$680$	392193.	0.0325257
$681$	−1.87908e6	−0.155266
$682$	8.39045e6	0.690756
$683$	1.39622e7	1.14525	0.572626	−	0.819817i	$-0.305925\pi$
$683$	1.39622e7	1.14525	0.572626	+	0.819817i	$0.305925\pi$
$684$	2.70351e6	0.220947
$685$	−9.20564e6	−0.749597
$686$	6.55306e6	0.531660
$687$	−783802.	−0.0633599
$688$	−7.46599e6	−0.601335
$689$	−2.78349e7	−2.23378
$690$	1.53515e6	0.122752
$691$	−1.46954e7	−1.17081	−0.585405	−	0.810741i	$-0.699064\pi$
$691$	−1.46954e7	−1.17081	−0.585405	+	0.810741i	$0.699064\pi$
$692$	−2.43310e6	−0.193150
$693$	4.46574e6	0.353232
$694$	−1.00883e7	−0.795097
$695$	−1.11781e7	−0.877821
$696$	−684631.	−0.0535714
$697$	−6.69685e6	−0.522142
$698$	2.10737e7	1.63720
$699$	6.70899e6	0.519355
$700$	3.66329e6	0.282570
$701$	3.51221e6	0.269951	0.134976	−	0.990849i	$-0.456904\pi$
$701$	3.51221e6	0.269951	0.134976	+	0.990849i	$0.456904\pi$
$702$	−2.16613e7	−1.65898
$703$	2.24099e6	0.171022
$704$	4.55536e6	0.346411
$705$	2.28494e6	0.173142
$706$	−2.52113e6	−0.190363
$707$	2.45059e7	1.84384
$708$	−5.74689e6	−0.430873
$709$	−1.39266e7	−1.04047	−0.520235	−	0.854023i	$-0.674156\pi$
$709$	−1.39266e7	−1.04047	−0.520235	+	0.854023i	$0.674156\pi$
$710$	8.43756e6	0.628161
$711$	−1.14779e7	−0.851508
$712$	−2.38629e6	−0.176410
$713$	1.25975e7	0.928024
$714$	−5.45072e6	−0.400137
$715$	−3.43515e6	−0.251293
$716$	−3.30401e6	−0.240857
$717$	−2.73198e6	−0.198463
$718$	3.15857e7	2.28654
$719$	−7.87767e6	−0.568297	−0.284149	−	0.958780i	$-0.591711\pi$
$719$	−7.87767e6	−0.568297	−0.284149	+	0.958780i	$0.591711\pi$
$720$	−5.09357e6	−0.366177
$721$	2.63269e7	1.88609
$722$	−1.06263e6	−0.0758646
$723$	1.73626e6	0.123529
$724$	−4.81047e6	−0.341068
$725$	4.15088e6	0.293289
$726$	−606919.	−0.0427355
$727$	−2.61320e7	−1.83374	−0.916869	−	0.399189i	$-0.869292\pi$
$727$	−2.61320e7	−1.83374	−0.916869	+	0.399189i	$0.869292\pi$
$728$	3.91348e6	0.273675
$729$	−5.98636e6	−0.417199
$730$	4.35460e6	0.302441
$731$	6.15644e6	0.426124
$732$	−5.52670e6	−0.381231
$733$	2.42788e7	1.66904	0.834521	−	0.550976i	$-0.185745\pi$
$733$	2.42788e7	1.66904	0.834521	+	0.550976i	$0.185745\pi$
$734$	−9.05418e6	−0.620310
$735$	−1.53511e6	−0.104814
$736$	1.22938e7	0.836552
$737$	−2.94186e6	−0.199505
$738$	−1.53268e7	−1.03588
$739$	311400.	0.0209753	0.0104876	−	0.999945i	$-0.496662\pi$
$739$	311400.	0.0209753	0.0104876	+	0.999945i	$0.496662\pi$
$740$	5.35212e6	0.359291
$741$	2.08411e6	0.139436
$742$	−3.39684e7	−2.26498
$743$	7.97137e6	0.529738	0.264869	−	0.964284i	$-0.414671\pi$
$743$	7.97137e6	0.529738	0.264869	+	0.964284i	$0.414671\pi$
$744$	−876655.	−0.0580626
$745$	1.29855e7	0.857175
$746$	−1.30469e7	−0.858343
$747$	1.95551e7	1.28221
$748$	−3.22845e6	−0.210979
$749$	−3.06918e7	−1.99902
$750$	647709.	0.0420462
$751$	1.71898e7	1.11217	0.556085	−	0.831125i	$-0.312303\pi$
$751$	1.71898e7	1.11217	0.556085	+	0.831125i	$0.312303\pi$
$752$	1.68677e7	1.08771
$753$	−2.70718e6	−0.173992
$754$	6.14962e7	3.93931
$755$	4.04884e6	0.258502
$756$	−1.37116e7	−0.872535
$757$	1.78534e6	0.113235	0.0566177	−	0.998396i	$-0.481968\pi$
$757$	1.78534e6	0.113235	0.0566177	+	0.998396i	$0.481968\pi$
$758$	−1.14899e6	−0.0726346
$759$	−911230.	−0.0574148
$760$	−183000.	−0.0114926
$761$	1.55230e7	0.971659	0.485829	−	0.874054i	$-0.338518\pi$
$761$	1.55230e7	0.971659	0.485829	+	0.874054i	$0.338518\pi$
$762$	1.10835e6	0.0691494
$763$	−2.44187e7	−1.51849
$764$	−5.68808e6	−0.352559
$765$	4.20015e6	0.259484
$766$	−9.13040e6	−0.562235
$767$	3.72228e7	2.28465
$768$	4.40838e6	0.269697
$769$	−1.13166e7	−0.690084	−0.345042	−	0.938587i	$-0.612135\pi$
$769$	−1.13166e7	−0.690084	−0.345042	+	0.938587i	$0.612135\pi$
$770$	−4.19210e6	−0.254803
$771$	748974.	0.0453765
$772$	3.64009e6	0.219821
$773$	−2.47761e7	−1.49137	−0.745684	−	0.666300i	$-0.767877\pi$
$773$	−2.47761e7	−1.49137	−0.745684	+	0.666300i	$0.767877\pi$
$774$	1.40900e7	0.845392
$775$	5.31511e6	0.317876
$776$	2.56020e6	0.152623
$777$	−5.36370e6	−0.318722
$778$	3.30646e6	0.195846
$779$	3.12480e6	0.184492
$780$	4.97743e6	0.292933
$781$	−5.00835e6	−0.293810
$782$	−9.34488e6	−0.546458
$783$	−1.55366e7	−0.905632
$784$	−1.13324e7	−0.658462
$785$	619224.	0.0358652
$786$	347792.	0.0200800
$787$	−2.21341e7	−1.27387	−0.636936	−	0.770917i	$-0.719798\pi$
$787$	−2.21341e7	−1.27387	−0.636936	+	0.770917i	$0.719798\pi$
$788$	−2.99621e7	−1.71893
$789$	2.13377e6	0.122027
$790$	1.07746e7	0.614234
$791$	−2.58037e7	−1.46636
$792$	−532793.	−0.0301818
$793$	3.57966e7	2.02143
$794$	1.99056e7	1.12053
$795$	−3.11531e6	−0.174817
$796$	1.89761e7	1.06151
$797$	−1.70173e7	−0.948955	−0.474477	−	0.880268i	$-0.657363\pi$
$797$	−1.70173e7	−0.948955	−0.474477	+	0.880268i	$0.657363\pi$
$798$	2.54335e6	0.141383
$799$	−1.39091e7	−0.770782
$800$	5.18701e6	0.286544
$801$	−2.55558e7	−1.40737
$802$	1.93107e7	1.06014
$803$	−2.58479e6	−0.141461
$804$	4.26267e6	0.232563
$805$	−6.29404e6	−0.342326
$806$	7.87446e7	4.26956
$807$	−7.96387e6	−0.430467
$808$	−2.92373e6	−0.157546
$809$	1.15150e7	0.618577	0.309288	−	0.950968i	$-0.399909\pi$
$809$	1.15150e7	0.618577	0.309288	+	0.950968i	$0.399909\pi$
$810$	8.33244e6	0.446231
$811$	2.19777e6	0.117336	0.0586679	−	0.998278i	$-0.481315\pi$
$811$	2.19777e6	0.117336	0.0586679	+	0.998278i	$0.481315\pi$
$812$	3.89271e7	2.07187
$813$	1.25471e6	0.0665757
$814$	−6.12472e6	−0.323985
$815$	3.48013e6	0.183528
$816$	−3.69030e6	−0.194015
$817$	−2.87264e6	−0.150566
$818$	3.14801e7	1.64495
$819$	4.19110e7	2.18333
$820$	7.46290e6	0.387590
$821$	2.02077e7	1.04630	0.523152	−	0.852239i	$-0.324756\pi$
$821$	2.02077e7	1.04630	0.523152	+	0.852239i	$0.324756\pi$
$822$	−1.52642e7	−0.787942
$823$	3.43940e7	1.77004	0.885021	−	0.465551i	$-0.154144\pi$
$823$	3.43940e7	1.77004	0.885021	+	0.465551i	$0.154144\pi$
$824$	−3.14098e6	−0.161156
$825$	−384466.	−0.0196663
$826$	4.54249e7	2.31656
$827$	−2.63575e7	−1.34011	−0.670055	−	0.742312i	$-0.733729\pi$
$827$	−2.63575e7	−1.34011	−0.670055	+	0.742312i	$0.733729\pi$
$828$	−1.10936e7	−0.562336
$829$	−2.14313e7	−1.08309	−0.541543	−	0.840673i	$-0.682160\pi$
$829$	−2.14313e7	−1.08309	−0.541543	+	0.840673i	$0.682160\pi$
$830$	−1.83569e7	−0.924918
$831$	6.79950e6	0.341566
$832$	4.27522e7	2.14116
$833$	9.34465e6	0.466606
$834$	−1.85348e7	−0.922726
$835$	−6.95174e6	−0.345046
$836$	1.50642e6	0.0745469
$837$	−1.98943e7	−0.981555
$838$	4.65568e7	2.29020
$839$	−1.08900e7	−0.534102	−0.267051	−	0.963682i	$-0.586049\pi$
$839$	−1.08900e7	−0.534102	−0.267051	+	0.963682i	$0.586049\pi$
$840$	438001.	0.0214179
$841$	2.35972e7	1.15046
$842$	−9.48641e6	−0.461128
$843$	−7.68244e6	−0.372332
$844$	526158.	0.0254250
$845$	−2.29566e7	−1.10603
$846$	−3.18332e7	−1.52916
$847$	2.48834e6	0.119179
$848$	−2.29976e7	−1.09823
$849$	760400.	0.0362054
$850$	−3.94279e6	−0.187178
$851$	−9.19568e6	−0.435271
$852$	7.25695e6	0.342496
$853$	−3.95075e7	−1.85912	−0.929558	−	0.368676i	$-0.879811\pi$
$853$	−3.95075e7	−1.85912	−0.929558	+	0.368676i	$0.879811\pi$
$854$	4.36845e7	2.04966
$855$	−1.95982e6	−0.0916855
$856$	3.66174e6	0.170806
$857$	−1.09851e6	−0.0510921	−0.0255460	−	0.999674i	$-0.508132\pi$
$857$	−1.09851e6	−0.0510921	−0.0255460	+	0.999674i	$0.508132\pi$
$858$	−5.69594e6	−0.264148
$859$	−1.29245e7	−0.597626	−0.298813	−	0.954312i	$-0.596591\pi$
$859$	−1.29245e7	−0.597626	−0.298813	+	0.954312i	$0.596591\pi$
$860$	−6.86067e6	−0.316315
$861$	−7.47904e6	−0.343825
$862$	−3.72194e7	−1.70608
$863$	1.25385e7	0.573085	0.286542	−	0.958068i	$-0.407494\pi$
$863$	1.25385e7	0.573085	0.286542	+	0.958068i	$0.407494\pi$
$864$	−1.94148e7	−0.884807
$865$	1.76380e6	0.0801508
$866$	−3.67638e7	−1.66581
$867$	−4.17532e6	−0.188644
$868$	4.98453e7	2.24556
$869$	−6.39557e6	−0.287296
$870$	6.88272e6	0.308292
$871$	−2.76094e7	−1.23314
$872$	2.91332e6	0.129747
$873$	2.74182e7	1.21760
$874$	4.36039e6	0.193084
$875$	−2.65558e6	−0.117257
$876$	3.74529e6	0.164902
$877$	−1.33156e7	−0.584606	−0.292303	−	0.956326i	$-0.594422\pi$
$877$	−1.33156e7	−0.584606	−0.292303	+	0.956326i	$0.594422\pi$
$878$	5.00504e7	2.19115
$879$	−8.21781e6	−0.358743
$880$	−2.83817e6	−0.123547
$881$	2.26552e7	0.983397	0.491698	−	0.870766i	$-0.336376\pi$
$881$	2.26552e7	0.983397	0.491698	+	0.870766i	$0.336376\pi$
$882$	2.13867e7	0.925705
$883$	−6.26479e6	−0.270399	−0.135199	−	0.990818i	$-0.543167\pi$
$883$	−6.26479e6	−0.270399	−0.135199	+	0.990818i	$0.543167\pi$
$884$	−3.02990e7	−1.30406
$885$	4.16601e6	0.178798
$886$	1.04302e7	0.446386
$887$	−5.59125e6	−0.238616	−0.119308	−	0.992857i	$-0.538068\pi$
$887$	−5.59125e6	−0.238616	−0.119308	+	0.992857i	$0.538068\pi$
$888$	639926.	0.0272331
$889$	−4.54417e6	−0.192841
$890$	2.39899e7	1.01520
$891$	−4.94595e6	−0.208716
$892$	−1.27036e7	−0.534584
$893$	6.49008e6	0.272346
$894$	2.15318e7	0.901024
$895$	2.39513e6	0.0999473
$896$	7.03654e6	0.292812
$897$	−8.55191e6	−0.354880
$898$	3.41531e7	1.41332
$899$	5.64797e7	2.33074
$900$	−4.68060e6	−0.192617
$901$	1.89637e7	0.778237
$902$	−8.54020e6	−0.349504
$903$	6.87551e6	0.280599
$904$	3.07856e6	0.125293
$905$	3.48718e6	0.141532
$906$	6.71352e6	0.271725
$907$	1.56969e7	0.633571	0.316785	−	0.948497i	$-0.397397\pi$
$907$	1.56969e7	0.633571	0.316785	+	0.948497i	$0.397397\pi$
$908$	−1.27469e7	−0.513086
$909$	−3.13113e7	−1.25687
$910$	−3.93430e7	−1.57494
$911$	−3.68246e7	−1.47008	−0.735042	−	0.678022i	$-0.762837\pi$
$911$	−3.68246e7	−1.47008	−0.735042	+	0.678022i	$0.762837\pi$
$912$	1.72192e6	0.0685529
$913$	1.08962e7	0.432613
$914$	5.68966e7	2.25279
$915$	4.00639e6	0.158198
$916$	−5.31700e6	−0.209377
$917$	−1.42593e6	−0.0559984
$918$	1.47577e7	0.577979
$919$	−2.43690e7	−0.951807	−0.475903	−	0.879498i	$-0.657879\pi$
$919$	−2.43690e7	−0.951807	−0.475903	+	0.879498i	$0.657879\pi$
$920$	750921.	0.0292499
$921$	1.28001e7	0.497238
$922$	3.25749e6	0.126199
$923$	−4.70035e7	−1.81604
$924$	−3.60553e6	−0.138928
$925$	−3.87984e6	−0.149094
$926$	−3.24126e6	−0.124219
$927$	−3.36380e7	−1.28567
$928$	5.51185e7	2.10101
$929$	−2.24096e7	−0.851913	−0.425956	−	0.904744i	$-0.640062\pi$
$929$	−2.24096e7	−0.851913	−0.425956	+	0.904744i	$0.640062\pi$
$930$	8.81317e6	0.334137
$931$	−4.36028e6	−0.164870
$932$	4.55111e7	1.71624
$933$	−9.16256e6	−0.344598
$934$	−6.55877e7	−2.46011
$935$	2.34035e6	0.0875492
$936$	−5.00027e6	−0.186554
$937$	−3.37812e7	−1.25697	−0.628487	−	0.777820i	$-0.716325\pi$
$937$	−3.37812e7	−1.25697	−0.628487	+	0.777820i	$0.716325\pi$
$938$	−3.36933e7	−1.25036
$939$	−1.89935e6	−0.0702978
$940$	1.55001e7	0.572158
$941$	1.70647e7	0.628240	0.314120	−	0.949383i	$-0.398291\pi$
$941$	1.70647e7	0.628240	0.314120	+	0.949383i	$0.398291\pi$
$942$	1.02676e6	0.0376999
$943$	−1.28223e7	−0.469555
$944$	3.07540e7	1.12324
$945$	9.93973e6	0.362072
$946$	7.85103e6	0.285233
$947$	1.49189e7	0.540581	0.270291	−	0.962779i	$-0.412880\pi$
$947$	1.49189e7	0.540581	0.270291	+	0.962779i	$0.412880\pi$
$948$	9.26698e6	0.334902
$949$	−2.42583e7	−0.874370
$950$	1.83973e6	0.0661372
$951$	−1.79173e7	−0.642423
$952$	−2.66623e6	−0.0953467
$953$	−3.79742e7	−1.35443	−0.677214	−	0.735786i	$-0.736813\pi$
$953$	−3.79742e7	−1.35443	−0.677214	+	0.735786i	$0.736813\pi$
$954$	4.34015e7	1.54395
$955$	4.12337e6	0.146300
$956$	−1.85327e7	−0.655833
$957$	−4.08543e6	−0.144198
$958$	1.35758e7	0.477915
$959$	6.25825e7	2.19739
$960$	4.78487e6	0.167568
$961$	4.36919e7	1.52613
$962$	−5.74806e7	−2.00255
$963$	3.92150e7	1.36266
$964$	1.17781e7	0.408210
$965$	−2.63876e6	−0.0912181
$966$	−1.04364e7	−0.359837
$967$	3.10291e7	1.06710	0.533548	−	0.845770i	$-0.320858\pi$
$967$	3.10291e7	1.06710	0.533548	+	0.845770i	$0.320858\pi$
$968$	−296876.	−0.0101832
$969$	−1.41989e6	−0.0485787
$970$	−2.57382e7	−0.878311
$971$	−2.40250e7	−0.817739	−0.408870	−	0.912593i	$-0.634077\pi$
$971$	−2.40250e7	−0.817739	−0.408870	+	0.912593i	$0.634077\pi$
$972$	2.67710e7	0.908864
$973$	7.59918e7	2.57327
$974$	−3.87244e7	−1.30794
$975$	−3.60822e6	−0.121557
$976$	2.95757e7	0.993825
$977$	−2.27379e7	−0.762104	−0.381052	−	0.924554i	$-0.624438\pi$
$977$	−2.27379e7	−0.762104	−0.381052	+	0.924554i	$0.624438\pi$
$978$	5.77053e6	0.192916
$979$	−1.42399e7	−0.474842
$980$	−1.04136e7	−0.346366
$981$	3.11999e7	1.03510
$982$	−4.97663e7	−1.64686
$983$	−4.75940e7	−1.57097	−0.785486	−	0.618879i	$-0.787587\pi$
$983$	−4.75940e7	−1.57097	−0.785486	+	0.618879i	$0.787587\pi$
$984$	892300.	0.0293781
$985$	2.17200e7	0.713296
$986$	−4.18971e7	−1.37243
$987$	−1.55337e7	−0.507553
$988$	1.41378e7	0.460774
$989$	1.17876e7	0.383207
$990$	5.35626e6	0.173690
$991$	−163666.	−0.00529388	−0.00264694	−	0.999996i	$-0.500843\pi$
$991$	−163666.	−0.00529388	−0.00264694	+	0.999996i	$0.500843\pi$
$992$	7.05780e7	2.27714
$993$	−3.32239e6	−0.106925
$994$	−5.73609e7	−1.84141
$995$	−1.37560e7	−0.440490
$996$	−1.57883e7	−0.504298
$997$	−1.38053e7	−0.439853	−0.219926	−	0.975516i	$-0.570582\pi$
$997$	−1.38053e7	−0.439853	−0.219926	+	0.975516i	$0.570582\pi$
$998$	−3.57403e6	−0.113588
$999$	1.45221e7	0.460379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.7	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-8.15394 q^{2} +5.08384 q^{3} +34.4868 q^{4} -25.0000 q^{5} -41.4534 q^{6} +169.957 q^{7} -20.2770 q^{8} -217.155 q^{9} +O(q^{10})\)	\(q-8.15394 q^{2} +5.08384 q^{3} +34.4868 q^{4} -25.0000 q^{5} -41.4534 q^{6} +169.957 q^{7} -20.2770 q^{8} -217.155 q^{9} +203.849 q^{10} -121.000 q^{11} +175.325 q^{12} -1135.59 q^{13} -1385.82 q^{14} -127.096 q^{15} -938.239 q^{16} +773.670 q^{17} +1770.67 q^{18} -361.000 q^{19} -862.169 q^{20} +864.034 q^{21} +986.627 q^{22} +1481.33 q^{23} -103.085 q^{24} +625.000 q^{25} +9259.51 q^{26} -2339.35 q^{27} +5861.26 q^{28} +6641.41 q^{29} +1036.33 q^{30} +8504.18 q^{31} +8299.21 q^{32} -615.145 q^{33} -6308.46 q^{34} -4248.92 q^{35} -7488.96 q^{36} -6207.74 q^{37} +2943.57 q^{38} -5773.15 q^{39} +506.925 q^{40} -8655.95 q^{41} -7045.29 q^{42} +7957.45 q^{43} -4172.90 q^{44} +5428.86 q^{45} -12078.6 q^{46} -17978.1 q^{47} -4769.86 q^{48} +12078.3 q^{49} -5096.21 q^{50} +3933.22 q^{51} -39162.7 q^{52} +24511.4 q^{53} +19075.0 q^{54} +3025.00 q^{55} -3446.22 q^{56} -1835.27 q^{57} -54153.7 q^{58} -32778.4 q^{59} -4383.13 q^{60} -31522.5 q^{61} -69342.6 q^{62} -36906.9 q^{63} -37647.6 q^{64} +28389.7 q^{65} +5015.86 q^{66} +24312.9 q^{67} +26681.4 q^{68} +7530.83 q^{69} +34645.5 q^{70} +41391.3 q^{71} +4403.24 q^{72} +21361.9 q^{73} +50617.6 q^{74} +3177.40 q^{75} -12449.7 q^{76} -20564.8 q^{77} +47073.9 q^{78} +52855.9 q^{79} +23456.0 q^{80} +40875.6 q^{81} +70580.1 q^{82} -90051.5 q^{83} +29797.8 q^{84} -19341.7 q^{85} -64884.6 q^{86} +33763.9 q^{87} +2453.52 q^{88} +117685. q^{89} -44266.6 q^{90} -193001. q^{91} +51086.1 q^{92} +43233.9 q^{93} +146592. q^{94} +9025.00 q^{95} +42191.9 q^{96} -126261. q^{97} -98486.1 q^{98} +26275.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

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