LMFDB - Embedded newform 165.6.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 143x^{3} + 71x^{2} + 4216x - 3740 $ x^5 - x^4 - 143x^3 + 71x^2 + 4216*x - 3740
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.898099$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.898099 q^{2} -9.00000 q^{3} -31.1934 q^{4} -25.0000 q^{5} +8.08289 q^{6} +120.732 q^{7} +56.7540 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-0.898099 q^{2} -9.00000 q^{3} -31.1934 q^{4} -25.0000 q^{5} +8.08289 q^{6} +120.732 q^{7} +56.7540 q^{8} +81.0000 q^{9} +22.4525 q^{10} -121.000 q^{11} +280.741 q^{12} +667.387 q^{13} -108.430 q^{14} +225.000 q^{15} +947.219 q^{16} -74.5586 q^{17} -72.7460 q^{18} -708.549 q^{19} +779.835 q^{20} -1086.59 q^{21} +108.670 q^{22} +1238.63 q^{23} -510.786 q^{24} +625.000 q^{25} -599.380 q^{26} -729.000 q^{27} -3766.06 q^{28} -3855.89 q^{29} -202.072 q^{30} -8236.92 q^{31} -2666.82 q^{32} +1089.00 q^{33} +66.9611 q^{34} -3018.31 q^{35} -2526.67 q^{36} -5725.33 q^{37} +636.348 q^{38} -6006.49 q^{39} -1418.85 q^{40} +672.977 q^{41} +975.867 q^{42} +16058.1 q^{43} +3774.40 q^{44} -2025.00 q^{45} -1112.41 q^{46} -7572.96 q^{47} -8524.97 q^{48} -2230.69 q^{49} -561.312 q^{50} +671.028 q^{51} -20818.1 q^{52} -5420.79 q^{53} +654.714 q^{54} +3025.00 q^{55} +6852.04 q^{56} +6376.94 q^{57} +3462.97 q^{58} -33128.4 q^{59} -7018.52 q^{60} +18038.6 q^{61} +7397.57 q^{62} +9779.32 q^{63} -27915.9 q^{64} -16684.7 q^{65} -978.030 q^{66} -60276.1 q^{67} +2325.74 q^{68} -11147.7 q^{69} +2710.74 q^{70} +12430.5 q^{71} +4597.07 q^{72} -1230.79 q^{73} +5141.92 q^{74} -5625.00 q^{75} +22102.1 q^{76} -14608.6 q^{77} +5394.42 q^{78} +47015.0 q^{79} -23680.5 q^{80} +6561.00 q^{81} -604.401 q^{82} -29681.0 q^{83} +33894.5 q^{84} +1863.97 q^{85} -14421.7 q^{86} +34703.0 q^{87} -6867.23 q^{88} -125061. q^{89} +1818.65 q^{90} +80575.2 q^{91} -38637.2 q^{92} +74132.3 q^{93} +6801.27 q^{94} +17713.7 q^{95} +24001.4 q^{96} +74465.3 q^{97} +2003.38 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.898099	−0.158763	−0.0793815	−	0.996844i	$-0.525295\pi$
$2$	−0.898099	−0.158763	−0.0793815	+	0.996844i	$0.525295\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.1934	−0.974794
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	8.08289	0.0916619
$7$	120.732	0.931277	0.465638	−	0.884975i	$-0.345825\pi$
$7$	120.732	0.931277	0.465638	+	0.884975i	$0.345825\pi$
$8$	56.7540	0.313524
$9$	81.0000	0.333333
$10$	22.4525	0.0710010
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	280.741	0.562798
$13$	667.387	1.09527	0.547633	−	0.836719i	$-0.315529\pi$
$13$	667.387	1.09527	0.547633	+	0.836719i	$0.315529\pi$
$14$	−108.430	−0.147852
$15$	225.000	0.258199
$16$	947.219	0.925018
$17$	−74.5586	−0.0625714	−0.0312857	−	0.999510i	$-0.509960\pi$
$17$	−74.5586	−0.0625714	−0.0312857	+	0.999510i	$0.509960\pi$
$18$	−72.7460	−0.0529210
$19$	−708.549	−0.450283	−0.225142	−	0.974326i	$-0.572285\pi$
$19$	−708.549	−0.450283	−0.225142	+	0.974326i	$0.572285\pi$
$20$	779.835	0.435941
$21$	−1086.59	−0.537673
$22$	108.670	0.0478689
$23$	1238.63	0.488228	0.244114	−	0.969747i	$-0.421503\pi$
$23$	1238.63	0.488228	0.244114	+	0.969747i	$0.421503\pi$
$24$	−510.786	−0.181013
$25$	625.000	0.200000
$26$	−599.380	−0.173888
$27$	−729.000	−0.192450
$28$	−3766.06	−0.907803
$29$	−3855.89	−0.851392	−0.425696	−	0.904866i	$-0.639971\pi$
$29$	−3855.89	−0.851392	−0.425696	+	0.904866i	$0.639971\pi$
$30$	−202.072	−0.0409924
$31$	−8236.92	−1.53943	−0.769716	−	0.638387i	$-0.779602\pi$
$31$	−8236.92	−1.53943	−0.769716	+	0.638387i	$0.779602\pi$
$32$	−2666.82	−0.460383
$33$	1089.00	0.174078
$34$	66.9611	0.00993402
$35$	−3018.31	−0.416480
$36$	−2526.67	−0.324931
$37$	−5725.33	−0.687538	−0.343769	−	0.939054i	$-0.611704\pi$
$37$	−5725.33	−0.687538	−0.343769	+	0.939054i	$0.611704\pi$
$38$	636.348	0.0714884
$39$	−6006.49	−0.632352
$40$	−1418.85	−0.140212
$41$	672.977	0.0625231	0.0312616	−	0.999511i	$-0.490048\pi$
$41$	672.977	0.0625231	0.0312616	+	0.999511i	$0.490048\pi$
$42$	975.867	0.0853626
$43$	16058.1	1.32441	0.662204	−	0.749323i	$-0.269621\pi$
$43$	16058.1	1.32441	0.662204	+	0.749323i	$0.269621\pi$
$44$	3774.40	0.293912
$45$	−2025.00	−0.149071
$46$	−1112.41	−0.0775125
$47$	−7572.96	−0.500059	−0.250029	−	0.968238i	$-0.580440\pi$
$47$	−7572.96	−0.500059	−0.250029	+	0.968238i	$0.580440\pi$
$48$	−8524.97	−0.534060
$49$	−2230.69	−0.132724
$50$	−561.312	−0.0317526
$51$	671.028	0.0361256
$52$	−20818.1	−1.06766
$53$	−5420.79	−0.265078	−0.132539	−	0.991178i	$-0.542313\pi$
$53$	−5420.79	−0.265078	−0.132539	+	0.991178i	$0.542313\pi$
$54$	654.714	0.0305540
$55$	3025.00	0.134840
$56$	6852.04	0.291978
$57$	6376.94	0.259971
$58$	3462.97	0.135170
$59$	−33128.4	−1.23900	−0.619499	−	0.784997i	$-0.712664\pi$
$59$	−33128.4	−1.23900	−0.619499	+	0.784997i	$0.712664\pi$
$60$	−7018.52	−0.251691
$61$	18038.6	0.620695	0.310348	−	0.950623i	$-0.399555\pi$
$61$	18038.6	0.620695	0.310348	+	0.950623i	$0.399555\pi$
$62$	7397.57	0.244405
$63$	9779.32	0.310426
$64$	−27915.9	−0.851926
$65$	−16684.7	−0.489818
$66$	−978.030	−0.0276371
$67$	−60276.1	−1.64043	−0.820216	−	0.572054i	$-0.806147\pi$
$67$	−60276.1	−1.64043	−0.820216	+	0.572054i	$0.806147\pi$
$68$	2325.74	0.0609942
$69$	−11147.7	−0.281878
$70$	2710.74	0.0661216
$71$	12430.5	0.292646	0.146323	−	0.989237i	$-0.453256\pi$
$71$	12430.5	0.292646	0.146323	+	0.989237i	$0.453256\pi$
$72$	4597.07	0.104508
$73$	−1230.79	−0.0270320	−0.0135160	−	0.999909i	$-0.504302\pi$
$73$	−1230.79	−0.0270320	−0.0135160	+	0.999909i	$0.504302\pi$
$74$	5141.92	0.109156
$75$	−5625.00	−0.115470
$76$	22102.1	0.438934
$77$	−14608.6	−0.280790
$78$	5394.42	0.100394
$79$	47015.0	0.847557	0.423778	−	0.905766i	$-0.360704\pi$
$79$	47015.0	0.847557	0.423778	+	0.905766i	$0.360704\pi$
$80$	−23680.5	−0.413681
$81$	6561.00	0.111111
$82$	−604.401	−0.00992636
$83$	−29681.0	−0.472915	−0.236457	−	0.971642i	$-0.575986\pi$
$83$	−29681.0	−0.472915	−0.236457	+	0.971642i	$0.575986\pi$
$84$	33894.5	0.524120
$85$	1863.97	0.0279828
$86$	−14421.7	−0.210267
$87$	34703.0	0.491551
$88$	−6867.23	−0.0945311
$89$	−125061.	−1.67358	−0.836791	−	0.547522i	$-0.815571\pi$
$89$	−125061.	−1.67358	−0.836791	+	0.547522i	$0.815571\pi$
$90$	1818.65	0.0236670
$91$	80575.2	1.02000
$92$	−38637.2	−0.475922
$93$	74132.3	0.888791
$94$	6801.27	0.0793908
$95$	17713.7	0.201373
$96$	24001.4	0.265802
$97$	74465.3	0.803572	0.401786	−	0.915734i	$-0.368390\pi$
$97$	74465.3	0.803572	0.401786	+	0.915734i	$0.368390\pi$
$98$	2003.38	0.0210717
$99$	−9801.00	−0.100504
$100$	−19495.9	−0.194959
$101$	−65393.5	−0.637868	−0.318934	−	0.947777i	$-0.603325\pi$
$101$	−65393.5	−0.637868	−0.318934	+	0.947777i	$0.603325\pi$
$102$	−602.650	−0.00573541
$103$	−35955.1	−0.333939	−0.166969	−	0.985962i	$-0.553398\pi$
$103$	−35955.1	−0.333939	−0.166969	+	0.985962i	$0.553398\pi$
$104$	37876.9	0.343392
$105$	27164.8	0.240455
$106$	4868.41	0.0420845
$107$	−118141.	−0.997565	−0.498783	−	0.866727i	$-0.666219\pi$
$107$	−118141.	−0.997565	−0.498783	+	0.866727i	$0.666219\pi$
$108$	22740.0	0.187599
$109$	216333.	1.74404	0.872019	−	0.489472i	$-0.162811\pi$
$109$	216333.	1.74404	0.872019	+	0.489472i	$0.162811\pi$
$110$	−2716.75	−0.0214076
$111$	51528.0	0.396950
$112$	114360.	0.861448
$113$	−82987.0	−0.611384	−0.305692	−	0.952130i	$-0.598888\pi$
$113$	−82987.0	−0.611384	−0.305692	+	0.952130i	$0.598888\pi$
$114$	−5727.13	−0.0412738
$115$	−30965.8	−0.218342
$116$	120278.	0.829932
$117$	54058.4	0.365089
$118$	29752.6	0.196707
$119$	−9001.64	−0.0582712
$120$	12769.6	0.0809516
$121$	14641.0	0.0909091
$122$	−16200.5	−0.0985434
$123$	−6056.80	−0.0360978
$124$	256938.	1.50063
$125$	−15625.0	−0.0894427
$126$	−8782.80	−0.0492841
$127$	−112754.	−0.620330	−0.310165	−	0.950683i	$-0.600384\pi$
$127$	−112754.	−0.620330	−0.310165	+	0.950683i	$0.600384\pi$
$128$	110410.	0.595637
$129$	−144523.	−0.764648
$130$	14984.5	0.0777650
$131$	177226.	0.902297	0.451149	−	0.892449i	$-0.351014\pi$
$131$	177226.	0.902297	0.451149	+	0.892449i	$0.351014\pi$
$132$	−33969.6	−0.169690
$133$	−85544.8	−0.419338
$134$	54133.9	0.260440
$135$	18225.0	0.0860663
$136$	−4231.50	−0.0196176
$137$	−179083.	−0.815181	−0.407590	−	0.913165i	$-0.633631\pi$
$137$	−179083.	−0.815181	−0.407590	+	0.913165i	$0.633631\pi$
$138$	10011.7	0.0447519
$139$	140181.	0.615392	0.307696	−	0.951485i	$-0.400442\pi$
$139$	140181.	0.615392	0.307696	+	0.951485i	$0.400442\pi$
$140$	94151.4	0.405982
$141$	68156.6	0.288709
$142$	−11163.8	−0.0464614
$143$	−80753.9	−0.330235
$144$	76724.7	0.308339
$145$	96397.2	0.380754
$146$	1105.37	0.00429168
$147$	20076.2	0.0766283
$148$	178593.	0.670208
$149$	−300863.	−1.11020	−0.555102	−	0.831783i	$-0.687321\pi$
$149$	−300863.	−1.11020	−0.555102	+	0.831783i	$0.687321\pi$
$150$	5051.81	0.0183324
$151$	225360.	0.804330	0.402165	−	0.915567i	$-0.368258\pi$
$151$	225360.	0.804330	0.402165	+	0.915567i	$0.368258\pi$
$152$	−40213.0	−0.141175
$153$	−6039.25	−0.0208571
$154$	13120.0	0.0445791
$155$	205923.	0.688455
$156$	187363.	0.616413
$157$	−344938.	−1.11684	−0.558421	−	0.829558i	$-0.688593\pi$
$157$	−344938.	−1.11684	−0.558421	+	0.829558i	$0.688593\pi$
$158$	−42224.2	−0.134561
$159$	48787.1	0.153043
$160$	66670.6	0.205890
$161$	149543.	0.454675
$162$	−5892.43	−0.0176403
$163$	−134781.	−0.397337	−0.198669	−	0.980067i	$-0.563662\pi$
$163$	−134781.	−0.397337	−0.198669	+	0.980067i	$0.563662\pi$
$164$	−20992.5	−0.0609472
$165$	−27225.0	−0.0778499
$166$	26656.5	0.0750814
$167$	476574.	1.32233	0.661163	−	0.750242i	$-0.270063\pi$
$167$	476574.	1.32233	0.661163	+	0.750242i	$0.270063\pi$
$168$	−61668.4	−0.168573
$169$	74112.7	0.199607
$170$	−1674.03	−0.00444263
$171$	−57392.5	−0.150094
$172$	−500906.	−1.29103
$173$	−607031.	−1.54204	−0.771020	−	0.636811i	$-0.780253\pi$
$173$	−607031.	−1.54204	−0.771020	+	0.636811i	$0.780253\pi$
$174$	−31166.7	−0.0780402
$175$	75457.7	0.186255
$176$	−114613.	−0.278903
$177$	298156.	0.715336
$178$	112317.	0.265703
$179$	−588915.	−1.37379	−0.686895	−	0.726757i	$-0.741027\pi$
$179$	−588915.	−1.37379	−0.686895	+	0.726757i	$0.741027\pi$
$180$	63166.7	0.145314
$181$	−403724.	−0.915984	−0.457992	−	0.888956i	$-0.651431\pi$
$181$	−403724.	−0.915984	−0.457992	+	0.888956i	$0.651431\pi$
$182$	−72364.6	−0.161938
$183$	−162347.	−0.358358
$184$	70297.3	0.153071
$185$	143133.	0.307476
$186$	−66578.1	−0.141107
$187$	9021.60	0.0188660
$188$	236226.	0.487454
$189$	−88013.9	−0.179224
$190$	−15908.7	−0.0319706
$191$	−395279.	−0.784007	−0.392004	−	0.919964i	$-0.628218\pi$
$191$	−395279.	−0.784007	−0.392004	+	0.919964i	$0.628218\pi$
$192$	251243.	0.491860
$193$	192334.	0.371675	0.185837	−	0.982581i	$-0.440500\pi$
$193$	192334.	0.371675	0.185837	+	0.982581i	$0.440500\pi$
$194$	−66877.3	−0.127578
$195$	150162.	0.282796
$196$	69582.9	0.129379
$197$	−537571.	−0.986894	−0.493447	−	0.869776i	$-0.664263\pi$
$197$	−537571.	−0.986894	−0.493447	+	0.869776i	$0.664263\pi$
$198$	8802.27	0.0159563
$199$	−619032.	−1.10810	−0.554052	−	0.832482i	$-0.686919\pi$
$199$	−619032.	−1.10810	−0.554052	+	0.832482i	$0.686919\pi$
$200$	35471.2	0.0627049
$201$	542485.	0.947104
$202$	58729.8	0.101270
$203$	−465530.	−0.792881
$204$	−20931.6	−0.0352150
$205$	−16824.4	−0.0279612
$206$	32291.2	0.0530172
$207$	100329.	0.162743
$208$	632162.	1.01314
$209$	85734.5	0.135766
$210$	−24396.7	−0.0381753
$211$	937975.	1.45039	0.725196	−	0.688543i	$-0.241749\pi$
$211$	937975.	1.45039	0.725196	+	0.688543i	$0.241749\pi$
$212$	169093.	0.258396
$213$	−111874.	−0.168959
$214$	106102.	0.158376
$215$	−401452.	−0.592294
$216$	−41373.6	−0.0603378
$217$	−994463.	−1.43364
$218$	−194288.	−0.276889
$219$	11077.1	0.0156069
$220$	−94360.1	−0.131441
$221$	−49759.5	−0.0685323
$222$	−46277.3	−0.0630210
$223$	−1.05781e6	−1.42445	−0.712224	−	0.701952i	$-0.752312\pi$
$223$	−1.05781e6	−1.42445	−0.712224	+	0.701952i	$0.752312\pi$
$224$	−321972.	−0.428744
$225$	50625.0	0.0666667
$226$	74530.6	0.0970651
$227$	−1.38495e6	−1.78389	−0.891945	−	0.452145i	$-0.850659\pi$
$227$	−1.38495e6	−1.78389	−0.891945	+	0.452145i	$0.850659\pi$
$228$	−198919.	−0.253419
$229$	−56996.7	−0.0718225	−0.0359113	−	0.999355i	$-0.511433\pi$
$229$	−56996.7	−0.0718225	−0.0359113	+	0.999355i	$0.511433\pi$
$230$	27810.4	0.0346647
$231$	131478.	0.162114
$232$	−218837.	−0.266932
$233$	−27988.8	−0.0337750	−0.0168875	−	0.999857i	$-0.505376\pi$
$233$	−27988.8	−0.0337750	−0.0168875	+	0.999857i	$0.505376\pi$
$234$	−48549.8	−0.0579626
$235$	189324.	0.223633
$236$	1.03339e6	1.20777
$237$	−423135.	−0.489337
$238$	8084.37	0.00925132
$239$	−1.21406e6	−1.37482	−0.687408	−	0.726272i	$-0.741252\pi$
$239$	−1.21406e6	−1.37482	−0.687408	+	0.726272i	$0.741252\pi$
$240$	213124.	0.238839
$241$	1.06213e6	1.17797	0.588987	−	0.808142i	$-0.299527\pi$
$241$	1.06213e6	1.17797	0.588987	+	0.808142i	$0.299527\pi$
$242$	−13149.1	−0.0144330
$243$	−59049.0	−0.0641500
$244$	−562686.	−0.605050
$245$	55767.3	0.0593560
$246$	5439.60	0.00573099
$247$	−472877.	−0.493180
$248$	−467478.	−0.482649
$249$	267129.	0.273037
$250$	14032.8	0.0142002
$251$	−75353.1	−0.0754948	−0.0377474	−	0.999287i	$-0.512018\pi$
$251$	−75353.1	−0.0754948	−0.0377474	+	0.999287i	$0.512018\pi$
$252$	−305050.	−0.302601
$253$	−149874.	−0.147206
$254$	101264.	0.0984855
$255$	−16775.7	−0.0161559
$256$	794151.	0.757361
$257$	1.14147e6	1.07803	0.539016	−	0.842296i	$-0.318796\pi$
$257$	1.14147e6	1.07803	0.539016	+	0.842296i	$0.318796\pi$
$258$	129796.	0.121398
$259$	−691233.	−0.640288
$260$	520452.	0.477472
$261$	−312327.	−0.283797
$262$	−159167.	−0.143251
$263$	−780299.	−0.695619	−0.347810	−	0.937565i	$-0.613074\pi$
$263$	−780299.	−0.695619	−0.347810	+	0.937565i	$0.613074\pi$
$264$	61805.1	0.0545776
$265$	135520.	0.118546
$266$	76827.8	0.0665754
$267$	1.12555e6	0.966244
$268$	1.88022e6	1.59908
$269$	210163.	0.177082	0.0885411	−	0.996073i	$-0.471780\pi$
$269$	210163.	0.177082	0.0885411	+	0.996073i	$0.471780\pi$
$270$	−16367.9	−0.0136641
$271$	−4596.78	−0.00380216	−0.00190108	−	0.999998i	$-0.500605\pi$
$271$	−4596.78	−0.00380216	−0.00190108	+	0.999998i	$0.500605\pi$
$272$	−70623.3	−0.0578797
$273$	−725177.	−0.588895
$274$	160835.	0.129421
$275$	−75625.0	−0.0603023
$276$	347734.	0.274774
$277$	−689589.	−0.539996	−0.269998	−	0.962861i	$-0.587023\pi$
$277$	−689589.	−0.539996	−0.269998	+	0.962861i	$0.587023\pi$
$278$	−125896.	−0.0977016
$279$	−667190.	−0.513144
$280$	−171301.	−0.130576
$281$	1.95020e6	1.47338	0.736688	−	0.676233i	$-0.236389\pi$
$281$	1.95020e6	1.47338	0.736688	+	0.676233i	$0.236389\pi$
$282$	−61211.4	−0.0458363
$283$	307845.	0.228489	0.114245	−	0.993453i	$-0.463555\pi$
$283$	307845.	0.228489	0.114245	+	0.993453i	$0.463555\pi$
$284$	−387750.	−0.285270
$285$	−159424.	−0.116263
$286$	72525.0	0.0524291
$287$	81250.2	0.0582263
$288$	−216013.	−0.153461
$289$	−1.41430e6	−0.996085
$290$	−86574.2	−0.0604496
$291$	−670188.	−0.463942
$292$	38392.7	0.0263506
$293$	2.19630e6	1.49459	0.747297	−	0.664491i	$-0.231351\pi$
$293$	2.19630e6	1.49459	0.747297	+	0.664491i	$0.231351\pi$
$294$	−18030.5	−0.0121657
$295$	828210.	0.554097
$296$	−324935.	−0.215560
$297$	88209.0	0.0580259
$298$	270204.	0.176259
$299$	826647.	0.534739
$300$	175463.	0.112560
$301$	1.93873e6	1.23339
$302$	−202396.	−0.127698
$303$	588541.	0.368273
$304$	−671151.	−0.416520
$305$	−450965.	−0.277583
$306$	5423.85	0.00331134
$307$	−905979.	−0.548621	−0.274310	−	0.961641i	$-0.588450\pi$
$307$	−905979.	−0.548621	−0.274310	+	0.961641i	$0.588450\pi$
$308$	455693.	0.273713
$309$	323596.	0.192800
$310$	−184939.	−0.109301
$311$	1.05496e6	0.618495	0.309247	−	0.950982i	$-0.399923\pi$
$311$	1.05496e6	0.618495	0.309247	+	0.950982i	$0.399923\pi$
$312$	−340892.	−0.198258
$313$	2.98094e6	1.71985	0.859927	−	0.510417i	$-0.170509\pi$
$313$	2.98094e6	1.71985	0.859927	+	0.510417i	$0.170509\pi$
$314$	309788.	0.177313
$315$	−244483.	−0.138827
$316$	−1.46656e6	−0.826194
$317$	−272200.	−0.152139	−0.0760694	−	0.997103i	$-0.524237\pi$
$317$	−272200.	−0.152139	−0.0760694	+	0.997103i	$0.524237\pi$
$318$	−43815.7	−0.0242975
$319$	466562.	0.256704
$320$	697898.	0.380993
$321$	1.06327e6	0.575944
$322$	−134304.	−0.0721856
$323$	52828.5	0.0281749
$324$	−204660.	−0.108310
$325$	417117.	0.219053
$326$	121047.	0.0630824
$327$	−1.94699e6	−1.00692
$328$	38194.1	0.0196025
$329$	−914301.	−0.465693
$330$	24450.8	0.0123597
$331$	−984627.	−0.493971	−0.246986	−	0.969019i	$-0.579440\pi$
$331$	−984627.	−0.493971	−0.246986	+	0.969019i	$0.579440\pi$
$332$	925851.	0.460995
$333$	−463752.	−0.229179
$334$	−428010.	−0.209937
$335$	1.50690e6	0.733623
$336$	−1.02924e6	−0.497357
$337$	−366865.	−0.175967	−0.0879836	−	0.996122i	$-0.528042\pi$
$337$	−366865.	−0.175967	−0.0879836	+	0.996122i	$0.528042\pi$
$338$	−66560.6	−0.0316902
$339$	746883.	0.352983
$340$	−58143.5	−0.0272774
$341$	996667.	0.464156
$342$	51544.2	0.0238295
$343$	−2.29847e6	−1.05488
$344$	911359.	0.415234
$345$	278692.	0.126060
$346$	545174.	0.244819
$347$	−558457.	−0.248981	−0.124490	−	0.992221i	$-0.539730\pi$
$347$	−558457.	−0.248981	−0.124490	+	0.992221i	$0.539730\pi$
$348$	−1.08250e6	−0.479161
$349$	1.53340e6	0.673895	0.336947	−	0.941524i	$-0.390606\pi$
$349$	1.53340e6	0.673895	0.336947	+	0.941524i	$0.390606\pi$
$350$	−67768.5	−0.0295705
$351$	−486525.	−0.210784
$352$	322686.	0.138811
$353$	2.43850e6	1.04156	0.520781	−	0.853690i	$-0.325641\pi$
$353$	2.43850e6	1.04156	0.520781	+	0.853690i	$0.325641\pi$
$354$	−267773.	−0.113569
$355$	−310762.	−0.130875
$356$	3.90108e6	1.63140
$357$	81014.8	0.0336429
$358$	528904.	0.218107
$359$	1.17648e6	0.481778	0.240889	−	0.970553i	$-0.422561\pi$
$359$	1.17648e6	0.481778	0.240889	+	0.970553i	$0.422561\pi$
$360$	−114927.	−0.0467374
$361$	−1.97406e6	−0.797245
$362$	362584.	0.145424
$363$	−131769.	−0.0524864
$364$	−2.51342e6	−0.994286
$365$	30769.8	0.0120891
$366$	145804.	0.0568941
$367$	−2.74188e6	−1.06263	−0.531316	−	0.847174i	$-0.678302\pi$
$367$	−2.74188e6	−1.06263	−0.531316	+	0.847174i	$0.678302\pi$
$368$	1.17325e6	0.451620
$369$	54511.2	0.0208410
$370$	−128548.	−0.0488159
$371$	−654465.	−0.246861
$372$	−2.31244e6	−0.866389
$373$	3.46639e6	1.29005	0.645023	−	0.764163i	$-0.276848\pi$
$373$	3.46639e6	1.29005	0.645023	+	0.764163i	$0.276848\pi$
$374$	−8102.29	−0.00299522
$375$	140625.	0.0516398
$376$	−429795.	−0.156781
$377$	−2.57337e6	−0.932500
$378$	79045.2	0.0284542
$379$	4.07201e6	1.45617	0.728083	−	0.685489i	$-0.240412\pi$
$379$	4.07201e6	1.45617	0.728083	+	0.685489i	$0.240412\pi$
$380$	−552552.	−0.196297
$381$	1.01479e6	0.358148
$382$	355000.	0.124471
$383$	436616.	0.152091	0.0760454	−	0.997104i	$-0.475771\pi$
$383$	436616.	0.152091	0.0760454	+	0.997104i	$0.475771\pi$
$384$	−993687.	−0.343891
$385$	365215.	0.125573
$386$	−172735.	−0.0590082
$387$	1.30070e6	0.441470
$388$	−2.32283e6	−0.783317
$389$	4.27642e6	1.43287	0.716435	−	0.697654i	$-0.245773\pi$
$389$	4.27642e6	1.43287	0.716435	+	0.697654i	$0.245773\pi$
$390$	−134861.	−0.0448976
$391$	−92350.7	−0.0305491
$392$	−126601.	−0.0416122
$393$	−1.59504e6	−0.520942
$394$	482792.	0.156682
$395$	−1.17538e6	−0.379039
$396$	305727.	0.0979705
$397$	−1.61356e6	−0.513817	−0.256909	−	0.966436i	$-0.582704\pi$
$397$	−1.61356e6	−0.513817	−0.256909	+	0.966436i	$0.582704\pi$
$398$	555952.	0.175926
$399$	769903.	0.242105
$400$	592012.	0.185004
$401$	4.58182e6	1.42291	0.711455	−	0.702732i	$-0.248037\pi$
$401$	4.58182e6	1.42291	0.711455	+	0.702732i	$0.248037\pi$
$402$	−487205.	−0.150365
$403$	−5.49721e6	−1.68609
$404$	2.03985e6	0.621790
$405$	−164025.	−0.0496904
$406$	418093.	0.125880
$407$	692766.	0.207300
$408$	38083.5	0.0113263
$409$	2.55861e6	0.756304	0.378152	−	0.925743i	$-0.376560\pi$
$409$	2.55861e6	0.756304	0.378152	+	0.925743i	$0.376560\pi$
$410$	15110.0	0.00443920
$411$	1.61175e6	0.470645
$412$	1.12156e6	0.325522
$413$	−3.99967e6	−1.15385
$414$	−90105.6	−0.0258375
$415$	742024.	0.211494
$416$	−1.77980e6	−0.504242
$417$	−1.26163e6	−0.355297
$418$	−76998.1	−0.0215546
$419$	−4.36111e6	−1.21356	−0.606781	−	0.794869i	$-0.707540\pi$
$419$	−4.36111e6	−1.21356	−0.606781	+	0.794869i	$0.707540\pi$
$420$	−847362.	−0.234394
$421$	−4.39997e6	−1.20989	−0.604943	−	0.796269i	$-0.706804\pi$
$421$	−4.39997e6	−1.20989	−0.604943	+	0.796269i	$0.706804\pi$
$422$	−842395.	−0.230269
$423$	−613410.	−0.166686
$424$	−307651.	−0.0831083
$425$	−46599.2	−0.0125143
$426$	100474.	0.0268245
$427$	2.17784e6	0.578039
$428$	3.68522e6	0.972421
$429$	726785.	0.190661
$430$	360543.	0.0940343
$431$	5.08667e6	1.31899	0.659493	−	0.751711i	$-0.270771\pi$
$431$	5.08667e6	1.31899	0.659493	+	0.751711i	$0.270771\pi$
$432$	−690522.	−0.178020
$433$	1.75095e6	0.448800	0.224400	−	0.974497i	$-0.427958\pi$
$433$	1.75095e6	0.448800	0.224400	+	0.974497i	$0.427958\pi$
$434$	893126.	0.227609
$435$	−867575.	−0.219828
$436$	−6.74816e6	−1.70008
$437$	−877631.	−0.219841
$438$	−9948.37	−0.00247780
$439$	−2.66084e6	−0.658957	−0.329479	−	0.944163i	$-0.606873\pi$
$439$	−2.66084e6	−0.658957	−0.329479	+	0.944163i	$0.606873\pi$
$440$	171681.	0.0422756
$441$	−180686.	−0.0442414
$442$	44689.0	0.0108804
$443$	−6.98400e6	−1.69081	−0.845406	−	0.534125i	$-0.820641\pi$
$443$	−6.98400e6	−1.69081	−0.845406	+	0.534125i	$0.820641\pi$
$444$	−1.60733e6	−0.386945
$445$	3.12653e6	0.748449
$446$	950021.	0.226150
$447$	2.70776e6	0.640976
$448$	−3.37036e6	−0.793379
$449$	7.66547e6	1.79441	0.897207	−	0.441610i	$-0.145593\pi$
$449$	7.66547e6	1.79441	0.897207	+	0.441610i	$0.145593\pi$
$450$	−45466.3	−0.0105842
$451$	−81430.3	−0.0188514
$452$	2.58865e6	0.595973
$453$	−2.02824e6	−0.464380
$454$	1.24382e6	0.283216
$455$	−2.01438e6	−0.456156
$456$	361917.	0.0815073
$457$	3.50188e6	0.784351	0.392175	−	0.919890i	$-0.371723\pi$
$457$	3.50188e6	0.784351	0.392175	+	0.919890i	$0.371723\pi$
$458$	51188.7	0.0114028
$459$	54353.2	0.0120419
$460$	965929.	0.212839
$461$	−6.63603e6	−1.45431	−0.727153	−	0.686475i	$-0.759157\pi$
$461$	−6.63603e6	−1.45431	−0.727153	+	0.686475i	$0.759157\pi$
$462$	−118080.	−0.0257378
$463$	1.13310e6	0.245649	0.122825	−	0.992428i	$-0.460805\pi$
$463$	1.13310e6	0.245649	0.122825	+	0.992428i	$0.460805\pi$
$464$	−3.65237e6	−0.787553
$465$	−1.85331e6	−0.397480
$466$	25136.8	0.00536222
$467$	1.37315e6	0.291358	0.145679	−	0.989332i	$-0.453463\pi$
$467$	1.37315e6	0.291358	0.145679	+	0.989332i	$0.453463\pi$
$468$	−1.68627e6	−0.355886
$469$	−7.27728e6	−1.52770
$470$	−170032.	−0.0355047
$471$	3.10444e6	0.644809
$472$	−1.88017e6	−0.388456
$473$	−1.94303e6	−0.399324
$474$	380017.	0.0776887
$475$	−442843.	−0.0900567
$476$	280792.	0.0568025
$477$	−439084.	−0.0883592
$478$	1.09034e6	0.218270
$479$	−7.71987e6	−1.53735	−0.768673	−	0.639642i	$-0.779082\pi$
$479$	−7.71987e6	−1.53735	−0.768673	+	0.639642i	$0.779082\pi$
$480$	−600035.	−0.118870
$481$	−3.82102e6	−0.753037
$482$	−953900.	−0.187019
$483$	−1.34589e6	−0.262507
$484$	−456703.	−0.0886177
$485$	−1.86163e6	−0.359368
$486$	53031.9	0.0101847
$487$	2.76688e6	0.528650	0.264325	−	0.964434i	$-0.414851\pi$
$487$	2.76688e6	0.528650	0.264325	+	0.964434i	$0.414851\pi$
$488$	1.02376e6	0.194603
$489$	1.21303e6	0.229403
$490$	−50084.6	−0.00942354
$491$	−2.58549e6	−0.483993	−0.241997	−	0.970277i	$-0.577802\pi$
$491$	−2.58549e6	−0.483993	−0.241997	+	0.970277i	$0.577802\pi$
$492$	188932.	0.0351879
$493$	287490.	0.0532727
$494$	424690.	0.0782988
$495$	245025.	0.0449467
$496$	−7.80216e6	−1.42400
$497$	1.50076e6	0.272534
$498$	−239908.	−0.0433483
$499$	−580259.	−0.104321	−0.0521604	−	0.998639i	$-0.516611\pi$
$499$	−580259.	−0.104321	−0.0521604	+	0.998639i	$0.516611\pi$
$500$	487397.	0.0871883
$501$	−4.28916e6	−0.763446
$502$	67674.6	0.0119858
$503$	−8.01677e6	−1.41280	−0.706398	−	0.707815i	$-0.749681\pi$
$503$	−8.01677e6	−1.41280	−0.706398	+	0.707815i	$0.749681\pi$
$504$	555015.	0.0973260
$505$	1.63484e6	0.285263
$506$	134602.	0.0233709
$507$	−667015.	−0.115243
$508$	3.51718e6	0.604694
$509$	−375241.	−0.0641971	−0.0320986	−	0.999485i	$-0.510219\pi$
$509$	−375241.	−0.0641971	−0.0320986	+	0.999485i	$0.510219\pi$
$510$	15066.2	0.00256495
$511$	−148597.	−0.0251743
$512$	−4.24633e6	−0.715878
$513$	516532.	0.0866571
$514$	−1.02515e6	−0.171152
$515$	898877.	0.149342
$516$	4.50815e6	0.745374
$517$	916328.	0.150773
$518$	620796.	0.101654
$519$	5.46328e6	0.890298
$520$	−946922.	−0.153570
$521$	−4.40189e6	−0.710469	−0.355235	−	0.934777i	$-0.615599\pi$
$521$	−4.40189e6	−0.710469	−0.355235	+	0.934777i	$0.615599\pi$
$522$	280501.	0.0450565
$523$	3.26635e6	0.522166	0.261083	−	0.965316i	$-0.415920\pi$
$523$	3.26635e6	0.522166	0.261083	+	0.965316i	$0.415920\pi$
$524$	−5.52829e6	−0.879554
$525$	−679120.	−0.107535
$526$	700786.	0.110439
$527$	614133.	0.0963244
$528$	1.03152e6	0.161025
$529$	−4.90213e6	−0.761634
$530$	−121710.	−0.0188208
$531$	−2.68340e6	−0.412999
$532$	2.66844e6	0.408769
$533$	449136.	0.0684795
$534$	−1.01086e6	−0.153404
$535$	2.95353e6	0.446125
$536$	−3.42091e6	−0.514315
$537$	5.30024e6	0.793158
$538$	−188747.	−0.0281141
$539$	269914.	0.0400178
$540$	−568500.	−0.0838969
$541$	8.43137e6	1.23853	0.619263	−	0.785184i	$-0.287432\pi$
$541$	8.43137e6	1.23853	0.619263	+	0.785184i	$0.287432\pi$
$542$	4128.37	0.000603643 0
$543$	3.63351e6	0.528844
$544$	198835.	0.0288068
$545$	−5.40832e6	−0.779957
$546$	651281.	0.0934947
$547$	−4.69753e6	−0.671276	−0.335638	−	0.941991i	$-0.608952\pi$
$547$	−4.69753e6	−0.671276	−0.335638	+	0.941991i	$0.608952\pi$
$548$	5.58622e6	0.794633
$549$	1.46113e6	0.206898
$550$	67918.8	0.00957377
$551$	2.73209e6	0.383368
$552$	−632675.	−0.0883758
$553$	5.67623e6	0.789310
$554$	619319.	0.0857315
$555$	−1.28820e6	−0.177521
$556$	−4.37272e6	−0.599881
$557$	1.06786e7	1.45840	0.729200	−	0.684300i	$-0.239892\pi$
$557$	1.06786e7	1.45840	0.729200	+	0.684300i	$0.239892\pi$
$558$	599203.	0.0814683
$559$	1.07169e7	1.45058
$560$	−2.85900e6	−0.385251
$561$	−81194.4	−0.0108923
$562$	−1.75147e6	−0.233917
$563$	6.73487e6	0.895485	0.447742	−	0.894163i	$-0.352228\pi$
$563$	6.73487e6	0.895485	0.447742	+	0.894163i	$0.352228\pi$
$564$	−2.12604e6	−0.281432
$565$	2.07467e6	0.273419
$566$	−276475.	−0.0362756
$567$	792125.	0.103475
$568$	705480.	0.0917516
$569$	6.36492e6	0.824161	0.412081	−	0.911147i	$-0.364802\pi$
$569$	6.36492e6	0.824161	0.412081	+	0.911147i	$0.364802\pi$
$570$	143178.	0.0184582
$571$	−3.10897e6	−0.399049	−0.199524	−	0.979893i	$-0.563940\pi$
$571$	−3.10897e6	−0.399049	−0.199524	+	0.979893i	$0.563940\pi$
$572$	2.51899e6	0.321911
$573$	3.55751e6	0.452647
$574$	−72970.7	−0.00924419
$575$	774145.	0.0976456
$576$	−2.26119e6	−0.283975
$577$	1.35678e7	1.69656	0.848280	−	0.529548i	$-0.177639\pi$
$577$	1.35678e7	1.69656	0.848280	+	0.529548i	$0.177639\pi$
$578$	1.27018e6	0.158141
$579$	−1.73101e6	−0.214586
$580$	−3.00696e6	−0.371157
$581$	−3.58345e6	−0.440414
$582$	601895.	0.0736569
$583$	655916.	0.0799239
$584$	−69852.4	−0.00847519
$585$	−1.35146e6	−0.163273
$586$	−1.97250e6	−0.237286
$587$	1.34652e7	1.61293	0.806466	−	0.591280i	$-0.201377\pi$
$587$	1.34652e7	1.61293	0.806466	+	0.591280i	$0.201377\pi$
$588$	−626247.	−0.0746968
$589$	5.83626e6	0.693181
$590$	−743815.	−0.0879701
$591$	4.83814e6	0.569783
$592$	−5.42314e6	−0.635985
$593$	1.49874e7	1.75021	0.875105	−	0.483933i	$-0.160792\pi$
$593$	1.49874e7	1.75021	0.875105	+	0.483933i	$0.160792\pi$
$594$	−79220.4	−0.00921237
$595$	225041.	0.0260597
$596$	9.38493e6	1.08222
$597$	5.57129e6	0.639764
$598$	−742411.	−0.0848968
$599$	4.88452e6	0.556231	0.278115	−	0.960548i	$-0.410290\pi$
$599$	4.88452e6	0.556231	0.278115	+	0.960548i	$0.410290\pi$
$600$	−319241.	−0.0362027
$601$	−801632.	−0.0905293	−0.0452646	−	0.998975i	$-0.514413\pi$
$601$	−801632.	−0.0905293	−0.0452646	+	0.998975i	$0.514413\pi$
$602$	−1.74117e6	−0.195817
$603$	−4.88236e6	−0.546811
$604$	−7.02975e6	−0.784056
$605$	−366025.	−0.0406558
$606$	−528569.	−0.0584682
$607$	1.38864e7	1.52974	0.764872	−	0.644182i	$-0.222802\pi$
$607$	1.38864e7	1.52974	0.764872	+	0.644182i	$0.222802\pi$
$608$	1.88958e6	0.207303
$609$	4.18977e6	0.457770
$610$	405011.	0.0440700
$611$	−5.05410e6	−0.547697
$612$	188385.	0.0203314
$613$	1.48685e6	0.159815	0.0799073	−	0.996802i	$-0.474538\pi$
$613$	1.48685e6	0.159815	0.0799073	+	0.996802i	$0.474538\pi$
$614$	813659.	0.0871007
$615$	151420.	0.0161434
$616$	−829097.	−0.0880346
$617$	2.96802e6	0.313873	0.156937	−	0.987609i	$-0.449838\pi$
$617$	2.96802e6	0.313873	0.156937	+	0.987609i	$0.449838\pi$
$618$	−290621.	−0.0306095
$619$	−1.40553e7	−1.47440	−0.737198	−	0.675677i	$-0.763851\pi$
$619$	−1.40553e7	−1.47440	−0.737198	+	0.675677i	$0.763851\pi$
$620$	−6.42344e6	−0.671102
$621$	−902962.	−0.0939595
$622$	−947461.	−0.0981941
$623$	−1.50989e7	−1.55857
$624$	−5.68945e6	−0.584937
$625$	390625.	0.0400000
$626$	−2.67718e6	−0.273049
$627$	−771610.	−0.0783843
$628$	1.07598e7	1.08869
$629$	426873.	0.0430202
$630$	219570.	0.0220405
$631$	−7.30424e6	−0.730301	−0.365150	−	0.930949i	$-0.618982\pi$
$631$	−7.30424e6	−0.730301	−0.365150	+	0.930949i	$0.618982\pi$
$632$	2.66829e6	0.265730
$633$	−8.44178e6	−0.837384
$634$	244463.	0.0241540
$635$	2.81885e6	0.277420
$636$	−1.52184e6	−0.149185
$637$	−1.48874e6	−0.145368
$638$	−419019.	−0.0407551
$639$	1.00687e6	0.0975487
$640$	−2.76024e6	−0.266377
$641$	−7.28278e6	−0.700087	−0.350043	−	0.936733i	$-0.613833\pi$
$641$	−7.28278e6	−0.700087	−0.350043	+	0.936733i	$0.613833\pi$
$642$	−954921.	−0.0914387
$643$	1.44225e7	1.37567	0.687833	−	0.725869i	$-0.258562\pi$
$643$	1.44225e7	1.37567	0.687833	+	0.725869i	$0.258562\pi$
$644$	−4.66476e6	−0.443215
$645$	3.61306e6	0.341961
$646$	−47445.2	−0.00447313
$647$	−1.62591e6	−0.152699	−0.0763495	−	0.997081i	$-0.524326\pi$
$647$	−1.62591e6	−0.152699	−0.0763495	+	0.997081i	$0.524326\pi$
$648$	372363.	0.0348360
$649$	4.00854e6	0.373572
$650$	−374613.	−0.0347775
$651$	8.95016e6	0.827711
$652$	4.20427e6	0.387322
$653$	−1.73130e7	−1.58887	−0.794435	−	0.607349i	$-0.792233\pi$
$653$	−1.73130e7	−1.58887	−0.794435	+	0.607349i	$0.792233\pi$
$654$	1.74859e6	0.159862
$655$	−4.43065e6	−0.403520
$656$	637457.	0.0578350
$657$	−99694.3	−0.00901066
$658$	821133.	0.0739348
$659$	2.47926e6	0.222387	0.111193	−	0.993799i	$-0.464533\pi$
$659$	2.47926e6	0.222387	0.111193	+	0.993799i	$0.464533\pi$
$660$	849241.	0.0758876
$661$	−7.28403e6	−0.648437	−0.324219	−	0.945982i	$-0.605101\pi$
$661$	−7.28403e6	−0.648437	−0.324219	+	0.945982i	$0.605101\pi$
$662$	884293.	0.0784244
$663$	447835.	0.0395671
$664$	−1.68451e6	−0.148270
$665$	2.13862e6	0.187534
$666$	416495.	0.0363852
$667$	−4.77602e6	−0.415673
$668$	−1.48660e7	−1.28900
$669$	9.52032e6	0.822406
$670$	−1.35335e6	−0.116472
$671$	−2.18267e6	−0.187147
$672$	2.89775e6	0.247535
$673$	1.73888e7	1.47990	0.739951	−	0.672661i	$-0.234849\pi$
$673$	1.73888e7	1.47990	0.739951	+	0.672661i	$0.234849\pi$
$674$	329481.	0.0279371
$675$	−455625.	−0.0384900
$676$	−2.31183e6	−0.194576
$677$	−1.51982e7	−1.27444	−0.637221	−	0.770681i	$-0.719916\pi$
$677$	−1.51982e7	−1.27444	−0.637221	+	0.770681i	$0.719916\pi$
$678$	−670775.	−0.0560406
$679$	8.99038e6	0.748348
$680$	105787.	0.00877328
$681$	1.24645e7	1.02993
$682$	−895106.	−0.0736908
$683$	−2.02075e7	−1.65753	−0.828765	−	0.559596i	$-0.810956\pi$
$683$	−2.02075e7	−1.65753	−0.828765	+	0.559596i	$0.810956\pi$
$684$	1.79027e6	0.146311
$685$	4.47708e6	0.364560
$686$	2.06425e6	0.167476
$687$	512970.	0.0414668
$688$	1.52105e7	1.22510
$689$	−3.61777e6	−0.290330
$690$	−250293.	−0.0200137
$691$	−1.88904e7	−1.50503	−0.752517	−	0.658573i	$-0.771160\pi$
$691$	−1.88904e7	−1.50503	−0.752517	+	0.658573i	$0.771160\pi$
$692$	1.89354e7	1.50317
$693$	−1.18330e6	−0.0935968
$694$	501550.	0.0395290
$695$	−3.50453e6	−0.275212
$696$	1.96953e6	0.154113
$697$	−50176.3	−0.00391216
$698$	−1.37715e6	−0.106990
$699$	251900.	0.0195000
$700$	−2.35378e6	−0.181561
$701$	−1.63467e7	−1.25642	−0.628210	−	0.778044i	$-0.716212\pi$
$701$	−1.63467e7	−1.25642	−0.628210	+	0.778044i	$0.716212\pi$
$702$	436948.	0.0334647
$703$	4.05668e6	0.309587
$704$	3.37783e6	0.256865
$705$	−1.70392e6	−0.129115
$706$	−2.19001e6	−0.165362
$707$	−7.89511e6	−0.594032
$708$	−9.30050e6	−0.697305
$709$	2.28062e7	1.70387	0.851936	−	0.523646i	$-0.175429\pi$
$709$	2.28062e7	1.70387	0.851936	+	0.523646i	$0.175429\pi$
$710$	279095.	0.0207782
$711$	3.80822e6	0.282519
$712$	−7.09771e6	−0.524709
$713$	−1.02025e7	−0.751594
$714$	−72759.3	−0.00534125
$715$	2.01885e6	0.147686
$716$	1.83703e7	1.33916
$717$	1.09265e7	0.793750
$718$	−1.05659e6	−0.0764886
$719$	1.42246e6	0.102617	0.0513083	−	0.998683i	$-0.483661\pi$
$719$	1.42246e6	0.102617	0.0513083	+	0.998683i	$0.483661\pi$
$720$	−1.91812e6	−0.137894
$721$	−4.34094e6	−0.310989
$722$	1.77290e6	0.126573
$723$	−9.55919e6	−0.680104
$724$	1.25935e7	0.892896
$725$	−2.40993e6	−0.170278
$726$	118342.	0.00833290
$727$	1.58260e7	1.11054	0.555272	−	0.831669i	$-0.312614\pi$
$727$	1.58260e7	1.11054	0.555272	+	0.831669i	$0.312614\pi$
$728$	4.57297e6	0.319793
$729$	531441.	0.0370370
$730$	−27634.4	−0.00191930
$731$	−1.19727e6	−0.0828701
$732$	5.06417e6	0.349326
$733$	1.04557e7	0.718776	0.359388	−	0.933188i	$-0.382985\pi$
$733$	1.04557e7	0.718776	0.359388	+	0.933188i	$0.382985\pi$
$734$	2.46248e6	0.168707
$735$	−501906.	−0.0342692
$736$	−3.30321e6	−0.224772
$737$	7.29341e6	0.494609
$738$	−48956.4	−0.00330879
$739$	−5.11969e6	−0.344852	−0.172426	−	0.985023i	$-0.555160\pi$
$739$	−5.11969e6	−0.344852	−0.172426	+	0.985023i	$0.555160\pi$
$740$	−4.46482e6	−0.299726
$741$	4.25589e6	0.284738
$742$	587775.	0.0391923
$743$	−4.44877e6	−0.295643	−0.147822	−	0.989014i	$-0.547226\pi$
$743$	−4.44877e6	−0.295643	−0.147822	+	0.989014i	$0.547226\pi$
$744$	4.20730e6	0.278658
$745$	7.52156e6	0.496498
$746$	−3.11316e6	−0.204812
$747$	−2.40416e6	−0.157638
$748$	−281414.	−0.0183904
$749$	−1.42634e7	−0.929009
$750$	−126295.	−0.00819849
$751$	−1.91736e7	−1.24052	−0.620262	−	0.784395i	$-0.712974\pi$
$751$	−1.91736e7	−1.24052	−0.620262	+	0.784395i	$0.712974\pi$
$752$	−7.17325e6	−0.462563
$753$	678178.	0.0435869
$754$	2.31114e6	0.148047
$755$	−5.63400e6	−0.359707
$756$	2.74545e6	0.174707
$757$	−1.24339e7	−0.788621	−0.394310	−	0.918977i	$-0.629017\pi$
$757$	−1.24339e7	−0.788621	−0.394310	+	0.918977i	$0.629017\pi$
$758$	−3.65707e6	−0.231185
$759$	1.34887e6	0.0849896
$760$	1.00532e6	0.0631353
$761$	−1.41772e7	−0.887421	−0.443710	−	0.896170i	$-0.646338\pi$
$761$	−1.41772e7	−0.887421	−0.443710	+	0.896170i	$0.646338\pi$
$762$	−911379.	−0.0568606
$763$	2.61184e7	1.62418
$764$	1.23301e7	0.764246
$765$	150981.	0.00932759
$766$	−392125.	−0.0241464
$767$	−2.21095e7	−1.35703
$768$	−7.14736e6	−0.437263
$769$	−4.53694e6	−0.276660	−0.138330	−	0.990386i	$-0.544174\pi$
$769$	−4.53694e6	−0.276660	−0.138330	+	0.990386i	$0.544174\pi$
$770$	−328000.	−0.0199364
$771$	−1.02732e7	−0.622402
$772$	−5.99956e6	−0.362306
$773$	−2.11780e7	−1.27479	−0.637393	−	0.770539i	$-0.719987\pi$
$773$	−2.11780e7	−1.27479	−0.637393	+	0.770539i	$0.719987\pi$
$774$	−1.16816e6	−0.0700890
$775$	−5.14807e6	−0.307886
$776$	4.22620e6	0.251939
$777$	6.22110e6	0.369670
$778$	−3.84065e6	−0.227487
$779$	−476838.	−0.0281531
$780$	−4.68407e6	−0.275668
$781$	−1.50409e6	−0.0882361
$782$	82940.1	0.00485007
$783$	2.81094e6	0.163850
$784$	−2.11295e6	−0.122772
$785$	8.62344e6	0.499467
$786$	1.43250e6	0.0827063
$787$	−2.73190e7	−1.57228	−0.786138	−	0.618051i	$-0.787922\pi$
$787$	−2.73190e7	−1.57228	−0.786138	+	0.618051i	$0.787922\pi$
$788$	1.67687e7	0.962018
$789$	7.02269e6	0.401616
$790$	1.05560e6	0.0601774
$791$	−1.00192e7	−0.569367
$792$	−556246.	−0.0315104
$793$	1.20387e7	0.679826
$794$	1.44914e6	0.0815752
$795$	−1.21968e6	−0.0684427
$796$	1.93097e7	1.08017
$797$	−8.71204e6	−0.485818	−0.242909	−	0.970049i	$-0.578102\pi$
$797$	−8.71204e6	−0.485818	−0.242909	+	0.970049i	$0.578102\pi$
$798$	−691450.	−0.0384373
$799$	564630.	0.0312894
$800$	−1.66676e6	−0.0920766
$801$	−1.01299e7	−0.557861
$802$	−4.11493e6	−0.225905
$803$	148926.	0.00815045
$804$	−1.69220e7	−0.923231
$805$	−3.73857e6	−0.203337
$806$	4.93704e6	0.267688
$807$	−1.89146e6	−0.102238
$808$	−3.71134e6	−0.199987
$809$	−8.30436e6	−0.446103	−0.223051	−	0.974807i	$-0.571602\pi$
$809$	−8.30436e6	−0.446103	−0.223051	+	0.974807i	$0.571602\pi$
$810$	147311.	0.00788900
$811$	−2.16579e7	−1.15629	−0.578143	−	0.815936i	$-0.696222\pi$
$811$	−2.16579e7	−1.15629	−0.578143	+	0.815936i	$0.696222\pi$
$812$	1.45215e7	0.772896
$813$	41371.0	0.00219518
$814$	−622172.	−0.0329116
$815$	3.36952e6	0.177695
$816$	635610.	0.0334168
$817$	−1.13779e7	−0.596359
$818$	−2.29789e6	−0.120073
$819$	6.52660e6	0.339998
$820$	524812.	0.0272564
$821$	−4.66524e6	−0.241555	−0.120777	−	0.992680i	$-0.538539\pi$
$821$	−4.66524e6	−0.241555	−0.120777	+	0.992680i	$0.538539\pi$
$822$	−1.44751e6	−0.0747210
$823$	−3.86223e7	−1.98765	−0.993823	−	0.110977i	$-0.964602\pi$
$823$	−3.86223e7	−1.98765	−0.993823	+	0.110977i	$0.964602\pi$
$824$	−2.04059e6	−0.104698
$825$	680625.	0.0348155
$826$	3.59210e6	0.183189
$827$	1.64856e7	0.838187	0.419094	−	0.907943i	$-0.362348\pi$
$827$	1.64856e7	0.838187	0.419094	+	0.907943i	$0.362348\pi$
$828$	−3.12961e6	−0.158641
$829$	1.17447e7	0.593546	0.296773	−	0.954948i	$-0.404089\pi$
$829$	1.17447e7	0.593546	0.296773	+	0.954948i	$0.404089\pi$
$830$	−666411.	−0.0335774
$831$	6.20630e6	0.311767
$832$	−1.86307e7	−0.933086
$833$	166317.	0.00830473
$834$	1.13307e6	0.0564080
$835$	−1.19143e7	−0.591363
$836$	−2.67435e6	−0.132344
$837$	6.00471e6	0.296264
$838$	3.91671e6	0.192669
$839$	2.08153e7	1.02089	0.510444	−	0.859911i	$-0.329481\pi$
$839$	2.08153e7	1.02089	0.510444	+	0.859911i	$0.329481\pi$
$840$	1.54171e6	0.0753884
$841$	−5.64328e6	−0.275132
$842$	3.95161e6	0.192085
$843$	−1.75518e7	−0.850653
$844$	−2.92587e7	−1.41383
$845$	−1.85282e6	−0.0892670
$846$	550903.	0.0264636
$847$	1.76764e6	0.0846615
$848$	−5.13467e6	−0.245202
$849$	−2.77060e6	−0.131918
$850$	41850.7	0.00198680
$851$	−7.09158e6	−0.335675
$852$	3.48975e6	0.164700
$853$	4.06291e6	0.191190	0.0955950	−	0.995420i	$-0.469525\pi$
$853$	4.06291e6	0.191190	0.0955950	+	0.995420i	$0.469525\pi$
$854$	−1.95592e6	−0.0917712
$855$	1.43481e6	0.0671243
$856$	−6.70497e6	−0.312761
$857$	66823.3	0.00310796	0.00155398	−	0.999999i	$-0.499505\pi$
$857$	66823.3	0.00310796	0.00155398	+	0.999999i	$0.499505\pi$
$858$	−652725.	−0.0302700
$859$	9.60662e6	0.444209	0.222105	−	0.975023i	$-0.428707\pi$
$859$	9.60662e6	0.444209	0.222105	+	0.975023i	$0.428707\pi$
$860$	1.25226e7	0.577364
$861$	−731251.	−0.0336170
$862$	−4.56833e6	−0.209406
$863$	−3.62555e6	−0.165709	−0.0828547	−	0.996562i	$-0.526404\pi$
$863$	−3.62555e6	−0.165709	−0.0828547	+	0.996562i	$0.526404\pi$
$864$	1.94411e6	0.0886008
$865$	1.51758e7	0.689621
$866$	−1.57252e6	−0.0712529
$867$	1.27287e7	0.575090
$868$	3.10207e7	1.39750
$869$	−5.68882e6	−0.255548
$870$	779168.	0.0349006
$871$	−4.02275e7	−1.79671
$872$	1.22777e7	0.546798
$873$	6.03169e6	0.267857
$874$	788200.	0.0349026
$875$	−1.88644e6	−0.0832959
$876$	−345534.	−0.0152135
$877$	−6.29358e6	−0.276311	−0.138156	−	0.990411i	$-0.544117\pi$
$877$	−6.29358e6	−0.276311	−0.138156	+	0.990411i	$0.544117\pi$
$878$	2.38970e6	0.104618
$879$	−1.97667e7	−0.862904
$880$	2.86534e6	0.124729
$881$	2.35769e7	1.02340	0.511701	−	0.859163i	$-0.329015\pi$
$881$	2.35769e7	1.02340	0.511701	+	0.859163i	$0.329015\pi$
$882$	162274.	0.00702389
$883$	1.08516e7	0.468372	0.234186	−	0.972192i	$-0.424758\pi$
$883$	1.08516e7	0.468372	0.234186	+	0.972192i	$0.424758\pi$
$884$	1.55217e6	0.0668049
$885$	−7.45389e6	−0.319908
$886$	6.27233e6	0.268438
$887$	−2.44367e7	−1.04288	−0.521439	−	0.853289i	$-0.674604\pi$
$887$	−2.44367e7	−1.04288	−0.521439	+	0.853289i	$0.674604\pi$
$888$	2.92442e6	0.124454
$889$	−1.36131e7	−0.577699
$890$	−2.80793e6	−0.118826
$891$	−793881.	−0.0335013
$892$	3.29968e7	1.38854
$893$	5.36581e6	0.225168
$894$	−2.43184e6	−0.101763
$895$	1.47229e7	0.614377
$896$	1.33300e7	0.554703
$897$	−7.43982e6	−0.308732
$898$	−6.88435e6	−0.284887
$899$	3.17606e7	1.31066
$900$	−1.57917e6	−0.0649863
$901$	404167.	0.0165863
$902$	73132.5	0.00299291
$903$	−1.74486e7	−0.712098
$904$	−4.70984e6	−0.191684
$905$	1.00931e7	0.409641
$906$	1.82156e6	0.0737264
$907$	−4.71119e7	−1.90157	−0.950785	−	0.309850i	$-0.899721\pi$
$907$	−4.71119e7	−1.90157	−0.950785	+	0.309850i	$0.899721\pi$
$908$	4.32012e7	1.73893
$909$	−5.29687e6	−0.212623
$910$	1.80911e6	0.0724207
$911$	4.74577e7	1.89457	0.947286	−	0.320390i	$-0.103814\pi$
$911$	4.74577e7	1.89457	0.947286	+	0.320390i	$0.103814\pi$
$912$	6.04036e6	0.240478
$913$	3.59140e6	0.142589
$914$	−3.14503e6	−0.124526
$915$	4.05869e6	0.160263
$916$	1.77792e6	0.0700122
$917$	2.13969e7	0.840288
$918$	−48814.6	−0.00191180
$919$	1.88222e7	0.735159	0.367580	−	0.929992i	$-0.380187\pi$
$919$	1.88222e7	0.735159	0.367580	+	0.929992i	$0.380187\pi$
$920$	−1.75743e6	−0.0684556
$921$	8.15381e6	0.316746
$922$	5.95982e6	0.230890
$923$	8.29595e6	0.320525
$924$	−4.10123e6	−0.158028
$925$	−3.57833e6	−0.137508
$926$	−1.01764e6	−0.0390001
$927$	−2.91236e6	−0.111313
$928$	1.02830e7	0.391966
$929$	1.80487e7	0.686132	0.343066	−	0.939311i	$-0.388535\pi$
$929$	1.80487e7	0.686132	0.343066	+	0.939311i	$0.388535\pi$
$930$	1.66445e6	0.0631051
$931$	1.58056e6	0.0597634
$932$	873067.	0.0329237
$933$	−9.49466e6	−0.357088
$934$	−1.23323e6	−0.0462569
$935$	−225540.	−0.00843712
$936$	3.06803e6	0.114464
$937$	−5.09381e7	−1.89537	−0.947685	−	0.319208i	$-0.896583\pi$
$937$	−5.09381e7	−1.89537	−0.947685	+	0.319208i	$0.896583\pi$
$938$	6.53572e6	0.242542
$939$	−2.68284e7	−0.992958
$940$	−5.90566e6	−0.217996
$941$	4.08876e7	1.50528	0.752641	−	0.658431i	$-0.228779\pi$
$941$	4.08876e7	1.50528	0.752641	+	0.658431i	$0.228779\pi$
$942$	−2.78810e6	−0.102372
$943$	833571.	0.0305255
$944$	−3.13799e7	−1.14610
$945$	2.20035e6	0.0801515
$946$	1.74503e6	0.0633979
$947$	−1.33924e6	−0.0485271	−0.0242636	−	0.999706i	$-0.507724\pi$
$947$	−1.33924e6	−0.0485271	−0.0242636	+	0.999706i	$0.507724\pi$
$948$	1.31990e7	0.477003
$949$	−821416.	−0.0296072
$950$	397717.	0.0142977
$951$	2.44980e6	0.0878374
$952$	−510879.	−0.0182695
$953$	1.17556e6	0.0419288	0.0209644	−	0.999780i	$-0.493326\pi$
$953$	1.17556e6	0.0419288	0.0209644	+	0.999780i	$0.493326\pi$
$954$	394341.	0.0140282
$955$	9.88197e6	0.350619
$956$	3.78706e7	1.34016
$957$	−4.19906e6	−0.148208
$958$	6.93321e6	0.244074
$959$	−2.16212e7	−0.759159
$960$	−6.28108e6	−0.219966
$961$	3.92177e7	1.36985
$962$	3.43165e6	0.119554
$963$	−9.56942e6	−0.332522
$964$	−3.31315e7	−1.14828
$965$	−4.80835e6	−0.166218
$966$	1.20874e6	0.0416764
$967$	−1.01207e7	−0.348053	−0.174026	−	0.984741i	$-0.555678\pi$
$967$	−1.01207e7	−0.348053	−0.174026	+	0.984741i	$0.555678\pi$
$968$	830935.	0.0285022
$969$	−475456.	−0.0162668
$970$	1.67193e6	0.0570544
$971$	−2.71903e7	−0.925476	−0.462738	−	0.886495i	$-0.653133\pi$
$971$	−2.71903e7	−0.925476	−0.462738	+	0.886495i	$0.653133\pi$
$972$	1.84194e6	0.0625331
$973$	1.69244e7	0.573101
$974$	−2.48493e6	−0.0839300
$975$	−3.75405e6	−0.126470
$976$	1.70865e7	0.574154
$977$	2.41360e7	0.808962	0.404481	−	0.914546i	$-0.367452\pi$
$977$	2.41360e7	0.808962	0.404481	+	0.914546i	$0.367452\pi$
$978$	−1.08942e6	−0.0364207
$979$	1.51324e7	0.504604
$980$	−1.73957e6	−0.0578599
$981$	1.75229e7	0.581346
$982$	2.32203e6	0.0768402
$983$	−2.27328e7	−0.750359	−0.375180	−	0.926952i	$-0.622419\pi$
$983$	−2.27328e7	−0.750359	−0.375180	+	0.926952i	$0.622419\pi$
$984$	−343747.	−0.0113175
$985$	1.34393e7	0.441352
$986$	−258194.	−0.00845774
$987$	8.22871e6	0.268868
$988$	1.47506e7	0.480749
$989$	1.98900e7	0.646613
$990$	−220057.	−0.00713587
$991$	−1.42957e6	−0.0462403	−0.0231202	−	0.999733i	$-0.507360\pi$
$991$	−1.42957e6	−0.0462403	−0.0231202	+	0.999733i	$0.507360\pi$
$992$	2.19664e7	0.708728
$993$	8.86164e6	0.285194
$994$	−1.34783e6	−0.0432684
$995$	1.54758e7	0.495559
$996$	−8.33266e6	−0.266155
$997$	−3.51095e6	−0.111863	−0.0559316	−	0.998435i	$-0.517813\pi$
$997$	−3.51095e6	−0.111863	−0.0559316	+	0.998435i	$0.517813\pi$
$998$	521130.	0.0165623
$999$	4.17377e6	0.132317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.g.1.3	✓	5
3.2	odd	2		495.6.a.i.1.3		5
5.4	even	2		825.6.a.k.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.g.1.3	✓	5	1.1	even	1	trivial
495.6.a.i.1.3		5	3.2	odd	2
825.6.a.k.1.3		5	5.4	even	2

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q-0.898099 q^{2} -9.00000 q^{3} -31.1934 q^{4} -25.0000 q^{5} +8.08289 q^{6} +120.732 q^{7} +56.7540 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-0.898099 q^{2} -9.00000 q^{3} -31.1934 q^{4} -25.0000 q^{5} +8.08289 q^{6} +120.732 q^{7} +56.7540 q^{8} +81.0000 q^{9} +22.4525 q^{10} -121.000 q^{11} +280.741 q^{12} +667.387 q^{13} -108.430 q^{14} +225.000 q^{15} +947.219 q^{16} -74.5586 q^{17} -72.7460 q^{18} -708.549 q^{19} +779.835 q^{20} -1086.59 q^{21} +108.670 q^{22} +1238.63 q^{23} -510.786 q^{24} +625.000 q^{25} -599.380 q^{26} -729.000 q^{27} -3766.06 q^{28} -3855.89 q^{29} -202.072 q^{30} -8236.92 q^{31} -2666.82 q^{32} +1089.00 q^{33} +66.9611 q^{34} -3018.31 q^{35} -2526.67 q^{36} -5725.33 q^{37} +636.348 q^{38} -6006.49 q^{39} -1418.85 q^{40} +672.977 q^{41} +975.867 q^{42} +16058.1 q^{43} +3774.40 q^{44} -2025.00 q^{45} -1112.41 q^{46} -7572.96 q^{47} -8524.97 q^{48} -2230.69 q^{49} -561.312 q^{50} +671.028 q^{51} -20818.1 q^{52} -5420.79 q^{53} +654.714 q^{54} +3025.00 q^{55} +6852.04 q^{56} +6376.94 q^{57} +3462.97 q^{58} -33128.4 q^{59} -7018.52 q^{60} +18038.6 q^{61} +7397.57 q^{62} +9779.32 q^{63} -27915.9 q^{64} -16684.7 q^{65} -978.030 q^{66} -60276.1 q^{67} +2325.74 q^{68} -11147.7 q^{69} +2710.74 q^{70} +12430.5 q^{71} +4597.07 q^{72} -1230.79 q^{73} +5141.92 q^{74} -5625.00 q^{75} +22102.1 q^{76} -14608.6 q^{77} +5394.42 q^{78} +47015.0 q^{79} -23680.5 q^{80} +6561.00 q^{81} -604.401 q^{82} -29681.0 q^{83} +33894.5 q^{84} +1863.97 q^{85} -14421.7 q^{86} +34703.0 q^{87} -6867.23 q^{88} -125061. q^{89} +1818.65 q^{90} +80575.2 q^{91} -38637.2 q^{92} +74132.3 q^{93} +6801.27 q^{94} +17713.7 q^{95} +24001.4 q^{96} +74465.3 q^{97} +2003.38 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * q^99

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