LMFDB - Embedded newform 1045.6.a.c.1.4

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			1.4
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)

$f(q)$	$=$	$q-10.2487 q^{2} +19.1450 q^{3} +73.0349 q^{4} -25.0000 q^{5} -196.210 q^{6} -226.466 q^{7} -420.553 q^{8} +123.531 q^{9} +O(q^{10})$	\(q-10.2487 q^{2} +19.1450 q^{3} +73.0349 q^{4} -25.0000 q^{5} -196.210 q^{6} -226.466 q^{7} -420.553 q^{8} +123.531 q^{9} +256.216 q^{10} -121.000 q^{11} +1398.25 q^{12} +1029.61 q^{13} +2320.98 q^{14} -478.625 q^{15} +1972.98 q^{16} +514.131 q^{17} -1266.02 q^{18} -361.000 q^{19} -1825.87 q^{20} -4335.70 q^{21} +1240.09 q^{22} +1808.72 q^{23} -8051.48 q^{24} +625.000 q^{25} -10552.1 q^{26} -2287.24 q^{27} -16540.0 q^{28} +935.441 q^{29} +4905.26 q^{30} -4403.24 q^{31} -6762.74 q^{32} -2316.54 q^{33} -5269.15 q^{34} +5661.66 q^{35} +9022.06 q^{36} -12196.3 q^{37} +3699.76 q^{38} +19711.8 q^{39} +10513.8 q^{40} +7895.89 q^{41} +44435.1 q^{42} +1087.67 q^{43} -8837.23 q^{44} -3088.27 q^{45} -18536.9 q^{46} -19730.2 q^{47} +37772.8 q^{48} +34480.1 q^{49} -6405.41 q^{50} +9843.03 q^{51} +75197.2 q^{52} +14101.3 q^{53} +23441.1 q^{54} +3025.00 q^{55} +95241.1 q^{56} -6911.34 q^{57} -9587.01 q^{58} +6033.65 q^{59} -34956.3 q^{60} +49608.6 q^{61} +45127.3 q^{62} -27975.6 q^{63} +6173.47 q^{64} -25740.2 q^{65} +23741.5 q^{66} +18528.3 q^{67} +37549.5 q^{68} +34627.9 q^{69} -58024.4 q^{70} -12554.9 q^{71} -51951.2 q^{72} -17938.4 q^{73} +124995. q^{74} +11965.6 q^{75} -26365.6 q^{76} +27402.4 q^{77} -202020. q^{78} +70167.0 q^{79} -49324.6 q^{80} -73807.1 q^{81} -80922.3 q^{82} -49179.8 q^{83} -316658. q^{84} -12853.3 q^{85} -11147.2 q^{86} +17909.0 q^{87} +50886.9 q^{88} -81454.5 q^{89} +31650.6 q^{90} -233171. q^{91} +132100. q^{92} -84300.0 q^{93} +202208. q^{94} +9025.00 q^{95} -129473. q^{96} +112553. q^{97} -353374. q^{98} -14947.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.2487	−1.81172	−0.905862	−	0.423574i	$-0.860775\pi$
$2$	−10.2487	−1.81172	−0.905862	+	0.423574i	$0.860775\pi$
$3$	19.1450	1.22815	0.614076	−	0.789247i	$-0.289529\pi$
$3$	19.1450	1.22815	0.614076	+	0.789247i	$0.289529\pi$
$4$	73.0349	2.28234
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−196.210	−2.22507
$7$	−226.466	−1.74686	−0.873432	−	0.486947i	$-0.838110\pi$
$7$	−226.466	−1.74686	−0.873432	+	0.486947i	$0.838110\pi$
$8$	−420.553	−2.32325
$9$	123.531	0.508357
$10$	256.216	0.810227
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	1398.25	2.80306
$13$	1029.61	1.68971	0.844856	−	0.534993i	$-0.179686\pi$
$13$	1029.61	1.68971	0.844856	+	0.534993i	$0.179686\pi$
$14$	2320.98	3.16483
$15$	−478.625	−0.549246
$16$	1972.98	1.92674
$17$	514.131	0.431471	0.215735	−	0.976452i	$-0.430785\pi$
$17$	514.131	0.431471	0.215735	+	0.976452i	$0.430785\pi$
$18$	−1266.02	−0.921002
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−1825.87	−1.02069
$21$	−4335.70	−2.14541
$22$	1240.09	0.546255
$23$	1808.72	0.712938	0.356469	−	0.934307i	$-0.383981\pi$
$23$	1808.72	0.712938	0.356469	+	0.934307i	$0.383981\pi$
$24$	−8051.48	−2.85330
$25$	625.000	0.200000
$26$	−10552.1	−3.06129
$27$	−2287.24	−0.603812
$28$	−16540.0	−3.98694
$29$	935.441	0.206548	0.103274	−	0.994653i	$-0.467068\pi$
$29$	935.441	0.206548	0.103274	+	0.994653i	$0.467068\pi$
$30$	4905.26	0.995082
$31$	−4403.24	−0.822939	−0.411470	−	0.911423i	$-0.634984\pi$
$31$	−4403.24	−0.822939	−0.411470	+	0.911423i	$0.634984\pi$
$32$	−6762.74	−1.16747
$33$	−2316.54	−0.370302
$34$	−5269.15	−0.781706
$35$	5661.66	0.781221
$36$	9022.06	1.16024
$37$	−12196.3	−1.46461	−0.732306	−	0.680975i	$-0.761556\pi$
$37$	−12196.3	−1.46461	−0.732306	+	0.680975i	$0.761556\pi$
$38$	3699.76	0.415638
$39$	19711.8	2.07522
$40$	10513.8	1.03899
$41$	7895.89	0.733570	0.366785	−	0.930306i	$-0.380458\pi$
$41$	7895.89	0.733570	0.366785	+	0.930306i	$0.380458\pi$
$42$	44435.1	3.88690
$43$	1087.67	0.0897072	0.0448536	−	0.998994i	$-0.485718\pi$
$43$	1087.67	0.0897072	0.0448536	+	0.998994i	$0.485718\pi$
$44$	−8837.23	−0.688152
$45$	−3088.27	−0.227344
$46$	−18536.9	−1.29165
$47$	−19730.2	−1.30283	−0.651415	−	0.758722i	$-0.725824\pi$
$47$	−19730.2	−1.30283	−0.651415	+	0.758722i	$0.725824\pi$
$48$	37772.8	2.36633
$49$	34480.1	2.05153
$50$	−6405.41	−0.362345
$51$	9843.03	0.529912
$52$	75197.2	3.85650
$53$	14101.3	0.689556	0.344778	−	0.938684i	$-0.387954\pi$
$53$	14101.3	0.689556	0.344778	+	0.938684i	$0.387954\pi$
$54$	23441.1	1.09394
$55$	3025.00	0.134840
$56$	95241.1	4.05840
$57$	−6911.34	−0.281757
$58$	−9587.01	−0.374208
$59$	6033.65	0.225658	0.112829	−	0.993614i	$-0.464009\pi$
$59$	6033.65	0.225658	0.112829	+	0.993614i	$0.464009\pi$
$60$	−34956.3	−1.25357
$61$	49608.6	1.70700	0.853498	−	0.521096i	$-0.174476\pi$
$61$	49608.6	1.70700	0.853498	+	0.521096i	$0.174476\pi$
$62$	45127.3	1.49094
$63$	−27975.6	−0.888030
$64$	6173.47	0.188399
$65$	−25740.2	−0.755663
$66$	23741.5	0.670884
$67$	18528.3	0.504252	0.252126	−	0.967694i	$-0.418870\pi$
$67$	18528.3	0.504252	0.252126	+	0.967694i	$0.418870\pi$
$68$	37549.5	0.984764
$69$	34627.9	0.875596
$70$	−58024.4	−1.41536
$71$	−12554.9	−0.295575	−0.147787	−	0.989019i	$-0.547215\pi$
$71$	−12554.9	−0.295575	−0.147787	+	0.989019i	$0.547215\pi$
$72$	−51951.2	−1.18104
$73$	−17938.4	−0.393982	−0.196991	−	0.980405i	$-0.563117\pi$
$73$	−17938.4	−0.393982	−0.196991	+	0.980405i	$0.563117\pi$
$74$	124995.	2.65347
$75$	11965.6	0.245630
$76$	−26365.6	−0.523605
$77$	27402.4	0.526699
$78$	−202020.	−3.75973
$79$	70167.0	1.26493	0.632463	−	0.774590i	$-0.282044\pi$
$79$	70167.0	1.26493	0.632463	+	0.774590i	$0.282044\pi$
$80$	−49324.6	−0.861665
$81$	−73807.1	−1.24993
$82$	−80922.3	−1.32903
$83$	−49179.8	−0.783595	−0.391797	−	0.920051i	$-0.628147\pi$
$83$	−49179.8	−0.783595	−0.391797	+	0.920051i	$0.628147\pi$
$84$	−316658.	−4.89657
$85$	−12853.3	−0.192960
$86$	−11147.2	−0.162525
$87$	17909.0	0.253673
$88$	50886.9	0.700486
$89$	−81454.5	−1.09003	−0.545017	−	0.838425i	$-0.683477\pi$
$89$	−81454.5	−1.09003	−0.545017	+	0.838425i	$0.683477\pi$
$90$	31650.6	0.411885
$91$	−233171.	−2.95170
$92$	132100.	1.62717
$93$	−84300.0	−1.01069
$94$	202208.	2.36037
$95$	9025.00	0.102598
$96$	−129473.	−1.43384
$97$	112553.	1.21459	0.607295	−	0.794477i	$-0.292255\pi$
$97$	112553.	1.21459	0.607295	+	0.794477i	$0.292255\pi$
$98$	−353374.	−3.71681
$99$	−14947.2	−0.153275
$100$	45646.8	0.456468
$101$	62513.0	0.609772	0.304886	−	0.952389i	$-0.401382\pi$
$101$	62513.0	0.609772	0.304886	+	0.952389i	$0.401382\pi$
$102$	−100878.	−0.960053
$103$	88050.5	0.817784	0.408892	−	0.912583i	$-0.365915\pi$
$103$	88050.5	0.817784	0.408892	+	0.912583i	$0.365915\pi$
$104$	−433004.	−3.92562
$105$	108392.	0.959458
$106$	−144519.	−1.24929
$107$	190010.	1.60441	0.802206	−	0.597047i	$-0.203659\pi$
$107$	190010.	1.60441	0.802206	+	0.597047i	$0.203659\pi$
$108$	−167048.	−1.37811
$109$	−83036.9	−0.669429	−0.334715	−	0.942320i	$-0.608640\pi$
$109$	−83036.9	−0.669429	−0.334715	+	0.942320i	$0.608640\pi$
$110$	−31002.2	−0.244293
$111$	−233498.	−1.79877
$112$	−446815.	−3.36575
$113$	34745.1	0.255975	0.127987	−	0.991776i	$-0.459148\pi$
$113$	34745.1	0.255975	0.127987	+	0.991776i	$0.459148\pi$
$114$	70832.0	0.510466
$115$	−45218.0	−0.318835
$116$	68319.9	0.471414
$117$	127188.	0.858977
$118$	−61836.8	−0.408829
$119$	−116433.	−0.753720
$120$	201287.	1.27604
$121$	14641.0	0.0909091
$122$	−508422.	−3.09261
$123$	151167.	0.900935
$124$	−321590.	−1.87823
$125$	−15625.0	−0.0894427
$126$	286712.	1.60886
$127$	133078.	0.732144	0.366072	−	0.930587i	$-0.380702\pi$
$127$	133078.	0.732144	0.366072	+	0.930587i	$0.380702\pi$
$128$	153138.	0.826147
$129$	20823.5	0.110174
$130$	263802.	1.36905
$131$	−212215.	−1.08043	−0.540216	−	0.841526i	$-0.681658\pi$
$131$	−212215.	−1.08043	−0.540216	+	0.841526i	$0.681658\pi$
$132$	−169189.	−0.845155
$133$	81754.4	0.400758
$134$	−189890.	−0.913565
$135$	57180.9	0.270033
$136$	−216219.	−1.00241
$137$	−128221.	−0.583659	−0.291829	−	0.956470i	$-0.594264\pi$
$137$	−128221.	−0.583659	−0.291829	+	0.956470i	$0.594264\pi$
$138$	−354890.	−1.58634
$139$	239525.	1.05151	0.525755	−	0.850636i	$-0.323783\pi$
$139$	239525.	1.05151	0.525755	+	0.850636i	$0.323783\pi$
$140$	413499.	1.78301
$141$	−377735.	−1.60007
$142$	128671.	0.535499
$143$	−124582.	−0.509468
$144$	243724.	0.979473
$145$	−23386.0	−0.0923712
$146$	183844.	0.713786
$147$	660121.	2.51959
$148$	−890754.	−3.34275
$149$	−54788.1	−0.202172	−0.101086	−	0.994878i	$-0.532232\pi$
$149$	−54788.1	−0.202172	−0.101086	+	0.994878i	$0.532232\pi$
$150$	−122632.	−0.445014
$151$	−66399.5	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$151$	−66399.5	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$152$	151820.	0.532990
$153$	63511.0	0.219341
$154$	−280838.	−0.954233
$155$	110081.	0.368030
$156$	1.43965e6	4.73637
$157$	228128.	0.738634	0.369317	−	0.929304i	$-0.379592\pi$
$157$	228128.	0.738634	0.369317	+	0.929304i	$0.379592\pi$
$158$	−719118.	−2.29170
$159$	269969.	0.846880
$160$	169068.	0.522111
$161$	−409614.	−1.24540
$162$	756424.	2.26453
$163$	15686.4	0.0462439	0.0231220	−	0.999733i	$-0.492639\pi$
$163$	15686.4	0.0462439	0.0231220	+	0.999733i	$0.492639\pi$
$164$	576676.	1.67426
$165$	57913.6	0.165604
$166$	504027.	1.41966
$167$	537033.	1.49008	0.745040	−	0.667020i	$-0.232430\pi$
$167$	537033.	1.49008	0.745040	+	0.667020i	$0.232430\pi$
$168$	1.82339e6	4.98433
$169$	688797.	1.85513
$170$	131729.	0.349589
$171$	−44594.6	−0.116625
$172$	79438.2	0.204743
$173$	−242455.	−0.615909	−0.307954	−	0.951401i	$-0.599644\pi$
$173$	−242455.	−0.615909	−0.307954	+	0.951401i	$0.599644\pi$
$174$	−183543.	−0.459585
$175$	−141542.	−0.349373
$176$	−238731.	−0.580934
$177$	115514.	0.277142
$178$	834799.	1.97484
$179$	−330379.	−0.770689	−0.385345	−	0.922773i	$-0.625917\pi$
$179$	−330379.	−0.770689	−0.385345	+	0.922773i	$0.625917\pi$
$180$	−225552.	−0.518877
$181$	−813572.	−1.84586	−0.922931	−	0.384965i	$-0.874214\pi$
$181$	−813572.	−1.84586	−0.922931	+	0.384965i	$0.874214\pi$
$182$	2.38969e6	5.34766
$183$	949757.	2.09645
$184$	−760662.	−1.65633
$185$	304907.	0.654995
$186$	863961.	1.83110
$187$	−62209.8	−0.130093
$188$	−1.44100e6	−2.97350
$189$	517983.	1.05478
$190$	−92494.1	−0.185879
$191$	−514741.	−1.02095	−0.510476	−	0.859892i	$-0.670531\pi$
$191$	−514741.	−1.02095	−0.510476	+	0.859892i	$0.670531\pi$
$192$	118191.	0.231383
$193$	−368038.	−0.711213	−0.355607	−	0.934636i	$-0.615726\pi$
$193$	−368038.	−0.711213	−0.355607	+	0.934636i	$0.615726\pi$
$194$	−1.15352e6	−2.20050
$195$	−492795.	−0.928068
$196$	2.51825e6	4.68229
$197$	−329760.	−0.605386	−0.302693	−	0.953088i	$-0.597886\pi$
$197$	−329760.	−0.605386	−0.302693	+	0.953088i	$0.597886\pi$
$198$	153189.	0.277693
$199$	−770627.	−1.37947	−0.689734	−	0.724063i	$-0.742272\pi$
$199$	−770627.	−1.37947	−0.689734	+	0.724063i	$0.742272\pi$
$200$	−262846.	−0.464650
$201$	354723.	0.619298
$202$	−640675.	−1.10474
$203$	−211846.	−0.360811
$204$	718885.	1.20944
$205$	−197397.	−0.328062
$206$	−902399.	−1.48160
$207$	223432.	0.362427
$208$	2.03140e6	3.25564
$209$	43681.0	0.0691714
$210$	−1.11088e6	−1.73827
$211$	−851423.	−1.31656	−0.658278	−	0.752775i	$-0.728715\pi$
$211$	−851423.	−1.31656	−0.658278	+	0.752775i	$0.728715\pi$
$212$	1.02989e6	1.57380
$213$	−240363.	−0.363011
$214$	−1.94734e6	−2.90675
$215$	−27191.8	−0.0401183
$216$	961904.	1.40281
$217$	997186.	1.43756
$218$	851016.	1.21282
$219$	−343430.	−0.483869
$220$	220931.	0.307751
$221$	529353.	0.729062
$222$	2.39304e6	3.25887
$223$	1.04967e6	1.41348	0.706741	−	0.707473i	$-0.250165\pi$
$223$	1.04967e6	1.41348	0.706741	+	0.707473i	$0.250165\pi$
$224$	1.53153e6	2.03942
$225$	77206.7	0.101671
$226$	−356090.	−0.463755
$227$	−40872.2	−0.0526458	−0.0263229	−	0.999653i	$-0.508380\pi$
$227$	−40872.2	−0.0526458	−0.0263229	+	0.999653i	$0.508380\pi$
$228$	−504769.	−0.643067
$229$	55609.4	0.0700744	0.0350372	−	0.999386i	$-0.488845\pi$
$229$	55609.4	0.0700744	0.0350372	+	0.999386i	$0.488845\pi$
$230$	463424.	0.577642
$231$	524620.	0.646866
$232$	−393402.	−0.479863
$233$	−1.48513e6	−1.79215	−0.896073	−	0.443907i	$-0.853592\pi$
$233$	−1.48513e6	−1.79215	−0.896073	+	0.443907i	$0.853592\pi$
$234$	−1.30351e6	−1.55623
$235$	493256.	0.582643
$236$	440667.	0.515028
$237$	1.34335e6	1.55352
$238$	1.19329e6	1.36553
$239$	−1.39515e6	−1.57989	−0.789945	−	0.613178i	$-0.789891\pi$
$239$	−1.39515e6	−1.57989	−0.789945	+	0.613178i	$0.789891\pi$
$240$	−944319.	−1.05826
$241$	774428.	0.858892	0.429446	−	0.903093i	$-0.358709\pi$
$241$	774428.	0.858892	0.429446	+	0.903093i	$0.358709\pi$
$242$	−150051.	−0.164702
$243$	−857238.	−0.931292
$244$	3.62316e6	3.89595
$245$	−862002.	−0.917472
$246$	−1.54926e6	−1.63225
$247$	−371688.	−0.387647
$248$	1.85179e6	1.91189
$249$	−941547.	−0.962374
$250$	160135.	0.162045
$251$	−795269.	−0.796764	−0.398382	−	0.917220i	$-0.630428\pi$
$251$	−795269.	−0.796764	−0.398382	+	0.917220i	$0.630428\pi$
$252$	−2.04319e6	−2.02679
$253$	−218855.	−0.214959
$254$	−1.36387e6	−1.32644
$255$	−246076.	−0.236984
$256$	−1.76701e6	−1.68515
$257$	240787.	0.227405	0.113702	−	0.993515i	$-0.463729\pi$
$257$	240787.	0.227405	0.113702	+	0.993515i	$0.463729\pi$
$258$	−213413.	−0.199605
$259$	2.76205e6	2.55848
$260$	−1.87993e6	−1.72468
$261$	115556.	0.105000
$262$	2.17492e6	1.95744
$263$	−1.42334e6	−1.26888	−0.634440	−	0.772972i	$-0.718769\pi$
$263$	−1.42334e6	−1.26888	−0.634440	+	0.772972i	$0.718769\pi$
$264$	974229.	0.860303
$265$	−352533.	−0.308379
$266$	−837873.	−0.726062
$267$	−1.55945e6	−1.33873
$268$	1.35321e6	1.15088
$269$	184238.	0.155238	0.0776189	−	0.996983i	$-0.475268\pi$
$269$	184238.	0.155238	0.0776189	+	0.996983i	$0.475268\pi$
$270$	−586028.	−0.489225
$271$	1.16733e6	0.965544	0.482772	−	0.875746i	$-0.339630\pi$
$271$	1.16733e6	0.965544	0.482772	+	0.875746i	$0.339630\pi$
$272$	1.01437e6	0.831333
$273$	−4.46406e6	−3.62513
$274$	1.31410e6	1.05743
$275$	−75625.0	−0.0603023
$276$	2.52905e6	1.99841
$277$	1.06504e6	0.833999	0.416999	−	0.908907i	$-0.363082\pi$
$277$	1.06504e6	0.833999	0.416999	+	0.908907i	$0.363082\pi$
$278$	−2.45481e6	−1.90505
$279$	−543935.	−0.418347
$280$	−2.38103e6	−1.81497
$281$	−1.36798e6	−1.03351	−0.516754	−	0.856134i	$-0.672860\pi$
$281$	−1.36798e6	−1.03351	−0.516754	+	0.856134i	$0.672860\pi$
$282$	3.87128e6	2.89889
$283$	−1.46688e6	−1.08875	−0.544375	−	0.838842i	$-0.683233\pi$
$283$	−1.46688e6	−1.08875	−0.544375	+	0.838842i	$0.683233\pi$
$284$	−916946.	−0.674602
$285$	172784.	0.126006
$286$	1.27680e6	0.923014
$287$	−1.78815e6	−1.28145
$288$	−835406.	−0.593494
$289$	−1.15553e6	−0.813833
$290$	239675.	0.167351
$291$	2.15484e6	1.49170
$292$	−1.31013e6	−0.899201
$293$	2.43745e6	1.65870	0.829348	−	0.558732i	$-0.188712\pi$
$293$	2.43745e6	1.65870	0.829348	+	0.558732i	$0.188712\pi$
$294$	−6.76535e6	−4.56480
$295$	−150841.	−0.100917
$296$	5.12918e6	3.40266
$297$	276756.	0.182056
$298$	561505.	0.366280
$299$	1.86227e6	1.20466
$300$	873908.	0.560612
$301$	−246322.	−0.156706
$302$	680505.	0.429353
$303$	1.19681e6	0.748892
$304$	−712247.	−0.442025
$305$	−1.24022e6	−0.763392
$306$	−650902.	−0.397386
$307$	−1.04123e6	−0.630520	−0.315260	−	0.949005i	$-0.602092\pi$
$307$	−1.04123e6	−0.630520	−0.315260	+	0.949005i	$0.602092\pi$
$308$	2.00134e6	1.20211
$309$	1.68573e6	1.00436
$310$	−1.12818e6	−0.666768
$311$	−1.42216e6	−0.833773	−0.416887	−	0.908959i	$-0.636879\pi$
$311$	−1.42216e6	−0.833773	−0.416887	+	0.908959i	$0.636879\pi$
$312$	−8.28986e6	−4.82126
$313$	−2.34585e6	−1.35344	−0.676719	−	0.736241i	$-0.736599\pi$
$313$	−2.34585e6	−1.35344	−0.676719	+	0.736241i	$0.736599\pi$
$314$	−2.33800e6	−1.33820
$315$	699389.	0.397139
$316$	5.12464e6	2.88699
$317$	−2.42848e6	−1.35734	−0.678668	−	0.734445i	$-0.737442\pi$
$317$	−2.42848e6	−1.35734	−0.678668	+	0.734445i	$0.737442\pi$
$318$	−2.76682e6	−1.53431
$319$	−113188.	−0.0622766
$320$	−154337.	−0.0842548
$321$	3.63773e6	1.97046
$322$	4.19800e6	2.25633
$323$	−185601.	−0.0989862
$324$	−5.39050e6	−2.85277
$325$	643504.	0.337943
$326$	−160765.	−0.0837812
$327$	−1.58974e6	−0.822161
$328$	−3.32064e6	−1.70427
$329$	4.46824e6	2.27586
$330$	−593537.	−0.300029
$331$	1.13183e6	0.567819	0.283910	−	0.958851i	$-0.408368\pi$
$331$	1.13183e6	0.567819	0.283910	+	0.958851i	$0.408368\pi$
$332$	−3.59184e6	−1.78843
$333$	−1.50661e6	−0.744546
$334$	−5.50386e6	−2.69961
$335$	−463206.	−0.225508
$336$	−8.55426e6	−4.13366
$337$	2.31726e6	1.11148	0.555738	−	0.831358i	$-0.312436\pi$
$337$	2.31726e6	1.11148	0.555738	+	0.831358i	$0.312436\pi$
$338$	−7.05924e6	−3.36098
$339$	665194.	0.314376
$340$	−938738.	−0.440400
$341$	532792.	0.248126
$342$	457035.	0.211292
$343$	−4.00236e6	−1.83688
$344$	−457424.	−0.208412
$345$	−865698.	−0.391578
$346$	2.48484e6	1.11586
$347$	2.16415e6	0.964859	0.482429	−	0.875935i	$-0.339754\pi$
$347$	2.16415e6	0.964859	0.482429	+	0.875935i	$0.339754\pi$
$348$	1.30798e6	0.578968
$349$	−4.43186e6	−1.94770	−0.973850	−	0.227192i	$-0.927046\pi$
$349$	−4.43186e6	−1.94770	−0.973850	+	0.227192i	$0.927046\pi$
$350$	1.45061e6	0.632967
$351$	−2.35496e6	−1.02027
$352$	818291.	0.352007
$353$	2.07054e6	0.884395	0.442197	−	0.896918i	$-0.354199\pi$
$353$	2.07054e6	0.884395	0.442197	+	0.896918i	$0.354199\pi$
$354$	−1.18387e6	−0.502105
$355$	313872.	0.132185
$356$	−5.94902e6	−2.48783
$357$	−2.22912e6	−0.925683
$358$	3.38594e6	1.39628
$359$	−4.42853e6	−1.81352	−0.906762	−	0.421643i	$-0.861453\pi$
$359$	−4.42853e6	−1.81352	−0.906762	+	0.421643i	$0.861453\pi$
$360$	1.29878e6	0.528177
$361$	130321.	0.0526316
$362$	8.33802e6	3.34419
$363$	280302.	0.111650
$364$	−1.70297e7	−6.73678
$365$	448459.	0.176194
$366$	−9.73373e6	−3.79819
$367$	−4.16415e6	−1.61384	−0.806921	−	0.590660i	$-0.798868\pi$
$367$	−4.16415e6	−1.61384	−0.806921	+	0.590660i	$0.798868\pi$
$368$	3.56857e6	1.37365
$369$	975385.	0.372915
$370$	−3.12488e6	−1.18667
$371$	−3.19347e6	−1.20456
$372$	−6.15684e6	−2.30675
$373$	−679140.	−0.252748	−0.126374	−	0.991983i	$-0.540334\pi$
$373$	−679140.	−0.252748	−0.126374	+	0.991983i	$0.540334\pi$
$374$	637567.	0.235693
$375$	−299141.	−0.109849
$376$	8.29761e6	3.02680
$377$	963136.	0.349007
$378$	−5.30863e6	−1.91096
$379$	−3.28895e6	−1.17614	−0.588070	−	0.808810i	$-0.700112\pi$
$379$	−3.28895e6	−1.17614	−0.588070	+	0.808810i	$0.700112\pi$
$380$	659140.	0.234163
$381$	2.54777e6	0.899184
$382$	5.27540e6	1.84968
$383$	−2.16707e6	−0.754876	−0.377438	−	0.926035i	$-0.623195\pi$
$383$	−2.16707e6	−0.754876	−0.377438	+	0.926035i	$0.623195\pi$
$384$	2.93182e6	1.01463
$385$	−685061.	−0.235547
$386$	3.77190e6	1.28852
$387$	134361.	0.0456033
$388$	8.22034e6	2.77211
$389$	−932848.	−0.312562	−0.156281	−	0.987713i	$-0.549951\pi$
$389$	−932848.	−0.312562	−0.156281	+	0.987713i	$0.549951\pi$
$390$	5.05049e6	1.68140
$391$	929919.	0.307612
$392$	−1.45007e7	−4.76621
$393$	−4.06285e6	−1.32693
$394$	3.37960e6	1.09679
$395$	−1.75418e6	−0.565692
$396$	−1.09167e6	−0.349827
$397$	2.98835e6	0.951601	0.475801	−	0.879553i	$-0.342158\pi$
$397$	2.98835e6	0.951601	0.475801	+	0.879553i	$0.342158\pi$
$398$	7.89789e6	2.49921
$399$	1.56519e6	0.492192
$400$	1.23311e6	0.385348
$401$	5.42725e6	1.68546	0.842730	−	0.538336i	$-0.180947\pi$
$401$	5.42725e6	1.68546	0.842730	+	0.538336i	$0.180947\pi$
$402$	−3.63544e6	−1.12200
$403$	−4.53360e6	−1.39053
$404$	4.56564e6	1.39171
$405$	1.84518e6	0.558986
$406$	2.17114e6	0.653691
$407$	1.47575e6	0.441597
$408$	−4.13952e6	−1.23112
$409$	−1.11747e6	−0.330316	−0.165158	−	0.986267i	$-0.552813\pi$
$409$	−1.11747e6	−0.330316	−0.165158	+	0.986267i	$0.552813\pi$
$410$	2.02306e6	0.594358
$411$	−2.45480e6	−0.716822
$412$	6.43076e6	1.86646
$413$	−1.36642e6	−0.394193
$414$	−2.28988e6	−0.656617
$415$	1.22950e6	0.350434
$416$	−6.96296e6	−1.97270
$417$	4.58570e6	1.29141
$418$	−447672.	−0.125320
$419$	−1.68412e6	−0.468640	−0.234320	−	0.972160i	$-0.575286\pi$
$419$	−1.68412e6	−0.468640	−0.234320	+	0.972160i	$0.575286\pi$
$420$	7.91644e6	2.18981
$421$	−121881.	−0.0335143	−0.0167572	−	0.999860i	$-0.505334\pi$
$421$	−121881.	−0.0335143	−0.0167572	+	0.999860i	$0.505334\pi$
$422$	8.72594e6	2.38523
$423$	−2.43729e6	−0.662302
$424$	−5.93035e6	−1.60201
$425$	321332.	0.0862942
$426$	2.46340e6	0.657675
$427$	−1.12347e7	−2.98189
$428$	1.38773e7	3.66182
$429$	−2.38513e6	−0.625704
$430$	278680.	0.0726832
$431$	−3.38224e6	−0.877024	−0.438512	−	0.898725i	$-0.644494\pi$
$431$	−3.38224e6	−0.877024	−0.438512	+	0.898725i	$0.644494\pi$
$432$	−4.51268e6	−1.16339
$433$	6.30799e6	1.61685	0.808427	−	0.588596i	$-0.200319\pi$
$433$	6.30799e6	1.61685	0.808427	+	0.588596i	$0.200319\pi$
$434$	−1.02198e7	−2.60447
$435$	−447725.	−0.113446
$436$	−6.06459e6	−1.52787
$437$	−652948.	−0.163559
$438$	3.51970e6	0.876637
$439$	−7.20788e6	−1.78503	−0.892517	−	0.451014i	$-0.851063\pi$
$439$	−7.20788e6	−1.78503	−0.892517	+	0.451014i	$0.851063\pi$
$440$	−1.27217e6	−0.313267
$441$	4.25935e6	1.04291
$442$	−5.42515e6	−1.32086
$443$	−2.62397e6	−0.635256	−0.317628	−	0.948215i	$-0.602886\pi$
$443$	−2.62397e6	−0.635256	−0.317628	+	0.948215i	$0.602886\pi$
$444$	−1.70535e7	−4.10540
$445$	2.03636e6	0.487478
$446$	−1.07577e7	−2.56084
$447$	−1.04892e6	−0.248298
$448$	−1.39808e6	−0.329108
$449$	−3.32084e6	−0.777379	−0.388689	−	0.921369i	$-0.627072\pi$
$449$	−3.32084e6	−0.777379	−0.388689	+	0.921369i	$0.627072\pi$
$450$	−791265.	−0.184200
$451$	−955403.	−0.221180
$452$	2.53760e6	0.584222
$453$	−1.27122e6	−0.291055
$454$	418885.	0.0953796
$455$	5.82928e6	1.32004
$456$	2.90658e6	0.654592
$457$	4.24435e6	0.950651	0.475326	−	0.879810i	$-0.342330\pi$
$457$	4.24435e6	0.950651	0.475326	+	0.879810i	$0.342330\pi$
$458$	−569922.	−0.126955
$459$	−1.17594e6	−0.260527
$460$	−3.30249e6	−0.727691
$461$	−1.16115e6	−0.254470	−0.127235	−	0.991873i	$-0.540610\pi$
$461$	−1.16115e6	−0.254470	−0.127235	+	0.991873i	$0.540610\pi$
$462$	−5.37665e6	−1.17194
$463$	4.18158e6	0.906543	0.453272	−	0.891372i	$-0.350257\pi$
$463$	4.18158e6	0.906543	0.453272	+	0.891372i	$0.350257\pi$
$464$	1.84561e6	0.397965
$465$	2.10750e6	0.451996
$466$	1.52205e7	3.24687
$467$	−5.70494e6	−1.21048	−0.605242	−	0.796041i	$-0.706924\pi$
$467$	−5.70494e6	−1.21048	−0.605242	+	0.796041i	$0.706924\pi$
$468$	9.28917e6	1.96048
$469$	−4.19603e6	−0.880859
$470$	−5.05521e6	−1.05559
$471$	4.36751e6	0.907154
$472$	−2.53747e6	−0.524259
$473$	−131608.	−0.0270477
$474$	−1.37675e7	−2.81455
$475$	−225625.	−0.0458831
$476$	−8.50371e6	−1.72025
$477$	1.74195e6	0.350541
$478$	1.42984e7	2.86232
$479$	9.18940e6	1.82999	0.914994	−	0.403467i	$-0.132195\pi$
$479$	9.18940e6	1.82999	0.914994	+	0.403467i	$0.132195\pi$
$480$	3.23681e6	0.641231
$481$	−1.25574e7	−2.47477
$482$	−7.93685e6	−1.55607
$483$	−7.84206e6	−1.52955
$484$	1.06930e6	0.207486
$485$	−2.81384e6	−0.543181
$486$	8.78554e6	1.68724
$487$	9.00944e6	1.72138	0.860688	−	0.509133i	$-0.170034\pi$
$487$	9.00944e6	1.72138	0.860688	+	0.509133i	$0.170034\pi$
$488$	−2.08631e7	−3.96578
$489$	300316.	0.0567946
$490$	8.83436e6	1.66221
$491$	−8.85530e6	−1.65768	−0.828838	−	0.559489i	$-0.810998\pi$
$491$	−8.85530e6	−1.65768	−0.828838	+	0.559489i	$0.810998\pi$
$492$	1.10405e7	2.05624
$493$	480939.	0.0891195
$494$	3.80930e6	0.702309
$495$	373681.	0.0685468
$496$	−8.68751e6	−1.58559
$497$	2.84326e6	0.516328
$498$	9.64959e6	1.74355
$499$	−1.44653e6	−0.260062	−0.130031	−	0.991510i	$-0.541508\pi$
$499$	−1.44653e6	−0.260062	−0.130031	+	0.991510i	$0.541508\pi$
$500$	−1.14117e6	−0.204139
$501$	1.02815e7	1.83004
$502$	8.15044e6	1.44352
$503$	−3.15842e6	−0.556608	−0.278304	−	0.960493i	$-0.589772\pi$
$503$	−3.15842e6	−0.556608	−0.278304	+	0.960493i	$0.589772\pi$
$504$	1.17652e7	2.06311
$505$	−1.56283e6	−0.272698
$506$	2.24297e6	0.389446
$507$	1.31870e7	2.27838
$508$	9.71933e6	1.67100
$509$	139247.	0.0238227	0.0119113	−	0.999929i	$-0.496208\pi$
$509$	139247.	0.0238227	0.0119113	+	0.999929i	$0.496208\pi$
$510$	2.52195e6	0.429349
$511$	4.06244e6	0.688232
$512$	1.32090e7	2.22688
$513$	825693.	0.138524
$514$	−2.46774e6	−0.411995
$515$	−2.20126e6	−0.365724
$516$	1.52084e6	0.251455
$517$	2.38736e6	0.392818
$518$	−2.83073e7	−4.63525
$519$	−4.64180e6	−0.756429
$520$	1.08251e7	1.75559
$521$	620841.	0.100204	0.0501021	−	0.998744i	$-0.484045\pi$
$521$	620841.	0.100204	0.0501021	+	0.998744i	$0.484045\pi$
$522$	−1.18429e6	−0.190231
$523$	−3.39334e6	−0.542467	−0.271234	−	0.962514i	$-0.587432\pi$
$523$	−3.39334e6	−0.542467	−0.271234	+	0.962514i	$0.587432\pi$
$524$	−1.54991e7	−2.46592
$525$	−2.70981e6	−0.429083
$526$	1.45874e7	2.29886
$527$	−2.26384e6	−0.355074
$528$	−4.57050e6	−0.713476
$529$	−3.16488e6	−0.491720
$530$	3.61299e6	0.558697
$531$	745342.	0.114715
$532$	5.97093e6	0.914666
$533$	8.12966e6	1.23952
$534$	1.59822e7	2.42540
$535$	−4.75024e6	−0.717515
$536$	−7.79211e6	−1.17150
$537$	−6.32510e6	−0.946524
$538$	−1.88819e6	−0.281248
$539$	−4.17209e6	−0.618560
$540$	4.17621e6	0.616308
$541$	−3.38009e6	−0.496518	−0.248259	−	0.968694i	$-0.579858\pi$
$541$	−3.38009e6	−0.496518	−0.248259	+	0.968694i	$0.579858\pi$
$542$	−1.19636e7	−1.74930
$543$	−1.55758e7	−2.26700
$544$	−3.47693e6	−0.503731
$545$	2.07592e6	0.299378
$546$	4.57507e7	6.56774
$547$	−8.22914e6	−1.17594	−0.587971	−	0.808882i	$-0.700073\pi$
$547$	−8.22914e6	−1.17594	−0.587971	+	0.808882i	$0.700073\pi$
$548$	−9.36464e6	−1.33211
$549$	6.12819e6	0.867764
$550$	775055.	0.109251
$551$	−337694.	−0.0473854
$552$	−1.45629e7	−2.03423
$553$	−1.58905e7	−2.20965
$554$	−1.09152e7	−1.51098
$555$	5.83744e6	0.804433
$556$	1.74937e7	2.39991
$557$	2.10502e6	0.287487	0.143743	−	0.989615i	$-0.454086\pi$
$557$	2.10502e6	0.287487	0.143743	+	0.989615i	$0.454086\pi$
$558$	5.57460e6	0.757929
$559$	1.11988e6	0.151579
$560$	1.11704e7	1.50521
$561$	−1.19101e6	−0.159774
$562$	1.40200e7	1.87243
$563$	−3.58774e6	−0.477035	−0.238518	−	0.971138i	$-0.576661\pi$
$563$	−3.58774e6	−0.477035	−0.238518	+	0.971138i	$0.576661\pi$
$564$	−2.75879e7	−3.65191
$565$	−868627.	−0.114475
$566$	1.50335e7	1.97251
$567$	1.67148e7	2.18346
$568$	5.28000e6	0.686693
$569$	1.19720e7	1.55020	0.775098	−	0.631841i	$-0.217700\pi$
$569$	1.19720e7	1.55020	0.775098	+	0.631841i	$0.217700\pi$
$570$	−1.77080e6	−0.228288
$571$	4.06731e6	0.522056	0.261028	−	0.965331i	$-0.415939\pi$
$571$	4.06731e6	0.522056	0.261028	+	0.965331i	$0.415939\pi$
$572$	−9.09887e6	−1.16278
$573$	−9.85472e6	−1.25388
$574$	1.83262e7	2.32163
$575$	1.13045e6	0.142588
$576$	762614.	0.0957742
$577$	2.85923e6	0.357528	0.178764	−	0.983892i	$-0.442790\pi$
$577$	2.85923e6	0.357528	0.178764	+	0.983892i	$0.442790\pi$
$578$	1.18426e7	1.47444
$579$	−7.04609e6	−0.873478
$580$	−1.70800e6	−0.210823
$581$	1.11376e7	1.36883
$582$	−2.20842e7	−2.70255
$583$	−1.70626e6	−0.207909
$584$	7.54403e6	0.915317
$585$	−3.17970e6	−0.384146
$586$	−2.49806e7	−3.00510
$587$	3.72894e6	0.446673	0.223336	−	0.974741i	$-0.428305\pi$
$587$	3.72894e6	0.446673	0.223336	+	0.974741i	$0.428305\pi$
$588$	4.82119e7	5.75057
$589$	1.58957e6	0.188795
$590$	1.54592e6	0.182834
$591$	−6.31325e6	−0.743506
$592$	−2.40630e7	−2.82193
$593$	−4.70537e6	−0.549486	−0.274743	−	0.961518i	$-0.588593\pi$
$593$	−4.70537e6	−0.549486	−0.274743	+	0.961518i	$0.588593\pi$
$594$	−2.83637e6	−0.329836
$595$	2.91084e6	0.337074
$596$	−4.00145e6	−0.461425
$597$	−1.47536e7	−1.69420
$598$	−1.90858e7	−2.18251
$599$	6.46469e6	0.736174	0.368087	−	0.929791i	$-0.380013\pi$
$599$	6.46469e6	0.736174	0.368087	+	0.929791i	$0.380013\pi$
$600$	−5.03218e6	−0.570660
$601$	−1.50554e6	−0.170022	−0.0850110	−	0.996380i	$-0.527093\pi$
$601$	−1.50554e6	−0.170022	−0.0850110	+	0.996380i	$0.527093\pi$
$602$	2.52446e6	0.283908
$603$	2.28881e6	0.256340
$604$	−4.84948e6	−0.540882
$605$	−366025.	−0.0406558
$606$	−1.22657e7	−1.35679
$607$	1.16453e7	1.28286	0.641430	−	0.767181i	$-0.278341\pi$
$607$	1.16453e7	1.28286	0.641430	+	0.767181i	$0.278341\pi$
$608$	2.44135e6	0.267837
$609$	−4.05579e6	−0.443131
$610$	1.27105e7	1.38306
$611$	−2.03144e7	−2.20141
$612$	4.63852e6	0.500612
$613$	1.29279e7	1.38956	0.694780	−	0.719222i	$-0.255502\pi$
$613$	1.29279e7	1.38956	0.694780	+	0.719222i	$0.255502\pi$
$614$	1.06712e7	1.14233
$615$	−3.77917e6	−0.402911
$616$	−1.15242e7	−1.22365
$617$	−1.84878e7	−1.95512	−0.977559	−	0.210662i	$-0.932438\pi$
$617$	−1.84878e7	−1.95512	−0.977559	+	0.210662i	$0.932438\pi$
$618$	−1.72764e7	−1.81963
$619$	1.31694e7	1.38147	0.690734	−	0.723109i	$-0.257288\pi$
$619$	1.31694e7	1.38147	0.690734	+	0.723109i	$0.257288\pi$
$620$	8.03975e6	0.839970
$621$	−4.13697e6	−0.430481
$622$	1.45752e7	1.51057
$623$	1.84467e7	1.90414
$624$	3.88911e7	3.99842
$625$	390625.	0.0400000
$626$	2.40418e7	2.45206
$627$	836272.	0.0849530
$628$	1.66613e7	1.68581
$629$	−6.27048e6	−0.631938
$630$	−7.16780e6	−0.719506
$631$	5.42106e6	0.542014	0.271007	−	0.962577i	$-0.412643\pi$
$631$	5.42106e6	0.542014	0.271007	+	0.962577i	$0.412643\pi$
$632$	−2.95089e7	−2.93874
$633$	−1.63005e7	−1.61693
$634$	2.48887e7	2.45912
$635$	−3.32695e6	−0.327425
$636$	1.97172e7	1.93287
$637$	3.55009e7	3.46650
$638$	1.16003e6	0.112828
$639$	−1.55092e6	−0.150257
$640$	−3.82844e6	−0.369464
$641$	−1.27442e7	−1.22508	−0.612542	−	0.790438i	$-0.709853\pi$
$641$	−1.27442e7	−1.22508	−0.612542	+	0.790438i	$0.709853\pi$
$642$	−3.72819e7	−3.56993
$643$	−1.90118e7	−1.81341	−0.906704	−	0.421767i	$-0.861410\pi$
$643$	−1.90118e7	−1.81341	−0.906704	+	0.421767i	$0.861410\pi$
$644$	−2.99162e7	−2.84244
$645$	−520588.	−0.0492713
$646$	1.90216e6	0.179336
$647$	−9.68650e6	−0.909717	−0.454858	−	0.890564i	$-0.650310\pi$
$647$	−9.68650e6	−0.909717	−0.454858	+	0.890564i	$0.650310\pi$
$648$	3.10398e7	2.90390
$649$	−730072.	−0.0680384
$650$	−6.59505e6	−0.612259
$651$	1.90911e7	1.76555
$652$	1.14566e6	0.105544
$653$	1.76050e7	1.61567	0.807834	−	0.589410i	$-0.200640\pi$
$653$	1.76050e7	1.61567	0.807834	+	0.589410i	$0.200640\pi$
$654$	1.62927e7	1.48953
$655$	5.30537e6	0.483184
$656$	1.55785e7	1.41340
$657$	−2.21594e6	−0.200283
$658$	−4.57934e7	−4.12324
$659$	−7.89694e6	−0.708346	−0.354173	−	0.935180i	$-0.615238\pi$
$659$	−7.89694e6	−0.708346	−0.354173	+	0.935180i	$0.615238\pi$
$660$	4.22972e6	0.377965
$661$	−1.41356e7	−1.25838	−0.629188	−	0.777253i	$-0.716612\pi$
$661$	−1.41356e7	−1.25838	−0.629188	+	0.777253i	$0.716612\pi$
$662$	−1.15997e7	−1.02873
$663$	1.01345e7	0.895399
$664$	2.06827e7	1.82049
$665$	−2.04386e6	−0.179224
$666$	1.54408e7	1.34891
$667$	1.69195e6	0.147256
$668$	3.92222e7	3.40087
$669$	2.00959e7	1.73597
$670$	4.74724e6	0.408559
$671$	−6.00264e6	−0.514679
$672$	2.93212e7	2.50472
$673$	1.66554e7	1.41748	0.708742	−	0.705467i	$-0.249263\pi$
$673$	1.66554e7	1.41748	0.708742	+	0.705467i	$0.249263\pi$
$674$	−2.37488e7	−2.01369
$675$	−1.42952e6	−0.120762
$676$	5.03062e7	4.23404
$677$	−2.03737e7	−1.70844	−0.854218	−	0.519915i	$-0.825964\pi$
$677$	−2.03737e7	−1.70844	−0.854218	+	0.519915i	$0.825964\pi$
$678$	−6.81735e6	−0.569562
$679$	−2.54896e7	−2.12172
$680$	5.40548e6	0.448293
$681$	−782498.	−0.0646570
$682$	−5.46040e6	−0.449535
$683$	−1.80662e7	−1.48189	−0.740944	−	0.671567i	$-0.765621\pi$
$683$	−1.80662e7	−1.48189	−0.740944	+	0.671567i	$0.765621\pi$
$684$	−3.25696e6	−0.266178
$685$	3.20553e6	0.261020
$686$	4.10188e7	3.32792
$687$	1.06464e6	0.0860620
$688$	2.14596e6	0.172843
$689$	1.45188e7	1.16515
$690$	8.87224e6	0.709432
$691$	−1.45077e7	−1.15586	−0.577928	−	0.816088i	$-0.696139\pi$
$691$	−1.45077e7	−1.15586	−0.577928	+	0.816088i	$0.696139\pi$
$692$	−1.77077e7	−1.40571
$693$	3.38504e6	0.267751
$694$	−2.21796e7	−1.74806
$695$	−5.98812e6	−0.470250
$696$	−7.53169e6	−0.589344
$697$	4.05952e6	0.316514
$698$	4.54206e7	3.52869
$699$	−2.84327e7	−2.20103
$700$	−1.03375e7	−0.797388
$701$	−1.95381e7	−1.50172	−0.750858	−	0.660464i	$-0.770360\pi$
$701$	−1.95381e7	−1.50172	−0.750858	+	0.660464i	$0.770360\pi$
$702$	2.41351e7	1.84845
$703$	4.40285e6	0.336005
$704$	−746990.	−0.0568046
$705$	9.44338e6	0.715574
$706$	−2.12202e7	−1.60228
$707$	−1.41571e7	−1.06519
$708$	8.43657e6	0.632533
$709$	2.18959e7	1.63587	0.817934	−	0.575312i	$-0.195120\pi$
$709$	2.18959e7	1.63587	0.817934	+	0.575312i	$0.195120\pi$
$710$	−3.21677e6	−0.239483
$711$	8.66779e6	0.643034
$712$	3.42559e7	2.53242
$713$	−7.96422e6	−0.586705
$714$	2.28455e7	1.67708
$715$	3.11456e6	0.227841
$716$	−2.41292e7	−1.75898
$717$	−2.67102e7	−1.94034
$718$	4.53864e7	3.28560
$719$	3.46163e6	0.249723	0.124861	−	0.992174i	$-0.460151\pi$
$719$	3.46163e6	0.249723	0.124861	+	0.992174i	$0.460151\pi$
$720$	−6.09310e6	−0.438033
$721$	−1.99405e7	−1.42856
$722$	−1.33561e6	−0.0953539
$723$	1.48264e7	1.05485
$724$	−5.94192e7	−4.21289
$725$	584651.	0.0413096
$726$	−2.87272e6	−0.202279
$727$	−6.37468e6	−0.447324	−0.223662	−	0.974667i	$-0.571801\pi$
$727$	−6.37468e6	−0.447324	−0.223662	+	0.974667i	$0.571801\pi$
$728$	9.80609e7	6.85753
$729$	1.52331e6	0.106162
$730$	−4.59611e6	−0.319215
$731$	559207.	0.0387060
$732$	6.93654e7	4.78482
$733$	−1.55616e6	−0.106978	−0.0534891	−	0.998568i	$-0.517034\pi$
$733$	−1.55616e6	−0.106978	−0.0534891	+	0.998568i	$0.517034\pi$
$734$	4.26769e7	2.92383
$735$	−1.65030e7	−1.12680
$736$	−1.22319e7	−0.832337
$737$	−2.24192e6	−0.152038
$738$	−9.99639e6	−0.675620
$739$	7.24508e6	0.488014	0.244007	−	0.969773i	$-0.421538\pi$
$739$	7.24508e6	0.488014	0.244007	+	0.969773i	$0.421538\pi$
$740$	2.22688e7	1.49492
$741$	−7.11596e6	−0.476089
$742$	3.27288e7	2.18233
$743$	−1.05140e7	−0.698710	−0.349355	−	0.936991i	$-0.613599\pi$
$743$	−1.05140e7	−0.698710	−0.349355	+	0.936991i	$0.613599\pi$
$744$	3.54526e7	2.34809
$745$	1.36970e6	0.0904140
$746$	6.96027e6	0.457909
$747$	−6.07522e6	−0.398346
$748$	−4.54349e6	−0.296917
$749$	−4.30308e7	−2.80269
$750$	3.06579e6	0.199016
$751$	−1.04665e7	−0.677174	−0.338587	−	0.940935i	$-0.609949\pi$
$751$	−1.04665e7	−0.677174	−0.338587	+	0.940935i	$0.609949\pi$
$752$	−3.89274e7	−2.51022
$753$	−1.52254e7	−0.978547
$754$	−9.87085e6	−0.632305
$755$	1.65999e6	0.105983
$756$	3.78308e7	2.40736
$757$	1.00845e7	0.639609	0.319804	−	0.947484i	$-0.396383\pi$
$757$	1.00845e7	0.639609	0.319804	+	0.947484i	$0.396383\pi$
$758$	3.37073e7	2.13084
$759$	−4.18998e6	−0.264002
$760$	−3.79549e6	−0.238360
$761$	−979090.	−0.0612860	−0.0306430	−	0.999530i	$-0.509755\pi$
$761$	−979090.	−0.0612860	−0.0306430	+	0.999530i	$0.509755\pi$
$762$	−2.61113e7	−1.62907
$763$	1.88051e7	1.16940
$764$	−3.75941e7	−2.33016
$765$	−1.58777e6	−0.0980924
$766$	2.22095e7	1.36763
$767$	6.21229e6	0.381297
$768$	−3.38293e7	−2.06962
$769$	−1.41069e7	−0.860232	−0.430116	−	0.902774i	$-0.641527\pi$
$769$	−1.41069e7	−0.860232	−0.430116	+	0.902774i	$0.641527\pi$
$770$	7.02096e6	0.426746
$771$	4.60986e6	0.279288
$772$	−2.68797e7	−1.62323
$773$	−1.54564e7	−0.930378	−0.465189	−	0.885211i	$-0.654014\pi$
$773$	−1.54564e7	−0.930378	−0.465189	+	0.885211i	$0.654014\pi$
$774$	−1.37702e6	−0.0826206
$775$	−2.75202e6	−0.164588
$776$	−4.73347e7	−2.82179
$777$	5.28794e7	3.14220
$778$	9.56043e6	0.566277
$779$	−2.85042e6	−0.168292
$780$	−3.59913e7	−2.11817
$781$	1.51914e6	0.0891191
$782$	−9.53042e6	−0.557308
$783$	−2.13958e6	−0.124716
$784$	6.80286e7	3.95277
$785$	−5.70320e6	−0.330327
$786$	4.16388e7	2.40404
$787$	2.45503e7	1.41293	0.706464	−	0.707749i	$-0.250289\pi$
$787$	2.45503e7	1.41293	0.706464	+	0.707749i	$0.250289\pi$
$788$	−2.40840e7	−1.38170
$789$	−2.72499e7	−1.55838
$790$	1.79779e7	1.02488
$791$	−7.86860e6	−0.447153
$792$	6.28610e6	0.356097
$793$	5.10774e7	2.88433
$794$	−3.06266e7	−1.72404
$795$	−6.74924e6	−0.378736
$796$	−5.62827e7	−3.14842
$797$	−1.97274e7	−1.10008	−0.550041	−	0.835138i	$-0.685388\pi$
$797$	−1.97274e7	−1.10008	−0.550041	+	0.835138i	$0.685388\pi$
$798$	−1.60411e7	−0.891715
$799$	−1.01439e7	−0.562133
$800$	−4.22671e6	−0.233495
$801$	−1.00621e7	−0.554126
$802$	−5.56220e7	−3.05359
$803$	2.17054e6	0.118790
$804$	2.59072e7	1.41345
$805$	1.02404e7	0.556962
$806$	4.64633e7	2.51926
$807$	3.52723e6	0.190656
$808$	−2.62900e7	−1.41665
$809$	1.17207e7	0.629623	0.314812	−	0.949154i	$-0.398059\pi$
$809$	1.17207e7	0.629623	0.314812	+	0.949154i	$0.398059\pi$
$810$	−1.89106e7	−1.01273
$811$	−1.88333e6	−0.100548	−0.0502740	−	0.998735i	$-0.516009\pi$
$811$	−1.88333e6	−0.100548	−0.0502740	+	0.998735i	$0.516009\pi$
$812$	−1.54722e7	−0.823495
$813$	2.23486e7	1.18583
$814$	−1.51244e7	−0.800052
$815$	−392160.	−0.0206809
$816$	1.94201e7	1.02100
$817$	−392650.	−0.0205802
$818$	1.14526e7	0.598441
$819$	−2.88038e7	−1.50052
$820$	−1.44169e7	−0.748751
$821$	2.13435e7	1.10512	0.552559	−	0.833474i	$-0.313651\pi$
$821$	2.13435e7	1.10512	0.552559	+	0.833474i	$0.313651\pi$
$822$	2.51584e7	1.29868
$823$	−9.66947e6	−0.497626	−0.248813	−	0.968552i	$-0.580040\pi$
$823$	−9.66947e6	−0.497626	−0.248813	+	0.968552i	$0.580040\pi$
$824$	−3.70299e7	−1.89992
$825$	−1.44784e6	−0.0740603
$826$	1.40040e7	0.714169
$827$	−2.25871e7	−1.14841	−0.574205	−	0.818711i	$-0.694689\pi$
$827$	−2.25871e7	−1.14841	−0.574205	+	0.818711i	$0.694689\pi$
$828$	1.63184e7	0.827182
$829$	1.75412e7	0.886489	0.443244	−	0.896401i	$-0.353827\pi$
$829$	1.75412e7	0.886489	0.443244	+	0.896401i	$0.353827\pi$
$830$	−1.26007e7	−0.634890
$831$	2.03901e7	1.02428
$832$	6.35625e6	0.318341
$833$	1.77273e7	0.885175
$834$	−4.69973e7	−2.33969
$835$	−1.34258e7	−0.666384
$836$	3.19024e6	0.157873
$837$	1.00713e7	0.496901
$838$	1.72600e7	0.849045
$839$	2.14013e7	1.04963	0.524815	−	0.851216i	$-0.324135\pi$
$839$	2.14013e7	1.04963	0.524815	+	0.851216i	$0.324135\pi$
$840$	−4.55848e7	−2.22906
$841$	−1.96361e7	−0.957338
$842$	1.24911e6	0.0607186
$843$	−2.61900e7	−1.26931
$844$	−6.21836e7	−3.00483
$845$	−1.72199e7	−0.829639
$846$	2.49789e7	1.19991
$847$	−3.31570e6	−0.158806
$848$	2.78217e7	1.32860
$849$	−2.80834e7	−1.33715
$850$	−3.29322e6	−0.156341
$851$	−2.20596e7	−1.04418
$852$	−1.75549e7	−0.828514
$853$	−5.51456e6	−0.259501	−0.129750	−	0.991547i	$-0.541418\pi$
$853$	−5.51456e6	−0.259501	−0.129750	+	0.991547i	$0.541418\pi$
$854$	1.15140e8	5.40236
$855$	1.11487e6	0.0521563
$856$	−7.99091e7	−3.72745
$857$	−2.41762e7	−1.12444	−0.562219	−	0.826988i	$-0.690052\pi$
$857$	−2.41762e7	−1.12444	−0.562219	+	0.826988i	$0.690052\pi$
$858$	2.44444e7	1.13360
$859$	−1.54456e7	−0.714202	−0.357101	−	0.934066i	$-0.616235\pi$
$859$	−1.54456e7	−0.714202	−0.357101	+	0.934066i	$0.616235\pi$
$860$	−1.98595e6	−0.0915636
$861$	−3.42342e7	−1.57381
$862$	3.46634e7	1.58892
$863$	2.24641e7	1.02675	0.513373	−	0.858166i	$-0.328396\pi$
$863$	2.24641e7	1.02675	0.513373	+	0.858166i	$0.328396\pi$
$864$	1.54680e7	0.704935
$865$	6.06138e6	0.275443
$866$	−6.46484e7	−2.92929
$867$	−2.21225e7	−0.999510
$868$	7.28294e7	3.28101
$869$	−8.49021e6	−0.381390
$870$	4.58858e6	0.205532
$871$	1.90768e7	0.852041
$872$	3.49214e7	1.55525
$873$	1.39038e7	0.617445
$874$	6.69184e6	0.296324
$875$	3.53854e6	0.156244
$876$	−2.50824e7	−1.10435
$877$	3.82920e6	0.168116	0.0840580	−	0.996461i	$-0.473212\pi$
$877$	3.82920e6	0.168116	0.0840580	+	0.996461i	$0.473212\pi$
$878$	7.38711e7	3.23399
$879$	4.66650e7	2.03713
$880$	5.96827e6	0.259802
$881$	−1.30681e7	−0.567246	−0.283623	−	0.958936i	$-0.591536\pi$
$881$	−1.30681e7	−0.567246	−0.283623	+	0.958936i	$0.591536\pi$
$882$	−4.36526e7	−1.88946
$883$	−3.59290e6	−0.155076	−0.0775378	−	0.996989i	$-0.524706\pi$
$883$	−3.59290e6	−0.155076	−0.0775378	+	0.996989i	$0.524706\pi$
$884$	3.86612e7	1.66397
$885$	−2.88786e6	−0.123942
$886$	2.68921e7	1.15091
$887$	3.23184e7	1.37924	0.689622	−	0.724169i	$-0.257777\pi$
$887$	3.23184e7	1.37924	0.689622	+	0.724169i	$0.257777\pi$
$888$	9.81980e7	4.17898
$889$	−3.01377e7	−1.27895
$890$	−2.08700e7	−0.883175
$891$	8.93066e6	0.376868
$892$	7.66625e7	3.22605
$893$	7.12261e6	0.298890
$894$	1.07500e7	0.449847
$895$	8.25947e6	0.344663
$896$	−3.46806e7	−1.44317
$897$	3.56531e7	1.47951
$898$	3.40342e7	1.40839
$899$	−4.11897e6	−0.169977
$900$	5.63879e6	0.232049
$901$	7.24992e6	0.297523
$902$	9.79159e6	0.400716
$903$	−4.71583e6	−0.192459
$904$	−1.46121e7	−0.594693
$905$	2.03393e7	0.825495
$906$	1.30283e7	0.527310
$907$	7.00957e6	0.282926	0.141463	−	0.989944i	$-0.454819\pi$
$907$	7.00957e6	0.282926	0.141463	+	0.989944i	$0.454819\pi$
$908$	−2.98510e6	−0.120156
$909$	7.72228e6	0.309982
$910$	−5.97423e7	−2.39155
$911$	−4.45857e7	−1.77992	−0.889958	−	0.456043i	$-0.849266\pi$
$911$	−4.45857e7	−1.77992	−0.889958	+	0.456043i	$0.849266\pi$
$912$	−1.36360e7	−0.542874
$913$	5.95076e6	0.236263
$914$	−4.34989e7	−1.72232
$915$	−2.37439e7	−0.937561
$916$	4.06143e6	0.159934
$917$	4.80596e7	1.88737
$918$	1.20518e7	0.472004
$919$	2.62052e7	1.02352	0.511762	−	0.859127i	$-0.328993\pi$
$919$	2.62052e7	1.02352	0.511762	+	0.859127i	$0.328993\pi$
$920$	1.90166e7	0.740734
$921$	−1.99342e7	−0.774374
$922$	1.19002e7	0.461029
$923$	−1.29266e7	−0.499436
$924$	3.83156e7	1.47637
$925$	−7.62267e6	−0.292922
$926$	−4.28556e7	−1.64241
$927$	1.08769e7	0.415726
$928$	−6.32614e6	−0.241140
$929$	−5.11664e7	−1.94512	−0.972559	−	0.232657i	$-0.925258\pi$
$929$	−5.11664e7	−1.94512	−0.972559	+	0.232657i	$0.925258\pi$
$930$	−2.15990e7	−0.818892
$931$	−1.24473e7	−0.470653
$932$	−1.08466e8	−4.09029
$933$	−2.72273e7	−1.02400
$934$	5.84680e7	2.19306
$935$	1.55525e6	0.0581795
$936$	−5.34893e7	−1.99562
$937$	3.65112e6	0.135855	0.0679277	−	0.997690i	$-0.478361\pi$
$937$	3.65112e6	0.135855	0.0679277	+	0.997690i	$0.478361\pi$
$938$	4.30037e7	1.59587
$939$	−4.49112e7	−1.66223
$940$	3.60249e7	1.32979
$941$	2.03978e7	0.750947	0.375473	−	0.926833i	$-0.377480\pi$
$941$	2.03978e7	0.750947	0.375473	+	0.926833i	$0.377480\pi$
$942$	−4.47611e7	−1.64351
$943$	1.42815e7	0.522990
$944$	1.19043e7	0.434784
$945$	−1.29496e7	−0.471711
$946$	1.34881e6	0.0490030
$947$	−3.98271e7	−1.44312	−0.721562	−	0.692350i	$-0.756575\pi$
$947$	−3.98271e7	−1.44312	−0.721562	+	0.692350i	$0.756575\pi$
$948$	9.81113e7	3.54567
$949$	−1.84695e7	−0.665716
$950$	2.31235e6	0.0831276
$951$	−4.64933e7	−1.66701
$952$	4.89664e7	1.75108
$953$	3.52920e7	1.25876	0.629382	−	0.777096i	$-0.283308\pi$
$953$	3.52920e7	1.25876	0.629382	+	0.777096i	$0.283308\pi$
$954$	−1.78526e7	−0.635083
$955$	1.28685e7	0.456584
$956$	−1.01895e8	−3.60585
$957$	−2.16699e6	−0.0764852
$958$	−9.41790e7	−3.31543
$959$	2.90378e7	1.01957
$960$	−2.95478e6	−0.103478
$961$	−9.24065e6	−0.322771
$962$	1.28696e8	4.48361
$963$	2.34720e7	0.815615
$964$	5.65603e7	1.96029
$965$	9.20096e6	0.318064
$966$	8.03706e7	2.77111
$967$	4.33723e6	0.149158	0.0745789	−	0.997215i	$-0.476239\pi$
$967$	4.33723e6	0.149158	0.0745789	+	0.997215i	$0.476239\pi$
$968$	−6.15731e6	−0.211204
$969$	−3.55333e6	−0.121570
$970$	2.88380e7	0.984094
$971$	−1.57244e6	−0.0535214	−0.0267607	−	0.999642i	$-0.508519\pi$
$971$	−1.57244e6	−0.0535214	−0.0267607	+	0.999642i	$0.508519\pi$
$972$	−6.26083e7	−2.12553
$973$	−5.42443e7	−1.83684
$974$	−9.23347e7	−3.11866
$975$	1.23199e7	0.415045
$976$	9.78770e7	3.28894
$977$	1.68910e7	0.566132	0.283066	−	0.959100i	$-0.408648\pi$
$977$	1.68910e7	0.566132	0.283066	+	0.959100i	$0.408648\pi$
$978$	−3.07784e6	−0.102896
$979$	9.85599e6	0.328658
$980$	−6.29562e7	−2.09399
$981$	−1.02576e7	−0.340309
$982$	9.07549e7	3.00325
$983$	2.64658e7	0.873577	0.436788	−	0.899564i	$-0.356116\pi$
$983$	2.64658e7	0.873577	0.436788	+	0.899564i	$0.356116\pi$
$984$	−6.35736e7	−2.09310
$985$	8.24400e6	0.270737
$986$	−4.92898e6	−0.161460
$987$	8.55444e7	2.79511
$988$	−2.71462e7	−0.884742
$989$	1.96730e6	0.0639557
$990$	−3.82972e6	−0.124188
$991$	3.28541e7	1.06269	0.531343	−	0.847157i	$-0.321688\pi$
$991$	3.28541e7	1.06269	0.531343	+	0.847157i	$0.321688\pi$
$992$	2.97779e7	0.960761
$993$	2.16688e7	0.697368
$994$	−2.91396e7	−0.935444
$995$	1.92657e7	0.616916
$996$	−6.87658e7	−2.19647
$997$	−1.88872e7	−0.601767	−0.300884	−	0.953661i	$-0.597282\pi$
$997$	−1.88872e7	−0.601767	−0.300884	+	0.953661i	$0.597282\pi$
$998$	1.48250e7	0.471161
$999$	2.78958e7	0.884351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.4	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-10.2487 q^{2} +19.1450 q^{3} +73.0349 q^{4} -25.0000 q^{5} -196.210 q^{6} -226.466 q^{7} -420.553 q^{8} +123.531 q^{9} +O(q^{10})\)	\(q-10.2487 q^{2} +19.1450 q^{3} +73.0349 q^{4} -25.0000 q^{5} -196.210 q^{6} -226.466 q^{7} -420.553 q^{8} +123.531 q^{9} +256.216 q^{10} -121.000 q^{11} +1398.25 q^{12} +1029.61 q^{13} +2320.98 q^{14} -478.625 q^{15} +1972.98 q^{16} +514.131 q^{17} -1266.02 q^{18} -361.000 q^{19} -1825.87 q^{20} -4335.70 q^{21} +1240.09 q^{22} +1808.72 q^{23} -8051.48 q^{24} +625.000 q^{25} -10552.1 q^{26} -2287.24 q^{27} -16540.0 q^{28} +935.441 q^{29} +4905.26 q^{30} -4403.24 q^{31} -6762.74 q^{32} -2316.54 q^{33} -5269.15 q^{34} +5661.66 q^{35} +9022.06 q^{36} -12196.3 q^{37} +3699.76 q^{38} +19711.8 q^{39} +10513.8 q^{40} +7895.89 q^{41} +44435.1 q^{42} +1087.67 q^{43} -8837.23 q^{44} -3088.27 q^{45} -18536.9 q^{46} -19730.2 q^{47} +37772.8 q^{48} +34480.1 q^{49} -6405.41 q^{50} +9843.03 q^{51} +75197.2 q^{52} +14101.3 q^{53} +23441.1 q^{54} +3025.00 q^{55} +95241.1 q^{56} -6911.34 q^{57} -9587.01 q^{58} +6033.65 q^{59} -34956.3 q^{60} +49608.6 q^{61} +45127.3 q^{62} -27975.6 q^{63} +6173.47 q^{64} -25740.2 q^{65} +23741.5 q^{66} +18528.3 q^{67} +37549.5 q^{68} +34627.9 q^{69} -58024.4 q^{70} -12554.9 q^{71} -51951.2 q^{72} -17938.4 q^{73} +124995. q^{74} +11965.6 q^{75} -26365.6 q^{76} +27402.4 q^{77} -202020. q^{78} +70167.0 q^{79} -49324.6 q^{80} -73807.1 q^{81} -80922.3 q^{82} -49179.8 q^{83} -316658. q^{84} -12853.3 q^{85} -11147.2 q^{86} +17909.0 q^{87} +50886.9 q^{88} -81454.5 q^{89} +31650.6 q^{90} -233171. q^{91} +132100. q^{92} -84300.0 q^{93} +202208. q^{94} +9025.00 q^{95} -129473. q^{96} +112553. q^{97} -353374. q^{98} -14947.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 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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