LMFDB - Embedded newform 309.6.a.b.1.8

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 475 x^{18} + 1732 x^{17} + 94501 x^{16} - 304042 x^{15} - 10274267 x^{14} + \cdots - 108537388253184 $ x^20 - 4x^19 - 475x^18 + 1732x^17 + 94501x^16 - 304042x^15 - 10274267x^14 + 27738506x^13 + 668854800x^12 - 1394251104x^11 - 26886918880x^10 + 36931823776x^9 + 663067133248x^8 - 391924258816x^7 - 9543181747968x^6 - 2051078115840x^5 + 69736119883776x^4 + 68811719589888x^3 - 164566613229568x^2 - 286519559659520*x - 108537388253184
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-3.29162$ of defining polynomial
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)

$f(q)$	$=$	$q-3.29162 q^{2} -9.00000 q^{3} -21.1653 q^{4} -24.8129 q^{5} +29.6246 q^{6} +226.920 q^{7} +175.000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-3.29162 q^{2} -9.00000 q^{3} -21.1653 q^{4} -24.8129 q^{5} +29.6246 q^{6} +226.920 q^{7} +175.000 q^{8} +81.0000 q^{9} +81.6747 q^{10} +745.590 q^{11} +190.487 q^{12} +94.9159 q^{13} -746.935 q^{14} +223.316 q^{15} +101.256 q^{16} -716.536 q^{17} -266.621 q^{18} +414.811 q^{19} +525.172 q^{20} -2042.28 q^{21} -2454.20 q^{22} -2349.27 q^{23} -1575.00 q^{24} -2509.32 q^{25} -312.427 q^{26} -729.000 q^{27} -4802.83 q^{28} +5465.99 q^{29} -735.072 q^{30} +5208.20 q^{31} -5933.29 q^{32} -6710.31 q^{33} +2358.56 q^{34} -5630.56 q^{35} -1714.39 q^{36} -4387.02 q^{37} -1365.40 q^{38} -854.243 q^{39} -4342.25 q^{40} +16504.1 q^{41} +6722.41 q^{42} -1481.96 q^{43} -15780.6 q^{44} -2009.85 q^{45} +7732.91 q^{46} +16168.5 q^{47} -911.305 q^{48} +34685.8 q^{49} +8259.72 q^{50} +6448.82 q^{51} -2008.92 q^{52} -8972.07 q^{53} +2399.59 q^{54} -18500.3 q^{55} +39711.0 q^{56} -3733.30 q^{57} -17991.9 q^{58} -3120.13 q^{59} -4726.55 q^{60} +25387.6 q^{61} -17143.4 q^{62} +18380.5 q^{63} +16289.9 q^{64} -2355.14 q^{65} +22087.8 q^{66} -69739.1 q^{67} +15165.7 q^{68} +21143.5 q^{69} +18533.6 q^{70} +7774.55 q^{71} +14175.0 q^{72} -3762.77 q^{73} +14440.4 q^{74} +22583.9 q^{75} -8779.58 q^{76} +169190. q^{77} +2811.84 q^{78} -5426.32 q^{79} -2512.46 q^{80} +6561.00 q^{81} -54325.3 q^{82} -72586.0 q^{83} +43225.4 q^{84} +17779.3 q^{85} +4878.04 q^{86} -49193.9 q^{87} +130478. q^{88} -52195.8 q^{89} +6615.65 q^{90} +21538.4 q^{91} +49723.0 q^{92} -46873.8 q^{93} -53220.6 q^{94} -10292.7 q^{95} +53399.6 q^{96} -134593. q^{97} -114173. q^{98} +60392.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.29162	−0.581881	−0.290941	−	0.956741i	$-0.593968\pi$
$2$	−3.29162	−0.581881	−0.290941	+	0.956741i	$0.593968\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−21.1653	−0.661414
$5$	−24.8129	−0.443867	−0.221934	−	0.975062i	$-0.571237\pi$
$5$	−24.8129	−0.443867	−0.221934	+	0.975062i	$0.571237\pi$
$6$	29.6246	0.335949
$7$	226.920	1.75036	0.875182	−	0.483794i	$-0.160742\pi$
$7$	226.920	1.75036	0.875182	+	0.483794i	$0.160742\pi$
$8$	175.000	0.966746
$9$	81.0000	0.333333
$10$	81.6747	0.258278
$11$	745.590	1.85788	0.928941	−	0.370227i	$-0.120720\pi$
$11$	745.590	1.85788	0.928941	+	0.370227i	$0.120720\pi$
$12$	190.487	0.381868
$13$	94.9159	0.155769	0.0778844	−	0.996962i	$-0.475183\pi$
$13$	94.9159	0.155769	0.0778844	+	0.996962i	$0.475183\pi$
$14$	−746.935	−1.01850
$15$	223.316	0.256267
$16$	101.256	0.0988830
$17$	−716.536	−0.601334	−0.300667	−	0.953729i	$-0.597209\pi$
$17$	−716.536	−0.601334	−0.300667	+	0.953729i	$0.597209\pi$
$18$	−266.621	−0.193960
$19$	414.811	0.263613	0.131806	−	0.991275i	$-0.457922\pi$
$19$	414.811	0.263613	0.131806	+	0.991275i	$0.457922\pi$
$20$	525.172	0.293580
$21$	−2042.28	−1.01057
$22$	−2454.20	−1.08107
$23$	−2349.27	−0.926006	−0.463003	−	0.886357i	$-0.653228\pi$
$23$	−2349.27	−0.926006	−0.463003	+	0.886357i	$0.653228\pi$
$24$	−1575.00	−0.558151
$25$	−2509.32	−0.802982
$26$	−312.427	−0.0906390
$27$	−729.000	−0.192450
$28$	−4802.83	−1.15772
$29$	5465.99	1.20691	0.603453	−	0.797398i	$-0.293791\pi$
$29$	5465.99	1.20691	0.603453	+	0.797398i	$0.293791\pi$
$30$	−735.072	−0.149117
$31$	5208.20	0.973383	0.486691	−	0.873574i	$-0.338204\pi$
$31$	5208.20	0.973383	0.486691	+	0.873574i	$0.338204\pi$
$32$	−5933.29	−1.02428
$33$	−6710.31	−1.07265
$34$	2358.56	0.349905
$35$	−5630.56	−0.776929
$36$	−1714.39	−0.220471
$37$	−4387.02	−0.526824	−0.263412	−	0.964683i	$-0.584848\pi$
$37$	−4387.02	−0.526824	−0.263412	+	0.964683i	$0.584848\pi$
$38$	−1365.40	−0.153391
$39$	−854.243	−0.0899332
$40$	−4342.25	−0.429107
$41$	16504.1	1.53332	0.766661	−	0.642052i	$-0.221917\pi$
$41$	16504.1	1.53332	0.766661	+	0.642052i	$0.221917\pi$
$42$	6722.41	0.588034
$43$	−1481.96	−0.122226	−0.0611132	−	0.998131i	$-0.519465\pi$
$43$	−1481.96	−0.122226	−0.0611132	+	0.998131i	$0.519465\pi$
$44$	−15780.6	−1.22883
$45$	−2009.85	−0.147956
$46$	7732.91	0.538826
$47$	16168.5	1.06764	0.533821	−	0.845597i	$-0.320756\pi$
$47$	16168.5	1.06764	0.533821	+	0.845597i	$0.320756\pi$
$48$	−911.305	−0.0570901
$49$	34685.8	2.06377
$50$	8259.72	0.467240
$51$	6448.82	0.347180
$52$	−2008.92	−0.103028
$53$	−8972.07	−0.438736	−0.219368	−	0.975642i	$-0.570399\pi$
$53$	−8972.07	−0.438736	−0.219368	+	0.975642i	$0.570399\pi$
$54$	2399.59	0.111983
$55$	−18500.3	−0.824653
$56$	39711.0	1.69216
$57$	−3733.30	−0.152197
$58$	−17991.9	−0.702276
$59$	−3120.13	−0.116693	−0.0583463	−	0.998296i	$-0.518583\pi$
$59$	−3120.13	−0.116693	−0.0583463	+	0.998296i	$0.518583\pi$
$60$	−4726.55	−0.169499
$61$	25387.6	0.873567	0.436784	−	0.899567i	$-0.356118\pi$
$61$	25387.6	0.873567	0.436784	+	0.899567i	$0.356118\pi$
$62$	−17143.4	−0.566393
$63$	18380.5	0.583455
$64$	16289.9	0.497129
$65$	−2355.14	−0.0691407
$66$	22087.8	0.624154
$67$	−69739.1	−1.89797	−0.948985	−	0.315320i	$-0.897888\pi$
$67$	−69739.1	−1.89797	−0.948985	+	0.315320i	$0.897888\pi$
$68$	15165.7	0.397731
$69$	21143.5	0.534630
$70$	18533.6	0.452080
$71$	7774.55	0.183033	0.0915165	−	0.995804i	$-0.470829\pi$
$71$	7774.55	0.183033	0.0915165	+	0.995804i	$0.470829\pi$
$72$	14175.0	0.322249
$73$	−3762.77	−0.0826419	−0.0413210	−	0.999146i	$-0.513157\pi$
$73$	−3762.77	−0.0826419	−0.0413210	+	0.999146i	$0.513157\pi$
$74$	14440.4	0.306549
$75$	22583.9	0.463602
$76$	−8779.58	−0.174357
$77$	169190.	3.25197
$78$	2811.84	0.0523304
$79$	−5426.32	−0.0978223	−0.0489112	−	0.998803i	$-0.515575\pi$
$79$	−5426.32	−0.0978223	−0.0489112	+	0.998803i	$0.515575\pi$
$80$	−2512.46	−0.0438909
$81$	6561.00	0.111111
$82$	−54325.3	−0.892211
$83$	−72586.0	−1.15653	−0.578266	−	0.815848i	$-0.696270\pi$
$83$	−72586.0	−1.15653	−0.578266	+	0.815848i	$0.696270\pi$
$84$	43225.4	0.668407
$85$	17779.3	0.266912
$86$	4878.04	0.0711212
$87$	−49193.9	−0.696808
$88$	130478.	1.79610
$89$	−52195.8	−0.698491	−0.349246	−	0.937031i	$-0.613562\pi$
$89$	−52195.8	−0.698491	−0.349246	+	0.937031i	$0.613562\pi$
$90$	6615.65	0.0860927
$91$	21538.4	0.272652
$92$	49723.0	0.612474
$93$	−46873.8	−0.561983
$94$	−53220.6	−0.621241
$95$	−10292.7	−0.117009
$96$	53399.6	0.591371
$97$	−134593.	−1.45242	−0.726211	−	0.687472i	$-0.758720\pi$
$97$	−134593.	−1.45242	−0.726211	+	0.687472i	$0.758720\pi$
$98$	−114173.	−1.20087
$99$	60392.8	0.619294
$100$	53110.4	0.531104
$101$	−134854.	−1.31541	−0.657703	−	0.753277i	$-0.728472\pi$
$101$	−134854.	−1.31541	−0.657703	+	0.753277i	$0.728472\pi$
$102$	−21227.1	−0.202018
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	16610.3	0.150589
$105$	50675.0	0.448560
$106$	29532.6	0.255292
$107$	115619.	0.976267	0.488134	−	0.872769i	$-0.337678\pi$
$107$	115619.	0.976267	0.488134	+	0.872769i	$0.337678\pi$
$108$	15429.5	0.127289
$109$	214828.	1.73190	0.865952	−	0.500127i	$-0.166713\pi$
$109$	214828.	1.73190	0.865952	+	0.500127i	$0.166713\pi$
$110$	60895.8	0.479850
$111$	39483.2	0.304162
$112$	22977.1	0.173081
$113$	183364.	1.35089	0.675444	−	0.737412i	$-0.263952\pi$
$113$	183364.	1.35089	0.675444	+	0.737412i	$0.263952\pi$
$114$	12288.6	0.0885605
$115$	58292.4	0.411024
$116$	−115689.	−0.798265
$117$	7688.19	0.0519230
$118$	10270.3	0.0679012
$119$	−162597.	−1.05255
$120$	39080.3	0.247745
$121$	394853.	2.45173
$122$	−83566.1	−0.508312
$123$	−148537.	−0.885264
$124$	−110233.	−0.643809
$125$	139804.	0.800285
$126$	−60501.7	−0.339501
$127$	34761.4	0.191244	0.0956221	−	0.995418i	$-0.469516\pi$
$127$	34761.4	0.191244	0.0956221	+	0.995418i	$0.469516\pi$
$128$	136245.	0.735014
$129$	13337.6	0.0705674
$130$	7752.23	0.0402317
$131$	183856.	0.936050	0.468025	−	0.883715i	$-0.344966\pi$
$131$	183856.	0.936050	0.468025	+	0.883715i	$0.344966\pi$
$132$	142025.	0.709465
$133$	94129.1	0.461418
$134$	229555.	1.10439
$135$	18088.6	0.0854223
$136$	−125394.	−0.581337
$137$	245141.	1.11587	0.557936	−	0.829884i	$-0.311593\pi$
$137$	245141.	1.11587	0.557936	+	0.829884i	$0.311593\pi$
$138$	−69596.2	−0.311091
$139$	−42476.9	−0.186473	−0.0932365	−	0.995644i	$-0.529721\pi$
$139$	−42476.9	−0.186473	−0.0932365	+	0.995644i	$0.529721\pi$
$140$	119172.	0.513872
$141$	−145517.	−0.616404
$142$	−25590.8	−0.106503
$143$	70768.4	0.289400
$144$	8201.75	0.0329610
$145$	−135627.	−0.535706
$146$	12385.6	0.0480878
$147$	−312173.	−1.19152
$148$	92852.4	0.348449
$149$	365689.	1.34942	0.674708	−	0.738085i	$-0.264269\pi$
$149$	365689.	1.34942	0.674708	+	0.738085i	$0.264269\pi$
$150$	−74337.4	−0.269761
$151$	−372127.	−1.32815	−0.664077	−	0.747664i	$-0.731175\pi$
$151$	−372127.	−1.32815	−0.664077	+	0.747664i	$0.731175\pi$
$152$	72591.8	0.254847
$153$	−58039.4	−0.200445
$154$	−556907.	−1.89226
$155$	−129231.	−0.432053
$156$	18080.3	0.0594831
$157$	311740.	1.00936	0.504678	−	0.863308i	$-0.331611\pi$
$157$	311740.	1.00936	0.504678	+	0.863308i	$0.331611\pi$
$158$	17861.4	0.0569210
$159$	80748.6	0.253304
$160$	147222.	0.454646
$161$	−533098.	−1.62085
$162$	−21596.3	−0.0646535
$163$	−399646.	−1.17817	−0.589083	−	0.808073i	$-0.700511\pi$
$163$	−399646.	−1.17817	−0.589083	+	0.808073i	$0.700511\pi$
$164$	−349314.	−1.01416
$165$	166502.	0.476114
$166$	238925.	0.672965
$167$	496467.	1.37752	0.688762	−	0.724987i	$-0.258154\pi$
$167$	496467.	1.37752	0.688762	+	0.724987i	$0.258154\pi$
$168$	−357399.	−0.976967
$169$	−362284.	−0.975736
$170$	−58522.8	−0.155311
$171$	33599.7	0.0878709
$172$	31366.0	0.0808422
$173$	10458.8	0.0265684	0.0132842	−	0.999912i	$-0.495771\pi$
$173$	10458.8	0.0265684	0.0132842	+	0.999912i	$0.495771\pi$
$174$	161927.	0.405459
$175$	−569415.	−1.40551
$176$	75495.6	0.183713
$177$	28081.2	0.0673725
$178$	171809.	0.406439
$179$	393978.	0.919050	0.459525	−	0.888165i	$-0.348020\pi$
$179$	393978.	0.919050	0.459525	+	0.888165i	$0.348020\pi$
$180$	42538.9	0.0978600
$181$	24020.3	0.0544983	0.0272491	−	0.999629i	$-0.491325\pi$
$181$	24020.3	0.0544983	0.0272491	+	0.999629i	$0.491325\pi$
$182$	−70896.0	−0.158651
$183$	−228488.	−0.504354
$184$	−411122.	−0.895213
$185$	108855.	0.233840
$186$	154291.	0.327007
$187$	−534242.	−1.11721
$188$	−342211.	−0.706154
$189$	−165425.	−0.336858
$190$	33879.6	0.0680854
$191$	868637.	1.72288	0.861440	−	0.507859i	$-0.169563\pi$
$191$	868637.	1.72288	0.861440	+	0.507859i	$0.169563\pi$
$192$	−146609.	−0.287017
$193$	−762531.	−1.47355	−0.736774	−	0.676139i	$-0.763652\pi$
$193$	−762531.	−1.47355	−0.736774	+	0.676139i	$0.763652\pi$
$194$	443028.	0.845137
$195$	21196.3	0.0399184
$196$	−734135.	−1.36501
$197$	658743.	1.20935	0.604673	−	0.796474i	$-0.293304\pi$
$197$	658743.	1.20935	0.604673	+	0.796474i	$0.293304\pi$
$198$	−198790.	−0.360356
$199$	−466230.	−0.834580	−0.417290	−	0.908773i	$-0.637020\pi$
$199$	−466230.	−0.834580	−0.417290	+	0.908773i	$0.637020\pi$
$200$	−439130.	−0.776279
$201$	627652.	1.09579
$202$	443887.	0.765410
$203$	1.24034e6	2.11253
$204$	−136491.	−0.229630
$205$	−409516.	−0.680591
$206$	−34920.8	−0.0573345
$207$	−190291.	−0.308669
$208$	9610.82	0.0154029
$209$	309279.	0.489762
$210$	−166803.	−0.261009
$211$	441785.	0.683132	0.341566	−	0.939858i	$-0.389043\pi$
$211$	441785.	0.683132	0.341566	+	0.939858i	$0.389043\pi$
$212$	189896.	0.290186
$213$	−69970.9	−0.105674
$214$	−380573.	−0.568071
$215$	36771.7	0.0542523
$216$	−127575.	−0.186050
$217$	1.18185e6	1.70377
$218$	−707130.	−1.00776
$219$	33864.9	0.0477133
$220$	391563.	0.545437
$221$	−68010.6	−0.0936691
$222$	−129964.	−0.176986
$223$	−813947.	−1.09606	−0.548030	−	0.836459i	$-0.684622\pi$
$223$	−813947.	−1.09606	−0.548030	+	0.836459i	$0.684622\pi$
$224$	−1.34638e6	−1.79287
$225$	−203255.	−0.267661
$226$	−603566.	−0.786056
$227$	278157.	0.358283	0.179141	−	0.983823i	$-0.442668\pi$
$227$	278157.	0.358283	0.179141	+	0.983823i	$0.442668\pi$
$228$	79016.3	0.100665
$229$	−462455.	−0.582747	−0.291374	−	0.956609i	$-0.594112\pi$
$229$	−462455.	−0.582747	−0.291374	+	0.956609i	$0.594112\pi$
$230$	−191876.	−0.239167
$231$	−1.52271e6	−1.87753
$232$	956546.	1.16677
$233$	347636.	0.419503	0.209752	−	0.977755i	$-0.432734\pi$
$233$	347636.	0.419503	0.209752	+	0.977755i	$0.432734\pi$
$234$	−25306.6	−0.0302130
$235$	−401189.	−0.473891
$236$	66038.4	0.0771821
$237$	48836.9	0.0564777
$238$	535206.	0.612461
$239$	−1.32539e6	−1.50089	−0.750445	−	0.660933i	$-0.770161\pi$
$239$	−1.32539e6	−1.50089	−0.750445	+	0.660933i	$0.770161\pi$
$240$	22612.2	0.0253404
$241$	1.12084e6	1.24308	0.621541	−	0.783381i	$-0.286507\pi$
$241$	1.12084e6	1.24308	0.621541	+	0.783381i	$0.286507\pi$
$242$	−1.29971e6	−1.42661
$243$	−59049.0	−0.0641500
$244$	−537334.	−0.577790
$245$	−860657.	−0.916041
$246$	488928.	0.515118
$247$	39372.2	0.0410627
$248$	911434.	0.941014
$249$	653274.	0.667724
$250$	−460181.	−0.465671
$251$	−524254.	−0.525240	−0.262620	−	0.964899i	$-0.584587\pi$
$251$	−524254.	−0.525240	−0.262620	+	0.964899i	$0.584587\pi$
$252$	−389029.	−0.385905
$253$	−1.75159e6	−1.72041
$254$	−114421.	−0.111281
$255$	−160014.	−0.154102
$256$	−969744.	−0.924820
$257$	86869.9	0.0820420	0.0410210	−	0.999158i	$-0.486939\pi$
$257$	86869.9	0.0820420	0.0410210	+	0.999158i	$0.486939\pi$
$258$	−43902.4	−0.0410619
$259$	−995504.	−0.922133
$260$	49847.2	0.0457306
$261$	442745.	0.402302
$262$	−605183.	−0.544670
$263$	957047.	0.853187	0.426593	−	0.904444i	$-0.359714\pi$
$263$	957047.	0.853187	0.426593	+	0.904444i	$0.359714\pi$
$264$	−1.17430e6	−1.03698
$265$	222623.	0.194740
$266$	−309837.	−0.268491
$267$	469763.	0.403274
$268$	1.47605e6	1.25534
$269$	351856.	0.296472	0.148236	−	0.988952i	$-0.452640\pi$
$269$	351856.	0.296472	0.148236	+	0.988952i	$0.452640\pi$
$270$	−59540.8	−0.0497056
$271$	1.81167e6	1.49850	0.749250	−	0.662287i	$-0.230414\pi$
$271$	1.81167e6	1.49850	0.749250	+	0.662287i	$0.230414\pi$
$272$	−72553.6	−0.0594617
$273$	−193845.	−0.157416
$274$	−806911.	−0.649306
$275$	−1.87092e6	−1.49185
$276$	−447507.	−0.353612
$277$	1.24759e6	0.976951	0.488476	−	0.872578i	$-0.337553\pi$
$277$	1.24759e6	0.976951	0.488476	+	0.872578i	$0.337553\pi$
$278$	139818.	0.108505
$279$	421864.	0.324461
$280$	−985346.	−0.751093
$281$	2.12003e6	1.60168	0.800842	−	0.598876i	$-0.204386\pi$
$281$	2.12003e6	1.60168	0.800842	+	0.598876i	$0.204386\pi$
$282$	478985.	0.358674
$283$	242928.	0.180306	0.0901532	−	0.995928i	$-0.471264\pi$
$283$	242928.	0.180306	0.0901532	+	0.995928i	$0.471264\pi$
$284$	−164550.	−0.121061
$285$	92634.1	0.0675552
$286$	−232942.	−0.168397
$287$	3.74513e6	2.68387
$288$	−480596.	−0.341428
$289$	−906434.	−0.638398
$290$	446433.	0.311717
$291$	1.21134e6	0.838556
$292$	79640.0	0.0546605
$293$	671455.	0.456928	0.228464	−	0.973552i	$-0.426630\pi$
$293$	671455.	0.456928	0.228464	+	0.973552i	$0.426630\pi$
$294$	1.02755e6	0.693323
$295$	77419.7	0.0517960
$296$	−767727.	−0.509305
$297$	−543535.	−0.357550
$298$	−1.20371e6	−0.785200
$299$	−222983.	−0.144243
$300$	−477993.	−0.306633
$301$	−336286.	−0.213941
$302$	1.22490e6	0.772828
$303$	1.21368e6	0.759450
$304$	42002.2	0.0260668
$305$	−629940.	−0.387748
$306$	191043.	0.116635
$307$	−850547.	−0.515054	−0.257527	−	0.966271i	$-0.582908\pi$
$307$	−850547.	−0.515054	−0.257527	+	0.966271i	$0.582908\pi$
$308$	−3.58094e6	−2.15090
$309$	−95481.0	−0.0568880
$310$	425378.	0.251403
$311$	131903.	0.0773309	0.0386654	−	0.999252i	$-0.487689\pi$
$311$	131903.	0.0773309	0.0386654	+	0.999252i	$0.487689\pi$
$312$	−149492.	−0.0869425
$313$	−2.86656e6	−1.65387	−0.826933	−	0.562300i	$-0.809916\pi$
$313$	−2.86656e6	−1.65387	−0.826933	+	0.562300i	$0.809916\pi$
$314$	−1.02613e6	−0.587325
$315$	−456075.	−0.258976
$316$	114850.	0.0647011
$317$	−2.72387e6	−1.52243	−0.761216	−	0.648498i	$-0.775397\pi$
$317$	−2.72387e6	−1.52243	−0.761216	+	0.648498i	$0.775397\pi$
$318$	−265794.	−0.147393
$319$	4.07538e6	2.24229
$320$	−404200.	−0.220659
$321$	−1.04057e6	−0.563648
$322$	1.75475e6	0.943141
$323$	−297227.	−0.158519
$324$	−138865.	−0.0734905
$325$	−238174.	−0.125080
$326$	1.31548e6	0.685552
$327$	−1.93345e6	−0.999916
$328$	2.88822e6	1.48233
$329$	3.66897e6	1.86876
$330$	−548062.	−0.277042
$331$	399235.	0.200290	0.100145	−	0.994973i	$-0.468069\pi$
$331$	399235.	0.200290	0.100145	+	0.994973i	$0.468069\pi$
$332$	1.53630e6	0.764947
$333$	−355349.	−0.175608
$334$	−1.63418e6	−0.801556
$335$	1.73043e6	0.842447
$336$	−206794.	−0.0999285
$337$	992346.	0.475980	0.237990	−	0.971268i	$-0.423512\pi$
$337$	992346.	0.475980	0.237990	+	0.971268i	$0.423512\pi$
$338$	1.19250e6	0.567763
$339$	−1.65028e6	−0.779935
$340$	−376304.	−0.176540
$341$	3.88318e6	1.80843
$342$	−110597.	−0.0511304
$343$	4.05707e6	1.86199
$344$	−259342.	−0.118162
$345$	−524631.	−0.237305
$346$	−34426.3	−0.0154597
$347$	−2.43422e6	−1.08527	−0.542633	−	0.839970i	$-0.682573\pi$
$347$	−2.43422e6	−1.08527	−0.542633	+	0.839970i	$0.682573\pi$
$348$	1.04120e6	0.460878
$349$	720195.	0.316509	0.158255	−	0.987398i	$-0.449413\pi$
$349$	720195.	0.316509	0.158255	+	0.987398i	$0.449413\pi$
$350$	1.87430e6	0.817840
$351$	−69193.7	−0.0299777
$352$	−4.42380e6	−1.90300
$353$	1.82361e6	0.778924	0.389462	−	0.921042i	$-0.372661\pi$
$353$	1.82361e6	0.778924	0.389462	+	0.921042i	$0.372661\pi$
$354$	−92432.6	−0.0392028
$355$	−192909.	−0.0812423
$356$	1.10474e6	0.461992
$357$	1.46337e6	0.607692
$358$	−1.29682e6	−0.534778
$359$	−2.31986e6	−0.950005	−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−2.31986e6	−0.950005	−0.475002	+	0.879985i	$0.657553\pi$
$360$	−351723.	−0.143036
$361$	−2.30403e6	−0.930508
$362$	−79065.7	−0.0317115
$363$	−3.55368e6	−1.41551
$364$	−455865.	−0.180336
$365$	93365.3	0.0366820
$366$	752095.	0.293474
$367$	4.54986e6	1.76333	0.881663	−	0.471880i	$-0.156424\pi$
$367$	4.54986e6	1.76333	0.881663	+	0.471880i	$0.156424\pi$
$368$	−237878.	−0.0915663
$369$	1.33684e6	0.511107
$370$	−358308.	−0.136067
$371$	−2.03594e6	−0.767947
$372$	992096.	0.371703
$373$	3.88896e6	1.44731	0.723654	−	0.690162i	$-0.242461\pi$
$373$	3.88896e6	1.44731	0.723654	+	0.690162i	$0.242461\pi$
$374$	1.75852e6	0.650082
$375$	−1.25824e6	−0.462044
$376$	2.82949e6	1.03214
$377$	518809.	0.187998
$378$	544516.	0.196011
$379$	4.29052e6	1.53430	0.767152	−	0.641465i	$-0.221673\pi$
$379$	4.29052e6	1.53430	0.767152	+	0.641465i	$0.221673\pi$
$380$	217847.	0.0773915
$381$	−312853.	−0.110415
$382$	−2.85922e6	−1.00251
$383$	−1.46110e6	−0.508958	−0.254479	−	0.967078i	$-0.581904\pi$
$383$	−1.46110e6	−0.508958	−0.254479	+	0.967078i	$0.581904\pi$
$384$	−1.22621e6	−0.424361
$385$	−4.19809e6	−1.44344
$386$	2.50996e6	0.857430
$387$	−120039.	−0.0407421
$388$	2.84869e6	0.960652
$389$	−1.97098e6	−0.660400	−0.330200	−	0.943911i	$-0.607116\pi$
$389$	−1.97098e6	−0.660400	−0.330200	+	0.943911i	$0.607116\pi$
$390$	−69770.0	−0.0232278
$391$	1.68334e6	0.556839
$392$	6.07001e6	1.99514
$393$	−1.65470e6	−0.540429
$394$	−2.16833e6	−0.703696
$395$	134643.	0.0434201
$396$	−1.27823e6	−0.409610
$397$	−4.26343e6	−1.35763	−0.678817	−	0.734307i	$-0.737507\pi$
$397$	−4.26343e6	−1.35763	−0.678817	+	0.734307i	$0.737507\pi$
$398$	1.53465e6	0.485626
$399$	−847162.	−0.266400
$400$	−254084.	−0.0794012
$401$	4.23588e6	1.31547	0.657737	−	0.753248i	$-0.271514\pi$
$401$	4.23588e6	1.31547	0.657737	+	0.753248i	$0.271514\pi$
$402$	−2.06599e6	−0.637622
$403$	494341.	0.151623
$404$	2.85422e6	0.870028
$405$	−162798.	−0.0493186
$406$	−4.08274e6	−1.22924
$407$	−3.27092e6	−0.978777
$408$	1.12854e6	0.335635
$409$	4.57302e6	1.35174	0.675872	−	0.737019i	$-0.263767\pi$
$409$	4.57302e6	1.35174	0.675872	+	0.737019i	$0.263767\pi$
$410$	1.34797e6	0.396023
$411$	−2.20627e6	−0.644250
$412$	−224542.	−0.0651711
$413$	−708022.	−0.204254
$414$	626366.	0.179609
$415$	1.80107e6	0.513347
$416$	−563163.	−0.159552
$417$	382292.	0.107660
$418$	−1.01803e6	−0.284983
$419$	4.79718e6	1.33491	0.667454	−	0.744651i	$-0.267384\pi$
$419$	4.79718e6	1.33491	0.667454	+	0.744651i	$0.267384\pi$
$420$	−1.07255e6	−0.296684
$421$	2.12067e6	0.583134	0.291567	−	0.956550i	$-0.405823\pi$
$421$	2.12067e6	0.583134	0.291567	+	0.956550i	$0.405823\pi$
$422$	−1.45419e6	−0.397502
$423$	1.30965e6	0.355881
$424$	−1.57011e6	−0.424146
$425$	1.79802e6	0.482860
$426$	230318.	0.0614898
$427$	5.76095e6	1.52906
$428$	−2.44710e6	−0.645717
$429$	−636915.	−0.167085
$430$	−121038.	−0.0315684
$431$	1.38713e6	0.359685	0.179843	−	0.983695i	$-0.442441\pi$
$431$	1.38713e6	0.359685	0.179843	+	0.983695i	$0.442441\pi$
$432$	−73815.7	−0.0190300
$433$	−2.66015e6	−0.681847	−0.340923	−	0.940091i	$-0.610740\pi$
$433$	−2.66015e6	−0.681847	−0.340923	+	0.940091i	$0.610740\pi$
$434$	−3.89019e6	−0.991394
$435$	1.22064e6	0.309290
$436$	−4.54688e6	−1.14551
$437$	−974505.	−0.244107
$438$	−111470.	−0.0277635
$439$	−1.94590e6	−0.481901	−0.240951	−	0.970537i	$-0.577459\pi$
$439$	−1.94590e6	−0.481901	−0.240951	+	0.970537i	$0.577459\pi$
$440$	−3.23754e6	−0.797230
$441$	2.80955e6	0.687925
$442$	223865.	0.0545043
$443$	5.38726e6	1.30424	0.652122	−	0.758114i	$-0.273879\pi$
$443$	5.38726e6	1.30424	0.652122	+	0.758114i	$0.273879\pi$
$444$	−835672.	−0.201177
$445$	1.29513e6	0.310037
$446$	2.67920e6	0.637776
$447$	−3.29120e6	−0.779086
$448$	3.69651e6	0.870156
$449$	−5.19843e6	−1.21690	−0.608452	−	0.793591i	$-0.708209\pi$
$449$	−5.19843e6	−1.21690	−0.608452	+	0.793591i	$0.708209\pi$
$450$	669037.	0.155747
$451$	1.23053e7	2.84873
$452$	−3.88096e6	−0.893496
$453$	3.34914e6	0.766810
$454$	−915588.	−0.208478
$455$	−534430.	−0.121021
$456$	−653326.	−0.147136
$457$	5.63608e6	1.26237	0.631185	−	0.775633i	$-0.282569\pi$
$457$	5.63608e6	1.26237	0.631185	+	0.775633i	$0.282569\pi$
$458$	1.52222e6	0.339090
$459$	522355.	0.115727
$460$	−1.23377e6	−0.271857
$461$	−6.42542e6	−1.40815	−0.704075	−	0.710125i	$-0.748638\pi$
$461$	−6.42542e6	−1.40815	−0.704075	+	0.710125i	$0.748638\pi$
$462$	5.01216e6	1.09250
$463$	1.08211e6	0.234595	0.117297	−	0.993097i	$-0.462577\pi$
$463$	1.08211e6	0.234595	0.117297	+	0.993097i	$0.462577\pi$
$464$	553465.	0.119342
$465$	1.16308e6	0.249446
$466$	−1.14429e6	−0.244101
$467$	6.49303e6	1.37770	0.688851	−	0.724903i	$-0.258116\pi$
$467$	6.49303e6	1.37770	0.688851	+	0.724903i	$0.258116\pi$
$468$	−162722.	−0.0343426
$469$	−1.58252e7	−3.32214
$470$	1.32056e6	0.275749
$471$	−2.80566e6	−0.582751
$472$	−546022.	−0.112812
$473$	−1.10493e6	−0.227082
$474$	−160752.	−0.0328633
$475$	−1.04089e6	−0.211676
$476$	3.44140e6	0.696173
$477$	−726737.	−0.146245
$478$	4.36267e6	0.873339
$479$	782831.	0.155894	0.0779470	−	0.996958i	$-0.475164\pi$
$479$	782831.	0.155894	0.0779470	+	0.996958i	$0.475164\pi$
$480$	−1.32500e6	−0.262490
$481$	−416398.	−0.0820627
$482$	−3.68937e6	−0.723327
$483$	4.79788e6	0.935797
$484$	−8.35717e6	−1.62161
$485$	3.33964e6	0.644682
$486$	194367.	0.0373277
$487$	−9.41924e6	−1.79967	−0.899836	−	0.436228i	$-0.856314\pi$
$487$	−9.41924e6	−1.79967	−0.899836	+	0.436228i	$0.856314\pi$
$488$	4.44281e6	0.844517
$489$	3.59681e6	0.680214
$490$	2.83296e6	0.533027
$491$	−8.84443e6	−1.65564	−0.827820	−	0.560993i	$-0.810419\pi$
$491$	−8.84443e6	−1.65564	−0.827820	+	0.560993i	$0.810419\pi$
$492$	3.14383e6	0.585526
$493$	−3.91657e6	−0.725753
$494$	−129598.	−0.0238936
$495$	−1.49852e6	−0.274884
$496$	527363.	0.0962510
$497$	1.76420e6	0.320374
$498$	−2.15033e6	−0.388536
$499$	−7.13996e6	−1.28364	−0.641821	−	0.766854i	$-0.721821\pi$
$499$	−7.13996e6	−1.28364	−0.641821	+	0.766854i	$0.721821\pi$
$500$	−2.95899e6	−0.529320
$501$	−4.46820e6	−0.795314
$502$	1.72564e6	0.305627
$503$	7.35727e6	1.29657	0.648286	−	0.761397i	$-0.275486\pi$
$503$	7.35727e6	1.29657	0.648286	+	0.761397i	$0.275486\pi$
$504$	3.21659e6	0.564052
$505$	3.34612e6	0.583866
$506$	5.76558e6	1.00108
$507$	3.26056e6	0.563341
$508$	−735735.	−0.126492
$509$	769831.	0.131705	0.0658523	−	0.997829i	$-0.479023\pi$
$509$	769831.	0.131705	0.0658523	+	0.997829i	$0.479023\pi$
$510$	526705.	0.0896690
$511$	−853849.	−0.144653
$512$	−1.16782e6	−0.196879
$513$	−302397.	−0.0507323
$514$	−285942.	−0.0477387
$515$	−263240.	−0.0437355
$516$	−282294.	−0.0466743
$517$	1.20551e7	1.98355
$518$	3.27682e6	0.536572
$519$	−94129.0	−0.0153393
$520$	−412149.	−0.0668415
$521$	−1.13794e7	−1.83664	−0.918320	−	0.395839i	$-0.870454\pi$
$521$	−1.13794e7	−1.83664	−0.918320	+	0.395839i	$0.870454\pi$
$522$	−1.45735e6	−0.234092
$523$	408345.	0.0652789	0.0326394	−	0.999467i	$-0.489609\pi$
$523$	408345.	0.0652789	0.0326394	+	0.999467i	$0.489609\pi$
$524$	−3.89135e6	−0.619117
$525$	5.12474e6	0.811472
$526$	−3.15023e6	−0.496453
$527$	−3.73186e6	−0.585328
$528$	−679460.	−0.106067
$529$	−917257.	−0.142512
$530$	−732791.	−0.113316
$531$	−252731.	−0.0388975
$532$	−1.99227e6	−0.305189
$533$	1.56651e6	0.238844
$534$	−1.54628e6	−0.234658
$535$	−2.86884e6	−0.433333
$536$	−1.22043e7	−1.83486
$537$	−3.54580e6	−0.530613
$538$	−1.15817e6	−0.172512
$539$	2.58614e7	3.83425
$540$	−382850.	−0.0564995
$541$	3.92923e6	0.577184	0.288592	−	0.957452i	$-0.406813\pi$
$541$	3.92923e6	0.577184	0.288592	+	0.957452i	$0.406813\pi$
$542$	−5.96334e6	−0.871950
$543$	−216183.	−0.0314646
$544$	4.25141e6	0.615936
$545$	−5.33050e6	−0.768736
$546$	638064.	0.0915973
$547$	−2.44810e6	−0.349833	−0.174916	−	0.984583i	$-0.555966\pi$
$547$	−2.44810e6	−0.349833	−0.174916	+	0.984583i	$0.555966\pi$
$548$	−5.18847e6	−0.738054
$549$	2.05639e6	0.291189
$550$	6.15836e6	0.868077
$551$	2.26735e6	0.318156
$552$	3.70010e6	0.516851
$553$	−1.23134e6	−0.171225
$554$	−4.10659e6	−0.568469
$555$	−979693.	−0.135007
$556$	899035.	0.123336
$557$	−4.99138e6	−0.681683	−0.340842	−	0.940121i	$-0.610712\pi$
$557$	−4.99138e6	−0.681683	−0.340842	+	0.940121i	$0.610712\pi$
$558$	−1.38862e6	−0.188798
$559$	−140661.	−0.0190391
$560$	−570129.	−0.0768251
$561$	4.80818e6	0.645020
$562$	−6.97834e6	−0.931990
$563$	−1.17260e7	−1.55912	−0.779558	−	0.626330i	$-0.784556\pi$
$563$	−1.17260e7	−1.55912	−0.779558	+	0.626330i	$0.784556\pi$
$564$	3.07990e6	0.407698
$565$	−4.54981e6	−0.599614
$566$	−799625.	−0.104917
$567$	1.48882e6	0.194485
$568$	1.36054e6	0.176946
$569$	−3.16127e6	−0.409337	−0.204668	−	0.978831i	$-0.565612\pi$
$569$	−3.16127e6	−0.409337	−0.204668	+	0.978831i	$0.565612\pi$
$570$	−304916.	−0.0393091
$571$	1.21431e7	1.55862	0.779311	−	0.626638i	$-0.215569\pi$
$571$	1.21431e7	1.55862	0.779311	+	0.626638i	$0.215569\pi$
$572$	−1.49783e6	−0.191413
$573$	−7.81774e6	−0.994705
$574$	−1.23275e7	−1.56169
$575$	5.89508e6	0.743566
$576$	1.31948e6	0.165710
$577$	−1.45157e6	−0.181509	−0.0907543	−	0.995873i	$-0.528928\pi$
$577$	−1.45157e6	−0.181509	−0.0907543	+	0.995873i	$0.528928\pi$
$578$	2.98363e6	0.371472
$579$	6.86278e6	0.850753
$580$	2.87058e6	0.354324
$581$	−1.64712e7	−2.02435
$582$	−3.98725e6	−0.487940
$583$	−6.68948e6	−0.815119
$584$	−658483.	−0.0798937
$585$	−190766.	−0.0230469
$586$	−2.21017e6	−0.265878
$587$	1.44454e7	1.73035	0.865175	−	0.501471i	$-0.167207\pi$
$587$	1.44454e7	1.73035	0.865175	+	0.501471i	$0.167207\pi$
$588$	6.60721e6	0.788089
$589$	2.16042e6	0.256596
$590$	−254836.	−0.0301391
$591$	−5.92869e6	−0.698216
$592$	−444213.	−0.0520939
$593$	−881514.	−0.102942	−0.0514710	−	0.998674i	$-0.516391\pi$
$593$	−881514.	−0.102942	−0.0514710	+	0.998674i	$0.516391\pi$
$594$	1.78911e6	0.208051
$595$	4.03450e6	0.467194
$596$	−7.73990e6	−0.892523
$597$	4.19607e6	0.481845
$598$	733976.	0.0839323
$599$	132857.	0.0151292	0.00756462	−	0.999971i	$-0.497592\pi$
$599$	132857.	0.0151292	0.00756462	+	0.999971i	$0.497592\pi$
$600$	3.95217e6	0.448185
$601$	−3.84466e6	−0.434181	−0.217091	−	0.976151i	$-0.569657\pi$
$601$	−3.84466e6	−0.434181	−0.217091	+	0.976151i	$0.569657\pi$
$602$	1.10693e6	0.124488
$603$	−5.64887e6	−0.632657
$604$	7.87615e6	0.878460
$605$	−9.79747e6	−1.08824
$606$	−3.99499e6	−0.441910
$607$	8.88565e6	0.978853	0.489426	−	0.872045i	$-0.337206\pi$
$607$	8.88565e6	0.978853	0.489426	+	0.872045i	$0.337206\pi$
$608$	−2.46119e6	−0.270014
$609$	−1.11631e7	−1.21967
$610$	2.07352e6	0.225623
$611$	1.53465e6	0.166305
$612$	1.22842e6	0.132577
$613$	−5.80320e6	−0.623759	−0.311879	−	0.950122i	$-0.600958\pi$
$613$	−5.80320e6	−0.623759	−0.311879	+	0.950122i	$0.600958\pi$
$614$	2.79968e6	0.299700
$615$	3.68565e6	0.392940
$616$	2.96081e7	3.14383
$617$	2.15641e6	0.228044	0.114022	−	0.993478i	$-0.463627\pi$
$617$	2.15641e6	0.228044	0.114022	+	0.993478i	$0.463627\pi$
$618$	314287.	0.0331021
$619$	−6.34791e6	−0.665893	−0.332946	−	0.942946i	$-0.608043\pi$
$619$	−6.34791e6	−0.665893	−0.332946	+	0.942946i	$0.608043\pi$
$620$	2.73520e6	0.285766
$621$	1.71262e6	0.178210
$622$	−434174.	−0.0449974
$623$	−1.18443e7	−1.22261
$624$	−86497.4	−0.00889286
$625$	4.37267e6	0.447762
$626$	9.43562e6	0.962354
$627$	−2.78351e6	−0.282764
$628$	−6.59806e6	−0.667602
$629$	3.14346e6	0.316797
$630$	1.50123e6	0.150693
$631$	791174.	0.0791040	0.0395520	−	0.999218i	$-0.487407\pi$
$631$	791174.	0.0791040	0.0395520	+	0.999218i	$0.487407\pi$
$632$	−949605.	−0.0945693
$633$	−3.97606e6	−0.394407
$634$	8.96593e6	0.885875
$635$	−862533.	−0.0848870
$636$	−1.70906e6	−0.167539
$637$	3.29224e6	0.321472
$638$	−1.34146e7	−1.30475
$639$	629738.	0.0610110
$640$	−3.38064e6	−0.326249
$641$	4.57771e6	0.440051	0.220026	−	0.975494i	$-0.429386\pi$
$641$	4.57771e6	0.440051	0.220026	+	0.975494i	$0.429386\pi$
$642$	3.42515e6	0.327976
$643$	6.61242e6	0.630714	0.315357	−	0.948973i	$-0.397876\pi$
$643$	6.61242e6	0.630714	0.315357	+	0.948973i	$0.397876\pi$
$644$	1.12832e7	1.07205
$645$	−330946.	−0.0313226
$646$	978358.	0.0922394
$647$	−8.53209e6	−0.801299	−0.400649	−	0.916231i	$-0.631215\pi$
$647$	−8.53209e6	−0.801299	−0.400649	+	0.916231i	$0.631215\pi$
$648$	1.14817e6	0.107416
$649$	−2.32634e6	−0.216801
$650$	783979.	0.0727815
$651$	−1.06366e7	−0.983674
$652$	8.45861e6	0.779255
$653$	1.52937e6	0.140356	0.0701779	−	0.997534i	$-0.477643\pi$
$653$	1.52937e6	0.140356	0.0701779	+	0.997534i	$0.477643\pi$
$654$	6.36417e6	0.581832
$655$	−4.56200e6	−0.415482
$656$	1.67115e6	0.151619
$657$	−304784.	−0.0275473
$658$	−1.20768e7	−1.08740
$659$	−6.03034e6	−0.540914	−0.270457	−	0.962732i	$-0.587175\pi$
$659$	−6.03034e6	−0.540914	−0.270457	+	0.962732i	$0.587175\pi$
$660$	−3.52407e6	−0.314908
$661$	−1.32680e7	−1.18114	−0.590570	−	0.806987i	$-0.701097\pi$
$661$	−1.32680e7	−1.18114	−0.590570	+	0.806987i	$0.701097\pi$
$662$	−1.31413e6	−0.116545
$663$	612096.	0.0540799
$664$	−1.27025e7	−1.11807
$665$	−2.33562e6	−0.204808
$666$	1.16967e6	0.102183
$667$	−1.28411e7	−1.11760
$668$	−1.05079e7	−0.911114
$669$	7.32552e6	0.632810
$670$	−5.69592e6	−0.490204
$671$	1.89287e7	1.62299
$672$	1.21175e7	1.03511
$673$	−4.28027e6	−0.364279	−0.182139	−	0.983273i	$-0.558302\pi$
$673$	−4.28027e6	−0.364279	−0.182139	+	0.983273i	$0.558302\pi$
$674$	−3.26642e6	−0.276964
$675$	1.82929e6	0.154534
$676$	7.66783e6	0.645366
$677$	3.77876e6	0.316868	0.158434	−	0.987370i	$-0.449356\pi$
$677$	3.77876e6	0.316868	0.158434	+	0.987370i	$0.449356\pi$
$678$	5.43209e6	0.453830
$679$	−3.05419e7	−2.54227
$680$	3.11138e6	0.258036
$681$	−2.50342e6	−0.206855
$682$	−1.27820e7	−1.05229
$683$	2.89853e6	0.237753	0.118876	−	0.992909i	$-0.462071\pi$
$683$	2.89853e6	0.237753	0.118876	+	0.992909i	$0.462071\pi$
$684$	−711146.	−0.0581191
$685$	−6.08267e6	−0.495299
$686$	−1.33543e7	−1.08346
$687$	4.16209e6	0.336449
$688$	−150057.	−0.0120861
$689$	−851592.	−0.0683413
$690$	1.72689e6	0.138083
$691$	2.30794e7	1.83878	0.919389	−	0.393351i	$-0.128684\pi$
$691$	2.30794e7	1.83878	0.919389	+	0.393351i	$0.128684\pi$
$692$	−221363.	−0.0175727
$693$	1.37044e7	1.08399
$694$	8.01253e6	0.631496
$695$	1.05398e6	0.0827692
$696$	−8.60891e6	−0.673636
$697$	−1.18258e7	−0.922038
$698$	−2.37061e6	−0.184171
$699$	−3.12873e6	−0.242200
$700$	1.20518e7	0.929625
$701$	3.02077e6	0.232179	0.116090	−	0.993239i	$-0.462964\pi$
$701$	3.02077e6	0.232179	0.116090	+	0.993239i	$0.462964\pi$
$702$	227759.	0.0174435
$703$	−1.81978e6	−0.138877
$704$	1.21456e7	0.923607
$705$	3.61070e6	0.273601
$706$	−6.00263e6	−0.453242
$707$	−3.06011e7	−2.30244
$708$	−594346.	−0.0445611
$709$	6.18653e6	0.462202	0.231101	−	0.972930i	$-0.425767\pi$
$709$	6.18653e6	0.462202	0.231101	+	0.972930i	$0.425767\pi$
$710$	634984.	0.0472734
$711$	−439532.	−0.0326074
$712$	−9.13426e6	−0.675263
$713$	−1.22355e7	−0.901359
$714$	−4.81685e6	−0.353604
$715$	−1.75597e6	−0.128455
$716$	−8.33864e6	−0.607872
$717$	1.19285e7	0.866539
$718$	7.63609e6	0.552790
$719$	1.63237e7	1.17760	0.588799	−	0.808279i	$-0.299601\pi$
$719$	1.63237e7	1.17760	0.588799	+	0.808279i	$0.299601\pi$
$720$	−203509.	−0.0146303
$721$	2.40740e6	0.172468
$722$	7.58399e6	0.541445
$723$	−1.00875e7	−0.717694
$724$	−508396.	−0.0360459
$725$	−1.37159e7	−0.969124
$726$	1.16974e7	0.823657
$727$	−719985.	−0.0505228	−0.0252614	−	0.999681i	$-0.508042\pi$
$727$	−719985.	−0.0505228	−0.0252614	+	0.999681i	$0.508042\pi$
$728$	3.76920e6	0.263585
$729$	531441.	0.0370370
$730$	−307323.	−0.0213446
$731$	1.06188e6	0.0734988
$732$	4.83601e6	0.333587
$733$	−2.07809e7	−1.42858	−0.714290	−	0.699850i	$-0.753250\pi$
$733$	−2.07809e7	−1.42858	−0.714290	+	0.699850i	$0.753250\pi$
$734$	−1.49764e7	−1.02605
$735$	7.74592e6	0.528877
$736$	1.39389e7	0.948493
$737$	−5.19968e7	−3.52621
$738$	−4.40035e6	−0.297404
$739$	−1.25025e7	−0.842145	−0.421073	−	0.907027i	$-0.638346\pi$
$739$	−1.25025e7	−0.842145	−0.421073	+	0.907027i	$0.638346\pi$
$740$	−2.30394e6	−0.154665
$741$	−354350.	−0.0237075
$742$	6.70155e6	0.446854
$743$	−5.49382e6	−0.365092	−0.182546	−	0.983197i	$-0.558434\pi$
$743$	−5.49382e6	−0.365092	−0.182546	+	0.983197i	$0.558434\pi$
$744$	−8.20290e6	−0.543294
$745$	−9.07381e6	−0.598962
$746$	−1.28010e7	−0.842162
$747$	−5.87947e6	−0.385511
$748$	1.13074e7	0.738937
$749$	2.62362e7	1.70882
$750$	4.14163e6	0.268855
$751$	−8.98674e6	−0.581437	−0.290718	−	0.956809i	$-0.593894\pi$
$751$	−8.98674e6	−0.581437	−0.290718	+	0.956809i	$0.593894\pi$
$752$	1.63716e6	0.105572
$753$	4.71829e6	0.303247
$754$	−1.70772e6	−0.109393
$755$	9.23355e6	0.589524
$756$	3.50126e6	0.222802
$757$	2.83059e7	1.79530	0.897652	−	0.440705i	$-0.145271\pi$
$757$	2.83059e7	1.79530	0.897652	+	0.440705i	$0.145271\pi$
$758$	−1.41227e7	−0.892783
$759$	1.57644e7	0.993280
$760$	−1.80122e6	−0.113118
$761$	2.04391e7	1.27938	0.639691	−	0.768632i	$-0.279062\pi$
$761$	2.04391e7	1.27938	0.639691	+	0.768632i	$0.279062\pi$
$762$	1.02979e6	0.0642484
$763$	4.87488e7	3.03146
$764$	−1.83849e7	−1.13954
$765$	1.44013e6	0.0889708
$766$	4.80937e6	0.296153
$767$	−296150.	−0.0181771
$768$	8.72769e6	0.533945
$769$	−9.14083e6	−0.557403	−0.278702	−	0.960378i	$-0.589904\pi$
$769$	−9.14083e6	−0.557403	−0.278702	+	0.960378i	$0.589904\pi$
$770$	1.38185e7	0.839913
$771$	−781829.	−0.0473670
$772$	1.61392e7	0.974626
$773$	−835007.	−0.0502622	−0.0251311	−	0.999684i	$-0.508000\pi$
$773$	−835007.	−0.0502622	−0.0251311	+	0.999684i	$0.508000\pi$
$774$	395121.	0.0237071
$775$	−1.30690e7	−0.781609
$776$	−2.35537e7	−1.40412
$777$	8.95954e6	0.532394
$778$	6.48770e6	0.384274
$779$	6.84610e6	0.404203
$780$	−448625.	−0.0264026
$781$	5.79663e6	0.340054
$782$	−5.54091e6	−0.324014
$783$	−3.98470e6	−0.232269
$784$	3.51216e6	0.204072
$785$	−7.73519e6	−0.448020
$786$	5.44664e6	0.314465
$787$	−2.77481e7	−1.59697	−0.798485	−	0.602015i	$-0.794365\pi$
$787$	−2.77481e7	−1.59697	−0.798485	+	0.602015i	$0.794365\pi$
$788$	−1.39425e7	−0.799879
$789$	−8.61342e6	−0.492587
$790$	−443193.	−0.0252654
$791$	4.16091e7	2.36454
$792$	1.05687e7	0.598700
$793$	2.40968e6	0.136075
$794$	1.40336e7	0.789982
$795$	−2.00361e6	−0.112433
$796$	9.86789e6	0.552003
$797$	1.82898e7	1.01991	0.509956	−	0.860200i	$-0.329662\pi$
$797$	1.82898e7	1.01991	0.509956	+	0.860200i	$0.329662\pi$
$798$	2.78853e6	0.155013
$799$	−1.15853e7	−0.642009
$800$	1.48885e7	0.822481
$801$	−4.22786e6	−0.232830
$802$	−1.39429e7	−0.765450
$803$	−2.80548e6	−0.153539
$804$	−1.32844e7	−0.724774
$805$	1.32277e7	0.719441
$806$	−1.62718e6	−0.0882264
$807$	−3.16670e6	−0.171168
$808$	−2.35994e7	−1.27166
$809$	−2.11881e7	−1.13820	−0.569102	−	0.822267i	$-0.692709\pi$
$809$	−2.11881e7	−1.13820	−0.569102	+	0.822267i	$0.692709\pi$
$810$	535868.	0.0286976
$811$	3.34252e7	1.78452	0.892262	−	0.451518i	$-0.149117\pi$
$811$	3.34252e7	1.78452	0.892262	+	0.451518i	$0.149117\pi$
$812$	−2.62522e7	−1.39725
$813$	−1.63051e7	−0.865160
$814$	1.07666e7	0.569532
$815$	9.91638e6	0.522949
$816$	652983.	0.0343302
$817$	−614733.	−0.0322204
$818$	−1.50526e7	−0.786555
$819$	1.74461e6	0.0908841
$820$	8.66751e6	0.450153
$821$	−1.21603e7	−0.629630	−0.314815	−	0.949153i	$-0.601942\pi$
$821$	−1.21603e7	−0.629630	−0.314815	+	0.949153i	$0.601942\pi$
$822$	7.26220e6	0.374877
$823$	3.57215e6	0.183836	0.0919179	−	0.995767i	$-0.470700\pi$
$823$	3.57215e6	0.183836	0.0919179	+	0.995767i	$0.470700\pi$
$824$	1.85657e6	0.0952563
$825$	1.68383e7	0.861318
$826$	2.33054e6	0.118852
$827$	−2.50284e7	−1.27253	−0.636266	−	0.771469i	$-0.719522\pi$
$827$	−2.50284e7	−1.27253	−0.636266	+	0.771469i	$0.719522\pi$
$828$	4.02756e6	0.204158
$829$	3.36102e7	1.69858	0.849288	−	0.527929i	$-0.177031\pi$
$829$	3.36102e7	1.69858	0.849288	+	0.527929i	$0.177031\pi$
$830$	−5.92844e6	−0.298707
$831$	−1.12283e7	−0.564043
$832$	1.54617e6	0.0774372
$833$	−2.48536e7	−1.24102
$834$	−1.25836e6	−0.0626455
$835$	−1.23188e7	−0.611438
$836$	−6.54597e6	−0.323935
$837$	−3.79678e6	−0.187328
$838$	−1.57905e7	−0.776758
$839$	1.98591e7	0.973993	0.486996	−	0.873404i	$-0.338092\pi$
$839$	1.98591e7	0.973993	0.486996	+	0.873404i	$0.338092\pi$
$840$	8.86811e6	0.433644
$841$	9.36585e6	0.456623
$842$	−6.98045e6	−0.339315
$843$	−1.90803e7	−0.924733
$844$	−9.35049e6	−0.451833
$845$	8.98933e6	0.433097
$846$	−4.31087e6	−0.207080
$847$	8.96003e7	4.29142
$848$	−908477.	−0.0433835
$849$	−2.18635e6	−0.104100
$850$	−5.91838e6	−0.280967
$851$	1.03063e7	0.487842
$852$	1.48095e6	0.0698944
$853$	5.17882e6	0.243702	0.121851	−	0.992548i	$-0.461117\pi$
$853$	5.17882e6	0.243702	0.121851	+	0.992548i	$0.461117\pi$
$854$	−1.89629e7	−0.889732
$855$	−833707.	−0.0390030
$856$	2.02332e7	0.943802
$857$	1.25514e7	0.583768	0.291884	−	0.956454i	$-0.405718\pi$
$857$	1.25514e7	0.583768	0.291884	+	0.956454i	$0.405718\pi$
$858$	2.09648e6	0.0972238
$859$	−233230.	−0.0107845	−0.00539227	−	0.999985i	$-0.501716\pi$
$859$	−233230.	−0.0107845	−0.00539227	+	0.999985i	$0.501716\pi$
$860$	−778283.	−0.0358832
$861$	−3.37061e7	−1.54953
$862$	−4.56589e6	−0.209294
$863$	−3.20351e7	−1.46420	−0.732098	−	0.681199i	$-0.761459\pi$
$863$	−3.20351e7	−1.46420	−0.732098	+	0.681199i	$0.761459\pi$
$864$	4.32537e6	0.197124
$865$	−259513.	−0.0117928
$866$	8.75620e6	0.396754
$867$	8.15790e6	0.368579
$868$	−2.50141e7	−1.12690
$869$	−4.04581e6	−0.181742
$870$	−4.01789e6	−0.179970
$871$	−6.61935e6	−0.295645
$872$	3.75948e7	1.67431
$873$	−1.09020e7	−0.484140
$874$	3.20770e6	0.142041
$875$	3.17244e7	1.40079
$876$	−716760.	−0.0315583
$877$	3.12594e7	1.37241	0.686203	−	0.727410i	$-0.259276\pi$
$877$	3.12594e7	1.37241	0.686203	+	0.727410i	$0.259276\pi$
$878$	6.40514e6	0.280409
$879$	−6.04309e6	−0.263807
$880$	−1.87327e6	−0.0815442
$881$	197716.	0.00858228	0.00429114	−	0.999991i	$-0.498634\pi$
$881$	197716.	0.00858228	0.00429114	+	0.999991i	$0.498634\pi$
$882$	−9.24798e6	−0.400290
$883$	−1.28542e7	−0.554807	−0.277404	−	0.960753i	$-0.589474\pi$
$883$	−1.28542e7	−0.554807	−0.277404	+	0.960753i	$0.589474\pi$
$884$	1.43946e6	0.0619540
$885$	−696777.	−0.0299044
$886$	−1.77328e7	−0.758915
$887$	2.02784e7	0.865415	0.432708	−	0.901534i	$-0.357558\pi$
$887$	2.02784e7	0.865415	0.432708	+	0.901534i	$0.357558\pi$
$888$	6.90954e6	0.294047
$889$	7.88808e6	0.334747
$890$	−4.26308e6	−0.180405
$891$	4.89182e6	0.206431
$892$	1.72274e7	0.724949
$893$	6.70689e6	0.281444
$894$	1.08334e7	0.453335
$895$	−9.77574e6	−0.407936
$896$	3.09168e7	1.28654
$897$	2.00685e6	0.0832787
$898$	1.71112e7	0.708093
$899$	2.84680e7	1.17478
$900$	4.30194e6	0.177035
$901$	6.42881e6	0.263826
$902$	−4.05044e7	−1.65762
$903$	3.02658e6	0.123519
$904$	3.20887e7	1.30596
$905$	−596015.	−0.0241900
$906$	−1.10241e7	−0.446192
$907$	3.26861e7	1.31930	0.659651	−	0.751572i	$-0.270704\pi$
$907$	3.26861e7	1.31930	0.659651	+	0.751572i	$0.270704\pi$
$908$	−5.88727e6	−0.236973
$909$	−1.09232e7	−0.438469
$910$	1.75914e6	0.0704201
$911$	2.29243e7	0.915168	0.457584	−	0.889166i	$-0.348715\pi$
$911$	2.29243e7	0.915168	0.457584	+	0.889166i	$0.348715\pi$
$912$	−378020.	−0.0150497
$913$	−5.41194e7	−2.14870
$914$	−1.85518e7	−0.734549
$915$	5.66946e6	0.223866
$916$	9.78797e6	0.385437
$917$	4.17206e7	1.63843
$918$	−1.71939e6	−0.0673392
$919$	2.89979e7	1.13260	0.566302	−	0.824198i	$-0.308374\pi$
$919$	2.89979e7	1.13260	0.566302	+	0.824198i	$0.308374\pi$
$920$	1.02011e7	0.397356
$921$	7.65493e6	0.297366
$922$	2.11500e7	0.819376
$923$	737928.	0.0285108
$924$	3.22285e7	1.24182
$925$	1.10084e7	0.423030
$926$	−3.56189e6	−0.136506
$927$	859329.	0.0328443
$928$	−3.24313e7	−1.23621
$929$	9.87538e6	0.375418	0.187709	−	0.982225i	$-0.439894\pi$
$929$	9.87538e6	0.375418	0.187709	+	0.982225i	$0.439894\pi$
$930$	−3.82840e6	−0.145148
$931$	1.43881e7	0.544037
$932$	−7.35781e6	−0.277465
$933$	−1.18713e6	−0.0446470
$934$	−2.13726e7	−0.801659
$935$	1.32561e7	0.495892
$936$	1.34543e6	0.0501963
$937$	2.77027e7	1.03080	0.515398	−	0.856951i	$-0.327644\pi$
$937$	2.77027e7	1.03080	0.515398	+	0.856951i	$0.327644\pi$
$938$	5.20906e7	1.93309
$939$	2.57990e7	0.954860
$940$	8.49126e6	0.313439
$941$	−453527.	−0.0166966	−0.00834831	−	0.999965i	$-0.502657\pi$
$941$	−453527.	−0.0166966	−0.00834831	+	0.999965i	$0.502657\pi$
$942$	9.23517e6	0.339092
$943$	−3.87728e7	−1.41987
$944$	−315933.	−0.0115389
$945$	4.10468e6	0.149520
$946$	3.63702e6	0.132135
$947$	−3.28736e7	−1.19117	−0.595584	−	0.803293i	$-0.703079\pi$
$947$	−3.28736e7	−1.19117	−0.595584	+	0.803293i	$0.703079\pi$
$948$	−1.03365e6	−0.0373552
$949$	−357147.	−0.0128730
$950$	3.42622e6	0.123170
$951$	2.45148e7	0.878976
$952$	−2.84543e7	−1.01755
$953$	1.72053e7	0.613664	0.306832	−	0.951764i	$-0.400731\pi$
$953$	1.72053e7	0.613664	0.306832	+	0.951764i	$0.400731\pi$
$954$	2.39214e6	0.0850973
$955$	−2.15534e7	−0.764730
$956$	2.80522e7	0.992710
$957$	−3.66785e7	−1.29459
$958$	−2.57678e6	−0.0907118
$959$	5.56275e7	1.95318
$960$	3.63780e6	0.127398
$961$	−1.50378e6	−0.0525260
$962$	1.37062e6	0.0477508
$963$	9.36511e6	0.325422
$964$	−2.37228e7	−0.822193
$965$	1.89206e7	0.654060
$966$	−1.57928e7	−0.544523
$967$	−4.53431e6	−0.155935	−0.0779677	−	0.996956i	$-0.524843\pi$
$967$	−4.53431e6	−0.155935	−0.0779677	+	0.996956i	$0.524843\pi$
$968$	6.90992e7	2.37020
$969$	2.67504e6	0.0915211
$970$	−1.09928e7	−0.375128
$971$	−4.77221e7	−1.62432	−0.812161	−	0.583434i	$-0.801709\pi$
$971$	−4.77221e7	−1.62432	−0.812161	+	0.583434i	$0.801709\pi$
$972$	1.24979e6	0.0424297
$973$	−9.63888e6	−0.326396
$974$	3.10045e7	1.04720
$975$	2.14357e6	0.0722147
$976$	2.57065e6	0.0863809
$977$	−4.80851e7	−1.61166	−0.805832	−	0.592145i	$-0.798281\pi$
$977$	−4.80851e7	−1.61166	−0.805832	+	0.592145i	$0.798281\pi$
$978$	−1.18393e7	−0.395804
$979$	−3.89167e7	−1.29771
$980$	1.82160e7	0.605883
$981$	1.74010e7	0.577302
$982$	2.91125e7	0.963386
$983$	−2.04900e7	−0.676329	−0.338164	−	0.941087i	$-0.609806\pi$
$983$	−2.04900e7	−0.676329	−0.338164	+	0.941087i	$0.609806\pi$
$984$	−2.59940e7	−0.855825
$985$	−1.63453e7	−0.536789
$986$	1.28919e7	0.422302
$987$	−3.30207e7	−1.07893
$988$	−833322.	−0.0271594
$989$	3.48153e6	0.113182
$990$	4.93256e6	0.159950
$991$	−3.59896e7	−1.16411	−0.582053	−	0.813151i	$-0.697750\pi$
$991$	−3.59896e7	−1.16411	−0.582053	+	0.813151i	$0.697750\pi$
$992$	−3.09018e7	−0.997020
$993$	−3.59311e6	−0.115637
$994$	−5.80708e6	−0.186420
$995$	1.15685e7	0.370443
$996$	−1.38267e7	−0.441642
$997$	−2.08478e7	−0.664236	−0.332118	−	0.943238i	$-0.607763\pi$
$997$	−2.08478e7	−0.664236	−0.332118	+	0.943238i	$0.607763\pi$
$998$	2.35020e7	0.746928
$999$	3.19814e6	0.101387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.8	✓	20
3.2	odd	2		927.6.a.c.1.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.8	✓	20	1.1	even	1	trivial
927.6.a.c.1.13		20	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)

\(f(q)\)	\(=\)	\(q-3.29162 q^{2} -9.00000 q^{3} -21.1653 q^{4} -24.8129 q^{5} +29.6246 q^{6} +226.920 q^{7} +175.000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-3.29162 q^{2} -9.00000 q^{3} -21.1653 q^{4} -24.8129 q^{5} +29.6246 q^{6} +226.920 q^{7} +175.000 q^{8} +81.0000 q^{9} +81.6747 q^{10} +745.590 q^{11} +190.487 q^{12} +94.9159 q^{13} -746.935 q^{14} +223.316 q^{15} +101.256 q^{16} -716.536 q^{17} -266.621 q^{18} +414.811 q^{19} +525.172 q^{20} -2042.28 q^{21} -2454.20 q^{22} -2349.27 q^{23} -1575.00 q^{24} -2509.32 q^{25} -312.427 q^{26} -729.000 q^{27} -4802.83 q^{28} +5465.99 q^{29} -735.072 q^{30} +5208.20 q^{31} -5933.29 q^{32} -6710.31 q^{33} +2358.56 q^{34} -5630.56 q^{35} -1714.39 q^{36} -4387.02 q^{37} -1365.40 q^{38} -854.243 q^{39} -4342.25 q^{40} +16504.1 q^{41} +6722.41 q^{42} -1481.96 q^{43} -15780.6 q^{44} -2009.85 q^{45} +7732.91 q^{46} +16168.5 q^{47} -911.305 q^{48} +34685.8 q^{49} +8259.72 q^{50} +6448.82 q^{51} -2008.92 q^{52} -8972.07 q^{53} +2399.59 q^{54} -18500.3 q^{55} +39711.0 q^{56} -3733.30 q^{57} -17991.9 q^{58} -3120.13 q^{59} -4726.55 q^{60} +25387.6 q^{61} -17143.4 q^{62} +18380.5 q^{63} +16289.9 q^{64} -2355.14 q^{65} +22087.8 q^{66} -69739.1 q^{67} +15165.7 q^{68} +21143.5 q^{69} +18533.6 q^{70} +7774.55 q^{71} +14175.0 q^{72} -3762.77 q^{73} +14440.4 q^{74} +22583.9 q^{75} -8779.58 q^{76} +169190. q^{77} +2811.84 q^{78} -5426.32 q^{79} -2512.46 q^{80} +6561.00 q^{81} -54325.3 q^{82} -72586.0 q^{83} +43225.4 q^{84} +17779.3 q^{85} +4878.04 q^{86} -49193.9 q^{87} +130478. q^{88} -52195.8 q^{89} +6615.65 q^{90} +21538.4 q^{91} +49723.0 q^{92} -46873.8 q^{93} -53220.6 q^{94} -10292.7 q^{95} +53399.6 q^{96} -134593. q^{97} -114173. q^{98} +60392.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * q^99

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