LMFDB - Embedded newform 309.6.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,6,Mod(1,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("309.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	309.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:	$49.5586003222$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.95711 q^{2} +9.00000 q^{3} -23.2555 q^{4} +59.9608 q^{5} -26.6140 q^{6} +248.119 q^{7} +163.397 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-2.95711 q^{2} +9.00000 q^{3} -23.2555 q^{4} +59.9608 q^{5} -26.6140 q^{6} +248.119 q^{7} +163.397 q^{8} +81.0000 q^{9} -177.311 q^{10} -134.294 q^{11} -209.300 q^{12} +1029.61 q^{13} -733.714 q^{14} +539.647 q^{15} +260.995 q^{16} +469.774 q^{17} -239.526 q^{18} +1870.91 q^{19} -1394.42 q^{20} +2233.07 q^{21} +397.123 q^{22} +1279.08 q^{23} +1470.57 q^{24} +470.296 q^{25} -3044.66 q^{26} +729.000 q^{27} -5770.13 q^{28} -4379.58 q^{29} -1595.79 q^{30} -1542.39 q^{31} -6000.48 q^{32} -1208.65 q^{33} -1389.17 q^{34} +14877.4 q^{35} -1883.70 q^{36} -12810.8 q^{37} -5532.48 q^{38} +9266.48 q^{39} +9797.38 q^{40} +12053.1 q^{41} -6603.43 q^{42} -19040.0 q^{43} +3123.08 q^{44} +4856.82 q^{45} -3782.37 q^{46} -12124.4 q^{47} +2348.96 q^{48} +44756.0 q^{49} -1390.72 q^{50} +4227.97 q^{51} -23944.1 q^{52} -11753.6 q^{53} -2155.73 q^{54} -8052.39 q^{55} +40541.8 q^{56} +16838.2 q^{57} +12950.9 q^{58} +18789.1 q^{59} -12549.8 q^{60} +1038.63 q^{61} +4561.02 q^{62} +20097.6 q^{63} +9392.22 q^{64} +61736.1 q^{65} +3574.10 q^{66} +29220.7 q^{67} -10924.8 q^{68} +11511.7 q^{69} -43994.1 q^{70} -80818.5 q^{71} +13235.1 q^{72} +46807.0 q^{73} +37882.8 q^{74} +4232.66 q^{75} -43508.9 q^{76} -33321.0 q^{77} -27402.0 q^{78} -43240.3 q^{79} +15649.5 q^{80} +6561.00 q^{81} -35642.4 q^{82} +60829.3 q^{83} -51931.2 q^{84} +28168.0 q^{85} +56303.3 q^{86} -39416.2 q^{87} -21943.2 q^{88} -102267. q^{89} -14362.2 q^{90} +255465. q^{91} -29745.6 q^{92} -13881.5 q^{93} +35853.2 q^{94} +112181. q^{95} -54004.3 q^{96} +77328.7 q^{97} -132348. q^{98} -10877.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) $ 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9} + 693 q^{10} + 1470 q^{11} + 4374 q^{12} + 2515 q^{13} + 254 q^{14} + 423 q^{15} + 11542 q^{16} + 880 q^{17} + 1134 q^{18} + 7412 q^{19} + 1927 q^{20} + 3618 q^{21} + 5461 q^{22} + 5567 q^{23} + 3078 q^{24} + 31584 q^{25} + 18502 q^{26} + 18225 q^{27} + 25011 q^{28} + 17230 q^{29} + 6237 q^{30} + 22821 q^{31} + 50233 q^{32} + 13230 q^{33} + 38342 q^{34} + 30664 q^{35} + 39366 q^{36} + 13342 q^{37} + 25860 q^{38} + 22635 q^{39} + 40701 q^{40} + 36374 q^{41} + 2286 q^{42} + 48371 q^{43} - 4133 q^{44} + 3807 q^{45} + 30489 q^{46} + 17740 q^{47} + 103878 q^{48} + 119201 q^{49} - 9505 q^{50} + 7920 q^{51} + 50699 q^{52} - 52204 q^{53} + 10206 q^{54} + 90638 q^{55} - 80285 q^{56} + 66708 q^{57} + 15313 q^{58} + 34099 q^{59} + 17343 q^{60} + 71175 q^{61} - 92130 q^{62} + 32562 q^{63} + 289374 q^{64} - 32899 q^{65} + 49149 q^{66} + 85201 q^{67} - 41169 q^{68} + 50103 q^{69} - 92312 q^{70} + 102652 q^{71} + 27702 q^{72} + 186396 q^{73} - 258113 q^{74} + 284256 q^{75} + 148369 q^{76} - 109016 q^{77} + 166518 q^{78} + 210994 q^{79} + 17955 q^{80} + 164025 q^{81} + 635103 q^{82} + 68429 q^{83} + 225099 q^{84} + 375692 q^{85} + 360833 q^{86} + 155070 q^{87} + 556985 q^{88} + 163508 q^{89} + 56133 q^{90} + 591882 q^{91} + 388500 q^{92} + 205389 q^{93} + 205288 q^{94} + 87988 q^{95} + 452097 q^{96} + 385683 q^{97} - 61147 q^{98} + 119070 q^{99}+O(q^{100}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9 + 693 * q^10 + 1470 * q^11 + 4374 * q^12 + 2515 * q^13 + 254 * q^14 + 423 * q^15 + 11542 * q^16 + 880 * q^17 + 1134 * q^18 + 7412 * q^19 + 1927 * q^20 + 3618 * q^21 + 5461 * q^22 + 5567 * q^23 + 3078 * q^24 + 31584 * q^25 + 18502 * q^26 + 18225 * q^27 + 25011 * q^28 + 17230 * q^29 + 6237 * q^30 + 22821 * q^31 + 50233 * q^32 + 13230 * q^33 + 38342 * q^34 + 30664 * q^35 + 39366 * q^36 + 13342 * q^37 + 25860 * q^38 + 22635 * q^39 + 40701 * q^40 + 36374 * q^41 + 2286 * q^42 + 48371 * q^43 - 4133 * q^44 + 3807 * q^45 + 30489 * q^46 + 17740 * q^47 + 103878 * q^48 + 119201 * q^49 - 9505 * q^50 + 7920 * q^51 + 50699 * q^52 - 52204 * q^53 + 10206 * q^54 + 90638 * q^55 - 80285 * q^56 + 66708 * q^57 + 15313 * q^58 + 34099 * q^59 + 17343 * q^60 + 71175 * q^61 - 92130 * q^62 + 32562 * q^63 + 289374 * q^64 - 32899 * q^65 + 49149 * q^66 + 85201 * q^67 - 41169 * q^68 + 50103 * q^69 - 92312 * q^70 + 102652 * q^71 + 27702 * q^72 + 186396 * q^73 - 258113 * q^74 + 284256 * q^75 + 148369 * q^76 - 109016 * q^77 + 166518 * q^78 + 210994 * q^79 + 17955 * q^80 + 164025 * q^81 + 635103 * q^82 + 68429 * q^83 + 225099 * q^84 + 375692 * q^85 + 360833 * q^86 + 155070 * q^87 + 556985 * q^88 + 163508 * q^89 + 56133 * q^90 + 591882 * q^91 + 388500 * q^92 + 205389 * q^93 + 205288 * q^94 + 87988 * q^95 + 452097 * q^96 + 385683 * q^97 - 61147 * q^98 + 119070 * 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 $

$2$	−2.95711	−0.522748	−0.261374	−	0.965238i	$-0.584176\pi$
$2$	−2.95711	−0.522748	−0.261374	+	0.965238i	$0.584176\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−23.2555	−0.726735
$5$	59.9608	1.07261	0.536306	−	0.844024i	$-0.319819\pi$
$5$	59.9608	1.07261	0.536306	+	0.844024i	$0.319819\pi$
$6$	−26.6140	−0.301809
$7$	248.119	1.91388	0.956940	−	0.290286i	$-0.0937504\pi$
$7$	248.119	1.91388	0.956940	+	0.290286i	$0.0937504\pi$
$8$	163.397	0.902647
$9$	81.0000	0.333333
$10$	−177.311	−0.560705
$11$	−134.294	−0.334638	−0.167319	−	0.985903i	$-0.553511\pi$
$11$	−134.294	−0.334638	−0.167319	+	0.985903i	$0.553511\pi$
$12$	−209.300	−0.419580
$13$	1029.61	1.68972	0.844858	−	0.534990i	$-0.179685\pi$
$13$	1029.61	1.68972	0.844858	+	0.534990i	$0.179685\pi$
$14$	−733.714	−1.00048
$15$	539.647	0.619272
$16$	260.995	0.254878
$17$	469.774	0.394246	0.197123	−	0.980379i	$-0.436840\pi$
$17$	469.774	0.394246	0.197123	+	0.980379i	$0.436840\pi$
$18$	−239.526	−0.174249
$19$	1870.91	1.18896	0.594482	−	0.804109i	$-0.297357\pi$
$19$	1870.91	1.18896	0.594482	+	0.804109i	$0.297357\pi$
$20$	−1394.42	−0.779504
$21$	2233.07	1.10498
$22$	397.123	0.174932
$23$	1279.08	0.504170	0.252085	−	0.967705i	$-0.418884\pi$
$23$	1279.08	0.504170	0.252085	+	0.967705i	$0.418884\pi$
$24$	1470.57	0.521143
$25$	470.296	0.150495
$26$	−3044.66	−0.883296
$27$	729.000	0.192450
$28$	−5770.13	−1.39088
$29$	−4379.58	−0.967025	−0.483512	−	0.875338i	$-0.660639\pi$
$29$	−4379.58	−0.967025	−0.483512	+	0.875338i	$0.660639\pi$
$30$	−1595.79	−0.323723
$31$	−1542.39	−0.288264	−0.144132	−	0.989558i	$-0.546039\pi$
$31$	−1542.39	−0.288264	−0.144132	+	0.989558i	$0.546039\pi$
$32$	−6000.48	−1.03588
$33$	−1208.65	−0.193204
$34$	−1389.17	−0.206091
$35$	14877.4	2.05285
$36$	−1883.70	−0.242245
$37$	−12810.8	−1.53840	−0.769202	−	0.639006i	$-0.779346\pi$
$37$	−12810.8	−1.53840	−0.769202	+	0.639006i	$0.779346\pi$
$38$	−5532.48	−0.621528
$39$	9266.48	0.975558
$40$	9797.38	0.968189
$41$	12053.1	1.11980	0.559899	−	0.828561i	$-0.310840\pi$
$41$	12053.1	1.11980	0.559899	+	0.828561i	$0.310840\pi$
$42$	−6603.43	−0.577625
$43$	−19040.0	−1.57035	−0.785173	−	0.619276i	$-0.787426\pi$
$43$	−19040.0	−1.57035	−0.785173	+	0.619276i	$0.787426\pi$
$44$	3123.08	0.243193
$45$	4856.82	0.357537
$46$	−3782.37	−0.263554
$47$	−12124.4	−0.800602	−0.400301	−	0.916384i	$-0.631094\pi$
$47$	−12124.4	−0.800602	−0.400301	+	0.916384i	$0.631094\pi$
$48$	2348.96	0.147154
$49$	44756.0	2.66294
$50$	−1390.72	−0.0786708
$51$	4227.97	0.227618
$52$	−23944.1	−1.22798
$53$	−11753.6	−0.574751	−0.287376	−	0.957818i	$-0.592783\pi$
$53$	−11753.6	−0.574751	−0.287376	+	0.957818i	$0.592783\pi$
$54$	−2155.73	−0.100603
$55$	−8052.39	−0.358937
$56$	40541.8	1.72756
$57$	16838.2	0.686449
$58$	12950.9	0.505510
$59$	18789.1	0.702711	0.351356	−	0.936242i	$-0.385721\pi$
$59$	18789.1	0.702711	0.351356	+	0.936242i	$0.385721\pi$
$60$	−12549.8	−0.450047
$61$	1038.63	0.0357383	0.0178692	−	0.999840i	$-0.494312\pi$
$61$	1038.63	0.0357383	0.0178692	+	0.999840i	$0.494312\pi$
$62$	4561.02	0.150689
$63$	20097.6	0.637960
$64$	9392.22	0.286628
$65$	61736.1	1.81241
$66$	3574.10	0.100997
$67$	29220.7	0.795251	0.397626	−	0.917548i	$-0.369834\pi$
$67$	29220.7	0.795251	0.397626	+	0.917548i	$0.369834\pi$
$68$	−10924.8	−0.286512
$69$	11511.7	0.291083
$70$	−43994.1	−1.07312
$71$	−80818.5	−1.90268	−0.951338	−	0.308151i	$-0.900290\pi$
$71$	−80818.5	−1.90268	−0.951338	+	0.308151i	$0.900290\pi$
$72$	13235.1	0.300882
$73$	46807.0	1.02803	0.514013	−	0.857783i	$-0.328158\pi$
$73$	46807.0	1.02803	0.514013	+	0.857783i	$0.328158\pi$
$74$	37882.8	0.804197
$75$	4232.66	0.0868882
$76$	−43508.9	−0.864061
$77$	−33321.0	−0.640458
$78$	−27402.0	−0.509971
$79$	−43240.3	−0.779508	−0.389754	−	0.920919i	$-0.627440\pi$
$79$	−43240.3	−0.779508	−0.389754	+	0.920919i	$0.627440\pi$
$80$	15649.5	0.273385
$81$	6561.00	0.111111
$82$	−35642.4	−0.585372
$83$	60829.3	0.969209	0.484605	−	0.874733i	$-0.338963\pi$
$83$	60829.3	0.969209	0.484605	+	0.874733i	$0.338963\pi$
$84$	−51931.2	−0.803027
$85$	28168.0	0.422872
$86$	56303.3	0.820895
$87$	−39416.2	−0.558312
$88$	−21943.2	−0.302060
$89$	−102267.	−1.36855	−0.684276	−	0.729223i	$-0.739882\pi$
$89$	−102267.	−1.36855	−0.684276	+	0.729223i	$0.739882\pi$
$90$	−14362.2	−0.186902
$91$	255465.	3.23391
$92$	−29745.6	−0.366398
$93$	−13881.5	−0.166429
$94$	35853.2	0.418513
$95$	112181.	1.27530
$96$	−54004.3	−0.598068
$97$	77328.7	0.834471	0.417235	−	0.908798i	$-0.362999\pi$
$97$	77328.7	0.834471	0.417235	+	0.908798i	$0.362999\pi$
$98$	−132348.	−1.39204
$99$	−10877.8	−0.111546
$100$	−10937.0	−0.109370
$101$	−49023.5	−0.478191	−0.239095	−	0.970996i	$-0.576851\pi$
$101$	−49023.5	−0.478191	−0.239095	+	0.970996i	$0.576851\pi$
$102$	−12502.6	−0.118987
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	168234.	1.52522
$105$	133897.	1.18521
$106$	34756.6	0.300450
$107$	150624.	1.27185	0.635923	−	0.771753i	$-0.280620\pi$
$107$	150624.	1.27185	0.635923	+	0.771753i	$0.280620\pi$
$108$	−16953.3	−0.139860
$109$	−9507.27	−0.0766460	−0.0383230	−	0.999265i	$-0.512202\pi$
$109$	−9507.27	−0.0766460	−0.0383230	+	0.999265i	$0.512202\pi$
$110$	23811.8	0.187634
$111$	−115297.	−0.888198
$112$	64757.8	0.487806
$113$	84838.9	0.625027	0.312514	−	0.949913i	$-0.398829\pi$
$113$	84838.9	0.625027	0.312514	+	0.949913i	$0.398829\pi$
$114$	−49792.3	−0.358839
$115$	76694.4	0.540778
$116$	101849.	0.702771
$117$	83398.3	0.563239
$118$	−55561.5	−0.367341
$119$	116560.	0.754539
$120$	88176.5	0.558984
$121$	−143016.	−0.888017
$122$	−3071.33	−0.0186821
$123$	108478.	0.646516
$124$	35869.1	0.209491
$125$	−159178.	−0.911189
$126$	−59430.9	−0.333492
$127$	305269.	1.67947	0.839736	−	0.542995i	$-0.182710\pi$
$127$	305269.	1.67947	0.839736	+	0.542995i	$0.182710\pi$
$128$	164242.	0.886050
$129$	−171360.	−0.906640
$130$	−182560.	−0.947433
$131$	52817.5	0.268906	0.134453	−	0.990920i	$-0.457072\pi$
$131$	52817.5	0.268906	0.134453	+	0.990920i	$0.457072\pi$
$132$	28107.7	0.140408
$133$	464208.	2.27553
$134$	−86408.9	−0.415716
$135$	43711.4	0.206424
$136$	76759.5	0.355865
$137$	−20045.8	−0.0912479	−0.0456240	−	0.998959i	$-0.514528\pi$
$137$	−20045.8	−0.0912479	−0.0456240	+	0.998959i	$0.514528\pi$
$138$	−34041.3	−0.152163
$139$	96383.4	0.423122	0.211561	−	0.977365i	$-0.432145\pi$
$139$	96383.4	0.423122	0.211561	+	0.977365i	$0.432145\pi$
$140$	−345982.	−1.49188
$141$	−109120.	−0.462228
$142$	238989.	0.994619
$143$	−138271.	−0.565444
$144$	21140.6	0.0849594
$145$	−262603.	−1.03724
$146$	−138413.	−0.537398
$147$	402804.	1.53745
$148$	297921.	1.11801
$149$	−427634.	−1.57800	−0.788998	−	0.614395i	$-0.789400\pi$
$149$	−427634.	−1.57800	−0.788998	+	0.614395i	$0.789400\pi$
$150$	−12516.4	−0.0454206
$151$	−460566.	−1.64380	−0.821900	−	0.569631i	$-0.807086\pi$
$151$	−460566.	−1.64380	−0.821900	+	0.569631i	$0.807086\pi$
$152$	305700.	1.07321
$153$	38051.7	0.131415
$154$	98533.7	0.334798
$155$	−92483.0	−0.309195
$156$	−215497.	−0.708972
$157$	193436.	0.626307	0.313154	−	0.949702i	$-0.398615\pi$
$157$	193436.	0.626307	0.313154	+	0.949702i	$0.398615\pi$
$158$	127866.	0.407486
$159$	−105782.	−0.331833
$160$	−359793.	−1.11110
$161$	317363.	0.964921
$162$	−19401.6	−0.0580831
$163$	−46509.0	−0.137110	−0.0685548	−	0.997647i	$-0.521839\pi$
$163$	−46509.0	−0.137110	−0.0685548	+	0.997647i	$0.521839\pi$
$164$	−280301.	−0.813796
$165$	−72471.5	−0.207232
$166$	−179879.	−0.506652
$167$	−381215.	−1.05774	−0.528870	−	0.848703i	$-0.677384\pi$
$167$	−381215.	−1.05774	−0.528870	+	0.848703i	$0.677384\pi$
$168$	364876.	0.997406
$169$	688801.	1.85514
$170$	−83295.9	−0.221056
$171$	151544.	0.396321
$172$	442785.	1.14123
$173$	203107.	0.515951	0.257976	−	0.966151i	$-0.416945\pi$
$173$	203107.	0.515951	0.257976	+	0.966151i	$0.416945\pi$
$174$	116558.	0.291856
$175$	116689.	0.288029
$176$	−35050.2	−0.0852920
$177$	169102.	0.405711
$178$	302415.	0.715408
$179$	−428076.	−0.998592	−0.499296	−	0.866431i	$-0.666408\pi$
$179$	−428076.	−0.998592	−0.499296	+	0.866431i	$0.666408\pi$
$180$	−112948.	−0.259835
$181$	287414.	0.652095	0.326048	−	0.945353i	$-0.394283\pi$
$181$	287414.	0.652095	0.326048	+	0.945353i	$0.394283\pi$
$182$	−755439.	−1.69052
$183$	9347.63	0.0206335
$184$	208997.	0.455087
$185$	−768143.	−1.65011
$186$	41049.1	0.0870005
$187$	−63088.0	−0.131930
$188$	281960.	0.581825
$189$	180879.	0.368326
$190$	−331732.	−0.666658
$191$	−361742.	−0.717490	−0.358745	−	0.933436i	$-0.616795\pi$
$191$	−361742.	−0.717490	−0.358745	+	0.933436i	$0.616795\pi$
$192$	84530.0	0.165485
$193$	−122696.	−0.237102	−0.118551	−	0.992948i	$-0.537825\pi$
$193$	−122696.	−0.237102	−0.118551	+	0.992948i	$0.537825\pi$
$194$	−228669.	−0.436218
$195$	555625.	1.04639
$196$	−1.04082e6	−1.93525
$197$	−512178.	−0.940276	−0.470138	−	0.882593i	$-0.655796\pi$
$197$	−512178.	−0.940276	−0.470138	+	0.882593i	$0.655796\pi$
$198$	32166.9	0.0583105
$199$	555039.	0.993552	0.496776	−	0.867879i	$-0.334517\pi$
$199$	555039.	0.993552	0.496776	+	0.867879i	$0.334517\pi$
$200$	76844.7	0.135844
$201$	262987.	0.459138
$202$	144968.	0.249973
$203$	−1.08666e6	−1.85077
$204$	−98323.5	−0.165418
$205$	722714.	1.20111
$206$	31372.0	0.0515079
$207$	103605.	0.168057
$208$	268723.	0.430672
$209$	−251252.	−0.397873
$210$	−395947.	−0.619567
$211$	−246115.	−0.380567	−0.190284	−	0.981729i	$-0.560941\pi$
$211$	−246115.	−0.380567	−0.190284	+	0.981729i	$0.560941\pi$
$212$	273335.	0.417692
$213$	−727366.	−1.09851
$214$	−445411.	−0.664855
$215$	−1.14165e6	−1.68437
$216$	119116.	0.173714
$217$	−382696.	−0.551702
$218$	28114.0	0.0400665
$219$	421263.	0.593531
$220$	187262.	0.260852
$221$	483684.	0.666163
$222$	340945.	0.464304
$223$	−777560.	−1.04706	−0.523530	−	0.852007i	$-0.675385\pi$
$223$	−777560.	−1.04706	−0.523530	+	0.852007i	$0.675385\pi$
$224$	−1.48883e6	−1.98256
$225$	38094.0	0.0501649
$226$	−250878.	−0.326732
$227$	−1.13228e6	−1.45844	−0.729221	−	0.684278i	$-0.760117\pi$
$227$	−1.13228e6	−1.45844	−0.729221	+	0.684278i	$0.760117\pi$
$228$	−391580.	−0.498866
$229$	108599.	0.136848	0.0684238	−	0.997656i	$-0.478203\pi$
$229$	108599.	0.136848	0.0684238	+	0.997656i	$0.478203\pi$
$230$	−226794.	−0.282691
$231$	−299889.	−0.369769
$232$	−715608.	−0.872882
$233$	−1.25937e6	−1.51973	−0.759863	−	0.650084i	$-0.774734\pi$
$233$	−1.25937e6	−1.51973	−0.759863	+	0.650084i	$0.774734\pi$
$234$	−246618.	−0.294432
$235$	−726990.	−0.858735
$236$	−436951.	−0.510685
$237$	−389162.	−0.450049
$238$	−344680.	−0.394433
$239$	1.45271e6	1.64506	0.822532	−	0.568719i	$-0.192561\pi$
$239$	1.45271e6	1.64506	0.822532	+	0.568719i	$0.192561\pi$
$240$	140845.	0.157839
$241$	−227764.	−0.252605	−0.126303	−	0.991992i	$-0.540311\pi$
$241$	−227764.	−0.252605	−0.126303	+	0.991992i	$0.540311\pi$
$242$	422914.	0.464209
$243$	59049.0	0.0641500
$244$	−24153.8	−0.0259723
$245$	2.68360e6	2.85630
$246$	−320781.	−0.337965
$247$	1.92630e6	2.00901
$248$	−252021.	−0.260200
$249$	547464.	0.559573
$250$	470707.	0.476322
$251$	462265.	0.463134	0.231567	−	0.972819i	$-0.425615\pi$
$251$	462265.	0.463134	0.231567	+	0.972819i	$0.425615\pi$
$252$	−467381.	−0.463628
$253$	−171773.	−0.168715
$254$	−902712.	−0.877940
$255$	253512.	0.244145
$256$	−786231.	−0.749808
$257$	1.20768e6	1.14056	0.570280	−	0.821450i	$-0.306835\pi$
$257$	1.20768e6	1.14056	0.570280	+	0.821450i	$0.306835\pi$
$258$	506730.	0.473944
$259$	−3.17859e6	−2.94432
$260$	−1.43571e6	−1.31714
$261$	−354746.	−0.322342
$262$	−156187.	−0.140570
$263$	500093.	0.445822	0.222911	−	0.974839i	$-0.428444\pi$
$263$	500093.	0.445822	0.222911	+	0.974839i	$0.428444\pi$
$264$	−197489.	−0.174395
$265$	−704753.	−0.616485
$266$	−1.37271e6	−1.18953
$267$	−920405.	−0.790134
$268$	−679543.	−0.577937
$269$	373030.	0.314314	0.157157	−	0.987574i	$-0.449767\pi$
$269$	373030.	0.314314	0.157157	+	0.987574i	$0.449767\pi$
$270$	−129259.	−0.107908
$271$	−367100.	−0.303641	−0.151821	−	0.988408i	$-0.548514\pi$
$271$	−367100.	−0.303641	−0.151821	+	0.988408i	$0.548514\pi$
$272$	122609.	0.100485
$273$	2.29919e6	1.86710
$274$	59277.7	0.0476996
$275$	−63158.1	−0.0503613
$276$	−267710.	−0.211540
$277$	−315710.	−0.247223	−0.123611	−	0.992331i	$-0.539448\pi$
$277$	−315710.	−0.247223	−0.123611	+	0.992331i	$0.539448\pi$
$278$	−285016.	−0.221186
$279$	−124934.	−0.0960879
$280$	2.43092e6	1.85300
$281$	1.40049e6	1.05807	0.529036	−	0.848599i	$-0.322554\pi$
$281$	1.40049e6	1.05807	0.529036	+	0.848599i	$0.322554\pi$
$282$	322679.	0.241629
$283$	856091.	0.635410	0.317705	−	0.948190i	$-0.397088\pi$
$283$	856091.	0.635410	0.317705	+	0.948190i	$0.397088\pi$
$284$	1.87947e6	1.38274
$285$	1.00963e6	0.736292
$286$	408881.	0.295585
$287$	2.99060e6	2.14316
$288$	−486039.	−0.345295
$289$	−1.19917e6	−0.844570
$290$	776546.	0.542216
$291$	695958.	0.481782
$292$	−1.08852e6	−0.747102
$293$	315784.	0.214892	0.107446	−	0.994211i	$-0.465733\pi$
$293$	315784.	0.214892	0.107446	+	0.994211i	$0.465733\pi$
$294$	−1.19113e6	−0.803697
$295$	1.12661e6	0.753736
$296$	−2.09323e6	−1.38864
$297$	−97900.5	−0.0644012
$298$	1.26456e6	0.824894
$299$	1.31695e6	0.851904
$300$	−98432.8	−0.0631446
$301$	−4.72418e6	−3.00545
$302$	1.36194e6	0.859293
$303$	−441212.	−0.276083
$304$	488298.	0.303041
$305$	62276.8	0.0383333
$306$	−112523.	−0.0686970
$307$	2.78851e6	1.68860	0.844299	−	0.535873i	$-0.180017\pi$
$307$	2.78851e6	1.68860	0.844299	+	0.535873i	$0.180017\pi$
$308$	774896.	0.465443
$309$	−95481.0	−0.0568880
$310$	273482.	0.161631
$311$	−2.57843e6	−1.51166	−0.755831	−	0.654767i	$-0.772767\pi$
$311$	−2.57843e6	−1.51166	−0.755831	+	0.654767i	$0.772767\pi$
$312$	1.51411e6	0.880585
$313$	2.28595e6	1.31888	0.659440	−	0.751757i	$-0.270793\pi$
$313$	2.28595e6	1.31888	0.659440	+	0.751757i	$0.270793\pi$
$314$	−572010.	−0.327401
$315$	1.20507e6	0.684283
$316$	1.00557e6	0.566496
$317$	−856451.	−0.478690	−0.239345	−	0.970935i	$-0.576933\pi$
$317$	−856451.	−0.478690	−0.239345	+	0.970935i	$0.576933\pi$
$318$	312809.	0.173465
$319$	588153.	0.323604
$320$	563165.	0.307440
$321$	1.35562e6	0.734301
$322$	−938477.	−0.504410
$323$	878905.	0.468744
$324$	−152579.	−0.0807483
$325$	484221.	0.254293
$326$	137532.	0.0716737
$327$	−85565.4	−0.0442516
$328$	1.96944e6	1.01078
$329$	−3.00830e6	−1.53226
$330$	214306.	0.108330
$331$	911002.	0.457035	0.228517	−	0.973540i	$-0.426612\pi$
$331$	911002.	0.457035	0.228517	+	0.973540i	$0.426612\pi$
$332$	−1.41462e6	−0.704358
$333$	−1.03767e6	−0.512801
$334$	1.12729e6	0.552931
$335$	1.75210e6	0.852995
$336$	582821.	0.281635
$337$	1.62022e6	0.777142	0.388571	−	0.921419i	$-0.372969\pi$
$337$	1.62022e6	0.777142	0.388571	+	0.921419i	$0.372969\pi$
$338$	−2.03686e6	−0.969771
$339$	763550.	0.360860
$340$	−655062.	−0.307316
$341$	207134.	0.0964642
$342$	−448131.	−0.207176
$343$	6.93467e6	3.18266
$344$	−3.11107e6	−1.41747
$345$	690250.	0.312219
$346$	−600608.	−0.269712
$347$	−3.70908e6	−1.65364	−0.826822	−	0.562463i	$-0.809854\pi$
$347$	−3.70908e6	−1.65364	−0.826822	+	0.562463i	$0.809854\pi$
$348$	916645.	0.405745
$349$	−13888.4	−0.00610363	−0.00305182	−	0.999995i	$-0.500971\pi$
$349$	−13888.4	−0.00610363	−0.00305182	+	0.999995i	$0.500971\pi$
$350$	−345063.	−0.150566
$351$	750585.	0.325186
$352$	805830.	0.346647
$353$	1.10307e6	0.471156	0.235578	−	0.971855i	$-0.424302\pi$
$353$	1.10307e6	0.471156	0.235578	+	0.971855i	$0.424302\pi$
$354$	−500054.	−0.212084
$355$	−4.84594e6	−2.04083
$356$	2.37828e6	0.994574
$357$	1.04904e6	0.435633
$358$	1.26587e6	0.522012
$359$	−3.56295e6	−1.45906	−0.729532	−	0.683947i	$-0.760262\pi$
$359$	−3.56295e6	−1.45906	−0.729532	+	0.683947i	$0.760262\pi$
$360$	793588.	0.322730
$361$	1.02420e6	0.413635
$362$	−849913.	−0.340881
$363$	−1.28714e6	−0.512697
$364$	−5.94098e6	−2.35020
$365$	2.80659e6	1.10267
$366$	−27641.9	−0.0107861
$367$	−1.68908e6	−0.654614	−0.327307	−	0.944918i	$-0.606141\pi$
$367$	−1.68908e6	−0.654614	−0.327307	+	0.944918i	$0.606141\pi$
$368$	333833.	0.128502
$369$	976302.	0.373266
$370$	2.27148e6	0.862591
$371$	−2.91628e6	−1.10001
$372$	322822.	0.120950
$373$	−477244.	−0.177611	−0.0888053	−	0.996049i	$-0.528305\pi$
$373$	−477244.	−0.177611	−0.0888053	+	0.996049i	$0.528305\pi$
$374$	186558.	0.0689660
$375$	−1.43260e6	−0.526075
$376$	−1.98109e6	−0.722661
$377$	−4.50926e6	−1.63400
$378$	−534878.	−0.192542
$379$	−3.13215e6	−1.12007	−0.560035	−	0.828469i	$-0.689212\pi$
$379$	−3.13215e6	−1.12007	−0.560035	+	0.828469i	$0.689212\pi$
$380$	−2.60883e6	−0.926802
$381$	2.74742e6	0.969644
$382$	1.06971e6	0.375066
$383$	−3.68832e6	−1.28479	−0.642395	−	0.766374i	$-0.722059\pi$
$383$	−3.68832e6	−1.28479	−0.642395	+	0.766374i	$0.722059\pi$
$384$	1.47817e6	0.511561
$385$	−1.99795e6	−0.686962
$386$	362824.	0.123945
$387$	−1.54224e6	−0.523449
$388$	−1.79832e6	−0.606439
$389$	−2.69364e6	−0.902539	−0.451270	−	0.892388i	$-0.649029\pi$
$389$	−2.69364e6	−0.902539	−0.451270	+	0.892388i	$0.649029\pi$
$390$	−1.64304e6	−0.547001
$391$	600877.	0.198767
$392$	7.31297e6	2.40369
$393$	475358.	0.155253
$394$	1.51457e6	0.491527
$395$	−2.59272e6	−0.836109
$396$	252970.	0.0810645
$397$	5.21624e6	1.66104	0.830522	−	0.556986i	$-0.188042\pi$
$397$	5.21624e6	1.66104	0.830522	+	0.556986i	$0.188042\pi$
$398$	−1.64131e6	−0.519377
$399$	4.17787e6	1.31378
$400$	122745.	0.0383578
$401$	1.29465e6	0.402060	0.201030	−	0.979585i	$-0.435571\pi$
$401$	1.29465e6	0.402060	0.201030	+	0.979585i	$0.435571\pi$
$402$	−777680.	−0.240014
$403$	−1.58806e6	−0.487084
$404$	1.14007e6	0.347518
$405$	393403.	0.119179
$406$	3.21336e6	0.967486
$407$	1.72041e6	0.514809
$408$	690835.	0.205458
$409$	−2.96251e6	−0.875692	−0.437846	−	0.899050i	$-0.644259\pi$
$409$	−2.96251e6	−0.875692	−0.437846	+	0.899050i	$0.644259\pi$
$410$	−2.13714e6	−0.627876
$411$	−180413.	−0.0526820
$412$	246718.	0.0716073
$413$	4.66194e6	1.34491
$414$	−306372.	−0.0878513
$415$	3.64737e6	1.03958
$416$	−6.17815e6	−1.75035
$417$	867451.	0.244290
$418$	742980.	0.207987
$419$	2.05229e6	0.571088	0.285544	−	0.958366i	$-0.407826\pi$
$419$	2.05229e6	0.571088	0.285544	+	0.958366i	$0.407826\pi$
$420$	−3.11383e6	−0.861335
$421$	6.55299e6	1.80191	0.900957	−	0.433908i	$-0.142866\pi$
$421$	6.55299e6	1.80191	0.900957	+	0.433908i	$0.142866\pi$
$422$	727788.	0.198941
$423$	−982079.	−0.266867
$424$	−1.92049e6	−0.518798
$425$	220933.	0.0593319
$426$	2.15090e6	0.574244
$427$	257702.	0.0683989
$428$	−3.50284e6	−0.924295
$429$	−1.24444e6	−0.326459
$430$	3.37599e6	0.880501
$431$	1.12328e6	0.291269	0.145634	−	0.989338i	$-0.453478\pi$
$431$	1.12328e6	0.291269	0.145634	+	0.989338i	$0.453478\pi$
$432$	190266.	0.0490513
$433$	3.82293e6	0.979888	0.489944	−	0.871754i	$-0.337017\pi$
$433$	3.82293e6	0.979888	0.489944	+	0.871754i	$0.337017\pi$
$434$	1.13167e6	0.288401
$435$	−2.36343e6	−0.598852
$436$	221096.	0.0557013
$437$	2.39304e6	0.599440
$438$	−1.24572e6	−0.310267
$439$	1.87051e6	0.463231	0.231616	−	0.972807i	$-0.425599\pi$
$439$	1.87051e6	0.463231	0.231616	+	0.972807i	$0.425599\pi$
$440$	−1.31573e6	−0.323993
$441$	3.62523e6	0.887646
$442$	−1.43030e6	−0.348235
$443$	7.35860e6	1.78150	0.890750	−	0.454493i	$-0.150180\pi$
$443$	7.35860e6	1.78150	0.890750	+	0.454493i	$0.150180\pi$
$444$	2.68129e6	0.645484
$445$	−6.13202e6	−1.46792
$446$	2.29933e6	0.547348
$447$	−3.84870e6	−0.911057
$448$	2.33039e6	0.548571
$449$	5.30216e6	1.24119	0.620593	−	0.784133i	$-0.286892\pi$
$449$	5.30216e6	1.24119	0.620593	+	0.784133i	$0.286892\pi$
$450$	−112648.	−0.0262236
$451$	−1.61866e6	−0.374727
$452$	−1.97297e6	−0.454229
$453$	−4.14509e6	−0.949049
$454$	3.34828e6	0.762398
$455$	1.53179e7	3.46873
$456$	2.75130e6	0.619621
$457$	−2.95191e6	−0.661168	−0.330584	−	0.943777i	$-0.607246\pi$
$457$	−2.95191e6	−0.661168	−0.330584	+	0.943777i	$0.607246\pi$
$458$	−321139.	−0.0715368
$459$	342465.	0.0758726
$460$	−1.78357e6	−0.393002
$461$	434684.	0.0952624	0.0476312	−	0.998865i	$-0.484833\pi$
$461$	434684.	0.0952624	0.0476312	+	0.998865i	$0.484833\pi$
$462$	886803.	0.193296
$463$	2.65847e6	0.576341	0.288171	−	0.957579i	$-0.406953\pi$
$463$	2.65847e6	0.576341	0.288171	+	0.957579i	$0.406953\pi$
$464$	−1.14305e6	−0.246473
$465$	−832347.	−0.178514
$466$	3.72411e6	0.794433
$467$	6.89602e6	1.46321	0.731604	−	0.681730i	$-0.238772\pi$
$467$	6.89602e6	1.46321	0.731604	+	0.681730i	$0.238772\pi$
$468$	−1.93947e6	−0.409325
$469$	7.25022e6	1.52202
$470$	2.14979e6	0.448902
$471$	1.74092e6	0.361599
$472$	3.07008e6	0.634300
$473$	2.55696e6	0.525498
$474$	1.15080e6	0.235262
$475$	879881.	0.178933
$476$	−2.71066e6	−0.548350
$477$	−952039.	−0.191584
$478$	−4.29581e6	−0.859953
$479$	−9.42133e6	−1.87618	−0.938088	−	0.346397i	$-0.887405\pi$
$479$	−9.42133e6	−1.87618	−0.938088	+	0.346397i	$0.887405\pi$
$480$	−3.23814e6	−0.641494
$481$	−1.31901e7	−2.59947
$482$	673522.	0.132049
$483$	2.85627e6	0.557097
$484$	3.32591e6	0.645353
$485$	4.63669e6	0.895063
$486$	−174614.	−0.0335343
$487$	3.69942e6	0.706823	0.353412	−	0.935468i	$-0.385022\pi$
$487$	3.69942e6	0.706823	0.353412	+	0.935468i	$0.385022\pi$
$488$	169708.	0.0322591
$489$	−418581.	−0.0791602
$490$	−7.93571e6	−1.49312
$491$	3.38672e6	0.633981	0.316990	−	0.948429i	$-0.397328\pi$
$491$	3.38672e6	0.633981	0.316990	+	0.948429i	$0.397328\pi$
$492$	−2.52271e6	−0.469845
$493$	−2.05741e6	−0.381245
$494$	−5.69629e6	−1.05021
$495$	−652244.	−0.119646
$496$	−402557.	−0.0734721
$497$	−2.00526e7	−3.64149
$498$	−1.61891e6	−0.292516
$499$	2.84805e6	0.512032	0.256016	−	0.966673i	$-0.417590\pi$
$499$	2.84805e6	0.512032	0.256016	+	0.966673i	$0.417590\pi$
$500$	3.70177e6	0.662193
$501$	−3.43093e6	−0.610686
$502$	−1.36697e6	−0.242102
$503$	−29060.7	−0.00512138	−0.00256069	−	0.999997i	$-0.500815\pi$
$503$	−29060.7	−0.00512138	−0.00256069	+	0.999997i	$0.500815\pi$
$504$	3.28388e6	0.575853
$505$	−2.93949e6	−0.512913
$506$	507950.	0.0881952
$507$	6.19921e6	1.07107
$508$	−7.09918e6	−1.22053
$509$	−9.31590e6	−1.59379	−0.796894	−	0.604120i	$-0.793525\pi$
$509$	−9.31590e6	−1.59379	−0.796894	+	0.604120i	$0.793525\pi$
$510$	−749663.	−0.127626
$511$	1.16137e7	1.96752
$512$	−2.93076e6	−0.494089
$513$	1.36389e6	0.228816
$514$	−3.57123e6	−0.596226
$515$	−636124.	−0.105688
$516$	3.98506e6	0.658887
$517$	1.62824e6	0.267912
$518$	9.39944e6	1.53914
$519$	1.82796e6	0.297885
$520$	1.00875e7	1.63596
$521$	−7.53656e6	−1.21641	−0.608203	−	0.793781i	$-0.708110\pi$
$521$	−7.53656e6	−1.21641	−0.608203	+	0.793781i	$0.708110\pi$
$522$	1.04902e6	0.168503
$523$	9.74032e6	1.55711	0.778554	−	0.627577i	$-0.215953\pi$
$523$	9.74032e6	1.55711	0.778554	+	0.627577i	$0.215953\pi$
$524$	−1.22830e6	−0.195423
$525$	1.05020e6	0.166294
$526$	−1.47883e6	−0.233052
$527$	−724575.	−0.113647
$528$	−315452.	−0.0492434
$529$	−4.80031e6	−0.745813
$530$	2.08403e6	0.322266
$531$	1.52192e6	0.234237
$532$	−1.07954e7	−1.65371
$533$	1.24100e7	1.89214
$534$	2.72174e6	0.413041
$535$	9.03153e6	1.36420
$536$	4.77457e6	0.717831
$537$	−3.85268e6	−0.576538
$538$	−1.10309e6	−0.164307
$539$	−6.01047e6	−0.891121
$540$	−1.01653e6	−0.150016
$541$	−3.92135e6	−0.576026	−0.288013	−	0.957626i	$-0.592995\pi$
$541$	−3.92135e6	−0.576026	−0.288013	+	0.957626i	$0.592995\pi$
$542$	1.08555e6	0.158728
$543$	2.58672e6	0.376487
$544$	−2.81887e6	−0.408393
$545$	−570063.	−0.0822114
$546$	−6.79895e6	−0.976023
$547$	−9.08624e6	−1.29842	−0.649211	−	0.760608i	$-0.724901\pi$
$547$	−9.08624e6	−1.29842	−0.649211	+	0.760608i	$0.724901\pi$
$548$	466176.	0.0663130
$549$	84128.6	0.0119128
$550$	186765.	0.0263263
$551$	−8.19380e6	−1.14976
$552$	1.88097e6	0.262745
$553$	−1.07287e7	−1.49189
$554$	933588.	0.129235
$555$	−6.91329e6	−0.952691
$556$	−2.24145e6	−0.307497
$557$	−3.77236e6	−0.515198	−0.257599	−	0.966252i	$-0.582931\pi$
$557$	−3.77236e6	−0.515198	−0.257599	+	0.966252i	$0.582931\pi$
$558$	369442.	0.0502298
$559$	−1.96037e7	−2.65344
$560$	3.88293e6	0.523226
$561$	−567792.	−0.0761697
$562$	−4.14141e6	−0.553105
$563$	−4.99427e6	−0.664050	−0.332025	−	0.943271i	$-0.607732\pi$
$563$	−4.99427e6	−0.664050	−0.332025	+	0.943271i	$0.607732\pi$
$564$	2.53764e6	0.335917
$565$	5.08701e6	0.670411
$566$	−2.53156e6	−0.332159
$567$	1.62791e6	0.212653
$568$	−1.32055e7	−1.71744
$569$	9.89330e6	1.28103	0.640517	−	0.767944i	$-0.278720\pi$
$569$	9.89330e6	1.28103	0.640517	+	0.767944i	$0.278720\pi$
$570$	−2.98559e6	−0.384895
$571$	−762405.	−0.0978578	−0.0489289	−	0.998802i	$-0.515581\pi$
$571$	−762405.	−0.0978578	−0.0489289	+	0.998802i	$0.515581\pi$
$572$	3.21555e6	0.410928
$573$	−3.25568e6	−0.414243
$574$	−8.84354e6	−1.12033
$575$	601545.	0.0758749
$576$	760770.	0.0955426
$577$	375393.	0.0469404	0.0234702	−	0.999725i	$-0.492529\pi$
$577$	375393.	0.0469404	0.0234702	+	0.999725i	$0.492529\pi$
$578$	3.54607e6	0.441497
$579$	−1.10426e6	−0.136891
$580$	6.10697e6	0.753800
$581$	1.50929e7	1.85495
$582$	−2.05802e6	−0.251850
$583$	1.57844e6	0.192334
$584$	7.64810e6	0.927944
$585$	5.00063e6	0.604136
$586$	−933808.	−0.112335
$587$	4.25843e6	0.510099	0.255049	−	0.966928i	$-0.417908\pi$
$587$	4.25843e6	0.510099	0.255049	+	0.966928i	$0.417908\pi$
$588$	−9.36741e6	−1.11732
$589$	−2.88567e6	−0.342735
$590$	−3.33151e6	−0.394014
$591$	−4.60960e6	−0.542868
$592$	−3.34355e6	−0.392106
$593$	−1.10296e7	−1.28802	−0.644011	−	0.765016i	$-0.722731\pi$
$593$	−1.10296e7	−1.28802	−0.644011	+	0.765016i	$0.722731\pi$
$594$	289502.	0.0336656
$595$	6.98902e6	0.809327
$596$	9.94484e6	1.14678
$597$	4.99535e6	0.573628
$598$	−3.89436e6	−0.445331
$599$	7.34712e6	0.836662	0.418331	−	0.908295i	$-0.362615\pi$
$599$	7.34712e6	0.836662	0.418331	+	0.908295i	$0.362615\pi$
$600$	691603.	0.0784293
$601$	−2.02961e6	−0.229206	−0.114603	−	0.993411i	$-0.536560\pi$
$601$	−2.02961e6	−0.229206	−0.114603	+	0.993411i	$0.536560\pi$
$602$	1.39699e7	1.57109
$603$	2.36688e6	0.265084
$604$	1.07107e7	1.19461
$605$	−8.57535e6	−0.952497
$606$	1.30471e6	0.144322
$607$	537523.	0.0592141	0.0296071	−	0.999562i	$-0.490574\pi$
$607$	537523.	0.0592141	0.0296071	+	0.999562i	$0.490574\pi$
$608$	−1.12263e7	−1.23163
$609$	−9.77991e6	−1.06854
$610$	−184159.	−0.0200387
$611$	−1.24834e7	−1.35279
$612$	−884912.	−0.0955040
$613$	−1.19085e7	−1.27999	−0.639994	−	0.768380i	$-0.721063\pi$
$613$	−1.19085e7	−1.27999	−0.639994	+	0.768380i	$0.721063\pi$
$614$	−8.24592e6	−0.882711
$615$	6.50443e6	0.693460
$616$	−5.44453e6	−0.578107
$617$	1.25765e7	1.32999	0.664995	−	0.746848i	$-0.268434\pi$
$617$	1.25765e7	1.32999	0.664995	+	0.746848i	$0.268434\pi$
$618$	282348.	0.0297381
$619$	1.82999e7	1.91965	0.959825	−	0.280599i	$-0.0905332\pi$
$619$	1.82999e7	1.91965	0.959825	+	0.280599i	$0.0905332\pi$
$620$	2.15074e6	0.224703
$621$	932447.	0.0970276
$622$	7.62470e6	0.790218
$623$	−2.53744e7	−2.61924
$624$	2.41851e6	0.248648
$625$	−1.10141e7	−1.12785
$626$	−6.75979e6	−0.689442
$627$	−2.26127e6	−0.229712
$628$	−4.49845e6	−0.455159
$629$	−6.01816e6	−0.606509
$630$	−3.56352e6	−0.357707
$631$	1.52799e7	1.52773	0.763867	−	0.645373i	$-0.223298\pi$
$631$	1.52799e7	1.52773	0.763867	+	0.645373i	$0.223298\pi$
$632$	−7.06531e6	−0.703621
$633$	−2.21503e6	−0.219721
$634$	2.53262e6	0.250234
$635$	1.83041e7	1.80142
$636$	2.46002e6	0.241155
$637$	4.60811e7	4.49961
$638$	−1.73923e6	−0.169163
$639$	−6.54629e6	−0.634225
$640$	9.84805e6	0.950387
$641$	1.46971e7	1.41282	0.706410	−	0.707803i	$-0.250314\pi$
$641$	1.46971e7	1.41282	0.706410	+	0.707803i	$0.250314\pi$
$642$	−4.00870e6	−0.383854
$643$	−1.13188e7	−1.07963	−0.539813	−	0.841785i	$-0.681505\pi$
$643$	−1.13188e7	−1.07963	−0.539813	+	0.841785i	$0.681505\pi$
$644$	−7.38044e6	−0.701242
$645$	−1.02749e7	−0.972472
$646$	−2.59902e6	−0.245035
$647$	2.72329e6	0.255760	0.127880	−	0.991790i	$-0.459183\pi$
$647$	2.72329e6	0.255760	0.127880	+	0.991790i	$0.459183\pi$
$648$	1.07204e6	0.100294
$649$	−2.52327e6	−0.235154
$650$	−1.43189e6	−0.132931
$651$	−3.44427e6	−0.318526
$652$	1.08159e6	0.0996423
$653$	−7.98805e6	−0.733091	−0.366545	−	0.930400i	$-0.619460\pi$
$653$	−7.98805e6	−0.733091	−0.366545	+	0.930400i	$0.619460\pi$
$654$	253026.	0.0231324
$655$	3.16698e6	0.288431
$656$	3.14580e6	0.285412
$657$	3.79137e6	0.342675
$658$	8.89587e6	0.800984
$659$	−4.68271e6	−0.420033	−0.210017	−	0.977698i	$-0.567352\pi$
$659$	−4.68271e6	−0.420033	−0.210017	+	0.977698i	$0.567352\pi$
$660$	1.68536e6	0.150603
$661$	−7.40240e6	−0.658975	−0.329488	−	0.944160i	$-0.606876\pi$
$661$	−7.40240e6	−0.658975	−0.329488	+	0.944160i	$0.606876\pi$
$662$	−2.69393e6	−0.238914
$663$	4.35315e6	0.384610
$664$	9.93930e6	0.874854
$665$	2.78343e7	2.44076
$666$	3.06851e6	0.268066
$667$	−5.60182e6	−0.487545
$668$	8.86535e6	0.768696
$669$	−6.99804e6	−0.604521
$670$	−5.18115e6	−0.445901
$671$	−139481.	−0.0119594
$672$	−1.33995e7	−1.14463
$673$	4.00204e6	0.340600	0.170300	−	0.985392i	$-0.445526\pi$
$673$	4.00204e6	0.340600	0.170300	+	0.985392i	$0.445526\pi$
$674$	−4.79118e6	−0.406249
$675$	342846.	0.0289627
$676$	−1.60184e7	−1.34820
$677$	2.30621e7	1.93387	0.966936	−	0.255020i	$-0.0820822\pi$
$677$	2.30621e7	1.93387	0.966936	+	0.255020i	$0.0820822\pi$
$678$	−2.25790e6	−0.188639
$679$	1.91867e7	1.59708
$680$	4.60256e6	0.381704
$681$	−1.01905e7	−0.842032
$682$	−612518.	−0.0504264
$683$	−2.09563e7	−1.71895	−0.859473	−	0.511182i	$-0.829208\pi$
$683$	−2.09563e7	−1.71895	−0.859473	+	0.511182i	$0.829208\pi$
$684$	−3.52422e6	−0.288020
$685$	−1.20196e6	−0.0978735
$686$	−2.05066e7	−1.66373
$687$	977391.	0.0790090
$688$	−4.96934e6	−0.400247
$689$	−1.21016e7	−0.971167
$690$	−2.04114e6	−0.163212
$691$	−6447.76	−0.000513705 0	−0.000256853	−	1.00000i	$-0.500082\pi$
$691$	−6447.76	−0.000513705 0	−0.000256853		1.00000i	$0.500082\pi$
$692$	−4.72335e6	−0.374960
$693$	−2.69900e6	−0.213486
$694$	1.09681e7	0.864439
$695$	5.77923e6	0.453845
$696$	−6.44048e6	−0.503959
$697$	5.66224e6	0.441475
$698$	41069.5	0.00319066
$699$	−1.13344e7	−0.877414
$700$	−2.71367e6	−0.209321
$701$	−2.52861e7	−1.94351	−0.971754	−	0.235997i	$-0.924164\pi$
$701$	−2.52861e7	−1.94351	−0.971754	+	0.235997i	$0.924164\pi$
$702$	−2.21956e6	−0.169990
$703$	−2.39678e7	−1.82911
$704$	−1.26132e6	−0.0959167
$705$	−6.54291e6	−0.495791
$706$	−3.26189e6	−0.246296
$707$	−1.21637e7	−0.915199
$708$	−3.93256e6	−0.294844
$709$	−2.55980e7	−1.91246	−0.956228	−	0.292624i	$-0.905472\pi$
$709$	−2.55980e7	−1.91246	−0.956228	+	0.292624i	$0.905472\pi$
$710$	1.43300e7	1.06684
$711$	−3.50246e6	−0.259836
$712$	−1.67101e7	−1.23532
$713$	−1.97284e6	−0.145334
$714$	−3.10212e6	−0.227726
$715$	−8.29081e6	−0.606502
$716$	9.95513e6	0.725712
$717$	1.30743e7	0.949778
$718$	1.05360e7	0.762722
$719$	3.54365e6	0.255640	0.127820	−	0.991797i	$-0.459202\pi$
$719$	3.54365e6	0.255640	0.127820	+	0.991797i	$0.459202\pi$
$720$	1.26761e6	0.0911284
$721$	−2.63229e6	−0.188580
$722$	−3.02867e6	−0.216227
$723$	−2.04987e6	−0.145842
$724$	−6.68395e6	−0.473900
$725$	−2.05970e6	−0.145532
$726$	3.80623e6	0.268011
$727$	−4.44708e6	−0.312060	−0.156030	−	0.987752i	$-0.549870\pi$
$727$	−4.44708e6	−0.312060	−0.156030	+	0.987752i	$0.549870\pi$
$728$	4.17422e7	2.91908
$729$	531441.	0.0370370
$730$	−8.29938e6	−0.576419
$731$	−8.94449e6	−0.619102
$732$	−217384.	−0.0149951
$733$	9.95425e6	0.684303	0.342152	−	0.939645i	$-0.388844\pi$
$733$	9.95425e6	0.684303	0.342152	+	0.939645i	$0.388844\pi$
$734$	4.99480e6	0.342198
$735$	2.41524e7	1.64908
$736$	−7.67507e6	−0.522262
$737$	−3.92418e6	−0.266122
$738$	−2.88703e6	−0.195124
$739$	−4.34840e6	−0.292900	−0.146450	−	0.989218i	$-0.546785\pi$
$739$	−4.34840e6	−0.292900	−0.146450	+	0.989218i	$0.546785\pi$
$740$	1.78636e7	1.19919
$741$	1.73367e7	1.15990
$742$	8.62376e6	0.575025
$743$	−2.41502e7	−1.60491	−0.802453	−	0.596716i	$-0.796472\pi$
$743$	−2.41502e7	−1.60491	−0.802453	+	0.596716i	$0.796472\pi$
$744$	−2.26819e6	−0.150227
$745$	−2.56412e7	−1.69258
$746$	1.41126e6	0.0928455
$747$	4.92717e6	0.323070
$748$	1.46714e6	0.0958779
$749$	3.73726e7	2.43416
$750$	4.23636e6	0.275005
$751$	−2.89247e7	−1.87141	−0.935706	−	0.352780i	$-0.885236\pi$
$751$	−2.89247e7	−1.87141	−0.935706	+	0.352780i	$0.885236\pi$
$752$	−3.16442e6	−0.204056
$753$	4.16039e6	0.267391
$754$	1.33344e7	0.854169
$755$	−2.76159e7	−1.76316
$756$	−4.20643e6	−0.267676
$757$	835927.	0.0530187	0.0265093	−	0.999649i	$-0.491561\pi$
$757$	835927.	0.0530187	0.0265093	+	0.999649i	$0.491561\pi$
$758$	9.26212e6	0.585514
$759$	−1.54595e6	−0.0974075
$760$	1.83300e7	1.15114
$761$	−2.45759e7	−1.53832	−0.769162	−	0.639054i	$-0.779326\pi$
$761$	−2.45759e7	−1.53832	−0.769162	+	0.639054i	$0.779326\pi$
$762$	−8.12441e6	−0.506879
$763$	−2.35893e6	−0.146691
$764$	8.41250e6	0.521425
$765$	2.28161e6	0.140957
$766$	1.09068e7	0.671621
$767$	1.93455e7	1.18738
$768$	−7.07608e6	−0.432902
$769$	2.15694e7	1.31529	0.657646	−	0.753327i	$-0.271552\pi$
$769$	2.15694e7	1.31529	0.657646	+	0.753327i	$0.271552\pi$
$770$	5.90816e6	0.359108
$771$	1.08691e7	0.658503
$772$	2.85335e6	0.172311
$773$	−5.77826e6	−0.347815	−0.173908	−	0.984762i	$-0.555639\pi$
$773$	−5.77826e6	−0.347815	−0.173908	+	0.984762i	$0.555639\pi$
$774$	4.56057e6	0.273632
$775$	−725380.	−0.0433822
$776$	1.26352e7	0.753232
$777$	−2.86073e7	−1.69990
$778$	7.96539e6	0.471800
$779$	2.25503e7	1.33140
$780$	−1.29214e7	−0.760451
$781$	1.08535e7	0.636708
$782$	−1.77686e6	−0.103905
$783$	−3.19271e6	−0.186104
$784$	1.16811e7	0.678724
$785$	1.15986e7	0.671784
$786$	−1.40568e6	−0.0811580
$787$	3.12901e7	1.80082	0.900408	−	0.435046i	$-0.143268\pi$
$787$	3.12901e7	1.80082	0.900408	+	0.435046i	$0.143268\pi$
$788$	1.19110e7	0.683331
$789$	4.50083e6	0.257395
$790$	7.66696e6	0.437074
$791$	2.10501e7	1.19623
$792$	−1.77740e6	−0.100687
$793$	1.06938e6	0.0603876
$794$	−1.54250e7	−0.868307
$795$	−6.34278e6	−0.355928
$796$	−1.29077e7	−0.722049
$797$	3.32279e7	1.85292	0.926461	−	0.376390i	$-0.122835\pi$
$797$	3.32279e7	1.85292	0.926461	+	0.376390i	$0.122835\pi$
$798$	−1.23544e7	−0.686776
$799$	−5.69574e6	−0.315634
$800$	−2.82200e6	−0.155895
$801$	−8.28364e6	−0.456184
$802$	−3.82842e6	−0.210176
$803$	−6.28592e6	−0.344017
$804$	−6.11589e6	−0.333672
$805$	1.90293e7	1.03498
$806$	4.69606e6	0.254622
$807$	3.35727e6	0.181469
$808$	−8.01027e6	−0.431637
$809$	−8.47500e6	−0.455270	−0.227635	−	0.973747i	$-0.573099\pi$
$809$	−8.47500e6	−0.455270	−0.227635	+	0.973747i	$0.573099\pi$
$810$	−1.16333e6	−0.0623006
$811$	−2.26625e6	−0.120992	−0.0604960	−	0.998168i	$-0.519268\pi$
$811$	−2.26625e6	−0.120992	−0.0604960	+	0.998168i	$0.519268\pi$
$812$	2.52708e7	1.34502
$813$	−3.30390e6	−0.175307
$814$	−5.08744e6	−0.269115
$815$	−2.78871e6	−0.147065
$816$	1.10348e6	0.0580148
$817$	−3.56221e7	−1.86708
$818$	8.76046e6	0.457766
$819$	2.06927e7	1.07797
$820$	−1.68071e7	−0.872887
$821$	−2.97775e7	−1.54181	−0.770903	−	0.636952i	$-0.780195\pi$
$821$	−2.97775e7	−1.54181	−0.770903	+	0.636952i	$0.780195\pi$
$822$	533500.	0.0275394
$823$	1.41941e7	0.730481	0.365241	−	0.930913i	$-0.380987\pi$
$823$	1.41941e7	0.730481	0.365241	+	0.930913i	$0.380987\pi$
$824$	−1.73347e6	−0.0889404
$825$	−568423.	−0.0290761
$826$	−1.37859e7	−0.703046
$827$	3.58218e7	1.82131	0.910655	−	0.413168i	$-0.135578\pi$
$827$	3.58218e7	1.82131	0.910655	+	0.413168i	$0.135578\pi$
$828$	−2.40939e6	−0.122133
$829$	−1.92739e7	−0.974056	−0.487028	−	0.873386i	$-0.661919\pi$
$829$	−1.92739e7	−0.974056	−0.487028	+	0.873386i	$0.661919\pi$
$830$	−1.07857e7	−0.543441
$831$	−2.84139e6	−0.142734
$832$	9.67031e6	0.484320
$833$	2.10252e7	1.04985
$834$	−2.56515e6	−0.127702
$835$	−2.28579e7	−1.13454
$836$	5.84300e6	0.289148
$837$	−1.12440e6	−0.0554764
$838$	−6.06883e6	−0.298535
$839$	−4.07405e6	−0.199812	−0.0999060	−	0.994997i	$-0.531854\pi$
$839$	−4.07405e6	−0.199812	−0.0999060	+	0.994997i	$0.531854\pi$
$840$	2.18782e7	1.06983
$841$	−1.33042e6	−0.0648631
$842$	−1.93779e7	−0.941947
$843$	1.26044e7	0.610878
$844$	5.72352e6	0.276571
$845$	4.13011e7	1.98985
$846$	2.90411e6	0.139504
$847$	−3.54850e7	−1.69956
$848$	−3.06763e6	−0.146492
$849$	7.70482e6	0.366854
$850$	−653323.	−0.0310156
$851$	−1.63859e7	−0.775617
$852$	1.69153e7	0.798325
$853$	−1.77196e7	−0.833838	−0.416919	−	0.908944i	$-0.636890\pi$
$853$	−1.77196e7	−0.833838	−0.416919	+	0.908944i	$0.636890\pi$
$854$	−762054.	−0.0357554
$855$	9.08667e6	0.425099
$856$	2.46114e7	1.14803
$857$	1.91069e7	0.888664	0.444332	−	0.895862i	$-0.353441\pi$
$857$	1.91069e7	0.888664	0.444332	+	0.895862i	$0.353441\pi$
$858$	3.67993e6	0.170656
$859$	1.72887e6	0.0799428	0.0399714	−	0.999201i	$-0.487273\pi$
$859$	1.72887e6	0.0799428	0.0399714	+	0.999201i	$0.487273\pi$
$860$	2.65497e7	1.22409
$861$	2.69154e7	1.23735
$862$	−3.32166e6	−0.152260
$863$	−1.01315e7	−0.463072	−0.231536	−	0.972826i	$-0.574375\pi$
$863$	−1.01315e7	−0.463072	−0.231536	+	0.972826i	$0.574375\pi$
$864$	−4.37435e6	−0.199356
$865$	1.21784e7	0.553415
$866$	−1.13048e7	−0.512234
$867$	−1.07925e7	−0.487613
$868$	8.89980e6	0.400941
$869$	5.80692e6	0.260853
$870$	6.98891e6	0.313048
$871$	3.00859e7	1.34375
$872$	−1.55345e6	−0.0691843
$873$	6.26362e6	0.278157
$874$	−7.07647e6	−0.313356
$875$	−3.94951e7	−1.74391
$876$	−9.79669e6	−0.431339
$877$	−3.20077e7	−1.40525	−0.702627	−	0.711558i	$-0.747990\pi$
$877$	−3.20077e7	−1.40525	−0.702627	+	0.711558i	$0.747990\pi$
$878$	−5.53129e6	−0.242153
$879$	2.84206e6	0.124068
$880$	−2.10164e6	−0.0914852
$881$	−2.59719e7	−1.12736	−0.563682	−	0.825992i	$-0.690616\pi$
$881$	−2.59719e7	−1.12736	−0.563682	+	0.825992i	$0.690616\pi$
$882$	−1.07202e7	−0.464015
$883$	867569.	0.0374457	0.0187229	−	0.999825i	$-0.494040\pi$
$883$	867569.	0.0374457	0.0187229	+	0.999825i	$0.494040\pi$
$884$	−1.12483e7	−0.484124
$885$	1.01395e7	0.435170
$886$	−2.17602e7	−0.931275
$887$	3.59743e7	1.53527	0.767633	−	0.640890i	$-0.221435\pi$
$887$	3.59743e7	1.53527	0.767633	+	0.640890i	$0.221435\pi$
$888$	−1.88391e7	−0.801729
$889$	7.57429e7	3.21431
$890$	1.81331e7	0.767354
$891$	−881105.	−0.0371821
$892$	1.80826e7	0.760935
$893$	−2.26837e7	−0.951887
$894$	1.13810e7	0.476253
$895$	−2.56678e7	−1.07110
$896$	4.07514e7	1.69579
$897$	1.18525e7	0.491847
$898$	−1.56791e7	−0.648827
$899$	6.75503e6	0.278758
$900$	−885895.	−0.0364566
$901$	−5.52152e6	−0.226593
$902$	4.78657e6	0.195888
$903$	−4.25176e7	−1.73520
$904$	1.38624e7	0.564179
$905$	1.72336e7	0.699445
$906$	1.22575e7	0.496113
$907$	3.69887e7	1.49297	0.746484	−	0.665404i	$-0.231741\pi$
$907$	3.69887e7	1.49297	0.746484	+	0.665404i	$0.231741\pi$
$908$	2.63318e7	1.05990
$909$	−3.97091e6	−0.159397
$910$	−4.52967e7	−1.81327
$911$	−3.27738e7	−1.30837	−0.654186	−	0.756334i	$-0.726989\pi$
$911$	−3.27738e7	−1.30837	−0.654186	+	0.756334i	$0.726989\pi$
$912$	4.39468e6	0.174961
$913$	−8.16903e6	−0.324335
$914$	8.72910e6	0.345624
$915$	560491.	0.0221318
$916$	−2.52553e6	−0.0994519
$917$	1.31050e7	0.514653
$918$	−1.01271e6	−0.0396622
$919$	−2.59127e7	−1.01210	−0.506050	−	0.862504i	$-0.668895\pi$
$919$	−2.59127e7	−1.01210	−0.506050	+	0.862504i	$0.668895\pi$
$920$	1.25316e7	0.488132
$921$	2.50966e7	0.974912
$922$	−1.28541e6	−0.0497982
$923$	−8.32114e7	−3.21498
$924$	6.97406e6	0.268724
$925$	−6.02485e6	−0.231522
$926$	−7.86139e6	−0.301281
$927$	−859329.	−0.0328443
$928$	2.62796e7	1.00173
$929$	2.64144e7	1.00416	0.502078	−	0.864822i	$-0.332569\pi$
$929$	2.64144e7	1.00416	0.502078	+	0.864822i	$0.332569\pi$
$930$	2.46134e6	0.0933177
$931$	8.37343e7	3.16613
$932$	2.92874e7	1.10444
$933$	−2.32059e7	−0.872758
$934$	−2.03923e7	−0.764889
$935$	−3.78281e6	−0.141509
$936$	1.36270e7	0.508406
$937$	−4.87434e7	−1.81371	−0.906853	−	0.421447i	$-0.861523\pi$
$937$	−4.87434e7	−1.81371	−0.906853	+	0.421447i	$0.861523\pi$
$938$	−2.14397e7	−0.795630
$939$	2.05735e7	0.761456
$940$	1.69065e7	0.624072
$941$	8.16328e6	0.300532	0.150266	−	0.988646i	$-0.451987\pi$
$941$	8.16328e6	0.300532	0.150266	+	0.988646i	$0.451987\pi$
$942$	−5.14809e6	−0.189025
$943$	1.54169e7	0.564568
$944$	4.90388e6	0.179106
$945$	1.08456e7	0.395071
$946$	−7.56121e6	−0.274703
$947$	3.20271e7	1.16049	0.580247	−	0.814441i	$-0.302956\pi$
$947$	3.20271e7	1.16049	0.580247	+	0.814441i	$0.302956\pi$
$948$	9.05017e6	0.327066
$949$	4.81929e7	1.73707
$950$	−2.60190e6	−0.0935367
$951$	−7.70806e6	−0.276372
$952$	1.90455e7	0.681082
$953$	−716685.	−0.0255621	−0.0127810	−	0.999918i	$-0.504068\pi$
$953$	−716685.	−0.0255621	−0.0127810	+	0.999918i	$0.504068\pi$
$954$	2.81528e6	0.100150
$955$	−2.16904e7	−0.769588
$956$	−3.37834e7	−1.19553
$957$	5.29338e6	0.186833
$958$	2.78599e7	0.980767
$959$	−4.97375e6	−0.174638
$960$	5.06848e6	0.177501
$961$	−2.62502e7	−0.916904
$962$	3.90045e7	1.35887
$963$	1.22005e7	0.423949
$964$	5.29677e6	0.183577
$965$	−7.35693e6	−0.254319
$966$	−8.44629e6	−0.291221
$967$	1.76696e7	0.607659	0.303829	−	0.952726i	$-0.401735\pi$
$967$	1.76696e7	0.607659	0.303829	+	0.952726i	$0.401735\pi$
$968$	−2.33683e7	−0.801566
$969$	7.91014e6	0.270629
$970$	−1.37112e7	−0.467892
$971$	−4.82287e7	−1.64156	−0.820781	−	0.571243i	$-0.806461\pi$
$971$	−4.82287e7	−1.64156	−0.820781	+	0.571243i	$0.806461\pi$
$972$	−1.37321e6	−0.0466201
$973$	2.39146e7	0.809804
$974$	−1.09396e7	−0.369490
$975$	4.35799e6	0.146816
$976$	271076.	0.00910892
$977$	3.47262e7	1.16392	0.581958	−	0.813219i	$-0.302287\pi$
$977$	3.47262e7	1.16392	0.581958	+	0.813219i	$0.302287\pi$
$978$	1.23779e6	0.0413808
$979$	1.37339e7	0.457970
$980$	−6.24086e7	−2.07577
$981$	−770089.	−0.0255487
$982$	−1.00149e7	−0.331412
$983$	3.57773e6	0.118093	0.0590464	−	0.998255i	$-0.481194\pi$
$983$	3.57773e6	0.118093	0.0590464	+	0.998255i	$0.481194\pi$
$984$	1.77249e7	0.583575
$985$	−3.07106e7	−1.00855
$986$	6.08400e6	0.199295
$987$	−2.70747e7	−0.884649
$988$	−4.47972e7	−1.46002
$989$	−2.43536e7	−0.791722
$990$	1.92876e6	0.0625445
$991$	4.08290e7	1.32064	0.660321	−	0.750984i	$-0.270420\pi$
$991$	4.08290e7	1.32064	0.660321	+	0.750984i	$0.270420\pi$
$992$	9.25508e6	0.298608
$993$	8.19902e6	0.263869
$994$	5.92977e7	1.90358
$995$	3.32806e7	1.06570
$996$	−1.27315e7	−0.406661
$997$	1.24925e6	0.0398025	0.0199013	−	0.999802i	$-0.493665\pi$
$997$	1.24925e6	0.0398025	0.0199013	+	0.999802i	$0.493665\pi$
$998$	−8.42200e6	−0.267663
$999$	−9.33904e6	−0.296066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.d.1.10	✓	25
3.2	odd	2		927.6.a.f.1.16		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.d.1.10	✓	25	1.1	even	1	trivial
927.6.a.f.1.16		25	3.2	odd	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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	309.a (trivial)

\(f(q)\)	\(=\)	\(q-2.95711 q^{2} +9.00000 q^{3} -23.2555 q^{4} +59.9608 q^{5} -26.6140 q^{6} +248.119 q^{7} +163.397 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-2.95711 q^{2} +9.00000 q^{3} -23.2555 q^{4} +59.9608 q^{5} -26.6140 q^{6} +248.119 q^{7} +163.397 q^{8} +81.0000 q^{9} -177.311 q^{10} -134.294 q^{11} -209.300 q^{12} +1029.61 q^{13} -733.714 q^{14} +539.647 q^{15} +260.995 q^{16} +469.774 q^{17} -239.526 q^{18} +1870.91 q^{19} -1394.42 q^{20} +2233.07 q^{21} +397.123 q^{22} +1279.08 q^{23} +1470.57 q^{24} +470.296 q^{25} -3044.66 q^{26} +729.000 q^{27} -5770.13 q^{28} -4379.58 q^{29} -1595.79 q^{30} -1542.39 q^{31} -6000.48 q^{32} -1208.65 q^{33} -1389.17 q^{34} +14877.4 q^{35} -1883.70 q^{36} -12810.8 q^{37} -5532.48 q^{38} +9266.48 q^{39} +9797.38 q^{40} +12053.1 q^{41} -6603.43 q^{42} -19040.0 q^{43} +3123.08 q^{44} +4856.82 q^{45} -3782.37 q^{46} -12124.4 q^{47} +2348.96 q^{48} +44756.0 q^{49} -1390.72 q^{50} +4227.97 q^{51} -23944.1 q^{52} -11753.6 q^{53} -2155.73 q^{54} -8052.39 q^{55} +40541.8 q^{56} +16838.2 q^{57} +12950.9 q^{58} +18789.1 q^{59} -12549.8 q^{60} +1038.63 q^{61} +4561.02 q^{62} +20097.6 q^{63} +9392.22 q^{64} +61736.1 q^{65} +3574.10 q^{66} +29220.7 q^{67} -10924.8 q^{68} +11511.7 q^{69} -43994.1 q^{70} -80818.5 q^{71} +13235.1 q^{72} +46807.0 q^{73} +37882.8 q^{74} +4232.66 q^{75} -43508.9 q^{76} -33321.0 q^{77} -27402.0 q^{78} -43240.3 q^{79} +15649.5 q^{80} +6561.00 q^{81} -35642.4 q^{82} +60829.3 q^{83} -51931.2 q^{84} +28168.0 q^{85} +56303.3 q^{86} -39416.2 q^{87} -21943.2 q^{88} -102267. q^{89} -14362.2 q^{90} +255465. q^{91} -29745.6 q^{92} -13881.5 q^{93} +35853.2 q^{94} +112181. q^{95} -54004.3 q^{96} +77328.7 q^{97} -132348. q^{98} -10877.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9} + 693 q^{10} + 1470 q^{11} + 4374 q^{12} + 2515 q^{13} + 254 q^{14} + 423 q^{15} + 11542 q^{16} + 880 q^{17} + 1134 q^{18} + 7412 q^{19} + 1927 q^{20} + 3618 q^{21} + 5461 q^{22} + 5567 q^{23} + 3078 q^{24} + 31584 q^{25} + 18502 q^{26} + 18225 q^{27} + 25011 q^{28} + 17230 q^{29} + 6237 q^{30} + 22821 q^{31} + 50233 q^{32} + 13230 q^{33} + 38342 q^{34} + 30664 q^{35} + 39366 q^{36} + 13342 q^{37} + 25860 q^{38} + 22635 q^{39} + 40701 q^{40} + 36374 q^{41} + 2286 q^{42} + 48371 q^{43} - 4133 q^{44} + 3807 q^{45} + 30489 q^{46} + 17740 q^{47} + 103878 q^{48} + 119201 q^{49} - 9505 q^{50} + 7920 q^{51} + 50699 q^{52} - 52204 q^{53} + 10206 q^{54} + 90638 q^{55} - 80285 q^{56} + 66708 q^{57} + 15313 q^{58} + 34099 q^{59} + 17343 q^{60} + 71175 q^{61} - 92130 q^{62} + 32562 q^{63} + 289374 q^{64} - 32899 q^{65} + 49149 q^{66} + 85201 q^{67} - 41169 q^{68} + 50103 q^{69} - 92312 q^{70} + 102652 q^{71} + 27702 q^{72} + 186396 q^{73} - 258113 q^{74} + 284256 q^{75} + 148369 q^{76} - 109016 q^{77} + 166518 q^{78} + 210994 q^{79} + 17955 q^{80} + 164025 q^{81} + 635103 q^{82} + 68429 q^{83} + 225099 q^{84} + 375692 q^{85} + 360833 q^{86} + 155070 q^{87} + 556985 q^{88} + 163508 q^{89} + 56133 q^{90} + 591882 q^{91} + 388500 q^{92} + 205389 q^{93} + 205288 q^{94} + 87988 q^{95} + 452097 q^{96} + 385683 q^{97} - 61147 q^{98} + 119070 q^{99}+O(q^{100}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9 + 693 * q^10 + 1470 * q^11 + 4374 * q^12 + 2515 * q^13 + 254 * q^14 + 423 * q^15 + 11542 * q^16 + 880 * q^17 + 1134 * q^18 + 7412 * q^19 + 1927 * q^20 + 3618 * q^21 + 5461 * q^22 + 5567 * q^23 + 3078 * q^24 + 31584 * q^25 + 18502 * q^26 + 18225 * q^27 + 25011 * q^28 + 17230 * q^29 + 6237 * q^30 + 22821 * q^31 + 50233 * q^32 + 13230 * q^33 + 38342 * q^34 + 30664 * q^35 + 39366 * q^36 + 13342 * q^37 + 25860 * q^38 + 22635 * q^39 + 40701 * q^40 + 36374 * q^41 + 2286 * q^42 + 48371 * q^43 - 4133 * q^44 + 3807 * q^45 + 30489 * q^46 + 17740 * q^47 + 103878 * q^48 + 119201 * q^49 - 9505 * q^50 + 7920 * q^51 + 50699 * q^52 - 52204 * q^53 + 10206 * q^54 + 90638 * q^55 - 80285 * q^56 + 66708 * q^57 + 15313 * q^58 + 34099 * q^59 + 17343 * q^60 + 71175 * q^61 - 92130 * q^62 + 32562 * q^63 + 289374 * q^64 - 32899 * q^65 + 49149 * q^66 + 85201 * q^67 - 41169 * q^68 + 50103 * q^69 - 92312 * q^70 + 102652 * q^71 + 27702 * q^72 + 186396 * q^73 - 258113 * q^74 + 284256 * q^75 + 148369 * q^76 - 109016 * q^77 + 166518 * q^78 + 210994 * q^79 + 17955 * q^80 + 164025 * q^81 + 635103 * q^82 + 68429 * q^83 + 225099 * q^84 + 375692 * q^85 + 360833 * q^86 + 155070 * q^87 + 556985 * q^88 + 163508 * q^89 + 56133 * q^90 + 591882 * q^91 + 388500 * q^92 + 205389 * q^93 + 205288 * q^94 + 87988 * q^95 + 452097 * q^96 + 385683 * q^97 - 61147 * q^98 + 119070 * q^99

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