LMFDB - Embedded newform 309.6.a.b.1.3

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			1.3
Root			$-8.44075$ 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)

$f(q)$	$=$	$q-8.44075 q^{2} -9.00000 q^{3} +39.2463 q^{4} -67.3508 q^{5} +75.9668 q^{6} -63.5218 q^{7} -61.1646 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-8.44075 q^{2} -9.00000 q^{3} +39.2463 q^{4} -67.3508 q^{5} +75.9668 q^{6} -63.5218 q^{7} -61.1646 q^{8} +81.0000 q^{9} +568.492 q^{10} +619.488 q^{11} -353.217 q^{12} -508.947 q^{13} +536.172 q^{14} +606.158 q^{15} -739.608 q^{16} -1273.41 q^{17} -683.701 q^{18} +1699.70 q^{19} -2643.27 q^{20} +571.696 q^{21} -5228.94 q^{22} -1461.97 q^{23} +550.481 q^{24} +1411.14 q^{25} +4295.90 q^{26} -729.000 q^{27} -2493.00 q^{28} -558.544 q^{29} -5116.43 q^{30} -4373.05 q^{31} +8200.11 q^{32} -5575.39 q^{33} +10748.6 q^{34} +4278.25 q^{35} +3178.95 q^{36} -4716.88 q^{37} -14346.7 q^{38} +4580.52 q^{39} +4119.49 q^{40} +4085.85 q^{41} -4825.55 q^{42} -22734.5 q^{43} +24312.6 q^{44} -5455.42 q^{45} +12340.1 q^{46} -23974.1 q^{47} +6656.47 q^{48} -12772.0 q^{49} -11911.1 q^{50} +11460.7 q^{51} -19974.3 q^{52} +22798.1 q^{53} +6153.31 q^{54} -41723.0 q^{55} +3885.28 q^{56} -15297.3 q^{57} +4714.53 q^{58} -2104.72 q^{59} +23789.5 q^{60} -47060.1 q^{61} +36911.9 q^{62} -5145.26 q^{63} -45547.7 q^{64} +34278.0 q^{65} +47060.5 q^{66} -50737.1 q^{67} -49976.7 q^{68} +13157.7 q^{69} -36111.6 q^{70} +28480.8 q^{71} -4954.33 q^{72} +47181.9 q^{73} +39814.0 q^{74} -12700.2 q^{75} +66707.0 q^{76} -39351.0 q^{77} -38663.1 q^{78} +4091.33 q^{79} +49813.2 q^{80} +6561.00 q^{81} -34487.6 q^{82} +31403.4 q^{83} +22437.0 q^{84} +85765.4 q^{85} +191896. q^{86} +5026.89 q^{87} -37890.7 q^{88} +125068. q^{89} +46047.9 q^{90} +32329.2 q^{91} -57376.8 q^{92} +39357.5 q^{93} +202359. q^{94} -114476. q^{95} -73801.0 q^{96} +49947.0 q^{97} +107805. q^{98} +50178.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.44075	−1.49213	−0.746064	−	0.665874i	$-0.768059\pi$
$2$	−8.44075	−1.49213	−0.746064	+	0.665874i	$0.768059\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	39.2463	1.22645
$5$	−67.3508	−1.20481	−0.602404	−	0.798191i	$-0.705790\pi$
$5$	−67.3508	−1.20481	−0.602404	+	0.798191i	$0.705790\pi$
$6$	75.9668	0.861481
$7$	−63.5218	−0.489979	−0.244990	−	0.969526i	$-0.578785\pi$
$7$	−63.5218	−0.489979	−0.244990	+	0.969526i	$0.578785\pi$
$8$	−61.1646	−0.337890
$9$	81.0000	0.333333
$10$	568.492	1.79773
$11$	619.488	1.54366	0.771829	−	0.635830i	$-0.219342\pi$
$11$	619.488	1.54366	0.771829	+	0.635830i	$0.219342\pi$
$12$	−353.217	−0.708090
$13$	−508.947	−0.835246	−0.417623	−	0.908620i	$-0.637137\pi$
$13$	−508.947	−0.835246	−0.417623	+	0.908620i	$0.637137\pi$
$14$	536.172	0.731112
$15$	606.158	0.695597
$16$	−739.608	−0.722273
$17$	−1273.41	−1.06868	−0.534339	−	0.845271i	$-0.679439\pi$
$17$	−1273.41	−1.06868	−0.534339	+	0.845271i	$0.679439\pi$
$18$	−683.701	−0.497376
$19$	1699.70	1.08016	0.540080	−	0.841614i	$-0.318394\pi$
$19$	1699.70	1.08016	0.540080	+	0.841614i	$0.318394\pi$
$20$	−2643.27	−1.47764
$21$	571.696	0.282890
$22$	−5228.94	−2.30334
$23$	−1461.97	−0.576259	−0.288130	−	0.957591i	$-0.593033\pi$
$23$	−1461.97	−0.576259	−0.288130	+	0.957591i	$0.593033\pi$
$24$	550.481	0.195081
$25$	1411.14	0.451564
$26$	4295.90	1.24629
$27$	−729.000	−0.192450
$28$	−2493.00	−0.600934
$29$	−558.544	−0.123328	−0.0616641	−	0.998097i	$-0.519641\pi$
$29$	−558.544	−0.123328	−0.0616641	+	0.998097i	$0.519641\pi$
$30$	−5116.43	−1.03792
$31$	−4373.05	−0.817298	−0.408649	−	0.912692i	$-0.634000\pi$
$31$	−4373.05	−0.817298	−0.408649	+	0.912692i	$0.634000\pi$
$32$	8200.11	1.41561
$33$	−5575.39	−0.891231
$34$	10748.6	1.59460
$35$	4278.25	0.590331
$36$	3178.95	0.408816
$37$	−4716.88	−0.566436	−0.283218	−	0.959056i	$-0.591402\pi$
$37$	−4716.88	−0.566436	−0.283218	+	0.959056i	$0.591402\pi$
$38$	−14346.7	−1.61174
$39$	4580.52	0.482229
$40$	4119.49	0.407092
$41$	4085.85	0.379597	0.189798	−	0.981823i	$-0.439217\pi$
$41$	4085.85	0.379597	0.189798	+	0.981823i	$0.439217\pi$
$42$	−4825.55	−0.422108
$43$	−22734.5	−1.87506	−0.937528	−	0.347909i	$-0.886892\pi$
$43$	−22734.5	−1.87506	−0.937528	+	0.347909i	$0.886892\pi$
$44$	24312.6	1.89322
$45$	−5455.42	−0.401603
$46$	12340.1	0.859853
$47$	−23974.1	−1.58306	−0.791530	−	0.611130i	$-0.790715\pi$
$47$	−23974.1	−1.58306	−0.791530	+	0.611130i	$0.790715\pi$
$48$	6656.47	0.417005
$49$	−12772.0	−0.759920
$50$	−11911.1	−0.673791
$51$	11460.7	0.617001
$52$	−19974.3	−1.02439
$53$	22798.1	1.11483	0.557415	−	0.830234i	$-0.311793\pi$
$53$	22798.1	1.11483	0.557415	+	0.830234i	$0.311793\pi$
$54$	6153.31	0.287160
$55$	−41723.0	−1.85981
$56$	3885.28	0.165559
$57$	−15297.3	−0.623631
$58$	4714.53	0.184021
$59$	−2104.72	−0.0787162	−0.0393581	−	0.999225i	$-0.512531\pi$
$59$	−2104.72	−0.0787162	−0.0393581	+	0.999225i	$0.512531\pi$
$60$	23789.5	0.853113
$61$	−47060.1	−1.61930	−0.809651	−	0.586912i	$-0.800344\pi$
$61$	−47060.1	−1.61930	−0.809651	+	0.586912i	$0.800344\pi$
$62$	36911.9	1.21951
$63$	−5145.26	−0.163326
$64$	−45547.7	−1.39001
$65$	34278.0	1.00631
$66$	47060.5	1.32983
$67$	−50737.1	−1.38082	−0.690412	−	0.723416i	$-0.742571\pi$
$67$	−50737.1	−1.38082	−0.690412	+	0.723416i	$0.742571\pi$
$68$	−49976.7	−1.31068
$69$	13157.7	0.332703
$70$	−36111.6	−0.880850
$71$	28480.8	0.670511	0.335255	−	0.942127i	$-0.391177\pi$
$71$	28480.8	0.670511	0.335255	+	0.942127i	$0.391177\pi$
$72$	−4954.33	−0.112630
$73$	47181.9	1.03626	0.518129	−	0.855302i	$-0.326629\pi$
$73$	47181.9	1.03626	0.518129	+	0.855302i	$0.326629\pi$
$74$	39814.0	0.845195
$75$	−12700.2	−0.260710
$76$	66707.0	1.32476
$77$	−39351.0	−0.756360
$78$	−38663.1	−0.719548
$79$	4091.33	0.0737558	0.0368779	−	0.999320i	$-0.488259\pi$
$79$	4091.33	0.0737558	0.0368779	+	0.999320i	$0.488259\pi$
$80$	49813.2	0.870201
$81$	6561.00	0.111111
$82$	−34487.6	−0.566407
$83$	31403.4	0.500359	0.250179	−	0.968200i	$-0.419510\pi$
$83$	31403.4	0.500359	0.250179	+	0.968200i	$0.419510\pi$
$84$	22437.0	0.346949
$85$	85765.4	1.28755
$86$	191896.	2.79783
$87$	5026.89	0.0712035
$88$	−37890.7	−0.521586
$89$	125068.	1.67368	0.836840	−	0.547447i	$-0.184400\pi$
$89$	125068.	1.67368	0.836840	+	0.547447i	$0.184400\pi$
$90$	46047.9	0.599243
$91$	32329.2	0.409253
$92$	−57376.8	−0.706752
$93$	39357.5	0.471867
$94$	202359.	2.36213
$95$	−114476.	−1.30139
$96$	−73801.0	−0.817305
$97$	49947.0	0.538989	0.269495	−	0.963002i	$-0.413143\pi$
$97$	49947.0	0.538989	0.269495	+	0.963002i	$0.413143\pi$
$98$	107805.	1.13390
$99$	50178.5	0.514553
$100$	55382.0	0.553820
$101$	97309.2	0.949184	0.474592	−	0.880206i	$-0.342596\pi$
$101$	97309.2	0.949184	0.474592	+	0.880206i	$0.342596\pi$
$102$	−96737.0	−0.920645
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	31129.5	0.282221
$105$	−38504.2	−0.340828
$106$	−192433.	−1.66347
$107$	−215683.	−1.82120	−0.910598	−	0.413294i	$-0.864378\pi$
$107$	−215683.	−1.82120	−0.910598	+	0.413294i	$0.864378\pi$
$108$	−28610.6	−0.236030
$109$	−36582.9	−0.294925	−0.147463	−	0.989068i	$-0.547111\pi$
$109$	−36582.9	−0.294925	−0.147463	+	0.989068i	$0.547111\pi$
$110$	352174.	2.77508
$111$	42451.9	0.327032
$112$	46981.2	0.353899
$113$	−139673.	−1.02901	−0.514503	−	0.857489i	$-0.672024\pi$
$113$	−139673.	−1.02901	−0.514503	+	0.857489i	$0.672024\pi$
$114$	129121.	0.930537
$115$	98464.7	0.694282
$116$	−21920.8	−0.151256
$117$	−41224.7	−0.278415
$118$	17765.4	0.117455
$119$	80889.4	0.523629
$120$	−37075.4	−0.235035
$121$	222714.	1.38288
$122$	397222.	2.41621
$123$	−36772.6	−0.219160
$124$	−171626.	−1.00237
$125$	115430.	0.660761
$126$	43429.9	0.243704
$127$	−66121.3	−0.363774	−0.181887	−	0.983319i	$-0.558221\pi$
$127$	−66121.3	−0.363774	−0.181887	+	0.983319i	$0.558221\pi$
$128$	122053.	0.658453
$129$	204611.	1.08256
$130$	−289332.	−1.50155
$131$	96460.9	0.491104	0.245552	−	0.969383i	$-0.421031\pi$
$131$	96460.9	0.491104	0.245552	+	0.969383i	$0.421031\pi$
$132$	−218814.	−1.09305
$133$	−107968.	−0.529256
$134$	428259.	2.06037
$135$	49098.8	0.231866
$136$	77887.7	0.361095
$137$	263519.	1.19953	0.599764	−	0.800177i	$-0.295261\pi$
$137$	263519.	1.19953	0.599764	+	0.800177i	$0.295261\pi$
$138$	−111061.	−0.496436
$139$	−98176.1	−0.430991	−0.215496	−	0.976505i	$-0.569137\pi$
$139$	−98176.1	−0.430991	−0.215496	+	0.976505i	$0.569137\pi$
$140$	167905.	0.724010
$141$	215767.	0.913980
$142$	−240399.	−1.00049
$143$	−315286.	−1.28933
$144$	−59908.2	−0.240758
$145$	37618.4	0.148587
$146$	−398251.	−1.54623
$147$	114948.	0.438740
$148$	−185120.	−0.694704
$149$	−124357.	−0.458886	−0.229443	−	0.973322i	$-0.573691\pi$
$149$	−124357.	−0.458886	−0.229443	+	0.973322i	$0.573691\pi$
$150$	107200.	0.389014
$151$	134798.	0.481108	0.240554	−	0.970636i	$-0.422671\pi$
$151$	134798.	0.481108	0.240554	+	0.970636i	$0.422671\pi$
$152$	−103961.	−0.364975
$153$	−103146.	−0.356226
$154$	332152.	1.12859
$155$	294529.	0.984688
$156$	179769.	0.591429
$157$	579706.	1.87698	0.938488	−	0.345312i	$-0.112227\pi$
$157$	579706.	1.87698	0.938488	+	0.345312i	$0.112227\pi$
$158$	−34533.9	−0.110053
$159$	−205183.	−0.643647
$160$	−552285.	−1.70554
$161$	92866.7	0.282355
$162$	−55379.8	−0.165792
$163$	385881.	1.13759	0.568793	−	0.822481i	$-0.307410\pi$
$163$	385881.	1.13759	0.568793	+	0.822481i	$0.307410\pi$
$164$	160355.	0.465556
$165$	375507.	1.07376
$166$	−265068.	−0.746599
$167$	549222.	1.52390	0.761950	−	0.647636i	$-0.224242\pi$
$167$	549222.	1.52390	0.761950	+	0.647636i	$0.224242\pi$
$168$	−34967.5	−0.0955855
$169$	−112266.	−0.302365
$170$	−723924.	−1.92119
$171$	137676.	0.360053
$172$	−892246.	−2.29966
$173$	−443436.	−1.12646	−0.563229	−	0.826301i	$-0.690441\pi$
$173$	−443436.	−1.12646	−0.563229	+	0.826301i	$0.690441\pi$
$174$	−42430.8	−0.106245
$175$	−89637.9	−0.221257
$176$	−458178.	−1.11494
$177$	18942.5	0.0454468
$178$	−1.05567e6	−2.49735
$179$	−657931.	−1.53478	−0.767392	−	0.641178i	$-0.778446\pi$
$179$	−657931.	−1.53478	−0.767392	+	0.641178i	$0.778446\pi$
$180$	−214105.	−0.492545
$181$	−589037.	−1.33643	−0.668215	−	0.743968i	$-0.732941\pi$
$181$	−589037.	−1.33643	−0.668215	+	0.743968i	$0.732941\pi$
$182$	−272883.	−0.610658
$183$	423540.	0.934904
$184$	89420.6	0.194712
$185$	317686.	0.682447
$186$	−332207.	−0.704087
$187$	−788863.	−1.64967
$188$	−940895.	−1.94154
$189$	46307.4	0.0942965
$190$	966266.	1.94184
$191$	−568595.	−1.12777	−0.563884	−	0.825854i	$-0.690694\pi$
$191$	−568595.	−1.12777	−0.563884	+	0.825854i	$0.690694\pi$
$192$	409929.	0.802520
$193$	321650.	0.621570	0.310785	−	0.950480i	$-0.399408\pi$
$193$	321650.	0.621570	0.310785	+	0.950480i	$0.399408\pi$
$194$	−421590.	−0.804241
$195$	−308502.	−0.580994
$196$	−501254.	−0.932003
$197$	−527177.	−0.967812	−0.483906	−	0.875120i	$-0.660782\pi$
$197$	−527177.	−0.967812	−0.483906	+	0.875120i	$0.660782\pi$
$198$	−423544.	−0.767779
$199$	412047.	0.737588	0.368794	−	0.929511i	$-0.379771\pi$
$199$	412047.	0.737588	0.368794	+	0.929511i	$0.379771\pi$
$200$	−86311.6	−0.152579
$201$	456634.	0.797219
$202$	−821363.	−1.41630
$203$	35479.7	0.0604282
$204$	449791.	0.756720
$205$	−275185.	−0.457341
$206$	−89548.0	−0.147024
$207$	−118419.	−0.192086
$208$	376421.	0.603276
$209$	1.05294e6	1.66740
$210$	325005.	0.508559
$211$	−156457.	−0.241930	−0.120965	−	0.992657i	$-0.538599\pi$
$211$	−156457.	−0.241930	−0.120965	+	0.992657i	$0.538599\pi$
$212$	894741.	1.36728
$213$	−256327.	−0.387120
$214$	1.82053e6	2.71746
$215$	1.53119e6	2.25908
$216$	44589.0	0.0650269
$217$	277784.	0.400459
$218$	308787.	0.440066
$219$	−424637.	−0.598284
$220$	−1.63748e6	−2.28096
$221$	648099.	0.892608
$222$	−358326.	−0.487974
$223$	−238661.	−0.321380	−0.160690	−	0.987005i	$-0.551372\pi$
$223$	−238661.	−0.321380	−0.160690	+	0.987005i	$0.551372\pi$
$224$	−520886.	−0.693621
$225$	114302.	0.150521
$226$	1.17895e6	1.53541
$227$	480857.	0.619372	0.309686	−	0.950839i	$-0.399776\pi$
$227$	480857.	0.619372	0.309686	+	0.950839i	$0.399776\pi$
$228$	−600363.	−0.764851
$229$	−574555.	−0.724007	−0.362003	−	0.932177i	$-0.617907\pi$
$229$	−574555.	−0.724007	−0.362003	+	0.932177i	$0.617907\pi$
$230$	−831116.	−1.03596
$231$	354159.	0.436685
$232$	34163.1	0.0416713
$233$	532496.	0.642579	0.321290	−	0.946981i	$-0.395884\pi$
$233$	532496.	0.642579	0.321290	+	0.946981i	$0.395884\pi$
$234$	347968.	0.415431
$235$	1.61468e6	1.90728
$236$	−82602.5	−0.0965414
$237$	−36821.9	−0.0425829
$238$	−682767.	−0.781323
$239$	807632.	0.914574	0.457287	−	0.889319i	$-0.348821\pi$
$239$	807632.	0.914574	0.457287	+	0.889319i	$0.348821\pi$
$240$	−448319.	−0.502411
$241$	−1.27214e6	−1.41088	−0.705442	−	0.708768i	$-0.749251\pi$
$241$	−1.27214e6	−1.41088	−0.705442	+	0.708768i	$0.749251\pi$
$242$	−1.87987e6	−2.06343
$243$	−59049.0	−0.0641500
$244$	−1.84693e6	−1.98599
$245$	860204.	0.915559
$246$	310389.	0.327015
$247$	−865057.	−0.902199
$248$	267476.	0.276157
$249$	−282631.	−0.288882
$250$	−974317.	−0.985940
$251$	1.31015e6	1.31261	0.656306	−	0.754495i	$-0.272118\pi$
$251$	1.31015e6	1.31261	0.656306	+	0.754495i	$0.272118\pi$
$252$	−201933.	−0.200311
$253$	−905671.	−0.889547
$254$	558114.	0.542798
$255$	−771888.	−0.743368
$256$	427304.	0.407509
$257$	−549272.	−0.518746	−0.259373	−	0.965777i	$-0.583516\pi$
$257$	−549272.	−0.518746	−0.259373	+	0.965777i	$0.583516\pi$
$258$	−1.72707e6	−1.61533
$259$	299625.	0.277542
$260$	1.34529e6	1.23419
$261$	−45242.0	−0.0411094
$262$	−814203.	−0.732790
$263$	393262.	0.350584	0.175292	−	0.984516i	$-0.443913\pi$
$263$	393262.	0.350584	0.175292	+	0.984516i	$0.443913\pi$
$264$	341016.	0.301138
$265$	−1.53547e6	−1.34316
$266$	911331.	0.789718
$267$	−1.12562e6	−0.966300
$268$	−1.99124e6	−1.69351
$269$	795154.	0.669993	0.334997	−	0.942219i	$-0.391265\pi$
$269$	795154.	0.669993	0.334997	+	0.942219i	$0.391265\pi$
$270$	−414431.	−0.345973
$271$	1.72832e6	1.42956	0.714778	−	0.699352i	$-0.246528\pi$
$271$	1.72832e6	1.42956	0.714778	+	0.699352i	$0.246528\pi$
$272$	941825.	0.771877
$273$	−290963.	−0.236282
$274$	−2.22430e6	−1.78985
$275$	874182.	0.697060
$276$	516392.	0.408044
$277$	−1.39355e6	−1.09124	−0.545622	−	0.838031i	$-0.683707\pi$
$277$	−1.39355e6	−1.09124	−0.545622	+	0.838031i	$0.683707\pi$
$278$	828680.	0.643095
$279$	−354217.	−0.272433
$280$	−261677.	−0.199467
$281$	−1.86366e6	−1.40800	−0.703998	−	0.710202i	$-0.748604\pi$
$281$	−1.86366e6	−1.40800	−0.703998	+	0.710202i	$0.748604\pi$
$282$	−1.82123e6	−1.36378
$283$	1.68406e6	1.24995	0.624974	−	0.780646i	$-0.285110\pi$
$283$	1.68406e6	1.24995	0.624974	+	0.780646i	$0.285110\pi$
$284$	1.11777e6	0.822347
$285$	1.03029e6	0.751356
$286$	2.66126e6	1.92385
$287$	−259540.	−0.185994
$288$	664209.	0.471871
$289$	201720.	0.142071
$290$	−317528.	−0.221711
$291$	−449523.	−0.311186
$292$	1.85172e6	1.27092
$293$	−2.63509e6	−1.79319	−0.896595	−	0.442852i	$-0.853967\pi$
$293$	−2.63509e6	−1.79319	−0.896595	+	0.442852i	$0.853967\pi$
$294$	−970247.	−0.654657
$295$	141755.	0.0948380
$296$	288506.	0.191393
$297$	−451607.	−0.297077
$298$	1.04967e6	0.684718
$299$	744064.	0.481318
$300$	−498438.	−0.319748
$301$	1.44414e6	0.918738
$302$	−1.13780e6	−0.717874
$303$	−875782.	−0.548011
$304$	−1.25711e6	−0.780171
$305$	3.16953e6	1.95095
$306$	870633.	0.531535
$307$	1.02137e6	0.618493	0.309247	−	0.950982i	$-0.399923\pi$
$307$	1.02137e6	0.618493	0.309247	+	0.950982i	$0.399923\pi$
$308$	−1.54438e6	−0.927636
$309$	−95481.0	−0.0568880
$310$	−2.48605e6	−1.46928
$311$	−634228.	−0.371830	−0.185915	−	0.982566i	$-0.559525\pi$
$311$	−634228.	−0.371830	−0.185915	+	0.982566i	$0.559525\pi$
$312$	−280166.	−0.162940
$313$	2.10013e6	1.21167	0.605835	−	0.795590i	$-0.292839\pi$
$313$	2.10013e6	1.21167	0.605835	+	0.795590i	$0.292839\pi$
$314$	−4.89316e6	−2.80069
$315$	346538.	0.196777
$316$	160570.	0.0904577
$317$	2.71441e6	1.51715	0.758573	−	0.651589i	$-0.225897\pi$
$317$	2.71441e6	1.51715	0.758573	+	0.651589i	$0.225897\pi$
$318$	1.73190e6	0.960405
$319$	−346011.	−0.190376
$320$	3.06768e6	1.67469
$321$	1.94115e6	1.05147
$322$	−783865.	−0.421310
$323$	−2.16442e6	−1.15434
$324$	257495.	0.136272
$325$	−718194.	−0.377167
$326$	−3.25713e6	−1.69743
$327$	329246.	0.170275
$328$	−249909.	−0.128262
$329$	1.52288e6	0.775666
$330$	−3.16956e6	−1.60219
$331$	779109.	0.390866	0.195433	−	0.980717i	$-0.437389\pi$
$331$	779109.	0.390866	0.195433	+	0.980717i	$0.437389\pi$
$332$	1.23247e6	0.613664
$333$	−382067.	−0.188812
$334$	−4.63585e6	−2.27386
$335$	3.41719e6	1.66363
$336$	−422831.	−0.204324
$337$	−1.71326e6	−0.821769	−0.410884	−	0.911687i	$-0.634780\pi$
$337$	−1.71326e6	−0.821769	−0.410884	+	0.911687i	$0.634780\pi$
$338$	947609.	0.451167
$339$	1.25706e6	0.594097
$340$	3.36598e6	1.57911
$341$	−2.70905e6	−1.26163
$342$	−1.16209e6	−0.537246
$343$	1.87891e6	0.862324
$344$	1.39055e6	0.633562
$345$	−886182.	−0.400844
$346$	3.74293e6	1.68082
$347$	2.52575e6	1.12608	0.563038	−	0.826431i	$-0.309633\pi$
$347$	2.52575e6	1.12608	0.563038	+	0.826431i	$0.309633\pi$
$348$	197287.	0.0873274
$349$	1.00925e6	0.443542	0.221771	−	0.975099i	$-0.428816\pi$
$349$	1.00925e6	0.443542	0.221771	+	0.975099i	$0.428816\pi$
$350$	756612.	0.330144
$351$	371022.	0.160743
$352$	5.07987e6	2.18522
$353$	1.07060e6	0.457290	0.228645	−	0.973510i	$-0.426570\pi$
$353$	1.07060e6	0.457290	0.228645	+	0.973510i	$0.426570\pi$
$354$	−159889.	−0.0678125
$355$	−1.91820e6	−0.807837
$356$	4.90848e6	2.05268
$357$	−728004.	−0.302318
$358$	5.55343e6	2.29010
$359$	−1.63716e6	−0.670432	−0.335216	−	0.942141i	$-0.608809\pi$
$359$	−1.63716e6	−0.670432	−0.335216	+	0.942141i	$0.608809\pi$
$360$	333678.	0.135697
$361$	412880.	0.166746
$362$	4.97192e6	1.99413
$363$	−2.00443e6	−0.798405
$364$	1.26880e6	0.501927
$365$	−3.17774e6	−1.24849
$366$	−3.57500e6	−1.39500
$367$	−2.09506e6	−0.811952	−0.405976	−	0.913884i	$-0.633068\pi$
$367$	−2.09506e6	−0.811952	−0.405976	+	0.913884i	$0.633068\pi$
$368$	1.08128e6	0.416217
$369$	330954.	0.126532
$370$	−2.68151e6	−1.01830
$371$	−1.44817e6	−0.546243
$372$	1.54464e6	0.578721
$373$	3.64987e6	1.35833	0.679165	−	0.733985i	$-0.262342\pi$
$373$	3.64987e6	1.35833	0.679165	+	0.733985i	$0.262342\pi$
$374$	6.65860e6	2.46152
$375$	−1.03887e6	−0.381490
$376$	1.46636e6	0.534900
$377$	284269.	0.103009
$378$	−390869.	−0.140703
$379$	1.80884e6	0.646849	0.323425	−	0.946254i	$-0.395166\pi$
$379$	1.80884e6	0.646849	0.323425	+	0.946254i	$0.395166\pi$
$380$	−4.49277e6	−1.59608
$381$	595092.	0.210025
$382$	4.79937e6	1.68278
$383$	148634.	0.0517753	0.0258876	−	0.999665i	$-0.491759\pi$
$383$	148634.	0.0517753	0.0258876	+	0.999665i	$0.491759\pi$
$384$	−1.09848e6	−0.380158
$385$	2.65032e6	0.911269
$386$	−2.71497e6	−0.927463
$387$	−1.84149e6	−0.625019
$388$	1.96024e6	0.661042
$389$	−745777.	−0.249882	−0.124941	−	0.992164i	$-0.539874\pi$
$389$	−745777.	−0.249882	−0.124941	+	0.992164i	$0.539874\pi$
$390$	2.60399e6	0.866918
$391$	1.86169e6	0.615835
$392$	781193.	0.256769
$393$	−868148.	−0.283539
$394$	4.44977e6	1.44410
$395$	−275554.	−0.0888616
$396$	1.96932e6	0.631072
$397$	1.92103e6	0.611728	0.305864	−	0.952075i	$-0.401055\pi$
$397$	1.92103e6	0.611728	0.305864	+	0.952075i	$0.401055\pi$
$398$	−3.47798e6	−1.10058
$399$	971712.	0.305566
$400$	−1.04369e6	−0.326152
$401$	3.39442e6	1.05416	0.527078	−	0.849817i	$-0.323288\pi$
$401$	3.39442e6	1.05416	0.527078	+	0.849817i	$0.323288\pi$
$402$	−3.85433e6	−1.18955
$403$	2.22565e6	0.682645
$404$	3.81903e6	1.16412
$405$	−441889.	−0.133868
$406$	−299475.	−0.0901667
$407$	−2.92205e6	−0.874383
$408$	−700989.	−0.208478
$409$	5.84662e6	1.72821	0.864105	−	0.503312i	$-0.167885\pi$
$409$	5.84662e6	1.72821	0.864105	+	0.503312i	$0.167885\pi$
$410$	2.32277e6	0.682412
$411$	−2.37167e6	−0.692548
$412$	416364.	0.120846
$413$	133696.	0.0385693
$414$	999548.	0.286618
$415$	−2.11504e6	−0.602836
$416$	−4.17342e6	−1.18239
$417$	883585.	0.248833
$418$	−8.88763e6	−2.48797
$419$	−809741.	−0.225326	−0.112663	−	0.993633i	$-0.535938\pi$
$419$	−809741.	−0.225326	−0.112663	+	0.993633i	$0.535938\pi$
$420$	−1.51115e6	−0.418008
$421$	−199631.	−0.0548938	−0.0274469	−	0.999623i	$-0.508738\pi$
$421$	−199631.	−0.0548938	−0.0274469	+	0.999623i	$0.508738\pi$
$422$	1.32062e6	0.360990
$423$	−1.94190e6	−0.527687
$424$	−1.39443e6	−0.376690
$425$	−1.79696e6	−0.482576
$426$	2.16359e6	0.577632
$427$	2.98934e6	0.793424
$428$	−8.46477e6	−2.23360
$429$	2.83758e6	0.744397
$430$	−1.29244e7	−3.37084
$431$	−3.08342e6	−0.799538	−0.399769	−	0.916616i	$-0.630910\pi$
$431$	−3.08342e6	−0.799538	−0.399769	+	0.916616i	$0.630910\pi$
$432$	539174.	0.139002
$433$	−457642.	−0.117302	−0.0586511	−	0.998279i	$-0.518680\pi$
$433$	−457642.	−0.117302	−0.0586511	+	0.998279i	$0.518680\pi$
$434$	−2.34471e6	−0.597536
$435$	−338566.	−0.0857866
$436$	−1.43575e6	−0.361711
$437$	−2.48490e6	−0.622452
$438$	3.58425e6	0.892717
$439$	226826.	0.0561734	0.0280867	−	0.999605i	$-0.491059\pi$
$439$	226826.	0.0561734	0.0280867	+	0.999605i	$0.491059\pi$
$440$	2.55197e6	0.628411
$441$	−1.03453e6	−0.253307
$442$	−5.47045e6	−1.33189
$443$	−2.55689e6	−0.619017	−0.309509	−	0.950897i	$-0.600165\pi$
$443$	−2.55689e6	−0.619017	−0.309509	+	0.950897i	$0.600165\pi$
$444$	1.66608e6	0.401088
$445$	−8.42346e6	−2.01646
$446$	2.01448e6	0.479541
$447$	1.11921e6	0.264938
$448$	2.89327e6	0.681074
$449$	3.75449e6	0.878891	0.439446	−	0.898269i	$-0.355175\pi$
$449$	3.75449e6	0.878891	0.439446	+	0.898269i	$0.355175\pi$
$450$	−964796.	−0.224597
$451$	2.53113e6	0.585967
$452$	−5.48167e6	−1.26202
$453$	−1.21318e6	−0.277768
$454$	−4.05880e6	−0.924183
$455$	−2.17740e6	−0.493071
$456$	935653.	0.210718
$457$	6.99059e6	1.56575	0.782877	−	0.622177i	$-0.213752\pi$
$457$	6.99059e6	1.56575	0.782877	+	0.622177i	$0.213752\pi$
$458$	4.84967e6	1.08031
$459$	928317.	0.205667
$460$	3.86438e6	0.851501
$461$	8.57700e6	1.87968	0.939838	−	0.341620i	$-0.110976\pi$
$461$	8.57700e6	1.87968	0.939838	+	0.341620i	$0.110976\pi$
$462$	−2.98937e6	−0.651590
$463$	−4.85789e6	−1.05316	−0.526581	−	0.850125i	$-0.676526\pi$
$463$	−4.85789e6	−1.05316	−0.526581	+	0.850125i	$0.676526\pi$
$464$	413103.	0.0890766
$465$	−2.65076e6	−0.568510
$466$	−4.49467e6	−0.958811
$467$	280549.	0.0595273	0.0297636	−	0.999557i	$-0.490525\pi$
$467$	280549.	0.0595273	0.0297636	+	0.999557i	$0.490525\pi$
$468$	−1.61792e6	−0.341462
$469$	3.22291e6	0.676575
$470$	−1.36291e7	−2.84591
$471$	−5.21735e6	−1.08367
$472$	128734.	0.0265974
$473$	−1.40837e7	−2.89445
$474$	310805.	0.0635392
$475$	2.39851e6	0.487761
$476$	3.17461e6	0.642204
$477$	1.84664e6	0.371610
$478$	−6.81703e6	−1.36466
$479$	−3.66669e6	−0.730189	−0.365095	−	0.930970i	$-0.618963\pi$
$479$	−3.66669e6	−0.730189	−0.365095	+	0.930970i	$0.618963\pi$
$480$	4.97056e6	0.984696
$481$	2.40064e6	0.473113
$482$	1.07378e7	2.10522
$483$	−835801.	−0.163018
$484$	8.74071e6	1.69603
$485$	−3.36397e6	−0.649379
$486$	498418.	0.0957201
$487$	408938.	0.0781331	0.0390665	−	0.999237i	$-0.487562\pi$
$487$	408938.	0.0781331	0.0390665	+	0.999237i	$0.487562\pi$
$488$	2.87841e6	0.547145
$489$	−3.47293e6	−0.656786
$490$	−7.26077e6	−1.36613
$491$	−4.99561e6	−0.935158	−0.467579	−	0.883951i	$-0.654874\pi$
$491$	−4.99561e6	−0.935158	−0.467579	+	0.883951i	$0.654874\pi$
$492$	−1.44319e6	−0.268789
$493$	711256.	0.131798
$494$	7.30174e6	1.34620
$495$	−3.37956e6	−0.619937
$496$	3.23434e6	0.590312
$497$	−1.80915e6	−0.328536
$498$	2.38561e6	0.431049
$499$	6.96204e6	1.25166	0.625828	−	0.779961i	$-0.284761\pi$
$499$	6.96204e6	1.25166	0.625828	+	0.779961i	$0.284761\pi$
$500$	4.53021e6	0.810389
$501$	−4.94300e6	−0.879824
$502$	−1.10587e7	−1.95859
$503$	5.85427e6	1.03170	0.515850	−	0.856679i	$-0.327476\pi$
$503$	5.85427e6	1.03170	0.515850	+	0.856679i	$0.327476\pi$
$504$	314708.	0.0551863
$505$	−6.55385e6	−1.14358
$506$	7.64454e6	1.32732
$507$	1.01039e6	0.174570
$508$	−2.59502e6	−0.446151
$509$	5.21236e6	0.891743	0.445871	−	0.895097i	$-0.352894\pi$
$509$	5.21236e6	0.891743	0.445871	+	0.895097i	$0.352894\pi$
$510$	6.51532e6	1.10920
$511$	−2.99708e6	−0.507745
$512$	−7.51248e6	−1.26651
$513$	−1.23908e6	−0.207877
$514$	4.63627e6	0.774036
$515$	−714525.	−0.118713
$516$	8.03021e6	1.32771
$517$	−1.48517e7	−2.44370
$518$	−2.52906e6	−0.414128
$519$	3.99092e6	0.650361
$520$	−2.09660e6	−0.340022
$521$	8.63489e6	1.39368	0.696839	−	0.717227i	$-0.254589\pi$
$521$	8.63489e6	1.39368	0.696839	+	0.717227i	$0.254589\pi$
$522$	381877.	0.0613405
$523$	1.18996e7	1.90229	0.951145	−	0.308745i	$-0.0999090\pi$
$523$	1.18996e7	1.90229	0.951145	+	0.308745i	$0.0999090\pi$
$524$	3.78574e6	0.602313
$525$	806741.	0.127743
$526$	−3.31943e6	−0.523117
$527$	5.56870e6	0.873428
$528$	4.12360e6	0.643712
$529$	−4.29900e6	−0.667925
$530$	1.29605e7	2.00416
$531$	−170482.	−0.0262387
$532$	−4.23735e6	−0.649105
$533$	−2.07948e6	−0.317056
$534$	9.50104e6	1.44184
$535$	1.45264e7	2.19419
$536$	3.10331e6	0.466566
$537$	5.92138e6	0.886108
$538$	−6.71170e6	−0.999716
$539$	−7.91209e6	−1.17306
$540$	1.92695e6	0.284371
$541$	1.13432e6	0.166625	0.0833126	−	0.996523i	$-0.473450\pi$
$541$	1.13432e6	0.166625	0.0833126	+	0.996523i	$0.473450\pi$
$542$	−1.45883e7	−2.13308
$543$	5.30133e6	0.771588
$544$	−1.04421e7	−1.51283
$545$	2.46389e6	0.355329
$546$	2.45595e6	0.352564
$547$	5.77134e6	0.824724	0.412362	−	0.911020i	$-0.364704\pi$
$547$	5.77134e6	0.824724	0.412362	+	0.911020i	$0.364704\pi$
$548$	1.03422e7	1.47116
$549$	−3.81186e6	−0.539767
$550$	−7.37876e6	−1.04010
$551$	−949357.	−0.133214
$552$	−804785.	−0.112417
$553$	−259888.	−0.0361388
$554$	1.17626e7	1.62828
$555$	−2.85917e6	−0.394011
$556$	−3.85305e6	−0.528589
$557$	−8.28207e6	−1.13110	−0.565550	−	0.824714i	$-0.691336\pi$
$557$	−8.28207e6	−1.13110	−0.565550	+	0.824714i	$0.691336\pi$
$558$	2.98986e6	0.406505
$559$	1.15707e7	1.56613
$560$	−3.16422e6	−0.426380
$561$	7.09977e6	0.952438
$562$	1.57307e7	2.10091
$563$	−6.89743e6	−0.917099	−0.458550	−	0.888669i	$-0.651631\pi$
$563$	−6.89743e6	−0.917099	−0.458550	+	0.888669i	$0.651631\pi$
$564$	8.46806e6	1.12095
$565$	9.40713e6	1.23975
$566$	−1.42147e7	−1.86508
$567$	−416766.	−0.0544421
$568$	−1.74201e6	−0.226559
$569$	1.01546e7	1.31486	0.657432	−	0.753514i	$-0.271643\pi$
$569$	1.01546e7	1.31486	0.657432	+	0.753514i	$0.271643\pi$
$570$	−8.69639e6	−1.12112
$571$	−6.86311e6	−0.880908	−0.440454	−	0.897775i	$-0.645183\pi$
$571$	−6.86311e6	−0.880908	−0.440454	+	0.897775i	$0.645183\pi$
$572$	−1.23738e7	−1.58130
$573$	5.11736e6	0.651117
$574$	2.19072e6	0.277528
$575$	−2.06304e6	−0.260218
$576$	−3.68936e6	−0.463335
$577$	−7.77680e6	−0.972437	−0.486219	−	0.873837i	$-0.661624\pi$
$577$	−7.77680e6	−0.972437	−0.486219	+	0.873837i	$0.661624\pi$
$578$	−1.70267e6	−0.211988
$579$	−2.89485e6	−0.358864
$580$	1.47638e6	0.182234
$581$	−1.99480e6	−0.245165
$582$	3.79431e6	0.464329
$583$	1.41231e7	1.72092
$584$	−2.88586e6	−0.350141
$585$	2.77652e6	0.335437
$586$	2.22421e7	2.67567
$587$	7.89145e6	0.945283	0.472641	−	0.881255i	$-0.343301\pi$
$587$	7.89145e6	0.945283	0.472641	+	0.881255i	$0.343301\pi$
$588$	4.51128e6	0.538092
$589$	−7.43288e6	−0.882813
$590$	−1.19652e6	−0.141510
$591$	4.74459e6	0.558766
$592$	3.48864e6	0.409121
$593$	1.45671e7	1.70112	0.850561	−	0.525876i	$-0.176262\pi$
$593$	1.45671e7	1.70112	0.850561	+	0.525876i	$0.176262\pi$
$594$	3.81190e6	0.443277
$595$	−5.44797e6	−0.630873
$596$	−4.88056e6	−0.562800
$597$	−3.70842e6	−0.425846
$598$	−6.28046e6	−0.718189
$599$	−3.92053e6	−0.446455	−0.223228	−	0.974766i	$-0.571659\pi$
$599$	−3.92053e6	−0.446455	−0.223228	+	0.974766i	$0.571659\pi$
$600$	776804.	0.0880914
$601$	−1.34193e7	−1.51546	−0.757730	−	0.652568i	$-0.773692\pi$
$601$	−1.34193e7	−1.51546	−0.757730	+	0.652568i	$0.773692\pi$
$602$	−1.21896e7	−1.37088
$603$	−4.10970e6	−0.460275
$604$	5.29034e6	0.590053
$605$	−1.50000e7	−1.66610
$606$	7.39226e6	0.817704
$607$	−1.17981e7	−1.29969	−0.649847	−	0.760065i	$-0.725167\pi$
$607$	−1.17981e7	−1.29969	−0.649847	+	0.760065i	$0.725167\pi$
$608$	1.39377e7	1.52909
$609$	−319317.	−0.0348882
$610$	−2.67533e7	−2.91107
$611$	1.22015e7	1.32224
$612$	−4.04812e6	−0.436892
$613$	−3.67184e6	−0.394669	−0.197335	−	0.980336i	$-0.563229\pi$
$613$	−3.67184e6	−0.394669	−0.197335	+	0.980336i	$0.563229\pi$
$614$	−8.62109e6	−0.922872
$615$	2.47667e6	0.264046
$616$	2.40688e6	0.255566
$617$	−4.96891e6	−0.525470	−0.262735	−	0.964868i	$-0.584624\pi$
$617$	−4.96891e6	−0.525470	−0.262735	+	0.964868i	$0.584624\pi$
$618$	805932.	0.0848842
$619$	3.18867e6	0.334489	0.167245	−	0.985915i	$-0.446513\pi$
$619$	3.18867e6	0.334489	0.167245	+	0.985915i	$0.446513\pi$
$620$	1.15592e7	1.20767
$621$	1.06577e6	0.110901
$622$	5.35337e6	0.554819
$623$	−7.94457e6	−0.820068
$624$	−3.38779e6	−0.348301
$625$	−1.21841e7	−1.24765
$626$	−1.77267e7	−1.80797
$627$	−9.47649e6	−0.962672
$628$	2.27513e7	2.30201
$629$	6.00653e6	0.605337
$630$	−2.92504e6	−0.293617
$631$	−1.21879e7	−1.21858	−0.609291	−	0.792947i	$-0.708546\pi$
$631$	−1.21879e7	−1.21858	−0.609291	+	0.792947i	$0.708546\pi$
$632$	−250244.	−0.0249213
$633$	1.40811e6	0.139678
$634$	−2.29117e7	−2.26378
$635$	4.45333e6	0.438279
$636$	−8.05267e6	−0.789400
$637$	6.50026e6	0.634720
$638$	2.92059e6	0.284066
$639$	2.30694e6	0.223504
$640$	−8.22039e6	−0.793310
$641$	1.47914e7	1.42188	0.710942	−	0.703251i	$-0.248269\pi$
$641$	1.47914e7	1.42188	0.710942	+	0.703251i	$0.248269\pi$
$642$	−1.63847e7	−1.56893
$643$	3.59362e6	0.342772	0.171386	−	0.985204i	$-0.445176\pi$
$643$	3.59362e6	0.342772	0.171386	+	0.985204i	$0.445176\pi$
$644$	3.64468e6	0.346294
$645$	−1.37807e7	−1.30428
$646$	1.82693e7	1.72243
$647$	−4.66265e6	−0.437897	−0.218948	−	0.975736i	$-0.570263\pi$
$647$	−4.66265e6	−0.437897	−0.218948	+	0.975736i	$0.570263\pi$
$648$	−401301.	−0.0375433
$649$	−1.30385e6	−0.121511
$650$	6.06210e6	0.562781
$651$	−2.50006e6	−0.231205
$652$	1.51444e7	1.39519
$653$	−3.49885e6	−0.321101	−0.160551	−	0.987028i	$-0.551327\pi$
$653$	−3.49885e6	−0.321101	−0.160551	+	0.987028i	$0.551327\pi$
$654$	−2.77909e6	−0.254073
$655$	−6.49673e6	−0.591686
$656$	−3.02192e6	−0.274173
$657$	3.82173e6	0.345419
$658$	−1.28542e7	−1.15739
$659$	7.78150e6	0.697991	0.348996	−	0.937124i	$-0.386523\pi$
$659$	7.78150e6	0.697991	0.348996	+	0.937124i	$0.386523\pi$
$660$	1.47373e7	1.31691
$661$	4.81826e6	0.428930	0.214465	−	0.976732i	$-0.431199\pi$
$661$	4.81826e6	0.428930	0.214465	+	0.976732i	$0.431199\pi$
$662$	−6.57627e6	−0.583223
$663$	−5.83289e6	−0.515347
$664$	−1.92077e6	−0.169066
$665$	7.27173e6	0.637652
$666$	3.22494e6	0.281732
$667$	816572.	0.0710690
$668$	2.15549e7	1.86898
$669$	2.14795e6	0.185549
$670$	−2.88436e7	−2.48235
$671$	−2.91531e7	−2.49965
$672$	4.68797e6	0.400463
$673$	−1.23818e7	−1.05377	−0.526884	−	0.849937i	$-0.676640\pi$
$673$	−1.23818e7	−1.05377	−0.526884	+	0.849937i	$0.676640\pi$
$674$	1.44612e7	1.22618
$675$	−1.02872e6	−0.0869035
$676$	−4.40603e6	−0.370835
$677$	−9.06626e6	−0.760250	−0.380125	−	0.924935i	$-0.624119\pi$
$677$	−9.06626e6	−0.760250	−0.380125	+	0.924935i	$0.624119\pi$
$678$	−1.06105e7	−0.886469
$679$	−3.17272e6	−0.264093
$680$	−5.24580e6	−0.435050
$681$	−4.32771e6	−0.357595
$682$	2.28664e7	1.88251
$683$	4.24338e6	0.348065	0.174032	−	0.984740i	$-0.444320\pi$
$683$	4.24338e6	0.348065	0.174032	+	0.984740i	$0.444320\pi$
$684$	5.40327e6	0.441587
$685$	−1.77482e7	−1.44520
$686$	−1.58594e7	−1.28670
$687$	5.17099e6	0.418005
$688$	1.68146e7	1.35430
$689$	−1.16030e7	−0.931157
$690$	7.48005e6	0.598111
$691$	1.78704e7	1.42377	0.711885	−	0.702297i	$-0.247842\pi$
$691$	1.78704e7	1.42377	0.711885	+	0.702297i	$0.247842\pi$
$692$	−1.74032e7	−1.38154
$693$	−3.18743e6	−0.252120
$694$	−2.13193e7	−1.68025
$695$	6.61224e6	0.519262
$696$	−307468.	−0.0240589
$697$	−5.20296e6	−0.405666
$698$	−8.51883e6	−0.661822
$699$	−4.79246e6	−0.370993
$700$	−3.51796e6	−0.271360
$701$	5.86012e6	0.450414	0.225207	−	0.974311i	$-0.427694\pi$
$701$	5.86012e6	0.450414	0.225207	+	0.974311i	$0.427694\pi$
$702$	−3.13171e6	−0.239849
$703$	−8.01728e6	−0.611841
$704$	−2.82162e7	−2.14569
$705$	−1.45321e7	−1.10117
$706$	−9.03670e6	−0.682336
$707$	−6.18125e6	−0.465080
$708$	743423.	0.0557382
$709$	2.07718e7	1.55188	0.775942	−	0.630805i	$-0.217275\pi$
$709$	2.07718e7	1.55188	0.775942	+	0.630805i	$0.217275\pi$
$710$	1.61911e7	1.20540
$711$	331397.	0.0245853
$712$	−7.64975e6	−0.565519
$713$	6.39326e6	0.470976
$714$	6.14491e6	0.451097
$715$	2.12348e7	1.55340
$716$	−2.58214e7	−1.88233
$717$	−7.26869e6	−0.528030
$718$	1.38189e7	1.00037
$719$	1.94052e7	1.39989	0.699947	−	0.714194i	$-0.253207\pi$
$719$	1.94052e7	1.39989	0.699947	+	0.714194i	$0.253207\pi$
$720$	4.03487e6	0.290067
$721$	−673903.	−0.0482791
$722$	−3.48502e6	−0.248807
$723$	1.14492e7	0.814574
$724$	−2.31176e7	−1.63906
$725$	−788182.	−0.0556905
$726$	1.69189e7	1.19132
$727$	2.03479e6	0.142785	0.0713927	−	0.997448i	$-0.477256\pi$
$727$	2.03479e6	0.142785	0.0713927	+	0.997448i	$0.477256\pi$
$728$	−1.97740e6	−0.138282
$729$	531441.	0.0370370
$730$	2.68225e7	1.86291
$731$	2.89504e7	2.00383
$732$	1.66224e7	1.14661
$733$	−2.36929e7	−1.62876	−0.814381	−	0.580331i	$-0.802923\pi$
$733$	−2.36929e7	−1.62876	−0.814381	+	0.580331i	$0.802923\pi$
$734$	1.76839e7	1.21154
$735$	−7.74184e6	−0.528598
$736$	−1.19883e7	−0.815761
$737$	−3.14310e7	−2.13152
$738$	−2.79350e6	−0.188802
$739$	1.34563e7	0.906387	0.453194	−	0.891412i	$-0.350285\pi$
$739$	1.34563e7	0.906387	0.453194	+	0.891412i	$0.350285\pi$
$740$	1.24680e7	0.836985
$741$	7.78551e6	0.520885
$742$	1.22237e7	0.815066
$743$	−3.75271e6	−0.249387	−0.124693	−	0.992195i	$-0.539795\pi$
$743$	−3.75271e6	−0.249387	−0.124693	+	0.992195i	$0.539795\pi$
$744$	−2.40728e6	−0.159439
$745$	8.37556e6	0.552870
$746$	−3.08077e7	−2.02680
$747$	2.54367e6	0.166786
$748$	−3.09600e7	−2.02324
$749$	1.37006e7	0.892348
$750$	8.76886e6	0.569233
$751$	−2.49492e7	−1.61420	−0.807099	−	0.590417i	$-0.798963\pi$
$751$	−2.49492e7	−1.61420	−0.807099	+	0.590417i	$0.798963\pi$
$752$	1.77314e7	1.14340
$753$	−1.17913e7	−0.757837
$754$	−2.39945e6	−0.153703
$755$	−9.07878e6	−0.579642
$756$	1.81740e6	0.115650
$757$	2.26904e7	1.43914	0.719569	−	0.694421i	$-0.244340\pi$
$757$	2.26904e7	1.43914	0.719569	+	0.694421i	$0.244340\pi$
$758$	−1.52680e7	−0.965182
$759$	8.15103e6	0.513580
$760$	7.00189e6	0.439725
$761$	1.46992e7	0.920093	0.460046	−	0.887895i	$-0.347833\pi$
$761$	1.46992e7	0.920093	0.460046	+	0.887895i	$0.347833\pi$
$762$	−5.02302e6	−0.313385
$763$	2.32381e6	0.144507
$764$	−2.23153e7	−1.38315
$765$	6.94699e6	0.429184
$766$	−1.25459e6	−0.0772554
$767$	1.07119e6	0.0657474
$768$	−3.84574e6	−0.235275
$769$	−119834.	−0.00730744	−0.00365372	−	0.999993i	$-0.501163\pi$
$769$	−119834.	−0.00730744	−0.00365372	+	0.999993i	$0.501163\pi$
$770$	−2.23707e7	−1.35973
$771$	4.94345e6	0.299498
$772$	1.26236e7	0.762324
$773$	5.04604e6	0.303740	0.151870	−	0.988400i	$-0.451470\pi$
$773$	5.04604e6	0.303740	0.151870	+	0.988400i	$0.451470\pi$
$774$	1.55436e7	0.932609
$775$	−6.17098e6	−0.369062
$776$	−3.05499e6	−0.182119
$777$	−2.69662e6	−0.160239
$778$	6.29492e6	0.372856
$779$	6.94471e6	0.410025
$780$	−1.21076e7	−0.712559
$781$	1.76435e7	1.03504
$782$	−1.57140e7	−0.918905
$783$	407178.	0.0237345
$784$	9.44626e6	0.548870
$785$	−3.90437e7	−2.26140
$786$	7.32783e6	0.423076
$787$	−6.12320e6	−0.352404	−0.176202	−	0.984354i	$-0.556381\pi$
$787$	−6.12320e6	−0.352404	−0.176202	+	0.984354i	$0.556381\pi$
$788$	−2.06898e7	−1.18697
$789$	−3.53936e6	−0.202410
$790$	2.32589e6	0.132593
$791$	8.87231e6	0.504191
$792$	−3.06915e6	−0.173862
$793$	2.39511e7	1.35251
$794$	−1.62150e7	−0.912777
$795$	1.38192e7	0.775472
$796$	1.61713e7	0.904613
$797$	8.48543e6	0.473182	0.236591	−	0.971609i	$-0.423970\pi$
$797$	8.48543e6	0.473182	0.236591	+	0.971609i	$0.423970\pi$
$798$	−8.20198e6	−0.455944
$799$	3.05289e7	1.69178
$800$	1.15715e7	0.639240
$801$	1.01305e7	0.557893
$802$	−2.86515e7	−1.57294
$803$	2.92286e7	1.59963
$804$	1.79212e7	0.977748
$805$	−6.25465e6	−0.340184
$806$	−1.87862e7	−1.01859
$807$	−7.15639e6	−0.386821
$808$	−5.95187e6	−0.320719
$809$	1.26284e7	0.678386	0.339193	−	0.940717i	$-0.389846\pi$
$809$	1.26284e7	0.678386	0.339193	+	0.940717i	$0.389846\pi$
$810$	3.72988e6	0.199748
$811$	2.50216e7	1.33587	0.667933	−	0.744221i	$-0.267179\pi$
$811$	2.50216e7	1.33587	0.667933	+	0.744221i	$0.267179\pi$
$812$	1.39245e6	0.0741121
$813$	−1.55549e7	−0.825354
$814$	2.46643e7	1.30469
$815$	−2.59894e7	−1.37057
$816$	−8.47643e6	−0.445643
$817$	−3.86418e7	−2.02536
$818$	−4.93499e7	−2.57871
$819$	2.61867e6	0.136418
$820$	−1.08000e7	−0.560905
$821$	−1.90801e7	−0.987924	−0.493962	−	0.869483i	$-0.664452\pi$
$821$	−1.90801e7	−0.987924	−0.493962	+	0.869483i	$0.664452\pi$
$822$	2.00187e7	1.03337
$823$	1.96524e7	1.01138	0.505692	−	0.862714i	$-0.331237\pi$
$823$	1.96524e7	1.01138	0.505692	+	0.862714i	$0.331237\pi$
$824$	−648895.	−0.0332933
$825$	−7.86764e6	−0.402448
$826$	−1.12849e6	−0.0575504
$827$	3.10992e7	1.58119	0.790597	−	0.612337i	$-0.209770\pi$
$827$	3.10992e7	1.58119	0.790597	+	0.612337i	$0.209770\pi$
$828$	−4.64752e6	−0.235584
$829$	1.82914e7	0.924403	0.462201	−	0.886775i	$-0.347060\pi$
$829$	1.82914e7	0.924403	0.462201	+	0.886775i	$0.347060\pi$
$830$	1.78526e7	0.899509
$831$	1.25419e7	0.630030
$832$	2.31814e7	1.16100
$833$	1.62640e7	0.812110
$834$	−7.45812e6	−0.371291
$835$	−3.69906e7	−1.83601
$836$	4.13242e7	2.04498
$837$	3.18796e6	0.157289
$838$	6.83483e6	0.336215
$839$	−4.72957e6	−0.231962	−0.115981	−	0.993251i	$-0.537001\pi$
$839$	−4.72957e6	−0.231962	−0.115981	+	0.993251i	$0.537001\pi$
$840$	2.35509e6	0.115162
$841$	−2.01992e7	−0.984790
$842$	1.68504e6	0.0819086
$843$	1.67730e7	0.812907
$844$	−6.14037e6	−0.296714
$845$	7.56120e6	0.364292
$846$	1.63911e7	0.787377
$847$	−1.41472e7	−0.677582
$848$	−1.68616e7	−0.805212
$849$	−1.51566e7	−0.721658
$850$	1.51677e7	0.720065
$851$	6.89592e6	0.326414
$852$	−1.00599e7	−0.474782
$853$	−8.00535e6	−0.376711	−0.188355	−	0.982101i	$-0.560316\pi$
$853$	−8.00535e6	−0.376711	−0.188355	+	0.982101i	$0.560316\pi$
$854$	−2.52323e7	−1.18389
$855$	−9.27257e6	−0.433795
$856$	1.31922e7	0.615363
$857$	−2.26461e7	−1.05327	−0.526636	−	0.850091i	$-0.676547\pi$
$857$	−2.26461e7	−1.05327	−0.526636	+	0.850091i	$0.676547\pi$
$858$	−2.39513e7	−1.11074
$859$	−27497.5	−0.00127148	−0.000635742	−	1.00000i	$-0.500202\pi$
$859$	−27497.5	−0.00127148	−0.000635742		1.00000i	$0.500202\pi$
$860$	6.00935e7	2.77065
$861$	2.33586e6	0.107384
$862$	2.60264e7	1.19301
$863$	−3.41485e7	−1.56079	−0.780396	−	0.625285i	$-0.784983\pi$
$863$	−3.41485e7	−1.56079	−0.780396	+	0.625285i	$0.784983\pi$
$864$	−5.97788e6	−0.272435
$865$	2.98658e7	1.35717
$866$	3.86284e6	0.175030
$867$	−1.81548e6	−0.0820246
$868$	1.09020e7	0.491142
$869$	2.53453e6	0.113854
$870$	2.85775e6	0.128005
$871$	2.58225e7	1.15333
$872$	2.23758e6	0.0996522
$873$	4.04571e6	0.179663
$874$	2.09745e7	0.928779
$875$	−7.33233e6	−0.323759
$876$	−1.66654e7	−0.733764
$877$	−2.04513e7	−0.897887	−0.448943	−	0.893560i	$-0.648200\pi$
$877$	−2.04513e7	−0.897887	−0.448943	+	0.893560i	$0.648200\pi$
$878$	−1.91458e6	−0.0838179
$879$	2.37158e7	1.03530
$880$	3.08587e7	1.34329
$881$	2.03900e7	0.885068	0.442534	−	0.896752i	$-0.354080\pi$
$881$	2.03900e7	0.885068	0.442534	+	0.896752i	$0.354080\pi$
$882$	8.73222e6	0.377966
$883$	1.24947e7	0.539293	0.269647	−	0.962959i	$-0.413093\pi$
$883$	1.24947e7	0.539293	0.269647	+	0.962959i	$0.413093\pi$
$884$	2.54355e7	1.09474
$885$	−1.27579e6	−0.0547547
$886$	2.15821e7	0.923654
$887$	1.66296e7	0.709698	0.354849	−	0.934924i	$-0.384532\pi$
$887$	1.66296e7	0.709698	0.354849	+	0.934924i	$0.384532\pi$
$888$	−2.59655e6	−0.110501
$889$	4.20014e6	0.178242
$890$	7.11004e7	3.00882
$891$	4.06446e6	0.171518
$892$	−9.36657e6	−0.394156
$893$	−4.07487e7	−1.70996
$894$	−9.44702e6	−0.395322
$895$	4.43122e7	1.84912
$896$	−7.75304e6	−0.322628
$897$	−6.69657e6	−0.277889
$898$	−3.16907e7	−1.31142
$899$	2.44254e6	0.100796
$900$	4.48594e6	0.184607
$901$	−2.90313e7	−1.19139
$902$	−2.13647e7	−0.874339
$903$	−1.29972e7	−0.530434
$904$	8.54307e6	0.347690
$905$	3.96722e7	1.61014
$906$	1.02402e7	0.414465
$907$	4.32646e7	1.74628	0.873141	−	0.487467i	$-0.162079\pi$
$907$	4.32646e7	1.74628	0.873141	+	0.487467i	$0.162079\pi$
$908$	1.88719e7	0.759627
$909$	7.88204e6	0.316395
$910$	1.83789e7	0.735726
$911$	−1.65819e7	−0.661969	−0.330984	−	0.943636i	$-0.607381\pi$
$911$	−1.65819e7	−0.661969	−0.330984	+	0.943636i	$0.607381\pi$
$912$	1.13140e7	0.450432
$913$	1.94540e7	0.772382
$914$	−5.90059e7	−2.33631
$915$	−2.85258e7	−1.12638
$916$	−2.25492e7	−0.887957
$917$	−6.12737e6	−0.240631
$918$	−7.83570e6	−0.306882
$919$	2.83501e7	1.10730	0.553651	−	0.832748i	$-0.313234\pi$
$919$	2.83501e7	1.10730	0.553651	+	0.832748i	$0.313234\pi$
$920$	−6.02255e6	−0.234591
$921$	−9.19229e6	−0.357087
$922$	−7.23963e7	−2.80472
$923$	−1.44952e7	−0.560041
$924$	1.38994e7	0.535571
$925$	−6.65617e6	−0.255782
$926$	4.10042e7	1.57145
$927$	859329.	0.0328443
$928$	−4.58012e6	−0.174585
$929$	9.29396e6	0.353314	0.176657	−	0.984272i	$-0.443472\pi$
$929$	9.29396e6	0.353314	0.176657	+	0.984272i	$0.443472\pi$
$930$	2.23744e7	0.848290
$931$	−2.17085e7	−0.820836
$932$	2.08985e7	0.788090
$933$	5.70806e6	0.214676
$934$	−2.36804e6	−0.0888224
$935$	5.31306e7	1.98754
$936$	2.52149e6	0.0940736
$937$	−1.71641e7	−0.638664	−0.319332	−	0.947643i	$-0.603459\pi$
$937$	−1.71641e7	−0.638664	−0.319332	+	0.947643i	$0.603459\pi$
$938$	−2.72038e7	−1.00954
$939$	−1.89011e7	−0.699558
$940$	6.33701e7	2.33919
$941$	7.32288e6	0.269593	0.134796	−	0.990873i	$-0.456962\pi$
$941$	7.32288e6	0.269593	0.134796	+	0.990873i	$0.456962\pi$
$942$	4.40384e7	1.61698
$943$	−5.97337e6	−0.218746
$944$	1.55667e6	0.0568546
$945$	−3.11884e6	−0.113609
$946$	1.18877e8	4.31888
$947$	1.05642e7	0.382790	0.191395	−	0.981513i	$-0.438699\pi$
$947$	1.05642e7	0.382790	0.191395	+	0.981513i	$0.438699\pi$
$948$	−1.44513e6	−0.0522258
$949$	−2.40131e7	−0.865530
$950$	−2.02452e7	−0.727803
$951$	−2.44297e7	−0.875924
$952$	−4.94756e6	−0.176929
$953$	−3.13574e7	−1.11843	−0.559214	−	0.829024i	$-0.688897\pi$
$953$	−3.13574e7	−1.11843	−0.559214	+	0.829024i	$0.688897\pi$
$954$	−1.55871e7	−0.554490
$955$	3.82954e7	1.35874
$956$	3.16966e7	1.12168
$957$	3.11410e6	0.109914
$958$	3.09496e7	1.08954
$959$	−1.67392e7	−0.587744
$960$	−2.76091e7	−0.966883
$961$	−9.50556e6	−0.332024
$962$	−2.02632e7	−0.705946
$963$	−1.74703e7	−0.607065
$964$	−4.99267e7	−1.73038
$965$	−2.16634e7	−0.748873
$966$	7.05479e6	0.243243
$967$	−5.27937e7	−1.81558	−0.907791	−	0.419423i	$-0.862233\pi$
$967$	−5.27937e7	−1.81558	−0.907791	+	0.419423i	$0.862233\pi$
$968$	−1.36222e7	−0.467261
$969$	1.94798e7	0.666460
$970$	2.83945e7	0.968957
$971$	−4.03246e7	−1.37253	−0.686265	−	0.727351i	$-0.740751\pi$
$971$	−4.03246e7	−1.37253	−0.686265	+	0.727351i	$0.740751\pi$
$972$	−2.31746e6	−0.0786767
$973$	6.23632e6	0.211177
$974$	−3.45175e6	−0.116585
$975$	6.46375e6	0.217757
$976$	3.48060e7	1.16958
$977$	−1.73921e7	−0.582930	−0.291465	−	0.956581i	$-0.594143\pi$
$977$	−1.73921e7	−0.582930	−0.291465	+	0.956581i	$0.594143\pi$
$978$	2.93141e7	0.980009
$979$	7.74783e7	2.58359
$980$	3.37599e7	1.12289
$981$	−2.96322e6	−0.0983084
$982$	4.21667e7	1.39538
$983$	8.72795e6	0.288090	0.144045	−	0.989571i	$-0.453989\pi$
$983$	8.72795e6	0.288090	0.144045	+	0.989571i	$0.453989\pi$
$984$	2.24918e6	0.0740520
$985$	3.55058e7	1.16603
$986$	−6.00354e6	−0.196660
$987$	−1.37059e7	−0.447831
$988$	−3.39503e7	−1.10650
$989$	3.32371e7	1.08052
$990$	2.85261e7	0.925026
$991$	−1.71313e7	−0.554121	−0.277061	−	0.960852i	$-0.589360\pi$
$991$	−1.71313e7	−0.554121	−0.277061	+	0.960852i	$0.589360\pi$
$992$	−3.58595e7	−1.15698
$993$	−7.01198e6	−0.225667
$994$	1.52706e7	0.490218
$995$	−2.77517e7	−0.888652
$996$	−1.10922e7	−0.354299
$997$	−2.97778e7	−0.948756	−0.474378	−	0.880321i	$-0.657327\pi$
$997$	−2.97778e7	−0.948756	−0.474378	+	0.880321i	$0.657327\pi$
$998$	−5.87649e7	−1.86763
$999$	3.43861e6	0.109011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.3	✓	20
3.2	odd	2		927.6.a.c.1.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.3	✓	20	1.1	even	1	trivial
927.6.a.c.1.18		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)

\(f(q)\)	\(=\)	\(q-8.44075 q^{2} -9.00000 q^{3} +39.2463 q^{4} -67.3508 q^{5} +75.9668 q^{6} -63.5218 q^{7} -61.1646 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-8.44075 q^{2} -9.00000 q^{3} +39.2463 q^{4} -67.3508 q^{5} +75.9668 q^{6} -63.5218 q^{7} -61.1646 q^{8} +81.0000 q^{9} +568.492 q^{10} +619.488 q^{11} -353.217 q^{12} -508.947 q^{13} +536.172 q^{14} +606.158 q^{15} -739.608 q^{16} -1273.41 q^{17} -683.701 q^{18} +1699.70 q^{19} -2643.27 q^{20} +571.696 q^{21} -5228.94 q^{22} -1461.97 q^{23} +550.481 q^{24} +1411.14 q^{25} +4295.90 q^{26} -729.000 q^{27} -2493.00 q^{28} -558.544 q^{29} -5116.43 q^{30} -4373.05 q^{31} +8200.11 q^{32} -5575.39 q^{33} +10748.6 q^{34} +4278.25 q^{35} +3178.95 q^{36} -4716.88 q^{37} -14346.7 q^{38} +4580.52 q^{39} +4119.49 q^{40} +4085.85 q^{41} -4825.55 q^{42} -22734.5 q^{43} +24312.6 q^{44} -5455.42 q^{45} +12340.1 q^{46} -23974.1 q^{47} +6656.47 q^{48} -12772.0 q^{49} -11911.1 q^{50} +11460.7 q^{51} -19974.3 q^{52} +22798.1 q^{53} +6153.31 q^{54} -41723.0 q^{55} +3885.28 q^{56} -15297.3 q^{57} +4714.53 q^{58} -2104.72 q^{59} +23789.5 q^{60} -47060.1 q^{61} +36911.9 q^{62} -5145.26 q^{63} -45547.7 q^{64} +34278.0 q^{65} +47060.5 q^{66} -50737.1 q^{67} -49976.7 q^{68} +13157.7 q^{69} -36111.6 q^{70} +28480.8 q^{71} -4954.33 q^{72} +47181.9 q^{73} +39814.0 q^{74} -12700.2 q^{75} +66707.0 q^{76} -39351.0 q^{77} -38663.1 q^{78} +4091.33 q^{79} +49813.2 q^{80} +6561.00 q^{81} -34487.6 q^{82} +31403.4 q^{83} +22437.0 q^{84} +85765.4 q^{85} +191896. q^{86} +5026.89 q^{87} -37890.7 q^{88} +125068. q^{89} +46047.9 q^{90} +32329.2 q^{91} -57376.8 q^{92} +39357.5 q^{93} +202359. q^{94} -114476. q^{95} -73801.0 q^{96} +49947.0 q^{97} +107805. q^{98} +50178.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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